LMFDB - Embedded newform 105.3.e.a.34.14

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			34.14
Root			$-0.366025 - 0.842173i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30086i q^{2} +1.73205 q^{3} -1.29396 q^{4} +(3.65761 - 3.40909i) q^{5} +3.98521i q^{6} +(6.39480 - 2.84720i) q^{7} +6.22623i q^{8} +3.00000 q^{9} +O(q^{10})$	\(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} +(13.6833 - 32.2144i) 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} +(74.1208 + 31.4834i) 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	$0.195082\pi$
$2$			2.30086i			1.15043i	−0.818002	+	0.575215i	$0.804918\pi$
$3$	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	$-0.546515\pi$
$13$	−3.78588			−0.291221			−0.145611	+	0.989342i	$0.546515\pi$
$14$	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	$-0.643946\pi$
$17$	−14.8567			−0.873926			−0.436963	+	0.899479i	$0.643946\pi$
$18$			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	$0.339650\pi$
$23$			40.2857i			1.75155i	−0.482716	+	0.875777i	$0.660350\pi$
$24$			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
$35$	13.6833	−	32.2144i	0.390952	−	0.920411i
$36$	−3.88187			−0.107830
$37$			30.4393i			0.822683i	0.911481	+	0.411342i	$0.134940\pi$
$37$			30.4393i			0.822683i	−0.911481	+	0.411342i	$0.865060\pi$
$38$	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	$-0.902117\pi$
$43$		−	26.0309i		−	0.605370i	0.953091	−	0.302685i	$-0.0978831\pi$
$44$	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	$-0.581142\pi$
$47$	−23.7033			−0.504326			−0.252163	+	0.967685i	$0.581142\pi$
$48$	−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	$-0.810171\pi$
$53$		−	59.5338i		−	1.12328i	0.827382	−	0.561640i	$-0.189829\pi$
$54$			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	$0.0717647\pi$
$67$			29.9557i			0.447101i	−0.974692	+	0.223550i	$0.928235\pi$
$68$	19.2240			0.282705
$69$			69.7770i			1.01126i
$70$	74.1208	+	31.4834i	1.05887	+	0.449762i
$71$	−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	$-0.548662\pi$
$73$	−22.2333			−0.304566			−0.152283	+	0.988337i	$0.548662\pi$
$74$	−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	$-0.0793252\pi$
$83$	160.872			1.93822			0.969108	+	0.246636i	$0.0793252\pi$
$84$	−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	$-0.574773\pi$
$97$	−45.1538			−0.465503			−0.232751	+	0.972536i	$0.574773\pi$
$98$	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	$-0.506302\pi$
$103$	−4.07795			−0.0395917			−0.0197959	+	0.999804i	$0.506302\pi$
$104$		−	23.5717i		−	0.226651i
$105$	23.7002	−	55.7970i	0.225716	−	0.531400i
$106$	136.979			1.29225
$107$			31.3454i			0.292948i	0.989215	+	0.146474i	$0.0467924\pi$
$107$			31.3454i			0.292948i	−0.989215	+	0.146474i	$0.953208\pi$
$108$	−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	$0.0883131\pi$
$113$			61.9010i			0.547796i	−0.961759	+	0.273898i	$0.911687\pi$
$114$	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	$0.260278\pi$
$127$			185.310i			1.45913i	−0.683910	+	0.729566i	$0.739722\pi$
$128$		−	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	$-0.894779\pi$
$137$		−	88.9332i		−	0.649147i	0.945860	−	0.324574i	$-0.105221\pi$
$138$	−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	$0.956214\pi$
$140$	−17.7056	+	41.6840i	−0.126468	+	0.297743i
$141$	−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	$-0.530010\pi$
$157$	−29.5598			−0.188279			−0.0941396	+	0.995559i	$0.530010\pi$
$158$			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	$0.263609\pi$
$163$			240.158i			1.47337i	−0.676239	+	0.736683i	$0.736391\pi$
$164$			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	$-0.286822\pi$
$167$	207.335			1.24153			0.620764	+	0.783997i	$0.286822\pi$
$168$	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	$-0.436683\pi$
$173$	68.3717			0.395212			0.197606	+	0.980282i	$0.436683\pi$
$174$			39.4091i			0.226489i
$175$	−59.7735	−	164.475i	−0.341563	−	0.939859i
$176$	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	$0.0887156\pi$
$193$			106.194i			0.550228i	−0.961412	+	0.275114i	$0.911284\pi$
$194$		−	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	$-0.938537\pi$
$197$		−	75.6061i		−	0.383787i	0.981416	−	0.191894i	$-0.0614629\pi$
$198$		−	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
$210$	128.381	+	54.5308i	0.611338	+	0.259670i
$211$	−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	$-0.887554\pi$
$223$	−418.459			−1.87650			−0.938250	+	0.345958i	$0.887554\pi$
$224$	−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	$-0.641403\pi$
$227$	−195.112			−0.859525			−0.429762	+	0.902942i	$0.641403\pi$
$228$			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	$0.0499117\pi$
$233$			72.7709i			0.312321i	−0.987732	+	0.156161i	$0.950088\pi$
$234$		−	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
$245$	−4.21900	−	244.964i	−0.0172204	−	0.999852i
$246$	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	$-0.770042\pi$
$257$	−385.602			−1.50040			−0.750198	+	0.661214i	$0.770042\pi$
$258$	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	$-0.928357\pi$
$263$		−	117.392i		−	0.446358i	0.974777	−	0.223179i	$-0.0716434\pi$
$264$		−	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	$0.0404135\pi$
$277$			70.1485i			0.253244i	−0.991951	+	0.126622i	$0.959587\pi$
$278$	−87.7099			−0.315503
$279$		−	104.329i		−	0.373939i
$280$	200.574	+	85.1954i	0.716336	+	0.304269i
$281$	−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	$-0.475250\pi$
$283$	43.9638			0.155349			0.0776746	+	0.996979i	$0.475250\pi$
$284$	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	$-0.606570\pi$
$293$	−192.547			−0.657157			−0.328579	+	0.944477i	$0.606570\pi$
$294$	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	$-0.297938\pi$
$307$	364.110			1.18603			0.593013	+	0.805193i	$0.297938\pi$
$308$	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	$-0.308729\pi$
$313$	353.929			1.13076			0.565381	+	0.824830i	$0.308729\pi$
$314$		−	68.0130i		−	0.216602i
$315$	41.0499	−	96.6432i	0.130317	−	0.306804i
$316$	−184.776			−0.584733
$317$		−	115.117i		−	0.363144i	−0.983378	−	0.181572i	$-0.941881\pi$
$317$		−	115.117i		−	0.363144i	0.983378	−	0.181572i	$-0.0581186\pi$
$318$	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	$-0.875127\pi$
$337$		−	257.680i		−	0.764629i	0.924032	−	0.382315i	$-0.124873\pi$
$338$		−	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	$0.0401399\pi$
$347$			87.2838i			0.251538i	−0.992060	+	0.125769i	$0.959860\pi$
$348$	−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	$0.985728\pi$
$350$	378.435	−	137.530i	1.08124	−	0.392944i
$351$	−19.6720			−0.0560456
$352$			277.547i			0.788486i
$353$	174.245			0.493611			0.246806	−	0.969065i	$-0.420619\pi$
$353$	174.245			0.493611			0.246806	+	0.969065i	$0.420619\pi$
$354$	−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	$-0.661345\pi$
$367$	−356.321			−0.970903			−0.485451	+	0.874264i	$0.661345\pi$
$368$		−	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	$0.305695\pi$
$373$			611.275i			1.63881i	−0.573217	+	0.819404i	$0.694305\pi$
$374$			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	$-0.641950\pi$
$383$	−330.386			−0.862626			−0.431313	+	0.902202i	$0.641950\pi$
$384$		−	266.124i		−	0.693031i
$385$	−190.218	+	447.828i	−0.494073	+	1.16319i
$386$	−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	$-0.314706\pi$
$397$	436.537			1.09959			0.549795	+	0.835299i	$0.314706\pi$
$398$	−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	$0.767010\pi$
$420$	−30.6670	+	72.1988i	−0.0730166	+	0.171902i
$421$	−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	$-0.548690\pi$
$433$	−131.951			−0.304736			−0.152368	+	0.988324i	$0.548690\pi$
$434$	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	$-0.889157\pi$
$443$		−	302.328i		−	0.682457i	0.939980	−	0.341228i	$-0.110843\pi$
$444$		−	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
$455$	−51.8033	+	121.960i	−0.113853	+	0.268043i
$456$	74.9396			0.164341
$457$		−	501.515i		−	1.09741i	−0.836017	−	0.548703i	$-0.815122\pi$
$457$		−	501.515i		−	1.09741i	0.836017	−	0.548703i	$-0.184878\pi$
$458$	−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	$-0.930404\pi$
$463$		−	200.854i		−	0.433810i	0.976193	−	0.216905i	$-0.0695963\pi$
$464$	−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	$-0.450010\pi$
$467$	146.079			0.312804			0.156402	+	0.987694i	$0.450010\pi$
$468$	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	$-0.689272\pi$
$487$		−	806.827i		−	1.65673i	0.560189	−	0.828365i	$-0.310728\pi$
$488$	−490.934			−1.00601
$489$			415.967i			0.850648i
$490$	563.627	−	9.70732i	1.15026	−	0.0198109i
$491$	−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	$-0.694520\pi$
$503$	−577.214			−1.14754			−0.573771	+	0.819016i	$0.694520\pi$
$504$	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	$-0.515504\pi$
$523$	−50.9274			−0.0973755			−0.0486878	+	0.998814i	$0.515504\pi$
$524$		−	120.103i		−	0.229205i
$525$	−103.531	−	284.880i	−0.197201	−	0.542628i
$526$	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	$0.147645\pi$
$547$			489.442i			0.894775i	−0.894340	+	0.447387i	$0.852355\pi$
$548$			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	$0.144836\pi$
$557$			489.578i			0.878955i	−0.898254	+	0.439478i	$0.855164\pi$
$558$	240.047			0.430191
$559$			98.5499i			0.176297i
$560$	−266.845	+	628.229i	−0.476509	+	1.12184i
$561$	357.722			0.637650
$562$		−	425.620i		−	0.757331i
$563$	−301.482			−0.535492			−0.267746	−	0.963490i	$-0.586279\pi$
$563$	−301.482			−0.535492			−0.267746	+	0.963490i	$0.586279\pi$
$564$	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	$-0.266517\pi$
$577$	772.580			1.33896			0.669480	+	0.742830i	$0.266517\pi$
$578$		−	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	$-0.429400\pi$
$587$	258.261			0.439967			0.219984	+	0.975504i	$0.429400\pi$
$588$	−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	$-0.360670\pi$
$593$	502.713			0.847745			0.423873	+	0.905722i	$0.360670\pi$
$594$		−	166.201i		−	0.279799i
$595$	−203.289	+	478.601i	−0.341663	+	0.804372i
$596$	−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	$-0.823384\pi$
$607$	−1031.87			−1.69995			−0.849976	+	0.526821i	$0.823384\pi$
$608$	−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	$-0.979643\pi$
$613$		−	78.3530i		−	0.127819i	0.997956	−	0.0639094i	$-0.0203569\pi$
$614$			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	$-0.880909\pi$
$617$		−	450.989i		−	0.730938i	0.930823	−	0.365469i	$-0.119091\pi$
$618$		−	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
$630$	222.362	+	94.4501i	0.352956	+	0.149921i
$631$	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	$-0.489357\pi$
$643$	42.9913			0.0668605			0.0334302	+	0.999441i	$0.489357\pi$
$644$	−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	$-0.722606\pi$
$647$	−832.962			−1.28742			−0.643711	+	0.765269i	$0.722606\pi$
$648$			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	$-0.623154\pi$
$653$		−	1209.46i		−	1.85217i	0.377319	−	0.926083i	$-0.376846\pi$
$654$			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
$665$	−223.860	−	95.0861i	−0.336631	−	0.142987i
$666$	−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	$-0.789548\pi$
$673$		−	826.484i		−	1.22806i	0.789283	−	0.614030i	$-0.210452\pi$
$674$	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	$-0.528722\pi$
$677$	−122.010			−0.180221			−0.0901106	+	0.995932i	$0.528722\pi$
$678$	−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	$-0.956742\pi$
$683$		−	185.065i		−	0.270960i	0.990780	−	0.135480i	$-0.0432576\pi$
$684$			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
$700$	77.3442	+	212.824i	0.110492	+	0.304034i
$701$	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	$-0.833618\pi$
$727$	−1259.85			−1.73295			−0.866473	+	0.499224i	$0.833618\pi$
$728$	−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	$-0.807117\pi$
$733$	−1204.99			−1.64391			−0.821955	+	0.569552i	$0.807117\pi$
$734$		−	819.845i		−	1.11696i
$735$	−7.30752	−	424.290i	−0.00994220	−	0.577265i
$736$	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	$0.00473600\pi$
$743$			22.1088i			0.0297561i	−0.999889	+	0.0148780i	$0.995264\pi$
$744$	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	$0.275601\pi$
$757$			1153.11i			1.52326i	−0.648011	+	0.761631i	$0.724399\pi$
$758$			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	$-0.0916191\pi$
$770$	−1030.39	−	437.665i	−1.33817	−	0.568396i
$771$	−667.881			−0.866254
$772$		−	137.410i		−	0.177993i
$773$	−852.655			−1.10305			−0.551524	−	0.834159i	$-0.685953\pi$
$773$	−852.655			−1.10305			−0.551524	+	0.834159i	$0.685953\pi$
$774$	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	$-0.317488\pi$
$787$	853.855			1.08495			0.542474	+	0.840072i	$0.317488\pi$
$788$			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	$-0.573340\pi$
$797$	−364.023			−0.456741			−0.228371	+	0.973574i	$0.573340\pi$
$798$	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
$805$	1297.78	+	551.242i	1.61215	+	0.684773i
$806$	−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	$0.143950\pi$
$823$			719.260i			0.873948i	−0.899474	+	0.436974i	$0.856050\pi$
$824$		−	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	$0.132382\pi$
$827$			668.223i			0.808008i	−0.914757	+	0.404004i	$0.867618\pi$
$828$		−	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	$-0.0409398\pi$
$840$	347.405	+	147.563i	0.413577	+	0.175670i
$841$	−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	$-0.641201\pi$
$853$	−732.200			−0.858382			−0.429191	+	0.903214i	$0.641201\pi$
$854$	−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	$-0.455441\pi$
$857$	239.155			0.279061			0.139530	+	0.990218i	$0.455441\pi$
$858$			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	$0.00471912\pi$
$863$			25.5880i			0.0296500i	−0.999890	+	0.0148250i	$0.995281\pi$
$864$		−	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
$875$	−779.339	−	397.814i	−0.890673	−	0.454644i
$876$	49.8292			0.0568826
$877$		−	289.049i		−	0.329589i	−0.986328	−	0.164794i	$-0.947304\pi$
$877$		−	289.049i		−	0.329589i	0.986328	−	0.164794i	$-0.0526960\pi$
$878$	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	$0.295023\pi$
$883$			1412.32i			1.59946i	−0.600362	+	0.799729i	$0.704977\pi$
$884$	−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	$-0.591948\pi$
$887$	−505.344			−0.569722			−0.284861	+	0.958569i	$0.591948\pi$
$888$	−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	$-0.874635\pi$
$907$		−	696.108i		−	0.767484i	0.923440	−	0.383742i	$-0.125365\pi$
$908$	252.466			0.278047
$909$		−	390.663i		−	0.429772i
$910$	−280.612	−	119.192i	−0.308365	−	0.130980i
$911$	−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	$-0.538489\pi$
$937$	−226.044			−0.241242			−0.120621	+	0.992699i	$0.538489\pi$
$938$	−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
$945$	71.1005	−	167.391i	0.0752387	−	0.177133i
$946$	−832.608			−0.880135
$947$		−	483.972i		−	0.511058i	−0.966801	−	0.255529i	$-0.917750\pi$
$947$		−	483.972i		−	0.511058i	0.966801	−	0.255529i	$-0.0822496\pi$
$948$	−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	$0.181385\pi$
$953$			1028.28i			1.07899i	−0.841989	+	0.539495i	$0.818615\pi$
$954$	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	$0.275017\pi$
$967$			1470.69i			1.52088i	−0.649407	+	0.760441i	$0.724983\pi$
$968$			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	$-0.970101\pi$
$977$		−	183.273i		−	0.187587i	0.995592	−	0.0937936i	$-0.0298994\pi$
$978$	−957.081			−0.978610
$979$			922.841i			0.942637i
$980$	5.45919	+	316.972i	0.00557061	+	0.323441i
$981$	187.332			0.190960
$982$		−	849.642i		−	0.865216i
$983$	−973.748			−0.990588			−0.495294	−	0.868725i	$-0.664940\pi$
$983$	−973.748			−0.990588			−0.495294	+	0.868725i	$0.664940\pi$
$984$	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	$-0.385216\pi$
$997$	703.562			0.705679			0.352839	+	0.935684i	$0.385216\pi$
$998$			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.34.14	yes	16
3.2	odd	2		315.3.e.e.244.3		16
4.3	odd	2		1680.3.bd.c.769.5		16
5.2	odd	4		525.3.h.e.76.3		16
5.3	odd	4		525.3.h.e.76.14		16
5.4	even	2	inner	105.3.e.a.34.3	✓	16
7.6	odd	2	inner	105.3.e.a.34.13	yes	16
15.14	odd	2		315.3.e.e.244.14		16
20.19	odd	2		1680.3.bd.c.769.11		16
21.20	even	2		315.3.e.e.244.4		16
28.27	even	2		1680.3.bd.c.769.12		16
35.13	even	4		525.3.h.e.76.13		16
35.27	even	4		525.3.h.e.76.4		16
35.34	odd	2	inner	105.3.e.a.34.4	yes	16
105.104	even	2		315.3.e.e.244.13		16
140.139	even	2		1680.3.bd.c.769.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.3	✓	16	5.4	even	2	inner
105.3.e.a.34.4	yes	16	35.34	odd	2	inner
105.3.e.a.34.13	yes	16	7.6	odd	2	inner
105.3.e.a.34.14	yes	16	1.1	even	1	trivial
315.3.e.e.244.3		16	3.2	odd	2
315.3.e.e.244.4		16	21.20	even	2
315.3.e.e.244.13		16	105.104	even	2
315.3.e.e.244.14		16	15.14	odd	2
525.3.h.e.76.3		16	5.2	odd	4
525.3.h.e.76.4		16	35.27	even	4
525.3.h.e.76.13		16	35.13	even	4
525.3.h.e.76.14		16	5.3	odd	4
1680.3.bd.c.769.5		16	4.3	odd	2
1680.3.bd.c.769.6		16	140.139	even	2
1680.3.bd.c.769.11		16	20.19	odd	2
1680.3.bd.c.769.12		16	28.27	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} +(13.6833 - 32.2144i) 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} +(74.1208 + 31.4834i) 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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Database

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