LMFDB - Embedded newform 1350.3.i.b.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,3,Mod(251,1350)]

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([1, 0]))

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

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

chi := DirichletCharacter("1350.251");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1350.i (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1350.1151
Dual form			1350.3.i.b.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.17423 - 7.22999i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.17423 - 7.22999i) q^{7} -2.82843i q^{8} +(-0.825765 + 0.476756i) q^{11} +(-4.84847 + 8.39780i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} +18.8776i q^{17} -24.6969 q^{19} +(-0.674235 + 1.16781i) q^{22} +(0.825765 + 0.476756i) q^{23} +13.7135i q^{26} -16.6969 q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(13.3485 + 23.1202i) q^{34} -46.6969 q^{37} +(-30.2474 + 17.4634i) q^{38} +(9.45459 + 5.45861i) q^{41} +(22.5227 + 39.0105i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(39.2196 - 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(9.69694 + 16.7956i) q^{52} +94.3879i q^{53} +(-20.4495 + 11.8065i) q^{56} +(-9.67423 + 16.7563i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +4.30686i q^{62} -8.00000 q^{64} +(37.5227 - 64.9912i) q^{67} +(32.6969 + 18.8776i) q^{68} +18.0204i q^{71} +7.90918 q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(6.89388 + 3.98018i) q^{77} +(21.8712 + 37.8820i) q^{79} +15.4393 q^{82} +(-112.871 + 65.1662i) q^{83} +(55.1691 + 31.8519i) q^{86} +(1.34847 + 2.33562i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(1.65153 - 0.953512i) q^{92} +(32.0227 - 55.4650i) q^{94} +(-54.9393 - 95.1576i) q^{97} +29.2699i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q + 4 * q^4 - 2 * q^7	$ 4 q + 4 q^{4} - 2 q^{7} - 18 q^{11} + 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 12 q^{22} + 18 q^{23} - 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} - 128 q^{37} - 72 q^{38} + 126 q^{41} + 46 q^{43} - 24 q^{46} + 54 q^{47} - 12 q^{49} - 20 q^{52} - 72 q^{56} - 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} + 106 q^{67} + 72 q^{68} + 208 q^{73} - 72 q^{74} - 40 q^{76} - 90 q^{77} + 14 q^{79} - 144 q^{82} - 378 q^{83} + 108 q^{86} - 24 q^{88} + 412 q^{91} + 36 q^{92} + 84 q^{94} - 14 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 - 2 * q^7 - 18 * q^11 + 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 12 * q^22 + 18 * q^23 - 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 - 128 * q^37 - 72 * q^38 + 126 * q^41 + 46 * q^43 - 24 * q^46 + 54 * q^47 - 12 * q^49 - 20 * q^52 - 72 * q^56 - 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 + 106 * q^67 + 72 * q^68 + 208 * q^73 - 72 * q^74 - 40 * q^76 - 90 * q^77 + 14 * q^79 - 144 * q^82 - 378 * q^83 + 108 * q^86 - 24 * q^88 + 412 * q^91 + 36 * q^92 + 84 * q^94 - 14 * q^97

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	−0.993359	−	0.115054i	$-0.963296\pi$
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	0.397040	−	0.917801i	$-0.370037\pi$
$8$		−	2.82843i		−	0.353553i
$9$		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
$13$	−4.84847	+	8.39780i	−0.372959	+	0.645984i	−0.990019	−	0.140932i	$-0.954990\pi$
$13$	−4.84847	+	8.39780i	−0.372959	+	0.645984i	0.617060	+	0.786916i	$0.288324\pi$
$14$	−10.2247	−	5.90326i	−0.730339	−	0.421661i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			18.8776i			1.11045i	0.831701	+	0.555223i	$0.187367\pi$
$17$			18.8776i			1.11045i	−0.831701	+	0.555223i	$0.812633\pi$
$18$		0			0
$19$	−24.6969			−1.29984			−0.649919	−	0.760003i	$-0.725197\pi$
$19$	−24.6969			−1.29984			−0.649919	+	0.760003i	$0.725197\pi$
$20$		0			0
$21$		0			0
$22$	−0.674235	+	1.16781i	−0.0306470	+	0.0530822i
$23$	0.825765	+	0.476756i	0.0359028	+	0.0207285i	0.517844	−	0.855475i	$-0.326735\pi$
$23$	0.825765	+	0.476756i	0.0359028	+	0.0207285i	−0.481941	+	0.876204i	$0.660068\pi$
$24$		0			0
$25$		0			0
$26$			13.7135i			0.527444i
$27$		0			0
$28$	−16.6969			−0.596319
$29$	−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	$0.182308\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	13.3485	+	23.1202i	0.392602	+	0.680007i
$35$		0			0
$36$		0			0
$37$	−46.6969			−1.26208			−0.631040	−	0.775751i	$-0.717372\pi$
$37$	−46.6969			−1.26208			−0.631040	+	0.775751i	$0.717372\pi$
$38$	−30.2474	+	17.4634i	−0.795985	+	0.459562i
$39$		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
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	0.999617	+	0.0276845i	$0.00881337\pi$
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	−0.475833	+	0.879536i	$0.657853\pi$
$44$			1.90702i			0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	39.2196	−	22.6435i	0.834460	−	0.481776i	−0.0209170	−	0.999781i	$-0.506659\pi$
$47$	39.2196	−	22.6435i	0.834460	−	0.481776i	0.855377	+	0.518005i	$0.173325\pi$
$48$		0			0
$49$	−10.3485	+	17.9241i	−0.211193	+	0.365797i
$50$		0			0
$51$		0			0
$52$	9.69694	+	16.7956i	0.186480	+	0.322992i
$53$			94.3879i			1.78090i	0.455077	+	0.890452i	$0.349612\pi$
$53$			94.3879i			1.78090i	−0.455077	+	0.890452i	$0.650388\pi$
$54$		0			0
$55$		0			0
$56$	−20.4495	+	11.8065i	−0.365169	+	0.210831i
$57$		0			0
$58$	−9.67423	+	16.7563i	−0.166797	+	0.288901i
$59$	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	$0.867554\pi$
$62$			4.30686i			0.0694654i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	−0.437452	−	0.899242i	$-0.644119\pi$
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	0.997492	−	0.0707765i	$-0.0225477\pi$
$68$	32.6969	+	18.8776i	0.480837	+	0.277612i
$69$		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
$73$	7.90918			0.108345			0.0541725	−	0.998532i	$-0.482748\pi$
$73$	7.90918			0.108345			0.0541725	+	0.998532i	$0.482748\pi$
$74$	−57.1918	+	33.0197i	−0.772863	+	0.446212i
$75$		0			0
$76$	−24.6969	+	42.7764i	−0.324960	+	0.562847i
$77$	6.89388	+	3.98018i	0.0895309	+	0.0516907i
$78$		0			0
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	0.970600	−	0.240697i	$-0.0773761\pi$
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	−0.693750	+	0.720216i	$0.744043\pi$
$80$		0			0
$81$		0			0
$82$	15.4393			0.188284
$83$	−112.871	+	65.1662i	−1.35989	+	0.785135i	−0.989609	−	0.143783i	$-0.954073\pi$
$83$	−112.871	+	65.1662i	−1.35989	+	0.785135i	−0.370284	+	0.928918i	$0.620740\pi$
$84$		0			0
$85$		0			0
$86$	55.1691	+	31.8519i	0.641502	+	0.370371i
$87$		0			0
$88$	1.34847	+	2.33562i	0.0153235	+	0.0265411i
$89$			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
$92$	1.65153	−	0.953512i	0.0179514	−	0.0103643i
$93$		0			0
$94$	32.0227	−	55.4650i	0.340667	−	0.590053i
$95$		0			0
$96$		0			0
$97$	−54.9393	−	95.1576i	−0.566384	−	0.981007i	−0.996919	−	0.0784327i	$-0.975008\pi$
$97$	−54.9393	−	95.1576i	−0.566384	−	0.981007i	0.430535	−	0.902574i	$-0.358325\pi$
$98$			29.2699i			0.298672i
$99$		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
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	0.499338	+	0.866407i	$0.333576\pi$
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	−1.00000		0.000763745i	$0.999757\pi$
$104$	23.7526	+	13.7135i	0.228390	+	0.131861i
$105$		0			0
$106$	66.7423	+	115.601i	0.629645	+	1.09058i
$107$		−	36.0408i		−	0.336830i	−0.985716	−	0.168415i	$-0.946135\pi$
$107$		−	36.0408i		−	0.336830i	0.985716	−	0.168415i	$-0.0538649\pi$
$108$		0			0
$109$	−148.272			−1.36030			−0.680149	−	0.733074i	$-0.738085\pi$
$109$	−148.272			−1.36030			−0.680149	+	0.733074i	$0.738085\pi$
$110$		0			0
$111$		0			0
$112$	−16.6969	+	28.9199i	−0.149080	+	0.258214i
$113$	−148.166	−	85.5439i	−1.31121	−	0.757025i	−0.328910	−	0.944361i	$-0.606681\pi$
$113$	−148.166	−	85.5439i	−1.31121	−	0.757025i	−0.982296	+	0.187336i	$0.940015\pi$
$114$		0			0
$115$		0			0
$116$			27.3629i			0.235887i
$117$		0			0
$118$	26.5607			0.225091
$119$	136.485	−	78.7995i	1.14693	−	0.662180i
$120$		0			0
$121$	−60.0454	+	104.002i	−0.496243	+	0.859518i
$122$	−16.0329	−	9.25660i	−0.131417	−	0.0758738i
$123$		0			0
$124$	3.04541	+	5.27480i	0.0245597	+	0.0425387i
$125$		0			0
$126$		0			0
$127$	78.0908			0.614888			0.307444	−	0.951566i	$-0.400526\pi$
$127$	78.0908			0.614888			0.307444	+	0.951566i	$0.400526\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		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
$133$	103.091	+	178.559i	0.775119	+	1.34255i
$134$		−	106.130i		−	0.792017i
$135$		0			0
$136$	53.3939			0.392602
$137$	129.758	−	74.9156i	0.947136	−	0.546829i	0.0549460	−	0.998489i	$-0.482501\pi$
$137$	129.758	−	74.9156i	0.947136	−	0.546829i	0.892190	+	0.451660i	$0.149168\pi$
$138$		0			0
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	−0.672988	−	0.739654i	$-0.734989\pi$
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	0.977053	+	0.212998i	$0.0683226\pi$
$140$		0			0
$141$		0			0
$142$	12.7423	+	22.0704i	0.0897348	+	0.155425i
$143$		−	9.24614i		−	0.0646584i
$144$		0			0
$145$		0			0
$146$	9.68673	−	5.59264i	0.0663475	−	0.0383057i
$147$		0			0
$148$	−46.6969	+	80.8815i	−0.315520	+	0.546496i
$149$	−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	$0.764528\pi$
$152$			69.8535i			0.459562i
$153$		0			0
$154$	11.2577			0.0731016
$155$		0			0
$156$		0			0
$157$	−10.4092	+	18.0292i	−0.0663005	+	0.114836i	−0.897270	−	0.441482i	$-0.854453\pi$
$157$	−10.4092	+	18.0292i	−0.0663005	+	0.114836i	0.830970	+	0.556318i	$0.187786\pi$
$158$	53.5732	+	30.9305i	0.339071	+	0.195763i
$159$		0			0
$160$		0			0
$161$		−	7.96036i		−	0.0494433i
$162$		0			0
$163$	−133.060			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$163$	−133.060			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$164$	18.9092	−	10.9172i	0.115300	−	0.0665684i
$165$		0			0
$166$	−92.1589	+	159.624i	−0.555174	+	0.961590i
$167$	−255.053	−	147.255i	−1.52726	−	0.881765i	−0.999475	−	0.0323885i	$-0.989689\pi$
$167$	−255.053	−	147.255i	−1.52726	−	0.881765i	−0.527787	−	0.849377i	$-0.676978\pi$
$168$		0			0
$169$	37.4847	+	64.9254i	0.221803	+	0.384174i
$170$		0			0
$171$		0			0
$172$	90.0908			0.523784
$173$	−59.9847	+	34.6322i	−0.346732	+	0.200186i	−0.663245	−	0.748402i	$-0.730821\pi$
$173$	−59.9847	+	34.6322i	−0.346732	+	0.200186i	0.316513	+	0.948588i	$0.397488\pi$
$174$		0			0
$175$		0			0
$176$	3.30306	+	1.90702i	0.0187674	+	0.0108354i
$177$		0			0
$178$	102.742	+	177.955i	0.577204	+	0.999747i
$179$			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	$0.265893\pi$
$182$	99.1487	−	57.2435i	0.544773	−	0.314525i
$183$		0			0
$184$	1.34847	−	2.33562i	0.00732864	−	0.0126936i
$185$		0			0
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.0481283	−	0.0833607i
$188$		−	90.5739i		−	0.481776i
$189$		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
$193$	172.727	−	299.172i	0.894959	−	1.55011i	0.0611031	−	0.998131i	$-0.480538\pi$
$193$	172.727	−	299.172i	0.894959	−	1.55011i	0.833856	−	0.551983i	$-0.186129\pi$
$194$	−134.573	−	77.6959i	−0.693676	−	0.400494i
$195$		0			0
$196$	20.6969	+	35.8481i	0.105597	+	0.182899i
$197$		−	77.2247i		−	0.392004i	−0.980604	−	0.196002i	$-0.937204\pi$
$197$		−	77.2247i		−	0.392004i	0.980604	−	0.196002i	$-0.0627959\pi$
$198$		0			0
$199$	153.485			0.771280			0.385640	−	0.922649i	$-0.373981\pi$
$199$	153.485			0.771280			0.385640	+	0.922649i	$0.373981\pi$
$200$		0			0
$201$		0			0
$202$	−104.326	+	180.698i	−0.516464	+	0.894542i
$203$	98.9166	+	57.1095i	0.487274	+	0.281328i
$204$		0			0
$205$		0			0
$206$			145.857i			0.708042i
$207$		0			0
$208$	38.7878			0.186480
$209$	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	$0.127678\pi$
$212$	163.485	+	94.3879i	0.771154	+	0.445226i
$213$		0			0
$214$	−25.4847	−	44.1408i	−0.119087	−	0.206265i
$215$		0			0
$216$		0			0
$217$	25.4245			0.117164
$218$	−181.596	+	104.844i	−0.833009	+	0.480938i
$219$		0			0
$220$		0			0
$221$	−158.530	−	91.5274i	−0.717331	−	0.414151i
$222$		0			0
$223$	156.614	+	271.263i	0.702303	+	1.21642i	0.967656	+	0.252273i	$0.0811781\pi$
$223$	156.614	+	271.263i	0.702303	+	1.21642i	−0.265353	+	0.964151i	$0.585489\pi$
$224$			47.2261i			0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	−66.0528	+	38.1356i	−0.290982	+	0.167998i	−0.638384	−	0.769718i	$-0.720397\pi$
$227$	−66.0528	+	38.1356i	−0.290982	+	0.167998i	0.347403	+	0.937716i	$0.387064\pi$
$228$		0			0
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	−0.702282	−	0.711899i	$-0.747835\pi$
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	0.967664	+	0.252244i	$0.0811686\pi$
$230$		0			0
$231$		0			0
$232$	19.3485	+	33.5125i	0.0833986	+	0.144451i
$233$			151.021i			0.648157i	0.946030	+	0.324079i	$0.105054\pi$
$233$			151.021i			0.648157i	−0.946030	+	0.324079i	$0.894946\pi$
$234$		0			0
$235$		0			0
$236$	32.5301	−	18.7813i	0.137839	−	0.0795816i
$237$		0			0
$238$	111.439	−	193.019i	0.468232	−	0.811002i
$239$	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	$0.970829\pi$
$242$			169.834i			0.701794i
$243$		0			0
$244$	−26.1816			−0.107302
$245$		0			0
$246$		0			0
$247$	119.742	−	207.400i	0.484787	−	0.839675i
$248$	7.45969	+	4.30686i	0.0300794	+	0.0173664i
$249$		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
$253$	−0.909185			−0.00359362
$254$	95.6413	−	55.2185i	0.376541	−	0.217396i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−69.8939	−	40.3532i	−0.271961	−	0.157017i	0.357818	−	0.933791i	$-0.383521\pi$
$257$	−69.8939	−	40.3532i	−0.271961	−	0.157017i	−0.629778	+	0.776775i	$0.716854\pi$
$258$		0			0
$259$	194.924	+	337.618i	0.752602	+	1.30355i
$260$		0			0
$261$		0			0
$262$	−331.015			−1.26342
$263$	401.614	−	231.872i	1.52705	−	0.881641i	0.527564	−	0.849515i	$-0.323106\pi$
$263$	401.614	−	231.872i	1.52705	−	0.881641i	0.999484	−	0.0321259i	$-0.0102278\pi$
$264$		0			0
$265$		0			0
$266$	252.520	+	145.792i	0.949323	+	0.548092i
$267$		0			0
$268$	−75.0454	−	129.982i	−0.280020	−	0.485009i
$269$		−	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	$0.717835\pi$
$272$	65.3939	−	37.7552i	0.240419	−	0.138806i
$273$		0			0
$274$	105.947	−	183.505i	0.386667	−	0.669726i
$275$		0			0
$276$		0			0
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	0.818407	−	0.574638i	$-0.194857\pi$
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	−0.906855	+	0.421442i	$0.861524\pi$
$278$		−	119.544i		−	0.430013i
$279$		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
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	−0.814980	−	0.579489i	$-0.803252\pi$
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	0.909342	+	0.416049i	$0.136586\pi$
$284$	31.2122	+	18.0204i	0.109902	+	0.0634521i
$285$		0			0
$286$	−6.53801	−	11.3242i	−0.0228602	−	0.0395950i
$287$		−	91.1421i		−	0.317568i
$288$		0			0
$289$	−67.3633			−0.233091
$290$		0			0
$291$		0			0
$292$	7.90918	−	13.6991i	0.0270862	−	0.0469148i
$293$	−12.9245	−	7.46196i	−0.0441109	−	0.0254674i	0.477782	−	0.878478i	$-0.341441\pi$
$293$	−12.9245	−	7.46196i	−0.0441109	−	0.0254674i	−0.521893	+	0.853011i	$0.674774\pi$
$294$		0			0
$295$		0			0
$296$			132.079i			0.446212i
$297$		0			0
$298$	−163.348			−0.548149
$299$	−8.00740	+	4.62307i	−0.0267806	+	0.0154618i
$300$		0			0
$301$	188.030	−	325.678i	0.624685	−	1.08199i
$302$	79.3304	+	45.8014i	0.262683	+	0.151660i
$303$		0			0
$304$	49.3939	+	85.5527i	0.162480	+	0.281423i
$305$		0			0
$306$		0			0
$307$	−65.9092			−0.214688			−0.107344	−	0.994222i	$-0.534235\pi$
$307$	−65.9092			−0.214688			−0.107344	+	0.994222i	$0.534235\pi$
$308$	13.7878	−	7.96036i	0.0447654	−	0.0258453i
$309$		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
$313$	−213.197	−	369.268i	−0.681140	−	1.17977i	−0.974633	−	0.223808i	$-0.928151\pi$
$313$	−213.197	−	369.268i	−0.681140	−	1.17977i	0.293493	−	0.955961i	$-0.405182\pi$
$314$			29.4416i			0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	−401.818	+	231.990i	−1.26756	+	0.731829i	−0.974527	−	0.224272i	$-0.927999\pi$
$317$	−401.818	+	231.990i	−1.26756	+	0.731829i	−0.293038	+	0.956101i	$0.594666\pi$
$318$		0			0
$319$	6.52270	−	11.2977i	0.0204473	−	0.0354158i
$320$		0			0
$321$		0			0
$322$	−5.62883	−	9.74941i	−0.0174808	−	0.0302777i
$323$		−	466.219i		−	1.44340i
$324$		0			0
$325$		0			0
$326$	−162.965	+	94.0878i	−0.499892	+	0.288613i
$327$		0			0
$328$	15.4393	−	26.7416i	0.0470710	−	0.0815293i
$329$	−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	$-0.419877\pi$
$332$			260.665i			0.785135i
$333$		0			0
$334$	−416.499			−1.24700
$335$		0			0
$336$		0			0
$337$	152.803	−	264.663i	0.453422	−	0.785349i	−0.545174	−	0.838323i	$-0.683537\pi$
$337$	152.803	−	264.663i	0.453422	−	0.785349i	0.998596	+	0.0529735i	$0.0168699\pi$
$338$	91.8184	+	53.0114i	0.271652	+	0.156838i
$339$		0			0
$340$		0			0
$341$		−	2.90383i		−	0.00851564i
$342$		0			0
$343$	−236.287			−0.688884
$344$	110.338	−	63.7038i	0.320751	−	0.185186i
$345$		0			0
$346$	−48.9773	+	84.8312i	−0.141553	+	0.245177i
$347$	115.766	+	66.8373i	0.333618	+	0.192615i	0.657446	−	0.753501i	$-0.271637\pi$
$347$	115.766	+	66.8373i	0.333618	+	0.192615i	−0.323828	+	0.946116i	$0.604970\pi$
$348$		0			0
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	0.928056	−	0.372440i	$-0.121479\pi$
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	−0.786570	+	0.617500i	$0.788145\pi$
$350$		0			0
$351$		0			0
$352$	5.39388			0.0153235
$353$	−282.424	+	163.058i	−0.800068	+	0.461919i	−0.843495	−	0.537137i	$-0.819506\pi$
$353$	−282.424	+	163.058i	−0.800068	+	0.461919i	0.0434270	+	0.999057i	$0.486172\pi$
$354$		0			0
$355$		0			0
$356$	251.666	+	145.300i	0.706928	+	0.408145i
$357$		0			0
$358$	33.5755	+	58.1545i	0.0937863	+	0.162443i
$359$		−	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
$362$	297.464	−	171.741i	0.821725	−	0.474423i
$363$		0			0
$364$	80.9546	−	140.217i	0.222403	−	0.385213i
$365$		0			0
$366$		0			0
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	0.964917	−	0.262557i	$-0.0845656\pi$
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	−0.709839	+	0.704364i	$0.751232\pi$
$368$		−	3.81405i		−	0.0103643i
$369$		0			0
$370$		0			0
$371$	682.423	−	393.997i	1.83942	−	1.06199i
$372$		0			0
$373$	225.515	−	390.603i	0.604597	−	1.04719i	−0.387518	−	0.921862i	$-0.626667\pi$
$373$	225.515	−	390.603i	0.604597	−	1.04719i	0.992115	−	0.125331i	$-0.0399993\pi$
$374$	−22.0454	−	12.7279i	−0.0589449	−	0.0340319i
$375$		0			0
$376$	−64.0454	−	110.930i	−0.170334	−	0.295026i
$377$		−	132.668i		−	0.351905i
$378$		0			0
$379$	−489.666			−1.29200			−0.645998	−	0.763339i	$-0.723558\pi$
$379$	−489.666			−1.29200			−0.645998	+	0.763339i	$0.723558\pi$
$380$		0			0
$381$		0			0
$382$	−5.32577	+	9.22450i	−0.0139418	+	0.0241479i
$383$	89.2492	+	51.5281i	0.233027	+	0.134538i	0.611968	−	0.790883i	$-0.290378\pi$
$383$	89.2492	+	51.5281i	0.233027	+	0.134538i	−0.378941	+	0.925421i	$0.623712\pi$
$384$		0			0
$385$		0			0
$386$		−	488.546i		−	1.26566i
$387$		0			0
$388$	−219.757			−0.566384
$389$	−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
$392$	50.6969	+	29.2699i	0.129329	+	0.0746681i
$393$		0			0
$394$	−54.6061	−	94.5806i	−0.138594	−	0.240052i
$395$		0			0
$396$		0			0
$397$	−8.27245			−0.0208374			−0.0104187	−	0.999946i	$-0.503316\pi$
$397$	−8.27245			−0.0208374			−0.0104187	+	0.999946i	$0.503316\pi$
$398$	187.980	−	108.530i	0.472311	−	0.272689i
$399$		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
$403$	−14.7656	−	25.5747i	−0.0366391	−	0.0634608i
$404$			295.078i			0.730391i
$405$		0			0
$406$	161.530			0.397857
$407$	38.5607	−	22.2630i	0.0947438	−	0.0547003i
$408$		0			0
$409$	163.106	−	282.508i	0.398792	−	0.690729i	−0.594785	−	0.803885i	$-0.702763\pi$
$409$	163.106	−	282.508i	0.398792	−	0.690729i	0.993577	+	0.113156i	$0.0360960\pi$
$410$		0			0
$411$		0			0
$412$	103.136	+	178.637i	0.250331	+	0.433585i
$413$		−	156.795i		−	0.379648i
$414$		0			0
$415$		0			0
$416$	47.5051	−	27.4271i	0.114195	−	0.0659305i
$417$		0			0
$418$	16.6515	−	28.8413i	0.0398362	−	0.0689983i
$419$	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	$0.942723\pi$
$422$		−	72.9179i		−	0.172791i
$423$		0			0
$424$	266.969			0.629645
$425$		0			0
$426$		0			0
$427$	−54.6441	+	94.6464i	−0.127972	+	0.221654i
$428$	−62.4245	−	36.0408i	−0.145852	−	0.0842075i
$429$		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
$433$	−476.272			−1.09994			−0.549968	−	0.835186i	$-0.685360\pi$
$433$	−476.272			−1.09994			−0.549968	+	0.835186i	$0.685360\pi$
$434$	31.1385	−	17.9778i	0.0717477	−	0.0414236i
$435$		0			0
$436$	−148.272	+	256.815i	−0.340074	+	0.589026i
$437$	−20.3939	−	11.7744i	−0.0466679	−	0.0269437i
$438$		0			0
$439$	278.931	+	483.123i	0.635379	+	1.10051i	0.986435	+	0.164154i	$0.0524894\pi$
$439$	278.931	+	483.123i	0.635379	+	1.10051i	−0.351056	+	0.936355i	$0.614177\pi$
$440$		0			0
$441$		0			0
$442$	−258.879			−0.585698
$443$	720.400	−	415.923i	1.62619	−	0.938879i	0.640969	−	0.767567i	$-0.278533\pi$
$443$	720.400	−	415.923i	1.62619	−	0.938879i	0.985217	−	0.171312i	$-0.0548005\pi$
$444$		0			0
$445$		0			0
$446$	383.623	+	221.485i	0.860142	+	0.496603i
$447$		0			0
$448$	33.3939	+	57.8399i	0.0745399	+	0.129107i
$449$			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
$452$	−296.333	+	171.088i	−0.655603	+	0.378513i
$453$		0			0
$454$	−53.9319	+	93.4128i	−0.118793	+	0.205755i
$455$		0			0
$456$		0			0
$457$	354.818	+	614.563i	0.776407	+	1.34478i	0.934000	+	0.357272i	$0.116293\pi$
$457$	354.818	+	614.563i	0.776407	+	1.34478i	−0.157594	+	0.987504i	$0.550374\pi$
$458$		−	171.890i		−	0.375307i
$459$		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
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	−0.894290	−	0.447488i	$-0.852319\pi$
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	0.834681	+	0.550733i	$0.185652\pi$
$464$	47.3939	+	27.3629i	0.102142	+	0.0589717i
$465$		0			0
$466$	106.788	+	184.962i	0.229158	+	0.396914i
$467$			625.811i			1.34007i	0.742331	+	0.670033i	$0.233720\pi$
$467$			625.811i			1.34007i	−0.742331	+	0.670033i	$0.766280\pi$
$468$		0			0
$469$	−626.514			−1.33585
$470$		0			0
$471$		0			0
$472$	26.5607	−	46.0045i	0.0562727	−	0.0974672i
$473$	−37.1969	−	21.4757i	−0.0786405	−	0.0454031i
$474$		0			0
$475$		0			0
$476$		−	315.198i		−	0.662180i
$477$		0			0
$478$	124.045			0.259509
$479$	−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
$482$	−247.139	−	142.685i	−0.512736	−	0.296028i
$483$		0			0
$484$	120.091	+	208.003i	0.248122	+	0.429759i
$485$		0			0
$486$		0			0
$487$	28.3337			0.0581800			0.0290900	−	0.999577i	$-0.490739\pi$
$487$	28.3337			0.0581800			0.0290900	+	0.999577i	$0.490739\pi$
$488$	−32.0658	+	18.5132i	−0.0657086	+	0.0379369i
$489$		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
$493$	−129.136	−	223.670i	−0.261940	−	0.453693i
$494$		−	338.682i		−	0.685592i
$495$		0			0
$496$	12.1816			0.0245597
$497$	130.287	−	75.2214i	0.262147	−	0.151351i
$498$		0			0
$499$	280.113	−	485.170i	0.561349	−	0.972284i	−0.436030	−	0.899932i	$-0.643616\pi$
$499$	280.113	−	485.170i	0.561349	−	0.972284i	0.997379	−	0.0723525i	$-0.0230507\pi$
$500$		0			0
$501$		0			0
$502$	37.2122	+	64.4535i	0.0741280	+	0.128393i
$503$			897.832i			1.78495i	0.451094	+	0.892477i	$0.351034\pi$
$503$			897.832i			1.78495i	−0.451094	+	0.892477i	$0.648966\pi$
$504$		0			0
$505$		0			0
$506$	−1.11352	+	0.642891i	−0.00220063	+	0.00127053i
$507$		0			0
$508$	78.0908	−	135.257i	0.153722	−	0.266254i
$509$	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
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−114.136			−0.222055
$515$		0			0
$516$		0			0
$517$	−21.5908	+	37.3964i	−0.0417617	+	0.0723334i
$518$	477.464	+	275.664i	0.921746	+	0.532170i
$519$		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
$523$	−91.1827			−0.174345			−0.0871727	−	0.996193i	$-0.527783\pi$
$523$	−91.1827			−0.174345			−0.0871727	+	0.996193i	$0.527783\pi$
$524$	−405.409	+	234.063i	−0.773681	+	0.446685i
$525$		0			0
$526$	327.916	−	567.967i	0.623415	−	1.07979i
$527$	−49.7878	−	28.7450i	−0.0944739	−	0.0545445i
$528$		0			0
$529$	−264.045	−	457.340i	−0.499141	−	0.864537i
$530$		0			0
$531$		0			0
$532$	412.363			0.775119
$533$	−91.6806	+	52.9318i	−0.172009	+	0.0993092i
$534$		0			0
$535$		0			0
$536$	−183.823	−	106.130i	−0.342953	−	0.198004i
$537$		0			0
$538$	−30.7423	−	53.2473i	−0.0571419	−	0.0989727i
$539$		−	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	$0.511431\pi$
$542$	−419.641	+	242.280i	−0.774246	+	0.447011i
$543$		0			0
$544$	53.3939	−	92.4809i	0.0981505	−	0.170002i
$545$		0			0
$546$		0			0
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	0.570513	−	0.821289i	$-0.306744\pi$
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	−0.996513	+	0.0834344i	$0.973411\pi$
$548$		−	299.662i		−	0.546829i
$549$		0			0
$550$		0			0
$551$	292.621	−	168.945i	0.531072	−	0.306615i
$552$		0			0
$553$	182.591	−	316.257i	0.330182	−	0.571893i
$554$	−60.0125	−	34.6482i	−0.108326	−	0.0625419i
$555$		0			0
$556$	−84.5301	−	146.410i	−0.152033	−	0.263328i
$557$		−	695.042i		−	1.24783i	−0.781492	−	0.623916i	$-0.785541\pi$
$557$		−	695.042i		−	1.24783i	0.781492	−	0.623916i	$-0.214459\pi$
$558$		0			0
$559$	−436.803			−0.781400
$560$		0			0
$561$		0			0
$562$	14.5982	−	25.2848i	0.0259755	−	0.0449908i
$563$	−473.780	−	273.537i	−0.841528	−	0.485857i	0.0162552	−	0.999868i	$-0.494826\pi$
$563$	−473.780	−	273.537i	−0.841528	−	0.485857i	−0.857783	+	0.514011i	$0.828159\pi$
$564$		0			0
$565$		0			0
$566$		−	75.5313i		−	0.133447i
$567$		0			0
$568$	50.9694			0.0897348
$569$	−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	$0.187261\pi$
$572$	−16.0148	−	9.24614i	−0.0279979	−	0.0161646i
$573$		0			0
$574$	−64.4472	−	111.626i	−0.112277	−	0.194470i
$575$		0			0
$576$		0			0
$577$	43.9092			0.0760991			0.0380496	−	0.999276i	$-0.487886\pi$
$577$	43.9092			0.0760991			0.0380496	+	0.999276i	$0.487886\pi$
$578$	−82.5028	+	47.6330i	−0.142738	+	0.0824101i
$579$		0			0
$580$		0			0
$581$	942.302	+	544.038i	1.62186	+	0.936382i
$582$		0			0
$583$	−45.0000	−	77.9423i	−0.0771870	−	0.133692i
$584$		−	22.3706i		−	0.0383057i
$585$		0			0
$586$	−21.1056			−0.0360164
$587$	−381.386	+	220.194i	−0.649721	+	0.375117i	−0.788349	−	0.615228i	$-0.789064\pi$
$587$	−381.386	+	220.194i	−0.649721	+	0.375117i	0.138628	+	0.990345i	$0.455731\pi$
$588$		0			0
$589$	37.6061	−	65.1357i	0.0638474	−	0.110587i
$590$		0			0
$591$		0			0
$592$	93.3939	+	161.763i	0.157760	+	0.273248i
$593$			347.232i			0.585551i	0.956181	+	0.292776i	$0.0945789\pi$
$593$			347.232i			0.585551i	−0.956181	+	0.292776i	$0.905421\pi$
$594$		0			0
$595$		0			0
$596$	−200.060	+	115.505i	−0.335671	+	0.193800i
$597$		0			0
$598$	−6.53801	+	11.3242i	−0.0109331	+	0.0189367i
$599$	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	$0.633205\pi$
$602$		−	531.829i		−	0.883438i
$603$		0			0
$604$	129.546			0.214480
$605$		0			0
$606$		0			0
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.332048	+	0.943263i	$0.607739\pi$
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.650866	+	0.759193i	$0.725594\pi$
$608$	120.990	+	69.8535i	0.198996	+	0.114891i
$609$		0			0
$610$		0			0
$611$			439.145i			0.718731i
$612$		0			0
$613$	−629.181			−1.02640			−0.513198	−	0.858270i	$-0.671539\pi$
$613$	−629.181			−1.02640			−0.513198	+	0.858270i	$0.671539\pi$
$614$	−80.7219	+	46.6048i	−0.131469	+	0.0759036i
$615$		0			0
$616$	11.2577	−	19.4988i	0.0182754	−	0.0316539i
$617$	166.909	+	96.3648i	0.270516	+	0.156183i	0.629122	−	0.777306i	$-0.283414\pi$
$617$	166.909	+	96.3648i	0.270516	+	0.156183i	−0.358606	+	0.933489i	$0.616748\pi$
$618$		0			0
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	0.921165	−	0.389172i	$-0.127239\pi$
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	−0.797615	+	0.603166i	$0.793905\pi$
$620$		0			0
$621$		0			0
$622$	353.803			0.568814
$623$	1050.51	−	606.515i	1.68622	−	0.973539i
$624$		0			0
$625$		0			0
$626$	−522.224	−	301.506i	−0.834223	−	0.481639i
$627$		0			0
$628$	20.8184	+	36.0585i	0.0331503	+	0.0574180i
$629$		−	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	$0.488678\pi$
$632$	107.146	−	61.8610i	0.169535	−	0.0978814i
$633$		0			0
$634$	−328.083	+	568.256i	−0.517481	+	0.896303i
$635$		0			0
$636$		0			0
$637$	−100.348	−	173.809i	−0.157533	−	0.272855i
$638$		−	18.4490i		−	0.0289169i
$639$		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
$643$	395.704	−	685.380i	0.615403	−	1.06591i	−0.374910	−	0.927061i	$-0.622326\pi$
$643$	395.704	−	685.380i	0.615403	−	1.06591i	0.990314	−	0.138849i	$-0.0443402\pi$
$644$	−13.7878	−	7.96036i	−0.0214096	−	0.0123608i
$645$		0			0
$646$	−329.666	−	570.999i	−0.510319	−	0.883899i
$647$		−	294.028i		−	0.454448i	−0.973842	−	0.227224i	$-0.927035\pi$
$647$		−	294.028i		−	0.454448i	0.973842	−	0.227224i	$-0.0729650\pi$
$648$		0			0
$649$	−17.9082			−0.0275935
$650$		0			0
$651$		0			0
$652$	−133.060	+	230.467i	−0.204080	+	0.353477i
$653$	−665.379	−	384.156i	−1.01896	−	0.588295i	−0.105155	−	0.994456i	$-0.533534\pi$
$653$	−665.379	−	384.156i	−1.01896	−	0.588295i	−0.913802	+	0.406161i	$0.866867\pi$
$654$		0			0
$655$		0			0
$656$		−	43.6689i		−	0.0665684i
$657$		0			0
$658$	−534.681			−0.812585
$659$	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	$0.889053\pi$
$662$	−579.062	−	334.322i	−0.874717	−	0.505018i
$663$		0			0
$664$	184.318	+	319.248i	0.277587	+	0.480795i
$665$		0			0
$666$		0			0
$667$	−13.0454			−0.0195583
$668$	−510.106	+	294.510i	−0.763631	+	0.440883i
$669$		0			0
$670$		0			0
$671$	10.8099	+	6.24112i	0.0161102	+	0.00930123i
$672$		0			0
$673$	281.606	+	487.755i	0.418433	+	0.724748i	0.995782	−	0.0917499i	$-0.0292460\pi$
$673$	281.606	+	487.755i	0.418433	+	0.724748i	−0.577349	+	0.816498i	$0.695913\pi$
$674$		−	432.192i		−	0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	−303.227	+	175.068i	−0.447897	+	0.258594i	−0.706942	−	0.707272i	$-0.749926\pi$
$677$	−303.227	+	175.068i	−0.447897	+	0.258594i	0.259044	+	0.965865i	$0.416592\pi$
$678$		0			0
$679$	−458.659	+	794.421i	−0.675492	+	1.16999i
$680$		0			0
$681$		0			0
$682$	−2.05332	−	3.55645i	−0.00301073	−	0.00521474i
$683$		−	502.818i		−	0.736190i	−0.929788	−	0.368095i	$-0.880010\pi$
$683$		−	502.818i		−	0.736190i	0.929788	−	0.368095i	$-0.119990\pi$
$684$		0			0
$685$		0			0
$686$	−289.392	+	167.080i	−0.421854	+	0.243557i
$687$		0			0
$688$	90.0908	−	156.042i	0.130946	−	0.226805i
$689$	−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	$0.921118\pi$
$692$			138.529i			0.200186i
$693$		0			0
$694$	189.044			0.272398
$695$		0			0
$696$		0			0
$697$	−103.045	+	178.480i	−0.147841	+	0.256069i
$698$	120.952	+	69.8318i	0.173284	+	0.100046i
$699$		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
$703$	1153.27			1.64050
$704$	6.60612	−	3.81405i	0.00938370	−	0.00541768i
$705$		0			0
$706$	−230.598	+	399.408i	−0.326626	+	0.565733i
$707$	1066.70	+	615.862i	1.50878	+	0.871092i
$708$		0			0
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	0.649055	−	0.760741i	$-0.275164\pi$
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	−0.983349	+	0.181728i	$0.941831\pi$
$710$		0			0
$711$		0			0
$712$	410.969			0.577204
$713$	−2.51479	+	1.45192i	−0.00352706	+	0.00203635i
$714$		0			0
$715$		0			0
$716$	82.2429	+	47.4829i	0.114864	+	0.0663170i
$717$		0			0
$718$	−296.091	−	512.844i	−0.412383	−	0.714268i
$719$		−	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
$722$	304.886	−	176.026i	0.422280	−	0.243804i
$723$		0			0
$724$	242.879	−	420.678i	0.335468	−	0.581047i
$725$		0			0
$726$		0			0
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	0.671662	−	0.740858i	$-0.265581\pi$
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	−0.977433	+	0.211247i	$0.932248\pi$
$728$		−	228.974i		−	0.314525i
$729$		0			0
$730$		0			0
$731$	−736.423	+	425.174i	−1.00742	+	0.581634i
$732$		0			0
$733$	−358.181	+	620.388i	−0.488651	+	0.846368i	−0.999915	−	0.0130556i	$-0.995844\pi$
$733$	−358.181	+	620.388i	−0.488651	+	0.846368i	0.511264	+	0.859424i	$0.329177\pi$
$734$	229.305	+	132.390i	0.312405	+	0.180367i
$735$		0			0
$736$	−2.69694	−	4.67123i	−0.00366432	−	0.00634679i
$737$			71.5567i			0.0970918i
$738$		0			0
$739$	933.362			1.26301			0.631504	−	0.775373i	$-0.282438\pi$
$739$	933.362			1.26301			0.631504	+	0.775373i	$0.282438\pi$
$740$		0			0
$741$		0			0
$742$	557.196	−	965.093i	0.750939	−	1.30066i
$743$	−13.7793	−	7.95550i	−0.0185455	−	0.0107073i	0.490699	−	0.871329i	$-0.336742\pi$
$743$	−13.7793	−	7.95550i	−0.0185455	−	0.0107073i	−0.509244	+	0.860622i	$0.670075\pi$
$744$		0			0
$745$		0			0
$746$		−	637.852i		−	0.855030i
$747$		0			0
$748$	−36.0000			−0.0481283
$749$	−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	$0.985405\pi$
$752$	−156.879	−	90.5739i	−0.208615	−	0.120444i
$753$		0			0
$754$	−93.8105	−	162.484i	−0.124417	−	0.215497i
$755$		0			0
$756$		0			0
$757$	−689.637			−0.911013			−0.455506	−	0.890232i	$-0.650542\pi$
$757$	−689.637			−0.911013			−0.455506	+	0.890232i	$0.650542\pi$
$758$	−599.716	+	346.246i	−0.791182	+	0.456789i
$759$		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
$763$	618.924	+	1072.01i	0.811172	+	1.40499i
$764$			15.0635i			0.0197167i
$765$		0			0
$766$	145.743			0.190266
$767$	−157.721	+	91.0604i	−0.205634	+	0.118723i
$768$		0			0
$769$	328.348	−	568.715i	0.426980	−	0.739552i	−0.569623	−	0.821906i	$-0.692911\pi$
$769$	328.348	−	568.715i	0.426980	−	0.739552i	0.996603	+	0.0823545i	$0.0262440\pi$
$770$		0			0
$771$		0			0
$772$	−345.454	−	598.344i	−0.447479	−	0.775057i
$773$			278.021i			0.359665i	0.983697	+	0.179832i	$0.0575555\pi$
$773$			278.021i			0.359665i	−0.983697	+	0.179832i	$0.942445\pi$
$774$		0			0
$775$		0			0
$776$	−269.146	+	155.392i	−0.346838	+	0.200247i
$777$		0			0
$778$	−24.2350	+	41.9762i	−0.0311503	+	0.0539539i
$779$	−233.499	−	134.811i	−0.299743	−	0.173056i
$780$		0			0
$781$	−8.59133	−	14.8806i	−0.0110004	−	0.0190533i
$782$			25.4558i			0.0325522i
$783$		0			0
$784$	82.7878			0.105597
$785$		0			0
$786$		0			0
$787$	410.977	−	711.833i	0.522207	−	0.904489i	−0.477459	−	0.878654i	$-0.658442\pi$
$787$	410.977	−	711.833i	0.522207	−	0.904489i	0.999666	−	0.0258350i	$-0.00822444\pi$
$788$	−133.757	−	77.2247i	−0.169743	−	0.0980009i
$789$		0			0
$790$		0			0
$791$			1428.32i			1.80572i
$792$		0			0
$793$	126.941			0.160077
$794$	−10.1316	+	5.84950i	−0.0127602	+	0.00736713i
$795$		0			0
$796$	153.485	−	265.843i	0.192820	−	0.333974i
$797$	1145.33	+	661.257i	1.43705	+	0.829683i	0.997644	−	0.0686043i	$-0.0218546\pi$
$797$	1145.33	+	661.257i	1.43705	+	0.829683i	0.439409	+	0.898287i	$0.355188\pi$
$798$		0			0
$799$	427.454	+	740.372i	0.534986	+	0.926624i
$800$		0			0
$801$		0			0
$802$	−585.650			−0.730238
$803$	−6.53113	+	3.77075i	−0.00813341	+	0.00469583i
$804$		0			0
$805$		0			0
$806$	−36.1681	−	20.8817i	−0.0448736	−	0.0259078i
$807$		0			0
$808$	208.652	+	361.395i	0.258232	+	0.447271i
$809$			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	$0.617948\pi$
$812$	197.833	−	114.219i	0.243637	−	0.140664i
$813$		0			0
$814$	31.4847	−	54.5331i	0.0386790	−	0.0669940i
$815$		0			0
$816$		0			0
$817$	−556.242	−	963.439i	−0.680835	−	1.17924i
$818$		−	461.334i		−	0.563978i
$819$		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
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.325520	+	0.945535i	$0.605539\pi$
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.656097	+	0.754676i	$0.727794\pi$
$824$	252.631	+	145.857i	0.306591	+	0.177010i
$825$		0			0
$826$	−110.871	−	192.034i	−0.134226	−	0.232486i
$827$		−	582.354i		−	0.704177i	−0.935967	−	0.352088i	$-0.885472\pi$
$827$		−	582.354i		−	0.704177i	0.935967	−	0.352088i	$-0.114528\pi$
$828$		0			0
$829$	877.121			1.05805			0.529024	−	0.848607i	$-0.322558\pi$
$829$	877.121			1.05805			0.529024	+	0.848607i	$0.322558\pi$
$830$		0			0
$831$		0			0
$832$	38.7878	−	67.1824i	0.0466199	−	0.0807480i
$833$	−338.363	−	195.354i	−0.406198	−	0.234519i
$834$		0			0
$835$		0			0
$836$		−	47.0976i		−	0.0563369i
$837$		0			0
$838$	764.772			0.912616
$839$	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
$842$	−347.456	−	200.604i	−0.412656	−	0.238247i
$843$		0			0
$844$	−51.5607	−	89.3058i	−0.0610909	−	0.105813i
$845$		0			0
$846$		0			0
$847$	1002.57			1.18368
$848$	326.969	−	188.776i	0.385577	−	0.222613i
$849$		0			0
$850$		0			0
$851$	−38.5607	−	22.2630i	−0.0453122	−	0.0261610i
$852$		0			0
$853$	−159.909	−	276.970i	−0.187466	−	0.324701i	0.756939	−	0.653486i	$-0.226694\pi$
$853$	−159.909	−	276.970i	−0.187466	−	0.324701i	−0.944405	+	0.328785i	$0.893361\pi$
$854$			154.557i			0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	691.061	−	398.984i	0.806372	−	0.465559i	−0.0393225	−	0.999227i	$-0.512520\pi$
$857$	691.061	−	398.984i	0.806372	−	0.465559i	0.845694	+	0.533668i	$0.179187\pi$
$858$		0			0
$859$	233.901	−	405.128i	0.272294	−	0.471627i	−0.697155	−	0.716921i	$-0.745551\pi$
$859$	233.901	−	405.128i	0.272294	−	0.471627i	0.969449	+	0.245293i	$0.0788843\pi$
$860$		0			0
$861$		0			0
$862$	−182.030	−	315.284i	−0.211171	−	0.365759i
$863$			1304.85i			1.51199i	0.654578	+	0.755994i	$0.272846\pi$
$863$			1304.85i			1.51199i	−0.654578	+	0.755994i	$0.727154\pi$
$864$		0			0
$865$		0			0
$866$	−583.312	+	336.775i	−0.673571	+	0.388886i
$867$		0			0
$868$	25.4245	−	44.0365i	0.0292909	−	0.0507333i
$869$	−36.1209	−	20.8544i	−0.0415661	−	0.0239982i
$870$		0			0
$871$	363.855	+	630.216i	0.417744	+	0.723554i
$872$			419.378i			0.480938i
$873$		0			0
$874$	−33.3031			−0.0381042
$875$		0			0
$876$		0			0
$877$	−186.878	+	323.682i	−0.213088	+	0.369079i	−0.952679	−	0.303977i	$-0.901685\pi$
$877$	−186.878	+	323.682i	−0.213088	+	0.369079i	0.739592	+	0.673056i	$0.235019\pi$
$878$	683.240	+	394.469i	0.778177	+	0.449281i
$879$		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
$883$	1381.79			1.56488			0.782439	−	0.622728i	$-0.213976\pi$
$883$	1381.79			1.56488			0.782439	+	0.622728i	$0.213976\pi$
$884$	−317.060	+	183.055i	−0.358665	+	0.207076i
$885$		0			0
$886$	588.204	−	1018.80i	0.663888	−	1.14989i
$887$	758.794	+	438.090i	0.855461	+	0.493901i	0.862490	−	0.506075i	$-0.168904\pi$
$887$	758.794	+	438.090i	0.855461	+	0.493901i	−0.00702852	+	0.999975i	$0.502237\pi$
$888$		0			0
$889$	−325.969	−	564.596i	−0.366670	−	0.635091i
$890$		0			0
$891$		0			0
$892$	626.454			0.702303
$893$	−968.605	+	559.224i	−1.08466	+	0.626231i
$894$		0			0
$895$		0			0
$896$	81.7980	+	47.2261i	0.0912924	+	0.0527077i
$897$		0			0
$898$	516.136	+	893.974i	0.574762	+	0.995517i
$899$		−	41.6655i		−	0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$	−12.7492	+	7.36077i	−0.0141344	+	0.00816050i
$903$		0			0
$904$	−241.955	+	419.078i	−0.267649	+	0.463581i
$905$		0			0
$906$		0			0
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	0.982993	+	0.183644i	$0.0587894\pi$
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	−0.332456	+	0.943119i	$0.607877\pi$
$908$			152.542i			0.167998i
$909$		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
$913$	62.1367	−	107.624i	0.0680578	−	0.117880i
$914$	869.123	+	501.788i	0.950900	+	0.549002i
$915$		0			0
$916$	−121.545	−	210.522i	−0.132691	−	0.229827i
$917$			1954.07i			2.13093i
$918$		0			0
$919$	1316.63			1.43268			0.716340	−	0.697751i	$-0.245816\pi$
$919$	1316.63			1.43268			0.716340	+	0.697751i	$0.245816\pi$
$920$		0			0
$921$		0			0
$922$	6.50740	−	11.2711i	0.00705791	−	0.0122247i
$923$	−151.332	−	87.3713i	−0.163956	−	0.0946602i
$924$		0			0
$925$		0			0
$926$			78.0610i			0.0842991i
$927$		0			0
$928$	77.3939			0.0833986
$929$	−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
$932$	261.576	+	151.021i	0.280660	+	0.162039i
$933$		0			0
$934$	442.515	+	766.459i	0.473785	+	0.820620i
$935$		0			0
$936$		0			0
$937$	−469.789			−0.501375			−0.250688	−	0.968068i	$-0.580657\pi$
$937$	−469.789			−0.501375			−0.250688	+	0.968068i	$0.580657\pi$
$938$	−767.320	+	443.012i	−0.818039	+	0.472295i
$939$		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
$943$	5.20485	+	9.01506i	0.00551946	+	0.00955998i
$944$		−	75.1250i		−	0.0795816i
$945$		0			0
$946$	−60.7423			−0.0642097
$947$	−3.14465	+	1.81556i	−0.00332064	+	0.00191717i	−0.501659	−	0.865065i	$-0.667277\pi$
$947$	−3.14465	+	1.81556i	−0.00332064	+	0.00191717i	0.498339	+	0.866982i	$0.333944\pi$
$948$		0			0
$949$	−38.3474	+	66.4197i	−0.0404083	+	0.0699892i
$950$		0			0
$951$		0			0
$952$	−222.879	−	386.037i	−0.234116	−	0.405501i
$953$			719.641i			0.755132i	0.925983	+	0.377566i	$0.123239\pi$
$953$			719.641i			0.755132i	−0.925983	+	0.377566i	$0.876761\pi$
$954$		0			0
$955$		0			0
$956$	151.924	−	87.7133i	0.158916	−	0.0917504i
$957$		0			0
$958$	−218.704	+	378.806i	−0.228292	+	0.395413i
$959$	−1083.28	−	625.431i	−1.12959	−	0.652170i
$960$		0			0
$961$	475.863	+	824.218i	0.495175	+	0.857667i
$962$		−	640.380i		−	0.665676i
$963$		0			0
$964$	−403.576			−0.418647
$965$		0			0
$966$		0			0
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	−0.857162	−	0.515047i	$-0.827774\pi$
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	0.874625	+	0.484800i	$0.161108\pi$
$968$	294.161	+	169.834i	0.303886	+	0.175448i
$969$		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
$973$	−705.697			−0.725279
$974$	34.7015	−	20.0349i	0.0356278	−	0.0205697i
$975$		0			0
$976$	−26.1816	+	45.3479i	−0.0268254	+	0.0464630i
$977$	−1359.92	−	785.151i	−1.39194	−	0.803635i	−0.398406	−	0.917209i	$-0.630437\pi$
$977$	−1359.92	−	785.151i	−1.39194	−	0.803635i	−0.993529	+	0.113574i	$0.963770\pi$
$978$		0			0
$979$	−69.2724	−	119.983i	−0.0707584	−	0.122557i
$980$		0			0
$981$		0			0
$982$	−1343.07			−1.36769
$983$	−671.930	+	387.939i	−0.683551	+	0.394648i	−0.801192	−	0.598408i	$-0.795800\pi$
$983$	−671.930	+	387.939i	−0.683551	+	0.394648i	0.117641	+	0.993056i	$0.462467\pi$
$984$		0			0
$985$		0			0
$986$	−316.318	−	182.626i	−0.320809	−	0.185219i
$987$		0			0
$988$	−239.485	−	414.800i	−0.242393	−	0.419838i
$989$			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	$0.355269\pi$
$992$	14.9194	−	8.61371i	0.0150397	−	0.00868318i
$993$		0			0
$994$	106.379	−	184.254i	0.107021	−	0.185366i
$995$		0			0
$996$		0			0
$997$	622.499	+	1078.20i	0.624372	+	1.08144i	0.988662	+	0.150159i	$0.0479784\pi$
$997$	622.499	+	1078.20i	0.624372	+	1.08144i	−0.364290	+	0.931286i	$0.618688\pi$
$998$		−	792.279i		−	0.793867i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.3.i.b.1151.2		4
3.2	odd	2		450.3.i.b.401.1		4
5.2	odd	4		1350.3.k.a.449.4		8
5.3	odd	4		1350.3.k.a.449.1		8
5.4	even	2		54.3.d.a.17.1		4
9.2	odd	6	inner	1350.3.i.b.251.2		4
9.7	even	3		450.3.i.b.101.1		4
15.2	even	4		450.3.k.a.149.1		8
15.8	even	4		450.3.k.a.149.4		8
15.14	odd	2		18.3.d.a.5.2	✓	4
20.19	odd	2		432.3.q.d.17.1		4
40.19	odd	2		1728.3.q.c.449.1		4
40.29	even	2		1728.3.q.d.449.2		4
45.2	even	12		1350.3.k.a.899.1		8
45.4	even	6		162.3.b.a.161.1		4
45.7	odd	12		450.3.k.a.299.4		8
45.14	odd	6		162.3.b.a.161.4		4
45.29	odd	6		54.3.d.a.35.1		4
45.34	even	6		18.3.d.a.11.2	yes	4
45.38	even	12		1350.3.k.a.899.4		8
45.43	odd	12		450.3.k.a.299.1		8
60.59	even	2		144.3.q.c.113.2		4
120.29	odd	2		576.3.q.f.257.2		4
120.59	even	2		576.3.q.e.257.1		4
180.59	even	6		1296.3.e.g.161.4		4
180.79	odd	6		144.3.q.c.65.2		4
180.119	even	6		432.3.q.d.305.1		4
180.139	odd	6		1296.3.e.g.161.2		4
360.29	odd	6		1728.3.q.d.1601.2		4
360.259	odd	6		576.3.q.e.65.1		4
360.299	even	6		1728.3.q.c.1601.1		4
360.349	even	6		576.3.q.f.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	15.14	odd	2
18.3.d.a.11.2	yes	4	45.34	even	6
54.3.d.a.17.1		4	5.4	even	2
54.3.d.a.35.1		4	45.29	odd	6
144.3.q.c.65.2		4	180.79	odd	6
144.3.q.c.113.2		4	60.59	even	2
162.3.b.a.161.1		4	45.4	even	6
162.3.b.a.161.4		4	45.14	odd	6
432.3.q.d.17.1		4	20.19	odd	2
432.3.q.d.305.1		4	180.119	even	6
450.3.i.b.101.1		4	9.7	even	3
450.3.i.b.401.1		4	3.2	odd	2
450.3.k.a.149.1		8	15.2	even	4
450.3.k.a.149.4		8	15.8	even	4
450.3.k.a.299.1		8	45.43	odd	12
450.3.k.a.299.4		8	45.7	odd	12
576.3.q.e.65.1		4	360.259	odd	6
576.3.q.e.257.1		4	120.59	even	2
576.3.q.f.65.2		4	360.349	even	6
576.3.q.f.257.2		4	120.29	odd	2
1296.3.e.g.161.2		4	180.139	odd	6
1296.3.e.g.161.4		4	180.59	even	6
1350.3.i.b.251.2		4	9.2	odd	6	inner
1350.3.i.b.1151.2		4	1.1	even	1	trivial
1350.3.k.a.449.1		8	5.3	odd	4
1350.3.k.a.449.4		8	5.2	odd	4
1350.3.k.a.899.1		8	45.2	even	12
1350.3.k.a.899.4		8	45.38	even	12
1728.3.q.c.449.1		4	40.19	odd	2
1728.3.q.c.1601.1		4	360.299	even	6
1728.3.q.d.449.2		4	40.29	even	2
1728.3.q.d.1601.2		4	360.29	odd	6

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.17423 - 7.22999i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.17423 - 7.22999i) q^{7} -2.82843i q^{8} +(-0.825765 + 0.476756i) q^{11} +(-4.84847 + 8.39780i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} +18.8776i q^{17} -24.6969 q^{19} +(-0.674235 + 1.16781i) q^{22} +(0.825765 + 0.476756i) q^{23} +13.7135i q^{26} -16.6969 q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(13.3485 + 23.1202i) q^{34} -46.6969 q^{37} +(-30.2474 + 17.4634i) q^{38} +(9.45459 + 5.45861i) q^{41} +(22.5227 + 39.0105i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(39.2196 - 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(9.69694 + 16.7956i) q^{52} +94.3879i q^{53} +(-20.4495 + 11.8065i) q^{56} +(-9.67423 + 16.7563i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} +4.30686i q^{62} -8.00000 q^{64} +(37.5227 - 64.9912i) q^{67} +(32.6969 + 18.8776i) q^{68} +18.0204i q^{71} +7.90918 q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(6.89388 + 3.98018i) q^{77} +(21.8712 + 37.8820i) q^{79} +15.4393 q^{82} +(-112.871 + 65.1662i) q^{83} +(55.1691 + 31.8519i) q^{86} +(1.34847 + 2.33562i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(1.65153 - 0.953512i) q^{92} +(32.0227 - 55.4650i) q^{94} +(-54.9393 - 95.1576i) q^{97} +29.2699i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q + 4 * q^4 - 2 * q^7	\( 4 q + 4 q^{4} - 2 q^{7} - 18 q^{11} + 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 12 q^{22} + 18 q^{23} - 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} - 128 q^{37} - 72 q^{38} + 126 q^{41} + 46 q^{43} - 24 q^{46} + 54 q^{47} - 12 q^{49} - 20 q^{52} - 72 q^{56} - 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} + 106 q^{67} + 72 q^{68} + 208 q^{73} - 72 q^{74} - 40 q^{76} - 90 q^{77} + 14 q^{79} - 144 q^{82} - 378 q^{83} + 108 q^{86} - 24 q^{88} + 412 q^{91} + 36 q^{92} + 84 q^{94} - 14 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 - 2 * q^7 - 18 * q^11 + 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 12 * q^22 + 18 * q^23 - 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 - 128 * q^37 - 72 * q^38 + 126 * q^41 + 46 * q^43 - 24 * q^46 + 54 * q^47 - 12 * q^49 - 20 * q^52 - 72 * q^56 - 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 + 106 * q^67 + 72 * q^68 + 208 * q^73 - 72 * q^74 - 40 * q^76 - 90 * q^77 + 14 * q^79 - 144 * q^82 - 378 * q^83 + 108 * q^86 - 24 * q^88 + 412 * q^91 + 36 * q^92 + 84 * q^94 - 14 * q^97

Introduction

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