LMFDB - Embedded newform 276.2.o.a.95.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			95.19
Character	$\chi$	$=$	276.95
Dual form			276.2.o.a.215.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.338952 - 1.37299i) q^{2} +(1.70321 + 0.314759i) q^{3} +(-1.77022 + 0.930758i) q^{4} +(0.479018 + 0.415071i) q^{5} +(-0.145145 - 2.44519i) q^{6} +(1.80972 + 2.81598i) q^{7} +(1.87795 + 2.11502i) q^{8} +(2.80185 + 1.07220i) q^{9} +O(q^{10})$	\(q+(-0.338952 - 1.37299i) q^{2} +(1.70321 + 0.314759i) q^{3} +(-1.77022 + 0.930758i) q^{4} +(0.479018 + 0.415071i) q^{5} +(-0.145145 - 2.44519i) q^{6} +(1.80972 + 2.81598i) q^{7} +(1.87795 + 2.11502i) q^{8} +(2.80185 + 1.07220i) q^{9} +(0.407526 - 0.798378i) q^{10} +(-0.284937 + 1.98178i) q^{11} +(-3.30803 + 1.02808i) q^{12} +(-1.90049 - 1.22137i) q^{13} +(3.25291 - 3.43922i) q^{14} +(0.685221 + 0.857730i) q^{15} +(2.26738 - 3.29530i) q^{16} +(1.27320 - 4.33612i) q^{17} +(0.522433 - 4.21035i) q^{18} +(-0.200766 - 0.683747i) q^{19} +(-1.23430 - 0.288919i) q^{20} +(2.19598 + 5.36583i) q^{21} +(2.81755 - 0.280512i) q^{22} +(-4.70393 + 0.934357i) q^{23} +(2.53282 + 4.19343i) q^{24} +(-0.654400 - 4.55145i) q^{25} +(-1.03276 + 3.02335i) q^{26} +(4.43466 + 2.70810i) q^{27} +(-5.82461 - 3.30050i) q^{28} +(-0.681251 + 2.32013i) q^{29} +(0.945400 - 1.23153i) q^{30} +(4.45897 - 2.03634i) q^{31} +(-5.29296 - 1.99615i) q^{32} +(-1.10909 + 3.28570i) q^{33} +(-6.38502 - 0.278358i) q^{34} +(-0.301944 + 2.10007i) q^{35} +(-5.95787 + 0.709811i) q^{36} +(-5.26579 - 6.07704i) q^{37} +(-0.870730 + 0.507408i) q^{38} +(-2.85250 - 2.67845i) q^{39} +(0.0216849 + 1.79262i) q^{40} +(-6.37875 - 5.52722i) q^{41} +(6.62292 - 4.83383i) q^{42} +(7.30327 + 3.33529i) q^{43} +(-1.34016 - 3.77340i) q^{44} +(0.897097 + 1.67657i) q^{45} +(2.87727 + 6.14177i) q^{46} +1.79521 q^{47} +(4.89905 - 4.89891i) q^{48} +(-1.74675 + 3.82485i) q^{49} +(-6.02731 + 2.44121i) q^{50} +(3.53336 - 6.98458i) q^{51} +(4.50110 + 0.393202i) q^{52} +(5.97309 + 9.29431i) q^{53} +(2.21506 - 7.00668i) q^{54} +(-0.959071 + 0.831039i) q^{55} +(-2.55730 + 9.11586i) q^{56} +(-0.126731 - 1.22776i) q^{57} +(3.41643 + 0.148941i) q^{58} +(-12.5418 - 8.06011i) q^{59} +(-2.01133 - 0.880597i) q^{60} +(-0.377953 - 0.827602i) q^{61} +(-4.30726 - 5.43191i) q^{62} +(2.05127 + 9.83035i) q^{63} +(-0.946635 + 7.94380i) q^{64} +(-0.403413 - 1.37390i) q^{65} +(4.88718 + 0.409079i) q^{66} +(-3.50773 + 0.504335i) q^{67} +(1.78203 + 8.86095i) q^{68} +(-8.30588 + 0.110800i) q^{69} +(2.98573 - 0.297255i) q^{70} +(0.747908 + 5.20181i) q^{71} +(2.99400 + 7.93952i) q^{72} +(-5.36692 + 1.57587i) q^{73} +(-6.55889 + 9.28972i) q^{74} +(0.318031 - 7.95806i) q^{75} +(0.991805 + 1.02352i) q^{76} +(-6.09631 + 2.78409i) q^{77} +(-2.71064 + 4.82433i) q^{78} +(-0.930478 + 1.44785i) q^{79} +(2.45390 - 0.637384i) q^{80} +(6.70076 + 6.00831i) q^{81} +(-5.42675 + 10.6315i) q^{82} +(7.69187 + 8.87689i) q^{83} +(-8.88167 - 7.45479i) q^{84} +(2.40969 - 1.54861i) q^{85} +(2.10387 - 11.1578i) q^{86} +(-1.89060 + 3.73724i) q^{87} +(-4.72661 + 3.11903i) q^{88} +(0.443256 + 0.202428i) q^{89} +(1.99785 - 1.79999i) q^{90} -7.56209i q^{91} +(7.45735 - 6.03224i) q^{92} +(8.23552 - 2.06482i) q^{93} +(-0.608490 - 2.46481i) q^{94} +(0.187633 - 0.410860i) q^{95} +(-8.38672 - 5.06586i) q^{96} +(7.32224 - 8.45031i) q^{97} +(5.84356 + 1.10184i) q^{98} +(-2.92322 + 5.24715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.338952	−	1.37299i	−0.239675	−	0.970853i
$2$	−0.338952	−	1.37299i	−0.239675	−	0.970853i
$3$	1.70321	+	0.314759i	0.983349	+	0.181726i
$3$	1.70321	+	0.314759i	0.983349	+	0.181726i
$4$	−1.77022	+	0.930758i	−0.885111	+	0.465379i
$5$	0.479018	+	0.415071i	0.214223	+	0.185626i	0.755362	−	0.655308i	$-0.227461\pi$
$5$	0.479018	+	0.415071i	0.214223	+	0.185626i	−0.541139	+	0.840933i	$0.682007\pi$
$6$	−0.145145	−	2.44519i	−0.0592550	−	0.998243i
$7$	1.80972	+	2.81598i	0.684010	+	1.06434i	0.993543	+	0.113452i	$0.0361908\pi$
$7$	1.80972	+	2.81598i	0.684010	+	1.06434i	−0.309533	+	0.950889i	$0.600173\pi$
$8$	1.87795	+	2.11502i	0.663954	+	0.747773i
$9$	2.80185	+	1.07220i	0.933951	+	0.357401i
$10$	0.407526	−	0.798378i	0.128871	−	0.252469i
$11$	−0.284937	+	1.98178i	−0.0859118	+	0.597529i	0.900700	+	0.434442i	$0.143054\pi$
$11$	−0.284937	+	1.98178i	−0.0859118	+	0.597529i	−0.986612	+	0.163087i	$0.947855\pi$
$12$	−3.30803	+	1.02808i	−0.954945	+	0.296782i
$13$	−1.90049	−	1.22137i	−0.527102	−	0.338748i	0.249874	−	0.968278i	$-0.419611\pi$
$13$	−1.90049	−	1.22137i	−0.527102	−	0.338748i	−0.776976	+	0.629531i	$0.783247\pi$
$14$	3.25291	−	3.43922i	0.869378	−	0.919170i
$15$	0.685221	+	0.857730i	0.176923	+	0.221465i
$16$	2.26738	−	3.29530i	0.566844	−	0.823825i
$17$	1.27320	−	4.33612i	0.308797	−	1.05166i	−0.648177	−	0.761490i	$-0.724468\pi$
$17$	1.27320	−	4.33612i	0.308797	−	1.05166i	0.956974	−	0.290175i	$-0.0937135\pi$
$18$	0.522433	−	4.21035i	0.123139	−	0.992389i
$19$	−0.200766	−	0.683747i	−0.0460589	−	0.156862i	0.933253	−	0.359221i	$-0.116958\pi$
$19$	−0.200766	−	0.683747i	−0.0460589	−	0.156862i	−0.979312	+	0.202359i	$0.935139\pi$
$20$	−1.23430	−	0.288919i	−0.275998	−	0.0646042i
$21$	2.19598	+	5.36583i	0.479202	+	1.17092i
$22$	2.81755	−	0.280512i	0.600704	−	0.0598054i
$23$	−4.70393	+	0.934357i	−0.980838	+	0.194827i
$23$	−4.70393	+	0.934357i	−0.980838	+	0.194827i
$24$	2.53282	+	4.19343i	0.517009	+	0.855980i
$25$	−0.654400	−	4.55145i	−0.130880	−	0.910291i
$26$	−1.03276	+	3.02335i	−0.202541	+	0.592928i
$27$	4.43466	+	2.70810i	0.853451	+	0.521173i
$28$	−5.82461	−	3.30050i	−1.10075	−	0.623736i
$29$	−0.681251	+	2.32013i	−0.126505	+	0.430837i	−0.998251	−	0.0591218i	$-0.981170\pi$
$29$	−0.681251	+	2.32013i	−0.126505	+	0.430837i	0.871746	+	0.489959i	$0.162988\pi$
$30$	0.945400	−	1.23153i	0.172606	−	0.224846i
$31$	4.45897	−	2.03634i	0.800855	−	0.365738i	0.0274279	−	0.999624i	$-0.491268\pi$
$31$	4.45897	−	2.03634i	0.800855	−	0.365738i	0.773427	+	0.633886i	$0.218541\pi$
$32$	−5.29296	−	1.99615i	−0.935672	−	0.352872i
$33$	−1.10909	+	3.28570i	−0.193068	+	0.571968i
$34$	−6.38502	−	0.278358i	−1.09502	−	0.0477380i
$35$	−0.301944	+	2.10007i	−0.0510379	+	0.354976i
$36$	−5.95787	+	0.709811i	−0.992978	+	0.118302i
$37$	−5.26579	−	6.07704i	−0.865690	−	0.999060i	−0.999967	−	0.00811574i	$-0.997417\pi$
$37$	−5.26579	−	6.07704i	−0.865690	−	0.999060i	0.134277	−	0.990944i	$-0.457129\pi$
$38$	−0.870730	+	0.507408i	−0.141251	+	0.0823125i
$39$	−2.85250	−	2.67845i	−0.456766	−	0.428896i
$40$	0.0216849	+	1.79262i	0.00342869	+	0.283437i
$41$	−6.37875	−	5.52722i	−0.996194	−	0.863207i	−0.00559220	−	0.999984i	$-0.501780\pi$
$41$	−6.37875	−	5.52722i	−0.996194	−	0.863207i	−0.990602	+	0.136777i	$0.956326\pi$
$42$	6.62292	−	4.83383i	1.02194	−	0.745876i
$43$	7.30327	+	3.33529i	1.11374	+	0.508627i	0.885341	−	0.464941i	$-0.153925\pi$
$43$	7.30327	+	3.33529i	1.11374	+	0.508627i	0.228396	+	0.973568i	$0.426652\pi$
$44$	−1.34016	−	3.77340i	−0.202036	−	0.568862i
$45$	0.897097	+	1.67657i	0.133731	+	0.249929i
$46$	2.87727	+	6.14177i	0.424231	+	0.905554i
$47$	1.79521			0.261858			0.130929	−	0.991392i	$-0.458204\pi$
$47$	1.79521			0.261858			0.130929	+	0.991392i	$0.458204\pi$
$48$	4.89905	−	4.89891i	0.707117	−	0.707097i
$49$	−1.74675	+	3.82485i	−0.249536	+	0.546407i
$50$	−6.02731	+	2.44121i	−0.852390	+	0.345240i
$51$	3.53336	−	6.98458i	0.494770	−	0.978037i
$52$	4.50110	+	0.393202i	0.624190	+	0.0545273i
$53$	5.97309	+	9.29431i	0.820467	+	1.27667i	0.958170	+	0.286198i	$0.0923916\pi$
$53$	5.97309	+	9.29431i	0.820467	+	1.27667i	−0.137703	+	0.990474i	$0.543972\pi$
$54$	2.21506	−	7.00668i	0.301432	−	0.953488i
$55$	−0.959071	+	0.831039i	−0.129321	+	0.112057i
$56$	−2.55730	+	9.11586i	−0.341734	+	1.21816i
$57$	−0.126731	−	1.22776i	−0.0167860	−	0.162621i
$58$	3.41643	+	0.148941i	0.448600	+	0.0195569i
$59$	−12.5418	−	8.06011i	−1.63280	−	1.04934i	−0.946844	−	0.321694i	$-0.895748\pi$
$59$	−12.5418	−	8.06011i	−1.63280	−	1.04934i	−0.685956	−	0.727643i	$-0.740616\pi$
$60$	−2.01133	−	0.880597i	−0.259662	−	0.113685i
$61$	−0.377953	−	0.827602i	−0.0483920	−	0.105964i	0.883892	−	0.467692i	$-0.154914\pi$
$61$	−0.377953	−	0.827602i	−0.0483920	−	0.105964i	−0.932284	+	0.361728i	$0.882187\pi$
$62$	−4.30726	−	5.43191i	−0.547023	−	0.689854i
$63$	2.05127	+	9.83035i	0.258436	+	1.23851i
$64$	−0.946635	+	7.94380i	−0.118329	+	0.992974i
$65$	−0.403413	−	1.37390i	−0.0500373	−	0.170411i
$66$	4.88718	+	0.409079i	0.601570	+	0.0503542i
$67$	−3.50773	+	0.504335i	−0.428537	+	0.0616143i	−0.353209	−	0.935544i	$-0.614910\pi$
$67$	−3.50773	+	0.504335i	−0.428537	+	0.0616143i	−0.0753281	+	0.997159i	$0.524000\pi$
$68$	1.78203	+	8.86095i	0.216103	+	1.07455i
$69$	−8.30588	+	0.110800i	−0.999911	+	0.0133387i
$70$	2.98573	−	0.297255i	0.356862	−	0.0355288i
$71$	0.747908	+	5.20181i	0.0887603	+	0.617342i	0.984842	+	0.173453i	$0.0554924\pi$
$71$	0.747908	+	5.20181i	0.0887603	+	0.617342i	−0.896082	+	0.443889i	$0.853598\pi$
$72$	2.99400	+	7.93952i	0.352846	+	0.935681i
$73$	−5.36692	+	1.57587i	−0.628151	+	0.184442i	−0.580287	−	0.814412i	$-0.697060\pi$
$73$	−5.36692	+	1.57587i	−0.628151	+	0.184442i	−0.0478638	+	0.998854i	$0.515241\pi$
$74$	−6.55889	+	9.28972i	−0.762455	+	1.07991i
$75$	0.318031	−	7.95806i	0.0367231	−	0.918918i
$76$	0.991805	+	1.02352i	0.113768	+	0.117406i
$77$	−6.09631	+	2.78409i	−0.694739	+	0.317277i
$78$	−2.71064	+	4.82433i	−0.306919	+	0.546248i
$79$	−0.930478	+	1.44785i	−0.104687	+	0.162896i	−0.889645	−	0.456653i	$-0.849048\pi$
$79$	−0.930478	+	1.44785i	−0.104687	+	0.162896i	0.784958	+	0.619549i	$0.212684\pi$
$80$	2.45390	−	0.637384i	0.274354	−	0.0712617i
$81$	6.70076	+	6.00831i	0.744529	+	0.667590i
$82$	−5.42675	+	10.6315i	−0.599284	+	1.17405i
$83$	7.69187	+	8.87689i	0.844292	+	0.974365i	0.999910	−	0.0134522i	$-0.00428209\pi$
$83$	7.69187	+	8.87689i	0.844292	+	0.974365i	−0.155617	+	0.987817i	$0.549737\pi$
$84$	−8.88167	−	7.45479i	−0.969069	−	0.813385i
$85$	2.40969	−	1.54861i	0.261367	−	0.167971i
$86$	2.10387	−	11.1578i	0.226866	−	1.20318i
$87$	−1.89060	+	3.73724i	−0.202693	+	0.400674i
$88$	−4.72661	+	3.11903i	−0.503858	+	0.332490i
$89$	0.443256	+	0.202428i	0.0469851	+	0.0214574i	0.438769	−	0.898600i	$-0.355415\pi$
$89$	0.443256	+	0.202428i	0.0469851	+	0.0214574i	−0.391784	+	0.920057i	$0.628142\pi$
$90$	1.99785	−	1.79999i	0.210592	−	0.189735i
$91$		−	7.56209i		−	0.792723i
$92$	7.45735	−	6.03224i	0.777482	−	0.628905i
$93$	8.23552	−	2.06482i	0.853984	−	0.214112i
$94$	−0.608490	−	2.46481i	−0.0627610	−	0.254226i
$95$	0.187633	−	0.410860i	0.0192508	−	0.0421533i
$96$	−8.38672	−	5.06586i	−0.855966	−	0.517033i
$97$	7.32224	−	8.45031i	0.743461	−	0.857999i	−0.250457	−	0.968128i	$-0.580581\pi$
$97$	7.32224	−	8.45031i	0.743461	−	0.857999i	0.993917	+	0.110128i	$0.0351262\pi$
$98$	5.84356	+	1.10184i	0.590289	+	0.111302i
$99$	−2.92322	+	5.24715i	−0.293795	+	0.527358i
$100$	5.39474	+	7.44800i	0.539474	+	0.744800i
$101$	−9.23081	+	7.99854i	−0.918500	+	0.795884i	−0.979331	−	0.202264i	$-0.935170\pi$
$101$	−9.23081	+	7.99854i	−0.918500	+	0.795884i	0.0608316	+	0.998148i	$0.480625\pi$
$102$	−10.7874	−	2.48385i	−1.06811	−	0.245938i
$103$	−17.8137	−	2.56123i	−1.75524	−	0.252365i	−0.811805	−	0.583928i	$-0.801515\pi$
$103$	−17.8137	−	2.56123i	−1.75524	−	0.252365i	−0.943433	+	0.331563i	$0.892424\pi$
$104$	−0.985794	−	6.31326i	−0.0966650	−	0.619066i
$105$	−1.17529	+	3.48182i	−0.114697	+	0.339791i
$106$	10.7364	−	11.3513i	1.04281	−	1.10254i
$107$	−4.19653	−	9.18913i	−0.405694	−	0.888347i	−0.996661	−	0.0816507i	$-0.973981\pi$
$107$	−4.19653	−	9.18913i	−0.405694	−	0.888347i	0.590967	−	0.806696i	$-0.298746\pi$
$108$	−10.3709	−	0.666337i	−0.997942	−	0.0641183i
$109$	−1.02468	−	0.300872i	−0.0981462	−	0.0288183i	0.232291	−	0.972646i	$-0.425378\pi$
$109$	−1.02468	−	0.300872i	−0.0981462	−	0.0288183i	−0.330437	+	0.943828i	$0.607196\pi$
$110$	1.46609	+	1.03512i	0.139786	+	0.0986944i
$111$	−7.05594	−	12.0079i	−0.669720	−	1.13974i
$112$	13.3828	+	0.421318i	1.26456	+	0.0398108i
$113$	15.8146	−	2.27380i	1.48772	−	0.213901i	0.649969	−	0.759961i	$-0.274782\pi$
$113$	15.8146	−	2.27380i	1.48772	−	0.213901i	0.837747	+	0.546059i	$0.183873\pi$
$114$	−1.64275	+	0.590153i	−0.153858	+	0.0552729i
$115$	−2.64109	−	1.50489i	−0.246283	−	0.140332i
$116$	−0.953513	−	4.74122i	−0.0885314	−	0.440212i
$117$	−4.01534	−	5.45982i	−0.371219	−	0.504761i
$118$	−6.81541	+	19.9518i	−0.627410	+	1.83671i
$119$	14.5146	−	4.26186i	1.33055	−	0.390684i
$120$	−0.527308	+	3.06003i	−0.0481365	+	0.279341i
$121$	6.70816	+	1.96969i	0.609832	+	0.179063i
$122$	−1.00818	+	0.799445i	−0.0912767	+	0.0723784i
$123$	−9.12462	−	11.4218i	−0.822739	−	1.02987i
$124$	−5.99803	+	7.75500i	−0.538639	+	0.696420i
$125$	3.28909	−	5.11792i	0.294185	−	0.457760i
$126$	12.8017	−	6.14840i	1.14047	−	0.547743i
$127$	−10.2848	−	1.47873i	−0.912625	−	0.131216i	−0.330023	−	0.943973i	$-0.607056\pi$
$127$	−10.2848	−	1.47873i	−0.912625	−	0.131216i	−0.582602	+	0.812757i	$0.697965\pi$
$128$	11.2276	−	1.39284i	0.992393	−	0.123111i
$129$	11.3892	+	7.97947i	1.00276	+	0.702553i
$130$	−1.74962	+	1.01957i	−0.153452	+	0.0894222i
$131$	9.70608	−	6.23772i	0.848024	−	0.544992i	−0.0429338	−	0.999078i	$-0.513670\pi$
$131$	9.70608	−	6.23772i	0.848024	−	0.544992i	0.890958	+	0.454086i	$0.150034\pi$
$132$	−1.09486	−	6.84872i	−0.0952951	−	0.596105i
$133$	1.56209	−	1.80275i	0.135450	−	0.156318i
$134$	1.88140	+	4.64514i	0.162528	+	0.401279i
$135$	1.00023	+	3.13793i	0.0860860	+	0.270070i
$136$	11.5620	−	5.45016i	0.991433	−	0.467347i
$137$		−	12.1743i		−	1.04012i	−0.854130	−	0.520060i	$-0.825910\pi$
$137$		−	12.1743i		−	1.04012i	0.854130	−	0.520060i	$-0.174090\pi$
$138$	2.96743	+	11.3664i	0.252604	+	0.967570i
$139$		−	14.3593i		−	1.21794i	−0.793193	−	0.608970i	$-0.791583\pi$
$139$		−	14.3593i		−	1.21794i	0.793193	−	0.608970i	$-0.208417\pi$
$140$	−1.42015	−	3.99863i	−0.120024	−	0.337946i
$141$	3.05762	+	0.565059i	0.257498	+	0.0475865i
$142$	6.88855	−	2.79004i	0.578074	−	0.234135i
$143$	2.96201	−	3.41835i	0.247696	−	0.285856i
$144$	9.88609	−	6.80186i	0.823841	−	0.566821i
$145$	−1.28935	+	0.828615i	−0.107075	+	0.0688127i
$146$	3.98279	+	6.83460i	0.329618	+	0.565636i
$147$	−4.17899	+	5.96472i	−0.344677	+	0.491962i
$148$	14.9779	+	5.85654i	1.23117	+	0.481405i
$149$	14.4884	+	2.08311i	1.18693	+	0.170655i	0.707364	−	0.706849i	$-0.249884\pi$
$149$	14.4884	+	2.08311i	1.18693	+	0.170655i	0.479569	+	0.877504i	$0.340793\pi$
$150$	−11.0342	+	2.26075i	−0.900936	+	0.184589i
$151$	−4.20134	+	6.53741i	−0.341900	+	0.532007i	−0.969041	−	0.246898i	$-0.920589\pi$
$151$	−4.20134	+	6.53741i	−0.341900	+	0.532007i	0.627141	+	0.778906i	$0.284225\pi$
$152$	1.06911	−	1.70867i	0.0867164	−	0.138591i
$153$	8.21653	−	10.7841i	0.664267	−	0.871839i
$154$	5.88890	+	7.42652i	0.474541	+	0.598446i
$155$	2.98115	+	0.875346i	0.239452	+	0.0703095i
$156$	7.54255	+	2.08647i	0.603888	+	0.167051i
$157$	−15.8765	+	4.66175i	−1.26708	+	0.372048i	−0.845125	−	0.534568i	$-0.820474\pi$
$157$	−15.8765	+	4.66175i	−1.26708	+	0.372048i	−0.421955	+	0.906617i	$0.638656\pi$
$158$	2.30328	+	0.786788i	0.183239	+	0.0625935i
$159$	7.24796	+	17.7103i	0.574801	+	1.40451i
$160$	−1.70688	−	3.15315i	−0.134941	−	0.249278i
$161$	−11.1439	−	11.5553i	−0.878265	−	0.910682i
$162$	5.97813	−	11.2366i	0.469686	−	0.882833i
$163$	−11.1181	+	1.59854i	−0.870836	+	0.125207i	−0.563224	−	0.826305i	$-0.690439\pi$
$163$	−11.1181	+	1.59854i	−0.870836	+	0.125207i	−0.307612	+	0.951512i	$0.599530\pi$
$164$	16.4363	+	3.84733i	1.28346	+	0.300426i
$165$	−1.89508	+	1.11356i	−0.147532	+	0.0866904i
$166$	9.58074	−	13.5697i	0.743609	−	1.05322i
$167$	−0.795819	−	0.233673i	−0.0615823	−	0.0180822i	0.250796	−	0.968040i	$-0.419308\pi$
$167$	−0.795819	−	0.233673i	−0.0615823	−	0.0180822i	−0.312379	+	0.949958i	$0.601126\pi$
$168$	−7.22492	+	14.7213i	−0.557415	+	1.13577i
$169$	−3.28027	−	7.18280i	−0.252329	−	0.552523i
$170$	−2.94300	−	2.78358i	−0.225718	−	0.213491i
$171$	0.170598	−	2.13102i	0.0130460	−	0.162963i
$172$	−16.0328	+	0.893371i	−1.22249	+	0.0681189i
$173$	7.52999	+	1.08265i	0.572494	+	0.0823123i	0.422481	−	0.906372i	$-0.361159\pi$
$173$	7.52999	+	1.08265i	0.572494	+	0.0823123i	0.150013	+	0.988684i	$0.452068\pi$
$174$	5.77202	+	1.32903i	0.437576	+	0.100754i
$175$	11.6325	−	10.0796i	0.879336	−	0.761949i
$176$	5.88450	+	5.43240i	0.443561	+	0.409482i
$177$	−18.8243	−	17.6757i	−1.41492	−	1.32859i
$178$	0.127690	−	0.677202i	0.00957078	−	0.0507584i
$179$	−7.14441	+	8.24509i	−0.533999	+	0.616267i	−0.957080	−	0.289825i	$-0.906403\pi$
$179$	−7.14441	+	8.24509i	−0.533999	+	0.616267i	0.423081	+	0.906092i	$0.360949\pi$
$180$	−3.14855	−	2.13293i	−0.234679	−	0.158979i
$181$	−2.67920	+	5.86663i	−0.199143	+	0.436063i	−0.982687	−	0.185274i	$-0.940683\pi$
$181$	−2.67920	+	5.86663i	−0.199143	+	0.436063i	0.783544	+	0.621337i	$0.213410\pi$
$182$	−10.3827	+	2.56319i	−0.769617	+	0.189996i
$183$	−0.383239	−	1.52855i	−0.0283298	−	0.112993i
$184$	−10.8099	−	8.19425i	−0.796918	−	0.604088i
$185$		−	5.09669i		−	0.374716i
$186$	−5.62643	−	10.6074i	−0.412550	−	0.777776i
$187$	8.23046	+	3.75873i	0.601871	+	0.274865i
$188$	−3.17792	+	1.67091i	−0.231774	+	0.121863i
$189$	0.399549	+	17.3888i	0.0290629	+	1.26485i
$190$	−0.627706	−	0.118358i	−0.0455386	−	0.00858656i
$191$	11.9990	−	7.71127i	0.868215	−	0.557968i	−0.0289912	−	0.999580i	$-0.509229\pi$
$191$	11.9990	−	7.71127i	0.868215	−	0.557968i	0.897206	+	0.441612i	$0.145593\pi$
$192$	−4.11270	+	13.2320i	−0.296809	+	0.954937i
$193$	−8.79516	−	10.1502i	−0.633089	−	0.730624i	0.345048	−	0.938585i	$-0.387863\pi$
$193$	−8.79516	−	10.1502i	−0.633089	−	0.730624i	−0.978137	+	0.207961i	$0.933317\pi$
$194$	−14.0841	−	7.18913i	−1.01118	−	0.516150i
$195$	−0.254650	−	2.46702i	−0.0182359	−	0.176667i
$196$	−0.467874	−	8.39664i	−0.0334196	−	0.599760i
$197$	−14.7781	+	22.9952i	−1.05290	+	1.63834i	−0.334958	+	0.942233i	$0.608722\pi$
$197$	−14.7781	+	22.9952i	−1.05290	+	1.63834i	−0.717938	+	0.696107i	$0.754914\pi$
$198$	8.19513	+	2.23503i	0.582403	+	0.158837i
$199$	13.4248	−	6.13089i	0.951657	−	0.434607i	0.121782	−	0.992557i	$-0.461139\pi$
$199$	13.4248	−	6.13089i	0.951657	−	0.434607i	0.829875	+	0.557950i	$0.188412\pi$
$200$	8.39750	−	9.93146i	0.593793	−	0.702260i
$201$	−6.13314	−	0.245101i	−0.432598	−	0.0172881i
$202$	14.1107	+	9.96272i	0.992829	+	0.700974i
$203$	−7.76631	+	2.28039i	−0.545088	+	0.160052i
$204$	0.246115	+	15.6530i	0.0172315	+	1.09593i
$205$	−0.761346	−	5.29528i	−0.0531747	−	0.369838i
$206$	2.52145	+	25.3263i	0.175678	+	1.76456i
$207$	−14.1815	−	2.42564i	−0.985686	−	0.168594i
$208$	−8.33392	+	3.49338i	−0.577854	+	0.242222i
$209$	1.41224	−	0.203050i	0.0976869	−	0.0140453i
$210$	5.17888	+	0.433496i	0.357377	+	0.0299141i
$211$	7.30040	+	24.8629i	0.502581	+	1.71163i	0.685117	+	0.728433i	$0.259751\pi$
$211$	7.30040	+	24.8629i	0.502581	+	1.71163i	−0.182537	+	0.983199i	$0.558431\pi$
$212$	−19.2245	−	10.8935i	−1.32034	−	0.748168i
$213$	−0.363475	+	9.09520i	−0.0249049	+	0.623193i
$214$	−11.1942	+	8.87649i	−0.765219	+	0.606784i
$215$	2.11401	+	4.62904i	0.144174	+	0.315698i
$216$	2.60037	+	14.4651i	0.176933	+	0.984223i
$217$	13.8038	+	8.87116i	0.937062	+	0.602213i
$218$	−0.0657792	+	1.50886i	−0.00445513	+	0.102193i
$219$	−9.63702	+	0.994750i	−0.651209	+	0.0672190i
$220$	0.924272	−	2.36379i	0.0623144	−	0.159367i
$221$	−7.71573	+	6.68572i	−0.519016	+	0.449730i
$222$	−14.0952	+	13.7579i	−0.946008	+	0.923368i
$223$	9.71188	+	15.1120i	0.650355	+	1.01197i	0.997253	+	0.0740696i	$0.0235987\pi$
$223$	9.71188	+	15.1120i	0.650355	+	1.01197i	−0.346898	+	0.937903i	$0.612765\pi$
$224$	−3.95767	−	18.5173i	−0.264433	−	1.23724i
$225$	3.04655	−	13.4542i	0.203103	−	0.896944i
$226$	−8.48232	−	20.9427i	−0.564236	−	1.39309i
$227$	−5.88440	+	12.8850i	−0.390562	+	0.855211i	0.607579	+	0.794259i	$0.292141\pi$
$227$	−5.88440	+	12.8850i	−0.390562	+	0.855211i	−0.998141	+	0.0609514i	$0.980587\pi$
$228$	1.36709	+	2.05545i	0.0905377	+	0.136125i
$229$	18.3512			1.21268			0.606342	−	0.795204i	$-0.292636\pi$
$229$	18.3512			1.21268			0.606342	+	0.795204i	$0.292636\pi$
$230$	−1.17101	+	4.13629i	−0.0772138	+	0.272739i
$231$	−11.2596	+	2.82302i	−0.740829	+	0.185741i
$232$	−6.18647	+	2.91622i	−0.406162	+	0.191459i
$233$	−4.41105	−	2.01446i	−0.288978	−	0.131972i	0.265652	−	0.964069i	$-0.414413\pi$
$233$	−4.41105	−	2.01446i	−0.288978	−	0.131972i	−0.554630	+	0.832097i	$0.687140\pi$
$234$	−6.13529	+	7.36366i	−0.401076	+	0.481377i
$235$	0.859938	+	0.745140i	0.0560961	+	0.0486076i
$236$	29.7037	+	2.59483i	1.93355	+	0.168909i
$237$	−2.04053	+	2.17312i	−0.132546	+	0.141159i
$238$	−10.7713	−	18.4839i	−0.698197	−	1.19813i
$239$	−11.4850	−	13.2544i	−0.742905	−	0.857358i	0.250955	−	0.967999i	$-0.419255\pi$
$239$	−11.4850	−	13.2544i	−0.742905	−	0.857358i	−0.993861	+	0.110640i	$0.964710\pi$
$240$	4.38013	−	0.313212i	0.282736	−	0.0202177i
$241$	−0.920414	+	6.40162i	−0.0592891	+	0.412365i	0.938465	+	0.345375i	$0.112248\pi$
$241$	−0.920414	+	6.40162i	−0.0592891	+	0.412365i	−0.997754	+	0.0669893i	$0.978661\pi$
$242$	0.430631	−	9.87789i	0.0276820	−	0.634975i
$243$	9.52164	+	12.3425i	0.610813	+	0.791775i
$244$	1.43936	+	1.11326i	0.0921455	+	0.0712690i
$245$	−2.42431	+	1.10715i	−0.154884	+	0.0707329i
$246$	−12.5892	+	16.3995i	−0.802661	+	1.04559i
$247$	−0.453555	+	1.54467i	−0.0288590	+	0.0982848i
$248$	12.6806	+	5.60667i	0.805220	+	0.356024i
$249$	10.3068	+	17.5403i	0.653166	+	1.11157i
$250$	−8.14171	−	2.78116i	−0.514927	−	0.175896i
$251$	0.545543	+	3.79434i	0.0344344	+	0.239496i	0.999768	−	0.0215214i	$-0.00685099\pi$
$251$	0.545543	+	3.79434i	0.0344344	+	0.239496i	−0.965334	+	0.261018i	$0.915942\pi$
$252$	−12.7809	−	15.4927i	−0.805120	−	0.975947i
$253$	−0.511365	−	9.58840i	−0.0321493	−	0.602817i
$254$	1.45576	+	14.6221i	0.0913427	+	0.917474i
$255$	4.59165	−	1.87914i	0.287540	−	0.117676i
$256$	−5.71800	−	14.9434i	−0.357375	−	0.933961i
$257$	−5.24478	−	17.8621i	−0.327160	−	1.11421i	−0.944774	−	0.327724i	$-0.893718\pi$
$257$	−5.24478	−	17.8621i	−0.327160	−	1.11421i	0.617613	−	0.786482i	$-0.288100\pi$
$258$	7.09537	−	18.3419i	0.441739	−	1.14192i
$259$	7.58323	−	25.8261i	0.471199	−	1.60476i
$260$	1.99290	+	2.05663i	0.123594	+	0.127547i
$261$	−4.39641	+	5.77022i	−0.272131	+	0.357168i
$262$	−11.8542	−	11.2121i	−0.732358	−	0.692686i
$263$	0.758584	+	0.487512i	0.0467763	+	0.0300613i	0.563820	−	0.825898i	$-0.309331\pi$
$263$	0.758584	+	0.487512i	0.0467763	+	0.0300613i	−0.517044	+	0.855959i	$0.672968\pi$
$264$	−9.03215	+	3.82462i	−0.555890	+	0.235389i
$265$	−0.996585	+	6.93140i	−0.0612197	+	0.425793i
$266$	−3.00463	−	1.53369i	−0.184226	−	0.0940367i
$267$	0.691243	+	0.484297i	0.0423034	+	0.0296385i
$268$	5.74004	−	4.15763i	0.350629	−	0.253968i
$269$	6.21544	+	9.67141i	0.378962	+	0.589677i	0.977376	−	0.211511i	$-0.0678384\pi$
$269$	6.21544	+	9.67141i	0.378962	+	0.589677i	−0.598414	+	0.801187i	$0.704202\pi$
$270$	3.96933	−	2.43692i	0.241565	−	0.148306i
$271$	13.7428	+	11.9082i	0.834817	+	0.723373i	0.963326	−	0.268335i	$-0.0864735\pi$
$271$	13.7428	+	11.9082i	0.834817	+	0.723373i	−0.128508	+	0.991708i	$0.541019\pi$
$272$	−11.4020	−	14.0272i	−0.691348	−	0.850524i
$273$	2.38024	−	12.8798i	0.144059	−	0.779523i
$274$	−16.7152	+	4.12650i	−1.00980	+	0.249291i
$275$	9.20645			0.555170
$276$	14.6001	−	7.92691i	0.878825	−	0.477144i
$277$	1.74144			0.104633			0.0523164	−	0.998631i	$-0.483340\pi$
$277$	1.74144			0.104633			0.0523164	+	0.998631i	$0.483340\pi$
$278$	−19.7152	+	4.86712i	−1.18244	+	0.291910i
$279$	14.6767	−	0.924614i	0.878674	−	0.0553552i
$280$	−5.00873	+	3.30520i	−0.299329	+	0.197523i
$281$	21.7980	+	18.8881i	1.30036	+	1.12677i	0.984008	+	0.178125i	$0.0570030\pi$
$281$	21.7980	+	18.8881i	1.30036	+	1.12677i	0.316350	+	0.948642i	$0.397542\pi$
$282$	−0.260565	−	4.38962i	−0.0155164	−	0.261398i
$283$	7.96234	+	12.3896i	0.473312	+	0.736487i	0.993031	−	0.117849i	$-0.0376000\pi$
$283$	7.96234	+	12.3896i	0.473312	+	0.736487i	−0.519720	+	0.854337i	$0.673964\pi$
$284$	−6.16560	−	8.51225i	−0.365861	−	0.505109i
$285$	0.448901	−	0.640721i	0.0265906	−	0.0379530i
$286$	−5.69735	−	2.90817i	−0.336891	−	0.171964i
$287$	4.02078	−	27.9652i	0.237339	−	1.65073i
$288$	−12.6898	−	11.2680i	−0.747755	−	0.663975i
$289$	−2.87962	−	1.85062i	−0.169389	−	0.108860i
$290$	1.57471	+	1.48941i	0.0924703	+	0.0874611i
$291$	15.1311	−	12.0879i	0.887003	−	0.708607i
$292$	8.03389	−	7.78495i	0.470148	−	0.455580i
$293$	−3.28842	+	11.1993i	−0.192112	+	0.654272i	0.805947	+	0.591988i	$0.201657\pi$
$293$	−3.28842	+	11.1993i	−0.192112	+	0.654272i	−0.998058	+	0.0622844i	$0.980161\pi$
$294$	9.60600	+	3.71597i	0.560233	+	0.216720i
$295$	−2.66221	−	9.06667i	−0.155000	−	0.527882i
$296$	2.96421	−	22.5496i	0.172291	−	1.31067i
$297$	−6.63045	+	8.01689i	−0.384738	+	0.465187i
$298$	−2.05076	−	20.5985i	−0.118798	−	1.19324i
$299$	10.0810	+	3.96952i	0.582998	+	0.229563i
$300$	6.84405	+	14.3836i	0.395141	+	0.830435i
$301$	3.82476	+	26.6018i	0.220456	+	1.53330i
$302$	10.3999	+	3.55254i	0.598446	+	0.204426i
$303$	−18.2396	+	10.7177i	−1.04784	+	0.615717i
$304$	−2.70836	−	0.888728i	−0.155335	−	0.0509720i
$305$	0.162468	−	0.553314i	0.00930287	−	0.0316827i
$306$	−17.5914	−	7.62596i	−1.00564	−	0.435947i
$307$	−9.89518	+	4.51898i	−0.564748	+	0.257912i	−0.677266	−	0.735738i	$-0.736835\pi$
$307$	−9.89518	+	4.51898i	−0.564748	+	0.257912i	0.112519	+	0.993650i	$0.464108\pi$
$308$	8.20051	−	10.6027i	0.467268	−	0.604142i
$309$	−29.5344	−	9.96934i	−1.68015	−	0.567136i
$310$	0.191375	−	4.38981i	0.0108694	−	0.249324i
$311$	−2.63055	+	18.2959i	−0.149165	+	1.03747i	0.768426	+	0.639939i	$0.221040\pi$
$311$	−2.63055	+	18.2959i	−0.149165	+	1.03747i	−0.917591	+	0.397526i	$0.869869\pi$
$312$	0.308141	−	11.0631i	0.0174451	−	0.626324i
$313$	−4.96211	−	5.72658i	−0.280475	−	0.323685i	0.597980	−	0.801511i	$-0.295970\pi$
$313$	−4.96211	−	5.72658i	−0.280475	−	0.323685i	−0.878455	+	0.477826i	$0.841425\pi$
$314$	11.7819	+	20.2182i	0.664892	+	1.14098i
$315$	−3.09770	+	5.56034i	−0.174536	+	0.313290i
$316$	0.299553	−	3.42907i	0.0168512	−	0.192900i
$317$	−21.2813	−	18.4403i	−1.19528	−	1.03571i	−0.998472	−	0.0552688i	$-0.982398\pi$
$317$	−21.2813	−	18.4403i	−1.19528	−	1.03571i	−0.196804	−	0.980443i	$-0.563056\pi$
$318$	21.8594	−	15.9543i	1.22581	−	0.894675i
$319$	−4.40387	−	2.01118i	−0.246569	−	0.112604i
$320$	−3.75070	+	3.41230i	−0.209670	+	0.190753i
$321$	−4.25522	−	16.9719i	−0.237503	−	0.947280i
$322$	−12.0880	+	19.2172i	−0.673640	+	1.07093i
$323$	−3.22043			−0.179189
$324$	−17.4541	−	4.39926i	−0.969674	−	0.244403i
$325$	−4.31534	+	9.44927i	−0.239372	+	0.524151i
$326$	5.96328	+	14.7232i	0.330276	+	0.815444i
$327$	−1.65054	−	0.834975i	−0.0912749	−	0.0461742i
$328$	−0.288763	−	23.8710i	−0.0159443	−	1.31806i
$329$	3.24883	+	5.05527i	0.179114	+	0.278706i
$330$	2.17125	+	2.22449i	0.119523	+	0.122454i
$331$	−18.8475	+	16.3314i	−1.03595	+	0.897656i	−0.994836	−	0.101498i	$-0.967636\pi$
$331$	−18.8475	+	16.3314i	−1.03595	+	0.897656i	−0.0411149	+	0.999154i	$0.513091\pi$
$332$	−21.8786	−	8.55480i	−1.20074	−	0.469506i
$333$	−8.23814	−	22.6730i	−0.451447	−	1.24247i
$334$	−0.0510876	+	1.17186i	−0.00279539	+	0.0641212i
$335$	−1.88960	−	1.21437i	−0.103240	−	0.0663482i
$336$	22.6611	+	4.92996i	1.23627	+	0.268951i
$337$	13.6721	+	29.9377i	0.744767	+	1.63081i	0.775550	+	0.631286i	$0.217473\pi$
$337$	13.6721	+	29.9377i	0.744767	+	1.63081i	−0.0307831	+	0.999526i	$0.509800\pi$
$338$	−8.75008	+	6.93842i	−0.475942	+	0.377400i
$339$	27.6514	+	1.10504i	1.50182	+	0.0600176i
$340$	−2.82430	+	4.98423i	−0.153169	+	0.270308i
$341$	2.76506	+	9.41693i	0.149736	+	0.509955i
$342$	−2.98370	+	0.488084i	−0.161340	+	0.0263926i
$343$	9.26120	−	1.33156i	0.500058	−	0.0718975i
$344$	6.66093	+	21.7101i	0.359133	+	1.17053i
$345$	−4.02466	−	3.39446i	−0.216680	−	0.182752i
$346$	−1.06584	−	10.7056i	−0.0572997	−	0.575536i
$347$	2.28747	+	15.9097i	0.122798	+	0.854078i	0.954363	+	0.298650i	$0.0965363\pi$
$347$	2.28747	+	15.9097i	0.122798	+	0.854078i	−0.831565	+	0.555428i	$0.812555\pi$
$348$	−0.131689	−	8.37543i	−0.00705925	−	0.448970i
$349$	26.1618	−	7.68180i	1.40041	−	0.411197i	0.507584	−	0.861602i	$-0.330539\pi$
$349$	26.1618	−	7.68180i	1.40041	−	0.411197i	0.892824	+	0.450405i	$0.148720\pi$
$350$	−17.7821	−	12.5549i	−0.950496	−	0.671086i
$351$	−5.12044	−	10.5631i	−0.273309	−	0.563816i
$352$	5.46408	−	9.92071i	0.291237	−	0.528775i
$353$	−9.85856	+	4.50225i	−0.524718	+	0.239631i	−0.660120	−	0.751160i	$-0.729495\pi$
$353$	−9.85856	+	4.50225i	−0.524718	+	0.239631i	0.135402	+	0.990791i	$0.456767\pi$
$354$	−17.8881	+	31.8368i	−0.950741	+	1.69211i
$355$	−1.80086	+	2.80220i	−0.0955799	+	0.148725i
$356$	−0.973075	+	0.0542213i	−0.0515729	+	0.00287372i
$357$	26.0628	−	2.69025i	1.37939	−	0.142383i
$358$	13.7421	+	7.01454i	0.726291	+	0.370730i
$359$	−7.33523	−	8.46530i	−0.387138	−	0.446782i	0.528410	−	0.848989i	$-0.322788\pi$
$359$	−7.33523	−	8.46530i	−0.387138	−	0.446782i	−0.915548	+	0.402208i	$0.868243\pi$
$360$	−1.86129	+	5.04590i	−0.0980986	+	0.265942i
$361$	15.5566	−	9.99763i	0.818769	−	0.526191i
$362$	8.96297	+	1.69002i	0.471083	+	0.0888253i
$363$	10.8054	+	5.46626i	0.567138	+	0.286904i
$364$	7.03848	+	13.3866i	0.368917	+	0.701648i
$365$	−3.22495	−	1.47279i	−0.168802	−	0.0770891i
$366$	−1.96878	+	1.04429i	−0.102910	+	0.0545858i
$367$		−	22.1415i		−	1.15578i	−0.816115	−	0.577889i	$-0.803877\pi$
$367$		−	22.1415i		−	1.15578i	0.816115	−	0.577889i	$-0.196123\pi$
$368$	−7.58660	+	17.6194i	−0.395479	+	0.918475i
$369$	−11.9460	−	22.3258i	−0.621885	−	1.16223i
$370$	−6.99772	+	1.72753i	−0.363794	+	0.0898103i
$371$	−15.3630	+	33.6402i	−0.797606	+	1.74651i
$372$	−12.6569	+	11.3205i	−0.656228	+	0.586939i
$373$	−17.0478	+	19.6742i	−0.882703	+	1.01869i	0.116970	+	0.993135i	$0.462682\pi$
$373$	−17.0478	+	19.6742i	−0.882703	+	1.01869i	−0.999673	+	0.0255584i	$0.991864\pi$
$374$	2.37097	−	12.5744i	0.122600	−	0.650207i
$375$	7.21292	−	7.68162i	0.372473	−	0.396677i
$376$	3.37131	+	3.79691i	0.173862	+	0.195811i
$377$	4.12845	−	3.57733i	0.212626	−	0.184242i
$378$	23.7393	−	6.44256i	1.22102	−	0.331369i
$379$	−2.31495	−	0.332839i	−0.118911	−	0.0170968i	0.0826025	−	0.996583i	$-0.473677\pi$
$379$	−2.31495	−	0.332839i	−0.118911	−	0.0170968i	−0.201513	+	0.979486i	$0.564586\pi$
$380$	0.0502583	+	0.901954i	0.00257820	+	0.0462693i
$381$	−17.0517	−	5.75581i	−0.873584	−	0.294879i
$382$	−14.6546	−	13.8608i	−0.749795	−	0.709178i
$383$	−8.58287	−	18.7939i	−0.438564	−	0.960322i	−0.991860	−	0.127337i	$-0.959357\pi$
$383$	−8.58287	−	18.7939i	−0.438564	−	0.960322i	0.553295	−	0.832985i	$-0.313370\pi$
$384$	19.5615	+	1.16170i	0.998241	+	0.0592827i
$385$	−4.07584	−	1.19677i	−0.207724	−	0.0609933i
$386$	−10.9550	+	15.5161i	−0.557593	+	0.789749i
$387$	16.8866	+	17.1756i	0.858393	+	0.873083i
$388$	−5.09679	+	21.7742i	−0.258750	+	1.10542i
$389$	31.8181	−	4.57475i	1.61324	−	0.231949i	0.724137	−	0.689656i	$-0.242238\pi$
$389$	31.8181	−	4.57475i	1.61324	−	0.231949i	0.889103	+	0.457707i	$0.151329\pi$
$390$	−3.30089	+	1.18583i	−0.167147	+	0.0600471i
$391$	−1.93756	+	21.5865i	−0.0979868	+	1.09167i
$392$	−11.3699	+	3.48845i	−0.574269	+	0.176193i
$393$	18.4949	−	7.56907i	0.932943	−	0.381809i
$394$	36.5813	+	12.4960i	1.84294	+	0.629538i
$395$	−1.04668	+	0.307332i	−0.0526641	+	0.0154636i
$396$	0.290928	−	12.0094i	0.0146197	−	0.603497i
$397$	−2.55415	−	0.749966i	−0.128189	−	0.0376397i	0.217009	−	0.976170i	$-0.430370\pi$
$397$	−2.55415	−	0.749966i	−0.128189	−	0.0376397i	−0.345198	+	0.938530i	$0.612188\pi$
$398$	−12.9680	−	16.3540i	−0.650029	−	0.819754i
$399$	3.22800	−	2.57877i	0.161602	−	0.129100i
$400$	−16.4822	−	8.16342i	−0.824109	−	0.408171i
$401$	8.40018	−	13.0709i	0.419485	−	0.652731i	−0.565624	−	0.824663i	$-0.691365\pi$
$401$	8.40018	−	13.0709i	0.419485	−	0.652731i	0.985109	+	0.171932i	$0.0550010\pi$
$402$	1.74232	+	8.50384i	0.0868990	+	0.424133i
$403$	−10.9614	−	1.57601i	−0.546025	−	0.0785065i
$404$	8.89588	−	22.7508i	0.442586	−	1.13190i
$405$	0.715908	+	5.65938i	0.0355737	+	0.281217i
$406$	5.76337	+	9.89015i	0.286031	+	0.490840i
$407$	13.5438	−	8.70406i	0.671340	−	0.431444i
$408$	21.4080	−	5.64352i	1.05985	−	0.279396i
$409$	−18.6006	+	21.4663i	−0.919741	+	1.06144i	0.0781764	+	0.996940i	$0.475090\pi$
$409$	−18.6006	+	21.4663i	−0.919741	+	1.06144i	−0.997918	+	0.0644986i	$0.979455\pi$
$410$	−7.01232	+	2.84017i	−0.346314	+	0.140266i
$411$	3.83197	−	20.7354i	0.189017	−	1.02280i
$412$	33.9181	−	12.0463i	1.67103	−	0.593480i
$413$		−	49.9039i		−	2.45561i
$414$	1.47648	+	20.2933i	0.0725650	+	0.997364i
$415$			7.44487i			0.365454i
$416$	7.62119	+	10.2583i	0.373660	+	0.502956i
$417$	4.51973	−	24.4569i	0.221332	−	1.19766i
$418$	−0.757469	−	1.87018i	−0.0370490	−	0.0914733i
$419$	−16.3739	+	18.8965i	−0.799919	+	0.923156i	−0.998377	−	0.0569535i	$-0.981861\pi$
$419$	−16.3739	+	18.8965i	−0.799919	+	0.923156i	0.198458	+	0.980109i	$0.436407\pi$
$420$	−1.16021	−	7.25751i	−0.0566123	−	0.354130i
$421$	−0.320765	+	0.206143i	−0.0156331	+	0.0100468i	−0.548434	−	0.836194i	$-0.684776\pi$
$421$	−0.320765	+	0.206143i	−0.0156331	+	0.0100468i	0.532801	+	0.846241i	$0.321139\pi$
$422$	31.6621	−	18.4507i	1.54129	−	0.898168i
$423$	5.02991	+	1.92483i	0.244563	+	0.0935884i
$424$	−8.44053	+	30.0874i	−0.409908	+	1.46118i
$425$	−20.5689	−	2.95735i	−0.997736	−	0.143453i
$426$	12.6108	−	2.58379i	0.610997	−	0.125185i
$427$	1.64652	−	2.56204i	0.0796808	−	0.123986i
$428$	15.9817	+	12.3608i	0.772503	+	0.597484i
$429$	6.12089	−	4.88984i	0.295519	−	0.236084i
$430$	5.63909	−	4.47155i	0.271941	−	0.215637i
$431$	−25.9929	−	7.63222i	−1.25204	−	0.367631i	−0.412511	−	0.910952i	$-0.635348\pi$
$431$	−25.9929	−	7.63222i	−1.25204	−	0.367631i	−0.839525	+	0.543321i	$0.817167\pi$
$432$	18.9790	−	8.47326i	0.913129	−	0.407670i
$433$	26.5919	−	7.80809i	1.27793	−	0.375233i	0.428789	−	0.903405i	$-0.358940\pi$
$433$	26.5919	−	7.80809i	1.27793	−	0.375233i	0.849138	+	0.528172i	$0.177122\pi$
$434$	7.50122	−	21.9594i	0.360070	−	1.05409i
$435$	−2.45685	+	1.00547i	−0.117797	+	0.0482087i
$436$	2.09394	−	0.421116i	0.100282	−	0.0201678i
$437$	1.58325	+	3.02871i	0.0757373	+	0.144883i
$438$	4.63227	+	12.8944i	0.221339	+	0.616118i
$439$	5.85606	−	0.841974i	0.279495	−	0.0401852i	−0.00114207	−	0.999999i	$-0.500364\pi$
$439$	5.85606	−	0.841974i	0.279495	−	0.0401852i	0.280637	+	0.959814i	$0.409454\pi$
$440$	−3.55875	−	0.467808i	−0.169657	−	0.0223019i
$441$	−8.99515	+	8.84380i	−0.428341	+	0.421133i
$442$	11.7947	+	8.32751i	0.561017	+	0.396099i
$443$	−1.96019	−	0.575565i	−0.0931316	−	0.0273459i	0.234835	−	0.972035i	$-0.424545\pi$
$443$	−1.96019	−	0.575565i	−0.0931316	−	0.0273459i	−0.327966	+	0.944689i	$0.606363\pi$
$444$	23.6671	+	14.6894i	1.12319	+	0.697126i
$445$	0.128306	+	0.280950i	0.00608227	+	0.0133183i
$446$	17.4568	−	18.4566i	0.826602	−	0.873944i
$447$	24.0211	+	8.10833i	1.13616	+	0.383511i
$448$	−24.0827	+	11.7103i	−1.13780	+	0.553262i
$449$	26.2162	+	3.76933i	1.23722	+	0.177885i	0.729708	−	0.683759i	$-0.239656\pi$
$449$	26.2162	+	3.76933i	1.23722	+	0.177885i	0.507513	+	0.861644i	$0.330565\pi$
$450$	−19.5051	+	0.377424i	−0.919479	+	0.0177920i
$451$	12.7713	−	11.0664i	0.601376	−	0.521096i
$452$	−25.8791	+	18.7447i	−1.21725	+	0.881678i
$453$	−9.21348	+	9.81218i	−0.432887	+	0.461017i
$454$	19.6856	+	3.71183i	0.923892	+	0.174205i
$455$	3.13881	−	3.62238i	0.147150	−	0.169820i
$456$	2.35874	−	2.57370i	0.110458	−	0.120525i
$457$	−6.18652	+	13.5466i	−0.289393	+	0.633682i	−0.997364	−	0.0725591i	$-0.976883\pi$
$457$	−6.18652	+	13.5466i	−0.289393	+	0.633682i	0.707971	+	0.706241i	$0.249611\pi$
$458$	−6.22020	−	25.1961i	−0.290651	−	1.17734i
$459$	17.3889	−	15.7813i	0.811642	−	0.736607i
$460$	6.07602	+	0.205779i	0.283296	+	0.00959447i
$461$		−	11.2247i		−	0.522789i	−0.965232	−	0.261394i	$-0.915818\pi$
$461$		−	11.2247i		−	0.522789i	0.965232	−	0.261394i	$-0.0841823\pi$
$462$	7.69247	+	14.5025i	0.357886	+	0.674718i
$463$	−17.2728	−	7.88822i	−0.802735	−	0.366597i	−0.0285790	−	0.999592i	$-0.509098\pi$
$463$	−17.2728	−	7.88822i	−0.802735	−	0.366597i	−0.774156	+	0.632995i	$0.781825\pi$
$464$	6.10086	+	7.50553i	0.283225	+	0.348436i
$465$	4.80201	+	2.42924i	0.222688	+	0.112654i
$466$	−1.27070	+	6.73915i	−0.0588642	+	0.312185i
$467$	−5.93860	+	3.81651i	−0.274806	+	0.176607i	−0.670784	−	0.741653i	$-0.734042\pi$
$467$	−5.93860	+	3.81651i	−0.274806	+	0.176607i	0.395978	+	0.918260i	$0.370406\pi$
$468$	12.1898	+	5.92778i	0.563475	+	0.274012i
$469$	−7.76820	−	8.96498i	−0.358702	−	0.413964i
$470$	0.731595	−	1.43326i	0.0337460	−	0.0661112i
$471$	−28.5083	+	2.94268i	−1.31359	+	0.135591i
$472$	−6.50547	−	41.6626i	−0.299439	−	1.91768i
$473$	−8.69078	+	13.5231i	−0.399603	+	0.621794i
$474$	3.67532	+	2.06504i	0.168813	+	0.0948506i
$475$	−2.98066	+	1.36122i	−0.136762	+	0.0624572i
$476$	−21.7273	+	21.0540i	−0.995868	+	0.965009i
$477$	6.77034	+	32.4457i	0.309992	+	1.48558i
$478$	−14.3054	+	20.2615i	−0.654313	+	0.926739i
$479$	25.7152	−	7.55066i	1.17496	−	0.344999i	0.364729	−	0.931114i	$-0.381162\pi$
$479$	25.7152	−	7.55066i	1.17496	−	0.344999i	0.810228	+	0.586115i	$0.199343\pi$
$480$	−1.91469	−	5.90773i	−0.0873934	−	0.269650i
$481$	2.58526	+	17.9809i	0.117878	+	0.819857i
$482$	9.10136	−	0.906121i	0.414556	−	0.0412727i
$483$	−15.3433	−	23.1887i	−0.698146	−	1.05512i
$484$	−13.7082	+	2.75688i	−0.623102	+	0.125313i
$485$	7.01497	−	1.00860i	0.318533	−	0.0457982i
$486$	13.7189	−	17.2567i	0.622300	−	0.782779i
$487$	0.814854	+	2.77514i	0.0369245	+	0.125753i	0.975893	−	0.218250i	$-0.0700349\pi$
$487$	0.814854	+	2.77514i	0.0369245	+	0.125753i	−0.938968	+	0.344004i	$0.888217\pi$
$488$	1.04062	−	2.35357i	0.0471067	−	0.106541i
$489$	−19.4396	−	0.776872i	−0.879089	−	0.0351314i
$490$	2.34183	+	2.95329i	0.105793	+	0.133416i
$491$	2.11047	+	4.62129i	0.0952443	+	0.208556i	0.951257	−	0.308398i	$-0.0997930\pi$
$491$	2.11047	+	4.62129i	0.0952443	+	0.208556i	−0.856013	+	0.516954i	$0.827066\pi$
$492$	26.7835	+	11.7263i	1.20750	+	0.528663i
$493$	9.19299	+	5.90798i	0.414032	+	0.266082i
$494$	2.27455	+	0.0991600i	0.102337	+	0.00446142i
$495$	−3.57822	+	1.30013i	−0.160829	+	0.0584366i
$496$	3.39980	−	19.3108i	0.152656	−	0.867080i
$497$	−13.2947	+	11.5199i	−0.596349	+	0.516739i
$498$	20.5892	−	20.0965i	0.922625	−	0.900545i
$499$	−12.7144	−	19.7840i	−0.569176	−	0.885655i	0.430682	−	0.902504i	$-0.358273\pi$
$499$	−12.7144	−	19.7840i	−0.569176	−	0.885655i	−0.999858	+	0.0168490i	$0.994637\pi$
$500$	−1.05887	+	12.1212i	−0.0473541	+	0.542076i
$501$	−1.28190	−	0.648486i	−0.0572709	−	0.0289722i
$502$	5.02469	−	2.03513i	0.224263	−	0.0908321i
$503$	−7.03255	+	15.3991i	−0.313566	+	0.686613i	−0.999143	−	0.0413863i	$-0.986823\pi$
$503$	−7.03255	+	15.3991i	−0.313566	+	0.686613i	0.685577	+	0.728000i	$0.259550\pi$
$504$	−16.9392	+	22.7993i	−0.754533	+	1.01556i
$505$	−7.74169			−0.344501
$506$	−12.9915	+	3.95211i	−0.577542	+	0.175693i
$507$	−3.32614	−	13.2663i	−0.147719	−	0.589178i
$508$	19.5827	−	6.95496i	0.868840	−	0.308576i
$509$	−34.5346	−	15.7714i	−1.53072	−	0.699055i	−0.540859	−	0.841113i	$-0.681901\pi$
$509$	−34.5346	−	15.7714i	−1.53072	−	0.699055i	−0.989858	+	0.142058i	$0.954628\pi$
$510$	−4.13640	−	5.66736i	−0.183163	−	0.250955i
$511$	−14.1502	−	12.2613i	−0.625970	−	0.542406i
$512$	−18.5790	+	12.9159i	−0.821085	+	0.570806i
$513$	0.961323	−	3.57588i	0.0424435	−	0.157879i
$514$	−22.7468	+	13.2554i	−1.00332	+	0.584672i
$515$	−7.47000	−	8.62084i	−0.329168	−	0.379880i
$516$	−27.5884	−	3.52486i	−1.21451	−	0.155173i
$517$	−0.511522	+	3.55771i	−0.0224967	+	0.156468i
$518$	−38.0294	−	1.65791i	−1.67092	−	0.0728443i
$519$	12.4844	+	4.21411i	0.548003	+	0.184979i
$520$	2.14824	−	3.43334i	0.0942065	−	0.150562i
$521$	19.8686	−	9.07369i	0.870460	−	0.397526i	0.0704521	−	0.997515i	$-0.477556\pi$
$521$	19.8686	−	9.07369i	0.870460	−	0.397526i	0.800008	+	0.599989i	$0.204829\pi$
$522$	9.41265	+	4.08042i	0.411980	+	0.178595i
$523$	−3.70332	+	12.6124i	−0.161935	+	0.551500i	0.838048	+	0.545597i	$0.183697\pi$
$523$	−3.70332	+	12.6124i	−0.161935	+	0.551500i	−0.999983	+	0.00590262i	$0.998121\pi$
$524$	−11.3761	+	20.0762i	−0.496968	+	0.877031i
$525$	22.9853	−	13.5063i	1.00316	−	0.589463i
$526$	0.412227	−	1.20677i	0.0179740	−	0.0526178i
$527$	−3.15267	−	21.9273i	−0.137333	−	0.955169i
$528$	8.31265	+	11.1047i	0.361762	+	0.483271i
$529$	21.2540	−	8.79030i	0.924085	−	0.382187i
$530$	9.85457	−	0.981109i	0.428055	−	0.0426167i
$531$	−26.4981	−	36.0306i	−1.14992	−	1.56359i
$532$	−1.08732	+	4.64519i	−0.0471414	+	0.201394i
$533$	5.37198	+	18.2953i	0.232686	+	0.792457i
$534$	0.430639	−	1.11323i	0.0186356	−	0.0481740i
$535$	1.80393	−	6.14362i	0.0779907	−	0.265612i
$536$	−7.65400	−	6.47180i	−0.330603	−	0.279539i
$537$	−14.7637	+	11.7944i	−0.637099	+	0.508964i
$538$	11.1721	−	11.8119i	0.481661	−	0.509248i
$539$	−7.08230	−	4.55152i	−0.305056	−	0.196048i
$540$	−4.69128	−	4.62386i	−0.201881	−	0.198979i
$541$	4.77593	−	33.2173i	0.205333	−	1.42812i	−0.582798	−	0.812617i	$-0.698042\pi$
$541$	4.77593	−	33.2173i	0.205333	−	1.42812i	0.788131	−	0.615508i	$-0.211049\pi$
$542$	11.6918	−	22.9051i	0.502204	−	0.983860i
$543$	−6.40982	+	9.14880i	−0.275072	+	0.392613i
$544$	−15.3945	+	20.4094i	−0.660035	+	0.875047i
$545$	−0.365955	−	0.569437i	−0.0156758	−	0.0243920i
$546$	−18.4907	+	1.09760i	−0.791330	+	0.0469728i
$547$	−7.62958	−	6.61107i	−0.326217	−	0.282669i	0.476318	−	0.879273i	$-0.341971\pi$
$547$	−7.62958	−	6.61107i	−0.326217	−	0.282669i	−0.802536	+	0.596604i	$0.796516\pi$
$548$	11.3313	+	21.5512i	0.484050	+	0.920621i
$549$	−0.171612	−	2.72406i	−0.00732422	−	0.116260i
$550$	−3.12055	−	12.6404i	−0.133061	−	0.538988i
$551$	1.72315			0.0734088
$552$	−15.8324	−	17.3591i	−0.673870	−	0.738850i
$553$	−5.76103			−0.244984
$554$	−0.590264	−	2.39098i	−0.0250779	−	0.101583i
$555$	1.60423	−	8.68074i	0.0680958	−	0.368477i
$556$	13.3651	+	25.4192i	0.566804	+	1.07801i
$557$	−3.97384	−	3.44335i	−0.168377	−	0.145900i	0.566596	−	0.823996i	$-0.308260\pi$
$557$	−3.97384	−	3.44335i	−0.168377	−	0.145900i	−0.734973	+	0.678096i	$0.762805\pi$
$558$	−6.24421	−	19.8377i	−0.264338	−	0.839796i
$559$	−9.80617	−	15.2587i	−0.414757	−	0.645374i
$560$	6.23573	+	5.75664i	0.263508	+	0.243263i
$561$	12.8351	+	8.99252i	0.541899	+	0.379664i
$562$	18.5447	−	36.3306i	0.782261	−	1.53252i
$563$	1.03426	−	7.19345i	0.0435889	−	0.303168i	−0.956351	−	0.292220i	$-0.905606\pi$
$563$	1.03426	−	7.19345i	0.0435889	−	0.303168i	0.999940	−	0.0109477i	$-0.00348485\pi$
$564$	−5.93860	+	1.84563i	−0.250060	+	0.0777148i
$565$	8.51929	+	5.47501i	0.358409	+	0.230335i
$566$	14.3120	−	15.1317i	0.601580	−	0.636034i
$567$	−4.79277	+	29.7426i	−0.201278	+	1.24907i
$568$	−9.59742	+	11.3506i	−0.402699	+	0.476259i
$569$	−12.8649	+	43.8138i	−0.539325	+	1.83677i	0.00817757	+	0.999967i	$0.497397\pi$
$569$	−12.8649	+	43.8138i	−0.539325	+	1.83677i	−0.547502	+	0.836804i	$0.684421\pi$
$570$	−1.03186	−	0.399164i	−0.0432199	−	0.0167191i
$571$	−5.86507	−	19.9746i	−0.245446	−	0.835911i	−0.986401	−	0.164357i	$-0.947445\pi$
$571$	−5.86507	−	19.9746i	−0.245446	−	0.835911i	0.740955	−	0.671554i	$-0.234373\pi$
$572$	−2.06177	+	8.80815i	−0.0862069	+	0.368287i
$573$	22.8640	−	9.35713i	0.955156	−	0.390900i
$574$	−39.7589	+	3.95835i	−1.65950	+	0.165218i
$575$	7.33094	+	20.7983i	0.305721	+	0.867349i
$576$	−11.1697	+	21.2424i	−0.465404	+	0.885098i
$577$	−1.87027	−	13.0080i	−0.0778602	−	0.541529i	−0.990998	−	0.133878i	$-0.957257\pi$
$577$	−1.87027	−	13.0080i	−0.0778602	−	0.541529i	0.913138	−	0.407651i	$-0.133652\pi$
$578$	−1.56483	+	4.58097i	−0.0650885	+	0.190543i
$579$	−11.7852	−	20.0562i	−0.489774	−	0.833507i
$580$	1.51120	−	2.66691i	0.0627490	−	0.110737i
$581$	−11.0770	+	37.7248i	−0.459552	+	1.56509i
$582$	−21.7254	−	16.6777i	−0.900546	−	0.691314i
$583$	−20.1212	+	9.18906i	−0.833337	+	0.380572i
$584$	−13.4118	−	8.39175i	−0.554984	−	0.347253i
$585$	0.342794	−	4.28201i	0.0141728	−	0.177039i
$586$	16.4912	+	0.718942i	0.681247	+	0.0296992i
$587$	0.144760	−	1.00683i	0.00597489	−	0.0415563i	−0.986616	−	0.163062i	$-0.947863\pi$
$587$	0.144760	−	1.00683i	0.00597489	−	0.0415563i	0.992591	+	0.121505i	$0.0387722\pi$
$588$	1.84603	−	14.4485i	0.0761291	−	0.595847i
$589$	−2.28755	−	2.63998i	−0.0942570	−	0.108778i
$590$	−11.5461	+	6.72837i	−0.475346	+	0.277003i
$591$	−32.4082	+	34.5141i	−1.33309	+	1.41972i
$592$	−31.9652	+	3.57340i	−1.31376	+	0.146866i
$593$	−2.01098	−	1.74253i	−0.0825813	−	0.0715571i	0.612592	−	0.790399i	$-0.290127\pi$
$593$	−2.01098	−	1.74253i	−0.0825813	−	0.0715571i	−0.695173	+	0.718842i	$0.744672\pi$
$594$	13.2545	+	6.38623i	0.543840	+	0.262030i
$595$	8.72172	+	3.98308i	0.357556	+	0.163290i
$596$	−27.5865	+	9.79760i	−1.12999	+	0.401325i
$597$	24.7950	−	6.21662i	1.01479	−	0.254429i
$598$	2.03315	−	15.1866i	0.0831415	−	0.621026i
$599$	37.0408			1.51345			0.756724	−	0.653735i	$-0.226799\pi$
$599$	37.0408			1.51345			0.756724	+	0.653735i	$0.226799\pi$
$600$	17.4287	−	14.2722i	0.711525	−	0.582659i
$601$	10.8272	−	23.7083i	0.441651	−	0.967080i	−0.549641	−	0.835401i	$-0.685236\pi$
$601$	10.8272	−	23.7083i	0.441651	−	0.967080i	0.991292	−	0.131680i	$-0.0420371\pi$
$602$	35.2277	−	14.2681i	1.43577	−	0.581525i
$603$	−10.3689	−	2.34792i	−0.422254	−	0.0956148i
$604$	1.35256	−	15.4831i	0.0550347	−	0.629999i
$605$	2.39576	+	3.72788i	0.0974017	+	0.151560i
$606$	20.8977	+	21.4101i	0.848912	+	0.869726i
$607$	11.6147	−	10.0642i	0.471425	−	0.408492i	−0.386482	−	0.922297i	$-0.626310\pi$
$607$	11.6147	−	10.0642i	0.471425	−	0.408492i	0.857907	+	0.513805i	$0.171764\pi$
$608$	−0.302211	+	4.01980i	−0.0122563	+	0.163025i
$609$	−13.9454	+	1.43947i	−0.565098	+	0.0583304i
$610$	−0.814765	−	0.0355200i	−0.0329889	−	0.00143816i
$611$	−3.41178	−	2.19262i	−0.138026	−	0.0887039i
$612$	−4.50773	+	26.7378i	−0.182214	+	1.08081i
$613$	0.479407	+	1.04975i	0.0193631	+	0.0423992i	0.919066	−	0.394103i	$-0.128945\pi$
$613$	0.479407	+	1.04975i	0.0193631	+	0.0423992i	−0.899703	+	0.436502i	$0.856217\pi$
$614$	9.55852	+	12.0543i	0.385750	+	0.486472i
$615$	0.370005	−	9.25861i	0.0149201	−	0.373343i
$616$	−17.3370	−	7.66546i	−0.698526	−	0.308850i
$617$	4.32432	+	14.7273i	0.174091	+	0.592898i	0.999594	+	0.0285007i	$0.00907328\pi$
$617$	4.32432	+	14.7273i	0.174091	+	0.592898i	−0.825503	+	0.564398i	$0.809109\pi$
$618$	−3.67711	+	43.9296i	−0.147915	+	1.76711i
$619$	12.4796	−	1.79429i	0.501597	−	0.0721188i	0.113128	−	0.993580i	$-0.463913\pi$
$619$	12.4796	−	1.79429i	0.501597	−	0.0721188i	0.388469	+	0.921462i	$0.373004\pi$
$620$	−6.09204	+	1.22518i	−0.244662	+	0.0492043i
$621$	−23.3907	−	8.59515i	−0.938635	−	0.344911i
$622$	26.0118	−	2.58970i	1.04298	−	0.103838i
$623$	0.232136	+	1.61454i	0.00930033	+	0.0646852i
$624$	−15.2940	+	3.32678i	−0.612250	+	0.133178i
$625$	−18.3601	+	5.39103i	−0.734406	+	0.215641i
$626$	−6.18064	+	8.75398i	−0.247028	+	0.349879i
$627$	2.46926	+	0.0986799i	0.0986127	+	0.00394090i
$628$	23.7659	−	23.0295i	0.948364	−	0.918977i
$629$	−33.0552	+	15.0958i	−1.31800	+	0.601909i
$630$	8.68428	+	2.36844i	0.345990	+	0.0943608i
$631$	−6.55479	+	10.1995i	−0.260942	+	0.406034i	−0.946860	−	0.321645i	$-0.895764\pi$
$631$	−6.55479	+	10.1995i	−0.260942	+	0.406034i	0.685918	+	0.727679i	$0.259401\pi$
$632$	−4.80963	+	0.751007i	−0.191317	+	0.0298735i
$633$	4.60830	+	44.6446i	0.183163	+	1.77446i
$634$	−18.1051	+	35.4694i	−0.719046	+	1.40867i
$635$	−4.31281	−	4.97725i	−0.171149	−	0.197516i
$636$	−29.3145	−	24.6050i	−1.16239	−	0.975652i
$637$	7.99125	−	5.13567i	0.316625	−	0.203483i
$638$	−1.26864	+	6.72818i	−0.0502258	+	0.266371i
$639$	−3.48187	+	15.3766i	−0.137741	+	0.608290i
$640$	5.95637	+	3.99308i	0.235446	+	0.157840i
$641$	−0.0514433	−	0.0234934i	−0.00203189	−	0.000927933i	0.414399	−	0.910095i	$-0.363992\pi$
$641$	−0.0514433	−	0.0234934i	−0.00203189	−	0.000927933i	−0.416431	+	0.909167i	$0.636719\pi$
$642$	−21.8600	+	11.5951i	−0.862746	+	0.457620i
$643$			26.9023i			1.06092i	0.847709	+	0.530462i	$0.177981\pi$
$643$			26.9023i			1.06092i	−0.847709	+	0.530462i	$0.822019\pi$
$644$	30.4824	+	10.0831i	1.20117	+	0.397328i
$645$	2.14357	+	8.54964i	0.0844032	+	0.336642i
$646$	1.09157	+	4.42163i	0.0429473	+	0.173967i
$647$	12.0641	−	26.4167i	0.474288	−	1.03855i	−0.509706	−	0.860349i	$-0.670246\pi$
$647$	12.0641	−	26.4167i	0.474288	−	1.03855i	0.983995	−	0.178198i	$-0.0570269\pi$
$648$	−0.124035	+	25.4555i	−0.00487256	+	0.999988i
$649$	19.5470	−	22.5584i	0.767286	−	0.885495i
$650$	14.4365	+	2.72208i	0.566245	+	0.106769i
$651$	20.7185	+	19.4543i	0.812021	+	0.762475i
$652$	18.1936	−	13.1780i	0.712518	−	0.516091i
$653$	16.1460	−	13.9906i	0.631841	−	0.547493i	−0.278979	−	0.960297i	$-0.589996\pi$
$653$	16.1460	−	13.9906i	0.631841	−	0.547493i	0.910820	+	0.412804i	$0.135451\pi$
$654$	−0.586962	+	2.54919i	−0.0229520	+	0.0996814i
$655$	7.23849	+	1.04074i	0.282831	+	0.0406650i
$656$	−32.6769	+	8.48761i	−1.27582	+	0.331385i
$657$	−16.7270	−	1.33907i	−0.652581	−	0.0522421i
$658$	5.83966	−	6.17412i	0.227654	−	0.240692i
$659$	5.94003	+	13.0069i	0.231391	+	0.506675i	0.989337	−	0.145641i	$-0.0465246\pi$
$659$	5.94003	+	13.0069i	0.231391	+	0.506675i	−0.757947	+	0.652316i	$0.773797\pi$
$660$	2.31825	−	3.73511i	0.0902379	−	0.145389i
$661$	−15.4076	−	4.52408i	−0.599287	−	0.175966i	−0.0320014	−	0.999488i	$-0.510188\pi$
$661$	−15.4076	−	4.52408i	−0.599287	−	0.175966i	−0.567285	+	0.823521i	$0.692006\pi$
$662$	28.8113	+	20.3419i	1.11978	+	0.790610i
$663$	−15.2459	+	8.95859i	−0.592102	+	0.347923i
$664$	−4.32990	+	32.9388i	−0.168033	+	1.27827i
$665$	1.49654	−	0.215169i	0.0580332	−	0.00834391i
$666$	−28.3375	+	18.9960i	−1.09806	+	0.736079i
$667$	1.03673	−	11.5503i	0.0401424	−	0.447228i
$668$	1.62627	−	0.327061i	0.0629223	−	0.0126544i
$669$	11.7847	+	28.7958i	0.455624	+	1.11331i
$670$	−1.02684	+	3.00602i	−0.0396703	+	0.116133i
$671$	1.74782	−	0.513206i	0.0674738	−	0.0198121i
$672$	−0.912243	−	32.7846i	−0.0351905	−	1.26469i
$673$	−26.7692	−	7.86014i	−1.03188	−	0.302986i	−0.278403	−	0.960464i	$-0.589805\pi$
$673$	−26.7692	−	7.86014i	−1.03188	−	0.302986i	−0.753474	+	0.657478i	$0.771623\pi$
$674$	36.4701	−	28.9192i	1.40478	−	1.11392i
$675$	9.42373	−	21.9563i	0.362720	−	0.845100i
$676$	12.4923	+	9.66201i	0.480472	+	0.371616i
$677$	27.5787	−	42.9134i	1.05994	−	1.64929i	0.363643	−	0.931538i	$-0.381533\pi$
$677$	27.5787	−	42.9134i	1.05994	−	1.64929i	0.696294	−	0.717756i	$-0.254831\pi$
$678$	−7.85527	−	38.3397i	−0.301680	−	1.47243i
$679$	37.0471	+	5.32657i	1.42174	+	0.204415i
$680$	7.80061	+	2.18833i	0.299140	+	0.0839187i
$681$	−14.0781	+	20.0938i	−0.539473	+	0.769995i
$682$	11.9922	−	6.98830i	0.459204	−	0.267596i
$683$	−0.694923	+	0.446600i	−0.0265905	+	0.0170887i	−0.553869	−	0.832604i	$-0.686849\pi$
$683$	−0.694923	+	0.446600i	−0.0265905	+	0.0170887i	0.527278	+	0.849693i	$0.323213\pi$
$684$	1.68147	+	3.93117i	0.0642926	+	0.150312i
$685$	5.05320	−	5.83170i	0.193073	−	0.222818i
$686$	−4.96733	−	12.2642i	−0.189654	−	0.468251i
$687$	31.2560	+	5.77623i	1.19249	+	0.220377i
$688$	27.5500	−	16.5041i	1.05034	−	0.629212i
$689$		−	24.9591i		−	0.950868i
$690$	−3.29641	+	6.67639i	−0.125492	+	0.254166i
$691$			3.43178i			0.130551i	0.997867	+	0.0652755i	$0.0207926\pi$
$691$			3.43178i			0.130551i	−0.997867	+	0.0652755i	$0.979207\pi$
$692$	−14.3374	+	5.09207i	−0.545028	+	0.193571i
$693$	−20.0661	+	1.26413i	−0.762247	+	0.0480205i
$694$	21.0686	−	8.53331i	0.799752	−	0.323920i
$695$	5.96014	−	6.87837i	0.226081	−	0.260911i
$696$	−11.4548	+	3.01968i	−0.434192	+	0.114461i
$697$	−32.0882	+	20.6218i	−1.21543	+	0.781107i
$698$	−19.4147	−	33.3162i	−0.734855	−	1.26104i
$699$	−6.87888	−	4.81947i	−0.260183	−	0.182289i
$700$	−11.2104	+	28.6703i	−0.423715	+	1.08363i
$701$	0.957326	+	0.137643i	0.0361577	+	0.00519869i	0.160370	−	0.987057i	$-0.448731\pi$
$701$	0.957326	+	0.137643i	0.0361577	+	0.00519869i	−0.124212	+	0.992256i	$0.539640\pi$
$702$	−12.7675	+	10.6107i	−0.481877	+	0.400476i
$703$	−3.09797	+	4.82053i	−0.116842	+	0.181810i
$704$	−15.4731	−	4.13950i	−0.583165	−	0.156013i
$705$	1.23012	+	1.53980i	0.0463288	+	0.0579924i
$706$	9.52314	+	12.0097i	0.358408	+	0.451991i
$707$	−39.2289	−	11.5186i	−1.47535	−	0.433203i
$708$	49.7750	+	13.7691i	1.87066	+	0.517473i
$709$	−45.9636	+	13.4961i	−1.72620	+	0.506858i	−0.986173	−	0.165718i	$-0.947006\pi$
$709$	−45.9636	+	13.4961i	−1.72620	+	0.506858i	−0.740028	+	0.672576i	$0.765188\pi$
$710$	4.45781	+	1.52276i	0.167298	+	0.0571483i
$711$	−4.15945	+	3.05901i	−0.155992	+	0.114722i
$712$	0.404271	+	1.31765i	0.0151507	+	0.0493809i
$713$	−19.0720	+	13.7451i	−0.714253	+	0.514758i
$714$	−12.5278	−	34.8722i	−0.468840	−	1.30506i
$715$	2.83772	−	0.408002i	0.106125	−	0.0152584i
$716$	4.97301	−	21.2454i	0.185850	−	0.793977i
$717$	−15.3895	−	26.1901i	−0.574731	−	0.978088i
$718$	−9.13651	+	12.9406i	−0.340972	+	0.482937i
$719$	16.0578	+	4.71500i	0.598856	+	0.175840i	0.567091	−	0.823655i	$-0.308069\pi$
$719$	16.0578	+	4.71500i	0.598856	+	0.175840i	0.0317653	+	0.999495i	$0.489887\pi$
$720$	7.55887	+	0.845221i	0.281703	+	0.0314995i
$721$	−25.0255	−	54.7982i	−0.931998	−	2.04079i
$722$	−18.9996	−	17.9704i	−0.707093	−	0.668790i
$723$	−3.58263	+	10.6136i	−0.133239	+	0.394724i
$724$	−0.717635	−	12.8789i	−0.0266707	−	0.478642i
$725$	11.0058	+	1.58239i	0.408744	+	0.0587685i
$726$	3.84261	−	16.6886i	0.142613	−	0.619371i
$727$	2.72140	−	2.35811i	0.100931	−	0.0874574i	−0.602933	−	0.797791i	$-0.706002\pi$
$727$	2.72140	−	2.35811i	0.100931	−	0.0874574i	0.703865	+	0.710334i	$0.251456\pi$
$728$	15.9940	−	14.2012i	0.592777	−	0.526332i
$729$	12.3324	+	24.0190i	0.456756	+	0.889592i
$730$	−0.929021	+	4.92704i	−0.0343846	+	0.182358i
$731$	23.7608	−	27.4214i	0.878823	−	1.01422i
$732$	2.10112	+	2.34916i	0.0776598	+	0.0868276i
$733$	−9.88241	+	21.6395i	−0.365015	+	0.799272i	0.634635	+	0.772812i	$0.281151\pi$
$733$	−9.88241	+	21.6395i	−0.365015	+	0.799272i	−0.999650	+	0.0264594i	$0.991577\pi$
$734$	−30.4002	+	7.50492i	−1.12209	+	0.277012i
$735$	−4.47760	+	1.12263i	−0.165159	+	0.0414088i
$736$	26.7628	+	4.44422i	0.986491	+	0.163816i
$737$		−	7.09525i		−	0.261357i
$738$	−26.6040	+	23.9692i	−0.979308	+	0.882318i
$739$	28.7388	+	13.1246i	1.05717	+	0.482795i	0.866665	−	0.498890i	$-0.166259\pi$
$739$	28.7388	+	13.1246i	1.05717	+	0.482795i	0.190509	+	0.981685i	$0.438986\pi$
$740$	4.74379	+	9.02228i	0.174385	+	0.331666i
$741$	−1.25870	+	2.48813i	−0.0462394	+	0.0914038i
$742$	51.3951	+	9.69083i	1.88677	+	0.355762i
$743$	−20.3641	+	13.0872i	−0.747085	+	0.480122i	−0.857963	−	0.513712i	$-0.828270\pi$
$743$	−20.3641	+	13.0872i	−0.747085	+	0.480122i	0.110878	+	0.993834i	$0.464634\pi$
$744$	19.8330	+	13.5407i	0.727113	+	0.496426i
$745$	6.07555	+	7.01156i	0.222591	+	0.256884i
$746$	32.7910	+	16.7379i	1.20056	+	0.612819i
$747$	12.0337	+	33.1190i	0.440289	+	1.21176i
$748$	−18.0682	+	1.00679i	−0.660640	+	0.0368119i
$749$	18.2818	−	28.4471i	0.668004	−	1.03943i
$750$	−12.9917	−	7.29959i	−0.474388	−	0.266543i
$751$	−39.3854	+	17.9867i	−1.43719	+	0.656344i	−0.973298	−	0.229545i	$-0.926276\pi$
$751$	−39.3854	+	17.9867i	−1.43719	+	0.656344i	−0.463896	+	0.885890i	$0.653549\pi$
$752$	4.07042	−	5.91575i	0.148433	−	0.215725i
$753$	−0.265128	+	6.63427i	−0.00966179	+	0.241766i
$754$	−6.31099	−	4.45580i	−0.229833	−	0.162271i
$755$	−4.72601	+	1.38768i	−0.171997	+	0.0505029i
$756$	−16.8921	−	30.4102i	−0.614359	−	1.10601i
$757$	−4.76789	−	33.1614i	−0.173292	−	1.20527i	−0.871870	−	0.489737i	$-0.837093\pi$
$757$	−4.76789	−	33.1614i	−0.173292	−	1.20527i	0.698578	−	0.715534i	$-0.253816\pi$
$758$	0.327670	+	3.29122i	0.0119015	+	0.119543i
$759$	2.14707	−	16.4920i	0.0779338	−	0.598622i
$760$	1.22134	−	0.374724i	0.0443027	−	0.0135927i
$761$	19.5135	−	2.80562i	0.707364	−	0.101704i	0.220763	−	0.975328i	$-0.429145\pi$
$761$	19.5135	−	2.80562i	0.707364	−	0.101704i	0.486602	+	0.873624i	$0.338236\pi$
$762$	−2.12298	+	25.3628i	−0.0769075	+	0.918797i
$763$	−1.00713	−	3.42996i	−0.0364605	−	0.124173i
$764$	−14.0635	+	24.8188i	−0.508800	+	0.897913i
$765$	8.41202	−	1.75531i	0.304137	−	0.0634634i
$766$	−22.8947	+	18.1545i	−0.827218	+	0.655947i
$767$	13.9912	+	30.6364i	0.505191	+	1.10621i
$768$	−5.03539	−	27.2515i	−0.181699	−	0.983354i
$769$	39.9710	+	25.6878i	1.44139	+	0.926326i	0.999573	+	0.0292214i	$0.00930277\pi$
$769$	39.9710	+	25.6878i	1.44139	+	0.926326i	0.441818	+	0.897105i	$0.354334\pi$
$770$	−0.261649	+	6.00175i	−0.00942917	+	0.216288i
$771$	−3.31071	−	32.0737i	−0.119232	−	1.15511i
$772$	25.0167	+	9.78186i	0.900372	+	0.352057i
$773$	−11.1126	+	9.62909i	−0.399691	+	0.346334i	−0.831396	−	0.555681i	$-0.812458\pi$
$773$	−11.1126	+	9.62909i	−0.399691	+	0.346334i	0.431705	+	0.902015i	$0.357912\pi$
$774$	17.8582	−	29.0069i	0.641900	−	1.04263i
$775$	−12.1863	−	18.9622i	−0.437744	−	0.681143i
$776$	31.6234	−	0.382542i	1.13521	−	0.0137325i
$777$	21.0448	−	41.6004i	0.754979	−	1.49241i
$778$	−17.0659	−	42.1354i	−0.611843	−	1.51063i
$779$	−2.49858	+	5.47114i	−0.0895211	+	0.196024i
$780$	2.74699	+	4.13016i	0.0983579	+	0.147883i
$781$	−10.5220			−0.376505
$782$	30.2948	−	4.65651i	1.08334	−	0.166517i
$783$	−9.30425	+	8.44409i	−0.332507	+	0.301767i
$784$	8.64348	+	14.4284i	0.308696	+	0.515302i
$785$	−9.54007	−	4.35681i	−0.340500	−	0.155501i
$786$	−16.6612	−	22.8278i	−0.594284	−	0.814240i
$787$	20.2390	+	17.5372i	0.721443	+	0.625134i	0.936173	−	0.351539i	$-0.114342\pi$
$787$	20.2390	+	17.5372i	0.721443	+	0.625134i	−0.214730	+	0.976674i	$0.568887\pi$
$788$	4.75758	−	54.4615i	0.169482	−	1.94011i
$789$	1.13858	+	1.06911i	0.0405345	+	0.0380612i
$790$	0.776739	+	1.33291i	0.0276351	+	0.0474228i
$791$	35.0230	+	40.4188i	1.24528	+	1.43713i
$792$	−16.5875	+	3.67118i	−0.589411	+	0.130450i
$793$	−0.292513	+	2.03447i	−0.0103874	+	0.0722463i
$794$	−0.163964	+	3.76103i	−0.00581885	+	0.133474i
$795$	−3.87912	+	11.4920i	−0.137578	+	0.407578i
$796$	−18.0585	+	23.3483i	−0.640065	+	0.827557i
$797$	26.6591	−	12.1748i	0.944315	−	0.431254i	0.117088	−	0.993122i	$-0.462644\pi$
$797$	26.6591	−	12.1748i	0.944315	−	0.431254i	0.827227	+	0.561868i	$0.189917\pi$
$798$	−4.63478	−	3.55794i	−0.164069	−	0.125950i
$799$	2.28566	−	7.78425i	0.0808609	−	0.275387i
$800$	−5.62165	+	25.3969i	−0.198755	+	0.897917i
$801$	1.02490	+	1.04244i	0.0362129	+	0.0368327i
$802$	−20.7936	−	7.10297i	−0.734246	−	0.250815i
$803$	−1.59379	−	11.0851i	−0.0562438	−	0.391184i
$804$	11.0852	−	5.27459i	0.390943	−	0.186020i
$805$	−0.541888	−	10.1607i	−0.0190990	−	0.358118i
$806$	1.55153	+	15.5841i	0.0546504	+	0.548926i
$807$	7.54204	+	18.4288i	0.265492	+	0.648725i
$808$	−34.2520	−	4.50253i	−1.20498	−	0.158398i
$809$	1.01119	+	3.44378i	0.0355514	+	0.121077i	0.975357	−	0.220633i	$-0.0708122\pi$
$809$	1.01119	+	3.44378i	0.0355514	+	0.121077i	−0.939806	+	0.341710i	$0.888994\pi$
$810$	7.52764	−	2.90120i	0.264494	−	0.101938i
$811$	−6.81745	+	23.2181i	−0.239393	+	0.815298i	0.748894	+	0.662690i	$0.230585\pi$
$811$	−6.81745	+	23.2181i	−0.239393	+	0.815298i	−0.988287	+	0.152608i	$0.951233\pi$
$812$	11.6256	−	11.2654i	0.407979	−	0.395337i
$813$	19.6587	+	24.6079i	0.689461	+	0.863037i
$814$	−16.5413	−	15.6453i	−0.579773	−	0.548366i
$815$	−5.98927	−	3.84907i	−0.209795	−	0.134827i
$816$	−15.0048	−	27.4802i	−0.525274	−	0.961999i
$817$	0.814245	−	5.66320i	0.0284868	−	0.198130i
$818$	35.7778	+	18.2625i	1.25094	+	0.638533i
$819$	8.10810	−	21.1879i	0.283320	−	0.740364i
$820$	6.27638	+	8.66519i	0.219181	+	0.302602i
$821$	−6.61086	−	10.2867i	−0.230721	−	0.359008i	0.706519	−	0.707694i	$-0.250264\pi$
$821$	−6.61086	−	10.2867i	−0.230721	−	0.359008i	−0.937240	+	0.348686i	$0.886628\pi$
$822$	−29.7684	+	1.76703i	−1.03829	+	0.0616323i
$823$	−0.0568924	−	0.0492976i	−0.00198315	−	0.00171841i	0.653869	−	0.756608i	$-0.273145\pi$
$823$	−0.0568924	−	0.0492976i	−0.00198315	−	0.00171841i	−0.655852	+	0.754890i	$0.727690\pi$
$824$	−28.0362	−	42.4863i	−0.976686	−	1.48008i
$825$	15.6805	+	2.89781i	0.545926	+	0.100889i
$826$	−68.5178	+	16.9150i	−2.38404	+	0.588550i
$827$	−27.7068			−0.963461			−0.481731	−	0.876319i	$-0.659992\pi$
$827$	−27.7068			−0.963461			−0.481731	+	0.876319i	$0.659992\pi$
$828$	27.3622	−	8.90567i	0.950902	−	0.309494i
$829$	37.5877			1.30547			0.652737	−	0.757584i	$-0.273621\pi$
$829$	37.5877			1.30547			0.652737	+	0.757584i	$0.273621\pi$
$830$	10.2218	−	2.52345i	0.354802	−	0.0875904i
$831$	2.96603	+	0.548133i	0.102891	+	0.0190145i
$832$	11.5014	−	13.9409i	0.398739	−	0.483315i
$833$	14.3611	+	12.4439i	0.497581	+	0.431157i
$834$	−35.1112	+	2.08418i	−1.21580	+	0.0721691i
$835$	−0.284220	−	0.442255i	−0.00983585	−	0.0153049i
$836$	−2.31099	+	1.67390i	−0.0799274	+	0.0578931i
$837$	25.2886	+	3.04483i	0.874103	+	0.105245i
$838$	31.4948	+	16.0763i	1.08797	+	0.555346i
$839$	−0.311859	+	2.16903i	−0.0107666	+	0.0748831i	−0.994496	−	0.104771i	$-0.966589\pi$
$839$	−0.311859	+	2.16903i	−0.0107666	+	0.0748831i	0.983730	+	0.179655i	$0.0574980\pi$
$840$	−9.57126	+	4.05290i	−0.330240	+	0.139838i
$841$	19.4775	+	12.5174i	0.671637	+	0.431635i
$842$	0.391758	+	0.370536i	0.0135009	+	0.0127695i
$843$	31.1814	+	39.0315i	1.07394	+	1.34431i
$844$	−36.0647	−	37.2179i	−1.24140	−	1.28109i
$845$	1.41006	−	4.80224i	0.0485077	−	0.165202i
$846$	0.937877	−	7.55846i	0.0322449	−	0.259865i
$847$	6.59327	+	22.4546i	0.226548	+	0.771550i
$848$	44.1708	+	1.39058i	1.51683	+	0.0477529i
$849$	9.66178	+	23.6084i	0.331592	+	0.810238i
$850$	2.91143	+	29.2433i	0.0998612	+	1.00304i
$851$	30.4480	+	23.6659i	1.04375	+	0.811256i
$852$	−7.82200	−	16.4388i	−0.267977	−	0.563185i
$853$	−1.30029	−	9.04372i	−0.0445211	−	0.309651i	−0.999898	−	0.0142624i	$-0.995460\pi$
$853$	−1.30029	−	9.04372i	−0.0445211	−	0.309651i	0.955377	−	0.295389i	$-0.0954491\pi$
$854$	−4.07575	−	1.39226i	−0.139469	−	0.0476420i
$855$	0.966246	−	0.949987i	0.0330449	−	0.0324889i
$856$	11.5543	−	26.1325i	0.394919	−	0.893189i
$857$	−12.0757	+	41.1260i	−0.412497	+	1.40484i	0.447383	+	0.894342i	$0.352356\pi$
$857$	−12.0757	+	41.1260i	−0.412497	+	1.40484i	−0.859881	+	0.510495i	$0.829462\pi$
$858$	−8.78841	−	6.74652i	−0.300031	−	0.230322i
$859$	37.4168	−	17.0877i	1.27664	−	0.583024i	0.342366	−	0.939567i	$-0.388772\pi$
$859$	37.4168	−	17.0877i	1.27664	−	0.583024i	0.934279	+	0.356542i	$0.116044\pi$
$860$	−8.05079	−	6.22680i	−0.274530	−	0.212332i
$861$	15.6505	−	46.3650i	0.533369	−	1.58011i
$862$	−1.66862	+	38.2751i	−0.0568334	+	1.30366i
$863$	5.21860	−	36.2961i	0.177643	−	1.23554i	−0.684554	−	0.728962i	$-0.740003\pi$
$863$	5.21860	−	36.2961i	0.177643	−	1.23554i	0.862197	−	0.506573i	$-0.169088\pi$
$864$	−18.0667	−	23.1861i	−0.614642	−	0.788806i
$865$	3.15762	+	3.64409i	0.107362	+	0.123903i
$866$	−19.7339	−	33.8640i	−0.670584	−	1.15074i
$867$	−4.32210	−	4.05838i	−0.146786	−	0.137830i
$868$	−32.6927	−	2.85593i	−1.10966	−	0.0969366i
$869$	−2.60420	−	2.25655i	−0.0883414	−	0.0765482i
$870$	2.21326	+	3.03243i	0.0750366	+	0.102809i
$871$	7.28239	+	3.32576i	0.246754	+	0.112689i
$872$	−1.28794	−	2.73223i	−0.0436150	−	0.0925251i
$873$	29.5763	−	15.8256i	1.00101	−	0.535616i
$874$	3.62176	−	3.20039i	0.122508	−	0.108255i
$875$	20.3643			0.688438
$876$	16.1338	−	10.7307i	0.545110	−	0.362556i
$877$	−7.76387	+	17.0005i	−0.262167	+	0.574066i	−0.994242	−	0.107158i	$-0.965825\pi$
$877$	−7.76387	+	17.0005i	−0.262167	+	0.574066i	0.732075	+	0.681224i	$0.238552\pi$
$878$	−3.14095	−	7.75494i	−0.106002	−	0.261717i
$879$	−9.12597	+	18.0398i	−0.307811	+	0.608467i
$880$	0.563949	+	5.04471i	0.0190107	+	0.170057i
$881$	−12.7173	−	19.7885i	−0.428456	−	0.666690i	0.558164	−	0.829731i	$-0.311506\pi$
$881$	−12.7173	−	19.7885i	−0.428456	−	0.666690i	−0.986619	+	0.163041i	$0.947870\pi$
$882$	15.1914	+	9.35266i	0.511521	+	0.314921i
$883$	16.6146	−	14.3966i	0.559126	−	0.484486i	−0.328846	−	0.944384i	$-0.606660\pi$
$883$	16.6146	−	14.3966i	0.559126	−	0.484486i	0.887972	+	0.459898i	$0.152114\pi$
$884$	7.43577	−	19.0167i	0.250092	−	0.639601i
$885$	−1.68049	−	16.2804i	−0.0564892	−	0.547260i
$886$	−0.125835	+	2.88642i	−0.00422750	+	0.0969712i
$887$	−43.3141	−	27.8363i	−1.45435	−	0.934652i	−0.999017	−	0.0443285i	$-0.985885\pi$
$887$	−43.3141	−	27.8363i	−1.45435	−	0.934652i	−0.455329	−	0.890323i	$-0.650478\pi$
$888$	12.1464	−	37.4737i	0.407606	−	1.25754i
$889$	−14.4485	−	31.6378i	−0.484587	−	1.06110i
$890$	0.342253	−	0.271391i	0.0114723	−	0.00909706i
$891$	−13.8164	+	11.5675i	−0.462868	+	0.387524i
$892$	−31.2578	−	17.7121i	−1.04659	−	0.593047i
$893$	−0.360418	−	1.22747i	−0.0120609	−	0.0410757i
$894$	2.99069	−	35.7291i	0.100024	−	1.19496i
$895$	−6.84461	+	0.984106i	−0.228790	+	0.0328950i
$896$	24.2411	+	29.0962i	0.809839	+	0.972035i
$897$	15.9206	+	9.93401i	0.531573	+	0.331687i
$898$	−3.71079	−	37.2723i	−0.123831	−	1.24379i
$899$	1.68690	+	11.7326i	0.0562612	+	0.391305i
$900$	7.12950	+	26.6525i	0.237650	+	0.888415i
$901$	47.9062	−	14.0665i	1.59599	−	0.468624i
$902$	−19.5229	−	13.7839i	−0.650042	−	0.458954i
$903$	−1.85879	+	46.5123i	−0.0618566	+	1.54783i
$904$	34.5082	+	29.1782i	1.14772	+	0.970453i
$905$	−3.71846	+	1.69816i	−0.123606	+	0.0564488i
$906$	16.5950	+	9.32419i	0.551332	+	0.309775i
$907$	6.64723	−	10.3433i	0.220718	−	0.343443i	−0.713182	−	0.700979i	$-0.752747\pi$
$907$	6.64723	−	10.3433i	0.220718	−	0.343443i	0.933899	+	0.357536i	$0.116383\pi$
$908$	−1.57616	−	28.2864i	−0.0523067	−	0.938716i
$909$	−34.4394	+	12.5134i	−1.14228	+	0.415044i
$910$	−6.03741	−	3.08175i	−0.200138	−	0.102159i
$911$	4.61847	+	5.32999i	0.153017	+	0.176591i	0.827082	−	0.562081i	$-0.189999\pi$
$911$	4.61847	+	5.32999i	0.153017	+	0.176591i	−0.674066	+	0.738671i	$0.735454\pi$
$912$	−4.33318	−	2.36617i	−0.143486	−	0.0783518i
$913$	−19.7837	+	12.7142i	−0.654747	+	0.420780i
$914$	20.6963	+	3.90240i	0.684573	+	0.129080i
$915$	0.450877	−	0.891272i	0.0149055	−	0.0294645i
$916$	−32.4858	+	17.0806i	−1.07336	+	0.564358i
$917$	35.1306	+	16.0436i	1.16011	+	0.529806i
$918$	−27.5616	−	18.5257i	−0.909668	−	0.611439i
$919$			3.87984i			0.127984i	0.997950	+	0.0639921i	$0.0203833\pi$
$919$			3.87984i			0.127984i	−0.997950	+	0.0639921i	$0.979617\pi$
$920$	−1.77695	−	8.41208i	−0.0585842	−	0.277338i
$921$	−18.2760	+	4.58217i	−0.602213	+	0.150988i
$922$	−15.4115	+	3.80465i	−0.507551	+	0.125300i
$923$	4.93196	−	10.7995i	0.162337	−	0.355469i
$924$	17.3045	−	15.4774i	0.569276	−	0.509168i
$925$	−24.2134	+	27.9438i	−0.796133	+	0.918787i
$926$	−4.97583	+	26.3892i	−0.163516	+	0.867202i
$927$	−47.1653	−	26.2761i	−1.54911	−	0.863021i
$928$	8.23715	−	10.9205i	0.270398	−	0.358482i
$929$	8.70066	−	7.53916i	0.285459	−	0.247352i	−0.500346	−	0.865825i	$-0.666794\pi$
$929$	8.70066	−	7.53916i	0.285459	−	0.247352i	0.785806	+	0.618473i	$0.212249\pi$
$930$	1.70769	−	7.41653i	0.0559972	−	0.243198i
$931$	2.96592	+	0.426435i	0.0972041	+	0.0139758i
$932$	9.68352	−	0.539581i	0.317194	−	0.0176746i
$933$	−10.2392	+	30.3338i	−0.335216	+	0.993083i
$934$	7.25295	+	6.86005i	0.237324	+	0.224468i
$935$	2.38240	+	5.21673i	0.0779128	+	0.170605i
$936$	4.00704	−	18.7458i	0.130974	−	0.612725i
$937$	−44.2662	−	12.9977i	−1.44611	−	0.424617i	−0.537859	−	0.843035i	$-0.680767\pi$
$937$	−44.2662	−	12.9977i	−1.44611	−	0.424617i	−0.908255	+	0.418418i	$0.862585\pi$
$938$	−9.67581	+	13.7044i	−0.315927	+	0.447464i
$939$	−6.64902	−	11.3154i	−0.216983	−	0.369265i
$940$	−2.21583	−	0.518670i	−0.0722723	−	0.0169171i
$941$	3.16822	−	0.455522i	0.103281	−	0.0148496i	−0.0904804	−	0.995898i	$-0.528840\pi$
$941$	3.16822	−	0.455522i	0.103281	−	0.0148496i	0.193762	+	0.981049i	$0.437931\pi$
$942$	13.7032	+	38.1443i	0.446475	+	1.24281i
$943$	35.1696	+	20.0396i	1.14528	+	0.652581i
$944$	−54.9974	+	23.0536i	−1.79001	+	0.750331i
$945$	−7.02621	+	8.49540i	−0.228563	+	0.276355i
$946$	21.5129	+	7.34870i	0.699445	+	0.238927i
$947$	−17.0328	+	5.00129i	−0.553493	+	0.162520i	−0.546506	−	0.837455i	$-0.684042\pi$
$947$	−17.0328	+	5.00129i	−0.553493	+	0.162520i	−0.00698736	+	0.999976i	$0.502224\pi$
$948$	1.58953	−	5.74614i	0.0516257	−	0.186626i
$949$	12.1245	+	3.56008i	0.393578	+	0.115565i
$950$	2.87925	+	3.63104i	0.0934153	+	0.117807i
$951$	−30.4422	−	38.1062i	−0.987157	−	1.23568i
$952$	36.2715	+	22.6951i	1.17557	+	0.735552i
$953$	−23.5590	+	36.6586i	−0.763152	+	1.18749i	0.214390	+	0.976748i	$0.431224\pi$
$953$	−23.5590	+	36.6586i	−0.763152	+	1.18749i	−0.977542	+	0.210740i	$0.932413\pi$
$954$	42.2529	−	20.2932i	1.36799	−	0.657015i
$955$	8.94845	+	1.28659i	0.289565	+	0.0416332i
$956$	32.6678	+	12.7735i	1.05655	+	0.413125i
$957$	−6.86768	−	4.81162i	−0.222001	−	0.155538i
$958$	−19.0832	−	32.7475i	−0.616551	−	1.05802i
$959$	34.2825	−	22.0321i	1.10704	−	0.711452i
$960$	−7.46228	+	4.63130i	−0.240844	+	0.149475i
$961$	−4.56497	+	5.26825i	−0.147257	+	0.169944i
$962$	23.8113	−	9.64420i	0.767708	−	0.310941i
$963$	−1.90546	−	30.2461i	−0.0614027	−	0.974668i
$964$	−4.32903	−	12.1890i	−0.139429	−	0.392581i
$965$		−	8.51273i		−	0.274034i
$966$	−26.6373	+	28.9262i	−0.857040	+	0.930684i
$967$			0.984345i			0.0316544i	0.999875	+	0.0158272i	$0.00503816\pi$
$967$			0.984345i			0.0316544i	−0.999875	+	0.0158272i	$0.994962\pi$
$968$	8.43162	+	17.8869i	0.271002	+	0.574906i
$969$	−5.48507	−	1.01366i	−0.176206	−	0.0325634i
$970$	−3.76254	−	9.28964i	−0.120808	−	0.298272i
$971$	29.8162	−	34.4097i	0.956847	−	1.10426i	−0.0376289	−	0.999292i	$-0.511980\pi$
$971$	29.8162	−	34.4097i	0.956847	−	1.10426i	0.994476	−	0.104968i	$-0.0334741\pi$
$972$	−28.3433	−	12.9867i	−0.909113	−	0.416549i
$973$	40.4355	−	25.9863i	1.29630	−	0.833084i
$974$	3.53405	−	2.05943i	0.113238	−	0.0659883i
$975$	−10.3242	+	14.7358i	−0.330638	+	0.471924i
$976$	−3.58416	−	0.631017i	−0.114726	−	0.0201984i
$977$	−20.4952	−	2.94677i	−0.655700	−	0.0942754i	−0.193568	−	0.981087i	$-0.562006\pi$
$977$	−20.4952	−	2.94677i	−0.655700	−	0.0942754i	−0.462132	+	0.886811i	$0.652915\pi$
$978$	5.52245	+	26.9538i	0.176589	+	0.861886i
$979$	−0.527469	+	0.820758i	−0.0168580	+	0.0262315i
$980$	3.26109	−	4.21634i	0.104172	−	0.134686i
$981$	−2.54840	−	1.94166i	−0.0813641	−	0.0619925i
$982$	5.62965	−	4.46406i	0.179649	−	0.142454i
$983$	−21.0695	−	6.18657i	−0.672013	−	0.197321i	−0.0721140	−	0.997396i	$-0.522975\pi$
$983$	−21.0695	−	6.18657i	−0.672013	−	0.197321i	−0.599899	+	0.800075i	$0.704793\pi$
$984$	7.02180	−	40.7483i	0.223847	−	1.29901i
$985$	−16.6236	+	4.88114i	−0.529673	+	0.155526i
$986$	4.99563	−	14.6244i	0.159093	−	0.465737i
$987$	3.94224	+	9.63279i	0.125483	+	0.306615i
$988$	−0.634818	−	3.15656i	−0.0201963	−	0.100423i
$989$	−37.4704	−	8.86512i	−1.19149	−	0.281894i
$990$	2.99792	+	4.47219i	0.0952801	+	0.142135i
$991$	33.8137	−	4.86167i	1.07413	−	0.154436i	0.417519	−	0.908668i	$-0.362900\pi$
$991$	33.8137	−	4.86167i	1.07413	−	0.154436i	0.656608	+	0.754232i	$0.271991\pi$
$992$	−27.6660	+	1.87753i	−0.878396	+	0.0596116i
$993$	−37.2417	+	21.8834i	−1.18183	+	0.694450i
$994$	20.3230	+	14.3488i	0.644608	+	0.455117i
$995$	8.97547	+	2.63543i	0.284541	+	0.0835489i
$996$	−34.5711	−	21.4571i	−1.09543	−	0.679895i
$997$	2.14359	+	4.69380i	0.0678881	+	0.148654i	0.940534	−	0.339699i	$-0.110325\pi$
$997$	2.14359	+	4.69380i	0.0678881	+	0.148654i	−0.872646	+	0.488353i	$0.837598\pi$
$998$	−22.8538	+	24.1627i	−0.723423	+	0.764856i
$999$	−6.89476	−	41.2099i	−0.218140	−	1.30382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.95.19	✓	440
3.2	odd	2	inner	276.2.o.a.95.26	yes	440
4.3	odd	2	inner	276.2.o.a.95.23	yes	440
12.11	even	2	inner	276.2.o.a.95.22	yes	440
23.8	even	11	inner	276.2.o.a.215.22	yes	440
69.8	odd	22	inner	276.2.o.a.215.23	yes	440
92.31	odd	22	inner	276.2.o.a.215.26	yes	440
276.215	even	22	inner	276.2.o.a.215.19	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.95.19	✓	440	1.1	even	1	trivial
276.2.o.a.95.22	yes	440	12.11	even	2	inner
276.2.o.a.95.23	yes	440	4.3	odd	2	inner
276.2.o.a.95.26	yes	440	3.2	odd	2	inner
276.2.o.a.215.19	yes	440	276.215	even	22	inner
276.2.o.a.215.22	yes	440	23.8	even	11	inner
276.2.o.a.215.23	yes	440	69.8	odd	22	inner
276.2.o.a.215.26	yes	440	92.31	odd	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.338952 - 1.37299i) q^{2} +(1.70321 + 0.314759i) q^{3} +(-1.77022 + 0.930758i) q^{4} +(0.479018 + 0.415071i) q^{5} +(-0.145145 - 2.44519i) q^{6} +(1.80972 + 2.81598i) q^{7} +(1.87795 + 2.11502i) q^{8} +(2.80185 + 1.07220i) q^{9} +O(q^{10})\)	\(q+(-0.338952 - 1.37299i) q^{2} +(1.70321 + 0.314759i) q^{3} +(-1.77022 + 0.930758i) q^{4} +(0.479018 + 0.415071i) q^{5} +(-0.145145 - 2.44519i) q^{6} +(1.80972 + 2.81598i) q^{7} +(1.87795 + 2.11502i) q^{8} +(2.80185 + 1.07220i) q^{9} +(0.407526 - 0.798378i) q^{10} +(-0.284937 + 1.98178i) q^{11} +(-3.30803 + 1.02808i) q^{12} +(-1.90049 - 1.22137i) q^{13} +(3.25291 - 3.43922i) q^{14} +(0.685221 + 0.857730i) q^{15} +(2.26738 - 3.29530i) q^{16} +(1.27320 - 4.33612i) q^{17} +(0.522433 - 4.21035i) q^{18} +(-0.200766 - 0.683747i) q^{19} +(-1.23430 - 0.288919i) q^{20} +(2.19598 + 5.36583i) q^{21} +(2.81755 - 0.280512i) q^{22} +(-4.70393 + 0.934357i) q^{23} +(2.53282 + 4.19343i) q^{24} +(-0.654400 - 4.55145i) q^{25} +(-1.03276 + 3.02335i) q^{26} +(4.43466 + 2.70810i) q^{27} +(-5.82461 - 3.30050i) q^{28} +(-0.681251 + 2.32013i) q^{29} +(0.945400 - 1.23153i) q^{30} +(4.45897 - 2.03634i) q^{31} +(-5.29296 - 1.99615i) q^{32} +(-1.10909 + 3.28570i) q^{33} +(-6.38502 - 0.278358i) q^{34} +(-0.301944 + 2.10007i) q^{35} +(-5.95787 + 0.709811i) q^{36} +(-5.26579 - 6.07704i) q^{37} +(-0.870730 + 0.507408i) q^{38} +(-2.85250 - 2.67845i) q^{39} +(0.0216849 + 1.79262i) q^{40} +(-6.37875 - 5.52722i) q^{41} +(6.62292 - 4.83383i) q^{42} +(7.30327 + 3.33529i) q^{43} +(-1.34016 - 3.77340i) q^{44} +(0.897097 + 1.67657i) q^{45} +(2.87727 + 6.14177i) q^{46} +1.79521 q^{47} +(4.89905 - 4.89891i) q^{48} +(-1.74675 + 3.82485i) q^{49} +(-6.02731 + 2.44121i) q^{50} +(3.53336 - 6.98458i) q^{51} +(4.50110 + 0.393202i) q^{52} +(5.97309 + 9.29431i) q^{53} +(2.21506 - 7.00668i) q^{54} +(-0.959071 + 0.831039i) q^{55} +(-2.55730 + 9.11586i) q^{56} +(-0.126731 - 1.22776i) q^{57} +(3.41643 + 0.148941i) q^{58} +(-12.5418 - 8.06011i) q^{59} +(-2.01133 - 0.880597i) q^{60} +(-0.377953 - 0.827602i) q^{61} +(-4.30726 - 5.43191i) q^{62} +(2.05127 + 9.83035i) q^{63} +(-0.946635 + 7.94380i) q^{64} +(-0.403413 - 1.37390i) q^{65} +(4.88718 + 0.409079i) q^{66} +(-3.50773 + 0.504335i) q^{67} +(1.78203 + 8.86095i) q^{68} +(-8.30588 + 0.110800i) q^{69} +(2.98573 - 0.297255i) q^{70} +(0.747908 + 5.20181i) q^{71} +(2.99400 + 7.93952i) q^{72} +(-5.36692 + 1.57587i) q^{73} +(-6.55889 + 9.28972i) q^{74} +(0.318031 - 7.95806i) q^{75} +(0.991805 + 1.02352i) q^{76} +(-6.09631 + 2.78409i) q^{77} +(-2.71064 + 4.82433i) q^{78} +(-0.930478 + 1.44785i) q^{79} +(2.45390 - 0.637384i) q^{80} +(6.70076 + 6.00831i) q^{81} +(-5.42675 + 10.6315i) q^{82} +(7.69187 + 8.87689i) q^{83} +(-8.88167 - 7.45479i) q^{84} +(2.40969 - 1.54861i) q^{85} +(2.10387 - 11.1578i) q^{86} +(-1.89060 + 3.73724i) q^{87} +(-4.72661 + 3.11903i) q^{88} +(0.443256 + 0.202428i) q^{89} +(1.99785 - 1.79999i) q^{90} -7.56209i q^{91} +(7.45735 - 6.03224i) q^{92} +(8.23552 - 2.06482i) q^{93} +(-0.608490 - 2.46481i) q^{94} +(0.187633 - 0.410860i) q^{95} +(-8.38672 - 5.06586i) q^{96} +(7.32224 - 8.45031i) q^{97} +(5.84356 + 1.10184i) q^{98} +(-2.92322 + 5.24715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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