LMFDB - Embedded newform 23.3.d.a.15.1

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			15.1
Character	$\chi$	$=$	23.15
Dual form			23.3.d.a.20.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.387684 + 2.69640i) q^{2} +(-0.141551 - 0.309954i) q^{3} +(-3.28232 - 0.963778i) q^{4} +(-0.353921 + 0.306674i) q^{5} +(0.890639 - 0.261515i) q^{6} +(4.93105 - 7.67286i) q^{7} +(-0.655341 + 1.43500i) q^{8} +(5.81771 - 6.71400i) q^{9} +O(q^{10})$	\(q+(-0.387684 + 2.69640i) q^{2} +(-0.141551 - 0.309954i) q^{3} +(-3.28232 - 0.963778i) q^{4} +(-0.353921 + 0.306674i) q^{5} +(0.890639 - 0.261515i) q^{6} +(4.93105 - 7.67286i) q^{7} +(-0.655341 + 1.43500i) q^{8} +(5.81771 - 6.71400i) q^{9} +(-0.689708 - 1.07321i) q^{10} +(-9.31650 + 1.33951i) q^{11} +(0.165891 + 1.15379i) q^{12} +(-15.9918 + 10.2773i) q^{13} +(18.7774 + 16.2708i) q^{14} +(0.145153 + 0.0662892i) q^{15} +(-15.1266 - 9.72129i) q^{16} +(2.33367 + 7.94773i) q^{17} +(15.8482 + 18.2898i) q^{18} +(4.88047 - 16.6214i) q^{19} +(1.45725 - 0.665504i) q^{20} +(-3.07623 - 0.442296i) q^{21} -25.6404i q^{22} +(22.6732 + 3.86340i) q^{23} +0.537548 q^{24} +(-3.52666 + 24.5285i) q^{25} +(-21.5119 - 47.1046i) q^{26} +(-5.84704 - 1.71684i) q^{27} +(-23.5802 + 20.4324i) q^{28} +(-20.1778 + 5.92475i) q^{29} +(-0.235016 + 0.365692i) q^{30} +(8.08126 - 17.6955i) q^{31} +(27.9446 - 32.2498i) q^{32} +(1.73395 + 2.69808i) q^{33} +(-22.3350 + 3.21129i) q^{34} +(0.607868 + 4.22781i) q^{35} +(-25.5664 + 16.4305i) q^{36} +(48.8134 + 42.2971i) q^{37} +(42.9259 + 19.6036i) q^{38} +(5.44914 + 3.50195i) q^{39} +(-0.208138 - 0.708852i) q^{40} +(-12.8853 - 14.8704i) q^{41} +(2.38522 - 8.12330i) q^{42} +(13.8027 - 6.30346i) q^{43} +(31.8708 + 4.58232i) q^{44} +4.16037i q^{45} +(-19.2073 + 59.6383i) q^{46} -66.5445 q^{47} +(-0.871962 + 6.06463i) q^{48} +(-14.2022 - 31.0986i) q^{49} +(-64.7714 - 19.0186i) q^{50} +(2.13310 - 1.84834i) q^{51} +(62.3951 - 18.3209i) q^{52} +(-13.4576 + 20.9404i) q^{53} +(6.89611 - 15.1004i) q^{54} +(2.88651 - 3.33121i) q^{55} +(7.77901 + 12.1044i) q^{56} +(-5.84270 + 0.840054i) q^{57} +(-8.15288 - 56.7045i) q^{58} +(43.0416 - 27.6611i) q^{59} +(-0.412551 - 0.357478i) q^{60} +(-54.7720 - 25.0135i) q^{61} +(44.5812 + 28.6506i) q^{62} +(-22.8282 - 77.7455i) q^{63} +(29.0244 + 33.4959i) q^{64} +(2.50804 - 8.54160i) q^{65} +(-7.94734 + 3.62943i) q^{66} +(70.5025 + 10.1367i) q^{67} -28.3362i q^{68} +(-2.01195 - 7.57453i) q^{69} -11.6356 q^{70} +(-2.48696 + 17.2972i) q^{71} +(5.82198 + 12.7484i) q^{72} +(56.1087 + 16.4750i) q^{73} +(-132.974 + 115.223i) q^{74} +(8.10191 - 2.37893i) q^{75} +(-32.0386 + 49.8530i) q^{76} +(-35.6622 + 78.0894i) q^{77} +(-11.5552 + 13.3354i) q^{78} +(44.6512 + 69.4787i) q^{79} +(8.33490 - 1.19838i) q^{80} +(-11.0833 - 77.0859i) q^{81} +(45.0920 - 28.9789i) q^{82} +(-92.3345 - 80.0083i) q^{83} +(9.67092 + 4.41656i) q^{84} +(-3.26330 - 2.09719i) q^{85} +(11.6456 + 39.6613i) q^{86} +(4.69260 + 5.41555i) q^{87} +(4.18329 - 14.2470i) q^{88} +(160.216 - 73.1683i) q^{89} +(-11.2180 - 1.61291i) q^{90} +173.380i q^{91} +(-70.6974 - 34.5329i) q^{92} -6.62871 q^{93} +(25.7983 - 179.431i) q^{94} +(3.37004 + 7.37937i) q^{95} +(-13.9515 - 4.09654i) q^{96} +(71.9579 - 62.3518i) q^{97} +(89.3603 - 26.2385i) q^{98} +(-45.2072 + 70.3438i) 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 $

$2$	−0.387684	+	2.69640i	−0.193842	+	1.34820i	0.627878	+	0.778311i	$0.283924\pi$
$2$	−0.387684	+	2.69640i	−0.193842	+	1.34820i	−0.821721	+	0.569891i	$0.806986\pi$
$3$	−0.141551	−	0.309954i	−0.0471838	−	0.103318i	0.884572	−	0.466404i	$-0.154451\pi$
$3$	−0.141551	−	0.309954i	−0.0471838	−	0.103318i	−0.931756	+	0.363086i	$0.881723\pi$
$4$	−3.28232	−	0.963778i	−0.820581	−	0.240944i
$5$	−0.353921	+	0.306674i	−0.0707842	+	0.0613349i	−0.689534	−	0.724253i	$-0.742185\pi$
$5$	−0.353921	+	0.306674i	−0.0707842	+	0.0613349i	0.618750	+	0.785588i	$0.287639\pi$
$6$	0.890639	−	0.261515i	0.148440	−	0.0435859i
$7$	4.93105	−	7.67286i	0.704436	−	1.09612i	−0.286011	−	0.958226i	$-0.592329\pi$
$7$	4.93105	−	7.67286i	0.704436	−	1.09612i	0.990447	−	0.137897i	$-0.0440342\pi$
$8$	−0.655341	+	1.43500i	−0.0819176	+	0.179375i
$9$	5.81771	−	6.71400i	0.646412	−	0.746000i
$10$	−0.689708	−	1.07321i	−0.0689708	−	0.107321i
$11$	−9.31650	+	1.33951i	−0.846954	+	0.121774i	−0.552110	−	0.833772i	$-0.686177\pi$
$11$	−9.31650	+	1.33951i	−0.846954	+	0.121774i	−0.294845	+	0.955545i	$0.595268\pi$
$12$	0.165891	+	1.15379i	0.0138242	+	0.0961496i
$13$	−15.9918	+	10.2773i	−1.23014	+	0.790560i	−0.983912	−	0.178653i	$-0.942826\pi$
$13$	−15.9918	+	10.2773i	−1.23014	+	0.790560i	−0.246223	+	0.969213i	$0.579190\pi$
$14$	18.7774	+	16.2708i	1.34125	+	1.16220i
$15$	0.145153	+	0.0662892i	0.00967687	+	0.00441928i
$16$	−15.1266	−	9.72129i	−0.945414	−	0.607581i
$17$	2.33367	+	7.94773i	0.137274	+	0.467514i	0.999220	−	0.0394869i	$-0.0125723\pi$
$17$	2.33367	+	7.94773i	0.137274	+	0.467514i	−0.861946	+	0.507001i	$0.830754\pi$
$18$	15.8482	+	18.2898i	0.880456	+	1.01610i
$19$	4.88047	−	16.6214i	0.256867	−	0.874809i	−0.725559	−	0.688159i	$-0.758419\pi$
$19$	4.88047	−	16.6214i	0.256867	−	0.874809i	0.982427	−	0.186650i	$-0.0597629\pi$
$20$	1.45725	−	0.665504i	0.0728625	−	0.0332752i
$21$	−3.07623	−	0.442296i	−0.146487	−	0.0210617i
$22$		−	25.6404i		−	1.16547i
$23$	22.6732	+	3.86340i	0.985791	+	0.167974i
$23$	22.6732	+	3.86340i	0.985791	+	0.167974i
$24$	0.537548			0.0223978
$25$	−3.52666	+	24.5285i	−0.141066	+	0.981138i
$26$	−21.5119	−	47.1046i	−0.827382	−	1.81171i
$27$	−5.84704	−	1.71684i	−0.216557	−	0.0635868i
$28$	−23.5802	+	20.4324i	−0.842151	+	0.729728i
$29$	−20.1778	+	5.92475i	−0.695788	+	0.204302i	−0.610455	−	0.792051i	$-0.709013\pi$
$29$	−20.1778	+	5.92475i	−0.695788	+	0.204302i	−0.0853325	+	0.996353i	$0.527195\pi$
$30$	−0.235016	+	0.365692i	−0.00783387	+	0.0121897i
$31$	8.08126	−	17.6955i	0.260686	−	0.570822i	−0.733353	−	0.679848i	$-0.762046\pi$
$31$	8.08126	−	17.6955i	0.260686	−	0.570822i	0.994039	+	0.109026i	$0.0347731\pi$
$32$	27.9446	−	32.2498i	0.873268	−	1.00780i
$33$	1.73395	+	2.69808i	0.0525440	+	0.0817600i
$34$	−22.3350	+	3.21129i	−0.656913	+	0.0944498i
$35$	0.607868	+	4.22781i	0.0173676	+	0.120795i
$36$	−25.5664	+	16.4305i	−0.710178	+	0.456404i
$37$	48.8134	+	42.2971i	1.31928	+	1.14316i	0.979229	+	0.202758i	$0.0649906\pi$
$37$	48.8134	+	42.2971i	1.31928	+	1.14316i	0.340053	+	0.940406i	$0.389555\pi$
$38$	42.9259	+	19.6036i	1.12963	+	0.515884i
$39$	5.44914	+	3.50195i	0.139722	+	0.0897936i
$40$	−0.208138	−	0.708852i	−0.00520344	−	0.0177213i
$41$	−12.8853	−	14.8704i	−0.314275	−	0.362693i	0.576532	−	0.817075i	$-0.304406\pi$
$41$	−12.8853	−	14.8704i	−0.314275	−	0.362693i	−0.890807	+	0.454382i	$0.849860\pi$
$42$	2.38522	−	8.12330i	0.0567909	−	0.193412i
$43$	13.8027	−	6.30346i	0.320992	−	0.146592i	−0.248402	−	0.968657i	$-0.579905\pi$
$43$	13.8027	−	6.30346i	0.320992	−	0.146592i	0.569394	+	0.822065i	$0.307178\pi$
$44$	31.8708	+	4.58232i	0.724336	+	0.104144i
$45$			4.16037i			0.0924526i
$46$	−19.2073	+	59.6383i	−0.417551	+	1.29649i
$47$	−66.5445			−1.41584			−0.707920	−	0.706293i	$-0.750366\pi$
$47$	−66.5445			−1.41584			−0.707920	+	0.706293i	$0.750366\pi$
$48$	−0.871962	+	6.06463i	−0.0181659	+	0.126346i
$49$	−14.2022	−	31.0986i	−0.289841	−	0.634664i
$50$	−64.7714	−	19.0186i	−1.29543	−	0.380372i
$51$	2.13310	−	1.84834i	0.0418255	−	0.0362420i
$52$	62.3951	−	18.3209i	1.19991	−	0.352324i
$53$	−13.4576	+	20.9404i	−0.253917	+	0.395102i	−0.944688	−	0.327971i	$-0.893635\pi$
$53$	−13.4576	+	20.9404i	−0.253917	+	0.395102i	0.690771	+	0.723074i	$0.257271\pi$
$54$	6.89611	−	15.1004i	0.127706	−	0.279637i
$55$	2.88651	−	3.33121i	0.0524820	−	0.0605675i
$56$	7.77901	+	12.1044i	0.138911	+	0.216150i
$57$	−5.84270	+	0.840054i	−0.102504	+	0.0147378i
$58$	−8.15288	−	56.7045i	−0.140567	−	0.977665i
$59$	43.0416	−	27.6611i	0.729518	−	0.468833i	−0.122418	−	0.992479i	$-0.539065\pi$
$59$	43.0416	−	27.6611i	0.729518	−	0.468833i	0.851936	+	0.523646i	$0.175428\pi$
$60$	−0.412551	−	0.357478i	−0.00687586	−	0.00595796i
$61$	−54.7720	−	25.0135i	−0.897902	−	0.410058i	−0.0876578	−	0.996151i	$-0.527938\pi$
$61$	−54.7720	−	25.0135i	−0.897902	−	0.410058i	−0.810244	+	0.586093i	$0.800665\pi$
$62$	44.5812	+	28.6506i	0.719052	+	0.462106i
$63$	−22.8282	−	77.7455i	−0.362352	−	1.23406i
$64$	29.0244	+	33.4959i	0.453505	+	0.523373i
$65$	2.50804	−	8.54160i	0.0385852	−	0.131409i
$66$	−7.94734	+	3.62943i	−0.120414	+	0.0549913i
$67$	70.5025	+	10.1367i	1.05228	+	0.151295i	0.646683	−	0.762759i	$-0.276156\pi$
$67$	70.5025	+	10.1367i	1.05228	+	0.151295i	0.405594	+	0.914054i	$0.367065\pi$
$68$		−	28.3362i		−	0.416709i
$69$	−2.01195	−	7.57453i	−0.0291586	−	0.109776i
$70$	−11.6356			−0.166222
$71$	−2.48696	+	17.2972i	−0.0350277	+	0.243623i	−0.999811	−	0.0194217i	$-0.993817\pi$
$71$	−2.48696	+	17.2972i	−0.0350277	+	0.243623i	0.964784	+	0.263044i	$0.0847266\pi$
$72$	5.82198	+	12.7484i	0.0808608	+	0.177061i
$73$	56.1087	+	16.4750i	0.768612	+	0.225685i	0.642453	−	0.766325i	$-0.277917\pi$
$73$	56.1087	+	16.4750i	0.768612	+	0.225685i	0.126159	+	0.992010i	$0.459735\pi$
$74$	−132.974	+	115.223i	−1.79695	+	1.55707i
$75$	8.10191	−	2.37893i	0.108025	−	0.0317191i
$76$	−32.0386	+	49.8530i	−0.421561	+	0.655961i
$77$	−35.6622	+	78.0894i	−0.463146	+	1.01415i
$78$	−11.5552	+	13.3354i	−0.148144	+	0.170967i
$79$	44.6512	+	69.4787i	0.565205	+	0.879477i	0.999776	−	0.0211610i	$-0.00673627\pi$
$79$	44.6512	+	69.4787i	0.565205	+	0.879477i	−0.434571	+	0.900638i	$0.643100\pi$
$80$	8.33490	−	1.19838i	0.104186	−	0.0149797i
$81$	−11.0833	−	77.0859i	−0.136831	−	0.951677i
$82$	45.0920	−	28.9789i	0.549903	−	0.353401i
$83$	−92.3345	−	80.0083i	−1.11246	−	0.963955i	−0.112903	−	0.993606i	$-0.536015\pi$
$83$	−92.3345	−	80.0083i	−1.11246	−	0.963955i	−0.999560	+	0.0296510i	$0.990560\pi$
$84$	9.67092	+	4.41656i	0.115130	+	0.0525781i
$85$	−3.26330	−	2.09719i	−0.0383918	−	0.0246729i
$86$	11.6456	+	39.6613i	0.135414	+	0.461178i
$87$	4.69260	+	5.41555i	0.0539380	+	0.0622477i
$88$	4.18329	−	14.2470i	0.0475374	−	0.161898i
$89$	160.216	−	73.1683i	1.80018	−	0.822116i	0.840082	−	0.542460i	$-0.182507\pi$
$89$	160.216	−	73.1683i	1.80018	−	0.822116i	0.960100	−	0.279655i	$-0.0902202\pi$
$90$	−11.2180	−	1.61291i	−0.124645	−	0.0179212i
$91$			173.380i			1.90528i
$92$	−70.6974	−	34.5329i	−0.768450	−	0.375357i
$93$	−6.62871			−0.0712764
$94$	25.7983	−	179.431i	0.274450	−	1.90884i
$95$	3.37004	+	7.37937i	0.0354742	+	0.0776776i
$96$	−13.9515	−	4.09654i	−0.145329	−	0.0426723i
$97$	71.9579	−	62.3518i	0.741834	−	0.642803i	−0.199648	−	0.979868i	$-0.563980\pi$
$97$	71.9579	−	62.3518i	0.741834	−	0.642803i	0.941481	+	0.337065i	$0.109434\pi$
$98$	89.3603	−	26.2385i	0.911839	−	0.267740i
$99$	−45.2072	+	70.3438i	−0.456639	+	0.710544i
$100$	35.2156	−	77.1115i	0.352156	−	0.771115i
$101$	−18.0665	+	20.8498i	−0.178876	+	0.206434i	−0.838106	−	0.545507i	$-0.816337\pi$
$101$	−18.0665	+	20.8498i	−0.178876	+	0.206434i	0.659230	+	0.751941i	$0.270882\pi$
$102$	4.15691	+	6.46828i	0.0407540	+	0.0634145i
$103$	−113.344	+	16.2964i	−1.10043	+	0.158218i	−0.668516	−	0.743698i	$-0.733070\pi$
$103$	−113.344	+	16.2964i	−1.10043	+	0.158218i	−0.431912	+	0.901916i	$0.642161\pi$
$104$	−4.26781	−	29.6832i	−0.0410366	−	0.285416i
$105$	1.22438	−	0.786864i	0.0116608	−	0.00749394i
$106$	−51.2465	−	44.4054i	−0.483458	−	0.418919i
$107$	−67.5833	−	30.8643i	−0.631620	−	0.288451i	0.0737650	−	0.997276i	$-0.476499\pi$
$107$	−67.5833	−	30.8643i	−0.631620	−	0.288451i	−0.705385	+	0.708825i	$0.749226\pi$
$108$	17.5372	+	11.2705i	0.162382	+	0.104356i
$109$	−13.7415	−	46.7994i	−0.126069	−	0.429352i	0.872134	−	0.489266i	$-0.162735\pi$
$109$	−13.7415	−	46.7994i	−0.126069	−	0.429352i	−0.998204	+	0.0599145i	$0.980917\pi$
$110$	7.86324	+	9.07466i	0.0714840	+	0.0824969i
$111$	6.20055	−	21.1171i	0.0558609	−	0.190245i
$112$	−149.180	+	68.1284i	−1.33197	+	0.608289i
$113$	−42.0781	−	6.04991i	−0.372372	−	0.0535391i	−0.0464117	−	0.998922i	$-0.514779\pi$
$113$	−42.0781	−	6.04991i	−0.372372	−	0.0535391i	−0.325961	+	0.945383i	$0.605688\pi$
$114$		−	16.0800i		−	0.141052i
$115$	−9.20933	+	5.58595i	−0.0800811	+	0.0485735i
$116$	71.9404			0.620176
$117$	−24.0338	+	167.159i	−0.205417	+	1.42871i
$118$	57.8991	+	126.781i	0.490670	+	1.07442i
$119$	72.4893	+	21.2848i	0.609154	+	0.178864i
$120$	−0.190250	+	0.164852i	−0.00158541	+	0.00137377i
$121$	−31.0958	+	9.13055i	−0.256990	+	0.0754591i
$122$	88.6809	−	137.990i	0.726892	−	1.13107i
$123$	−2.78522	+	6.09877i	−0.0226440	+	0.0495835i
$124$	−43.5798	+	50.2938i	−0.351450	+	0.405595i
$125$	−12.6037	−	19.6117i	−0.100830	−	0.156894i
$126$	218.484	−	31.4132i	1.73400	−	0.249311i
$127$	23.2120	+	161.443i	0.182772	+	1.27120i	0.850172	+	0.526505i	$0.176498\pi$
$127$	23.2120	+	161.443i	0.182772	+	1.27120i	−0.667400	+	0.744699i	$0.732593\pi$
$128$	42.0230	−	27.0065i	0.328304	−	0.210988i
$129$	−3.90757	−	3.38593i	−0.0302912	−	0.0262475i
$130$	22.0593	+	10.0741i	0.169687	+	0.0774934i
$131$	69.7887	+	44.8505i	0.532738	+	0.342370i	0.779193	−	0.626784i	$-0.215629\pi$
$131$	69.7887	+	44.8505i	0.532738	+	0.342370i	−0.246455	+	0.969154i	$0.579266\pi$
$132$	−3.09104	−	10.5271i	−0.0234170	−	0.0797509i
$133$	−103.468	−	119.408i	−0.777952	−	0.897805i
$134$	−54.6655	+	186.173i	−0.407951	+	1.38935i
$135$	2.59590	−	1.18551i	0.0192289	−	0.00878154i
$136$	−12.9343	−	1.85967i	−0.0951053	−	0.0136741i
$137$		−	144.682i		−	1.05607i	−0.849223	−	0.528035i	$-0.822929\pi$
$137$		−	144.682i		−	1.05607i	0.849223	−	0.528035i	$-0.177071\pi$
$138$	21.2040	−	2.48849i	0.153652	−	0.0180326i
$139$	−41.5862			−0.299181			−0.149590	−	0.988748i	$-0.547796\pi$
$139$	−41.5862			−0.299181			−0.149590	+	0.988748i	$0.547796\pi$
$140$	2.07945	−	14.4629i	0.0148532	−	0.103306i
$141$	9.41947	+	20.6258i	0.0668047	+	0.146282i
$142$	−45.6761	−	13.4117i	−0.321663	−	0.0944487i
$143$	135.221	−	117.169i	0.945599	−	0.819366i
$144$	−153.271	+	45.0045i	−1.06438	+	0.312531i
$145$	5.32439	−	8.28492i	0.0367199	−	0.0571374i
$146$	−66.1757	+	144.905i	−0.453258	+	0.992497i
$147$	−7.62879	+	8.80409i	−0.0518965	+	0.0598918i
$148$	−119.457	−	185.878i	−0.807139	−	1.25593i
$149$	73.9613	−	10.6340i	0.496385	−	0.0713693i	0.110424	−	0.993885i	$-0.464779\pi$
$149$	73.9613	−	10.6340i	0.496385	−	0.0713693i	0.385961	+	0.922515i	$0.373870\pi$
$150$	3.27359	+	22.7683i	0.0218239	+	0.151789i
$151$	−62.1008	+	39.9097i	−0.411263	+	0.264303i	−0.729873	−	0.683583i	$-0.760421\pi$
$151$	−62.1008	+	39.9097i	−0.411263	+	0.264303i	0.318609	+	0.947886i	$0.396784\pi$
$152$	20.6532	+	17.8961i	0.135877	+	0.117738i
$153$	66.9377	+	30.5694i	0.437501	+	0.199800i
$154$	−196.735	−	126.434i	−1.27750	−	0.820999i
$155$	2.56662	+	8.74112i	0.0165589	+	0.0563943i
$156$	−14.5108	−	16.7463i	−0.0930176	−	0.107348i
$157$	19.2942	−	65.7099i	0.122893	−	0.418535i	−0.874948	−	0.484217i	$-0.839104\pi$
$157$	19.2942	−	65.7099i	0.122893	−	0.418535i	0.997841	+	0.0656828i	$0.0209225\pi$
$158$	−204.653	+	93.4620i	−1.29527	+	0.591531i
$159$	8.39552	+	1.20709i	0.0528020	+	0.00759178i
$160$			19.9837i			0.124898i
$161$	141.446	−	154.918i	0.878547	−	0.962222i
$162$	212.151			1.30958
$163$	15.8506	−	110.244i	0.0972432	−	0.676341i	−0.881640	−	0.471922i	$-0.843560\pi$
$163$	15.8506	−	110.244i	0.0972432	−	0.676341i	0.978883	−	0.204419i	$-0.0655305\pi$
$164$	27.9619	+	61.2280i	0.170499	+	0.373341i
$165$	−1.44111	−	0.423149i	−0.00873402	−	0.00256454i
$166$	251.531	−	217.953i	1.51525	−	1.31297i
$167$	−204.013	+	59.9036i	−1.22163	+	0.358704i	−0.828087	−	0.560600i	$-0.810571\pi$
$167$	−204.013	+	59.9036i	−1.22163	+	0.358704i	−0.393548	+	0.919304i	$0.628752\pi$
$168$	2.65068	−	4.12453i	0.0157778	−	0.0245508i
$169$	79.9087	−	174.976i	0.472832	−	1.03536i
$170$	6.92002	−	7.98612i	0.0407060	−	0.0469772i
$171$	−83.2026	−	129.466i	−0.486565	−	0.757110i
$172$	−51.3799	+	7.38732i	−0.298721	+	0.0429495i
$173$	35.5277	+	247.100i	0.205362	+	1.42833i	0.788041	+	0.615623i	$0.211096\pi$
$173$	35.5277	+	247.100i	0.205362	+	1.42833i	−0.582678	+	0.812703i	$0.697995\pi$
$174$	−16.4218	+	10.5536i	−0.0943780	+	0.0606530i
$175$	170.813	+	148.011i	0.976076	+	0.845775i
$176$	153.949	+	70.3061i	0.874710	+	0.399467i
$177$	−14.6663	−	9.42545i	−0.0828604	−	0.0532511i
$178$	135.178	+	460.374i	0.759427	+	2.58637i
$179$	−10.3913	−	11.9922i	−0.0580522	−	0.0669958i	0.725981	−	0.687715i	$-0.241386\pi$
$179$	−10.3913	−	11.9922i	−0.0580522	−	0.0669958i	−0.784033	+	0.620719i	$0.786841\pi$
$180$	4.00967	−	13.6557i	0.0222759	−	0.0758649i
$181$	3.71504	−	1.69660i	0.0205251	−	0.00937350i	−0.405126	−	0.914261i	$-0.632772\pi$
$181$	3.71504	−	1.69660i	0.0205251	−	0.00937350i	0.425651	+	0.904887i	$0.360045\pi$
$182$	−467.503	−	67.2168i	−2.56870	−	0.369323i
$183$			20.5175i			0.112118i
$184$	−20.4027	+	30.0041i	−0.110884	+	0.163066i
$185$	−30.2475			−0.163500
$186$	2.56985	−	17.8737i	0.0138164	−	0.0960950i
$187$	−32.3877	−	70.9191i	−0.173196	−	0.379246i
$188$	218.421	+	64.1341i	1.16181	+	0.341139i
$189$	−42.0051	+	36.3977i	−0.222249	+	0.192580i
$190$	−21.2043	+	6.22614i	−0.111601	+	0.0327691i
$191$	89.0866	−	138.621i	0.466422	−	0.725767i	−0.525751	−	0.850639i	$-0.676216\pi$
$191$	89.0866	−	138.621i	0.466422	−	0.725767i	0.992173	+	0.124872i	$0.0398520\pi$
$192$	6.27376	−	13.7376i	0.0326758	−	0.0715501i
$193$	−80.4770	+	92.8754i	−0.416979	+	0.481220i	−0.924914	−	0.380176i	$-0.875864\pi$
$193$	−80.4770	+	92.8754i	−0.416979	+	0.481220i	0.507935	+	0.861395i	$0.330409\pi$
$194$	140.229	+	218.200i	0.722829	+	1.12474i
$195$	−3.00252	+	0.431698i	−0.0153976	+	0.00221383i
$196$	16.6443	+	115.763i	0.0849197	+	0.590629i
$197$	−200.867	+	129.089i	−1.01963	+	0.655276i	−0.939868	−	0.341537i	$-0.889052\pi$
$197$	−200.867	+	129.089i	−1.01963	+	0.655276i	−0.0797619	+	0.996814i	$0.525416\pi$
$198$	−172.149	−	149.168i	−0.869441	−	0.753375i
$199$	−214.713	−	98.0561i	−1.07896	−	0.492744i	−0.205009	−	0.978760i	$-0.565722\pi$
$199$	−214.713	−	98.0561i	−1.07896	−	0.492744i	−0.873950	+	0.486016i	$0.838450\pi$
$200$	−32.8871	−	21.1353i	−0.164435	−	0.105676i
$201$	−6.83781	−	23.2874i	−0.0340189	−	0.115858i
$202$	−49.2155	−	56.7977i	−0.243641	−	0.281177i
$203$	−54.0381	+	184.037i	−0.266198	+	0.906586i
$204$	−8.78292	+	4.01103i	−0.0430535	+	0.0196619i
$205$	9.12074	+	1.31136i	0.0444914	+	0.00639690i
$206$		−	311.939i		−	1.51427i
$207$	157.845	−	129.752i	0.762536	−	0.626820i
$208$	341.810			1.64332
$209$	−23.2044	+	161.390i	−0.111026	+	0.772203i
$210$	1.64703	+	3.60649i	0.00784300	+	0.0171738i
$211$	156.480	+	45.9468i	0.741613	+	0.217757i	0.630650	−	0.776067i	$-0.282788\pi$
$211$	156.480	+	45.9468i	0.741613	+	0.217757i	0.110963	+	0.993825i	$0.464606\pi$
$212$	64.3541	−	55.7631i	0.303557	−	0.263034i
$213$	5.71338	−	1.67760i	0.0268234	−	0.00787605i
$214$	109.424	−	170.266i	0.511325	−	0.795637i
$215$	−2.95194	+	6.46385i	−0.0137300	+	0.0300644i
$216$	6.29547	−	7.26536i	0.0291457	−	0.0336359i
$217$	−95.9259	−	149.264i	−0.442055	−	0.687851i
$218$	131.517	−	18.9093i	0.603291	−	0.0867401i
$219$	−2.83577	−	19.7232i	−0.0129487	−	0.0900602i
$220$	−12.6850	+	8.15216i	−0.0576592	+	0.0370553i
$221$	−119.000	−	103.115i	−0.538464	−	0.466581i
$222$	54.5365	+	24.9060i	0.245660	+	0.112189i
$223$	−127.214	−	81.7553i	−0.570465	−	0.366616i	0.223384	−	0.974731i	$-0.428290\pi$
$223$	−127.214	−	81.7553i	−0.570465	−	0.366616i	−0.793849	+	0.608115i	$0.791926\pi$
$224$	−109.652	−	373.440i	−0.489517	−	1.66714i
$225$	144.167	+	166.377i	0.640742	+	0.739456i
$226$	32.6260	−	111.114i	0.144363	−	0.491655i
$227$	37.3463	−	17.0555i	0.164521	−	0.0751343i	−0.331452	−	0.943472i	$-0.607539\pi$
$227$	37.3463	−	17.0555i	0.164521	−	0.0751343i	0.495973	+	0.868338i	$0.334811\pi$
$228$	19.9873	+	2.87374i	0.0876635	+	0.0126041i
$229$			237.490i			1.03708i	0.855055	+	0.518538i	$0.173523\pi$
$229$			237.490i			1.03708i	−0.855055	+	0.518538i	$0.826477\pi$
$230$	−11.4917	−	26.9977i	−0.0499638	−	0.117381i
$231$	29.2522			0.126633
$232$	4.72137	−	32.8379i	0.0203507	−	0.141543i
$233$	61.7638	+	135.244i	0.265081	+	0.580446i	0.994631	−	0.103481i	$-0.0329980\pi$
$233$	61.7638	+	135.244i	0.265081	+	0.580446i	−0.729551	+	0.683927i	$0.760271\pi$
$234$	−441.410	−	129.610i	−1.88637	−	0.553888i
$235$	23.5515	−	20.4075i	0.100219	−	0.0868404i
$236$	−167.936	+	49.3104i	−0.711592	+	0.208942i
$237$	15.2148	−	23.6746i	0.0641973	−	0.0998930i
$238$	−85.4953	+	187.209i	−0.359224	+	0.786591i
$239$	116.313	−	134.232i	0.486664	−	0.561640i	−0.458307	−	0.888794i	$-0.651544\pi$
$239$	116.313	−	134.232i	0.486664	−	0.561640i	0.944971	+	0.327154i	$0.106089\pi$
$240$	−1.55126	−	2.41381i	−0.00646358	−	0.0100575i
$241$	−100.909	+	14.5085i	−0.418708	+	0.0602011i	−0.348449	−	0.937328i	$-0.613292\pi$
$241$	−100.909	+	14.5085i	−0.418708	+	0.0602011i	−0.0702586	+	0.997529i	$0.522382\pi$
$242$	−12.5643	−	87.3866i	−0.0519186	−	0.361102i
$243$	−68.4627	+	43.9983i	−0.281740	+	0.181063i
$244$	155.672	+	134.891i	0.638000	+	0.552830i
$245$	14.5636	+	6.65097i	0.0594432	+	0.0271468i
$246$	−15.3650	−	9.87447i	−0.0624592	−	0.0401401i
$247$	92.7751	+	315.963i	0.375608	+	1.27920i
$248$	20.0970	+	23.1932i	0.0810362	+	0.0935208i
$249$	−11.7288	+	39.9448i	−0.0471038	+	0.160421i
$250$	57.7675	−	26.3815i	0.231070	−	0.105526i
$251$	96.2996	+	13.8458i	0.383664	+	0.0551625i	0.331448	−	0.943473i	$-0.392463\pi$
$251$	96.2996	+	13.8458i	0.383664	+	0.0551625i	0.0522152	+	0.998636i	$0.483372\pi$
$252$			277.187i			1.09995i
$253$	−216.410	−	5.62237i	−0.855375	−	0.0222228i
$254$	−444.314			−1.74927
$255$	−0.188110	+	1.30833i	−0.000737687	+	0.00513072i
$256$	130.176	+	285.046i	0.508500	+	1.11346i
$257$	99.0376	+	29.0801i	0.385360	+	0.113152i	0.468674	−	0.883371i	$-0.344732\pi$
$257$	99.0376	+	29.0801i	0.385360	+	0.113152i	−0.0833132	+	0.996523i	$0.526550\pi$
$258$	10.6447	−	9.22372i	0.0412587	−	0.0357508i
$259$	565.241	−	165.970i	2.18240	−	0.640810i
$260$	−16.4644	+	25.6191i	−0.0633247	+	0.0985351i
$261$	−77.6101	+	169.942i	−0.297357	+	0.651120i
$262$	−147.991	+	170.791i	−0.564851	+	0.651873i
$263$	−118.300	−	184.079i	−0.449811	−	0.699920i	0.540101	−	0.841600i	$-0.318386\pi$
$263$	−118.300	−	184.079i	−0.449811	−	0.699920i	−0.989913	+	0.141680i	$0.954750\pi$
$264$	−5.00807	+	0.720051i	−0.0189699	+	0.00272747i
$265$	−1.65896	−	11.5384i	−0.00626024	−	0.0435410i
$266$	362.085	−	232.698i	1.36122	−	0.874804i
$267$	−45.3577	−	39.3026i	−0.169879	−	0.147201i
$268$	−221.643	−	101.221i	−0.827025	−	0.377690i
$269$	421.925	+	271.155i	1.56849	+	1.00801i	0.979878	+	0.199596i	$0.0639630\pi$
$269$	421.925	+	271.155i	1.56849	+	1.00801i	0.588615	+	0.808413i	$0.299673\pi$
$270$	2.19022	+	7.45920i	0.00811192	+	0.0276267i
$271$	−130.961	−	151.137i	−0.483250	−	0.557700i	0.460799	−	0.887504i	$-0.347563\pi$
$271$	−130.961	−	151.137i	−0.483250	−	0.557700i	−0.944049	+	0.329804i	$0.893017\pi$
$272$	41.9618	−	142.909i	0.154271	−	0.525400i
$273$	53.7400	−	24.5422i	0.196850	−	0.0898983i
$274$	390.120	+	56.0908i	1.42380	+	0.204711i
$275$		−	233.243i		−	0.848158i
$276$	−0.696298	+	26.8011i	−0.00252282	+	0.0971055i
$277$	−29.3463			−0.105943			−0.0529716	−	0.998596i	$-0.516869\pi$
$277$	−29.3463			−0.105943			−0.0529716	+	0.998596i	$0.516869\pi$
$278$	16.1223	−	112.133i	0.0579939	−	0.403356i
$279$	−71.7930	−	157.205i	−0.257323	−	0.563458i
$280$	−6.46526	−	1.89837i	−0.0230902	−	0.00677990i
$281$	−259.400	+	224.772i	−0.923133	+	0.799899i	−0.980106	−	0.198476i	$-0.936401\pi$
$281$	−259.400	+	224.772i	−0.923133	+	0.799899i	0.0569726	+	0.998376i	$0.481855\pi$
$282$	−59.2671	+	17.4024i	−0.210167	+	0.0617107i
$283$	−134.946	+	209.980i	−0.476841	+	0.741980i	−0.993453	−	0.114240i	$-0.963557\pi$
$283$	−134.946	+	209.980i	−0.476841	+	0.741980i	0.516612	+	0.856220i	$0.327193\pi$
$284$	24.8337	−	54.3782i	0.0874426	−	0.191472i
$285$	1.81023	−	2.08912i	0.00635169	−	0.00733024i
$286$	263.513	+	410.034i	0.921374	+	1.43369i
$287$	−177.636	+	25.5403i	−0.618942	+	0.0889904i
$288$	−53.9513	−	375.240i	−0.187331	−	1.30292i
$289$	185.402	−	119.150i	0.641529	−	0.412285i
$290$	20.2753	+	17.5686i	0.0699148	+	0.0605815i
$291$	−29.5120	−	13.4777i	−0.101416	−	0.0463150i
$292$	−168.289	−	108.153i	−0.576331	−	0.370385i
$293$	−127.834	−	435.363i	−0.436293	−	1.48588i	−0.825327	−	0.564655i	$-0.809009\pi$
$293$	−127.834	−	435.363i	−0.436293	−	1.48588i	0.389033	−	0.921224i	$-0.372809\pi$
$294$	−20.7818	−	23.9835i	−0.0706865	−	0.0815765i
$295$	−6.75036	+	22.9896i	−0.0228826	+	0.0779309i
$296$	−92.6856	+	42.3281i	−0.313127	+	0.143000i
$297$	56.7736	+	8.16282i	0.191157	+	0.0274842i
$298$			203.552i			0.683061i
$299$	−402.290	+	171.236i	−1.34545	+	0.572696i
$300$	−28.8859			−0.0962862
$301$	19.6960	−	136.989i	0.0654351	−	0.455111i
$302$	−83.5373	−	182.921i	−0.276614	−	0.605699i
$303$	9.01983	+	2.64846i	0.0297684	+	0.00874080i
$304$	−235.406	+	203.981i	−0.774363	+	0.670989i
$305$	27.0560	−	7.94435i	0.0887081	−	0.0260471i
$306$	−108.378	+	168.640i	−0.354177	+	0.551110i
$307$	195.965	−	429.104i	0.638322	−	1.39773i	−0.263091	−	0.964771i	$-0.584742\pi$
$307$	195.965	−	429.104i	0.638322	−	1.39773i	0.901413	−	0.432960i	$-0.142531\pi$
$308$	192.316	−	221.944i	0.624402	−	0.720598i
$309$	21.0952	+	32.8247i	0.0682691	+	0.106229i
$310$	−24.5646	+	3.53186i	−0.0792407	+	0.0113931i
$311$	9.54582	+	66.3926i	0.0306939	+	0.213481i	0.999396	−	0.0347444i	$-0.0110617\pi$
$311$	9.54582	+	66.3926i	0.0306939	+	0.213481i	−0.968702	+	0.248225i	$0.920153\pi$
$312$	−8.59634	+	5.52453i	−0.0275524	+	0.0177068i
$313$	−394.759	−	342.060i	−1.26121	−	1.09284i	−0.991528	−	0.129896i	$-0.958536\pi$
$313$	−394.759	−	342.060i	−1.26121	−	1.09284i	−0.269683	−	0.962949i	$-0.586919\pi$
$314$	169.701	+	77.4996i	0.540448	+	0.246814i
$315$	31.9219	+	20.5150i	0.101339	+	0.0651269i
$316$	−79.5978	−	271.085i	−0.251892	−	0.857865i
$317$	145.820	+	168.285i	0.459999	+	0.530867i	0.937603	−	0.347708i	$-0.113040\pi$
$317$	145.820	+	168.285i	0.459999	+	0.530867i	−0.477604	+	0.878575i	$0.658495\pi$
$318$	−6.50962	+	22.1697i	−0.0204705	+	0.0697161i
$319$	180.051	−	82.2263i	0.564422	−	0.257763i
$320$	−20.5447	−	2.95388i	−0.0642020	−	0.00923086i
$321$			25.3166i			0.0788680i
$322$	362.884	+	441.455i	1.12697	+	1.37098i
$323$	143.492			0.444247
$324$	−37.9147	+	263.703i	−0.117021	+	0.813897i
$325$	−195.688	−	428.498i	−0.602118	−	1.31845i
$326$	291.116	+	85.4795i	0.892995	+	0.262207i
$327$	−12.5605	+	10.8838i	−0.0384114	+	0.0332837i
$328$	29.7832	−	8.74514i	0.0908025	−	0.0266620i
$329$	−328.134	+	510.587i	−0.997368	+	1.55194i
$330$	1.69968	−	3.72178i	0.00515054	−	0.0112781i
$331$	−194.363	+	224.307i	−0.587200	+	0.677665i	−0.969137	−	0.246523i	$-0.920712\pi$
$331$	−194.363	+	224.307i	−0.587200	+	0.677665i	0.381936	+	0.924189i	$0.375257\pi$
$332$	225.962	+	351.603i	0.680607	+	1.05905i
$333$	567.965	−	81.6610i	1.70560	−	0.245228i
$334$	−82.4317	−	573.325i	−0.246802	−	1.71654i
$335$	−28.0610	+	18.0337i	−0.0837642	+	0.0538320i
$336$	42.2334	+	36.5954i	0.125695	+	0.108915i
$337$	173.346	+	79.1644i	0.514379	+	0.234909i	0.655654	−	0.755061i	$-0.272393\pi$
$337$	173.346	+	79.1644i	0.514379	+	0.234909i	−0.141275	+	0.989970i	$0.545120\pi$
$338$	440.826	+	283.301i	1.30422	+	0.838170i
$339$	4.08101	+	13.8987i	0.0120384	+	0.0409990i
$340$	8.68998	+	10.0288i	0.0255588	+	0.0294964i
$341$	−51.5857	+	175.685i	−0.151278	+	0.515205i
$342$	381.349	−	174.156i	1.11505	−	0.509228i
$343$	133.721	+	19.2262i	0.389857	+	0.0560530i
$344$			23.9377i			0.0695863i
$345$	3.03498	+	2.06377i	0.00879705	+	0.00598195i
$346$	−680.056			−1.96548
$347$	37.5707	−	261.310i	0.108273	−	0.753055i	−0.861273	−	0.508143i	$-0.830332\pi$
$347$	37.5707	−	261.310i	0.108273	−	0.753055i	0.969545	−	0.244911i	$-0.0787589\pi$
$348$	−10.1833	−	22.2982i	−0.0292622	−	0.0640754i
$349$	−442.351	−	129.886i	−1.26748	−	0.372166i	−0.422207	−	0.906499i	$-0.638745\pi$
$349$	−442.351	−	129.886i	−1.26748	−	0.372166i	−0.845274	+	0.534333i	$0.820563\pi$
$350$	−465.318	+	403.200i	−1.32948	+	1.15200i
$351$	111.149	−	32.6363i	0.316663	−	0.0929808i
$352$	−217.147	+	337.887i	−0.616894	+	0.959906i
$353$	−25.3592	+	55.5289i	−0.0718391	+	0.157306i	−0.942145	−	0.335206i	$-0.891194\pi$
$353$	−25.3592	+	55.5289i	−0.0718391	+	0.157306i	0.870306	+	0.492512i	$0.163921\pi$
$354$	31.1007	−	35.8921i	0.0878551	−	0.101390i
$355$	−4.42442	−	6.88453i	−0.0124632	−	0.0193931i
$356$	−596.400	+	85.7493i	−1.67528	+	0.240869i
$357$	−3.66365	−	25.4813i	−0.0102623	−	0.0713761i
$358$	36.3645	−	23.3701i	0.101577	−	0.0652795i
$359$	360.187	+	312.104i	1.00331	+	0.869369i	0.991440	−	0.130560i	$-0.0416776\pi$
$359$	360.187	+	312.104i	1.00331	+	0.869369i	0.0118653	+	0.999930i	$0.496223\pi$
$360$	−5.97011	−	2.72646i	−0.0165837	−	0.00757350i
$361$	51.2416	+	32.9310i	0.141943	+	0.0912215i
$362$	3.13446	+	10.6750i	0.00865874	+	0.0294890i
$363$	7.23171	+	8.34583i	0.0199221	+	0.0229913i
$364$	167.100	−	569.090i	0.459066	−	1.56344i
$365$	−24.9105	+	11.3762i	−0.0682479	+	0.0311678i
$366$	−55.3235	−	7.95432i	−0.151157	−	0.0217331i
$367$		−	40.2222i		−	0.109597i	−0.998497	−	0.0547986i	$-0.982548\pi$
$367$		−	40.2222i		−	0.109597i	0.998497	−	0.0547986i	$-0.0174517\pi$
$368$	−305.412	−	278.853i	−0.829924	−	0.757753i
$369$	−174.803			−0.473720
$370$	11.7265	−	81.5596i	0.0316932	−	0.220431i
$371$	94.3129	+	206.517i	0.254213	+	0.556648i
$372$	21.7576	+	6.38860i	0.0584881	+	0.0171737i
$373$	36.2141	−	31.3797i	0.0970887	−	0.0841278i	−0.604964	−	0.796253i	$-0.706813\pi$
$373$	36.2141	−	31.3797i	0.0970887	−	0.0841278i	0.702053	+	0.712125i	$0.252267\pi$
$374$	203.783	−	59.8360i	0.544874	−	0.159989i
$375$	−4.29467	+	6.68264i	−0.0114525	+	0.0178204i
$376$	43.6093	−	95.4911i	0.115982	−	0.253966i
$377$	261.789	−	302.120i	0.694400	−	0.801380i
$378$	−81.8581	−	127.374i	−0.216556	−	0.336967i
$379$	−369.037	+	53.0595i	−0.973712	+	0.139999i	−0.610766	−	0.791811i	$-0.709138\pi$
$379$	−369.037	+	53.0595i	−0.973712	+	0.139999i	−0.362946	+	0.931810i	$0.618229\pi$
$380$	−3.94951	−	27.4695i	−0.0103935	−	0.0722880i
$381$	46.7543	−	30.0471i	0.122715	−	0.0788639i
$382$	339.242	+	293.955i	0.888068	+	0.769515i
$383$	188.143	+	85.9220i	0.491235	+	0.224340i	0.645602	−	0.763674i	$-0.276607\pi$
$383$	188.143	+	85.9220i	0.491235	+	0.224340i	−0.154367	+	0.988014i	$0.549334\pi$
$384$	−14.3192	−	9.20239i	−0.0372896	−	0.0239646i
$385$	−11.3264	−	38.5742i	−0.0294192	−	0.100193i
$386$	−219.230	−	253.005i	−0.567953	−	0.655453i
$387$	37.9784	−	129.343i	0.0981355	−	0.334219i
$388$	−296.282	+	135.308i	−0.763614	+	0.348731i
$389$	506.962	+	72.8901i	1.30324	+	0.187378i	0.758747	−	0.651385i	$-0.225812\pi$
$389$	506.962	+	72.8901i	1.30324	+	0.187378i	0.544496	+	0.838763i	$0.316721\pi$
$390$		−	8.26338i		−	0.0211882i
$391$	22.2064	+	189.216i	0.0567938	+	0.483930i
$392$	53.9336			0.137586
$393$	4.02291	−	27.9800i	0.0102364	−	0.0711958i
$394$	−270.204	−	591.665i	−0.685798	−	1.50169i
$395$	−37.1103	−	10.8966i	−0.0939502	−	0.0275863i
$396$	216.181	−	187.322i	0.545911	−	0.473034i
$397$	−7.31471	+	2.14779i	−0.0184250	+	0.00541006i	−0.290932	−	0.956744i	$-0.593965\pi$
$397$	−7.31471	+	2.14779i	−0.0184250	+	0.00541006i	0.272507	+	0.962154i	$0.412147\pi$
$398$	347.640	−	540.938i	0.873466	−	1.35914i
$399$	−22.3650	+	48.9726i	−0.0560527	+	0.122738i
$400$	291.795	−	336.749i	0.729487	−	0.841873i
$401$	−64.7009	−	100.677i	−0.161349	−	0.251064i	0.751160	−	0.660120i	$-0.229494\pi$
$401$	−64.7009	−	100.677i	−0.161349	−	0.251064i	−0.912509	+	0.409056i	$0.865858\pi$
$402$	65.4432	−	9.40932i	0.162794	−	0.0234063i
$403$	52.6279	+	366.035i	0.130590	+	0.908276i
$404$	79.3947	−	51.0239i	0.196522	−	0.126297i
$405$	27.5629	+	23.8833i	0.0680564	+	0.0589712i
$406$	−475.288	−	217.057i	−1.17066	−	0.534623i
$407$	−511.428	−	328.675i	−1.25658	−	0.807554i
$408$	1.25446	+	4.27229i	0.00307465	+	0.0104713i
$409$	426.672	+	492.406i	1.04321	+	1.20393i	0.978548	+	0.206019i	$0.0660510\pi$
$409$	426.672	+	492.406i	1.04321	+	1.20393i	0.0646606	+	0.997907i	$0.479404\pi$
$410$	−7.07193	+	24.0848i	−0.0172486	+	0.0587434i
$411$	−44.8447	+	20.4799i	−0.109111	+	0.0498294i
$412$	387.738	+	55.7483i	0.941112	+	0.135312i
$413$		−	466.651i		−	1.12990i
$414$	288.669	+	475.917i	0.697268	+	1.14956i
$415$	57.2156			0.137869
$416$	−115.443	+	802.924i	−0.277507	+	1.93011i
$417$	5.88658	+	12.8898i	0.0141165	+	0.0309108i
$418$	−426.178	−	125.137i	−1.01956	−	0.299371i
$419$	−513.670	+	445.097i	−1.22594	+	1.06228i	−0.229917	+	0.973210i	$0.573846\pi$
$419$	−513.670	+	445.097i	−1.22594	+	1.06228i	−0.996025	+	0.0890747i	$0.971609\pi$
$420$	−4.77719	+	1.40271i	−0.0113743	+	0.00333978i
$421$	279.094	−	434.278i	0.662930	−	1.03154i	−0.333132	−	0.942880i	$-0.608105\pi$
$421$	279.094	−	434.278i	0.662930	−	1.03154i	0.996062	−	0.0886592i	$-0.0282582\pi$
$422$	−184.556	+	404.122i	−0.437337	+	0.957634i
$423$	−387.137	+	446.780i	−0.915217	+	1.05622i
$424$	−21.2301	−	33.0347i	−0.0500711	−	0.0779121i
$425$	−203.176	+	29.2123i	−0.478061	+	0.0687347i
$426$	2.30850	+	16.0560i	0.00541901	+	0.0376900i
$427$	−462.009	+	296.915i	−1.08199	+	0.695352i
$428$	192.084	+	166.442i	0.448795	+	0.388883i
$429$	−55.4578	−	25.3267i	−0.129272	−	0.0590367i
$430$	−16.2847	−	10.4656i	−0.0378714	−	0.0243385i
$431$	38.4188	+	130.842i	0.0891388	+	0.303579i	0.991980	−	0.126395i	$-0.0403408\pi$
$431$	38.4188	+	130.842i	0.0891388	+	0.303579i	−0.902841	+	0.429974i	$0.858523\pi$
$432$	71.7560	+	82.8108i	0.166102	+	0.191692i
$433$	−128.407	+	437.315i	−0.296553	+	1.00997i	0.667579	+	0.744539i	$0.267331\pi$
$433$	−128.407	+	437.315i	−0.296553	+	1.00997i	−0.964131	+	0.265426i	$0.914487\pi$
$434$	439.664	−	200.788i	1.01305	−	0.462645i
$435$	−3.32162	−	0.477577i	−0.00763591	−	0.00109788i
$436$			166.854i			0.382694i
$437$	174.871	−	358.004i	0.400162	−	0.819232i
$438$	54.2811			0.123929
$439$	−34.2498	+	238.213i	−0.0780178	+	0.542626i	0.912903	+	0.408177i	$0.133835\pi$
$439$	−34.2498	+	238.213i	−0.0780178	+	0.542626i	−0.990921	+	0.134449i	$0.957074\pi$
$440$	2.88863	+	6.32521i	0.00656507	+	0.0143755i
$441$	−291.420	−	85.5687i	−0.660817	−	0.194033i
$442$	324.173	−	280.898i	0.733423	−	0.635515i
$443$	154.156	−	45.2642i	0.347981	−	0.102177i	−0.103071	−	0.994674i	$-0.532867\pi$
$443$	154.156	−	45.2642i	0.347981	−	0.102177i	0.451052	+	0.892497i	$0.351049\pi$
$444$	−40.7045	+	63.3374i	−0.0916767	+	0.142652i
$445$	−34.2650	+	75.0300i	−0.0770001	+	0.168607i
$446$	269.764	−	311.324i	0.604852	−	0.698036i
$447$	−13.7654	−	21.4194i	−0.0307951	−	0.0479180i
$448$	400.130	−	57.5300i	0.893147	−	0.128415i
$449$	−39.0879	−	271.862i	−0.0870554	−	0.605483i	−0.985915	−	0.167247i	$-0.946512\pi$
$449$	−39.0879	−	271.862i	−0.0870554	−	0.605483i	0.898860	−	0.438237i	$-0.144397\pi$
$450$	−504.512	+	324.230i	−1.12114	+	0.720512i
$451$	139.965	+	121.280i	0.310343	+	0.268914i
$452$	132.283	+	60.4117i	0.292662	+	0.133654i
$453$	21.1607	+	13.5991i	0.0467123	+	0.0300201i
$454$	31.5099	+	107.313i	0.0694050	+	0.236372i
$455$	−53.1713	−	61.3629i	−0.116860	−	0.134864i
$456$	2.62349	−	8.93478i	0.00575327	−	0.0195938i
$457$	−88.5556	+	40.4420i	−0.193776	+	0.0884945i	−0.509940	−	0.860210i	$-0.670332\pi$
$457$	−88.5556	+	40.4420i	−0.193776	+	0.0884945i	0.316164	+	0.948705i	$0.397605\pi$
$458$	−640.370	−	92.0713i	−1.39819	−	0.201029i
$459$		−	50.4772i		−	0.109972i
$460$	35.6116	−	9.45916i	0.0774166	−	0.0205634i
$461$	351.537			0.762552			0.381276	−	0.924461i	$-0.375485\pi$
$461$	351.537			0.762552			0.381276	+	0.924461i	$0.375485\pi$
$462$	−11.3406	+	78.8757i	−0.0245468	+	0.170727i
$463$	82.3203	+	180.256i	0.177798	+	0.389322i	0.977458	−	0.211130i	$-0.0677144\pi$
$463$	82.3203	+	180.256i	0.177798	+	0.389322i	−0.799660	+	0.600453i	$0.794987\pi$
$464$	362.819	+	106.533i	0.781937	+	0.229597i
$465$	2.34604	−	2.03285i	0.00504524	−	0.00437173i
$466$	−388.617	+	114.108i	−0.833942	+	0.244868i
$467$	382.921	−	595.837i	0.819960	−	1.27588i	−0.138416	−	0.990374i	$-0.544201\pi$
$467$	382.921	−	595.837i	0.819960	−	1.27588i	0.958376	−	0.285509i	$-0.0921625\pi$
$468$	239.991	−	525.506i	0.512801	−	1.12288i
$469$	425.429	−	490.971i	0.907098	−	1.04685i
$470$	45.8963	+	71.4160i	0.0976517	+	0.151949i
$471$	−23.0982	+	3.32102i	−0.0490408	+	0.00705100i
$472$	11.4867	+	79.8920i	0.0243363	+	0.169263i
$473$	−120.149	+	77.2150i	−0.254015	+	0.163245i
$474$	57.9379	+	50.2035i	0.122232	+	0.105914i
$475$	390.485	+	178.328i	0.822073	+	0.375428i
$476$	−217.420	−	139.727i	−0.456764	−	0.293544i
$477$	62.3015	+	212.180i	0.130611	+	0.444821i
$478$	316.851	+	365.666i	0.662869	+	0.764991i
$479$	224.063	−	763.088i	0.467772	−	1.59309i	−0.301040	−	0.953612i	$-0.597334\pi$
$479$	224.063	−	763.088i	0.467772	−	1.59309i	0.768812	−	0.639475i	$-0.220848\pi$
$480$	6.19405	−	2.82873i	0.0129043	−	0.00589318i
$481$	−1215.31	−	174.735i	−2.52663	−	0.363275i
$482$		−	277.715i		−	0.576172i
$483$	−68.0393	−	21.9130i	−0.140868	−	0.0453685i
$484$	110.866			0.229063
$485$	−6.34569	+	44.1353i	−0.0130839	+	0.0910005i
$486$	−92.0954	−	201.661i	−0.189497	−	0.414940i
$487$	116.101	+	34.0904i	0.238401	+	0.0700008i	0.398750	−	0.917059i	$-0.369444\pi$
$487$	116.101	+	34.0904i	0.238401	+	0.0700008i	−0.160350	+	0.987060i	$0.551262\pi$
$488$	71.7887	−	62.2053i	0.147108	−	0.127470i
$489$	−36.4142	+	10.6922i	−0.0744666	+	0.0218654i
$490$	−23.5798	+	36.6909i	−0.0481220	+	0.0748793i
$491$	21.1738	−	46.3641i	0.0431238	−	0.0944279i	−0.886844	−	0.462069i	$-0.847107\pi$
$491$	21.1738	−	46.3641i	0.0431238	−	0.0944279i	0.929968	+	0.367641i	$0.119835\pi$
$492$	15.0198	−	17.3338i	0.0305281	−	0.0352313i
$493$	−94.1767	−	146.542i	−0.191028	−	0.297245i
$494$	−887.931	+	127.665i	−1.79743	+	0.258432i
$495$	−5.57285	−	38.7601i	−0.0112583	−	0.0783031i
$496$	−294.265	+	189.113i	−0.593277	+	0.381276i
$497$	120.456	+	104.376i	0.242366	+	0.210011i
$498$	−103.160	−	47.1116i	−0.207149	−	0.0946017i
$499$	−28.8726	−	18.5553i	−0.0578609	−	0.0371850i	0.511391	−	0.859348i	$-0.329131\pi$
$499$	−28.8726	−	18.5553i	−0.0578609	−	0.0371850i	−0.569251	+	0.822163i	$0.692767\pi$
$500$	22.4681	+	76.5193i	0.0449362	+	0.153039i
$501$	47.4457	+	54.7553i	0.0947020	+	0.109292i
$502$	−74.6677	+	254.295i	−0.148740	+	0.506563i
$503$	−553.123	+	252.603i	−1.09965	+	0.502192i	−0.880763	−	0.473558i	$-0.842969\pi$
$503$	−553.123	+	252.603i	−1.09965	+	0.502192i	−0.218885	+	0.975751i	$0.570242\pi$
$504$	126.525	+	18.1915i	0.251041	+	0.0360943i
$505$		−	12.9197i		−	0.0255836i
$506$	99.0589	−	581.349i	0.195769	−	1.14891i
$507$	−65.5456			−0.129281
$508$	79.4058	−	552.279i	0.156311	−	1.08716i
$509$	−202.942	−	444.381i	−0.398707	−	0.873047i	−0.997400	−	0.0720679i	$-0.977040\pi$
$509$	−202.942	−	444.381i	−0.398707	−	0.873047i	0.598693	−	0.800979i	$-0.295687\pi$
$510$	−3.45487	−	1.01444i	−0.00677426	−	0.00198910i
$511$	403.085	−	349.275i	0.788816	−	0.683513i
$512$	−627.348	+	184.206i	−1.22529	+	0.359777i
$513$	−57.0726	+	88.8067i	−0.111253	+	0.173113i
$514$	−116.807	+	255.772i	−0.227251	+	0.497610i
$515$	35.1172	−	40.5274i	0.0681886	−	0.0786939i
$516$	9.56263	+	14.8797i	0.0185322	+	0.0288367i
$517$	619.962	−	89.1370i	1.19915	−	0.172412i
$518$	228.386	+	1588.46i	0.440900	+	3.06653i
$519$	71.5609	−	45.9894i	0.137882	−	0.0886115i
$520$	10.6136	+	9.19670i	0.0204107	+	0.0176860i
$521$	86.8680	+	39.6713i	0.166733	+	0.0761445i	0.497033	−	0.867731i	$-0.334423\pi$
$521$	86.8680	+	39.6713i	0.166733	+	0.0761445i	−0.330300	+	0.943876i	$0.607150\pi$
$522$	−428.145	−	275.152i	−0.820202	−	0.527112i
$523$	212.883	+	725.014i	0.407043	+	1.38626i	0.866995	+	0.498316i	$0.166048\pi$
$523$	212.883	+	725.014i	0.407043	+	1.38626i	−0.459953	+	0.887943i	$0.652134\pi$
$524$	−185.843	−	214.475i	−0.354663	−	0.409303i
$525$	21.6977	−	73.8955i	0.0413289	−	0.140753i
$526$	542.215	−	247.621i	1.03083	−	0.470763i
$527$	159.498	+	22.9323i	0.302653	+	0.0435149i
$528$		−	57.6691i		−	0.109222i
$529$	499.148	+	175.191i	0.943570	+	0.331174i
$530$	31.7552			0.0599155
$531$	64.6867	−	449.906i	0.121820	−	0.847280i
$532$	224.532	+	491.656i	0.422052	+	0.924165i
$533$	358.885	+	105.378i	0.673331	+	0.197708i
$534$	123.560	−	107.066i	0.231386	−	0.200497i
$535$	33.3844	−	9.80255i	0.0624008	−	0.0183225i
$536$	−60.7494	+	94.5279i	−0.113338	+	0.176358i
$537$	−2.24614	+	4.91836i	−0.00418276	+	0.00915896i
$538$	−894.716	+	1032.56i	−1.66304	+	1.91925i
$539$	173.972	+	270.706i	0.322768	+	0.502237i
$540$	−9.66316	+	1.38935i	−0.0178947	+	0.00257287i
$541$	−87.7272	−	610.156i	−0.162158	−	1.12783i	−0.894557	−	0.446955i	$-0.852508\pi$
$541$	−87.7272	−	610.156i	−0.162158	−	1.12783i	0.732399	−	0.680876i	$-0.238401\pi$
$542$	458.297	−	294.530i	0.845567	−	0.543413i
$543$	−1.05174	−	0.911337i	−0.00193690	−	0.00167834i
$544$	321.526	+	146.836i	0.591040	+	0.269919i
$545$	19.2156	+	12.3491i	0.0352579	+	0.0226589i
$546$	45.3416	+	154.419i	0.0830432	+	0.282819i
$547$	−519.689	−	599.753i	−0.950072	−	1.09644i	−0.995239	−	0.0974619i	$-0.968928\pi$
$547$	−519.689	−	599.753i	−0.950072	−	1.09644i	0.0451675	−	0.998979i	$-0.485618\pi$
$548$	−139.441	+	474.892i	−0.254454	+	0.866592i
$549$	−486.589	+	222.218i	−0.886318	+	0.404768i
$550$	628.918	+	90.4248i	1.14349	+	0.164409i
$551$			364.299i			0.661160i
$552$	12.1879	+	2.07676i	0.0220796	+	0.00376225i
$553$	753.278			1.36217
$554$	11.3771	−	79.1294i	0.0205363	−	0.142833i
$555$	4.28158	+	9.37535i	0.00771456	+	0.0168925i
$556$	136.499	+	40.0798i	0.245502	+	0.0720860i
$557$	−9.26934	+	8.03193i	−0.0166415	+	0.0144200i	−0.663142	−	0.748494i	$-0.730777\pi$
$557$	−9.26934	+	8.03193i	−0.0166415	+	0.0144200i	0.646500	+	0.762914i	$0.276232\pi$
$558$	451.721	−	132.637i	0.809535	−	0.237701i
$559$	−155.946	+	242.657i	−0.278974	+	0.434091i
$560$	31.9048	−	69.8618i	0.0569729	−	0.124753i
$561$	−17.3972	+	20.0774i	−0.0310110	+	0.0357886i
$562$	−505.510	−	786.589i	−0.899484	−	1.39962i
$563$	148.434	−	21.3417i	0.263649	−	0.0379070i	−0.00922250	−	0.999957i	$-0.502936\pi$
$563$	148.434	−	21.3417i	0.263649	−	0.0379070i	0.272872	+	0.962050i	$0.412027\pi$
$564$	−11.0391	−	76.7787i	−0.0195729	−	0.136132i
$565$	16.7477	−	10.7631i	0.0296419	−	0.0190497i
$566$	−513.875	−	445.275i	−0.907907	−	0.786706i
$567$	−646.121	−	295.074i	−1.13954	−	0.520412i
$568$	−23.1916	−	14.9044i	−0.0408303	−	0.0262401i
$569$	−78.4612	−	267.214i	−0.137893	−	0.469621i	0.861371	−	0.507976i	$-0.169606\pi$
$569$	−78.4612	−	267.214i	−0.137893	−	0.469621i	−0.999264	+	0.0383553i	$0.987788\pi$
$570$	4.93131	+	5.69104i	0.00865143	+	0.00998428i
$571$	−14.1059	+	48.0404i	−0.0247039	+	0.0841338i	−0.970922	−	0.239395i	$-0.923051\pi$
$571$	−14.1059	+	48.0404i	−0.0247039	+	0.0841338i	0.946218	+	0.323529i	$0.104869\pi$
$572$	−556.763	+	254.265i	−0.973362	+	0.444520i
$573$	−55.5767	−	7.99072i	−0.0969924	−	0.0139454i
$574$		−	488.881i		−	0.851709i
$575$	−174.724	+	542.514i	−0.303868	+	0.943502i
$576$	393.747			0.683588
$577$	−144.084	+	1002.13i	−0.249712	+	1.73679i	0.350159	+	0.936690i	$0.386128\pi$
$577$	−144.084	+	1002.13i	−0.249712	+	1.73679i	−0.599871	+	0.800097i	$0.704782\pi$
$578$	249.401	+	546.111i	0.431489	+	0.944829i
$579$	40.1788	+	11.7976i	0.0693934	+	0.0203757i
$580$	−25.4612	+	22.0623i	−0.0438986	+	0.0380384i
$581$	−1069.20	+	313.945i	−1.84027	+	0.540353i
$582$	47.7826	−	74.3511i	0.0821006	−	0.127751i
$583$	97.3277	−	213.118i	0.166943	−	0.365554i
$584$	−60.4119	+	69.7190i	−0.103445	+	0.119382i
$585$	−42.7572	−	66.5316i	−0.0730893	−	0.113729i
$586$	1223.47	−	175.909i	2.08784	−	0.300186i
$587$	12.7990	+	89.0189i	0.0218041	+	0.151651i	0.997815	−	0.0660713i	$-0.0210465\pi$
$587$	12.7990	+	89.0189i	0.0218041	+	0.151651i	−0.976011	+	0.217722i	$0.930137\pi$
$588$	33.5253	−	21.5454i	0.0570159	−	0.0366419i
$589$	−254.683	−	220.684i	−0.432399	−	0.374676i
$590$	−59.3723	−	27.1144i	−0.100631	−	0.0459566i
$591$	68.4449	+	43.9868i	0.115812	+	0.0744278i
$592$	−327.200	−	1114.34i	−0.552703	−	1.88233i
$593$	−273.187	−	315.274i	−0.460686	−	0.531660i	0.477112	−	0.878843i	$-0.341684\pi$
$593$	−273.187	−	315.274i	−0.460686	−	0.531660i	−0.937797	+	0.347183i	$0.887138\pi$
$594$	−44.0205	+	149.920i	−0.0741086	+	0.252391i
$595$	−32.1830	+	14.6975i	−0.0540890	+	0.0247016i
$596$	−253.014	−	36.3779i	−0.424520	−	0.0610367i
$597$			80.4311i			0.134726i
$598$	−305.761	−	1151.12i	−0.511306	−	1.92495i
$599$	−1025.94			−1.71276			−0.856380	−	0.516346i	$-0.827292\pi$
$599$	−1025.94			−1.71276			−0.856380	+	0.516346i	$0.827292\pi$
$600$	−1.89575	+	13.1852i	−0.00315958	+	0.0219754i
$601$	359.429	+	787.040i	0.598052	+	1.30955i	0.930452	+	0.366413i	$0.119414\pi$
$601$	359.429	+	787.040i	0.598052	+	1.30955i	−0.332400	+	0.943138i	$0.607858\pi$
$602$	361.741	+	106.217i	0.600898	+	0.176440i
$603$	478.221	−	414.381i	0.793070	−	0.687199i
$604$	242.299	−	71.1454i	0.401157	−	0.117790i
$605$	8.20535	−	12.7678i	0.0135626	−	0.0211038i
$606$	−10.6382	+	23.2944i	−0.0175547	+	0.0384395i
$607$	66.0178	−	76.1886i	0.108761	−	0.125517i	−0.698759	−	0.715357i	$-0.746264\pi$
$607$	66.0178	−	76.1886i	0.108761	−	0.125517i	0.807520	+	0.589841i	$0.200809\pi$
$608$	−399.652	−	621.871i	−0.657323	−	1.02281i
$609$	64.6922	−	9.30134i	0.106227	−	0.0152731i
$610$	10.9320	+	76.0337i	0.0179213	+	0.124645i
$611$	1064.16	−	683.896i	1.74167	−	1.11931i
$612$	−190.249	−	164.852i	−0.310864	−	0.269366i
$613$	442.304	+	201.994i	0.721540	+	0.329516i	0.742116	−	0.670272i	$-0.233823\pi$
$613$	442.304	+	201.994i	0.721540	+	0.329516i	−0.0205754	+	0.999788i	$0.506550\pi$
$614$	1081.06	+	694.758i	1.76069	+	1.13153i
$615$	−0.884590	−	3.01264i	−0.00143836	−	0.00489860i
$616$	−88.6871	−	102.350i	−0.143973	−	0.166153i
$617$	−231.396	+	788.063i	−0.375035	+	1.27725i	0.528573	+	0.848888i	$0.322727\pi$
$617$	−231.396	+	788.063i	−0.375035	+	1.27725i	−0.903607	+	0.428362i	$0.859091\pi$
$618$	−96.6869	+	44.1554i	−0.156451	+	0.0714489i
$619$	−387.350	−	55.6926i	−0.625768	−	0.0899718i	−0.177866	−	0.984055i	$-0.556919\pi$
$619$	−387.350	−	55.6926i	−0.625768	−	0.0899718i	−0.447902	+	0.894083i	$0.647829\pi$
$620$		−	31.1648i		−	0.0502659i
$621$	−125.938	−	61.5158i	−0.202799	−	0.0990593i
$622$	−182.722			−0.293765
$623$	228.624	−	1590.11i	0.366972	−	2.55235i
$624$	−48.3836	−	105.945i	−0.0775379	−	0.169784i
$625$	−583.947	−	171.462i	−0.934316	−	0.274340i
$626$	1075.38	−	931.818i	1.71785	−	1.48853i
$627$	53.3083	−	15.6527i	0.0850212	−	0.0249645i
$628$	−126.660	+	197.086i	−0.201687	+	0.313831i
$629$	−222.252	+	486.664i	−0.353341	+	0.773710i
$630$	−67.6923	+	78.1211i	−0.107448	+	0.124002i
$631$	462.303	+	719.357i	0.732651	+	1.14003i	0.985027	+	0.172398i	$0.0551514\pi$
$631$	462.303	+	719.357i	0.732651	+	1.14003i	−0.252377	+	0.967629i	$0.581212\pi$
$632$	−128.963	+	18.5421i	−0.204056	+	0.0293388i
$633$	−7.90861	−	55.0056i	−0.0124939	−	0.0868967i
$634$	−510.296	+	327.947i	−0.804883	+	0.517267i
$635$	−57.7256	−	50.0195i	−0.0909065	−	0.0787709i
$636$	−26.3934	−	12.0535i	−0.0414991	−	0.0189520i
$637$	546.727	+	351.360i	0.858284	+	0.551586i
$638$	151.913	+	517.367i	0.238108	+	0.810920i
$639$	101.665	+	117.328i	0.159100	+	0.183611i
$640$	−6.59060	+	22.4455i	−0.0102978	+	0.0350711i
$641$	289.323	−	132.130i	0.451362	−	0.206130i	−0.176745	−	0.984257i	$-0.556557\pi$
$641$	289.323	−	132.130i	0.451362	−	0.206130i	0.628108	+	0.778126i	$0.283830\pi$
$642$	−68.2639	−	9.81486i	−0.106330	−	0.0152879i
$643$			690.168i			1.07336i	0.843787	+	0.536678i	$0.180321\pi$
$643$			690.168i			1.07336i	−0.843787	+	0.536678i	$0.819679\pi$
$644$	−613.578	+	372.168i	−0.952761	+	0.577900i
$645$	2.42135			0.00375403
$646$	−55.6295	+	386.911i	−0.0861137	+	0.598934i
$647$	332.017	+	727.016i	0.513164	+	1.12367i	0.971963	+	0.235132i	$0.0755523\pi$
$647$	332.017	+	727.016i	0.513164	+	1.12367i	−0.458800	+	0.888540i	$0.651720\pi$
$648$	117.881	+	34.6131i	0.181916	+	0.0534152i
$649$	−363.944	+	315.360i	−0.560777	+	0.485916i
$650$	1231.27	−	361.533i	1.89426	−	0.556204i
$651$	−32.6865	+	50.8611i	−0.0502096	+	0.0781277i
$652$	−158.277	+	346.579i	−0.242757	+	0.531563i
$653$	−401.727	+	463.618i	−0.615203	+	0.709982i	−0.974789	−	0.223130i	$-0.928372\pi$
$653$	−401.727	+	463.618i	−0.615203	+	0.709982i	0.359586	+	0.933112i	$0.382918\pi$
$654$	−24.4775	−	38.0877i	−0.0374274	−	0.0582381i
$655$	−38.4542	+	5.52888i	−0.0587087	+	0.00844103i
$656$	50.3512	+	350.200i	0.0767549	+	0.533842i
$657$	437.037	−	280.867i	0.665201	−	0.427499i
$658$	−1249.54	−	1082.73i	−1.89899	−	1.64548i
$659$	−422.228	−	192.825i	−0.640710	−	0.292603i	0.0684451	−	0.997655i	$-0.478196\pi$
$659$	−422.228	−	192.825i	−0.640710	−	0.292603i	−0.709155	+	0.705052i	$0.750923\pi$
$660$	4.32238	+	2.77783i	0.00654906	+	0.00420883i
$661$	−190.915	−	650.196i	−0.288827	−	0.983656i	−0.968266	−	0.249923i	$-0.919595\pi$
$661$	−190.915	−	650.196i	−0.288827	−	0.983656i	0.679438	−	0.733733i	$-0.262224\pi$
$662$	−529.471	−	611.043i	−0.799806	−	0.923025i
$663$	−15.1161	+	51.4807i	−0.0227996	+	0.0776481i
$664$	175.322	−	80.0670i	0.264039	−	0.120583i
$665$	73.2387	+	10.5301i	0.110133	+	0.0158348i
$666$			1563.12i			2.34703i
$667$	−480.386	+	56.3780i	−0.720219	+	0.0845247i
$668$	727.371			1.08888
$669$	−7.33312	+	51.0030i	−0.0109613	+	0.0762377i
$670$	−37.7474	−	82.6552i	−0.0563393	−	0.123366i
$671$	543.789	+	159.671i	0.810416	+	0.237960i
$672$	−100.228	+	86.8480i	−0.149149	+	0.129238i
$673$	−633.971	+	186.151i	−0.942007	+	0.276598i	−0.716455	−	0.697633i	$-0.754237\pi$
$673$	−633.971	+	186.151i	−0.942007	+	0.276598i	−0.225552	+	0.974231i	$0.572418\pi$
$674$	−280.663	+	436.720i	−0.416413	+	0.647952i
$675$	62.7321	−	137.364i	0.0929364	−	0.203502i
$676$	−430.924	+	497.313i	−0.637461	+	0.735669i
$677$	570.315	+	887.428i	0.842415	+	1.31082i	0.948600	+	0.316477i	$0.102500\pi$
$677$	570.315	+	887.428i	0.842415	+	1.31082i	−0.106185	+	0.994346i	$0.533864\pi$
$678$	−39.0585	+	5.61577i	−0.0576085	+	0.00828285i
$679$	−123.589	−	859.583i	−0.182017	−	1.26595i
$680$	5.14804	−	3.30845i	0.00757065	−	0.00486536i
$681$	−10.5728	−	9.16142i	−0.0155255	−	0.0134529i
$682$	−453.719	−	207.206i	−0.665276	−	0.303822i
$683$	−893.631	−	574.301i	−1.30839	−	0.840851i	−0.314291	−	0.949327i	$-0.601767\pi$
$683$	−893.631	−	574.301i	−1.30839	−	0.840851i	−0.994099	+	0.108475i	$0.965403\pi$
$684$	148.322	+	505.138i	0.216845	+	0.738506i
$685$	44.3701	+	51.2059i	0.0647739	+	0.0747531i
$686$	−103.683	+	353.112i	−0.151141	+	0.514740i
$687$	73.6112	−	33.6171i	0.107149	−	0.0489332i
$688$	−270.065	−	38.8295i	−0.392537	−	0.0564383i
$689$		−	473.182i		−	0.686766i
$690$	−6.74138	+	7.38345i	−0.00977011	+	0.0107006i
$691$	739.711			1.07049			0.535247	−	0.844696i	$-0.320219\pi$
$691$	739.711			1.07049			0.535247	+	0.844696i	$0.320219\pi$
$692$	121.536	−	845.305i	0.175631	−	1.22154i
$693$	316.819	+	693.738i	0.457171	+	1.00106i
$694$	690.032	+	202.612i	0.994282	+	0.291948i
$695$	14.7182	−	12.7534i	0.0211773	−	0.0183502i
$696$	−10.8466	+	3.18484i	−0.0155841	+	0.00457591i
$697$	88.1160	−	137.111i	0.126422	−	0.196716i
$698$	521.718	−	1142.40i	0.747447	−	1.63668i
$699$	33.1767	−	38.2879i	0.0474631	−	0.0547753i
$700$	−418.016	−	650.445i	−0.597165	−	0.929207i
$701$	486.698	−	69.9767i	0.694292	−	0.0998241i	0.213870	−	0.976862i	$-0.431393\pi$
$701$	486.698	−	69.9767i	0.694292	−	0.0998241i	0.480421	+	0.877038i	$0.340484\pi$
$702$	44.9098	+	312.355i	0.0639741	+	0.444950i
$703$	941.268	−	604.916i	1.33893	−	0.860478i
$704$	−315.273	−	273.186i	−0.447832	−	0.388048i
$705$	−9.65913	−	4.41118i	−0.0137009	−	0.00625699i
$706$	−139.897	−	89.9064i	−0.198155	−	0.127346i
$707$	70.8912	+	241.433i	0.100270	+	0.341490i
$708$	39.0555	+	45.0724i	0.0551631	+	0.0636616i
$709$	295.656	−	1006.91i	0.417004	−	1.42018i	−0.436786	−	0.899566i	$-0.643883\pi$
$709$	295.656	−	1006.91i	0.417004	−	1.42018i	0.853789	−	0.520619i	$-0.174299\pi$
$710$	20.2788	−	9.26100i	0.0285616	−	0.0130437i
$711$	726.247	+	104.419i	1.02145	+	0.146862i
$712$			277.860i			0.390253i
$713$	251.593	−	369.992i	0.352865	−	0.518923i
$714$	70.1281			0.0982187
$715$	−11.9246	+	82.9374i	−0.0166778	+	0.115996i
$716$	22.5499	+	49.3774i	0.0314943	+	0.0689628i
$717$	−58.0700	−	17.0509i	−0.0809903	−	0.0237809i
$718$	−981.196	+	850.211i	−1.36657	+	1.18414i
$719$	646.809	−	189.920i	0.899596	−	0.264145i	0.200940	−	0.979603i	$-0.435600\pi$
$719$	646.809	−	189.920i	0.899596	−	0.264145i	0.698655	+	0.715458i	$0.253782\pi$
$720$	40.4441	−	62.9323i	0.0561724	−	0.0874060i
$721$	−433.865	+	950.032i	−0.601755	+	1.31766i
$722$	−108.661	+	125.401i	−0.150500	+	0.173686i
$723$	18.7807	+	29.2233i	0.0259761	+	0.0404196i
$724$	−13.8291	+	1.98833i	−0.0191010	+	0.00274631i
$725$	−74.1646	−	515.826i	−0.102296	−	0.711484i
$726$	−25.3074	+	16.2641i	−0.0348586	+	0.0224023i
$727$	−654.266	−	566.925i	−0.899954	−	0.779814i	0.0761551	−	0.997096i	$-0.475736\pi$
$727$	−654.266	−	566.925i	−0.899954	−	0.779814i	−0.976109	+	0.217281i	$0.930281\pi$
$728$	−248.800	−	113.623i	−0.341759	−	0.156076i
$729$	−566.312	−	363.947i	−0.776834	−	0.499241i
$730$	−21.0175	−	71.5792i	−0.0287911	−	0.0980536i
$731$	82.3090	+	94.9897i	0.112598	+	0.129945i
$732$	19.7743	−	67.3452i	0.0270141	−	0.0920016i
$733$	169.351	−	77.3402i	0.231039	−	0.105512i	−0.296532	−	0.955023i	$-0.595830\pi$
$733$	169.351	−	77.3402i	0.231039	−	0.105512i	0.527571	+	0.849511i	$0.323103\pi$
$734$	108.455	+	15.5935i	0.147759	+	0.0212446i
$735$		−	5.45550i		−	0.00742245i
$736$	758.187	−	623.244i	1.03014	−	0.846799i
$737$	−670.415			−0.909654
$738$	67.7682	−	471.338i	0.0918269	−	0.638670i
$739$	−251.085	−	549.801i	−0.339764	−	0.743979i	0.660211	−	0.751080i	$-0.270467\pi$
$739$	−251.085	−	549.801i	−0.339764	−	0.743979i	−0.999975	+	0.00710119i	$0.997740\pi$
$740$	99.2822	+	29.1519i	0.134165	+	0.0393944i
$741$	84.8016	−	73.4810i	0.114442	−	0.0991647i
$742$	−593.416	+	174.243i	−0.799752	+	0.234828i
$743$	207.269	−	322.517i	0.278962	−	0.434074i	−0.673293	−	0.739375i	$-0.735121\pi$
$743$	207.269	−	322.517i	0.278962	−	0.434074i	0.952256	+	0.305302i	$0.0987573\pi$
$744$	4.34406	−	9.51217i	0.00583880	−	0.0127852i
$745$	−22.9153	+	26.4456i	−0.0307588	+	0.0354975i
$746$	70.5727	+	109.813i	0.0946014	+	0.147203i
$747$	−1074.35	+	154.468i	−1.43822	+	0.206785i
$748$	37.9566	+	263.994i	0.0507441	+	0.352933i
$749$	−570.074	+	366.364i	−0.761113	+	0.489138i
$750$	−16.3541	−	14.1709i	−0.0218055	−	0.0188946i
$751$	−366.129	−	167.206i	−0.487522	−	0.222644i	0.156460	−	0.987684i	$-0.449992\pi$
$751$	−366.129	−	167.206i	−0.487522	−	0.222644i	−0.643982	+	0.765040i	$0.722719\pi$
$752$	1006.59	+	646.898i	1.33856	+	0.860237i
$753$	−9.33978	−	31.8084i	−0.0124034	−	0.0422422i
$754$	713.147	+	823.016i	0.945819	+	1.09153i
$755$	9.73948	−	33.1696i	0.0129000	−	0.0439333i
$756$	172.954	−	78.9853i	0.228775	−	0.104478i
$757$	−723.924	−	104.085i	−0.956306	−	0.137496i	−0.353545	−	0.935418i	$-0.615024\pi$
$757$	−723.924	−	104.085i	−0.956306	−	0.137496i	−0.602761	+	0.797921i	$0.705933\pi$
$758$		−	1015.64i		−	1.33990i
$759$	28.8905	+	67.8731i	0.0380638	+	0.0894243i
$760$	−12.7979			−0.0168393
$761$	−37.4250	+	260.297i	−0.0491788	+	0.342046i	0.950345	+	0.311197i	$0.100730\pi$
$761$	−37.4250	+	260.297i	−0.0491788	+	0.342046i	−0.999524	+	0.0308485i	$0.990179\pi$
$762$	62.8933	+	137.717i	0.0825372	+	0.180731i
$763$	−426.845	−	125.333i	−0.559430	−	0.164263i
$764$	−426.011	+	369.141i	−0.557607	+	0.483169i
$765$	−33.0655	+	9.70891i	−0.0432229	+	0.0126914i
$766$	−304.621	+	473.999i	−0.397677	+	0.618798i
$767$	−404.029	+	884.700i	−0.526766	+	1.15346i
$768$	69.9245	−	80.6972i	0.0910476	−	0.105074i
$769$	405.091	+	630.333i	0.526776	+	0.819679i	0.998057	−	0.0623038i	$-0.0198448\pi$
$769$	405.091	+	630.333i	0.526776	+	0.819679i	−0.471281	+	0.881983i	$0.656208\pi$
$770$	108.403	−	15.5859i	0.140783	−	0.0202415i
$771$	−5.00542	−	34.8135i	−0.00649212	−	0.0451537i
$772$	353.663	−	227.285i	0.458113	−	0.294411i
$773$	112.697	+	97.6524i	0.145792	+	0.126329i	0.724703	−	0.689061i	$-0.241977\pi$
$773$	112.697	+	97.6524i	0.145792	+	0.126329i	−0.578912	+	0.815390i	$0.696522\pi$
$774$	334.037	+	152.549i	0.431572	+	0.197092i
$775$	405.543	+	260.627i	0.523281	+	0.336293i
$776$	42.3178	+	144.121i	0.0545332	+	0.185723i
$777$	−131.454	−	151.706i	−0.169181	−	0.195245i
$778$	−393.082	+	1338.71i	−0.505247	+	1.72071i
$779$	−310.053	+	141.596i	−0.398014	+	0.181767i
$780$	10.2713	+	1.47679i	0.0131684	+	0.00189332i
$781$		−	164.481i		−	0.210603i
$782$	−518.813	−	13.4789i	−0.663444	−	0.0172364i
$783$	128.152			0.163669
$784$	−87.4863	+	608.480i	−0.111590	+	0.776123i
$785$	13.3229	+	29.1732i	0.0169719	+	0.0371633i
$786$	73.8857	+	21.6948i	0.0940021	+	0.0276015i
$787$	841.548	−	729.205i	1.06931	−	0.926563i	0.0718244	−	0.997417i	$-0.477118\pi$
$787$	841.548	−	729.205i	1.06931	−	0.926563i	0.997487	+	0.0708539i	$0.0225724\pi$
$788$	783.725	−	230.122i	0.994575	−	0.292033i
$789$	−40.3105	+	62.7244i	−0.0510906	+	0.0794986i
$790$	43.7687	−	95.8400i	0.0554034	−	0.121316i
$791$	−253.909	+	293.027i	−0.320998	+	0.370451i
$792$	−71.3170	−	110.971i	−0.0900467	−	0.140115i
$793$	1132.97	−	162.897i	1.42872	−	0.205418i
$794$	−2.95552	−	20.5561i	−0.00372232	−	0.0258893i
$795$	−3.34153	+	2.14747i	−0.00420319	+	0.00270122i
$796$	610.253	+	528.787i	0.766649	+	0.664306i
$797$	872.629	+	398.516i	1.09489	+	0.500020i	0.879206	−	0.476443i	$-0.158074\pi$
$797$	872.629	+	398.516i	1.09489	+	0.500020i	0.215686	+	0.976463i	$0.430801\pi$
$798$	−123.379	−	79.2911i	−0.154611	−	0.0993623i
$799$	−155.293	−	528.878i	−0.194359	−	0.661925i
$800$	692.486	+	799.171i	0.865607	+	0.998964i
$801$	440.840	−	1501.36i	0.550362	−	1.87436i
$802$	296.548	−	135.429i	0.369761	−	0.168864i
$803$	−544.805	−	78.3311i	−0.678462	−	0.0975481i
$804$			83.0270i			0.103267i
$805$	−2.55142	+	98.2065i	−0.00316947	+	0.121996i
$806$	−1007.38			−1.24985
$807$	24.3215	−	169.160i	0.0301382	−	0.209615i
$808$	−18.0797	−	39.5891i	−0.0223759	−	0.0489964i
$809$	−298.589	−	87.6736i	−0.369084	−	0.108373i	0.0919305	−	0.995765i	$-0.470696\pi$
$809$	−298.589	−	87.6736i	−0.369084	−	0.108373i	−0.461015	+	0.887393i	$0.652514\pi$
$810$	−75.0849	+	65.0614i	−0.0926973	+	0.0803227i
$811$	−821.180	+	241.120i	−1.01255	+	0.297312i	−0.745597	−	0.666397i	$-0.767836\pi$
$811$	−821.180	+	241.120i	−1.01255	+	0.297312i	−0.266955	+	0.963709i	$0.586018\pi$
$812$	354.741	−	551.988i	0.436874	−	0.679789i
$813$	−28.3078	+	61.9855i	−0.0348190	+	0.0762429i
$814$	1084.51	−	1251.59i	1.33232	−	1.53758i
$815$	28.1990	+	43.8785i	0.0346000	+	0.0538387i
$816$	−50.2349	+	7.22269i	−0.0615624	+	0.00885134i
$817$	−37.4087	−	260.183i	−0.0457878	−	0.318461i
$818$	−1493.14	+	959.583i	−1.82535	+	1.17308i
$819$	1164.07	+	1008.68i	1.42134	+	1.23160i
$820$	−28.6734	−	13.0947i	−0.0349675	−	0.0159691i
$821$	−585.596	−	376.340i	−0.713271	−	0.458392i	0.133019	−	0.991113i	$-0.457533\pi$
$821$	−585.596	−	376.340i	−0.713271	−	0.458392i	−0.846290	+	0.532722i	$0.821169\pi$
$822$	−37.8365	−	128.859i	−0.0460298	−	0.156763i
$823$	−10.8013	−	12.4654i	−0.0131243	−	0.0151463i	0.749149	−	0.662401i	$-0.230462\pi$
$823$	−10.8013	−	12.4654i	−0.0131243	−	0.0151463i	−0.762274	+	0.647255i	$0.775917\pi$
$824$	50.8937	−	173.328i	0.0617642	−	0.210350i
$825$	−72.2948	+	33.0159i	−0.0876301	+	0.0400193i
$826$	1258.28	+	180.913i	1.52334	+	0.219023i
$827$			666.193i			0.805554i	0.915298	+	0.402777i	$0.131955\pi$
$827$			666.193i			0.805554i	−0.915298	+	0.402777i	$0.868045\pi$
$828$	−643.150	+	273.760i	−0.776752	+	0.330628i
$829$	199.457			0.240599			0.120299	−	0.992738i	$-0.461615\pi$
$829$	199.457			0.240599			0.120299	+	0.992738i	$0.461615\pi$
$830$	−22.1816	+	154.276i	−0.0267248	+	0.185875i
$831$	4.15401	+	9.09600i	0.00499880	+	0.0109459i
$832$	−808.397	−	237.367i	−0.971631	−	0.285297i
$833$	214.020	−	185.449i	0.256927	−	0.222628i
$834$	−37.0383	+	10.8754i	−0.0444104	+	0.0130401i
$835$	53.8336	−	83.7667i	0.0644714	−	0.100319i
$836$	231.709	−	507.372i	0.277164	−	0.606904i
$837$	−77.6318	+	89.5919i	−0.0927501	+	0.107039i
$838$	−1001.02	−	1557.62i	−1.19454	−	1.85873i
$839$	−1183.61	+	170.178i	−1.41074	+	0.202834i	−0.805212	−	0.592987i	$-0.797949\pi$
$839$	−1183.61	+	170.178i	−1.41074	+	0.202834i	−0.605532	+	0.795821i	$0.707039\pi$
$840$	0.326758	+	2.27265i	0.000388998	+	0.00270554i
$841$	−335.452	+	215.582i	−0.398872	+	0.256340i
$842$	1062.79	+	920.912i	1.26222	+	1.09372i
$843$	106.387	+	48.5855i	0.126201	+	0.0576341i
$844$	−469.337	−	301.625i	−0.556086	−	0.357375i
$845$	25.3792	+	86.4335i	0.0300345	+	0.102288i
$846$	−1054.61	−	1217.09i	−1.24659	−	1.43864i
$847$	−83.2774	+	283.617i	−0.0983205	+	0.334849i
$848$	407.136	−	185.933i	0.480113	−	0.219260i
$849$	84.1861	+	12.1041i	0.0991592	+	0.0142569i
$850$		−	559.169i		−	0.657846i
$851$	943.346	+	1147.60i	1.10852	+	1.34853i
$852$	−20.3700			−0.0239084
$853$	−173.828	+	1209.00i	−0.203785	+	1.41735i	0.589139	+	0.808032i	$0.299467\pi$
$853$	−173.828	+	1209.00i	−0.203785	+	1.41735i	−0.792923	+	0.609321i	$0.791442\pi$
$854$	−621.490	−	1360.87i	−0.727740	−	1.59353i
$855$	69.1510	+	20.3046i	0.0808784	+	0.0237480i
$856$	88.5803	−	76.7552i	0.103482	−	0.0896673i
$857$	408.996	−	120.092i	0.477242	−	0.140131i	−0.0342602	−	0.999413i	$-0.510907\pi$
$857$	408.996	−	120.092i	0.477242	−	0.140131i	0.511502	+	0.859282i	$0.329089\pi$
$858$	89.7913	−	139.718i	0.104652	−	0.162841i
$859$	435.337	−	953.256i	0.506795	−	1.10973i	−0.467405	−	0.884043i	$-0.654811\pi$
$859$	435.337	−	953.256i	0.506795	−	1.10973i	0.974201	−	0.225684i	$-0.0724617\pi$
$860$	15.9189	−	18.3714i	0.0185104	−	0.0213621i
$861$	33.0610	+	51.4439i	0.0383984	+	0.0597490i
$862$	−367.699	+	52.8671i	−0.426564	+	0.0613307i
$863$	108.107	+	751.901i	0.125269	+	0.871264i	0.951438	+	0.307842i	$0.0996067\pi$
$863$	108.107	+	751.901i	0.125269	+	0.871264i	−0.826169	+	0.563423i	$0.809484\pi$
$864$	−218.761	+	140.589i	−0.253195	+	0.162719i
$865$	−88.3533	−	76.5586i	−0.102143	−	0.0885071i
$866$	−1129.40	−	515.778i	−1.30415	−	0.595587i
$867$	−63.1751	−	40.6002i	−0.0728663	−	0.0468283i
$868$	171.003	+	582.383i	0.197008	+	0.670948i
$869$	−509.060	−	587.487i	−0.585800	−	0.676050i
$870$	2.57548	−	8.77128i	0.00296032	−	0.0100819i
$871$	−1231.64	+	562.470i	−1.41405	+	0.645775i
$872$	76.1623	+	10.9505i	0.0873421	+	0.0125579i
$873$		−	845.870i		−	0.968923i
$874$	897.530	+	610.316i	1.02692	+	0.698302i
$875$	−212.628			−0.243003
$876$	−9.70086	+	67.4710i	−0.0110740	+	0.0770216i
$877$	−477.491	−	1045.56i	−0.544460	−	1.19220i	−0.959321	−	0.282316i	$-0.908897\pi$
$877$	−477.491	−	1045.56i	−0.544460	−	1.19220i	0.414861	−	0.909885i	$-0.363830\pi$
$878$	−629.039	−	184.703i	−0.716446	−	0.210367i
$879$	−116.847	+	101.249i	−0.132932	+	0.115186i
$880$	−76.0469	+	22.3294i	−0.0864169	+	0.0253743i
$881$	665.744	−	1035.92i	0.755669	−	1.17584i	−0.223876	−	0.974618i	$-0.571871\pi$
$881$	665.744	−	1035.92i	0.755669	−	1.17584i	0.979545	−	0.201226i	$-0.0644925\pi$
$882$	343.707	−	752.613i	0.389690	−	0.853302i
$883$	1037.56	−	1197.41i	1.17504	−	1.35607i	0.253716	−	0.967279i	$-0.418347\pi$
$883$	1037.56	−	1197.41i	1.17504	−	1.35607i	0.921326	−	0.388792i	$-0.127108\pi$
$884$	291.219	+	453.145i	0.329433	+	0.512608i
$885$	8.08125	−	1.16191i	0.00913136	−	0.00131289i
$886$	62.2869	+	433.215i	0.0703012	+	0.488955i
$887$	196.041	−	125.988i	0.221016	−	0.142039i	−0.425448	−	0.904983i	$-0.639883\pi$
$887$	196.041	−	125.988i	0.221016	−	0.142039i	0.646464	+	0.762944i	$0.276247\pi$
$888$	26.2396	+	22.7367i	0.0295491	+	0.0256044i
$889$	1353.19	+	617.981i	1.52215	+	0.695141i
$890$	−189.027	−	121.480i	−0.212390	−	0.136495i
$891$	206.515	+	703.324i	0.231778	+	0.789365i
$892$	338.763	+	390.953i	0.379779	+	0.438288i
$893$	−324.769	+	1106.06i	−0.363683	+	1.23859i
$894$	63.0919	−	28.8131i	0.0705726	−	0.0322294i
$895$	7.35543	+	1.05755i	0.00821836	+	0.00118162i
$896$		−	455.607i		−	0.508490i
$897$	110.020	+	100.453i	0.122653	+	0.111987i
$898$	748.204			0.833189
$899$	−58.2210	+	404.936i	−0.0647620	+	0.450429i
$900$	−312.852	−	685.050i	−0.347613	−	0.761166i
$901$	−197.834	−	58.0894i	−0.219572	−	0.0644722i
$902$	−381.282	+	330.383i	−0.422708	+	0.366278i
$903$	−45.2482	+	13.2861i	−0.0501087	+	0.0147133i
$904$	36.2571	−	56.4171i	0.0401074	−	0.0624083i
$905$	−0.794527	+	1.73977i	−0.000877931	+	0.00192240i
$906$	−44.8724	+	51.7855i	−0.0495280	+	0.0571584i
$907$	549.031	+	854.309i	0.605327	+	0.941907i	0.999736	+	0.0229719i	$0.00731284\pi$
$907$	549.031	+	854.309i	0.605327	+	0.941907i	−0.394409	+	0.918935i	$0.629051\pi$
$908$	−139.020	+	19.9881i	−0.153106	+	0.0220133i
$909$	34.8801	+	242.597i	0.0383720	+	0.266883i
$910$	186.073	−	119.582i	0.204476	−	0.131409i
$911$	729.931	+	632.489i	0.801242	+	0.694280i	0.955901	−	0.293688i	$-0.0948827\pi$
$911$	729.931	+	632.489i	0.801242	+	0.694280i	−0.154660	+	0.987968i	$0.549428\pi$
$912$	96.5468	+	44.0915i	0.105863	+	0.0483459i
$913$	967.406	+	621.714i	1.05959	+	0.680957i
$914$	−74.7163	−	254.460i	−0.0817465	−	0.278403i
$915$	−6.29220	−	7.26158i	−0.00687672	−	0.00793616i
$916$	228.888	−	779.520i	0.249878	−	0.851005i
$917$	688.263	−	314.319i	0.750560	−	0.342769i
$918$	136.107	+	19.5692i	0.148265	+	0.0213173i
$919$		−	451.409i		−	0.491195i	−0.969372	−	0.245598i	$-0.921016\pi$
$919$		−	451.409i		−	0.491195i	0.969372	−	0.245598i	$-0.0789842\pi$
$920$	−1.98057	−	16.8761i	−0.00215279	−	0.0183435i
$921$	−160.742			−0.174529
$922$	−136.285	+	947.885i	−0.147815	+	1.02807i
$923$	−137.997	−	302.172i	−0.149510	−	0.327380i
$924$	−96.0152	−	28.1926i	−0.103913	−	0.0305115i
$925$	−1209.63	+	1048.15i	−1.30771	+	1.13314i
$926$	−517.958	+	152.086i	−0.559350	+	0.164240i
$927$	−549.989	+	855.800i	−0.593300	+	0.923193i
$928$	−372.789	+	816.295i	−0.401713	+	0.879628i
$929$	530.203	−	611.887i	0.570724	−	0.658651i	−0.394860	−	0.918741i	$-0.629207\pi$
$929$	530.203	−	611.887i	0.570724	−	0.658651i	0.965584	+	0.260090i	$0.0837523\pi$
$930$	4.57187	+	7.11397i	0.00491599	+	0.00764943i
$931$	−586.214	+	84.2849i	−0.629661	+	0.0905316i
$932$	−72.3839	−	503.441i	−0.0776651	−	0.540173i
$933$	19.2275	−	12.3567i	0.0206082	−	0.0132441i
$934$	1458.17	+	1263.51i	1.56120	+	1.35279i
$935$	33.2117	+	15.1673i	0.0355206	+	0.0162217i
$936$	−224.122	−	144.035i	−0.239447	−	0.153883i
$937$	−212.936	−	725.193i	−0.227253	−	0.773952i	−0.991622	−	0.129173i	$-0.958768\pi$
$937$	−212.936	−	725.193i	−0.227253	−	0.773952i	0.764369	−	0.644779i	$-0.223051\pi$
$938$	1158.93	+	1337.47i	1.23553	+	1.42588i
$939$	−50.1445	+	170.776i	−0.0534020	+	0.181870i
$940$	−96.9719	+	44.2856i	−0.103162	+	0.0471123i
$941$	−671.463	−	96.5418i	−0.713563	−	0.102595i	−0.224034	−	0.974581i	$-0.571923\pi$
$941$	−671.463	−	96.5418i	−0.713563	−	0.102595i	−0.489530	+	0.871987i	$0.662832\pi$
$942$		−	63.5696i		−	0.0674837i
$943$	−234.700	−	386.940i	−0.248887	−	0.410329i
$944$	−919.976			−0.974551
$945$	3.70427	−	25.7638i	0.00391987	−	0.0272633i
$946$	−161.623	−	353.905i	−0.170849	−	0.374107i
$947$	301.741	+	88.5992i	0.318628	+	0.0935577i	0.437136	−	0.899395i	$-0.355993\pi$
$947$	301.741	+	88.5992i	0.318628	+	0.0935577i	−0.118508	+	0.992953i	$0.537811\pi$
$948$	−72.7569	+	63.0442i	−0.0767478	+	0.0665023i
$949$	−1066.59	+	313.180i	−1.12391	+	0.330011i
$950$	−632.230	+	983.770i	−0.665506	+	1.03555i
$951$	31.5196	−	69.0184i	0.0331437	−	0.0725745i
$952$	−78.0488	+	90.0731i	−0.0819840	+	0.0946146i
$953$	−832.848	−	1295.94i	−0.873922	−	1.35985i	−0.932350	−	0.361557i	$-0.882245\pi$
$953$	−832.848	−	1295.94i	−0.873922	−	1.35985i	0.0584279	−	0.998292i	$-0.481391\pi$
$954$	−596.275	+	85.7314i	−0.625027	+	0.0898652i
$955$	10.9820	+	76.3816i	0.0114995	+	0.0799807i
$956$	−511.146	+	328.494i	−0.534671	+	0.343612i
$957$	−50.9728	−	44.1682i	−0.0532631	−	0.0461528i
$958$	1970.73	+	900.002i	2.05713	+	0.939459i
$959$	−1110.12	−	713.432i	−1.15758	−	0.743934i
$960$	1.99256	+	6.78603i	0.00207558	+	0.00706878i
$961$	381.498	+	440.272i	0.396980	+	0.458139i
$962$	942.315	−	3209.23i	0.979537	−	3.33600i
$963$	−600.403	+	274.195i	−0.623471	+	0.284730i
$964$	345.197	+	49.6319i	0.358089	+	0.0514854i
$965$		−	57.5508i		−	0.0596381i
$966$	85.4640	−	174.966i	0.0884721	−	0.181124i
$967$	−243.442			−0.251749			−0.125875	−	0.992046i	$-0.540174\pi$
$967$	−243.442			−0.251749			−0.125875	+	0.992046i	$0.540174\pi$
$968$	7.27604	−	50.6060i	0.00751657	−	0.0522789i
$969$	−20.3114	−	44.4759i	−0.0209612	−	0.0458987i
$970$	−116.546	−	34.2211i	−0.120151	−	0.0352795i
$971$	277.640	−	240.576i	0.285932	−	0.247761i	−0.500071	−	0.865985i	$-0.666693\pi$
$971$	277.640	−	240.576i	0.285932	−	0.247761i	0.786003	+	0.618223i	$0.212147\pi$
$972$	267.122	−	78.4340i	0.274816	−	0.0806934i
$973$	−205.063	+	319.085i	−0.210754	+	0.327939i
$974$	−136.932	+	299.840i	−0.140587	+	0.307843i
$975$	−105.115	+	121.309i	−0.107810	+	0.124419i
$976$	585.352	+	910.825i	0.599746	+	0.933223i
$977$	1069.34	−	153.748i	1.09451	−	0.157367i	0.428671	−	0.903461i	$-0.358982\pi$
$977$	1069.34	−	153.748i	1.09451	−	0.157367i	0.665841	+	0.746093i	$0.268073\pi$
$978$	−14.7132	−	102.333i	−0.0150442	−	0.104634i
$979$	−1394.64	+	896.283i	−1.42456	+	0.915509i
$980$	−41.3924	−	35.8667i	−0.0422371	−	0.0365987i
$981$	−394.155	−	180.005i	−0.401789	−	0.183491i
$982$	116.808	+	75.0677i	0.118949	+	0.0764437i
$983$	344.325	+	1172.66i	0.350280	+	1.19294i	0.926704	+	0.375793i	$0.122630\pi$
$983$	344.325	+	1172.66i	0.350280	+	1.19294i	−0.576424	+	0.817151i	$0.695552\pi$
$984$	−6.92645	−	7.99355i	−0.00703908	−	0.00812353i
$985$	31.5027	−	107.288i	0.0319824	−	0.108922i
$986$	431.647	−	197.126i	0.437775	−	0.199925i
$987$	204.706	+	29.4323i	0.207403	+	0.0298200i
$988$		−	1126.51i		−	1.14019i
$989$	337.303	−	89.5945i	0.341055	−	0.0905910i
$990$	106.673			0.107751
$991$	139.165	−	967.914i	0.140429	−	0.976704i	−0.790749	−	0.612140i	$-0.790309\pi$
$991$	139.165	−	967.914i	0.140429	−	0.976704i	0.931178	−	0.364564i	$-0.118782\pi$
$992$	−344.848	−	755.111i	−0.347629	−	0.761201i
$993$	97.0374	+	28.4928i	0.0977215	+	0.0286936i
$994$	−328.137	+	284.333i	−0.330118	+	0.286049i
$995$	106.063	−	31.1428i	0.106596	−	0.0312993i
$996$	76.9957	−	119.808i	0.0773049	−	0.120289i
$997$	233.396	−	511.067i	0.234099	−	0.512604i	−0.755728	−	0.654886i	$-0.772717\pi$
$997$	233.396	−	511.067i	0.234099	−	0.512604i	0.989826	+	0.142282i	$0.0454439\pi$
$998$	61.2260	−	70.6586i	0.0613487	−	0.0708002i
$999$	−212.796	−	331.118i	−0.213009	−	0.331449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.15.1	✓	30
3.2	odd	2		207.3.j.a.199.3		30
4.3	odd	2		368.3.p.a.337.2		30
23.7	odd	22		529.3.b.b.528.27		30
23.16	even	11		529.3.b.b.528.28		30
23.20	odd	22	inner	23.3.d.a.20.1	yes	30
69.20	even	22		207.3.j.a.181.3		30
92.43	even	22		368.3.p.a.273.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.15.1	✓	30	1.1	even	1	trivial
23.3.d.a.20.1	yes	30	23.20	odd	22	inner
207.3.j.a.181.3		30	69.20	even	22
207.3.j.a.199.3		30	3.2	odd	2
368.3.p.a.273.2		30	92.43	even	22
368.3.p.a.337.2		30	4.3	odd	2
529.3.b.b.528.27		30	23.7	odd	22
529.3.b.b.528.28		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)

\(f(q)\)	\(=\)	\(q+(-0.387684 + 2.69640i) q^{2} +(-0.141551 - 0.309954i) q^{3} +(-3.28232 - 0.963778i) q^{4} +(-0.353921 + 0.306674i) q^{5} +(0.890639 - 0.261515i) q^{6} +(4.93105 - 7.67286i) q^{7} +(-0.655341 + 1.43500i) q^{8} +(5.81771 - 6.71400i) q^{9} +O(q^{10})\)	\(q+(-0.387684 + 2.69640i) q^{2} +(-0.141551 - 0.309954i) q^{3} +(-3.28232 - 0.963778i) q^{4} +(-0.353921 + 0.306674i) q^{5} +(0.890639 - 0.261515i) q^{6} +(4.93105 - 7.67286i) q^{7} +(-0.655341 + 1.43500i) q^{8} +(5.81771 - 6.71400i) q^{9} +(-0.689708 - 1.07321i) q^{10} +(-9.31650 + 1.33951i) q^{11} +(0.165891 + 1.15379i) q^{12} +(-15.9918 + 10.2773i) q^{13} +(18.7774 + 16.2708i) q^{14} +(0.145153 + 0.0662892i) q^{15} +(-15.1266 - 9.72129i) q^{16} +(2.33367 + 7.94773i) q^{17} +(15.8482 + 18.2898i) q^{18} +(4.88047 - 16.6214i) q^{19} +(1.45725 - 0.665504i) q^{20} +(-3.07623 - 0.442296i) q^{21} -25.6404i q^{22} +(22.6732 + 3.86340i) q^{23} +0.537548 q^{24} +(-3.52666 + 24.5285i) q^{25} +(-21.5119 - 47.1046i) q^{26} +(-5.84704 - 1.71684i) q^{27} +(-23.5802 + 20.4324i) q^{28} +(-20.1778 + 5.92475i) q^{29} +(-0.235016 + 0.365692i) q^{30} +(8.08126 - 17.6955i) q^{31} +(27.9446 - 32.2498i) q^{32} +(1.73395 + 2.69808i) q^{33} +(-22.3350 + 3.21129i) q^{34} +(0.607868 + 4.22781i) q^{35} +(-25.5664 + 16.4305i) q^{36} +(48.8134 + 42.2971i) q^{37} +(42.9259 + 19.6036i) q^{38} +(5.44914 + 3.50195i) q^{39} +(-0.208138 - 0.708852i) q^{40} +(-12.8853 - 14.8704i) q^{41} +(2.38522 - 8.12330i) q^{42} +(13.8027 - 6.30346i) q^{43} +(31.8708 + 4.58232i) q^{44} +4.16037i q^{45} +(-19.2073 + 59.6383i) q^{46} -66.5445 q^{47} +(-0.871962 + 6.06463i) q^{48} +(-14.2022 - 31.0986i) q^{49} +(-64.7714 - 19.0186i) q^{50} +(2.13310 - 1.84834i) q^{51} +(62.3951 - 18.3209i) q^{52} +(-13.4576 + 20.9404i) q^{53} +(6.89611 - 15.1004i) q^{54} +(2.88651 - 3.33121i) q^{55} +(7.77901 + 12.1044i) q^{56} +(-5.84270 + 0.840054i) q^{57} +(-8.15288 - 56.7045i) q^{58} +(43.0416 - 27.6611i) q^{59} +(-0.412551 - 0.357478i) q^{60} +(-54.7720 - 25.0135i) q^{61} +(44.5812 + 28.6506i) q^{62} +(-22.8282 - 77.7455i) q^{63} +(29.0244 + 33.4959i) q^{64} +(2.50804 - 8.54160i) q^{65} +(-7.94734 + 3.62943i) q^{66} +(70.5025 + 10.1367i) q^{67} -28.3362i q^{68} +(-2.01195 - 7.57453i) q^{69} -11.6356 q^{70} +(-2.48696 + 17.2972i) q^{71} +(5.82198 + 12.7484i) q^{72} +(56.1087 + 16.4750i) q^{73} +(-132.974 + 115.223i) q^{74} +(8.10191 - 2.37893i) q^{75} +(-32.0386 + 49.8530i) q^{76} +(-35.6622 + 78.0894i) q^{77} +(-11.5552 + 13.3354i) q^{78} +(44.6512 + 69.4787i) q^{79} +(8.33490 - 1.19838i) q^{80} +(-11.0833 - 77.0859i) q^{81} +(45.0920 - 28.9789i) q^{82} +(-92.3345 - 80.0083i) q^{83} +(9.67092 + 4.41656i) q^{84} +(-3.26330 - 2.09719i) q^{85} +(11.6456 + 39.6613i) q^{86} +(4.69260 + 5.41555i) q^{87} +(4.18329 - 14.2470i) q^{88} +(160.216 - 73.1683i) q^{89} +(-11.2180 - 1.61291i) q^{90} +173.380i q^{91} +(-70.6974 - 34.5329i) q^{92} -6.62871 q^{93} +(25.7983 - 179.431i) q^{94} +(3.37004 + 7.37937i) q^{95} +(-13.9515 - 4.09654i) q^{96} +(71.9579 - 62.3518i) q^{97} +(89.3603 - 26.2385i) q^{98} +(-45.2072 + 70.3438i) 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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