LMFDB - Embedded newform 930.2.br.a.761.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.8
Character	$\chi$	$=$	930.761
Dual form			930.2.br.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.991446 + 1.42022i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.504048 - 1.65709i) q^{6} +(-0.310184 + 2.95121i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.03407 + 2.81615i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.991446 + 1.42022i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.504048 - 1.65709i) q^{6} +(-0.310184 + 2.95121i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.03407 + 2.81615i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(5.85567 - 2.60711i) q^{11} +(-0.0326902 + 1.73174i) q^{12} +(-0.0533559 + 0.251020i) q^{13} +(1.20698 - 2.71091i) q^{14} +(0.148505 + 1.72567i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.128731 + 0.0573147i) q^{17} +(1.85370 - 2.35877i) q^{18} +(3.33397 - 0.708656i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-4.49890 + 2.48543i) q^{21} +(-6.37472 + 0.670010i) q^{22} +(0.218421 - 0.158692i) q^{23} +(0.566228 - 1.63688i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.128314 - 0.222246i) q^{26} +(-5.02479 + 1.32345i) q^{27} +(-1.98562 + 2.20525i) q^{28} +(-1.06871 + 3.28916i) q^{29} +(0.392025 - 1.68710i) q^{30} +(5.50287 - 0.847624i) q^{31} -1.00000i q^{32} +(9.50827 + 5.73155i) q^{33} +(-0.104719 - 0.0942896i) q^{34} +(-1.74423 + 2.40073i) q^{35} +(-2.49187 + 1.67050i) q^{36} +(-2.58554 + 1.49276i) q^{37} +(-3.38978 - 0.356280i) q^{38} +(-0.409403 + 0.173095i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-4.27156 + 3.84613i) q^{41} +(5.04675 - 0.973546i) q^{42} +(-0.105304 - 0.495415i) q^{43} +(6.26976 + 1.33268i) q^{44} +(-2.30361 + 1.92182i) q^{45} +(-0.256769 + 0.0834292i) q^{46} +(-11.6458 + 3.78394i) q^{47} +(-1.04434 + 1.38179i) q^{48} +(-1.76636 - 0.375452i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(0.0462300 + 0.239651i) q^{51} +(-0.190711 + 0.171717i) q^{52} +(-0.682747 - 6.49590i) q^{53} +(5.18782 + 0.294072i) q^{54} +(6.37472 + 0.670010i) q^{55} +(2.56990 - 1.48373i) q^{56} +(4.31190 + 4.03238i) q^{57} +(2.03281 - 2.79793i) q^{58} +(-1.28184 - 1.15417i) q^{59} +(-0.894182 + 1.48339i) q^{60} -10.3488i q^{61} +(-5.49547 - 0.894340i) q^{62} +(-7.99028 - 3.92528i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.171717 + 0.190711i) q^{65} +(-7.27175 - 8.38925i) q^{66} +(2.56939 - 4.45032i) q^{67} +(0.0704568 + 0.122035i) q^{68} +(0.441930 + 0.152872i) q^{69} +(2.40073 - 1.74423i) q^{70} +(-3.18552 + 0.334811i) q^{71} +(2.88612 - 0.818710i) q^{72} +(2.49424 + 5.60216i) q^{73} +(2.92029 - 0.620726i) q^{74} +(-0.734227 + 1.56873i) q^{75} +(3.11377 + 1.38634i) q^{76} +(5.87779 + 18.0900i) q^{77} +(0.442855 - 0.0381105i) q^{78} +(-6.36960 + 14.3063i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-6.86139 - 5.82420i) q^{81} +(5.25101 - 2.33790i) q^{82} +(-3.61823 - 4.01845i) q^{83} +(-5.10059 - 0.633634i) q^{84} +(0.0828269 + 0.114002i) q^{85} +(-0.0529419 + 0.503709i) q^{86} +(-5.73091 + 1.74321i) q^{87} +(-5.55108 - 3.20492i) q^{88} +(6.43221 + 4.67328i) q^{89} +(2.78474 - 1.11591i) q^{90} +(-0.724260 - 0.235326i) q^{91} +0.269983 q^{92} +(6.65961 + 6.97493i) q^{93} +12.2451 q^{94} +(3.24163 + 1.05327i) q^{95} +(1.42022 - 0.991446i) q^{96} +(3.37411 + 2.45144i) q^{97} +(1.56389 + 0.902913i) q^{98} +(1.28684 + 19.1864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.991446	+	1.42022i	0.572411	+	0.819967i
$3$	0.991446	+	1.42022i	0.572411	+	0.819967i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−0.504048	−	1.65709i	−0.205777	−	0.676503i
$7$	−0.310184	+	2.95121i	−0.117239	+	1.11545i	0.764798	+	0.644270i	$0.222839\pi$
$7$	−0.310184	+	2.95121i	−0.117239	+	1.11545i	−0.882037	+	0.471181i	$0.843828\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−1.03407	+	2.81615i	−0.344690	+	0.938716i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	5.85567	−	2.60711i	1.76555	−	0.786074i	0.778103	−	0.628137i	$-0.216182\pi$
$11$	5.85567	−	2.60711i	1.76555	−	0.786074i	0.987449	−	0.157937i	$-0.0504844\pi$
$12$	−0.0326902	+	1.73174i	−0.00943683	+	0.499911i
$13$	−0.0533559	+	0.251020i	−0.0147983	+	0.0696203i	−0.984927	−	0.172970i	$-0.944664\pi$
$13$	−0.0533559	+	0.251020i	−0.0147983	+	0.0696203i	0.970129	+	0.242590i	$0.0779970\pi$
$14$	1.20698	−	2.71091i	0.322578	−	0.724521i
$15$	0.148505	+	1.72567i	0.0383439	+	0.445567i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.128731	+	0.0573147i	0.0312219	+	0.0139009i	0.422288	−	0.906462i	$-0.361227\pi$
$17$	0.128731	+	0.0573147i	0.0312219	+	0.0139009i	−0.391066	+	0.920362i	$0.627894\pi$
$18$	1.85370	−	2.35877i	0.436921	−	0.555968i
$19$	3.33397	−	0.708656i	0.764864	−	0.162577i	0.191070	−	0.981576i	$-0.438804\pi$
$19$	3.33397	−	0.708656i	0.764864	−	0.162577i	0.573794	+	0.819000i	$0.305471\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	−4.49890	+	2.48543i	−0.981741	+	0.542365i
$22$	−6.37472	+	0.670010i	−1.35909	+	0.142847i
$23$	0.218421	−	0.158692i	0.0455438	−	0.0330895i	−0.564780	−	0.825241i	$-0.691039\pi$
$23$	0.218421	−	0.158692i	0.0455438	−	0.0330895i	0.610324	+	0.792152i	$0.291039\pi$
$24$	0.566228	−	1.63688i	0.115581	−	0.334127i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.128314	−	0.222246i	0.0251644	−	0.0435860i
$27$	−5.02479	+	1.32345i	−0.967021	+	0.254698i
$28$	−1.98562	+	2.20525i	−0.375247	+	0.416754i
$29$	−1.06871	+	3.28916i	−0.198455	+	0.610782i	0.801464	+	0.598043i	$0.204055\pi$
$29$	−1.06871	+	3.28916i	−0.198455	+	0.610782i	−0.999919	+	0.0127384i	$0.995945\pi$
$30$	0.392025	−	1.68710i	0.0715737	−	0.308021i
$31$	5.50287	−	0.847624i	0.988344	−	0.152238i
$31$	5.50287	−	0.847624i	0.988344	−	0.152238i
$32$		−	1.00000i		−	0.176777i
$33$	9.50827	+	5.73155i	1.65518	+	0.997736i
$34$	−0.104719	−	0.0942896i	−0.0179592	−	0.0161705i
$35$	−1.74423	+	2.40073i	−0.294829	+	0.405797i
$36$	−2.49187	+	1.67050i	−0.415312	+	0.278417i
$37$	−2.58554	+	1.49276i	−0.425060	+	0.245409i	−0.697240	−	0.716838i	$-0.745589\pi$
$37$	−2.58554	+	1.49276i	−0.425060	+	0.245409i	0.272180	+	0.962246i	$0.412256\pi$
$38$	−3.38978	−	0.356280i	−0.549894	−	0.0577962i
$39$	−0.409403	+	0.173095i	−0.0655570	+	0.0277174i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−4.27156	+	3.84613i	−0.667105	+	0.600664i	−0.931496	−	0.363752i	$-0.881496\pi$
$41$	−4.27156	+	3.84613i	−0.667105	+	0.600664i	0.264391	+	0.964416i	$0.414829\pi$
$42$	5.04675	−	0.973546i	0.778730	−	0.150221i
$43$	−0.105304	−	0.495415i	−0.0160587	−	0.0755501i	0.969389	−	0.245532i	$-0.0789625\pi$
$43$	−0.105304	−	0.495415i	−0.0160587	−	0.0755501i	−0.985447	+	0.169982i	$0.945629\pi$
$44$	6.26976	+	1.33268i	0.945202	+	0.200909i
$45$	−2.30361	+	1.92182i	−0.343401	+	0.286488i
$46$	−0.256769	+	0.0834292i	−0.0378585	+	0.0123010i
$47$	−11.6458	+	3.78394i	−1.69871	+	0.551944i	−0.988390	−	0.151937i	$-0.951449\pi$
$47$	−11.6458	+	3.78394i	−1.69871	+	0.551944i	−0.710318	+	0.703881i	$0.751449\pi$
$48$	−1.04434	+	1.38179i	−0.150737	+	0.199445i
$49$	−1.76636	−	0.375452i	−0.252338	−	0.0536361i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	0.0462300	+	0.239651i	0.00647350	+	0.0335579i
$52$	−0.190711	+	0.171717i	−0.0264469	+	0.0238129i
$53$	−0.682747	−	6.49590i	−0.0937825	−	0.892281i	−0.935729	−	0.352720i	$-0.885257\pi$
$53$	−0.682747	−	6.49590i	−0.0937825	−	0.892281i	0.841946	−	0.539561i	$-0.181410\pi$
$54$	5.18782	+	0.294072i	0.705973	+	0.0400181i
$55$	6.37472	+	0.670010i	0.859567	+	0.0903441i
$56$	2.56990	−	1.48373i	0.343417	−	0.198272i
$57$	4.31190	+	4.03238i	0.571125	+	0.534102i
$58$	2.03281	−	2.79793i	0.266921	−	0.367386i
$59$	−1.28184	−	1.15417i	−0.166881	−	0.150260i	0.581459	−	0.813576i	$-0.302482\pi$
$59$	−1.28184	−	1.15417i	−0.166881	−	0.150260i	−0.748340	+	0.663315i	$0.769149\pi$
$60$	−0.894182	+	1.48339i	−0.115438	+	0.191505i
$61$		−	10.3488i		−	1.32503i	−0.749048	−	0.662516i	$-0.769489\pi$
$61$		−	10.3488i		−	1.32503i	0.749048	−	0.662516i	$-0.230511\pi$
$62$	−5.49547	−	0.894340i	−0.697925	−	0.113581i
$63$	−7.99028	−	3.92528i	−1.00668	−	0.494539i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−0.171717	+	0.190711i	−0.0212989	+	0.0236548i
$66$	−7.27175	−	8.38925i	−0.895091	−	1.03265i
$67$	2.56939	−	4.45032i	0.313901	−	0.543693i	−0.665302	−	0.746574i	$-0.731697\pi$
$67$	2.56939	−	4.45032i	0.313901	−	0.543693i	0.979203	+	0.202881i	$0.0650305\pi$
$68$	0.0704568	+	0.122035i	0.00854414	+	0.0147989i
$69$	0.441930	+	0.152872i	0.0532021	+	0.0184036i
$70$	2.40073	−	1.74423i	0.286942	−	0.208475i
$71$	−3.18552	+	0.334811i	−0.378051	+	0.0397348i	−0.291649	−	0.956526i	$-0.594204\pi$
$71$	−3.18552	+	0.334811i	−0.378051	+	0.0397348i	−0.0864026	+	0.996260i	$0.527537\pi$
$72$	2.88612	−	0.818710i	0.340133	−	0.0964859i
$73$	2.49424	+	5.60216i	0.291929	+	0.655683i	0.998657	−	0.0518019i	$-0.0164964\pi$
$73$	2.49424	+	5.60216i	0.291929	+	0.655683i	−0.706729	+	0.707485i	$0.749830\pi$
$74$	2.92029	−	0.620726i	0.339476	−	0.0721579i
$75$	−0.734227	+	1.56873i	−0.0847812	+	0.181141i
$76$	3.11377	+	1.38634i	0.357174	+	0.159024i
$77$	5.87779	+	18.0900i	0.669836	+	2.06154i
$78$	0.442855	−	0.0381105i	0.0501435	−	0.00431517i
$79$	−6.36960	+	14.3063i	−0.716636	+	1.60959i	0.0739674	+	0.997261i	$0.476434\pi$
$79$	−6.36960	+	14.3063i	−0.716636	+	1.60959i	−0.790603	+	0.612329i	$0.790233\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	−6.86139	−	5.82420i	−0.762377	−	0.647133i
$82$	5.25101	−	2.33790i	0.579877	−	0.258178i
$83$	−3.61823	−	4.01845i	−0.397152	−	0.441082i	0.511090	−	0.859527i	$-0.329242\pi$
$83$	−3.61823	−	4.01845i	−0.397152	−	0.441082i	−0.908242	+	0.418445i	$0.862575\pi$
$84$	−5.10059	−	0.633634i	−0.556520	−	0.0691352i
$85$	0.0828269	+	0.114002i	0.00898384	+	0.0123652i
$86$	−0.0529419	+	0.503709i	−0.00570887	+	0.0543163i
$87$	−5.73091	+	1.74321i	−0.614418	+	0.186892i
$88$	−5.55108	−	3.20492i	−0.591747	−	0.341645i
$89$	6.43221	+	4.67328i	0.681813	+	0.495366i	0.873959	−	0.486000i	$-0.161545\pi$
$89$	6.43221	+	4.67328i	0.681813	+	0.495366i	−0.192146	+	0.981366i	$0.561545\pi$
$90$	2.78474	−	1.11591i	0.293537	−	0.117627i
$91$	−0.724260	−	0.235326i	−0.0759231	−	0.0246689i
$92$	0.269983			0.0281476
$93$	6.65961	+	6.97493i	0.690569	+	0.723266i
$94$	12.2451			1.26298
$95$	3.24163	+	1.05327i	0.332584	+	0.108063i
$96$	1.42022	−	0.991446i	0.144951	−	0.101189i
$97$	3.37411	+	2.45144i	0.342589	+	0.248906i	0.745754	−	0.666222i	$-0.232090\pi$
$97$	3.37411	+	2.45144i	0.342589	+	0.248906i	−0.403164	+	0.915128i	$0.632090\pi$
$98$	1.56389	+	0.902913i	0.157977	+	0.0912080i
$99$	1.28684	+	19.1864i	0.129332	+	1.92830i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	0.233398	+	0.321245i	0.0232240	+	0.0319651i	0.820471	−	0.571688i	$-0.193711\pi$
$101$	0.233398	+	0.321245i	0.0232240	+	0.0319651i	−0.797247	+	0.603653i	$0.793711\pi$
$102$	0.0300889	−	0.242208i	0.00297925	−	0.0239821i
$103$	−6.85604	−	7.61441i	−0.675546	−	0.750270i	0.303739	−	0.952755i	$-0.401765\pi$
$103$	−6.85604	−	7.61441i	−0.675546	−	0.750270i	−0.979285	+	0.202485i	$0.935098\pi$
$104$	0.234441	−	0.104380i	0.0229888	−	0.0102353i
$105$	−5.13888	−	0.0970068i	−0.501503	−	0.00946689i
$106$	−1.35801	+	6.38895i	−0.131902	+	0.620550i
$107$	−0.978911	+	2.19867i	−0.0946349	+	0.212553i	−0.954660	−	0.297698i	$-0.903781\pi$
$107$	−0.978911	+	2.19867i	−0.0946349	+	0.212553i	0.860025	+	0.510252i	$0.170448\pi$
$108$	−4.84304	−	1.88280i	−0.466022	−	0.181173i
$109$	−4.84728	−	14.9184i	−0.464285	−	1.42892i	−0.859880	−	0.510497i	$-0.829461\pi$
$109$	−4.84728	−	14.9184i	−0.464285	−	1.42892i	0.395595	−	0.918425i	$-0.370539\pi$
$110$	−5.85567	−	2.60711i	−0.558317	−	0.248579i
$111$	−4.68348	−	2.19205i	−0.444536	−	0.208061i
$112$	−2.90262	+	0.616970i	−0.274271	+	0.0582982i
$113$	3.09800	+	6.95822i	0.291435	+	0.654574i	0.998623	−	0.0524512i	$-0.0167034\pi$
$113$	3.09800	+	6.95822i	0.291435	+	0.654574i	−0.707188	+	0.707025i	$0.750037\pi$
$114$	−2.85478	−	5.16747i	−0.267375	−	0.483978i
$115$	0.268504	−	0.0282209i	0.0250381	−	0.00263161i
$116$	−2.79793	+	2.03281i	−0.259781	+	0.188742i
$117$	−0.651735	−	0.409830i	−0.0602529	−	0.0378888i
$118$	0.862441	+	1.49379i	0.0793941	+	0.137515i
$119$	−0.209078	+	0.362133i	−0.0191661	+	0.0331967i
$120$	1.30881	−	1.13447i	0.119477	−	0.103562i
$121$	20.1314	−	22.3582i	1.83013	−	2.03257i
$122$	−3.19797	+	9.84233i	−0.289530	+	0.891082i
$123$	−9.69738	−	2.25334i	−0.874383	−	0.203177i
$124$	4.95013	+	2.54876i	0.444535	+	0.228885i
$125$			1.00000i			0.0894427i
$126$	6.38623	+	6.20230i	0.568931	+	0.552544i
$127$	14.5990	+	13.1450i	1.29545	+	1.16643i	0.975744	+	0.218916i	$0.0702521\pi$
$127$	14.5990	+	13.1450i	1.29545	+	1.16643i	0.319710	+	0.947515i	$0.396415\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.599198	−	0.640732i	0.0527564	−	0.0564133i
$130$	0.222246	−	0.128314i	0.0194923	−	0.0112539i
$131$	10.6941	+	1.12399i	0.934345	+	0.0982036i	0.559450	−	0.828864i	$-0.311012\pi$
$131$	10.6941	+	1.12399i	0.934345	+	0.0982036i	0.374895	+	0.927067i	$0.377679\pi$
$132$	4.32343	+	10.2257i	0.376306	+	0.890037i
$133$	1.05725	+	10.0590i	0.0916749	+	0.872229i
$134$	−3.81886	+	3.43852i	−0.329900	+	0.297043i
$135$	−5.01332	−	1.36625i	−0.431478	−	0.117588i
$136$	−0.0292976	−	0.137834i	−0.00251225	−	0.0118192i
$137$	20.8872	+	4.43972i	1.78452	+	0.379311i	0.977453	−	0.211153i	$-0.0677218\pi$
$137$	20.8872	+	4.43972i	1.78452	+	0.379311i	0.807064	+	0.590464i	$0.201055\pi$
$138$	−0.373061	−	0.281954i	−0.0317570	−	0.0240015i
$139$	−9.92018	+	3.22326i	−0.841419	+	0.273394i	−0.697847	−	0.716246i	$-0.745859\pi$
$139$	−9.92018	+	3.22326i	−0.841419	+	0.273394i	−0.143571	+	0.989640i	$0.545859\pi$
$140$	−2.82222	+	0.916996i	−0.238521	+	0.0775003i
$141$	−16.9202	−	12.7880i	−1.42494	−	1.07695i
$142$	3.13307	+	0.665954i	0.262921	+	0.0558857i
$143$	0.342002	+	1.60899i	0.0285997	+	0.134551i
$144$	−2.99786	−	0.113222i	−0.249822	−	0.00943515i
$145$	−2.57011	+	2.31414i	−0.213436	+	0.192179i
$146$	−0.641003	−	6.09873i	−0.0530497	−	0.504735i
$147$	−1.21803	−	2.88087i	−0.100461	−	0.237610i
$148$	−2.96917	−	0.312073i	−0.244064	−	0.0256522i
$149$	2.88082	−	1.66324i	0.236006	−	0.136258i	−0.377334	−	0.926077i	$-0.623159\pi$
$149$	2.88082	−	1.66324i	0.236006	−	0.136258i	0.613340	+	0.789819i	$0.289826\pi$
$150$	1.18306	−	1.26506i	0.0965961	−	0.103292i
$151$	3.20473	−	4.41093i	0.260797	−	0.358956i	−0.658459	−	0.752617i	$-0.728791\pi$
$151$	3.20473	−	4.41093i	0.260797	−	0.358956i	0.919256	+	0.393660i	$0.128791\pi$
$152$	−2.53297	−	2.28070i	−0.205451	−	0.184989i
$153$	−0.294524	+	0.303258i	−0.0238108	+	0.0245170i
$154$		−	19.0209i		−	1.53275i
$155$	5.18943	+	2.01737i	0.416825	+	0.162039i
$156$	−0.432957	−	0.100604i	−0.0346643	−	0.00805480i
$157$	3.42703	−	10.5473i	0.273507	−	0.841767i	−0.716104	−	0.697994i	$-0.754076\pi$
$157$	3.42703	−	10.5473i	0.273507	−	0.841767i	0.989611	−	0.143773i	$-0.0459236\pi$
$158$	10.4788	−	11.6378i	0.833645	−	0.925856i
$159$	8.54873	−	7.40999i	0.677958	−	0.587650i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.400582	+	0.693828i	0.0315703	+	0.0546813i
$162$	4.72580	+	7.65943i	0.371294	+	0.601781i
$163$	−9.88759	+	7.18376i	−0.774456	+	0.562675i	−0.903310	−	0.428988i	$-0.858870\pi$
$163$	−9.88759	+	7.18376i	−0.774456	+	0.562675i	0.128854	+	0.991664i	$0.458870\pi$
$164$	−5.71646	+	0.600824i	−0.446380	+	0.0469165i
$165$	5.36862	+	9.71780i	0.417947	+	0.756530i
$166$	2.19937	+	4.93987i	0.170704	+	0.383408i
$167$	−10.1755	+	2.16287i	−0.787403	+	0.167368i	−0.584028	−	0.811733i	$-0.698524\pi$
$167$	−10.1755	+	2.16287i	−0.787403	+	0.167368i	−0.203375	+	0.979101i	$0.565191\pi$
$168$	4.65514	+	2.17879i	0.359152	+	0.168097i
$169$	11.8159	+	5.26079i	0.908917	+	0.404676i
$170$	−0.0435447	−	0.134017i	−0.00333973	−	0.0102786i
$171$	−1.45187	+	10.1217i	−0.111028	+	0.774029i
$172$	0.206005	−	0.462695i	0.0157078	−	0.0352802i
$173$	4.65615	−	21.9055i	0.354001	−	1.66544i	−0.336174	−	0.941800i	$-0.609133\pi$
$173$	4.65615	−	21.9055i	0.354001	−	1.66544i	0.690175	−	0.723643i	$-0.257534\pi$
$174$	5.98910	+	0.113057i	0.454033	+	0.00857079i
$175$	−2.71091	+	1.20698i	−0.204926	+	0.0912388i
$176$	4.28901	+	4.76343i	0.323297	+	0.359057i
$177$	0.368309	−	2.96479i	0.0276838	−	0.222847i
$178$	−4.67328	−	6.43221i	−0.350277	−	0.482115i
$179$	2.45758	−	23.3823i	0.183688	−	1.74767i	−0.383006	−	0.923746i	$-0.625111\pi$
$179$	2.45758	−	23.3823i	0.183688	−	1.74767i	0.566694	−	0.823928i	$-0.308222\pi$
$180$	−2.99328	+	0.200760i	−0.223106	+	0.0149638i
$181$	3.88655	+	2.24390i	0.288885	+	0.166788i	0.637439	−	0.770501i	$-0.279994\pi$
$181$	3.88655	+	2.24390i	0.288885	+	0.166788i	−0.348554	+	0.937289i	$0.613327\pi$
$182$	0.616093	+	0.447617i	0.0456678	+	0.0331796i
$183$	14.6977	−	10.2603i	1.08648	−	0.758464i
$184$	−0.256769	−	0.0834292i	−0.0189292	−	0.00615049i
$185$	−2.98553			−0.219500
$186$	−4.17829	−	8.69148i	−0.306367	−	0.637290i
$187$	0.903233			0.0660509
$188$	−11.6458	−	3.78394i	−0.849354	−	0.275972i
$189$	−2.34715	−	15.2397i	−0.170730	−	1.10852i
$190$	−2.75749	−	2.00344i	−0.200050	−	0.145345i
$191$	−14.1596	−	8.17505i	−1.02455	−	0.591526i	−0.109133	−	0.994027i	$-0.534808\pi$
$191$	−14.1596	−	8.17505i	−1.02455	−	0.591526i	−0.915419	+	0.402501i	$0.868141\pi$
$192$	−1.65709	+	0.504048i	−0.119590	+	0.0363765i
$193$	1.27720	−	12.1518i	0.0919351	−	0.874704i	−0.847227	−	0.531231i	$-0.821730\pi$
$193$	1.27720	−	12.1518i	0.0919351	−	0.874704i	0.939162	−	0.343473i	$-0.111604\pi$
$194$	−2.45144	−	3.37411i	−0.176003	−	0.242247i
$195$	−0.441101	−	0.0547970i	−0.0315879	−	0.00392410i
$196$	−1.20833	−	1.34199i	−0.0863095	−	0.0958565i
$197$	−20.3188	+	9.04653i	−1.44766	+	0.644539i	−0.971976	−	0.235079i	$-0.924465\pi$
$197$	−20.3188	+	9.04653i	−1.44766	+	0.644539i	−0.475681	+	0.879618i	$0.657798\pi$
$198$	4.70506	−	18.6450i	0.334374	−	1.32504i
$199$	3.98258	−	18.7366i	0.282318	−	1.32820i	−0.576994	−	0.816748i	$-0.695775\pi$
$199$	3.98258	−	18.7366i	0.282318	−	1.32820i	0.859312	−	0.511452i	$-0.170892\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	8.86787	−	0.763137i	0.625491	−	0.0538275i
$202$	−0.122705	−	0.377646i	−0.00863347	−	0.0265711i
$203$	−9.37549	−	4.17424i	−0.658030	−	0.292974i
$204$	−0.103463	+	0.221055i	−0.00724383	+	0.0154770i
$205$	−5.62234	+	1.19507i	−0.392681	+	0.0834670i
$206$	4.16750	+	9.36037i	0.290364	+	0.652168i
$207$	0.221038	+	0.779204i	0.0153632	+	0.0541584i
$208$	−0.255222	+	0.0268249i	−0.0176964	+	0.00185997i
$209$	17.6751	−	12.8417i	1.22261	−	0.888278i
$210$	4.85739	+	1.68026i	0.335192	+	0.115949i
$211$	−13.2921	−	23.0226i	−0.915067	−	1.58494i	−0.806803	−	0.590820i	$-0.798804\pi$
$211$	−13.2921	−	23.0226i	−0.915067	−	1.58494i	−0.108264	−	0.994122i	$-0.534529\pi$
$212$	3.26584	−	5.65660i	0.224299	−	0.388497i
$213$	−3.63377	−	4.19220i	−0.248982	−	0.287245i
$214$	1.61043	−	1.78856i	0.110086	−	0.122263i
$215$	0.156512	−	0.481694i	0.0106740	−	0.0328513i
$216$	4.02419	+	3.28724i	0.273811	+	0.223668i
$217$	0.794612	+	16.5030i	0.0539417	+	1.12030i
$218$			15.6861i			1.06240i
$219$	−5.48341	+	9.09662i	−0.370535	+	0.614692i
$220$	4.76343	+	4.28901i	0.321151	+	0.289165i
$221$	−0.0212557	+	0.0292559i	−0.00142981	+	0.00196797i
$222$	3.77687	+	3.53204i	0.253487	+	0.237055i
$223$	20.4355	−	11.7985i	1.36847	−	0.790084i	0.377733	−	0.925914i	$-0.376704\pi$
$223$	20.4355	−	11.7985i	1.36847	−	0.790084i	0.990732	+	0.135831i	$0.0433703\pi$
$224$	2.95121	+	0.310184i	0.197186	+	0.0207251i
$225$	−2.95589	+	0.512543i	−0.197059	+	0.0341695i
$226$	−0.796164	−	7.57499i	−0.0529600	−	0.503881i
$227$	−12.1905	+	10.9763i	−0.809110	+	0.728526i	−0.965847	−	0.259115i	$-0.916569\pi$
$227$	−12.1905	+	10.9763i	−0.809110	+	0.728526i	0.156737	+	0.987640i	$0.449903\pi$
$228$	1.11822	+	5.79674i	0.0740561	+	0.383898i
$229$	0.658256	+	3.09685i	0.0434988	+	0.204646i	0.994530	−	0.104448i	$-0.0333076\pi$
$229$	0.658256	+	3.09685i	0.0434988	+	0.204646i	−0.951032	+	0.309094i	$0.899974\pi$
$230$	−0.264083	−	0.0561326i	−0.0174131	−	0.00370127i
$231$	−19.8643	+	26.2830i	−1.30698	+	1.72929i
$232$	3.28916	−	1.06871i	0.215944	−	0.0701644i
$233$	3.93413	−	1.27828i	0.257733	−	0.0837426i	−0.177300	−	0.984157i	$-0.556736\pi$
$233$	3.93413	−	1.27828i	0.257733	−	0.0837426i	0.435034	+	0.900414i	$0.356736\pi$
$234$	0.493192	+	0.591169i	0.0322410	+	0.0386459i
$235$	−11.9775	−	2.54589i	−0.781325	−	0.166076i
$236$	−0.358623	−	1.68719i	−0.0233444	−	0.109827i
$237$	−26.6333	+	5.13771i	−1.73002	+	0.333730i
$238$	0.310750	−	0.279801i	0.0201429	−	0.0181368i
$239$	−0.873628	−	8.31201i	−0.0565103	−	0.537659i	−0.985754	−	0.168192i	$-0.946207\pi$
$239$	−0.873628	−	8.31201i	−0.0565103	−	0.537659i	0.929244	−	0.369467i	$-0.120460\pi$
$240$	−1.59532	+	0.674499i	−0.102978	+	0.0435387i
$241$	−10.5496	−	1.10881i	−0.679559	−	0.0714245i	−0.241541	−	0.970391i	$-0.577653\pi$
$241$	−10.5496	−	1.10881i	−0.679559	−	0.0714245i	−0.438018	+	0.898966i	$0.644319\pi$
$242$	−26.0552	+	15.0430i	−1.67489	+	0.966999i
$243$	1.46896	−	15.5191i	0.0942339	−	0.995550i
$244$	6.08289	−	8.37238i	0.389417	−	0.535987i
$245$	−1.34199	−	1.20833i	−0.0857366	−	0.0771976i
$246$	8.52643	+	5.13971i	0.543625	+	0.327696i
$247$			0.874702i			0.0556559i
$248$	−3.92025	−	3.95369i	−0.248936	−	0.251060i
$249$	2.11982	−	9.12277i	0.134338	−	0.578132i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	4.56472	−	5.06964i	0.288123	−	0.319993i	−0.581656	−	0.813435i	$-0.697595\pi$
$251$	4.56472	−	5.06964i	0.288123	−	0.319993i	0.869779	+	0.493442i	$0.164262\pi$
$252$	−4.15705	−	7.87219i	−0.261870	−	0.495901i
$253$	0.865272	−	1.49869i	0.0543992	−	0.0942221i
$254$	−9.82246	−	17.0130i	−0.616316	−	1.06749i
$255$	−0.0797892	+	0.230659i	−0.00499660	+	0.0144444i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−8.43770	+	0.886838i	−0.526330	+	0.0553195i	−0.363967	−	0.931412i	$-0.618578\pi$
$257$	−8.43770	+	0.886838i	−0.526330	+	0.0553195i	−0.162362	+	0.986731i	$0.551911\pi$
$258$	−0.767868	+	0.424210i	−0.0478054	+	0.0264102i
$259$	−3.60346	−	8.09350i	−0.223908	−	0.502905i
$260$	−0.251020	+	0.0533559i	−0.0155676	+	0.00330899i
$261$	−8.15764	−	6.41088i	−0.504945	−	0.396823i
$262$	−9.82333	−	4.37363i	−0.606887	−	0.270204i
$263$	6.72004	+	20.6822i	0.414376	+	1.27532i	0.912808	+	0.408388i	$0.133909\pi$
$263$	6.72004	+	20.6822i	0.414376	+	1.27532i	−0.498433	+	0.866928i	$0.666091\pi$
$264$	−0.951894	−	11.0613i	−0.0585850	−	0.680774i
$265$	2.65668	−	5.96699i	0.163198	−	0.366549i
$266$	2.10291	−	9.89341i	0.128938	−	0.606604i
$267$	−0.259908	+	13.7685i	−0.0159061	+	0.842617i
$268$	4.69452	−	2.09013i	0.286763	−	0.127675i
$269$	−2.54091	−	2.82197i	−0.154922	−	0.172059i	0.660687	−	0.750661i	$-0.270265\pi$
$269$	−2.54091	−	2.82197i	−0.154922	−	0.172059i	−0.815610	+	0.578603i	$0.803598\pi$
$270$	4.34575	+	2.84859i	0.264474	+	0.173359i
$271$	2.67624	+	3.68353i	0.162570	+	0.223759i	0.882529	−	0.470258i	$-0.155839\pi$
$271$	2.67624	+	3.68353i	0.162570	+	0.223759i	−0.719959	+	0.694017i	$0.755839\pi$
$272$	−0.0147295	+	0.140142i	−0.000893106	+	0.00849734i
$273$	−0.383849	−	1.26192i	−0.0232316	−	0.0763752i
$274$	−18.4930	−	10.6769i	−1.11720	−	0.645017i
$275$	5.18566	+	3.76760i	0.312707	+	0.227195i
$276$	0.267673	+	0.383436i	0.0161120	+	0.0230801i
$277$	−8.83358	−	2.87020i	−0.530758	−	0.172454i	0.0313639	−	0.999508i	$-0.490015\pi$
$277$	−8.83358	−	2.87020i	−0.530758	−	0.172454i	−0.562122	+	0.827054i	$0.690015\pi$
$278$	10.4307			0.625592
$279$	−3.30332	+	16.3734i	−0.197764	+	0.980250i
$280$	2.96746			0.177340
$281$	20.0881	+	6.52702i	1.19836	+	0.389369i	0.839156	−	0.543891i	$-0.183050\pi$
$281$	20.0881	+	6.52702i	1.19836	+	0.389369i	0.359200	+	0.933261i	$0.383050\pi$
$282$	12.1403	+	17.3907i	0.722946	+	1.03560i
$283$	−3.75448	−	2.72779i	−0.223180	−	0.162150i	0.470577	−	0.882359i	$-0.344046\pi$
$283$	−3.75448	−	2.72779i	−0.223180	−	0.162150i	−0.693757	+	0.720209i	$0.744046\pi$
$284$	−2.77393	−	1.60153i	−0.164603	−	0.0950334i
$285$	1.71802	+	5.64809i	0.101767	+	0.334564i
$286$	0.171943	−	1.63593i	0.0101672	−	0.0967345i
$287$	−10.0257	−	13.7992i	−0.591801	−	0.814544i
$288$	2.81615	+	1.03407i	0.165943	+	0.0609332i
$289$	−11.3619	−	12.6187i	−0.668349	−	0.742277i
$290$	3.15943	−	1.40667i	0.185528	−	0.0826024i
$291$	−0.136339	+	7.22246i	−0.00799232	+	0.423388i
$292$	−1.27498	+	5.99832i	−0.0746127	+	0.351025i
$293$	2.93664	−	6.59581i	0.171561	−	0.385331i	−0.807218	−	0.590254i	$-0.799028\pi$
$293$	2.93664	−	6.59581i	0.171561	−	0.385331i	0.978778	+	0.204923i	$0.0656943\pi$
$294$	0.268175	+	3.11626i	0.0156403	+	0.181744i
$295$	−0.533018	−	1.64046i	−0.0310335	−	0.0955112i
$296$	2.72741	+	1.21432i	0.158528	+	0.0705811i
$297$	−25.9731	+	20.8499i	−1.50711	+	1.20983i
$298$	−3.25379	+	0.691615i	−0.188487	+	0.0400642i
$299$	0.0281807	+	0.0632950i	0.00162973	+	0.00366044i
$300$	−1.51608	+	0.837561i	−0.0875308	+	0.0483566i
$301$	1.49474	−	0.157103i	0.0861551	−	0.00905527i
$302$	−4.41093	+	3.20473i	−0.253820	+	0.184411i
$303$	−0.224838	+	0.649975i	−0.0129166	+	0.0373401i
$304$	1.70422	+	2.95180i	0.0977440	+	0.169298i
$305$	5.17442	−	8.96235i	0.296286	−	0.513183i
$306$	0.373821	−	0.197403i	0.0213699	−	0.0112848i
$307$	20.1392	−	22.3668i	1.14940	−	1.27654i	0.194080	−	0.980986i	$-0.437828\pi$
$307$	20.1392	−	22.3668i	1.14940	−	1.27654i	0.955325	−	0.295557i	$-0.0955053\pi$
$308$	−5.87779	+	18.0900i	−0.334918	+	1.03077i
$309$	4.01677	−	17.2864i	0.228506	−	0.983388i
$310$	−4.31204	−	3.52225i	−0.244908	−	0.200051i
$311$			5.29491i			0.300247i	0.988667	+	0.150123i	$0.0479671\pi$
$311$			5.29491i			0.300247i	−0.988667	+	0.150123i	$0.952033\pi$
$312$	0.380678	+	0.229472i	0.0215517	+	0.0129913i
$313$	6.74152	+	6.07010i	0.381053	+	0.343102i	0.837293	−	0.546755i	$-0.184137\pi$
$313$	6.74152	+	6.07010i	0.381053	+	0.343102i	−0.456239	+	0.889857i	$0.650804\pi$
$314$	−6.51860	+	8.97208i	−0.367866	+	0.506324i
$315$	−4.95715	−	7.39453i	−0.279304	−	0.416635i
$316$	−13.5622	+	7.83012i	−0.762932	+	0.440479i
$317$	15.4790	+	1.62691i	0.869386	+	0.0913762i	0.528708	−	0.848804i	$-0.322677\pi$
$317$	15.4790	+	1.62691i	0.869386	+	0.0913762i	0.340678	+	0.940180i	$0.389343\pi$
$318$	−10.4201	+	4.40561i	−0.584332	+	0.247055i
$319$	2.31718	+	22.0465i	0.129737	+	1.23437i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	−4.09314	+	0.789589i	−0.228457	+	0.0440706i
$322$	−0.166571	−	0.783656i	−0.00928265	−	0.0436714i
$323$	0.469801	+	0.0998593i	0.0261404	+	0.00555632i
$324$	−2.12761	−	8.74490i	−0.118200	−	0.485828i
$325$	−0.244067	+	0.0793023i	−0.0135384	+	0.00439890i
$326$	11.6236	−	3.77672i	0.643769	−	0.209173i
$327$	16.3816	−	21.6750i	0.905906	−	1.19863i
$328$	5.62234	+	1.19507i	0.310442	+	0.0659864i
$329$	−7.55484	−	35.5427i	−0.416512	−	1.95953i
$330$	−2.10290	−	10.9012i	−0.115761	−	0.600090i
$331$	6.98624	−	6.29044i	0.383998	−	0.345754i	−0.454413	−	0.890791i	$-0.650151\pi$
$331$	6.98624	−	6.29044i	0.383998	−	0.345754i	0.838412	+	0.545037i	$0.183484\pi$
$332$	−0.565223	−	5.37774i	−0.0310206	−	0.295142i
$333$	−1.53021	−	8.82490i	−0.0838550	−	0.483601i
$334$	10.3458	+	1.08739i	0.566099	+	0.0594994i
$335$	4.45032	−	2.56939i	0.243147	−	0.140381i
$336$	−3.75402	−	3.51067i	−0.204799	−	0.191523i
$337$	17.5658	−	24.1772i	0.956869	−	1.31702i	0.00846184	−	0.999964i	$-0.497306\pi$
$337$	17.5658	−	24.1772i	0.956869	−	1.31702i	0.948408	−	0.317054i	$-0.102694\pi$
$338$	−9.61194	−	8.65463i	−0.522821	−	0.470750i
$339$	−6.81073	+	11.2985i	−0.369908	+	0.613653i
$340$			0.140914i			0.00764211i
$341$	30.0131	−	19.3100i	1.62530	−	1.04570i
$342$	4.50861	−	9.17770i	0.243798	−	0.496273i
$343$	−4.76304	+	14.6591i	−0.257180	+	0.791518i
$344$	−0.338903	+	0.376390i	−0.0182724	+	0.0202936i
$345$	0.306287	+	0.353356i	0.0164899	+	0.0190240i
$346$	−11.1974	+	19.3945i	−0.601978	+	1.04266i
$347$	−8.23955	−	14.2713i	−0.442322	−	0.766124i	0.555539	−	0.831490i	$-0.312512\pi$
$347$	−8.23955	−	14.2713i	−0.442322	−	0.766124i	−0.997861	+	0.0653659i	$0.979179\pi$
$348$	−5.66104	−	1.95826i	−0.303464	−	0.104974i
$349$	−24.0897	+	17.5022i	−1.28949	+	0.936872i	−0.999795	−	0.0202459i	$-0.993555\pi$
$349$	−24.0897	+	17.5022i	−1.28949	+	0.936872i	−0.289699	+	0.957118i	$0.593555\pi$
$350$	2.95121	−	0.310184i	0.157749	−	0.0165800i
$351$	−0.0641093	−	1.33193i	−0.00342190	−	0.0710934i
$352$	−2.60711	−	5.85567i	−0.138960	−	0.312108i
$353$	25.4413	−	5.40772i	1.35410	−	0.287824i	0.526997	−	0.849867i	$-0.323318\pi$
$353$	25.4413	−	5.40772i	1.35410	−	0.287824i	0.827108	+	0.562044i	$0.189985\pi$
$354$	−1.26645	+	2.70587i	−0.0673113	+	0.143815i
$355$	−2.92614	−	1.30280i	−0.155304	−	0.0691456i
$356$	2.45689	+	7.56152i	0.130215	+	0.400760i
$357$	−0.721600	+	0.0620983i	−0.0381911	+	0.00328659i
$358$	−9.56282	+	21.4784i	−0.505411	+	1.13517i
$359$	−0.543205	+	2.55558i	−0.0286693	+	0.134878i	−0.990155	−	0.139978i	$-0.955297\pi$
$359$	−0.543205	+	2.55558i	−0.0286693	+	0.134878i	0.961485	+	0.274856i	$0.0886302\pi$
$360$	2.90881	+	0.734038i	0.153308	+	0.0386872i
$361$	−6.74423	+	3.00272i	−0.354959	+	0.158038i
$362$	−3.00292	−	3.33509i	−0.157830	−	0.175288i
$363$	51.7129	+	6.42418i	2.71422	+	0.337182i
$364$	−0.447617	−	0.616093i	−0.0234615	−	0.0322920i
$365$	−0.641003	+	6.09873i	−0.0335516	+	0.319222i
$366$	−17.1489	+	5.21631i	−0.896388	+	0.272661i
$367$	16.7269	+	9.65731i	0.873140	+	0.504107i	0.868390	−	0.495881i	$-0.165155\pi$
$367$	16.7269	+	9.65731i	0.873140	+	0.504107i	0.00474934	+	0.999989i	$0.498488\pi$
$368$	0.218421	+	0.158692i	0.0113860	+	0.00827238i
$369$	−6.41417	−	16.0065i	−0.333909	−	0.833265i
$370$	2.83940	+	0.922578i	0.147614	+	0.0479626i
$371$	19.3825			1.00629
$372$	1.28798	+	9.55725i	0.0667785	+	0.495521i
$373$	5.10909			0.264539			0.132269	−	0.991214i	$-0.457774\pi$
$373$	5.10909			0.264539			0.132269	+	0.991214i	$0.457774\pi$
$374$	−0.859025	−	0.279114i	−0.0444191	−	0.0144327i
$375$	−1.42022	+	0.991446i	−0.0733400	+	0.0511980i
$376$	9.90647	+	7.19747i	0.510887	+	0.371181i
$377$	−0.768621	−	0.443764i	−0.0395860	−	0.0228550i
$378$	−2.47705	+	15.2191i	−0.127406	+	0.782787i
$379$	−1.52625	+	14.5213i	−0.0783983	+	0.745910i	0.882743	+	0.469855i	$0.155694\pi$
$379$	−1.52625	+	14.5213i	−0.0783983	+	0.745910i	−0.961142	+	0.276055i	$0.910973\pi$
$380$	2.00344	+	2.75749i	0.102774	+	0.141456i
$381$	−4.19473	+	33.7664i	−0.214902	+	1.72991i
$382$	10.9404	+	12.1505i	0.559757	+	0.621673i
$383$	−22.9609	+	10.2228i	−1.17325	+	0.522363i	−0.898423	−	0.439132i	$-0.855286\pi$
$383$	−22.9609	+	10.2228i	−1.17325	+	0.522363i	−0.274824	+	0.961495i	$0.588620\pi$
$384$	1.73174	+	0.0326902i	0.0883726	+	0.00166821i
$385$	−3.95467	+	18.6053i	−0.201549	+	0.948213i
$386$	−4.96980	+	11.1623i	−0.252956	+	0.568149i
$387$	1.50405	+	0.215743i	0.0764554	+	0.0109669i
$388$	1.28880	+	3.96651i	0.0654288	+	0.201369i
$389$	27.8643	+	12.4060i	1.41278	+	0.629008i	0.964306	−	0.264790i	$-0.0853026\pi$
$389$	27.8643	+	12.4060i	1.41278	+	0.629008i	0.448469	+	0.893798i	$0.351969\pi$
$390$	0.402579	+	0.188423i	0.0203854	+	0.00954116i
$391$	0.0372129	−	0.00790984i	0.00188194	−	0.000400018i
$392$	0.734496	+	1.64970i	0.0370976	+	0.0833226i
$393$	9.00627	+	16.3023i	0.454306	+	0.822344i
$394$	22.1199	−	2.32490i	1.11438	−	0.117127i
$395$	−12.6694	+	9.20486i	−0.637467	+	0.463147i
$396$	−10.2364	+	16.2785i	−0.514399	+	0.818025i
$397$	−0.671490	−	1.16305i	−0.0337011	−	0.0583720i	0.848683	−	0.528902i	$-0.177396\pi$
$397$	−0.671490	−	1.16305i	−0.0337011	−	0.0583720i	−0.882384	+	0.470530i	$0.844063\pi$
$398$	−9.57758	+	16.5888i	−0.480080	+	0.831524i
$399$	−13.2379	+	11.4745i	−0.662722	+	0.574444i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	8.37871	−	25.7870i	0.418413	−	1.28774i	−0.490750	−	0.871301i	$-0.663277\pi$
$401$	8.37871	−	25.7870i	0.418413	−	1.28774i	0.909162	−	0.416442i	$-0.136723\pi$
$402$	−8.66966	−	2.01453i	−0.432404	−	0.100476i
$403$	−0.0808398	+	1.42655i	−0.00402692	+	0.0710617i
$404$			0.397081i			0.0197555i
$405$	−3.03004	−	8.47460i	−0.150564	−	0.421106i
$406$	7.62671	+	6.86712i	0.378507	+	0.340809i
$407$	−11.2483	+	15.4819i	−0.557557	+	0.767411i
$408$	0.166709	−	0.178264i	0.00825331	−	0.00882540i
$409$	−27.4210	+	15.8315i	−1.35588	+	0.782818i	−0.989066	−	0.147477i	$-0.952885\pi$
$409$	−27.4210	+	15.8315i	−1.35588	+	0.782818i	−0.366814	+	0.930294i	$0.619552\pi$
$410$	5.71646	+	0.600824i	0.282316	+	0.0296726i
$411$	14.4032	+	34.0663i	0.710456	+	1.68037i
$412$	−1.07102	−	10.1901i	−0.0527653	−	0.502029i
$413$	3.80380	−	3.42496i	0.187173	−	0.168531i
$414$	0.0305679	−	0.809371i	0.00150233	−	0.0397784i
$415$	−1.12425	−	5.28919i	−0.0551874	−	0.259636i
$416$	0.251020	+	0.0533559i	0.0123072	+	0.00261599i
$417$	−14.4131	−	10.8932i	−0.705811	−	0.533442i
$418$	−20.7783	+	6.75127i	−1.01630	+	0.330216i
$419$	13.2118	−	4.29277i	0.645438	−	0.209715i	0.0320362	−	0.999487i	$-0.489801\pi$
$419$	13.2118	−	4.29277i	0.645438	−	0.209715i	0.613401	+	0.789771i	$0.289801\pi$
$420$	−4.10042	−	3.09904i	−0.200080	−	0.151218i
$421$	36.5161	+	7.76173i	1.77968	+	0.378283i	0.976171	−	0.217004i	$-0.0696284\pi$
$421$	36.5161	+	7.76173i	1.77968	+	0.378283i	0.803513	+	0.595287i	$0.202962\pi$
$422$	5.52717	+	26.0033i	0.269059	+	1.26582i
$423$	1.38641	−	36.7091i	0.0674096	−	1.78486i
$424$	−4.85399	+	4.37055i	−0.235730	+	0.212253i
$425$	0.0147295	+	0.140142i	0.000714485	+	0.00679787i
$426$	2.16046	+	5.10992i	0.104675	+	0.247576i
$427$	30.5415	+	3.21004i	1.47801	+	0.155345i
$428$	−2.08430	+	1.20337i	−0.100748	+	0.0581672i
$429$	−1.94605	+	2.08095i	−0.0939564	+	0.100469i
$430$	−0.297703	+	0.409753i	−0.0143565	+	0.0197601i
$431$	−7.85858	−	7.07589i	−0.378534	−	0.340834i	0.457798	−	0.889056i	$-0.348638\pi$
$431$	−7.85858	−	7.07589i	−0.378534	−	0.340834i	−0.836333	+	0.548222i	$0.815305\pi$
$432$	−2.81142	−	4.36989i	−0.135264	−	0.210246i
$433$			0.696606i			0.0334767i	0.999860	+	0.0167384i	$0.00532824\pi$
$433$			0.696606i			0.0334767i	−0.999860	+	0.0167384i	$0.994672\pi$
$434$	4.34399	−	15.9408i	0.208518	−	0.765185i
$435$	−5.83472	−	1.35579i	−0.279754	−	0.0650052i
$436$	4.84728	−	14.9184i	0.232142	−	0.714461i
$437$	0.615749	−	0.683858i	0.0294553	−	0.0327134i
$438$	8.02604	−	6.95693i	0.383499	−	0.332415i
$439$	−15.1086	+	26.1689i	−0.721096	+	1.24898i	0.239465	+	0.970905i	$0.423028\pi$
$439$	−15.1086	+	26.1689i	−0.721096	+	1.24898i	−0.960561	+	0.278070i	$0.910305\pi$
$440$	−3.20492	−	5.55108i	−0.152788	−	0.264637i
$441$	2.88388	−	4.58610i	0.137327	−	0.218386i
$442$	0.0292559	−	0.0212557i	0.00139156	−	0.00101103i
$443$	22.0683	−	2.31948i	1.04850	−	0.110202i	0.435423	−	0.900226i	$-0.356599\pi$
$443$	22.0683	−	2.31948i	1.04850	−	0.110202i	0.613075	+	0.790024i	$0.289932\pi$
$444$	−2.50056	−	4.52629i	−0.118671	−	0.214808i
$445$	3.23382	+	7.26328i	0.153298	+	0.344313i
$446$	−23.0813	+	4.90608i	−1.09293	+	0.232310i
$447$	5.21836	+	2.44240i	0.246820	+	0.115521i
$448$	−2.71091	−	1.20698i	−0.128078	−	0.0570242i
$449$	−3.01743	−	9.28669i	−0.142401	−	0.438266i	0.854266	−	0.519836i	$-0.174007\pi$
$449$	−3.01743	−	9.28669i	−0.142401	−	0.438266i	−0.996668	+	0.0815694i	$0.974007\pi$
$450$	2.96961	+	0.425964i	0.139989	+	0.0200801i
$451$	−14.9855	+	33.6581i	−0.705642	+	1.58490i
$452$	−1.58360	+	7.45027i	−0.0744865	+	0.350431i
$453$	9.44182	+	0.178233i	0.443615	+	0.00837414i
$454$	14.9857	−	6.67206i	0.703314	−	0.313135i
$455$	−0.509565	−	0.565929i	−0.0238888	−	0.0265311i
$456$	0.727797	−	5.85857i	0.0340822	−	0.274353i
$457$	−16.7874	−	23.1059i	−0.785284	−	1.08085i	−0.994679	−	0.103019i	$-0.967150\pi$
$457$	−16.7874	−	23.1059i	−0.785284	−	1.08085i	0.209396	−	0.977831i	$-0.432850\pi$
$458$	0.330941	−	3.14869i	0.0154638	−	0.147129i
$459$	−0.722699	−	0.117626i	−0.0337327	−	0.00549030i
$460$	0.233812	+	0.134991i	0.0109015	+	0.00629400i
$461$	12.9289	+	9.39336i	0.602157	+	0.437492i	0.846644	−	0.532160i	$-0.178620\pi$
$461$	12.9289	+	9.39336i	0.602157	+	0.437492i	−0.244487	+	0.969653i	$0.578620\pi$
$462$	27.0140	−	18.8582i	1.25680	−	0.877364i
$463$	−13.9863	−	4.54442i	−0.649997	−	0.211197i	−0.0345844	−	0.999402i	$-0.511011\pi$
$463$	−13.9863	−	4.54442i	−0.649997	−	0.211197i	−0.615413	+	0.788205i	$0.711011\pi$
$464$	−3.45843			−0.160553
$465$	2.27993	+	9.37027i	0.105729	+	0.434536i
$466$	−4.13659			−0.191624
$467$	−25.9318	−	8.42577i	−1.19998	−	0.389898i	−0.360228	−	0.932864i	$-0.617301\pi$
$467$	−25.9318	−	8.42577i	−1.19998	−	0.389898i	−0.839755	+	0.542966i	$0.817301\pi$
$468$	−0.286373	−	0.714640i	−0.0132376	−	0.0330342i
$469$	12.3368	+	8.96323i	0.569662	+	0.413883i
$470$	10.6045	+	6.12254i	0.489151	+	0.282412i
$471$	18.3773	−	5.58994i	0.846779	−	0.257571i
$472$	−0.180299	+	1.71543i	−0.00829894	+	0.0789592i
$473$	−1.90823	−	2.62645i	−0.0877404	−	0.120764i
$474$	26.9174	+	3.34389i	1.23636	+	0.153590i
$475$	2.28070	+	2.53297i	0.104646	+	0.116221i
$476$	−0.382004	+	0.170079i	−0.0175091	+	0.00779557i
$477$	18.9994	+	4.79451i	0.869925	+	0.219525i
$478$	−1.73768	+	8.17516i	−0.0794798	+	0.373923i
$479$	−6.64610	+	14.9274i	−0.303668	+	0.682049i	−0.999341	−	0.0363096i	$-0.988440\pi$
$479$	−6.64610	+	14.9274i	−0.303668	+	0.682049i	0.695673	+	0.718359i	$0.255106\pi$
$480$	1.72567	−	0.148505i	0.0787658	−	0.00677831i
$481$	−0.236759	−	0.728669i	−0.0107953	−	0.0332245i
$482$	9.69062	+	4.31454i	0.441396	+	0.196522i
$483$	−0.588236	+	1.25681i	−0.0267656	+	0.0571867i
$484$	29.4285	−	6.25522i	1.33766	−	0.284328i
$485$	1.69635	+	3.81006i	0.0770273	+	0.173006i
$486$	−6.19273	+	14.3056i	−0.280908	+	0.648915i
$487$	8.27105	−	0.869322i	0.374797	−	0.0393927i	0.0847425	−	0.996403i	$-0.472993\pi$
$487$	8.27105	−	0.869322i	0.374797	−	0.0393927i	0.290054	+	0.957010i	$0.406327\pi$
$488$	−8.37238	+	6.08289i	−0.379000	+	0.275360i
$489$	−20.0055	−	6.92029i	−0.904682	−	0.312946i
$490$	0.902913	+	1.56389i	0.0407895	+	0.0706494i
$491$	−5.38717	+	9.33085i	−0.243120	+	0.421095i	−0.961601	−	0.274451i	$-0.911504\pi$
$491$	−5.38717	+	9.33085i	−0.243120	+	0.421095i	0.718482	+	0.695546i	$0.244837\pi$
$492$	−6.52086	−	7.52296i	−0.293983	−	0.339161i
$493$	−0.326094	+	0.362164i	−0.0146865	+	0.0163110i
$494$	0.270298	−	0.831891i	0.0121613	−	0.0374285i
$495$	−8.47876	+	17.2593i	−0.381092	+	0.775749i
$496$	2.50662	+	4.97161i	0.112550	+	0.223232i
$497$		−	9.50497i		−	0.426356i
$498$	−4.83516	+	8.02121i	−0.216669	+	0.359439i
$499$	−18.9389	−	17.0527i	−0.847822	−	0.763383i	0.125677	−	0.992071i	$-0.459890\pi$
$499$	−18.9389	−	17.0527i	−0.847822	−	0.763383i	−0.973500	+	0.228689i	$0.926556\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	−13.1602	−	12.3071i	−0.587955	−	0.549841i
$502$	−5.90792	+	3.41094i	−0.263683	+	0.152238i
$503$	−3.00457	−	0.315793i	−0.133967	−	0.0140805i	0.0373075	−	0.999304i	$-0.488122\pi$
$503$	−3.00457	−	0.315793i	−0.133967	−	0.0140805i	−0.171275	+	0.985223i	$0.554789\pi$
$504$	1.52095	+	8.77150i	0.0677486	+	0.390713i
$505$	0.0415062	+	0.394905i	0.00184700	+	0.0175731i
$506$	−1.28604	+	1.15796i	−0.0571717	+	0.0514776i
$507$	4.24335	+	21.9970i	0.188454	+	0.976923i
$508$	4.08441	+	19.2156i	0.181216	+	0.852556i
$509$	−0.368881	−	0.0784080i	−0.0163504	−	0.00347537i	0.199729	−	0.979851i	$-0.435994\pi$
$509$	−0.368881	−	0.0784080i	−0.0163504	−	0.00347537i	−0.216080	+	0.976376i	$0.569327\pi$
$510$	0.147162	−	0.194714i	0.00651643	−	0.00862206i
$511$	−17.3068	+	5.62332i	−0.765607	+	0.248761i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−15.8146	+	7.97317i	−0.698232	+	0.352024i
$514$	8.29878	+	1.76396i	0.366044	+	0.0778050i
$515$	−2.13030	−	10.0223i	−0.0938724	−	0.441635i
$516$	0.861374	−	0.166164i	0.0379199	−	0.00731495i
$517$	−58.3286	+	52.5193i	−2.56529	+	2.30980i
$518$	0.926063	+	8.81090i	0.0406889	+	0.387129i
$519$	35.7270	−	15.1053i	1.56824	−	0.663050i
$520$	0.255222	+	0.0268249i	0.0111922	+	0.00117635i
$521$	32.5754	−	18.8074i	1.42715	−	0.823967i	0.430258	−	0.902706i	$-0.358423\pi$
$521$	32.5754	−	18.8074i	1.42715	−	0.823967i	0.996895	+	0.0787386i	$0.0250893\pi$
$522$	5.77731	+	8.61796i	0.252866	+	0.377198i
$523$	−15.2004	+	20.9216i	−0.664669	+	0.914838i	−0.999625	−	0.0273955i	$-0.991279\pi$
$523$	−15.2004	+	20.9216i	−0.664669	+	0.914838i	0.334956	+	0.942234i	$0.391279\pi$
$524$	7.99102	+	7.19514i	0.349089	+	0.314321i
$525$	−4.40190	−	2.65345i	−0.192114	−	0.115806i
$526$		−	21.7465i		−	0.948193i
$527$	0.756971	+	0.206280i	0.0329742	+	0.00898569i
$528$	−2.51282	+	10.8140i	−0.109356	+	0.470621i
$529$	−7.08487	+	21.8050i	−0.308038	+	0.948042i
$530$	−4.37055	+	4.85399i	−0.189845	+	0.210844i
$531$	4.57583	−	2.41635i	0.198574	−	0.104861i
$532$	−5.05722	+	8.75936i	−0.219258	+	0.379766i
$533$	−0.737541	−	1.27746i	−0.0319464	−	0.0553328i
$534$	4.50188	−	13.0143i	0.194815	−	0.563183i
$535$	−1.94710	+	1.41465i	−0.0841803	+	0.0611606i
$536$	−5.11064	+	0.537150i	−0.220746	+	0.0232013i
$537$	35.6446	−	19.6920i	1.53818	−	0.849771i
$538$	1.54452	+	3.46904i	0.0665888	+	0.149561i
$539$	−11.3221	+	2.40659i	−0.487677	+	0.103659i
$540$	−3.25279	−	4.05208i	−0.139978	−	0.174374i
$541$	10.0784	+	4.48718i	0.433303	+	0.192919i	0.611785	−	0.791024i	$-0.290452\pi$
$541$	10.0784	+	4.48718i	0.433303	+	0.192919i	−0.178482	+	0.983943i	$0.557119\pi$
$542$	−1.40698	−	4.33025i	−0.0604351	−	0.186000i
$543$	0.666462	+	7.74447i	0.0286006	+	0.332347i
$544$	0.0573147	−	0.128731i	0.00245735	−	0.00551930i
$545$	3.26133	−	15.3433i	0.139700	−	0.657236i
$546$	−0.0248946	+	1.31878i	−0.00106539	+	0.0564385i
$547$	26.0680	−	11.6062i	1.11459	−	0.496246i	0.235005	−	0.971994i	$-0.424489\pi$
$547$	26.0680	−	11.6062i	1.11459	−	0.496246i	0.879581	+	0.475749i	$0.157823\pi$
$548$	14.2885	+	15.8690i	0.610376	+	0.677891i
$549$	29.1439	+	10.7014i	1.24383	+	0.456726i
$550$	−3.76760	−	5.18566i	−0.160651	−	0.221117i
$551$	−1.23217	+	11.7233i	−0.0524921	+	0.499429i
$552$	−0.136084	−	0.447385i	−0.00579213	−	0.0190420i
$553$	−40.2452	−	23.2356i	−1.71140	−	0.988078i
$554$	7.51429	+	5.45945i	0.319252	+	0.231950i
$555$	−2.95999	−	4.24012i	−0.125644	−	0.179983i
$556$	−9.92018	−	3.22326i	−0.420709	−	0.136697i
$557$	−28.2244			−1.19590			−0.597952	−	0.801532i	$-0.704019\pi$
$557$	−28.2244			−1.19590			−0.597952	+	0.801532i	$0.704019\pi$
$558$	8.20130	−	14.5512i	0.347189	−	0.616003i
$559$	0.129978			0.00549746
$560$	−2.82222	−	0.916996i	−0.119261	−	0.0387502i
$561$	0.895506	+	1.28279i	0.0378083	+	0.0541595i
$562$	−17.0880	−	12.4151i	−0.720812	−	0.523701i
$563$	17.1685	+	9.91222i	0.723565	+	0.417750i	0.816063	−	0.577962i	$-0.196152\pi$
$563$	17.1685	+	9.91222i	0.723565	+	0.417750i	−0.0924984	+	0.995713i	$0.529485\pi$
$564$	−6.17210	−	20.2911i	−0.259892	−	0.854411i
$565$	−0.796164	+	7.57499i	−0.0334949	+	0.318682i
$566$	2.72779	+	3.75448i	0.114657	+	0.157812i
$567$	19.3167	−	18.4428i	0.811225	−	0.774525i
$568$	2.14327	+	2.38034i	0.0899295	+	0.0998769i
$569$	−37.4164	+	16.6589i	−1.56858	+	0.698376i	−0.992862	−	0.119272i	$-0.961944\pi$
$569$	−37.4164	+	16.6589i	−1.56858	+	0.698376i	−0.575717	+	0.817649i	$0.695277\pi$
$570$	0.111423	−	5.90255i	0.00466698	−	0.247231i
$571$	−9.25762	+	43.5537i	−0.387419	+	1.82266i	0.161603	+	0.986856i	$0.448334\pi$
$571$	−9.25762	+	43.5537i	−0.387419	+	1.82266i	−0.549022	+	0.835808i	$0.685000\pi$
$572$	−0.669057	+	1.50273i	−0.0279747	+	0.0628322i
$573$	−2.42808	−	28.2149i	−0.101434	−	1.17870i
$574$	5.27084	+	16.2220i	0.220001	+	0.677093i
$575$	0.246641	+	0.109812i	0.0102857	+	0.00457947i
$576$	−2.35877	−	1.85370i	−0.0982822	−	0.0772374i
$577$	8.59621	−	1.82718i	0.357865	−	0.0760665i	−0.0254710	−	0.999676i	$-0.508109\pi$
$577$	8.59621	−	1.82718i	0.357865	−	0.0760665i	0.383336	+	0.923609i	$0.374775\pi$
$578$	6.90645	+	15.5121i	0.287270	+	0.645220i
$579$	18.5245	−	10.2339i	0.769853	−	0.425307i
$580$	−3.43948	+	0.361504i	−0.142817	+	0.0150106i
$581$	12.9816	−	9.43168i	0.538567	−	0.391292i
$582$	2.36153	−	6.82684i	0.0978886	−	0.282982i
$583$	−20.9335	−	36.2579i	−0.866977	−	1.50165i
$584$	3.06616	−	5.31075i	0.126879	−	0.219760i
$585$	−0.359504	−	0.680791i	−0.0148637	−	0.0281472i
$586$	−4.83113	+	5.36552i	−0.199572	+	0.221647i
$587$	1.60954	−	4.95366i	0.0664329	−	0.204459i	−0.912330	−	0.409456i	$-0.865718\pi$
$587$	1.60954	−	4.95366i	0.0664329	−	0.204459i	0.978763	+	0.204997i	$0.0657184\pi$
$588$	0.707929	−	3.04661i	0.0291945	−	0.125640i
$589$	17.7457	−	6.72559i	0.731198	−	0.277123i
$590$			1.72488i			0.0710122i
$591$	−32.9931	−	19.8882i	−1.35716	−	0.818090i
$592$	−2.21868	−	1.99771i	−0.0911871	−	0.0821053i
$593$	−8.51531	+	11.7203i	−0.349682	+	0.481296i	−0.947238	−	0.320531i	$-0.896139\pi$
$593$	−8.51531	+	11.7203i	−0.349682	+	0.481296i	0.597556	+	0.801827i	$0.296139\pi$
$594$	31.1449	−	11.8033i	1.27789	−	0.484294i
$595$	−0.362133	+	0.209078i	−0.0148460	+	0.00857136i
$596$	3.30826	+	0.347712i	0.135512	+	0.0142429i
$597$	30.5586	−	12.9201i	1.25068	−	0.528786i
$598$	−0.00724225	−	0.0689054i	−0.000296158	−	0.00281775i
$599$	−31.5334	+	28.3928i	−1.28842	+	1.16010i	−0.310627	+	0.950532i	$0.600539\pi$
$599$	−31.5334	+	28.3928i	−1.28842	+	1.16010i	−0.977794	+	0.209568i	$0.932794\pi$
$600$	1.70070	−	0.328074i	0.0694306	−	0.0133936i
$601$	2.71216	+	12.7597i	0.110631	+	0.520480i	0.998209	+	0.0598218i	$0.0190532\pi$
$601$	2.71216	+	12.7597i	0.110631	+	0.520480i	−0.887578	+	0.460658i	$0.847613\pi$
$602$	−1.47013	−	0.312485i	−0.0599178	−	0.0127359i
$603$	9.87583	+	11.8377i	0.402175	+	0.482070i
$604$	5.18536	−	1.68482i	0.210989	−	0.0685545i
$605$	28.6134	−	9.29707i	1.16330	−	0.377980i
$606$	0.414687	−	0.548684i	0.0168455	−	0.0222888i
$607$	−44.9720	−	9.55908i	−1.82536	−	0.387991i	−0.837891	−	0.545837i	$-0.816212\pi$
$607$	−44.9720	−	9.55908i	−1.82536	−	0.387991i	−0.987464	+	0.157846i	$0.949545\pi$
$608$	−0.708656	−	3.33397i	−0.0287398	−	0.135210i
$609$	−3.36694	−	17.4538i	−0.136435	−	0.707264i
$610$	−7.69068	+	6.92472i	−0.311387	+	0.280374i
$611$	−0.328473	−	3.12521i	−0.0132886	−	0.126432i
$612$	−0.416525	+	0.0722243i	−0.0168370	+	0.00291949i
$613$	37.1749	+	3.90724i	1.50148	+	0.157812i	0.819297	−	0.573369i	$-0.194364\pi$
$613$	37.1749	+	3.90724i	1.50148	+	0.157812i	0.682184	+	0.731181i	$0.261030\pi$
$614$	−26.0652	+	15.0488i	−1.05191	+	0.607319i
$615$	−7.27150	−	6.80014i	−0.293215	−	0.274208i
$616$	11.1802	−	15.3883i	0.450464	−	0.620010i
$617$	17.3969	+	15.6642i	0.700373	+	0.630618i	0.940369	−	0.340155i	$-0.110480\pi$
$617$	17.3969	+	15.6642i	0.700373	+	0.630618i	−0.239997	+	0.970774i	$0.577146\pi$
$618$	−9.16196	+	15.1991i	−0.368548	+	0.611397i
$619$		−	28.5570i		−	1.14780i	−0.818925	−	0.573900i	$-0.805430\pi$
$619$		−	28.5570i		−	1.14780i	0.818925	−	0.573900i	$-0.194570\pi$
$620$	3.01256	+	4.68236i	0.120987	+	0.188048i
$621$	−0.887497	+	1.08646i	−0.0356140	+	0.0435982i
$622$	1.63622	−	5.03576i	0.0656063	−	0.201915i
$623$	−15.7870	+	17.5332i	−0.632491	+	0.702453i
$624$	−0.291136	−	0.335877i	−0.0116548	−	0.0134458i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.53581	−	7.85625i	−0.181287	−	0.313999i
$627$	35.7619	+	12.3707i	1.42819	+	0.494039i
$628$	8.97208	−	6.51860i	0.358025	−	0.260120i
$629$	−0.418397	+	0.0439753i	−0.0166826	+	0.00175341i
$630$	2.42949	+	8.56446i	0.0967932	+	0.341216i
$631$	11.7545	+	26.4010i	0.467938	+	1.05101i	0.981239	+	0.192797i	$0.0617560\pi$
$631$	11.7545	+	26.4010i	0.467938	+	1.05101i	−0.513301	+	0.858209i	$0.671577\pi$
$632$	15.3180	−	3.25595i	0.609319	−	0.129515i
$633$	19.5189	−	41.7035i	0.775805	−	1.65756i
$634$	−14.2186	−	6.33055i	−0.564694	−	0.251418i
$635$	6.07061	+	18.6834i	0.240905	+	0.741429i
$636$	11.2715	−	0.969990i	0.446946	−	0.0384626i
$637$	0.188492	−	0.423360i	0.00746832	−	0.0167741i
$638$	4.60897	−	21.6835i	0.182471	−	0.858459i
$639$	2.35117	−	9.31711i	0.0930109	−	0.368579i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	10.6851	+	11.8670i	0.422036	+	0.468719i	0.916241	−	0.400627i	$-0.131208\pi$
$641$	10.6851	+	11.8670i	0.422036	+	0.468719i	−0.494205	+	0.869345i	$0.664541\pi$
$642$	4.13680	+	0.513906i	0.163267	+	0.0202822i
$643$	−4.07102	−	5.60327i	−0.160545	−	0.220972i	0.721164	−	0.692764i	$-0.243607\pi$
$643$	−4.07102	−	5.60327i	−0.160545	−	0.220972i	−0.881710	+	0.471792i	$0.843607\pi$
$644$	−0.0837444	+	0.796774i	−0.00329999	+	0.0313973i
$645$	0.839286	−	0.255292i	0.0330469	−	0.0100521i
$646$	−0.415949	−	0.240148i	−0.0163653	−	0.00944851i
$647$	−14.4912	−	10.5285i	−0.569707	−	0.413917i	0.265291	−	0.964168i	$-0.414532\pi$
$647$	−14.4912	−	10.5285i	−0.569707	−	0.413917i	−0.834999	+	0.550252i	$0.814532\pi$
$648$	−0.678847	+	8.97436i	−0.0266676	+	0.352546i
$649$	−10.5151	−	3.41655i	−0.412753	−	0.134111i
$650$	0.256628			0.0100658
$651$	−22.6501	+	17.4904i	−0.887729	+	0.685501i
$652$	−12.2217			−0.478640
$653$	−15.6971	−	5.10030i	−0.614276	−	0.199590i	−0.0146786	−	0.999892i	$-0.504673\pi$
$653$	−15.6971	−	5.10030i	−0.614276	−	0.199590i	−0.599597	+	0.800302i	$0.704673\pi$
$654$	−22.2778	+	15.5519i	−0.871131	+	0.608129i
$655$	8.69934	+	6.32044i	0.339911	+	0.246960i
$656$	−4.97787	−	2.87397i	−0.194353	−	0.112210i
$657$	−18.3557	+	1.23113i	−0.716125	+	0.0480309i
$658$	−3.79823	+	36.1377i	−0.148070	+	1.40880i
$659$	12.2545	+	16.8669i	0.477369	+	0.657043i	0.977997	−	0.208620i	$-0.0668973\pi$
$659$	12.2545	+	16.8669i	0.477369	+	0.657043i	−0.500627	+	0.865663i	$0.666897\pi$
$660$	−1.36868	+	11.0175i	−0.0532756	+	0.428854i
$661$	−21.1234	−	23.4599i	−0.821605	−	0.912485i	0.175804	−	0.984425i	$-0.443747\pi$
$661$	−21.1234	−	23.4599i	−0.821605	−	0.912485i	−0.997409	+	0.0719405i	$0.977081\pi$
$662$	−8.58816	+	3.82370i	−0.333788	+	0.148612i
$663$	−0.0626238	−	0.00118215i	−0.00243211	−	4.59110e-5i
$664$	−1.12425	+	5.28919i	−0.0436295	+	0.205261i
$665$	−4.11391	+	9.24000i	−0.159531	+	0.358312i
$666$	−1.27173	+	8.86584i	−0.0492784	+	0.343544i
$667$	0.288534	+	0.888016i	0.0111721	+	0.0343841i
$668$	−9.50345	−	4.23121i	−0.367700	−	0.163710i
$669$	37.0172	+	17.3255i	1.43117	+	0.669843i
$670$	−5.02649	+	1.06841i	−0.194190	+	0.0412764i
$671$	−26.9806	−	60.5994i	−1.04157	−	2.33941i
$672$	2.48543	+	4.49890i	0.0958775	+	0.173549i
$673$	−0.236402	+	0.0248468i	−0.00911263	+	0.000957776i	−0.109084	−	0.994033i	$-0.534792\pi$
$673$	−0.236402	+	0.0248468i	−0.00911263	+	0.000957776i	0.0999711	+	0.994990i	$0.468125\pi$
$674$	−24.1772	+	17.5658i	−0.931272	+	0.676609i
$675$	−3.65853	−	3.68987i	−0.140817	−	0.142023i
$676$	6.46707	+	11.2013i	0.248734	+	0.430819i
$677$	3.27774	−	5.67721i	0.125974	−	0.218193i	−0.796139	−	0.605113i	$-0.793128\pi$
$677$	3.27774	−	5.67721i	0.125974	−	0.218193i	0.922113	+	0.386920i	$0.126461\pi$
$678$	9.96883	−	8.64092i	0.382851	−	0.331853i
$679$	−8.28129	+	9.19731i	−0.317807	+	0.352960i
$680$	0.0435447	−	0.134017i	0.00166986	−	0.00513931i
$681$	−27.6750	−	6.43074i	−1.06051	−	0.246426i
$682$	−34.5113	+	9.09034i	−1.32151	+	0.348087i
$683$		−	21.3045i		−	0.815194i	−0.913162	−	0.407597i	$-0.866367\pi$
$683$		−	21.3045i		−	0.815194i	0.913162	−	0.407597i	$-0.133633\pi$
$684$	−7.12400	+	7.33527i	−0.272393	+	0.280471i
$685$	15.8690	+	14.2885i	0.606324	+	0.545937i
$686$	9.05983	−	12.4698i	0.345906	−	0.476099i
$687$	−3.74559	+	4.00523i	−0.142903	+	0.152809i
$688$	0.438627	−	0.253242i	0.0167225	−	0.00965474i
$689$	1.66703	+	0.175212i	0.0635087	+	0.00667503i
$690$	−0.182103	−	0.430709i	−0.00693255	−	0.0163968i
$691$	−1.20982	−	11.5106i	−0.0460236	−	0.437885i	−0.993134	−	0.116979i	$-0.962679\pi$
$691$	−1.20982	−	11.5106i	−0.0460236	−	0.437885i	0.947111	−	0.320907i	$-0.103988\pi$
$692$	16.6426	−	14.9851i	0.632658	−	0.569648i
$693$	−57.0221	−	2.15358i	−2.16609	−	0.0818079i
$694$	3.42620	+	16.1190i	0.130057	+	0.611868i
$695$	−10.2028	−	2.16866i	−0.387013	−	0.0822621i
$696$	4.77883	+	3.61177i	0.181141	+	0.136904i
$697$	−0.770321	+	0.250293i	−0.0291780	+	0.00948051i
$698$	28.3192	−	9.20146i	1.07190	−	0.348280i
$699$	5.71591	+	4.32000i	0.216196	+	0.163397i
$700$	−2.90262	−	0.616970i	−0.109709	−	0.0233193i
$701$	2.04055	+	9.60001i	0.0770703	+	0.362587i	0.999735	−	0.0230156i	$-0.00732675\pi$
$701$	2.04055	+	9.60001i	0.0770703	+	0.362587i	−0.922665	+	0.385603i	$0.873993\pi$
$702$	−0.350619	+	1.28656i	−0.0132332	+	0.0485579i
$703$	−7.56225	+	6.80908i	−0.285216	+	0.256809i
$704$	0.670010	+	6.37472i	0.0252519	+	0.240256i
$705$	−8.25929	−	19.5348i	−0.311063	−	0.735724i
$706$	−25.8672	−	2.71875i	−0.973525	−	0.102322i
$707$	−1.02046	+	0.589161i	−0.0383782	+	0.0221577i
$708$	2.04063	−	2.18208i	0.0766916	−	0.0820076i
$709$	12.4227	−	17.0983i	0.466543	−	0.642141i	−0.509307	−	0.860585i	$-0.670098\pi$
$709$	12.4227	−	17.0983i	0.466543	−	0.642141i	0.975849	+	0.218444i	$0.0700982\pi$
$710$	2.38034	+	2.14327i	0.0893326	+	0.0804354i
$711$	−33.7022	−	32.7315i	−1.26393	−	1.22753i
$712$		−	7.95065i		−	0.297963i
$713$	1.06743	−	1.05840i	0.0399755	−	0.0396373i
$714$	0.705472	+	0.163928i	0.0264016	+	0.00613484i
$715$	−0.508314	+	1.56443i	−0.0190099	+	0.0585064i
$716$	15.7320	−	17.4721i	0.587932	−	0.652965i
$717$	10.9388	−	9.48165i	0.408516	−	0.354099i
$718$	1.30634	−	2.26264i	0.0487520	−	0.0844409i
$719$	23.8175	+	41.2531i	0.888242	+	1.53848i	0.841952	+	0.539552i	$0.181406\pi$
$719$	23.8175	+	41.2531i	0.888242	+	1.53848i	0.0462892	+	0.998928i	$0.485260\pi$
$720$	−2.53961	−	1.59698i	−0.0946458	−	0.0595161i
$721$	24.5983	−	17.8717i	0.916089	−	0.665578i
$722$	7.34204	−	0.771679i	0.273242	−	0.0287189i
$723$	−8.88460	−	16.0821i	−0.330422	−	0.598100i
$724$	1.82535	+	4.09981i	0.0678387	+	0.152368i
$725$	−3.38285	+	0.719047i	−0.125636	+	0.0267047i
$726$	−47.1967	−	22.0899i	−1.75163	−	0.819834i
$727$	−4.34575	−	1.93485i	−0.161175	−	0.0717596i	0.324564	−	0.945864i	$-0.394783\pi$
$727$	−4.34575	−	1.93485i	−0.161175	−	0.0717596i	−0.485738	+	0.874104i	$0.661449\pi$
$728$	0.235326	+	0.724260i	0.00872178	+	0.0268429i
$729$	23.4970	−	13.3001i	0.870258	−	0.492596i
$730$	2.49424	−	5.60216i	0.0923160	−	0.207345i
$731$	0.0148387	−	0.0698108i	0.000548830	−	0.00258204i
$732$	17.9215	+	0.338305i	0.662398	+	0.0125041i
$733$	39.6919	−	17.6720i	1.46605	−	0.652729i	0.490290	−	0.871559i	$-0.336891\pi$
$733$	39.6919	−	17.6720i	1.46605	−	0.652729i	0.975763	+	0.218830i	$0.0702241\pi$
$734$	−12.9240	−	14.3536i	−0.477034	−	0.529799i
$735$	0.385593	−	3.10392i	0.0142228	−	0.114490i
$736$	−0.158692	−	0.218421i	−0.00584946	−	0.00805109i
$737$	3.44304	−	32.7583i	0.126826	−	1.20667i
$738$	1.15396	+	17.2052i	0.0424778	+	0.633332i
$739$	−36.7939	−	21.2430i	−1.35349	−	0.781436i	−0.364751	−	0.931105i	$-0.618846\pi$
$739$	−36.7939	−	21.2430i	−1.35349	−	0.781436i	−0.988736	+	0.149669i	$0.952179\pi$
$740$	−2.41534	−	1.75485i	−0.0887897	−	0.0645095i
$741$	−1.24227	+	0.867219i	−0.0456360	+	0.0318581i
$742$	−18.4339	−	5.98953i	−0.676729	−	0.219882i
$743$	−47.4483			−1.74071			−0.870354	−	0.492426i	$-0.836110\pi$
$743$	−47.4483			−1.74071			−0.870354	+	0.492426i	$0.836110\pi$
$744$	1.72841	−	9.48750i	0.0633668	−	0.347828i
$745$	3.32649			0.121873
$746$	−4.85904	−	1.57880i	−0.177902	−	0.0578038i
$747$	15.0581	−	6.03411i	0.550946	−	0.220777i
$748$	0.730731	+	0.530907i	0.0267182	+	0.0194119i
$749$	−6.18508	−	3.57096i	−0.225998	−	0.130480i
$750$	1.65709	−	0.504048i	0.0605082	−	0.0184052i
$751$	−0.906080	+	8.62078i	−0.0330633	+	0.314577i	0.965474	+	0.260501i	$0.0838878\pi$
$751$	−0.906080	+	8.62078i	−0.0330633	+	0.314577i	−0.998537	+	0.0540754i	$0.982779\pi$
$752$	−7.19747	−	9.90647i	−0.262465	−	0.361252i
$753$	11.7257	+	1.45666i	0.427308	+	0.0530835i
$754$	0.593872	+	0.659562i	0.0216275	+	0.0240198i
$755$	4.98084	−	2.21761i	0.181271	−	0.0807072i
$756$	7.05878	−	13.7088i	0.256725	−	0.498584i
$757$	−7.35513	+	34.6031i	−0.267327	+	1.25767i	0.615561	+	0.788089i	$0.288929\pi$
$757$	−7.35513	+	34.6031i	−0.267327	+	1.25767i	−0.882888	+	0.469584i	$0.844404\pi$
$758$	5.93889	−	13.3390i	0.215710	−	0.484493i
$759$	2.98635	−	0.256995i	0.108398	−	0.00932832i
$760$	−1.05327	−	3.24163i	−0.0382061	−	0.117586i
$761$	−17.3365	−	7.71872i	−0.628448	−	0.279803i	0.0676950	−	0.997706i	$-0.478436\pi$
$761$	−17.3365	−	7.71872i	−0.628448	−	0.279803i	−0.696143	+	0.717903i	$0.745102\pi$
$762$	14.4238	−	30.8176i	0.522520	−	1.11640i
$763$	45.5308	−	9.67786i	1.64832	−	0.350362i
$764$	−6.65018	−	14.9366i	−0.240595	−	0.540386i
$765$	−0.406694	+	0.115367i	−0.0147041	+	0.00417112i
$766$	24.9961	−	2.62720i	0.903147	−	0.0949246i
$767$	0.358113	−	0.260184i	0.0129307	−	0.00939471i
$768$	−1.63688	−	0.566228i	−0.0590659	−	0.0204320i
$769$	−9.50285	−	16.4594i	−0.342681	−	0.593542i	0.642248	−	0.766497i	$-0.278002\pi$
$769$	−9.50285	−	16.4594i	−0.342681	−	0.593542i	−0.984930	+	0.172955i	$0.944668\pi$
$770$	9.51046	−	16.4726i	0.342733	−	0.593632i
$771$	−9.62503	−	11.1042i	−0.346637	−	0.399907i
$772$	8.17591	−	9.08027i	0.294258	−	0.326806i
$773$	9.32942	−	28.7130i	0.335556	−	1.03273i	−0.630892	−	0.775871i	$-0.717311\pi$
$773$	9.32942	−	28.7130i	0.335556	−	1.03273i	0.966448	−	0.256864i	$-0.0826892\pi$
$774$	−1.36377	−	0.669963i	−0.0490198	−	0.0240813i
$775$	3.48550	+	4.34181i	0.125203	+	0.155962i
$776$		−	4.17063i		−	0.149717i
$777$	7.92194	−	13.1420i	0.284198	−	0.471466i
$778$	−22.6669	−	20.4093i	−0.812646	−	0.731710i
$779$	−11.5156	+	15.8499i	−0.412591	+	0.567882i
$780$	−0.324650	−	0.303605i	−0.0116243	−	0.0108708i
$781$	−17.7805	+	10.2656i	−0.636235	+	0.367330i
$782$	−0.0378358	−	0.00397671i	−0.00135301	−	0.000142207i
$783$	1.01703	−	17.9417i	0.0363455	−	0.641184i
$784$	−0.188760	−	1.79593i	−0.00674144	−	0.0641405i
$785$	8.24155	−	7.42072i	0.294154	−	0.264857i
$786$	−3.52777	−	18.2875i	−0.125831	−	0.652295i
$787$	−7.10619	−	33.4320i	−0.253308	−	1.19172i	−0.902362	−	0.430979i	$-0.858168\pi$
$787$	−7.10619	−	33.4320i	−0.253308	−	1.19172i	0.649054	−	0.760743i	$-0.275165\pi$
$788$	−21.7557	−	4.62432i	−0.775015	−	0.164735i
$789$	−22.7107	+	30.0492i	−0.808524	+	1.06978i
$790$	14.8938	−	4.83928i	0.529897	−	0.172174i
$791$	−21.4961	+	6.98450i	−0.764313	+	0.248340i
$792$	14.7657	−	12.3186i	0.524677	−	0.437721i
$793$	2.59776	+	0.552171i	0.0922492	+	0.0196082i
$794$	0.279221	+	1.31363i	0.00990918	+	0.0466190i
$795$	11.1084	−	2.14287i	0.393975	−	0.0759999i
$796$	14.2351	−	12.8173i	0.504548	−	0.454297i
$797$	−2.12985	−	20.2642i	−0.0754433	−	0.717795i	−0.965227	−	0.261413i	$-0.915812\pi$
$797$	−2.12985	−	20.2642i	−0.0754433	−	0.717795i	0.889784	−	0.456382i	$-0.150855\pi$
$798$	16.1358	−	6.82218i	0.571201	−	0.241503i
$799$	−1.71605	−	0.180364i	−0.0607093	−	0.00638081i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−19.8120	+	13.2816i	−0.700023	+	0.469281i
$802$	−15.9373	+	21.9358i	−0.562764	+	0.774578i
$803$	29.2109	+	26.3016i	1.03083	+	0.928164i
$804$	7.62282	+	4.59501i	0.268836	+	0.162054i
$805$			0.801163i			0.0282373i
$806$	0.517712	−	1.33175i	0.0182356	−	0.0469090i
$807$	1.48865	−	6.40650i	0.0524030	−	0.225519i
$808$	0.122705	−	0.377646i	0.00431674	−	0.0132855i
$809$	25.3526	−	28.1570i	0.891352	−	0.989946i	−0.108640	−	0.994081i	$-0.534650\pi$
$809$	25.3526	−	28.1570i	0.891352	−	0.989946i	0.999991	+	0.00413496i	$0.00131620\pi$
$810$	0.262948	+	8.99616i	0.00923905	+	0.316093i
$811$	−15.7300	+	27.2451i	−0.552353	+	0.956704i	0.445751	+	0.895157i	$0.352937\pi$
$811$	−15.7300	+	27.2451i	−0.552353	+	0.956704i	−0.998104	+	0.0615471i	$0.980397\pi$
$812$	−5.13137	−	8.88780i	−0.180076	−	0.311901i
$813$	−2.57809	+	7.45288i	−0.0904176	+	0.261384i
$814$	15.4819	−	11.2483i	0.542642	−	0.394252i
$815$	−12.1548	+	1.27752i	−0.425763	+	0.0447495i
$816$	−0.213636	+	0.118024i	−0.00747876	+	0.00413166i
$817$	−0.702158	−	1.57707i	−0.0245654	−	0.0551748i
$818$	30.9711	−	6.58311i	1.08288	−	0.230173i
$819$	1.41165	−	1.79628i	0.0493271	−	0.0627671i
$820$	−5.25101	−	2.33790i	−0.183373	−	0.0816430i
$821$	15.7652	+	48.5204i	0.550210	+	1.69337i	0.708269	+	0.705943i	$0.249476\pi$
$821$	15.7652	+	48.5204i	0.550210	+	1.69337i	−0.158059	+	0.987430i	$0.550524\pi$
$822$	−3.17116	−	36.8498i	−0.110607	−	1.28528i
$823$	−20.5355	+	46.1234i	−0.715822	+	1.60776i	0.0760714	+	0.997102i	$0.475762\pi$
$823$	−20.5355	+	46.1234i	−0.715822	+	1.60776i	−0.791893	+	0.610660i	$0.790904\pi$
$824$	−2.13030	+	10.0223i	−0.0742127	+	0.349143i
$825$	−0.209538	+	11.1002i	−0.00729519	+	0.386459i
$826$	−4.67600	+	2.08189i	−0.162699	+	0.0724382i
$827$	3.27057	+	3.63233i	0.113729	+	0.126309i	0.797321	−	0.603556i	$-0.206250\pi$
$827$	3.27057	+	3.63233i	0.113729	+	0.126309i	−0.683592	+	0.729864i	$0.739583\pi$
$828$	−0.279181	+	0.760312i	−0.00970222	+	0.0264227i
$829$	−14.1159	−	19.4288i	−0.490264	−	0.674791i	0.490173	−	0.871625i	$-0.336934\pi$
$829$	−14.1159	−	19.4288i	−0.490264	−	0.674791i	−0.980437	+	0.196835i	$0.936934\pi$
$830$	−0.565223	+	5.37774i	−0.0196192	+	0.186664i
$831$	−4.68168	−	15.3913i	−0.162406	−	0.533918i
$832$	−0.222246	−	0.128314i	−0.00770499	−	0.00444848i
$833$	−0.205867	−	0.149571i	−0.00713287	−	0.00518233i
$834$	10.3415	+	14.8139i	0.358096	+	0.512964i
$835$	−9.89367	−	3.21465i	−0.342385	−	0.111248i
$836$	21.8476			0.755614
$837$	−26.5289	+	11.5419i	−0.916974	+	0.398946i
$838$	−13.8917			−0.479880
$839$	−33.9618	−	11.0349i	−1.17249	−	0.380966i	−0.342920	−	0.939365i	$-0.611416\pi$
$839$	−33.9618	−	11.0349i	−1.17249	−	0.380966i	−0.829573	+	0.558399i	$0.811416\pi$
$840$	2.94208	+	4.21446i	0.101511	+	0.145413i
$841$	13.7851	+	10.0154i	0.475347	+	0.345360i
$842$	−32.3303	−	18.6659i	−1.11418	−	0.643270i
$843$	10.6464	+	35.0008i	0.366683	+	1.20549i
$844$	2.77881	−	26.4386i	0.0956505	−	0.910054i
$845$	7.60250	+	10.4639i	0.261534	+	0.359971i
$846$	−12.6623	+	34.4840i	−0.435338	+	1.18558i
$847$	59.7392	+	66.3471i	2.05266	+	2.27971i
$848$	5.96699	−	2.65668i	0.204907	−	0.0912306i
$849$	0.151708	−	8.03665i	0.00520661	−	0.275817i
$850$	0.0292976	−	0.137834i	0.00100490	−	0.00472768i
$851$	−0.327846	+	0.736355i	−0.0112384	+	0.0252419i
$852$	−0.475672	−	5.52744i	−0.0162963	−	0.189367i
$853$	−8.85037	−	27.2386i	−0.303031	−	0.932633i	−0.980405	−	0.196994i	$-0.936882\pi$
$853$	−8.85037	−	27.2386i	−0.303031	−	0.932633i	0.677374	−	0.735639i	$-0.263118\pi$
$854$	−28.0548	−	12.4908i	−0.960014	−	0.427426i
$855$	−6.31823	+	8.03975i	−0.216079	+	0.274954i
$856$	2.35415	−	0.500390i	0.0804632	−	0.0171030i
$857$	2.19386	+	4.92748i	0.0749407	+	0.168320i	0.947131	−	0.320847i	$-0.103968\pi$
$857$	2.19386	+	4.92748i	0.0749407	+	0.168320i	−0.872190	+	0.489167i	$0.837301\pi$
$858$	2.49386	−	1.37774i	0.0851389	−	0.0470351i
$859$	9.07361	−	0.953675i	0.309587	−	0.0325390i	0.0515392	−	0.998671i	$-0.483587\pi$
$859$	9.07361	−	0.953675i	0.309587	−	0.0325390i	0.258048	+	0.966132i	$0.416921\pi$
$860$	0.409753	−	0.297703i	0.0139725	−	0.0101516i
$861$	9.65804	−	27.9200i	0.329145	−	0.951511i
$862$	5.28738	+	9.15801i	0.180089	+	0.311923i
$863$	−7.41453	+	12.8423i	−0.252394	+	0.437159i	−0.964184	−	0.265233i	$-0.914551\pi$
$863$	−7.41453	+	12.8423i	−0.252394	+	0.437159i	0.711791	+	0.702392i	$0.247884\pi$
$864$	1.32345	+	5.02479i	0.0450246	+	0.170947i
$865$	14.9851	−	16.6426i	0.509508	−	0.565866i
$866$	0.215263	−	0.662511i	0.00731494	−	0.0225131i
$867$	6.65665	−	28.6472i	0.226072	−	0.972912i
$868$	−9.05737	+	13.8183i	−0.307427	+	0.469023i
$869$			100.380i			3.40514i
$870$	5.13019	+	3.09246i	0.173930	+	0.104844i
$871$	0.980026	+	0.882419i	0.0332069	+	0.0298996i
$872$	−9.22007	+	12.6903i	−0.312231	+	0.429749i
$873$	−10.3927	+	6.96705i	−0.351739	+	0.235799i
$874$	−0.796936	+	0.460111i	−0.0269568	+	0.0155635i
$875$	−2.95121	−	0.310184i	−0.0997689	−	0.0104861i
$876$	−9.78303	+	4.13625i	−0.330538	+	0.139751i
$877$	−3.88037	−	36.9192i	−0.131031	−	1.24667i	−0.840451	−	0.541888i	$-0.817710\pi$
$877$	−3.88037	−	36.9192i	−0.131031	−	1.24667i	0.709420	−	0.704786i	$-0.248957\pi$
$878$	22.4558	−	20.2193i	0.757847	−	0.682369i
$879$	12.2790	−	2.36870i	0.414162	−	0.0798941i
$880$	1.33268	+	6.26976i	0.0449246	+	0.211354i
$881$	44.4835	+	9.45525i	1.49869	+	0.318555i	0.882976	−	0.469418i	$-0.155536\pi$
$881$	44.4835	+	9.45525i	1.49869	+	0.318555i	0.615709	+	0.787973i	$0.288870\pi$
$882$	−4.15991	+	3.47048i	−0.140072	+	0.116857i
$883$	−1.59190	+	0.517241i	−0.0535719	+	0.0174065i	−0.335680	−	0.941976i	$-0.608966\pi$
$883$	−1.59190	+	0.517241i	−0.0535719	+	0.0174065i	0.282108	+	0.959383i	$0.408966\pi$
$884$	−0.0343924	+	0.0111748i	−0.00115674	+	0.000375848i
$885$	1.80136	−	2.38343i	0.0605521	−	0.0801181i
$886$	−21.7050	−	4.61354i	−0.729194	−	0.154995i
$887$	−4.15934	−	19.5682i	−0.139657	−	0.657035i	−0.991159	−	0.132683i	$-0.957641\pi$
$887$	−4.15934	−	19.5682i	−0.139657	−	0.657035i	0.851501	−	0.524352i	$-0.175692\pi$
$888$	0.979473	+	5.07747i	0.0328690	+	0.170389i
$889$	−43.3220	+	39.0073i	−1.45297	+	1.30826i
$890$	−0.831069	−	7.90710i	−0.0278575	−	0.265046i
$891$	−55.3624	−	16.2162i	−1.85471	−	0.543262i
$892$	23.4677	+	2.46655i	0.785756	+	0.0825863i
$893$	−36.1450	+	20.8684i	−1.20955	+	0.698333i
$894$	−4.20821	−	3.93542i	−0.140744	−	0.131620i
$895$	13.8195	−	19.0209i	0.461934	−	0.635797i
$896$	2.20525	+	1.98562i	0.0736723	+	0.0663349i
$897$	−0.0619534	+	0.102777i	−0.00206856	+	0.00343161i
$898$			9.76461i			0.325849i
$899$	−3.09301	+	19.0057i	−0.103158	+	0.633875i
$900$	−2.69263	−	1.32277i	−0.0897544	−	0.0440925i
$901$	0.284420	−	0.875355i	0.00947541	−	0.0291623i
$902$	24.6530	−	27.3800i	0.820856	−	0.911653i
$903$	1.70507	+	1.96710i	0.0567412	+	0.0654610i
$904$	3.80836	−	6.59627i	0.126664	−	0.219389i
$905$	2.24390	+	3.88655i	0.0745898	+	0.129193i
$906$	−8.92462	−	3.08719i	−0.296501	−	0.102565i
$907$	39.2846	−	28.5419i	1.30442	−	0.947719i	0.304435	−	0.952533i	$-0.401532\pi$
$907$	39.2846	−	28.5419i	1.30442	−	0.947719i	0.999988	+	0.00481376i	$0.00153227\pi$
$908$	−16.3140	+	1.71467i	−0.541400	+	0.0569034i
$909$	−1.14602	+	0.325094i	−0.0380112	+	0.0107827i
$910$	0.309743	+	0.695694i	0.0102679	+	0.0230620i
$911$	19.0303	−	4.04501i	0.630500	−	0.134017i	0.118433	−	0.992962i	$-0.462213\pi$
$911$	19.0303	−	4.04501i	0.630500	−	0.134017i	0.512068	+	0.858945i	$0.328880\pi$
$912$	−2.50257	+	5.34693i	−0.0828685	+	0.177055i
$913$	−31.6637	−	14.0976i	−1.04792	−	0.466562i
$914$	8.82568	+	27.1627i	0.291928	+	0.898461i
$915$	17.8587	−	1.53686i	0.590390	−	0.0508069i
$916$	−1.28774	+	2.89232i	−0.0425482	+	0.0955648i
$917$	−6.63426	+	31.2117i	−0.219083	+	1.03070i
$918$	0.650979	+	0.335195i	0.0214855	+	0.0110631i
$919$	40.0269	−	17.8211i	1.32037	−	0.587865i	0.379045	−	0.925378i	$-0.376252\pi$
$919$	40.0269	−	17.8211i	1.32037	−	0.587865i	0.941321	+	0.337513i	$0.109586\pi$
$920$	−0.180654	−	0.200636i	−0.00595598	−	0.00661478i
$921$	51.7328	+	6.42665i	1.70465	+	0.211765i
$922$	−9.39336	−	12.9289i	−0.309354	−	0.425789i
$923$	0.0859218	−	0.817491i	0.00282815	−	0.0269081i
$924$	−31.5193	+	9.58745i	−1.03691	+	0.315404i
$925$	−2.58554	−	1.49276i	−0.0850121	−	0.0490818i
$926$	11.8974	+	8.64399i	0.390974	+	0.284059i
$927$	28.5329	−	11.4338i	0.937145	−	0.375536i
$928$	3.28916	+	1.06871i	0.107972	+	0.0350822i
$929$	−20.1282			−0.660385			−0.330192	−	0.943914i	$-0.607114\pi$
$929$	−20.1282			−0.660385			−0.330192	+	0.943914i	$0.607114\pi$
$930$	0.727233	−	9.61619i	0.0238469	−	0.315327i
$931$	−6.15507			−0.201724
$932$	3.93413	+	1.27828i	0.128867	+	0.0418713i
$933$	−7.51995	+	5.24961i	−0.246192	+	0.171865i
$934$	22.0589	+	16.0268i	0.721791	+	0.524412i
$935$	0.782222	+	0.451616i	0.0255814	+	0.0147694i
$936$	0.0515206	+	0.768157i	0.00168400	+	0.0251080i
$937$	0.954056	−	9.07724i	0.0311677	−	0.296540i	−0.967823	−	0.251631i	$-0.919033\pi$
$937$	0.954056	−	9.07724i	0.0311677	−	0.296540i	0.998991	−	0.0449100i	$-0.0143001\pi$
$938$	−8.96323	−	12.3368i	−0.292660	−	0.402812i
$939$	−1.93704	+	15.5926i	−0.0632129	+	0.508847i
$940$	−8.19355	−	9.09986i	−0.267244	−	0.296805i
$941$	2.27688	−	1.01373i	0.0742241	−	0.0330467i	−0.369289	−	0.929315i	$-0.620399\pi$
$941$	2.27688	−	1.01373i	0.0742241	−	0.0330467i	0.443513	+	0.896268i	$0.353732\pi$
$942$	−19.2052	−	0.362537i	−0.625739	−	0.0118121i
$943$	−0.322647	+	1.51793i	−0.0105068	+	0.0494307i
$944$	0.701572	−	1.57576i	0.0228342	−	0.0512865i
$945$	5.58715	−	14.3715i	0.181750	−	0.467506i
$946$	1.00321	+	3.08758i	0.0326173	+	0.100386i
$947$	29.7943	+	13.2653i	0.968185	+	0.431064i	0.829028	−	0.559206i	$-0.188894\pi$
$947$	29.7943	+	13.2653i	0.968185	+	0.431064i	0.139157	+	0.990270i	$0.455561\pi$
$948$	−24.5667	−	11.4982i	−0.797889	−	0.373443i
$949$	−1.53933	+	0.327196i	−0.0499689	+	0.0106212i
$950$	−1.38634	−	3.11377i	−0.0449788	−	0.101024i
$951$	13.0360	+	23.5966i	0.422721	+	0.765172i
$952$	0.415865	−	0.0437092i	0.0134783	−	0.00141662i
$953$	−23.7218	+	17.2349i	−0.768426	+	0.558294i	−0.901483	−	0.432814i	$-0.857521\pi$
$953$	−23.7218	+	17.2349i	−0.768426	+	0.558294i	0.133057	+	0.991108i	$0.457521\pi$
$954$	−16.5880	−	10.4310i	−0.537055	−	0.337716i
$955$	−8.17505	−	14.1596i	−0.264538	−	0.458194i
$956$	4.17890	−	7.23806i	0.135155	−	0.234096i
$957$	−29.0136	+	25.1488i	−0.937877	+	0.812946i
$958$	10.9336	−	12.1430i	0.353250	−	0.392323i
$959$	−19.5814	+	60.2654i	−0.632317	+	1.94607i
$960$	−1.68710	−	0.392025i	−0.0544510	−	0.0126526i
$961$	29.5631	−	9.32873i	0.953647	−	0.300927i
$962$			0.766168i			0.0247023i
$963$	−5.17952	−	5.03034i	−0.166908	−	0.162100i
$964$	−7.88306	−	7.09794i	−0.253896	−	0.228609i
$965$	7.18198	−	9.88515i	0.231196	−	0.318214i
$966$	0.947820	−	1.01352i	0.0304956	−	0.0326095i
$967$	11.6612	−	6.73259i	0.374998	−	0.216505i	−0.300642	−	0.953737i	$-0.597201\pi$
$967$	11.6612	−	6.73259i	0.374998	−	0.216505i	0.675640	+	0.737232i	$0.263867\pi$
$968$	−29.9211	−	3.14484i	−0.961702	−	0.101079i
$969$	0.323960	+	0.766228i	0.0104071	+	0.0246148i
$970$	−0.435950	−	4.14779i	−0.0139975	−	0.133177i
$971$	−32.0427	+	28.8514i	−1.02830	+	0.925885i	−0.997285	−	0.0736335i	$-0.976541\pi$
$971$	−32.0427	+	28.8514i	−1.02830	+	0.925885i	−0.0310146	+	0.999519i	$0.509874\pi$
$972$	10.3103	−	11.6918i	0.330703	−	0.375014i
$973$	−6.43543	−	30.2763i	−0.206310	−	0.970613i
$974$	−8.13487	−	1.72912i	−0.260658	−	0.0554046i
$975$	−0.354606	−	0.268006i	−0.0113565	−	0.00858307i
$976$	9.84233	−	3.19797i	0.315045	−	0.102364i
$977$	14.4407	−	4.69206i	0.461998	−	0.150112i	−0.0687643	−	0.997633i	$-0.521906\pi$
$977$	14.4407	−	4.69206i	0.461998	−	0.150112i	0.530762	+	0.847521i	$0.321906\pi$
$978$	16.8879	+	12.7636i	0.540016	+	0.408136i
$979$	49.8487	+	10.5957i	1.59317	+	0.338639i
$980$	−0.375452	−	1.76636i	−0.0119934	−	0.0564244i
$981$	47.0248	+	1.77601i	1.50139	+	0.0567037i
$982$	8.00689	−	7.20944i	0.255510	−	0.230062i
$983$	−4.28930	−	40.8099i	−0.136807	−	1.30163i	−0.820408	−	0.571779i	$-0.806254\pi$
$983$	−4.28930	−	40.8099i	−0.136807	−	1.30163i	0.683601	−	0.729856i	$-0.260413\pi$
$984$	3.87698	+	9.16982i	0.123594	+	0.292323i
$985$	−22.1199	−	2.32490i	−0.704799	−	0.0740773i
$986$	0.422048	−	0.243670i	0.0134408	−	0.00776002i
$987$	42.9884	−	45.9683i	1.36834	−	1.46319i
$988$	−0.514137	+	0.707649i	−0.0163569	+	0.0225133i
$989$	−0.101619	−	0.0914980i	−0.00323129	−	0.00290947i
$990$	13.3972	−	13.7945i	0.425791	−	0.438418i
$991$		−	51.2431i		−	1.62779i	−0.581011	−	0.813896i	$-0.697343\pi$
$991$		−	51.2431i		−	1.62779i	0.581011	−	0.813896i	$-0.302657\pi$
$992$	−0.847624	−	5.50287i	−0.0269121	−	0.174716i
$993$	15.8603	+	3.68540i	0.503312	+	0.116952i
$994$	−2.93720	+	9.03976i	−0.0931622	+	0.286724i
$995$	12.8173	−	14.2351i	0.406336	−	0.451281i
$996$	7.07720	−	6.13448i	0.224250	−	0.194378i
$997$	−13.0046	+	22.5246i	−0.411860	+	0.713362i	−0.995093	−	0.0989425i	$-0.968454\pi$
$997$	−13.0046	+	22.5246i	−0.411860	+	0.713362i	0.583233	+	0.812305i	$0.301787\pi$
$998$	12.7424	+	22.0705i	0.403354	+	0.698630i
$999$	11.0162	−	10.9226i	0.348537	−	0.345577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.761.8	yes	176
3.2	odd	2	inner	930.2.br.a.761.21	yes	176
31.11	odd	30	inner	930.2.br.a.11.21	yes	176
93.11	even	30	inner	930.2.br.a.11.8	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.8	✓	176	93.11	even	30	inner
930.2.br.a.11.21	yes	176	31.11	odd	30	inner
930.2.br.a.761.8	yes	176	1.1	even	1	trivial
930.2.br.a.761.21	yes	176	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.991446 + 1.42022i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.504048 - 1.65709i) q^{6} +(-0.310184 + 2.95121i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.03407 + 2.81615i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.991446 + 1.42022i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.504048 - 1.65709i) q^{6} +(-0.310184 + 2.95121i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.03407 + 2.81615i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(5.85567 - 2.60711i) q^{11} +(-0.0326902 + 1.73174i) q^{12} +(-0.0533559 + 0.251020i) q^{13} +(1.20698 - 2.71091i) q^{14} +(0.148505 + 1.72567i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.128731 + 0.0573147i) q^{17} +(1.85370 - 2.35877i) q^{18} +(3.33397 - 0.708656i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-4.49890 + 2.48543i) q^{21} +(-6.37472 + 0.670010i) q^{22} +(0.218421 - 0.158692i) q^{23} +(0.566228 - 1.63688i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.128314 - 0.222246i) q^{26} +(-5.02479 + 1.32345i) q^{27} +(-1.98562 + 2.20525i) q^{28} +(-1.06871 + 3.28916i) q^{29} +(0.392025 - 1.68710i) q^{30} +(5.50287 - 0.847624i) q^{31} -1.00000i q^{32} +(9.50827 + 5.73155i) q^{33} +(-0.104719 - 0.0942896i) q^{34} +(-1.74423 + 2.40073i) q^{35} +(-2.49187 + 1.67050i) q^{36} +(-2.58554 + 1.49276i) q^{37} +(-3.38978 - 0.356280i) q^{38} +(-0.409403 + 0.173095i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-4.27156 + 3.84613i) q^{41} +(5.04675 - 0.973546i) q^{42} +(-0.105304 - 0.495415i) q^{43} +(6.26976 + 1.33268i) q^{44} +(-2.30361 + 1.92182i) q^{45} +(-0.256769 + 0.0834292i) q^{46} +(-11.6458 + 3.78394i) q^{47} +(-1.04434 + 1.38179i) q^{48} +(-1.76636 - 0.375452i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(0.0462300 + 0.239651i) q^{51} +(-0.190711 + 0.171717i) q^{52} +(-0.682747 - 6.49590i) q^{53} +(5.18782 + 0.294072i) q^{54} +(6.37472 + 0.670010i) q^{55} +(2.56990 - 1.48373i) q^{56} +(4.31190 + 4.03238i) q^{57} +(2.03281 - 2.79793i) q^{58} +(-1.28184 - 1.15417i) q^{59} +(-0.894182 + 1.48339i) q^{60} -10.3488i q^{61} +(-5.49547 - 0.894340i) q^{62} +(-7.99028 - 3.92528i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.171717 + 0.190711i) q^{65} +(-7.27175 - 8.38925i) q^{66} +(2.56939 - 4.45032i) q^{67} +(0.0704568 + 0.122035i) q^{68} +(0.441930 + 0.152872i) q^{69} +(2.40073 - 1.74423i) q^{70} +(-3.18552 + 0.334811i) q^{71} +(2.88612 - 0.818710i) q^{72} +(2.49424 + 5.60216i) q^{73} +(2.92029 - 0.620726i) q^{74} +(-0.734227 + 1.56873i) q^{75} +(3.11377 + 1.38634i) q^{76} +(5.87779 + 18.0900i) q^{77} +(0.442855 - 0.0381105i) q^{78} +(-6.36960 + 14.3063i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-6.86139 - 5.82420i) q^{81} +(5.25101 - 2.33790i) q^{82} +(-3.61823 - 4.01845i) q^{83} +(-5.10059 - 0.633634i) q^{84} +(0.0828269 + 0.114002i) q^{85} +(-0.0529419 + 0.503709i) q^{86} +(-5.73091 + 1.74321i) q^{87} +(-5.55108 - 3.20492i) q^{88} +(6.43221 + 4.67328i) q^{89} +(2.78474 - 1.11591i) q^{90} +(-0.724260 - 0.235326i) q^{91} +0.269983 q^{92} +(6.65961 + 6.97493i) q^{93} +12.2451 q^{94} +(3.24163 + 1.05327i) q^{95} +(1.42022 - 0.991446i) q^{96} +(3.37411 + 2.45144i) q^{97} +(1.56389 + 0.902913i) q^{98} +(1.28684 + 19.1864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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