LMFDB - Embedded newform 690.2.m.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	690.31
Dual form			690.2.m.a.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(2.31329 + 1.48666i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(2.31329 + 1.48666i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.0200026 + 0.139121i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-3.76788 + 2.42147i) q^{13} +(-1.80075 + 2.07817i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.08458 - 0.318463i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(4.66608 + 1.37008i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.391340 + 2.72183i) q^{21} -0.140551 q^{22} +(-3.77831 + 2.95371i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-1.86060 - 4.07414i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-1.80075 - 2.07817i) q^{28} +(9.35640 - 2.74729i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(-1.52257 + 3.33397i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.118239 + 0.0759879i) q^{33} +(0.160869 + 1.11887i) q^{34} +(0.391340 + 2.72183i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-4.25023 + 4.90502i) q^{37} +(-2.02019 + 4.42360i) q^{38} +(-3.76788 - 2.42147i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-7.94313 - 9.16686i) q^{41} +(-2.63843 - 0.774713i) q^{42} +(2.22997 + 4.88295i) q^{43} +(0.0200026 - 0.139121i) q^{44} -1.00000 q^{45} +(-2.38594 - 4.16021i) q^{46} -4.61230 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.233250 + 0.510747i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(0.740237 + 0.854279i) q^{51} +(4.29746 - 1.26185i) q^{52} +(-0.688254 - 0.442314i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-0.0920417 + 0.106222i) q^{55} +(2.31329 - 1.48666i) q^{56} +(0.692086 + 4.81356i) q^{57} +(1.38777 + 9.65214i) q^{58} +(-2.53773 + 1.63090i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-4.87918 + 10.6839i) q^{61} +(-3.08335 - 1.98155i) q^{62} +(-2.63843 + 0.774713i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-4.29746 - 1.26185i) q^{65} +(-0.0583872 - 0.127850i) q^{66} +(1.15334 - 8.02167i) q^{67} -1.13037 q^{68} +(-4.25635 - 2.20985i) q^{69} -2.74982 q^{70} +(1.03413 - 7.19254i) q^{71} +(0.415415 + 0.909632i) q^{72} +(8.86793 + 2.60386i) q^{73} +(-4.25023 - 4.90502i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-4.09107 - 2.62917i) q^{76} +(-0.160554 + 0.351564i) q^{77} +(2.93305 - 3.38492i) q^{78} +(10.3764 - 6.66849i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(10.2040 - 6.55770i) q^{82} +(10.5332 - 12.1560i) q^{83} +(1.14231 - 2.50132i) q^{84} +(0.950930 + 0.611126i) q^{85} +(-5.15061 + 1.51235i) q^{86} +(6.38581 + 7.36962i) q^{87} +(0.134858 + 0.0395979i) q^{88} +(2.26912 + 4.96867i) q^{89} +(0.142315 - 0.989821i) q^{90} -12.3161 q^{91} +(4.45741 - 1.76959i) q^{92} -3.66519 q^{93} +(0.656399 - 4.56535i) q^{94} +(2.02019 + 4.42360i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(6.94688 + 8.01713i) q^{97} +(-0.538744 + 0.158189i) q^{98} +(-0.118239 - 0.0759879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	2.31329	+	1.48666i	0.874342	+	0.561906i	0.899078	−	0.437788i	$-0.144238\pi$
$7$	2.31329	+	1.48666i	0.874342	+	0.561906i	−0.0247357	+	0.999694i	$0.507874\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	0.0200026	+	0.139121i	0.00603100	+	0.0419465i	0.992615	−	0.121310i	$-0.0387094\pi$
$11$	0.0200026	+	0.139121i	0.00603100	+	0.0419465i	−0.986584	+	0.163256i	$0.947800\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	−3.76788	+	2.42147i	−1.04502	+	0.671595i	−0.946224	−	0.323512i	$-0.895136\pi$
$13$	−3.76788	+	2.42147i	−1.04502	+	0.671595i	−0.0987987	+	0.995107i	$0.531500\pi$
$14$	−1.80075	+	2.07817i	−0.481270	+	0.555415i
$15$	−0.415415	+	0.909632i	−0.107260	+	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	1.08458	−	0.318463i	0.263050	−	0.0772386i	−0.147548	−	0.989055i	$-0.547138\pi$
$17$	1.08458	−	0.318463i	0.263050	−	0.0772386i	0.410598	+	0.911816i	$0.365320\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	4.66608	+	1.37008i	1.07047	+	0.314319i	0.769061	−	0.639176i	$-0.220724\pi$
$19$	4.66608	+	1.37008i	1.07047	+	0.314319i	0.301410	+	0.953494i	$0.402543\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	−0.391340	+	2.72183i	−0.0853973	+	0.593951i
$22$	−0.140551			−0.0299657
$23$	−3.77831	+	2.95371i	−0.787831	+	0.615891i
$23$	−3.77831	+	2.95371i	−0.787831	+	0.615891i
$24$	1.00000			0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−1.86060	−	4.07414i	−0.364893	−	0.799005i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	−1.80075	−	2.07817i	−0.340309	−	0.392738i
$29$	9.35640	−	2.74729i	1.73744	−	0.510158i	0.749104	−	0.662452i	$-0.230484\pi$
$29$	9.35640	−	2.74729i	1.73744	−	0.510158i	0.988335	+	0.152294i	$0.0486660\pi$
$30$	−0.841254	−	0.540641i	−0.153591	−	0.0987071i
$31$	−1.52257	+	3.33397i	−0.273462	+	0.598799i	−0.995678	−	0.0928686i	$-0.970396\pi$
$31$	−1.52257	+	3.33397i	−0.273462	+	0.598799i	0.722216	+	0.691668i	$0.243124\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−0.118239	+	0.0759879i	−0.0205828	+	0.0132278i
$34$	0.160869	+	1.11887i	0.0275888	+	0.191884i
$35$	0.391340	+	2.72183i	0.0661485	+	0.460073i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−4.25023	+	4.90502i	−0.698733	+	0.806381i	−0.988581	−	0.150692i	$-0.951850\pi$
$37$	−4.25023	+	4.90502i	−0.698733	+	0.806381i	0.289848	+	0.957073i	$0.406395\pi$
$38$	−2.02019	+	4.42360i	−0.327718	+	0.717602i
$39$	−3.76788	−	2.42147i	−0.603344	−	0.387746i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	−7.94313	−	9.16686i	−1.24051	−	1.43162i	−0.862683	−	0.505745i	$-0.831218\pi$
$41$	−7.94313	−	9.16686i	−1.24051	−	1.43162i	−0.377825	−	0.925877i	$-0.623328\pi$
$42$	−2.63843	−	0.774713i	−0.407118	−	0.119541i
$43$	2.22997	+	4.88295i	0.340067	+	0.744643i	0.999978	−	0.00670123i	$-0.00213308\pi$
$43$	2.22997	+	4.88295i	0.340067	+	0.744643i	−0.659910	+	0.751344i	$0.729406\pi$
$44$	0.0200026	−	0.139121i	0.00301550	−	0.0209733i
$45$	−1.00000			−0.149071
$46$	−2.38594	−	4.16021i	−0.351787	−	0.613389i
$47$	−4.61230			−0.672773			−0.336387	−	0.941724i	$-0.609205\pi$
$47$	−4.61230			−0.672773			−0.336387	+	0.941724i	$0.609205\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	0.233250	+	0.510747i	0.0333215	+	0.0729639i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	0.740237	+	0.854279i	0.103654	+	0.119623i
$52$	4.29746	−	1.26185i	0.595951	−	0.174987i
$53$	−0.688254	−	0.442314i	−0.0945389	−	0.0607565i	0.492517	−	0.870303i	$-0.336077\pi$
$53$	−0.688254	−	0.442314i	−0.0945389	−	0.0607565i	−0.587056	+	0.809546i	$0.699713\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	−0.0920417	+	0.106222i	−0.0124109	+	0.0143229i
$56$	2.31329	−	1.48666i	0.309127	−	0.198664i
$57$	0.692086	+	4.81356i	0.0916690	+	0.637572i
$58$	1.38777	+	9.65214i	0.182223	+	1.26739i
$59$	−2.53773	+	1.63090i	−0.330384	+	0.212325i	−0.695307	−	0.718713i	$-0.744732\pi$
$59$	−2.53773	+	1.63090i	−0.330384	+	0.212325i	0.364923	+	0.931038i	$0.381095\pi$
$60$	0.654861	−	0.755750i	0.0845422	−	0.0975669i
$61$	−4.87918	+	10.6839i	−0.624715	+	1.36794i	0.287325	+	0.957833i	$0.407234\pi$
$61$	−4.87918	+	10.6839i	−0.624715	+	1.36794i	−0.912040	+	0.410102i	$0.865493\pi$
$62$	−3.08335	−	1.98155i	−0.391586	−	0.251657i
$63$	−2.63843	+	0.774713i	−0.332411	+	0.0976046i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−4.29746	−	1.26185i	−0.533035	−	0.156513i
$66$	−0.0583872	−	0.127850i	−0.00718697	−	0.0157373i
$67$	1.15334	−	8.02167i	0.140903	−	0.980003i	−0.789574	−	0.613655i	$-0.789699\pi$
$67$	1.15334	−	8.02167i	0.140903	−	0.980003i	0.930478	−	0.366349i	$-0.119392\pi$
$68$	−1.13037			−0.137078
$69$	−4.25635	−	2.20985i	−0.512405	−	0.266035i
$70$	−2.74982			−0.328666
$71$	1.03413	−	7.19254i	0.122729	−	0.853597i	−0.831714	−	0.555204i	$-0.812640\pi$
$71$	1.03413	−	7.19254i	0.122729	−	0.853597i	0.954443	−	0.298393i	$-0.0964507\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	8.86793	+	2.60386i	1.03791	+	0.304759i	0.755924	−	0.654659i	$-0.227188\pi$
$73$	8.86793	+	2.60386i	1.03791	+	0.304759i	0.281988	+	0.959418i	$0.409006\pi$
$74$	−4.25023	−	4.90502i	−0.494079	−	0.570198i
$75$	−0.959493	+	0.281733i	−0.110793	+	0.0325317i
$76$	−4.09107	−	2.62917i	−0.469278	−	0.301587i
$77$	−0.160554	+	0.351564i	−0.0182968	+	0.0400645i
$78$	2.93305	−	3.38492i	0.332103	−	0.383267i
$79$	10.3764	−	6.66849i	1.16743	−	0.750264i	0.194399	−	0.980923i	$-0.437725\pi$
$79$	10.3764	−	6.66849i	1.16743	−	0.750264i	0.973035	+	0.230659i	$0.0740881\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	10.2040	−	6.55770i	1.12684	−	0.724176i
$83$	10.5332	−	12.1560i	1.15617	−	1.33429i	0.223019	−	0.974814i	$-0.428409\pi$
$83$	10.5332	−	12.1560i	1.15617	−	1.33429i	0.933153	−	0.359480i	$-0.117046\pi$
$84$	1.14231	−	2.50132i	0.124637	−	0.272916i
$85$	0.950930	+	0.611126i	0.103143	+	0.0662859i
$86$	−5.15061	+	1.51235i	−0.555404	+	0.163081i
$87$	6.38581	+	7.36962i	0.684630	+	0.790106i
$88$	0.134858	+	0.0395979i	0.0143759	+	0.00422115i
$89$	2.26912	+	4.96867i	0.240526	+	0.526678i	0.990942	−	0.134287i	$-0.0428744\pi$
$89$	2.26912	+	4.96867i	0.240526	+	0.526678i	−0.750417	+	0.660965i	$0.770147\pi$
$90$	0.142315	−	0.989821i	0.0150013	−	0.104336i
$91$	−12.3161			−1.29108
$92$	4.45741	−	1.76959i	0.464718	−	0.184493i
$93$	−3.66519			−0.380062
$94$	0.656399	−	4.56535i	0.0677024	−	0.470880i
$95$	2.02019	+	4.42360i	0.207267	+	0.453852i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	6.94688	+	8.01713i	0.705349	+	0.814016i	0.989465	−	0.144774i	$-0.0462454\pi$
$97$	6.94688	+	8.01713i	0.705349	+	0.814016i	−0.284116	+	0.958790i	$0.591700\pi$
$98$	−0.538744	+	0.158189i	−0.0544213	+	0.0159795i
$99$	−0.118239	−	0.0759879i	−0.0118835	−	0.00763707i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	4.28353	−	4.94346i	0.426227	−	0.491892i	−0.501497	−	0.865160i	$-0.667217\pi$
$101$	4.28353	−	4.94346i	0.426227	−	0.491892i	0.927724	+	0.373267i	$0.121763\pi$
$102$	−0.950930	+	0.611126i	−0.0941561	+	0.0605105i
$103$	−1.80061	−	12.5235i	−0.177419	−	1.23398i	−0.862707	−	0.505705i	$-0.831233\pi$
$103$	−1.80061	−	12.5235i	−0.177419	−	1.23398i	0.685287	−	0.728273i	$-0.259677\pi$
$104$	0.637413	+	4.43330i	0.0625035	+	0.434721i
$105$	−2.31329	+	1.48666i	−0.225754	+	0.145083i
$106$	0.535760	−	0.618300i	0.0520376	−	0.0600546i
$107$	2.85921	−	6.26079i	0.276410	−	0.605254i	−0.719610	−	0.694378i	$-0.755680\pi$
$107$	2.85921	−	6.26079i	0.276410	−	0.605254i	0.996021	+	0.0891244i	$0.0284069\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	−0.358844	+	0.105366i	−0.0343711	+	0.0100923i	−0.298873	−	0.954293i	$-0.596611\pi$
$109$	−0.358844	+	0.105366i	−0.0343711	+	0.0100923i	0.264502	+	0.964385i	$0.414792\pi$
$110$	−0.0920417	−	0.106222i	−0.00877583	−	0.0101278i
$111$	−6.22738	−	1.82852i	−0.591076	−	0.173556i
$112$	1.14231	+	2.50132i	0.107939	+	0.236353i
$113$	−2.65538	+	18.4685i	−0.249797	+	1.73737i	0.349580	+	0.936907i	$0.386324\pi$
$113$	−2.65538	+	18.4685i	−0.249797	+	1.73737i	−0.599376	+	0.800467i	$0.704585\pi$
$114$	−4.86306			−0.455468
$115$	−4.70653	−	0.921186i	−0.438886	−	0.0859010i
$116$	−9.75140			−0.905395
$117$	0.637413	−	4.43330i	0.0589288	−	0.409859i
$118$	−1.25314	−	2.74400i	−0.115361	−	0.252605i
$119$	2.98241	+	0.875714i	0.273397	+	0.0802766i
$120$	0.654861	+	0.755750i	0.0597803	+	0.0689902i
$121$	10.5355	−	3.09349i	0.957770	−	0.281227i
$122$	−9.88079	−	6.35000i	−0.894565	−	0.574902i
$123$	5.03877	−	11.0334i	0.454331	−	0.994846i
$124$	2.40019	−	2.76996i	0.215543	−	0.248750i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	−0.391340	−	2.72183i	−0.0348633	−	0.242480i
$127$	2.74578	+	19.0973i	0.243649	+	1.69461i	0.633506	+	0.773738i	$0.281615\pi$
$127$	2.74578	+	19.0973i	0.243649	+	1.69461i	−0.389858	+	0.920875i	$0.627476\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−3.51533	+	4.05690i	−0.309507	+	0.357190i
$130$	1.86060	−	4.07414i	0.163185	−	0.357326i
$131$	−14.5182	−	9.33026i	−1.26846	−	0.815189i	−0.279040	−	0.960279i	$-0.590016\pi$
$131$	−14.5182	−	9.33026i	−1.26846	−	0.815189i	−0.989418	+	0.145090i	$0.953653\pi$
$132$	0.134858	−	0.0395979i	0.0117379	−	0.00344656i
$133$	8.75714	+	10.1063i	0.759341	+	0.876326i
$134$	7.77589	+	2.28321i	0.671734	+	0.197239i
$135$	−0.415415	−	0.909632i	−0.0357532	−	0.0782887i
$136$	0.160869	−	1.11887i	0.0137944	−	0.0959421i
$137$	7.78305			0.664951			0.332476	−	0.943112i	$-0.392116\pi$
$137$	7.78305			0.664951			0.332476	+	0.943112i	$0.392116\pi$
$138$	2.79310	−	3.89854i	0.237765	−	0.331865i
$139$	19.4854			1.65273			0.826363	−	0.563138i	$-0.190406\pi$
$139$	19.4854			1.65273			0.826363	+	0.563138i	$0.190406\pi$
$140$	0.391340	−	2.72183i	0.0330742	−	0.230036i
$141$	−1.91602	−	4.19550i	−0.161358	−	0.353325i
$142$	6.97216	+	2.04721i	0.585090	+	0.171798i
$143$	−0.412245	−	0.475756i	−0.0344736	−	0.0397847i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	8.20340	+	5.27200i	0.681255	+	0.437816i
$146$	−3.83939	+	8.40710i	−0.317750	+	0.695776i
$147$	−0.367696	+	0.424344i	−0.0303271	+	0.0349993i
$148$	5.45997	−	3.50891i	0.448807	−	0.288431i
$149$	−0.388560	−	2.70249i	−0.0318321	−	0.221397i	0.967696	−	0.252120i	$-0.0811279\pi$
$149$	−0.388560	−	2.70249i	−0.0318321	−	0.221397i	−0.999528	+	0.0307236i	$0.990219\pi$
$150$	−0.142315	−	0.989821i	−0.0116200	−	0.0808186i
$151$	0.155823	−	0.100141i	0.0126807	−	0.00814936i	−0.534285	−	0.845304i	$-0.679419\pi$
$151$	0.155823	−	0.100141i	0.0126807	−	0.00814936i	0.546966	+	0.837155i	$0.315783\pi$
$152$	3.18463	−	3.67526i	0.258308	−	0.298103i
$153$	−0.469574	+	1.02822i	−0.0379628	+	0.0831269i
$154$	−0.325137	−	0.208953i	−0.0262003	−	0.0168379i
$155$	−3.51672	+	1.03260i	−0.282470	+	0.0829406i
$156$	2.93305	+	3.38492i	0.234832	+	0.271011i
$157$	17.9585	+	5.27309i	1.43325	+	0.420839i	0.903964	−	0.427608i	$-0.140644\pi$
$157$	17.9585	+	5.27309i	1.43325	+	0.420839i	0.529281	+	0.848447i	$0.322462\pi$
$158$	5.12390	+	11.2198i	0.407636	+	0.892598i
$159$	0.116432	−	0.809801i	0.00923365	−	0.0642214i
$160$	−1.00000			−0.0790569
$161$	−13.1315	+	1.21573i	−1.03491	+	0.0958126i
$162$	1.00000			0.0785674
$163$	2.11812	−	14.7319i	0.165904	−	1.15389i	−0.721338	−	0.692583i	$-0.756472\pi$
$163$	2.11812	−	14.7319i	0.165904	−	1.15389i	0.887242	−	0.461304i	$-0.152618\pi$
$164$	5.03877	+	11.0334i	0.393462	+	0.861561i
$165$	−0.134858	−	0.0395979i	−0.0104987	−	0.00308269i
$166$	10.5332	+	12.1560i	0.817537	+	0.943488i
$167$	16.0137	−	4.70203i	1.23917	−	0.363854i	0.404469	−	0.914552i	$-0.367456\pi$
$167$	16.0137	−	4.70203i	1.23917	−	0.363854i	0.834705	+	0.550698i	$0.185638\pi$
$168$	2.31329	+	1.48666i	0.178474	+	0.114699i
$169$	2.93302	−	6.42243i	0.225617	−	0.494033i
$170$	−0.740237	+	0.854279i	−0.0567736	+	0.0655202i
$171$	−4.09107	+	2.62917i	−0.312852	+	0.201058i
$172$	−0.763953	−	5.31341i	−0.0582509	−	0.405144i
$173$	−0.0732807	−	0.509678i	−0.00557143	−	0.0387501i	0.986846	−	0.161663i	$-0.0516856\pi$
$173$	−0.0732807	−	0.509678i	−0.00557143	−	0.0387501i	−0.992418	+	0.122913i	$0.960777\pi$
$174$	−8.20340	+	5.27200i	−0.621898	+	0.399670i
$175$	−1.80075	+	2.07817i	−0.136124	+	0.157095i
$176$	−0.0583872	+	0.127850i	−0.00440110	+	0.00963707i
$177$	−2.53773	−	1.63090i	−0.190747	−	0.122586i
$178$	−5.24103	+	1.53890i	−0.392832	+	0.115346i
$179$	−7.14833	−	8.24961i	−0.534291	−	0.616605i	0.422859	−	0.906195i	$-0.361026\pi$
$179$	−7.14833	−	8.24961i	−0.534291	−	0.616605i	−0.957151	+	0.289590i	$0.906481\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	−6.83414	−	14.9647i	−0.507978	−	1.11232i	−0.973793	−	0.227435i	$-0.926966\pi$
$181$	−6.83414	−	14.9647i	−0.507978	−	1.11232i	0.465815	−	0.884882i	$-0.345761\pi$
$182$	1.75277	−	12.1908i	0.129924	−	0.903640i
$183$	−11.7453			−0.868239
$184$	1.11722	+	4.66388i	0.0823628	+	0.343826i
$185$	−6.49028			−0.477175
$186$	0.521610	−	3.62788i	0.0382463	−	0.266009i
$187$	0.0659993	+	0.144518i	0.00482635	+	0.0105682i
$188$	4.42547	+	1.29944i	0.322761	+	0.0947711i
$189$	−1.80075	−	2.07817i	−0.130985	−	0.151165i
$190$	−4.66608	+	1.37008i	−0.338513	+	0.0993963i
$191$	3.02110	+	1.94154i	0.218599	+	0.140485i	0.645358	−	0.763881i	$-0.276708\pi$
$191$	3.02110	+	1.94154i	0.218599	+	0.140485i	−0.426759	+	0.904365i	$0.640345\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	−4.45883	+	5.14576i	−0.320953	+	0.370400i	−0.893183	−	0.449694i	$-0.851533\pi$
$193$	−4.45883	+	5.14576i	−0.320953	+	0.370400i	0.572230	+	0.820093i	$0.306079\pi$
$194$	−8.92417	+	5.73522i	−0.640718	+	0.411765i
$195$	−0.637413	−	4.43330i	−0.0456461	−	0.317475i
$196$	−0.0799081	−	0.555773i	−0.00570772	−	0.0396981i
$197$	6.91862	−	4.44633i	0.492931	−	0.316788i	−0.270452	−	0.962733i	$-0.587173\pi$
$197$	6.91862	−	4.44633i	0.492931	−	0.316788i	0.763383	+	0.645946i	$0.223537\pi$
$198$	0.0920417	−	0.106222i	0.00654112	−	0.00754885i
$199$	0.837181	−	1.83317i	0.0593462	−	0.129950i	−0.877635	−	0.479329i	$-0.840880\pi$
$199$	0.837181	−	1.83317i	0.0593462	−	0.129950i	0.936982	+	0.349379i	$0.113607\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	7.77589	−	2.28321i	0.548469	−	0.161045i
$202$	4.28353	+	4.94346i	0.301388	+	0.347820i
$203$	25.7284	+	7.55453i	1.80578	+	0.530224i
$204$	−0.469574	−	1.02822i	−0.0328768	−	0.0719900i
$205$	1.72621	−	12.0060i	0.120563	−	0.838537i
$206$	12.6523			0.881527
$207$	0.242000	−	4.78972i	0.0168202	−	0.332909i
$208$	−4.47889			−0.310555
$209$	−0.0972737	+	0.676554i	−0.00672857	+	0.0467982i
$210$	−1.14231	−	2.50132i	−0.0788272	−	0.172608i
$211$	9.04233	+	2.65507i	0.622499	+	0.182782i	0.577747	−	0.816216i	$-0.303932\pi$
$211$	9.04233	+	2.65507i	0.622499	+	0.182782i	0.0447523	+	0.998998i	$0.485750\pi$
$212$	0.535760	+	0.618300i	0.0367962	+	0.0424650i
$213$	6.97216	−	2.04721i	0.477724	−	0.140273i
$214$	5.79016	+	3.72111i	0.395807	+	0.254370i
$215$	−2.22997	+	4.88295i	−0.152083	+	0.333014i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	−8.47865	+	5.44890i	−0.575568	+	0.369895i
$218$	−0.0532249	−	0.370187i	−0.00360484	−	0.0250722i
$219$	1.31532	+	9.14823i	0.0888809	+	0.618180i
$220$	0.118239	−	0.0759879i	0.00797170	−	0.00512310i
$221$	−3.31544	+	3.82622i	−0.223021	+	0.257380i
$222$	2.69616	−	5.90376i	0.180954	−	0.396235i
$223$	−14.6686	−	9.42697i	−0.982285	−	0.631276i	−0.0522065	−	0.998636i	$-0.516625\pi$
$223$	−14.6686	−	9.42697i	−0.982285	−	0.631276i	−0.930079	+	0.367360i	$0.880262\pi$
$224$	−2.63843	+	0.774713i	−0.176287	+	0.0517627i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−17.9027	−	5.25669i	−1.19087	−	0.349670i
$227$	−1.88163	−	4.12020i	−0.124888	−	0.273467i	0.836852	−	0.547429i	$-0.184393\pi$
$227$	−1.88163	−	4.12020i	−0.124888	−	0.273467i	−0.961741	+	0.273961i	$0.911666\pi$
$228$	0.692086	−	4.81356i	0.0458345	−	0.318786i
$229$	4.65320			0.307492			0.153746	−	0.988110i	$-0.450866\pi$
$229$	4.65320			0.307492			0.153746	+	0.988110i	$0.450866\pi$
$230$	1.58162	−	4.52753i	0.104289	−	0.298536i
$231$	−0.386491			−0.0254292
$232$	1.38777	−	9.65214i	0.0911115	−	0.633694i
$233$	1.25494	+	2.74793i	0.0822136	+	0.180023i	0.946274	−	0.323365i	$-0.104814\pi$
$233$	1.25494	+	2.74793i	0.0822136	+	0.180023i	−0.864061	+	0.503387i	$0.832087\pi$
$234$	4.29746	+	1.26185i	0.280934	+	0.0824897i
$235$	−3.02041	−	3.48574i	−0.197030	−	0.227385i
$236$	2.89441	−	0.849875i	0.188410	−	0.0553222i
$237$	10.3764	+	6.66849i	0.674018	+	0.433165i
$238$	−1.29124	+	2.82743i	−0.0836988	+	0.183275i
$239$	5.55461	−	6.41036i	0.359298	−	0.414652i	−0.547106	−	0.837063i	$-0.684271\pi$
$239$	5.55461	−	6.41036i	0.359298	−	0.414652i	0.906404	+	0.422411i	$0.138816\pi$
$240$	−0.841254	+	0.540641i	−0.0543027	+	0.0348982i
$241$	−1.03161	−	7.17500i	−0.0664518	−	0.462182i	−0.995693	−	0.0927092i	$-0.970447\pi$
$241$	−1.03161	−	7.17500i	−0.0664518	−	0.462182i	0.929241	−	0.369473i	$-0.120462\pi$
$242$	1.56265	+	10.8685i	0.100451	+	0.698652i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	7.69155	−	8.87652i	0.492401	−	0.568261i
$245$	−0.233250	+	0.510747i	−0.0149018	+	0.0326305i
$246$	10.2040	+	6.55770i	0.650582	+	0.418103i
$247$	−20.8988	+	6.13645i	−1.32976	+	0.390453i
$248$	2.40019	+	2.76996i	0.152412	+	0.175893i
$249$	15.4331	+	4.53158i	0.978036	+	0.287177i
$250$	−0.415415	−	0.909632i	−0.0262732	−	0.0575302i
$251$	2.84328	−	19.7755i	0.179467	−	1.24822i	−0.678534	−	0.734569i	$-0.737384\pi$
$251$	2.84328	−	19.7755i	0.179467	−	1.24822i	0.858001	−	0.513648i	$-0.171706\pi$
$252$	2.74982			0.173222
$253$	−0.486498	−	0.466560i	−0.0305859	−	0.0293324i
$254$	−19.2937			−1.21059
$255$	−0.160869	+	1.11887i	−0.0100740	+	0.0700662i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	2.59282	+	0.761322i	0.161736	+	0.0474899i	0.361598	−	0.932334i	$-0.382231\pi$
$257$	2.59282	+	0.761322i	0.161736	+	0.0474899i	−0.199862	+	0.979824i	$0.564049\pi$
$258$	−3.51533	−	4.05690i	−0.218855	−	0.252572i
$259$	−17.1241	+	5.02810i	−1.06404	+	0.312431i
$260$	3.76788	+	2.42147i	0.233674	+	0.150173i
$261$	−4.05088	+	8.87018i	−0.250743	+	0.549051i
$262$	11.3014	−	13.0426i	0.698206	−	0.805772i
$263$	−1.97111	+	1.26676i	−0.121544	+	0.0781116i	−0.600000	−	0.800000i	$-0.704833\pi$
$263$	−1.97111	+	1.26676i	−0.121544	+	0.0781116i	0.478456	+	0.878111i	$0.341197\pi$
$264$	0.0200026	+	0.139121i	0.00123107	+	0.00856230i
$265$	−0.116432	−	0.809801i	−0.00715235	−	0.0497457i
$266$	−11.2497	+	7.22974i	−0.689763	+	0.443284i
$267$	−3.57704	+	4.12812i	−0.218911	+	0.252637i
$268$	−3.36659	+	7.37180i	−0.205647	+	0.450305i
$269$	2.43170	+	1.56276i	0.148263	+	0.0952829i	0.612669	−	0.790339i	$-0.290096\pi$
$269$	2.43170	+	1.56276i	0.148263	+	0.0952829i	−0.464406	+	0.885622i	$0.653732\pi$
$270$	0.959493	−	0.281733i	0.0583929	−	0.0171457i
$271$	−0.708223	−	0.817333i	−0.0430215	−	0.0496494i	0.733831	−	0.679332i	$-0.237730\pi$
$271$	−0.708223	−	0.817333i	−0.0430215	−	0.0496494i	−0.776852	+	0.629683i	$0.783185\pi$
$272$	1.08458	+	0.318463i	0.0657626	+	0.0193096i
$273$	−5.11630	−	11.2031i	−0.309653	−	0.678045i
$274$	−1.10764	+	7.70383i	−0.0669152	+	0.465406i
$275$	−0.140551			−0.00847557
$276$	3.46135	+	3.31949i	0.208349	+	0.199810i
$277$	−10.8637			−0.652739			−0.326370	−	0.945242i	$-0.605825\pi$
$277$	−10.8637			−0.652739			−0.326370	+	0.945242i	$0.605825\pi$
$278$	−2.77305	+	19.2870i	−0.166317	+	1.15676i
$279$	−1.52257	−	3.33397i	−0.0911541	−	0.199600i
$280$	2.63843	+	0.774713i	0.157676	+	0.0462979i
$281$	−3.36030	−	3.87800i	−0.200459	−	0.231342i	0.646616	−	0.762816i	$-0.276184\pi$
$281$	−3.36030	−	3.87800i	−0.200459	−	0.231342i	−0.847075	+	0.531474i	$0.821638\pi$
$282$	4.42547	−	1.29944i	0.263533	−	0.0773803i
$283$	−24.0176	−	15.4352i	−1.42770	−	0.917525i	−0.999907	−	0.0136471i	$-0.995656\pi$
$283$	−24.0176	−	15.4352i	−1.42770	−	0.917525i	−0.427790	−	0.903878i	$-0.640708\pi$
$284$	−3.01861	+	6.60984i	−0.179122	+	0.392222i
$285$	−3.18463	+	3.67526i	−0.188641	+	0.217704i
$286$	0.529582	−	0.340341i	0.0313148	−	0.0201248i
$287$	−4.74675	−	33.0144i	−0.280192	−	1.94878i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−13.2264	+	8.50009i	−0.778024	+	0.500006i
$290$	−6.38581	+	7.36962i	−0.374988	+	0.432759i
$291$	−4.40680	+	9.64954i	−0.258331	+	0.565666i
$292$	−7.77512	−	4.99677i	−0.455005	−	0.292414i
$293$	−3.08111	+	0.904696i	−0.180000	+	0.0528529i	−0.370491	−	0.928836i	$-0.620810\pi$
$293$	−3.08111	+	0.904696i	−0.180000	+	0.0528529i	0.190490	+	0.981689i	$0.438992\pi$
$294$	−0.367696	−	0.424344i	−0.0214445	−	0.0247483i
$295$	−2.89441	−	0.849875i	−0.168519	−	0.0494816i
$296$	2.69616	+	5.90376i	0.156711	+	0.343149i
$297$	0.0200026	−	0.139121i	0.00116067	−	0.00807261i
$298$	2.73028			0.158161
$299$	7.08390	−	20.2783i	0.409672	−	1.17272i
$300$	1.00000			0.0577350
$301$	−2.10073	+	14.6109i	−0.121084	+	0.842159i
$302$	0.0769459	+	0.168488i	0.00442774	+	0.00969540i
$303$	6.27617	+	1.84285i	0.360557	+	0.105869i
$304$	3.18463	+	3.67526i	0.182651	+	0.210791i
$305$	−11.2695	+	3.30904i	−0.645292	+	0.189475i
$306$	−0.950930	−	0.611126i	−0.0543611	−	0.0349357i
$307$	2.17816	−	4.76950i	0.124314	−	0.272210i	−0.837235	−	0.546843i	$-0.815829\pi$
$307$	2.17816	−	4.76950i	0.124314	−	0.272210i	0.961549	+	0.274634i	$0.0885566\pi$
$308$	0.253098	−	0.292090i	0.0144216	−	0.0166434i
$309$	10.6438	−	6.84034i	0.605503	−	0.389133i
$310$	−0.521610	−	3.62788i	−0.0296255	−	0.206050i
$311$	−0.0531382	−	0.369585i	−0.00301319	−	0.0209572i	0.988259	−	0.152785i	$-0.0488244\pi$
$311$	−0.0531382	−	0.369585i	−0.00301319	−	0.0209572i	−0.991273	+	0.131828i	$0.957915\pi$
$312$	−3.76788	+	2.42147i	−0.213314	+	0.137089i
$313$	−10.4650	+	12.0773i	−0.591519	+	0.682649i	−0.970041	−	0.242943i	$-0.921887\pi$
$313$	−10.4650	+	12.0773i	−0.591519	+	0.682649i	0.378522	+	0.925592i	$0.376433\pi$
$314$	−7.77518	+	17.0253i	−0.438779	+	0.960792i
$315$	−2.31329	−	1.48666i	−0.130339	−	0.0837640i
$316$	−11.8348	+	3.47501i	−0.665759	+	0.195484i
$317$	20.0703	+	23.1624i	1.12726	+	1.30093i	0.948408	+	0.317051i	$0.102693\pi$
$317$	20.0703	+	23.1624i	1.12726	+	1.30093i	0.178852	+	0.983876i	$0.442762\pi$
$318$	0.784989	+	0.230493i	0.0440200	+	0.0129254i
$319$	0.569357	+	1.24672i	0.0318779	+	0.0698028i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	6.88278			0.384159
$322$	0.665456	−	13.1709i	0.0370844	−	0.733983i
$323$	5.49708			0.305865
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−1.86060	−	4.07414i	−0.103207	−	0.225993i
$326$	14.2805	+	4.19312i	0.790922	+	0.232236i
$327$	−0.244914	−	0.282646i	−0.0135438	−	0.0156303i
$328$	−11.6382	+	3.41727i	−0.642610	+	0.188687i
$329$	−10.6696	−	6.85694i	−0.588234	−	0.378035i
$330$	0.0583872	−	0.127850i	0.00321411	−	0.00703792i
$331$	−20.4834	+	23.6391i	−1.12587	+	1.29932i	−0.176802	+	0.984246i	$0.556575\pi$
$331$	−20.4834	+	23.6391i	−1.12587	+	1.29932i	−0.949067	+	0.315076i	$0.897970\pi$
$332$	−13.5313	+	8.69604i	−0.742626	+	0.477257i
$333$	−0.923663	−	6.42422i	−0.0506164	−	0.352045i
$334$	2.37519	+	16.5198i	0.129965	+	0.903925i
$335$	6.81765	−	4.38144i	0.372488	−	0.239384i
$336$	−1.80075	+	2.07817i	−0.0982388	+	0.113374i
$337$	1.20760	−	2.64427i	0.0657821	−	0.144043i	−0.873885	−	0.486132i	$-0.838407\pi$
$337$	1.20760	−	2.64427i	0.0657821	−	0.144043i	0.939667	+	0.342090i	$0.111135\pi$
$338$	5.93964	+	3.81718i	0.323074	+	0.207627i
$339$	−17.9027	+	5.25669i	−0.972339	+	0.285504i
$340$	−0.740237	−	0.854279i	−0.0401450	−	0.0463298i
$341$	−0.494280	−	0.145134i	−0.0267668	−	0.00785944i
$342$	−2.02019	−	4.42360i	−0.109239	−	0.239201i
$343$	2.51964	−	17.5245i	0.136048	−	0.946235i
$344$	5.36805			0.289426
$345$	−1.11722	−	4.66388i	−0.0601493	−	0.251095i
$346$	0.514919			0.0276822
$347$	−2.97274	+	20.6759i	−0.159585	+	1.10994i	0.739814	+	0.672811i	$0.234913\pi$
$347$	−2.97274	+	20.6759i	−0.159585	+	1.10994i	−0.899399	+	0.437128i	$0.855996\pi$
$348$	−4.05088	−	8.87018i	−0.217150	−	0.475492i
$349$	−9.93367	−	2.91679i	−0.531737	−	0.156132i	0.00483224	−	0.999988i	$-0.498462\pi$
$349$	−9.93367	−	2.91679i	−0.531737	−	0.156132i	−0.536569	+	0.843856i	$0.680280\pi$
$350$	−1.80075	−	2.07817i	−0.0962539	−	0.111083i
$351$	4.29746	−	1.26185i	0.229382	−	0.0673525i
$352$	−0.118239	−	0.0759879i	−0.00630218	−	0.00405017i
$353$	−7.52924	+	16.4867i	−0.400741	+	0.877501i	0.596453	+	0.802648i	$0.296576\pi$
$353$	−7.52924	+	16.4867i	−0.400741	+	0.877501i	−0.997195	+	0.0748531i	$0.976151\pi$
$354$	1.97545	−	2.27980i	0.104994	−	0.121170i
$355$	6.11297	−	3.92857i	0.324443	−	0.208507i
$356$	−0.777365	−	5.40669i	−0.0412003	−	0.286554i
$357$	0.442360	+	3.07668i	0.0234122	+	0.162835i
$358$	9.18296	−	5.90153i	0.485334	−	0.311905i
$359$	−13.4359	+	15.5059i	−0.709121	+	0.818369i	−0.989954	−	0.141387i	$-0.954844\pi$
$359$	−13.4359	+	15.5059i	−0.709121	+	0.818369i	0.280833	+	0.959757i	$0.409389\pi$
$360$	−0.415415	+	0.909632i	−0.0218943	+	0.0479418i
$361$	3.91131	+	2.51365i	0.205859	+	0.132297i
$362$	15.7850	−	4.63489i	0.829640	−	0.243604i
$363$	7.19053	+	8.29832i	0.377405	+	0.435549i
$364$	11.8172	+	3.46985i	0.619392	+	0.181870i
$365$	3.83939	+	8.40710i	0.200963	+	0.440048i
$366$	1.67153	−	11.6258i	0.0873724	−	0.607688i
$367$	3.38363			0.176624			0.0883119	−	0.996093i	$-0.471853\pi$
$367$	3.38363			0.176624			0.0883119	+	0.996093i	$0.471853\pi$
$368$	−4.77541	+	0.442111i	−0.248935	+	0.0230467i
$369$	12.1295			0.631436
$370$	0.923663	−	6.42422i	0.0480189	−	0.333979i
$371$	−0.934561	−	2.04640i	−0.0485200	−	0.106244i
$372$	3.51672	+	1.03260i	0.182333	+	0.0535379i
$373$	−5.23299	−	6.03919i	−0.270954	−	0.312697i	0.603923	−	0.797042i	$-0.293603\pi$
$373$	−5.23299	−	6.03919i	−0.270954	−	0.312697i	−0.874877	+	0.484345i	$0.839058\pi$
$374$	−0.152440	+	0.0447604i	−0.00788249	+	0.00231451i
$375$	−0.841254	−	0.540641i	−0.0434421	−	0.0279186i
$376$	−1.91602	+	4.19550i	−0.0988111	+	0.216366i
$377$	−28.6013	+	33.0077i	−1.47304	+	1.69998i
$378$	2.31329	−	1.48666i	0.118983	−	0.0764657i
$379$	−1.30600	−	9.08346i	−0.0670849	−	0.466586i	−0.995478	−	0.0949874i	$-0.969719\pi$
$379$	−1.30600	−	9.08346i	−0.0670849	−	0.466586i	0.928394	−	0.371598i	$-0.121190\pi$
$380$	−0.692086	−	4.81356i	−0.0355033	−	0.246931i
$381$	−16.2309	+	10.4310i	−0.831534	+	0.534394i
$382$	−2.35172	+	2.71403i	−0.120325	+	0.138862i
$383$	−3.77911	+	8.27509i	−0.193103	+	0.422837i	−0.981273	−	0.192620i	$-0.938301\pi$
$383$	−3.77911	+	8.27509i	−0.193103	+	0.422837i	0.788170	+	0.615457i	$0.211029\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	−0.370835	+	0.108887i	−0.0188995	+	0.00554940i
$386$	−4.45883	−	5.14576i	−0.226948	−	0.261912i
$387$	−5.15061	−	1.51235i	−0.261820	−	0.0768773i
$388$	−4.40680	−	9.64954i	−0.223721	−	0.489881i
$389$	3.81746	−	26.5510i	0.193553	−	1.34619i	−0.628958	−	0.777439i	$-0.716518\pi$
$389$	3.81746	−	26.5510i	0.193553	−	1.34619i	0.822511	−	0.568750i	$-0.192573\pi$
$390$	4.47889			0.226797
$391$	−3.15725	+	4.40680i	−0.159669	+	0.222861i
$392$	0.561488			0.0283594
$393$	2.45604	−	17.0821i	0.123891	−	0.861679i
$394$	3.41645	+	7.48097i	0.172118	+	0.376886i
$395$	11.8348	+	3.47501i	0.595473	+	0.174847i
$396$	0.0920417	+	0.106222i	0.00462527	+	0.00533784i
$397$	3.23465	−	0.949778i	0.162342	−	0.0476680i	−0.199551	−	0.979887i	$-0.563949\pi$
$397$	3.23465	−	0.949778i	0.162342	−	0.0476680i	0.361894	+	0.932219i	$0.382130\pi$
$398$	1.69537	+	1.08955i	0.0849811	+	0.0546140i
$399$	−5.55515	+	12.1641i	−0.278105	+	0.608966i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	26.4736	−	17.0136i	1.32203	−	0.849617i	0.326604	−	0.945161i	$-0.394096\pi$
$401$	26.4736	−	17.0136i	1.32203	−	0.849617i	0.995425	+	0.0955448i	$0.0304593\pi$
$402$	1.15334	+	8.02167i	0.0575235	+	0.400085i
$403$	−2.33624	−	16.2489i	−0.116376	−	0.809414i
$404$	−5.50275	+	3.53640i	−0.273772	+	0.175943i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	−11.1392	+	24.3914i	−0.552828	+	1.21052i
$407$	−0.767407	−	0.493182i	−0.0380389	−	0.0244461i
$408$	1.08458	−	0.318463i	0.0536950	−	0.0157663i
$409$	−4.65115	−	5.36771i	−0.229985	−	0.265416i	0.629014	−	0.777394i	$-0.283459\pi$
$409$	−4.65115	−	5.36771i	−0.229985	−	0.265416i	−0.858999	+	0.511977i	$0.828913\pi$
$410$	11.6382	+	3.41727i	0.574768	+	0.168767i
$411$	3.23320	+	7.07971i	0.159482	+	0.349217i
$412$	−1.80061	+	12.5235i	−0.0887096	+	0.616989i
$413$	−8.29510			−0.408175
$414$	4.70653	+	0.921186i	0.231313	+	0.0452738i
$415$	16.0847			0.789566
$416$	0.637413	−	4.43330i	0.0312517	−	0.217361i
$417$	8.09451	+	17.7245i	0.396390	+	0.867973i
$418$	−0.655824	−	0.192567i	−0.0320774	−	0.00941877i
$419$	−14.9641	−	17.2695i	−0.731044	−	0.843669i	0.261545	−	0.965191i	$-0.415768\pi$
$419$	−14.9641	−	17.2695i	−0.731044	−	0.843669i	−0.992589	+	0.121522i	$0.961223\pi$
$420$	2.63843	−	0.774713i	0.128742	−	0.0378021i
$421$	8.89816	+	5.71850i	0.433670	+	0.278703i	0.739208	−	0.673477i	$-0.235200\pi$
$421$	8.89816	+	5.71850i	0.433670	+	0.278703i	−0.305538	+	0.952180i	$0.598836\pi$
$422$	−3.91490	+	8.57243i	−0.190574	+	0.417300i
$423$	3.02041	−	3.48574i	0.146858	−	0.169483i
$424$	−0.688254	+	0.442314i	−0.0334246	+	0.0214807i
$425$	0.160869	+	1.11887i	0.00780329	+	0.0542730i
$426$	1.03413	+	7.19254i	0.0501038	+	0.348480i
$427$	−27.1703	+	17.4613i	−1.31487	+	0.845013i
$428$	−4.50726	+	5.20165i	−0.217867	+	0.251431i
$429$	0.261510	−	0.572627i	0.0126258	−	0.0276467i
$430$	−4.51589	−	2.90219i	−0.217776	−	0.139956i
$431$	−34.5933	+	10.1575i	−1.66630	+	0.489270i	−0.972889	−	0.231273i	$-0.925711\pi$
$431$	−34.5933	+	10.1575i	−1.66630	+	0.489270i	−0.693410	+	0.720543i	$0.743893\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	−35.2234	−	10.3425i	−1.69273	−	0.497030i	−0.713648	−	0.700504i	$-0.752958\pi$
$433$	−35.2234	−	10.3425i	−1.69273	−	0.497030i	−0.979080	+	0.203474i	$0.934777\pi$
$434$	−4.18680	−	9.16781i	−0.200973	−	0.440069i
$435$	−1.38777	+	9.65214i	−0.0665384	+	0.462785i
$436$	0.373994			0.0179111
$437$	−21.6767	+	8.60563i	−1.03694	+	0.411663i
$438$	−9.24231			−0.441614
$439$	−0.513135	+	3.56893i	−0.0244906	+	0.170336i	−0.998396	−	0.0566191i	$-0.981968\pi$
$439$	−0.513135	+	3.56893i	−0.0244906	+	0.170336i	0.973905	+	0.226955i	$0.0728770\pi$
$440$	0.0583872	+	0.127850i	0.00278350	+	0.00609502i
$441$	−0.538744	−	0.158189i	−0.0256545	−	0.00753283i
$442$	−3.31544	−	3.82622i	−0.157699	−	0.181995i
$443$	34.4981	−	10.1296i	1.63905	−	0.481270i	0.673008	−	0.739636i	$-0.265002\pi$
$443$	34.4981	−	10.1296i	1.63905	−	0.481270i	0.966047	+	0.258366i	$0.0831840\pi$
$444$	5.45997	+	3.50891i	0.259119	+	0.166525i
$445$	−2.26912	+	4.96867i	−0.107566	+	0.235538i
$446$	11.4186	−	13.1777i	0.540686	−	0.623984i
$447$	2.29686	−	1.47610i	0.108638	−	0.0698173i
$448$	−0.391340	−	2.72183i	−0.0184891	−	0.128594i
$449$	−0.300298	−	2.08862i	−0.0141720	−	0.0985681i	0.981508	−	0.191422i	$-0.0613100\pi$
$449$	−0.300298	−	2.08862i	−0.0141720	−	0.0985681i	−0.995680	+	0.0928543i	$0.970401\pi$
$450$	0.841254	−	0.540641i	0.0396571	−	0.0254861i
$451$	1.11642	−	1.28842i	0.0525701	−	0.0606691i
$452$	7.75100	−	16.9723i	0.364577	−	0.798311i
$453$	0.155823	+	0.100141i	0.00732118	+	0.00470504i
$454$	4.34604	−	1.27611i	0.203970	−	0.0598910i
$455$	−8.06535	−	9.30791i	−0.378109	−	0.436361i
$456$	4.66608	+	1.37008i	0.218509	+	0.0641600i
$457$	5.96259	+	13.0563i	0.278918	+	0.610746i	0.996301	−	0.0859335i	$-0.0273873\pi$
$457$	5.96259	+	13.0563i	0.278918	+	0.610746i	−0.717383	+	0.696679i	$0.754660\pi$
$458$	−0.662220	+	4.60584i	−0.0309435	+	0.215217i
$459$	−1.13037			−0.0527613
$460$	4.25635	+	2.20985i	0.198454	+	0.103035i
$461$	−31.8633			−1.48402			−0.742011	−	0.670388i	$-0.766128\pi$
$461$	−31.8633			−1.48402			−0.742011	+	0.670388i	$0.766128\pi$
$462$	0.0550034	−	0.382557i	0.00255899	−	0.0177982i
$463$	1.72985	+	3.78783i	0.0803928	+	0.176036i	0.945560	−	0.325448i	$-0.105515\pi$
$463$	1.72985	+	3.78783i	0.0803928	+	0.176036i	−0.865167	+	0.501484i	$0.832788\pi$
$464$	9.35640	+	2.74729i	0.434360	+	0.127540i
$465$	−2.40019	−	2.76996i	−0.111306	−	0.128454i
$466$	−2.89855	+	0.851091i	−0.134273	+	0.0394260i
$467$	−4.64280	−	2.98375i	−0.214843	−	0.138071i	0.428793	−	0.903403i	$-0.358939\pi$
$467$	−4.64280	−	2.98375i	−0.214843	−	0.138071i	−0.643637	+	0.765331i	$0.722575\pi$
$468$	−1.86060	+	4.07414i	−0.0860062	+	0.188327i
$469$	14.5935	−	16.8418i	0.673867	−	0.777684i
$470$	3.88011	−	2.49360i	0.178976	−	0.115021i
$471$	2.66366	+	18.5262i	0.122735	+	0.853640i
$472$	0.429307	+	2.98590i	0.0197605	+	0.137437i
$473$	−0.634715	+	0.407907i	−0.0291842	+	0.0187556i
$474$	−8.07733	+	9.32173i	−0.371004	+	0.428161i
$475$	−2.02019	+	4.42360i	−0.0926927	+	0.202969i
$476$	−2.61488	−	1.68048i	−0.119853	−	0.0770248i
$477$	0.784989	−	0.230493i	0.0359422	−	0.0105536i
$478$	5.55461	+	6.41036i	0.254062	+	0.293203i
$479$	14.6140	+	4.29107i	0.667733	+	0.196064i	0.597993	−	0.801501i	$-0.295965\pi$
$479$	14.6140	+	4.29107i	0.667733	+	0.196064i	0.0697396	+	0.997565i	$0.477783\pi$
$480$	−0.415415	−	0.909632i	−0.0189610	−	0.0415188i
$481$	4.13699	−	28.7734i	0.188630	−	1.31195i
$482$	7.24878			0.330173
$483$	−6.56088	−	11.4398i	−0.298531	−	0.520529i
$484$	−10.9802			−0.499102
$485$	−1.50970	+	10.5002i	−0.0685520	+	0.476790i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	−19.0807	−	5.60261i	−0.864630	−	0.253878i	−0.180800	−	0.983520i	$-0.557869\pi$
$487$	−19.0807	−	5.60261i	−0.864630	−	0.253878i	−0.683830	+	0.729642i	$0.739687\pi$
$488$	7.69155	+	8.87652i	0.348180	+	0.401821i
$489$	14.2805	−	4.19312i	0.645785	−	0.189620i
$490$	−0.472354	−	0.303563i	−0.0213388	−	0.0137136i
$491$	4.10183	−	8.98176i	0.185113	−	0.405341i	−0.794210	−	0.607643i	$-0.792115\pi$
$491$	4.10183	−	8.98176i	0.185113	−	0.405341i	0.979323	+	0.202302i	$0.0648423\pi$
$492$	−7.94313	+	9.16686i	−0.358104	+	0.413274i
$493$	9.27290	−	5.95933i	0.417630	−	0.268395i
$494$	−3.09978	−	21.5594i	−0.139466	−	0.970005i
$495$	−0.0200026	−	0.139121i	−0.000899048	−	0.00625302i
$496$	−3.08335	+	1.98155i	−0.138447	+	0.0889742i
$497$	13.0851	−	15.1010i	0.586948	−	0.677374i
$498$	−6.68182	+	14.6311i	−0.299419	+	0.655637i
$499$	−8.69043	−	5.58500i	−0.389037	−	0.250019i	0.331471	−	0.943465i	$-0.392455\pi$
$499$	−8.69043	−	5.58500i	−0.389037	−	0.250019i	−0.720508	+	0.693446i	$0.756091\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	10.9294	+	12.6132i	0.488291	+	0.563518i
$502$	19.1696	+	5.62869i	0.855579	+	0.251221i
$503$	3.16542	+	6.93131i	0.141139	+	0.309052i	0.966980	−	0.254851i	$-0.0820265\pi$
$503$	3.16542	+	6.93131i	0.141139	+	0.309052i	−0.825841	+	0.563903i	$0.809299\pi$
$504$	−0.391340	+	2.72183i	−0.0174317	+	0.121240i
$505$	6.54113			0.291077
$506$	0.531047	−	0.415148i	0.0236079	−	0.0184556i
$507$	7.06047			0.313566
$508$	2.74578	−	19.0973i	0.121824	−	0.847306i
$509$	16.9220	+	37.0540i	0.750053	+	1.64239i	0.766269	+	0.642520i	$0.222111\pi$
$509$	16.9220	+	37.0540i	0.750053	+	1.64239i	−0.0162158	+	0.999869i	$0.505162\pi$
$510$	−1.08458	−	0.318463i	−0.0480262	−	0.0141018i
$511$	16.6431	+	19.2071i	0.736245	+	0.849672i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−4.09107	−	2.62917i	−0.180625	−	0.116081i
$514$	−1.12257	+	2.45809i	−0.0495144	+	0.108421i
$515$	8.28548	−	9.56196i	0.365102	−	0.421350i
$516$	4.51589	−	2.90219i	0.198801	−	0.127762i
$517$	−0.0922578	−	0.641667i	−0.00405750	−	0.0282205i
$518$	−2.53990	−	17.6654i	−0.111597	−	0.776174i
$519$	0.433178	−	0.278386i	0.0190144	−	0.0122198i
$520$	−2.93305	+	3.38492i	−0.128623	+	0.148439i
$521$	−12.2855	+	26.9015i	−0.538238	+	1.17858i	0.423824	+	0.905745i	$0.360688\pi$
$521$	−12.2855	+	26.9015i	−0.538238	+	1.17858i	−0.962062	+	0.272832i	$0.912040\pi$
$522$	−8.20340	−	5.27200i	−0.359053	−	0.230749i
$523$	2.39105	−	0.702074i	0.104553	−	0.0306996i	−0.229038	−	0.973418i	$-0.573558\pi$
$523$	2.39105	−	0.702074i	0.104553	−	0.0306996i	0.333591	+	0.942718i	$0.391740\pi$
$524$	11.3014	+	13.0426i	0.493706	+	0.569767i
$525$	−2.63843	−	0.774713i	−0.115150	−	0.0338112i
$526$	−0.973345	−	2.13133i	−0.0424398	−	0.0929303i
$527$	−0.589614	+	4.10086i	−0.0256840	+	0.178636i
$528$	−0.140551			−0.00611672
$529$	5.55120	−	22.3200i	0.241357	−	0.970436i
$530$	0.818129			0.0355372
$531$	0.429307	−	2.98590i	0.0186303	−	0.129577i
$532$	−5.55515	−	12.1641i	−0.240846	−	0.527380i
$533$	52.1260	+	15.3056i	2.25783	+	0.662959i
$534$	−3.57704	−	4.12812i	−0.154794	−	0.178641i
$535$	6.60397	−	1.93910i	0.285515	−	0.0838347i
$536$	−6.81765	−	4.38144i	−0.294478	−	0.189249i
$537$	4.53459	−	9.92936i	0.195682	−	0.428484i
$538$	−1.89292	+	2.18454i	−0.0816094	+	0.0941823i
$539$	−0.0663900	+	0.0426663i	−0.00285962	+	0.00183777i
$540$	0.142315	+	0.989821i	0.00612426	+	0.0425951i
$541$	3.87766	+	26.9697i	0.166714	+	1.15952i	0.885620	+	0.464411i	$0.153734\pi$
$541$	3.87766	+	26.9697i	0.166714	+	1.15952i	−0.718906	+	0.695107i	$0.755357\pi$
$542$	0.909804	−	0.584696i	0.0390794	−	0.0251148i
$543$	10.7734	−	12.4331i	0.462329	−	0.533556i
$544$	−0.469574	+	1.02822i	−0.0201328	+	0.0440847i
$545$	−0.314624	−	0.202196i	−0.0134770	−	0.00866114i
$546$	11.8172	−	3.46985i	0.505731	−	0.148496i
$547$	−5.22164	−	6.02610i	−0.223261	−	0.257657i	0.633058	−	0.774105i	$-0.281800\pi$
$547$	−5.22164	−	6.02610i	−0.223261	−	0.257657i	−0.856319	+	0.516447i	$0.827254\pi$
$548$	−7.46779	−	2.19274i	−0.319008	−	0.0936692i
$549$	−4.87918	−	10.6839i	−0.208238	−	0.455978i
$550$	0.0200026	−	0.139121i	0.000852912	−	0.00593213i
$551$	47.4217			2.02023
$552$	−3.77831	+	2.95371i	−0.160815	+	0.125718i
$553$	33.9174			1.44231
$554$	1.54607	−	10.7532i	0.0656863	−	0.456858i
$555$	−2.69616	−	5.90376i	−0.114446	−	0.250601i
$556$	−18.6961	−	5.48966i	−0.792890	−	0.232813i
$557$	−17.8270	−	20.5734i	−0.755352	−	0.871723i	0.239724	−	0.970841i	$-0.422943\pi$
$557$	−17.8270	−	20.5734i	−0.755352	−	0.871723i	−0.995076	+	0.0991184i	$0.968398\pi$
$558$	3.51672	−	1.03260i	0.148875	−	0.0437135i
$559$	−20.2262	−	12.9986i	−0.855477	−	0.549781i
$560$	−1.14231	+	2.50132i	−0.0482716	+	0.105700i
$561$	−0.104041	+	0.120070i	−0.00439263	+	0.00506937i
$562$	4.31675	−	2.77420i	0.182091	−	0.117023i
$563$	−6.18173	−	42.9949i	−0.260529	−	1.81202i	−0.528878	−	0.848698i	$-0.677387\pi$
$563$	−6.18173	−	42.9949i	−0.260529	−	1.81202i	0.268349	−	0.963322i	$-0.413522\pi$
$564$	0.656399	+	4.56535i	0.0276394	+	0.192236i
$565$	−15.6965	+	10.0875i	−0.660356	+	0.424385i
$566$	18.6961	−	21.5765i	0.785856	−	0.906926i
$567$	1.14231	−	2.50132i	0.0479727	−	0.105046i
$568$	−6.11297	−	3.92857i	−0.256494	−	0.164839i
$569$	−12.9805	+	3.81141i	−0.544170	+	0.159783i	−0.542253	−	0.840215i	$-0.682429\pi$
$569$	−12.9805	+	3.81141i	−0.544170	+	0.159783i	−0.00191738	+	0.999998i	$0.500610\pi$
$570$	−3.18463	−	3.67526i	−0.133389	−	0.153940i
$571$	27.1660	+	7.97666i	1.13686	+	0.333813i	0.795401	−	0.606083i	$-0.207260\pi$
$571$	27.1660	+	7.97666i	1.13686	+	0.333813i	0.341461	+	0.939896i	$0.389078\pi$
$572$	0.261510	+	0.572627i	0.0109343	+	0.0239427i
$573$	−0.511079	+	3.55463i	−0.0213506	+	0.148497i
$574$	33.3539			1.39216
$575$	−2.38594	−	4.16021i	−0.0995004	−	0.173493i
$576$	1.00000			0.0416667
$577$	3.53868	−	24.6121i	0.147317	−	1.02461i	−0.773270	−	0.634077i	$-0.781380\pi$
$577$	3.53868	−	24.6121i	0.147317	−	1.02461i	0.920587	−	0.390537i	$-0.127711\pi$
$578$	−6.53126	−	14.3015i	−0.271665	−	0.594863i
$579$	−6.53301	−	1.91826i	−0.271503	−	0.0797204i
$580$	−6.38581	−	7.36962i	−0.265156	−	0.306007i
$581$	42.4383	−	12.4610i	1.76064	−	0.516970i
$582$	−8.92417	−	5.73522i	−0.369919	−	0.237732i
$583$	0.0477682	−	0.104598i	0.00197836	−	0.00433200i
$584$	6.05242	−	6.98487i	0.250451	−	0.289036i
$585$	3.76788	−	2.42147i	0.155783	−	0.100116i
$586$	−0.457000	−	3.17850i	−0.0188785	−	0.131303i
$587$	−2.91282	−	20.2591i	−0.120225	−	0.836183i	−0.957300	−	0.289095i	$-0.906646\pi$
$587$	−2.91282	−	20.2591i	−0.120225	−	0.836183i	0.837075	−	0.547087i	$-0.184263\pi$
$588$	0.472354	−	0.303563i	0.0194795	−	0.0125187i
$589$	−11.6723	+	13.4705i	−0.480947	+	0.555043i
$590$	1.25314	−	2.74400i	0.0515910	−	0.112969i
$591$	6.91862	+	4.44633i	0.284594	+	0.182897i
$592$	−6.22738	+	1.82852i	−0.255944	+	0.0751518i
$593$	19.1744	+	22.1284i	0.787398	+	0.908706i	0.997620	−	0.0689475i	$-0.0219641\pi$
$593$	19.1744	+	22.1284i	0.787398	+	0.908706i	−0.210222	+	0.977654i	$0.567419\pi$
$594$	0.134858	+	0.0395979i	0.00553330	+	0.00162472i
$595$	1.29124	+	2.82743i	0.0529358	+	0.115913i
$596$	−0.388560	+	2.70249i	−0.0159160	+	0.110698i
$597$	2.01529			0.0824802
$598$	19.0637	+	9.89769i	0.779575	+	0.404747i
$599$	8.58343			0.350709			0.175355	−	0.984505i	$-0.443893\pi$
$599$	8.58343			0.350709			0.175355	+	0.984505i	$0.443893\pi$
$600$	−0.142315	+	0.989821i	−0.00580998	+	0.0404093i
$601$	−6.85536	−	15.0111i	−0.279636	−	0.612317i	0.716743	−	0.697337i	$-0.245632\pi$
$601$	−6.85536	−	15.0111i	−0.279636	−	0.612317i	−0.996379	+	0.0850198i	$0.972905\pi$
$602$	−14.1632	−	4.15870i	−0.577250	−	0.169496i
$603$	5.30710	+	6.12472i	0.216122	+	0.249418i
$604$	−0.177724	+	0.0521844i	−0.00723147	+	0.00212335i
$605$	9.23717	+	5.93637i	0.375544	+	0.241348i
$606$	−2.71728	+	5.95002i	−0.110382	+	0.241703i
$607$	−24.4132	+	28.1744i	−0.990902	+	1.14356i	−0.00126060	+	0.999999i	$0.500401\pi$
$607$	−24.4132	+	28.1744i	−0.990902	+	1.14356i	−0.989641	+	0.143562i	$0.954144\pi$
$608$	−4.09107	+	2.62917i	−0.165915	+	0.106627i
$609$	3.81611	+	26.5416i	0.154637	+	1.07552i
$610$	−1.67153	−	11.6258i	−0.0676784	−	0.470713i
$611$	17.3786	−	11.1686i	0.703063	−	0.451831i
$612$	0.740237	−	0.854279i	0.0299223	−	0.0345322i
$613$	−6.12978	+	13.4223i	−0.247579	+	0.542123i	−0.992096	−	0.125481i	$-0.959953\pi$
$613$	−6.12978	+	13.4223i	−0.247579	+	0.542123i	0.744517	+	0.667604i	$0.232680\pi$
$614$	4.41097	+	2.83476i	0.178012	+	0.114401i
$615$	11.6382	−	3.41727i	0.469296	−	0.137798i
$616$	0.253098	+	0.292090i	0.0101976	+	0.0117687i
$617$	−4.86024	−	1.42709i	−0.195666	−	0.0574527i	0.182431	−	0.983219i	$-0.441603\pi$
$617$	−4.86024	−	1.42709i	−0.195666	−	0.0574527i	−0.378097	+	0.925766i	$0.623421\pi$
$618$	5.25595	+	11.5089i	0.211425	+	0.462957i
$619$	5.17339	−	35.9817i	0.207936	−	1.44623i	−0.571942	−	0.820294i	$-0.693810\pi$
$619$	5.17339	−	35.9817i	0.207936	−	1.44623i	0.779878	−	0.625932i	$-0.215281\pi$
$620$	3.66519			0.147197
$621$	4.45741	−	1.76959i	0.178870	−	0.0710112i
$622$	0.373385			0.0149714
$623$	−2.13761	+	14.8674i	−0.0856415	+	0.595650i
$624$	−1.86060	−	4.07414i	−0.0744836	−	0.163096i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	−10.4650	−	12.0773i	−0.418267	−	0.482706i
$627$	−0.655824	+	0.192567i	−0.0261911	+	0.00769040i
$628$	−15.7455	−	10.1190i	−0.628312	−	0.403792i
$629$	−3.04767	+	6.67346i	−0.121518	+	0.266088i
$630$	1.80075	−	2.07817i	0.0717435	−	0.0827964i
$631$	−7.18211	+	4.61566i	−0.285915	+	0.183747i	−0.675735	−	0.737145i	$-0.736174\pi$
$631$	−7.18211	+	4.61566i	−0.285915	+	0.183747i	0.389820	+	0.920891i	$0.372537\pi$
$632$	−1.75537	−	12.2089i	−0.0698249	−	0.485643i
$633$	1.34118	+	9.32814i	0.0533073	+	0.370760i
$634$	−25.7829	+	16.5697i	−1.02397	+	0.658065i
$635$	−12.6347	+	14.5812i	−0.501392	+	0.578637i
$636$	−0.339863	+	0.744196i	−0.0134764	+	0.0295093i
$637$	−2.11562	−	1.35963i	−0.0838239	−	0.0538704i
$638$	−1.31506	+	0.386135i	−0.0520636	+	0.0152872i
$639$	4.75855	+	5.49165i	0.188245	+	0.217247i
$640$	0.959493	+	0.281733i	0.0379273	+	0.0111365i
$641$	−18.2516	−	39.9655i	−0.720896	−	1.57854i	−0.812644	−	0.582760i	$-0.801973\pi$
$641$	−18.2516	−	39.9655i	−0.720896	−	1.57854i	0.0917485	−	0.995782i	$-0.470754\pi$
$642$	−0.979521	+	6.81272i	−0.0386586	+	0.268877i
$643$	−11.5862			−0.456914			−0.228457	−	0.973554i	$-0.573368\pi$
$643$	−11.5862			−0.456914			−0.228457	+	0.973554i	$0.573368\pi$
$644$	12.9421	+	2.53309i	0.509990	+	0.0998178i
$645$	−5.36805			−0.211367
$646$	−0.782315	+	5.44112i	−0.0307798	+	0.214078i
$647$	17.7297	+	38.8226i	0.697026	+	1.52627i	0.843541	+	0.537065i	$0.180467\pi$
$647$	17.7297	+	38.8226i	0.697026	+	1.52627i	−0.146515	+	0.989208i	$0.546806\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−0.277653	−	0.320429i	−0.0108988	−	0.0125779i
$650$	4.29746	−	1.26185i	0.168560	−	0.0494938i
$651$	−8.47865	−	5.44890i	−0.332304	−	0.213559i
$652$	−6.18276	+	13.5384i	−0.242136	+	0.530203i
$653$	−27.1940	+	31.3836i	−1.06418	+	1.22813i	−0.0915482	+	0.995801i	$0.529182\pi$
$653$	−27.1940	+	31.3836i	−1.06418	+	1.22813i	−0.972636	+	0.232334i	$0.925364\pi$
$654$	0.314624	−	0.202196i	0.0123028	−	0.00790650i
$655$	−2.45604	−	17.0821i	−0.0959654	−	0.667454i
$656$	−1.72621	−	12.0060i	−0.0673970	−	0.468757i
$657$	−7.77512	+	4.99677i	−0.303336	+	0.194942i
$658$	8.30559	−	9.58516i	0.323785	−	0.373668i
$659$	12.4565	−	27.2759i	0.485236	−	1.06252i	−0.495755	−	0.868463i	$-0.665108\pi$
$659$	12.4565	−	27.2759i	0.485236	−	1.06252i	0.980991	−	0.194056i	$-0.0621643\pi$
$660$	0.118239	+	0.0759879i	0.00460246	+	0.00295782i
$661$	45.5770	−	13.3826i	1.77274	−	0.520523i	0.778493	−	0.627653i	$-0.215984\pi$
$661$	45.5770	−	13.3826i	1.77274	−	0.520523i	0.994245	+	0.107130i	$0.0341661\pi$
$662$	−20.4834	−	23.6391i	−0.796110	−	0.918759i
$663$	−4.85774	−	1.42636i	−0.188659	−	0.0553953i
$664$	−6.68182	−	14.6311i	−0.259305	−	0.567799i
$665$	−1.90311	+	13.2364i	−0.0737994	+	0.513286i
$666$	6.49028			0.251493
$667$	−27.2367	+	38.0162i	−1.05461	+	1.47199i
$668$	−16.6897			−0.645744
$669$	2.48149	−	17.2592i	0.0959401	−	0.667278i
$670$	3.36659	+	7.37180i	0.130063	+	0.284798i
$671$	−1.58395	−	0.465090i	−0.0611478	−	0.0179546i
$672$	−1.80075	−	2.07817i	−0.0694653	−	0.0801672i
$673$	−6.90082	+	2.02626i	−0.266007	+	0.0781067i	−0.412016	−	0.911177i	$-0.635175\pi$
$673$	−6.90082	+	2.02626i	−0.266007	+	0.0781067i	0.146009	+	0.989283i	$0.453357\pi$
$674$	2.44550	+	1.57163i	0.0941971	+	0.0605368i
$675$	0.415415	−	0.909632i	0.0159893	−	0.0350118i
$676$	−4.62362	+	5.33595i	−0.177832	+	0.205229i
$677$	27.7557	−	17.8375i	1.06674	−	0.685551i	0.115282	−	0.993333i	$-0.463223\pi$
$677$	27.7557	−	17.8375i	1.06674	−	0.685551i	0.951457	+	0.307782i	$0.0995866\pi$
$678$	−2.65538	−	18.4685i	−0.101979	−	0.709280i
$679$	4.15140	+	28.8736i	0.159316	+	1.10807i
$680$	0.950930	−	0.611126i	0.0364665	−	0.0234356i
$681$	2.96621	−	3.42318i	0.113665	−	0.131177i
$682$	0.214000	−	0.468595i	0.00819448	−	0.0179434i
$683$	−7.44885	−	4.78709i	−0.285022	−	0.183173i	0.390316	−	0.920681i	$-0.372366\pi$
$683$	−7.44885	−	4.78709i	−0.285022	−	0.183173i	−0.675338	+	0.737508i	$0.736002\pi$
$684$	4.66608	−	1.37008i	0.178412	−	0.0523864i
$685$	5.09682	+	5.88204i	0.194739	+	0.224741i
$686$	16.9876	+	4.98800i	0.648588	+	0.190443i
$687$	1.93301	+	4.23270i	0.0737490	+	0.161488i
$688$	−0.763953	+	5.31341i	−0.0291254	+	0.202572i
$689$	3.66431			0.139599
$690$	4.77541	−	0.442111i	0.181797	−	0.0168309i
$691$	49.3593			1.87772			0.938859	−	0.344303i	$-0.111885\pi$
$691$	49.3593			1.87772			0.938859	+	0.344303i	$0.111885\pi$
$692$	−0.0732807	+	0.509678i	−0.00278571	+	0.0193751i
$693$	−0.160554	−	0.351564i	−0.00609894	−	0.0133548i
$694$	−20.0424	−	5.88497i	−0.760797	−	0.223390i
$695$	12.7602	+	14.7260i	0.484022	+	0.558591i
$696$	9.35640	−	2.74729i	0.354653	−	0.104136i
$697$	−11.5343	−	7.41264i	−0.436893	−	0.280774i
$698$	4.30081	−	9.41746i	0.162788	−	0.356456i
$699$	−1.97828	+	2.28306i	−0.0748255	+	0.0863532i
$700$	2.31329	−	1.48666i	0.0874342	−	0.0561906i
$701$	0.255722	+	1.77858i	0.00965848	+	0.0671762i	0.994081	−	0.108645i	$-0.0346511\pi$
$701$	0.255722	+	1.77858i	0.00965848	+	0.0671762i	−0.984422	+	0.175821i	$0.943742\pi$
$702$	0.637413	+	4.43330i	0.0240576	+	0.167324i
$703$	−26.5522	+	17.0640i	−1.00143	+	0.643583i
$704$	0.0920417	−	0.106222i	0.00346895	−	0.00400338i
$705$	1.91602	−	4.19550i	0.0721615	−	0.158012i
$706$	−15.2474	−	9.79892i	−0.573844	−	0.368787i
$707$	17.2583	−	5.06750i	0.649066	−	0.190583i
$708$	1.97545	+	2.27980i	0.0742421	+	0.0856800i
$709$	35.8509	+	10.5268i	1.34641	+	0.395342i	0.873952	−	0.486012i	$-0.161549\pi$
$709$	35.8509	+	10.5268i	1.34641	+	0.395342i	0.472458	+	0.881353i	$0.343367\pi$
$710$	3.01861	+	6.60984i	0.113287	+	0.248063i
$711$	−1.75537	+	12.2089i	−0.0658315	+	0.457868i
$712$	5.46229			0.204708
$713$	−4.09483	−	17.0940i	−0.153353	−	0.640176i
$714$	−3.10832			−0.116326
$715$	0.0895893	−	0.623107i	0.00335045	−	0.0233029i
$716$	4.53459	+	9.92936i	0.169466	+	0.371078i
$717$	8.13854	+	2.38969i	0.303939	+	0.0892446i
$718$	−13.4359	−	15.5059i	−0.501424	−	0.578675i
$719$	−14.1239	+	4.14714i	−0.526731	+	0.154662i	−0.534277	−	0.845309i	$-0.679416\pi$
$719$	−14.1239	+	4.14714i	−0.526731	+	0.154662i	0.00754601	+	0.999972i	$0.497598\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	14.4529	−	31.6474i	0.538254	−	1.17861i
$722$	−3.04470	+	3.51377i	−0.113312	+	0.130769i
$723$	6.09806	−	3.91899i	0.226789	−	0.145749i
$724$	2.34127	+	16.2839i	0.0870127	+	0.605187i
$725$	1.38777	+	9.65214i	0.0515404	+	0.358472i
$726$	−9.23717	+	5.93637i	−0.342824	+	0.220319i
$727$	−1.45577	+	1.68004i	−0.0539914	+	0.0623094i	−0.782103	−	0.623149i	$-0.785853\pi$
$727$	−1.45577	+	1.68004i	−0.0539914	+	0.0623094i	0.728111	+	0.685459i	$0.240398\pi$
$728$	−5.11630	+	11.2031i	−0.189623	+	0.415216i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−8.86793	+	2.60386i	−0.328217	+	0.0963731i
$731$	3.97363	+	4.58581i	0.146970	+	0.169612i
$732$	11.2695	+	3.30904i	0.416534	+	0.122306i
$733$	6.18170	+	13.5360i	0.228326	+	0.499965i	0.988771	−	0.149438i	$-0.0477463\pi$
$733$	6.18170	+	13.5360i	0.228326	+	0.499965i	−0.760445	+	0.649403i	$0.775019\pi$
$734$	−0.481540	+	3.34919i	−0.0177740	+	0.123621i
$735$	−0.561488			−0.0207108
$736$	0.242000	−	4.78972i	0.00892025	−	0.176551i
$737$	1.13905			0.0419575
$738$	−1.72621	+	12.0060i	−0.0635425	+	0.441948i
$739$	10.9062	+	23.8812i	0.401191	+	0.878485i	0.997148	+	0.0754689i	$0.0240454\pi$
$739$	10.9062	+	23.8812i	0.401191	+	0.878485i	−0.595958	+	0.803016i	$0.703227\pi$
$740$	6.22738	+	1.82852i	0.228923	+	0.0672178i
$741$	−14.2636	−	16.4611i	−0.523987	−	0.604713i
$742$	2.15857	−	0.633815i	0.0792438	−	0.0232681i
$743$	−3.22038	−	2.06962i	−0.118144	−	0.0759268i	0.480234	−	0.877140i	$-0.340552\pi$
$743$	−3.22038	−	2.06962i	−0.118144	−	0.0759268i	−0.598379	+	0.801214i	$0.704188\pi$
$744$	−1.52257	+	3.33397i	−0.0558203	+	0.122229i
$745$	1.78796	−	2.06341i	0.0655056	−	0.0755975i
$746$	6.72245	−	4.32026i	0.246126	−	0.158176i
$747$	2.28909	+	15.9210i	0.0837534	+	0.582518i
$748$	−0.0226104	−	0.157258i	−0.000826717	−	0.00574994i
$749$	15.9219	−	10.2324i	0.581773	−	0.373883i
$750$	0.654861	−	0.755750i	0.0239121	−	0.0275961i
$751$	−6.08374	+	13.3215i	−0.221999	+	0.486110i	−0.987558	−	0.157256i	$-0.949735\pi$
$751$	−6.08374	+	13.3215i	−0.221999	+	0.486110i	0.765559	+	0.643366i	$0.222462\pi$
$752$	−3.88011	−	2.49360i	−0.141493	−	0.0909322i
$753$	19.1696	−	5.62869i	0.698577	−	0.205121i
$754$	−28.6013	−	33.0077i	−1.04160	−	1.20207i
$755$	0.177724	+	0.0521844i	0.00646803	+	0.00189918i
$756$	1.14231	+	2.50132i	0.0415456	+	0.0909722i
$757$	6.16770	−	42.8973i	0.224169	−	1.55913i	−0.497855	−	0.867261i	$-0.665879\pi$
$757$	6.16770	−	42.8973i	0.224169	−	1.55913i	0.722024	−	0.691869i	$-0.243212\pi$
$758$	9.17687			0.333319
$759$	0.222299	−	0.636350i	0.00806894	−	0.0230981i
$760$	4.86306			0.176402
$761$	−2.55526	+	17.7722i	−0.0926280	+	0.644242i	0.889626	+	0.456689i	$0.150965\pi$
$761$	−2.55526	+	17.7722i	−0.0926280	+	0.644242i	−0.982254	+	0.187553i	$0.939944\pi$
$762$	−8.01489	−	17.5502i	−0.290349	−	0.635775i
$763$	−0.986756	−	0.289738i	−0.0357230	−	0.0104892i
$764$	−2.35172	−	2.71403i	−0.0850824	−	0.0981903i
$765$	−1.08458	+	0.318463i	−0.0392133	+	0.0115140i
$766$	−7.65304	−	4.91831i	−0.276515	−	0.177706i
$767$	5.61269	−	12.2901i	0.202662	−	0.443769i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	−23.7253	+	15.2473i	−0.855556	+	0.549833i	−0.893303	−	0.449455i	$-0.851618\pi$
$769$	−23.7253	+	15.2473i	−0.855556	+	0.549833i	0.0377468	+	0.999287i	$0.487982\pi$
$770$	−0.0550034	−	0.382557i	−0.00198218	−	0.0137864i
$771$	0.384575	+	2.67478i	0.0138501	+	0.0963298i
$772$	5.72794	−	3.68112i	0.206153	−	0.132487i
$773$	−26.5945	+	30.6916i	−0.956536	+	1.10390i	0.0379761	+	0.999279i	$0.487909\pi$
$773$	−26.5945	+	30.6916i	−0.956536	+	1.10390i	−0.994512	+	0.104623i	$0.966637\pi$
$774$	2.22997	−	4.88295i	0.0801546	−	0.175514i
$775$	−3.08335	−	1.98155i	−0.110757	−	0.0711794i
$776$	10.1785	−	2.98867i	0.365386	−	0.107287i
$777$	−11.6873	−	13.4879i	−0.419281	−	0.483876i
$778$	25.7375	+	7.55720i	0.922733	+	0.270939i
$779$	−24.5039	−	53.6560i	−0.877942	−	1.92243i
$780$	−0.637413	+	4.43330i	−0.0228230	+	0.158738i
$781$	1.02132			0.0365456
$782$	−3.91262	−	3.75226i	−0.139915	−	0.134181i
$783$	−9.75140			−0.348487
$784$	−0.0799081	+	0.555773i	−0.00285386	+	0.0198490i
$785$	7.77518	+	17.0253i	0.277508	+	0.607658i
$786$	16.5587	+	4.86208i	0.590630	+	0.173425i
$787$	−34.6042	−	39.9354i	−1.23351	−	1.42354i	−0.870798	−	0.491641i	$-0.836397\pi$
$787$	−34.6042	−	39.9354i	−1.23351	−	1.42354i	−0.362709	−	0.931902i	$-0.618148\pi$
$788$	−7.89104	+	2.31702i	−0.281107	+	0.0825404i
$789$	−1.97111	−	1.26676i	−0.0701734	−	0.0450977i
$790$	−5.12390	+	11.2198i	−0.182300	+	0.399182i
$791$	−33.5992	+	38.7755i	−1.19465	+	1.37870i
$792$	−0.118239	+	0.0759879i	−0.00420146	+	0.00270011i
$793$	−7.48661	−	52.0705i	−0.265857	−	1.84908i
$794$	0.479772	+	3.33689i	0.0170265	+	0.118422i
$795$	0.688254	−	0.442314i	0.0244098	−	0.0156873i
$796$	−1.31973	+	1.52305i	−0.0467767	+	0.0539832i
$797$	−9.21534	+	20.1788i	−0.326424	+	0.714769i	−0.999697	−	0.0246251i	$-0.992161\pi$
$797$	−9.21534	+	20.1788i	−0.326424	+	0.714769i	0.673273	+	0.739394i	$0.264888\pi$
$798$	−11.2497	−	7.22974i	−0.398235	−	0.255930i
$799$	−5.00243	+	1.46885i	−0.176973	+	0.0519641i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	−5.24103	−	1.53890i	−0.185183	−	0.0543745i
$802$	13.0728	+	28.6254i	0.461616	+	1.01080i
$803$	−0.184870	+	1.28580i	−0.00652391	+	0.0453748i
$804$	−8.10416			−0.285812
$805$	−9.51809	−	9.12799i	−0.335468	−	0.321719i
$806$	16.4160			0.578228
$807$	−0.411370	+	2.86114i	−0.0144809	+	0.100717i
$808$	−2.71728	−	5.95002i	−0.0955937	−	0.209321i
$809$	−9.32568	−	2.73827i	−0.327874	−	0.0962724i	0.113653	−	0.993520i	$-0.463745\pi$
$809$	−9.32568	−	2.73827i	−0.327874	−	0.0962724i	−0.441527	+	0.897248i	$0.645563\pi$
$810$	0.654861	+	0.755750i	0.0230095	+	0.0265543i
$811$	46.2793	−	13.5888i	1.62509	−	0.477168i	0.662707	−	0.748879i	$-0.269408\pi$
$811$	46.2793	−	13.5888i	1.62509	−	0.477168i	0.962379	+	0.271711i	$0.0875895\pi$
$812$	−22.5578	−	14.4970i	−0.791625	−	0.508746i
$813$	0.449266	−	0.983754i	0.0157564	−	0.0345018i
$814$	0.597376	−	0.689409i	0.0209380	−	0.0241638i
$815$	12.5207	−	8.04654i	0.438580	−	0.281858i
$816$	0.160869	+	1.11887i	0.00563154	+	0.0391682i
$817$	3.71515	+	25.8395i	0.129977	+	0.904008i
$818$	5.97501	−	3.83990i	0.208911	−	0.134259i
$819$	8.06535	−	9.30791i	0.281826	−	0.325245i
$820$	−5.03877	+	11.0334i	−0.175962	+	0.385302i
$821$	21.6311	+	13.9015i	0.754931	+	0.485165i	0.860628	−	0.509233i	$-0.170071\pi$
$821$	21.6311	+	13.9015i	0.754931	+	0.485165i	−0.105697	+	0.994398i	$0.533707\pi$
$822$	−7.46779	+	2.19274i	−0.260469	+	0.0764806i
$823$	26.1886	+	30.2232i	0.912877	+	1.05352i	0.998364	+	0.0571766i	$0.0182098\pi$
$823$	26.1886	+	30.2232i	0.912877	+	1.05352i	−0.0854874	+	0.996339i	$0.527245\pi$
$824$	−12.1398	−	3.56456i	−0.422909	−	0.124177i
$825$	−0.0583872	−	0.127850i	−0.00203278	−	0.00445117i
$826$	1.18052	−	8.21067i	0.0410754	−	0.285686i
$827$	7.40168			0.257382			0.128691	−	0.991685i	$-0.458923\pi$
$827$	7.40168			0.257382			0.128691	+	0.991685i	$0.458923\pi$
$828$	−1.58162	+	4.52753i	−0.0549650	+	0.157342i
$829$	−36.8880			−1.28117			−0.640586	−	0.767887i	$-0.721308\pi$
$829$	−36.8880			−1.28117			−0.640586	+	0.767887i	$0.721308\pi$
$830$	−2.28909	+	15.9210i	−0.0794554	+	0.552625i
$831$	−4.51296	−	9.88201i	−0.156553	−	0.342803i
$832$	4.29746	+	1.26185i	0.148988	+	0.0437468i
$833$	0.415634	+	0.479667i	0.0144009	+	0.0166195i
$834$	−18.6961	+	5.48966i	−0.647392	+	0.190091i
$835$	14.0403	+	9.02314i	0.485884	+	0.312258i
$836$	0.283941	−	0.621743i	0.00982029	−	0.0215034i
$837$	2.40019	−	2.76996i	0.0829626	−	0.0957439i
$838$	19.2233	−	12.3541i	0.664058	−	0.426764i
$839$	−0.599066	−	4.16659i	−0.0206820	−	0.143847i	0.976864	−	0.213862i	$-0.0686043\pi$
$839$	−0.599066	−	4.16659i	−0.0206820	−	0.143847i	−0.997546	+	0.0700153i	$0.977695\pi$
$840$	0.391340	+	2.72183i	0.0135025	+	0.0939119i
$841$	55.5983	−	35.7308i	1.91718	−	1.23210i
$842$	−6.92663	+	7.99376i	−0.238708	+	0.275483i
$843$	2.13163	−	4.66762i	0.0734172	−	0.160761i
$844$	−7.92803	−	5.09504i	−0.272894	−	0.175378i
$845$	6.77447	−	1.98916i	0.233049	−	0.0684293i
$846$	3.02041	+	3.48574i	0.103844	+	0.119842i
$847$	28.9706	+	8.50654i	0.995442	+	0.292288i
$848$	−0.339863	−	0.744196i	−0.0116709	−	0.0255558i
$849$	4.06305	−	28.2592i	0.139444	−	0.969852i
$850$	−1.13037			−0.0387715
$851$	1.57065	−	31.0866i	0.0538412	−	1.06564i
$852$	−7.26650			−0.248946
$853$	−2.05210	+	14.2727i	−0.0702627	+	0.488688i	0.924057	+	0.382254i	$0.124852\pi$
$853$	−2.05210	+	14.2727i	−0.0702627	+	0.488688i	−0.994320	+	0.106433i	$0.966057\pi$
$854$	−13.4168	−	29.3788i	−0.459115	−	1.00532i
$855$	−4.66608	−	1.37008i	−0.159576	−	0.0468559i
$856$	−4.50726	−	5.20165i	−0.154055	−	0.177789i
$857$	−48.1569	+	14.1401i	−1.64501	+	0.483018i	−0.967579	−	0.252569i	$-0.918725\pi$
$857$	−48.1569	+	14.1401i	−1.64501	+	0.483018i	−0.677430	+	0.735587i	$0.736906\pi$
$858$	0.529582	+	0.340341i	0.0180796	+	0.0116191i
$859$	18.1898	−	39.8302i	0.620629	−	1.35899i	−0.294432	−	0.955672i	$-0.595130\pi$
$859$	18.1898	−	39.8302i	0.620629	−	1.35899i	0.915061	−	0.403315i	$-0.132142\pi$
$860$	3.51533	−	4.05690i	0.119872	−	0.138339i
$861$	28.0591	−	18.0325i	0.956250	−	0.614545i
$862$	−5.13098	−	35.6867i	−0.174762	−	1.21549i
$863$	1.50391	+	10.4600i	0.0511938	+	0.356061i	0.999276	+	0.0380365i	$0.0121103\pi$
$863$	1.50391	+	10.4600i	0.0511938	+	0.356061i	−0.948083	+	0.318024i	$0.896981\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	0.337201	−	0.389150i	0.0114652	−	0.0132315i
$866$	15.2501	−	33.3930i	0.518218	−	1.13474i
$867$	−13.2264	−	8.50009i	−0.449192	−	0.288678i
$868$	9.67034	−	2.83947i	0.328233	−	0.0963778i
$869$	1.13528	+	1.31018i	0.0385117	+	0.0444449i
$870$	−9.35640	−	2.74729i	−0.317212	−	0.0931417i
$871$	15.0786	+	33.0175i	0.510919	+	1.11876i
$872$	−0.0532249	+	0.370187i	−0.00180242	+	0.0125361i
$873$	−10.6082			−0.359033
$874$	−5.43313	−	22.6808i	−0.183778	−	0.767188i
$875$	−2.74982			−0.0929607
$876$	1.31532	−	9.14823i	0.0444405	−	0.309090i
$877$	−12.0045	−	26.2861i	−0.405363	−	0.887620i	−0.996698	−	0.0811946i	$-0.974126\pi$
$877$	−12.0045	−	26.2861i	−0.405363	−	0.887620i	0.591336	−	0.806425i	$-0.298601\pi$
$878$	−3.45958	−	1.01582i	−0.116755	−	0.0342824i
$879$	−2.10288	−	2.42685i	−0.0709284	−	0.0818557i
$880$	−0.134858	+	0.0395979i	−0.00454607	+	0.00133485i
$881$	−27.2558	−	17.5162i	−0.918271	−	0.590137i	−0.00611581	−	0.999981i	$-0.501947\pi$
$881$	−27.2558	−	17.5162i	−0.918271	−	0.590137i	−0.912156	+	0.409844i	$0.865583\pi$
$882$	0.233250	−	0.510747i	0.00785395	−	0.0171978i
$883$	13.4350	−	15.5048i	0.452122	−	0.521777i	−0.483231	−	0.875493i	$-0.660537\pi$
$883$	13.4350	−	15.5048i	0.452122	−	0.521777i	0.935353	+	0.353716i	$0.115082\pi$
$884$	4.25911	−	2.73717i	0.143249	−	0.0920609i
$885$	−0.429307	−	2.98590i	−0.0144310	−	0.100370i
$886$	5.11686	+	35.5886i	0.171904	+	1.19562i
$887$	−16.6315	+	10.6884i	−0.558430	+	0.358881i	−0.789209	−	0.614125i	$-0.789509\pi$
$887$	−16.6315	+	10.6884i	−0.558430	+	0.358881i	0.230779	+	0.973006i	$0.425873\pi$
$888$	−4.25023	+	4.90502i	−0.142628	+	0.164602i
$889$	−22.0395	+	48.2597i	−0.739180	+	1.61858i
$890$	−4.59517	−	2.95314i	−0.154030	−	0.0989894i
$891$	0.134858	−	0.0395979i	0.00451792	−	0.00132658i
$892$	11.4186	+	13.1777i	0.382322	+	0.441224i
$893$	−21.5213	−	6.31924i	−0.720184	−	0.211465i
$894$	1.13420	+	2.48355i	0.0379333	+	0.0830625i
$895$	1.55348	−	10.8047i	0.0519271	−	0.361161i
$896$	2.74982			0.0918649
$897$	21.3885	−	1.98017i	0.714143	−	0.0661159i
$898$	2.11010			0.0704149
$899$	−5.08643	+	35.3769i	−0.169642	+	1.17989i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	−0.887330	−	0.260544i	−0.0295613	−	0.00867997i
$902$	1.11642	+	1.28842i	0.0371727	+	0.0428995i
$903$	−14.1632	+	4.15870i	−0.471322	+	0.138393i
$904$	15.6965	+	10.0875i	0.522058	+	0.335506i
$905$	6.83414	−	14.9647i	0.227175	−	0.497443i
$906$	−0.121298	+	0.139985i	−0.00402984	+	0.00465069i
$907$	−0.228930	+	0.147124i	−0.00760148	+	0.00488517i	−0.544436	−	0.838802i	$-0.683256\pi$
$907$	−0.228930	+	0.147124i	−0.00760148	+	0.00488517i	0.536835	+	0.843688i	$0.319620\pi$
$908$	0.644618	+	4.48342i	0.0213924	+	0.148787i
$909$	0.930900	+	6.47455i	0.0308760	+	0.214747i
$910$	10.3610	−	6.65860i	0.343463	−	0.220730i
$911$	−24.8347	+	28.6608i	−0.822811	+	0.949574i	−0.999397	−	0.0347110i	$-0.988949\pi$
$911$	−24.8347	+	28.6608i	−0.822811	+	0.949574i	0.176587	+	0.984285i	$0.443494\pi$
$912$	−2.02019	+	4.42360i	−0.0668952	+	0.146480i
$913$	1.90184	+	1.22224i	0.0629419	+	0.0404503i
$914$	−13.7719	+	4.04380i	−0.455535	+	0.133757i
$915$	−7.69155	−	8.87652i	−0.254275	−	0.293449i
$916$	−4.46472	−	1.31096i	−0.147518	−	0.0433153i
$917$	−19.7138	−	43.1673i	−0.651008	−	1.42551i
$918$	0.160869	−	1.11887i	0.00530946	−	0.0369281i
$919$	−9.08529			−0.299696			−0.149848	−	0.988709i	$-0.547878\pi$
$919$	−9.08529			−0.299696			−0.149848	+	0.988709i	$0.547878\pi$
$920$	−2.79310	+	3.89854i	−0.0920859	+	0.128531i
$921$	5.24333			0.172773
$922$	4.53462	−	31.5390i	0.149340	−	1.03868i
$923$	13.5200	+	29.6048i	0.445018	+	0.974453i
$924$	0.370835	+	0.108887i	0.0121996	+	0.00358212i
$925$	−4.25023	−	4.90502i	−0.139747	−	0.161276i
$926$	−3.99546	+	1.17317i	−0.131299	+	0.0385529i
$927$	10.6438	+	6.84034i	0.349588	+	0.224666i
$928$	−4.05088	+	8.87018i	−0.132977	+	0.291178i
$929$	−36.3957	+	42.0029i	−1.19410	+	1.37807i	−0.286588	+	0.958054i	$0.592521\pi$
$929$	−36.3957	+	42.0029i	−1.19410	+	1.37807i	−0.907517	+	0.420016i	$0.862024\pi$
$930$	3.08335	−	1.98155i	0.101107	−	0.0649776i
$931$	0.388598	+	2.70276i	0.0127358	+	0.0885793i
$932$	−0.429922	−	2.99017i	−0.0140826	−	0.0979463i
$933$	0.314112	−	0.201867i	0.0102836	−	0.00660884i
$934$	3.61412	−	4.17092i	0.118258	−	0.136477i
$935$	−0.0659993	+	0.144518i	−0.00215841	+	0.00472626i
$936$	−3.76788	−	2.42147i	−0.123157	−	0.0791483i
$937$	37.1829	−	10.9179i	1.21471	−	0.356672i	0.389252	−	0.921132i	$-0.372734\pi$
$937$	37.1829	−	10.9179i	1.21471	−	0.356672i	0.825461	+	0.564460i	$0.190916\pi$
$938$	14.5935	+	16.8418i	0.476496	+	0.549906i
$939$	−15.3332	−	4.50224i	−0.500381	−	0.146925i
$940$	1.91602	+	4.19550i	0.0624937	+	0.136842i
$941$	3.03733	−	21.1251i	0.0990142	−	0.688659i	−0.878493	−	0.477756i	$-0.841450\pi$
$941$	3.03733	−	21.1251i	0.0990142	−	0.688659i	0.977507	−	0.210903i	$-0.0676404\pi$
$942$	−18.7167			−0.609822
$943$	57.0878	+	11.1735i	1.85903	+	0.363860i
$944$	−3.01660			−0.0981820
$945$	0.391340	−	2.72183i	0.0127303	−	0.0885410i
$946$	−0.313425	−	0.686306i	−0.0101903	−	0.0223137i
$947$	8.19219	+	2.40544i	0.266210	+	0.0781664i	0.412114	−	0.911132i	$-0.364791\pi$
$947$	8.19219	+	2.40544i	0.266210	+	0.0781664i	−0.145903	+	0.989299i	$0.546609\pi$
$948$	−8.07733	−	9.32173i	−0.262339	−	0.302756i
$949$	−39.7185	+	11.6624i	−1.28932	+	0.378578i
$950$	−4.09107	−	2.62917i	−0.132732	−	0.0853016i
$951$	−12.7317	+	27.8786i	−0.412854	+	0.904025i
$952$	2.03552	−	2.34911i	0.0659714	−	0.0761351i
$953$	−35.9748	+	23.1196i	−1.16534	+	0.748918i	−0.972635	−	0.232339i	$-0.925362\pi$
$953$	−35.9748	+	23.1196i	−1.16534	+	0.748918i	−0.192704	+	0.981257i	$0.561726\pi$
$954$	0.116432	+	0.809801i	0.00376962	+	0.0262183i
$955$	0.511079	+	3.55463i	0.0165381	+	0.115025i
$956$	−7.13562	+	4.58578i	−0.230782	+	0.148315i
$957$	−0.897535	+	1.03581i	−0.0290132	+	0.0334830i
$958$	−6.32719	+	13.8546i	−0.204422	+	0.447622i
$959$	18.0045	+	11.5708i	0.581395	+	0.373640i
$960$	0.959493	−	0.281733i	0.0309675	−	0.00909288i
$961$	11.5035	+	13.2758i	0.371082	+	0.428252i
$962$	27.8917	+	8.18975i	0.899266	+	0.264048i
$963$	2.85921	+	6.26079i	0.0921367	+	0.201751i
$964$	−1.03161	+	7.17500i	−0.0332259	+	0.231091i
$965$	−6.80881			−0.219183
$966$	12.2571	−	4.86605i	0.394365	−	0.156563i
$967$	−49.3229			−1.58612			−0.793058	−	0.609146i	$-0.791512\pi$
$967$	−49.3229			−1.58612			−0.793058	+	0.609146i	$0.791512\pi$
$968$	1.56265	−	10.8685i	0.0502255	−	0.349326i
$969$	2.28357	+	5.00032i	0.0733588	+	0.160633i
$970$	−10.1785	−	2.98867i	−0.326811	−	0.0959604i
$971$	15.9587	+	18.4173i	0.512139	+	0.591040i	0.951645	−	0.307200i	$-0.0993920\pi$
$971$	15.9587	+	18.4173i	0.512139	+	0.591040i	−0.439506	+	0.898239i	$0.644847\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	45.0753	+	28.9681i	1.44505	+	0.928676i
$974$	8.26105	−	18.0892i	0.264701	−	0.579615i
$975$	2.93305	−	3.38492i	0.0939328	−	0.108404i
$976$	−9.88079	+	6.35000i	−0.316276	+	0.203258i
$977$	3.79324	+	26.3825i	0.121356	+	0.844052i	0.956022	+	0.293295i	$0.0947518\pi$
$977$	3.79324	+	26.3825i	0.121356	+	0.844052i	−0.834666	+	0.550757i	$0.814339\pi$
$978$	2.11812	+	14.7319i	0.0677300	+	0.471073i
$979$	−0.645858	+	0.415068i	−0.0206417	+	0.0132656i
$980$	0.367696	−	0.424344i	0.0117456	−	0.0135552i
$981$	0.155363	−	0.340197i	0.00496035	−	0.0108616i
$982$	8.30659	+	5.33832i	0.265074	+	0.170353i
$983$	19.3863	−	5.69232i	0.618326	−	0.181557i	0.0424562	−	0.999098i	$-0.486482\pi$
$983$	19.3863	−	5.69232i	0.618326	−	0.181557i	0.575870	+	0.817541i	$0.304664\pi$
$984$	−7.94313	−	9.16686i	−0.253218	−	0.292229i
$985$	7.89104	+	2.31702i	0.251429	+	0.0738263i
$986$	4.57900	+	10.0266i	0.145825	+	0.319313i
$987$	1.80498	−	12.5539i	0.0574530	−	0.399595i
$988$	21.7811			0.692950
$989$	−22.8483	−	11.8626i	−0.726534	−	0.377209i
$990$	0.140551			0.00446702
$991$	1.02283	−	7.11397i	0.0324914	−	0.225983i	−0.967105	−	0.254376i	$-0.918130\pi$
$991$	1.02283	−	7.11397i	0.0324914	−	0.225983i	0.999597	+	0.0283933i	$0.00903907\pi$
$992$	−1.52257	−	3.33397i	−0.0483418	−	0.105854i
$993$	−30.0120	−	8.81231i	−0.952401	−	0.279650i
$994$	13.0851	+	15.1010i	0.415035	+	0.478976i
$995$	1.93365	−	0.567772i	0.0613010	−	0.0179996i
$996$	−13.5313	−	8.69604i	−0.428756	−	0.275544i
$997$	−14.6401	+	32.0574i	−0.463657	+	1.01527i	0.522981	+	0.852344i	$0.324820\pi$
$997$	−14.6401	+	32.0574i	−0.463657	+	1.01527i	−0.986639	+	0.162924i	$0.947908\pi$
$998$	6.76493	−	7.80715i	0.214140	−	0.247131i
$999$	5.45997	−	3.50891i	0.172746	−	0.111017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.a.31.1	✓	10
23.3	even	11	inner	690.2.m.a.601.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.a.31.1	✓	10	1.1	even	1	trivial
690.2.m.a.601.1	yes	10	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(2.31329 + 1.48666i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(2.31329 + 1.48666i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.0200026 + 0.139121i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-3.76788 + 2.42147i) q^{13} +(-1.80075 + 2.07817i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.08458 - 0.318463i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(4.66608 + 1.37008i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.391340 + 2.72183i) q^{21} -0.140551 q^{22} +(-3.77831 + 2.95371i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-1.86060 - 4.07414i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-1.80075 - 2.07817i) q^{28} +(9.35640 - 2.74729i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(-1.52257 + 3.33397i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.118239 + 0.0759879i) q^{33} +(0.160869 + 1.11887i) q^{34} +(0.391340 + 2.72183i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-4.25023 + 4.90502i) q^{37} +(-2.02019 + 4.42360i) q^{38} +(-3.76788 - 2.42147i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-7.94313 - 9.16686i) q^{41} +(-2.63843 - 0.774713i) q^{42} +(2.22997 + 4.88295i) q^{43} +(0.0200026 - 0.139121i) q^{44} -1.00000 q^{45} +(-2.38594 - 4.16021i) q^{46} -4.61230 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.233250 + 0.510747i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(0.740237 + 0.854279i) q^{51} +(4.29746 - 1.26185i) q^{52} +(-0.688254 - 0.442314i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-0.0920417 + 0.106222i) q^{55} +(2.31329 - 1.48666i) q^{56} +(0.692086 + 4.81356i) q^{57} +(1.38777 + 9.65214i) q^{58} +(-2.53773 + 1.63090i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-4.87918 + 10.6839i) q^{61} +(-3.08335 - 1.98155i) q^{62} +(-2.63843 + 0.774713i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-4.29746 - 1.26185i) q^{65} +(-0.0583872 - 0.127850i) q^{66} +(1.15334 - 8.02167i) q^{67} -1.13037 q^{68} +(-4.25635 - 2.20985i) q^{69} -2.74982 q^{70} +(1.03413 - 7.19254i) q^{71} +(0.415415 + 0.909632i) q^{72} +(8.86793 + 2.60386i) q^{73} +(-4.25023 - 4.90502i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-4.09107 - 2.62917i) q^{76} +(-0.160554 + 0.351564i) q^{77} +(2.93305 - 3.38492i) q^{78} +(10.3764 - 6.66849i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(10.2040 - 6.55770i) q^{82} +(10.5332 - 12.1560i) q^{83} +(1.14231 - 2.50132i) q^{84} +(0.950930 + 0.611126i) q^{85} +(-5.15061 + 1.51235i) q^{86} +(6.38581 + 7.36962i) q^{87} +(0.134858 + 0.0395979i) q^{88} +(2.26912 + 4.96867i) q^{89} +(0.142315 - 0.989821i) q^{90} -12.3161 q^{91} +(4.45741 - 1.76959i) q^{92} -3.66519 q^{93} +(0.656399 - 4.56535i) q^{94} +(2.02019 + 4.42360i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(6.94688 + 8.01713i) q^{97} +(-0.538744 + 0.158189i) q^{98} +(-0.118239 - 0.0759879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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