LMFDB - Embedded newform 418.2.n.e.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	418.49
Dual form			418.2.n.e.273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(-2.93761 + 1.30791i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.74891 + 1.94236i) q^{5} +(3.14534 - 0.668563i) q^{6} +(0.517306 - 0.375844i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(4.91153 - 5.45480i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(-2.93761 + 1.30791i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.74891 + 1.94236i) q^{5} +(3.14534 - 0.668563i) q^{6} +(0.517306 - 0.375844i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(4.91153 - 5.45480i) q^{9} +(-1.30685 - 2.26353i) q^{10} +(2.68025 + 1.95352i) q^{11} -3.21561 q^{12} +(2.87476 - 3.19275i) q^{13} +(-0.584144 + 0.260077i) q^{14} +(-7.67803 - 3.41848i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.83119 - 2.03374i) q^{17} +(-5.93831 + 4.31444i) q^{18} +(-0.0648390 + 4.35842i) q^{19} +(0.807679 + 2.48578i) q^{20} +(-1.02807 + 1.78067i) q^{21} +(-2.21552 - 2.46809i) q^{22} +(3.27542 + 5.67319i) q^{23} +(3.14534 + 0.668563i) q^{24} +(-0.191438 + 1.82141i) q^{25} +(-3.47575 + 2.52528i) q^{26} +(-4.31272 + 13.2732i) q^{27} +(0.625452 - 0.132944i) q^{28} +(6.54498 + 2.91401i) q^{29} +(6.79951 + 4.94013i) q^{30} +(-1.22509 - 3.77044i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-10.4286 - 2.23317i) q^{33} +(1.36833 + 2.37002i) q^{34} +(1.63475 + 0.347476i) q^{35} +(6.70557 - 2.98551i) q^{36} +(-3.35767 + 2.43949i) q^{37} +(0.969588 - 4.24969i) q^{38} +(-4.26910 + 13.1390i) q^{39} +(-0.273206 - 2.59938i) q^{40} +(2.37850 - 1.05898i) q^{41} +(1.37583 - 1.52801i) q^{42} +(-2.67234 + 4.62862i) q^{43} +(1.65396 + 2.87479i) q^{44} +19.1850 q^{45} +(-2.02432 - 6.23022i) q^{46} +(0.156121 - 1.48539i) q^{47} +(-2.93761 - 1.30791i) q^{48} +(-2.03677 + 6.26854i) q^{49} +(0.565947 - 1.74181i) q^{50} +(8.03925 + 3.57930i) q^{51} +(3.92483 - 1.74745i) q^{52} +(-7.85252 + 8.72111i) q^{53} +(6.97814 - 12.0865i) q^{54} +(0.893069 + 8.62255i) q^{55} -0.639425 q^{56} +(-5.50993 - 12.8881i) q^{57} +(-5.79610 - 4.21111i) q^{58} +(0.104294 + 0.992295i) q^{59} +(-5.62381 - 6.24588i) q^{60} +(2.90268 - 0.616984i) q^{61} +(0.414401 + 3.94276i) q^{62} +(0.490602 - 4.66777i) q^{63} +(0.309017 + 0.951057i) q^{64} +11.2292 q^{65} +(9.73636 + 4.35258i) q^{66} +(-2.63234 - 4.55935i) q^{67} +(-0.845676 - 2.60272i) q^{68} +(-17.0419 - 12.3817i) q^{69} +(-1.52678 - 0.679765i) q^{70} +(-4.76067 - 5.28726i) q^{71} +(-7.17976 + 1.52611i) q^{72} +(-0.367487 - 3.49641i) q^{73} +(3.79150 - 1.68808i) q^{74} +(-1.81987 - 5.60097i) q^{75} +(-1.83196 + 3.95524i) q^{76} +(2.12073 + 0.00321097i) q^{77} +(6.90756 - 11.9642i) q^{78} +(1.02274 + 0.217390i) q^{79} +(-0.273206 + 2.59938i) q^{80} +(-2.38926 - 22.7323i) q^{81} +(-2.54670 + 0.541318i) q^{82} +(4.22540 - 13.0044i) q^{83} +(-1.66345 + 1.20857i) q^{84} +(0.747674 - 7.11364i) q^{85} +(3.57629 - 3.97187i) q^{86} -23.0378 q^{87} +(-1.02012 - 3.15585i) q^{88} +(7.55400 + 13.0839i) q^{89} +(-18.7658 - 3.98879i) q^{90} +(0.287154 - 2.73209i) q^{91} +(0.684749 + 6.51495i) q^{92} +(8.53022 + 9.47377i) q^{93} +(-0.461539 + 1.42047i) q^{94} +(-8.57901 + 7.49653i) q^{95} +(2.60148 + 1.89009i) q^{96} +(-16.5586 - 3.51963i) q^{97} +(3.29557 - 5.70809i) q^{98} +(23.8202 - 5.02546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	−2.93761	+	1.30791i	−1.69603	+	0.755121i	−0.696743	+	0.717321i	$0.745368\pi$
$3$	−2.93761	+	1.30791i	−1.69603	+	0.755121i	−0.999285	+	0.0378000i	$0.987965\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	1.74891	+	1.94236i	0.782136	+	0.868650i	0.994082	−	0.108632i	$-0.0346469\pi$
$5$	1.74891	+	1.94236i	0.782136	+	0.868650i	−0.211946	+	0.977281i	$0.567980\pi$
$6$	3.14534	−	0.668563i	1.28408	−	0.272940i
$7$	0.517306	−	0.375844i	0.195523	−	0.142056i	−0.485716	−	0.874116i	$-0.661441\pi$
$7$	0.517306	−	0.375844i	0.195523	−	0.142056i	0.681240	+	0.732061i	$0.261441\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	4.91153	−	5.45480i	1.63718	−	1.81827i
$10$	−1.30685	−	2.26353i	−0.413263	−	0.715792i
$11$	2.68025	+	1.95352i	0.808126	+	0.589010i
$11$	2.68025	+	1.95352i	0.808126	+	0.589010i
$12$	−3.21561			−0.928267
$13$	2.87476	−	3.19275i	0.797315	−	0.885508i	−0.198195	−	0.980163i	$-0.563508\pi$
$13$	2.87476	−	3.19275i	0.797315	−	0.885508i	0.995510	+	0.0946544i	$0.0301746\pi$
$14$	−0.584144	+	0.260077i	−0.156119	+	0.0695086i
$15$	−7.67803	−	3.41848i	−1.98246	−	0.882648i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−1.83119	−	2.03374i	−0.444128	−	0.493254i	0.478963	−	0.877835i	$-0.341013\pi$
$17$	−1.83119	−	2.03374i	−0.444128	−	0.493254i	−0.923091	+	0.384581i	$0.874346\pi$
$18$	−5.93831	+	4.31444i	−1.39967	+	1.01692i
$19$	−0.0648390	+	4.35842i	−0.0148751	+	0.999889i
$19$	−0.0648390	+	4.35842i	−0.0148751	+	0.999889i
$20$	0.807679	+	2.48578i	0.180602	+	0.555837i
$21$	−1.02807	+	1.78067i	−0.224343	+	0.388574i
$22$	−2.21552	−	2.46809i	−0.472351	−	0.526199i
$23$	3.27542	+	5.67319i	0.682972	+	1.18294i	0.974070	+	0.226249i	$0.0726463\pi$
$23$	3.27542	+	5.67319i	0.682972	+	1.18294i	−0.291097	+	0.956693i	$0.594020\pi$
$24$	3.14534	+	0.668563i	0.642040	+	0.136470i
$25$	−0.191438	+	1.82141i	−0.0382876	+	0.364282i
$26$	−3.47575	+	2.52528i	−0.681651	+	0.495248i
$27$	−4.31272	+	13.2732i	−0.829984	+	2.55443i
$28$	0.625452	−	0.132944i	0.118199	−	0.0251240i
$29$	6.54498	+	2.91401i	1.21537	+	0.541118i	0.911384	−	0.411558i	$-0.135015\pi$
$29$	6.54498	+	2.91401i	1.21537	+	0.541118i	0.303988	+	0.952676i	$0.401682\pi$
$30$	6.79951	+	4.94013i	1.24141	+	0.901941i
$31$	−1.22509	−	3.77044i	−0.220033	−	0.677191i	−0.998758	−	0.0498259i	$-0.984133\pi$
$31$	−1.22509	−	3.77044i	−0.220033	−	0.677191i	0.778725	−	0.627365i	$-0.215867\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−10.4286	−	2.23317i	−1.81538	−	0.388744i
$34$	1.36833	+	2.37002i	0.234667	+	0.406455i
$35$	1.63475	+	0.347476i	0.276322	+	0.0587341i
$36$	6.70557	−	2.98551i	1.11759	−	0.497585i
$37$	−3.35767	+	2.43949i	−0.551998	+	0.401050i	−0.828521	−	0.559957i	$-0.810818\pi$
$37$	−3.35767	+	2.43949i	−0.551998	+	0.401050i	0.276524	+	0.961007i	$0.410818\pi$
$38$	0.969588	−	4.24969i	0.157288	−	0.689391i
$39$	−4.26910	+	13.1390i	−0.683604	+	2.10392i
$40$	−0.273206	−	2.59938i	−0.0431977	−	0.410999i
$41$	2.37850	−	1.05898i	0.371460	−	0.165385i	−0.212512	−	0.977158i	$-0.568164\pi$
$41$	2.37850	−	1.05898i	0.371460	−	0.165385i	0.583972	+	0.811774i	$0.301498\pi$
$42$	1.37583	−	1.52801i	0.212295	−	0.235777i
$43$	−2.67234	+	4.62862i	−0.407528	+	0.705859i	−0.994612	−	0.103667i	$-0.966942\pi$
$43$	−2.67234	+	4.62862i	−0.407528	+	0.705859i	0.587084	+	0.809526i	$0.300276\pi$
$44$	1.65396	+	2.87479i	0.249344	+	0.433391i
$45$	19.1850			2.85993
$46$	−2.02432	−	6.23022i	−0.298470	−	0.918595i
$47$	0.156121	−	1.48539i	0.0227726	−	0.216666i	−0.977218	−	0.212240i	$-0.931924\pi$
$47$	0.156121	−	1.48539i	0.0227726	−	0.216666i	0.999990	−	0.00442676i	$-0.00140909\pi$
$48$	−2.93761	−	1.30791i	−0.424007	−	0.188780i
$49$	−2.03677	+	6.26854i	−0.290968	+	0.895506i
$50$	0.565947	−	1.74181i	0.0800370	−	0.246329i
$51$	8.03925	+	3.57930i	1.12572	+	0.501203i
$52$	3.92483	−	1.74745i	0.544276	−	0.242327i
$53$	−7.85252	+	8.72111i	−1.07863	+	1.19794i	−0.0994255	+	0.995045i	$0.531700\pi$
$53$	−7.85252	+	8.72111i	−1.07863	+	1.19794i	−0.979201	+	0.202891i	$0.934966\pi$
$54$	6.97814	−	12.0865i	0.949604	−	1.64476i
$55$	0.893069	+	8.62255i	0.120421	+	1.16266i
$56$	−0.639425			−0.0854467
$57$	−5.50993	−	12.8881i	−0.729808	−	1.70707i
$58$	−5.79610	−	4.21111i	−0.761065	−	0.552946i
$59$	0.104294	+	0.992295i	0.0135780	+	0.129186i	0.999211	−	0.0397149i	$-0.0126450\pi$
$59$	0.104294	+	0.992295i	0.0135780	+	0.129186i	−0.985633	+	0.168901i	$0.945978\pi$
$60$	−5.62381	−	6.24588i	−0.726031	−	0.806339i
$61$	2.90268	−	0.616984i	0.371650	−	0.0789966i	−0.0183003	−	0.999833i	$-0.505826\pi$
$61$	2.90268	−	0.616984i	0.371650	−	0.0789966i	0.389950	+	0.920836i	$0.372492\pi$
$62$	0.414401	+	3.94276i	0.0526289	+	0.500731i
$63$	0.490602	−	4.66777i	0.0618101	−	0.588084i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	11.2292			1.39281
$66$	9.73636	+	4.35258i	1.19846	+	0.535766i
$67$	−2.63234	−	4.55935i	−0.321592	−	0.557014i	0.659225	−	0.751946i	$-0.270885\pi$
$67$	−2.63234	−	4.55935i	−0.321592	−	0.557014i	−0.980817	+	0.194932i	$0.937551\pi$
$68$	−0.845676	−	2.60272i	−0.102553	−	0.315626i
$69$	−17.0419	−	12.3817i	−2.05160	−	1.49058i
$70$	−1.52678	−	0.679765i	−0.182485	−	0.0812475i
$71$	−4.76067	−	5.28726i	−0.564987	−	0.627482i	0.391176	−	0.920316i	$-0.372068\pi$
$71$	−4.76067	−	5.28726i	−0.564987	−	0.627482i	−0.956163	+	0.292834i	$0.905402\pi$
$72$	−7.17976	+	1.52611i	−0.846143	+	0.179853i
$73$	−0.367487	−	3.49641i	−0.0430111	−	0.409224i	−0.994752	−	0.102320i	$-0.967374\pi$
$73$	−0.367487	−	3.49641i	−0.0430111	−	0.409224i	0.951740	−	0.306904i	$-0.0992931\pi$
$74$	3.79150	−	1.68808i	0.440752	−	0.196236i
$75$	−1.81987	−	5.60097i	−0.210140	−	0.646745i
$76$	−1.83196	+	3.95524i	−0.210140	+	0.453697i
$77$	2.12073	+	0.00321097i	0.241680	+	0.000365925i
$78$	6.90756	−	11.9642i	0.782127	−	1.35468i
$79$	1.02274	+	0.217390i	0.115067	+	0.0244582i	0.265085	−	0.964225i	$-0.414600\pi$
$79$	1.02274	+	0.217390i	0.115067	+	0.0244582i	−0.150018	+	0.988683i	$0.547933\pi$
$80$	−0.273206	+	2.59938i	−0.0305454	+	0.290620i
$81$	−2.38926	−	22.7323i	−0.265473	−	2.52581i
$82$	−2.54670	+	0.541318i	−0.281236	+	0.0597786i
$83$	4.22540	−	13.0044i	0.463798	−	1.42742i	−0.396691	−	0.917952i	$-0.629841\pi$
$83$	4.22540	−	13.0044i	0.463798	−	1.42742i	0.860488	−	0.509470i	$-0.170159\pi$
$84$	−1.66345	+	1.20857i	−0.181498	+	0.131866i
$85$	0.747674	−	7.11364i	0.0810966	−	0.771583i
$86$	3.57629	−	3.97187i	0.385641	−	0.428298i
$87$	−23.0378			−2.46991
$88$	−1.02012	−	3.15585i	−0.108745	−	0.336414i
$89$	7.55400	+	13.0839i	0.800723	+	1.38689i	0.919141	+	0.393929i	$0.128884\pi$
$89$	7.55400	+	13.0839i	0.800723	+	1.38689i	−0.118418	+	0.992964i	$0.537782\pi$
$90$	−18.7658	−	3.98879i	−1.97808	−	0.420455i
$91$	0.287154	−	2.73209i	0.0301019	−	0.286401i
$92$	0.684749	+	6.51495i	0.0713900	+	0.679231i
$93$	8.53022	+	9.47377i	0.884543	+	0.982384i
$94$	−0.461539	+	1.42047i	−0.0476041	+	0.146510i
$95$	−8.57901	+	7.49653i	−0.880188	+	0.769128i
$96$	2.60148	+	1.89009i	0.265513	+	0.192906i
$97$	−16.5586	−	3.51963i	−1.68127	−	0.357365i	−0.734333	−	0.678789i	$-0.762505\pi$
$97$	−16.5586	−	3.51963i	−1.68127	−	0.357365i	−0.946935	+	0.321425i	$0.895838\pi$
$98$	3.29557	−	5.70809i	0.332903	−	0.576604i
$99$	23.8202	−	5.02546i	2.39402	−	0.505078i
$100$	−0.915722	+	1.58608i	−0.0915722	+	0.158608i
$101$	8.73074	−	9.69647i	0.868741	−	0.964835i	−0.130906	−	0.991395i	$-0.541789\pi$
$101$	8.73074	−	9.69647i	0.868741	−	0.964835i	0.999647	+	0.0265599i	$0.00845526\pi$
$102$	−7.11939	−	5.17254i	−0.704925	−	0.512158i
$103$	3.29070	−	2.39084i	0.324243	−	0.235576i	−0.413741	−	0.910395i	$-0.635778\pi$
$103$	3.29070	−	2.39084i	0.324243	−	0.235576i	0.737984	+	0.674818i	$0.235778\pi$
$104$	−4.20238	+	0.893243i	−0.412077	+	0.0875897i
$105$	−5.25671	+	1.11735i	−0.513002	+	0.109042i
$106$	9.49415	−	6.89790i	0.922153	−	0.669983i
$107$	15.0975	+	10.9690i	1.45953	+	1.06041i	0.983485	+	0.180988i	$0.0579294\pi$
$107$	15.0975	+	10.9690i	1.45953	+	1.06041i	0.476043	+	0.879422i	$0.342071\pi$
$108$	−9.33857	+	10.3715i	−0.898604	+	0.998001i
$109$	1.50222	−	2.60192i	0.143887	−	0.249219i	−0.785070	−	0.619407i	$-0.787373\pi$
$109$	1.50222	−	2.60192i	0.143887	−	0.249219i	0.928957	+	0.370188i	$0.120707\pi$
$110$	0.919175	−	8.61980i	0.0876399	−	0.821866i
$111$	6.67289	−	11.5578i	0.633363	−	1.09702i
$112$	0.625452	+	0.132944i	0.0590996	+	0.0125620i
$113$	15.7742	+	11.4606i	1.48391	+	1.07813i	0.976270	+	0.216558i	$0.0694830\pi$
$113$	15.7742	+	11.4606i	1.48391	+	1.07813i	0.507643	+	0.861568i	$0.330517\pi$
$114$	2.70994	+	13.7521i	0.253809	+	1.28800i
$115$	−5.29097	+	16.2839i	−0.493386	+	1.51849i
$116$	4.79390	+	5.32416i	0.445102	+	0.494336i
$117$	−3.29633	−	31.3625i	−0.304746	−	2.89946i
$118$	0.104294	−	0.992295i	0.00960108	−	0.0913482i
$119$	−1.71165	−	0.363823i	−0.156907	−	0.0333516i
$120$	4.20233	+	7.27864i	0.383618	+	0.664446i
$121$	3.36749	+	10.4719i	0.306136	+	0.951988i
$122$	−2.96753			−0.268667
$123$	−5.60207	+	6.22173i	−0.505121	+	0.560994i
$124$	0.414401	−	3.94276i	0.0372143	−	0.354070i
$125$	6.70001	−	4.86784i	0.599267	−	0.435393i
$126$	−1.45037	+	4.46377i	−0.129209	+	0.397664i
$127$	−10.9843	+	2.33478i	−0.974698	+	0.207178i	−0.667617	−	0.744505i	$-0.732686\pi$
$127$	−10.9843	+	2.33478i	−0.974698	+	0.207178i	−0.307081	+	0.951683i	$0.599352\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	1.79647	−	17.0923i	0.158170	−	1.50489i
$130$	−10.9838	−	2.33467i	−0.963340	−	0.204764i
$131$	−5.80405	+	10.0529i	−0.507102	+	0.878327i	0.492864	+	0.870106i	$0.335950\pi$
$131$	−5.80405	+	10.0529i	−0.507102	+	0.878327i	−0.999966	+	0.00822062i	$0.997383\pi$
$132$	−8.61865	−	6.28177i	−0.750157	−	0.546758i
$133$	1.60455	+	2.27900i	0.139132	+	0.197615i
$134$	1.62688	+	5.00702i	0.140541	+	0.432540i
$135$	−33.3239	+	14.8368i	−2.86806	+	1.27694i
$136$	0.286059	+	2.72167i	0.0245294	+	0.233381i
$137$	−16.0399	+	3.40939i	−1.37038	+	0.291284i	−0.833568	−	0.552417i	$-0.813705\pi$
$137$	−16.0399	+	3.40939i	−1.37038	+	0.291284i	−0.536814	+	0.843701i	$0.680372\pi$
$138$	14.0952	+	15.6543i	1.19986	+	1.33258i
$139$	−16.0130	−	7.12946i	−1.35821	−	0.604713i	−0.407046	−	0.913408i	$-0.633441\pi$
$139$	−16.0130	−	7.12946i	−1.35821	−	0.604713i	−0.951161	+	0.308695i	$0.900108\pi$
$140$	1.35208	+	0.982346i	0.114272	+	0.0830234i
$141$	1.48413	+	4.56769i	0.124986	+	0.384668i
$142$	3.55735	+	6.16152i	0.298526	+	0.517063i
$143$	13.9422	−	2.94145i	1.16590	−	0.245976i
$144$	7.34016			0.611680
$145$	5.78651	+	17.8090i	0.480543	+	1.47896i
$146$	−0.367487	+	3.49641i	−0.0304135	+	0.289365i
$147$	−2.21543	−	21.0784i	−0.182726	−	1.73852i
$148$	−4.05961	+	0.862898i	−0.333698	+	0.0709298i
$149$	14.2909	+	15.8717i	1.17076	+	1.30026i	0.945375	+	0.325986i	$0.105696\pi$
$149$	14.2909	+	15.8717i	1.17076	+	1.30026i	0.225382	+	0.974271i	$0.427637\pi$
$150$	0.615590	+	5.85695i	0.0502627	+	0.478218i
$151$	11.9380	+	8.67345i	0.971499	+	0.705835i	0.955793	−	0.294041i	$-0.0950004\pi$
$151$	11.9380	+	8.67345i	0.971499	+	0.705835i	0.0157062	+	0.999877i	$0.495000\pi$
$152$	2.61427	−	3.48792i	0.212045	−	0.282908i
$153$	−20.0876			−1.62398
$154$	−2.07372	−	0.444065i	−0.167105	−	0.0357838i
$155$	5.18098	−	8.97372i	0.416146	−	0.720787i
$156$	−9.24412	+	10.2666i	−0.740122	+	0.821988i
$157$	7.36819	−	3.28053i	0.588046	−	0.261815i	−0.0910719	−	0.995844i	$-0.529029\pi$
$157$	7.36819	−	3.28053i	0.588046	−	0.261815i	0.679118	+	0.734030i	$0.262363\pi$
$158$	−0.955190	−	0.425278i	−0.0759909	−	0.0338333i
$159$	11.6612	−	35.8896i	0.924795	−	2.84623i
$160$	0.807679	−	2.48578i	0.0638526	−	0.196518i
$161$	3.82663	+	1.70373i	0.301581	+	0.134272i
$162$	−2.38926	+	22.7323i	−0.187718	+	1.78601i
$163$	−3.05995	−	9.41757i	−0.239674	−	0.737641i	−0.996467	−	0.0839861i	$-0.973235\pi$
$163$	−3.05995	−	9.41757i	−0.239674	−	0.737641i	0.756793	−	0.653655i	$-0.226765\pi$
$164$	2.60360			0.203307
$165$	−13.9010	−	24.1616i	−1.08219	−	1.88098i
$166$	−6.83684	+	11.8417i	−0.530641	+	0.919098i
$167$	1.70606	−	1.89478i	0.132019	−	0.146622i	−0.673510	−	0.739178i	$-0.735214\pi$
$167$	1.70606	−	1.89478i	0.132019	−	0.146622i	0.805529	+	0.592556i	$0.201881\pi$
$168$	1.87838	−	0.836308i	0.144920	−	0.0645226i
$169$	−0.570503	−	5.42797i	−0.0438849	−	0.417536i
$170$	−2.21035	+	6.80274i	−0.169526	+	0.521747i
$171$	23.4558	+	21.7602i	1.79371	+	1.66404i
$172$	−4.32393	+	3.14152i	−0.329697	+	0.239539i
$173$	3.32034	−	1.47831i	0.252441	−	0.112394i	−0.276615	−	0.960981i	$-0.589213\pi$
$173$	3.32034	−	1.47831i	0.252441	−	0.112394i	0.529056	+	0.848587i	$0.322546\pi$
$174$	22.5344	+	4.78983i	1.70833	+	0.363116i
$175$	0.585535	+	1.01418i	0.0442623	+	0.0766646i
$176$	0.341687	+	3.29898i	0.0257556	+	0.248670i
$177$	−1.60421	−	2.77857i	−0.120579	−	0.208850i
$178$	−4.66863	−	14.3686i	−0.349929	−	1.07697i
$179$	−8.90740	−	6.47161i	−0.665771	−	0.483711i	0.202836	−	0.979213i	$-0.434984\pi$
$179$	−8.90740	−	6.47161i	−0.665771	−	0.483711i	−0.868607	+	0.495502i	$0.834984\pi$
$180$	17.5264	+	7.80324i	1.30634	+	0.581619i
$181$	23.3652	−	4.96643i	1.73672	−	0.369152i	0.772659	−	0.634821i	$-0.218926\pi$
$181$	23.3652	−	4.96643i	1.73672	−	0.369152i	0.964064	+	0.265669i	$0.0855929\pi$
$182$	−0.848912	+	2.61268i	−0.0629255	+	0.193665i
$183$	−7.71998	+	5.60889i	−0.570677	+	0.414621i
$184$	0.684749	−	6.51495i	0.0504804	−	0.480289i
$185$	−10.6106	−	2.25536i	−0.780109	−	0.165817i
$186$	−6.37411	−	11.0403i	−0.467372	−	0.809512i
$187$	−0.935083	−	9.02819i	−0.0683800	−	0.660207i
$188$	0.746786	−	1.29347i	0.0544650	−	0.0943361i
$189$	2.75766	+	8.48721i	0.200590	+	0.617354i
$190$	9.95016	−	5.54904i	0.721860	−	0.402570i
$191$	−5.74887	+	4.17680i	−0.415974	+	0.302223i	−0.776016	−	0.630714i	$-0.782762\pi$
$191$	−5.74887	+	4.17680i	−0.415974	+	0.302223i	0.360042	+	0.932936i	$0.382762\pi$
$192$	−2.15166	−	2.38967i	−0.155283	−	0.172459i
$193$	2.38740	+	2.65148i	0.171849	+	0.190858i	0.822917	−	0.568162i	$-0.192345\pi$
$193$	2.38740	+	2.65148i	0.171849	+	0.190858i	−0.651068	+	0.759020i	$0.725679\pi$
$194$	15.4650	+	6.88544i	1.11032	+	0.494346i
$195$	−32.9869	+	14.6867i	−2.36224	+	1.05174i
$196$	−4.41033	+	4.89817i	−0.315024	+	0.349869i
$197$	0.606210			0.0431906			0.0215953	−	0.999767i	$-0.493125\pi$
$197$	0.606210			0.0431906			0.0215953	+	0.999767i	$0.493125\pi$
$198$	−24.3445	−	0.0368598i	−1.73009	−	0.00261951i
$199$	−11.3379	−	19.6377i	−0.803719	−	1.39208i	−0.917152	−	0.398537i	$-0.869518\pi$
$199$	−11.3379	−	19.6377i	−0.803719	−	1.39208i	0.113433	−	0.993546i	$-0.463815\pi$
$200$	1.22548	−	1.36103i	0.0866542	−	0.0962392i
$201$	13.6960	+	9.95073i	0.966042	+	0.701871i
$202$	−10.5560	+	7.66936i	−0.742715	+	0.539614i
$203$	4.48097	−	0.952459i	0.314502	−	0.0668495i
$204$	5.88838	+	6.53971i	0.412269	+	0.457871i
$205$	6.21670	+	2.76785i	0.434193	+	0.193315i
$206$	−3.71588	+	1.65442i	−0.258897	+	0.115269i
$207$	47.0334	+	9.99727i	3.26905	+	0.694858i
$208$	4.29626			0.297892
$209$	−8.68805	+	11.5550i	−0.600965	+	0.799275i
$210$	5.37414			0.370851
$211$	−4.28671	−	0.911169i	−0.295109	−	0.0627275i	0.0579777	−	0.998318i	$-0.481535\pi$
$211$	−4.28671	−	0.911169i	−0.295109	−	0.0627275i	−0.353087	+	0.935590i	$0.614868\pi$
$212$	−10.7208	+	4.77322i	−0.736310	+	0.327826i
$213$	20.9002	+	9.30538i	1.43206	+	0.637594i
$214$	−12.4870	−	13.8682i	−0.853593	−	0.948011i
$215$	−13.6641	+	2.90440i	−0.931886	+	0.198078i
$216$	11.2909	−	8.20329i	0.768246	−	0.558163i
$217$	−2.05085	−	1.49003i	−0.139220	−	0.101150i
$218$	−2.01036	+	2.23274i	−0.136159	+	0.151220i
$219$	5.65251	+	9.79044i	0.381961	+	0.661576i
$220$	−2.69125	+	8.24033i	−0.181444	+	0.555563i
$221$	−11.7574			−0.790890
$222$	−8.93007	+	9.91785i	−0.599347	+	0.665643i
$223$	7.64380	−	3.40324i	0.511866	−	0.227898i	−0.134516	−	0.990911i	$-0.542948\pi$
$223$	7.64380	−	3.40324i	0.511866	−	0.227898i	0.646382	+	0.763014i	$0.276281\pi$
$224$	−0.584144	−	0.260077i	−0.0390297	−	0.0173772i
$225$	8.99518	+	9.99016i	0.599679	+	0.666011i
$226$	−13.0467	−	14.4898i	−0.867854	−	0.963849i
$227$	17.4042	−	12.6449i	1.15516	−	0.839270i	0.165998	−	0.986126i	$-0.446915\pi$
$227$	17.4042	−	12.6449i	1.15516	−	0.839270i	0.989158	+	0.146856i	$0.0469153\pi$
$228$	0.208497	−	14.0150i	0.0138081	−	0.928164i
$229$	−2.41014	−	7.41765i	−0.159267	−	0.490172i	0.839302	−	0.543666i	$-0.182964\pi$
$229$	−2.41014	−	7.41765i	−0.159267	−	0.490172i	−0.998568	+	0.0534939i	$0.982964\pi$
$230$	8.56097	−	14.8280i	0.564494	−	0.977732i
$231$	−6.23407	+	2.76429i	−0.410172	+	0.181877i
$232$	−3.58218	−	6.20453i	−0.235182	−	0.407347i
$233$	−9.87041	−	2.09802i	−0.646632	−	0.137446i	−0.127091	−	0.991891i	$-0.540564\pi$
$233$	−9.87041	−	2.09802i	−0.646632	−	0.137446i	−0.519541	+	0.854445i	$0.673897\pi$
$234$	−3.29633	+	31.3625i	−0.215488	+	2.05023i
$235$	3.15820	−	2.29457i	0.206018	−	0.149681i
$236$	−0.308325	+	0.948927i	−0.0200703	+	0.0617699i
$237$	−3.28873	+	0.699040i	−0.213626	+	0.0454076i
$238$	1.59861	+	0.711745i	0.103622	+	0.0461356i
$239$	−10.8428	−	7.87777i	−0.701364	−	0.509571i	0.179012	−	0.983847i	$-0.442710\pi$
$239$	−10.8428	−	7.87777i	−0.701364	−	0.509571i	−0.880376	+	0.474276i	$0.842710\pi$
$240$	−2.59718	−	7.99330i	−0.167647	−	0.515965i
$241$	−4.93605	−	8.54949i	−0.317959	−	0.550721i	0.662103	−	0.749413i	$-0.269664\pi$
$241$	−4.93605	−	8.54949i	−0.317959	−	0.550721i	−0.980062	+	0.198692i	$0.936331\pi$
$242$	−1.11668	−	10.9432i	−0.0717829	−	0.703454i
$243$	15.8160	+	27.3941i	1.01459	+	1.75733i
$244$	2.90268	+	0.616984i	0.185825	+	0.0394983i
$245$	−15.7379	+	7.00696i	−1.00546	+	0.447658i
$246$	6.77322	−	4.92103i	0.431845	−	0.313753i
$247$	13.7289	+	12.7364i	0.873550	+	0.810399i
$248$	−1.22509	+	3.77044i	−0.0777933	+	0.239423i
$249$	4.59604	+	43.7284i	0.291262	+	2.77117i
$250$	−7.56568	+	3.36846i	−0.478495	+	0.213040i
$251$	−3.54891	+	3.94147i	−0.224005	+	0.248783i	−0.844663	−	0.535299i	$-0.820199\pi$
$251$	−3.54891	+	3.94147i	−0.224005	+	0.248783i	0.620658	+	0.784082i	$0.286866\pi$
$252$	2.34674	−	4.06467i	0.147831	−	0.256050i
$253$	−2.30377	+	21.6042i	−0.144837	+	1.35824i
$254$	11.2297			0.704613
$255$	7.10761	+	21.8750i	0.445096	+	1.36986i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−8.89457	−	3.96012i	−0.554828	−	0.247025i	0.110116	−	0.993919i	$-0.464878\pi$
$257$	−8.89457	−	3.96012i	−0.554828	−	0.247025i	−0.664944	+	0.746893i	$0.731545\pi$
$258$	−5.31089	+	16.3452i	−0.330642	+	1.01761i
$259$	−0.820073	+	2.52392i	−0.0509568	+	0.156829i
$260$	10.2583	+	4.56731i	0.636195	+	0.283252i
$261$	48.0412	−	21.3893i	2.97367	−	1.32397i
$262$	7.76734	−	8.62650i	0.479868	−	0.532947i
$263$	11.4080	−	19.7593i	0.703448	−	1.21841i	−0.263801	−	0.964577i	$-0.584976\pi$
$263$	11.4080	−	19.7593i	0.703448	−	1.21841i	0.967249	−	0.253830i	$-0.0816905\pi$
$264$	7.12426	+	7.93642i	0.438468	+	0.488453i
$265$	−30.6729			−1.88422
$266$	−1.09565	−	2.56280i	−0.0671787	−	0.157136i
$267$	−39.3033	−	28.5555i	−2.40532	−	1.74757i
$268$	−0.550310	−	5.23585i	−0.0336155	−	0.319830i
$269$	−15.5911	−	17.3156i	−0.950604	−	1.05575i	−0.998380	−	0.0568947i	$-0.981880\pi$
$269$	−15.5911	−	17.3156i	−0.950604	−	1.05575i	0.0477761	−	0.998858i	$-0.484787\pi$
$270$	35.6804	−	7.58411i	2.17144	−	0.461554i
$271$	1.28696	+	12.2446i	0.0781770	+	0.743804i	0.961456	+	0.274957i	$0.0886637\pi$
$271$	1.28696	+	12.2446i	0.0781770	+	0.743804i	−0.883279	+	0.468847i	$0.844670\pi$
$272$	0.286059	−	2.72167i	0.0173449	−	0.165026i
$273$	2.72977	+	8.40137i	0.165213	+	0.508474i
$274$	16.3982			0.990654
$275$	−4.07127	+	4.50786i	−0.245507	+	0.271834i
$276$	−10.5325	−	18.2428i	−0.633981	−	1.09809i
$277$	−0.488912	−	1.50472i	−0.0293759	−	0.0904096i	0.935294	−	0.353873i	$-0.115135\pi$
$277$	−0.488912	−	1.50472i	−0.0293759	−	0.0904096i	−0.964670	+	0.263463i	$0.915135\pi$
$278$	14.1808	+	10.3030i	0.850508	+	0.617930i
$279$	−26.5841	−	11.8360i	−1.59155	−	0.708602i
$280$	−1.11830	−	1.24199i	−0.0668309	−	0.0742233i
$281$	−18.5034	+	3.93303i	−1.10382	+	0.234625i	−0.723565	−	0.690256i	$-0.757498\pi$
$281$	−18.5034	+	3.93303i	−1.10382	+	0.234625i	−0.380257	+	0.924881i	$0.624164\pi$
$282$	−0.502024	−	4.77644i	−0.0298951	−	0.284433i
$283$	16.0977	−	7.16716i	0.956910	−	0.426044i	0.131963	−	0.991255i	$-0.457872\pi$
$283$	16.0977	−	7.16716i	0.956910	−	0.426044i	0.824946	+	0.565211i	$0.191205\pi$
$284$	−2.19857	−	6.76649i	−0.130461	−	0.401517i
$285$	15.3970	−	33.2424i	0.912040	−	1.96911i
$286$	−14.2491	−	0.0215744i	−0.842565	−	0.00127572i
$287$	0.832402	−	1.44176i	0.0491352	−	0.0851046i
$288$	−7.17976	−	1.52611i	−0.423071	−	0.0899266i
$289$	0.994136	−	9.45857i	0.0584786	−	0.556386i
$290$	−1.95735	−	18.6230i	−0.114940	−	1.09358i
$291$	53.2459	−	11.3178i	3.12133	−	0.663460i
$292$	1.08640	−	3.34360i	0.0635768	−	0.195669i
$293$	−15.9671	+	11.6008i	−0.932809	+	0.677725i	−0.946679	−	0.322178i	$-0.895585\pi$
$293$	−15.9671	+	11.6008i	−0.932809	+	0.677725i	0.0138700	+	0.999904i	$0.495585\pi$
$294$	−2.21543	+	21.0784i	−0.129207	+	1.22932i
$295$	−1.74499	+	1.93801i	−0.101597	+	0.112835i
$296$	4.15031			0.241232
$297$	−37.4887	+	27.1505i	−2.17531	+	1.57543i
$298$	−10.6787	−	18.4961i	−0.618601	−	1.07145i
$299$	27.5291	+	5.85149i	1.59205	+	0.338401i
$300$	0.615590	−	5.85695i	0.0355411	−	0.338151i
$301$	0.357228	+	3.39880i	0.0205903	+	0.195903i
$302$	−9.87379	−	10.9660i	−0.568173	−	0.631020i
$303$	−12.9654	+	39.9034i	−0.744843	+	2.29239i
$304$	−3.28232	+	2.86817i	−0.188254	+	0.164501i
$305$	6.27493	+	4.55900i	0.359301	+	0.261048i
$306$	19.6486	+	4.17644i	1.12324	+	0.238751i
$307$	−5.57548	+	9.65701i	−0.318209	+	0.551154i	−0.980114	−	0.198433i	$-0.936415\pi$
$307$	−5.57548	+	9.65701i	−0.318209	+	0.551154i	0.661905	+	0.749587i	$0.269748\pi$
$308$	1.93608	+	0.865512i	0.110318	+	0.0493171i
$309$	−6.53981	+	11.3273i	−0.372037	+	0.644386i
$310$	−6.93351	+	7.70044i	−0.393797	+	0.437356i
$311$	−5.82851	−	4.23466i	−0.330504	−	0.240125i	0.410140	−	0.912022i	$-0.365480\pi$
$311$	−5.82851	−	4.23466i	−0.330504	−	0.240125i	−0.740645	+	0.671897i	$0.765480\pi$
$312$	11.1767	−	8.12032i	0.632754	−	0.459723i
$313$	1.54754	−	0.328940i	0.0874721	−	0.0185928i	−0.163968	−	0.986466i	$-0.552429\pi$
$313$	1.54754	−	0.328940i	0.0874721	−	0.0185928i	0.251440	+	0.967873i	$0.419096\pi$
$314$	−7.88924	+	1.67691i	−0.445215	+	0.0946335i
$315$	9.92451	−	7.21058i	0.559183	−	0.406270i
$316$	0.845897	+	0.614580i	0.0475854	+	0.0345728i
$317$	−2.45899	+	2.73099i	−0.138111	+	0.153388i	−0.808232	−	0.588864i	$-0.799575\pi$
$317$	−2.45899	+	2.73099i	−0.138111	+	0.153388i	0.670121	+	0.742252i	$0.266242\pi$
$318$	−18.8683	+	32.6808i	−1.05808	+	1.83265i
$319$	11.8496	+	20.5960i	0.663450	+	1.15316i
$320$	−1.30685	+	2.26353i	−0.0730552	+	0.126535i
$321$	−58.6969	−	12.4764i	−3.27614	−	0.696365i
$322$	−3.38878	−	2.46210i	−0.188850	−	0.137207i
$323$	8.98261	−	7.84921i	0.499806	−	0.436741i
$324$	7.06335	−	21.7387i	0.392408	−	1.20771i
$325$	5.26496	+	5.84733i	0.292048	+	0.324352i
$326$	1.03506	+	9.84797i	0.0573269	+	0.545429i
$327$	−1.00986	+	9.60819i	−0.0558455	+	0.531334i
$328$	−2.54670	−	0.541318i	−0.140618	−	0.0298893i
$329$	−0.477514	−	0.827078i	−0.0263262	−	0.0455983i
$330$	8.57373	+	26.5238i	0.471968	+	1.46009i
$331$	1.79323			0.0985650			0.0492825	−	0.998785i	$-0.484307\pi$
$331$	1.79323			0.0985650			0.0492825	+	0.998785i	$0.484307\pi$
$332$	9.14947	−	10.1615i	0.502143	−	0.557686i
$333$	−3.18435	+	30.2970i	−0.174501	+	1.66027i
$334$	−2.06273	+	1.49866i	−0.112867	+	0.0820030i
$335$	4.25218	−	13.0869i	0.232321	−	0.715011i
$336$	−2.01121	+	0.427496i	−0.109721	+	0.0233218i
$337$	0.596302	+	5.67344i	0.0324827	+	0.309052i	0.998685	+	0.0512669i	$0.0163259\pi$
$337$	0.596302	+	5.67344i	0.0324827	+	0.309052i	−0.966202	+	0.257785i	$0.917007\pi$
$338$	−0.570503	+	5.42797i	−0.0310313	+	0.295243i
$339$	−61.3279	−	13.0356i	−3.33087	−	0.707999i
$340$	3.57641	−	6.19453i	0.193958	−	0.335946i
$341$	4.08209	−	12.4990i	0.221058	−	0.676857i
$342$	−18.4191	−	26.1614i	−0.995990	−	1.41465i
$343$	2.68552	+	8.26517i	0.145004	+	0.446277i
$344$	4.88260	−	2.17388i	0.263252	−	0.117208i
$345$	−5.75508	−	54.7559i	−0.309843	−	2.94796i
$346$	−3.55514	+	0.755669i	−0.191126	+	0.0406250i
$347$	17.2061	+	19.1093i	0.923670	+	1.02584i	0.999587	+	0.0287253i	$0.00914479\pi$
$347$	17.2061	+	19.1093i	0.923670	+	1.02584i	−0.0759174	+	0.997114i	$0.524189\pi$
$348$	−21.0461	−	9.37033i	−1.12819	−	0.502302i
$349$	−22.9627	−	16.6833i	−1.22916	−	0.893039i	−0.232336	−	0.972636i	$-0.574637\pi$
$349$	−22.9627	−	16.6833i	−1.22916	−	0.893039i	−0.996827	+	0.0795967i	$0.974637\pi$
$350$	−0.361881	−	1.11375i	−0.0193433	−	0.0595327i
$351$	29.9799	+	51.9267i	1.60021	+	2.77164i
$352$	0.351675	−	3.29793i	0.0187444	−	0.175780i
$353$	18.3213			0.975146			0.487573	−	0.873082i	$-0.337882\pi$
$353$	18.3213			0.975146			0.487573	+	0.873082i	$0.337882\pi$
$354$	0.991454	+	3.05138i	0.0526952	+	0.162179i
$355$	1.94378	−	18.4939i	0.103165	−	0.981552i
$356$	1.57922	+	15.0252i	0.0836983	+	0.796336i
$357$	5.50401	−	1.16991i	0.291303	−	0.0619184i
$358$	7.36723	+	8.18214i	0.389370	+	0.432440i
$359$	−2.68759	−	25.5707i	−0.141845	−	1.34957i	−0.801497	−	0.597998i	$-0.795963\pi$
$359$	−2.68759	−	25.5707i	−0.141845	−	1.34957i	0.659652	−	0.751571i	$-0.270704\pi$
$360$	−15.5210	−	11.2767i	−0.818028	−	0.594332i
$361$	−18.9916	−	0.565191i	−0.999557	−	0.0297469i
$362$	−23.8872			−1.25548
$363$	−23.5886	−	26.3579i	−1.23808	−	1.38343i
$364$	1.37357	−	2.37909i	0.0719945	−	0.124698i
$365$	6.14858	−	6.82869i	0.321831	−	0.357430i
$366$	8.71743	−	3.88125i	0.455667	−	0.202876i
$367$	4.25308	+	1.89359i	0.222009	+	0.0988447i	0.514727	−	0.857354i	$-0.327893\pi$
$367$	4.25308	+	1.89359i	0.222009	+	0.0988447i	−0.292718	+	0.956199i	$0.594560\pi$
$368$	−2.02432	+	6.23022i	−0.105525	+	0.324773i
$369$	5.90557	−	18.1755i	0.307432	−	0.946177i
$370$	9.90984	+	4.41215i	0.515188	+	0.229377i
$371$	−0.784372	+	7.46280i	−0.0407226	+	0.387449i
$372$	3.93941	+	12.1243i	0.204249	+	0.628614i
$373$	9.02478			0.467285			0.233643	−	0.972323i	$-0.424935\pi$
$373$	9.02478			0.467285			0.233643	+	0.972323i	$0.424935\pi$
$374$	−0.962418	+	9.02532i	−0.0497654	+	0.466688i
$375$	−13.3153	+	23.0628i	−0.687600	+	1.19096i
$376$	−0.999395	+	1.10994i	−0.0515399	+	0.0572408i
$377$	28.1189	−	12.5194i	1.44820	−	0.644780i
$378$	−0.932810	−	8.87510i	−0.0479786	−	0.456486i
$379$	4.83258	−	14.8732i	0.248233	−	0.763983i	−0.746855	−	0.664987i	$-0.768437\pi$
$379$	4.83258	−	14.8732i	0.248233	−	0.763983i	0.995088	−	0.0989958i	$-0.0315630\pi$
$380$	−10.8864	+	3.35902i	−0.558462	+	0.172314i
$381$	29.2139	−	21.2251i	1.49667	−	1.08740i
$382$	6.49165	−	2.89027i	0.332142	−	0.147879i
$383$	7.39420	+	1.57169i	0.377826	+	0.0803094i	0.392910	−	0.919577i	$-0.371468\pi$
$383$	7.39420	+	1.57169i	0.377826	+	0.0803094i	−0.0150843	+	0.999886i	$0.504802\pi$
$384$	1.60781	+	2.78480i	0.0820480	+	0.142111i
$385$	3.70273	+	4.12484i	0.188708	+	0.210221i
$386$	−1.78396	−	3.08990i	−0.0908010	−	0.157272i
$387$	12.1230	+	37.3107i	0.616245	+	1.89661i
$388$	−13.6954	−	9.95032i	−0.695281	−	0.505151i
$389$	−17.6888	−	7.87558i	−0.896860	−	0.399308i	−0.0940673	−	0.995566i	$-0.529987\pi$
$389$	−17.6888	−	7.87558i	−0.896860	−	0.399308i	−0.802793	+	0.596258i	$0.796654\pi$
$390$	35.3195	−	7.50740i	1.78847	−	0.380152i
$391$	5.53989	−	17.0500i	0.280164	−	0.862256i
$392$	5.33234	−	3.87417i	0.269324	−	0.195675i
$393$	3.90175	−	37.1227i	0.196817	−	1.87259i
$394$	−0.592962	−	0.126038i	−0.0298730	−	0.00634971i
$395$	1.36643	+	2.36672i	0.0687523	+	0.119083i
$396$	23.8049	+	5.09757i	1.19624	+	0.256162i
$397$	−4.04839	+	7.01202i	−0.203183	+	0.351923i	−0.949552	−	0.313609i	$-0.898462\pi$
$397$	−4.04839	+	7.01202i	−0.203183	+	0.351923i	0.746369	+	0.665532i	$0.231795\pi$
$398$	7.00718	+	21.5659i	0.351238	+	1.08100i
$399$	−7.69425	−	4.59622i	−0.385194	−	0.230099i
$400$	−1.48167	+	1.07650i	−0.0740835	+	0.0538248i
$401$	−22.6855	−	25.1947i	−1.13286	−	1.25817i	−0.962054	−	0.272860i	$-0.912030\pi$
$401$	−22.6855	−	25.1947i	−1.13286	−	1.25817i	−0.170804	−	0.985305i	$-0.554636\pi$
$402$	−11.3278	−	12.5808i	−0.564982	−	0.627476i
$403$	−15.5599	−	6.92771i	−0.775094	−	0.345094i
$404$	11.9198	−	5.30705i	0.593034	−	0.264036i
$405$	39.9756	−	44.3974i	1.98640	−	2.20613i
$406$	−4.58108			−0.227355
$407$	−13.7650	−	0.0208414i	−0.682306	−	0.00103307i
$408$	−4.40003	−	7.62107i	−0.217834	−	0.377299i
$409$	10.0644	−	11.1776i	0.497652	−	0.552699i	−0.441025	−	0.897495i	$-0.645385\pi$
$409$	10.0644	−	11.1776i	0.497652	−	0.552699i	0.938678	+	0.344796i	$0.112052\pi$
$410$	−5.50538	−	3.99990i	−0.271892	−	0.197541i
$411$	42.6598	−	30.9941i	2.10425	−	1.52883i
$412$	3.97865	−	0.845688i	0.196014	−	0.0416641i
$413$	0.426901	+	0.474121i	0.0210064	+	0.0233300i
$414$	−43.9271	−	19.5576i	−2.15890	−	0.961204i
$415$	32.6491	−	14.5363i	1.60268	−	0.713560i
$416$	−4.20238	−	0.893243i	−0.206039	−	0.0437949i
$417$	56.3647			2.76019
$418$	10.9006	−	9.49613i	0.533167	−	0.464471i
$419$	−31.3653			−1.53229			−0.766146	−	0.642666i	$-0.777828\pi$
$419$	−31.3653			−1.53229			−0.766146	+	0.642666i	$0.777828\pi$
$420$	−5.25671	−	1.11735i	−0.256501	−	0.0545210i
$421$	9.98132	−	4.44397i	0.486460	−	0.216586i	−0.148825	−	0.988864i	$-0.547549\pi$
$421$	9.98132	−	4.44397i	0.486460	−	0.216586i	0.635285	+	0.772278i	$0.280883\pi$
$422$	4.00360	+	1.78252i	0.194892	+	0.0867715i
$423$	−7.33572	−	8.14714i	−0.356675	−	0.396128i
$424$	11.4790	−	2.43993i	0.557468	−	0.118493i
$425$	4.05483	−	2.94601i	0.196688	−	0.142902i
$426$	−18.5088	−	13.4474i	−0.896754	−	0.651530i
$427$	1.26968	−	1.41012i	0.0614442	−	0.0682407i
$428$	9.33076	+	16.1613i	0.451019	+	0.781188i
$429$	−37.1095	+	26.8759i	−1.79166	+	1.29758i
$430$	13.9694			0.673664
$431$	18.2194	−	20.2346i	0.877596	−	0.974669i	−0.122245	−	0.992500i	$-0.539010\pi$
$431$	18.2194	−	20.2346i	0.877596	−	0.974669i	0.999841	+	0.0178313i	$0.00567618\pi$
$432$	−12.7497	+	5.67653i	−0.613420	+	0.273112i
$433$	32.1231	+	14.3021i	1.54374	+	0.687316i	0.989432	−	0.144998i	$-0.0463175\pi$
$433$	32.1231	+	14.3021i	1.54374	+	0.687316i	0.554305	+	0.832314i	$0.312984\pi$
$434$	1.69624	+	1.88386i	0.0814219	+	0.0904282i
$435$	−40.2911	−	44.7478i	−1.93181	−	2.14549i
$436$	2.43064	−	1.76597i	0.116407	−	0.0845745i
$437$	−24.9385	+	13.9078i	−1.19297	+	0.665300i
$438$	−3.49344	−	10.7517i	−0.166923	−	0.513737i
$439$	7.64477	−	13.2411i	0.364865	−	0.631965i	−0.623889	−	0.781513i	$-0.714448\pi$
$439$	7.64477	−	13.2411i	0.364865	−	0.631965i	0.988755	+	0.149548i	$0.0477818\pi$
$440$	4.34570	−	7.50072i	0.207173	−	0.357583i
$441$	24.1900	+	41.8983i	1.15190	+	1.99516i
$442$	11.5005	+	2.44451i	0.547023	+	0.116273i
$443$	0.277381	−	2.63911i	0.0131788	−	0.125388i	−0.985954	−	0.167014i	$-0.946587\pi$
$443$	0.277381	−	2.63911i	0.0131788	−	0.125388i	0.999133	+	0.0416267i	$0.0132540\pi$
$444$	10.7970	−	7.84445i	0.512401	−	0.372281i
$445$	−12.2024	+	37.5552i	−0.578450	+	1.78029i
$446$	−8.18433	+	1.73963i	−0.387539	+	0.0823740i
$447$	−62.7397	−	27.9335i	−2.96749	−	1.32121i
$448$	0.517306	+	0.375844i	0.0244404	+	0.0177570i
$449$	4.66954	+	14.3714i	0.220369	+	0.678226i	0.998729	+	0.0504076i	$0.0160520\pi$
$449$	4.66954	+	14.3714i	0.220369	+	0.678226i	−0.778360	+	0.627819i	$0.783948\pi$
$450$	−6.72154	−	11.6421i	−0.316857	−	0.548812i
$451$	8.44373	+	1.80814i	0.397600	+	0.0851418i
$452$	9.74900	+	16.8858i	0.458554	+	0.794239i
$453$	−46.4132	−	9.86542i	−2.18068	−	0.463518i
$454$	−19.6529	+	8.75003i	−0.922355	+	0.410659i
$455$	5.80890	−	4.22042i	0.272326	−	0.197856i
$456$	−3.11782	+	13.6654i	−0.146005	+	0.639939i
$457$	4.79955	−	14.7715i	0.224513	−	0.690981i	−0.773827	−	0.633397i	$-0.781660\pi$
$457$	4.79955	−	14.7715i	0.224513	−	0.690981i	0.998341	−	0.0575843i	$-0.0183398\pi$
$458$	0.815257	+	7.75666i	0.0380945	+	0.362445i
$459$	34.8916	−	15.5347i	1.62860	−	0.725100i
$460$	−11.4568	+	12.7241i	−0.534177	+	0.593264i
$461$	−6.15905	+	10.6678i	−0.286856	+	0.496848i	−0.973057	−	0.230563i	$-0.925943\pi$
$461$	−6.15905	+	10.6678i	−0.286856	+	0.496848i	0.686202	+	0.727411i	$0.259277\pi$
$462$	6.67257	−	1.40774i	0.310436	−	0.0654941i
$463$	27.3486			1.27100			0.635498	−	0.772103i	$-0.280795\pi$
$463$	27.3486			1.27100			0.635498	+	0.772103i	$0.280795\pi$
$464$	2.21391	+	6.81372i	0.102778	+	0.316319i
$465$	−3.48289	+	33.1375i	−0.161515	+	1.53672i
$466$	9.21851	+	4.10435i	0.427039	+	0.190130i
$467$	−8.87602	+	27.3176i	−0.410733	+	1.26411i	0.505279	+	0.862956i	$0.331390\pi$
$467$	−8.87602	+	27.3176i	−0.410733	+	1.26411i	−0.916012	+	0.401151i	$0.868610\pi$
$468$	9.74493	−	29.9918i	0.450460	−	1.38637i
$469$	−3.07533	−	1.36923i	−0.142006	−	0.0632250i
$470$	−3.56626	+	1.58780i	−0.164499	+	0.0732397i
$471$	−17.3542	+	19.2738i	−0.799640	+	0.888091i
$472$	0.498880	−	0.864086i	0.0229628	−	0.0397728i
$473$	−16.2047	+	7.18540i	−0.745091	+	0.330385i
$474$	3.36220			0.154431
$475$	−7.92605	−	0.952465i	−0.363672	−	0.0437021i
$476$	−1.41569	−	1.02856i	−0.0648881	−	0.0471440i
$477$	9.00406	+	85.6679i	0.412268	+	3.92246i
$478$	8.96800	+	9.95997i	0.410187	+	0.455559i
$479$	−13.6740	+	2.90650i	−0.624781	+	0.132801i	−0.509414	−	0.860522i	$-0.670138\pi$
$479$	−13.6740	+	2.90650i	−0.624781	+	0.132801i	−0.115367	+	0.993323i	$0.536804\pi$
$480$	0.878526	+	8.35861i	0.0400990	+	0.381517i
$481$	−1.86383	+	17.7331i	−0.0849832	+	0.808562i
$482$	3.05065	+	9.38893i	0.138953	+	0.427654i
$483$	−13.4695			−0.612881
$484$	−1.18294	+	10.9362i	−0.0537698	+	0.497100i
$485$	−22.1230	−	38.3182i	−1.00456	−	1.73994i
$486$	−9.77481	−	30.0838i	−0.443394	−	1.36463i
$487$	−2.88514	−	2.09617i	−0.130738	−	0.0949867i	0.520494	−	0.853865i	$-0.325748\pi$
$487$	−2.88514	−	2.09617i	−0.130738	−	0.0949867i	−0.651232	+	0.758878i	$0.725748\pi$
$488$	−2.71097	−	1.20700i	−0.122720	−	0.0546384i
$489$	21.3062	+	23.6630i	0.963502	+	1.07008i
$490$	16.8508	−	3.58175i	0.761242	−	0.161807i
$491$	0.622236	+	5.92018i	0.0280811	+	0.267174i	0.999550	+	0.0300057i	$0.00955255\pi$
$491$	0.622236	+	5.92018i	0.0280811	+	0.267174i	−0.971469	+	0.237168i	$0.923781\pi$
$492$	−7.64835	+	3.40526i	−0.344814	+	0.153521i
$493$	−6.05873	−	18.6469i	−0.272872	−	0.839812i
$494$	−10.7809	−	15.3125i	−0.485054	−	0.688942i
$495$	51.4206	+	37.4783i	2.31118	+	1.68453i
$496$	1.98224	−	3.43334i	0.0890051	−	0.154161i
$497$	−4.44991	−	0.945857i	−0.199606	−	0.0424275i
$498$	4.59604	−	43.7284i	0.205953	−	1.95951i
$499$	−0.822638	−	7.82687i	−0.0368263	−	0.350379i	−0.997383	−	0.0722956i	$-0.976968\pi$
$499$	−0.822638	−	7.82687i	−0.0368263	−	0.350379i	0.960557	−	0.278083i	$-0.0896992\pi$
$500$	8.10069	−	1.72186i	0.362274	−	0.0770037i
$501$	−2.53355	+	7.79748i	−0.113191	+	0.348366i
$502$	4.29084	−	3.11748i	0.191509	−	0.139140i
$503$	1.05733	−	10.0598i	0.0471441	−	0.448546i	−0.945332	−	0.326109i	$-0.894262\pi$
$503$	1.05733	−	10.0598i	0.0471441	−	0.448546i	0.992476	−	0.122437i	$-0.0390709\pi$
$504$	−3.14055	+	3.48794i	−0.139891	+	0.155365i
$505$	34.1033			1.51758
$506$	6.74519	−	20.6531i	0.299860	−	0.918142i
$507$	8.77520	+	15.1991i	0.389720	+	0.675015i
$508$	−10.9843	−	2.33478i	−0.487349	−	0.103589i
$509$	−4.35313	+	41.4172i	−0.192949	+	1.83579i	0.286338	+	0.958129i	$0.407562\pi$
$509$	−4.35313	+	41.4172i	−0.192949	+	1.83579i	−0.479287	+	0.877658i	$0.659105\pi$
$510$	−2.40423	−	22.8747i	−0.106461	−	1.01291i
$511$	−1.50421	−	1.67059i	−0.0665423	−	0.0739027i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−57.5705	−	19.6573i	−2.54180	−	0.867890i
$514$	7.87685	+	5.72287i	0.347433	+	0.252425i
$515$	10.3990	+	2.21038i	0.458235	+	0.0974008i
$516$	8.59320	−	14.8839i	0.378295	−	0.655225i
$517$	3.32019	−	3.67623i	0.146022	−	0.161681i
$518$	1.32691	−	2.29827i	0.0583009	−	0.100980i
$519$	−7.82037	+	8.68540i	−0.343276	+	0.381247i
$520$	−9.08458	−	6.60033i	−0.398385	−	0.289444i
$521$	16.5916	−	12.0545i	0.726893	−	0.528119i	−0.161686	−	0.986842i	$-0.551693\pi$
$521$	16.5916	−	12.0545i	0.726893	−	0.528119i	0.888579	+	0.458723i	$0.151693\pi$
$522$	−51.4384	+	10.9336i	−2.25140	+	0.478550i
$523$	1.01088	−	0.214870i	0.0442028	−	0.00939560i	−0.185757	−	0.982596i	$-0.559474\pi$
$523$	1.01088	−	0.214870i	0.0442028	−	0.00939560i	0.229960	+	0.973200i	$0.426140\pi$
$524$	−9.39115	+	6.82307i	−0.410254	+	0.298067i
$525$	−3.04652	−	2.21343i	−0.132961	−	0.0966019i
$526$	−15.2669	+	16.9556i	−0.665668	+	0.739299i
$527$	−5.42472	+	9.39589i	−0.236304	+	0.409291i
$528$	−5.31850	−	9.24421i	−0.231458	−	0.402302i
$529$	−9.95674	+	17.2456i	−0.432902	+	0.749808i
$530$	30.0026	+	6.37725i	1.30323	+	0.277010i
$531$	5.92502	+	4.30478i	0.257124	+	0.186811i
$532$	0.538871	+	2.73460i	0.0233630	+	0.118560i
$533$	3.45658	−	10.6383i	0.149721	−	0.460795i
$534$	32.5074	+	36.1031i	1.40673	+	1.56233i
$535$	5.09844	+	48.5085i	0.220425	+	2.09720i
$536$	−0.550310	+	5.23585i	−0.0237698	+	0.226154i
$537$	34.6307	+	7.36099i	1.49443	+	0.317650i
$538$	11.6502	+	20.1788i	0.502278	+	0.869970i
$539$	−17.7048	+	12.8224i	−0.762600	+	0.552299i
$540$	−36.4775			−1.56974
$541$	11.6345	−	12.9214i	0.500206	−	0.555535i	−0.439179	−	0.898400i	$-0.644731\pi$
$541$	11.6345	−	12.9214i	0.500206	−	0.555535i	0.939385	+	0.342865i	$0.111397\pi$
$542$	1.28696	−	12.2446i	0.0552795	−	0.525949i
$543$	−62.1422	+	45.1490i	−2.66678	+	1.93753i
$544$	−0.845676	+	2.60272i	−0.0362580	+	0.111591i
$545$	7.68112	−	1.63267i	0.329023	−	0.0699360i
$546$	−0.923376	−	8.78533i	−0.0395168	−	0.375978i
$547$	2.12525	−	20.2204i	0.0908690	−	0.864561i	−0.850226	−	0.526418i	$-0.823535\pi$
$547$	2.12525	−	20.2204i	0.0908690	−	0.864561i	0.941095	−	0.338143i	$-0.109799\pi$
$548$	−16.0399	−	3.40939i	−0.685191	−	0.145642i
$549$	10.8911	−	18.8639i	0.464819	−	0.805090i
$550$	4.91954	−	3.56289i	0.209770	−	0.151922i
$551$	−13.1248	+	28.3368i	−0.559137	+	1.20719i
$552$	6.50943	+	20.0340i	0.277060	+	0.852702i
$553$	0.610772	−	0.271933i	0.0259727	−	0.0115638i
$554$	0.165380	+	1.57348i	0.00702632	+	0.0668509i
$555$	34.1197	−	7.25236i	1.44830	−	0.307845i
$556$	−11.7288	−	13.0262i	−0.497413	−	0.552433i
$557$	30.9897	+	13.7975i	1.31307	+	0.584619i	0.939362	−	0.342926i	$-0.111418\pi$
$557$	30.9897	+	13.7975i	1.31307	+	0.584619i	0.373712	+	0.927545i	$0.378085\pi$
$558$	23.5423	+	17.1045i	0.996625	+	0.724090i
$559$	7.09569	+	21.8383i	0.300116	+	0.923661i
$560$	0.835633	+	1.44736i	0.0353120	+	0.0611621i
$561$	14.5549	+	25.2983i	0.614510	+	1.06809i
$562$	18.9168			0.797957
$563$	−7.49477	−	23.0665i	−0.315867	−	0.972138i	−0.975396	−	0.220459i	$-0.929244\pi$
$563$	−7.49477	−	23.0665i	−0.315867	−	0.972138i	0.659529	−	0.751679i	$-0.270756\pi$
$564$	−0.502024	+	4.77644i	−0.0211390	+	0.201124i
$565$	5.32698	+	50.6828i	0.224108	+	2.13224i
$566$	−17.2361	+	3.66364i	−0.724486	+	0.153994i
$567$	−9.77977	−	10.8615i	−0.410712	−	0.456141i
$568$	0.743689	+	7.07573i	0.0312045	+	0.296891i
$569$	−16.8203	−	12.2206i	−0.705142	−	0.512316i	0.176461	−	0.984308i	$-0.443535\pi$
$569$	−16.8203	−	12.2206i	−0.705142	−	0.512316i	−0.881603	+	0.471992i	$0.843535\pi$
$570$	−21.9720	+	29.3148i	−0.920307	+	1.22786i
$571$	−5.01454			−0.209852			−0.104926	−	0.994480i	$-0.533461\pi$
$571$	−5.01454			−0.209852			−0.104926	+	0.994480i	$0.533461\pi$
$572$	13.9332	+	2.98365i	0.582577	+	0.124753i
$573$	11.4251	−	19.7888i	0.477289	−	0.826688i
$574$	−1.11397	+	1.23719i	−0.0464963	+	0.0516393i
$575$	−10.9603	+	4.87982i	−0.457074	+	0.203503i
$576$	6.70557	+	2.98551i	0.279399	+	0.124396i
$577$	7.49796	−	23.0763i	0.312144	−	0.960681i	−0.664770	−	0.747048i	$-0.731470\pi$
$577$	7.49796	−	23.0763i	0.312144	−	0.960681i	0.976914	−	0.213633i	$-0.0685295\pi$
$578$	−2.93896	+	9.04518i	−0.122245	+	0.376230i
$579$	−10.4811	−	4.66650i	−0.435581	−	0.193933i
$580$	−1.95735	+	18.6230i	−0.0812746	+	0.773276i
$581$	−2.70182	−	8.31536i	−0.112091	−	0.344979i
$582$	−54.4355			−2.25642
$583$	−38.0836	+	8.03468i	−1.57726	+	0.332762i
$584$	−1.75783	+	3.04466i	−0.0727397	+	0.125989i
$585$	55.1523	−	61.2528i	2.28027	−	2.53249i
$586$	18.0301	−	8.02753i	0.744818	−	0.331614i
$587$	−0.198387	−	1.88752i	−0.00818830	−	0.0779065i	0.989665	−	0.143401i	$-0.0458040\pi$
$587$	−0.198387	−	1.88752i	−0.00818830	−	0.0779065i	−0.997853	+	0.0654950i	$0.979137\pi$
$588$	6.54947	−	20.1572i	0.270096	−	0.831269i
$589$	16.5126	−	5.09498i	0.680389	−	0.209935i
$590$	2.10980	−	1.53286i	0.0868589	−	0.0631067i
$591$	−1.78081	+	0.792866i	−0.0732526	+	0.0326141i
$592$	−4.05961	−	0.862898i	−0.166849	−	0.0354649i
$593$	−16.0905	−	27.8696i	−0.660759	−	1.14447i	−0.980417	−	0.196935i	$-0.936901\pi$
$593$	−16.0905	−	27.8696i	−0.660759	−	1.14447i	0.319658	−	0.947533i	$-0.396432\pi$
$594$	42.3144	−	18.7629i	1.73618	−	0.769850i
$595$	−2.28685	−	3.96094i	−0.0937516	−	0.162383i
$596$	6.59981	+	20.3121i	0.270339	+	0.832017i
$597$	58.9905	+	42.8591i	2.41432	+	1.75411i
$598$	−25.7109	−	11.4472i	−1.05140	−	0.468113i
$599$	0.0231194	−	0.00491418i	0.000944634	−	0.000200788i	−0.207439	−	0.978248i	$-0.566513\pi$
$599$	0.0231194	−	0.00491418i	0.000944634	−	0.000200788i	0.208384	+	0.978047i	$0.433180\pi$
$600$	−1.81987	+	5.60097i	−0.0742957	+	0.228659i
$601$	−11.1436	+	8.09631i	−0.454558	+	0.330255i	−0.791393	−	0.611308i	$-0.790644\pi$
$601$	−11.1436	+	8.09631i	−0.454558	+	0.330255i	0.336835	+	0.941564i	$0.390644\pi$
$602$	0.357228	−	3.39880i	0.0145595	−	0.138525i
$603$	−37.7992	−	8.03447i	−1.53930	−	0.327189i
$604$	7.37808	+	12.7792i	0.300210	+	0.519978i
$605$	−14.4507	+	24.8552i	−0.587504	+	1.01051i
$606$	20.9785	−	36.3358i	0.852192	−	1.47604i
$607$	−4.85798	−	14.9513i	−0.197179	−	0.606856i	−0.999944	−	0.0105601i	$-0.996639\pi$
$607$	−4.85798	−	14.9513i	−0.197179	−	0.606856i	0.802765	−	0.596296i	$-0.203361\pi$
$608$	3.80692	−	2.12306i	0.154391	−	0.0861013i
$609$	−11.9176	+	8.65864i	−0.482925	+	0.350866i
$610$	−5.18993	−	5.76401i	−0.210134	−	0.233378i
$611$	−4.29366	−	4.76860i	−0.173703	−	0.192917i
$612$	−18.3509	−	8.17034i	−0.741791	−	0.330267i
$613$	−6.30057	+	2.80520i	−0.254478	+	0.113301i	−0.530011	−	0.847991i	$-0.677812\pi$
$613$	−6.30057	+	2.80520i	−0.254478	+	0.113301i	0.275533	+	0.961292i	$0.411146\pi$
$614$	7.46144	−	8.28677i	0.301119	−	0.334427i
$615$	−21.8823			−0.882381
$616$	−1.71382	−	1.24913i	−0.0690517	−	0.0503289i
$617$	−5.98694	−	10.3697i	−0.241025	−	0.417468i	0.719981	−	0.693993i	$-0.244150\pi$
$617$	−5.98694	−	10.3697i	−0.241025	−	0.417468i	−0.961007	+	0.276525i	$0.910817\pi$
$618$	8.75197	−	9.72005i	0.352056	−	0.390998i
$619$	31.5987	+	22.9578i	1.27006	+	0.922751i	0.999205	−	0.0398700i	$-0.0126944\pi$
$619$	31.5987	+	22.9578i	1.27006	+	0.922751i	0.270853	+	0.962621i	$0.412694\pi$
$620$	8.38300	−	6.09061i	0.336670	−	0.244605i
$621$	−89.4274	+	19.0084i	−3.58860	+	0.762780i
$622$	4.82071	+	5.35394i	0.193293	+	0.214673i
$623$	8.82525	+	3.92925i	0.353576	+	0.157422i
$624$	−12.6207	+	5.61911i	−0.505234	+	0.224945i
$625$	30.1299	+	6.40431i	1.20520	+	0.256172i
$626$	−1.58211			−0.0632339
$627$	10.4092	−	45.3072i	0.415705	−	1.80939i
$628$	8.06549			0.321848
$629$	11.1098	+	2.36146i	0.442977	+	0.0941576i
$630$	−11.2068	+	4.98959i	−0.446489	+	0.198790i
$631$	14.4996	+	6.45563i	0.577219	+	0.256994i	0.674515	−	0.738261i	$-0.264353\pi$
$631$	14.4996	+	6.45563i	0.577219	+	0.256994i	−0.0972961	+	0.995255i	$0.531019\pi$
$632$	−0.699634	−	0.777022i	−0.0278299	−	0.0309083i
$633$	13.7844	−	2.92997i	0.547881	−	0.116456i
$634$	2.97306	−	2.16006i	0.118075	−	0.0857868i
$635$	−23.7455	−	17.2521i	−0.942312	−	0.684630i
$636$	25.2507	−	28.0437i	1.00125	−	1.11201i
$637$	14.1586	+	24.5235i	0.560985	+	0.971655i
$638$	−7.30849	−	22.6096i	−0.289346	−	0.895124i
$639$	−52.2231			−2.06591
$640$	1.74891	−	1.94236i	0.0691317	−	0.0767785i
$641$	28.5819	−	12.7255i	1.12892	−	0.502626i	0.244651	−	0.969611i	$-0.421327\pi$
$641$	28.5819	−	12.7255i	1.12892	−	0.502626i	0.884265	+	0.466985i	$0.154660\pi$
$642$	54.8202	+	24.4075i	2.16358	+	0.963288i
$643$	−4.12682	−	4.58330i	−0.162746	−	0.180748i	0.656256	−	0.754538i	$-0.272139\pi$
$643$	−4.12682	−	4.58330i	−0.162746	−	0.180748i	−0.819002	+	0.573790i	$0.805472\pi$
$644$	2.80283	+	3.11286i	0.110447	+	0.122664i
$645$	36.3412	−	26.4034i	1.43093	−	1.03963i
$646$	−10.4183	+	5.81009i	−0.409901	+	0.228595i
$647$	5.97277	+	18.3823i	0.234814	+	0.722683i	0.997146	+	0.0754968i	$0.0240543\pi$
$647$	5.97277	+	18.3823i	0.234814	+	0.722683i	−0.762332	+	0.647186i	$0.775946\pi$
$648$	−11.4287	+	19.7951i	−0.448963	+	0.777627i
$649$	−1.65894	+	2.86334i	−0.0651190	+	0.112396i
$650$	−3.93418	−	6.81420i	−0.154311	−	0.267275i
$651$	7.97339	+	1.69480i	0.312502	+	0.0664243i
$652$	1.03506	−	9.84797i	0.0405362	−	0.385676i
$653$	−8.16152	+	5.92969i	−0.319385	+	0.232047i	−0.735913	−	0.677076i	$-0.763247\pi$
$653$	−8.16152	+	5.92969i	−0.319385	+	0.232047i	0.416528	+	0.909123i	$0.363247\pi$
$654$	2.98545	−	9.18827i	0.116740	−	0.359290i
$655$	−29.6771	+	6.30807i	−1.15958	+	0.246477i
$656$	2.37850	+	1.05898i	0.0928650	+	0.0413462i
$657$	−20.8771	−	15.1681i	−0.814495	−	0.591765i
$658$	0.295120	+	0.908285i	0.0115050	+	0.0354086i
$659$	−10.7080	−	18.5467i	−0.417123	−	0.722478i	0.578526	−	0.815664i	$-0.303628\pi$
$659$	−10.7080	−	18.5467i	−0.417123	−	0.722478i	−0.995649	+	0.0931861i	$0.970295\pi$
$660$	−2.87176	−	27.7268i	−0.111783	−	1.07926i
$661$	−14.0187	−	24.2811i	−0.545263	−	0.944424i	−0.998590	−	0.0530795i	$-0.983096\pi$
$661$	−14.0187	−	24.2811i	−0.545263	−	0.944424i	0.453327	−	0.891344i	$-0.350237\pi$
$662$	−1.75405	−	0.372834i	−0.0681730	−	0.0144906i
$663$	34.5387	−	15.3776i	1.34137	−	0.597217i
$664$	−11.0622	+	8.03718i	−0.429298	+	0.311903i
$665$	−1.62044	+	7.10237i	−0.0628380	+	0.275418i
$666$	9.41387	−	28.9729i	0.364780	−	1.12268i
$667$	4.90579	+	46.6755i	0.189953	+	1.80728i
$668$	2.32924	−	1.03704i	0.0901210	−	0.0401245i
$669$	−18.0034	+	19.9948i	−0.696050	+	0.773042i
$670$	−6.88017	+	11.9168i	−0.265804	+	0.460386i
$671$	8.98520	+	4.01678i	0.346870	+	0.155066i
$672$	2.05614			0.0793174
$673$	−5.84191	−	17.9796i	−0.225189	−	0.693061i	−0.998272	−	0.0587562i	$-0.981287\pi$
$673$	−5.84191	−	17.9796i	−0.225189	−	0.693061i	0.773083	−	0.634305i	$-0.218713\pi$
$674$	0.596302	−	5.67344i	0.0229687	−	0.218533i
$675$	−23.3503	−	10.3962i	−0.898755	−	0.400151i
$676$	1.68658	−	5.19075i	0.0648683	−	0.199644i
$677$	5.94836	−	18.3072i	0.228614	−	0.703602i	−0.769290	−	0.638899i	$-0.779390\pi$
$677$	5.94836	−	18.3072i	0.228614	−	0.703602i	0.997905	−	0.0647028i	$-0.0206099\pi$
$678$	57.2774	+	25.5016i	2.19973	+	0.979382i
$679$	−9.88868	+	4.40272i	−0.379493	+	0.168961i
$680$	−4.78618	+	5.31559i	−0.183541	+	0.203843i
$681$	−34.5883	+	59.9088i	−1.32543	+	2.29571i
$682$	−6.59157	+	11.3771i	−0.252404	+	0.435653i
$683$	44.4555			1.70104			0.850520	−	0.525942i	$-0.176287\pi$
$683$	44.4555			1.70104			0.850520	+	0.525942i	$0.176287\pi$
$684$	12.5773	+	29.4192i	0.480906	+	1.12487i
$685$	−34.6746	−	25.1926i	−1.32485	−	0.962558i
$686$	−0.908406	−	8.64290i	−0.0346831	−	0.329988i
$687$	16.7817	+	18.6379i	0.640260	+	0.711081i
$688$	−5.22788	+	1.11122i	−0.199311	+	0.0423649i
$689$	5.27016	+	50.1422i	0.200777	+	1.91027i
$690$	−5.75508	+	54.7559i	−0.219092	+	2.08452i
$691$	7.13662	+	21.9642i	0.271490	+	0.835559i	0.990127	+	0.140174i	$0.0447662\pi$
$691$	7.13662	+	21.9642i	0.271490	+	0.835559i	−0.718637	+	0.695385i	$0.755234\pi$
$692$	3.63457			0.138165
$693$	10.4335	−	11.5524i	0.396337	−	0.438839i
$694$	−12.8570	−	22.2690i	−0.488046	−	0.845321i
$695$	−14.1573	−	43.5718i	−0.537019	−	1.65277i
$696$	18.6380	+	13.5413i	0.706471	+	0.513282i
$697$	−6.50917	−	2.89807i	−0.246552	−	0.109772i
$698$	18.9922	+	21.0930i	0.718865	+	0.798381i
$699$	31.7394	−	6.74642i	1.20049	−	0.255173i
$700$	0.122410	+	1.16466i	0.00462667	+	0.0440198i
$701$	10.6283	−	4.73201i	0.401424	−	0.178725i	−0.196087	−	0.980587i	$-0.562823\pi$
$701$	10.6283	−	4.73201i	0.401424	−	0.178725i	0.597510	+	0.801861i	$0.296157\pi$
$702$	−18.5286	−	57.0252i	−0.699317	−	2.15228i
$703$	−10.4146	−	14.7923i	−0.392794	−	0.557902i
$704$	−1.02967	+	3.15274i	−0.0388071	+	0.118823i
$705$	−6.27648	+	10.8712i	−0.236386	+	0.409432i
$706$	−17.9210	−	3.80922i	−0.674465	−	0.143362i
$707$	0.872096	−	8.29744i	0.0327985	−	0.312057i
$708$	−0.335370	−	3.19084i	−0.0126040	−	0.119919i
$709$	−46.2236	+	9.82513i	−1.73596	+	0.368990i	−0.963840	−	0.266482i	$-0.914139\pi$
$709$	−46.2236	+	9.82513i	−1.73596	+	0.368990i	−0.772124	+	0.635472i	$0.780805\pi$
$710$	−5.74640	+	17.6856i	−0.215658	+	0.663728i
$711$	6.20902	−	4.51112i	0.232856	−	0.169180i
$712$	1.57922	−	15.0252i	0.0591837	−	0.563095i
$713$	17.3777	−	19.2999i	0.650802	−	0.722789i
$714$	−5.62697			−0.210584
$715$	30.0970	+	21.9364i	1.12556	+	0.820376i
$716$	−5.50508	−	9.53507i	−0.205734	−	0.356342i
$717$	42.1554	+	8.96040i	1.57432	+	0.334632i
$718$	−2.68759	+	25.5707i	−0.100300	+	0.954290i
$719$	−2.47485	−	23.5466i	−0.0922962	−	0.878140i	−0.938500	−	0.345280i	$-0.887784\pi$
$719$	−2.47485	−	23.5466i	−0.0922962	−	0.878140i	0.846204	−	0.532860i	$-0.178883\pi$
$720$	12.8373	+	14.2572i	0.478417	+	0.531336i
$721$	0.803717	−	2.47359i	0.0299320	−	0.0921212i
$722$	18.4591	+	4.50141i	0.686975	+	0.167525i
$723$	25.6821	+	18.6592i	0.955128	+	0.693941i
$724$	23.3652	+	4.96643i	0.868362	+	0.184576i
$725$	−6.56057	+	11.3632i	−0.243653	+	0.422020i
$726$	17.5930	+	30.6862i	0.652938	+	1.13887i
$727$	6.43295	−	11.1422i	0.238585	−	0.413241i	−0.721724	−	0.692181i	$-0.756650\pi$
$727$	6.43295	−	11.1422i	0.238585	−	0.413241i	0.960308	+	0.278940i	$0.0899832\pi$
$728$	−1.83819	+	2.04152i	−0.0681280	+	0.0756638i
$729$	−26.8138	−	19.4813i	−0.993102	−	0.721531i
$730$	−7.43398	+	5.40111i	−0.275144	+	0.199904i
$731$	14.3070	−	3.04104i	0.529162	−	0.112477i
$732$	−9.33389	+	1.98398i	−0.344990	+	0.0733300i
$733$	33.3186	−	24.2074i	1.23065	−	0.894119i	0.233711	−	0.972306i	$-0.424913\pi$
$733$	33.3186	−	24.2074i	1.23065	−	0.894119i	0.996939	+	0.0781867i	$0.0249130\pi$
$734$	−3.76644	−	2.73648i	−0.139022	−	0.101005i
$735$	37.0673	−	41.1674i	1.36725	−	1.51848i
$736$	3.27542	−	5.67319i	0.120734	−	0.209117i
$737$	1.85146	−	17.3626i	0.0681995	−	0.639558i
$738$	−9.55541	+	16.5505i	−0.351739	+	0.609231i
$739$	17.9492	+	3.81522i	0.660271	+	0.140345i	0.525847	−	0.850579i	$-0.323748\pi$
$739$	17.9492	+	3.81522i	0.660271	+	0.140345i	0.134424	+	0.990924i	$0.457082\pi$
$740$	−8.77595	−	6.37610i	−0.322610	−	0.234390i
$741$	−56.9882	−	19.4585i	−2.09351	−	0.714824i
$742$	2.31884	−	7.13664i	0.0851272	−	0.261994i
$743$	−17.6081	−	19.5557i	−0.645978	−	0.717431i	0.327847	−	0.944731i	$-0.393677\pi$
$743$	−17.6081	−	19.5557i	−0.645978	−	0.717431i	−0.973825	+	0.227300i	$0.927010\pi$
$744$	−1.33255	−	12.6784i	−0.0488537	−	0.464812i
$745$	−5.83498	+	55.5162i	−0.213777	+	2.03395i
$746$	−8.82757	−	1.87636i	−0.323200	−	0.0686983i
$747$	−50.1835	−	86.9203i	−1.83612	−	3.18025i
$748$	2.81786	−	8.62800i	0.103031	−	0.315471i
$749$	11.9326			0.436009
$750$	17.8194	−	19.7904i	0.650671	−	0.722644i
$751$	1.06778	−	10.1592i	0.0389638	−	0.370715i	−0.957614	−	0.288055i	$-0.906992\pi$
$751$	1.06778	−	10.1592i	0.0389638	−	0.370715i	0.996578	−	0.0826608i	$-0.0263418\pi$
$752$	1.20833	−	0.877900i	0.0440631	−	0.0320137i
$753$	5.27024	−	16.2201i	0.192058	−	0.591094i
$754$	−30.1074	+	6.39952i	−1.09645	+	0.233057i
$755$	4.03147	+	38.3569i	0.146720	+	1.39595i
$756$	−0.932810	+	8.87510i	−0.0339260	+	0.322784i
$757$	−42.2971	−	8.99052i	−1.53731	−	0.326766i	−0.640075	−	0.768312i	$-0.721097\pi$
$757$	−42.2971	−	8.99052i	−1.53731	−	0.326766i	−0.897239	+	0.441546i	$0.854430\pi$
$758$	−7.81928	+	13.5434i	−0.284009	+	0.491918i
$759$	−21.4887	−	66.4777i	−0.779991	−	2.41299i
$760$	11.3469	−	1.02221i	0.411596	−	0.0370793i
$761$	−12.1632	−	37.4344i	−0.440914	−	1.35699i	−0.886903	−	0.461956i	$-0.847148\pi$
$761$	−12.1632	−	37.4344i	−0.440914	−	1.35699i	0.445989	−	0.895039i	$-0.352852\pi$
$762$	−32.9884	+	14.6874i	−1.19504	+	0.532068i
$763$	−0.200811	−	1.91059i	−0.00726985	−	0.0691680i
$764$	−6.95071	+	1.47742i	−0.251468	+	0.0534511i
$765$	−35.1313	−	39.0173i	−1.27017	−	1.41067i
$766$	−6.90585	−	3.07468i	−0.249518	−	0.111093i
$767$	3.46797	+	2.51963i	0.125221	+	0.0909784i
$768$	−0.993679	−	3.05823i	−0.0358563	−	0.110354i
$769$	−18.3333	−	31.7542i	−0.661116	−	1.14509i	−0.980323	−	0.197401i	$-0.936750\pi$
$769$	−18.3333	−	31.7542i	−0.661116	−	1.14509i	0.319207	−	0.947685i	$-0.396583\pi$
$770$	−2.76421	−	4.80454i	−0.0996152	−	0.173144i
$771$	31.3082			1.12754
$772$	1.10255	+	3.39329i	0.0396815	+	0.122127i
$773$	−4.48602	+	42.6816i	−0.161351	+	1.53515i	0.551702	+	0.834041i	$0.313979\pi$
$773$	−4.48602	+	42.6816i	−0.161351	+	1.53515i	−0.713053	+	0.701110i	$0.752688\pi$
$774$	−4.10073	−	39.0159i	−0.147398	−	1.40240i
$775$	7.10205	−	1.50959i	0.255113	−	0.0542260i
$776$	11.3274	+	12.5803i	0.406629	+	0.451607i
$777$	−0.892007	−	8.48688i	−0.0320006	−	0.304465i
$778$	15.6649	+	11.3812i	0.561613	+	0.408036i
$779$	4.46125	+	10.4352i	0.159841	+	0.373879i
$780$	−36.1086			−1.29290
$781$	−2.43100	−	23.4713i	−0.0869881	−	0.839867i
$782$	−8.96372	+	15.5256i	−0.320542	+	0.555195i
$783$	−66.9049	+	74.3055i	−2.39099	+	2.65546i
$784$	−6.02130	+	2.68086i	−0.215047	+	0.0957449i
$785$	19.2583	+	8.57433i	0.687357	+	0.306031i
$786$	−11.5347	+	35.5002i	−0.411430	+	1.26625i
$787$	−3.20144	+	9.85302i	−0.114119	+	0.351222i	−0.991762	−	0.128092i	$-0.959115\pi$
$787$	−3.20144	+	9.85302i	−0.114119	+	0.351222i	0.877643	+	0.479315i	$0.159115\pi$
$788$	0.553800	+	0.246568i	0.0197283	+	0.00878361i
$789$	−7.66899	+	72.9655i	−0.273023	+	2.59764i
$790$	−0.844497	−	2.59910i	−0.0300459	−	0.0924717i
$791$	12.4675			0.443293
$792$	−22.2248	−	9.93548i	−0.789725	−	0.353042i
$793$	6.37464	−	11.0412i	0.226370	−	0.392084i
$794$	5.41781	−	6.01708i	0.192271	−	0.213538i
$795$	90.1049	−	40.1173i	3.19569	−	1.42281i
$796$	−2.37026	−	22.5515i	−0.0840115	−	0.799316i
$797$	−10.1376	+	31.2004i	−0.359093	+	1.10518i	0.594504	+	0.804092i	$0.297348\pi$
$797$	−10.1376	+	31.2004i	−0.359093	+	1.10518i	−0.953598	+	0.301084i	$0.902652\pi$
$798$	6.57050	+	6.09550i	0.232593	+	0.215779i
$799$	−3.30678	+	2.40252i	−0.116985	+	0.0849949i
$800$	1.67311	−	0.744915i	0.0591533	−	0.0263367i
$801$	108.472	+	23.0564i	3.83267	+	0.814658i
$802$	16.9514	+	29.3607i	0.598576	+	1.03676i
$803$	5.84536	−	10.0891i	0.206278	−	0.356038i
$804$	8.46460	+	14.6611i	0.298523	+	0.517058i
$805$	3.38318	+	10.4124i	0.119241	+	0.366987i
$806$	13.7795	+	10.0114i	0.485363	+	0.352637i
$807$	68.4477	+	30.4749i	2.40947	+	1.07277i
$808$	−12.7628	+	2.71281i	−0.448992	+	0.0954363i
$809$	2.20659	−	6.79119i	0.0775796	−	0.238766i	−0.904744	−	0.425956i	$-0.859938\pi$
$809$	2.20659	−	6.79119i	0.0775796	−	0.238766i	0.982324	+	0.187190i	$0.0599380\pi$
$810$	−48.3328	+	35.1158i	−1.69824	+	1.23384i
$811$	0.220825	−	2.10101i	0.00775423	−	0.0737766i	−0.989960	−	0.141345i	$-0.954857\pi$
$811$	0.220825	−	2.10101i	0.00775423	−	0.0737766i	0.997715	+	0.0675683i	$0.0215240\pi$
$812$	4.48097	+	0.952459i	0.157251	+	0.0334248i
$813$	−19.7953	−	34.2865i	−0.694252	−	1.20248i
$814$	13.4599	+	2.88229i	0.471768	+	0.101024i
$815$	12.9407	−	22.4140i	0.453294	−	0.785128i
$816$	2.71937	+	8.36935i	0.0951968	+	0.292986i
$817$	−20.0002	−	11.9473i	−0.699719	−	0.417982i
$818$	−12.1684	+	8.84088i	−0.425459	+	0.309114i
$819$	−13.4926	−	14.9851i	−0.471471	−	0.523621i
$820$	4.55345	+	5.05712i	0.159013	+	0.176602i
$821$	17.5677	+	7.82166i	0.613118	+	0.272978i	0.689711	−	0.724085i	$-0.257738\pi$
$821$	17.5677	+	7.82166i	0.613118	+	0.272978i	−0.0765930	+	0.997062i	$0.524404\pi$
$822$	−48.1716	+	21.4474i	−1.68018	+	0.748063i
$823$	−17.9988	+	19.9897i	−0.627399	+	0.696797i	−0.970116	−	0.242642i	$-0.921986\pi$
$823$	−17.9988	+	19.9897i	−0.627399	+	0.696797i	0.342717	+	0.939439i	$0.388653\pi$
$824$	−4.06753			−0.141699
$825$	6.06393	−	18.5672i	0.211119	−	0.646426i
$826$	−0.318997	−	0.552518i	−0.0110993	−	0.0192246i
$827$	26.9871	−	29.9722i	0.938432	−	1.04223i	−0.0605961	−	0.998162i	$-0.519300\pi$
$827$	26.9871	−	29.9722i	0.938432	−	1.04223i	0.999028	−	0.0440723i	$-0.0140332\pi$
$828$	38.9009	+	28.2632i	1.35190	+	0.982214i
$829$	−4.00944	+	2.91303i	−0.139254	+	0.101174i	−0.655231	−	0.755428i	$-0.727429\pi$
$829$	−4.00944	+	2.91303i	−0.139254	+	0.101174i	0.515978	+	0.856602i	$0.327429\pi$
$830$	−34.9579	+	7.43054i	−1.21341	+	0.257918i
$831$	3.40426	+	3.78081i	0.118092	+	0.131155i
$832$	3.92483	+	1.74745i	0.136069	+	0.0605818i
$833$	16.4783	−	7.33660i	0.570939	−	0.254198i
$834$	−55.1330	−	11.7189i	−1.90910	−	0.405791i
$835$	6.66408			0.230620
$836$	−12.6368	+	7.02226i	−0.437052	+	0.242870i
$837$	55.3293			1.91246
$838$	30.6798	+	6.52120i	1.05982	+	0.225271i
$839$	−42.3257	+	18.8446i	−1.46125	+	0.650589i	−0.974792	−	0.223117i	$-0.928377\pi$
$839$	−42.3257	+	18.8446i	−1.46125	+	0.650589i	−0.486454	+	0.873706i	$0.661710\pi$
$840$	4.90953	+	2.18586i	0.169395	+	0.0754194i
$841$	14.9405	+	16.5931i	0.515189	+	0.572175i
$842$	−10.6872	+	2.27163i	−0.368304	+	0.0782854i
$843$	49.2118	−	35.7545i	1.69494	−	1.23145i
$844$	−3.54550	−	2.57596i	−0.122041	−	0.0886681i
$845$	9.54532	−	10.6012i	0.328369	−	0.364691i
$846$	5.48153	+	9.49429i	0.188459	+	0.326420i
$847$	5.67782	+	4.15150i	0.195092	+	0.142647i
$848$	−11.7354			−0.402996
$849$	−37.9148	+	42.1086i	−1.30123	+	1.44516i
$850$	−4.57873	+	2.03858i	−0.157049	+	0.0699228i
$851$	−24.8375	−	11.0584i	−0.851418	−	0.379076i
$852$	15.3085	+	17.0018i	0.524459	+	0.582471i
$853$	23.1722	+	25.7353i	0.793401	+	0.881161i	0.995159	−	0.0982741i	$-0.0313322\pi$
$853$	23.1722	+	25.7353i	0.793401	+	0.881161i	−0.201758	+	0.979435i	$0.564666\pi$
$854$	−1.53512	+	1.11533i	−0.0525307	+	0.0381658i
$855$	−1.24394	+	83.6162i	−0.0425417	+	2.85961i
$856$	−5.76672	−	17.7482i	−0.197103	−	0.606619i
$857$	−9.60546	+	16.6372i	−0.328116	+	0.568314i	−0.982138	−	0.188162i	$-0.939747\pi$
$857$	−9.60546	+	16.6372i	−0.328116	+	0.568314i	0.654022	+	0.756476i	$0.273080\pi$
$858$	41.8864	−	18.5731i	1.42998	−	0.634075i
$859$	9.48677	+	16.4316i	0.323684	+	0.560638i	0.981245	−	0.192764i	$-0.0617450\pi$
$859$	9.48677	+	16.4316i	0.323684	+	0.560638i	−0.657561	+	0.753402i	$0.728412\pi$
$860$	−13.6641	−	2.90440i	−0.465943	−	0.0990392i
$861$	−0.559579	+	5.32404i	−0.0190704	+	0.181443i
$862$	−22.0282	+	16.0045i	−0.750285	+	0.545114i
$863$	−1.48848	+	4.58106i	−0.0506683	+	0.155941i	−0.973189	−	0.230006i	$-0.926125\pi$
$863$	−1.48848	+	4.58106i	−0.0506683	+	0.155941i	0.922521	+	0.385947i	$0.126125\pi$
$864$	13.6513	−	2.90167i	0.464426	−	0.0987169i
$865$	8.67839	+	3.86387i	0.295074	+	0.131375i
$866$	−28.4475	−	20.6683i	−0.966687	−	0.702339i
$867$	9.45055	+	29.0858i	0.320957	+	0.987806i
$868$	−1.26749	−	2.19536i	−0.0430215	−	0.0745154i
$869$	2.31652	+	2.58060i	0.0785825	+	0.0875409i
$870$	30.1070	+	52.1469i	1.02072	+	1.76795i
$871$	−22.1242	−	4.70265i	−0.749651	−	0.159343i
$872$	−2.74469	+	1.22202i	−0.0929471	+	0.0413827i
$873$	−100.527	+	73.0370i	−3.40232	+	2.47193i
$874$	27.2851	−	8.41887i	0.922934	−	0.284773i
$875$	1.63640	−	5.03632i	0.0553204	−	0.170259i
$876$	1.18170	+	11.2431i	0.0399258	+	0.379869i
$877$	−6.61331	+	2.94444i	−0.223316	+	0.0994266i	−0.515345	−	0.856983i	$-0.672336\pi$
$877$	−6.61331	+	2.94444i	−0.223316	+	0.0994266i	0.292029	+	0.956409i	$0.405670\pi$
$878$	−10.2307	+	11.3623i	−0.345269	+	0.383461i
$879$	31.7324	−	54.9621i	1.07031	−	1.85382i
$880$	−5.81022	+	6.43329i	−0.195863	+	0.216866i
$881$	−32.4066			−1.09181			−0.545904	−	0.837848i	$-0.683814\pi$
$881$	−32.4066			−1.09181			−0.545904	+	0.837848i	$0.683814\pi$
$882$	−14.9502	−	46.0121i	−0.503401	−	1.54931i
$883$	2.23452	−	21.2600i	0.0751976	−	0.715457i	−0.890358	−	0.455261i	$-0.849546\pi$
$883$	2.23452	−	21.2600i	0.0751976	−	0.715457i	0.965556	−	0.260197i	$-0.0837873\pi$
$884$	−10.7409	−	4.78218i	−0.361257	−	0.160842i
$885$	2.59137	−	7.97540i	0.0871078	−	0.268090i
$886$	−0.820021	+	2.52376i	−0.0275491	+	0.0847875i
$887$	−39.8419	−	17.7388i	−1.33776	−	0.595609i	−0.391847	−	0.920030i	$-0.628164\pi$
$887$	−39.8419	−	17.7388i	−1.33776	−	0.595609i	−0.945913	+	0.324421i	$0.894831\pi$
$888$	−12.1920	+	5.42822i	−0.409136	+	0.182159i
$889$	−4.80472	+	5.33618i	−0.161145	+	0.178970i
$890$	19.7439	−	34.1975i	0.661818	−	1.14630i
$891$	38.0042	−	65.5956i	1.27319	−	2.19754i
$892$	8.36718			0.280154
$893$	6.46383	+	0.776751i	0.216304	+	0.0259930i
$894$	55.5610	+	40.3674i	1.85824	+	1.35009i
$895$	−3.00804	−	28.6196i	−0.100548	−	0.956649i
$896$	−0.427859	−	0.475185i	−0.0142938	−	0.0158748i
$897$	−88.5229	+	18.8161i	−2.95569	+	0.628252i
$898$	−1.57952	−	15.0282i	−0.0527094	−	0.501496i
$899$	2.96892	−	28.2474i	0.0990190	−	0.942103i
$900$	4.15414	+	12.7851i	0.138471	+	0.426171i
$901$	32.1159			1.06993
$902$	−7.88328	−	3.52417i	−0.262484	−	0.117342i
$903$	−5.49471	−	9.51711i	−0.182852	−	0.316710i
$904$	−6.02521	−	18.5437i	−0.200396	−	0.616754i
$905$	50.5102	+	36.6978i	1.67902	+	1.21988i
$906$	43.3478	+	19.2997i	1.44013	+	0.641189i
$907$	−24.3172	−	27.0069i	−0.807438	−	0.896751i	0.188922	−	0.981992i	$-0.439501\pi$
$907$	−24.3172	−	27.0069i	−0.807438	−	0.896751i	−0.996360	+	0.0852411i	$0.972834\pi$
$908$	21.0426	−	4.47275i	0.698325	−	0.148434i
$909$	−10.0111	−	95.2489i	−0.332046	−	3.15921i
$910$	−6.55944	+	2.92045i	−0.217443	+	0.0968120i
$911$	6.55882	+	20.1860i	0.217303	+	0.668791i	0.998982	+	0.0451096i	$0.0143637\pi$
$911$	6.55882	+	20.1860i	0.217303	+	0.668791i	−0.781679	+	0.623681i	$0.785636\pi$
$912$	5.89088	−	12.7185i	0.195066	−	0.421152i
$913$	36.7296	−	26.6007i	1.21557	−	0.880356i
$914$	−7.76583	+	13.4508i	−0.256871	+	0.444913i
$915$	−24.3960	−	5.18553i	−0.806507	−	0.171428i
$916$	0.815257	−	7.75666i	0.0269369	−	0.256287i
$917$	0.775864	+	7.38185i	0.0256213	+	0.243770i
$918$	−37.3590	+	7.94090i	−1.23303	+	0.262089i
$919$	14.9484	−	46.0065i	0.493103	−	1.51761i	−0.326789	−	0.945097i	$-0.605967\pi$
$919$	14.9484	−	46.0065i	0.493103	−	1.51761i	0.819892	−	0.572518i	$-0.194033\pi$
$920$	13.8519	−	10.0640i	0.456685	−	0.331801i
$921$	3.74809	−	35.6607i	0.123504	−	1.17506i
$922$	8.24242	−	9.15413i	0.271450	−	0.301475i
$923$	−30.5666			−1.00611
$924$	−6.81944	−	0.0103252i	−0.224343	−	0.000339676i
$925$	−3.80053	−	6.58271i	−0.124961	−	0.216438i
$926$	−26.7509	−	5.68609i	−0.879090	−	0.186856i
$927$	3.12084	−	29.6928i	0.102502	−	0.975239i
$928$	−0.748880	−	7.12512i	−0.0245832	−	0.233894i
$929$	−5.25521	−	5.83650i	−0.172418	−	0.191489i	0.650742	−	0.759299i	$-0.274458\pi$
$929$	−5.25521	−	5.83650i	−0.172418	−	0.191489i	−0.823160	+	0.567809i	$0.807791\pi$
$930$	10.2965	−	31.6892i	0.337634	−	1.03913i
$931$	−27.1889	−	9.28355i	−0.891079	−	0.304256i
$932$	−8.16373	−	5.93129i	−0.267412	−	0.194286i
$933$	22.6604	+	4.81662i	0.741869	+	0.157689i
$934$	14.3617	−	24.8752i	0.469929	−	0.813941i
$935$	15.9006	−	17.6058i	0.520006	−	0.575770i
$936$	−15.7676	+	27.3103i	−0.515381	+	0.892666i
$937$	2.51597	−	2.79427i	0.0821932	−	0.0912847i	−0.700645	−	0.713510i	$-0.747104\pi$
$937$	2.51597	−	2.79427i	0.0821932	−	0.0912847i	0.782838	+	0.622225i	$0.213771\pi$
$938$	2.72345	+	1.97870i	0.0889239	+	0.0646070i
$939$	−4.11584	+	2.99033i	−0.134315	+	0.0975858i
$940$	3.81845	−	0.811636i	0.124544	−	0.0264727i
$941$	−46.3174	+	9.84506i	−1.50990	+	0.320940i	−0.887151	−	0.461480i	$-0.847319\pi$
$941$	−46.3174	+	9.84506i	−1.50990	+	0.320940i	−0.622752	+	0.782419i	$0.713985\pi$
$942$	20.9822	−	15.2445i	0.683638	−	0.496692i
$943$	13.7984	+	10.0251i	0.449337	+	0.326463i
$944$	−0.667632	+	0.741481i	−0.0217296	+	0.0241331i
$945$	−11.6623	+	20.1997i	−0.379375	+	0.657098i
$946$	17.3445	−	3.65924i	0.563918	−	0.118972i
$947$	−5.31788	+	9.21083i	−0.172808	+	0.299312i	−0.939400	−	0.342822i	$-0.888617\pi$
$947$	−5.31788	+	9.21083i	−0.172808	+	0.299312i	0.766593	+	0.642134i	$0.221951\pi$
$948$	−3.28873	−	0.699040i	−0.106813	−	0.0227038i
$949$	−12.2196	−	8.87804i	−0.396664	−	0.288193i
$950$	7.55482	+	2.57957i	0.245111	+	0.0836923i
$951$	3.65168	−	11.2387i	0.118414	−	0.364440i
$952$	1.17091	+	1.30042i	0.0379493	+	0.0421469i
$953$	3.48790	+	33.1852i	0.112984	+	1.07497i	0.893261	+	0.449539i	$0.148412\pi$
$953$	3.48790	+	33.1852i	0.112984	+	1.07497i	−0.780276	+	0.625435i	$0.784922\pi$
$954$	9.00406	−	85.6679i	0.291517	−	2.77360i
$955$	−18.1671	−	3.86153i	−0.587873	−	0.124956i
$956$	−6.70123	−	11.6069i	−0.216733	−	0.375393i
$957$	−61.7472	−	45.0049i	−1.99600	−	1.45480i
$958$	13.9795			0.451657
$959$	−7.01613	+	7.79220i	−0.226563	+	0.251623i
$960$	0.878526	−	8.35861i	0.0283543	−	0.269773i
$961$	12.3642	−	8.98308i	0.398844	−	0.289777i
$962$	5.51003	−	16.9581i	0.177650	−	0.546752i
$963$	133.985	−	28.4794i	4.31761	−	0.917737i
$964$	−1.03192	−	9.81802i	−0.0332358	−	0.316217i
$965$	−0.974777	+	9.27438i	−0.0313792	+	0.298553i
$966$	13.1751	+	2.80046i	0.423902	+	0.0901032i
$967$	−30.3479	+	52.5642i	−0.975924	+	1.69035i	−0.299071	+	0.954231i	$0.596677\pi$
$967$	−30.3479	+	52.5642i	−0.975924	+	1.69035i	−0.676853	+	0.736118i	$0.736657\pi$
$968$	3.43085	−	10.4513i	0.110272	−	0.335917i
$969$	−16.1213	+	34.8063i	−0.517892	+	1.11814i
$970$	13.6728	+	42.0805i	0.439007	+	1.35112i
$971$	−5.02489	+	2.23723i	−0.161256	+	0.0717960i	−0.485778	−	0.874082i	$-0.661464\pi$
$971$	−5.02489	+	2.23723i	−0.161256	+	0.0717960i	0.324521	+	0.945878i	$0.394797\pi$
$972$	3.30644	+	31.4587i	0.106054	+	1.00904i
$973$	−10.9632	+	2.33030i	−0.351464	+	0.0747060i
$974$	2.38627	+	2.65022i	0.0764610	+	0.0849186i
$975$	−23.1142	−	10.2911i	−0.740246	−	0.329579i
$976$	2.40078	+	1.74427i	0.0768471	+	0.0558327i
$977$	−9.82729	−	30.2453i	−0.314403	−	0.967633i	−0.975999	−	0.217773i	$-0.930121\pi$
$977$	−9.82729	−	30.2453i	−0.314403	−	0.967633i	0.661596	−	0.749860i	$-0.269879\pi$
$978$	−15.9208	−	27.5757i	−0.509092	−	0.881774i
$979$	−5.31312	+	49.8251i	−0.169808	+	1.59242i
$980$	−17.2273			−0.550305
$981$	−6.81478	−	20.9737i	−0.217579	−	0.669640i
$982$	0.622236	−	5.92018i	0.0198563	−	0.188920i
$983$	−0.707257	−	6.72910i	−0.0225580	−	0.214625i	−0.999994	−	0.00339431i	$-0.998920\pi$
$983$	−0.707257	−	6.72910i	−0.0225580	−	0.214625i	0.977436	−	0.211231i	$-0.0677471\pi$
$984$	8.18921	−	1.74067i	0.261062	−	0.0554905i
$985$	1.06021	+	1.17748i	0.0337809	+	0.0375175i
$986$	2.04943	+	19.4991i	0.0652673	+	0.620977i
$987$	2.48449	+	1.80509i	0.0790821	+	0.0574565i
$988$	7.36162	+	17.2194i	0.234204	+	0.547821i
$989$	−35.0121			−1.11332
$990$	−42.5048	−	47.3503i	−1.35089	−	1.50489i
$991$	−13.4569	+	23.3080i	−0.427473	+	0.740404i	−0.996648	−	0.0818120i	$-0.973929\pi$
$991$	−13.4569	+	23.3080i	−0.427473	+	0.740404i	0.569175	+	0.822216i	$0.307263\pi$
$992$	−2.65275	+	2.94618i	−0.0842250	+	0.0935413i
$993$	−5.26782	+	2.34538i	−0.167169	+	0.0744285i
$994$	4.15601	+	1.85038i	0.131821	+	0.0586903i
$995$	18.3147	−	56.3668i	0.580615	−	1.78695i
$996$	−13.5872	+	41.8172i	−0.430528	+	1.32503i
$997$	−43.2911	−	19.2744i	−1.37104	−	0.610427i	−0.416673	−	0.909056i	$-0.636804\pi$
$997$	−43.2911	−	19.2744i	−1.37104	−	0.610427i	−0.954369	+	0.298629i	$0.903471\pi$
$998$	−0.822638	+	7.82687i	−0.0260401	+	0.247755i
$999$	−17.8991	−	55.0879i	−0.566304	−	1.74290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.e.49.1	✓	72
11.9	even	5	inner	418.2.n.e.163.9	yes	72
19.7	even	3	inner	418.2.n.e.159.9	yes	72
209.64	even	15	inner	418.2.n.e.273.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.e.49.1	✓	72	1.1	even	1	trivial
418.2.n.e.159.9	yes	72	19.7	even	3	inner
418.2.n.e.163.9	yes	72	11.9	even	5	inner
418.2.n.e.273.1	yes	72	209.64	even	15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-2.93761 + 1.30791i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.74891 + 1.94236i) q^{5} +(3.14534 - 0.668563i) q^{6} +(0.517306 - 0.375844i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(4.91153 - 5.45480i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-2.93761 + 1.30791i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.74891 + 1.94236i) q^{5} +(3.14534 - 0.668563i) q^{6} +(0.517306 - 0.375844i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(4.91153 - 5.45480i) q^{9} +(-1.30685 - 2.26353i) q^{10} +(2.68025 + 1.95352i) q^{11} -3.21561 q^{12} +(2.87476 - 3.19275i) q^{13} +(-0.584144 + 0.260077i) q^{14} +(-7.67803 - 3.41848i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.83119 - 2.03374i) q^{17} +(-5.93831 + 4.31444i) q^{18} +(-0.0648390 + 4.35842i) q^{19} +(0.807679 + 2.48578i) q^{20} +(-1.02807 + 1.78067i) q^{21} +(-2.21552 - 2.46809i) q^{22} +(3.27542 + 5.67319i) q^{23} +(3.14534 + 0.668563i) q^{24} +(-0.191438 + 1.82141i) q^{25} +(-3.47575 + 2.52528i) q^{26} +(-4.31272 + 13.2732i) q^{27} +(0.625452 - 0.132944i) q^{28} +(6.54498 + 2.91401i) q^{29} +(6.79951 + 4.94013i) q^{30} +(-1.22509 - 3.77044i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-10.4286 - 2.23317i) q^{33} +(1.36833 + 2.37002i) q^{34} +(1.63475 + 0.347476i) q^{35} +(6.70557 - 2.98551i) q^{36} +(-3.35767 + 2.43949i) q^{37} +(0.969588 - 4.24969i) q^{38} +(-4.26910 + 13.1390i) q^{39} +(-0.273206 - 2.59938i) q^{40} +(2.37850 - 1.05898i) q^{41} +(1.37583 - 1.52801i) q^{42} +(-2.67234 + 4.62862i) q^{43} +(1.65396 + 2.87479i) q^{44} +19.1850 q^{45} +(-2.02432 - 6.23022i) q^{46} +(0.156121 - 1.48539i) q^{47} +(-2.93761 - 1.30791i) q^{48} +(-2.03677 + 6.26854i) q^{49} +(0.565947 - 1.74181i) q^{50} +(8.03925 + 3.57930i) q^{51} +(3.92483 - 1.74745i) q^{52} +(-7.85252 + 8.72111i) q^{53} +(6.97814 - 12.0865i) q^{54} +(0.893069 + 8.62255i) q^{55} -0.639425 q^{56} +(-5.50993 - 12.8881i) q^{57} +(-5.79610 - 4.21111i) q^{58} +(0.104294 + 0.992295i) q^{59} +(-5.62381 - 6.24588i) q^{60} +(2.90268 - 0.616984i) q^{61} +(0.414401 + 3.94276i) q^{62} +(0.490602 - 4.66777i) q^{63} +(0.309017 + 0.951057i) q^{64} +11.2292 q^{65} +(9.73636 + 4.35258i) q^{66} +(-2.63234 - 4.55935i) q^{67} +(-0.845676 - 2.60272i) q^{68} +(-17.0419 - 12.3817i) q^{69} +(-1.52678 - 0.679765i) q^{70} +(-4.76067 - 5.28726i) q^{71} +(-7.17976 + 1.52611i) q^{72} +(-0.367487 - 3.49641i) q^{73} +(3.79150 - 1.68808i) q^{74} +(-1.81987 - 5.60097i) q^{75} +(-1.83196 + 3.95524i) q^{76} +(2.12073 + 0.00321097i) q^{77} +(6.90756 - 11.9642i) q^{78} +(1.02274 + 0.217390i) q^{79} +(-0.273206 + 2.59938i) q^{80} +(-2.38926 - 22.7323i) q^{81} +(-2.54670 + 0.541318i) q^{82} +(4.22540 - 13.0044i) q^{83} +(-1.66345 + 1.20857i) q^{84} +(0.747674 - 7.11364i) q^{85} +(3.57629 - 3.97187i) q^{86} -23.0378 q^{87} +(-1.02012 - 3.15585i) q^{88} +(7.55400 + 13.0839i) q^{89} +(-18.7658 - 3.98879i) q^{90} +(0.287154 - 2.73209i) q^{91} +(0.684749 + 6.51495i) q^{92} +(8.53022 + 9.47377i) q^{93} +(-0.461539 + 1.42047i) q^{94} +(-8.57901 + 7.49653i) q^{95} +(2.60148 + 1.89009i) q^{96} +(-16.5586 - 3.51963i) q^{97} +(3.29557 - 5.70809i) q^{98} +(23.8202 - 5.02546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Introduction

L-functions

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Database

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