LMFDB - Embedded newform 750.2.m.c.91.1

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			91.1
Character	$\chi$	$=$	750.91
Dual form			750.2.m.c.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 - 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.58297 - 1.57930i) q^{5} +(0.968583 - 0.248690i) q^{6} +(0.654948 + 2.01572i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(-0.728969 - 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.58297 - 1.57930i) q^{5} +(0.968583 - 0.248690i) q^{6} +(0.654948 + 2.01572i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(0.0728305 + 2.23488i) q^{10} +(0.508965 + 0.477950i) q^{11} +(-0.876307 - 0.481754i) q^{12} +(-1.55394 - 3.30228i) q^{13} +(0.902421 - 1.91774i) q^{14} +(2.18165 - 0.490316i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.191949 - 3.05094i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(3.12308 + 4.92119i) q^{19} +(1.47679 - 1.67901i) q^{20} +(-2.05287 - 0.527087i) q^{21} +(-0.0438402 - 0.696820i) q^{22} +(0.582162 + 3.05180i) q^{23} +(0.309017 + 0.951057i) q^{24} +(0.0116064 + 4.99999i) q^{25} +(-1.12780 + 3.47100i) q^{26} +(0.992115 + 0.125333i) q^{27} +(-1.97062 + 0.780224i) q^{28} +(5.05022 - 1.99952i) q^{29} +(-1.92600 - 1.13602i) q^{30} +(-0.468947 + 7.45371i) q^{31} +(0.809017 + 0.587785i) q^{32} +(-0.676263 + 0.173635i) q^{33} +(-2.22844 + 2.09264i) q^{34} +(2.14667 - 4.22520i) q^{35} +(0.876307 - 0.481754i) q^{36} +(10.5077 - 1.32743i) q^{37} +(1.09216 - 5.72529i) q^{38} +(3.62085 + 0.457420i) q^{39} +(-2.22590 + 0.213016i) q^{40} +(0.336427 - 1.76361i) q^{41} +(1.13566 + 1.78952i) q^{42} +(-4.53228 + 3.29290i) q^{43} +(-0.445048 + 0.537971i) q^{44} +(-0.754999 + 2.10475i) q^{45} +(1.66472 - 2.62319i) q^{46} +(-1.01228 - 1.22363i) q^{47} +(0.425779 - 0.904827i) q^{48} +(2.02894 - 1.47411i) q^{49} +(3.41427 - 3.65278i) q^{50} +(2.47314 + 1.79684i) q^{51} +(3.19819 - 1.75822i) q^{52} +(3.96820 + 1.01886i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(-0.0508501 - 1.56039i) q^{55} +(1.97062 + 0.780224i) q^{56} -5.82853 q^{57} +(-5.05022 - 1.99952i) q^{58} +(12.1545 + 6.68202i) q^{59} +(0.626335 + 2.14656i) q^{60} +(1.45156 + 7.60936i) q^{61} +(5.44426 - 5.11250i) q^{62} +(1.54502 - 1.45087i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.75546 + 7.68156i) q^{65} +(0.611836 + 0.336360i) q^{66} +(8.92686 + 3.53440i) q^{67} +3.05697 q^{68} +(-2.88866 - 1.14370i) q^{69} +(-4.45720 + 1.61054i) q^{70} +(5.23753 + 6.33109i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(-3.06897 + 1.68718i) q^{73} +(-8.56847 - 6.22536i) q^{74} +(-4.22785 - 2.66933i) q^{75} +(-4.71538 + 3.42592i) q^{76} +(-0.630068 + 1.33896i) q^{77} +(-2.32636 - 2.81209i) q^{78} +(3.99113 - 6.28902i) q^{79} +(1.76843 + 1.36845i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-1.45252 + 1.05532i) q^{82} +(-3.17591 - 5.00443i) q^{83} +(0.397147 - 2.08191i) q^{84} +(-5.12221 + 4.52641i) q^{85} +(5.55803 + 0.702143i) q^{86} +(-1.01779 + 5.33544i) q^{87} +(0.692693 - 0.0875074i) q^{88} +(3.71923 - 2.04466i) q^{89} +(1.99117 - 1.01747i) q^{90} +(5.63874 - 5.29513i) q^{91} +(-3.00923 + 0.772638i) q^{92} +(-6.04210 - 4.38984i) q^{93} +(-0.0997159 + 1.58494i) q^{94} +(2.82829 - 12.7224i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(-9.72601 + 3.85080i) q^{97} +(-2.48813 - 0.314324i) q^{98} +(0.215755 - 0.664026i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{6}{25}\right)$	$1$

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 $

$2$	−0.728969	−	0.684547i	−0.515459	−	0.484048i
$2$	−0.728969	−	0.684547i	−0.515459	−	0.484048i
$3$	−0.535827	+	0.844328i	−0.309360	+	0.487473i
$3$	−0.535827	+	0.844328i	−0.309360	+	0.487473i
$4$	0.0627905	+	0.998027i	0.0313953	+	0.499013i
$5$	−1.58297	−	1.57930i	−0.707927	−	0.706286i
$5$	−1.58297	−	1.57930i	−0.707927	−	0.706286i
$6$	0.968583	−	0.248690i	0.395422	−	0.101527i
$7$	0.654948	+	2.01572i	0.247547	+	0.761872i	0.995207	+	0.0977899i	$0.0311773\pi$
$7$	0.654948	+	2.01572i	0.247547	+	0.761872i	−0.747660	+	0.664082i	$0.768823\pi$
$8$	0.637424	−	0.770513i	0.225363	−	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	0.0728305	+	2.23488i	0.0230310	+	0.706732i
$11$	0.508965	+	0.477950i	0.153459	+	0.144107i	0.757474	−	0.652866i	$-0.226433\pi$
$11$	0.508965	+	0.477950i	0.153459	+	0.144107i	−0.604015	+	0.796973i	$0.706433\pi$
$12$	−0.876307	−	0.481754i	−0.252968	−	0.139070i
$13$	−1.55394	−	3.30228i	−0.430984	−	0.915888i	−0.995876	−	0.0907231i	$-0.971082\pi$
$13$	−1.55394	−	3.30228i	−0.430984	−	0.915888i	0.564892	−	0.825165i	$-0.308918\pi$
$14$	0.902421	−	1.91774i	0.241182	−	0.512538i
$15$	2.18165	−	0.490316i	0.563299	−	0.126599i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	0.191949	−	3.05094i	0.0465545	−	0.739962i	−0.903638	−	0.428298i	$-0.859114\pi$
$17$	0.191949	−	3.05094i	0.0465545	−	0.739962i	0.950192	−	0.311664i	$-0.100886\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	3.12308	+	4.92119i	0.716484	+	1.12900i	0.986120	+	0.166036i	$0.0530967\pi$
$19$	3.12308	+	4.92119i	0.716484	+	1.12900i	−0.269636	+	0.962962i	$0.586903\pi$
$20$	1.47679	−	1.67901i	0.330220	−	0.375439i
$21$	−2.05287	−	0.527087i	−0.447973	−	0.115020i
$22$	−0.0438402	−	0.696820i	−0.00934677	−	0.148563i
$23$	0.582162	+	3.05180i	0.121389	+	0.636345i	0.990025	+	0.140893i	$0.0449974\pi$
$23$	0.582162	+	3.05180i	0.121389	+	0.636345i	−0.868636	+	0.495452i	$0.835003\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	0.0116064	+	4.99999i	0.00232128	+	0.999997i
$26$	−1.12780	+	3.47100i	−0.221179	+	0.680719i
$27$	0.992115	+	0.125333i	0.190933	+	0.0241204i
$28$	−1.97062	+	0.780224i	−0.372412	+	0.147448i
$29$	5.05022	−	1.99952i	0.937803	−	0.371302i	0.151019	−	0.988531i	$-0.451745\pi$
$29$	5.05022	−	1.99952i	0.937803	−	0.371302i	0.786784	+	0.617229i	$0.211745\pi$
$30$	−1.92600	−	1.13602i	−0.351637	−	0.207407i
$31$	−0.468947	+	7.45371i	−0.0842254	+	1.33873i	0.698165	+	0.715937i	$0.254000\pi$
$31$	−0.468947	+	7.45371i	−0.0842254	+	1.33873i	−0.782390	+	0.622788i	$0.786000\pi$
$32$	0.809017	+	0.587785i	0.143015	+	0.103907i
$33$	−0.676263	+	0.173635i	−0.117722	+	0.0302259i
$34$	−2.22844	+	2.09264i	−0.382174	+	0.358885i
$35$	2.14667	−	4.22520i	0.362854	−	0.714188i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	10.5077	−	1.32743i	1.72746	−	0.218228i	0.802063	−	0.597239i	$-0.203736\pi$
$37$	10.5077	−	1.32743i	1.72746	−	0.218228i	0.925392	+	0.379011i	$0.123736\pi$
$38$	1.09216	−	5.72529i	0.177171	−	0.928764i
$39$	3.62085	+	0.457420i	0.579800	+	0.0732457i
$40$	−2.22590	+	0.213016i	−0.351945	+	0.0336808i
$41$	0.336427	−	1.76361i	0.0525411	−	0.275430i	−0.946315	−	0.323246i	$-0.895226\pi$
$41$	0.336427	−	1.76361i	0.0525411	−	0.275430i	0.998856	+	0.0478156i	$0.0152260\pi$
$42$	1.13566	+	1.78952i	0.175236	+	0.276128i
$43$	−4.53228	+	3.29290i	−0.691167	+	0.502162i	−0.877043	−	0.480411i	$-0.840487\pi$
$43$	−4.53228	+	3.29290i	−0.691167	+	0.502162i	0.185877	+	0.982573i	$0.440487\pi$
$44$	−0.445048	+	0.537971i	−0.0670935	+	0.0811022i
$45$	−0.754999	+	2.10475i	−0.112549	+	0.313758i
$46$	1.66472	−	2.62319i	0.245450	−	0.386768i
$47$	−1.01228	−	1.22363i	−0.147656	−	0.178485i	0.691500	−	0.722377i	$-0.256950\pi$
$47$	−1.01228	−	1.22363i	−0.147656	−	0.178485i	−0.839155	+	0.543892i	$0.816950\pi$
$48$	0.425779	−	0.904827i	0.0614559	−	0.130601i
$49$	2.02894	−	1.47411i	0.289848	−	0.210587i
$50$	3.41427	−	3.65278i	0.482850	−	0.516581i
$51$	2.47314	+	1.79684i	0.346309	+	0.251609i
$52$	3.19819	−	1.75822i	0.443509	−	0.243821i
$53$	3.96820	+	1.01886i	0.545074	+	0.139951i	0.511179	−	0.859474i	$-0.329209\pi$
$53$	3.96820	+	1.01886i	0.545074	+	0.139951i	0.0338948	+	0.999425i	$0.489209\pi$
$54$	−0.637424	−	0.770513i	−0.0867424	−	0.104854i
$55$	−0.0508501	−	1.56039i	−0.00685663	−	0.210403i
$56$	1.97062	+	0.780224i	0.263335	+	0.104262i
$57$	−5.82853			−0.772007
$58$	−5.05022	−	1.99952i	−0.663127	−	0.262550i
$59$	12.1545	+	6.68202i	1.58239	+	0.869925i	0.998303	+	0.0582311i	$0.0185460\pi$
$59$	12.1545	+	6.68202i	1.58239	+	0.869925i	0.584084	+	0.811693i	$0.301454\pi$
$60$	0.626335	+	2.14656i	0.0808595	+	0.277119i
$61$	1.45156	+	7.60936i	0.185854	+	0.974279i	0.945912	+	0.324424i	$0.105170\pi$
$61$	1.45156	+	7.60936i	0.185854	+	0.974279i	−0.760058	+	0.649855i	$0.774830\pi$
$62$	5.44426	−	5.11250i	0.691422	−	0.649288i
$63$	1.54502	−	1.45087i	0.194654	−	0.182792i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	−2.75546	+	7.68156i	−0.341773	+	0.952780i
$66$	0.611836	+	0.336360i	0.0753118	+	0.0414030i
$67$	8.92686	+	3.53440i	1.09059	+	0.431795i	0.843463	−	0.537188i	$-0.180513\pi$
$67$	8.92686	+	3.53440i	1.09059	+	0.431795i	0.247127	+	0.968983i	$0.420513\pi$
$68$	3.05697			0.370713
$69$	−2.88866	−	1.14370i	−0.347754	−	0.137685i
$70$	−4.45720	+	1.61054i	−0.532737	+	0.192496i
$71$	5.23753	+	6.33109i	0.621580	+	0.751362i	0.983512	−	0.180843i	$-0.0578826\pi$
$71$	5.23753	+	6.33109i	0.621580	+	0.751362i	−0.361932	+	0.932205i	$0.617883\pi$
$72$	−0.968583	−	0.248690i	−0.114149	−	0.0293084i
$73$	−3.06897	+	1.68718i	−0.359196	+	0.197469i	−0.651125	−	0.758970i	$-0.725703\pi$
$73$	−3.06897	+	1.68718i	−0.359196	+	0.197469i	0.291930	+	0.956440i	$0.405703\pi$
$74$	−8.56847	−	6.22536i	−0.996065	−	0.723683i
$75$	−4.22785	−	2.66933i	−0.488190	−	0.308227i
$76$	−4.71538	+	3.42592i	−0.540891	+	0.392980i
$77$	−0.630068	+	1.33896i	−0.0718030	+	0.152589i
$78$	−2.32636	−	2.81209i	−0.263408	−	0.318406i
$79$	3.99113	−	6.28902i	0.449037	−	0.707569i	−0.542114	−	0.840305i	$-0.682376\pi$
$79$	3.99113	−	6.28902i	0.449037	−	0.707569i	0.991152	+	0.132735i	$0.0423760\pi$
$80$	1.76843	+	1.36845i	0.197716	+	0.152997i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	−1.45252	+	1.05532i	−0.160404	+	0.116540i
$83$	−3.17591	−	5.00443i	−0.348601	−	0.549307i	0.624107	−	0.781339i	$-0.285463\pi$
$83$	−3.17591	−	5.00443i	−0.348601	−	0.549307i	−0.972708	+	0.232031i	$0.925463\pi$
$84$	0.397147	−	2.08191i	0.0433322	−	0.227156i
$85$	−5.12221	+	4.52641i	−0.555582	+	0.490958i
$86$	5.55803	+	0.702143i	0.599338	+	0.0757140i
$87$	−1.01779	+	5.33544i	−0.109119	+	0.572019i
$88$	0.692693	−	0.0875074i	0.0738413	−	0.00932832i
$89$	3.71923	−	2.04466i	0.394237	−	0.216734i	−0.272289	−	0.962216i	$-0.587781\pi$
$89$	3.71923	−	2.04466i	0.394237	−	0.216734i	0.666526	+	0.745482i	$0.267781\pi$
$90$	1.99117	−	1.01747i	0.209888	−	0.107250i
$91$	5.63874	−	5.29513i	0.591100	−	0.555080i
$92$	−3.00923	+	0.772638i	−0.313733	+	0.0805531i
$93$	−6.04210	−	4.38984i	−0.626536	−	0.455205i
$94$	−0.0997159	+	1.58494i	−0.0102849	+	0.163474i
$95$	2.82829	−	12.7224i	0.290177	−	1.30529i
$96$	−0.929776	+	0.368125i	−0.0948949	+	0.0375716i
$97$	−9.72601	+	3.85080i	−0.987527	+	0.390990i	−0.805689	−	0.592339i	$-0.798205\pi$
$97$	−9.72601	+	3.85080i	−0.987527	+	0.390990i	−0.181838	+	0.983328i	$0.558205\pi$
$98$	−2.48813	−	0.314324i	−0.251339	−	0.0317515i
$99$	0.215755	−	0.664026i	0.0216842	−	0.0667371i
$100$	−4.98939	+	0.325535i	−0.498939	+	0.0325535i
$101$	4.74412	+	14.6009i	0.472057	+	1.45284i	0.849886	+	0.526967i	$0.176671\pi$
$101$	4.74412	+	14.6009i	0.472057	+	1.45284i	−0.377828	+	0.925876i	$0.623329\pi$
$102$	−0.572820	−	3.00283i	−0.0567176	−	0.297324i
$103$	−0.766930	−	12.1900i	−0.0755678	−	1.20112i	−0.834896	−	0.550408i	$-0.814472\pi$
$103$	−0.766930	−	12.1900i	−0.0755678	−	1.20112i	0.759328	−	0.650708i	$-0.225528\pi$
$104$	−3.53497	−	0.907625i	−0.346632	−	0.0890000i
$105$	2.41721	+	4.07647i	0.235895	+	0.397822i
$106$	−2.19523	−	3.45914i	−0.213220	−	0.335981i
$107$	1.05253	−	3.23935i	0.101752	−	0.313160i	−0.887203	−	0.461380i	$-0.847354\pi$
$107$	1.05253	−	3.23935i	0.101752	−	0.313160i	0.988954	+	0.148220i	$0.0473544\pi$
$108$	−0.0627905	+	0.998027i	−0.00604202	+	0.0960352i
$109$	10.3528	−	1.30787i	0.991621	−	0.125271i	0.387251	−	0.921974i	$-0.373425\pi$
$109$	10.3528	−	1.30787i	0.991621	−	0.125271i	0.604370	+	0.796704i	$0.293425\pi$
$110$	−1.03109	+	1.17228i	−0.0983108	+	0.111773i
$111$	−4.50952	+	9.58322i	−0.428025	+	0.909599i
$112$	−0.902421	−	1.91774i	−0.0852707	−	0.181210i
$113$	−15.5663	−	8.55764i	−1.46435	−	0.805035i	−0.467477	−	0.884005i	$-0.654837\pi$
$113$	−15.5663	−	8.55764i	−1.46435	−	0.805035i	−0.996877	+	0.0789701i	$0.974837\pi$
$114$	4.24881	+	3.98990i	0.397938	+	0.373689i
$115$	3.89817	−	5.75033i	0.363506	−	0.536221i
$116$	2.31268	+	4.91470i	0.214727	+	0.456319i
$117$	−2.32636	+	2.81209i	−0.215072	+	0.259977i
$118$	−4.28613	−	13.1913i	−0.394570	−	1.21436i
$119$	6.27557	−	1.61129i	0.575281	−	0.147707i
$120$	1.01284	−	1.99353i	0.0924593	−	0.181983i
$121$	−0.660087	−	10.4918i	−0.0600079	−	0.953798i
$122$	4.15082	−	6.54065i	0.375798	−	0.592163i
$123$	1.30880	+	1.22905i	0.118011	+	0.110819i
$124$	−7.46844			−0.670686
$125$	7.87812	−	7.93317i	0.704640	−	0.709565i
$126$	−2.11946			−0.188816
$127$	−0.749312	−	0.703651i	−0.0664907	−	0.0624389i	0.650590	−	0.759430i	$-0.274522\pi$
$127$	−0.749312	−	0.703651i	−0.0664907	−	0.0624389i	−0.717080	+	0.696991i	$0.754522\pi$
$128$	−0.535827	+	0.844328i	−0.0473608	+	0.0746288i
$129$	−0.351766	−	5.59116i	−0.0309712	−	0.492274i
$130$	7.26703	−	3.71337i	0.637361	−	0.325684i
$131$	−14.1454	+	3.63191i	−1.23589	+	0.317322i	−0.809446	−	0.587194i	$-0.800233\pi$
$131$	−14.1454	+	3.63191i	−1.23589	+	0.317322i	−0.426440	+	0.904516i	$0.640233\pi$
$132$	−0.215755	−	0.664026i	−0.0187791	−	0.0577960i
$133$	−7.87430	+	9.51839i	−0.682788	+	0.825349i
$134$	−4.08794	−	8.68732i	−0.353145	−	0.750470i
$135$	−1.37255	−	1.76525i	−0.118130	−	0.151928i
$136$	−2.22844	−	2.09264i	−0.191087	−	0.179443i
$137$	0.616767	+	0.339071i	0.0526940	+	0.0289688i	0.507883	−	0.861426i	$-0.330428\pi$
$137$	0.616767	+	0.339071i	0.0526940	+	0.0289688i	−0.455189	+	0.890395i	$0.650428\pi$
$138$	1.32283	+	2.81115i	0.112606	+	0.239301i
$139$	−5.65266	+	12.0125i	−0.479452	+	1.01889i	0.508056	+	0.861324i	$0.330364\pi$
$139$	−5.65266	+	12.0125i	−0.479452	+	1.01889i	−0.987509	+	0.157564i	$0.949636\pi$
$140$	4.35165	+	1.87713i	0.367781	+	0.158647i
$141$	1.57555	−	0.199038i	0.132685	−	0.0167621i
$142$	0.515932	−	8.20050i	0.0432960	−	0.688171i
$143$	0.787426	−	2.42345i	0.0658478	−	0.202659i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	−11.1522	−	4.81064i	−0.926141	−	0.399502i
$146$	3.39214	+	0.870953i	0.280735	+	0.0720806i
$147$	0.157473	+	2.50296i	0.0129881	+	0.206440i
$148$	1.98460	+	10.4036i	0.163133	+	0.855172i
$149$	1.72925	+	5.32208i	0.141666	+	0.436002i	0.996567	−	0.0827883i	$-0.0263825\pi$
$149$	1.72925	+	5.32208i	0.141666	+	0.436002i	−0.854902	+	0.518790i	$0.826383\pi$
$150$	1.25469	+	4.84002i	0.102445	+	0.395186i
$151$	0.227731	−	0.700883i	0.0185325	−	0.0570371i	−0.941363	−	0.337397i	$-0.890454\pi$
$151$	0.227731	−	0.700883i	0.0185325	−	0.0570371i	0.959895	+	0.280359i	$0.0904537\pi$
$152$	5.78257	+	0.730508i	0.469028	+	0.0592520i
$153$	−2.84230	+	1.12535i	−0.229787	+	0.0909789i
$154$	1.37588	−	0.544751i	0.110872	−	0.0438973i
$155$	12.5140	−	11.0584i	1.00515	−	0.888232i
$156$	−0.229162	+	3.64243i	−0.0183476	+	0.291627i
$157$	−4.56577	−	3.31723i	−0.364388	−	0.264743i	0.390492	−	0.920606i	$-0.372305\pi$
$157$	−4.56577	−	3.31723i	−0.364388	−	0.264743i	−0.754880	+	0.655863i	$0.772305\pi$
$158$	−7.21454	+	1.85238i	−0.573958	+	0.147367i
$159$	−2.98652	+	2.80453i	−0.236846	+	0.222414i
$160$	−0.352361	−	2.20813i	−0.0278566	−	0.174568i
$161$	−5.77030	+	3.17225i	−0.454763	+	0.250008i
$162$	0.992115	−	0.125333i	0.0779479	−	0.00984711i
$163$	−3.88358	+	20.3585i	−0.304186	+	1.59460i	0.421669	+	0.906750i	$0.361444\pi$
$163$	−3.88358	+	20.3585i	−0.304186	+	1.59460i	−0.725855	+	0.687848i	$0.758556\pi$
$164$	1.78126	+	0.225025i	0.139093	+	0.0175715i
$165$	1.34473	+	0.793165i	0.104687	+	0.0617478i
$166$	−1.11063	+	5.82213i	−0.0862017	+	0.451885i
$167$	−12.8629	−	20.2687i	−0.995362	−	1.56844i	−0.810553	−	0.585665i	$-0.800833\pi$
$167$	−12.8629	−	20.2687i	−0.995362	−	1.56844i	−0.184809	−	0.982774i	$-0.559167\pi$
$168$	−1.71468	+	1.24579i	−0.132290	+	0.0961144i
$169$	−0.203833	+	0.246392i	−0.0156795	+	0.0189532i
$170$	6.83247	+	0.206782i	0.524027	+	0.0158594i
$171$	3.12308	−	4.92119i	0.238828	−	0.376333i
$172$	−3.57098	−	4.31658i	−0.272285	−	0.329136i
$173$	−6.43791	+	13.6812i	−0.489465	+	1.04017i	0.495690	+	0.868499i	$0.334915\pi$
$173$	−6.43791	+	13.6812i	−0.489465	+	1.04017i	−0.985155	+	0.171666i	$0.945085\pi$
$174$	4.39430	−	3.19264i	0.333131	−	0.242034i
$175$	−10.0710	+	3.29813i	−0.761295	+	0.249315i
$176$	−0.564854	−	0.410391i	−0.0425775	−	0.0309344i
$177$	−12.1545	+	6.68202i	−0.913591	+	0.502251i
$178$	−4.11087	−	1.05549i	−0.308123	−	0.0791125i
$179$	−9.88934	−	11.9542i	−0.739164	−	0.893496i	0.258197	−	0.966092i	$-0.416872\pi$
$179$	−9.88934	−	11.9542i	−0.739164	−	0.893496i	−0.997361	+	0.0725963i	$0.976872\pi$
$180$	−2.14800	−	0.621350i	−0.160103	−	0.0463127i
$181$	5.30687	+	2.10114i	0.394456	+	0.156176i	0.556975	−	0.830529i	$-0.311962\pi$
$181$	5.30687	+	2.10114i	0.394456	+	0.156176i	−0.162519	+	0.986705i	$0.551962\pi$
$182$	−7.73522			−0.573373
$183$	−7.20258	−	2.85170i	−0.532430	−	0.210804i
$184$	2.72254	+	1.49673i	0.200708	+	0.110340i
$185$	−18.7298	−	14.4936i	−1.37704	−	1.06559i
$186$	1.39945	+	7.33616i	0.102612	+	0.537913i
$187$	1.55589	−	1.46108i	0.113778	−	0.106845i
$188$	1.15766	−	1.08711i	0.0844307	−	0.0792857i
$189$	0.397147	+	2.08191i	0.0288882	+	0.151437i
$190$	−10.7708	+	7.33813i	−0.781397	+	0.532364i
$191$	−4.04329	−	2.22282i	−0.292562	−	0.160837i	0.328713	−	0.944430i	$-0.393385\pi$
$191$	−4.04329	−	2.22282i	−0.292562	−	0.160837i	−0.621275	+	0.783592i	$0.713385\pi$
$192$	0.929776	+	0.368125i	0.0671008	+	0.0265671i
$193$	12.8900			0.927840			0.463920	−	0.885877i	$-0.346442\pi$
$193$	12.8900			0.927840			0.463920	+	0.885877i	$0.346442\pi$
$194$	9.72601	+	3.85080i	0.698287	+	0.276471i
$195$	−5.00930	−	6.44250i	−0.358724	−	0.461357i
$196$	1.59860	+	1.93237i	0.114186	+	0.138027i
$197$	5.58587	+	1.43421i	0.397976	+	0.102183i	0.442373	−	0.896831i	$-0.354137\pi$
$197$	5.58587	+	1.43421i	0.397976	+	0.102183i	−0.0443969	+	0.999014i	$0.514137\pi$
$198$	−0.611836	+	0.336360i	−0.0434813	+	0.0239040i
$199$	13.9843	+	10.1602i	0.991324	+	0.720239i	0.960211	−	0.279277i	$-0.0900948\pi$
$199$	13.9843	+	10.1602i	0.991324	+	0.720239i	0.0311131	+	0.999516i	$0.490095\pi$
$200$	3.85995	+	3.17817i	0.272940	+	0.224730i
$201$	−7.76744	+	5.64338i	−0.547873	+	0.398053i
$202$	6.53669	−	13.8912i	0.459920	−	0.977379i
$203$	7.33812	+	8.87026i	0.515035	+	0.622570i
$204$	−1.63801	+	2.58109i	−0.114684	+	0.180712i
$205$	−3.31783	+	2.26043i	−0.231728	+	0.157875i
$206$	−7.78556	+	9.41112i	−0.542446	+	0.655704i
$207$	2.51348	−	1.82615i	0.174699	−	0.126926i
$208$	1.95557	+	3.08148i	0.135594	+	0.213662i
$209$	−0.762542	+	3.99739i	−0.0527461	+	0.276505i
$210$	1.02847	−	4.62631i	0.0709709	−	0.319246i
$211$	−17.0658	−	2.15591i	−1.17486	−	0.148419i	−0.486428	−	0.873721i	$-0.661700\pi$
$211$	−17.0658	−	2.15591i	−1.17486	−	0.148419i	−0.688431	+	0.725301i	$0.741700\pi$
$212$	−0.767684	+	4.02434i	−0.0527248	+	0.276393i
$213$	−8.15192	+	1.02983i	−0.558560	+	0.0705626i
$214$	−2.98475	+	1.64088i	−0.204033	+	0.112168i
$215$	12.3750	+	1.94528i	0.843965	+	0.132667i
$216$	0.728969	−	0.684547i	0.0496000	−	0.0465775i
$217$	−15.3317	+	3.93652i	−1.04079	+	0.267229i
$218$	−8.44218	−	6.13360i	−0.571777	−	0.415420i
$219$	0.219903	−	3.49525i	0.0148596	−	0.236187i
$220$	1.55412	−	0.148728i	0.104779	−	0.0100272i
$221$	−10.3733	+	4.10710i	−0.697787	+	0.276273i
$222$	9.84746	−	3.89889i	0.660918	−	0.261676i
$223$	12.3165	+	1.55593i	0.824771	+	0.104193i	0.526379	−	0.850250i	$-0.323549\pi$
$223$	12.3165	+	1.55593i	0.824771	+	0.104193i	0.298393	+	0.954443i	$0.403549\pi$
$224$	−0.654948	+	2.01572i	−0.0437606	+	0.134681i
$225$	4.51918	−	2.13939i	0.301279	−	0.142626i
$226$	5.48923	+	16.8941i	0.365138	+	1.12378i
$227$	−3.93619	−	20.6342i	−0.261254	−	1.36954i	−0.834883	−	0.550427i	$-0.814465\pi$
$227$	−3.93619	−	20.6342i	−0.261254	−	1.36954i	0.573629	−	0.819115i	$-0.305535\pi$
$228$	−0.365976	−	5.81703i	−0.0242374	−	0.385242i
$229$	−14.8487	−	3.81249i	−0.981229	−	0.251937i	−0.276188	−	0.961104i	$-0.589071\pi$
$229$	−14.8487	−	3.81249i	−0.981229	−	0.251937i	−0.705041	+	0.709167i	$0.749071\pi$
$230$	−6.77802	+	1.52333i	−0.446929	+	0.100445i
$231$	−0.792917	−	1.24944i	−0.0521701	−	0.0822069i
$232$	1.67847	−	5.16581i	0.110197	−	0.339152i
$233$	−0.160674	+	2.55385i	−0.0105261	+	0.167308i	0.989252	+	0.146224i	$0.0467119\pi$
$233$	−0.160674	+	2.55385i	−0.0105261	+	0.167308i	−0.999778	+	0.0210844i	$0.993288\pi$
$234$	3.62085	−	0.457420i	0.236702	−	0.0299025i
$235$	−0.330079	+	3.53566i	−0.0215320	+	0.230641i
$236$	−5.90564	+	12.5501i	−0.384425	+	0.816944i
$237$	3.17144	+	6.73965i	0.206007	+	0.437787i
$238$	−5.67770	−	3.12134i	−0.368031	−	0.202327i
$239$	−2.63317	−	2.47272i	−0.170326	−	0.159947i	0.594697	−	0.803950i	$-0.297272\pi$
$239$	−2.63317	−	2.47272i	−0.170326	−	0.159947i	−0.765022	+	0.644004i	$0.777272\pi$
$240$	−2.10299	+	0.759882i	−0.135748	+	0.0490502i
$241$	−11.1064	−	23.6022i	−0.715423	−	1.52035i	−0.848471	−	0.529242i	$-0.822476\pi$
$241$	−11.1064	−	23.6022i	−0.715423	−	1.52035i	0.133048	−	0.991110i	$-0.457524\pi$
$242$	−6.70093	+	8.10004i	−0.430752	+	0.520690i
$243$	−0.309017	−	0.951057i	−0.0198234	−	0.0610103i
$244$	−7.50320	+	1.92649i	−0.480343	+	0.123331i
$245$	−5.53982	−	0.870831i	−0.353926	−	0.0556354i
$246$	−0.112735	−	1.79187i	−0.00718772	−	0.114246i
$247$	11.3981	−	17.9605i	0.725243	−	1.14280i
$248$	5.44426	+	5.11250i	0.345711	+	0.324644i
$249$	5.92712			0.375616
$250$	−11.1735	+	0.390091i	−0.706676	+	0.0246715i
$251$	−0.352160			−0.0222281			−0.0111141	−	0.999938i	$-0.503538\pi$
$251$	−0.352160			−0.0222281			−0.0111141	+	0.999938i	$0.503538\pi$
$252$	1.54502	+	1.45087i	0.0973269	+	0.0913961i
$253$	−1.16231	+	1.83150i	−0.0730736	+	0.115146i
$254$	0.0645428	+	1.02588i	0.00404978	+	0.0643693i
$255$	−1.07716	−	6.75020i	−0.0674543	−	0.422714i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	9.08753	+	27.9685i	0.566865	+	1.74463i	0.662345	+	0.749199i	$0.269561\pi$
$257$	9.08753	+	27.9685i	0.566865	+	1.74463i	−0.0954805	+	0.995431i	$0.530439\pi$
$258$	−3.57098	+	4.31658i	−0.222320	+	0.268738i
$259$	9.55773	+	20.3112i	0.593888	+	1.26208i
$260$	−7.83942	−	2.26770i	−0.486180	−	0.140637i
$261$	−3.95950	−	3.71822i	−0.245087	−	0.230152i
$262$	12.7977	+	7.03562i	0.790647	+	0.434662i
$263$	3.99564	+	8.49117i	0.246382	+	0.523588i	0.989318	−	0.145775i	$-0.0465674\pi$
$263$	3.99564	+	8.49117i	0.246382	+	0.523588i	−0.742936	+	0.669362i	$0.766567\pi$
$264$	−0.297278	+	0.631749i	−0.0182962	+	0.0388814i
$265$	−4.67246	−	7.87981i	−0.287027	−	0.484053i
$266$	12.2559	−	1.54828i	0.751457	−	0.0949311i
$267$	−0.266496	+	4.23583i	−0.0163093	+	0.259229i
$268$	−2.96690	+	9.13118i	−0.181232	+	0.557775i
$269$	4.28576	+	6.75328i	0.261307	+	0.411755i	0.949497	−	0.313776i	$-0.101594\pi$
$269$	4.28576	+	6.75328i	0.261307	+	0.411755i	−0.688189	+	0.725531i	$0.741594\pi$
$270$	−0.207849	+	2.22639i	−0.0126493	+	0.135494i
$271$	−6.05917	−	1.55573i	−0.368068	−	0.0945039i	0.0601254	−	0.998191i	$-0.480850\pi$
$271$	−6.05917	−	1.55573i	−0.368068	−	0.0945039i	−0.428194	+	0.903687i	$0.640850\pi$
$272$	0.191949	+	3.05094i	0.0116386	+	0.184991i
$273$	1.44944	+	7.59821i	0.0877239	+	0.459865i
$274$	−0.217494	−	0.669378i	−0.0131393	−	0.0404386i
$275$	−2.38383	+	2.55036i	−0.143751	+	0.153793i
$276$	0.960064	−	2.95477i	0.0577891	−	0.177856i
$277$	22.9366	+	2.89757i	1.37813	+	0.174098i	0.779236	−	0.626731i	$-0.215607\pi$
$277$	22.9366	+	2.89757i	1.37813	+	0.174098i	0.598893	+	0.800829i	$0.295607\pi$
$278$	12.3437	−	4.88723i	0.740328	−	0.293117i
$279$	6.94398	−	2.74932i	0.415725	−	0.164597i
$280$	−1.88723	−	4.34728i	−0.112784	−	0.259800i
$281$	−0.516850	+	8.21510i	−0.0308327	+	0.490072i	0.952062	+	0.305904i	$0.0989588\pi$
$281$	−0.516850	+	8.21510i	−0.0308327	+	0.490072i	−0.982895	+	0.184167i	$0.941041\pi$
$282$	−1.28478	−	0.933446i	−0.0765074	−	0.0555859i
$283$	−3.62637	+	0.931095i	−0.215566	+	0.0553478i	−0.354928	−	0.934894i	$-0.615495\pi$
$283$	−3.62637	+	0.931095i	−0.215566	+	0.0553478i	0.139363	+	0.990241i	$0.455495\pi$
$284$	−5.98973	+	5.62473i	−0.355425	+	0.333766i
$285$	9.22640	+	9.20501i	0.546525	+	0.545258i
$286$	−2.23297	+	1.22759i	−0.132038	+	0.0725887i
$287$	3.77530	−	0.476931i	0.222849	−	0.0281523i
$288$	0.187381	−	0.982287i	0.0110415	−	0.0578818i
$289$	7.59455	+	0.959415i	0.446738	+	0.0564362i
$290$	4.83651	+	11.1410i	0.284010	+	0.654223i
$291$	1.96012	−	10.2753i	0.114904	−	0.602349i
$292$	−1.87655	−	2.95697i	−0.109817	−	0.173044i
$293$	−2.38630	+	1.73375i	−0.139409	+	0.101287i	−0.655304	−	0.755365i	$-0.727459\pi$
$293$	−2.38630	+	1.73375i	−0.139409	+	0.101287i	0.515895	+	0.856652i	$0.327459\pi$
$294$	1.59860	−	1.93237i	0.0932322	−	0.112698i
$295$	−8.68739	−	29.7732i	−0.505799	−	1.73346i
$296$	5.67506	−	8.94246i	0.329856	−	0.519770i
$297$	0.445048	+	0.537971i	0.0258243	+	0.0312162i
$298$	2.38265	−	5.06338i	0.138023	−	0.293314i
$299$	9.17327	−	6.66477i	0.530504	−	0.385433i
$300$	2.39859	−	4.38711i	0.138483	−	0.253290i
$301$	−9.60598	−	6.97915i	−0.553679	−	0.402272i
$302$	−0.645796	+	0.355029i	−0.0371614	+	0.0204297i
$303$	−14.8700	−	3.81796i	−0.854257	−	0.219336i
$304$	−3.71524	−	4.49096i	−0.213084	−	0.257574i
$305$	9.71970	−	14.3379i	0.556548	−	0.820984i
$306$	2.84230	+	1.12535i	0.162484	+	0.0643318i
$307$	27.5604			1.57296			0.786478	−	0.617619i	$-0.211902\pi$
$307$	27.5604			1.57296			0.786478	+	0.617619i	$0.211902\pi$
$308$	−1.37588	−	0.544751i	−0.0783982	−	0.0310401i
$309$	10.7033	+	5.88419i	0.608889	+	0.334740i
$310$	−16.6923	−	0.505185i	−0.948059	−	0.0286926i
$311$	−1.74136	−	9.12854i	−0.0987436	−	0.517632i	−0.996949	−	0.0780560i	$-0.975129\pi$
$311$	−1.74136	−	9.12854i	−0.0987436	−	0.517632i	0.898205	−	0.439576i	$-0.144871\pi$
$312$	2.66046	−	2.49834i	0.150619	−	0.141441i
$313$	11.1162	−	10.4388i	0.628323	−	0.590034i	−0.303552	−	0.952815i	$-0.598173\pi$
$313$	11.1162	−	10.4388i	0.628323	−	0.590034i	0.931875	+	0.362781i	$0.118173\pi$
$314$	1.05751	+	5.54364i	0.0596785	+	0.312846i
$315$	−4.73708	−	0.143365i	−0.266904	−	0.00807773i
$316$	6.52721	+	3.58836i	0.367184	+	0.201861i
$317$	−16.6369	−	6.58701i	−0.934421	−	0.369963i	−0.148938	−	0.988847i	$-0.547585\pi$
$317$	−16.6369	−	6.58701i	−0.934421	−	0.369963i	−0.785483	+	0.618883i	$0.787585\pi$
$318$	4.09691			0.229743
$319$	3.52606	+	1.39606i	0.197421	+	0.0781646i
$320$	−1.25471	+	1.85087i	−0.0701404	+	0.103467i
$321$	2.17110	+	2.62441i	0.121179	+	0.146480i
$322$	6.37792	+	1.63757i	0.355428	+	0.0912583i
$323$	15.6137	−	8.58372i	0.868771	−	0.477611i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	16.4933	−	7.80798i	0.914885	−	0.433109i
$326$	16.7673	−	12.1822i	0.928657	−	0.674709i
$327$	−4.44305	+	9.44197i	−0.245701	+	0.522142i
$328$	−1.14444	−	1.38339i	−0.0631911	−	0.0763850i
$329$	1.80351	−	2.84188i	0.0994309	−	0.156678i
$330$	−0.437306	−	1.49872i	−0.0240729	−	0.0825019i
$331$	19.2360	−	23.2523i	1.05731	−	1.27806i	0.0981558	−	0.995171i	$-0.468706\pi$
$331$	19.2360	−	23.2523i	1.05731	−	1.27806i	0.959151	−	0.282894i	$-0.0912943\pi$
$332$	4.79514	−	3.48387i	0.263167	−	0.191202i
$333$	−5.67506	−	8.94246i	−0.310991	−	0.490044i
$334$	−4.49822	+	23.5805i	−0.246132	+	1.29027i
$335$	−8.54910	−	19.6931i	−0.467087	−	1.07595i
$336$	2.10274	+	0.265638i	0.114714	+	0.0144918i
$337$	1.55666	−	8.16032i	0.0847969	−	0.444521i	−0.914413	−	0.404782i	$-0.867347\pi$
$337$	1.55666	−	8.16032i	0.0847969	−	0.444521i	0.999210	−	0.0397390i	$-0.0126526\pi$
$338$	0.317255	−	0.0400786i	0.0172564	−	0.00217999i
$339$	15.5663	−	8.55764i	0.845445	−	0.464787i
$340$	−4.83911	−	4.82789i	−0.262437	−	0.261829i
$341$	−3.80117	+	3.56954i	−0.205845	+	0.193301i
$342$	−5.64541	+	1.44950i	−0.305269	+	0.0783798i
$343$	16.3030	+	11.8448i	0.880278	+	0.639559i
$344$	−0.351766	+	5.59116i	−0.0189659	+	0.301455i
$345$	2.76642	+	6.37252i	0.148939	+	0.343085i
$346$	14.0585	−	5.56615i	0.755789	−	0.299238i
$347$	1.84148	−	0.729094i	0.0988559	−	0.0391398i	−0.318176	−	0.948032i	$-0.603070\pi$
$347$	1.84148	−	0.729094i	0.0988559	−	0.0391398i	0.417032	+	0.908892i	$0.363070\pi$
$348$	−5.38882	−	0.680766i	−0.288871	−	0.0364929i
$349$	4.11543	−	12.6660i	0.220294	−	0.677996i	−0.778441	−	0.627718i	$-0.783989\pi$
$349$	4.11543	−	12.6660i	0.220294	−	0.677996i	0.998735	−	0.0502781i	$-0.0160108\pi$
$350$	9.59916	+	4.48983i	0.513096	+	0.239992i
$351$	−1.12780	−	3.47100i	−0.0601973	−	0.185268i
$352$	0.130829	+	0.685831i	0.00697322	+	0.0365549i
$353$	0.387427	+	6.15797i	0.0206206	+	0.327756i	0.994791	+	0.101940i	$0.0325049\pi$
$353$	0.387427	+	6.15797i	0.0206206	+	0.327756i	−0.974170	+	0.225816i	$0.927495\pi$
$354$	13.4344	+	3.44938i	0.714032	+	0.183332i
$355$	1.70783	−	18.2936i	0.0906424	−	0.970923i
$356$	2.27416	+	3.58350i	0.120530	+	0.189925i
$357$	−2.00216	+	6.16201i	−0.105965	+	0.326128i
$358$	−0.974166	+	15.4839i	−0.0514863	+	0.818351i
$359$	−1.73015	+	0.218569i	−0.0913140	+	0.0115356i	−0.170857	−	0.985296i	$-0.554654\pi$
$359$	−1.73015	+	0.218569i	−0.0913140	+	0.0115356i	0.0795435	+	0.996831i	$0.474654\pi$
$360$	1.14048	+	1.92336i	0.0601088	+	0.101370i
$361$	−6.37465	+	13.5468i	−0.335508	+	0.712991i
$362$	−2.43021	−	5.16446i	−0.127729	−	0.271438i
$363$	9.21219	+	5.06444i	0.483515	+	0.265814i
$364$	5.63874	+	5.29513i	0.295550	+	0.277540i
$365$	7.52266	+	2.17607i	0.393754	+	0.113901i
$366$	3.29833	+	7.00931i	0.172407	+	0.366383i
$367$	14.5475	−	17.5850i	0.759376	−	0.917927i	−0.239217	−	0.970966i	$-0.576891\pi$
$367$	14.5475	−	17.5850i	0.759376	−	0.917927i	0.998592	+	0.0530388i	$0.0168907\pi$
$368$	−0.960064	−	2.95477i	−0.0500468	−	0.154028i
$369$	−1.73901	+	0.446501i	−0.0905292	+	0.0232439i
$370$	3.73193	+	23.3868i	0.194014	+	1.21582i
$371$	0.545224	+	8.66609i	0.0283066	+	0.449921i
$372$	4.00179	−	6.30582i	0.207483	−	0.326941i
$373$	19.4561	+	18.2705i	1.00740	+	0.946011i	0.998544	−	0.0539495i	$-0.0171810\pi$
$373$	19.4561	+	18.2705i	1.00740	+	0.946011i	0.00885599	+	0.999961i	$0.497181\pi$
$374$	−2.13437			−0.110366
$375$	2.47689	+	10.9025i	0.127906	+	0.563004i
$376$	−1.58807			−0.0818986
$377$	−14.4507	−	13.5701i	−0.744249	−	0.698897i
$378$	1.13566	−	1.78952i	0.0584121	−	0.0920428i
$379$	−0.514896	−	8.18403i	−0.0264484	−	0.420386i	−0.988866	−	0.148811i	$-0.952456\pi$
$379$	−0.514896	−	8.18403i	−0.0264484	−	0.420386i	0.962417	−	0.271575i	$-0.0875445\pi$
$380$	12.8749	+	2.02387i	0.660468	+	0.103822i
$381$	0.995613	−	0.255630i	0.0510068	−	0.0130963i
$382$	1.42581	+	4.38819i	0.0729507	+	0.224519i
$383$	−18.1605	+	21.9522i	−0.927956	+	1.12171i	0.0643540	+	0.997927i	$0.479501\pi$
$383$	−18.1605	+	21.9522i	−0.927956	+	1.12171i	−0.992310	+	0.123779i	$0.960499\pi$
$384$	−0.425779	−	0.904827i	−0.0217280	−	0.0461743i
$385$	3.11201	−	1.12447i	0.158603	−	0.0573085i
$386$	−9.39638	−	8.82379i	−0.478263	−	0.449119i
$387$	4.90925	+	2.69889i	0.249551	+	0.137192i
$388$	−4.45390	−	9.46503i	−0.226113	−	0.480514i
$389$	6.35506	−	13.5052i	0.322214	−	0.684740i	−0.676446	−	0.736493i	$-0.736481\pi$
$389$	6.35506	−	13.5052i	0.322214	−	0.684740i	0.998660	+	0.0517522i	$0.0164806\pi$
$390$	−0.758570	+	8.12548i	−0.0384117	+	0.411450i
$391$	9.42262	−	1.19035i	0.476522	−	0.0601988i
$392$	0.157473	−	2.50296i	0.00795357	−	0.126418i
$393$	4.51294	−	13.8894i	0.227648	−	0.700628i
$394$	−3.09014	−	4.86928i	−0.155679	−	0.245311i
$395$	−16.2501	+	3.65214i	−0.817632	+	0.183759i
$396$	0.676263	+	0.173635i	0.0339835	+	0.00872548i
$397$	−0.595662	−	9.46777i	−0.0298954	−	0.475174i	−0.984282	−	0.176602i	$-0.943490\pi$
$397$	−0.595662	−	9.46777i	−0.0298954	−	0.475174i	0.954387	−	0.298572i	$-0.0965104\pi$
$398$	−3.23900	−	16.9794i	−0.162356	−	0.851101i
$399$	−3.81738	−	11.7487i	−0.191108	−	0.588170i
$400$	−0.638179	−	4.95911i	−0.0319090	−	0.247955i
$401$	−8.14649	+	25.0723i	−0.406816	+	1.25205i	0.512553	+	0.858656i	$0.328700\pi$
$401$	−8.14649	+	25.0723i	−0.406816	+	1.25205i	−0.919369	+	0.393396i	$0.871300\pi$
$402$	9.52538	+	1.20334i	0.475083	+	0.0600169i
$403$	25.3429	−	10.0340i	1.26242	−	0.499828i
$404$	−14.2742	+	5.65155i	−0.710168	+	0.281175i
$405$	2.22590	−	0.213016i	0.110606	−	0.0105849i
$406$	0.722854	−	11.4894i	0.0358746	−	0.570211i
$407$	5.98249	+	4.34653i	0.296541	+	0.215450i
$408$	2.96093	−	0.760239i	0.146588	−	0.0376374i
$409$	−8.77739	+	8.24252i	−0.434014	+	0.407566i	−0.870518	−	0.492136i	$-0.836216\pi$
$409$	−8.77739	+	8.24252i	−0.434014	+	0.407566i	0.436504	+	0.899702i	$0.356216\pi$
$410$	3.96597	+	0.623430i	0.195865	+	0.0307890i
$411$	−0.616767	+	0.339071i	−0.0304229	+	0.0167251i
$412$	12.1178	−	1.53083i	0.597001	−	0.0754187i
$413$	−5.50850	+	28.8766i	−0.271056	+	1.42092i
$414$	−3.08233	−	0.389389i	−0.151488	−	0.0191374i
$415$	−2.87613	+	12.9376i	−0.141184	+	0.635082i
$416$	0.683872	−	3.58498i	0.0335296	−	0.175768i
$417$	−7.11365	−	11.2093i	−0.348357	−	0.548923i
$418$	3.29227	−	2.39197i	0.161030	−	0.116995i
$419$	−14.1022	+	17.0467i	−0.688939	+	0.832784i	−0.992781	−	0.119938i	$-0.961730\pi$
$419$	−14.1022	+	17.0467i	−0.688939	+	0.832784i	0.303843	+	0.952722i	$0.401730\pi$
$420$	−3.91665	+	2.66840i	−0.191113	+	0.130205i
$421$	8.41645	−	13.2622i	0.410193	−	0.646360i	−0.574932	−	0.818201i	$-0.694972\pi$
$421$	8.41645	−	13.2622i	0.410193	−	0.646360i	0.985125	+	0.171841i	$0.0549716\pi$
$422$	10.9646	+	13.2540i	0.533749	+	0.645192i
$423$	−0.676169	+	1.43693i	−0.0328764	+	0.0698660i
$424$	3.31447	−	2.40810i	0.160965	−	0.116948i
$425$	15.2569	+	0.924332i	0.740068	+	0.0448367i
$426$	6.64746	+	4.82966i	0.322071	+	0.233998i
$427$	−14.3877	+	7.90969i	−0.696268	+	0.382777i
$428$	3.29905	+	0.847052i	0.159466	+	0.0409438i
$429$	1.62426	+	1.96339i	0.0784200	+	0.0947935i
$430$	−7.68932	−	9.88929i	−0.370812	−	0.476904i
$431$	−5.84123	−	2.31270i	−0.281362	−	0.111399i	0.223205	−	0.974771i	$-0.428348\pi$
$431$	−5.84123	−	2.31270i	−0.281362	−	0.111399i	−0.504567	+	0.863372i	$0.668348\pi$
$432$	−1.00000			−0.0481125
$433$	−14.3627	−	5.68660i	−0.690228	−	0.273280i	−0.00328764	−	0.999995i	$-0.501046\pi$
$433$	−14.3627	−	5.68660i	−0.690228	−	0.273280i	−0.686940	+	0.726714i	$0.741046\pi$
$434$	13.8711	+	7.62570i	0.665834	+	0.366045i
$435$	10.0374	−	6.83846i	0.481257	−	0.327879i
$436$	1.95534	+	10.2503i	0.0936440	+	0.490899i
$437$	−13.2004	+	12.3960i	−0.631459	+	0.592979i
$438$	−2.55297	+	2.39740i	−0.121985	+	0.114552i
$439$	5.35842	+	28.0898i	0.255743	+	1.34065i	0.845890	+	0.533357i	$0.179070\pi$
$439$	5.35842	+	28.0898i	0.255743	+	1.34065i	−0.590147	+	0.807296i	$0.700930\pi$
$440$	−1.23471	−	0.955449i	−0.0588627	−	0.0455493i
$441$	−2.19769	−	1.20819i	−0.104652	−	0.0575330i
$442$	10.3733	+	4.10710i	0.493410	+	0.195355i
$443$	−18.5636			−0.881982			−0.440991	−	0.897512i	$-0.645373\pi$
$443$	−18.5636			−0.881982			−0.440991	+	0.897512i	$0.645373\pi$
$444$	−9.84746	−	3.89889i	−0.467340	−	0.185033i
$445$	−9.11658	−	2.63714i	−0.432167	−	0.125012i
$446$	−7.91321	−	9.56542i	−0.374701	−	0.452936i
$447$	−5.42016	−	1.39166i	−0.256365	−	0.0658233i
$448$	1.85729	−	1.02106i	0.0877489	−	0.0482404i
$449$	12.7649	+	9.27425i	0.602413	+	0.437679i	0.846735	−	0.532016i	$-0.178565\pi$
$449$	12.7649	+	9.27425i	0.602413	+	0.437679i	−0.244321	+	0.969694i	$0.578565\pi$
$450$	−4.75886	−	1.53404i	−0.224335	−	0.0723155i
$451$	1.01415	−	0.736821i	0.0477543	−	0.0346956i
$452$	7.56334	−	16.0729i	0.355750	−	0.756006i
$453$	0.469751	+	0.567832i	0.0220708	+	0.0266791i
$454$	−11.2558	+	17.7362i	−0.528259	+	0.832402i
$455$	−17.2886	−	0.523230i	−0.810501	−	0.0245294i
$456$	−3.71524	+	4.49096i	−0.173982	+	0.210308i
$457$	−25.5130	+	18.5363i	−1.19345	+	0.867090i	−0.993624	−	0.112742i	$-0.964037\pi$
$457$	−25.5130	+	18.5363i	−1.19345	+	0.867090i	−0.199823	+	0.979832i	$0.564037\pi$
$458$	8.21439	+	12.9438i	0.383833	+	0.604825i
$459$	0.572820	−	3.00283i	0.0267369	−	0.140160i
$460$	5.98375	+	3.52941i	0.278994	+	0.164560i
$461$	20.4640	+	2.58520i	0.953102	+	0.120405i	0.586479	−	0.809965i	$-0.300514\pi$
$461$	20.4640	+	2.58520i	0.953102	+	0.120405i	0.366623	+	0.930369i	$0.380514\pi$
$462$	−0.277287	+	1.45359i	−0.0129006	+	0.0676271i
$463$	−1.78583	+	0.225603i	−0.0829945	+	0.0104846i	−0.166721	−	0.986004i	$-0.553318\pi$
$463$	−1.78583	+	0.225603i	−0.0829945	+	0.0104846i	0.0837263	+	0.996489i	$0.473318\pi$
$464$	−4.75979	+	2.61672i	−0.220968	+	0.121478i
$465$	2.63159	+	16.4913i	0.122037	+	0.764766i
$466$	1.86535	−	1.75168i	0.0864109	−	0.0811452i
$467$	−3.28582	+	0.843654i	−0.152049	+	0.0390397i	−0.323947	−	0.946075i	$-0.605010\pi$
$467$	−3.28582	+	0.843654i	−0.152049	+	0.0390397i	0.171898	+	0.985115i	$0.445010\pi$
$468$	−2.95261	−	2.14520i	−0.136484	−	0.0991618i
$469$	−1.27773	+	20.3089i	−0.0590001	+	0.937779i
$470$	2.66095	−	2.35143i	0.122740	−	0.108464i
$471$	5.24729	−	2.07755i	0.241782	−	0.0957284i
$472$	12.8962	−	5.10596i	0.593595	−	0.235021i
$473$	−3.88061	−	0.490235i	−0.178431	−	0.0225410i
$474$	2.30173	−	7.08399i	0.105722	−	0.325378i
$475$	−24.5696	+	15.6725i	−1.12733	+	0.719103i
$476$	2.00216	+	6.16201i	0.0917688	+	0.282435i
$477$	−0.767684	−	4.02434i	−0.0351499	−	0.184262i
$478$	0.226811	+	3.60506i	0.0103741	+	0.164892i
$479$	−6.85529	−	1.76014i	−0.313226	−	0.0804228i	0.0888044	−	0.996049i	$-0.471695\pi$
$479$	−6.85529	−	1.76014i	−0.313226	−	0.0804228i	−0.402030	+	0.915626i	$0.631695\pi$
$480$	2.05319	+	0.885667i	0.0937149	+	0.0404250i
$481$	−20.7118	−	32.6366i	−0.944379	−	1.48810i
$482$	−8.06064	+	24.8081i	−0.367152	+	1.12998i
$483$	0.413463	−	6.57180i	0.0188132	−	0.299027i
$484$	10.4296	−	1.31757i	0.474074	−	0.0598895i
$485$	21.4776	+	9.26461i	0.975247	+	0.420684i
$486$	−0.425779	+	0.904827i	−0.0193137	+	0.0410438i
$487$	0.293664	+	0.624069i	0.0133072	+	0.0282792i	0.911370	−	0.411588i	$-0.135026\pi$
$487$	0.293664	+	0.624069i	0.0133072	+	0.0282792i	−0.898063	+	0.439867i	$0.855026\pi$
$488$	6.78838	+	3.73194i	0.307295	+	0.168937i
$489$	−15.1083	−	14.1876i	−0.683220	−	0.641587i
$490$	3.44223	+	4.42708i	0.155504	+	0.199995i
$491$	7.95073	+	16.8962i	0.358812	+	0.762514i	0.999988	−	0.00487995i	$-0.00155334\pi$
$491$	7.95073	+	16.8962i	0.358812	+	0.762514i	−0.641176	+	0.767393i	$0.721553\pi$
$492$	−1.14444	+	1.38339i	−0.0515954	+	0.0623681i
$493$	−5.13105	−	15.7917i	−0.231091	−	0.711224i
$494$	−20.6037	+	5.29012i	−0.927002	+	0.238014i
$495$	−1.39023	+	0.710392i	−0.0624863	+	0.0319298i
$496$	−0.468947	−	7.45371i	−0.0210564	−	0.334681i
$497$	−9.33140	+	14.7039i	−0.418571	+	0.659562i
$498$	−4.32068	−	4.05739i	−0.193614	−	0.181816i
$499$	2.32306			0.103995			0.0519973	−	0.998647i	$-0.483441\pi$
$499$	2.32306			0.103995			0.0519973	+	0.998647i	$0.483441\pi$
$500$	8.41219	+	7.36445i	0.376205	+	0.329348i
$501$	24.0057			1.07250
$502$	0.256713	+	0.241070i	0.0114577	+	0.0107595i
$503$	6.60651	−	10.4102i	0.294570	−	0.464167i	−0.664520	−	0.747271i	$-0.731364\pi$
$503$	6.60651	−	10.4102i	0.294570	−	0.464167i	0.959089	+	0.283103i	$0.0913639\pi$
$504$	−0.133082	−	2.11527i	−0.00592793	−	0.0942218i
$505$	15.5494	−	30.6052i	0.691940	−	1.36191i
$506$	2.10104	−	0.539454i	0.0934024	−	0.0239817i
$507$	−0.0988164	−	0.304126i	−0.00438859	−	0.0135067i
$508$	0.655212	−	0.792016i	0.0290704	−	0.0351400i
$509$	−7.84410	−	16.6696i	−0.347684	−	0.738865i	0.652131	−	0.758106i	$-0.273875\pi$
$509$	−7.84410	−	16.6696i	−0.347684	−	0.738865i	−0.999815	+	0.0192408i	$0.993875\pi$
$510$	−3.83561	+	5.65805i	−0.169844	+	0.250543i
$511$	−5.41090	−	5.08118i	−0.239364	−	0.224778i
$512$	−0.876307	−	0.481754i	−0.0387276	−	0.0212907i
$513$	2.48167	+	5.27381i	0.109568	+	0.232844i
$514$	12.5213	−	26.6090i	0.552289	−	1.17367i
$515$	−18.0377	+	20.5076i	−0.794835	+	0.903675i
$516$	5.55803	−	0.702143i	0.244679	−	0.0309101i
$517$	0.0696215	−	1.10660i	0.00306195	−	0.0486683i
$518$	6.93670	−	21.3490i	0.304781	−	0.938019i
$519$	−8.10186	−	12.7665i	−0.355632	−	0.560386i
$520$	4.16234	+	7.01953i	0.182531	+	0.307827i
$521$	−39.2351	−	10.0739i	−1.71892	−	0.441344i	−0.744786	−	0.667303i	$-0.767448\pi$
$521$	−39.2351	−	10.0739i	−1.71892	−	0.441344i	−0.974137	+	0.225959i	$0.927448\pi$
$522$	0.341056	+	5.42093i	0.0149276	+	0.237268i
$523$	4.68682	+	24.5692i	0.204940	+	1.07433i	0.924869	+	0.380286i	$0.124175\pi$
$523$	4.68682	+	24.5692i	0.204940	+	1.07433i	−0.719928	+	0.694048i	$0.755825\pi$
$524$	−4.51294	−	13.8894i	−0.197149	−	0.606761i
$525$	2.61160	−	10.2704i	0.113980	−	0.448239i
$526$	2.89991	−	8.92500i	0.126442	−	0.389148i
$527$	22.6508	+	2.86146i	0.986685	+	0.124647i
$528$	0.649168	−	0.257024i	0.0282514	−	0.0111855i
$529$	12.4103	−	4.91358i	0.539577	−	0.213634i
$530$	−1.98803	+	8.94266i	−0.0863543	+	0.388444i
$531$	0.870917	−	13.8428i	0.0377946	−	0.600727i
$532$	−9.99404	−	7.26109i	−0.433296	−	0.314808i
$533$	−6.34673	+	1.62956i	−0.274907	+	0.0705842i
$534$	3.09390	−	2.90536i	0.133886	−	0.125727i
$535$	−6.78204	+	3.46555i	−0.293213	+	0.149829i
$536$	8.41350	−	4.62536i	0.363408	−	0.199785i
$537$	15.3922	−	1.94449i	0.664223	−	0.0839108i
$538$	1.49875	−	7.85673i	0.0646158	−	0.338728i
$539$	1.73721	+	0.219460i	0.0748268	+	0.00945282i
$540$	1.67558	−	1.48068i	0.0721056	−	0.0637185i
$541$	−0.153572	+	0.805055i	−0.00660260	+	0.0346120i	−0.985436	−	0.170046i	$-0.945608\pi$
$541$	−0.153572	+	0.805055i	−0.00660260	+	0.0346120i	0.978833	+	0.204658i	$0.0656083\pi$
$542$	3.35197	+	5.28187i	0.143980	+	0.226876i
$543$	−4.61761	+	3.35489i	−0.198161	+	0.143972i
$544$	1.94859	−	2.35544i	0.0835450	−	0.100989i
$545$	−18.4538	−	14.2799i	−0.790472	−	0.611685i
$546$	4.14474	−	6.53107i	0.177379	−	0.279504i
$547$	13.5704	+	16.4038i	0.580227	+	0.701374i	0.976196	−	0.216890i	$-0.0695912\pi$
$547$	13.5704	+	16.4038i	0.580227	+	0.701374i	−0.395969	+	0.918264i	$0.629591\pi$
$548$	−0.299674	+	0.636840i	−0.0128015	+	0.0272045i
$549$	6.26711	−	4.55332i	0.267474	−	0.194331i
$550$	3.48358	−	0.227288i	0.148541	−	0.00969160i
$551$	25.6123	+	18.6084i	1.09112	+	0.792745i
$552$	−2.72254	+	1.49673i	−0.115879	+	0.0637050i
$553$	15.2909	+	3.92603i	0.650235	+	0.166952i
$554$	−14.7366	−	17.8134i	−0.626097	−	0.756821i
$555$	22.2732	−	8.04808i	0.945447	−	0.341622i
$556$	−12.3437	−	4.88723i	−0.523491	−	0.207265i
$557$	9.15053			0.387720			0.193860	−	0.981029i	$-0.437899\pi$
$557$	9.15053			0.387720			0.193860	+	0.981029i	$0.437899\pi$
$558$	−6.94398	−	2.74932i	−0.293962	−	0.116388i
$559$	17.9169	+	9.84992i	0.757806	+	0.416607i
$560$	−1.60019	+	4.46093i	−0.0676202	+	0.188509i
$561$	0.399942	+	2.09657i	0.0168856	+	0.0885172i
$562$	6.00039	−	5.63474i	0.253111	−	0.237687i
$563$	17.0215	−	15.9843i	0.717371	−	0.673656i	−0.237260	−	0.971446i	$-0.576249\pi$
$563$	17.0215	−	15.9843i	0.717371	−	0.673656i	0.954631	+	0.297790i	$0.0962495\pi$
$564$	0.297575	+	1.55994i	0.0125302	+	0.0656855i
$565$	11.1259	+	38.1304i	0.468071	+	1.60416i
$566$	3.28089	+	1.80369i	0.137906	+	0.0758145i
$567$	−1.97062	−	0.780224i	−0.0827583	−	0.0327663i
$568$	8.21671			0.344766
$569$	17.5032	+	6.92999i	0.733770	+	0.290520i	0.705138	−	0.709070i	$-0.250885\pi$
$569$	17.5032	+	6.92999i	0.733770	+	0.290520i	0.0286321	+	0.999590i	$0.490885\pi$
$570$	−0.424495	−	13.0261i	−0.0177801	−	0.545602i
$571$	−22.0613	−	26.6675i	−0.923236	−	1.11600i	−0.992962	−	0.118434i	$-0.962212\pi$
$571$	−22.0613	−	26.6675i	−0.923236	−	1.11600i	0.0697259	−	0.997566i	$-0.477788\pi$
$572$	2.46811	+	0.633702i	0.103197	+	0.0264964i
$573$	4.04329	−	2.22282i	0.168911	−	0.0928595i
$574$	−3.07855	−	2.23670i	−0.128496	−	0.0933581i
$575$	−15.2522	+	2.94622i	−0.636061	+	0.122866i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	12.3409	−	26.2257i	0.513757	−	1.09179i	−0.464724	−	0.885455i	$-0.653847\pi$
$577$	12.3409	−	26.2257i	0.513757	−	1.09179i	0.978482	−	0.206334i	$-0.0661535\pi$
$578$	−4.87942	−	5.89821i	−0.202957	−	0.245333i
$579$	−6.90679	+	10.8834i	−0.287036	+	0.452297i
$580$	4.10089	−	11.4323i	0.170280	−	0.474699i
$581$	8.00749	−	9.67939i	0.332207	−	0.401569i
$582$	−8.46280	+	6.14858i	−0.350794	+	0.254867i
$583$	1.53271	+	2.41516i	0.0634783	+	0.100026i
$584$	−0.656240	+	3.44013i	−0.0271554	+	0.142354i
$585$	8.12370	−	0.777430i	0.335874	−	0.0321428i
$586$	2.92637	+	0.369687i	0.120887	+	0.0152716i
$587$	−1.17529	+	6.16110i	−0.0485095	+	0.254296i	−0.998278	−	0.0586570i	$-0.981318\pi$
$587$	−1.17529	+	6.16110i	−0.0485095	+	0.254296i	0.949769	+	0.312953i	$0.101318\pi$
$588$	−2.48813	+	0.314324i	−0.102609	+	0.0129625i
$589$	−38.1457	+	20.9707i	−1.57176	+	0.864085i
$590$	−14.0483	+	27.6506i	−0.578359	+	1.13836i
$591$	−4.20400	+	3.94782i	−0.172929	+	0.162391i
$592$	−10.2585	+	2.63393i	−0.421621	+	0.108254i
$593$	−37.7828	−	27.4508i	−1.55155	−	1.12727i	−0.942533	−	0.334113i	$-0.891563\pi$
$593$	−37.7828	−	27.4508i	−1.55155	−	1.12727i	−0.609019	−	0.793156i	$-0.708437\pi$
$594$	0.0438402	−	0.696820i	0.00179879	−	0.0285909i
$595$	−12.4788	−	7.36039i	−0.511580	−	0.301747i
$596$	−5.20300	+	2.06001i	−0.213123	+	0.0843815i
$597$	−16.0717	+	6.36325i	−0.657773	+	0.260431i
$598$	−11.2494	−	1.42113i	−0.460021	−	0.0581142i
$599$	9.11025	−	28.0385i	0.372235	−	1.14562i	−0.573091	−	0.819492i	$-0.694256\pi$
$599$	9.11025	−	28.0385i	0.372235	−	1.14562i	0.945325	−	0.326129i	$-0.105744\pi$
$600$	−4.75168	+	1.55612i	−0.193987	+	0.0635283i
$601$	6.11024	+	18.8054i	0.249242	+	0.767088i	0.994910	+	0.100770i	$0.0321306\pi$
$601$	6.11024	+	18.8054i	0.249242	+	0.767088i	−0.745668	+	0.666318i	$0.767869\pi$
$602$	2.22490	+	11.6633i	0.0906801	+	0.475362i
$603$	−0.602857	−	9.58214i	−0.0245502	−	0.390215i
$604$	0.713800	+	0.183273i	0.0290441	+	0.00745726i
$605$	−15.5248	+	17.6507i	−0.631172	+	0.717602i
$606$	8.22617	+	12.9624i	0.334165	+	0.526560i
$607$	−10.9283	+	33.6338i	−0.443565	+	1.36515i	0.440485	+	0.897760i	$0.354806\pi$
$607$	−10.9283	+	33.6338i	−0.443565	+	1.36515i	−0.884050	+	0.467392i	$0.845194\pi$
$608$	−0.365976	+	5.81703i	−0.0148423	+	0.235912i
$609$	−11.4214	+	1.44285i	−0.462817	+	0.0584674i
$610$	−16.9003	+	3.79827i	−0.684273	+	0.153787i
$611$	−2.46776	+	5.24426i	−0.0998350	+	0.212160i
$612$	−1.30160	−	2.76603i	−0.0526139	−	0.111810i
$613$	26.6590	+	14.6559i	1.07675	+	0.591947i	0.918487	−	0.395450i	$-0.129411\pi$
$613$	26.6590	+	14.6559i	1.07675	+	0.591947i	0.158261	+	0.987397i	$0.449411\pi$
$614$	−20.0907	−	18.8664i	−0.810794	−	0.761386i
$615$	−0.130761	−	4.01254i	−0.00527279	−	0.161801i
$616$	0.630068	+	1.33896i	0.0253862	+	0.0539484i
$617$	−28.9153	+	34.9526i	−1.16408	+	1.40714i	−0.267905	+	0.963445i	$0.586331\pi$
$617$	−28.9153	+	34.9526i	−1.16408	+	1.40714i	−0.896180	+	0.443692i	$0.853669\pi$
$618$	−3.77436	−	11.6163i	−0.151827	−	0.467276i
$619$	−47.4758	+	12.1897i	−1.90821	+	0.489946i	−0.911272	+	0.411805i	$0.864899\pi$
$619$	−47.4758	+	12.1897i	−1.90821	+	0.489946i	−0.996942	+	0.0781416i	$0.975101\pi$
$620$	11.8223	+	11.7949i	0.474797	+	0.473696i
$621$	0.195080	+	3.10070i	0.00782828	+	0.124427i
$622$	−4.97952	+	7.84646i	−0.199660	+	0.314615i
$623$	6.55738	+	6.15779i	0.262716	+	0.246706i
$624$	−3.64963			−0.146102
$625$	−24.9997	+	0.116064i	−0.999989	+	0.00464255i
$626$	−15.2492			−0.609479
$627$	−2.96651	−	2.78574i	−0.118471	−	0.111252i
$628$	3.02399	−	4.76505i	0.120670	−	0.190146i
$629$	−2.03297	−	32.3132i	−0.0810599	−	1.28841i
$630$	3.35504	+	3.34726i	0.133668	+	0.133358i
$631$	30.6718	−	7.87519i	1.22103	−	0.313506i	0.417445	−	0.908702i	$-0.362926\pi$
$631$	30.6718	−	7.87519i	1.22103	−	0.313506i	0.803581	+	0.595196i	$0.202926\pi$
$632$	−2.30173	−	7.08399i	−0.0915578	−	0.281786i
$633$	10.9646	−	13.2540i	0.435805	−	0.526797i
$634$	7.61865	+	16.1905i	0.302575	+	0.643005i
$635$	0.0748630	+	2.29725i	0.00297085	+	0.0911636i
$636$	−2.98652	−	2.80453i	−0.118423	−	0.111207i
$637$	−8.02076	−	4.40945i	−0.317794	−	0.174709i
$638$	−1.61471	−	3.43144i	−0.0639271	−	0.135852i
$639$	3.49851	−	7.43470i	0.138399	−	0.294112i
$640$	2.18165	−	0.490316i	0.0862372	−	0.0193814i
$641$	37.2449	−	4.70513i	1.47109	−	0.185841i	0.651435	−	0.758704i	$-0.274167\pi$
$641$	37.2449	−	4.70513i	1.47109	−	0.185841i	0.819651	+	0.572863i	$0.194167\pi$
$642$	0.213868	−	3.39934i	0.00844070	−	0.134161i
$643$	−11.0871	+	34.1225i	−0.437231	+	1.34566i	0.453552	+	0.891230i	$0.350157\pi$
$643$	−11.0871	+	34.1225i	−0.437231	+	1.34566i	−0.890783	+	0.454429i	$0.849843\pi$
$644$	−3.52831	−	5.55973i	−0.139035	−	0.219084i
$645$	−8.27329	+	9.40619i	−0.325760	+	0.370368i
$646$	−17.2579	−	4.43107i	−0.679002	−	0.174338i
$647$	−2.35125	−	37.3720i	−0.0924370	−	1.46924i	−0.721783	−	0.692119i	$-0.756677\pi$
$647$	−2.35125	−	37.3720i	−0.0924370	−	1.46924i	0.629346	−	0.777125i	$-0.283323\pi$
$648$	0.187381	+	0.982287i	0.00736103	+	0.0385879i
$649$	2.99257	+	9.21017i	0.117468	+	0.361531i
$650$	−17.3681	−	5.59868i	−0.681231	−	0.219598i
$651$	4.89144	−	15.0543i	0.191711	−	0.590025i
$652$	−20.5621	−	2.59760i	−0.805275	−	0.101730i
$653$	28.0962	−	11.1241i	1.09949	−	0.435319i	0.252861	−	0.967503i	$-0.418628\pi$
$653$	28.0962	−	11.1241i	1.09949	−	0.435319i	0.846629	+	0.532184i	$0.178628\pi$
$654$	9.70232	−	3.84142i	0.379391	−	0.150211i
$655$	28.1276	+	16.5906i	1.09904	+	0.648248i
$656$	−0.112735	+	1.79187i	−0.00440156	+	0.0699608i
$657$	2.83331	+	2.05852i	0.110538	+	0.0803105i
$658$	−3.26011	+	0.837053i	−0.127092	+	0.0326317i
$659$	−24.7471	+	23.2391i	−0.964010	+	0.905265i	−0.995550	−	0.0942372i	$-0.969959\pi$
$659$	−24.7471	+	23.2391i	−0.964010	+	0.905265i	0.0315402	+	0.999502i	$0.489959\pi$
$660$	−0.707163	+	1.39188i	−0.0275263	+	0.0541788i
$661$	−8.87604	+	4.87964i	−0.345238	+	0.189796i	−0.644933	−	0.764239i	$-0.723115\pi$
$661$	−8.87604	+	4.87964i	−0.345238	+	0.189796i	0.299695	+	0.954035i	$0.403115\pi$
$662$	−29.9398	+	3.78227i	−1.16364	+	0.147002i
$663$	2.09058	−	10.9592i	0.0811913	−	0.425620i
$664$	−5.88038	−	0.742865i	−0.228203	−	0.0288287i
$665$	27.4972	−	2.63145i	1.06630	−	0.102043i
$666$	−1.98460	+	10.4036i	−0.0769015	+	0.403132i
$667$	9.04220	+	14.2482i	0.350115	+	0.551694i
$668$	19.4210	−	14.1102i	0.751423	−	0.545941i
$669$	−7.91321	+	9.56542i	−0.305942	+	0.369821i
$670$	−7.24881	+	20.2079i	−0.280046	+	0.780699i
$671$	−2.89810	+	4.56667i	−0.111880	+	0.176294i
$672$	−1.35099	−	1.63307i	−0.0521157	−	0.0629970i
$673$	8.22154	−	17.4717i	0.316917	−	0.673483i	−0.681373	−	0.731936i	$-0.738617\pi$
$673$	8.22154	−	17.4717i	0.316917	−	0.673483i	0.998290	+	0.0584532i	$0.0186169\pi$
$674$	−6.72089	+	4.88301i	−0.258879	+	0.188086i
$675$	−0.615150	+	4.96201i	−0.0236771	+	0.190988i
$676$	−0.258705	−	0.187960i	−0.00995018	−	0.00722923i
$677$	9.52024	−	5.23380i	0.365893	−	0.201151i	−0.288192	−	0.957573i	$-0.593054\pi$
$677$	9.52024	−	5.23380i	0.365893	−	0.201151i	0.654084	+	0.756422i	$0.273054\pi$
$678$	−17.2054	−	4.41761i	−0.660771	−	0.169657i
$679$	−14.1322	−	17.0829i	−0.542343	−	0.655581i
$680$	0.222641	+	6.83198i	0.00853789	+	0.261994i
$681$	19.5312	+	7.73294i	0.748437	+	0.296327i
$682$	5.21445			0.199672
$683$	−14.5876	−	5.77565i	−0.558180	−	0.220999i	0.0720590	−	0.997400i	$-0.477043\pi$
$683$	−14.5876	−	5.77565i	−0.558180	−	0.220999i	−0.630239	+	0.776401i	$0.717043\pi$
$684$	5.10758	+	2.80791i	0.195293	+	0.107363i
$685$	−0.440830	−	1.51080i	−0.0168433	−	0.0577247i
$686$	−3.77603	−	19.7946i	−0.144170	−	0.755763i
$687$	11.1753	−	10.4943i	0.426365	−	0.400383i
$688$	4.08384	−	3.83498i	0.155695	−	0.146207i
$689$	−2.80176	−	14.6873i	−0.106739	−	0.559543i
$690$	2.34565	−	6.53911i	0.0892975	−	0.248940i
$691$	−43.2881	−	23.7978i	−1.64676	−	0.905312i	−0.988270	−	0.152719i	$-0.951197\pi$
$691$	−43.2881	−	23.7978i	−1.64676	−	0.905312i	−0.658486	−	0.752593i	$-0.728803\pi$
$692$	−14.0585	−	5.56615i	−0.534424	−	0.211593i
$693$	1.47980			0.0562130
$694$	−1.84148	−	0.729094i	−0.0699017	−	0.0276760i
$695$	27.9194	−	10.0882i	1.05904	−	0.382668i
$696$	3.46226	+	4.18516i	0.131237	+	0.158638i
$697$	−5.31610	−	1.36494i	−0.201362	−	0.0517009i
$698$	−11.6705	+	6.41591i	−0.441735	+	0.242846i
$699$	−2.07019	−	1.50408i	−0.0783018	−	0.0568896i
$700$	−3.92398	−	9.84402i	−0.148313	−	0.372069i
$701$	−30.3904	+	22.0799i	−1.14783	+	0.833946i	−0.988191	−	0.153230i	$-0.951032\pi$
$701$	−30.3904	+	22.0799i	−1.14783	+	0.833946i	−0.159637	+	0.987176i	$0.551032\pi$
$702$	−1.55394	+	3.30228i	−0.0586495	+	0.124637i
$703$	39.3489	+	47.5647i	1.48407	+	1.79394i
$704$	0.374113	−	0.589508i	0.0140999	−	0.0222179i
$705$	−2.80840	−	2.17320i	−0.105770	−	0.0818474i
$706$	3.93300	−	4.75418i	0.148020	−	0.178926i
$707$	−26.3242	+	19.1257i	−0.990023	+	0.719294i
$708$	−7.43202	−	11.7110i	−0.279312	−	0.440126i
$709$	6.08430	−	31.8950i	0.228501	−	1.19784i	−0.664326	−	0.747443i	$-0.731282\pi$
$709$	6.08430	−	31.8950i	0.228501	−	1.19784i	0.892827	−	0.450400i	$-0.148718\pi$
$710$	−13.7678	+	12.1664i	−0.516695	+	0.456595i
$711$	−7.38981	−	0.933550i	−0.277140	−	0.0350109i
$712$	0.795285	−	4.16903i	0.0298046	−	0.156241i
$713$	−23.0202	+	2.90813i	−0.862115	+	0.108910i
$714$	5.67770	−	3.12134i	0.212483	−	0.116813i
$715$	−5.07383	+	2.59267i	−0.189750	+	0.0969603i
$716$	11.3096	−	10.6204i	0.422660	−	0.396904i
$717$	3.49871	−	0.898316i	0.130662	−	0.0335482i
$718$	1.41085	+	1.02504i	0.0526524	+	0.0382542i
$719$	−2.70667	+	43.0213i	−0.100942	+	1.60442i	0.543257	+	0.839566i	$0.317191\pi$
$719$	−2.70667	+	43.0213i	−0.100942	+	1.60442i	−0.644199	+	0.764858i	$0.722809\pi$
$720$	0.485250	−	2.18278i	0.0180842	−	0.0813474i
$721$	24.0694	−	9.52973i	0.896390	−	0.354906i
$722$	13.9204	−	5.51146i	0.518062	−	0.205115i
$723$	25.8791	+	3.26929i	0.962453	+	0.121586i
$724$	−1.76377	+	5.42833i	−0.0655500	+	0.201742i
$725$	10.0562	+	25.2278i	0.373478	+	0.936938i
$726$	−3.24855	−	9.99800i	−0.120565	−	0.371061i
$727$	−0.169150	−	0.886717i	−0.00627344	−	0.0328865i	0.979013	−	0.203798i	$-0.0653287\pi$
$727$	−0.169150	−	0.886717i	−0.00627344	−	0.0328865i	−0.985286	+	0.170912i	$0.945329\pi$
$728$	−0.485699	−	7.71996i	−0.0180012	−	0.286121i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	−3.99416	−	6.73590i	−0.147831	−	0.249307i
$731$	9.17647	+	14.4598i	0.339404	+	0.534815i
$732$	2.39382	−	7.36743i	0.0884783	−	0.272308i
$733$	1.03754	−	16.4913i	0.0383226	−	0.609120i	−0.931260	−	0.364355i	$-0.881289\pi$
$733$	1.03754	−	16.4913i	0.0383226	−	0.609120i	0.969583	−	0.244765i	$-0.0787107\pi$
$734$	−22.6424	+	2.86040i	−0.835748	+	0.105579i
$735$	3.70365	−	4.21081i	0.136611	−	0.155318i
$736$	−1.32283	+	2.81115i	−0.0487600	+	0.103620i
$737$	2.85419	+	6.06547i	0.105136	+	0.223425i
$738$	1.57333	+	0.864948i	0.0579152	+	0.0318392i
$739$	−36.6611	−	34.4271i	−1.34860	−	1.26642i	−0.934396	−	0.356236i	$-0.884060\pi$
$739$	−36.6611	−	34.4271i	−1.34860	−	1.26642i	−0.414204	−	0.910184i	$-0.635940\pi$
$740$	13.2889	−	19.6029i	0.488510	−	0.720618i
$741$	9.05716	+	19.2474i	0.332723	+	0.707072i
$742$	5.53489	−	6.69054i	0.203192	−	0.245617i
$743$	−4.75602	−	14.6375i	−0.174481	−	0.536998i	0.825128	−	0.564946i	$-0.191103\pi$
$743$	−4.75602	−	14.6375i	−0.174481	−	0.536998i	−0.999609	+	0.0279474i	$0.991103\pi$
$744$	−7.23381	+	1.85733i	−0.265204	+	0.0680929i
$745$	5.66782	−	11.1557i	0.207653	−	0.408714i
$746$	−1.67587	−	26.6373i	−0.0613581	−	0.975259i
$747$	−3.17591	+	5.00443i	−0.116200	+	0.183102i
$748$	1.55589	+	1.46108i	0.0568890	+	0.0534223i
$749$	7.21899			0.263776
$750$	5.65771	−	9.64315i	0.206590	−	0.352118i
$751$	−35.3137			−1.28862			−0.644308	−	0.764766i	$-0.722854\pi$
$751$	−35.3137			−1.28862			−0.644308	+	0.764766i	$0.722854\pi$
$752$	1.15766	+	1.08711i	0.0422153	+	0.0396429i
$753$	0.188697	−	0.297338i	0.00687649	−	0.0108356i
$754$	1.24473	+	19.7844i	0.0453303	+	0.720505i
$755$	−1.46740	+	0.749823i	−0.0534041	+	0.0272889i
$756$	−2.05287	+	0.527087i	−0.0746622	+	0.0191700i
$757$	14.1104	+	43.4275i	0.512853	+	1.57840i	0.787155	+	0.616755i	$0.211553\pi$
$757$	14.1104	+	43.4275i	0.512853	+	1.57840i	−0.274303	+	0.961643i	$0.588447\pi$
$758$	−5.22701	+	6.31837i	−0.189854	+	0.229494i
$759$	−0.923594	−	1.96274i	−0.0335243	−	0.0712428i
$760$	−7.99995	−	10.2888i	−0.290189	−	0.373214i
$761$	−29.6895	−	27.8803i	−1.07624	−	1.01066i	−0.999908	−	0.0135760i	$-0.995678\pi$
$761$	−29.6895	−	27.8803i	−1.07624	−	1.01066i	−0.0763339	−	0.997082i	$-0.524322\pi$
$762$	−0.900762	−	0.495198i	−0.0326311	−	0.0179391i
$763$	9.41686	+	20.0118i	0.340913	+	0.724477i
$764$	1.96455	−	4.17488i	0.0710749	−	0.151042i
$765$	6.27655	+	2.70746i	0.226929	+	0.0978885i
$766$	28.2657	−	3.57079i	1.02128	−	0.129018i
$767$	3.17852	−	50.5211i	0.114770	−	1.82421i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	−25.3191	−	39.8965i	−0.913031	−	1.43871i	−0.898580	−	0.438811i	$-0.855400\pi$
$769$	−25.3191	−	39.8965i	−0.913031	−	1.43871i	−0.0144511	−	0.999896i	$-0.504600\pi$
$770$	−3.03831	−	1.31061i	−0.109493	−	0.0472311i
$771$	−28.4840	−	7.31344i	−1.02583	−	0.263387i
$772$	0.809368	+	12.8645i	0.0291298	+	0.463005i
$773$	6.40078	+	33.5540i	0.230220	+	1.20686i	0.890199	+	0.455571i	$0.150565\pi$
$773$	6.40078	+	33.5540i	0.230220	+	1.20686i	−0.659979	+	0.751284i	$0.729435\pi$
$774$	−1.73118	−	5.32802i	−0.0622259	−	0.191512i
$775$	−37.2739	−	2.25822i	−1.33892	−	0.0811177i
$776$	−3.23250	+	9.94862i	−0.116040	+	0.357135i
$777$	−22.2706	−	2.81343i	−0.798954	−	0.100931i
$778$	−13.8776	+	5.49452i	−0.497535	+	0.196988i
$779$	9.72976	−	3.85228i	0.348605	−	0.138022i
$780$	6.11525	−	5.40394i	0.218961	−	0.193492i
$781$	−0.360223	+	5.72557i	−0.0128898	+	0.204877i
$782$	−7.68364	−	5.58249i	−0.274767	−	0.199630i
$783$	5.26101	−	1.35080i	0.188013	−	0.0482735i
$784$	−1.82818	+	1.71678i	−0.0652923	+	0.0613135i
$785$	1.98859	+	12.4618i	0.0709757	+	0.444781i
$786$	−12.7977	+	7.03562i	−0.456480	+	0.250952i
$787$	1.08181	−	0.136664i	0.0385623	−	0.00487156i	−0.106028	−	0.994363i	$-0.533813\pi$
$787$	1.08181	−	0.136664i	0.0385623	−	0.00487156i	0.144591	+	0.989492i	$0.453813\pi$
$788$	−1.08064	+	5.66490i	−0.0384961	+	0.201804i
$789$	−9.31030	−	1.17616i	−0.331455	−	0.0418726i
$790$	14.3459	+	8.46167i	0.510404	+	0.301053i
$791$	7.05472	−	36.9821i	0.250837	−	1.31493i
$792$	−0.374113	−	0.589508i	−0.0132935	−	0.0209473i
$793$	22.8726	−	16.6179i	0.812230	−	0.590120i
$794$	−6.04692	+	7.30947i	−0.214597	+	0.259403i
$795$	9.15678	+	0.277125i	0.324757	+	0.00982863i
$796$	−9.26209	+	14.5947i	−0.328286	+	0.517296i
$797$	5.26853	+	6.36856i	0.186621	+	0.225586i	0.855523	−	0.517764i	$-0.173236\pi$
$797$	5.26853	+	6.36856i	0.186621	+	0.225586i	−0.668902	+	0.743350i	$0.733236\pi$
$798$	−5.25978	+	11.1776i	−0.186194	+	0.395683i
$799$	−3.92753	+	2.85352i	−0.138946	+	0.100950i
$800$	−2.92953	+	4.05190i	−0.103574	+	0.143256i
$801$	−3.43364	−	2.49468i	−0.121322	−	0.0881453i
$802$	23.1017	−	12.7003i	0.815750	−	0.448462i
$803$	−2.36838	−	0.608097i	−0.0835784	−	0.0214593i
$804$	−6.11996	−	7.39776i	−0.215834	−	0.260899i
$805$	14.1442	+	4.09147i	0.498517	+	0.144205i
$806$	−25.3429	−	10.0340i	−0.892667	−	0.353432i
$807$	−7.99841			−0.281557
$808$	14.2742	+	5.65155i	0.502164	+	0.198821i
$809$	−6.27382	−	3.44906i	−0.220576	−	0.121263i	0.367635	−	0.929970i	$-0.380168\pi$
$809$	−6.27382	−	3.44906i	−0.220576	−	0.121263i	−0.588211	+	0.808708i	$0.700168\pi$
$810$	−1.76843	−	1.36845i	−0.0621363	−	0.0480824i
$811$	−4.38604	−	22.9924i	−0.154015	−	0.807373i	−0.972510	−	0.232860i	$-0.925192\pi$
$811$	−4.38604	−	22.9924i	−0.154015	−	0.807373i	0.818496	−	0.574513i	$-0.194808\pi$
$812$	−8.39199	+	7.88061i	−0.294501	+	0.276555i
$813$	4.56021	−	4.28232i	0.159934	−	0.150188i
$814$	−1.38564	−	7.26378i	−0.0485667	−	0.254596i
$815$	38.2998	−	26.0935i	1.34158	−	0.914017i
$816$	−2.67885	−	1.47271i	−0.0937784	−	0.0515551i
$817$	−30.3596	−	12.0202i	−1.06215	−	0.420535i
$818$	12.0408			0.420998
$819$	−7.19203	−	2.84753i	−0.251310	−	0.0995006i
$820$	−2.46430	−	3.16935i	−0.0860571	−	0.110679i
$821$	4.43284	+	5.35838i	0.154707	+	0.187009i	0.842172	−	0.539209i	$-0.181277\pi$
$821$	4.43284	+	5.35838i	0.154707	+	0.187009i	−0.687465	+	0.726217i	$0.741277\pi$
$822$	0.681714	+	0.175034i	0.0237775	+	0.00610502i
$823$	−14.1913	+	7.80171i	−0.494676	+	0.271950i	−0.709504	−	0.704701i	$-0.751081\pi$
$823$	−14.1913	+	7.80171i	−0.494676	+	0.271950i	0.214828	+	0.976652i	$0.431081\pi$
$824$	−9.88141	−	7.17927i	−0.344235	−	0.250102i
$825$	−0.876021	−	3.37929i	−0.0304991	−	0.117652i
$826$	23.7829	−	17.2793i	0.827513	−	0.601223i
$827$	−0.921299	+	1.95786i	−0.0320367	+	0.0680814i	−0.920205	−	0.391437i	$-0.871978\pi$
$827$	−0.921299	+	1.95786i	−0.0320367	+	0.0680814i	0.888168	+	0.459519i	$0.151978\pi$
$828$	1.98037	+	2.39386i	0.0688226	+	0.0831922i
$829$	−17.8627	+	28.1471i	−0.620397	+	0.977589i	0.378256	+	0.925701i	$0.376524\pi$
$829$	−17.8627	+	28.1471i	−0.620397	+	0.977589i	−0.998653	+	0.0518880i	$0.983476\pi$
$830$	10.9530	−	7.46225i	0.380184	−	0.259019i
$831$	−14.7366	+	17.8134i	−0.511206	+	0.617942i
$832$	−2.95261	+	2.14520i	−0.102363	+	0.0743713i
$833$	−4.10797	−	6.47312i	−0.142333	−	0.224280i
$834$	−2.48768	+	13.0409i	−0.0861413	+	0.451569i
$835$	−11.6488	+	52.3992i	−0.403123	+	1.81335i
$836$	−4.03738	−	0.510039i	−0.139636	−	0.0176401i
$837$	−1.39945	+	7.33616i	−0.0483720	+	0.253575i
$838$	21.9493	−	2.77284i	0.758227	−	0.0957863i
$839$	20.0731	−	11.0353i	0.693001	−	0.380980i	−0.0959926	−	0.995382i	$-0.530603\pi$
$839$	20.0731	−	11.0353i	0.693001	−	0.380980i	0.788993	+	0.614402i	$0.210603\pi$
$840$	4.68176	+	0.735948i	0.161536	+	0.0253926i
$841$	0.366550	−	0.344213i	0.0126396	−	0.0118694i
$842$	−15.2139	+	3.90627i	−0.524306	+	0.134619i
$843$	−6.65929	−	4.83826i	−0.229358	−	0.166639i
$844$	1.08009	−	17.1675i	0.0371782	−	0.590930i
$845$	0.711790	−	0.0681176i	0.0244863	−	0.00234332i
$846$	1.47655	−	0.584609i	0.0507649	−	0.0200993i
$847$	20.7162	−	8.20212i	0.711817	−	0.281828i
$848$	−4.06460	−	0.513479i	−0.139579	−	0.0176329i
$849$	1.15696	−	3.56075i	0.0397067	−	0.122205i
$850$	−10.4890	−	11.1179i	−0.359771	−	0.381340i
$851$	10.1682	+	31.2946i	0.348563	+	1.07277i
$852$	−1.53966	−	8.07117i	−0.0527478	−	0.276514i
$853$	−2.20871	−	35.1064i	−0.0756248	−	1.20202i	−0.834583	−	0.550882i	$-0.814291\pi$
$853$	−2.20871	−	35.1064i	−0.0756248	−	1.20202i	0.758958	−	0.651140i	$-0.225709\pi$
$854$	15.9027	+	4.08312i	0.544180	+	0.139722i
$855$	−12.7158	+	2.85782i	−0.434871	+	0.0977353i
$856$	−1.82506	−	2.87583i	−0.0623792	−	0.0982938i
$857$	−2.64088	+	8.12780i	−0.0902108	+	0.277640i	−0.985976	−	0.166887i	$-0.946628\pi$
$857$	−2.64088	+	8.12780i	−0.0902108	+	0.277640i	0.895765	+	0.444527i	$0.146628\pi$
$858$	0.160000	−	2.54313i	0.00546233	−	0.0868212i
$859$	44.3578	−	5.60369i	1.51347	−	0.191196i	0.675682	−	0.737193i	$-0.263849\pi$
$859$	44.3578	−	5.60369i	1.51347	−	0.191196i	0.837787	+	0.545998i	$0.183849\pi$
$860$	−1.16441	+	12.4727i	−0.0397061	+	0.425315i
$861$	−1.62022	+	3.44314i	−0.0552169	+	0.117342i
$862$	2.67491	+	5.68448i	0.0911080	+	0.193614i
$863$	−17.7682	−	9.76813i	−0.604835	−	0.332511i	0.149739	−	0.988726i	$-0.452157\pi$
$863$	−17.7682	−	9.76813i	−0.604835	−	0.332511i	−0.754574	+	0.656214i	$0.772157\pi$
$864$	0.728969	+	0.684547i	0.0248000	+	0.0232888i
$865$	31.7979	−	11.4896i	1.08116	−	0.390659i
$866$	6.57722	+	13.9773i	0.223503	+	0.474968i
$867$	−4.87942	+	5.89821i	−0.165714	+	0.200314i
$868$	−4.89144	−	15.0543i	−0.166026	−	0.510977i
$869$	5.03718	−	1.29333i	0.170874	−	0.0438731i
$870$	−11.9982	−	1.88606i	−0.406777	−	0.0639433i
$871$	−2.20020	−	34.9712i	−0.0745511	−	1.18496i
$872$	5.59141	−	8.81065i	0.189349	−	0.298366i
$873$	7.62544	+	7.16077i	0.258082	+	0.242355i
$874$	18.1083			0.612521
$875$	21.1508	+	10.6843i	0.715029	+	0.361195i
$876$	3.50216			0.118327
$877$	−30.0916	−	28.2579i	−1.01612	−	0.954200i	−0.0171629	−	0.999853i	$-0.505463\pi$
$877$	−30.0916	−	28.2579i	−1.01612	−	0.954200i	−0.998957	+	0.0456523i	$0.985463\pi$
$878$	15.3227	−	24.1447i	0.517115	−	0.814843i
$879$	−0.185209	−	2.94381i	−0.00624694	−	0.0992922i
$880$	0.246018	+	1.54171i	0.00829326	+	0.0519711i
$881$	55.3300	−	14.2063i	1.86412	−	0.478624i	0.864408	−	0.502792i	$-0.167694\pi$
$881$	55.3300	−	14.2063i	1.86412	−	0.478624i	0.999708	+	0.0241680i	$0.00769368\pi$
$882$	0.774985	+	2.38516i	0.0260951	+	0.0803125i
$883$	−2.57759	+	3.11577i	−0.0867427	+	0.104854i	−0.812099	−	0.583520i	$-0.801675\pi$
$883$	−2.57759	+	3.11577i	−0.0867427	+	0.104854i	0.725356	+	0.688374i	$0.241675\pi$
$884$	−4.75034	−	10.0950i	−0.159771	−	0.339531i
$885$	29.7932	+	8.61825i	1.00149	+	0.289699i
$886$	13.5323	+	12.7076i	0.454625	+	0.426921i
$887$	−20.6764	−	11.3669i	−0.694245	−	0.381664i	0.0952233	−	0.995456i	$-0.469643\pi$
$887$	−20.6764	−	11.3669i	−0.694245	−	0.381664i	−0.789468	+	0.613792i	$0.789643\pi$
$888$	4.50952	+	9.58322i	0.151330	+	0.321592i
$889$	0.927604	−	1.97126i	0.0311108	−	0.0661139i
$890$	4.84045	+	8.16312i	0.162252	+	0.273628i
$891$	−0.692693	+	0.0875074i	−0.0232061	+	0.00293161i
$892$	−0.779504	+	12.3899i	−0.0260997	+	0.414843i
$893$	2.86030	−	8.80310i	0.0957163	−	0.294584i
$894$	2.99847	+	4.72483i	0.100284	+	0.158022i
$895$	−3.22468	+	34.5414i	−0.107789	+	1.15459i
$896$	−2.05287	−	0.527087i	−0.0685816	−	0.0176088i
$897$	0.711968	+	11.3164i	0.0237719	+	0.377844i
$898$	−2.95656	−	15.4988i	−0.0986616	−	0.517202i
$899$	12.5356	+	38.5805i	0.418085	+	1.28673i
$900$	2.41893	+	4.37593i	0.0806311	+	0.145864i
$901$	3.87017	−	11.9112i	0.128934	−	0.396819i
$902$	−1.24367	−	0.157112i	−0.0414097	−	0.00523126i
$903$	11.0398	−	4.37098i	0.367383	−	0.145457i
$904$	−16.5161	+	6.53919i	−0.549318	+	0.217490i
$905$	−5.08229	−	11.7072i	−0.168941	−	0.389160i
$906$	0.0462736	−	0.735498i	0.00153734	−	0.0244353i
$907$	−2.58538	−	1.87839i	−0.0858461	−	0.0623708i	0.544034	−	0.839063i	$-0.316896\pi$
$907$	−2.58538	−	1.87839i	−0.0858461	−	0.0623708i	−0.629880	+	0.776692i	$0.716896\pi$
$908$	20.3464	−	5.22406i	0.675218	−	0.173367i
$909$	11.1913	−	10.5094i	0.371193	−	0.348574i
$910$	12.2447	+	12.2163i	0.405906	+	0.404965i
$911$	−16.4278	+	9.03129i	−0.544279	+	0.299220i	−0.730073	−	0.683369i	$-0.760514\pi$
$911$	−16.4278	+	9.03129i	−0.544279	+	0.299220i	0.185794	+	0.982589i	$0.440514\pi$
$912$	5.78257	−	0.730508i	0.191480	−	0.0241895i
$913$	0.775440	−	4.06500i	0.0256633	−	0.134532i
$914$	31.2871	+	3.95248i	1.03489	+	0.130737i
$915$	6.89779	+	15.8892i	0.228034	+	0.525282i
$916$	2.87262	−	15.0588i	0.0949139	−	0.497556i
$917$	−16.5854	−	26.1344i	−0.547698	−	0.863035i
$918$	−2.47314	+	1.79684i	−0.0816259	+	0.0593047i
$919$	−19.0736	+	23.0561i	−0.629181	+	0.760549i	−0.984726	−	0.174110i	$-0.944295\pi$
$919$	−19.0736	+	23.0561i	−0.629181	+	0.760549i	0.355545	+	0.934659i	$0.384295\pi$
$920$	−1.94592	−	6.66899i	−0.0641550	−	0.219870i
$921$	−14.7676	+	23.2700i	−0.486609	+	0.766773i
$922$	−13.1479	−	15.8931i	−0.433003	−	0.523411i
$923$	12.7682	−	27.1339i	0.420272	−	0.893123i
$924$	1.19718	−	0.869805i	0.0393845	−	0.0286145i
$925$	6.75909	+	52.5229i	0.222238	+	1.72694i
$926$	1.45625	+	1.05803i	0.0478553	+	0.0347689i
$927$	−10.7033	+	5.88419i	−0.351542	+	0.193262i
$928$	5.26101	+	1.35080i	0.172701	+	0.0443421i
$929$	−26.2610	−	31.7441i	−0.861595	−	1.04149i	−0.998702	−	0.0509335i	$-0.983780\pi$
$929$	−26.2610	−	31.7441i	−0.861595	−	1.04149i	0.137107	−	0.990556i	$-0.456220\pi$
$930$	9.37073	−	13.8231i	0.307278	−	0.453277i
$931$	13.5909	+	5.38102i	0.445424	+	0.176356i
$932$	−2.55890			−0.0838194
$933$	8.64055	+	3.42104i	0.282879	+	0.112000i
$934$	2.97278	+	1.63430i	0.0972722	+	0.0534759i
$935$	−4.77042	−	0.144374i	−0.156009	−	0.00472155i
$936$	0.683872	+	3.58498i	0.0223531	+	0.117179i
$937$	25.3744	−	23.8281i	0.828944	−	0.778430i	−0.148659	−	0.988889i	$-0.547496\pi$
$937$	25.3744	−	23.8281i	0.828944	−	0.778430i	0.977603	+	0.210458i	$0.0674956\pi$
$938$	14.8338	−	13.9299i	0.484342	−	0.454828i
$939$	2.85741	+	14.9791i	0.0932480	+	0.488823i
$940$	−3.54941	−	0.107421i	−0.115769	−	0.00350370i
$941$	34.6289	+	19.0374i	1.12887	+	0.620602i	0.932946	−	0.360017i	$-0.117229\pi$
$941$	34.6289	+	19.0374i	1.12887	+	0.620602i	0.195925	+	0.980619i	$0.437229\pi$
$942$	−5.24729	−	2.07755i	−0.170966	−	0.0676902i
$943$	5.57805			0.181646
$944$	−12.8962	−	5.10596i	−0.419735	−	0.166185i
$945$	2.65930	−	3.92283i	0.0865071	−	0.127610i
$946$	2.49325	+	3.01383i	0.0810627	+	0.0979879i
$947$	54.4104	+	13.9702i	1.76810	+	0.453971i	0.985658	−	0.168754i	$-0.0539744\pi$
$947$	54.4104	+	13.9702i	1.76810	+	0.453971i	0.782441	+	0.622725i	$0.213974\pi$
$948$	−6.52721	+	3.58836i	−0.211994	+	0.116545i
$949$	10.3405	+	7.51283i	0.335668	+	0.243877i
$950$	28.6390	+	5.39432i	0.929173	+	0.175015i
$951$	14.4761	−	10.5175i	0.469419	−	0.341053i
$952$	2.75868	−	5.86249i	0.0894092	−	0.190004i
$953$	−1.77191	−	2.14187i	−0.0573978	−	0.0693820i	0.741033	−	0.671469i	$-0.234336\pi$
$953$	−1.77191	−	2.14187i	−0.0573978	−	0.0693820i	−0.798431	+	0.602087i	$0.794336\pi$
$954$	−2.19523	+	3.45914i	−0.0710733	+	0.111994i
$955$	2.88992	+	9.90424i	0.0935155	+	0.320494i
$956$	2.30250	−	2.78324i	0.0744681	−	0.0900165i
$957$	−3.06809	+	2.22910i	−0.0991773	+	0.0720565i
$958$	3.79239	+	5.97585i	0.122527	+	0.193071i
$959$	−0.279522	+	1.46530i	−0.00902623	+	0.0473172i
$960$	−0.890431	−	2.05113i	−0.0287385	−	0.0661999i
$961$	−24.5823	−	3.10546i	−0.792976	−	0.100176i
$962$	−7.24303	+	37.9693i	−0.233525	+	1.22418i
$963$	−3.37920	+	0.426892i	−0.108893	+	0.0137564i
$964$	22.8583	−	12.5664i	0.736215	−	0.404738i
$965$	−20.4045	−	20.3572i	−0.656843	−	0.655320i
$966$	−4.80011	+	4.50760i	−0.154441	+	0.145030i
$967$	−24.8217	+	6.37314i	−0.798213	+	0.204946i	−0.625703	−	0.780061i	$-0.715188\pi$
$967$	−24.8217	+	6.37314i	−0.798213	+	0.204946i	−0.172510	+	0.985008i	$0.555188\pi$
$968$	−8.50481	−	6.17910i	−0.273355	−	0.198604i
$969$	−1.11878	+	17.7825i	−0.0359404	+	0.571256i
$970$	−9.31444	−	21.4560i	−0.299069	−	0.688912i
$971$	−6.77249	+	2.68142i	−0.217340	+	0.0860508i	−0.474271	−	0.880379i	$-0.657288\pi$
$971$	−6.77249	+	2.68142i	−0.217340	+	0.0860508i	0.256932	+	0.966430i	$0.417288\pi$
$972$	0.929776	−	0.368125i	0.0298226	−	0.0118076i
$973$	−27.9161	−	3.52662i	−0.894949	−	0.113058i
$974$	0.213132	−	0.655953i	0.00682920	−	0.0210181i
$975$	−2.24507	+	18.1095i	−0.0718997	+	0.579968i
$976$	−2.39382	−	7.36743i	−0.0766244	−	0.235826i
$977$	8.52775	+	44.7040i	0.272827	+	1.43021i	0.809848	+	0.586640i	$0.199550\pi$
$977$	8.52775	+	44.7040i	0.272827	+	1.43021i	−0.537021	+	0.843569i	$0.680450\pi$
$978$	1.30137	+	20.6847i	0.0416132	+	0.661423i
$979$	2.87020	+	0.736942i	0.0917320	+	0.0235528i
$980$	0.521265	−	5.58357i	0.0166512	−	0.178360i
$981$	−5.59141	−	8.81065i	−0.178520	−	0.281303i
$982$	5.77039	−	17.7594i	0.184141	−	0.566726i
$983$	−2.44659	+	38.8875i	−0.0780341	+	1.24032i	0.742942	+	0.669355i	$0.233430\pi$
$983$	−2.44659	+	38.8875i	−0.0780341	+	1.24032i	−0.820977	+	0.570962i	$0.806570\pi$
$984$	1.78126	−	0.225025i	0.0567844	−	0.00717354i
$985$	−6.57723	−	11.0921i	−0.209568	−	0.353423i
$986$	−7.06982	+	15.0241i	−0.225149	+	0.478466i
$987$	1.43311	+	3.04551i	0.0456164	+	0.0969398i
$988$	18.6408	+	10.2478i	0.593041	+	0.326027i
$989$	−12.6878	−	11.9146i	−0.403448	−	0.378863i
$990$	1.49973	+	0.433826i	0.0476646	+	0.0137879i
$991$	13.1788	+	28.0063i	0.418638	+	0.889650i	0.997254	+	0.0740508i	$0.0235927\pi$
$991$	13.1788	+	28.0063i	0.418638	+	0.889650i	−0.578617	+	0.815600i	$0.696407\pi$
$992$	−4.76056	+	5.75453i	−0.151148	+	0.182707i
$993$	9.32543	+	28.7007i	0.295934	+	0.910790i
$994$	16.8678	−	4.33093i	0.535015	−	0.137369i
$995$	−6.09077	−	38.1689i	−0.193090	−	1.21003i
$996$	0.372167	+	5.91542i	0.0117926	+	0.187437i
$997$	−29.8161	+	46.9826i	−0.944285	+	1.48795i	−0.0729088	+	0.997339i	$0.523228\pi$
$997$	−29.8161	+	46.9826i	−0.944285	+	1.48795i	−0.871376	+	0.490616i	$0.836772\pi$
$998$	−1.69344	−	1.59025i	−0.0536049	−	0.0503384i
$999$	10.5912			0.335091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.c.91.1	✓	120
125.11	even	25	inner	750.2.m.c.511.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.c.91.1	✓	120	1.1	even	1	trivial
750.2.m.c.511.1	yes	120	125.11	even	25	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.728969 - 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.58297 - 1.57930i) q^{5} +(0.968583 - 0.248690i) q^{6} +(0.654948 + 2.01572i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(-0.728969 - 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.58297 - 1.57930i) q^{5} +(0.968583 - 0.248690i) q^{6} +(0.654948 + 2.01572i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(0.0728305 + 2.23488i) q^{10} +(0.508965 + 0.477950i) q^{11} +(-0.876307 - 0.481754i) q^{12} +(-1.55394 - 3.30228i) q^{13} +(0.902421 - 1.91774i) q^{14} +(2.18165 - 0.490316i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.191949 - 3.05094i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(3.12308 + 4.92119i) q^{19} +(1.47679 - 1.67901i) q^{20} +(-2.05287 - 0.527087i) q^{21} +(-0.0438402 - 0.696820i) q^{22} +(0.582162 + 3.05180i) q^{23} +(0.309017 + 0.951057i) q^{24} +(0.0116064 + 4.99999i) q^{25} +(-1.12780 + 3.47100i) q^{26} +(0.992115 + 0.125333i) q^{27} +(-1.97062 + 0.780224i) q^{28} +(5.05022 - 1.99952i) q^{29} +(-1.92600 - 1.13602i) q^{30} +(-0.468947 + 7.45371i) q^{31} +(0.809017 + 0.587785i) q^{32} +(-0.676263 + 0.173635i) q^{33} +(-2.22844 + 2.09264i) q^{34} +(2.14667 - 4.22520i) q^{35} +(0.876307 - 0.481754i) q^{36} +(10.5077 - 1.32743i) q^{37} +(1.09216 - 5.72529i) q^{38} +(3.62085 + 0.457420i) q^{39} +(-2.22590 + 0.213016i) q^{40} +(0.336427 - 1.76361i) q^{41} +(1.13566 + 1.78952i) q^{42} +(-4.53228 + 3.29290i) q^{43} +(-0.445048 + 0.537971i) q^{44} +(-0.754999 + 2.10475i) q^{45} +(1.66472 - 2.62319i) q^{46} +(-1.01228 - 1.22363i) q^{47} +(0.425779 - 0.904827i) q^{48} +(2.02894 - 1.47411i) q^{49} +(3.41427 - 3.65278i) q^{50} +(2.47314 + 1.79684i) q^{51} +(3.19819 - 1.75822i) q^{52} +(3.96820 + 1.01886i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(-0.0508501 - 1.56039i) q^{55} +(1.97062 + 0.780224i) q^{56} -5.82853 q^{57} +(-5.05022 - 1.99952i) q^{58} +(12.1545 + 6.68202i) q^{59} +(0.626335 + 2.14656i) q^{60} +(1.45156 + 7.60936i) q^{61} +(5.44426 - 5.11250i) q^{62} +(1.54502 - 1.45087i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.75546 + 7.68156i) q^{65} +(0.611836 + 0.336360i) q^{66} +(8.92686 + 3.53440i) q^{67} +3.05697 q^{68} +(-2.88866 - 1.14370i) q^{69} +(-4.45720 + 1.61054i) q^{70} +(5.23753 + 6.33109i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(-3.06897 + 1.68718i) q^{73} +(-8.56847 - 6.22536i) q^{74} +(-4.22785 - 2.66933i) q^{75} +(-4.71538 + 3.42592i) q^{76} +(-0.630068 + 1.33896i) q^{77} +(-2.32636 - 2.81209i) q^{78} +(3.99113 - 6.28902i) q^{79} +(1.76843 + 1.36845i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-1.45252 + 1.05532i) q^{82} +(-3.17591 - 5.00443i) q^{83} +(0.397147 - 2.08191i) q^{84} +(-5.12221 + 4.52641i) q^{85} +(5.55803 + 0.702143i) q^{86} +(-1.01779 + 5.33544i) q^{87} +(0.692693 - 0.0875074i) q^{88} +(3.71923 - 2.04466i) q^{89} +(1.99117 - 1.01747i) q^{90} +(5.63874 - 5.29513i) q^{91} +(-3.00923 + 0.772638i) q^{92} +(-6.04210 - 4.38984i) q^{93} +(-0.0997159 + 1.58494i) q^{94} +(2.82829 - 12.7224i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(-9.72601 + 3.85080i) q^{97} +(-2.48813 - 0.314324i) q^{98} +(0.215755 - 0.664026i) 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

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