LMFDB - Embedded newform 105.3.e.a.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(34,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("105.34");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + \cdots + 1849 $ x^16 - 8x^15 + 72x^14 - 292x^13 + 1148x^12 - 2304x^11 + 4996x^10 - 4490x^9 + 9786x^8 - 5744x^7 + 8608x^6 + 4740x^5 + 22841x^4 + 22790x^3 + 18930x^2 + 8170*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.3
Root			$1.36603 - 3.14303i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30086i q^{2} -1.73205 q^{3} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +3.98521i q^{6} +(-6.39480 + 2.84720i) q^{7} -6.22623i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.30086i q^{2} -1.73205 q^{3} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +3.98521i q^{6} +(-6.39480 + 2.84720i) q^{7} -6.22623i q^{8} +3.00000 q^{9} +(-7.84383 + 8.41565i) q^{10} -13.9015 q^{11} +2.24120 q^{12} +3.78588 q^{13} +(6.55102 + 14.7135i) q^{14} +(6.33517 + 5.90471i) q^{15} -19.5015 q^{16} +14.8567 q^{17} -6.90258i q^{18} -6.94906i q^{19} +(4.73278 + 4.41121i) q^{20} +(11.0761 - 4.93150i) q^{21} +31.9853i q^{22} -40.2857i q^{23} +10.7841i q^{24} +(1.75623 + 24.9382i) q^{25} -8.71077i q^{26} -5.19615 q^{27} +(8.27458 - 3.68415i) q^{28} +9.88885 q^{29} +(13.5859 - 14.5763i) q^{30} -34.7764i q^{31} +19.9653i q^{32} +24.0781 q^{33} -34.1833i q^{34} +(33.0960 + 11.3865i) q^{35} -3.88187 q^{36} -30.4393i q^{37} -15.9888 q^{38} -6.55733 q^{39} +(-21.2258 + 22.7731i) q^{40} -44.6778i q^{41} +(-11.3467 - 25.4846i) q^{42} +26.0309i q^{43} +17.9879 q^{44} +(-10.9728 - 10.2273i) q^{45} -92.6918 q^{46} +23.7033 q^{47} +33.7776 q^{48} +(32.7869 - 36.4146i) q^{49} +(57.3794 - 4.04085i) q^{50} -25.7326 q^{51} -4.89875 q^{52} +59.5338i q^{53} +11.9556i q^{54} +(50.8462 + 47.3914i) q^{55} +(17.7273 + 39.8155i) q^{56} +12.0361i q^{57} -22.7529i q^{58} +81.0347i q^{59} +(-8.19742 - 7.64043i) q^{60} +78.8493i q^{61} -80.0155 q^{62} +(-19.1844 + 8.54161i) q^{63} -32.0687 q^{64} +(-13.8473 - 12.9064i) q^{65} -55.4002i q^{66} -29.9557i q^{67} -19.2240 q^{68} +69.7770i q^{69} +(26.1986 - 76.1494i) q^{70} -117.475 q^{71} -18.6787i q^{72} +22.2333 q^{73} -70.0365 q^{74} +(-3.04189 - 43.1943i) q^{75} +8.99177i q^{76} +(88.8971 - 39.5803i) q^{77} +15.0875i q^{78} +142.799 q^{79} +(71.3289 + 66.4823i) q^{80} +9.00000 q^{81} -102.797 q^{82} -160.872 q^{83} +(-14.3320 + 6.38114i) q^{84} +(-54.3402 - 50.6480i) q^{85} +59.8935 q^{86} -17.1280 q^{87} +86.5538i q^{88} -66.3844i q^{89} +(-23.5315 + 25.2469i) q^{90} +(-24.2099 + 10.7792i) q^{91} +52.1279i q^{92} +60.2344i q^{93} -54.5380i q^{94} +(-23.6899 + 25.4169i) q^{95} -34.5809i q^{96} +45.1538 q^{97} +(-83.7849 - 75.4379i) q^{98} -41.7044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.30086i		−	1.15043i	−0.818002	−	0.575215i	$-0.804918\pi$
$2$		−	2.30086i		−	1.15043i	0.818002	−	0.575215i	$-0.195082\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−1.29396			−0.323489
$5$	−3.65761	−	3.40909i	−0.731522	−	0.681818i
$5$	−3.65761	−	3.40909i	−0.731522	−	0.681818i
$6$			3.98521i			0.664201i
$7$	−6.39480	+	2.84720i	−0.913542	+	0.406744i
$7$	−6.39480	+	2.84720i	−0.913542	+	0.406744i
$8$		−	6.22623i		−	0.778279i
$9$	3.00000			0.333333
$10$	−7.84383	+	8.41565i	−0.784383	+	0.841565i
$11$	−13.9015			−1.26377			−0.631885	−	0.775062i	$-0.717719\pi$
$11$	−13.9015			−1.26377			−0.631885	+	0.775062i	$0.717719\pi$
$12$	2.24120			0.186766
$13$	3.78588			0.291221			0.145611	−	0.989342i	$-0.453485\pi$
$13$	3.78588			0.291221			0.145611	+	0.989342i	$0.453485\pi$
$14$	6.55102	+	14.7135i	0.467930	+	1.05097i
$15$	6.33517	+	5.90471i	0.422345	+	0.393648i
$16$	−19.5015			−1.21884
$17$	14.8567			0.873926			0.436963	−	0.899479i	$-0.356054\pi$
$17$	14.8567			0.873926			0.436963	+	0.899479i	$0.356054\pi$
$18$		−	6.90258i		−	0.383477i
$19$		−	6.94906i		−	0.365740i	−0.983137	−	0.182870i	$-0.941461\pi$
$19$		−	6.94906i		−	0.365740i	0.983137	−	0.182870i	$-0.0585387\pi$
$20$	4.73278	+	4.41121i	0.236639	+	0.220560i
$21$	11.0761	−	4.93150i	0.527434	−	0.234833i
$22$			31.9853i			1.45388i
$23$		−	40.2857i		−	1.75155i	−0.482716	−	0.875777i	$-0.660350\pi$
$23$		−	40.2857i		−	1.75155i	0.482716	−	0.875777i	$-0.339650\pi$
$24$			10.7841i			0.449339i
$25$	1.75623	+	24.9382i	0.0702494	+	0.997529i
$26$		−	8.71077i		−	0.335030i
$27$	−5.19615			−0.192450
$28$	8.27458	−	3.68415i	0.295521	−	0.131577i
$29$	9.88885			0.340995			0.170497	−	0.985358i	$-0.445463\pi$
$29$	9.88885			0.340995			0.170497	+	0.985358i	$0.445463\pi$
$30$	13.5859	−	14.5763i	0.452864	−	0.485878i
$31$		−	34.7764i		−	1.12182i	−0.827877	−	0.560909i	$-0.810452\pi$
$31$		−	34.7764i		−	1.12182i	0.827877	−	0.560909i	$-0.189548\pi$
$32$			19.9653i			0.623916i
$33$	24.0781			0.729638
$34$		−	34.1833i		−	1.00539i
$35$	33.0960	+	11.3865i	0.945601	+	0.325327i
$36$	−3.88187			−0.107830
$37$		−	30.4393i		−	0.822683i	−0.911481	−	0.411342i	$-0.865060\pi$
$37$		−	30.4393i		−	0.822683i	0.911481	−	0.411342i	$-0.134940\pi$
$38$	−15.9888			−0.420758
$39$	−6.55733			−0.168137
$40$	−21.2258	+	22.7731i	−0.530644	+	0.569328i
$41$		−	44.6778i		−	1.08970i	−0.838532	−	0.544852i	$-0.816586\pi$
$41$		−	44.6778i		−	1.08970i	0.838532	−	0.544852i	$-0.183414\pi$
$42$	−11.3467	−	25.4846i	−0.270159	−	0.606776i
$43$			26.0309i			0.605370i	0.953091	+	0.302685i	$0.0978831\pi$
$43$			26.0309i			0.605370i	−0.953091	+	0.302685i	$0.902117\pi$
$44$	17.9879			0.408816
$45$	−10.9728	−	10.2273i	−0.243841	−	0.227273i
$46$	−92.6918			−2.01504
$47$	23.7033			0.504326			0.252163	−	0.967685i	$-0.418858\pi$
$47$	23.7033			0.504326			0.252163	+	0.967685i	$0.418858\pi$
$48$	33.7776			0.703700
$49$	32.7869	−	36.4146i	0.669119	−	0.743155i
$50$	57.3794	−	4.04085i	1.14759	−	0.0808170i
$51$	−25.7326			−0.504562
$52$	−4.89875			−0.0942068
$53$			59.5338i			1.12328i	0.827382	+	0.561640i	$0.189829\pi$
$53$			59.5338i			1.12328i	−0.827382	+	0.561640i	$0.810171\pi$
$54$			11.9556i			0.221400i
$55$	50.8462	+	47.3914i	0.924476	+	0.861661i
$56$	17.7273	+	39.8155i	0.316560	+	0.710991i
$57$			12.0361i			0.211160i
$58$		−	22.7529i		−	0.392291i
$59$			81.0347i			1.37347i	0.726908	+	0.686735i	$0.240957\pi$
$59$			81.0347i			1.37347i	−0.726908	+	0.686735i	$0.759043\pi$
$60$	−8.19742	−	7.64043i	−0.136624	−	0.127341i
$61$			78.8493i			1.29261i	0.763079	+	0.646306i	$0.223687\pi$
$61$			78.8493i			1.29261i	−0.763079	+	0.646306i	$0.776313\pi$
$62$	−80.0155			−1.29057
$63$	−19.1844	+	8.54161i	−0.304514	+	0.135581i
$64$	−32.0687			−0.501073
$65$	−13.8473	−	12.9064i	−0.213035	−	0.198560i
$66$		−	55.4002i		−	0.839398i
$67$		−	29.9557i		−	0.447101i	−0.974692	−	0.223550i	$-0.928235\pi$
$67$		−	29.9557i		−	0.447101i	0.974692	−	0.223550i	$-0.0717647\pi$
$68$	−19.2240			−0.282705
$69$			69.7770i			1.01126i
$70$	26.1986	−	76.1494i	0.374266	−	1.08785i
$71$	−117.475			−1.65457			−0.827286	−	0.561780i	$-0.810117\pi$
$71$	−117.475			−1.65457			−0.827286	+	0.561780i	$0.810117\pi$
$72$		−	18.6787i		−	0.259426i
$73$	22.2333			0.304566			0.152283	−	0.988337i	$-0.451338\pi$
$73$	22.2333			0.304566			0.152283	+	0.988337i	$0.451338\pi$
$74$	−70.0365			−0.946439
$75$	−3.04189	−	43.1943i	−0.0405585	−	0.575924i
$76$			8.99177i			0.118313i
$77$	88.8971	−	39.5803i	1.15451	−	0.514030i
$78$			15.0875i			0.193429i
$79$	142.799			1.80758			0.903791	−	0.427974i	$-0.140772\pi$
$79$	142.799			1.80758			0.903791	+	0.427974i	$0.140772\pi$
$80$	71.3289	+	66.4823i	0.891611	+	0.831029i
$81$	9.00000			0.111111
$82$	−102.797			−1.25363
$83$	−160.872			−1.93822			−0.969108	−	0.246636i	$-0.920675\pi$
$83$	−160.872			−1.93822			−0.969108	+	0.246636i	$0.920675\pi$
$84$	−14.3320	+	6.38114i	−0.170619	+	0.0759660i
$85$	−54.3402	−	50.6480i	−0.639296	−	0.595858i
$86$	59.8935			0.696436
$87$	−17.1280			−0.196873
$88$			86.5538i			0.983566i
$89$		−	66.3844i		−	0.745892i	−0.927853	−	0.372946i	$-0.878348\pi$
$89$		−	66.3844i		−	0.745892i	0.927853	−	0.372946i	$-0.121652\pi$
$90$	−23.5315	+	25.2469i	−0.261461	+	0.280522i
$91$	−24.2099	+	10.7792i	−0.266043	+	0.118452i
$92$			52.1279i			0.566608i
$93$			60.2344i			0.647682i
$94$		−	54.5380i		−	0.580192i
$95$	−23.6899	+	25.4169i	−0.249368	+	0.267547i
$96$		−	34.5809i		−	0.360218i
$97$	45.1538			0.465503			0.232751	−	0.972536i	$-0.425227\pi$
$97$	45.1538			0.465503			0.232751	+	0.972536i	$0.425227\pi$
$98$	−83.7849	−	75.4379i	−0.854948	−	0.769775i
$99$	−41.7044			−0.421257
$100$	−2.27249	−	32.2690i	−0.0227249	−	0.322690i
$101$		−	130.221i		−	1.28932i	−0.764471	−	0.644658i	$-0.777000\pi$
$101$		−	130.221i		−	1.28932i	0.764471	−	0.644658i	$-0.223000\pi$
$102$			59.2072i			0.580463i
$103$	4.07795			0.0395917			0.0197959	−	0.999804i	$-0.493698\pi$
$103$	4.07795			0.0395917			0.0197959	+	0.999804i	$0.493698\pi$
$104$		−	23.5717i		−	0.226651i
$105$	−57.3240	−	19.7219i	−0.545943	−	0.187828i
$106$	136.979			1.29225
$107$		−	31.3454i		−	0.292948i	−0.989215	−	0.146474i	$-0.953208\pi$
$107$		−	31.3454i		−	0.292948i	0.989215	−	0.146474i	$-0.0467924\pi$
$108$	6.72359			0.0622554
$109$	62.4441			0.572881			0.286441	−	0.958098i	$-0.407528\pi$
$109$	62.4441			0.572881			0.286441	+	0.958098i	$0.407528\pi$
$110$	109.041	−	116.990i	0.991281	−	1.06354i
$111$			52.7224i			0.474976i
$112$	124.708	−	55.5248i	1.11347	−	0.495757i
$113$		−	61.9010i		−	0.547796i	−0.961759	−	0.273898i	$-0.911687\pi$
$113$		−	61.9010i		−	0.547796i	0.961759	−	0.273898i	$-0.0883131\pi$
$114$	27.6934			0.242925
$115$	−137.338	+	147.350i	−1.19424	+	1.28130i
$116$	−12.7957			−0.110308
$117$	11.3576			0.0970738
$118$	186.450			1.58008
$119$	−95.0059	+	42.3002i	−0.798369	+	0.355464i
$120$	36.7641	−	39.4442i	0.306368	−	0.328702i
$121$	72.2510			0.597116
$122$	181.421			1.48706
$123$			77.3843i			0.629141i
$124$			44.9990i			0.362896i
$125$	78.5930	−	97.2015i	0.628744	−	0.777612i
$126$	19.6531	+	44.1406i	0.155977	+	0.350322i
$127$		−	185.310i		−	1.45913i	−0.683910	−	0.729566i	$-0.739722\pi$
$127$		−	185.310i		−	1.45913i	0.683910	−	0.729566i	$-0.260278\pi$
$128$			153.647i			1.20036i
$129$		−	45.0869i		−	0.349511i
$130$	−29.6958	+	31.8606i	−0.228429	+	0.245082i
$131$			92.8188i			0.708541i	0.935143	+	0.354270i	$0.115271\pi$
$131$			92.8188i			0.708541i	−0.935143	+	0.354270i	$0.884729\pi$
$132$	−31.1559			−0.236030
$133$	19.7854	+	44.4378i	0.148762	+	0.334119i
$134$	−68.9240			−0.514358
$135$	19.0055	+	17.7141i	0.140782	+	0.131216i
$136$		−	92.5015i		−	0.680158i
$137$			88.9332i			0.649147i	0.945860	+	0.324574i	$0.105221\pi$
$137$			88.9332i			0.649147i	−0.945860	+	0.324574i	$0.894779\pi$
$138$	160.547			1.16338
$139$			38.1205i			0.274248i	0.990554	+	0.137124i	$0.0437859\pi$
$139$			38.1205i			0.274248i	−0.990554	+	0.137124i	$0.956214\pi$
$140$	−42.8248	−	14.7336i	−0.305891	−	0.105240i
$141$	−41.0554			−0.291173
$142$			270.293i			1.90347i
$143$	−52.6293			−0.368037
$144$	−58.5045			−0.406281
$145$	−36.1696	−	33.7120i	−0.249445	−	0.232496i
$146$		−	51.1557i		−	0.350381i
$147$	−56.7885	+	63.0719i	−0.386316	+	0.429061i
$148$			39.3871i			0.266129i
$149$	132.122			0.886724			0.443362	−	0.896343i	$-0.353786\pi$
$149$	132.122			0.886724			0.443362	+	0.896343i	$0.353786\pi$
$150$	−99.3840	+	6.99896i	−0.662560	+	0.0466597i
$151$	149.537			0.990310			0.495155	−	0.868805i	$-0.335111\pi$
$151$	149.537			0.990310			0.495155	+	0.868805i	$0.335111\pi$
$152$	−43.2664			−0.284647
$153$	44.5702			0.291309
$154$	−91.0688	−	204.540i	−0.591356	−	1.32818i
$155$	−118.556	+	127.198i	−0.764875	+	0.820635i
$156$	8.48489			0.0543903
$157$	29.5598			0.188279			0.0941396	−	0.995559i	$-0.469990\pi$
$157$	29.5598			0.188279			0.0941396	+	0.995559i	$0.469990\pi$
$158$		−	328.560i		−	2.07950i
$159$		−	103.116i		−	0.648526i
$160$	68.0635	−	73.0253i	0.425397	−	0.456408i
$161$	114.702	+	257.619i	0.712433	+	1.60012i
$162$		−	20.7077i		−	0.127826i
$163$		−	240.158i		−	1.47337i	−0.676239	−	0.736683i	$-0.736391\pi$
$163$		−	240.158i		−	1.47337i	0.676239	−	0.736683i	$-0.263609\pi$
$164$			57.8111i			0.352507i
$165$	−88.0682	−	82.0842i	−0.533747	−	0.497480i
$166$			370.144i			2.22978i
$167$	−207.335			−1.24153			−0.620764	−	0.783997i	$-0.713178\pi$
$167$	−207.335			−1.24153			−0.620764	+	0.783997i	$0.713178\pi$
$168$	−30.7047	−	68.9624i	−0.182766	−	0.410491i
$169$	−154.667			−0.915190
$170$	−116.534	+	125.029i	−0.685493	+	0.735466i
$171$		−	20.8472i		−	0.121913i
$172$		−	33.6828i		−	0.195831i
$173$	−68.3717			−0.395212			−0.197606	−	0.980282i	$-0.563317\pi$
$173$	−68.3717			−0.395212			−0.197606	+	0.980282i	$0.563317\pi$
$174$			39.4091i			0.226489i
$175$	−82.2350	−	154.475i	−0.469914	−	0.882712i
$176$	271.100			1.54034
$177$		−	140.356i		−	0.792973i
$178$	−152.741			−0.858097
$179$	142.187			0.794342			0.397171	−	0.917745i	$-0.369992\pi$
$179$	142.187			0.794342			0.397171	+	0.917745i	$0.369992\pi$
$180$	14.1984	+	13.2336i	0.0788797	+	0.0735201i
$181$		−	266.458i		−	1.47214i	−0.676903	−	0.736072i	$-0.736678\pi$
$181$		−	266.458i		−	1.47214i	0.676903	−	0.736072i	$-0.263322\pi$
$182$	24.8013	+	55.7036i	0.136271	+	0.306064i
$183$		−	136.571i		−	0.746289i
$184$	−250.828			−1.36320
$185$	−103.770	+	111.335i	−0.560920	+	0.601811i
$186$	138.591			0.745113
$187$	−206.531			−1.10444
$188$	−30.6710			−0.163144
$189$	33.2283	−	14.7945i	0.175811	−	0.0782778i
$190$	58.4808	+	54.5072i	0.307794	+	0.286880i
$191$	−32.5201			−0.170262			−0.0851312	−	0.996370i	$-0.527131\pi$
$191$	−32.5201			−0.170262			−0.0851312	+	0.996370i	$0.527131\pi$
$192$	55.5445			0.289294
$193$		−	106.194i		−	0.550228i	−0.961412	−	0.275114i	$-0.911284\pi$
$193$		−	106.194i		−	0.550228i	0.961412	−	0.275114i	$-0.0887156\pi$
$194$		−	103.892i		−	0.535528i
$195$	23.9842	+	22.3545i	0.122996	+	0.114639i
$196$	−42.4247	+	47.1188i	−0.216453	+	0.240402i
$197$			75.6061i			0.383787i	0.981416	+	0.191894i	$0.0614629\pi$
$197$			75.6061i			0.383787i	−0.981416	+	0.191894i	$0.938537\pi$
$198$			95.9560i			0.484626i
$199$			319.273i			1.60439i	0.597065	+	0.802193i	$0.296333\pi$
$199$			319.273i			1.60439i	−0.597065	+	0.802193i	$0.703667\pi$
$200$	155.271	−	10.9347i	0.776356	−	0.0546736i
$201$			51.8849i			0.258134i
$202$	−299.620			−1.48327
$203$	−63.2372	+	28.1556i	−0.311513	+	0.138697i
$204$	33.2969			0.163220
$205$	−152.311	+	163.414i	−0.742979	+	0.797142i
$206$		−	9.38279i		−	0.0455475i
$207$		−	120.857i		−	0.583851i
$208$	−73.8303			−0.354953
$209$			96.6021i			0.462211i
$210$	−45.3774	+	131.895i	−0.216083	+	0.628069i
$211$	−57.1113			−0.270670			−0.135335	−	0.990800i	$-0.543211\pi$
$211$	−57.1113			−0.270670			−0.135335	+	0.990800i	$0.543211\pi$
$212$		−	77.0341i		−	0.363368i
$213$	203.472			0.955268
$214$	−72.1214			−0.337016
$215$	88.7417	−	95.2110i	0.412752	−	0.442842i
$216$			32.3524i			0.149780i
$217$	99.0154	+	222.388i	0.456292	+	1.02483i
$218$		−	143.675i		−	0.659060i
$219$	−38.5092			−0.175841
$220$	−65.7927	−	61.3223i	−0.299058	−	0.278738i
$221$	56.2458			0.254506
$222$	121.307			0.546427
$223$	418.459			1.87650			0.938250	−	0.345958i	$-0.112446\pi$
$223$	418.459			1.87650			0.938250	+	0.345958i	$0.112446\pi$
$224$	−56.8453	−	127.674i	−0.253774	−	0.569973i
$225$	5.26870	+	74.8147i	0.0234165	+	0.332510i
$226$	−142.425			−0.630201
$227$	195.112			0.859525			0.429762	−	0.902942i	$-0.358597\pi$
$227$	195.112			0.859525			0.429762	+	0.902942i	$0.358597\pi$
$228$		−	15.5742i		−	0.0683079i
$229$			133.938i			0.584883i	0.956283	+	0.292441i	$0.0944676\pi$
$229$			133.938i			0.584883i	−0.956283	+	0.292441i	$0.905532\pi$
$230$	339.031	+	315.995i	1.47405	+	1.37389i
$231$	−153.974	+	68.5552i	−0.666555	+	0.296776i
$232$		−	61.5703i		−	0.265389i
$233$		−	72.7709i		−	0.312321i	−0.987732	−	0.156161i	$-0.950088\pi$
$233$		−	72.7709i		−	0.312321i	0.987732	−	0.156161i	$-0.0499117\pi$
$234$		−	26.1323i		−	0.111677i
$235$	−86.6975	−	80.8067i	−0.368926	−	0.343858i
$236$		−	104.855i		−	0.444302i
$237$	−247.335			−1.04361
$238$	97.3268	+	218.595i	0.408936	+	0.918467i
$239$	257.788			1.07861			0.539305	−	0.842111i	$-0.318687\pi$
$239$	257.788			1.07861			0.539305	+	0.842111i	$0.318687\pi$
$240$	−123.545	−	115.151i	−0.514772	−	0.479795i
$241$		−	241.558i		−	1.00231i	−0.865357	−	0.501157i	$-0.832908\pi$
$241$		−	241.558i		−	1.00231i	0.865357	−	0.501157i	$-0.167092\pi$
$242$		−	166.239i		−	0.686940i
$243$	−15.5885			−0.0641500
$244$		−	102.027i		−	0.418145i
$245$	−244.062	+	21.4171i	−0.996172	+	0.0874168i
$246$	178.050			0.723782
$247$		−	26.3083i		−	0.106511i
$248$	−216.526			−0.873087
$249$	278.638			1.11903
$250$	−223.647	−	180.832i	−0.894588	−	0.723326i
$251$			202.953i			0.808577i	0.914631	+	0.404289i	$0.132481\pi$
$251$			202.953i			0.808577i	−0.914631	+	0.404289i	$0.867519\pi$
$252$	24.8237	−	11.0525i	0.0985069	−	0.0438590i
$253$			560.031i			2.21356i
$254$	−426.372			−1.67863
$255$	94.1200	+	87.7248i	0.369098	+	0.344019i
$256$	225.245			0.879862
$257$	385.602			1.50040			0.750198	−	0.661214i	$-0.229958\pi$
$257$	385.602			1.50040			0.750198	+	0.661214i	$0.229958\pi$
$258$	−103.739			−0.402088
$259$	86.6668	+	194.653i	0.334621	+	0.751556i
$260$	17.9177	+	16.7003i	0.0689144	+	0.0642319i
$261$	29.6666			0.113665
$262$	213.563			0.815126
$263$			117.392i			0.446358i	0.974777	+	0.223179i	$0.0716434\pi$
$263$			117.392i			0.446358i	−0.974777	+	0.223179i	$0.928357\pi$
$264$		−	149.916i		−	0.567862i
$265$	202.956	−	217.752i	0.765872	−	0.821704i
$266$	102.245	−	45.5234i	0.384380	−	0.171141i
$267$			114.981i			0.430641i
$268$			38.7614i			0.144632i
$269$		−	372.769i		−	1.38576i	−0.721054	−	0.692879i	$-0.756342\pi$
$269$		−	372.769i		−	1.38576i	0.721054	−	0.692879i	$-0.243658\pi$
$270$	40.7578	−	43.7290i	0.150955	−	0.161959i
$271$		−	98.6583i		−	0.364053i	−0.983294	−	0.182026i	$-0.941734\pi$
$271$		−	98.6583i		−	0.364053i	0.983294	−	0.182026i	$-0.0582656\pi$
$272$	−289.729			−1.06518
$273$	41.9328	−	18.6701i	0.153600	−	0.0683885i
$274$	204.623			0.746798
$275$	−24.4143	−	346.678i	−0.0887791	−	1.26065i
$276$		−	90.2882i		−	0.327131i
$277$		−	70.1485i		−	0.253244i	−0.991951	−	0.126622i	$-0.959587\pi$
$277$		−	70.1485i		−	0.253244i	0.991951	−	0.126622i	$-0.0404135\pi$
$278$	87.7099			0.315503
$279$		−	104.329i		−	0.373939i
$280$	70.8947	−	206.064i	0.253195	−	0.735941i
$281$	−184.983			−0.658303			−0.329151	−	0.944277i	$-0.606763\pi$
$281$	−184.983			−0.658303			−0.329151	+	0.944277i	$0.606763\pi$
$282$			94.4626i			0.334974i
$283$	−43.9638			−0.155349			−0.0776746	−	0.996979i	$-0.524750\pi$
$283$	−43.9638			−0.155349			−0.0776746	+	0.996979i	$0.524750\pi$
$284$	152.007			0.535236
$285$	41.0322	−	44.0234i	0.143973	−	0.154468i
$286$			121.093i			0.423401i
$287$	127.207	+	285.706i	0.443230	+	0.995490i
$288$			59.8959i			0.207972i
$289$	−68.2771			−0.236253
$290$	−77.5665	+	83.2211i	−0.267471	+	0.286969i
$291$	−78.2086			−0.268758
$292$	−28.7689			−0.0985236
$293$	192.547			0.657157			0.328579	−	0.944477i	$-0.393430\pi$
$293$	192.547			0.657157			0.328579	+	0.944477i	$0.393430\pi$
$294$	145.120	+	130.662i	0.493604	+	0.444430i
$295$	276.255	−	296.393i	0.936456	−	1.00472i
$296$	−189.522			−0.640277
$297$	72.2342			0.243213
$298$		−	303.994i		−	1.02011i
$299$		−	152.517i		−	0.510090i
$300$	3.93607	+	55.8915i	0.0131202	+	0.186305i
$301$	−74.1154	−	166.462i	−0.246230	−	0.553032i
$302$		−	344.063i		−	1.13928i
$303$			225.549i			0.744387i
$304$			135.517i			0.445780i
$305$	268.804	−	288.400i	0.881325	−	0.945574i
$306$		−	102.550i		−	0.335130i
$307$	−364.110			−1.18603			−0.593013	−	0.805193i	$-0.702062\pi$
$307$	−364.110			−1.18603			−0.593013	+	0.805193i	$0.702062\pi$
$308$	−115.029	+	51.2152i	−0.373470	+	0.166283i
$309$	−7.06321			−0.0228583
$310$	292.666	+	272.780i	0.944083	+	0.879935i
$311$		−	400.969i		−	1.28929i	−0.764482	−	0.644645i	$-0.777005\pi$
$311$		−	400.969i		−	1.28929i	0.764482	−	0.644645i	$-0.222995\pi$
$312$			40.8274i			0.130857i
$313$	−353.929			−1.13076			−0.565381	−	0.824830i	$-0.691271\pi$
$313$	−353.929			−1.13076			−0.565381	+	0.824830i	$0.691271\pi$
$314$		−	68.0130i		−	0.216602i
$315$	99.2881	+	34.1594i	0.315200	+	0.108442i
$316$	−184.776			−0.584733
$317$			115.117i			0.363144i	0.983378	+	0.181572i	$0.0581186\pi$
$317$			115.117i			0.363144i	−0.983378	+	0.181572i	$0.941881\pi$
$318$	−237.255			−0.746084
$319$	−137.470			−0.430939
$320$	117.295	+	109.325i	0.366546	+	0.341640i
$321$			54.2918i			0.169133i
$322$	592.745	−	263.913i	1.84082	−	0.819604i
$323$		−	103.240i		−	0.319630i
$324$	−11.6456			−0.0359432
$325$	6.64889	+	94.4131i	0.0204581	+	0.290502i
$326$	−552.571			−1.69500
$327$	−108.156			−0.330753
$328$	−278.174			−0.848093
$329$	−151.578	+	67.4882i	−0.460723	+	0.205131i
$330$	−188.864	+	202.633i	−0.572316	+	0.614038i
$331$	−217.808			−0.658031			−0.329016	−	0.944324i	$-0.606717\pi$
$331$	−217.808			−0.658031			−0.329016	+	0.944324i	$0.606717\pi$
$332$	208.161			0.626991
$333$		−	91.3178i		−	0.274228i
$334$			477.049i			1.42829i
$335$	−102.122	+	109.566i	−0.304841	+	0.327064i
$336$	−216.001	+	96.1717i	−0.642860	+	0.286225i
$337$			257.680i			0.764629i	0.924032	+	0.382315i	$0.124873\pi$
$337$			257.680i			0.764629i	−0.924032	+	0.382315i	$0.875127\pi$
$338$			355.867i			1.05286i
$339$			107.216i			0.316270i
$340$	70.3138	+	65.5362i	0.206805	+	0.192753i
$341$			483.443i			1.41772i
$342$	−47.9664			−0.140253
$343$	−105.985	+	326.215i	−0.308996	+	0.951063i
$344$	162.075			0.471147
$345$	237.876	−	255.217i	0.689495	−	0.739759i
$346$			157.314i			0.454664i
$347$		−	87.2838i		−	0.251538i	−0.992060	−	0.125769i	$-0.959860\pi$
$347$		−	87.2838i		−	0.251538i	0.992060	−	0.125769i	$-0.0401399\pi$
$348$	22.1629			0.0636864
$349$			31.2851i			0.0896421i	0.998995	+	0.0448211i	$0.0142718\pi$
$349$			31.2851i			0.0896421i	−0.998995	+	0.0448211i	$0.985728\pi$
$350$	−355.424	+	189.211i	−1.01550	+	0.540604i
$351$	−19.6720			−0.0560456
$352$		−	277.547i		−	0.788486i
$353$	−174.245			−0.493611			−0.246806	−	0.969065i	$-0.579381\pi$
$353$	−174.245			−0.493611			−0.246806	+	0.969065i	$0.579381\pi$
$354$	−322.940			−0.912260
$355$	429.677	+	400.482i	1.21036	+	1.12812i
$356$			85.8984i			0.241288i
$357$	164.555	−	73.2661i	0.460938	−	0.205227i
$358$		−	327.153i		−	0.913835i
$359$	251.691			0.701089			0.350545	−	0.936546i	$-0.385996\pi$
$359$	251.691			0.701089			0.350545	+	0.936546i	$0.385996\pi$
$360$	−63.6773	+	68.3194i	−0.176881	+	0.189776i
$361$	312.711			0.866234
$362$	−613.083			−1.69360
$363$	−125.142			−0.344745
$364$	31.3265	−	13.9478i	0.0860619	−	0.0383180i
$365$	−81.3207	−	75.7953i	−0.222797	−	0.207658i
$366$	−314.231			−0.858554
$367$	356.321			0.970903			0.485451	−	0.874264i	$-0.338655\pi$
$367$	356.321			0.970903			0.485451	+	0.874264i	$0.338655\pi$
$368$			785.632i			2.13487i
$369$		−	134.034i		−	0.363234i
$370$	256.166	+	238.761i	0.692341	+	0.645299i
$371$	−169.505	−	380.707i	−0.456887	−	1.02616i
$372$		−	77.9406i		−	0.209518i
$373$		−	611.275i		−	1.63881i	−0.573217	−	0.819404i	$-0.694305\pi$
$373$		−	611.275i		−	1.63881i	0.573217	−	0.819404i	$-0.305695\pi$
$374$			475.198i			1.27058i
$375$	−136.127	+	168.358i	−0.363006	+	0.448955i
$376$		−	147.582i		−	0.392506i
$377$	37.4380			0.0993050
$378$	−34.0401	−	76.4537i	−0.0900531	−	0.202259i
$379$	157.934			0.416713			0.208356	−	0.978053i	$-0.433189\pi$
$379$	157.934			0.416713			0.208356	+	0.978053i	$0.433189\pi$
$380$	30.6537	−	32.8884i	0.0806677	−	0.0865484i
$381$			320.966i			0.842430i
$382$			74.8243i			0.195875i
$383$	330.386			0.862626			0.431313	−	0.902202i	$-0.358050\pi$
$383$	330.386			0.862626			0.431313	+	0.902202i	$0.358050\pi$
$384$		−	266.124i		−	0.693031i
$385$	−460.084	−	158.289i	−1.19502	−	0.411139i
$386$	−244.337			−0.632999
$387$			78.0928i			0.201790i
$388$	−58.4269			−0.150585
$389$	−43.6493			−0.112209			−0.0561046	−	0.998425i	$-0.517868\pi$
$389$	−43.6493			−0.112209			−0.0561046	+	0.998425i	$0.517868\pi$
$390$	51.4346	−	55.1842i	0.131884	−	0.141498i
$391$		−	598.515i		−	1.53073i
$392$	−226.726	−	204.138i	−0.578382	−	0.520761i
$393$		−	160.767i		−	0.409076i
$394$	173.959			0.441520
$395$	−522.303	−	486.814i	−1.32229	−	1.23244i
$396$	53.9637			0.136272
$397$	−436.537			−1.09959			−0.549795	−	0.835299i	$-0.685294\pi$
$397$	−436.537			−1.09959			−0.549795	+	0.835299i	$0.685294\pi$
$398$	734.602			1.84573
$399$	−34.2693	−	76.9685i	−0.0858879	−	0.192904i
$400$	−34.2492	−	486.333i	−0.0856230	−	1.21583i
$401$	662.494			1.65210			0.826052	−	0.563593i	$-0.190581\pi$
$401$	662.494			1.65210			0.826052	+	0.563593i	$0.190581\pi$
$402$	119.380			0.296965
$403$		−	131.659i		−	0.326697i
$404$			168.500i			0.417079i
$405$	−32.9185	−	30.6818i	−0.0812802	−	0.0757575i
$406$	64.7820	+	145.500i	0.159562	+	0.358374i
$407$			423.151i			1.03968i
$408$			160.217i			0.392690i
$409$		−	6.80523i		−	0.0166387i	−0.999965	−	0.00831936i	$-0.997352\pi$
$409$		−	6.80523i		−	0.0166387i	0.999965	−	0.00831936i	$-0.00264816\pi$
$410$	375.993	+	350.446i	0.917056	+	0.854745i
$411$		−	154.037i		−	0.374785i
$412$	−5.27668			−0.0128075
$413$	−230.722	−	518.201i	−0.558650	−	1.25472i
$414$	−278.076			−0.671680
$415$	588.407	+	548.427i	1.41785	+	1.32151i
$416$			75.5862i			0.181697i
$417$		−	66.0266i		−	0.158337i
$418$	222.268			0.531742
$419$			560.059i			1.33666i	0.743867	+	0.668328i	$0.232990\pi$
$419$			560.059i			1.33666i	−0.743867	+	0.668328i	$0.767010\pi$
$420$	74.1747	+	25.5193i	0.176607	+	0.0607602i
$421$	−374.770			−0.890191			−0.445095	−	0.895483i	$-0.646830\pi$
$421$	−374.770			−0.890191			−0.445095	+	0.895483i	$0.646830\pi$
$422$			131.405i			0.311387i
$423$	71.1100			0.168109
$424$	370.671			0.874225
$425$	26.0919	+	370.501i	0.0613928	+	0.871767i
$426$		−	468.161i		−	1.09897i
$427$	−224.500	−	504.225i	−0.525761	−	1.18086i
$428$			40.5596i			0.0947653i
$429$	91.1566			0.212486
$430$	−219.067	−	204.182i	−0.509458	−	0.474842i
$431$	−710.190			−1.64777			−0.823887	−	0.566755i	$-0.808199\pi$
$431$	−710.190			−1.64777			−0.823887	+	0.566755i	$0.808199\pi$
$432$	101.333			0.234567
$433$	131.951			0.304736			0.152368	−	0.988324i	$-0.451310\pi$
$433$	131.951			0.304736			0.152368	+	0.988324i	$0.451310\pi$
$434$	511.683	−	227.821i	1.17899	−	0.524932i
$435$	62.6475	+	58.3908i	0.144017	+	0.134232i
$436$	−80.7998			−0.185321
$437$	−279.948			−0.640613
$438$			88.6043i			0.202293i
$439$		−	792.806i		−	1.80594i	−0.429707	−	0.902968i	$-0.641383\pi$
$439$		−	792.806i		−	1.80594i	0.429707	−	0.902968i	$-0.358617\pi$
$440$	295.069	−	316.580i	0.670612	−	0.719500i
$441$	98.3606	−	109.244i	0.223040	−	0.247718i
$442$		−	129.414i		−	0.292791i
$443$			302.328i			0.682457i	0.939980	+	0.341228i	$0.110843\pi$
$443$			302.328i			0.682457i	−0.939980	+	0.341228i	$0.889157\pi$
$444$		−	68.2204i		−	0.153649i
$445$	−226.310	+	242.808i	−0.508562	+	0.545637i
$446$		−	962.816i		−	2.15878i
$447$	−228.842			−0.511950
$448$	205.073	−	91.3060i	0.457751	−	0.203808i
$449$	−72.8787			−0.162313			−0.0811567	−	0.996701i	$-0.525861\pi$
$449$	−72.8787			−0.162313			−0.0811567	+	0.996701i	$0.525861\pi$
$450$	172.138	−	12.1225i	0.382529	−	0.0269390i
$451$			621.088i			1.37713i
$452$			80.0971i			0.177206i
$453$	−259.005			−0.571756
$454$		−	448.926i		−	0.988823i
$455$	125.298	+	43.1077i	0.275379	+	0.0947423i
$456$	74.9396			0.164341
$457$			501.515i			1.09741i	0.836017	+	0.548703i	$0.184878\pi$
$457$			501.515i			1.09741i	−0.836017	+	0.548703i	$0.815122\pi$
$458$	308.173			0.672867
$459$	−77.1979			−0.168187
$460$	177.709	−	190.664i	0.386323	−	0.414486i
$461$			225.746i			0.489688i	0.969562	+	0.244844i	$0.0787368\pi$
$461$			225.746i			0.489688i	−0.969562	+	0.244844i	$0.921263\pi$
$462$	157.736	+	354.273i	0.341420	+	0.766825i
$463$			200.854i			0.433810i	0.976193	+	0.216905i	$0.0695963\pi$
$463$			200.854i			0.433810i	−0.976193	+	0.216905i	$0.930404\pi$
$464$	−192.847			−0.415619
$465$	205.344	−	220.314i	0.441601	−	0.473794i
$466$	−167.436			−0.359304
$467$	−146.079			−0.312804			−0.156402	−	0.987694i	$-0.549990\pi$
$467$	−146.079			−0.312804			−0.156402	+	0.987694i	$0.549990\pi$
$468$	−14.6963			−0.0314023
$469$	85.2901	+	191.561i	0.181855	+	0.408445i
$470$	−185.925	+	199.479i	−0.395585	+	0.424423i
$471$	−51.1991			−0.108703
$472$	504.541			1.06894
$473$		−	361.868i		−	0.765049i
$474$			569.083i			1.20060i
$475$	173.297	−	12.2042i	0.364836	−	0.0256930i
$476$	122.933	−	54.7346i	0.258263	−	0.114989i
$477$			178.602i			0.374427i
$478$		−	593.133i		−	1.24086i
$479$		−	609.973i		−	1.27343i	−0.771099	−	0.636715i	$-0.780293\pi$
$479$		−	609.973i		−	1.27343i	0.771099	−	0.636715i	$-0.219707\pi$
$480$	−117.889	+	126.484i	−0.245603	+	0.263507i
$481$		−	115.239i		−	0.239583i
$482$	−555.790			−1.15309
$483$	−198.669	−	446.209i	−0.411324	−	0.923829i
$484$	−93.4896			−0.193160
$485$	−165.155	−	153.933i	−0.340526	−	0.317388i
$486$			35.8669i			0.0738001i
$487$			806.827i			1.65673i	0.560189	+	0.828365i	$0.310728\pi$
$487$			806.827i			1.65673i	−0.560189	+	0.828365i	$0.689272\pi$
$488$	490.934			1.00601
$489$			415.967i			0.850648i
$490$	49.2778	+	561.553i	0.100567	+	1.14603i
$491$	−369.272			−0.752081			−0.376040	−	0.926603i	$-0.622715\pi$
$491$	−369.272			−0.752081			−0.376040	+	0.926603i	$0.622715\pi$
$492$		−	100.132i		−	0.203520i
$493$	146.916			0.298004
$494$	−60.5316			−0.122534
$495$	152.539	+	142.174i	0.308159	+	0.287220i
$496$			678.191i			1.36732i
$497$	751.227	−	334.474i	1.51152	−	0.672987i
$498$		−	641.108i		−	1.28737i
$499$	417.437			0.836547			0.418274	−	0.908321i	$-0.362635\pi$
$499$	417.437			0.836547			0.418274	+	0.908321i	$0.362635\pi$
$500$	−101.696	+	125.774i	−0.203392	+	0.251549i
$501$	359.115			0.716797
$502$	466.966			0.930212
$503$	577.214			1.14754			0.573771	−	0.819016i	$-0.305480\pi$
$503$	577.214			1.14754			0.573771	+	0.819016i	$0.305480\pi$
$504$	53.1820	+	119.446i	0.105520	+	0.236997i
$505$	−443.934	+	476.297i	−0.879078	+	0.943163i
$506$	1288.55			2.54655
$507$	267.891			0.528385
$508$			239.783i			0.472013i
$509$			241.834i			0.475116i	0.971373	+	0.237558i	$0.0763469\pi$
$509$			241.834i			0.475116i	−0.971373	+	0.237558i	$0.923653\pi$
$510$	201.843	−	216.557i	0.395770	−	0.424621i
$511$	−142.177	+	63.3027i	−0.278234	+	0.123880i
$512$			96.3300i			0.188145i
$513$			36.1084i			0.0703867i
$514$		−	887.215i		−	1.72610i
$515$	−14.9155	−	13.9021i	−0.0289622	−	0.0269943i
$516$			58.3404i			0.113063i
$517$	−329.511			−0.637352
$518$	447.869	−	199.408i	0.864612	−	0.384958i
$519$	118.423			0.228176
$520$	−80.3581	+	86.2162i	−0.154535	+	0.165800i
$521$			811.283i			1.55716i	0.627543	+	0.778582i	$0.284061\pi$
$521$			811.283i			1.55716i	−0.627543	+	0.778582i	$0.715939\pi$
$522$		−	68.2586i		−	0.130764i
$523$	50.9274			0.0973755			0.0486878	−	0.998814i	$-0.484496\pi$
$523$	50.9274			0.0973755			0.0486878	+	0.998814i	$0.484496\pi$
$524$		−	120.103i		−	0.229205i
$525$	142.435	+	267.558i	0.271305	+	0.509634i
$526$	270.103			0.513503
$527$		−	516.664i		−	0.980386i
$528$	−469.558			−0.889315
$529$	−1093.94			−2.06794
$530$	−501.016	−	466.974i	−0.945313	−	0.881082i
$531$			243.104i			0.457823i
$532$	−25.6014	−	57.5005i	−0.0481229	−	0.108084i
$533$		−	169.145i		−	0.317345i
$534$	264.556			0.495422
$535$	−106.859	+	114.649i	−0.199737	+	0.214298i
$536$	−186.511			−0.347969
$537$	−246.276			−0.458614
$538$	−857.688			−1.59422
$539$	−455.786	+	506.217i	−0.845613	+	0.939177i
$540$	−24.5923	−	22.9213i	−0.0455412	−	0.0424469i
$541$	222.529			0.411329			0.205665	−	0.978623i	$-0.434064\pi$
$541$	222.529			0.411329			0.205665	+	0.978623i	$0.434064\pi$
$542$	−226.999			−0.418817
$543$			461.519i			0.849943i
$544$			296.619i			0.545256i
$545$	−228.396	−	212.877i	−0.419075	−	0.390601i
$546$	−42.9572	−	96.4815i	−0.0786762	−	0.176706i
$547$		−	489.442i		−	0.894775i	−0.894340	−	0.447387i	$-0.852355\pi$
$547$		−	489.442i		−	0.894775i	0.894340	−	0.447387i	$-0.147645\pi$
$548$		−	115.076i		−	0.209992i
$549$			236.548i			0.430870i
$550$	−797.658	+	56.1738i	−1.45029	+	0.102134i
$551$		−	68.7182i		−	0.124715i
$552$	434.447			0.787042
$553$	−913.171	+	406.578i	−1.65130	+	0.735222i
$554$	−161.402			−0.291339
$555$	179.735	−	192.838i	0.323847	−	0.347456i
$556$		−	49.3262i		−	0.0887162i
$557$		−	489.578i		−	0.878955i	−0.898254	−	0.439478i	$-0.855164\pi$
$557$		−	489.578i		−	0.878955i	0.898254	−	0.439478i	$-0.144836\pi$
$558$	−240.047			−0.430191
$559$			98.5499i			0.176297i
$560$	−645.423	−	222.053i	−1.15254	−	0.396523i
$561$	357.722			0.637650
$562$			425.620i			0.757331i
$563$	301.482			0.535492			0.267746	−	0.963490i	$-0.413721\pi$
$563$	301.482			0.535492			0.267746	+	0.963490i	$0.413721\pi$
$564$	53.1238			0.0941911
$565$	−211.026	+	226.410i	−0.373497	+	0.400725i
$566$			101.155i			0.178718i
$567$	−57.5532	+	25.6248i	−0.101505	+	0.0451937i
$568$			731.424i			1.28772i
$569$	−847.144			−1.48883			−0.744415	−	0.667718i	$-0.767271\pi$
$569$	−847.144			−1.48883			−0.744415	+	0.667718i	$0.767271\pi$
$570$	−101.292	−	94.4093i	−0.177705	−	0.165630i
$571$	−220.035			−0.385350			−0.192675	−	0.981263i	$-0.561716\pi$
$571$	−220.035			−0.385350			−0.192675	+	0.981263i	$0.561716\pi$
$572$	68.0999			0.119056
$573$	56.3265			0.0983011
$574$	657.369	−	292.685i	1.14524	−	0.509905i
$575$	1004.66	−	70.7512i	1.74723	−	0.123046i
$576$	−96.2060			−0.167024
$577$	−772.580			−1.33896			−0.669480	−	0.742830i	$-0.733483\pi$
$577$	−772.580			−1.33896			−0.669480	+	0.742830i	$0.733483\pi$
$578$			157.096i			0.271792i
$579$			183.933i			0.317674i
$580$	46.8018	+	43.6218i	0.0806928	+	0.0752099i
$581$	1028.74	−	458.035i	1.77064	−	0.788357i
$582$			179.947i			0.309187i
$583$		−	827.608i		−	1.41957i
$584$		−	138.430i		−	0.237037i
$585$	−41.5418	−	38.7192i	−0.0710116	−	0.0661866i
$586$		−	443.024i		−	0.756013i
$587$	−258.261			−0.439967			−0.219984	−	0.975504i	$-0.570600\pi$
$587$	−258.261			−0.439967			−0.219984	+	0.975504i	$0.570600\pi$
$588$	73.4818	−	81.6122i	0.124969	−	0.138796i
$589$	−241.663			−0.410294
$590$	−681.960	−	635.623i	−1.15586	−	1.07733i
$591$		−	130.954i		−	0.221580i
$592$			593.612i			1.00272i
$593$	−502.713			−0.847745			−0.423873	−	0.905722i	$-0.639330\pi$
$593$	−502.713			−0.847745			−0.423873	+	0.905722i	$0.639330\pi$
$594$		−	166.201i		−	0.279799i
$595$	491.700	+	169.166i	0.826386	+	0.284312i
$596$	−170.960			−0.286845
$597$		−	552.997i		−	0.926292i
$598$	−350.920			−0.586823
$599$	−122.194			−0.203997			−0.101998	−	0.994785i	$-0.532524\pi$
$599$	−122.194			−0.203997			−0.101998	+	0.994785i	$0.532524\pi$
$600$	−268.938	+	18.9395i	−0.448229	+	0.0315658i
$601$			703.680i			1.17085i	0.810727	+	0.585424i	$0.199072\pi$
$601$			703.680i			1.17085i	−0.810727	+	0.585424i	$0.800928\pi$
$602$	−383.007	+	170.529i	−0.636224	+	0.283271i
$603$		−	89.8672i		−	0.149034i
$604$	−193.494			−0.320354
$605$	−264.266	−	246.310i	−0.436804	−	0.407124i
$606$	518.957			0.856365
$607$	1031.87			1.69995			0.849976	−	0.526821i	$-0.176616\pi$
$607$	1031.87			1.69995			0.849976	+	0.526821i	$0.176616\pi$
$608$	138.740			0.228191
$609$	109.530	−	48.7669i	0.179852	−	0.0800770i
$610$	−663.568	−	618.481i	−1.08782	−	1.01390i
$611$	89.7379			0.146870
$612$	−57.6719			−0.0942351
$613$			78.3530i			0.127819i	0.997956	+	0.0639094i	$0.0203569\pi$
$613$			78.3530i			0.127819i	−0.997956	+	0.0639094i	$0.979643\pi$
$614$			837.766i			1.36444i
$615$	263.810	−	283.042i	0.428959	−	0.460230i
$616$	−246.436	−	553.494i	−0.400059	−	0.898529i
$617$			450.989i			0.730938i	0.930823	+	0.365469i	$0.119091\pi$
$617$			450.989i			0.730938i	−0.930823	+	0.365469i	$0.880909\pi$
$618$			16.2515i			0.0262969i
$619$		−	574.725i		−	0.928473i	−0.885711	−	0.464237i	$-0.846329\pi$
$619$		−	574.725i		−	0.928473i	0.885711	−	0.464237i	$-0.153671\pi$
$620$	153.406	−	164.589i	0.247429	−	0.265466i
$621$			209.331i			0.337087i
$622$	−922.574			−1.48324
$623$	189.010	+	424.515i	0.303387	+	0.681404i
$624$	127.878			0.204932
$625$	−618.831	+	87.5948i	−0.990130	+	0.140152i
$626$			814.340i			1.30086i
$627$		−	167.320i		−	0.266858i
$628$	−38.2491			−0.0609062
$629$		−	452.229i		−	0.718964i
$630$	78.5959	−	228.448i	0.124755	−	0.362616i
$631$	1094.51			1.73456			0.867279	−	0.497823i	$-0.165867\pi$
$631$	1094.51			1.73456			0.867279	+	0.497823i	$0.165867\pi$
$632$		−	889.099i		−	1.40680i
$633$	98.9198			0.156271
$634$	264.867			0.417772
$635$	−631.737	+	677.791i	−0.994862	+	1.06739i
$636$			133.427i			0.209791i
$637$	124.127	−	137.861i	0.194862	−	0.216423i
$638$			316.298i			0.495765i
$639$	−352.424			−0.551524
$640$	523.795	−	561.980i	0.818430	−	0.878093i
$641$	145.856			0.227544			0.113772	−	0.993507i	$-0.463707\pi$
$641$	145.856			0.227544			0.113772	+	0.993507i	$0.463707\pi$
$642$	124.918			0.194576
$643$	−42.9913			−0.0668605			−0.0334302	−	0.999441i	$-0.510643\pi$
$643$	−42.9913			−0.0668605			−0.0334302	+	0.999441i	$0.510643\pi$
$644$	−148.419	−	333.348i	−0.230464	−	0.517620i
$645$	−153.705	+	164.910i	−0.238303	+	0.255675i
$646$	−237.542			−0.367711
$647$	832.962			1.28742			0.643711	−	0.765269i	$-0.277394\pi$
$647$	832.962			1.28742			0.643711	+	0.765269i	$0.277394\pi$
$648$		−	56.0361i		−	0.0864754i
$649$		−	1126.50i		−	1.73575i
$650$	217.231	−	15.2982i	0.334202	−	0.0235356i
$651$	−171.500	−	385.187i	−0.263440	−	0.591685i
$652$			310.754i			0.476617i
$653$			1209.46i			1.85217i	0.377319	+	0.926083i	$0.376846\pi$
$653$			1209.46i			1.85217i	−0.377319	+	0.926083i	$0.623154\pi$
$654$			248.852i			0.380508i
$655$	316.428	−	339.495i	0.483096	−	0.518313i
$656$			871.285i			1.32818i
$657$	66.6999			0.101522
$658$	155.281	+	348.760i	0.235989	+	0.530030i
$659$	370.831			0.562718			0.281359	−	0.959603i	$-0.409215\pi$
$659$	370.831			0.562718			0.281359	+	0.959603i	$0.409215\pi$
$660$	113.956	+	106.213i	0.172661	+	0.160929i
$661$			1199.95i			1.81536i	0.419663	+	0.907680i	$0.362148\pi$
$661$			1199.95i			1.81536i	−0.419663	+	0.907680i	$0.637852\pi$
$662$			501.146i			0.757019i
$663$	−97.4206			−0.146939
$664$			1001.63i			1.50847i
$665$	79.1252	−	229.986i	0.118985	−	0.345844i
$666$	−210.109			−0.315480
$667$		−	398.380i		−	0.597271i
$668$	268.282			0.401620
$669$	−724.793			−1.08340
$670$	252.097	+	234.968i	0.376264	+	0.350698i
$671$		−	1096.12i		−	1.63356i
$672$	98.4589	+	221.138i	0.146516	+	0.329074i
$673$			826.484i			1.22806i	0.789283	+	0.614030i	$0.210452\pi$
$673$			826.484i			1.22806i	−0.789283	+	0.614030i	$0.789548\pi$
$674$	592.886			0.879653
$675$	−9.12566	−	129.583i	−0.0135195	−	0.191975i
$676$	200.132			0.296054
$677$	122.010			0.180221			0.0901106	−	0.995932i	$-0.471278\pi$
$677$	122.010			0.180221			0.0901106	+	0.995932i	$0.471278\pi$
$678$	246.688			0.363847
$679$	−288.749	+	128.562i	−0.425256	+	0.189340i
$680$	−315.346	+	338.335i	−0.463744	+	0.497551i
$681$	−337.944			−0.496247
$682$	1112.33			1.63099
$683$			185.065i			0.270960i	0.990780	+	0.135480i	$0.0432576\pi$
$683$			185.065i			0.270960i	−0.990780	+	0.135480i	$0.956742\pi$
$684$			26.9753i			0.0394376i
$685$	303.181	−	325.283i	0.442600	−	0.474866i
$686$	750.574	+	243.858i	1.09413	+	0.355478i
$687$		−	231.988i		−	0.337682i
$688$		−	507.642i		−	0.737852i
$689$			225.388i			0.327123i
$690$	−587.218	−	547.319i	−0.851041	−	0.793216i
$691$		−	1052.60i		−	1.52329i	−0.647993	−	0.761647i	$-0.724391\pi$
$691$		−	1052.60i		−	1.52329i	0.647993	−	0.761647i	$-0.275609\pi$
$692$	88.4699			0.127847
$693$	266.691	−	118.741i	0.384836	−	0.171343i
$694$	−200.828			−0.289377
$695$	129.956	−	139.430i	0.186987	−	0.200619i
$696$			106.643i			0.153222i
$697$		−	663.767i		−	0.952320i
$698$	71.9826			0.103127
$699$			126.043i			0.180319i
$700$	106.408	+	199.883i	0.152012	+	0.285547i
$701$	658.867			0.939896			0.469948	−	0.882694i	$-0.344273\pi$
$701$	658.867			0.939896			0.469948	+	0.882694i	$0.344273\pi$
$702$			45.2625i			0.0644765i
$703$	−211.524			−0.300888
$704$	445.802			0.633241
$705$	150.165	+	139.961i	0.212999	+	0.198527i
$706$			400.913i			0.567865i
$707$	370.765	+	832.736i	0.524421	+	1.17784i
$708$			181.615i			0.256518i
$709$	−277.453			−0.391331			−0.195665	−	0.980671i	$-0.562687\pi$
$709$	−277.453			−0.391331			−0.195665	+	0.980671i	$0.562687\pi$
$710$	921.452	−	988.626i	1.29782	−	1.39243i
$711$	428.397			0.602527
$712$	−413.325			−0.580512
$713$	−1400.99			−1.96492
$714$	−168.575	−	378.618i	−0.236099	−	0.530277i
$715$	192.497	+	179.418i	0.269227	+	0.250934i
$716$	−183.984			−0.256961
$717$	−446.501			−0.622735
$718$		−	579.106i		−	0.806554i
$719$		−	159.264i		−	0.221507i	−0.993848	−	0.110753i	$-0.964674\pi$
$719$		−	159.264i		−	0.221507i	0.993848	−	0.110753i	$-0.0353264\pi$
$720$	213.987	+	199.447i	0.297204	+	0.277010i
$721$	−26.0777	+	11.6108i	−0.0361687	+	0.0161037i
$722$		−	719.503i		−	0.996542i
$723$			418.390i			0.578686i
$724$			344.785i			0.476222i
$725$	17.3671	+	246.610i	0.0239547	+	0.340152i
$726$			287.935i			0.396605i
$727$	1259.85			1.73295			0.866473	−	0.499224i	$-0.166382\pi$
$727$	1259.85			1.73295			0.866473	+	0.499224i	$0.166382\pi$
$728$	67.1136	+	150.736i	0.0921889	+	0.207056i
$729$	27.0000			0.0370370
$730$	−174.394	+	187.108i	−0.238896	+	0.256312i
$731$			386.735i			0.529049i
$732$			176.717i			0.241416i
$733$	1204.99			1.64391			0.821955	−	0.569552i	$-0.192883\pi$
$733$	1204.99			1.64391			0.821955	+	0.569552i	$0.192883\pi$
$734$		−	819.845i		−	1.11696i
$735$	422.728	−	37.0955i	0.575140	−	0.0504701i
$736$	804.317			1.09282
$737$			416.429i			0.565033i
$738$	−308.392			−0.417876
$739$	400.880			0.542463			0.271232	−	0.962514i	$-0.412569\pi$
$739$	400.880			0.542463			0.271232	+	0.962514i	$0.412569\pi$
$740$	134.274	−	144.063i	0.181451	−	0.194679i
$741$			45.5673i			0.0614943i
$742$	−875.953	+	390.007i	−1.18053	+	0.525616i
$743$		−	22.1088i		−	0.0297561i	−0.999889	−	0.0148780i	$-0.995264\pi$
$743$		−	22.1088i		−	0.0297561i	0.999889	−	0.0148780i	$-0.00473600\pi$
$744$	375.033			0.504077
$745$	−483.250	−	450.415i	−0.648658	−	0.604584i
$746$	−1406.46			−1.88533
$747$	−482.616			−0.646072
$748$	267.241			0.357275
$749$	89.2468	+	200.448i	0.119155	+	0.267620i
$750$	387.368	+	313.209i	0.516491	+	0.417613i
$751$	−616.731			−0.821213			−0.410606	−	0.911813i	$-0.634683\pi$
$751$	−616.731			−0.821213			−0.410606	+	0.911813i	$0.634683\pi$
$752$	−462.250			−0.614695
$753$		−	351.525i		−	0.466832i
$754$		−	86.1395i		−	0.114243i
$755$	−546.947	−	509.784i	−0.724434	−	0.675211i
$756$	−42.9960	+	19.1434i	−0.0568730	+	0.0253220i
$757$		−	1153.11i		−	1.52326i	−0.648011	−	0.761631i	$-0.724399\pi$
$757$		−	1153.11i		−	1.52326i	0.648011	−	0.761631i	$-0.275601\pi$
$758$		−	363.384i		−	0.479399i
$759$		−	970.003i		−	1.27800i
$760$	158.252	+	147.499i	0.208226	+	0.194078i
$761$		−	974.653i		−	1.28075i	−0.768061	−	0.640377i	$-0.778778\pi$
$761$		−	974.653i		−	1.28075i	0.768061	−	0.640377i	$-0.221222\pi$
$762$	738.498			0.969157
$763$	−399.317	+	177.791i	−0.523351	+	0.233016i
$764$	42.0796			0.0550780
$765$	−163.021	−	151.944i	−0.213099	−	0.198619i
$766$		−	760.172i		−	0.992391i
$767$			306.787i			0.399984i
$768$	−390.135			−0.507989
$769$		−	436.595i		−	0.567744i	−0.958862	−	0.283872i	$-0.908381\pi$
$769$		−	436.595i		−	0.567744i	0.958862	−	0.283872i	$-0.0916191\pi$
$770$	−364.200	+	1058.59i	−0.472987	+	1.37479i
$771$	−667.881			−0.866254
$772$			137.410i			0.177993i
$773$	852.655			1.10305			0.551524	−	0.834159i	$-0.314047\pi$
$773$	852.655			1.10305			0.551524	+	0.834159i	$0.314047\pi$
$774$	179.681			0.232145
$775$	867.261	−	61.0755i	1.11905	−	0.0788070i
$776$		−	281.138i		−	0.362291i
$777$	−150.111	−	337.149i	−0.193194	−	0.433911i
$778$			100.431i			0.129089i
$779$	−310.469			−0.398548
$780$	−31.0344	−	28.9257i	−0.0397877	−	0.0370843i
$781$	1633.07			2.09100
$782$	−1377.10			−1.76100
$783$	−51.3840			−0.0656245
$784$	−639.393	+	710.139i	−0.815552	+	0.905790i
$785$	−108.118	−	100.772i	−0.137730	−	0.128372i
$786$	−369.902			−0.470613
$787$	−853.855			−1.08495			−0.542474	−	0.840072i	$-0.682512\pi$
$787$	−853.855			−1.08495			−0.542474	+	0.840072i	$0.682512\pi$
$788$		−	97.8309i		−	0.124151i
$789$		−	203.329i		−	0.257705i
$790$	−1120.09	+	1201.75i	−1.41784	+	1.52120i
$791$	176.245	+	395.844i	0.222812	+	0.500435i
$792$			259.661i			0.327855i
$793$			298.514i			0.376436i
$794$			1004.41i			1.26500i
$795$	−351.530	+	377.157i	−0.442176	+	0.474411i
$796$		−	413.125i		−	0.519001i
$797$	364.023			0.456741			0.228371	−	0.973574i	$-0.426660\pi$
$797$	364.023			0.456741			0.228371	+	0.973574i	$0.426660\pi$
$798$	−177.094	+	78.8488i	−0.221922	+	0.0988081i
$799$	352.154			0.440744
$800$	−497.899	+	35.0638i	−0.622374	+	0.0438297i
$801$		−	199.153i		−	0.248631i
$802$		−	1524.31i		−	1.90063i
$803$	−309.076			−0.384901
$804$		−	67.1367i		−	0.0835034i
$805$	458.712	−	1333.30i	0.569829	−	1.65627i
$806$	−302.929			−0.375842
$807$			645.654i			0.800067i
$808$	−810.785			−1.00345
$809$	1240.40			1.53325			0.766623	−	0.642097i	$-0.221936\pi$
$809$	1240.40			1.53325			0.766623	+	0.642097i	$0.221936\pi$
$810$	−70.5945	+	75.7408i	−0.0871537	+	0.0935072i
$811$			468.274i			0.577403i	0.957419	+	0.288701i	$0.0932235\pi$
$811$			468.274i			0.577403i	−0.957419	+	0.288701i	$0.906777\pi$
$812$	81.8261	−	36.4321i	0.100771	−	0.0448671i
$813$			170.881i			0.210186i
$814$	973.611			1.19608
$815$	−818.722	+	878.406i	−1.00457	+	1.07780i
$816$	501.825			0.614982
$817$	180.890			0.221408
$818$	−15.6579			−0.0191417
$819$	−72.6297	+	32.3375i	−0.0886810	+	0.0394841i
$820$	197.083	−	211.451i	0.240345	−	0.257867i
$821$	−542.526			−0.660811			−0.330406	−	0.943839i	$-0.607186\pi$
$821$	−542.526			−0.660811			−0.330406	+	0.943839i	$0.607186\pi$
$822$	−354.417			−0.431164
$823$		−	719.260i		−	0.873948i	−0.899474	−	0.436974i	$-0.856050\pi$
$823$		−	719.260i		−	0.873948i	0.899474	−	0.436974i	$-0.143950\pi$
$824$		−	25.3902i		−	0.0308134i
$825$	42.2867	+	600.464i	0.0512566	+	0.727836i
$826$	−1192.31	+	530.860i	−1.44347	+	0.642688i
$827$		−	668.223i		−	0.808008i	−0.914757	−	0.404004i	$-0.867618\pi$
$827$		−	668.223i		−	0.808008i	0.914757	−	0.404004i	$-0.132382\pi$
$828$			156.384i			0.188869i
$829$			122.101i			0.147287i	0.997285	+	0.0736437i	$0.0234628\pi$
$829$			122.101i			0.147287i	−0.997285	+	0.0736437i	$0.976537\pi$
$830$	1261.85	−	1353.84i	1.52030	−	1.63113i
$831$			121.501i			0.146210i
$832$	−121.408			−0.145923
$833$	487.106	−	541.002i	0.584761	−	0.649463i
$834$	−151.918			−0.182156
$835$	758.351	+	706.824i	0.908205	+	0.846496i
$836$		−	124.999i		−	0.149520i
$837$			180.703i			0.215894i
$838$	1288.62			1.53773
$839$		−	215.223i		−	0.256524i	−0.991740	−	0.128262i	$-0.959060\pi$
$839$		−	215.223i		−	0.256524i	0.991740	−	0.128262i	$-0.0409398\pi$
$840$	−122.793	+	356.913i	−0.146182	+	0.424896i
$841$	−743.211			−0.883723
$842$			862.294i			1.02410i
$843$	320.400			0.380071
$844$	73.8995			0.0875587
$845$	565.712	+	527.274i	0.669482	+	0.623993i
$846$		−	163.614i		−	0.193397i
$847$	−462.031	+	205.713i	−0.545491	+	0.242873i
$848$		−	1161.00i		−	1.36910i
$849$	76.1476			0.0896909
$850$	852.471	−	60.0339i	1.00291	−	0.0706281i
$851$	−1226.27			−1.44097
$852$	−263.284			−0.309018
$853$	732.200			0.858382			0.429191	−	0.903214i	$-0.358799\pi$
$853$	732.200			0.858382			0.429191	+	0.903214i	$0.358799\pi$
$854$	−1160.15	+	516.543i	−1.35849	+	0.604851i
$855$	−71.0698	+	76.2508i	−0.0831226	+	0.0891823i
$856$	−195.164			−0.227995
$857$	−239.155			−0.279061			−0.139530	−	0.990218i	$-0.544559\pi$
$857$	−239.155			−0.279061			−0.139530	+	0.990218i	$0.544559\pi$
$858$		−	209.738i		−	0.244450i
$859$			1157.68i			1.34770i	0.738867	+	0.673851i	$0.235361\pi$
$859$			1157.68i			1.34770i	−0.738867	+	0.673851i	$0.764639\pi$
$860$	−114.828	+	123.199i	−0.133521	+	0.143254i
$861$	−220.329	−	494.857i	−0.255899	−	0.574747i
$862$			1634.05i			1.89565i
$863$		−	25.5880i		−	0.0296500i	−0.999890	−	0.0148250i	$-0.995281\pi$
$863$		−	25.5880i		−	0.0296500i	0.999890	−	0.0148250i	$-0.00471912\pi$
$864$		−	103.743i		−	0.120073i
$865$	250.077	+	233.085i	0.289106	+	0.269462i
$866$		−	303.600i		−	0.350578i
$867$	118.259			0.136401
$868$	−128.121	−	287.760i	−0.147605	−	0.331520i
$869$	−1985.12			−2.28437
$870$	134.349	−	144.143i	0.154424	−	0.165682i
$871$		−	113.409i		−	0.130205i
$872$		−	388.791i		−	0.445861i
$873$	135.461			0.155168
$874$			644.121i			0.736980i
$875$	−225.834	+	845.354i	−0.258096	+	0.966119i
$876$	49.8292			0.0568826
$877$			289.049i			0.329589i	0.986328	+	0.164794i	$0.0526960\pi$
$877$			289.049i			0.329589i	−0.986328	+	0.164794i	$0.947304\pi$
$878$	−1824.14			−2.07760
$879$	−333.501			−0.379410
$880$	−991.577	−	924.203i	−1.12679	−	1.05023i
$881$			700.483i			0.795100i	0.917580	+	0.397550i	$0.130140\pi$
$881$			700.483i			0.795100i	−0.917580	+	0.397550i	$0.869860\pi$
$882$	−251.355	−	226.314i	−0.284983	−	0.256592i
$883$		−	1412.32i		−	1.59946i	−0.600362	−	0.799729i	$-0.704977\pi$
$883$		−	1412.32i		−	1.59946i	0.600362	−	0.799729i	$-0.295023\pi$
$884$	−72.7796			−0.0823298
$885$	−478.487	+	513.369i	−0.540663	+	0.580077i
$886$	695.615			0.785119
$887$	505.344			0.569722			0.284861	−	0.958569i	$-0.408052\pi$
$887$	505.344			0.569722			0.284861	+	0.958569i	$0.408052\pi$
$888$	328.262			0.369664
$889$	527.615	+	1185.02i	0.593493	+	1.33298i
$890$	558.668	+	520.708i	0.627717	+	0.585065i
$891$	−125.113			−0.140419
$892$	−541.468			−0.607027
$893$		−	164.716i		−	0.184452i
$894$			526.533i			0.588963i
$895$	−520.066	−	484.729i	−0.581079	−	0.541597i
$896$	−437.463	−	982.539i	−0.488240	−	1.09658i
$897$			264.167i			0.294500i
$898$			167.684i			0.186730i
$899$		−	343.898i		−	0.382534i
$900$	−6.81747	−	96.8069i	−0.00757496	−	0.107563i
$901$			884.479i			0.981664i
$902$	1429.04			1.58430
$903$	128.372	+	288.321i	0.142161	+	0.319293i
$904$	−385.410			−0.426338
$905$	−908.379	+	974.600i	−1.00373	+	1.07691i
$906$			595.935i			0.657765i
$907$			696.108i			0.767484i	0.923440	+	0.383742i	$0.125365\pi$
$907$			696.108i			0.767484i	−0.923440	+	0.383742i	$0.874635\pi$
$908$	−252.466			−0.278047
$909$		−	390.663i		−	0.429772i
$910$	99.1848	−	288.292i	0.108994	−	0.316805i
$911$	−214.709			−0.235685			−0.117843	−	0.993032i	$-0.537598\pi$
$911$	−214.709			−0.235685			−0.117843	+	0.993032i	$0.537598\pi$
$912$		−	234.722i		−	0.257371i
$913$	2236.36			2.44946
$914$	1153.92			1.26249
$915$	−465.582	+	499.523i	−0.508833	+	0.545927i
$916$		−	173.310i		−	0.189203i
$917$	−264.274	−	593.558i	−0.288194	−	0.647282i
$918$			177.622i			0.193488i
$919$	−564.974			−0.614771			−0.307385	−	0.951585i	$-0.599454\pi$
$919$	−564.974			−0.614771			−0.307385	+	0.951585i	$0.599454\pi$
$920$	917.432	+	855.096i	0.997209	+	0.929452i
$921$	630.657			0.684753
$922$	519.411			0.563352
$923$	−444.745			−0.481847
$924$	199.236	−	88.7073i	0.215623	−	0.0960036i
$925$	759.102	−	53.4585i	0.820651	−	0.0577930i
$926$	462.137			0.499068
$927$	12.2338			0.0131972
$928$			197.434i			0.212752i
$929$		−	1302.09i		−	1.40160i	−0.713356	−	0.700802i	$-0.752826\pi$
$929$		−	1302.09i		−	1.40160i	0.713356	−	0.700802i	$-0.247174\pi$
$930$	−506.912	−	472.469i	−0.545066	−	0.508031i
$931$	−253.047	−	227.838i	−0.271801	−	0.244724i
$932$			94.1622i			0.101032i
$933$			694.499i			0.744372i
$934$			336.108i			0.359859i
$935$	755.409	+	704.081i	0.807924	+	0.753028i
$936$		−	70.7152i		−	0.0755504i
$937$	226.044			0.241242			0.120621	−	0.992699i	$-0.461511\pi$
$937$	226.044			0.241242			0.120621	+	0.992699i	$0.461511\pi$
$938$	440.755	−	196.241i	0.469888	−	0.209212i
$939$	613.022			0.652846
$940$	112.183	+	104.560i	0.119343	+	0.111234i
$941$		−	415.187i		−	0.441219i	−0.975362	−	0.220610i	$-0.929195\pi$
$941$		−	415.187i		−	0.441219i	0.975362	−	0.220610i	$-0.0708047\pi$
$942$			117.802i			0.125055i
$943$	−1799.88			−1.90867
$944$		−	1580.30i		−	1.67405i
$945$	−171.972	−	59.1658i	−0.181981	−	0.0626093i
$946$	−832.608			−0.880135
$947$			483.972i			0.511058i	0.966801	+	0.255529i	$0.0822496\pi$
$947$			483.972i			0.511058i	−0.966801	+	0.255529i	$0.917750\pi$
$948$	320.041			0.337596
$949$	84.1725			0.0886960
$950$	−28.0801	−	398.733i	−0.0295580	−	0.419718i
$951$		−	199.388i		−	0.209661i
$952$	263.371	+	591.528i	0.276650	+	0.621353i
$953$		−	1028.28i		−	1.07899i	−0.841989	−	0.539495i	$-0.818615\pi$
$953$		−	1028.28i		−	1.07899i	0.841989	−	0.539495i	$-0.181385\pi$
$954$	410.937			0.430752
$955$	118.946	+	110.864i	0.124551	+	0.116088i
$956$	−333.566			−0.348918
$957$	238.104			0.248803
$958$	−1403.46			−1.46499
$959$	−253.211	−	568.709i	−0.264036	−	0.593023i
$960$	−203.160	−	189.356i	−0.211625	−	0.197246i
$961$	−248.395			−0.258476
$962$	−265.150			−0.275623
$963$		−	94.0362i		−	0.0976492i
$964$			312.565i			0.324237i
$965$	−362.025	+	388.416i	−0.375155	+	0.402504i
$966$	−1026.67	+	457.110i	−1.06280	+	0.473199i
$967$		−	1470.69i		−	1.52088i	−0.649407	−	0.760441i	$-0.724983\pi$
$967$		−	1470.69i		−	1.52088i	0.649407	−	0.760441i	$-0.275017\pi$
$968$		−	449.851i		−	0.464723i
$969$			178.818i			0.184538i
$970$	−354.179	+	379.998i	−0.365133	+	0.391751i
$971$			1218.45i			1.25484i	0.778680	+	0.627422i	$0.215890\pi$
$971$			1218.45i			1.25484i	−0.778680	+	0.627422i	$0.784110\pi$
$972$	20.1708			0.0207518
$973$	−108.537	−	243.773i	−0.111549	−	0.250537i
$974$	1856.40			1.90595
$975$	−11.5162	−	163.528i	−0.0118115	−	0.167721i
$976$		−	1537.68i		−	1.57549i
$977$			183.273i			0.187587i	0.995592	+	0.0937936i	$0.0298994\pi$
$977$			183.273i			0.187587i	−0.995592	+	0.0937936i	$0.970101\pi$
$978$	957.081			0.978610
$979$			922.841i			0.942637i
$980$	315.805	−	27.7128i	0.322250	−	0.0282784i
$981$	187.332			0.190960
$982$			849.642i			0.865216i
$983$	973.748			0.990588			0.495294	−	0.868725i	$-0.335060\pi$
$983$	973.748			0.990588			0.495294	+	0.868725i	$0.335060\pi$
$984$	481.812			0.489647
$985$	257.748	−	276.538i	0.261673	−	0.280749i
$986$		−	338.033i		−	0.342833i
$987$	262.541	−	116.893i	0.265999	−	0.118433i
$988$			34.0417i			0.0344552i
$989$	1048.68			1.06034
$990$	327.123	−	350.970i	0.330427	−	0.354515i
$991$	−1177.71			−1.18841			−0.594205	−	0.804313i	$-0.702533\pi$
$991$	−1177.71			−1.18841			−0.594205	+	0.804313i	$0.702533\pi$
$992$	694.320			0.699920
$993$	377.255			0.379914
$994$	−769.579	−	1728.47i	−0.774224	−	1.73890i
$995$	1088.43	−	1167.78i	1.09390	−	1.17364i
$996$	−360.546			−0.361994
$997$	−703.562			−0.705679			−0.352839	−	0.935684i	$-0.614784\pi$
$997$	−703.562			−0.705679			−0.352839	+	0.935684i	$0.614784\pi$
$998$		−	960.464i		−	0.962389i
$999$			158.167i			0.158325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.e.a.34.3	✓	16
3.2	odd	2		315.3.e.e.244.14		16
4.3	odd	2		1680.3.bd.c.769.11		16
5.2	odd	4		525.3.h.e.76.14		16
5.3	odd	4		525.3.h.e.76.3		16
5.4	even	2	inner	105.3.e.a.34.14	yes	16
7.6	odd	2	inner	105.3.e.a.34.4	yes	16
15.14	odd	2		315.3.e.e.244.3		16
20.19	odd	2		1680.3.bd.c.769.5		16
21.20	even	2		315.3.e.e.244.13		16
28.27	even	2		1680.3.bd.c.769.6		16
35.13	even	4		525.3.h.e.76.4		16
35.27	even	4		525.3.h.e.76.13		16
35.34	odd	2	inner	105.3.e.a.34.13	yes	16
105.104	even	2		315.3.e.e.244.4		16
140.139	even	2		1680.3.bd.c.769.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.3	✓	16	1.1	even	1	trivial
105.3.e.a.34.4	yes	16	7.6	odd	2	inner
105.3.e.a.34.13	yes	16	35.34	odd	2	inner
105.3.e.a.34.14	yes	16	5.4	even	2	inner
315.3.e.e.244.3		16	15.14	odd	2
315.3.e.e.244.4		16	105.104	even	2
315.3.e.e.244.13		16	21.20	even	2
315.3.e.e.244.14		16	3.2	odd	2
525.3.h.e.76.3		16	5.3	odd	4
525.3.h.e.76.4		16	35.13	even	4
525.3.h.e.76.13		16	35.27	even	4
525.3.h.e.76.14		16	5.2	odd	4
1680.3.bd.c.769.5		16	20.19	odd	2
1680.3.bd.c.769.6		16	28.27	even	2
1680.3.bd.c.769.11		16	4.3	odd	2
1680.3.bd.c.769.12		16	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.30086i q^{2} -1.73205 q^{3} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +3.98521i q^{6} +(-6.39480 + 2.84720i) q^{7} -6.22623i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.30086i q^{2} -1.73205 q^{3} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +3.98521i q^{6} +(-6.39480 + 2.84720i) q^{7} -6.22623i q^{8} +3.00000 q^{9} +(-7.84383 + 8.41565i) q^{10} -13.9015 q^{11} +2.24120 q^{12} +3.78588 q^{13} +(6.55102 + 14.7135i) q^{14} +(6.33517 + 5.90471i) q^{15} -19.5015 q^{16} +14.8567 q^{17} -6.90258i q^{18} -6.94906i q^{19} +(4.73278 + 4.41121i) q^{20} +(11.0761 - 4.93150i) q^{21} +31.9853i q^{22} -40.2857i q^{23} +10.7841i q^{24} +(1.75623 + 24.9382i) q^{25} -8.71077i q^{26} -5.19615 q^{27} +(8.27458 - 3.68415i) q^{28} +9.88885 q^{29} +(13.5859 - 14.5763i) q^{30} -34.7764i q^{31} +19.9653i q^{32} +24.0781 q^{33} -34.1833i q^{34} +(33.0960 + 11.3865i) q^{35} -3.88187 q^{36} -30.4393i q^{37} -15.9888 q^{38} -6.55733 q^{39} +(-21.2258 + 22.7731i) q^{40} -44.6778i q^{41} +(-11.3467 - 25.4846i) q^{42} +26.0309i q^{43} +17.9879 q^{44} +(-10.9728 - 10.2273i) q^{45} -92.6918 q^{46} +23.7033 q^{47} +33.7776 q^{48} +(32.7869 - 36.4146i) q^{49} +(57.3794 - 4.04085i) q^{50} -25.7326 q^{51} -4.89875 q^{52} +59.5338i q^{53} +11.9556i q^{54} +(50.8462 + 47.3914i) q^{55} +(17.7273 + 39.8155i) q^{56} +12.0361i q^{57} -22.7529i q^{58} +81.0347i q^{59} +(-8.19742 - 7.64043i) q^{60} +78.8493i q^{61} -80.0155 q^{62} +(-19.1844 + 8.54161i) q^{63} -32.0687 q^{64} +(-13.8473 - 12.9064i) q^{65} -55.4002i q^{66} -29.9557i q^{67} -19.2240 q^{68} +69.7770i q^{69} +(26.1986 - 76.1494i) q^{70} -117.475 q^{71} -18.6787i q^{72} +22.2333 q^{73} -70.0365 q^{74} +(-3.04189 - 43.1943i) q^{75} +8.99177i q^{76} +(88.8971 - 39.5803i) q^{77} +15.0875i q^{78} +142.799 q^{79} +(71.3289 + 66.4823i) q^{80} +9.00000 q^{81} -102.797 q^{82} -160.872 q^{83} +(-14.3320 + 6.38114i) q^{84} +(-54.3402 - 50.6480i) q^{85} +59.8935 q^{86} -17.1280 q^{87} +86.5538i q^{88} -66.3844i q^{89} +(-23.5315 + 25.2469i) q^{90} +(-24.2099 + 10.7792i) q^{91} +52.1279i q^{92} +60.2344i q^{93} -54.5380i q^{94} +(-23.6899 + 25.4169i) q^{95} -34.5809i q^{96} +45.1538 q^{97} +(-83.7849 - 75.4379i) q^{98} -41.7044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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