LMFDB - Embedded newform 23.3.d.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, 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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	23.15
Dual form			23.3.d.a.20.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.123822 - 0.861198i) q^{2} +(-1.04228 - 2.28229i) q^{3} +(3.11164 + 0.913660i) q^{4} +(-1.80972 + 1.56813i) q^{5} +(-2.09456 + 0.615017i) q^{6} +(-6.61670 + 10.2958i) q^{7} +(2.61786 - 5.73232i) q^{8} +(1.77128 - 2.04416i) q^{9} +O(q^{10})$	\(q+(0.123822 - 0.861198i) q^{2} +(-1.04228 - 2.28229i) q^{3} +(3.11164 + 0.913660i) q^{4} +(-1.80972 + 1.56813i) q^{5} +(-2.09456 + 0.615017i) q^{6} +(-6.61670 + 10.2958i) q^{7} +(2.61786 - 5.73232i) q^{8} +(1.77128 - 2.04416i) q^{9} +(1.12639 + 1.75270i) q^{10} +(-4.49352 + 0.646071i) q^{11} +(-1.15798 - 8.05395i) q^{12} +(1.78452 - 1.14684i) q^{13} +(8.04742 + 6.97313i) q^{14} +(5.46517 + 2.49586i) q^{15} +(6.30025 + 4.04892i) q^{16} +(-6.95262 - 23.6785i) q^{17} +(-1.54111 - 1.77853i) q^{18} +(3.08688 - 10.5129i) q^{19} +(-7.06394 + 3.22599i) q^{20} +(30.3944 + 4.37005i) q^{21} +3.94981i q^{22} +(-14.6235 + 17.7525i) q^{23} -15.8114 q^{24} +(-2.74182 + 19.0698i) q^{25} +(-0.766694 - 1.67883i) q^{26} +(-28.1780 - 8.27382i) q^{27} +(-29.9956 + 25.9914i) q^{28} +(29.6135 - 8.69529i) q^{29} +(2.82613 - 4.39755i) q^{30} +(-0.235011 + 0.514601i) q^{31} +(20.7742 - 23.9748i) q^{32} +(6.15805 + 9.58211i) q^{33} +(-21.2527 + 3.05568i) q^{34} +(-4.17077 - 29.0083i) q^{35} +(7.37925 - 4.74236i) q^{36} +(10.3686 + 8.98442i) q^{37} +(-8.67149 - 3.96014i) q^{38} +(-4.47739 - 2.87744i) q^{39} +(4.25144 + 14.4791i) q^{40} +(38.9498 + 44.9505i) q^{41} +(7.52696 - 25.6345i) q^{42} +(67.7877 - 30.9576i) q^{43} +(-14.5725 - 2.09521i) q^{44} +6.47696i q^{45} +(13.4777 + 14.7919i) q^{46} -44.3115 q^{47} +(2.67415 - 18.5991i) q^{48} +(-41.8671 - 91.6762i) q^{49} +(16.0834 + 4.72250i) q^{50} +(-46.7944 + 40.5476i) q^{51} +(6.60060 - 1.93811i) q^{52} +(-11.9498 + 18.5942i) q^{53} +(-10.6144 + 23.2424i) q^{54} +(7.11890 - 8.21564i) q^{55} +(41.6971 + 64.8820i) q^{56} +(-27.2109 + 3.91234i) q^{57} +(-3.82158 - 26.5797i) q^{58} +(-57.2139 + 36.7691i) q^{59} +(14.7253 + 12.7595i) q^{60} +(-17.5399 - 8.01019i) q^{61} +(0.414074 + 0.266109i) q^{62} +(9.32625 + 31.7623i) q^{63} +(1.54260 + 1.78025i) q^{64} +(-1.43108 + 4.87382i) q^{65} +(9.01459 - 4.11683i) q^{66} +(50.4336 + 7.25125i) q^{67} -80.0312i q^{68} +(55.7582 + 14.8718i) q^{69} -25.4984 q^{70} +(-4.48515 + 31.1949i) q^{71} +(-7.08084 - 15.5049i) q^{72} +(-77.3652 - 22.7165i) q^{73} +(9.02122 - 7.81693i) q^{74} +(46.3804 - 13.6185i) q^{75} +(19.2105 - 29.8921i) q^{76} +(23.0805 - 50.5392i) q^{77} +(-3.03245 + 3.49963i) q^{78} +(-57.8562 - 90.0260i) q^{79} +(-17.7509 + 2.55220i) q^{80} +(7.02190 + 48.8384i) q^{81} +(43.5341 - 27.9777i) q^{82} +(75.8317 + 65.7085i) q^{83} +(90.5837 + 41.3682i) q^{84} +(49.7133 + 31.9488i) q^{85} +(-18.2671 - 62.2119i) q^{86} +(-50.7108 - 58.5234i) q^{87} +(-8.05994 + 27.4496i) q^{88} +(-61.6477 + 28.1536i) q^{89} +(5.57795 + 0.801988i) q^{90} +25.9613i q^{91} +(-61.7229 + 41.8786i) q^{92} +1.41942 q^{93} +(-5.48672 + 38.1610i) q^{94} +(10.8993 + 23.8661i) q^{95} +(-76.3699 - 22.4242i) q^{96} +(44.7263 - 38.7555i) q^{97} +(-84.1354 + 24.7044i) q^{98} +(-6.63860 + 10.3299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{17}{22}\right)$

Coefficient data

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

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

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

$2$	0.123822	−	0.861198i	0.0619108	−	0.430599i	−0.935167	−	0.354207i	$-0.884751\pi$
$2$	0.123822	−	0.861198i	0.0619108	−	0.430599i	0.997078	−	0.0763920i	$-0.0243401\pi$
$3$	−1.04228	−	2.28229i	−0.347428	−	0.760762i	−0.999995	−	0.00303088i	$-0.999035\pi$
$3$	−1.04228	−	2.28229i	−0.347428	−	0.760762i	0.652567	−	0.757731i	$-0.273692\pi$
$4$	3.11164	+	0.913660i	0.777910	+	0.228415i
$5$	−1.80972	+	1.56813i	−0.361944	+	0.313626i	−0.816780	−	0.576949i	$-0.804243\pi$
$5$	−1.80972	+	1.56813i	−0.361944	+	0.313626i	0.454836	+	0.890575i	$0.349698\pi$
$6$	−2.09456	+	0.615017i	−0.349093	+	0.102503i
$7$	−6.61670	+	10.2958i	−0.945242	+	1.47083i	−0.0641176	+	0.997942i	$0.520423\pi$
$7$	−6.61670	+	10.2958i	−0.945242	+	1.47083i	−0.881125	+	0.472884i	$0.843213\pi$
$8$	2.61786	−	5.73232i	0.327233	−	0.716540i
$9$	1.77128	−	2.04416i	0.196809	−	0.227129i
$10$	1.12639	+	1.75270i	0.112639	+	0.175270i
$11$	−4.49352	+	0.646071i	−0.408502	+	0.0587337i	−0.343503	−	0.939152i	$-0.611614\pi$
$11$	−4.49352	+	0.646071i	−0.408502	+	0.0587337i	−0.0649991	+	0.997885i	$0.520704\pi$
$12$	−1.15798	−	8.05395i	−0.0964986	−	0.671162i
$13$	1.78452	−	1.14684i	0.137271	−	0.0882184i	−0.470203	−	0.882558i	$-0.655819\pi$
$13$	1.78452	−	1.14684i	0.137271	−	0.0882184i	0.607474	+	0.794340i	$0.292183\pi$
$14$	8.04742	+	6.97313i	0.574815	+	0.498080i
$15$	5.46517	+	2.49586i	0.364345	+	0.166391i
$16$	6.30025	+	4.04892i	0.393765	+	0.253058i
$17$	−6.95262	−	23.6785i	−0.408978	−	1.39285i	−0.864503	−	0.502628i	$-0.832367\pi$
$17$	−6.95262	−	23.6785i	−0.408978	−	1.39285i	0.455525	−	0.890223i	$-0.349451\pi$
$18$	−1.54111	−	1.77853i	−0.0856171	−	0.0988073i
$19$	3.08688	−	10.5129i	0.162467	−	0.553312i	−0.837509	−	0.546423i	$-0.815989\pi$
$19$	3.08688	−	10.5129i	0.162467	−	0.553312i	0.999976	−	0.00688891i	$-0.00219282\pi$
$20$	−7.06394	+	3.22599i	−0.353197	+	0.161300i
$21$	30.3944	+	4.37005i	1.44735	+	0.208098i
$22$			3.94981i			0.179537i
$23$	−14.6235	+	17.7525i	−0.635805	+	0.771850i
$23$	−14.6235	+	17.7525i	−0.635805	+	0.771850i
$24$	−15.8114			−0.658807
$25$	−2.74182	+	19.0698i	−0.109673	+	0.762791i
$26$	−0.766694	−	1.67883i	−0.0294882	−	0.0645702i
$27$	−28.1780	−	8.27382i	−1.04363	−	0.306438i
$28$	−29.9956	+	25.9914i	−1.07127	+	0.928263i
$29$	29.6135	−	8.69529i	1.02115	−	0.299838i	0.272045	−	0.962285i	$-0.412300\pi$
$29$	29.6135	−	8.69529i	1.02115	−	0.299838i	0.749109	+	0.662447i	$0.230482\pi$
$30$	2.82613	−	4.39755i	0.0942045	−	0.146585i
$31$	−0.235011	+	0.514601i	−0.00758099	+	0.0166000i	−0.913385	−	0.407098i	$-0.866541\pi$
$31$	−0.235011	+	0.514601i	−0.00758099	+	0.0166000i	0.905804	+	0.423698i	$0.139268\pi$
$32$	20.7742	−	23.9748i	0.649195	−	0.749211i
$33$	6.15805	+	9.58211i	0.186608	+	0.290367i
$34$	−21.2527	+	3.05568i	−0.625080	+	0.0898730i
$35$	−4.17077	−	29.0083i	−0.119165	−	0.828810i
$36$	7.37925	−	4.74236i	0.204979	−	0.131732i
$37$	10.3686	+	8.98442i	0.280232	+	0.242822i	0.783623	−	0.621236i	$-0.213369\pi$
$37$	10.3686	+	8.98442i	0.280232	+	0.242822i	−0.503392	+	0.864058i	$0.667915\pi$
$38$	−8.67149	−	3.96014i	−0.228197	−	0.104214i
$39$	−4.47739	−	2.87744i	−0.114805	−	0.0737806i
$40$	4.25144	+	14.4791i	0.106286	+	0.361977i
$41$	38.9498	+	44.9505i	0.949996	+	1.09635i	0.995247	+	0.0973784i	$0.0310457\pi$
$41$	38.9498	+	44.9505i	0.949996	+	1.09635i	−0.0452512	+	0.998976i	$0.514409\pi$
$42$	7.52696	−	25.6345i	0.179213	−	0.610345i
$43$	67.7877	−	30.9576i	1.57646	−	0.719945i	0.580890	−	0.813982i	$-0.302705\pi$
$43$	67.7877	−	30.9576i	1.57646	−	0.719945i	0.995569	+	0.0940376i	$0.0299774\pi$
$44$	−14.5725	−	2.09521i	−0.331194	−	0.0476185i
$45$			6.47696i			0.143933i
$46$	13.4777	+	14.7919i	0.292994	+	0.321563i
$47$	−44.3115			−0.942798			−0.471399	−	0.881920i	$-0.656251\pi$
$47$	−44.3115			−0.942798			−0.471399	+	0.881920i	$0.656251\pi$
$48$	2.67415	−	18.5991i	0.0557114	−	0.387481i
$49$	−41.8671	−	91.6762i	−0.854431	−	1.87094i
$50$	16.0834	+	4.72250i	0.321667	+	0.0944500i
$51$	−46.7944	+	40.5476i	−0.917537	+	0.795050i
$52$	6.60060	−	1.93811i	0.126935	−	0.0372714i
$53$	−11.9498	+	18.5942i	−0.225468	+	0.350835i	−0.935495	−	0.353339i	$-0.885046\pi$
$53$	−11.9498	+	18.5942i	−0.225468	+	0.350835i	0.710028	+	0.704174i	$0.248682\pi$
$54$	−10.6144	+	23.2424i	−0.196564	+	0.430414i
$55$	7.11890	−	8.21564i	0.129434	−	0.149375i
$56$	41.6971	+	64.8820i	0.744592	+	1.15861i
$57$	−27.2109	+	3.91234i	−0.477384	+	0.0686375i
$58$	−3.82158	−	26.5797i	−0.0658894	−	0.458271i
$59$	−57.2139	+	36.7691i	−0.969727	+	0.623206i	−0.926674	−	0.375867i	$-0.877345\pi$
$59$	−57.2139	+	36.7691i	−0.969727	+	0.623206i	−0.0430534	+	0.999073i	$0.513709\pi$
$60$	14.7253	+	12.7595i	0.245421	+	0.212659i
$61$	−17.5399	−	8.01019i	−0.287539	−	0.131315i	0.266424	−	0.963856i	$-0.414158\pi$
$61$	−17.5399	−	8.01019i	−0.287539	−	0.131315i	−0.553963	+	0.832541i	$0.686885\pi$
$62$	0.414074	+	0.266109i	0.00667862	+	0.00429209i
$63$	9.32625	+	31.7623i	0.148036	+	0.504164i
$64$	1.54260	+	1.78025i	0.0241031	+	0.0278165i
$65$	−1.43108	+	4.87382i	−0.0220166	+	0.0749818i
$66$	9.01459	−	4.11683i	0.136585	−	0.0623762i
$67$	50.4336	+	7.25125i	0.752740	+	0.108228i	0.507995	−	0.861360i	$-0.330387\pi$
$67$	50.4336	+	7.25125i	0.752740	+	0.108228i	0.244745	+	0.969588i	$0.421296\pi$
$68$		−	80.0312i		−	1.17693i
$69$	55.7582	+	14.8718i	0.808090	+	0.215534i
$70$	−25.4984			−0.364262
$71$	−4.48515	+	31.1949i	−0.0631712	+	0.439365i	0.933550	+	0.358448i	$0.116694\pi$
$71$	−4.48515	+	31.1949i	−0.0631712	+	0.439365i	−0.996721	+	0.0809170i	$0.974215\pi$
$72$	−7.08084	−	15.5049i	−0.0983450	−	0.215346i
$73$	−77.3652	−	22.7165i	−1.05980	−	0.311184i	−0.295028	−	0.955489i	$-0.595329\pi$
$73$	−77.3652	−	22.7165i	−1.05980	−	0.311184i	−0.764769	+	0.644304i	$0.777147\pi$
$74$	9.02122	−	7.81693i	0.121908	−	0.105634i
$75$	46.3804	−	13.6185i	0.618406	−	0.181580i
$76$	19.2105	−	29.8921i	0.252770	−	0.393317i
$77$	23.0805	−	50.5392i	0.299746	−	0.656353i
$78$	−3.03245	+	3.49963i	−0.0388775	+	0.0448670i
$79$	−57.8562	−	90.0260i	−0.732357	−	1.13957i	−0.985091	−	0.172033i	$-0.944966\pi$
$79$	−57.8562	−	90.0260i	−0.732357	−	1.13957i	0.252735	−	0.967536i	$-0.418670\pi$
$80$	−17.7509	+	2.55220i	−0.221887	+	0.0319025i
$81$	7.02190	+	48.8384i	0.0866902	+	0.602943i
$82$	43.5341	−	27.9777i	0.530904	−	0.341191i
$83$	75.8317	+	65.7085i	0.913635	+	0.791669i	0.978505	−	0.206225i	$-0.0661177\pi$
$83$	75.8317	+	65.7085i	0.913635	+	0.791669i	−0.0648697	+	0.997894i	$0.520663\pi$
$84$	90.5837	+	41.3682i	1.07838	+	0.492479i
$85$	49.7133	+	31.9488i	0.584862	+	0.375868i
$86$	−18.2671	−	62.2119i	−0.212408	−	0.723394i
$87$	−50.7108	−	58.5234i	−0.582883	−	0.672682i
$88$	−8.05994	+	27.4496i	−0.0915903	+	0.311928i
$89$	−61.6477	+	28.1536i	−0.692671	+	0.316332i	−0.730462	−	0.682954i	$-0.760695\pi$
$89$	−61.6477	+	28.1536i	−0.692671	+	0.316332i	0.0377912	+	0.999286i	$0.487968\pi$
$90$	5.57795	+	0.801988i	0.0619772	+	0.00891097i
$91$			25.9613i			0.285289i
$92$	−61.7229	+	41.8786i	−0.670902	+	0.455202i
$93$	1.41942			0.0152625
$94$	−5.48672	+	38.1610i	−0.0583694	+	0.405968i
$95$	10.8993	+	23.8661i	0.114729	+	0.251222i
$96$	−76.3699	−	22.4242i	−0.795520	−	0.233586i
$97$	44.7263	−	38.7555i	0.461096	−	0.399542i	−0.393098	−	0.919497i	$-0.628597\pi$
$97$	44.7263	−	38.7555i	0.461096	−	0.399542i	0.854194	+	0.519955i	$0.174051\pi$
$98$	−84.1354	+	24.7044i	−0.858524	+	0.252085i
$99$	−6.63860	+	10.3299i	−0.0670566	+	0.104342i
$100$	−25.9549	+	56.8332i	−0.259549	+	0.568332i
$101$	43.2437	−	49.9059i	0.428156	−	0.494118i	−0.500149	−	0.865940i	$-0.666721\pi$
$101$	43.2437	−	49.9059i	0.428156	−	0.494118i	0.928304	+	0.371822i	$0.121267\pi$
$102$	29.1253	+	45.3199i	0.285542	+	0.444313i
$103$	67.5002	−	9.70506i	0.655341	−	0.0942239i	0.193380	−	0.981124i	$-0.438055\pi$
$103$	67.5002	−	9.70506i	0.655341	−	0.0942239i	0.461961	+	0.886900i	$0.347146\pi$
$104$	−1.90243	−	13.2317i	−0.0182926	−	0.127228i
$105$	−61.8582	+	39.7538i	−0.589126	+	0.378608i
$106$	14.5337	+	12.5935i	0.137110	+	0.118807i
$107$	−45.6552	−	20.8500i	−0.426684	−	0.194860i	0.190486	−	0.981690i	$-0.438994\pi$
$107$	−45.6552	−	20.8500i	−0.426684	−	0.194860i	−0.617170	+	0.786830i	$0.711721\pi$
$108$	−80.1205	−	51.4903i	−0.741856	−	0.476762i
$109$	1.47593	+	5.02657i	0.0135407	+	0.0461153i	0.965986	−	0.258594i	$-0.0832590\pi$
$109$	1.47593	+	5.02657i	0.0135407	+	0.0461153i	−0.952446	+	0.304709i	$0.901441\pi$
$110$	−6.19382	−	7.14805i	−0.0563075	−	0.0649823i
$111$	9.69801	−	33.0284i	0.0873694	−	0.297553i
$112$	−83.3736	+	38.0755i	−0.744407	+	0.339959i
$113$	−38.9422	−	5.59905i	−0.344622	−	0.0495491i	−0.0321689	−	0.999482i	$-0.510241\pi$
$113$	−38.9422	−	5.59905i	−0.344622	−	0.0495491i	−0.312453	+	0.949933i	$0.601151\pi$
$114$			23.9184i			0.209811i
$115$	−1.37385	−	55.0588i	−0.0119465	−	0.478772i
$116$	100.091			0.862853
$117$	0.816548	−	5.67921i	0.00697904	−	0.0485403i
$118$	24.5812	+	53.8253i	0.208315	+	0.456147i
$119$	289.792	+	85.0905i	2.43522	+	0.715046i
$120$	28.6141	−	24.7943i	0.238451	−	0.206619i
$121$	−96.3243	+	28.2834i	−0.796069	+	0.233747i
$122$	−9.07017	+	14.1135i	−0.0743457	+	0.115684i
$123$	61.9931	−	135.746i	0.504009	−	1.10363i
$124$	−1.20144	+	1.38654i	−0.00968903	+	0.0111817i
$125$	−57.3075	−	89.1722i	−0.458460	−	0.713378i
$126$	28.5084	−	4.09889i	0.226257	−	0.0325309i
$127$	7.32301	+	50.9327i	0.0576615	+	0.401045i	0.998128	+	0.0611584i	$0.0194795\pi$
$127$	7.32301	+	50.9327i	0.0576615	+	0.401045i	−0.940467	+	0.339886i	$0.889611\pi$
$128$	108.473	−	69.7114i	0.847445	−	0.544620i
$129$	−141.308	−	122.444i	−1.09541	−	0.949180i
$130$	4.02012	+	1.83593i	0.0309240	+	0.0141225i
$131$	−39.0736	−	25.1111i	−0.298272	−	0.191688i	0.382942	−	0.923773i	$-0.374911\pi$
$131$	−39.0736	−	25.1111i	−0.298272	−	0.191688i	−0.681213	+	0.732085i	$0.738547\pi$
$132$	10.4068	+	35.4425i	0.0788397	+	0.268503i
$133$	87.8139	+	101.343i	0.660255	+	0.761975i
$134$	12.4895	−	42.5354i	0.0932054	−	0.317429i
$135$	63.9688	−	29.2136i	0.473843	−	0.216397i
$136$	−153.934	−	22.1323i	−1.13186	−	0.162738i
$137$			43.5024i			0.317536i	0.987316	+	0.158768i	$0.0507521\pi$
$137$			43.5024i			0.317536i	−0.987316	+	0.158768i	$0.949248\pi$
$138$	19.7117	−	46.1774i	0.142838	−	0.334619i
$139$	121.389			0.873305			0.436653	−	0.899630i	$-0.356164\pi$
$139$	121.389			0.873305			0.436653	+	0.899630i	$0.356164\pi$
$140$	13.5258	−	94.0743i	0.0966131	−	0.671959i
$141$	46.1852	+	101.131i	0.327555	+	0.717245i
$142$	26.3096	+	7.72521i	0.185279	+	0.0544029i
$143$	−7.27783	+	6.30627i	−0.0508939	+	0.0440998i
$144$	19.4361	−	5.70697i	0.134973	−	0.0396317i
$145$	−39.9567	+	62.1739i	−0.275564	+	0.428785i
$146$	−29.1429	+	63.8139i	−0.199609	+	0.437082i
$147$	−165.594	+	191.105i	−1.12649	+	1.30004i
$148$	24.0546	+	37.4297i	0.162531	+	0.252903i
$149$	−110.763	+	15.9253i	−0.743375	+	0.106881i	−0.503588	−	0.863944i	$-0.667987\pi$
$149$	−110.763	+	15.9253i	−0.743375	+	0.106881i	−0.239788	+	0.970825i	$0.577078\pi$
$150$	−5.98534	−	41.6290i	−0.0399023	−	0.277527i
$151$	−51.1532	+	32.8742i	−0.338763	+	0.217710i	−0.698950	−	0.715170i	$-0.746349\pi$
$151$	−51.1532	+	32.8742i	−0.338763	+	0.217710i	0.360187	+	0.932880i	$0.382713\pi$
$152$	−52.1825	−	45.2164i	−0.343306	−	0.297476i
$153$	−60.7177	−	27.7288i	−0.396848	−	0.181234i
$154$	−40.6664	−	26.1347i	−0.264067	−	0.169706i
$155$	−0.381659	−	1.29981i	−0.00246232	−	0.00838589i
$156$	−11.3030	−	13.0444i	−0.0724553	−	0.0836179i
$157$	−26.3159	+	89.6237i	−0.167617	+	0.570851i	0.832248	+	0.554404i	$0.187054\pi$
$157$	−26.3159	+	89.6237i	−0.167617	+	0.570851i	−0.999865	+	0.0164473i	$0.994764\pi$
$158$	−84.6940	+	38.6785i	−0.536038	+	0.244800i
$159$	54.8924	+	7.89234i	0.345235	+	0.0496374i
$160$			75.9644i			0.474777i
$161$	−86.0169	−	268.024i	−0.534267	−	1.66474i
$162$	42.9290			0.264994
$163$	9.47497	−	65.8999i	0.0581287	−	0.404294i	−0.939895	−	0.341462i	$-0.889078\pi$
$163$	9.47497	−	65.8999i	0.0581287	−	0.404294i	0.998024	−	0.0628315i	$-0.0200131\pi$
$164$	80.1285	+	175.457i	0.488588	+	1.06986i
$165$	−26.1704	−	7.68431i	−0.158608	−	0.0465716i
$166$	65.9777	−	57.1700i	0.397456	−	0.344397i
$167$	57.0364	−	16.7474i	0.341535	−	0.100284i	−0.106467	−	0.994316i	$-0.533954\pi$
$167$	57.0364	−	16.7474i	0.341535	−	0.100284i	0.448002	+	0.894032i	$0.352136\pi$
$168$	104.619	−	162.790i	0.622732	−	0.968990i
$169$	−68.3359	+	149.635i	−0.404354	+	0.885412i
$170$	33.6698	−	38.8570i	0.198058	−	0.228571i
$171$	−16.0224	−	24.9314i	−0.0936985	−	0.145798i
$172$	239.216	−	34.3940i	1.39079	−	0.199965i
$173$	43.4850	+	302.445i	0.251358	+	1.74823i	0.590077	+	0.807347i	$0.299097\pi$
$173$	43.4850	+	302.445i	0.251358	+	1.74823i	−0.338719	+	0.940888i	$0.609993\pi$
$174$	−56.6793	+	36.4256i	−0.325743	+	0.209342i
$175$	−178.196	−	154.408i	−1.01827	−	0.882332i
$176$	−30.9262	−	14.1235i	−0.175717	−	0.0802472i
$177$	143.551	+	92.2545i	0.811022	+	0.521212i
$178$	16.6125	+	56.5769i	0.0933285	+	0.317848i
$179$	−209.257	−	241.495i	−1.16903	−	1.34914i	−0.925274	−	0.379300i	$-0.876165\pi$
$179$	−209.257	−	241.495i	−1.16903	−	1.34914i	−0.243759	−	0.969836i	$-0.578381\pi$
$180$	−5.91775	+	20.1540i	−0.0328764	+	0.111967i
$181$	127.639	−	58.2909i	0.705190	−	0.322049i	−0.0303421	−	0.999540i	$-0.509660\pi$
$181$	127.639	−	58.2909i	0.705190	−	0.322049i	0.735532	+	0.677490i	$0.236932\pi$
$182$	22.3578	+	3.21457i	0.122845	+	0.0176625i
$183$			48.3799i			0.264371i
$184$	63.4809	+	130.300i	0.345005	+	0.708155i
$185$	−32.8530			−0.177584
$186$	0.175754	−	1.22240i	0.000944915	−	0.00657203i
$187$	46.5397	+	101.908i	0.248876	+	0.544961i
$188$	−137.882	−	40.4857i	−0.733412	−	0.215349i
$189$	271.631	−	235.370i	1.43720	−	1.24534i
$190$	21.9030	−	6.43130i	0.115279	−	0.0338490i
$191$	78.7925	−	122.604i	0.412526	−	0.641903i	−0.571360	−	0.820700i	$-0.693584\pi$
$191$	78.7925	−	122.604i	0.412526	−	0.641903i	0.983886	+	0.178796i	$0.0572203\pi$
$192$	2.45522	−	5.37618i	0.0127876	−	0.0280010i
$193$	−94.6152	+	109.192i	−0.490234	+	0.565760i	−0.945928	−	0.324376i	$-0.894846\pi$
$193$	−94.6152	+	109.192i	−0.490234	+	0.565760i	0.455694	+	0.890136i	$0.349391\pi$
$194$	−27.8381	−	43.3169i	−0.143495	−	0.223283i
$195$	12.6150	−	1.81377i	0.0646925	−	0.00930138i
$196$	−46.5145	−	323.516i	−0.237319	−	1.65059i
$197$	257.129	−	165.247i	1.30522	−	0.838815i	0.311451	−	0.950262i	$-0.399185\pi$
$197$	257.129	−	165.247i	1.30522	−	0.838815i	0.993770	+	0.111447i	$0.0355486\pi$
$198$	8.07406	+	6.99621i	0.0407781	+	0.0353344i
$199$	−89.4230	−	40.8381i	−0.449362	−	0.205217i	0.177862	−	0.984055i	$-0.443082\pi$
$199$	−89.4230	−	40.8381i	−0.449362	−	0.205217i	−0.627224	+	0.778839i	$0.715809\pi$
$200$	102.136	+	65.6391i	0.510682	+	0.328195i
$201$	−36.0167	−	122.662i	−0.179188	−	0.610257i
$202$	−37.6244	−	43.4208i	−0.186259	−	0.214955i
$203$	−106.418	+	362.428i	−0.524229	+	1.78536i
$204$	−182.654	+	83.4153i	−0.895363	+	0.408899i
$205$	−140.977	−	20.2694i	−0.687691	−	0.0988751i
$206$		−	59.3327i		−	0.288023i
$207$	10.3868	+	61.3375i	0.0501777	+	0.296317i
$208$	15.8864			0.0763767
$209$	−7.07884	+	49.2344i	−0.0338701	+	0.235571i
$210$	26.5766	+	58.1945i	0.126555	+	0.277117i
$211$	59.7448	+	17.5426i	0.283151	+	0.0831405i	0.420224	−	0.907420i	$-0.361951\pi$
$211$	59.7448	+	17.5426i	0.283151	+	0.0831405i	−0.137073	+	0.990561i	$0.543770\pi$
$212$	−54.1723	+	46.9406i	−0.255530	+	0.221418i
$213$	75.8705	−	22.2776i	0.356200	−	0.104590i
$214$	−23.6091	+	36.7365i	−0.110323	+	0.171666i
$215$	−74.1312	+	162.325i	−0.344796	+	0.754999i
$216$	−121.194	+	139.866i	−0.561085	+	0.647527i
$217$	−3.74323	−	5.82458i	−0.0172499	−	0.0268414i
$218$	4.51162	−	0.648673i	0.0206955	−	0.00297557i
$219$	28.7911	+	200.246i	0.131466	+	0.914367i
$220$	29.6578	−	19.0599i	0.134808	−	0.0866359i
$221$	−39.5625	−	34.2811i	−0.179016	−	0.155118i
$222$	−27.2431	−	12.4415i	−0.122717	−	0.0560429i
$223$	−62.4181	−	40.1137i	−0.279902	−	0.179882i	0.393156	−	0.919472i	$-0.371383\pi$
$223$	−62.4181	−	40.1137i	−0.279902	−	0.179882i	−0.673058	+	0.739590i	$0.735020\pi$
$224$	109.382	+	372.521i	0.488312	+	1.66304i
$225$	34.1252	+	39.3826i	0.151668	+	0.175034i
$226$	−9.64378	+	32.8437i	−0.0426716	+	0.145326i
$227$	110.735	−	50.5709i	0.487819	−	0.222779i	−0.156293	−	0.987711i	$-0.549954\pi$
$227$	110.735	−	50.5709i	0.487819	−	0.222779i	0.644112	+	0.764931i	$0.277227\pi$
$228$	−88.2452	−	12.6877i	−0.387040	−	0.0556480i
$229$		−	164.911i		−	0.720137i	−0.932926	−	0.360069i	$-0.882753\pi$
$229$		−	164.911i		−	0.720137i	0.932926	−	0.360069i	$-0.117247\pi$
$230$	−47.5866	−	5.63430i	−0.206898	−	0.0244970i
$231$	−139.401			−0.603469
$232$	27.6798	−	192.517i	0.119309	−	0.829815i
$233$	−117.197	−	256.625i	−0.502991	−	1.10140i	−0.975486	−	0.220063i	$-0.929374\pi$
$233$	−117.197	−	256.625i	−0.502991	−	1.10140i	0.472495	−	0.881334i	$-0.343354\pi$
$234$	−4.78982	−	1.40642i	−0.0204693	−	0.00601034i
$235$	80.1914	−	69.4863i	0.341240	−	0.295686i
$236$	−211.624	+	62.1383i	−0.896710	+	0.263298i
$237$	−145.162	+	225.877i	−0.612499	+	0.953067i
$238$	109.162	−	239.032i	0.458665	−	1.00434i
$239$	110.212	−	127.191i	0.461136	−	0.532179i	−0.476789	−	0.879018i	$-0.658199\pi$
$239$	110.212	−	127.191i	0.461136	−	0.532179i	0.937925	+	0.346839i	$0.112745\pi$
$240$	24.3264	+	37.8526i	0.101360	+	0.157719i
$241$	294.634	−	42.3620i	1.22255	−	0.175776i	0.499340	−	0.866406i	$-0.333576\pi$
$241$	294.634	−	42.3620i	1.22255	−	0.175776i	0.723208	+	0.690630i	$0.242667\pi$
$242$	12.4306	+	86.4564i	0.0513659	+	0.357258i
$243$	−118.206	+	75.9665i	−0.486445	+	0.312619i
$244$	−47.2592	−	40.9503i	−0.193685	−	0.167829i
$245$	219.528	+	100.255i	0.896033	+	0.409205i
$246$	−109.228	−	70.1966i	−0.444016	−	0.285352i
$247$	−6.54806	−	22.3007i	−0.0265104	−	0.0902860i
$248$	2.33464	+	2.69431i	0.00941385	+	0.0108642i
$249$	70.9274	−	241.557i	0.284849	−	0.970107i
$250$	−83.8908	+	38.3117i	−0.335563	+	0.153247i
$251$	18.0981	+	2.60212i	0.0721041	+	0.0103670i	0.178272	−	0.983981i	$-0.442949\pi$
$251$	18.0981	+	2.60212i	0.0721041	+	0.0103670i	−0.106168	+	0.994348i	$0.533858\pi$
$252$			107.354i			0.426008i
$253$	54.2417	−	89.2193i	0.214394	−	0.352645i
$254$	44.7698			0.176259
$255$	21.1008	−	146.760i	0.0827484	−	0.575528i
$256$	−42.6898	−	93.4775i	−0.166757	−	0.365147i
$257$	348.455	+	102.315i	1.35585	+	0.398115i	0.877300	−	0.479943i	$-0.159343\pi$
$257$	348.455	+	102.315i	1.35585	+	0.398115i	0.478555	+	0.878058i	$0.341161\pi$
$258$	−122.946	+	106.533i	−0.476534	+	0.412919i
$259$	−161.107	+	47.3054i	−0.622036	+	0.182646i
$260$	−8.90603	+	13.8580i	−0.0342540	+	0.0533002i
$261$	34.6790	−	75.9365i	0.132870	−	0.290945i
$262$	−26.4638	+	30.5408i	−0.101007	+	0.116568i
$263$	3.61970	+	5.63237i	0.0137631	+	0.0214158i	0.848067	−	0.529889i	$-0.177766\pi$
$263$	3.61970	+	5.63237i	0.0137631	+	0.0214158i	−0.834304	+	0.551305i	$0.814130\pi$
$264$	71.0487	−	10.2153i	0.269124	−	0.0386942i
$265$	−7.53243	−	52.3892i	−0.0284243	−	0.197695i
$266$	98.1494	−	63.0768i	0.368983	−	0.237131i
$267$	128.509	+	111.354i	0.481307	+	0.417055i
$268$	150.306	+	68.6425i	0.560843	+	0.256129i
$269$	120.490	+	77.4339i	0.447917	+	0.287859i	0.745089	−	0.666965i	$-0.232407\pi$
$269$	120.490	+	77.4339i	0.447917	+	0.287859i	−0.297172	+	0.954824i	$0.596044\pi$
$270$	−17.2380	−	58.7071i	−0.0638443	−	0.217434i
$271$	54.9410	+	63.4053i	0.202734	+	0.233968i	0.848008	−	0.529984i	$-0.177802\pi$
$271$	54.9410	+	63.4053i	0.202734	+	0.233968i	−0.645273	+	0.763952i	$0.723257\pi$
$272$	52.0690	−	177.331i	0.191430	−	0.651951i
$273$	59.2511	−	27.0590i	0.217037	−	0.0991174i
$274$	37.4642	+	5.38653i	0.136731	+	0.0196589i
$275$		−	87.4619i		−	0.318043i
$276$	159.912	+	97.2199i	0.579391	+	0.352246i
$277$	−52.1867			−0.188400			−0.0941999	−	0.995553i	$-0.530029\pi$
$277$	−52.1867			−0.188400			−0.0941999	+	0.995553i	$0.530029\pi$
$278$	15.0306	−	104.540i	0.0540670	−	0.376044i
$279$	0.635660	+	1.39190i	0.00227835	+	0.00498890i
$280$	−177.204	−	52.0317i	−0.632870	−	0.185828i
$281$	−267.253	+	231.576i	−0.951080	+	0.824115i	−0.984510	−	0.175326i	$-0.943902\pi$
$281$	−267.253	+	231.576i	−0.951080	+	0.824115i	0.0334309	+	0.999441i	$0.489357\pi$
$282$	92.8129	−	27.2523i	0.329124	−	0.0966395i
$283$	6.20268	−	9.65156i	0.0219176	−	0.0341045i	−0.830122	−	0.557582i	$-0.811729\pi$
$283$	6.20268	−	9.65156i	0.0219176	−	0.0341045i	0.852039	+	0.523478i	$0.175366\pi$
$284$	−42.4578	+	92.9695i	−0.149499	+	0.327357i
$285$	43.1091	−	49.7505i	0.151260	−	0.174563i
$286$	4.52980	+	7.04850i	0.0158384	+	0.0246451i
$287$	−720.520	+	103.595i	−2.51052	+	0.360959i
$288$	−12.2114	−	84.9319i	−0.0424006	−	0.294903i
$289$	−269.208	+	173.010i	−0.931516	+	0.598649i
$290$	48.5965	+	42.1091i	0.167574	+	0.145204i
$291$	−135.069	−	61.6838i	−0.464154	−	0.211972i
$292$	−219.978	−	141.371i	−0.753348	−	0.484147i
$293$	−63.9782	−	217.890i	−0.218356	−	0.743651i	−0.993696	−	0.112107i	$-0.964240\pi$
$293$	−63.9782	−	217.890i	−0.218356	−	0.743651i	0.775340	−	0.631543i	$-0.217578\pi$
$294$	144.075	+	166.272i	0.490053	+	0.565551i
$295$	45.8823	−	156.261i	0.155533	−	0.529698i
$296$	78.6451	−	35.9160i	0.265693	−	0.121338i
$297$	131.964	+	18.9736i	0.444323	+	0.0638841i
$298$			97.3607i			0.326714i
$299$	−5.73660	+	48.4505i	−0.0191859	+	0.162042i
$300$	156.762			0.522540
$301$	−129.798	+	902.765i	−0.431223	+	2.99922i
$302$	21.9773	+	48.1236i	0.0727725	+	0.159350i
$303$	−158.972	−	46.6783i	−0.524659	−	0.154054i
$304$	62.0141	−	53.7355i	0.203994	−	0.176762i
$305$	44.3033	−	13.0086i	0.145257	−	0.0426512i
$306$	−31.3982	+	48.8565i	−0.102608	+	0.159662i
$307$	105.691	−	231.430i	0.344269	−	0.753845i	−0.655730	−	0.754996i	$-0.727639\pi$
$307$	105.691	−	231.430i	0.344269	−	0.753845i	0.999999	+	0.00115063i	$0.000366258\pi$
$308$	117.994	−	136.172i	0.383097	−	0.442117i
$309$	−92.5041	−	143.939i	−0.299366	−	0.465823i
$310$	−1.16665	+	0.167739i	−0.00376340	+	0.000541095i
$311$	14.8679	+	103.409i	0.0478068	+	0.332504i	0.999663	+	0.0259589i	$0.00826391\pi$
$311$	14.8679	+	103.409i	0.0478068	+	0.332504i	−0.951856	+	0.306545i	$0.900827\pi$
$312$	−28.2156	+	18.1331i	−0.0904347	+	0.0581189i
$313$	285.213	+	247.138i	0.911223	+	0.789579i	0.978090	−	0.208183i	$-0.0667550\pi$
$313$	285.213	+	247.138i	0.911223	+	0.789579i	−0.0668673	+	0.997762i	$0.521300\pi$
$314$	73.9252	+	33.7605i	0.235431	+	0.107518i
$315$	−66.6854	−	42.8561i	−0.211700	−	0.136051i
$316$	−97.7745	−	332.989i	−0.309413	−	1.05376i
$317$	−59.7464	−	68.9510i	−0.188474	−	0.217511i	0.653646	−	0.756800i	$-0.273238\pi$
$317$	−59.7464	−	68.9510i	−0.188474	−	0.217511i	−0.842121	+	0.539289i	$0.818693\pi$
$318$	13.5937	−	46.2960i	0.0427476	−	0.145585i
$319$	−127.451	+	58.2049i	−0.399533	+	0.182460i
$320$	−5.58335	−	0.802764i	−0.0174480	−	0.00250864i
$321$			125.930i			0.392305i
$322$	−241.472	+	40.8905i	−0.749914	+	0.126989i
$323$	−270.392			−0.837127
$324$	−22.7721	+	158.383i	−0.0702842	+	0.488837i
$325$	16.9771	+	37.1748i	0.0522374	+	0.114384i
$326$	−55.5796	−	16.3197i	−0.170490	−	0.0500603i
$327$	9.93372	−	8.60762i	0.0303784	−	0.0263230i
$328$	359.636	−	105.599i	1.09645	−	0.321947i
$329$	293.196	−	456.222i	0.891173	−	1.38669i
$330$	−9.85817	+	21.5864i	−0.0298732	+	0.0654133i
$331$	361.889	−	417.642i	1.09332	−	1.26176i	0.130549	−	0.991442i	$-0.458326\pi$
$331$	361.889	−	417.642i	1.09332	−	1.26176i	0.962771	−	0.270317i	$-0.0871285\pi$
$332$	175.926	+	273.746i	0.529897	+	0.824536i
$333$	36.7313	−	5.28116i	0.110304	−	0.0158593i
$334$	−7.36048	−	51.1933i	−0.0220374	−	0.153273i
$335$	−102.642	+	65.9637i	−0.306393	+	0.196907i
$336$	173.798	+	150.597i	0.517256	+	0.448205i
$337$	−286.003	−	130.613i	−0.848675	−	0.387577i	−0.0568927	−	0.998380i	$-0.518119\pi$
$337$	−286.003	−	130.613i	−0.848675	−	0.387577i	−0.791782	+	0.610803i	$0.790847\pi$
$338$	120.404	+	77.3787i	0.356224	+	0.228931i
$339$	27.8103	+	94.7131i	0.0820362	+	0.279390i
$340$	125.500	+	144.834i	0.369116	+	0.425983i
$341$	0.723556	−	2.46421i	0.00212187	−	0.00722641i
$342$	−23.4548	+	10.7114i	−0.0685813	+	0.0313200i
$343$	627.312	+	90.1938i	1.82890	+	0.262956i
$344$		−	469.624i		−	1.36519i
$345$	−124.228	+	60.5224i	−0.360081	+	0.175427i
$346$	265.849			0.768350
$347$	45.6680	−	317.628i	0.131608	−	0.915354i	−0.811851	−	0.583865i	$-0.801540\pi$
$347$	45.6680	−	317.628i	0.131608	−	0.915354i	0.943459	−	0.331489i	$-0.107551\pi$
$348$	−104.323	−	228.436i	−0.299780	−	0.656426i
$349$	−440.960	−	129.478i	−1.26350	−	0.370996i	−0.419702	−	0.907662i	$-0.637865\pi$
$349$	−440.960	−	129.478i	−1.26350	−	0.370996i	−0.843795	+	0.536666i	$0.819683\pi$
$350$	−155.040	+	134.343i	−0.442973	+	0.383838i
$351$	−59.7729	+	17.5509i	−0.170293	+	0.0500026i
$352$	−77.8601	+	121.153i	−0.221194	+	0.344184i
$353$	−64.7628	+	141.811i	−0.183464	+	0.401730i	−0.978909	−	0.204295i	$-0.934510\pi$
$353$	−64.7628	+	141.811i	−0.183464	+	0.401730i	0.795445	+	0.606025i	$0.207237\pi$
$354$	97.2241	−	112.203i	0.274644	−	0.316956i
$355$	−40.8009	−	63.4874i	−0.114932	−	0.178838i
$356$	−217.548	+	31.2787i	−0.611091	+	0.0878616i
$357$	−107.845	−	750.076i	−0.302086	−	2.10105i
$358$	−233.886	+	150.309i	−0.653312	+	0.419858i
$359$	390.136	+	338.055i	1.08673	+	0.941657i	0.998517	−	0.0544442i	$-0.0173387\pi$
$359$	390.136	+	338.055i	1.08673	+	0.941657i	0.0882137	+	0.996102i	$0.471884\pi$
$360$	37.1280	+	16.9558i	0.103133	+	0.0470995i
$361$	202.700	+	130.267i	0.561495	+	0.360851i
$362$	−34.3955	−	117.140i	−0.0950153	−	0.323592i
$363$	164.948	+	190.360i	0.454402	+	0.524408i
$364$	−23.7198	+	80.7822i	−0.0651643	+	0.221929i
$365$	175.632	−	80.2084i	0.481183	−	0.219749i
$366$	41.6646	+	5.99047i	0.113838	+	0.0163674i
$367$			503.034i			1.37067i	0.728230	+	0.685333i	$0.240343\pi$
$367$			503.034i			1.37067i	−0.728230	+	0.685333i	$0.759657\pi$
$368$	−164.010	+	52.6359i	−0.445680	+	0.143032i
$369$	160.877			0.435982
$370$	−4.06791	+	28.2929i	−0.0109943	+	0.0764674i
$371$	−112.374	−	246.065i	−0.302895	−	0.663248i
$372$	4.41671	+	1.29686i	0.0118729	+	0.00348619i
$373$	−446.896	+	387.237i	−1.19811	+	1.03817i	−0.199815	+	0.979834i	$0.564034\pi$
$373$	−446.896	+	387.237i	−1.19811	+	1.03817i	−0.998297	+	0.0583358i	$0.981421\pi$
$374$	93.5254	−	27.4615i	0.250068	−	0.0734266i
$375$	−143.786	+	223.735i	−0.383429	+	0.596627i
$376$	−116.002	+	254.008i	−0.308515	+	0.675553i
$377$	42.8736	−	49.4788i	0.113723	−	0.131243i
$378$	−169.066	−	263.072i	−0.447264	−	0.695957i
$379$	−267.421	+	38.4494i	−0.705598	+	0.101450i	−0.485767	−	0.874088i	$-0.661460\pi$
$379$	−267.421	+	38.4494i	−0.705598	+	0.101450i	−0.219831	+	0.975538i	$0.570550\pi$
$380$	12.1092	+	84.2210i	0.0318662	+	0.221634i
$381$	108.610	−	69.7995i	0.285066	−	0.183201i
$382$	−95.8297	−	83.0369i	−0.250863	−	0.217374i
$383$	42.0115	+	19.1860i	0.109691	+	0.0500940i	0.469505	−	0.882930i	$-0.344433\pi$
$383$	42.0115	+	19.1860i	0.109691	+	0.0500940i	−0.359814	+	0.933024i	$0.617160\pi$
$384$	−272.161	−	174.907i	−0.708753	−	0.455488i
$385$	37.4829	+	127.655i	0.0973582	+	0.331572i
$386$	82.3203	+	95.0027i	0.213265	+	0.246121i
$387$	56.7885	−	193.404i	0.146740	−	0.499751i
$388$	174.582	−	79.7287i	0.449952	−	0.205486i
$389$	−510.299	−	73.3699i	−1.31182	−	0.188612i	−0.549329	−	0.835606i	$-0.685116\pi$
$389$	−510.299	−	73.3699i	−1.31182	−	0.188612i	−0.762494	+	0.646995i	$0.776026\pi$
$390$		−	11.0886i		−	0.0284324i
$391$	522.025	+	222.836i	1.33510	+	0.569912i
$392$	−635.120			−1.62020
$393$	−16.5848	+	115.350i	−0.0422006	+	0.293511i
$394$	−110.472	−	241.900i	−0.280386	−	0.613959i
$395$	245.876	+	72.1957i	0.622471	+	0.182774i
$396$	−30.0949	+	26.0774i	−0.0759973	+	0.0658521i
$397$	−12.3055	+	3.61323i	−0.0309963	+	0.00910134i	−0.297194	−	0.954817i	$-0.596051\pi$
$397$	−12.3055	+	3.61323i	−0.0309963	+	0.00910134i	0.266198	+	0.963918i	$0.414233\pi$
$398$	−46.2422	+	71.9543i	−0.116186	+	0.180790i
$399$	139.766	−	306.044i	0.350290	−	0.767029i
$400$	−94.4862	+	109.043i	−0.236215	+	0.272607i
$401$	403.883	+	628.454i	1.00719	+	1.56722i	0.809642	+	0.586925i	$0.199662\pi$
$401$	403.883	+	628.454i	1.00719	+	1.56722i	0.197548	+	0.980293i	$0.436702\pi$
$402$	−110.096	+	15.8294i	−0.273870	+	0.0393765i
$403$	0.170785	+	1.18783i	0.000423783	+	0.00294748i
$404$	180.156	−	115.779i	0.445931	−	0.286582i
$405$	−89.2928	−	77.3726i	−0.220476	−	0.191043i
$406$	298.945	+	136.524i	0.736318	+	0.336265i
$407$	−52.3960	−	33.6729i	−0.128737	−	0.0827343i
$408$	109.930	+	374.389i	0.269437	+	0.917619i
$409$	−8.58539	−	9.90807i	−0.0209912	−	0.0242251i	0.745157	−	0.666889i	$-0.232375\pi$
$409$	−8.58539	−	9.90807i	−0.0209912	−	0.0242251i	−0.766148	+	0.642664i	$0.777829\pi$
$410$	−34.9119	+	118.899i	−0.0851510	+	0.289998i
$411$	99.2849	−	45.3419i	0.241569	−	0.110321i
$412$	218.903	+	31.4736i	0.531319	+	0.0763921i
$413$		−	832.352i		−	2.01538i
$414$	54.1099	−	1.35017i	0.130700	−	0.00326129i
$415$	−240.274			−0.578973
$416$	9.57680	−	66.6081i	0.0230211	−	0.160116i
$417$	−126.522	−	277.045i	−0.303411	−	0.664377i
$418$	41.5241	+	12.1926i	0.0993399	+	0.0291688i
$419$	−75.1530	+	65.1205i	−0.179363	+	0.155419i	−0.739915	−	0.672700i	$-0.765134\pi$
$419$	−75.1530	+	65.1205i	−0.179363	+	0.155419i	0.560552	+	0.828119i	$0.310589\pi$
$420$	−228.802	+	67.1823i	−0.544767	+	0.159958i
$421$	−370.039	+	575.791i	−0.878951	+	1.36768i	0.0504974	+	0.998724i	$0.483919\pi$
$421$	−370.039	+	575.791i	−0.878951	+	1.36768i	−0.929449	+	0.368951i	$0.879717\pi$
$422$	22.5054	−	49.2799i	0.0533303	−	0.116777i
$423$	−78.4880	+	90.5800i	−0.185551	+	0.214137i
$424$	75.3052	+	117.177i	0.177607	+	0.276361i
$425$	470.606	−	67.6629i	1.10731	−	0.159207i
$426$	−9.79101	−	68.0980i	−0.0229836	−	0.159854i
$427$	198.527	−	127.586i	0.464935	−	0.298795i
$428$	−123.013	−	106.591i	−0.287413	−	0.249045i
$429$	21.9783	+	10.0371i	0.0512314	+	0.0233966i
$430$	130.615	+	83.9410i	0.303755	+	0.195212i
$431$	−55.7675	−	189.927i	−0.129391	−	0.440665i	0.869157	−	0.494536i	$-0.164662\pi$
$431$	−55.7675	−	189.927i	−0.129391	−	0.440665i	−0.998548	+	0.0538713i	$0.982844\pi$
$432$	−144.028	−	166.218i	−0.333399	−	0.384763i
$433$	162.096	−	552.047i	0.374355	−	1.27494i	−0.529943	−	0.848033i	$-0.677787\pi$
$433$	162.096	−	552.047i	0.374355	−	1.27494i	0.904298	−	0.426902i	$-0.140395\pi$
$434$	−5.47961	+	2.50245i	−0.0126258	+	0.00576602i
$435$	183.545	+	26.3898i	0.421942	+	0.0606661i
$436$			16.9894i			0.0389665i
$437$	141.490	+	208.536i	0.323776	+	0.477199i
$438$	176.017			0.401865
$439$	85.4054	−	594.008i	0.194545	−	1.35309i	−0.625245	−	0.780429i	$-0.715001\pi$
$439$	85.4054	−	594.008i	0.194545	−	1.35309i	0.819790	−	0.572664i	$-0.194090\pi$
$440$	−28.4584	−	62.3153i	−0.0646782	−	0.141626i
$441$	−261.559	−	76.8008i	−0.593105	−	0.174151i
$442$	−34.4215	+	29.8264i	−0.0778766	+	0.0674805i
$443$	567.112	−	166.519i	1.28016	−	0.375890i	0.430200	−	0.902733i	$-0.358443\pi$
$443$	567.112	−	166.519i	1.28016	−	0.375890i	0.849962	+	0.526844i	$0.176625\pi$
$444$	60.3534	−	93.9118i	0.135931	−	0.211513i
$445$	67.4166	−	147.622i	0.151498	−	0.331734i
$446$	−42.2745	+	48.7874i	−0.0947859	+	0.109389i
$447$	151.793	+	236.194i	0.339581	+	0.528398i
$448$	−28.5360	+	4.10286i	−0.0636965	+	0.00915817i
$449$	13.1362	+	91.3646i	0.0292567	+	0.203485i	0.999207	−	0.0398187i	$-0.0126780\pi$
$449$	13.1362	+	91.3646i	0.0292567	+	0.203485i	−0.969950	+	0.243303i	$0.921769\pi$
$450$	38.1416	−	24.5121i	0.0847592	−	0.0544714i
$451$	−204.063	−	176.822i	−0.452468	−	0.392066i
$452$	−116.059	−	53.0022i	−0.256767	−	0.117262i
$453$	128.344	+	82.4820i	0.283321	+	0.182079i
$454$	−29.8402	−	101.626i	−0.0657273	−	0.223847i
$455$	−40.7107	−	46.9827i	−0.0894741	−	0.103259i
$456$	−48.8077	+	166.224i	−0.107034	+	0.364526i
$457$	266.623	−	121.763i	0.583420	−	0.266439i	−0.101765	−	0.994809i	$-0.532449\pi$
$457$	266.623	−	121.763i	0.583420	−	0.266439i	0.685185	+	0.728370i	$0.259722\pi$
$458$	−142.021	−	20.4196i	−0.310090	−	0.0445843i
$459$			724.737i			1.57895i
$460$	46.0301	−	172.578i	0.100065	−	0.375170i
$461$	−713.769			−1.54831			−0.774153	−	0.632998i	$-0.781824\pi$
$461$	−713.769			−1.54831			−0.774153	+	0.632998i	$0.781824\pi$
$462$	−17.2609	+	120.052i	−0.0373612	+	0.259853i
$463$	−105.877	−	231.839i	−0.228677	−	0.500733i	0.760160	−	0.649736i	$-0.225121\pi$
$463$	−105.877	−	231.839i	−0.228677	−	0.500733i	−0.988837	+	0.149003i	$0.952393\pi$
$464$	221.779	+	65.1201i	0.477971	+	0.140345i
$465$	−2.56875	+	2.22583i	−0.00552418	+	0.00478673i
$466$	−235.517	+	69.1540i	−0.505401	+	0.148399i
$467$	232.143	−	361.221i	0.497094	−	0.773493i	−0.498537	−	0.866868i	$-0.666129\pi$
$467$	232.143	−	361.221i	0.497094	−	0.773493i	0.995631	+	0.0933754i	$0.0297657\pi$
$468$	7.72968	−	16.9256i	0.0165164	−	0.0361659i
$469$	−408.361	+	471.274i	−0.870706	+	1.00485i
$470$	−49.9120	−	77.6646i	−0.106196	−	0.165244i
$471$	231.975	−	33.3530i	0.492517	−	0.0708132i
$472$	60.9944	+	424.225i	0.129225	+	0.898782i
$473$	−284.605	+	182.904i	−0.601701	+	0.386690i
$474$	176.551	+	152.982i	0.372470	+	0.322747i
$475$	192.016	+	87.6906i	0.404243	+	0.184612i
$476$	823.984	+	529.542i	1.73106	+	1.11248i
$477$	16.8433	+	57.3629i	0.0353108	+	0.120258i
$478$	−95.8899	−	110.663i	−0.200607	−	0.231512i
$479$	−148.535	+	505.865i	−0.310095	+	1.05609i	0.646075	+	0.763274i	$0.276409\pi$
$479$	−148.535	+	505.865i	−0.310095	+	1.05609i	−0.956170	+	0.292812i	$0.905409\pi$
$480$	173.372	−	79.1765i	0.361193	−	0.164951i
$481$	28.8066	+	4.14176i	0.0598889	+	0.00861073i
$482$		−	258.984i		−	0.537311i
$483$	−522.053	+	475.672i	−1.08085	+	0.984829i
$484$	−325.568			−0.672662
$485$	−20.1683	+	140.273i	−0.0415841	+	0.289224i
$486$	50.7857	+	111.205i	0.104497	+	0.228817i
$487$	−354.273	−	104.024i	−0.727460	−	0.213601i	−0.103025	−	0.994679i	$-0.532852\pi$
$487$	−354.273	−	104.024i	−0.727460	−	0.213601i	−0.624434	+	0.781077i	$0.714670\pi$
$488$	−91.8340	+	79.5746i	−0.188184	+	0.163063i
$489$	−160.278	+	47.0618i	−0.327767	+	0.0962410i
$490$	113.522	−	176.643i	0.231677	−	0.360497i
$491$	−150.421	+	329.376i	−0.306356	+	0.670827i	−0.998712	−	0.0507292i	$-0.983845\pi$
$491$	−150.421	+	329.376i	−0.306356	+	0.670827i	0.692356	+	0.721556i	$0.256573\pi$
$492$	316.926	−	365.752i	0.644158	−	0.743398i
$493$	−411.782	−	640.746i	−0.835258	−	1.29969i
$494$	−20.0161	+	2.87788i	−0.0405184	+	0.00582566i
$495$	−4.18458	−	29.1044i	−0.00845369	−	0.0587967i
$496$	−3.56420	+	2.29058i	−0.00718590	+	0.00461810i
$497$	−291.499	−	252.585i	−0.586517	−	0.508220i
$498$	−199.246	−	90.9925i	−0.400092	−	0.182716i
$499$	−584.451	−	375.604i	−1.17124	−	0.752713i	−0.197488	−	0.980305i	$-0.563278\pi$
$499$	−584.451	−	375.604i	−1.17124	−	0.752713i	−0.973757	+	0.227592i	$0.926915\pi$
$500$	−96.8473	−	329.832i	−0.193695	−	0.659663i
$501$	−97.6705	−	112.718i	−0.194951	−	0.224985i
$502$	4.48188	−	15.2639i	0.00892804	−	0.0304061i
$503$	−500.244	+	228.454i	−0.994520	+	0.454182i	−0.845110	−	0.534593i	$-0.820465\pi$
$503$	−500.244	+	228.454i	−0.994520	+	0.454182i	−0.149411	+	0.988775i	$0.547738\pi$
$504$	206.487	+	29.6883i	0.409696	+	0.0589054i
$505$			158.128i			0.313124i
$506$	−70.1192	−	57.7601i	−0.138575	−	0.114150i
$507$	412.735			0.814072
$508$	−23.7486	+	165.175i	−0.0467492	+	0.325148i
$509$	311.954	+	683.084i	0.612877	+	1.34201i	0.920589	+	0.390533i	$0.127709\pi$
$509$	311.954	+	683.084i	0.612877	+	1.34201i	−0.307712	+	0.951479i	$0.599563\pi$
$510$	−123.776	−	36.3440i	−0.242699	−	0.0712627i
$511$	745.786	−	646.227i	1.45946	−	1.26463i
$512$	409.088	−	120.119i	0.798999	−	0.234607i
$513$	−173.964	+	270.693i	−0.339111	+	0.527668i
$514$	131.260	−	287.419i	0.255370	−	0.559182i
$515$	−106.938	+	123.413i	−0.207646	+	0.239636i
$516$	−327.828	−	510.110i	−0.635326	−	0.988586i
$517$	199.115	−	28.6284i	0.385135	−	0.0553740i
$518$	20.7907	+	144.603i	0.0401366	+	0.279156i
$519$	644.941	−	414.479i	1.24266	−	0.798610i
$520$	24.1919	+	20.9624i	0.0465229	+	0.0403123i
$521$	353.923	+	161.631i	0.679314	+	0.310232i	0.725025	−	0.688722i	$-0.241828\pi$
$521$	353.923	+	161.631i	0.679314	+	0.310232i	−0.0457109	+	0.998955i	$0.514555\pi$
$522$	−61.1024	−	39.2681i	−0.117054	−	0.0752262i
$523$	152.109	+	518.037i	0.290840	+	0.990510i	0.967216	+	0.253954i	$0.0817312\pi$
$523$	152.109	+	518.037i	0.290840	+	0.990510i	−0.676376	+	0.736556i	$0.736451\pi$
$524$	−98.6400	−	113.837i	−0.188244	−	0.217246i
$525$	−166.672	+	567.632i	−0.317470	+	1.08120i
$526$	5.29878	−	2.41987i	0.0100737	−	0.00460052i
$527$	13.8189	+	1.98686i	0.0262218	+	0.00377013i
$528$			85.3031i			0.161559i
$529$	−101.306	−	519.209i	−0.191504	−	0.981492i
$530$	−46.0502			−0.0868871
$531$	−26.1796	+	182.083i	−0.0493024	+	0.342906i
$532$	180.653	+	395.574i	0.339573	+	0.743561i
$533$	121.058	+	35.5457i	0.227125	+	0.0666899i
$534$	111.810	−	96.8836i	0.209381	−	0.181430i
$535$	115.319	−	33.8607i	0.215549	−	0.0632909i
$536$	173.595	−	270.119i	0.323871	−	0.503953i
$537$	−333.056	+	729.291i	−0.620216	+	1.35808i
$538$	81.6052	−	94.1774i	0.151682	−	0.175051i
$539$	247.360	+	384.900i	0.458924	+	0.714100i
$540$	225.739	−	32.4564i	0.418036	−	0.0601045i
$541$	−102.749	−	714.635i	−0.189924	−	1.32095i	−0.832199	−	0.554478i	$-0.812918\pi$
$541$	−102.749	−	714.635i	−0.189924	−	1.32095i	0.642274	−	0.766475i	$-0.277991\pi$
$542$	61.4074	−	39.4642i	0.113298	−	0.0728121i
$543$	−266.073	−	230.554i	−0.490006	−	0.424592i
$544$	−712.121	−	325.215i	−1.30905	−	0.597821i
$545$	−10.5534	−	6.78223i	−0.0193639	−	0.0124445i
$546$	−15.9666	−	54.3774i	−0.0292429	−	0.0995923i
$547$	8.27616	+	9.55120i	0.0151301	+	0.0174611i	0.763264	−	0.646087i	$-0.223595\pi$
$547$	8.27616	+	9.55120i	0.0151301	+	0.0174611i	−0.748134	+	0.663548i	$0.769050\pi$
$548$	−39.7464	+	135.364i	−0.0725299	+	0.247014i
$549$	−47.4421	+	21.6661i	−0.0864155	+	0.0394646i
$550$	−75.3220	−	10.8297i	−0.136949	−	0.0196903i
$551$		−	338.165i		−	0.613730i
$552$	231.218	−	280.692i	0.418873	−	0.508500i
$553$	1309.70			2.36836
$554$	−6.46184	+	44.9431i	−0.0116640	+	0.0811247i
$555$	34.2422	+	74.9799i	0.0616976	+	0.135099i
$556$	377.720	+	110.909i	0.679353	+	0.199476i
$557$	108.021	−	93.6010i	0.193934	−	0.168045i	−0.552481	−	0.833525i	$-0.686319\pi$
$557$	108.021	−	93.6010i	0.193934	−	0.168045i	0.746415	+	0.665481i	$0.231773\pi$
$558$	1.27741	−	0.375082i	0.00228927	−	0.000672190i
$559$	85.4649	−	132.986i	0.152889	−	0.237900i
$560$	91.1757	−	199.647i	0.162814	−	0.356512i
$561$	184.075	−	212.434i	0.328119	−	0.378670i
$562$	166.341	+	258.832i	0.295981	+	0.460555i
$563$	−509.510	+	73.2565i	−0.904992	+	0.130118i	−0.579069	−	0.815278i	$-0.696584\pi$
$563$	−509.510	+	73.2565i	−0.904992	+	0.130118i	−0.325922	+	0.945397i	$0.605675\pi$
$564$	51.3120	+	356.883i	0.0909787	+	0.632771i
$565$	79.2546	−	50.9338i	0.140274	−	0.0901484i
$566$	−7.54388	−	6.53681i	−0.0133284	−	0.0115491i
$567$	−549.291	−	250.853i	−0.968768	−	0.442421i
$568$	167.078	+	107.374i	0.294151	+	0.189039i
$569$	−115.294	−	392.657i	−0.202626	−	0.690082i	−0.996620	−	0.0821554i	$-0.973820\pi$
$569$	−115.294	−	392.657i	−0.202626	−	0.690082i	0.793993	−	0.607927i	$-0.207999\pi$
$570$	−37.5072	−	43.2857i	−0.0658022	−	0.0759397i
$571$	220.842	−	752.119i	0.386764	−	1.31720i	−0.504382	−	0.863480i	$-0.668280\pi$
$571$	220.842	−	752.119i	0.386764	−	1.31720i	0.891146	−	0.453716i	$-0.149902\pi$
$572$	−28.4078	+	12.9734i	−0.0496639	+	0.0226808i
$573$	−361.940	−	52.0392i	−0.631659	−	0.0908188i
$574$			633.338i			1.10338i
$575$	−298.442	−	327.541i	−0.519029	−	0.569637i
$576$	6.37150			0.0110616
$577$	47.3749	−	329.499i	0.0821055	−	0.571056i	−0.906692	−	0.421793i	$-0.861401\pi$
$577$	47.3749	−	329.499i	0.0821055	−	0.571056i	0.988798	−	0.149263i	$-0.0476901\pi$
$578$	115.662	+	253.264i	0.200107	+	0.438173i
$579$	347.823	+	102.130i	0.600730	+	0.176390i
$580$	−181.137	+	156.956i	−0.312305	+	0.270614i
$581$	−1178.28	+	345.973i	−2.02801	+	0.595479i
$582$	−69.8464	+	108.683i	−0.120011	+	0.186741i
$583$	41.6834	−	91.2740i	0.0714982	−	0.156559i
$584$	−332.750	+	384.014i	−0.569777	+	0.657558i
$585$	7.42803	+	11.5582i	0.0126975	+	0.0197577i
$586$	−195.568	+	28.1184i	−0.333734	+	0.0479837i
$587$	58.8637	+	409.406i	0.100279	+	0.697455i	0.976496	+	0.215538i	$0.0691504\pi$
$587$	58.8637	+	409.406i	0.100279	+	0.697455i	−0.876217	+	0.481917i	$0.839941\pi$
$588$	−689.874	+	443.355i	−1.17325	+	0.754005i
$589$	4.68452	+	4.05916i	0.00795335	+	0.00689161i
$590$	−128.890	−	58.8622i	−0.218458	−	0.0997665i
$591$	−645.141	−	414.607i	−1.09161	−	0.701535i
$592$	28.9473	+	98.5856i	0.0488975	+	0.166530i
$593$	400.260	+	461.925i	0.674975	+	0.778962i	0.985146	−	0.171718i	$-0.0549319\pi$
$593$	400.260	+	461.925i	0.674975	+	0.778962i	−0.310171	+	0.950681i	$0.600386\pi$
$594$	32.6800	−	111.298i	0.0550168	−	0.187370i
$595$	−657.875	+	300.442i	−1.10567	+	0.504944i
$596$	−359.205	−	51.6459i	−0.602693	−	0.0866541i
$597$			246.654i			0.413155i
$598$	41.0152	+	10.9396i	0.0685873	+	0.0182936i
$599$	911.211			1.52122			0.760611	−	0.649208i	$-0.224900\pi$
$599$	911.211			1.52122			0.760611	+	0.649208i	$0.224900\pi$
$600$	43.3519	−	301.519i	0.0722532	−	0.502532i
$601$	209.931	+	459.686i	0.349304	+	0.764868i	0.999985	+	0.00551708i	$0.00175615\pi$
$601$	209.931	+	459.686i	0.349304	+	0.764868i	−0.650681	+	0.759351i	$0.725517\pi$
$602$	761.387	+	223.563i	1.26476	+	0.371368i
$603$	104.155	−	90.2505i	0.172727	−	0.149669i
$604$	−189.206	+	55.5560i	−0.313255	+	0.0919801i
$605$	129.968	−	202.234i	0.214823	−	0.334271i
$606$	−59.8834	+	131.126i	−0.0988175	+	0.216380i
$607$	−640.509	+	739.187i	−1.05520	+	1.21777i	−0.0799232	+	0.996801i	$0.525468\pi$
$607$	−640.509	+	739.187i	−1.05520	+	1.21777i	−0.975281	+	0.220969i	$0.929078\pi$
$608$	−187.918	−	292.405i	−0.309075	−	0.480930i
$609$	938.082	−	134.876i	1.54036	−	0.221471i
$610$	−5.71729	−	39.7647i	−0.00937261	−	0.0651880i
$611$	−79.0746	+	50.8182i	−0.129418	+	0.0831721i
$612$	−163.597	−	141.758i	−0.267315	−	0.231630i
$613$	931.140	+	425.237i	1.51899	+	0.693699i	0.988110	−	0.153749i	$-0.0491349\pi$
$613$	931.140	+	425.237i	1.51899	+	0.693699i	0.530878	+	0.847448i	$0.321862\pi$
$614$	−186.221	−	119.677i	−0.303291	−	0.194913i
$615$	100.677	+	342.876i	0.163703	+	0.557521i
$616$	−229.285	−	264.609i	−0.372217	−	0.429561i
$617$	−41.8410	+	142.497i	−0.0678137	+	0.230952i	−0.986426	−	0.164209i	$-0.947493\pi$
$617$	−41.8410	+	142.497i	−0.0678137	+	0.230952i	0.918612	+	0.395161i	$0.129311\pi$
$618$	−135.414	+	61.8416i	−0.219117	+	0.100067i
$619$	−843.470	−	121.273i	−1.36263	−	0.195917i	−0.578080	−	0.815980i	$-0.696198\pi$
$619$	−843.470	−	121.273i	−1.36263	−	0.195917i	−0.784552	+	0.620063i	$0.787107\pi$
$620$		−	4.39326i		−	0.00708590i
$621$	558.943	−	379.239i	0.900069	−	0.610691i
$622$	90.8963			0.146136
$623$	118.041	−	820.995i	0.189472	−	1.31781i
$624$	−16.5581	−	36.2572i	−0.0265354	−	0.0581045i
$625$	−218.592	−	64.1845i	−0.349748	−	0.102695i
$626$	248.150	−	215.024i	0.396406	−	0.343488i
$627$	119.745	−	35.1604i	0.190981	−	0.0560771i
$628$	−163.771	+	254.833i	−0.260782	+	0.405785i
$629$	140.648	−	307.977i	0.223606	−	0.489630i
$630$	−45.1647	+	52.1228i	−0.0716900	+	0.0827346i
$631$	139.235	+	216.654i	0.220658	+	0.343350i	0.933879	−	0.357589i	$-0.116401\pi$
$631$	139.235	+	216.654i	0.220658	+	0.343350i	−0.713221	+	0.700939i	$0.752765\pi$
$632$	−667.518	+	95.9745i	−1.05620	+	0.151858i
$633$	−22.2337	−	154.639i	−0.0351244	−	0.244296i
$634$	−66.7783	+	42.9158i	−0.105329	+	0.0676906i
$635$	−93.1217	−	80.6905i	−0.146648	−	0.127072i
$636$	163.595	+	74.7112i	0.257224	+	0.117470i
$637$	−179.850	−	115.583i	−0.282340	−	0.181449i
$638$	34.3448	+	116.967i	0.0538319	+	0.183335i
$639$	55.8231	+	64.4233i	0.0873600	+	0.100819i
$640$	−86.9892	+	296.258i	−0.135921	+	0.462903i
$641$	−257.646	+	117.663i	−0.401944	+	0.183561i	−0.606121	−	0.795372i	$-0.707275\pi$
$641$	−257.646	+	117.663i	−0.401944	+	0.183561i	0.204177	+	0.978934i	$0.434548\pi$
$642$	108.451	+	15.5928i	0.168926	+	0.0242879i
$643$		−	572.137i		−	0.889793i	−0.895582	−	0.444897i	$-0.853240\pi$
$643$		−	572.137i		−	0.889793i	0.895582	−	0.444897i	$-0.146760\pi$
$644$	−22.7712	−	912.584i	−0.0353590	−	1.41706i
$645$	447.737			0.694166
$646$	−33.4803	+	232.861i	−0.0518272	+	0.360466i
$647$	367.952	+	805.702i	0.568704	+	1.24529i	0.947484	+	0.319802i	$0.103616\pi$
$647$	367.952	+	805.702i	0.568704	+	1.24529i	−0.378780	+	0.925487i	$0.623656\pi$
$648$	298.340	+	87.6005i	0.460401	+	0.135186i
$649$	233.336	−	202.187i	0.359532	−	0.311536i
$650$	34.1170	−	10.0176i	0.0524876	−	0.0154118i
$651$	−9.39184	+	14.6140i	−0.0144268	+	0.0224485i
$652$	89.6928	−	196.400i	0.137566	−	0.301227i
$653$	758.899	−	875.817i	1.16217	−	1.34122i	0.232605	−	0.972571i	$-0.425275\pi$
$653$	758.899	−	875.817i	1.16217	−	1.34122i	0.929569	−	0.368649i	$-0.120179\pi$
$654$	−6.18285	−	9.62071i	−0.00945391	−	0.0147106i
$655$	110.090	−	15.8285i	0.168076	−	0.0241657i
$656$	63.3924	+	440.904i	0.0966348	+	0.672110i
$657$	−183.471	+	117.910i	−0.279256	+	0.179467i
$658$	−356.593	−	308.990i	−0.541935	−	0.469589i
$659$	94.4209	+	43.1206i	0.143279	+	0.0654334i	0.485764	−	0.874090i	$-0.338541\pi$
$659$	94.4209	+	43.1206i	0.143279	+	0.0654334i	−0.342485	+	0.939523i	$0.611269\pi$
$660$	−74.4119	−	47.8216i	−0.112745	−	0.0724570i
$661$	−40.9257	−	139.380i	−0.0619148	−	0.210863i	0.922725	−	0.385458i	$-0.125956\pi$
$661$	−40.9257	−	139.380i	−0.0619148	−	0.210863i	−0.984640	+	0.174595i	$0.944138\pi$
$662$	−314.863	−	363.371i	−0.475624	−	0.548899i
$663$	−37.0038	+	126.023i	−0.0558127	+	0.190081i
$664$	575.180	−	262.676i	0.866235	−	0.395596i
$665$	−317.837	−	45.6981i	−0.477951	−	0.0687190i
$666$		−	32.2868i		−	0.0484787i
$667$	−278.689	+	652.870i	−0.417825	+	0.978815i
$668$	192.778			0.288590
$669$	−26.4934	+	184.266i	−0.0396015	+	0.275435i
$670$	44.0986	+	96.5625i	0.0658188	+	0.144123i
$671$	83.9909	+	24.6620i	0.125173	+	0.0367540i
$672$	736.192	−	637.914i	1.09552	−	0.949276i
$673$	238.304	−	69.9723i	0.354092	−	0.103971i	−0.0998491	−	0.995003i	$-0.531836\pi$
$673$	238.304	−	69.9723i	0.354092	−	0.103971i	0.453941	+	0.891032i	$0.350018\pi$
$674$	−147.897	+	230.133i	−0.219432	+	0.341443i
$675$	235.039	−	514.663i	0.348206	−	0.762464i
$676$	−349.352	+	403.174i	−0.516793	+	0.596411i
$677$	−295.679	−	460.086i	−0.436750	−	0.679596i	0.551200	−	0.834373i	$-0.314170\pi$
$677$	−295.679	−	460.086i	−0.436750	−	0.679596i	−0.987949	+	0.154778i	$0.950534\pi$
$678$	85.0102	−	12.2226i	0.125384	−	0.0180275i
$679$	103.078	+	716.926i	0.151809	+	1.05586i
$680$	313.283	−	201.335i	0.460711	−	0.296081i
$681$	−230.834	−	200.019i	−0.338964	−	0.293714i
$682$	−2.03258	−	0.928247i	−0.00298032	−	0.00136107i
$683$	234.136	+	150.470i	0.342805	+	0.220307i	0.700703	−	0.713453i	$-0.252870\pi$
$683$	234.136	+	150.470i	0.342805	+	0.220307i	−0.357898	+	0.933761i	$0.616506\pi$
$684$	−27.0773	−	92.2167i	−0.0395866	−	0.134820i
$685$	−68.2175	−	78.7272i	−0.0995876	−	0.114930i
$686$	155.349	−	529.071i	0.226457	−	0.771241i
$687$	−376.375	+	171.885i	−0.547853	+	0.250196i
$688$	552.424	+	79.4266i	0.802942	+	0.115446i
$689$			46.8862i			0.0680497i
$690$	36.7397	+	114.479i	0.0532459	+	0.165911i
$691$	−614.217			−0.888881			−0.444441	−	0.895808i	$-0.646598\pi$
$691$	−614.217			−0.888881			−0.444441	+	0.895808i	$0.646598\pi$
$692$	−141.022	+	980.830i	−0.203789	+	1.41738i
$693$	−62.4284	−	136.699i	−0.0900843	−	0.197257i
$694$	−267.886	−	78.6584i	−0.386003	−	0.113341i
$695$	−219.681	+	190.355i	−0.316088	+	0.273892i
$696$	−468.229	+	137.484i	−0.672743	+	0.197535i
$697$	793.555	−	1234.80i	1.13853	−	1.77159i
$698$	−166.106	+	363.722i	−0.237974	+	0.521091i
$699$	−463.540	+	534.954i	−0.663147	+	0.765313i
$700$	−413.407	−	643.274i	−0.590581	−	0.918962i
$701$	679.288	−	97.6669i	0.969027	−	0.139325i	0.360414	−	0.932792i	$-0.382635\pi$
$701$	679.288	−	97.6669i	0.969027	−	0.139325i	0.608613	+	0.793467i	$0.291726\pi$
$702$	7.71363	+	53.6495i	0.0109881	+	0.0764237i
$703$	126.459	−	81.2703i	0.179885	−	0.115605i
$704$	−8.08188	−	7.00299i	−0.0114799	−	0.00994742i
$705$	−242.170	−	110.595i	−0.343503	−	0.156873i
$706$	114.108	+	73.3328i	0.161626	+	0.103871i
$707$	227.690	+	775.440i	0.322051	+	1.09680i
$708$	362.389	+	418.220i	0.511850	+	0.590706i
$709$	−296.712	+	1010.51i	−0.418494	+	1.42526i	0.433237	+	0.901280i	$0.357371\pi$
$709$	−296.712	+	1010.51i	−0.418494	+	1.42526i	−0.851731	+	0.523979i	$0.824447\pi$
$710$	−59.7272	+	27.2765i	−0.0841229	+	0.0384176i
$711$	−286.507	−	41.1935i	−0.402964	−	0.0579374i
$712$			427.087i			0.599841i
$713$	−5.69880	−	11.6973i	−0.00799271	−	0.0164058i
$714$	−659.317			−0.923413
$715$	3.28177	−	22.8252i	0.00458988	−	0.0319233i
$716$	−430.488	−	942.637i	−0.601240	−	1.31653i
$717$	−405.158	−	118.965i	−0.565073	−	0.165921i
$718$	339.440	−	294.126i	0.472757	−	0.409646i
$719$	−534.036	+	156.807i	−0.742748	+	0.218090i	−0.631148	−	0.775663i	$-0.717416\pi$
$719$	−534.036	+	156.807i	−0.742748	+	0.218090i	−0.111600	+	0.993753i	$0.535598\pi$
$720$	−26.2247	+	40.8065i	−0.0364232	+	0.0566756i
$721$	−346.707	+	759.182i	−0.480870	+	1.05296i
$722$	137.284	−	158.435i	0.190145	−	0.219438i
$723$	−403.775	−	628.286i	−0.558472	−	0.868999i
$724$	450.426	−	64.7615i	0.622135	−	0.0894496i
$725$	84.6225	+	588.563i	0.116721	+	0.811811i
$726$	184.362	−	118.482i	0.253942	−	0.163199i
$727$	973.708	+	843.723i	1.33935	+	1.16055i	0.973190	+	0.230003i	$0.0738735\pi$
$727$	973.708	+	843.723i	1.33935	+	1.16055i	0.366161	+	0.930552i	$0.380672\pi$
$728$	148.818	+	67.9631i	0.204421	+	0.0933559i
$729$	670.154	+	430.682i	0.919278	+	0.590784i
$730$	−47.3283	−	161.185i	−0.0648332	−	0.220802i
$731$	−1204.33	−	1389.87i	−1.64751	−	1.90133i
$732$	−44.2028	+	150.541i	−0.0603863	+	0.205657i
$733$	−1119.54	+	511.277i	−1.52734	+	0.697513i	−0.989366	−	0.145449i	$-0.953537\pi$
$733$	−1119.54	+	511.277i	−1.52734	+	0.697513i	−0.537974	+	0.842961i	$0.680810\pi$
$734$	433.212	+	62.2865i	0.590207	+	0.0848590i
$735$		−	605.520i		−	0.823837i
$736$	121.820	+	719.391i	0.165517	+	0.977433i
$737$	−231.309			−0.313852
$738$	19.9201	−	138.547i	0.0269920	−	0.187733i
$739$	153.018	+	335.062i	0.207060	+	0.453399i	0.984460	−	0.175608i	$-0.0561891\pi$
$739$	153.018	+	335.062i	0.207060	+	0.453399i	−0.777400	+	0.629007i	$0.783462\pi$
$740$	−102.227	−	30.0165i	−0.138144	−	0.0405628i
$741$	−44.0715	+	38.1882i	−0.0594757	+	0.0515360i
$742$	−225.825	+	66.3082i	−0.304346	+	0.0893641i
$743$	10.3856	−	16.1603i	0.0139780	−	0.0217501i	−0.834194	−	0.551471i	$-0.814067\pi$
$743$	10.3856	−	16.1603i	0.0139780	−	0.0217501i	0.848172	+	0.529721i	$0.177703\pi$
$744$	3.71584	−	8.13655i	0.00499440	−	0.0109362i
$745$	175.477	−	202.511i	0.235540	−	0.271827i
$746$	278.153	+	432.814i	0.372859	+	0.580179i
$747$	268.638	−	38.6243i	0.359623	−	0.0517059i
$748$	51.7058	+	359.622i	0.0691255	+	0.480778i
$749$	516.754	−	332.098i	0.689925	−	0.443388i
$750$	174.876	+	151.531i	0.233168	+	0.202042i
$751$	−719.664	−	328.660i	−0.958274	−	0.437629i	−0.126023	−	0.992027i	$-0.540221\pi$
$751$	−719.664	−	328.660i	−0.958274	−	0.437629i	−0.832252	+	0.554398i	$0.812949\pi$
$752$	−279.173	−	179.414i	−0.371241	−	0.238582i
$753$	−12.9246	−	44.0172i	−0.0171642	−	0.0584558i
$754$	−37.3023	−	43.0492i	−0.0494726	−	0.0570944i
$755$	41.0220	−	139.708i	0.0543337	−	0.185044i
$756$	1060.27	−	484.207i	1.40247	−	0.640486i
$757$	−173.205	−	24.9032i	−0.228805	−	0.0328972i	0.0269585	−	0.999637i	$-0.491418\pi$
$757$	−173.205	−	24.9032i	−0.228805	−	0.0328972i	−0.255764	+	0.966739i	$0.582327\pi$
$758$			235.064i			0.310110i
$759$	−260.159	−	30.8031i	−0.342766	−	0.0405838i
$760$	165.341			0.217554
$761$	−31.5438	+	219.392i	−0.0414504	+	0.288294i	0.958544	+	0.284945i	$0.0919752\pi$
$761$	−31.5438	+	219.392i	−0.0414504	+	0.288294i	−0.999994	+	0.00334942i	$0.998934\pi$
$762$	−46.6629	−	102.178i	−0.0612374	−	0.134091i
$763$	−61.5183	−	18.0634i	−0.0806268	−	0.0236742i
$764$	357.192	−	309.509i	0.467529	−	0.405116i
$765$	153.365	−	45.0319i	0.200476	−	0.0588652i
$766$	21.7249	−	33.8046i	0.0283615	−	0.0441313i
$767$	−59.9309	+	131.230i	−0.0781367	+	0.171096i
$768$	−168.848	+	194.860i	−0.219854	+	0.253725i
$769$	309.055	+	480.899i	0.401892	+	0.625357i	0.981933	−	0.189231i	$-0.0605995\pi$
$769$	309.055	+	480.899i	0.401892	+	0.625357i	−0.580040	+	0.814588i	$0.696963\pi$
$770$	114.577	−	16.4737i	0.148802	−	0.0213945i
$771$	−129.676	−	901.915i	−0.168192	−	1.16980i
$772$	−394.173	+	253.319i	−0.510586	+	0.328134i
$773$	−616.249	−	533.983i	−0.797217	−	0.690793i	0.157758	−	0.987478i	$-0.449573\pi$
$773$	−616.249	−	533.983i	−0.797217	−	0.690793i	−0.954975	+	0.296685i	$0.904119\pi$
$774$	−159.527	−	72.8537i	−0.206108	−	0.0941262i
$775$	−9.16897	−	5.89254i	−0.0118309	−	0.00760328i
$776$	−105.072	−	357.842i	−0.135402	−	0.461137i
$777$	275.884	+	318.387i	0.355063	+	0.409765i
$778$	−126.372	+	430.384i	−0.162432	+	0.553192i
$779$	592.795	−	270.720i	0.760969	−	0.347523i
$780$	40.9106	+	5.88206i	0.0524495	+	0.00754110i
$781$		−	143.073i		−	0.183192i
$782$	256.543	−	421.975i	0.328061	−	0.539610i
$783$	−906.392			−1.15759
$784$	107.417	−	747.099i	0.137011	−	0.952932i
$785$	−92.9173	−	203.461i	−0.118366	−	0.259185i
$786$	97.2856	+	28.5656i	0.123773	+	0.0363430i
$787$	103.291	−	89.5026i	0.131247	−	0.113726i	−0.586764	−	0.809758i	$-0.699598\pi$
$787$	103.291	−	89.5026i	0.131247	−	0.113726i	0.718011	+	0.696032i	$0.245053\pi$
$788$	951.071	−	279.260i	1.20694	−	0.354391i
$789$	9.08191	−	14.1317i	0.0115107	−	0.0179109i
$790$	92.6196	−	202.809i	0.117240	−	0.256720i
$791$	315.316	−	363.894i	0.398629	−	0.460042i
$792$	41.8352	+	65.0968i	0.0528222	+	0.0821929i
$793$	−40.4866	+	5.82109i	−0.0510550	+	0.00734059i
$794$	1.58802	+	11.0449i	0.00200002	+	0.0139105i
$795$	−111.716	+	71.7957i	−0.140524	+	0.0903090i
$796$	−240.940	−	208.776i	−0.302689	−	0.262281i
$797$	1077.16	+	491.921i	1.35152	+	0.617216i	0.953841	−	0.300311i	$-0.0970903\pi$
$797$	1077.16	+	491.921i	1.35152	+	0.617216i	0.397674	+	0.917527i	$0.369818\pi$
$798$	−246.259	−	158.261i	−0.308595	−	0.198322i
$799$	308.081	+	1049.23i	0.385583	+	1.31318i
$800$	400.234	+	461.895i	0.500293	+	0.577368i
$801$	−51.6447	+	175.886i	−0.0644753	+	0.219583i
$802$	591.233	−	270.007i	0.737198	−	0.336667i
$803$	362.319	+	52.0936i	0.451206	+	0.0648737i
$804$		−	414.586i		−	0.515654i
$805$	575.963	+	350.162i	0.715482	+	0.434984i
$806$	1.04411			0.00129542
$807$	51.1419	−	355.700i	0.0633729	−	0.440768i
$808$	−172.871	−	378.534i	−0.213949	−	0.468483i
$809$	−291.078	−	85.4683i	−0.359800	−	0.105647i	0.0968362	−	0.995300i	$-0.469128\pi$
$809$	−291.078	−	85.4683i	−0.359800	−	0.105647i	−0.456636	+	0.889654i	$0.650946\pi$
$810$	−77.6895	+	67.3183i	−0.0959130	+	0.0831091i
$811$	1117.44	−	328.109i	1.37785	−	0.404573i	0.492829	−	0.870126i	$-0.335963\pi$
$811$	1117.44	−	328.109i	1.37785	−	0.404573i	0.885020	+	0.465553i	$0.154144\pi$
$812$	−662.272	+	1030.52i	−0.815606	+	1.26911i
$813$	87.4449	−	191.478i	0.107558	−	0.235520i
$814$	−35.4868	+	40.9539i	−0.0435955	+	0.0503119i
$815$	86.1927	+	134.118i	0.105758	+	0.164562i
$816$	−458.990	+	65.9928i	−0.562488	+	0.0808735i
$817$	−116.203	−	808.210i	−0.142231	−	0.989241i
$818$	−9.59587	+	6.16689i	−0.0117309	+	0.00753898i
$819$	53.0691	+	45.9846i	0.0647974	+	0.0561473i
$820$	−420.150	−	191.876i	−0.512378	−	0.233995i
$821$	−36.7567	−	23.6221i	−0.0447707	−	0.0287724i	0.518064	−	0.855342i	$-0.326653\pi$
$821$	−36.7567	−	23.6221i	−0.0447707	−	0.0287724i	−0.562835	+	0.826569i	$0.690289\pi$
$822$	−26.7547	−	91.1182i	−0.0325483	−	0.110849i
$823$	483.809	+	558.345i	0.587860	+	0.678427i	0.969276	−	0.245977i	$-0.0791088\pi$
$823$	483.809	+	558.345i	0.587860	+	0.678427i	−0.381416	+	0.924404i	$0.624563\pi$
$824$	121.074	−	412.339i	0.146934	−	0.500412i
$825$	−199.613	+	91.1602i	−0.241955	+	0.110497i
$826$	−716.820	−	103.063i	−0.867821	−	0.124774i
$827$			24.4729i			0.0295923i	0.999891	+	0.0147962i	$0.00470994\pi$
$827$			24.4729i			0.0295923i	−0.999891	+	0.0147962i	$0.995290\pi$
$828$	−23.7217	+	200.350i	−0.0286494	+	0.241969i
$829$	−407.964			−0.492115			−0.246058	−	0.969255i	$-0.579135\pi$
$829$	−407.964			−0.492115			−0.246058	+	0.969255i	$0.579135\pi$
$830$	−29.7511	+	206.923i	−0.0358447	+	0.249305i
$831$	54.3934	+	119.105i	0.0654554	+	0.143327i
$832$	4.79446	+	1.40778i	0.00576257	+	0.00169204i
$833$	−1879.66	+	1628.74i	−2.25650	+	1.95527i
$834$	−254.257	+	74.6566i	−0.304864	+	0.0895163i
$835$	−76.9578	+	119.749i	−0.0921650	+	0.143412i
$836$	−67.0104	+	146.732i	−0.0801560	+	0.175517i
$837$	10.8799	−	12.5560i	0.0129986	−	0.0150012i
$838$	46.7760	+	72.7850i	0.0558187	+	0.0868555i
$839$	−1150.22	+	165.376i	−1.37094	+	0.197111i	−0.788135	−	0.615503i	$-0.788953\pi$
$839$	−1150.22	+	165.376i	−1.37094	+	0.197111i	−0.582802	+	0.812614i	$0.698044\pi$
$840$	65.9455	+	458.661i	0.0785066	+	0.546025i
$841$	93.8541	−	60.3164i	0.111598	−	0.0717198i
$842$	450.051	+	389.972i	0.534503	+	0.463149i
$843$	807.077	+	368.580i	0.957387	+	0.437224i
$844$	169.876	+	109.173i	0.201275	+	0.129352i
$845$	−110.978	−	377.957i	−0.131335	−	0.447286i
$846$	68.2888	+	78.8094i	0.0807196	+	0.0931554i
$847$	346.149	−	1178.88i	0.408677	−	1.39183i
$848$	−150.573	+	68.7645i	−0.177563	+	0.0810902i
$849$	−28.4926	−	4.09661i	−0.0335602	−	0.00482522i
$850$		−	413.663i		−	0.486662i
$851$	−311.121	+	52.6847i	−0.365595	+	0.0619092i
$852$	256.436			0.300981
$853$	147.210	−	1023.87i	0.172580	−	1.20032i	−0.700829	−	0.713330i	$-0.747186\pi$
$853$	147.210	−	1023.87i	0.172580	−	1.20032i	0.873408	−	0.486989i	$-0.161905\pi$
$854$	−85.2945	−	186.769i	−0.0998765	−	0.218699i
$855$	68.0919	+	19.9936i	0.0796396	+	0.0233843i
$856$	−239.038	+	207.128i	−0.279250	+	0.241972i
$857$	−1194.74	+	350.809i	−1.39410	+	0.409345i	−0.890654	−	0.454681i	$-0.849753\pi$
$857$	−1194.74	+	350.809i	−1.39410	+	0.409345i	−0.503447	+	0.864026i	$0.667935\pi$
$858$	11.3654	−	17.6848i	0.0132463	−	0.0206117i
$859$	139.752	−	306.015i	0.162692	−	0.356245i	−0.810676	−	0.585495i	$-0.800900\pi$
$859$	139.752	−	306.015i	0.162692	−	0.356245i	0.973368	+	0.229250i	$0.0736273\pi$
$860$	−378.980	+	437.366i	−0.440674	+	0.508565i
$861$	987.421	+	1536.46i	1.14683	+	1.78450i
$862$	−170.470	+	24.5098i	−0.197761	+	0.0284337i
$863$	−160.978	−	1119.63i	−0.186533	−	1.29736i	−0.840901	−	0.541189i	$-0.817975\pi$
$863$	−160.978	−	1119.63i	−0.186533	−	1.29736i	0.654368	−	0.756176i	$-0.272935\pi$
$864$	−783.740	+	503.679i	−0.907107	+	0.582962i
$865$	−552.969	−	479.150i	−0.639270	−	0.553931i
$866$	−455.351	−	207.952i	−0.525809	−	0.240129i
$867$	675.449	+	434.085i	0.779064	+	0.500674i
$868$	−6.32590	−	21.5440i	−0.00728791	−	0.0248203i
$869$	318.141	+	367.154i	0.366100	+	0.422502i
$870$	45.4536	−	154.801i	0.0522455	−	0.177932i
$871$	98.3156	−	44.8992i	0.112877	−	0.0515490i
$872$	32.6777	+	4.69835i	0.0374744	+	0.00538801i
$873$		−	160.075i		−	0.183362i
$874$	197.110	−	96.0299i	0.225527	−	0.109874i
$875$	1297.28			1.48261
$876$	−93.3697	+	649.401i	−0.106586	+	0.741325i
$877$	−579.210	−	1268.29i	−0.660445	−	1.44617i	−0.882107	−	0.471049i	$-0.843876\pi$
$877$	−579.210	−	1268.29i	−0.660445	−	1.44617i	0.221663	−	0.975123i	$-0.428852\pi$
$878$	−500.983	−	147.102i	−0.570596	−	0.167542i
$879$	−430.603	+	373.120i	−0.489878	+	0.424482i
$880$	78.1153	−	22.9367i	0.0887674	−	0.0260645i
$881$	85.9392	−	133.724i	0.0975474	−	0.151787i	−0.789050	−	0.614330i	$-0.789427\pi$
$881$	85.9392	−	133.724i	0.0975474	−	0.151787i	0.886597	+	0.462543i	$0.153063\pi$
$882$	−98.5273	+	215.745i	−0.111709	+	0.244609i
$883$	−98.8702	+	114.102i	−0.111971	+	0.129221i	−0.808968	−	0.587853i	$-0.799974\pi$
$883$	−98.8702	+	114.102i	−0.111971	+	0.129221i	0.696997	+	0.717074i	$0.254519\pi$
$884$	−91.7829	−	142.817i	−0.103827	−	0.161558i
$885$	−404.454	+	58.1517i	−0.457010	+	0.0657082i
$886$	−73.1852	−	509.014i	−0.0826018	−	0.574508i
$887$	193.743	−	124.511i	0.218425	−	0.140373i	−0.426853	−	0.904321i	$-0.640378\pi$
$887$	193.743	−	124.511i	0.218425	−	0.140373i	0.645278	+	0.763948i	$0.276741\pi$
$888$	−163.941	−	142.056i	−0.184619	−	0.159973i
$889$	−572.846	−	261.610i	−0.644371	−	0.294274i
$890$	−118.784	−	76.3378i	−0.133465	−	0.0857728i
$891$	−63.1062	−	214.920i	−0.0708262	−	0.241212i
$892$	−157.572	−	181.848i	−0.176651	−	0.203866i
$893$	−136.784	+	465.844i	−0.153174	+	0.521662i
$894$	222.205	−	101.478i	0.248551	−	0.113510i
$895$	757.393	+	108.897i	0.846249	+	0.121672i
$896$			1578.07i			1.76124i
$897$	116.557	−	37.4067i	0.129941	−	0.0417020i
$898$	80.3096			0.0894316
$899$	−2.48486	+	17.2826i	−0.00276403	+	0.0192243i
$900$	70.2031	+	153.723i	0.0780035	+	0.170804i
$901$	523.365	+	153.674i	0.580872	+	0.170559i
$902$	−177.546	+	153.844i	−0.196836	+	0.170559i
$903$	2195.65	−	644.702i	2.43151	−	0.713956i
$904$	−134.041	+	208.572i	−0.148275	+	0.230721i
$905$	−139.584	+	305.646i	−0.154236	+	0.337730i
$906$	86.9251	−	100.317i	0.0959438	−	0.110725i
$907$	534.275	+	831.349i	0.589058	+	0.916592i	0.999988	+	0.00492501i	$0.00156769\pi$
$907$	534.275	+	831.349i	0.589058	+	0.916592i	−0.410930	+	0.911667i	$0.634796\pi$
$908$	390.772	−	56.1845i	0.430365	−	0.0618772i
$909$	−25.4192	−	176.794i	−0.0279639	−	0.194493i
$910$	−45.5022	+	29.2425i	−0.0500025	+	0.0321346i
$911$	1251.47	+	1084.40i	1.37373	+	1.19034i	0.960020	+	0.279932i	$0.0903120\pi$
$911$	1251.47	+	1084.40i	1.37373	+	1.19034i	0.413708	+	0.910410i	$0.364233\pi$
$912$	−187.276	−	85.5262i	−0.205347	−	0.0937787i
$913$	−383.204	−	246.270i	−0.419719	−	0.269737i
$914$	−71.8480	−	244.692i	−0.0786084	−	0.267715i
$915$	−75.8660	−	87.5541i	−0.0829137	−	0.0956875i
$916$	150.673	−	513.145i	0.164490	−	0.560202i
$917$	517.076	−	236.141i	0.563878	−	0.257514i
$918$	624.142	+	89.7381i	0.679893	+	0.0977539i
$919$			225.730i			0.245626i	0.992430	+	0.122813i	$0.0391915\pi$
$919$			225.730i			0.245626i	−0.992430	+	0.122813i	$0.960808\pi$
$920$	−319.211	−	136.261i	−0.346969	−	0.148110i
$921$	−638.350			−0.693105
$922$	−88.3801	+	614.697i	−0.0958569	+	0.666699i
$923$	27.7717	+	60.8116i	0.0300885	+	0.0658847i
$924$	−433.767	−	127.365i	−0.469445	−	0.137841i
$925$	−199.760	+	173.093i	−0.215956	+	0.187127i
$926$	−212.769	+	62.4748i	−0.229773	+	0.0674673i
$927$	99.7228	−	155.172i	0.107576	−	0.167391i
$928$	406.730	−	890.614i	0.438286	−	0.959713i
$929$	980.710	−	1131.80i	1.05566	−	1.21830i	0.0805117	−	0.996754i	$-0.474345\pi$
$929$	980.710	−	1131.80i	1.05566	−	1.21830i	0.975150	−	0.221545i	$-0.0711100\pi$
$930$	1.59881	+	2.48780i	0.00171916	+	0.00267506i
$931$	−1093.02	+	157.153i	−1.17403	+	0.168800i
$932$	−130.206	−	905.605i	−0.139706	−	0.971679i
$933$	220.512	−	141.714i	0.236347	−	0.151891i
$934$	−282.339	−	244.648i	−0.302290	−	0.261936i
$935$	−244.029	−	111.444i	−0.260993	−	0.119192i
$936$	−30.4175	−	19.5481i	−0.0324973	−	0.0208848i
$937$	−481.933	−	1641.31i	−0.514336	−	1.75167i	−0.649012	−	0.760778i	$-0.724817\pi$
$937$	−481.933	−	1641.31i	−0.514336	−	1.75167i	0.134676	−	0.990890i	$-0.457001\pi$
$938$	355.296	+	410.033i	0.378780	+	0.437136i
$939$	266.767	−	908.525i	0.284097	−	0.967545i
$940$	313.014	−	142.949i	0.332994	−	0.152073i
$941$	1552.86	+	223.268i	1.65022	+	0.237266i	0.903723	−	0.428118i	$-0.140823\pi$
$941$	1552.86	+	223.268i	1.65022	+	0.237266i	0.746501	+	0.665385i	$0.231732\pi$
$942$		−	203.907i		−	0.216461i
$943$	−1367.57	+	34.1242i	−1.45023	+	0.0361868i
$944$	−509.337			−0.539552
$945$	−122.486	+	851.906i	−0.129614	+	0.901488i
$946$	122.277	+	267.749i	0.129257	+	0.283032i
$947$	−299.799	−	88.0289i	−0.316578	−	0.0929556i	0.119584	−	0.992824i	$-0.461844\pi$
$947$	−299.799	−	88.0289i	−0.316578	−	0.0929556i	−0.436161	+	0.899869i	$0.643662\pi$
$948$	−658.068	+	570.219i	−0.694165	+	0.601497i
$949$	−164.112	+	48.1875i	−0.172931	+	0.0507771i
$950$	99.2946	−	154.505i	0.104521	−	0.162637i
$951$	−95.0931	+	208.225i	−0.0999927	+	0.218954i
$952$	1246.40	−	1438.42i	1.30925	−	1.51095i
$953$	−819.707	−	1275.49i	−0.860133	−	1.33839i	−0.939854	−	0.341576i	$-0.889039\pi$
$953$	−819.707	−	1275.49i	−0.860133	−	1.33839i	0.0797209	−	0.996817i	$-0.474597\pi$
$954$	51.4864	−	7.40262i	0.0539689	−	0.00775956i
$955$	49.6661	+	345.435i	0.0520064	+	0.361712i
$956$	459.148	−	295.076i	0.480280	−	0.308657i
$957$	265.680	+	230.213i	0.277618	+	0.240557i
$958$	417.258	+	190.555i	0.435551	+	0.198910i
$959$	−447.891	−	287.842i	−0.467040	−	0.300148i
$960$	3.98730	+	13.5795i	0.00415344	+	0.0141453i
$961$	629.112	+	726.033i	0.654643	+	0.755498i
$962$	7.13375	−	24.2953i	0.00741554	−	0.0252550i
$963$	−123.489	+	56.3955i	−0.128234	+	0.0585623i
$964$	955.501	+	137.380i	0.991183	+	0.142511i
$965$		−	345.976i		−	0.358524i
$966$	345.007	+	508.489i	0.357150	+	0.526386i
$967$	−1342.02			−1.38781			−0.693907	−	0.720065i	$-0.744112\pi$
$967$	−1342.02			−1.38781			−0.693907	+	0.720065i	$0.744112\pi$
$968$	−90.0346	+	626.204i	−0.0930109	+	0.646905i
$969$	281.825	+	617.112i	0.290841	+	0.636854i
$970$	118.306	+	34.7377i	0.121965	+	0.0358121i
$971$	695.073	−	602.284i	0.715832	−	0.620272i	−0.218849	−	0.975759i	$-0.570230\pi$
$971$	695.073	−	602.284i	0.715832	−	0.620272i	0.934681	+	0.355487i	$0.115685\pi$
$972$	−437.223	+	128.380i	−0.449818	+	0.132078i
$973$	−803.197	+	1249.80i	−0.825485	+	1.28448i
$974$	−133.452	+	292.219i	−0.137014	+	0.300019i
$975$	67.1484	−	77.4934i	0.0688701	−	0.0794804i
$976$	−78.0728	−	121.484i	−0.0799927	−	0.124471i
$977$	58.5229	−	8.41432i	0.0599006	−	0.00861241i	−0.112299	−	0.993674i	$-0.535822\pi$
$977$	58.5229	−	8.41432i	0.0599006	−	0.00861241i	0.172200	+	0.985062i	$0.444912\pi$
$978$	20.6837	+	143.858i	0.0211490	+	0.147094i
$979$	258.826	−	166.337i	0.264378	−	0.169905i
$980$	591.494	+	512.532i	0.603565	+	0.522992i
$981$	12.8894	+	5.88640i	0.0131391	+	0.00600041i
$982$	265.033	+	170.326i	0.269891	+	0.173448i
$983$	−102.544	−	349.232i	−0.104317	−	0.355271i	0.890748	−	0.454498i	$-0.150181\pi$
$983$	−102.544	−	349.232i	−0.104317	−	0.355271i	−0.995065	+	0.0992267i	$0.968363\pi$
$984$	−615.850	−	710.729i	−0.625864	−	0.722285i
$985$	−206.203	+	702.262i	−0.209343	+	0.712956i
$986$	−602.796	+	275.288i	−0.611355	+	0.279197i
$987$	−1346.82	−	193.644i	−1.36456	−	0.196194i
$988$		−	75.3743i		−	0.0762898i
$989$	−441.718	+	1656.11i	−0.446631	+	1.67453i
$990$	−25.5828			−0.0258412
$991$	−71.3199	+	496.041i	−0.0719676	+	0.500546i	0.921675	+	0.387963i	$0.126821\pi$
$991$	−71.3199	+	496.041i	−0.0719676	+	0.500546i	−0.993642	+	0.112582i	$0.964088\pi$
$992$	7.45528	+	16.3248i	0.00751540	+	0.0164564i
$993$	−1330.37	−	390.632i	−1.33975	−	0.393386i
$994$	−253.620	+	219.763i	−0.255151	+	0.221089i
$995$	225.870	−	66.3215i	0.227005	−	0.0666548i
$996$	441.401	−	686.834i	0.443174	−	0.689592i
$997$	−193.733	+	424.217i	−0.194316	+	0.425493i	−0.981561	−	0.191147i	$-0.938779\pi$
$997$	−193.733	+	424.217i	−0.194316	+	0.425493i	0.787245	+	0.616640i	$0.211507\pi$
$998$	−395.837	+	456.820i	−0.396630	+	0.457736i
$999$	−217.831	−	338.951i	−0.218049	−	0.339290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.15.2	✓	30
3.2	odd	2		207.3.j.a.199.2		30
4.3	odd	2		368.3.p.a.337.3		30
23.7	odd	22		529.3.b.b.528.11		30
23.16	even	11		529.3.b.b.528.12		30
23.20	odd	22	inner	23.3.d.a.20.2	yes	30
69.20	even	22		207.3.j.a.181.2		30
92.43	even	22		368.3.p.a.273.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.15.2	✓	30	1.1	even	1	trivial
23.3.d.a.20.2	yes	30	23.20	odd	22	inner
207.3.j.a.181.2		30	69.20	even	22
207.3.j.a.199.2		30	3.2	odd	2
368.3.p.a.273.3		30	92.43	even	22
368.3.p.a.337.3		30	4.3	odd	2
529.3.b.b.528.11		30	23.7	odd	22
529.3.b.b.528.12		30	23.16	even	11

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.123822 - 0.861198i) q^{2} +(-1.04228 - 2.28229i) q^{3} +(3.11164 + 0.913660i) q^{4} +(-1.80972 + 1.56813i) q^{5} +(-2.09456 + 0.615017i) q^{6} +(-6.61670 + 10.2958i) q^{7} +(2.61786 - 5.73232i) q^{8} +(1.77128 - 2.04416i) q^{9} +O(q^{10})\)	\(q+(0.123822 - 0.861198i) q^{2} +(-1.04228 - 2.28229i) q^{3} +(3.11164 + 0.913660i) q^{4} +(-1.80972 + 1.56813i) q^{5} +(-2.09456 + 0.615017i) q^{6} +(-6.61670 + 10.2958i) q^{7} +(2.61786 - 5.73232i) q^{8} +(1.77128 - 2.04416i) q^{9} +(1.12639 + 1.75270i) q^{10} +(-4.49352 + 0.646071i) q^{11} +(-1.15798 - 8.05395i) q^{12} +(1.78452 - 1.14684i) q^{13} +(8.04742 + 6.97313i) q^{14} +(5.46517 + 2.49586i) q^{15} +(6.30025 + 4.04892i) q^{16} +(-6.95262 - 23.6785i) q^{17} +(-1.54111 - 1.77853i) q^{18} +(3.08688 - 10.5129i) q^{19} +(-7.06394 + 3.22599i) q^{20} +(30.3944 + 4.37005i) q^{21} +3.94981i q^{22} +(-14.6235 + 17.7525i) q^{23} -15.8114 q^{24} +(-2.74182 + 19.0698i) q^{25} +(-0.766694 - 1.67883i) q^{26} +(-28.1780 - 8.27382i) q^{27} +(-29.9956 + 25.9914i) q^{28} +(29.6135 - 8.69529i) q^{29} +(2.82613 - 4.39755i) q^{30} +(-0.235011 + 0.514601i) q^{31} +(20.7742 - 23.9748i) q^{32} +(6.15805 + 9.58211i) q^{33} +(-21.2527 + 3.05568i) q^{34} +(-4.17077 - 29.0083i) q^{35} +(7.37925 - 4.74236i) q^{36} +(10.3686 + 8.98442i) q^{37} +(-8.67149 - 3.96014i) q^{38} +(-4.47739 - 2.87744i) q^{39} +(4.25144 + 14.4791i) q^{40} +(38.9498 + 44.9505i) q^{41} +(7.52696 - 25.6345i) q^{42} +(67.7877 - 30.9576i) q^{43} +(-14.5725 - 2.09521i) q^{44} +6.47696i q^{45} +(13.4777 + 14.7919i) q^{46} -44.3115 q^{47} +(2.67415 - 18.5991i) q^{48} +(-41.8671 - 91.6762i) q^{49} +(16.0834 + 4.72250i) q^{50} +(-46.7944 + 40.5476i) q^{51} +(6.60060 - 1.93811i) q^{52} +(-11.9498 + 18.5942i) q^{53} +(-10.6144 + 23.2424i) q^{54} +(7.11890 - 8.21564i) q^{55} +(41.6971 + 64.8820i) q^{56} +(-27.2109 + 3.91234i) q^{57} +(-3.82158 - 26.5797i) q^{58} +(-57.2139 + 36.7691i) q^{59} +(14.7253 + 12.7595i) q^{60} +(-17.5399 - 8.01019i) q^{61} +(0.414074 + 0.266109i) q^{62} +(9.32625 + 31.7623i) q^{63} +(1.54260 + 1.78025i) q^{64} +(-1.43108 + 4.87382i) q^{65} +(9.01459 - 4.11683i) q^{66} +(50.4336 + 7.25125i) q^{67} -80.0312i q^{68} +(55.7582 + 14.8718i) q^{69} -25.4984 q^{70} +(-4.48515 + 31.1949i) q^{71} +(-7.08084 - 15.5049i) q^{72} +(-77.3652 - 22.7165i) q^{73} +(9.02122 - 7.81693i) q^{74} +(46.3804 - 13.6185i) q^{75} +(19.2105 - 29.8921i) q^{76} +(23.0805 - 50.5392i) q^{77} +(-3.03245 + 3.49963i) q^{78} +(-57.8562 - 90.0260i) q^{79} +(-17.7509 + 2.55220i) q^{80} +(7.02190 + 48.8384i) q^{81} +(43.5341 - 27.9777i) q^{82} +(75.8317 + 65.7085i) q^{83} +(90.5837 + 41.3682i) q^{84} +(49.7133 + 31.9488i) q^{85} +(-18.2671 - 62.2119i) q^{86} +(-50.7108 - 58.5234i) q^{87} +(-8.05994 + 27.4496i) q^{88} +(-61.6477 + 28.1536i) q^{89} +(5.57795 + 0.801988i) q^{90} +25.9613i q^{91} +(-61.7229 + 41.8786i) q^{92} +1.41942 q^{93} +(-5.48672 + 38.1610i) q^{94} +(10.8993 + 23.8661i) q^{95} +(-76.3699 - 22.4242i) q^{96} +(44.7263 - 38.7555i) q^{97} +(-84.1354 + 24.7044i) q^{98} +(-6.63860 + 10.3299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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