LMFDB - Embedded newform 414.2.m.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(-1.60283 - 0.656460i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.587955 + 0.825667i) q^{5} +(-1.14459 + 1.29997i) q^{6} +(0.631846 + 2.60451i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.13812 + 2.10439i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(-1.60283 - 0.656460i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.587955 + 0.825667i) q^{5} +(-1.14459 + 1.29997i) q^{6} +(0.631846 + 2.60451i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.13812 + 2.10439i) q^{9} +(0.972558 - 0.285569i) q^{10} +(4.21366 + 0.812116i) q^{11} +(0.854112 + 1.50682i) q^{12} +(0.329783 - 1.35938i) q^{13} +(2.66792 + 0.254755i) q^{14} +(-0.400374 - 1.70937i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.106552 - 0.741088i) q^{17} +(2.68796 - 1.33225i) q^{18} +(0.115012 - 0.799923i) q^{19} +(0.0482298 - 1.01247i) q^{20} +(0.697013 - 4.58936i) q^{21} +(2.14560 - 3.71629i) q^{22} +(2.80451 + 3.89034i) q^{23} +(1.70329 - 0.314305i) q^{24} +(1.29930 - 3.75409i) q^{25} +(-1.17676 - 0.756256i) q^{26} +(-2.04559 - 4.77656i) q^{27} +(1.11333 - 2.43786i) q^{28} +(2.88066 - 2.26538i) q^{29} +(-1.74631 - 0.180728i) q^{30} +(0.320023 + 6.71811i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(-6.22065 - 4.06778i) q^{33} +(-0.735179 - 0.141694i) q^{34} +(-1.77896 + 2.05303i) q^{35} +(-0.379830 - 2.97586i) q^{36} +(-2.92193 - 6.39814i) q^{37} +(-0.718311 - 0.370315i) q^{38} +(-1.42097 + 1.96237i) q^{39} +(-0.941009 - 0.376723i) q^{40} +(5.20925 + 7.31537i) q^{41} +(-4.10898 - 2.15971i) q^{42} +(-0.0982038 + 2.06155i) q^{43} +(-2.81014 - 3.24308i) q^{44} +(-0.480405 + 3.00266i) q^{45} +(4.59364 - 1.37786i) q^{46} +(0.747026 + 1.29389i) q^{47} +(0.260074 - 1.71241i) q^{48} +(-0.162372 + 0.0837086i) q^{49} +(-3.12266 - 2.45569i) q^{50} +(-0.315710 + 1.25779i) q^{51} +(-1.09954 + 0.864689i) q^{52} +(8.52409 + 2.50290i) q^{53} +(-5.18290 + 0.370828i) q^{54} +(1.80690 + 3.95657i) q^{55} +(-1.93964 - 1.84945i) q^{56} +(-0.709462 + 1.20664i) q^{57} +(-1.19861 - 3.46316i) q^{58} +(-1.25344 + 5.16674i) q^{59} +(-0.741949 + 1.59115i) q^{60} +(-0.00565540 - 0.00291556i) q^{61} +(6.45329 + 1.89486i) q^{62} +(-4.12992 + 6.89839i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.31630 - 0.526965i) q^{65} +(-5.87863 + 4.54808i) q^{66} +(-7.39116 + 1.42453i) q^{67} +(-0.374355 + 0.648401i) q^{68} +(-1.94130 - 8.07659i) q^{69} +(1.35827 + 2.35260i) q^{70} +(2.75020 + 3.17390i) q^{71} +(-2.93642 - 0.614368i) q^{72} +(1.29317 - 8.99417i) q^{73} +(-7.00192 + 0.668602i) q^{74} +(-4.54698 + 5.16423i) q^{75} +(-0.584885 + 0.557687i) q^{76} +(0.547223 + 11.4876i) q^{77} +(1.38969 + 1.98464i) q^{78} +(-7.62846 - 7.27372i) q^{79} +(-0.663777 + 0.766040i) q^{80} +(0.143114 + 8.99886i) q^{81} +(8.61681 - 2.53012i) q^{82} +(-6.36949 + 8.94469i) q^{83} +(-3.38484 + 3.17661i) q^{84} +(0.549244 - 0.523703i) q^{85} +(1.91605 + 0.767070i) q^{86} +(-6.10434 + 1.73997i) q^{87} +(-3.98382 + 1.59488i) q^{88} +(-8.01953 - 5.15384i) q^{89} +(2.68039 + 1.43606i) q^{90} +3.74889 q^{91} +(0.200352 - 4.79164i) q^{92} +(3.89723 - 10.9781i) q^{93} +(1.46705 - 0.282751i) q^{94} +(0.728092 - 0.375358i) q^{95} +(-1.53317 - 0.805846i) q^{96} +(-11.5216 + 1.10018i) q^{97} +(0.0259980 + 0.180820i) q^{98} +(7.30030 + 10.6036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	−1.60283	−	0.656460i	−0.925394	−	0.379007i
$3$	−1.60283	−	0.656460i	−0.925394	−	0.379007i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	0.587955	+	0.825667i	0.262941	+	0.369250i	0.924848	−	0.380337i	$-0.124192\pi$
$5$	0.587955	+	0.825667i	0.262941	+	0.369250i	−0.661907	+	0.749586i	$0.730252\pi$
$6$	−1.14459	+	1.29997i	−0.467277	+	0.530709i
$7$	0.631846	+	2.60451i	0.238815	+	0.984411i	0.957353	+	0.288922i	$0.0932969\pi$
$7$	0.631846	+	2.60451i	0.238815	+	0.984411i	−0.718537	+	0.695489i	$0.755188\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	2.13812	+	2.10439i	0.712707	+	0.701462i
$10$	0.972558	−	0.285569i	0.307550	−	0.0903047i
$11$	4.21366	+	0.812116i	1.27047	+	0.244862i	0.779547	−	0.626343i	$-0.215449\pi$
$11$	4.21366	+	0.812116i	1.27047	+	0.244862i	0.490918	+	0.871206i	$0.336661\pi$
$12$	0.854112	+	1.50682i	0.246561	+	0.434980i
$13$	0.329783	−	1.35938i	0.0914653	−	0.377025i	−0.907620	−	0.419793i	$-0.862103\pi$
$13$	0.329783	−	1.35938i	0.0914653	−	0.377025i	0.999085	+	0.0427683i	$0.0136177\pi$
$14$	2.66792	+	0.254755i	0.713031	+	0.0680862i
$15$	−0.400374	−	1.70937i	−0.103376	−	0.441358i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.106552	−	0.741088i	−0.0258428	−	0.179740i	0.972812	−	0.231597i	$-0.0743951\pi$
$17$	−0.106552	−	0.741088i	−0.0258428	−	0.179740i	−0.998655	+	0.0518569i	$0.983486\pi$
$18$	2.68796	−	1.33225i	0.633558	−	0.314014i
$19$	0.115012	−	0.799923i	0.0263855	−	0.183515i	−0.972367	−	0.233460i	$-0.924995\pi$
$19$	0.115012	−	0.799923i	0.0263855	−	0.183515i	0.998752	+	0.0499445i	$0.0159045\pi$
$20$	0.0482298	−	1.01247i	0.0107845	−	0.226395i
$21$	0.697013	−	4.58936i	0.152101	−	1.00148i
$22$	2.14560	−	3.71629i	0.457444	−	0.792316i
$23$	2.80451	+	3.89034i	0.584781	+	0.811191i
$23$	2.80451	+	3.89034i	0.584781	+	0.811191i
$24$	1.70329	−	0.314305i	0.347684	−	0.0641573i
$25$	1.29930	−	3.75409i	0.259861	−	0.750819i
$26$	−1.17676	−	0.756256i	−0.230781	−	0.148314i
$27$	−2.04559	−	4.77656i	−0.393675	−	0.919250i
$28$	1.11333	−	2.43786i	0.210400	−	0.460712i
$29$	2.88066	−	2.26538i	0.534926	−	0.420670i	−0.313811	−	0.949485i	$-0.601606\pi$
$29$	2.88066	−	2.26538i	0.534926	−	0.420670i	0.848737	+	0.528815i	$0.177364\pi$
$30$	−1.74631	−	0.180728i	−0.318831	−	0.0329962i
$31$	0.320023	+	6.71811i	0.0574778	+	1.20661i	0.824829	+	0.565382i	$0.191271\pi$
$31$	0.320023	+	6.71811i	0.0574778	+	1.20661i	−0.767352	+	0.641227i	$0.778426\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	−6.22065	−	4.06778i	−1.08288	−	0.708110i
$34$	−0.735179	−	0.141694i	−0.126082	−	0.0243003i
$35$	−1.77896	+	2.05303i	−0.300699	+	0.347025i
$36$	−0.379830	−	2.97586i	−0.0633051	−	0.495976i
$37$	−2.92193	−	6.39814i	−0.480363	−	1.05185i	−0.982364	−	0.186980i	$-0.940130\pi$
$37$	−2.92193	−	6.39814i	−0.480363	−	1.05185i	0.502001	−	0.864867i	$-0.332597\pi$
$38$	−0.718311	−	0.370315i	−0.116526	−	0.0600731i
$39$	−1.42097	+	1.96237i	−0.227537	+	0.314231i
$40$	−0.941009	−	0.376723i	−0.148787	−	0.0595651i
$41$	5.20925	+	7.31537i	0.813548	+	1.14247i	0.987485	+	0.157712i	$0.0504117\pi$
$41$	5.20925	+	7.31537i	0.813548	+	1.14247i	−0.173937	+	0.984757i	$0.555649\pi$
$42$	−4.10898	−	2.15971i	−0.634029	−	0.333250i
$43$	−0.0982038	+	2.06155i	−0.0149759	+	0.314383i	0.978933	+	0.204181i	$0.0654530\pi$
$43$	−0.0982038	+	2.06155i	−0.0149759	+	0.314383i	−0.993909	+	0.110203i	$0.964850\pi$
$44$	−2.81014	−	3.24308i	−0.423645	−	0.488912i
$45$	−0.480405	+	3.00266i	−0.0716145	+	0.447610i
$46$	4.59364	−	1.37786i	0.677295	−	0.203155i
$47$	0.747026	+	1.29389i	0.108965	+	0.188733i	0.915351	−	0.402656i	$-0.131913\pi$
$47$	0.747026	+	1.29389i	0.108965	+	0.188733i	−0.806386	+	0.591389i	$0.798580\pi$
$48$	0.260074	−	1.71241i	0.0375385	−	0.247166i
$49$	−0.162372	+	0.0837086i	−0.0231960	+	0.0119584i
$50$	−3.12266	−	2.45569i	−0.441611	−	0.347287i
$51$	−0.315710	+	1.25779i	−0.0442082	+	0.176125i
$52$	−1.09954	+	0.864689i	−0.152479	+	0.119911i
$53$	8.52409	+	2.50290i	1.17087	+	0.343800i	0.808649	−	0.588291i	$-0.200199\pi$
$53$	8.52409	+	2.50290i	1.17087	+	0.343800i	0.362225	+	0.932091i	$0.382017\pi$
$54$	−5.18290	+	0.370828i	−0.705304	+	0.0504633i
$55$	1.80690	+	3.95657i	0.243643	+	0.533504i
$56$	−1.93964	−	1.84945i	−0.259196	−	0.247143i
$57$	−0.709462	+	1.20664i	−0.0939705	+	0.159823i
$58$	−1.19861	−	3.46316i	−0.157385	−	0.454735i
$59$	−1.25344	+	5.16674i	−0.163184	+	0.672652i	0.830166	+	0.557516i	$0.188245\pi$
$59$	−1.25344	+	5.16674i	−0.163184	+	0.672652i	−0.993350	+	0.115136i	$0.963270\pi$
$60$	−0.741949	+	1.59115i	−0.0957852	+	0.205417i
$61$	−0.00565540	−	0.00291556i	−0.000724100	−	0.000373299i	0.457864	−	0.889022i	$-0.348615\pi$
$61$	−0.00565540	−	0.00291556i	−0.000724100	−	0.000373299i	−0.458589	+	0.888649i	$0.651645\pi$
$62$	6.45329	+	1.89486i	0.819568	+	0.240647i
$63$	−4.12992	+	6.89839i	−0.520321	+	0.869116i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	1.31630	−	0.526965i	0.163266	−	0.0653620i
$66$	−5.87863	+	4.54808i	−0.723610	+	0.559830i
$67$	−7.39116	+	1.42453i	−0.902974	+	0.174034i	−0.619547	−	0.784960i	$-0.712684\pi$
$67$	−7.39116	+	1.42453i	−0.902974	+	0.174034i	−0.283427	+	0.958994i	$0.591471\pi$
$68$	−0.374355	+	0.648401i	−0.0453972	+	0.0786302i
$69$	−1.94130	−	8.07659i	−0.233705	−	0.972308i
$70$	1.35827	+	2.35260i	0.162345	+	0.281189i
$71$	2.75020	+	3.17390i	0.326389	+	0.376672i	0.895101	−	0.445864i	$-0.147104\pi$
$71$	2.75020	+	3.17390i	0.326389	+	0.376672i	−0.568712	+	0.822537i	$0.692558\pi$
$72$	−2.93642	−	0.614368i	−0.346060	−	0.0724039i
$73$	1.29317	−	8.99417i	0.151354	−	1.05269i	−0.762600	−	0.646870i	$-0.776078\pi$
$73$	1.29317	−	8.99417i	0.151354	−	1.05269i	0.913954	−	0.405818i	$-0.133013\pi$
$74$	−7.00192	+	0.668602i	−0.813956	+	0.0777234i
$75$	−4.54698	+	5.16423i	−0.525039	+	0.596314i
$76$	−0.584885	+	0.557687i	−0.0670909	+	0.0639710i
$77$	0.547223	+	11.4876i	0.0623619	+	1.30914i
$78$	1.38969	+	1.98464i	0.157351	+	0.224717i
$79$	−7.62846	−	7.27372i	−0.858269	−	0.818357i	0.126547	−	0.991961i	$-0.459611\pi$
$79$	−7.62846	−	7.27372i	−0.858269	−	0.818357i	−0.984816	+	0.173603i	$0.944459\pi$
$80$	−0.663777	+	0.766040i	−0.0742126	+	0.0856459i
$81$	0.143114	+	8.99886i	0.0159016	+	0.999874i
$82$	8.61681	−	2.53012i	0.951567	−	0.279405i
$83$	−6.36949	+	8.94469i	−0.699142	+	0.981807i	0.300466	+	0.953793i	$0.402858\pi$
$83$	−6.36949	+	8.94469i	−0.699142	+	0.981807i	−0.999608	+	0.0280148i	$0.991081\pi$
$84$	−3.38484	+	3.17661i	−0.369317	+	0.346597i
$85$	0.549244	−	0.523703i	0.0595739	−	0.0568036i
$86$	1.91605	+	0.767070i	0.206613	+	0.0827153i
$87$	−6.10434	+	1.73997i	−0.654454	+	0.186545i
$88$	−3.98382	+	1.59488i	−0.424676	+	0.170015i
$89$	−8.01953	−	5.15384i	−0.850069	−	0.546306i	0.0415273	−	0.999137i	$-0.486778\pi$
$89$	−8.01953	−	5.15384i	−0.850069	−	0.546306i	−0.891596	+	0.452831i	$0.850414\pi$
$90$	2.68039	+	1.43606i	0.282538	+	0.151374i
$91$	3.74889			0.392991
$92$	0.200352	−	4.79164i	0.0208881	−	0.499563i
$93$	3.89723	−	10.9781i	0.404124	−	1.13837i
$94$	1.46705	−	0.282751i	0.151315	−	0.0291636i
$95$	0.728092	−	0.375358i	0.0747007	−	0.0385109i
$96$	−1.53317	−	0.805846i	−0.156479	−	0.0822463i
$97$	−11.5216	+	1.10018i	−1.16984	+	0.111706i	−0.661835	−	0.749649i	$-0.730222\pi$
$97$	−11.5216	+	1.10018i	−1.16984	+	0.111706i	−0.508003	+	0.861355i	$0.669616\pi$
$98$	0.0259980	+	0.180820i	0.00262620	+	0.0182656i
$99$	7.30030	+	10.6036i	0.733708	+	1.06570i
$100$	−3.34195	+	2.14774i	−0.334195	+	0.214774i
$101$	−4.19248	+	5.88752i	−0.417168	+	0.585830i	−0.968673	−	0.248342i	$-0.920114\pi$
$101$	−4.19248	+	5.88752i	−0.417168	+	0.585830i	0.551505	+	0.834172i	$0.314054\pi$
$102$	1.08535	+	0.709727i	0.107466	+	0.0702735i
$103$	−2.23095	−	6.44590i	−0.219822	−	0.635134i	−0.999955	−	0.00951979i	$-0.996970\pi$
$103$	−2.23095	−	6.44590i	−0.219822	−	0.635134i	0.780133	−	0.625614i	$-0.215152\pi$
$104$	0.457507	+	1.32188i	0.0448623	+	0.129621i
$105$	4.19910	−	2.12284i	0.409790	−	0.207168i
$106$	5.15320	−	7.23666i	0.500523	−	0.702886i
$107$	12.3023	−	7.90623i	1.18931	−	0.764324i	0.212237	−	0.977218i	$-0.431925\pi$
$107$	12.3023	−	7.90623i	1.18931	−	0.764324i	0.977075	+	0.212894i	$0.0682889\pi$
$108$	−1.34473	+	5.01913i	−0.129397	+	0.482966i
$109$	−1.32120	−	9.18917i	−0.126548	−	0.880163i	−0.949883	−	0.312607i	$-0.898798\pi$
$109$	−1.32120	−	9.18917i	−0.126548	−	0.880163i	0.823334	−	0.567557i	$-0.192111\pi$
$110$	4.32994	−	0.413459i	0.412844	−	0.0394218i
$111$	0.483233	+	12.1733i	0.0458665	+	1.15543i
$112$	−2.38213	+	1.22807i	−0.225090	+	0.116042i
$113$	−8.53344	+	1.64469i	−0.802759	+	0.154719i	−0.574097	−	0.818787i	$-0.694647\pi$
$113$	−8.53344	+	1.64469i	−0.802759	+	0.154719i	−0.228661	+	0.973506i	$0.573435\pi$
$114$	0.908233	+	1.06509i	0.0850638	+	0.0997553i
$115$	−1.56320	+	4.60294i	−0.145769	+	0.429226i
$116$	−3.66472			−0.340261
$117$	3.56578	−	2.21253i	0.329657	−	0.204549i
$118$	4.47261	+	2.87437i	0.411737	+	0.264607i
$119$	1.86284	−	0.745770i	0.170767	−	0.0683646i
$120$	1.26097	+	1.22156i	0.115110	+	0.111512i
$121$	6.88334	+	2.75567i	0.625758	+	0.250516i
$122$	−0.00460491	+	0.00439077i	−0.000416909	+	0.000397522i
$123$	−3.54729	−	15.1449i	−0.319848	−	1.36557i
$124$	3.90130	−	5.47862i	0.350348	−	0.491994i
$125$	8.72635	−	2.56229i	0.780509	−	0.229178i
$126$	5.16822	+	6.15903i	0.460422	+	0.548690i
$127$	−9.63810	+	11.1230i	−0.855243	+	0.987003i	−0.999997	−	0.00246436i	$-0.999216\pi$
$127$	−9.63810	+	11.1230i	−0.855243	+	0.987003i	0.144754	+	0.989468i	$0.453761\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	1.51073	−	3.23985i	0.133012	−	0.285252i
$130$	−0.0674645	−	1.41625i	−0.00591703	−	0.124214i
$131$	0.820246	−	0.782103i	0.0716652	−	0.0683326i	−0.653400	−	0.757013i	$-0.726658\pi$
$131$	0.820246	−	0.782103i	0.0716652	−	0.0683326i	0.725065	+	0.688680i	$0.241810\pi$
$132$	2.37523	+	7.04284i	0.206737	+	0.613001i
$133$	2.15607	−	0.205880i	0.186955	−	0.0178521i
$134$	−1.07123	+	7.45057i	−0.0925402	+	0.643631i
$135$	2.74113	−	4.49738i	0.235919	−	0.387073i
$136$	0.490300	+	0.565837i	0.0420429	+	0.0485201i
$137$	−10.1373	−	17.5583i	−0.866089	−	1.50011i	−0.865962	−	0.500110i	$-0.833293\pi$
$137$	−10.1373	−	17.5583i	−0.866089	−	1.50011i	−0.000126540	−	1.00000i	$-0.500040\pi$
$138$	−8.26732	−	0.807064i	−0.703761	−	0.0687019i
$139$	5.66942	−	9.81972i	0.480874	−	0.832898i	−0.518885	−	0.854844i	$-0.673653\pi$
$139$	5.66942	−	9.81972i	0.480874	−	0.832898i	0.999759	+	0.0219458i	$0.00698611\pi$
$140$	2.66745	−	0.514109i	0.225441	−	0.0434502i
$141$	−0.347969	−	2.56427i	−0.0293043	−	0.215951i
$142$	3.89884	−	1.56086i	0.327183	−	0.130984i
$143$	2.49357	−	5.46015i	0.208523	−	0.456601i
$144$	−1.54099	+	2.57398i	−0.128416	+	0.214498i
$145$	3.56415	+	1.04653i	0.295986	+	0.0869095i
$146$	−8.07654	−	4.16375i	−0.668419	−	0.344594i
$147$	0.315206	−	0.0275798i	0.0259978	−	0.00227474i
$148$	−1.65827	+	6.83549i	−0.136309	+	0.561874i
$149$	2.01196	+	5.81317i	0.164826	+	0.476233i	0.996922	−	0.0783980i	$-0.0249805\pi$
$149$	2.01196	+	5.81317i	0.164826	+	0.476233i	−0.832096	+	0.554631i	$0.812859\pi$
$150$	3.39303	+	5.98595i	0.277040	+	0.488751i
$151$	14.0050	+	13.3537i	1.13971	+	1.08671i	0.995265	+	0.0971953i	$0.0309872\pi$
$151$	14.0050	+	13.3537i	1.13971	+	1.08671i	0.144442	+	0.989513i	$0.453861\pi$
$152$	0.335717	+	0.735118i	0.0272303	+	0.0596260i
$153$	1.33171	−	1.80876i	0.107663	−	0.146230i
$154$	11.0348	+	3.24011i	0.889209	+	0.261095i
$155$	−5.35876	+	4.21418i	−0.430426	+	0.338491i
$156$	2.33001	−	0.664143i	0.186550	−	0.0531740i
$157$	12.8602	+	10.1134i	1.02636	+	0.807136i	0.981423	−	0.191854i	$-0.0614501\pi$
$157$	12.8602	+	10.1134i	1.02636	+	0.807136i	0.0449332	+	0.998990i	$0.485693\pi$
$158$	−9.36870	+	4.82990i	−0.745333	+	0.384246i
$159$	−12.0196	−	9.60745i	−0.953217	−	0.761920i
$160$	0.506808	+	0.877817i	0.0400667	+	0.0693976i
$161$	−8.36038	+	9.76246i	−0.658890	+	0.769390i
$162$	8.55074	+	2.80800i	0.671810	+	0.220617i
$163$	−11.6882	−	13.4889i	−0.915492	−	1.05653i	−0.998201	−	0.0599601i	$-0.980903\pi$
$163$	−11.6882	−	13.4889i	−0.915492	−	1.05653i	0.0827090	−	0.996574i	$-0.473643\pi$
$164$	0.427313	−	8.97041i	0.0333676	−	0.700472i
$165$	−0.298828	−	7.52786i	−0.0232638	−	0.586043i
$166$	6.36949	+	8.94469i	0.494368	+	0.694243i
$167$	−22.9515	−	9.18840i	−1.77604	−	0.711020i	−0.996398	−	0.0847962i	$-0.972976\pi$
$167$	−22.9515	−	9.18840i	−1.77604	−	0.711020i	−0.779643	−	0.626224i	$-0.784600\pi$
$168$	1.89483	+	4.23765i	0.146189	+	0.326942i
$169$	9.81569	+	5.06034i	0.755053	+	0.389257i
$170$	−0.315260	−	0.690323i	−0.0241793	−	0.0529454i
$171$	1.92926	−	1.46830i	0.147534	−	0.112284i
$172$	1.35156	−	1.55978i	0.103055	−	0.118932i
$173$	−9.03048	−	1.74048i	−0.686575	−	0.132326i	−0.165978	−	0.986129i	$-0.553078\pi$
$173$	−9.03048	−	1.74048i	−0.686575	−	0.132326i	−0.520596	+	0.853803i	$0.674290\pi$
$174$	−0.352258	+	6.33770i	−0.0267046	+	0.480459i
$175$	10.5985	+	1.01204i	0.801173	+	0.0765027i
$176$	0.204184	+	4.28635i	0.0153909	+	0.323095i
$177$	5.40080	−	7.45856i	0.405949	−	0.560620i
$178$	−7.49332	+	5.89281i	−0.561648	+	0.441685i
$179$	10.4189	−	22.8142i	0.778746	−	1.70522i	0.0723713	−	0.997378i	$-0.476943\pi$
$179$	10.4189	−	22.8142i	0.778746	−	1.70522i	0.706375	−	0.707838i	$-0.250329\pi$
$180$	2.23375	−	2.06328i	0.166494	−	0.153788i
$181$	−19.1610	−	12.3140i	−1.42423	−	0.915295i	−0.999952	−	0.00976140i	$-0.996893\pi$
$181$	−19.1610	−	12.3140i	−1.42423	−	0.915295i	−0.424275	−	0.905534i	$-0.639471\pi$
$182$	1.22614	−	3.54271i	0.0908878	−	0.262603i
$183$	0.00715069	+	0.00838569i	0.000528594	+	0.000619888i
$184$	−4.46258	−	1.75653i	−0.328986	−	0.129493i
$185$	3.56477	−	6.17436i	0.262087	−	0.453948i
$186$	−9.09962	−	7.27346i	−0.667216	−	0.533316i
$187$	0.152874	−	3.20923i	0.0111793	−	0.234682i
$188$	0.212626	−	1.47884i	0.0155073	−	0.107856i
$189$	11.1481	−	8.34581i	0.810904	−	0.607069i
$190$	−0.116578	−	0.810815i	−0.00845743	−	0.0588227i
$191$	1.70605	+	7.03243i	0.123445	+	0.508849i	0.999638	+	0.0268886i	$0.00855994\pi$
$191$	1.70605	+	7.03243i	0.123445	+	0.508849i	−0.876193	+	0.481960i	$0.839925\pi$
$192$	−1.26298	+	1.18528i	−0.0911475	+	0.0855403i
$193$	−15.6749	−	1.49677i	−1.12830	−	0.107740i	−0.485832	−	0.874052i	$-0.661483\pi$
$193$	−15.6749	−	1.49677i	−1.12830	−	0.107740i	−0.642468	+	0.766312i	$0.722090\pi$
$194$	−2.72867	+	11.2477i	−0.195907	+	0.807540i
$195$	−2.45573	−	0.0194606i	−0.175858	−	0.00139360i
$196$	0.179378	+	0.0345723i	0.0128127	+	0.00246945i
$197$	18.9585	−	5.56673i	1.35074	−	0.396613i	0.475250	−	0.879851i	$-0.342358\pi$
$197$	18.9585	−	5.56673i	1.35074	−	0.396613i	0.875489	+	0.483238i	$0.160539\pi$
$198$	12.4081	−	3.43070i	0.881803	−	0.243809i
$199$	−4.92387	+	3.16438i	−0.349044	+	0.224317i	−0.703401	−	0.710793i	$-0.748336\pi$
$199$	−4.92387	+	3.16438i	−0.349044	+	0.224317i	0.354357	+	0.935110i	$0.384700\pi$
$200$	0.936572	+	3.86060i	0.0662256	+	0.272986i
$201$	12.7819	+	2.56873i	0.901566	+	0.181184i
$202$	4.19248	+	5.88752i	0.294982	+	0.414244i
$203$	7.72033	+	6.07133i	0.541861	+	0.426124i
$204$	1.02568	−	0.793527i	0.0718117	−	0.0555580i
$205$	−2.97726	+	8.60222i	−0.207941	+	0.600805i
$206$	−6.82106			−0.475246
$207$	−2.19039	+	14.2198i	−0.152243	+	0.988343i
$208$	1.39881			0.0969903
$209$	1.13425	−	3.27720i	0.0784577	−	0.226689i
$210$	−0.632692	−	4.66246i	−0.0436599	−	0.321740i
$211$	6.61483	+	5.20196i	0.455384	+	0.358118i	0.819349	−	0.573295i	$-0.194335\pi$
$211$	6.61483	+	5.20196i	0.455384	+	0.358118i	−0.363966	+	0.931412i	$0.618577\pi$
$212$	−5.15320	−	7.23666i	−0.353923	−	0.497016i
$213$	−2.32456	−	6.89261i	−0.159276	−	0.472274i
$214$	−3.44770	−	14.2116i	−0.235680	−	0.971485i
$215$	−1.75989	+	1.13102i	−0.120024	+	0.0771346i
$216$	4.30327	+	2.91237i	0.292800	+	0.198162i
$217$	−17.2951	+	5.07831i	−1.17407	+	0.344738i
$218$	−9.11590	−	1.75695i	−0.617407	−	0.118995i
$219$	−7.97703	+	13.5672i	−0.539038	+	0.916786i
$220$	1.02547	−	4.22703i	0.0691369	−	0.284986i
$221$	−1.04256	−	0.0995526i	−0.0701303	−	0.00669663i
$222$	11.6618	+	3.52482i	0.782688	+	0.236571i
$223$	0.175211	+	0.722229i	0.0117330	+	0.0483640i	0.977377	−	0.211504i	$-0.0678361\pi$
$223$	0.175211	+	0.722229i	0.0117330	+	0.0483640i	−0.965644	+	0.259868i	$0.916321\pi$
$224$	0.381411	+	2.65277i	0.0254841	+	0.177246i
$225$	10.6781	−	5.29246i	0.711876	−	0.352831i
$226$	−1.23679	+	8.60203i	−0.0822698	+	0.572199i
$227$	0.646770	−	13.5774i	0.0429277	−	0.901162i	−0.870003	−	0.493047i	$-0.835883\pi$
$227$	0.646770	−	13.5774i	0.0429277	−	0.901162i	0.912930	−	0.408115i	$-0.133814\pi$
$228$	1.30357	−	0.509923i	0.0863310	−	0.0337704i
$229$	5.31164	−	9.20004i	0.351003	−	0.607956i	−0.635422	−	0.772165i	$-0.719174\pi$
$229$	5.31164	−	9.20004i	0.351003	−	0.607956i	0.986426	+	0.164209i	$0.0525073\pi$
$230$	3.83851	+	2.98270i	0.253104	+	0.196673i
$231$	6.66407	−	18.7719i	0.438463	−	1.23510i
$232$	−1.19861	+	3.46316i	−0.0786927	+	0.227368i
$233$	9.90789	+	6.36741i	0.649087	+	0.417143i	0.823333	−	0.567559i	$-0.192112\pi$
$233$	9.90789	+	6.36741i	0.649087	+	0.417143i	−0.174245	+	0.984702i	$0.555749\pi$
$234$	−0.924593	−	4.09332i	−0.0604425	−	0.267588i
$235$	−0.629102	+	1.37754i	−0.0410381	+	0.0898609i
$236$	4.17913	−	3.28651i	0.272038	−	0.213933i
$237$	7.45220	+	16.6663i	0.484073	+	1.08259i
$238$	−0.0954769	−	2.00431i	−0.00618885	−	0.129920i
$239$	−6.28128	−	0.599789i	−0.406302	−	0.0387971i	−0.110095	−	0.993921i	$-0.535116\pi$
$239$	−6.28128	−	0.599789i	−0.406302	−	0.0387971i	−0.296207	+	0.955124i	$0.595722\pi$
$240$	1.56680	−	0.792087i	0.101136	−	0.0511290i
$241$	−23.8924	−	4.60488i	−1.53905	−	0.296627i	−0.651968	−	0.758247i	$-0.726056\pi$
$241$	−23.8924	−	4.60488i	−1.53905	−	0.296627i	−0.887078	+	0.461620i	$0.847268\pi$
$242$	4.85543	−	5.60347i	0.312119	−	0.360205i
$243$	5.67801	−	14.5176i	0.364244	−	0.931303i
$244$	0.00264316	+	0.00578772i	0.000169211	+	0.000370521i
$245$	−0.164583	−	0.0848484i	−0.0105148	−	0.00542077i
$246$	−15.4722	−	1.60124i	−0.986471	−	0.102091i
$247$	−1.04947	−	0.420146i	−0.0667764	−	0.0267332i
$248$	−3.90130	−	5.47862i	−0.247733	−	0.347892i
$249$	16.0810	−	10.1555i	1.01909	−	0.643578i
$250$	0.432746	−	9.08445i	0.0273693	−	0.574551i
$251$	−7.94602	−	9.17019i	−0.501548	−	0.578817i	0.447366	−	0.894351i	$-0.352362\pi$
$251$	−7.94602	−	9.17019i	−0.501548	−	0.578817i	−0.948914	+	0.315533i	$0.897817\pi$
$252$	7.51064	−	2.86955i	0.473126	−	0.180765i
$253$	8.65785	+	18.6701i	0.544314	+	1.17378i
$254$	7.35889	+	12.7460i	0.461738	+	0.799754i
$255$	−1.22414	+	0.478850i	−0.0766583	+	0.0299867i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	1.91120	+	1.50298i	0.119217	+	0.0937535i	0.675988	−	0.736913i	$-0.263717\pi$
$257$	1.91120	+	1.50298i	0.119217	+	0.0937535i	−0.556770	+	0.830666i	$0.687960\pi$
$258$	−2.56755	−	2.48729i	−0.159848	−	0.154852i
$259$	14.8178	−	11.6528i	0.920732	−	0.724071i
$260$	−1.36043	−	0.399457i	−0.0843701	−	0.0247733i
$261$	10.9264	+	1.21838i	0.676329	+	0.0754157i
$262$	−0.470812	−	1.03093i	−0.0290868	−	0.0636913i
$263$	−1.40718	−	1.34175i	−0.0867707	−	0.0827357i	0.645453	−	0.763800i	$-0.276669\pi$
$263$	−1.40718	−	1.34175i	−0.0867707	−	0.0827357i	−0.732223	+	0.681065i	$0.761517\pi$
$264$	7.43235	+	0.0588982i	0.457430	+	0.00362493i
$265$	2.94522	+	8.50966i	0.180924	+	0.522744i
$266$	0.510626	−	2.10483i	0.0313085	−	0.129055i
$267$	9.47065	+	13.5252i	0.579594	+	0.827731i
$268$	6.69043	+	3.44916i	0.408683	+	0.210691i
$269$	16.2558	+	4.77314i	0.991135	+	0.291023i	0.736813	−	0.676096i	$-0.236330\pi$
$269$	16.2558	+	4.77314i	0.991135	+	0.291023i	0.254321	+	0.967120i	$0.418148\pi$
$270$	−3.35349	−	4.06132i	−0.204087	−	0.247164i
$271$	−7.45720	+	16.3290i	−0.452993	+	0.991916i	0.536036	+	0.844195i	$0.319921\pi$
$271$	−7.45720	+	16.3290i	−0.452993	+	0.991916i	−0.989029	+	0.147721i	$0.952806\pi$
$272$	0.695078	−	0.278267i	0.0421453	−	0.0168724i
$273$	−6.00883	−	2.46100i	−0.363671	−	0.148946i
$274$	−19.9082	+	3.83700i	−1.20270	+	0.231801i
$275$	8.52358	−	14.7633i	0.513991	−	0.890259i
$276$	−3.46665	+	7.54866i	−0.208668	+	0.454376i
$277$	−1.46309	−	2.53415i	−0.0879088	−	0.152263i	0.818718	−	0.574196i	$-0.194685\pi$
$277$	−1.46309	−	2.53415i	−0.0879088	−	0.152263i	−0.906627	+	0.421933i	$0.861352\pi$
$278$	−7.42536	−	8.56932i	−0.445344	−	0.513954i
$279$	−13.4533	+	15.0376i	−0.805425	+	0.900276i
$280$	0.386605	−	2.68889i	0.0231040	−	0.160692i
$281$	7.29452	−	0.696542i	0.435155	−	0.0415522i	0.124820	−	0.992179i	$-0.460165\pi$
$281$	7.29452	−	0.696542i	0.435155	−	0.0415522i	0.310335	+	0.950627i	$0.399559\pi$
$282$	−2.53705	−	0.509860i	−0.151079	−	0.0303617i
$283$	7.03879	−	6.71148i	0.418413	−	0.398956i	−0.451413	−	0.892315i	$-0.649080\pi$
$283$	7.03879	−	6.71148i	0.418413	−	0.398956i	0.869826	+	0.493359i	$0.164231\pi$
$284$	−0.199828	−	4.19491i	−0.0118576	−	0.248922i
$285$	−1.41341	+	0.123670i	−0.0837234	+	0.00732560i
$286$	−4.34428	−	4.14227i	−0.256883	−	0.244937i
$287$	−15.7615	+	18.1897i	−0.930370	+	1.07370i
$288$	1.92840	+	2.29810i	0.113632	+	0.135417i
$289$	15.7735	−	4.63152i	0.927854	−	0.272443i
$290$	2.15469	−	3.02584i	0.126528	−	0.177683i
$291$	19.1893	+	5.80006i	1.12490	+	0.340005i
$292$	−6.57632	+	6.27051i	−0.384850	+	0.366954i
$293$	3.39046	+	1.35734i	0.198073	+	0.0792964i	0.468578	−	0.883422i	$-0.344766\pi$
$293$	3.39046	+	1.35734i	0.198073	+	0.0792964i	−0.270505	+	0.962719i	$0.587191\pi$
$294$	0.0770309	−	0.306890i	0.00449253	−	0.0178982i
$295$	−5.00297	+	2.00289i	−0.291284	+	0.116613i
$296$	5.91718	+	3.80274i	0.343929	+	0.221030i
$297$	−4.74031	−	21.7881i	−0.275061	−	1.26427i
$298$	6.15150			0.356347
$299$	6.21334	−	2.52944i	0.359327	−	0.146281i
$300$	6.76648	−	1.24860i	0.390663	−	0.0720881i
$301$	−5.43137	+	1.04681i	−0.313059	+	0.0603372i
$302$	17.1998	−	8.86713i	0.989739	−	0.510246i
$303$	10.5848	−	6.68449i	0.608078	−	0.384014i
$304$	0.804490	−	0.0768194i	0.0461406	−	0.00440590i
$305$	−0.000917837	−	0.00638370i	−5.25552e−5	−	0.000365529i
$306$	−1.27372	−	1.85006i	−0.0728138	−	0.105761i
$307$	−13.9444	+	8.96150i	−0.795847	+	0.511460i	−0.874258	−	0.485461i	$-0.838652\pi$
$307$	−13.9444	+	8.96150i	−0.795847	+	0.511460i	0.0784114	+	0.996921i	$0.475015\pi$
$308$	6.67104	−	9.36816i	0.380117	−	0.533800i
$309$	−0.655650	+	11.7962i	−0.0372986	+	0.671063i
$310$	2.22972	+	6.44236i	0.126640	+	0.365901i
$311$	−4.02144	−	11.6192i	−0.228035	−	0.658864i	−0.999738	−	0.0228808i	$-0.992716\pi$
$311$	−4.02144	−	11.6192i	−0.228035	−	0.658864i	0.771703	−	0.635983i	$-0.219405\pi$
$312$	0.134456	−	2.41908i	0.00761207	−	0.136954i
$313$	−9.87881	+	13.8728i	−0.558383	+	0.784139i	−0.993205	−	0.116377i	$-0.962872\pi$
$313$	−9.87881	+	13.8728i	−0.558383	+	0.784139i	0.434822	+	0.900516i	$0.356811\pi$
$314$	13.7633	−	8.84515i	0.776709	−	0.499161i
$315$	−8.12399	+	0.646003i	−0.457735	+	0.0363981i
$316$	1.50006	+	10.4331i	0.0843848	+	0.586909i
$317$	7.52411	−	0.718466i	0.422596	−	0.0403531i	0.118408	−	0.992965i	$-0.462221\pi$
$317$	7.52411	−	0.718466i	0.422596	−	0.0403531i	0.304188	+	0.952612i	$0.401615\pi$
$318$	−13.0103	+	8.21625i	−0.729580	+	0.460745i
$319$	13.9779	−	7.20610i	0.782611	−	0.403464i
$320$	0.995299	−	0.191828i	0.0556389	−	0.0107235i
$321$	−24.9087	+	4.59634i	−1.39027	+	0.256543i
$322$	6.49112	+	11.0936i	0.361736	+	0.618220i
$323$	−0.605069			−0.0336669
$324$	5.45023	−	7.16205i	0.302791	−	0.397892i
$325$	−4.67476	−	3.00429i	−0.259309	−	0.166648i
$326$	−16.5699	+	6.63358i	−0.917721	+	0.367400i
$327$	−3.91466	+	15.5960i	−0.216481	+	0.862460i
$328$	−8.33729	−	3.33775i	−0.460350	−	0.184296i
$329$	−2.89793	+	2.76317i	−0.159768	+	0.152339i
$330$	−7.21157	−	2.17973i	−0.396984	−	0.119990i
$331$	9.98905	−	14.0277i	0.549048	−	0.771030i	−0.443050	−	0.896497i	$-0.646104\pi$
$331$	9.98905	−	14.0277i	0.549048	−	0.771030i	0.992098	+	0.125467i	$0.0400430\pi$
$332$	10.5360	−	3.09365i	0.578238	−	0.169786i
$333$	7.21671	−	19.8289i	0.395474	−	1.08661i
$334$	−16.1898	+	18.6840i	−0.885864	+	1.02234i
$335$	−5.52186	−	5.26508i	−0.301691	−	0.287662i
$336$	4.62432	−	0.404617i	0.252277	−	0.0220737i
$337$	1.01751	+	21.3602i	0.0554274	+	1.16356i	0.839666	+	0.543104i	$0.182751\pi$
$337$	1.01751	+	21.3602i	0.0554274	+	1.16356i	−0.784238	+	0.620460i	$0.786946\pi$
$338$	7.99243	−	7.62076i	0.434731	−	0.414515i
$339$	14.7573	+	2.96571i	0.801507	+	0.161076i
$340$	−0.755467	+	0.0721384i	−0.0409710	+	0.00391225i
$341$	−4.10742	+	28.5677i	−0.222429	+	1.54703i
$342$	−0.756550	−	2.30338i	−0.0409095	−	0.124553i
$343$	11.9648	+	13.8081i	0.646039	+	0.745569i
$344$	−1.03194	−	1.78738i	−0.0556387	−	0.0963690i
$345$	5.52718	−	6.35154i	0.297573	−	0.341956i
$346$	−4.59834	+	7.96456i	−0.247208	+	0.428177i
$347$	−28.3076	+	5.45583i	−1.51963	+	0.292885i	−0.879692	−	0.475543i	$-0.842252\pi$
$347$	−28.3076	+	5.45583i	−1.51963	+	0.292885i	−0.639937	+	0.768428i	$0.721039\pi$
$348$	5.87392	+	2.40574i	0.314875	+	0.128961i
$349$	−12.4838	+	4.99778i	−0.668245	+	0.267525i	−0.680880	−	0.732395i	$-0.738402\pi$
$349$	−12.4838	+	4.99778i	−0.668245	+	0.267525i	0.0126349	+	0.999920i	$0.495978\pi$
$350$	4.42281	−	9.68460i	0.236409	−	0.517664i
$351$	−7.16778	+	1.20552i	−0.382588	+	0.0643458i
$352$	4.11738	+	1.20897i	0.219457	+	0.0644384i
$353$	−27.4312	−	14.1418i	−1.46002	−	0.752692i	−0.468599	−	0.883411i	$-0.655241\pi$
$353$	−27.4312	−	14.1418i	−1.46002	−	0.752692i	−0.991419	+	0.130720i	$0.958271\pi$
$354$	−5.28192	−	7.54322i	−0.280731	−	0.400918i
$355$	−1.00359	+	4.13686i	−0.0532651	+	0.219562i
$356$	3.11789	+	9.00854i	0.165248	+	0.477452i
$357$	−3.47539	−	0.0275410i	−0.183937	−	0.00145762i
$358$	−18.1518	−	17.3077i	−0.959351	−	0.914740i
$359$	4.19013	+	9.17511i	0.221147	+	0.484244i	0.987390	−	0.158307i	$-0.0506035\pi$
$359$	4.19013	+	9.17511i	0.221147	+	0.484244i	−0.766243	+	0.642551i	$0.777876\pi$
$360$	−1.21922	−	2.78573i	−0.0642585	−	0.146821i
$361$	17.6037	+	5.16892i	0.926511	+	0.272048i
$362$	−17.9037	+	14.0796i	−0.940999	+	0.740010i
$363$	−9.22382	−	8.93551i	−0.484125	−	0.468993i
$364$	−2.94683	−	2.31741i	−0.154456	−	0.121465i
$365$	8.18651	−	4.22044i	0.428502	−	0.220908i
$366$	0.0102632	−	0.00401471i	0.000536468	−	0.000209852i
$367$	16.1750	+	28.0159i	0.844327	+	1.46242i	0.886205	+	0.463294i	$0.153333\pi$
$367$	16.1750	+	28.0159i	0.844327	+	1.46242i	−0.0418778	+	0.999123i	$0.513334\pi$
$368$	−3.11949	+	3.64264i	−0.162614	+	0.189886i
$369$	−4.25636	+	26.6034i	−0.221577	+	1.38492i
$370$	−4.66885	−	5.38815i	−0.242722	−	0.280116i
$371$	−1.13290	+	23.7825i	−0.0588172	+	1.23473i
$372$	−9.84962	+	6.22023i	−0.510679	+	0.322504i
$373$	−18.9105	−	26.5561i	−0.979149	−	1.37502i	−0.926452	−	0.376412i	$-0.877158\pi$
$373$	−18.9105	−	26.5561i	−0.979149	−	1.37502i	−0.0526973	−	0.998611i	$-0.516782\pi$
$374$	−2.98272	−	1.19410i	−0.154233	−	0.0617455i
$375$	−15.6689	−	1.62159i	−0.809138	−	0.0837387i
$376$	−1.32797	−	0.684614i	−0.0684846	−	0.0353063i
$377$	−2.12952	−	4.66301i	−0.109676	−	0.240157i
$378$	−4.24062	−	13.2646i	−0.218114	−	0.682257i
$379$	−8.86625	+	10.2322i	−0.455429	+	0.525593i	−0.936301	−	0.351198i	$-0.885774\pi$
$379$	−8.86625	+	10.2322i	−0.455429	+	0.525593i	0.480873	+	0.876790i	$0.340320\pi$
$380$	−0.804350	−	0.155026i	−0.0412623	−	0.00795265i
$381$	22.7500	−	11.5012i	1.16552	−	0.589223i
$382$	7.20365	+	0.687865i	0.368571	+	0.0351942i
$383$	−1.31632	−	27.6329i	−0.0672608	−	1.41198i	−0.740254	−	0.672328i	$-0.765295\pi$
$383$	−1.31632	−	27.6329i	−0.0672608	−	1.41198i	0.672993	−	0.739649i	$-0.265008\pi$
$384$	0.707012	+	1.58118i	0.0360796	+	0.0806893i
$385$	−9.16322	+	7.20603i	−0.467001	+	0.367254i
$386$	−6.54119	+	14.3232i	−0.332938	+	0.729032i
$387$	−4.54827	+	4.20118i	−0.231202	+	0.213558i
$388$	9.73665	+	6.25737i	0.494304	+	0.317670i
$389$	−0.772641	+	2.23240i	−0.0391745	+	0.113187i	−0.962892	−	0.269887i	$-0.913014\pi$
$389$	−0.772641	+	2.23240i	−0.0391745	+	0.113187i	0.923717	+	0.383075i	$0.125135\pi$
$390$	−0.821580	+	2.31430i	−0.0416023	+	0.117189i
$391$	2.58426	−	2.49292i	0.130691	−	0.126072i
$392$	0.0913398	−	0.158205i	0.00461336	−	0.00799057i
$393$	−1.82813	+	0.715118i	−0.0922171	+	0.0360729i
$394$	0.940167	−	19.7365i	0.0473649	−	0.994312i
$395$	1.52048	−	10.5752i	0.0765038	−	0.532096i
$396$	0.816266	−	12.8477i	0.0410189	−	0.645622i
$397$	0.184103	+	1.28046i	0.00923987	+	0.0642647i	0.993920	−	0.110107i	$-0.0351195\pi$
$397$	0.184103	+	1.28046i	0.00923987	+	0.0642647i	−0.984680	+	0.174372i	$0.944210\pi$
$398$	1.37990	+	5.68803i	0.0691681	+	0.285115i
$399$	−3.59097	−	1.08539i	−0.179773	−	0.0543373i
$400$	3.95459	+	0.377618i	0.197730	+	0.0188809i
$401$	−2.94571	+	12.1424i	−0.147102	+	0.606361i	0.849758	+	0.527173i	$0.176748\pi$
$401$	−2.94571	+	12.1424i	−0.147102	+	0.606361i	−0.996860	+	0.0791882i	$0.974767\pi$
$402$	6.60800	−	11.2388i	0.329577	−	0.560539i
$403$	9.23802	+	1.78048i	0.460179	+	0.0886922i
$404$	6.93494	−	2.03628i	0.345026	−	0.101309i
$405$	−7.34592	+	5.40909i	−0.365022	+	0.268780i
$406$	8.26249	−	5.30998i	0.410060	−	0.263530i
$407$	−7.11599	−	29.3325i	−0.352727	−	1.45396i
$408$	−0.414418	−	1.22880i	−0.0205168	−	0.0608348i
$409$	−13.3531	−	18.7518i	−0.660268	−	0.927216i	0.339643	−	0.940554i	$-0.389694\pi$
$409$	−13.3531	−	18.7518i	−0.660268	−	0.927216i	−0.999911	+	0.0133380i	$0.995754\pi$
$410$	7.15534	+	5.62702i	0.353377	+	0.277899i
$411$	4.72202	+	34.7977i	0.232920	+	1.71645i
$412$	−2.23095	+	6.44590i	−0.109911	+	0.317567i
$413$	−14.2488			−0.701136
$414$	12.7213	+	6.72076i	0.625218	+	0.330307i
$415$	−11.1303			−0.546365
$416$	0.457507	−	1.32188i	0.0224311	−	0.0648105i
$417$	−15.5334	+	12.0176i	−0.760672	+	0.588504i
$418$	−2.72598	−	2.14373i	−0.133332	−	0.104853i
$419$	6.44464	+	9.05023i	0.314841	+	0.442133i	0.941425	−	0.337221i	$-0.109487\pi$
$419$	6.44464	+	9.05023i	0.314841	+	0.442133i	−0.626584	+	0.779354i	$0.715548\pi$
$420$	−4.61296	−	0.927047i	−0.225090	−	0.0452353i
$421$	5.66759	+	23.3621i	0.276222	+	1.13860i	0.925711	+	0.378230i	$0.123467\pi$
$421$	5.66759	+	23.3621i	0.276222	+	1.13860i	−0.649490	+	0.760370i	$0.725018\pi$
$422$	7.07935	−	4.54962i	0.344618	−	0.221472i
$423$	−1.12561	+	4.33852i	−0.0547289	+	0.210946i
$424$	−8.52409	+	2.50290i	−0.413967	+	0.121552i
$425$	−2.92056	−	0.562892i	−0.141668	−	0.0273043i
$426$	−7.27381	−	0.0576418i	−0.352417	−	0.00279276i
$427$	0.00402025	−	0.0165717i	0.000194554	−	0.000801961i
$428$	−14.5576	−	1.39008i	−0.703668	−	0.0671922i
$429$	−7.58114	+	7.11476i	−0.366021	+	0.343504i
$430$	0.493205	+	2.03302i	0.0237845	+	0.0980410i
$431$	−4.28300	−	29.7890i	−0.206305	−	1.43488i	−0.785079	−	0.619395i	$-0.787378\pi$
$431$	−4.28300	−	29.7890i	−0.206305	−	1.43488i	0.578774	−	0.815488i	$-0.303531\pi$
$432$	4.15965	−	3.11405i	0.200131	−	0.149825i
$433$	−1.20285	+	8.36601i	−0.0578053	+	0.402045i	0.940291	+	0.340371i	$0.110553\pi$
$433$	−1.20285	+	8.36601i	−0.0578053	+	0.402045i	−0.998096	+	0.0616734i	$0.980356\pi$
$434$	−0.857678	+	18.0049i	−0.0411699	+	0.864262i
$435$	−5.02572	−	4.01713i	−0.240965	−	0.192607i
$436$	−4.64183	+	8.03989i	−0.222304	+	0.385041i
$437$	3.43452	−	1.79596i	0.164295	−	0.0859124i
$438$	10.2120	+	11.9757i	0.487947	+	0.572221i
$439$	2.22529	−	6.42954i	0.106207	−	0.306865i	−0.879358	−	0.476161i	$-0.842028\pi$
$439$	2.22529	−	6.42954i	0.106207	−	0.306865i	0.985565	+	0.169295i	$0.0541492\pi$
$440$	−3.65915	−	2.35159i	−0.174443	−	0.112108i
$441$	−0.523326	−	0.162715i	−0.0249203	−	0.00774831i
$442$	−0.435066	+	0.952662i	−0.0206940	+	0.0453135i
$443$	−9.62649	+	7.57036i	−0.457368	+	0.359678i	−0.820105	−	0.572213i	$-0.806085\pi$
$443$	−9.62649	+	7.57036i	−0.457368	+	0.359678i	0.362736	+	0.931892i	$0.381843\pi$
$444$	7.14516	−	9.86754i	0.339094	−	0.468293i
$445$	−0.459767	−	9.65170i	−0.0217950	−	0.457534i
$446$	0.739813	+	0.0706436i	0.0350312	+	0.00334507i
$447$	0.591291	−	10.6383i	0.0279671	−	0.503174i
$448$	2.63162	+	0.507203i	0.124332	+	0.0239631i
$449$	−20.9740	+	24.2053i	−0.989826	+	1.14232i	−5.87273e−6		1.00000i	$0.500002\pi$
$449$	−20.9740	+	24.2053i	−0.989826	+	1.14232i	−0.989821	+	0.142321i	$0.954544\pi$
$450$	−1.50891	−	11.8218i	−0.0711306	−	0.557287i
$451$	16.0091	+	35.0550i	0.753838	+	1.65067i
$452$	7.72442	+	3.98221i	0.363326	+	0.187308i
$453$	−13.6814	−	30.5974i	−0.642807	−	1.43759i
$454$	−12.6191	−	5.05192i	−0.592244	−	0.237099i
$455$	2.20418	+	3.09534i	0.103334	+	0.145112i
$456$	−0.0555214	−	1.39865i	−0.00260003	−	0.0654980i
$457$	1.49878	−	31.4634i	0.0701102	−	1.47179i	−0.640365	−	0.768071i	$-0.721217\pi$
$457$	1.49878	−	31.4634i	0.0701102	−	1.47179i	0.710475	−	0.703723i	$-0.248480\pi$
$458$	−6.95677	−	8.02854i	−0.325069	−	0.375149i
$459$	−3.32189	+	2.02492i	−0.155053	+	0.0945152i
$460$	4.07410	−	2.65185i	0.189956	−	0.123643i
$461$	8.38647	+	14.5258i	0.390597	+	0.676534i	0.992528	−	0.122014i	$-0.0389353\pi$
$461$	8.38647	+	14.5258i	0.390597	+	0.676534i	−0.601931	+	0.798548i	$0.705602\pi$
$462$	−15.5599	−	12.4372i	−0.723912	−	0.578633i
$463$	−8.42876	+	4.34533i	−0.391718	+	0.201945i	−0.642822	−	0.766015i	$-0.722237\pi$
$463$	−8.42876	+	4.34533i	−0.391718	+	0.201945i	0.251104	+	0.967960i	$0.419206\pi$
$464$	2.88066	+	2.26538i	0.133731	+	0.105168i
$465$	11.3556	−	3.23679i	0.526604	−	0.150103i
$466$	9.25776	−	7.28038i	0.428857	−	0.337257i
$467$	−20.0948	−	5.90037i	−0.929877	−	0.273037i	−0.218492	−	0.975839i	$-0.570114\pi$
$467$	−20.0948	−	5.90037i	−0.929877	−	0.273037i	−0.711385	+	0.702802i	$0.751932\pi$
$468$	−4.17059	−	0.465052i	−0.192786	−	0.0214970i
$469$	−8.38027	−	18.3502i	−0.386965	−	0.847335i
$470$	1.09602	+	1.04505i	0.0505556	+	0.0482047i
$471$	−13.9737	−	24.6522i	−0.643873	−	1.13592i
$472$	−1.73889	−	5.02419i	−0.0800389	−	0.231257i
$473$	−2.08802	+	8.60692i	−0.0960070	+	0.395746i
$474$	18.1871	−	1.59132i	0.835359	−	0.0730919i
$475$	−2.85355	−	1.47111i	−0.130930	−	0.0674991i
$476$	−1.92530	−	0.565319i	−0.0882459	−	0.0259113i
$477$	12.9585	+	23.2895i	0.593327	+	1.06635i
$478$	−2.62121	+	5.73964i	−0.119891	+	0.262525i
$479$	9.41661	−	3.76984i	0.430256	−	0.172248i	−0.146418	−	0.989223i	$-0.546775\pi$
$479$	9.41661	−	3.76984i	0.430256	−	0.172248i	0.576674	+	0.816974i	$0.304350\pi$
$480$	−0.236074	−	1.73969i	−0.0107753	−	0.0794056i
$481$	−9.66112	+	1.86203i	−0.440509	+	0.0849012i
$482$	−12.1661	+	21.0722i	−0.554149	+	0.959814i
$483$	19.8089	−	10.1593i	0.901337	−	0.462264i
$484$	−3.70722	−	6.42110i	−0.168510	−	0.291868i
$485$	−7.68255	−	8.86613i	−0.348846	−	0.402590i
$486$	−11.8620	−	10.1140i	−0.538073	−	0.458778i
$487$	6.06529	−	42.1851i	0.274845	−	1.91159i	−0.119881	−	0.992788i	$-0.538251\pi$
$487$	6.06529	−	42.1851i	0.274845	−	1.91159i	0.394726	−	0.918799i	$-0.370840\pi$
$488$	0.00633390		0.000604814i	0.000286722		2.73786e-5i
$489$	9.87927	+	29.2933i	0.446756	+	1.32469i
$490$	−0.134012	+	0.127780i	−0.00605403	+	0.00577251i
$491$	1.02966	+	21.6153i	0.0464680	+	0.975484i	0.894924	+	0.446218i	$0.147230\pi$
$491$	1.02966	+	21.6153i	0.0464680	+	0.975484i	−0.848456	+	0.529266i	$0.822467\pi$
$492$	−6.57363	+	14.0975i	−0.296362	+	0.635565i
$493$	−1.98579	−	1.89344i	−0.0894353	−	0.0852764i
$494$	−0.740287	+	0.854337i	−0.0333071	+	0.0384384i
$495$	−4.46277	+	12.2620i	−0.200587	+	0.551138i
$496$	−6.45329	+	1.89486i	−0.289761	+	0.0850816i
$497$	−6.52873	+	9.16832i	−0.292854	+	0.411256i
$498$	−4.33736	−	18.5181i	−0.194362	−	0.829817i
$499$	−5.83964	+	5.56809i	−0.261418	+	0.249262i	−0.809440	−	0.587202i	$-0.800229\pi$
$499$	−5.83964	+	5.56809i	−0.261418	+	0.249262i	0.548022	+	0.836464i	$0.315381\pi$
$500$	−8.44328	−	3.38018i	−0.377595	−	0.151166i
$501$	30.7555	+	29.7942i	1.37406	+	1.33111i
$502$	−11.2647	+	4.50972i	−0.502769	+	0.201278i
$503$	0.943244	+	0.606186i	0.0420572	+	0.0270285i	0.561500	−	0.827476i	$-0.310224\pi$
$503$	0.943244	+	0.606186i	0.0420572	+	0.0270285i	−0.519443	+	0.854505i	$0.673861\pi$
$504$	−0.255241	−	8.03610i	−0.0113693	−	0.357957i
$505$	−7.32613			−0.326008
$506$	20.4750	−	2.07527i	0.910225	−	0.0922570i
$507$	−12.4110	−	14.5545i	−0.551190	−	0.646387i
$508$	14.4518	−	2.78536i	0.641196	−	0.123580i
$509$	32.2133	−	16.6071i	1.42783	−	0.736097i	0.440945	−	0.897534i	$-0.354643\pi$
$509$	32.2133	−	16.6071i	1.42783	−	0.736097i	0.986883	+	0.161437i	$0.0516129\pi$
$510$	0.0521381	+	1.31343i	0.00230872	+	0.0581594i
$511$	24.2424	−	2.31487i	1.07242	−	0.102404i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−4.05615	+	1.08696i	−0.179083	+	0.0479904i
$514$	2.04541	−	1.31451i	0.0902193	−	0.0579804i
$515$	4.01047	−	5.63192i	0.176723	−	0.248172i
$516$	−3.19025	+	1.61282i	−0.140443	+	0.0710004i
$517$	2.09693	+	6.05867i	0.0922227	+	0.266460i
$518$	−6.16551	−	17.8141i	−0.270897	−	0.782706i
$519$	13.3318	+	8.71785i	0.585199	+	0.382671i
$520$	−0.822440	+	1.15495i	−0.0360664	+	0.0506481i
$521$	3.84657	−	2.47204i	0.168522	−	0.108302i	−0.453661	−	0.891174i	$-0.649882\pi$
$521$	3.84657	−	2.47204i	0.168522	−	0.108302i	0.622183	+	0.782872i	$0.286246\pi$
$522$	4.72505	−	9.92700i	0.206810	−	0.434493i
$523$	−2.17237	−	15.1092i	−0.0949911	−	0.660678i	−0.980567	−	0.196183i	$-0.937145\pi$
$523$	−2.17237	−	15.1092i	−0.0949911	−	0.660678i	0.885576	−	0.464494i	$-0.153764\pi$
$524$	−1.12822	+	0.107732i	−0.0492865	+	0.00470629i
$525$	−16.3232	−	8.57963i	−0.712405	−	0.374446i
$526$	−1.72820	+	0.890948i	−0.0753530	+	0.0388472i
$527$	4.94461	−	0.952996i	0.215391	−	0.0415132i
$528$	2.48654	−	7.00432i	0.108213	−	0.304824i
$529$	−7.26943	+	21.8210i	−0.316062	+	0.948738i
$530$	9.00492			0.391149
$531$	−13.5528	+	8.40939i	−0.588142	+	0.364936i
$532$	−1.82206	−	1.17096i	−0.0789961	−	0.0507677i
$533$	11.6623	−	4.66888i	0.505151	−	0.202232i
$534$	15.8789	−	4.52610i	0.687147	−	0.195864i
$535$	13.7611	+	5.50913i	0.594946	+	0.238180i
$536$	5.44768	−	5.19435i	0.235304	−	0.224362i
$537$	−31.6764	+	29.7277i	−1.36694	+	1.28285i
$538$	9.82738	−	13.8006i	0.423688	−	0.594987i
$539$	−0.752162	+	0.220855i	−0.0323979	+	0.00951288i
$540$	−4.93478	+	1.84073i	−0.212359	+	0.0792122i
$541$	19.7542	−	22.7976i	0.849300	−	0.980145i	−0.150664	−	0.988585i	$-0.548141\pi$
$541$	19.7542	−	22.7976i	0.849300	−	0.980145i	0.999964	+	0.00844036i	$0.00268668\pi$
$542$	12.9919	+	12.3878i	0.558050	+	0.532100i
$543$	22.6281	+	32.3157i	0.971067	+	1.38680i
$544$	−0.0356250	−	0.747861i	−0.00152741	−	0.0320643i
$545$	6.81039	−	6.49370i	0.291725	−	0.278159i
$546$	−4.29094	+	4.87344i	−0.183635	+	0.208564i
$547$	24.8547	−	2.37333i	1.06271	−	0.101476i	0.450972	−	0.892538i	$-0.351077\pi$
$547$	24.8547	−	2.37333i	1.06271	−	0.101476i	0.611736	+	0.791062i	$0.290471\pi$
$548$	−2.88538	+	20.0682i	−0.123257	+	0.857273i
$549$	−0.00595646	−	0.0181350i	−0.000254215	−	0.000773981i
$550$	−11.1635	−	12.8834i	−0.476014	−	0.549350i
$551$	−1.48082	−	2.56485i	−0.0630850	−	0.109266i
$552$	5.99966	+	5.74492i	0.255363	+	0.244520i
$553$	14.1244	−	24.4642i	0.600632	−	1.04033i
$554$	−2.87331	+	0.553785i	−0.122075	+	0.0235281i
$555$	−9.76694	+	7.55631i	−0.414583	+	0.320748i
$556$	−10.5266	+	4.21422i	−0.446428	+	0.178723i
$557$	9.66999	−	21.1743i	0.409730	−	0.897185i	−0.586460	−	0.809978i	$-0.699479\pi$
$557$	9.66999	−	21.1743i	0.409730	−	0.897185i	0.996190	−	0.0872062i	$-0.0277939\pi$
$558$	9.81039	+	17.6316i	0.415307	+	0.746407i
$559$	2.77005	+	0.813360i	0.117161	+	0.0344015i
$560$	−2.41456	−	1.24479i	−0.102034	−	0.0526021i
$561$	−2.35176	+	5.04348i	−0.0992914	+	0.212936i
$562$	1.72757	−	7.12115i	0.0728732	−	0.300387i
$563$	13.6774	+	39.5182i	0.576432	+	1.66549i	0.734939	+	0.678134i	$0.237211\pi$
$563$	13.6774	+	39.5182i	0.576432	+	1.66549i	−0.158506	+	0.987358i	$0.550668\pi$
$564$	−1.31161	+	2.23075i	−0.0552285	+	0.0939317i
$565$	−6.37524	−	6.07878i	−0.268209	−	0.255736i
$566$	−4.04019	−	8.84677i	−0.169822	−	0.371858i
$567$	−23.3472	+	6.05864i	−0.980489	+	0.254439i
$568$	−4.02955	−	1.18318i	−0.169076	−	0.0496453i
$569$	5.52279	−	4.34317i	0.231527	−	0.182075i	−0.495655	−	0.868520i	$-0.665072\pi$
$569$	5.52279	−	4.34317i	0.231527	−	0.182075i	0.727182	+	0.686444i	$0.240830\pi$
$570$	−0.345414	+	1.37613i	−0.0144678	+	0.0576396i
$571$	2.79140	+	2.19518i	0.116816	+	0.0918653i	0.674858	−	0.737947i	$-0.264205\pi$
$571$	2.79140	+	2.19518i	0.116816	+	0.0918653i	−0.558042	+	0.829813i	$0.688447\pi$
$572$	−5.33532	+	2.75055i	−0.223081	+	0.115006i
$573$	1.88201	−	12.3917i	0.0786220	−	0.517672i
$574$	12.0342	+	20.8439i	0.502299	+	0.870007i
$575$	18.2486	−	5.47367i	0.761019	−	0.228268i
$576$	2.80242	−	1.07071i	0.116768	−	0.0446129i
$577$	−20.4360	−	23.5844i	−0.850760	−	0.981830i	0.149216	−	0.988805i	$-0.452325\pi$
$577$	−20.4360	−	23.5844i	−0.850760	−	0.981830i	−0.999976	+	0.00697516i	$0.997780\pi$
$578$	0.782220	−	16.4208i	0.0325361	−	0.683016i
$579$	24.1415	+	12.6890i	1.00329	+	0.527336i
$580$	−2.15469	−	3.02584i	−0.0894686	−	0.125641i
$581$	−27.3210	−	10.9377i	−1.13347	−	0.453772i
$582$	11.7573	−	16.2369i	0.487355	−	0.673042i
$583$	33.8850	+	17.4689i	1.40337	+	0.723489i
$584$	3.77473	+	8.26551i	0.156200	+	0.342029i
$585$	3.92334	+	1.64328i	0.162210	+	0.0679413i
$586$	2.39159	−	2.76005i	0.0987959	−	0.114017i
$587$	23.8627	+	4.59916i	0.984920	+	0.189828i	0.656190	−	0.754596i	$-0.272167\pi$
$587$	23.8627	+	4.59916i	0.984920	+	0.189828i	0.328730	+	0.944424i	$0.393379\pi$
$588$	−0.264817	−	0.173168i	−0.0109209	−	0.00714134i
$589$	5.41078	+	0.516667i	0.222947	+	0.0212889i
$590$	0.256419	+	5.38289i	0.0105566	+	0.221610i
$591$	−34.0416	−	3.52301i	−1.40028	−	0.144917i
$592$	5.52891	−	4.34798i	0.227237	−	0.178701i
$593$	−5.26961	+	11.5388i	−0.216397	+	0.473843i	−0.986435	−	0.164155i	$-0.947510\pi$
$593$	−5.26961	+	11.5388i	−0.216397	+	0.473843i	0.770038	+	0.637999i	$0.220237\pi$
$594$	−22.1401	−	2.64658i	−0.908421	−	0.108590i
$595$	1.71103	+	1.09961i	0.0701453	+	0.0450796i
$596$	2.01196	−	5.81317i	0.0824130	−	0.238117i
$597$	9.96941	−	1.83963i	0.408021	−	0.0752911i
$598$	−0.358139	−	6.69891i	−0.0146454	−	0.273939i
$599$	9.87511	−	17.1042i	0.403486	−	0.698858i	−0.590658	−	0.806922i	$-0.701132\pi$
$599$	9.87511	−	17.1042i	0.403486	−	0.698858i	0.994144	+	0.108064i	$0.0344651\pi$
$600$	1.03317	−	6.80271i	0.0421789	−	0.277719i
$601$	0.100015	−	2.09958i	0.00407971	−	0.0856436i	−0.995909	−	0.0903600i	$-0.971198\pi$
$601$	0.100015	−	2.09958i	0.00407971	−	0.0856436i	0.999989	+	0.00471635i	$0.00150127\pi$
$602$	−0.787190	+	5.47503i	−0.0320835	+	0.223145i
$603$	−18.8009	−	12.5080i	−0.765634	−	0.509367i
$604$	−2.75393	−	19.1540i	−0.112056	−	0.779365i
$605$	1.77182	+	7.30356i	0.0720349	+	0.296932i
$606$	−2.85491	−	12.1889i	−0.115973	−	0.495140i
$607$	28.0639	+	2.67978i	1.13908	+	0.108769i	0.647500	−	0.762065i	$-0.275814\pi$
$607$	28.0639	+	2.67978i	1.13908	+	0.108769i	0.491577	+	0.870834i	$0.336421\pi$
$608$	0.190528	−	0.785369i	0.00772694	−	0.0318509i
$609$	−8.38877	−	14.7994i	−0.339930	−	0.599702i
$610$	−0.00633279	−	0.00122055i	−0.000256407	−	4.94185e-5i
$611$	2.00524	−	0.588793i	0.0811235	−	0.0238200i
$612$	−2.16490	+	0.598573i	−0.0875110	+	0.0241959i
$613$	38.3880	−	24.6705i	1.55048	−	0.996430i	0.565299	−	0.824886i	$-0.308761\pi$
$613$	38.3880	−	24.6705i	1.55048	−	0.996430i	0.985176	−	0.171544i	$-0.0548756\pi$
$614$	3.90787	+	16.1084i	0.157709	+	0.650084i
$615$	10.4190	−	11.8334i	0.420136	−	0.477170i
$616$	−6.67104	−	9.36816i	−0.268784	−	0.377454i
$617$	29.5772	+	23.2597i	1.19073	+	0.936402i	0.998985	−	0.0450430i	$-0.0143425\pi$
$617$	29.5772	+	23.2597i	1.19073	+	0.936402i	0.191746	+	0.981445i	$0.438585\pi$
$618$	10.9330	+	4.47775i	0.439789	+	0.180122i
$619$	0.946205	−	2.73388i	0.0380312	−	0.109884i	−0.924387	−	0.381457i	$-0.875423\pi$
$619$	0.946205	−	2.73388i	0.0380312	−	0.109884i	0.962418	+	0.271573i	$0.0875438\pi$
$620$	6.81731			0.273790
$621$	12.8455	−	21.3540i	0.515474	−	0.856905i
$622$	−12.2954			−0.493002
$623$	8.35610	−	24.1434i	0.334780	−	0.967283i
$624$	−2.24206	−	0.918265i	−0.0897542	−	0.0367600i
$625$	−8.36700	−	6.57988i	−0.334680	−	0.263195i
$626$	9.87881	+	13.8728i	0.394837	+	0.554470i
$627$	−3.96936	+	4.50820i	−0.158521	+	0.180040i
$628$	−3.85713	−	15.8993i	−0.153916	−	0.634452i
$629$	−4.43025	+	2.84715i	−0.176645	+	0.113523i
$630$	−2.04662	+	7.88846i	−0.0815394	+	0.314284i
$631$	19.1633	−	5.62686i	0.762880	−	0.224002i	0.122927	−	0.992416i	$-0.460772\pi$
$631$	19.1633	−	5.62686i	0.762880	−	0.224002i	0.639953	+	0.768414i	$0.278954\pi$
$632$	10.3499	+	1.99479i	0.411698	+	0.0793484i
$633$	−7.18756	−	12.6802i	−0.285680	−	0.503994i
$634$	1.78195	−	7.34528i	0.0707701	−	0.291718i
$635$	−14.8506	−	1.41806i	−0.589330	−	0.0562742i
$636$	3.50912	+	14.9820i	0.139146	+	0.594075i
$637$	0.0602446	+	0.248332i	0.00238698	+	0.00983926i
$638$	−2.23805	−	15.5660i	−0.0886053	−	0.616263i
$639$	−0.798854	+	12.5737i	−0.0316022	+	0.497406i
$640$	0.144253	−	1.00330i	0.00570209	−	0.0396589i
$641$	−1.20736	+	25.3455i	−0.0476877	+	1.00109i	0.840559	+	0.541721i	$0.182227\pi$
$641$	−1.20736	+	25.3455i	−0.0476877	+	1.00109i	−0.888246	+	0.459368i	$0.848076\pi$
$642$	−3.80328	+	25.0420i	−0.150104	+	0.988330i
$643$	2.91798	−	5.05408i	0.115074	−	0.199314i	−0.802735	−	0.596335i	$-0.796623\pi$
$643$	2.91798	−	5.05408i	0.115074	−	0.199314i	0.917809	+	0.397022i	$0.129956\pi$
$644$	12.6065	−	2.50577i	0.496764	−	0.0987410i
$645$	3.56328	−	0.657523i	0.140304	−	0.0258900i
$646$	−0.197899	+	0.571790i	−0.00778621	+	0.0224968i
$647$	7.17989	+	4.61424i	0.282271	+	0.181404i	0.674113	−	0.738628i	$-0.264526\pi$
$647$	7.17989	+	4.61424i	0.282271	+	0.181404i	−0.391843	+	0.920032i	$0.628162\pi$
$648$	−4.98555	−	7.49295i	−0.195851	−	0.294351i
$649$	−9.47754	+	20.7529i	−0.372026	+	0.814624i
$650$	−4.36802	+	3.43505i	−0.171328	+	0.134734i
$651$	31.0549	+	3.21391i	1.21714	+	0.125963i
$652$	0.849261	+	17.8282i	0.0332596	+	0.698206i
$653$	−3.45101	−	0.329532i	−0.135049	−	0.0128956i	0.0273129	−	0.999627i	$-0.491305\pi$
$653$	−3.45101	−	0.329532i	−0.135049	−	0.0128956i	−0.162361	+	0.986731i	$0.551911\pi$
$654$	13.4579	+	8.80031i	0.526244	+	0.344119i
$655$	1.12802	+	0.217409i	0.0440756	+	0.00849487i
$656$	−5.88103	+	6.78707i	−0.229616	+	0.264991i
$657$	21.6921	−	16.5093i	0.846291	−	0.644089i
$658$	1.66338	+	3.64229i	0.0648452	+	0.141991i
$659$	−23.7391	−	12.2383i	−0.924744	−	0.476738i	−0.0710258	−	0.997474i	$-0.522627\pi$
$659$	−23.7391	−	12.2383i	−0.924744	−	0.476738i	−0.853718	+	0.520736i	$0.825658\pi$
$660$	−4.41852	+	6.10202i	−0.171991	+	0.237521i
$661$	22.2680	+	8.91476i	0.866125	+	0.346744i	0.761810	−	0.647800i	$-0.224311\pi$
$661$	22.2680	+	8.91476i	0.866125	+	0.346744i	0.104315	+	0.994544i	$0.466735\pi$
$662$	−9.98905	−	14.0277i	−0.388235	−	0.545200i
$663$	1.60570	+	0.843966i	0.0623601	+	0.0327769i
$664$	0.522487	−	10.9684i	0.0202764	−	0.425655i
$665$	1.43766	+	1.65915i	0.0557502	+	0.0643391i
$666$	−16.3779	−	13.3052i	−0.634632	−	0.515565i
$667$	16.8919	+	4.85347i	0.654058	+	0.187927i
$668$	12.3612	+	21.4103i	0.478270	+	0.828388i
$669$	0.193282	−	1.27263i	0.00747270	−	0.0492027i
$670$	−6.78153	+	3.49612i	−0.261993	+	0.135067i
$671$	−0.0214621	−	0.0168780i	−0.000828537	−	0.000651569i
$672$	1.13010	−	4.50232i	0.0435947	−	0.173681i
$673$	35.9689	−	28.2862i	1.38650	−	1.09035i	0.401868	−	0.915698i	$-0.368361\pi$
$673$	35.9689	−	28.2862i	1.38650	−	1.09035i	0.984630	−	0.174656i	$-0.0558813\pi$
$674$	20.5182	+	6.02468i	0.790331	+	0.232062i
$675$	−20.5895	+	1.47314i	−0.792491	+	0.0567013i
$676$	−4.58756	−	10.0454i	−0.176445	−	0.386360i
$677$	17.4248	+	16.6145i	0.669689	+	0.638547i	0.946623	−	0.322342i	$-0.104470\pi$
$677$	17.4248	+	16.6145i	0.669689	+	0.638547i	−0.276935	+	0.960889i	$0.589319\pi$
$678$	7.62925	−	12.9757i	0.293000	−	0.498328i
$679$	−10.1453	−	29.3129i	−0.389340	−	1.12492i
$680$	−0.178918	+	0.737511i	−0.00686120	+	0.0282823i
$681$	−9.94967	+	21.3376i	−0.381272	+	0.817660i
$682$	25.6531	+	13.2251i	0.982308	+	0.506415i
$683$	−41.6006	−	12.2150i	−1.59180	−	0.467396i	−0.638553	−	0.769577i	$-0.720467\pi$
$683$	−41.6006	−	12.2150i	−1.59180	−	0.467396i	−0.953250	+	0.302182i	$0.902285\pi$
$684$	−2.42414	−	0.0384230i	−0.0926894	−	0.00146914i
$685$	8.53706	−	18.6936i	0.326184	−	0.714244i
$686$	16.9620	−	6.79056i	0.647612	−	0.259265i
$687$	−14.5531	+	11.2592i	−0.555236	+	0.429565i
$688$	−2.02659	+	0.390593i	−0.0772631	+	0.0148912i
$689$	6.21350	−	10.7621i	0.236715	−	0.410003i
$690$	−4.19445	−	7.30058i	−0.159680	−	0.277928i
$691$	−24.7588	−	42.8834i	−0.941868	−	1.63136i	−0.761905	−	0.647689i	$-0.775736\pi$
$691$	−24.7588	−	42.8834i	−0.941868	−	1.63136i	−0.179963	−	0.983673i	$-0.557598\pi$
$692$	6.02254	+	6.95039i	0.228943	+	0.264214i
$693$	−23.0044	+	25.7135i	−0.873864	+	0.976775i
$694$	−4.10273	+	28.5351i	−0.155737	+	1.08318i
$695$	11.4412	−	1.09250i	0.433989	−	0.0414409i
$696$	4.19460	−	4.76401i	0.158996	−	0.180579i
$697$	4.86628	−	4.63998i	0.184323	−	0.175752i
$698$	0.639838	+	13.4319i	0.0242182	+	0.508403i
$699$	−11.7007	−	16.7100i	−0.442561	−	0.632030i
$700$	−7.70540	−	7.34708i	−0.291237	−	0.277694i
$701$	−32.6409	+	37.6696i	−1.23283	+	1.42276i	−0.361275	+	0.932459i	$0.617658\pi$
$701$	−32.6409	+	37.6696i	−1.23283	+	1.42276i	−0.871553	+	0.490301i	$0.836887\pi$
$702$	−1.20514	+	7.16784i	−0.0454849	+	0.270533i
$703$	−5.45407	+	1.60146i	−0.205704	+	0.0604002i
$704$	2.48914	−	3.49551i	0.0938131	−	0.131742i
$705$	1.91264	−	1.79498i	0.0720344	−	0.0676030i
$706$	−22.3359	+	21.2972i	−0.840622	+	0.801532i
$707$	−17.9831	−	7.19934i	−0.676323	−	0.270759i
$708$	−8.85589	+	2.52427i	−0.332825	+	0.0948680i
$709$	−34.6950	+	13.8898i	−1.30300	+	0.521641i	−0.916273	−	0.400555i	$-0.868817\pi$
$709$	−34.6950	+	13.8898i	−1.30300	+	0.521641i	−0.386723	+	0.922196i	$0.626393\pi$
$710$	3.58109	+	2.30143i	0.134396	+	0.0863711i
$711$	−1.00384	−	31.6053i	−0.0376469	−	1.18529i
$712$	9.53284			0.357258
$713$	−25.2382	+	20.0860i	−0.945178	+	0.752227i
$714$	−1.16271	+	3.27524i	−0.0435135	+	0.122573i
$715$	5.97438	−	1.15147i	0.223429	−	0.0430624i
$716$	−22.2926	+	11.4927i	−0.833115	+	0.429501i
$717$	9.67408	+	5.08477i	0.361285	+	0.189894i
$718$	10.0409	−	0.958794i	0.374725	−	0.0357819i
$719$	3.03705	+	21.1232i	0.113263	+	0.787761i	0.964709	+	0.263319i	$0.0848171\pi$
$719$	3.03705	+	21.1232i	0.113263	+	0.787761i	−0.851446	+	0.524442i	$0.824274\pi$
$720$	−3.03128	+	0.241041i	−0.112969	+	0.00898307i
$721$	15.3788	−	9.88334i	0.572736	−	0.368075i
$722$	10.6422	−	14.9449i	0.396063	−	0.556193i
$723$	35.2725	+	23.0653i	1.31180	+	0.857806i
$724$	7.44954	+	21.5240i	0.276860	+	0.799935i
$725$	−4.76158	−	13.7577i	−0.176841	−	0.510948i
$726$	−11.4609	+	5.79400i	−0.425353	+	0.215036i
$727$	−18.8824	+	26.5166i	−0.700310	+	0.983448i	0.299261	+	0.954171i	$0.403260\pi$
$727$	−18.8824	+	26.5166i	−0.700310	+	0.983448i	−0.999571	+	0.0292768i	$0.990680\pi$
$728$	−3.15377	+	2.02680i	−0.116886	+	0.0751184i
$729$	−18.6311	+	19.5418i	−0.690040	+	0.723771i
$730$	−1.31077	−	9.11663i	−0.0485139	−	0.337422i
$731$	1.53825	−	0.146886i	0.0568944	−	0.00543276i
$732$	−0.000437130	−	0.0110119i	−1.61568e−5	−	0.000407010i
$733$	−9.74756	+	5.02522i	−0.360034	+	0.185611i	−0.628747	−	0.777610i	$-0.716432\pi$
$733$	−9.74756	+	5.02522i	−0.360034	+	0.185611i	0.268713	+	0.963220i	$0.413402\pi$
$734$	31.7653	−	6.12227i	1.17248	−	0.225977i
$735$	0.208099	+	0.244040i	0.00767584	+	0.00900154i
$736$	2.42201	+	4.13931i	0.0892766	+	0.152577i
$737$	−32.3007			−1.18981
$738$	23.7481	+	12.7234i	0.874181	+	0.468354i
$739$	−26.6613	−	17.1342i	−0.980751	−	0.630290i	−0.0510851	−	0.998694i	$-0.516268\pi$
$739$	−26.6613	−	17.1342i	−0.980751	−	0.630290i	−0.929666	+	0.368404i	$0.879904\pi$
$740$	−6.61883	+	2.64978i	−0.243313	+	0.0974079i
$741$	1.40632	+	1.36236i	0.0516623	+	0.0500475i
$742$	22.1039	+	8.84909i	0.811461	+	0.324860i
$743$	6.24163	−	5.95138i	0.228983	−	0.218335i	−0.566898	−	0.823788i	$-0.691857\pi$
$743$	6.24163	−	5.95138i	0.228983	−	0.218335i	0.795881	+	0.605453i	$0.207008\pi$
$744$	2.65663	+	11.3423i	0.0973968	+	0.415830i
$745$	−3.61680	+	5.07909i	−0.132509	+	0.186083i
$746$	−31.2806	+	9.18480i	−1.14526	+	0.336280i
$747$	−32.4418	+	5.72096i	−1.18698	+	0.209319i
$748$	−2.10398	+	2.42812i	−0.0769291	+	0.0887809i
$749$	28.3650	+	27.0460i	1.03644	+	0.988239i
$750$	−6.65720	+	14.2767i	−0.243087	+	0.521313i
$751$	−0.354660	−	7.44524i	−0.0129417	−	0.271681i	−0.996058	−	0.0887004i	$-0.971729\pi$
$751$	−0.354660	−	7.44524i	−0.0129417	−	0.271681i	0.983117	−	0.182980i	$-0.0585744\pi$
$752$	−1.08130	+	1.03101i	−0.0394308	+	0.0375972i
$753$	6.71624	+	19.9145i	0.244753	+	0.725724i
$754$	−5.10304	+	0.487282i	−0.185842	+	0.0177458i
$755$	−2.79143	+	19.4148i	−0.101590	+	0.706577i
$756$	−13.9220	−	0.331034i	−0.506339	−	0.0120396i
$757$	10.3392	+	11.9321i	0.375786	+	0.433680i	0.911867	−	0.410487i	$-0.134641\pi$
$757$	10.3392	+	11.9321i	0.375786	+	0.433680i	−0.536081	+	0.844167i	$0.680096\pi$
$758$	6.76957	+	11.7252i	0.245882	+	0.425880i
$759$	−1.62085	−	35.6086i	−0.0588330	−	1.29251i
$760$	−0.409576	+	0.709407i	−0.0148569	+	0.0257329i
$761$	8.64969	−	1.66709i	0.313551	−	0.0604320i	−0.0300479	−	0.999548i	$-0.509566\pi$
$761$	8.64969	−	1.66709i	0.313551	−	0.0604320i	0.343599	+	0.939116i	$0.388354\pi$
$762$	−3.42782	−	25.2604i	−0.124177	−	0.915089i
$763$	23.0985	−	9.24723i	0.836220	−	0.334772i
$764$	3.00612	−	6.58248i	0.108757	−	0.238146i
$765$	2.27643	+	0.0360817i	0.0823043	+	0.00130453i
$766$	−26.5437	−	7.79392i	−0.959062	−	0.281606i
$767$	6.61021	+	3.40780i	0.238681	+	0.123049i
$768$	1.72546	−	0.150974i	0.0622621	−	0.00544779i
$769$	1.59796	−	6.58688i	0.0576239	−	0.237529i	−0.935715	−	0.352756i	$-0.885244\pi$
$769$	1.59796	−	6.58688i	0.0576239	−	0.237529i	0.993339	+	0.115227i	$0.0367596\pi$
$770$	3.81271	+	11.0161i	0.137401	+	0.396993i
$771$	−2.07668	−	3.66365i	−0.0747897	−	0.131943i
$772$	11.3960	+	10.8661i	0.410152	+	0.391079i
$773$	−5.15871	−	11.2960i	−0.185546	−	0.406289i	0.793885	−	0.608068i	$-0.208055\pi$
$773$	−5.15871	−	11.2960i	−0.185546	−	0.406289i	−0.979431	+	0.201779i	$0.935328\pi$
$774$	2.48253	+	5.67219i	0.0892326	+	0.203883i
$775$	25.6362	+	7.52747i	0.920880	+	0.270395i
$776$	9.09776	−	7.15456i	0.326591	−	0.256834i
$777$	−31.4000	+	8.95021i	−1.12647	+	0.321087i
$778$	1.85691	+	1.46029i	0.0665736	+	0.0523541i
$779$	6.45086	−	3.32565i	0.231126	−	0.119154i
$780$	1.91830	+	1.53333i	0.0686863	+	0.0549019i
$781$	9.01082	+	15.6072i	0.322433	+	0.558470i
$782$	−1.51058	−	3.25748i	−0.0540182	−	0.116487i
$783$	−16.7134	−	9.12562i	−0.597288	−	0.326123i
$784$	−0.119630	−	0.138060i	−0.00427249	−	0.00493072i
$785$	−0.789063	+	16.5645i	−0.0281629	+	0.591211i
$786$	0.0778635	+	1.96148i	0.00277730	+	0.0699636i
$787$	−20.1405	−	28.2833i	−0.717930	−	1.00819i	−0.998825	−	0.0484533i	$-0.984571\pi$
$787$	−20.1405	−	28.2833i	−0.717930	−	1.00819i	0.280895	−	0.959738i	$-0.409369\pi$
$788$	−18.3435	−	7.34364i	−0.653461	−	0.261606i
$789$	1.37467	+	3.07435i	0.0489396	+	0.109450i
$790$	−9.49626	−	4.89566i	−0.337862	−	0.174180i
$791$	−9.67542	−	21.1862i	−0.344018	−	0.753295i
$792$	−11.8741	−	4.97345i	−0.421929	−	0.176724i
$793$	−0.00582842	+	0.00672635i	−0.000206973	+	0.000238860i
$794$	1.27025	+	0.244821i	0.0450796	+	0.00868839i
$795$	0.865567	−	15.5729i	0.0306985	−	0.552316i
$796$	5.82651	+	0.556364i	0.206515	+	0.0197198i
$797$	−1.27665	−	26.8001i	−0.0452211	−	0.949308i	−0.901496	−	0.432788i	$-0.857530\pi$
$797$	−1.27665	−	26.8001i	−0.0452211	−	0.949308i	0.856275	−	0.516521i	$-0.172773\pi$
$798$	−2.20018	+	3.03847i	−0.0778856	+	0.107561i
$799$	0.879287	−	0.691479i	0.0311069	−	0.0244628i
$800$	1.65027	−	3.61359i	0.0583459	−	0.127760i
$801$	−6.30105	−	27.8957i	−0.222637	−	0.985647i
$802$	10.5111	+	6.75507i	0.371160	+	0.238530i
$803$	12.7533	−	36.8481i	0.450053	−	1.30034i
$804$	−8.45938	−	9.92041i	−0.298339	−	0.349866i
$805$	−12.9761	−	1.16301i	−0.457347	−	0.0409906i
$806$	4.70402	−	8.14760i	0.165692	−	0.286987i
$807$	−22.9219	−	18.3218i	−0.806890	−	0.644959i
$808$	0.343908	−	7.21952i	0.0120987	−	0.253982i
$809$	−3.77199	+	26.2348i	−0.132616	+	0.922365i	0.809510	+	0.587106i	$0.199733\pi$
$809$	−3.77199	+	26.2348i	−0.132616	+	0.922365i	−0.942126	+	0.335259i	$0.891176\pi$
$810$	2.70898	+	8.71104i	0.0951839	+	0.306075i
$811$	−5.86749	−	40.8093i	−0.206035	−	1.43301i	−0.785930	−	0.618316i	$-0.787815\pi$
$811$	−5.86749	−	40.8093i	−0.206035	−	1.43301i	0.579894	−	0.814692i	$-0.303094\pi$
$812$	−2.31554	−	9.54478i	−0.0812595	−	0.334956i
$813$	22.6720	−	21.2772i	0.795140	−	0.746225i
$814$	−30.0467	−	2.86911i	−1.05313	−	0.100562i
$815$	4.26522	−	17.5815i	0.149404	−	0.615852i
$816$	−1.29676	−	0.0102763i	−0.0453957	−	0.000359742i
$817$	1.63779	+	0.315658i	0.0572989	+	0.0110435i
$818$	−22.0878	+	6.48557i	−0.772283	+	0.226763i
$819$	8.01558	+	7.88912i	0.280087	+	0.275668i
$820$	7.65782	−	4.92138i	0.267423	−	0.171862i
$821$	−9.34599	−	38.5247i	−0.326177	−	1.34452i	−0.864861	−	0.502012i	$-0.832593\pi$
$821$	−9.34599	−	38.5247i	−0.326177	−	1.34452i	0.538683	−	0.842508i	$-0.318922\pi$
$822$	34.4283	+	6.91891i	1.20083	+	0.241325i
$823$	−17.6683	−	24.8116i	−0.615877	−	0.864878i	0.382373	−	0.924008i	$-0.375107\pi$
$823$	−17.6683	−	24.8116i	−0.615877	−	0.864878i	−0.998250	+	0.0591296i	$0.981167\pi$
$824$	5.36171	+	4.21650i	0.186784	+	0.146889i
$825$	−23.3534	+	18.0676i	−0.813059	+	0.629034i
$826$	−4.66032	+	13.4651i	−0.162153	+	0.468511i
$827$	−12.3166			−0.428291			−0.214146	−	0.976802i	$-0.568697\pi$
$827$	−12.3166			−0.428291			−0.214146	+	0.976802i	$0.568697\pi$
$828$	10.5118	−	9.82349i	0.365312	−	0.341390i
$829$	9.51140			0.330345			0.165172	−	0.986265i	$-0.447182\pi$
$829$	9.51140			0.330345			0.165172	+	0.986265i	$0.447182\pi$
$830$	−3.64037	+	10.5182i	−0.126359	+	0.365090i
$831$	0.681519	+	5.02228i	0.0236416	+	0.174221i
$832$	−1.09954	−	0.864689i	−0.0381198	−	0.0299777i
$833$	0.0793366	+	0.111413i	0.00274885	+	0.00386022i
$834$	6.27616	+	18.6096i	0.217326	+	0.644398i
$835$	−5.90790	−	24.3527i	−0.204451	−	0.842759i
$836$	−2.91741	+	1.87491i	−0.100901	+	0.0648450i
$837$	31.4348	−	15.2711i	1.08655	−	0.527848i
$838$	10.6603	−	3.13015i	0.368254	−	0.108129i
$839$	24.5597	+	4.73349i	0.847894	+	0.163418i	0.594651	−	0.803984i	$-0.297290\pi$
$839$	24.5597	+	4.73349i	0.847894	+	0.163418i	0.253244	+	0.967402i	$0.418503\pi$
$840$	−2.38481	+	4.05605i	−0.0822839	+	0.139947i
$841$	−3.67073	+	15.1310i	−0.126577	+	0.521757i
$842$	23.9309	+	2.28513i	0.824714	+	0.0787506i
$843$	−12.1491	−	3.67213i	−0.418438	−	0.126475i
$844$	−1.98397	−	8.17803i	−0.0682910	−	0.281499i
$845$	1.59303	+	11.0798i	0.0548018	+	0.381155i
$846$	3.73175	+	2.48269i	0.128300	+	0.0853566i
$847$	−2.82795	+	19.6689i	−0.0971696	+	0.675830i
$848$	−0.422716	+	8.87389i	−0.0145161	+	0.304731i
$849$	−15.6878	+	6.13666i	−0.538404	+	0.210610i
$850$	−1.48715	+	2.57583i	−0.0510090	+	0.0883501i
$851$	16.6963	−	29.3109i	0.572342	−	1.00477i
$852$	−2.43350	+	6.85491i	−0.0833704	+	0.234845i
$853$	−13.8738	+	40.0856i	−0.475028	+	1.37250i	0.412166	+	0.911109i	$0.364772\pi$
$853$	−13.8738	+	40.0856i	−0.475028	+	1.37250i	−0.887194	+	0.461396i	$0.847349\pi$
$854$	−0.0143454	−	0.00921922i	−0.000490889	−	0.000315475i
$855$	2.34665	+	0.729628i	0.0802536	+	0.0249527i
$856$	−6.07495	+	13.3023i	−0.207638	+	0.454663i
$857$	8.58011	−	6.74748i	0.293091	−	0.230489i	−0.460776	−	0.887517i	$-0.652429\pi$
$857$	8.58011	−	6.74748i	0.293091	−	0.230489i	0.753867	+	0.657027i	$0.228186\pi$
$858$	4.24391	+	9.49119i	0.144885	+	0.324024i
$859$	−0.252821	−	5.30736i	−0.00862613	−	0.181085i	−0.999068	−	0.0431564i	$-0.986259\pi$
$859$	−0.252821	−	5.30736i	−0.00862613	−	0.181085i	0.990442	−	0.137928i	$-0.0440444\pi$
$860$	2.08252	+	0.198856i	0.0710133	+	0.00678094i
$861$	37.2038	−	18.8082i	1.26790	−	0.640982i
$862$	−29.5514	−	5.69557i	−1.00653	−	0.193992i
$863$	30.8391	−	35.5903i	1.04978	−	1.21151i	0.0729805	−	0.997333i	$-0.476749\pi$
$863$	30.8391	−	35.5903i	1.04978	−	1.21151i	0.976796	−	0.214173i	$-0.0687056\pi$
$864$	−1.58229	−	4.94938i	−0.0538306	−	0.168381i
$865$	−3.87246	−	8.47950i	−0.131668	−	0.288312i
$866$	7.51247	+	3.87295i	0.255284	+	0.131608i
$867$	−28.3227	−	2.93115i	−0.961888	−	0.0995471i
$868$	16.7341	+	6.69933i	0.567993	+	0.227390i
$869$	−26.2366	−	36.8442i	−0.890016	−	1.24985i
$870$	−5.43994	+	3.43543i	−0.184431	+	0.116472i
$871$	−0.500996	+	10.5172i	−0.0169756	+	0.356362i
$872$	6.07951	+	7.01613i	0.205878	+	0.237596i
$873$	−26.9497	−	21.8935i	−0.912109	−	0.740984i
$874$	−0.573862	−	3.83303i	−0.0194112	−	0.129654i
$875$	12.1872	+	21.1089i	0.412003	+	0.713610i
$876$	14.6571	−	5.73346i	0.495216	−	0.193716i
$877$	2.00160	−	1.03190i	0.0675893	−	0.0348447i	−0.424101	−	0.905615i	$-0.639410\pi$
$877$	2.00160	−	1.03190i	0.0675893	−	0.0348447i	0.491690	+	0.870770i	$0.336379\pi$
$878$	−5.34810	−	4.20580i	−0.180490	−	0.141939i
$879$	−4.54329	−	4.40128i	−0.153241	−	0.148451i
$880$	−3.41904	+	2.68877i	−0.115256	+	0.0906383i
$881$	9.56533	+	2.80863i	0.322264	+	0.0946253i	0.438864	−	0.898554i	$-0.355381\pi$
$881$	9.56533	+	2.80863i	0.322264	+	0.0946253i	−0.116599	+	0.993179i	$0.537199\pi$
$882$	−0.324929	+	0.441325i	−0.0109409	+	0.0148602i
$883$	13.8393	+	30.3038i	0.465728	+	1.01980i	0.986144	+	0.165890i	$0.0530496\pi$
$883$	13.8393	+	30.3038i	0.465728	+	1.01980i	−0.520416	+	0.853913i	$0.674223\pi$
$884$	0.757970	+	0.722723i	0.0254933	+	0.0243078i
$885$	9.33372	+	0.0739657i	0.313750	+	0.00248633i
$886$	4.00548	+	11.5731i	0.134567	+	0.388805i
$887$	−13.1007	+	54.0016i	−0.439877	+	1.81320i	0.130057	+	0.991507i	$0.458484\pi$
$887$	−13.1007	+	54.0016i	−0.439877	+	1.81320i	−0.569934	+	0.821691i	$0.693031\pi$
$888$	−6.98788	−	9.97953i	−0.234498	−	0.334891i
$889$	−35.0596	−	18.0745i	−1.17586	−	0.606199i
$890$	−9.27124	−	2.72228i	−0.310773	−	0.0912510i
$891$	−6.70509	+	38.0344i	−0.224629	+	1.27420i
$892$	0.308727	−	0.676018i	0.0103370	−	0.0226348i
$893$	1.12093	−	0.448751i	0.0375104	−	0.0150169i
$894$	−9.85980	−	4.03821i	−0.329761	−	0.135058i
$895$	24.9628	−	4.81119i	0.834415	−	0.160820i
$896$	1.34003	−	2.32099i	0.0447671	−	0.0775389i
$897$	−11.6194	−	0.0245502i	−0.387960	−	0.000819708i
$898$	16.0141	+	27.7373i	0.534398	+	0.925605i
$899$	16.1409	+	18.6276i	0.538330	+	0.621266i
$900$	−11.6652	−	2.44063i	−0.388839	−	0.0813542i
$901$	0.946607	−	6.58380i	0.0315361	−	0.219338i
$902$	38.3630	−	3.66323i	1.27735	−	0.121972i
$903$	9.39274	+	1.88762i	0.312571	+	0.0628161i
$904$	6.28960	−	5.99712i	0.209189	−	0.199461i
$905$	−1.09852	−	23.0607i	−0.0365160	−	0.766564i
$906$	−33.3893	+	2.92148i	−1.10929	+	0.0970598i
$907$	−12.8601	−	12.2621i	−0.427012	−	0.407155i	0.445861	−	0.895102i	$-0.352898\pi$
$907$	−12.8601	−	12.2621i	−0.427012	−	0.407155i	−0.872873	+	0.487947i	$0.837746\pi$
$908$	−8.90138	+	10.2727i	−0.295403	+	0.340913i
$909$	−21.3537	+	3.76562i	−0.708256	+	0.124898i
$910$	3.64601	−	1.07057i	0.120864	−	0.0354889i
$911$	8.62016	−	12.1053i	0.285599	−	0.401067i	−0.646707	−	0.762738i	$-0.723854\pi$
$911$	8.62016	−	12.1053i	0.285599	−	0.401067i	0.932306	+	0.361671i	$0.117794\pi$
$912$	−1.33989	−	0.404987i	−0.0443681	−	0.0134105i
$913$	−34.1030	+	32.5171i	−1.12864	+	1.07616i
$914$	−29.2427	−	11.7070i	−0.967262	−	0.387233i
$915$	−0.00271951	+	0.0108345i	−8.99041e−5	+	0.000358177i
$916$	−9.86232	+	3.94828i	−0.325860	+	0.130455i
$917$	2.55526	+	1.64217i	0.0843821	+	0.0542291i
$918$	0.827067	+	3.80148i	0.0272973	+	0.125467i
$919$	−41.1277			−1.35668			−0.678338	−	0.734750i	$-0.737300\pi$
$919$	−41.1277			−1.35668			−0.678338	+	0.734750i	$0.737300\pi$
$920$	−1.17349	−	4.71736i	−0.0386888	−	0.155527i
$921$	28.2333	−	5.20983i	0.930318	−	0.171670i
$922$	16.4698	−	3.17430i	0.542405	−	0.104540i
$923$	5.22151	−	2.69188i	0.171868	−	0.0886042i
$924$	−16.8423	+	10.6363i	−0.554073	+	0.349908i
$925$	−27.8157	+	2.65608i	−0.914574	+	0.0873312i
$926$	1.34956	+	9.38640i	0.0443493	+	0.308456i
$927$	8.79464	−	18.4769i	0.288854	−	0.606861i
$928$	3.08296	−	1.98130i	0.101203	−	0.0650392i
$929$	−23.5653	+	33.0929i	−0.773153	+	1.08574i	0.220733	+	0.975334i	$0.429155\pi$
$929$	−23.5653	+	33.0929i	−0.773153	+	1.08574i	−0.993886	+	0.110407i	$0.964784\pi$
$930$	0.655290	−	11.7897i	0.0214878	−	0.386600i
$931$	0.0482858	+	0.139513i	0.00158250	+	0.00457234i
$932$	−3.85205	−	11.1298i	−0.126178	−	0.364568i
$933$	−1.18185	+	21.2635i	−0.0386922	+	0.696135i
$934$	−12.1482	+	17.0598i	−0.397502	+	0.558214i
$935$	2.73964	−	1.76066i	0.0895957	−	0.0575797i
$936$	−1.80354	+	3.78911i	−0.0589506	+	0.123851i
$937$	4.88646	+	33.9861i	0.159634	+	1.11028i	0.899309	+	0.437313i	$0.144070\pi$
$937$	4.88646	+	33.9861i	0.159634	+	1.11028i	−0.739676	+	0.672963i	$0.765021\pi$
$938$	−20.0819	+	1.91759i	−0.655697	+	0.0626115i
$939$	24.9410	−	15.7507i	0.813919	−	0.514006i
$940$	1.34605	−	0.693936i	0.0439032	−	0.0226337i
$941$	−3.01437	+	0.580972i	−0.0982657	+	0.0189392i	−0.238147	−	0.971229i	$-0.576540\pi$
$941$	−3.01437	+	0.580972i	−0.0982657	+	0.0189392i	0.139881	+	0.990168i	$0.455328\pi$
$942$	−27.8667	+	5.14219i	−0.907947	+	0.167541i
$943$	−13.8498	+	40.7818i	−0.451013	+	1.32804i
$944$	−5.31660			−0.173041
$945$	13.4454	+	4.29764i	0.437380	+	0.139802i
$946$	7.45062	+	4.78822i	0.242241	+	0.155679i
$947$	−0.939388	+	0.376074i	−0.0305260	+	0.0122208i	−0.386875	−	0.922132i	$-0.626446\pi$
$947$	−0.939388	+	0.376074i	−0.0305260	+	0.0122208i	0.356349	+	0.934353i	$0.384021\pi$
$948$	4.44460	−	17.7073i	0.144354	−	0.575105i
$949$	−11.8001	−	4.72403i	−0.383046	−	0.153348i
$950$	−2.32350	+	2.21546i	−0.0753844	+	0.0718789i
$951$	−12.5315	−	3.78770i	−0.406362	−	0.122825i
$952$	−1.16393	+	1.63451i	−0.0377232	+	0.0529748i
$953$	−49.6573	+	14.5807i	−1.60856	+	0.472315i	−0.957911	−	0.287066i	$-0.907320\pi$
$953$	−49.6573	+	14.5807i	−1.60856	+	0.472315i	−0.650646	+	0.759381i	$0.725502\pi$
$954$	26.2469	−	4.62852i	0.849774	−	0.149854i
$955$	−4.80337	+	5.54338i	−0.155433	+	0.179380i
$956$	4.56665	+	4.35429i	0.147696	+	0.140828i
$957$	−27.1347	+	2.37422i	−0.877139	+	0.0767476i
$958$	−0.482632	−	10.1317i	−0.0155931	−	0.327340i
$959$	39.3256	−	37.4968i	1.26989	−	1.21084i
$960$	−1.72122	−	0.345906i	−0.0555522	−	0.0111641i
$961$	−14.1710	+	1.35316i	−0.457128	+	0.0436504i
$962$	−1.40023	+	9.73878i	−0.0451451	+	0.313991i
$963$	42.9416	+	8.98440i	1.38378	+	0.289518i
$964$	15.9341	+	18.3890i	0.513204	+	0.592269i
$965$	−7.98028	−	13.8222i	−0.256894	−	0.444954i
$966$	−3.12167	−	22.0422i	−0.100438	−	0.709197i
$967$	−14.5477	+	25.1974i	−0.467824	+	0.810295i	−0.999324	−	0.0367634i	$-0.988295\pi$
$967$	−14.5477	+	25.1974i	−0.467824	+	0.810295i	0.531500	+	0.847058i	$0.321629\pi$
$968$	−7.28046	+	1.40319i	−0.234003	+	0.0451004i
$969$	0.969821	+	0.397203i	0.0311551	+	0.0127600i
$970$	−10.8912	+	4.36019i	−0.349696	+	0.139997i
$971$	0.446416	−	0.977514i	0.0143262	−	0.0313699i	−0.902334	−	0.431038i	$-0.858147\pi$
$971$	0.446416	−	0.977514i	0.0143262	−	0.0313699i	0.916660	+	0.399668i	$0.130875\pi$
$972$	−13.4374	+	7.90168i	−0.431004	+	0.253447i
$973$	29.1577	+	8.56148i	0.934754	+	0.274469i
$974$	−37.8811	−	19.5291i	−1.21379	−	0.625752i
$975$	5.52065	+	7.88416i	0.176802	+	0.252495i
$976$	0.00150006	−	0.00618335i	4.80159e−5	−	0.000197924i
$977$	12.0546	+	34.8294i	0.385660	+	1.11429i	0.956122	+	0.292968i	$0.0946428\pi$
$977$	12.0546	+	34.8294i	0.385660	+	1.11429i	−0.570462	+	0.821324i	$0.693236\pi$
$978$	30.9134	+	0.244975i	0.988500	+	0.00783344i
$979$	−29.6061	−	28.2293i	−0.946214	−	0.902213i
$980$	0.0769212	+	0.168434i	0.00245716	+	0.00538042i
$981$	16.5127	−	22.4279i	0.527209	−	0.716067i
$982$	20.7632	+	6.09663i	0.662581	+	0.194551i
$983$	−5.19249	+	4.08342i	−0.165615	+	0.130241i	−0.697527	−	0.716559i	$-0.745716\pi$
$983$	−5.19249	+	4.08342i	−0.165615	+	0.130241i	0.531912	+	0.846800i	$0.321474\pi$
$984$	11.1721	+	10.8229i	0.356155	+	0.345022i
$985$	15.7430	+	12.3805i	0.501615	+	0.394474i
$986$	−2.43879	+	1.25729i	−0.0776670	+	0.0400401i
$987$	6.45880	−	2.52651i	0.205586	−	0.0804198i
$988$	0.565225	+	0.978998i	0.0179822	+	0.0311461i
$989$	−8.29554	+	5.39960i	−0.263783	+	0.171697i
$990$	10.1280	+	8.22784i	0.321889	+	0.261498i
$991$	−6.79727	−	7.84447i	−0.215922	−	0.249188i	0.637447	−	0.770494i	$-0.279990\pi$
$991$	−6.79727	−	7.84447i	−0.215922	−	0.249188i	−0.853370	+	0.521306i	$0.825445\pi$
$992$	−0.320023	+	6.71811i	−0.0101607	+	0.213300i
$993$	−25.2193	+	15.9265i	−0.800311	+	0.505413i
$994$	6.52873	+	9.16832i	0.207079	+	0.290802i
$995$	−5.50774	−	2.20497i	−0.174607	−	0.0699021i
$996$	−18.9183	−	1.95787i	−0.599448	−	0.0620376i
$997$	48.7922	+	25.1541i	1.54526	+	0.796639i	0.999156	−	0.0410763i	$-0.0130787\pi$
$997$	48.7922	+	25.1541i	1.54526	+	0.796639i	0.546108	+	0.837715i	$0.316109\pi$
$998$	3.35189	+	7.33961i	0.106102	+	0.232331i
$999$	−24.5840	+	27.0448i	−0.777804	+	0.855659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.1	✓	240
9.7	even	3	inner	414.2.m.a.151.4	yes	240
23.16	even	11	inner	414.2.m.a.85.4	yes	240
207.16	even	33	inner	414.2.m.a.223.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.1	✓	240	1.1	even	1	trivial
414.2.m.a.85.4	yes	240	23.16	even	11	inner
414.2.m.a.151.4	yes	240	9.7	even	3	inner
414.2.m.a.223.1	yes	240	207.16	even	33	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(-1.60283 - 0.656460i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.587955 + 0.825667i) q^{5} +(-1.14459 + 1.29997i) q^{6} +(0.631846 + 2.60451i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.13812 + 2.10439i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(-1.60283 - 0.656460i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.587955 + 0.825667i) q^{5} +(-1.14459 + 1.29997i) q^{6} +(0.631846 + 2.60451i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.13812 + 2.10439i) q^{9} +(0.972558 - 0.285569i) q^{10} +(4.21366 + 0.812116i) q^{11} +(0.854112 + 1.50682i) q^{12} +(0.329783 - 1.35938i) q^{13} +(2.66792 + 0.254755i) q^{14} +(-0.400374 - 1.70937i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.106552 - 0.741088i) q^{17} +(2.68796 - 1.33225i) q^{18} +(0.115012 - 0.799923i) q^{19} +(0.0482298 - 1.01247i) q^{20} +(0.697013 - 4.58936i) q^{21} +(2.14560 - 3.71629i) q^{22} +(2.80451 + 3.89034i) q^{23} +(1.70329 - 0.314305i) q^{24} +(1.29930 - 3.75409i) q^{25} +(-1.17676 - 0.756256i) q^{26} +(-2.04559 - 4.77656i) q^{27} +(1.11333 - 2.43786i) q^{28} +(2.88066 - 2.26538i) q^{29} +(-1.74631 - 0.180728i) q^{30} +(0.320023 + 6.71811i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(-6.22065 - 4.06778i) q^{33} +(-0.735179 - 0.141694i) q^{34} +(-1.77896 + 2.05303i) q^{35} +(-0.379830 - 2.97586i) q^{36} +(-2.92193 - 6.39814i) q^{37} +(-0.718311 - 0.370315i) q^{38} +(-1.42097 + 1.96237i) q^{39} +(-0.941009 - 0.376723i) q^{40} +(5.20925 + 7.31537i) q^{41} +(-4.10898 - 2.15971i) q^{42} +(-0.0982038 + 2.06155i) q^{43} +(-2.81014 - 3.24308i) q^{44} +(-0.480405 + 3.00266i) q^{45} +(4.59364 - 1.37786i) q^{46} +(0.747026 + 1.29389i) q^{47} +(0.260074 - 1.71241i) q^{48} +(-0.162372 + 0.0837086i) q^{49} +(-3.12266 - 2.45569i) q^{50} +(-0.315710 + 1.25779i) q^{51} +(-1.09954 + 0.864689i) q^{52} +(8.52409 + 2.50290i) q^{53} +(-5.18290 + 0.370828i) q^{54} +(1.80690 + 3.95657i) q^{55} +(-1.93964 - 1.84945i) q^{56} +(-0.709462 + 1.20664i) q^{57} +(-1.19861 - 3.46316i) q^{58} +(-1.25344 + 5.16674i) q^{59} +(-0.741949 + 1.59115i) q^{60} +(-0.00565540 - 0.00291556i) q^{61} +(6.45329 + 1.89486i) q^{62} +(-4.12992 + 6.89839i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.31630 - 0.526965i) q^{65} +(-5.87863 + 4.54808i) q^{66} +(-7.39116 + 1.42453i) q^{67} +(-0.374355 + 0.648401i) q^{68} +(-1.94130 - 8.07659i) q^{69} +(1.35827 + 2.35260i) q^{70} +(2.75020 + 3.17390i) q^{71} +(-2.93642 - 0.614368i) q^{72} +(1.29317 - 8.99417i) q^{73} +(-7.00192 + 0.668602i) q^{74} +(-4.54698 + 5.16423i) q^{75} +(-0.584885 + 0.557687i) q^{76} +(0.547223 + 11.4876i) q^{77} +(1.38969 + 1.98464i) q^{78} +(-7.62846 - 7.27372i) q^{79} +(-0.663777 + 0.766040i) q^{80} +(0.143114 + 8.99886i) q^{81} +(8.61681 - 2.53012i) q^{82} +(-6.36949 + 8.94469i) q^{83} +(-3.38484 + 3.17661i) q^{84} +(0.549244 - 0.523703i) q^{85} +(1.91605 + 0.767070i) q^{86} +(-6.10434 + 1.73997i) q^{87} +(-3.98382 + 1.59488i) q^{88} +(-8.01953 - 5.15384i) q^{89} +(2.68039 + 1.43606i) q^{90} +3.74889 q^{91} +(0.200352 - 4.79164i) q^{92} +(3.89723 - 10.9781i) q^{93} +(1.46705 - 0.282751i) q^{94} +(0.728092 - 0.375358i) q^{95} +(-1.53317 - 0.805846i) q^{96} +(-11.5216 + 1.10018i) q^{97} +(0.0259980 + 0.180820i) q^{98} +(7.30030 + 10.6036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

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