LMFDB - Embedded newform 483.2.q.f.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	483.85
Dual form			483.2.q.f.358.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0321112 - 0.0370583i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.284287 + 1.97726i) q^{4} +(1.63623 + 3.58284i) q^{5} +(0.00697843 - 0.0485360i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.164905 + 0.105978i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.0321112 - 0.0370583i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.284287 + 1.97726i) q^{4} +(1.63623 + 3.58284i) q^{5} +(0.00697843 - 0.0485360i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.164905 + 0.105978i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.185315 + 0.0544134i) q^{10} +(-0.874709 - 1.00947i) q^{11} +(1.30815 + 1.50968i) q^{12} +(-1.75596 - 0.515597i) q^{13} +(0.0203699 - 0.0446039i) q^{14} +(3.31351 + 2.12946i) q^{15} +(-3.82414 + 1.12287i) q^{16} +(-0.359295 + 2.49895i) q^{17} +(-0.0203699 - 0.0446039i) q^{18} +(-0.518322 - 3.60501i) q^{19} +(-6.61906 + 4.25381i) q^{20} +(0.654861 - 0.755750i) q^{21} -0.0654971 q^{22} +(4.22309 - 2.27278i) q^{23} +0.196023 q^{24} +(-6.88519 + 7.94594i) q^{25} +(-0.0754932 + 0.0485166i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.829831 + 1.81708i) q^{28} +(0.0321640 - 0.223705i) q^{29} +(0.185315 - 0.0544134i) q^{30} +(-2.14464 - 1.37828i) q^{31} +(-0.244048 + 0.534390i) q^{32} +(-1.28161 - 0.376315i) q^{33} +(0.0810694 + 0.0935591i) q^{34} +(2.57935 + 2.97673i) q^{35} +(1.91668 + 0.562788i) q^{36} +(1.53409 - 3.35919i) q^{37} +(-0.150239 - 0.0965530i) q^{38} +(-1.75596 + 0.515597i) q^{39} +(-0.109880 + 0.764231i) q^{40} +(0.330944 + 0.724667i) q^{41} +(-0.00697843 - 0.0485360i) q^{42} +(5.06906 - 3.25769i) q^{43} +(1.74731 - 2.01651i) q^{44} +3.93878 q^{45} +(0.0513830 - 0.229482i) q^{46} +7.23733 q^{47} +(-2.61000 + 3.01210i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.0733711 + 0.510307i) q^{50} +(1.04878 + 2.29650i) q^{51} +(0.520273 - 3.61858i) q^{52} +(6.61732 - 1.94302i) q^{53} +(-0.0412510 - 0.0265104i) q^{54} +(2.18554 - 4.78566i) q^{55} +(0.188082 + 0.0552260i) q^{56} +(-2.38505 - 2.75250i) q^{57} +(-0.00725731 - 0.00837538i) q^{58} +(13.7957 + 4.05079i) q^{59} +(-3.26852 + 7.15706i) q^{60} +(-0.665804 - 0.427886i) q^{61} +(-0.119944 + 0.0352187i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-3.29937 - 7.22462i) q^{64} +(-1.02585 - 7.13497i) q^{65} +(-0.0550997 + 0.0354104i) q^{66} +(-7.78104 + 8.97980i) q^{67} -5.04322 q^{68} +(2.32393 - 4.19516i) q^{69} +0.193139 q^{70} +(0.598824 - 0.691079i) q^{71} +(0.164905 - 0.105978i) q^{72} +(-0.454168 - 3.15881i) q^{73} +(-0.0752244 - 0.164719i) q^{74} +(-1.49630 + 10.4070i) q^{75} +(6.98070 - 2.04972i) q^{76} +(-1.12368 - 0.722143i) q^{77} +(-0.0372789 + 0.0816295i) q^{78} +(-12.0627 - 3.54193i) q^{79} +(-10.2802 - 11.8640i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(0.0374819 + 0.0110057i) q^{82} +(0.946462 - 2.07246i) q^{83} +(1.68048 + 1.07998i) q^{84} +(-9.54122 + 2.80156i) q^{85} +(0.0420493 - 0.292459i) q^{86} +(-0.0938861 - 0.205582i) q^{87} +(-0.0372624 - 0.259166i) q^{88} +(-2.14901 + 1.38108i) q^{89} +(0.126479 - 0.145964i) q^{90} -1.83009 q^{91} +(5.69446 + 7.70403i) q^{92} -2.54934 q^{93} +(0.232399 - 0.268203i) q^{94} +(12.0681 - 7.75568i) q^{95} +(0.0836070 + 0.581499i) q^{96} +(-2.38519 - 5.22284i) q^{97} +(0.00697843 - 0.0485360i) q^{98} +(-1.28161 + 0.376315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	0.0321112	−	0.0370583i	0.0227060	−	0.0262042i	−0.744283	−	0.667864i	$-0.767209\pi$
$2$	0.0321112	−	0.0370583i	0.0227060	−	0.0262042i	0.766989	+	0.641660i	$0.221754\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	0.284287	+	1.97726i	0.142144	+	0.988631i
$5$	1.63623	+	3.58284i	0.731743	+	1.60229i	0.796677	+	0.604405i	$0.206589\pi$
$5$	1.63623	+	3.58284i	0.731743	+	1.60229i	−0.0649339	+	0.997890i	$0.520684\pi$
$6$	0.00697843	−	0.0485360i	0.00284893	−	0.0198148i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.164905	+	0.105978i	0.0583027	+	0.0374688i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	0.185315	+	0.0544134i	0.0586018	+	0.0172070i
$11$	−0.874709	−	1.00947i	−0.263735	−	0.304366i	0.608401	−	0.793629i	$-0.291811\pi$
$11$	−0.874709	−	1.00947i	−0.263735	−	0.304366i	−0.872136	+	0.489264i	$0.837266\pi$
$12$	1.30815	+	1.50968i	0.377629	+	0.435808i
$13$	−1.75596	−	0.515597i	−0.487017	−	0.143001i	0.0290003	−	0.999579i	$-0.490768\pi$
$13$	−1.75596	−	0.515597i	−0.487017	−	0.143001i	−0.516017	+	0.856578i	$0.672586\pi$
$14$	0.0203699	−	0.0446039i	0.00544410	−	0.0119209i
$15$	3.31351	+	2.12946i	0.855545	+	0.549825i
$16$	−3.82414	+	1.12287i	−0.956034	+	0.280717i
$17$	−0.359295	+	2.49895i	−0.0871418	+	0.606084i	0.898720	+	0.438523i	$0.144498\pi$
$17$	−0.359295	+	2.49895i	−0.0871418	+	0.606084i	−0.985862	+	0.167561i	$0.946411\pi$
$18$	−0.0203699	−	0.0446039i	−0.00480124	−	0.0105133i
$19$	−0.518322	−	3.60501i	−0.118911	−	0.827046i	−0.958758	−	0.284223i	$-0.908265\pi$
$19$	−0.518322	−	3.60501i	−0.118911	−	0.827046i	0.839847	−	0.542823i	$-0.182645\pi$
$20$	−6.61906	+	4.25381i	−1.48007	+	0.951181i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	−0.0654971			−0.0139640
$23$	4.22309	−	2.27278i	0.880575	−	0.473907i
$23$	4.22309	−	2.27278i	0.880575	−	0.473907i
$24$	0.196023			0.0400130
$25$	−6.88519	+	7.94594i	−1.37704	+	1.58919i
$26$	−0.0754932	+	0.0485166i	−0.0148054	+	0.00951488i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	0.829831	+	1.81708i	0.156823	+	0.343395i
$29$	0.0321640	−	0.223705i	0.00597270	−	0.0415410i	−0.986617	−	0.163054i	$-0.947866\pi$
$29$	0.0321640	−	0.223705i	0.00597270	−	0.0415410i	0.992590	+	0.121513i	$0.0387746\pi$
$30$	0.185315	−	0.0544134i	0.0338338	−	0.00993449i
$31$	−2.14464	−	1.37828i	−0.385189	−	0.247546i	0.333687	−	0.942684i	$-0.391707\pi$
$31$	−2.14464	−	1.37828i	−0.385189	−	0.247546i	−0.718877	+	0.695138i	$0.755343\pi$
$32$	−0.244048	+	0.534390i	−0.0431419	+	0.0944676i
$33$	−1.28161	−	0.376315i	−0.223100	−	0.0655080i
$34$	0.0810694	+	0.0935591i	0.0139033	+	0.0160453i
$35$	2.57935	+	2.97673i	0.435990	+	0.503159i
$36$	1.91668	+	0.562788i	0.319446	+	0.0937980i
$37$	1.53409	−	3.35919i	0.252203	−	0.552248i	−0.740608	−	0.671937i	$-0.765463\pi$
$37$	1.53409	−	3.35919i	0.252203	−	0.552248i	0.992811	+	0.119689i	$0.0381898\pi$
$38$	−0.150239	−	0.0965530i	−0.0243720	−	0.0156630i
$39$	−1.75596	+	0.515597i	−0.281179	+	0.0825616i
$40$	−0.109880	+	0.764231i	−0.0173735	+	0.120836i
$41$	0.330944	+	0.724667i	0.0516848	+	0.113174i	0.933713	−	0.358023i	$-0.116549\pi$
$41$	0.330944	+	0.724667i	0.0516848	+	0.113174i	−0.882028	+	0.471197i	$0.843822\pi$
$42$	−0.00697843	−	0.0485360i	−0.00107680	−	0.00748927i
$43$	5.06906	−	3.25769i	0.773025	−	0.496793i	−0.0936871	−	0.995602i	$-0.529865\pi$
$43$	5.06906	−	3.25769i	0.773025	−	0.496793i	0.866712	+	0.498809i	$0.166229\pi$
$44$	1.74731	−	2.01651i	0.263418	−	0.304000i
$45$	3.93878			0.587159
$46$	0.0513830	−	0.229482i	0.00757602	−	0.0338353i
$47$	7.23733			1.05567			0.527836	−	0.849346i	$-0.323003\pi$
$47$	7.23733			1.05567			0.527836	+	0.849346i	$0.323003\pi$
$48$	−2.61000	+	3.01210i	−0.376721	+	0.434759i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.0733711	+	0.510307i	0.0103762	+	0.0721683i
$51$	1.04878	+	2.29650i	0.146858	+	0.321574i
$52$	0.520273	−	3.61858i	0.0721489	−	0.501807i
$53$	6.61732	−	1.94302i	0.908959	−	0.266894i	0.206356	−	0.978477i	$-0.433839\pi$
$53$	6.61732	−	1.94302i	0.908959	−	0.266894i	0.702603	+	0.711583i	$0.252021\pi$
$54$	−0.0412510	−	0.0265104i	−0.00561355	−	0.00360761i
$55$	2.18554	−	4.78566i	0.294698	−	0.645298i
$56$	0.188082	+	0.0552260i	0.0251336	+	0.00737988i
$57$	−2.38505	−	2.75250i	−0.315908	−	0.364577i
$58$	−0.00725731	−	0.00837538i	−0.000952932	−	0.00109974i
$59$	13.7957	+	4.05079i	1.79605	+	0.527368i	0.997242	−	0.0742166i	$-0.0236456\pi$
$59$	13.7957	+	4.05079i	1.79605	+	0.527368i	0.798809	+	0.601585i	$0.205464\pi$
$60$	−3.26852	+	7.15706i	−0.421964	+	0.923973i
$61$	−0.665804	−	0.427886i	−0.0852475	−	0.0547852i	0.497323	−	0.867566i	$-0.334317\pi$
$61$	−0.665804	−	0.427886i	−0.0852475	−	0.0547852i	−0.582570	+	0.812780i	$0.697953\pi$
$62$	−0.119944	+	0.0352187i	−0.0152329	+	0.00447277i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	−3.29937	−	7.22462i	−0.412421	−	0.903077i
$65$	−1.02585	−	7.13497i	−0.127241	−	0.884984i
$66$	−0.0550997	+	0.0354104i	−0.00678230	+	0.00435872i
$67$	−7.78104	+	8.97980i	−0.950605	+	1.09706i	0.0445764	+	0.999006i	$0.485806\pi$
$67$	−7.78104	+	8.97980i	−0.950605	+	1.09706i	−0.995181	+	0.0980507i	$0.968739\pi$
$68$	−5.04322			−0.611581
$69$	2.32393	−	4.19516i	0.279768	−	0.505038i
$70$	0.193139			0.0230845
$71$	0.598824	−	0.691079i	0.0710673	−	0.0820160i	−0.719103	−	0.694904i	$-0.755447\pi$
$71$	0.598824	−	0.691079i	0.0710673	−	0.0820160i	0.790170	+	0.612888i	$0.209992\pi$
$72$	0.164905	−	0.105978i	0.0194342	−	0.0124896i
$73$	−0.454168	−	3.15881i	−0.0531563	−	0.369710i	−0.998985	−	0.0450442i	$-0.985657\pi$
$73$	−0.454168	−	3.15881i	−0.0531563	−	0.369710i	0.945829	−	0.324666i	$-0.105252\pi$
$74$	−0.0752244	−	0.164719i	−0.00874466	−	0.0191481i
$75$	−1.49630	+	10.4070i	−0.172777	+	1.20169i
$76$	6.98070	−	2.04972i	0.800741	−	0.235119i
$77$	−1.12368	−	0.722143i	−0.128055	−	0.0822958i
$78$	−0.0372789	+	0.0816295i	−0.00422101	+	0.00924272i
$79$	−12.0627	−	3.54193i	−1.35716	−	0.398499i	−0.479400	−	0.877596i	$-0.659146\pi$
$79$	−12.0627	−	3.54193i	−1.35716	−	0.398499i	−0.877762	+	0.479098i	$0.840964\pi$
$80$	−10.2802	−	11.8640i	−1.14936	−	1.32643i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	0.0374819	+	0.0110057i	0.00413919	+	0.00121538i
$83$	0.946462	−	2.07246i	0.103888	−	0.227482i	−0.850549	−	0.525896i	$-0.823730\pi$
$83$	0.946462	−	2.07246i	0.103888	−	0.227482i	0.954437	+	0.298413i	$0.0964574\pi$
$84$	1.68048	+	1.07998i	0.183356	+	0.117836i
$85$	−9.54122	+	2.80156i	−1.03489	+	0.303871i
$86$	0.0420493	−	0.292459i	0.00453429	−	0.0315367i
$87$	−0.0938861	−	0.205582i	−0.0100657	−	0.0220407i
$88$	−0.0372624	−	0.259166i	−0.00397219	−	0.0276272i
$89$	−2.14901	+	1.38108i	−0.227794	+	0.146394i	−0.649560	−	0.760310i	$-0.725047\pi$
$89$	−2.14901	+	1.38108i	−0.227794	+	0.146394i	0.421766	+	0.906705i	$0.361410\pi$
$90$	0.126479	−	0.145964i	0.0133320	−	0.0153860i
$91$	−1.83009			−0.191846
$92$	5.69446	+	7.70403i	0.593688	+	0.803201i
$93$	−2.54934			−0.264355
$94$	0.232399	−	0.268203i	0.0239702	−	0.0276630i
$95$	12.0681	−	7.75568i	1.23816	−	0.795716i
$96$	0.0836070	+	0.581499i	0.00853310	+	0.0593490i
$97$	−2.38519	−	5.22284i	−0.242180	−	0.530299i	0.749040	−	0.662525i	$-0.230515\pi$
$97$	−2.38519	−	5.22284i	−0.242180	−	0.530299i	−0.991220	+	0.132225i	$0.957788\pi$
$98$	0.00697843	−	0.0485360i	0.000704928	−	0.00490288i
$99$	−1.28161	+	0.376315i	−0.128807	+	0.0378211i
$100$	−17.6686	−	11.3549i	−1.76686	−	1.13549i
$101$	−7.76665	+	17.0066i	−0.772810	+	1.69222i	−0.0524446	+	0.998624i	$0.516701\pi$
$101$	−7.76665	+	17.0066i	−0.772810	+	1.69222i	−0.720366	+	0.693595i	$0.756026\pi$
$102$	0.118782	+	0.0348775i	0.0117612	+	0.00345339i
$103$	1.42655	+	1.64633i	0.140562	+	0.162218i	0.821666	−	0.569970i	$-0.193045\pi$
$103$	1.42655	+	1.64633i	0.140562	+	0.162218i	−0.681103	+	0.732187i	$0.738500\pi$
$104$	−0.234925	−	0.271118i	−0.0230363	−	0.0265853i
$105$	3.77923	+	1.10968i	0.368815	+	0.108294i
$106$	0.140485	−	0.307619i	0.0136451	−	0.0298786i
$107$	−10.5958	−	6.80951i	−1.02433	−	0.658300i	−0.0832703	−	0.996527i	$-0.526536\pi$
$107$	−10.5958	−	6.80951i	−1.02433	−	0.658300i	−0.941065	+	0.338227i	$0.890173\pi$
$108$	1.91668	−	0.562788i	0.184433	−	0.0541543i
$109$	2.36372	−	16.4401i	0.226404	−	1.57467i	−0.486672	−	0.873585i	$-0.661789\pi$
$109$	2.36372	−	16.4401i	0.226404	−	1.57467i	0.713076	−	0.701087i	$-0.247302\pi$
$110$	−0.107168	−	0.234666i	−0.0102181	−	0.0223745i
$111$	−0.525557	−	3.65533i	−0.0498836	−	0.346948i
$112$	−3.35288	+	2.15477i	−0.316818	+	0.203606i
$113$	−12.3413	+	14.2426i	−1.16097	+	1.33983i	−0.230669	+	0.973032i	$0.574091\pi$
$113$	−12.3413	+	14.2426i	−1.16097	+	1.33983i	−0.930301	+	0.366798i	$0.880454\pi$
$114$	−0.178590			−0.0167265
$115$	15.0529	+	11.4119i	1.40369	+	1.06416i
$116$	0.451468			0.0419177
$117$	−1.19846	+	1.38309i	−0.110797	+	0.127867i
$118$	0.593113	−	0.381171i	0.0546005	−	0.0350896i
$119$	0.359295	+	2.49895i	0.0329365	+	0.229078i
$120$	0.320738	+	0.702318i	0.0292792	+	0.0641126i
$121$	1.31155	−	9.12206i	0.119232	−	0.829278i
$122$	−0.0372365	+	0.0109336i	−0.00337124	+	0.000989884i
$123$	0.670192	+	0.430707i	0.0604292	+	0.0388355i
$124$	2.11552	−	4.63235i	0.189980	−	0.415997i
$125$	−20.8386	−	6.11877i	−1.86386	−	0.547279i
$126$	−0.0321112	−	0.0370583i	−0.00286069	−	0.00330142i
$127$	−13.7000	−	15.8107i	−1.21568	−	1.40297i	−0.889046	−	0.457817i	$-0.848631\pi$
$127$	−13.7000	−	15.8107i	−1.21568	−	1.40297i	−0.326633	−	0.945151i	$-0.605914\pi$
$128$	−1.50104	−	0.440746i	−0.132675	−	0.0389568i
$129$	2.50313	−	5.48109i	0.220388	−	0.482583i
$130$	−0.297351	−	0.191096i	−0.0260794	−	0.0167602i
$131$	11.1566	−	3.27588i	0.974760	−	0.286215i	0.244700	−	0.969599i	$-0.421310\pi$
$131$	11.1566	−	3.27588i	0.974760	−	0.286215i	0.730060	+	0.683383i	$0.239492\pi$
$132$	0.379728	−	2.64106i	0.0330510	−	0.229875i
$133$	−1.51297	−	3.31295i	−0.131192	−	0.287269i
$134$	0.0829175	+	0.576704i	0.00716298	+	0.0498196i
$135$	3.31351	−	2.12946i	0.285182	−	0.183275i
$136$	−0.324083	+	0.374011i	−0.0277899	+	0.0320712i
$137$	16.3830			1.39970			0.699848	−	0.714292i	$-0.253251\pi$
$137$	16.3830			1.39970			0.699848	+	0.714292i	$0.253251\pi$
$138$	−0.0808412	−	0.220832i	−0.00688166	−	0.0187985i
$139$	16.8325			1.42771			0.713857	−	0.700291i	$-0.246947\pi$
$139$	16.8325			1.42771			0.713857	+	0.700291i	$0.246947\pi$
$140$	−5.15250	+	5.94630i	−0.435466	+	0.502554i
$141$	6.08843	−	3.91279i	0.512738	−	0.329517i
$142$	−0.00638128	−	0.0443828i	−0.000535505	−	0.00372452i
$143$	1.01548	+	2.22359i	0.0849185	+	0.185946i
$144$	−0.567207	+	3.94501i	−0.0472673	+	0.328751i
$145$	0.854128	−	0.250794i	0.0709314	−	0.0208273i
$146$	−0.131644	−	0.0846024i	−0.0108949	−	0.00700174i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	7.07813	+	2.07833i	0.581819	+	0.170837i
$149$	−7.60013	−	8.77102i	−0.622627	−	0.718550i	0.353577	−	0.935405i	$-0.384965\pi$
$149$	−7.60013	−	8.77102i	−0.622627	−	0.718550i	−0.976204	+	0.216856i	$0.930420\pi$
$150$	0.337617	+	0.389630i	0.0275663	+	0.0318132i
$151$	19.3167	+	5.67189i	1.57197	+	0.461572i	0.947574	−	0.319537i	$-0.103527\pi$
$151$	19.3167	+	5.67189i	1.57197	+	0.461572i	0.624395	+	0.781109i	$0.285345\pi$
$152$	0.296577	−	0.649414i	0.0240556	−	0.0526744i
$153$	2.12387	+	1.36493i	0.171705	+	0.110348i
$154$	−0.0628440	+	0.0184527i	−0.00506411	+	0.00148696i
$155$	1.42903	−	9.93909i	0.114782	−	0.798327i
$156$	−1.51867	−	3.32542i	−0.121591	−	0.266247i
$157$	2.44101	+	16.9776i	0.194814	+	1.35496i	0.819049	+	0.573723i	$0.194501\pi$
$157$	2.44101	+	16.9776i	0.194814	+	1.35496i	−0.624235	+	0.781236i	$0.714589\pi$
$158$	−0.518606	+	0.333288i	−0.0412581	+	0.0265150i
$159$	4.51637	−	5.21217i	0.358171	−	0.413352i
$160$	−2.31395			−0.182934
$161$	3.41171	−	3.37050i	0.268880	−	0.265632i
$162$	−0.0490352			−0.00385257
$163$	−11.8412	+	13.6654i	−0.927471	+	1.07036i	0.0698758	+	0.997556i	$0.477740\pi$
$163$	−11.8412	+	13.6654i	−0.927471	+	1.07036i	−0.997346	+	0.0728024i	$0.976806\pi$
$164$	−1.33877	+	0.860378i	−0.104541	+	0.0671842i
$165$	−0.748732	−	5.20754i	−0.0582887	−	0.405407i
$166$	−0.0464099	−	0.101624i	−0.00360211	−	0.00788752i
$167$	1.20372	−	8.37206i	0.0931467	−	0.647849i	−0.888744	−	0.458403i	$-0.848422\pi$
$167$	1.20372	−	8.37206i	0.0931467	−	0.647849i	0.981891	−	0.189446i	$-0.0606693\pi$
$168$	0.188082	−	0.0552260i	0.0145109	−	0.00426078i
$169$	−8.11873	−	5.21759i	−0.624518	−	0.401353i
$170$	−0.202559	+	0.443543i	−0.0155356	+	0.0340182i
$171$	−3.49455	−	1.02609i	−0.267235	−	0.0784672i
$172$	7.88238	+	9.09675i	0.601026	+	0.693621i
$173$	−1.62961	−	1.88067i	−0.123897	−	0.142984i	0.690412	−	0.723416i	$-0.257429\pi$
$173$	−1.62961	−	1.88067i	−0.123897	−	0.142984i	−0.814309	+	0.580432i	$0.802884\pi$
$174$	−0.0106333	−	0.00312222i	−0.000806110	−	0.000236695i
$175$	−4.36767	+	9.56385i	−0.330164	+	0.722959i
$176$	4.47850	+	2.87816i	0.337580	+	0.216949i
$177$	13.7957	−	4.05079i	1.03695	−	0.304476i
$178$	−0.0178266	+	0.123987i	−0.00133616	+	0.00929320i
$179$	−4.52855	−	9.91613i	−0.338479	−	0.741166i	0.661482	−	0.749961i	$-0.269928\pi$
$179$	−4.52855	−	9.91613i	−0.338479	−	0.741166i	−0.999961	+	0.00879466i	$0.997201\pi$
$180$	1.11975	+	7.78800i	0.0834609	+	0.580483i
$181$	6.85863	−	4.40777i	0.509798	−	0.327627i	−0.260327	−	0.965521i	$-0.583830\pi$
$181$	6.85863	−	4.40777i	0.509798	−	0.327627i	0.770125	+	0.637893i	$0.220194\pi$
$182$	−0.0587665	+	0.0678202i	−0.00435607	+	0.00502717i
$183$	−0.791443			−0.0585051
$184$	0.937272	+	0.0727615i	0.0690966	+	0.00536405i
$185$	14.5456			1.06941
$186$	−0.0818625	+	0.0944743i	−0.00600245	+	0.00692719i
$187$	2.83689	−	1.82316i	0.207454	−	0.133322i
$188$	2.05748	+	14.3101i	0.150057	+	1.04367i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	0.100108	−	0.696266i	0.00726260	−	0.0505125i
$191$	−0.779692	+	0.228938i	−0.0564165	+	0.0165654i	−0.309819	−	0.950796i	$-0.600268\pi$
$191$	−0.779692	+	0.228938i	−0.0564165	+	0.0165654i	0.253403	+	0.967361i	$0.418450\pi$
$192$	−6.68153	−	4.29396i	−0.482198	−	0.309890i
$193$	−3.30067	+	7.22747i	−0.237588	+	0.520244i	−0.990440	−	0.137945i	$-0.955950\pi$
$193$	−3.30067	+	7.22747i	−0.237588	+	0.520244i	0.752852	+	0.658190i	$0.228677\pi$
$194$	−0.270141	−	0.0793206i	−0.0193950	−	0.00569488i
$195$	−4.72046	−	5.44770i	−0.338039	−	0.390118i
$196$	1.30815	+	1.50968i	0.0934391	+	0.107834i
$197$	−22.8263	−	6.70242i	−1.62631	−	0.477527i	−0.663605	−	0.748083i	$-0.730974\pi$
$197$	−22.8263	−	6.70242i	−1.62631	−	0.477527i	−0.962704	+	0.270556i	$0.912792\pi$
$198$	−0.0272085	+	0.0595783i	−0.00193362	+	0.00423404i
$199$	−5.60377	−	3.60133i	−0.397241	−	0.255291i	0.326736	−	0.945116i	$-0.394051\pi$
$199$	−5.60377	−	3.60133i	−0.397241	−	0.255291i	−0.723977	+	0.689824i	$0.757688\pi$
$200$	−1.97749	+	0.580645i	−0.139830	+	0.0410578i
$201$	−1.69098	+	11.7610i	−0.119273	+	0.829559i
$202$	0.380839	+	0.833920i	0.0267957	+	0.0586744i
$203$	−0.0321640	−	0.223705i	−0.00225747	−	0.0157010i
$204$	−4.24263	+	2.72657i	−0.297043	+	0.190898i
$205$	−2.05486	+	2.37144i	−0.143518	+	0.165629i
$206$	0.106819			0.00744240
$207$	−0.313060	−	4.78560i	−0.0217591	−	0.332622i
$208$	7.29399			0.505747
$209$	−3.18576	+	3.67656i	−0.220363	+	0.254313i
$210$	0.162479	−	0.104419i	0.0112121	−	0.00720557i
$211$	−0.331889	−	2.30834i	−0.0228482	−	0.158913i	0.975203	−	0.221312i	$-0.0710339\pi$
$211$	−0.331889	−	2.30834i	−0.0228482	−	0.158913i	−0.998051	+	0.0623992i	$0.980125\pi$
$212$	5.72308	+	12.5318i	0.393063	+	0.860688i
$213$	0.130137	−	0.905121i	0.00891683	−	0.0620179i
$214$	−0.592593	+	0.174001i	−0.0405088	+	0.0118945i
$215$	19.9659	+	12.8313i	1.36166	+	0.875089i
$216$	0.0814308	−	0.178309i	0.00554066	−	0.0121324i
$217$	−2.44608	−	0.718233i	−0.166050	−	0.0487568i
$218$	−0.533339	−	0.615505i	−0.0361222	−	0.0416873i
$219$	−2.08985	−	2.41182i	−0.141219	−	0.162975i
$220$	10.0838	+	2.96088i	0.679852	+	0.199622i
$221$	1.91936	−	4.20281i	0.129110	−	0.282712i
$222$	−0.152336	−	0.0979007i	−0.0102241	−	0.00657066i
$223$	−9.36777	+	2.75063i	−0.627312	+	0.184196i	−0.579910	−	0.814680i	$-0.696912\pi$
$223$	−9.36777	+	2.75063i	−0.627312	+	0.184196i	−0.0474021	+	0.998876i	$0.515094\pi$
$224$	−0.0836070	+	0.581499i	−0.00558623	+	0.0388531i
$225$	4.36767	+	9.56385i	0.291178	+	0.637590i
$226$	0.131513	+	0.914693i	0.00874812	+	0.0608445i
$227$	−17.5802	+	11.2981i	−1.16684	+	0.749881i	−0.972921	−	0.231137i	$-0.925755\pi$
$227$	−17.5802	+	11.2981i	−1.16684	+	0.749881i	−0.193916	+	0.981018i	$0.562119\pi$
$228$	4.76437	−	5.49838i	0.315528	−	0.364139i
$229$	−28.9896			−1.91568			−0.957842	−	0.287296i	$-0.907244\pi$
$229$	−28.9896			−1.91568			−0.957842	+	0.287296i	$0.907244\pi$
$230$	0.906272	−	0.191388i	0.0597578	−	0.0126197i
$231$	−1.33572			−0.0878837
$232$	0.0290118	−	0.0334814i	0.00190472	−	0.00219816i
$233$	8.60510	−	5.53016i	0.563739	−	0.362293i	−0.227521	−	0.973773i	$-0.573062\pi$
$233$	8.60510	−	5.53016i	0.563739	−	0.362293i	0.791260	+	0.611480i	$0.209426\pi$
$234$	0.0127712	+	0.0888256i	0.000834879	+	0.00580671i
$235$	11.8419	+	25.9302i	0.772481	+	1.69150i
$236$	−4.08753	+	28.4294i	−0.266075	+	1.85059i
$237$	−12.0627	+	3.54193i	−0.783558	+	0.230073i
$238$	0.104144	+	0.0669294i	0.00675067	+	0.00433839i
$239$	4.99820	−	10.9445i	0.323307	−	0.707942i	−0.676282	−	0.736643i	$-0.736410\pi$
$239$	4.99820	−	10.9445i	0.323307	−	0.707942i	0.999588	+	0.0287008i	$0.00913699\pi$
$240$	−15.0624	−	4.42273i	−0.972275	−	0.285486i
$241$	14.2779	+	16.4776i	0.919722	+	1.06142i	0.997919	+	0.0644783i	$0.0205383\pi$
$241$	14.2779	+	16.4776i	0.919722	+	1.06142i	−0.0781967	+	0.996938i	$0.524916\pi$
$242$	−0.295932	−	0.341524i	−0.0190232	−	0.0219540i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	0.656764	−	1.43811i	0.0420450	−	0.0920657i
$245$	3.31351	+	2.12946i	0.211693	+	0.136047i
$246$	0.0374819	−	0.0110057i	0.00238976	−	0.000701697i
$247$	−0.948578	+	6.59751i	−0.0603566	+	0.419789i
$248$	−0.207595	−	0.454570i	−0.0131823	−	0.0288652i
$249$	−0.324243	−	2.25516i	−0.0205481	−	0.142915i
$250$	−0.895904	+	0.575762i	−0.0566619	+	0.0364144i
$251$	4.48584	−	5.17694i	0.283144	−	0.326765i	−0.596306	−	0.802757i	$-0.703365\pi$
$251$	4.48584	−	5.17694i	0.283144	−	0.326765i	0.879450	+	0.475992i	$0.157911\pi$
$252$	1.99760			0.125837
$253$	−5.98827	−	2.27505i	−0.376479	−	0.143031i
$254$	−1.02584			−0.0643669
$255$	−6.51195	+	7.51519i	−0.407794	+	0.470620i
$256$	13.2985	−	8.54645i	0.831158	−	0.534153i
$257$	0.253469	+	1.76291i	0.0158109	+	0.109968i	0.996199	−	0.0871113i	$-0.0277636\pi$
$257$	0.253469	+	1.76291i	0.0158109	+	0.109968i	−0.980388	+	0.197079i	$0.936854\pi$
$258$	−0.122741	−	0.268766i	−0.00764154	−	0.0167326i
$259$	0.525557	−	3.65533i	0.0326565	−	0.227131i
$260$	13.8161	−	4.05676i	0.856836	−	0.251590i
$261$	−0.190128	−	0.122188i	−0.0117686	−	0.00756324i
$262$	0.236854	−	0.518639i	0.0146329	−	0.0320416i
$263$	−20.8562	−	6.12392i	−1.28605	−	0.377617i	−0.433919	−	0.900952i	$-0.642869\pi$
$263$	−20.8562	−	6.12392i	−1.28605	−	0.377617i	−0.852127	+	0.523335i	$0.824688\pi$
$264$	−0.171463	−	0.197879i	−0.0105528	−	0.0121786i
$265$	17.7890	+	20.5296i	1.09277	+	1.26112i
$266$	−0.171356	−	0.0503146i	−0.0105065	−	0.00308499i
$267$	−1.06119	+	2.32368i	−0.0649438	+	0.142207i
$268$	−19.9675	−	12.8323i	−1.21971	−	0.783858i
$269$	0.268136	−	0.0787319i	0.0163486	−	0.00480037i	−0.273548	−	0.961858i	$-0.588197\pi$
$269$	0.268136	−	0.0787319i	0.0163486	−	0.00480037i	0.289897	+	0.957058i	$0.406379\pi$
$270$	0.0274865	−	0.191173i	0.00167277	−	0.0116344i
$271$	7.50313	+	16.4296i	0.455783	+	0.998025i	0.988429	+	0.151687i	$0.0484705\pi$
$271$	7.50313	+	16.4296i	0.455783	+	0.998025i	−0.532646	+	0.846338i	$0.678802\pi$
$272$	−1.43200	−	9.95976i	−0.0868276	−	0.603899i
$273$	−1.53957	+	0.989424i	−0.0931792	+	0.0598827i
$274$	0.526078	−	0.607127i	0.0317815	−	0.0366779i
$275$	14.0437			0.846867
$276$	8.95559	+	3.40239i	0.539063	+	0.204800i
$277$	9.80975			0.589411			0.294705	−	0.955588i	$-0.404779\pi$
$277$	9.80975			0.589411			0.294705	+	0.955588i	$0.404779\pi$
$278$	0.540512	−	0.623784i	0.0324177	−	0.0374121i
$279$	−2.14464	+	1.37828i	−0.128396	+	0.0825154i
$280$	0.109880	+	0.764231i	0.00656658	+	0.0456716i
$281$	−1.74372	−	3.81820i	−0.104021	−	0.227775i	0.850464	−	0.526034i	$-0.176321\pi$
$281$	−1.74372	−	3.81820i	−0.104021	−	0.227775i	−0.954485	+	0.298259i	$0.903594\pi$
$282$	0.0505052	−	0.351271i	0.00300754	−	0.0209179i
$283$	−15.1883	+	4.45970i	−0.902853	+	0.265102i	−0.700030	−	0.714114i	$-0.746830\pi$
$283$	−15.1883	+	4.45970i	−0.902853	+	0.265102i	−0.202824	+	0.979215i	$0.565012\pi$
$284$	1.53668	+	0.987566i	0.0911854	+	0.0586013i
$285$	5.95927	−	13.0490i	0.352997	−	0.772955i
$286$	0.115010	+	0.0337701i	0.00680071	+	0.00199687i
$287$	0.521701	+	0.602075i	0.0307950	+	0.0355394i
$288$	0.384717	+	0.443987i	0.0226697	+	0.0261622i
$289$	10.1957	+	2.99374i	0.599749	+	0.176102i
$290$	0.0181330	−	0.0397058i	0.00106481	−	0.00233161i
$291$	−4.83023	−	3.10420i	−0.283153	−	0.181972i
$292$	6.11668	−	1.79602i	0.357951	−	0.105104i
$293$	0.849993	−	5.91183i	0.0496571	−	0.345373i	−0.949813	−	0.312819i	$-0.898727\pi$
$293$	0.849993	−	5.91183i	0.0496571	−	0.345373i	0.999470	−	0.0325541i	$-0.0103641\pi$
$294$	−0.0203699	−	0.0446039i	−0.00118800	−	0.00260136i
$295$	8.05962	+	56.0559i	0.469249	+	3.26370i
$296$	0.608979	−	0.391367i	0.0353962	−	0.0227478i
$297$	−0.874709	+	1.00947i	−0.0507557	+	0.0585753i
$298$	−0.569088			−0.0329664
$299$	−8.58743	+	1.81351i	−0.496624	+	0.104878i
$300$	−21.0027			−1.21259
$301$	3.94593	−	4.55385i	0.227440	−	0.262480i
$302$	0.830472	−	0.533712i	0.0477883	−	0.0307117i
$303$	2.66073	+	18.5058i	0.152855	+	1.06313i
$304$	6.03008	+	13.2040i	0.345849	+	0.757303i
$305$	0.443641	−	3.08559i	0.0254028	−	0.176680i
$306$	0.118782	−	0.0348775i	0.00679030	−	0.00199381i
$307$	23.6199	+	15.1796i	1.34806	+	0.866345i	0.997532	−	0.0702081i	$-0.0223663\pi$
$307$	23.6199	+	15.1796i	1.34806	+	0.866345i	0.350526	+	0.936553i	$0.386003\pi$
$308$	1.10842	−	2.42710i	0.0631581	−	0.138297i
$309$	2.09017	+	0.613728i	0.118905	+	0.0349138i
$310$	−0.322438	−	0.372113i	−0.0183133	−	0.0211346i
$311$	16.1388	+	18.6252i	0.915149	+	1.05614i	0.998223	+	0.0595948i	$0.0189809\pi$
$311$	16.1388	+	18.6252i	0.915149	+	1.05614i	−0.0830737	+	0.996543i	$0.526474\pi$
$312$	−0.344209	−	0.101069i	−0.0194870	−	0.00572189i
$313$	8.02193	−	17.5656i	0.453426	−	0.992865i	−0.535511	−	0.844528i	$-0.679881\pi$
$313$	8.02193	−	17.5656i	0.453426	−	0.992865i	0.988937	−	0.148337i	$-0.0473919\pi$
$314$	0.707544	+	0.454711i	0.0399290	+	0.0256608i
$315$	3.77923	−	1.10968i	0.212936	−	0.0625235i
$316$	3.57405	−	24.8581i	0.201056	−	1.39838i
$317$	−7.97356	−	17.4597i	−0.447839	−	0.980632i	−0.990093	−	0.140416i	$-0.955156\pi$
$317$	−7.97356	−	17.4597i	−0.447839	−	0.980632i	0.542253	−	0.840215i	$-0.317571\pi$
$318$	−0.0481280	−	0.334738i	−0.00269889	−	0.0187712i
$319$	−0.253957	+	0.163208i	−0.0142189	+	0.00913792i
$320$	20.4861	−	23.6422i	1.14521	−	1.32164i
$321$	−12.5953			−0.702999
$322$	−0.0153509	−	0.234663i	−0.000855474	−	0.0130772i
$323$	9.19496			0.511621
$324$	1.30815	−	1.50968i	0.0726748	−	0.0838712i
$325$	16.1870	−	10.4028i	0.897896	−	0.577043i
$326$	0.126184	+	0.877626i	0.00698866	+	0.0486072i
$327$	−6.89967	−	15.1082i	−0.381553	−	0.835484i
$328$	−0.0222244	+	0.154574i	−0.00122713	+	0.00853491i
$329$	6.94416	−	2.03899i	0.382844	−	0.112413i
$330$	−0.217025	−	0.139474i	−0.0119469	−	0.00767778i
$331$	6.89074	−	15.0886i	0.378749	−	0.829345i	−0.620241	−	0.784411i	$-0.712965\pi$
$331$	6.89074	−	15.0886i	0.378749	−	0.829345i	0.998990	−	0.0449334i	$-0.0143076\pi$
$332$	4.36687	+	1.28223i	0.239663	+	0.0703715i
$333$	−2.41834	−	2.79092i	−0.132524	−	0.152941i
$334$	−0.271601	−	0.313445i	−0.0148614	−	0.0171509i
$335$	−44.9047	−	13.1852i	−2.45341	−	0.720385i
$336$	−1.65567	+	3.62541i	−0.0903242	+	0.197782i
$337$	0.465497	+	0.299157i	0.0253572	+	0.0162961i	0.553258	−	0.833010i	$-0.313384\pi$
$337$	0.465497	+	0.299157i	0.0253572	+	0.0162961i	−0.527901	+	0.849306i	$0.677021\pi$
$338$	−0.454057	+	0.133323i	−0.0246975	+	0.00725183i
$339$	−2.68202	+	18.6538i	−0.145667	+	1.01314i
$340$	−8.25186	−	18.0691i	−0.447520	−	0.979932i
$341$	0.484611	+	3.37054i	0.0262431	+	0.182525i
$342$	−0.150239	+	0.0965530i	−0.00812402	+	0.00522099i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	1.18116			0.0636837
$345$	18.8331	+	1.46203i	1.01394	+	0.0787132i
$346$	−0.122023			−0.00655999
$347$	−22.3838	+	25.8322i	−1.20162	+	1.38675i	−0.300161	+	0.953889i	$0.597040\pi$
$347$	−22.3838	+	25.8322i	−1.20162	+	1.38675i	−0.901462	+	0.432858i	$0.857505\pi$
$348$	0.379799	−	0.244082i	0.0203594	−	0.0130842i
$349$	−2.90937	−	20.2351i	−0.155735	−	1.08316i	−0.906382	−	0.422458i	$-0.861167\pi$
$349$	−2.90937	−	20.2351i	−0.155735	−	1.08316i	0.750647	−	0.660703i	$-0.229742\pi$
$350$	0.214169	+	0.468965i	0.0114478	+	0.0250672i
$351$	−0.260450	+	1.81147i	−0.0139018	+	0.0966890i
$352$	0.752920	−	0.221077i	0.0401307	−	0.0117835i
$353$	0.966687	+	0.621252i	0.0514516	+	0.0330659i	0.566114	−	0.824327i	$-0.308446\pi$
$353$	0.966687	+	0.621252i	0.0514516	+	0.0330659i	−0.514662	+	0.857393i	$0.672083\pi$
$354$	0.292882	−	0.641322i	0.0155665	−	0.0340859i
$355$	3.45584	+	1.01473i	0.183417	+	0.0538560i
$356$	−3.34170	−	3.85653i	−0.177110	−	0.204395i
$357$	1.65329	+	1.90800i	0.0875015	+	0.100982i
$358$	−0.512892	−	0.150599i	−0.0271072	−	0.00795939i
$359$	−5.70291	+	12.4876i	−0.300988	+	0.659072i	−0.998336	−	0.0576607i	$-0.981636\pi$
$359$	−5.70291	+	12.4876i	−0.300988	+	0.659072i	0.697348	+	0.716732i	$0.254363\pi$
$360$	0.649524	+	0.417423i	0.0342329	+	0.0220001i
$361$	5.50294	−	1.61581i	0.289629	−	0.0850426i
$362$	0.0568942	−	0.395708i	0.00299029	−	0.0207979i
$363$	−3.82841	−	8.38304i	−0.200939	−	0.439996i
$364$	−0.520273	−	3.61858i	−0.0272697	−	0.189665i
$365$	10.5744	−	6.79574i	0.553488	−	0.355705i
$366$	−0.0254142	+	0.0293295i	−0.00132842	+	0.00153308i
$367$	−21.3601			−1.11499			−0.557495	−	0.830180i	$-0.688238\pi$
$367$	−21.3601			−1.11499			−0.557495	+	0.830180i	$0.688238\pi$
$368$	−13.5976	+	13.4334i	−0.708825	+	0.700264i
$369$	0.796659			0.0414724
$370$	0.467076	−	0.539034i	0.0242821	−	0.0280231i
$371$	5.80186	−	3.72863i	0.301218	−	0.193581i
$372$	−0.724746	−	5.04072i	−0.0375763	−	0.261349i
$373$	−9.15818	−	20.0536i	−0.474193	−	1.03834i	−0.984020	−	0.178060i	$-0.943018\pi$
$373$	−9.15818	−	20.0536i	−0.474193	−	1.03834i	0.509827	−	0.860277i	$-0.329709\pi$
$374$	0.0235328	−	0.163674i	0.00121685	−	0.00846338i
$375$	−20.8386	+	6.11877i	−1.07610	+	0.315972i
$376$	1.19347	+	0.766997i	0.0615485	+	0.0395548i
$377$	−0.171821	+	0.376235i	−0.00884921	+	0.0193771i
$378$	−0.0470489	−	0.0138148i	−0.00241993	−	0.000710557i
$379$	5.04713	+	5.82469i	0.259253	+	0.299194i	0.870422	−	0.492306i	$-0.163846\pi$
$379$	5.04713	+	5.82469i	0.259253	+	0.299194i	−0.611169	+	0.791500i	$0.709300\pi$
$380$	18.7658	+	21.6569i	0.962666	+	1.11098i
$381$	−20.0731	−	5.89398i	−1.02837	−	0.301958i
$382$	−0.0165528	+	0.0362455i	−0.000846914	+	0.00185448i
$383$	13.3972	+	8.60985i	0.684565	+	0.439943i	0.836150	−	0.548501i	$-0.184801\pi$
$383$	13.3972	+	8.60985i	0.684565	+	0.439943i	−0.151585	+	0.988444i	$0.548438\pi$
$384$	−1.50104	+	0.440746i	−0.0765998	+	0.0224917i
$385$	0.748732	−	5.20754i	0.0381589	−	0.265401i
$386$	0.161849	+	0.354400i	0.00823790	+	0.0180385i
$387$	−0.857533	−	5.96428i	−0.0435909	−	0.303181i
$388$	9.64885	−	6.20094i	0.489846	−	0.314805i
$389$	−24.8763	+	28.7088i	−1.26128	+	1.45559i	−0.427000	+	0.904252i	$0.640430\pi$
$389$	−24.8763	+	28.7088i	−1.26128	+	1.45559i	−0.834279	+	0.551342i	$0.814116\pi$
$390$	−0.353462			−0.0178982
$391$	4.16223	+	11.3699i	0.210493	+	0.575000i
$392$	0.196023			0.00990064
$393$	7.61448	−	8.78758i	0.384100	−	0.443275i
$394$	−0.981361	+	0.630682i	−0.0494403	+	0.0317733i
$395$	−7.04718	−	49.0142i	−0.354582	−	2.46617i
$396$	−1.10842	−	2.42710i	−0.0557002	−	0.121966i
$397$	−4.60088	+	31.9998i	−0.230912	+	1.60603i	0.463264	+	0.886220i	$0.346678\pi$
$397$	−4.60088	+	31.9998i	−0.230912	+	1.60603i	−0.694176	+	0.719805i	$0.744231\pi$
$398$	−0.313403	+	0.0920234i	−0.0157095	+	0.00461272i
$399$	−3.06391	−	1.96906i	−0.153387	−	0.0985761i
$400$	17.4077	−	38.1175i	0.870384	−	1.90587i
$401$	−15.6775	−	4.60332i	−0.782895	−	0.229879i	−0.134227	−	0.990951i	$-0.542855\pi$
$401$	−15.6775	−	4.60332i	−0.782895	−	0.229879i	−0.648668	+	0.761072i	$0.724673\pi$
$402$	0.381544	+	0.440326i	0.0190297	+	0.0219614i
$403$	3.05528	+	3.52598i	0.152194	+	0.175642i
$404$	−35.8344	−	10.5219i	−1.78283	−	0.523486i
$405$	1.63623	−	3.58284i	0.0813048	−	0.178033i
$406$	−0.00932296	−	0.00599150i	−0.000462691	−	0.000297353i
$407$	−4.73288	+	1.38970i	−0.234600	+	0.0688848i
$408$	−0.0704299	+	0.489851i	−0.00348680	+	0.0242512i
$409$	−9.51693	−	20.8392i	−0.470582	−	1.03043i	−0.984947	−	0.172859i	$-0.944700\pi$
$409$	−9.51693	−	20.8392i	−0.470582	−	1.03043i	0.514365	−	0.857571i	$-0.328028\pi$
$410$	0.0218974	+	0.152300i	0.00108143	+	0.00752154i
$411$	13.7823	−	8.85733i	0.679829	−	0.436900i
$412$	−2.84968	+	3.28870i	−0.140393	+	0.162023i
$413$	14.3781			0.707502
$414$	−0.187399	−	0.142070i	−0.00921016	−	0.00698236i
$415$	8.97393			0.440513
$416$	0.704068	−	0.812538i	0.0345198	−	0.0398380i
$417$	14.1604	−	9.10034i	0.693438	−	0.445645i
$418$	0.0339486	+	0.236118i	0.00166048	+	0.0115489i
$419$	−11.1980	−	24.5202i	−0.547058	−	1.19789i	−0.958142	−	0.286293i	$-0.907577\pi$
$419$	−11.1980	−	24.5202i	−0.547058	−	1.19789i	0.411084	−	0.911598i	$-0.365150\pi$
$420$	−1.11975	+	7.78800i	−0.0546380	+	0.380016i
$421$	−19.7736	+	5.80604i	−0.963704	+	0.282969i	−0.725482	−	0.688241i	$-0.758383\pi$
$421$	−19.7736	+	5.80604i	−0.963704	+	0.282969i	−0.238223	+	0.971211i	$0.576565\pi$
$422$	−0.0962006	−	0.0618244i	−0.00468297	−	0.00300956i
$423$	3.00649	−	6.58330i	0.146181	−	0.320091i
$424$	1.29715	+	0.380876i	0.0629949	+	0.0184970i
$425$	−17.3827	−	20.0607i	−0.843184	−	0.973086i
$426$	−0.0293634	−	0.0338872i	−0.00142266	−	0.00164184i
$427$	−0.759384	−	0.222975i	−0.0367492	−	0.0107905i
$428$	10.4519	−	22.8865i	0.505213	−	1.10626i
$429$	2.05643	+	1.32159i	0.0992856	+	0.0638070i
$430$	1.11664	−	0.327874i	0.0538490	−	0.0158115i
$431$	−3.08153	+	21.4325i	−0.148432	+	1.03237i	0.770355	+	0.637615i	$0.220079\pi$
$431$	−3.08153	+	21.4325i	−0.148432	+	1.03237i	−0.918787	+	0.394753i	$0.870830\pi$
$432$	1.65567	+	3.62541i	0.0796584	+	0.174428i
$433$	4.55985	+	31.7145i	0.219132	+	1.52410i	0.741252	+	0.671227i	$0.234232\pi$
$433$	4.55985	+	31.7145i	0.219132	+	1.52410i	−0.522119	+	0.852872i	$0.674858\pi$
$434$	−0.105163	+	0.0675841i	−0.00504798	+	0.00324414i
$435$	0.582948	−	0.672758i	0.0279502	−	0.0322563i
$436$	33.1783			1.58895
$437$	−10.3823	−	14.0462i	−0.496653	−	0.671922i
$438$	−0.156485			−0.00747716
$439$	22.0112	−	25.4023i	1.05054	−	1.21238i	0.0739490	−	0.997262i	$-0.476440\pi$
$439$	22.0112	−	25.4023i	1.05054	−	1.21238i	0.976587	−	0.215121i	$-0.0690147\pi$
$440$	0.867580	−	0.557560i	0.0413602	−	0.0265806i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−0.0941161	−	0.206086i	−0.00447665	−	0.00980249i
$443$	−2.17495	+	15.1271i	−0.103335	+	0.718711i	0.870618	+	0.491960i	$0.163719\pi$
$443$	−2.17495	+	15.1271i	−0.103335	+	0.718711i	−0.973953	+	0.226751i	$0.927190\pi$
$444$	7.07813	−	2.07833i	0.335913	−	0.0986330i
$445$	−8.46446	−	5.43978i	−0.401254	−	0.257870i
$446$	−0.198877	+	0.435480i	−0.00941709	+	0.0206206i
$447$	−11.1356	−	3.26971i	−0.526696	−	0.154652i
$448$	−5.20113	−	6.00243i	−0.245730	−	0.283588i
$449$	13.6261	+	15.7253i	0.643054	+	0.742124i	0.979912	−	0.199432i	$-0.0639096\pi$
$449$	13.6261	+	15.7253i	0.643054	+	0.742124i	−0.336858	+	0.941556i	$0.609364\pi$
$450$	0.494671	+	0.145249i	0.0233190	+	0.00684708i
$451$	0.442048	−	0.967950i	0.0208152	−	0.0455790i
$452$	−31.6698	−	20.3530i	−1.48962	−	0.957322i
$453$	19.3167	−	5.67189i	0.907577	−	0.266489i
$454$	−0.145832	+	1.01429i	−0.00684426	+	0.0476028i
$455$	−2.99445	−	6.55694i	−0.140382	−	0.307394i
$456$	−0.101603	−	0.706663i	−0.00475799	−	0.0330925i
$457$	−2.30030	+	1.47831i	−0.107604	+	0.0691526i	−0.593336	−	0.804955i	$-0.702189\pi$
$457$	−2.30030	+	1.47831i	−0.107604	+	0.0691526i	0.485732	+	0.874108i	$0.338553\pi$
$458$	−0.930889	+	1.07430i	−0.0434976	+	0.0501989i
$459$	2.52465			0.117840
$460$	−18.2849	+	33.0079i	−0.852537	+	1.53900i
$461$	5.79204			0.269762			0.134881	−	0.990862i	$-0.456935\pi$
$461$	5.79204			0.269762			0.134881	+	0.990862i	$0.456935\pi$
$462$	−0.0428915	+	0.0494994i	−0.00199549	+	0.00230292i
$463$	−21.3907	+	13.7470i	−0.994109	+	0.638875i	−0.933234	−	0.359270i	$-0.883026\pi$
$463$	−21.3907	+	13.7470i	−0.994109	+	0.638875i	−0.0608757	+	0.998145i	$0.519389\pi$
$464$	0.128192	+	0.891595i	0.00595116	+	0.0413913i
$465$	−4.17131	−	9.13389i	−0.193440	−	0.423574i
$466$	0.0713817	−	0.496470i	0.00330669	−	0.0229985i
$467$	−21.9075	+	6.43262i	−1.01376	+	0.297666i	−0.746090	−	0.665845i	$-0.768071\pi$
$467$	−21.9075	+	6.43262i	−1.01376	+	0.297666i	−0.267668	+	0.963511i	$0.586253\pi$
$468$	−3.07545	−	1.97647i	−0.142163	−	0.0913623i
$469$	−4.93595	+	10.8082i	−0.227921	+	0.499077i
$470$	1.34119	+	0.393808i	0.0618643	+	0.0181650i
$471$	11.2323	+	12.9628i	0.517556	+	0.597292i
$472$	1.84569	+	2.13004i	0.0849547	+	0.0980429i
$473$	−7.72249	−	2.26753i	−0.355080	−	0.104261i
$474$	−0.256090	+	0.560760i	−0.0117626	+	0.0257565i
$475$	32.2139	+	20.7026i	1.47808	+	0.949901i
$476$	−4.83894	+	1.42084i	−0.221792	+	0.0651241i
$477$	0.981500	−	6.82649i	0.0449398	−	0.312563i
$478$	−0.245087	−	0.536667i	−0.0112100	−	0.0245466i
$479$	3.93291	+	27.3540i	0.179699	+	1.24984i	0.857459	+	0.514552i	$0.172042\pi$
$479$	3.93291	+	27.3540i	0.179699	+	1.24984i	−0.677760	+	0.735284i	$0.737049\pi$
$480$	−1.94662	+	1.25102i	−0.0888506	+	0.0571008i
$481$	−4.42580	+	5.10765i	−0.201799	+	0.232889i
$482$	1.06911			0.0486968
$483$	1.04788	−	4.67995i	0.0476803	−	0.212945i
$484$	18.4096			0.836798
$485$	14.8099	−	17.0915i	0.672482	−	0.776086i
$486$	−0.0412510	+	0.0265104i	−0.00187118	+	0.00120254i
$487$	−2.41877	−	16.8229i	−0.109605	−	0.762320i	−0.968292	−	0.249820i	$-0.919629\pi$
$487$	−2.41877	−	16.8229i	−0.109605	−	0.762320i	0.858687	−	0.512500i	$-0.171281\pi$
$488$	−0.0644478	−	0.141121i	−0.00291742	−	0.00638825i
$489$	−2.57333	+	17.8979i	−0.116370	+	0.809371i
$490$	0.185315	−	0.0544134i	0.00837169	−	0.00245815i
$491$	30.3382	+	19.4971i	1.36914	+	0.879894i	0.998799	−	0.0490012i	$-0.0156038\pi$
$491$	30.3382	+	19.4971i	1.36914	+	0.879894i	0.370343	+	0.928895i	$0.379240\pi$
$492$	−0.661093	+	1.44759i	−0.0298044	+	0.0652625i
$493$	0.547472	+	0.160752i	0.0246569	+	0.00723992i
$494$	0.214032	+	0.247007i	0.00962977	+	0.0111133i
$495$	−3.44528	−	3.97607i	−0.154854	−	0.178711i
$496$	9.74903	+	2.86257i	0.437744	+	0.128533i
$497$	0.379867	−	0.831794i	0.0170394	−	0.0373110i
$498$	−0.0939843	−	0.0604001i	−0.00421154	−	0.00270659i
$499$	−29.1995	+	8.57376i	−1.30715	+	0.383814i	−0.859840	−	0.510564i	$-0.829437\pi$
$499$	−29.1995	+	8.57376i	−1.30715	+	0.383814i	−0.447311	+	0.894378i	$0.647618\pi$
$500$	6.17426	−	42.9429i	0.276121	−	1.92046i
$501$	−3.51364	−	7.69381i	−0.156978	−	0.343734i
$502$	−0.0478027	−	0.332475i	−0.00213354	−	0.0148391i
$503$	3.26090	−	2.09565i	0.145396	−	0.0934405i	−0.465920	−	0.884827i	$-0.654277\pi$
$503$	3.26090	−	2.09565i	0.145396	−	0.0934405i	0.611316	+	0.791386i	$0.290640\pi$
$504$	0.128368	−	0.148144i	0.00571795	−	0.00659886i
$505$	−73.6399			−3.27693
$506$	−0.276600	+	0.148860i	−0.0122964	+	0.00661766i
$507$	−9.65075			−0.428605
$508$	27.3671	−	31.5833i	1.21422	−	1.40128i
$509$	−12.8465	+	8.25595i	−0.569411	+	0.365938i	−0.793444	−	0.608643i	$-0.791714\pi$
$509$	−12.8465	+	8.25595i	−0.569411	+	0.365938i	0.224033	+	0.974582i	$0.428078\pi$
$510$	0.0693937	+	0.482644i	0.00307280	+	0.0213718i
$511$	−1.32571	−	2.90290i	−0.0586459	−	0.128417i
$512$	0.555593	−	3.86424i	0.0245540	−	0.170777i
$513$	−3.49455	+	1.02609i	−0.154288	+	0.0453031i
$514$	0.0734698	+	0.0472161i	0.00324061	+	0.00208261i
$515$	−3.56437	+	7.80488i	−0.157065	+	0.343924i
$516$	11.5492	+	3.39114i	0.508423	+	0.149287i
$517$	−6.33055	−	7.30585i	−0.278417	−	0.321311i
$518$	−0.118584	−	0.136853i	−0.00521028	−	0.00601298i
$519$	−2.38768	−	0.701085i	−0.104807	−	0.0307742i
$520$	0.586981	−	1.28531i	0.0257408	−	0.0563645i
$521$	−9.86172	−	6.33774i	−0.432050	−	0.277662i	0.306487	−	0.951875i	$-0.400846\pi$
$521$	−9.86172	−	6.33774i	−0.432050	−	0.277662i	−0.738537	+	0.674213i	$0.764483\pi$
$522$	−0.0106333	+	0.00312222i	−0.000465408	+	0.000136656i
$523$	2.90871	−	20.2306i	0.127189	−	0.884620i	−0.821904	−	0.569626i	$-0.807088\pi$
$523$	2.90871	−	20.2306i	0.127189	−	0.884620i	0.949093	−	0.314995i	$-0.102003\pi$
$524$	9.64898	+	21.1283i	0.421518	+	0.922995i
$525$	1.49630	+	10.4070i	0.0653037	+	0.454197i
$526$	−0.896658	+	0.576247i	−0.0390962	+	0.0251256i
$527$	4.21481	−	4.86415i	0.183600	−	0.211886i
$528$	5.32361			0.231680
$529$	12.6689	−	19.1963i	0.550823	−	0.834622i
$530$	1.33202			0.0578591
$531$	9.41568	−	10.8663i	0.408606	−	0.471556i
$532$	6.12046	−	3.93338i	0.265355	−	0.170534i
$533$	−0.207490	−	1.44312i	−0.00898737	−	0.0625086i
$534$	0.0520356	+	0.113942i	0.00225180	+	0.00493076i
$535$	7.06023	−	49.1050i	0.305240	−	2.12299i
$536$	−2.23479	+	0.656194i	−0.0965282	+	0.0283432i
$537$	−9.17072	−	5.89366i	−0.395746	−	0.254330i
$538$	0.00569251	−	0.0124649i	0.000245421	−	0.000537398i
$539$	−1.28161	−	0.376315i	−0.0552029	−	0.0162090i
$540$	5.15250	+	5.94630i	0.221728	+	0.255888i
$541$	2.47965	+	2.86167i	0.106608	+	0.123033i	0.806546	−	0.591171i	$-0.201334\pi$
$541$	2.47965	+	2.86167i	0.106608	+	0.123033i	−0.699938	+	0.714204i	$0.746789\pi$
$542$	0.849786	+	0.249520i	0.0365014	+	0.0107178i
$543$	3.38682	−	7.41611i	0.145342	−	0.318256i
$544$	−1.24773	−	0.801866i	−0.0534959	−	0.0343797i
$545$	62.7697	−	18.4308i	2.68876	−	0.789490i
$546$	−0.0127712	+	0.0888256i	−0.000546556	+	0.00380138i
$547$	7.53970	+	16.5096i	0.322374	+	0.705901i	0.999552	−	0.0299180i	$-0.00952462\pi$
$547$	7.53970	+	16.5096i	0.322374	+	0.705901i	−0.677178	+	0.735819i	$0.736797\pi$
$548$	4.65749	+	32.3935i	0.198958	+	1.38378i
$549$	−0.665804	+	0.427886i	−0.0284158	+	0.0182617i
$550$	0.450960	−	0.520436i	0.0192290	−	0.0221915i
$551$	−0.823130			−0.0350665
$552$	0.827821	−	0.445517i	0.0352344	−	0.0189624i
$553$	−12.5720			−0.534615
$554$	0.315003	−	0.363533i	0.0133832	−	0.0154450i
$555$	12.2365	−	7.86393i	0.519411	−	0.333805i
$556$	4.78527	+	33.2823i	0.202941	+	1.41148i
$557$	−4.05852	−	8.88692i	−0.171965	−	0.376551i	0.803952	−	0.594695i	$-0.202727\pi$
$557$	−4.05852	−	8.88692i	−0.171965	−	0.376551i	−0.975917	+	0.218144i	$0.930000\pi$
$558$	−0.0177904	+	0.123735i	−0.000753128	+	0.00523812i
$559$	−10.5807	+	3.10679i	−0.447518	+	0.131403i
$560$	−13.2063	−	8.48715i	−0.558066	−	0.358648i
$561$	1.40087	−	3.06747i	0.0591447	−	0.129509i
$562$	−0.197489	−	0.0579880i	−0.00833057	−	0.00244608i
$563$	−11.2632	−	12.9984i	−0.474688	−	0.547819i	0.467022	−	0.884246i	$-0.345327\pi$
$563$	−11.2632	−	12.9984i	−0.474688	−	0.547819i	−0.941710	+	0.336427i	$0.890782\pi$
$564$	9.46749	+	10.9261i	0.398653	+	0.460070i
$565$	−71.2220	−	20.9127i	−2.99633	−	0.879803i
$566$	−0.322447	+	0.706060i	−0.0135535	+	0.0296779i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	0.171988	−	0.0505002i	0.00721646	−	0.00211894i
$569$	−0.427896	+	2.97608i	−0.0179383	+	0.124764i	−0.996823	−	0.0796499i	$-0.974620\pi$
$569$	−0.427896	+	2.97608i	−0.0179383	+	0.124764i	0.978885	+	0.204414i	$0.0655288\pi$
$570$	−0.292214	−	0.639859i	−0.0122395	−	0.0268007i
$571$	3.70542	+	25.7717i	0.155067	+	1.07851i	0.907563	+	0.419916i	$0.137941\pi$
$571$	3.70542	+	25.7717i	0.155067	+	1.07851i	−0.752496	+	0.658597i	$0.771150\pi$
$572$	−4.10793	+	2.64000i	−0.171761	+	0.110384i
$573$	−0.532145	+	0.614128i	−0.0222307	+	0.0256556i
$574$	0.0390643			0.00163051
$575$	−11.0174	+	49.2049i	−0.459458	+	2.05199i
$576$	−7.94235			−0.330931
$577$	−9.89593	+	11.4205i	−0.411973	+	0.475442i	−0.923375	−	0.383899i	$-0.874581\pi$
$577$	−9.89593	+	11.4205i	−0.411973	+	0.475442i	0.511402	+	0.859342i	$0.329126\pi$
$578$	0.438340	−	0.281704i	0.0182325	−	0.0117173i
$579$	1.13076	+	7.86461i	0.0469928	+	0.326842i
$580$	0.738704	+	1.61754i	0.0306730	+	0.0671646i
$581$	0.324243	−	2.25516i	0.0134519	−	0.0935599i
$582$	−0.270141	+	0.0793206i	−0.0111977	+	0.00328794i
$583$	−7.74964	−	4.98039i	−0.320957	−	0.206267i
$584$	0.259869	−	0.569034i	0.0107535	−	0.0235468i
$585$	−6.91635	−	2.03082i	−0.285956	−	0.0839642i
$586$	−0.191788	−	0.221335i	−0.00792269	−	0.00914327i
$587$	−9.28652	−	10.7172i	−0.383296	−	0.442347i	0.531014	−	0.847363i	$-0.321811\pi$
$587$	−9.28652	−	10.7172i	−0.383296	−	0.442347i	−0.914309	+	0.405016i	$0.867266\pi$
$588$	1.91668	+	0.562788i	0.0790425	+	0.0232090i
$589$	−3.85709	+	8.44585i	−0.158929	+	0.348005i
$590$	2.33614	+	1.50135i	0.0961774	+	0.0618095i
$591$	−22.8263	+	6.70242i	−0.938950	+	0.275701i
$592$	−2.09465	+	14.5686i	−0.0860895	+	0.598765i
$593$	3.88369	+	8.50410i	0.159484	+	0.349221i	0.972458	−	0.233079i	$-0.0748800\pi$
$593$	3.88369	+	8.50410i	0.159484	+	0.349221i	−0.812974	+	0.582300i	$0.802153\pi$
$594$	0.00932121	+	0.0648304i	0.000382454	+	0.00266002i
$595$	−8.36545	+	5.37615i	−0.342950	+	0.220400i
$596$	15.1820	−	17.5209i	0.621878	−	0.717686i
$597$	−6.66122			−0.272626
$598$	−0.208547	+	0.376469i	−0.00852813	+	0.0153950i
$599$	35.4682			1.44919			0.724595	−	0.689174i	$-0.242027\pi$
$599$	35.4682			1.44919			0.724595	+	0.689174i	$0.242027\pi$
$600$	−1.34965	+	1.55758i	−0.0550994	+	0.0635881i
$601$	32.3076	−	20.7628i	1.31785	−	0.846933i	0.322818	−	0.946461i	$-0.395370\pi$
$601$	32.3076	−	20.7628i	1.31785	−	0.846933i	0.995035	+	0.0995284i	$0.0317334\pi$
$602$	−0.0420493	−	0.292459i	−0.00171380	−	0.0119197i
$603$	4.93595	+	10.8082i	0.201007	+	0.440145i
$604$	−5.72333	+	39.8066i	−0.232879	+	1.61971i
$605$	34.8289	−	10.2267i	1.41599	−	0.415774i
$606$	0.771233	+	0.495642i	0.0313292	+	0.0201341i
$607$	6.10043	−	13.3581i	0.247609	−	0.542188i	−0.744492	−	0.667632i	$-0.767308\pi$
$607$	6.10043	−	13.3581i	0.247609	−	0.542188i	0.992101	+	0.125444i	$0.0400354\pi$
$608$	2.05297	+	0.602808i	0.0832591	+	0.0244471i
$609$	−0.148002	−	0.170804i	−0.00599735	−	0.00692131i
$610$	−0.100101	−	0.115523i	−0.00405296	−	0.00467737i
$611$	−12.7085	−	3.73155i	−0.514130	−	0.150962i
$612$	−2.09503	+	4.58748i	−0.0846866	+	0.185438i
$613$	−20.8321	−	13.3880i	−0.841401	−	0.540736i	0.0474805	−	0.998872i	$-0.484881\pi$
$613$	−20.8321	−	13.3880i	−0.841401	−	0.540736i	−0.888882	+	0.458136i	$0.848517\pi$
$614$	1.32099	−	0.387878i	0.0533109	−	0.0156535i
$615$	−0.446565	+	3.10593i	−0.0180072	+	0.125243i
$616$	−0.108768	−	0.238170i	−0.00438241	−	0.00959613i
$617$	−1.23711	−	8.60427i	−0.0498041	−	0.346395i	−0.999453	−	0.0330782i	$-0.989469\pi$
$617$	−1.23711	−	8.60427i	−0.0498041	−	0.346395i	0.949649	−	0.313317i	$-0.101440\pi$
$618$	0.0898615	−	0.0577505i	0.00361476	−	0.00232306i
$619$	−2.46559	+	2.84544i	−0.0991004	+	0.114368i	−0.803133	−	0.595799i	$-0.796835\pi$
$619$	−2.46559	+	2.84544i	−0.0991004	+	0.114368i	0.704033	+	0.710167i	$0.251381\pi$
$620$	20.0585			0.805567
$621$	−2.85065	−	3.85665i	−0.114393	−	0.154762i
$622$	1.20846			0.0484546
$623$	−1.67286	+	1.93058i	−0.0670217	+	0.0773472i
$624$	6.13609	−	3.94343i	0.245640	−	0.157863i
$625$	−4.69267	−	32.6383i	−0.187707	−	1.30553i
$626$	−0.393357	−	0.861331i	−0.0157217	−	0.0344257i
$627$	−0.692331	+	4.81527i	−0.0276491	+	0.192303i
$628$	−32.8752	+	9.65303i	−1.31186	+	0.385198i
$629$	7.84326	+	5.04056i	0.312731	+	0.200980i
$630$	0.0802327	−	0.175685i	0.00319655	−	0.00699946i
$631$	9.97823	+	2.92987i	0.397227	+	0.116636i	0.474244	−	0.880393i	$-0.342721\pi$
$631$	9.97823	+	2.92987i	0.397227	+	0.116636i	−0.0770170	+	0.997030i	$0.524540\pi$
$632$	−1.61383	−	1.86246i	−0.0641949	−	0.0740848i
$633$	−1.52719	−	1.76247i	−0.0607002	−	0.0700518i
$634$	−0.903065	−	0.265164i	−0.0358653	−	0.0105310i
$635$	34.2307	−	74.9548i	1.35840	−	2.97449i
$636$	11.5898	+	7.44829i	0.459564	+	0.295344i
$637$	−1.75596	+	0.515597i	−0.0695738	+	0.0204287i
$638$	−0.00210665	+	0.0146520i	−8.34029e−5	+	0.000580080i
$639$	−0.379867	−	0.831794i	−0.0150273	−	0.0329053i
$640$	−0.876926	−	6.09916i	−0.0346635	−	0.241090i
$641$	−19.0646	+	12.2521i	−0.753007	+	0.483928i	−0.859976	−	0.510334i	$-0.829522\pi$
$641$	−19.0646	+	12.2521i	−0.753007	+	0.483928i	0.106970	+	0.994262i	$0.465885\pi$
$642$	−0.404449	+	0.466759i	−0.0159623	+	0.0184215i
$643$	15.4839			0.610624			0.305312	−	0.952252i	$-0.401239\pi$
$643$	15.4839			0.610624			0.305312	+	0.952252i	$0.401239\pi$
$644$	7.63427	+	5.78765i	0.300832	+	0.228065i
$645$	23.7335			0.934507
$646$	0.295261	−	0.340750i	0.0116169	−	0.0134066i
$647$	5.35128	−	3.43906i	0.210380	−	0.135203i	−0.431207	−	0.902253i	$-0.641912\pi$
$647$	5.35128	−	3.43906i	0.210380	−	0.135203i	0.641588	+	0.767049i	$0.278276\pi$
$648$	−0.0278969	−	0.194027i	−0.00109590	−	0.00762212i
$649$	−7.97810	−	17.4696i	−0.313168	−	0.685742i
$650$	0.134276	−	0.933910i	0.00526674	−	0.0366310i
$651$	−2.44608	+	0.718233i	−0.0958693	+	0.0281498i
$652$	−30.3864	−	19.5282i	−1.19002	−	0.764782i
$653$	−15.0326	+	32.9168i	−0.588272	+	1.28814i	0.348209	+	0.937417i	$0.386790\pi$
$653$	−15.0326	+	32.9168i	−0.588272	+	1.28814i	−0.936481	+	0.350719i	$0.885937\pi$
$654$	−0.781440	−	0.229452i	−0.0305567	−	0.00897227i
$655$	29.9918	+	34.6124i	1.17188	+	1.35242i
$656$	−2.07928	−	2.39962i	−0.0811823	−	0.0936893i
$657$	−3.06202	−	0.899090i	−0.119461	−	0.0350768i
$658$	0.147424	−	0.322813i	0.00574718	−	0.0125846i
$659$	−40.8717	−	26.2666i	−1.59214	−	1.02320i	−0.970871	−	0.239602i	$-0.922983\pi$
$659$	−40.8717	−	26.2666i	−1.59214	−	1.02320i	−0.621264	−	0.783602i	$-0.713380\pi$
$660$	10.0838	−	2.96088i	0.392512	−	0.115252i
$661$	2.67799	−	18.6258i	0.104162	−	0.724460i	−0.869079	−	0.494673i	$-0.835288\pi$
$661$	2.67799	−	18.6258i	0.104162	−	0.724460i	0.973241	−	0.229787i	$-0.0738030\pi$
$662$	−0.337888	−	0.739872i	−0.0131324	−	0.0287559i
$663$	−0.657543	−	4.57331i	−0.0255369	−	0.177613i
$664$	0.375711	−	0.241455i	0.0145804	−	0.00937027i
$665$	9.39420	−	10.8415i	0.364292	−	0.420415i
$666$	−0.181083			−0.00701681
$667$	−0.372602	−	1.01783i	−0.0144272	−	0.0394105i
$668$	16.8960			0.653725
$669$	−6.39357	+	7.37857i	−0.247190	+	0.285272i
$670$	−1.93057	+	1.24070i	−0.0745843	+	0.0479324i
$671$	0.150447	+	1.04638i	0.00580795	+	0.0403952i
$672$	0.244048	+	0.534390i	0.00941434	+	0.0206145i
$673$	−1.30864	+	9.10181i	−0.0504445	+	0.350849i	0.948930	+	0.315486i	$0.102168\pi$
$673$	−1.30864	+	9.10181i	−0.0504445	+	0.350849i	−0.999375	+	0.0353625i	$0.988741\pi$
$674$	0.0260339	−	0.00764424i	0.00100279	−	0.000294445i
$675$	8.84492	+	5.68429i	0.340441	+	0.218788i
$676$	8.00850	−	17.5362i	0.308019	−	0.674468i
$677$	28.7718	+	8.44816i	1.10579	+	0.324689i	0.783150	−	0.621833i	$-0.213612\pi$
$677$	28.7718	+	8.44816i	1.10579	+	0.324689i	0.322640	+	0.946522i	$0.395430\pi$
$678$	0.605156	+	0.698388i	0.0232409	+	0.0268214i
$679$	−3.76002	−	4.33929i	−0.144296	−	0.166527i
$680$	−1.87030	−	0.549169i	−0.0717226	−	0.0210597i
$681$	−8.68118	+	19.0091i	−0.332663	+	0.728431i
$682$	0.140468	+	0.0902733i	0.00537879	+	0.00345674i
$683$	30.0150	−	8.81321i	1.14849	−	0.337228i	0.348542	−	0.937293i	$-0.386677\pi$
$683$	30.0150	−	8.81321i	1.14849	−	0.337228i	0.799951	+	0.600065i	$0.204859\pi$
$684$	1.03540	−	7.20135i	0.0395894	−	0.275350i
$685$	26.8063	+	58.6977i	1.02422	+	2.24272i
$686$	−0.00697843	−	0.0485360i	−0.000266438	−	0.00185311i
$687$	−24.3876	+	15.6729i	−0.930444	+	0.597960i
$688$	−15.7268	+	18.1497i	−0.599580	+	0.691952i
$689$	−12.6216			−0.480844
$690$	0.658932	−	0.650973i	0.0250851	−	0.0247821i
$691$	−6.25370			−0.237902			−0.118951	−	0.992900i	$-0.537953\pi$
$691$	−6.25370			−0.237902			−0.118951	+	0.992900i	$0.537953\pi$
$692$	3.25529	−	3.75681i	0.123748	−	0.142812i
$693$	−1.12368	+	0.722143i	−0.0426849	+	0.0274319i
$694$	0.238529	+	1.65901i	0.00905445	+	0.0629751i
$695$	27.5418	+	60.3082i	1.04472	+	2.28762i
$696$	0.00630487	−	0.0438513i	0.000238985	−	0.00166218i
$697$	−1.92981	+	0.566644i	−0.0730968	+	0.0214632i
$698$	−0.843303	−	0.541958i	−0.0319195	−	0.0205134i
$699$	4.24924	−	9.30453i	0.160721	−	0.351930i
$700$	−20.1519	−	5.91714i	−0.761671	−	0.223647i
$701$	18.5949	+	21.4597i	0.702320	+	0.810520i	0.989064	−	0.147487i	$-0.0471184\pi$
$701$	18.5949	+	21.4597i	0.702320	+	0.810520i	−0.286744	+	0.958007i	$0.592573\pi$
$702$	0.0587665	+	0.0678202i	0.00221800	+	0.00255971i
$703$	−12.9051	−	3.78927i	−0.486724	−	0.142915i
$704$	−4.40703	+	9.65004i	−0.166096	+	0.363700i
$705$	23.9810	+	15.4116i	0.903175	+	0.580436i
$706$	0.0540640	−	0.0158746i	0.00203473	−	0.000597450i
$707$	−2.66073	+	18.5058i	−0.100067	+	0.695983i
$708$	11.9314	+	26.1262i	0.448411	+	0.981883i
$709$	−0.224490	−	1.56136i	−0.00843091	−	0.0586383i	0.985172	−	0.171572i	$-0.0548845\pi$
$709$	−0.224490	−	1.56136i	−0.00843091	−	0.0586383i	−0.993603	+	0.112933i	$0.963975\pi$
$710$	0.148575	−	0.0954834i	0.00557592	−	0.00358343i
$711$	−8.23289	+	9.50126i	−0.308758	+	0.356325i
$712$	−0.500746			−0.0187662
$713$	−12.1895	−	0.946289i	−0.456502	−	0.0354388i
$714$	0.123796			0.00463297
$715$	−6.30520	+	7.27658i	−0.235801	+	0.272129i
$716$	18.3194	−	11.7732i	0.684628	−	0.439984i
$717$	−1.71231	−	11.9094i	−0.0639472	−	0.444763i
$718$	0.279643	+	0.612333i	0.0104362	+	0.0228521i
$719$	−6.64617	+	46.2251i	−0.247860	+	1.72391i	0.362674	+	0.931916i	$0.381864\pi$
$719$	−6.64617	+	46.2251i	−0.247860	+	1.72391i	−0.610535	+	0.791990i	$0.709045\pi$
$720$	−15.0624	+	4.42273i	−0.561343	+	0.164825i
$721$	1.83259	+	1.17774i	0.0682493	+	0.0438612i
$722$	0.116827	−	0.255815i	0.00434785	−	0.00952046i
$723$	20.9198	+	6.14262i	0.778017	+	0.228446i
$724$	10.6651	+	12.3082i	0.396367	+	0.457432i
$725$	1.55609	+	1.79583i	0.0577918	+	0.0666953i
$726$	−0.433596	−	0.127315i	−0.0160923	−	0.00472511i
$727$	15.1003	−	33.0651i	0.560041	−	1.22632i	−0.391892	−	0.920011i	$-0.628179\pi$
$727$	15.1003	−	33.0651i	0.560041	−	1.22632i	0.951933	−	0.306307i	$-0.0990934\pi$
$728$	−0.301791	−	0.193950i	−0.0111851	−	0.00718825i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.0877174	−	0.610088i	0.00324656	−	0.0225804i
$731$	6.31951	+	13.8378i	0.233736	+	0.511810i
$732$	−0.224997	−	1.56489i	−0.00831614	−	0.0578400i
$733$	−26.4266	+	16.9833i	−0.976087	+	0.627293i	−0.928405	−	0.371569i	$-0.878820\pi$
$733$	−26.4266	+	16.9833i	−0.976087	+	0.627293i	−0.0476820	+	0.998863i	$0.515183\pi$
$734$	−0.685900	+	0.791571i	−0.0253170	+	0.0292174i
$735$	3.93878			0.145284
$736$	0.183916	+	2.81144i	0.00677923	+	0.103631i
$737$	15.8710			0.584614
$738$	0.0255817	−	0.0295228i	0.000941675	−	0.00108675i
$739$	5.71274	−	3.67136i	0.210147	−	0.135053i	−0.431334	−	0.902192i	$-0.641957\pi$
$739$	5.71274	−	3.67136i	0.210147	−	0.135053i	0.641480	+	0.767139i	$0.278321\pi$
$740$	4.13512	+	28.7604i	0.152010	+	1.05725i
$741$	2.76889	+	6.06302i	0.101718	+	0.222730i
$742$	0.0481280	−	0.334738i	0.00176684	−	0.0122886i
$743$	48.4579	−	14.2285i	1.77775	−	0.521994i	0.782791	−	0.622284i	$-0.213795\pi$
$743$	48.4579	−	14.2285i	1.77775	−	0.521994i	0.994958	+	0.100290i	$0.0319770\pi$
$744$	−0.420399	−	0.270174i	−0.0154126	−	0.00990506i
$745$	18.9896	−	41.5814i	0.695725	−	1.52343i
$746$	−1.03723	−	0.304559i	−0.0379758	−	0.0111507i
$747$	−1.49200	−	1.72186i	−0.0545896	−	0.0629997i
$748$	4.41135	+	5.09097i	0.161295	+	0.186144i
$749$	−12.0851	−	3.54849i	−0.441578	−	0.129659i
$750$	−0.442401	+	0.968724i	−0.0161542	+	0.0353728i
$751$	16.0042	+	10.2853i	0.584001	+	0.375315i	0.799028	−	0.601293i	$-0.205348\pi$
$751$	16.0042	+	10.2853i	0.584001	+	0.375315i	−0.215027	+	0.976608i	$0.568984\pi$
$752$	−27.6765	+	8.12656i	−1.00926	+	0.296345i
$753$	0.974866	−	6.78034i	0.0355261	−	0.247089i
$754$	0.00842525	+	0.0184487i	0.000306829	+	0.000671863i
$755$	11.2850	+	78.4891i	0.410704	+	2.85651i
$756$	1.68048	−	1.07998i	0.0611186	−	0.0392786i
$757$	8.74920	−	10.0971i	0.317995	−	0.366986i	−0.574138	−	0.818759i	$-0.694663\pi$
$757$	8.74920	−	10.0971i	0.317995	−	0.366986i	0.892133	+	0.451773i	$0.149208\pi$
$758$	0.377923			0.0137268
$759$	−6.26764	+	1.32361i	−0.227501	+	0.0480440i
$760$	2.81201			0.102002
$761$	3.69225	−	4.26109i	0.133844	−	0.154464i	−0.684871	−	0.728664i	$-0.740141\pi$
$761$	3.69225	−	4.26109i	0.133844	−	0.154464i	0.818715	+	0.574200i	$0.194687\pi$
$762$	−0.862991	+	0.554611i	−0.0312629	+	0.0200914i
$763$	−2.36372	−	16.4401i	−0.0855725	−	0.595170i
$764$	−0.674327	−	1.47657i	−0.0243963	−	0.0534205i
$765$	−1.41518	+	9.84281i	−0.0511660	+	0.355868i
$766$	0.749266	−	0.220004i	0.0270721	−	0.00794909i
$767$	−22.1362	−	14.2261i	−0.799292	−	0.513674i
$768$	6.56688	−	14.3795i	0.236962	−	0.518874i
$769$	−32.2690	−	9.47503i	−1.16365	−	0.341678i	−0.357799	−	0.933798i	$-0.616473\pi$
$769$	−32.2690	−	9.47503i	−1.16365	−	0.341678i	−0.805850	+	0.592120i	$0.798291\pi$
$770$	−0.168940	−	0.194967i	−0.00608818	−	0.00702613i
$771$	1.16633	+	1.34602i	0.0420045	+	0.0484758i
$772$	−15.2289	−	4.47162i	−0.548102	−	0.160937i
$773$	−10.8650	+	23.7911i	−0.390788	+	0.855706i	0.607334	+	0.794447i	$0.292239\pi$
$773$	−10.8650	+	23.7911i	−0.390788	+	0.855706i	−0.998122	+	0.0612594i	$0.980488\pi$
$774$	−0.248562	−	0.159741i	−0.00893439	−	0.00574178i
$775$	25.7180	−	7.55149i	0.923818	−	0.271257i
$776$	0.160176	−	1.11405i	0.00574999	−	0.0399920i
$777$	−1.53409	−	3.35919i	−0.0550352	−	0.120510i
$778$	0.265091	+	1.84375i	0.00950397	+	0.0661016i
$779$	2.44089	−	1.56867i	0.0874541	−	0.0562033i
$780$	9.42957	−	10.8823i	0.337633	−	0.389649i
$781$	−1.22142			−0.0437058
$782$	0.555003	+	0.210855i	0.0198469	+	0.00754017i
$783$	−0.226006			−0.00807678
$784$	−2.61000	+	3.01210i	−0.0932143	+	0.107575i
$785$	−56.8339	+	36.5250i	−2.02849	+	1.30363i
$786$	−0.0811427	−	0.564360i	−0.00289426	−	0.0201300i
$787$	1.60763	+	3.52022i	0.0573059	+	0.125482i	0.936119	−	0.351685i	$-0.114391\pi$
$787$	1.60763	+	3.52022i	0.0573059	+	0.125482i	−0.878813	+	0.477167i	$0.841664\pi$
$788$	6.76320	−	47.0391i	0.240929	−	1.67570i
$789$	−20.8562	+	6.12392i	−0.742499	+	0.218017i
$790$	−2.04268	−	1.31275i	−0.0726752	−	0.0467055i
$791$	−7.82876	+	17.1426i	−0.278359	+	0.609521i
$792$	−0.251225	−	0.0737663i	−0.00892689	−	0.00262117i
$793$	0.948511	+	1.09464i	0.0336826	+	0.0388718i
$794$	1.03812	+	1.19805i	0.0368415	+	0.0425173i
$795$	26.0642	+	7.65313i	0.924401	+	0.271428i
$796$	5.52769	−	12.1039i	0.195924	−	0.429013i
$797$	8.50406	+	5.46523i	0.301229	+	0.193588i	0.682520	−	0.730867i	$-0.260884\pi$
$797$	8.50406	+	5.46523i	0.301229	+	0.193588i	−0.381291	+	0.924455i	$0.624520\pi$
$798$	−0.171356	+	0.0503146i	−0.00606593	+	0.00178112i
$799$	−2.60033	+	18.0857i	−0.0919932	+	0.639827i
$800$	−2.56591	−	5.61856i	−0.0907187	−	0.198646i
$801$	0.363547	+	2.52853i	0.0128453	+	0.0893411i
$802$	−0.674013	+	0.433162i	−0.0238002	+	0.0152955i
$803$	−2.79145	+	3.22150i	−0.0985081	+	0.113684i
$804$	−23.7354			−0.837082
$805$	17.6583	+	6.70869i	0.622373	+	0.236450i
$806$	0.228775			0.00805827
$807$	0.183005	−	0.211199i	0.00644208	−	0.00743456i
$808$	−3.08308	+	1.98137i	−0.108462	+	0.0697045i
$809$	1.48229	+	10.3095i	0.0521144	+	0.362464i	0.999146	+	0.0413229i	$0.0131572\pi$
$809$	1.48229	+	10.3095i	0.0521144	+	0.362464i	−0.947031	+	0.321141i	$0.895934\pi$
$810$	−0.0802327	−	0.175685i	−0.00281909	−	0.00617294i
$811$	−4.05632	+	28.2123i	−0.142437	+	0.990669i	0.785747	+	0.618548i	$0.212279\pi$
$811$	−4.05632	+	28.2123i	−0.142437	+	0.990669i	−0.928184	+	0.372121i	$0.878631\pi$
$812$	0.433180	−	0.127193i	0.0152016	−	0.00446361i
$813$	15.1945	+	9.76493i	0.532895	+	0.342471i
$814$	−0.100479	+	0.220017i	−0.00352177	+	0.00771161i
$815$	−68.3358	−	20.0652i	−2.39370	−	0.702854i
$816$	−6.58933	−	7.60449i	−0.230673	−	0.266210i
$817$	−14.3714	−	16.5855i	−0.502792	−	0.580253i
$818$	−1.07786	−	0.316489i	−0.0376866	−	0.0110658i
$819$	−0.760249	+	1.66471i	−0.0265652	+	0.0581698i
$820$	−5.27313	−	3.38884i	−0.184146	−	0.118343i
$821$	21.6405	−	6.35423i	0.755259	−	0.221764i	0.118634	−	0.992938i	$-0.462148\pi$
$821$	21.6405	−	6.35423i	0.755259	−	0.221764i	0.636624	+	0.771174i	$0.280330\pi$
$822$	0.114328	−	0.795167i	0.00398764	−	0.0277346i
$823$	−18.9097	−	41.4064i	−0.659150	−	1.44334i	−0.883312	−	0.468785i	$-0.844692\pi$
$823$	−18.9097	−	41.4064i	−0.659150	−	1.44334i	0.224162	−	0.974552i	$-0.428035\pi$
$824$	0.0607709	+	0.422671i	0.00211705	+	0.0147244i
$825$	11.8143	−	7.59260i	0.411322	−	0.264340i
$826$	0.461700	−	0.532830i	0.0160646	−	0.0185395i
$827$	−33.0056			−1.14772			−0.573858	−	0.818955i	$-0.694554\pi$
$827$	−33.0056			−1.14772			−0.573858	+	0.818955i	$0.694554\pi$
$828$	9.37340	−	1.97949i	0.325748	−	0.0687920i
$829$	−51.0006			−1.77132			−0.885662	−	0.464330i	$-0.846295\pi$
$829$	−51.0006			−1.77132			−0.885662	+	0.464330i	$0.846295\pi$
$830$	0.288164	−	0.332559i	0.0100023	−	0.0115433i
$831$	8.25249	−	5.30355i	0.286276	−	0.183978i
$832$	2.06858	+	14.3873i	0.0717152	+	0.498790i
$833$	1.04878	+	2.29650i	0.0363379	+	0.0795690i
$834$	0.117464	−	0.816983i	0.00406746	−	0.0282898i
$835$	31.9653	−	9.38586i	1.10621	−	0.324811i
$836$	−8.17520	−	5.25388i	−0.282745	−	0.181709i
$837$	−1.05904	+	2.31896i	−0.0366056	+	0.0801551i
$838$	−1.26826	−	0.372394i	−0.0438113	−	0.0128641i
$839$	−8.91535	−	10.2889i	−0.307792	−	0.355211i	0.580688	−	0.814126i	$-0.302784\pi$
$839$	−8.91535	−	10.2889i	−0.307792	−	0.355211i	−0.888480	+	0.458915i	$0.848238\pi$
$840$	0.505612	+	0.583507i	0.0174453	+	0.0201329i
$841$	27.7763	+	8.15585i	0.957803	+	0.281236i
$842$	−0.419791	+	0.919214i	−0.0144669	+	0.0316782i
$843$	−3.53118	−	2.26935i	−0.121620	−	0.0781607i
$844$	4.46985	−	1.31247i	0.153858	−	0.0451769i
$845$	5.40970	−	37.6253i	0.186099	−	1.29435i
$846$	−0.147424	−	0.322813i	−0.00506854	−	0.0110986i
$847$	−1.31155	−	9.12206i	−0.0450655	−	0.313438i
$848$	−23.1238	+	14.8607i	−0.794074	+	0.510320i
$849$	−10.3662	+	11.9632i	−0.355765	+	0.410575i
$850$	−1.30159			−0.0446443
$851$	−1.15610	−	17.6728i	−0.0396307	−	0.605816i
$852$	1.82666			0.0625803
$853$	−21.5280	+	24.8447i	−0.737106	+	0.850666i	−0.993252	−	0.115972i	$-0.963002\pi$
$853$	−21.5280	+	24.8447i	−0.737106	+	0.850666i	0.256146	+	0.966638i	$0.417547\pi$
$854$	−0.0326478	+	0.0209815i	−0.00111719	+	0.000717971i
$855$	−2.04156	−	14.1993i	−0.0698197	−	0.485607i
$856$	−1.02564	−	2.24584i	−0.0350557	−	0.0767613i
$857$	−2.69059	+	18.7134i	−0.0919087	+	0.639239i	0.890843	+	0.454311i	$0.150114\pi$
$857$	−2.69059	+	18.7134i	−0.0919087	+	0.639239i	−0.982752	+	0.184928i	$0.940795\pi$
$858$	0.115010	−	0.0337701i	0.00392639	−	0.00115289i
$859$	39.0065	+	25.0679i	1.33088	+	0.855307i	0.996206	−	0.0870261i	$-0.0277364\pi$
$859$	39.0065	+	25.0679i	1.33088	+	0.855307i	0.334677	+	0.942333i	$0.391373\pi$
$860$	−19.6948	+	43.1257i	−0.671588	+	1.47057i
$861$	0.764389	+	0.224445i	0.0260503	+	0.00764906i
$862$	0.695301	+	0.802420i	0.0236820	+	0.0273305i
$863$	12.9390	+	14.9324i	0.440449	+	0.508305i	0.931957	−	0.362568i	$-0.118100\pi$
$863$	12.9390	+	14.9324i	0.440449	+	0.508305i	−0.491509	+	0.870873i	$0.663554\pi$
$864$	0.563682	+	0.165512i	0.0191768	+	0.00563083i
$865$	4.07172	−	8.91582i	0.138443	−	0.303147i
$866$	1.32171	+	0.849409i	0.0449134	+	0.0288641i
$867$	10.1957	−	2.99374i	0.346265	−	0.101673i
$868$	0.724746	−	5.04072i	0.0245995	−	0.171093i
$869$	6.97590	+	15.2751i	0.236641	+	0.518172i
$870$	−0.00621210	−	0.0432061i	−0.000210610	−	0.00146482i
$871$	18.2932	−	11.7563i	0.619841	−	0.398347i
$872$	2.13207	−	2.46054i	0.0722011	−	0.0833245i
$873$	−5.74171			−0.194327
$874$	−0.853918	−	0.0662907i	−0.0288842	−	0.00224231i
$875$	−21.7183			−0.734214
$876$	4.17468	−	4.81783i	0.141049	−	0.162779i
$877$	13.7889	−	8.86161i	0.465619	−	0.299235i	−0.286716	−	0.958016i	$-0.592564\pi$
$877$	13.7889	−	8.86161i	0.465619	−	0.299235i	0.752335	+	0.658780i	$0.228927\pi$
$878$	−0.234559	−	1.63139i	−0.00791598	−	0.0550569i
$879$	−2.48112	−	5.43289i	−0.0836860	−	0.183247i
$880$	−2.98413	+	20.7551i	−0.100595	+	0.699654i
$881$	0.113455	−	0.0333135i	0.00382241	−	0.00112236i	−0.279821	−	0.960052i	$-0.590275\pi$
$881$	0.113455	−	0.0333135i	0.00382241	−	0.00112236i	0.283643	+	0.958930i	$0.408457\pi$
$882$	−0.0412510	−	0.0265104i	−0.00138899	−	0.000892652i
$883$	15.9918	−	35.0172i	0.538168	−	1.17842i	−0.423924	−	0.905698i	$-0.639347\pi$
$883$	15.9918	−	35.0172i	0.538168	−	1.17842i	0.962092	−	0.272726i	$-0.0879253\pi$
$884$	8.85571	+	2.60027i	0.297850	+	0.0874566i
$885$	37.0863	+	42.7999i	1.24664	+	1.43870i
$886$	0.490745	+	0.566350i	0.0164869	+	0.0190269i
$887$	4.49889	+	1.32099i	0.151058	+	0.0443546i	0.356387	−	0.934338i	$-0.384008\pi$
$887$	4.49889	+	1.32099i	0.151058	+	0.0443546i	−0.205329	+	0.978693i	$0.565827\pi$
$888$	0.300717	−	0.658478i	0.0100914	−	0.0220971i
$889$	−17.5994	−	11.3105i	−0.590266	−	0.379341i
$890$	−0.473393	+	0.139001i	−0.0158682	+	0.00465931i
$891$	−0.190092	+	1.32212i	−0.00636833	+	0.0442927i
$892$	−8.10185	−	17.7406i	−0.271270	−	0.593999i
$893$	−3.75126	−	26.0906i	−0.125531	−	0.873089i
$894$	−0.478747	+	0.307672i	−0.0160117	+	0.0102901i
$895$	28.1182	−	32.4501i	0.939887	−	1.08469i
$896$	−1.56441			−0.0522633
$897$	−6.24375	+	6.16833i	−0.208473	+	0.205955i
$898$	1.02030			0.0340480
$899$	−0.377308	+	0.435437i	−0.0125839	+	0.0145226i
$900$	−17.6686	+	11.3549i	−0.588953	+	0.378497i
$901$	2.47794	+	17.2345i	0.0825522	+	0.574163i
$902$	−0.0216759	−	0.0474636i	−0.000721728	−	0.00158036i
$903$	0.857533	−	5.96428i	0.0285369	−	0.198479i
$904$	−3.54453	+	1.04077i	−0.117889	+	0.0346155i
$905$	27.0146	+	17.3612i	0.897996	+	0.577107i
$906$	0.410091	−	0.897974i	0.0136244	−	0.0298332i
$907$	−31.6414	−	9.29076i	−1.05064	−	0.308495i	−0.289562	−	0.957159i	$-0.593510\pi$
$907$	−31.6414	−	9.29076i	−1.05064	−	0.308495i	−0.761074	+	0.648665i	$0.775328\pi$
$908$	−27.3371	−	31.5487i	−0.907215	−	1.04698i
$909$	12.2434	+	14.1296i	0.406086	+	0.468649i
$910$	−0.339144	−	0.0995818i	−0.0112425	−	0.00330110i
$911$	18.1594	−	39.7636i	0.601649	−	1.31743i	−0.326492	−	0.945200i	$-0.605867\pi$
$911$	18.1594	−	39.7636i	0.601649	−	1.31743i	0.928141	−	0.372228i	$-0.121406\pi$
$912$	12.2115	+	7.84783i	0.404362	+	0.259868i
$913$	−2.91996	+	0.857378i	−0.0966367	+	0.0283751i
$914$	−0.0190816	+	0.132716i	−0.000631164	+	0.00438984i
$915$	−1.29498	−	2.83561i	−0.0428108	−	0.0937425i
$916$	−8.24137	−	57.3200i	−0.272302	−	1.89391i
$917$	9.78179	−	6.28638i	0.323023	−	0.207594i
$918$	0.0810694	−	0.0935591i	0.00267569	−	0.00308791i
$919$	46.4640			1.53270			0.766352	−	0.642421i	$-0.222070\pi$
$919$	46.4640			1.53270			0.766352	+	0.642421i	$0.222070\pi$
$920$	1.27290	+	3.47715i	0.0419662	+	0.114638i
$921$	28.0770			0.925169
$922$	0.185989	−	0.214643i	0.00612523	−	0.00706889i
$923$	−1.40783	+	0.904758i	−0.0463393	+	0.0297805i
$924$	−0.379728	−	2.64106i	−0.0124921	−	0.0868846i
$925$	16.1294	+	35.3185i	0.530332	+	1.16126i
$926$	−0.177442	+	1.23413i	−0.00583109	+	0.0405561i
$927$	2.09017	−	0.613728i	0.0686501	−	0.0201575i
$928$	0.111696	+	0.0717828i	0.00366661	+	0.00235639i
$929$	17.6547	−	38.6584i	0.579232	−	1.26834i	−0.362503	−	0.931983i	$-0.618078\pi$
$929$	17.6547	−	38.6584i	0.579232	−	1.26834i	0.941734	−	0.336358i	$-0.109195\pi$
$930$	−0.472432	−	0.138719i	−0.0154917	−	0.00454876i
$931$	−2.38505	−	2.75250i	−0.0781670	−	0.0902095i
$932$	13.3809	+	15.4424i	0.438306	+	0.505832i
$933$	23.6464	+	6.94321i	0.774148	+	0.227310i
$934$	−0.465094	+	1.01841i	−0.0152183	+	0.0333235i
$935$	11.1739	+	7.18101i	0.365425	+	0.234844i
$936$	−0.344209	+	0.101069i	−0.0112508	+	0.00330354i
$937$	0.0537934	−	0.374141i	0.00175735	−	0.0122227i	−0.988924	−	0.148423i	$-0.952580\pi$
$937$	0.0537934	−	0.374141i	0.00175735	−	0.0122227i	0.990681	+	0.136201i	$0.0434892\pi$
$938$	0.242035	+	0.529983i	0.00790273	+	0.0173046i
$939$	−2.74819	−	19.1141i	−0.0896838	−	0.623765i
$940$	−47.9043	+	30.7862i	−1.56247	+	1.00414i
$941$	−26.7609	+	30.8837i	−0.872379	+	1.00678i	0.127509	+	0.991837i	$0.459302\pi$
$941$	−26.7609	+	30.8837i	−0.872379	+	1.00678i	−0.999888	+	0.0149417i	$0.995244\pi$
$942$	0.841060			0.0274032
$943$	3.04462	+	2.30817i	0.0991463	+	0.0751643i
$944$	−57.3052			−1.86513
$945$	2.57935	−	2.97673i	0.0839063	−	0.0968331i
$946$	−0.332009	+	0.213369i	−0.0107945	+	0.00693723i
$947$	0.724926	+	5.04197i	0.0235569	+	0.163842i	0.998204	−	0.0599056i	$-0.0190800\pi$
$947$	0.724926	+	5.04197i	0.0235569	+	0.163842i	−0.974647	+	0.223748i	$0.928171\pi$
$948$	−10.4326	−	22.8442i	−0.338836	−	0.741947i
$949$	−0.831170	+	5.78092i	−0.0269809	+	0.187656i
$950$	1.80163	−	0.529007i	0.0584526	−	0.0171632i
$951$	−16.1472	−	10.3772i	−0.523608	−	0.336503i
$952$	−0.205584	+	0.450166i	−0.00666301	+	0.0145900i
$953$	49.4403	+	14.5170i	1.60153	+	0.470252i	0.955972	−	0.293460i	$-0.0948066\pi$
$953$	49.4403	+	14.5170i	1.60153	+	0.470252i	0.645558	+	0.763711i	$0.276625\pi$
$954$	−0.221461	−	0.255579i	−0.00717006	−	0.00827469i
$955$	−2.09600	−	2.41891i	−0.0678250	−	0.0782742i
$956$	23.0611	+	6.77136i	0.745850	+	0.219001i
$957$	−0.125405	+	0.274599i	−0.00405378	+	0.00887654i
$958$	1.13998	+	0.732623i	0.0368312	+	0.0236700i
$959$	15.7194	−	4.61563i	0.507605	−	0.149046i
$960$	4.45206	−	30.9647i	0.143690	−	0.999383i
$961$	−10.1780	−	22.2868i	−0.328323	−	0.718928i
$962$	0.0471629	+	0.328025i	0.00152059	+	0.0105760i
$963$	−10.5958	+	6.80951i	−0.341445	+	0.219433i
$964$	−28.5215	+	32.9156i	−0.918617	+	1.06014i
$965$	−31.2955			−1.00744
$966$	−0.139782	−	0.189112i	−0.00449742	−	0.00608456i
$967$	−21.4425			−0.689543			−0.344772	−	0.938687i	$-0.612044\pi$
$967$	−21.4425			−0.689543			−0.344772	+	0.938687i	$0.612044\pi$
$968$	1.18302	−	1.36528i	0.0380236	−	0.0438816i
$969$	7.73529	−	4.97117i	0.248493	−	0.159697i
$970$	−0.157819	−	1.09766i	−0.00506728	−	0.0352437i
$971$	0.316761	+	0.693611i	0.0101654	+	0.0222590i	0.914647	−	0.404254i	$-0.132469\pi$
$971$	0.316761	+	0.693611i	0.0101654	+	0.0222590i	−0.904481	+	0.426513i	$0.859742\pi$
$972$	0.284287	−	1.97726i	0.00911853	−	0.0634207i
$973$	16.1507	−	4.74226i	0.517767	−	0.152030i
$974$	−0.701099	−	0.450569i	−0.0224647	−	0.0144372i
$975$	7.99324	−	17.5028i	0.255989	−	0.560537i
$976$	3.02658	+	0.888685i	0.0968786	+	0.0284461i
$977$	−7.10455	−	8.19908i	−0.227295	−	0.262312i	0.630635	−	0.776080i	$-0.282795\pi$
$977$	−7.10455	−	8.19908i	−0.227295	−	0.262312i	−0.857929	+	0.513768i	$0.828249\pi$
$978$	0.580633	+	0.670086i	0.0185666	+	0.0214270i
$979$	3.27391	+	0.961307i	0.104635	+	0.0307235i
$980$	−3.26852	+	7.15706i	−0.104409	+	0.228624i
$981$	−13.9725	−	8.97956i	−0.446107	−	0.286695i
$982$	1.69673	−	0.498204i	0.0541447	−	0.0158983i
$983$	3.37780	−	23.4931i	0.107735	−	0.749313i	−0.862309	−	0.506383i	$-0.830982\pi$
$983$	3.37780	−	23.4931i	0.107735	−	0.749313i	0.970044	−	0.242930i	$-0.0781087\pi$
$984$	0.0648726	+	0.142051i	0.00206806	+	0.00452843i
$985$	−13.3354	−	92.7498i	−0.424901	−	2.95525i
$986$	0.0235372	−	0.0151264i	0.000749576	−	0.000481724i
$987$	4.73944	−	5.46961i	0.150858	−	0.174099i
$988$	−13.3147			−0.423596
$989$	14.0031	−	25.2784i	0.445272	−	0.803806i
$990$	−0.257979			−0.00819910
$991$	2.47627	−	2.85777i	0.0786612	−	0.0907799i	−0.715055	−	0.699069i	$-0.753598\pi$
$991$	2.47627	−	2.85777i	0.0786612	−	0.0907799i	0.793716	+	0.608289i	$0.208144\pi$
$992$	1.25993	−	0.809710i	0.0400029	−	0.0257083i
$993$	−2.36066	−	16.4188i	−0.0749133	−	0.521033i
$994$	−0.0186269	−	0.0407871i	−0.000590808	−	0.00129369i
$995$	3.73392	−	25.9700i	0.118373	−	0.823305i
$996$	4.36687	−	1.28223i	0.138370	−	0.0406290i
$997$	−31.7363	−	20.3957i	−1.00510	−	0.645937i	−0.0689783	−	0.997618i	$-0.521974\pi$
$997$	−31.7363	−	20.3957i	−1.00510	−	0.645937i	−0.936120	+	0.351681i	$0.885610\pi$
$998$	−0.619903	+	1.35740i	−0.0196227	+	0.0429677i
$999$	−3.54333	−	1.04041i	−0.112106	−	0.0329172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.85.4	✓	80
23.13	even	11	inner	483.2.q.f.358.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.85.4	✓	80	1.1	even	1	trivial
483.2.q.f.358.4	yes	80	23.13	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0321112 - 0.0370583i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.284287 + 1.97726i) q^{4} +(1.63623 + 3.58284i) q^{5} +(0.00697843 - 0.0485360i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.164905 + 0.105978i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.0321112 - 0.0370583i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.284287 + 1.97726i) q^{4} +(1.63623 + 3.58284i) q^{5} +(0.00697843 - 0.0485360i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.164905 + 0.105978i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.185315 + 0.0544134i) q^{10} +(-0.874709 - 1.00947i) q^{11} +(1.30815 + 1.50968i) q^{12} +(-1.75596 - 0.515597i) q^{13} +(0.0203699 - 0.0446039i) q^{14} +(3.31351 + 2.12946i) q^{15} +(-3.82414 + 1.12287i) q^{16} +(-0.359295 + 2.49895i) q^{17} +(-0.0203699 - 0.0446039i) q^{18} +(-0.518322 - 3.60501i) q^{19} +(-6.61906 + 4.25381i) q^{20} +(0.654861 - 0.755750i) q^{21} -0.0654971 q^{22} +(4.22309 - 2.27278i) q^{23} +0.196023 q^{24} +(-6.88519 + 7.94594i) q^{25} +(-0.0754932 + 0.0485166i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.829831 + 1.81708i) q^{28} +(0.0321640 - 0.223705i) q^{29} +(0.185315 - 0.0544134i) q^{30} +(-2.14464 - 1.37828i) q^{31} +(-0.244048 + 0.534390i) q^{32} +(-1.28161 - 0.376315i) q^{33} +(0.0810694 + 0.0935591i) q^{34} +(2.57935 + 2.97673i) q^{35} +(1.91668 + 0.562788i) q^{36} +(1.53409 - 3.35919i) q^{37} +(-0.150239 - 0.0965530i) q^{38} +(-1.75596 + 0.515597i) q^{39} +(-0.109880 + 0.764231i) q^{40} +(0.330944 + 0.724667i) q^{41} +(-0.00697843 - 0.0485360i) q^{42} +(5.06906 - 3.25769i) q^{43} +(1.74731 - 2.01651i) q^{44} +3.93878 q^{45} +(0.0513830 - 0.229482i) q^{46} +7.23733 q^{47} +(-2.61000 + 3.01210i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.0733711 + 0.510307i) q^{50} +(1.04878 + 2.29650i) q^{51} +(0.520273 - 3.61858i) q^{52} +(6.61732 - 1.94302i) q^{53} +(-0.0412510 - 0.0265104i) q^{54} +(2.18554 - 4.78566i) q^{55} +(0.188082 + 0.0552260i) q^{56} +(-2.38505 - 2.75250i) q^{57} +(-0.00725731 - 0.00837538i) q^{58} +(13.7957 + 4.05079i) q^{59} +(-3.26852 + 7.15706i) q^{60} +(-0.665804 - 0.427886i) q^{61} +(-0.119944 + 0.0352187i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-3.29937 - 7.22462i) q^{64} +(-1.02585 - 7.13497i) q^{65} +(-0.0550997 + 0.0354104i) q^{66} +(-7.78104 + 8.97980i) q^{67} -5.04322 q^{68} +(2.32393 - 4.19516i) q^{69} +0.193139 q^{70} +(0.598824 - 0.691079i) q^{71} +(0.164905 - 0.105978i) q^{72} +(-0.454168 - 3.15881i) q^{73} +(-0.0752244 - 0.164719i) q^{74} +(-1.49630 + 10.4070i) q^{75} +(6.98070 - 2.04972i) q^{76} +(-1.12368 - 0.722143i) q^{77} +(-0.0372789 + 0.0816295i) q^{78} +(-12.0627 - 3.54193i) q^{79} +(-10.2802 - 11.8640i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(0.0374819 + 0.0110057i) q^{82} +(0.946462 - 2.07246i) q^{83} +(1.68048 + 1.07998i) q^{84} +(-9.54122 + 2.80156i) q^{85} +(0.0420493 - 0.292459i) q^{86} +(-0.0938861 - 0.205582i) q^{87} +(-0.0372624 - 0.259166i) q^{88} +(-2.14901 + 1.38108i) q^{89} +(0.126479 - 0.145964i) q^{90} -1.83009 q^{91} +(5.69446 + 7.70403i) q^{92} -2.54934 q^{93} +(0.232399 - 0.268203i) q^{94} +(12.0681 - 7.75568i) q^{95} +(0.0836070 + 0.581499i) q^{96} +(-2.38519 - 5.22284i) q^{97} +(0.00697843 - 0.0485360i) q^{98} +(-1.28161 + 0.376315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more