LMFDB - Embedded newform 64.2.i.a.61.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			61.6
Character	$\chi$	$=$	64.61
Dual form			64.2.i.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19357 - 0.758552i) q^{2} +(-0.599600 + 3.01439i) q^{3} +(0.849199 - 1.81076i) q^{4} +(-1.78465 - 1.19247i) q^{5} +(1.57091 + 4.05270i) q^{6} +(1.99271 - 0.825409i) q^{7} +(-0.359981 - 2.80543i) q^{8} +(-5.95540 - 2.46681i) q^{9} +O(q^{10})$	\(q+(1.19357 - 0.758552i) q^{2} +(-0.599600 + 3.01439i) q^{3} +(0.849199 - 1.81076i) q^{4} +(-1.78465 - 1.19247i) q^{5} +(1.57091 + 4.05270i) q^{6} +(1.99271 - 0.825409i) q^{7} +(-0.359981 - 2.80543i) q^{8} +(-5.95540 - 2.46681i) q^{9} +(-3.03465 - 0.0695368i) q^{10} +(-3.15038 + 0.626650i) q^{11} +(4.94917 + 3.64555i) q^{12} +(0.0943077 - 0.0630144i) q^{13} +(1.75232 - 2.49676i) q^{14} +(4.66465 - 4.66465i) q^{15} +(-2.55772 - 3.07540i) q^{16} +(2.42319 + 2.42319i) q^{17} +(-8.97937 + 1.57318i) q^{18} +(1.93596 + 2.89737i) q^{19} +(-3.67480 + 2.21894i) q^{20} +(1.29328 + 6.50174i) q^{21} +(-3.28485 + 3.13768i) q^{22} +(-1.33543 + 3.22402i) q^{23} +(8.67250 + 0.597008i) q^{24} +(-0.150405 - 0.363110i) q^{25} +(0.0647628 - 0.146749i) q^{26} +(5.88424 - 8.80639i) q^{27} +(0.197591 - 4.30927i) q^{28} +(2.01879 + 0.401561i) q^{29} +(2.02919 - 9.10594i) q^{30} +4.16617i q^{31} +(-5.38566 - 1.73052i) q^{32} -9.87224i q^{33} +(4.73035 + 1.05412i) q^{34} +(-4.54058 - 0.903177i) q^{35} +(-9.52413 + 8.68901i) q^{36} +(5.48499 - 8.20886i) q^{37} +(4.50850 + 1.98968i) q^{38} +(0.133403 + 0.322064i) q^{39} +(-2.70294 + 5.43598i) q^{40} +(0.347569 - 0.839106i) q^{41} +(6.47551 + 6.77923i) q^{42} +(0.925855 + 4.65459i) q^{43} +(-1.54059 + 6.23675i) q^{44} +(7.68675 + 11.5040i) q^{45} +(0.851658 + 4.86108i) q^{46} +(-8.31575 - 8.31575i) q^{47} +(10.8041 - 5.86597i) q^{48} +(-1.66014 + 1.66014i) q^{49} +(-0.454956 - 0.319306i) q^{50} +(-8.75739 + 5.85150i) q^{51} +(-0.0340181 - 0.224281i) q^{52} +(0.565279 - 0.112441i) q^{53} +(0.343130 - 14.9745i) q^{54} +(6.36961 + 2.63838i) q^{55} +(-3.03296 - 5.29328i) q^{56} +(-9.89462 + 4.09848i) q^{57} +(2.71416 - 1.05206i) q^{58} +(-0.649771 - 0.434163i) q^{59} +(-4.48535 - 12.4078i) q^{60} +(-0.528753 + 2.65822i) q^{61} +(3.16025 + 4.97260i) q^{62} -13.9035 q^{63} +(-7.74083 + 2.01980i) q^{64} -0.243449 q^{65} +(-7.48860 - 11.7832i) q^{66} +(0.971210 - 4.88260i) q^{67} +(6.44559 - 2.33005i) q^{68} +(-8.91774 - 5.95864i) q^{69} +(-6.10459 + 2.36626i) q^{70} +(9.38522 - 3.88748i) q^{71} +(-4.77662 + 17.5955i) q^{72} +(12.6303 + 5.23165i) q^{73} +(0.319848 - 13.9585i) q^{74} +(1.18474 - 0.235659i) q^{75} +(6.89047 - 1.04512i) q^{76} +(-5.76057 + 3.84909i) q^{77} +(0.403528 + 0.283211i) q^{78} +(-3.50532 + 3.50532i) q^{79} +(0.897337 + 8.53852i) q^{80} +(9.34353 + 9.34353i) q^{81} +(-0.221658 - 1.26518i) q^{82} +(-8.25513 - 12.3547i) q^{83} +(12.8713 + 3.17945i) q^{84} +(-1.43498 - 7.21413i) q^{85} +(4.63581 + 4.85325i) q^{86} +(-2.42093 + 5.84464i) q^{87} +(2.89210 + 8.61259i) q^{88} +(4.98881 + 12.0441i) q^{89} +(17.9010 + 7.90003i) q^{90} +(0.135916 - 0.203412i) q^{91} +(4.70389 + 5.15599i) q^{92} +(-12.5585 - 2.49803i) q^{93} +(-16.2333 - 3.61747i) q^{94} -7.47938i q^{95} +(8.44572 - 15.1969i) q^{96} +4.06140i q^{97} +(-0.722186 + 3.24079i) q^{98} +(20.3076 + 4.03944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	1.19357	−	0.758552i	0.843979	−	0.536377i
$2$	1.19357	−	0.758552i	0.843979	−	0.536377i
$3$	−0.599600	+	3.01439i	−0.346179	+	1.74036i	0.279377	+	0.960181i	$0.409872\pi$
$3$	−0.599600	+	3.01439i	−0.346179	+	1.74036i	−0.625556	+	0.780179i	$0.715128\pi$
$4$	0.849199	−	1.81076i	0.424600	−	0.905381i
$5$	−1.78465	−	1.19247i	−0.798122	−	0.533288i	0.0883396	−	0.996090i	$-0.471844\pi$
$5$	−1.78465	−	1.19247i	−0.798122	−	0.533288i	−0.886461	+	0.462802i	$0.846844\pi$
$6$	1.57091	+	4.05270i	0.641321	+	1.65451i
$7$	1.99271	−	0.825409i	0.753175	−	0.311975i	0.0271386	−	0.999632i	$-0.491360\pi$
$7$	1.99271	−	0.825409i	0.753175	−	0.311975i	0.726036	+	0.687656i	$0.241360\pi$
$8$	−0.359981	−	2.80543i	−0.127273	−	0.991868i
$9$	−5.95540	−	2.46681i	−1.98513	−	0.822270i
$10$	−3.03465	−	0.0695368i	−0.959641	−	0.0219895i
$11$	−3.15038	+	0.626650i	−0.949877	+	0.188942i	−0.645629	−	0.763651i	$-0.723405\pi$
$11$	−3.15038	+	0.626650i	−0.949877	+	0.188942i	−0.304247	+	0.952593i	$0.598405\pi$
$12$	4.94917	+	3.64555i	1.42870	+	1.05238i
$13$	0.0943077	−	0.0630144i	0.0261563	−	0.0174770i	−0.542423	−	0.840105i	$-0.682493\pi$
$13$	0.0943077	−	0.0630144i	0.0261563	−	0.0174770i	0.568580	+	0.822628i	$0.307493\pi$
$14$	1.75232	−	2.49676i	0.468327	−	0.667286i
$15$	4.66465	−	4.66465i	1.20441	−	1.20441i
$16$	−2.55772	−	3.07540i	−0.639430	−	0.768849i
$17$	2.42319	+	2.42319i	0.587710	+	0.587710i	0.937011	−	0.349301i	$-0.113581\pi$
$17$	2.42319	+	2.42319i	0.587710	+	0.587710i	−0.349301	+	0.937011i	$0.613581\pi$
$18$	−8.97937	+	1.57318i	−2.11646	+	0.370802i
$19$	1.93596	+	2.89737i	0.444140	+	0.664702i	0.984228	−	0.176906i	$-0.0566089\pi$
$19$	1.93596	+	2.89737i	0.444140	+	0.664702i	−0.540088	+	0.841609i	$0.681609\pi$
$20$	−3.67480	+	2.21894i	−0.821711	+	0.496171i
$21$	1.29328	+	6.50174i	0.282216	+	1.41879i
$22$	−3.28485	+	3.13768i	−0.700331	+	0.668955i
$23$	−1.33543	+	3.22402i	−0.278457	+	0.672255i	−0.999793	−	0.0203301i	$-0.993528\pi$
$23$	−1.33543	+	3.22402i	−0.278457	+	0.672255i	0.721336	+	0.692585i	$0.243528\pi$
$24$	8.67250	+	0.597008i	1.77027	+	0.121864i
$25$	−0.150405	−	0.363110i	−0.0300810	−	0.0726220i
$26$	0.0647628	−	0.146749i	0.0127010	−	0.0287799i
$27$	5.88424	−	8.80639i	1.13242	−	1.69479i
$28$	0.197591	−	4.30927i	0.0373412	−	0.814375i
$29$	2.01879	+	0.401561i	0.374879	+	0.0745681i	0.378934	−	0.925424i	$-0.376291\pi$
$29$	2.01879	+	0.401561i	0.374879	+	0.0745681i	−0.00405495	+	0.999992i	$0.501291\pi$
$30$	2.02919	−	9.10594i	0.370477	−	1.66251i
$31$			4.16617i			0.748266i	0.927375	+	0.374133i	$0.122060\pi$
$31$			4.16617i			0.748266i	−0.927375	+	0.374133i	$0.877940\pi$
$32$	−5.38566	−	1.73052i	−0.952058	−	0.305916i
$33$		−	9.87224i		−	1.71854i
$34$	4.73035	+	1.05412i	0.811248	+	0.180781i
$35$	−4.54058	−	0.903177i	−0.767498	−	0.152665i
$36$	−9.52413	+	8.68901i	−1.58736	+	1.44817i
$37$	5.48499	−	8.20886i	0.901726	−	1.34953i	−0.0349711	−	0.999388i	$-0.511134\pi$
$37$	5.48499	−	8.20886i	0.901726	−	1.34953i	0.936697	−	0.350140i	$-0.113866\pi$
$38$	4.50850	+	1.98968i	0.731376	+	0.322768i
$39$	0.133403	+	0.322064i	0.0213616	+	0.0515715i
$40$	−2.70294	+	5.43598i	−0.427372	+	0.859504i
$41$	0.347569	−	0.839106i	0.0542812	−	0.131046i	−0.894413	−	0.447243i	$-0.852406\pi$
$41$	0.347569	−	0.839106i	0.0542812	−	0.131046i	0.948694	+	0.316197i	$0.102406\pi$
$42$	6.47551	+	6.77923i	0.999193	+	1.04606i
$43$	0.925855	+	4.65459i	0.141192	+	0.709818i	0.984915	+	0.173039i	$0.0553588\pi$
$43$	0.925855	+	4.65459i	0.141192	+	0.709818i	−0.843723	+	0.536778i	$0.819641\pi$
$44$	−1.54059	+	6.23675i	−0.232253	+	0.940225i
$45$	7.68675	+	11.5040i	1.14587	+	1.71492i
$46$	0.851658	+	4.86108i	0.125570	+	0.716727i
$47$	−8.31575	−	8.31575i	−1.21298	−	1.21298i	−0.970043	−	0.242935i	$-0.921890\pi$
$47$	−8.31575	−	8.31575i	−1.21298	−	1.21298i	−0.242935	−	0.970043i	$-0.578110\pi$
$48$	10.8041	−	5.86597i	1.55943	−	0.846680i
$49$	−1.66014	+	1.66014i	−0.237163	+	0.237163i
$50$	−0.454956	−	0.319306i	−0.0643405	−	0.0451566i
$51$	−8.75739	+	5.85150i	−1.22628	+	0.819374i
$52$	−0.0340181	−	0.224281i	−0.00471746	−	0.0311021i
$53$	0.565279	−	0.112441i	0.0776470	−	0.0154450i	−0.156114	−	0.987739i	$-0.549897\pi$
$53$	0.565279	−	0.112441i	0.0776470	−	0.0154450i	0.233761	+	0.972294i	$0.424897\pi$
$54$	0.343130	−	14.9745i	0.0466941	−	2.03777i
$55$	6.36961	+	2.63838i	0.858878	+	0.355759i
$56$	−3.03296	−	5.29328i	−0.405297	−	0.707344i
$57$	−9.89462	+	4.09848i	−1.31057	+	0.542857i
$58$	2.71416	−	1.05206i	0.356386	−	0.138143i
$59$	−0.649771	−	0.434163i	−0.0845930	−	0.0565232i	0.512554	−	0.858655i	$-0.328699\pi$
$59$	−0.649771	−	0.434163i	−0.0845930	−	0.0565232i	−0.597147	+	0.802132i	$0.703699\pi$
$60$	−4.48535	−	12.4078i	−0.579056	−	1.60184i
$61$	−0.528753	+	2.65822i	−0.0676999	+	0.340350i	−0.999759	−	0.0219561i	$-0.993011\pi$
$61$	−0.528753	+	2.65822i	−0.0676999	+	0.340350i	0.932059	+	0.362306i	$0.118011\pi$
$62$	3.16025	+	4.97260i	0.401353	+	0.631520i
$63$	−13.9035			−1.75168
$64$	−7.74083	+	2.01980i	−0.967603	+	0.252475i
$65$	−0.243449			−0.0301962
$66$	−7.48860	−	11.7832i	−0.921783	−	1.45041i
$67$	0.971210	−	4.88260i	0.118652	−	0.596505i	−0.875011	−	0.484104i	$-0.839146\pi$
$67$	0.971210	−	4.88260i	0.118652	−	0.596505i	0.993663	−	0.112401i	$-0.0358542\pi$
$68$	6.44559	−	2.33005i	0.781643	−	0.282560i
$69$	−8.91774	−	5.95864i	−1.07357	−	0.717336i
$70$	−6.10459	+	2.36626i	−0.729638	+	0.282822i
$71$	9.38522	−	3.88748i	1.11382	−	0.461360i	0.251569	−	0.967839i	$-0.419054\pi$
$71$	9.38522	−	3.88748i	1.11382	−	0.461360i	0.862252	+	0.506480i	$0.169054\pi$
$72$	−4.77662	+	17.5955i	−0.562930	+	2.07364i
$73$	12.6303	+	5.23165i	1.47827	+	0.612318i	0.968727	−	0.248129i	$-0.0798158\pi$
$73$	12.6303	+	5.23165i	1.47827	+	0.612318i	0.509539	+	0.860447i	$0.329816\pi$
$74$	0.319848	−	13.9585i	0.0371816	−	1.62264i
$75$	1.18474	−	0.235659i	0.136802	−	0.0272116i
$76$	6.89047	−	1.04512i	0.790391	−	0.119884i
$77$	−5.76057	+	3.84909i	−0.656478	+	0.438645i
$78$	0.403528	+	0.283211i	0.0456905	+	0.0320674i
$79$	−3.50532	+	3.50532i	−0.394379	+	0.394379i	−0.876245	−	0.481866i	$-0.839959\pi$
$79$	−3.50532	+	3.50532i	−0.394379	+	0.394379i	0.481866	+	0.876245i	$0.339959\pi$
$80$	0.897337	+	8.53852i	0.100325	+	0.954636i
$81$	9.34353	+	9.34353i	1.03817	+	1.03817i
$82$	−0.221658	−	1.26518i	−0.0244781	−	0.139715i
$83$	−8.25513	−	12.3547i	−0.906118	−	1.35610i	−0.934296	−	0.356499i	$-0.883970\pi$
$83$	−8.25513	−	12.3547i	−0.906118	−	1.35610i	0.0281778	−	0.999603i	$-0.491030\pi$
$84$	12.8713	+	3.17945i	1.40438	+	0.346907i
$85$	−1.43498	−	7.21413i	−0.155645	−	0.782483i
$86$	4.63581	+	4.85325i	0.499892	+	0.523339i
$87$	−2.42093	+	5.84464i	−0.259551	+	0.626611i
$88$	2.89210	+	8.61259i	0.308299	+	0.918105i
$89$	4.98881	+	12.0441i	0.528813	+	1.27667i	0.932301	+	0.361683i	$0.117798\pi$
$89$	4.98881	+	12.0441i	0.528813	+	1.27667i	−0.403488	+	0.914985i	$0.632202\pi$
$90$	17.9010	+	7.90003i	1.88694	+	0.832736i
$91$	0.135916	−	0.203412i	0.0142478	−	0.0213234i
$92$	4.70389	+	5.15599i	0.490414	+	0.537549i
$93$	−12.5585	−	2.49803i	−1.30225	−	0.259034i
$94$	−16.2333	−	3.61747i	−1.67434	−	0.373114i
$95$		−	7.47938i		−	0.767368i
$96$	8.44572	−	15.1969i	0.861988	−	1.55102i
$97$			4.06140i			0.412373i	0.978513	+	0.206187i	$0.0661054\pi$
$97$			4.06140i			0.412373i	−0.978513	+	0.206187i	$0.933895\pi$
$98$	−0.722186	+	3.24079i	−0.0729518	+	0.327369i
$99$	20.3076	+	4.03944i	2.04099	+	0.405979i
$100$	−0.785230	−	0.0360048i	−0.0785230	−	0.00360048i
$101$	3.05636	−	4.57417i	0.304119	−	0.455147i	−0.647660	−	0.761929i	$-0.724252\pi$
$101$	3.05636	−	4.57417i	0.304119	−	0.455147i	0.951780	+	0.306782i	$0.0992524\pi$
$102$	−6.01386	+	13.6271i	−0.595461	+	1.34928i
$103$	−5.12950	−	12.3837i	−0.505425	−	1.22020i	−0.946491	−	0.322730i	$-0.895400\pi$
$103$	−5.12950	−	12.3837i	−0.505425	−	1.22020i	0.441066	−	0.897475i	$-0.354600\pi$
$104$	−0.210731	−	0.241889i	−0.0206639	−	0.0237192i
$105$	5.44506	−	13.1455i	0.531384	−	1.28287i
$106$	0.589405	−	0.562999i	0.0572481	−	0.0546833i
$107$	1.35370	+	6.80550i	0.130867	+	0.657913i	0.989407	+	0.145167i	$0.0463718\pi$
$107$	1.35370	+	6.80550i	0.130867	+	0.657913i	−0.858540	+	0.512746i	$0.828628\pi$
$108$	−10.9494	−	18.1334i	−1.05361	−	1.74488i
$109$	−11.0688	−	16.5656i	−1.06020	−	1.58670i	−0.778973	−	0.627057i	$-0.784259\pi$
$109$	−11.0688	−	16.5656i	−1.06020	−	1.58670i	−0.281225	−	0.959642i	$-0.590741\pi$
$110$	9.60390	−	1.68260i	0.915695	−	0.160429i
$111$	21.4559	+	21.4559i	2.03651	+	2.03651i
$112$	−7.63526	−	4.01722i	−0.721465	−	0.379591i
$113$	6.43123	−	6.43123i	0.605000	−	0.605000i	−0.336635	−	0.941635i	$-0.609289\pi$
$113$	6.43123	−	6.43123i	0.605000	−	0.605000i	0.941635	+	0.336635i	$0.109289\pi$
$114$	−8.70097	+	12.3974i	−0.814920	+	1.16112i
$115$	6.22783	−	4.16130i	0.580748	−	0.388044i
$116$	2.44148	−	3.31454i	0.226686	−	0.307747i
$117$	−0.717085	+	0.142637i	−0.0662945	+	0.0131868i
$118$	−1.10488	−	0.0253175i	−0.101712	−	0.00233067i
$119$	6.82884	+	2.82860i	0.625999	+	0.259297i
$120$	−14.7655	−	11.4071i	−1.34790	−	1.04132i
$121$	−0.630442	+	0.261137i	−0.0573129	+	0.0237398i
$122$	1.38530	+	3.57385i	0.125419	+	0.323561i
$123$	2.32099	+	1.55084i	0.209277	+	0.139834i
$124$	7.54394	+	3.53791i	0.677466	+	0.317713i
$125$	−2.25827	+	11.3531i	−0.201986	+	1.01545i
$126$	−16.5948	+	10.5466i	−1.47838	+	0.939561i
$127$	−5.12090			−0.454406			−0.227203	−	0.973847i	$-0.572958\pi$
$127$	−5.12090			−0.454406			−0.227203	+	0.973847i	$0.572958\pi$
$128$	−7.70706	+	8.28258i	−0.681215	+	0.732084i
$129$	−14.5859			−1.28422
$130$	−0.290573	+	0.184669i	−0.0254849	+	0.0161965i
$131$	−2.39632	+	12.0471i	−0.209368	+	1.05256i	0.722944	+	0.690907i	$0.242789\pi$
$131$	−2.39632	+	12.0471i	−0.209368	+	1.05256i	−0.932312	+	0.361656i	$0.882211\pi$
$132$	−17.8763	−	8.38350i	−1.55593	−	0.729690i
$133$	6.24933	+	4.17567i	0.541886	+	0.362076i
$134$	−2.54450	−	6.56442i	−0.219812	−	0.567080i
$135$	−21.0027	+	8.69960i	−1.80762	+	0.748742i
$136$	5.92578	−	7.67038i	0.508131	−	0.657730i
$137$	−1.03177	−	0.427371i	−0.0881496	−	0.0365128i	0.338173	−	0.941084i	$-0.390191\pi$
$137$	−1.03177	−	0.427371i	−0.0881496	−	0.0365128i	−0.426323	+	0.904571i	$0.640191\pi$
$138$	−15.1638	−	0.347469i	−1.29083	−	0.0295785i
$139$	3.00073	−	0.596882i	0.254518	−	0.0506269i	−0.0661819	−	0.997808i	$-0.521082\pi$
$139$	3.00073	−	0.596882i	0.254518	−	0.0506269i	0.320700	+	0.947181i	$0.396082\pi$
$140$	−5.49130	+	7.45493i	−0.464099	+	0.630057i
$141$	30.0531	−	20.0808i	2.53093	−	1.69111i
$142$	8.25302	−	11.7591i	0.692578	−	0.986805i
$143$	−0.257618	+	0.257618i	−0.0215431	+	0.0215431i
$144$	7.64585	+	24.6246i	0.637154	+	2.05205i
$145$	−3.12399	−	3.12399i	−0.259433	−	0.259433i
$146$	19.0436	−	3.33643i	1.57606	−	0.276125i
$147$	−4.00890	−	5.99974i	−0.330648	−	0.494850i
$148$	−10.2065	−	16.9030i	−0.838965	−	1.38942i
$149$	−0.649276	−	3.26413i	−0.0531907	−	0.267408i	0.945034	−	0.326973i	$-0.106029\pi$
$149$	−0.649276	−	3.26413i	−0.0531907	−	0.267408i	−0.998224	+	0.0595651i	$0.981029\pi$
$150$	1.23530	−	1.17996i	0.100862	−	0.0963434i
$151$	−1.38074	+	3.33339i	−0.112363	+	0.271268i	−0.970051	−	0.242903i	$-0.921900\pi$
$151$	−1.38074	+	3.33339i	−0.112363	+	0.271268i	0.857688	+	0.514171i	$0.171900\pi$
$152$	7.43145	−	6.47420i	0.602770	−	0.525127i
$153$	−8.45353	−	20.4086i	−0.683427	−	1.64994i
$154$	−3.95589	+	8.96383i	−0.318774	+	0.722326i
$155$	4.96802	−	7.43517i	0.399041	−	0.597207i
$156$	0.696467	+	0.0319348i	0.0557620	+	0.00255683i
$157$	−14.8431	−	2.95247i	−1.18460	−	0.235633i	−0.436805	−	0.899556i	$-0.643890\pi$
$157$	−14.8431	−	2.95247i	−1.18460	−	0.235633i	−0.747800	+	0.663924i	$0.768890\pi$
$158$	−1.52487	+	6.84280i	−0.121312	+	0.544384i
$159$			1.77139i			0.140481i
$160$	7.54794	+	9.51061i	0.596717	+	0.751880i
$161$			7.52683i			0.593197i
$162$	18.2397	+	4.06457i	1.43304	+	0.319343i
$163$	14.0586	+	2.79643i	1.10115	+	0.219033i	0.712027	−	0.702152i	$-0.247777\pi$
$163$	14.0586	+	2.79643i	1.10115	+	0.219033i	0.389126	+	0.921185i	$0.372777\pi$
$164$	−1.22427	−	1.34193i	−0.0955991	−	0.104787i
$165$	−11.7723	+	17.6185i	−0.916474	+	1.37160i
$166$	−19.2247	−	8.48418i	−1.49213	−	0.658500i
$167$	2.52271	+	6.09036i	0.195213	+	0.471286i	0.990929	−	0.134383i	$-0.0429053\pi$
$167$	2.52271	+	6.09036i	0.195213	+	0.471286i	−0.795716	+	0.605670i	$0.792905\pi$
$168$	17.7746	−	5.96869i	1.37134	−	0.460495i
$169$	−4.96996	+	11.9985i	−0.382305	+	0.922965i
$170$	−7.18504	−	7.52204i	−0.551067	−	0.576914i
$171$	−4.38217	−	22.0307i	−0.335113	−	1.68473i
$172$	9.21458	+	2.27617i	0.702605	+	0.173556i
$173$	10.9283	+	16.3554i	0.830866	+	1.24348i	0.967503	+	0.252858i	$0.0813706\pi$
$173$	10.9283	+	16.3554i	0.830866	+	1.24348i	−0.136637	+	0.990621i	$0.543629\pi$
$174$	1.54392	+	8.81236i	0.117044	+	0.668063i
$175$	−0.599428	−	0.599428i	−0.0453125	−	0.0453125i
$176$	9.98500	+	8.08588i	0.752648	+	0.609496i
$177$	1.69834	−	1.69834i	0.127655	−	0.127655i
$178$	15.0905	+	10.5911i	1.13108	+	0.793837i
$179$	1.59347	−	1.06472i	0.119102	−	0.0795812i	−0.494593	−	0.869125i	$-0.664683\pi$
$179$	1.59347	−	1.06472i	0.119102	−	0.0795812i	0.613694	+	0.789544i	$0.289683\pi$
$180$	27.3587	−	4.14966i	2.03919	−	0.309297i
$181$	−19.2000	+	3.81912i	−1.42713	+	0.283873i	−0.847408	−	0.530943i	$-0.821838\pi$
$181$	−19.2000	+	3.81912i	−1.42713	+	0.283873i	−0.579720	+	0.814816i	$0.696838\pi$
$182$	0.00792570	−	0.345885i	0.000587492	−	0.0256387i
$183$	−7.69588	−	3.18774i	−0.568896	−	0.235644i
$184$	9.52548	+	2.58587i	0.702228	+	0.190633i
$185$	−19.5776	+	8.10931i	−1.43937	+	0.596209i
$186$	−16.8842	+	6.54468i	−1.23801	+	0.479879i
$187$	−9.15247	−	6.11549i	−0.669295	−	0.447209i
$188$	−22.1196	+	7.99612i	−1.61324	+	0.583177i
$189$	4.45674	−	22.4055i	0.324180	−	1.62976i
$190$	−5.67349	−	8.92713i	−0.411599	−	0.647642i
$191$	12.6604			0.916073			0.458037	−	0.888933i	$-0.348553\pi$
$191$	12.6604			0.916073			0.458037	+	0.888933i	$0.348553\pi$
$192$	−1.44708	−	24.5450i	−0.104434	−	1.77138i
$193$	6.31378			0.454476			0.227238	−	0.973839i	$-0.427030\pi$
$193$	6.31378			0.454476			0.227238	+	0.973839i	$0.427030\pi$
$194$	3.08078	+	4.84755i	0.221187	+	0.348034i
$195$	0.145972	−	0.733852i	0.0104533	−	0.0525522i
$196$	1.59633	+	4.41591i	0.114024	+	0.315422i
$197$	19.2658	+	12.8730i	1.37263	+	0.917163i	0.999942	−	0.0107926i	$-0.00343545\pi$
$197$	19.2658	+	12.8730i	1.37263	+	0.917163i	0.372690	+	0.927956i	$0.378435\pi$
$198$	27.3026	−	10.5831i	1.94031	−	0.752105i
$199$	−13.5609	+	5.61712i	−0.961309	+	0.398187i	−0.807470	−	0.589909i	$-0.799164\pi$
$199$	−13.5609	+	5.61712i	−0.961309	+	0.398187i	−0.153839	+	0.988096i	$0.549164\pi$
$200$	−0.964535	+	0.552663i	−0.0682029	+	0.0390792i
$201$	14.1357	+	5.85522i	0.997059	+	0.412995i
$202$	0.178227	−	7.77798i	0.0125400	−	0.547257i
$203$	4.35431	−	0.866127i	0.305613	−	0.0607902i
$204$	3.15891	+	20.8266i	0.221168	+	1.45816i
$205$	−1.62090	+	1.08305i	−0.113208	+	0.0756434i
$206$	−15.5161	−	10.8898i	−1.08106	−	0.758728i
$207$	15.9061	−	15.9061i	1.10555	−	1.10555i
$208$	−0.435007	−	0.128860i	−0.0301623	−	0.00893485i
$209$	−7.91466	−	7.91466i	−0.547469	−	0.547469i
$210$	−3.47253	−	19.8204i	−0.239627	−	1.36774i
$211$	1.35601	+	2.02941i	0.0933516	+	0.139711i	0.875206	−	0.483751i	$-0.160726\pi$
$211$	1.35601	+	2.02941i	0.0933516	+	0.139711i	−0.781854	+	0.623461i	$0.785726\pi$
$212$	0.276430	−	1.11907i	0.0189853	−	0.0768581i
$213$	6.09103	+	30.6217i	0.417350	+	2.09816i
$214$	6.77805	+	7.09597i	0.463338	+	0.485070i
$215$	3.89811	−	9.41088i	0.265849	−	0.641817i
$216$	−26.8239	−	13.3377i	−1.82514	−	0.907514i
$217$	3.43879	+	8.30198i	0.233440	+	0.563575i
$218$	−25.7772	−	11.3759i	−1.74585	−	0.770474i
$219$	−23.3434	+	34.9358i	−1.57740	+	2.36074i
$220$	10.1865	−	9.29334i	0.686777	−	0.626557i
$221$	0.381221	+	0.0758296i	0.0256437	+	0.00510085i
$222$	41.8845	+	9.33364i	2.81110	+	0.626433i
$223$			7.01617i			0.469838i	0.972015	+	0.234919i	$0.0754824\pi$
$223$			7.01617i			0.469838i	−0.972015	+	0.234919i	$0.924518\pi$
$224$	−12.1605	+	0.996928i	−0.812505	+	0.0666101i
$225$			2.53349i			0.168899i
$226$	2.79768	−	12.5545i	0.186099	−	0.835115i
$227$	−16.9611	−	3.37378i	−1.12575	−	0.223925i	−0.403110	−	0.915151i	$-0.632071\pi$
$227$	−16.9611	−	3.37378i	−1.12575	−	0.223925i	−0.722638	+	0.691226i	$0.757071\pi$
$228$	−0.981119	+	21.3972i	−0.0649762	+	1.41707i
$229$	1.93254	−	2.89225i	0.127706	−	0.191126i	−0.762107	−	0.647451i	$-0.775835\pi$
$229$	1.93254	−	2.89225i	0.127706	−	0.191126i	0.889813	+	0.456326i	$0.150835\pi$
$230$	4.27676	−	9.69092i	0.282001	−	0.639000i
$231$	−8.14863	−	19.6725i	−0.536141	−	1.29436i
$232$	0.399826	−	5.80811i	0.0262498	−	0.381321i
$233$	10.0866	−	24.3511i	0.660794	−	1.59530i	−0.135769	−	0.990741i	$-0.543350\pi$
$233$	10.0866	−	24.3511i	0.660794	−	1.59530i	0.796563	−	0.604556i	$-0.206650\pi$
$234$	−0.747691	+	0.714193i	−0.0488781	+	0.0466882i
$235$	4.92448	+	24.7570i	0.321238	+	1.61497i
$236$	−1.33795	+	0.807890i	−0.0870932	+	0.0525891i
$237$	−8.46462	−	12.6682i	−0.549836	−	0.822888i
$238$	10.2963	−	1.80391i	0.667411	−	0.116930i
$239$	−11.2250	−	11.2250i	−0.726085	−	0.726085i	0.243752	−	0.969838i	$-0.421622\pi$
$239$	−11.2250	−	11.2250i	−0.726085	−	0.726085i	−0.969838	+	0.243752i	$0.921622\pi$
$240$	−26.2765	−	2.41477i	−1.69614	−	0.155873i
$241$	−15.1085	+	15.1085i	−0.973222	+	0.973222i	−0.999651	−	0.0264284i	$-0.991587\pi$
$241$	−15.1085	+	15.1085i	−0.973222	+	0.973222i	0.0264284	+	0.999651i	$0.491587\pi$
$242$	−0.554387	+	0.789907i	−0.0356374	+	0.0507772i
$243$	−7.34826	+	4.90995i	−0.471391	+	0.314973i
$244$	4.36439	+	3.21480i	0.279401	+	0.205807i
$245$	4.94245	−	0.983113i	0.315761	−	0.0628088i
$246$	3.94665	+	0.0904345i	0.251629	+	0.00576590i
$247$	0.365152	+	0.151251i	0.0232341	+	0.00962387i
$248$	11.6879	−	1.49974i	0.742181	−	0.0952338i
$249$	42.1916	−	17.4763i	2.67378	−	1.10752i
$250$	5.91651	+	15.2637i	0.374193	+	0.965360i
$251$	−0.246229	−	0.164525i	−0.0155419	−	0.0103847i	0.547775	−	0.836626i	$-0.315475\pi$
$251$	−0.246229	−	0.164525i	−0.0155419	−	0.0103847i	−0.563317	+	0.826241i	$0.690475\pi$
$252$	−11.8069	+	25.1760i	−0.743763	+	1.58594i
$253$	2.18679	−	10.9938i	0.137483	−	0.691172i
$254$	−6.11213	+	3.88446i	−0.383509	+	0.243733i
$255$	22.6066			1.41568
$256$	−2.91612	+	15.7320i	−0.182258	+	0.983251i
$257$	0.958734			0.0598042			0.0299021	−	0.999553i	$-0.490480\pi$
$257$	0.958734			0.0598042			0.0299021	+	0.999553i	$0.490480\pi$
$258$	−17.4092	+	11.0641i	−1.08385	+	0.688824i
$259$	4.15434	−	20.8853i	0.258138	−	1.29775i
$260$	−0.206737	+	0.440829i	−0.0128213	+	0.0273391i
$261$	−11.0321	−	7.37142i	−0.682870	−	0.456279i
$262$	6.27820	+	16.1968i	0.387868	+	1.00064i
$263$	4.44089	−	1.83948i	0.273837	−	0.113427i	−0.241539	−	0.970391i	$-0.577652\pi$
$263$	4.44089	−	1.83948i	0.273837	−	0.113427i	0.515376	+	0.856964i	$0.327652\pi$
$264$	−27.6958	+	3.55382i	−1.70456	+	0.218723i
$265$	−1.14291	−	0.473409i	−0.0702084	−	0.0290813i
$266$	10.6264	+	0.243497i	0.651549	+	0.0149298i
$267$	−39.2968	+	7.81663i	−2.40493	+	0.478370i
$268$	−8.01648	−	5.90493i	−0.489685	−	0.360701i
$269$	−3.61121	+	2.41293i	−0.220179	+	0.147119i	−0.660769	−	0.750590i	$-0.729770\pi$
$269$	−3.61121	+	2.41293i	−0.220179	+	0.147119i	0.440589	+	0.897709i	$0.354770\pi$
$270$	−18.4690	+	26.3152i	−1.12399	+	1.60149i
$271$	−10.6599	+	10.6599i	−0.647540	+	0.647540i	−0.952398	−	0.304858i	$-0.901391\pi$
$271$	−10.6599	+	10.6599i	−0.647540	+	0.647540i	0.304858	+	0.952398i	$0.401391\pi$
$272$	1.25442	−	13.6501i	0.0760606	−	0.827660i
$273$	0.531669	+	0.531669i	0.0321781	+	0.0321781i
$274$	−1.55566	+	0.272551i	−0.0939810	+	0.0164654i
$275$	0.701377	+	1.04968i	0.0422946	+	0.0632984i
$276$	−18.3626	+	11.0878i	−1.10530	+	0.667409i
$277$	0.0750905	+	0.377506i	0.00451175	+	0.0226821i	0.982976	−	0.183736i	$-0.0588192\pi$
$277$	0.0750905	+	0.377506i	0.00451175	+	0.0226821i	−0.978464	+	0.206418i	$0.933819\pi$
$278$	3.12880	−	2.98862i	0.187653	−	0.179246i
$279$	10.2771	−	24.8112i	0.615276	−	1.48541i
$280$	−0.899273	+	13.0634i	−0.0537418	+	0.780686i
$281$	−1.58445	−	3.82519i	−0.0945201	−	0.228192i	0.869547	−	0.493850i	$-0.164411\pi$
$281$	−1.58445	−	3.82519i	−0.0945201	−	0.228192i	−0.964067	+	0.265658i	$0.914411\pi$
$282$	20.6380	−	46.7646i	1.22897	−	2.78479i
$283$	5.06218	−	7.57609i	0.300915	−	0.450352i	−0.649941	−	0.759985i	$-0.725206\pi$
$283$	5.06218	−	7.57609i	0.300915	−	0.450352i	0.950856	+	0.309633i	$0.100206\pi$
$284$	0.930609	−	20.2957i	0.0552215	−	1.20433i
$285$	22.5458	+	4.48464i	1.33550	+	0.265647i
$286$	−0.112067	+	0.502900i	−0.00662668	+	0.0297371i
$287$		−	1.95898i		−	0.115635i
$288$	27.8049	+	23.5914i	1.63842	+	1.39013i
$289$		−	5.25630i		−	0.309194i
$290$	−6.09839	−	1.35898i	−0.358110	−	0.0798020i
$291$	−12.2427	−	2.43522i	−0.717678	−	0.142755i
$292$	20.1989	−	18.4278i	1.18205	−	1.07840i
$293$	9.97915	−	14.9349i	0.582988	−	0.872504i	−0.416338	−	0.909210i	$-0.636687\pi$
$293$	9.97915	−	14.9349i	0.582988	−	0.872504i	0.999326	+	0.0367064i	$0.0116866\pi$
$294$	−9.33600	−	4.12013i	−0.544486	−	0.240291i
$295$	0.641891	+	1.54966i	0.0373723	+	0.0902248i
$296$	−25.0038	−	12.4327i	−1.45332	−	0.722635i
$297$	−13.0191	+	31.4309i	−0.755445	+	1.82381i
$298$	−3.25096	−	3.40344i	−0.188323	−	0.197156i
$299$	0.0772181	+	0.388202i	0.00446564	+	0.0224503i
$300$	0.579357	−	2.34540i	0.0334492	−	0.135412i
$301$	5.68690	+	8.51105i	0.327787	+	0.490568i
$302$	0.880550	+	5.02598i	0.0506699	+	0.289213i
$303$	11.9557	+	11.9557i	0.686840	+	0.686840i
$304$	3.95891	−	13.3645i	0.227059	−	0.766508i
$305$	4.11348	−	4.11348i	0.235537	−	0.235537i
$306$	−25.5708	−	17.9466i	−1.46179	−	1.02594i
$307$	19.6650	−	13.1398i	1.12234	−	0.749925i	0.151219	−	0.988500i	$-0.451680\pi$
$307$	19.6650	−	13.1398i	1.12234	−	0.749925i	0.971124	+	0.238575i	$0.0766803\pi$
$308$	2.07792	+	13.6997i	0.118400	+	0.780611i
$309$	40.4050	−	8.03706i	2.29856	−	0.457213i
$310$	0.289702	−	12.6429i	0.0164540	−	0.718067i
$311$	−5.33022	−	2.20785i	−0.302249	−	0.125196i	0.226404	−	0.974033i	$-0.427303\pi$
$311$	−5.33022	−	2.20785i	−0.302249	−	0.125196i	−0.528654	+	0.848838i	$0.677303\pi$
$312$	0.855504	−	0.490190i	0.0484334	−	0.0277515i
$313$	6.66540	−	2.76090i	0.376751	−	0.156055i	−0.186269	−	0.982499i	$-0.559640\pi$
$313$	6.66540	−	2.76090i	0.376751	−	0.156055i	0.563020	+	0.826444i	$0.309640\pi$
$314$	−19.9558	+	7.73526i	−1.12617	+	0.436526i
$315$	24.8130	+	16.5795i	1.39806	+	0.934151i
$316$	3.37059	+	9.32402i	0.189610	+	0.524517i
$317$	−6.63635	+	33.3632i	−0.372734	+	1.87386i	0.103632	+	0.994616i	$0.466954\pi$
$317$	−6.63635	+	33.3632i	−0.372734	+	1.87386i	−0.476366	+	0.879247i	$0.658046\pi$
$318$	1.34369	+	2.11427i	0.0753505	+	0.118563i
$319$	−6.61159			−0.370178
$320$	16.2233	+	5.62604i	0.906907	+	0.314505i
$321$	−21.3261			−1.19031
$322$	5.70949	+	8.98377i	0.318177	+	0.500646i
$323$	−2.32968	+	11.7121i	−0.129627	+	0.651678i
$324$	24.8534	−	8.98439i	1.38075	−	0.499133i
$325$	−0.0370655	−	0.0247664i	−0.00205603	−	0.00137379i
$326$	18.9011	−	7.32644i	1.04683	−	0.405774i
$327$	56.5721	−	23.4330i	3.12845	−	1.29585i
$328$	−2.47917	−	0.673017i	−0.136889	−	0.0371611i
$329$	−23.4348	−	9.70702i	−1.29200	−	0.535165i
$330$	−0.686484	+	29.9588i	−0.0377897	+	1.64918i
$331$	14.2233	−	2.82918i	0.781781	−	0.155506i	0.211964	−	0.977277i	$-0.432014\pi$
$331$	14.2233	−	2.82918i	0.781781	−	0.155506i	0.569817	+	0.821772i	$0.307014\pi$
$332$	−29.3816	+	4.45650i	−1.61253	+	0.244582i
$333$	−52.9150	+	35.3567i	−2.89972	+	1.93753i
$334$	7.63087	+	5.35564i	0.417543	+	0.293048i
$335$	−7.55562	+	7.55562i	−0.412808	+	0.412808i
$336$	16.6876	−	20.6070i	0.910382	−	1.12420i
$337$	−22.7689	−	22.7689i	−1.24030	−	1.24030i	−0.959877	−	0.280423i	$-0.909525\pi$
$337$	−22.7689	−	22.7689i	−1.24030	−	1.24030i	−0.280423	−	0.959877i	$-0.590475\pi$
$338$	3.16954	+	18.0910i	0.172400	+	0.984022i
$339$	15.5301	+	23.2424i	0.843479	+	1.26236i
$340$	−14.2817	−	3.52783i	−0.774532	−	0.191323i
$341$	−2.61073	−	13.1250i	−0.141379	−	0.710760i
$342$	−21.9418	−	22.9709i	−1.18648	−	1.24213i
$343$	−7.71575	+	18.6275i	−0.416611	+	1.00579i
$344$	12.7248	−	4.27298i	0.686075	−	0.230384i
$345$	8.80959	+	21.2682i	0.474293	+	1.14504i
$346$	25.4501	+	11.2316i	1.36821	+	0.603812i
$347$	5.44427	−	8.14793i	0.292264	−	0.437404i	−0.656060	−	0.754709i	$-0.727778\pi$
$347$	5.44427	−	8.14793i	0.292264	−	0.437404i	0.948323	+	0.317305i	$0.102778\pi$
$348$	8.52740	+	9.34699i	0.457117	+	0.501051i
$349$	33.0492	+	6.57390i	1.76909	+	0.351893i	0.968822	−	0.247756i	$-0.0796931\pi$
$349$	33.0492	+	6.57390i	1.76909	+	0.351893i	0.800263	+	0.599649i	$0.204693\pi$
$350$	−1.17015	−	0.260760i	−0.0625474	−	0.0139382i
$351$		−	1.20130i		−	0.0641208i
$352$	18.0513	+	2.07689i	0.962139	+	0.110699i
$353$		−	17.4677i		−	0.929711i	−0.885387	−	0.464856i	$-0.846106\pi$
$353$		−	17.4677i		−	0.929711i	0.885387	−	0.464856i	$-0.153894\pi$
$354$	0.738802	−	3.31536i	0.0392669	−	0.176209i
$355$	−21.3851	−	4.25376i	−1.13500	−	0.225766i
$356$	26.0454	+	1.19425i	1.38041	+	0.0632952i
$357$	−12.6211	+	18.8888i	−0.667979	+	0.999701i
$358$	1.09427	−	2.47955i	0.0578337	−	0.131048i
$359$	6.92204	+	16.7113i	0.365331	+	0.881987i	0.994502	+	0.104720i	$0.0333947\pi$
$359$	6.92204	+	16.7113i	0.365331	+	0.881987i	−0.629171	+	0.777267i	$0.716605\pi$
$360$	29.5066	−	25.7058i	1.55514	−	1.35482i
$361$	2.62417	−	6.33532i	0.138114	−	0.333438i
$362$	−20.0195	+	19.1226i	−1.05220	+	1.00506i
$363$	−0.409158	−	2.05698i	−0.0214752	−	0.107963i
$364$	−0.252911	−	0.418848i	−0.0132562	−	0.0219536i
$365$	−16.3022	−	24.3979i	−0.853295	−	1.27705i
$366$	−11.6036	+	2.03295i	−0.606530	+	0.106264i
$367$	−22.7264	−	22.7264i	−1.18631	−	1.18631i	−0.978081	−	0.208226i	$-0.933231\pi$
$367$	−22.7264	−	22.7264i	−1.18631	−	1.18631i	−0.208226	−	0.978081i	$-0.566769\pi$
$368$	13.3308	−	4.13916i	0.694916	−	0.215769i
$369$	−4.13983	+	4.13983i	−0.215511	+	0.215511i
$370$	−17.2158	+	24.5296i	−0.895009	+	1.27523i
$371$	1.03363	−	0.690649i	0.0536633	−	0.0358567i
$372$	−15.1880	+	20.6191i	−0.787460	+	1.06905i
$373$	−4.36804	+	0.868856i	−0.226168	+	0.0449877i	−0.306873	−	0.951750i	$-0.599283\pi$
$373$	−4.36804	+	0.868856i	−0.226168	+	0.0449877i	0.0807051	+	0.996738i	$0.474283\pi$
$374$	−15.5630	−	0.356615i	−0.804743	−	0.0184401i
$375$	−32.8686	−	13.6146i	−1.69733	−	0.703057i
$376$	−20.3357	+	26.3227i	−1.04873	+	1.35749i
$377$	0.215691	−	0.0893422i	0.0111087	−	0.00460136i
$378$	−11.6763	−	30.1231i	−0.600566	−	1.54937i
$379$	−19.0406	−	12.7225i	−0.978052	−	0.653513i	−0.0397061	−	0.999211i	$-0.512642\pi$
$379$	−19.0406	−	12.7225i	−0.978052	−	0.653513i	−0.938346	+	0.345698i	$0.887642\pi$
$380$	−13.5434	−	6.35148i	−0.694761	−	0.325824i
$381$	3.07049	−	15.4364i	0.157306	−	0.790830i
$382$	15.1110	−	9.60355i	0.773146	−	0.491360i
$383$	−9.58576			−0.489809			−0.244905	−	0.969547i	$-0.578757\pi$
$383$	−9.58576			−0.489809			−0.244905	+	0.969547i	$0.578757\pi$
$384$	−20.3458	−	28.1984i	−1.03827	−	1.43899i
$385$	14.8705			0.757873
$386$	7.53592	−	4.78933i	0.383568	−	0.243770i
$387$	5.96814	−	30.0038i	0.303377	−	1.52518i
$388$	7.35424	+	3.44894i	0.373355	+	0.175093i
$389$	−10.2676	−	6.86062i	−0.520590	−	0.347847i	0.267349	−	0.963600i	$-0.413852\pi$
$389$	−10.2676	−	6.86062i	−0.520590	−	0.347847i	−0.787940	+	0.615752i	$0.788852\pi$
$390$	−0.382437	−	0.986628i	−0.0193655	−	0.0499599i
$391$	−11.0484	+	4.57641i	−0.558743	+	0.231439i
$392$	5.25502	+	4.05978i	0.265419	+	0.205050i
$393$	−34.8779	−	14.4469i	−1.75936	−	0.728751i
$394$	32.7598	+	0.750668i	1.65042	+	0.0378181i
$395$	10.4358	−	2.07580i	0.525081	−	0.104445i
$396$	24.5597	−	33.3420i	1.23417	−	1.67550i
$397$	6.79289	−	4.53886i	0.340925	−	0.227799i	−0.373307	−	0.927708i	$-0.621776\pi$
$397$	6.79289	−	4.53886i	0.340925	−	0.227799i	0.714232	+	0.699909i	$0.246776\pi$
$398$	−11.9250	+	16.9911i	−0.597746	+	0.851685i
$399$	−16.3342	+	16.3342i	−0.817733	+	0.817733i
$400$	−0.732013	+	1.39129i	−0.0366006	+	0.0695645i
$401$	6.63465	+	6.63465i	0.331319	+	0.331319i	0.853087	−	0.521769i	$-0.174728\pi$
$401$	6.63465	+	6.63465i	0.331319	+	0.331319i	−0.521769	+	0.853087i	$0.674728\pi$
$402$	21.3134	−	3.73410i	1.06302	−	0.186240i
$403$	0.262529	+	0.392902i	0.0130775	+	0.0195718i
$404$	−5.68727	−	9.41873i	−0.282952	−	0.468599i
$405$	−5.53311	−	27.8168i	−0.274943	−	1.38223i
$406$	4.54016	−	4.33675i	0.225324	−	0.215229i
$407$	−12.1357	+	29.2982i	−0.601546	+	1.45226i
$408$	19.5684	+	22.4618i	0.968782	+	1.11202i
$409$	−3.09518	−	7.47242i	−0.153047	−	0.369487i	0.828697	−	0.559698i	$-0.189083\pi$
$409$	−3.09518	−	7.47242i	−0.153047	−	0.369487i	−0.981743	+	0.190211i	$0.939083\pi$
$410$	−1.11310	+	2.52222i	−0.0549721	+	0.124564i
$411$	1.90691	−	2.85389i	0.0940610	−	0.140772i
$412$	−26.7799	−	1.22793i	−1.31935	−	0.0604958i
$413$	−1.65317	−	0.328836i	−0.0813471	−	0.0161809i
$414$	6.91938	−	31.0506i	0.340069	−	1.52605i
$415$			31.8928i			1.56556i
$416$	−0.616957	+	0.176172i	−0.0302488	+	0.00863754i
$417$			9.40326i			0.460480i
$418$	−15.4503	−	3.44299i	−0.755701	−	0.168402i
$419$	−2.86945	−	0.570769i	−0.140182	−	0.0278839i	0.124501	−	0.992220i	$-0.460267\pi$
$419$	−2.86945	−	0.570769i	−0.140182	−	0.0278839i	−0.264682	+	0.964336i	$0.585267\pi$
$420$	−19.1795	−	21.0229i	−0.935864	−	1.02581i
$421$	−11.9038	+	17.8153i	−0.580157	+	0.868266i	−0.999212	−	0.0396948i	$-0.987361\pi$
$421$	−11.9038	+	17.8153i	−0.580157	+	0.868266i	0.419055	+	0.907961i	$0.362361\pi$
$422$	3.15790	+	1.39363i	0.153724	+	0.0678411i
$423$	29.0103	+	70.0371i	1.41053	+	3.40532i
$424$	−0.518935	−	1.54537i	−0.0252017	−	0.0750499i
$425$	0.515424	−	1.24434i	0.0250018	−	0.0603596i
$426$	30.4982	+	31.9286i	1.47764	+	1.54695i
$427$	1.14047	+	5.73351i	0.0551910	+	0.277464i
$428$	13.4727	+	3.32800i	0.651228	+	0.160865i
$429$	−0.622093	−	0.931028i	−0.0300349	−	0.0449505i
$430$	−2.48598	−	14.1894i	−0.119885	−	0.684275i
$431$	8.75609	+	8.75609i	0.421766	+	0.421766i	0.885811	−	0.464045i	$-0.153603\pi$
$431$	8.75609	+	8.75609i	0.421766	+	0.421766i	−0.464045	+	0.885811i	$0.653603\pi$
$432$	−42.1334	+	4.42792i	−2.02714	+	0.213038i
$433$	−13.9449	+	13.9449i	−0.670149	+	0.670149i	−0.957750	−	0.287601i	$-0.907142\pi$
$433$	−13.9449	+	13.9449i	−0.670149	+	0.670149i	0.287601	+	0.957750i	$0.407142\pi$
$434$	10.4019	+	7.30046i	0.499307	+	0.350433i
$435$	11.2901	−	7.54378i	0.541317	−	0.361696i
$436$	−39.3960	+	5.97545i	−1.88673	+	0.286172i
$437$	−11.9265	+	2.37233i	−0.570523	+	0.113484i
$438$	−1.36123	+	59.4054i	−0.0650421	+	2.83850i
$439$	−9.84033	−	4.07600i	−0.469653	−	0.194537i	0.135289	−	0.990806i	$-0.456804\pi$
$439$	−9.84033	−	4.07600i	−0.469653	−	0.194537i	−0.604942	+	0.796270i	$0.706804\pi$
$440$	5.10883	−	18.8192i	0.243554	−	0.897172i
$441$	13.9821	−	5.79156i	0.665813	−	0.275789i
$442$	0.512533	−	0.198668i	0.0243787	−	0.00944969i
$443$	16.3602	+	10.9315i	0.777294	+	0.519371i	0.879790	−	0.475362i	$-0.157683\pi$
$443$	16.3602	+	10.9315i	0.777294	+	0.519371i	−0.102496	+	0.994733i	$0.532683\pi$
$444$	57.0720	−	20.6312i	2.70852	−	0.979115i
$445$	5.45885	−	27.4435i	0.258774	−	1.30095i
$446$	5.32213	+	8.37426i	0.252010	+	0.396533i
$447$	10.2287			0.483800
$448$	−13.7581	+	10.4142i	−0.650008	+	0.492026i
$449$	30.9457			1.46042			0.730209	−	0.683224i	$-0.239423\pi$
$449$	30.9457			1.46042			0.730209	+	0.683224i	$0.239423\pi$
$450$	1.92178	+	3.02388i	0.0905936	+	0.142547i
$451$	−0.569150	+	2.86131i	−0.0268002	+	0.134734i
$452$	−6.18404	−	17.1068i	−0.290873	−	0.804638i
$453$	−9.22026	−	6.16078i	−0.433206	−	0.289459i
$454$	−22.8034	+	8.83905i	−1.07022	+	0.414837i
$455$	−0.485125	+	0.200945i	−0.0227430	+	0.00942046i
$456$	15.0599	+	26.2832i	0.705243	+	1.23083i
$457$	36.3997	+	15.0773i	1.70271	+	0.705285i	0.999981	−	0.00617459i	$-0.00196544\pi$
$457$	36.3997	+	15.0773i	1.70271	+	0.705285i	0.702727	+	0.711459i	$0.251965\pi$
$458$	0.112693	−	4.91803i	0.00526580	−	0.229804i
$459$	35.5982	−	7.08092i	1.66158	−	0.330509i
$460$	−2.24646	−	14.8109i	−0.104742	−	0.690562i
$461$	7.22960	−	4.83066i	0.336716	−	0.224986i	−0.375704	−	0.926740i	$-0.622599\pi$
$461$	7.22960	−	4.83066i	0.336716	−	0.224986i	0.712420	+	0.701753i	$0.247599\pi$
$462$	−24.6486	−	17.2993i	−1.14675	−	0.804837i
$463$	25.2338	−	25.2338i	1.17271	−	1.17271i	0.191154	−	0.981560i	$-0.438777\pi$
$463$	25.2338	−	25.2338i	1.17271	−	1.17271i	0.981560	−	0.191154i	$-0.0612228\pi$
$464$	−3.92853	−	7.23565i	−0.182377	−	0.335906i
$465$	19.4337	+	19.4337i	0.901216	+	0.901216i
$466$	−6.43261	−	36.7159i	−0.297985	−	1.70083i
$467$	20.5128	+	30.6996i	0.949220	+	1.42061i	0.906825	+	0.421507i	$0.138499\pi$
$467$	20.5128	+	30.6996i	0.949220	+	1.42061i	0.0423942	+	0.999101i	$0.486501\pi$
$468$	−0.350666	+	1.41960i	−0.0162096	+	0.0656209i
$469$	−2.09480	−	10.5313i	−0.0967289	−	0.486289i
$470$	24.6572	+	25.8137i	1.13735	+	1.19070i
$471$	17.7998	−	42.9725i	0.820171	−	1.98007i
$472$	−0.984107	+	1.97917i	−0.0452972	+	0.0910989i
$473$	−5.83360	−	14.0835i	−0.268229	−	0.647562i
$474$	−19.7126	−	8.69948i	−0.905428	−	0.399581i
$475$	0.760886	−	1.13875i	0.0349118	−	0.0522493i
$476$	10.9210	−	9.96337i	0.500562	−	0.456670i
$477$	−3.64383	−	0.724804i	−0.166840	−	0.0331865i
$478$	−21.9125	−	4.88304i	−1.00226	−	0.223345i
$479$		−	22.3832i		−	1.02271i	−0.859368	−	0.511357i	$-0.829143\pi$
$479$		−	22.3832i		−	1.02271i	0.859368	−	0.511357i	$-0.170857\pi$
$480$	−33.1945	+	17.0499i	−1.51511	+	0.778218i
$481$		−	1.11979i		−	0.0510581i
$482$	−6.57240	+	29.4935i	−0.299365	+	1.34339i
$483$	−22.6888	−	4.51309i	−1.03238	−	0.205353i
$484$	−0.0625126	+	1.36334i	−0.00284148	+	0.0619699i
$485$	4.84310	−	7.24821i	0.219914	−	0.329124i
$486$	−5.04618	+	11.4344i	−0.228899	+	0.518674i
$487$	−13.3025	−	32.1150i	−0.602792	−	1.45527i	−0.870695	−	0.491824i	$-0.836330\pi$
$487$	−13.3025	−	32.1150i	−0.602792	−	1.45527i	0.267902	−	0.963446i	$-0.413670\pi$
$488$	7.64778	+	0.526467i	0.346199	+	0.0238321i
$489$	−16.8591	+	40.7014i	−0.762393	+	1.84058i
$490$	5.15339	−	4.92251i	0.232807	−	0.222376i
$491$	−5.09965	−	25.6377i	−0.230144	−	1.15701i	−0.907076	−	0.420966i	$-0.861691\pi$
$491$	−5.09965	−	25.6377i	−0.230144	−	1.15701i	0.676933	−	0.736045i	$-0.263309\pi$
$492$	4.77918	−	2.88580i	0.215462	−	0.130102i
$493$	3.91884	+	5.86496i	0.176496	+	0.264144i
$494$	0.550565	−	0.0964587i	0.0247711	−	0.00433988i
$495$	−31.4252	−	31.4252i	−1.41246	−	1.41246i
$496$	12.8126	−	10.6559i	0.575304	−	0.478464i
$497$	15.4933	−	15.4933i	0.694969	−	0.694969i
$498$	37.1018	−	52.8637i	1.66257	−	2.36888i
$499$	−27.9332	+	18.6644i	−1.25046	+	0.835532i	−0.991468	−	0.130347i	$-0.958391\pi$
$499$	−27.9332	+	18.6644i	−1.25046	+	0.835532i	−0.258994	+	0.965879i	$0.583391\pi$
$500$	18.6400	+	13.7302i	0.833608	+	0.614035i
$501$	−19.8714	+	3.95266i	−0.887787	+	0.176592i
$502$	−0.418692	−	0.00959402i	−0.0186871	−	0.000428202i
$503$	20.0549	+	8.30702i	0.894205	+	0.370392i	0.781989	−	0.623292i	$-0.214205\pi$
$503$	20.0549	+	8.30702i	0.894205	+	0.370392i	0.112216	+	0.993684i	$0.464205\pi$
$504$	5.00501	+	39.0053i	0.222941	+	1.73744i
$505$	−10.9091	+	4.51870i	−0.485449	+	0.201079i
$506$	−5.72925	−	14.7806i	−0.254696	−	0.657077i
$507$	−33.1883	−	22.1757i	−1.47395	−	0.984859i
$508$	−4.34866	+	9.27273i	−0.192941	+	0.411411i
$509$	−0.581805	+	2.92493i	−0.0257881	+	0.129645i	−0.991535	−	0.129841i	$-0.958553\pi$
$509$	−0.581805	+	2.92493i	−0.0257881	+	0.129645i	0.965747	+	0.259486i	$0.0835533\pi$
$510$	26.9825	−	17.1483i	1.19481	−	0.759340i
$511$	29.4868			1.30442
$512$	8.45296	+	20.9892i	0.373571	+	0.927601i
$513$	36.9071			1.62949
$514$	1.14431	−	0.727249i	0.0504734	−	0.0320776i
$515$	−5.61280	+	28.2174i	−0.247329	+	1.24341i
$516$	−12.3863	+	26.4116i	−0.545278	+	1.16271i
$517$	31.4089	+	20.9868i	1.38136	+	0.922996i
$518$	−10.8841	−	28.0792i	−0.478219	−	1.23373i
$519$	−55.8543	+	23.1356i	−2.45173	+	1.01554i
$520$	0.0876372	+	0.682979i	0.00384315	+	0.0299506i
$521$	−18.7789	−	7.77848i	−0.822719	−	0.340781i	−0.0687028	−	0.997637i	$-0.521886\pi$
$521$	−18.7789	−	7.77848i	−0.822719	−	0.340781i	−0.754016	+	0.656856i	$0.771886\pi$
$522$	−18.7592	−	0.429852i	−0.821066	−	0.0188141i
$523$	13.4384	−	2.67306i	0.587620	−	0.116885i	0.107679	−	0.994186i	$-0.465658\pi$
$523$	13.4384	−	2.67306i	0.587620	−	0.116885i	0.479941	+	0.877301i	$0.340658\pi$
$524$	19.7795	+	14.5696i	0.864073	+	0.636475i
$525$	2.16633	−	1.44750i	0.0945464	−	0.0631739i
$526$	3.90516	−	5.56419i	0.170273	−	0.242610i
$527$	−10.0954	+	10.0954i	−0.439763	+	0.439763i
$528$	−30.3610	+	25.2504i	−1.32129	+	1.09888i
$529$	7.65252	+	7.65252i	0.332718	+	0.332718i
$530$	−1.72324	+	0.301911i	−0.0748529	+	0.0131142i
$531$	2.79865	+	4.18848i	0.121451	+	0.181764i
$532$	12.8681	−	7.77008i	0.557902	−	0.336876i
$533$	−0.0200973	−	0.101036i	−0.000870511	−	0.00437635i
$534$	−40.9740	+	39.1383i	−1.77312	+	1.69368i
$535$	5.69946	−	13.7597i	0.246409	−	0.594884i
$536$	−14.0474	−	0.967012i	−0.606755	−	0.0417686i
$537$	2.25405	+	5.44176i	0.0972694	+	0.234829i
$538$	−2.47988	+	5.61928i	−0.106915	+	0.242264i
$539$	4.18976	−	6.27041i	0.180466	−	0.270086i
$540$	−2.08256	+	45.4186i	−0.0896191	+	1.95450i
$541$	7.53938	+	1.49968i	0.324143	+	0.0644761i	0.354480	−	0.935064i	$-0.384658\pi$
$541$	7.53938	+	1.49968i	0.324143	+	0.0644761i	−0.0303365	+	0.999540i	$0.509658\pi$
$542$	−4.63719	+	20.8093i	−0.199184	+	0.893836i
$543$		−	60.1664i		−	2.58199i
$544$	−8.85707	−	17.2439i	−0.379744	−	0.739324i
$545$			42.7631i			1.83177i
$546$	1.03788	+	0.231284i	0.0444172	+	0.00989802i
$547$	23.2900	+	4.63267i	0.995809	+	0.198079i	0.665986	−	0.745964i	$-0.268011\pi$
$547$	23.2900	+	4.63267i	0.995809	+	0.198079i	0.329823	+	0.944043i	$0.393011\pi$
$548$	−1.65004	+	1.50536i	−0.0704863	+	0.0643057i
$549$	9.70626	−	14.5264i	0.414253	−	0.619974i
$550$	1.63338	+	0.720837i	0.0696475	+	0.0307366i
$551$	2.74482	+	6.62658i	0.116933	+	0.282302i
$552$	−13.5063	+	27.1631i	−0.574867	+	1.15614i
$553$	−4.09178	+	9.87842i	−0.174000	+	0.420073i
$554$	0.375983	+	0.393618i	0.0159740	+	0.0167232i
$555$	−12.7059	−	63.8770i	−0.539336	−	2.71143i
$556$	1.46740	−	5.94048i	0.0622318	−	0.251932i
$557$	−7.86803	−	11.7753i	−0.333379	−	0.498937i	0.626473	−	0.779443i	$-0.284498\pi$
$557$	−7.86803	−	11.7753i	−0.333379	−	0.498937i	−0.959852	+	0.280506i	$0.909498\pi$
$558$	−6.55414	−	37.4096i	−0.277459	−	1.58367i
$559$	0.380621	+	0.380621i	0.0160986	+	0.0160986i
$560$	8.83591	+	16.2742i	0.373385	+	0.687708i
$561$	23.9223	−	23.9223i	1.01000	−	1.01000i
$562$	−4.79275	−	3.36373i	−0.202170	−	0.141891i
$563$	−5.80935	+	3.88168i	−0.244835	+	0.163593i	−0.671933	−	0.740612i	$-0.734536\pi$
$563$	−5.80935	+	3.88168i	−0.244835	+	0.163593i	0.427098	+	0.904205i	$0.359536\pi$
$564$	−10.8406	−	71.4716i	−0.456470	−	3.00950i
$565$	−19.1466	+	3.80849i	−0.805502	+	0.160224i
$566$	0.295193	−	12.8825i	0.0124079	−	0.541491i
$567$	26.3312	+	10.9067i	1.10581	+	0.458040i
$568$	−14.2846	−	24.9301i	−0.599367	−	1.04604i
$569$	−17.1266	+	7.09406i	−0.717983	+	0.297398i	−0.711603	−	0.702581i	$-0.752031\pi$
$569$	−17.1266	+	7.09406i	−0.717983	+	0.297398i	−0.00637952	+	0.999980i	$0.502031\pi$
$570$	30.3117	−	11.7494i	1.26962	−	0.492130i
$571$	1.16513	+	0.778514i	0.0487591	+	0.0325798i	0.579711	−	0.814822i	$-0.303165\pi$
$571$	1.16513	+	0.778514i	0.0487591	+	0.0325798i	−0.530952	+	0.847402i	$0.678165\pi$
$572$	0.247716	+	0.685253i	0.0103575	+	0.0286519i
$573$	−7.59116	+	38.1634i	−0.317125	+	1.59430i
$574$	−1.48599	−	2.33818i	−0.0620240	−	0.0975936i
$575$	1.37153			0.0571968
$576$	51.0822	+	7.06641i	2.12843	+	0.294434i
$577$	28.1108			1.17027			0.585135	−	0.810936i	$-0.301042\pi$
$577$	28.1108			1.17027			0.585135	+	0.810936i	$0.301042\pi$
$578$	−3.98718	−	6.27375i	−0.165845	−	0.260953i
$579$	−3.78574	+	19.0322i	−0.157330	+	0.790952i
$580$	−8.30968	+	3.00391i	−0.345041	+	0.124731i
$581$	−26.6478	−	17.8055i	−1.10554	−	0.738695i
$582$	−16.4597	+	6.38010i	−0.682275	+	0.264464i
$583$	−1.71038	+	0.708464i	−0.0708369	+	0.0293416i
$584$	10.1303	−	37.3167i	0.419196	−	1.54418i
$585$	1.44984	+	0.600543i	0.0599435	+	0.0248294i
$586$	0.581918	−	25.3954i	0.0240388	−	1.04908i
$587$	11.1359	−	2.21507i	0.459629	−	0.0914258i	0.0401553	−	0.999193i	$-0.487215\pi$
$587$	11.1359	−	2.21507i	0.459629	−	0.0914258i	0.419473	+	0.907768i	$0.362215\pi$
$588$	−14.2685	+	2.16419i	−0.588421	+	0.0892496i
$589$	−12.0709	+	8.06554i	−0.497374	+	0.332335i
$590$	1.94164	+	1.36272i	0.0799360	+	0.0561021i
$591$	−50.3561	+	50.3561i	−2.07137	+	2.07137i
$592$	−39.2746	+	4.12748i	−1.61417	+	0.169638i
$593$	5.38627	+	5.38627i	0.221188	+	0.221188i	0.808998	−	0.587811i	$-0.200010\pi$
$593$	5.38627	+	5.38627i	0.221188	+	0.221188i	−0.587811	+	0.808998i	$0.700010\pi$
$594$	8.30279	+	47.3905i	0.340668	+	1.94446i
$595$	−8.81411	−	13.1913i	−0.361343	−	0.540789i
$596$	−6.46193	−	1.59621i	−0.264691	−	0.0653834i
$597$	−8.80108	−	44.2460i	−0.360204	−	1.81087i
$598$	0.386636	+	0.404770i	0.0158107	+	0.0165523i
$599$	−10.9367	+	26.4036i	−0.446863	+	1.07882i	0.526627	+	0.850096i	$0.323456\pi$
$599$	−10.9367	+	26.4036i	−0.446863	+	1.07882i	−0.973491	+	0.228727i	$0.926544\pi$
$600$	−1.08761	−	3.23886i	−0.0444014	−	0.132226i
$601$	−8.76796	−	21.1677i	−0.357653	−	0.863450i	−0.995629	−	0.0933942i	$-0.970228\pi$
$601$	−8.76796	−	21.1677i	−0.357653	−	0.863450i	0.637977	−	0.770056i	$-0.279772\pi$
$602$	13.2438	+	5.84469i	0.539775	+	0.238212i
$603$	−17.8284	+	26.6821i	−0.726029	+	1.08658i
$604$	4.86346	+	5.33090i	0.197891	+	0.216911i
$605$	1.43652	+	0.285741i	0.0584028	+	0.0116170i
$606$	23.3390	+	5.20092i	0.948083	+	0.211273i
$607$			27.1652i			1.10260i	0.834306	+	0.551301i	$0.185868\pi$
$607$			27.1652i			1.10260i	−0.834306	+	0.551301i	$0.814132\pi$
$608$	−5.41245	−	18.9545i	−0.219504	−	0.768705i
$609$			13.6449i			0.552921i
$610$	1.78943	−	8.03000i	0.0724517	−	0.325125i
$611$	−1.30825	−	0.260227i	−0.0529262	−	0.0105277i
$612$	−44.1339	−	2.02365i	−1.78401	−	0.0818014i
$613$	−4.77987	+	7.15358i	−0.193057	+	0.288930i	−0.915352	−	0.402655i	$-0.868087\pi$
$613$	−4.77987	+	7.15358i	−0.193057	+	0.288930i	0.722295	+	0.691585i	$0.243087\pi$
$614$	13.5043	−	30.6001i	0.544990	−	1.23492i
$615$	−2.29285	−	5.53542i	−0.0924564	−	0.223210i
$616$	12.8720	+	14.7753i	0.518629	+	0.595312i
$617$	−3.84308	+	9.27803i	−0.154717	+	0.373519i	−0.982165	−	0.188023i	$-0.939792\pi$
$617$	−3.84308	+	9.27803i	−0.154717	+	0.373519i	0.827448	+	0.561543i	$0.189792\pi$
$618$	42.1296	−	40.2421i	1.69470	−	1.61877i
$619$	−0.956021	−	4.80624i	−0.0384257	−	0.193179i	0.956805	−	0.290732i	$-0.0938987\pi$
$619$	−0.956021	−	4.80624i	−0.0384257	−	0.193179i	−0.995230	+	0.0975524i	$0.968899\pi$
$620$	−9.24449	−	15.3099i	−0.371268	−	0.614858i
$621$	20.5340	+	30.7313i	0.824000	+	1.23320i
$622$	−8.03674	+	1.40803i	−0.322244	+	0.0564570i
$623$	19.8826	+	19.8826i	0.796578	+	0.796578i
$624$	0.649266	−	1.23402i	0.0259914	−	0.0494002i
$625$	16.1789	−	16.1789i	0.647155	−	0.647155i
$626$	5.86131	−	8.35137i	0.234265	−	0.333788i
$627$	28.6035	−	19.1123i	1.14231	−	0.763270i
$628$	−17.9509	+	24.3700i	−0.716320	+	0.972469i
$629$	33.1828	−	6.60047i	1.32308	−	0.263178i
$630$	42.1924	+	0.966808i	1.68099	+	0.0385186i
$631$	4.21091	+	1.74421i	0.167634	+	0.0694361i	0.464922	−	0.885352i	$-0.346082\pi$
$631$	4.21091	+	1.74421i	0.167634	+	0.0694361i	−0.297289	+	0.954788i	$0.596082\pi$
$632$	11.0958	+	8.57207i	0.441366	+	0.340979i
$633$	−6.93051	+	2.87071i	−0.275463	+	0.114101i
$634$	17.3868	+	44.8552i	0.690517	+	1.78143i
$635$	9.13903	+	6.10650i	0.362671	+	0.242329i
$636$	3.20757	+	1.50426i	0.127188	+	0.0596480i
$637$	−0.0519513	+	0.261177i	−0.00205839	+	0.0103482i
$638$	−7.89137	+	5.01523i	−0.312422	+	0.198555i
$639$	−65.4825			−2.59045
$640$	23.6312	−	5.59112i	0.934104	−	0.221008i
$641$	−18.0849			−0.714310			−0.357155	−	0.934045i	$-0.616253\pi$
$641$	−18.0849			−0.714310			−0.357155	+	0.934045i	$0.616253\pi$
$642$	−25.4542	+	16.1770i	−1.00460	+	0.638454i
$643$	−1.42112	+	7.14443i	−0.0560433	+	0.281749i	−0.998637	−	0.0521929i	$-0.983379\pi$
$643$	−1.42112	+	7.14443i	−0.0560433	+	0.281749i	0.942594	+	0.333942i	$0.108379\pi$
$644$	13.6293	+	6.39178i	0.537070	+	0.251871i
$645$	26.0308	+	17.3932i	1.02496	+	0.684857i
$646$	6.10359	+	15.7463i	0.240143	+	0.619531i
$647$	3.05247	−	1.26437i	0.120005	−	0.0497076i	−0.321873	−	0.946783i	$-0.604312\pi$
$647$	3.05247	−	1.26437i	0.120005	−	0.0497076i	0.441878	+	0.897075i	$0.354312\pi$
$648$	22.8491	−	29.5761i	0.897596	−	1.16186i
$649$	2.31910	+	0.960601i	0.0910325	+	0.0377069i
$650$	−0.0630267	−	0.00144421i	−0.00247211	−	5.66466e-5i
$651$	−27.0873	+	5.38800i	−1.06164	+	0.211172i
$652$	17.0022	−	23.0820i	0.665858	−	0.903962i
$653$	10.1827	−	6.80383i	0.398478	−	0.266254i	−0.340145	−	0.940373i	$-0.610476\pi$
$653$	10.1827	−	6.80383i	0.398478	−	0.266254i	0.738623	+	0.674118i	$0.235476\pi$
$654$	49.7475	−	70.8817i	1.94528	−	2.77169i
$655$	18.6424	−	18.6424i	0.728420	−	0.728420i
$656$	−3.46957	+	1.07729i	−0.135464	+	0.0420610i
$657$	−62.3131	−	62.3131i	−2.43107	−	2.43107i
$658$	−35.3343	+	6.19055i	−1.37747	+	0.241333i
$659$	−14.7692	−	22.1037i	−0.575328	−	0.861039i	0.423669	−	0.905817i	$-0.360742\pi$
$659$	−14.7692	−	22.1037i	−0.575328	−	0.861039i	−0.998997	+	0.0447783i	$0.985742\pi$
$660$	21.9059	+	36.2785i	0.852687	+	1.41214i
$661$	2.82505	+	14.2025i	0.109882	+	0.552412i	0.996031	+	0.0890116i	$0.0283708\pi$
$661$	2.82505	+	14.2025i	0.109882	+	0.552412i	−0.886149	+	0.463400i	$0.846629\pi$
$662$	14.8303	−	14.1659i	0.576397	−	0.550573i
$663$	−0.457161	+	1.10368i	−0.0177546	+	0.0428635i
$664$	−31.6884	+	27.6066i	−1.22975	+	1.07134i
$665$	−6.17355	−	14.9043i	−0.239400	−	0.577962i
$666$	−36.3377	+	82.3393i	−1.40806	+	3.19058i
$667$	−3.99060	+	5.97235i	−0.154516	+	0.231250i
$668$	13.1705	+	0.603901i	0.509581	+	0.0233656i
$669$	−21.1495	−	4.20690i	−0.817687	−	0.162648i
$670$	−3.28681	+	14.7495i	−0.126980	+	0.569822i
$671$		−	8.70576i		−	0.336082i
$672$	4.28628	−	37.2541i	0.165347	−	1.43711i
$673$			26.9629i			1.03934i	0.854366	+	0.519671i	$0.173946\pi$
$673$			26.9629i			1.03934i	−0.854366	+	0.519671i	$0.826054\pi$
$674$	−44.4475	−	9.90479i	−1.71205	−	0.381518i
$675$	−4.08271	−	0.812101i	−0.157144	−	0.0312578i
$676$	17.5060	+	19.1886i	0.673309	+	0.738022i
$677$	−9.17925	+	13.7377i	−0.352787	+	0.527984i	−0.964842	−	0.262832i	$-0.915343\pi$
$677$	−9.17925	+	13.7377i	−0.352787	+	0.527984i	0.612054	+	0.790816i	$0.290343\pi$
$678$	36.1668	+	15.9610i	1.38898	+	0.612978i
$679$	3.35232	+	8.09321i	0.128650	+	0.310589i
$680$	−19.7221	+	6.62268i	−0.756310	+	0.253968i
$681$	20.3398	−	49.1045i	0.779422	−	1.88169i
$682$	−13.0721	−	13.6852i	−0.500556	−	0.524034i
$683$	−3.67420	−	18.4714i	−0.140589	−	0.706790i	−0.985200	−	0.171409i	$-0.945168\pi$
$683$	−3.67420	−	18.4714i	−0.140589	−	0.706790i	0.844611	−	0.535381i	$-0.179832\pi$
$684$	−43.6136	−	10.7734i	−1.66761	−	0.411929i
$685$	1.33172	+	1.99306i	0.0508823	+	0.0761508i
$686$	4.92064	+	28.0859i	0.187871	+	1.07233i
$687$	7.55964	+	7.55964i	0.288418	+	0.288418i
$688$	11.9466	−	14.7525i	0.455460	−	0.562434i
$689$	0.0462248	−	0.0462248i	0.00176102	−	0.00176102i
$690$	26.6479	+	18.7025i	1.01447	+	0.711993i
$691$	−22.5013	+	15.0349i	−0.855989	+	0.571953i	−0.904309	−	0.426879i	$-0.859613\pi$
$691$	−22.5013	+	15.0349i	−0.855989	+	0.571953i	0.0483204	+	0.998832i	$0.484613\pi$
$692$	38.8961	−	5.89962i	1.47861	−	0.224270i
$693$	43.8015	−	8.71266i	1.66388	−	0.330967i
$694$	0.317474	−	13.8548i	0.0120511	−	0.525923i
$695$	−6.06703	−	2.51304i	−0.230135	−	0.0953252i
$696$	17.2682	+	4.68777i	0.654549	+	0.177690i
$697$	2.87554	−	1.19109i	0.108919	−	0.0451156i
$698$	44.4331	−	17.2232i	1.68182	−	0.651907i
$699$	67.3560	+	45.0058i	2.54764	+	1.70228i
$700$	−1.59446	+	0.576388i	−0.0602648	+	0.0217854i
$701$	−4.62224	+	23.2376i	−0.174579	+	0.877670i	0.789844	+	0.613308i	$0.210162\pi$
$701$	−4.62224	+	23.2376i	−0.174579	+	0.877670i	−0.964423	+	0.264362i	$0.914838\pi$
$702$	−0.911250	−	1.43383i	−0.0343929	−	0.0541166i
$703$	34.4028			1.29753
$704$	23.1209	−	11.2139i	0.871401	−	0.422641i
$705$	−77.5801			−2.92184
$706$	−13.2501	−	20.8488i	−0.498676	−	0.784656i
$707$	2.31489	−	11.6378i	0.0870605	−	0.437683i
$708$	−1.63306	−	4.51752i	−0.0613742	−	0.169779i
$709$	16.3280	+	10.9100i	0.613211	+	0.409734i	0.823024	−	0.568007i	$-0.192285\pi$
$709$	16.3280	+	10.9100i	0.613211	+	0.409734i	−0.209813	+	0.977742i	$0.567285\pi$
$710$	−28.7512	+	11.1445i	−1.07901	+	0.418247i
$711$	29.5226	−	12.2286i	1.10718	−	0.458610i
$712$	31.9928	−	18.3314i	1.19898	−	0.686998i
$713$	−13.4318	−	5.56364i	−0.503025	−	0.208360i
$714$	−0.735978	+	32.1188i	−0.0275433	+	1.20201i
$715$	0.766959	−	0.152558i	0.0286826	−	0.00570533i
$716$	−0.574787	−	3.78956i	−0.0214808	−	0.141623i
$717$	40.5671	−	27.1061i	1.51501	−	1.01229i
$718$	20.9383	+	14.6953i	0.781409	+	0.548423i
$719$	3.45757	−	3.45757i	0.128946	−	0.128946i	−0.639689	−	0.768634i	$-0.720937\pi$
$719$	3.45757	−	3.45757i	0.128946	−	0.128946i	0.768634	+	0.639689i	$0.220937\pi$
$720$	15.7189	−	53.0639i	0.585809	−	1.97758i
$721$	−20.4433	−	20.4433i	−0.761347	−	0.761347i
$722$	−1.67354	−	9.55219i	−0.0622827	−	0.355496i
$723$	−36.4838	−	54.6019i	−1.35685	−	2.03067i
$724$	−9.38913	+	38.0099i	−0.348944	+	1.41263i
$725$	−0.157825	−	0.793438i	−0.00586146	−	0.0294676i
$726$	−2.04868	−	2.14477i	−0.0760336	−	0.0795999i
$727$	14.0936	−	34.0251i	0.522704	−	1.26192i	−0.413513	−	0.910498i	$-0.635698\pi$
$727$	14.0936	−	34.0251i	0.522704	−	1.26192i	0.936217	−	0.351421i	$-0.114302\pi$
$728$	−0.619584	−	0.308077i	−0.0229633	−	0.0114181i
$729$	4.77554	+	11.5292i	0.176872	+	0.427007i
$730$	−37.9648	−	16.7545i	−1.40514	−	0.620112i
$731$	−9.03542	+	13.5225i	−0.334187	+	0.500146i
$732$	−12.3076	+	11.2284i	−0.454901	+	0.415013i
$733$	−9.93170	−	1.97554i	−0.366836	−	0.0729681i	0.00823071	−	0.999966i	$-0.497380\pi$
$733$	−9.93170	−	1.97554i	−0.366836	−	0.0729681i	−0.375066	+	0.926998i	$0.622380\pi$
$734$	−44.3645	−	9.88630i	−1.63753	−	0.364910i
$735$			15.4879i			0.571281i
$736$	12.7714	−	15.0525i	0.470761	−	0.554841i
$737$			15.9907i			0.589025i
$738$	−1.80088	+	8.08143i	−0.0662915	+	0.297482i
$739$	47.0664	+	9.36209i	1.73137	+	0.344390i	0.957384	−	0.288817i	$-0.0932620\pi$
$739$	47.0664	+	9.36209i	1.73137	+	0.344390i	0.773982	+	0.633207i	$0.218262\pi$
$740$	−1.94125	+	42.3368i	−0.0713619	+	1.55633i
$741$	−0.674875	+	1.01002i	−0.0247922	+	0.0371041i
$742$	0.709811	−	1.60840i	0.0260580	−	0.0590461i
$743$	−8.63374	−	20.8437i	−0.316741	−	0.764681i	−0.999423	−	0.0339651i	$-0.989186\pi$
$743$	−8.63374	−	20.8437i	−0.316741	−	0.764681i	0.682682	−	0.730716i	$-0.260814\pi$
$744$	−2.48724	+	36.1311i	−0.0911865	+	1.32463i
$745$	−2.73364	+	6.59958i	−0.100153	+	0.241790i
$746$	−4.55447	+	4.35042i	−0.166751	+	0.159280i
$747$	18.6860	+	93.9409i	0.683685	+	3.43712i
$748$	−18.8460	+	11.3797i	−0.689077	+	0.416083i
$749$	8.31486	+	12.4441i	0.303818	+	0.454696i
$750$	−49.5583	+	8.68259i	−1.80961	+	0.317043i
$751$	6.86892	+	6.86892i	0.250650	+	0.250650i	0.821237	−	0.570587i	$-0.193284\pi$
$751$	6.86892	+	6.86892i	0.250650	+	0.250650i	−0.570587	+	0.821237i	$0.693284\pi$
$752$	−4.30486	+	46.8436i	−0.156982	+	1.70821i
$753$	0.643583	−	0.643583i	0.0234535	−	0.0234535i
$754$	0.189671	−	0.270249i	0.00690741	−	0.00984188i
$755$	6.43910	−	4.30247i	0.234343	−	0.156583i
$756$	−36.7864	−	27.0968i	−1.33791	−	0.985503i
$757$	−20.6195	+	4.10147i	−0.749428	+	0.149070i	−0.555005	−	0.831847i	$-0.687284\pi$
$757$	−20.6195	+	4.10147i	−0.749428	+	0.149070i	−0.194423	+	0.980918i	$0.562284\pi$
$758$	−32.3770	−	0.741895i	−1.17598	−	0.0269468i
$759$	31.8283	+	13.1837i	1.15529	+	0.478539i
$760$	−20.9828	+	2.69244i	−0.761128	+	0.0976649i
$761$	−2.27046	+	0.940453i	−0.0823039	+	0.0340914i	−0.423456	−	0.905917i	$-0.639183\pi$
$761$	−2.27046	+	0.940453i	−0.0823039	+	0.0340914i	0.341152	+	0.940008i	$0.389183\pi$
$762$	−8.04447	−	20.7535i	−0.291420	−	0.751819i
$763$	−35.7303	−	23.8743i	−1.29353	−	0.864306i
$764$	10.7512	−	22.9249i	0.388964	−	0.829395i
$765$	−9.25000	+	46.5029i	−0.334435	+	1.68132i
$766$	−11.4412	+	7.27129i	−0.413389	+	0.262722i
$767$	−0.0886369			−0.00320049
$768$	−45.6740	−	18.2233i	−1.64812	−	0.657575i
$769$	−3.66124			−0.132028			−0.0660139	−	0.997819i	$-0.521028\pi$
$769$	−3.66124			−0.132028			−0.0660139	+	0.997819i	$0.521028\pi$
$770$	17.7490	−	11.2801i	0.639629	−	0.406506i
$771$	−0.574857	+	2.89000i	−0.0207030	+	0.104081i
$772$	5.36166	−	11.4328i	0.192970	−	0.411474i
$773$	−35.7598	−	23.8939i	−1.28619	−	0.859404i	−0.290938	−	0.956742i	$-0.593967\pi$
$773$	−35.7598	−	23.8939i	−1.28619	−	0.859404i	−0.995251	+	0.0973381i	$0.968967\pi$
$774$	−15.6361	−	40.3387i	−0.562028	−	1.44994i
$775$	1.51278	−	0.626613i	0.0543406	−	0.0225086i
$776$	11.3940	−	1.46203i	0.409020	−	0.0524838i
$777$	60.4654	+	25.0456i	2.16919	+	0.898506i
$778$	−17.4592	−	0.400066i	−0.625944	−	0.0143431i
$779$	3.10408	−	0.617440i	0.111215	−	0.0221221i
$780$	−1.20487	−	0.887508i	−0.0431413	−	0.0317779i
$781$	−27.1310	+	18.1283i	−0.970822	+	0.648682i
$782$	−9.71558	+	13.8430i	−0.347428	+	0.495026i
$783$	15.4153	−	15.4153i	0.550899	−	0.550899i
$784$	9.35177	+	0.859413i	0.333992	+	0.0306933i
$785$	22.9690	+	22.9690i	0.819799	+	0.819799i
$786$	−52.5879	+	9.21337i	−1.87575	+	0.328630i
$787$	17.0932	+	25.5818i	0.609308	+	0.911894i	0.999963	−	0.00864361i	$-0.00275138\pi$
$787$	17.0932	+	25.5818i	0.609308	+	0.911894i	−0.390655	+	0.920537i	$0.627751\pi$
$788$	39.6705	−	23.9541i	1.41320	−	0.853328i
$789$	2.88215	+	14.4895i	0.102607	+	0.515842i
$790$	10.8812	−	10.3937i	0.387135	−	0.369790i
$791$	7.50721	−	18.1240i	0.266926	−	0.644415i
$792$	4.02198	−	58.4257i	0.142915	−	2.07607i
$793$	0.117641	+	0.284010i	0.00417754	+	0.0100855i
$794$	4.66480	−	10.5702i	0.165547	−	0.375122i
$795$	2.11233	−	3.16132i	0.0749166	−	0.112121i
$796$	−1.34466	+	29.3257i	−0.0476602	+	1.03942i
$797$	−3.59248	−	0.714589i	−0.127252	−	0.0253120i	0.131053	−	0.991375i	$-0.458164\pi$
$797$	−3.59248	−	0.714589i	−0.127252	−	0.0253120i	−0.258306	+	0.966063i	$0.583164\pi$
$798$	−7.10562	+	31.8863i	−0.251536	+	1.12876i
$799$		−	40.3013i		−	1.42576i
$800$	0.181659	+	2.21587i	0.00642262	+	0.0783427i
$801$		−	84.0337i		−	2.96919i
$802$	12.9516	+	2.88617i	0.457337	+	0.101914i
$803$	−43.0688	−	8.56691i	−1.51986	−	0.302320i
$804$	22.6065	−	20.6242i	0.797269	−	0.727361i
$805$	8.97550	−	13.4328i	0.316345	−	0.473444i
$806$	0.611381	+	0.269813i	0.0215350	+	0.00950375i
$807$	−5.10825	−	12.3324i	−0.179819	−	0.434121i
$808$	−13.9327	−	6.92778i	−0.490152	−	0.243719i
$809$	−4.56231	+	11.0144i	−0.160402	+	0.387245i	−0.983564	−	0.180562i	$-0.942208\pi$
$809$	−4.56231	+	11.0144i	−0.160402	+	0.387245i	0.823161	+	0.567808i	$0.192208\pi$
$810$	−27.7046	−	29.0041i	−0.973441	−	1.01910i
$811$	0.413214	+	2.07737i	0.0145099	+	0.0729462i	0.987362	−	0.158482i	$-0.0506601\pi$
$811$	0.413214	+	2.07737i	0.0145099	+	0.0729462i	−0.972852	+	0.231428i	$0.925660\pi$
$812$	2.12933	−	8.62014i	0.0747248	−	0.302508i
$813$	−25.7413	−	38.5246i	−0.902788	−	1.35112i
$814$	7.73943	+	44.1750i	0.271267	+	1.54833i
$815$	−21.7551	−	21.7551i	−0.762047	−	0.762047i
$816$	40.3946	+	11.9659i	1.41410	+	0.418891i
$817$	−11.6936	+	11.6936i	−0.409109	+	0.409109i
$818$	−9.36252	−	6.57098i	−0.327353	−	0.229749i
$819$	−1.31121	+	0.876123i	−0.0458174	+	0.0306142i
$820$	0.584680	+	3.85478i	0.0204179	+	0.134615i
$821$	−46.0479	+	9.15949i	−1.60708	+	0.319668i	−0.915403	−	0.402538i	$-0.868128\pi$
$821$	−46.0479	+	9.15949i	−1.60708	+	0.319668i	−0.691678	+	0.722206i	$0.743128\pi$
$822$	0.111198	−	4.85280i	0.00387849	−	0.169261i
$823$	43.8242	+	18.1526i	1.52761	+	0.632759i	0.979099	−	0.203382i	$-0.0651933\pi$
$823$	43.8242	+	18.1526i	1.52761	+	0.632759i	0.548515	+	0.836141i	$0.315193\pi$
$824$	−32.8951	+	18.8484i	−1.14595	+	0.656613i
$825$	−3.58471	+	1.48483i	−0.124804	+	0.0516953i
$826$	−2.22260	+	0.861527i	−0.0773343	+	0.0299763i
$827$	−7.79161	−	5.20619i	−0.270941	−	0.181037i	0.412676	−	0.910878i	$-0.364594\pi$
$827$	−7.79161	−	5.20619i	−0.270941	−	0.181037i	−0.683617	+	0.729841i	$0.739594\pi$
$828$	−15.2947	−	42.3096i	−0.531528	−	1.47036i
$829$	10.9119	−	54.8578i	0.378986	−	1.90529i	−0.0437617	−	0.999042i	$-0.513934\pi$
$829$	10.9119	−	54.8578i	0.378986	−	1.90529i	0.422747	−	0.906248i	$-0.361066\pi$
$830$	24.1923	+	38.0662i	0.839728	+	1.32130i
$831$	−1.18297			−0.0410369
$832$	−0.602743	+	0.678266i	−0.0208964	+	0.0235147i
$833$	−8.04568			−0.278766
$834$	7.13286	+	11.2234i	0.246991	+	0.388635i
$835$	2.76040	−	13.8774i	0.0955274	−	0.480249i
$836$	−21.0527	+	7.61045i	−0.728123	+	0.263213i
$837$	36.6889	+	24.5147i	1.26815	+	0.847354i
$838$	−3.85783	+	1.49537i	−0.133267	+	0.0516568i
$839$	38.4928	−	15.9443i	1.32892	−	0.550457i	0.398573	−	0.917137i	$-0.369506\pi$
$839$	38.4928	−	15.9443i	1.32892	−	0.550457i	0.930347	+	0.366680i	$0.119506\pi$
$840$	−38.8390	−	10.5436i	−1.34007	−	0.363788i
$841$	−22.8783	−	9.47649i	−0.788906	−	0.326775i
$842$	−0.694152	+	30.2934i	−0.0239221	+	1.04398i
$843$	12.4807	−	2.48256i	0.429857	−	0.0855038i
$844$	4.82631	−	0.732037i	0.166128	−	0.0251978i
$845$	23.1776	−	15.4867i	0.797332	−	0.532760i
$846$	87.7524	+	61.5880i	3.01699	+	2.11744i
$847$	−1.04074	+	1.04074i	−0.0357604	+	0.0357604i
$848$	−1.79163	−	1.45086i	−0.0615247	−	0.0498229i
$849$	19.8020	+	19.8020i	0.679604	+	0.679604i
$850$	−0.328706	−	1.87618i	−0.0112745	−	0.0643525i
$851$	19.1407	+	28.6461i	0.656135	+	0.981976i
$852$	60.6211	+	14.9745i	2.07684	+	0.513018i
$853$	−3.22130	−	16.1946i	−0.110295	−	0.554491i	−0.995932	−	0.0901121i	$-0.971277\pi$
$853$	−3.22130	−	16.1946i	−0.110295	−	0.554491i	0.885636	−	0.464379i	$-0.153723\pi$
$854$	5.71038	+	5.97822i	0.195405	+	0.204570i
$855$	−18.4502	+	44.5427i	−0.630984	+	1.52333i
$856$	18.6050	−	6.24756i	0.635907	−	0.213537i
$857$	−3.26603	−	7.88490i	−0.111566	−	0.269343i	0.858229	−	0.513267i	$-0.171565\pi$
$857$	−3.26603	−	7.88490i	−0.111566	−	0.269343i	−0.969794	+	0.243924i	$0.921565\pi$
$858$	−1.44874	−	0.639354i	−0.0494592	−	0.0218272i
$859$	−3.93549	+	5.88988i	−0.134277	+	0.200960i	−0.892515	−	0.451019i	$-0.851061\pi$
$859$	−3.93549	+	5.88988i	−0.134277	+	0.200960i	0.758237	+	0.651979i	$0.226061\pi$
$860$	−13.7306	−	15.0503i	−0.468209	−	0.513210i
$861$	5.90515	+	1.17461i	0.201247	+	0.0400305i
$862$	17.0929	+	3.80903i	0.582187	+	0.129736i
$863$		−	17.7071i		−	0.602756i	−0.953505	−	0.301378i	$-0.902553\pi$
$863$		−	17.7071i		−	0.602756i	0.953505	−	0.301378i	$-0.0974466\pi$
$864$	−46.9302	+	37.2454i	−1.59660	+	1.26711i
$865$		−	42.2205i		−	1.43554i
$866$	−6.06623	+	27.2221i	−0.206139	+	0.925044i
$867$	15.8446	+	3.15168i	0.538110	+	0.107037i
$868$	17.9531	+	0.823198i	0.609369	+	0.0279412i
$869$	8.84650	−	13.2397i	0.300097	−	0.449127i
$870$	7.75309	−	17.5681i	0.262854	−	0.595614i
$871$	−0.216082	−	0.521667i	−0.00732165	−	0.0176760i
$872$	−42.4891	+	37.0160i	−1.43886	+	1.25352i
$873$	10.0187	−	24.1873i	0.339082	−	0.818616i
$874$	−12.4356	+	11.8784i	−0.420639	+	0.401794i
$875$	4.87086	+	24.4875i	0.164665	+	0.827827i
$876$	43.4373	+	71.9368i	1.46761	+	2.43052i
$877$	23.3455	+	34.9391i	0.788323	+	1.17981i	0.980126	+	0.198375i	$0.0635664\pi$
$877$	23.3455	+	34.9391i	0.788323	+	1.17981i	−0.191804	+	0.981433i	$0.561434\pi$
$878$	−14.8369	+	2.59942i	−0.500722	+	0.0877263i
$879$	39.0360	+	39.0360i	1.31665	+	1.31665i
$880$	−8.17763	−	26.3373i	−0.275668	−	0.887831i
$881$	−22.0191	+	22.0191i	−0.741844	+	0.741844i	−0.972933	−	0.231089i	$-0.925771\pi$
$881$	−22.0191	+	22.0191i	−0.741844	+	0.741844i	0.231089	+	0.972933i	$0.425771\pi$
$882$	12.2953	−	17.5187i	0.414005	−	0.589886i
$883$	−37.7422	+	25.2185i	−1.27012	+	0.848670i	−0.993668	−	0.112356i	$-0.964160\pi$
$883$	−37.7422	+	25.2185i	−1.27012	+	0.848670i	−0.276457	+	0.961026i	$0.589160\pi$
$884$	0.461042	−	0.625907i	0.0155065	−	0.0210515i
$885$	−5.05617	+	1.00573i	−0.169961	+	0.0338074i
$886$	27.8190	+	0.637453i	0.934599	+	0.0214156i
$887$	−44.8061	−	18.5593i	−1.50444	−	0.623160i	−0.530040	−	0.847973i	$-0.677823\pi$
$887$	−44.8061	−	18.5593i	−1.50444	−	0.623160i	−0.974402	+	0.224812i	$0.927823\pi$
$888$	52.4693	−	67.9168i	1.76075	−	2.27914i
$889$	−10.2045	+	4.22683i	−0.342247	+	0.141763i
$890$	−14.3018	−	36.8964i	−0.479398	−	1.23677i
$891$	−35.2908	−	23.5806i	−1.18229	−	0.789979i
$892$	12.7046	+	5.95813i	0.425382	+	0.199493i
$893$	7.99485	−	40.1928i	0.267537	−	1.34500i
$894$	12.2086	−	7.75897i	0.408316	−	0.259499i
$895$	−4.11345			−0.137497
$896$	−8.52145	+	22.8663i	−0.284682	+	0.763909i
$897$	−1.21649			−0.0406175
$898$	36.9358	−	23.4739i	1.23256	−	0.783335i
$899$	−1.67297	+	8.41060i	−0.0557968	+	0.280509i
$900$	4.58754	+	2.15144i	0.152918	+	0.0717145i
$901$	1.64224	+	1.09731i	0.0547111	+	0.0365568i
$902$	1.49113	+	3.84689i	0.0496493	+	0.128087i
$903$	−29.0655	+	12.0393i	−0.967239	+	0.400644i
$904$	−20.3575	−	15.7272i	−0.677080	−	0.523080i
$905$	38.8196	+	16.0796i	1.29041	+	0.534504i
$906$	−15.6783	−	0.359256i	−0.520875	−	0.0119355i
$907$	−47.1400	+	9.37673i	−1.56526	+	0.311349i	−0.900212	−	0.435453i	$-0.856588\pi$
$907$	−47.1400	+	9.37673i	−1.56526	+	0.311349i	−0.665047	+	0.746802i	$0.731588\pi$
$908$	−20.5125	+	27.8475i	−0.680730	+	0.924153i
$909$	−29.4855	+	19.7016i	−0.977972	+	0.653460i
$910$	−0.426601	+	0.607834i	−0.0141417	+	0.0201495i
$911$	36.2741	−	36.2741i	1.20182	−	1.20182i	0.228202	−	0.973614i	$-0.426715\pi$
$911$	36.2741	−	36.2741i	1.20182	−	1.20182i	0.973614	−	0.228202i	$-0.0732847\pi$
$912$	37.9121	+	19.9471i	1.25540	+	0.660514i
$913$	33.7489	+	33.7489i	1.11693	+	1.11693i
$914$	54.8824	−	9.61537i	1.81535	−	0.318048i
$915$	9.93321	+	14.8661i	0.328382	+	0.491458i
$916$	−3.59607	−	5.95548i	−0.118818	−	0.196774i
$917$	5.16862	+	25.9844i	0.170683	+	0.858081i
$918$	37.1176	−	35.4546i	1.22506	−	1.17018i
$919$	11.2124	−	27.0692i	0.369864	−	0.892932i	−0.623907	−	0.781498i	$-0.714456\pi$
$919$	11.2124	−	27.0692i	0.369864	−	0.892932i	0.993772	−	0.111433i	$-0.0355442\pi$
$920$	−13.9161	−	15.9737i	−0.458801	−	0.526638i
$921$	27.8172	+	67.1567i	0.916609	+	2.21289i
$922$	4.96470	−	11.2497i	0.163504	−	0.370490i
$923$	0.640131	−	0.958024i	0.0210702	−	0.0315337i
$924$	−42.5421	−	1.95067i	−1.39953	−	0.0641722i
$925$	−3.80569	−	0.756999i	−0.125130	−	0.0248900i
$926$	10.9771	−	49.2593i	0.360729	−	1.61876i
$927$			86.4036i			2.83787i
$928$	−10.1776	−	5.65623i	−0.334095	−	0.185675i
$929$		−	42.1312i		−	1.38228i	−0.722722	−	0.691139i	$-0.757109\pi$
$929$		−	42.1312i		−	1.38228i	0.722722	−	0.691139i	$-0.242891\pi$
$930$	37.9369	+	8.45394i	1.24400	+	0.277216i
$931$	−8.02402	−	1.59608i	−0.262976	−	0.0523093i
$932$	−35.5286	−	38.9434i	−1.16378	−	1.27563i
$933$	9.85133	−	14.7436i	0.322518	−	0.482682i
$934$	47.7706	+	21.0820i	1.56310	+	0.689823i
$935$	9.04148	+	21.8281i	0.295688	+	0.713854i
$936$	0.658295	+	1.96038i	0.0215170	+	0.0640771i
$937$	11.2961	−	27.2713i	0.369028	−	0.890913i	−0.624882	−	0.780719i	$-0.714853\pi$
$937$	11.2961	−	27.2713i	0.369028	−	0.890913i	0.993910	−	0.110194i	$-0.0351472\pi$
$938$	−10.4888	−	10.9808i	−0.342471	−	0.358534i
$939$	4.32586	+	21.7476i	0.141169	+	0.709705i
$940$	49.0109	+	12.1066i	1.59856	+	0.394873i
$941$	−6.97461	−	10.4382i	−0.227366	−	0.340277i	0.700193	−	0.713953i	$-0.253097\pi$
$941$	−6.97461	−	10.4382i	−0.227366	−	0.340277i	−0.927559	+	0.373676i	$0.878097\pi$
$942$	−11.3516	−	64.7926i	−0.369856	−	2.11106i
$943$	2.24114	+	2.24114i	0.0729815	+	0.0729815i
$944$	0.326710	+	3.10877i	0.0106335	+	0.101182i
$945$	−34.6716	+	34.6716i	−1.12787	+	1.12787i
$946$	−17.6459	−	12.3846i	−0.573717	−	0.402657i
$947$	−12.5016	+	8.35333i	−0.406249	+	0.271447i	−0.741861	−	0.670553i	$-0.766057\pi$
$947$	−12.5016	+	8.35333i	−0.406249	+	0.271447i	0.335612	+	0.942000i	$0.391057\pi$
$948$	−30.1273	+	4.56959i	−0.978488	+	0.148413i
$949$	1.52080	−	0.302507i	0.0493674	−	0.00981979i
$950$	0.0443698	−	1.93634i	0.00143955	−	0.0628232i
$951$	−96.5906	−	40.0091i	−3.13216	−	1.29738i
$952$	5.47717	−	20.1761i	0.177516	−	0.653910i
$953$	42.7086	−	17.6905i	1.38347	−	0.573051i	0.438062	−	0.898945i	$-0.355665\pi$
$953$	42.7086	−	17.6905i	1.38347	−	0.573051i	0.945407	+	0.325893i	$0.105665\pi$
$954$	−4.89896	+	1.89894i	−0.158610	+	0.0614803i
$955$	−22.5944	−	15.0971i	−0.731138	−	0.488531i
$956$	−29.8581	+	10.7936i	−0.965680	+	0.349089i
$957$	3.96431	−	19.9299i	0.128148	−	0.644243i
$958$	−16.9788	−	26.7158i	−0.548560	−	0.863149i
$959$	−2.40877			−0.0777832
$960$	−26.6866	+	45.5299i	−0.861305	+	1.46947i
$961$	13.6430			0.440098
$962$	−0.849420	−	1.33655i	−0.0273864	−	0.0430920i
$963$	8.72606	−	43.8688i	0.281193	−	1.41365i
$964$	14.5278	+	40.1880i	0.467907	+	1.29437i
$965$	−11.2679	−	7.52898i	−0.362727	−	0.242367i
$966$	−30.5040	+	11.8240i	−0.981450	+	0.380430i
$967$	−35.3386	+	14.6377i	−1.13641	+	0.470718i	−0.869956	−	0.493129i	$-0.835853\pi$
$967$	−35.3386	+	14.6377i	−1.13641	+	0.470718i	−0.266457	+	0.963847i	$0.585853\pi$
$968$	0.959549	+	1.67465i	0.0308411	+	0.0538254i
$969$	−33.9079	−	14.0451i	−1.08928	−	0.451194i
$970$	0.282417	−	12.3249i	0.00906787	−	0.395730i
$971$	0.620988	−	0.123522i	0.0199285	−	0.00396402i	−0.185116	−	0.982717i	$-0.559266\pi$
$971$	0.620988	−	0.123522i	0.0199285	−	0.00396402i	0.205044	+	0.978753i	$0.434266\pi$
$972$	2.65062	+	17.4755i	0.0850186	+	0.560526i
$973$	5.48692	−	3.66624i	0.175903	−	0.117534i
$974$	−40.2383	−	28.2408i	−1.28932	−	0.904893i
$975$	0.0968801	−	0.0968801i	0.00310265	−	0.00310265i
$976$	9.52748	−	5.17286i	0.304967	−	0.165579i
$977$	14.4692	+	14.4692i	0.462911	+	0.462911i	0.899608	−	0.436697i	$-0.143852\pi$
$977$	14.4692	+	14.4692i	0.462911	+	0.462911i	−0.436697	+	0.899608i	$0.643852\pi$
$978$	10.7517	+	61.3682i	0.343801	+	1.96234i
$979$	−23.2641	−	34.8172i	−0.743524	−	1.11276i
$980$	2.41694	−	9.78445i	0.0772062	−	0.312553i
$981$	25.0549	+	125.960i	0.799942	+	4.02158i
$982$	−25.5342	−	26.7319i	−0.814831	−	0.853049i
$983$	−6.41367	+	15.4840i	−0.204564	+	0.493862i	−0.992551	−	0.121831i	$-0.961124\pi$
$983$	−6.41367	+	15.4840i	−0.204564	+	0.493862i	0.787987	+	0.615692i	$0.211124\pi$
$984$	3.51524	−	7.06964i	0.112062	−	0.225372i
$985$	−19.0322	−	45.9477i	−0.606415	−	1.46402i
$986$	9.12627	+	4.02757i	0.290640	+	0.128264i
$987$	43.3123	−	64.8214i	1.37864	−	2.06329i
$988$	0.583967	−	0.532762i	0.0185785	−	0.0169494i
$989$	−16.2429	−	3.23091i	−0.516494	−	0.102737i
$990$	−61.3457	−	13.6704i	−1.94970	−	0.434475i
$991$			53.4671i			1.69844i	0.528041	+	0.849219i	$0.322927\pi$
$991$			53.4671i			1.69844i	−0.528041	+	0.849219i	$0.677073\pi$
$992$	7.20966	−	22.4375i	0.228907	−	0.712393i
$993$			44.5709i			1.41441i
$994$	6.73980	−	30.2447i	0.213774	−	0.959304i
$995$	30.8998	+	6.14636i	0.979590	+	0.194853i
$996$	4.18359	−	91.2399i	0.132562	−	2.89105i
$997$	−17.9595	+	26.8783i	−0.568783	+	0.851244i	−0.998666	−	0.0516411i	$-0.983555\pi$
$997$	−17.9595	+	26.8783i	−0.568783	+	0.851244i	0.429883	+	0.902885i	$0.358555\pi$
$998$	−19.1822	+	43.4659i	−0.607203	+	1.37589i
$999$	−40.0155	−	96.6059i	−1.26603	−	3.05648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.61.6	yes	56
3.2	odd	2		576.2.bd.a.253.2		56
4.3	odd	2		256.2.i.a.81.7		56
8.3	odd	2		512.2.i.a.417.1		56
8.5	even	2		512.2.i.b.417.7		56
64.11	odd	16		512.2.i.a.97.1		56
64.21	even	16	inner	64.2.i.a.21.6	✓	56
64.43	odd	16		256.2.i.a.177.7		56
64.53	even	16		512.2.i.b.97.7		56
192.149	odd	16		576.2.bd.a.469.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.6	✓	56	64.21	even	16	inner
64.2.i.a.61.6	yes	56	1.1	even	1	trivial
256.2.i.a.81.7		56	4.3	odd	2
256.2.i.a.177.7		56	64.43	odd	16
512.2.i.a.97.1		56	64.11	odd	16
512.2.i.a.417.1		56	8.3	odd	2
512.2.i.b.97.7		56	64.53	even	16
512.2.i.b.417.7		56	8.5	even	2
576.2.bd.a.253.2		56	3.2	odd	2
576.2.bd.a.469.2		56	192.149	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19357 - 0.758552i) q^{2} +(-0.599600 + 3.01439i) q^{3} +(0.849199 - 1.81076i) q^{4} +(-1.78465 - 1.19247i) q^{5} +(1.57091 + 4.05270i) q^{6} +(1.99271 - 0.825409i) q^{7} +(-0.359981 - 2.80543i) q^{8} +(-5.95540 - 2.46681i) q^{9} +O(q^{10})\)	\(q+(1.19357 - 0.758552i) q^{2} +(-0.599600 + 3.01439i) q^{3} +(0.849199 - 1.81076i) q^{4} +(-1.78465 - 1.19247i) q^{5} +(1.57091 + 4.05270i) q^{6} +(1.99271 - 0.825409i) q^{7} +(-0.359981 - 2.80543i) q^{8} +(-5.95540 - 2.46681i) q^{9} +(-3.03465 - 0.0695368i) q^{10} +(-3.15038 + 0.626650i) q^{11} +(4.94917 + 3.64555i) q^{12} +(0.0943077 - 0.0630144i) q^{13} +(1.75232 - 2.49676i) q^{14} +(4.66465 - 4.66465i) q^{15} +(-2.55772 - 3.07540i) q^{16} +(2.42319 + 2.42319i) q^{17} +(-8.97937 + 1.57318i) q^{18} +(1.93596 + 2.89737i) q^{19} +(-3.67480 + 2.21894i) q^{20} +(1.29328 + 6.50174i) q^{21} +(-3.28485 + 3.13768i) q^{22} +(-1.33543 + 3.22402i) q^{23} +(8.67250 + 0.597008i) q^{24} +(-0.150405 - 0.363110i) q^{25} +(0.0647628 - 0.146749i) q^{26} +(5.88424 - 8.80639i) q^{27} +(0.197591 - 4.30927i) q^{28} +(2.01879 + 0.401561i) q^{29} +(2.02919 - 9.10594i) q^{30} +4.16617i q^{31} +(-5.38566 - 1.73052i) q^{32} -9.87224i q^{33} +(4.73035 + 1.05412i) q^{34} +(-4.54058 - 0.903177i) q^{35} +(-9.52413 + 8.68901i) q^{36} +(5.48499 - 8.20886i) q^{37} +(4.50850 + 1.98968i) q^{38} +(0.133403 + 0.322064i) q^{39} +(-2.70294 + 5.43598i) q^{40} +(0.347569 - 0.839106i) q^{41} +(6.47551 + 6.77923i) q^{42} +(0.925855 + 4.65459i) q^{43} +(-1.54059 + 6.23675i) q^{44} +(7.68675 + 11.5040i) q^{45} +(0.851658 + 4.86108i) q^{46} +(-8.31575 - 8.31575i) q^{47} +(10.8041 - 5.86597i) q^{48} +(-1.66014 + 1.66014i) q^{49} +(-0.454956 - 0.319306i) q^{50} +(-8.75739 + 5.85150i) q^{51} +(-0.0340181 - 0.224281i) q^{52} +(0.565279 - 0.112441i) q^{53} +(0.343130 - 14.9745i) q^{54} +(6.36961 + 2.63838i) q^{55} +(-3.03296 - 5.29328i) q^{56} +(-9.89462 + 4.09848i) q^{57} +(2.71416 - 1.05206i) q^{58} +(-0.649771 - 0.434163i) q^{59} +(-4.48535 - 12.4078i) q^{60} +(-0.528753 + 2.65822i) q^{61} +(3.16025 + 4.97260i) q^{62} -13.9035 q^{63} +(-7.74083 + 2.01980i) q^{64} -0.243449 q^{65} +(-7.48860 - 11.7832i) q^{66} +(0.971210 - 4.88260i) q^{67} +(6.44559 - 2.33005i) q^{68} +(-8.91774 - 5.95864i) q^{69} +(-6.10459 + 2.36626i) q^{70} +(9.38522 - 3.88748i) q^{71} +(-4.77662 + 17.5955i) q^{72} +(12.6303 + 5.23165i) q^{73} +(0.319848 - 13.9585i) q^{74} +(1.18474 - 0.235659i) q^{75} +(6.89047 - 1.04512i) q^{76} +(-5.76057 + 3.84909i) q^{77} +(0.403528 + 0.283211i) q^{78} +(-3.50532 + 3.50532i) q^{79} +(0.897337 + 8.53852i) q^{80} +(9.34353 + 9.34353i) q^{81} +(-0.221658 - 1.26518i) q^{82} +(-8.25513 - 12.3547i) q^{83} +(12.8713 + 3.17945i) q^{84} +(-1.43498 - 7.21413i) q^{85} +(4.63581 + 4.85325i) q^{86} +(-2.42093 + 5.84464i) q^{87} +(2.89210 + 8.61259i) q^{88} +(4.98881 + 12.0441i) q^{89} +(17.9010 + 7.90003i) q^{90} +(0.135916 - 0.203412i) q^{91} +(4.70389 + 5.15599i) q^{92} +(-12.5585 - 2.49803i) q^{93} +(-16.2333 - 3.61747i) q^{94} -7.47938i q^{95} +(8.44572 - 15.1969i) q^{96} +4.06140i q^{97} +(-0.722186 + 3.24079i) q^{98} +(20.3076 + 4.03944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more