LMFDB - Embedded newform 450.3.k.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(149,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, 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("450.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.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:	$12.2616118962$
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			149.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.149
Dual form			450.3.k.a.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(7.22999 - 4.17423i) q^{7} +2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(7.22999 - 4.17423i) q^{7} +2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(5.97469 - 0.550510i) q^{12} +(8.39780 + 4.84847i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} +18.8776 q^{17} +(12.5136 - 2.32577i) q^{18} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-1.16781 - 0.674235i) q^{22} +(-0.476756 + 0.825765i) q^{23} +(-4.89898 - 6.92820i) q^{24} -13.7135i q^{26} +(25.9808 - 7.34847i) q^{27} +16.6969i q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-2.59808 - 1.19694i) q^{33} +(-13.3485 - 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} -46.6969i q^{37} +(-17.4634 - 30.2474i) q^{38} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(3.24980 + 35.2702i) q^{42} +(39.0105 - 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(-22.6435 - 39.2196i) q^{47} +(-5.02118 + 10.8990i) q^{48} +(10.3485 - 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(-16.7956 + 9.69694i) q^{52} -94.3879 q^{53} +(-27.3712 - 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(-42.7764 - 60.4949i) q^{57} +(16.7563 + 9.67423i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +4.30686 q^{62} +(13.7296 + 73.8712i) q^{63} +8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(64.9912 + 37.5227i) q^{67} +(-18.8776 + 32.6969i) q^{68} +(2.84847 - 0.262459i) q^{69} -18.0204i q^{71} +(-8.48528 + 24.0000i) q^{72} -7.90918i q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(3.98018 - 6.89388i) q^{77} +(-33.5912 + 23.7526i) q^{78} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +15.4393i q^{82} +(-65.1662 - 112.871i) q^{83} +(40.8990 - 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(37.2784 + 17.1742i) q^{87} +(2.33562 - 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(-0.953512 - 1.65153i) q^{92} +(9.09769 - 0.838264i) q^{93} +(-32.0227 + 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(95.1576 - 54.9393i) q^{97} -29.2699 q^{98} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9	$ 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51} - 72 q^{54} + 144 q^{56} - 252 q^{59} + 124 q^{61} + 64 q^{64} - 144 q^{66} - 36 q^{69} - 144 q^{74} - 80 q^{76} - 28 q^{79} - 504 q^{81} + 288 q^{84} - 216 q^{86} + 824 q^{91} - 168 q^{94} + 96 q^{96} - 252 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−1.73205	−	2.44949i	−0.577350	−	0.816497i
$3$	−1.73205	−	2.44949i	−0.577350	−	0.816497i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.77526	+	3.85337i	−0.295876	+	0.642229i
$7$	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
$9$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$10$		0			0
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	−0.461995	−	0.886882i	$-0.652866\pi$
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	0.537065	+	0.843541i	$0.319533\pi$
$12$	5.97469	−	0.550510i	0.497891	−	0.0458759i
$13$	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	$-0.312633\pi$
$17$	18.8776			1.11045			0.555223	+	0.831701i	$0.312633\pi$
$18$	12.5136	−	2.32577i	0.695201	−	0.129209i
$19$	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
$21$	−22.7474	−	10.4798i	−1.08321	−	0.499038i
$22$	−1.16781	−	0.674235i	−0.0530822	−	0.0306470i
$23$	−0.476756	+	0.825765i	−0.0207285	+	0.0359028i	−0.876204	−	0.481941i	$-0.839932\pi$
$23$	−0.476756	+	0.825765i	−0.0207285	+	0.0359028i	0.855475	+	0.517844i	$0.173265\pi$
$24$	−4.89898	−	6.92820i	−0.204124	−	0.288675i
$25$		0			0
$26$		−	13.7135i		−	0.527444i
$27$	25.9808	−	7.34847i	0.962250	−	0.272166i
$28$			16.6969i			0.596319i
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	−0.690174	−	0.723643i	$-0.742466\pi$
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	0.281606	+	0.959530i	$0.409133\pi$
$30$		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
$33$	−2.59808	−	1.19694i	−0.0787296	−	0.0362709i
$34$	−13.3485	−	23.1202i	−0.392602	−	0.680007i
$35$		0			0
$36$	−11.6969	−	13.6814i	−0.324915	−	0.380040i
$37$		−	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
$39$	−2.66913	−	28.9681i	−0.0684393	−	0.742772i
$40$		0			0
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	0.380249	−	0.924884i	$-0.375838\pi$
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	−0.610849	+	0.791747i	$0.709172\pi$
$42$	3.24980	+	35.2702i	0.0773763	+	0.839766i
$43$	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	0.518005	−	0.855377i	$-0.326675\pi$
$47$	−22.6435	−	39.2196i	−0.481776	−	0.834460i	−0.999781	+	0.0209170i	$0.993341\pi$
$48$	−5.02118	+	10.8990i	−0.104608	+	0.227062i
$49$	10.3485	−	17.9241i	0.211193	−	0.365797i
$50$		0			0
$51$	−32.6969	−	46.2405i	−0.641116	−	0.906676i
$52$	−16.7956	+	9.69694i	−0.322992	+	0.186480i
$53$	−94.3879			−1.78090			−0.890452	−	0.455077i	$-0.849612\pi$
$53$	−94.3879			−1.78090			−0.890452	+	0.455077i	$0.849612\pi$
$54$	−27.3712	−	26.6237i	−0.506874	−	0.493031i
$55$		0			0
$56$	20.4495	−	11.8065i	0.365169	−	0.210831i
$57$	−42.7764	−	60.4949i	−0.750462	−	1.06131i
$58$	16.7563	+	9.67423i	0.288901	+	0.166797i
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	0.631466	−	0.775404i	$-0.282454\pi$
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	−0.355787	+	0.934567i	$0.615787\pi$
$60$		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
$63$	13.7296	+	73.8712i	0.217930	+	1.17256i
$64$	8.00000			0.125000
$65$		0			0
$66$	0.371173	+	4.02834i	0.00562383	+	0.0610355i
$67$	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
$69$	2.84847	−	0.262459i	0.0412822	−	0.00380375i
$70$		0			0
$71$		−	18.0204i		−	0.253808i	−0.991915	−	0.126904i	$-0.959496\pi$
$71$		−	18.0204i		−	0.253808i	0.991915	−	0.126904i	$-0.0405041\pi$
$72$	−8.48528	+	24.0000i	−0.117851	+	0.333333i
$73$		−	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
$78$	−33.5912	+	23.7526i	−0.430656	+	0.304520i
$79$	−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
$81$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$82$			15.4393i			0.188284i
$83$	−65.1662	−	112.871i	−0.785135	−	1.35989i	−0.928918	−	0.370284i	$-0.879260\pi$
$83$	−65.1662	−	112.871i	−0.785135	−	1.35989i	0.143783	−	0.989609i	$-0.454073\pi$
$84$	40.8990	−	28.9199i	0.486893	−	0.344285i
$85$		0			0
$86$	−55.1691	−	31.8519i	−0.641502	−	0.370371i
$87$	37.2784	+	17.1742i	0.428488	+	0.197405i
$88$	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
$93$	9.09769	−	0.838264i	0.0978246	−	0.00901359i
$94$	−32.0227	+	55.4650i	−0.340667	+	0.590053i
$95$		0			0
$96$	16.8990	−	1.55708i	0.176031	−	0.0162196i
$97$	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
$99$	1.56811	+	8.43712i	0.0158395	+	0.0852234i
$100$		0			0
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.291022	−	0.956716i	$-0.406005\pi$
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.974052	+	0.226326i	$0.0726714\pi$
$102$	−33.5125	+	72.7423i	−0.328554	+	0.713160i
$103$	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	$-0.553865\pi$
$107$	−36.0408			−0.336830			−0.168415	+	0.985716i	$0.553865\pi$
$108$	−13.2528	+	52.3485i	−0.122711	+	0.484708i
$109$	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
$111$	−114.384	+	80.8815i	−1.03048	+	0.728662i
$112$	−28.9199	−	16.6969i	−0.258214	−	0.149080i
$113$	85.5439	−	148.166i	0.757025	−	1.31121i	−0.187336	−	0.982296i	$-0.559985\pi$
$113$	85.5439	−	148.166i	0.757025	−	1.31121i	0.944361	−	0.328910i	$-0.106681\pi$
$114$	−43.8434	+	95.1665i	−0.384591	+	0.834794i
$115$		0			0
$116$		−	27.3629i		−	0.235887i
$117$	−66.3340	+	56.7122i	−0.566957	+	0.484720i
$118$		−	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
$123$	3.00502	+	32.6135i	0.0244311	+	0.265151i
$124$	−3.04541	−	5.27480i	−0.0245597	−	0.0425387i
$125$		0			0
$126$	80.7650	−	69.0501i	0.640992	−	0.548016i
$127$			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
$129$	−122.737	−	56.5453i	−0.951452	−	0.438335i
$130$		0			0
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.998342	+	0.0575598i	$0.0183320\pi$
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.549019	+	0.835810i	$0.315001\pi$
$132$	4.67123	−	3.30306i	0.0353881	−	0.0250232i
$133$	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	$-0.982501\pi$
$137$	−74.9156	−	129.758i	−0.546829	−	0.947136i	0.451660	−	0.892190i	$-0.350832\pi$
$138$	−2.33562	−	3.30306i	−0.0169248	−	0.0239352i
$139$	−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
$141$	−56.8485	+	123.395i	−0.403181	+	0.875144i
$142$	−22.0704	+	12.7423i	−0.155425	+	0.0897348i
$143$	9.24614			0.0646584
$144$	35.3939	−	6.57826i	0.245791	−	0.0456823i
$145$		0			0
$146$	−9.68673	+	5.59264i	−0.0663475	+	0.0383057i
$147$	−61.8289	+	5.69694i	−0.420605	+	0.0387547i
$148$	80.8815	+	46.6969i	0.546496	+	0.315520i
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	0.125242	−	0.992126i	$-0.460029\pi$
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	−0.796585	+	0.604526i	$0.793362\pi$
$150$		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
$153$	−56.6328	+	160.182i	−0.370149	+	1.04694i
$154$	−11.2577			−0.0731016
$155$		0			0
$156$	52.8434	+	24.3450i	0.338740	+	0.156058i
$157$	−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
$159$	163.485	+	231.202i	1.02821	+	1.45410i
$160$		0			0
$161$			7.96036i			0.0494433i
$162$	−17.8061	+	113.159i	−0.109914	+	0.698512i
$163$			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	$0.510311\pi$
$167$	−147.255	+	255.053i	−0.881765	+	1.52726i	−0.849377	+	0.527787i	$0.823022\pi$
$168$	−64.3395	−	29.6413i	−0.382973	−	0.176436i
$169$	−37.4847	−	64.9254i	−0.221803	−	0.384174i
$170$		0			0
$171$	−74.0908	+	209.560i	−0.433280	+	1.22550i
$172$			90.0908i			0.523784i
$173$	−34.6322	−	59.9847i	−0.200186	−	0.346732i	0.748402	−	0.663245i	$-0.230821\pi$
$173$	−34.6322	−	59.9847i	−0.200186	−	0.346732i	−0.948588	+	0.316513i	$0.897488\pi$
$174$	−5.32577	−	57.8006i	−0.0306078	−	0.332187i
$175$		0			0
$176$	−3.30306	−	1.90702i	−0.0187674	−	0.0108354i
$177$	−5.16964	−	56.1061i	−0.0292070	−	0.316984i
$178$	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
$183$	−16.4328	+	35.6691i	−0.0897969	+	0.194913i
$184$	−1.34847	+	2.33562i	−0.00732864	+	0.0126936i
$185$		0			0
$186$	−7.45969	−	10.5496i	−0.0401059	−	0.0567183i
$187$	15.5885	−	9.00000i	0.0833607	−	0.0481283i
$188$	90.5739			0.481776
$189$	157.166	−	161.579i	0.831568	−	0.854916i
$190$		0			0
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	−0.482828	−	0.875715i	$-0.660390\pi$
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	0.516978	+	0.855999i	$0.327057\pi$
$192$	−13.8564	−	19.5959i	−0.0721688	−	0.102062i
$193$	−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	$-0.562796\pi$
$197$	−77.2247			−0.392004			−0.196002	+	0.980604i	$0.562796\pi$
$198$	9.22450	−	7.88648i	0.0465884	−	0.0398307i
$199$	−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
$201$	−20.6566	−	224.187i	−0.102769	−	1.11536i
$202$	−180.698	−	104.326i	−0.894542	−	0.516464i
$203$	−57.1095	+	98.9166i	−0.281328	+	0.487274i
$204$	112.788	−	10.3923i	0.552881	−	0.0509427i
$205$		0			0
$206$		−	145.857i		−	0.708042i
$207$	−5.57658	−	6.52270i	−0.0269400	−	0.0315106i
$208$		−	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
$213$	−44.1408	+	31.2122i	−0.207234	+	0.146536i
$214$	25.4847	+	44.1408i	0.119087	+	0.206265i
$215$		0			0
$216$	73.4847	−	20.7846i	0.340207	−	0.0962250i
$217$			25.4245i			0.117164i
$218$	−104.844	−	181.596i	−0.480938	−	0.833009i
$219$	−19.3735	+	13.6991i	−0.0884633	+	0.0625530i
$220$		0			0
$221$	158.530	+	91.5274i	0.717331	+	0.414151i
$222$	179.941	+	82.8990i	0.810543	+	0.373419i
$223$	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	0.937716	−	0.347403i	$-0.112936\pi$
$227$	38.1356	+	66.0528i	0.167998	+	0.290982i	−0.769718	+	0.638384i	$0.779603\pi$
$228$	147.557	−	13.5959i	0.647178	−	0.0596312i
$229$	−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
$231$	−23.7804	+	2.19113i	−0.102945	+	0.00948541i
$232$	−33.5125	+	19.3485i	−0.144451	+	0.0833986i
$233$	−151.021			−0.648157			−0.324079	−	0.946030i	$-0.605054\pi$
$233$	−151.021			−0.648157			−0.324079	+	0.946030i	$0.605054\pi$
$234$	116.363	+	41.1406i	0.497279	+	0.175815i
$235$		0			0
$236$	−32.5301	+	18.7813i	−0.137839	+	0.0795816i
$237$	−54.9095	+	119.187i	−0.231686	+	0.502898i
$238$	−193.019	−	111.439i	−0.811002	−	0.468232i
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	0.650426	−	0.759570i	$-0.274590\pi$
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	−0.332593	+	0.943070i	$0.607924\pi$
$240$		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
$243$	−15.5885	+	242.499i	−0.0641500	+	0.997940i
$244$	26.1816			0.107302
$245$		0			0
$246$	37.8184	−	26.7416i	0.153733	−	0.108706i
$247$	207.400	+	119.742i	0.839675	+	0.484787i
$248$	−4.30686	+	7.45969i	−0.0173664	+	0.0300794i
$249$	−163.606	+	355.123i	−0.657051	+	1.42619i
$250$		0			0
$251$		−	52.6261i		−	0.209666i	−0.994490	−	0.104833i	$-0.966569\pi$
$251$		−	52.6261i		−	0.209666i	0.994490	−	0.104833i	$-0.0334307\pi$
$252$	−141.678	−	50.0908i	−0.562215	−	0.198773i
$253$			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	$-0.883521\pi$
$257$	−40.3532	+	69.8939i	−0.157017	+	0.271961i	0.776775	+	0.629778i	$0.216854\pi$
$258$	17.5348	+	190.305i	0.0679644	+	0.737618i
$259$	−194.924	−	337.618i	−0.752602	−	1.30355i
$260$		0			0
$261$	−22.5000	−	121.060i	−0.0862069	−	0.463830i
$262$		−	331.015i		−	1.26342i
$263$	231.872	+	401.614i	0.881641	+	1.52705i	0.849515	+	0.527564i	$0.176894\pi$
$263$	231.872	+	401.614i	0.881641	+	1.52705i	0.0321259	+	0.999484i	$0.489772\pi$
$264$	−7.34847	−	3.38545i	−0.0278351	−	0.0128237i
$265$		0			0
$266$	−252.520	−	145.792i	−0.949323	−	0.548092i
$267$	355.910	−	251.666i	1.33300	−	0.942570i
$268$	−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
$273$	−140.217	−	198.297i	−0.513617	−	0.726364i
$274$	−105.947	+	183.505i	−0.386667	+	0.669726i
$275$		0			0
$276$	−2.39388	+	5.19615i	−0.00867347	+	0.0188266i
$277$	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
$279$	−17.8110	−	20.8328i	−0.0638386	−	0.0746694i
$280$		0			0
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	−0.531476	−	0.847073i	$-0.678362\pi$
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	0.467849	+	0.883808i	$0.345029\pi$
$282$	191.326	−	17.6288i	0.678460	−	0.0625136i
$283$	−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
$288$	−33.0839	−	38.6969i	−0.114875	−	0.134364i
$289$	67.3633			0.233091
$290$		0			0
$291$	−299.391	−	137.930i	−1.02884	−	0.473986i
$292$	13.6991	+	7.90918i	0.0469148	+	0.0270862i
$293$	7.46196	−	12.9245i	0.0254674	−	0.0441109i	−0.853011	−	0.521893i	$-0.825226\pi$
$293$	7.46196	−	12.9245i	0.0254674	−	0.0441109i	0.878478	+	0.477782i	$0.158559\pi$
$294$	50.6969	+	71.6963i	0.172439	+	0.243865i
$295$		0			0
$296$		−	132.079i		−	0.446212i
$297$	17.9506	−	18.4546i	0.0604397	−	0.0621367i
$298$			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
$303$	−402.006	−	185.205i	−1.32675	−	0.611237i
$304$	−49.3939	−	85.5527i	−0.162480	−	0.281423i
$305$		0			0
$306$	236.227	−	43.9048i	0.771984	−	0.143480i
$307$		−	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
$309$	−28.3888	−	308.104i	−0.0918731	−	0.997099i
$310$		0			0
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	0.109447	−	0.993993i	$-0.465092\pi$
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	−0.806099	+	0.591780i	$0.798425\pi$
$312$	−7.54945	−	81.9342i	−0.0241969	−	0.262610i
$313$	−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	$0.0946661\pi$
$317$	231.990	+	401.818i	0.731829	+	1.26756i	−0.224272	+	0.974527i	$0.572001\pi$
$318$	167.563	−	363.712i	0.526927	−	1.14375i
$319$	−6.52270	+	11.2977i	−0.0204473	+	0.0354158i
$320$		0			0
$321$	62.4245	+	88.2816i	0.194469	+	0.275020i
$322$	9.74941	−	5.62883i	0.0302777	−	0.0174808i
$323$	466.219			1.44340
$324$	151.182	−	58.2075i	0.466610	−	0.179653i
$325$		0			0
$326$	162.965	−	94.0878i	0.499892	−	0.288613i
$327$	−256.815	−	363.192i	−0.785368	−	1.11068i
$328$	−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
$333$	396.237	+	140.091i	1.18990	+	0.420693i
$334$	416.499			1.24700
$335$		0			0
$336$	9.19184	+	99.7591i	0.0273567	+	0.296902i
$337$	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
$339$	−511.098	+	47.0928i	−1.50766	+	0.138917i
$340$		0			0
$341$			2.90383i			0.00851564i
$342$	309.048	−	57.4393i	0.903650	−	0.167951i
$343$			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	$-0.771637\pi$
$347$	66.8373	−	115.766i	0.192615	−	0.333618i	0.946116	+	0.323828i	$0.104970\pi$
$348$	−67.0251	+	47.3939i	−0.192601	+	0.136189i
$349$	−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
$351$	253.810	+	64.2560i	0.723105	+	0.183065i
$352$			5.39388i			0.0153235i
$353$	−163.058	−	282.424i	−0.461919	−	0.800068i	0.537137	−	0.843495i	$-0.319506\pi$
$353$	−163.058	−	282.424i	−0.461919	−	0.800068i	−0.999057	+	0.0434270i	$0.986172\pi$
$354$	−65.0602	+	46.0045i	−0.183786	+	0.129956i
$355$		0			0
$356$	−251.666	−	145.300i	−0.706928	−	0.408145i
$357$	−429.417	−	197.833i	−1.20285	−	0.554155i
$358$	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
$363$	358.753	−	33.0556i	0.988300	−	0.0910623i
$364$	−80.9546	+	140.217i	−0.222403	+	0.385213i
$365$		0			0
$366$	55.3054	−	5.09586i	0.151108	−	0.0139231i
$367$	−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
$369$	74.6816	−	63.8490i	0.202389	−	0.173033i
$370$		0			0
$371$	−682.423	+	393.997i	−1.83942	+	1.06199i
$372$	−7.64577	+	16.5959i	−0.0205531	+	0.0446127i
$373$	−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
$378$	−309.027	−	78.2350i	−0.817531	−	0.206971i
$379$	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
$381$	191.283	−	135.257i	0.502054	−	0.355006i
$382$	−9.22450	−	5.32577i	−0.0241479	−	0.0139418i
$383$	−51.5281	+	89.2492i	−0.134538	+	0.233027i	−0.925421	−	0.378941i	$-0.876288\pi$
$383$	−51.5281	+	89.2492i	−0.134538	+	0.233027i	0.790883	+	0.611968i	$0.209622\pi$
$384$	−14.2020	+	30.8270i	−0.0369845	+	0.0802786i
$385$		0			0
$386$			488.546i			1.26566i
$387$	74.0801	+	398.583i	0.191421	+	1.02993i
$388$			219.757i			0.566384i
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	−0.537666	−	0.843158i	$-0.680694\pi$
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	0.461363	+	0.887211i	$0.347360\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	29.2699	−	50.6969i	0.0746681	−	0.129329i
$393$	−64.4270	−	699.227i	−0.163936	−	1.77920i
$394$	54.6061	+	94.5806i	0.138594	+	0.240052i
$395$		0			0
$396$	−16.1816	−	5.72107i	−0.0408627	−	0.0144471i
$397$		−	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
$399$	−561.792	−	258.819i	−1.40800	−	0.648669i
$400$		0			0
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.875364	−	0.483464i	$-0.160622\pi$
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.0189903	+	0.999820i	$0.493955\pi$
$402$	−259.965	+	183.823i	−0.646679	+	0.457271i
$403$	−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
$408$	−92.4809	−	130.788i	−0.226669	−	0.320558i
$409$	−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
$411$	−188.082	+	408.252i	−0.457621	+	0.993314i
$412$	−178.637	+	103.136i	−0.433585	+	0.250331i
$413$	156.795			0.379648
$414$	−4.04541	+	11.4421i	−0.00977152	+	0.0276380i
$415$		0			0
$416$	−47.5051	+	27.4271i	−0.114195	+	0.0659305i
$417$	252.521	−	23.2673i	0.605565	−	0.0557970i
$418$	−28.8413	−	16.6515i	−0.0689983	−	0.0398362i
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.940818	−	0.338912i	$-0.110059\pi$
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.176903	+	0.984228i	$0.443392\pi$
$420$		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
$423$	400.720	−	74.4773i	0.947329	−	0.176069i
$424$	−266.969			−0.629645
$425$		0			0
$426$	69.4393	+	31.9908i	0.163003	+	0.0750958i
$427$	−94.6464	−	54.6441i	−0.221654	−	0.127972i
$428$	36.0408	−	62.4245i	0.0842075	−	0.145852i
$429$	−16.0148	−	22.6483i	−0.0373305	−	0.0527933i
$430$		0			0
$431$			257.429i			0.597282i	0.954365	+	0.298641i	$0.0965334\pi$
$431$			257.429i			0.597282i	−0.954365	+	0.298641i	$0.903467\pi$
$432$	−77.4174	−	75.3031i	−0.179207	−	0.174313i
$433$			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
$438$	30.4770	+	14.0408i	0.0695822	+	0.0320567i
$439$	−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
$441$	121.045	+	141.582i	0.274479	+	0.321047i
$442$		−	258.879i		−	0.585698i
$443$	415.923	+	720.400i	0.938879	+	1.62619i	0.767567	+	0.640969i	$0.221467\pi$
$443$	415.923	+	720.400i	0.938879	+	1.62619i	0.171312	+	0.985217i	$0.445199\pi$
$444$	−25.7071	−	279.000i	−0.0578990	−	0.628378i
$445$		0			0
$446$	−383.623	−	221.485i	−0.860142	−	0.496603i
$447$	31.7933	+	345.053i	0.0711259	+	0.771930i
$448$	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
$453$	81.3092	−	176.490i	0.179490	−	0.389602i
$454$	53.9319	−	93.4128i	0.118793	−	0.205755i
$455$		0			0
$456$	−120.990	−	171.105i	−0.265328	−	0.375231i
$457$	−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
$459$	490.454	−	138.721i	1.06853	−	0.302225i
$460$		0			0
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	−0.508619	−	0.860992i	$-0.669844\pi$
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	0.491331	+	0.870973i	$0.336511\pi$
$462$	19.4988	+	27.5755i	0.0422053	+	0.0596872i
$463$	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	$-0.266280\pi$
$467$	625.811			1.34007			0.670033	+	0.742331i	$0.266280\pi$
$468$	−31.8945	−	171.606i	−0.0681506	−	0.366680i
$469$	626.514			1.33585
$470$		0			0
$471$	5.73036	+	62.1917i	0.0121664	+	0.132042i
$472$	46.0045	+	26.5607i	0.0974672	+	0.0562727i
$473$	21.4757	−	37.1969i	0.0454031	−	0.0786405i
$474$	184.800	−	17.0276i	0.389874	−	0.0359231i
$475$		0			0
$476$			315.198i			0.662180i
$477$	283.164	−	800.908i	0.593635	−	1.67905i
$478$		−	124.045i		−	0.259509i
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	−0.752824	−	0.658222i	$-0.771309\pi$
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	0.193625	+	0.981076i	$0.437976\pi$
$480$		0			0
$481$	226.409	−	392.151i	0.470704	−	0.815283i
$482$	−142.685	+	247.139i	−0.296028	+	0.512736i
$483$	19.4988	−	13.7878i	0.0403702	−	0.0285461i
$484$	−120.091	−	208.003i	−0.248122	−	0.429759i
$485$		0			0
$486$	308.023	−	152.381i	0.633792	−	0.313541i
$487$			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
$489$	325.930	−	230.467i	0.666523	−	0.471303i
$490$		0			0
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.964727	+	0.263254i	$0.0847956\pi$
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.710348	+	0.703851i	$0.248538\pi$
$492$	−59.4933	−	27.4087i	−0.120921	−	0.0557087i
$493$	−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
$498$	550.621	−	50.7344i	1.10566	−	0.101876i
$499$	−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
$501$	879.802	−	81.0653i	1.75609	−	0.161807i
$502$	−64.4535	+	37.2122i	−0.128393	+	0.0741280i
$503$	−897.832			−1.78495			−0.892477	−	0.451094i	$-0.851034\pi$
$503$	−897.832			−1.78495			−0.892477	+	0.451094i	$0.851034\pi$
$504$	38.8332	+	208.939i	0.0770499	+	0.414562i
$505$		0			0
$506$	1.11352	−	0.642891i	0.00220063	−	0.00127053i
$507$	−94.1087	+	204.272i	−0.185619	+	0.402904i
$508$	−135.257	−	78.0908i	−0.266254	−	0.153722i
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	0.658005	−	0.753013i	$-0.271400\pi$
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	−0.323126	+	0.946356i	$0.604734\pi$
$510$		0			0
$511$	−33.0148	−	57.1833i	−0.0646082	−	0.111905i
$512$	22.6274			0.0441942
$513$	641.645	−	181.485i	1.25077	−	0.353771i
$514$	114.136			0.222055
$515$		0			0
$516$	220.677	−	156.042i	0.427668	−	0.302407i
$517$	−37.3964	−	21.5908i	−0.0723334	−	0.0417617i
$518$	−275.664	+	477.464i	−0.532170	+	0.921746i
$519$	−86.9472	+	188.728i	−0.167528	+	0.363637i
$520$		0			0
$521$			375.837i			0.721377i	0.932686	+	0.360688i	$0.117458\pi$
$521$			375.837i			0.721377i	−0.932686	+	0.360688i	$0.882542\pi$
$522$	−132.357	+	113.159i	−0.253558	+	0.216780i
$523$			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
$528$	1.04984	+	11.3939i	0.00198833	+	0.0215793i
$529$	264.045	+	457.340i	0.499141	+	0.864537i
$530$		0			0
$531$	−128.477	+	109.842i	−0.241953	+	0.206858i
$532$			412.363i			0.775119i
$533$	−52.9318	−	91.6806i	−0.0993092	−	0.172009i
$534$	−559.893	−	257.944i	−1.04849	−	0.483041i
$535$		0			0
$536$	183.823	+	106.130i	0.342953	+	0.198004i
$537$	116.309	−	82.2429i	0.216590	−	0.153152i
$538$	−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
$543$	−420.678	−	594.929i	−0.774729	−	1.09563i
$544$	−53.3939	+	92.4809i	−0.0981505	+	0.170002i
$545$		0			0
$546$	−143.715	+	311.948i	−0.263214	+	0.571333i
$547$	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
$549$	115.834	−	21.5287i	0.210990	−	0.0392144i
$550$		0			0
$551$	−292.621	+	168.945i	−0.531072	+	0.306615i
$552$	8.05669	−	0.742346i	0.0145954	−	0.00134483i
$553$	−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	$-0.714459\pi$
$557$	−695.042			−1.24783			−0.623916	+	0.781492i	$0.714459\pi$
$558$	−12.9206	+	36.5449i	−0.0231551	+	0.0654926i
$559$	436.803			0.781400
$560$		0			0
$561$	−49.0454	−	22.5953i	−0.0874250	−	0.0402768i
$562$	25.2848	+	14.5982i	0.0449908	+	0.0259755i
$563$	273.537	−	473.780i	0.485857	−	0.841528i	−0.514011	−	0.857783i	$-0.671841\pi$
$563$	273.537	−	473.780i	0.485857	−	0.841528i	0.999868	+	0.0162552i	$0.00517442\pi$
$564$	−156.879	−	221.860i	−0.278153	−	0.393368i
$565$		0			0
$566$			75.5313i			0.133447i
$567$	−668.006	−	105.114i	−1.17814	−	0.185386i
$568$		−	50.9694i		−	0.0897348i
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	−0.677615	−	0.735417i	$-0.736986\pi$
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	0.298082	+	0.954540i	$0.403653\pi$
$570$		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
$573$	−20.5222	−	9.45459i	−0.0358153	−	0.0165002i
$574$	64.4472	+	111.626i	0.112277	+	0.194470i
$575$		0			0
$576$	−24.0000	+	67.8823i	−0.0416667	+	0.117851i
$577$			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
$579$	95.0880	+	1031.99i	0.164228	+	1.78237i
$580$		0			0
$581$	−942.302	−	544.038i	−1.62186	−	0.936382i
$582$	42.7724	+	464.209i	0.0734921	+	0.797610i
$583$	−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	$-0.0442693\pi$
$587$	220.194	+	381.386i	0.375117	+	0.649721i	−0.615228	+	0.788349i	$0.710936\pi$
$588$	51.9615	−	112.788i	0.0883699	−	0.191816i
$589$	−37.6061	+	65.1357i	−0.0638474	+	0.110587i
$590$		0			0
$591$	133.757	+	189.161i	0.226323	+	0.320070i
$592$	−161.763	+	93.3939i	−0.273248	+	0.157760i
$593$	−347.232			−0.585551			−0.292776	−	0.956181i	$-0.594579\pi$
$593$	−347.232			−0.585551			−0.292776	+	0.956181i	$0.594579\pi$
$594$	−35.2951	−	8.93552i	−0.0594194	−	0.0150430i
$595$		0			0
$596$	200.060	−	115.505i	0.335671	−	0.193800i
$597$	265.843	+	375.959i	0.445299	+	0.629747i
$598$	11.3242	+	6.53801i	0.0189367	+	0.0109331i
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.946936	−	0.321423i	$-0.104161\pi$
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.195107	+	0.980782i	$0.437495\pi$
$600$		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
$603$	−513.364	+	438.901i	−0.851351	+	0.727862i
$604$	−129.546			−0.214480
$605$		0			0
$606$	57.4324	+	623.314i	0.0947729	+	1.02857i
$607$	−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
$609$	341.212	−	31.4394i	0.560282	−	0.0516246i
$610$		0			0
$611$		−	439.145i		−	0.718731i
$612$	−220.810	−	258.272i	−0.360801	−	0.422014i
$613$			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	−0.777306	−	0.629122i	$-0.783414\pi$
$617$	96.3648	−	166.909i	0.156183	−	0.270516i	0.933489	+	0.358606i	$0.116748\pi$
$618$	−357.274	+	252.631i	−0.578114	+	0.408788i
$619$	−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
$621$	−6.31837	+	24.9574i	−0.0101745	+	0.0401891i
$622$			353.803i			0.568814i
$623$	606.515	+	1050.51i	0.973539	+	1.68622i
$624$	−95.0102	+	67.1824i	−0.152260	+	0.107664i
$625$		0			0
$626$	522.224	+	301.506i	0.834223	+	0.481639i
$627$	−64.1645	−	29.5607i	−0.102336	−	0.0471463i
$628$	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
$633$	−154.030	+	14.1924i	−0.243333	+	0.0224208i
$634$	328.083	−	568.256i	0.517481	−	0.896303i
$635$		0			0
$636$	−563.939	+	51.9615i	−0.886696	+	0.0817005i
$637$	173.809	−	100.348i	0.272855	−	0.157533i
$638$	18.4490			0.0289169
$639$	152.908	+	54.0612i	0.239293	+	0.0846028i
$640$		0			0
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	−0.654161	−	0.756355i	$-0.726978\pi$
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	0.327942	+	0.944698i	$0.393645\pi$
$642$	63.9816	−	138.879i	0.0996598	−	0.216322i
$643$	−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	$-0.572965\pi$
$647$	−294.028			−0.454448			−0.227224	+	0.973842i	$0.572965\pi$
$648$	−178.191	−	144.000i	−0.274986	−	0.222222i
$649$	17.9082			0.0275935
$650$		0			0
$651$	62.2770	−	44.0365i	0.0956636	−	0.0676444i
$652$	−230.467	−	133.060i	−0.353477	−	0.204080i
$653$	384.156	−	665.379i	0.588295	−	1.01896i	−0.406161	−	0.913802i	$-0.633133\pi$
$653$	384.156	−	665.379i	0.588295	−	1.01896i	0.994456	−	0.105155i	$-0.0335339\pi$
$654$	−263.221	+	571.349i	−0.402479	+	0.873622i
$655$		0			0
$656$			43.6689i			0.0665684i
$657$	67.1117	+	23.7276i	0.102149	+	0.0361150i
$658$			534.681i			0.812585i
$659$	373.204	−	215.469i	0.566318	−	0.326964i	−0.189359	−	0.981908i	$-0.560641\pi$
$659$	373.204	−	215.469i	0.566318	−	0.326964i	0.755678	+	0.654944i	$0.227308\pi$
$660$		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
$663$	−50.3868	−	546.848i	−0.0759981	−	0.824808i
$664$	−184.318	−	319.248i	−0.277587	−	0.480795i
$665$		0			0
$666$	−108.606	−	584.348i	−0.163072	−	0.877399i
$667$		−	13.0454i		−	0.0195583i
$668$	−294.510	−	510.106i	−0.440883	−	0.763631i
$669$	−853.464	−	393.192i	−1.27573	−	0.587731i
$670$		0			0
$671$	−10.8099	−	6.24112i	−0.0161102	−	0.00930123i
$672$	115.680	−	81.7980i	0.172143	−	0.121723i
$673$	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	0.965865	−	0.259044i	$-0.0834076\pi$
$677$	175.068	+	303.227i	0.258594	+	0.447897i	−0.707272	+	0.706942i	$0.750074\pi$
$678$	419.078	+	592.665i	0.618109	+	0.874138i
$679$	458.659	−	794.421i	0.675492	−	1.16999i
$680$		0			0
$681$	95.7429	−	207.820i	0.140592	−	0.305168i
$682$	3.55645	−	2.05332i	0.00521474	−	0.00301073i
$683$	502.818			0.736190			0.368095	−	0.929788i	$-0.380010\pi$
$683$	502.818			0.736190			0.368095	+	0.929788i	$0.380010\pi$
$684$	−288.879	−	337.890i	−0.422337	−	0.493991i
$685$		0			0
$686$	289.392	−	167.080i	0.421854	−	0.243557i
$687$	363.097	−	33.4559i	0.528525	−	0.0486985i
$688$	−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
$693$	46.5559	+	54.4546i	0.0671803	+	0.0785781i
$694$	−189.044			−0.272398
$695$		0			0
$696$	105.439	+	48.5761i	0.151493	+	0.0697932i
$697$	−178.480	−	103.045i	−0.256069	−	0.147841i
$698$	−69.8318	+	120.952i	−0.100046	+	0.173284i
$699$	261.576	+	369.924i	0.374214	+	0.529218i
$700$		0			0
$701$		−	489.681i		−	0.698546i	−0.937021	−	0.349273i	$-0.886429\pi$
$701$		−	489.681i		−	0.698546i	0.937021	−	0.349273i	$-0.113571\pi$
$702$	−100.774	−	356.288i	−0.143552	−	0.507533i
$703$		−	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
$708$	102.348	+	47.1520i	0.144560	+	0.0665989i
$709$	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
$711$	387.053	−	71.9371i	0.544378	−	0.101177i
$712$			410.969i			0.577204i
$713$	−1.45192	−	2.51479i	−0.00203635	−	0.00352706i
$714$	61.3485	+	665.815i	0.0859222	+	0.932514i
$715$		0			0
$716$	−82.2429	−	47.4829i	−0.114864	−	0.0663170i
$717$	−24.1435	−	262.030i	−0.0336730	−	0.365453i
$718$	−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
$723$	−253.303	+	549.820i	−0.350350	+	0.760470i
$724$	−242.879	+	420.678i	−0.335468	+	0.581047i
$725$		0			0
$726$	−294.161	−	416.007i	−0.405181	−	0.573012i
$727$	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
$729$	621.000	−	381.838i	0.851852	−	0.523783i
$730$		0			0
$731$	736.423	−	425.174i	1.00742	−	0.581634i
$732$	−45.3479	−	64.1316i	−0.0619507	−	0.0876115i
$733$	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
$738$	−131.007	−	46.3179i	−0.177516	−	0.0627613i
$739$	−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
$741$	−65.9194	−	715.424i	−0.0889600	−	0.965484i
$742$	965.093	+	557.196i	1.30066	+	0.750939i
$743$	7.95550	−	13.7793i	0.0107073	−	0.0185455i	−0.860622	−	0.509244i	$-0.829925\pi$
$743$	7.95550	−	13.7793i	0.0107073	−	0.0185455i	0.871329	+	0.490699i	$0.163258\pi$
$744$	25.7321	−	2.37097i	0.0345862	−	0.00318679i
$745$		0			0
$746$			637.852i			0.855030i
$747$	1153.24	−	214.340i	1.54383	−	0.286934i
$748$			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
$753$	−128.907	+	91.1510i	−0.171191	+	0.121050i
$754$	93.8105	+	162.484i	0.124417	+	0.215497i
$755$		0			0
$756$	122.697	+	433.799i	0.162298	+	0.573808i
$757$		−	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
$759$	2.22704	−	1.57475i	0.00293417	−	0.00207477i
$760$		0			0
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.152479	−	0.988307i	$-0.548726\pi$
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.932138	+	0.362103i	$0.882059\pi$
$762$	−300.913	−	138.631i	−0.394899	−	0.181931i
$763$	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
$768$	47.7975	−	4.40408i	0.0622364	−	0.00573448i
$769$	−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
$771$	241.098	−	22.2149i	0.312708	−	0.0288131i
$772$	598.344	−	345.454i	0.775057	−	0.447479i
$773$	−278.021			−0.359665			−0.179832	−	0.983697i	$-0.557555\pi$
$773$	−278.021			−0.359665			−0.179832	+	0.983697i	$0.557555\pi$
$774$	435.780	−	372.570i	0.563023	−	0.481356i
$775$		0			0
$776$	269.146	−	155.392i	0.346838	−	0.200247i
$777$	−489.374	+	1062.24i	−0.629825	+	1.36710i
$778$	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
$783$	−257.563	+	264.795i	−0.328944	+	0.338180i
$784$	−82.7878			−0.105597
$785$		0			0
$786$	−810.817	+	573.334i	−1.03157	+	0.729433i
$787$	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
$789$	582.135	−	1263.58i	0.737813	−	1.60150i
$790$		0			0
$791$		−	1428.32i		−	1.80572i
$792$	4.43529	+	23.8638i	0.00560011	+	0.0301310i
$793$		−	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	$-0.521855\pi$
$797$	661.257	−	1145.33i	0.829683	−	1.43705i	0.898287	−	0.439409i	$-0.144812\pi$
$798$	80.2602	+	871.065i	0.100577	+	1.09156i
$799$	−427.454	−	740.372i	−0.534986	−	0.926624i
$800$		0			0
$801$	−1232.91	−	435.899i	−1.53921	−	0.544193i
$802$		−	585.650i		−	0.730238i
$803$	−3.77075	−	6.53113i	−0.00469583	−	0.00813341i
$804$	408.959	+	188.408i	0.508656	+	0.234339i
$805$		0			0
$806$	36.1681	+	20.8817i	0.0448736	+	0.0259078i
$807$	−106.495	+	75.3031i	−0.131964	+	0.0933123i
$808$	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
$813$	593.462	+	839.283i	0.729966	+	1.03233i
$814$	−31.4847	+	54.5331i	−0.0386790	+	0.0669940i
$815$		0			0
$816$	−94.7878	+	205.746i	−0.116161	+	0.252140i
$817$	963.439	−	556.242i	1.17924	−	0.680835i
$818$	461.334			0.563978
$819$	−242.864	+	686.922i	−0.296537	+	0.838733i
$820$		0			0
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.906967	−	0.421202i	$-0.861608\pi$
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.0887121	+	0.996057i	$0.528275\pi$
$822$	632.999	−	58.3247i	0.770071	−	0.0709547i
$823$	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	$-0.614528\pi$
$827$	−582.354			−0.704177			−0.352088	+	0.935967i	$0.614528\pi$
$828$	16.8742	−	3.13622i	0.0203795	−	0.00378771i
$829$	−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
$831$	−133.512	−	61.5095i	−0.160665	−	0.0740186i
$832$	67.1824	+	38.7878i	0.0807480	+	0.0466199i
$833$	195.354	−	338.363i	0.234519	−	0.406198i
$834$	−207.056	−	292.821i	−0.248268	−	0.351104i
$835$		0			0
$836$			47.0976i			0.0563369i
$837$	−20.1802	+	79.7112i	−0.0241101	+	0.0952344i
$838$		−	764.772i		−	0.912616i
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.219191	−	0.975682i	$-0.429658\pi$
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.954561	+	0.298016i	$0.0963247\pi$
$840$		0			0
$841$	−326.909	+	566.223i	−0.388715	+	0.673274i
$842$	−200.604	+	347.456i	−0.238247	+	0.412656i
$843$	56.2523	+	25.9155i	0.0667287	+	0.0307421i
$844$	51.5607	+	89.3058i	0.0610909	+	0.105813i
$845$		0			0
$846$	−374.568	−	438.117i	−0.442751	−	0.517868i
$847$			1002.57i			1.18368i
$848$	188.776	+	326.969i	0.222613	+	0.385577i
$849$	14.7010	+	159.550i	0.0173157	+	0.187927i
$850$		0			0
$851$	38.5607	+	22.2630i	0.0453122	+	0.0261610i
$852$	−9.92041	−	107.666i	−0.0116437	−	0.126369i
$853$	−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	0.533668	−	0.845694i	$-0.320813\pi$
$857$	−398.984	−	691.061i	−0.465559	−	0.806372i	−0.999227	+	0.0393225i	$0.987480\pi$
$858$	−16.4143	+	35.6288i	−0.0191308	+	0.0415254i
$859$	−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
$861$	157.863	+	223.252i	0.183348	+	0.259293i
$862$	315.284	−	182.030i	0.365759	−	0.211171i
$863$	−1304.85			−1.51199			−0.755994	−	0.654578i	$-0.772846\pi$
$863$	−1304.85			−1.51199			−0.755994	+	0.654578i	$0.772846\pi$
$864$	−37.4847	+	148.064i	−0.0433851	+	0.171370i
$865$		0			0
$866$	583.312	−	336.775i	0.673571	−	0.388886i
$867$	−116.677	−	165.006i	−0.134575	−	0.190318i
$868$	−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
$873$	180.702	+	972.257i	0.206990	+	1.11370i
$874$	33.3031			0.0381042
$875$		0			0
$876$	−4.35409	−	47.2549i	−0.00497042	−	0.0539440i
$877$	−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
$879$	−44.5829	+	4.10789i	−0.0507200	+	0.00467336i
$880$		0			0
$881$		−	229.979i		−	0.261043i	−0.991445	−	0.130522i	$-0.958335\pi$
$881$		−	229.979i		−	0.261043i	0.991445	−	0.130522i	$-0.0416652\pi$
$882$	87.8097	−	248.363i	0.0995575	−	0.281591i
$883$		−	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	−0.506075	−	0.862490i	$-0.668904\pi$
$887$	438.090	−	758.794i	0.493901	−	0.855461i	0.999975	+	0.00702852i	$0.00223726\pi$
$888$	−323.526	+	228.767i	−0.364331	+	0.257621i
$889$	325.969	+	564.596i	0.366670	+	0.635091i
$890$		0			0
$891$	−76.2957	−	12.0055i	−0.0856293	−	0.0134742i
$892$			626.454i			0.702303i
$893$	−559.224	−	968.605i	−0.626231	−	1.08466i
$894$	400.120	−	282.928i	0.447562	−	0.316474i
$895$		0			0
$896$	−81.7980	−	47.2261i	−0.0912924	−	0.0527077i
$897$	25.1934	+	11.6066i	0.0280863	+	0.0129394i
$898$	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
$903$	−1123.42	+	103.512i	−1.24410	+	0.114632i
$904$	241.955	−	419.078i	0.267649	−	0.463581i
$905$		0			0
$906$	−273.649	+	25.2141i	−0.302041	+	0.0278302i
$907$	−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
$909$	242.637	+	1305.49i	0.266928	+	1.43619i
$910$		0			0
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.245368	−	0.969430i	$-0.421091\pi$
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.962235	+	0.272220i	$0.0877578\pi$
$912$	−124.008	+	269.171i	−0.135973	+	0.295144i
$913$	−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
$918$	−516.702	−	502.590i	−0.562856	−	0.547484i
$919$	−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
$921$	−161.444	+	114.158i	−0.175292	+	0.123950i
$922$	11.2711	+	6.50740i	0.0122247	+	0.00705791i
$923$	87.3713	−	151.332i	0.0946602	−	0.163956i
$924$	19.9852	−	43.3799i	0.0216290	−	0.0469480i
$925$		0			0
$926$		−	78.0610i		−	0.0842991i
$927$	−705.526	+	603.189i	−0.761085	+	0.650689i
$928$		−	77.3939i		−	0.0833986i
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	−0.763100	−	0.646280i	$-0.776324\pi$
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	0.178145	+	0.984004i	$0.442991\pi$
$930$		0			0
$931$	255.576	−	442.670i	0.274517	−	0.475478i
$932$	151.021	−	261.576i	0.162039	−	0.280660i
$933$	68.8623	+	747.363i	0.0738074	+	0.801032i
$934$	−442.515	−	766.459i	−0.473785	−	0.820620i
$935$		0			0
$936$	−187.621	+	160.406i	−0.200450	+	0.171374i
$937$		−	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
$939$	1161.81	+	535.250i	1.23729	+	0.570021i
$940$		0			0
$941$	805.984	+	465.335i	0.856518	+	0.494511i	0.862845	−	0.505469i	$-0.168680\pi$
$941$	805.984	+	465.335i	0.856518	+	0.494511i	−0.00632656	+	0.999980i	$0.502014\pi$
$942$	72.1169	−	50.9944i	0.0765573	−	0.0541342i
$943$	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	$-0.166056\pi$
$947$	1.81556	+	3.14465i	0.00191717	+	0.00332064i	−0.865065	+	0.501659i	$0.832723\pi$
$948$	−151.528	−	214.293i	−0.159840	−	0.226047i
$949$	38.3474	−	66.4197i	0.0404083	−	0.0699892i
$950$		0			0
$951$	582.431	−	1264.23i	0.612440	−	1.32936i
$952$	386.037	−	222.879i	0.405501	−	0.234116i
$953$	−719.641			−0.755132			−0.377566	−	0.925983i	$-0.623239\pi$
$953$	−719.641			−0.755132			−0.377566	+	0.925983i	$0.623239\pi$
$954$	−1181.14	+	219.524i	−1.23809	+	0.230109i
$955$		0			0
$956$	−151.924	+	87.7133i	−0.158916	+	0.0917504i
$957$	38.9711	−	3.59082i	0.0407222	−	0.00375216i
$958$	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
$963$	108.122	−	305.816i	0.112277	−	0.317566i
$964$	403.576			0.418647
$965$		0			0
$966$	−30.6742	−	14.1317i	−0.0317539	−	0.0146291i
$967$	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
$969$	−807.514	−	1142.00i	−0.833348	−	1.17853i
$970$		0			0
$971$		−	970.472i		−	0.999456i	−0.866182	−	0.499728i	$-0.833433\pi$
$971$		−	970.472i		−	0.999456i	0.866182	−	0.499728i	$-0.166567\pi$
$972$	−404.433	−	269.499i	−0.416083	−	0.277263i
$973$			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	$0.463770\pi$
$977$	−785.151	+	1359.92i	−0.803635	+	1.39194i	−0.917209	+	0.398406i	$0.869563\pi$
$978$	−512.730	−	236.216i	−0.524264	−	0.241529i
$979$	69.2724	+	119.983i	0.0707584	+	0.122557i
$980$		0			0
$981$	−444.817	+	1258.13i	−0.453433	+	1.28250i
$982$		−	1343.07i		−	1.36769i
$983$	−387.939	−	671.930i	−0.394648	−	0.683551i	0.598408	−	0.801192i	$-0.295800\pi$
$983$	−387.939	−	671.930i	−0.394648	−	0.683551i	−0.993056	+	0.117641i	$0.962467\pi$
$984$	8.49948	+	92.2450i	0.00863769	+	0.0937449i
$985$		0			0
$986$	316.318	+	182.626i	0.320809	+	0.185219i
$987$	104.068	+	1129.45i	0.105438	+	1.14432i
$988$	−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
$993$	−593.507	+	1288.27i	−0.597690	+	1.29735i
$994$	−106.379	+	184.254i	−0.107021	+	0.185366i
$995$		0			0
$996$	−451.485	−	638.496i	−0.453298	−	0.641060i
$997$	−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
$999$	−343.151	−	1213.22i	−0.343495	−	1.21444i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	5.2	odd	4
18.3.d.a.11.2	yes	4	45.2	even	12
54.3.d.a.17.1		4	15.2	even	4
54.3.d.a.35.1		4	45.7	odd	12
144.3.q.c.65.2		4	180.47	odd	12
144.3.q.c.113.2		4	20.7	even	4
162.3.b.a.161.1		4	45.32	even	12
162.3.b.a.161.4		4	45.22	odd	12
432.3.q.d.17.1		4	60.47	odd	4
432.3.q.d.305.1		4	180.7	even	12
450.3.i.b.101.1		4	45.38	even	12
450.3.i.b.401.1		4	5.3	odd	4
450.3.k.a.149.1		8	1.1	even	1	trivial
450.3.k.a.149.4		8	5.4	even	2	inner
450.3.k.a.299.1		8	45.29	odd	6	inner
450.3.k.a.299.4		8	9.2	odd	6	inner
576.3.q.e.65.1		4	360.227	odd	12
576.3.q.e.257.1		4	40.27	even	4
576.3.q.f.65.2		4	360.317	even	12
576.3.q.f.257.2		4	40.37	odd	4
1296.3.e.g.161.2		4	180.167	odd	12
1296.3.e.g.161.4		4	180.67	even	12
1350.3.i.b.251.2		4	45.43	odd	12
1350.3.i.b.1151.2		4	15.8	even	4
1350.3.k.a.449.1		8	15.14	odd	2
1350.3.k.a.449.4		8	3.2	odd	2
1350.3.k.a.899.1		8	9.7	even	3
1350.3.k.a.899.4		8	45.34	even	6
1728.3.q.c.449.1		4	120.107	odd	4
1728.3.q.c.1601.1		4	360.187	even	12
1728.3.q.d.449.2		4	120.77	even	4
1728.3.q.d.1601.2		4	360.277	odd	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(7.22999 - 4.17423i) q^{7} +2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(7.22999 - 4.17423i) q^{7} +2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(5.97469 - 0.550510i) q^{12} +(8.39780 + 4.84847i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} +18.8776 q^{17} +(12.5136 - 2.32577i) q^{18} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-1.16781 - 0.674235i) q^{22} +(-0.476756 + 0.825765i) q^{23} +(-4.89898 - 6.92820i) q^{24} -13.7135i q^{26} +(25.9808 - 7.34847i) q^{27} +16.6969i q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-2.59808 - 1.19694i) q^{33} +(-13.3485 - 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} -46.6969i q^{37} +(-17.4634 - 30.2474i) q^{38} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(3.24980 + 35.2702i) q^{42} +(39.0105 - 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(-22.6435 - 39.2196i) q^{47} +(-5.02118 + 10.8990i) q^{48} +(10.3485 - 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(-16.7956 + 9.69694i) q^{52} -94.3879 q^{53} +(-27.3712 - 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(-42.7764 - 60.4949i) q^{57} +(16.7563 + 9.67423i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +4.30686 q^{62} +(13.7296 + 73.8712i) q^{63} +8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(64.9912 + 37.5227i) q^{67} +(-18.8776 + 32.6969i) q^{68} +(2.84847 - 0.262459i) q^{69} -18.0204i q^{71} +(-8.48528 + 24.0000i) q^{72} -7.90918i q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(3.98018 - 6.89388i) q^{77} +(-33.5912 + 23.7526i) q^{78} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +15.4393i q^{82} +(-65.1662 - 112.871i) q^{83} +(40.8990 - 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(37.2784 + 17.1742i) q^{87} +(2.33562 - 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(-0.953512 - 1.65153i) q^{92} +(9.09769 - 0.838264i) q^{93} +(-32.0227 + 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(95.1576 - 54.9393i) q^{97} -29.2699 q^{98} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9	\( 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51} - 72 q^{54} + 144 q^{56} - 252 q^{59} + 124 q^{61} + 64 q^{64} - 144 q^{66} - 36 q^{69} - 144 q^{74} - 80 q^{76} - 28 q^{79} - 504 q^{81} + 288 q^{84} - 216 q^{86} + 824 q^{91} - 168 q^{94} + 96 q^{96} - 252 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Introduction

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