LMFDB - Embedded newform 750.2.m.d.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:	$140$
Relative dimension:	$7$ 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.d.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.20812 + 0.352409i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.260934 - 0.803073i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.20812 + 0.352409i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.260934 - 0.803073i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(1.85089 + 1.25467i) q^{10} +(3.77146 + 3.54163i) q^{11} +(0.876307 + 0.481754i) q^{12} +(0.988843 + 2.10140i) q^{13} +(-0.359529 + 0.764037i) q^{14} +(-0.885623 + 2.05321i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(-0.463236 + 7.36292i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-3.98926 - 6.28607i) q^{19} +(-0.490363 - 2.18164i) q^{20} +(-0.817873 - 0.209994i) q^{21} +(-0.324859 - 5.16348i) q^{22} +(0.928613 + 4.86796i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.75162 - 1.55633i) q^{25} +(0.717670 - 2.20876i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(0.785104 - 0.310845i) q^{28} +(8.23645 - 3.26104i) q^{29} +(2.05111 - 0.890475i) q^{30} +(0.00135602 - 0.0215533i) q^{31} +(0.809017 + 0.587785i) q^{32} +(5.01115 - 1.28664i) q^{33} +(5.37795 - 5.05023i) q^{34} +(0.859186 + 1.68133i) q^{35} +(0.876307 - 0.481754i) q^{36} +(6.09628 - 0.770139i) q^{37} +(-1.39506 + 7.31318i) q^{38} +(2.30412 + 0.291078i) q^{39} +(-1.13597 + 1.92602i) q^{40} +(0.650581 - 3.41046i) q^{41} +(0.452453 + 0.712952i) q^{42} +(-1.92789 + 1.40070i) q^{43} +(-3.29783 + 3.98640i) q^{44} +(1.25904 + 1.84792i) q^{45} +(2.65542 - 4.18427i) q^{46} +(7.89005 + 9.53743i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(5.08628 - 3.69540i) q^{49} +(-4.52916 - 2.11819i) q^{50} +(5.96851 + 4.33637i) q^{51} +(-2.03516 + 1.11884i) q^{52} +(-0.993889 - 0.255187i) q^{53} +(0.637424 + 0.770513i) q^{54} +(-9.57595 - 6.49127i) q^{55} +(-0.785104 - 0.310845i) q^{56} -7.44505 q^{57} +(-8.23645 - 3.26104i) q^{58} +(-5.03392 - 2.76742i) q^{59} +(-2.10477 - 0.754953i) q^{60} +(2.34855 + 12.3115i) q^{61} +(-0.0157427 + 0.0147834i) q^{62} +(-0.615542 + 0.578032i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.92404 - 4.29167i) q^{65} +(-4.53374 - 2.49244i) q^{66} +(10.3170 + 4.08480i) q^{67} -7.37748 q^{68} +(4.60773 + 1.82433i) q^{69} +(0.524630 - 1.81379i) q^{70} +(-1.94952 - 2.35657i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(1.48557 - 0.816698i) q^{73} +(-4.97119 - 3.61178i) q^{74} +(1.23199 - 4.84584i) q^{75} +(6.02318 - 4.37609i) q^{76} +(1.86009 - 3.95289i) q^{77} +(-1.48037 - 1.78946i) q^{78} +(0.306935 - 0.483652i) q^{79} +(2.14654 - 0.626381i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-2.80888 + 2.04077i) q^{82} +(1.46915 + 2.31501i) q^{83} +(0.158225 - 0.829445i) q^{84} +(-1.57188 - 16.4215i) q^{85} +(2.36422 + 0.298670i) q^{86} +(1.65992 - 8.70162i) q^{87} +(5.13289 - 0.648435i) q^{88} +(-2.43013 + 1.33597i) q^{89} +(0.347187 - 2.20895i) q^{90} +(1.42955 - 1.34244i) q^{91} +(-4.80004 + 1.23244i) q^{92} +(-0.0174714 - 0.0126937i) q^{93} +(0.777223 - 12.3536i) q^{94} +(11.0240 + 12.4746i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-16.0511 + 6.35508i) q^{97} +(-6.23741 - 0.787968i) q^{98} +(1.59876 - 4.92047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) $ 140 * q - 20 * q^5 + 5 * q^7	$ 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) $ 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * 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
$5$	−2.20812	+	0.352409i	−0.987503	+	0.157602i
$5$	−2.20812	+	0.352409i	−0.987503	+	0.157602i
$6$	−0.968583	+	0.248690i	−0.395422	+	0.101527i
$7$	−0.260934	−	0.803073i	−0.0986239	−	0.303533i	0.889557	−	0.456824i	$-0.151013\pi$
$7$	−0.260934	−	0.803073i	−0.0986239	−	0.303533i	−0.988181	+	0.153291i	$0.951013\pi$
$8$	0.637424	−	0.770513i	0.225363	−	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	1.85089	+	1.25467i	0.585304	+	0.396761i
$11$	3.77146	+	3.54163i	1.13714	+	1.06784i	0.996976	+	0.0777145i	$0.0247623\pi$
$11$	3.77146	+	3.54163i	1.13714	+	1.06784i	0.140162	+	0.990129i	$0.455238\pi$
$12$	0.876307	+	0.481754i	0.252968	+	0.139070i
$13$	0.988843	+	2.10140i	0.274256	+	0.582823i	0.993744	−	0.111682i	$-0.0356237\pi$
$13$	0.988843	+	2.10140i	0.274256	+	0.582823i	−0.719488	+	0.694504i	$0.755624\pi$
$14$	−0.359529	+	0.764037i	−0.0960881	+	0.204198i
$15$	−0.885623	+	2.05321i	−0.228667	+	0.530137i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	−0.463236	+	7.36292i	−0.112351	+	1.78577i	0.389709	+	0.920938i	$0.372576\pi$
$17$	−0.463236	+	7.36292i	−0.112351	+	1.78577i	−0.502060	+	0.864833i	$0.667424\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−3.98926	−	6.28607i	−0.915199	−	1.44212i	−0.896872	−	0.442291i	$-0.854166\pi$
$19$	−3.98926	−	6.28607i	−0.915199	−	1.44212i	−0.0183272	−	0.999832i	$-0.505834\pi$
$20$	−0.490363	−	2.18164i	−0.109648	−	0.487829i
$21$	−0.817873	−	0.209994i	−0.178474	−	0.0458245i
$22$	−0.324859	−	5.16348i	−0.0692601	−	1.10086i
$23$	0.928613	+	4.86796i	0.193629	+	1.01504i	0.937833	+	0.347087i	$0.112829\pi$
$23$	0.928613	+	4.86796i	0.193629	+	1.01504i	−0.744204	+	0.667953i	$0.767171\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	4.75162	−	1.55633i	0.950323	−	0.311265i
$26$	0.717670	−	2.20876i	0.140747	−	0.433174i
$27$	−0.992115	−	0.125333i	−0.190933	−	0.0241204i
$28$	0.785104	−	0.310845i	0.148371	−	0.0587442i
$29$	8.23645	−	3.26104i	1.52947	−	0.605560i	0.555355	−	0.831613i	$-0.312582\pi$
$29$	8.23645	−	3.26104i	1.52947	−	0.605560i	0.974115	+	0.226053i	$0.0725822\pi$
$30$	2.05111	−	0.890475i	0.374480	−	0.162578i
$31$	0.00135602	−	0.0215533i	0.000243548	−	0.00387108i	−0.997903	−	0.0647259i	$-0.979383\pi$
$31$	0.00135602	−	0.0215533i	0.000243548	−	0.00387108i	0.998147	+	0.0608549i	$0.0193827\pi$
$32$	0.809017	+	0.587785i	0.143015	+	0.103907i
$33$	5.01115	−	1.28664i	0.872329	−	0.223976i
$34$	5.37795	−	5.05023i	0.922311	−	0.866108i
$35$	0.859186	+	1.68133i	0.145229	+	0.284197i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	6.09628	−	0.770139i	1.00222	−	0.126610i	0.392940	−	0.919564i	$-0.371458\pi$
$37$	6.09628	−	0.770139i	1.00222	−	0.126610i	0.609282	+	0.792954i	$0.291458\pi$
$38$	−1.39506	+	7.31318i	−0.226309	+	1.18635i
$39$	2.30412	+	0.291078i	0.368954	+	0.0466097i
$40$	−1.13597	+	1.92602i	−0.179613	+	0.304531i
$41$	0.650581	−	3.41046i	0.101604	−	0.532625i	−0.894696	−	0.446676i	$-0.852608\pi$
$41$	0.650581	−	3.41046i	0.101604	−	0.532625i	0.996300	−	0.0859492i	$-0.0273923\pi$
$42$	0.452453	+	0.712952i	0.0698150	+	0.110011i
$43$	−1.92789	+	1.40070i	−0.294001	+	0.213604i	−0.725001	−	0.688748i	$-0.758161\pi$
$43$	−1.92789	+	1.40070i	−0.294001	+	0.213604i	0.431000	+	0.902352i	$0.358161\pi$
$44$	−3.29783	+	3.98640i	−0.497167	+	0.600972i
$45$	1.25904	+	1.84792i	0.187687	+	0.275472i
$46$	2.65542	−	4.18427i	0.391520	−	0.616937i
$47$	7.89005	+	9.53743i	1.15088	+	1.39118i	0.906873	+	0.421405i	$0.138463\pi$
$47$	7.89005	+	9.53743i	1.15088	+	1.39118i	0.244010	+	0.969773i	$0.421537\pi$
$48$	−0.425779	+	0.904827i	−0.0614559	+	0.130601i
$49$	5.08628	−	3.69540i	0.726611	−	0.527914i
$50$	−4.52916	−	2.11819i	−0.640519	−	0.299558i
$51$	5.96851	+	4.33637i	0.835758	+	0.607214i
$52$	−2.03516	+	1.11884i	−0.282226	+	0.155155i
$53$	−0.993889	−	0.255187i	−0.136521	−	0.0350527i	0.179811	−	0.983701i	$-0.442451\pi$
$53$	−0.993889	−	0.255187i	−0.136521	−	0.0350527i	−0.316332	+	0.948649i	$0.602451\pi$
$54$	0.637424	+	0.770513i	0.0867424	+	0.104854i
$55$	−9.57595	−	6.49127i	−1.29122	−	0.875283i
$56$	−0.785104	−	0.310845i	−0.104914	−	0.0415384i
$57$	−7.44505			−0.986122
$58$	−8.23645	−	3.26104i	−1.08150	−	0.428196i
$59$	−5.03392	−	2.76742i	−0.655361	−	0.360288i	0.119125	−	0.992879i	$-0.461991\pi$
$59$	−5.03392	−	2.76742i	−0.655361	−	0.360288i	−0.774486	+	0.632592i	$0.781991\pi$
$60$	−2.10477	−	0.754953i	−0.271724	−	0.0974640i
$61$	2.34855	+	12.3115i	0.300701	+	1.57633i	0.736596	+	0.676333i	$0.236432\pi$
$61$	2.34855	+	12.3115i	0.300701	+	1.57633i	−0.435895	+	0.899997i	$0.643568\pi$
$62$	−0.0157427	+	0.0147834i	−0.00199933	+	0.00187749i
$63$	−0.615542	+	0.578032i	−0.0775510	+	0.0728252i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	−2.92404	−	4.29167i	−0.362682	−	0.532316i
$66$	−4.53374	−	2.49244i	−0.558065	−	0.306799i
$67$	10.3170	+	4.08480i	1.26043	+	0.499038i	0.900871	−	0.434087i	$-0.142929\pi$
$67$	10.3170	+	4.08480i	1.26043	+	0.499038i	0.359554	+	0.933124i	$0.382929\pi$
$68$	−7.37748			−0.894651
$69$	4.60773	+	1.82433i	0.554705	+	0.219623i
$70$	0.524630	−	1.81379i	0.0627053	−	0.216789i
$71$	−1.94952	−	2.35657i	−0.231366	−	0.279673i	0.642035	−	0.766675i	$-0.278090\pi$
$71$	−1.94952	−	2.35657i	−0.231366	−	0.279673i	−0.873401	+	0.487002i	$0.838090\pi$
$72$	−0.968583	−	0.248690i	−0.114149	−	0.0293084i
$73$	1.48557	−	0.816698i	0.173873	−	0.0955872i	−0.392441	−	0.919777i	$-0.628369\pi$
$73$	1.48557	−	0.816698i	0.173873	−	0.0955872i	0.566313	+	0.824190i	$0.308369\pi$
$74$	−4.97119	−	3.61178i	−0.577889	−	0.419861i
$75$	1.23199	−	4.84584i	0.142258	−	0.559550i
$76$	6.02318	−	4.37609i	0.690906	−	0.501972i
$77$	1.86009	−	3.95289i	0.211977	−	0.450474i
$78$	−1.48037	−	1.78946i	−0.167619	−	0.202617i
$79$	0.306935	−	0.483652i	0.0345329	−	0.0544151i	−0.826623	−	0.562756i	$-0.809741\pi$
$79$	0.306935	−	0.483652i	0.0345329	−	0.0544151i	0.861156	+	0.508341i	$0.169741\pi$
$80$	2.14654	−	0.626381i	0.239991	−	0.0700316i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	−2.80888	+	2.04077i	−0.310189	+	0.225365i
$83$	1.46915	+	2.31501i	0.161260	+	0.254106i	0.915344	−	0.402673i	$-0.131919\pi$
$83$	1.46915	+	2.31501i	0.161260	+	0.254106i	−0.754084	+	0.656778i	$0.771919\pi$
$84$	0.158225	−	0.829445i	0.0172638	−	0.0904998i
$85$	−1.57188	−	16.4215i	−0.170494	−	1.78116i
$86$	2.36422	+	0.298670i	0.254940	+	0.0322064i
$87$	1.65992	−	8.70162i	0.177962	−	0.932911i
$88$	5.13289	−	0.648435i	0.547168	−	0.0691234i
$89$	−2.43013	+	1.33597i	−0.257593	+	0.141613i	−0.605318	−	0.795984i	$-0.706954\pi$
$89$	−2.43013	+	1.33597i	−0.257593	+	0.141613i	0.347725	+	0.937596i	$0.386954\pi$
$90$	0.347187	−	2.20895i	0.0365967	−	0.232844i
$91$	1.42955	−	1.34244i	0.149858	−	0.140726i
$92$	−4.80004	+	1.23244i	−0.500439	+	0.128491i
$93$	−0.0174714	−	0.0126937i	−0.00181170	−	0.00131628i
$94$	0.777223	−	12.3536i	0.0801644	−	1.27418i
$95$	11.0240	+	12.4746i	1.13104	+	1.27986i
$96$	0.929776	−	0.368125i	0.0948949	−	0.0375716i
$97$	−16.0511	+	6.35508i	−1.62974	+	0.645260i	−0.992143	−	0.125109i	$-0.960072\pi$
$97$	−16.0511	+	6.35508i	−1.62974	+	0.645260i	−0.637598	+	0.770369i	$0.720072\pi$
$98$	−6.23741	−	0.787968i	−0.630074	−	0.0795968i
$99$	1.59876	−	4.92047i	0.160681	−	0.494526i
$100$	1.85161	+	4.64452i	0.185161	+	0.464452i
$101$	2.47790	+	7.62620i	0.246560	+	0.758835i	0.995376	+	0.0960564i	$0.0306229\pi$
$101$	2.47790	+	7.62620i	0.246560	+	0.758835i	−0.748815	+	0.662779i	$0.769377\pi$
$102$	−1.38240	−	7.24680i	−0.136878	−	0.717541i
$103$	0.473549	+	7.52684i	0.0466601	+	0.741642i	0.949909	+	0.312525i	$0.101175\pi$
$103$	0.473549	+	7.52684i	0.0466601	+	0.741642i	−0.903249	+	0.429116i	$0.858825\pi$
$104$	2.24947	+	0.577565i	0.220578	+	0.0566349i
$105$	1.87997	+	0.175467i	0.183466	+	0.0171238i
$106$	0.549826	+	0.866387i	0.0534038	+	0.0841509i
$107$	3.24353	−	9.98255i	0.313564	−	0.965049i	−0.662778	−	0.748816i	$-0.730623\pi$
$107$	3.24353	−	9.98255i	0.313564	−	0.965049i	0.976342	−	0.216233i	$-0.0693772\pi$
$108$	0.0627905	−	0.998027i	0.00604202	−	0.0960352i
$109$	−1.11529	+	0.140894i	−0.106826	+	0.0134952i	−0.178564	−	0.983928i	$-0.557145\pi$
$109$	−1.11529	+	0.140894i	−0.106826	+	0.0134952i	0.0717385	+	0.997423i	$0.477145\pi$
$110$	2.53699	+	11.2871i	0.241892	+	1.07618i
$111$	2.61630	−	5.55992i	0.248328	−	0.527724i
$112$	0.359529	+	0.764037i	0.0339723	+	0.0721947i
$113$	4.45184	+	2.44742i	0.418794	+	0.230234i	0.677195	−	0.735804i	$-0.263196\pi$
$113$	4.45184	+	2.44742i	0.418794	+	0.230234i	−0.258401	+	0.966038i	$0.583196\pi$
$114$	5.42721	+	5.09649i	0.508305	+	0.477330i
$115$	−3.76600	−	10.4218i	−0.351182	−	0.971838i
$116$	3.77178	+	8.01544i	0.350201	+	0.744214i
$117$	1.48037	−	1.78946i	0.136861	−	0.165436i
$118$	1.77514	+	5.46332i	0.163415	+	0.502940i
$119$	6.03384	−	1.54923i	0.553121	−	0.142017i
$120$	1.01751	+	1.99115i	0.0928854	+	0.181766i
$121$	0.990023	+	15.7360i	0.0900021	+	1.43054i
$122$	6.71580	−	10.5824i	0.608020	−	0.958087i
$123$	−2.53095	−	2.37672i	−0.228208	−	0.214302i
$124$	0.0215959			0.00193937
$125$	−9.94369	+	5.11107i	−0.889391	+	0.457148i
$126$	0.844401			0.0752252
$127$	−10.6862	−	10.0350i	−0.948243	−	0.890459i	0.0458551	−	0.998948i	$-0.485399\pi$
$127$	−10.6862	−	10.0350i	−0.948243	−	0.890459i	−0.994098	+	0.108489i	$0.965399\pi$
$128$	−0.535827	+	0.844328i	−0.0473608	+	0.0746288i
$129$	0.149630	+	2.37831i	0.0131742	+	0.209398i
$130$	−0.806317	+	5.13013i	−0.0707187	+	0.449942i
$131$	−18.9126	+	4.85593i	−1.65240	+	0.424265i	−0.955995	−	0.293382i	$-0.905219\pi$
$131$	−18.9126	+	4.85593i	−1.65240	+	0.424265i	−0.696407	+	0.717647i	$0.745219\pi$
$132$	1.59876	+	4.92047i	0.139154	+	0.428272i
$133$	−4.00724	+	4.84392i	−0.347472	+	0.420021i
$134$	−4.72455	−	10.0402i	−0.408139	−	0.867339i
$135$	2.23488	−	0.0728790i	0.192348	−	0.00627243i
$136$	5.37795	+	5.05023i	0.461156	+	0.433054i
$137$	−12.9493	−	7.11891i	−1.10633	−	0.608210i	−0.179525	−	0.983753i	$-0.557456\pi$
$137$	−12.9493	−	7.11891i	−1.10633	−	0.608210i	−0.926805	+	0.375544i	$0.877456\pi$
$138$	−2.11005	−	4.48409i	−0.179619	−	0.381711i
$139$	2.07546	−	4.41057i	0.176038	−	0.374100i	−0.797263	−	0.603632i	$-0.793720\pi$
$139$	2.07546	−	4.41057i	0.176038	−	0.374100i	0.973301	+	0.229532i	$0.0737196\pi$
$140$	−1.62406	+	0.963062i	−0.137258	+	0.0813936i
$141$	12.2804	−	1.55138i	1.03420	−	0.130650i
$142$	−0.192041	+	3.05240i	−0.0161157	+	0.256152i
$143$	−3.71300	+	11.4275i	−0.310497	+	0.955612i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	−17.0379	+	10.1034i	−1.41492	+	0.839040i
$146$	−1.64200	−	0.421594i	−0.135893	−	0.0348914i
$147$	−0.394763	−	6.27458i	−0.0325595	−	0.517519i
$148$	1.15141	+	6.03589i	0.0946451	+	0.496147i
$149$	4.08712	+	12.5789i	0.334830	+	1.03050i	0.966806	+	0.255512i	$0.0822441\pi$
$149$	4.08712	+	12.5789i	0.334830	+	1.03050i	−0.631976	+	0.774988i	$0.717756\pi$
$150$	−4.21529	+	2.68911i	−0.344177	+	0.219565i
$151$	5.17691	−	15.9329i	0.421291	−	1.29660i	−0.485211	−	0.874397i	$-0.661257\pi$
$151$	5.17691	−	15.9329i	0.421291	−	1.29660i	0.906502	−	0.422202i	$-0.138743\pi$
$152$	−7.38635	−	0.933113i	−0.599112	−	0.0756854i
$153$	6.85941	−	2.71583i	0.554550	−	0.219562i
$154$	−4.06189	+	1.60822i	−0.327316	+	0.129594i
$155$	0.00460132	+	0.0480701i	0.000369587	+	0.00386109i
$156$	−0.145827	+	2.31785i	−0.0116755	+	0.185576i
$157$	15.1574	+	11.0125i	1.20969	+	0.878893i	0.995203	−	0.0978328i	$-0.0311911\pi$
$157$	15.1574	+	11.0125i	1.20969	+	0.878893i	0.214490	+	0.976726i	$0.431191\pi$
$158$	−0.554828	+	0.142456i	−0.0441398	+	0.0113332i
$159$	−0.748014	+	0.702432i	−0.0593214	+	0.0557065i
$160$	−1.99355	−	1.01280i	−0.157604	−	0.0800687i
$161$	3.66702	−	2.01596i	0.289002	−	0.158880i
$162$	0.992115	−	0.125333i	0.0779479	−	0.00984711i
$163$	0.261724	−	1.37201i	0.0204998	−	0.107464i	−0.970567	−	0.240833i	$-0.922580\pi$
$163$	0.261724	−	1.37201i	0.0204998	−	0.107464i	0.991066	+	0.133369i	$0.0425795\pi$
$164$	3.44459	+	0.435152i	0.268977	+	0.0339797i
$165$	−10.6118	+	4.60704i	−0.826128	+	0.358658i
$166$	0.513770	−	2.69327i	0.0398763	−	0.209039i
$167$	−3.36907	−	5.30881i	−0.260707	−	0.410808i	0.688609	−	0.725133i	$-0.258222\pi$
$167$	−3.36907	−	5.30881i	−0.260707	−	0.410808i	−0.949315	+	0.314325i	$0.898222\pi$
$168$	−0.683135	+	0.496327i	−0.0527050	+	0.0382924i
$169$	4.84845	−	5.86077i	0.372958	−	0.450828i
$170$	−10.0954	+	13.0468i	−0.774284	+	1.00064i
$171$	−3.98926	+	6.28607i	−0.305066	+	0.480708i
$172$	−1.51899	−	1.83614i	−0.115822	−	0.140004i
$173$	−4.96217	+	10.5452i	−0.377267	+	0.801733i	0.622550	+	0.782580i	$0.286097\pi$
$173$	−4.96217	+	10.5452i	−0.377267	+	0.801733i	−0.999817	+	0.0191528i	$0.993903\pi$
$174$	−7.16670	+	5.20691i	−0.543306	+	0.394735i
$175$	−2.48970	−	3.40980i	−0.188204	−	0.257756i
$176$	−4.18560	−	3.04102i	−0.315502	−	0.229225i
$177$	−5.03392	+	2.76742i	−0.378373	+	0.208012i
$178$	2.68602	+	0.689653i	0.201326	+	0.0516917i
$179$	−12.0598	−	14.5778i	−0.901393	−	1.08960i	−0.995568	−	0.0940410i	$-0.970022\pi$
$179$	−12.0598	−	14.5778i	−0.901393	−	1.08960i	0.0941757	−	0.995556i	$-0.469978\pi$
$180$	−1.76522	+	1.37259i	−0.131572	+	0.102307i
$181$	15.2555	+	6.04008i	1.13393	+	0.448956i	0.858729	−	0.512430i	$-0.171255\pi$
$181$	15.2555	+	6.04008i	1.13393	+	0.448956i	0.275204	+	0.961386i	$0.411255\pi$
$182$	−1.96106			−0.145364
$183$	11.6534	+	4.61390i	0.861443	+	0.341069i
$184$	4.34275	+	2.38744i	0.320151	+	0.176005i
$185$	−13.1899	+	3.84895i	−0.969743	+	0.282980i
$186$	0.00404667	+	0.0212134i	0.000296716	+	0.00155544i
$187$	−27.8239	+	26.1283i	−2.03468	+	1.91069i
$188$	−9.02319	+	8.47334i	−0.658084	+	0.617982i
$189$	0.158225	+	0.829445i	0.0115092	+	0.0603332i
$190$	0.503242	−	16.6400i	0.0365090	−	1.20720i
$191$	5.69192	+	3.12916i	0.411853	+	0.226418i	0.674190	−	0.738558i	$-0.264493\pi$
$191$	5.69192	+	3.12916i	0.411853	+	0.226418i	−0.262337	+	0.964976i	$0.584493\pi$
$192$	−0.929776	−	0.368125i	−0.0671008	−	0.0265671i
$193$	−12.2703			−0.883234			−0.441617	−	0.897204i	$-0.645595\pi$
$193$	−12.2703			−0.883234			−0.441617	+	0.897204i	$0.645595\pi$
$194$	16.0511	+	6.35508i	1.15240	+	0.456268i
$195$	−5.19035	+	0.169256i	−0.371689	+	0.0121207i
$196$	4.00748	+	4.84421i	0.286248	+	0.346015i
$197$	−20.2592	−	5.20167i	−1.44341	−	0.370604i	−0.555842	−	0.831288i	$-0.687604\pi$
$197$	−20.2592	−	5.20167i	−1.44341	−	0.370604i	−0.887564	+	0.460685i	$0.847604\pi$
$198$	−4.53374	+	2.49244i	−0.322199	+	0.177130i
$199$	−9.13326	−	6.63570i	−0.647440	−	0.470392i	0.214958	−	0.976623i	$-0.431038\pi$
$199$	−9.13326	−	6.63570i	−0.647440	−	0.470392i	−0.862398	+	0.506231i	$0.831038\pi$
$200$	1.82962	−	4.65322i	0.129374	−	0.329032i
$201$	8.97705	−	6.52221i	0.633192	−	0.460041i
$202$	3.41418	−	7.25550i	0.240221	−	0.510495i
$203$	−4.76803	−	5.76356i	−0.334650	−	0.404522i
$204$	−3.95305	+	6.22901i	−0.276769	+	0.436118i
$205$	−0.234684	+	7.76000i	−0.0163911	+	0.541982i
$206$	4.80727	−	5.81100i	0.334939	−	0.404871i
$207$	4.00928	−	2.91291i	0.278664	−	0.202461i
$208$	−1.24442	−	1.96089i	−0.0862850	−	0.135963i
$209$	7.21763	−	37.8361i	0.499254	−	2.61718i
$210$	−1.25032	−	1.41484i	−0.0862804	−	0.0976330i
$211$	18.6283	+	2.35331i	1.28243	+	0.162008i	0.736853	−	0.676053i	$-0.236311\pi$
$211$	18.6283	+	2.35331i	1.28243	+	0.162008i	0.545576	+	0.838062i	$0.316311\pi$
$212$	0.192277	−	1.00795i	0.0132056	−	0.0692263i
$213$	−3.03432	+	0.383324i	−0.207908	+	0.0262649i
$214$	−9.19795	+	5.05662i	−0.628759	+	0.345663i
$215$	3.76341	−	3.77232i	0.256662	−	0.257270i
$216$	−0.728969	+	0.684547i	−0.0496000	+	0.0465775i
$217$	−0.0176627	+	0.00453501i	−0.00119902	+	0.000307856i
$218$	0.909464	+	0.660764i	0.0615966	+	0.0447526i
$219$	0.106446	−	1.69191i	0.00719297	−	0.114329i
$220$	5.87718	−	9.96464i	0.396240	−	0.671816i
$221$	−15.9305	+	6.30733i	−1.07160	+	0.424277i
$222$	−5.71323	+	2.26203i	−0.383447	+	0.151817i
$223$	14.1064	+	1.78205i	0.944635	+	0.119335i	0.582536	−	0.812805i	$-0.302060\pi$
$223$	14.1064	+	1.78205i	0.944635	+	0.119335i	0.362099	+	0.932140i	$0.382060\pi$
$224$	0.260934	−	0.803073i	0.0174344	−	0.0536576i
$225$	−3.43134	−	3.63674i	−0.228756	−	0.242449i
$226$	−1.56988	−	4.83159i	−0.104427	−	0.321392i
$227$	0.278750	+	1.46126i	0.0185013	+	0.0969871i	0.990340	−	0.138659i	$-0.0442793\pi$
$227$	0.278750	+	1.46126i	0.0185013	+	0.0969871i	−0.971839	+	0.235646i	$0.924279\pi$
$228$	−0.467479	−	7.43036i	−0.0309595	−	0.492088i
$229$	−21.6473	−	5.55807i	−1.43049	−	0.367288i	−0.547551	−	0.836772i	$-0.684440\pi$
$229$	−21.6473	−	5.55807i	−1.43049	−	0.367288i	−0.882941	+	0.469484i	$0.844440\pi$
$230$	−4.38891	+	10.1752i	−0.289396	+	0.670931i
$231$	−2.34085	−	3.68859i	−0.154017	−	0.242691i
$232$	2.73744	−	8.42496i	0.179721	−	0.553126i
$233$	−1.13725	+	18.0761i	−0.0745037	+	1.18420i	0.766162	+	0.642648i	$0.222164\pi$
$233$	−1.13725	+	18.0761i	−0.0745037	+	1.18420i	−0.840666	+	0.541554i	$0.817836\pi$
$234$	−2.30412	+	0.291078i	−0.150625	+	0.0190283i
$235$	−20.7833	−	18.2793i	−1.35575	−	1.19241i
$236$	2.44588	−	5.19776i	0.159213	−	0.338345i
$237$	−0.243897	−	0.518307i	−0.0158428	−	0.0336677i
$238$	−5.45900	−	3.00111i	−0.353854	−	0.194533i
$239$	15.7258	+	14.7675i	1.01722	+	0.955232i	0.999005	−	0.0446018i	$-0.0142019\pi$
$239$	15.7258	+	14.7675i	1.01722	+	0.955232i	0.0182143	+	0.999834i	$0.494202\pi$
$240$	0.621304	−	2.14802i	0.0401050	−	0.138654i
$241$	3.05167	+	6.48513i	0.196575	+	0.417744i	0.978677	−	0.205408i	$-0.0658520\pi$
$241$	3.05167	+	6.48513i	0.196575	+	0.417744i	−0.782101	+	0.623151i	$0.785852\pi$
$242$	10.0503	−	12.1487i	0.646058	−	0.780951i
$243$	0.309017	+	0.951057i	0.0198234	+	0.0610103i
$244$	−12.1398	+	3.11696i	−0.777169	+	0.199543i
$245$	−9.92884	+	9.95234i	−0.634330	+	0.635832i
$246$	0.218006	+	3.46511i	0.0138996	+	0.220927i
$247$	9.26478	−	14.5990i	0.589504	−	0.928909i
$248$	−0.0157427	−	0.0147834i	−0.000999664	−	0.000938747i
$249$	2.74184			0.173757
$250$	10.7474	+	3.08111i	0.679726	+	0.194867i
$251$	−9.32881			−0.588829			−0.294415	−	0.955678i	$-0.595125\pi$
$251$	−9.32881			−0.588829			−0.294415	+	0.955678i	$0.595125\pi$
$252$	−0.615542	−	0.578032i	−0.0387755	−	0.0364126i
$253$	−13.7383	+	21.6481i	−0.863720	+	1.36100i
$254$	0.920463	+	14.6303i	0.0577550	+	0.917990i
$255$	−14.7074	−	7.47189i	−0.921012	−	0.467908i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	−5.71950	−	17.6028i	−0.356773	−	1.09803i	−0.954975	−	0.296688i	$-0.904118\pi$
$257$	−5.71950	−	17.6028i	−0.356773	−	1.09803i	0.598202	−	0.801345i	$-0.295882\pi$
$258$	1.51899	−	1.83614i	0.0945680	−	0.114313i
$259$	−2.20921	−	4.69480i	−0.137273	−	0.291721i
$260$	4.09960	−	3.18774i	0.254246	−	0.197696i
$261$	−6.45759	−	6.06408i	−0.399715	−	0.375357i
$262$	17.1108	+	9.40675i	1.05711	+	0.581151i
$263$	−6.48754	−	13.7867i	−0.400039	−	0.850126i	−0.998789	−	0.0491903i	$-0.984336\pi$
$263$	−6.48754	−	13.7867i	−0.400039	−	0.850126i	0.598751	−	0.800936i	$-0.295664\pi$
$264$	2.20285	−	4.68130i	0.135576	−	0.288114i
$265$	2.28456	+	0.213229i	0.140339	+	0.0130986i
$266$	6.23704	−	0.787922i	0.382418	−	0.0483106i
$267$	−0.174127	+	2.76767i	−0.0106564	+	0.169379i
$268$	−3.42893	+	10.5532i	−0.209455	+	0.644636i
$269$	13.7536	+	21.6722i	0.838570	+	1.32137i	0.945005	+	0.327055i	$0.106056\pi$
$269$	13.7536	+	21.6722i	0.838570	+	1.32137i	−0.106435	+	0.994320i	$0.533944\pi$
$270$	−1.67905	−	1.47675i	−0.102184	−	0.0898724i
$271$	−1.03252	−	0.265105i	−0.0627209	−	0.0161040i	0.217199	−	0.976127i	$-0.430308\pi$
$271$	−1.03252	−	0.265105i	−0.0627209	−	0.0161040i	−0.279920	+	0.960023i	$0.590308\pi$
$272$	−0.463236	−	7.36292i	−0.0280878	−	0.446443i
$273$	−0.367467	−	1.92633i	−0.0222401	−	0.116587i
$274$	4.56637	+	14.0538i	0.275864	+	0.849024i
$275$	23.4325	+	10.9589i	1.41303	+	0.660845i
$276$	−1.53141	+	4.71319i	−0.0921799	+	0.283700i
$277$	−1.24912	−	0.157800i	−0.0750523	−	0.00948131i	0.0877174	−	0.996145i	$-0.472043\pi$
$277$	−1.24912	−	0.157800i	−0.0750523	−	0.00948131i	−0.162770	+	0.986664i	$0.552043\pi$
$278$	−4.53219	+	1.79442i	−0.271823	+	0.107622i
$279$	−0.0200793	+	0.00794998i	−0.00120212	+	0.000475953i
$280$	1.84315	+	0.409706i	0.110149	+	0.0244846i
$281$	−1.05374	+	16.7487i	−0.0628606	+	0.999141i	0.832564	+	0.553928i	$0.186872\pi$
$281$	−1.05374	+	16.7487i	−0.0628606	+	0.999141i	−0.895425	+	0.445213i	$0.853128\pi$
$282$	−10.0140	−	7.27562i	−0.596327	−	0.433257i
$283$	16.2980	−	4.18461i	0.968815	−	0.248749i	0.269053	−	0.963125i	$-0.413289\pi$
$283$	16.2980	−	4.18461i	0.968815	−	0.248749i	0.699762	+	0.714376i	$0.253289\pi$
$284$	2.22951	−	2.09364i	0.132297	−	0.124235i
$285$	16.4396	−	2.62370i	0.973798	−	0.155415i
$286$	10.5293	−	5.78853i	0.622610	−	0.342283i
$287$	−2.90861	+	0.367443i	−0.171690	+	0.0216895i
$288$	0.187381	−	0.982287i	0.0110415	−	0.0578818i
$289$	−37.1321	−	4.69087i	−2.18424	−	0.275934i
$290$	19.3363	+	4.29818i	1.13547	+	0.252398i
$291$	−3.23484	+	16.9576i	−0.189629	+	0.994072i
$292$	0.908366	+	1.43136i	0.0531581	+	0.0837637i
$293$	10.7111	−	7.78204i	0.625747	−	0.454632i	−0.229177	−	0.973385i	$-0.573604\pi$
$293$	10.7111	−	7.78204i	0.625747	−	0.454632i	0.854924	+	0.518753i	$0.173604\pi$
$294$	−4.00748	+	4.84421i	−0.233721	+	0.282520i
$295$	12.0908	+	4.33681i	0.703953	+	0.252499i
$296$	3.29251	−	5.18817i	0.191373	−	0.301556i
$297$	−3.29783	−	3.98640i	−0.191360	−	0.231314i
$298$	5.63144	−	11.9674i	0.326220	−	0.693254i
$299$	−9.31126	+	6.76503i	−0.538484	+	0.391232i
$300$	4.91364	+	0.925290i	0.283689	+	0.0534216i
$301$	1.62792	+	1.18275i	0.0938316	+	0.0681726i
$302$	−14.6806	+	8.07073i	−0.844774	+	0.464419i
$303$	7.76674	+	1.99416i	0.446187	+	0.114561i
$304$	4.74566	+	5.73651i	0.272182	+	0.329012i
$305$	−9.52458	−	26.3577i	−0.545376	−	1.50924i
$306$	−6.85941	−	2.71583i	−0.392126	−	0.155254i
$307$	5.27855			0.301263			0.150631	−	0.988590i	$-0.451869\pi$
$307$	5.27855			0.301263			0.150631	+	0.988590i	$0.451869\pi$
$308$	4.06189	+	1.60822i	0.231448	+	0.0916366i
$309$	6.60886	+	3.63325i	0.375965	+	0.206688i
$310$	0.0295521	−	0.0381914i	0.00167844	−	0.00216913i
$311$	−1.59434	−	8.35782i	−0.0904067	−	0.473928i	−0.998480	−	0.0551169i	$-0.982447\pi$
$311$	−1.59434	−	8.35782i	−0.0904067	−	0.473928i	0.908073	−	0.418811i	$-0.137553\pi$
$312$	1.69298	−	1.58981i	0.0958461	−	0.0900054i
$313$	−6.74527	+	6.33423i	−0.381265	+	0.358032i	−0.851358	−	0.524585i	$-0.824220\pi$
$313$	−6.74527	+	6.33423i	−0.381265	+	0.358032i	0.470093	+	0.882617i	$0.344220\pi$
$314$	−3.51070	−	18.4037i	−0.198120	−	1.03858i
$315$	1.15549	−	1.49329i	0.0651044	−	0.0841373i
$316$	0.501970	+	0.275960i	0.0282380	+	0.0155240i
$317$	22.6020	+	8.94876i	1.26945	+	0.502612i	0.903727	−	0.428110i	$-0.140820\pi$
$317$	22.6020	+	8.94876i	1.26945	+	0.502612i	0.365727	+	0.930722i	$0.380820\pi$
$318$	1.02613			0.0575423
$319$	42.6128	+	16.8716i	2.38586	+	0.944629i
$320$	0.759928	+	2.10298i	0.0424813	+	0.117560i
$321$	−6.69057	−	8.08752i	−0.373431	−	0.451401i
$322$	−4.05316	−	1.04068i	−0.225874	−	0.0579946i
$323$	48.1318	−	26.4607i	2.67812	−	1.47231i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	7.96906	+	8.44607i	0.442044	+	0.468504i
$326$	−1.12999	+	0.820987i	−0.0625844	+	0.0454703i
$327$	−0.478644	+	1.01717i	−0.0264690	+	0.0562496i
$328$	−2.21311	−	2.67519i	−0.122199	−	0.147713i
$329$	5.60047	−	8.82493i	0.308764	−	0.486534i
$330$	10.8894	+	3.90589i	0.599443	+	0.215012i
$331$	13.2565	−	16.0244i	0.728645	−	0.880781i	−0.267933	−	0.963438i	$-0.586341\pi$
$331$	13.2565	−	16.0244i	0.728645	−	0.880781i	0.996578	+	0.0826570i	$0.0263406\pi$
$332$	−2.21820	+	1.61161i	−0.121739	+	0.0884488i
$333$	−3.29251	−	5.18817i	−0.180429	−	0.284310i
$334$	−1.17818	+	6.17625i	−0.0644673	+	0.337949i
$335$	−24.2208	−	5.38393i	−1.32332	−	0.294155i
$336$	0.837743	+	0.105832i	0.0457026	+	0.00577358i
$337$	2.58048	−	13.5274i	0.140568	−	0.736882i	−0.840287	−	0.542142i	$-0.817614\pi$
$337$	2.58048	−	13.5274i	0.140568	−	0.736882i	0.980855	−	0.194740i	$-0.0623864\pi$
$338$	−7.54634	+	0.953324i	−0.410467	+	0.0518540i
$339$	4.45184	−	2.44742i	0.241791	−	0.132926i
$340$	16.2904	−	2.59989i	0.883470	−	0.140999i
$341$	0.0814480	−	0.0764847i	0.00441066	−	0.00414188i
$342$	7.21115	−	1.85151i	0.389935	−	0.100118i
$343$	−9.07681	−	6.59469i	−0.490101	−	0.356080i
$344$	−0.149630	+	2.37831i	−0.00806753	+	0.128230i
$345$	−10.8173	−	2.40454i	−0.582386	−	0.129456i
$346$	10.8359	−	4.29025i	0.582543	−	0.230645i
$347$	19.5622	−	7.74524i	1.05016	−	0.415786i	0.221275	−	0.975211i	$-0.428978\pi$
$347$	19.5622	−	7.74524i	1.05016	−	0.415786i	0.828881	+	0.559425i	$0.188978\pi$
$348$	8.78868	+	1.11027i	0.471122	+	0.0595166i
$349$	9.32802	−	28.7087i	0.499318	−	1.53674i	−0.310800	−	0.950475i	$-0.600597\pi$
$349$	9.32802	−	28.7087i	0.499318	−	1.53674i	0.810118	−	0.586267i	$-0.199403\pi$
$350$	−0.519251	+	4.18995i	−0.0277552	+	0.223962i
$351$	−0.717670	−	2.20876i	−0.0383064	−	0.117895i
$352$	0.969453	+	5.08205i	0.0516720	+	0.270874i
$353$	−1.72399	−	27.4021i	−0.0917589	−	1.45847i	−0.727258	−	0.686364i	$-0.759206\pi$
$353$	−1.72399	−	27.4021i	−0.0917589	−	1.45847i	0.635499	−	0.772102i	$-0.280794\pi$
$354$	5.56400	+	1.42859i	0.295723	+	0.0759289i
$355$	5.13526	+	4.51656i	0.272551	+	0.239714i
$356$	−1.48593	−	2.34144i	−0.0787539	−	0.124096i
$357$	1.92504	−	5.92466i	0.101884	−	0.313566i
$358$	−1.18797	+	18.8823i	−0.0627863	+	0.997959i
$359$	20.1854	−	2.55001i	1.06535	−	0.134584i	0.426936	−	0.904282i	$-0.359593\pi$
$359$	20.1854	−	2.55001i	1.06535	−	0.134584i	0.638409	+	0.769697i	$0.279593\pi$
$360$	2.22639	+	0.207800i	0.117341	+	0.0109520i
$361$	−15.5106	+	32.9618i	−0.816350	+	1.73483i
$362$	−6.98607	−	14.8461i	−0.367180	−	0.780296i
$363$	13.8168	+	7.59585i	0.725194	+	0.398679i
$364$	1.42955	+	1.34244i	0.0749290	+	0.0703630i
$365$	−2.99250	+	2.32690i	−0.156635	+	0.121795i
$366$	−5.33652	−	11.3407i	−0.278944	−	0.592787i
$367$	−13.3992	+	16.1968i	−0.699431	+	0.845467i	−0.993910	−	0.110191i	$-0.964854\pi$
$367$	−13.3992	+	16.1968i	−0.699431	+	0.845467i	0.294479	+	0.955658i	$0.404854\pi$
$368$	−1.53141	−	4.71319i	−0.0798301	−	0.245692i
$369$	−3.36288	+	0.863442i	−0.175065	+	0.0449490i
$370$	12.2498	+	6.22337i	0.636838	+	0.323537i
$371$	0.0544056	+	0.864753i	0.00282460	+	0.0448957i
$372$	0.0115717	−	0.0182340i	0.000599962	−	0.000945389i
$373$	−12.2700	−	11.5223i	−0.635315	−	0.596600i	0.298477	−	0.954417i	$-0.403521\pi$
$373$	−12.2700	−	11.5223i	−0.635315	−	0.596600i	−0.933792	+	0.357816i	$0.883521\pi$
$374$	38.1688			1.97366
$375$	−1.01268	+	11.1344i	−0.0522944	+	0.574977i
$376$	12.3780			0.638348
$377$	14.9973	+	14.0834i	0.772400	+	0.725332i
$378$	0.452453	−	0.712952i	0.0232717	−	0.0366703i
$379$	0.884178	+	14.0536i	0.0454172	+	0.721885i	0.953180	+	0.302402i	$0.0977886\pi$
$379$	0.884178	+	14.0536i	0.0454172	+	0.721885i	−0.907763	+	0.419483i	$0.862211\pi$
$380$	−11.7577	+	11.7856i	−0.603159	+	0.604587i
$381$	−14.1987	+	3.64561i	−0.727423	+	0.186770i
$382$	−2.00718	−	6.17745i	−0.102696	−	0.316066i
$383$	18.3193	−	22.1442i	0.936071	−	1.13152i	−0.0550412	−	0.998484i	$-0.517529\pi$
$383$	18.3193	−	22.1442i	0.936071	−	1.13152i	0.991112	−	0.133031i	$-0.0424710\pi$
$384$	0.425779	+	0.904827i	0.0217280	+	0.0461743i
$385$	−2.71427	+	9.38398i	−0.138332	+	0.478252i
$386$	8.94464	+	8.39958i	0.455270	+	0.427527i
$387$	2.08825	+	1.14802i	0.106152	+	0.0583573i
$388$	−7.35039	−	15.6204i	−0.373160	−	0.793005i
$389$	−10.5762	+	22.4756i	−0.536235	+	1.13956i	0.434779	+	0.900537i	$0.356826\pi$
$389$	−10.5762	+	22.4756i	−0.536235	+	1.13956i	−0.971014	+	0.239021i	$0.923174\pi$
$390$	3.89947	+	3.42966i	0.197457	+	0.173668i
$391$	−36.2726	+	4.58229i	−1.83438	+	0.231736i
$392$	0.394763	−	6.27458i	0.0199385	−	0.316914i
$393$	−6.03388	+	18.5704i	−0.304369	+	0.936752i
$394$	11.2075	+	17.6602i	0.564626	+	0.889708i
$395$	−0.507307	+	1.17613i	−0.0255254	+	0.0591775i
$396$	5.01115	+	1.28664i	0.251820	+	0.0646563i
$397$	0.624110	+	9.91994i	0.0313232	+	0.497867i	0.982145	+	0.188128i	$0.0602419\pi$
$397$	0.624110	+	9.91994i	0.0313232	+	0.497867i	−0.950821	+	0.309740i	$0.899758\pi$
$398$	2.11541	+	11.0894i	0.106036	+	0.555860i
$399$	1.94267	+	5.97892i	0.0972552	+	0.299321i
$400$	−4.51909	+	2.13959i	−0.225954	+	0.106979i
$401$	12.0253	−	37.0099i	0.600513	−	1.84819i	0.0754045	−	0.997153i	$-0.475975\pi$
$401$	12.0253	−	37.0099i	0.600513	−	1.84819i	0.525108	−	0.851035i	$-0.324025\pi$
$402$	−11.0087	−	1.39073i	−0.549066	−	0.0693632i
$403$	0.0466329	−	0.0184633i	0.00232295	−	0.000919721i
$404$	−7.45556	+	2.95186i	−0.370928	+	0.146861i
$405$	1.13597	−	1.92602i	0.0564470	−	0.0957048i
$406$	−0.469683	+	7.46539i	−0.0233100	+	0.370501i
$407$	25.7194	+	18.6862i	1.27486	+	0.926243i
$408$	7.14570	−	1.83470i	0.353765	−	0.0908314i
$409$	−5.41003	+	5.08036i	−0.267509	+	0.251208i	−0.806680	−	0.590989i	$-0.798738\pi$
$409$	−5.41003	+	5.08036i	−0.267509	+	0.251208i	0.539171	+	0.842196i	$0.318738\pi$
$410$	5.48316	−	5.49614i	0.270794	−	0.271435i
$411$	−12.9493	+	7.11891i	−0.638740	+	0.351150i
$412$	−7.48225	+	0.945228i	−0.368624	+	0.0465681i
$413$	−0.908920	+	4.76473i	−0.0447250	+	0.234457i
$414$	−4.91666	−	0.621119i	−0.241641	−	0.0305263i
$415$	−4.05990	−	4.59409i	−0.199293	−	0.225515i
$416$	−0.435180	+	2.28129i	−0.0213365	+	0.111850i
$417$	−2.61188	−	4.11567i	−0.127904	−	0.201545i
$418$	−31.1620	+	22.6406i	−1.52419	+	1.10739i
$419$	19.1532	−	23.1522i	0.935695	−	1.13106i	−0.0554746	−	0.998460i	$-0.517667\pi$
$419$	19.1532	−	23.1522i	0.935695	−	1.13106i	0.991170	−	0.132601i	$-0.0423328\pi$
$420$	−0.0570765	+	1.88728i	−0.00278505	+	0.0920896i
$421$	11.2524	−	17.7309i	0.548408	−	0.864153i	−0.451192	−	0.892427i	$-0.649001\pi$
$421$	11.2524	−	17.7309i	0.548408	−	0.864153i	0.999600	+	0.0282737i	$0.00900099\pi$
$422$	−11.9685	−	14.4675i	−0.582619	−	0.704265i
$423$	5.27031	−	11.2000i	0.256251	−	0.544561i
$424$	−0.830154	+	0.603142i	−0.0403158	+	0.0292912i
$425$	9.25798	+	35.7067i	0.449078	+	1.73203i
$426$	2.47433	+	1.79770i	0.119882	+	0.0870991i
$427$	9.27425	−	5.09856i	0.448812	−	0.246737i
$428$	10.1665	+	2.61032i	0.491417	+	0.126174i
$429$	7.65899	+	9.25813i	0.369780	+	0.446987i
$430$	−5.32574	+	0.173671i	−0.256830	+	0.00837518i
$431$	−27.6572	−	10.9503i	−1.33220	−	0.527456i	−0.409268	−	0.912414i	$-0.634216\pi$
$431$	−27.6572	−	10.9503i	−1.33220	−	0.527456i	−0.922934	+	0.384958i	$0.874216\pi$
$432$	1.00000			0.0481125
$433$	10.1125	+	4.00382i	0.485975	+	0.192411i	0.598319	−	0.801258i	$-0.295836\pi$
$433$	10.1125	+	4.00382i	0.485975	+	0.192411i	−0.112343	+	0.993669i	$0.535836\pi$
$434$	0.0159800	+	0.00878506i	0.000767063	+	0.000421697i
$435$	−0.598784	+	19.7992i	−0.0287095	+	0.949300i
$436$	−0.210646	−	1.10425i	−0.0100881	−	0.0528838i
$437$	26.8958	−	25.2569i	1.28660	−	1.20820i
$438$	−1.23579	+	1.16049i	−0.0590484	+	0.0554501i
$439$	−3.23510	−	16.9590i	−0.154403	−	0.809408i	−0.972245	−	0.233965i	$-0.924830\pi$
$439$	−3.23510	−	16.9590i	−0.154403	−	0.809408i	0.817842	−	0.575442i	$-0.195170\pi$
$440$	−11.1055	+	3.24070i	−0.529436	+	0.154494i
$441$	−5.50933	−	3.02878i	−0.262349	−	0.144228i
$442$	15.9305	+	6.30733i	0.757736	+	0.300009i
$443$	−25.8743			−1.22932			−0.614662	−	0.788791i	$-0.710707\pi$
$443$	−25.8743			−1.22932			−0.614662	+	0.788791i	$0.710707\pi$
$444$	5.71323	+	2.26203i	0.271138	+	0.107351i
$445$	4.89521	−	3.80639i	0.232055	−	0.180440i
$446$	−9.06323	−	10.9556i	−0.429156	−	0.518761i
$447$	12.8107	+	3.28922i	0.605924	+	0.155575i
$448$	−0.739954	+	0.406793i	−0.0349596	+	0.0192192i
$449$	−23.2343	−	16.8807i	−1.09650	−	0.796651i	−0.116012	−	0.993248i	$-0.537011\pi$
$449$	−23.2343	−	16.8807i	−1.09650	−	0.796651i	−0.980484	+	0.196597i	$0.937011\pi$
$450$	0.0118233	+	4.99999i	0.000557354	+	0.235702i
$451$	14.5323	−	10.5583i	0.684297	−	0.497171i
$452$	−2.16306	+	4.59673i	−0.101742	+	0.216212i
$453$	−10.6787	−	12.9083i	−0.501727	−	0.606483i
$454$	0.797100	−	1.25603i	0.0374098	−	0.0589483i
$455$	−2.68354	+	3.46806i	−0.125806	+	0.162585i
$456$	−4.74566	+	5.73651i	−0.222236	+	0.268637i
$457$	5.87390	−	4.26764i	0.274769	−	0.199632i	−0.441863	−	0.897082i	$-0.645682\pi$
$457$	5.87390	−	4.26764i	0.274769	−	0.199632i	0.716633	+	0.697451i	$0.245682\pi$
$458$	11.9754	+	18.8702i	0.559574	+	0.881748i
$459$	1.38240	−	7.24680i	0.0645250	−	0.338252i
$460$	10.1648	−	4.41296i	0.473935	−	0.205755i
$461$	7.40274	+	0.935183i	0.344780	+	0.0435558i	0.295817	−	0.955245i	$-0.404408\pi$
$461$	7.40274	+	0.935183i	0.344780	+	0.0435558i	0.0489632	+	0.998801i	$0.484408\pi$
$462$	−0.818607	+	4.29129i	−0.0380851	+	0.199649i
$463$	−4.56096	+	0.576183i	−0.211966	+	0.0267775i	−0.230599	−	0.973049i	$-0.574069\pi$
$463$	−4.56096	+	0.576183i	−0.211966	+	0.0267775i	0.0186333	+	0.999826i	$0.494069\pi$
$464$	−7.76279	+	4.26763i	−0.360378	+	0.198120i
$465$	0.0430525	+	0.0218723i	0.00199651	+	0.00101430i
$466$	13.2029	−	12.3984i	0.611614	−	0.574344i
$467$	12.7678	−	3.27822i	0.590825	−	0.151698i	0.0585716	−	0.998283i	$-0.481345\pi$
$467$	12.7678	−	3.27822i	0.590825	−	0.151698i	0.532253	+	0.846585i	$0.321345\pi$
$468$	1.87889	+	1.36509i	0.0868515	+	0.0631013i
$469$	0.588327	−	9.35119i	0.0271664	−	0.431798i
$470$	2.63732	+	27.5522i	0.121650	+	1.27089i
$471$	17.4199	−	6.89703i	0.802667	−	0.317798i
$472$	−5.34108	+	2.11468i	−0.245843	+	0.0973362i
$473$	−12.2317	−	1.54523i	−0.562416	−	0.0710496i
$474$	−0.177013	+	0.544789i	−0.00813046	+	0.0250230i
$475$	−28.7386	−	23.6604i	−1.31862	−	1.08561i
$476$	1.92504	+	5.92466i	0.0882340	+	0.271556i
$477$	0.192277	+	1.00795i	0.00880375	+	0.0461509i
$478$	−1.35456	−	21.5301i	−0.0619562	−	0.984766i
$479$	−17.2024	−	4.41682i	−0.785996	−	0.201809i	−0.165699	−	0.986176i	$-0.552988\pi$
$479$	−17.2024	−	4.41682i	−0.785996	−	0.201809i	−0.620297	+	0.784367i	$0.712988\pi$
$480$	−1.92333	+	1.14053i	−0.0877876	+	0.0520577i
$481$	7.64663	+	12.0492i	0.348656	+	0.549394i
$482$	2.21480	−	6.81647i	0.100882	−	0.310482i
$483$	0.262755	−	4.17637i	0.0119558	−	0.190032i
$484$	−15.6427	+	1.97614i	−0.711034	+	0.0898245i
$485$	33.2032	−	19.6893i	1.50768	−	0.894047i
$486$	0.425779	−	0.904827i	0.0193137	−	0.0410438i
$487$	−13.9046	−	29.5488i	−0.630078	−	1.33898i	−0.923720	−	0.383068i	$-0.874867\pi$
$487$	−13.9046	−	29.5488i	−0.630078	−	1.33898i	0.293642	−	0.955915i	$-0.405133\pi$
$488$	10.9832	+	6.03808i	0.497187	+	0.273331i
$489$	−1.01818	−	0.956138i	−0.0460439	−	0.0432381i
$490$	14.0507	−	0.458189i	0.634744	−	0.0206989i
$491$	−6.33310	−	13.4585i	−0.285809	−	0.607375i	0.709437	−	0.704769i	$-0.248949\pi$
$491$	−6.33310	−	13.4585i	−0.285809	−	0.607375i	−0.995246	+	0.0973942i	$0.968949\pi$
$492$	2.21311	−	2.67519i	0.0997748	−	0.120607i
$493$	20.1954	+	62.1550i	0.909554	+	2.79932i
$494$	−16.7474	+	4.30000i	−0.753501	+	0.193466i
$495$	−1.79624	+	11.4284i	−0.0807348	+	0.513670i
$496$	0.00135602	+	0.0215533i	6.08870e−5	+	0.000967770i
$497$	−1.38380	+	2.18052i	−0.0620719	+	0.0978096i
$498$	−1.99872	−	1.87692i	−0.0895646	−	0.0841067i
$499$	−9.57029			−0.428425			−0.214212	−	0.976787i	$-0.568718\pi$
$499$	−9.57029			−0.428425			−0.214212	+	0.976787i	$0.568718\pi$
$500$	−5.72535	−	9.60314i	−0.256046	−	0.429466i
$501$	−6.28762			−0.280910
$502$	6.80041	+	6.38601i	0.303517	+	0.285022i
$503$	−17.1742	+	27.0622i	−0.765760	+	1.20664i	0.207791	+	0.978173i	$0.433373\pi$
$503$	−17.1742	+	27.0622i	−0.765760	+	1.20664i	−0.973551	+	0.228471i	$0.926627\pi$
$504$	0.0530204	+	0.842735i	0.00236172	+	0.0375384i
$505$	−8.15905	−	15.9663i	−0.363073	−	0.710493i
$506$	24.8339	−	6.37627i	1.10400	−	0.283460i
$507$	−2.35048	−	7.23404i	−0.104389	−	0.321275i
$508$	9.34417	−	11.2952i	0.414581	−	0.501142i
$509$	−4.43764	−	9.43047i	−0.196695	−	0.417998i	0.782011	−	0.623264i	$-0.214194\pi$
$509$	−4.43764	−	9.43047i	−0.196695	−	0.417998i	−0.978706	+	0.205266i	$0.934194\pi$
$510$	5.60635	+	15.5147i	0.248253	+	0.687001i
$511$	−1.04350	−	0.979915i	−0.0461619	−	0.0433489i
$512$	−0.876307	−	0.481754i	−0.0387276	−	0.0212907i
$513$	3.16995	+	6.73649i	0.139957	+	0.297423i
$514$	−7.88062	+	16.7472i	−0.347599	+	0.738686i
$515$	−3.69818	−	16.4533i	−0.162961	−	0.725019i
$516$	−2.36422	+	0.298670i	−0.104079	+	0.0131482i
$517$	−4.02111	+	63.9137i	−0.176848	+	2.81092i
$518$	−1.60337	+	4.93467i	−0.0704481	+	0.216817i
$519$	6.24470	+	9.84008i	0.274112	+	0.431931i
$520$	−5.17064	−	0.482602i	−0.226748	−	0.0211635i
$521$	6.34717	+	1.62968i	0.278075	+	0.0713975i	0.385152	−	0.922853i	$-0.374149\pi$
$521$	6.34717	+	1.62968i	0.278075	+	0.0713975i	−0.107077	+	0.994251i	$0.534149\pi$
$522$	0.556232	+	8.84105i	0.0243456	+	0.386962i
$523$	−3.81017	−	19.9736i	−0.166607	−	0.873386i	−0.963183	−	0.268847i	$-0.913357\pi$
$523$	−3.81017	−	19.9736i	−0.166607	−	0.873386i	0.796576	−	0.604539i	$-0.206643\pi$
$524$	−6.03388	−	18.5704i	−0.263591	−	0.811251i
$525$	−4.21304	+	0.275065i	−0.183872	+	0.0120048i
$526$	−4.70845	+	14.4911i	−0.205298	+	0.631843i
$527$	0.158067	+	0.0199685i	0.00688550	+	0.000869841i
$528$	−4.81038	+	1.90456i	−0.209345	+	0.0828854i
$529$	−1.44983	+	0.574028i	−0.0630361	+	0.0249577i
$530$	−1.51941	−	1.71933i	−0.0659988	−	0.0746827i
$531$	−0.360699	+	5.73314i	−0.0156530	+	0.248797i
$532$	−5.08598	−	3.69518i	−0.220505	−	0.160206i
$533$	7.81007	−	2.00528i	0.338291	−	0.0868585i
$534$	2.02154	−	1.89835i	0.0874804	−	0.0821496i
$535$	−3.64417	+	23.1857i	−0.157551	+	1.00241i
$536$	9.72371	−	5.34566i	0.420000	−	0.230897i
$537$	−18.7704	+	2.37126i	−0.810003	+	0.102327i
$538$	4.80969	−	25.2133i	0.207361	−	1.08702i
$539$	32.2704	+	4.07670i	1.38999	+	0.175596i
$540$	0.213064	+	2.22589i	0.00916883	+	0.0957872i
$541$	−0.718771	+	3.76793i	−0.0309024	+	0.161996i	−0.994393	−	0.105745i	$-0.966277\pi$
$541$	−0.718771	+	3.76793i	−0.0309024	+	0.161996i	0.963491	+	0.267741i	$0.0862772\pi$
$542$	0.571195	+	0.900060i	0.0245349	+	0.0386609i
$543$	13.2741	−	9.64421i	0.569647	−	0.413873i
$544$	−4.70258	+	5.68445i	−0.201622	+	0.243719i
$545$	2.41306	−	0.704152i	0.103364	−	0.0301626i
$546$	−1.05079	+	1.65578i	−0.0449697	+	0.0708609i
$547$	−24.8874	−	30.0837i	−1.06411	−	1.28629i	−0.956386	−	0.292106i	$-0.905644\pi$
$547$	−24.8874	−	30.0837i	−1.06411	−	1.28629i	−0.107723	−	0.994181i	$-0.534356\pi$
$548$	6.29178	−	13.3707i	0.268771	−	0.571168i
$549$	10.1398	−	7.36703i	0.432758	−	0.314417i
$550$	−9.57966	−	24.0293i	−0.408478	−	1.02461i
$551$	−53.3565	−	38.7657i	−2.27306	−	1.65148i
$552$	4.34275	−	2.38744i	0.184840	−	0.101616i
$553$	−0.468498	−	0.120290i	−0.0199226	−	0.00511524i
$554$	0.802547	+	0.970113i	0.0340970	+	0.0412161i
$555$	−3.81775	+	13.1990i	−0.162054	+	0.560266i
$556$	4.53219	+	1.79442i	0.192208	+	0.0761004i
$557$	4.16593			0.176516			0.0882581	−	0.996098i	$-0.471870\pi$
$557$	4.16593			0.176516			0.0882581	+	0.996098i	$0.471870\pi$
$558$	0.0200793	+	0.00794998i	0.000850027	+	0.000336549i
$559$	−4.84981	−	2.66620i	−0.205125	−	0.112768i
$560$	−1.06314	−	1.56039i	−0.0449257	−	0.0659384i
$561$	7.15212	+	37.4927i	0.301963	+	1.58294i
$562$	12.2334	−	11.4879i	0.516034	−	0.484588i
$563$	21.7197	−	20.3962i	0.915378	−	0.859597i	−0.0751127	−	0.997175i	$-0.523932\pi$
$563$	21.7197	−	20.3962i	0.915378	−	0.859597i	0.990491	+	0.137578i	$0.0439317\pi$
$564$	2.31941	+	12.1588i	0.0976648	+	0.511977i
$565$	−10.6927	−	3.83533i	−0.449845	−	0.161354i
$566$	−14.7453	−	8.10629i	−0.619790	−	0.340733i
$567$	0.785104	+	0.310845i	0.0329713	+	0.0130543i
$568$	−3.05844			−0.128329
$569$	−14.9220	−	5.90804i	−0.625563	−	0.247678i	0.0338878	−	0.999426i	$-0.489211\pi$
$569$	−14.9220	−	5.90804i	−0.625563	−	0.247678i	−0.659451	+	0.751748i	$0.729211\pi$
$570$	−13.7800	−	9.34108i	−0.577181	−	0.391255i
$571$	14.4962	+	17.5228i	0.606645	+	0.733308i	0.981007	−	0.193975i	$-0.0621380\pi$
$571$	14.4962	+	17.5228i	0.606645	+	0.733308i	−0.374361	+	0.927283i	$0.622138\pi$
$572$	−11.6380	−	2.98814i	−0.486611	−	0.124941i
$573$	5.69192	−	3.12916i	0.237783	−	0.130723i
$574$	2.37182	+	1.72323i	0.0989978	+	0.0719261i
$575$	11.9885	+	21.6854i	0.499956	+	0.904345i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−12.2498	+	26.0321i	−0.509966	+	1.08373i	0.469650	+	0.882853i	$0.344380\pi$
$577$	−12.2498	+	26.0321i	−0.509966	+	1.08373i	−0.979616	+	0.200880i	$0.935620\pi$
$578$	23.8570	+	28.8382i	0.992320	+	1.19951i
$579$	−6.57474	+	10.3601i	−0.273237	+	0.430553i
$580$	−11.1533	−	16.3699i	−0.463114	−	0.679721i
$581$	1.47577	−	1.78390i	0.0612254	−	0.0740087i
$582$	13.9664	−	10.1472i	0.578925	−	0.420614i
$583$	−2.84463	−	4.48242i	−0.117813	−	0.185643i
$584$	0.317660	−	1.66523i	0.0131449	−	0.0689078i
$585$	−2.63822	+	4.47305i	−0.109077	+	0.184938i
$586$	−13.1352	−	1.65936i	−0.542610	−	0.0685476i
$587$	0.173695	−	0.910541i	0.00716916	−	0.0375821i	−0.978523	−	0.206138i	$-0.933910\pi$
$587$	0.173695	−	0.910541i	0.00716916	−	0.0375821i	0.985692	+	0.168556i	$0.0539104\pi$
$588$	6.23741	−	0.787968i	0.257227	−	0.0324953i
$589$	−0.140895	+	0.0774576i	−0.00580547	+	0.00319158i
$590$	−5.84505	−	11.4381i	−0.240637	−	0.470900i
$591$	−15.2473	+	14.3182i	−0.627191	+	0.588971i
$592$	−5.95168	+	1.52813i	−0.244613	+	0.0628059i
$593$	1.02196	+	0.742495i	0.0419667	+	0.0304906i	0.608571	−	0.793500i	$-0.291743\pi$
$593$	1.02196	+	0.742495i	0.0419667	+	0.0304906i	−0.566604	+	0.823990i	$0.691743\pi$
$594$	−0.324859	+	5.16348i	−0.0133291	+	0.211860i
$595$	−12.7775	+	5.54726i	−0.523826	+	0.227416i
$596$	−12.2974	+	4.86889i	−0.503721	+	0.199437i
$597$	−10.4966	+	4.15588i	−0.429595	+	0.170089i
$598$	11.4186	+	1.44250i	0.466941	+	0.0589884i
$599$	−0.468336	+	1.44139i	−0.0191357	+	0.0588936i	−0.960168	−	0.279422i	$-0.909857\pi$
$599$	−0.468336	+	1.44139i	−0.0191357	+	0.0588936i	0.941033	+	0.338316i	$0.109857\pi$
$600$	−2.94848	−	4.03812i	−0.120371	−	0.164856i
$601$	−10.4884	−	32.2800i	−0.427830	−	1.31673i	−0.900258	−	0.435357i	$-0.856622\pi$
$601$	−10.4884	−	32.2800i	−0.427830	−	1.31673i	0.472427	−	0.881370i	$-0.343378\pi$
$602$	−0.377052	−	1.97657i	−0.0153675	−	0.0805591i
$603$	−0.696739	−	11.0743i	−0.0283734	−	0.450982i
$604$	16.2265	+	4.16626i	0.660247	+	0.169523i
$605$	−7.73159	−	34.3980i	−0.314334	−	1.39848i
$606$	−4.29661	−	6.77038i	−0.174538	−	0.275028i
$607$	−7.30356	+	22.4780i	−0.296442	+	0.912356i	0.686291	+	0.727327i	$0.259238\pi$
$607$	−7.30356	+	22.4780i	−0.296442	+	0.912356i	−0.982733	+	0.185029i	$0.940762\pi$
$608$	0.467479	−	7.43036i	0.0189588	−	0.301341i
$609$	−7.42117	+	0.937512i	−0.300721	+	0.0379899i
$610$	−11.1000	+	25.7340i	−0.449425	+	1.04194i
$611$	−12.2399	+	26.0112i	−0.495174	+	1.05230i
$612$	3.14118	+	6.67534i	0.126975	+	0.269835i
$613$	4.04677	+	2.22473i	0.163447	+	0.0898560i	0.561378	−	0.827560i	$-0.310271\pi$
$613$	4.04677	+	2.22473i	0.163447	+	0.0898560i	−0.397930	+	0.917416i	$0.630271\pi$
$614$	−3.84790	−	3.61342i	−0.155289	−	0.145826i
$615$	6.42623	+	4.35616i	0.259131	+	0.175658i
$616$	−1.86009	−	3.95289i	−0.0749451	−	0.159267i
$617$	−3.16407	+	3.82470i	−0.127381	+	0.153977i	−0.830348	−	0.557246i	$-0.811858\pi$
$617$	−3.16407	+	3.82470i	−0.127381	+	0.153977i	0.702967	+	0.711222i	$0.251858\pi$
$618$	−2.33052	−	7.17260i	−0.0937473	−	0.288524i
$619$	28.2128	−	7.24381i	1.13397	−	0.291153i	0.365355	−	0.930868i	$-0.380948\pi$
$619$	28.2128	−	7.24381i	1.13397	−	0.291153i	0.768612	+	0.639715i	$0.220948\pi$
$620$	−0.0476864	+	0.00761059i	−0.00191513	+	0.000305648i
$621$	−0.311173	−	4.94596i	−0.0124870	−	0.198474i
$622$	−4.55910	+	7.18399i	−0.182803	+	0.288052i
$623$	1.70699	+	1.60297i	0.0683890	+	0.0642215i
$624$	−2.32243			−0.0929716
$625$	20.1557	−	14.7901i	0.806228	−	0.591605i
$626$	9.25316			0.369831
$627$	−28.0787	−	26.3677i	−1.12136	−	1.05302i
$628$	−10.0390	+	15.8190i	−0.400601	+	0.631246i
$629$	2.84646	+	45.2432i	0.113496	+	1.80396i
$630$	−1.86454	+	0.297575i	−0.0742851	+	0.0118557i
$631$	−9.85868	+	2.53128i	−0.392468	+	0.100769i	−0.439766	−	0.898112i	$-0.644939\pi$
$631$	−9.85868	+	2.53128i	−0.392468	+	0.100769i	0.0472986	+	0.998881i	$0.484939\pi$
$632$	−0.177013	−	0.544789i	−0.00704118	−	0.0216705i
$633$	11.9685	−	14.4675i	0.475706	−	0.575030i
$634$	−10.3503	−	21.9955i	−0.411062	−	0.873552i
$635$	27.1327	+	18.3925i	1.07673	+	0.729886i
$636$	−0.748014	−	0.702432i	−0.0296607	−	0.0278532i
$637$	12.7950	+	7.03413i	0.506958	+	0.278702i
$638$	−19.5140	−	41.4694i	−0.772567	−	1.64179i
$639$	−1.30222	+	2.76736i	−0.0515150	+	0.109475i
$640$	0.885623	−	2.05321i	0.0350073	−	0.0811603i
$641$	−41.7765	+	5.27760i	−1.65007	+	0.208453i	−0.894644	−	0.446779i	$-0.852571\pi$
$641$	−41.7765	+	5.27760i	−1.65007	+	0.208453i	−0.755428	+	0.655232i	$0.772571\pi$
$642$	−0.659066	+	10.4756i	−0.0260113	+	0.413437i
$643$	3.75075	−	11.5436i	0.147915	−	0.455236i	−0.849459	−	0.527654i	$-0.823072\pi$
$643$	3.75075	−	11.5436i	0.147915	−	0.455236i	0.997374	+	0.0724185i	$0.0230717\pi$
$644$	2.24224	+	3.53320i	0.0883565	+	0.139228i
$645$	−1.16854	−	5.19886i	−0.0460112	−	0.204705i
$646$	−53.2001	−	13.6595i	−2.09313	−	0.537425i
$647$	0.0687613	+	1.09293i	0.00270328	+	0.0429675i	0.999147	−	0.0412922i	$-0.0131475\pi$
$647$	0.0687613	+	1.09293i	0.00270328	+	0.0429675i	−0.996444	+	0.0842597i	$0.973147\pi$
$648$	0.187381	+	0.982287i	0.00736103	+	0.0385879i
$649$	−9.18403	−	28.2655i	−0.360505	−	1.10952i
$650$	−0.0274587	−	11.6121i	−0.00107702	−	0.455465i
$651$	−0.00563511	+	0.0173431i	−0.000220857	+	0.000679729i
$652$	1.38573	+	0.175059i	0.0542695	+	0.00685583i
$653$	−8.07569	+	3.19739i	−0.316026	+	0.125124i	−0.520783	−	0.853689i	$-0.674360\pi$
$653$	−8.07569	+	3.19739i	−0.316026	+	0.125124i	0.204756	+	0.978813i	$0.434360\pi$
$654$	1.04522	−	0.413830i	0.0408712	−	0.0161821i
$655$	40.0501	−	17.3875i	1.56489	−	0.679385i
$656$	−0.218006	+	3.46511i	−0.00851172	+	0.135290i
$657$	−1.37149	−	0.996449i	−0.0535071	−	0.0388752i
$658$	−10.1237	+	2.59931i	−0.394661	+	0.101332i
$659$	−7.56946	+	7.10819i	−0.294864	+	0.276896i	−0.817833	−	0.575456i	$-0.804825\pi$
$659$	−7.56946	+	7.10819i	−0.294864	+	0.276896i	0.522968	+	0.852352i	$0.324825\pi$
$660$	−5.26427	−	10.3016i	−0.204912	−	0.400989i
$661$	13.5144	−	7.42962i	0.525650	−	0.288979i	−0.196750	−	0.980454i	$-0.563039\pi$
$661$	13.5144	−	7.42962i	0.525650	−	0.288979i	0.722400	+	0.691475i	$0.243039\pi$
$662$	−20.6331	+	2.60656i	−0.801926	+	0.101307i
$663$	−3.21053	+	16.8302i	−0.124687	+	0.653631i
$664$	2.72022	+	0.343644i	0.105565	+	0.0133360i
$665$	7.14143	−	12.1082i	0.276933	−	0.469534i
$666$	−1.15141	+	6.03589i	−0.0446161	+	0.233886i
$667$	23.5231	+	37.0664i	0.910817	+	1.43522i
$668$	5.08679	−	3.69577i	0.196814	−	0.142994i
$669$	9.06323	−	10.9556i	0.350405	−	0.423566i
$670$	13.9706	+	20.5050i	0.539733	+	0.792176i
$671$	−34.7455	+	54.7501i	−1.34133	+	2.11361i
$672$	−0.538242	−	0.650622i	−0.0207631	−	0.0250983i
$673$	−5.50206	+	11.6925i	−0.212089	+	0.450711i	−0.982359	−	0.187006i	$-0.940121\pi$
$673$	−5.50206	+	11.6925i	−0.212089	+	0.450711i	0.770270	+	0.637718i	$0.220121\pi$
$674$	−11.1412	+	8.09455i	−0.429143	+	0.311791i
$675$	−4.90921	+	0.948518i	−0.188955	+	0.0365085i
$676$	6.15364	+	4.47088i	0.236678	+	0.171957i
$677$	−37.4692	+	20.5989i	−1.44006	+	0.791680i	−0.994616	−	0.103630i	$-0.966954\pi$
$677$	−37.4692	+	20.5989i	−1.44006	+	0.791680i	−0.445444	+	0.895310i	$0.646954\pi$
$678$	−4.92063	−	1.26340i	−0.188975	−	0.0485207i
$679$	9.29187	+	11.2319i	0.356589	+	0.431043i
$680$	−13.6549	−	9.25630i	−0.523643	−	0.354963i
$681$	1.38314	+	0.547625i	0.0530021	+	0.0209850i
$682$	−0.111730			−0.00427838
$683$	20.6021	+	8.15697i	0.788319	+	0.312118i	0.727568	−	0.686035i	$-0.240650\pi$
$683$	20.6021	+	8.15697i	0.788319	+	0.312118i	0.0607510	+	0.998153i	$0.480650\pi$
$684$	−6.52415	−	3.58668i	−0.249457	−	0.137140i
$685$	31.1023	+	11.1560i	1.18836	+	0.426249i
$686$	2.10233	+	11.0208i	0.0802675	+	0.420777i
$687$	−16.2920	+	15.2992i	−0.621579	+	0.583702i
$688$	1.73714	−	1.63128i	0.0662278	−	0.0621920i
$689$	−0.446550	−	2.34090i	−0.0170122	−	0.0891810i
$690$	6.23948	+	9.15781i	0.237533	+	0.348632i
$691$	15.5740	+	8.56190i	0.592464	+	0.325710i	0.749625	−	0.661863i	$-0.230234\pi$
$691$	15.5740	+	8.56190i	0.592464	+	0.325710i	−0.157160	+	0.987573i	$0.550234\pi$
$692$	−10.8359	−	4.29025i	−0.411920	−	0.163091i
$693$	−4.36867			−0.165952
$694$	−19.5622	−	7.74524i	−0.742573	−	0.294005i
$695$	−3.02854	+	10.4705i	−0.114879	+	0.397169i
$696$	−5.64664	−	6.82561i	−0.214035	−	0.258724i
$697$	24.8096	+	6.37003i	0.939731	+	0.241282i
$698$	−26.4523	+	14.5423i	−1.00123	+	0.550433i
$699$	14.6528	+	10.6458i	0.554218	+	0.402663i
$700$	3.24674	−	2.69889i	0.122715	−	0.102009i
$701$	13.7385	−	9.98160i	0.518896	−	0.377000i	−0.297292	−	0.954787i	$-0.596083\pi$
$701$	13.7385	−	9.98160i	0.518896	−	0.377000i	0.816188	+	0.577787i	$0.196083\pi$
$702$	−0.988843	+	2.10140i	−0.0373215	+	0.0793121i
$703$	−29.1608	−	35.2493i	−1.09982	−	1.32945i
$704$	2.77220	−	4.36829i	0.104481	−	0.164636i
$705$	−26.5700	+	7.75337i	−1.00068	+	0.292009i
$706$	−17.5013	+	21.1554i	−0.658669	+	0.796194i
$707$	5.47783	−	3.97987i	0.206015	−	0.149679i
$708$	−3.07804	−	4.85022i	−0.115680	−	0.182283i
$709$	0.728211	−	3.81742i	0.0273486	−	0.143366i	−0.965994	−	0.258565i	$-0.916750\pi$
$709$	0.728211	−	3.81742i	0.0273486	−	0.143366i	0.993342	+	0.115199i	$0.0367505\pi$
$710$	−0.651644	−	6.80776i	−0.0244558	−	0.255491i
$711$	−0.568308	−	0.0717940i	−0.0213132	−	0.00269248i
$712$	−0.519636	+	2.72402i	−0.0194742	+	0.102087i
$713$	0.106180	−	0.0134136i	0.00397646	−	0.000502343i
$714$	−5.45900	+	3.00111i	−0.204298	+	0.112314i
$715$	4.17163	−	26.5417i	0.156010	−	0.992604i
$716$	13.7918	−	12.9514i	0.515424	−	0.484015i
$717$	20.8950	−	5.36491i	0.780337	−	0.200356i
$718$	−16.4601	−	11.9590i	−0.614287	−	0.446305i
$719$	−2.38142	+	37.8517i	−0.0888121	+	1.41163i	0.661203	+	0.750207i	$0.270046\pi$
$719$	−2.38142	+	37.8517i	−0.0888121	+	1.41163i	−0.750015	+	0.661421i	$0.769954\pi$
$720$	−1.48072	−	1.67555i	−0.0551832	−	0.0624441i
$721$	5.92104	−	2.34431i	0.220511	−	0.0873065i
$722$	33.8707	−	13.4103i	1.26054	−	0.499081i
$723$	7.11074	+	0.898296i	0.264451	+	0.0334080i
$724$	−5.07026	+	15.6047i	−0.188435	+	0.579943i
$725$	34.0612	−	28.3138i	1.26500	−	1.05155i
$726$	−4.87229	−	14.9954i	−0.180828	−	0.556531i
$727$	1.07777	+	5.64985i	0.0399722	+	0.209541i	0.996670	−	0.0815417i	$-0.0259844\pi$
$727$	1.07777	+	5.64985i	0.0399722	+	0.209541i	−0.956698	+	0.291083i	$0.905984\pi$
$728$	−0.123136	−	1.95719i	−0.00456373	−	0.0725384i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	3.77431	+	0.352276i	0.139694	+	0.0130383i
$731$	−9.42016	−	14.8438i	−0.348417	−	0.549018i
$732$	−3.87308	+	11.9201i	−0.143153	+	0.440580i
$733$	−0.968621	+	15.3958i	−0.0357768	+	0.568656i	0.938780	+	0.344517i	$0.111957\pi$
$733$	−0.968621	+	15.3958i	−0.0357768	+	0.568656i	−0.974557	+	0.224140i	$0.928043\pi$
$734$	20.8551	−	2.63461i	0.769775	−	0.0972452i
$735$	3.08290	+	13.7159i	0.113715	+	0.505920i
$736$	−2.11005	+	4.48409i	−0.0777775	+	0.165286i
$737$	24.4434	+	51.9448i	0.900383	+	1.91341i
$738$	3.04250	+	1.67263i	0.111996	+	0.0615704i
$739$	−9.78549	−	9.18919i	−0.359965	−	0.338030i	0.483372	−	0.875415i	$-0.339412\pi$
$739$	−9.78549	−	9.18919i	−0.359965	−	0.338030i	−0.843337	+	0.537386i	$0.819412\pi$
$740$	−4.66955	−	12.9222i	−0.171656	−	0.475030i
$741$	−7.36199	−	15.6450i	−0.270449	−	0.574734i
$742$	0.552304	−	0.667621i	0.0202757	−	0.0245091i
$743$	−2.09606	−	6.45102i	−0.0768971	−	0.236665i	0.905218	−	0.424948i	$-0.139708\pi$
$743$	−2.09606	−	6.45102i	−0.0768971	−	0.236665i	−0.982115	+	0.188283i	$0.939708\pi$
$744$	−0.0209174	+	0.00537068i	−0.000766869	+	0.000196899i
$745$	−13.4578	−	26.3353i	−0.493054	−	0.964852i
$746$	1.05689	+	16.7987i	0.0386954	+	0.615046i
$747$	1.46915	−	2.31501i	0.0537534	−	0.0847019i
$748$	−27.8239	−	26.1283i	−1.01734	−	0.955347i
$749$	−8.86306			−0.323849
$750$	8.36022	−	7.42339i	0.305272	−	0.271064i
$751$	7.60338			0.277451			0.138726	−	0.990331i	$-0.455699\pi$
$751$	7.60338			0.277451			0.138726	+	0.990331i	$0.455699\pi$
$752$	−9.02319	−	8.47334i	−0.329042	−	0.308991i
$753$	−4.99863	+	7.87658i	−0.182160	+	0.287038i
$754$	−1.29181	−	20.5327i	−0.0470449	−	0.747757i
$755$	−5.81636	+	37.0062i	−0.211679	+	1.34679i
$756$	−0.817873	+	0.209994i	−0.0297457	+	0.00763741i
$757$	−2.94247	−	9.05598i	−0.106946	−	0.329145i	0.883236	−	0.468928i	$-0.155360\pi$
$757$	−2.94247	−	9.05598i	−0.106946	−	0.329145i	−0.990182	+	0.139783i	$0.955360\pi$
$758$	8.97582	−	10.8499i	0.326016	−	0.394086i
$759$	10.9167	+	23.1993i	0.396253	+	0.842080i
$760$	16.6388	−	0.542588i	0.603553	−	0.0196817i
$761$	−13.5994	−	12.7707i	−0.492977	−	0.462936i	0.397738	−	0.917499i	$-0.369795\pi$
$761$	−13.5994	−	12.7707i	−0.492977	−	0.462936i	−0.890715	+	0.454563i	$0.849795\pi$
$762$	12.8460	+	7.06216i	0.465362	+	0.255835i
$763$	0.404167	+	0.858899i	0.0146318	+	0.0310942i
$764$	−2.76559	+	5.87717i	−0.100055	+	0.212629i
$765$	−14.1893	+	8.41421i	−0.513016	+	0.304216i
$766$	−28.5129	+	3.60202i	−1.03021	+	0.130146i
$767$	0.837698	−	13.3148i	0.0302475	−	0.480770i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	−16.0532	−	25.2957i	−0.578892	−	0.912188i	−0.999987	−	0.00517097i	$-0.998354\pi$
$769$	−16.0532	−	25.2957i	−0.578892	−	0.912188i	0.421095	−	0.907017i	$-0.361646\pi$
$770$	8.40240	−	4.98258i	0.302801	−	0.179560i
$771$	−17.9272	−	4.60292i	−0.645633	−	0.165770i
$772$	−0.770457	−	12.2461i	−0.0277294	−	0.440745i
$773$	−8.40835	−	44.0781i	−0.302427	−	1.58538i	−0.731326	−	0.682028i	$-0.761098\pi$
$773$	−8.40835	−	44.0781i	−0.302427	−	1.58538i	0.428899	−	0.903353i	$-0.358902\pi$
$774$	−0.736390	−	2.26638i	−0.0264690	−	0.0814632i
$775$	−0.0271006	−	0.104523i	−0.000973483	−	0.00375459i
$776$	−5.33468	+	16.4185i	−0.191504	+	0.589388i
$777$	−5.14771	−	0.650306i	−0.184673	−	0.0233296i
$778$	23.0953	−	9.14409i	0.828008	−	0.327831i
$779$	−24.0337	+	9.51563i	−0.861098	+	0.340933i
$780$	−0.494827	−	5.16948i	−0.0177177	−	0.185097i
$781$	0.993560	−	15.7922i	0.0355524	−	0.565089i
$782$	29.5783	+	21.4899i	1.05772	+	0.768478i
$783$	−8.58022	+	2.20303i	−0.306632	+	0.0787297i
$784$	−4.58302	+	4.30374i	−0.163679	+	0.153705i
$785$	−37.3503	−	18.9754i	−1.33309	−	0.677259i
$786$	17.1108	−	9.40675i	0.610322	−	0.335528i
$787$	30.5134	−	3.85474i	1.08768	−	0.137406i	0.439017	−	0.898479i	$-0.355327\pi$
$787$	30.5134	−	3.85474i	1.08768	−	0.137406i	0.648667	+	0.761072i	$0.275327\pi$
$788$	3.91932	−	20.5458i	0.139620	−	0.731914i
$789$	−15.1167	−	1.90969i	−0.538169	−	0.0679866i
$790$	1.17493	−	0.510086i	0.0418020	−	0.0181481i
$791$	0.803820	−	4.21377i	0.0285805	−	0.149824i
$792$	−2.77220	−	4.36829i	−0.0985059	−	0.155220i
$793$	−23.5491	+	17.1094i	−0.836252	+	0.607573i
$794$	6.33571	−	7.65856i	0.224846	−	0.271792i
$795$	1.40416	−	1.81466i	0.0498005	−	0.0643595i
$796$	6.04913	−	9.53190i	0.214406	−	0.337849i
$797$	32.4426	+	39.2164i	1.14918	+	1.38911i	0.908175	+	0.418590i	$0.137475\pi$
$797$	32.4426	+	39.2164i	1.14918	+	1.38911i	0.241000	+	0.970525i	$0.422525\pi$
$798$	2.67671	−	5.68830i	0.0947545	−	0.201364i
$799$	−73.8783	+	53.6758i	−2.61363	+	1.89891i
$800$	4.75892	+	1.53384i	0.168253	+	0.0542293i
$801$	2.24352	+	1.63001i	0.0792709	+	0.0575937i
$802$	−34.1011	+	18.7472i	−1.20415	+	0.661988i
$803$	8.49520	+	2.18120i	0.299789	+	0.0769728i
$804$	7.07301	+	8.54980i	0.249446	+	0.301528i
$805$	−7.38679	+	5.74378i	−0.260350	+	0.202442i
$806$	−0.0466329	−	0.0184633i	−0.00164257	−	0.000650341i
$807$	25.6679			0.903554
$808$	7.45556	+	2.95186i	0.262286	+	0.103846i
$809$	−0.186760	−	0.102672i	−0.00656613	−	0.00360976i	0.478467	−	0.878105i	$-0.341193\pi$
$809$	−0.186760	−	0.102672i	−0.00656613	−	0.00360976i	−0.485033	+	0.874496i	$0.661193\pi$
$810$	−2.14654	+	0.626381i	−0.0754218	+	0.0220088i
$811$	−4.48834	−	23.5287i	−0.157607	−	0.826205i	−0.970002	−	0.243097i	$-0.921837\pi$
$811$	−4.48834	−	23.5287i	−0.157607	−	0.826205i	0.812395	−	0.583108i	$-0.198163\pi$
$812$	5.45280	−	5.12052i	0.191356	−	0.179695i
$813$	−0.777086	+	0.729732i	−0.0272536	+	0.0255928i
$814$	−5.95703	−	31.2278i	−0.208794	−	1.09453i
$815$	−0.0944118	+	3.12179i	−0.00330710	+	0.109352i
$816$	−6.46493	−	3.55413i	−0.226318	−	0.124419i
$817$	16.4958	+	6.53113i	0.577113	+	0.228495i
$818$	7.42149			0.259486
$819$	−1.82335	−	0.721916i	−0.0637130	−	0.0252258i
$820$	−7.75942	+	0.253033i	−0.270971	+	0.00883630i
$821$	2.96813	+	3.58785i	0.103588	+	0.125217i	0.819760	−	0.572708i	$-0.194107\pi$
$821$	2.96813	+	3.58785i	0.103588	+	0.125217i	−0.716171	+	0.697925i	$0.754107\pi$
$822$	14.3128	+	3.67491i	0.499217	+	0.128177i
$823$	2.49947	−	1.37410i	0.0871262	−	0.0478980i	−0.437595	−	0.899172i	$-0.644170\pi$
$823$	2.49947	−	1.37410i	0.0871262	−	0.0478980i	0.524721	+	0.851274i	$0.324170\pi$
$824$	6.10138	+	4.43291i	0.212552	+	0.154428i
$825$	21.8086	−	13.9126i	0.759279	−	0.484375i
$826$	3.92425	−	2.85114i	0.136542	−	0.0992037i
$827$	1.76905	−	3.75943i	0.0615161	−	0.130728i	−0.871705	−	0.490031i	$-0.836985\pi$
$827$	1.76905	−	3.75943i	0.0615161	−	0.130728i	0.933221	+	0.359303i	$0.116985\pi$
$828$	3.15891	+	3.81846i	0.109780	+	0.132701i
$829$	−1.28974	+	2.03230i	−0.0447945	+	0.0705848i	−0.865987	−	0.500066i	$-0.833309\pi$
$829$	−1.28974	+	2.03230i	−0.0447945	+	0.0705848i	0.821193	+	0.570651i	$0.193309\pi$
$830$	−0.185332	+	6.12814i	−0.00643297	+	0.212711i
$831$	−0.802547	+	0.970113i	−0.0278400	+	0.0336528i
$832$	1.87889	−	1.36509i	0.0651386	−	0.0473260i
$833$	24.8528	+	39.1617i	0.861098	+	1.35687i
$834$	−0.913389	+	4.78815i	−0.0316281	+	0.165800i
$835$	9.31021	+	10.5352i	0.322193	+	0.364586i
$836$	38.2147	+	4.82764i	1.32168	+	0.166967i
$837$	−0.00404667	+	0.0212134i	−0.000139873	+	0.000733241i
$838$	−29.8109	+	3.76599i	−1.02980	+	0.130094i
$839$	11.0476	−	6.07347i	0.381406	−	0.209680i	−0.279505	−	0.960144i	$-0.590170\pi$
$839$	11.0476	−	6.07347i	0.381406	−	0.209680i	0.660911	+	0.750465i	$0.270170\pi$
$840$	1.33354	−	1.33669i	0.0460114	−	0.0461203i
$841$	36.0646	−	33.8669i	1.24361	−	1.16783i
$842$	−20.3403	+	5.22250i	−0.700973	+	0.179979i
$843$	13.5767	+	9.86408i	0.467608	+	0.339737i
$844$	−1.17898	+	18.7394i	−0.0405822	+	0.645035i
$845$	−8.64058	+	14.6499i	−0.297245	+	0.503973i
$846$	−11.5088	+	4.55666i	−0.395681	+	0.156661i
$847$	12.3788	−	4.90111i	0.425341	−	0.168404i
$848$	1.01803	+	0.128608i	0.0349595	+	0.00441641i
$849$	5.19971	−	16.0031i	0.178454	−	0.549224i
$850$	17.6942	−	32.3666i	0.606904	−	1.11017i
$851$	9.41008	+	28.9613i	0.322574	+	0.992779i
$852$	−0.573094	−	3.00426i	−0.0196339	−	0.102924i
$853$	−0.644649	−	10.2464i	−0.0220724	−	0.350830i	−0.993526	−	0.113602i	$-0.963761\pi$
$853$	−0.644649	−	10.2464i	−0.0220724	−	0.350830i	0.971454	−	0.237228i	$-0.0762389\pi$
$854$	−10.2508	−	2.63197i	−0.350776	−	0.0900641i
$855$	6.59351	−	15.2863i	0.225493	−	0.522779i
$856$	−5.62418	−	8.86229i	−0.192231	−	0.302907i
$857$	−3.82243	+	11.7642i	−0.130572	+	0.401858i	−0.994875	−	0.101113i	$-0.967760\pi$
$857$	−3.82243	+	11.7642i	−0.130572	+	0.401858i	0.864303	+	0.502971i	$0.167760\pi$
$858$	0.754462	−	11.9918i	0.0257569	−	0.409394i
$859$	−30.5360	+	3.85760i	−1.04188	+	0.131620i	−0.627603	−	0.778533i	$-0.715964\pi$
$859$	−30.5360	+	3.85760i	−1.04188	+	0.131620i	−0.414273	+	0.910153i	$0.635964\pi$
$860$	4.00118	+	3.51912i	0.136439	+	0.120001i
$861$	−1.24827	+	2.65271i	−0.0425409	+	0.0904041i
$862$	12.6653	+	26.9151i	0.431381	+	0.916732i
$863$	−30.1147	−	16.5557i	−1.02512	−	0.563563i	−0.121808	−	0.992554i	$-0.538869\pi$
$863$	−30.1147	−	16.5557i	−1.02512	−	0.563563i	−0.903309	+	0.428991i	$0.858869\pi$
$864$	−0.728969	−	0.684547i	−0.0248000	−	0.0232888i
$865$	7.24088	−	25.0337i	0.246197	−	0.851172i
$866$	−4.63089	−	9.84114i	−0.157364	−	0.334415i
$867$	−23.8570	+	28.8382i	−0.810226	+	0.979395i
$868$	−0.00563511	−	0.0173431i	−0.000191268	−	0.000588662i
$869$	2.87051	−	0.737022i	0.0973754	−	0.0250018i
$870$	13.9900	−	14.0231i	0.474305	−	0.475428i
$871$	1.61813	+	25.7194i	0.0548282	+	0.871469i
$872$	−0.602354	+	0.949159i	−0.0203983	+	0.0321426i
$873$	12.5845	+	11.8176i	0.425920	+	0.399965i
$874$	−36.8957			−1.24802
$875$	6.69921	+	6.65186i	0.226475	+	0.224874i
$876$	1.69526			0.0572775
$877$	−9.34126	−	8.77203i	−0.315432	−	0.296210i	0.510617	−	0.859808i	$-0.329417\pi$
$877$	−9.34126	−	8.77203i	−0.315432	−	0.296210i	−0.826049	+	0.563598i	$0.809417\pi$
$878$	−9.25093	+	14.5771i	−0.312204	+	0.491954i
$879$	−0.831321	−	13.2135i	−0.0280398	−	0.445679i
$880$	10.3140	+	5.23990i	0.347685	+	0.176637i
$881$	−19.7426	+	5.06903i	−0.665144	+	0.170780i	−0.566143	−	0.824307i	$-0.691565\pi$
$881$	−19.7426	+	5.06903i	−0.665144	+	0.170780i	−0.0990017	+	0.995087i	$0.531565\pi$
$882$	1.94279	+	5.97928i	0.0654170	+	0.201333i
$883$	−16.3947	+	19.8177i	−0.551724	+	0.666920i	−0.970481	−	0.241178i	$-0.922466\pi$
$883$	−16.3947	+	19.8177i	−0.551724	+	0.666920i	0.418756	+	0.908099i	$0.362466\pi$
$884$	−7.29517	−	15.5030i	−0.245363	−	0.521423i
$885$	10.1403	−	7.88481i	0.340861	−	0.265045i
$886$	18.8615	+	17.7122i	0.633665	+	0.595051i
$887$	−39.1613	−	21.5291i	−1.31491	−	0.722877i	−0.338944	−	0.940807i	$-0.610070\pi$
$887$	−39.1613	−	21.5291i	−1.31491	−	0.722877i	−0.975965	+	0.217929i	$0.930070\pi$
$888$	−2.61630	−	5.55992i	−0.0877973	−	0.186579i
$889$	−5.27043	+	11.2002i	−0.176764	+	0.375644i
$890$	−6.17411	−	0.576261i	−0.206957	−	0.0193163i
$891$	−5.13289	+	0.648435i	−0.171958	+	0.0217234i
$892$	−0.892789	+	14.1905i	−0.0298928	+	0.475132i
$893$	28.4775	−	87.6447i	0.952963	−	2.93292i
$894$	−7.08695	−	11.1672i	−0.237023	−	0.373488i
$895$	31.7669	+	27.9396i	1.06185	+	0.933918i
$896$	0.817873	+	0.209994i	0.0273232	+	0.00701541i
$897$	0.722678	+	11.4866i	0.0241295	+	0.383528i
$898$	5.38145	+	28.2105i	0.179581	+	0.941398i
$899$	−0.0591173	−	0.181944i	−0.00197167	−	0.00606819i
$900$	3.41411	−	3.65293i	0.113804	−	0.121764i
$901$	2.33933	−	7.19971i	0.0779343	−	0.239857i
$902$	−17.8212	−	2.25134i	−0.593382	−	0.0749615i
$903$	1.87091	−	0.740746i	0.0622600	−	0.0246505i
$904$	4.72348	−	1.87016i	0.157101	−	0.0622005i
$905$	−35.8146	−	7.96107i	−1.19052	−	0.264635i
$906$	−1.05192	+	16.7198i	−0.0349476	+	0.555477i
$907$	19.1618	+	13.9219i	0.636257	+	0.462268i	0.858562	−	0.512709i	$-0.171358\pi$
$907$	19.1618	+	13.9219i	0.636257	+	0.462268i	−0.222305	+	0.974977i	$0.571358\pi$
$908$	−1.44087	+	0.369953i	−0.0478170	+	0.0122773i
$909$	5.84535	−	5.48915i	0.193878	−	0.182064i
$910$	4.33027	−	0.691096i	0.143547	−	0.0229096i
$911$	19.1617	−	10.5342i	0.634856	−	0.349015i	−0.131608	−	0.991302i	$-0.542014\pi$
$911$	19.1617	−	10.5342i	0.634856	−	0.349015i	0.766464	+	0.642287i	$0.222014\pi$
$912$	7.38635	−	0.933113i	0.244586	−	0.0308985i
$913$	−2.65808	+	13.9342i	−0.0879698	+	0.461154i
$914$	−7.20329	−	0.909987i	−0.238264	−	0.0300997i
$915$	−27.3581	−	6.08130i	−0.904431	−	0.201042i
$916$	4.18786	−	21.9535i	0.138371	−	0.725366i
$917$	8.83462	+	13.9211i	0.291745	+	0.459716i
$918$	−5.96851	+	4.33637i	−0.196990	+	0.143122i
$919$	3.93583	−	4.75760i	0.129831	−	0.156939i	−0.701592	−	0.712579i	$-0.747527\pi$
$919$	3.93583	−	4.75760i	0.129831	−	0.156939i	0.831423	+	0.555640i	$0.187527\pi$
$920$	−10.4307	−	3.74135i	−0.343889	−	0.123349i
$921$	2.82839	−	4.45683i	0.0931986	−	0.146857i
$922$	−4.75619	−	5.74924i	−0.156637	−	0.189341i
$923$	3.02431	−	6.42699i	0.0995465	−	0.211547i
$924$	3.53433	−	2.56784i	0.116271	−	0.0844757i
$925$	27.7686	−	13.1472i	0.913025	−	0.432277i
$926$	3.71922	+	2.70217i	0.122221	+	0.0887988i
$927$	6.60886	−	3.63325i	0.217063	−	0.119332i
$928$	8.58022	+	2.20303i	0.281660	+	0.0723179i
$929$	13.3466	+	16.1333i	0.437888	+	0.529316i	0.942579	−	0.333984i	$-0.108393\pi$
$929$	13.3466	+	16.1333i	0.437888	+	0.529316i	−0.504690	+	0.863301i	$0.668393\pi$
$930$	−0.0164113	−	0.0454156i	−0.000538148	−	0.00148924i
$931$	−43.5200	−	17.2308i	−1.42631	−	0.564716i
$932$	−18.1118			−0.593272
$933$	−7.91103	−	3.13220i	−0.258995	−	0.102544i
$934$	−11.5514	−	6.35046i	−0.377975	−	0.207793i
$935$	52.2306	−	67.5000i	1.70812	−	2.20749i
$936$	−0.435180	−	2.28129i	−0.0142243	−	0.0745664i
$937$	14.9186	−	14.0095i	0.487368	−	0.457669i	−0.401482	−	0.915867i	$-0.631505\pi$
$937$	14.9186	−	14.0095i	0.487368	−	0.457669i	0.888850	+	0.458198i	$0.151505\pi$
$938$	−6.83020	+	6.41399i	−0.223014	+	0.209424i
$939$	1.73387	+	9.08926i	0.0565827	+	0.296617i
$940$	16.9382	−	21.8900i	0.552465	−	0.713974i
$941$	17.5514	+	9.64895i	0.572159	+	0.314547i	0.741438	−	0.671021i	$-0.234144\pi$
$941$	17.5514	+	9.64895i	0.572159	+	0.314547i	−0.169280	+	0.985568i	$0.554144\pi$
$942$	−17.4199	−	6.89703i	−0.567571	−	0.224717i
$943$	17.2061			0.560309
$944$	5.34108	+	2.11468i	0.173837	+	0.0688271i
$945$	−0.641684	−	1.77576i	−0.0208740	−	0.0577653i
$946$	7.85877	+	9.49962i	0.255511	+	0.308859i
$947$	19.2316	+	4.93783i	0.624943	+	0.160458i	0.547865	−	0.836567i	$-0.315441\pi$
$947$	19.2316	+	4.93783i	0.624943	+	0.160458i	0.0770781	+	0.997025i	$0.475441\pi$
$948$	0.501970	−	0.275960i	0.0163032	−	0.00896278i
$949$	3.18520	+	2.31418i	0.103396	+	0.0751216i
$950$	4.75288	+	36.9206i	0.154204	+	1.19786i
$951$	19.6664	−	14.2885i	0.637728	−	0.463336i
$952$	2.65241	−	5.63667i	0.0859653	−	0.182685i
$953$	−33.9909	−	41.0879i	−1.10107	−	1.33097i	−0.938894	−	0.344205i	$-0.888148\pi$
$953$	−33.9909	−	41.0879i	−1.10107	−	1.33097i	−0.162177	−	0.986762i	$-0.551852\pi$
$954$	0.549826	−	0.866387i	0.0178013	−	0.0280503i
$955$	−13.6712	−	4.90369i	−0.442390	−	0.158680i
$956$	−13.7510	+	16.6221i	−0.444738	+	0.537596i
$957$	37.0783	−	26.9390i	1.19857	−	0.870813i
$958$	9.51646	+	14.9955i	0.307463	+	0.484484i
$959$	−2.33810	+	12.2568i	−0.0755013	+	0.395792i
$960$	2.18279	+	0.485203i	0.0704493	+	0.0156598i
$961$	30.7551	+	3.88527i	0.992100	+	0.125331i
$962$	2.67406	−	14.0179i	0.0862153	−	0.451956i
$963$	−10.4135	+	1.31553i	−0.335571	+	0.0423924i
$964$	−6.28072	+	3.45285i	−0.202288	+	0.111209i
$965$	27.0943	−	4.32416i	0.872196	−	0.139200i
$966$	−3.05046	+	2.86458i	−0.0981471	+	0.0921663i
$967$	7.71466	−	1.98079i	0.248087	−	0.0636978i	−0.122599	−	0.992456i	$-0.539123\pi$
$967$	7.71466	−	1.98079i	0.248087	−	0.0636978i	0.370685	+	0.928758i	$0.379123\pi$
$968$	12.7558	+	9.26765i	0.409988	+	0.297874i
$969$	3.44882	−	54.8174i	0.110792	−	1.76099i
$970$	−37.6824	−	8.37624i	−1.20991	−	0.268945i
$971$	−14.4223	+	5.71020i	−0.462835	+	0.183249i	−0.587957	−	0.808892i	$-0.700068\pi$
$971$	−14.4223	+	5.71020i	−0.462835	+	0.183249i	0.125123	+	0.992141i	$0.460068\pi$
$972$	−0.929776	+	0.368125i	−0.0298226	+	0.0118076i
$973$	−4.08357	−	0.515875i	−0.130913	−	0.0165382i
$974$	−10.0915	+	31.0585i	−0.323353	+	0.995179i
$975$	11.4013	−	2.20287i	0.365134	−	0.0705482i
$976$	−3.87308	−	11.9201i	−0.123974	−	0.381553i
$977$	6.83741	+	35.8430i	0.218748	+	1.14672i	0.906963	+	0.421211i	$0.138395\pi$
$977$	6.83741	+	35.8430i	0.218748	+	1.14672i	−0.688215	+	0.725507i	$0.741605\pi$
$978$	0.0877024	+	1.39399i	0.00280441	+	0.0445749i
$979$	−13.8966	−	3.56805i	−0.444139	−	0.114035i
$980$	−10.5561	−	9.28433i	−0.337204	−	0.296577i
$981$	0.602354	+	0.949159i	0.0192317	+	0.0303043i
$982$	−4.59636	+	14.1461i	−0.146676	+	0.451422i
$983$	−0.657878	+	10.4567i	−0.0209830	+	0.333516i	0.973505	+	0.228666i	$0.0734363\pi$
$983$	−0.657878	+	10.4567i	−0.0209830	+	0.333516i	−0.994488	+	0.104850i	$0.966564\pi$
$984$	−3.44459	+	0.435152i	−0.109809	+	0.0138721i
$985$	46.5678	+	4.34641i	1.48377	+	0.138488i
$986$	27.8262	−	59.1337i	0.886167	−	1.88320i
$987$	−4.45025	−	9.45727i	−0.141653	−	0.301028i
$988$	15.1519	+	8.32982i	0.482046	+	0.265007i
$989$	−8.60880	−	8.08420i	−0.273744	−	0.257063i
$990$	9.13270	−	7.10136i	0.290256	−	0.225696i
$991$	−4.77229	−	10.1416i	−0.151597	−	0.322160i	0.814575	−	0.580058i	$-0.196970\pi$
$991$	−4.77229	−	10.1416i	−0.151597	−	0.322160i	−0.966172	+	0.257898i	$0.916970\pi$
$992$	0.0137657	−	0.0166399i	0.000437063	−	0.000528318i
$993$	−6.42664	−	19.7792i	−0.203943	−	0.627673i
$994$	2.50141	−	0.642254i	0.0793400	−	0.0203711i
$995$	22.5058	+	11.4338i	0.713483	+	0.362476i
$996$	0.172162	+	2.73643i	0.00545515	+	0.0867071i
$997$	−2.64205	+	4.16321i	−0.0836747	+	0.131850i	−0.883588	−	0.468266i	$-0.844879\pi$
$997$	−2.64205	+	4.16321i	−0.0836747	+	0.131850i	0.799913	+	0.600116i	$0.204879\pi$
$998$	6.97644	+	6.55131i	0.220835	+	0.207378i
$999$	−6.14473			−0.194411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.d.91.1	✓	140
125.11	even	25	inner	750.2.m.d.511.1	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.d.91.1	✓	140	1.1	even	1	trivial
750.2.m.d.511.1	yes	140	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)

\(f(q)\)	\(=\)	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.20812 + 0.352409i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.260934 - 0.803073i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.20812 + 0.352409i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.260934 - 0.803073i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(1.85089 + 1.25467i) q^{10} +(3.77146 + 3.54163i) q^{11} +(0.876307 + 0.481754i) q^{12} +(0.988843 + 2.10140i) q^{13} +(-0.359529 + 0.764037i) q^{14} +(-0.885623 + 2.05321i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(-0.463236 + 7.36292i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-3.98926 - 6.28607i) q^{19} +(-0.490363 - 2.18164i) q^{20} +(-0.817873 - 0.209994i) q^{21} +(-0.324859 - 5.16348i) q^{22} +(0.928613 + 4.86796i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.75162 - 1.55633i) q^{25} +(0.717670 - 2.20876i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(0.785104 - 0.310845i) q^{28} +(8.23645 - 3.26104i) q^{29} +(2.05111 - 0.890475i) q^{30} +(0.00135602 - 0.0215533i) q^{31} +(0.809017 + 0.587785i) q^{32} +(5.01115 - 1.28664i) q^{33} +(5.37795 - 5.05023i) q^{34} +(0.859186 + 1.68133i) q^{35} +(0.876307 - 0.481754i) q^{36} +(6.09628 - 0.770139i) q^{37} +(-1.39506 + 7.31318i) q^{38} +(2.30412 + 0.291078i) q^{39} +(-1.13597 + 1.92602i) q^{40} +(0.650581 - 3.41046i) q^{41} +(0.452453 + 0.712952i) q^{42} +(-1.92789 + 1.40070i) q^{43} +(-3.29783 + 3.98640i) q^{44} +(1.25904 + 1.84792i) q^{45} +(2.65542 - 4.18427i) q^{46} +(7.89005 + 9.53743i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(5.08628 - 3.69540i) q^{49} +(-4.52916 - 2.11819i) q^{50} +(5.96851 + 4.33637i) q^{51} +(-2.03516 + 1.11884i) q^{52} +(-0.993889 - 0.255187i) q^{53} +(0.637424 + 0.770513i) q^{54} +(-9.57595 - 6.49127i) q^{55} +(-0.785104 - 0.310845i) q^{56} -7.44505 q^{57} +(-8.23645 - 3.26104i) q^{58} +(-5.03392 - 2.76742i) q^{59} +(-2.10477 - 0.754953i) q^{60} +(2.34855 + 12.3115i) q^{61} +(-0.0157427 + 0.0147834i) q^{62} +(-0.615542 + 0.578032i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.92404 - 4.29167i) q^{65} +(-4.53374 - 2.49244i) q^{66} +(10.3170 + 4.08480i) q^{67} -7.37748 q^{68} +(4.60773 + 1.82433i) q^{69} +(0.524630 - 1.81379i) q^{70} +(-1.94952 - 2.35657i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(1.48557 - 0.816698i) q^{73} +(-4.97119 - 3.61178i) q^{74} +(1.23199 - 4.84584i) q^{75} +(6.02318 - 4.37609i) q^{76} +(1.86009 - 3.95289i) q^{77} +(-1.48037 - 1.78946i) q^{78} +(0.306935 - 0.483652i) q^{79} +(2.14654 - 0.626381i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-2.80888 + 2.04077i) q^{82} +(1.46915 + 2.31501i) q^{83} +(0.158225 - 0.829445i) q^{84} +(-1.57188 - 16.4215i) q^{85} +(2.36422 + 0.298670i) q^{86} +(1.65992 - 8.70162i) q^{87} +(5.13289 - 0.648435i) q^{88} +(-2.43013 + 1.33597i) q^{89} +(0.347187 - 2.20895i) q^{90} +(1.42955 - 1.34244i) q^{91} +(-4.80004 + 1.23244i) q^{92} +(-0.0174714 - 0.0126937i) q^{93} +(0.777223 - 12.3536i) q^{94} +(11.0240 + 12.4746i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-16.0511 + 6.35508i) q^{97} +(-6.23741 - 0.787968i) q^{98} +(1.59876 - 4.92047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) \) 140 * q - 20 * q^5 + 5 * q^7	\( 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) \) 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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