LMFDB - Embedded newform 750.2.m.c.481.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			481.5
Character	$\chi$	$=$	750.481
Dual form			750.2.m.c.421.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535827 + 0.844328i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(1.46645 - 1.68806i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.898597 + 0.652869i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +O(q^{10})$	\(q+(-0.535827 + 0.844328i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(1.46645 - 1.68806i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.898597 + 0.652869i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(0.639513 + 2.14267i) q^{10} +(-1.91846 + 3.02301i) q^{11} +(0.929776 + 0.368125i) q^{12} +(0.0937155 - 1.48956i) q^{13} +(-0.0697431 - 1.10853i) q^{14} +(0.0865613 + 2.23439i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(1.77890 - 3.78036i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.75788 + 3.52889i) q^{19} +(-2.15178 - 0.608140i) q^{20} +(0.208129 - 1.09105i) q^{21} +(-1.52445 - 3.23962i) q^{22} +(3.35390 + 0.861136i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.699072 - 4.95089i) q^{25} +(1.20747 + 0.877275i) q^{26} +(0.637424 + 0.770513i) q^{27} +(0.973337 + 0.535097i) q^{28} +(8.64605 + 4.75320i) q^{29} +(-1.93294 - 1.12416i) q^{30} +(0.381626 - 0.810996i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(-0.670896 - 3.51696i) q^{33} +(2.23868 + 3.52759i) q^{34} +(-0.215664 + 2.47428i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(4.32642 - 5.22975i) q^{37} +(-4.99311 + 1.28201i) q^{38} +(0.951362 + 1.15000i) q^{39} +(1.66645 - 1.49095i) q^{40} +(9.37795 - 2.40785i) q^{41} +(0.809685 + 0.760345i) q^{42} +(1.80794 - 5.56427i) q^{43} +(3.55215 + 0.448741i) q^{44} +(-1.59265 - 1.56955i) q^{45} +(-2.52419 + 2.37037i) q^{46} +(-3.25535 + 0.411247i) q^{47} +(-0.0627905 - 0.998027i) q^{48} +(-1.78188 + 5.48406i) q^{49} +(4.55476 + 2.06257i) q^{50} +(1.29107 + 3.97350i) q^{51} +(-1.38770 + 0.549430i) q^{52} +(-1.95250 + 10.2354i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(2.28970 + 7.67156i) q^{55} +(-0.973337 + 0.535097i) q^{56} -5.15507 q^{57} +(-8.64605 + 4.75320i) q^{58} +(7.69449 + 3.04647i) q^{59} +(1.98488 - 1.02968i) q^{60} +(-3.64713 - 0.936424i) q^{61} +(0.480261 + 0.756771i) q^{62} +(0.595157 + 0.937817i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.37704 - 2.34256i) q^{65} +(3.32895 + 1.31803i) q^{66} +(3.66857 - 2.01681i) q^{67} -4.17799 q^{68} +(-3.03438 + 1.66816i) q^{69} +(-1.97354 - 1.50788i) q^{70} +(11.2064 - 1.41570i) q^{71} +(0.187381 - 0.982287i) q^{72} +(-6.39374 + 2.53146i) q^{73} +(2.09741 + 6.45516i) q^{74} +(3.89872 + 3.13049i) q^{75} +(1.59300 - 4.90276i) q^{76} +(-0.249707 - 3.96897i) q^{77} +(-1.48074 + 0.187061i) q^{78} +(-12.8793 + 12.0945i) q^{79} +(0.365922 + 2.20592i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-2.99194 + 9.20825i) q^{82} +(5.37880 + 5.05103i) q^{83} +(-1.07583 + 0.276226i) q^{84} +(-3.77279 - 8.54657i) q^{85} +(3.72932 + 4.50798i) q^{86} +(-9.55649 + 2.45369i) q^{87} +(-2.28222 + 2.75873i) q^{88} +(-2.11606 + 0.837805i) q^{89} +(2.17859 - 0.503711i) q^{90} +(0.888278 + 1.39970i) q^{91} +(-0.648843 - 3.40135i) q^{92} +(0.276972 + 0.852432i) q^{93} +(1.39708 - 2.96894i) q^{94} +(11.4677 - 1.16860i) q^{95} +(0.876307 + 0.481754i) q^{96} +(-9.13798 - 5.02364i) q^{97} +(-3.67557 - 4.44300i) q^{98} +(2.89659 + 2.10449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) $ 120 * q + 20 * q^5 - 5 * q^7	$ 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) $ 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{25}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.535827	+	0.844328i	−0.378887	+	0.597030i
$2$	−0.535827	+	0.844328i	−0.378887	+	0.597030i
$3$	−0.728969	+	0.684547i	−0.420870	+	0.395223i
$3$	−0.728969	+	0.684547i	−0.420870	+	0.395223i
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	1.46645	−	1.68806i	0.655815	−	0.754922i
$5$	1.46645	−	1.68806i	0.655815	−	0.754922i
$6$	−0.187381	−	0.982287i	−0.0764981	−	0.401017i
$7$	−0.898597	+	0.652869i	−0.339638	+	0.246761i	−0.744509	−	0.667613i	$-0.767316\pi$
$7$	−0.898597	+	0.652869i	−0.339638	+	0.246761i	0.404871	+	0.914374i	$0.367316\pi$
$8$	0.992115	+	0.125333i	0.350766	+	0.0443120i
$9$	0.0627905	−	0.998027i	0.0209302	−	0.332676i
$10$	0.639513	+	2.14267i	0.202232	+	0.677571i
$11$	−1.91846	+	3.02301i	−0.578438	+	0.911473i	0.421551	+	0.906805i	$0.361486\pi$
$11$	−1.91846	+	3.02301i	−0.578438	+	0.911473i	−0.999989	+	0.00466825i	$0.998514\pi$
$12$	0.929776	+	0.368125i	0.268403	+	0.106268i
$13$	0.0937155	−	1.48956i	0.0259920	−	0.413131i	−0.963420	−	0.267996i	$-0.913638\pi$
$13$	0.0937155	−	1.48956i	0.0259920	−	0.413131i	0.989412	−	0.145135i	$-0.0463615\pi$
$14$	−0.0697431	−	1.10853i	−0.0186396	−	0.296268i
$15$	0.0865613	+	2.23439i	0.0223500	+	0.576918i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	1.77890	−	3.78036i	0.431447	−	0.916871i	−0.564372	−	0.825521i	$-0.690882\pi$
$17$	1.77890	−	3.78036i	0.431447	−	0.916871i	0.995819	−	0.0913505i	$-0.0291184\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	3.75788	+	3.52889i	0.862117	+	0.809582i	0.983099	−	0.183073i	$-0.0586043\pi$
$19$	3.75788	+	3.52889i	0.862117	+	0.809582i	−0.120982	+	0.992655i	$0.538604\pi$
$20$	−2.15178	−	0.608140i	−0.481153	−	0.135984i
$21$	0.208129	−	1.09105i	0.0454176	−	0.238087i
$22$	−1.52445	−	3.23962i	−0.325014	−	0.690690i
$23$	3.35390	+	0.861136i	0.699337	+	0.179559i	0.581587	−	0.813484i	$-0.302432\pi$
$23$	3.35390	+	0.861136i	0.699337	+	0.179559i	0.117750	+	0.993043i	$0.462432\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−0.699072	−	4.95089i	−0.139814	−	0.990178i
$26$	1.20747	+	0.877275i	0.236804	+	0.172048i
$27$	0.637424	+	0.770513i	0.122672	+	0.148285i
$28$	0.973337	+	0.535097i	0.183943	+	0.101124i
$29$	8.64605	+	4.75320i	1.60553	+	0.882648i	0.995949	+	0.0899245i	$0.0286626\pi$
$29$	8.64605	+	4.75320i	1.60553	+	0.882648i	0.609582	+	0.792723i	$0.291337\pi$
$30$	−1.93294	−	1.12416i	−0.352905	−	0.205243i
$31$	0.381626	−	0.810996i	0.0685420	−	0.145659i	−0.867620	−	0.497227i	$-0.834351\pi$
$31$	0.381626	−	0.810996i	0.0685420	−	0.145659i	0.936162	+	0.351568i	$0.114351\pi$
$32$	−0.309017	−	0.951057i	−0.0546270	−	0.168125i
$33$	−0.670896	−	3.51696i	−0.116788	−	0.612224i
$34$	2.23868	+	3.52759i	0.383930	+	0.604977i
$35$	−0.215664	+	2.47428i	−0.0364539	+	0.418229i
$36$	−0.929776	+	0.368125i	−0.154963	+	0.0613541i
$37$	4.32642	−	5.22975i	0.711260	−	0.859765i	−0.283816	−	0.958879i	$-0.591601\pi$
$37$	4.32642	−	5.22975i	0.711260	−	0.859765i	0.995076	+	0.0991134i	$0.0316007\pi$
$38$	−4.99311	+	1.28201i	−0.809990	+	0.207970i
$39$	0.951362	+	1.15000i	0.152340	+	0.184147i
$40$	1.66645	−	1.49095i	0.263489	−	0.235740i
$41$	9.37795	−	2.40785i	1.46459	−	0.376043i	0.569523	−	0.821975i	$-0.307128\pi$
$41$	9.37795	−	2.40785i	1.46459	−	0.376043i	0.895067	+	0.445933i	$0.147128\pi$
$42$	0.809685	+	0.760345i	0.124937	+	0.117324i
$43$	1.80794	−	5.56427i	0.275708	−	0.848543i	−0.713323	−	0.700836i	$-0.752811\pi$
$43$	1.80794	−	5.56427i	0.275708	−	0.848543i	0.989031	−	0.147707i	$-0.0471894\pi$
$44$	3.55215	+	0.448741i	0.535506	+	0.0676502i
$45$	−1.59265	−	1.56955i	−0.237418	−	0.233974i
$46$	−2.52419	+	2.37037i	−0.372172	+	0.349492i
$47$	−3.25535	+	0.411247i	−0.474842	+	0.0599865i	−0.359113	−	0.933294i	$-0.616921\pi$
$47$	−3.25535	+	0.411247i	−0.474842	+	0.0599865i	−0.115730	+	0.993281i	$0.536921\pi$
$48$	−0.0627905	−	0.998027i	−0.00906303	−	0.144053i
$49$	−1.78188	+	5.48406i	−0.254554	+	0.783438i
$50$	4.55476	+	2.06257i	0.644140	+	0.291692i
$51$	1.29107	+	3.97350i	0.180786	+	0.556402i
$52$	−1.38770	+	0.549430i	−0.192439	+	0.0761922i
$53$	−1.95250	+	10.2354i	−0.268197	+	1.40594i	0.551993	+	0.833848i	$0.313867\pi$
$53$	−1.95250	+	10.2354i	−0.268197	+	1.40594i	−0.820191	+	0.572090i	$0.806133\pi$
$54$	−0.992115	+	0.125333i	−0.135010	+	0.0170557i
$55$	2.28970	+	7.67156i	0.308743	+	1.03443i
$56$	−0.973337	+	0.535097i	−0.130068	+	0.0715053i
$57$	−5.15507			−0.682805
$58$	−8.64605	+	4.75320i	−1.13528	+	0.624126i
$59$	7.69449	+	3.04647i	1.00174	+	0.396616i	0.811013	−	0.585028i	$-0.198916\pi$
$59$	7.69449	+	3.04647i	1.00174	+	0.396616i	0.190724	+	0.981644i	$0.438916\pi$
$60$	1.98488	−	1.02968i	0.256247	−	0.132931i
$61$	−3.64713	−	0.936424i	−0.466967	−	0.119897i	0.00787256	−	0.999969i	$-0.497494\pi$
$61$	−3.64713	−	0.936424i	−0.466967	−	0.119897i	−0.474840	+	0.880072i	$0.657494\pi$
$62$	0.480261	+	0.756771i	0.0609932	+	0.0961100i
$63$	0.595157	+	0.937817i	0.0749827	+	0.118154i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−2.37704	−	2.34256i	−0.294836	−	0.290559i
$66$	3.32895	+	1.31803i	0.409766	+	0.162238i
$67$	3.66857	−	2.01681i	0.448187	−	0.246393i	−0.241641	−	0.970366i	$-0.577686\pi$
$67$	3.66857	−	2.01681i	0.448187	−	0.246393i	0.689829	+	0.723972i	$0.257686\pi$
$68$	−4.17799			−0.506655
$69$	−3.03438	+	1.66816i	−0.365296	+	0.200823i
$70$	−1.97354	−	1.50788i	−0.235884	−	0.180226i
$71$	11.2064	−	1.41570i	1.32996	−	0.168013i	0.571968	−	0.820276i	$-0.306180\pi$
$71$	11.2064	−	1.41570i	1.32996	−	0.168013i	0.757993	+	0.652263i	$0.226180\pi$
$72$	0.187381	−	0.982287i	0.0220831	−	0.115764i
$73$	−6.39374	+	2.53146i	−0.748331	+	0.296285i	−0.711166	−	0.703024i	$-0.751833\pi$
$73$	−6.39374	+	2.53146i	−0.748331	+	0.296285i	−0.0371647	+	0.999309i	$0.511833\pi$
$74$	2.09741	+	6.45516i	0.243819	+	0.750397i
$75$	3.89872	+	3.13049i	0.450185	+	0.361478i
$76$	1.59300	−	4.90276i	0.182730	−	0.562385i
$77$	−0.249707	−	3.96897i	−0.0284567	−	0.452307i
$78$	−1.48074	+	0.187061i	−0.167661	+	0.0211805i
$79$	−12.8793	+	12.0945i	−1.44903	+	1.36073i	−0.648981	+	0.760805i	$0.724804\pi$
$79$	−12.8793	+	12.0945i	−1.44903	+	1.36073i	−0.800054	+	0.599929i	$0.795196\pi$
$80$	0.365922	+	2.20592i	0.0409114	+	0.246630i
$81$	−0.992115	−	0.125333i	−0.110235	−	0.0139259i
$82$	−2.99194	+	9.20825i	−0.330405	+	1.01688i
$83$	5.37880	+	5.05103i	0.590400	+	0.554423i	0.921106	−	0.389311i	$-0.127287\pi$
$83$	5.37880	+	5.05103i	0.590400	+	0.554423i	−0.330706	+	0.943734i	$0.607287\pi$
$84$	−1.07583	+	0.276226i	−0.117383	+	0.0301388i
$85$	−3.77279	−	8.54657i	−0.409217	−	0.927006i
$86$	3.72932	+	4.50798i	0.402143	+	0.486108i
$87$	−9.55649	+	2.45369i	−1.02456	+	0.263063i
$88$	−2.28222	+	2.75873i	−0.243285	+	0.294082i
$89$	−2.11606	+	0.837805i	−0.224301	+	0.0888072i	−0.477587	−	0.878584i	$-0.658489\pi$
$89$	−2.11606	+	0.837805i	−0.224301	+	0.0888072i	0.253286	+	0.967391i	$0.418489\pi$
$90$	2.17859	−	0.503711i	0.229644	−	0.0530958i
$91$	0.888278	+	1.39970i	0.0931168	+	0.146729i
$92$	−0.648843	−	3.40135i	−0.0676466	−	0.354616i
$93$	0.276972	+	0.852432i	0.0287206	+	0.0883930i
$94$	1.39708	−	2.96894i	0.144098	−	0.306223i
$95$	11.4677	−	1.16860i	1.17656	−	0.119896i
$96$	0.876307	+	0.481754i	0.0894377	+	0.0491688i
$97$	−9.13798	−	5.02364i	−0.927821	−	0.510074i	−0.0552018	−	0.998475i	$-0.517580\pi$
$97$	−9.13798	−	5.02364i	−0.927821	−	0.510074i	−0.872619	+	0.488401i	$0.837580\pi$
$98$	−3.67557	−	4.44300i	−0.371289	−	0.448811i
$99$	2.89659	+	2.10449i	0.291118	+	0.211510i
$100$	−4.18205	+	2.74053i	−0.418205	+	0.274053i
$101$	−1.57679	+	1.14561i	−0.156897	+	0.113992i	−0.663464	−	0.748209i	$-0.730914\pi$
$101$	−1.57679	+	1.14561i	−0.156897	+	0.113992i	0.506567	+	0.862201i	$0.330914\pi$
$102$	−4.04673	−	1.03902i	−0.400686	−	0.102879i
$103$	−5.02107	−	10.6703i	−0.494741	−	1.05138i	−0.983824	−	0.179140i	$-0.942668\pi$
$103$	−5.02107	−	10.6703i	−0.494741	−	1.05138i	0.489083	−	0.872237i	$-0.337332\pi$
$104$	0.279668	−	1.46607i	0.0274238	−	0.143760i
$105$	−1.53655	−	1.95130i	−0.149952	−	0.190428i
$106$	−7.59582	−	7.13295i	−0.737771	−	0.692813i
$107$	1.17053	+	0.850440i	0.113159	+	0.0822152i	0.642926	−	0.765929i	$-0.277720\pi$
$107$	1.17053	+	0.850440i	0.113159	+	0.0822152i	−0.529766	+	0.848144i	$0.677720\pi$
$108$	0.425779	−	0.904827i	0.0409706	−	0.0870670i
$109$	9.41372	−	11.3792i	0.901671	−	1.08993i	−0.0938686	−	0.995585i	$-0.529923\pi$
$109$	9.41372	−	11.3792i	0.901671	−	1.08993i	0.995539	−	0.0943480i	$-0.0300766\pi$
$110$	−7.70420	−	2.17737i	−0.734566	−	0.207604i
$111$	0.426182	+	6.77396i	0.0404514	+	0.642956i
$112$	0.0697431	−	1.10853i	0.00659010	−	0.104747i
$113$	15.6888	+	6.21165i	1.47588	+	0.584343i	0.961886	−	0.273449i	$-0.0881646\pi$
$113$	15.6888	+	6.21165i	1.47588	+	0.584343i	0.513996	+	0.857792i	$0.328165\pi$
$114$	2.76222	−	4.35257i	0.258706	−	0.407655i
$115$	6.37196	−	4.39877i	0.594188	−	0.410187i
$116$	0.619520	−	9.84699i	0.0575210	−	0.914270i
$117$	−1.48074	−	0.187061i	−0.136895	−	0.0172938i
$118$	−6.69513	+	4.86430i	−0.616337	+	0.447795i
$119$	0.869562	+	4.55840i	0.0797126	+	0.417868i
$120$	−0.194165	+	2.22762i	−0.0177247	+	0.203353i
$121$	−0.774542	−	1.64599i	−0.0704129	−	0.149635i
$122$	2.74488	−	2.57761i	0.248510	−	0.233366i
$123$	−5.18795	+	8.17489i	−0.467781	+	0.737105i
$124$	−0.896300			−0.0804901
$125$	−9.38253	−	6.08014i	−0.839199	−	0.543824i
$126$	−1.11073			−0.0989514
$127$	7.33382	−	11.5563i	0.650772	−	1.02545i	−0.345436	−	0.938442i	$-0.612269\pi$
$127$	7.33382	−	11.5563i	0.650772	−	1.02545i	0.996207	−	0.0870098i	$-0.0277311\pi$
$128$	−0.728969	+	0.684547i	−0.0644323	+	0.0605060i
$129$	2.49107	+	5.29380i	0.219327	+	0.466093i
$130$	3.25157	−	0.751794i	0.285182	−	0.0659367i
$131$	−3.89085	−	20.3965i	−0.339945	−	1.78205i	−0.583445	−	0.812153i	$-0.698296\pi$
$131$	−3.89085	−	20.3965i	−0.339945	−	1.78205i	0.243500	−	0.969901i	$-0.421704\pi$
$132$	−2.89659	+	2.10449i	−0.252116	+	0.183173i
$133$	−5.68072	−	0.717642i	−0.492581	−	0.0622274i
$134$	−0.262866	+	4.17814i	−0.0227082	+	0.360936i
$135$	2.23542	+	0.0539081i	0.192394	+	0.00463967i
$136$	2.23868	−	3.52759i	0.191965	−	0.302489i
$137$	−1.15579	−	0.457609i	−0.0987456	−	0.0390961i	0.318232	−	0.948013i	$-0.396911\pi$
$137$	−1.15579	−	0.457609i	−0.0987456	−	0.0390961i	−0.416978	+	0.908917i	$0.636911\pi$
$138$	0.217424	−	3.45586i	0.0185084	−	0.294182i
$139$	−0.0590291	−	0.938241i	−0.00500678	−	0.0795805i	0.994730	−	0.102531i	$-0.0326940\pi$
$139$	−0.0590291	−	0.938241i	−0.00500678	−	0.0795805i	−0.999737	+	0.0229503i	$0.992694\pi$
$140$	2.33062	−	0.858358i	0.196973	−	0.0725445i
$141$	2.09153	−	2.52823i	0.176139	−	0.212915i
$142$	−4.80940	+	10.2205i	−0.403596	+	0.857684i
$143$	4.32319	+	3.14098i	0.361523	+	0.262662i
$144$	0.728969	+	0.684547i	0.0607474	+	0.0570456i
$145$	20.7026	−	7.62470i	1.71926	−	0.633197i
$146$	1.28855	−	6.75484i	0.106642	−	0.559034i
$147$	−2.45517	−	5.21749i	−0.202499	−	0.430332i
$148$	−6.57412	−	1.68795i	−0.540389	−	0.138748i
$149$	−8.96054	+	6.51021i	−0.734076	+	0.533337i	−0.890850	−	0.454297i	$-0.849890\pi$
$149$	−8.96054	+	6.51021i	−0.734076	+	0.533337i	0.156774	+	0.987634i	$0.449890\pi$
$150$	−4.73220	+	1.61439i	−0.386383	+	0.131815i
$151$	−13.4090	−	9.74222i	−1.09121	−	0.792810i	−0.111607	−	0.993752i	$-0.535600\pi$
$151$	−13.4090	−	9.74222i	−1.09121	−	0.792810i	−0.979603	+	0.200942i	$0.935600\pi$
$152$	3.28596	+	3.97205i	0.266527	+	0.322176i
$153$	−3.66120	−	2.01276i	−0.295990	−	0.162722i
$154$	3.48492	+	1.91585i	0.280822	+	0.154383i
$155$	−0.809374	−	1.83349i	−0.0650105	−	0.147269i
$156$	0.635480	−	1.35046i	0.0508791	−	0.108124i
$157$	−0.0659263	−	0.202900i	−0.00526149	−	0.0161932i	0.948391	−	0.317102i	$-0.102710\pi$
$157$	−0.0659263	−	0.202900i	−0.00526149	−	0.0161932i	−0.953653	+	0.300909i	$0.902710\pi$
$158$	−3.31062	−	17.3549i	−0.263379	−	1.38068i
$159$	−5.58329	−	8.79786i	−0.442784	−	0.697716i
$160$	−2.05859	−	0.873035i	−0.162746	−	0.0690195i
$161$	−3.57601	+	1.41584i	−0.281829	+	0.111584i
$162$	0.637424	−	0.770513i	0.0500808	−	0.0605372i
$163$	−16.1201	+	4.13895i	−1.26263	+	0.324187i	−0.819919	−	0.572479i	$-0.805982\pi$
$163$	−16.1201	+	4.13895i	−1.26263	+	0.324187i	−0.442707	+	0.896666i	$0.645982\pi$
$164$	−6.17162	−	7.46021i	−0.481923	−	0.582545i
$165$	−6.92066	−	4.02492i	−0.538773	−	0.313340i
$166$	−7.14684	+	1.83500i	−0.554702	+	0.142423i
$167$	−5.49300	−	5.15827i	−0.425061	−	0.399159i	0.442277	−	0.896879i	$-0.354171\pi$
$167$	−5.49300	−	5.15827i	−0.425061	−	0.399159i	−0.867338	+	0.497720i	$0.834171\pi$
$168$	0.343233	−	1.05636i	0.0264810	−	0.0815002i
$169$	10.6875	+	1.35014i	0.822113	+	0.103857i
$170$	9.23768	+	1.39401i	0.708497	+	0.106915i
$171$	3.75788	−	3.52889i	0.287372	−	0.269861i
$172$	−5.80449	+	0.733277i	−0.442588	+	0.0559118i
$173$	0.145430	+	2.31154i	0.0110568	+	0.175743i	0.999679	+	0.0253250i	$0.00806206\pi$
$173$	0.145430	+	2.31154i	0.0110568	+	0.175743i	−0.988622	+	0.150418i	$0.951938\pi$
$174$	3.04890	−	9.38356i	0.231137	−	0.711366i
$175$	3.86046	+	3.99245i	0.291824	+	0.301801i
$176$	−1.10640	−	3.40514i	−0.0833979	−	0.256672i
$177$	−7.69449	+	3.04647i	−0.578354	+	0.228986i
$178$	0.426456	−	2.23556i	0.0319643	−	0.167563i
$179$	11.9054	−	1.50400i	0.889853	−	0.112415i	0.332903	−	0.942961i	$-0.391972\pi$
$179$	11.9054	−	1.50400i	0.889853	−	0.112415i	0.556949	+	0.830546i	$0.311972\pi$
$180$	−0.742052	+	2.10935i	−0.0553093	+	0.157222i
$181$	−10.0395	+	5.51926i	−0.746230	+	0.410244i	−0.809018	−	0.587783i	$-0.800001\pi$
$181$	−10.0395	+	5.51926i	−0.746230	+	0.410244i	0.0627881	+	0.998027i	$0.480001\pi$
$182$	−1.65777			−0.122882
$183$	3.29967	−	1.81401i	0.243919	−	0.134095i
$184$	3.21953	+	1.27470i	0.237347	+	0.0939722i
$185$	−2.48365	−	14.9724i	−0.182601	−	1.10079i
$186$	−0.868141	−	0.222901i	−0.0636552	−	0.0163439i
$187$	8.01532	+	12.6301i	0.586138	+	0.923606i
$188$	1.75817	+	2.77043i	0.128228	+	0.202055i
$189$	−1.07583	−	0.276226i	−0.0782552	−	0.0200925i
$190$	−5.15802	+	10.3087i	−0.374202	+	0.747869i
$191$	−2.04185	−	0.808425i	−0.147743	−	0.0584956i	0.293089	−	0.956085i	$-0.405317\pi$
$191$	−2.04185	−	0.808425i	−0.147743	−	0.0584956i	−0.440832	+	0.897589i	$0.645317\pi$
$192$	−0.876307	+	0.481754i	−0.0632420	+	0.0347676i
$193$	4.01795			0.289218			0.144609	−	0.989489i	$-0.453808\pi$
$193$	4.01795			0.289218			0.144609	+	0.989489i	$0.453808\pi$
$194$	9.13798	−	5.02364i	0.656068	−	0.360677i
$195$	3.33638	+	0.0804584i	0.238923	+	0.00576175i
$196$	5.72082	−	0.722707i	0.408630	−	0.0516220i
$197$	4.12429	−	21.6203i	0.293844	−	1.54038i	−0.462746	−	0.886491i	$-0.653136\pi$
$197$	4.12429	−	21.6203i	0.293844	−	1.54038i	0.756589	−	0.653891i	$-0.226864\pi$
$198$	−3.32895	+	1.31803i	−0.236578	+	0.0936680i
$199$	1.75071	+	5.38812i	0.124104	+	0.381954i	0.993737	−	0.111746i	$-0.0356442\pi$
$199$	1.75071	+	5.38812i	0.124104	+	0.381954i	−0.869632	+	0.493700i	$0.835644\pi$
$200$	−0.0730489	−	4.99947i	−0.00516533	−	0.353516i
$201$	−1.29367	+	3.98151i	−0.0912484	+	0.280834i
$202$	−0.122380	−	1.94518i	−0.00861063	−	0.136862i
$203$	−10.8725	+	1.37352i	−0.763102	+	0.0964021i
$204$	3.04562	−	2.86003i	0.213236	−	0.200242i
$205$	9.68767	−	19.3615i	0.676616	−	1.35227i
$206$	11.6997	+	1.47801i	0.815155	+	0.102978i
$207$	1.07003	−	3.29321i	0.0743722	−	0.228894i
$208$	1.08799	+	1.02169i	0.0754387	+	0.0708417i
$209$	−17.8772	+	4.59009i	−1.23659	+	0.317503i
$210$	2.47086	−	0.251790i	0.170506	−	0.0173751i
$211$	9.26796	+	11.2030i	0.638033	+	0.771249i	0.986088	−	0.166225i	$-0.0531577\pi$
$211$	9.26796	+	11.2030i	0.638033	+	0.771249i	−0.348055	+	0.937474i	$0.613158\pi$
$212$	10.0926	−	2.59134i	0.693162	−	0.177974i
$213$	−7.20003	+	8.70334i	−0.493338	+	0.596343i
$214$	−1.34525	+	0.532623i	−0.0919595	+	0.0364094i
$215$	−6.74156	−	11.2116i	−0.459770	−	0.764625i
$216$	0.535827	+	0.844328i	0.0364584	+	0.0574492i
$217$	0.186546	+	0.977910i	0.0126636	+	0.0663848i
$218$	4.56368	+	14.0456i	0.309091	+	0.951285i
$219$	2.92793	−	6.22217i	0.197851	−	0.420455i
$220$	5.96653	−	5.33817i	0.402263	−	0.359900i
$221$	−5.46438	−	3.00407i	−0.367574	−	0.202075i
$222$	−5.94781	−	3.26983i	−0.399191	−	0.219457i
$223$	10.0806	+	12.1853i	0.675046	+	0.815990i	0.991152	−	0.132734i	$-0.0423755\pi$
$223$	10.0806	+	12.1853i	0.675046	+	0.815990i	−0.316106	+	0.948724i	$0.602375\pi$
$224$	0.898597	+	0.652869i	0.0600400	+	0.0436216i
$225$	−4.98501	+	0.386824i	−0.332334	+	0.0257883i
$226$	−13.6512	+	9.91816i	−0.908063	+	0.659746i
$227$	−26.0143	−	6.67934i	−1.72663	−	0.443323i	−0.750565	−	0.660797i	$-0.770218\pi$
$227$	−26.0143	−	6.67934i	−1.72663	−	0.443323i	−0.976066	+	0.217474i	$0.930218\pi$
$228$	2.19492	+	4.66444i	0.145362	+	0.308910i
$229$	0.767835	−	4.02513i	0.0507400	−	0.265988i	−0.947872	−	0.318650i	$-0.896771\pi$
$229$	0.767835	−	4.02513i	0.0507400	−	0.265988i	0.998612	+	0.0526618i	$0.0167705\pi$
$230$	0.299735	+	7.73700i	0.0197639	+	0.510163i
$231$	2.89898	+	2.72232i	0.190739	+	0.179116i
$232$	7.98213	+	5.79936i	0.524053	+	0.380747i
$233$	−0.344848	+	0.732840i	−0.0225918	+	0.0480100i	−0.915804	−	0.401624i	$-0.868446\pi$
$233$	−0.344848	+	0.732840i	−0.0225918	+	0.0480100i	0.893213	+	0.449634i	$0.148446\pi$
$234$	0.951362	−	1.15000i	0.0621925	−	0.0751778i
$235$	−4.07959	+	6.09829i	−0.266123	+	0.397809i
$236$	−0.519632	−	8.25931i	−0.0338251	−	0.537635i
$237$	1.10937	−	17.6330i	0.0720615	−	1.14538i
$238$	−4.31472	−	1.70832i	−0.279682	−	0.110734i
$239$	−13.5457	+	21.3445i	−0.876196	+	1.38066i	0.0480420	+	0.998845i	$0.484702\pi$
$239$	−13.5457	+	21.3445i	−0.876196	+	1.38066i	−0.924238	+	0.381818i	$0.875298\pi$
$240$	−1.77680	−	1.35756i	−0.114692	−	0.0876300i
$241$	−0.170251	+	2.70606i	−0.0109668	+	0.174313i	0.988730	+	0.149707i	$0.0478330\pi$
$241$	−0.170251	+	2.70606i	−0.0109668	+	0.174313i	−0.999697	+	0.0246056i	$0.992167\pi$
$242$	1.80477	+	0.227996i	0.116015	+	0.0146561i
$243$	0.809017	−	0.587785i	0.0518985	−	0.0377064i
$244$	0.705571	+	3.69873i	0.0451696	+	0.236787i
$245$	6.64438	+	11.0500i	0.424494	+	0.705959i
$246$	−4.12245	−	8.76065i	−0.262838	−	0.558559i
$247$	5.60868	−	5.26690i	0.356872	−	0.335125i
$248$	0.480261	−	0.756771i	0.0304966	−	0.0480550i
$249$	−7.37865			−0.467603
$250$	10.1610	−	4.66403i	0.642641	−	0.294979i
$251$	−0.796228			−0.0502574			−0.0251287	−	0.999684i	$-0.508000\pi$
$251$	−0.796228			−0.0502574			−0.0251287	+	0.999684i	$0.508000\pi$
$252$	0.595157	−	0.937817i	0.0374914	−	0.0590769i
$253$	−9.03756	+	8.48683i	−0.568187	+	0.533563i
$254$	5.82761	+	12.3843i	0.365657	+	0.777060i
$255$	8.60078	+	3.64753i	0.538602	+	0.228417i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	−12.8141	+	9.30998i	−0.799321	+	0.580741i	−0.910715	−	0.413036i	$-0.864468\pi$
$257$	−12.8141	+	9.30998i	−0.799321	+	0.580741i	0.111394	+	0.993776i	$0.464468\pi$
$258$	−5.80449	−	0.733277i	−0.361371	−	0.0456518i
$259$	−0.473371	+	7.52402i	−0.0294139	+	0.467520i
$260$	−1.10752	+	3.14823i	−0.0686855	+	0.195245i
$261$	5.28671	−	8.33053i	0.327239	−	0.515647i
$262$	19.3062	+	7.64386i	1.19274	+	0.472239i
$263$	−1.64382	+	26.1277i	−0.101362	+	1.61110i	0.538508	+	0.842620i	$0.318988\pi$
$263$	−1.64382	+	26.1277i	−0.101362	+	1.61110i	−0.639870	+	0.768483i	$0.721012\pi$
$264$	−0.224814	−	3.57331i	−0.0138363	−	0.219922i
$265$	14.4147	+	18.3056i	0.885487	+	1.12450i
$266$	3.64981	−	4.41186i	0.223784	−	0.270508i
$267$	0.969020	−	2.05927i	0.0593031	−	0.126025i
$268$	−3.38687	−	2.46071i	−0.206886	−	0.150312i
$269$	−12.7554	−	11.9782i	−0.777713	−	0.730321i	0.190162	−	0.981753i	$-0.439099\pi$
$269$	−12.7554	−	11.9782i	−0.777713	−	0.730321i	−0.967875	+	0.251432i	$0.919099\pi$
$270$	−1.24331	+	1.85854i	−0.0756656	+	0.113107i
$271$	1.76568	−	9.25602i	0.107257	−	0.562263i	−0.887569	−	0.460675i	$-0.847607\pi$
$271$	1.76568	−	9.25602i	0.107257	−	0.562263i	0.994826	−	0.101589i	$-0.0323926\pi$
$272$	1.77890	+	3.78036i	0.107862	+	0.229218i
$273$	−1.60569	−	0.412271i	−0.0971807	−	0.0249518i
$274$	1.00567	−	0.730665i	0.0607550	−	0.0441411i
$275$	16.3078	+	7.38479i	0.983394	+	0.445320i
$276$	2.80137	+	2.03532i	0.168623	+	0.122512i
$277$	−15.3311	−	18.5322i	−0.921159	−	1.11349i	−0.993239	−	0.116091i	$-0.962964\pi$
$277$	−15.3311	−	18.5322i	−0.921159	−	1.11349i	0.0720800	−	0.997399i	$-0.477036\pi$
$278$	0.823812	+	0.452895i	0.0494090	+	0.0271628i
$279$	−0.785433	−	0.431796i	−0.0470227	−	0.0258509i
$280$	−0.524073	+	2.42774i	−0.0313193	+	0.145085i
$281$	0.271173	−	0.576271i	0.0161768	−	0.0343775i	−0.896575	−	0.442891i	$-0.853953\pi$
$281$	0.271173	−	0.576271i	0.0161768	−	0.0343775i	0.912752	+	0.408514i	$0.133953\pi$
$282$	1.01396	+	3.12063i	0.0603801	+	0.185831i
$283$	−3.16103	−	16.5707i	−0.187904	−	0.985027i	−0.943845	−	0.330388i	$-0.892821\pi$
$283$	−3.16103	−	16.5707i	−0.187904	−	0.985027i	0.755941	−	0.654639i	$-0.227179\pi$
$284$	−6.05244	−	9.53712i	−0.359146	−	0.565924i
$285$	−7.55963	+	8.70205i	−0.447794	+	0.515465i
$286$	−4.96849	+	1.96717i	−0.293793	+	0.116321i
$287$	−6.85498	+	8.28625i	−0.404637	+	0.489122i
$288$	−0.968583	+	0.248690i	−0.0570743	+	0.0146542i
$289$	−0.290399	−	0.351033i	−0.0170823	−	0.0206490i
$290$	−4.65528	+	21.5653i	−0.273367	+	1.26636i
$291$	10.1002	−	2.59330i	0.592085	−	0.152022i
$292$	5.01286	+	4.70739i	0.293355	+	0.275479i
$293$	−1.93154	+	5.94467i	−0.112842	+	0.347291i	−0.991491	−	0.130177i	$-0.958445\pi$
$293$	−1.93154	+	5.94467i	−0.112842	+	0.347291i	0.878649	+	0.477468i	$0.158445\pi$
$294$	5.72082	+	0.722707i	0.333645	+	0.0421491i
$295$	16.4262	−	8.52127i	0.956368	−	0.496127i
$296$	4.94777	−	4.64626i	0.287583	−	0.270059i
$297$	−3.55215	+	0.448741i	−0.206116	+	0.0260386i
$298$	−0.695457	−	11.0540i	−0.0402868	−	0.640340i
$299$	1.59703	−	4.91515i	0.0923586	−	0.284251i
$300$	1.17256	−	4.86057i	0.0676979	−	0.280625i
$301$	2.00813	+	6.18038i	0.115747	+	0.356231i
$302$	15.4105	−	6.10146i	0.886777	−	0.351100i
$303$	0.365210	−	1.91450i	0.0209808	−	0.109985i
$304$	−5.11442	+	0.646101i	−0.293332	+	0.0370565i
$305$	−6.92906	+	4.78335i	−0.396757	+	0.273894i
$306$	3.66120	−	2.01276i	0.209297	−	0.115062i
$307$	−25.2262			−1.43974			−0.719869	−	0.694110i	$-0.755798\pi$
$307$	−25.2262			−1.43974			−0.719869	+	0.694110i	$0.755798\pi$
$308$	−3.48492	+	1.91585i	−0.198571	+	0.109166i
$309$	10.9645	+	4.34117i	0.623751	+	0.246960i
$310$	1.98175	+	0.299055i	0.112556	+	0.0169852i
$311$	2.32655	+	0.597358i	0.131927	+	0.0338731i	0.314076	−	0.949398i	$-0.398305\pi$
$311$	2.32655	+	0.597358i	0.131927	+	0.0338731i	−0.182149	+	0.983271i	$0.558305\pi$
$312$	0.799727	+	1.26017i	0.0452756	+	0.0713430i
$313$	3.37774	+	5.32247i	0.190921	+	0.300844i	0.926281	−	0.376833i	$-0.122987\pi$
$313$	3.37774	+	5.32247i	0.190921	+	0.300844i	−0.735360	+	0.677677i	$0.762987\pi$
$314$	0.206639	+	0.0530560i	0.0116613	+	0.00299412i
$315$	2.45585	+	0.370600i	0.138372	+	0.0208809i
$316$	16.4271	+	6.50396i	0.924099	+	0.365877i
$317$	−15.8366	+	8.70625i	−0.889473	+	0.488992i	−0.859837	−	0.510569i	$-0.829435\pi$
$317$	−15.8366	+	8.70625i	−0.889473	+	0.488992i	−0.0296360	+	0.999561i	$0.509435\pi$
$318$	10.4200			0.584322
$319$	−30.9561	+	17.0183i	−1.73321	+	0.952840i
$320$	1.84018	−	1.27033i	0.102869	−	0.0710138i
$321$	−1.43545	+	0.181339i	−0.0801188	+	0.0101214i
$322$	0.720687	−	3.77797i	0.0401623	−	0.210538i
$323$	20.0254	−	7.92860i	1.11424	−	0.441159i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−7.44018	+	0.577338i	−0.412707	+	0.0320250i
$326$	5.14297	−	15.8284i	0.284843	−	0.876656i
$327$	0.927314	+	14.7392i	0.0512806	+	0.815082i
$328$	9.60579	−	1.21349i	0.530391	−	0.0670039i
$329$	2.65676	−	2.49486i	0.146472	−	0.137546i
$330$	7.10663	−	3.68665i	0.391207	−	0.202943i
$331$	−1.53917	−	0.194442i	−0.0846004	−	0.0106875i	0.0829190	−	0.996556i	$-0.473576\pi$
$331$	−1.53917	−	0.194442i	−0.0846004	−	0.0106875i	−0.167519	+	0.985869i	$0.553576\pi$
$332$	2.28013	−	7.01751i	0.125138	−	0.385136i
$333$	−4.94777	−	4.64626i	−0.271136	−	0.254614i
$334$	7.29857	−	1.87395i	0.399360	−	0.102538i
$335$	1.97527	−	9.15031i	0.107920	−	0.499935i
$336$	0.708004	+	0.855829i	0.0386248	+	0.0466893i
$337$	8.75780	−	2.24862i	0.477068	−	0.122490i	−0.00249663	−	0.999997i	$-0.500795\pi$
$337$	8.75780	−	2.24862i	0.477068	−	0.122490i	0.479564	+	0.877507i	$0.340795\pi$
$338$	−6.86660	+	8.30029i	−0.373494	+	0.451476i
$339$	−15.6888	+	6.21165i	−0.852101	+	0.337371i
$340$	−6.12679	+	7.05268i	−0.332272	+	0.382485i
$341$	1.71952	+	2.70953i	0.0931171	+	0.146729i
$342$	0.965963	+	5.06376i	0.0522333	+	0.273817i
$343$	−4.38182	−	13.4858i	−0.236596	−	0.728167i
$344$	2.49107	−	5.29380i	0.134310	−	0.285422i
$345$	−1.63380	+	7.56847i	−0.0879606	+	0.407473i
$346$	−2.02963	−	1.11580i	−0.109113	−	0.0599856i
$347$	20.2693	+	11.1431i	1.08811	+	0.598196i	0.921717	−	0.387863i	$-0.126787\pi$
$347$	20.2693	+	11.1431i	1.08811	+	0.598196i	0.166397	+	0.986059i	$0.446787\pi$
$348$	6.28912	+	7.60224i	0.337132	+	0.407523i
$349$	−3.94316	−	2.86487i	−0.211072	−	0.153353i	0.477226	−	0.878780i	$-0.341642\pi$
$349$	−3.94316	−	2.86487i	−0.211072	−	0.153353i	−0.688299	+	0.725427i	$0.741642\pi$
$350$	−5.43948	+	1.12024i	−0.290752	+	0.0598791i
$351$	1.20747	−	0.877275i	0.0644498	−	0.0468255i
$352$	3.46790	+	0.890404i	0.184839	+	0.0474587i
$353$	−5.56348	−	11.8230i	−0.296114	−	0.629274i	0.700303	−	0.713845i	$-0.253048\pi$
$353$	−5.56348	−	11.8230i	−0.296114	−	0.629274i	−0.996417	+	0.0845709i	$0.973048\pi$
$354$	1.55070	−	8.12905i	0.0824188	−	0.432054i
$355$	14.0439	−	20.9932i	0.745371	−	1.11420i
$356$	1.65904	+	1.55794i	0.0879290	+	0.0825708i
$357$	−3.75433	−	2.72768i	−0.198700	−	0.144364i
$358$	−5.10937	+	10.8580i	−0.270038	+	0.573861i
$359$	7.71880	−	9.33043i	0.407383	−	0.492441i	−0.526422	−	0.850223i	$-0.676467\pi$
$359$	7.71880	−	9.33043i	0.407383	−	0.492441i	0.933805	+	0.357782i	$0.116467\pi$
$360$	−1.38337	−	1.75678i	−0.0729101	−	0.0925905i
$361$	0.475621	+	7.55978i	0.0250327	+	0.397883i
$362$	0.719366	−	11.4340i	0.0378091	−	0.600958i
$363$	1.69137	+	0.669661i	0.0887740	+	0.0351481i
$364$	0.888278	−	1.39970i	0.0465584	−	0.0733643i
$365$	−5.10283	+	14.5052i	−0.267094	+	0.759239i
$366$	−0.236433	+	3.75800i	−0.0123586	+	0.196434i
$367$	1.69998	+	0.214757i	0.0887380	+	0.0112102i	0.169577	−	0.985517i	$-0.445760\pi$
$367$	1.69998	+	0.214757i	0.0887380	+	0.0112102i	−0.0808388	+	0.996727i	$0.525760\pi$
$368$	−2.80137	+	2.03532i	−0.146032	+	0.106098i
$369$	−1.81425	−	9.51063i	−0.0944461	−	0.495104i
$370$	13.9724	+	5.92560i	0.726391	+	0.308057i
$371$	−4.92785	−	10.4722i	−0.255841	−	0.543690i
$372$	0.653374	−	0.613559i	0.0338759	−	0.0318116i
$373$	6.17264	−	9.72653i	0.319607	−	0.503621i	−0.646100	−	0.763253i	$-0.723601\pi$
$373$	6.17264	−	9.72653i	0.319607	−	0.503621i	0.965708	+	0.259632i	$0.0836012\pi$
$374$	−14.9588			−0.773500
$375$	11.0017	−	1.99056i	0.568126	−	0.102792i
$376$	−3.28123			−0.169216
$377$	7.89047	−	12.4334i	0.406380	−	0.640352i
$378$	0.809685	−	0.760345i	0.0416457	−	0.0391079i
$379$	9.66608	+	20.5415i	0.496513	+	1.05514i	0.983362	+	0.181658i	$0.0581462\pi$
$379$	9.66608	+	20.5415i	0.496513	+	1.05514i	−0.486849	+	0.873486i	$0.661854\pi$
$380$	−5.94009	−	9.87872i	−0.304720	−	0.506767i
$381$	2.56468	+	13.4445i	0.131392	+	0.688783i
$382$	1.77665	−	1.29081i	0.0909015	−	0.0660438i
$383$	−2.45230	−	0.309798i	−0.125307	−	0.0158299i	0.0624297	−	0.998049i	$-0.480115\pi$
$383$	−2.45230	−	0.309798i	−0.125307	−	0.0158299i	−0.187736	+	0.982219i	$0.560115\pi$
$384$	0.0627905	−	0.998027i	0.00320427	−	0.0509303i
$385$	−7.06604	−	5.39877i	−0.360119	−	0.275147i
$386$	−2.15293	+	3.39247i	−0.109581	+	0.172672i
$387$	−5.43977	−	2.15376i	−0.276519	−	0.109482i
$388$	−0.654769	+	10.4073i	−0.0332408	+	0.528348i
$389$	−1.16917	−	18.5835i	−0.0592794	−	0.942219i	−0.909477	−	0.415755i	$-0.863517\pi$
$389$	−1.16917	−	18.5835i	−0.0592794	−	0.942219i	0.850197	−	0.526464i	$-0.176483\pi$
$390$	−1.85566	+	2.77389i	−0.0939648	+	0.140461i
$391$	9.22166	−	11.1471i	0.466359	−	0.563731i
$392$	−2.45517	+	5.21749i	−0.124005	+	0.263523i
$393$	16.7987	+	12.2050i	0.847382	+	0.615659i
$394$	16.0447	+	15.0670i	0.808321	+	0.759064i
$395$	1.52935	+	39.4769i	0.0769500	+	1.98630i
$396$	0.670896	−	3.51696i	0.0337138	−	0.176734i
$397$	12.6794	+	26.9452i	0.636363	+	1.35234i	0.919435	+	0.393241i	$0.128646\pi$
$397$	12.6794	+	26.9452i	0.636363	+	1.35234i	−0.283072	+	0.959099i	$0.591354\pi$
$398$	−5.48742	−	1.40893i	−0.275060	−	0.0706233i
$399$	4.63233	−	3.36558i	0.231906	−	0.168490i
$400$	4.26033	+	2.61717i	0.213017	+	0.130859i
$401$	−11.3727	−	8.26272i	−0.567924	−	0.412621i	0.266427	−	0.963855i	$-0.414157\pi$
$401$	−11.3727	−	8.26272i	−0.567924	−	0.412621i	−0.834350	+	0.551234i	$0.814157\pi$
$402$	−2.66851	−	3.22568i	−0.133093	−	0.160882i
$403$	−1.17227	−	0.644459i	−0.0583948	−	0.0321028i
$404$	1.70794	+	0.938948i	0.0849732	+	0.0467144i
$405$	−1.66645	+	1.49095i	−0.0828067	+	0.0740860i
$406$	4.66609	−	9.91594i	0.231574	−	0.492120i
$407$	7.50952	+	23.1119i	0.372233	+	1.14562i
$408$	0.782877	+	4.10398i	0.0387582	+	0.203177i
$409$	12.5658	+	19.8005i	0.621338	+	0.979072i	0.998596	+	0.0529637i	$0.0168668\pi$
$409$	12.5658	+	19.8005i	0.621338	+	0.979072i	−0.377259	+	0.926108i	$0.623133\pi$
$410$	11.1565	+	18.5540i	0.550982	+	0.916316i
$411$	1.15579	−	0.457609i	0.0570108	−	0.0225722i
$412$	−7.51692	+	9.08640i	−0.370332	+	0.447655i
$413$	−8.90319	+	2.28595i	−0.438097	+	0.112484i
$414$	2.20720	+	2.66805i	0.108478	+	0.131127i
$415$	16.4142	−	1.67266i	0.805739	−	0.0821076i
$416$	−1.44562	+	0.371172i	−0.0708774	+	0.0181982i
$417$	0.685300	+	0.643540i	0.0335593	+	0.0315143i
$418$	5.70356	−	17.5537i	0.278970	−	0.858582i
$419$	0.812932	+	0.102697i	0.0397144	+	0.00501709i	0.145165	−	0.989407i	$-0.453629\pi$
$419$	0.812932	+	0.102697i	0.0397144	+	0.00501709i	−0.105451	+	0.994425i	$0.533629\pi$
$420$	−1.11136	+	2.22113i	−0.0542289	+	0.108380i
$421$	5.84375	−	5.48765i	0.284807	−	0.267452i	−0.528955	−	0.848650i	$-0.677416\pi$
$421$	5.84375	−	5.48765i	0.284807	−	0.267452i	0.813762	+	0.581198i	$0.197416\pi$
$422$	−14.4251	+	1.82231i	−0.702201	+	0.0887086i
$423$	0.206030	+	3.27475i	0.0100175	+	0.159224i
$424$	−3.21994	+	9.90997i	−0.156374	+	0.481271i
$425$	−19.9597	−	6.16440i	−0.968188	−	0.299017i
$426$	−3.49051	−	10.7427i	−0.169116	−	0.520484i
$427$	3.88866	−	1.53963i	0.188186	−	0.0745079i
$428$	0.271114	−	1.42123i	0.0131048	−	0.0686976i
$429$	−5.30161	+	0.669750i	−0.255964	+	0.0323358i
$430$	13.0786	+	0.315396i	0.630705	+	0.0152097i
$431$	−30.4432	+	16.7363i	−1.46640	+	0.806159i	−0.997043	−	0.0768502i	$-0.975514\pi$
$431$	−30.4432	+	16.7363i	−1.46640	+	0.806159i	−0.469355	+	0.883009i	$0.655514\pi$
$432$	−1.00000			−0.0481125
$433$	−6.09736	+	3.35205i	−0.293020	+	0.161089i	−0.621483	−	0.783428i	$-0.713470\pi$
$433$	−6.09736	+	3.35205i	−0.293020	+	0.161089i	0.328463	+	0.944517i	$0.393470\pi$
$434$	−0.925633	−	0.366484i	−0.0444318	−	0.0175918i
$435$	−9.87211	+	19.7301i	−0.473331	+	0.945986i
$436$	−14.3044	−	3.67275i	−0.685057	−	0.175893i
$437$	9.56472	+	15.0716i	0.457543	+	0.720972i
$438$	3.68469	+	5.80614i	0.176061	+	0.277428i
$439$	−16.9132	−	4.34257i	−0.807223	−	0.207260i	−0.177542	−	0.984113i	$-0.556814\pi$
$439$	−16.9132	−	4.34257i	−0.807223	−	0.207260i	−0.629681	+	0.776854i	$0.716814\pi$
$440$	1.31014	+	7.89804i	0.0624585	+	0.376525i
$441$	5.36136	+	2.12271i	0.255303	+	0.101082i
$442$	5.46438	−	3.00407i	0.259914	−	0.142889i
$443$	31.9681			1.51885			0.759425	−	0.650595i	$-0.225480\pi$
$443$	31.9681			1.51885			0.759425	+	0.650595i	$0.225480\pi$
$444$	5.94781	−	3.26983i	0.282270	−	0.155179i
$445$	−1.68882	+	4.80062i	−0.0800576	+	0.227571i
$446$	−15.6899	+	1.98209i	−0.742937	+	0.0938547i
$447$	2.07540	−	10.8797i	0.0981633	−	0.514590i
$448$	−1.03273	+	0.408886i	−0.0487918	+	0.0193180i
$449$	7.13104	+	21.9471i	0.336535	+	1.03575i	0.965961	+	0.258687i	$0.0832900\pi$
$449$	7.13104	+	21.9471i	0.336535	+	1.03575i	−0.629426	+	0.777060i	$0.716710\pi$
$450$	2.34450	−	4.41626i	0.110521	−	0.208184i
$451$	−10.7123	+	32.9690i	−0.504422	+	1.55245i
$452$	−1.05951	−	16.8405i	−0.0498353	−	0.792110i
$453$	16.4438	−	2.07733i	0.772595	−	0.0976014i
$454$	19.5787	−	18.3856i	0.918875	−	0.862881i
$455$	3.66539	+	0.553124i	0.171836	+	0.0259308i
$456$	−5.11442	−	0.646101i	−0.239505	−	0.0302565i
$457$	−3.47472	+	10.6941i	−0.162541	+	0.500249i	−0.998847	−	0.0480143i	$-0.984711\pi$
$457$	−3.47472	+	10.6941i	−0.162541	+	0.500249i	0.836306	+	0.548263i	$0.184711\pi$
$458$	2.98710	+	2.80508i	0.139578	+	0.131073i
$459$	4.04673	−	1.03902i	0.188885	−	0.0484975i
$460$	−6.69317	−	3.89262i	−0.312071	−	0.181494i
$461$	24.8888	+	30.0853i	1.15919	+	1.40121i	0.900280	+	0.435312i	$0.143362\pi$
$461$	24.8888	+	30.0853i	1.15919	+	1.40121i	0.258905	+	0.965903i	$0.416638\pi$
$462$	−3.85188	+	0.988995i	−0.179206	+	0.0460122i
$463$	−1.59117	+	1.92339i	−0.0739477	+	0.0893875i	−0.806190	−	0.591657i	$-0.798474\pi$
$463$	−1.59117	+	1.92339i	−0.0739477	+	0.0893875i	0.732242	+	0.681044i	$0.238474\pi$
$464$	−9.17360	+	3.63209i	−0.425874	+	0.168615i
$465$	1.84512	+	0.782501i	0.0855653	+	0.0362876i
$466$	−0.433978	−	0.683841i	−0.0201037	−	0.0316783i
$467$	−4.58542	−	24.0376i	−0.212188	−	1.11233i	−0.915766	−	0.401711i	$-0.868416\pi$
$467$	−4.58542	−	24.0376i	−0.212188	−	1.11233i	0.703578	−	0.710618i	$-0.251584\pi$
$468$	0.461211	+	1.41946i	0.0213195	+	0.0656146i
$469$	−1.97985	+	4.20740i	−0.0914210	+	0.194280i
$470$	−2.96300	−	6.71214i	−0.136673	−	0.309608i
$471$	0.186953	+	0.102778i	0.00861434	+	0.00473577i
$472$	7.25200	+	3.98682i	0.333800	+	0.183508i
$473$	13.3524	+	16.1403i	0.613944	+	0.742131i
$474$	14.2936	+	10.3849i	0.656526	+	0.476994i
$475$	14.8441	−	21.0718i	0.681094	−	0.966841i
$476$	3.75433	−	2.72768i	0.172079	−	0.125023i
$477$	10.0926	+	2.59134i	0.462108	+	0.118649i
$478$	−10.7637	−	22.8739i	−0.492318	−	1.04623i
$479$	−4.27015	+	22.3849i	−0.195108	+	1.02279i	0.741113	+	0.671381i	$0.234298\pi$
$479$	−4.27015	+	22.3849i	−0.195108	+	1.02279i	−0.936221	+	0.351412i	$0.885702\pi$
$480$	2.09828	−	0.772790i	0.0957731	−	0.0352729i
$481$	−7.38460	−	6.93460i	−0.336709	−	0.316190i
$482$	−2.19358	−	1.59373i	−0.0999146	−	0.0725922i
$483$	1.63759	−	3.48005i	0.0745129	−	0.158348i
$484$	−1.15955	+	1.40165i	−0.0527067	+	0.0637115i
$485$	−21.8805	+	8.05852i	−0.993544	+	0.365919i
$486$	0.0627905	+	0.998027i	0.00284824	+	0.0452714i
$487$	−1.15762	+	18.3998i	−0.0524566	+	0.833774i	0.880559	+	0.473937i	$0.157168\pi$
$487$	−1.15762	+	18.3998i	−0.0524566	+	0.833774i	−0.933015	+	0.359837i	$0.882832\pi$
$488$	−3.50101	−	1.38615i	−0.158483	−	0.0627479i
$489$	8.91777	−	14.0522i	0.403275	−	0.635460i
$490$	−12.8901	−	0.310850i	−0.582314	−	0.0140428i
$491$	0.732729	−	11.6464i	0.0330676	−	0.525594i	−0.946272	−	0.323372i	$-0.895184\pi$
$491$	0.732729	−	11.6464i	0.0330676	−	0.525594i	0.979340	−	0.202223i	$-0.0648164\pi$
$492$	9.60579	+	1.21349i	0.433062	+	0.0547085i
$493$	33.3493	−	24.2297i	1.50198	−	1.09125i
$494$	1.44171	+	7.55771i	0.0648656	+	0.340037i
$495$	7.80020	−	1.80348i	0.350593	−	0.0810603i
$496$	0.381626	+	0.810996i	0.0171355	+	0.0364148i
$497$	−9.14580	+	8.58848i	−0.410245	+	0.385246i
$498$	3.95368	−	6.23000i	0.177169	−	0.279173i
$499$	−11.0904			−0.496474			−0.248237	−	0.968699i	$-0.579851\pi$
$499$	−11.0904			−0.496474			−0.248237	+	0.968699i	$0.579851\pi$
$500$	−1.50658	+	11.0784i	−0.0673765	+	0.495440i
$501$	7.53531			0.336653
$502$	0.426640	−	0.672277i	0.0190419	−	0.0300052i
$503$	11.9213	−	11.1948i	0.531544	−	0.499153i	−0.371657	−	0.928370i	$-0.621210\pi$
$503$	11.9213	−	11.1948i	0.531544	−	0.499153i	0.903201	+	0.429217i	$0.141210\pi$
$504$	0.472924	+	1.00502i	0.0210657	+	0.0447669i
$505$	−0.378431	+	4.34168i	−0.0168400	+	0.193202i
$506$	−2.32310	−	12.1781i	−0.103275	−	0.541384i
$507$	−8.71507	+	6.33187i	−0.387050	+	0.281208i
$508$	−13.5790	−	1.71543i	−0.602471	−	0.0761098i
$509$	2.39220	−	38.0230i	0.106033	−	1.68534i	−0.481741	−	0.876314i	$-0.659995\pi$
$509$	2.39220	−	38.0230i	0.106033	−	1.68534i	0.587773	−	0.809026i	$-0.300005\pi$
$510$	−7.68824	+	5.30744i	−0.340441	+	0.235017i
$511$	4.09268	−	6.44903i	0.181050	−	0.285289i
$512$	0.929776	+	0.368125i	0.0410907	+	0.0162690i
$513$	−0.323689	+	5.14490i	−0.0142912	+	0.227153i
$514$	−0.994544	−	15.8078i	−0.0438675	−	0.697254i
$515$	−25.3752	−	7.17159i	−1.11817	−	0.316018i
$516$	3.72932	−	4.50798i	0.164174	−	0.198453i
$517$	5.00207	−	10.6299i	0.219991	−	0.467504i
$518$	−6.09909	−	4.43125i	−0.267979	−	0.194698i
$519$	−1.68837	−	1.58549i	−0.0741114	−	0.0695952i
$520$	−2.06470	−	2.62201i	−0.0905429	−	0.114983i
$521$	8.05223	−	42.2113i	0.352775	−	1.84931i	−0.155128	−	0.987894i	$-0.549579\pi$
$521$	8.05223	−	42.2113i	0.352775	−	1.84931i	0.507902	−	0.861415i	$-0.330421\pi$
$522$	4.20093	+	8.92744i	0.183870	+	0.390743i
$523$	23.4688	+	6.02576i	1.02622	+	0.263488i	0.724036	−	0.689762i	$-0.242285\pi$
$523$	23.4688	+	6.02576i	1.02622	+	0.263488i	0.302183	+	0.953250i	$0.402285\pi$
$524$	−16.7987	+	12.2050i	−0.733854	+	0.533176i
$525$	−5.54718	−	0.267701i	−0.242099	−	0.0116834i
$526$	−21.1795	−	15.3878i	−0.923472	−	0.670942i
$527$	−2.38698	−	2.88536i	−0.103978	−	0.125688i
$528$	3.13751	+	1.72486i	0.136543	+	0.0750649i
$529$	−9.64795	−	5.30401i	−0.419476	−	0.230609i
$530$	−23.1797	+	2.36209i	−1.00686	+	0.102603i
$531$	3.52360	−	7.48802i	0.152911	−	0.324952i
$532$	1.76939	+	5.44563i	0.0767128	+	0.236098i
$533$	−2.70779	−	14.1947i	−0.117287	−	0.614841i
$534$	1.21947	+	1.92158i	0.0527718	+	0.0831551i
$535$	3.15211	−	0.728797i	0.136278	−	0.0315087i
$536$	3.89242	−	1.54112i	0.168127	−	0.0665661i
$537$	−7.64911	+	9.24619i	−0.330084	+	0.399003i
$538$	16.9482	−	4.35156i	0.730689	−	0.187609i
$539$	−13.1599	−	15.9076i	−0.566838	−	0.685190i
$540$	−0.903017	−	2.04562i	−0.0388597	−	0.0880295i
$541$	11.8659	−	3.04666i	0.510157	−	0.130986i	0.0151673	−	0.999885i	$-0.495172\pi$
$541$	11.8659	−	3.04666i	0.510157	−	0.130986i	0.494989	+	0.868899i	$0.335172\pi$
$542$	6.86902	+	6.45044i	0.295050	+	0.277070i
$543$	3.54029	−	10.8959i	0.151928	−	0.467587i
$544$	−4.14504	−	0.523641i	−0.177717	−	0.0224509i
$545$	−5.40408	−	32.5779i	−0.231485	−	1.39548i
$546$	1.20846	−	1.13482i	0.0517174	−	0.0485659i
$547$	8.43741	−	1.06589i	0.360758	−	0.0455743i	0.0571345	−	0.998366i	$-0.481804\pi$
$547$	8.43741	−	1.06589i	0.360758	−	0.0455743i	0.303623	+	0.952792i	$0.401804\pi$
$548$	0.0780537	+	1.24063i	0.00333429	+	0.0529970i
$549$	−1.16358	+	3.58114i	−0.0496605	+	0.152839i
$550$	−14.9733	+	9.81212i	−0.638464	+	0.418390i
$551$	15.7173	+	48.3729i	0.669580	+	2.06075i
$552$	−3.21953	+	1.27470i	−0.137032	+	0.0542549i
$553$	3.67720	−	19.2765i	0.156370	−	0.819722i
$554$	23.8621	−	3.01448i	1.01380	−	0.128073i
$555$	12.0598	+	9.21423i	0.511910	+	0.391122i
$556$	−0.823812	+	0.452895i	−0.0349374	+	0.0192070i
$557$	−39.6821			−1.68138			−0.840692	−	0.541514i	$-0.817851\pi$
$557$	−39.6821			−1.68138			−0.840692	+	0.541514i	$0.817851\pi$
$558$	0.785433	−	0.431796i	0.0332500	−	0.0182794i
$559$	−8.11891	−	3.21450i	−0.343393	−	0.135959i
$560$	−1.76900	−	1.74334i	−0.0747537	−	0.0736694i
$561$	−14.4888	−	3.72010i	−0.611719	−	0.157063i
$562$	0.341260	+	0.537740i	0.0143952	+	0.0226832i
$563$	8.41658	+	13.2624i	0.354717	+	0.558944i	0.974092	−	0.226151i	$-0.0726142\pi$
$563$	8.41658	+	13.2624i	0.354717	+	0.558944i	−0.619376	+	0.785095i	$0.712614\pi$
$564$	−3.17814	−	0.816008i	−0.133824	−	0.0343601i
$565$	33.4925	−	17.3746i	1.40904	−	0.730955i
$566$	15.6849	+	6.21009i	0.659285	+	0.261029i
$567$	0.973337	−	0.535097i	0.0408763	−	0.0224719i
$568$	11.2955			0.473949
$569$	13.5312	−	7.43883i	0.567257	−	0.311852i	−0.172194	−	0.985063i	$-0.555085\pi$
$569$	13.5312	−	7.43883i	0.567257	−	0.311852i	0.739450	+	0.673211i	$0.235085\pi$
$570$	−3.29673	−	11.0456i	−0.138085	−	0.462649i
$571$	−32.4292	+	4.09675i	−1.35712	+	0.171444i	−0.769993	−	0.638053i	$-0.779740\pi$
$571$	−32.4292	+	4.09675i	−1.35712	+	0.171444i	−0.587125	+	0.809496i	$0.699740\pi$
$572$	1.00132	−	5.24910i	0.0418673	−	0.219476i
$573$	2.04185	−	0.808425i	0.0852995	−	0.0337724i
$574$	−3.32323	−	10.2279i	−0.138709	−	0.426902i
$575$	1.91877	−	17.2068i	0.0800181	−	0.717573i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	0.725774	+	11.5359i	0.0302144	+	0.480244i	0.983817	+	0.179176i	$0.0573431\pi$
$577$	0.725774	+	11.5359i	0.0302144	+	0.480244i	−0.953603	+	0.301068i	$0.902657\pi$
$578$	0.451990	−	0.0570997i	0.0188003	−	0.00237503i
$579$	−2.92896	+	2.75048i	−0.121723	+	0.114306i
$580$	−15.7138	−	15.4859i	−0.652480	−	0.643016i
$581$	−8.13104	−	1.02719i	−0.337332	−	0.0426150i
$582$	−3.22238	+	9.91745i	−0.133572	+	0.411092i
$583$	−27.1959	−	25.5387i	−1.12634	−	1.05770i
$584$	−6.66060	+	1.71015i	−0.275618	+	0.0707666i
$585$	−2.48720	+	2.22526i	−0.102833	+	0.0920032i
$586$	−3.98428	−	4.81616i	−0.164589	−	0.198954i
$587$	29.6661	−	7.61696i	1.22445	−	0.314386i	0.419516	−	0.907748i	$-0.362200\pi$
$587$	29.6661	−	7.61696i	1.22445	−	0.314386i	0.804936	+	0.593362i	$0.202200\pi$
$588$	−3.67557	+	4.44300i	−0.151578	+	0.183226i
$589$	4.29602	−	1.70091i	0.177014	−	0.0700849i
$590$	−1.60684	+	18.4350i	−0.0661525	+	0.758957i
$591$	11.7936	+	18.5838i	0.485125	+	0.764435i
$592$	1.27182	+	6.66713i	0.0522716	+	0.274017i
$593$	14.5755	+	44.8588i	0.598545	+	1.84213i	0.536225	+	0.844075i	$0.319850\pi$
$593$	14.5755	+	44.8588i	0.598545	+	1.84213i	0.0623195	+	0.998056i	$0.480150\pi$
$594$	1.52445	−	3.23962i	0.0625490	−	0.132923i
$595$	8.97001	+	5.21678i	0.367735	+	0.213867i
$596$	9.70583	+	5.33582i	0.397566	+	0.218564i
$597$	−4.96464	−	2.72933i	−0.203189	−	0.111704i
$598$	3.29427	+	3.98209i	0.134713	+	0.162840i
$599$	−22.7648	−	16.5396i	−0.930144	−	0.675789i	0.0158843	−	0.999874i	$-0.494944\pi$
$599$	−22.7648	−	16.5396i	−0.930144	−	0.675789i	−0.946028	+	0.324085i	$0.894944\pi$
$600$	3.47562	+	3.59445i	0.141892	+	0.146743i
$601$	−26.6251	+	19.3443i	−1.08606	+	0.789070i	−0.978730	−	0.205153i	$-0.934231\pi$
$601$	−26.6251	+	19.3443i	−1.08606	+	0.789070i	−0.107332	+	0.994223i	$0.534231\pi$
$602$	−6.29428	−	1.61610i	−0.256536	−	0.0658671i
$603$	−1.78248	−	3.78797i	−0.0725883	−	0.154258i
$604$	−3.10574	+	16.2809i	−0.126371	+	0.662459i
$605$	−3.91434	−	1.10628i	−0.159141	−	0.0449766i
$606$	1.42078	+	1.33420i	0.0577151	+	0.0541981i
$607$	8.92751	+	6.48622i	0.362356	+	0.263267i	0.754034	−	0.656835i	$-0.228105\pi$
$607$	8.92751	+	6.48622i	0.362356	+	0.263267i	−0.391678	+	0.920102i	$0.628105\pi$
$608$	2.19492	−	4.66444i	0.0890158	−	0.189168i
$609$	6.98549	−	8.44401i	0.283066	−	0.342168i
$610$	−0.325941	−	8.41345i	−0.0131969	−	0.340650i
$611$	0.307502	+	4.88760i	0.0124402	+	0.197731i
$612$	−0.262338	+	4.16974i	−0.0106044	+	0.168552i
$613$	−13.4766	−	5.33575i	−0.544314	−	0.215509i	0.0798441	−	0.996807i	$-0.474558\pi$
$613$	−13.4766	−	5.33575i	−0.544314	−	0.215509i	−0.624158	+	0.781298i	$0.714558\pi$
$614$	13.5169	−	21.2992i	0.545498	−	0.859567i
$615$	6.19184	+	20.7456i	0.249679	+	0.836543i
$616$	0.249707	−	3.96897i	0.0100610	−	0.159915i
$617$	−32.0312	−	4.04648i	−1.28953	−	0.162905i	−0.549507	−	0.835489i	$-0.685184\pi$
$617$	−32.0312	−	4.04648i	−1.28953	−	0.162905i	−0.740021	+	0.672584i	$0.765184\pi$
$618$	−9.54046	+	6.93155i	−0.383774	+	0.278828i
$619$	1.16408	+	6.10233i	0.0467884	+	0.245273i	0.997996	−	0.0632785i	$-0.0201556\pi$
$619$	1.16408	+	6.10233i	0.0467884	+	0.245273i	−0.951208	+	0.308552i	$0.900156\pi$
$620$	−1.31437	+	1.51300i	−0.0527866	+	0.0607637i
$621$	1.47434	+	3.13313i	0.0591633	+	0.125728i
$622$	−1.75100	+	1.64429i	−0.0702086	+	0.0659302i
$623$	1.35450	−	2.13436i	0.0542670	−	0.0855111i
$624$	−1.49251			−0.0597482
$625$	−24.0226	+	6.92206i	−0.960904	+	0.276882i
$626$	−6.30379			−0.251950
$627$	9.88981	−	15.5838i	0.394961	−	0.622359i
$628$	−0.155520	+	0.146043i	−0.00620591	+	0.00582774i
$629$	−12.0740	−	25.6586i	−0.481423	−	1.02308i
$630$	−1.62882	+	1.87497i	−0.0648938	+	0.0747006i
$631$	−1.23392	−	6.46841i	−0.0491214	−	0.257503i	0.949252	−	0.314516i	$-0.101842\pi$
$631$	−1.23392	−	6.46841i	−0.0491214	−	0.257503i	−0.998373	+	0.0570130i	$0.981842\pi$
$632$	−14.2936	+	10.3849i	−0.568568	+	0.413089i
$633$	−14.4251	−	1.82231i	−0.573345	−	0.0724303i
$634$	1.13475	−	18.0363i	0.0450667	−	0.716314i
$635$	−8.75296	−	29.3265i	−0.347351	−	1.16379i
$636$	−5.58329	+	8.79786i	−0.221392	+	0.348858i
$637$	8.00188	+	3.16817i	0.317046	+	0.125527i
$638$	2.21812	−	35.2560i	0.0878161	−	1.39580i
$639$	−0.709251	−	11.2732i	−0.0280575	−	0.445962i
$640$	0.0865613	+	2.23439i	0.00342164	+	0.0883221i
$641$	−17.1315	+	20.7084i	−0.676654	+	0.817934i	−0.991348	−	0.131259i	$-0.958098\pi$
$641$	−17.1315	+	20.7084i	−0.676654	+	0.817934i	0.314694	+	0.949193i	$0.398098\pi$
$642$	0.616041	−	1.30915i	0.0243132	−	0.0516682i
$643$	−34.2938	−	24.9159i	−1.35242	−	0.982588i	−0.998887	−	0.0471639i	$-0.984982\pi$
$643$	−34.2938	−	24.9159i	−1.35242	−	0.982588i	−0.353529	−	0.935424i	$-0.615018\pi$
$644$	2.80369	+	2.63284i	0.110481	+	0.103748i
$645$	12.5893	+	3.55800i	0.495701	+	0.140096i
$646$	−4.03578	+	21.1563i	−0.158786	+	0.832384i
$647$	−5.98376	−	12.7161i	−0.235246	−	0.499923i	0.751993	−	0.659172i	$-0.229093\pi$
$647$	−5.98376	−	12.7161i	−0.235246	−	0.499923i	−0.987239	+	0.159248i	$0.949093\pi$
$648$	−0.968583	−	0.248690i	−0.0380495	−	0.00976946i
$649$	−23.9711	+	17.4160i	−0.940949	+	0.683639i
$650$	3.49919	−	6.59131i	0.137249	−	0.258532i
$651$	−0.805412	−	0.585166i	−0.0315666	−	0.0229345i
$652$	10.6087	+	12.8237i	0.415467	+	0.502213i
$653$	1.11106	+	0.610813i	0.0434793	+	0.0239030i	0.503345	−	0.864086i	$-0.332102\pi$
$653$	1.11106	+	0.610813i	0.0434793	+	0.0239030i	−0.459866	+	0.887988i	$0.652102\pi$
$654$	−12.9416	−	7.11472i	−0.506058	−	0.278208i
$655$	−40.1362	−	23.3424i	−1.56825	−	0.912065i
$656$	−4.12245	+	8.76065i	−0.160955	+	0.342046i
$657$	2.12500	+	6.54008i	0.0829041	+	0.255153i
$658$	0.682920	+	3.57999i	0.0266230	+	0.139563i
$659$	−1.21851	−	1.92007i	−0.0474664	−	0.0747952i	0.819766	−	0.572699i	$-0.194103\pi$
$659$	−1.21851	−	1.92007i	−0.0474664	−	0.0747952i	−0.867233	+	0.497903i	$0.834103\pi$
$660$	−0.695184	+	7.97573i	−0.0270600	+	0.310455i
$661$	6.27104	−	2.48288i	0.243915	−	0.0965729i	−0.242986	−	0.970030i	$-0.578127\pi$
$661$	6.27104	−	2.48288i	0.243915	−	0.0965729i	0.486902	+	0.873457i	$0.338127\pi$
$662$	0.988902	−	1.19538i	0.0384348	−	0.0464596i
$663$	6.03978	−	1.55075i	0.234566	−	0.0602262i
$664$	4.70333	+	5.68535i	0.182525	+	0.220634i
$665$	−9.54189	+	8.53700i	−0.370019	+	0.331050i
$666$	6.57412	−	1.68795i	0.254742	−	0.0654066i
$667$	24.9048	+	23.3872i	0.964319	+	0.905556i
$668$	−2.32854	+	7.16650i	−0.0900938	+	0.277280i
$669$	−15.6899	−	1.98209i	−0.606605	−	0.0766321i
$670$	6.66746	+	6.57075i	0.257587	+	0.253850i
$671$	9.82771	−	9.22884i	0.379395	−	0.356275i
$672$	−1.10197	+	0.139211i	−0.0425093	+	0.00537018i
$673$	−1.61656	−	25.6944i	−0.0623137	−	0.990447i	−0.897650	−	0.440708i	$-0.854727\pi$
$673$	−1.61656	−	25.6944i	−0.0623137	−	0.990447i	0.835337	−	0.549739i	$-0.185273\pi$
$674$	−2.79409	+	8.59933i	−0.107624	+	0.331234i
$675$	3.36912	−	3.69446i	0.129677	−	0.142200i
$676$	−3.32886	−	10.2452i	−0.128033	−	0.394045i
$677$	−14.1751	+	5.61231i	−0.544793	+	0.215699i	−0.624368	−	0.781130i	$-0.714644\pi$
$677$	−14.1751	+	5.61231i	−0.544793	+	0.215699i	0.0795755	+	0.996829i	$0.474644\pi$
$678$	3.16183	−	16.5749i	0.121429	−	0.636555i
$679$	11.4911	−	1.45167i	0.440989	−	0.0557099i
$680$	−2.67188	−	8.95204i	−0.102462	−	0.343295i
$681$	23.5359	−	12.9390i	0.901899	−	0.495823i
$682$	−3.20909			−0.122882
$683$	−7.50902	+	4.12812i	−0.287325	+	0.157958i	−0.618898	−	0.785471i	$-0.712421\pi$
$683$	−7.50902	+	4.12812i	−0.287325	+	0.157958i	0.331573	+	0.943429i	$0.392421\pi$
$684$	−4.79306	−	1.89771i	−0.183267	−	0.0725606i
$685$	−2.46737	+	1.27998i	−0.0942733	+	0.0489054i
$686$	13.7344	+	3.52639i	0.524381	+	0.134638i
$687$	2.19566	+	3.45981i	0.0837698	+	0.132000i
$688$	3.13492	+	4.93984i	0.119518	+	0.188330i
$689$	15.0633	+	3.86760i	0.573866	+	0.147344i
$690$	−5.51484	−	5.43485i	−0.209946	−	0.206901i
$691$	20.1024	+	7.95909i	0.764730	+	0.302778i	0.717920	−	0.696126i	$-0.245094\pi$
$691$	20.1024	+	7.95909i	0.764730	+	0.302778i	0.0468102	+	0.998904i	$0.485094\pi$
$692$	2.02963	−	1.11580i	0.0771548	−	0.0424162i
$693$	−3.97682			−0.151067
$694$	−20.2693	+	11.1431i	−0.769413	+	0.422988i
$695$	−1.67037	−	1.27623i	−0.0633606	−	0.0484104i
$696$	−9.78866	+	1.23660i	−0.371038	+	0.0468730i
$697$	7.57992	−	39.7353i	0.287110	−	1.50508i
$698$	4.53174	−	1.79424i	0.171529	−	0.0679131i
$699$	−0.250280	−	0.770283i	−0.00946646	−	0.0291348i
$700$	1.96877	−	5.19295i	0.0744125	−	0.196275i
$701$	10.3191	−	31.7588i	0.389745	−	1.19951i	−0.543234	−	0.839581i	$-0.682800\pi$
$701$	10.3191	−	31.7588i	0.389745	−	1.19951i	0.932979	−	0.359931i	$-0.117200\pi$
$702$	0.0937155	+	1.48956i	0.00353706	+	0.0562200i
$703$	34.7134	−	4.38532i	1.30924	−	0.165395i
$704$	−2.60998	+	2.45094i	−0.0983675	+	0.0923732i
$705$	−1.20067	−	7.23814i	−0.0452200	−	0.272604i
$706$	12.9635	+	1.63768i	0.487889	+	0.0616348i
$707$	0.668969	−	2.05888i	0.0251592	−	0.0774320i
$708$	6.03268	+	5.66506i	0.226722	+	0.212906i
$709$	46.8488	−	12.0287i	1.75944	−	0.451748i	0.775666	−	0.631143i	$-0.217414\pi$
$709$	46.8488	−	12.0287i	1.75944	−	0.451748i	0.983777	+	0.179395i	$0.0574139\pi$
$710$	10.2000	+	23.1063i	0.382801	+	0.867165i
$711$	11.2619	+	13.6133i	0.422354	+	0.510539i
$712$	−2.20437	+	0.565987i	−0.0826124	+	0.0212113i
$713$	1.97831	−	2.39137i	0.0740884	−	0.0895575i
$714$	4.31472	−	1.70832i	0.161474	−	0.0639322i
$715$	11.6419	−	2.69171i	0.435381	−	0.100664i
$716$	−6.42994	−	10.1320i	−0.240298	−	0.378649i
$717$	−4.73698	−	24.8321i	−0.176906	−	0.927373i
$718$	3.74200	+	11.5167i	0.139650	+	0.429799i
$719$	−0.199611	+	0.424195i	−0.00744424	+	0.0158198i	−0.908515	−	0.417853i	$-0.862783\pi$
$719$	−0.199611	+	0.424195i	−0.00744424	+	0.0158198i	0.901070	+	0.433673i	$0.142783\pi$
$720$	2.22455	−	0.226689i	0.0829040	−	0.00844821i
$721$	11.4782	+	6.31021i	0.427472	+	0.235005i
$722$	−6.63778	−	3.64915i	−0.247033	−	0.135807i
$723$	−1.72832	−	2.08918i	−0.0642768	−	0.0776973i
$724$	9.26859	+	6.73403i	0.344464	+	0.250268i
$725$	17.4884	−	46.1284i	0.649502	−	1.71317i
$726$	−1.47170	+	1.06925i	−0.0546197	+	0.0396836i
$727$	−43.2520	−	11.1052i	−1.60413	−	0.411870i	−0.662646	−	0.748933i	$-0.730567\pi$
$727$	−43.2520	−	11.1052i	−1.60413	−	0.411870i	−0.941482	+	0.337063i	$0.890567\pi$
$728$	0.705844	+	1.50000i	0.0261603	+	0.0555935i
$729$	−0.187381	+	0.982287i	−0.00694005	+	0.0363810i
$730$	−9.51296	−	12.0808i	−0.352090	−	0.447129i
$731$	−17.8188	−	16.7329i	−0.659051	−	0.618890i
$732$	−3.04630	−	2.21326i	−0.112594	−	0.0818046i
$733$	17.7272	−	37.6723i	0.654770	−	1.39146i	−0.251125	−	0.967955i	$-0.580800\pi$
$733$	17.7272	−	37.6723i	0.654770	−	1.39146i	0.905895	−	0.423503i	$-0.139200\pi$
$734$	−1.09222	+	1.32026i	−0.0403145	+	0.0487318i
$735$	−12.4078	−	3.50671i	−0.457668	−	0.129347i
$736$	−0.217424	−	3.45586i	−0.00801435	−	0.127385i
$737$	−0.941161	+	14.9593i	−0.0346681	+	0.551034i
$738$	9.00222	+	3.56423i	0.331376	+	0.131201i
$739$	−24.4951	+	38.5981i	−0.901068	+	1.41986i	0.00651310	+	0.999979i	$0.497927\pi$
$739$	−24.4951	+	38.5981i	−0.901068	+	1.41986i	−0.907581	+	0.419877i	$0.862073\pi$
$740$	−12.4899	+	8.62220i	−0.459139	+	0.316959i
$741$	−0.483110	+	7.67881i	−0.0177475	+	0.282088i
$742$	11.4825	+	1.45057i	0.421534	+	0.0532522i
$743$	9.53864	−	6.93023i	0.349939	−	0.254245i	−0.398905	−	0.916992i	$-0.630610\pi$
$743$	9.53864	−	6.93023i	0.349939	−	0.254245i	0.748843	+	0.662747i	$0.230610\pi$
$744$	0.167950	+	0.880424i	0.00615734	+	0.0322779i
$745$	−2.15054	+	24.6728i	−0.0787896	+	0.903940i
$746$	4.90491	+	10.4235i	0.179582	+	0.381630i
$747$	5.37880	−	5.05103i	0.196800	−	0.184808i
$748$	8.01532	−	12.6301i	0.293069	−	0.461803i
$749$	−1.60706			−0.0587207
$750$	−4.21433	+	10.3556i	−0.153886	+	0.378135i
$751$	−5.08026			−0.185381			−0.0926906	−	0.995695i	$-0.529547\pi$
$751$	−5.08026			−0.185381			−0.0926906	+	0.995695i	$0.529547\pi$
$752$	1.75817	−	2.77043i	0.0641138	−	0.101027i
$753$	0.580425	−	0.545055i	0.0211519	−	0.0198629i
$754$	6.26994	+	13.3243i	0.228338	+	0.485242i
$755$	−36.1090	+	8.34874i	−1.31414	+	0.303842i
$756$	0.208129	+	1.09105i	0.00756959	+	0.0396812i
$757$	19.0055	−	13.8083i	0.690766	−	0.501871i	−0.186146	−	0.982522i	$-0.559600\pi$
$757$	19.0055	−	13.8083i	0.690766	−	0.501871i	0.876912	+	0.480651i	$0.159600\pi$
$758$	−22.5231	−	2.84533i	−0.818075	−	0.103347i
$759$	0.778460	−	12.3733i	0.0282563	−	0.449121i
$760$	11.5237	+	0.277900i	0.418010	+	0.0100805i
$761$	−27.5898	+	43.4745i	−1.00013	+	1.57595i	−0.196773	+	0.980449i	$0.563046\pi$
$761$	−27.5898	+	43.4745i	−1.00013	+	1.57595i	−0.803355	+	0.595501i	$0.796954\pi$
$762$	−12.7258	−	5.03850i	−0.461007	−	0.182525i
$763$	−1.02999	+	16.3713i	−0.0372882	+	0.592679i
$764$	0.137892	+	2.19173i	0.00498876	+	0.0792940i
$765$	−8.76661	+	3.22871i	−0.316957	+	0.116734i
$766$	1.57558	−	1.90455i	0.0569280	−	0.0688141i
$767$	5.25900	−	11.1759i	0.189892	−	0.403540i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	−17.1213	−	16.0779i	−0.617408	−	0.579785i	0.311431	−	0.950269i	$-0.399192\pi$
$769$	−17.1213	−	16.0779i	−0.617408	−	0.579785i	−0.928839	+	0.370484i	$0.879192\pi$
$770$	8.34450	−	3.07325i	0.300715	−	0.110752i
$771$	2.96795	−	15.5585i	0.106888	−	0.560327i
$772$	−1.71076	−	3.63555i	−0.0615716	−	0.130846i
$773$	4.19672	+	1.07753i	0.150946	+	0.0387562i	0.323407	−	0.946260i	$-0.395172\pi$
$773$	4.19672	+	1.07753i	0.150946	+	0.0387562i	−0.172461	+	0.985016i	$0.555172\pi$
$774$	4.73325	−	3.43891i	0.170133	−	0.123609i
$775$	−4.28194	−	1.32244i	−0.153812	−	0.0475035i
$776$	−8.43629	−	6.12932i	−0.302845	−	0.220030i
$777$	−4.80547	−	5.80882i	−0.172395	−	0.208390i
$778$	16.3170	+	8.97036i	0.584993	+	0.321603i
$779$	43.7383	+	24.0453i	1.56709	+	0.861513i
$780$	−1.34776	−	3.05311i	−0.0482576	−	0.109319i
$781$	−17.2195	+	36.5932i	−0.616161	+	1.30941i
$782$	4.47057	+	13.7590i	0.159867	+	0.492021i
$783$	1.84879	+	9.69170i	0.0660704	+	0.346353i
$784$	−3.08973	−	4.86864i	−0.110348	−	0.173880i
$785$	−0.439185	−	0.186255i	−0.0156752	−	0.00664772i
$786$	−19.3062	+	7.64386i	−0.688629	+	0.272647i
$787$	−5.71784	+	6.91169i	−0.203819	+	0.246375i	−0.862512	−	0.506037i	$-0.831110\pi$
$787$	−5.71784	+	6.91169i	−0.203819	+	0.246375i	0.658692	+	0.752412i	$0.271110\pi$
$788$	−21.3187	+	5.47370i	−0.759446	+	0.194993i
$789$	−16.6874	−	20.1715i	−0.594086	−	0.718126i
$790$	−34.1509	−	19.8615i	−1.21503	−	0.706640i
$791$	−18.1533	+	4.66099i	−0.645458	+	0.165726i
$792$	2.60998	+	2.45094i	0.0927417	+	0.0870903i
$793$	−1.73666	+	5.34488i	−0.0616705	+	0.189802i
$794$	−29.5446	−	3.73235i	−1.04850	−	0.132456i
$795$	−23.0389	−	3.47667i	−0.817105	−	0.123305i
$796$	4.12991	−	3.87824i	0.146381	−	0.137461i
$797$	50.9131	−	6.43182i	1.80343	−	0.227827i	0.849447	−	0.527674i	$-0.176936\pi$
$797$	50.9131	−	6.43182i	1.80343	−	0.227827i	0.953987	+	0.299847i	$0.0969356\pi$
$798$	0.359530	+	5.71457i	0.0127272	+	0.202294i
$799$	−4.23629	+	13.0380i	−0.149869	+	0.461250i
$800$	−4.49255	+	2.19477i	−0.158836	+	0.0775967i
$801$	0.703284	+	2.16449i	0.0248493	+	0.0764783i
$802$	13.0702	−	5.17487i	0.461526	−	0.182731i
$803$	4.61351	−	24.1849i	0.162807	−	0.853466i
$804$	4.15339	−	0.524695i	0.146479	−	0.0185046i
$805$	−2.85400	+	8.11277i	−0.100590	+	0.285938i
$806$	1.17227	−	0.644459i	0.0412913	−	0.0227001i
$807$	17.4979			0.615956
$808$	−1.70794	+	0.938948i	−0.0600851	+	0.0330321i
$809$	−17.4525	−	6.90994i	−0.613598	−	0.242941i	0.0407073	−	0.999171i	$-0.487039\pi$
$809$	−17.4525	−	6.90994i	−0.613598	−	0.242941i	−0.654305	+	0.756230i	$0.727039\pi$
$810$	−0.365922	−	2.20592i	−0.0128572	−	0.0775083i
$811$	−44.0103	−	11.2999i	−1.54541	−	0.396794i	−0.622755	−	0.782417i	$-0.713987\pi$
$811$	−44.0103	−	11.2999i	−1.54541	−	0.396794i	−0.922657	+	0.385622i	$0.873987\pi$
$812$	5.87209	+	9.25294i	0.206070	+	0.324714i
$813$	5.04906	+	7.95604i	0.177078	+	0.279031i
$814$	−23.5378	−	6.04349i	−0.825001	−	0.211824i
$815$	−16.6525	+	33.2813i	−0.583313	+	1.16579i
$816$	−3.88459	−	1.53802i	−0.135988	−	0.0538415i
$817$	26.4297	−	14.5299i	0.924658	−	0.508335i
$818$	−23.4512			−0.819952
$819$	1.45272	−	0.798637i	0.0507620	−	0.0279066i
$820$	−21.6436	−	0.521946i	−0.755828	−	0.0182271i
$821$	11.0931	−	1.40138i	0.387151	−	0.0489085i	0.0706511	−	0.997501i	$-0.477492\pi$
$821$	11.0931	−	1.40138i	0.387151	−	0.0489085i	0.316500	+	0.948593i	$0.397492\pi$
$822$	−0.232930	+	1.22106i	−0.00812437	+	0.0425894i
$823$	−17.0285	+	6.74205i	−0.593575	+	0.235013i	−0.645654	−	0.763630i	$-0.723415\pi$
$823$	−17.0285	+	6.74205i	−0.593575	+	0.235013i	0.0520790	+	0.998643i	$0.483415\pi$
$824$	−3.64413	−	11.2155i	−0.126949	−	0.390710i
$825$	−16.9431	+	5.78014i	−0.589882	+	0.201239i
$826$	2.84048	−	8.74208i	0.0988328	−	0.304176i
$827$	1.42099	+	22.5860i	0.0494126	+	0.785391i	0.942229	+	0.334970i	$0.108726\pi$
$827$	1.42099	+	22.5860i	0.0494126	+	0.785391i	−0.892816	+	0.450421i	$0.851274\pi$
$828$	−3.43538	+	0.433990i	−0.119388	+	0.0150822i
$829$	5.02739	−	4.72103i	0.174608	−	0.163968i	−0.592316	−	0.805706i	$-0.701786\pi$
$829$	5.02739	−	4.72103i	0.174608	−	0.163968i	0.766924	+	0.641738i	$0.221786\pi$
$830$	−7.38287	+	14.7552i	−0.256263	+	0.512160i
$831$	23.8621	+	3.01448i	0.827765	+	0.104571i
$832$	0.461211	−	1.41946i	0.0159896	−	0.0492110i
$833$	17.5619	+	16.4918i	0.608485	+	0.571405i
$834$	−0.910561	+	0.233792i	−0.0315301	+	0.00809557i
$835$	−16.7626	+	1.70817i	−0.580095	+	0.0591137i
$836$	11.7650	+	14.2214i	0.406901	+	0.491859i
$837$	0.868141	−	0.222901i	0.0300073	−	0.00770457i
$838$	−0.522301	+	0.631354i	−0.0180426	+	0.0218098i
$839$	0.288660	−	0.114289i	0.00996566	−	0.00394569i	−0.363136	−	0.931736i	$-0.618294\pi$
$839$	0.288660	−	0.114289i	0.00996566	−	0.00394569i	0.373102	+	0.927790i	$0.378294\pi$
$840$	−1.27987	−	2.12850i	−0.0441597	−	0.0734401i
$841$	36.6222	+	57.7073i	1.26283	+	1.98991i
$842$	1.50214	+	7.87447i	0.0517670	+	0.271372i
$843$	0.196808	+	0.605714i	0.00677844	+	0.0208619i
$844$	6.19071	−	13.1559i	0.213093	−	0.452846i
$845$	17.9517	−	16.0611i	0.617558	−	0.552520i
$846$	−2.87536	−	1.58074i	−0.0988570	−	0.0543471i
$847$	1.77061	+	0.973403i	0.0608390	+	0.0334465i
$848$	−6.64193	−	8.02871i	−0.228085	−	0.275707i
$849$	13.6477	+	9.91566i	0.468389	+	0.340304i
$850$	15.8997	−	13.5495i	0.545356	−	0.464744i
$851$	19.0139	−	13.8144i	0.651789	−	0.473552i
$852$	10.9406	+	2.80908i	0.374820	+	0.0962375i
$853$	10.0429	+	21.3423i	0.343863	+	0.730745i	0.999708	−	0.0241496i	$-0.00768779\pi$
$853$	10.0429	+	21.3423i	0.343863	+	0.730745i	−0.655846	+	0.754895i	$0.727688\pi$
$854$	−0.783697	+	4.10828i	−0.0268175	+	0.140582i
$855$	−0.446229	−	11.5184i	−0.0152607	−	0.393922i
$856$	1.05471	+	0.990441i	0.0360493	+	0.0338526i
$857$	5.64324	+	4.10005i	0.192769	+	0.140055i	0.679984	−	0.733227i	$-0.261987\pi$
$857$	5.64324	+	4.10005i	0.192769	+	0.140055i	−0.487214	+	0.873282i	$0.661987\pi$
$858$	2.27526	−	4.83517i	0.0776761	−	0.165070i
$859$	33.9592	−	41.0496i	1.15867	−	1.40060i	0.257974	−	0.966152i	$-0.416945\pi$
$859$	33.9592	−	41.0496i	1.15867	−	1.40060i	0.900699	−	0.434444i	$-0.143055\pi$
$860$	−7.27415	+	10.8736i	−0.248046	+	0.370787i
$861$	−0.675262	−	10.7330i	−0.0230129	−	0.365779i
$862$	2.18137	−	34.6718i	0.0742976	−	1.18093i
$863$	−28.0184	−	11.0933i	−0.953757	−	0.377619i	−0.160862	−	0.986977i	$-0.551427\pi$
$863$	−28.0184	−	11.0933i	−0.953757	−	0.377619i	−0.792895	+	0.609358i	$0.791427\pi$
$864$	0.535827	−	0.844328i	0.0182292	−	0.0287246i
$865$	4.11528	+	3.14426i	0.139924	+	0.106908i
$866$	0.436898	−	6.94429i	0.0148464	−	0.235977i
$867$	0.451990	+	0.0570997i	0.0153504	+	0.00193921i
$868$	0.805412	−	0.585166i	0.0273375	−	0.0198618i
$869$	−11.8533	−	62.1371i	−0.402095	−	2.10786i
$870$	−11.3689	−	18.9072i	−0.385443	−	0.641014i
$871$	−2.66037	−	5.65358i	−0.0901433	−	0.191564i
$872$	10.7657	−	10.1097i	0.364572	−	0.342356i
$873$	−5.58751	+	8.80451i	−0.189109	+	0.297987i
$874$	−17.8504			−0.603799
$875$	12.4006	−	0.661971i	0.419218	−	0.0223787i
$876$	−6.87664			−0.232340
$877$	−1.30960	+	2.06361i	−0.0442222	+	0.0696830i	−0.865720	−	0.500529i	$-0.833139\pi$
$877$	−1.30960	+	2.06361i	−0.0442222	+	0.0696830i	0.821498	+	0.570212i	$0.193139\pi$
$878$	12.7291	−	11.9534i	0.429586	−	0.403408i
$879$	−2.66137	−	5.65570i	−0.0897659	−	0.190762i
$880$	−7.37055	−	3.12580i	−0.248461	−	0.105371i
$881$	10.7973	+	56.6015i	0.363771	+	1.90695i	0.418044	+	0.908427i	$0.362716\pi$
$881$	10.7973	+	56.6015i	0.363771	+	1.90695i	−0.0542736	+	0.998526i	$0.517284\pi$
$882$	−4.66502	+	3.38934i	−0.157080	+	0.114125i
$883$	−23.2100	−	2.93210i	−0.781078	−	0.0986731i	−0.275325	−	0.961351i	$-0.588785\pi$
$883$	−23.2100	−	2.93210i	−0.781078	−	0.0986731i	−0.505753	+	0.862678i	$0.668785\pi$
$884$	−0.391542	+	6.22338i	−0.0131690	+	0.209315i
$885$	−6.14095	+	17.4562i	−0.206426	+	0.586784i
$886$	−17.1294	+	26.9915i	−0.575472	+	0.906799i
$887$	41.1533	+	16.2937i	1.38179	+	0.547090i	0.937247	−	0.348666i	$-0.113365\pi$
$887$	41.1533	+	16.2937i	1.38179	+	0.547090i	0.444545	+	0.895757i	$0.353365\pi$
$888$	−0.426182	+	6.77396i	−0.0143017	+	0.227319i
$889$	0.954569	+	15.1724i	0.0320152	+	0.508867i
$890$	−3.14838	−	3.99822i	−0.105534	−	0.134020i
$891$	2.28222	−	2.75873i	0.0764572	−	0.0924209i
$892$	6.73352	−	14.3094i	0.225455	−	0.479116i
$893$	−13.6845	−	9.94236i	−0.457934	−	0.332708i
$894$	8.07394	+	7.58193i	0.270033	+	0.253578i
$895$	14.9198	−	22.3026i	0.498714	−	0.745492i
$896$	0.208129	−	1.09105i	0.00695311	−	0.0364495i
$897$	2.20047	+	4.67623i	0.0734715	+	0.156135i
$898$	−22.3516	−	5.73890i	−0.745881	−	0.191510i
$899$	7.15438	−	5.19796i	0.238612	−	0.173362i
$900$	2.47252	+	4.34587i	0.0824175	+	0.144862i
$901$	35.2201	+	25.5889i	1.17335	+	0.852490i
$902$	−22.0968	−	26.7104i	−0.735741	−	0.889359i
$903$	−5.69462	−	3.13065i	−0.189505	−	0.104181i
$904$	14.7866	+	8.12901i	0.491795	+	0.270367i
$905$	−5.40556	+	25.0410i	−0.179687	+	0.832389i
$906$	−7.05706	+	14.9970i	−0.234455	+	0.498242i
$907$	3.49813	+	10.7661i	0.116153	+	0.357483i	0.992186	−	0.124769i	$-0.0398189\pi$
$907$	3.49813	+	10.7661i	0.116153	+	0.357483i	−0.876032	+	0.482252i	$0.839819\pi$
$908$	5.03271	+	26.3824i	0.167016	+	0.875530i
$909$	1.04434	+	1.64561i	0.0346385	+	0.0545816i
$910$	−2.43103	+	2.79841i	−0.0805879	+	0.0927664i
$911$	14.9406	−	5.91540i	0.495004	−	0.195986i	−0.107341	−	0.994222i	$-0.534234\pi$
$911$	14.9406	−	5.91540i	0.495004	−	0.195986i	0.602344	+	0.798237i	$0.294234\pi$
$912$	3.28596	−	3.97205i	0.108809	−	0.131528i
$913$	−25.5884	+	6.56998i	−0.846852	+	0.217435i
$914$	−7.16747	−	8.66399i	−0.237079	−	0.286579i
$915$	1.77664	−	8.23018i	0.0587339	−	0.272081i
$916$	−3.96898	+	1.01906i	−0.131139	+	0.0336707i
$917$	16.8126	+	15.7880i	0.555200	+	0.521367i
$918$	−1.29107	+	3.97350i	−0.0426116	+	0.131145i
$919$	−56.0917	−	7.08603i	−1.85029	−	0.233746i	−0.879880	−	0.475196i	$-0.842377\pi$
$919$	−56.0917	−	7.08603i	−1.85029	−	0.233746i	−0.970413	+	0.241449i	$0.922377\pi$
$920$	6.87303	−	3.56546i	0.226597	−	0.117550i
$921$	18.3891	−	17.2686i	0.605943	−	0.569018i
$922$	−38.7380	+	4.89374i	−1.27577	+	0.161167i
$923$	−1.05856	−	16.8254i	−0.0348431	−	0.553815i
$924$	1.22891	−	3.78218i	0.0404280	−	0.124425i
$925$	−28.9164	−	17.7637i	−0.950765	−	0.584066i
$926$	−0.771382	−	2.37407i	−0.0253492	−	0.0780167i
$927$	−10.9645	+	4.34117i	−0.360123	+	0.142583i
$928$	1.84879	−	9.69170i	0.0606895	−	0.318146i
$929$	49.6336	−	6.27018i	1.62843	−	0.205718i	0.742599	−	0.669736i	$-0.233593\pi$
$929$	49.6336	−	6.27018i	1.62843	−	0.205718i	0.885826	+	0.464018i	$0.153593\pi$
$930$	−1.64935	+	1.13860i	−0.0540843	+	0.0373361i
$931$	−26.0487	+	14.3204i	−0.853713	+	0.469333i
$932$	0.809923			0.0265299
$933$	−2.10491	+	1.15718i	−0.0689115	+	0.0378844i
$934$	22.7526	+	9.00841i	0.744489	+	0.294764i
$935$	33.0744	+	4.99108i	1.08165	+	0.163226i
$936$	−1.44562	−	0.371172i	−0.0472516	−	0.0121321i
$937$	17.3325	+	27.3117i	0.566230	+	0.892235i	0.999961	−	0.00880705i	$-0.00280341\pi$
$937$	17.3325	+	27.3117i	0.566230	+	0.892235i	−0.433732	+	0.901042i	$0.642803\pi$
$938$	−2.49157	−	3.92608i	−0.0813525	−	0.128191i
$939$	−6.10575	−	1.56769i	−0.199254	−	0.0511596i
$940$	7.25491	+	1.09480i	0.236629	+	0.0357084i
$941$	−21.2560	−	8.41584i	−0.692926	−	0.274349i	−0.00485062	−	0.999988i	$-0.501544\pi$
$941$	−21.2560	−	8.41584i	−0.692926	−	0.274349i	−0.688075	+	0.725640i	$0.741544\pi$
$942$	−0.186953	+	0.102778i	−0.00609126	+	0.00334870i
$943$	33.5262			1.09176
$944$	−7.25200	+	3.98682i	−0.236032	+	0.129760i
$945$	−2.04393	+	1.41099i	−0.0664892	+	0.0458996i
$946$	−20.7823	+	2.62541i	−0.675690	+	0.0853594i
$947$	−9.10824	+	47.7471i	−0.295978	+	1.55157i	0.454543	+	0.890725i	$0.349802\pi$
$947$	−9.10824	+	47.7471i	−0.295978	+	1.55157i	−0.750521	+	0.660846i	$0.770198\pi$
$948$	−16.4271	+	6.50396i	−0.533529	+	0.211239i
$949$	3.17158	+	9.76113i	0.102954	+	0.316860i
$950$	9.83765	+	23.8241i	0.319176	+	0.772957i
$951$	5.58455	−	17.1875i	0.181092	−	0.557343i
$952$	0.291386	+	4.63144i	0.00944387	+	0.150106i
$953$	−52.9253	+	6.68602i	−1.71442	+	0.216582i	−0.920309	−	0.391192i	$-0.872063\pi$
$953$	−52.9253	+	6.68602i	−1.71442	+	0.216582i	−0.794110	+	0.607774i	$0.792063\pi$
$954$	−7.59582	+	7.13295i	−0.245924	+	0.230938i
$955$	−4.35893	+	2.26125i	−0.141052	+	0.0731722i
$956$	25.0806	+	3.16841i	0.811164	+	0.102474i
$957$	10.9162	−	33.5967i	0.352872	−	1.08603i
$958$	−16.6121	−	15.5998i	−0.536714	−	0.504008i
$959$	1.33734	−	0.343372i	0.0431851	−	0.0110881i
$960$	−0.471829	+	2.18572i	−0.0152282	+	0.0705439i
$961$	19.2481	+	23.2669i	0.620905	+	0.750546i
$962$	9.81194	−	2.51928i	0.316350	−	0.0812248i
$963$	0.922260	−	1.11482i	0.0297194	−	0.0359246i
$964$	2.52100	−	0.998136i	0.0811961	−	0.0321478i
$965$	5.89211	−	6.78253i	0.189674	−	0.218337i
$966$	2.06084	+	3.24737i	0.0663065	+	0.104482i
$967$	5.10058	+	26.7382i	0.164024	+	0.859842i	0.965220	+	0.261440i	$0.0841973\pi$
$967$	5.10058	+	26.7382i	0.164024	+	0.859842i	−0.801196	+	0.598402i	$0.795803\pi$
$968$	−0.562138	−	1.73008i	−0.0180678	−	0.0556069i
$969$	−9.17035	+	19.4880i	−0.294594	+	0.626045i
$970$	4.92015	−	22.7923i	0.157977	−	0.731818i
$971$	17.2308	+	9.47269i	0.552961	+	0.303993i	0.733628	−	0.679551i	$-0.237825\pi$
$971$	17.2308	+	9.47269i	0.552961	+	0.303993i	−0.180667	+	0.983544i	$0.557825\pi$
$972$	−0.876307	−	0.481754i	−0.0281075	−	0.0154523i
$973$	0.665591	+	0.804562i	0.0213379	+	0.0257931i
$974$	−14.9152	−	10.8365i	−0.477913	−	0.347224i
$975$	5.02844	−	5.51402i	0.161039	−	0.176590i
$976$	3.04630	−	2.21326i	0.0975096	−	0.0708449i
$977$	−22.2502	−	5.71288i	−0.711847	−	0.182771i	−0.124633	−	0.992203i	$-0.539775\pi$
$977$	−22.2502	−	5.71288i	−0.711847	−	0.182771i	−0.587214	+	0.809432i	$0.699775\pi$
$978$	7.08625	+	15.0590i	0.226593	+	0.481535i
$979$	1.52688	−	8.00416i	0.0487992	−	0.255814i
$980$	7.16930	−	10.7169i	0.229015	−	0.342338i
$981$	−10.7657	−	10.1097i	−0.343722	−	0.322776i
$982$	9.44076	+	6.85911i	0.301267	+	0.218883i
$983$	10.9538	−	23.2780i	0.349372	−	0.742452i	−0.650483	−	0.759521i	$-0.725433\pi$
$983$	10.9538	−	23.2780i	0.349372	−	0.742452i	0.999854	+	0.0170687i	$0.00543338\pi$
$984$	−6.17162	+	7.46021i	−0.196744	+	0.237823i
$985$	−30.4482	−	38.6670i	−0.970161	−	1.23203i
$986$	2.58835	+	41.1406i	0.0824298	+	1.31018i
$987$	−0.228843	+	3.63735i	−0.00728415	+	0.115778i
$988$	−7.15369	−	2.83235i	−0.227589	−	0.0901090i
$989$	10.8552	−	17.1051i	0.345177	−	0.543911i
$990$	−2.65683	+	7.55227i	−0.0844395	+	0.240027i
$991$	−0.981801	+	15.6053i	−0.0311879	+	0.495718i	0.951165	+	0.308682i	$0.0998880\pi$
$991$	−0.981801	+	15.6053i	−0.0311879	+	0.495718i	−0.982353	+	0.187036i	$0.940112\pi$
$992$	−0.889232	−	0.112336i	−0.0282331	−	0.00356668i
$993$	1.25511	−	0.911892i	0.0398298	−	0.0289380i
$994$	−2.35093	−	12.3240i	−0.0745669	−	0.390893i
$995$	11.6628	+	4.94610i	0.369735	+	0.156802i
$996$	3.14168	+	6.67640i	0.0995478	+	0.211550i
$997$	23.9813	−	22.5200i	0.759496	−	0.713215i	−0.204577	−	0.978850i	$-0.565582\pi$
$997$	23.9813	−	22.5200i	0.759496	−	0.713215i	0.964073	+	0.265636i	$0.0855819\pi$
$998$	5.94253	−	9.36393i	0.188107	−	0.296410i
$999$	6.78736			0.214742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.c.481.5	yes	120
125.46	even	25	inner	750.2.m.c.421.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.c.421.5	✓	120	125.46	even	25	inner
750.2.m.c.481.5	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.535827 + 0.844328i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(1.46645 - 1.68806i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.898597 + 0.652869i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +O(q^{10})\)	\(q+(-0.535827 + 0.844328i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(1.46645 - 1.68806i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.898597 + 0.652869i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(0.639513 + 2.14267i) q^{10} +(-1.91846 + 3.02301i) q^{11} +(0.929776 + 0.368125i) q^{12} +(0.0937155 - 1.48956i) q^{13} +(-0.0697431 - 1.10853i) q^{14} +(0.0865613 + 2.23439i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(1.77890 - 3.78036i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.75788 + 3.52889i) q^{19} +(-2.15178 - 0.608140i) q^{20} +(0.208129 - 1.09105i) q^{21} +(-1.52445 - 3.23962i) q^{22} +(3.35390 + 0.861136i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.699072 - 4.95089i) q^{25} +(1.20747 + 0.877275i) q^{26} +(0.637424 + 0.770513i) q^{27} +(0.973337 + 0.535097i) q^{28} +(8.64605 + 4.75320i) q^{29} +(-1.93294 - 1.12416i) q^{30} +(0.381626 - 0.810996i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(-0.670896 - 3.51696i) q^{33} +(2.23868 + 3.52759i) q^{34} +(-0.215664 + 2.47428i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(4.32642 - 5.22975i) q^{37} +(-4.99311 + 1.28201i) q^{38} +(0.951362 + 1.15000i) q^{39} +(1.66645 - 1.49095i) q^{40} +(9.37795 - 2.40785i) q^{41} +(0.809685 + 0.760345i) q^{42} +(1.80794 - 5.56427i) q^{43} +(3.55215 + 0.448741i) q^{44} +(-1.59265 - 1.56955i) q^{45} +(-2.52419 + 2.37037i) q^{46} +(-3.25535 + 0.411247i) q^{47} +(-0.0627905 - 0.998027i) q^{48} +(-1.78188 + 5.48406i) q^{49} +(4.55476 + 2.06257i) q^{50} +(1.29107 + 3.97350i) q^{51} +(-1.38770 + 0.549430i) q^{52} +(-1.95250 + 10.2354i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(2.28970 + 7.67156i) q^{55} +(-0.973337 + 0.535097i) q^{56} -5.15507 q^{57} +(-8.64605 + 4.75320i) q^{58} +(7.69449 + 3.04647i) q^{59} +(1.98488 - 1.02968i) q^{60} +(-3.64713 - 0.936424i) q^{61} +(0.480261 + 0.756771i) q^{62} +(0.595157 + 0.937817i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.37704 - 2.34256i) q^{65} +(3.32895 + 1.31803i) q^{66} +(3.66857 - 2.01681i) q^{67} -4.17799 q^{68} +(-3.03438 + 1.66816i) q^{69} +(-1.97354 - 1.50788i) q^{70} +(11.2064 - 1.41570i) q^{71} +(0.187381 - 0.982287i) q^{72} +(-6.39374 + 2.53146i) q^{73} +(2.09741 + 6.45516i) q^{74} +(3.89872 + 3.13049i) q^{75} +(1.59300 - 4.90276i) q^{76} +(-0.249707 - 3.96897i) q^{77} +(-1.48074 + 0.187061i) q^{78} +(-12.8793 + 12.0945i) q^{79} +(0.365922 + 2.20592i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-2.99194 + 9.20825i) q^{82} +(5.37880 + 5.05103i) q^{83} +(-1.07583 + 0.276226i) q^{84} +(-3.77279 - 8.54657i) q^{85} +(3.72932 + 4.50798i) q^{86} +(-9.55649 + 2.45369i) q^{87} +(-2.28222 + 2.75873i) q^{88} +(-2.11606 + 0.837805i) q^{89} +(2.17859 - 0.503711i) q^{90} +(0.888278 + 1.39970i) q^{91} +(-0.648843 - 3.40135i) q^{92} +(0.276972 + 0.852432i) q^{93} +(1.39708 - 2.96894i) q^{94} +(11.4677 - 1.16860i) q^{95} +(0.876307 + 0.481754i) q^{96} +(-9.13798 - 5.02364i) q^{97} +(-3.67557 - 4.44300i) q^{98} +(2.89659 + 2.10449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) \) 120 * q + 20 * q^5 - 5 * q^7	\( 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) \) 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

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