LMFDB - Embedded newform 574.2.s.a.387.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.6
Character	$\chi$	$=$	574.387
Dual form			574.2.s.a.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(-0.184992 - 0.320416i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.227337 + 2.16297i) q^{5} +(-0.114331 - 0.351876i) q^{6} +(1.04208 - 2.43189i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43156 - 2.47953i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(-0.184992 - 0.320416i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.227337 + 2.16297i) q^{5} +(-0.114331 - 0.351876i) q^{6} +(1.04208 - 2.43189i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43156 - 2.47953i) q^{9} +(-0.227337 + 2.16297i) q^{10} +(0.315493 - 3.00171i) q^{11} +(-0.0386739 - 0.367957i) q^{12} +(0.267854 + 0.824370i) q^{13} +(1.52492 - 2.16208i) q^{14} +(0.650993 - 0.472974i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.138757 + 1.32019i) q^{17} +(1.91580 - 2.12771i) q^{18} +(4.18033 + 4.64273i) q^{19} +(-0.672076 + 2.06844i) q^{20} +(-0.971991 + 0.115981i) q^{21} +(0.932690 - 2.87053i) q^{22} +(4.43766 + 0.943253i) q^{23} +(0.0386739 - 0.367957i) q^{24} +(0.263990 - 0.0561127i) q^{25} +(0.0906046 + 0.862046i) q^{26} -2.16926 q^{27} +(1.94112 - 1.79779i) q^{28} +(-8.19493 + 5.95396i) q^{29} +(0.735104 - 0.327289i) q^{30} +(-0.0632244 + 0.601540i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.02016 + 0.454204i) q^{33} +(-0.410208 + 1.26249i) q^{34} +(5.49700 + 1.70113i) q^{35} +(2.31631 - 1.68289i) q^{36} +(0.140764 + 1.33928i) q^{37} +(3.12371 + 5.41042i) q^{38} +(0.214590 - 0.238326i) q^{39} +(-1.08744 + 1.88350i) q^{40} +(0.0789962 - 6.40264i) q^{41} +(-0.974864 - 0.0886415i) q^{42} +(-1.18220 - 3.63844i) q^{43} +(1.50912 - 2.61388i) q^{44} +(5.68858 + 2.53272i) q^{45} +(4.14457 + 1.84528i) q^{46} +(2.19694 + 0.466975i) q^{47} +(0.114331 - 0.351876i) q^{48} +(-4.82814 - 5.06844i) q^{49} +0.269887 q^{50} +(0.448678 - 0.199764i) q^{51} +(-0.0906046 + 0.862046i) q^{52} +(-12.9667 - 5.77315i) q^{53} +(-2.12185 - 0.451014i) q^{54} +6.56434 q^{55} +(2.27249 - 1.35492i) q^{56} +(0.714275 - 2.19831i) q^{57} +(-9.25375 + 4.12003i) q^{58} +(-0.841194 + 0.934241i) q^{59} +(0.787088 - 0.167301i) q^{60} +(1.25769 + 1.39681i) q^{61} +(-0.186910 + 0.575249i) q^{62} +(-4.53813 - 6.06524i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.72219 + 0.766770i) q^{65} +(-1.09230 + 0.232176i) q^{66} +(-2.06222 - 0.918158i) q^{67} +(-0.663731 + 1.14961i) q^{68} +(-0.518698 - 1.59639i) q^{69} +(5.02319 + 2.80684i) q^{70} +(-6.90001 - 5.01315i) q^{71} +(2.61558 - 1.16453i) q^{72} +(3.17557 + 5.50025i) q^{73} +(-0.140764 + 1.33928i) q^{74} +(-0.0668154 - 0.0742060i) q^{75} +(1.93056 + 5.94164i) q^{76} +(-6.97106 - 3.89527i) q^{77} +(0.259452 - 0.188503i) q^{78} +(0.169176 - 0.293022i) q^{79} +(-1.45528 + 1.61625i) q^{80} +(-3.89337 - 6.74352i) q^{81} +(1.40845 - 6.24630i) q^{82} -4.32199 q^{83} +(-0.935131 - 0.289390i) q^{84} -2.88707 q^{85} +(-0.399893 - 3.80472i) q^{86} +(3.42374 + 1.52435i) q^{87} +(2.01960 - 2.24300i) q^{88} +(-1.18476 - 1.31581i) q^{89} +(5.03769 + 3.66010i) q^{90} +(2.28390 + 0.207668i) q^{91} +(3.67035 + 2.66666i) q^{92} +(0.204439 - 0.0910219i) q^{93} +(2.05185 + 0.913541i) q^{94} +(-9.09174 + 10.0974i) q^{95} +(0.184992 - 0.320416i) q^{96} +(-2.24069 + 1.62795i) q^{97} +(-3.66885 - 5.96151i) q^{98} +(-6.99119 - 5.07940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	−0.184992	−	0.320416i	−0.106805	−	0.184992i	0.807669	−	0.589636i	$-0.200729\pi$
$3$	−0.184992	−	0.320416i	−0.106805	−	0.184992i	−0.914474	+	0.404644i	$0.867395\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	0.227337	+	2.16297i	0.101668	+	0.967309i	0.919829	+	0.392319i	$0.128327\pi$
$5$	0.227337	+	2.16297i	0.101668	+	0.967309i	−0.818161	+	0.574989i	$0.805006\pi$
$6$	−0.114331	−	0.351876i	−0.0466756	−	0.143653i
$7$	1.04208	−	2.43189i	0.393869	−	0.919167i
$7$	1.04208	−	2.43189i	0.393869	−	0.919167i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.43156	−	2.47953i	0.477185	−	0.826509i
$10$	−0.227337	+	2.16297i	−0.0718903	+	0.683991i
$11$	0.315493	−	3.00171i	0.0951247	−	0.905051i	−0.838042	−	0.545606i	$-0.816299\pi$
$11$	0.315493	−	3.00171i	0.0951247	−	0.905051i	0.933166	−	0.359445i	$-0.117034\pi$
$12$	−0.0386739	−	0.367957i	−0.0111642	−	0.106220i
$13$	0.267854	+	0.824370i	0.0742894	+	0.228639i	0.981305	−	0.192457i	$-0.0616456\pi$
$13$	0.267854	+	0.824370i	0.0742894	+	0.228639i	−0.907016	+	0.421096i	$0.861646\pi$
$14$	1.52492	−	2.16208i	0.407553	−	0.577841i
$15$	0.650993	−	0.472974i	0.168086	−	0.122121i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.138757	+	1.32019i	−0.0336536	+	0.320193i	0.964724	+	0.263262i	$0.0847982\pi$
$17$	−0.138757	+	1.32019i	−0.0336536	+	0.320193i	−0.998378	+	0.0569312i	$0.981868\pi$
$18$	1.91580	−	2.12771i	0.451557	−	0.501505i
$19$	4.18033	+	4.64273i	0.959035	+	1.06512i	0.997828	+	0.0658685i	$0.0209818\pi$
$19$	4.18033	+	4.64273i	0.959035	+	1.06512i	−0.0387938	+	0.999247i	$0.512352\pi$
$20$	−0.672076	+	2.06844i	−0.150281	+	0.462516i
$21$	−0.971991	+	0.115981i	−0.212106	+	0.0253092i
$22$	0.932690	−	2.87053i	0.198850	−	0.611998i
$23$	4.43766	+	0.943253i	0.925316	+	0.196682i	0.645842	−	0.763471i	$-0.276507\pi$
$23$	4.43766	+	0.943253i	0.925316	+	0.196682i	0.279474	+	0.960153i	$0.409840\pi$
$24$	0.0386739	−	0.367957i	0.00789427	−	0.0751090i
$25$	0.263990	−	0.0561127i	0.0527979	−	0.0112225i
$26$	0.0906046	+	0.862046i	0.0177690	+	0.169061i
$27$	−2.16926			−0.417474
$28$	1.94112	−	1.79779i	0.366838	−	0.339750i
$29$	−8.19493	+	5.95396i	−1.52176	+	1.10562i	−0.561154	+	0.827712i	$0.689642\pi$
$29$	−8.19493	+	5.95396i	−1.52176	+	1.10562i	−0.960607	+	0.277912i	$0.910358\pi$
$30$	0.735104	−	0.327289i	0.134211	−	0.0597546i
$31$	−0.0632244	+	0.601540i	−0.0113554	+	0.108040i	−0.998731	−	0.0503543i	$-0.983965\pi$
$31$	−0.0632244	+	0.601540i	−0.0113554	+	0.108040i	0.987376	+	0.158394i	$0.0506316\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.02016	+	0.454204i	−0.177587	+	0.0790668i
$34$	−0.410208	+	1.26249i	−0.0703501	+	0.216515i
$35$	5.49700	+	1.70113i	0.929162	+	0.287543i
$36$	2.31631	−	1.68289i	0.386051	−	0.280482i
$37$	0.140764	+	1.33928i	0.0231414	+	0.220176i	0.999981	+	0.00620193i	$0.00197415\pi$
$37$	0.140764	+	1.33928i	0.0231414	+	0.220176i	−0.976839	+	0.213974i	$0.931359\pi$
$38$	3.12371	+	5.41042i	0.506732	+	0.877686i
$39$	0.214590	−	0.238326i	0.0343619	−	0.0381628i
$40$	−1.08744	+	1.88350i	−0.171940	+	0.297808i
$41$	0.0789962	−	6.40264i	0.0123371	−	0.999924i
$41$	0.0789962	−	6.40264i	0.0123371	−	0.999924i
$42$	−0.974864	−	0.0886415i	−0.150425	−	0.0136777i
$43$	−1.18220	−	3.63844i	−0.180284	−	0.554857i	0.819551	−	0.573006i	$-0.194223\pi$
$43$	−1.18220	−	3.63844i	−0.180284	−	0.554857i	−0.999835	+	0.0181489i	$0.994223\pi$
$44$	1.50912	−	2.61388i	0.227509	−	0.394057i
$45$	5.68858	+	2.53272i	0.848004	+	0.377556i
$46$	4.14457	+	1.84528i	0.611084	+	0.272072i
$47$	2.19694	+	0.466975i	0.320457	+	0.0681153i	0.365332	−	0.930877i	$-0.380955\pi$
$47$	2.19694	+	0.466975i	0.320457	+	0.0681153i	−0.0448746	+	0.998993i	$0.514289\pi$
$48$	0.114331	−	0.351876i	0.0165023	−	0.0507889i
$49$	−4.82814	−	5.06844i	−0.689735	−	0.724062i
$50$	0.269887			0.0381678
$51$	0.448678	−	0.199764i	0.0628275	−	0.0279726i
$52$	−0.0906046	+	0.862046i	−0.0125646	+	0.119544i
$53$	−12.9667	−	5.77315i	−1.78111	−	0.793003i	−0.981228	−	0.192852i	$-0.938226\pi$
$53$	−12.9667	−	5.77315i	−1.78111	−	0.793003i	−0.799886	−	0.600151i	$-0.795107\pi$
$54$	−2.12185	−	0.451014i	−0.288748	−	0.0613752i
$55$	6.56434			0.885135
$56$	2.27249	−	1.35492i	0.303674	−	0.181059i
$57$	0.714275	−	2.19831i	0.0946080	−	0.291174i
$58$	−9.25375	+	4.12003i	−1.21508	+	0.540987i
$59$	−0.841194	+	0.934241i	−0.109514	+	0.121628i	−0.795409	−	0.606072i	$-0.792744\pi$
$59$	−0.841194	+	0.934241i	−0.109514	+	0.121628i	0.685895	+	0.727700i	$0.259411\pi$
$60$	0.787088	−	0.167301i	0.101613	−	0.0215984i
$61$	1.25769	+	1.39681i	0.161031	+	0.178843i	0.818261	−	0.574847i	$-0.194938\pi$
$61$	1.25769	+	1.39681i	0.161031	+	0.178843i	−0.657230	+	0.753690i	$0.728272\pi$
$62$	−0.186910	+	0.575249i	−0.0237376	+	0.0730567i
$63$	−4.53813	−	6.06524i	−0.571751	−	0.764149i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.72219	+	0.766770i	−0.213612	+	0.0951061i
$66$	−1.09230	+	0.232176i	−0.134453	+	0.0285789i
$67$	−2.06222	−	0.918158i	−0.251940	−	0.112171i	0.276881	−	0.960904i	$-0.410699\pi$
$67$	−2.06222	−	0.918158i	−0.251940	−	0.112171i	−0.528821	+	0.848733i	$0.677366\pi$
$68$	−0.663731	+	1.14961i	−0.0804891	+	0.139411i
$69$	−0.518698	−	1.59639i	−0.0624439	−	0.192183i
$70$	5.02319	+	2.80684i	0.600386	+	0.335482i
$71$	−6.90001	−	5.01315i	−0.818880	−	0.594951i	0.0975111	−	0.995234i	$-0.468912\pi$
$71$	−6.90001	−	5.01315i	−0.818880	−	0.594951i	−0.916392	+	0.400283i	$0.868912\pi$
$72$	2.61558	−	1.16453i	0.308249	−	0.137241i
$73$	3.17557	+	5.50025i	0.371673	+	0.643756i	0.989823	−	0.142304i	$-0.0454510\pi$
$73$	3.17557	+	5.50025i	0.371673	+	0.643756i	−0.618150	+	0.786060i	$0.712118\pi$
$74$	−0.140764	+	1.33928i	−0.0163635	+	0.155688i
$75$	−0.0668154	−	0.0742060i	−0.00771517	−	0.00856857i
$76$	1.93056	+	5.94164i	0.221450	+	0.681553i
$77$	−6.97106	−	3.89527i	−0.794426	−	0.443907i
$78$	0.259452	−	0.188503i	0.0293771	−	0.0213437i
$79$	0.169176	−	0.293022i	0.0190338	−	0.0329676i	−0.856352	−	0.516393i	$-0.827274\pi$
$79$	0.169176	−	0.293022i	0.0190338	−	0.0329676i	0.875385	+	0.483426i	$0.160608\pi$
$80$	−1.45528	+	1.61625i	−0.162705	+	0.180703i
$81$	−3.89337	−	6.74352i	−0.432597	−	0.749280i
$82$	1.40845	−	6.24630i	0.155538	−	0.689788i
$83$	−4.32199			−0.474400			−0.237200	−	0.971461i	$-0.576230\pi$
$83$	−4.32199			−0.474400			−0.237200	+	0.971461i	$0.576230\pi$
$84$	−0.935131	−	0.289390i	−0.102031	−	0.0315750i
$85$	−2.88707			−0.313147
$86$	−0.399893	−	3.80472i	−0.0431215	−	0.410274i
$87$	3.42374	+	1.52435i	0.367063	+	0.163427i
$88$	2.01960	−	2.24300i	0.215290	−	0.239104i
$89$	−1.18476	−	1.31581i	−0.125585	−	0.139476i	0.677073	−	0.735916i	$-0.263248\pi$
$89$	−1.18476	−	1.31581i	−0.125585	−	0.139476i	−0.802658	+	0.596440i	$0.796581\pi$
$90$	5.03769	+	3.66010i	0.531019	+	0.385808i
$91$	2.28390	+	0.207668i	0.239418	+	0.0217695i
$92$	3.67035	+	2.66666i	0.382660	+	0.278019i
$93$	0.204439	−	0.0910219i	0.0211993	−	0.00943854i
$94$	2.05185	+	0.913541i	0.211632	+	0.0942246i
$95$	−9.09174	+	10.0974i	−0.932792	+	1.03597i
$96$	0.184992	−	0.320416i	0.0188807	−	0.0327023i
$97$	−2.24069	+	1.62795i	−0.227507	+	0.165294i	−0.695699	−	0.718333i	$-0.744905\pi$
$97$	−2.24069	+	1.62795i	−0.227507	+	0.165294i	0.468192	+	0.883627i	$0.344905\pi$
$98$	−3.66885	−	5.96151i	−0.370610	−	0.602203i
$99$	−6.99119	−	5.07940i	−0.702641	−	0.510498i
$100$	0.263990	+	0.0561127i	0.0263990	+	0.00561127i
$101$	−15.5127	+	3.29732i	−1.54357	+	0.328096i	−0.899518	−	0.436885i	$-0.856082\pi$
$101$	−15.5127	+	3.29732i	−1.54357	+	0.328096i	−0.644053	+	0.764981i	$0.722748\pi$
$102$	0.480407	−	0.102114i	0.0475674	−	0.0101108i
$103$	1.97890	+	2.19779i	0.194986	+	0.216554i	0.832708	−	0.553713i	$-0.186789\pi$
$103$	1.97890	+	2.19779i	0.194986	+	0.216554i	−0.637721	+	0.770267i	$0.720123\pi$
$104$	−0.267854	+	0.824370i	−0.0262653	+	0.0808361i
$105$	−0.471833	−	2.07602i	−0.0460462	−	0.202599i
$106$	−11.4830	−	8.34292i	−1.11533	−	0.810336i
$107$	10.7594	+	11.9496i	1.04015	+	1.15521i	0.987664	+	0.156586i	$0.0500489\pi$
$107$	10.7594	+	11.9496i	1.04015	+	1.15521i	0.0524894	+	0.998621i	$0.483284\pi$
$108$	−1.98172	−	0.882317i	−0.190691	−	0.0849010i
$109$	5.75182	+	9.96245i	0.550925	+	0.954230i	0.998208	+	0.0598375i	$0.0190583\pi$
$109$	5.75182	+	9.96245i	0.550925	+	0.954230i	−0.447283	+	0.894392i	$0.647608\pi$
$110$	6.42089	+	1.36480i	0.612208	+	0.130129i
$111$	0.403086	−	0.292859i	0.0382592	−	0.0277969i
$112$	2.50453	−	0.852834i	0.236656	−	0.0805852i
$113$	−2.66782	−	1.93828i	−0.250967	−	0.182338i	0.455188	−	0.890395i	$-0.349572\pi$
$113$	−2.66782	−	1.93828i	−0.250967	−	0.182338i	−0.706155	+	0.708057i	$0.749572\pi$
$114$	1.15572	−	2.00177i	0.108243	−	0.187483i
$115$	−1.03138	+	9.81295i	−0.0961769	+	0.915062i
$116$	−9.90814	+	2.10604i	−0.919947	+	0.195541i
$117$	2.42750	+	0.515980i	0.224422	+	0.0477024i
$118$	−1.01705	+	0.738931i	−0.0936272	+	0.0680241i
$119$	3.06595	+	1.71318i	0.281055	+	0.157047i
$120$	0.804672			0.0734561
$121$	1.84887	+	0.392989i	0.168079	+	0.0357263i
$122$	0.939797	+	1.62778i	0.0850852	+	0.147372i
$123$	−2.06612	+	1.15913i	−0.186296	+	0.104515i
$124$	−0.302426	+	0.523818i	−0.0271587	+	0.0470402i
$125$	3.54176	+	10.9004i	0.316785	+	0.974964i
$126$	−3.17793	−	6.87624i	−0.283113	−	0.612584i
$127$	0.355294	−	0.258136i	0.0315273	−	0.0229059i	−0.571910	−	0.820316i	$-0.693797\pi$
$127$	0.355294	−	0.258136i	0.0315273	−	0.0229059i	0.603437	+	0.797410i	$0.293797\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.947115	+	1.05188i	−0.0833888	+	0.0926127i
$130$	−1.84398	+	0.391950i	−0.161728	+	0.0343763i
$131$	−20.1479	+	8.97044i	−1.76033	+	0.783751i	−0.771226	+	0.636561i	$0.780356\pi$
$131$	−20.1479	+	8.97044i	−1.76033	+	0.783751i	−0.989108	+	0.147190i	$0.952977\pi$
$132$	−1.11670			−0.0971966
$133$	15.6468	−	5.32801i	1.35675	−	0.461997i
$134$	−1.82626	−	1.32685i	−0.157765	−	0.114623i
$135$	−0.493153	−	4.69204i	−0.0424438	−	0.403826i
$136$	−0.888245	+	0.986496i	−0.0761664	+	0.0845913i
$137$	1.25832	+	2.17947i	0.107506	+	0.186205i	0.914759	−	0.404000i	$-0.132380\pi$
$137$	1.25832	+	2.17947i	0.107506	+	0.186205i	−0.807254	+	0.590205i	$0.799047\pi$
$138$	−0.175455	−	1.66935i	−0.0149358	−	0.142104i
$139$	1.27474	−	3.92325i	0.108122	−	0.332766i	−0.882328	−	0.470634i	$-0.844025\pi$
$139$	1.27474	−	3.92325i	0.108122	−	0.332766i	0.990451	+	0.137868i	$0.0440251\pi$
$140$	4.32985	+	3.78989i	0.365939	+	0.320304i
$141$	−0.256791	−	0.790322i	−0.0216257	−	0.0665571i
$142$	−5.70694	−	6.33819i	−0.478915	−	0.531889i
$143$	2.55903	−	0.543939i	0.213997	−	0.0454864i
$144$	2.80055	−	0.595274i	0.233379	−	0.0496062i
$145$	−14.7412	−	16.3718i	−1.22419	−	1.35961i
$146$	1.96261	+	6.04030i	0.162427	+	0.499899i
$147$	−0.730838	+	2.48463i	−0.0602785	+	0.204929i
$148$	−0.416139	+	1.28075i	−0.0342065	+	0.105277i
$149$	−2.13609	−	20.3236i	−0.174996	−	1.66497i	−0.631594	−	0.775299i	$-0.717599\pi$
$149$	−2.13609	−	20.3236i	−0.174996	−	1.66497i	0.456599	−	0.889673i	$-0.349067\pi$
$150$	−0.0499270	−	0.0864761i	−0.00407652	−	0.00706074i
$151$	−13.3290	+	14.8033i	−1.08470	+	1.20468i	−0.107089	+	0.994249i	$0.534153\pi$
$151$	−13.3290	+	14.8033i	−1.08470	+	1.20468i	−0.977609	+	0.210429i	$0.932514\pi$
$152$	0.653032	+	6.21319i	0.0529679	+	0.503956i
$153$	3.07481	+	2.23398i	0.248583	+	0.180606i
$154$	−6.00885	−	5.25951i	−0.484207	−	0.423823i
$155$	−1.31548			−0.105662
$156$	0.292974	−	0.130440i	0.0234567	−	0.0104436i
$157$	−13.8806	+	2.95041i	−1.10779	+	0.235468i	−0.725261	−	0.688474i	$-0.758281\pi$
$157$	−13.8806	+	2.95041i	−1.10779	+	0.235468i	−0.382531	+	0.923943i	$0.624947\pi$
$158$	0.226402	−	0.251445i	0.0180116	−	0.0200039i
$159$	0.548930	+	5.22272i	0.0435330	+	0.414189i
$160$	−1.75952	+	1.27836i	−0.139102	+	0.101064i
$161$	6.91828	−	9.80894i	0.545236	−	0.773052i
$162$	−2.40624	−	7.40563i	−0.189052	−	0.581842i
$163$	6.40302	−	11.0904i	0.501523	−	0.868663i	−0.498475	−	0.866904i	$-0.666107\pi$
$163$	6.40302	−	11.0904i	0.501523	−	0.868663i	0.999998	−	0.00175947i	$-0.000560056\pi$
$164$	2.67635	−	5.81697i	0.208988	−	0.454229i
$165$	−1.21435	−	2.10332i	−0.0945370	−	0.163743i
$166$	−4.22755	−	0.898593i	−0.328121	−	0.0697443i
$167$	10.1902			0.788540			0.394270	−	0.918995i	$-0.370998\pi$
$167$	10.1902			0.788540			0.394270	+	0.918995i	$0.370998\pi$
$168$	−0.854529	−	0.477491i	−0.0659283	−	0.0368392i
$169$	9.90938	−	7.19959i	0.762260	−	0.553814i
$170$	−2.82398	−	0.600256i	−0.216590	−	0.0460375i
$171$	17.4962	−	3.71892i	1.33797	−	0.284393i
$172$	0.399893	−	3.80472i	0.0304915	−	0.290108i
$173$	0.0513074	−	0.0888670i	0.00390083	−	0.00675643i	−0.864068	−	0.503374i	$-0.832092\pi$
$173$	0.0513074	−	0.0888670i	0.00390083	−	0.00675643i	0.867969	+	0.496618i	$0.165425\pi$
$174$	3.03199	+	2.20287i	0.229855	+	0.166999i
$175$	0.138638	−	0.700467i	0.0104801	−	0.0529503i
$176$	2.44181	−	1.77408i	0.184059	−	0.133726i
$177$	0.454959	+	0.0967046i	0.0341968	+	0.00726876i
$178$	−0.885301	−	1.53339i	−0.0663561	−	0.114932i
$179$	11.9955	+	5.34075i	0.896587	+	0.399186i	0.802690	−	0.596396i	$-0.203401\pi$
$179$	11.9955	+	5.34075i	0.896587	+	0.399186i	0.0938963	+	0.995582i	$0.470068\pi$
$180$	4.16663	+	4.62751i	0.310562	+	0.344914i
$181$	−6.50141	−	4.72355i	−0.483246	−	0.351099i	0.319335	−	0.947642i	$-0.396540\pi$
$181$	−6.50141	−	4.72355i	−0.483246	−	0.351099i	−0.802581	+	0.596543i	$0.796540\pi$
$182$	2.19081	+	0.677979i	0.162394	+	0.0502552i
$183$	0.214896	−	0.661383i	0.0158856	−	0.0488909i
$184$	3.03571	+	3.37150i	0.223796	+	0.248550i
$185$	−2.86482	+	0.608935i	−0.210625	+	0.0447698i
$186$	0.218896	−	0.0465277i	0.0160502	−	0.00341158i
$187$	3.91905	+	0.833021i	0.286590	+	0.0609165i
$188$	1.81707	+	1.32018i	0.132524	+	0.0962841i
$189$	−2.26054	+	5.27539i	−0.164430	+	0.383728i
$190$	−10.9924	+	7.98646i	−0.797474	+	0.579399i
$191$	−4.46170	+	7.72789i	−0.322837	+	0.559171i	−0.981072	−	0.193642i	$-0.937970\pi$
$191$	−4.46170	+	7.72789i	−0.322837	+	0.559171i	0.658235	+	0.752813i	$0.271303\pi$
$192$	0.247568	−	0.274952i	0.0178667	−	0.0198429i
$193$	−10.6215	−	4.72901i	−0.764554	−	0.340401i	−0.0128634	−	0.999917i	$-0.504095\pi$
$193$	−10.6215	−	4.72901i	−0.764554	−	0.340401i	−0.751691	+	0.659516i	$0.770761\pi$
$194$	−2.53019	+	1.12651i	−0.181657	+	0.0808790i
$195$	0.564277	+	0.409971i	0.0404087	+	0.0293586i
$196$	−2.34921	−	6.59403i	−0.167801	−	0.471002i
$197$	−6.97652	−	5.06874i	−0.497057	−	0.361133i	0.310835	−	0.950464i	$-0.399391\pi$
$197$	−6.97652	−	5.06874i	−0.497057	−	0.361133i	−0.807892	+	0.589331i	$0.799391\pi$
$198$	−5.78235	−	6.42195i	−0.410934	−	0.456388i
$199$	13.4881	−	14.9800i	0.956144	−	1.06191i	−0.0418830	−	0.999123i	$-0.513336\pi$
$199$	13.4881	−	14.9800i	0.956144	−	1.06191i	0.998027	−	0.0627832i	$-0.0199977\pi$
$200$	0.246554	+	0.109773i	0.0174340	+	0.00776213i
$201$	0.0873015	+	0.830618i	0.00615777	+	0.0585873i
$202$	−15.8593			−1.11585
$203$	5.93960	+	26.1336i	0.416878	+	1.83422i
$204$	0.491139			0.0343866
$205$	13.8667	−	1.28469i	0.968489	−	0.0897267i
$206$	1.47871	+	2.56120i	0.103026	+	0.178447i
$207$	8.69158	−	9.65298i	0.604106	−	0.670928i
$208$	−0.433397	+	0.750666i	−0.0300507	+	0.0520493i
$209$	15.2550	−	11.0834i	1.05521	−	0.766656i
$210$	−0.0298941	−	2.12875i	−0.00206289	−	0.146898i
$211$	−4.10901	−	12.6462i	−0.282876	−	0.870602i	−0.987027	−	0.160552i	$-0.948673\pi$
$211$	−4.10901	−	12.6462i	−0.282876	−	0.870602i	0.704152	−	0.710049i	$-0.251327\pi$
$212$	−9.49753	−	10.5481i	−0.652293	−	0.724444i
$213$	−0.329845	+	3.13826i	−0.0226006	+	0.215030i
$214$	8.03986	+	13.9254i	0.549594	+	0.951924i
$215$	7.60107	−	3.38421i	0.518389	−	0.230802i
$216$	−1.75497	−	1.27506i	−0.119410	−	0.0867567i
$217$	1.39699	+	0.780606i	0.0948339	+	0.0529910i
$218$	3.55482	+	10.9406i	0.240763	+	0.740992i
$219$	1.17491	−	2.03501i	0.0793932	−	0.137513i
$220$	5.99682	+	2.66996i	0.404305	+	0.180008i
$221$	−1.12549	+	0.239231i	−0.0757087	+	0.0160924i
$222$	0.455166	−	0.202653i	0.0305487	−	0.0136012i
$223$	−1.39840	−	4.30383i	−0.0936436	−	0.288205i	0.893254	−	0.449552i	$-0.148416\pi$
$223$	−1.39840	−	4.30383i	−0.0936436	−	0.288205i	−0.986898	+	0.161346i	$0.948416\pi$
$224$	2.62711	−	0.313476i	0.175531	−	0.0209450i
$225$	0.238783	−	0.734898i	0.0159189	−	0.0489932i
$226$	−2.20653	−	2.45060i	−0.146776	−	0.163011i
$227$	19.8726	−	4.22404i	1.31899	−	0.280360i	0.505946	−	0.862565i	$-0.331143\pi$
$227$	19.8726	−	4.22404i	1.31899	−	0.280360i	0.813042	+	0.582205i	$0.197810\pi$
$228$	1.54666	−	1.71774i	0.102430	−	0.113760i
$229$	−20.5417	+	9.14574i	−1.35743	+	0.604368i	−0.950965	−	0.309298i	$-0.899906\pi$
$229$	−20.5417	+	9.14574i	−1.35743	+	0.604368i	−0.406467	+	0.913665i	$0.633239\pi$
$230$	−3.04907	+	9.38408i	−0.201050	+	0.618768i
$231$	0.0414864	+	2.95423i	0.00272960	+	0.194374i
$232$	−10.1295			−0.665034
$233$	20.5437	+	4.36670i	1.34586	+	0.286072i	0.823822	−	0.566848i	$-0.191837\pi$
$233$	20.5437	+	4.36670i	1.34586	+	0.286072i	0.522041	+	0.852920i	$0.325171\pi$
$234$	2.26717	+	1.00941i	0.148210	+	0.0659872i
$235$	−0.510605	+	4.85808i	−0.0333082	+	0.316906i
$236$	−1.14846	+	0.511327i	−0.0747583	+	0.0332845i
$237$	−0.125185			−0.00813165
$238$	2.64276	+	2.31319i	0.171305	+	0.149942i
$239$	−3.80705	+	11.7169i	−0.246258	+	0.757903i	0.749169	+	0.662379i	$0.230453\pi$
$239$	−3.80705	+	11.7169i	−0.246258	+	0.757903i	−0.995427	+	0.0955248i	$0.969547\pi$
$240$	0.787088	+	0.167301i	0.0508063	+	0.0107992i
$241$	11.3241	+	5.04180i	0.729448	+	0.324771i	0.737639	−	0.675195i	$-0.235941\pi$
$241$	11.3241	+	5.04180i	0.729448	+	0.324771i	−0.00819124	+	0.999966i	$0.502607\pi$
$242$	1.72676	+	0.768803i	0.111000	+	0.0494206i
$243$	−4.69437	+	8.13089i	−0.301144	+	0.521597i
$244$	0.580826	+	1.78760i	0.0371836	+	0.114439i
$245$	9.86525	−	11.5954i	0.630268	−	0.740800i
$246$	−2.26196	+	0.704225i	−0.144218	+	0.0448998i
$247$	−2.70761	+	4.68972i	−0.172281	+	0.298400i
$248$	−0.404726	+	0.449493i	−0.0257001	+	0.0285429i
$249$	0.799534	+	1.38483i	0.0506684	+	0.0877603i
$250$	1.19804	+	11.3986i	0.0757708	+	0.720911i
$251$	−13.8095	+	10.0332i	−0.871647	+	0.633289i	−0.931028	−	0.364946i	$-0.881087\pi$
$251$	−13.8095	+	10.0332i	−0.871647	+	0.633289i	0.0593811	+	0.998235i	$0.481087\pi$
$252$	−1.67884	−	7.38670i	−0.105757	−	0.465319i
$253$	4.23143	−	13.0230i	0.266028	−	0.818748i
$254$	0.401200	−	0.178626i	0.0251735	−	0.0112080i
$255$	0.534085	+	0.925063i	0.0334457	+	0.0579297i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−24.6296	+	10.9658i	−1.53635	+	0.684028i	−0.988315	−	0.152426i	$-0.951292\pi$
$257$	−24.6296	+	10.9658i	−1.53635	+	0.684028i	−0.548038	+	0.836454i	$0.684625\pi$
$258$	−1.14512	+	0.831975i	−0.0712918	+	0.0517965i
$259$	3.40366	+	1.05331i	0.211493	+	0.0654496i
$260$	−1.88517			−0.116914
$261$	3.03152	+	28.8430i	0.187646	+	1.78534i
$262$	−21.5727	+	4.58542i	−1.33277	+	0.283288i
$263$	0.510163	−	4.85387i	0.0314580	−	0.299303i	−0.967469	−	0.252990i	$-0.918586\pi$
$263$	0.510163	−	4.85387i	0.0314580	−	0.299303i	0.998927	−	0.0463131i	$-0.0147472\pi$
$264$	−1.09230	−	0.232176i	−0.0672265	−	0.0142894i
$265$	9.53933	−	29.3590i	0.585996	−	1.80351i
$266$	16.4127	−	1.95842i	1.00633	−	0.120078i
$267$	−0.202435	+	0.623032i	−0.0123888	+	0.0381289i
$268$	−1.51048	−	1.67756i	−0.0922673	−	0.102473i
$269$	−12.1533	+	13.4976i	−0.740998	+	0.822962i	−0.989327	−	0.145714i	$-0.953452\pi$
$269$	−12.1533	+	13.4976i	−0.740998	+	0.822962i	0.248328	+	0.968676i	$0.420119\pi$
$270$	0.493153	−	4.69204i	0.0300123	−	0.285548i
$271$	12.3782	+	13.7474i	0.751922	+	0.835094i	0.990712	−	0.135977i	$-0.0434174\pi$
$271$	12.3782	+	13.7474i	0.751922	+	0.835094i	−0.238790	+	0.971071i	$0.576751\pi$
$272$	−1.07394	+	0.780262i	−0.0651171	+	0.0473103i
$273$	−0.355963	−	0.770214i	−0.0215439	−	0.0466155i
$274$	0.777685	+	2.39347i	0.0469816	+	0.144595i
$275$	−0.0851475	−	0.810125i	−0.00513459	−	0.0488523i
$276$	0.175455	−	1.66935i	0.0105612	−	0.100483i
$277$	0.493672	−	4.69698i	0.0296619	−	0.282214i	−0.969630	−	0.244578i	$-0.921351\pi$
$277$	0.493672	−	4.69698i	0.0296619	−	0.282214i	0.999292	−	0.0376360i	$-0.0119827\pi$
$278$	2.06258	−	3.57249i	0.123705	−	0.214264i
$279$	1.40102	+	1.01790i	0.0838771	+	0.0609403i
$280$	3.44727	+	4.60729i	0.206014	+	0.275338i
$281$	−3.01874	−	9.29073i	−0.180083	−	0.554239i	0.819746	−	0.572727i	$-0.194115\pi$
$281$	−3.01874	−	9.29073i	−0.180083	−	0.554239i	−0.999829	+	0.0184886i	$0.994115\pi$
$282$	−0.0868625	−	0.826441i	−0.00517259	−	0.0492139i
$283$	9.80578	+	4.36582i	0.582893	+	0.259521i	0.676929	−	0.736048i	$-0.263310\pi$
$283$	9.80578	+	4.36582i	0.582893	+	0.259521i	−0.0940361	+	0.995569i	$0.529977\pi$
$284$	−4.26444	−	7.38623i	−0.253048	−	0.438292i
$285$	4.91726	+	1.04520i	0.291273	+	0.0619121i
$286$	2.61620			0.154699
$287$	−15.4882	−	6.86416i	−0.914237	−	0.405179i
$288$	2.86311			0.168710
$289$	14.9049	+	3.16813i	0.876757	+	0.186360i
$290$	−11.0152	−	19.0789i	−0.646836	−	1.12035i
$291$	0.936131	+	0.416792i	0.0548770	+	0.0244328i
$292$	0.663876	+	6.31635i	0.0388504	+	0.369637i
$293$	8.33214	+	25.6437i	0.486769	+	1.49812i	0.829402	+	0.558652i	$0.188681\pi$
$293$	8.33214	+	25.6437i	0.486769	+	1.49812i	−0.342633	+	0.939469i	$0.611319\pi$
$294$	−1.23145	+	2.27839i	−0.0718197	+	0.132878i
$295$	−2.21197	−	1.60709i	−0.128786	−	0.0935683i
$296$	−0.673328	+	1.16624i	−0.0391364	+	0.0677862i
$297$	−0.684385	+	6.51149i	−0.0397121	+	0.377835i
$298$	2.13609	−	20.3236i	0.123741	−	1.17731i
$299$	0.411055	+	3.91093i	0.0237719	+	0.226175i
$300$	−0.0308566	−	0.0949668i	−0.00178151	−	0.00548291i
$301$	−10.0802	−	0.916564i	−0.581014	−	0.0528299i
$302$	−16.1155	+	11.7086i	−0.927343	+	0.673754i
$303$	3.92624	+	4.36053i	0.225557	+	0.250506i
$304$	−0.653032	+	6.21319i	−0.0374540	+	0.356351i
$305$	−2.73534	+	3.03790i	−0.156625	+	0.173950i
$306$	2.54314	+	2.82445i	0.145382	+	0.161463i
$307$	4.30240	−	13.2414i	0.245551	−	0.755729i	−0.749994	−	0.661444i	$-0.769944\pi$
$307$	4.30240	−	13.2414i	0.245551	−	0.755729i	0.995545	−	0.0942843i	$-0.0300563\pi$
$308$	−4.78403	−	6.39389i	−0.272596	−	0.364326i
$309$	0.338125	−	1.04064i	0.0192353	−	0.0592001i
$310$	−1.28674	−	0.273504i	−0.0730818	−	0.0155340i
$311$	−1.82774	+	17.3898i	−0.103642	+	0.986086i	0.811882	+	0.583822i	$0.198443\pi$
$311$	−1.82774	+	17.3898i	−0.103642	+	0.986086i	−0.915524	+	0.402264i	$0.868223\pi$
$312$	0.313692	−	0.0666773i	0.0177593	−	0.00377486i
$313$	−3.39234	−	32.2759i	−0.191746	−	1.82434i	−0.492126	−	0.870524i	$-0.663780\pi$
$313$	−3.39234	−	32.2759i	−0.191746	−	1.82434i	0.300380	−	0.953820i	$-0.402887\pi$
$314$	−14.1907			−0.800827
$315$	12.0872	−	11.1947i	0.681039	−	0.630750i
$316$	0.273733	−	0.198879i	0.0153987	−	0.0111878i
$317$	25.8554	−	11.5115i	1.45218	−	0.646553i	0.479257	−	0.877675i	$-0.340906\pi$
$317$	25.8554	−	11.5115i	1.45218	−	0.646553i	0.972925	+	0.231122i	$0.0742396\pi$
$318$	−0.548930	+	5.22272i	−0.0307825	+	0.292876i
$319$	15.2867	+	26.4773i	0.855889	+	1.48244i
$320$	−1.98685	+	0.884604i	−0.111069	+	0.0494509i
$321$	1.83842	−	5.65806i	0.102610	−	0.315802i
$322$	8.80649	−	8.15620i	0.490766	−	0.454527i
$323$	−6.70934	+	4.87462i	−0.373317	+	0.271231i
$324$	−0.813936	−	7.74409i	−0.0452187	−	0.430227i
$325$	0.116968	+	0.202595i	0.00648824	+	0.0112380i
$326$	8.56891	−	9.51674i	0.474588	−	0.527083i
$327$	2.12808	−	3.68595i	0.117683	−	0.203833i
$328$	3.82728	−	5.13341i	0.211326	−	0.283445i
$329$	3.42502	−	4.85610i	0.188827	−	0.267725i
$330$	−0.750509	−	2.30983i	−0.0413142	−	0.127152i
$331$	−0.251994	+	0.436466i	−0.0138508	+	0.0239904i	−0.872868	−	0.487957i	$-0.837742\pi$
$331$	−0.251994	+	0.436466i	−0.0138508	+	0.0239904i	0.859017	+	0.511947i	$0.171076\pi$
$332$	−3.94834	−	1.75791i	−0.216693	−	0.0964780i
$333$	3.52229	+	1.56822i	0.193020	+	0.0859382i
$334$	9.96750	+	2.11866i	0.545397	+	0.115928i
$335$	1.51713	−	4.66924i	0.0828896	−	0.255108i
$336$	−0.736579	−	0.644723i	−0.0401837	−	0.0351725i
$337$	−18.2134			−0.992146			−0.496073	−	0.868281i	$-0.665225\pi$
$337$	−18.2134			−0.992146			−0.496073	+	0.868281i	$0.665225\pi$
$338$	11.1897	−	4.98198i	0.608640	−	0.270984i
$339$	−0.127531	+	1.21338i	−0.00692654	+	0.0659016i
$340$	−2.63747	−	1.17428i	−0.143037	−	0.0636842i
$341$	1.78570	+	0.379563i	0.0967012	+	0.0205545i
$342$	17.8870			0.967220
$343$	−17.3572	+	6.45978i	−0.937199	+	0.348796i
$344$	1.18220	−	3.63844i	0.0637400	−	0.196172i
$345$	3.33502	−	1.48485i	0.179551	−	0.0799414i
$346$	0.0686627	−	0.0762576i	0.00369133	−	0.00409964i
$347$	19.2074	−	4.08266i	1.03111	−	0.219169i	0.338866	−	0.940835i	$-0.389957\pi$
$347$	19.2074	−	4.08266i	1.03111	−	0.219169i	0.692242	+	0.721666i	$0.256623\pi$
$348$	2.50773	+	2.78512i	0.134429	+	0.149298i
$349$	1.52603	−	4.69664i	0.0816865	−	0.251405i	−0.901869	−	0.432009i	$-0.857805\pi$
$349$	1.52603	−	4.69664i	0.0816865	−	0.251405i	0.983556	+	0.180603i	$0.0578050\pi$
$350$	0.281244	−	0.656335i	0.0150331	−	0.0350826i
$351$	−0.581044	−	1.78827i	−0.0310139	−	0.0954508i
$352$	2.75731	−	1.22763i	0.146965	−	0.0654330i
$353$	−11.7314	+	2.49358i	−0.624398	+	0.132720i	−0.509236	−	0.860627i	$-0.670072\pi$
$353$	−11.7314	+	2.49358i	−0.624398	+	0.132720i	−0.115162	+	0.993347i	$0.536739\pi$
$354$	0.424911	+	0.189183i	0.0225838	+	0.0100550i
$355$	9.27466	−	16.0642i	0.492248	−	0.852598i
$356$	−0.547146	−	1.68394i	−0.0289987	−	0.0892488i
$357$	−0.0182462	−	1.29930i	−0.000965691	−	0.0687665i
$358$	10.6230	+	7.71805i	0.561442	+	0.407911i
$359$	8.96486	−	3.99141i	0.473147	−	0.210659i	−0.156288	−	0.987712i	$-0.549953\pi$
$359$	8.96486	−	3.99141i	0.473147	−	0.210659i	0.629436	+	0.777053i	$0.283286\pi$
$360$	3.11347	+	5.39268i	0.164094	+	0.284219i
$361$	−2.09372	+	19.9204i	−0.110196	+	1.04844i
$362$	−5.37725	−	5.97204i	−0.282622	−	0.313884i
$363$	−0.216106	−	0.665107i	−0.0113426	−	0.0349090i
$364$	2.00198	+	1.11866i	0.104932	+	0.0586337i
$365$	−11.1749	+	8.11908i	−0.584924	+	0.424972i
$366$	0.347710	−	0.602251i	0.0181751	−	0.0314802i
$367$	14.0994	−	15.6590i	0.735984	−	0.817393i	−0.252678	−	0.967550i	$-0.581311\pi$
$367$	14.0994	−	15.6590i	0.735984	−	0.817393i	0.988662	+	0.150157i	$0.0479780\pi$
$368$	2.26840	+	3.92898i	0.118248	+	0.204812i
$369$	−15.7624	−	9.36161i	−0.820559	−	0.487346i
$370$	−2.92882			−0.152262
$371$	−27.5520	+	25.5175i	−1.43043	+	1.32480i
$372$	0.223786			0.0116028
$373$	1.34682	+	12.8141i	0.0697358	+	0.663492i	0.972428	+	0.233204i	$0.0749211\pi$
$373$	1.34682	+	12.8141i	0.0697358	+	0.663492i	−0.902692	+	0.430287i	$0.858412\pi$
$374$	3.66022	+	1.62963i	0.189265	+	0.0842664i
$375$	2.83747	−	3.15133i	0.146526	−	0.162734i
$376$	1.50288	+	1.66912i	0.0775054	+	0.0860784i
$377$	−7.10332	−	5.16086i	−0.365839	−	0.265798i
$378$	−3.30795	+	4.69012i	−0.170143	+	0.241234i
$379$	13.1480	+	9.55262i	0.675370	+	0.490685i	0.871818	−	0.489829i	$-0.162941\pi$
$379$	13.1480	+	9.55262i	0.675370	+	0.490685i	−0.196449	+	0.980514i	$0.562941\pi$
$380$	−12.4127	+	5.52649i	−0.636758	+	0.283503i
$381$	−0.148437	−	0.0660886i	−0.00760468	−	0.00338582i
$382$	−5.97092	+	6.63138i	−0.305499	+	0.339291i
$383$	5.79799	−	10.0424i	0.296263	−	0.513143i	−0.679015	−	0.734125i	$-0.737593\pi$
$383$	5.79799	−	10.0424i	0.296263	−	0.513143i	0.975278	+	0.220982i	$0.0709261\pi$
$384$	0.299323	−	0.217471i	0.0152748	−	0.0110978i
$385$	6.84056	−	15.9637i	0.348627	−	0.813586i
$386$	−9.40620	−	6.83401i	−0.478763	−	0.347842i
$387$	−10.7140	−	2.27733i	−0.544623	−	0.115763i
$388$	−2.70912	+	0.575841i	−0.137535	+	0.0292339i
$389$	23.2361	−	4.93899i	1.17812	−	0.250417i	0.423077	−	0.906094i	$-0.360950\pi$
$389$	23.2361	−	4.93899i	1.17812	−	0.250417i	0.755041	+	0.655677i	$0.227617\pi$
$390$	0.466708	+	0.518332i	0.0236327	+	0.0262468i
$391$	−1.86103	+	5.72766i	−0.0941164	+	0.289660i
$392$	−0.926898	−	6.93836i	−0.0468154	−	0.350440i
$393$	6.60148	+	4.79626i	0.333001	+	0.241939i
$394$	−5.77022	−	6.40848i	−0.290699	−	0.322854i
$395$	0.672257	+	0.299308i	0.0338249	+	0.0150598i
$396$	−4.32079	−	7.48383i	−0.217128	−	0.376077i
$397$	35.2258	+	7.48747i	1.76793	+	0.375785i	0.972980	−	0.230889i	$-0.0741635\pi$
$397$	35.2258	+	7.48747i	1.76793	+	0.375785i	0.794950	+	0.606674i	$0.207497\pi$
$398$	16.3078	−	11.8483i	0.817439	−	0.593904i
$399$	−4.60172	−	4.02785i	−0.230374	−	0.201645i
$400$	0.218343	+	0.158636i	0.0109172	+	0.00793179i
$401$	−9.63740	+	16.6925i	−0.481269	+	0.833582i	−0.999769	−	0.0214953i	$-0.993157\pi$
$401$	−9.63740	+	16.6925i	−0.481269	+	0.833582i	0.518500	+	0.855078i	$0.326491\pi$
$402$	−0.0873015	+	0.830618i	−0.00435420	+	0.0414275i
$403$	−0.512826	+	0.109005i	−0.0255457	+	0.00542990i
$404$	−15.5127	−	3.29732i	−0.771785	−	0.164048i
$405$	13.7009	−	9.95429i	0.680804	−	0.494633i
$406$	0.376318	+	26.7975i	0.0186763	+	1.32994i
$407$	4.06454			0.201472
$408$	0.480407	+	0.102114i	0.0237837	+	0.00505538i
$409$	−2.29580	−	3.97644i	−0.113520	−	0.196623i	0.803667	−	0.595079i	$-0.202879\pi$
$409$	−2.29580	−	3.97644i	−0.113520	−	0.196623i	−0.917187	+	0.398457i	$0.869546\pi$
$410$	13.8307	+	1.62642i	0.683052	+	0.0803233i
$411$	0.465558	−	0.806371i	0.0229643	−	0.0397753i
$412$	0.913891	+	2.81267i	0.0450242	+	0.138570i
$413$	1.39538	+	3.01924i	0.0686620	+	0.148567i
$414$	10.5086	−	7.63495i	0.516470	−	0.375238i
$415$	−0.982549	−	9.34833i	−0.0482315	−	0.458892i
$416$	−0.579998	+	0.644153i	−0.0284368	+	0.0315822i
$417$	−1.49289	+	0.317323i	−0.0731071	+	0.0155394i
$418$	17.2260	−	7.66952i	0.842553	−	0.375129i
$419$	−10.2829			−0.502354			−0.251177	−	0.967941i	$-0.580818\pi$
$419$	−10.2829			−0.502354			−0.251177	+	0.967941i	$0.580818\pi$
$420$	0.413351	−	2.08845i	0.0201695	−	0.101906i
$421$	6.09367	+	4.42731i	0.296988	+	0.215774i	0.726293	−	0.687385i	$-0.241242\pi$
$421$	6.09367	+	4.42731i	0.296988	+	0.215774i	−0.429305	+	0.903159i	$0.641242\pi$
$422$	−1.38992	−	13.2242i	−0.0676601	−	0.643743i
$423$	4.30293	−	4.77888i	0.209215	−	0.232357i
$424$	−7.09691	−	12.2922i	−0.344657	−	0.596963i
$425$	0.0374489	+	0.356302i	0.00181654	+	0.0172832i
$426$	−0.975118	+	3.00111i	−0.0472446	+	0.145404i
$427$	4.70750	−	1.60298i	0.227812	−	0.0775737i
$428$	4.96891	+	15.2927i	0.240181	+	0.739202i
$429$	−0.647686	−	0.719329i	−0.0312706	−	0.0347295i
$430$	8.13859	−	1.72991i	0.392477	−	0.0834237i
$431$	−12.5075	+	2.65856i	−0.602467	+	0.128058i	−0.499040	−	0.866579i	$-0.666314\pi$
$431$	−12.5075	+	2.65856i	−0.602467	+	0.128058i	−0.103426	+	0.994637i	$0.532981\pi$
$432$	−1.45152	−	1.61207i	−0.0698361	−	0.0775609i
$433$	4.60291	+	14.1663i	0.221202	+	0.680789i	0.998655	+	0.0518482i	$0.0165112\pi$
$433$	4.60291	+	14.1663i	0.221202	+	0.680789i	−0.777453	+	0.628941i	$0.783489\pi$
$434$	1.20417	+	1.05400i	0.0578018	+	0.0505936i
$435$	−2.51877	+	7.75198i	−0.120766	+	0.371679i
$436$	1.20246	+	11.4406i	0.0575873	+	0.547907i
$437$	14.1716	+	24.5460i	0.677921	+	1.17419i
$438$	1.57234	−	1.74626i	0.0751292	−	0.0834395i
$439$	−2.15937	−	20.5451i	−0.103061	−	0.980562i	−0.916804	−	0.399337i	$-0.869240\pi$
$439$	−2.15937	−	20.5451i	−0.103061	−	0.980562i	0.813743	−	0.581225i	$-0.197426\pi$
$440$	5.31066	+	3.85842i	0.253176	+	0.183943i
$441$	−19.4791	+	4.71576i	−0.927575	+	0.224560i
$442$	−1.15064			−0.0547301
$443$	0.610615	−	0.271863i	0.0290112	−	0.0129166i	−0.392180	−	0.919889i	$-0.628279\pi$
$443$	0.610615	−	0.271863i	0.0290112	−	0.0129166i	0.421191	+	0.906972i	$0.361612\pi$
$444$	0.487353	−	0.103590i	0.0231288	−	0.00491617i
$445$	2.57672	−	2.86174i	0.122148	−	0.135660i
$446$	−0.473024	−	4.50052i	−0.0223983	−	0.213106i
$447$	−6.11683	+	4.44414i	−0.289316	+	0.210200i
$448$	2.63488	+	0.239582i	0.124486	+	0.0113192i
$449$	4.05286	+	12.4734i	0.191266	+	0.588657i	1.00000		0.000482002i	$0.000153426\pi$
$449$	4.05286	+	12.4734i	0.191266	+	0.588657i	−0.808734	+	0.588175i	$0.799847\pi$
$450$	0.386359	−	0.669193i	0.0182131	−	0.0315461i
$451$	−19.1940	−	2.25711i	−0.903808	−	0.106283i
$452$	−1.64880	−	2.85581i	−0.0775532	−	0.134326i
$453$	7.20898	+	1.53232i	0.338707	+	0.0719945i
$454$	20.3165			0.953502
$455$	0.0700356	+	4.98721i	0.00328332	+	0.233804i
$456$	1.87000	−	1.35863i	0.0875706	−	0.0636238i
$457$	2.37293	+	0.504383i	0.111001	+	0.0235940i	0.263077	−	0.964775i	$-0.415263\pi$
$457$	2.37293	+	0.504383i	0.111001	+	0.0235940i	−0.152076	+	0.988369i	$0.548596\pi$
$458$	−21.9943	+	4.67503i	−1.02773	+	0.218450i
$459$	0.301001	−	2.86383i	0.0140495	−	0.133672i
$460$	−4.93350	+	8.54507i	−0.230026	+	0.398416i
$461$	−28.9375	−	21.0244i	−1.34776	−	0.979202i	−0.999120	−	0.0419436i	$-0.986645\pi$
$461$	−28.9375	−	21.0244i	−1.34776	−	0.979202i	−0.348636	−	0.937258i	$-0.613355\pi$
$462$	−0.573639	+	2.89830i	−0.0266881	+	0.134841i
$463$	9.38833	−	6.82102i	0.436313	−	0.317000i	−0.347855	−	0.937548i	$-0.613090\pi$
$463$	9.38833	−	6.82102i	0.436313	−	0.317000i	0.784168	+	0.620548i	$0.213090\pi$
$464$	−9.90814	−	2.10604i	−0.459974	−	0.0977704i
$465$	0.243354	+	0.421502i	0.0112853	+	0.0195467i
$466$	19.1869	+	8.54255i	0.888816	+	0.395726i
$467$	−6.78820	−	7.53906i	−0.314120	−	0.348866i	0.565323	−	0.824870i	$-0.308752\pi$
$467$	−6.78820	−	7.53906i	−0.314120	−	0.348866i	−0.879443	+	0.476004i	$0.842085\pi$
$468$	2.00776	+	1.45872i	0.0928087	+	0.0674295i
$469$	−4.38185	+	4.05828i	−0.202335	+	0.187394i
$470$	−1.50950	+	4.64576i	−0.0696280	+	0.214293i
$471$	3.51316	+	3.90175i	0.161878	+	0.179783i
$472$	−1.22967	+	0.261375i	−0.0566003	+	0.0120308i
$473$	−11.2945	+	2.40073i	−0.519323	+	0.110386i
$474$	−0.122450	−	0.0260274i	−0.00562429	−	0.00119548i
$475$	1.36408	+	0.991063i	0.0625883	+	0.0454731i
$476$	2.10407	+	2.81211i	0.0964400	+	0.128893i
$477$	−32.8773	+	23.8867i	−1.50535	+	1.09370i
$478$	−6.15994	+	10.6693i	−0.281749	+	0.488004i
$479$	26.4900	−	29.4201i	1.21036	−	1.34424i	0.288129	−	0.957592i	$-0.406967\pi$
$479$	26.4900	−	29.4201i	1.21036	−	1.34424i	0.922228	−	0.386646i	$-0.126367\pi$
$480$	0.735104	+	0.327289i	0.0335528	+	0.0149387i
$481$	−1.06636	+	0.474773i	−0.0486217	+	0.0216478i
$482$	10.0284	+	7.28603i	0.456780	+	0.331870i
$483$	−4.42276	−	0.402148i	−0.201243	−	0.0182984i
$484$	1.52918	+	1.11102i	0.0695083	+	0.0505008i
$485$	−4.03060	−	4.47644i	−0.183020	−	0.203265i
$486$	−6.28230	+	6.97720i	−0.284971	+	0.316492i
$487$	−12.7849	−	5.69220i	−0.579338	−	0.257938i	0.0960791	−	0.995374i	$-0.469370\pi$
$487$	−12.7849	−	5.69220i	−0.579338	−	0.257938i	−0.675417	+	0.737436i	$0.736036\pi$
$488$	0.196471	+	1.86930i	0.00889383	+	0.0846191i
$489$	−4.73803			−0.214261
$490$	12.0605	−	9.29087i	0.544837	−	0.419719i
$491$	10.1294			0.457133			0.228567	−	0.973528i	$-0.426596\pi$
$491$	10.1294			0.457133			0.228567	+	0.973528i	$0.426596\pi$
$492$	−2.35895	+	0.218547i	−0.106350	+	0.00985288i
$493$	−6.72325	−	11.6450i	−0.302800	−	0.524465i
$494$	−3.62349	+	4.02429i	−0.163028	+	0.181061i
$495$	9.39721	−	16.2765i	0.422373	−	0.731572i
$496$	−0.489336	+	0.355524i	−0.0219718	+	0.0159635i
$497$	−19.3818	+	11.5559i	−0.869391	+	0.518355i
$498$	0.494139	+	1.52080i	0.0221429	+	0.0681489i
$499$	−18.4566	−	20.4982i	−0.826233	−	0.917625i	0.171482	−	0.985187i	$-0.445144\pi$
$499$	−18.4566	−	20.4982i	−0.826233	−	0.917625i	−0.997715	+	0.0675627i	$0.978478\pi$
$500$	−1.19804	+	11.3986i	−0.0535780	+	0.509761i
$501$	−1.88510	−	3.26509i	−0.0842201	−	0.145874i
$502$	−15.5937	+	6.94278i	−0.695983	+	0.309871i
$503$	18.7853	+	13.6483i	0.837596	+	0.608549i	0.921698	−	0.387908i	$-0.126802\pi$
$503$	18.7853	+	13.6483i	0.837596	+	0.608549i	−0.0841019	+	0.996457i	$0.526802\pi$
$504$	−0.106367	−	7.57434i	−0.00473795	−	0.337388i
$505$	−10.6586	−	32.8039i	−0.474302	−	1.45975i
$506$	6.84659	−	11.8586i	0.304368	−	0.527181i
$507$	−4.14002	−	1.84325i	−0.183865	−	0.0818618i
$508$	0.429571	−	0.0913081i	0.0190591	−	0.00405114i
$509$	−27.2483	+	12.1317i	−1.20776	+	0.537730i	−0.909079	−	0.416623i	$-0.863213\pi$
$509$	−27.2483	+	12.1317i	−1.20776	+	0.537730i	−0.298681	+	0.954353i	$0.596547\pi$
$510$	0.330083	+	1.01589i	0.0146163	+	0.0449844i
$511$	16.6852	−	1.99093i	0.738109	−	0.0880737i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−9.06822	−	10.0713i	−0.400372	−	0.444658i
$514$	−26.3713	+	5.60539i	−1.16319	+	0.247243i
$515$	−4.30387	+	4.77993i	−0.189651	+	0.210629i
$516$	−1.29307	+	0.575712i	−0.0569242	+	0.0253443i
$517$	2.09485	−	6.44727i	0.0921312	−	0.283551i
$518$	3.11029	+	1.73796i	0.136658	+	0.0763614i
$519$	−0.0379658			−0.00166651
$520$	−1.84398	−	0.391950i	−0.0808638	−	0.0171881i
$521$	−38.3569	−	17.0776i	−1.68045	−	0.748183i	−0.999880	−	0.0154970i	$-0.995067\pi$
$521$	−38.3569	−	17.0776i	−1.68045	−	0.748183i	−0.680567	−	0.732686i	$-0.738266\pi$
$522$	−3.03152	+	28.8430i	−0.132686	+	1.26242i
$523$	38.7544	−	17.2546i	1.69461	−	0.754489i	0.695248	−	0.718769i	$-0.255294\pi$
$523$	38.7544	−	17.2546i	1.69461	−	0.754489i	0.999362	−	0.0357196i	$-0.0113723\pi$
$524$	−22.0547			−0.963463
$525$	−0.250087	+	0.0851589i	−0.0109147	+	0.00371664i
$526$	1.50819	−	4.64174i	0.0657603	−	0.202389i
$527$	−0.785373	−	0.166936i	−0.0342114	−	0.00727185i
$528$	−1.02016	−	0.454204i	−0.0443968	−	0.0197667i
$529$	−2.20846	−	0.983272i	−0.0960202	−	0.0427509i
$530$	15.4350	−	26.7341i	0.670452	−	1.16126i
$531$	1.11226	+	3.42318i	0.0482679	+	0.148553i
$532$	16.4612	+	1.49677i	0.713683	+	0.0648931i
$533$	5.29930	−	1.64985i	0.229538	−	0.0714629i
$534$	−0.327547	+	0.567329i	−0.0141744	+	0.0245507i
$535$	−23.4005	+	25.9889i	−1.01169	+	1.12360i
$536$	−1.12869	−	1.95495i	−0.0487519	−	0.0844408i
$537$	−0.507816	−	4.83154i	−0.0219139	−	0.208497i
$538$	−14.6940	+	10.6758i	−0.633503	+	0.460267i
$539$	−16.7372	+	12.8936i	−0.720924	+	0.555369i
$540$	1.45791	−	4.48697i	0.0627382	−	0.193088i
$541$	25.1528	−	11.1987i	1.08140	−	0.481471i	0.212858	−	0.977083i	$-0.431723\pi$
$541$	25.1528	−	11.1987i	1.08140	−	0.481471i	0.868544	+	0.495612i	$0.165056\pi$
$542$	9.24946	+	16.0205i	0.397299	+	0.688141i
$543$	−0.310790	+	2.95697i	−0.0133373	+	0.126896i
$544$	−1.21270	+	0.539927i	−0.0519939	+	0.0231492i
$545$	−20.2409	+	14.7058i	−0.867023	+	0.629929i
$546$	−0.188048	−	0.827392i	−0.00804771	−	0.0354091i
$547$	38.1459			1.63100			0.815501	−	0.578756i	$-0.196462\pi$
$547$	38.1459			1.63100			0.815501	+	0.578756i	$0.196462\pi$
$548$	0.263061	+	2.50285i	0.0112374	+	0.106917i
$549$	5.26389	−	1.11887i	0.224657	−	0.0477524i
$550$	0.0851475	−	0.810125i	0.00363070	−	0.0345438i
$551$	−61.9002	−	13.1573i	−2.63704	−	0.560520i
$552$	0.518698	−	1.59639i	0.0220773	−	0.0679468i
$553$	−0.536301	−	0.716770i	−0.0228058	−	0.0304802i
$554$	1.45944	−	4.49170i	0.0620057	−	0.190834i
$555$	0.725080	+	0.805283i	0.0307779	+	0.0341824i
$556$	2.76027	−	3.06559i	0.117061	−	0.130010i
$557$	−2.69283	+	25.6206i	−0.114099	+	1.08558i	0.776289	+	0.630377i	$0.217100\pi$
$557$	−2.69283	+	25.6206i	−0.114099	+	1.08558i	−0.890388	+	0.455202i	$0.849567\pi$
$558$	1.15877	+	1.28695i	0.0490548	+	0.0544809i
$559$	2.68276	−	1.94914i	0.113469	−	0.0824399i
$560$	2.41403	+	5.22334i	0.102011	+	0.220726i
$561$	−0.458081	−	1.40983i	−0.0193402	−	0.0595230i
$562$	−1.02112	−	9.71534i	−0.0430735	−	0.409817i
$563$	1.05347	−	10.0231i	0.0443986	−	0.422425i	−0.949636	−	0.313356i	$-0.898547\pi$
$563$	1.05347	−	10.0231i	0.0443986	−	0.422425i	0.994034	−	0.109068i	$-0.0347867\pi$
$564$	0.0868625	−	0.826441i	0.00365757	−	0.0347995i
$565$	3.58595	−	6.21105i	0.150862	−	0.261301i
$566$	8.68380	+	6.30915i	0.365007	+	0.265193i
$567$	−20.4567	+	2.44096i	−0.859100	+	0.102511i
$568$	−2.63557	−	8.11145i	−0.110586	−	0.340349i
$569$	−0.284039	−	2.70245i	−0.0119075	−	0.113293i	0.986954	−	0.161005i	$-0.0514735\pi$
$569$	−0.284039	−	2.70245i	−0.0119075	−	0.113293i	−0.998861	+	0.0477125i	$0.984807\pi$
$570$	4.59250	+	2.04471i	0.192359	+	0.0856436i
$571$	−19.5328	−	33.8318i	−0.817423	−	1.41582i	−0.907575	−	0.419890i	$-0.862069\pi$
$571$	−19.5328	−	33.8318i	−0.817423	−	1.41582i	0.0901524	−	0.995928i	$-0.471265\pi$
$572$	2.55903	+	0.543939i	0.106998	+	0.0227432i
$573$	3.30152			0.137923
$574$	−13.7226	−	9.93434i	−0.572769	−	0.414651i
$575$	1.22442			0.0510620
$576$	2.80055	+	0.595274i	0.116689	+	0.0248031i
$577$	−10.3153	−	17.8666i	−0.429431	−	0.743797i	0.567391	−	0.823448i	$-0.307953\pi$
$577$	−10.3153	−	17.8666i	−0.429431	−	0.743797i	−0.996823	+	0.0796513i	$0.974619\pi$
$578$	13.9205	+	6.19779i	0.579015	+	0.257794i
$579$	0.449650	+	4.27813i	0.0186868	+	0.177793i
$580$	−6.80778	−	20.9522i	−0.282678	−	0.869993i
$581$	−4.50386	+	10.5106i	−0.186852	+	0.436053i
$582$	0.829018	+	0.602317i	0.0343639	+	0.0249668i
$583$	−21.4203	+	37.1010i	−0.887136	+	1.53657i
$584$	−0.663876	+	6.31635i	−0.0274714	+	0.261373i
$585$	−0.564189	+	5.36790i	−0.0233263	+	0.221935i
$586$	2.81844	+	26.8157i	0.116429	+	1.10775i
$587$	−12.5704	−	38.6877i	−0.518836	−	1.59681i	−0.776193	−	0.630496i	$-0.782852\pi$
$587$	−12.5704	−	38.6877i	−0.518836	−	1.59681i	0.257357	−	0.966316i	$-0.417148\pi$
$588$	−1.67824	+	1.97257i	−0.0692096	+	0.0813472i
$589$	−3.05709	+	2.22110i	−0.125965	+	0.0915189i
$590$	−1.82950	−	2.03186i	−0.0753192	−	0.0836505i
$591$	−0.333502	+	3.17306i	−0.0137185	+	0.130522i
$592$	−0.901089	+	1.00076i	−0.0370345	+	0.0411310i
$593$	5.44396	+	6.04613i	0.223557	+	0.248285i	0.844481	−	0.535586i	$-0.179909\pi$
$593$	5.44396	+	6.04613i	0.223557	+	0.248285i	−0.620924	+	0.783871i	$0.713242\pi$
$594$	−2.02325	+	6.22691i	−0.0830148	+	0.255493i
$595$	−3.00856	+	7.02103i	−0.123339	+	0.287834i
$596$	6.31492	−	19.4353i	0.258669	−	0.796102i
$597$	−7.29502	−	1.55060i	−0.298565	−	0.0634620i
$598$	−0.411055	+	3.91093i	−0.0168093	+	0.159930i
$599$	32.9839	−	7.01095i	1.34769	−	0.286460i	0.523137	−	0.852249i	$-0.324762\pi$
$599$	32.9839	−	7.01095i	1.34769	−	0.286460i	0.824550	+	0.565789i	$0.191428\pi$
$600$	−0.0104376	−	0.0993070i	−0.000426113	−	0.00405419i
$601$	−9.42023			−0.384259			−0.192130	−	0.981370i	$-0.561539\pi$
$601$	−9.42023			−0.384259			−0.192130	+	0.981370i	$0.561539\pi$
$602$	−9.66938	−	2.99233i	−0.394094	−	0.121958i
$603$	−5.22878	+	3.79893i	−0.212932	+	0.154704i
$604$	−18.1977	+	8.10214i	−0.740454	+	0.329671i
$605$	−0.429707	+	4.08839i	−0.0174701	+	0.166217i
$606$	2.93384	+	5.08155i	0.119179	+	0.206424i
$607$	−39.5109	+	17.5914i	−1.60370	+	0.714012i	−0.996737	−	0.0807213i	$-0.974278\pi$
$607$	−39.5109	+	17.5914i	−1.60370	+	0.714012i	−0.606959	+	0.794733i	$0.707611\pi$
$608$	−1.93056	+	5.94164i	−0.0782944	+	0.240965i
$609$	7.27485	−	6.73766i	0.294792	−	0.273024i
$610$	−3.30718	+	2.40280i	−0.133904	+	0.0972867i
$611$	0.203500	+	1.93618i	0.00823274	+	0.0783293i
$612$	1.90033	+	3.29148i	0.0768165	+	0.133050i
$613$	9.35387	−	10.3885i	0.377799	−	0.419588i	−0.524017	−	0.851708i	$-0.675567\pi$
$613$	9.35387	−	10.3885i	0.377799	−	0.419588i	0.901817	+	0.432119i	$0.142234\pi$
$614$	6.96144	−	12.0576i	0.280941	−	0.486604i
$615$	−2.97686	−	4.20544i	−0.120038	−	0.169580i
$616$	−3.35013	−	7.24882i	−0.134980	−	0.292063i
$617$	3.40609	+	10.4829i	0.137124	+	0.422024i	0.995914	−	0.0903028i	$-0.0287835\pi$
$617$	3.40609	+	10.4829i	0.137124	+	0.422024i	−0.858790	+	0.512327i	$0.828783\pi$
$618$	0.547098	−	0.947601i	0.0220075	−	0.0381181i
$619$	−5.68143	−	2.52953i	−0.228356	−	0.101671i	0.289369	−	0.957217i	$-0.406554\pi$
$619$	−5.68143	−	2.52953i	−0.228356	−	0.101671i	−0.517725	+	0.855547i	$0.673221\pi$
$620$	−1.20175	−	0.535056i	−0.0482636	−	0.0214883i
$621$	−9.62642	−	2.04616i	−0.386295	−	0.0821096i
$622$	−5.40335	+	16.6298i	−0.216655	+	0.666794i
$623$	−4.43453	+	1.51003i	−0.177666	+	0.0604981i
$624$	0.320700			0.0128383
$625$	−21.5393	+	9.58992i	−0.861573	+	0.383597i
$626$	3.39234	−	32.2759i	0.135585	−	1.29001i
$627$	−6.37336	−	2.83760i	−0.254527	−	0.113323i
$628$	−13.8806	−	2.95041i	−0.553896	−	0.117734i
$629$	−1.78763			−0.0712776
$630$	14.1506	−	8.43699i	0.563774	−	0.336138i
$631$	−11.5234	+	35.4655i	−0.458741	+	1.41186i	0.407946	+	0.913006i	$0.366245\pi$
$631$	−11.5234	+	35.4655i	−0.458741	+	1.41186i	−0.866687	+	0.498853i	$0.833755\pi$
$632$	0.309101	−	0.137620i	0.0122954	−	0.00547425i
$633$	−3.29191	+	3.65604i	−0.130842	+	0.145314i
$634$	27.6837	−	5.88436i	1.09946	−	0.233698i
$635$	0.639112	+	0.709806i	0.0253624	+	0.0281678i
$636$	−1.62280	+	4.99446i	−0.0643482	+	0.198043i
$637$	2.88503	−	5.33778i	0.114309	−	0.211490i
$638$	9.44768	+	29.0770i	0.374037	+	1.15117i
$639$	−22.3080	+	9.93216i	−0.882491	+	0.392910i
$640$	−2.12736	+	0.452183i	−0.0840911	+	0.0178741i
$641$	−20.6987	−	9.21564i	−0.817548	−	0.363996i	−0.0450277	−	0.998986i	$-0.514338\pi$
$641$	−20.6987	−	9.21564i	−0.817548	−	0.363996i	−0.772521	+	0.634990i	$0.781004\pi$
$642$	2.97462	−	5.15219i	0.117399	−	0.203341i
$643$	1.40389	+	4.32072i	0.0553639	+	0.170393i	0.974915	−	0.222578i	$-0.0714473\pi$
$643$	1.40389	+	4.32072i	0.0553639	+	0.170393i	−0.919551	+	0.392971i	$0.871447\pi$
$644$	10.3098	−	6.14699i	0.406264	−	0.242225i
$645$	−2.49049	−	1.80945i	−0.0980630	−	0.0712470i
$646$	−7.57621	+	3.37315i	−0.298082	+	0.132715i
$647$	−14.3558	−	24.8650i	−0.564386	−	0.977545i	−0.997107	−	0.0760171i	$-0.975780\pi$
$647$	−14.3558	−	24.8650i	−0.564386	−	0.977545i	0.432720	−	0.901528i	$-0.357554\pi$
$648$	0.813936	−	7.74409i	0.0319744	−	0.304217i
$649$	2.53893	+	2.81977i	0.0996618	+	0.110686i
$650$	0.0722904	+	0.222487i	0.00283546	+	0.00872666i
$651$	−0.00831381	−	0.592024i	−0.000325844	−	0.0232032i
$652$	10.3603	−	7.52720i	0.405741	−	0.294788i
$653$	18.9584	−	32.8369i	0.741900	−	1.28501i	−0.209730	−	0.977759i	$-0.567258\pi$
$653$	18.9584	−	32.8369i	0.741900	−	1.28501i	0.951629	−	0.307249i	$-0.0994083\pi$
$654$	2.84793	−	3.16295i	0.111363	−	0.123681i
$655$	−23.9832	−	41.5401i	−0.937100	−	1.62310i
$656$	4.81095	−	4.22549i	0.187836	−	0.164978i
$657$	18.1840			0.709427
$658$	4.35981	−	4.03788i	0.169963	−	0.157413i
$659$	−3.31344			−0.129073			−0.0645366	−	0.997915i	$-0.520557\pi$
$659$	−3.31344			−0.129073			−0.0645366	+	0.997915i	$0.520557\pi$
$660$	−0.253868	−	2.41539i	−0.00988181	−	0.0940191i
$661$	−2.25294	−	1.00307i	−0.0876293	−	0.0390151i	0.362454	−	0.932002i	$-0.381939\pi$
$661$	−2.25294	−	1.00307i	−0.0876293	−	0.0390151i	−0.450083	+	0.892987i	$0.648606\pi$
$662$	−0.337234	+	0.374536i	−0.0131070	+	0.0145568i
$663$	0.284860	+	0.316369i	0.0110630	+	0.0122868i
$664$	−3.49657	−	2.54040i	−0.135693	−	0.0985868i
$665$	15.0814	+	32.6324i	0.584832	+	1.26543i
$666$	3.11927	+	2.26628i	0.120869	+	0.0878166i
$667$	−41.9824	+	18.6918i	−1.62556	+	0.723748i
$668$	9.30919	+	4.14472i	0.360183	+	0.160364i
$669$	−1.12032	+	1.24424i	−0.0433141	+	0.0481052i
$670$	2.45477	−	4.25178i	0.0948359	−	0.164261i
$671$	4.58962	−	3.33455i	0.177180	−	0.128729i
$672$	−0.586438	−	0.783778i	−0.0226223	−	0.0302349i
$673$	27.3843	+	19.8959i	1.05559	+	0.766929i	0.973267	−	0.229677i	$-0.0737668\pi$
$673$	27.3843	+	19.8959i	1.05559	+	0.766929i	0.0823207	+	0.996606i	$0.473767\pi$
$674$	−17.8154	−	3.78678i	−0.686223	−	0.145861i
$675$	−0.572661	+	0.121723i	−0.0220418	+	0.00468512i
$676$	11.9810	−	2.54664i	0.460808	−	0.0979477i
$677$	31.3685	+	34.8382i	1.20559	+	1.33894i	0.925398	+	0.378997i	$0.123731\pi$
$677$	31.3685	+	34.8382i	1.20559	+	1.33894i	0.280191	+	0.959944i	$0.409602\pi$
$678$	−0.377020	+	1.16035i	−0.0144794	+	0.0445629i
$679$	1.62403	+	7.14555i	0.0623244	+	0.274221i
$680$	−2.33569	−	1.69698i	−0.0895696	−	0.0650761i
$681$	−5.02971	−	5.58606i	−0.192739	−	0.214058i
$682$	1.66777	+	0.742537i	0.0638620	+	0.0284332i
$683$	17.5044	+	30.3185i	0.669788	+	1.16011i	0.977963	+	0.208777i	$0.0669482\pi$
$683$	17.5044	+	30.3185i	0.669788	+	1.16011i	−0.308176	+	0.951329i	$0.599718\pi$
$684$	17.4962	+	3.71892i	0.668983	+	0.142197i
$685$	−4.42807	+	3.21718i	−0.169188	+	0.122922i
$686$	−18.3209	+	2.70986i	−0.699497	+	0.103463i
$687$	6.73049	+	4.88998i	0.256784	+	0.186565i
$688$	1.91284	−	3.31314i	0.0729264	−	0.126312i
$689$	1.28603	−	12.2357i	0.0489937	−	0.466144i
$690$	3.57086	−	0.759009i	0.135940	−	0.0288950i
$691$	4.07933	+	0.867088i	0.155185	+	0.0329856i	0.284849	−	0.958572i	$-0.408057\pi$
$691$	4.07933	+	0.867088i	0.155185	+	0.0329856i	−0.129664	+	0.991558i	$0.541390\pi$
$692$	0.0830171	−	0.0603155i	0.00315584	−	0.00229285i
$693$	−19.6379	+	11.7086i	−0.745981	+	0.444775i
$694$	19.6365			0.745392
$695$	8.77567	+	1.86533i	0.332880	+	0.0707559i
$696$	1.87387	+	3.24565i	0.0710290	+	0.123026i
$697$	8.44173	+	0.992704i	0.319753	+	0.0376013i
$698$	2.46917	−	4.27673i	0.0934594	−	0.161876i
$699$	−2.40126	−	7.39033i	−0.0908241	−	0.279528i
$700$	0.411558	−	0.583519i	0.0155554	−	0.0220549i
$701$	3.24204	−	2.35548i	0.122450	−	0.0889651i	−0.524875	−	0.851180i	$-0.675888\pi$
$701$	3.24204	−	2.35548i	0.122450	−	0.0889651i	0.647325	+	0.762214i	$0.275888\pi$
$702$	−0.196545	−	1.87000i	−0.00741811	−	0.0705786i
$703$	−5.62947	+	6.25216i	−0.212320	+	0.235805i
$704$	2.95229	−	0.627529i	0.111269	−	0.0236509i
$705$	1.65106	−	0.735101i	0.0621826	−	0.0276855i
$706$	−11.9935			−0.451380
$707$	−8.14673	+	41.1612i	−0.306389	+	1.54803i
$708$	0.376293	+	0.273393i	0.0141420	+	0.0102747i
$709$	3.79839	+	36.1393i	0.142652	+	1.35724i	0.798340	+	0.602207i	$0.205712\pi$
$709$	3.79839	+	36.1393i	0.142652	+	1.35724i	−0.655688	+	0.755032i	$0.727621\pi$
$710$	12.4119	−	13.7848i	0.465811	−	0.517335i
$711$	−0.484371	−	0.838955i	−0.0181653	−	0.0314633i
$712$	−0.185078	−	1.76090i	−0.00693610	−	0.0659926i
$713$	−0.847972	+	2.60979i	−0.0317568	+	0.0977374i
$714$	0.252293	−	1.27471i	0.00944183	−	0.0477046i
$715$	1.75828	+	5.41144i	0.0657561	+	0.202376i
$716$	8.78617	+	9.75803i	0.328355	+	0.364675i
$717$	4.45855	−	0.947694i	0.166508	−	0.0353923i
$718$	9.59882	−	2.04029i	0.358225	−	0.0761430i
$719$	34.2183	+	38.0033i	1.27613	+	1.41728i	0.861874	+	0.507123i	$0.169291\pi$
$719$	34.2183	+	38.0033i	1.27613	+	1.41728i	0.414255	+	0.910161i	$0.364042\pi$
$720$	1.92423	+	5.92216i	0.0717117	+	0.220706i
$721$	7.40693	−	2.52218i	0.275849	−	0.0939310i
$722$	−6.18966	+	19.0498i	−0.230355	+	0.708961i
$723$	−0.479391	−	4.56110i	−0.0178287	−	0.169629i
$724$	−4.01809	−	6.95954i	−0.149331	−	0.258649i
$725$	−1.82928	+	2.03162i	−0.0679379	+	0.0754526i
$726$	−0.0731004	−	0.695504i	−0.00271301	−	0.0258126i
$727$	13.6212	+	9.89637i	0.505182	+	0.367036i	0.810993	−	0.585056i	$-0.198928\pi$
$727$	13.6212	+	9.89637i	0.505182	+	0.367036i	−0.305811	+	0.952092i	$0.598928\pi$
$728$	1.72565	+	1.51045i	0.0639568	+	0.0559810i
$729$	−19.8865			−0.736539
$730$	−12.6188	+	5.61825i	−0.467043	+	0.207941i
$731$	4.96747	−	1.05587i	0.183728	−	0.0390527i
$732$	0.465327	−	0.516798i	0.0171990	−	0.0191014i
$733$	−3.90631	−	37.1661i	−0.144283	−	1.37276i	−0.791833	−	0.610738i	$-0.790873\pi$
$733$	−3.90631	−	37.1661i	−0.144283	−	1.37276i	0.647550	−	0.762023i	$-0.275794\pi$
$734$	17.0470	−	12.3854i	0.629217	−	0.457153i
$735$	−5.54033	−	1.01593i	−0.204358	−	0.0374731i
$736$	1.40195	+	4.31475i	0.0516765	+	0.159044i
$737$	−3.40666	+	5.90051i	−0.125486	+	0.217348i
$738$	−13.4716	−	12.4342i	−0.495896	−	0.457710i
$739$	−23.0092	−	39.8532i	−0.846409	−	1.46602i	−0.884392	−	0.466745i	$-0.845427\pi$
$739$	−23.0092	−	39.8532i	−0.846409	−	1.46602i	0.0379832	−	0.999278i	$-0.487907\pi$
$740$	−2.86482	−	0.608935i	−0.105313	−	0.0223849i
$741$	2.00354			0.0736020
$742$	−32.2553	+	19.2315i	−1.18413	+	0.706010i
$743$	18.1860	−	13.2129i	0.667181	−	0.484736i	−0.201899	−	0.979406i	$-0.564711\pi$
$743$	18.1860	−	13.2129i	0.667181	−	0.484736i	0.869080	+	0.494671i	$0.164711\pi$
$744$	0.218896	+	0.0465277i	0.00802510	+	0.00170579i
$745$	43.4736	−	9.24060i	1.59275	−	0.338549i
$746$	−1.34682	+	12.8141i	−0.0493106	+	0.469159i
$747$	−6.18718	+	10.7165i	−0.226377	+	0.392096i
$748$	3.24141	+	2.35502i	0.118518	+	0.0861082i
$749$	40.2722	−	13.7133i	1.47151	−	0.501074i
$750$	3.43066	−	2.49252i	0.125270	−	0.0910140i
$751$	−15.8839	−	3.37623i	−0.579612	−	0.123200i	−0.0912291	−	0.995830i	$-0.529080\pi$
$751$	−15.8839	−	3.37623i	−0.579612	−	0.123200i	−0.488382	+	0.872630i	$0.662413\pi$
$752$	1.12301	+	1.94512i	0.0409521	+	0.0709311i
$753$	5.76943	+	2.56872i	0.210250	+	0.0936093i
$754$	−5.87509	−	6.52495i	−0.213958	−	0.237625i
$755$	−35.0493	−	25.4648i	−1.27558	−	0.926760i
$756$	−4.21080	+	3.89986i	−0.153145	+	0.141837i
$757$	5.06188	−	15.5789i	0.183977	−	0.566223i	−0.815952	−	0.578119i	$-0.803787\pi$
$757$	5.06188	−	15.5789i	0.183977	−	0.566223i	0.999929	+	0.0118964i	$0.00378682\pi$
$758$	10.8746	+	12.0775i	0.394984	+	0.438675i
$759$	−4.95555	+	1.05333i	−0.179875	+	0.0382336i
$760$	−13.2905	+	2.82498i	−0.482096	+	0.102473i
$761$	−23.1433	−	4.91927i	−0.838945	−	0.178323i	−0.231650	−	0.972799i	$-0.574412\pi$
$761$	−23.1433	−	4.91927i	−0.838945	−	0.178323i	−0.607296	+	0.794476i	$0.707746\pi$
$762$	−0.131453	−	0.0955063i	−0.00476205	−	0.00345983i
$763$	30.2214	−	3.60612i	1.09409	−	0.130550i
$764$	−7.21918	+	5.24504i	−0.261181	+	0.189759i
$765$	−4.13300	+	7.15857i	−0.149429	+	0.258819i
$766$	7.75922	−	8.61749i	0.280352	−	0.311362i
$767$	−0.995477	−	0.443215i	−0.0359446	−	0.0160036i
$768$	0.337997	−	0.150486i	0.0121964	−	0.00543020i
$769$	−3.15817	−	2.29454i	−0.113886	−	0.0827433i	0.529384	−	0.848382i	$-0.322423\pi$
$769$	−3.15817	−	2.29454i	−0.113886	−	0.0827433i	−0.643271	+	0.765639i	$0.722423\pi$
$770$	10.0101	−	14.1926i	0.360740	−	0.511467i
$771$	8.06990	+	5.86312i	0.290630	+	0.211155i
$772$	−7.77978	−	8.64033i	−0.280001	−	0.310972i
$773$	31.2460	−	34.7022i	1.12384	−	1.24815i	0.158442	−	0.987368i	$-0.449353\pi$
$773$	31.2460	−	34.7022i	1.12384	−	1.24815i	0.965398	−	0.260782i	$-0.0839804\pi$
$774$	−10.0064	−	4.45513i	−0.359672	−	0.160136i
$775$	0.0170634	+	0.162348i	0.000612937	+	0.00583171i
$776$	−2.76964			−0.0994243
$777$	−0.292152	−	1.28544i	−0.0104809	−	0.0461149i
$778$	23.7552			0.851666
$779$	30.0560	−	26.3984i	1.07687	−	0.945821i
$780$	0.348742	+	0.604039i	0.0124870	+	0.0216281i
$781$	−17.2249	+	19.1302i	−0.616357	+	0.684534i
$782$	−3.01121	+	5.21557i	−0.107681	+	0.186508i
$783$	17.7769	−	12.9157i	0.635295	−	0.461569i
$784$	0.535924	−	6.97945i	0.0191401	−	0.249266i
$785$	−9.53722	−	29.3525i	−0.340398	−	1.04764i
$786$	5.46002	+	6.06397i	0.194753	+	0.216295i
$787$	5.69902	−	54.2226i	0.203148	−	1.93283i	−0.133203	−	0.991089i	$-0.542526\pi$
$787$	5.69902	−	54.2226i	0.203148	−	1.93283i	0.336351	−	0.941737i	$-0.390807\pi$
$788$	−4.31173	−	7.46813i	−0.153599	−	0.266041i
$789$	−1.64963	+	0.734464i	−0.0587285	+	0.0261476i
$790$	0.595337	+	0.432538i	0.0211812	+	0.0153890i
$791$	−7.49377	+	4.46799i	−0.266448	+	0.158863i
$792$	−2.67040	−	8.21863i	−0.0948884	−	0.292036i
$793$	−0.814610	+	1.41095i	−0.0289277	+	0.0501042i
$794$	32.8993	+	14.6477i	1.16755	+	0.519827i
$795$	−11.1718	+	2.37464i	−0.396222	+	0.0842197i
$796$	18.4149	−	8.19884i	0.652699	−	0.290600i
$797$	−1.68878	−	5.19752i	−0.0598195	−	0.184105i	0.916681	−	0.399619i	$-0.130858\pi$
$797$	−1.68878	−	5.19752i	−0.0598195	−	0.184105i	−0.976501	+	0.215513i	$0.930858\pi$
$798$	−3.66372	−	4.89658i	−0.129694	−	0.173337i
$799$	−0.921338	+	2.83559i	−0.0325946	+	0.100316i
$800$	0.180590	+	0.200565i	0.00638481	+	0.00709106i
$801$	−4.95865	+	1.05399i	−0.175205	+	0.0372411i
$802$	−12.8974	+	14.3240i	−0.455422	+	0.505797i
$803$	17.5121	−	7.79687i	0.617987	−	0.275146i
$804$	−0.258089	+	0.794316i	−0.00910210	+	0.0280134i
$805$	22.7892	+	12.7341i	0.803214	+	0.448817i
$806$	−0.524283			−0.0184671
$807$	6.57309	+	1.39715i	0.231384	+	0.0491822i
$808$	−14.4882	−	6.45054i	−0.509691	−	0.226929i
$809$	0.634722	−	6.03898i	0.0223156	−	0.212319i	−0.977682	−	0.210091i	$-0.932624\pi$
$809$	0.634722	−	6.03898i	0.0223156	−	0.212319i	0.999998	−	0.00222830i	$-0.000709290\pi$
$810$	15.4711	−	6.88819i	0.543600	−	0.242026i
$811$	−6.77608			−0.237940			−0.118970	−	0.992898i	$-0.537959\pi$
$811$	−6.77608			−0.237940			−0.118970	+	0.992898i	$0.537959\pi$
$812$	−5.20341	+	26.2901i	−0.182604	+	0.922602i
$813$	2.11501	−	6.50932i	0.0741766	−	0.228292i
$814$	3.97572	+	0.845066i	0.139349	+	0.0296195i
$815$	25.4437	+	11.3283i	0.891254	+	0.396812i
$816$	0.448678	+	0.199764i	0.0157069	+	0.00699315i
$817$	11.9503	−	20.6985i	0.418088	−	0.724150i
$818$	−1.41888	−	4.36687i	−0.0496101	−	0.152684i
$819$	3.78445	−	5.36570i	0.132239	−	0.187493i
$820$	13.1904	+	4.46645i	0.460627	+	0.155975i
$821$	−3.77294	+	6.53493i	−0.131677	+	0.228071i	−0.924323	−	0.381611i	$-0.875369\pi$
$821$	−3.77294	+	6.53493i	−0.131677	+	0.228071i	0.792646	+	0.609682i	$0.208703\pi$
$822$	0.623039	−	0.691955i	0.0217310	−	0.0241347i
$823$	−4.98467	−	8.63369i	−0.173755	−	0.300952i	0.765975	−	0.642870i	$-0.222257\pi$
$823$	−4.98467	−	8.63369i	−0.173755	−	0.300952i	−0.939730	+	0.341919i	$0.888923\pi$
$824$	0.309134	+	2.94121i	0.0107692	+	0.102462i
$825$	−0.243825	+	0.177149i	−0.00848889	+	0.00616754i
$826$	0.737149	+	3.24338i	0.0256487	+	0.112852i
$827$	5.56289	−	17.1208i	0.193441	−	0.595349i	−0.806551	−	0.591165i	$-0.798668\pi$
$827$	5.56289	−	17.1208i	0.193441	−	0.595349i	0.999991	−	0.00418390i	$-0.00133178\pi$
$828$	11.8664	−	5.28325i	0.412385	−	0.183606i
$829$	17.1824	+	29.7608i	0.596770	+	1.03364i	0.993294	+	0.115612i	$0.0368828\pi$
$829$	17.1824	+	29.7608i	0.596770	+	1.03364i	−0.396525	+	0.918024i	$0.629784\pi$
$830$	0.982549	−	9.34833i	0.0341048	−	0.324485i
$831$	−1.59631	+	0.710723i	−0.0553754	+	0.0246547i
$832$	−0.701251	+	0.509489i	−0.0243115	+	0.0176633i
$833$	7.36123	−	5.67078i	0.255052	−	0.196481i
$834$	−1.52624			−0.0528494
$835$	2.31661	+	22.0410i	0.0801694	+	0.762761i
$836$	18.4442	−	3.92043i	0.637906	−	0.135591i
$837$	0.137150	−	1.30489i	0.00474059	−	0.0451037i
$838$	−10.0582	−	2.13794i	−0.347456	−	0.0738540i
$839$	−8.64668	+	26.6118i	−0.298517	+	0.918740i	0.683501	+	0.729950i	$0.260457\pi$
$839$	−8.64668	+	26.6118i	−0.298517	+	0.918740i	−0.982017	+	0.188790i	$0.939543\pi$
$840$	0.838531	−	1.95687i	0.0289321	−	0.0675184i
$841$	22.7457	−	70.0040i	0.784334	−	2.41393i
$842$	5.04002	+	5.59751i	0.173691	+	0.192903i
$843$	−2.41845	+	2.68596i	−0.0832959	+	0.0925095i
$844$	1.38992	−	13.2242i	0.0478429	−	0.455195i
$845$	17.8252	+	19.7969i	0.613207	+	0.681035i
$846$	5.20248	−	3.77983i	0.178865	−	0.129953i
$847$	2.88237	−	4.08672i	0.0990396	−	0.140421i
$848$	−4.38613	−	13.4991i	−0.150620	−	0.463562i
$849$	−0.415116	−	3.94957i	−0.0142468	−	0.135549i
$850$	−0.0374489	+	0.356302i	−0.00128449	+	0.0122211i
$851$	−0.638617	+	6.07604i	−0.0218915	+	0.208284i
$852$	−1.57777	+	2.73279i	−0.0540537	+	0.0936237i
$853$	38.7648	+	28.1643i	1.32728	+	0.964328i	0.999811	+	0.0194668i	$0.00619687\pi$
$853$	38.7648	+	28.1643i	1.32728	+	0.964328i	0.327472	+	0.944861i	$0.393803\pi$
$854$	4.93791	−	0.589208i	0.168972	−	0.0201623i
$855$	12.0214	+	36.9982i	0.411125	+	1.26531i
$856$	1.68079	+	15.9916i	0.0574482	+	0.546583i
$857$	−3.95014	−	1.75871i	−0.134934	−	0.0600765i	0.338159	−	0.941089i	$-0.390196\pi$
$857$	−3.95014	−	1.75871i	−0.134934	−	0.0600765i	−0.473093	+	0.881012i	$0.656863\pi$
$858$	−0.483976	−	0.838271i	−0.0165227	−	0.0286181i
$859$	30.6615	+	6.51731i	1.04616	+	0.222368i	0.698764	−	0.715352i	$-0.253734\pi$
$859$	30.6615	+	6.51731i	1.04616	+	0.222368i	0.347393	+	0.937720i	$0.387067\pi$
$860$	8.32041			0.283724
$861$	0.665802	+	6.23246i	0.0226905	+	0.212402i
$862$	−12.7870			−0.435526
$863$	−33.5609	−	7.13360i	−1.14243	−	0.242831i	−0.402437	−	0.915448i	$-0.631837\pi$
$863$	−33.5609	−	7.13360i	−1.14243	−	0.242831i	−0.739991	+	0.672617i	$0.765170\pi$
$864$	−1.08463	−	1.87863i	−0.0368998	−	0.0639124i
$865$	0.203881	+	0.0907735i	0.00693215	+	0.00308639i
$866$	1.55699	+	14.8137i	0.0529085	+	0.503391i
$867$	−1.74216	−	5.36183i	−0.0591670	−	0.182097i
$868$	0.958714	+	1.28133i	0.0325409	+	0.0434911i
$869$	−0.826195	−	0.600266i	−0.0280267	−	0.0203626i
$870$	−4.07546	+	7.05890i	−0.138171	+	0.239319i
$871$	0.204529	−	1.94596i	0.00693020	−	0.0659364i
$872$	−1.20246	+	11.4406i	−0.0407204	+	0.387429i
$873$	0.828889	+	7.88635i	0.0280536	+	0.266912i
$874$	8.75854	+	26.9560i	0.296262	+	0.911801i
$875$	30.1994	+	2.74594i	1.02093	+	0.0928297i
$876$	1.90105	−	1.38119i	0.0642304	−	0.0466661i
$877$	33.9421	+	37.6965i	1.14614	+	1.27292i	0.956715	+	0.291027i	$0.0939971\pi$
$877$	33.9421	+	37.6965i	1.14614	+	1.27292i	0.189429	+	0.981894i	$0.439336\pi$
$878$	2.15937	−	20.5451i	0.0728753	−	0.693362i
$879$	6.67526	−	7.41363i	0.225151	−	0.250055i
$880$	4.39240	+	4.87825i	0.148068	+	0.164446i
$881$	5.33962	−	16.4336i	0.179896	−	0.553664i	−0.819927	−	0.572468i	$-0.805986\pi$
$881$	5.33962	−	16.4336i	0.179896	−	0.553664i	0.999823	+	0.0188045i	$0.00598602\pi$
$882$	−20.0339	+	0.562784i	−0.674576	+	0.0189499i
$883$	−8.05708	+	24.7971i	−0.271142	+	0.834490i	0.719072	+	0.694936i	$0.244567\pi$
$883$	−8.05708	+	24.7971i	−0.271142	+	0.834490i	−0.990214	+	0.139555i	$0.955433\pi$
$884$	−1.12549	−	0.239231i	−0.0378544	−	0.00804619i
$885$	−0.105740	+	1.00605i	−0.00355441	+	0.0338179i
$886$	0.653795	−	0.138968i	0.0219647	−	0.00466873i
$887$	−2.75581	−	26.2198i	−0.0925311	−	0.880375i	−0.938067	−	0.346455i	$-0.887385\pi$
$887$	−2.75581	−	26.2198i	−0.0925311	−	0.880375i	0.845535	−	0.533919i	$-0.179281\pi$
$888$	0.498241			0.0167199
$889$	−0.257514	−	1.13303i	−0.00863673	−	0.0380007i
$890$	3.11540	−	2.26347i	0.104429	−	0.0758718i
$891$	−21.4704	+	9.55926i	−0.719287	+	0.320247i
$892$	0.473024	−	4.50052i	0.0158380	−	0.150689i
$893$	7.01592	+	12.1519i	0.234779	+	0.406649i
$894$	−6.90715	+	3.07526i	−0.231010	+	0.102852i
$895$	−8.82484	+	27.1601i	−0.294982	+	0.907861i
$896$	2.52749	+	0.782169i	0.0844376	+	0.0261304i
$897$	1.17708	−	0.855199i	0.0393016	−	0.0285542i
$898$	1.37093	+	13.0435i	0.0457484	+	0.435267i
$899$	−3.06343	−	5.30601i	−0.102171	−	0.176965i
$900$	0.517049	−	0.574241i	0.0172350	−	0.0191414i
$901$	9.42088	−	16.3174i	0.313855	−	0.543613i
$902$	−18.3053	−	6.19844i	−0.609498	−	0.206385i
$903$	1.57108	+	3.39942i	0.0522822	+	0.113125i
$904$	−1.01902	−	3.13621i	−0.0338920	−	0.104309i
$905$	8.73887	−	15.1362i	0.290490	−	0.503143i
$906$	6.73286	+	2.99766i	0.223684	+	0.0995906i
$907$	−33.4290	−	14.8835i	−1.10999	−	0.494200i	−0.231922	−	0.972734i	$-0.574501\pi$
$907$	−33.4290	−	14.8835i	−1.10999	−	0.494200i	−0.878069	+	0.478535i	$0.841168\pi$
$908$	19.8726	+	4.22404i	0.659494	+	0.140180i
$909$	−14.0315	+	43.1845i	−0.465395	+	1.43234i
$910$	−0.968394	+	4.89279i	−0.0321020	+	0.162194i
$911$	−11.8632			−0.393045			−0.196522	−	0.980499i	$-0.562965\pi$
$911$	−11.8632			−0.393045			−0.196522	+	0.980499i	$0.562965\pi$
$912$	2.11161	−	0.940148i	0.0699223	−	0.0311314i
$913$	−1.36356	+	12.9734i	−0.0451272	+	0.429357i
$914$	2.21621	+	0.986721i	0.0733058	+	0.0326378i
$915$	1.47941	+	0.314457i	0.0489076	+	0.0103956i
$916$	−22.4857			−0.742947
$917$	0.819347	+	58.3454i	0.0270572	+	1.92674i
$918$	0.889847	−	2.73867i	0.0293693	−	0.0903895i
$919$	10.1105	−	4.50149i	0.333515	−	0.148490i	−0.233145	−	0.972442i	$-0.574902\pi$
$919$	10.1105	−	4.50149i	0.333515	−	0.148490i	0.566660	+	0.823951i	$0.308235\pi$
$920$	−6.60231	+	7.33261i	−0.217672	+	0.241749i
$921$	−5.03867	+	1.07100i	−0.166030	+	0.0352907i
$922$	−23.9340	−	26.5814i	−0.788224	−	0.875411i
$923$	2.28450	−	7.03095i	0.0751951	−	0.231427i
$924$	−1.16369	+	2.71570i	−0.0382827	+	0.0893399i
$925$	0.112311	+	0.345657i	0.00369275	+	0.0113651i
$926$	10.6013	−	4.72002i	0.348382	−	0.155110i
$927$	8.28237	−	1.76047i	0.272029	−	0.0578215i
$928$	−9.25375	−	4.12003i	−0.303769	−	0.135247i
$929$	−4.99452	+	8.65076i	−0.163865	+	0.283822i	−0.936252	−	0.351330i	$-0.885729\pi$
$929$	−4.99452	+	8.65076i	−0.163865	+	0.283822i	0.772387	+	0.635153i	$0.219063\pi$
$930$	0.150401	+	0.462887i	0.00493184	+	0.0151787i
$931$	3.34814	−	43.6035i	0.109731	−	1.42905i
$932$	16.9915	+	12.3451i	0.556576	+	0.404376i
$933$	5.91008	−	2.63134i	0.193487	−	0.0861462i
$934$	−5.07240	−	8.78566i	−0.165974	−	0.287476i
$935$	−0.910850	+	8.66616i	−0.0297880	+	0.283414i
$936$	1.66060	+	1.84428i	0.0542784	+	0.0602823i
$937$	7.54744	+	23.2286i	0.246564	+	0.758846i	0.995375	+	0.0960627i	$0.0306249\pi$
$937$	7.54744	+	23.2286i	0.246564	+	0.758846i	−0.748811	+	0.662783i	$0.769375\pi$
$938$	−5.12986	+	3.05856i	−0.167496	+	0.0998656i
$939$	−9.71416	+	7.05775i	−0.317010	+	0.230321i
$940$	−2.44242	+	4.23040i	−0.0796630	+	0.137980i
$941$	24.8228	−	27.5685i	0.809199	−	0.898707i	−0.187300	−	0.982303i	$-0.559974\pi$
$941$	24.8228	−	27.5685i	0.809199	−	0.898707i	0.996500	+	0.0835958i	$0.0266404\pi$
$942$	2.62516	+	4.54692i	0.0855325	+	0.148147i
$943$	6.38987	−	28.3382i	0.208083	−	0.922819i
$944$	−1.25714			−0.0409166
$945$	−11.9244	−	3.69018i	−0.387901	−	0.120042i
$946$	−11.5469			−0.375421
$947$	3.51240	+	33.4183i	0.114138	+	1.08595i	0.890287	+	0.455399i	$0.150504\pi$
$947$	3.51240	+	33.4183i	0.114138	+	1.08595i	−0.776149	+	0.630549i	$0.782830\pi$
$948$	−0.114362	−	0.0509174i	−0.00371431	−	0.00165372i
$949$	−3.68365	+	4.09111i	−0.119576	+	0.132803i
$950$	1.12822	+	1.25301i	0.0366043	+	0.0406532i
$951$	−8.47151	−	6.15492i	−0.274708	−	0.199587i
$952$	1.47342	+	3.18812i	0.0477540	+	0.103327i
$953$	3.84040	+	2.79021i	0.124403	+	0.0903839i	0.648247	−	0.761430i	$-0.275503\pi$
$953$	3.84040	+	2.79021i	0.124403	+	0.0903839i	−0.523844	+	0.851814i	$0.675503\pi$
$954$	−37.1251	+	16.5292i	−1.20197	+	0.535152i
$955$	−17.7295	−	7.89368i	−0.573713	−	0.255433i
$956$	−8.24361	+	9.15545i	−0.266617	+	0.296109i
$957$	5.65582	−	9.79617i	0.182827	−	0.316665i
$958$	32.0279	−	23.2696i	1.03477	−	0.751807i
$959$	6.61150	−	0.788907i	0.213497	−	0.0254751i
$960$	0.650993	+	0.472974i	0.0210107	+	0.0152652i
$961$	29.9647	+	6.36920i	0.966604	+	0.205458i
$962$	−1.14177	+	0.242690i	−0.0368120	+	0.00782463i
$963$	45.0320	−	9.57185i	1.45114	−	0.308448i
$964$	8.29437	+	9.21183i	0.267144	+	0.296693i
$965$	7.81403	−	24.0491i	0.251542	−	0.774168i
$966$	−4.24250	−	1.31290i	−0.136500	−	0.0422420i
$967$	42.8339	+	31.1207i	1.37745	+	1.00077i	0.997114	+	0.0759243i	$0.0241907\pi$
$967$	42.8339	+	31.1207i	1.37745	+	1.00077i	0.380333	+	0.924849i	$0.375809\pi$
$968$	1.26477	+	1.40467i	0.0406514	+	0.0451479i
$969$	2.80308	+	1.24801i	0.0900478	+	0.0400919i
$970$	−3.01182	−	5.21663i	−0.0967037	−	0.167496i
$971$	37.8970	+	8.05525i	1.21617	+	0.258505i	0.770939	−	0.636909i	$-0.219787\pi$
$971$	37.8970	+	8.05525i	1.21617	+	0.258505i	0.445233	+	0.895415i	$0.353121\pi$
$972$	−7.59565	+	5.51857i	−0.243631	+	0.177008i
$973$	−8.21253	−	7.18837i	−0.263281	−	0.230449i
$974$	−11.3220	−	8.22593i	−0.362781	−	0.263576i
$975$	0.0432764	−	0.0749569i	0.00138595	−	0.00240054i
$976$	−0.196471	+	1.86930i	−0.00628889	+	0.0598347i
$977$	12.7654	−	2.71336i	0.408400	−	0.0868081i	0.000869404	−	1.00000i	$-0.499723\pi$
$977$	12.7654	−	2.71336i	0.408400	−	0.0868081i	0.407531	+	0.913191i	$0.366390\pi$
$978$	−4.63449	−	0.985091i	−0.148195	−	0.0314997i
$979$	−4.32348	+	3.14119i	−0.138179	+	0.100393i
$980$	13.7286	−	6.58033i	0.438544	−	0.210201i
$981$	32.9362			1.05157
$982$	9.90805	+	2.10602i	0.316179	+	0.0672058i
$983$	−25.6093	−	44.3567i	−0.816811	−	1.41476i	−0.908020	−	0.418927i	$-0.862406\pi$
$983$	−25.6093	−	44.3567i	−0.816811	−	1.41476i	0.0912088	−	0.995832i	$-0.470927\pi$
$984$	−2.35284	−	0.276682i	−0.0750058	−	0.00882030i
$985$	9.37750	−	16.2423i	0.298792	−	0.517523i
$986$	−4.15520	−	12.7884i	−0.132328	−	0.407265i
$987$	−2.18957	−	0.199091i	−0.0696948	−	0.00633714i
$988$	−4.38100	+	3.18299i	−0.139378	+	0.101264i
$989$	−1.81423	−	17.2613i	−0.0576892	−	0.548876i
$990$	12.5759	−	13.9670i	0.399689	−	0.443900i
$991$	−17.0042	+	3.61435i	−0.540156	+	0.114814i	−0.469907	−	0.882716i	$-0.655713\pi$
$991$	−17.0042	+	3.61435i	−0.540156	+	0.114814i	−0.0702488	+	0.997530i	$0.522379\pi$
$992$	−0.552561	+	0.246016i	−0.0175438	+	0.00781101i
$993$	0.186468			0.00591737
$994$	−21.3608	+	7.27372i	−0.677525	+	0.230708i
$995$	35.4677	+	25.7688i	1.12440	+	0.816924i
$996$	0.167148	+	1.59031i	0.00529629	+	0.0503909i
$997$	−8.07833	+	8.97189i	−0.255843	+	0.284143i	−0.857360	−	0.514718i	$-0.827897\pi$
$997$	−8.07833	+	8.97189i	−0.255843	+	0.284143i	0.601517	+	0.798860i	$0.294563\pi$
$998$	−13.7915	−	23.8876i	−0.436563	−	0.756149i
$999$	−0.305353	−	2.90524i	−0.00966094	−	0.0919177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.a.387.6	yes	112
7.4	even	3	inner	574.2.s.a.305.6	yes	112
41.16	even	5	inner	574.2.s.a.303.6	yes	112
287.221	even	15	inner	574.2.s.a.221.6	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.a.221.6	✓	112	287.221	even	15	inner
574.2.s.a.303.6	yes	112	41.16	even	5	inner
574.2.s.a.305.6	yes	112	7.4	even	3	inner
574.2.s.a.387.6	yes	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.184992 - 0.320416i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.227337 + 2.16297i) q^{5} +(-0.114331 - 0.351876i) q^{6} +(1.04208 - 2.43189i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43156 - 2.47953i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.184992 - 0.320416i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.227337 + 2.16297i) q^{5} +(-0.114331 - 0.351876i) q^{6} +(1.04208 - 2.43189i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43156 - 2.47953i) q^{9} +(-0.227337 + 2.16297i) q^{10} +(0.315493 - 3.00171i) q^{11} +(-0.0386739 - 0.367957i) q^{12} +(0.267854 + 0.824370i) q^{13} +(1.52492 - 2.16208i) q^{14} +(0.650993 - 0.472974i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.138757 + 1.32019i) q^{17} +(1.91580 - 2.12771i) q^{18} +(4.18033 + 4.64273i) q^{19} +(-0.672076 + 2.06844i) q^{20} +(-0.971991 + 0.115981i) q^{21} +(0.932690 - 2.87053i) q^{22} +(4.43766 + 0.943253i) q^{23} +(0.0386739 - 0.367957i) q^{24} +(0.263990 - 0.0561127i) q^{25} +(0.0906046 + 0.862046i) q^{26} -2.16926 q^{27} +(1.94112 - 1.79779i) q^{28} +(-8.19493 + 5.95396i) q^{29} +(0.735104 - 0.327289i) q^{30} +(-0.0632244 + 0.601540i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.02016 + 0.454204i) q^{33} +(-0.410208 + 1.26249i) q^{34} +(5.49700 + 1.70113i) q^{35} +(2.31631 - 1.68289i) q^{36} +(0.140764 + 1.33928i) q^{37} +(3.12371 + 5.41042i) q^{38} +(0.214590 - 0.238326i) q^{39} +(-1.08744 + 1.88350i) q^{40} +(0.0789962 - 6.40264i) q^{41} +(-0.974864 - 0.0886415i) q^{42} +(-1.18220 - 3.63844i) q^{43} +(1.50912 - 2.61388i) q^{44} +(5.68858 + 2.53272i) q^{45} +(4.14457 + 1.84528i) q^{46} +(2.19694 + 0.466975i) q^{47} +(0.114331 - 0.351876i) q^{48} +(-4.82814 - 5.06844i) q^{49} +0.269887 q^{50} +(0.448678 - 0.199764i) q^{51} +(-0.0906046 + 0.862046i) q^{52} +(-12.9667 - 5.77315i) q^{53} +(-2.12185 - 0.451014i) q^{54} +6.56434 q^{55} +(2.27249 - 1.35492i) q^{56} +(0.714275 - 2.19831i) q^{57} +(-9.25375 + 4.12003i) q^{58} +(-0.841194 + 0.934241i) q^{59} +(0.787088 - 0.167301i) q^{60} +(1.25769 + 1.39681i) q^{61} +(-0.186910 + 0.575249i) q^{62} +(-4.53813 - 6.06524i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.72219 + 0.766770i) q^{65} +(-1.09230 + 0.232176i) q^{66} +(-2.06222 - 0.918158i) q^{67} +(-0.663731 + 1.14961i) q^{68} +(-0.518698 - 1.59639i) q^{69} +(5.02319 + 2.80684i) q^{70} +(-6.90001 - 5.01315i) q^{71} +(2.61558 - 1.16453i) q^{72} +(3.17557 + 5.50025i) q^{73} +(-0.140764 + 1.33928i) q^{74} +(-0.0668154 - 0.0742060i) q^{75} +(1.93056 + 5.94164i) q^{76} +(-6.97106 - 3.89527i) q^{77} +(0.259452 - 0.188503i) q^{78} +(0.169176 - 0.293022i) q^{79} +(-1.45528 + 1.61625i) q^{80} +(-3.89337 - 6.74352i) q^{81} +(1.40845 - 6.24630i) q^{82} -4.32199 q^{83} +(-0.935131 - 0.289390i) q^{84} -2.88707 q^{85} +(-0.399893 - 3.80472i) q^{86} +(3.42374 + 1.52435i) q^{87} +(2.01960 - 2.24300i) q^{88} +(-1.18476 - 1.31581i) q^{89} +(5.03769 + 3.66010i) q^{90} +(2.28390 + 0.207668i) q^{91} +(3.67035 + 2.66666i) q^{92} +(0.204439 - 0.0910219i) q^{93} +(2.05185 + 0.913541i) q^{94} +(-9.09174 + 10.0974i) q^{95} +(0.184992 - 0.320416i) q^{96} +(-2.24069 + 1.62795i) q^{97} +(-3.66885 - 5.96151i) q^{98} +(-6.99119 - 5.07940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Introduction

L-functions

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