LMFDB - Embedded newform 99.2.p.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	99.2
Dual form			99.2.p.a.50.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02662 - 1.14018i) q^{2} +(-0.926210 + 1.46360i) q^{3} +(-0.0369992 + 0.352024i) q^{4} +(-2.07594 - 1.86918i) q^{5} +(2.61964 - 0.446523i) q^{6} +(-1.07503 - 2.41456i) q^{7} +(-2.04313 + 1.48442i) q^{8} +(-1.28427 - 2.71121i) q^{9} +O(q^{10})$	\(q+(-1.02662 - 1.14018i) q^{2} +(-0.926210 + 1.46360i) q^{3} +(-0.0369992 + 0.352024i) q^{4} +(-2.07594 - 1.86918i) q^{5} +(2.61964 - 0.446523i) q^{6} +(-1.07503 - 2.41456i) q^{7} +(-2.04313 + 1.48442i) q^{8} +(-1.28427 - 2.71121i) q^{9} +4.28588i q^{10} +(-0.894961 - 3.19359i) q^{11} +(-0.480955 - 0.380200i) q^{12} +(0.824813 + 3.88044i) q^{13} +(-1.64938 + 3.70458i) q^{14} +(4.65849 - 1.30709i) q^{15} +(4.48249 + 0.952784i) q^{16} +(0.950349 + 2.92487i) q^{17} +(-1.77280 + 4.24769i) q^{18} +(-3.46908 - 4.77479i) q^{19} +(0.734805 - 0.661621i) q^{20} +(4.52967 + 0.662970i) q^{21} +(-2.72248 + 4.29903i) q^{22} +(6.81163 - 3.93270i) q^{23} +(-0.280237 - 4.36523i) q^{24} +(0.293029 + 2.78799i) q^{25} +(3.57763 - 4.92418i) q^{26} +(5.15764 + 0.631484i) q^{27} +(0.889760 - 0.289101i) q^{28} +(-1.62991 + 0.725684i) q^{29} +(-6.27283 - 3.96963i) q^{30} +(0.336898 - 0.0716100i) q^{31} +(-0.990031 - 1.71478i) q^{32} +(5.50308 + 1.64807i) q^{33} +(2.35923 - 4.08631i) q^{34} +(-2.28156 + 7.02191i) q^{35} +(1.00193 - 0.351782i) q^{36} +(-0.830542 - 0.603424i) q^{37} +(-1.88267 + 8.85728i) q^{38} +(-6.44338 - 2.38690i) q^{39} +(7.01607 + 0.737419i) q^{40} +(-0.905030 - 0.402945i) q^{41} +(-3.89436 - 5.84526i) q^{42} +(-6.81106 - 3.93236i) q^{43} +(1.15733 - 0.196887i) q^{44} +(-2.40167 + 8.02883i) q^{45} +(-11.4770 - 3.72909i) q^{46} +(-4.08522 + 0.429374i) q^{47} +(-5.54623 + 5.67812i) q^{48} +(0.00949289 - 0.0105429i) q^{49} +(2.87798 - 3.19632i) q^{50} +(-5.16108 - 1.31811i) q^{51} +(-1.39653 + 0.146781i) q^{52} +(0.543068 + 0.176453i) q^{53} +(-4.57494 - 6.52893i) q^{54} +(-4.11152 + 8.30254i) q^{55} +(5.78067 + 3.33747i) q^{56} +(10.2015 - 0.654912i) q^{57} +(2.50071 + 1.11339i) q^{58} +(5.35030 + 0.562340i) q^{59} +(0.287768 + 1.68826i) q^{60} +(0.638862 - 3.00561i) q^{61} +(-0.427516 - 0.310608i) q^{62} +(-5.16575 + 6.01559i) q^{63} +(1.89345 - 5.82744i) q^{64} +(5.54099 - 9.59727i) q^{65} +(-3.77049 - 7.96644i) q^{66} +(-6.19123 - 10.7235i) q^{67} +(-1.06479 + 0.226328i) q^{68} +(-0.553090 + 13.6120i) q^{69} +(10.3485 - 4.60746i) q^{70} +(6.04945 - 1.96559i) q^{71} +(6.64852 + 3.63296i) q^{72} +(2.35594 - 3.24267i) q^{73} +(0.164641 + 1.56646i) q^{74} +(-4.35192 - 2.15338i) q^{75} +(1.80919 - 1.04454i) q^{76} +(-6.74902 + 5.59416i) q^{77} +(3.89342 + 9.79705i) q^{78} +(2.19900 - 1.97999i) q^{79} +(-7.52445 - 10.3565i) q^{80} +(-5.70130 + 6.96385i) q^{81} +(0.469694 + 1.44557i) q^{82} +(-4.50447 - 0.957455i) q^{83} +(-0.400976 + 1.57002i) q^{84} +(3.49425 - 7.84822i) q^{85} +(2.50878 + 11.8029i) q^{86} +(0.447528 - 3.05768i) q^{87} +(6.56917 + 5.19644i) q^{88} -13.1208i q^{89} +(11.6199 - 5.50423i) q^{90} +(8.48287 - 6.16317i) q^{91} +(1.13238 + 2.54336i) q^{92} +(-0.207230 + 0.559411i) q^{93} +(4.68355 + 4.21708i) q^{94} +(-1.72334 + 16.3965i) q^{95} +(3.42674 + 0.139237i) q^{96} +(7.37347 + 8.18907i) q^{97} -0.0217664 q^{98} +(-7.50913 + 6.52786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.02662	−	1.14018i	−0.725932	−	0.806229i	0.261344	−	0.965246i	$-0.415834\pi$
$2$	−1.02662	−	1.14018i	−0.725932	−	0.806229i	−0.987276	+	0.159017i	$0.949168\pi$
$3$	−0.926210	+	1.46360i	−0.534747	+	0.845012i
$3$	−0.926210	+	1.46360i	−0.534747	+	0.845012i
$4$	−0.0369992	+	0.352024i	−0.0184996	+	0.176012i
$5$	−2.07594	−	1.86918i	−0.928387	−	0.835923i	0.0583428	−	0.998297i	$-0.481418\pi$
$5$	−2.07594	−	1.86918i	−0.928387	−	0.835923i	−0.986729	+	0.162374i	$0.948085\pi$
$6$	2.61964	−	0.446523i	1.06946	−	0.182292i
$7$	−1.07503	−	2.41456i	−0.406324	−	0.912619i	−0.994583	−	0.103946i	$-0.966853\pi$
$7$	−1.07503	−	2.41456i	−0.406324	−	0.912619i	0.588259	−	0.808673i	$-0.299814\pi$
$8$	−2.04313	+	1.48442i	−0.722357	+	0.524823i
$9$	−1.28427	−	2.71121i	−0.428090	−	0.903736i
$10$			4.28588i			1.35531i
$11$	−0.894961	−	3.19359i	−0.269841	−	0.962905i
$11$	−0.894961	−	3.19359i	−0.269841	−	0.962905i
$12$	−0.480955	−	0.380200i	−0.138840	−	0.109754i
$13$	0.824813	+	3.88044i	0.228762	+	1.07624i	0.931204	+	0.364499i	$0.118760\pi$
$13$	0.824813	+	3.88044i	0.228762	+	1.07624i	−0.702442	+	0.711741i	$0.747907\pi$
$14$	−1.64938	+	3.70458i	−0.440816	+	0.990089i
$15$	4.65849	−	1.30709i	1.20282	−	0.337490i
$16$	4.48249	+	0.952784i	1.12062	+	0.238196i
$17$	0.950349	+	2.92487i	0.230493	+	0.709386i	0.997687	+	0.0679706i	$0.0216524\pi$
$17$	0.950349	+	2.92487i	0.230493	+	0.709386i	−0.767194	+	0.641415i	$0.778348\pi$
$18$	−1.77280	+	4.24769i	−0.417854	+	1.00119i
$19$	−3.46908	−	4.77479i	−0.795863	−	1.09541i	−0.993353	−	0.115106i	$-0.963279\pi$
$19$	−3.46908	−	4.77479i	−0.795863	−	1.09541i	0.197491	−	0.980305i	$-0.436721\pi$
$20$	0.734805	−	0.661621i	0.164307	−	0.147943i
$21$	4.52967	+	0.662970i	0.988455	+	0.144672i
$22$	−2.72248	+	4.29903i	−0.580436	+	0.916557i
$23$	6.81163	−	3.93270i	1.42032	−	0.820024i	0.423997	−	0.905664i	$-0.360627\pi$
$23$	6.81163	−	3.93270i	1.42032	−	0.820024i	0.996326	+	0.0856397i	$0.0272934\pi$
$24$	−0.280237	−	4.36523i	−0.0572032	−	0.891048i
$25$	0.293029	+	2.78799i	0.0586059	+	0.557598i
$26$	3.57763	−	4.92418i	0.701631	−	0.965712i
$27$	5.15764	+	0.631484i	0.992588	+	0.121529i
$28$	0.889760	−	0.289101i	0.168149	−	0.0546349i
$29$	−1.62991	+	0.725684i	−0.302667	+	0.134756i	−0.552451	−	0.833546i	$-0.686307\pi$
$29$	−1.62991	+	0.725684i	−0.302667	+	0.134756i	0.249783	+	0.968302i	$0.419641\pi$
$30$	−6.27283	−	3.96963i	−1.14526	−	0.724751i
$31$	0.336898	−	0.0716100i	0.0605087	−	0.0128615i	−0.177558	−	0.984110i	$-0.556820\pi$
$31$	0.336898	−	0.0716100i	0.0605087	−	0.0128615i	0.238067	+	0.971249i	$0.423486\pi$
$32$	−0.990031	−	1.71478i	−0.175014	−	0.303134i
$33$	5.50308	+	1.64807i	0.957963	+	0.286892i
$34$	2.35923	−	4.08631i	0.404605	−	0.700796i
$35$	−2.28156	+	7.02191i	−0.385653	+	1.18692i
$36$	1.00193	−	0.351782i	0.166988	−	0.0586303i
$37$	−0.830542	−	0.603424i	−0.136540	−	0.0992023i	0.517419	−	0.855732i	$-0.326893\pi$
$37$	−0.830542	−	0.603424i	−0.136540	−	0.0992023i	−0.653959	+	0.756530i	$0.726893\pi$
$38$	−1.88267	+	8.85728i	−0.305410	+	1.43684i
$39$	−6.44338	−	2.38690i	−1.03177	−	0.382210i
$40$	7.01607	+	0.737419i	1.10934	+	0.116596i
$41$	−0.905030	−	0.402945i	−0.141342	−	0.0629295i	0.334847	−	0.942273i	$-0.391315\pi$
$41$	−0.905030	−	0.402945i	−0.141342	−	0.0629295i	−0.476189	+	0.879343i	$0.657982\pi$
$42$	−3.89436	−	5.84526i	−0.600912	−	0.901943i
$43$	−6.81106	−	3.93236i	−1.03868	−	0.599680i	−0.119218	−	0.992868i	$-0.538039\pi$
$43$	−6.81106	−	3.93236i	−1.03868	−	0.599680i	−0.919458	+	0.393188i	$0.871372\pi$
$44$	1.15733	−	0.196887i	0.174475	−	0.0296819i
$45$	−2.40167	+	8.02883i	−0.358020	+	1.19687i
$46$	−11.4770	−	3.72909i	−1.69218	−	0.549824i
$47$	−4.08522	+	0.429374i	−0.595891	+	0.0626307i	−0.397673	−	0.917527i	$-0.630182\pi$
$47$	−4.08522	+	0.429374i	−0.595891	+	0.0626307i	−0.198218	+	0.980158i	$0.563515\pi$
$48$	−5.54623	+	5.67812i	−0.800529	+	0.819566i
$49$	0.00949289	−	0.0105429i	0.00135613	−	0.00150613i
$50$	2.87798	−	3.19632i	0.407007	−	0.452028i
$51$	−5.16108	−	1.31811i	−0.722695	−	0.184573i
$52$	−1.39653	+	0.146781i	−0.193663	+	0.0203548i
$53$	0.543068	+	0.176453i	0.0745961	+	0.0242377i	0.346077	−	0.938206i	$-0.387513\pi$
$53$	0.543068	+	0.176453i	0.0745961	+	0.0242377i	−0.271481	+	0.962444i	$0.587513\pi$
$54$	−4.57494	−	6.52893i	−0.622571	−	0.888475i
$55$	−4.11152	+	8.30254i	−0.554398	+	1.11951i
$56$	5.78067	+	3.33747i	0.772475	+	0.445989i
$57$	10.2015	−	0.654912i	1.35122	−	0.0867452i
$58$	2.50071	+	1.11339i	0.328360	+	0.146195i
$59$	5.35030	+	0.562340i	0.696550	+	0.0732104i	0.446185	−	0.894941i	$-0.352782\pi$
$59$	5.35030	+	0.562340i	0.696550	+	0.0732104i	0.250366	+	0.968151i	$0.419449\pi$
$60$	0.287768	+	1.68826i	0.0371507	+	0.217954i
$61$	0.638862	−	3.00561i	0.0817979	−	0.384829i	−0.918137	−	0.396264i	$-0.870307\pi$
$61$	0.638862	−	3.00561i	0.0817979	−	0.384829i	0.999935	+	0.0114349i	$0.00363994\pi$
$62$	−0.427516	−	0.310608i	−0.0542945	−	0.0394473i
$63$	−5.16575	+	6.01559i	−0.650823	+	0.757893i
$64$	1.89345	−	5.82744i	0.236681	−	0.728430i
$65$	5.54099	−	9.59727i	0.687275	−	1.19039i
$66$	−3.77049	−	7.96644i	−0.464115	−	0.980601i
$67$	−6.19123	−	10.7235i	−0.756380	−	1.31009i	−0.944686	−	0.327977i	$-0.893633\pi$
$67$	−6.19123	−	10.7235i	−0.756380	−	1.31009i	0.188306	−	0.982110i	$-0.439700\pi$
$68$	−1.06479	+	0.226328i	−0.129124	+	0.0274463i
$69$	−0.553090	+	13.6120i	−0.0665842	+	1.63870i
$70$	10.3485	−	4.60746i	1.23689	−	0.550697i
$71$	6.04945	−	1.96559i	0.717938	−	0.233272i	0.0728088	−	0.997346i	$-0.476804\pi$
$71$	6.04945	−	1.96559i	0.717938	−	0.233272i	0.645129	+	0.764074i	$0.276804\pi$
$72$	6.64852	+	3.63296i	0.783536	+	0.428148i
$73$	2.35594	−	3.24267i	0.275742	−	0.379526i	−0.648576	−	0.761150i	$-0.724635\pi$
$73$	2.35594	−	3.24267i	0.275742	−	0.379526i	0.924318	+	0.381624i	$0.124635\pi$
$74$	0.164641	+	1.56646i	0.0191391	+	0.182097i
$75$	−4.35192	−	2.15338i	−0.502516	−	0.248651i
$76$	1.80919	−	1.04454i	0.207529	−	0.119817i
$77$	−6.74902	+	5.59416i	−0.769123	+	0.637514i
$78$	3.89342	+	9.79705i	0.440843	+	1.10930i
$79$	2.19900	−	1.97999i	0.247407	−	0.222766i	−0.536092	−	0.844160i	$-0.680100\pi$
$79$	2.19900	−	1.97999i	0.247407	−	0.222766i	0.783499	+	0.621394i	$0.213433\pi$
$80$	−7.52445	−	10.3565i	−0.841259	−	1.15789i
$81$	−5.70130	+	6.96385i	−0.633477	+	0.773761i
$82$	0.469694	+	1.44557i	0.0518690	+	0.159636i
$83$	−4.50447	−	0.957455i	−0.494430	−	0.105094i	−0.0460533	−	0.998939i	$-0.514664\pi$
$83$	−4.50447	−	0.957455i	−0.494430	−	0.105094i	−0.448377	+	0.893845i	$0.647998\pi$
$84$	−0.400976	+	1.57002i	−0.0437500	+	0.171304i
$85$	3.49425	−	7.84822i	0.379005	−	0.851259i
$86$	2.50878	+	11.8029i	0.270529	+	1.27274i
$87$	0.447528	−	3.05768i	0.0479800	−	0.327818i
$88$	6.56917	+	5.19644i	0.700276	+	0.553943i
$89$		−	13.1208i		−	1.39080i	−0.718622	−	0.695401i	$-0.755227\pi$
$89$		−	13.1208i		−	1.39080i	0.718622	−	0.695401i	$-0.244773\pi$
$90$	11.6199	−	5.50423i	1.22485	−	0.580197i
$91$	8.48287	−	6.16317i	0.889246	−	0.646075i
$92$	1.13238	+	2.54336i	0.118059	+	0.265164i
$93$	−0.207230	+	0.559411i	−0.0214887	+	0.0580083i
$94$	4.68355	+	4.21708i	0.483071	+	0.434959i
$95$	−1.72334	+	16.3965i	−0.176811	+	1.68224i
$96$	3.42674	+	0.139237i	0.349740	+	0.0142108i
$97$	7.37347	+	8.18907i	0.748663	+	0.831474i	0.990308	−	0.138890i	$-0.0443536\pi$
$97$	7.37347	+	8.18907i	0.748663	+	0.831474i	−0.241645	+	0.970365i	$0.577687\pi$
$98$	−0.0217664			−0.00219874
$99$	−7.50913	+	6.52786i	−0.754696	+	0.656075i
$100$	−0.992281			−0.0992281
$101$	6.41814	+	7.12806i	0.638629	+	0.709269i	0.972383	−	0.233391i	$-0.0749823\pi$
$101$	6.41814	+	7.12806i	0.638629	+	0.709269i	−0.333754	+	0.942660i	$0.608316\pi$
$102$	3.79559	+	7.23776i	0.375820	+	0.716645i
$103$	−1.52616	+	14.5205i	−0.150377	+	1.43074i	0.615693	+	0.787986i	$0.288876\pi$
$103$	−1.52616	+	14.5205i	−0.150377	+	1.43074i	−0.766070	+	0.642757i	$0.777790\pi$
$104$	−7.44543	−	6.70389i	−0.730084	−	0.657371i
$105$	−8.16409	−	9.84306i	−0.796734	−	0.960584i
$106$	−0.356337	−	0.800346i	−0.0346105	−	0.0777364i
$107$	−3.05515	+	2.21970i	−0.295353	+	0.214586i	−0.725586	−	0.688131i	$-0.758431\pi$
$107$	−3.05515	+	2.21970i	−0.295353	+	0.214586i	0.430234	+	0.902718i	$0.358431\pi$
$108$	−0.413126	+	1.79225i	−0.0397531	+	0.172459i
$109$			17.8297i			1.70777i	0.520460	+	0.853886i	$0.325760\pi$
$109$			17.8297i			1.70777i	−0.520460	+	0.853886i	$0.674240\pi$
$110$	13.6874	−	3.83570i	1.30504	−	0.365719i
$111$	1.65243	−	0.656687i	0.156842	−	0.0623300i
$112$	−2.51827	−	11.8475i	−0.237954	−	1.11949i
$113$	5.06020	−	11.3654i	0.476023	−	1.06917i	−0.502790	−	0.864409i	$-0.667693\pi$
$113$	5.06020	−	11.3654i	0.476023	−	1.06917i	0.978813	−	0.204757i	$-0.0656404\pi$
$114$	−11.2198	−	10.9592i	−1.05083	−	1.02642i
$115$	−21.4914	−	4.56814i	−2.00409	−	0.425982i
$116$	−0.195153	−	0.600618i	−0.0181195	−	0.0557660i
$117$	9.46140	−	7.21978i	0.874707	−	0.667469i
$118$	−4.85157	−	6.67762i	−0.446624	−	0.614725i
$119$	6.04063	−	5.43901i	0.553744	−	0.498593i
$120$	−7.57765	+	9.58575i	−0.691741	+	0.875055i
$121$	−9.39809	+	5.71628i	−0.854372	+	0.519662i
$122$	−4.08280	+	2.35721i	−0.369640	+	0.213412i
$123$	1.42800	−	0.951393i	0.128758	−	0.0857842i
$124$	0.0127435	+	0.121246i	0.00114440	+	0.0108882i
$125$	−3.60679	+	4.96432i	−0.322601	+	0.444022i
$126$	12.1621	−	0.285858i	1.08349	−	0.0254662i
$127$	5.84705	−	1.89982i	0.518842	−	0.168582i	−0.0378780	−	0.999282i	$-0.512060\pi$
$127$	5.84705	−	1.89982i	0.518842	−	0.168582i	0.556719	+	0.830701i	$0.312060\pi$
$128$	−12.2059	+	5.43444i	−1.07886	+	0.480341i
$129$	12.0639	−	6.32649i	1.06217	−	0.557016i
$130$	−16.6311	+	3.53505i	−1.45865	+	0.310045i
$131$	−3.27124	−	5.66595i	−0.285810	−	0.495037i	0.686996	−	0.726662i	$-0.258929\pi$
$131$	−3.27124	−	5.66595i	−0.285810	−	0.495037i	−0.972805	+	0.231625i	$0.925596\pi$
$132$	−0.783770	+	1.87624i	−0.0682184	+	0.163306i
$133$	−7.79964	+	13.5094i	−0.676315	+	1.17141i
$134$	−5.87069	+	18.0681i	−0.507151	+	1.56085i
$135$	−9.52657	−	10.9515i	−0.819916	−	0.942553i
$136$	−6.28344	−	4.56519i	−0.538801	−	0.391462i
$137$	1.33907	−	6.29981i	0.114404	−	0.538229i	−0.883197	−	0.469003i	$-0.844613\pi$
$137$	1.33907	−	6.29981i	0.114404	−	0.538229i	0.997601	−	0.0692268i	$-0.0220532\pi$
$138$	16.0880	−	13.3438i	1.36950	−	1.13590i
$139$	20.2352	+	2.12680i	1.71633	+	0.180393i	0.910991	−	0.412427i	$-0.135319\pi$
$139$	20.2352	+	2.12680i	1.71633	+	0.180393i	0.805335	+	0.592820i	$0.201986\pi$
$140$	−2.38747	−	1.06297i	−0.201778	−	0.0898372i
$141$	3.15534	−	6.37684i	0.265728	−	0.537027i
$142$	−8.45162	−	4.87955i	−0.709244	−	0.409482i
$143$	11.6544	−	6.10696i	0.974588	−	0.510690i
$144$	−3.17354	−	13.3766i	−0.264462	−	1.11472i
$145$	4.74003	+	1.54013i	0.393638	+	0.127901i
$146$	−6.11589	+	0.642806i	−0.506155	+	0.0531990i
$147$	0.00663825	+	0.0236588i	0.000547514	+	0.00195134i
$148$	0.243149	−	0.270045i	0.0199867	−	0.0221975i
$149$	3.49745	−	3.88431i	0.286522	−	0.318215i	−0.582651	−	0.812722i	$-0.697985\pi$
$149$	3.49745	−	3.88431i	0.286522	−	0.318215i	0.869174	+	0.494507i	$0.164651\pi$
$150$	2.01253	+	7.17268i	0.164322	+	0.585647i
$151$	3.60133	−	0.378515i	0.293072	−	0.0308031i	0.0431486	−	0.999069i	$-0.486261\pi$
$151$	3.60133	−	0.378515i	0.293072	−	0.0308031i	0.249924	+	0.968266i	$0.419594\pi$
$152$	14.1756	+	4.60594i	1.14979	+	0.373591i
$153$	6.70943	−	6.33292i	0.542425	−	0.511986i
$154$	13.3070	+	1.95201i	1.07231	+	0.157298i
$155$	−0.833231	−	0.481066i	−0.0669267	−	0.0386402i
$156$	1.07865	−	2.17991i	0.0863609	−	0.174533i
$157$	−9.66974	−	4.30524i	−0.771729	−	0.343596i	−0.0171911	−	0.999852i	$-0.505472\pi$
$157$	−9.66974	−	4.30524i	−0.771729	−	0.343596i	−0.754538	+	0.656256i	$0.772139\pi$
$158$	−4.51508	−	0.474555i	−0.359201	−	0.0377535i
$159$	−0.761252	+	0.631403i	−0.0603712	+	0.0500735i
$160$	−1.15000	+	5.41033i	−0.0909156	+	0.427724i
$161$	−16.8185	−	12.2193i	−1.32548	−	0.963019i
$162$	13.7931	−	0.648743i	1.08369	−	0.0509701i
$163$	−4.87570	+	15.0059i	−0.381894	+	1.17535i	0.556814	+	0.830637i	$0.312023\pi$
$163$	−4.87570	+	15.0059i	−0.381894	+	1.17535i	−0.938708	+	0.344712i	$0.887977\pi$
$164$	0.175332	−	0.303684i	0.0136911	−	0.0237137i
$165$	−8.34349	−	13.7075i	−0.649540	−	1.06713i
$166$	3.53272	+	6.11885i	0.274192	+	0.474915i
$167$	−6.06696	+	1.28957i	−0.469475	+	0.0997900i	−0.436574	−	0.899669i	$-0.643808\pi$
$167$	−6.06696	+	1.28957i	−0.469475	+	0.0997900i	−0.0329016	+	0.999459i	$0.510475\pi$
$168$	−10.2389	+	5.36941i	−0.789945	+	0.414259i
$169$	−2.50141	+	1.11370i	−0.192416	+	0.0856693i
$170$	−12.5357	+	4.07308i	−0.961441	+	0.312391i
$171$	−8.49019	+	15.5375i	−0.649261	+	1.18818i
$172$	1.63629	−	2.25216i	0.124766	−	0.171726i
$173$	1.53964	+	14.6487i	0.117056	+	1.11372i	0.882532	+	0.470252i	$0.155837\pi$
$173$	1.53964	+	14.6487i	0.117056	+	1.11372i	−0.765476	+	0.643465i	$0.777496\pi$
$174$	−3.94575	+	2.62882i	−0.299126	+	0.199291i
$175$	6.41676	−	3.70472i	0.485061	−	0.280050i
$176$	−0.968852	−	15.1680i	−0.0730300	−	1.14333i
$177$	−5.77855	+	7.30988i	−0.434342	+	0.549444i
$178$	−14.9601	+	13.4701i	−1.12130	+	1.00963i
$179$	7.32242	+	10.0784i	0.547303	+	0.753299i	0.989643	−	0.143549i	$-0.0458515\pi$
$179$	7.32242	+	10.0784i	0.547303	+	0.753299i	−0.442340	+	0.896848i	$0.645851\pi$
$180$	−2.73748	−	1.14251i	−0.204040	−	0.0851575i
$181$	0.342305	+	1.05351i	0.0254433	+	0.0783064i	0.962972	−	0.269602i	$-0.0868921\pi$
$181$	0.342305	+	1.05351i	0.0254433	+	0.0783064i	−0.937529	+	0.347908i	$0.886892\pi$
$182$	−15.7358	−	3.34475i	−1.16642	−	0.247929i
$183$	3.80730	+	3.71886i	0.281444	+	0.274906i
$184$	−8.07929	+	18.1464i	−0.595613	+	1.33777i
$185$	0.596243	+	2.80510i	0.0438367	+	0.206235i
$186$	0.850576	−	0.338025i	0.0623673	−	0.0247852i
$187$	8.49033	−	5.65267i	0.620875	−	0.413364i
$188$		−	1.45398i		−	0.106043i
$189$	−4.01987	−	13.1323i	−0.292403	−	0.955235i
$190$	20.4642	−	14.8681i	1.48463	−	1.07864i
$191$	−7.96099	−	17.8807i	−0.576037	−	1.29380i	−0.933066	−	0.359706i	$-0.882877\pi$
$191$	−7.96099	−	17.8807i	−0.576037	−	1.29380i	0.357029	−	0.934093i	$-0.383790\pi$
$192$	6.77533	+	8.16870i	0.488968	+	0.589525i
$193$	−7.07067	−	6.36646i	−0.508958	−	0.458268i	0.374197	−	0.927349i	$-0.377918\pi$
$193$	−7.07067	−	6.36646i	−0.508958	−	0.458268i	−0.883155	+	0.469081i	$0.844585\pi$
$194$	1.76724	−	16.8142i	0.126880	−	1.20719i
$195$	8.91448	+	16.9989i	0.638379	+	1.21732i
$196$	0.00336013	+	0.00373181i	0.000240010	+	0.000266558i
$197$	0.576409			0.0410674			0.0205337	−	0.999789i	$-0.493463\pi$
$197$	0.576409			0.0410674			0.0205337	+	0.999789i	$0.493463\pi$
$198$	15.1520	+	1.86010i	1.07680	+	0.132192i
$199$	21.9796			1.55809			0.779047	−	0.626965i	$-0.215703\pi$
$199$	21.9796			1.55809			0.779047	+	0.626965i	$0.215703\pi$
$200$	−4.73726	−	5.26126i	−0.334975	−	0.372027i
$201$	21.4294	+	0.870728i	1.51151	+	0.0614164i
$202$	1.53827	−	14.6357i	0.108232	−	1.02976i
$203$	3.50442	+	3.15539i	0.245962	+	0.221465i
$204$	0.654963	−	1.76805i	0.0458566	−	0.123789i
$205$	1.12561	+	2.52815i	0.0786157	+	0.176574i
$206$	18.1227	−	13.1669i	1.26267	−	0.917384i
$207$	−19.4103	−	13.4171i	−1.34911	−	0.932553i
$208$			18.1799i			1.26055i
$209$	−12.1440	+	15.3521i	−0.840020	+	1.06193i
$210$	−2.84141	+	19.4136i	−0.196076	+	1.33967i
$211$	−5.00050	−	23.5255i	−0.344248	−	1.61956i	−0.720785	−	0.693159i	$-0.756218\pi$
$211$	−5.00050	−	23.5255i	−0.344248	−	1.61956i	0.376536	−	0.926402i	$-0.377115\pi$
$212$	−0.0822089	+	0.184644i	−0.00564613	+	0.0126814i
$213$	−2.72622	+	10.6745i	−0.186798	+	0.731407i
$214$	5.66734	+	1.20463i	0.387411	+	0.0823468i
$215$	6.78901	+	20.8944i	0.463007	+	1.42499i
$216$	−11.4751	+	6.36592i	−0.780784	+	0.433146i
$217$	−0.535084	−	0.736479i	−0.0363238	−	0.0499955i
$218$	20.3290	−	18.3043i	1.37685	−	1.23973i
$219$	2.56389	+	6.45156i	0.173252	+	0.435956i
$220$	−2.77057	−	1.75454i	−0.186792	−	0.118291i
$221$	−10.5659	+	6.10024i	−0.710742	+	0.410347i
$222$	−2.44516	−	1.20990i	−0.164109	−	0.0812030i
$223$	−0.502411	−	4.78012i	−0.0336439	−	0.320101i	−0.998381	−	0.0568843i	$-0.981883\pi$
$223$	−0.502411	−	4.78012i	−0.0336439	−	0.320101i	0.964737	−	0.263216i	$-0.0847833\pi$
$224$	−3.07614	+	4.23394i	−0.205533	+	0.282892i
$225$	7.18249	−	4.37500i	0.478832	−	0.291666i
$226$	−18.1535	+	5.89843i	−1.20755	+	0.392358i
$227$	2.61886	−	1.16599i	0.173820	−	0.0773896i	−0.317982	−	0.948097i	$-0.603005\pi$
$227$	2.61886	−	1.16599i	0.173820	−	0.0773896i	0.491802	+	0.870707i	$0.336338\pi$
$228$	−0.146903	+	3.61540i	−0.00972886	+	0.239436i
$229$	11.6992	−	2.48673i	0.773102	−	0.164328i	0.195563	−	0.980691i	$-0.437347\pi$
$229$	11.6992	−	2.48673i	0.773102	−	0.164328i	0.577539	+	0.816363i	$0.304013\pi$
$230$	16.8551	+	29.1938i	1.11139	+	1.92499i
$231$	−1.93662	−	15.0593i	−0.127420	−	0.990827i
$232$	2.25291	−	3.90215i	0.147911	−	0.256189i
$233$	−0.512177	+	1.57632i	−0.0335538	+	0.103268i	−0.966431	−	0.256927i	$-0.917290\pi$
$233$	−0.512177	+	1.57632i	−0.0335538	+	0.103268i	0.932877	+	0.360195i	$0.117290\pi$
$234$	−17.9451	−	3.37571i	−1.17311	−	0.220677i
$235$	9.28324	+	6.74467i	0.605572	+	0.439974i
$236$	−0.395914	+	1.86263i	−0.0257718	+	0.121247i
$237$	0.861183	+	5.05235i	0.0559398	+	0.328185i
$238$	−12.4029	−	1.30360i	−0.803961	−	0.0844997i
$239$	−3.66975	−	1.63388i	−0.237377	−	0.105687i	0.284601	−	0.958646i	$-0.408139\pi$
$239$	−3.66975	−	1.63388i	−0.237377	−	0.105687i	−0.521978	+	0.852959i	$0.674806\pi$
$240$	22.1270	−	1.42050i	1.42829	−	0.0916931i
$241$	13.5055	+	7.79739i	0.869964	+	0.502274i	0.867336	−	0.497722i	$-0.165830\pi$
$241$	13.5055	+	7.79739i	0.869964	+	0.502274i	0.00262792	+	0.999997i	$0.499164\pi$
$242$	16.1659	+	4.84705i	1.03918	+	0.311580i
$243$	−4.91172	−	14.7944i	−0.315087	−	0.949063i
$244$	1.03441	+	0.336100i	0.0662213	+	0.0215166i
$245$	−0.0394133	+	0.00414250i	−0.00251802	+	0.000264655i
$246$	−2.55077	−	0.651454i	−0.162631	−	0.0415352i
$247$	15.6669	−	17.3999i	0.996863	−	1.10713i
$248$	−0.582029	+	0.646409i	−0.0369589	+	0.0410470i
$249$	5.57342	−	5.70596i	0.353201	−	0.361600i
$250$	9.36303	−	0.984094i	0.592170	−	0.0622396i
$251$	−22.7610	−	7.39551i	−1.43666	−	0.466800i	−0.515808	−	0.856704i	$-0.672508\pi$
$251$	−22.7610	−	7.39551i	−1.43666	−	0.466800i	−0.920856	+	0.389904i	$0.872508\pi$
$252$	−1.92650	−	2.04104i	−0.121358	−	0.128573i
$253$	−18.6556	−	18.2340i	−1.17287	−	1.14636i
$254$	−8.16885	−	4.71629i	−0.512559	−	0.295926i
$255$	8.25027	+	12.3833i	0.516652	+	0.775472i
$256$	7.53193	+	3.35343i	0.470746	+	0.209589i
$257$	17.5165	+	1.84106i	1.09265	+	0.114842i	0.633670	−	0.773603i	$-0.281548\pi$
$257$	17.5165	+	1.84106i	1.09265	+	0.114842i	0.458982	+	0.888446i	$0.348214\pi$
$258$	−19.5984	−	7.26008i	−1.22014	−	0.451993i
$259$	−0.564146	+	2.65410i	−0.0350543	+	0.164918i
$260$	3.17346	+	2.30565i	0.196809	+	0.142990i
$261$	4.06073	+	3.48706i	0.251353	+	0.215843i
$262$	−3.10188	+	9.54659i	−0.191635	+	0.589791i
$263$	2.29478	−	3.97468i	0.141502	−	0.245089i	−0.786560	−	0.617514i	$-0.788140\pi$
$263$	2.29478	−	3.97468i	0.141502	−	0.245089i	0.928063	+	0.372424i	$0.121473\pi$
$264$	−13.6900	+	4.80167i	−0.842559	+	0.295522i
$265$	−0.797550	−	1.38140i	−0.0489931	−	0.0848586i
$266$	23.4104	−	4.97604i	1.43538	−	0.305100i
$267$	19.2036	+	12.1526i	1.17524	+	0.743727i
$268$	4.00401	−	1.78270i	0.244584	−	0.108896i
$269$	−7.71837	+	2.50785i	−0.470597	+	0.152906i	−0.534709	−	0.845036i	$-0.679579\pi$
$269$	−7.71837	+	2.50785i	−0.470597	+	0.152906i	0.0641114	+	0.997943i	$0.479579\pi$
$270$	−2.70646	+	22.1050i	−0.164710	+	1.34527i
$271$	2.83543	−	3.90264i	0.172240	−	0.237068i	−0.714166	−	0.699976i	$-0.753194\pi$
$271$	2.83543	−	3.90264i	0.172240	−	0.237068i	0.886406	+	0.462908i	$0.153194\pi$
$272$	1.47316	+	14.0162i	0.0893236	+	0.849857i
$273$	1.16351	+	18.1239i	0.0704191	+	1.09691i
$274$	−8.55764	+	4.94075i	−0.516986	+	0.298482i
$275$	8.64145	−	3.43096i	0.521099	−	0.206894i
$276$	−4.77130	−	0.698335i	−0.287198	−	0.0420348i
$277$	−8.12722	+	7.31778i	−0.488317	+	0.439683i	−0.876144	−	0.482049i	$-0.839893\pi$
$277$	−8.12722	+	7.31778i	−0.488317	+	0.439683i	0.387827	+	0.921732i	$0.373226\pi$
$278$	−18.3489	−	25.2552i	−1.10050	−	1.51470i
$279$	−0.626818	−	0.821435i	−0.0375266	−	0.0491780i
$280$	−5.76197	−	17.7335i	−0.344343	−	1.05978i
$281$	−4.08803	−	0.868937i	−0.243871	−	0.0518365i	0.0843542	−	0.996436i	$-0.473117\pi$
$281$	−4.08803	−	0.868937i	−0.243871	−	0.0518365i	−0.328226	+	0.944599i	$0.606451\pi$
$282$	−10.5101	+	2.94895i	−0.625866	+	0.175607i
$283$	4.57216	−	10.2692i	0.271787	−	0.610443i	−0.725155	−	0.688585i	$-0.758232\pi$
$283$	4.57216	−	10.2692i	0.271787	−	0.610443i	0.996942	+	0.0781419i	$0.0248987\pi$
$284$	0.468108	+	2.20228i	0.0277771	+	0.130681i
$285$	−22.4018	−	17.7089i	−1.32697	−	1.04898i
$286$	−18.9277	−	7.01854i	−1.11922	−	0.415015i
$287$			2.61843i			0.154561i
$288$	−3.37767	+	4.88643i	−0.199031	+	0.287936i
$289$	6.10157	−	4.43305i	0.358916	−	0.260768i
$290$	−3.11020	−	6.98561i	−0.182637	−	0.410209i
$291$	−18.8149	+	3.20704i	−1.10295	+	0.188000i
$292$	1.05433	+	0.949324i	0.0617001	+	0.0555550i
$293$	2.90062	−	27.5976i	0.169456	−	1.61227i	−0.497700	−	0.867349i	$-0.665822\pi$
$293$	2.90062	−	27.5976i	0.169456	−	1.61227i	0.667156	−	0.744918i	$-0.267511\pi$
$294$	0.0201603	−	0.0318574i	0.00117577	−	0.00185796i
$295$	−10.0558	−	11.1681i	−0.585470	−	0.650230i
$296$	2.59265			0.150695
$297$	−2.59918	−	17.0366i	−0.150820	−	0.988561i
$298$	−8.01937			−0.464550
$299$	20.8789	+	23.1884i	1.20746	+	1.34102i
$300$	0.919060	−	1.45231i	0.0530620	−	0.0838489i
$301$	−2.17284	+	20.6731i	−0.125240	+	1.19158i
$302$	−4.12879	−	3.71757i	−0.237585	−	0.213922i
$303$	−16.3772	+	2.79153i	−0.940846	+	0.160369i
$304$	−11.0008	−	24.7082i	−0.630940	−	1.41711i
$305$	−6.94426	+	5.04530i	−0.397627	+	0.288893i
$306$	−14.1087	−	1.14844i	−0.806542	−	0.0656519i
$307$		−	29.0972i		−	1.66067i	−0.557266	−	0.830334i	$-0.688150\pi$
$307$		−	29.0972i		−	1.66067i	0.557266	−	0.830334i	$-0.311850\pi$
$308$	−1.71957	−	2.58280i	−0.0979816	−	0.147169i
$309$	−19.8387	−	15.6827i	−1.12858	−	0.892157i
$310$	0.306912	+	1.44391i	0.0174314	+	0.0820084i
$311$	−8.70355	+	19.5485i	−0.493533	+	1.10849i	0.479440	+	0.877575i	$0.340840\pi$
$311$	−8.70355	+	19.5485i	−0.493533	+	1.10849i	−0.972973	+	0.230919i	$0.925827\pi$
$312$	16.7079	−	4.68794i	0.945897	−	0.265402i
$313$	3.30408	+	0.702304i	0.186758	+	0.0396966i	0.300341	−	0.953832i	$-0.402900\pi$
$313$	3.30408	+	0.702304i	0.186758	+	0.0396966i	−0.113583	+	0.993528i	$0.536233\pi$
$314$	5.01842	+	15.4451i	0.283206	+	0.871617i
$315$	21.9680	−	2.83226i	1.23776	−	0.159580i
$316$	0.615642	+	0.847359i	0.0346326	+	0.0476677i
$317$	−14.5334	+	13.0860i	−0.816279	+	0.734981i	−0.967323	−	0.253546i	$-0.918403\pi$
$317$	−14.5334	+	13.0860i	−0.816279	+	0.734981i	0.151045	+	0.988527i	$0.451736\pi$
$318$	1.50143	+	0.219752i	0.0841961	+	0.0123231i
$319$	3.77625	+	4.55582i	0.211429	+	0.255077i
$320$	−14.8232	+	8.55819i	−0.828644	+	0.478418i
$321$	−0.419046	−	6.52743i	−0.0233889	−	0.364326i
$322$	3.33398	+	31.7207i	0.185796	+	1.76773i
$323$	10.6688	−	14.6843i	0.593628	−	0.817059i
$324$	−2.24050	−	2.26465i	−0.124472	−	0.125814i
$325$	−10.5769	+	3.43665i	−0.586702	+	0.190631i
$326$	22.1149	−	9.84617i	1.22483	−	0.545329i
$327$	−26.0956	−	16.5140i	−1.44309	−	0.913227i
$328$	2.44724	−	0.520177i	0.135126	−	0.0287220i
$329$	5.42850	+	9.40244i	0.299283	+	0.518373i
$330$	−7.06344	+	23.5855i	−0.388829	+	1.29834i
$331$	−15.4873	+	26.8248i	−0.851259	+	1.47442i	0.0288134	+	0.999585i	$0.490827\pi$
$331$	−15.4873	+	26.8248i	−0.851259	+	1.47442i	−0.880073	+	0.474839i	$0.842506\pi$
$332$	0.503709	−	1.55026i	0.0276446	−	0.0850815i
$333$	−0.569367	+	3.02673i	−0.0312011	+	0.165864i
$334$	7.69882	+	5.59352i	0.421260	+	0.306064i
$335$	−7.19162	+	33.8339i	−0.392920	+	1.84854i
$336$	19.6726	+	7.28756i	1.07323	+	0.397569i
$337$	−29.5939	−	3.11044i	−1.61208	−	0.169437i	−0.744811	−	0.667275i	$-0.767460\pi$
$337$	−29.5939	−	3.11044i	−1.61208	−	0.169437i	−0.867270	+	0.497839i	$0.834127\pi$
$338$	3.83782	+	1.70871i	0.208750	+	0.0929415i
$339$	11.9476	+	17.9329i	0.648906	+	0.973979i
$340$	2.63348	+	1.52044i	0.142820	+	0.0824574i
$341$	−0.530204	−	1.01183i	−0.0287122	−	0.0547936i
$342$	26.4318	−	6.27083i	1.42927	−	0.339088i
$343$	−17.6316	−	5.72886i	−0.952018	−	0.309329i
$344$	19.7532	−	2.07615i	1.06502	−	0.111938i
$345$	26.5915	−	27.2239i	1.43164	−	1.46568i
$346$	15.1215	−	16.7941i	0.812936	−	0.902857i
$347$	18.0631	−	20.0611i	0.969676	−	1.07693i	−0.0273308	−	0.999626i	$-0.508701\pi$
$347$	18.0631	−	20.0611i	0.969676	−	1.07693i	0.997007	−	0.0773083i	$-0.0246326\pi$
$348$	1.05982	+	0.270672i	0.0568123	+	0.0145096i
$349$	24.2742	−	2.55132i	1.29937	−	0.136569i	0.570541	−	0.821269i	$-0.306733\pi$
$349$	24.2742	−	2.55132i	1.29937	−	0.136569i	0.728825	+	0.684700i	$0.240067\pi$
$350$	−10.8116	−	3.51291i	−0.577906	−	0.187773i
$351$	1.80365	+	20.5348i	0.0962718	+	1.09606i
$352$	−4.59029	+	4.69642i	−0.244663	+	0.250320i
$353$	0.733079	+	0.423243i	0.0390178	+	0.0225270i	0.519382	−	0.854542i	$-0.326162\pi$
$353$	0.733079	+	0.423243i	0.0390178	+	0.0225270i	−0.480364	+	0.877069i	$0.659496\pi$
$354$	14.2670	−	0.915905i	0.758280	−	0.0486798i
$355$	−16.2323	−	7.22709i	−0.861521	−	0.383574i
$356$	4.61884	+	0.485459i	0.244798	+	0.0257293i
$357$	2.36566	+	13.8788i	0.125204	+	0.734542i
$358$	3.97388	−	18.6956i	0.210026	−	0.988095i
$359$	19.5043	+	14.1707i	1.02940	+	0.747902i	0.968188	−	0.250223i	$-0.0805040\pi$
$359$	19.5043	+	14.1707i	1.02940	+	0.747902i	0.0612103	+	0.998125i	$0.480504\pi$
$360$	−7.01124	−	19.9691i	−0.369525	−	1.05246i
$361$	−4.89271	+	15.0582i	−0.257511	+	0.792537i
$362$	0.849768	−	1.47184i	0.0446628	−	0.0773582i
$363$	0.338231	−	19.0496i	0.0177525	−	0.999842i
$364$	1.85572	+	3.21421i	0.0972663	+	0.168470i
$365$	−10.9519	+	2.32790i	−0.573250	+	0.121848i
$366$	0.331515	−	8.15888i	0.0173286	−	0.426471i
$367$	−5.86539	+	2.61144i	−0.306171	+	0.136316i	−0.554071	−	0.832470i	$-0.686926\pi$
$367$	−5.86539	+	2.61144i	−0.306171	+	0.136316i	0.247900	+	0.968786i	$0.420260\pi$
$368$	34.2801	−	11.1383i	1.78697	−	0.580623i
$369$	0.0698351	+	2.97121i	0.00363547	+	0.154675i
$370$	2.58620	−	3.55961i	0.134450	−	0.185055i
$371$	−0.157758	−	1.50096i	−0.00819037	−	0.0779262i
$372$	−0.189259	−	0.0936477i	−0.00981262	−	0.00485541i
$373$	25.7002	−	14.8380i	1.33071	−	0.768284i	0.345299	−	0.938493i	$-0.387778\pi$
$373$	25.7002	−	14.8380i	1.33071	−	0.768284i	0.985408	+	0.170209i	$0.0544443\pi$
$374$	−15.1614	−	3.87734i	−0.783979	−	0.200493i
$375$	−3.92515	−	9.87691i	−0.202694	−	0.510042i
$376$	7.70929	−	6.94147i	0.397576	−	0.357979i
$377$	−4.16035	−	5.72623i	−0.214269	−	0.294916i
$378$	−10.8463	+	18.0653i	−0.557874	+	0.929179i
$379$	8.27226	+	25.4594i	0.424917	+	1.30776i	0.903073	+	0.429486i	$0.141305\pi$
$379$	8.27226	+	25.4594i	0.424917	+	1.30776i	−0.478156	+	0.878275i	$0.658695\pi$
$380$	−5.70820	−	1.21332i	−0.292824	−	0.0622417i
$381$	−2.63501	+	10.3174i	−0.134996	+	0.528576i
$382$	−12.2142	+	27.4337i	−0.624935	+	1.40363i
$383$	2.11948	+	9.97137i	0.108300	+	0.509513i	0.998540	+	0.0540205i	$0.0172036\pi$
$383$	2.11948	+	9.97137i	0.108300	+	0.509513i	−0.890239	+	0.455493i	$0.849463\pi$
$384$	3.35140	−	22.8981i	0.171026	−	1.16851i
$385$	24.4670	+	1.00203i	1.24696	+	0.0510684i
$386$			14.5978i			0.743008i
$387$	−1.91422	+	23.5164i	−0.0973052	+	1.19541i
$388$	−3.15556	+	2.29265i	−0.160199	+	0.116392i
$389$	−6.01530	−	13.5106i	−0.304988	−	0.685014i	0.694415	−	0.719575i	$-0.255663\pi$
$389$	−6.01530	−	13.5106i	−0.304988	−	0.685014i	−0.999403	+	0.0345611i	$0.988997\pi$
$390$	10.2300	−	27.6156i	0.518015	−	1.39837i
$391$	17.9761	+	16.1857i	0.909088	+	0.818547i
$392$	−0.00374508	+	0.0356321i	−0.000189155	+	0.00179969i
$393$	11.3226	+	0.460063i	0.571148	+	0.0232071i
$394$	−0.591754	−	0.657210i	−0.0298122	−	0.0331097i
$395$	−8.26594			−0.415904
$396$	−2.02013	−	2.88492i	−0.101516	−	0.144973i
$397$	8.81189			0.442256			0.221128	−	0.975245i	$-0.429026\pi$
$397$	8.81189			0.442256			0.221128	+	0.975245i	$0.429026\pi$
$398$	−22.5648	−	25.0607i	−1.13107	−	1.25618i
$399$	−12.5483	−	23.9281i	−0.628199	−	1.19790i
$400$	−1.34285	+	12.7763i	−0.0671424	+	0.638817i
$401$	0.121426	+	0.109332i	0.00606372	+	0.00545980i	0.672157	−	0.740409i	$-0.265368\pi$
$401$	0.121426	+	0.109332i	0.00606372	+	0.00545980i	−0.666093	+	0.745869i	$0.732035\pi$
$402$	−21.0071	−	25.3273i	−1.04774	−	1.26321i
$403$	0.555756	+	1.24825i	0.0276842	+	0.0621797i
$404$	−2.74672	+	1.99561i	−0.136654	+	0.0992851i
$405$	24.8522	−	3.79975i	1.23492	−	0.188811i
$406$		−	7.23507i		−	0.359070i
$407$	−1.18379	+	3.19246i	−0.0586783	+	0.158244i
$408$	12.5014	−	4.96815i	0.618912	−	0.245960i
$409$	2.34770	+	11.0450i	0.116086	+	0.546143i	0.997301	+	0.0734259i	$0.0233932\pi$
$409$	2.34770	+	11.0450i	0.116086	+	0.546143i	−0.881214	+	0.472717i	$0.843273\pi$
$410$	1.72698	−	3.87885i	0.0852892	−	0.191563i
$411$	7.98017	+	7.79481i	0.393633	+	0.384490i
$412$	−5.05508	−	1.07449i	−0.249046	−	0.0529364i
$413$	−4.39395	−	13.5232i	−0.216212	−	0.665432i
$414$	4.62918	+	35.9056i	0.227512	+	1.76466i
$415$	7.56134	+	10.4073i	0.371172	+	0.510874i
$416$	5.83753	−	5.25613i	0.286208	−	0.257703i
$417$	−21.8548	+	27.6464i	−1.07023	+	1.35385i
$418$	29.9715	−	1.91442i	1.46595	−	0.0936375i
$419$	−19.0677	+	11.0087i	−0.931518	+	0.537812i	−0.887291	−	0.461209i	$-0.847416\pi$
$419$	−19.0677	+	11.0087i	−0.931518	+	0.537812i	−0.0442268	+	0.999022i	$0.514082\pi$
$420$	3.76706	−	2.50977i	0.183814	−	0.122464i
$421$	−1.02902	−	9.79050i	−0.0501515	−	0.477160i	−0.990557	−	0.137104i	$-0.956221\pi$
$421$	−1.02902	−	9.79050i	−0.0501515	−	0.477160i	0.940405	−	0.340056i	$-0.110446\pi$
$422$	−21.6897	+	29.8532i	−1.05584	+	1.45323i
$423$	6.41066	+	10.5245i	0.311697	+	0.511717i
$424$	−1.37149	+	0.445625i	−0.0666055	+	0.0216414i
$425$	−7.87603	+	3.50663i	−0.382044	+	0.170097i
$426$	14.9697	−	7.85034i	0.725284	−	0.380350i
$427$	−7.94403	+	1.68856i	−0.384439	+	0.0817149i
$428$	−0.668348	−	1.15761i	−0.0323058	−	0.0559554i
$429$	−1.85623	+	22.7137i	−0.0896196	+	1.09663i
$430$	16.8537	−	29.1914i	0.812755	−	1.40773i
$431$	6.08766	−	18.7359i	0.293232	−	0.902476i	−0.690577	−	0.723259i	$-0.742643\pi$
$431$	6.08766	−	18.7359i	0.293232	−	0.902476i	0.983809	−	0.179218i	$-0.0573566\pi$
$432$	22.5174	+	7.74474i	1.08337	+	0.372619i
$433$	−11.7898	−	8.56581i	−0.566583	−	0.411647i	0.267279	−	0.963619i	$-0.413875\pi$
$433$	−11.7898	−	8.56581i	−0.566583	−	0.411647i	−0.833862	+	0.551973i	$0.813875\pi$
$434$	−0.290390	+	1.36618i	−0.0139392	+	0.0655786i
$435$	−6.64440	+	5.51104i	−0.318574	+	0.264234i
$436$	−6.27647	−	0.659683i	−0.300588	−	0.0315931i
$437$	−42.4079	−	18.8812i	−2.02865	−	0.903211i
$438$	4.72379	−	9.54662i	0.225711	−	0.456155i
$439$	−9.94159	−	5.73978i	−0.474486	−	0.273945i	0.243630	−	0.969868i	$-0.421662\pi$
$439$	−9.94159	−	5.73978i	−0.474486	−	0.273945i	−0.718116	+	0.695924i	$0.754995\pi$
$440$	−3.92409	−	23.0665i	−0.187074	−	1.09965i
$441$	−0.0407755	−	0.0121972i	−0.00194169	−	0.000580821i
$442$	17.8026	+	5.78442i	0.846783	+	0.275137i
$443$	9.37521	−	0.985374i	0.445430	−	0.0468165i	0.120841	−	0.992672i	$-0.461441\pi$
$443$	9.37521	−	0.985374i	0.445430	−	0.0468165i	0.324588	+	0.945855i	$0.394774\pi$
$444$	0.170031	+	0.605992i	0.00806931	+	0.0287591i
$445$	−24.5251	+	27.2379i	−1.16260	+	1.29120i
$446$	−4.93441	+	5.48022i	−0.233651	+	0.259496i
$447$	2.44572	+	8.71656i	0.115679	+	0.412279i
$448$	−16.1063	+	1.69284i	−0.760949	+	0.0799790i
$449$	0.636449	+	0.206795i	0.0300359	+	0.00975924i	0.323996	−	0.946058i	$-0.394973\pi$
$449$	0.636449	+	0.206795i	0.0300359	+	0.00975924i	−0.293961	+	0.955818i	$0.594973\pi$
$450$	−12.3620	−	3.69786i	−0.582749	−	0.174319i
$451$	−0.476877	+	3.25092i	−0.0224553	+	0.153080i
$452$	3.81367	+	2.20182i	0.179380	+	0.103565i
$453$	−2.78159	+	5.62151i	−0.130691	+	0.264122i
$454$	−4.01802	−	1.78894i	−0.188575	−	0.0839591i
$455$	−29.1300	−	3.06168i	−1.36563	−	0.143534i
$456$	−19.8709	+	16.4814i	−0.930538	+	0.771813i
$457$	4.84463	−	22.7922i	0.226622	−	1.06617i	−0.706805	−	0.707408i	$-0.749864\pi$
$457$	4.84463	−	22.7922i	0.226622	−	1.06617i	0.933428	−	0.358766i	$-0.116802\pi$
$458$	−14.8459	−	10.7862i	−0.693705	−	0.504006i
$459$	3.05454	+	15.6856i	0.142574	+	0.732139i
$460$	2.40326	−	7.39648i	0.112053	−	0.344863i
$461$	10.1561	−	17.5909i	0.473017	−	0.819290i	−0.526506	−	0.850172i	$-0.676498\pi$
$461$	10.1561	−	17.5909i	0.473017	−	0.819290i	0.999523	+	0.0308815i	$0.00983144\pi$
$462$	−15.1821	+	17.6683i	−0.706335	+	0.822002i
$463$	17.3328	+	30.0213i	0.805524	+	1.39521i	0.915936	+	0.401323i	$0.131450\pi$
$463$	17.3328	+	30.0213i	0.805524	+	1.39521i	−0.110412	+	0.993886i	$0.535217\pi$
$464$	−7.99749	+	1.69992i	−0.371274	+	0.0789168i
$465$	1.47584	−	0.773952i	0.0684403	−	0.0358912i
$466$	2.32310	−	1.03431i	0.107616	−	0.0479135i
$467$	23.4499	−	7.61935i	1.08513	−	0.352581i	0.288770	−	0.957399i	$-0.406754\pi$
$467$	23.4499	−	7.61935i	1.08513	−	0.352581i	0.796364	+	0.604817i	$0.206754\pi$
$468$	2.19147	+	3.59777i	0.101301	+	0.166307i
$469$	−19.2369	+	26.4773i	−0.888276	+	1.22261i
$470$	−1.84025	−	17.5088i	−0.0848843	−	0.807620i
$471$	15.2574	−	10.1651i	0.703023	−	0.468383i
$472$	−11.7661	+	6.79319i	−0.541581	+	0.312682i
$473$	−6.46275	+	25.2711i	−0.297158	+	1.16196i
$474$	4.87648	−	6.16876i	0.223984	−	0.283340i
$475$	12.2955	−	11.0709i	0.564156	−	0.507969i
$476$	1.69116	+	2.32769i	0.0775144	+	0.106689i
$477$	−0.219044	−	1.69898i	−0.0100293	−	0.0777911i
$478$	1.90453	+	5.86155i	0.0871114	+	0.268101i
$479$	11.9927	+	2.54914i	0.547962	+	0.116473i	0.473570	−	0.880756i	$-0.342965\pi$
$479$	11.9927	+	2.54914i	0.547962	+	0.116473i	0.0743922	+	0.997229i	$0.476298\pi$
$480$	−6.85344	−	6.69425i	−0.312815	−	0.305549i
$481$	1.65651	−	3.72058i	0.0755303	−	0.169644i
$482$	−4.97460	−	23.4036i	−0.226587	−	1.06601i
$483$	33.4617	−	13.2979i	1.52256	−	0.605076i
$484$	−1.66455	−	3.51985i	−0.0756612	−	0.159993i
$485$		−	30.7823i		−	1.39775i
$486$	−11.8258	+	20.7885i	−0.536430	+	0.942987i
$487$	−2.20321	+	1.60073i	−0.0998371	+	0.0725359i	−0.636584	−	0.771208i	$-0.719653\pi$
$487$	−2.20321	+	1.60073i	−0.0998371	+	0.0725359i	0.536747	+	0.843743i	$0.319653\pi$
$488$	3.15632	+	7.08921i	0.142880	+	0.320913i
$489$	−17.4467	−	21.0347i	−0.788967	−	0.951220i
$490$	0.0451857	+	0.0406854i	0.00204128	+	0.00183798i
$491$	−1.09258	+	10.3952i	−0.0493073	+	0.469127i	0.941811	+	0.336143i	$0.109123\pi$
$491$	−1.09258	+	10.3952i	−0.0493073	+	0.469127i	−0.991118	+	0.132984i	$0.957544\pi$
$492$	0.282078	+	0.537891i	0.0127171	+	0.0242500i
$493$	−3.67152	−	4.07763i	−0.165357	−	0.183647i
$494$	−35.9230			−1.61625
$495$	27.7902	+	0.484488i	1.24908	+	0.0217761i
$496$	1.57837			0.0708711
$497$	−11.2494	−	12.4937i	−0.504604	−	0.560420i
$498$	−12.2276	−	0.496838i	−0.547933	−	0.0222638i
$499$	1.14982	−	10.9398i	0.0514729	−	0.489732i	−0.938169	−	0.346177i	$-0.887480\pi$
$499$	1.14982	−	10.9398i	0.0514729	−	0.489732i	0.989642	−	0.143555i	$-0.0458535\pi$
$500$	−1.61411	−	1.45335i	−0.0721853	−	0.0649959i
$501$	3.73185	−	10.0740i	0.166727	−	0.450075i
$502$	14.9348	+	33.5441i	0.666572	+	1.49714i
$503$	−6.64248	+	4.82604i	−0.296173	+	0.215183i	−0.725941	−	0.687757i	$-0.758595\pi$
$503$	−6.64248	+	4.82604i	−0.296173	+	0.215183i	0.429768	+	0.902940i	$0.358595\pi$
$504$	1.62463	−	19.9588i	0.0723669	−	0.889037i
$505$		−	26.7941i		−	1.19232i
$506$	−1.63777	+	39.9901i	−0.0728079	+	1.77778i
$507$	0.686816	−	4.69260i	0.0305026	−	0.208406i
$508$	0.452446	+	2.12859i	0.0200741	+	0.0944410i
$509$	−8.98615	+	20.1832i	−0.398304	+	0.894605i	0.597394	+	0.801948i	$0.296203\pi$
$509$	−8.98615	+	20.1832i	−0.398304	+	0.894605i	−0.995698	+	0.0926575i	$0.970464\pi$
$510$	5.64927	−	22.1198i	0.250154	−	0.979480i
$511$	−10.3624	−	2.20259i	−0.458404	−	0.0974367i
$512$	4.34866	+	13.3838i	0.192186	+	0.591486i
$513$	−14.8771	−	26.8173i	−0.656839	−	1.18401i
$514$	−15.8837	−	21.8621i	−0.700601	−	0.964295i
$515$	30.3096	−	27.2909i	1.33560	−	1.20258i
$516$	1.78072	+	4.48085i	0.0783919	+	0.197259i
$517$	5.02736	+	12.6623i	0.221103	+	0.556886i
$518$	3.60531	−	2.08153i	0.158408	−	0.0914571i
$519$	−22.8659	−	11.3143i	−1.00370	−	0.496643i
$520$	2.92544	+	27.8337i	0.128289	+	1.22059i
$521$	−14.3440	+	19.7428i	−0.628422	+	0.864949i	−0.997932	−	0.0642780i	$-0.979526\pi$
$521$	−14.3440	+	19.7428i	−0.628422	+	0.864949i	0.369510	+	0.929227i	$0.379526\pi$
$522$	−0.192964	−	8.20985i	−0.00844579	−	0.359335i
$523$	−11.4006	+	3.70428i	−0.498513	+	0.161977i	−0.547472	−	0.836824i	$-0.684410\pi$
$523$	−11.4006	+	3.70428i	−0.498513	+	0.161977i	0.0489586	+	0.998801i	$0.484410\pi$
$524$	2.11559	−	0.941919i	0.0924198	−	0.0411479i
$525$	−0.521027	+	12.8229i	−0.0227395	+	0.559639i
$526$	−6.88773	+	1.46403i	−0.300319	+	0.0638348i
$527$	0.529621	+	0.917330i	0.0230706	+	0.0399595i
$528$	23.0973	+	12.6307i	1.00518	+	0.549681i
$529$	19.4322	−	33.6576i	0.844879	−	1.46337i
$530$	−0.756258	+	2.32752i	−0.0328498	+	0.101101i
$531$	−5.34662	−	15.2280i	−0.232024	−	0.660838i
$532$	−4.46705	−	3.24550i	−0.193671	−	0.140710i
$533$	0.817124	−	3.84427i	0.0353936	−	0.166514i
$534$	−5.85873	−	34.3717i	−0.253532	−	1.48741i
$535$	10.4913	+	1.10268i	0.453579	+	0.0476731i
$536$	28.5678	+	12.7192i	1.23394	+	0.549386i
$537$	−21.5330	+	1.38236i	−0.929215	+	0.0596534i
$538$	10.7833	+	6.22572i	0.464899	+	0.268410i
$539$	−0.0421656	−	0.0208809i	−0.00181620	−	0.000899406i
$540$	4.20766	−	2.94838i	0.181069	−	0.126878i
$541$	13.9239	+	4.52415i	0.598635	+	0.194508i	0.592631	−	0.805474i	$-0.298089\pi$
$541$	13.9239	+	4.52415i	0.598635	+	0.194508i	0.00600328	+	0.999982i	$0.498089\pi$
$542$	−7.36063	+	0.773633i	−0.316166	+	0.0332304i
$543$	−1.85896	−	0.474769i	−0.0797756	−	0.0203743i
$544$	4.07465	−	4.52536i	0.174699	−	0.194023i
$545$	33.3269	−	37.0132i	1.42757	−	1.58547i
$546$	19.4701	−	19.9331i	0.833242	−	0.853056i
$547$	−6.49674	+	0.682835i	−0.277781	+	0.0291959i	−0.242394	−	0.970178i	$-0.577933\pi$
$547$	−6.49674	+	0.682835i	−0.277781	+	0.0291959i	−0.0353862	+	0.999374i	$0.511266\pi$
$548$	2.16814	+	0.704472i	0.0926184	+	0.0300936i
$549$	−8.96930	+	2.12793i	−0.382800	+	0.0908178i
$550$	−12.7834	−	6.33051i	−0.545087	−	0.269934i
$551$	9.11929	+	5.26502i	0.388495	+	0.224298i
$552$	−19.0760	−	28.6322i	−0.811928	−	1.21867i
$553$	−7.14480	−	3.18107i	−0.303828	−	0.135273i
$554$	16.6872	+	1.75389i	0.708970	+	0.0745157i
$555$	−4.65780	−	1.72545i	−0.197713	−	0.0732413i
$556$	−1.49737	+	7.04458i	−0.0635027	+	0.298757i
$557$	31.9814	+	23.2358i	1.35509	+	0.984533i	0.998740	+	0.0501824i	$0.0159803\pi$
$557$	31.9814	+	23.2358i	1.35509	+	0.984533i	0.356354	+	0.934351i	$0.384020\pi$
$558$	−0.293078	+	1.55799i	−0.0124070	+	0.0659549i
$559$	9.64146	−	29.6734i	0.407790	−	1.25505i
$560$	−16.9174	+	29.3018i	−0.714892	+	1.23823i
$561$	0.409446	+	17.6620i	0.0172868	+	0.745692i
$562$	3.20612	+	5.55316i	0.135242	+	0.234246i
$563$	37.4467	−	7.95954i	1.57819	−	0.335454i	0.666233	−	0.745743i	$-0.267905\pi$
$563$	37.4467	−	7.95954i	1.57819	−	0.335454i	0.911956	+	0.410289i	$0.134572\pi$
$564$	2.12806	+	1.34669i	0.0896073	+	0.0567060i
$565$	−31.7486	+	14.1354i	−1.33567	+	0.594680i
$566$	−16.4027	+	5.32955i	−0.689456	+	0.224018i
$567$	22.9437	+	6.27977i	0.963547	+	0.263726i
$568$	−9.44208	+	12.9959i	−0.396181	+	0.545296i
$569$	−2.58578	−	24.6020i	−0.108401	−	1.03137i	−0.904579	−	0.426307i	$-0.859814\pi$
$569$	−2.58578	−	24.6020i	−0.108401	−	1.03137i	0.796177	−	0.605064i	$-0.206852\pi$
$570$	2.80688	+	43.7224i	0.117567	+	1.83133i
$571$	−29.2614	+	16.8941i	−1.22455	+	0.706994i	−0.965885	−	0.258973i	$-0.916616\pi$
$571$	−29.2614	+	16.8941i	−1.22455	+	0.706994i	−0.258665	+	0.965967i	$0.583283\pi$
$572$	1.71859	+	4.32857i	0.0718580	+	0.180987i
$573$	33.5438	+	4.90952i	1.40131	+	0.205098i
$574$	2.98548	−	2.68814i	0.124612	−	0.112201i
$575$	12.9603	+	17.8383i	0.540483	+	0.743911i
$576$	−18.2311	+	2.35048i	−0.759630	+	0.0979365i
$577$	−1.28480	−	3.95422i	−0.0534871	−	0.164616i	0.920745	−	0.390166i	$-0.127582\pi$
$577$	−1.28480	−	3.95422i	−0.0534871	−	0.164616i	−0.974232	+	0.225549i	$0.927582\pi$
$578$	−11.3185	−	2.40582i	−0.470787	−	0.100069i
$579$	15.8669	−	4.45198i	0.659406	−	0.185018i
$580$	−0.717540	+	1.61162i	−0.0297942	+	0.0669189i
$581$	2.53062	+	11.9056i	0.104988	+	0.493929i
$582$	22.9724	+	18.1600i	0.952239	+	0.752756i
$583$	0.0774963	−	1.89226i	0.00320957	−	0.0783692i
$584$			10.1224i			0.418869i
$585$	−33.1363	−	2.69727i	−1.37002	−	0.111518i
$586$	−34.4440	+	25.0251i	−1.42287	+	1.03378i
$587$	3.28105	+	7.36936i	0.135423	+	0.304166i	0.968509	−	0.248978i	$-0.0800947\pi$
$587$	3.28105	+	7.36936i	0.135423	+	0.304166i	−0.833086	+	0.553144i	$0.813428\pi$
$588$	−0.00857407	+	0.00146147i	−0.000353589	+	6.02699e-5i
$589$	−1.51065	−	1.36020i	−0.0622453	−	0.0560459i
$590$	−2.41012	+	22.9308i	−0.0992231	+	0.944045i
$591$	−0.533876	+	0.843634i	−0.0219607	+	0.0347025i
$592$	−3.14797	−	3.49617i	−0.129381	−	0.143692i
$593$	3.24653			0.133319			0.0666596	−	0.997776i	$-0.478766\pi$
$593$	3.24653			0.133319			0.0666596	+	0.997776i	$0.478766\pi$
$594$	−16.7564	+	20.4536i	−0.687522	+	0.839223i
$595$	−22.7065			−0.930874
$596$	1.23797	+	1.37490i	0.0507091	+	0.0563182i
$597$	−20.3577	+	32.1695i	−0.833187	+	1.31661i
$598$	5.00416	−	47.6114i	0.204635	−	1.94698i
$599$	−11.5274	−	10.3793i	−0.470997	−	0.424087i	0.399146	−	0.916887i	$-0.369307\pi$
$599$	−11.5274	−	10.3793i	−0.470997	−	0.424087i	−0.870143	+	0.492800i	$0.835973\pi$
$600$	12.0881	−	2.06044i	0.493494	−	0.0841170i
$601$	5.22040	+	11.7252i	0.212945	+	0.478281i	0.988162	−	0.153413i	$-0.0490265\pi$
$601$	5.22040	+	11.7252i	0.212945	+	0.478281i	−0.775218	+	0.631694i	$0.782360\pi$
$602$	25.8018	−	18.7461i	1.05160	−	0.764034i
$603$	−21.1225	+	30.5576i	−0.860175	+	1.24440i
$604$			1.28176i			0.0521541i
$605$	30.1946	+	5.70010i	1.22758	+	0.231742i
$606$	19.9960	+	15.8071i	0.812284	+	0.642120i
$607$	1.89078	+	8.89542i	0.0767444	+	0.361054i	0.999716	−	0.0238130i	$-0.00758062\pi$
$607$	1.89078	+	8.89542i	0.0767444	+	0.361054i	−0.922972	+	0.384867i	$0.874247\pi$
$608$	−4.75323	+	10.6759i	−0.192769	+	0.432966i
$609$	−7.86407	+	2.20652i	−0.318668	+	0.0894129i
$610$	12.8817	+	2.73809i	0.521564	+	0.110862i
$611$	−5.03571	−	15.4983i	−0.203723	−	0.626995i
$612$	1.98110	+	2.59619i	0.0800811	+	0.104945i
$613$	−2.23663	−	3.07846i	−0.0903368	−	0.124338i	0.761456	−	0.648216i	$-0.224485\pi$
$613$	−2.23663	−	3.07846i	−0.0903368	−	0.124338i	−0.851793	+	0.523878i	$0.824485\pi$
$614$	−33.1761	+	29.8719i	−1.33888	+	1.20553i
$615$	−4.74276	−	0.694158i	−0.191247	−	0.0279912i
$616$	5.48506	−	21.4480i	0.220999	−	0.864166i
$617$	32.5274	−	18.7797i	1.30950	−	0.756043i	0.327491	−	0.944854i	$-0.393797\pi$
$617$	32.5274	−	18.7797i	1.30950	−	0.756043i	0.982013	+	0.188811i	$0.0604634\pi$
$618$	2.48572	+	38.7198i	0.0999904	+	1.55754i
$619$	−3.07333	−	29.2408i	−0.123527	−	1.17529i	−0.864104	−	0.503313i	$-0.832114\pi$
$619$	−3.07333	−	29.2408i	−0.123527	−	1.17529i	0.740577	−	0.671972i	$-0.234552\pi$
$620$	0.200176	−	0.275518i	0.00803925	−	0.0110651i
$621$	37.6154	−	15.9820i	1.50945	−	0.641335i
$622$	31.2241	−	10.1453i	1.25197	−	0.406790i
$623$	−31.6810	+	14.1053i	−1.26927	+	0.565116i
$624$	−26.6082	−	16.8384i	−1.06518	−	0.674076i
$625$	30.4771	−	6.47811i	1.21908	−	0.259124i
$626$	−2.59129	−	4.48825i	−0.103569	−	0.179387i
$627$	−11.2215	−	31.9933i	−0.448142	−	1.27769i
$628$	1.87332	−	3.24469i	0.0747537	−	0.129477i
$629$	0.975634	−	3.00269i	0.0389011	−	0.119725i
$630$	−25.7821	−	22.1398i	−1.02718	−	0.882071i
$631$	2.62503	+	1.90720i	0.104501	+	0.0759243i	0.638808	−	0.769366i	$-0.279428\pi$
$631$	2.62503	+	1.90720i	0.104501	+	0.0759243i	−0.534308	+	0.845290i	$0.679428\pi$
$632$	−1.55371	+	7.30963i	−0.0618033	+	0.290762i
$633$	39.0635	+	14.4708i	1.55263	+	0.575162i
$634$	29.8407	+	3.13638i	1.18512	+	0.124562i
$635$	−15.6892	−	6.98528i	−0.622607	−	0.277202i
$636$	−0.194103	−	0.291341i	−0.00769669	−	0.0115524i
$637$	0.0487411	+	0.0281407i	0.00193119	+	0.00111497i
$638$	1.31767	−	8.98271i	0.0521672	−	0.355629i
$639$	−13.0982	−	13.8770i	−0.518158	−	0.548965i
$640$	35.4967	+	11.5336i	1.40313	+	0.455905i
$641$	29.2722	−	3.07663i	1.15618	−	0.121520i	0.493036	−	0.870009i	$-0.335887\pi$
$641$	29.2722	−	3.07663i	1.15618	−	0.121520i	0.663147	+	0.748489i	$0.269220\pi$
$642$	−7.01224	+	7.17900i	−0.276751	+	0.283332i
$643$	−11.0951	+	12.3224i	−0.437548	+	0.485946i	−0.921076	−	0.389383i	$-0.872688\pi$
$643$	−11.0951	+	12.3224i	−0.437548	+	0.485946i	0.483528	+	0.875329i	$0.339355\pi$
$644$	4.92377	−	5.46840i	0.194024	−	0.215485i
$645$	−36.8692	−	9.41620i	−1.45172	−	0.370763i
$646$	−27.6956	+	2.91093i	−1.08967	+	0.114529i
$647$	−40.6801	−	13.2178i	−1.59930	−	0.519643i	−0.632364	−	0.774671i	$-0.717915\pi$
$647$	−40.6801	−	13.2178i	−1.59930	−	0.519643i	−0.966934	+	0.255028i	$0.917915\pi$
$648$	1.31121	−	22.6912i	0.0515091	−	0.891396i
$649$	−2.99243	−	17.5900i	−0.117463	−	0.690467i
$650$	14.7769	+	8.53145i	0.579598	+	0.334631i
$651$	1.57351	−	0.101016i	0.0616709	−	0.00395912i
$652$	−5.10202	−	2.27157i	−0.199811	−	0.0889614i
$653$	32.1081	+	3.37470i	1.25649	+	0.132062i	0.709276	−	0.704931i	$-0.249022\pi$
$653$	32.1081	+	3.37470i	1.25649	+	0.132062i	0.547213	+	0.836993i	$0.315689\pi$
$654$	7.96135	+	46.7073i	0.311313	+	1.82640i
$655$	−3.79981	+	17.8767i	−0.148471	+	0.698500i
$656$	−3.67287	−	2.66850i	−0.143402	−	0.104187i
$657$	−11.8172	−	2.22297i	−0.461034	−	0.0867264i
$658$	5.14745	−	15.8422i	0.200668	−	0.617594i
$659$	−2.69601	+	4.66962i	−0.105022	+	0.181903i	−0.913747	−	0.406284i	$-0.866824\pi$
$659$	−2.69601	+	4.66962i	−0.105022	+	0.181903i	0.808725	+	0.588186i	$0.200158\pi$
$660$	5.13409	−	2.42994i	0.199844	−	0.0945854i
$661$	−3.48556	−	6.03716i	−0.135572	−	0.234818i	0.790244	−	0.612793i	$-0.209954\pi$
$661$	−3.48556	−	6.03716i	−0.135572	−	0.234818i	−0.925816	+	0.377975i	$0.876621\pi$
$662$	46.4847	−	9.88063i	1.80668	−	0.384021i
$663$	0.857931	−	21.1144i	0.0333193	−	0.820017i
$664$	10.6245	−	4.73034i	0.412311	−	0.183573i
$665$	41.4430	−	13.4657i	1.60709	−	0.522176i
$666$	4.03554	−	2.45813i	0.156374	−	0.0952506i
$667$	−8.24847	+	11.3530i	−0.319382	+	0.439592i
$668$	−0.229487	−	2.18343i	−0.00887914	−	0.0844794i
$669$	7.46154	+	3.69207i	0.288480	+	0.142743i
$670$	45.9598	−	26.5349i	1.77558	−	1.02513i
$671$	−10.1705	+	0.649636i	−0.392626	+	0.0250789i
$672$	−3.34766	−	8.42377i	−0.129139	−	0.324954i
$673$	−7.03354	+	6.33302i	−0.271123	+	0.244120i	−0.793465	−	0.608616i	$-0.791725\pi$
$673$	−7.03354	+	6.33302i	−0.271123	+	0.244120i	0.522342	+	0.852736i	$0.325058\pi$
$674$	26.8353	+	36.9356i	1.03366	+	1.42271i
$675$	−0.249230	+	14.5645i	−0.00959286	+	0.560587i
$676$	−0.299499	−	0.921763i	−0.0115192	−	0.0354524i
$677$	−39.2051	−	8.33329i	−1.50677	−	0.320275i	−0.620784	−	0.783981i	$-0.713186\pi$
$677$	−39.2051	−	8.33329i	−1.50677	−	0.320275i	−0.885989	+	0.463707i	$0.846519\pi$
$678$	8.18098	−	32.0327i	0.314189	−	1.23021i
$679$	11.8463	−	26.6072i	0.454620	−	1.02109i
$680$	4.51086	+	21.2219i	0.172984	+	0.813824i
$681$	−0.719065	+	4.91293i	−0.0275546	+	0.188264i
$682$	−0.609347	+	1.64329i	−0.0233331	+	0.0629250i
$683$			18.6808i			0.714802i	0.933951	+	0.357401i	$0.116337\pi$
$683$			18.6808i			0.714802i	−0.933951	+	0.357401i	$0.883663\pi$
$684$	−5.15545	−	3.56363i	−0.197124	−	0.136259i
$685$	−14.5553	+	10.5751i	−0.556130	+	0.404052i
$686$	11.5691	+	25.9846i	0.441710	+	0.992096i
$687$	−7.19628	+	19.4262i	−0.274555	+	0.741154i
$688$	−26.7838	−	24.1163i	−1.02112	−	0.919424i
$689$	−0.236787	+	2.25288i	−0.00902088	+	0.0858280i
$690$	−58.3396	−	2.37048i	−2.22095	−	0.0902425i
$691$	5.41523	+	6.01422i	0.206005	+	0.228792i	0.837290	−	0.546759i	$-0.184139\pi$
$691$	5.41523	+	6.01422i	0.206005	+	0.228792i	−0.631285	+	0.775551i	$0.717472\pi$
$692$	−5.21365			−0.198193
$693$	23.8345	+	11.1136i	0.905398	+	0.422170i
$694$	−41.4172			−1.57217
$695$	−38.0315	−	42.2383i	−1.44262	−	1.60219i
$696$	3.62454	+	6.91158i	0.137388	+	0.261983i
$697$	0.318469	−	3.03003i	0.0120629	−	0.114771i
$698$	−27.8294	−	25.0577i	−1.05336	−	0.948447i
$699$	−1.83272	−	2.20963i	−0.0693199	−	0.0835758i
$700$	1.06673	+	2.39593i	0.0403188	+	0.0905575i
$701$	13.7719	−	10.0059i	0.520157	−	0.377916i	−0.296506	−	0.955031i	$-0.595821\pi$
$701$	13.7719	−	10.0059i	0.520157	−	0.377916i	0.816663	+	0.577115i	$0.195821\pi$
$702$	21.5617	−	23.1379i	0.813792	−	0.873285i
$703$			6.05899i			0.228519i
$704$	−20.3051	−	0.831582i	−0.765275	−	0.0313414i
$705$	−18.4697	+	7.34000i	−0.695611	+	0.276441i
$706$	−0.270022	−	1.27035i	−0.0101624	−	0.0478103i
$707$	10.3115	−	23.1599i	0.387802	−	0.871018i
$708$	−2.35945	−	2.30465i	−0.0886736	−	0.0866140i
$709$	33.8792	+	7.20125i	1.27236	+	0.270449i	0.794110	−	0.607774i	$-0.207938\pi$
$709$	33.8792	+	7.20125i	1.27236	+	0.270449i	0.478251	+	0.878223i	$0.341271\pi$
$710$	8.42427	+	25.9272i	0.316157	+	0.973032i
$711$	−8.19227	−	3.41910i	−0.307234	−	0.128226i
$712$	19.4768	+	26.8076i	0.729925	+	1.00466i
$713$	2.01321	−	1.81270i	0.0753952	−	0.0678861i
$714$	13.3956	−	16.9455i	0.501319	−	0.634170i
$715$	−35.6088	−	9.10648i	−1.33169	−	0.340563i
$716$	−3.81878	+	2.20477i	−0.142715	+	0.0823963i
$717$	5.79031	−	3.85775i	0.216243	−	0.144070i
$718$	−3.86641	−	36.7864i	−0.144293	−	1.37286i
$719$	18.8375	−	25.9276i	0.702521	−	0.966937i	−0.297405	−	0.954751i	$-0.596121\pi$
$719$	18.8375	−	25.9276i	0.702521	−	0.966937i	0.999926	−	0.0121856i	$-0.00387890\pi$
$720$	−18.4152	+	33.7009i	−0.686295	+	1.25596i
$721$	36.7012	−	11.9250i	1.36683	−	0.444109i
$722$	22.1920	−	9.88052i	0.825901	−	0.367715i
$723$	−23.9212	+	12.5446i	−0.889639	+	0.466540i
$724$	−0.383524	+	0.0815206i	−0.0142536	+	0.00302969i
$725$	−2.50081	−	4.33153i	−0.0928778	−	0.160869i
$726$	−22.0672	+	19.1711i	−0.818989	+	0.711505i
$727$	−21.5410	+	37.3100i	−0.798910	+	1.38375i	0.121417	+	0.992602i	$0.461256\pi$
$727$	−21.5410	+	37.3100i	−0.798910	+	1.38375i	−0.920327	+	0.391151i	$0.872077\pi$
$728$	−8.18289	+	25.1844i	−0.303278	+	0.933394i
$729$	26.2025	+	6.51393i	0.970461	+	0.241257i
$730$	13.8977	+	10.0973i	0.514378	+	0.373717i
$731$	5.02879	−	23.6586i	0.185996	−	0.875044i
$732$	−1.45000	+	1.20267i	−0.0535934	+	0.0444518i
$733$	−34.2830	−	3.60329i	−1.26627	−	0.133090i	−0.552526	−	0.833496i	$-0.686336\pi$
$733$	−34.2830	−	3.60329i	−1.26627	−	0.133090i	−0.713745	+	0.700405i	$0.753003\pi$
$734$	8.99905	+	4.00664i	0.332161	+	0.147888i
$735$	0.0304420	−	0.0615222i	0.00112287	−	0.00226928i
$736$	−13.4875	−	7.78699i	−0.497154	−	0.287032i
$737$	−28.7057	+	29.3694i	−1.05739	+	1.08184i
$738$	3.31602	−	3.12994i	0.122065	−	0.115215i
$739$	0.742336	+	0.241200i	0.0273073	+	0.00887267i	0.322639	−	0.946522i	$-0.395430\pi$
$739$	0.742336	+	0.241200i	0.0273073	+	0.00887267i	−0.295332	+	0.955395i	$0.595430\pi$
$740$	−1.00952	+	0.106105i	−0.0371108	+	0.00390051i
$741$	10.9557	+	39.0461i	0.402467	+	1.43439i
$742$	−1.54941	+	1.72080i	−0.0568807	+	0.0631724i
$743$	−15.0742	+	16.7416i	−0.553018	+	0.614188i	−0.953234	−	0.302232i	$-0.902268\pi$
$743$	−15.0742	+	16.7416i	−0.553018	+	0.614188i	0.400217	+	0.916421i	$0.368935\pi$
$744$	−0.407005	−	1.45057i	−0.0149215	−	0.0531805i
$745$	−14.5210	+	1.52621i	−0.532007	+	0.0559161i
$746$	−43.3024	−	14.0698i	−1.58541	−	0.515132i
$747$	3.18910	+	13.4422i	0.116683	+	0.491824i
$748$	1.67574	+	3.19795i	0.0612712	+	0.116928i
$749$	8.64399	+	4.99061i	0.315844	+	0.182353i
$750$	−7.23181	+	14.6152i	−0.264068	+	0.533673i
$751$	1.01539	+	0.452083i	0.0370523	+	0.0164967i	0.425179	−	0.905109i	$-0.360211\pi$
$751$	1.01539	+	0.452083i	0.0370523	+	0.0164967i	−0.388127	+	0.921606i	$0.626878\pi$
$752$	−18.7211	−	1.96767i	−0.682688	−	0.0717534i
$753$	31.9056	−	26.4633i	1.16270	−	0.964377i
$754$	−2.25782	+	10.6222i	−0.0822250	+	0.386838i
$755$	−8.18365	−	5.94577i	−0.297834	−	0.216389i
$756$	4.77162	−	0.929207i	0.173542	−	0.0337949i
$757$	16.0853	−	49.5054i	0.584629	−	1.79930i	−0.0161240	−	0.999870i	$-0.505133\pi$
$757$	16.0853	−	49.5054i	0.584629	−	1.79930i	0.600753	−	0.799434i	$-0.294867\pi$
$758$	20.5358	−	35.5690i	0.745894	−	1.29193i
$759$	43.9663	−	10.4159i	1.59588	−	0.378073i
$760$	−20.8183	−	36.0584i	−0.755160	−	1.30798i
$761$	−48.4796	+	10.3047i	−1.75739	+	0.373544i	−0.970036	−	0.242963i	$-0.921881\pi$
$761$	−48.4796	+	10.3047i	−1.75739	+	0.373544i	−0.787350	+	0.616507i	$0.788547\pi$
$762$	14.4688	−	7.58768i	0.524151	−	0.274873i
$763$	43.0508	−	19.1675i	1.55855	−	0.693909i
$764$	6.58898	−	2.14089i	0.238381	−	0.0774546i
$765$	−25.7657	+	0.605595i	−0.931562	+	0.0218953i
$766$	9.19325	−	12.6534i	0.332166	−	0.457187i
$767$	2.23088	+	21.2254i	0.0805523	+	0.766403i
$768$	−11.8842	+	7.91778i	−0.428836	+	0.285708i
$769$	−35.4296	+	20.4553i	−1.27763	+	0.737637i	−0.976411	−	0.215919i	$-0.930725\pi$
$769$	−35.4296	+	20.4553i	−1.27763	+	0.737637i	−0.301214	+	0.953557i	$0.597392\pi$
$770$	−23.9759	−	28.9255i	−0.864032	−	1.04240i
$771$	−18.9186	+	23.9321i	−0.681336	+	0.861892i
$772$	2.50276	−	2.25349i	0.0900762	−	0.0811050i
$773$	21.1418	+	29.0992i	0.760417	+	1.04662i	0.997179	+	0.0750568i	$0.0239138\pi$
$773$	21.1418	+	29.0992i	0.760417	+	1.04662i	−0.236762	+	0.971568i	$0.576086\pi$
$774$	28.7781	−	21.9599i	1.03441	−	0.789333i
$775$	0.298369	+	0.918285i	0.0107177	+	0.0329858i
$776$	−27.2211	−	5.78602i	−0.977179	−	0.207706i
$777$	−3.36203	−	3.28394i	−0.120612	−	0.117811i
$778$	−9.22905	+	20.7288i	−0.330878	+	0.743163i
$779$	1.21565	+	5.71917i	0.0435551	+	0.204911i
$780$	−6.31385	+	2.50917i	−0.226072	+	0.0898426i
$781$	−11.6913	−	17.5604i	−0.418348	−	0.628359i
$782$		−	37.1126i		−	1.32714i
$783$	−8.86476	+	2.71355i	−0.316801	+	0.0969744i
$784$	0.0525970	−	0.0382139i	0.00187846	−	0.00136478i
$785$	12.0265	+	27.0119i	0.429243	+	0.964096i
$786$	−11.0994	−	13.3821i	−0.395904	−	0.477323i
$787$	16.0402	+	14.4427i	0.571772	+	0.514826i	0.903522	−	0.428541i	$-0.140972\pi$
$787$	16.0402	+	14.4427i	0.571772	+	0.514826i	−0.331750	+	0.943367i	$0.607639\pi$
$788$	−0.0213267	+	0.202910i	−0.000759732	+	0.00722836i
$789$	3.69191	+	7.04004i	0.131435	+	0.250632i
$790$	8.48600	+	9.42465i	0.301918	+	0.335314i
$791$	−32.8823			−1.16916
$792$	5.65204	−	24.4840i	0.200836	−	0.870002i
$793$	12.1900			0.432881
$794$	−9.04648	−	10.0471i	−0.321048	−	0.356559i
$795$	2.76052	+	0.112166i	0.0979054	+	0.00397814i
$796$	−0.813229	+	7.73736i	−0.0288241	+	0.274243i
$797$	26.5002	+	23.8609i	0.938685	+	0.845195i	0.988136	−	0.153581i	$-0.0490806\pi$
$797$	26.5002	+	23.8609i	0.938685	+	0.845195i	−0.0494515	+	0.998777i	$0.515747\pi$
$798$	−14.4000	+	38.8724i	−0.509755	+	1.37607i
$799$	−5.13825	−	11.5407i	−0.181778	−	0.408281i
$800$	4.49069	−	3.26268i	0.158770	−	0.115353i
$801$	−35.5732	+	16.8507i	−1.25692	+	0.595389i
$802$		−	0.250691i		−	0.00885219i
$803$	−12.4643	−	4.62185i	−0.439854	−	0.163102i
$804$	−1.09939	+	7.51144i	−0.0387724	+	0.264908i
$805$	12.0739	+	56.8033i	0.425550	+	2.00205i
$806$	0.852676	−	1.91514i	0.0300342	−	0.0674580i
$807$	3.47833	−	13.6194i	0.122443	−	0.479427i
$808$	−23.6942	−	5.03636i	−0.833559	−	0.177178i
$809$	11.2240	+	34.5440i	0.394615	+	1.21450i	0.929261	+	0.369424i	$0.120445\pi$
$809$	11.2240	+	34.5440i	0.394615	+	1.21450i	−0.534646	+	0.845076i	$0.679555\pi$
$810$	−29.8462	−	24.4351i	−1.04869	−	0.858561i
$811$	10.9328	+	15.0477i	0.383902	+	0.528396i	0.956613	−	0.291361i	$-0.0941082\pi$
$811$	10.9328	+	15.0477i	0.383902	+	0.528396i	−0.572711	+	0.819757i	$0.694108\pi$
$812$	−1.24044	+	1.11689i	−0.0435307	+	0.0391953i
$813$	3.08571	+	7.76461i	0.108221	+	0.272317i
$814$	4.85528	−	1.92771i	0.170177	−	0.0675663i
$815$	38.1703	−	22.0376i	1.33705	−	0.771944i
$816$	−21.8786	−	10.8258i	−0.765905	−	0.378979i
$817$	4.85193	+	46.1630i	0.169748	+	1.61504i
$818$	10.1831	−	14.0159i	0.356045	−	0.490054i
$819$	−27.6039	−	15.0836i	−0.964559	−	0.527065i
$820$	−0.931617	+	0.302701i	−0.0325335	+	0.0105708i
$821$	−1.35082	+	0.601422i	−0.0471438	+	0.0209898i	−0.430173	−	0.902746i	$-0.641547\pi$
$821$	−1.35082	+	0.601422i	−0.0471438	+	0.0209898i	0.383029	+	0.923736i	$0.374881\pi$
$822$	0.694862	−	17.1012i	0.0242361	−	0.596472i
$823$	25.7543	−	5.47425i	0.897740	−	0.190820i	0.264143	−	0.964484i	$-0.414911\pi$
$823$	25.7543	−	5.47425i	0.897740	−	0.190820i	0.633597	+	0.773663i	$0.281578\pi$
$824$	−18.4364	−	31.9327i	−0.642261	−	1.11243i
$825$	−2.98224	+	15.8254i	−0.103828	+	0.550971i
$826$	−10.9079	+	18.8931i	−0.379536	+	0.657375i
$827$	12.8224	−	39.4633i	0.445879	−	1.37227i	−0.435639	−	0.900122i	$-0.643477\pi$
$827$	12.8224	−	39.4633i	0.445879	−	1.37227i	0.881517	−	0.472152i	$-0.156523\pi$
$828$	5.44131	−	6.33648i	0.189099	−	0.220208i
$829$	−24.3273	−	17.6748i	−0.844922	−	0.613871i	0.0788195	−	0.996889i	$-0.474885\pi$
$829$	−24.3273	−	17.6748i	−0.844922	−	0.613871i	−0.923741	+	0.383017i	$0.874885\pi$
$830$	4.10354	−	19.3056i	0.142436	−	0.670109i
$831$	−3.18282	−	18.6728i	−0.110411	−	0.647753i
$832$	24.1748	+	2.54087i	0.838110	+	0.0880889i
$833$	0.0398583	+	0.0177460i	0.00138101	+	0.000614864i
$834$	53.9585	−	3.46401i	1.86843	−	0.119949i
$835$	15.0051	+	8.66317i	0.519271	+	0.299801i
$836$	−4.95499	−	4.84301i	−0.171372	−	0.167499i
$837$	1.78282	−	0.156592i	0.0616233	−	0.00541262i
$838$	32.1273	+	10.4388i	1.10982	+	0.360602i
$839$	−43.5765	+	4.58008i	−1.50443	+	0.158122i	−0.820592	−	0.571514i	$-0.806356\pi$
$839$	−43.5765	+	4.58008i	−1.50443	+	0.158122i	−0.683836	+	0.729636i	$0.739690\pi$
$840$	31.2916	+	7.99171i	1.07966	+	0.275740i
$841$	−17.2748	+	19.1856i	−0.595682	+	0.661572i
$842$	−10.1065	+	11.2244i	−0.348293	+	0.386819i
$843$	5.05815	−	5.17844i	0.174212	−	0.178355i
$844$	8.46655	−	0.889870i	0.291431	−	0.0306306i
$845$	7.27448	+	2.36362i	0.250250	+	0.0813110i
$846$	5.41845	−	18.1139i	0.186290	−	0.622770i
$847$	23.9056	+	16.5471i	0.821406	+	0.568565i
$848$	2.26618	+	1.30838i	0.0778208	+	0.0449299i
$849$	10.7953	+	16.2033i	0.370495	+	0.556096i
$850$	12.0839	+	5.38010i	0.414474	+	0.184536i
$851$	−8.03043	−	0.844032i	−0.275280	−	0.0289330i
$852$	−3.65683	−	1.35465i	−0.125281	−	0.0464094i
$853$	−4.92066	+	23.1499i	−0.168480	+	0.792636i	0.810022	+	0.586399i	$0.199455\pi$
$853$	−4.92066	+	23.1499i	−0.168480	+	0.792636i	−0.978502	+	0.206237i	$0.933878\pi$
$854$	10.0808	+	7.32411i	0.344957	+	0.250626i
$855$	46.6675	−	16.3852i	1.59600	−	0.560362i
$856$	2.94711	−	9.07028i	0.100730	−	0.310016i
$857$	6.80091	−	11.7795i	0.232315	−	0.402381i	−0.726174	−	0.687511i	$-0.758703\pi$
$857$	6.80091	−	11.7795i	0.232315	−	0.402381i	0.958489	+	0.285130i	$0.0920367\pi$
$858$	27.8034	−	21.2020i	0.949191	−	0.723823i
$859$	−21.4372	−	37.1303i	−0.731428	−	1.26687i	−0.956273	−	0.292476i	$-0.905521\pi$
$859$	−21.4372	−	37.1303i	−0.731428	−	1.26687i	0.224845	−	0.974395i	$-0.427812\pi$
$860$	−7.60653	+	1.61682i	−0.259381	+	0.0551330i
$861$	−3.83234	−	2.42522i	−0.130606	−	0.0826511i
$862$	−27.6120	+	12.2937i	−0.940469	+	0.418724i
$863$	−44.3529	+	14.4111i	−1.50979	+	0.490561i	−0.942856	−	0.333202i	$-0.891871\pi$
$863$	−44.3529	+	14.4111i	−1.50979	+	0.490561i	−0.566935	+	0.823762i	$0.691871\pi$
$864$	−4.02336	−	9.46943i	−0.136878	−	0.322156i
$865$	24.1848	−	33.2875i	0.822308	−	1.13181i
$866$	2.33714	+	22.2364i	0.0794191	+	0.755623i
$867$	0.836895	+	13.0362i	0.0284224	+	0.442733i
$868$	0.279056	−	0.161113i	0.00947178	−	0.00546854i
$869$	−8.29130	−	5.25070i	−0.281263	−	0.178118i
$870$	13.1049	+	1.91805i	0.444296	+	0.0650280i
$871$	36.5054	−	32.8696i	1.23694	−	1.11374i
$872$	−26.4668	−	36.4284i	−0.896278	−	1.23362i
$873$	12.7327	−	30.5080i	0.430938	−	1.03254i
$874$	22.0089	+	67.7365i	0.744463	+	2.29122i
$875$	15.8641	+	3.37202i	0.536304	+	0.113995i
$876$	−2.36597	+	0.663850i	−0.0799386	+	0.0224294i
$877$	15.3460	−	34.4678i	0.518199	−	1.16389i	−0.445105	−	0.895478i	$-0.646834\pi$
$877$	15.3460	−	34.4678i	0.518199	−	1.16389i	0.963303	−	0.268415i	$-0.0864998\pi$
$878$	3.66188	+	17.2278i	0.123582	+	0.581410i
$879$	37.7053	+	29.8065i	1.27177	+	1.00535i
$880$	−26.3404	+	33.2987i	−0.887935	+	1.12250i
$881$			26.0806i			0.878678i	0.898321	+	0.439339i	$0.144787\pi$
$881$			26.0806i			0.878678i	−0.898321	+	0.439339i	$0.855213\pi$
$882$	0.0279540	+	0.0590133i	0.000941260	+	0.00198708i
$883$	−37.3267	+	27.1194i	−1.25614	+	0.912642i	−0.998562	−	0.0536143i	$-0.982926\pi$
$883$	−37.3267	+	27.1194i	−1.25614	+	0.912642i	−0.257582	+	0.966256i	$0.582926\pi$
$884$	−1.75650	−	3.94517i	−0.0590775	−	0.132690i
$885$	25.6594	−	4.37369i	0.862531	−	0.147020i
$886$	−10.7483	−	9.67781i	−0.361096	−	0.325133i
$887$	−2.22458	+	21.1655i	−0.0746942	+	0.710668i	0.891529	+	0.452963i	$0.149633\pi$
$887$	−2.22458	+	21.1655i	−0.0746942	+	0.710668i	−0.966224	+	0.257705i	$0.917034\pi$
$888$	−2.40133	+	3.79461i	−0.0805835	+	0.127339i
$889$	−10.8730	−	12.0757i	−0.364669	−	0.405006i
$890$	56.2342			1.88497
$891$	27.3422	+	11.9753i	0.915997	+	0.401186i
$892$	1.70131			0.0569640
$893$	16.2222	+	18.0165i	0.542854	+	0.602900i
$894$	7.42762	−	11.7372i	0.248417	−	0.392550i
$895$	3.63757	−	34.6091i	0.121590	−	1.15686i
$896$	26.2436	+	23.6298i	0.876737	+	0.789417i
$897$	−53.2769	+	9.08115i	−1.77886	+	0.303211i
$898$	−0.417609	−	0.937966i	−0.0139358	−	0.0313003i
$899$	−0.497149	+	0.361200i	−0.0165808	+	0.0120467i
$900$	1.27436	+	2.69028i	0.0424786	+	0.0896760i
$901$			1.75610i			0.0585040i
$902$	4.19620	−	2.79374i	0.139718	−	0.0930213i
$903$	−28.2448	−	22.3278i	−0.939928	−	0.743024i
$904$	6.53239	+	30.7325i	0.217264	+	1.02215i
$905$	1.25859	−	2.82684i	0.0418369	−	0.0939673i
$906$	9.26518	−	2.59965i	0.307815	−	0.0863676i
$907$	−1.24600	−	0.264846i	−0.0413729	−	0.00879408i	0.187179	−	0.982326i	$-0.440066\pi$
$907$	−1.24600	−	0.264846i	−0.0413729	−	0.00879408i	−0.228552	+	0.973532i	$0.573399\pi$
$908$	0.313562	+	0.965043i	0.0104059	+	0.0320261i
$909$	11.0830	−	26.5553i	0.367601	−	0.880783i
$910$	26.4146	+	36.3566i	0.875636	+	1.20521i
$911$	19.4487	−	17.5117i	0.644365	−	0.580189i	−0.280794	−	0.959768i	$-0.590598\pi$
$911$	19.4487	−	17.5117i	0.644365	−	0.580189i	0.925159	+	0.379579i	$0.123931\pi$
$912$	46.3521	+	6.78418i	1.53487	+	0.224647i
$913$	0.973602	+	15.2423i	0.0322215	+	0.504448i
$914$	−30.9608	+	17.8752i	−1.02409	+	0.591260i
$915$	−0.952478	−	14.8367i	−0.0314880	−	0.490485i
$916$	0.442530	+	4.21039i	0.0146216	+	0.139115i
$917$	−10.1641	+	13.9897i	−0.335649	+	0.461981i
$918$	14.7485	−	19.5859i	0.486773	−	0.646430i
$919$	−44.7124	+	14.5279i	−1.47493	+	0.479233i	−0.932593	−	0.360931i	$-0.882459\pi$
$919$	−44.7124	+	14.5279i	−1.47493	+	0.479233i	−0.542333	+	0.840163i	$0.682459\pi$
$920$	50.6909	−	22.5691i	1.67123	−	0.744080i
$921$	42.5868	+	26.9502i	1.40328	+	0.888038i
$922$	−30.4833	+	6.47942i	−1.00391	+	0.213388i
$923$	12.6170	+	21.8533i	0.415294	+	0.719310i
$924$	5.37288	−	0.124555i	0.176755	−	0.00409757i
$925$	1.43897	−	2.49236i	0.0473129	−	0.0819484i
$926$	16.4354	−	50.5831i	0.540102	−	1.66226i
$927$	41.3280	−	14.5105i	1.35739	−	0.476586i
$928$	2.85806	+	2.07650i	0.0938203	+	0.0681644i
$929$	−1.46900	+	6.91111i	−0.0481964	+	0.226746i	−0.995653	−	0.0931373i	$-0.970310\pi$
$929$	−1.46900	+	6.91111i	−0.0481964	+	0.226746i	0.947457	+	0.319884i	$0.103644\pi$
$930$	−2.39757	−	0.888163i	−0.0786195	−	0.0291240i
$931$	−0.0832719	−	0.00875222i	−0.00272912	−	0.000286843i
$932$	−0.535952	−	0.238621i	−0.0175557	−	0.00781630i
$933$	−20.5499	−	30.8446i	−0.672775	−	1.00981i
$934$	−32.7617	−	18.9150i	−1.07199	−	0.618916i
$935$	−28.1913	−	4.13538i	−0.921953	−	0.135241i
$936$	−8.61370	+	28.7957i	−0.281548	+	0.941217i
$937$	−30.3985	−	9.87708i	−0.993076	−	0.322670i	−0.232981	−	0.972481i	$-0.574848\pi$
$937$	−30.3985	−	9.87708i	−0.993076	−	0.322670i	−0.760095	+	0.649811i	$0.774848\pi$
$938$	49.9379	−	5.24868i	1.63053	−	0.171375i
$939$	−4.08817	+	4.18539i	−0.133412	+	0.136585i
$940$	−2.71776	+	3.01838i	−0.0886435	+	0.0984486i
$941$	−20.8640	+	23.1718i	−0.680146	+	0.755378i	−0.980085	−	0.198580i	$-0.936367\pi$
$941$	−20.8640	+	23.1718i	−0.680146	+	0.755378i	0.299939	+	0.953958i	$0.403034\pi$
$942$	−27.2536	−	6.96043i	−0.887971	−	0.226783i
$943$	−7.74939	+	0.814493i	−0.252355	+	0.0265236i
$944$	23.4469	+	7.61837i	0.763132	+	0.247957i
$945$	−16.2017	+	34.7757i	−0.527040	+	1.13125i
$946$	35.4484	−	18.5751i	1.15253	−	0.603930i
$947$	23.5597	+	13.6022i	0.765587	+	0.442012i	0.831298	−	0.555827i	$-0.187598\pi$
$947$	23.5597	+	13.6022i	0.765587	+	0.442012i	−0.0657109	+	0.997839i	$0.520932\pi$
$948$	−1.81041	+	0.116224i	−0.0587994	+	0.00377478i
$949$	14.5262	+	6.46749i	0.471541	+	0.209944i
$950$	−25.2457	−	2.65343i	−0.819078	−	0.0860886i
$951$	−5.69165	−	33.3915i	−0.184564	−	1.08279i
$952$	−4.26803	+	20.0795i	−0.138328	+	0.650780i
$953$	−1.81421	−	1.31810i	−0.0587681	−	0.0426975i	0.558013	−	0.829832i	$-0.311564\pi$
$953$	−1.81421	−	1.31810i	−0.0587681	−	0.0426975i	−0.616781	+	0.787134i	$0.711564\pi$
$954$	−1.71227	+	1.99396i	−0.0554368	+	0.0645570i
$955$	−16.8957	+	51.9996i	−0.546732	+	1.68267i
$956$	0.710943	−	1.23139i	0.0229935	−	0.0398260i
$957$	−10.1655	+	1.30728i	−0.328604	+	0.0422585i
$958$	−9.40555	−	16.2909i	−0.303879	−	0.526335i
$959$	−16.6508	+	3.53925i	−0.537684	+	0.114288i
$960$	1.20361	−	29.6220i	0.0388465	−	0.956046i
$961$	−28.2115	+	12.5606i	−0.910050	+	0.405180i
$962$	−5.94274	+	1.93091i	−0.191602	+	0.0622551i
$963$	9.94170	+	5.43246i	0.320367	+	0.175058i
$964$	−3.24456	+	4.46576i	−0.104500	+	0.143832i
$965$	2.77819	+	26.4327i	0.0894331	+	0.850900i
$966$	−49.5145	−	24.5004i	−1.59310	−	0.788288i
$967$	−3.38525	+	1.95447i	−0.108862	+	0.0628516i	−0.553443	−	0.832887i	$-0.686686\pi$
$967$	−3.38525	+	1.95447i	−0.108862	+	0.0628516i	0.444580	+	0.895739i	$0.353353\pi$
$968$	10.7162	−	25.6299i	0.344431	−	0.823776i
$969$	11.6105	+	29.2157i	0.372983	+	0.938543i
$970$	−35.0974	+	31.6018i	−1.12691	+	1.01467i
$971$	−8.82768	−	12.1503i	−0.283294	−	0.389920i	0.643528	−	0.765423i	$-0.277470\pi$
$971$	−8.82768	−	12.1503i	−0.283294	−	0.389920i	−0.926821	+	0.375502i	$0.877470\pi$
$972$	5.38972	−	1.18166i	0.172875	−	0.0379018i
$973$	−16.6182	−	51.1455i	−0.532754	−	1.63965i
$974$	4.08698	+	0.868715i	0.130955	+	0.0278354i
$975$	4.76656	−	18.6635i	0.152652	−	0.597710i
$976$	5.72739	−	12.8639i	0.183329	−	0.411764i
$977$	3.29317	+	15.4931i	0.105358	+	0.495670i	0.998909	+	0.0467074i	$0.0148728\pi$
$977$	3.29317	+	15.4931i	0.105358	+	0.495670i	−0.893551	+	0.448962i	$0.851794\pi$
$978$	−6.07211	+	41.4870i	−0.194165	+	1.32661i
$979$	−41.9025	+	11.7426i	−1.33921	+	0.375295i
$980$		−	0.0140277i		−	0.000448098i
$981$	48.3399	−	22.8981i	1.54337	−	0.731080i
$982$	12.9740	−	9.42618i	0.414018	−	0.300801i
$983$	−8.91585	−	20.0253i	−0.284371	−	0.638709i	0.713722	−	0.700429i	$-0.247008\pi$
$983$	−8.91585	−	20.0253i	−0.284371	−	0.638709i	−0.998093	+	0.0617204i	$0.980341\pi$
$984$	−1.50532	+	4.06358i	−0.0479880	+	0.129542i
$985$	−1.19659	−	1.07741i	−0.0381265	−	0.0343292i
$986$	−0.879973	+	8.37238i	−0.0280240	+	0.266631i
$987$	−18.7894	−	0.763458i	−0.598072	−	0.0243011i
$988$	5.54551	+	6.15892i	0.176426	+	0.195941i
$989$	−61.8592			−1.96701
$990$	−27.9777	−	32.1832i	−0.889188	−	1.02285i
$991$	29.5878			0.939888			0.469944	−	0.882696i	$-0.344274\pi$
$991$	29.5878			0.939888			0.469944	+	0.882696i	$0.344274\pi$
$992$	−0.456336	−	0.506812i	−0.0144887	−	0.0160913i
$993$	−24.9164	−	47.5127i	−0.790697	−	1.50777i
$994$	−2.69620	+	25.6526i	−0.0855183	+	0.813653i
$995$	−45.6283	−	41.0839i	−1.44651	−	1.30245i
$996$	1.80242	+	2.17310i	0.0571120	+	0.0688572i
$997$	−15.0669	−	33.8408i	−0.477173	−	1.07175i	−0.978454	−	0.206464i	$-0.933804\pi$
$997$	−15.0669	−	33.8408i	−0.477173	−	1.07175i	0.501281	−	0.865284i	$-0.332862\pi$
$998$	−13.6537	+	9.92003i	−0.432202	+	0.314013i
$999$	−3.90258	−	3.63672i	−0.123472	−	0.115061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.2.3	✓	80
3.2	odd	2		297.2.t.a.35.8		80
9.2	odd	6		891.2.k.a.728.16		80
9.4	even	3		297.2.t.a.233.8		80
9.5	odd	6	inner	99.2.p.a.68.3	yes	80
9.7	even	3		891.2.k.a.728.5		80
11.6	odd	10	inner	99.2.p.a.83.3	yes	80
33.17	even	10		297.2.t.a.116.8		80
99.50	even	30	inner	99.2.p.a.50.3	yes	80
99.61	odd	30		891.2.k.a.809.16		80
99.83	even	30		891.2.k.a.809.5		80
99.94	odd	30		297.2.t.a.17.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.3	✓	80	1.1	even	1	trivial
99.2.p.a.50.3	yes	80	99.50	even	30	inner
99.2.p.a.68.3	yes	80	9.5	odd	6	inner
99.2.p.a.83.3	yes	80	11.6	odd	10	inner
297.2.t.a.17.8		80	99.94	odd	30
297.2.t.a.35.8		80	3.2	odd	2
297.2.t.a.116.8		80	33.17	even	10
297.2.t.a.233.8		80	9.4	even	3
891.2.k.a.728.5		80	9.7	even	3
891.2.k.a.728.16		80	9.2	odd	6
891.2.k.a.809.5		80	99.83	even	30
891.2.k.a.809.16		80	99.61	odd	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02662 - 1.14018i) q^{2} +(-0.926210 + 1.46360i) q^{3} +(-0.0369992 + 0.352024i) q^{4} +(-2.07594 - 1.86918i) q^{5} +(2.61964 - 0.446523i) q^{6} +(-1.07503 - 2.41456i) q^{7} +(-2.04313 + 1.48442i) q^{8} +(-1.28427 - 2.71121i) q^{9} +O(q^{10})\)	\(q+(-1.02662 - 1.14018i) q^{2} +(-0.926210 + 1.46360i) q^{3} +(-0.0369992 + 0.352024i) q^{4} +(-2.07594 - 1.86918i) q^{5} +(2.61964 - 0.446523i) q^{6} +(-1.07503 - 2.41456i) q^{7} +(-2.04313 + 1.48442i) q^{8} +(-1.28427 - 2.71121i) q^{9} +4.28588i q^{10} +(-0.894961 - 3.19359i) q^{11} +(-0.480955 - 0.380200i) q^{12} +(0.824813 + 3.88044i) q^{13} +(-1.64938 + 3.70458i) q^{14} +(4.65849 - 1.30709i) q^{15} +(4.48249 + 0.952784i) q^{16} +(0.950349 + 2.92487i) q^{17} +(-1.77280 + 4.24769i) q^{18} +(-3.46908 - 4.77479i) q^{19} +(0.734805 - 0.661621i) q^{20} +(4.52967 + 0.662970i) q^{21} +(-2.72248 + 4.29903i) q^{22} +(6.81163 - 3.93270i) q^{23} +(-0.280237 - 4.36523i) q^{24} +(0.293029 + 2.78799i) q^{25} +(3.57763 - 4.92418i) q^{26} +(5.15764 + 0.631484i) q^{27} +(0.889760 - 0.289101i) q^{28} +(-1.62991 + 0.725684i) q^{29} +(-6.27283 - 3.96963i) q^{30} +(0.336898 - 0.0716100i) q^{31} +(-0.990031 - 1.71478i) q^{32} +(5.50308 + 1.64807i) q^{33} +(2.35923 - 4.08631i) q^{34} +(-2.28156 + 7.02191i) q^{35} +(1.00193 - 0.351782i) q^{36} +(-0.830542 - 0.603424i) q^{37} +(-1.88267 + 8.85728i) q^{38} +(-6.44338 - 2.38690i) q^{39} +(7.01607 + 0.737419i) q^{40} +(-0.905030 - 0.402945i) q^{41} +(-3.89436 - 5.84526i) q^{42} +(-6.81106 - 3.93236i) q^{43} +(1.15733 - 0.196887i) q^{44} +(-2.40167 + 8.02883i) q^{45} +(-11.4770 - 3.72909i) q^{46} +(-4.08522 + 0.429374i) q^{47} +(-5.54623 + 5.67812i) q^{48} +(0.00949289 - 0.0105429i) q^{49} +(2.87798 - 3.19632i) q^{50} +(-5.16108 - 1.31811i) q^{51} +(-1.39653 + 0.146781i) q^{52} +(0.543068 + 0.176453i) q^{53} +(-4.57494 - 6.52893i) q^{54} +(-4.11152 + 8.30254i) q^{55} +(5.78067 + 3.33747i) q^{56} +(10.2015 - 0.654912i) q^{57} +(2.50071 + 1.11339i) q^{58} +(5.35030 + 0.562340i) q^{59} +(0.287768 + 1.68826i) q^{60} +(0.638862 - 3.00561i) q^{61} +(-0.427516 - 0.310608i) q^{62} +(-5.16575 + 6.01559i) q^{63} +(1.89345 - 5.82744i) q^{64} +(5.54099 - 9.59727i) q^{65} +(-3.77049 - 7.96644i) q^{66} +(-6.19123 - 10.7235i) q^{67} +(-1.06479 + 0.226328i) q^{68} +(-0.553090 + 13.6120i) q^{69} +(10.3485 - 4.60746i) q^{70} +(6.04945 - 1.96559i) q^{71} +(6.64852 + 3.63296i) q^{72} +(2.35594 - 3.24267i) q^{73} +(0.164641 + 1.56646i) q^{74} +(-4.35192 - 2.15338i) q^{75} +(1.80919 - 1.04454i) q^{76} +(-6.74902 + 5.59416i) q^{77} +(3.89342 + 9.79705i) q^{78} +(2.19900 - 1.97999i) q^{79} +(-7.52445 - 10.3565i) q^{80} +(-5.70130 + 6.96385i) q^{81} +(0.469694 + 1.44557i) q^{82} +(-4.50447 - 0.957455i) q^{83} +(-0.400976 + 1.57002i) q^{84} +(3.49425 - 7.84822i) q^{85} +(2.50878 + 11.8029i) q^{86} +(0.447528 - 3.05768i) q^{87} +(6.56917 + 5.19644i) q^{88} -13.1208i q^{89} +(11.6199 - 5.50423i) q^{90} +(8.48287 - 6.16317i) q^{91} +(1.13238 + 2.54336i) q^{92} +(-0.207230 + 0.559411i) q^{93} +(4.68355 + 4.21708i) q^{94} +(-1.72334 + 16.3965i) q^{95} +(3.42674 + 0.139237i) q^{96} +(7.37347 + 8.18907i) q^{97} -0.0217664 q^{98} +(-7.50913 + 6.52786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more