LMFDB - Embedded newform 418.2.n.d.125.7

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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	418.125
Dual form			418.2.n.d.311.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(1.35422 + 1.50401i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.371716 + 3.53664i) q^{5} +(-1.84887 - 0.823172i) q^{6} +(1.09191 + 3.36056i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.114558 + 1.08994i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(1.35422 + 1.50401i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.371716 + 3.53664i) q^{5} +(-1.84887 - 0.823172i) q^{6} +(1.09191 + 3.36056i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.114558 + 1.08994i) q^{9} +(-1.77806 - 3.07970i) q^{10} +(1.87278 - 2.73728i) q^{11} +2.02384 q^{12} +(-0.150718 + 1.43399i) q^{13} +(-2.36437 - 2.62590i) q^{14} +(-4.81576 + 5.34845i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.409591 - 3.89700i) q^{17} +(-0.338666 - 1.04231i) q^{18} +(-2.73750 - 3.39206i) q^{19} +(2.87697 + 2.09024i) q^{20} +(-3.57563 + 6.19317i) q^{21} +(-0.597523 + 3.26236i) q^{22} +(-1.32206 - 2.28987i) q^{23} +(-1.84887 + 0.823172i) q^{24} +(-7.47894 + 1.58970i) q^{25} +(-0.445568 - 1.37132i) q^{26} +(3.11755 - 2.26504i) q^{27} +(3.22802 + 1.43721i) q^{28} +(5.66846 - 6.29547i) q^{29} +(2.22401 - 6.84480i) q^{30} +(3.85512 + 2.80091i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.65304 - 0.890179i) q^{33} +(1.95923 + 3.39349i) q^{34} +(-11.4792 + 5.11088i) q^{35} +(0.733331 + 0.814446i) q^{36} +(3.32582 + 10.2358i) q^{37} +(3.88051 + 1.98536i) q^{38} +(-2.36084 + 1.71525i) q^{39} +(-3.47842 - 0.739360i) q^{40} +(-5.28591 - 5.87060i) q^{41} +(0.747510 - 7.11208i) q^{42} +(-0.894200 + 1.54880i) q^{43} +(-0.781056 - 3.22334i) q^{44} -3.89732 q^{45} +(2.13913 + 1.55417i) q^{46} +(-7.35484 + 1.56332i) q^{47} +(1.35422 - 1.50401i) q^{48} +(-4.43798 + 3.22438i) q^{49} +(6.18577 - 4.49422i) q^{50} +(5.30645 - 5.89341i) q^{51} +(0.964812 + 1.07153i) q^{52} +(-0.373475 + 3.55337i) q^{53} +(-1.92675 + 3.33724i) q^{54} +(10.3769 + 5.60588i) q^{55} -3.53350 q^{56} +(1.39453 - 8.71081i) q^{57} +(-2.61780 + 8.05677i) q^{58} +(4.65202 + 0.988818i) q^{59} +(0.752296 + 7.15762i) q^{60} +(-10.3719 - 4.61786i) q^{61} +(-4.66106 - 0.990740i) q^{62} +(-3.78790 + 0.805144i) q^{63} +(-0.809017 - 0.587785i) q^{64} -5.12754 q^{65} +(-5.71579 + 3.51926i) q^{66} +(3.02219 + 5.23459i) q^{67} +(-3.17011 - 2.30322i) q^{68} +(1.65363 - 5.08936i) q^{69} +(8.40801 - 9.33805i) q^{70} +(0.367570 + 3.49719i) q^{71} +(-1.00120 - 0.445761i) q^{72} +(2.28065 + 0.484766i) q^{73} +(-7.20157 - 7.99815i) q^{74} +(-12.5190 - 9.09561i) q^{75} +(-4.35254 - 0.235377i) q^{76} +(11.2437 + 3.30474i) q^{77} +(1.45908 - 2.52720i) q^{78} +(-5.66245 + 2.52109i) q^{79} +(3.47842 - 0.739360i) q^{80} +(10.8445 + 2.30506i) q^{81} +(7.21671 + 3.21309i) q^{82} +(11.2442 - 8.16939i) q^{83} +(2.20986 + 6.80125i) q^{84} +(13.6301 - 2.89716i) q^{85} +(0.186939 - 1.77860i) q^{86} +17.1448 q^{87} +(2.02458 + 2.62699i) q^{88} +(0.165534 + 0.286714i) q^{89} +(3.56038 - 1.58518i) q^{90} +(-4.98358 + 1.05929i) q^{91} +(-2.58633 - 0.549742i) q^{92} +(1.00807 + 9.59118i) q^{93} +(6.08312 - 4.41965i) q^{94} +(10.9790 - 10.9424i) q^{95} +(-0.625402 + 1.92479i) q^{96} +(5.04577 - 2.24652i) q^{97} +(2.74282 - 4.75070i) q^{98} +(2.76893 + 2.35480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	1.35422	+	1.50401i	0.781857	+	0.868340i	0.994054	−	0.108887i	$-0.0347286\pi$
$3$	1.35422	+	1.50401i	0.781857	+	0.868340i	−0.212197	+	0.977227i	$0.568062\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.371716	+	3.53664i	0.166237	+	1.58164i	0.686178	+	0.727434i	$0.259287\pi$
$5$	0.371716	+	3.53664i	0.166237	+	1.58164i	−0.519941	+	0.854202i	$0.674046\pi$
$6$	−1.84887	−	0.823172i	−0.754800	−	0.336058i
$7$	1.09191	+	3.36056i	0.412704	+	1.27017i	0.914288	+	0.405064i	$0.132751\pi$
$7$	1.09191	+	3.36056i	0.412704	+	1.27017i	−0.501584	+	0.865109i	$0.667249\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.114558	+	1.08994i	−0.0381858	+	0.363314i
$10$	−1.77806	−	3.07970i	−0.562273	−	0.973885i
$11$	1.87278	−	2.73728i	0.564666	−	0.825320i
$11$	1.87278	−	2.73728i	0.564666	−	0.825320i
$12$	2.02384			0.584234
$13$	−0.150718	+	1.43399i	−0.0418018	+	0.397717i	0.953537	+	0.301276i	$0.0974126\pi$
$13$	−0.150718	+	1.43399i	−0.0418018	+	0.397717i	−0.995339	+	0.0964410i	$0.969254\pi$
$14$	−2.36437	−	2.62590i	−0.631906	−	0.701802i
$15$	−4.81576	+	5.34845i	−1.24342	+	1.38096i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.409591	−	3.89700i	−0.0993405	−	0.945162i	−0.924737	−	0.380608i	$-0.875715\pi$
$17$	−0.409591	−	3.89700i	−0.0993405	−	0.945162i	0.825396	−	0.564554i	$-0.190952\pi$
$18$	−0.338666	−	1.04231i	−0.0798243	−	0.245674i
$19$	−2.73750	−	3.39206i	−0.628025	−	0.778193i
$19$	−2.73750	−	3.39206i	−0.628025	−	0.778193i
$20$	2.87697	+	2.09024i	0.643309	+	0.467391i
$21$	−3.57563	+	6.19317i	−0.780266	+	1.35146i
$22$	−0.597523	+	3.26236i	−0.127392	+	0.695537i
$23$	−1.32206	−	2.28987i	−0.275668	−	0.477470i	0.694636	−	0.719362i	$-0.255566\pi$
$23$	−1.32206	−	2.28987i	−0.275668	−	0.477470i	−0.970303	+	0.241891i	$0.922232\pi$
$24$	−1.84887	+	0.823172i	−0.377400	+	0.168029i
$25$	−7.47894	+	1.58970i	−1.49579	+	0.317940i
$26$	−0.445568	−	1.37132i	−0.0873831	−	0.268937i
$27$	3.11755	−	2.26504i	0.599974	−	0.435906i
$28$	3.22802	+	1.43721i	0.610038	+	0.271606i
$29$	5.66846	−	6.29547i	1.05261	−	1.16904i	0.0673905	−	0.997727i	$-0.478533\pi$
$29$	5.66846	−	6.29547i	1.05261	−	1.16904i	0.985217	−	0.171312i	$-0.0548007\pi$
$30$	2.22401	−	6.84480i	0.406047	−	1.24968i
$31$	3.85512	+	2.80091i	0.692401	+	0.503058i	0.877448	−	0.479671i	$-0.159244\pi$
$31$	3.85512	+	2.80091i	0.692401	+	0.503058i	−0.185048	+	0.982730i	$0.559244\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	6.65304	−	0.890179i	1.15815	−	0.154960i
$34$	1.95923	+	3.39349i	0.336006	+	0.581979i
$35$	−11.4792	+	5.11088i	−1.94034	+	0.863897i
$36$	0.733331	+	0.814446i	0.122222	+	0.135741i
$37$	3.32582	+	10.2358i	0.546761	+	1.68276i	0.716765	+	0.697315i	$0.245622\pi$
$37$	3.32582	+	10.2358i	0.546761	+	1.68276i	−0.170003	+	0.985443i	$0.554378\pi$
$38$	3.88051	+	1.98536i	0.629501	+	0.322069i
$39$	−2.36084	+	1.71525i	−0.378037	+	0.274660i
$40$	−3.47842	−	0.739360i	−0.549986	−	0.116903i
$41$	−5.28591	−	5.87060i	−0.825521	−	0.916834i	0.172148	−	0.985071i	$-0.444929\pi$
$41$	−5.28591	−	5.87060i	−0.825521	−	0.916834i	−0.997669	+	0.0682373i	$0.978262\pi$
$42$	0.747510	−	7.11208i	0.115343	−	1.09742i
$43$	−0.894200	+	1.54880i	−0.136364	+	0.236190i	−0.926118	−	0.377234i	$-0.876875\pi$
$43$	−0.894200	+	1.54880i	−0.136364	+	0.236190i	0.789754	+	0.613424i	$0.210208\pi$
$44$	−0.781056	−	3.22334i	−0.117749	−	0.485938i
$45$	−3.89732			−0.580978
$46$	2.13913	+	1.55417i	0.315398	+	0.229150i
$47$	−7.35484	+	1.56332i	−1.07281	+	0.228034i	−0.710267	−	0.703932i	$-0.751426\pi$
$47$	−7.35484	+	1.56332i	−1.07281	+	0.228034i	−0.362547	+	0.931966i	$0.618093\pi$
$48$	1.35422	−	1.50401i	0.195464	−	0.217085i
$49$	−4.43798	+	3.22438i	−0.633997	+	0.460626i
$50$	6.18577	−	4.49422i	0.874800	−	0.635579i
$51$	5.30645	−	5.89341i	0.743052	−	0.825243i
$52$	0.964812	+	1.07153i	0.133795	+	0.148595i
$53$	−0.373475	+	3.55337i	−0.0513007	+	0.488094i	0.938463	+	0.345379i	$0.112250\pi$
$53$	−0.373475	+	3.55337i	−0.0513007	+	0.488094i	−0.989764	+	0.142714i	$0.954417\pi$
$54$	−1.92675	+	3.33724i	−0.262198	+	0.454140i
$55$	10.3769	+	5.60588i	1.39922	+	0.755897i
$56$	−3.53350			−0.472184
$57$	1.39453	−	8.71081i	0.184710	−	1.15378i
$58$	−2.61780	+	8.05677i	−0.343734	+	1.05791i
$59$	4.65202	+	0.988818i	0.605642	+	0.128733i	0.500518	−	0.865726i	$-0.333143\pi$
$59$	4.65202	+	0.988818i	0.605642	+	0.128733i	0.105124	+	0.994459i	$0.466476\pi$
$60$	0.752296	+	7.15762i	0.0971210	+	0.924045i
$61$	−10.3719	−	4.61786i	−1.32798	−	0.591257i	−0.384638	−	0.923067i	$-0.625674\pi$
$61$	−10.3719	−	4.61786i	−1.32798	−	0.591257i	−0.943346	+	0.331811i	$0.892341\pi$
$62$	−4.66106	−	0.990740i	−0.591956	−	0.125824i
$63$	−3.78790	+	0.805144i	−0.477231	+	0.101439i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−5.12754			−0.635993
$66$	−5.71579	+	3.51926i	−0.703565	+	0.433190i
$67$	3.02219	+	5.23459i	0.369220	+	0.639507i	0.989444	−	0.144917i	$-0.0462917\pi$
$67$	3.02219	+	5.23459i	0.369220	+	0.639507i	−0.620224	+	0.784425i	$0.712958\pi$
$68$	−3.17011	−	2.30322i	−0.384432	−	0.279306i
$69$	1.65363	−	5.08936i	0.199074	−	0.612687i
$70$	8.40801	−	9.33805i	1.00495	−	1.11611i
$71$	0.367570	+	3.49719i	0.0436225	+	0.415041i	0.994441	+	0.105293i	$0.0335780\pi$
$71$	0.367570	+	3.49719i	0.0436225	+	0.415041i	−0.950819	+	0.309748i	$0.899755\pi$
$72$	−1.00120	−	0.445761i	−0.117992	−	0.0525335i
$73$	2.28065	+	0.484766i	0.266930	+	0.0567376i	0.339432	−	0.940631i	$-0.389765\pi$
$73$	2.28065	+	0.484766i	0.266930	+	0.0567376i	−0.0725024	+	0.997368i	$0.523099\pi$
$74$	−7.20157	−	7.99815i	−0.837166	−	0.929767i
$75$	−12.5190	−	9.09561i	−1.44557	−	1.05027i
$76$	−4.35254	−	0.235377i	−0.499270	−	0.0269996i
$77$	11.2437	+	3.30474i	1.28134	+	0.376610i
$78$	1.45908	−	2.52720i	0.165208	−	0.286149i
$79$	−5.66245	+	2.52109i	−0.637076	+	0.283644i	−0.699748	−	0.714390i	$-0.746704\pi$
$79$	−5.66245	+	2.52109i	−0.637076	+	0.283644i	0.0626724	+	0.998034i	$0.480038\pi$
$80$	3.47842	−	0.739360i	0.388899	−	0.0826630i
$81$	10.8445	+	2.30506i	1.20494	+	0.256118i
$82$	7.21671	+	3.21309i	0.796952	+	0.354826i
$83$	11.2442	−	8.16939i	1.23421	−	0.896707i	0.237013	−	0.971507i	$-0.423832\pi$
$83$	11.2442	−	8.16939i	1.23421	−	0.896707i	0.997199	+	0.0747996i	$0.0238317\pi$
$84$	2.20986	+	6.80125i	0.241116	+	0.742077i
$85$	13.6301	−	2.89716i	1.47839	−	0.314241i
$86$	0.186939	−	1.77860i	0.0201581	−	0.191792i
$87$	17.1448			1.83811
$88$	2.02458	+	2.62699i	0.215821	+	0.280038i
$89$	0.165534	+	0.286714i	0.0175466	+	0.0303916i	0.874665	−	0.484727i	$-0.161081\pi$
$89$	0.165534	+	0.286714i	0.0175466	+	0.0303916i	−0.857119	+	0.515119i	$0.827748\pi$
$90$	3.56038	−	1.58518i	0.375297	−	0.167093i
$91$	−4.98358	+	1.05929i	−0.522421	+	0.111044i
$92$	−2.58633	−	0.549742i	−0.269644	−	0.0573145i
$93$	1.00807	+	9.59118i	0.104532	+	0.994559i
$94$	6.08312	−	4.41965i	0.627426	−	0.455852i
$95$	10.9790	−	10.9424i	1.12642	−	1.12267i
$96$	−0.625402	+	1.92479i	−0.0638299	+	0.196448i
$97$	5.04577	−	2.24652i	0.512320	−	0.228100i	−0.134259	−	0.990946i	$-0.542866\pi$
$97$	5.04577	−	2.24652i	0.512320	−	0.228100i	0.646579	+	0.762847i	$0.276199\pi$
$98$	2.74282	−	4.75070i	0.277067	−	0.479894i
$99$	2.76893	+	2.35480i	0.278288	+	0.236666i
$100$	−3.82301	+	6.62166i	−0.382301	+	0.662166i
$101$	0.460610	−	4.38242i	0.0458325	−	0.436067i	−0.947411	−	0.320019i	$-0.896311\pi$
$101$	0.460610	−	4.38242i	0.0458325	−	0.436067i	0.993244	−	0.116048i	$-0.0370226\pi$
$102$	−2.45062	+	7.54223i	−0.242647	+	0.746792i
$103$	−3.21690	−	9.90060i	−0.316970	−	0.975535i	−0.974936	−	0.222487i	$-0.928583\pi$
$103$	−3.21690	−	9.90060i	−0.316970	−	0.975535i	0.657965	−	0.753048i	$-0.271417\pi$
$104$	−1.31723	−	0.586469i	−0.129165	−	0.0575080i
$105$	−23.2322	−	10.3436i	−2.26723	−	1.00943i
$106$	−1.10410	−	3.39808i	−0.107240	−	0.330050i
$107$	−4.44870	+	13.6917i	−0.430072	+	1.32363i	0.467980	+	0.883739i	$0.344982\pi$
$107$	−4.44870	+	13.6917i	−0.430072	+	1.32363i	−0.898053	+	0.439888i	$0.855018\pi$
$108$	0.402801	−	3.83240i	0.0387596	−	0.368773i
$109$	4.51425	−	7.81891i	0.432387	−	0.748916i	−0.564692	−	0.825302i	$-0.691005\pi$
$109$	4.51425	−	7.81891i	0.432387	−	0.748916i	0.997078	+	0.0763863i	$0.0243382\pi$
$110$	−11.7599	−	0.900554i	−1.12126	−	0.0858645i
$111$	−10.8909	+	18.8636i	−1.03372	+	1.79045i
$112$	3.22802	−	1.43721i	0.305019	−	0.135803i
$113$	3.63516	−	11.1879i	0.341967	−	1.05247i	−0.621221	−	0.783636i	$-0.713363\pi$
$113$	3.63516	−	11.1879i	0.341967	−	1.05247i	0.963188	−	0.268830i	$-0.0866371\pi$
$114$	2.26904	+	8.52493i	0.212515	+	0.798433i
$115$	7.60702	−	5.52682i	0.709358	−	0.515379i
$116$	−0.885501	−	8.42498i	−0.0822167	−	0.782240i
$117$	−1.54570	−	0.328549i	−0.142900	−	0.0303743i
$118$	−4.65202	+	0.988818i	−0.428254	+	0.0910281i
$119$	12.6489	−	5.63164i	1.15952	−	0.516252i
$120$	−3.59852	−	6.23282i	−0.328499	−	0.568976i
$121$	−3.98536	−	10.2527i	−0.362306	−	0.932059i
$122$	11.3534			1.02789
$123$	1.67117	−	15.9001i	0.150684	−	1.43367i
$124$	4.66106	−	0.990740i	0.418576	−	0.0889710i
$125$	−2.90773	−	8.94907i	−0.260075	−	0.800429i
$126$	3.13294	−	2.27621i	0.279105	−	0.202781i
$127$	12.4552	+	5.54540i	1.10522	+	0.492074i	0.876492	−	0.481417i	$-0.159878\pi$
$127$	12.4552	+	5.54540i	1.10522	+	0.492074i	0.228725	+	0.973491i	$0.426544\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	−3.54035	+	0.752525i	−0.311711	+	0.0662561i
$130$	4.68424	−	2.08556i	0.410835	−	0.182915i
$131$	−4.37286	+	7.57402i	−0.382059	+	0.661745i	−0.991356	−	0.131196i	$-0.958118\pi$
$131$	−4.37286	+	7.57402i	−0.382059	+	0.661745i	0.609297	+	0.792942i	$0.291452\pi$
$132$	3.79022	−	5.53982i	0.329897	−	0.482180i
$133$	8.41013	−	12.9034i	0.729251	−	1.11886i
$134$	−4.89001	−	3.55280i	−0.422433	−	0.306915i
$135$	9.16947	+	10.1837i	0.789183	+	0.876476i
$136$	3.83284	+	0.814695i	0.328663	+	0.0698595i
$137$	−18.9268	−	8.42673i	−1.61702	−	0.719944i	−0.619157	−	0.785267i	$-0.712526\pi$
$137$	−18.9268	−	8.42673i	−1.61702	−	0.719944i	−0.997864	+	0.0653225i	$0.979192\pi$
$138$	0.559360	+	5.32195i	0.0476159	+	0.453035i
$139$	−6.47823	+	7.19481i	−0.549477	+	0.610256i	−0.952353	−	0.304999i	$-0.901344\pi$
$139$	−6.47823	+	7.19481i	−0.549477	+	0.610256i	0.402876	+	0.915255i	$0.368011\pi$
$140$	−3.88298	+	11.9506i	−0.328171	+	1.01001i
$141$	−12.3113	−	8.94468i	−1.03680	−	0.753278i
$142$	−1.75823	−	3.04534i	−0.147547	−	0.255559i
$143$	3.64296	+	3.09811i	0.304640	+	0.259077i
$144$	1.09595			0.0913288
$145$	24.3719	+	17.7072i	2.02398	+	1.47050i
$146$	−2.28065	+	0.484766i	−0.188748	+	0.0401196i
$147$	−10.8595	−	2.30825i	−0.895675	−	0.190381i
$148$	9.83210	+	4.37754i	0.808194	+	0.359831i
$149$	−1.43826	−	13.6841i	−0.117827	−	1.12105i	−0.880428	−	0.474179i	$-0.842745\pi$
$149$	−1.43826	−	13.6841i	−0.117827	−	1.12105i	0.762602	−	0.646869i	$-0.223922\pi$
$150$	15.1362	+	3.21730i	1.23587	+	0.262692i
$151$	−1.95374	+	6.01298i	−0.158993	+	0.489330i	−0.998544	−	0.0539517i	$-0.982818\pi$
$151$	−1.95374	+	6.01298i	−0.158993	+	0.489330i	0.839551	+	0.543281i	$0.182818\pi$
$152$	4.07198	−	1.55531i	0.330281	−	0.126152i
$153$	4.29443			0.347184
$154$	−11.6158	+	1.55420i	−0.936027	+	0.125241i
$155$	−8.47281	+	14.6753i	−0.680553	+	1.17875i
$156$	−0.305031	+	2.90217i	−0.0244220	+	0.232360i
$157$	−7.62889	−	8.47274i	−0.608851	−	0.676198i	0.357355	−	0.933969i	$-0.383679\pi$
$157$	−7.62889	−	8.47274i	−0.608851	−	0.676198i	−0.966206	+	0.257771i	$0.917012\pi$
$158$	4.14749	−	4.60625i	0.329956	−	0.366454i
$159$	−5.85007	+	4.25033i	−0.463941	+	0.337073i
$160$	−2.87697	+	2.09024i	−0.227444	+	0.165248i
$161$	6.25167	−	6.94318i	0.492701	−	0.547199i
$162$	−10.8445	+	2.30506i	−0.852022	+	0.181103i
$163$	7.05786	+	5.12784i	0.552815	+	0.401643i	0.828822	−	0.559512i	$-0.189011\pi$
$163$	7.05786	+	5.12784i	0.552815	+	0.401643i	−0.276008	+	0.961155i	$0.589011\pi$
$164$	−7.89967			−0.616861
$165$	5.62129	+	23.1986i	0.437617	+	1.80601i
$166$	−6.94930	+	12.0365i	−0.539370	+	0.934216i
$167$	−2.32708	+	22.1407i	−0.180075	+	1.71330i	0.415161	+	0.909748i	$0.363725\pi$
$167$	−2.32708	+	22.1407i	−0.180075	+	1.71330i	−0.595236	+	0.803551i	$0.702941\pi$
$168$	−4.78513	−	5.31442i	−0.369181	−	0.410017i
$169$	10.6823	+	2.27059i	0.821716	+	0.174661i
$170$	−11.2733	+	8.19053i	−0.864622	+	0.628185i
$171$	4.01076	−	2.59513i	0.306710	−	0.198454i
$172$	0.552646	+	1.70087i	0.0421389	+	0.129690i
$173$	−8.77055	−	9.74068i	−0.666813	−	0.740570i	0.310918	−	0.950437i	$-0.399364\pi$
$173$	−8.77055	−	9.74068i	−0.666813	−	0.740570i	−0.977730	+	0.209867i	$0.932697\pi$
$174$	−15.6625	+	6.97340i	−1.18737	+	0.528652i
$175$	−13.5086	−	23.3976i	−1.02116	−	1.76870i
$176$	−2.91804	−	1.57640i	−0.219956	−	0.118826i
$177$	4.81265	+	8.33576i	0.361741	+	0.626554i
$178$	−0.267840	−	0.194597i	−0.0200754	−	0.0145857i
$179$	7.46714	−	22.9815i	0.558120	−	1.71772i	−0.129437	−	0.991588i	$-0.541317\pi$
$179$	7.46714	−	22.9815i	0.558120	−	1.71772i	0.687558	−	0.726130i	$-0.258683\pi$
$180$	−2.60782	+	2.89627i	−0.194375	+	0.215875i
$181$	−0.728997	−	0.324570i	−0.0541859	−	0.0241251i	0.379465	−	0.925206i	$-0.376108\pi$
$181$	−0.728997	−	0.324570i	−0.0541859	−	0.0241251i	−0.433651	+	0.901081i	$0.642775\pi$
$182$	4.12187	−	2.99472i	0.305534	−	0.221983i
$183$	−7.10047	−	21.8530i	−0.524882	−	1.61542i
$184$	2.58633	−	0.549742i	0.190667	−	0.0405275i
$185$	−34.9642	+	15.5671i	−2.57062	+	1.14451i
$186$	−4.82201	−	8.35196i	−0.353567	−	0.612395i
$187$	−11.4342	−	6.17708i	−0.836155	−	0.451713i
$188$	−3.75958	+	6.51178i	−0.274195	+	0.474920i
$189$	11.0159	+	8.00351i	0.801288	+	0.582170i
$190$	−5.57908	+	14.4620i	−0.404749	+	1.04918i
$191$	6.70498	+	20.6358i	0.485155	+	1.49315i	0.831756	+	0.555141i	$0.187336\pi$
$191$	6.70498	+	20.6358i	0.485155	+	1.49315i	−0.346601	+	0.938013i	$0.612664\pi$
$192$	−0.211549	−	2.01276i	−0.0152673	−	0.145258i
$193$	2.33754	+	22.2402i	0.168260	+	1.60089i	0.674354	+	0.738409i	$0.264422\pi$
$193$	2.33754	+	22.2402i	0.168260	+	1.60089i	−0.506094	+	0.862479i	$0.668911\pi$
$194$	−3.69580	+	4.10460i	−0.265343	+	0.294693i
$195$	−6.94379	−	7.71186i	−0.497255	−	0.552258i
$196$	−0.573406	+	5.45559i	−0.0409575	+	0.389685i
$197$	−24.4898			−1.74483			−0.872413	−	0.488770i	$-0.837446\pi$
$197$	−24.4898			−1.74483			−0.872413	+	0.488770i	$0.837446\pi$
$198$	−3.48733	−	1.02499i	−0.247834	−	0.0728430i
$199$	2.83922	+	4.91767i	0.201267	+	0.348604i	0.948937	−	0.315466i	$-0.102161\pi$
$199$	2.83922	+	4.91767i	0.201267	+	0.348604i	−0.747670	+	0.664070i	$0.768828\pi$
$200$	0.799228	−	7.60414i	0.0565139	−	0.537694i
$201$	−3.78017	+	11.6342i	−0.266633	+	0.820612i
$202$	1.36170	+	4.19088i	0.0958089	+	0.294870i
$203$	27.3458	+	12.1751i	1.91930	+	0.854526i
$204$	−0.828949	−	7.88692i	−0.0580381	−	0.552195i
$205$	18.7974	−	20.8766i	1.31287	−	1.45808i
$206$	6.96572	+	7.73621i	0.485325	+	0.539008i
$207$	2.64727	−	1.17864i	0.183998	−	0.0819213i
$208$	1.44189			0.0999770
$209$	−14.4118	+	1.14068i	−0.996882	+	0.0789028i
$210$	25.4308			1.75489
$211$	0.332904	−	0.148218i	0.0229180	−	0.0102038i	−0.395246	−	0.918575i	$-0.629341\pi$
$211$	0.332904	−	0.148218i	0.0229180	−	0.0102038i	0.418164	+	0.908372i	$0.362674\pi$
$212$	2.39077	+	2.65522i	0.164199	+	0.182361i
$213$	−4.76204	+	5.28878i	−0.326290	+	0.362382i
$214$	−1.50482	−	14.3174i	−0.102868	−	0.978720i
$215$	−5.80995	−	2.58675i	−0.396235	−	0.176415i
$216$	1.19080	+	3.66491i	0.0810237	+	0.249365i
$217$	−5.20317	+	16.0137i	−0.353215	+	1.08708i
$218$	−0.943735	+	8.97904i	−0.0639178	+	0.608137i
$219$	2.35940	+	4.08659i	0.159433	+	0.276146i
$220$	11.1095	−	3.96049i	0.749002	−	0.267016i
$221$	5.64999			0.380060
$222$	2.27682	−	21.6625i	0.152810	−	1.45389i
$223$	−13.4636	−	14.9529i	−0.901591	−	1.00132i	−0.999981	−	0.00617048i	$-0.998036\pi$
$223$	−13.4636	−	14.9529i	−0.901591	−	1.00132i	0.0983898	−	0.995148i	$-0.468631\pi$
$224$	−2.36437	+	2.62590i	−0.157976	+	0.175451i
$225$	−0.875910	−	8.33373i	−0.0583940	−	0.555582i
$226$	1.22963	+	11.6992i	0.0817940	+	0.778218i
$227$	5.64102	+	17.3613i	0.374408	+	1.15231i	0.943877	+	0.330296i	$0.107149\pi$
$227$	5.64102	+	17.3613i	0.374408	+	1.15231i	−0.569469	+	0.822012i	$0.692851\pi$
$228$	−5.54027	−	6.86501i	−0.366913	−	0.454646i
$229$	−16.5982	−	12.0593i	−1.09684	−	0.796898i	−0.116296	−	0.993215i	$-0.537102\pi$
$229$	−16.5982	−	12.0593i	−1.09684	−	0.796898i	−0.980541	+	0.196316i	$0.937102\pi$
$230$	−4.70140	+	8.14306i	−0.310001	+	0.536937i
$231$	10.2560	+	21.3860i	0.674798	+	1.40709i
$232$	4.23569	+	7.33644i	0.278087	+	0.481661i
$233$	8.56983	−	3.81553i	0.561428	−	0.249964i	−0.106344	−	0.994329i	$-0.533915\pi$
$233$	8.56983	−	3.81553i	0.561428	−	0.249964i	0.667773	+	0.744365i	$0.267248\pi$
$234$	1.54570	−	0.328549i	0.101046	−	0.0214779i
$235$	−8.26282	−	25.4304i	−0.539007	−	1.65889i
$236$	3.84765	−	2.79548i	0.250461	−	0.181970i
$237$	−11.4599	−	5.10229i	−0.744402	−	0.331429i
$238$	−9.26473	+	10.2895i	−0.600543	+	0.666971i
$239$	−0.821090	+	2.52706i	−0.0531119	+	0.163462i	−0.974094	−	0.226143i	$-0.927388\pi$
$239$	−0.821090	+	2.52706i	−0.0531119	+	0.163462i	0.920982	+	0.389605i	$0.127388\pi$
$240$	5.82253	+	4.23032i	0.375843	+	0.273066i
$241$	5.38079	+	9.31980i	0.346607	+	0.600341i	0.985644	−	0.168835i	$-0.0540004\pi$
$241$	5.38079	+	9.31980i	0.346607	+	0.600341i	−0.639037	+	0.769176i	$0.720667\pi$
$242$	7.81094	+	7.74527i	0.502106	+	0.497885i
$243$	5.43865	+	9.42002i	0.348890	+	0.604295i
$244$	−10.3719	+	4.61786i	−0.663992	+	0.295628i
$245$	−13.0532	−	14.4970i	−0.833935	−	0.926179i
$246$	4.94047	+	15.2052i	0.314993	+	0.969449i
$247$	5.27678	−	3.41430i	0.335753	−	0.217247i
$248$	−3.85512	+	2.80091i	−0.244801	+	0.177858i
$249$	27.5139	+	5.84826i	1.74362	+	0.370619i
$250$	6.29626	+	6.99270i	0.398210	+	0.442257i
$251$	1.59263	−	15.1528i	0.100526	−	0.956438i	−0.821735	−	0.569870i	$-0.806994\pi$
$251$	1.59263	−	15.1528i	0.100526	−	0.956438i	0.922261	−	0.386568i	$-0.126340\pi$
$252$	−1.93626	+	3.35371i	−0.121973	+	0.211264i
$253$	−8.74392	−	0.669595i	−0.549726	−	0.0420971i
$254$	−13.6339			−0.855465
$255$	22.8154	+	16.5764i	1.42876	+	1.03805i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−7.38724	+	8.20436i	−0.460803	+	0.511774i	−0.928102	−	0.372325i	$-0.878561\pi$
$257$	−7.38724	+	8.20436i	−0.460803	+	0.511774i	0.467299	+	0.884099i	$0.345227\pi$
$258$	2.92819	−	2.12746i	0.182301	−	0.132450i
$259$	−30.7666	+	22.3532i	−1.91174	+	1.38896i
$260$	−3.43099	+	3.81050i	−0.212781	+	0.236317i
$261$	6.21233	+	6.89949i	0.384533	+	0.427068i
$262$	0.914178	−	8.69782i	0.0564781	−	0.537353i
$263$	13.0077	−	22.5300i	0.802090	−	1.38926i	−0.116148	−	0.993232i	$-0.537055\pi$
$263$	13.0077	−	22.5300i	0.802090	−	1.38926i	0.918238	−	0.396029i	$-0.129612\pi$
$264$	−1.20929	+	6.60250i	−0.0744268	+	0.406356i
$265$	−12.7059			−0.780514
$266$	−2.43477	+	15.2085i	−0.149285	+	0.932494i
$267$	−0.207051	+	0.637237i	−0.0126713	+	0.0389983i
$268$	5.91230	+	1.25670i	0.361151	+	0.0767651i
$269$	0.625629	+	5.95246i	0.0381453	+	0.362928i	0.996899	+	0.0786902i	$0.0250738\pi$
$269$	0.625629	+	5.95246i	0.0381453	+	0.362928i	−0.958754	+	0.284238i	$0.908260\pi$
$270$	−12.5188	−	5.57374i	−0.761872	−	0.339207i
$271$	11.7681	+	2.50139i	0.714861	+	0.151948i	0.550964	−	0.834529i	$-0.314260\pi$
$271$	11.7681	+	2.50139i	0.714861	+	0.151948i	0.163897	+	0.986477i	$0.447594\pi$
$272$	−3.83284	+	0.814695i	−0.232400	+	0.0493982i
$273$	−8.34203	−	6.06084i	−0.504883	−	0.366819i
$274$	20.7179			1.25161
$275$	−9.65500	+	23.4491i	−0.582219	+	1.41403i
$276$	−2.67563	−	4.63433i	−0.161054	−	0.278954i
$277$	−5.25125	−	3.81525i	−0.315517	−	0.229236i	0.418743	−	0.908105i	$-0.362471\pi$
$277$	−5.25125	−	3.81525i	−0.315517	−	0.229236i	−0.734260	+	0.678868i	$0.762471\pi$
$278$	2.99177	−	9.20772i	0.179434	−	0.552242i
$279$	−3.49446	+	3.88100i	−0.209208	+	0.232349i
$280$	−1.31346	−	12.4967i	−0.0784943	−	0.746823i
$281$	8.31835	+	3.70357i	0.496231	+	0.220936i	0.639563	−	0.768738i	$-0.279115\pi$
$281$	8.31835	+	3.70357i	0.496231	+	0.220936i	−0.143332	+	0.989675i	$0.545782\pi$
$282$	14.8851	+	3.16392i	0.886392	+	0.188408i
$283$	4.95512	+	5.50322i	0.294551	+	0.327133i	0.872197	−	0.489155i	$-0.162695\pi$
$283$	4.95512	+	5.50322i	0.294551	+	0.327133i	−0.577645	+	0.816288i	$0.696028\pi$
$284$	2.84487	+	2.06692i	0.168812	+	0.122649i
$285$	31.3254	+	1.69402i	1.85556	+	0.100345i
$286$	−4.58813	−	1.34854i	−0.271302	−	0.0797407i
$287$	13.9568	−	24.1738i	0.823841	−	1.42693i
$288$	−1.00120	+	0.445761i	−0.0589961	+	0.0262667i
$289$	1.60965	−	0.342142i	0.0946854	−	0.0201260i
$290$	−29.4670	−	6.26340i	−1.73036	−	0.367800i
$291$	10.2118	+	4.54661i	0.598629	+	0.266527i
$292$	1.88630	−	1.37048i	0.110387	−	0.0802012i
$293$	−9.85645	−	30.3350i	−0.575820	−	1.77219i	−0.633370	−	0.773850i	$-0.718329\pi$
$293$	−9.85645	−	30.3350i	−0.575820	−	1.77219i	0.0575494	−	0.998343i	$-0.481671\pi$
$294$	10.8595	−	2.30825i	0.633338	−	0.134620i
$295$	−1.76787	+	16.8201i	−0.102929	+	0.979305i
$296$	−10.7626			−0.625562
$297$	−0.361523	−	12.7755i	−0.0209777	−	0.741311i
$298$	6.87975	+	11.9161i	0.398533	+	0.690280i
$299$	3.48290	−	1.55069i	0.201422	−	0.0896786i
$300$	−15.1362	+	3.21730i	−0.873890	+	0.185751i
$301$	−6.18123	−	1.31386i	−0.356280	−	0.0757297i
$302$	−0.660873	−	6.28779i	−0.0380290	−	0.361822i
$303$	7.21496	−	5.24198i	0.414489	−	0.301144i
$304$	−3.08734	+	3.07707i	−0.177071	+	0.176482i
$305$	12.4763	−	38.3982i	0.714393	−	2.19868i
$306$	−3.92316	+	1.74670i	−0.224272	+	0.0998523i
$307$	1.99611	−	3.45737i	0.113924	−	0.197322i	−0.803425	−	0.595406i	$-0.796991\pi$
$307$	1.99611	−	3.45737i	0.113924	−	0.197322i	0.917349	+	0.398084i	$0.130325\pi$
$308$	9.97940	−	6.14440i	0.568629	−	0.350109i
$309$	10.5342	−	18.2458i	0.599271	−	1.03797i
$310$	1.77130	−	16.8528i	0.100603	−	0.957175i
$311$	−7.82047	+	24.0689i	−0.443458	+	1.36482i	0.440708	+	0.897651i	$0.354728\pi$
$311$	−7.82047	+	24.0689i	−0.443458	+	1.36482i	−0.884166	+	0.467173i	$0.845272\pi$
$312$	−0.901760	−	2.77533i	−0.0510521	−	0.157122i
$313$	−25.2926	−	11.2610i	−1.42962	−	0.636508i	−0.461534	−	0.887123i	$-0.652701\pi$
$313$	−25.2926	−	11.2610i	−1.42962	−	0.636508i	−0.968087	+	0.250614i	$0.919367\pi$
$314$	10.4155	+	4.63728i	0.587781	+	0.261697i
$315$	−4.25553	−	13.0972i	−0.239772	−	0.737943i
$316$	−1.91539	+	5.89496i	−0.107749	+	0.331617i
$317$	0.791017	−	7.52602i	0.0444279	−	0.422703i	−0.949591	−	0.313492i	$-0.898501\pi$
$317$	0.791017	−	7.52602i	0.0444279	−	0.422703i	0.994019	−	0.109211i	$-0.0348324\pi$
$318$	3.61554	−	6.26231i	0.202750	−	0.351173i
$319$	−6.61662	−	27.3062i	−0.370460	−	1.52885i
$320$	1.77806	−	3.07970i	0.0993967	−	0.172160i
$321$	−26.6170	+	11.8506i	−1.48561	+	0.661438i
$322$	−2.88714	+	8.88570i	−0.160894	+	0.495180i
$323$	−12.0976	+	12.0574i	−0.673130	+	0.670891i
$324$	8.96936	−	6.51662i	0.498298	−	0.362035i
$325$	−1.15240	−	10.9643i	−0.0639235	−	0.608191i
$326$	−8.53336	−	1.81382i	−0.472619	−	0.100458i
$327$	17.8730	−	3.79902i	0.988378	−	0.210086i
$328$	7.21671	−	3.21309i	0.398476	−	0.177413i
$329$	−13.2845	−	23.0094i	−0.732397	−	1.26855i
$330$	−14.5710	−	18.9066i	−0.802108	−	1.04077i
$331$	−5.57872			−0.306634			−0.153317	−	0.988177i	$-0.548996\pi$
$331$	−5.57872			−0.306634			−0.153317	+	0.988177i	$0.548996\pi$
$332$	1.45280	−	13.8225i	0.0797327	−	0.758606i
$333$	−11.5374	+	2.45236i	−0.632248	+	0.134389i
$334$	−6.87954	−	21.1731i	−0.376432	−	1.15854i
$335$	−17.3895	+	12.6342i	−0.950090	+	0.690281i
$336$	6.53300	+	2.90868i	0.356404	+	0.158681i
$337$	2.90292	+	0.617035i	0.158132	+	0.0336120i	0.286297	−	0.958141i	$-0.407575\pi$
$337$	2.90292	+	0.617035i	0.158132	+	0.0336120i	−0.128165	+	0.991753i	$0.540909\pi$
$338$	−10.6823	+	2.27059i	−0.581041	+	0.123504i
$339$	21.7495	−	9.68348i	1.18127	−	0.525934i
$340$	6.96728	−	12.0677i	0.377854	−	0.654462i
$341$	14.8867	−	5.30704i	0.806159	−	0.287392i
$342$	−2.60847	+	4.00209i	−0.141050	+	0.216408i
$343$	4.32904	+	3.14523i	0.233746	+	0.169827i
$344$	−1.19667	−	1.32904i	−0.0645203	−	0.0716571i
$345$	18.6139	+	3.95651i	1.00214	+	0.213012i
$346$	11.9742	+	5.33125i	0.643736	+	0.286610i
$347$	−0.184103	−	1.75162i	−0.00988317	−	0.0940321i	0.988468	−	0.151428i	$-0.0483871\pi$
$347$	−0.184103	−	1.75162i	−0.00988317	−	0.0940321i	−0.998352	+	0.0573955i	$0.981720\pi$
$348$	11.4721	−	12.7410i	0.614968	−	0.682992i
$349$	−2.78704	+	8.57763i	−0.149187	+	0.459150i	−0.997526	−	0.0703037i	$-0.977603\pi$
$349$	−2.78704	+	8.57763i	−0.149187	+	0.459150i	0.848339	+	0.529454i	$0.177603\pi$
$350$	21.8574	+	15.8803i	1.16833	+	0.848840i
$351$	2.77817	+	4.81192i	0.148287	+	0.256841i
$352$	3.30694	+	0.253240i	0.176261	+	0.0134978i
$353$	−21.6566			−1.15267			−0.576333	−	0.817215i	$-0.695517\pi$
$353$	−21.6566			−1.15267			−0.576333	+	0.817215i	$0.695517\pi$
$354$	−7.78704	−	5.65761i	−0.413876	−	0.300699i
$355$	−12.2317	+	2.59993i	−0.649191	+	0.137990i
$356$	0.323834	+	0.0688330i	0.0171632	+	0.00364814i
$357$	25.5994	+	11.3976i	1.35486	+	0.603223i
$358$	2.52584	+	24.0318i	0.133495	+	1.27012i
$359$	−10.0059	−	2.12683i	−0.528093	−	0.112250i	−0.0638533	−	0.997959i	$-0.520339\pi$
$359$	−10.0059	−	2.12683i	−0.528093	−	0.112250i	−0.464240	+	0.885710i	$0.653672\pi$
$360$	1.20434	−	3.70657i	0.0634742	−	0.195354i
$361$	−4.01221	+	18.5715i	−0.211169	+	0.977450i
$362$	0.797987			0.0419413
$363$	10.0230	−	19.8783i	0.526073	−	1.04334i
$364$	−2.54746	+	4.41233i	−0.133523	+	0.231269i
$365$	−0.866693	+	8.24603i	−0.0453648	+	0.431617i
$366$	15.3750	+	17.0757i	0.803665	+	0.892561i
$367$	−8.23761	+	9.14879i	−0.430000	+	0.477563i	−0.918738	−	0.394867i	$-0.870791\pi$
$367$	−8.23761	+	9.14879i	−0.430000	+	0.477563i	0.488738	+	0.872430i	$0.337457\pi$
$368$	−2.13913	+	1.55417i	−0.111510	+	0.0810167i
$369$	7.00415	−	5.08882i	0.364622	−	0.264913i
$370$	25.6097	−	28.4424i	1.33138	−	1.47865i
$371$	−12.3491	+	2.62489i	−0.641135	+	0.136277i
$372$	7.80217	+	5.66861i	0.404524	+	0.293904i
$373$	−1.16088			−0.0601079			−0.0300540	−	0.999548i	$-0.509568\pi$
$373$	−1.16088			−0.0601079			−0.0300540	+	0.999548i	$0.509568\pi$
$374$	12.9581	+	0.992314i	0.670050	+	0.0513113i
$375$	9.52179	−	16.4922i	0.491703	−	0.851655i
$376$	0.785966	−	7.47796i	0.0405331	−	0.385647i
$377$	8.17329	+	9.07736i	0.420946	+	0.467508i
$378$	−13.3188	−	2.83101i	−0.685047	−	0.145611i
$379$	−3.80431	+	2.76399i	−0.195414	+	0.141977i	−0.681190	−	0.732107i	$-0.738537\pi$
$379$	−3.80431	+	2.76399i	−0.195414	+	0.141977i	0.485776	+	0.874084i	$0.338537\pi$
$380$	−0.785466	−	15.4809i	−0.0402936	−	0.794152i
$381$	8.52666	+	26.2423i	0.436834	+	1.34444i
$382$	−14.5186	−	16.1246i	−0.742838	−	0.825005i
$383$	8.29869	−	3.69481i	0.424043	−	0.188796i	−0.183609	−	0.982999i	$-0.558778\pi$
$383$	8.29869	−	3.69481i	0.424043	−	0.188796i	0.607652	+	0.794203i	$0.292111\pi$
$384$	1.01192	+	1.75270i	0.0516394	+	0.0894421i
$385$	−7.50822	+	40.9934i	−0.382654	+	2.08922i
$386$	−11.1814	−	19.3667i	−0.569117	−	0.985739i
$387$	−1.58567	−	1.15205i	−0.0806039	−	0.0585622i
$388$	1.70679	−	5.25295i	0.0866490	−	0.266678i
$389$	22.6054	−	25.1059i	1.14614	−	1.27292i	0.189424	−	0.981895i	$-0.439338\pi$
$389$	22.6054	−	25.1059i	1.14614	−	1.27292i	0.956716	−	0.291022i	$-0.0939953\pi$
$390$	9.48017	+	4.22084i	0.480047	+	0.213731i
$391$	−8.38211	+	6.08996i	−0.423902	+	0.307983i
$392$	−1.69516	−	5.21715i	−0.0856183	−	0.263506i
$393$	−17.3132	+	3.68004i	−0.873336	+	0.185633i
$394$	22.3725	−	9.96090i	1.12711	−	0.501823i
$395$	−11.0210	−	19.0890i	−0.554527	−	0.960469i
$396$	3.60273	−	0.482047i	0.181044	−	0.0242238i
$397$	12.4975	−	21.6464i	0.627234	−	1.08640i	−0.360870	−	0.932616i	$-0.617520\pi$
$397$	12.4975	−	21.6464i	0.627234	−	1.08640i	0.988104	−	0.153785i	$-0.0491464\pi$
$398$	−4.59395	−	3.33770i	−0.230274	−	0.167304i
$399$	30.7959	−	4.82503i	1.54172	−	0.241554i
$400$	2.36275	+	7.27181i	0.118138	+	0.363590i
$401$	2.72921	+	25.9667i	0.136290	+	1.29671i	0.822272	+	0.569095i	$0.192706\pi$
$401$	2.72921	+	25.9667i	0.136290	+	1.29671i	−0.685981	+	0.727619i	$0.740627\pi$
$402$	−1.27869	−	12.1659i	−0.0637751	−	0.606779i
$403$	−4.59751	+	5.10606i	−0.229019	+	0.254351i
$404$	−2.94856	−	3.27471i	−0.146696	−	0.162923i
$405$	−4.12112	+	39.2099i	−0.204780	+	1.94835i
$406$	−29.9337			−1.48558
$407$	34.2468	+	10.0658i	1.69755	+	0.498943i
$408$	3.96518	+	6.86790i	0.196306	+	0.340012i
$409$	1.67710	−	15.9566i	0.0829273	−	0.789001i	−0.871467	−	0.490453i	$-0.836831\pi$
$409$	1.67710	−	15.9566i	0.0829273	−	0.789001i	0.954395	−	0.298547i	$-0.0965021\pi$
$410$	−8.68097	+	26.7173i	−0.428723	+	1.31947i
$411$	−12.9570	−	39.8776i	−0.639123	−	1.96702i
$412$	−9.51010	−	4.23417i	−0.468529	−	0.208603i
$413$	1.75662	+	16.7131i	0.0864376	+	0.822399i
$414$	−1.93901	+	2.15349i	−0.0952970	+	0.105838i
$415$	33.0719	+	36.7300i	1.62343	+	1.80301i
$416$	−1.31723	+	0.586469i	−0.0645825	+	0.0287540i
$417$	−19.5940			−0.959522
$418$	12.7018	−	6.90386i	0.621267	−	0.337679i
$419$	−8.13292			−0.397319			−0.198659	−	0.980069i	$-0.563659\pi$
$419$	−8.13292			−0.397319			−0.198659	+	0.980069i	$0.563659\pi$
$420$	−23.2322	+	10.3436i	−1.13361	+	0.504717i
$421$	10.7704	+	11.9618i	0.524919	+	0.582981i	0.946051	−	0.324018i	$-0.105034\pi$
$421$	10.7704	+	11.9618i	0.524919	+	0.582981i	−0.421132	+	0.906999i	$0.638367\pi$
$422$	−0.243837	+	0.270808i	−0.0118698	+	0.0131827i
$423$	−0.861376	−	8.19544i	−0.0418815	−	0.398476i
$424$	−3.26405	−	1.45325i	−0.158516	−	0.0705760i
$425$	9.25837	+	28.4943i	0.449097	+	1.38218i
$426$	2.19920	−	6.76844i	0.106552	−	0.327932i
$427$	4.19341	−	39.8977i	0.202934	−	1.93078i
$428$	7.19815	+	12.4676i	0.347936	+	0.602643i
$429$	0.273772	+	9.67456i	0.0132178	+	0.467092i
$430$	6.35978			0.306696
$431$	−0.434469	+	4.13370i	−0.0209276	+	0.199113i	−0.999990	−	0.00444682i	$-0.998585\pi$
$431$	−0.434469	+	4.13370i	−0.0209276	+	0.199113i	0.979062	+	0.203560i	$0.0652512\pi$
$432$	−2.57850	−	2.86372i	−0.124058	−	0.137781i
$433$	2.93514	−	3.25981i	0.141054	−	0.156656i	−0.668478	−	0.743732i	$-0.733054\pi$
$433$	2.93514	−	3.25981i	0.141054	−	0.156656i	0.809532	+	0.587075i	$0.199721\pi$
$434$	−1.76003	−	16.7456i	−0.0844842	−	0.803814i
$435$	6.37299	+	60.6349i	0.305561	+	2.90722i
$436$	−2.78996	−	8.58661i	−0.133615	−	0.411224i
$437$	−4.14825	+	10.7530i	−0.198438	+	0.514386i
$438$	−3.81758	−	2.77364i	−0.182411	−	0.132529i
$439$	−9.28223	+	16.0773i	−0.443017	+	0.767327i	−0.997912	−	0.0645930i	$-0.979425\pi$
$439$	−9.28223	+	16.0773i	−0.443017	+	0.767327i	0.554895	+	0.831920i	$0.312758\pi$
$440$	−8.53815	+	8.13672i	−0.407040	+	0.387903i
$441$	−3.00598	−	5.20651i	−0.143142	−	0.247929i
$442$	−5.16153	+	2.29806i	−0.245509	+	0.109308i
$443$	27.8875	−	5.92767i	1.32498	−	0.281632i	0.509523	−	0.860457i	$-0.329822\pi$
$443$	27.8875	−	5.92767i	1.32498	−	0.281632i	0.815452	+	0.578825i	$0.196488\pi$
$444$	6.73094	+	20.7157i	0.319436	+	0.983124i
$445$	−0.952472	+	0.692012i	−0.0451515	+	0.0328045i
$446$	18.3815	+	8.18398i	0.870390	+	0.387523i
$447$	18.6333	−	20.6944i	0.881327	−	0.978813i
$448$	1.09191	−	3.36056i	0.0515880	−	0.158772i
$449$	15.4243	+	11.2064i	0.727917	+	0.528863i	0.888904	−	0.458094i	$-0.151468\pi$
$449$	15.4243	+	11.2064i	0.727917	+	0.528863i	−0.160987	+	0.986957i	$0.551468\pi$
$450$	4.18982	+	7.25698i	0.197510	+	0.342097i
$451$	−25.9688	+	3.47464i	−1.22282	+	0.163614i
$452$	−5.88181	−	10.1876i	−0.276657	−	0.479184i
$453$	−11.6894	+	5.20444i	−0.549214	+	0.244526i
$454$	−12.2148	−	13.5659i	−0.573269	−	0.636680i
$455$	−5.59882	−	17.2314i	−0.262477	−	0.807820i
$456$	7.85354	+	4.01807i	0.367776	+	0.188163i
$457$	15.0773	−	10.9543i	0.705286	−	0.512420i	−0.176364	−	0.984325i	$-0.556434\pi$
$457$	15.0773	−	10.9543i	0.705286	−	0.512420i	0.881649	+	0.471905i	$0.156434\pi$
$458$	20.0681	+	4.26561i	0.937721	+	0.199319i
$459$	−10.1038	−	11.2214i	−0.471604	−	0.523769i
$460$	0.982859	−	9.35128i	0.0458260	−	0.436006i
$461$	3.04252	−	5.26980i	0.141704	−	0.245439i	−0.786434	−	0.617674i	$-0.788075\pi$
$461$	3.04252	−	5.26980i	0.141704	−	0.245439i	0.928138	+	0.372235i	$0.121408\pi$
$462$	−18.0678	−	15.3655i	−0.840591	−	0.714869i
$463$	13.6584			0.634762			0.317381	−	0.948298i	$-0.397197\pi$
$463$	13.6584			0.634762			0.317381	+	0.948298i	$0.397197\pi$
$464$	−6.85350	−	4.97936i	−0.318166	−	0.231161i
$465$	−33.5459	+	7.13040i	−1.55565	+	0.330664i
$466$	−6.27701	+	6.97133i	−0.290777	+	0.322941i
$467$	3.65790	−	2.65762i	0.169267	−	0.122980i	−0.499926	−	0.866068i	$-0.666640\pi$
$467$	3.65790	−	2.65762i	0.169267	−	0.122980i	0.669194	+	0.743088i	$0.266640\pi$
$468$	−1.27843	+	0.928837i	−0.0590956	+	0.0429355i
$469$	−14.2912	+	15.8720i	−0.659906	+	0.732900i
$470$	17.8919	+	19.8710i	0.825293	+	0.916580i
$471$	2.41191	−	22.9478i	0.111135	−	1.05738i
$472$	−2.37798	+	4.11878i	−0.109455	+	0.189582i
$473$	2.56485	+	5.34824i	0.117932	+	0.245912i
$474$	12.5444			0.576185
$475$	25.8660	+	21.0173i	1.18681	+	0.964338i
$476$	4.27862	−	13.1682i	0.196110	−	0.603566i
$477$	−3.83019	−	0.814132i	−0.175372	−	0.0372765i
$478$	−0.277743	−	2.64255i	−0.0127037	−	0.120867i
$479$	6.91050	+	3.07675i	0.315749	+	0.140580i	0.558491	−	0.829510i	$-0.311380\pi$
$479$	6.91050	+	3.07675i	0.315749	+	0.140580i	−0.242743	+	0.970091i	$0.578047\pi$
$480$	−7.03977	−	1.49635i	−0.321320	−	0.0682987i
$481$	−15.1793	+	3.22646i	−0.692117	+	0.147114i
$482$	−8.70630	−	6.32550i	−0.396561	−	0.288119i
$483$	18.9087			0.860377
$484$	−10.2859	−	3.89866i	−0.467542	−	0.177212i
$485$	9.82074	+	17.0100i	0.445937	+	0.772385i
$486$	−8.79993	−	6.39352i	−0.399173	−	0.290016i
$487$	9.18957	−	28.2826i	0.416419	−	1.28161i	−0.494556	−	0.869146i	$-0.664669\pi$
$487$	9.18957	−	28.2826i	0.416419	−	1.28161i	0.910975	−	0.412461i	$-0.135331\pi$
$488$	7.59694	−	8.43726i	0.343897	−	0.381937i
$489$	1.84556	+	17.5593i	0.0834589	+	0.794059i
$490$	17.8211	+	7.93447i	0.805075	+	0.358443i
$491$	−17.9459	−	3.81452i	−0.809887	−	0.172147i	−0.215685	−	0.976463i	$-0.569198\pi$
$491$	−17.9459	−	3.81452i	−0.809887	−	0.172147i	−0.594201	+	0.804316i	$0.702532\pi$
$492$	−10.6979	−	11.8812i	−0.482297	−	0.535645i
$493$	−26.8552	−	19.5114i	−1.20950	−	0.878751i
$494$	−3.43186	+	5.26537i	−0.154406	+	0.236900i
$495$	−7.29884	+	10.6680i	−0.328058	+	0.479493i
$496$	2.38260	−	4.12678i	0.106982	−	0.185298i
$497$	−11.3512	+	5.05387i	−0.509170	+	0.226697i
$498$	−27.5139	+	5.84826i	−1.23293	+	0.262067i
$499$	−42.4301	−	9.01879i	−1.89943	−	0.403736i	−0.899951	−	0.435992i	$-0.856398\pi$
$499$	−42.4301	−	9.01879i	−1.89943	−	0.403736i	−0.999480	+	0.0322552i	$0.989731\pi$
$500$	−8.59611	−	3.82723i	−0.384430	−	0.171159i
$501$	−36.4512	+	26.4833i	−1.62852	+	1.18319i
$502$	4.70827	+	14.4906i	0.210141	+	0.646746i
$503$	−19.5759	+	4.16098i	−0.872844	+	0.185529i	−0.622492	−	0.782626i	$-0.713880\pi$
$503$	−19.5759	+	4.16098i	−0.872844	+	0.185529i	−0.250352	+	0.968155i	$0.580546\pi$
$504$	0.404789	−	3.85131i	0.0180307	−	0.171551i
$505$	15.6703			0.697318
$506$	8.26032	−	2.94477i	0.367216	−	0.130911i
$507$	11.0512	+	19.1412i	0.490799	+	0.850089i
$508$	12.4552	−	5.54540i	0.552609	−	0.246037i
$509$	3.03626	−	0.645377i	0.134580	−	0.0286058i	−0.140129	−	0.990133i	$-0.544752\pi$
$509$	3.03626	−	0.645377i	0.134580	−	0.0286058i	0.274709	+	0.961527i	$0.411418\pi$
$510$	−27.5851	−	5.86340i	−1.22149	−	0.259636i
$511$	0.861179	+	8.19357i	0.0380963	+	0.362462i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−16.2174	−	4.37441i	−0.716018	−	0.193135i
$514$	3.41157	−	10.4997i	0.150478	−	0.463123i
$515$	33.8191	−	15.0572i	1.49025	−	0.663501i
$516$	−1.80972	+	3.13453i	−0.0796686	+	0.137990i
$517$	−9.49479	+	23.0600i	−0.417580	+	1.01418i
$518$	19.0148	−	32.9346i	0.835462	−	1.44706i
$519$	2.77286	−	26.3820i	0.121715	−	1.15804i
$520$	1.58450	−	4.87658i	0.0694847	−	0.213852i
$521$	−6.99362	−	21.5241i	−0.306396	−	0.942990i	−0.979153	−	0.203126i	$-0.934890\pi$
$521$	−6.99362	−	21.5241i	−0.306396	−	0.942990i	0.672757	−	0.739864i	$-0.265110\pi$
$522$	−8.48152	−	3.77622i	−0.371226	−	0.165280i
$523$	−36.1336	−	16.0877i	−1.58001	−	0.703466i	−0.585754	−	0.810489i	$-0.699201\pi$
$523$	−36.1336	−	16.0877i	−1.58001	−	0.703466i	−0.994257	+	0.107023i	$0.965868\pi$
$524$	2.70258	+	8.31768i	0.118063	+	0.363360i
$525$	16.8967	−	52.0026i	0.737431	−	2.26958i
$526$	−2.71935	+	25.8729i	−0.118569	+	1.12811i
$527$	9.33613	−	16.1707i	0.406688	−	0.704405i
$528$	−1.58074	−	6.52355i	−0.0687927	−	0.283901i
$529$	8.00434	−	13.8639i	0.348015	−	0.602779i
$530$	11.6074	−	5.16793i	0.504192	−	0.224481i
$531$	−1.61068	+	4.95716i	−0.0698975	+	0.215122i
$532$	−3.96159	−	14.8840i	−0.171757	−	0.645303i
$533$	9.21506	−	6.69514i	0.399149	−	0.289999i
$534$	−0.0700373	−	0.666360i	−0.00303081	−	0.0288362i
$535$	−50.0764	−	10.6441i	−2.16499	−	0.460183i
$536$	−5.91230	+	1.25670i	−0.255373	+	0.0542811i
$537$	44.6765	−	19.8913i	1.92793	−	0.858371i
$538$	−2.99262	−	5.18338i	−0.129021	−	0.223471i
$539$	0.514644	+	18.1865i	0.0221673	+	0.783349i
$540$	13.7036			0.589707
$541$	−1.61714	+	15.3860i	−0.0695261	+	0.661497i	0.903149	+	0.429327i	$0.141249\pi$
$541$	−1.61714	+	15.3860i	−0.0695261	+	0.661497i	−0.972675	+	0.232170i	$0.925417\pi$
$542$	−11.7681	+	2.50139i	−0.505483	+	0.107444i
$543$	−0.499063	−	1.53596i	−0.0214168	−	0.0659142i
$544$	3.17011	−	2.30322i	0.135917	−	0.0987496i
$545$	29.3307	+	13.0589i	1.25639	+	0.559381i
$546$	10.0860	+	2.14384i	0.431641	+	0.0917480i
$547$	−18.7141	+	3.97780i	−0.800156	+	0.170078i	−0.589803	−	0.807547i	$-0.700795\pi$
$547$	−18.7141	+	3.97780i	−0.800156	+	0.170078i	−0.210353	+	0.977626i	$0.567461\pi$
$548$	−18.9268	+	8.42673i	−0.808511	+	0.359972i
$549$	6.22138	−	10.7757i	0.265522	−	0.459898i
$550$	−0.717325	−	25.3489i	−0.0305868	−	1.08088i
$551$	−36.8720	−	1.99397i	−1.57080	−	0.0849458i
$552$	4.32927	+	3.14540i	0.184266	+	0.133877i
$553$	−14.6552	−	16.2762i	−0.623201	−	0.692135i
$554$	6.34906	+	1.34953i	0.269746	+	0.0573362i
$555$	−70.7621	−	31.5053i	−3.00368	−	1.33733i
$556$	1.01200	+	9.62853i	0.0429183	+	0.408341i
$557$	13.3524	−	14.8294i	0.565761	−	0.628342i	−0.390589	−	0.920565i	$-0.627729\pi$
$557$	13.3524	−	14.8294i	0.565761	−	0.628342i	0.956350	+	0.292224i	$0.0943952\pi$
$558$	1.61381	−	4.96679i	0.0683180	−	0.210261i
$559$	−2.08619	−	1.51571i	−0.0882365	−	0.0641076i
$560$	6.28279	+	10.8821i	0.265496	+	0.459853i
$561$	−6.19406	−	25.5623i	−0.261513	−	1.07924i
$562$	−9.10557			−0.384095
$563$	4.09391	+	2.97440i	0.172538	+	0.125356i	0.670703	−	0.741726i	$-0.265993\pi$
$563$	4.09391	+	2.97440i	0.172538	+	0.125356i	−0.498165	+	0.867082i	$0.665993\pi$
$564$	−14.8851	+	3.16392i	−0.626774	+	0.133225i
$565$	40.9188	+	8.69755i	1.72147	+	0.365909i
$566$	−6.76509	−	3.01201i	−0.284358	−	0.126604i
$567$	4.09491	+	38.9604i	0.171970	+	1.63618i
$568$	−3.43961	−	0.731113i	−0.144323	−	0.0306768i
$569$	3.15857	−	9.72108i	0.132414	−	0.407529i	−0.862765	−	0.505606i	$-0.831269\pi$
$569$	3.15857	−	9.72108i	0.132414	−	0.407529i	0.995179	+	0.0980768i	$0.0312691\pi$
$570$	−29.3062	+	11.1936i	−1.22750	+	0.468850i
$571$	−23.4669			−0.982061			−0.491030	−	0.871142i	$-0.663380\pi$
$571$	−23.4669			−0.982061			−0.491030	+	0.871142i	$0.663380\pi$
$572$	4.73996	−	0.634208i	0.198188	−	0.0265176i
$573$	−21.9564	+	38.0297i	−0.917244	+	1.58871i
$574$	−2.91776	+	27.7606i	−0.121785	+	1.15870i
$575$	13.5278	+	15.0241i	0.564147	+	0.626549i
$576$	0.733331	−	0.814446i	0.0305555	−	0.0339353i
$577$	33.1644	−	24.0953i	1.38065	−	1.00310i	0.383833	−	0.923403i	$-0.374604\pi$
$577$	33.1644	−	24.0953i	1.38065	−	1.00310i	0.996819	−	0.0796996i	$-0.0253961\pi$
$578$	−1.33133	+	0.967267i	−0.0553760	+	0.0402330i
$579$	−30.2840	+	33.6338i	−1.25856	+	1.39777i
$580$	29.4670	−	6.26340i	1.22355	−	0.260074i
$581$	39.7314	+	28.8666i	1.64834	+	1.19759i
$582$	−11.1783			−0.463354
$583$	9.02713	+	7.67701i	0.373866	+	0.317949i
$584$	−1.16580	+	2.01922i	−0.0482411	+	0.0835560i
$585$	0.587398	−	5.58872i	0.0242859	−	0.231065i
$586$	21.3427	+	23.7035i	0.881658	+	0.979181i
$587$	−10.0105	−	2.12779i	−0.413177	−	0.0878235i	−0.00336686	−	0.999994i	$-0.501072\pi$
$587$	−10.0105	−	2.12779i	−0.413177	−	0.0878235i	−0.409810	+	0.912171i	$0.634405\pi$
$588$	−8.98177	+	6.52564i	−0.370402	+	0.269113i
$589$	−1.05252	−	20.7443i	−0.0433684	−	0.854755i
$590$	−5.22633	−	16.0850i	−0.215165	−	0.662209i
$591$	−33.1645	−	36.8329i	−1.36420	−	1.51510i
$592$	9.83210	−	4.37754i	0.404097	−	0.179916i
$593$	0.0569116	+	0.0985737i	0.00233708	+	0.00404794i	0.867192	−	0.497975i	$-0.165923\pi$
$593$	0.0569116	+	0.0985737i	0.00233708	+	0.00404794i	−0.864855	+	0.502023i	$0.832589\pi$
$594$	5.52654	+	11.5240i	0.226757	+	0.472835i
$595$	24.6189	+	42.6412i	1.00928	+	1.74812i
$596$	−11.1317	−	8.08764i	−0.455971	−	0.331282i
$597$	−3.55131	+	10.9298i	−0.145345	+	0.447327i
$598$	−2.55107	+	2.83325i	−0.104321	+	0.115860i
$599$	26.9884	+	12.0160i	1.10272	+	0.490960i	0.875663	−	0.482922i	$-0.160425\pi$
$599$	26.9884	+	12.0160i	1.10272	+	0.490960i	0.227052	+	0.973883i	$0.427091\pi$
$600$	12.5190	−	9.09561i	0.511087	−	0.371327i
$601$	6.17234	+	18.9965i	0.251775	+	0.774883i	0.994448	+	0.105229i	$0.0335577\pi$
$601$	6.17234	+	18.9965i	0.251775	+	0.774883i	−0.742673	+	0.669654i	$0.766442\pi$
$602$	6.18123	−	1.31386i	0.251928	−	0.0535490i
$603$	−6.05162	+	2.69435i	−0.246441	+	0.109723i
$604$	3.16121	+	5.47538i	0.128628	+	0.222790i
$605$	34.7786	−	17.9059i	1.41395	−	0.727978i
$606$	−4.45909	+	7.72337i	−0.181138	+	0.313741i
$607$	−13.8488	−	10.0617i	−0.562105	−	0.408393i	0.270124	−	0.962826i	$-0.412935\pi$
$607$	−13.8488	−	10.0617i	−0.562105	−	0.408393i	−0.832229	+	0.554433i	$0.812935\pi$
$608$	1.56887	−	4.06678i	0.0636259	−	0.164930i
$609$	18.7206	+	57.6160i	0.758596	+	2.33472i
$610$	4.22026	+	40.1531i	0.170873	+	1.62575i
$611$	−1.13327	−	10.7824i	−0.0458474	−	0.436209i
$612$	2.87353	−	3.19138i	0.116156	−	0.129004i
$613$	2.61904	+	2.90874i	0.105782	+	0.117483i	0.793711	−	0.608296i	$-0.208146\pi$
$613$	2.61904	+	2.90874i	0.105782	+	0.117483i	−0.687929	+	0.725778i	$0.741480\pi$
$614$	−0.417301	+	3.97035i	−0.0168409	+	0.160230i
$615$	56.8543			2.29259
$616$	−6.61749	+	9.67217i	−0.266626	+	0.389703i
$617$	0.547197	+	0.947774i	0.0220293	+	0.0381559i	0.876830	−	0.480801i	$-0.159654\pi$
$617$	0.547197	+	0.947774i	0.0220293	+	0.0381559i	−0.854801	+	0.518957i	$0.826321\pi$
$618$	−2.20225	+	20.9530i	−0.0885875	+	0.842854i
$619$	6.52816	−	20.0916i	0.262389	−	0.807551i	−0.729894	−	0.683560i	$-0.760431\pi$
$619$	6.52816	−	20.0916i	0.262389	−	0.807551i	0.992283	−	0.123991i	$-0.0395693\pi$
$620$	5.23649	+	16.1163i	0.210302	+	0.647244i
$621$	−9.30821	−	4.14428i	−0.373526	−	0.166304i
$622$	−2.64536	−	25.1689i	−0.106069	−	1.00918i
$623$	−0.782770	+	0.869354i	−0.0313610	+	0.0348299i
$624$	1.95263	+	2.16861i	0.0781677	+	0.0868140i
$625$	−4.35614	+	1.93948i	−0.174245	+	0.0775791i
$626$	27.6862			1.10656
$627$	−21.2322	−	20.1307i	−0.847934	−	0.803942i
$628$	−11.4012			−0.454957
$629$	38.5268	−	17.1532i	1.53616	−	0.683944i
$630$	9.21473	+	10.2340i	0.367124	+	0.407732i
$631$	−2.48549	+	2.76042i	−0.0989460	+	0.109891i	−0.790584	−	0.612354i	$-0.790223\pi$
$631$	−2.48549	+	2.76042i	−0.0989460	+	0.109891i	0.691638	+	0.722245i	$0.256889\pi$
$632$	−0.647901	−	6.16437i	−0.0257721	−	0.245205i
$633$	0.673745	+	0.299971i	0.0267790	+	0.0119228i
$634$	2.33848	+	7.19710i	0.0928728	+	0.285833i
$635$	−14.9823	+	46.1108i	−0.594555	+	1.82985i
$636$	−0.755855	+	7.19148i	−0.0299716	+	0.285161i
$637$	−3.95484	−	6.84999i	−0.156697	−	0.271406i
$638$	17.1510	+	22.2542i	0.679015	+	0.881053i
$639$	−3.85385			−0.152456
$640$	−0.371716	+	3.53664i	−0.0146934	+	0.139798i
$641$	2.14187	+	2.37879i	0.0845988	+	0.0939565i	0.783958	−	0.620814i	$-0.213198\pi$
$641$	2.14187	+	2.37879i	0.0845988	+	0.0939565i	−0.699359	+	0.714771i	$0.746531\pi$
$642$	19.4957	−	21.6522i	0.769435	−	0.854544i
$643$	2.09158	+	19.9001i	0.0824838	+	0.784781i	0.955082	+	0.296342i	$0.0957669\pi$
$643$	2.09158	+	19.9001i	0.0824838	+	0.784781i	−0.872598	+	0.488439i	$0.837566\pi$
$644$	−0.976607	−	9.29179i	−0.0384837	−	0.366148i
$645$	−3.97742	−	12.2412i	−0.156611	−	0.481998i
$646$	6.14755	−	15.9355i	0.241872	−	0.626975i
$647$	−22.4459	−	16.3079i	−0.882440	−	0.641130i	0.0514556	−	0.998675i	$-0.483614\pi$
$647$	−22.4459	−	16.3079i	−0.882440	−	0.641130i	−0.933896	+	0.357545i	$0.883614\pi$
$648$	−5.54337	+	9.60140i	−0.217764	+	0.377179i
$649$	11.4189	−	10.8820i	0.448231	−	0.427157i
$650$	5.51236	+	9.54769i	0.216213	+	0.374491i
$651$	−31.1310	+	13.8604i	−1.22012	+	0.543233i
$652$	8.53336	−	1.81382i	0.334192	−	0.0710347i
$653$	13.5386	+	41.6676i	0.529807	+	1.63058i	0.754609	+	0.656174i	$0.227826\pi$
$653$	13.5386	+	41.6676i	0.529807	+	1.63058i	−0.224802	+	0.974404i	$0.572174\pi$
$654$	−14.7826	+	10.7402i	−0.578045	+	0.419974i
$655$	−28.4121	−	12.6499i	−1.11015	−	0.494272i
$656$	−5.28591	+	5.87060i	−0.206380	+	0.229208i
$657$	−0.789633	+	2.43024i	−0.0308065	+	0.0948127i
$658$	21.4947	+	15.6168i	0.837952	+	0.608808i
$659$	19.5540	+	33.8685i	0.761715	+	1.31933i	0.941966	+	0.335709i	$0.108976\pi$
$659$	19.5540	+	33.8685i	0.761715	+	1.31933i	−0.180251	+	0.983621i	$0.557691\pi$
$660$	21.0013	+	11.3454i	0.817473	+	0.441620i
$661$	10.4741	+	18.1416i	0.407393	+	0.705626i	0.994597	−	0.103813i	$-0.0331045\pi$
$661$	10.4741	+	18.1416i	0.407393	+	0.705626i	−0.587203	+	0.809439i	$0.699771\pi$
$662$	5.09641	−	2.26907i	0.198078	−	0.0881899i
$663$	7.65131	+	8.49764i	0.297152	+	0.330021i
$664$	4.29490	+	13.2183i	0.166675	+	0.512971i
$665$	48.7608	+	24.9473i	1.89086	+	0.967413i
$666$	9.54252	−	6.93305i	0.369765	−	0.268650i
$667$	−21.9098	−	4.65707i	−0.848351	−	0.180323i
$668$	14.8966	+	16.5444i	0.576368	+	0.640121i
$669$	4.25660	−	40.4988i	0.164570	−	1.56578i
$670$	10.7473	−	18.6149i	0.415204	−	0.719155i
$671$	−32.0647	+	19.7425i	−1.23784	+	0.762150i
$672$	−7.15126			−0.275866
$673$	−7.79703	−	5.66488i	−0.300554	−	0.218365i	0.427279	−	0.904120i	$-0.359472\pi$
$673$	−7.79703	−	5.66488i	−0.300554	−	0.218365i	−0.727833	+	0.685755i	$0.759472\pi$
$674$	−2.90292	+	0.617035i	−0.111816	+	0.0237673i
$675$	−19.7153	+	21.8961i	−0.758842	+	0.842779i
$676$	8.83524	−	6.41918i	0.339817	−	0.246891i
$677$	−31.5586	+	22.9286i	−1.21289	+	0.881219i	−0.995490	−	0.0948630i	$-0.969759\pi$
$677$	−31.5586	+	22.9286i	−1.21289	+	0.881219i	−0.217403	+	0.976082i	$0.569759\pi$
$678$	−15.9305	+	17.6926i	−0.611807	+	0.679480i
$679$	13.0591	+	14.5036i	0.501162	+	0.556597i
$680$	−1.45656	+	13.8582i	−0.0558565	+	0.531439i
$681$	−18.4724	+	31.9951i	−0.707863	+	1.22605i
$682$	−11.4411	+	10.9032i	−0.438102	+	0.417504i
$683$	−30.7704			−1.17740			−0.588699	−	0.808352i	$-0.700360\pi$
$683$	−30.7704			−1.17740			−0.588699	+	0.808352i	$0.700360\pi$
$684$	0.755163	−	4.71705i	0.0288744	−	0.180361i
$685$	22.7670	−	70.0696i	0.869882	−	2.67722i
$686$	−5.23406	−	1.11253i	−0.199837	−	0.0424767i
$687$	−4.34024	−	41.2946i	−0.165590	−	1.57549i
$688$	1.63379	+	0.727408i	0.0622875	+	0.0277322i
$689$	−5.03921	−	1.07112i	−0.191979	−	0.0408063i
$690$	−18.6139	+	3.95651i	−0.708620	+	0.150622i
$691$	−30.1282	−	21.8894i	−1.14613	−	0.832714i	−0.158171	−	0.987412i	$-0.550560\pi$
$691$	−30.1282	−	21.8894i	−1.14613	−	0.832714i	−0.987962	+	0.154698i	$0.950560\pi$
$692$	−13.1074			−0.498268
$693$	−4.89002	+	11.8764i	−0.185757	+	0.451147i
$694$	0.880636	+	1.52531i	0.0334285	+	0.0578998i
$695$	−27.8535	−	20.2368i	−1.05654	−	0.767625i
$696$	−5.29802	+	16.3056i	−0.200821	+	0.618064i
$697$	−20.7127	+	23.0038i	−0.784549	+	0.871329i
$698$	−0.942748	−	8.96965i	−0.0356835	−	0.339506i
$699$	17.3440	+	7.72205i	0.656010	+	0.292075i
$700$	−26.4269	−	5.61721i	−0.998842	−	0.212310i
$701$	−8.39164	−	9.31986i	−0.316948	−	0.352006i	0.563528	−	0.826097i	$-0.309444\pi$
$701$	−8.39164	−	9.31986i	−0.316948	−	0.352006i	−0.880476	+	0.474091i	$0.842777\pi$
$702$	−4.49517	−	3.26593i	−0.169659	−	0.123265i
$703$	25.6161	−	39.3019i	0.966131	−	1.48230i
$704$	−3.12404	+	1.11371i	−0.117742	+	0.0419745i
$705$	27.0578	−	46.8656i	1.01906	−	1.76506i
$706$	19.7843	−	8.80854i	0.744592	−	0.331514i
$707$	15.2303	−	3.23730i	0.572795	−	0.121751i
$708$	9.41497	+	2.00121i	0.353836	+	0.0752102i
$709$	−38.7443	−	17.2501i	−1.45507	−	0.647840i	−0.481547	−	0.876420i	$-0.659925\pi$
$709$	−38.7443	−	17.2501i	−1.45507	−	0.647840i	−0.973525	+	0.228581i	$0.926592\pi$
$710$	10.1167	−	7.35023i	0.379674	−	0.275849i
$711$	−2.09916	−	6.46055i	−0.0787247	−	0.242290i
$712$	−0.323834	+	0.0688330i	−0.0121362	+	0.00257962i
$713$	1.31703	−	12.5307i	0.0493231	−	0.469278i
$714$	−28.0220			−1.04870
$715$	−9.60277	+	14.0355i	−0.359123	+	0.524897i
$716$	−12.0821	−	20.9268i	−0.451529	−	0.782071i
$717$	−4.91265	+	2.18725i	−0.183466	+	0.0816844i
$718$	10.0059	−	2.12683i	0.373418	−	0.0793725i
$719$	5.58863	+	1.18790i	0.208421	+	0.0443012i	0.310939	−	0.950430i	$-0.399357\pi$
$719$	5.58863	+	1.18790i	0.208421	+	0.0443012i	−0.102518	+	0.994731i	$0.532690\pi$
$720$	0.407381	+	3.87597i	0.0151822	+	0.144449i
$721$	29.7590	−	21.6212i	1.10828	−	0.805214i
$722$	−3.88839	−	18.5979i	−0.144711	−	0.692141i
$723$	−6.73032	+	20.7138i	−0.250303	+	0.770354i
$724$	−0.728997	+	0.324570i	−0.0270930	+	0.0120626i
$725$	−32.3862	+	56.0946i	−1.20279	+	2.08330i
$726$	−1.07126	+	22.2365i	−0.0397583	+	0.825274i
$727$	−11.2962	+	19.5657i	−0.418954	+	0.725650i	−0.995835	−	0.0911787i	$-0.970937\pi$
$727$	−11.2962	+	19.5657i	−0.418954	+	0.725650i	0.576880	+	0.816829i	$0.304270\pi$
$728$	0.532564	−	5.06701i	0.0197381	−	0.187796i
$729$	3.47528	−	10.6958i	0.128714	−	0.396141i
$730$	−2.56220	−	7.88564i	−0.0948313	−	0.291861i
$731$	6.40194	+	2.85033i	0.236784	+	0.105423i
$732$	−20.9911	−	9.34584i	−0.775853	−	0.345432i
$733$	1.64104	+	5.05061i	0.0606133	+	0.186549i	0.976778	−	0.214253i	$-0.0687317\pi$
$733$	1.64104	+	5.05061i	0.0606133	+	0.186549i	−0.916165	+	0.400802i	$0.868732\pi$
$734$	3.80428	−	11.7084i	0.140419	−	0.432164i
$735$	4.12683	−	39.2641i	0.152220	−	1.44828i
$736$	1.32206	−	2.28987i	0.0487316	−	0.0844056i
$737$	19.9884	+	1.53068i	0.736284	+	0.0563834i
$738$	−4.32881	+	7.49771i	−0.159346	+	0.275995i
$739$	16.8541	−	7.50393i	0.619988	−	0.276036i	−0.0726098	−	0.997360i	$-0.523133\pi$
$739$	16.8541	−	7.50393i	0.619988	−	0.276036i	0.692598	+	0.721324i	$0.256466\pi$
$740$	−11.8270	+	36.3999i	−0.434770	+	1.33809i
$741$	12.2810	+	3.31263i	0.451155	+	0.121692i
$742$	10.2139	−	7.42080i	0.374962	−	0.272426i
$743$	−4.48069	−	42.6309i	−0.164380	−	1.56398i	−0.696657	−	0.717405i	$-0.745330\pi$
$743$	−4.48069	−	42.6309i	−0.164380	−	1.56398i	0.532276	−	0.846571i	$-0.321337\pi$
$744$	−9.43327	−	2.00510i	−0.345840	−	0.0735106i
$745$	47.8613	−	10.1732i	1.75350	−	0.372718i
$746$	1.06051	−	0.472171i	0.0388282	−	0.0172874i
$747$	7.61605	+	13.1914i	0.278657	+	0.482648i
$748$	−12.2415	+	4.36403i	−0.447592	+	0.159565i
$749$	−50.8694			−1.85873
$750$	−1.99060	+	18.9393i	−0.0726863	+	0.691564i
$751$	42.0642	−	8.94103i	1.53495	−	0.326263i	0.638572	−	0.769562i	$-0.279525\pi$
$751$	42.0642	−	8.94103i	1.53495	−	0.326263i	0.896374	+	0.443299i	$0.146192\pi$
$752$	2.32355	+	7.15114i	0.0847310	+	0.260775i
$753$	24.9468	−	18.1249i	0.909110	−	0.660507i
$754$	−11.1588	−	4.96820i	−0.406378	−	0.180931i
$755$	−21.9920	−	4.67455i	−0.800371	−	0.170124i
$756$	13.3188	−	2.83101i	0.484401	−	0.102963i
$757$	−20.2497	+	9.01576i	−0.735989	+	0.327683i	−0.740272	−	0.672308i	$-0.765303\pi$
$757$	−20.2497	+	9.01576i	−0.735989	+	0.327683i	0.00428331	+	0.999991i	$0.498637\pi$
$758$	2.35119	−	4.07239i	0.0853992	−	0.147916i
$759$	−10.8341	−	14.0577i	−0.393252	−	0.510263i
$760$	7.01420	+	13.8230i	0.254432	+	0.501413i
$761$	−36.8568	−	26.7780i	−1.33606	−	0.970702i	−0.999579	−	0.0290099i	$-0.990765\pi$
$761$	−36.8568	−	26.7780i	−1.33606	−	0.970702i	−0.336477	−	0.941692i	$-0.609235\pi$
$762$	−18.4632	−	20.5055i	−0.668852	−	0.742835i
$763$	31.2051	+	6.63285i	1.12970	+	0.240125i
$764$	19.8219	+	8.82528i	0.717131	+	0.319287i
$765$	1.59631	+	15.1879i	0.0577147	+	0.549118i
$766$	−6.07841	+	6.75076i	−0.219622	+	0.243915i
$767$	−2.11910	+	6.52192i	−0.0765163	+	0.235493i
$768$	−1.63732	−	1.18959i	−0.0590819	−	0.0429255i
$769$	15.6054	+	27.0294i	0.562746	+	0.974704i	0.997255	+	0.0740370i	$0.0235883\pi$
$769$	15.6054	+	27.0294i	0.562746	+	0.974704i	−0.434510	+	0.900667i	$0.643078\pi$
$770$	−9.81442	−	40.5032i	−0.353687	−	1.45963i
$771$	−22.3434			−0.804676
$772$	18.0918	+	13.1445i	0.651139	+	0.473081i
$773$	6.99425	−	1.48667i	0.251566	−	0.0534719i	−0.0804027	−	0.996762i	$-0.525621\pi$
$773$	6.99425	−	1.48667i	0.251566	−	0.0534719i	0.331968	+	0.943291i	$0.392287\pi$
$774$	1.91716	+	0.407505i	0.0689109	+	0.0146475i
$775$	−33.2849	−	14.8194i	−1.19563	−	0.532328i
$776$	0.577340	+	5.49302i	0.0207253	+	0.197188i
$777$	−75.2841	−	16.0021i	−2.70080	−	0.574073i
$778$	−10.4396	+	32.1298i	−0.374278	+	1.15191i
$779$	−5.44328	+	34.0009i	−0.195026	+	1.21821i
$780$	−10.3773			−0.371568
$781$	10.2612	+	5.54335i	0.367173	+	0.198357i
$782$	5.18043	−	8.97277i	0.185252	−	0.320866i
$783$	3.41229	−	32.4657i	0.121945	−	1.16023i
$784$	3.67061	+	4.07663i	0.131093	+	0.145594i
$785$	27.1293	−	30.1301i	0.968285	−	1.07539i
$786$	14.3196	−	10.4038i	0.510763	−	0.371091i
$787$	40.6799	−	29.5557i	1.45008	−	1.05355i	0.464270	−	0.885694i	$-0.346317\pi$
$787$	40.6799	−	29.5557i	1.45008	−	1.05355i	0.985812	−	0.167853i	$-0.0536833\pi$
$788$	−16.3869	+	18.1995i	−0.583758	+	0.648329i
$789$	51.5006	−	10.9468i	1.83347	−	0.389716i
$790$	17.8324	+	12.9560i	0.634447	+	0.460953i
$791$	41.5668			1.47794
$792$	−3.09520	+	1.90574i	−0.109983	+	0.0677174i
$793$	8.18520	−	14.1772i	0.290665	−	0.503447i
$794$	−2.61270	+	24.8582i	−0.0927212	+	0.882184i
$795$	−17.2065	−	19.1097i	−0.610251	−	0.677752i
$796$	5.55435	+	1.18061i	0.196869	+	0.0418457i
$797$	−22.9308	+	16.6602i	−0.812251	+	0.590135i	−0.914482	−	0.404626i	$-0.867402\pi$
$797$	−22.9308	+	16.6602i	−0.812251	+	0.590135i	0.102231	+	0.994761i	$0.467402\pi$
$798$	−26.1710	+	16.9337i	−0.926442	+	0.599447i
$799$	9.10474	+	28.0215i	0.322103	+	0.991330i
$800$	−5.11619	−	5.68211i	−0.180885	−	0.200893i
$801$	−0.331464	+	0.147577i	−0.0117117	+	0.00521439i
$802$	−13.0549	−	22.6117i	−0.460983	−	0.798446i
$803$	5.59810	−	5.33490i	0.197553	−	0.188264i
$804$	6.11645	+	10.5940i	0.215711	+	0.373622i
$805$	26.8794	+	19.5290i	0.947375	+	0.688308i
$806$	2.12322	−	6.53459i	0.0747872	−	0.230171i
$807$	−8.10532	+	9.00187i	−0.285321	+	0.316881i
$808$	4.02559	+	1.79231i	0.141620	+	0.0630532i
$809$	−12.5702	+	9.13282i	−0.441946	+	0.321093i	−0.786408	−	0.617708i	$-0.788062\pi$
$809$	−12.5702	+	9.13282i	−0.441946	+	0.321093i	0.344462	+	0.938800i	$0.388062\pi$
$810$	−12.1833	−	37.4962i	−0.428076	−	1.31748i
$811$	−12.5604	+	2.66980i	−0.441057	+	0.0937495i	−0.423087	−	0.906089i	$-0.639054\pi$
$811$	−12.5604	+	2.66980i	−0.441057	+	0.0937495i	−0.0179697	+	0.999839i	$0.505720\pi$
$812$	27.3458	−	12.1751i	0.959648	−	0.427263i
$813$	12.1744	+	21.0867i	0.426976	+	0.739544i
$814$	−35.3801	+	4.73387i	−1.24007	+	0.165922i
$815$	−15.5118	+	26.8673i	−0.543355	+	0.941119i
$816$	−6.41580	−	4.66135i	−0.224598	−	0.163180i
$817$	7.70150	−	1.20665i	0.269442	−	0.0422155i
$818$	4.95801	+	15.2592i	0.173353	+	0.533525i
$819$	−0.583661	−	5.55316i	−0.0203948	−	0.194043i
$820$	−2.93644	−	27.9383i	−0.102545	−	0.975649i
$821$	−8.43635	+	9.36952i	−0.294431	+	0.326998i	−0.872151	−	0.489236i	$-0.837276\pi$
$821$	−8.43635	+	9.36952i	−0.294431	+	0.326998i	0.577721	+	0.816235i	$0.303942\pi$
$822$	28.0565	+	31.1599i	0.978584	+	1.08683i
$823$	−2.95709	+	28.1348i	−0.103078	+	0.980718i	0.813690	+	0.581298i	$0.197455\pi$
$823$	−2.95709	+	28.1348i	−0.103078	+	0.980718i	−0.916768	+	0.399420i	$0.869212\pi$
$824$	10.4101			0.362653
$825$	−48.3426	+	17.2339i	−1.68307	+	0.600009i
$826$	−8.40259	−	14.5537i	−0.292363	−	0.506388i
$827$	1.95258	−	18.5776i	0.0678980	−	0.646006i	−0.906659	−	0.421865i	$-0.861376\pi$
$827$	1.95258	−	18.5776i	0.0678980	−	0.646006i	0.974557	−	0.224141i	$-0.0719577\pi$
$828$	0.895470	−	2.75597i	0.0311197	−	0.0957767i
$829$	−4.84979	−	14.9261i	−0.168440	−	0.518406i	0.830833	−	0.556522i	$-0.187864\pi$
$829$	−4.84979	−	14.9261i	−0.168440	−	0.518406i	−0.999273	+	0.0381160i	$0.987864\pi$
$830$	−45.1521	−	20.1030i	−1.56725	−	0.697786i
$831$	−1.37315	−	13.0646i	−0.0476339	−	0.453206i
$832$	0.964812	−	1.07153i	0.0334488	−	0.0371487i
$833$	14.3832	+	15.9741i	0.498347	+	0.553471i
$834$	17.9000	−	7.96959i	0.619826	−	0.275964i
$835$	−79.1688			−2.73975
$836$	−8.79566	+	11.4733i	−0.304204	+	0.396812i
$837$	18.3627			0.634708
$838$	7.42979	−	3.30796i	0.256658	−	0.114271i
$839$	−22.9749	−	25.5162i	−0.793180	−	0.880916i	0.201959	−	0.979394i	$-0.435269\pi$
$839$	−22.9749	−	25.5162i	−0.793180	−	0.880916i	−0.995139	+	0.0984783i	$0.968603\pi$
$840$	17.0165	−	18.8987i	0.587125	−	0.652069i
$841$	−4.47010	−	42.5301i	−0.154141	−	1.46656i
$842$	−14.7046	−	6.54690i	−0.506753	−	0.225621i
$843$	5.69464	+	17.5263i	0.196134	+	0.603638i
$844$	0.112608	−	0.346573i	0.00387614	−	0.0119295i
$845$	−4.05950	+	38.6235i	−0.139651	+	1.32869i
$846$	4.12029	+	7.13656i	0.141659	+	0.245360i
$847$	30.1030	−	24.5880i	1.03435	−	0.844855i
$848$	3.57295			0.122696
$849$	−1.56659	+	14.9051i	−0.0537652	+	0.511542i
$850$	−20.0476	−	22.2652i	−0.687628	−	0.763688i
$851$	19.0418	−	21.1480i	0.652743	−	0.724944i
$852$	0.743904	+	7.07778i	0.0254857	+	0.242481i
$853$	1.39517	+	13.2741i	0.0477696	+	0.454498i	0.992095	+	0.125486i	$0.0400490\pi$
$853$	1.39517	+	13.2741i	0.0477696	+	0.454498i	−0.944326	+	0.329012i	$0.893284\pi$
$854$	12.3970	+	38.1539i	0.424216	+	1.30560i
$855$	10.6689	+	13.2200i	0.364869	+	0.452113i
$856$	−11.6469	−	8.46194i	−0.398081	−	0.289223i
$857$	−21.1950	+	36.7108i	−0.724007	+	1.25402i	0.235374	+	0.971905i	$0.424369\pi$
$857$	−21.1950	+	36.7108i	−0.724007	+	1.25402i	−0.959381	+	0.282113i	$0.908965\pi$
$858$	−4.18510	−	8.72680i	−0.142877	−	0.297928i
$859$	11.5412	+	19.9899i	0.393779	+	0.682045i	0.992945	−	0.118580i	$-0.0378342\pi$
$859$	11.5412	+	19.9899i	0.393779	+	0.682045i	−0.599166	+	0.800625i	$0.704501\pi$
$860$	−5.80995	+	2.58675i	−0.198118	+	0.0882076i
$861$	55.2581	−	11.7455i	1.88319	−	0.400285i
$862$	−1.28442	−	3.95303i	−0.0437475	−	0.134641i
$863$	−36.4584	+	26.4885i	−1.24106	+	0.901681i	−0.997668	−	0.0682483i	$-0.978259\pi$
$863$	−36.4584	+	26.4885i	−1.24106	+	0.901681i	−0.243388	+	0.969929i	$0.578259\pi$
$864$	3.52036	+	1.56736i	0.119765	+	0.0533228i
$865$	31.1892	−	34.6391i	1.06046	−	1.17776i
$866$	−1.35550	+	4.17181i	−0.0460619	+	0.141764i
$867$	2.69440	+	1.95760i	0.0915067	+	0.0664835i
$868$	8.41891	+	14.5820i	0.285757	+	0.494945i
$869$	−3.70364	+	20.2211i	−0.125637	+	0.685955i
$870$	−30.4845	−	52.8007i	−1.03352	−	1.79011i
$871$	−7.96185	+	3.54484i	−0.269777	+	0.120112i
$872$	6.04125	+	6.70948i	0.204582	+	0.227212i
$873$	1.87055	+	5.75695i	0.0633084	+	0.194843i
$874$	−0.584023	−	11.5106i	−0.0197549	−	0.389352i
$875$	26.8989	−	19.5432i	0.909349	−	0.660681i
$876$	4.61567	+	0.981092i	0.155949	+	0.0331480i
$877$	18.0118	+	20.0041i	0.608214	+	0.675490i	0.966068	−	0.258287i	$-0.0831582\pi$
$877$	18.0118	+	20.0041i	0.608214	+	0.675490i	−0.357854	+	0.933777i	$0.616492\pi$
$878$	1.94051	−	18.4628i	0.0654892	−	0.623088i
$879$	32.2764	−	55.9044i	1.08866	−	1.88561i
$880$	4.49049	−	10.9060i	0.151374	−	0.367643i
$881$	52.2281			1.75961			0.879804	−	0.475336i	$-0.157674\pi$
$881$	52.2281			1.75961			0.879804	+	0.475336i	$0.157674\pi$
$882$	4.86378	+	3.53374i	0.163772	+	0.118987i
$883$	39.8654	−	8.47366i	1.34158	−	0.285161i	0.519469	−	0.854490i	$-0.326130\pi$
$883$	39.8654	−	8.47366i	1.34158	−	0.285161i	0.822110	+	0.569328i	$0.192797\pi$
$884$	3.78058	−	4.19876i	0.127155	−	0.141220i
$885$	−27.6917	+	20.1192i	−0.930846	+	0.676299i
$886$	−23.0655	+	16.7581i	−0.774901	+	0.562998i
$887$	4.28969	−	4.76418i	0.144034	−	0.159966i	−0.666811	−	0.745227i	$-0.732341\pi$
$887$	4.28969	−	4.76418i	0.144034	−	0.159966i	0.810845	+	0.585261i	$0.199008\pi$
$888$	−14.5749	−	16.1870i	−0.489100	−	0.543201i
$889$	−5.03569	+	47.9114i	−0.168892	+	1.60690i
$890$	0.588660	−	1.01959i	0.0197319	−	0.0341767i
$891$	26.6189	−	25.3674i	0.891768	−	0.849841i
$892$	−20.1211			−0.673703
$893$	25.4368	+	20.6685i	0.851208	+	0.691646i
$894$	−8.60523	+	26.4842i	−0.287802	+	0.885763i
$895$	84.0530	+	17.8660i	2.80958	+	0.597195i
$896$	0.369352	+	3.51415i	0.0123392	+	0.117399i
$897$	7.04885	+	3.13835i	0.235354	+	0.104787i
$898$	−18.6488	−	3.96393i	−0.622320	−	0.132278i
$899$	39.4857	−	8.39294i	1.31692	−	0.279920i
$900$	−6.77927	−	4.92542i	−0.225976	−	0.164181i
$901$	14.0005			0.466424
$902$	22.3104	−	13.7367i	0.742856	−	0.457382i
$903$	−6.39466	−	11.0759i	−0.212801	−	0.368582i
$904$	9.51697	+	6.91448i	0.316530	+	0.229972i
$905$	0.876910	−	2.69885i	0.0291495	−	0.0897129i
$906$	8.56193	−	9.50899i	0.284451	−	0.315915i
$907$	−4.73096	−	45.0121i	−0.157089	−	1.49460i	−0.734757	−	0.678331i	$-0.762704\pi$
$907$	−4.73096	−	45.0121i	−0.157089	−	1.49460i	0.577668	−	0.816272i	$-0.303963\pi$
$908$	16.6765	+	7.42487i	0.553430	+	0.246403i
$909$	4.72381	+	1.00408i	0.156679	+	0.0333031i
$910$	12.1234	+	13.4644i	0.401887	+	0.446341i
$911$	−6.73577	−	4.89382i	−0.223166	−	0.162140i	0.470585	−	0.882355i	$-0.344043\pi$
$911$	−6.73577	−	4.89382i	−0.223166	−	0.162140i	−0.693751	+	0.720215i	$0.744043\pi$
$912$	−8.80886	−	0.476366i	−0.291691	−	0.0157740i
$913$	−1.30392	−	46.0780i	−0.0431534	−	1.52496i
$914$	−9.31827	+	16.1397i	−0.308221	+	0.533855i
$915$	74.6470	−	33.2350i	2.46775	−	1.09871i
$916$	−20.0681	+	4.26561i	−0.663069	+	0.140940i
$917$	−30.2278	−	6.42511i	−0.998208	−	0.212176i
$918$	13.7944	+	6.14166i	0.455283	+	0.202705i
$919$	12.1017	−	8.79241i	0.399199	−	0.290035i	−0.370016	−	0.929025i	$-0.620648\pi$
$919$	12.1017	−	8.79241i	0.399199	−	0.290035i	0.769215	+	0.638991i	$0.220648\pi$
$920$	2.90562	+	8.94258i	0.0957955	+	0.294828i
$921$	7.90308	−	1.67985i	0.260415	−	0.0553530i
$922$	−0.636060	+	6.05170i	−0.0209475	+	0.199302i
$923$	−5.07034			−0.166892
$924$	22.7555	+	6.68828i	0.748601	+	0.220028i
$925$	−41.1455	−	71.2661i	−1.35286	−	2.34321i
$926$	−12.4776	+	5.55539i	−0.410040	+	0.182561i
$927$	11.1596	−	2.37205i	0.366529	−	0.0779082i
$928$	8.28627	+	1.76130i	0.272010	+	0.0578175i
$929$	−3.71529	−	35.3486i	−0.121895	−	1.15975i	−0.868919	−	0.494955i	$-0.835185\pi$
$929$	−3.71529	−	35.3486i	−0.121895	−	1.15975i	0.747024	−	0.664797i	$-0.231482\pi$
$930$	27.7455	−	20.1583i	0.909811	−	0.661016i
$931$	23.0863	+	6.22717i	0.756621	+	0.204087i
$932$	2.89884	−	8.92172i	0.0949547	−	0.292241i
$933$	−46.7905	+	20.8325i	−1.53185	+	0.682025i
$934$	−2.26071	+	3.91566i	−0.0739725	+	0.128124i
$935$	17.5958	−	42.7350i	0.575445	−	1.39758i
$936$	0.790116	−	1.36852i	0.0258257	−	0.0447315i
$937$	−5.57883	+	53.0790i	−0.182252	+	1.73402i	0.396082	+	0.918215i	$0.370370\pi$
$937$	−5.57883	+	53.0790i	−0.182252	+	1.73402i	−0.578334	+	0.815800i	$0.696297\pi$
$938$	6.59994	−	20.3125i	0.215496	−	0.663228i
$939$	−17.3150	−	53.2901i	−0.565054	−	1.73906i
$940$	−24.4273	−	10.8758i	−0.796732	−	0.354728i
$941$	−20.6343	−	9.18700i	−0.672660	−	0.299488i	0.0418386	−	0.999124i	$-0.486678\pi$
$941$	−20.6343	−	9.18700i	−0.672660	−	0.299488i	−0.714499	+	0.699637i	$0.753345\pi$
$942$	7.13033	+	21.9449i	0.232319	+	0.715004i
$943$	−6.45463	+	19.8653i	−0.210192	+	0.646903i
$944$	0.497133	−	4.72990i	0.0161803	−	0.153945i
$945$	−24.2108	+	41.9343i	−0.787577	+	1.36412i
$946$	−4.51843	−	3.84264i	−0.146907	−	0.124935i
$947$	−11.6724	+	20.2172i	−0.379302	+	0.656971i	−0.990961	−	0.134151i	$-0.957169\pi$
$947$	−11.6724	+	20.2172i	−0.379302	+	0.656971i	0.611658	+	0.791122i	$0.290503\pi$
$948$	−11.4599	+	5.10229i	−0.372201	+	0.165715i
$949$	−1.03889	+	3.19736i	−0.0337236	+	0.103791i
$950$	−32.1782	−	8.67960i	−1.04400	−	0.281603i
$951$	12.3904	−	9.00216i	0.401787	−	0.291915i
$952$	1.44729	+	13.7701i	0.0469070	+	0.446290i
$953$	25.7214	+	5.46725i	0.833198	+	0.177102i	0.604711	−	0.796445i	$-0.293289\pi$
$953$	25.7214	+	5.46725i	0.833198	+	0.177102i	0.228487	+	0.973547i	$0.426622\pi$
$954$	3.83019	−	0.814132i	0.124007	−	0.0263585i
$955$	−70.4891	+	31.3838i	−2.28097	+	1.01556i
$956$	1.32855	+	2.30112i	0.0429684	+	0.0744235i
$957$	32.1084	−	46.9300i	1.03792	−	1.51703i
$958$	−7.56448			−0.244397
$959$	7.65219	−	72.8058i	0.247102	−	2.35102i
$960$	7.03977	−	1.49635i	0.227208	−	0.0482945i
$961$	−2.56265	−	7.88704i	−0.0826663	−	0.254421i
$962$	12.5547	−	9.12151i	0.404779	−	0.294089i
$963$	−14.4135	−	6.41732i	−0.464470	−	0.206795i
$964$	10.5264	+	2.23746i	0.339033	+	0.0720637i
$965$	−77.7869	+	16.5341i	−2.50405	+	0.532252i
$966$	−17.2740	+	7.69087i	−0.555781	+	0.247450i
$967$	−23.3168	+	40.3859i	−0.749818	+	1.29872i	0.198092	+	0.980183i	$0.436525\pi$
$967$	−23.3168	+	40.3859i	−0.749818	+	1.29872i	−0.947910	+	0.318539i	$0.896808\pi$
$968$	10.9824	−	0.622060i	0.352988	−	0.0199938i
$969$	−34.5172	−	1.86662i	−1.10885	−	0.0599646i
$970$	−15.8903	−	11.5450i	−0.510206	−	0.370687i
$971$	11.0442	+	12.2658i	0.354424	+	0.393628i	0.893821	−	0.448424i	$-0.148014\pi$
$971$	11.0442	+	12.2658i	0.354424	+	0.393628i	−0.539397	+	0.842052i	$0.681348\pi$
$972$	10.6396	+	2.26152i	0.341266	+	0.0725383i
$973$	−31.2522	−	13.9144i	−1.00190	−	0.446075i
$974$	3.10847	+	29.5752i	0.0996020	+	0.947649i
$975$	14.9299	−	16.5813i	0.478138	−	0.531026i
$976$	−3.50841	+	10.7978i	−0.112301	+	0.345628i
$977$	−4.45757	−	3.23862i	−0.142610	−	0.103613i	0.514193	−	0.857675i	$-0.328092\pi$
$977$	−4.45757	−	3.23862i	−0.142610	−	0.103613i	−0.656803	+	0.754062i	$0.728092\pi$
$978$	−8.82801	−	15.2906i	−0.282289	−	0.488938i
$979$	1.09482	+	0.0838398i	0.0349907	+	0.00267953i
$980$	−19.5076			−0.623148
$981$	8.00502	+	5.81599i	0.255581	+	0.185690i
$982$	17.9459	−	3.81452i	0.572676	−	0.121726i
$983$	22.3354	+	4.74753i	0.712388	+	0.151423i	0.549830	−	0.835276i	$-0.314692\pi$
$983$	22.3354	+	4.74753i	0.712388	+	0.151423i	0.162557	+	0.986699i	$0.448026\pi$
$984$	14.6055	+	6.50279i	0.465606	+	0.207301i
$985$	−9.10326	−	86.6117i	−0.290054	−	2.75968i
$986$	32.4695	+	6.90160i	1.03404	+	0.219792i
$987$	16.6163	−	51.1397i	0.528902	−	1.62779i
$988$	0.993535	−	6.20602i	0.0316086	−	0.197440i
$989$	4.72873			0.150365
$990$	2.32874	−	12.7144i	0.0740121	−	0.404092i
$991$	5.70030	−	9.87320i	0.181076	−	0.313633i	−0.761171	−	0.648551i	$-0.775375\pi$
$991$	5.70030	−	9.87320i	0.181076	−	0.313633i	0.942247	+	0.334918i	$0.108709\pi$
$992$	−0.498098	+	4.73909i	−0.0158146	+	0.150466i
$993$	−7.55479	−	8.39045i	−0.239744	−	0.266263i
$994$	8.31422	−	9.23388i	0.263711	−	0.292881i
$995$	−16.3367	+	11.8693i	−0.517907	+	0.376282i
$996$	22.7565	−	16.5336i	0.721068	−	0.523886i
$997$	12.9631	−	14.3970i	0.410545	−	0.455957i	−0.502039	−	0.864845i	$-0.667417\pi$
$997$	12.9631	−	14.3970i	0.410545	−	0.455957i	0.912585	+	0.408888i	$0.134083\pi$
$998$	42.4301	−	9.01879i	1.34310	−	0.285485i
$999$	33.5529	+	24.3776i	1.06157	+	0.771274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.125.7	✓	64
11.3	even	5	inner	418.2.n.d.201.2	yes	64
19.7	even	3	inner	418.2.n.d.235.2	yes	64
209.102	even	15	inner	418.2.n.d.311.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.125.7	✓	64	1.1	even	1	trivial
418.2.n.d.201.2	yes	64	11.3	even	5	inner
418.2.n.d.235.2	yes	64	19.7	even	3	inner
418.2.n.d.311.7	yes	64	209.102	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)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(1.35422 + 1.50401i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.371716 + 3.53664i) q^{5} +(-1.84887 - 0.823172i) q^{6} +(1.09191 + 3.36056i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.114558 + 1.08994i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(1.35422 + 1.50401i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.371716 + 3.53664i) q^{5} +(-1.84887 - 0.823172i) q^{6} +(1.09191 + 3.36056i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.114558 + 1.08994i) q^{9} +(-1.77806 - 3.07970i) q^{10} +(1.87278 - 2.73728i) q^{11} +2.02384 q^{12} +(-0.150718 + 1.43399i) q^{13} +(-2.36437 - 2.62590i) q^{14} +(-4.81576 + 5.34845i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.409591 - 3.89700i) q^{17} +(-0.338666 - 1.04231i) q^{18} +(-2.73750 - 3.39206i) q^{19} +(2.87697 + 2.09024i) q^{20} +(-3.57563 + 6.19317i) q^{21} +(-0.597523 + 3.26236i) q^{22} +(-1.32206 - 2.28987i) q^{23} +(-1.84887 + 0.823172i) q^{24} +(-7.47894 + 1.58970i) q^{25} +(-0.445568 - 1.37132i) q^{26} +(3.11755 - 2.26504i) q^{27} +(3.22802 + 1.43721i) q^{28} +(5.66846 - 6.29547i) q^{29} +(2.22401 - 6.84480i) q^{30} +(3.85512 + 2.80091i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.65304 - 0.890179i) q^{33} +(1.95923 + 3.39349i) q^{34} +(-11.4792 + 5.11088i) q^{35} +(0.733331 + 0.814446i) q^{36} +(3.32582 + 10.2358i) q^{37} +(3.88051 + 1.98536i) q^{38} +(-2.36084 + 1.71525i) q^{39} +(-3.47842 - 0.739360i) q^{40} +(-5.28591 - 5.87060i) q^{41} +(0.747510 - 7.11208i) q^{42} +(-0.894200 + 1.54880i) q^{43} +(-0.781056 - 3.22334i) q^{44} -3.89732 q^{45} +(2.13913 + 1.55417i) q^{46} +(-7.35484 + 1.56332i) q^{47} +(1.35422 - 1.50401i) q^{48} +(-4.43798 + 3.22438i) q^{49} +(6.18577 - 4.49422i) q^{50} +(5.30645 - 5.89341i) q^{51} +(0.964812 + 1.07153i) q^{52} +(-0.373475 + 3.55337i) q^{53} +(-1.92675 + 3.33724i) q^{54} +(10.3769 + 5.60588i) q^{55} -3.53350 q^{56} +(1.39453 - 8.71081i) q^{57} +(-2.61780 + 8.05677i) q^{58} +(4.65202 + 0.988818i) q^{59} +(0.752296 + 7.15762i) q^{60} +(-10.3719 - 4.61786i) q^{61} +(-4.66106 - 0.990740i) q^{62} +(-3.78790 + 0.805144i) q^{63} +(-0.809017 - 0.587785i) q^{64} -5.12754 q^{65} +(-5.71579 + 3.51926i) q^{66} +(3.02219 + 5.23459i) q^{67} +(-3.17011 - 2.30322i) q^{68} +(1.65363 - 5.08936i) q^{69} +(8.40801 - 9.33805i) q^{70} +(0.367570 + 3.49719i) q^{71} +(-1.00120 - 0.445761i) q^{72} +(2.28065 + 0.484766i) q^{73} +(-7.20157 - 7.99815i) q^{74} +(-12.5190 - 9.09561i) q^{75} +(-4.35254 - 0.235377i) q^{76} +(11.2437 + 3.30474i) q^{77} +(1.45908 - 2.52720i) q^{78} +(-5.66245 + 2.52109i) q^{79} +(3.47842 - 0.739360i) q^{80} +(10.8445 + 2.30506i) q^{81} +(7.21671 + 3.21309i) q^{82} +(11.2442 - 8.16939i) q^{83} +(2.20986 + 6.80125i) q^{84} +(13.6301 - 2.89716i) q^{85} +(0.186939 - 1.77860i) q^{86} +17.1448 q^{87} +(2.02458 + 2.62699i) q^{88} +(0.165534 + 0.286714i) q^{89} +(3.56038 - 1.58518i) q^{90} +(-4.98358 + 1.05929i) q^{91} +(-2.58633 - 0.549742i) q^{92} +(1.00807 + 9.59118i) q^{93} +(6.08312 - 4.41965i) q^{94} +(10.9790 - 10.9424i) q^{95} +(-0.625402 + 1.92479i) q^{96} +(5.04577 - 2.24652i) q^{97} +(2.74282 - 4.75070i) q^{98} +(2.76893 + 2.35480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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