LMFDB - Embedded newform 1350.3.k.a.449.4

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			449.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.449
Dual form			1350.3.k.a.899.4

$q$-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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.115054	−	0.993359i	$-0.463296\pi$
$7$	7.22999	−	4.17423i	1.03286	−	0.596319i	0.917801	+	0.397040i	$0.129963\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$		0			0
$11$	−0.825765	+	0.476756i	−0.0750696	+	0.0433414i	−0.537065	−	0.843541i	$-0.680467\pi$
$11$	−0.825765	+	0.476756i	−0.0750696	+	0.0433414i	0.461995	+	0.886882i	$0.347134\pi$
$12$		0			0
$13$	8.39780	+	4.84847i	0.645984	+	0.372959i	0.786916	−	0.617060i	$-0.211676\pi$
$13$	8.39780	+	4.84847i	0.645984	+	0.372959i	−0.140932	+	0.990019i	$0.545010\pi$
$14$	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	−0.855475	−	0.517844i	$-0.826735\pi$
$23$	0.476756	−	0.825765i	0.0207285	−	0.0359028i	0.876204	+	0.481941i	$0.160068\pi$
$24$		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	−0.281606	−	0.959530i	$-0.590867\pi$
$29$	11.8485	−	6.84072i	0.408568	−	0.235887i	0.690174	+	0.723643i	$0.257534\pi$
$30$		0			0
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	−0.889540	−	0.456858i	$-0.848975\pi$
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	0.840420	+	0.541935i	$0.182308\pi$
$32$	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	$-0.782628\pi$
$37$		−	46.6969i		−	1.26208i	0.775751	−	0.631040i	$-0.217372\pi$
$38$	17.4634	+	30.2474i	0.459562	+	0.795985i
$39$		0			0
$40$		0			0
$41$	9.45459	+	5.45861i	0.230600	+	0.133137i	0.610849	−	0.791747i	$-0.290828\pi$
$41$	9.45459	+	5.45861i	0.230600	+	0.133137i	−0.380249	+	0.924884i	$0.624162\pi$
$42$		0			0
$43$	39.0105	−	22.5227i	0.907220	−	0.523784i	0.0276845	−	0.999617i	$-0.491187\pi$
$43$	39.0105	−	22.5227i	0.907220	−	0.523784i	0.879536	+	0.475833i	$0.157853\pi$
$44$		−	1.90702i		−	0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	22.6435	+	39.2196i	0.481776	+	0.834460i	0.999781	−	0.0209170i	$-0.00665856\pi$
$47$	22.6435	+	39.2196i	0.481776	+	0.834460i	−0.518005	+	0.855377i	$0.673325\pi$
$48$		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	0.355787	−	0.934567i	$-0.384213\pi$
$59$	−16.2650	−	9.39063i	−0.275679	−	0.159163i	−0.631466	+	0.775404i	$0.717546\pi$
$60$		0			0
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	0.807375	−	0.590039i	$-0.200888\pi$
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	−0.914676	+	0.404187i	$0.867554\pi$
$62$	−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	0.899242	−	0.437452i	$-0.144119\pi$
$67$	64.9912	+	37.5227i	0.970018	+	0.560040i	0.0707765	+	0.997492i	$0.477452\pi$
$68$	18.8776	−	32.6969i	0.277612	−	0.480837i
$69$		0			0
$70$		0			0
$71$			18.0204i			0.253808i	0.991915	+	0.126904i	$0.0405041\pi$
$71$			18.0204i			0.253808i	−0.991915	+	0.126904i	$0.959496\pi$
$72$		0			0
$73$		−	7.90918i		−	0.108345i	−0.998532	−	0.0541725i	$-0.982748\pi$
$73$		−	7.90918i		−	0.108345i	0.998532	−	0.0541725i	$-0.0172521\pi$
$74$	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	0.693750	−	0.720216i	$-0.255957\pi$
$79$	−21.8712	−	37.8820i	−0.276850	−	0.479519i	−0.970600	+	0.240697i	$0.922624\pi$
$80$		0			0
$81$		0			0
$82$			15.4393i			0.188284i
$83$	65.1662	+	112.871i	0.785135	+	1.35989i	0.928918	+	0.370284i	$0.120740\pi$
$83$	65.1662	+	112.871i	0.785135	+	1.35989i	−0.143783	+	0.989609i	$0.545927\pi$
$84$		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	$-0.696027\pi$
$89$		−	145.300i		−	1.63258i	0.577642	−	0.816290i	$-0.303973\pi$
$90$		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	0.0784327	−	0.996919i	$-0.475008\pi$
$97$	95.1576	−	54.9393i	0.981007	−	0.566384i	0.902574	+	0.430535i	$0.141675\pi$
$98$	29.2699			0.298672
$99$		0			0
$100$		0			0
$101$	−127.772	+	73.7695i	−1.26507	+	0.730391i	−0.974052	−	0.226326i	$-0.927329\pi$
$101$	−127.772	+	73.7695i	−1.26507	+	0.730391i	−0.291022	+	0.956716i	$0.593995\pi$
$102$		0			0
$103$	89.3186	+	51.5681i	0.867171	+	0.500661i	0.866407	−	0.499338i	$-0.166424\pi$
$103$	89.3186	+	51.5681i	0.867171	+	0.500661i	0.000763745		1.00000i	$0.499757\pi$
$104$	−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	0.187336	+	0.982296i	$0.440015\pi$
$113$	−85.5439	+	148.166i	−0.757025	+	1.31121i	−0.944361	+	0.328910i	$0.893319\pi$
$114$		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	$0.0994737\pi$
$127$			78.0908i			0.614888i	−0.951566	+	0.307444i	$0.900526\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−202.704	−	117.031i	−1.54736	−	0.893369i	−0.998342	−	0.0575598i	$-0.981668\pi$
$131$	−202.704	−	117.031i	−1.54736	−	0.893369i	−0.549019	−	0.835810i	$-0.684999\pi$
$132$		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	0.998489	+	0.0549460i	$0.0174987\pi$
$137$	74.9156	+	129.758i	0.546829	+	0.947136i	−0.451660	+	0.892190i	$0.649168\pi$
$138$		0			0
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	−0.977053	−	0.212998i	$-0.931677\pi$
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	0.672988	+	0.739654i	$0.265011\pi$
$140$		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	0.796585	−	0.604526i	$-0.206638\pi$
$149$	100.030	+	57.7524i	0.671343	+	0.387600i	−0.125242	+	0.992126i	$0.539971\pi$
$150$		0			0
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	0.953112	−	0.302619i	$-0.0978610\pi$
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	−0.738632	+	0.674109i	$0.764528\pi$
$152$	−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	0.441482	−	0.897270i	$-0.354453\pi$
$157$	−18.0292	−	10.4092i	−0.114836	−	0.0663005i	−0.556318	+	0.830970i	$0.687786\pi$
$158$	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	$0.133829\pi$
$163$			133.060i			0.816320i	−0.912910	+	0.408160i	$0.866171\pi$
$164$	−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	0.0323885	−	0.999475i	$-0.489689\pi$
$167$	147.255	−	255.053i	0.881765	−	1.52726i	0.849377	−	0.527787i	$-0.176978\pi$
$168$		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	0.948588	−	0.316513i	$-0.102512\pi$
$173$	34.6322	+	59.9847i	0.200186	+	0.346732i	−0.748402	+	0.663245i	$0.769179\pi$
$174$		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	$-0.957657\pi$
$179$		−	47.4829i		−	0.265268i	0.991165	−	0.132634i	$-0.0423435\pi$
$180$		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	−0.516978	−	0.855999i	$-0.672943\pi$
$191$	−6.52270	+	3.76588i	−0.0341503	+	0.0197167i	0.482828	+	0.875715i	$0.339610\pi$
$192$		0			0
$193$	−299.172	−	172.727i	−1.55011	−	0.894959i	−0.998131	−	0.0611031i	$-0.980538\pi$
$193$	−299.172	−	172.727i	−1.55011	−	0.894959i	−0.551983	−	0.833856i	$-0.686129\pi$
$194$	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	−0.798446	−	0.602066i	$-0.794344\pi$
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	0.920628	+	0.390441i	$0.127678\pi$
$212$	−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	0.252273	−	0.967656i	$-0.418822\pi$
$223$	271.263	−	156.614i	1.21642	−	0.702303i	0.964151	+	0.265353i	$0.0854886\pi$
$224$		−	47.2261i		−	0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	−38.1356	−	66.0528i	−0.167998	−	0.290982i	0.769718	−	0.638384i	$-0.220397\pi$
$227$	−38.1356	−	66.0528i	−0.167998	−	0.290982i	−0.937716	+	0.347403i	$0.887064\pi$
$228$		0			0
$229$	−60.7724	+	105.261i	−0.265382	+	0.459655i	−0.967664	−	0.252244i	$-0.918831\pi$
$229$	−60.7724	+	105.261i	−0.265382	+	0.459655i	0.702282	+	0.711899i	$0.252165\pi$
$230$		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	0.332593	−	0.943070i	$-0.392076\pi$
$239$	−75.9620	−	43.8567i	−0.317833	−	0.183501i	−0.650426	+	0.759570i	$0.725410\pi$
$240$		0			0
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	0.577157	−	0.816633i	$-0.304162\pi$
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	−0.995804	+	0.0915158i	$0.970829\pi$
$242$	−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	$0.0334307\pi$
$251$			52.6261i			0.209666i	−0.994490	+	0.104833i	$0.966569\pi$
$252$		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	−0.776775	−	0.629778i	$-0.783146\pi$
$257$	40.3532	−	69.8939i	0.157017	−	0.271961i	0.933791	+	0.357818i	$0.116479\pi$
$258$		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	−0.849515	−	0.527564i	$-0.823106\pi$
$263$	−231.872	−	401.614i	−0.881641	−	1.52705i	−0.0321259	−	0.999484i	$-0.510228\pi$
$264$		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	$0.0257510\pi$
$269$			43.4762i			0.161622i	−0.996729	+	0.0808109i	$0.974249\pi$
$270$		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	−0.421442	−	0.906855i	$-0.638476\pi$
$277$	42.4352	−	24.5000i	0.153196	−	0.0884477i	0.574638	+	0.818407i	$0.305143\pi$
$278$	−119.544			−0.430013
$279$		0			0
$280$		0			0
$281$	17.8791	−	10.3225i	0.0636266	−	0.0367349i	−0.467849	−	0.883808i	$-0.654971\pi$
$281$	17.8791	−	10.3225i	0.0636266	−	0.0367349i	0.531476	+	0.847073i	$0.321638\pi$
$282$		0			0
$283$	−46.2533	−	26.7043i	−0.163439	−	0.0943616i	0.416049	−	0.909342i	$-0.363414\pi$
$283$	−46.2533	−	26.7043i	−0.163439	−	0.0943616i	−0.579489	+	0.814980i	$0.696748\pi$
$284$	−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	−0.878478	−	0.477782i	$-0.841441\pi$
$293$	−7.46196	+	12.9245i	−0.0254674	+	0.0441109i	0.853011	+	0.521893i	$0.174774\pi$
$294$		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	$-0.965765\pi$
$307$		−	65.9092i		−	0.214688i	0.994222	−	0.107344i	$-0.0342346\pi$
$308$	−7.96036	−	13.7878i	−0.0258453	−	0.0447654i
$309$		0			0
$310$		0			0
$311$	216.659	+	125.088i	0.696652	+	0.402213i	0.806099	−	0.591780i	$-0.201575\pi$
$311$	216.659	+	125.088i	0.696652	+	0.402213i	−0.109447	+	0.993993i	$0.534908\pi$
$312$		0			0
$313$	−369.268	+	213.197i	−1.17977	+	0.681140i	−0.955961	−	0.293493i	$-0.905182\pi$
$313$	−369.268	+	213.197i	−1.17977	+	0.681140i	−0.223808	+	0.974633i	$0.571849\pi$
$314$		−	29.4416i		−	0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	−231.990	−	401.818i	−0.731829	−	1.26756i	−0.956101	−	0.293038i	$-0.905334\pi$
$317$	−231.990	−	401.818i	−0.731829	−	1.26756i	0.224272	−	0.974527i	$-0.427999\pi$
$318$		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	−0.963266	−	0.268549i	$-0.913456\pi$
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	0.249063	−	0.968487i	$-0.419877\pi$
$332$	−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	0.838323	−	0.545174i	$-0.183537\pi$
$337$	264.663	+	152.803i	0.785349	+	0.453422i	−0.0529735	+	0.998596i	$0.516870\pi$
$338$	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	−0.946116	−	0.323828i	$-0.895030\pi$
$347$	−66.8373	+	115.766i	−0.192615	+	0.333618i	0.753501	+	0.657446i	$0.228363\pi$
$348$		0			0
$349$	−49.3786	−	85.5262i	−0.141486	−	0.245061i	0.786570	−	0.617500i	$-0.211855\pi$
$349$	−49.3786	−	85.5262i	−0.141486	−	0.245061i	−0.928056	+	0.372440i	$0.878521\pi$
$350$		0			0
$351$		0			0
$352$			5.39388i			0.0153235i
$353$	163.058	+	282.424i	0.461919	+	0.800068i	0.999057	−	0.0434270i	$-0.0138276\pi$
$353$	163.058	+	282.424i	0.461919	+	0.800068i	−0.537137	+	0.843495i	$0.680494\pi$
$354$		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	$0.198199\pi$
$359$			418.736i			1.16639i	−0.812331	+	0.583197i	$0.801801\pi$
$360$		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	−0.704364	−	0.709839i	$-0.748768\pi$
$367$	−162.143	+	93.6135i	−0.441808	+	0.255078i	0.262557	+	0.964917i	$0.415434\pi$
$368$	−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	−0.125331	−	0.992115i	$-0.539999\pi$
$373$	−390.603	−	225.515i	−1.04719	−	0.604597i	−0.921862	+	0.387518i	$0.873333\pi$
$374$	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	−0.790883	−	0.611968i	$-0.790378\pi$
$383$	51.5281	−	89.2492i	0.134538	−	0.233027i	0.925421	+	0.378941i	$0.123712\pi$
$384$		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	−0.461363	−	0.887211i	$-0.652640\pi$
$389$	29.6816	−	17.1367i	0.0763024	−	0.0440532i	0.537666	+	0.843158i	$0.319306\pi$
$390$		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	$-0.996684\pi$
$397$		−	8.27245i		−	0.0208374i	0.999946	−	0.0104187i	$-0.00331643\pi$
$398$	−108.530	−	187.980i	−0.272689	−	0.472311i
$399$		0			0
$400$		0			0
$401$	−358.636	−	207.059i	−0.894355	−	0.516356i	−0.0189903	−	0.999820i	$-0.506045\pi$
$401$	−358.636	−	207.059i	−0.894355	−	0.516356i	−0.875364	+	0.483464i	$0.839378\pi$
$402$		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	−0.993577	−	0.113156i	$-0.963904\pi$
$409$	−163.106	+	282.508i	−0.398792	+	0.690729i	0.594785	+	0.803885i	$0.297237\pi$
$410$		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	−0.176903	−	0.984228i	$-0.556608\pi$
$419$	−468.325	−	270.388i	−1.11772	−	0.645317i	−0.940818	+	0.338912i	$0.889941\pi$
$420$		0			0
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	0.646922	−	0.762556i	$-0.276056\pi$
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	−0.983854	+	0.178973i	$0.942723\pi$
$422$	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	$-0.903467\pi$
$431$		−	257.429i		−	0.597282i	0.954365	−	0.298641i	$-0.0965334\pi$
$432$		0			0
$433$			476.272i			1.09994i	0.835186	+	0.549968i	$0.185360\pi$
$433$			476.272i			1.09994i	−0.835186	+	0.549968i	$0.814640\pi$
$434$	−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	−0.986435	−	0.164154i	$-0.947511\pi$
$439$	−278.931	−	483.123i	−0.635379	−	1.10051i	0.351056	−	0.936355i	$-0.385823\pi$
$440$		0			0
$441$		0			0
$442$		−	258.879i		−	0.585698i
$443$	−415.923	−	720.400i	−0.938879	−	1.62619i	−0.767567	−	0.640969i	$-0.778533\pi$
$443$	−415.923	−	720.400i	−0.938879	−	1.62619i	−0.171312	−	0.985217i	$-0.554801\pi$
$444$		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	$-0.697922\pi$
$449$		−	729.927i		−	1.62567i	0.582492	−	0.812836i	$-0.302078\pi$
$450$		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	−0.987504	−	0.157594i	$-0.949626\pi$
$457$	−614.563	+	354.818i	−1.34478	+	0.776407i	−0.357272	+	0.934000i	$0.616293\pi$
$458$	−171.890			−0.375307
$459$		0			0
$460$		0			0
$461$	7.96990	−	4.60142i	0.0172883	−	0.00998140i	−0.491331	−	0.870973i	$-0.663489\pi$
$461$	7.96990	−	4.60142i	0.0172883	−	0.00998140i	0.508619	+	0.860992i	$0.330156\pi$
$462$		0			0
$463$	47.8024	+	27.5987i	0.103245	+	0.0596085i	0.550733	−	0.834681i	$-0.314348\pi$
$463$	47.8024	+	27.5987i	0.103245	+	0.0596085i	−0.447488	+	0.894290i	$0.647681\pi$
$464$	−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	−0.193625	−	0.981076i	$-0.562024\pi$
$479$	267.856	−	154.647i	0.559199	−	0.322854i	0.752824	+	0.658222i	$0.228691\pi$
$480$		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	$0.00926095\pi$
$487$			28.3337i			0.0581800i	−0.999577	+	0.0290900i	$0.990739\pi$
$488$	18.5132	+	32.0658i	0.0379369	+	0.0657086i
$489$		0			0
$490$		0			0
$491$	−822.461	−	474.848i	−1.67507	−	0.967105i	−0.964727	−	0.263254i	$-0.915204\pi$
$491$	−822.461	−	474.848i	−1.67507	−	0.967105i	−0.710348	−	0.703851i	$-0.751462\pi$
$492$		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	0.436030	+	0.899932i	$0.356384\pi$
$499$	−280.113	+	485.170i	−0.561349	+	0.972284i	−0.997379	+	0.0723525i	$0.976949\pi$
$500$		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	0.323126	−	0.946356i	$-0.395266\pi$
$509$	−170.454	−	98.4114i	−0.334879	−	0.193343i	−0.658005	+	0.753013i	$0.728600\pi$
$510$		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	$-0.882542\pi$
$521$		−	375.837i		−	0.721377i	0.932686	−	0.360688i	$-0.117458\pi$
$522$		0			0
$523$			91.1827i			0.174345i	0.996193	+	0.0871727i	$0.0277832\pi$
$523$			91.1827i			0.174345i	−0.996193	+	0.0871727i	$0.972217\pi$
$524$	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	−0.0834344	−	0.996513i	$-0.526589\pi$
$547$	403.606	−	233.022i	0.737854	−	0.426000i	0.821289	+	0.570513i	$0.193256\pi$
$548$	−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	−0.999868	−	0.0162552i	$-0.994826\pi$
$563$	−273.537	+	473.780i	−0.485857	+	0.841528i	0.514011	+	0.857783i	$0.328159\pi$
$564$		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	−0.298082	−	0.954540i	$-0.596347\pi$
$569$	215.954	−	124.681i	0.379533	−	0.219123i	0.677615	+	0.735417i	$0.263014\pi$
$570$		0			0
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	−0.896540	−	0.442963i	$-0.853927\pi$
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	0.831887	+	0.554945i	$0.187261\pi$
$572$	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	$0.0121145\pi$
$577$			43.9092i			0.0760991i	−0.999276	+	0.0380496i	$0.987886\pi$
$578$	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	0.615228	−	0.788349i	$-0.289064\pi$
$587$	−220.194	−	381.386i	−0.375117	−	0.649721i	−0.990345	+	0.138628i	$0.955731\pi$
$588$		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	−0.195107	−	0.980782i	$-0.562505\pi$
$599$	−684.083	−	394.956i	−1.14204	−	0.659359i	−0.946936	+	0.321423i	$0.895839\pi$
$600$		0			0
$601$	353.455	+	612.201i	0.588111	+	1.01864i	0.994480	+	0.104929i	$0.0334614\pi$
$601$	353.455	+	612.201i	0.588111	+	1.01864i	−0.406369	+	0.913709i	$0.633205\pi$
$602$	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	−0.943263	−	0.332048i	$-0.892261\pi$
$607$	−1033.39	−	596.628i	−1.70246	−	0.982913i	−0.759193	−	0.650866i	$-0.774406\pi$
$608$	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	$0.171539\pi$
$613$			629.181i			1.02640i	−0.858270	+	0.513198i	$0.828461\pi$
$614$	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	−0.933489	−	0.358606i	$-0.883252\pi$
$617$	−96.3648	+	166.909i	−0.156183	+	0.270516i	0.777306	+	0.629122i	$0.216586\pi$
$618$		0			0
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	0.797615	−	0.603166i	$-0.206095\pi$
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	−0.921165	+	0.389172i	$0.872761\pi$
$620$		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	−0.327942	−	0.944698i	$-0.606355\pi$
$641$	209.106	−	120.727i	0.326219	−	0.188342i	0.654161	+	0.756355i	$0.273022\pi$
$642$		0			0
$643$	−685.380	−	395.704i	−1.06591	−	0.615403i	−0.138849	−	0.990314i	$-0.544340\pi$
$643$	−685.380	−	395.704i	−1.06591	−	0.615403i	−0.927061	+	0.374910i	$0.877674\pi$
$644$	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	0.406161	+	0.913802i	$0.366867\pi$
$653$	−384.156	+	665.379i	−0.588295	+	1.01896i	−0.994456	+	0.105155i	$0.966466\pi$
$654$		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	−0.755678	−	0.654944i	$-0.772692\pi$
$659$	−373.204	+	215.469i	−0.566318	+	0.326964i	0.189359	+	0.981908i	$0.439359\pi$
$660$		0			0
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	0.174157	+	0.984718i	$0.444280\pi$
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	−0.939869	+	0.341534i	$0.889053\pi$
$662$	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	−0.0917499	−	0.995782i	$-0.529246\pi$
$673$	487.755	−	281.606i	0.724748	−	0.418433i	0.816498	+	0.577349i	$0.195913\pi$
$674$			432.192i			0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	−175.068	−	303.227i	−0.258594	−	0.447897i	0.707272	−	0.706942i	$-0.249926\pi$
$677$	−175.068	−	303.227i	−0.258594	−	0.447897i	−0.965865	+	0.259044i	$0.916592\pi$
$678$		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	0.697150	−	0.716925i	$-0.254451\pi$
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	−0.969450	+	0.245287i	$0.921118\pi$
$692$	−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	$0.113571\pi$
$701$			489.681i			0.698546i	−0.937021	+	0.349273i	$0.886429\pi$
$702$		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	0.983349	−	0.181728i	$-0.0581689\pi$
$709$	237.014	+	410.521i	0.334294	+	0.579014i	−0.649055	+	0.760741i	$0.724836\pi$
$710$		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	$0.0239561\pi$
$719$			108.122i			0.150379i	−0.997169	+	0.0751894i	$0.976044\pi$
$720$		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	−0.211247	−	0.977433i	$-0.567752\pi$
$727$	385.027	−	222.296i	0.529611	−	0.305771i	0.740858	+	0.671662i	$0.234419\pi$
$728$	−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	0.859424	−	0.511264i	$-0.170823\pi$
$733$	620.388	+	358.181i	0.846368	+	0.488651i	−0.0130556	+	0.999915i	$0.504156\pi$
$734$	−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	−0.871329	−	0.490699i	$-0.836742\pi$
$743$	−7.95550	+	13.7793i	−0.0107073	+	0.0185455i	0.860622	+	0.509244i	$0.170075\pi$
$744$		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	0.459781	+	0.888033i	$0.347928\pi$
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	−0.998949	+	0.0458347i	$0.985405\pi$
$752$	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	$-0.849458\pi$
$757$		−	689.637i		−	0.911013i	0.890232	−	0.455506i	$-0.150542\pi$
$758$	346.246	+	599.716i	0.456789	+	0.791182i
$759$		0			0
$760$		0			0
$761$	825.393	+	476.541i	1.08462	+	0.626204i	0.932138	−	0.362103i	$-0.117941\pi$
$761$	825.393	+	476.541i	1.08462	+	0.626204i	0.152479	+	0.988307i	$0.451274\pi$
$762$		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	−0.996603	−	0.0823545i	$-0.973756\pi$
$769$	−328.348	+	568.715i	−0.426980	+	0.739552i	0.569623	+	0.821906i	$0.307089\pi$
$770$		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	0.878654	−	0.477459i	$-0.158442\pi$
$787$	711.833	+	410.977i	0.904489	+	0.522207i	0.0258350	+	0.999666i	$0.491776\pi$
$788$	−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	0.0686043	+	0.997644i	$0.478145\pi$
$797$	−661.257	+	1145.33i	−0.829683	+	1.43705i	−0.898287	+	0.439409i	$0.855188\pi$
$798$		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	$-0.953469\pi$
$809$		−	235.681i		−	0.291324i	0.989334	−	0.145662i	$-0.0465311\pi$
$810$		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	0.0887121	−	0.996057i	$-0.471725\pi$
$821$	817.453	−	471.956i	0.995679	−	0.574856i	0.906967	+	0.421202i	$0.138392\pi$
$822$		0			0
$823$	1399.27	+	807.871i	1.70021	+	0.981617i	0.945535	+	0.325520i	$0.105539\pi$
$823$	1399.27	+	807.871i	1.70021	+	0.981617i	0.754676	+	0.656097i	$0.227794\pi$
$824$	−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	−0.954561	−	0.298016i	$-0.903675\pi$
$839$	−984.778	+	568.562i	−1.17375	+	0.677666i	−0.219191	+	0.975682i	$0.570342\pi$
$840$		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	−0.653486	−	0.756939i	$-0.726694\pi$
$853$	−276.970	+	159.909i	−0.324701	+	0.187466i	0.328785	+	0.944405i	$0.393361\pi$
$854$		−	154.557i		−	0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	398.984	+	691.061i	0.465559	+	0.806372i	0.999227	−	0.0393225i	$-0.0125200\pi$
$857$	398.984	+	691.061i	0.465559	+	0.806372i	−0.533668	+	0.845694i	$0.679187\pi$
$858$		0			0
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	−0.969449	−	0.245293i	$-0.921116\pi$
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	0.697155	+	0.716921i	$0.254449\pi$
$860$		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	0.303977	−	0.952679i	$-0.401685\pi$
$877$	−323.682	−	186.878i	−0.369079	−	0.213088i	−0.673056	+	0.739592i	$0.735019\pi$
$878$	394.469	−	683.240i	0.449281	−	0.778177i
$879$		0			0
$880$		0			0
$881$			229.979i			0.261043i	0.991445	+	0.130522i	$0.0416652\pi$
$881$			229.979i			0.261043i	−0.991445	+	0.130522i	$0.958335\pi$
$882$		0			0
$883$		−	1381.79i		−	1.56488i	−0.622728	−	0.782439i	$-0.713976\pi$
$883$		−	1381.79i		−	1.56488i	0.622728	−	0.782439i	$-0.286024\pi$
$884$	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	−0.999975	−	0.00702852i	$-0.997763\pi$
$887$	−438.090	+	758.794i	−0.493901	+	0.855461i	0.506075	+	0.862490i	$0.331096\pi$
$888$		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	−0.943119	−	0.332456i	$-0.892123\pi$
$907$	−1021.97	+	590.037i	−1.12676	+	0.650537i	−0.183644	+	0.982993i	$0.558789\pi$
$908$	152.542			0.167998
$909$		0			0
$910$		0			0
$911$	−1100.13	+	635.158i	−1.20760	+	0.697210i	−0.962235	−	0.272220i	$-0.912242\pi$
$911$	−1100.13	+	635.158i	−1.20760	+	0.697210i	−0.245368	+	0.969430i	$0.578909\pi$
$912$		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	−0.178145	−	0.984004i	$-0.557009\pi$
$929$	543.424	−	313.746i	0.584956	−	0.337724i	0.763100	+	0.646280i	$0.223676\pi$
$930$		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	$-0.919343\pi$
$937$		−	469.789i		−	0.501375i	0.968068	−	0.250688i	$-0.0806567\pi$
$938$	443.012	+	767.320i	0.472295	+	0.818039i
$939$		0			0
$940$		0			0
$941$	−805.984	−	465.335i	−0.856518	−	0.494511i	0.00632656	−	0.999980i	$-0.497986\pi$
$941$	−805.984	−	465.335i	−0.856518	−	0.494511i	−0.862845	+	0.505469i	$0.831320\pi$
$942$		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	0.865065	−	0.501659i	$-0.167277\pi$
$947$	−1.81556	−	3.14465i	−0.00191717	−	0.00332064i	−0.866982	+	0.498339i	$0.833944\pi$
$948$		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	0.515047	−	0.857162i	$-0.327774\pi$
$967$	29.2491	+	16.8870i	0.0302473	+	0.0174633i	−0.484800	+	0.874625i	$0.661108\pi$
$968$	169.834	−	294.161i	0.175448	−	0.303886i
$969$		0			0
$970$		0			0
$971$			970.472i			0.999456i	0.866182	+	0.499728i	$0.166567\pi$
$971$			970.472i			0.999456i	−0.866182	+	0.499728i	$0.833433\pi$
$972$		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	−0.113574	−	0.993529i	$-0.536230\pi$
$977$	785.151	−	1359.92i	0.803635	−	1.39194i	0.917209	−	0.398406i	$-0.130437\pi$
$978$		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	0.993056	−	0.117641i	$-0.0375331\pi$
$983$	387.939	+	671.930i	0.394648	+	0.683551i	−0.598408	+	0.801192i	$0.704200\pi$
$984$		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	−0.931286	−	0.364290i	$-0.881312\pi$
$997$	−1078.20	+	622.499i	−1.08144	+	0.624372i	−0.150159	+	0.988662i	$0.547978\pi$
$998$	−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.449.4		8
3.2	odd	2		450.3.k.a.149.1		8
5.2	odd	4		54.3.d.a.17.1		4
5.3	odd	4		1350.3.i.b.1151.2		4
5.4	even	2	inner	1350.3.k.a.449.1		8
9.2	odd	6	inner	1350.3.k.a.899.1		8
9.7	even	3		450.3.k.a.299.4		8
15.2	even	4		18.3.d.a.5.2	✓	4
15.8	even	4		450.3.i.b.401.1		4
15.14	odd	2		450.3.k.a.149.4		8
20.7	even	4		432.3.q.d.17.1		4
40.27	even	4		1728.3.q.c.449.1		4
40.37	odd	4		1728.3.q.d.449.2		4
45.2	even	12		54.3.d.a.35.1		4
45.7	odd	12		18.3.d.a.11.2	yes	4
45.22	odd	12		162.3.b.a.161.1		4
45.29	odd	6	inner	1350.3.k.a.899.4		8
45.32	even	12		162.3.b.a.161.4		4
45.34	even	6		450.3.k.a.299.1		8
45.38	even	12		1350.3.i.b.251.2		4
45.43	odd	12		450.3.i.b.101.1		4
60.47	odd	4		144.3.q.c.113.2		4
120.77	even	4		576.3.q.f.257.2		4
120.107	odd	4		576.3.q.e.257.1		4
180.7	even	12		144.3.q.c.65.2		4
180.47	odd	12		432.3.q.d.305.1		4
180.67	even	12		1296.3.e.g.161.2		4
180.167	odd	12		1296.3.e.g.161.4		4
360.187	even	12		576.3.q.e.65.1		4
360.227	odd	12		1728.3.q.c.1601.1		4
360.277	odd	12		576.3.q.f.65.2		4
360.317	even	12		1728.3.q.d.1601.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	15.2	even	4
18.3.d.a.11.2	yes	4	45.7	odd	12
54.3.d.a.17.1		4	5.2	odd	4
54.3.d.a.35.1		4	45.2	even	12
144.3.q.c.65.2		4	180.7	even	12
144.3.q.c.113.2		4	60.47	odd	4
162.3.b.a.161.1		4	45.22	odd	12
162.3.b.a.161.4		4	45.32	even	12
432.3.q.d.17.1		4	20.7	even	4
432.3.q.d.305.1		4	180.47	odd	12
450.3.i.b.101.1		4	45.43	odd	12
450.3.i.b.401.1		4	15.8	even	4
450.3.k.a.149.1		8	3.2	odd	2
450.3.k.a.149.4		8	15.14	odd	2
450.3.k.a.299.1		8	45.34	even	6
450.3.k.a.299.4		8	9.7	even	3
576.3.q.e.65.1		4	360.187	even	12
576.3.q.e.257.1		4	120.107	odd	4
576.3.q.f.65.2		4	360.277	odd	12
576.3.q.f.257.2		4	120.77	even	4
1296.3.e.g.161.2		4	180.67	even	12
1296.3.e.g.161.4		4	180.167	odd	12
1350.3.i.b.251.2		4	45.38	even	12
1350.3.i.b.1151.2		4	5.3	odd	4
1350.3.k.a.449.1		8	5.4	even	2	inner
1350.3.k.a.449.4		8	1.1	even	1	trivial
1350.3.k.a.899.1		8	9.2	odd	6	inner
1350.3.k.a.899.4		8	45.29	odd	6	inner
1728.3.q.c.449.1		4	40.27	even	4
1728.3.q.c.1601.1		4	360.227	odd	12
1728.3.q.d.449.2		4	40.37	odd	4
1728.3.q.d.1601.2		4	360.317	even	12

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

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Representations

Groups

Database

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