LMFDB - Embedded newform 215.2.q.b.56.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [215,2,Mod(31,215)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(215, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("215.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 215 = 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	215.q (of order $21$, degree $12$, 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:	$1.71678364346$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			56.3
Character	$\chi$	$=$	215.56
Dual form			215.2.q.b.96.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.262036 + 1.14805i) q^{2} +(0.317968 - 0.295032i) q^{3} +(0.552571 + 0.266104i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(0.255393 + 0.442354i) q^{6} +(-0.848432 + 1.46953i) q^{7} +(-1.91871 + 2.40599i) q^{8} +(-0.210130 + 2.80399i) q^{9} +O(q^{10})$	\(q+(-0.262036 + 1.14805i) q^{2} +(0.317968 - 0.295032i) q^{3} +(0.552571 + 0.266104i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(0.255393 + 0.442354i) q^{6} +(-0.848432 + 1.46953i) q^{7} +(-1.91871 + 2.40599i) q^{8} +(-0.210130 + 2.80399i) q^{9} +(0.430218 - 1.09618i) q^{10} +(3.63754 - 1.75175i) q^{11} +(0.254209 - 0.0784132i) q^{12} +(1.37847 + 3.51228i) q^{13} +(-1.46478 - 1.35912i) q^{14} +(-0.358389 + 0.244346i) q^{15} +(-1.49465 - 1.87424i) q^{16} +(3.80279 - 0.573179i) q^{17} +(-3.16407 - 0.975987i) q^{18} +(-0.0440464 - 0.587759i) q^{19} +(-0.506738 - 0.345488i) q^{20} +(0.163782 + 0.717578i) q^{21} +(1.05793 + 4.63511i) q^{22} +(-7.04653 - 4.80424i) q^{23} +(0.0997529 + 1.33111i) q^{24} +(0.955573 + 0.294755i) q^{25} +(-4.39349 + 0.662212i) q^{26} +(1.57179 + 1.97096i) q^{27} +(-0.859866 + 0.586247i) q^{28} +(-2.63396 - 2.44396i) q^{29} +(-0.186611 - 0.475478i) q^{30} +(5.26891 - 1.62524i) q^{31} +(-3.00186 + 1.44562i) q^{32} +(0.639802 - 1.63019i) q^{33} +(-0.338428 + 4.51601i) q^{34} +(1.05798 - 1.32666i) q^{35} +(-0.862265 + 1.49349i) q^{36} +(-3.23552 - 5.60408i) q^{37} +(0.686321 + 0.103446i) q^{38} +(1.47454 + 0.710102i) q^{39} +(2.25588 - 2.09315i) q^{40} +(2.47709 - 10.8528i) q^{41} -0.866735 q^{42} +(6.51489 + 0.745825i) q^{43} +2.47614 q^{44} +(0.625696 - 2.74135i) q^{45} +(7.36197 - 6.83091i) q^{46} +(-1.48694 - 0.716070i) q^{47} +(-1.02821 - 0.154978i) q^{48} +(2.06033 + 3.56859i) q^{49} +(-0.588790 + 1.01981i) q^{50} +(1.04006 - 1.30420i) q^{51} +(-0.172930 + 2.30760i) q^{52} +(-0.00247347 + 0.00630229i) q^{53} +(-2.67463 + 1.28803i) q^{54} +(-3.85799 + 1.19003i) q^{55} +(-1.90777 - 4.86092i) q^{56} +(-0.187413 - 0.173894i) q^{57} +(3.49599 - 2.38353i) q^{58} +(0.910284 + 1.14146i) q^{59} +(-0.263057 + 0.0396494i) q^{60} +(0.0218481 + 0.00673924i) q^{61} +(0.485224 + 6.47487i) q^{62} +(-3.94226 - 2.68779i) q^{63} +(-1.93993 - 8.49938i) q^{64} +(-0.839593 - 3.67850i) q^{65} +(1.70389 + 1.16170i) q^{66} +(0.506784 + 6.76257i) q^{67} +(2.25384 + 0.695217i) q^{68} +(-3.65798 + 0.551351i) q^{69} +(1.24585 + 1.56225i) q^{70} +(9.38143 - 6.39615i) q^{71} +(-6.34319 - 5.88562i) q^{72} +(0.970114 + 2.47181i) q^{73} +(7.28161 - 2.24608i) q^{74} +(0.390804 - 0.188201i) q^{75} +(0.132066 - 0.336499i) q^{76} +(-0.511965 + 6.83170i) q^{77} +(-1.20162 + 1.50678i) q^{78} +(3.44937 - 5.97449i) q^{79} +(1.19862 + 2.07607i) q^{80} +(-7.26007 - 1.09428i) q^{81} +(11.8106 + 5.68767i) q^{82} +(8.86570 - 8.22617i) q^{83} +(-0.100449 + 0.440096i) q^{84} -3.84575 q^{85} +(-2.56338 + 7.28401i) q^{86} -1.55856 q^{87} +(-2.76471 + 12.1130i) q^{88} +(-9.30715 + 8.63577i) q^{89} +(2.98327 + 1.43667i) q^{90} +(-6.33092 - 0.954233i) q^{91} +(-2.61528 - 4.52979i) q^{92} +(1.19585 - 2.07127i) q^{93} +(1.21172 - 1.51945i) q^{94} +(-0.0440464 + 0.587759i) q^{95} +(-0.527993 + 1.34531i) q^{96} +(-13.2171 + 6.36500i) q^{97} +(-4.63682 + 1.43027i) q^{98} +(4.14752 + 10.5677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9}+O(q^{10}) $ 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9} + 14 q^{10} - 24 q^{11} + 15 q^{12} - 17 q^{14} - 4 q^{15} - 2 q^{16} + 13 q^{17} + 14 q^{18} + q^{19} - 8 q^{20} + 30 q^{21} - 37 q^{22} - 14 q^{23} - 15 q^{24} + 8 q^{25} - 56 q^{26} - 18 q^{27} + 111 q^{28} - 15 q^{29} + 2 q^{30} - 43 q^{31} - 9 q^{32} - 19 q^{33} + 33 q^{34} + 3 q^{35} - 61 q^{36} + 19 q^{37} - 24 q^{38} + 19 q^{39} + 3 q^{40} + 40 q^{41} + 140 q^{42} - 53 q^{43} + 104 q^{44} - 32 q^{45} - 34 q^{46} - 18 q^{47} - 54 q^{48} - 78 q^{49} - 7 q^{50} + 59 q^{51} - 25 q^{52} + 51 q^{53} - 24 q^{54} + 12 q^{55} - 20 q^{56} - 113 q^{57} - 112 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 87 q^{62} - 38 q^{63} + 50 q^{64} - 96 q^{66} - 28 q^{67} - 149 q^{68} + 112 q^{69} - q^{70} + 51 q^{71} - 208 q^{72} + 24 q^{73} - 19 q^{74} + 8 q^{75} + 248 q^{76} + 7 q^{77} + 242 q^{78} - 138 q^{79} - 55 q^{80} - 15 q^{81} - 98 q^{82} + 43 q^{83} + 132 q^{84} + 44 q^{85} - 30 q^{86} - 22 q^{87} - 66 q^{88} + 7 q^{89} + 98 q^{90} - 5 q^{91} - 102 q^{92} - 2 q^{93} + 16 q^{94} + q^{95} + 486 q^{96} - 67 q^{97} + 62 q^{98} + 11 q^{99}+O(q^{100}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9 + 14 * q^10 - 24 * q^11 + 15 * q^12 - 17 * q^14 - 4 * q^15 - 2 * q^16 + 13 * q^17 + 14 * q^18 + q^19 - 8 * q^20 + 30 * q^21 - 37 * q^22 - 14 * q^23 - 15 * q^24 + 8 * q^25 - 56 * q^26 - 18 * q^27 + 111 * q^28 - 15 * q^29 + 2 * q^30 - 43 * q^31 - 9 * q^32 - 19 * q^33 + 33 * q^34 + 3 * q^35 - 61 * q^36 + 19 * q^37 - 24 * q^38 + 19 * q^39 + 3 * q^40 + 40 * q^41 + 140 * q^42 - 53 * q^43 + 104 * q^44 - 32 * q^45 - 34 * q^46 - 18 * q^47 - 54 * q^48 - 78 * q^49 - 7 * q^50 + 59 * q^51 - 25 * q^52 + 51 * q^53 - 24 * q^54 + 12 * q^55 - 20 * q^56 - 113 * q^57 - 112 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 87 * q^62 - 38 * q^63 + 50 * q^64 - 96 * q^66 - 28 * q^67 - 149 * q^68 + 112 * q^69 - q^70 + 51 * q^71 - 208 * q^72 + 24 * q^73 - 19 * q^74 + 8 * q^75 + 248 * q^76 + 7 * q^77 + 242 * q^78 - 138 * q^79 - 55 * q^80 - 15 * q^81 - 98 * q^82 + 43 * q^83 + 132 * q^84 + 44 * q^85 - 30 * q^86 - 22 * q^87 - 66 * q^88 + 7 * q^89 + 98 * q^90 - 5 * q^91 - 102 * q^92 - 2 * q^93 + 16 * q^94 + q^95 + 486 * q^96 - 67 * q^97 + 62 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/215\mathbb{Z}\right)^\times$.

$n$	$46$	$87$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.262036	+	1.14805i	−0.185287	+	0.811797i	0.793771	+	0.608217i	$0.208115\pi$
$2$	−0.262036	+	1.14805i	−0.185287	+	0.811797i	−0.979058	+	0.203580i	$0.934742\pi$
$3$	0.317968	−	0.295032i	0.183579	−	0.170337i	−0.583030	−	0.812451i	$-0.698133\pi$
$3$	0.317968	−	0.295032i	0.183579	−	0.170337i	0.766609	+	0.642114i	$0.221942\pi$
$4$	0.552571	+	0.266104i	0.276285	+	0.133052i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$6$	0.255393	+	0.442354i	0.104264	+	0.180590i
$7$	−0.848432	+	1.46953i	−0.320677	+	0.555429i	−0.980628	−	0.195880i	$-0.937244\pi$
$7$	−0.848432	+	1.46953i	−0.320677	+	0.555429i	0.659951	+	0.751309i	$0.270577\pi$
$8$	−1.91871	+	2.40599i	−0.678367	+	0.850646i
$9$	−0.210130	+	2.80399i	−0.0700433	+	0.934663i
$10$	0.430218	−	1.09618i	0.136047	−	0.346642i
$11$	3.63754	−	1.75175i	1.09676	−	0.528171i	0.204121	−	0.978946i	$-0.434566\pi$
$11$	3.63754	−	1.75175i	1.09676	−	0.528171i	0.892638	+	0.450775i	$0.148852\pi$
$12$	0.254209	−	0.0784132i	0.0733839	−	0.0226359i
$13$	1.37847	+	3.51228i	0.382318	+	0.974130i	0.984439	+	0.175725i	$0.0562271\pi$
$13$	1.37847	+	3.51228i	0.382318	+	0.974130i	−0.602121	+	0.798405i	$0.705678\pi$
$14$	−1.46478	−	1.35912i	−0.391478	−	0.363239i
$15$	−0.358389	+	0.244346i	−0.0925357	+	0.0630898i
$16$	−1.49465	−	1.87424i	−0.373664	−	0.468559i
$17$	3.80279	−	0.573179i	0.922313	−	0.139016i	0.329315	−	0.944220i	$-0.393182\pi$
$17$	3.80279	−	0.573179i	0.922313	−	0.139016i	0.592998	+	0.805204i	$0.297944\pi$
$18$	−3.16407	−	0.975987i	−0.745779	−	0.230042i
$19$	−0.0440464	−	0.587759i	−0.0101049	−	0.134841i	0.989870	−	0.141980i	$-0.0453468\pi$
$19$	−0.0440464	−	0.587759i	−0.0101049	−	0.134841i	−0.999975	+	0.00713854i	$0.997728\pi$
$20$	−0.506738	−	0.345488i	−0.113310	−	0.0772535i
$21$	0.163782	+	0.717578i	0.0357403	+	0.156588i
$22$	1.05793	+	4.63511i	0.225552	+	0.988209i
$23$	−7.04653	−	4.80424i	−1.46930	−	1.00175i	−0.992434	−	0.122778i	$-0.960820\pi$
$23$	−7.04653	−	4.80424i	−1.46930	−	1.00175i	−0.476868	−	0.878975i	$-0.658228\pi$
$24$	0.0997529	+	1.33111i	0.0203620	+	0.271712i
$25$	0.955573	+	0.294755i	0.191115	+	0.0589510i
$26$	−4.39349	+	0.662212i	−0.861635	+	0.129871i
$27$	1.57179	+	1.97096i	0.302490	+	0.379311i
$28$	−0.859866	+	0.586247i	−0.162499	+	0.110790i
$29$	−2.63396	−	2.44396i	−0.489114	−	0.453832i	0.396648	−	0.917971i	$-0.370173\pi$
$29$	−2.63396	−	2.44396i	−0.489114	−	0.453832i	−0.885762	+	0.464139i	$0.846364\pi$
$30$	−0.186611	−	0.475478i	−0.0340704	−	0.0868100i
$31$	5.26891	−	1.62524i	0.946324	−	0.291902i	0.217078	−	0.976154i	$-0.430347\pi$
$31$	5.26891	−	1.62524i	0.946324	−	0.291902i	0.729246	+	0.684252i	$0.239871\pi$
$32$	−3.00186	+	1.44562i	−0.530659	+	0.255552i
$33$	0.639802	−	1.63019i	0.111375	−	0.283779i
$34$	−0.338428	+	4.51601i	−0.0580399	+	0.774489i
$35$	1.05798	−	1.32666i	0.178831	−	0.224247i
$36$	−0.862265	+	1.49349i	−0.143711	+	0.248914i
$37$	−3.23552	−	5.60408i	−0.531916	−	0.921305i	−0.999306	−	0.0372537i	$-0.988139\pi$
$37$	−3.23552	−	5.60408i	−0.531916	−	0.921305i	0.467390	−	0.884051i	$-0.345194\pi$
$38$	0.686321	+	0.103446i	0.111336	+	0.0167812i
$39$	1.47454	+	0.710102i	0.236116	+	0.113707i
$40$	2.25588	−	2.09315i	0.356685	−	0.330956i
$41$	2.47709	−	10.8528i	0.386856	−	1.69493i	−0.288535	−	0.957469i	$-0.593168\pi$
$41$	2.47709	−	10.8528i	0.386856	−	1.69493i	0.675391	−	0.737460i	$-0.263975\pi$
$42$	−0.866735			−0.133740
$43$	6.51489	+	0.745825i	0.993511	+	0.113737i
$43$	6.51489	+	0.745825i	0.993511	+	0.113737i
$44$	2.47614			0.373293
$45$	0.625696	−	2.74135i	0.0932733	−	0.408657i
$46$	7.36197	−	6.83091i	1.08546	−	1.00716i
$47$	−1.48694	−	0.716070i	−0.216892	−	0.104450i	0.322283	−	0.946643i	$-0.395550\pi$
$47$	−1.48694	−	0.716070i	−0.216892	−	0.104450i	−0.539175	+	0.842194i	$0.681264\pi$
$48$	−1.02821	−	0.154978i	−0.148410	−	0.0223692i
$49$	2.06033	+	3.56859i	0.294332	+	0.509799i
$50$	−0.588790	+	1.01981i	−0.0832674	+	0.144223i
$51$	1.04006	−	1.30420i	0.145638	−	0.182624i
$52$	−0.172930	+	2.30760i	−0.0239811	+	0.320006i
$53$	−0.00247347	+	0.00630229i	−0.000339757	+	0.000865686i	−0.931044	−	0.364908i	$-0.881100\pi$
$53$	−0.00247347	+	0.00630229i	−0.000339757	+	0.000865686i	0.930704	+	0.365774i	$0.119196\pi$
$54$	−2.67463	+	1.28803i	−0.363971	+	0.175279i
$55$	−3.85799	+	1.19003i	−0.520212	+	0.160464i
$56$	−1.90777	−	4.86092i	−0.254937	−	0.649568i
$57$	−0.187413	−	0.173894i	−0.0248234	−	0.0230328i
$58$	3.49599	−	2.38353i	0.459046	−	0.312972i
$59$	0.910284	+	1.14146i	0.118509	+	0.148605i	0.837547	−	0.546365i	$-0.183989\pi$
$59$	0.910284	+	1.14146i	0.118509	+	0.148605i	−0.719038	+	0.694970i	$0.755417\pi$
$60$	−0.263057	+	0.0396494i	−0.0339605	+	0.00511872i
$61$	0.0218481	+	0.00673924i	0.00279736	+	0.000862871i	0.296154	−	0.955140i	$-0.404296\pi$
$61$	0.0218481	+	0.00673924i	0.00279736	+	0.000862871i	−0.293356	+	0.956003i	$0.594772\pi$
$62$	0.485224	+	6.47487i	0.0616235	+	0.822309i
$63$	−3.94226	−	2.68779i	−0.496678	−	0.338629i
$64$	−1.93993	−	8.49938i	−0.242491	−	1.06242i
$65$	−0.839593	−	3.67850i	−0.104139	−	0.456261i
$66$	1.70389	+	1.16170i	0.209735	+	0.142995i
$67$	0.506784	+	6.76257i	0.0619136	+	0.826179i	0.938576	+	0.345073i	$0.112146\pi$
$67$	0.506784	+	6.76257i	0.0619136	+	0.826179i	−0.876662	+	0.481106i	$0.840235\pi$
$68$	2.25384	+	0.695217i	0.273318	+	0.0843074i
$69$	−3.65798	+	0.551351i	−0.440369	+	0.0663749i
$70$	1.24585	+	1.56225i	0.148908	+	0.186724i
$71$	9.38143	−	6.39615i	1.11337	−	0.759083i	0.140419	−	0.990092i	$-0.455155\pi$
$71$	9.38143	−	6.39615i	1.11337	−	0.759083i	0.972952	+	0.231009i	$0.0742027\pi$
$72$	−6.34319	−	5.88562i	−0.747552	−	0.693627i
$73$	0.970114	+	2.47181i	0.113543	+	0.289304i	0.976338	−	0.216251i	$-0.0693831\pi$
$73$	0.970114	+	2.47181i	0.113543	+	0.289304i	−0.862794	+	0.505555i	$0.831288\pi$
$74$	7.28161	−	2.24608i	0.846470	−	0.261101i
$75$	0.390804	−	0.188201i	0.0451262	−	0.0217316i
$76$	0.132066	−	0.336499i	0.0151490	−	0.0385991i
$77$	−0.511965	+	6.83170i	−0.0583438	+	0.778544i
$78$	−1.20162	+	1.50678i	−0.136057	+	0.170609i
$79$	3.44937	−	5.97449i	0.388085	−	0.672183i	−0.604107	−	0.796903i	$-0.706470\pi$
$79$	3.44937	−	5.97449i	0.388085	−	0.672183i	0.992192	+	0.124720i	$0.0398034\pi$
$80$	1.19862	+	2.07607i	0.134010	+	0.232112i
$81$	−7.26007	−	1.09428i	−0.806674	−	0.121587i
$82$	11.8106	+	5.68767i	1.30426	+	0.628098i
$83$	8.86570	−	8.22617i	0.973137	−	0.902940i	−0.0221651	−	0.999754i	$-0.507056\pi$
$83$	8.86570	−	8.22617i	0.973137	−	0.902940i	0.995302	+	0.0968148i	$0.0308655\pi$
$84$	−0.100449	+	0.440096i	−0.0109599	+	0.0480184i
$85$	−3.84575			−0.417130
$86$	−2.56338	+	7.28401i	−0.276417	+	0.785455i
$87$	−1.55856			−0.167095
$88$	−2.76471	+	12.1130i	−0.294719	+	1.29125i
$89$	−9.30715	+	8.63577i	−0.986556	+	0.915390i	−0.996418	−	0.0845613i	$-0.973051\pi$
$89$	−9.30715	+	8.63577i	−0.986556	+	0.915390i	0.00986242	+	0.999951i	$0.496861\pi$
$90$	2.98327	+	1.43667i	0.314464	+	0.151438i
$91$	−6.33092	−	0.954233i	−0.663661	−	0.100031i
$92$	−2.61528	−	4.52979i	−0.272661	−	0.472263i
$93$	1.19585	−	2.07127i	0.124004	−	0.214781i
$94$	1.21172	−	1.51945i	0.124979	−	0.156719i
$95$	−0.0440464	+	0.587759i	−0.00451907	+	0.0603028i
$96$	−0.527993	+	1.34531i	−0.0538881	+	0.137305i
$97$	−13.2171	+	6.36500i	−1.34199	+	0.646268i	−0.960545	−	0.278125i	$-0.910287\pi$
$97$	−13.2171	+	6.36500i	−1.34199	+	0.646268i	−0.381443	+	0.924392i	$0.624573\pi$
$98$	−4.63682	+	1.43027i	−0.468389	+	0.144479i
$99$	4.14752	+	10.5677i	0.416841	+	1.06209i
$100$	0.449586	+	0.417155i	0.0449586	+	0.0417155i
$101$	−15.1750	+	10.3462i	−1.50997	+	1.02948i	−0.526139	+	0.850399i	$0.676361\pi$
$101$	−15.1750	+	10.3462i	−1.50997	+	1.02948i	−0.983834	+	0.179083i	$0.942687\pi$
$102$	1.22476	+	1.53580i	0.121269	+	0.152066i
$103$	−2.18166	+	0.328832i	−0.214965	+	0.0324008i	−0.255642	−	0.966772i	$-0.582287\pi$
$103$	−2.18166	+	0.328832i	−0.214965	+	0.0324008i	0.0406767	+	0.999172i	$0.487049\pi$
$104$	−11.0954	−	3.42247i	−1.08799	−	0.335601i
$105$	−0.0550037	−	0.733973i	−0.00536781	−	0.0716285i
$106$	−0.00658723	−	0.00449110i	−0.000639809	−	0.000436214i
$107$	−1.76500	−	7.73296i	−0.170629	−	0.747573i	−0.985741	−	0.168270i	$-0.946182\pi$
$107$	−1.76500	−	7.73296i	−0.170629	−	0.747573i	0.815112	−	0.579303i	$-0.196675\pi$
$108$	0.344043	+	1.50735i	0.0331056	+	0.145045i
$109$	10.7812	+	7.35051i	1.03265	+	0.704052i	0.956108	−	0.293014i	$-0.0946584\pi$
$109$	10.7812	+	7.35051i	1.03265	+	0.704052i	0.0765460	+	0.997066i	$0.475611\pi$
$110$	−0.355290	−	4.74102i	−0.0338756	−	0.452038i
$111$	−2.68217	−	0.827341i	−0.254581	−	0.0785277i
$112$	4.02236	−	0.606273i	0.380077	−	0.0572874i
$113$	5.57022	+	6.98484i	0.524003	+	0.657078i	0.971453	−	0.237230i	$-0.0762395\pi$
$113$	5.57022	+	6.98484i	0.524003	+	0.657078i	−0.447451	+	0.894308i	$0.647668\pi$
$114$	0.248748	−	0.169594i	0.0232974	−	0.0158839i
$115$	6.25179	+	5.80081i	0.582982	+	0.540928i
$116$	−0.805102	−	2.05137i	−0.0747519	−	0.190465i
$117$	−10.1380	+	3.12717i	−0.937262	+	0.289107i
$118$	−1.54899	+	0.745952i	−0.142596	+	0.0686704i
$119$	−2.38411	+	6.07461i	−0.218551	+	0.556859i
$120$	0.0997529	−	1.33111i	0.00910615	−	0.121513i
$121$	3.30467	−	4.14393i	0.300425	−	0.376721i
$122$	−0.0134620	+	0.0233169i	−0.00121879	+	0.00211101i
$123$	−2.41429	−	4.18168i	−0.217690	−	0.377050i
$124$	3.34393	+	0.504016i	0.300294	+	0.0452620i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	4.11874	−	3.82163i	0.366927	−	0.340458i
$127$	2.20570	−	9.66382i	0.195725	−	0.857525i	−0.777722	−	0.628609i	$-0.783625\pi$
$127$	2.20570	−	9.66382i	0.195725	−	0.857525i	0.973446	−	0.228916i	$-0.0735182\pi$
$128$	3.60245			0.318415
$129$	2.29157	−	1.68495i	0.201762	−	0.148351i
$130$	4.44312			0.389687
$131$	−3.46244	+	15.1699i	−0.302515	+	1.32540i	0.563803	+	0.825910i	$0.309338\pi$
$131$	−3.46244	+	15.1699i	−0.302515	+	1.32540i	−0.866317	+	0.499494i	$0.833519\pi$
$132$	0.787335	−	0.730541i	0.0685288	−	0.0635854i
$133$	0.901098	+	0.433946i	0.0781351	+	0.0376279i
$134$	−7.89659	−	1.19022i	−0.682162	−	0.102819i
$135$	−1.26047	−	2.18321i	−0.108484	−	0.187900i
$136$	−5.91741	+	10.2492i	−0.507413	+	0.878866i
$137$	8.21477	−	10.3010i	0.701835	−	0.880073i	−0.295324	−	0.955397i	$-0.595428\pi$
$137$	8.21477	−	10.3010i	0.701835	−	0.880073i	0.997159	+	0.0753238i	$0.0239990\pi$
$138$	0.325540	−	4.34403i	0.0277118	−	0.369788i
$139$	0.789279	−	2.01105i	0.0669457	−	0.170575i	−0.893486	−	0.449092i	$-0.851748\pi$
$139$	0.789279	−	2.01105i	0.0669457	−	0.170575i	0.960431	+	0.278517i	$0.0898428\pi$
$140$	0.937637	−	0.451542i	0.0792448	−	0.0381623i
$141$	−0.684062	+	0.211005i	−0.0576084	+	0.0177698i
$142$	4.88486	+	12.4464i	0.409928	+	1.04448i
$143$	11.1668	+	10.3613i	0.933818	+	0.866456i
$144$	5.56941	−	3.79716i	0.464118	−	0.316430i
$145$	2.24029	+	2.80923i	0.186046	+	0.233294i
$146$	−3.09198	+	0.466041i	−0.255894	+	0.0385698i
$147$	1.70797	+	0.526838i	0.140871	+	0.0434528i
$148$	−0.296584	−	3.95763i	−0.0243790	−	0.325315i
$149$	−10.7133	−	7.30420i	−0.877667	−	0.598383i	0.0384648	−	0.999260i	$-0.487753\pi$
$149$	−10.7133	−	7.30420i	−0.877667	−	0.598383i	−0.916132	+	0.400876i	$0.868706\pi$
$150$	0.113661	+	0.497980i	0.00928036	+	0.0406599i
$151$	−3.99334	−	17.4960i	−0.324974	−	1.42380i	−0.828580	−	0.559870i	$-0.810851\pi$
$151$	−3.99334	−	17.4960i	−0.324974	−	1.42380i	0.503607	−	0.863933i	$-0.332006\pi$
$152$	1.49865	+	1.02177i	0.121557	+	0.0828761i
$153$	0.808107	+	10.7834i	0.0653316	+	0.871789i
$154$	−7.70901	−	2.37791i	−0.621210	−	0.191618i
$155$	−5.45229	+	0.821800i	−0.437938	+	0.0660086i
$156$	0.625828	+	0.784763i	0.0501063	+	0.0628313i
$157$	−8.54316	+	5.82463i	−0.681818	+	0.464856i	−0.854043	−	0.520202i	$-0.825857\pi$
$157$	−8.54316	+	5.82463i	−0.681818	+	0.464856i	0.172225	+	0.985058i	$0.444904\pi$
$158$	5.95518	+	5.52560i	0.473769	+	0.439593i
$159$	0.00107289	+	0.00273368i	8.50857e−5	+	0.000216795i
$160$	3.18379	−	0.982069i	0.251701	−	0.0776394i
$161$	13.0385	−	6.27899i	1.02757	−	0.494854i
$162$	3.15869	−	8.04821i	0.248170	−	0.632327i
$163$	0.771171	−	10.2906i	0.0604027	−	0.806019i	−0.881938	−	0.471365i	$-0.843762\pi$
$163$	0.771171	−	10.2906i	0.0604027	−	0.806019i	0.942341	−	0.334654i	$-0.108619\pi$
$164$	4.25675	−	5.33780i	0.332397	−	0.416812i
$165$	−0.875623	+	1.51662i	−0.0681671	+	0.118069i
$166$	7.12096	+	12.3339i	0.552694	+	0.957294i
$167$	2.85637	+	0.430529i	0.221033	+	0.0333153i	0.258625	−	0.965978i	$-0.416731\pi$
$167$	2.85637	+	0.430529i	0.221033	+	0.0333153i	−0.0375922	+	0.999293i	$0.511969\pi$
$168$	−2.04074	−	0.982767i	−0.157446	−	0.0758221i
$169$	−0.906236	+	0.840864i	−0.0697104	+	0.0646818i
$170$	1.00772	−	4.41513i	0.0772889	−	0.338625i
$171$	1.65733			0.126739
$172$	3.40147	+	2.14576i	0.259360	+	0.163613i
$173$	18.7746			1.42740			0.713701	−	0.700450i	$-0.247017\pi$
$173$	18.7746			1.42740			0.713701	+	0.700450i	$0.247017\pi$
$174$	0.408399	−	1.78931i	0.0309607	−	0.135648i
$175$	−1.24389	+	1.15416i	−0.0940292	+	0.0872463i
$176$	−8.72005	−	4.19935i	−0.657298	−	0.316538i
$177$	0.626208	+	0.0943857i	0.0470687	+	0.00709446i
$178$	−7.47553	−	12.9480i	−0.560315	−	0.970494i
$179$	−5.94868	+	10.3034i	−0.444625	+	0.770114i	−0.998026	−	0.0628014i	$-0.979997\pi$
$179$	−5.94868	+	10.3034i	−0.444625	+	0.770114i	0.553401	+	0.832915i	$0.313330\pi$
$180$	1.07523	−	1.34829i	0.0801427	−	0.100496i
$181$	−0.946212	+	12.6263i	−0.0703314	+	0.938507i	0.844730	+	0.535193i	$0.179761\pi$
$181$	−0.946212	+	12.6263i	−0.0703314	+	0.938507i	−0.915061	+	0.403314i	$0.867858\pi$
$182$	2.75444	−	7.01820i	0.204173	−	0.520224i
$183$	0.00893529	−	0.00430301i	0.000660516	−	0.000318088i
$184$	25.0792	−	7.73591i	1.84886	−	0.570299i
$185$	2.36413	+	6.02371i	0.173815	+	0.442872i
$186$	2.06458	+	1.91565i	0.151382	+	0.140462i
$187$	12.8287	−	8.74648i	0.938130	−	0.639606i
$188$	−0.631088	−	0.791359i	−0.0460268	−	0.0577158i
$189$	−4.22993	+	0.637559i	−0.307682	+	0.0463756i
$190$	−0.663238	−	0.204582i	−0.0481163	−	0.0148419i
$191$	1.47334	+	19.6603i	0.106607	+	1.42257i	0.752222	+	0.658909i	$0.228982\pi$
$191$	1.47334	+	19.6603i	0.106607	+	1.42257i	−0.645615	+	0.763663i	$0.723399\pi$
$192$	−3.12442	−	2.13019i	−0.225486	−	0.153733i
$193$	−1.62748	−	7.13045i	−0.117148	−	0.513261i	−0.999119	−	0.0419570i	$-0.986641\pi$
$193$	−1.62748	−	7.13045i	−0.117148	−	0.513261i	0.881971	−	0.471304i	$-0.156216\pi$
$194$	−3.84402	−	16.8418i	−0.275985	−	1.20917i
$195$	−1.35224	−	0.921939i	−0.0968357	−	0.0660215i
$196$	0.188860	+	2.52016i	0.0134900	+	0.180011i
$197$	−22.0825	−	6.81156i	−1.57332	−	0.485303i	−0.619323	−	0.785136i	$-0.712593\pi$
$197$	−22.0825	−	6.81156i	−1.57332	−	0.485303i	−0.953992	+	0.299833i	$0.903069\pi$
$198$	−13.2191	+	1.99246i	−0.939441	+	0.141598i
$199$	−9.58469	−	12.0188i	−0.679441	−	0.851992i	0.315862	−	0.948805i	$-0.397706\pi$
$199$	−9.58469	−	12.0188i	−0.679441	−	0.851992i	−0.995303	+	0.0968136i	$0.969135\pi$
$200$	−2.54265	+	1.73355i	−0.179792	+	0.122580i
$201$	2.15631	+	2.00077i	0.152095	+	0.141123i
$202$	−7.90156	−	20.1328i	−0.555952	−	1.41654i
$203$	5.82620	−	1.79714i	0.408919	−	0.126135i
$204$	0.921760	−	0.443896i	0.0645361	−	0.0310790i
$205$	−4.06696	+	10.3624i	−0.284048	+	0.723744i
$206$	0.194156	−	2.59083i	0.0135275	−	0.180512i
$207$	14.9517	−	18.7489i	1.03922	−	1.30314i
$208$	4.52251	−	7.83321i	0.313579	−	0.543136i
$209$	−1.18982	−	2.06084i	−0.0823019	−	0.142551i
$210$	0.857055	+	0.129180i	0.0591424	+	0.00891428i
$211$	−15.5340	−	7.48078i	−1.06941	−	0.514998i	−0.185490	−	0.982646i	$-0.559387\pi$
$211$	−15.5340	−	7.48078i	−1.06941	−	0.514998i	−0.883915	+	0.467648i	$0.845102\pi$
$212$	−0.00304383	+	0.00282426i	−0.000209051	+	0.000193971i
$213$	1.09593	−	4.80159i	0.0750920	−	0.329000i
$214$	9.34035			0.638494
$215$	−6.33096	−	1.70849i	−0.431768	−	0.116518i
$216$	−7.75791			−0.527859
$217$	−2.08197	+	9.12171i	−0.141333	+	0.619222i
$218$	−11.2639	+	10.4513i	−0.762885	+	0.707854i
$219$	1.03773	+	0.499743i	0.0701232	+	0.0337695i
$220$	−2.44849	−	0.369050i	−0.165077	−	0.0248813i
$221$	7.25519	+	12.5663i	0.488037	+	0.845304i
$222$	1.65266	−	2.86249i	0.110919	−	0.192118i
$223$	9.56944	−	11.9997i	0.640817	−	0.803559i	−0.350288	−	0.936642i	$-0.613916\pi$
$223$	9.56944	−	11.9997i	0.640817	−	0.803559i	0.991105	+	0.133083i	$0.0424876\pi$
$224$	0.422497	−	5.63783i	0.0282292	−	0.376693i
$225$	−1.02729	+	2.61748i	−0.0684857	+	0.174499i
$226$	−9.47858	+	4.56464i	−0.630506	+	0.303635i
$227$	9.27798	−	2.86188i	0.615801	−	0.189950i	0.0288659	−	0.999583i	$-0.490810\pi$
$227$	9.27798	−	2.86188i	0.615801	−	0.189950i	0.586935	+	0.809634i	$0.300334\pi$
$228$	−0.0572850	−	0.145960i	−0.00379379	−	0.00966643i
$229$	3.70177	+	3.43474i	0.244620	+	0.226974i	0.792948	−	0.609289i	$-0.208545\pi$
$229$	3.70177	+	3.43474i	0.244620	+	0.226974i	−0.548328	+	0.836263i	$0.684736\pi$
$230$	−8.29784	+	5.65737i	−0.547143	+	0.373036i
$231$	1.85278	+	2.32331i	0.121904	+	0.152863i
$232$	10.9339	−	1.64803i	0.717849	−	0.108198i
$233$	−22.5135	−	6.94450i	−1.47491	−	0.454950i	−0.550010	−	0.835158i	$-0.685376\pi$
$233$	−22.5135	−	6.94450i	−1.47491	−	0.454950i	−0.924901	+	0.380209i	$0.875852\pi$
$234$	−0.933632	−	12.4585i	−0.0610335	−	0.814435i
$235$	1.36360	+	0.929689i	0.0889517	+	0.0606462i
$236$	0.199249	+	0.872967i	0.0129700	+	0.0568253i
$237$	−0.665872	−	2.91737i	−0.0432530	−	0.189504i
$238$	−6.34926	−	4.32886i	−0.411562	−	0.280598i
$239$	1.37490	+	18.3468i	0.0889352	+	1.18676i	0.845915	+	0.533318i	$0.179055\pi$
$239$	1.37490	+	18.3468i	0.0889352	+	1.18676i	−0.756979	+	0.653439i	$0.773326\pi$
$240$	0.993630	+	0.306494i	0.0641385	+	0.0197841i
$241$	13.4242	−	2.02337i	0.864728	−	0.130337i	0.298324	−	0.954465i	$-0.403572\pi$
$241$	13.4242	−	2.02337i	0.864728	−	0.130337i	0.566404	+	0.824128i	$0.308334\pi$
$242$	3.89151	+	4.87980i	0.250156	+	0.313686i
$243$	−8.88004	+	6.05431i	−0.569655	+	0.388384i
$244$	0.0102793	+	0.00953777i	0.000658063	+	0.000610593i
$245$	−1.50544	−	3.83581i	−0.0961793	−	0.245061i
$246$	5.43343	−	1.67599i	0.346423	−	0.106857i
$247$	2.00365	−	0.964909i	0.127489	−	0.0613957i
$248$	−6.19920	+	15.7953i	−0.393650	+	1.00300i
$249$	0.392034	−	5.23133i	0.0248441	−	0.331522i
$250$	0.734209	−	0.920668i	0.0464354	−	0.0582282i
$251$	−0.989949	+	1.71464i	−0.0624850	+	0.108227i	−0.895576	−	0.444909i	$-0.853236\pi$
$251$	−0.989949	+	1.71464i	−0.0624850	+	0.108227i	0.833091	+	0.553137i	$0.186569\pi$
$252$	−1.46315	−	2.53424i	−0.0921695	−	0.159642i
$253$	−34.0478	−	5.13188i	−2.14057	−	0.322639i
$254$	10.5166	+	5.06454i	0.659872	+	0.317777i
$255$	−1.22283	+	1.13462i	−0.0765764	+	0.0710525i
$256$	2.93588	−	12.8629i	0.183493	−	0.803934i
$257$	6.51941			0.406670			0.203335	−	0.979109i	$-0.434822\pi$
$257$	6.51941			0.406670			0.203335	+	0.979109i	$0.434822\pi$
$258$	1.33394	+	3.07237i	0.0830475	+	0.191277i
$259$	10.9805			0.682293
$260$	0.514928	−	2.25605i	0.0319345	−	0.139914i
$261$	7.40631	−	6.87205i	0.458439	−	0.425369i
$262$	−16.5086	−	7.95014i	−1.01991	−	0.491161i
$263$	25.3780	+	3.82512i	1.56488	+	0.235867i	0.873571	−	0.486696i	$-0.161798\pi$
$263$	25.3780	+	3.82512i	1.56488	+	0.235867i	0.691305	+	0.722563i	$0.257036\pi$
$264$	2.69462	+	4.66722i	0.165842	+	0.287247i
$265$	0.00338515	−	0.00586324i	0.000207948	−	0.000360176i
$266$	−0.734314	+	0.920800i	−0.0450237	+	0.0564579i
$267$	−0.411554	+	5.49181i	−0.0251867	+	0.336093i
$268$	−1.51951	+	3.87165i	−0.0928190	+	0.236499i
$269$	−27.5546	+	13.2696i	−1.68004	+	0.809063i	−0.683144	+	0.730284i	$0.739388\pi$
$269$	−27.5546	+	13.2696i	−1.68004	+	0.809063i	−0.996892	+	0.0787791i	$0.974898\pi$
$270$	2.83673	−	0.875015i	0.172638	−	0.0532517i
$271$	6.52766	+	16.6322i	0.396527	+	1.01034i	0.980141	+	0.198304i	$0.0635432\pi$
$271$	6.52766	+	16.6322i	0.396527	+	1.01034i	−0.583613	+	0.812032i	$0.698362\pi$
$272$	−6.75813	−	6.27063i	−0.409772	−	0.380213i
$273$	−2.29456	+	1.56441i	−0.138873	+	0.0946822i
$274$	9.67354	+	12.1302i	0.584400	+	0.732814i
$275$	3.99227	−	0.601737i	0.240743	−	0.0362861i
$276$	−2.16801	−	0.668742i	−0.130499	−	0.0402535i
$277$	−0.227465	−	3.03531i	−0.0136671	−	0.182374i	−0.999859	−	0.0167701i	$-0.994662\pi$
$277$	−0.227465	−	3.03531i	−0.0136671	−	0.182374i	0.986192	−	0.165604i	$-0.0529574\pi$
$278$	2.10197	+	1.43310i	0.126068	+	0.0859518i
$279$	3.45001	+	15.1155i	0.206547	+	0.904940i
$280$	1.16198	+	5.09097i	0.0694416	+	0.304243i
$281$	1.73192	+	1.18081i	0.103318	+	0.0704409i	0.613877	−	0.789402i	$-0.289609\pi$
$281$	1.73192	+	1.18081i	0.103318	+	0.0704409i	−0.510559	+	0.859843i	$0.670562\pi$
$282$	−0.0629966	−	0.840632i	−0.00375140	−	0.0500589i
$283$	−15.5231	−	4.78825i	−0.922755	−	0.284632i	−0.203256	−	0.979126i	$-0.565152\pi$
$283$	−15.5231	−	4.78825i	−0.922755	−	0.284632i	−0.719499	+	0.694494i	$0.755628\pi$
$284$	6.88594	−	1.03789i	0.408606	−	0.0615874i
$285$	0.159402	+	0.199884i	0.00944216	+	0.0118401i
$286$	−14.8215	+	10.1051i	−0.876411	+	0.597527i
$287$	13.8469	+	12.8480i	0.817357	+	0.758396i
$288$	−3.42272	−	8.72095i	−0.201686	−	0.513887i
$289$	−2.11204	+	0.651477i	−0.124237	+	0.0383222i
$290$	−3.81219	+	1.83585i	−0.223859	+	0.107805i
$291$	−2.32473	+	5.92332i	−0.136278	+	0.347231i
$292$	−0.121702	+	1.62400i	−0.00712208	+	0.0950375i
$293$	−0.656834	+	0.823644i	−0.0383727	+	0.0481178i	−0.800648	−	0.599136i	$-0.795511\pi$
$293$	−0.656834	+	0.823644i	−0.0383727	+	0.0481178i	0.762275	+	0.647253i	$0.224082\pi$
$294$	−1.05239	+	1.82279i	−0.0613765	+	0.106307i
$295$	−0.729991	−	1.26438i	−0.0425017	−	0.0736151i
$296$	19.6914	+	2.96800i	1.14454	+	0.172511i
$297$	9.17004	+	4.41606i	0.532100	+	0.256246i
$298$	11.1929	−	10.3855i	0.648387	−	0.601615i
$299$	7.16041	−	31.3718i	0.414097	−	1.81428i
$300$	0.266028			0.0153591
$301$	−6.62345	+	8.94102i	−0.381769	+	0.515352i
$302$	21.1327			1.21605
$303$	−1.77274	+	7.76687i	−0.101841	+	0.446195i
$304$	−1.03577	+	0.961050i	−0.0594052	+	0.0551200i
$305$	−0.0205996	−	0.00992026i	−0.00117953	−	0.000568032i
$306$	−12.5917	−	1.89790i	−0.719821	−	0.108496i
$307$	−2.14189	−	3.70986i	−0.122244	−	0.211733i	0.798408	−	0.602117i	$-0.205676\pi$
$307$	−2.14189	−	3.70986i	−0.122244	−	0.211733i	−0.920652	+	0.390383i	$0.872342\pi$
$308$	−2.10084	+	3.63876i	−0.119706	+	0.207338i
$309$	−0.596682	+	0.748216i	−0.0339441	+	0.0425645i
$310$	0.485224	−	6.47487i	0.0275589	−	0.367748i
$311$	−3.66318	+	9.33363i	−0.207720	+	0.529262i	−0.996326	−	0.0856364i	$-0.972708\pi$
$311$	−3.66318	+	9.33363i	−0.207720	+	0.529262i	0.788607	+	0.614898i	$0.210803\pi$
$312$	−4.53772	+	2.18525i	−0.256898	+	0.123715i
$313$	10.9720	−	3.38441i	0.620173	−	0.191298i	0.0312819	−	0.999511i	$-0.490041\pi$
$313$	10.9720	−	3.38441i	0.620173	−	0.191298i	0.588891	+	0.808213i	$0.299565\pi$
$314$	−4.44838	−	11.3343i	−0.251036	−	0.639630i
$315$	3.49763	+	3.24533i	0.197069	+	0.182854i
$316$	3.49586	−	2.38344i	0.196658	−	0.134079i
$317$	−9.06410	−	11.3660i	−0.509090	−	0.638379i	0.459162	−	0.888352i	$-0.348150\pi$
$317$	−9.06410	−	11.3660i	−0.509090	−	0.638379i	−0.968253	+	0.249973i	$0.919578\pi$
$318$	−0.00341955		0.000515414i	−0.000191759		2.89030e-5i
$319$	−13.8623	−	4.27596i	−0.776141	−	0.239408i
$320$	0.651493	+	8.69358i	0.0364196	+	0.485986i
$321$	−2.84268	−	1.93811i	−0.158663	−	0.108175i
$322$	3.79208	+	16.6142i	0.211324	+	0.925872i
$323$	−0.504390	−	2.20988i	−0.0280650	−	0.122961i
$324$	−3.72051	−	2.53660i	−0.206695	−	0.140922i
$325$	0.281964	+	3.76255i	0.0156405	+	0.208708i
$326$	11.6120	+	3.58184i	0.643132	+	0.198380i
$327$	5.59672	−	0.843570i	0.309500	−	0.0466496i
$328$	21.3590	+	26.7833i	1.17935	+	1.47886i
$329$	2.31385	−	1.57756i	0.127567	−	0.0869734i
$330$	−1.51172	−	1.40267i	−0.0832175	−	0.0772146i
$331$	3.03789	+	7.74043i	0.166978	+	0.425452i	0.989730	−	0.142947i	$-0.0456580\pi$
$331$	3.03789	+	7.74043i	0.166978	+	0.425452i	−0.822753	+	0.568400i	$0.807563\pi$
$332$	7.08795	−	2.18634i	0.389002	−	0.119991i
$333$	16.3937	−	7.89477i	0.898367	−	0.432631i
$334$	−1.24274	+	3.16646i	−0.0679998	+	0.173261i
$335$	0.506784	−	6.76257i	0.0276886	−	0.369478i
$336$	1.10011	−	1.37950i	0.0600161	−	0.0752578i
$337$	−9.80338	+	16.9799i	−0.534024	+	0.924957i	0.465186	+	0.885213i	$0.345987\pi$
$337$	−9.80338	+	16.9799i	−0.534024	+	0.924957i	−0.999210	+	0.0397437i	$0.987346\pi$
$338$	−0.727891	−	1.26074i	−0.0395921	−	0.0685755i
$339$	3.83190	+	0.577567i	0.208120	+	0.0313691i
$340$	−2.12505	−	1.02337i	−0.115247	−	0.0555000i
$341$	16.3188	−	15.1417i	0.883714	−	0.819967i
$342$	−0.434279	+	1.90270i	−0.0234831	+	0.102886i
$343$	−18.8702			−1.01890
$344$	−14.2946	+	14.2437i	−0.770715	+	0.767970i
$345$	3.69929			0.199163
$346$	−4.91961	+	21.5542i	−0.264480	+	1.15876i
$347$	10.3961	−	9.64613i	0.558089	−	0.517831i	−0.349921	−	0.936779i	$-0.613792\pi$
$347$	10.3961	−	9.64613i	0.558089	−	0.517831i	0.908010	+	0.418948i	$0.137601\pi$
$348$	−0.861215	−	0.414739i	−0.0461660	−	0.0222324i
$349$	−28.5513	−	4.30342i	−1.52832	−	0.230357i	−0.669567	−	0.742752i	$-0.733520\pi$
$349$	−28.5513	−	4.30342i	−1.52832	−	0.230357i	−0.858750	+	0.512395i	$0.828758\pi$
$350$	−0.999096	−	1.73048i	−0.0534039	−	0.0924983i
$351$	−4.75589	+	8.23744i	−0.253851	+	0.439682i
$352$	−8.38702	+	10.5170i	−0.447030	+	0.560557i
$353$	−0.341703	+	4.55971i	−0.0181870	+	0.242689i	0.980700	+	0.195519i	$0.0626392\pi$
$353$	−0.341703	+	4.55971i	−0.0181870	+	0.242689i	−0.998887	+	0.0471696i	$0.984980\pi$
$354$	−0.272449	+	0.694189i	−0.0144805	+	0.0368957i
$355$	−10.2299	+	4.92648i	−0.542949	+	0.261470i
$356$	−7.44087	+	2.29521i	−0.394365	+	0.121646i
$357$	1.03413	+	2.63492i	0.0547320	+	0.139455i
$358$	−10.2701	−	9.52928i	−0.542793	−	0.503638i
$359$	6.89119	−	4.69834i	0.363703	−	0.247969i	−0.367655	−	0.929962i	$-0.619839\pi$
$359$	6.89119	−	4.69834i	0.363703	−	0.247969i	0.731358	+	0.681994i	$0.238887\pi$
$360$	5.39514	+	6.76529i	0.284349	+	0.356562i
$361$	18.4443	−	2.78003i	0.970751	−	0.146317i
$362$	−14.2478	−	4.39485i	−0.748846	−	0.230988i
$363$	−0.171808	−	2.29262i	−0.00901760	−	0.120331i
$364$	−3.24436	−	2.21196i	−0.170050	−	0.115938i
$365$	−0.590874	−	2.58879i	−0.0309278	−	0.135503i
$366$	0.00259872	+	0.0113857i	0.000135837	+	0.000595143i
$367$	10.7327	+	7.31746i	0.560244	+	0.381968i	0.810079	−	0.586320i	$-0.199424\pi$
$367$	10.7327	+	7.31746i	0.560244	+	0.381968i	−0.249835	+	0.968288i	$0.580376\pi$
$368$	1.52783	+	20.3875i	0.0796439	+	1.06277i
$369$	29.9107	+	9.22624i	1.55709	+	0.480299i
$370$	−7.53504	+	1.13572i	−0.391728	+	0.0590435i
$371$	−0.00716282	−	0.00898189i	−0.000371875	−	0.000466316i
$372$	1.21196	−	0.826303i	0.0628374	−	0.0428418i
$373$	−16.3307	−	15.1527i	−0.845571	−	0.784575i	0.132863	−	0.991134i	$-0.457583\pi$
$373$	−16.3307	−	15.1527i	−0.845571	−	0.784575i	−0.978434	+	0.206559i	$0.933773\pi$
$374$	6.67985	+	17.0200i	0.345407	+	0.880082i
$375$	−0.414489	+	0.127853i	−0.0214041	+	0.00660230i
$376$	4.57586	−	2.20362i	0.235982	−	0.113643i
$377$	4.95303	−	12.6201i	0.255094	−	0.649969i
$378$	0.376441	−	5.02325i	0.0193620	−	0.258368i
$379$	11.0832	−	13.8979i	0.569305	−	0.713886i	−0.410942	−	0.911661i	$-0.634800\pi$
$379$	11.0832	−	13.8979i	0.569305	−	0.713886i	0.980247	+	0.197776i	$0.0633717\pi$
$380$	−0.180744	+	0.313057i	−0.00927196	+	0.0160595i
$381$	−2.14979	−	3.72354i	−0.110137	−	0.190763i
$382$	−22.9572	−	3.46024i	−1.17459	−	0.177041i
$383$	16.8247	+	8.10236i	0.859703	+	0.414011i	0.811170	−	0.584810i	$-0.198831\pi$
$383$	16.8247	+	8.10236i	0.859703	+	0.414011i	0.0485330	+	0.998822i	$0.484545\pi$
$384$	1.14547	−	1.06284i	0.0584543	−	0.0542377i
$385$	1.52446	−	6.67909i	0.0776936	−	0.340398i
$386$	8.61260			0.438370
$387$	−3.46026	+	18.1110i	−0.175895	+	0.920632i
$388$	−8.99711			−0.456759
$389$	−1.95349	+	8.55882i	−0.0990461	+	0.433949i	0.900954	+	0.433915i	$0.142868\pi$
$389$	−1.95349	+	8.55882i	−0.0990461	+	0.433949i	−1.00000		3.44863e-5i	$0.999989\pi$
$390$	1.41277	−	1.31086i	0.0715385	−	0.0663780i
$391$	−29.5502	−	14.2306i	−1.49442	−	0.719673i
$392$	−12.5392	−	1.88997i	−0.633323	−	0.0954582i
$393$	3.37467	+	5.84509i	0.170229	+	0.294846i
$394$	13.6065	−	23.5671i	0.685484	−	1.18729i
$395$	−4.30130	+	5.39366i	−0.216422	+	0.271384i
$396$	−0.520312	+	6.94308i	−0.0261467	+	0.348903i
$397$	0.812194	−	2.06944i	0.0407628	−	0.103862i	−0.909043	−	0.416703i	$-0.863185\pi$
$397$	0.812194	−	2.06944i	0.0407628	−	0.103862i	0.949805	+	0.312841i	$0.101281\pi$
$398$	16.3098	−	7.85439i	0.817536	−	0.393705i
$399$	0.414549	−	0.127871i	0.0207534	−	0.00640157i
$400$	−0.875810	−	2.23153i	−0.0437905	−	0.111576i
$401$	−16.1963	−	15.0280i	−0.808804	−	0.750461i	0.162905	−	0.986642i	$-0.447914\pi$
$401$	−16.1963	−	15.0280i	−0.808804	−	0.750461i	−0.971709	+	0.236181i	$0.924104\pi$
$402$	−2.86202	+	1.95129i	−0.142745	+	0.0973216i
$403$	12.9713	+	16.2655i	0.646147	+	0.810243i
$404$	−11.1384	+	1.67885i	−0.554158	+	0.0835259i
$405$	7.01588	+	2.16411i	0.348622	+	0.107536i
$406$	0.536546	+	7.15971i	0.0266283	+	0.355331i
$407$	−21.5862	−	14.7172i	−1.06999	−	0.729506i
$408$	1.14230	+	5.00476i	0.0565525	+	0.247773i
$409$	0.495552	+	2.17115i	0.0245035	+	0.107357i	0.985701	−	0.168505i	$-0.0538939\pi$
$409$	0.495552	+	2.17115i	0.0245035	+	0.107357i	−0.961197	+	0.275862i	$0.911037\pi$
$410$	−10.8310	−	7.38442i	−0.534903	−	0.364690i
$411$	−0.427082	−	5.69901i	−0.0210664	−	0.281111i
$412$	−1.29302	−	0.398845i	−0.0637027	−	0.0196497i
$413$	−2.44972	+	0.369236i	−0.120543	+	0.0181689i
$414$	17.6068	+	22.0783i	0.865329	+	1.08509i
$415$	−9.99273	+	6.81293i	−0.490524	+	0.334433i
$416$	−9.21538	−	8.55062i	−0.451821	−	0.419229i
$417$	−0.342357	−	0.872312i	−0.0167653	−	0.0427173i
$418$	2.67773	−	0.825970i	0.130972	−	0.0403995i
$419$	−10.7751	+	5.18902i	−0.526399	+	0.253500i	−0.678157	−	0.734917i	$-0.737221\pi$
$419$	−10.7751	+	5.18902i	−0.526399	+	0.253500i	0.151758	+	0.988418i	$0.451507\pi$
$420$	0.164920	−	0.420209i	0.00804727	−	0.0205041i
$421$	0.885066	−	11.8104i	0.0431355	−	0.575603i	−0.933202	−	0.359351i	$-0.882998\pi$
$421$	0.885066	−	11.8104i	0.0431355	−	0.575603i	0.976338	−	0.216251i	$-0.0693830\pi$
$422$	12.6588	−	15.8737i	0.616222	−	0.772718i
$423$	2.32030	−	4.01888i	0.112817	−	0.195405i
$424$	−0.0104174	−	0.0180434i	−0.000505912	−	0.000876265i
$425$	3.80279	+	0.573179i	0.184463	+	0.0278033i
$426$	5.22532	+	2.51638i	0.253167	+	0.121919i
$427$	−0.0284401	+	0.0263886i	−0.00137631	+	0.00127703i
$428$	1.08249	−	4.74268i	0.0523239	−	0.229246i
$429$	6.60762			0.319019
$430$	3.62038	−	6.82060i	0.174590	−	0.328919i
$431$	−5.73866			−0.276422			−0.138211	−	0.990403i	$-0.544135\pi$
$431$	−5.73866			−0.276422			−0.138211	+	0.990403i	$0.544135\pi$
$432$	1.34476	−	5.89180i	0.0647000	−	0.283469i
$433$	−6.35462	+	5.89622i	−0.305383	+	0.283354i	−0.817945	−	0.575296i	$-0.804887\pi$
$433$	−6.35462	+	5.89622i	−0.305383	+	0.283354i	0.512562	+	0.858650i	$0.328696\pi$
$434$	−9.92667	−	4.78043i	−0.476496	−	0.229468i
$435$	1.54115	+	0.232291i	0.0738926	+	0.0111375i
$436$	4.00139	+	6.93061i	0.191632	+	0.331916i
$437$	−2.51336	+	4.35327i	−0.120230	+	0.208245i
$438$	−0.845655	+	1.06042i	−0.0404070	+	0.0506687i
$439$	2.17747	−	29.0563i	0.103925	−	1.38678i	−0.664714	−	0.747098i	$-0.731447\pi$
$439$	2.17747	−	29.0563i	0.103925	−	1.38678i	0.768639	−	0.639683i	$-0.220934\pi$
$440$	4.53917	−	11.5656i	0.216397	−	0.551369i
$441$	−10.4392	+	5.02727i	−0.497106	+	0.239394i
$442$	−16.3280	+	5.03651i	−0.776643	+	0.239563i
$443$	−8.44795	−	21.5250i	−0.401374	−	1.02268i	−0.978540	−	0.206058i	$-0.933937\pi$
$443$	−8.44795	−	21.5250i	−0.401374	−	1.02268i	0.577166	−	0.816627i	$-0.304159\pi$
$444$	−1.26193	−	1.17090i	−0.0598886	−	0.0555685i
$445$	10.4903	−	7.15216i	0.497288	−	0.339045i
$446$	11.2688	+	14.1306i	0.533592	+	0.669103i
$447$	−5.56146	+	0.838255i	−0.263048	+	0.0396481i
$448$	14.1360	+	4.36037i	0.667861	+	0.206008i
$449$	−1.09180	−	14.5691i	−0.0515253	−	0.687557i	−0.961835	−	0.273630i	$-0.911776\pi$
$449$	−1.09180	−	14.5691i	−0.0515253	−	0.687557i	0.910310	−	0.413928i	$-0.135843\pi$
$450$	−2.73582	−	1.86525i	−0.128968	−	0.0879289i
$451$	−10.0009	−	43.8168i	−0.470924	−	2.06325i
$452$	1.21925	+	5.34188i	0.0573486	+	0.251261i
$453$	−6.43163	−	4.38501i	−0.302184	−	0.206026i
$454$	0.854428	+	11.4015i	0.0401003	+	0.535101i
$455$	6.11799	+	1.88715i	0.286816	+	0.0884709i
$456$	0.777978	−	0.117261i	0.0364321	−	0.00549126i
$457$	8.54488	+	10.7149i	0.399713	+	0.501224i	0.940433	−	0.339978i	$-0.110420\pi$
$457$	8.54488	+	10.7149i	0.399713	+	0.501224i	−0.540720	+	0.841202i	$0.681848\pi$
$458$	−4.91327	+	3.34981i	−0.229582	+	0.156526i
$459$	7.10689	+	6.59423i	0.331721	+	0.307792i
$460$	1.91094	+	4.86898i	0.0890978	+	0.227018i
$461$	27.1198	−	8.36536i	1.26310	−	0.389614i	0.410345	−	0.911930i	$-0.365408\pi$
$461$	27.1198	−	8.36536i	1.26310	−	0.389614i	0.852752	+	0.522317i	$0.174932\pi$
$462$	−3.15278	+	1.51830i	−0.146681	+	0.0706377i
$463$	2.14548	−	5.46660i	0.0997090	−	0.254054i	−0.872311	−	0.488951i	$-0.837380\pi$
$463$	2.14548	−	5.46660i	0.0997090	−	0.254054i	0.972020	+	0.234896i	$0.0754751\pi$
$464$	−0.643697	+	8.58954i	−0.0298829	+	0.398759i
$465$	−1.49120	+	1.86990i	−0.0691527	+	0.0867147i
$466$	13.8720	−	24.0271i	0.642609	−	1.11303i
$467$	8.16195	+	14.1369i	0.377690	+	0.654178i	0.990726	−	0.135877i	$-0.0433852\pi$
$467$	8.16195	+	14.1369i	0.377690	+	0.654178i	−0.613036	+	0.790055i	$0.710052\pi$
$468$	−6.43414	−	0.969790i	−0.297418	−	0.0448286i
$469$	−10.3677	−	4.99284i	−0.478738	−	0.230548i
$470$	−1.42465	+	1.32188i	−0.0657141	+	0.0609737i
$471$	−0.998006	+	4.37255i	−0.0459857	+	0.201476i
$472$	−4.49291			−0.206803
$473$	25.0046	−	8.69946i	1.14971	−	0.400001i
$474$	3.52379			0.161853
$475$	0.131155	−	0.574629i	0.00601782	−	0.0263658i
$476$	−2.93387	+	2.72223i	−0.134474	+	0.124773i
$477$	−0.0171518	−	0.00825987i	−0.000785327	−	0.000378194i
$478$	−21.4234	−	3.22906i	−0.979885	−	0.147694i
$479$	−16.7610	−	29.0309i	−0.765830	−	1.32646i	−0.939807	−	0.341706i	$-0.888995\pi$
$479$	−16.7610	−	29.0309i	−0.765830	−	1.32646i	0.173977	−	0.984750i	$-0.444338\pi$
$480$	0.722603	−	1.25159i	0.0329822	−	0.0571268i
$481$	15.2230	−	19.0891i	0.694110	−	0.870386i
$482$	−1.19468	+	15.9419i	−0.0544162	+	0.726134i
$483$	2.29332	−	5.84328i	0.104350	−	0.265878i
$484$	2.92878	−	1.41043i	0.133126	−	0.0641103i
$485$	14.0181	−	4.32401i	0.636528	−	0.196343i
$486$	−4.62379	−	11.7812i	−0.209739	−	0.534407i
$487$	−1.62856	−	1.51108i	−0.0737969	−	0.0684735i	0.642412	−	0.766359i	$-0.277934\pi$
$487$	−1.62856	−	1.51108i	−0.0737969	−	0.0684735i	−0.716209	+	0.697886i	$0.754124\pi$
$488$	−0.0581347	+	0.0396356i	−0.00263164	+	0.00179422i
$489$	−2.79083	−	3.49959i	−0.126206	−	0.158257i
$490$	4.79820	−	0.723212i	0.216760	−	0.0326714i
$491$	−22.3567	−	6.89614i	−1.00895	−	0.311219i	−0.254140	−	0.967167i	$-0.581793\pi$
$491$	−22.3567	−	6.89614i	−1.00895	−	0.311219i	−0.754805	+	0.655949i	$0.772269\pi$
$492$	−0.221306	−	2.95313i	−0.00997726	−	0.133137i
$493$	−11.4172	−	7.78414i	−0.514206	−	0.350580i
$494$	0.582739	+	2.55315i	0.0262187	+	0.114871i
$495$	−2.52616	−	11.0678i	−0.113542	−	0.497462i
$496$	−10.9213	−	7.44601i	−0.490380	−	0.334336i
$497$	1.43981	+	19.2130i	0.0645844	+	0.861819i
$498$	5.90312	+	1.82087i	0.264525	+	0.0815952i
$499$	−39.0722	+	5.88919i	−1.74911	+	0.263636i	−0.944109	−	0.329632i	$-0.893075\pi$
$499$	−39.0722	+	5.88919i	−1.74911	+	0.263636i	−0.805004	+	0.593269i	$0.797837\pi$
$500$	−0.382391	−	0.479503i	−0.0171010	−	0.0214440i
$501$	1.03526	−	0.705825i	0.0462518	−	0.0315339i
$502$	−1.70910	−	1.58581i	−0.0762809	−	0.0707783i
$503$	5.77003	+	14.7018i	0.257273	+	0.655521i	0.999899	−	0.0141848i	$-0.00451533\pi$
$503$	5.77003	+	14.7018i	0.257273	+	0.655521i	−0.742626	+	0.669706i	$0.766420\pi$
$504$	14.0308	−	4.32794i	0.624984	−	0.192782i
$505$	16.5476	−	7.96888i	0.736357	−	0.354611i
$506$	14.8134	−	37.7440i	0.658537	−	1.67793i
$507$	−0.0400730	+	0.534736i	−0.00177970	+	0.0237485i
$508$	3.79039	−	4.75300i	0.168171	−	0.210880i
$509$	−6.72900	+	11.6550i	−0.298258	+	0.516598i	−0.975737	−	0.218944i	$-0.929739\pi$
$509$	−6.72900	+	11.6550i	−0.298258	+	0.516598i	0.677480	+	0.735542i	$0.263072\pi$
$510$	−0.982178	−	1.70118i	−0.0434916	−	0.0753296i
$511$	−4.45547	−	0.671554i	−0.197098	−	0.0297078i
$512$	20.4894	+	9.86720i	0.905514	+	0.436073i
$513$	1.08922	−	1.01064i	0.0480900	−	0.0446210i
$514$	−1.70832	+	7.48464i	−0.0753508	+	0.330133i
$515$	2.20630			0.0972212
$516$	1.71463	−	0.321257i	0.0754822	−	0.0141426i
$517$	−6.66316			−0.293045
$518$	−2.87728	+	12.6062i	−0.126420	+	0.553883i
$519$	5.96972	−	5.53909i	0.262041	−	0.243139i
$520$	10.4614	+	5.03793i	0.458761	+	0.220928i
$521$	41.9641	+	6.32507i	1.83848	+	0.277107i	0.974164	−	0.225840i	$-0.0725128\pi$
$521$	41.9641	+	6.32507i	1.83848	+	0.277107i	0.864317	+	0.502947i	$0.167751\pi$
$522$	5.94877	+	10.3036i	0.260371	+	0.450975i
$523$	−10.0976	+	17.4896i	−0.441539	+	0.764768i	−0.997804	−	0.0662372i	$-0.978901\pi$
$523$	−10.0976	+	17.4896i	−0.441539	+	0.764768i	0.556265	+	0.831005i	$0.312234\pi$
$524$	−5.95003	+	7.46110i	−0.259928	+	0.325939i
$525$	−0.0550037	+	0.733973i	−0.00240056	+	0.0320332i
$526$	−11.0414	+	28.1330i	−0.481428	+	1.22666i
$527$	19.1050	−	9.20049i	0.832227	−	0.400780i
$528$	−4.01164	+	1.23743i	−0.174584	+	0.0538521i
$529$	18.1700	+	46.2963i	0.789998	+	2.01288i
$530$	0.00584430	+	0.00542271i	0.000253860	+	0.000235548i
$531$	−3.39192	+	2.31257i	−0.147197	+	0.100357i
$532$	0.382446	+	0.479572i	0.0165811	+	0.0207921i
$533$	41.5328	−	6.26006i	1.79898	−	0.271153i
$534$	−6.19705	−	1.91154i	−0.268173	−	0.0827203i
$535$	0.592746	+	7.90965i	0.0256267	+	0.341964i
$536$	−17.2430	−	11.7561i	−0.744786	−	0.507786i
$537$	1.14834	+	5.03121i	0.0495546	+	0.217113i
$538$	−8.01394	−	35.1114i	−0.345505	−	1.51376i
$539$	13.7458	+	9.37171i	0.592072	+	0.403668i
$540$	−0.115541	−	1.54179i	−0.00497211	−	0.0663482i
$541$	−26.7891	−	8.26335i	−1.15175	−	0.355269i	−0.340662	−	0.940186i	$-0.610651\pi$
$541$	−26.7891	−	8.26335i	−1.15175	−	0.355269i	−0.811093	+	0.584917i	$0.801127\pi$
$542$	−20.8052	+	3.13588i	−0.893659	+	0.134697i
$543$	3.42430	+	4.29393i	0.146951	+	0.184270i
$544$	−10.5869	+	7.21799i	−0.453908	+	0.309469i
$545$	−9.56527	−	8.87527i	−0.409731	−	0.380175i
$546$	−1.19477	−	3.04421i	−0.0511313	−	0.130280i
$547$	19.7154	−	6.08139i	0.842969	−	0.260021i	0.156951	−	0.987606i	$-0.449834\pi$
$547$	19.7154	−	6.08139i	0.842969	−	0.260021i	0.686018	+	0.727585i	$0.259357\pi$
$548$	7.28038	−	3.50605i	0.311002	−	0.149771i
$549$	−0.0234877	+	0.0598457i	−0.00100243	+	0.00255415i
$550$	−0.355290	+	4.74102i	−0.0151496	+	0.202158i
$551$	−1.32044	+	1.65578i	−0.0562527	+	0.0705386i
$552$	5.69206	−	9.85894i	0.242270	−	0.419624i
$553$	5.85312	+	10.1379i	0.248900	+	0.431107i
$554$	3.54431	+	0.534219i	0.150583	+	0.0226968i
$555$	2.52891	+	1.21786i	0.107346	+	0.0516952i
$556$	0.971281	−	0.901217i	0.0411915	−	0.0382201i
$557$	3.65663	−	16.0207i	0.154936	−	0.678820i	−0.836471	−	0.548011i	$-0.815385\pi$
$557$	3.65663	−	16.0207i	0.154936	−	0.678820i	0.991408	−	0.130809i	$-0.0417575\pi$
$558$	−18.2574			−0.772898
$559$	6.36101	+	23.9102i	0.269042	+	1.01129i
$560$	−4.06779			−0.171895
$561$	1.49864	−	6.56599i	0.0632728	−	0.277216i
$562$	−1.80946	+	1.67893i	−0.0763273	+	0.0708214i
$563$	21.7852	+	10.4912i	0.918136	+	0.442151i	0.832405	−	0.554167i	$-0.186963\pi$
$563$	21.7852	+	10.4912i	0.918136	+	0.442151i	0.0857308	+	0.996318i	$0.472678\pi$
$564$	−0.434142	−	0.0654364i	−0.0182807	−	0.00275537i
$565$	−4.46697	−	7.73702i	−0.187927	−	0.325499i
$566$	9.56480	−	16.5667i	0.402039	−	0.696351i
$567$	7.76774	−	9.74044i	0.326215	−	0.409060i
$568$	−2.61120	+	34.8440i	−0.109563	+	1.46202i
$569$	10.5079	−	26.7738i	0.440516	−	1.12242i	−0.522421	−	0.852688i	$-0.674971\pi$
$569$	10.5079	−	26.7738i	0.440516	−	1.12242i	0.962936	−	0.269728i	$-0.0869339\pi$
$570$	−0.271247	+	0.130626i	−0.0113613	+	0.00547130i
$571$	−28.6757	+	8.84528i	−1.20004	+	0.370163i	−0.829422	−	0.558622i	$-0.811330\pi$
$571$	−28.6757	+	8.84528i	−1.20004	+	0.370163i	−0.370618	+	0.928785i	$0.620854\pi$
$572$	3.41328	+	8.69690i	0.142716	+	0.363636i
$573$	6.26890	+	5.81669i	0.261887	+	0.242996i
$574$	−18.3787	+	12.5304i	−0.767110	+	0.523007i
$575$	−5.31739	−	6.66780i	−0.221751	−	0.278067i
$576$	24.2398	−	3.65356i	1.00999	−	0.152232i
$577$	−4.91455	−	1.51594i	−0.204596	−	0.0631094i	0.190763	−	0.981636i	$-0.438904\pi$
$577$	−4.91455	−	1.51594i	−0.204596	−	0.0631094i	−0.395359	+	0.918527i	$0.629380\pi$
$578$	−0.194502	−	2.59544i	−0.00809020	−	0.107956i
$579$	−2.62119	−	1.78710i	−0.108933	−	0.0742693i
$580$	0.490370	+	2.14845i	0.0203615	+	0.0892095i
$581$	4.56664	+	20.0077i	0.189456	+	0.830061i
$582$	−6.19113	−	4.22104i	−0.256631	−	0.174968i
$583$	0.00204268	+	0.0272577i	8.45992e−5	+	0.00112890i
$584$	−7.80852	−	2.40861i	−0.323119	−	0.0996690i
$585$	10.4909	−	1.58125i	0.433745	−	0.0653765i
$586$	−0.773474	−	0.969906i	−0.0319519	−	0.0400665i
$587$	−11.0778	+	7.55275i	−0.457232	+	0.311735i	−0.769943	−	0.638113i	$-0.779715\pi$
$587$	−11.0778	+	7.55275i	−0.457232	+	0.311735i	0.312711	+	0.949848i	$0.398763\pi$
$588$	0.803578	+	0.745612i	0.0331390	+	0.0307485i
$589$	−1.18733	−	3.02526i	−0.0489230	−	0.124654i
$590$	1.64286	−	0.506756i	0.0676356	−	0.0208628i
$591$	−9.03117	+	4.34918i	−0.371493	+	0.178902i
$592$	−5.66739	+	14.4403i	−0.232928	+	0.593492i
$593$	0.877773	−	11.7131i	0.0360458	−	0.480998i	−0.949745	−	0.313023i	$-0.898658\pi$
$593$	0.877773	−	11.7131i	0.0360458	−	0.480998i	0.985791	−	0.167975i	$-0.0537227\pi$
$594$	−7.47276	+	9.37054i	−0.306611	+	0.384478i
$595$	3.26285	−	5.65143i	0.133764	−	0.231686i
$596$	−3.97618	−	6.88694i	−0.162871	−	0.282100i
$597$	−6.59356	−	0.993820i	−0.269857	−	0.0406743i
$598$	34.1403	+	16.4411i	1.39610	+	0.672326i
$599$	−30.7055	+	28.4906i	−1.25459	+	1.16409i	−0.275364	+	0.961340i	$0.588798\pi$
$599$	−30.7055	+	28.4906i	−1.25459	+	1.16409i	−0.979230	+	0.202753i	$0.935011\pi$
$600$	−0.297030	+	1.30138i	−0.0121262	+	0.0531284i
$601$	8.37211			0.341505			0.170753	−	0.985314i	$-0.445380\pi$
$601$	8.37211			0.341505			0.170753	+	0.985314i	$0.445380\pi$
$602$	−8.52920	−	9.94695i	−0.347624	−	0.405407i
$603$	−19.0687			−0.776536
$604$	2.44915	−	10.7304i	0.0996544	−	0.436614i
$605$	−3.88538	+	3.60511i	−0.157963	+	0.146569i
$606$	−8.45227	−	4.07040i	−0.343350	−	0.165349i
$607$	17.8912	+	2.69666i	0.726181	+	0.109454i	0.501722	−	0.865029i	$-0.332700\pi$
$607$	17.8912	+	2.69666i	0.726181	+	0.109454i	0.224460	+	0.974483i	$0.427938\pi$
$608$	0.981897	+	1.70070i	0.0398212	+	0.0689723i
$609$	1.32233	−	2.29035i	0.0535836	−	0.0928096i
$610$	0.0167868	−	0.0210500i	0.000679679	−	0.000852291i
$611$	0.465346	−	6.20961i	0.0188259	−	0.251214i
$612$	−2.42298	+	6.17365i	−0.0979432	+	0.249555i
$613$	24.0114	−	11.5633i	0.969811	−	0.467037i	0.119222	−	0.992868i	$-0.461960\pi$
$613$	24.0114	−	11.5633i	0.969811	−	0.467037i	0.850589	+	0.525831i	$0.176246\pi$
$614$	4.82038	−	1.48689i	0.194535	−	0.0600060i
$615$	1.76408	+	4.49481i	0.0711347	+	0.181248i
$616$	−15.4547	−	14.3398i	−0.622687	−	0.577769i
$617$	−39.2142	+	26.7358i	−1.57871	+	1.07634i	−0.622917	+	0.782288i	$0.714053\pi$
$617$	−39.2142	+	26.7358i	−1.57871	+	1.07634i	−0.955788	+	0.294056i	$0.904995\pi$
$618$	−0.702641	−	0.881084i	−0.0282644	−	0.0354424i
$619$	14.9242	−	2.24946i	0.599854	−	0.0904135i	0.157906	−	0.987454i	$-0.449526\pi$
$619$	14.9242	−	2.24946i	0.599854	−	0.0904135i	0.441948	+	0.897041i	$0.354288\pi$
$620$	−3.23146	−	0.996773i	−0.129779	−	0.0400314i
$621$	−1.60668	−	21.4396i	−0.0644738	−	0.860343i
$622$	−9.75564	−	6.65128i	−0.391165	−	0.266692i
$623$	−4.79402	−	21.0040i	−0.192068	−	0.841507i
$624$	−0.873031	−	3.82500i	−0.0349492	−	0.153122i
$625$	0.826239	+	0.563320i	0.0330496	+	0.0225328i
$626$	1.01043	+	13.4833i	0.0403849	+	0.538899i
$627$	−0.986338	−	0.304245i	−0.0393906	−	0.0121504i
$628$	−6.27066	+	0.945149i	−0.250226	+	0.0377156i
$629$	−15.5161	−	19.4566i	−0.618669	−	0.775786i
$630$	−4.64232	+	3.16508i	−0.184955	+	0.126100i
$631$	−4.17771	−	3.87635i	−0.166312	−	0.154315i	0.592626	−	0.805478i	$-0.298091\pi$
$631$	−4.17771	−	3.87635i	−0.166312	−	0.154315i	−0.758938	+	0.651163i	$0.774282\pi$
$632$	7.75621	+	19.7625i	0.308525	+	0.786110i
$633$	−7.14639	+	2.20437i	−0.284044	+	0.0876159i
$634$	15.4239	−	7.42778i	0.612563	−	0.294995i
$635$	−3.62139	+	9.22714i	−0.143710	+	0.366168i
$636$	−0.000134595		0.00179605i	−5.33706e−6		7.12181e-5i
$637$	−9.69378	+	12.1556i	−0.384082	+	0.481623i
$638$	8.54146	−	14.7942i	0.338160	−	0.585710i
$639$	15.9634	+	27.6494i	0.631503	+	1.09380i
$640$	−3.56222	−	0.536918i	−0.140809	−	0.0212235i
$641$	14.1604	+	6.81930i	0.559303	+	0.269346i	0.692105	−	0.721796i	$-0.256683\pi$
$641$	14.1604	+	6.81930i	0.559303	+	0.269346i	−0.132803	+	0.991143i	$0.542398\pi$
$642$	2.96994	−	2.75570i	0.117214	−	0.108759i
$643$	−8.00808	+	35.0857i	−0.315808	+	1.38364i	0.529022	+	0.848608i	$0.322559\pi$
$643$	−8.00808	+	35.0857i	−0.315808	+	1.38364i	−0.844830	+	0.535036i	$0.820298\pi$
$644$	8.87554			0.349745
$645$	−2.51710	+	1.32459i	−0.0991109	+	0.0521556i
$646$	2.66923			0.105019
$647$	−10.1908	+	44.6490i	−0.400644	+	1.75533i	0.224160	+	0.974552i	$0.428036\pi$
$647$	−10.1908	+	44.6490i	−0.400644	+	1.75533i	−0.624804	+	0.780782i	$0.714821\pi$
$648$	16.5628	−	15.3680i	0.650648	−	0.603713i
$649$	5.31074	+	2.55752i	0.208465	+	0.100391i
$650$	−4.39349	−	0.662212i	−0.172327	−	0.0259741i
$651$	2.02919	+	3.51466i	0.0795303	+	0.137751i
$652$	3.16449	−	5.48105i	0.123931	−	0.214654i
$653$	−18.6779	+	23.4214i	−0.730923	+	0.916549i	−0.998901	−	0.0468765i	$-0.985073\pi$
$653$	−18.6779	+	23.4214i	−0.730923	+	0.916549i	0.267978	+	0.963425i	$0.413645\pi$
$654$	−0.498078	+	6.64639i	−0.0194764	+	0.259894i
$655$	5.68473	−	14.4845i	0.222121	−	0.565954i
$656$	−24.0432	+	11.5786i	−0.938729	+	0.452068i
$657$	−7.13478	+	2.20079i	−0.278354	+	0.0858609i
$658$	1.20481	+	3.06980i	0.0469683	+	0.119673i
$659$	1.68861	+	1.56680i	0.0657787	+	0.0610337i	0.712377	−	0.701797i	$-0.247619\pi$
$659$	1.68861	+	1.56680i	0.0657787	+	0.0610337i	−0.646598	+	0.762831i	$0.723809\pi$
$660$	−0.887423	+	0.605035i	−0.0345429	+	0.0235509i
$661$	7.51138	+	9.41898i	0.292159	+	0.366356i	0.906149	−	0.422958i	$-0.139008\pi$
$661$	7.51138	+	9.41898i	0.292159	+	0.366356i	−0.613990	+	0.789313i	$0.710437\pi$
$662$	−9.68247	+	1.45940i	−0.376320	+	0.0567211i
$663$	6.01439	+	1.85519i	0.233580	+	0.0720498i
$664$	2.78134	+	37.1144i	0.107937	+	1.44032i
$665$	−0.826357	−	0.563401i	−0.0320448	−	0.0218477i
$666$	4.76790	+	20.8895i	0.184752	+	0.809453i
$667$	6.81891	+	29.8756i	0.264029	+	1.15679i
$668$	1.46378	+	0.997989i	0.0566354	+	0.0386134i
$669$	−0.497510	−	6.63881i	−0.0192349	−	0.256671i
$670$	7.63100	+	2.35385i	0.294811	+	0.0909372i
$671$	0.0912786	−	0.0137580i	0.00352377	−	0.000531123i
$672$	−1.52900	−	1.91730i	−0.0589823	−	0.0739615i
$673$	−0.799261	+	0.544927i	−0.0308092	+	0.0210054i	−0.578627	−	0.815592i	$-0.696411\pi$
$673$	−0.799261	+	0.544927i	−0.0308092	+	0.0210054i	0.547818	+	0.836598i	$0.315459\pi$
$674$	−16.9251	−	15.7042i	−0.651929	−	0.604902i
$675$	0.921006	+	2.34668i	0.0354495	+	0.0903239i
$676$	−0.724517	+	0.223484i	−0.0278660	+	0.00859553i
$677$	−26.4223	+	12.7243i	−1.01549	+	0.489035i	−0.866168	−	0.499753i	$-0.833424\pi$
$677$	−26.4223	+	12.7243i	−1.01549	+	0.489035i	−0.149324	+	0.988788i	$0.547710\pi$
$678$	−1.66718	+	4.24789i	−0.0640275	+	0.163139i
$679$	1.86023	−	24.8231i	0.0713892	−	0.952623i
$680$	7.37888	−	9.25283i	0.282967	−	0.354830i
$681$	2.10576	−	3.64729i	0.0806930	−	0.139764i
$682$	13.1073	+	22.7026i	0.501906	+	0.869326i
$683$	−32.8364	−	4.94929i	−1.25645	−	0.189379i	−0.513127	−	0.858313i	$-0.671513\pi$
$683$	−32.8364	−	4.94929i	−1.25645	−	0.189379i	−0.743322	+	0.668933i	$0.766751\pi$
$684$	0.915790	+	0.441021i	0.0350161	+	0.0168629i
$685$	−9.65830	+	8.96159i	−0.369025	+	0.342405i
$686$	4.94468	−	21.6641i	0.188789	−	0.827138i
$687$	2.19040			0.0835691
$688$	−8.33965	−	13.3252i	−0.317946	−	0.508018i
$689$	−0.0255450			−0.000973185
$690$	−0.969348	+	4.24699i	−0.0369025	+	0.161680i
$691$	11.3355	−	10.5178i	0.431221	−	0.400115i	−0.434476	−	0.900684i	$-0.643066\pi$
$691$	11.3355	−	10.5178i	0.431221	−	0.400115i	0.865697	+	0.500569i	$0.166876\pi$
$692$	10.3743	+	4.99599i	0.394371	+	0.189919i
$693$	−19.0484	−	2.87109i	−0.723590	−	0.109064i
$694$	8.35014	+	14.4629i	0.316967	+	0.549003i
$695$	−1.08019	+	1.87095i	−0.0409741	+	0.0709692i
$696$	2.99043	−	3.74988i	0.113352	−	0.142139i
$697$	3.19924	−	42.6909i	0.121180	−	1.61703i
$698$	12.4220	−	31.6508i	0.470181	−	1.19800i
$699$	−9.20744	+	4.43407i	−0.348257	+	0.167712i
$700$	−0.994464	+	0.306751i	−0.0375872	+	0.0115941i
$701$	12.1459	+	30.9472i	0.458743	+	1.16886i	0.953919	+	0.300065i	$0.0970085\pi$
$701$	12.1459	+	30.9472i	0.458743	+	1.16886i	−0.495176	+	0.868793i	$0.664896\pi$
$702$	−8.21082	−	7.61853i	−0.309897	−	0.287543i
$703$	−3.15133	+	2.14854i	−0.118855	+	0.0810338i
$704$	−21.9453	−	27.5185i	−0.827094	−	1.03714i
$705$	0.707870	−	0.106694i	0.0266599	−	0.00401834i
$706$	−5.14525	−	1.58710i	−0.193644	−	0.0597313i
$707$	−2.32899	−	31.0781i	−0.0875905	−	1.16881i
$708$	0.320908	+	0.218791i	0.0120605	+	0.00822268i
$709$	5.41212	+	23.7120i	0.203256	+	0.890525i	0.968938	+	0.247305i	$0.0795448\pi$
$709$	5.41212	+	23.7120i	0.203256	+	0.890525i	−0.765681	+	0.643220i	$0.777598\pi$
$710$	−2.97526	−	13.0354i	−0.111659	−	0.489212i
$711$	16.0276	+	10.9274i	0.601082	+	0.409811i
$712$	−2.91983	−	38.9625i	−0.109425	−	1.46018i
$713$	−44.9355	−	13.8608i	−1.68285	−	0.519090i
$714$	−3.29602	+	0.496794i	−0.123350	+	0.0185921i
$715$	−9.49784	−	11.9099i	−0.355199	−	0.445405i
$716$	−6.02885	+	4.11040i	−0.225309	+	0.153613i
$717$	5.85007	+	5.42807i	0.218475	+	0.202715i
$718$	3.58821	+	9.14260i	0.133911	+	0.341199i
$719$	12.5977	−	3.88587i	0.469814	−	0.144919i	−0.0508029	−	0.998709i	$-0.516178\pi$
$719$	12.5977	−	3.88587i	0.469814	−	0.144919i	0.520617	+	0.853790i	$0.325702\pi$
$720$	−6.07315	+	2.92467i	−0.226333	+	0.108996i
$721$	1.36776	−	3.48500i	0.0509381	−	0.129788i
$722$	−1.64144	+	21.9035i	−0.0610881	+	0.815164i
$723$	3.67151	−	4.60393i	0.136545	−	0.171222i
$724$	−3.88276	+	6.72514i	−0.144302	+	0.249938i
$725$	−1.79657	−	3.11175i	−0.0667230	−	0.115568i
$726$	2.67708	+	0.403504i	0.0993556	+	0.0149754i
$727$	−33.5693	−	16.1661i	−1.24502	−	0.599568i	−0.308844	−	0.951113i	$-0.599942\pi$
$727$	−33.5693	−	16.1661i	−1.24502	−	0.599568i	−0.936171	+	0.351545i	$0.885657\pi$
$728$	14.4431	−	13.4012i	0.535297	−	0.496683i
$729$	3.86393	−	16.9290i	0.143109	−	0.627000i
$730$	3.12690			0.115732
$731$	25.2023	−	0.897977i	0.932139	−	0.0332129i
$732$	0.00608243			0.000224813
$733$	−9.60096	+	42.0645i	−0.354619	+	1.55369i	0.411755	+	0.911295i	$0.364916\pi$
$733$	−9.60096	+	42.0645i	−0.354619	+	1.55369i	−0.766374	+	0.642394i	$0.777941\pi$
$734$	−11.2132	+	10.4043i	−0.413887	+	0.384031i
$735$	−1.61037	−	0.775512i	−0.0593993	−	0.0286052i
$736$	28.0978	+	4.23506i	1.03570	+	0.156106i
$737$	13.6897	+	23.7113i	0.504268	+	0.873418i
$738$	−18.4299	+	31.9216i	−0.678415	+	1.17505i
$739$	27.5845	−	34.5899i	1.01471	−	1.27241i	0.0529301	−	0.998598i	$-0.483144\pi$
$739$	27.5845	−	34.5899i	1.01471	−	1.27241i	0.961783	−	0.273812i	$-0.0882846\pi$
$740$	−0.296584	+	3.95763i	−0.0109026	+	0.145486i
$741$	0.352420	−	0.897952i	0.0129465	−	0.0329871i
$742$	0.0121886	−	0.00586973i	0.000447458	−	0.000215484i
$743$	−11.2432	+	3.46807i	−0.412473	+	0.127231i	−0.494045	−	0.869436i	$-0.664482\pi$
$743$	−11.2432	+	3.46807i	−0.412473	+	0.127231i	0.0815718	+	0.996667i	$0.474006\pi$
$744$	2.68897	+	6.85137i	0.0985822	+	0.251183i
$745$	9.50500	+	8.81935i	0.348236	+	0.323116i
$746$	21.6753	−	14.7780i	0.793590	−	0.541060i
$747$	21.2031	+	26.5879i	0.775783	+	0.972801i
$748$	9.41626	−	1.41927i	0.344293	−	0.0518938i
$749$	12.8613	+	3.96718i	0.469941	+	0.144958i
$750$	−0.0381711	−	0.509358i	−0.00139381	−	0.0185991i
$751$	−6.12868	−	4.17847i	−0.223639	−	0.152474i	0.446318	−	0.894874i	$-0.352735\pi$
$751$	−6.12868	−	4.17847i	−0.223639	−	0.152474i	−0.669957	+	0.742400i	$0.733687\pi$
$752$	0.880369	+	3.85715i	0.0321038	+	0.140656i
$753$	0.191101	+	0.837268i	0.00696411	+	0.0305118i
$754$	13.1907	+	8.99327i	0.480377	+	0.327516i
$755$	1.34110	+	17.8957i	0.0488077	+	0.651293i
$756$	−2.50699	−	0.773305i	−0.0911784	−	0.0281248i
$757$	29.9574	−	4.51535i	1.08882	−	0.164113i	0.419990	−	0.907529i	$-0.362034\pi$
$757$	29.9574	−	4.51535i	1.08882	−	0.164113i	0.668830	+	0.743416i	$0.266796\pi$
$758$	13.0513	+	16.3658i	0.474046	+	0.594434i
$759$	−12.3402	+	8.41340i	−0.447921	+	0.305387i
$760$	−1.32963	−	1.23372i	−0.0482307	−	0.0447516i
$761$	1.66987	+	4.25476i	0.0605327	+	0.154235i	0.957940	−	0.286968i	$-0.0926473\pi$
$761$	1.66987	+	4.25476i	0.0605327	+	0.154235i	−0.897408	+	0.441203i	$0.854552\pi$
$762$	4.83815	−	1.49237i	0.175268	−	0.0540630i
$763$	−19.9489	+	9.60689i	−0.722199	+	0.347793i
$764$	−4.41757	+	11.2558i	−0.159822	+	0.407220i
$765$	0.808107	−	10.7834i	0.0292172	−	0.389876i
$766$	−13.7106	+	17.1926i	−0.495385	+	0.621194i
$767$	−2.75432	+	4.77063i	−0.0994529	+	0.172257i
$768$	−2.86146	−	4.95619i	−0.103254	−	0.178841i
$769$	24.7530	+	3.73091i	0.892615	+	0.134540i	0.579305	−	0.815111i	$-0.303324\pi$
$769$	24.7530	+	3.73091i	0.892615	+	0.134540i	0.313310	+	0.949651i	$0.398562\pi$
$770$	7.26850	+	3.50032i	0.261938	+	0.126143i
$771$	2.07297	−	1.92343i	0.0746561	−	0.0692708i
$772$	0.998144	−	4.37315i	0.0359240	−	0.157393i
$773$	−17.5769			−0.632198			−0.316099	−	0.948726i	$-0.602373\pi$
$773$	−17.5769			−0.632198			−0.316099	+	0.948726i	$0.602373\pi$
$774$	−19.8857	−	8.71829i	−0.714775	−	0.313372i
$775$	5.51387			0.198064
$776$	10.0456	−	44.0127i	0.360616	−	1.57996i
$777$	3.49144	−	3.23958i	0.125255	−	0.116219i
$778$	−9.31411	−	4.48544i	−0.333927	−	0.160811i
$779$	−6.48796	−	0.977903i	−0.232455	−	0.0350370i
$780$	−0.501875	−	0.869273i	−0.0179700	−	0.0311250i
$781$	22.9209	−	39.7001i	0.820173	−	1.42058i
$782$	24.0807	−	30.1963i	0.861125	−	1.07982i
$783$	0.676915	−	9.03280i	0.0241910	−	0.322806i
$784$	3.60891	−	9.19535i	0.128890	−	0.328405i
$785$	9.31585	−	4.48628i	0.332497	−	0.160122i
$786$	−7.59477	+	2.34268i	−0.270896	+	0.0835605i
$787$	−10.8292	−	27.5924i	−0.386019	−	0.983561i	−0.983375	−	0.181585i	$-0.941877\pi$
$787$	−10.8292	−	27.5924i	−0.386019	−	0.983561i	0.597356	−	0.801976i	$-0.296218\pi$
$788$	−10.3896	−	9.64012i	−0.370113	−	0.343415i
$789$	9.19794	−	6.27105i	0.327455	−	0.223255i
$790$	−5.06512	−	6.35146i	−0.180209	−	0.225975i
$791$	−14.9904	+	2.25943i	−0.532996	+	0.0803362i
$792$	−33.3837	−	10.2975i	−1.18624	−	0.365906i
$793$	0.00644678	+	0.0860263i	0.000228932	+	0.00305488i
$794$	2.16300	+	1.47471i	0.0767621	+	0.0523355i
$795$	−0.000653473	−	0.00286305i	−2.31763e−5	−	0.000101542i
$796$	−2.09796	−	9.19177i	−0.0743603	−	0.325794i
$797$	23.5387	+	16.0484i	0.833782	+	0.568463i	0.903247	−	0.429122i	$-0.141177\pi$
$797$	23.5387	+	16.0484i	0.833782	+	0.568463i	−0.0694649	+	0.997584i	$0.522129\pi$
$798$	0.0381766	+	0.509431i	0.00135144	+	0.0180337i
$799$	−6.06495	−	1.87079i	−0.214562	−	0.0661837i
$800$	−3.29460	+	0.496581i	−0.116482	+	0.0175568i
$801$	−22.2589	−	27.9118i	−0.786480	−	0.986215i
$802$	21.4969	−	14.6564i	0.759083	−	0.517534i
$803$	7.85881	+	7.29191i	0.277331	+	0.257326i
$804$	0.659104	+	1.67937i	0.0232448	+	0.0592268i
$805$	−13.8287	+	4.26558i	−0.487396	+	0.150342i
$806$	−22.0726	+	10.6296i	−0.777476	+	0.374413i
$807$	−4.84655	+	12.3488i	−0.170607	+	0.434699i
$808$	4.22377	−	56.3623i	0.148592	−	1.98282i
$809$	9.11999	−	11.4361i	0.320642	−	0.402072i	−0.595222	−	0.803561i	$-0.702936\pi$
$809$	9.11999	−	11.4361i	0.320642	−	0.402072i	0.915864	+	0.401489i	$0.131507\pi$
$810$	−4.32293	+	7.48754i	−0.151892	+	0.263085i
$811$	26.9268	+	46.6386i	0.945528	+	1.63770i	0.754691	+	0.656080i	$0.227787\pi$
$811$	26.9268	+	46.6386i	0.945528	+	1.63770i	0.190836	+	0.981622i	$0.438880\pi$
$812$	3.69761	+	0.557326i	0.129761	+	0.0195583i
$813$	6.98262	+	3.36265i	0.244891	+	0.117933i
$814$	22.5526	−	20.9257i	0.790467	−	0.733446i
$815$	−2.29628	+	10.0607i	−0.0804354	+	0.352410i
$816$	−3.99891			−0.139990
$817$	0.151408	−	3.86203i	0.00529708	−	0.135115i
$818$	−2.62246			−0.0916921
$819$	4.00597	−	17.5513i	0.139980	−	0.613293i
$820$	−5.00477	+	4.64374i	−0.174774	+	0.162167i
$821$	18.7417	+	9.02551i	0.654088	+	0.314992i	0.731334	−	0.682020i	$-0.238898\pi$
$821$	18.7417	+	9.02551i	0.654088	+	0.314992i	−0.0772454	+	0.997012i	$0.524613\pi$
$822$	6.65468	+	1.00303i	0.232109	+	0.0349848i
$823$	−3.72898	−	6.45878i	−0.129984	−	0.225139i	0.793686	−	0.608328i	$-0.208159\pi$
$823$	−3.72898	−	6.45878i	−0.129984	−	0.225139i	−0.923670	+	0.383189i	$0.874826\pi$
$824$	3.39481	−	5.87998i	0.118264	−	0.204839i
$825$	1.09188	−	1.36918i	0.0380145	−	0.0476687i
$826$	0.218012	−	2.90917i	0.00758560	−	0.101223i
$827$	5.05229	−	12.8730i	0.175685	−	0.447639i	−0.815723	−	0.578443i	$-0.803661\pi$
$827$	5.05229	−	12.8730i	0.175685	−	0.447639i	0.991408	+	0.130804i	$0.0417559\pi$
$828$	13.2510	−	6.38136i	0.460505	−	0.221768i
$829$	−30.7357	+	9.48072i	−1.06750	+	0.329279i	−0.778236	−	0.627972i	$-0.783885\pi$
$829$	−30.7357	+	9.48072i	−1.06750	+	0.329279i	−0.289260	+	0.957251i	$0.593409\pi$
$830$	−5.20316	−	13.2574i	−0.180604	−	0.460172i
$831$	−0.967840	−	0.898024i	−0.0335740	−	0.0311521i
$832$	27.1780	−	18.5297i	0.942228	−	0.642401i
$833$	9.88043	+	12.3897i	0.342337	+	0.429277i
$834$	1.09117	−	0.164468i	0.0377842	−	0.00569505i
$835$	−2.76030	−	0.851440i	−0.0955241	−	0.0294653i
$836$	−0.109065	−	1.45537i	−0.00377210	−	0.0503352i
$837$	11.4849	+	7.83026i	0.396975	+	0.270653i
$838$	−3.13381	−	13.7301i	−0.108256	−	0.474300i
$839$	−3.34371	−	14.6498i	−0.115438	−	0.505766i	−0.999279	−	0.0379782i	$-0.987908\pi$
$839$	−3.34371	−	14.6498i	−0.115438	−	0.505766i	0.883841	−	0.467788i	$-0.154949\pi$
$840$	1.87147	+	1.27595i	0.0645718	+	0.0440243i
$841$	−1.20236	−	16.0443i	−0.0414606	−	0.553253i
$842$	13.3270	+	4.11085i	0.459280	+	0.141669i
$843$	0.899072	−	0.135513i	0.0309657	−	0.00466733i
$844$	−6.59297	−	8.26733i	−0.226939	−	0.284573i
$845$	1.02144	−	0.696405i	0.0351385	−	0.0239570i
$846$	4.00590	+	3.71693i	0.137726	+	0.127791i
$847$	3.28583	+	8.37215i	0.112902	+	0.287670i
$848$	0.0155090	−	0.00478388i	0.000532580	−	0.000164279i
$849$	−6.34856	+	3.05730i	−0.217882	+	0.104926i
$850$	−1.65451	+	4.21562i	−0.0567492	+	0.144595i
$851$	−4.12419	+	55.0335i	−0.141375	+	1.88652i
$852$	1.88330	−	2.36159i	0.0645209	−	0.0809067i
$853$	−3.21266	+	5.56448i	−0.109999	+	0.190524i	−0.915770	−	0.401704i	$-0.868418\pi$
$853$	−3.21266	+	5.56448i	−0.109999	+	0.190524i	0.805770	+	0.592228i	$0.201752\pi$
$854$	−0.0228432	−	0.0395656i	−0.000781678	−	0.00135391i
$855$	−1.63881	−	0.247011i	−0.0560463	−	0.00844762i
$856$	21.9919	+	10.5908i	0.751669	+	0.361985i
$857$	22.1790	−	20.5791i	0.757619	−	0.702967i	−0.203509	−	0.979073i	$-0.565234\pi$
$857$	22.1790	−	20.5791i	0.757619	−	0.702967i	0.961127	+	0.276106i	$0.0890440\pi$
$858$	−1.73143	+	7.58590i	−0.0591102	+	0.258979i
$859$	29.1381			0.994178			0.497089	−	0.867700i	$-0.334402\pi$
$859$	29.1381			0.994178			0.497089	+	0.867700i	$0.334402\pi$
$860$	−3.04367	−	2.62876i	−0.103788	−	0.0896398i
$861$	8.19346			0.279232
$862$	1.50374	−	6.58830i	0.0512174	−	0.224398i
$863$	3.87157	−	3.59229i	0.131790	−	0.122283i	−0.611524	−	0.791226i	$-0.709443\pi$
$863$	3.87157	−	3.59229i	0.131790	−	0.122283i	0.743314	+	0.668943i	$0.233253\pi$
$864$	−7.56753	−	3.64433i	−0.257453	−	0.123983i
$865$	−18.5649	−	2.79820i	−0.631224	−	0.0951417i
$866$	−5.10405	−	8.84047i	−0.173443	−	0.300411i
$867$	−0.479355	+	0.830267i	−0.0162797	+	0.0281973i
$868$	−3.57776	+	4.48637i	−0.121437	+	0.152277i
$869$	2.08144	−	27.7749i	0.0706079	−	0.942198i
$870$	−0.670521	+	1.70846i	−0.0227328	+	0.0579222i
$871$	−23.0534	+	11.1019i	−0.781135	+	0.376175i
$872$	−38.3713	+	11.8360i	−1.29942	+	0.400817i
$873$	−15.0701	−	38.3980i	−0.510045	−	1.29957i
$874$	−4.33920	−	4.02619i	−0.146776	−	0.136188i
$875$	1.40201	−	0.955878i	0.0473968	−	0.0323146i
$876$	0.440434	+	0.552287i	0.0148809	+	0.0186601i
$877$	16.5522	−	2.49485i	0.558929	−	0.0842450i	0.136499	−	0.990640i	$-0.456415\pi$
$877$	16.5522	−	2.49485i	0.558929	−	0.0842450i	0.422431	+	0.906395i	$0.361177\pi$
$878$	32.7876	+	10.1136i	1.10653	+	0.341319i
$879$	0.0341485	+	0.455680i	0.00115180	+	0.0153697i
$880$	7.99677	+	5.45211i	0.269571	+	0.183790i
$881$	9.51470	+	41.6866i	0.320558	+	1.40446i	0.836562	+	0.547872i	$0.184562\pi$
$881$	9.51470	+	41.6866i	0.320558	+	1.40446i	−0.516004	+	0.856586i	$0.672581\pi$
$882$	−3.03612	−	13.3021i	−0.102232	−	0.447906i
$883$	−45.8649	−	31.2702i	−1.54348	−	1.05233i	−0.972941	−	0.231053i	$-0.925783\pi$
$883$	−45.8649	−	31.2702i	−1.54348	−	1.05233i	−0.570537	−	0.821272i	$-0.693265\pi$
$884$	0.665047	+	8.87443i	0.0223679	+	0.298479i
$885$	−0.605146	−	0.186663i	−0.0203418	−	0.00627461i
$886$	26.9256	−	4.05838i	0.904582	−	0.136344i
$887$	−22.1674	−	27.7970i	−0.744309	−	0.933334i	0.255128	−	0.966907i	$-0.417883\pi$
$887$	−22.1674	−	27.7970i	−0.744309	−	0.933334i	−0.999436	+	0.0335738i	$0.989311\pi$
$888$	7.13689	−	4.86585i	0.239498	−	0.163287i
$889$	12.3299	+	11.4404i	0.413530	+	0.383700i
$890$	5.46224	+	13.9176i	0.183095	+	0.466517i
$891$	−28.3257	+	8.73731i	−0.948945	+	0.292711i
$892$	8.48096	−	4.08422i	0.283964	−	0.136750i
$893$	−0.355383	+	0.905500i	−0.0118924	+	0.0303014i
$894$	0.494940	−	6.60451i	0.0165533	−	0.220888i
$895$	7.41789	−	9.30174i	0.247953	−	0.310923i
$896$	−3.05644	+	5.29390i	−0.102108	+	0.176857i
$897$	−6.97889	−	12.0878i	−0.233019	−	0.403600i
$898$	17.0122	+	2.56418i	0.567704	+	0.0855676i
$899$	−17.8501	−	8.59616i	−0.595335	−	0.286698i
$900$	−1.26417	+	1.17298i	−0.0421390	+	0.0390993i
$901$	−0.00579374	+	0.0253840i	−0.000193017	+	0.000845665i
$902$	52.9247			1.76220
$903$	0.531837	+	4.79709i	0.0176984	+	0.159637i
$904$	−27.4931			−0.914407
$905$	2.81750	−	12.3443i	0.0936568	−	0.410337i
$906$	6.71955	−	6.23483i	0.223242	−	0.207138i
$907$	−34.3068	−	16.5213i	−1.13914	−	0.548580i	−0.233385	−	0.972384i	$-0.574980\pi$
$907$	−34.3068	−	16.5213i	−1.13914	−	0.548580i	−0.905754	+	0.423804i	$0.860694\pi$
$908$	5.88830	+	0.887519i	0.195410	+	0.0294533i
$909$	−25.8218	−	44.7247i	−0.856455	−	1.48342i
$910$	−3.76968	+	6.52928i	−0.124964	+	0.216444i
$911$	−31.2018	+	39.1258i	−1.03376	+	1.29630i	−0.0796562	+	0.996822i	$0.525382\pi$
$911$	−31.2018	+	39.1258i	−1.03376	+	1.29630i	−0.954105	+	0.299473i	$0.903189\pi$
$912$	−0.0458006	+	0.611167i	−0.00151661	+	0.0202378i
$913$	17.8392	−	45.4534i	0.590390	−	1.50429i
$914$	−14.5404	+	7.00229i	−0.480954	+	0.231615i
$915$	−0.00947682	+	0.00292321i	−0.000313294	+	9.66384e-5i
$916$	1.13149	+	2.88299i	0.0373855	+	0.0952568i
$917$	−19.3550	−	17.9588i	−0.639158	−	0.593052i
$918$	−9.43279	+	6.43117i	−0.311329	+	0.212260i
$919$	21.8448	+	27.3925i	0.720592	+	0.903594i	0.998371	−	0.0570507i	$-0.0181697\pi$
$919$	21.8448	+	27.3925i	0.720592	+	0.903594i	−0.277779	+	0.960645i	$0.589598\pi$
$920$	−25.9521	+	3.91165i	−0.855615	+	0.128963i
$921$	−1.77558	−	0.547694i	−0.0585074	−	0.0180471i
$922$	2.49752	+	33.3271i	0.0822514	+	1.09757i
$923$	35.3970	+	24.1333i	1.16511	+	0.794357i
$924$	0.405549	+	1.77682i	0.0133416	+	0.0584533i
$925$	−1.43994	−	6.30879i	−0.0473449	−	0.207432i
$926$	5.71376	+	3.89558i	0.187766	+	0.128017i
$927$	−0.463610	−	6.18644i	−0.0152269	−	0.203189i
$928$	11.4398	+	3.52871i	0.375530	+	0.115836i
$929$	51.2731	−	7.72817i	1.68221	−	0.253553i	0.762741	−	0.646704i	$-0.223853\pi$
$929$	51.2731	−	7.72817i	1.68221	−	0.253553i	0.919474	+	0.393151i	$0.128615\pi$
$930$	−1.75600	−	2.20196i	−0.0575817	−	0.0722051i
$931$	2.00672	−	1.36816i	0.0657676	−	0.0448396i
$932$	−10.5924	−	9.82827i	−0.346964	−	0.321936i
$933$	1.58894	+	4.04856i	0.0520196	+	0.132544i
$934$	−18.3687	+	5.66598i	−0.601041	+	0.185397i
$935$	−13.9890	+	6.73677i	−0.457491	+	0.220316i
$936$	11.9280	−	30.3922i	0.389880	−	0.993399i
$937$	3.22092	−	42.9802i	0.105223	−	1.40410i	−0.655583	−	0.755123i	$-0.727577\pi$
$937$	3.22092	−	42.9802i	0.105223	−	1.40410i	0.760806	−	0.648979i	$-0.224804\pi$
$938$	8.44878	−	10.5944i	0.275863	−	0.345921i
$939$	2.49023	−	4.31321i	0.0812657	−	0.140756i
$940$	0.506093	+	0.876579i	0.0165069	+	0.0285909i
$941$	−35.2974	−	5.32023i	−1.15066	−	0.173434i	−0.454114	−	0.890944i	$-0.650044\pi$
$941$	−35.2974	−	5.32023i	−1.15066	−	0.173434i	−0.696549	+	0.717509i	$0.745282\pi$
$942$	−4.75841	−	2.29153i	−0.155037	−	0.0746621i
$943$	−69.5945	+	64.5743i	−2.26631	+	2.10283i
$944$	0.778807	−	3.41217i	0.0253480	−	0.111057i
$945$	4.27771			0.139154
$946$	3.43534	+	30.9863i	0.111692	+	1.00745i
$947$	−0.951783			−0.0309288			−0.0154644	−	0.999880i	$-0.504923\pi$
$947$	−0.951783			−0.0309288			−0.0154644	+	0.999880i	$0.504923\pi$
$948$	0.408384	−	1.78925i	0.0132637	−	0.0581121i
$949$	−7.34441	+	6.81462i	−0.238410	+	0.221212i
$950$	0.625338	+	0.301147i	0.0202887	+	0.00977050i
$951$	−6.23543	−	0.939840i	−0.202198	−	0.0304764i
$952$	−10.0410	−	17.3916i	−0.325432	−	0.563664i
$953$	−29.5090	+	51.1111i	−0.955890	+	1.65565i	−0.223572	+	0.974688i	$0.571772\pi$
$953$	−29.5090	+	51.1111i	−0.955890	+	1.65565i	−0.732318	+	0.680962i	$0.761562\pi$
$954$	0.0139772	−	0.0175268i	0.000452528	−	0.000567452i
$955$	1.47334	−	19.6603i	0.0476761	−	0.636194i
$956$	−4.12243	+	10.5038i	−0.133329	+	0.339717i
$957$	−5.66932	+	2.73020i	−0.183263	+	0.0882549i
$958$	37.7211	−	11.6354i	1.21871	−	0.375923i
$959$	8.16792	+	20.8115i	0.263756	+	0.672039i
$960$	2.77203	+	2.57207i	0.0894670	+	0.0830133i
$961$	−0.493434	+	0.336418i	−0.0159172	+	0.0108522i
$962$	17.9263	+	22.4789i	0.577967	+	0.724748i
$963$	22.0540	−	3.32411i	0.710681	−	0.107118i
$964$	7.95625	+	2.45418i	0.256253	+	0.0790437i
$965$	0.546562	+	7.29337i	0.0175945	+	0.234782i
$966$	6.10747	+	4.16400i	0.196505	+	0.133975i
$967$	−2.51019	−	10.9978i	−0.0807221	−	0.353667i	0.918396	−	0.395663i	$-0.129485\pi$
$967$	−2.51019	−	10.9978i	−0.0807221	−	0.353667i	−0.999118	+	0.0419966i	$0.986628\pi$
$968$	3.62953	+	15.9020i	0.116658	+	0.511110i
$969$	−0.812364	−	0.553861i	−0.0260969	−	0.0177926i
$970$	1.29095	+	17.2266i	0.0414500	+	0.553112i
$971$	−54.9705	−	16.9562i	−1.76409	−	0.544149i	−0.768659	−	0.639659i	$-0.779076\pi$
$971$	−54.9705	−	16.9562i	−1.76409	−	0.544149i	−0.995428	+	0.0955098i	$0.969552\pi$
$972$	−6.51792	+	0.982419i	−0.209062	+	0.0315111i
$973$	2.28564	+	2.86610i	0.0732743	+	0.0918831i
$974$	2.16154	−	1.47371i	0.0692603	−	0.0472208i
$975$	1.19973	+	1.11318i	0.0384220	+	0.0356504i
$976$	−0.0200244	−	0.0510213i	−0.000640965	−	0.00163315i
$977$	1.13812	−	0.351063i	0.0364116	−	0.0112315i	−0.276496	−	0.961015i	$-0.589173\pi$
$977$	1.13812	−	0.351063i	0.0364116	−	0.0112315i	0.312907	+	0.949784i	$0.398697\pi$
$978$	4.74902	−	2.28701i	0.151857	−	0.0731305i
$979$	−18.7274	+	47.7167i	−0.598531	+	1.52503i
$980$	0.188860	−	2.52016i	0.00603291	−	0.0805036i
$981$	−22.8762	+	28.6859i	−0.730382	+	0.915870i
$982$	13.7754	−	23.8597i	0.439591	−	0.761395i
$983$	−19.3299	−	33.4804i	−0.616528	−	1.06786i	−0.990114	−	0.140263i	$-0.955205\pi$
$983$	−19.3299	−	33.4804i	−0.616528	−	1.06786i	0.373586	−	0.927596i	$-0.378128\pi$
$984$	14.6934	+	2.21468i	0.468409	+	0.0706013i
$985$	20.8207	+	10.0267i	0.663402	+	0.319478i
$986$	11.9283	−	11.0679i	0.379876	−	0.352473i
$987$	0.270302	−	1.18427i	0.00860382	−	0.0376958i
$988$	1.36393			0.0433923
$989$	−42.3242	−	36.5546i	−1.34583	−	1.16237i
$990$	13.3684			0.424876
$991$	−4.38047	+	19.1921i	−0.139150	+	0.609657i	0.856472	+	0.516193i	$0.172651\pi$
$991$	−4.38047	+	19.1921i	−0.139150	+	0.609657i	−0.995623	+	0.0934641i	$0.970206\pi$
$992$	−13.4670	+	12.4956i	−0.427579	+	0.396735i
$993$	3.24963	+	1.56494i	0.103124	+	0.0496618i
$994$	−22.4348	−	3.38150i	−0.711589	−	0.107255i
$995$	7.68632	+	13.3131i	0.243673	+	0.422054i
$996$	1.60870	−	2.78636i	0.0509737	−	0.0882891i
$997$	−30.2352	+	37.9138i	−0.957560	+	1.20074i	0.0220344	+	0.999757i	$0.492986\pi$
$997$	−30.2352	+	37.9138i	−0.957560	+	1.20074i	−0.979594	+	0.200985i	$0.935586\pi$
$998$	3.47722	−	46.4003i	0.110069	−	1.46877i
$999$	5.95986	−	15.1855i	0.188562	−	0.480447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	215.2.q.b.56.3	✓	96
43.10	even	21	inner	215.2.q.b.96.3	yes	96
43.15	even	21		9245.2.a.bb.1.30		48
43.28	odd	42		9245.2.a.ba.1.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.q.b.56.3	✓	96	1.1	even	1	trivial
215.2.q.b.96.3	yes	96	43.10	even	21	inner
9245.2.a.ba.1.19		48	43.28	odd	42
9245.2.a.bb.1.30		48	43.15	even	21

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:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262036 + 1.14805i) q^{2} +(0.317968 - 0.295032i) q^{3} +(0.552571 + 0.266104i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(0.255393 + 0.442354i) q^{6} +(-0.848432 + 1.46953i) q^{7} +(-1.91871 + 2.40599i) q^{8} +(-0.210130 + 2.80399i) q^{9} +O(q^{10})\)	\(q+(-0.262036 + 1.14805i) q^{2} +(0.317968 - 0.295032i) q^{3} +(0.552571 + 0.266104i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(0.255393 + 0.442354i) q^{6} +(-0.848432 + 1.46953i) q^{7} +(-1.91871 + 2.40599i) q^{8} +(-0.210130 + 2.80399i) q^{9} +(0.430218 - 1.09618i) q^{10} +(3.63754 - 1.75175i) q^{11} +(0.254209 - 0.0784132i) q^{12} +(1.37847 + 3.51228i) q^{13} +(-1.46478 - 1.35912i) q^{14} +(-0.358389 + 0.244346i) q^{15} +(-1.49465 - 1.87424i) q^{16} +(3.80279 - 0.573179i) q^{17} +(-3.16407 - 0.975987i) q^{18} +(-0.0440464 - 0.587759i) q^{19} +(-0.506738 - 0.345488i) q^{20} +(0.163782 + 0.717578i) q^{21} +(1.05793 + 4.63511i) q^{22} +(-7.04653 - 4.80424i) q^{23} +(0.0997529 + 1.33111i) q^{24} +(0.955573 + 0.294755i) q^{25} +(-4.39349 + 0.662212i) q^{26} +(1.57179 + 1.97096i) q^{27} +(-0.859866 + 0.586247i) q^{28} +(-2.63396 - 2.44396i) q^{29} +(-0.186611 - 0.475478i) q^{30} +(5.26891 - 1.62524i) q^{31} +(-3.00186 + 1.44562i) q^{32} +(0.639802 - 1.63019i) q^{33} +(-0.338428 + 4.51601i) q^{34} +(1.05798 - 1.32666i) q^{35} +(-0.862265 + 1.49349i) q^{36} +(-3.23552 - 5.60408i) q^{37} +(0.686321 + 0.103446i) q^{38} +(1.47454 + 0.710102i) q^{39} +(2.25588 - 2.09315i) q^{40} +(2.47709 - 10.8528i) q^{41} -0.866735 q^{42} +(6.51489 + 0.745825i) q^{43} +2.47614 q^{44} +(0.625696 - 2.74135i) q^{45} +(7.36197 - 6.83091i) q^{46} +(-1.48694 - 0.716070i) q^{47} +(-1.02821 - 0.154978i) q^{48} +(2.06033 + 3.56859i) q^{49} +(-0.588790 + 1.01981i) q^{50} +(1.04006 - 1.30420i) q^{51} +(-0.172930 + 2.30760i) q^{52} +(-0.00247347 + 0.00630229i) q^{53} +(-2.67463 + 1.28803i) q^{54} +(-3.85799 + 1.19003i) q^{55} +(-1.90777 - 4.86092i) q^{56} +(-0.187413 - 0.173894i) q^{57} +(3.49599 - 2.38353i) q^{58} +(0.910284 + 1.14146i) q^{59} +(-0.263057 + 0.0396494i) q^{60} +(0.0218481 + 0.00673924i) q^{61} +(0.485224 + 6.47487i) q^{62} +(-3.94226 - 2.68779i) q^{63} +(-1.93993 - 8.49938i) q^{64} +(-0.839593 - 3.67850i) q^{65} +(1.70389 + 1.16170i) q^{66} +(0.506784 + 6.76257i) q^{67} +(2.25384 + 0.695217i) q^{68} +(-3.65798 + 0.551351i) q^{69} +(1.24585 + 1.56225i) q^{70} +(9.38143 - 6.39615i) q^{71} +(-6.34319 - 5.88562i) q^{72} +(0.970114 + 2.47181i) q^{73} +(7.28161 - 2.24608i) q^{74} +(0.390804 - 0.188201i) q^{75} +(0.132066 - 0.336499i) q^{76} +(-0.511965 + 6.83170i) q^{77} +(-1.20162 + 1.50678i) q^{78} +(3.44937 - 5.97449i) q^{79} +(1.19862 + 2.07607i) q^{80} +(-7.26007 - 1.09428i) q^{81} +(11.8106 + 5.68767i) q^{82} +(8.86570 - 8.22617i) q^{83} +(-0.100449 + 0.440096i) q^{84} -3.84575 q^{85} +(-2.56338 + 7.28401i) q^{86} -1.55856 q^{87} +(-2.76471 + 12.1130i) q^{88} +(-9.30715 + 8.63577i) q^{89} +(2.98327 + 1.43667i) q^{90} +(-6.33092 - 0.954233i) q^{91} +(-2.61528 - 4.52979i) q^{92} +(1.19585 - 2.07127i) q^{93} +(1.21172 - 1.51945i) q^{94} +(-0.0440464 + 0.587759i) q^{95} +(-0.527993 + 1.34531i) q^{96} +(-13.2171 + 6.36500i) q^{97} +(-4.63682 + 1.43027i) q^{98} +(4.14752 + 10.5677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9}+O(q^{10}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9} + 14 q^{10} - 24 q^{11} + 15 q^{12} - 17 q^{14} - 4 q^{15} - 2 q^{16} + 13 q^{17} + 14 q^{18} + q^{19} - 8 q^{20} + 30 q^{21} - 37 q^{22} - 14 q^{23} - 15 q^{24} + 8 q^{25} - 56 q^{26} - 18 q^{27} + 111 q^{28} - 15 q^{29} + 2 q^{30} - 43 q^{31} - 9 q^{32} - 19 q^{33} + 33 q^{34} + 3 q^{35} - 61 q^{36} + 19 q^{37} - 24 q^{38} + 19 q^{39} + 3 q^{40} + 40 q^{41} + 140 q^{42} - 53 q^{43} + 104 q^{44} - 32 q^{45} - 34 q^{46} - 18 q^{47} - 54 q^{48} - 78 q^{49} - 7 q^{50} + 59 q^{51} - 25 q^{52} + 51 q^{53} - 24 q^{54} + 12 q^{55} - 20 q^{56} - 113 q^{57} - 112 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 87 q^{62} - 38 q^{63} + 50 q^{64} - 96 q^{66} - 28 q^{67} - 149 q^{68} + 112 q^{69} - q^{70} + 51 q^{71} - 208 q^{72} + 24 q^{73} - 19 q^{74} + 8 q^{75} + 248 q^{76} + 7 q^{77} + 242 q^{78} - 138 q^{79} - 55 q^{80} - 15 q^{81} - 98 q^{82} + 43 q^{83} + 132 q^{84} + 44 q^{85} - 30 q^{86} - 22 q^{87} - 66 q^{88} + 7 q^{89} + 98 q^{90} - 5 q^{91} - 102 q^{92} - 2 q^{93} + 16 q^{94} + q^{95} + 486 q^{96} - 67 q^{97} + 62 q^{98} + 11 q^{99}+O(q^{100}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9 + 14 * q^10 - 24 * q^11 + 15 * q^12 - 17 * q^14 - 4 * q^15 - 2 * q^16 + 13 * q^17 + 14 * q^18 + q^19 - 8 * q^20 + 30 * q^21 - 37 * q^22 - 14 * q^23 - 15 * q^24 + 8 * q^25 - 56 * q^26 - 18 * q^27 + 111 * q^28 - 15 * q^29 + 2 * q^30 - 43 * q^31 - 9 * q^32 - 19 * q^33 + 33 * q^34 + 3 * q^35 - 61 * q^36 + 19 * q^37 - 24 * q^38 + 19 * q^39 + 3 * q^40 + 40 * q^41 + 140 * q^42 - 53 * q^43 + 104 * q^44 - 32 * q^45 - 34 * q^46 - 18 * q^47 - 54 * q^48 - 78 * q^49 - 7 * q^50 + 59 * q^51 - 25 * q^52 + 51 * q^53 - 24 * q^54 + 12 * q^55 - 20 * q^56 - 113 * q^57 - 112 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 87 * q^62 - 38 * q^63 + 50 * q^64 - 96 * q^66 - 28 * q^67 - 149 * q^68 + 112 * q^69 - q^70 + 51 * q^71 - 208 * q^72 + 24 * q^73 - 19 * q^74 + 8 * q^75 + 248 * q^76 + 7 * q^77 + 242 * q^78 - 138 * q^79 - 55 * q^80 - 15 * q^81 - 98 * q^82 + 43 * q^83 + 132 * q^84 + 44 * q^85 - 30 * q^86 - 22 * q^87 - 66 * q^88 + 7 * q^89 + 98 * q^90 - 5 * q^91 - 102 * q^92 - 2 * q^93 + 16 * q^94 + q^95 + 486 * q^96 - 67 * q^97 + 62 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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