LMFDB - Embedded newform 288.2.bf.a.11.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.40
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27367 + 0.614625i) q^{2} +(-1.05013 + 1.37740i) q^{3} +(1.24447 + 1.56566i) q^{4} +(0.0452073 + 0.343384i) q^{5} +(-2.18411 + 1.10891i) q^{6} +(0.358377 + 1.33748i) q^{7} +(0.622752 + 2.75902i) q^{8} +(-0.794441 - 2.89290i) q^{9} +O(q^{10})$	\(q+(1.27367 + 0.614625i) q^{2} +(-1.05013 + 1.37740i) q^{3} +(1.24447 + 1.56566i) q^{4} +(0.0452073 + 0.343384i) q^{5} +(-2.18411 + 1.10891i) q^{6} +(0.358377 + 1.33748i) q^{7} +(0.622752 + 2.75902i) q^{8} +(-0.794441 - 2.89290i) q^{9} +(-0.153473 + 0.465143i) q^{10} +(-1.53764 + 1.17987i) q^{11} +(-3.46339 + 0.0699788i) q^{12} +(1.07217 - 1.39728i) q^{13} +(-0.365595 + 1.92378i) q^{14} +(-0.520449 - 0.298330i) q^{15} +(-0.902582 + 3.89684i) q^{16} -0.574776 q^{17} +(0.766194 - 4.17288i) q^{18} +(-1.27313 + 0.527348i) q^{19} +(-0.481363 + 0.498111i) q^{20} +(-2.21858 - 0.910905i) q^{21} +(-2.68362 + 0.557696i) q^{22} +(2.80438 + 0.751432i) q^{23} +(-4.45423 - 2.03956i) q^{24} +(4.71376 - 1.26305i) q^{25} +(2.22440 - 1.12069i) q^{26} +(4.81894 + 1.94367i) q^{27} +(-1.64805 + 2.22555i) q^{28} +(-2.67785 - 0.352546i) q^{29} +(-0.479519 - 0.699856i) q^{30} +(4.87848 - 2.81659i) q^{31} +(-3.54469 + 4.40854i) q^{32} +(-0.0104253 - 3.35696i) q^{33} +(-0.732075 - 0.353272i) q^{34} +(-0.443068 + 0.183525i) q^{35} +(3.54064 - 4.84395i) q^{36} +(0.837849 - 2.02275i) q^{37} +(-1.94567 - 0.110831i) q^{38} +(0.798689 + 2.94414i) q^{39} +(-0.919249 + 0.338571i) q^{40} +(2.97203 - 11.0918i) q^{41} +(-2.26588 - 2.52379i) q^{42} +(4.52106 + 5.89196i) q^{43} +(-3.76083 - 0.939103i) q^{44} +(0.957460 - 0.403578i) q^{45} +(3.11001 + 2.68072i) q^{46} +(-4.21627 - 2.43427i) q^{47} +(-4.41966 - 5.33541i) q^{48} +(4.40176 - 2.54136i) q^{49} +(6.78008 + 1.28849i) q^{50} +(0.603591 - 0.791694i) q^{51} +(3.52196 - 0.0602207i) q^{52} +(-3.53239 + 8.52795i) q^{53} +(4.94311 + 5.43743i) q^{54} +(-0.474662 - 0.474662i) q^{55} +(-3.46695 + 1.82169i) q^{56} +(0.610590 - 2.30739i) q^{57} +(-3.19401 - 2.09490i) q^{58} +(5.62596 - 0.740672i) q^{59} +(-0.180600 - 1.18611i) q^{60} +(0.645484 - 4.90294i) q^{61} +(7.94472 - 0.588972i) q^{62} +(3.58449 - 2.09930i) q^{63} +(-7.22436 + 3.43637i) q^{64} +(0.528275 + 0.305000i) q^{65} +(2.05000 - 4.28207i) q^{66} +(4.11206 - 5.35894i) q^{67} +(-0.715292 - 0.899903i) q^{68} +(-3.98000 + 3.07364i) q^{69} +(-0.677121 - 0.0385707i) q^{70} +(-5.04976 - 5.04976i) q^{71} +(7.48682 - 3.99343i) q^{72} +(8.79899 - 8.79899i) q^{73} +(2.31038 - 2.06135i) q^{74} +(-3.21036 + 7.81908i) q^{75} +(-2.41002 - 1.33702i) q^{76} +(-2.12911 - 1.63372i) q^{77} +(-0.792279 + 4.24076i) q^{78} +(-6.57615 + 11.3902i) q^{79} +(-1.37891 - 0.133766i) q^{80} +(-7.73773 + 4.59647i) q^{81} +(10.6027 - 12.3006i) q^{82} +(-11.3315 - 1.49182i) q^{83} +(-1.33480 - 4.60714i) q^{84} +(-0.0259841 - 0.197369i) q^{85} +(2.13699 + 10.2832i) q^{86} +(3.29769 - 3.31824i) q^{87} +(-4.21286 - 3.50761i) q^{88} +(-8.74474 + 8.74474i) q^{89} +(1.46754 + 0.0744536i) q^{90} +(2.25308 + 0.933257i) q^{91} +(2.31349 + 5.32585i) q^{92} +(-1.24349 + 9.67740i) q^{93} +(-3.87398 - 5.69188i) q^{94} +(-0.238638 - 0.413332i) q^{95} +(-2.34991 - 9.51199i) q^{96} +(0.426263 - 0.738308i) q^{97} +(7.16837 - 0.531418i) q^{98} +(4.63481 + 3.51090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.27367	+	0.614625i	0.900621	+	0.434606i
$2$	1.27367	+	0.614625i	0.900621	+	0.434606i
$3$	−1.05013	+	1.37740i	−0.606295	+	0.795240i
$3$	−1.05013	+	1.37740i	−0.606295	+	0.795240i
$4$	1.24447	+	1.56566i	0.622236	+	0.782830i
$5$	0.0452073	+	0.343384i	0.0202173	+	0.153566i	0.998576	−	0.0533512i	$-0.0169903\pi$
$5$	0.0452073	+	0.343384i	0.0202173	+	0.153566i	−0.978358	+	0.206917i	$0.933657\pi$
$6$	−2.18411	+	1.10891i	−0.891657	+	0.452711i
$7$	0.358377	+	1.33748i	0.135454	+	0.505520i	0.999996	+	0.00295929i	$0.000941974\pi$
$7$	0.358377	+	1.33748i	0.135454	+	0.505520i	−0.864542	+	0.502561i	$0.832391\pi$
$8$	0.622752	+	2.75902i	0.220176	+	0.975460i
$9$	−0.794441	−	2.89290i	−0.264814	−	0.964300i
$10$	−0.153473	+	0.465143i	−0.0485325	+	0.147091i
$11$	−1.53764	+	1.17987i	−0.463616	+	0.355745i	−0.814004	−	0.580860i	$-0.802716\pi$
$11$	−1.53764	+	1.17987i	−0.463616	+	0.355745i	0.350388	+	0.936605i	$0.386050\pi$
$12$	−3.46339	+	0.0699788i	−0.999796	+	0.0202012i
$13$	1.07217	−	1.39728i	0.297368	−	0.387537i	−0.620643	−	0.784094i	$-0.713128\pi$
$13$	1.07217	−	1.39728i	0.297368	−	0.387537i	0.918010	+	0.396556i	$0.129795\pi$
$14$	−0.365595	+	1.92378i	−0.0977095	+	0.514151i
$15$	−0.520449	−	0.298330i	−0.134379	−	0.0770285i
$16$	−0.902582	+	3.89684i	−0.225645	+	0.974209i
$17$	−0.574776			−0.139404			−0.0697018	−	0.997568i	$-0.522205\pi$
$17$	−0.574776			−0.139404			−0.0697018	+	0.997568i	$0.522205\pi$
$18$	0.766194	−	4.17288i	0.180594	−	0.983558i
$19$	−1.27313	+	0.527348i	−0.292076	+	0.120982i	−0.523910	−	0.851773i	$-0.675527\pi$
$19$	−1.27313	+	0.527348i	−0.292076	+	0.120982i	0.231834	+	0.972755i	$0.425527\pi$
$20$	−0.481363	+	0.498111i	−0.107636	+	0.111381i
$21$	−2.21858	−	0.910905i	−0.484135	−	0.198776i
$22$	−2.68362	+	0.557696i	−0.572151	+	0.118901i
$23$	2.80438	+	0.751432i	0.584754	+	0.156684i	0.539055	−	0.842271i	$-0.318782\pi$
$23$	2.80438	+	0.751432i	0.584754	+	0.156684i	0.0456996	+	0.998955i	$0.485448\pi$
$24$	−4.45423	−	2.03956i	−0.909217	−	0.416323i
$25$	4.71376	−	1.26305i	0.942752	−	0.252610i
$26$	2.22440	−	1.12069i	0.436241	−	0.219786i
$27$	4.81894	+	1.94367i	0.927405	+	0.374059i
$28$	−1.64805	+	2.22555i	−0.311452	+	0.420590i
$29$	−2.67785	−	0.352546i	−0.497264	−	0.0654661i	−0.122277	−	0.992496i	$-0.539020\pi$
$29$	−2.67785	−	0.352546i	−0.497264	−	0.0654661i	−0.374987	+	0.927030i	$0.622353\pi$
$30$	−0.479519	−	0.699856i	−0.0875478	−	0.127776i
$31$	4.87848	−	2.81659i	0.876201	−	0.505875i	0.00679713	−	0.999977i	$-0.497836\pi$
$31$	4.87848	−	2.81659i	0.876201	−	0.505875i	0.869404	+	0.494102i	$0.164503\pi$
$32$	−3.54469	+	4.40854i	−0.626618	+	0.779327i
$33$	−0.0104253	−	3.35696i	−0.00181482	−	0.584372i
$34$	−0.732075	−	0.353272i	−0.125550	−	0.0605856i
$35$	−0.443068	+	0.183525i	−0.0748921	+	0.0310213i
$36$	3.54064	−	4.84395i	0.590106	−	0.807326i
$37$	0.837849	−	2.02275i	0.137742	−	0.332538i	−0.839924	−	0.542704i	$-0.817401\pi$
$37$	0.837849	−	2.02275i	0.137742	−	0.332538i	0.977666	+	0.210166i	$0.0674006\pi$
$38$	−1.94567	−	0.110831i	−0.315629	−	0.0179792i
$39$	0.798689	+	2.94414i	0.127893	+	0.471440i
$40$	−0.919249	+	0.338571i	−0.145346	+	0.0535327i
$41$	2.97203	−	11.0918i	0.464154	−	1.73224i	−0.195527	−	0.980698i	$-0.562642\pi$
$41$	2.97203	−	11.0918i	0.464154	−	1.73224i	0.659680	−	0.751546i	$-0.270692\pi$
$42$	−2.26588	−	2.52379i	−0.349633	−	0.389429i
$43$	4.52106	+	5.89196i	0.689455	+	0.898515i	0.998621	−	0.0524929i	$-0.0167167\pi$
$43$	4.52106	+	5.89196i	0.689455	+	0.898515i	−0.309166	+	0.951008i	$0.600050\pi$
$44$	−3.76083	−	0.939103i	−0.566966	−	0.141575i
$45$	0.957460	−	0.403578i	0.142730	−	0.0601619i
$46$	3.11001	+	2.68072i	0.458546	+	0.395251i
$47$	−4.21627	−	2.43427i	−0.615006	−	0.355074i	0.159916	−	0.987131i	$-0.448878\pi$
$47$	−4.21627	−	2.43427i	−0.615006	−	0.355074i	−0.774922	+	0.632057i	$0.782211\pi$
$48$	−4.41966	−	5.33541i	−0.637923	−	0.770100i
$49$	4.40176	−	2.54136i	0.628823	−	0.363051i
$50$	6.78008	+	1.28849i	0.958848	+	0.182220i
$51$	0.603591	−	0.791694i	0.0845197	−	0.110859i
$52$	3.52196	−	0.0602207i	0.488408	−	0.00835111i
$53$	−3.53239	+	8.52795i	−0.485211	+	1.17140i	0.471892	+	0.881657i	$0.343571\pi$
$53$	−3.53239	+	8.52795i	−0.485211	+	1.17140i	−0.957103	+	0.289748i	$0.906429\pi$
$54$	4.94311	+	5.43743i	0.672672	+	0.739941i
$55$	−0.474662	−	0.474662i	−0.0640034	−	0.0640034i
$56$	−3.46695	+	1.82169i	−0.463291	+	0.243433i
$57$	0.610590	−	2.30739i	0.0808746	−	0.305621i
$58$	−3.19401	−	2.09490i	−0.419395	−	0.275074i
$59$	5.62596	−	0.740672i	0.732438	−	0.0964273i	0.244924	−	0.969542i	$-0.421237\pi$
$59$	5.62596	−	0.740672i	0.732438	−	0.0964273i	0.487514	+	0.873115i	$0.337904\pi$
$60$	−0.180600	−	1.18611i	−0.0233154	−	0.153126i
$61$	0.645484	−	4.90294i	0.0826458	−	0.627757i	−0.899126	−	0.437691i	$-0.855796\pi$
$61$	0.645484	−	4.90294i	0.0826458	−	0.627757i	0.981771	−	0.190066i	$-0.0608702\pi$
$62$	7.94472	−	0.588972i	1.00898	−	0.0747995i
$63$	3.58449	−	2.09930i	0.451603	−	0.264486i
$64$	−7.22436	+	3.43637i	−0.903045	+	0.429546i
$65$	0.528275	+	0.305000i	0.0655245	+	0.0378306i
$66$	2.05000	−	4.28207i	0.252337	−	0.527086i
$67$	4.11206	−	5.35894i	0.502368	−	0.654699i	−0.471486	−	0.881874i	$-0.656282\pi$
$67$	4.11206	−	5.35894i	0.502368	−	0.654699i	0.973854	+	0.227175i	$0.0729489\pi$
$68$	−0.715292	−	0.899903i	−0.0867419	−	0.109129i
$69$	−3.98000	+	3.07364i	−0.479135	+	0.370023i
$70$	−0.677121	−	0.0385707i	−0.0809314	−	0.00461009i
$71$	−5.04976	−	5.04976i	−0.599296	−	0.599296i	0.340829	−	0.940125i	$-0.389292\pi$
$71$	−5.04976	−	5.04976i	−0.599296	−	0.599296i	−0.940125	+	0.340829i	$0.889292\pi$
$72$	7.48682	−	3.99343i	0.882330	−	0.470631i
$73$	8.79899	−	8.79899i	1.02984	−	1.02984i	0.0303035	−	0.999541i	$-0.490353\pi$
$73$	8.79899	−	8.79899i	1.02984	−	1.02984i	0.999541	−	0.0303035i	$-0.00964736\pi$
$74$	2.31038	−	2.06135i	0.268576	−	0.239627i
$75$	−3.21036	+	7.81908i	−0.370700	+	0.902870i
$76$	−2.41002	−	1.33702i	−0.276449	−	0.153367i
$77$	−2.12911	−	1.63372i	−0.242635	−	0.186180i
$78$	−0.792279	+	4.24076i	−0.0897080	+	0.480172i
$79$	−6.57615	+	11.3902i	−0.739875	+	1.28150i	0.212676	+	0.977123i	$0.431782\pi$
$79$	−6.57615	+	11.3902i	−0.739875	+	1.28150i	−0.952551	+	0.304379i	$0.901551\pi$
$80$	−1.37891	−	0.133766i	−0.154167	−	0.0149555i
$81$	−7.73773	+	4.59647i	−0.859748	+	0.510719i
$82$	10.6027	−	12.3006i	1.17087	−	1.35837i
$83$	−11.3315	−	1.49182i	−1.24379	−	0.163749i	−0.520242	−	0.854019i	$-0.674158\pi$
$83$	−11.3315	−	1.49182i	−1.24379	−	0.163749i	−0.723552	+	0.690270i	$0.757492\pi$
$84$	−1.33480	−	4.60714i	−0.145638	−	0.502680i
$85$	−0.0259841	−	0.197369i	−0.00281837	−	0.0214076i
$86$	2.13699	+	10.2832i	0.230438	+	1.10886i
$87$	3.29769	−	3.31824i	0.353550	−	0.355753i
$88$	−4.21286	−	3.50761i	−0.449092	−	0.373912i
$89$	−8.74474	+	8.74474i	−0.926941	+	0.926941i	−0.997507	−	0.0705665i	$-0.977519\pi$
$89$	−8.74474	+	8.74474i	−0.926941	+	0.926941i	0.0705665	+	0.997507i	$0.477519\pi$
$90$	1.46754	+	0.0744536i	0.154692	+	0.00784810i
$91$	2.25308	+	0.933257i	0.236187	+	0.0978320i
$92$	2.31349	+	5.32585i	0.241198	+	0.555258i
$93$	−1.24349	+	9.67740i	−0.128944	+	1.00350i
$94$	−3.87398	−	5.69188i	−0.399570	−	0.587072i
$95$	−0.238638	−	0.413332i	−0.0244837	−	0.0424070i
$96$	−2.34991	−	9.51199i	−0.239837	−	0.970813i
$97$	0.426263	−	0.738308i	0.0432804	−	0.0749639i	−0.843574	−	0.537013i	$-0.819552\pi$
$97$	0.426263	−	0.738308i	0.0432804	−	0.0749639i	0.886854	+	0.462050i	$0.152886\pi$
$98$	7.16837	−	0.531418i	0.724115	−	0.0536813i
$99$	4.63481	+	3.51090i	0.465816	+	0.352858i
$100$	7.84364	+	5.80832i	0.784364	+	0.580832i
$101$	−13.5511	+	10.3982i	−1.34839	+	1.03466i	−0.353317	+	0.935504i	$0.614946\pi$
$101$	−13.5511	+	10.3982i	−1.34839	+	1.03466i	−0.995072	+	0.0991519i	$0.968387\pi$
$102$	1.25537	−	0.637375i	0.124300	−	0.0631095i
$103$	−6.70552	−	1.79674i	−0.660714	−	0.177038i	−0.0871458	−	0.996196i	$-0.527775\pi$
$103$	−6.70552	−	1.79674i	−0.660714	−	0.177038i	−0.573568	+	0.819158i	$0.694441\pi$
$104$	4.52283	+	2.08799i	0.443500	+	0.204744i
$105$	0.212494	−	0.803005i	0.0207373	−	0.0783653i
$106$	−9.74060	+	8.69070i	−0.946091	+	0.844115i
$107$	1.16034	+	0.480630i	0.112175	+	0.0464642i	0.438065	−	0.898943i	$-0.355664\pi$
$107$	1.16034	+	0.480630i	0.112175	+	0.0464642i	−0.325890	+	0.945408i	$0.605664\pi$
$108$	2.95390	+	9.96366i	0.284239	+	0.958753i
$109$	−3.15151	−	7.60841i	−0.301860	−	0.728753i	−0.999919	−	0.0127138i	$-0.995953\pi$
$109$	−3.15151	−	7.60841i	−0.301860	−	0.728753i	0.698060	−	0.716040i	$-0.254047\pi$
$110$	−0.312823	−	0.896301i	−0.0298265	−	0.0854590i
$111$	1.90627	+	3.27820i	0.180935	+	0.311153i
$112$	−5.53541	+	0.189351i	−0.523047	+	0.0178920i
$113$	0.963528	+	1.66888i	0.0906411	+	0.156995i	0.907781	−	0.419444i	$-0.137775\pi$
$113$	0.963528	+	1.66888i	0.0906411	+	0.156995i	−0.817140	+	0.576439i	$0.804442\pi$
$114$	2.19587	−	2.56357i	0.205662	−	0.240100i
$115$	−0.131251	+	0.996950i	−0.0122392	+	0.0929661i
$116$	−2.78054	−	4.63133i	−0.258167	−	0.430009i
$117$	−4.89398	−	1.99163i	−0.452449	−	0.184126i
$118$	7.62086	+	2.51449i	0.701557	+	0.231477i
$119$	−0.205986	−	0.768751i	−0.0188827	−	0.0704713i
$120$	0.498988	−	1.62171i	0.0455511	−	0.148042i
$121$	−1.87477	+	6.99675i	−0.170434	+	0.636068i
$122$	3.83560	−	5.84800i	0.347259	−	0.529453i
$123$	12.1567	+	15.7415i	1.09614	+	1.41936i
$124$	10.4810	+	4.13287i	0.941218	+	0.371143i
$125$	1.30951	+	3.16144i	0.117126	+	0.282768i
$126$	5.85573	−	0.470695i	0.521670	−	0.0419329i
$127$		−	16.6034i		−	1.47332i	−0.676266	−	0.736658i	$-0.736403\pi$
$127$		−	16.6034i		−	1.47332i	0.676266	−	0.736658i	$-0.263597\pi$
$128$	−11.3135	−	0.0634754i	−0.999984	−	0.00561049i
$129$	−12.8633	+	0.0399480i	−1.13255	+	0.00351723i
$130$	0.485388	+	0.713160i	0.0425713	+	0.0625483i
$131$	−10.8684	−	8.33958i	−0.949573	−	0.728633i	0.0129266	−	0.999916i	$-0.495885\pi$
$131$	−10.8684	−	8.33958i	−0.949573	−	0.728633i	−0.962499	+	0.271284i	$0.912552\pi$
$132$	5.24289	−	4.19397i	0.456335	−	0.365038i
$133$	−1.16158	−	1.51380i	−0.100722	−	0.131263i
$134$	8.53115	−	4.29815i	0.736979	−	0.371303i
$135$	−0.449573	+	1.74261i	−0.0386931	+	0.149980i
$136$	−0.357943	−	1.58582i	−0.0306933	−	0.135983i
$137$	20.6862	−	5.54285i	1.76734	−	0.473558i	0.779157	−	0.626829i	$-0.215647\pi$
$137$	20.6862	−	5.54285i	1.76734	−	0.473558i	0.988184	+	0.153271i	$0.0489807\pi$
$138$	−6.95834	+	1.46860i	−0.592333	+	0.125016i
$139$	1.99544	−	0.262705i	0.169251	−	0.0222823i	−0.0454242	−	0.998968i	$-0.514464\pi$
$139$	1.99544	−	0.262705i	0.169251	−	0.0222823i	0.214675	+	0.976685i	$0.431131\pi$
$140$	−0.838722	−	0.465302i	−0.0708850	−	0.0393252i
$141$	7.78059	−	3.25117i	0.655244	−	0.273798i
$142$	−3.32802	−	9.53544i	−0.279281	−	0.800196i
$143$			3.41355i			0.285455i
$144$	11.9902	−	0.484729i	0.999184	−	0.0403941i
$145$		−	0.935468i		−	0.0776864i
$146$	16.6151	−	5.79893i	1.37508	−	0.479923i
$147$	−1.12198	+	8.73173i	−0.0925392	+	0.720181i
$148$	4.20961	−	1.20546i	0.346028	−	0.0990885i
$149$	−7.72366	+	1.01684i	−0.632747	+	0.0833027i	−0.440076	−	0.897961i	$-0.645048\pi$
$149$	−7.72366	+	1.01684i	−0.632747	+	0.0833027i	−0.192671	+	0.981263i	$0.561715\pi$
$150$	−8.89475	+	7.98577i	−0.726253	+	0.652035i
$151$	−20.7464	+	5.55899i	−1.68832	+	0.452384i	−0.969955	−	0.243283i	$-0.921776\pi$
$151$	−20.7464	+	5.55899i	−1.68832	+	0.452384i	−0.718365	+	0.695667i	$0.755109\pi$
$152$	−2.24781	−	3.18418i	−0.182321	−	0.258271i
$153$	0.456625	+	1.66277i	0.0369160	+	0.134427i
$154$	−1.70766	−	3.38943i	−0.137607	−	0.273128i
$155$	1.18772	+	1.54786i	0.0953996	+	0.124327i
$156$	−3.61558	+	4.91438i	−0.289478	+	0.393465i
$157$	−12.8538	−	9.86308i	−1.02585	−	0.787159i	−0.0485035	−	0.998823i	$-0.515445\pi$
$157$	−12.8538	−	9.86308i	−1.02585	−	0.787159i	−0.977343	+	0.211664i	$0.932112\pi$
$158$	−15.3766	+	10.4655i	−1.22329	+	0.832593i
$159$	−8.03688	−	13.8210i	−0.637366	−	1.09608i
$160$	−1.67407	−	1.01789i	−0.132347	−	0.0804712i
$161$			4.02010i			0.316828i
$162$	−12.6804	+	1.09859i	−0.996268	+	0.0863131i
$163$	5.42994	+	13.1090i	0.425305	+	1.02678i	0.980758	+	0.195230i	$0.0625452\pi$
$163$	5.42994	+	13.1090i	0.425305	+	1.02678i	−0.555452	+	0.831548i	$0.687455\pi$
$164$	21.0646	−	9.15021i	1.64487	−	0.714511i
$165$	1.15225	−	0.155339i	0.0897029	−	0.0120931i
$166$	−13.5157	−	8.86471i	−1.04902	−	0.688035i
$167$	3.82478	−	14.2743i	0.295970	−	1.10458i	−0.644474	−	0.764626i	$-0.722924\pi$
$167$	3.82478	−	14.2743i	0.295970	−	1.10458i	0.940444	−	0.339949i	$-0.110410\pi$
$168$	1.13158	−	6.68838i	0.0873031	−	0.516020i
$169$	2.56180	+	9.56077i	0.197062	+	0.735444i
$170$	0.0882126	−	0.267353i	0.00676560	−	0.0205050i
$171$	2.53699	+	3.26409i	0.194009	+	0.249611i
$172$	−3.59847	+	14.4108i	−0.274381	+	1.09881i
$173$	0.270838	−	2.05722i	0.0205915	−	0.156408i	−0.978060	−	0.208323i	$-0.933199\pi$
$173$	0.270838	−	2.05722i	0.0205915	−	0.156408i	0.998651	+	0.0519157i	$0.0165327\pi$
$174$	6.23965	−	2.19950i	0.473027	−	0.166743i
$175$	3.37860	+	5.85191i	0.255398	+	0.442363i
$176$	−3.20993	−	7.05686i	−0.241957	−	0.531931i
$177$	−4.88781	+	8.52698i	−0.367390	+	0.640927i
$178$	−16.5127	+	5.76318i	−1.23768	+	0.431968i
$179$	−0.700228	−	1.69050i	−0.0523375	−	0.126354i	0.895548	−	0.444965i	$-0.146784\pi$
$179$	−0.700228	−	1.69050i	−0.0523375	−	0.126354i	−0.947886	+	0.318611i	$0.896784\pi$
$180$	1.82340	+	0.996815i	0.135908	+	0.0742982i
$181$	19.7735	+	8.19045i	1.46975	+	0.608791i	0.966803	−	0.255525i	$-0.0822482\pi$
$181$	19.7735	+	8.19045i	1.46975	+	0.608791i	0.502949	+	0.864316i	$0.332248\pi$
$182$	2.29608	+	2.57346i	0.170197	+	0.190758i
$183$	6.07544	+	6.03783i	0.449110	+	0.446329i
$184$	−0.326780	+	8.20530i	−0.0240905	+	0.604903i
$185$	0.732455	+	0.196261i	0.0538512	+	0.0144294i
$186$	−7.53177	+	11.5615i	−0.552256	+	0.847733i
$187$	0.883798	−	0.678162i	0.0646297	−	0.0495921i
$188$	−1.43580	−	9.63062i	−0.104716	−	0.702385i
$189$	−0.872625	+	7.14180i	−0.0634741	+	0.519489i
$190$	−0.0499010	−	0.673122i	−0.00362020	−	0.0488334i
$191$	1.43851	−	2.49157i	0.104087	−	0.180284i	−0.809278	−	0.587426i	$-0.800141\pi$
$191$	1.43851	−	2.49157i	0.104087	−	0.180284i	0.913365	+	0.407142i	$0.133475\pi$
$192$	2.85330	−	13.5594i	0.205919	−	0.978569i
$193$	1.23668	+	2.14199i	0.0890182	+	0.154184i	0.907096	−	0.420923i	$-0.138294\pi$
$193$	1.23668	+	2.14199i	0.0890182	+	0.154184i	−0.818078	+	0.575107i	$0.804960\pi$
$194$	0.996701	−	0.678370i	0.0715589	−	0.0487041i
$195$	−0.974865	+	0.407354i	−0.0698115	+	0.0291712i
$196$	9.45676	+	3.72901i	0.675483	+	0.266358i
$197$	19.5836	+	8.11179i	1.39527	+	0.577941i	0.948520	−	0.316716i	$-0.102580\pi$
$197$	19.5836	+	8.11179i	1.39527	+	0.577941i	0.446753	+	0.894657i	$0.352580\pi$
$198$	3.74534	+	7.32040i	0.266170	+	0.520238i
$199$	−17.8549	+	17.8549i	−1.26570	+	1.26570i	−0.317417	+	0.948286i	$0.602815\pi$
$199$	−17.8549	+	17.8549i	−1.26570	+	1.26570i	−0.948286	+	0.317417i	$0.897185\pi$
$200$	6.42028	+	12.2188i	0.453982	+	0.863998i
$201$	3.06317	+	11.2915i	0.216060	+	0.796443i
$202$	−23.6507	+	4.91495i	−1.66405	+	0.345815i
$203$	−0.488156	−	3.70791i	−0.0342618	−	0.260245i
$204$	1.99068	−	0.0402221i	0.139375	−	0.00281611i
$205$	3.94309	+	0.519118i	0.275398	+	0.0362568i
$206$	−7.43629	−	6.40983i	−0.518111	−	0.446594i
$207$	−0.0540984	−	8.70977i	−0.00376010	−	0.605371i
$208$	4.47727	+	5.43925i	0.310443	+	0.377144i
$209$	1.33541	−	2.31300i	0.0923724	−	0.159994i
$210$	0.764194	−	0.892159i	0.0527344	−	0.0615648i
$211$	−3.60771	−	2.76830i	−0.248365	−	0.190577i	0.477075	−	0.878863i	$-0.341697\pi$
$211$	−3.60771	−	2.76830i	−0.248365	−	0.190577i	−0.725440	+	0.688285i	$0.758364\pi$
$212$	−17.7478	+	5.08227i	−1.21893	+	0.349051i
$213$	12.2584	−	1.65260i	0.839935	−	0.113234i
$214$	1.18249	+	1.32534i	0.0808331	+	0.0905984i
$215$	−1.81882	+	1.81882i	−0.124042	+	0.124042i
$216$	−2.36162	+	14.5060i	−0.160688	+	0.987005i
$217$	5.51547	+	5.51547i	0.374415	+	0.374415i
$218$	0.662341	−	11.6276i	0.0448594	−	0.787520i
$219$	2.87958	+	21.3598i	0.194584	+	1.44336i
$220$	0.152456	−	1.33386i	0.0102786	−	0.0899289i
$221$	−0.616260	+	0.803125i	−0.0414541	+	0.0540241i
$222$	0.413093	+	5.34699i	0.0277250	+	0.358867i
$223$	−18.5810	−	10.7277i	−1.24427	−	0.718381i	−0.274311	−	0.961641i	$-0.588450\pi$
$223$	−18.5810	−	10.7277i	−1.24427	−	0.718381i	−0.969961	+	0.243260i	$0.921783\pi$
$224$	−7.16666	−	3.16103i	−0.478843	−	0.211205i
$225$	−7.39867	−	12.6330i	−0.493245	−	0.842201i
$226$	0.201481	+	2.71781i	0.0134023	+	0.180786i
$227$	2.28759	−	17.3759i	0.151832	−	1.15328i	−0.730588	−	0.682819i	$-0.760754\pi$
$227$	2.28759	−	17.3759i	0.151832	−	1.15328i	0.882420	−	0.470462i	$-0.155913\pi$
$228$	4.37245	−	1.91551i	0.289573	−	0.126858i
$229$	−17.3524	+	2.28449i	−1.14668	+	0.150963i	−0.679828	−	0.733372i	$-0.737945\pi$
$229$	−17.3524	+	2.28449i	−1.14668	+	0.150963i	−0.466852	+	0.884335i	$0.654612\pi$
$230$	−0.779921	+	1.18912i	−0.0514265	+	0.0784079i
$231$	4.48613	−	1.21700i	0.295166	−	0.0800728i
$232$	−0.694957	−	7.60778i	−0.0456261	−	0.499475i
$233$	1.37102	+	1.37102i	0.0898185	+	0.0898185i	0.750588	−	0.660770i	$-0.229770\pi$
$233$	1.37102	+	1.37102i	0.0898185	+	0.0898185i	−0.660770	+	0.750588i	$0.729770\pi$
$234$	−5.00921	−	5.54465i	−0.327462	−	0.362465i
$235$	0.645281	−	1.55785i	0.0420935	−	0.101623i
$236$	8.16099	+	7.88660i	0.531235	+	0.513374i
$237$	−8.78303	−	21.0192i	−0.570519	−	1.36535i
$238$	0.210135	−	1.10574i	0.0136211	−	0.0716745i
$239$	16.0202	−	9.24926i	1.03626	−	0.598285i	0.117488	−	0.993074i	$-0.462516\pi$
$239$	16.0202	−	9.24926i	1.03626	−	0.598285i	0.918772	+	0.394789i	$0.129182\pi$
$240$	1.63229	−	1.75884i	0.105364	−	0.113533i
$241$	8.91419	+	5.14661i	0.574214	+	0.331522i	0.758830	−	0.651288i	$-0.225771\pi$
$241$	8.91419	+	5.14661i	0.574214	+	0.331522i	−0.184617	+	0.982811i	$0.559104\pi$
$242$	−6.68822	+	7.75927i	−0.429935	+	0.498785i
$243$	1.79448	−	15.4848i	0.115116	−	0.993352i
$244$	8.47962	−	5.09096i	0.542852	−	0.325915i
$245$	1.07165	+	1.39660i	0.0684654	+	0.0892258i
$246$	5.80855	+	27.5213i	0.370340	+	1.75470i
$247$	−0.628163	+	2.34434i	−0.0399690	+	0.149166i
$248$	10.8091	+	11.7058i	0.686379	+	0.743318i
$249$	13.9544	−	14.0414i	0.884325	−	0.889835i
$250$	−0.275216	+	4.83150i	−0.0174062	+	0.305571i
$251$	7.46406	−	18.0198i	0.471128	−	1.13740i	−0.492538	−	0.870291i	$-0.663931\pi$
$251$	7.46406	−	18.0198i	0.471128	−	1.13740i	0.963666	−	0.267112i	$-0.0860692\pi$
$252$	7.74757	+	2.99957i	0.488051	+	0.188955i
$253$	−5.19872	+	2.15338i	−0.326841	+	0.135382i
$254$	10.2049	−	21.1473i	0.640311	−	1.32690i
$255$	0.299142	+	0.171473i	0.0187330	+	0.0107381i
$256$	−14.3707	−	7.03443i	−0.898168	−	0.439652i
$257$	5.92640	−	3.42161i	0.369679	−	0.213434i	−0.303639	−	0.952787i	$-0.598202\pi$
$257$	5.92640	−	3.42161i	0.369679	−	0.213434i	0.673318	+	0.739353i	$0.264868\pi$
$258$	−16.4081	−	7.85521i	−1.02152	−	0.489044i
$259$	3.00565	+	0.395701i	0.186762	+	0.0245877i
$260$	0.179897	+	1.20666i	0.0111568	+	0.0748340i
$261$	1.10751	+	8.02682i	0.0685534	+	0.496848i
$262$	−8.71698	−	17.3018i	−0.538537	−	1.06891i
$263$	−13.1446	+	3.52208i	−0.810530	+	0.217181i	−0.640202	−	0.768206i	$-0.721149\pi$
$263$	−13.1446	+	3.52208i	−0.810530	+	0.217181i	−0.170328	+	0.985387i	$0.554483\pi$
$264$	9.25543	−	2.11932i	0.569632	−	0.130435i
$265$	−3.08805	−	0.827441i	−0.189697	−	0.0508293i
$266$	−0.549049	−	2.64201i	−0.0336643	−	0.161992i
$267$	−2.86183	−	21.2281i	−0.175141	−	1.29914i
$268$	13.5076	−	0.230962i	0.825109	−	0.0141082i
$269$	10.4025	−	4.30886i	0.634252	−	0.262716i	−0.0423066	−	0.999105i	$-0.513471\pi$
$269$	10.4025	−	4.30886i	0.634252	−	0.262716i	0.676558	+	0.736389i	$0.263471\pi$
$270$	−1.64366	+	1.94319i	−0.100030	+	0.118259i
$271$	7.69540			0.467462			0.233731	−	0.972301i	$-0.424906\pi$
$271$	7.69540			0.467462			0.233731	+	0.972301i	$0.424906\pi$
$272$	0.518782	−	2.23981i	0.0314558	−	0.135808i
$273$	−3.65150	+	2.12334i	−0.220999	+	0.128511i
$274$	29.7542	+	5.65450i	1.79752	+	0.341601i
$275$	−5.75783	+	7.50375i	−0.347210	+	0.452493i
$276$	−9.76527	−	2.40626i	−0.587800	−	0.144840i
$277$	14.2646	−	10.9456i	0.857079	−	0.657660i	−0.0837700	−	0.996485i	$-0.526696\pi$
$277$	14.2646	−	10.9456i	0.857079	−	0.657660i	0.940849	+	0.338825i	$0.110029\pi$
$278$	2.70300	+	0.891850i	0.162115	+	0.0534896i
$279$	−12.0238	−	11.8753i	−0.719845	−	0.710958i
$280$	−0.782269	−	1.10814i	−0.0467495	−	0.0662241i
$281$	−1.39007	−	5.18783i	−0.0829248	−	0.309480i	0.911988	−	0.410216i	$-0.134547\pi$
$281$	−1.39007	−	5.18783i	−0.0829248	−	0.309480i	−0.994913	+	0.100737i	$0.967880\pi$
$282$	11.9082	+	0.641228i	0.709121	+	0.0381846i
$283$	−2.38621	−	18.1250i	−0.141845	−	1.07742i	−0.903241	−	0.429134i	$-0.858819\pi$
$283$	−2.38621	−	18.1250i	−0.141845	−	1.07742i	0.761396	−	0.648288i	$-0.224515\pi$
$284$	1.62192	−	14.1905i	0.0962435	−	0.842051i
$285$	0.819924	+	0.105356i	0.0485681	+	0.00624073i
$286$	−2.09805	+	4.34774i	−0.124061	+	0.257087i
$287$	15.9001			0.938555
$288$	15.5695	+	6.75210i	0.917441	+	0.397871i
$289$	−16.6696			−0.980567
$290$	0.574962	−	1.19148i	0.0337629	−	0.0699660i
$291$	0.569311	+	1.36245i	0.0333736	+	0.0798685i
$292$	24.7263	+	2.82613i	1.44700	+	0.165387i
$293$	2.59169	+	19.6858i	0.151408	+	1.15006i	0.883358	+	0.468699i	$0.155277\pi$
$293$	2.59169	+	19.6858i	0.151408	+	1.15006i	−0.731950	+	0.681358i	$0.761390\pi$
$294$	−6.79577	+	10.4317i	−0.396337	+	0.608392i
$295$	0.508669	+	1.89838i	0.0296159	+	0.110528i
$296$	6.10257	+	1.05197i	0.354705	+	0.0611446i
$297$	−9.70307	+	2.69707i	−0.563029	+	0.156500i
$298$	−10.4624	−	3.45204i	−0.606069	−	0.199971i
$299$	4.05675	−	3.11286i	0.234608	−	0.180021i
$300$	−16.2372	+	4.70430i	−0.937457	+	0.271603i
$301$	−6.26013	+	8.15836i	−0.360828	+	0.470240i
$302$	−29.8408	−	5.67096i	−1.71714	−	0.326327i
$303$	−0.0918780	−	29.5847i	−0.00527825	−	1.69960i
$304$	−0.905885	−	5.43716i	−0.0519561	−	0.311842i
$305$	1.71277			0.0980729
$306$	−0.440390	+	2.39847i	−0.0251754	+	0.137111i
$307$	−3.32430	+	1.37697i	−0.189728	+	0.0785879i	−0.475525	−	0.879702i	$-0.657742\pi$
$307$	−3.32430	+	1.37697i	−0.189728	+	0.0785879i	0.285797	+	0.958290i	$0.407742\pi$
$308$	−0.0917612	−	5.36658i	−0.00522858	−	0.305789i
$309$	9.51650	−	7.34934i	0.541375	−	0.418089i
$310$	0.561403	+	2.70146i	0.0318856	+	0.153433i
$311$	24.9435	+	6.68359i	1.41442	+	0.378992i	0.883499	−	0.468433i	$-0.155181\pi$
$311$	24.9435	+	6.68359i	1.41442	+	0.378992i	0.530916	+	0.847424i	$0.321848\pi$
$312$	−7.62556	+	4.03707i	−0.431712	+	0.228554i
$313$	16.3338	−	4.37664i	0.923243	−	0.247382i	0.234272	−	0.972171i	$-0.424729\pi$
$313$	16.3338	−	4.37664i	0.923243	−	0.247382i	0.688971	+	0.724789i	$0.258063\pi$
$314$	−10.3094	−	20.4626i	−0.581794	−	1.15477i
$315$	0.882909	+	1.13595i	0.0497463	+	0.0640036i
$316$	−26.0171	+	3.87880i	−1.46357	+	0.218199i
$317$	−9.22696	−	1.21475i	−0.518238	−	0.0682273i	−0.133129	−	0.991099i	$-0.542503\pi$
$317$	−9.22696	−	1.21475i	−0.518238	−	0.0682273i	−0.385108	+	0.922871i	$0.625836\pi$
$318$	−1.74161	−	22.5431i	−0.0976646	−	1.26415i
$319$	4.53353	−	2.61743i	0.253829	−	0.146548i
$320$	−1.50659	−	2.32538i	−0.0842208	−	0.129993i
$321$	−1.88053	+	1.09353i	−0.104961	+	0.0610347i
$322$	−2.47086	+	5.12028i	−0.137695	+	0.285342i
$323$	0.731765	−	0.303107i	0.0407165	−	0.0168653i
$324$	−16.8259	−	6.39447i	−0.934772	−	0.355248i
$325$	3.28913	−	7.94067i	0.182448	−	0.440469i
$326$	−1.14119	+	20.0339i	−0.0632047	+	1.10958i
$327$	13.7893	+	3.64897i	0.762550	+	0.201789i
$328$	32.4533	+	1.29247i	1.79193	+	0.0713645i
$329$	1.74477	−	6.51156i	0.0961922	−	0.358994i
$330$	1.56307	+	0.510354i	0.0860441	+	0.0280941i
$331$	−11.0885	−	14.4509i	−0.609481	−	0.794291i	0.382053	−	0.924140i	$-0.375217\pi$
$331$	−11.0885	−	14.4509i	−0.609481	−	0.794291i	−0.991534	+	0.129850i	$0.958550\pi$
$332$	−11.7660	−	19.5978i	−0.645745	−	1.07557i
$333$	−6.51722	−	0.816861i	−0.357142	−	0.0447637i
$334$	13.6448	−	15.8299i	0.746612	−	0.866173i
$335$	2.02607	+	1.16975i	0.110696	+	0.0639103i
$336$	5.55210	−	7.82329i	0.302892	−	0.426796i
$337$	9.71791	−	5.61064i	0.529369	−	0.305631i	−0.211391	−	0.977402i	$-0.567799\pi$
$337$	9.71791	−	5.61064i	0.529369	−	0.305631i	0.740759	+	0.671771i	$0.234466\pi$
$338$	−2.61340	+	13.7518i	−0.142150	+	0.748000i
$339$	−3.31054	−	0.425386i	−0.179804	−	0.0231038i
$340$	0.276676	−	0.286302i	0.0150048	−	0.0155269i
$341$	−4.17813	+	10.0869i	−0.226258	+	0.546236i
$342$	1.22510	+	5.71668i	0.0662456	+	0.309122i
$343$	11.8302	+	11.8302i	0.638772	+	0.638772i
$344$	−13.4405	+	16.1429i	−0.724664	+	0.870367i
$345$	−1.23536	−	1.22771i	−0.0665098	−	0.0660979i
$346$	1.60938	−	2.45376i	0.0865208	−	0.131915i
$347$	−7.14581	+	0.940763i	−0.383607	+	0.0505028i	−0.319864	−	0.947464i	$-0.603637\pi$
$347$	−7.14581	+	0.940763i	−0.383607	+	0.0505028i	−0.0637431	+	0.997966i	$0.520304\pi$
$348$	9.29912	+	1.03361i	0.498485	+	0.0554074i
$349$	1.22262	−	9.28675i	0.0654456	−	0.497109i	−0.927060	−	0.374912i	$-0.877673\pi$
$349$	1.22262	−	9.28675i	0.0654456	−	0.497109i	0.992506	−	0.122196i	$-0.0389938\pi$
$350$	0.706493	+	9.52998i	0.0377636	+	0.509399i
$351$	7.88260	−	4.64947i	0.420742	−	0.248171i
$352$	0.248940	−	10.9610i	0.0132685	−	0.584224i
$353$	3.03528	+	1.75242i	0.161552	+	0.0932720i	0.578596	−	0.815614i	$-0.303601\pi$
$353$	3.03528	+	1.75242i	0.161552	+	0.0932720i	−0.417044	+	0.908886i	$0.636934\pi$
$354$	−11.4664	+	7.85639i	−0.609430	+	0.417562i
$355$	1.50572	−	1.96229i	0.0799153	−	0.104148i
$356$	−24.5739	−	2.80871i	−1.30241	−	0.148861i
$357$	1.27519	+	0.523566i	0.0674901	+	0.0277101i
$358$	0.147165	−	2.58352i	0.00777789	−	0.136543i
$359$	1.61533	+	1.61533i	0.0852541	+	0.0852541i	0.748448	−	0.663194i	$-0.230799\pi$
$359$	1.61533	+	1.61533i	0.0852541	+	0.0852541i	−0.663194	+	0.748448i	$0.730799\pi$
$360$	1.70974	+	2.39032i	0.0901112	+	0.125981i
$361$	−12.0923	+	12.0923i	−0.636435	+	0.636435i
$362$	20.1508	+	22.5852i	1.05911	+	1.18705i
$363$	−7.66853	−	9.92982i	−0.402494	−	0.521180i
$364$	1.34273	+	4.68897i	0.0703784	+	0.245769i
$365$	3.41921	+	2.62365i	0.178970	+	0.137328i
$366$	4.02711	+	11.4243i	0.210501	+	0.597159i
$367$	4.17945	−	7.23901i	0.218165	−	0.377873i	−0.736082	−	0.676893i	$-0.763326\pi$
$367$	4.17945	−	7.23901i	0.218165	−	0.377873i	0.954247	+	0.299019i	$0.0966595\pi$
$368$	−5.45939	+	10.2500i	−0.284591	+	0.534318i
$369$	−34.4485	+	0.213968i	−1.79332	+	0.0111387i
$370$	0.812280	+	0.700157i	0.0422284	+	0.0363994i
$371$	−12.6719	−	1.66829i	−0.657892	−	0.0866131i
$372$	−16.6990	+	10.0964i	−0.865803	+	0.523472i
$373$	3.43521	+	26.0930i	0.177869	+	1.35105i	0.814628	+	0.579984i	$0.196941\pi$
$373$	3.43521	+	26.0930i	0.177869	+	1.35105i	−0.636759	+	0.771063i	$0.719725\pi$
$374$	1.54248	−	0.320550i	0.0797599	−	0.0165753i
$375$	−5.72972	−	1.51622i	−0.295882	−	0.0782972i
$376$	4.09049	−	13.1487i	0.210951	−	0.678093i
$377$	−3.36373	+	3.36373i	−0.173241	+	0.173241i
$378$	−5.50097	+	8.55996i	−0.282939	+	0.440277i
$379$	−3.63491	−	1.50563i	−0.186713	−	0.0773389i	0.287368	−	0.957820i	$-0.407220\pi$
$379$	−3.63491	−	1.50563i	−0.186713	−	0.0773389i	−0.474081	+	0.880481i	$0.657220\pi$
$380$	0.350160	−	0.888006i	0.0179628	−	0.0455537i
$381$	22.8695	+	17.4358i	1.17164	+	0.893263i
$382$	3.36357	−	2.28930i	0.172095	−	0.117131i
$383$	17.3414	+	30.0361i	0.886102	+	1.53477i	0.844445	+	0.535642i	$0.179930\pi$
$383$	17.3414	+	30.0361i	0.886102	+	1.53477i	0.0416575	+	0.999132i	$0.486736\pi$
$384$	11.9681	−	15.5166i	0.610747	−	0.791826i
$385$	0.464743	−	0.804958i	0.0236855	−	0.0410245i
$386$	0.258600	+	3.48829i	0.0131624	+	0.177549i
$387$	13.4531	−	17.7598i	0.683861	−	0.902780i
$388$	1.68641	−	0.251422i	0.0856146	−	0.0127640i
$389$	−11.7666	+	9.02885i	−0.596592	+	0.457781i	−0.862388	−	0.506248i	$-0.831032\pi$
$389$	−11.7666	+	9.02885i	−0.596592	+	0.457781i	0.265796	+	0.964029i	$0.414365\pi$
$390$	−1.49203	−	0.0803422i	−0.0755517	−	0.00406829i
$391$	−1.61189	−	0.431905i	−0.0815169	−	0.0218424i
$392$	9.75285	+	10.5619i	0.492593	+	0.533456i
$393$	22.9001	−	6.21236i	1.15516	−	0.313372i
$394$	19.9573	+	22.3683i	1.00544	+	1.12690i
$395$	−4.20851	−	1.74322i	−0.211753	−	0.0877110i
$396$	0.271023	+	11.6258i	0.0136194	+	0.584216i
$397$	−11.9115	−	28.7569i	−0.597821	−	1.44327i	−0.875797	−	0.482679i	$-0.839664\pi$
$397$	−11.9115	−	28.7569i	−0.597821	−	1.44327i	0.277976	−	0.960588i	$-0.410336\pi$
$398$	−33.7154	+	11.7672i	−1.69000	+	0.589837i
$399$	3.30491	−	0.0102637i	0.165452	−	0.000513827i
$400$	0.667341	+	19.5088i	0.0333670	+	0.975438i
$401$	14.6435	+	25.3633i	0.731263	+	1.26658i	0.956344	+	0.292245i	$0.0944022\pi$
$401$	14.6435	+	25.3633i	0.731263	+	1.26658i	−0.225080	+	0.974340i	$0.572264\pi$
$402$	−3.03859	+	16.2644i	−0.151551	+	0.811194i
$403$	1.29500	−	9.83651i	0.0645086	−	0.489991i
$404$	−33.1440	−	8.27627i	−1.64898	−	0.411760i
$405$	−1.92816	−	2.44922i	−0.0958108	−	0.121703i
$406$	1.65723	−	5.02269i	0.0822469	−	0.249272i
$407$	1.09827	+	4.09881i	0.0544394	+	0.203171i
$408$	2.56019	+	1.17229i	0.126748	+	0.0580370i
$409$	−8.46074	+	31.5759i	−0.418356	+	1.56133i	0.359660	+	0.933083i	$0.382893\pi$
$409$	−8.46074	+	31.5759i	−0.418356	+	1.56133i	−0.778016	+	0.628244i	$0.783774\pi$
$410$	4.70314	+	3.08471i	0.232271	+	0.152343i
$411$	−14.0886	+	34.3138i	−0.694938	+	1.69258i
$412$	−5.53174	−	12.7345i	−0.272529	−	0.627386i
$413$	3.00685	+	7.25917i	0.147957	+	0.357200i
$414$	5.28434	−	11.1266i	0.259711	−	0.546843i
$415$		−	3.95849i		−	0.194315i
$416$	2.35946	+	9.67966i	0.115682	+	0.474584i
$417$	−1.73363	+	3.02439i	−0.0848963	+	0.148105i
$418$	3.12251	−	2.12522i	0.152727	−	0.103948i
$419$	−26.9905	−	20.7105i	−1.31857	−	1.01178i	−0.997912	−	0.0645817i	$-0.979429\pi$
$419$	−26.9905	−	20.7105i	−1.31857	−	1.01178i	−0.320660	−	0.947194i	$-0.603905\pi$
$420$	1.52168	−	0.666624i	0.0742502	−	0.0325279i
$421$	−8.36658	−	10.9035i	−0.407762	−	0.531406i	0.543656	−	0.839308i	$-0.317040\pi$
$421$	−8.36658	−	10.9035i	−0.407762	−	0.531406i	−0.951418	+	0.307902i	$0.900373\pi$
$422$	−2.89357	−	5.74329i	−0.140857	−	0.279579i
$423$	−3.69251	+	14.1311i	−0.179536	+	0.687079i
$424$	−25.7286	−	4.43514i	−1.24949	−	0.215389i
$425$	−2.70936	+	0.725970i	−0.131423	+	0.0352147i
$426$	16.6289	+	5.42948i	0.805675	+	0.263059i
$427$	6.78891	−	0.893777i	0.328538	−	0.0432529i
$428$	0.691511	+	2.41483i	0.0334254	+	0.116725i
$429$	−4.70181	−	3.58468i	−0.227006	−	0.173070i
$430$	−3.43447	+	1.19868i	−0.165625	+	0.0578056i
$431$			15.3879i			0.741209i	0.928791	+	0.370605i	$0.120849\pi$
$431$			15.3879i			0.741209i	−0.928791	+	0.370605i	$0.879151\pi$
$432$	−11.9236	+	17.0243i	−0.573677	+	0.819082i
$433$		−	10.2006i		−	0.490209i	−0.969497	−	0.245105i	$-0.921178\pi$
$433$		−	10.2006i		−	0.490209i	0.969497	−	0.245105i	$-0.0788223\pi$
$434$	3.63494	+	10.4148i	0.174483	+	0.499928i
$435$	1.28851	+	0.982366i	0.0617793	+	0.0471008i
$436$	7.99022	−	14.4026i	0.382662	−	0.689761i
$437$	−3.96661	+	0.522215i	−0.189749	+	0.0249809i
$438$	−9.46064	+	28.9752i	−0.452047	+	1.38449i
$439$	−9.53888	+	2.55594i	−0.455266	+	0.121988i	−0.479162	−	0.877726i	$-0.659059\pi$
$439$	−9.53888	+	2.55594i	−0.455266	+	0.121988i	0.0238964	+	0.999714i	$0.492393\pi$
$440$	1.01400	−	1.60520i	0.0483407	−	0.0765247i
$441$	−10.8488	−	10.7149i	−0.516611	−	0.510233i
$442$	−1.27853	+	0.644148i	−0.0608136	+	0.0306390i
$443$	10.3166	+	13.4449i	0.490157	+	0.638786i	0.971300	−	0.237857i	$-0.0764448\pi$
$443$	10.3166	+	13.4449i	0.490157	+	0.638786i	−0.481143	+	0.876642i	$0.659778\pi$
$444$	−2.76025	+	7.06420i	−0.130996	+	0.335252i
$445$	−3.39813	−	2.60748i	−0.161087	−	0.123606i
$446$	−17.0725	−	25.0839i	−0.808405	−	1.18776i
$447$	6.71028	−	11.7064i	0.317385	−	0.553692i
$448$	−7.18512	−	8.43092i	−0.339465	−	0.398324i
$449$		−	15.4753i		−	0.730324i	−0.930944	−	0.365162i	$-0.881014\pi$
$449$		−	15.4753i		−	0.730324i	0.930944	−	0.365162i	$-0.118986\pi$
$450$	−1.65890	−	20.6377i	−0.0782012	−	0.972871i
$451$	8.51697	+	20.5618i	0.401048	+	0.968216i
$452$	−1.41382	+	3.58543i	−0.0665003	+	0.168645i
$453$	14.1296	−	34.4137i	0.663866	−	1.61690i
$454$	13.5933	−	20.7252i	0.637966	−	0.972682i
$455$	−0.218610	+	0.815862i	−0.0102486	+	0.0382482i
$456$	6.74638	+	0.247696i	0.315928	+	0.0115994i
$457$	9.95193	+	37.1411i	0.465532	+	1.73739i	0.655120	+	0.755525i	$0.272618\pi$
$457$	9.95193	+	37.1411i	0.465532	+	1.73739i	−0.189588	+	0.981864i	$0.560715\pi$
$458$	−23.5054	−	7.75555i	−1.09833	−	0.362393i
$459$	−2.76981	−	1.11717i	−0.129284	−	0.0521452i
$460$	−1.72422	+	1.03518i	−0.0803923	+	0.0482656i
$461$	−2.92643	+	22.2284i	−0.136297	+	1.03528i	0.777434	+	0.628964i	$0.216521\pi$
$461$	−2.92643	+	22.2284i	−0.136297	+	1.03528i	−0.913732	+	0.406318i	$0.866813\pi$
$462$	6.46185	+	1.20723i	0.300633	+	0.0561656i
$463$	10.3861	+	17.9892i	0.482682	+	0.836030i	0.999802	−	0.0198831i	$-0.00632939\pi$
$463$	10.3861	+	17.9892i	0.482682	+	0.836030i	−0.517120	+	0.855913i	$0.672996\pi$
$464$	3.79079	−	10.1169i	0.175983	−	0.469667i
$465$	−3.37928	+	0.0104946i	−0.156710	+	0.000486677i
$466$	0.903563	+	2.58889i	0.0418568	+	0.119928i
$467$	5.06780	+	12.2348i	0.234510	+	0.566157i	0.996698	−	0.0811986i	$-0.0258748\pi$
$467$	5.06780	+	12.2348i	0.234510	+	0.566157i	−0.762188	+	0.647356i	$0.775875\pi$
$468$	−2.97220	−	10.1408i	−0.137390	−	0.468761i
$469$	8.64114	+	3.57928i	0.399011	+	0.165276i
$470$	1.77937	−	1.58758i	0.0820760	−	0.0732294i
$471$	27.0836	−	7.34725i	1.24795	−	0.338543i
$472$	5.54711	+	15.0609i	0.255326	+	0.693233i
$473$	−13.9035	−	3.72544i	−0.639284	−	0.171296i
$474$	1.73227	−	32.1698i	0.0795660	−	1.47761i
$475$	−5.33517	+	4.09382i	−0.244794	+	0.187837i
$476$	0.947259	−	1.27919i	0.0434175	−	0.0586317i
$477$	27.4768	+	3.44391i	1.25808	+	0.157686i
$478$	26.0893	−	1.93409i	1.19330	−	0.0884634i
$479$	−10.2347	+	17.7270i	−0.467635	+	0.809968i	−0.999316	−	0.0369770i	$-0.988227\pi$
$479$	−10.2347	+	17.7270i	−0.467635	+	0.809968i	0.531681	+	0.846945i	$0.321560\pi$
$480$	3.16003	−	1.23693i	0.144235	−	0.0564580i
$481$	−1.92803	−	3.33945i	−0.0879108	−	0.152266i
$482$	8.19050	+	12.0340i	0.373067	+	0.548133i
$483$	−5.53727	−	4.22164i	−0.251955	−	0.192091i
$484$	−13.2876	+	5.77200i	−0.603983	+	0.262363i
$485$	0.272793	+	0.112995i	0.0123869	+	0.00513082i
$486$	11.8029	−	18.6196i	0.535392	−	0.844603i
$487$	−24.3007	+	24.3007i	−1.10117	+	1.10117i	−0.106899	+	0.994270i	$0.534092\pi$
$487$	−24.3007	+	24.3007i	−1.10117	+	1.10117i	−0.994270	+	0.106899i	$0.965908\pi$
$488$	13.9293	−	1.27241i	0.630548	−	0.0575994i
$489$	−23.7585	−	6.28705i	−1.07440	−	0.284310i
$490$	0.506543	+	2.43748i	0.0228833	+	0.110114i
$491$	0.463090	+	3.51752i	0.0208990	+	0.158743i	0.998712	−	0.0507356i	$-0.0161566\pi$
$491$	0.463090	+	3.51752i	0.0208990	+	0.158743i	−0.977813	+	0.209479i	$0.932823\pi$
$492$	−9.51713	+	38.6232i	−0.429065	+	1.74127i
$493$	1.53916	+	0.202635i	0.0693204	+	0.00912621i
$494$	−2.24096	+	2.59983i	−0.100826	+	0.116972i
$495$	−0.996058	+	1.75024i	−0.0447695	+	0.0786674i
$496$	6.57258	+	21.5529i	0.295117	+	0.967752i
$497$	4.94424	−	8.56367i	0.221779	−	0.384133i
$498$	26.4035	−	9.30732i	1.18317	−	0.417071i
$499$	18.4485	+	14.1560i	0.825867	+	0.633710i	0.932735	−	0.360564i	$-0.117416\pi$
$499$	18.4485	+	14.1560i	0.825867	+	0.633710i	−0.106868	+	0.994273i	$0.534082\pi$
$500$	−3.32009	+	5.98458i	−0.148479	+	0.267638i
$501$	15.6448	+	20.2581i	0.698957	+	0.905065i
$502$	20.5822	−	18.3637i	0.918629	−	0.819614i
$503$	−12.0479	+	12.0479i	−0.537191	+	0.537191i	−0.922703	−	0.385512i	$-0.874025\pi$
$503$	−12.0479	+	12.0479i	−0.537191	+	0.537191i	0.385512	+	0.922703i	$0.374025\pi$
$504$	8.02424	+	8.58232i	0.357428	+	0.382287i
$505$	−4.18317	−	4.18317i	−0.186149	−	0.186149i
$506$	−7.94498	−	0.452569i	−0.353198	−	0.0201191i
$507$	−15.8592	−	6.51147i	−0.704332	−	0.289184i
$508$	25.9953	−	20.6625i	1.15336	−	0.916749i
$509$	21.9860	−	28.6527i	0.974513	−	1.27001i	0.0116744	−	0.999932i	$-0.496284\pi$
$509$	21.9860	−	28.6527i	0.974513	−	1.27001i	0.962838	−	0.270078i	$-0.0870495\pi$
$510$	0.275616	+	0.402260i	0.0122045	+	0.0178124i
$511$	14.9218	+	8.61512i	0.660103	+	0.381111i
$512$	−13.9800	−	17.7921i	−0.617834	−	0.786309i
$513$	−7.16013	+	0.0667109i	−0.316127	+	0.00294536i
$514$	9.65129	−	0.715486i	0.425700	−	0.0315587i
$515$	0.313832	−	2.38379i	0.0138291	−	0.105042i
$516$	−16.0705	−	20.0898i	−0.707465	−	0.884404i
$517$	9.35523	−	1.23164i	0.411442	−	0.0541674i
$518$	3.58500	+	2.35134i	0.157516	+	0.103312i
$519$	2.54919	+	2.53341i	0.111897	+	0.111204i
$520$	−0.512515	+	1.64746i	−0.0224753	+	0.0722459i
$521$	−13.4588	−	13.4588i	−0.589643	−	0.589643i	0.347892	−	0.937535i	$-0.386898\pi$
$521$	−13.4588	−	13.4588i	−0.589643	−	0.589643i	−0.937535	+	0.347892i	$0.886898\pi$
$522$	−3.52288	+	10.9042i	−0.154192	+	0.477265i
$523$	2.77801	−	6.70671i	0.121474	−	0.293264i	−0.851432	−	0.524465i	$-0.824265\pi$
$523$	2.77801	−	6.70671i	0.121474	−	0.293264i	0.972906	+	0.231201i	$0.0742655\pi$
$524$	−0.468409	−	27.3945i	−0.0204625	−	1.19674i
$525$	−11.6084	−	1.49161i	−0.506632	−	0.0650993i
$526$	−18.9066	−	3.59303i	−0.824369	−	0.156663i
$527$	−2.80403	+	1.61891i	−0.122146	+	0.0705208i
$528$	13.0909	+	2.98931i	0.569710	+	0.130093i
$529$	−12.6187	−	7.28539i	−0.548638	−	0.316756i
$530$	−3.42459	−	2.95188i	−0.148755	−	0.128221i
$531$	−6.61218	−	15.6869i	−0.286944	−	0.680754i
$532$	0.924542	−	3.70251i	0.0400840	−	0.160524i
$533$	−12.3118	−	16.0451i	−0.533285	−	0.694990i
$534$	9.40231	−	28.7966i	0.406878	−	1.24615i
$535$	−0.112584	+	0.420171i	−0.00486745	+	0.0181656i
$536$	17.3462	+	8.00795i	0.749242	+	0.345891i
$537$	3.06382	+	0.810759i	0.132214	+	0.0349868i
$538$	15.8977	+	0.905578i	0.685398	+	0.0390422i
$539$	−3.76984	+	9.10120i	−0.162379	+	0.392017i
$540$	−3.28782	+	1.46475i	−0.141485	+	0.0630329i
$541$	−25.2984	+	10.4790i	−1.08767	+	0.450526i	−0.853192	−	0.521597i	$-0.825337\pi$
$541$	−25.2984	+	10.4790i	−1.08767	+	0.450526i	−0.234473	+	0.972123i	$0.575337\pi$
$542$	9.80140	+	4.72979i	0.421006	+	0.203162i
$543$	−32.0463	+	18.6349i	−1.37524	+	0.799699i
$544$	2.03740	−	2.53392i	0.0873528	−	0.108641i
$545$	2.47013	−	1.42613i	0.105809	−	0.0610888i
$546$	−5.95587	+	0.460133i	−0.254888	+	0.0196919i
$547$	−8.53332	−	1.12343i	−0.364858	−	0.0480345i	−0.0541317	−	0.998534i	$-0.517239\pi$
$547$	−8.53332	−	1.12343i	−0.364858	−	0.0480345i	−0.310727	+	0.950499i	$0.600572\pi$
$548$	34.4216	+	25.4896i	1.47042	+	1.08886i
$549$	−14.6965	+	2.02777i	−0.627231	+	0.0865432i
$550$	−11.9456	+	6.01839i	−0.509361	+	0.256625i
$551$	3.59517	−	0.963322i	0.153159	−	0.0410389i
$552$	−10.9588	−	9.06676i	−0.466437	−	0.385907i
$553$	−17.5909	−	4.71348i	−0.748043	−	0.200438i
$554$	24.8959	−	5.17373i	1.05773	−	0.219811i
$555$	−1.03950	+	0.802781i	−0.0441245	+	0.0340762i
$556$	2.89458	+	2.79726i	0.122757	+	0.118630i
$557$	12.9331	−	5.35706i	0.547993	−	0.226986i	−0.0914705	−	0.995808i	$-0.529157\pi$
$557$	12.9331	−	5.35706i	0.547993	−	0.226986i	0.639463	+	0.768822i	$0.279157\pi$
$558$	−8.01545	−	22.5154i	−0.339321	−	0.953152i
$559$	13.0801			0.553229
$560$	−0.315261	−	1.89221i	−0.0133222	−	0.0799604i
$561$	0.00599223	+	1.92950i	0.000252992	+	0.0814636i
$562$	1.41807	−	7.46195i	0.0598178	−	0.314763i
$563$	−24.2298	+	31.5768i	−1.02116	+	1.33080i	−0.0785518	+	0.996910i	$0.525030\pi$
$563$	−24.2298	+	31.5768i	−1.02116	+	1.33080i	−0.942610	+	0.333895i	$0.891637\pi$
$564$	14.7730	+	8.13577i	0.622054	+	0.342578i
$565$	−0.529508	+	0.406306i	−0.0222766	+	0.0170934i
$566$	8.10087	−	24.5519i	0.340505	−	1.03200i
$567$	−8.92071	−	8.70179i	−0.374635	−	0.365441i
$568$	10.7876	−	17.0771i	0.452639	−	0.716540i
$569$	−5.63454	−	21.0284i	−0.236212	−	0.881555i	−0.977599	−	0.210477i	$-0.932498\pi$
$569$	−5.63454	−	21.0284i	−0.236212	−	0.881555i	0.741387	−	0.671078i	$-0.234168\pi$
$570$	0.979558	+	0.638134i	0.0410292	+	0.0267285i
$571$	−4.98912	−	37.8961i	−0.208788	−	1.58590i	−0.699533	−	0.714600i	$-0.746609\pi$
$571$	−4.98912	−	37.8961i	−0.208788	−	1.58590i	0.490745	−	0.871303i	$-0.336725\pi$
$572$	−5.34446	+	4.24806i	−0.223463	+	0.177620i
$573$	1.92126	+	4.59788i	0.0802616	+	0.192079i
$574$	20.2515	+	9.77263i	0.845283	+	0.407902i
$575$	14.1683			0.590858
$576$	15.6804	+	18.1694i	0.653350	+	0.757056i
$577$	−20.9424			−0.871843			−0.435921	−	0.899985i	$-0.643577\pi$
$577$	−20.9424			−0.871843			−0.435921	+	0.899985i	$0.643577\pi$
$578$	−21.2316	−	10.2456i	−0.883119	−	0.426160i
$579$	−4.24905	−	0.545979i	−0.176585	−	0.0226901i
$580$	1.46462	−	1.16416i	0.0608152	−	0.0483392i
$581$	−2.06567	−	15.6903i	−0.0856982	−	0.650943i
$582$	−0.112285	+	2.08523i	−0.00465436	+	0.0864356i
$583$	−4.63035	−	17.2807i	−0.191769	−	0.715693i
$584$	29.7562	+	18.7970i	1.23132	+	0.777825i
$585$	0.462650	−	1.77055i	0.0191282	−	0.0732033i
$586$	−8.79845	+	26.6662i	−0.363460	+	1.10157i
$587$	3.70294	−	2.84136i	0.152837	−	0.117276i	−0.529512	−	0.848302i	$-0.677625\pi$
$587$	3.70294	−	2.84136i	0.152837	−	0.117276i	0.682349	+	0.731027i	$0.260958\pi$
$588$	−15.0672	+	9.10975i	−0.621360	+	0.375680i
$589$	−4.72562	+	6.15855i	−0.194716	+	0.253759i
$590$	−0.518915	+	2.73055i	−0.0213634	+	0.112415i
$591$	−31.7385	+	18.4559i	−1.30555	+	0.759175i
$592$	7.12609	+	5.09066i	0.292881	+	0.209225i
$593$	6.68985			0.274719			0.137360	−	0.990521i	$-0.456138\pi$
$593$	6.68985			0.274719			0.137360	+	0.990521i	$0.456138\pi$
$594$	−14.0162	−	2.52858i	−0.575091	−	0.103749i
$595$	0.254665	−	0.105486i	0.0104402	−	0.00432448i
$596$	−11.2039	−	10.8272i	−0.458930	−	0.443499i
$597$	−5.84326	−	43.3434i	−0.239149	−	1.77393i
$598$	7.08020	−	1.47137i	0.289531	−	0.0601687i
$599$	16.8748	+	4.52158i	0.689484	+	0.184747i	0.586516	−	0.809938i	$-0.300499\pi$
$599$	16.8748	+	4.52158i	0.689484	+	0.184747i	0.102969	+	0.994685i	$0.467166\pi$
$600$	−23.5723	−	3.98809i	−0.962333	−	0.162813i
$601$	−7.02342	+	1.88192i	−0.286491	+	0.0767651i	−0.399203	−	0.916863i	$-0.630713\pi$
$601$	−7.02342	+	1.88192i	−0.286491	+	0.0767651i	0.112712	+	0.993628i	$0.464046\pi$
$602$	−12.9877	+	6.54343i	−0.529338	+	0.266690i
$603$	−18.7697	−	7.63841i	−0.764359	−	0.311060i
$604$	−34.5218	−	25.5638i	−1.40467	−	1.04018i
$605$	−2.48732	−	0.327462i	−0.101124	−	0.0133132i
$606$	18.0665	−	37.7377i	0.733902	−	1.53299i
$607$	−5.59768	+	3.23182i	−0.227203	+	0.131176i	−0.609281	−	0.792954i	$-0.708542\pi$
$607$	−5.59768	+	3.23182i	−0.227203	+	0.131176i	0.382078	+	0.924130i	$0.375209\pi$
$608$	2.18802	−	7.48193i	0.0887358	−	0.303432i
$609$	5.61990	+	3.22142i	0.227730	+	0.130539i
$610$	2.18150	+	1.05271i	0.0883265	+	0.0426231i
$611$	−7.92194	+	3.28137i	−0.320487	+	0.132750i
$612$	−2.03507	+	2.78419i	−0.0822629	+	0.112544i
$613$	13.5163	−	32.6313i	0.545920	−	1.31797i	−0.374570	−	0.927199i	$-0.622209\pi$
$613$	13.5163	−	32.6313i	0.545920	−	1.31797i	0.920489	−	0.390768i	$-0.127791\pi$
$614$	−5.08038	−	0.289393i	−0.205028	−	0.0116790i
$615$	−4.85581	+	4.88606i	−0.195805	+	0.197025i
$616$	3.18156	−	6.89166i	0.128189	−	0.277673i
$617$	1.49686	−	5.58635i	0.0602613	−	0.224898i	−0.929227	−	0.369508i	$-0.879526\pi$
$617$	1.49686	−	5.58635i	0.0602613	−	0.224898i	0.989489	+	0.144610i	$0.0461928\pi$
$618$	16.6380	−	3.51155i	0.669278	−	0.141255i
$619$	22.4216	+	29.2204i	0.901201	+	1.17447i	0.984048	+	0.177905i	$0.0569321\pi$
$619$	22.4216	+	29.2204i	0.901201	+	1.17447i	−0.0828470	+	0.996562i	$0.526401\pi$
$620$	−0.945346	+	3.78583i	−0.0379660	+	0.152042i
$621$	12.0536	+	9.07190i	0.483695	+	0.364043i
$622$	27.6619	+	23.8436i	1.10914	+	0.956041i
$623$	−14.8298	−	8.56200i	−0.594144	−	0.343029i
$624$	−12.1937	+	0.455031i	−0.488140	+	0.0182158i
$625$	20.1048	−	11.6075i	0.804193	−	0.464301i
$626$	23.4939	+	4.46480i	0.939006	+	0.178449i
$627$	1.78356	+	4.26835i	0.0712285	+	0.170462i
$628$	−0.553978	−	32.3990i	−0.0221061	−	1.29286i
$629$	−0.481575	+	1.16263i	−0.0192017	+	0.0463569i
$630$	0.426351	+	1.98948i	0.0169862	+	0.0792630i
$631$	17.9530	+	17.9530i	0.714696	+	0.714696i	0.967514	−	0.252818i	$-0.0813573\pi$
$631$	17.9530	+	17.9530i	0.714696	+	0.714696i	−0.252818	+	0.967514i	$0.581357\pi$
$632$	−35.5212	−	11.0504i	−1.41296	−	0.439563i
$633$	7.60162	−	2.06217i	0.302137	−	0.0819640i
$634$	−11.0055	−	7.21832i	−0.437084	−	0.286676i
$635$	5.70134	−	0.750596i	0.226251	−	0.0297865i
$636$	11.6373	−	29.7829i	0.461449	−	1.18097i
$637$	1.16845	−	8.87529i	0.0462958	−	0.351652i
$638$	7.38296	−	0.547326i	0.292294	−	0.0216688i
$639$	−10.5967	+	18.6202i	−0.419199	+	0.736603i
$640$	−0.489658	−	3.88775i	−0.0193554	−	0.153677i
$641$	−0.777343	−	0.448799i	−0.0307032	−	0.0177265i	0.484570	−	0.874753i	$-0.338976\pi$
$641$	−0.777343	−	0.448799i	−0.0307032	−	0.0177265i	−0.515273	+	0.857026i	$0.672309\pi$
$642$	−3.06729	+	0.236970i	−0.121056	+	0.00935244i
$643$	−3.03354	+	3.95338i	−0.119631	+	0.155906i	−0.849330	−	0.527863i	$-0.822994\pi$
$643$	−3.03354	+	3.95338i	−0.119631	+	0.155906i	0.729699	+	0.683769i	$0.239660\pi$
$644$	−6.29411	+	5.00290i	−0.248023	+	0.197142i
$645$	−0.595232	−	4.41523i	−0.0234372	−	0.173850i
$646$	1.11832	+	0.0637029i	0.0439999	+	0.00250636i
$647$	−1.28302	−	1.28302i	−0.0504409	−	0.0504409i	0.681436	−	0.731877i	$-0.261356\pi$
$647$	−1.28302	−	1.28302i	−0.0504409	−	0.0504409i	−0.731877	+	0.681436i	$0.761356\pi$
$648$	−17.5004	−	18.4861i	−0.687482	−	0.726201i
$649$	−7.77680	+	7.77680i	−0.305266	+	0.305266i
$650$	9.06981	−	8.09221i	0.355747	−	0.317403i
$651$	−13.3890	+	1.80501i	−0.524755	+	0.0707439i
$652$	−13.7669	+	24.8152i	−0.539152	+	0.971840i
$653$	−6.65434	−	5.10605i	−0.260404	−	0.199815i	0.470305	−	0.882504i	$-0.344144\pi$
$653$	−6.65434	−	5.10605i	−0.260404	−	0.199815i	−0.730709	+	0.682689i	$0.760811\pi$
$654$	15.3203	+	13.1228i	0.599070	+	0.513143i
$655$	2.37235	−	4.10903i	0.0926953	−	0.160553i
$656$	40.5404	+	21.5928i	1.58284	+	0.843056i
$657$	−32.4449	−	18.4643i	−1.26580	−	0.720362i
$658$	6.22443	−	7.22120i	0.242654	−	0.281512i
$659$	35.1818	+	4.63178i	1.37049	+	0.180428i	0.779577	−	0.626307i	$-0.215434\pi$
$659$	35.1818	+	4.63178i	1.37049	+	0.180428i	0.590913	+	0.806735i	$0.298768\pi$
$660$	1.67716	+	1.61072i	0.0652832	+	0.0626974i
$661$	−0.00813271	−	0.0617740i	−0.000316326	−	0.00240273i	0.991286	−	0.131727i	$-0.0420524\pi$
$661$	−0.00813271	−	0.0617740i	−0.000316326	−	0.00240273i	−0.991602	+	0.129325i	$0.958719\pi$
$662$	−5.24127	−	25.2209i	−0.203708	−	0.980238i
$663$	−0.459067	−	1.69222i	−0.0178287	−	0.0657205i
$664$	−2.94075	−	32.1928i	−0.114123	−	1.24932i
$665$	0.467302	−	0.467302i	0.0181212	−	0.0181212i
$666$	−7.79873	−	5.04606i	−0.302195	−	0.195531i
$667$	−7.24480	−	3.00090i	−0.280520	−	0.116195i
$668$	27.1085	−	11.7756i	1.04886	−	0.455612i
$669$	34.2888	−	14.3278i	1.32568	−	0.553945i
$670$	1.86158	+	2.73515i	0.0719193	+	0.105668i
$671$	4.79232	+	8.30054i	0.185005	+	0.320439i
$672$	11.8799	−	6.55183i	0.458279	−	0.252742i
$673$	−5.58320	+	9.67039i	−0.215217	+	0.372766i	−0.953340	−	0.301900i	$-0.902379\pi$
$673$	−5.58320	+	9.67039i	−0.215217	+	0.372766i	0.738123	+	0.674666i	$0.235712\pi$
$674$	15.8259	−	1.17323i	0.609589	−	0.0451911i
$675$	25.1703	+	3.07544i	0.968804	+	0.118374i
$676$	−11.7808	+	15.9090i	−0.453109	+	0.611885i
$677$	−0.878057	+	0.673756i	−0.0337465	+	0.0258946i	−0.625497	−	0.780227i	$-0.715104\pi$
$677$	−0.878057	+	0.673756i	−0.0337465	+	0.0258946i	0.591751	+	0.806121i	$0.298437\pi$
$678$	−3.95509	−	2.57654i	−0.151894	−	0.0989516i
$679$	1.14024	+	0.305525i	0.0437582	+	0.0117250i
$680$	0.528362	−	0.194602i	0.0202618	−	0.00746266i
$681$	21.5313	+	21.3980i	0.825080	+	0.819972i
$682$	−11.5212	+	10.2794i	−0.441170	+	0.393618i
$683$	27.8034	+	11.5165i	1.06387	+	0.440668i	0.844823	−	0.535046i	$-0.179706\pi$
$683$	27.8034	+	11.5165i	1.06387	+	0.440668i	0.219045	+	0.975715i	$0.429706\pi$
$684$	−1.95324	+	8.03414i	−0.0746842	+	0.307193i
$685$	2.83849	+	6.85273i	0.108453	+	0.261829i
$686$	7.79665	+	22.3390i	0.297677	+	0.852905i
$687$	15.0757	−	26.3002i	0.575174	−	1.00341i
$688$	−27.0406	+	12.2999i	−1.03091	+	0.468928i
$689$	8.12864	+	14.0792i	0.309676	+	0.536375i
$690$	−0.818862	−	2.32299i	−0.0311735	−	0.0884347i
$691$	5.47219	−	41.5654i	0.208172	−	1.58122i	−0.494158	−	0.869372i	$-0.664524\pi$
$691$	5.47219	−	41.5654i	0.208172	−	1.58122i	0.702330	−	0.711851i	$-0.252143\pi$
$692$	3.55796	−	2.13611i	0.135253	−	0.0812028i
$693$	−3.03475	+	7.45720i	−0.115280	+	0.283275i
$694$	−9.67962	−	3.19377i	−0.367433	−	0.121234i
$695$	0.180417	+	0.673326i	0.00684362	+	0.0255407i
$696$	11.2087	+	7.03196i	0.424866	+	0.266546i
$697$	−1.70825	+	6.37528i	−0.0647047	+	0.241481i
$698$	7.26509	−	11.0768i	0.274988	−	0.419263i
$699$	−3.32819	+	0.448684i	−0.125884	+	0.0169708i
$700$	−4.95753	+	12.5723i	−0.187377	+	0.475188i
$701$	−18.4529	−	44.5492i	−0.696956	−	1.68260i	−0.730274	−	0.683155i	$-0.760607\pi$
$701$	−18.4529	−	44.5492i	−0.696956	−	1.68260i	0.0333180	−	0.999445i	$-0.489393\pi$
$702$	12.8975	−	1.07705i	0.486785	−	0.0406507i
$703$			3.01706i			0.113791i
$704$	7.05399	−	13.8077i	0.265857	−	0.520398i
$705$	1.46814	+	2.52475i	0.0552933	+	0.0950877i
$706$	2.78887	+	4.09757i	0.104960	+	0.154214i
$707$	−18.7637	−	14.3979i	−0.705683	−	0.541490i
$708$	−19.4331	+	2.95894i	−0.730340	+	0.111204i
$709$	1.28644	+	1.67652i	0.0483133	+	0.0629631i	0.816885	−	0.576800i	$-0.195699\pi$
$709$	1.28644	+	1.67652i	0.0483133	+	0.0629631i	−0.768572	+	0.639763i	$0.779032\pi$
$710$	3.12386	−	1.57386i	0.117237	−	0.0590659i
$711$	38.1752	+	9.97529i	1.43168	+	0.374102i
$712$	−29.5727	−	18.6811i	−1.10828	−	0.700103i
$713$	15.7976	−	4.23296i	0.591625	−	0.158525i
$714$	1.30237	+	1.45061i	0.0487400	+	0.0542879i
$715$	−1.17216	+	0.154317i	−0.0438362	+	0.00577115i
$716$	1.77534	−	3.20010i	0.0663474	−	0.119593i
$717$	−4.08344	+	31.7791i	−0.152499	+	1.18681i
$718$	1.06458	+	3.05023i	0.0397297	+	0.113834i
$719$			49.4592i			1.84452i	0.386573	+	0.922259i	$0.373659\pi$
$719$			49.4592i			1.84452i	−0.386573	+	0.922259i	$0.626341\pi$
$720$	0.708493	+	4.09533i	0.0264040	+	0.152624i
$721$		−	9.61240i		−	0.357985i
$722$	−22.8338	+	7.96934i	−0.849785	+	0.296588i
$723$	−16.4500	+	6.87375i	−0.611783	+	0.255637i
$724$	11.7841	+	41.1513i	0.437952	+	1.52938i
$725$	−13.0680	+	1.72044i	−0.485334	+	0.0638955i
$726$	−3.66406	−	17.3606i	−0.135986	−	0.644312i
$727$	−5.58197	+	1.49568i	−0.207024	+	0.0554719i	−0.360841	−	0.932628i	$-0.617510\pi$
$727$	−5.58197	+	1.49568i	−0.207024	+	0.0554719i	0.153817	+	0.988099i	$0.450843\pi$
$728$	−1.17176	+	6.79748i	−0.0434284	+	0.251932i
$729$	19.4443	+	18.7328i	0.720159	+	0.693809i
$730$	2.74238	+	5.44320i	0.101500	+	0.201462i
$731$	−2.59859	−	3.38655i	−0.0961125	−	0.125256i
$732$	−1.89246	+	17.0260i	−0.0699475	+	0.629298i
$733$	−1.33408	−	1.02367i	−0.0492753	−	0.0378102i	0.583830	−	0.811876i	$-0.301553\pi$
$733$	−1.33408	−	1.02367i	−0.0492753	−	0.0378102i	−0.633105	+	0.774066i	$0.718220\pi$
$734$	9.77252	−	6.65132i	0.360710	−	0.245505i
$735$	−3.04906	+	0.00946911i	−0.112466	+	0.000349273i
$736$	−13.2534	+	9.69963i	−0.488526	+	0.357533i
$737$			13.0918i			0.482243i
$738$	−44.0075	−	20.9004i	−1.61994	−	0.769354i
$739$	6.12108	+	14.7776i	0.225168	+	0.543603i	0.995577	−	0.0939466i	$-0.0299483\pi$
$739$	6.12108	+	14.7776i	0.225168	+	0.543603i	−0.770410	+	0.637549i	$0.779948\pi$
$740$	0.604242	+	1.39102i	0.0222124	+	0.0511348i
$741$	−2.56942	−	3.32709i	−0.0943902	−	0.122224i
$742$	−15.1144	−	9.91331i	−0.554869	−	0.363929i
$743$	12.6215	−	47.1041i	0.463038	−	1.72808i	−0.200275	−	0.979740i	$-0.564184\pi$
$743$	12.6215	−	47.1041i	0.463038	−	1.72808i	0.663313	−	0.748342i	$-0.269150\pi$
$744$	−27.4745	+	2.59580i	−1.00726	+	0.0951668i
$745$	−0.698332	−	2.60621i	−0.0255849	−	0.0954842i
$746$	−11.6621	+	35.3453i	−0.426980	+	1.29408i
$747$	4.68652	+	33.9660i	0.171471	+	1.24275i
$748$	2.16163	+	0.539774i	0.0790371	+	0.0197361i
$749$	−0.226993	+	1.72418i	−0.00829414	+	0.0630002i
$750$	−6.36587	−	5.45280i	−0.232449	−	0.199108i
$751$	−1.99813	−	3.46086i	−0.0729128	−	0.126289i	0.827264	−	0.561814i	$-0.189896\pi$
$751$	−1.99813	−	3.46086i	−0.0729128	−	0.126289i	−0.900177	+	0.435525i	$0.856563\pi$
$752$	13.2915	−	14.2330i	0.484690	−	0.519024i
$753$	16.9822	+	29.2042i	0.618866	+	1.06426i
$754$	−6.35171	+	2.21685i	−0.231316	+	0.0807328i
$755$	−2.84676	−	6.87268i	−0.103604	−	0.250122i
$756$	−12.2676	+	7.52153i	−0.446168	+	0.273555i
$757$	−3.51002	−	1.45390i	−0.127574	−	0.0528429i	0.317983	−	0.948096i	$-0.396994\pi$
$757$	−3.51002	−	1.45390i	−0.127574	−	0.0528429i	−0.445557	+	0.895253i	$0.646994\pi$
$758$	−3.70428	−	4.15178i	−0.134545	−	0.150799i
$759$	2.49329	−	9.42204i	0.0905008	−	0.341998i
$760$	0.991780	−	0.915809i	0.0359756	−	0.0332199i
$761$	−32.6397	−	8.74579i	−1.18319	−	0.317035i	−0.386999	−	0.922080i	$-0.626488\pi$
$761$	−32.6397	−	8.74579i	−1.18319	−	0.317035i	−0.796191	+	0.605046i	$0.793155\pi$
$762$	18.4117	+	36.2636i	0.666985	+	1.31369i
$763$	9.04667	−	6.94175i	0.327511	−	0.251308i
$764$	5.69114	−	0.848473i	0.205898	−	0.0306967i
$765$	−0.550325	+	0.231967i	−0.0198970	+	0.00838678i
$766$	3.62622	+	48.9146i	0.131021	+	1.76735i
$767$	4.99708	−	8.65520i	0.180434	−	0.312521i
$768$	24.7803	−	12.4071i	0.894183	−	0.447701i
$769$	21.8485	+	37.8428i	0.787879	+	1.36465i	0.927264	+	0.374408i	$0.122154\pi$
$769$	21.8485	+	37.8428i	0.787879	+	1.36465i	−0.139386	+	0.990238i	$0.544513\pi$
$770$	1.08668	−	0.739608i	0.0391611	−	0.0266536i
$771$	−1.51060	+	11.7561i	−0.0544029	+	0.423387i
$772$	−1.81462	+	4.60187i	−0.0653096	+	0.165625i
$773$	15.0231	+	6.22279i	0.540345	+	0.223818i	0.636127	−	0.771584i	$-0.280535\pi$
$773$	15.0231	+	6.22279i	0.540345	+	0.223818i	−0.0957826	+	0.995402i	$0.530535\pi$
$774$	28.0505	−	14.3515i	1.00825	−	0.515853i
$775$	19.4385	−	19.4385i	0.698252	−	0.698252i
$776$	2.30246	+	0.716283i	0.0826536	+	0.0257131i
$777$	−3.70137	+	3.72443i	−0.132786	+	0.133613i
$778$	−20.5362	+	4.26771i	−0.736257	+	0.153005i
$779$	2.06544	+	15.6886i	0.0740021	+	0.562102i
$780$	−1.85097	−	1.01937i	−0.0662753	−	0.0364992i
$781$	13.7228	+	1.80664i	0.491040	+	0.0646466i
$782$	−1.78756	−	1.54081i	−0.0639230	−	0.0550994i
$783$	−12.2192	−	6.90375i	−0.436677	−	0.246720i
$784$	5.93031	+	19.4467i	0.211797	+	0.694526i
$785$	2.80573	−	4.85967i	0.100141	−	0.173449i
$786$	32.9855	+	6.16250i	1.17655	+	0.219809i
$787$	22.1614	+	17.0051i	0.789970	+	0.606165i	0.922935	−	0.384956i	$-0.125783\pi$
$787$	22.1614	+	17.0051i	0.789970	+	0.606165i	−0.132965	+	0.991121i	$0.542450\pi$
$788$	11.6709	+	40.7562i	0.415759	+	1.45188i
$789$	8.95227	−	21.8040i	0.318709	−	0.776242i
$790$	−4.28883	−	4.80695i	−0.152590	−	0.171024i
$791$	−1.88679	+	1.88679i	−0.0670864	+	0.0670864i
$792$	−6.80029	+	14.9740i	−0.241638	+	0.532076i
$793$	−6.15873	−	6.15873i	−0.218703	−	0.218703i
$794$	2.50340	−	43.9479i	0.0888423	−	1.55965i
$795$	4.38258	−	3.38455i	0.155434	−	0.120037i
$796$	−50.1747	−	5.73480i	−1.77840	−	0.203265i
$797$	20.1557	−	26.2674i	0.713952	−	0.930441i	−0.285659	−	0.958331i	$-0.592212\pi$
$797$	20.1557	−	26.2674i	0.713952	−	0.930441i	0.999611	+	0.0278909i	$0.00887909\pi$
$798$	4.21567	+	2.01821i	0.149233	+	0.0714438i
$799$	2.42341	+	1.39916i	0.0857341	+	0.0494986i
$800$	−11.1406	+	25.2579i	−0.393880	+	0.893002i
$801$	32.2448	+	18.3505i	1.13931	+	0.648382i
$802$	3.06208	+	41.3048i	0.108126	+	1.45852i
$803$	−3.14799	+	23.9114i	−0.111090	+	0.843814i
$804$	−13.8667	+	18.8479i	−0.489040	+	0.664713i
$805$	−1.38044	+	0.181738i	−0.0486540	+	0.00640543i
$806$	7.69517	−	11.7325i	0.271051	−	0.413261i
$807$	−4.98901	+	18.8532i	−0.175621	+	0.663666i
$808$	−37.1277	−	30.9124i	−1.30615	−	1.08749i
$809$	−39.3544	−	39.3544i	−1.38363	−	1.38363i	−0.838083	−	0.545543i	$-0.816324\pi$
$809$	−39.3544	−	39.3544i	−1.38363	−	1.38363i	−0.545543	−	0.838083i	$-0.683676\pi$
$810$	−0.950485	−	4.30459i	−0.0333966	−	0.151248i
$811$	5.95460	−	14.3757i	0.209094	−	0.504798i	−0.784187	−	0.620525i	$-0.786920\pi$
$811$	5.95460	−	14.3757i	0.209094	−	0.504798i	0.993281	+	0.115727i	$0.0369196\pi$
$812$	5.19784	−	5.37868i	0.182408	−	0.188755i
$813$	−8.08120	+	10.5996i	−0.283420	+	0.371745i
$814$	−1.12040	+	5.89556i	−0.0392698	+	0.206639i
$815$	−4.25595	+	2.45718i	−0.149080	+	0.0860711i
$816$	2.54031	+	3.06667i	0.0889287	+	0.107355i
$817$	−8.86301	−	5.11706i	−0.310077	−	0.179023i
$818$	−30.1835	+	35.0171i	−1.05534	+	1.22434i
$819$	0.909879	−	7.25936i	0.0317937	−	0.253663i
$820$	4.09431	+	6.81957i	0.142979	+	0.238150i
$821$	−7.15926	−	9.33013i	−0.249860	−	0.325624i	0.651538	−	0.758616i	$-0.274124\pi$
$821$	−7.15926	−	9.33013i	−0.249860	−	0.325624i	−0.901397	+	0.432993i	$0.857458\pi$
$822$	−39.0343	+	35.0453i	−1.36148	+	1.22235i
$823$	11.6735	−	43.5662i	0.406914	−	1.51862i	−0.393585	−	0.919288i	$-0.628765\pi$
$823$	11.6735	−	43.5662i	0.406914	−	1.51862i	0.800499	−	0.599334i	$-0.204568\pi$
$824$	0.781358	−	19.6196i	0.0272199	−	0.683480i
$825$	−4.28915	−	15.8107i	−0.149329	−	0.550460i
$826$	−0.631939	+	11.0939i	−0.0219880	+	0.386005i
$827$	19.2919	−	46.5749i	0.670846	−	1.61957i	−0.109329	−	0.994006i	$-0.534870\pi$
$827$	19.2919	−	46.5749i	0.670846	−	1.61957i	0.780175	−	0.625561i	$-0.215130\pi$
$828$	13.5692	−	10.9238i	0.471563	−	0.379627i
$829$	−25.4354	+	10.5357i	−0.883409	+	0.365920i	−0.777818	−	0.628490i	$-0.783674\pi$
$829$	−25.4354	+	10.5357i	−0.883409	+	0.365920i	−0.105591	+	0.994410i	$0.533674\pi$
$830$	2.43299	−	5.04182i	0.0844503	−	0.175004i
$831$	0.0967156	+	31.1425i	0.00335503	+	1.08032i
$832$	−2.94419	+	13.7789i	−0.102071	+	0.477696i
$833$	−2.53002	+	1.46071i	−0.0876601	+	0.0506106i
$834$	−4.06694	+	2.78654i	−0.140827	+	0.0964901i
$835$	5.07446	+	0.668065i	0.175609	+	0.0231193i
$836$	5.28326	−	0.787664i	0.182725	−	0.0272419i
$837$	28.9836	−	4.09082i	1.00182	−	0.141400i
$838$	−21.6478	−	42.9674i	−0.747810	−	1.48429i
$839$	30.1077	−	8.06733i	1.03943	−	0.278515i	0.301555	−	0.953449i	$-0.402494\pi$
$839$	30.1077	−	8.06733i	1.03943	−	0.278515i	0.737879	+	0.674934i	$0.235828\pi$
$840$	2.34784	+	0.0862016i	0.0810080	+	0.00297424i
$841$	−20.9653	−	5.61762i	−0.722940	−	0.193711i
$842$	−3.95467	−	19.0298i	−0.136287	−	0.655811i
$843$	8.60545	+	3.53323i	0.296388	+	0.121691i
$844$	−0.155487	−	9.09352i	−0.00535207	−	0.313012i
$845$	−3.16720	+	1.31190i	−0.108955	+	0.0451306i
$846$	−13.3884	+	15.7289i	−0.460302	+	0.540770i
$847$	−10.0299			−0.344631
$848$	−30.0438	−	21.4623i	−1.03171	−	0.737020i
$849$	27.4712	+	15.7470i	0.942809	+	0.540434i
$850$	−3.89702	−	0.740593i	−0.133667	−	0.0254021i
$851$	3.86961	−	5.04297i	0.132648	−	0.172871i
$852$	17.8427	+	17.1359i	0.611280	+	0.587067i
$853$	−35.9469	+	27.5830i	−1.23080	+	0.944425i	−0.999594	−	0.0284809i	$-0.990933\pi$
$853$	−35.9469	+	27.5830i	−1.23080	+	0.944425i	−0.231204	+	0.972905i	$0.574266\pi$
$854$	9.19617	+	3.03426i	0.314686	+	0.103830i
$855$	−1.00615	+	1.01872i	−0.0344095	+	0.0348396i
$856$	−0.603460	+	3.50072i	−0.0206258	+	0.119652i
$857$	1.89885	+	7.08660i	0.0648634	+	0.242074i	0.990744	−	0.135742i	$-0.0433419\pi$
$857$	1.89885	+	7.08660i	0.0648634	+	0.242074i	−0.925881	+	0.377816i	$0.876675\pi$
$858$	−3.78532	−	7.45555i	−0.129229	−	0.254528i
$859$	−2.36263	−	17.9459i	−0.0806118	−	0.612307i	−0.983297	−	0.182006i	$-0.941741\pi$
$859$	−2.36263	−	17.9459i	−0.0806118	−	0.612307i	0.902686	−	0.430301i	$-0.141593\pi$
$860$	−5.11112	−	0.584183i	−0.174288	−	0.0199205i
$861$	−16.6973	+	21.9008i	−0.569041	+	0.746377i
$862$	−9.45779	+	19.5991i	−0.322134	+	0.667548i
$863$	−46.9403			−1.59787			−0.798934	−	0.601419i	$-0.794602\pi$
$863$	−46.9403			−1.59787			−0.798934	+	0.601419i	$0.794602\pi$
$864$	−25.6504	+	14.3548i	−0.872643	+	0.488359i
$865$	0.718661			0.0244352
$866$	6.26954	−	12.9922i	0.213048	−	0.441493i
$867$	17.5053	−	22.9607i	0.594512	−	0.779786i
$868$	−1.77151	+	15.4992i	−0.0601288	+	0.526077i
$869$	−3.32727	−	25.2731i	−0.112870	−	0.857331i
$870$	1.03735	+	2.04316i	0.0351694	+	0.0692696i
$871$	−3.07912	−	11.4914i	−0.104332	−	0.389372i
$872$	19.0291	−	13.4332i	0.644408	−	0.454906i
$873$	−2.47449	−	0.646592i	−0.0837489	−	0.0218838i
$874$	−5.37312	−	1.77285i	−0.181749	−	0.0599676i
$875$	−3.75907	+	2.88443i	−0.127080	+	0.0975117i
$876$	−29.8586	+	31.0901i	−1.00883	+	1.05044i
$877$	−7.07932	+	9.22595i	−0.239052	+	0.311538i	−0.897437	−	0.441143i	$-0.854573\pi$
$877$	−7.07932	+	9.22595i	−0.239052	+	0.311538i	0.658385	+	0.752681i	$0.271240\pi$
$878$	−13.7203	−	2.60742i	−0.463039	−	0.0879961i
$879$	−29.8368	−	17.1029i	−1.00637	−	0.576868i
$880$	2.27810	−	1.42126i	0.0767947	−	0.0479106i
$881$	−21.2953			−0.717455			−0.358728	−	0.933442i	$-0.616789\pi$
$881$	−21.2953			−0.717455			−0.358728	+	0.933442i	$0.616789\pi$
$882$	−7.23218	−	20.3152i	−0.243520	−	0.684048i
$883$	8.06528	−	3.34075i	0.271418	−	0.112425i	−0.242823	−	0.970071i	$-0.578074\pi$
$883$	8.06528	−	3.34075i	0.271418	−	0.112425i	0.514241	+	0.857645i	$0.328074\pi$
$884$	−2.02434	+	0.0346134i	−0.0680859	+	0.00116417i
$885$	−3.14899	−	1.29291i	−0.105852	−	0.0434608i
$886$	4.87641	+	23.4652i	0.163826	+	0.788329i
$887$	−41.5311	−	11.1282i	−1.39448	−	0.373649i	−0.518119	−	0.855309i	$-0.673368\pi$
$887$	−41.5311	−	11.1282i	−1.39448	−	0.373649i	−0.876358	+	0.481660i	$0.840034\pi$
$888$	−7.85749	+	7.30094i	−0.263680	+	0.245004i
$889$	22.2067	−	5.95028i	0.744790	−	0.199566i
$890$	−2.72547	−	5.40964i	−0.0913581	−	0.181332i
$891$	6.47459	−	16.1972i	0.216907	−	0.542628i
$892$	−6.32751	−	42.4418i	−0.211861	−	1.42106i
$893$	6.65157	+	0.875696i	0.222586	+	0.0293040i
$894$	15.7417	−	10.7857i	0.526482	−	0.360729i
$895$	0.548835	−	0.316870i	0.0183455	−	0.0105918i
$896$	−3.96961	−	15.1544i	−0.132615	−	0.506272i
$897$	0.0275051	+	8.85667i	0.000918370	+	0.295716i
$898$	9.51151	−	19.7104i	0.317403	−	0.657745i
$899$	−14.0568	+	5.82252i	−0.468821	+	0.194192i
$900$	10.5716	−	27.3052i	0.352386	−	0.910174i
$901$	2.03033	−	4.90166i	0.0676402	−	0.163298i
$902$	−1.78998	+	31.4237i	−0.0595999	+	1.04629i
$903$	−4.66333	−	17.1901i	−0.155186	−	0.572049i
$904$	−4.00443	+	3.69769i	−0.133185	+	0.122983i
$905$	−1.91856	+	7.16016i	−0.0637751	+	0.238012i
$906$	39.1480	−	35.1473i	1.30060	−	1.16769i
$907$	−14.6059	−	19.0348i	−0.484982	−	0.632040i	0.485205	−	0.874401i	$-0.338745\pi$
$907$	−14.6059	−	19.0348i	−0.484982	−	0.632040i	−0.970186	+	0.242360i	$0.922078\pi$
$908$	30.0516	−	18.0423i	0.997299	−	0.598754i
$909$	40.8464	+	30.9414i	1.35479	+	1.02626i
$910$	−0.779886	+	0.904776i	−0.0258530	+	0.0299930i
$911$	−17.8426	−	10.3014i	−0.591151	−	0.341301i	0.174401	−	0.984675i	$-0.444201\pi$
$911$	−17.8426	−	10.3014i	−0.591151	−	0.341301i	−0.765553	+	0.643373i	$0.777534\pi$
$912$	8.44042	+	4.46198i	0.279490	+	0.147751i
$913$	19.1839	−	11.0758i	0.634895	−	0.366557i
$914$	−10.1524	+	53.4222i	−0.335811	+	1.76705i
$915$	−1.79864	+	2.35916i	−0.0594611	+	0.0779915i
$916$	−25.1713	−	24.3250i	−0.831684	−	0.803721i
$917$	7.25906	−	17.5249i	0.239715	−	0.578724i
$918$	−2.84118	−	3.12531i	−0.0937729	−	0.103150i
$919$	6.10597	+	6.10597i	0.201417	+	0.201417i	0.800607	−	0.599190i	$-0.204510\pi$
$919$	6.10597	+	6.10597i	0.201417	+	0.201417i	−0.599190	+	0.800607i	$0.704510\pi$
$920$	−2.83234	+	0.258729i	−0.0933795	+	0.00853004i
$921$	1.59432	−	6.02488i	0.0525348	−	0.198527i
$922$	−17.3895	+	26.5131i	−0.572692	+	0.873161i
$923$	−12.4702	+	1.64173i	−0.410461	+	0.0540382i
$924$	7.48827	+	5.50924i	0.246346	+	0.181241i
$925$	1.39459	−	10.5930i	0.0458540	−	0.348295i
$926$	2.17181	+	29.2959i	0.0713701	+	0.962722i
$927$	0.129354	+	20.8258i	0.00424853	+	0.684008i
$928$	11.0463	−	10.5557i	0.362614	−	0.346509i
$929$	3.80199	+	2.19508i	0.124739	+	0.0720182i	0.561071	−	0.827768i	$-0.310389\pi$
$929$	3.80199	+	2.19508i	0.124739	+	0.0720182i	−0.436332	+	0.899786i	$0.643723\pi$
$930$	−4.31053	−	2.06362i	−0.141348	−	0.0676688i
$931$	−4.26384	+	5.55674i	−0.139742	+	0.182115i
$932$	−0.440356	+	3.85274i	−0.0144243	+	0.126201i
$933$	−35.3999	+	27.3384i	−1.15894	+	0.895019i
$934$	−1.06508	+	18.6979i	−0.0348506	+	0.611812i
$935$	0.272824	+	0.272824i	0.00892230	+	0.00892230i
$936$	2.44721	−	14.7429i	0.0799896	−	0.481886i
$937$	1.77257	−	1.77257i	0.0579072	−	0.0579072i	−0.677560	−	0.735467i	$-0.736963\pi$
$937$	1.77257	−	1.77257i	0.0579072	−	0.0579072i	0.735467	+	0.677560i	$0.236963\pi$
$938$	8.80605	+	9.86988i	0.287528	+	0.322263i
$939$	−11.1243	+	27.0942i	−0.363029	+	0.884187i
$940$	3.24209	−	0.928404i	0.105745	−	0.0302812i
$941$	28.1056	+	21.5662i	0.916218	+	0.703039i	0.955125	−	0.296204i	$-0.0957209\pi$
$941$	28.1056	+	21.5662i	0.916218	+	0.703039i	−0.0389069	+	0.999243i	$0.512388\pi$
$942$	39.0114	+	7.28828i	1.27106	+	0.237465i
$943$	16.6694	−	28.8723i	0.542832	−	0.940212i
$944$	−2.19161	+	22.5920i	−0.0713309	+	0.735306i
$945$	−2.49183	+	0.0232163i	−0.0810591	+	0.000755228i
$946$	−15.4187	−	13.2904i	−0.501307	−	0.432109i
$947$	43.8566	+	5.77383i	1.42515	+	0.187624i	0.803328	−	0.595537i	$-0.203061\pi$
$947$	43.8566	+	5.77383i	1.42515	+	0.187624i	0.621819	+	0.783161i	$0.286394\pi$
$948$	21.9787	−	39.9091i	0.713836	−	1.29619i
$949$	−2.86064	−	21.7288i	−0.0928605	−	0.705345i
$950$	−9.31141	+	1.93504i	−0.302102	+	0.0627811i
$951$	11.3627	−	11.4335i	0.368462	−	0.370758i
$952$	1.99272	−	1.04706i	0.0645844	−	0.0339354i
$953$	−1.30796	+	1.30796i	−0.0423691	+	0.0423691i	−0.727974	−	0.685605i	$-0.759538\pi$
$953$	−1.30796	+	1.30796i	−0.0423691	+	0.0423691i	0.685605	+	0.727974i	$0.259538\pi$
$954$	32.8796	+	21.2743i	1.06452	+	0.688782i
$955$	0.920597	+	0.381324i	0.0297898	+	0.0123393i
$956$	34.4179	+	13.5717i	1.11315	+	0.438941i
$957$	−1.15556	+	8.99311i	−0.0373541	+	0.290706i
$958$	−23.9311	+	16.2879i	−0.773178	+	0.526237i
$959$	14.8269	+	25.6810i	0.478786	+	0.829281i
$960$	4.78509	+	0.366790i	0.154438	+	0.0118381i
$961$	0.366386	−	0.634599i	0.0118189	−	0.0204709i
$962$	−0.403167	−	5.43838i	−0.0129986	−	0.175340i
$963$	0.468590	−	3.73859i	0.0151001	−	0.120474i
$964$	3.03562	+	20.3614i	0.0977706	+	0.655797i
$965$	−0.679618	+	0.521490i	−0.0218777	+	0.0167873i
$966$	−4.45793	−	8.78033i	−0.143432	−	0.282502i
$967$	−10.6279	−	2.84775i	−0.341771	−	0.0915773i	0.0838509	−	0.996478i	$-0.473278\pi$
$967$	−10.6279	−	2.84775i	−0.341771	−	0.0915773i	−0.425622	+	0.904901i	$0.639945\pi$
$968$	−20.4717	−	0.815294i	−0.657984	−	0.0262045i
$969$	−0.350952	+	1.32623i	−0.0112742	+	0.0426047i
$970$	0.277999	+	0.311584i	0.00892602	+	0.0100043i
$971$	−39.4533	−	16.3421i	−1.26612	−	0.524443i	−0.354335	−	0.935119i	$-0.615293\pi$
$971$	−39.4533	−	16.3421i	−1.26612	−	0.524443i	−0.911781	+	0.410676i	$0.865293\pi$
$972$	26.4772	−	16.4609i	0.849255	−	0.527983i
$973$	1.06648	+	2.57472i	0.0341899	+	0.0825417i
$974$	−45.8869	+	16.0152i	−1.47031	+	0.513161i
$975$	7.48342	+	12.8692i	0.239661	+	0.412144i
$976$	18.5234	+	6.94065i	0.592918	+	0.222165i
$977$	15.0042	+	25.9880i	0.480027	+	0.831431i	0.999738	−	0.0229113i	$-0.00729354\pi$
$977$	15.0042	+	25.9880i	0.480027	+	0.831431i	−0.519711	+	0.854342i	$0.673960\pi$
$978$	−26.3963	−	22.6102i	−0.844060	−	0.722994i
$979$	3.12858	−	23.7639i	0.0999899	−	0.759499i
$980$	−0.852967	+	3.41588i	−0.0272470	+	0.109116i
$981$	−19.5067	+	15.1614i	−0.622800	+	0.484067i
$982$	−1.57213	+	4.76478i	−0.0501687	+	0.152050i
$983$	−4.32695	−	16.1484i	−0.138008	−	0.515053i	−0.999967	−	0.00807584i	$-0.997429\pi$
$983$	−4.32695	−	16.1484i	−0.138008	−	0.515053i	0.861959	−	0.506978i	$-0.169237\pi$
$984$	−35.8605	+	43.3437i	−1.14319	+	1.38175i
$985$	−1.90014	+	7.09140i	−0.0605434	+	0.225951i
$986$	1.83584	+	1.20410i	0.0584651	+	0.0383463i
$987$	7.13676	+	9.24124i	0.227166	+	0.294152i
$988$	−4.45216	+	1.93397i	−0.141642	+	0.0615278i
$989$	8.25137	+	19.9206i	0.262378	+	0.633437i
$990$	−2.34439	+	1.61702i	−0.0745096	+	0.0513924i
$991$		−	50.6354i		−	1.60849i	−0.594300	−	0.804244i	$-0.702571\pi$
$991$		−	50.6354i		−	1.60849i	0.594300	−	0.804244i	$-0.297429\pi$
$992$	−4.87564	+	31.4909i	−0.154802	+	0.999837i
$993$	31.5490	−	0.0979781i	1.00118	−	0.00310924i
$994$	11.5608	−	7.86844i	0.366686	−	0.249572i
$995$	−6.93827	−	5.32392i	−0.219958	−	0.168780i
$996$	39.3498	+	4.37380i	1.24685	+	0.138589i
$997$	28.2085	+	36.7621i	0.893373	+	1.16427i	0.985695	+	0.168537i	$0.0539043\pi$
$997$	28.2085	+	36.7621i	0.893373	+	1.16427i	−0.0923222	+	0.995729i	$0.529429\pi$
$998$	14.7966	+	29.3690i	0.468379	+	0.929658i
$999$	7.96910	−	8.11899i	0.252131	−	0.256873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.40	✓	368
3.2	odd	2		864.2.bn.a.683.7		368
9.4	even	3		864.2.bn.a.395.8		368
9.5	odd	6	inner	288.2.bf.a.203.39	yes	368
32.3	odd	8	inner	288.2.bf.a.227.39	yes	368
96.35	even	8		864.2.bn.a.35.8		368
288.67	odd	24		864.2.bn.a.611.7		368
288.131	even	24	inner	288.2.bf.a.131.40	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.40	✓	368	1.1	even	1	trivial
288.2.bf.a.131.40	yes	368	288.131	even	24	inner
288.2.bf.a.203.39	yes	368	9.5	odd	6	inner
288.2.bf.a.227.39	yes	368	32.3	odd	8	inner
864.2.bn.a.35.8		368	96.35	even	8
864.2.bn.a.395.8		368	9.4	even	3
864.2.bn.a.611.7		368	288.67	odd	24
864.2.bn.a.683.7		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27367 + 0.614625i) q^{2} +(-1.05013 + 1.37740i) q^{3} +(1.24447 + 1.56566i) q^{4} +(0.0452073 + 0.343384i) q^{5} +(-2.18411 + 1.10891i) q^{6} +(0.358377 + 1.33748i) q^{7} +(0.622752 + 2.75902i) q^{8} +(-0.794441 - 2.89290i) q^{9} +O(q^{10})\)	\(q+(1.27367 + 0.614625i) q^{2} +(-1.05013 + 1.37740i) q^{3} +(1.24447 + 1.56566i) q^{4} +(0.0452073 + 0.343384i) q^{5} +(-2.18411 + 1.10891i) q^{6} +(0.358377 + 1.33748i) q^{7} +(0.622752 + 2.75902i) q^{8} +(-0.794441 - 2.89290i) q^{9} +(-0.153473 + 0.465143i) q^{10} +(-1.53764 + 1.17987i) q^{11} +(-3.46339 + 0.0699788i) q^{12} +(1.07217 - 1.39728i) q^{13} +(-0.365595 + 1.92378i) q^{14} +(-0.520449 - 0.298330i) q^{15} +(-0.902582 + 3.89684i) q^{16} -0.574776 q^{17} +(0.766194 - 4.17288i) q^{18} +(-1.27313 + 0.527348i) q^{19} +(-0.481363 + 0.498111i) q^{20} +(-2.21858 - 0.910905i) q^{21} +(-2.68362 + 0.557696i) q^{22} +(2.80438 + 0.751432i) q^{23} +(-4.45423 - 2.03956i) q^{24} +(4.71376 - 1.26305i) q^{25} +(2.22440 - 1.12069i) q^{26} +(4.81894 + 1.94367i) q^{27} +(-1.64805 + 2.22555i) q^{28} +(-2.67785 - 0.352546i) q^{29} +(-0.479519 - 0.699856i) q^{30} +(4.87848 - 2.81659i) q^{31} +(-3.54469 + 4.40854i) q^{32} +(-0.0104253 - 3.35696i) q^{33} +(-0.732075 - 0.353272i) q^{34} +(-0.443068 + 0.183525i) q^{35} +(3.54064 - 4.84395i) q^{36} +(0.837849 - 2.02275i) q^{37} +(-1.94567 - 0.110831i) q^{38} +(0.798689 + 2.94414i) q^{39} +(-0.919249 + 0.338571i) q^{40} +(2.97203 - 11.0918i) q^{41} +(-2.26588 - 2.52379i) q^{42} +(4.52106 + 5.89196i) q^{43} +(-3.76083 - 0.939103i) q^{44} +(0.957460 - 0.403578i) q^{45} +(3.11001 + 2.68072i) q^{46} +(-4.21627 - 2.43427i) q^{47} +(-4.41966 - 5.33541i) q^{48} +(4.40176 - 2.54136i) q^{49} +(6.78008 + 1.28849i) q^{50} +(0.603591 - 0.791694i) q^{51} +(3.52196 - 0.0602207i) q^{52} +(-3.53239 + 8.52795i) q^{53} +(4.94311 + 5.43743i) q^{54} +(-0.474662 - 0.474662i) q^{55} +(-3.46695 + 1.82169i) q^{56} +(0.610590 - 2.30739i) q^{57} +(-3.19401 - 2.09490i) q^{58} +(5.62596 - 0.740672i) q^{59} +(-0.180600 - 1.18611i) q^{60} +(0.645484 - 4.90294i) q^{61} +(7.94472 - 0.588972i) q^{62} +(3.58449 - 2.09930i) q^{63} +(-7.22436 + 3.43637i) q^{64} +(0.528275 + 0.305000i) q^{65} +(2.05000 - 4.28207i) q^{66} +(4.11206 - 5.35894i) q^{67} +(-0.715292 - 0.899903i) q^{68} +(-3.98000 + 3.07364i) q^{69} +(-0.677121 - 0.0385707i) q^{70} +(-5.04976 - 5.04976i) q^{71} +(7.48682 - 3.99343i) q^{72} +(8.79899 - 8.79899i) q^{73} +(2.31038 - 2.06135i) q^{74} +(-3.21036 + 7.81908i) q^{75} +(-2.41002 - 1.33702i) q^{76} +(-2.12911 - 1.63372i) q^{77} +(-0.792279 + 4.24076i) q^{78} +(-6.57615 + 11.3902i) q^{79} +(-1.37891 - 0.133766i) q^{80} +(-7.73773 + 4.59647i) q^{81} +(10.6027 - 12.3006i) q^{82} +(-11.3315 - 1.49182i) q^{83} +(-1.33480 - 4.60714i) q^{84} +(-0.0259841 - 0.197369i) q^{85} +(2.13699 + 10.2832i) q^{86} +(3.29769 - 3.31824i) q^{87} +(-4.21286 - 3.50761i) q^{88} +(-8.74474 + 8.74474i) q^{89} +(1.46754 + 0.0744536i) q^{90} +(2.25308 + 0.933257i) q^{91} +(2.31349 + 5.32585i) q^{92} +(-1.24349 + 9.67740i) q^{93} +(-3.87398 - 5.69188i) q^{94} +(-0.238638 - 0.413332i) q^{95} +(-2.34991 - 9.51199i) q^{96} +(0.426263 - 0.738308i) q^{97} +(7.16837 - 0.531418i) q^{98} +(4.63481 + 3.51090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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