LMFDB - Embedded newform 799.2.k.b.256.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(18,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([0, 12]))

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

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

chi := DirichletCharacter("799.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.k (of order $23$, degree $22$, 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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$704$
Relative dimension:	$32$ over $\Q(\zeta_{23})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			256.11
Character	$\chi$	$=$	799.256
Dual form			799.2.k.b.103.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573945 - 1.10766i) q^{2} +(-0.697537 + 1.96268i) q^{3} +(0.255856 - 0.362465i) q^{4} +(-1.00567 - 0.436825i) q^{5} +(2.57434 - 0.353835i) q^{6} +(-0.732908 - 0.445691i) q^{7} +(-3.02016 - 0.415111i) q^{8} +(-1.03843 - 0.844825i) q^{9} +O(q^{10})$	\(q+(-0.573945 - 1.10766i) q^{2} +(-0.697537 + 1.96268i) q^{3} +(0.255856 - 0.362465i) q^{4} +(-1.00567 - 0.436825i) q^{5} +(2.57434 - 0.353835i) q^{6} +(-0.732908 - 0.445691i) q^{7} +(-3.02016 - 0.415111i) q^{8} +(-1.03843 - 0.844825i) q^{9} +(0.0933453 + 1.36466i) q^{10} +(4.39021 - 1.23008i) q^{11} +(0.532935 + 0.754996i) q^{12} +(0.0240487 + 0.115729i) q^{13} +(-0.0730270 + 1.06762i) q^{14} +(1.55884 - 1.66911i) q^{15} +(0.976448 + 2.74746i) q^{16} +(-0.962917 - 0.269797i) q^{17} +(-0.339780 + 1.63511i) q^{18} +(-0.551741 + 0.239655i) q^{19} +(-0.415641 + 0.252757i) q^{20} +(1.38598 - 1.12758i) q^{21} +(-3.88225 - 4.15687i) q^{22} +(-1.03769 + 2.00266i) q^{23} +(2.92140 - 5.63805i) q^{24} +(-2.59220 - 2.77557i) q^{25} +(0.114386 - 0.0930597i) q^{26} +(-2.95667 + 1.79799i) q^{27} +(-0.349066 + 0.151621i) q^{28} +(0.874347 - 4.20759i) q^{29} +(-2.74351 - 0.768694i) q^{30} +(-2.99208 - 8.41892i) q^{31} +(-1.67876 + 1.79752i) q^{32} +(-0.648081 + 9.47461i) q^{33} +(0.253817 + 1.22144i) q^{34} +(0.542376 + 0.768372i) q^{35} +(-0.571907 + 0.160241i) q^{36} +(-0.683453 - 9.99173i) q^{37} +(0.582125 + 0.473594i) q^{38} +(-0.243913 - 0.0335251i) q^{39} +(2.85596 + 1.73675i) q^{40} +(5.03326 - 0.691805i) q^{41} +(-2.04445 - 0.888031i) q^{42} +(2.78748 - 3.94896i) q^{43} +(0.677400 - 1.90602i) q^{44} +(0.675279 + 1.30323i) q^{45} +2.81385 q^{46} +(6.79248 + 0.928542i) q^{47} -6.07350 q^{48} +(-2.88194 - 5.56190i) q^{49} +(-1.58662 + 4.46431i) q^{50} +(1.20120 - 1.70171i) q^{51} +(0.0481006 + 0.0208930i) q^{52} +(11.8434 - 1.62784i) q^{53} +(3.68854 + 2.24305i) q^{54} +(-4.95244 - 0.680698i) q^{55} +(2.02848 + 1.65029i) q^{56} +(-0.0855064 - 1.25006i) q^{57} +(-5.16242 + 1.44644i) q^{58} +(-5.64717 - 8.00021i) q^{59} +(-0.206156 - 0.992079i) q^{60} +(0.881977 - 12.8940i) q^{61} +(-7.60803 + 8.14621i) q^{62} +(0.384542 + 1.08200i) q^{63} +(8.56994 + 2.40118i) q^{64} +(0.0263681 - 0.126890i) q^{65} +(10.8666 - 4.72005i) q^{66} +(-4.57135 + 2.77990i) q^{67} +(-0.344160 + 0.279995i) q^{68} +(-3.20675 - 3.43359i) q^{69} +(0.539803 - 1.04177i) q^{70} +(-2.50377 + 4.83207i) q^{71} +(2.78552 + 2.98257i) q^{72} +(-7.19619 + 5.85454i) q^{73} +(-10.6752 + 6.49174i) q^{74} +(7.25573 - 3.15161i) q^{75} +(-0.0542995 + 0.261304i) q^{76} +(-3.76585 - 1.05514i) q^{77} +(0.102858 + 0.289416i) q^{78} +(0.557398 - 0.596827i) q^{79} +(0.218174 - 3.18958i) q^{80} +(-2.28359 - 10.9892i) q^{81} +(-3.65510 - 5.17810i) q^{82} +(-0.242951 + 0.0680717i) q^{83} +(-0.0540968 - 0.790867i) q^{84} +(0.850526 + 0.691954i) q^{85} +(-5.97397 - 0.821104i) q^{86} +(7.64827 + 4.65102i) q^{87} +(-13.7697 + 1.89261i) q^{88} +(-3.52263 - 1.53009i) q^{89} +(1.05597 - 1.49596i) q^{90} +(0.0339538 - 0.0955367i) q^{91} +(0.460393 + 0.888519i) q^{92} +18.6108 q^{93} +(-2.87000 - 8.05671i) q^{94} +0.659558 q^{95} +(-2.35695 - 4.54871i) q^{96} +(3.39347 - 9.54831i) q^{97} +(-4.50663 + 6.38444i) q^{98} +(-5.59812 - 2.43161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 704 q - 2 q^{3} - 32 q^{4} - 2 q^{5} - 10 q^{6} - 21 q^{7} - 34 q^{9}+O(q^{10}) $ 704 * q - 2 * q^3 - 32 * q^4 - 2 * q^5 - 10 * q^6 - 21 * q^7 - 34 * q^9	\( 704 q - 2 q^{3} - 32 q^{4} - 2 q^{5} - 10 q^{6} - 21 q^{7} - 34 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 12 q^{13} + 2 q^{14} + 14 q^{15} - 32 q^{16} + 32 q^{17} - 6 q^{18} + 4 q^{19} - 14 q^{20} + 8 q^{22} - 2 q^{23} - 24 q^{24} - 42 q^{25} + 18 q^{26} - 8 q^{27} + 2 q^{28} - 12 q^{29} - 184 q^{30} + 12 q^{31} - 12 q^{33} - 6 q^{35} + 110 q^{36} - 472 q^{38} + 97 q^{39} + 142 q^{40} + 43 q^{41} + 18 q^{42} + 37 q^{43} - 20 q^{44} - 38 q^{45} - 136 q^{46} + 15 q^{47} - 24 q^{48} - 11 q^{49} + 68 q^{50} + 2 q^{51} - 4 q^{52} - 11 q^{53} - 551 q^{54} + 71 q^{55} + 186 q^{56} + 103 q^{57} + 20 q^{58} - 30 q^{59} + 208 q^{60} + 18 q^{61} - 228 q^{62} + 22 q^{63} - 92 q^{64} - 32 q^{65} - 52 q^{66} + 8 q^{67} + 32 q^{68} - 128 q^{69} - 706 q^{70} - 42 q^{71} - 34 q^{72} + 26 q^{73} + 46 q^{74} + 8 q^{75} + 46 q^{76} - 534 q^{77} - 118 q^{78} + 36 q^{79} - 84 q^{80} + 74 q^{81} + 173 q^{82} + 88 q^{83} + 90 q^{84} + 2 q^{85} + 224 q^{86} + 126 q^{87} + 22 q^{88} - 8 q^{89} + 390 q^{90} + 258 q^{91} + 215 q^{92} - 430 q^{93} - 8 q^{94} + 4 q^{95} + 72 q^{96} + 34 q^{97} + 165 q^{98} + 276 q^{99}+O(q^{100}) \) 704 * q - 2 * q^3 - 32 * q^4 - 2 * q^5 - 10 * q^6 - 21 * q^7 - 34 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 12 * q^13 + 2 * q^14 + 14 * q^15 - 32 * q^16 + 32 * q^17 - 6 * q^18 + 4 * q^19 - 14 * q^20 + 8 * q^22 - 2 * q^23 - 24 * q^24 - 42 * q^25 + 18 * q^26 - 8 * q^27 + 2 * q^28 - 12 * q^29 - 184 * q^30 + 12 * q^31 - 12 * q^33 - 6 * q^35 + 110 * q^36 - 472 * q^38 + 97 * q^39 + 142 * q^40 + 43 * q^41 + 18 * q^42 + 37 * q^43 - 20 * q^44 - 38 * q^45 - 136 * q^46 + 15 * q^47 - 24 * q^48 - 11 * q^49 + 68 * q^50 + 2 * q^51 - 4 * q^52 - 11 * q^53 - 551 * q^54 + 71 * q^55 + 186 * q^56 + 103 * q^57 + 20 * q^58 - 30 * q^59 + 208 * q^60 + 18 * q^61 - 228 * q^62 + 22 * q^63 - 92 * q^64 - 32 * q^65 - 52 * q^66 + 8 * q^67 + 32 * q^68 - 128 * q^69 - 706 * q^70 - 42 * q^71 - 34 * q^72 + 26 * q^73 + 46 * q^74 + 8 * q^75 + 46 * q^76 - 534 * q^77 - 118 * q^78 + 36 * q^79 - 84 * q^80 + 74 * q^81 + 173 * q^82 + 88 * q^83 + 90 * q^84 + 2 * q^85 + 224 * q^86 + 126 * q^87 + 22 * q^88 - 8 * q^89 + 390 * q^90 + 258 * q^91 + 215 * q^92 - 430 * q^93 - 8 * q^94 + 4 * q^95 + 72 * q^96 + 34 * q^97 + 165 * q^98 + 276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$e\left(\frac{3}{23}\right)$	$1$

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 $

$2$	−0.573945	−	1.10766i	−0.405840	−	0.783236i	0.593933	−	0.804514i	$-0.297574\pi$
$2$	−0.573945	−	1.10766i	−0.405840	−	0.783236i	−0.999774	+	0.0212782i	$0.993226\pi$
$3$	−0.697537	+	1.96268i	−0.402723	+	1.13316i	0.551530	+	0.834155i	$0.314044\pi$
$3$	−0.697537	+	1.96268i	−0.402723	+	1.13316i	−0.954253	+	0.299000i	$0.903347\pi$
$4$	0.255856	−	0.362465i	0.127928	−	0.181233i
$5$	−1.00567	−	0.436825i	−0.449751	−	0.195354i	0.161366	−	0.986895i	$-0.448410\pi$
$5$	−1.00567	−	0.436825i	−0.449751	−	0.195354i	−0.611117	+	0.791540i	$0.709279\pi$
$6$	2.57434	−	0.353835i	1.05097	−	0.144452i
$7$	−0.732908	−	0.445691i	−0.277013	−	0.168455i	0.374205	−	0.927346i	$-0.377916\pi$
$7$	−0.732908	−	0.445691i	−0.277013	−	0.168455i	−0.651218	+	0.758891i	$0.725742\pi$
$8$	−3.02016	−	0.415111i	−1.06779	−	0.146764i
$9$	−1.03843	−	0.844825i	−0.346143	−	0.281608i
$10$	0.0933453	+	1.36466i	0.0295184	+	0.431544i
$11$	4.39021	−	1.23008i	1.32370	−	0.370883i	0.465885	−	0.884845i	$-0.345736\pi$
$11$	4.39021	−	1.23008i	1.32370	−	0.370883i	0.857813	+	0.513963i	$0.171823\pi$
$12$	0.532935	+	0.754996i	0.153845	+	0.217949i
$13$	0.0240487	+	0.115729i	0.00666991	+	0.0320974i	0.982288	−	0.187380i	$-0.0599996\pi$
$13$	0.0240487	+	0.115729i	0.00666991	+	0.0320974i	−0.975618	+	0.219477i	$0.929565\pi$
$14$	−0.0730270	+	1.06762i	−0.0195173	+	0.285333i
$15$	1.55884	−	1.66911i	0.402492	−	0.430963i
$16$	0.976448	+	2.74746i	0.244112	+	0.686865i
$17$	−0.962917	−	0.269797i	−0.233542	−	0.0654353i
$17$	−0.962917	−	0.269797i	−0.233542	−	0.0654353i
$18$	−0.339780	+	1.63511i	−0.0800870	+	0.385400i
$19$	−0.551741	+	0.239655i	−0.126578	+	0.0549806i	−0.460741	−	0.887535i	$-0.652416\pi$
$19$	−0.551741	+	0.239655i	−0.126578	+	0.0549806i	0.334163	+	0.942515i	$0.391547\pi$
$20$	−0.415641	+	0.252757i	−0.0929402	+	0.0565182i
$21$	1.38598	−	1.12758i	0.302446	−	0.246058i
$22$	−3.88225	−	4.15687i	−0.827698	−	0.886249i
$23$	−1.03769	+	2.00266i	−0.216374	+	0.417583i	−0.971174	−	0.238372i	$-0.923386\pi$
$23$	−1.03769	+	2.00266i	−0.216374	+	0.417583i	0.754800	+	0.655955i	$0.227734\pi$
$24$	2.92140	−	5.63805i	0.596329	−	1.15086i
$25$	−2.59220	−	2.77557i	−0.518441	−	0.555115i
$26$	0.114386	−	0.0930597i	0.0224329	−	0.0182505i
$27$	−2.95667	+	1.79799i	−0.569012	+	0.346024i
$28$	−0.349066	+	0.151621i	−0.0659673	+	0.0286536i
$29$	0.874347	−	4.20759i	0.162362	−	0.781330i	−0.816586	−	0.577223i	$-0.804136\pi$
$29$	0.874347	−	4.20759i	0.162362	−	0.781330i	0.978949	−	0.204107i	$-0.0654289\pi$
$30$	−2.74351	−	0.768694i	−0.500893	−	0.140344i
$31$	−2.99208	−	8.41892i	−0.537394	−	1.51208i	−0.831065	−	0.556176i	$-0.812268\pi$
$31$	−2.99208	−	8.41892i	−0.537394	−	1.51208i	0.293671	−	0.955907i	$-0.405123\pi$
$32$	−1.67876	+	1.79752i	−0.296766	+	0.317759i
$33$	−0.648081	+	9.47461i	−0.112816	+	1.64932i
$34$	0.253817	+	1.22144i	0.0435293	+	0.209475i
$35$	0.542376	+	0.768372i	0.0916783	+	0.129879i
$36$	−0.571907	+	0.160241i	−0.0953179	+	0.0267068i
$37$	−0.683453	−	9.99173i	−0.112359	−	1.64263i	−0.622558	−	0.782574i	$-0.713907\pi$
$37$	−0.683453	−	9.99173i	−0.112359	−	1.64263i	0.510199	−	0.860056i	$-0.329572\pi$
$38$	0.582125	+	0.473594i	0.0944332	+	0.0768271i
$39$	−0.243913	−	0.0335251i	−0.0390574	−	0.00536832i
$40$	2.85596	+	1.73675i	0.451567	+	0.274604i
$41$	5.03326	−	0.691805i	0.786063	−	0.108042i	0.268039	−	0.963408i	$-0.413624\pi$
$41$	5.03326	−	0.691805i	0.786063	−	0.108042i	0.518024	+	0.855366i	$0.326668\pi$
$42$	−2.04445	−	0.888031i	−0.315466	−	0.137026i
$43$	2.78748	−	3.94896i	0.425087	−	0.602210i	−0.546914	−	0.837189i	$-0.684198\pi$
$43$	2.78748	−	3.94896i	0.425087	−	0.602210i	0.972001	+	0.234978i	$0.0755019\pi$
$44$	0.677400	−	1.90602i	0.102122	−	0.287343i
$45$	0.675279	+	1.30323i	0.100665	+	0.194274i
$46$	2.81385			0.414879
$47$	6.79248	+	0.928542i	0.990785	+	0.135442i
$47$	6.79248	+	0.928542i	0.990785	+	0.135442i
$48$	−6.07350			−0.876634
$49$	−2.88194	−	5.56190i	−0.411706	−	0.794557i
$50$	−1.58662	+	4.46431i	−0.224382	+	0.631349i
$51$	1.20120	−	1.70171i	0.168201	−	0.238287i
$52$	0.0481006	+	0.0208930i	0.00667035	+	0.00289734i
$53$	11.8434	−	1.62784i	1.62682	−	0.223601i	0.735680	−	0.677329i	$-0.236863\pi$
$53$	11.8434	−	1.62784i	1.62682	−	0.223601i	0.891140	+	0.453728i	$0.149906\pi$
$54$	3.68854	+	2.24305i	0.501946	+	0.305240i
$55$	−4.95244	−	0.680698i	−0.667787	−	0.0917853i
$56$	2.02848	+	1.65029i	0.271068	+	0.220530i
$57$	−0.0855064	−	1.25006i	−0.0113256	−	0.165574i
$58$	−5.16242	+	1.44644i	−0.677859	+	0.189927i
$59$	−5.64717	−	8.00021i	−0.735199	−	1.04154i	−0.997074	−	0.0764375i	$-0.975645\pi$
$59$	−5.64717	−	8.00021i	−0.735199	−	1.04154i	0.261876	−	0.965102i	$-0.415659\pi$
$60$	−0.206156	−	0.992079i	−0.0266147	−	0.128077i
$61$	0.881977	−	12.8940i	0.112926	−	1.65091i	−0.503862	−	0.863784i	$-0.668088\pi$
$61$	0.881977	−	12.8940i	0.112926	−	1.65091i	0.616788	−	0.787129i	$-0.288434\pi$
$62$	−7.60803	+	8.14621i	−0.966221	+	1.03457i
$63$	0.384542	+	1.08200i	0.0484477	+	0.136319i
$64$	8.56994	+	2.40118i	1.07124	+	0.300148i
$65$	0.0263681	−	0.126890i	0.00327056	−	0.0157388i
$66$	10.8666	−	4.72005i	1.33759	−	0.580998i
$67$	−4.57135	+	2.77990i	−0.558479	+	0.339619i	−0.770292	−	0.637692i	$-0.779889\pi$
$67$	−4.57135	+	2.77990i	−0.558479	+	0.339619i	0.211813	+	0.977310i	$0.432063\pi$
$68$	−0.344160	+	0.279995i	−0.0417355	+	0.0339544i
$69$	−3.20675	−	3.43359i	−0.386047	−	0.413356i
$70$	0.539803	−	1.04177i	0.0645188	−	0.124516i
$71$	−2.50377	+	4.83207i	−0.297143	+	0.573461i	−0.988885	−	0.148685i	$-0.952496\pi$
$71$	−2.50377	+	4.83207i	−0.297143	+	0.573461i	0.691741	+	0.722145i	$0.256844\pi$
$72$	2.78552	+	2.98257i	0.328277	+	0.351499i
$73$	−7.19619	+	5.85454i	−0.842251	+	0.685222i	−0.951116	−	0.308835i	$-0.900061\pi$
$73$	−7.19619	+	5.85454i	−0.842251	+	0.685222i	0.108865	+	0.994057i	$0.465278\pi$
$74$	−10.6752	+	6.49174i	−1.24097	+	0.754649i
$75$	7.25573	−	3.15161i	0.837819	−	0.363916i
$76$	−0.0542995	+	0.261304i	−0.00622859	+	0.0299736i
$77$	−3.76585	−	1.05514i	−0.429159	−	0.120245i
$78$	0.102858	+	0.289416i	0.0116464	+	0.0327699i
$79$	0.557398	−	0.596827i	0.0627121	−	0.0671483i	−0.698708	−	0.715407i	$-0.746241\pi$
$79$	0.557398	−	0.596827i	0.0627121	−	0.0671483i	0.761420	+	0.648258i	$0.224502\pi$
$80$	0.218174	−	3.18958i	0.0243925	−	0.356606i
$81$	−2.28359	−	10.9892i	−0.253732	−	1.22102i
$82$	−3.65510	−	5.17810i	−0.403638	−	0.571825i
$83$	−0.242951	+	0.0680717i	−0.0266674	+	0.00747184i	−0.283105	−	0.959089i	$-0.591364\pi$
$83$	−0.242951	+	0.0680717i	−0.0266674	+	0.00747184i	0.256437	+	0.966561i	$0.417451\pi$
$84$	−0.0540968	−	0.790867i	−0.00590244	−	0.0862906i
$85$	0.850526	+	0.691954i	0.0922525	+	0.0750530i
$86$	−5.97397	−	0.821104i	−0.644190	−	0.0885419i
$87$	7.64827	+	4.65102i	0.819981	+	0.498641i
$88$	−13.7697	+	1.89261i	−1.46786	+	0.201753i
$89$	−3.52263	−	1.53009i	−0.373398	−	0.162190i	0.203361	−	0.979104i	$-0.434813\pi$
$89$	−3.52263	−	1.53009i	−0.373398	−	0.162190i	−0.576759	+	0.816914i	$0.695683\pi$
$90$	1.05597	−	1.49596i	0.111309	−	0.157688i
$91$	0.0339538	−	0.0955367i	0.00355932	−	0.0100150i
$92$	0.460393	+	0.888519i	0.0479993	+	0.0926345i
$93$	18.6108			1.92984
$94$	−2.87000	−	8.05671i	−0.296018	−	0.830986i
$95$	0.659558			0.0676692
$96$	−2.35695	−	4.54871i	−0.240555	−	0.464251i
$97$	3.39347	−	9.54831i	0.344555	−	0.969484i	−0.635733	−	0.771909i	$-0.719302\pi$
$97$	3.39347	−	9.54831i	0.344555	−	0.969484i	0.980288	−	0.197575i	$-0.0633066\pi$
$98$	−4.50663	+	6.38444i	−0.455238	+	0.644926i
$99$	−5.59812	−	2.43161i	−0.562632	−	0.244386i
$100$	−1.66928	+	0.229437i	−0.166928	+	0.0229437i
$101$	3.67506	+	2.23486i	0.365683	+	0.222376i	0.690389	−	0.723438i	$-0.257439\pi$
$101$	3.67506	+	2.23486i	0.365683	+	0.222376i	−0.324706	+	0.945815i	$0.605265\pi$
$102$	−2.57434	−	0.353835i	−0.254897	−	0.0350349i
$103$	14.1521	+	11.5136i	1.39445	+	1.13447i	0.973842	+	0.227227i	$0.0729661\pi$
$103$	14.1521	+	11.5136i	1.39445	+	1.13447i	0.420609	+	0.907242i	$0.361817\pi$
$104$	−0.0245906	−	0.359502i	−0.00241130	−	0.0352520i
$105$	−1.88640	+	0.528544i	−0.184094	+	0.0515806i
$106$	−8.60057	−	12.1842i	−0.835361	−	1.18344i
$107$	−2.04105	−	9.82205i	−0.197315	−	0.949533i	−0.954930	−	0.296831i	$-0.904070\pi$
$107$	−2.04105	−	9.82205i	−0.197315	−	0.949533i	0.757615	−	0.652702i	$-0.226365\pi$
$108$	−0.104772	+	1.53172i	−0.0100817	+	0.147390i
$109$	−12.5259	+	13.4120i	−1.19977	+	1.28464i	−0.251247	+	0.967923i	$0.580841\pi$
$109$	−12.5259	+	13.4120i	−1.19977	+	1.28464i	−0.948521	+	0.316715i	$0.897420\pi$
$110$	2.08845	+	5.87632i	0.199125	+	0.560285i
$111$	20.0873	+	5.62820i	1.90660	+	0.534205i
$112$	0.508872	−	2.44883i	0.0480839	−	0.231393i
$113$	−16.8201	+	7.30602i	−1.58231	+	0.687292i	−0.992724	−	0.120416i	$-0.961577\pi$
$113$	−16.8201	+	7.30602i	−1.58231	+	0.687292i	−0.589582	+	0.807708i	$0.700708\pi$
$114$	−1.33557	+	0.812178i	−0.125088	+	0.0760674i
$115$	1.91839	−	1.56073i	0.178891	−	0.145539i
$116$	−1.30140	−	1.39346i	−0.120832	−	0.129379i
$117$	0.0727976	−	0.140493i	0.00673014	−	0.0129886i
$118$	−5.62038	+	10.8468i	−0.517398	+	0.998532i
$119$	0.585483	+	0.626900i	0.0536712	+	0.0574678i
$120$	−5.40082	+	4.39389i	−0.493025	+	0.401106i
$121$	8.36222	−	5.08518i	0.760202	−	0.462289i
$122$	−14.7885	+	6.42354i	−1.33888	+	0.581560i
$123$	−2.15309	+	10.3612i	−0.194138	+	0.934242i
$124$	−3.81711	−	1.06950i	−0.342786	−	0.0960442i
$125$	3.23036	+	9.08935i	0.288932	+	0.812976i
$126$	0.977782	−	1.04695i	0.0871078	−	0.0932696i
$127$	0.493838	−	7.21965i	0.0438210	−	0.640640i	−0.922938	−	0.384950i	$-0.874219\pi$
$127$	0.493838	−	7.21965i	0.0438210	−	0.640640i	0.966759	−	0.255691i	$-0.0823029\pi$
$128$	−1.25815	−	6.05457i	−0.111206	−	0.535154i
$129$	5.80618	+	8.22548i	0.511205	+	0.724213i
$130$	−0.155686	+	0.0436210i	−0.0136545	+	0.00382582i
$131$	0.717012	+	10.4823i	0.0626456	+	0.915846i	0.917691	+	0.397294i	$0.130051\pi$
$131$	0.717012	+	10.4823i	0.0626456	+	0.915846i	−0.855046	+	0.518553i	$0.826471\pi$
$132$	3.26840	+	2.65904i	0.284478	+	0.231440i
$133$	0.511187	+	0.0702610i	0.0443255	+	0.00609240i
$134$	5.70289	+	3.46800i	0.492655	+	0.299590i
$135$	3.75885	−	0.516643i	0.323511	−	0.0444655i
$136$	2.79617	+	1.21455i	0.239769	+	0.104146i
$137$	−6.21174	+	8.80003i	−0.530705	+	0.751838i	−0.990697	−	0.136085i	$-0.956548\pi$
$137$	−6.21174	+	8.80003i	−0.530705	+	0.751838i	0.459992	+	0.887923i	$0.347852\pi$
$138$	−1.96276	+	5.52269i	−0.167082	+	0.470122i
$139$	3.23300	+	6.23940i	0.274219	+	0.529219i	0.984648	−	0.174550i	$-0.0558470\pi$
$139$	3.23300	+	6.23940i	0.274219	+	0.529219i	−0.710429	+	0.703769i	$0.751499\pi$
$140$	0.417278			0.0352664
$141$	−6.56044	+	12.6838i	−0.552489	+	1.06817i
$142$	6.78933			0.569748
$143$	0.247934	+	0.478491i	0.0207333	+	0.0400134i
$144$	1.30715	−	3.67797i	0.108929	−	0.306497i
$145$	−2.71729	+	3.84952i	−0.225659	+	0.319685i
$146$	10.6151	+	4.61078i	0.878510	+	0.381591i
$147$	12.9265	−	1.77671i	1.06616	−	0.146540i
$148$	−3.79652	−	2.30871i	−0.312072	−	0.189775i
$149$	−0.284021	−	0.0390377i	−0.0232679	−	0.00319810i	0.124523	−	0.992217i	$-0.460260\pi$
$149$	−0.284021	−	0.0390377i	−0.0232679	−	0.00319810i	−0.147791	+	0.989019i	$0.547216\pi$
$150$	−7.65530	−	6.22805i	−0.625053	−	0.508518i
$151$	−0.920547	−	13.4579i	−0.0749130	−	1.09519i	−0.871413	−	0.490551i	$-0.836796\pi$
$151$	−0.920547	−	13.4579i	−0.0749130	−	1.09519i	0.796500	−	0.604639i	$-0.206683\pi$
$152$	1.76583	−	0.494761i	0.143227	−	0.0401304i
$153$	0.771990	+	1.09366i	0.0624117	+	0.0884173i
$154$	0.992649	+	4.77689i	0.0799899	+	0.384933i
$155$	−0.668539	+	9.77370i	−0.0536984	+	0.785042i
$156$	−0.0745584	+	0.0798325i	−0.00596945	+	0.00639172i
$157$	7.29848	+	20.5360i	0.582482	+	1.63895i	0.756341	+	0.654177i	$0.226985\pi$
$157$	7.29848	+	20.5360i	0.582482	+	1.63895i	−0.173859	+	0.984771i	$0.555624\pi$
$158$	−0.980999	−	0.274863i	−0.0780441	−	0.0218669i
$159$	−5.06630	+	24.3804i	−0.401784	+	1.93349i
$160$	2.47349	−	1.07439i	0.195546	−	0.0849377i
$161$	1.65310	−	1.00527i	0.130282	−	0.0792265i
$162$	−10.8617	+	8.83665i	−0.853375	+	0.694272i
$163$	−10.2333	−	10.9572i	−0.801536	−	0.858236i	0.190822	−	0.981625i	$-0.438885\pi$
$163$	−10.2333	−	10.9572i	−0.801536	−	0.858236i	−0.992358	+	0.123389i	$0.960624\pi$
$164$	1.03703	−	2.00138i	0.0809786	−	0.156282i
$165$	4.79051	−	9.24526i	0.372941	−	0.719743i
$166$	0.214841	+	0.230039i	0.0166749	+	0.0178545i
$167$	6.06543	−	4.93460i	0.469357	−	0.381851i	−0.366836	−	0.930286i	$-0.619559\pi$
$167$	6.06543	−	4.93460i	0.469357	−	0.381851i	0.836193	+	0.548435i	$0.184776\pi$
$168$	−4.65395	+	2.83013i	−0.359060	+	0.218349i
$169$	11.9109	−	5.17365i	0.916226	−	0.397973i
$170$	0.278297	−	1.33924i	0.0213444	−	0.102715i
$171$	0.775410	+	0.217260i	0.0592971	+	0.0166143i
$172$	−0.718167	−	2.02073i	−0.0547597	−	0.154079i
$173$	−8.13308	+	8.70840i	−0.618347	+	0.662088i	−0.960734	−	0.277471i	$-0.910504\pi$
$173$	−8.13308	+	8.70840i	−0.618347	+	0.662088i	0.342387	+	0.939559i	$0.388765\pi$
$174$	0.762074	−	11.1411i	0.0577727	−	0.844607i
$175$	0.662798	+	3.18956i	0.0501028	+	0.241108i
$176$	7.66640	+	10.8608i	0.577877	+	0.818665i
$177$	19.6410	−	5.50315i	1.47631	−	0.413642i
$178$	0.326966	+	4.78008i	0.0245072	+	0.358282i
$179$	7.48824	+	6.09214i	0.559697	+	0.455348i	0.868437	−	0.495799i	$-0.165125\pi$
$179$	7.48824	+	6.09214i	0.559697	+	0.455348i	−0.308740	+	0.951146i	$0.599907\pi$
$180$	0.645149	+	0.0886737i	0.0480866	+	0.00660935i
$181$	−4.66995	−	2.83986i	−0.347114	−	0.211085i	0.335195	−	0.942149i	$-0.391198\pi$
$181$	−4.66995	−	2.83986i	−0.347114	−	0.211085i	−0.682309	+	0.731064i	$0.739024\pi$
$182$	−0.125310	+	0.0172235i	−0.00928860	+	0.00127669i
$183$	24.6917	+	10.7251i	1.82526	+	0.792824i
$184$	3.96532	−	5.61758i	0.292327	−	0.414133i
$185$	−3.67731	+	10.3470i	−0.270361	+	0.760724i
$186$	−10.6815	−	20.6144i	−0.783209	−	1.51152i
$187$	−4.55928			−0.333407
$188$	2.07446	−	2.22446i	0.151296	−	0.162236i
$189$	2.96832			0.215913
$190$	−0.378550	−	0.730568i	−0.0274629	−	0.0530010i
$191$	1.70205	−	4.78912i	0.123156	−	0.346529i	−0.864616	−	0.502434i	$-0.832438\pi$
$191$	1.70205	−	4.78912i	0.123156	−	0.346529i	0.987772	+	0.155905i	$0.0498294\pi$
$192$	−10.6906	+	15.1452i	−0.771529	+	1.09301i
$193$	1.39919	+	0.607752i	0.100716	+	0.0437470i	0.448158	−	0.893954i	$-0.352080\pi$
$193$	1.39919	+	0.607752i	0.100716	+	0.0437470i	−0.347442	+	0.937701i	$0.612950\pi$
$194$	−12.5240	+	1.72138i	−0.899169	+	0.123588i
$195$	0.230653	+	0.140263i	0.0165174	+	0.0100444i
$196$	−2.75335	−	0.378440i	−0.196668	−	0.0270314i
$197$	−4.39742	−	3.57757i	−0.313304	−	0.254891i	0.461434	−	0.887175i	$-0.347335\pi$
$197$	−4.39742	−	3.57757i	−0.313304	−	0.254891i	−0.774737	+	0.632283i	$0.782118\pi$
$198$	0.519611	+	7.59644i	0.0369271	+	0.539855i
$199$	21.7944	−	6.10650i	1.54496	−	0.432878i	0.611409	−	0.791315i	$-0.290603\pi$
$199$	21.7944	−	6.10650i	1.54496	−	0.432878i	0.933554	+	0.358436i	$0.116690\pi$
$200$	6.67669	+	9.45872i	0.472113	+	0.668832i
$201$	−2.26737	−	10.9112i	−0.159928	−	0.769616i
$202$	0.366184	−	5.35342i	0.0257646	−	0.376665i
$203$	−2.51610	+	2.69409i	−0.176596	+	0.189088i
$204$	−0.309476	−	0.870783i	−0.0216677	−	0.0609670i
$205$	−5.36401	−	1.50292i	−0.374639	−	0.104969i
$206$	4.63066	−	22.2840i	0.322633	−	1.55260i
$207$	2.76946	−	1.20295i	0.192491	−	0.0836107i
$208$	−0.294478	+	0.179076i	−0.0204184	+	0.0124167i
$209$	−2.12746	+	1.73082i	−0.147160	+	0.119723i
$210$	1.66814	+	1.78614i	0.115112	+	0.123255i
$211$	5.15732	−	9.95318i	0.355045	−	0.685205i	−0.641601	−	0.767038i	$-0.721730\pi$
$211$	5.15732	−	9.95318i	0.355045	−	0.685205i	0.996646	+	0.0818330i	$0.0260774\pi$
$212$	2.44017	−	4.70932i	0.167592	−	0.323438i
$213$	−7.73733	−	8.28466i	−0.530153	−	0.567656i
$214$	−9.70808	+	7.89810i	−0.663630	+	0.539903i
$215$	−4.52830	+	2.75372i	−0.308827	+	0.187802i
$216$	9.67598	−	4.20287i	0.658367	−	0.285969i
$217$	−1.55931	+	7.50383i	−0.105853	+	0.509393i
$218$	22.0452	+	6.17677i	1.49309	+	0.418344i
$219$	−6.47098	−	18.2076i	−0.437268	−	1.23036i
$220$	−1.51384	+	1.62093i	−0.102063	+	0.109283i
$221$	0.00806632	−	0.117925i	0.000542599	−	0.00793252i
$222$	−5.29486	−	25.4803i	−0.355368	−	1.71012i
$223$	2.07138	+	2.93448i	0.138710	+	0.196507i	0.880395	−	0.474241i	$-0.157278\pi$
$223$	2.07138	+	2.93448i	0.138710	+	0.196507i	−0.741685	+	0.670748i	$0.765973\pi$
$224$	2.03151	−	0.569203i	0.135736	−	0.0380315i
$225$	0.346948	+	5.07219i	0.0231298	+	0.338146i
$226$	17.7464	+	14.4378i	1.18048	+	0.960388i
$227$	23.6169	+	3.24607i	1.56751	+	0.215449i	0.867041	−	0.498236i	$-0.166019\pi$
$227$	23.6169	+	3.24607i	1.56751	+	0.215449i	0.700466	+	0.713685i	$0.252975\pi$
$228$	−0.474980	−	0.288842i	−0.0314563	−	0.0191290i
$229$	−24.2752	+	3.33655i	−1.60415	+	0.220485i	−0.881999	−	0.471250i	$-0.843803\pi$
$229$	−24.2752	+	3.33655i	−1.60415	+	0.220485i	−0.722151	+	0.691736i	$0.756846\pi$
$230$	−2.82981	−	1.22916i	−0.186592	−	0.0810484i
$231$	4.69773	−	6.65517i	0.309088	−	0.437878i
$232$	−4.38728	+	12.3446i	−0.288039	+	0.810464i
$233$	−3.22626	−	6.22640i	−0.211359	−	0.407905i	0.758464	−	0.651715i	$-0.225950\pi$
$233$	−3.22626	−	6.22640i	−0.211359	−	0.407905i	−0.969823	+	0.243810i	$0.921603\pi$
$234$	−0.197401			−0.0129045
$235$	−6.42540	−	3.90094i	−0.419147	−	0.254469i
$236$	−4.34466			−0.282813
$237$	0.782576	+	1.51030i	0.0508338	+	0.0981048i
$238$	0.358358	−	1.00832i	0.0232289	−	0.0653599i
$239$	11.6168	−	16.4572i	0.751426	−	1.06453i	−0.244073	−	0.969757i	$-0.578484\pi$
$239$	11.6168	−	16.4572i	0.751426	−	1.06453i	0.995499	−	0.0947710i	$-0.0302119\pi$
$240$	6.10795	+	2.65306i	0.394267	+	0.171254i
$241$	−7.13690	+	0.980944i	−0.459728	+	0.0631882i	−0.362315	−	0.932056i	$-0.618013\pi$
$241$	−7.13690	+	0.980944i	−0.459728	+	0.0631882i	−0.0974134	+	0.995244i	$0.531057\pi$
$242$	−10.4321	−	6.34391i	−0.670602	−	0.407802i
$243$	12.8766	+	1.76984i	0.826033	+	0.113536i
$244$	−4.44798	−	3.61870i	−0.284753	−	0.231664i
$245$	0.468714	+	6.85235i	0.0299450	+	0.437781i
$246$	12.7125	−	3.56188i	0.810521	−	0.227097i
$247$	−0.0410036	−	0.0580888i	−0.00260900	−	0.00369610i
$248$	5.54178	+	26.6685i	0.351903	+	1.69345i
$249$	0.0358644	−	0.524318i	0.00227281	−	0.0332273i
$250$	8.21389	−	8.79493i	0.519492	−	0.556240i
$251$	9.82091	+	27.6334i	0.619890	+	1.74420i	0.666728	+	0.745302i	$0.267694\pi$
$251$	9.82091	+	27.6334i	0.619890	+	1.74420i	−0.0468372	+	0.998903i	$0.514914\pi$
$252$	0.490573	+	0.137452i	0.0309032	+	0.00865867i
$253$	−2.09226	+	10.0685i	−0.131539	+	0.633003i
$254$	−8.28038	+	3.59668i	−0.519557	+	0.225675i
$255$	−1.95136	+	1.18665i	−0.122199	+	0.0743108i
$256$	7.82331	−	6.36473i	0.488957	−	0.397796i
$257$	0.276837	+	0.296420i	0.0172686	+	0.0184902i	0.739412	−	0.673253i	$-0.235104\pi$
$257$	0.276837	+	0.296420i	0.0172686	+	0.0184902i	−0.722143	+	0.691744i	$0.756843\pi$
$258$	5.77864	−	11.1523i	0.359762	−	0.694309i
$259$	−3.95232	+	7.62762i	−0.245585	+	0.473957i
$260$	−0.0392469	−	0.0420231i	−0.00243399	−	0.00260616i
$261$	−4.46262	+	3.63061i	−0.276229	+	0.224729i
$262$	11.1994	−	6.81049i	0.691900	−	0.420754i
$263$	−12.1432	+	5.27454i	−0.748782	+	0.325242i	−0.738091	−	0.674701i	$-0.764273\pi$
$263$	−12.1432	+	5.27454i	−0.748782	+	0.325242i	−0.0106906	+	0.999943i	$0.503403\pi$
$264$	5.89032	−	28.3458i	0.362524	−	1.74456i
$265$	−12.6217	−	3.53643i	−0.775345	−	0.217241i
$266$	−0.215567	−	0.606549i	−0.0132173	−	0.0371899i
$267$	5.46026	−	5.84651i	0.334162	−	0.357800i
$268$	−0.161990	+	2.36821i	−0.00989510	+	0.144661i
$269$	3.40957	+	16.4078i	0.207885	+	1.00040i	0.945611	+	0.325299i	$0.105465\pi$
$269$	3.40957	+	16.4078i	0.207885	+	1.00040i	−0.737726	+	0.675100i	$0.764100\pi$
$270$	−2.72964	−	3.86702i	−0.166121	−	0.235339i
$271$	20.9243	−	5.86272i	1.27106	−	0.356135i	0.432844	−	0.901469i	$-0.357510\pi$
$271$	20.9243	−	5.86272i	1.27106	−	0.356135i	0.838219	+	0.545334i	$0.183597\pi$
$272$	−0.198982	−	2.90902i	−0.0120651	−	0.176385i
$273$	0.163824	+	0.133281i	0.00991509	+	0.00806652i
$274$	13.3127	+	1.82978i	0.804248	+	0.110541i
$275$	−14.7945	−	8.99673i	−0.892141	−	0.542523i
$276$	−2.06502	+	0.283831i	−0.124300	+	0.0170846i
$277$	−10.6219	−	4.61373i	−0.638206	−	0.277212i	0.0544097	−	0.998519i	$-0.482672\pi$
$277$	−10.6219	−	4.61373i	−0.638206	−	0.277212i	−0.692616	+	0.721307i	$0.743542\pi$
$278$	5.05559	−	7.16214i	0.303214	−	0.429557i
$279$	−4.00544	+	11.2702i	−0.239800	+	0.674731i
$280$	−1.31910	−	2.54575i	−0.0788314	−	0.152138i
$281$	33.0771			1.97322			0.986608	−	0.163107i	$-0.0521517\pi$
$281$	33.0771			1.97322			0.986608	+	0.163107i	$0.0521517\pi$
$282$	17.8147	−	0.0130345i	1.06085	−	0.000776195i
$283$	4.81755			0.286373			0.143187	−	0.989696i	$-0.454265\pi$
$283$	4.81755			0.286373			0.143187	+	0.989696i	$0.454265\pi$
$284$	1.11085	+	2.14384i	0.0659168	+	0.127214i
$285$	−0.460066	+	1.29450i	−0.0272520	+	0.0766797i
$286$	0.387707	−	0.549255i	0.0229256	−	0.0324781i
$287$	−3.99724	−	1.73625i	−0.235950	−	0.102487i
$288$	3.26186	−	0.448332i	0.192207	−	0.0264182i
$289$	0.854419	+	0.519584i	0.0502600	+	0.0305638i
$290$	5.82355	+	0.800428i	0.341970	+	0.0470028i
$291$	16.3732	+	13.3206i	0.959816	+	0.780868i
$292$	0.280878	+	4.10629i	0.0164371	+	0.240302i
$293$	7.05601	−	1.97700i	0.412217	−	0.115498i	−0.0574356	−	0.998349i	$-0.518292\pi$
$293$	7.05601	−	1.97700i	0.412217	−	0.115498i	0.469652	+	0.882852i	$0.344379\pi$
$294$	−9.38709	−	13.2985i	−0.547466	−	0.775583i
$295$	2.18451	+	10.5124i	0.127187	+	0.612057i
$296$	−2.08354	+	30.4603i	−0.121103	+	1.77047i
$297$	−10.7687	+	11.5305i	−0.624866	+	0.669068i
$298$	0.119772	+	0.337005i	0.00693818	+	0.0195222i
$299$	−0.256720	−	0.0719296i	−0.0148465	−	0.00415979i
$300$	0.714072	−	3.43630i	0.0412270	−	0.198395i
$301$	−3.80298	+	1.65187i	−0.219200	+	0.0952120i
$302$	−14.3785	+	8.74376i	−0.827389	+	0.503147i
$303$	−6.94981	+	5.65409i	−0.399256	+	0.324819i
$304$	−1.19719	−	1.28188i	−0.0686634	−	0.0735206i
$305$	−6.51943	+	12.5819i	−0.373301	+	0.720439i
$306$	0.768328	−	1.48281i	0.0439224	−	0.0847664i
$307$	−6.44529	−	6.90122i	−0.367852	−	0.393873i	0.519876	−	0.854242i	$-0.325978\pi$
$307$	−6.44529	−	6.90122i	−0.367852	−	0.393873i	−0.887728	+	0.460368i	$0.847717\pi$
$308$	−1.34597	+	1.09503i	−0.0766936	+	0.0623949i
$309$	−32.4692	+	19.7450i	−1.84711	+	1.12325i
$310$	11.2097	−	4.86905i	0.636666	−	0.276543i
$311$	−4.73104	+	22.7670i	−0.268273	+	1.29100i	0.602026	+	0.798476i	$0.294360\pi$
$311$	−4.73104	+	22.7670i	−0.268273	+	1.29100i	−0.870299	+	0.492523i	$0.836075\pi$
$312$	0.722740	+	0.202502i	0.0409171	+	0.0114644i
$313$	−4.05988	−	11.4234i	−0.229478	−	0.645688i	−0.999966	−	0.00823437i	$-0.997379\pi$
$313$	−4.05988	−	11.4234i	−0.229478	−	0.645688i	0.770488	−	0.637454i	$-0.220012\pi$
$314$	18.5580	−	19.8708i	1.04729	−	1.12137i
$315$	0.0859204	−	1.25611i	0.00484107	−	0.0707739i
$316$	−0.0737156	−	0.354739i	−0.00414683	−	0.0199556i
$317$	−5.91353	−	8.37756i	−0.332137	−	0.470531i	0.616293	−	0.787517i	$-0.288634\pi$
$317$	−5.91353	−	8.37756i	−0.332137	−	0.470531i	−0.948430	+	0.316986i	$0.897329\pi$
$318$	29.9130	−	8.38123i	1.67744	−	0.469996i
$319$	−1.33710	−	19.5477i	−0.0748632	−	1.09446i
$320$	−7.56966	−	6.15837i	−0.423157	−	0.344264i
$321$	20.7013	+	2.84532i	1.15543	+	0.158810i
$322$	−2.06229	−	1.25411i	−0.114927	−	0.0698886i
$323$	0.595939	−	0.0819099i	0.0331589	−	0.00455759i
$324$	−4.56748	−	1.98393i	−0.253749	−	0.110219i
$325$	0.258874	−	0.366741i	0.0143598	−	0.0203431i
$326$	−6.26354	+	17.6239i	−0.346905	+	0.976098i
$327$	−17.5862	−	33.9398i	−0.972519	−	1.87688i
$328$	−15.4884			−0.855204
$329$	−4.56442	−	3.70788i	−0.251645	−	0.204422i
$330$	−12.9901			−0.715083
$331$	2.01997	+	3.89837i	0.111028	+	0.214274i	0.936912	−	0.349567i	$-0.113671\pi$
$331$	2.01997	+	3.89837i	0.111028	+	0.214274i	−0.825884	+	0.563840i	$0.809323\pi$
$332$	−0.0374868	+	0.105478i	−0.00205736	+	0.00578885i
$333$	−7.73154	+	10.9531i	−0.423686	+	0.600226i
$334$	−8.94709	−	3.88627i	−0.489563	−	0.212647i
$335$	5.81161	−	0.798787i	0.317522	−	0.0436424i
$336$	4.45131	+	2.70690i	0.242839	+	0.147674i
$337$	−35.0107	−	4.81211i	−1.90716	−	0.262133i	−0.916660	−	0.399669i	$-0.869125\pi$
$337$	−35.0107	−	4.81211i	−1.90716	−	0.262133i	−0.990497	+	0.137536i	$0.956082\pi$
$338$	−12.5669	−	10.2239i	−0.683548	−	0.556107i
$339$	−2.60671	−	38.1088i	−0.141577	−	2.06979i
$340$	0.468421	−	0.131245i	0.0254037	−	0.00711778i
$341$	−23.4918	−	33.2803i	−1.27215	−	1.80223i
$342$	−0.204392	−	0.983588i	−0.0110522	−	0.0531863i
$343$	−0.776450	+	11.3513i	−0.0419244	+	0.612913i
$344$	−10.0579	+	10.7694i	−0.542284	+	0.580645i
$345$	1.72506	+	4.85386i	0.0928742	+	0.261323i
$346$	14.3139	+	4.01057i	0.769521	+	0.215610i
$347$	−2.10123	+	10.1117i	−0.112800	+	0.542823i	0.884313	+	0.466894i	$0.154627\pi$
$347$	−2.10123	+	10.1117i	−0.112800	+	0.542823i	−0.997113	+	0.0759289i	$0.975808\pi$
$348$	3.64269	−	1.58224i	0.195268	−	0.0848170i
$349$	−30.4282	+	18.5038i	−1.62878	+	0.990486i	−0.657224	+	0.753695i	$0.728269\pi$
$349$	−30.4282	+	18.5038i	−1.62878	+	0.990486i	−0.971561	+	0.236791i	$0.923904\pi$
$350$	3.15255	−	2.56479i	0.168511	−	0.137094i
$351$	−0.279183	−	0.298932i	−0.0149017	−	0.0159558i
$352$	−5.15903	+	9.95648i	−0.274977	+	0.530682i
$353$	5.15329	−	9.94541i	0.274282	−	0.529341i	−0.710379	−	0.703820i	$-0.751476\pi$
$353$	5.15329	−	9.94541i	0.274282	−	0.529341i	0.984661	+	0.174479i	$0.0558241\pi$
$354$	−17.3685	−	18.5971i	−0.923124	−	0.988424i
$355$	4.62875	−	3.76576i	0.245668	−	0.199866i
$356$	−1.45589	+	0.885347i	−0.0771621	+	0.0469233i
$357$	−1.63880	+	0.711832i	−0.0867346	+	0.0376741i
$358$	2.45020	−	11.7910i	0.129497	−	0.623173i
$359$	27.1128	+	7.59664i	1.43096	+	0.400935i	0.896042	−	0.443970i	$-0.146430\pi$
$359$	27.1128	+	7.59664i	1.43096	+	0.400935i	0.534916	+	0.844905i	$0.320343\pi$
$360$	−1.49846	−	4.21627i	−0.0789760	−	0.222217i
$361$	−12.7215	+	13.6214i	−0.669554	+	0.716917i
$362$	−0.465314	+	6.80265i	−0.0244563	+	0.357539i
$363$	4.14763	+	19.9595i	0.217694	+	1.04760i
$364$	−0.0259415	−	0.0367507i	−0.00135970	−	0.00192626i
$365$	9.79443	−	2.74427i	0.512664	−	0.143642i
$366$	−2.29185	−	33.5057i	−0.119797	−	1.75137i
$367$	10.0252	+	8.15612i	0.523312	+	0.425746i	0.855758	−	0.517377i	$-0.173091\pi$
$367$	10.0252	+	8.15612i	0.523312	+	0.425746i	−0.332446	+	0.943122i	$0.607874\pi$
$368$	−6.51547	−	0.895531i	−0.339642	−	0.0466828i
$369$	−5.81113	−	3.53383i	−0.302516	−	0.183964i
$370$	13.5715	−	1.86536i	0.705550	−	0.0969756i
$371$	−9.40565	−	4.08545i	−0.488317	−	0.212106i
$372$	4.76167	−	6.74575i	0.246881	−	0.349751i
$373$	10.4326	−	29.3546i	0.540181	−	1.51992i	−0.286969	−	0.957940i	$-0.592648\pi$
$373$	10.4326	−	29.3546i	0.540181	−	1.51992i	0.827149	−	0.561982i	$-0.189961\pi$
$374$	2.61677	+	5.05014i	0.135310	+	0.261137i
$375$	−20.0928			−1.03759
$376$	−20.1289	−	5.62397i	−1.03807	−	0.290034i
$377$	0.507966			0.0261616
$378$	−1.70365	−	3.28789i	−0.0876263	−	0.169111i
$379$	8.76675	−	24.6673i	0.450318	−	1.26707i	−0.472327	−	0.881423i	$-0.656586\pi$
$379$	8.76675	−	24.6673i	0.450318	−	1.26707i	0.922645	−	0.385650i	$-0.126023\pi$
$380$	0.168752	−	0.239067i	0.00865678	−	0.0122639i
$381$	13.8254	+	6.00522i	0.708297	+	0.307657i
$382$	−6.28162	+	0.863388i	−0.321396	+	0.0441748i
$383$	−22.7893	−	13.8585i	−1.16448	−	0.708136i	−0.201972	−	0.979391i	$-0.564735\pi$
$383$	−22.7893	−	13.8585i	−1.16448	−	0.708136i	−0.962507	+	0.271256i	$0.912561\pi$
$384$	12.7608	+	1.75393i	0.651197	+	0.0895050i
$385$	3.32630	+	2.70615i	0.169524	+	0.137918i
$386$	−0.129871	−	1.89864i	−0.00661025	−	0.0966384i
$387$	−6.23078	+	1.74578i	−0.316728	+	0.0887431i
$388$	−2.59269	−	3.67301i	−0.131624	−	0.186469i
$389$	−2.62591	−	12.6366i	−0.133139	−	0.640699i	−0.991762	−	0.128092i	$-0.959115\pi$
$389$	−2.62591	−	12.6366i	−0.133139	−	0.640699i	0.858623	−	0.512607i	$-0.171320\pi$
$390$	0.0229822	−	0.335988i	0.00116375	−	0.0170134i
$391$	1.53952	−	1.64843i	0.0778570	−	0.0833645i
$392$	6.39511	+	17.9941i	0.323002	+	0.908840i
$393$	−21.0736	−	5.90456i	−1.06302	−	0.297846i
$394$	−1.43886	+	6.92419i	−0.0724889	+	0.348836i
$395$	−0.821269	+	0.356728i	−0.0413225	+	0.0179489i
$396$	−2.31368	+	1.40698i	−0.116267	+	0.0707035i
$397$	−17.1129	+	13.9223i	−0.858870	+	0.698742i	−0.954993	−	0.296627i	$-0.904138\pi$
$397$	−17.1129	+	13.9223i	−0.858870	+	0.698742i	0.0961237	+	0.995369i	$0.469356\pi$
$398$	−19.2727	−	20.6360i	−0.966054	−	1.03439i
$399$	−0.494472	+	0.954288i	−0.0247546	+	0.0477741i
$400$	5.09462	−	9.83218i	0.254731	−	0.491609i
$401$	−18.8066	−	20.1369i	−0.939155	−	1.00559i	−0.999972	−	0.00744030i	$-0.997632\pi$
$401$	−18.8066	−	20.1369i	−0.939155	−	1.00559i	0.0608176	−	0.998149i	$-0.480629\pi$
$402$	−10.7846	+	8.77390i	−0.537885	+	0.437602i
$403$	0.902355	−	0.548734i	0.0449495	−	0.0273344i
$404$	1.75034	−	0.760282i	0.0870828	−	0.0378254i
$405$	−2.50383	+	12.0491i	−0.124416	+	0.598724i
$406$	4.42824	+	1.24074i	0.219770	+	0.0615766i
$407$	−15.2911	−	43.0251i	−0.757952	−	2.13267i
$408$	−4.33420	+	4.64079i	−0.214575	+	0.229753i
$409$	1.39220	−	20.3533i	0.0688399	−	1.00640i	−0.827050	−	0.562128i	$-0.809983\pi$
$409$	1.39220	−	20.3533i	0.0688399	−	1.00640i	0.895890	−	0.444276i	$-0.146539\pi$
$410$	1.41391	+	6.80411i	0.0698281	+	0.336031i
$411$	−12.9387	−	18.3300i	−0.638221	−	0.904154i
$412$	7.79418	−	2.18383i	0.383992	−	0.107589i
$413$	0.573229	+	8.38031i	0.0282067	+	0.412368i
$414$	−2.92198	−	2.37721i	−0.143607	−	0.116833i
$415$	0.274065	+	0.0376693i	0.0134533	+	0.00184912i
$416$	−0.248396	−	0.151053i	−0.0121786	−	0.00740598i
$417$	−14.5011	+	1.99313i	−0.710122	+	0.0976040i
$418$	3.13821	+	1.36312i	0.153495	+	0.0666722i
$419$	−17.8368	+	25.2690i	−0.871385	+	1.23447i	0.0995264	+	0.995035i	$0.468267\pi$
$419$	−17.8368	+	25.2690i	−0.871385	+	1.23447i	−0.970912	+	0.239437i	$0.923037\pi$
$420$	−0.291067	+	0.818984i	−0.0142026	+	0.0399623i
$421$	6.75020	+	13.0273i	0.328984	+	0.634911i	0.993686	−	0.112198i	$-0.0357891\pi$
$421$	6.75020	+	13.0273i	0.328984	+	0.634911i	−0.664701	+	0.747109i	$0.731441\pi$
$422$	−13.9848			−0.680769
$423$	−6.26905	−	6.70268i	−0.304812	−	0.325895i
$424$	−36.4447			−1.76991
$425$	1.74724	+	3.37202i	0.0847535	+	0.163567i
$426$	−4.73581	+	13.3253i	−0.229451	+	0.645613i
$427$	−6.39317	+	9.05705i	−0.309387	+	0.438302i
$428$	−4.08236	−	1.77322i	−0.197328	−	0.0857119i
$429$	−1.11207	+	0.152850i	−0.0536912	+	0.00737969i
$430$	5.64918	+	3.43535i	0.272428	+	0.165667i
$431$	14.4376	+	1.98440i	0.695434	+	0.0955852i	0.475221	−	0.879867i	$-0.342368\pi$
$431$	14.4376	+	1.98440i	0.695434	+	0.0955852i	0.220213	+	0.975452i	$0.429325\pi$
$432$	−7.82695	−	6.36770i	−0.376574	−	0.306366i
$433$	2.69060	+	39.3352i	0.129302	+	1.89033i	0.384037	+	0.923318i	$0.374533\pi$
$433$	2.69060	+	39.3352i	0.129302	+	1.89033i	−0.254735	+	0.967011i	$0.581988\pi$
$434$	9.20668	−	2.57959i	0.441935	−	0.123824i
$435$	−5.65998	−	8.01836i	−0.271375	−	0.384451i
$436$	1.65655	+	7.97176i	0.0793344	+	0.381778i
$437$	0.0925912	−	1.35364i	0.00442924	−	0.0647532i
$438$	−16.4539	+	17.6178i	−0.786198	+	0.841812i
$439$	6.07453	+	17.0921i	0.289922	+	0.815761i	0.994366	+	0.106002i	$0.0338050\pi$
$439$	6.07453	+	17.0921i	0.289922	+	0.815761i	−0.704444	+	0.709759i	$0.748804\pi$
$440$	14.6746	+	4.11163i	0.699584	+	0.196014i
$441$	−1.70613	+	8.21037i	−0.0812445	+	0.390970i
$442$	−0.135251	+	0.0587479i	−0.00643325	+	0.00279435i
$443$	1.29417	−	0.787000i	0.0614877	−	0.0373915i	−0.488504	−	0.872562i	$-0.662457\pi$
$443$	1.29417	−	0.787000i	0.0614877	−	0.0373915i	0.549991	+	0.835170i	$0.314631\pi$
$444$	7.17948	−	5.84094i	0.340723	−	0.277199i
$445$	2.87423	+	3.07755i	0.136252	+	0.145890i
$446$	2.06155	−	3.97862i	0.0976174	−	0.188393i
$447$	0.274734	−	0.530212i	0.0129945	−	0.0250782i
$448$	−5.21079	−	5.57939i	−0.246187	−	0.263601i
$449$	20.9096	−	17.0112i	0.986783	−	0.802808i	0.00641420	−	0.999979i	$-0.497958\pi$
$449$	20.9096	−	17.0112i	0.986783	−	0.802808i	0.980369	+	0.197172i	$0.0631757\pi$
$450$	5.41915	−	3.29546i	0.255461	−	0.155349i
$451$	21.2461	−	9.22847i	1.00044	−	0.434552i
$452$	−1.65535	+	7.96600i	−0.0778613	+	0.374689i
$453$	27.0557	+	7.58066i	1.27119	+	0.356170i
$454$	−9.95924	−	28.0226i	−0.467410	−	1.31517i
$455$	−0.0758792	+	0.0812468i	−0.00355727	+	0.00380891i
$456$	−0.260671	+	3.81087i	−0.0122070	+	0.178460i
$457$	−6.00951	−	28.9193i	−0.281113	−	1.35279i	−0.848437	−	0.529296i	$-0.822456\pi$
$457$	−6.00951	−	28.9193i	−0.281113	−	1.35279i	0.567324	−	0.823494i	$-0.307979\pi$
$458$	17.6284	+	24.9737i	0.823721	+	1.16695i
$459$	3.33212	−	0.933617i	0.155530	−	0.0435775i
$460$	−0.0748775	−	1.09467i	−0.00349118	−	0.0510393i
$461$	24.9745	+	20.3183i	1.16318	+	0.946317i	0.999194	−	0.0401458i	$-0.0127822\pi$
$461$	24.9745	+	20.3183i	1.16318	+	0.946317i	0.163986	+	0.986463i	$0.447565\pi$
$462$	−10.0679	−	1.38380i	−0.468402	−	0.0643804i
$463$	18.8105	+	11.4389i	0.874197	+	0.531611i	0.883546	−	0.468345i	$-0.155150\pi$
$463$	18.8105	+	11.4389i	0.874197	+	0.531611i	−0.00934817	+	0.999956i	$0.502976\pi$
$464$	12.4139	−	1.70626i	0.576303	−	0.0792110i
$465$	−18.7163	−	8.12965i	−0.867949	−	0.377003i
$466$	−5.04506	+	7.14722i	−0.233708	+	0.331088i
$467$	3.43412	−	9.66268i	0.158912	−	0.447135i	−0.835898	−	0.548885i	$-0.815053\pi$
$467$	3.43412	−	9.66268i	0.158912	−	0.447135i	0.994810	+	0.101749i	$0.0324439\pi$
$468$	−0.0322981	−	0.0623325i	−0.00149298	−	0.00288132i
$469$	4.58935			0.211916
$470$	−0.633098	+	9.35611i	−0.0292026	+	0.431565i
$471$	−45.3965			−2.09176
$472$	13.7344	+	26.5061i	0.632175	+	1.22004i
$473$	7.38008	−	20.7656i	0.339337	−	0.954802i
$474$	1.22375	−	1.73366i	0.0562088	−	0.0796297i
$475$	2.09540	+	0.910162i	0.0961437	+	0.0417611i
$476$	0.377028	−	0.0518214i	0.0172811	−	0.00237523i
$477$	−13.6738	−	8.31522i	−0.626080	−	0.380728i
$478$	−24.8964	−	3.42193i	−1.13874	−	0.156516i
$479$	−7.04360	−	5.73039i	−0.321830	−	0.261828i	0.456445	−	0.889752i	$-0.349123\pi$
$479$	−7.04360	−	5.73039i	−0.321830	−	0.261828i	−0.778275	+	0.627923i	$0.783905\pi$
$480$	0.383330	+	5.60409i	0.0174966	+	0.255791i
$481$	1.13989	−	0.319383i	0.0519747	−	0.0145626i
$482$	5.18274	+	7.34227i	0.236067	+	0.334431i
$483$	0.819931	+	3.94572i	0.0373081	+	0.179537i
$484$	0.296323	−	4.33209i	0.0134692	−	0.196913i
$485$	−7.58367	+	8.12012i	−0.344357	+	0.368716i
$486$	−5.43005	−	15.2787i	−0.246312	−	0.693056i
$487$	22.9320	+	6.42524i	1.03915	+	0.291156i	0.746725	−	0.665133i	$-0.231625\pi$
$487$	22.9320	+	6.42524i	1.03915	+	0.291156i	0.292423	+	0.956289i	$0.405538\pi$
$488$	−8.01617	+	38.5759i	−0.362875	+	1.74625i
$489$	28.6437	−	12.4417i	1.29531	−	0.562633i
$490$	7.32108	−	4.45205i	0.330733	−	0.201123i
$491$	−0.795240	+	0.646976i	−0.0358887	+	0.0291976i	−0.648863	−	0.760905i	$-0.724755\pi$
$491$	−0.795240	+	0.646976i	−0.0358887	+	0.0291976i	0.612975	+	0.790103i	$0.289973\pi$
$492$	3.20471	+	3.43140i	0.144479	+	0.154700i
$493$	−1.97712	+	3.81566i	−0.0890449	+	0.171849i
$494$	−0.0408091	+	0.0787579i	−0.00183609	+	0.00354349i
$495$	4.56769	+	4.89080i	0.205302	+	0.219825i
$496$	20.2090	−	16.4413i	0.907412	−	0.738235i
$497$	3.98864	−	2.42555i	0.178915	−	0.108801i
$498$	−0.601352	+	0.261204i	−0.0269472	+	0.0117048i
$499$	6.24593	−	30.0571i	0.279606	−	1.34554i	−0.571524	−	0.820585i	$-0.693648\pi$
$499$	6.24593	−	30.0571i	0.279606	−	1.34554i	0.851130	−	0.524954i	$-0.175918\pi$
$500$	4.12108	+	1.15467i	0.184300	+	0.0516385i
$501$	5.45418	+	15.3466i	0.243675	+	0.685635i
$502$	24.9718	−	26.7383i	1.11455	−	1.19339i
$503$	−1.19585	+	17.4828i	−0.0533205	+	0.779519i	0.891725	+	0.452579i	$0.149496\pi$
$503$	−1.19585	+	17.4828i	−0.0533205	+	0.779519i	−0.945045	+	0.326940i	$0.893982\pi$
$504$	−0.712227	−	3.42743i	−0.0317251	−	0.152670i
$505$	−2.71967	−	3.85290i	−0.121024	−	0.171452i
$506$	12.3534	−	3.46125i	0.549174	−	0.153871i
$507$	1.84591	+	26.9862i	0.0819796	+	1.19850i
$508$	−2.49052	−	2.02619i	−0.110499	−	0.0898976i
$509$	−2.66448	−	0.366225i	−0.118101	−	0.0162326i	0.0768740	−	0.997041i	$-0.475506\pi$
$509$	−2.66448	−	0.366225i	−0.118101	−	0.0162326i	−0.194975	+	0.980808i	$0.562463\pi$
$510$	2.43438	+	1.48038i	0.107796	+	0.0655523i
$511$	7.88346	−	1.08356i	0.348744	−	0.0479337i
$512$	−22.8840	−	9.93994i	−1.01134	−	0.439287i
$513$	1.20042	−	1.70061i	0.0529998	−	0.0750836i
$514$	0.169444	−	0.476770i	0.00747386	−	0.0210294i
$515$	−9.20297	−	17.7609i	−0.405531	−	0.782640i
$516$	4.46699			0.196648
$517$	30.9626	−	4.27879i	1.36173	−	0.188181i
$518$	10.7172			0.470889
$519$	−11.4187	−	22.0371i	−0.501225	−	0.967321i
$520$	−0.132309	+	0.372283i	−0.00580215	+	0.0163257i
$521$	−6.79847	+	9.63123i	−0.297846	+	0.421952i	−0.938182	−	0.346143i	$-0.887491\pi$
$521$	−6.79847	+	9.63123i	−0.297846	+	0.421952i	0.640335	+	0.768095i	$0.278795\pi$
$522$	6.58279	+	2.85931i	0.288121	+	0.125149i
$523$	−13.7132	+	1.88484i	−0.599637	+	0.0824182i	−0.429600	−	0.903019i	$-0.641345\pi$
$523$	−13.7132	+	1.88484i	−0.599637	+	0.0824182i	−0.170037	+	0.985438i	$0.554389\pi$
$524$	3.98293	+	2.42208i	0.173995	+	0.105809i
$525$	−6.72242	−	0.923975i	−0.293390	−	0.0403256i
$526$	12.8119	+	10.4233i	0.558627	+	0.454477i
$527$	0.609733	+	8.91398i	0.0265604	+	0.388299i
$528$	−26.6639	+	7.47088i	−1.16040	+	0.325128i
$529$	10.3298	+	14.6340i	0.449123	+	0.636262i
$530$	3.32698	+	16.0103i	0.144515	+	0.695443i
$531$	−0.894595	+	13.0785i	−0.0388221	+	0.567559i
$532$	0.156257	−	0.167311i	0.00677461	−	0.00725384i
$533$	0.201105	+	0.565855i	0.00871082	+	0.0245099i
$534$	−9.60984	−	2.69255i	−0.415859	−	0.116518i
$535$	−2.23790	+	10.7694i	−0.0967527	+	0.465600i
$536$	14.9601	−	6.49811i	0.646180	−	0.280676i
$537$	−17.1803	+	10.4475i	−0.741383	+	0.450845i
$538$	16.2174	−	13.1938i	0.699180	−	0.568825i
$539$	−19.4939	−	20.8729i	−0.839662	−	0.899058i
$540$	0.774460	−	1.49464i	0.0333274	−	0.0643190i
$541$	12.0854	−	23.3238i	0.519593	−	1.00277i	−0.472975	−	0.881076i	$-0.656820\pi$
$541$	12.0854	−	23.3238i	0.519593	−	1.00277i	0.992568	−	0.121692i	$-0.0388322\pi$
$542$	−18.5033	−	19.8122i	−0.794786	−	0.851008i
$543$	8.83120	−	7.18471i	0.378983	−	0.308325i
$544$	2.10147	−	1.27793i	0.0900999	−	0.0547910i
$545$	18.4557	−	8.01645i	0.790556	−	0.343387i
$546$	0.0536043	−	0.257958i	0.00229405	−	0.0110396i
$547$	−3.83309	−	1.07398i	−0.163891	−	0.0459202i	0.186872	−	0.982384i	$-0.440165\pi$
$547$	−3.83309	−	1.07398i	−0.163891	−	0.0459202i	−0.350764	+	0.936464i	$0.614078\pi$
$548$	1.60039	+	4.50308i	0.0683655	+	0.192362i
$549$	−11.8091	+	12.6444i	−0.503999	+	0.539651i
$550$	−1.47412	+	21.5509i	−0.0628569	+	0.918935i
$551$	0.525956	+	2.53104i	0.0224065	+	0.107826i
$552$	8.25956	+	11.7011i	0.351550	+	0.498033i
$553$	−0.674522	+	0.188992i	−0.0286836	+	0.00803676i
$554$	0.985909	+	14.4135i	0.0418872	+	0.612370i
$555$	−17.7427	−	14.4348i	−0.753137	−	0.612722i
$556$	3.08874	+	0.424538i	0.130992	+	0.0180044i
$557$	1.39145	+	0.846162i	0.0589578	+	0.0358530i	0.548754	−	0.835984i	$-0.315103\pi$
$557$	1.39145	+	0.846162i	0.0589578	+	0.0358530i	−0.489796	+	0.871837i	$0.662929\pi$
$558$	14.7825	−	2.03181i	0.625794	−	0.0860134i
$559$	0.524043	+	0.227624i	0.0221647	+	0.00962747i
$560$	−1.58147	+	2.24043i	−0.0668293	+	0.0946755i
$561$	3.18027	−	8.94842i	0.134271	−	0.377802i
$562$	−18.9844	−	36.6383i	−0.800811	−	1.54549i
$563$	−11.5073			−0.484974			−0.242487	−	0.970155i	$-0.577963\pi$
$563$	−11.5073			−0.484974			−0.242487	+	0.970155i	$0.577963\pi$
$564$	2.91890	+	5.62315i	0.122908	+	0.236777i
$565$	20.1070			0.845908
$566$	−2.76501	−	5.33622i	−0.116222	−	0.224298i
$567$	−3.22414	+	9.07185i	−0.135401	+	0.380982i
$568$	9.56763	−	13.5542i	0.401449	−	0.568724i
$569$	12.4106	+	5.39067i	0.520278	+	0.225989i	0.642180	−	0.766554i	$-0.278030\pi$
$569$	12.4106	+	5.39067i	0.520278	+	0.225989i	−0.121903	+	0.992542i	$0.538900\pi$
$570$	1.69793	−	0.233374i	0.0711183	−	0.00977498i
$571$	−16.5105	−	10.0402i	−0.690942	−	0.420171i	0.129746	−	0.991547i	$-0.458584\pi$
$571$	−16.5105	−	10.0402i	−0.690942	−	0.420171i	−0.820688	+	0.571376i	$0.806410\pi$
$572$	0.236872	+	0.0325573i	0.00990410	+	0.00136129i
$573$	8.21228	+	6.68118i	0.343073	+	0.279110i
$574$	0.371019	+	5.42411i	0.0154860	+	0.226398i
$575$	8.24843	−	2.31110i	0.343983	−	0.0963796i
$576$	−6.87069	−	9.73356i	−0.286279	−	0.405565i
$577$	−4.97537	−	23.9428i	−0.207127	−	0.996752i	−0.946313	−	0.323250i	$-0.895224\pi$
$577$	−4.97537	−	23.9428i	−0.207127	−	0.996752i	0.739186	−	0.673501i	$-0.235210\pi$
$578$	0.0851344	−	1.24462i	0.00354113	−	0.0517694i
$579$	−2.16881	+	2.32223i	−0.0901327	+	0.0965085i
$580$	0.700083	+	1.96984i	0.0290694	+	0.0817934i
$581$	0.208400	+	0.0583909i	0.00864588	+	0.00242246i
$582$	5.35742	−	25.7813i	0.222072	−	1.06867i
$583$	49.9927	−	21.7149i	2.07049	−	0.899340i
$584$	24.1639	−	14.6944i	0.999910	−	0.608059i
$585$	−0.134581	+	0.109490i	−0.00556426	+	0.00452686i
$586$	−6.23961	−	6.68099i	−0.257756	−	0.275989i
$587$	3.87091	−	7.47051i	0.159769	−	0.308341i	−0.794513	−	0.607247i	$-0.792274\pi$
$587$	3.87091	−	7.47051i	0.159769	−	0.308341i	0.954283	+	0.298906i	$0.0966217\pi$
$588$	2.66332	−	5.13998i	0.109834	−	0.211969i
$589$	3.66849	+	3.92799i	0.151157	+	0.161850i
$590$	10.3904	−	8.45325i	0.427768	−	0.348015i
$591$	10.0890	−	6.13526i	0.415006	−	0.252371i
$592$	26.7845	−	11.6342i	1.10084	−	0.478161i
$593$	2.56436	−	12.3404i	0.105306	−	0.506759i	−0.893077	−	0.449904i	$-0.851458\pi$
$593$	2.56436	−	12.3404i	0.105306	−	0.506759i	0.998382	−	0.0568547i	$-0.0181072\pi$
$594$	18.9526	+	5.31026i	0.777633	+	0.217883i
$595$	−0.314959	−	0.886210i	−0.0129121	−	0.0363311i
$596$	−0.0868182	+	0.0929595i	−0.00355621	+	0.00380777i
$597$	−3.21728	+	47.0350i	−0.131675	+	1.92501i
$598$	0.0676693	+	0.325643i	0.00276721	+	0.0133165i
$599$	−7.06330	−	10.0064i	−0.288599	−	0.408851i	0.646681	−	0.762760i	$-0.276156\pi$
$599$	−7.06330	−	10.0064i	−0.288599	−	0.408851i	−0.935280	+	0.353909i	$0.884852\pi$
$600$	−23.2217	+	6.50641i	−0.948022	+	0.265623i
$601$	2.11092	+	30.8605i	0.0861061	+	1.25883i	0.817121	+	0.576465i	$0.195568\pi$
$601$	2.11092	+	30.8605i	0.0861061	+	1.25883i	−0.731015	+	0.682361i	$0.760953\pi$
$602$	4.01241	+	3.26434i	0.163534	+	0.133045i
$603$	7.09555	+	0.975260i	0.288953	+	0.0397157i
$604$	−5.11355	−	3.10962i	−0.208067	−	0.126529i
$605$	−10.6310	+	1.46120i	−0.432211	+	0.0594061i
$606$	10.2516	+	4.45291i	0.416444	+	0.180887i
$607$	19.0763	−	27.0249i	0.774281	−	1.09691i	−0.218366	−	0.975867i	$-0.570073\pi$
$607$	19.0763	−	27.0249i	0.774281	−	1.09691i	0.992648	−	0.121040i	$-0.0386229\pi$
$608$	0.495458	−	1.39409i	0.0200935	−	0.0565376i
$609$	−3.53256	−	6.81753i	−0.143147	−	0.276260i
$610$	17.6783			0.715774
$611$	0.0558914	+	0.808415i	0.00226112	+	0.0327050i
$612$	0.593932			0.0240083
$613$	−3.72038	−	7.18002i	−0.150265	−	0.289998i	0.800833	−	0.598888i	$-0.204390\pi$
$613$	−3.72038	−	7.18002i	−0.150265	−	0.289998i	−0.951098	+	0.308890i	$0.900043\pi$
$614$	−3.94499	+	11.1001i	−0.159207	+	0.447965i
$615$	6.69136	−	9.47950i	0.269822	−	0.382250i
$616$	10.9355	+	4.74994i	0.440602	+	0.191381i
$617$	5.89014	−	0.809582i	0.237128	−	0.0325925i	−0.0166238	−	0.999862i	$-0.505292\pi$
$617$	5.89014	−	0.809582i	0.237128	−	0.0325925i	0.253752	+	0.967269i	$0.418335\pi$
$618$	40.5063	+	24.6324i	1.62940	+	0.990861i
$619$	−26.5295	−	3.64640i	−1.06631	−	0.146561i	−0.418389	−	0.908268i	$-0.637405\pi$
$619$	−26.5295	−	3.64640i	−1.06631	−	0.146561i	−0.647922	+	0.761707i	$0.724362\pi$
$620$	3.37157	+	2.74298i	0.135406	+	0.110161i
$621$	−0.532643	−	7.78696i	−0.0213742	−	0.312480i
$622$	27.9336	−	7.82661i	1.12003	−	0.313819i
$623$	1.89981	+	2.69142i	0.0761144	+	0.107830i
$624$	−0.146060	−	0.702878i	−0.00584707	−	0.0281376i
$625$	−0.574079	+	8.39274i	−0.0229632	+	0.335710i
$626$	−10.3231	+	11.0534i	−0.412595	+	0.441782i
$627$	−1.91306	−	5.38284i	−0.0764004	−	0.214970i
$628$	9.31093	+	2.60880i	0.371546	+	0.104102i
$629$	−2.03763	+	9.80560i	−0.0812455	+	0.390975i
$630$	−1.44066	+	0.625768i	−0.0573974	+	0.0249312i
$631$	−26.3084	+	15.9985i	−1.04732	+	0.636889i	−0.934221	−	0.356694i	$-0.883904\pi$
$631$	−26.3084	+	15.9985i	−1.04732	+	0.636889i	−0.113099	+	0.993584i	$0.536078\pi$
$632$	−1.93118	+	1.57113i	−0.0768181	+	0.0624962i
$633$	15.9375	+	17.0649i	0.633459	+	0.678269i
$634$	−5.88548	+	11.3585i	−0.233742	+	0.451102i
$635$	−3.65037	+	7.04489i	−0.144860	+	0.279568i
$636$	7.54079	+	8.07421i	0.299012	+	0.320163i
$637$	0.574364	−	0.467280i	0.0227571	−	0.0185143i
$638$	−20.8849	+	12.7004i	−0.826839	+	0.502812i
$639$	6.68224	−	2.90251i	0.264345	−	0.114821i
$640$	−1.37950	+	6.63851i	−0.0545295	+	0.262410i
$641$	−41.8844	−	11.7355i	−1.65433	−	0.463523i	−0.689047	−	0.724716i	$-0.741971\pi$
$641$	−41.8844	−	11.7355i	−1.65433	−	0.463523i	−0.965286	+	0.261194i	$0.915884\pi$
$642$	−8.72972	−	24.5631i	−0.344535	−	0.969428i
$643$	3.40672	−	3.64771i	0.134348	−	0.143852i	−0.660114	−	0.751165i	$-0.729492\pi$
$643$	3.40672	−	3.64771i	0.134348	−	0.143852i	0.794462	+	0.607314i	$0.207753\pi$
$644$	0.0585790	−	0.856395i	0.00230834	−	0.0337467i
$645$	−2.24602	−	10.8084i	−0.0884368	−	0.425581i
$646$	−0.432764	−	0.613088i	−0.0170269	−	0.0241216i
$647$	12.0410	−	3.37373i	0.473381	−	0.132635i	−0.0248287	−	0.999692i	$-0.507904\pi$
$647$	12.0410	−	3.37373i	0.473381	−	0.132635i	0.498210	+	0.867057i	$0.333991\pi$
$648$	2.33504	+	34.1371i	0.0917291	+	1.34103i
$649$	−34.6331	−	28.1761i	−1.35947	−	1.10601i
$650$	−0.554805	−	0.0762562i	−0.0217613	−	0.00299102i
$651$	−13.6400	−	8.29464i	−0.534592	−	0.325093i
$652$	−6.58986	+	0.905756i	−0.258079	+	0.0354721i
$653$	−9.49056	−	4.12233i	−0.371394	−	0.161319i	0.204453	−	0.978876i	$-0.434458\pi$
$653$	−9.49056	−	4.12233i	−0.371394	−	0.161319i	−0.575848	+	0.817557i	$0.695328\pi$
$654$	−27.5004	+	38.9592i	−1.07535	+	1.52342i
$655$	3.85787	−	10.8550i	0.150740	−	0.424141i
$656$	6.81542	+	13.1532i	0.266097	+	0.513545i
$657$	12.4188			0.484503
$658$	−1.48736	+	7.18396i	−0.0579834	+	0.280060i
$659$	−9.70246			−0.377954			−0.188977	−	0.981982i	$-0.560517\pi$
$659$	−9.70246			−0.377954			−0.188977	+	0.981982i	$0.560517\pi$
$660$	−2.12540	−	4.10184i	−0.0827313	−	0.159664i
$661$	−1.21646	+	3.42278i	−0.0473146	+	0.133131i	−0.963564	−	0.267478i	$-0.913810\pi$
$661$	−1.21646	+	3.42278i	−0.0473146	+	0.133131i	0.916249	+	0.400608i	$0.131201\pi$
$662$	3.15873	−	4.47490i	0.122767	−	0.173922i
$663$	0.225824	+	0.0980890i	0.00877026	+	0.00380946i
$664$	0.762008	−	0.104736i	0.0295716	−	0.00406453i
$665$	−0.483395	−	0.293959i	−0.0187453	−	0.0113992i
$666$	16.5698	+	2.27747i	0.642067	+	0.0882501i
$667$	7.51905	+	6.11720i	0.291139	+	0.236859i
$668$	−0.236742	−	3.46105i	−0.00915984	−	0.133912i
$669$	−7.20431	+	2.01855i	−0.278535	+	0.0780417i
$670$	−4.22033	−	5.97885i	−0.163046	−	0.230983i
$671$	−11.9886	−	57.6924i	−0.462816	−	2.22719i
$672$	−0.299891	+	4.38426i	−0.0115686	+	0.169126i
$673$	8.80444	−	9.42725i	0.339386	−	0.363394i	−0.538196	−	0.842819i	$-0.680894\pi$
$673$	8.80444	−	9.42725i	0.339386	−	0.363394i	0.877582	+	0.479426i	$0.159155\pi$
$674$	14.7640	+	41.5420i	0.568689	+	1.60014i
$675$	12.6548	+	3.54570i	0.487082	+	0.136474i
$676$	1.17221	−	5.64100i	0.0450852	−	0.216962i
$677$	14.0914	−	6.12078i	0.541578	−	0.235241i	−0.109854	−	0.993948i	$-0.535038\pi$
$677$	14.0914	−	6.12078i	0.541578	−	0.235241i	0.651432	+	0.758707i	$0.274169\pi$
$678$	−40.7156	+	24.7597i	−1.56367	+	0.950891i
$679$	−6.74270	+	5.48559i	−0.258761	+	0.210518i
$680$	−2.28148	−	2.44287i	−0.0874909	−	0.0936799i
$681$	−22.8447	+	44.0882i	−0.875409	+	1.68946i
$682$	−23.3804	+	45.1221i	−0.895281	+	1.72781i
$683$	11.9618	+	12.8079i	0.457704	+	0.490081i	0.917384	−	0.398004i	$-0.130297\pi$
$683$	11.9618	+	12.8079i	0.457704	+	0.490081i	−0.459680	+	0.888085i	$0.652036\pi$
$684$	0.277142	−	0.225472i	0.0105968	−	0.00862113i
$685$	10.0911	−	6.13651i	0.385560	−	0.234464i
$686$	13.0191	−	5.65498i	0.497070	−	0.215908i
$687$	10.3843	−	49.9719i	0.396185	−	1.90655i
$688$	13.5714	+	3.80254i	0.517406	+	0.144970i
$689$	0.473207	+	1.33148i	0.0180277	+	0.0507252i
$690$	4.38635	−	4.69663i	0.166985	−	0.178798i
$691$	−1.08795	+	15.9053i	−0.0413876	+	0.605066i	0.929999	+	0.367562i	$0.119807\pi$
$691$	−1.08795	+	15.9053i	−0.0413876	+	0.605066i	−0.971387	+	0.237504i	$0.923671\pi$
$692$	1.07560	+	5.17605i	0.0408880	+	0.196764i
$693$	3.01916	+	4.27717i	0.114688	+	0.162476i
$694$	12.4063	−	3.47608i	0.470937	−	0.131950i
$695$	−0.525809	−	7.68705i	−0.0199451	−	0.291586i
$696$	−21.1683	−	17.2217i	−0.802382	−	0.652786i
$697$	−5.03326	−	0.691805i	−0.190648	−	0.0262040i
$698$	37.9601	+	23.0840i	1.43681	+	0.873744i
$699$	14.4709	−	1.98898i	0.547339	−	0.0752300i
$700$	1.32568	+	0.575826i	0.0501062	+	0.0217642i
$701$	12.7791	−	18.1038i	0.482659	−	0.683772i	−0.500664	−	0.865642i	$-0.666911\pi$
$701$	12.7791	−	18.1038i	0.482659	−	0.683772i	0.983323	+	0.181870i	$0.0582149\pi$
$702$	−0.170881	+	0.480812i	−0.00644947	+	0.0181471i
$703$	2.77165	+	5.34905i	0.104535	+	0.201743i
$704$	40.5775			1.52932
$705$	12.1383	−	9.88998i	0.457153	−	0.372478i
$706$	−13.9739			−0.525913
$707$	−1.69743	−	3.27589i	−0.0638383	−	0.123202i
$708$	3.03056	−	8.52718i	0.113895	−	0.320471i
$709$	−26.2363	+	37.1684i	−0.985325	+	1.39589i	−0.0680276	+	0.997683i	$0.521671\pi$
$709$	−26.2363	+	37.1684i	−0.985325	+	1.39589i	−0.917297	+	0.398204i	$0.869634\pi$
$710$	−6.82784	−	2.96575i	−0.256244	−	0.111303i
$711$	−1.08303	+	0.148859i	−0.0406169	+	0.00558266i
$712$	10.0037	+	6.08341i	0.374906	+	0.227985i
$713$	19.9651	+	2.74414i	0.747698	+	0.102769i
$714$	1.72905	+	1.40669i	0.0647081	+	0.0526440i
$715$	−0.0403236	−	0.589510i	−0.00150802	−	0.0220464i
$716$	4.12410	−	1.15552i	0.154125	−	0.0431837i
$717$	24.1971	+	34.2795i	0.903658	+	1.28019i
$718$	−7.14671	−	34.3919i	−0.266713	−	1.28349i
$719$	0.667652	−	9.76073i	0.0248992	−	0.364014i	−0.968477	−	0.249104i	$-0.919864\pi$
$719$	0.667652	−	9.76073i	0.0248992	−	0.364014i	0.993376	−	0.114910i	$-0.0366579\pi$
$720$	−2.92120	+	3.12784i	−0.108867	+	0.116568i
$721$	−5.24069	−	14.7459i	−0.195173	−	0.549165i
$722$	22.3894	+	6.27322i	0.833247	+	0.233465i
$723$	3.05297	−	14.6917i	0.113541	−	0.546391i
$724$	−2.22418	+	0.966098i	−0.0826610	+	0.0359048i
$725$	−13.9450	+	8.48012i	−0.517903	+	0.314944i
$726$	19.7279	−	16.0498i	0.732170	−	0.595665i
$727$	32.4146	+	34.7076i	1.20219	+	1.28723i	0.947332	+	0.320254i	$0.103768\pi$
$727$	32.4146	+	34.7076i	1.20219	+	1.28723i	0.254859	+	0.966978i	$0.417971\pi$
$728$	−0.142204	+	0.274441i	−0.00527043	+	0.0101715i
$729$	3.03574	−	5.85871i	0.112435	−	0.216989i
$730$	−8.66119	−	9.27387i	−0.320565	−	0.343241i
$731$	−3.74953	+	3.05047i	−0.138681	+	0.112826i
$732$	10.2050	−	6.20579i	0.377187	−	0.229373i
$733$	45.6956	−	19.8484i	1.68781	−	0.733118i	0.687833	−	0.725869i	$-0.258562\pi$
$733$	45.6956	−	19.8484i	1.68781	−	0.733118i	0.999974	−	0.00724862i	$-0.00230733\pi$
$734$	3.28031	−	15.7857i	0.121078	−	0.582661i
$735$	−13.7759	−	3.85984i	−0.508133	−	0.142372i
$736$	−1.85777	−	5.22725i	−0.0684782	−	0.192679i
$737$	−16.6497	+	17.8274i	−0.613299	+	0.656682i
$738$	−0.579022	+	8.46500i	−0.0213141	+	0.311601i
$739$	9.06931	+	43.6439i	0.333620	+	1.60547i	0.727367	+	0.686249i	$0.240744\pi$
$739$	9.06931	+	43.6439i	0.333620	+	1.60547i	−0.393747	+	0.919219i	$0.628821\pi$
$740$	2.80955	+	3.98023i	0.103281	+	0.146316i
$741$	0.142611	−	0.0399579i	0.00523896	−	0.00146789i
$742$	0.873021	+	12.7631i	0.0320496	+	0.468549i
$743$	−19.2965	−	15.6989i	−0.707921	−	0.575936i	0.207597	−	0.978214i	$-0.433436\pi$
$743$	−19.2965	−	15.6989i	−0.707921	−	0.575936i	−0.915517	+	0.402278i	$0.868218\pi$
$744$	−56.2074	−	7.72553i	−2.06066	−	0.283232i
$745$	0.268579	+	0.163327i	0.00983998	+	0.00598383i
$746$	−38.5027	+	5.29208i	−1.40969	+	0.193757i
$747$	0.309796	+	0.134563i	0.0113348	+	0.00492342i
$748$	−1.16652	+	1.65258i	−0.0426521	+	0.0604243i
$749$	−2.88170	+	8.10833i	−0.105295	+	0.296272i
$750$	11.5322	+	22.2561i	0.421095	+	0.812676i
$751$	36.2919			1.32431			0.662156	−	0.749366i	$-0.269642\pi$
$751$	36.2919			1.32431			0.662156	+	0.749366i	$0.269642\pi$
$752$	4.08137	+	19.5687i	0.148832	+	0.713599i
$753$	−61.0860			−2.22610
$754$	−0.291544	−	0.562655i	−0.0106174	−	0.0204907i
$755$	−4.95299	+	13.9364i	−0.180258	+	0.507197i
$756$	0.759461	−	1.07591i	0.0276213	−	0.0391305i
$757$	−5.55247	−	2.41178i	−0.201808	−	0.0876576i	0.295079	−	0.955473i	$-0.404654\pi$
$757$	−5.55247	−	2.41178i	−0.201808	−	0.0876576i	−0.496887	+	0.867815i	$0.665524\pi$
$758$	−32.3547	+	4.44705i	−1.17517	+	0.161524i
$759$	−18.3019	−	11.1296i	−0.664316	−	0.403980i
$760$	−1.99197	−	0.273790i	−0.0722563	−	0.00993140i
$761$	−4.44813	−	3.61882i	−0.161245	−	0.131182i	0.547048	−	0.837101i	$-0.315752\pi$
$761$	−4.44813	−	3.61882i	−0.161245	−	0.131182i	−0.708292	+	0.705919i	$0.750534\pi$
$762$	−1.28326	−	18.7606i	−0.0464875	−	0.679623i
$763$	15.1580	−	4.24707i	0.548755	−	0.153754i
$764$	−1.30041	−	1.84226i	−0.0470471	−	0.0666506i
$765$	−0.298631	−	1.43709i	−0.0107970	−	0.0519581i
$766$	−2.27073	+	33.1969i	−0.0820448	+	1.19945i
$767$	0.790047	−	0.845934i	0.0285269	−	0.0305449i
$768$	7.03490	+	19.7943i	0.253850	+	0.714265i
$769$	−10.0183	−	2.80699i	−0.361269	−	0.101223i	0.0843727	−	0.996434i	$-0.473111\pi$
$769$	−10.0183	−	2.80699i	−0.361269	−	0.101223i	−0.445642	+	0.895211i	$0.647024\pi$
$770$	1.08839	−	5.23760i	0.0392227	−	0.188750i
$771$	−0.774882	+	0.336579i	−0.0279067	+	0.0121216i
$772$	0.578279	−	0.351659i	0.0208127	−	0.0126565i
$773$	−21.9229	+	17.8356i	−0.788510	+	0.641501i	−0.937754	−	0.347300i	$-0.887099\pi$
$773$	−21.9229	+	17.8356i	−0.788510	+	0.641501i	0.149244	+	0.988800i	$0.452316\pi$
$774$	5.50986	+	5.89962i	0.198048	+	0.212057i
$775$	−15.6112	+	30.1283i	−0.560772	+	1.08224i
$776$	−14.2124	+	27.4287i	−0.510196	+	0.984634i
$777$	−12.2137	−	13.0777i	−0.438164	−	0.469160i
$778$	−12.4899	+	10.1613i	−0.447786	+	0.364301i
$779$	−2.61126	+	1.58794i	−0.0935580	+	0.0568939i
$780$	0.109854	−	0.0477164i	0.00393341	−	0.00170852i
$781$	−5.04827	+	24.2936i	−0.180641	+	0.869294i
$782$	−2.70950	−	0.759167i	−0.0968916	−	0.0271478i
$783$	4.98006	+	14.0125i	0.177973	+	0.500767i
$784$	12.4670	−	13.3489i	0.445251	−	0.476747i
$785$	1.63074	−	23.8406i	0.0582037	−	0.850908i
$786$	5.55485	+	26.7314i	0.198135	+	0.953477i
$787$	4.43448	+	6.28223i	0.158072	+	0.223937i	0.888297	−	0.459270i	$-0.151889\pi$
$787$	4.43448	+	6.28223i	0.158072	+	0.223937i	−0.730225	+	0.683207i	$0.760585\pi$
$788$	−2.42185	+	0.678571i	−0.0862749	+	0.0241731i
$789$	−1.88190	−	27.5124i	−0.0669975	−	0.979468i
$790$	0.866497	+	0.704948i	0.0308286	+	0.0250809i
$791$	15.5838	+	2.14195i	0.554097	+	0.0761589i
$792$	15.8978	+	9.66767i	0.564904	+	0.343526i
$793$	1.51342	−	0.208015i	0.0537432	−	0.00738683i
$794$	25.2431	+	10.9646i	0.895844	+	0.389120i
$795$	15.7450	−	22.3056i	0.558418	−	0.791098i
$796$	3.36283	−	9.46209i	0.119192	−	0.335375i
$797$	2.49755	+	4.82005i	0.0884677	+	0.170735i	0.928006	−	0.372566i	$-0.121522\pi$
$797$	2.49755	+	4.82005i	0.0884677	+	0.170735i	−0.839538	+	0.543301i	$0.817174\pi$
$798$	1.34083			0.0474648
$799$	−6.29008	−	2.72670i	−0.222527	−	0.0964637i
$800$	9.34083			0.330248
$801$	2.36534	+	4.56490i	0.0835752	+	0.161293i
$802$	−11.5110	+	32.3888i	−0.406467	+	1.14369i
$803$	−24.3912	+	34.5545i	−0.860748	+	1.21940i
$804$	−4.53504	−	1.96985i	−0.159939	−	0.0694711i
$805$	−2.10161	+	0.288859i	−0.0740718	+	0.0101809i
$806$	−1.12571	−	0.684562i	−0.0396516	−	0.0241127i
$807$	−34.5815	−	4.75312i	−1.21733	−	0.167318i
$808$	−10.1716	−	8.27517i	−0.357834	−	0.291120i
$809$	0.510488	+	7.46307i	0.0179478	+	0.262387i	0.997979	+	0.0635439i	$0.0202403\pi$
$809$	0.510488	+	7.46307i	0.0179478	+	0.262387i	−0.980031	+	0.198844i	$0.936281\pi$
$810$	14.7834	−	4.14211i	0.519435	−	0.145539i
$811$	−19.4054	−	27.4912i	−0.681417	−	0.965348i	−0.999849	−	0.0174018i	$-0.994461\pi$
$811$	−19.4054	−	27.4912i	−0.681417	−	0.965348i	0.318432	−	0.947946i	$-0.396844\pi$
$812$	0.332753	+	1.60130i	0.0116773	+	0.0561945i
$813$	−3.08884	+	45.1573i	−0.108330	+	1.58374i
$814$	−38.8810	+	41.6314i	−1.36278	+	1.45918i
$815$	5.50499	+	15.4896i	0.192831	+	0.542575i
$816$	5.84828	+	1.63861i	0.204731	+	0.0573628i
$817$	−0.591579	+	2.84683i	−0.0206967	+	0.0995981i
$818$	−23.3436	+	10.1396i	−0.816190	+	0.354521i
$819$	−0.115970	+	0.0705231i	−0.00405233	+	0.00246428i
$820$	−1.91717	+	1.55973i	−0.0669505	+	0.0544683i
$821$	22.5188	+	24.1118i	0.785913	+	0.841508i	0.990525	−	0.137336i	$-0.0438539\pi$
$821$	22.5188	+	24.1118i	0.785913	+	0.841508i	−0.204611	+	0.978843i	$0.565593\pi$
$822$	−12.8774	+	24.8522i	−0.449150	+	0.866820i
$823$	−0.431888	+	0.833506i	−0.0150547	+	0.0290542i	−0.895294	−	0.445476i	$-0.853034\pi$
$823$	−0.431888	+	0.833506i	−0.0150547	+	0.0290542i	0.880239	+	0.474531i	$0.157382\pi$
$824$	−37.9622	−	40.6476i	−1.32248	−	1.41603i
$825$	27.9774	−	22.7613i	0.974049	−	0.792448i
$826$	8.95356	−	5.44478i	0.311534	−	0.189448i
$827$	−16.7512	+	7.27608i	−0.582497	+	0.253014i	−0.669031	−	0.743235i	$-0.733290\pi$
$827$	−16.7512	+	7.27608i	−0.582497	+	0.253014i	0.0865339	+	0.996249i	$0.472421\pi$
$828$	0.272557	−	1.31162i	0.00947200	−	0.0455818i
$829$	0.657737	+	0.184289i	0.0228441	+	0.00640063i	0.281200	−	0.959649i	$-0.409268\pi$
$829$	0.657737	+	0.184289i	0.0228441	+	0.00640063i	−0.258356	+	0.966050i	$0.583181\pi$
$830$	−0.115573	−	0.325192i	−0.00401160	−	0.0112876i
$831$	16.4644	−	17.6291i	0.571145	−	0.611547i
$832$	−0.0717900	+	1.04953i	−0.00248887	+	0.0363860i
$833$	1.27449	+	6.13318i	0.0441585	+	0.212502i
$834$	10.5305	+	14.9184i	0.364643	+	0.516581i
$835$	−8.25540	+	2.31305i	−0.285690	+	0.0800466i
$836$	0.0830379	+	1.21397i	0.00287192	+	0.0419861i
$837$	23.9838	+	19.5122i	0.829000	+	0.674442i
$838$	38.2269	+	5.25417i	1.32053	+	0.181502i
$839$	−26.5319	−	16.1344i	−0.915982	−	0.557021i	−0.0193571	−	0.999813i	$-0.506162\pi$
$839$	−26.5319	−	16.1344i	−0.915982	−	0.557021i	−0.896624	+	0.442792i	$0.853988\pi$
$840$	5.91662	−	0.813221i	0.204143	−	0.0280588i
$841$	9.65980	+	4.19584i	0.333097	+	0.144684i
$842$	10.5556	−	14.9539i	0.363770	−	0.515345i
$843$	−23.0725	+	64.9199i	−0.794661	+	2.23596i
$844$	−2.28815	−	4.41593i	−0.0787614	−	0.152003i
$845$	−14.2385			−0.489819
$846$	−3.82622	+	10.7910i	−0.131548	+	0.371001i
$847$	−8.39515			−0.288461
$848$	16.0369	+	30.9498i	0.550710	+	1.06282i
$849$	−3.36042	+	9.45531i	−0.115329	+	0.324506i
$850$	2.73224	−	3.87070i	0.0937150	−	0.132764i
$851$	20.7192	+	8.99962i	0.710245	+	0.308503i
$852$	−4.98254	+	0.684834i	−0.170699	+	0.0234620i
$853$	3.72230	+	2.26358i	0.127449	+	0.0775036i	0.581861	−	0.813288i	$-0.302325\pi$
$853$	3.72230	+	2.26358i	0.127449	+	0.0775036i	−0.454412	+	0.890792i	$0.650151\pi$
$854$	13.7015	+	1.88323i	0.468855	+	0.0644427i
$855$	−0.684904	−	0.557211i	−0.0234232	−	0.0190562i
$856$	2.08704	+	30.5114i	0.0713334	+	1.04286i
$857$	−2.27554	+	0.637577i	−0.0777310	+	0.0217792i	−0.308442	−	0.951243i	$-0.599808\pi$
$857$	−2.27554	+	0.637577i	−0.0777310	+	0.0217792i	0.230711	+	0.973022i	$0.425895\pi$
$858$	0.807573	+	1.14407i	0.0275701	+	0.0390579i
$859$	9.15685	+	44.0652i	0.312428	+	1.50348i	0.783501	+	0.621391i	$0.213432\pi$
$859$	9.15685	+	44.0652i	0.312428	+	1.50348i	−0.471073	+	0.882094i	$0.656133\pi$
$860$	−0.160464	+	2.34590i	−0.00547178	+	0.0799947i
$861$	6.19593	−	6.63422i	0.211157	−	0.226094i
$862$	−6.08833	−	17.1309i	−0.207369	−	0.583481i
$863$	4.26337	+	1.19454i	0.145127	+	0.0406626i	0.341593	−	0.939848i	$-0.389034\pi$
$863$	4.26337	+	1.19454i	0.145127	+	0.0406626i	−0.196466	+	0.980511i	$0.562947\pi$
$864$	1.73163	−	8.33307i	0.0589113	−	0.283497i
$865$	11.9833	−	5.20507i	0.407443	−	0.176978i
$866$	42.0259	−	25.5565i	1.42810	−	0.868445i
$867$	−1.61577	+	1.31452i	−0.0548743	+	0.0446436i
$868$	2.32092	+	2.48510i	0.0787771	+	0.0843497i
$869$	1.71295	−	3.30584i	0.0581078	−	0.112143i
$870$	−5.63313	+	10.8714i	−0.190981	+	0.368576i
$871$	−0.431649	−	0.462183i	−0.0146259	−	0.0156605i
$872$	43.3978	−	35.3067i	1.46963	−	1.19564i
$873$	−11.5905	+	7.04836i	−0.392280	+	0.238551i
$874$	−1.55251	+	0.674352i	−0.0525146	+	0.0228103i
$875$	1.68349	−	8.10140i	0.0569123	−	0.273877i
$876$	−8.25526	−	2.31301i	−0.278919	−	0.0781495i
$877$	−0.837605	−	2.35679i	−0.0282839	−	0.0795833i	0.927278	−	0.374373i	$-0.122142\pi$
$877$	−0.837605	−	2.35679i	−0.0282839	−	0.0795833i	−0.955562	+	0.294789i	$0.904751\pi$
$878$	15.4458	−	16.5385i	0.521272	−	0.558146i
$879$	−1.04161	+	15.2277i	−0.0351325	+	0.513619i
$880$	−2.96561	−	14.2713i	−0.0999708	−	0.481086i
$881$	−24.5400	−	34.7653i	−0.826775	−	1.17127i	−0.983010	−	0.183554i	$-0.941240\pi$
$881$	−24.5400	−	34.7653i	−0.826775	−	1.17127i	0.156235	−	0.987720i	$-0.450064\pi$
$882$	10.0736	−	2.82248i	0.339194	−	0.0950377i
$883$	1.82882	+	26.7364i	0.0615447	+	0.899752i	0.921252	+	0.388966i	$0.127168\pi$
$883$	1.82882	+	26.7364i	0.0615447	+	0.899752i	−0.859708	+	0.510787i	$0.829354\pi$
$884$	−0.0406800	−	0.0330957i	−0.00136822	−	0.00111313i
$885$	−22.1563	−	3.04532i	−0.744777	−	0.102367i
$886$	−1.61451	−	0.981806i	−0.0542406	−	0.0329844i
$887$	−16.4468	+	2.26056i	−0.552230	+	0.0759023i	−0.406886	−	0.913479i	$-0.633385\pi$
$887$	−16.4468	+	2.26056i	−0.552230	+	0.0759023i	−0.145344	+	0.989381i	$0.546429\pi$
$888$	−58.3305	−	25.3365i	−1.95744	−	0.850238i
$889$	−3.57967	+	5.07124i	−0.120058	+	0.170084i
$890$	1.75924	−	4.95002i	0.0589698	−	0.165925i
$891$	−23.5430	−	45.4360i	−0.788721	−	1.52216i
$892$	1.59362			0.0533583
$893$	−3.97022	+	1.11554i	−0.132858	+	0.0373300i
$894$	−0.744978			−0.0249158
$895$	−4.86952	−	9.39775i	−0.162770	−	0.314132i
$896$	−1.77636	+	4.99819i	−0.0593439	+	0.166978i
$897$	0.320247	−	0.453686i	0.0106927	−	0.0151481i
$898$	−30.8436	−	13.3973i	−1.02926	−	0.447073i
$899$	−38.0395	+	5.22841i	−1.26869	+	0.174377i
$900$	1.92726	+	1.17199i	0.0642420	+	0.0390664i
$901$	−11.8434	−	1.62784i	−0.394562	−	0.0542313i
$902$	−22.4161	−	18.2369i	−0.746375	−	0.607221i
$903$	−0.589370	−	8.61628i	−0.0196130	−	0.286732i
$904$	53.8323	−	15.0831i	1.79043	−	0.501656i
$905$	3.45592	+	4.89592i	0.114879	+	0.162746i
$906$	−7.13168	−	34.3195i	−0.236934	−	1.14019i
$907$	−0.904959	+	13.2300i	−0.0300487	+	0.439296i	0.958165	+	0.286216i	$0.0923975\pi$
$907$	−0.904959	+	13.2300i	−0.0300487	+	0.439296i	−0.988214	+	0.153080i	$0.951081\pi$
$908$	7.21910	−	7.72977i	0.239574	−	0.256521i
$909$	−1.92823	−	5.42552i	−0.0639554	−	0.179953i
$910$	0.133545	+	0.0374174i	0.00442696	+	0.00124038i
$911$	−7.56368	+	36.3984i	−0.250596	+	1.20593i	0.646088	+	0.763263i	$0.276404\pi$
$911$	−7.56368	+	36.3984i	−0.250596	+	1.20593i	−0.896684	+	0.442671i	$0.854031\pi$
$912$	3.35100	−	1.45554i	0.110963	−	0.0481979i
$913$	−0.982873	+	0.597698i	−0.0325283	+	0.0197809i
$914$	−28.5838	+	23.2546i	−0.945467	+	0.769194i
$915$	−20.1468	−	21.5719i	−0.666032	−	0.713146i
$916$	−5.00157	+	9.65259i	−0.165256	+	0.318930i
$917$	4.14638	−	8.00215i	0.136926	−	0.264254i
$918$	−2.94659	−	3.15503i	−0.0972519	−	0.104131i
$919$	17.9699	−	14.6196i	0.592773	−	0.482257i	−0.286819	−	0.957985i	$-0.592598\pi$
$919$	17.9699	−	14.6196i	0.592773	−	0.482257i	0.879593	+	0.475728i	$0.157815\pi$
$920$	−6.44172	+	3.91729i	−0.212377	+	0.129149i
$921$	18.0407	−	7.83620i	0.594462	−	0.258211i
$922$	8.17182	−	39.3249i	0.269124	−	1.29510i
$923$	−0.619421	−	0.173554i	−0.0203885	−	0.00571259i
$924$	−1.21032	−	3.40553i	−0.0398168	−	0.112034i
$925$	−25.9611	+	27.7976i	−0.853596	+	0.913979i
$926$	1.87428	−	27.4010i	0.0615926	−	0.900452i
$927$	−4.96900	−	23.9121i	−0.163203	−	0.785377i
$928$	6.09539	+	8.63519i	0.200091	+	0.283464i
$929$	30.3320	−	8.49862i	0.995160	−	0.278831i	0.266596	−	0.963808i	$-0.414101\pi$
$929$	30.3320	−	8.49862i	0.995160	−	0.278831i	0.728564	+	0.684978i	$0.240188\pi$
$930$	1.73723	+	25.3974i	0.0569659	+	0.832812i
$931$	2.92302	+	2.37805i	0.0957981	+	0.0779375i
$932$	−3.08231	−	0.423654i	−0.100964	−	0.0138772i
$933$	−41.3844	−	25.1664i	−1.35486	−	0.823910i
$934$	−12.6740	+	1.74200i	−0.414705	+	0.0569999i
$935$	4.58514	+	1.99161i	0.149950	+	0.0651326i
$936$	−0.278180	+	0.394092i	−0.00909260	+	0.0128813i
$937$	−11.9457	+	33.6120i	−0.390249	+	1.09806i	0.570658	+	0.821188i	$0.306688\pi$
$937$	−11.9457	+	33.6120i	−0.390249	+	1.09806i	−0.960908	+	0.276869i	$0.910703\pi$
$938$	−2.63403	−	5.08345i	−0.0860042	−	0.165981i
$939$	25.2524			0.824081
$940$	−3.05793	+	1.33091i	−0.0997387	+	0.0434094i
$941$	8.30538			0.270748			0.135374	−	0.990795i	$-0.456776\pi$
$941$	8.30538			0.270748			0.135374	+	0.990795i	$0.456776\pi$
$942$	26.0551	+	50.2841i	0.848921	+	1.63834i
$943$	−3.83753	+	10.7978i	−0.124967	+	0.351624i
$944$	16.4661	−	23.3272i	0.535926	−	0.759234i
$945$	−2.98516	−	1.29664i	−0.0971071	−	0.0421796i
$946$	−27.2370	+	3.74364i	−0.885552	+	0.121716i
$947$	−23.3066	−	14.1731i	−0.757363	−	0.460563i	0.0870842	−	0.996201i	$-0.472245\pi$
$947$	−23.3066	−	14.1731i	−0.757363	−	0.460563i	−0.844448	+	0.535638i	$0.820071\pi$
$948$	0.747659	+	0.102763i	0.0242828	+	0.00333760i
$949$	−0.850597	−	0.692012i	−0.0276115	−	0.0224637i
$950$	−0.194493	−	2.84338i	−0.00631018	−	0.0922516i
$951$	20.5674	−	5.76272i	0.666944	−	0.186869i
$952$	−1.50802	−	2.13638i	−0.0488752	−	0.0692403i
$953$	−9.72629	−	46.8055i	−0.315065	−	1.51618i	−0.777135	−	0.629334i	$-0.783328\pi$
$953$	−9.72629	−	46.8055i	−0.315065	−	1.51618i	0.462069	−	0.886844i	$-0.347107\pi$
$954$	−1.36246	+	19.9184i	−0.0441112	+	0.644883i
$955$	−3.80372	+	4.07279i	−0.123085	+	0.131792i
$956$	−2.99294	−	8.42134i	−0.0967987	−	0.272366i
$957$	39.2986	+	11.0110i	1.27034	+	0.355934i
$958$	−2.30471	+	11.0909i	−0.0744617	+	0.358330i
$959$	8.47473	−	3.68109i	0.273663	−	0.118869i
$960$	17.3670	−	10.5611i	0.560519	−	0.340859i
$961$	−37.8786	+	30.8165i	−1.22189	+	0.994081i
$962$	−1.00800	−	1.07931i	−0.0324994	−	0.0347983i
$963$	−6.17843	+	11.9238i	−0.199097	+	0.384240i
$964$	−1.47046	+	2.83786i	−0.0473603	+	0.0914012i
$965$	−1.14164	−	1.22240i	−0.0367508	−	0.0393505i
$966$	3.89994	−	3.17283i	0.125478	−	0.102084i
$967$	34.2202	−	20.8098i	1.10045	−	0.669197i	0.152717	−	0.988270i	$-0.451198\pi$
$967$	34.2202	−	20.8098i	1.10045	−	0.669197i	0.947730	+	0.319073i	$0.103371\pi$
$968$	−27.3661	+	11.8868i	−0.879581	+	0.382056i
$969$	−0.254926	+	1.22677i	−0.00818942	+	0.0394096i
$970$	13.3470	+	3.73964i	0.428545	+	0.120073i
$971$	−7.62280	−	21.4485i	−0.244627	−	0.688315i	−0.999475	−	0.0324146i	$-0.989680\pi$
$971$	−7.62280	−	21.4485i	−0.244627	−	0.688315i	0.754847	−	0.655901i	$-0.227711\pi$
$972$	3.93605	−	4.21448i	0.126249	−	0.135180i
$973$	0.411357	−	6.01382i	0.0131875	−	0.192794i
$974$	−6.04469	−	29.0887i	−0.193684	−	0.932061i
$975$	0.539222	+	0.763904i	0.0172689	+	0.0244645i
$976$	36.2871	−	10.1672i	1.16152	−	0.325443i
$977$	−1.04145	−	15.2255i	−0.0333191	−	0.487108i	−0.984143	−	0.177376i	$-0.943239\pi$
$977$	−1.04145	−	15.2255i	−0.0333191	−	0.487108i	0.950824	−	0.309732i	$-0.100239\pi$
$978$	−30.2211	−	24.5867i	−0.966364	−	0.786195i
$979$	−17.3472	−	2.38432i	−0.554420	−	0.0762032i
$980$	2.60366	+	1.58332i	0.0831709	+	0.0505774i
$981$	24.3381	−	3.34520i	0.777056	−	0.106804i
$982$	1.17305	+	0.509530i	0.0374337	+	0.0162597i
$983$	8.08311	−	11.4512i	0.257811	−	0.365235i	−0.667392	−	0.744706i	$-0.732590\pi$
$983$	8.08311	−	11.4512i	0.257811	−	0.365235i	0.925204	+	0.379471i	$0.123894\pi$
$984$	10.8037	−	30.3988i	0.344411	−	0.969079i
$985$	2.85960	+	5.51877i	0.0911144	+	0.175843i
$986$	5.36123			0.170736
$987$	10.4612	−	6.37212i	0.332985	−	0.202827i
$988$	−0.0315462			−0.00100362
$989$	5.01586	+	9.68017i	0.159495	+	0.307811i
$990$	2.79576	−	7.86651i	0.0888551	−	0.250014i
$991$	−8.21440	+	11.6372i	−0.260939	+	0.369667i	−0.926256	−	0.376894i	$-0.876992\pi$
$991$	−8.21440	+	11.6372i	−0.260939	+	0.369667i	0.665317	+	0.746561i	$0.268296\pi$
$992$	20.1561	+	8.75504i	0.639958	+	0.277973i
$993$	−9.06027	+	1.24531i	−0.287519	+	0.0395186i
$994$	−4.97595	−	3.02594i	−0.157828	−	0.0959771i
$995$	−24.5855	−	3.37920i	−0.779413	−	0.107128i
$996$	−0.180871	−	0.147149i	−0.00573112	−	0.00466261i
$997$	−2.76884	−	40.4790i	−0.0876900	−	1.28198i	−0.808354	−	0.588697i	$-0.799641\pi$
$997$	−2.76884	−	40.4790i	−0.0876900	−	1.28198i	0.720664	−	0.693285i	$-0.243837\pi$
$998$	−36.8779	+	10.3327i	−1.16735	+	0.327076i
$999$	19.9858	+	28.3134i	0.632323	+	0.895797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.k.b.256.11	yes	704
47.9	even	23	inner	799.2.k.b.103.11	✓	704

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.k.b.103.11	✓	704	47.9	even	23	inner
799.2.k.b.256.11	yes	704	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.k (of order \(23\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573945 - 1.10766i) q^{2} +(-0.697537 + 1.96268i) q^{3} +(0.255856 - 0.362465i) q^{4} +(-1.00567 - 0.436825i) q^{5} +(2.57434 - 0.353835i) q^{6} +(-0.732908 - 0.445691i) q^{7} +(-3.02016 - 0.415111i) q^{8} +(-1.03843 - 0.844825i) q^{9} +O(q^{10})\)	\(q+(-0.573945 - 1.10766i) q^{2} +(-0.697537 + 1.96268i) q^{3} +(0.255856 - 0.362465i) q^{4} +(-1.00567 - 0.436825i) q^{5} +(2.57434 - 0.353835i) q^{6} +(-0.732908 - 0.445691i) q^{7} +(-3.02016 - 0.415111i) q^{8} +(-1.03843 - 0.844825i) q^{9} +(0.0933453 + 1.36466i) q^{10} +(4.39021 - 1.23008i) q^{11} +(0.532935 + 0.754996i) q^{12} +(0.0240487 + 0.115729i) q^{13} +(-0.0730270 + 1.06762i) q^{14} +(1.55884 - 1.66911i) q^{15} +(0.976448 + 2.74746i) q^{16} +(-0.962917 - 0.269797i) q^{17} +(-0.339780 + 1.63511i) q^{18} +(-0.551741 + 0.239655i) q^{19} +(-0.415641 + 0.252757i) q^{20} +(1.38598 - 1.12758i) q^{21} +(-3.88225 - 4.15687i) q^{22} +(-1.03769 + 2.00266i) q^{23} +(2.92140 - 5.63805i) q^{24} +(-2.59220 - 2.77557i) q^{25} +(0.114386 - 0.0930597i) q^{26} +(-2.95667 + 1.79799i) q^{27} +(-0.349066 + 0.151621i) q^{28} +(0.874347 - 4.20759i) q^{29} +(-2.74351 - 0.768694i) q^{30} +(-2.99208 - 8.41892i) q^{31} +(-1.67876 + 1.79752i) q^{32} +(-0.648081 + 9.47461i) q^{33} +(0.253817 + 1.22144i) q^{34} +(0.542376 + 0.768372i) q^{35} +(-0.571907 + 0.160241i) q^{36} +(-0.683453 - 9.99173i) q^{37} +(0.582125 + 0.473594i) q^{38} +(-0.243913 - 0.0335251i) q^{39} +(2.85596 + 1.73675i) q^{40} +(5.03326 - 0.691805i) q^{41} +(-2.04445 - 0.888031i) q^{42} +(2.78748 - 3.94896i) q^{43} +(0.677400 - 1.90602i) q^{44} +(0.675279 + 1.30323i) q^{45} +2.81385 q^{46} +(6.79248 + 0.928542i) q^{47} -6.07350 q^{48} +(-2.88194 - 5.56190i) q^{49} +(-1.58662 + 4.46431i) q^{50} +(1.20120 - 1.70171i) q^{51} +(0.0481006 + 0.0208930i) q^{52} +(11.8434 - 1.62784i) q^{53} +(3.68854 + 2.24305i) q^{54} +(-4.95244 - 0.680698i) q^{55} +(2.02848 + 1.65029i) q^{56} +(-0.0855064 - 1.25006i) q^{57} +(-5.16242 + 1.44644i) q^{58} +(-5.64717 - 8.00021i) q^{59} +(-0.206156 - 0.992079i) q^{60} +(0.881977 - 12.8940i) q^{61} +(-7.60803 + 8.14621i) q^{62} +(0.384542 + 1.08200i) q^{63} +(8.56994 + 2.40118i) q^{64} +(0.0263681 - 0.126890i) q^{65} +(10.8666 - 4.72005i) q^{66} +(-4.57135 + 2.77990i) q^{67} +(-0.344160 + 0.279995i) q^{68} +(-3.20675 - 3.43359i) q^{69} +(0.539803 - 1.04177i) q^{70} +(-2.50377 + 4.83207i) q^{71} +(2.78552 + 2.98257i) q^{72} +(-7.19619 + 5.85454i) q^{73} +(-10.6752 + 6.49174i) q^{74} +(7.25573 - 3.15161i) q^{75} +(-0.0542995 + 0.261304i) q^{76} +(-3.76585 - 1.05514i) q^{77} +(0.102858 + 0.289416i) q^{78} +(0.557398 - 0.596827i) q^{79} +(0.218174 - 3.18958i) q^{80} +(-2.28359 - 10.9892i) q^{81} +(-3.65510 - 5.17810i) q^{82} +(-0.242951 + 0.0680717i) q^{83} +(-0.0540968 - 0.790867i) q^{84} +(0.850526 + 0.691954i) q^{85} +(-5.97397 - 0.821104i) q^{86} +(7.64827 + 4.65102i) q^{87} +(-13.7697 + 1.89261i) q^{88} +(-3.52263 - 1.53009i) q^{89} +(1.05597 - 1.49596i) q^{90} +(0.0339538 - 0.0955367i) q^{91} +(0.460393 + 0.888519i) q^{92} +18.6108 q^{93} +(-2.87000 - 8.05671i) q^{94} +0.659558 q^{95} +(-2.35695 - 4.54871i) q^{96} +(3.39347 - 9.54831i) q^{97} +(-4.50663 + 6.38444i) q^{98} +(-5.59812 - 2.43161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 704 q - 2 q^{3} - 32 q^{4} - 2 q^{5} - 10 q^{6} - 21 q^{7} - 34 q^{9}+O(q^{10}) \) 704 * q - 2 * q^3 - 32 * q^4 - 2 * q^5 - 10 * q^6 - 21 * q^7 - 34 * q^9	\( 704 q - 2 q^{3} - 32 q^{4} - 2 q^{5} - 10 q^{6} - 21 q^{7} - 34 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 12 q^{13} + 2 q^{14} + 14 q^{15} - 32 q^{16} + 32 q^{17} - 6 q^{18} + 4 q^{19} - 14 q^{20} + 8 q^{22} - 2 q^{23} - 24 q^{24} - 42 q^{25} + 18 q^{26} - 8 q^{27} + 2 q^{28} - 12 q^{29} - 184 q^{30} + 12 q^{31} - 12 q^{33} - 6 q^{35} + 110 q^{36} - 472 q^{38} + 97 q^{39} + 142 q^{40} + 43 q^{41} + 18 q^{42} + 37 q^{43} - 20 q^{44} - 38 q^{45} - 136 q^{46} + 15 q^{47} - 24 q^{48} - 11 q^{49} + 68 q^{50} + 2 q^{51} - 4 q^{52} - 11 q^{53} - 551 q^{54} + 71 q^{55} + 186 q^{56} + 103 q^{57} + 20 q^{58} - 30 q^{59} + 208 q^{60} + 18 q^{61} - 228 q^{62} + 22 q^{63} - 92 q^{64} - 32 q^{65} - 52 q^{66} + 8 q^{67} + 32 q^{68} - 128 q^{69} - 706 q^{70} - 42 q^{71} - 34 q^{72} + 26 q^{73} + 46 q^{74} + 8 q^{75} + 46 q^{76} - 534 q^{77} - 118 q^{78} + 36 q^{79} - 84 q^{80} + 74 q^{81} + 173 q^{82} + 88 q^{83} + 90 q^{84} + 2 q^{85} + 224 q^{86} + 126 q^{87} + 22 q^{88} - 8 q^{89} + 390 q^{90} + 258 q^{91} + 215 q^{92} - 430 q^{93} - 8 q^{94} + 4 q^{95} + 72 q^{96} + 34 q^{97} + 165 q^{98} + 276 q^{99}+O(q^{100}) \) 704 * q - 2 * q^3 - 32 * q^4 - 2 * q^5 - 10 * q^6 - 21 * q^7 - 34 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 12 * q^13 + 2 * q^14 + 14 * q^15 - 32 * q^16 + 32 * q^17 - 6 * q^18 + 4 * q^19 - 14 * q^20 + 8 * q^22 - 2 * q^23 - 24 * q^24 - 42 * q^25 + 18 * q^26 - 8 * q^27 + 2 * q^28 - 12 * q^29 - 184 * q^30 + 12 * q^31 - 12 * q^33 - 6 * q^35 + 110 * q^36 - 472 * q^38 + 97 * q^39 + 142 * q^40 + 43 * q^41 + 18 * q^42 + 37 * q^43 - 20 * q^44 - 38 * q^45 - 136 * q^46 + 15 * q^47 - 24 * q^48 - 11 * q^49 + 68 * q^50 + 2 * q^51 - 4 * q^52 - 11 * q^53 - 551 * q^54 + 71 * q^55 + 186 * q^56 + 103 * q^57 + 20 * q^58 - 30 * q^59 + 208 * q^60 + 18 * q^61 - 228 * q^62 + 22 * q^63 - 92 * q^64 - 32 * q^65 - 52 * q^66 + 8 * q^67 + 32 * q^68 - 128 * q^69 - 706 * q^70 - 42 * q^71 - 34 * q^72 + 26 * q^73 + 46 * q^74 + 8 * q^75 + 46 * q^76 - 534 * q^77 - 118 * q^78 + 36 * q^79 - 84 * q^80 + 74 * q^81 + 173 * q^82 + 88 * q^83 + 90 * q^84 + 2 * q^85 + 224 * q^86 + 126 * q^87 + 22 * q^88 - 8 * q^89 + 390 * q^90 + 258 * q^91 + 215 * q^92 - 430 * q^93 - 8 * q^94 + 4 * q^95 + 72 * q^96 + 34 * q^97 + 165 * q^98 + 276 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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