LMFDB - Embedded newform 819.2.dk.a.43.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(43,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 1]))

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

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

chi := DirichletCharacter("819.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dk (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.38
Character	$\chi$	$=$	819.43
Dual form			819.2.dk.a.400.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233987 + 0.135092i) q^{2} +(-0.921408 + 1.46663i) q^{3} +(-0.963500 + 1.66883i) q^{4} +(-1.02596 + 0.592341i) q^{5} +(0.0174666 - 0.467647i) q^{6} -1.00000i q^{7} -1.06101i q^{8} +(-1.30201 - 2.70273i) q^{9} +O(q^{10})$	\(q+(-0.233987 + 0.135092i) q^{2} +(-0.921408 + 1.46663i) q^{3} +(-0.963500 + 1.66883i) q^{4} +(-1.02596 + 0.592341i) q^{5} +(0.0174666 - 0.467647i) q^{6} -1.00000i q^{7} -1.06101i q^{8} +(-1.30201 - 2.70273i) q^{9} +(0.160041 - 0.277200i) q^{10} +(4.19316 - 2.42092i) q^{11} +(-1.55978 - 2.95077i) q^{12} +(-0.439844 - 3.57862i) q^{13} +(0.135092 + 0.233987i) q^{14} +(0.0765862 - 2.05050i) q^{15} +(-1.78367 - 3.08940i) q^{16} +(0.0680483 + 0.117863i) q^{17} +(0.669772 + 0.456511i) q^{18} +(2.44199 - 1.40988i) q^{19} -2.28288i q^{20} +(1.46663 + 0.921408i) q^{21} +(-0.654095 + 1.13293i) q^{22} -8.16325 q^{23} +(1.55612 + 0.977627i) q^{24} +(-1.79826 + 3.11469i) q^{25} +(0.586361 + 0.777930i) q^{26} +(5.16360 + 0.580743i) q^{27} +(1.66883 + 0.963500i) q^{28} +(0.654220 + 1.13314i) q^{29} +(0.259086 + 0.490135i) q^{30} +(8.25123 - 4.76385i) q^{31} +(2.67244 + 1.54293i) q^{32} +(-0.313011 + 8.38047i) q^{33} +(-0.0318448 - 0.0183856i) q^{34} +(0.592341 + 1.02596i) q^{35} +(5.76489 + 0.431239i) q^{36} +(8.80311 + 5.08248i) q^{37} +(-0.380929 + 0.659788i) q^{38} +(5.65380 + 2.65228i) q^{39} +(0.628482 + 1.08856i) q^{40} -8.38412i q^{41} +(-0.467647 - 0.0174666i) q^{42} -5.09614 q^{43} +9.33023i q^{44} +(2.93676 + 2.00167i) q^{45} +(1.91009 - 1.10279i) q^{46} +(-5.17441 - 2.98745i) q^{47} +(6.17449 + 0.230617i) q^{48} -1.00000 q^{49} -0.971726i q^{50} +(-0.235562 - 0.00879824i) q^{51} +(6.39591 + 2.71398i) q^{52} -0.0422456 q^{53} +(-1.28667 + 0.561676i) q^{54} +(-2.86802 + 4.96755i) q^{55} -1.06101 q^{56} +(-0.182290 + 4.88058i) q^{57} +(-0.306157 - 0.176760i) q^{58} +(-9.91918 - 5.72684i) q^{59} +(3.34815 + 2.10347i) q^{60} +9.74614 q^{61} +(-1.28712 + 2.22935i) q^{62} +(-2.70273 + 1.30201i) q^{63} +6.30091 q^{64} +(2.57103 + 3.41100i) q^{65} +(-1.05890 - 2.00320i) q^{66} +4.09863i q^{67} -0.262258 q^{68} +(7.52169 - 11.9725i) q^{69} +(-0.277200 - 0.160041i) q^{70} +(6.42863 - 3.71157i) q^{71} +(-2.86764 + 1.38146i) q^{72} -8.28011i q^{73} -2.74641 q^{74} +(-2.91116 - 5.50729i) q^{75} +5.43370i q^{76} +(-2.42092 - 4.19316i) q^{77} +(-1.68121 + 0.143185i) q^{78} +(-2.24974 + 3.89666i) q^{79} +(3.65996 + 2.11308i) q^{80} +(-5.60952 + 7.03799i) q^{81} +(1.13263 + 1.96177i) q^{82} +(8.79698 + 5.07894i) q^{83} +(-2.95077 + 1.55978i) q^{84} +(-0.139630 - 0.0806155i) q^{85} +(1.19243 - 0.688448i) q^{86} +(-2.26470 - 0.0845867i) q^{87} +(-2.56863 - 4.44900i) q^{88} +(-3.40348 - 1.96500i) q^{89} +(-0.957572 - 0.0716306i) q^{90} +(-3.57862 + 0.439844i) q^{91} +(7.86530 - 13.6231i) q^{92} +(-0.615938 + 16.4910i) q^{93} +1.61432 q^{94} +(-1.67026 + 2.89298i) q^{95} +(-4.72532 + 2.49781i) q^{96} -11.5939i q^{97} +(0.233987 - 0.135092i) q^{98} +(-12.0026 - 8.18090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 2 * q^9	$ 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) $ 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.233987	+	0.135092i	−0.165453	+	0.0955246i	−0.580440	−	0.814303i	$-0.697120\pi$
$2$	−0.233987	+	0.135092i	−0.165453	+	0.0955246i	0.414987	+	0.909827i	$0.363786\pi$
$3$	−0.921408	+	1.46663i	−0.531975	+	0.846760i
$3$	−0.921408	+	1.46663i	−0.531975	+	0.846760i
$4$	−0.963500	+	1.66883i	−0.481750	+	0.834416i
$5$	−1.02596	+	0.592341i	−0.458825	+	0.264903i	−0.711550	−	0.702635i	$-0.752007\pi$
$5$	−1.02596	+	0.592341i	−0.458825	+	0.264903i	0.252725	+	0.967538i	$0.418673\pi$
$6$	0.0174666	−	0.467647i	0.00713072	−	0.190916i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.06101i		−	0.375125i
$9$	−1.30201	−	2.70273i	−0.434005	−	0.900911i
$10$	0.160041	−	0.277200i	0.0506095	−	0.0876582i
$11$	4.19316	−	2.42092i	1.26428	−	0.729935i	0.290384	−	0.956910i	$-0.406217\pi$
$11$	4.19316	−	2.42092i	1.26428	−	0.729935i	0.973900	+	0.226976i	$0.0728838\pi$
$12$	−1.55978	−	2.95077i	−0.450271	−	0.851815i
$13$	−0.439844	−	3.57862i	−0.121991	−	0.992531i
$13$	−0.439844	−	3.57862i	−0.121991	−	0.992531i
$14$	0.135092	+	0.233987i	0.0361049	+	0.0625355i
$15$	0.0765862	−	2.05050i	0.0197745	−	0.529437i
$16$	−1.78367	−	3.08940i	−0.445916	−	0.772350i
$17$	0.0680483	+	0.117863i	0.0165041	+	0.0285860i	0.874160	−	0.485639i	$-0.161413\pi$
$17$	0.0680483	+	0.117863i	0.0165041	+	0.0285860i	−0.857655	+	0.514225i	$0.828080\pi$
$18$	0.669772	+	0.456511i	0.157867	+	0.107601i
$19$	2.44199	−	1.40988i	0.560231	−	0.323450i	−0.193007	−	0.981197i	$-0.561824\pi$
$19$	2.44199	−	1.40988i	0.560231	−	0.323450i	0.753238	+	0.657748i	$0.228491\pi$
$20$		−	2.28288i		−	0.510468i
$21$	1.46663	+	0.921408i	0.320045	+	0.201068i
$22$	−0.654095	+	1.13293i	−0.139453	+	0.241540i
$23$	−8.16325			−1.70216			−0.851078	−	0.525039i	$-0.824051\pi$
$23$	−8.16325			−1.70216			−0.851078	+	0.525039i	$0.824051\pi$
$24$	1.55612	+	0.977627i	0.317641	+	0.199557i
$25$	−1.79826	+	3.11469i	−0.359653	+	0.622937i
$26$	0.586361	+	0.777930i	0.114995	+	0.152565i
$27$	5.16360	+	0.580743i	0.993735	+	0.111764i
$28$	1.66883	+	0.963500i	0.315379	+	0.182084i
$29$	0.654220	+	1.13314i	0.121486	+	0.210419i	0.920354	−	0.391087i	$-0.127901\pi$
$29$	0.654220	+	1.13314i	0.121486	+	0.210419i	−0.798868	+	0.601506i	$0.794568\pi$
$30$	0.259086	+	0.490135i	0.0473025	+	0.0894861i
$31$	8.25123	−	4.76385i	1.48197	−	0.855613i	0.482174	−	0.876075i	$-0.339847\pi$
$31$	8.25123	−	4.76385i	1.48197	−	0.855613i	0.999791	+	0.0204623i	$0.00651381\pi$
$32$	2.67244	+	1.54293i	0.472425	+	0.272755i
$33$	−0.313011	+	8.38047i	−0.0544881	+	1.45885i
$34$	−0.0318448	−	0.0183856i	−0.00546133	−	0.00315310i
$35$	0.592341	+	1.02596i	0.100124	+	0.173420i
$36$	5.76489	+	0.431239i	0.960816	+	0.0718732i
$37$	8.80311	+	5.08248i	1.44722	+	0.835554i	0.998315	−	0.0580239i	$-0.0184799\pi$
$37$	8.80311	+	5.08248i	1.44722	+	0.835554i	0.448907	+	0.893578i	$0.351813\pi$
$38$	−0.380929	+	0.659788i	−0.0617948	+	0.107032i
$39$	5.65380	+	2.65228i	0.905332	+	0.424705i
$40$	0.628482	+	1.08856i	0.0993717	+	0.172117i
$41$		−	8.38412i		−	1.30938i	−0.755898	−	0.654690i	$-0.772799\pi$
$41$		−	8.38412i		−	1.30938i	0.755898	−	0.654690i	$-0.227201\pi$
$42$	−0.467647	−	0.0174666i	−0.0721595	−	0.00269516i
$43$	−5.09614			−0.777153			−0.388577	−	0.921416i	$-0.627033\pi$
$43$	−5.09614			−0.777153			−0.388577	+	0.921416i	$0.627033\pi$
$44$			9.33023i			1.40658i
$45$	2.93676	+	2.00167i	0.437786	+	0.298391i
$46$	1.91009	−	1.10279i	0.281628	−	0.162598i
$47$	−5.17441	−	2.98745i	−0.754766	−	0.435764i	0.0726476	−	0.997358i	$-0.476855\pi$
$47$	−5.17441	−	2.98745i	−0.754766	−	0.435764i	−0.827413	+	0.561594i	$0.810188\pi$
$48$	6.17449	+	0.230617i	0.891211	+	0.0332868i
$49$	−1.00000			−0.142857
$50$		−	0.971726i		−	0.137423i
$51$	−0.235562	−	0.00879824i	−0.0329853	−	0.00123200i
$52$	6.39591	+	2.71398i	0.886953	+	0.376361i
$53$	−0.0422456			−0.00580288			−0.00290144	−	0.999996i	$-0.500924\pi$
$53$	−0.0422456			−0.00580288			−0.00290144	+	0.999996i	$0.500924\pi$
$54$	−1.28667	+	0.561676i	−0.175093	+	0.0764344i
$55$	−2.86802	+	4.96755i	−0.386724	+	0.669825i
$56$	−1.06101			−0.141784
$57$	−0.182290	+	4.88058i	−0.0241449	+	0.646449i
$58$	−0.306157	−	0.176760i	−0.0402004	−	0.0232097i
$59$	−9.91918	−	5.72684i	−1.29137	−	0.745571i	−0.312470	−	0.949927i	$-0.601157\pi$
$59$	−9.91918	−	5.72684i	−1.29137	−	0.745571i	−0.978897	+	0.204356i	$0.934490\pi$
$60$	3.34815	+	2.10347i	0.432244	+	0.271556i
$61$	9.74614			1.24787			0.623933	−	0.781478i	$-0.285534\pi$
$61$	9.74614			1.24787			0.623933	+	0.781478i	$0.285534\pi$
$62$	−1.28712	+	2.22935i	−0.163464	+	0.283128i
$63$	−2.70273	+	1.30201i	−0.340512	+	0.164038i
$64$	6.30091			0.787614
$65$	2.57103	+	3.41100i	0.318897	+	0.423083i
$66$	−1.05890	−	2.00320i	−0.130341	−	0.246577i
$67$			4.09863i			0.500728i	0.968152	+	0.250364i	$0.0805503\pi$
$67$			4.09863i			0.500728i	−0.968152	+	0.250364i	$0.919450\pi$
$68$	−0.262258			−0.0318035
$69$	7.52169	−	11.9725i	0.905505	−	1.44132i
$70$	−0.277200	−	0.160041i	−0.0331317	−	0.0191286i
$71$	6.42863	−	3.71157i	0.762938	−	0.440483i	−0.0674115	−	0.997725i	$-0.521474\pi$
$71$	6.42863	−	3.71157i	0.762938	−	0.440483i	0.830350	+	0.557243i	$0.188141\pi$
$72$	−2.86764	+	1.38146i	−0.337954	+	0.162806i
$73$		−	8.28011i		−	0.969113i	−0.874760	−	0.484557i	$-0.838981\pi$
$73$		−	8.28011i		−	0.969113i	0.874760	−	0.484557i	$-0.161019\pi$
$74$	−2.74641			−0.319264
$75$	−2.91116	−	5.50729i	−0.336152	−	0.635927i
$76$			5.43370i			0.623288i
$77$	−2.42092	−	4.19316i	−0.275889	−	0.477854i
$78$	−1.68121	+	0.143185i	−0.190360	+	0.0162126i
$79$	−2.24974	+	3.89666i	−0.253116	+	0.438409i	−0.964382	−	0.264514i	$-0.914789\pi$
$79$	−2.24974	+	3.89666i	−0.253116	+	0.438409i	0.711266	+	0.702923i	$0.248122\pi$
$80$	3.65996	+	2.11308i	0.409195	+	0.236249i
$81$	−5.60952	+	7.03799i	−0.623279	+	0.781999i
$82$	1.13263	+	1.96177i	0.125078	+	0.216641i
$83$	8.79698	+	5.07894i	0.965594	+	0.557486i	0.897890	−	0.440220i	$-0.145099\pi$
$83$	8.79698	+	5.07894i	0.965594	+	0.557486i	0.0677036	+	0.997705i	$0.478433\pi$
$84$	−2.95077	+	1.55978i	−0.321956	+	0.170186i
$85$	−0.139630	−	0.0806155i	−0.0151450	−	0.00874398i
$86$	1.19243	−	0.688448i	0.128583	−	0.0742373i
$87$	−2.26470	−	0.0845867i	−0.242802	−	0.00906865i
$88$	−2.56863	−	4.44900i	−0.273817	−	0.474265i
$89$	−3.40348	−	1.96500i	−0.360768	−	0.208290i	0.308649	−	0.951176i	$-0.400123\pi$
$89$	−3.40348	−	1.96500i	−0.360768	−	0.208290i	−0.669418	+	0.742886i	$0.733456\pi$
$90$	−0.957572	−	0.0716306i	−0.100937	−	0.00755053i
$91$	−3.57862	+	0.439844i	−0.375142	+	0.0461082i
$92$	7.86530	−	13.6231i	0.820014	−	1.42031i
$93$	−0.615938	+	16.4910i	−0.0638698	+	1.71003i
$94$	1.61432			0.166505
$95$	−1.67026	+	2.89298i	−0.171366	+	0.296814i
$96$	−4.72532	+	2.49781i	−0.482276	+	0.254932i
$97$		−	11.5939i		−	1.17718i	−0.808432	−	0.588590i	$-0.799683\pi$
$97$		−	11.5939i		−	1.17718i	0.808432	−	0.588590i	$-0.200317\pi$
$98$	0.233987	−	0.135092i	0.0236362	−	0.0136464i
$99$	−12.0026	−	8.18090i	−1.20631	−	0.822211i
$100$	−3.46526	−	6.00200i	−0.346526	−	0.600200i
$101$	−4.94628	−	8.56720i	−0.492173	−	0.852469i	0.507786	−	0.861483i	$-0.330464\pi$
$101$	−4.94628	−	8.56720i	−0.492173	−	0.852469i	−0.999959	+	0.00901441i	$0.997131\pi$
$102$	0.0563069	−	0.0297639i	0.00557521	−	0.00294706i
$103$	6.01306	+	10.4149i	0.592484	+	1.02621i	0.993897	+	0.110315i	$0.0351860\pi$
$103$	6.01306	+	10.4149i	0.592484	+	1.02621i	−0.401413	+	0.915897i	$0.631481\pi$
$104$	−3.79697	+	0.466681i	−0.372323	+	0.0457618i
$105$	−2.05050	−	0.0765862i	−0.200108	−	0.00747405i
$106$	0.00988490	−	0.00570705i	0.000960106	−	0.000554318i
$107$	4.78159	−	8.28196i	0.462254	−	0.800648i	−0.536819	−	0.843698i	$-0.680374\pi$
$107$	4.78159	−	8.28196i	0.462254	−	0.800648i	0.999073	+	0.0430499i	$0.0137074\pi$
$108$	−5.94429	+	8.05763i	−0.571989	+	0.775346i
$109$		−	8.08902i		−	0.774787i	−0.921914	−	0.387394i	$-0.873375\pi$
$109$		−	8.08902i		−	0.774787i	0.921914	−	0.387394i	$-0.126625\pi$
$110$		−	1.54979i		−	0.147766i
$111$	−15.5654	+	8.22788i	−1.47740	+	0.780956i
$112$	−3.08940	+	1.78367i	−0.291921	+	0.168541i
$113$	7.32364	−	12.6849i	0.688950	−	1.19330i	−0.283228	−	0.959053i	$-0.591405\pi$
$113$	7.32364	−	12.6849i	0.688950	−	1.19330i	0.972178	−	0.234244i	$-0.0752613\pi$
$114$	−0.616675	−	1.16662i	−0.0577569	−	0.109264i
$115$	8.37521	−	4.83543i	0.780992	−	0.450906i
$116$	−2.52136			−0.234103
$117$	−9.09937	+	5.84820i	−0.841237	+	0.540666i
$118$	3.09461			0.284882
$119$	0.117863	−	0.0680483i	0.0108045	−	0.00623797i
$120$	−2.17561	−	0.0812590i	−0.198605	−	0.00741790i
$121$	6.22170	−	10.7763i	0.565609	−	0.979664i
$122$	−2.28046	+	1.31663i	−0.206464	+	0.119202i
$123$	12.2964	+	7.72519i	1.10873	+	0.696557i
$124$			18.3599i			1.64877i
$125$		−	10.1842i		−	0.910898i
$126$	0.456511	−	0.669772i	0.0406692	−	0.0596680i
$127$	2.08730	−	3.61531i	0.185218	−	0.320807i	−0.758432	−	0.651752i	$-0.774034\pi$
$127$	2.08730	−	3.61531i	0.185218	−	0.320807i	0.943650	+	0.330945i	$0.107368\pi$
$128$	−6.81920	+	3.93707i	−0.602738	+	0.347991i
$129$	4.69562	−	7.47415i	0.413426	−	0.658062i
$130$	−1.06239	−	0.450803i	−0.0931774	−	0.0395380i
$131$	6.14748	+	10.6478i	0.537108	+	0.930299i	0.999058	+	0.0433927i	$0.0138167\pi$
$131$	6.14748	+	10.6478i	0.537108	+	0.930299i	−0.461950	+	0.886906i	$0.652850\pi$
$132$	−13.6840	−	8.59694i	−1.19104	−	0.748268i
$133$	−1.40988	−	2.44199i	−0.122252	−	0.211748i
$134$	−0.553693	−	0.959025i	−0.0478318	−	0.0828472i
$135$	−5.64167	+	2.46279i	−0.485557	+	0.211963i
$136$	0.125054	−	0.0722002i	0.0107233	−	0.00619111i
$137$			3.66071i			0.312756i	0.987697	+	0.156378i	$0.0499818\pi$
$137$			3.66071i			0.312756i	−0.987697	+	0.156378i	$0.950018\pi$
$138$	−0.142584	+	3.81752i	−0.0121376	+	0.324969i
$139$	6.22485	−	10.7818i	0.527985	−	0.914497i	−0.471482	−	0.881875i	$-0.656281\pi$
$139$	6.22485	−	10.7818i	0.527985	−	0.914497i	0.999468	−	0.0326219i	$-0.0103857\pi$
$140$	−2.28288			−0.192939
$141$	9.14923	−	4.83630i	0.770504	−	0.407290i
$142$	−1.00281	+	1.73692i	−0.0841538	+	0.145759i
$143$	−10.5079	−	13.9409i	−0.878714	−	1.16580i
$144$	−6.02746	+	8.84321i	−0.502288	+	0.736934i
$145$	−1.34241	−	0.775042i	−0.111481	−	0.0643637i
$146$	1.11858	+	1.93743i	0.0925741	+	0.160343i
$147$	0.921408	−	1.46663i	0.0759964	−	0.120966i
$148$	−16.9636	+	9.79394i	−1.39440	+	0.805057i
$149$	−11.5914	−	6.69233i	−0.949608	−	0.548257i	−0.0566492	−	0.998394i	$-0.518042\pi$
$149$	−11.5914	−	6.69233i	−0.949608	−	0.548257i	−0.892959	+	0.450137i	$0.851375\pi$
$150$	1.42516	+	0.895356i	0.116364	+	0.0731055i
$151$	4.86810	+	2.81060i	0.396160	+	0.228723i	0.684826	−	0.728707i	$-0.259878\pi$
$151$	4.86810	+	2.81060i	0.396160	+	0.228723i	−0.288666	+	0.957430i	$0.593212\pi$
$152$	−1.49591	−	2.59099i	−0.121334	−	0.210157i
$153$	0.229952	−	0.337376i	0.0185905	−	0.0272752i
$154$	1.13293	+	0.654095i	0.0912937	+	0.0527084i
$155$	−5.64365	+	9.77508i	−0.453309	+	0.785154i
$156$	−9.87364	+	6.87976i	−0.790524	+	0.550821i
$157$	−0.235348	−	0.407635i	−0.0187828	−	0.0325328i	0.856481	−	0.516178i	$-0.172646\pi$
$157$	−0.235348	−	0.407635i	−0.0187828	−	0.0325328i	−0.875264	+	0.483645i	$0.839312\pi$
$158$		−	1.21569i		−	0.0967151i
$159$	0.0389254	−	0.0619587i	0.00308699	−	0.00491364i
$160$	−3.65577			−0.289014
$161$			8.16325i			0.643354i
$162$	0.361773	−	2.40460i	0.0284236	−	0.188923i
$163$	8.55740	−	4.94062i	0.670267	−	0.386979i	−0.125911	−	0.992042i	$-0.540185\pi$
$163$	8.55740	−	4.94062i	0.670267	−	0.386979i	0.796178	+	0.605063i	$0.206852\pi$
$164$	13.9917	+	8.07810i	1.09257	+	0.630794i
$165$	−4.64296	−	8.78347i	−0.361454	−	0.683792i
$166$	−2.74450			−0.213014
$167$			4.66322i			0.360851i	0.983589	+	0.180425i	$0.0577474\pi$
$167$			4.66322i			0.360851i	−0.983589	+	0.180425i	$0.942253\pi$
$168$	0.977627	−	1.55612i	0.0754255	−	0.120057i
$169$	−12.6131	+	3.14807i	−0.970236	+	0.242159i
$170$	0.0435621			0.00334106
$171$	−6.99005	−	4.76436i	−0.534542	−	0.364339i
$172$	4.91013	−	8.50459i	0.374394	−	0.648469i
$173$	−19.1388			−1.45509			−0.727547	−	0.686058i	$-0.759340\pi$
$173$	−19.1388			−1.45509			−0.727547	+	0.686058i	$0.759340\pi$
$174$	0.541337	−	0.286152i	0.0410387	−	0.0216931i
$175$	3.11469	+	1.79826i	0.235448	+	0.135936i
$176$	−14.9584	−	8.63622i	−1.12753	−	0.650980i
$177$	17.5388	−	9.27102i	1.31829	−	0.696853i
$178$	1.06183			0.0795872
$179$	−1.49542	+	2.59014i	−0.111773	+	0.193596i	−0.916485	−	0.400069i	$-0.868986\pi$
$179$	−1.49542	+	2.59014i	−0.111773	+	0.193596i	0.804712	+	0.593665i	$0.202320\pi$
$180$	−6.17002	+	2.97235i	−0.459886	+	0.221546i
$181$	11.3857			0.846291			0.423146	−	0.906062i	$-0.360926\pi$
$181$	11.3857			0.846291			0.423146	+	0.906062i	$0.360926\pi$
$182$	0.777930	−	0.586361i	0.0576640	−	0.0434640i
$183$	−8.98017	+	14.2940i	−0.663833	+	1.05664i
$184$			8.66133i			0.638521i
$185$	−12.0422			−0.885363
$186$	−2.08368	−	3.94187i	−0.152783	−	0.289032i
$187$	0.570674	+	0.329479i	0.0417318	+	0.0240939i
$188$	9.97110	−	5.75681i	0.727217	−	0.419859i
$189$	0.580743	−	5.16360i	0.0422428	−	0.375596i
$190$		−	0.902559i		−	0.0654785i
$191$	−13.6902			−0.990586			−0.495293	−	0.868726i	$-0.664939\pi$
$191$	−13.6902			−0.990586			−0.495293	+	0.868726i	$0.664939\pi$
$192$	−5.80571	+	9.24111i	−0.418991	+	0.666920i
$193$			25.5289i			1.83761i	0.394715	+	0.918804i	$0.370843\pi$
$193$			25.5289i			1.83761i	−0.394715	+	0.918804i	$0.629157\pi$
$194$	1.56624	+	2.71281i	0.112450	+	0.194768i
$195$	−7.37165	+	0.627827i	−0.527895	+	0.0449596i
$196$	0.963500	−	1.66883i	0.0688214	−	0.119202i
$197$	3.92644	+	2.26693i	0.279747	+	0.161512i	0.633309	−	0.773899i	$-0.281696\pi$
$197$	3.92644	+	2.26693i	0.279747	+	0.161512i	−0.353562	+	0.935411i	$0.615030\pi$
$198$	3.91363	+	0.292757i	0.278130	+	0.0208053i
$199$	−4.38276	−	7.59117i	−0.310686	−	0.538124i	0.667825	−	0.744318i	$-0.267225\pi$
$199$	−4.38276	−	7.59117i	−0.310686	−	0.538124i	−0.978511	+	0.206194i	$0.933892\pi$
$200$	3.30473	+	1.90798i	0.233679	+	0.134915i
$201$	−6.01119	−	3.77651i	−0.423996	−	0.266375i
$202$	2.31472	+	1.33641i	0.162863	+	0.0940292i
$203$	1.13314	−	0.654220i	0.0795310	−	0.0459172i
$204$	0.241647	−	0.384636i	0.0169187	−	0.0269299i
$205$	4.96626	+	8.60181i	0.346858	+	0.600776i
$206$	−2.81395	−	1.62463i	−0.196057	−	0.113194i
$207$	10.6287	+	22.0631i	0.738744	+	1.53349i
$208$	−10.2713	+	7.74192i	−0.712184	+	0.536806i
$209$	6.82643	−	11.8237i	0.472194	−	0.817864i
$210$	0.490135	−	0.259086i	0.0338226	−	0.0178787i
$211$	27.8120			1.91466			0.957328	−	0.289003i	$-0.0933239\pi$
$211$	27.8120			1.91466			0.957328	+	0.289003i	$0.0933239\pi$
$212$	0.0407036	−	0.0705008i	0.00279554	−	0.00484201i
$213$	−0.479884	+	12.8483i	−0.0328811	+	0.880351i
$214$			2.58382i			0.176627i
$215$	5.22845	−	3.01865i	0.356578	−	0.205870i
$216$	0.616176	−	5.47865i	0.0419255	−	0.372775i
$217$	−4.76385	−	8.25123i	−0.323391	−	0.560130i
$218$	1.09276	+	1.89272i	0.0740112	+	0.128191i
$219$	12.1439	+	7.62936i	0.820606	+	0.515544i
$220$	−5.52667	−	9.57248i	−0.372608	−	0.645376i
$221$	0.391857	−	0.295360i	0.0263591	−	0.0198681i
$222$	2.53057	−	4.02797i	0.169840	−	0.270340i
$223$	4.98407	−	2.87756i	0.333758	−	0.192695i	−0.323750	−	0.946143i	$-0.604944\pi$
$223$	4.98407	−	2.87756i	0.333758	−	0.192695i	0.657508	+	0.753447i	$0.271610\pi$
$224$	1.54293	−	2.67244i	0.103092	−	0.178560i
$225$	10.7595	+	0.804860i	0.717302	+	0.0536573i
$226$			3.95746i			0.263247i
$227$			0.852157i			0.0565597i	0.999600	+	0.0282798i	$0.00900295\pi$
$227$			0.852157i			0.0565597i	−0.999600	+	0.0282798i	$0.990997\pi$
$228$	−7.96923	−	5.00665i	−0.527775	−	0.331574i
$229$	−2.33495	+	1.34809i	−0.154298	+	0.0890841i	−0.575161	−	0.818040i	$-0.695061\pi$
$229$	−2.33495	+	1.34809i	−0.154298	+	0.0890841i	0.420863	+	0.907124i	$0.361727\pi$
$230$	−1.30646	+	2.26285i	−0.0861452	+	0.149208i
$231$	8.38047	+	0.313011i	0.551394	+	0.0205946i
$232$	1.20228	−	0.694136i	0.0789335	−	0.0455723i
$233$	3.92369			0.257049			0.128525	−	0.991706i	$-0.458976\pi$
$233$	3.92369			0.257049			0.128525	+	0.991706i	$0.458976\pi$
$234$	1.33908	−	2.59765i	0.0875387	−	0.169814i
$235$	7.07835			0.461741
$236$	19.1143	−	11.0356i	1.24423	−	0.718358i
$237$	−3.64204	−	6.88996i	−0.236576	−	0.447551i
$238$	−0.0183856	+	0.0318448i	−0.00119176	+	0.00206419i
$239$	−15.2475	+	8.80315i	−0.986279	+	0.569429i	−0.904160	−	0.427194i	$-0.859502\pi$
$239$	−15.2475	+	8.80315i	−0.986279	+	0.569429i	−0.0821192	+	0.996623i	$0.526169\pi$
$240$	−6.47142	+	3.42080i	−0.417728	+	0.220812i
$241$		−	6.15064i		−	0.396197i	−0.980182	−	0.198099i	$-0.936523\pi$
$241$		−	6.15064i		−	0.396197i	0.980182	−	0.198099i	$-0.0634767\pi$
$242$			3.36201i			0.216118i
$243$	−5.15349	−	14.7120i	−0.330596	−	0.943772i
$244$	−9.39041	+	16.2647i	−0.601159	+	1.04124i
$245$	1.02596	−	0.592341i	0.0655465	−	0.0378433i
$246$	−3.92081	−	0.146442i	−0.249982	−	0.00933682i
$247$	−6.11954	−	8.11884i	−0.389377	−	0.516589i
$248$	−5.05451	−	8.75467i	−0.320962	−	0.555922i
$249$	−15.5545	+	8.22215i	−0.985728	+	0.521057i
$250$	1.37580	+	2.38295i	0.0870132	+	0.150711i
$251$	−5.68229	−	9.84202i	−0.358663	−	0.621223i	0.629075	−	0.777345i	$-0.283434\pi$
$251$	−5.68229	−	9.84202i	−0.358663	−	0.621223i	−0.987738	+	0.156122i	$0.950101\pi$
$252$	0.431239	−	5.76489i	0.0271655	−	0.363154i
$253$	−34.2298	+	19.7626i	−2.15201	+	1.24246i
$254$			1.12791i			0.0707715i
$255$	0.246890	−	0.130506i	0.0154608	−	0.00817262i
$256$	−5.23718	+	9.07105i	−0.327323	+	0.566941i
$257$	12.3769			0.772052			0.386026	−	0.922488i	$-0.373848\pi$
$257$	12.3769			0.772052			0.386026	+	0.922488i	$0.373848\pi$
$258$	−0.0890123	+	2.38319i	−0.00554166	+	0.148371i
$259$	5.08248	−	8.80311i	0.315810	−	0.546999i
$260$	−8.16957	+	1.00411i	−0.506655	+	0.0622724i
$261$	2.21077	−	3.24355i	0.136843	−	0.200771i
$262$	−2.87686	−	1.66095i	−0.177733	−	0.102614i
$263$	7.26589	+	12.5849i	0.448034	+	0.776018i	0.998258	−	0.0589992i	$-0.0187909\pi$
$263$	7.26589	+	12.5849i	0.448034	+	0.776018i	−0.550224	+	0.835017i	$0.685458\pi$
$264$	8.89179	+	0.332109i	0.547252	+	0.0204399i
$265$	0.0433425	−	0.0250238i	0.00266251	−	0.00153720i
$266$	0.659788	+	0.380929i	0.0404542	+	0.0233562i
$267$	6.01793	−	3.18109i	0.368291	−	0.194679i
$268$	−6.83993	−	3.94904i	−0.417815	−	0.241226i
$269$	−14.9609	−	25.9130i	−0.912180	−	1.57994i	−0.810978	−	0.585077i	$-0.801064\pi$
$269$	−14.9609	−	25.9130i	−0.912180	−	1.57994i	−0.101202	−	0.994866i	$-0.532269\pi$
$270$	0.987370	−	1.33840i	0.0600894	−	0.0814527i
$271$	−4.48341	−	2.58850i	−0.272348	−	0.157240i	0.357606	−	0.933872i	$-0.383593\pi$
$271$	−4.48341	−	2.58850i	−0.272348	−	0.157240i	−0.629954	+	0.776632i	$0.716926\pi$
$272$	0.242751	−	0.420457i	0.0147189	−	0.0254939i
$273$	2.65228	−	5.65380i	0.160523	−	0.342183i
$274$	−0.494534	−	0.856558i	−0.0298759	−	0.0517466i
$275$			17.4138i			1.05009i
$276$	12.7329	+	24.0879i	0.766431	+	1.44992i
$277$	−24.8814			−1.49498			−0.747491	−	0.664272i	$-0.768741\pi$
$277$	−24.8814			−1.49498			−0.747491	+	0.664272i	$0.768741\pi$
$278$			3.36372i			0.201742i
$279$	−23.6186	−	16.0983i	−1.41401	−	0.963778i
$280$	1.08856	−	0.628482i	0.0650541	−	0.0375590i
$281$	18.1292	+	10.4669i	1.08150	+	0.624402i	0.931299	−	0.364255i	$-0.118676\pi$
$281$	18.1292	+	10.4669i	1.08150	+	0.624402i	0.150196	+	0.988656i	$0.452010\pi$
$282$	−1.48745	+	2.36762i	−0.0885764	+	0.140990i
$283$	−15.0630			−0.895404			−0.447702	−	0.894183i	$-0.647757\pi$
$283$	−15.0630			−0.895404			−0.447702	+	0.894183i	$0.647757\pi$
$284$			14.3044i			0.848810i
$285$	−2.70394	−	5.11528i	−0.160168	−	0.303003i
$286$	4.34201	+	1.84245i	0.256748	+	0.108946i
$287$	−8.38412			−0.494899
$288$	0.690579	−	9.23180i	0.0406928	−	0.543989i
$289$	8.49074	−	14.7064i	0.499455	−	0.865082i
$290$	0.418808			0.0245933
$291$	17.0039	+	10.6827i	0.996788	+	0.626230i
$292$	13.8181	+	7.97788i	0.808643	+	0.466870i
$293$	−17.3446	−	10.0139i	−1.01328	−	0.585019i	−0.101131	−	0.994873i	$-0.532246\pi$
$293$	−17.3446	−	10.0139i	−1.01328	−	0.585019i	−0.912151	+	0.409854i	$0.865580\pi$
$294$	−0.0174666	+	0.467647i	−0.00101867	+	0.0272737i
$295$	13.5690			0.790016
$296$	5.39258	−	9.34023i	0.313437	−	0.542890i
$297$	23.0577	−	10.0655i	1.33794	−	0.584060i
$298$	3.61632			0.209488
$299$	3.59056	+	29.2132i	0.207647	+	1.68944i
$300$	11.9956	+	0.448037i	0.692568	+	0.0258674i
$301$			5.09614i			0.293736i
$302$	−1.51876			−0.0873948
$303$	17.1225	+	0.639524i	0.983660	+	0.0367397i
$304$	−8.71139	−	5.02952i	−0.499633	−	0.288463i
$305$	−9.99919	+	5.77304i	−0.572552	+	0.330563i
$306$	−0.00822894	+	0.110006i	−0.000470417	+	0.00628863i
$307$		−	4.36732i		−	0.249256i	−0.992204	−	0.124628i	$-0.960226\pi$
$307$		−	4.36732i		−	0.249256i	0.992204	−	0.124628i	$-0.0397738\pi$
$308$	9.33023			0.531639
$309$	−20.8153	−	0.777453i	−1.18414	−	0.0442277i
$310$		−	3.04965i		−	0.173209i
$311$	13.3607	+	23.1414i	0.757616	+	1.31223i	0.944063	+	0.329764i	$0.106969\pi$
$311$	13.3607	+	23.1414i	0.757616	+	1.31223i	−0.186448	+	0.982465i	$0.559698\pi$
$312$	2.81411	−	5.99876i	0.159318	−	0.339613i
$313$	8.44243	−	14.6227i	0.477194	−	0.826524i	−0.522464	−	0.852661i	$-0.674987\pi$
$313$	8.44243	−	14.6227i	0.477194	−	0.826524i	0.999658	+	0.0261367i	$0.00832053\pi$
$314$	0.110137	+	0.0635874i	0.00621537	+	0.00358845i
$315$	2.00167	−	2.93676i	0.112781	−	0.165468i
$316$	−4.33525	−	7.50887i	−0.243877	−	0.422407i
$317$	−0.202225	−	0.116755i	−0.0113581	−	0.00655760i	0.494310	−	0.869286i	$-0.335421\pi$
$317$	−0.202225	−	0.116755i	−0.0113581	−	0.00655760i	−0.505668	+	0.862728i	$0.668754\pi$
$318$	−0.000737888		0.0197560i	−4.13787e−5		0.00110786i
$319$	5.48649	+	3.16763i	0.307184	+	0.177353i
$320$	−6.46451	+	3.73229i	−0.361377	+	0.208641i
$321$	7.74079	+	14.6439i	0.432049	+	0.817343i
$322$	−1.10279	−	1.91009i	−0.0614562	−	0.106445i
$323$	0.332347	+	0.191880i	0.0184923	+	0.0106765i
$324$	−6.34045	−	16.1424i	−0.352247	−	0.896802i
$325$	11.9372	+	5.06533i	0.662159	+	0.280974i
$326$	−1.33488	+	2.31207i	−0.0739320	+	0.128054i
$327$	11.8636	+	7.45328i	0.656059	+	0.412168i
$328$	−8.89567			−0.491181
$329$	−2.98745	+	5.17441i	−0.164703	+	0.285275i
$330$	2.27297	+	1.42799i	0.125123	+	0.0786081i
$331$		−	21.6743i		−	1.19133i	−0.803235	−	0.595663i	$-0.796889\pi$
$331$		−	21.6743i		−	1.19133i	0.803235	−	0.595663i	$-0.203111\pi$
$332$	−16.9518	+	9.78711i	−0.930350	+	0.537138i
$333$	2.27479	−	30.4099i	0.124658	−	1.66645i
$334$	−0.629964	−	1.09113i	−0.0344701	−	0.0597040i
$335$	−2.42779	−	4.20505i	−0.132644	−	0.229747i
$336$	0.230617	−	6.17449i	0.0125812	−	0.336846i
$337$	−16.6938	−	28.9144i	−0.909367	−	1.57507i	−0.814945	−	0.579538i	$-0.803233\pi$
$337$	−16.6938	−	28.9144i	−0.909367	−	1.57507i	−0.0944222	−	0.995532i	$-0.530100\pi$
$338$	2.52601	−	2.44053i	0.137397	−	0.132748i
$339$	11.8560	+	22.4291i	0.643931	+	1.21818i
$340$	0.269067	−	0.155346i	0.0145922	−	0.00842483i
$341$	23.0658	−	39.9511i	1.24908	−	2.16348i
$342$	2.27920	+	0.170494i	0.123245	+	0.00921928i
$343$			1.00000i			0.0539949i
$344$			5.40707i			0.291530i
$345$	−0.625192	+	16.7387i	−0.0336592	+	0.901184i
$346$	4.47821	−	2.58550i	0.240750	−	0.138997i
$347$	−12.6422	+	21.8969i	−0.678669	+	1.17549i	0.296714	+	0.954967i	$0.404109\pi$
$347$	−12.6422	+	21.8969i	−0.678669	+	1.17549i	−0.975382	+	0.220522i	$0.929224\pi$
$348$	2.32320	−	3.69791i	0.124537	−	0.198229i
$349$	−3.51509	+	2.02944i	−0.188159	+	0.108633i	−0.591120	−	0.806583i	$-0.701314\pi$
$349$	−3.51509	+	2.02944i	−0.188159	+	0.108633i	0.402962	+	0.915217i	$0.367981\pi$
$350$	−0.971726			−0.0519409
$351$	−0.192920	−	18.7340i	−0.0102973	−	0.999947i
$352$	14.9413			0.796372
$353$	10.9006	−	6.29348i	0.580181	−	0.334968i	−0.181024	−	0.983479i	$-0.557941\pi$
$353$	10.9006	−	6.29348i	0.580181	−	0.334968i	0.761205	+	0.648511i	$0.224608\pi$
$354$	−2.85139	+	4.53865i	−0.151550	+	0.241226i
$355$	−4.39703	+	7.61588i	−0.233370	+	0.404209i
$356$	6.55851	−	3.78656i	0.347600	−	0.200687i
$357$	−0.00879824	+	0.235562i	−0.000465652	+	0.0124673i
$358$		−	0.808078i		−	0.0427082i
$359$			11.6529i			0.615016i	0.951545	+	0.307508i	$0.0994951\pi$
$359$			11.6529i			0.615016i	−0.951545	+	0.307508i	$0.900505\pi$
$360$	2.12380	−	3.11594i	0.111934	−	0.164225i
$361$	−5.52445	+	9.56863i	−0.290761	+	0.503612i
$362$	−2.66410	+	1.53812i	−0.140022	+	0.0808416i
$363$	10.0721	+	19.0543i	0.528650	+	1.00009i
$364$	2.71398	−	6.39591i	0.142251	−	0.335237i
$365$	4.90465	+	8.49509i	0.256721	+	0.444654i
$366$	0.170232	−	4.55775i	0.00889817	−	0.238237i
$367$	−3.68933	−	6.39011i	−0.192582	−	0.333561i	0.753523	−	0.657421i	$-0.228353\pi$
$367$	−3.68933	−	6.39011i	−0.192582	−	0.333561i	−0.946105	+	0.323860i	$0.895019\pi$
$368$	14.5605	+	25.2195i	0.759019	+	1.31466i
$369$	−22.6600	+	10.9162i	−1.17963	+	0.568277i
$370$	2.81772	−	1.62681i	0.146486	−	0.0845740i
$371$			0.0422456i			0.00219328i
$372$	−26.9272	−	16.9169i	−1.39611	−	0.877103i
$373$	10.0065	−	17.3317i	0.518115	−	0.897401i	−0.481664	−	0.876356i	$-0.659967\pi$
$373$	10.0065	−	17.3317i	0.518115	−	0.897401i	0.999779	−	0.0210448i	$-0.00669927\pi$
$374$	−0.178040			−0.00920623
$375$	14.9364	+	9.38376i	0.771312	+	0.484575i
$376$	−3.16972	+	5.49012i	−0.163466	+	0.283132i
$377$	3.76733	−	2.83961i	0.194027	−	0.146247i
$378$	0.561676	+	1.28667i	0.0288895	+	0.0661790i
$379$	12.1513	+	7.01554i	0.624169	+	0.360364i	0.778490	−	0.627656i	$-0.215986\pi$
$379$	12.1513	+	7.01554i	0.624169	+	0.360364i	−0.154321	+	0.988021i	$0.549319\pi$
$380$	−3.21860	−	5.57478i	−0.165111	−	0.285980i
$381$	3.37907	+	6.39248i	0.173115	+	0.327496i
$382$	3.20332	−	1.84943i	0.163896	−	0.0946253i
$383$	20.2628	+	11.6988i	1.03538	+	0.597779i	0.918522	−	0.395370i	$-0.129383\pi$
$383$	20.2628	+	11.6988i	1.03538	+	0.597779i	0.116861	+	0.993148i	$0.462717\pi$
$384$	0.509040	−	13.6289i	0.0259768	−	0.695497i
$385$	4.96755	+	2.86802i	0.253170	+	0.146168i
$386$	−3.44875	−	5.97341i	−0.175537	−	0.304038i
$387$	6.63524	+	13.7735i	0.337288	+	0.700146i
$388$	19.3482	+	11.1707i	0.982257	+	0.567106i
$389$	7.73435	−	13.3963i	0.392147	−	0.679219i	−0.600585	−	0.799561i	$-0.705066\pi$
$389$	7.73435	−	13.3963i	0.392147	−	0.679219i	0.992733	+	0.120342i	$0.0383991\pi$
$390$	1.64005	−	1.14276i	0.0830472	−	0.0578657i
$391$	−0.555495	−	0.962146i	−0.0280926	−	0.0486578i
$392$			1.06101i			0.0535893i
$393$	−21.2807	−	0.794833i	−1.07347	−	0.0400940i
$394$	−1.22498			−0.0617135
$395$		−	5.33045i		−	0.268204i
$396$	25.2171	−	12.1481i	1.26721	−	0.610465i
$397$	−10.8447	+	6.26121i	−0.544282	+	0.314241i	−0.746812	−	0.665035i	$-0.768417\pi$
$397$	−10.8447	+	6.26121i	−0.544282	+	0.314241i	0.202531	+	0.979276i	$0.435083\pi$
$398$	2.05102	+	1.18415i	0.102808	+	0.0593563i
$399$	4.88058	+	0.182290i	0.244335	+	0.00912590i
$400$	12.8300			0.641501
$401$		−	34.5268i		−	1.72419i	−0.506748	−	0.862094i	$-0.669153\pi$
$401$		−	34.5268i		−	1.72419i	0.506748	−	0.862094i	$-0.330847\pi$
$402$	1.91671	+	0.0715893i	0.0955970	+	0.00357055i
$403$	−20.6773	−	27.4327i	−1.03001	−	1.36652i
$404$	19.0630			0.948418
$405$	1.58627	−	10.5435i	0.0788225	−	0.523910i
$406$	−0.176760	+	0.306157i	−0.00877245	+	0.0151943i
$407$	49.2171			2.43960
$408$	−0.00933506	+	0.249934i	−0.000462154	+	0.0123736i
$409$	−27.8058	−	16.0537i	−1.37491	−	0.793805i	−0.383368	−	0.923596i	$-0.625236\pi$
$409$	−27.8058	−	16.0537i	−1.37491	−	0.793805i	−0.991541	+	0.129791i	$0.958569\pi$
$410$	−2.32407	−	1.34180i	−0.114778	−	0.0662670i
$411$	−5.36892	−	3.37301i	−0.264829	−	0.166378i
$412$	−23.1743			−1.14172
$413$	−5.72684	+	9.91918i	−0.281799	+	0.488091i
$414$	−5.46752	−	3.72661i	−0.268714	−	0.183153i
$415$	−12.0338			−0.590718
$416$	4.34612	−	10.2423i	0.213086	−	0.502170i
$417$	10.0772	+	19.0640i	0.493485	+	0.933567i
$418$			3.68879i			0.180425i
$419$	−0.299223			−0.0146180			−0.00730900	−	0.999973i	$-0.502327\pi$
$419$	−0.299223			−0.0146180			−0.00730900	+	0.999973i	$0.502327\pi$
$420$	2.10347	−	3.34815i	0.102639	−	0.163373i
$421$	23.0210	+	13.2912i	1.12197	+	0.647772i	0.941904	−	0.335882i	$-0.109034\pi$
$421$	23.0210	+	13.2912i	1.12197	+	0.647772i	0.180070	+	0.983654i	$0.442368\pi$
$422$	−6.50763	+	3.75718i	−0.316786	+	0.182897i
$423$	−1.33711	+	17.8747i	−0.0650125	+	0.869100i
$424$			0.0448232i			0.00217681i
$425$	−0.489475			−0.0237430
$426$	−1.62342	−	3.07116i	−0.0786549	−	0.148798i
$427$		−	9.74614i		−	0.471649i
$428$	9.21413	+	15.9593i	0.445382	+	0.771424i
$429$	30.1282	−	2.56595i	1.45460	−	0.123885i
$430$	−0.815592	+	1.41265i	−0.0393313	+	0.0681239i
$431$	−30.0006	−	17.3208i	−1.44508	−	0.834315i	−0.446894	−	0.894587i	$-0.647470\pi$
$431$	−30.0006	−	17.3208i	−1.44508	−	0.834315i	−0.998182	+	0.0602720i	$0.980803\pi$
$432$	−7.41599	−	16.9883i	−0.356802	−	0.817348i
$433$	0.0401378	+	0.0695207i	0.00192890	+	0.00334095i	0.866988	−	0.498329i	$-0.166053\pi$
$433$	0.0401378	+	0.0695207i	0.00192890	+	0.00334095i	−0.865059	+	0.501670i	$0.832719\pi$
$434$	2.22935	+	1.28712i	0.107012	+	0.0617836i
$435$	2.37361	−	1.25469i	0.113806	−	0.0601580i
$436$	13.4992	+	7.79377i	0.646495	+	0.373254i
$437$	−19.9346	+	11.5092i	−0.953601	+	0.550562i
$438$	−3.87217	−	0.144625i	−0.185019	−	0.00691047i
$439$	18.9741	+	32.8640i	0.905582	+	1.56851i	0.820134	+	0.572172i	$0.193899\pi$
$439$	18.9741	+	32.8640i	0.905582	+	1.56851i	0.0854481	+	0.996343i	$0.472768\pi$
$440$	5.27065	+	3.04301i	0.251268	+	0.145070i
$441$	1.30201	+	2.70273i	0.0620007	+	0.128702i
$442$	−0.0517883	+	0.122047i	−0.00246332	+	0.00580519i
$443$	−18.6101	+	32.2336i	−0.884193	+	1.53147i	−0.0375561	+	0.999295i	$0.511957\pi$
$443$	−18.6101	+	32.2336i	−0.884193	+	1.53147i	−0.846636	+	0.532172i	$0.821376\pi$
$444$	1.26630	−	33.9036i	0.0600959	−	1.60899i
$445$	4.65580			0.220706
$446$	−0.777471	+	1.34662i	−0.0368143	+	0.0637642i
$447$	20.4956	−	10.8340i	0.969410	−	0.512432i
$448$		−	6.30091i		−	0.297690i
$449$	26.1521	−	15.0989i	1.23419	−	0.712562i	0.266292	−	0.963892i	$-0.414201\pi$
$449$	26.1521	−	15.0989i	1.23419	−	0.712562i	0.967901	+	0.251330i	$0.0808680\pi$
$450$	−2.62631	+	1.26520i	−0.123806	+	0.0596422i
$451$	−20.2973	−	35.1559i	−0.955762	−	1.65543i
$452$	14.1127	+	24.4438i	0.663803	+	1.14974i
$453$	−8.60762	+	4.55000i	−0.404421	+	0.213778i
$454$	−0.115120	−	0.199393i	−0.00540284	−	0.00935799i
$455$	3.41100	−	2.57103i	0.159910	−	0.120532i
$456$	5.17836	+	0.193412i	0.242499	+	0.00905734i
$457$	−4.56705	+	2.63679i	−0.213638	+	0.123344i	−0.603001	−	0.797741i	$-0.706028\pi$
$457$	−4.56705	+	2.63679i	−0.213638	+	0.123344i	0.389363	+	0.921084i	$0.372695\pi$
$458$	0.364232	−	0.630868i	0.0170194	−	0.0294785i
$459$	0.282926	+	0.648116i	0.0132058	+	0.0302515i
$460$			18.6357i			0.868896i
$461$			22.3456i			1.04074i	0.853941	+	0.520370i	$0.174206\pi$
$461$			22.3456i			1.04074i	−0.853941	+	0.520370i	$0.825794\pi$
$462$	−2.00320	+	1.05890i	−0.0931974	+	0.0492643i
$463$	−12.6181	+	7.28508i	−0.586414	+	0.338566i	−0.763678	−	0.645597i	$-0.776609\pi$
$463$	−12.6181	+	7.28508i	−0.586414	+	0.338566i	0.177264	+	0.984163i	$0.443275\pi$
$464$	2.33382	−	4.04229i	0.108345	−	0.187659i
$465$	−9.13634	−	17.2840i	−0.423688	−	0.801526i
$466$	−0.918091	+	0.530060i	−0.0425297	+	0.0245545i
$467$	10.9083			0.504778			0.252389	−	0.967626i	$-0.418784\pi$
$467$	10.9083			0.504778			0.252389	+	0.967626i	$0.418784\pi$
$468$	−0.992413	−	20.8201i	−0.0458743	−	0.962408i
$469$	4.09863			0.189257
$470$	−1.65624	+	0.956230i	−0.0763966	+	0.0441076i
$471$	0.814702	+	0.0304291i	0.0375395	+	0.00140210i
$472$	−6.07626	+	10.5244i	−0.279682	+	0.484424i
$473$	−21.3689	+	12.3373i	−0.982543	+	0.567271i
$474$	1.78297	+	1.12015i	0.0818944	+	0.0514500i
$475$			10.1414i			0.465318i
$476$			0.262258i			0.0120206i
$477$	0.0550044	+	0.114178i	0.00251848	+	0.00522787i
$478$	2.37847	−	4.11964i	0.108789	−	0.188428i
$479$	12.5843	−	7.26555i	0.574991	−	0.331971i	−0.184149	−	0.982898i	$-0.558953\pi$
$479$	12.5843	−	7.26555i	0.574991	−	0.331971i	0.759140	+	0.650927i	$0.225620\pi$
$480$	3.36845	−	5.36166i	0.153748	−	0.244725i
$481$	14.3163	−	33.7385i	0.652766	−	1.53834i
$482$	0.830903	+	1.43917i	0.0378466	+	0.0655522i
$483$	−11.9725	−	7.52169i	−0.544767	−	0.342249i
$484$	11.9892	+	20.7659i	0.544965	+	0.943907i
$485$	6.86752	+	11.8949i	0.311838	+	0.540120i
$486$	3.19332	+	2.74620i	0.144852	+	0.124570i
$487$	−25.1394	+	14.5142i	−1.13917	+	0.657702i	−0.946226	−	0.323507i	$-0.895138\pi$
$487$	−25.1394	+	14.5142i	−1.13917	+	0.657702i	−0.192948	+	0.981209i	$0.561805\pi$
$488$		−	10.3408i		−	0.468106i
$489$	−0.638792	+	17.1029i	−0.0288872	+	0.773418i
$490$	−0.160041	+	0.277200i	−0.00722993	+	0.0125226i
$491$	−17.2727			−0.779508			−0.389754	−	0.920919i	$-0.627440\pi$
$491$	−17.2727			−0.779508			−0.389754	+	0.920919i	$0.627440\pi$
$492$	−24.7396	+	13.0774i	−1.11535	+	0.589575i
$493$	−0.0890370	+	0.154217i	−0.00401003	+	0.00694557i
$494$	2.52868	+	1.07300i	0.113771	+	0.0482764i
$495$	17.1602	+	1.28366i	0.771292	+	0.0576960i
$496$	−29.4349	−	16.9942i	−1.32167	−	0.763064i
$497$	−3.71157	−	6.42863i	−0.166487	−	0.288364i
$498$	2.52880	−	4.02517i	0.113318	−	0.180372i
$499$	−13.6439	+	7.87730i	−0.610784	+	0.352636i	−0.773272	−	0.634074i	$-0.781381\pi$
$499$	−13.6439	+	7.87730i	−0.610784	+	0.352636i	0.162488	+	0.986710i	$0.448048\pi$
$500$	16.9956	+	9.81243i	0.760068	+	0.438825i
$501$	−6.83922	−	4.29672i	−0.305554	−	0.191963i
$502$	2.65916	+	1.53527i	0.118684	+	0.0685223i
$503$	15.9840	+	27.6851i	0.712691	+	1.23442i	0.963844	+	0.266469i	$0.0858569\pi$
$503$	15.9840	+	27.6851i	0.712691	+	1.23442i	−0.251153	+	0.967947i	$0.580810\pi$
$504$	1.38146	+	2.86764i	0.0615349	+	0.127735i
$505$	10.1494	+	5.85976i	0.451643	+	0.260756i
$506$	5.33954	−	9.24835i	0.237371	−	0.411139i
$507$	7.00473	−	21.3994i	0.311091	−	0.950380i
$508$	4.02223	+	6.96670i	0.178458	+	0.309097i
$509$		−	18.6131i		−	0.825013i	−0.910955	−	0.412507i	$-0.864653\pi$
$509$		−	18.6131i		−	0.825013i	0.910955	−	0.412507i	$-0.135347\pi$
$510$	−0.0401385	+	0.0638896i	−0.00177736	+	0.00282908i
$511$	−8.28011			−0.366290
$512$		−	18.5783i		−	0.821052i
$513$	13.4282	−	5.86191i	0.592871	−	0.258809i
$514$	−2.89604	+	1.67203i	−0.127739	+	0.0737499i
$515$	−12.3384	−	7.12356i	−0.543693	−	0.313902i
$516$	7.94887	+	15.0375i	0.349929	+	0.661991i
$517$	−28.9295			−1.27232
$518$			2.74641i			0.120670i
$519$	17.6346	−	28.0695i	0.774074	−	1.23212i
$520$	3.61912	−	2.72790i	0.158709	−	0.119626i
$521$	21.6205			0.947210			0.473605	−	0.880737i	$-0.342952\pi$
$521$	21.6205			0.947210			0.473605	+	0.880737i	$0.342952\pi$
$522$	−0.0791135	+	1.05760i	−0.00346270	+	0.0462901i
$523$	−2.42546	+	4.20103i	−0.106058	+	0.183698i	−0.914170	−	0.405331i	$-0.867156\pi$
$523$	−2.42546	+	4.20103i	−0.106058	+	0.183698i	0.808112	+	0.589029i	$0.200490\pi$
$524$	−23.6924			−1.03501
$525$	−5.50729	+	2.91116i	−0.240358	+	0.127053i
$526$	−3.40024	−	1.96313i	−0.148258	−	0.0855966i
$527$	1.12296	+	0.648344i	0.0489171	+	0.0282423i
$528$	26.4489	−	13.9809i	1.15104	−	0.608442i
$529$	43.6387			1.89733
$530$	−0.00676104	+	0.0117105i	−0.000293681	+	0.000508670i
$531$	−2.56320	+	34.2653i	−0.111233	+	1.48699i
$532$	5.43370			0.235581
$533$	−30.0036	+	3.68771i	−1.29960	+	0.159732i
$534$	−0.978374	+	1.55731i	−0.0423384	+	0.0673912i
$535$			11.3293i			0.489810i
$536$	4.34871			0.187836
$537$	−2.42089	−	4.57981i	−0.104469	−	0.197633i
$538$	7.00128	+	4.04219i	0.301847	+	0.174271i
$539$	−4.19316	+	2.42092i	−0.180612	+	0.104276i
$540$	1.32577	−	11.7879i	0.0570519	−	0.507270i
$541$			29.1335i			1.25255i	0.779603	+	0.626275i	$0.215421\pi$
$541$			29.1335i			1.25255i	−0.779603	+	0.626275i	$0.784579\pi$
$542$	1.39874			0.0600812
$543$	−10.4909	+	16.6986i	−0.450206	+	0.716605i
$544$			0.419976i			0.0180063i
$545$	4.79145	+	8.29904i	0.205243	+	0.355492i
$546$	0.143185	+	1.68121i	0.00612777	+	0.0719493i
$547$	−4.95822	+	8.58789i	−0.211998	+	0.367192i	−0.952340	−	0.305039i	$-0.901330\pi$
$547$	−4.95822	+	8.58789i	−0.211998	+	0.367192i	0.740342	+	0.672231i	$0.234664\pi$
$548$	−6.10912	−	3.52710i	−0.260968	−	0.150670i
$549$	−12.6896	−	26.3412i	−0.541580	−	1.12421i
$550$	−2.35247	−	4.07460i	−0.100310	−	0.173741i
$551$	3.19520	+	1.84475i	0.136120	+	0.0785889i
$552$	−12.7030	−	7.98061i	−0.540674	−	0.339677i
$553$	3.89666	+	2.24974i	0.165703	+	0.0956687i
$554$	5.82192	−	3.36129i	0.247350	−	0.142807i
$555$	11.0958	−	17.6615i	0.470991	−	0.749690i
$556$	11.9953	+	20.7765i	0.508714	+	0.881118i
$557$	−14.2831	−	8.24635i	−0.605194	−	0.349409i	0.165888	−	0.986145i	$-0.446951\pi$
$557$	−14.2831	−	8.24635i	−0.605194	−	0.349409i	−0.771082	+	0.636735i	$0.780284\pi$
$558$	7.70119	+	0.576083i	0.326017	+	0.0243875i
$559$	2.24151	+	18.2371i	0.0948056	+	0.771349i
$560$	2.11308	−	3.65996i	0.0892938	−	0.154661i
$561$	−1.00905	+	0.533384i	−0.0426020	+	0.0225195i
$562$	−5.65597			−0.238583
$563$	4.05790	−	7.02849i	0.171020	−	0.296216i	−0.767757	−	0.640742i	$-0.778627\pi$
$563$	4.05790	−	7.02849i	0.171020	−	0.296216i	0.938777	+	0.344526i	$0.111960\pi$
$564$	−0.744322	+	19.9283i	−0.0313416	+	0.839133i
$565$			17.3524i			0.730019i
$566$	3.52454	−	2.03490i	0.148148	−	0.0855331i
$567$	7.03799	+	5.60952i	0.295568	+	0.235577i
$568$	−3.93803	−	6.82087i	−0.165236	−	0.286197i
$569$	18.9307	+	32.7889i	0.793616	+	1.37458i	0.923714	+	0.383082i	$0.125137\pi$
$569$	18.9307	+	32.7889i	0.793616	+	1.37458i	−0.130098	+	0.991501i	$0.541529\pi$
$570$	1.32372	+	0.831625i	0.0554446	+	0.0348329i
$571$	−6.70098	−	11.6064i	−0.280427	−	0.485714i	0.691063	−	0.722795i	$-0.257143\pi$
$571$	−6.70098	−	11.6064i	−0.280427	−	0.485714i	−0.971490	+	0.237080i	$0.923810\pi$
$572$	33.3894	−	4.10385i	1.39608	−	0.171590i
$573$	12.6142	−	20.0784i	0.526967	−	0.838789i
$574$	1.96177	−	1.13263i	0.0818827	−	0.0472750i
$575$	14.6797	−	25.4260i	0.612185	−	1.06034i
$576$	−8.20388	−	17.0297i	−0.341828	−	0.709570i
$577$			35.9731i			1.49758i	0.662807	+	0.748790i	$0.269365\pi$
$577$			35.9731i			1.49758i	−0.662807	+	0.748790i	$0.730635\pi$
$578$			4.58813i			0.190841i
$579$	−37.4414	−	23.5225i	−1.55601	−	0.977561i
$580$	2.58683	−	1.49351i	0.107412	−	0.0620145i
$581$	5.07894	−	8.79698i	0.210710	−	0.364960i
$582$	−5.42184	−	0.202506i	−0.224742	−	0.00839413i
$583$	−0.177142	+	0.102273i	−0.00733649	+	0.00423572i
$584$	−8.78531			−0.363539
$585$	5.87150	−	11.3900i	0.242757	−	0.470918i
$586$	5.41120			0.223535
$587$	21.2219	−	12.2525i	0.875923	−	0.505714i	0.00661090	−	0.999978i	$-0.497896\pi$
$587$	21.2219	−	12.2525i	0.875923	−	0.505714i	0.869312	+	0.494264i	$0.164562\pi$
$588$	1.55978	+	2.95077i	0.0643244	+	0.121688i
$589$	13.4330	−	23.2666i	0.553495	−	0.958682i
$590$	−3.17496	+	1.83306i	−0.130711	+	0.0754659i
$591$	−6.94260	+	3.66987i	−0.285581	+	0.150958i
$592$		−	36.2618i		−	1.49035i
$593$		−	38.0338i		−	1.56186i	−0.624619	−	0.780930i	$-0.714746\pi$
$593$		−	38.0338i		−	1.56186i	0.624619	−	0.780930i	$-0.285254\pi$
$594$	−4.03542	+	5.47011i	−0.165575	+	0.224441i
$595$	−0.0806155	+	0.139630i	−0.00330492	+	0.00572428i
$596$	22.3367	−	12.8961i	0.914948	−	0.528245i
$597$	15.1718	+	0.566665i	0.620939	+	0.0231921i
$598$	−4.78662	−	6.35044i	−0.195739	−	0.259689i
$599$	13.3958	+	23.2021i	0.547336	+	0.948013i	0.998456	+	0.0555498i	$0.0176912\pi$
$599$	13.3958	+	23.2021i	0.547336	+	0.948013i	−0.451120	+	0.892463i	$0.648975\pi$
$600$	−5.84331	+	3.08878i	−0.238552	+	0.126099i
$601$	19.0278	+	32.9572i	0.776162	+	1.34435i	0.934139	+	0.356909i	$0.116169\pi$
$601$	19.0278	+	32.9572i	0.776162	+	1.34435i	−0.157977	+	0.987443i	$0.550497\pi$
$602$	−0.688448	−	1.19243i	−0.0280590	−	0.0485997i
$603$	11.0775	−	5.33648i	0.451111	−	0.217318i
$604$	−9.38083	+	5.41602i	−0.381701	+	0.220375i
$605$			14.7415i			0.599326i
$606$	−4.09282	+	2.16347i	−0.166260	+	0.0878850i
$607$	2.66099	−	4.60897i	0.108006	−	0.187072i	−0.806956	−	0.590611i	$-0.798887\pi$
$607$	2.66099	−	4.60897i	0.108006	−	0.187072i	0.914962	+	0.403539i	$0.132220\pi$
$608$	8.70143			0.352889
$609$	−0.0845867	+	2.26470i	−0.00342763	+	0.0917704i
$610$	1.55978	−	2.70162i	0.0631538	−	0.109386i
$611$	−8.41501	+	19.8313i	−0.340435	+	0.802288i
$612$	0.341464	+	0.708813i	0.0138029	+	0.0286521i
$613$	0.485771	+	0.280460i	0.0196201	+	0.0113277i	0.509778	−	0.860306i	$-0.329728\pi$
$613$	0.485771	+	0.280460i	0.0196201	+	0.0113277i	−0.490158	+	0.871634i	$0.663061\pi$
$614$	0.589991	+	1.02189i	0.0238101	+	0.0412403i
$615$	−17.1916	−	0.642108i	−0.693233	−	0.0258923i
$616$	−4.44900	+	2.56863i	−0.179255	+	0.103493i
$617$	21.9654	+	12.6817i	0.884293	+	0.510547i	0.872071	−	0.489378i	$-0.162776\pi$
$617$	21.9654	+	12.6817i	0.884293	+	0.510547i	0.0122215	+	0.999925i	$0.496110\pi$
$618$	4.97553	−	2.63007i	0.200145	−	0.105797i
$619$	−26.9080	−	15.5353i	−1.08152	−	0.624418i	−0.150217	−	0.988653i	$-0.547997\pi$
$619$	−26.9080	−	15.5353i	−1.08152	−	0.624418i	−0.931307	+	0.364235i	$0.881331\pi$
$620$	−10.8753	−	18.8366i	−0.436763	−	0.756496i
$621$	−42.1517	−	4.74075i	−1.69149	−	0.190240i
$622$	−6.25245	−	3.60985i	−0.250700	−	0.144742i
$623$	−1.96500	+	3.40348i	−0.0787261	+	0.136358i
$624$	−1.89052	−	22.1976i	−0.0756815	−	0.888616i
$625$	−2.95883	−	5.12485i	−0.118353	−	0.204994i
$626$			4.56202i			0.182335i
$627$	11.0511	+	20.9063i	0.441339	+	0.834919i
$628$	0.907032			0.0361945
$629$			1.38342i			0.0551604i
$630$	−0.0716306	+	0.957572i	−0.00285383	+	0.0381506i
$631$	4.17044	−	2.40780i	0.166023	−	0.0958532i	−0.414686	−	0.909964i	$-0.636109\pi$
$631$	4.17044	−	2.40780i	0.166023	−	0.0958532i	0.580709	+	0.814111i	$0.302775\pi$
$632$	4.13442	+	2.38701i	0.164458	+	0.0949500i
$633$	−25.6262	+	40.7899i	−1.01855	+	1.62125i
$634$	0.0630906			0.00250565
$635$			4.94557i			0.196259i
$636$	0.0658940	+	0.124657i	0.00261287	+	0.00494298i
$637$	0.439844	+	3.57862i	0.0174273	+	0.141790i
$638$	−1.71169			−0.0677663
$639$	−18.4016	−	12.5423i	−0.727954	−	0.496167i
$640$	4.66417	−	8.07859i	0.184368	−	0.319334i
$641$	−13.8883			−0.548556			−0.274278	−	0.961650i	$-0.588439\pi$
$641$	−13.8883			−0.548556			−0.274278	+	0.961650i	$0.588439\pi$
$642$	−3.78952	−	2.38076i	−0.149560	−	0.0939609i
$643$	−8.64843	−	4.99317i	−0.341061	−	0.196912i	0.319680	−	0.947525i	$-0.396425\pi$
$643$	−8.64843	−	4.99317i	−0.341061	−	0.196912i	−0.660741	+	0.750614i	$0.729758\pi$
$644$	−13.6231	−	7.86530i	−0.536825	−	0.309936i
$645$	−0.390294	+	10.4496i	−0.0153678	+	0.411453i
$646$	−0.103686			−0.00407948
$647$	−14.1482	+	24.5054i	−0.556223	+	0.963406i	0.441585	+	0.897220i	$0.354416\pi$
$647$	−14.1482	+	24.5054i	−0.556223	+	0.963406i	−0.997807	+	0.0661862i	$0.978917\pi$
$648$	7.46741	+	5.95177i	0.293348	+	0.233808i
$649$	−55.4569			−2.17687
$650$	−3.47744	+	0.427408i	−0.136396	+	0.0167643i
$651$	16.4910	+	0.615938i	0.646332	+	0.0241405i
$652$			19.0411i			0.745708i
$653$	−24.9742			−0.977315			−0.488658	−	0.872476i	$-0.662513\pi$
$653$	−24.9742			−0.977315			−0.488658	+	0.872476i	$0.662513\pi$
$654$	−3.78280	−	0.141288i	−0.147919	−	0.00552479i
$655$	−12.6142	−	7.28281i	−0.492878	−	0.284563i
$656$	−25.9019	+	14.9545i	−1.01130	+	0.583874i
$657$	−22.3789	+	10.7808i	−0.873084	+	0.420600i
$658$		−	1.61432i		−	0.0629329i
$659$	−22.2070			−0.865061			−0.432530	−	0.901619i	$-0.642379\pi$
$659$	−22.2070			−0.865061			−0.432530	+	0.901619i	$0.642379\pi$
$660$	19.1316	+	0.714566i	0.744697	+	0.0278145i
$661$		−	30.4918i		−	1.18599i	−0.805205	−	0.592996i	$-0.797945\pi$
$661$		−	30.4918i		−	1.18599i	0.805205	−	0.592996i	$-0.202055\pi$
$662$	2.92802	+	5.07149i	0.113801	+	0.197109i
$663$	0.0721250	+	0.846857i	0.00280110	+	0.0328892i
$664$	5.38882	−	9.33372i	0.209127	−	0.362218i
$665$	2.89298	+	1.67026i	0.112185	+	0.0647701i
$666$	3.57587	+	7.42282i	0.138562	+	0.287628i
$667$	−5.34056	−	9.25012i	−0.206787	−	0.358166i
$668$	−7.78212	−	4.49301i	−0.301099	−	0.173840i
$669$	−0.372051	+	9.96120i	−0.0143843	+	0.385122i
$670$	1.13614	+	0.655951i	0.0438929	+	0.0253416i
$671$	40.8671	−	23.5946i	1.57766	−	0.910860i
$672$	2.49781	+	4.72532i	0.0963551	+	0.182283i
$673$	−0.123050	−	0.213129i	−0.00474322	−	0.00821550i	0.863644	−	0.504102i	$-0.168176\pi$
$673$	−0.123050	−	0.213129i	−0.00474322	−	0.00821550i	−0.868387	+	0.495887i	$0.834843\pi$
$674$	7.81223	+	4.51039i	0.300916	+	0.173734i
$675$	−11.0943	+	15.0387i	−0.427022	+	0.578838i
$676$	6.89910	−	24.0823i	0.265350	−	0.926241i
$677$	2.41199	−	4.17768i	0.0927002	−	0.160561i	−0.815946	−	0.578128i	$-0.803784\pi$
$677$	2.41199	−	4.17768i	0.0927002	−	0.160561i	0.908646	+	0.417566i	$0.137117\pi$
$678$	−5.80414	−	3.64644i	−0.222907	−	0.140041i
$679$	−11.5939			−0.444932
$680$	−0.0855342	+	0.148150i	−0.00328009	+	0.00568128i
$681$	−1.24980	−	0.785184i	−0.0478925	−	0.0300883i
$682$			12.4640i			0.477273i
$683$	14.5572	−	8.40463i	0.557018	−	0.321594i	−0.194930	−	0.980817i	$-0.562448\pi$
$683$	14.5572	−	8.40463i	0.557018	−	0.321594i	0.751948	+	0.659223i	$0.229115\pi$
$684$	14.6858	−	7.07475i	0.561526	−	0.270510i
$685$	−2.16839	−	3.75576i	−0.0828500	−	0.143500i
$686$	−0.135092	−	0.233987i	−0.00515784	−	0.00893365i
$687$	0.174300	−	4.66666i	0.00664995	−	0.178044i
$688$	9.08980	+	15.7440i	0.346545	+	0.600234i
$689$	0.0185815	+	0.151181i	0.000707898	+	0.00575954i
$690$	−2.11499	−	4.00110i	−0.0805162	−	0.152319i
$691$	−25.3693	+	14.6470i	−0.965095	+	0.557198i	−0.897738	−	0.440531i	$-0.854790\pi$
$691$	−25.3693	+	14.6470i	−0.965095	+	0.557198i	−0.0673579	+	0.997729i	$0.521457\pi$
$692$	18.4402	−	31.9394i	0.700992	−	1.21415i
$693$	−8.18090	+	12.0026i	−0.310767	+	0.455943i
$694$		−	6.83145i		−	0.259318i
$695$			14.7489i			0.559459i
$696$	−0.0897477	+	2.40288i	−0.00340188	+	0.0910810i
$697$	0.988178	−	0.570525i	0.0374299	−	0.0216102i
$698$	0.548323	−	0.949723i	0.0207543	−	0.0359475i
$699$	−3.61532	+	5.75461i	−0.136744	+	0.217659i
$700$	−6.00200	+	3.46526i	−0.226854	+	0.130974i
$701$	−48.4840			−1.83121			−0.915607	−	0.402074i	$-0.868289\pi$
$701$	−48.4840			−1.83121			−0.915607	+	0.402074i	$0.868289\pi$
$702$	2.57596	+	4.35744i	0.0972233	+	0.164461i
$703$	28.6628			1.08104
$704$	26.4207	−	15.2540i	0.995767	−	0.574907i
$705$	−6.52205	+	10.3813i	−0.245635	+	0.390984i
$706$	−1.70040	+	2.94518i	−0.0639953	+	0.110843i
$707$	−8.56720	+	4.94628i	−0.322203	+	0.186024i
$708$	−1.42684	+	38.2019i	−0.0536240	+	1.43571i
$709$			14.0482i			0.527592i	0.964578	+	0.263796i	$0.0849746\pi$
$709$			14.0482i			0.527592i	−0.964578	+	0.263796i	$0.915025\pi$
$710$		−	2.37602i		−	0.0891704i
$711$	13.4608	+	1.00693i	0.504821	+	0.0377628i
$712$	−2.08489	+	3.61114i	−0.0781347	+	0.135333i
$713$	−67.3569	+	38.8885i	−2.52254	+	1.45639i
$714$	−0.0297639	−	0.0563069i	−0.00111389	−	0.00210723i
$715$	19.0385	+	8.07861i	0.711999	+	0.302123i
$716$	−2.88167	−	4.99120i	−0.107693	−	0.186530i
$717$	1.13820	−	30.4738i	0.0425067	−	1.13806i
$718$	−1.57422	−	2.72662i	−0.0587492	−	0.101757i
$719$	4.39578	+	7.61371i	0.163935	+	0.283943i	0.936276	−	0.351264i	$-0.114248\pi$
$719$	4.39578	+	7.61371i	0.163935	+	0.283943i	−0.772342	+	0.635207i	$0.780915\pi$
$720$	0.945762	−	12.6431i	0.0352465	−	0.471182i
$721$	10.4149	−	6.01306i	0.387872	−	0.223938i
$722$		−	2.98524i		−	0.111099i
$723$	9.02072	+	5.66725i	0.335484	+	0.210767i
$724$	−10.9701	+	19.0008i	−0.407701	+	0.706159i
$725$	−4.70584			−0.174771
$726$	−4.93083	−	3.09779i	−0.183000	−	0.114970i
$727$	7.62448	−	13.2060i	0.282776	−	0.489783i	−0.689291	−	0.724484i	$-0.742078\pi$
$727$	7.62448	−	13.2060i	0.282776	−	0.489783i	0.972067	+	0.234702i	$0.0754113\pi$
$728$	0.466681	+	3.79697i	0.0172963	+	0.140725i
$729$	26.3255	+	5.99744i	0.975018	+	0.222128i
$730$	−2.29524	−	1.32516i	−0.0849507	−	0.0490463i
$731$	−0.346783	−	0.600646i	−0.0128262	−	0.0222157i
$732$	−15.2019	−	28.7586i	−0.561877	−	1.06295i
$733$	−13.5244	+	7.80829i	−0.499533	+	0.288406i	−0.728521	−	0.685024i	$-0.759792\pi$
$733$	−13.5244	+	7.80829i	−0.499533	+	0.288406i	0.228987	+	0.973429i	$0.426459\pi$
$734$	1.72651	+	0.996800i	0.0637266	+	0.0367925i
$735$	−0.0765862	+	2.05050i	−0.00282492	+	0.0756338i
$736$	−21.8158	−	12.5953i	−0.804140	−	0.464271i
$737$	9.92246	+	17.1862i	0.365499	+	0.633062i
$738$	3.82744	−	5.61545i	0.140890	−	0.206707i
$739$	−5.58892	−	3.22676i	−0.205592	−	0.118698i	0.393669	−	0.919252i	$-0.371205\pi$
$739$	−5.58892	−	3.22676i	−0.205592	−	0.118698i	−0.599261	+	0.800554i	$0.704539\pi$
$740$	11.6027	−	20.0965i	0.426524	−	0.738761i
$741$	17.5459	−	1.49435i	0.644566	−	0.0548963i
$742$	−0.00570705	−	0.00988490i	−0.000209512	−	0.000362886i
$743$			31.6580i			1.16142i	0.814110	+	0.580710i	$0.197225\pi$
$743$			31.6580i			1.16142i	−0.814110	+	0.580710i	$0.802775\pi$
$744$	17.4971	+	0.653519i	0.641477	+	0.0239592i
$745$	15.8566			0.580939
$746$			5.40718i			0.197971i
$747$	2.27321	−	30.3887i	0.0831724	−	1.11187i
$748$	−1.09969	+	0.634906i	−0.0402086	+	0.0232145i
$749$	−8.28196	−	4.78159i	−0.302616	−	0.174716i
$750$	−4.76259	−	0.177883i	−0.173905	−	0.00649536i
$751$	−33.2020			−1.21156			−0.605779	−	0.795633i	$-0.707139\pi$
$751$	−33.2020			−1.21156			−0.605779	+	0.795633i	$0.707139\pi$
$752$			21.3144i			0.777258i
$753$	19.6703	+	0.734687i	0.716826	+	0.0267735i
$754$	−0.497896	+	1.17337i	−0.0181323	+	0.0427315i
$755$	−6.65933			−0.242358
$756$	8.05763	+	5.94429i	0.293053	+	0.216192i
$757$	−23.2558	+	40.2803i	−0.845247	+	1.46401i	0.0401596	+	0.999193i	$0.487213\pi$
$757$	−23.2558	+	40.2803i	−0.845247	+	1.46401i	−0.885407	+	0.464817i	$0.846120\pi$
$758$	−3.79098			−0.137695
$759$	2.55518	−	68.4119i	0.0927473	−	2.48319i
$760$	3.06950	+	1.77217i	0.111342	+	0.0642835i
$761$	24.2838	+	14.0202i	0.880286	+	0.508234i	0.870753	−	0.491721i	$-0.163632\pi$
$761$	24.2838	+	14.0202i	0.880286	+	0.508234i	0.00953362	+	0.999955i	$0.496965\pi$
$762$	−1.65423	−	1.03927i	−0.0599265	−	0.0376487i
$763$	−8.08902			−0.292842
$764$	13.1905	−	22.8466i	0.477215	−	0.826560i
$765$	−0.0360816	+	0.482346i	−0.00130453	+	0.0174392i
$766$	−6.32164			−0.228410
$767$	−16.1313	+	38.0159i	−0.582468	+	1.37267i
$768$	−8.47832	−	16.0391i	−0.305935	−	0.578763i
$769$			24.4073i			0.880148i	0.897961	+	0.440074i	$0.145048\pi$
$769$			24.4073i			0.880148i	−0.897961	+	0.440074i	$0.854952\pi$
$770$	−1.54979			−0.0558505
$771$	−11.4042	+	18.1524i	−0.410712	+	0.653743i
$772$	−42.6034	−	24.5971i	−1.53333	−	0.885268i
$773$	−36.5947	+	21.1280i	−1.31622	+	0.759920i	−0.983118	−	0.182971i	$-0.941428\pi$
$773$	−36.5947	+	21.1280i	−1.31622	+	0.759920i	−0.333101	+	0.942891i	$0.608095\pi$
$774$	−3.41325	−	2.32644i	−0.122687	−	0.0836222i
$775$			34.2667i			1.23089i
$776$	−12.3013			−0.441590
$777$	8.22788	+	15.5654i	0.295174	+	0.558405i
$778$			4.17940i			0.149839i
$779$	−11.8206	−	20.4739i	−0.423518	−	0.733555i
$780$	6.05485	−	12.9069i	0.216798	−	0.462143i
$781$	17.9708	−	31.1264i	0.643047	−	1.11379i
$782$	0.259957	+	0.150086i	0.00929604	+	0.00536707i
$783$	2.72006	+	6.23102i	0.0972071	+	0.222679i
$784$	1.78367	+	3.08940i	0.0637023	+	0.110336i
$785$	0.482918	+	0.278813i	0.0172361	+	0.00995125i
$786$	5.08677	−	2.68887i	0.181439	−	0.0959089i
$787$	10.6415	+	6.14388i	0.379329	+	0.219006i	0.677526	−	0.735499i	$-0.263052\pi$
$787$	10.6415	+	6.14388i	0.379329	+	0.219006i	−0.298197	+	0.954504i	$0.596385\pi$
$788$	−7.56625	+	4.36838i	−0.269536	+	0.155617i
$789$	−25.1523	−	0.939437i	−0.895444	−	0.0334449i
$790$	0.720102	+	1.24725i	0.0256201	+	0.0443753i
$791$	−12.6849	−	7.32364i	−0.451024	−	0.260399i
$792$	−8.68005	+	12.7350i	−0.308432	+	0.452518i
$793$	−4.28678	−	34.8777i	−0.152228	−	1.23854i
$794$	1.69168	−	2.93008i	0.0600355	−	0.103985i
$795$	−0.00323543	+	0.0866246i	−0.000114749	+	0.00307226i
$796$	16.8912			0.598692
$797$	10.3766	−	17.9728i	0.367559	−	0.636631i	−0.621624	−	0.783316i	$-0.713527\pi$
$797$	10.3766	−	17.9728i	0.367559	−	0.636631i	0.989183	+	0.146685i	$0.0468602\pi$
$798$	−1.16662	+	0.616675i	−0.0412978	+	0.0218301i
$799$		−	0.813163i		−	0.0287676i
$800$	−9.61150	+	5.54920i	−0.339818	+	0.196194i
$801$	−0.879487	+	11.7572i	−0.0310752	+	0.415419i
$802$	4.66431	+	8.07882i	0.164702	+	0.285273i
$803$	−20.0455	−	34.7198i	−0.707389	−	1.22523i
$804$	12.0941	−	6.39298i	0.426528	−	0.225463i
$805$	−4.83543	−	8.37521i	−0.170426	−	0.295187i
$806$	8.54415	+	3.62554i	0.300955	+	0.127704i
$807$	51.7899	+	1.93435i	1.82309	+	0.0680924i
$808$	−9.08992	+	5.24807i	−0.319782	+	0.184626i
$809$	12.7129	−	22.0194i	0.446962	−	0.774160i	−0.551225	−	0.834357i	$-0.685839\pi$
$809$	12.7129	−	22.0194i	0.446962	−	0.774160i	0.998187	+	0.0601965i	$0.0191727\pi$
$810$	1.05317	+	2.68132i	0.0370048	+	0.0942121i
$811$			11.6711i			0.409829i	0.978780	+	0.204914i	$0.0656916\pi$
$811$			11.6711i			0.409829i	−0.978780	+	0.204914i	$0.934308\pi$
$812$			2.52136i			0.0884825i
$813$	7.92742	−	4.19045i	0.278027	−	0.146965i
$814$	−11.5161	+	6.64884i	−0.403640	+	0.233042i
$815$	−5.85306	+	10.1378i	−0.205024	+	0.355111i
$816$	0.392982	+	0.743438i	0.0137571	+	0.0260255i
$817$	−12.4447	+	7.18496i	−0.435386	+	0.251370i
$818$	8.67492			0.303311
$819$	5.84820	+	9.09937i	0.204353	+	0.317958i
$820$	−19.1400			−0.668396
$821$	15.1600	−	8.75262i	0.529087	−	0.305468i	−0.211558	−	0.977366i	$-0.567854\pi$
$821$	15.1600	−	8.75262i	0.529087	−	0.305468i	0.740645	+	0.671897i	$0.234520\pi$
$822$	1.71192	+	0.0639403i	0.0597101	+	0.00223017i
$823$	−2.58910	+	4.48445i	−0.0902502	+	0.156318i	−0.907616	−	0.419801i	$-0.862100\pi$
$823$	−2.58910	+	4.48445i	−0.0902502	+	0.156318i	0.817366	+	0.576119i	$0.195433\pi$
$824$	11.0504	−	6.37994i	0.384958	−	0.222256i
$825$	−25.5396	−	16.0452i	−0.889176	−	0.558623i
$826$		−	3.09461i		−	0.107675i
$827$		−	37.9267i		−	1.31884i	−0.751774	−	0.659420i	$-0.770802\pi$
$827$		−	37.9267i		−	1.31884i	0.751774	−	0.659420i	$-0.229198\pi$
$828$	−47.0603	−	3.52032i	−1.63546	−	0.122339i
$829$	25.8844	−	44.8331i	0.899003	−	1.55712i	0.0702324	−	0.997531i	$-0.477626\pi$
$829$	25.8844	−	44.8331i	0.899003	−	1.55712i	0.828771	−	0.559588i	$-0.189041\pi$
$830$	2.81576	−	1.62568i	0.0977364	−	0.0564281i
$831$	22.9260	−	36.4919i	0.795293	−	1.26589i
$832$	−2.77142	−	22.5486i	−0.0960817	−	0.781731i
$833$	−0.0680483	−	0.117863i	−0.00235773	−	0.00408371i
$834$	−4.93333	−	3.09936i	−0.170827	−	0.107322i
$835$	−2.76221	−	4.78429i	−0.0955903	−	0.165567i
$836$	13.1545	+	22.7843i	0.454959	+	0.788013i
$837$	45.3726	−	19.8068i	1.56831	−	0.684622i
$838$	0.0700142	−	0.0404227i	0.00241860	−	0.00139638i
$839$		−	3.93681i		−	0.135914i	−0.997688	−	0.0679569i	$-0.978352\pi$
$839$		−	3.93681i		−	0.135914i	0.997688	−	0.0679569i	$-0.0216480\pi$
$840$	−0.0812590	+	2.17561i	−0.00280370	+	0.0750656i
$841$	13.6440	−	23.6321i	0.470483	−	0.814900i
$842$	−7.18213			−0.247513
$843$	−32.0554	+	16.9445i	−1.10405	+	0.583601i
$844$	−26.7969	+	46.4135i	−0.922386	+	1.59762i
$845$	11.0758	−	10.7011i	0.381020	−	0.368127i
$846$	−2.10187	−	4.36308i	−0.0722639	−	0.150006i
$847$	−10.7763	−	6.22170i	−0.370278	−	0.213780i
$848$	0.0753520	+	0.130514i	0.00258760	+	0.00448185i
$849$	13.8792	−	22.0919i	0.476333	−	0.758192i
$850$	0.114531	−	0.0661243i	0.00392837	−	0.00226804i
$851$	−71.8620	−	41.4896i	−2.46340	−	1.42224i
$852$	−20.9793	−	13.1802i	−0.718738	−	0.451546i
$853$	−0.721139	−	0.416350i	−0.0246913	−	0.0142555i	0.487604	−	0.873065i	$-0.337871\pi$
$853$	−0.721139	−	0.416350i	−0.0246913	−	0.0142555i	−0.512295	+	0.858810i	$0.671205\pi$
$854$	1.31663	+	2.28046i	0.0450540	+	0.0780359i
$855$	9.99366	+	0.747570i	0.341776	+	0.0255664i
$856$	−8.78728	−	5.07334i	−0.300343	−	0.173403i
$857$	−13.5242	+	23.4246i	−0.461978	+	0.800169i	−0.999059	−	0.0433610i	$-0.986193\pi$
$857$	−13.5242	+	23.4246i	−0.461978	+	0.800169i	0.537081	+	0.843530i	$0.319527\pi$
$858$	−6.70295	+	4.67048i	−0.228835	+	0.159448i
$859$	6.42438	+	11.1273i	0.219197	+	0.379660i	0.954563	−	0.298010i	$-0.0963229\pi$
$859$	6.42438	+	11.1273i	0.219197	+	0.379660i	−0.735366	+	0.677670i	$0.762990\pi$
$860$			11.6339i			0.396712i
$861$	7.72519	−	12.2964i	0.263274	−	0.419061i
$862$	9.35963			0.318790
$863$			30.8515i			1.05020i	0.851041	+	0.525099i	$0.175972\pi$
$863$			30.8515i			1.05020i	−0.851041	+	0.525099i	$0.824028\pi$
$864$	12.9033	+	9.51908i	0.438981	+	0.323846i
$865$	19.6357	−	11.3367i	0.667634	−	0.385459i
$866$	−0.0187834	−	0.0108446i	−0.000638286	−	0.000368515i
$867$	13.7454	+	26.0034i	0.466819	+	0.883121i
$868$	18.3599			0.623175
$869$			21.7858i			0.739031i
$870$	−0.385893	+	0.614238i	−0.0130830	+	0.0208246i
$871$	14.6675	−	1.80276i	0.496988	−	0.0610842i
$872$	−8.58256			−0.290642
$873$	−31.3351	+	15.0954i	−1.06053	+	0.510902i
$874$	3.10962	−	5.38601i	0.105184	−	0.182185i
$875$	−10.1842			−0.344287
$876$	−24.4327	+	12.9152i	−0.825505	+	0.436363i
$877$	2.19963	+	1.26996i	0.0742763	+	0.0428835i	0.536678	−	0.843787i	$-0.319679\pi$
$877$	2.19963	+	1.26996i	0.0742763	+	0.0428835i	−0.462402	+	0.886670i	$0.653012\pi$
$878$	−8.87934	−	5.12649i	−0.299663	−	0.173011i
$879$	30.6682	−	16.2112i	1.03441	−	0.546791i
$880$	20.4623			0.689786
$881$	−1.29367	+	2.24070i	−0.0435848	+	0.0754912i	−0.886995	−	0.461779i	$-0.847211\pi$
$881$	−1.29367	+	2.24070i	−0.0435848	+	0.0754912i	0.843410	+	0.537270i	$0.180545\pi$
$882$	−0.669772	−	0.456511i	−0.0225524	−	0.0153715i
$883$	24.5135			0.824946			0.412473	−	0.910970i	$-0.364665\pi$
$883$	24.5135			0.824946			0.412473	+	0.910970i	$0.364665\pi$
$884$	0.115353	+	0.938523i	0.00387973	+	0.0315659i
$885$	−12.5026	+	19.9007i	−0.420269	+	0.668954i
$886$		−	10.0563i		−	0.337849i
$887$	−13.6258			−0.457509			−0.228755	−	0.973484i	$-0.573465\pi$
$887$	−13.6258			−0.457509			−0.228755	+	0.973484i	$0.573465\pi$
$888$	8.72990	+	16.5151i	0.292956	+	0.554210i
$889$	−3.61531	−	2.08730i	−0.121254	−	0.0700058i
$890$	−1.08940	+	0.628963i	−0.0365166	+	0.0210829i
$891$	−6.48316	+	43.0916i	−0.217194	+	1.44362i
$892$			11.0901i			0.371324i
$893$	−16.8478			−0.563791
$894$	−3.33211	+	5.30381i	−0.111442	+	0.177386i
$895$		−	3.54319i		−	0.118436i
$896$	3.93707	+	6.81920i	0.131528	+	0.227814i
$897$	−46.1534	−	21.6512i	−1.54102	−	0.722914i
$898$	−4.07949	+	7.06589i	−0.136134	+	0.235792i
$899$	10.7962	+	6.23321i	0.360075	+	0.207889i
$900$	−11.7100	+	17.1804i	−0.390333	+	0.572678i
$901$	−0.00287474	−	0.00497919i	−9.57715e−5	−	0.000165881i
$902$	9.49858	+	5.48401i	0.316268	+	0.182597i
$903$	−7.47415	−	4.69562i	−0.248724	−	0.156260i
$904$	−13.4589	−	7.77048i	−0.447635	−	0.258442i
$905$	−11.6813	+	6.74421i	−0.388300	+	0.224185i
$906$	1.39940	−	2.22746i	0.0464919	−	0.0740024i
$907$	5.49170	+	9.51190i	0.182349	+	0.315837i	0.942680	−	0.333698i	$-0.108297\pi$
$907$	5.49170	+	9.51190i	0.182349	+	0.315837i	−0.760331	+	0.649536i	$0.774963\pi$
$908$	−1.42211	−	0.821054i	−0.0471943	−	0.0272476i
$909$	−16.7147	+	24.5231i	−0.554392	+	0.813379i
$910$	−0.450803	+	1.06239i	−0.0149440	+	0.0352177i
$911$	−15.9535	+	27.6322i	−0.528562	+	0.915496i	0.470883	+	0.882195i	$0.343935\pi$
$911$	−15.9535	+	27.6322i	−0.528562	+	0.915496i	−0.999445	+	0.0333007i	$0.989398\pi$
$912$	15.4032	−	8.14216i	0.510051	−	0.269614i
$913$	49.1828			1.62771
$914$	0.712419	−	1.23395i	0.0235647	−	0.0408153i
$915$	0.746419	−	19.9844i	0.0246759	−	0.660665i
$916$		−	5.19553i		−	0.171665i
$917$	10.6478	−	6.14748i	0.351620	−	0.203008i
$918$	−0.153756	−	0.113429i	−0.00507471	−	0.00374373i
$919$	−4.74942	−	8.22624i	−0.156669	−	0.271359i	0.776997	−	0.629505i	$-0.216742\pi$
$919$	−4.74942	−	8.22624i	−0.156669	−	0.271359i	−0.933665	+	0.358146i	$0.883409\pi$
$920$	−5.13046	−	8.88621i	−0.169146	−	0.292970i
$921$	6.40525	+	4.02408i	0.211060	+	0.132598i
$922$	−3.01872	−	5.22858i	−0.0994162	−	0.172194i
$923$	−16.1099	−	21.3731i	−0.530264	−	0.703505i
$924$	−8.59694	+	13.6840i	−0.282819	+	0.450171i
$925$	−31.6606	+	18.2793i	−1.04100	+	0.601019i
$926$	1.96831	−	3.40922i	0.0646828	−	0.112034i
$927$	20.3196	−	29.8121i	0.667385	−	0.979156i
$928$			4.03767i			0.132543i
$929$		−	23.4693i		−	0.770002i	−0.922916	−	0.385001i	$-0.874201\pi$
$929$		−	23.4693i		−	0.770002i	0.922916	−	0.385001i	$-0.125799\pi$
$930$	4.47271	+	2.80997i	0.146666	+	0.0921426i
$931$	−2.44199	+	1.40988i	−0.0800330	+	0.0462071i
$932$	−3.78048	+	6.54798i	−0.123834	+	0.214486i
$933$	−46.2506	−	1.72746i	−1.51418	−	0.0565545i
$934$	−2.55240	+	1.47363i	−0.0835172	+	0.0482187i
$935$	−0.780655			−0.0255301
$936$	6.20502	+	9.65456i	0.202817	+	0.315569i
$937$	2.39420			0.0782151			0.0391075	−	0.999235i	$-0.487549\pi$
$937$	2.39420			0.0782151			0.0391075	+	0.999235i	$0.487549\pi$
$938$	−0.959025	+	0.553693i	−0.0313133	+	0.0180787i
$939$	13.6672	+	25.8554i	0.446012	+	0.843759i
$940$	−6.81999	+	11.8126i	−0.222444	+	0.385284i
$941$	−19.5166	+	11.2679i	−0.636224	+	0.367324i	−0.783159	−	0.621822i	$-0.786393\pi$
$941$	−19.5166	+	11.2679i	−0.636224	+	0.367324i	0.146934	+	0.989146i	$0.453059\pi$
$942$	−0.194740	+	0.102940i	−0.00634497	+	0.00335396i
$943$			68.4417i			2.22877i
$944$			40.8591i			1.32985i
$945$	2.46279	+	5.64167i	0.0801145	+	0.183523i
$946$	3.33335	−	5.77354i	0.108377	−	0.187714i
$947$	−1.26690	+	0.731443i	−0.0411686	+	0.0237687i	−0.520443	−	0.853896i	$-0.674233\pi$
$947$	−1.26690	+	0.731443i	−0.0411686	+	0.0237687i	0.479274	+	0.877665i	$0.340900\pi$
$948$	15.0073	+	0.560522i	0.487414	+	0.0182049i
$949$	−29.6314	+	3.64196i	−0.961875	+	0.118223i
$950$	−1.37002	−	2.37295i	−0.0444494	−	0.0769885i
$951$	0.357568	−	0.189011i	0.0115949	−	0.00612910i
$952$	−0.0722002	−	0.125054i	−0.00234002	−	0.00405304i
$953$	6.26954	+	10.8592i	0.203090	+	0.351763i	0.949523	−	0.313699i	$-0.101568\pi$
$953$	6.26954	+	10.8592i	0.203090	+	0.351763i	−0.746432	+	0.665461i	$0.768235\pi$
$954$	−0.0282949	−	0.0192856i	−0.000916081	−	0.000624393i
$955$	14.0456	−	8.10925i	0.454506	−	0.262409i
$956$		−	33.9274i		−	1.09729i
$957$	−9.70103	+	5.12798i	−0.313590	+	0.165764i
$958$	−1.96304	+	3.40008i	−0.0634229	+	0.109852i
$959$	3.66071			0.118211
$960$	0.482563	−	12.9200i	0.0155746	−	0.416992i
$961$	29.8886	−	51.7685i	0.964147	−	1.66995i
$962$	1.20799	+	9.82837i	0.0389473	+	0.316879i
$963$	−28.6096	−	2.14013i	−0.921932	−	0.0689646i
$964$	10.2644	+	5.92614i	0.330593	+	0.190868i
$965$	−15.1218	−	26.1917i	−0.486788	−	0.843141i
$966$	3.81752	+	0.142584i	0.122827	+	0.00458758i
$967$	−15.1894	+	8.76962i	−0.488459	+	0.282012i	−0.723935	−	0.689868i	$-0.757668\pi$
$967$	−15.1894	+	8.76962i	−0.488459	+	0.282012i	0.235476	+	0.971880i	$0.424335\pi$
$968$	−11.4338	−	6.60131i	−0.367497	−	0.212174i
$969$	−0.587645	+	0.310630i	−0.0188779	+	0.00997887i
$970$	−3.21382	−	1.85550i	−0.103189	−	0.0595764i
$971$	9.78566	+	16.9493i	0.314037	+	0.543928i	0.979232	−	0.202742i	$-0.0649851\pi$
$971$	9.78566	+	16.9493i	0.314037	+	0.543928i	−0.665196	+	0.746669i	$0.731652\pi$
$972$	29.5172	+	5.57467i	0.946763	+	0.178808i
$973$	−10.7818	−	6.22485i	−0.345648	−	0.199560i
$974$	3.92152	−	6.79226i	0.125653	−	0.217638i
$975$	−18.4280	+	12.8403i	−0.590170	+	0.411218i
$976$	−17.3839	−	30.1097i	−0.556444	−	0.963788i
$977$		−	59.3669i		−	1.89932i	−0.313289	−	0.949658i	$-0.601431\pi$
$977$		−	59.3669i		−	1.89932i	0.313289	−	0.949658i	$-0.398569\pi$
$978$	−2.16099	−	4.08814i	−0.0691010	−	0.130724i
$979$	−19.0284			−0.608152
$980$			2.28288i			0.0729240i
$981$	−21.8624	+	10.5320i	−0.698014	+	0.336261i
$982$	4.04159	−	2.33341i	0.128972	−	0.0744622i
$983$	39.2250	+	22.6466i	1.25108	+	0.722313i	0.971325	−	0.237757i	$-0.0764123\pi$
$983$	39.2250	+	22.6466i	1.25108	+	0.722313i	0.279758	+	0.960070i	$0.409746\pi$
$984$	8.19654	−	13.0467i	0.261296	−	0.415913i
$985$	−5.37118			−0.171140
$986$		−	0.0481128i		−	0.00153222i
$987$	−4.83630	−	9.14923i	−0.153941	−	0.291223i
$988$	19.4451	−	2.38998i	0.618632	−	0.0760354i
$989$	41.6010			1.32284
$990$	−4.18866	+	2.01785i	−0.133124	+	0.0641314i
$991$	25.4426	−	44.0679i	0.808210	−	1.39986i	−0.105892	−	0.994378i	$-0.533770\pi$
$991$	25.4426	−	44.0679i	0.808210	−	1.39986i	0.914102	−	0.405484i	$-0.132897\pi$
$992$	29.4012			0.933489
$993$	31.7882	+	19.9708i	1.00877	+	0.633756i
$994$	1.73692	+	1.00281i	0.0550916	+	0.0318072i
$995$	8.99312	+	5.19218i	0.285101	+	0.164603i
$996$	1.26542	−	33.8799i	0.0400962	−	1.07353i
$997$	−61.7211			−1.95473			−0.977363	−	0.211568i	$-0.932143\pi$
$997$	−61.7211			−1.95473			−0.977363	+	0.211568i	$0.932143\pi$
$998$	2.12832	−	3.68636i	0.0673709	−	0.116690i
$999$	42.5041	+	31.3562i	1.34477	+	0.992067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dk.a.43.38	yes	168
9.4	even	3		819.2.bh.a.589.38	✓	168
13.10	even	6		819.2.bh.a.673.47	yes	168
117.49	even	6	inner	819.2.dk.a.400.38	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.38	✓	168	9.4	even	3
819.2.bh.a.673.47	yes	168	13.10	even	6
819.2.dk.a.43.38	yes	168	1.1	even	1	trivial
819.2.dk.a.400.38	yes	168	117.49	even	6	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.233987 + 0.135092i) q^{2} +(-0.921408 + 1.46663i) q^{3} +(-0.963500 + 1.66883i) q^{4} +(-1.02596 + 0.592341i) q^{5} +(0.0174666 - 0.467647i) q^{6} -1.00000i q^{7} -1.06101i q^{8} +(-1.30201 - 2.70273i) q^{9} +O(q^{10})\)	\(q+(-0.233987 + 0.135092i) q^{2} +(-0.921408 + 1.46663i) q^{3} +(-0.963500 + 1.66883i) q^{4} +(-1.02596 + 0.592341i) q^{5} +(0.0174666 - 0.467647i) q^{6} -1.00000i q^{7} -1.06101i q^{8} +(-1.30201 - 2.70273i) q^{9} +(0.160041 - 0.277200i) q^{10} +(4.19316 - 2.42092i) q^{11} +(-1.55978 - 2.95077i) q^{12} +(-0.439844 - 3.57862i) q^{13} +(0.135092 + 0.233987i) q^{14} +(0.0765862 - 2.05050i) q^{15} +(-1.78367 - 3.08940i) q^{16} +(0.0680483 + 0.117863i) q^{17} +(0.669772 + 0.456511i) q^{18} +(2.44199 - 1.40988i) q^{19} -2.28288i q^{20} +(1.46663 + 0.921408i) q^{21} +(-0.654095 + 1.13293i) q^{22} -8.16325 q^{23} +(1.55612 + 0.977627i) q^{24} +(-1.79826 + 3.11469i) q^{25} +(0.586361 + 0.777930i) q^{26} +(5.16360 + 0.580743i) q^{27} +(1.66883 + 0.963500i) q^{28} +(0.654220 + 1.13314i) q^{29} +(0.259086 + 0.490135i) q^{30} +(8.25123 - 4.76385i) q^{31} +(2.67244 + 1.54293i) q^{32} +(-0.313011 + 8.38047i) q^{33} +(-0.0318448 - 0.0183856i) q^{34} +(0.592341 + 1.02596i) q^{35} +(5.76489 + 0.431239i) q^{36} +(8.80311 + 5.08248i) q^{37} +(-0.380929 + 0.659788i) q^{38} +(5.65380 + 2.65228i) q^{39} +(0.628482 + 1.08856i) q^{40} -8.38412i q^{41} +(-0.467647 - 0.0174666i) q^{42} -5.09614 q^{43} +9.33023i q^{44} +(2.93676 + 2.00167i) q^{45} +(1.91009 - 1.10279i) q^{46} +(-5.17441 - 2.98745i) q^{47} +(6.17449 + 0.230617i) q^{48} -1.00000 q^{49} -0.971726i q^{50} +(-0.235562 - 0.00879824i) q^{51} +(6.39591 + 2.71398i) q^{52} -0.0422456 q^{53} +(-1.28667 + 0.561676i) q^{54} +(-2.86802 + 4.96755i) q^{55} -1.06101 q^{56} +(-0.182290 + 4.88058i) q^{57} +(-0.306157 - 0.176760i) q^{58} +(-9.91918 - 5.72684i) q^{59} +(3.34815 + 2.10347i) q^{60} +9.74614 q^{61} +(-1.28712 + 2.22935i) q^{62} +(-2.70273 + 1.30201i) q^{63} +6.30091 q^{64} +(2.57103 + 3.41100i) q^{65} +(-1.05890 - 2.00320i) q^{66} +4.09863i q^{67} -0.262258 q^{68} +(7.52169 - 11.9725i) q^{69} +(-0.277200 - 0.160041i) q^{70} +(6.42863 - 3.71157i) q^{71} +(-2.86764 + 1.38146i) q^{72} -8.28011i q^{73} -2.74641 q^{74} +(-2.91116 - 5.50729i) q^{75} +5.43370i q^{76} +(-2.42092 - 4.19316i) q^{77} +(-1.68121 + 0.143185i) q^{78} +(-2.24974 + 3.89666i) q^{79} +(3.65996 + 2.11308i) q^{80} +(-5.60952 + 7.03799i) q^{81} +(1.13263 + 1.96177i) q^{82} +(8.79698 + 5.07894i) q^{83} +(-2.95077 + 1.55978i) q^{84} +(-0.139630 - 0.0806155i) q^{85} +(1.19243 - 0.688448i) q^{86} +(-2.26470 - 0.0845867i) q^{87} +(-2.56863 - 4.44900i) q^{88} +(-3.40348 - 1.96500i) q^{89} +(-0.957572 - 0.0716306i) q^{90} +(-3.57862 + 0.439844i) q^{91} +(7.86530 - 13.6231i) q^{92} +(-0.615938 + 16.4910i) q^{93} +1.61432 q^{94} +(-1.67026 + 2.89298i) q^{95} +(-4.72532 + 2.49781i) q^{96} -11.5939i q^{97} +(0.233987 - 0.135092i) q^{98} +(-12.0026 - 8.18090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 2 * q^9	\( 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) \) 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Introduction

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