LMFDB - Embedded newform 392.2.z.a.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19828 - 0.751090i) q^{2} +(0.581041 + 0.626213i) q^{3} +(0.871727 + 1.80003i) q^{4} +(-0.147712 + 0.478871i) q^{5} +(-0.225904 - 1.18679i) q^{6} +(2.54532 - 0.722043i) q^{7} +(0.307412 - 2.81167i) q^{8} +(0.169656 - 2.26390i) q^{9} +O(q^{10})$	\(q+(-1.19828 - 0.751090i) q^{2} +(0.581041 + 0.626213i) q^{3} +(0.871727 + 1.80003i) q^{4} +(-0.147712 + 0.478871i) q^{5} +(-0.225904 - 1.18679i) q^{6} +(2.54532 - 0.722043i) q^{7} +(0.307412 - 2.81167i) q^{8} +(0.169656 - 2.26390i) q^{9} +(0.536675 - 0.462874i) q^{10} +(-1.85026 + 0.138658i) q^{11} +(-0.620690 + 1.59178i) q^{12} +(0.132527 - 0.275195i) q^{13} +(-3.59231 - 1.04656i) q^{14} +(-0.385702 + 0.185744i) q^{15} +(-2.48018 + 3.13826i) q^{16} +(5.30929 + 0.800247i) q^{17} +(-1.90369 + 2.58535i) q^{18} +(2.82642 + 1.63184i) q^{19} +(-0.990744 + 0.151559i) q^{20} +(1.93109 + 1.17438i) q^{21} +(2.32127 + 1.22356i) q^{22} +(1.54014 - 0.232139i) q^{23} +(1.93932 - 1.44119i) q^{24} +(3.92370 + 2.67513i) q^{25} +(-0.365501 + 0.230220i) q^{26} +(3.51991 - 2.80704i) q^{27} +(3.51852 + 3.95222i) q^{28} +(-1.53472 - 1.22390i) q^{29} +(0.601688 + 0.0671242i) q^{30} +(1.25229 + 2.16902i) q^{31} +(5.32906 - 1.89766i) q^{32} +(-1.16191 - 1.07809i) q^{33} +(-5.76093 - 4.94667i) q^{34} +(-0.0302091 + 1.32553i) q^{35} +(4.22297 - 1.66812i) q^{36} +(-7.96832 + 3.12733i) q^{37} +(-2.16118 - 4.07828i) q^{38} +(0.249335 - 0.0769096i) q^{39} +(1.30102 + 0.562529i) q^{40} +(-2.42235 - 10.6130i) q^{41} +(-1.43191 - 2.85765i) q^{42} +(11.6561 + 2.66042i) q^{43} +(-1.86251 - 3.20965i) q^{44} +(1.05906 + 0.415649i) q^{45} +(-2.01987 - 0.878620i) q^{46} +(-5.80626 + 3.95864i) q^{47} +(-3.40631 + 0.270336i) q^{48} +(5.95731 - 3.67566i) q^{49} +(-2.69240 - 6.15259i) q^{50} +(2.58379 + 3.78972i) q^{51} +(0.610886 - 0.00134317i) q^{52} +(-8.58578 - 3.36967i) q^{53} +(-6.32616 + 0.719831i) q^{54} +(0.206907 - 0.906519i) q^{55} +(-1.24769 - 7.37857i) q^{56} +(0.620390 + 2.71811i) q^{57} +(0.919762 + 2.61929i) q^{58} +(2.05306 + 6.65587i) q^{59} +(-0.670571 - 0.532355i) q^{60} +(8.93192 - 3.50552i) q^{61} +(0.128548 - 3.53967i) q^{62} +(-1.20281 - 5.88485i) q^{63} +(-7.81100 - 1.72868i) q^{64} +(0.112207 + 0.104113i) q^{65} +(0.582541 + 2.16455i) q^{66} +(1.84379 - 1.06451i) q^{67} +(3.18779 + 10.2545i) q^{68} +(1.04026 + 0.829576i) q^{69} +(1.03179 - 1.56567i) q^{70} +(3.67997 + 4.61453i) q^{71} +(-6.31319 - 1.17297i) q^{72} +(-9.40355 - 6.41123i) q^{73} +(11.8971 + 2.23752i) q^{74} +(0.604626 + 4.01143i) q^{75} +(-0.473476 + 6.51015i) q^{76} +(-4.60939 + 1.68890i) q^{77} +(-0.356538 - 0.0951140i) q^{78} +(-3.32010 + 5.75059i) q^{79} +(-1.13647 - 1.65125i) q^{80} +(-2.93166 - 0.441877i) q^{81} +(-5.06868 + 14.5367i) q^{82} +(0.776799 + 1.61304i) q^{83} +(-0.430525 + 4.49974i) q^{84} +(-1.16746 + 2.42426i) q^{85} +(-11.9690 - 11.9427i) q^{86} +(-0.125314 - 1.67220i) q^{87} +(-0.178932 + 5.24496i) q^{88} +(-0.590524 + 7.87999i) q^{89} +(-0.956851 - 1.29351i) q^{90} +(0.138621 - 0.796151i) q^{91} +(1.76044 + 2.56994i) q^{92} +(-0.630642 + 2.04449i) q^{93} +(9.93079 - 0.382517i) q^{94} +(-1.19894 + 1.11245i) q^{95} +(4.28474 + 2.23451i) q^{96} -4.65673 q^{97} +(-9.89925 - 0.0700191i) q^{98} +4.21234i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−1.19828	−	0.751090i	−0.847309	−	0.531101i
$2$	−1.19828	−	0.751090i	−0.847309	−	0.531101i
$3$	0.581041	+	0.626213i	0.335464	+	0.361544i	0.878145	−	0.478395i	$-0.158781\pi$
$3$	0.581041	+	0.626213i	0.335464	+	0.361544i	−0.542681	+	0.839939i	$0.682591\pi$
$4$	0.871727	+	1.80003i	0.435864	+	0.900013i
$5$	−0.147712	+	0.478871i	−0.0660589	+	0.214158i	−0.982584	−	0.185820i	$-0.940506\pi$
$5$	−0.147712	+	0.478871i	−0.0660589	+	0.214158i	0.916525	+	0.399978i	$0.130982\pi$
$6$	−0.225904	−	1.18679i	−0.0922251	−	0.484505i
$7$	2.54532	−	0.722043i	0.962041	−	0.272907i
$7$	2.54532	−	0.722043i	0.962041	−	0.272907i
$8$	0.307412	−	2.81167i	0.108687	−	0.994076i
$9$	0.169656	−	2.26390i	0.0565520	−	0.754634i
$10$	0.536675	−	0.462874i	0.169712	−	0.146374i
$11$	−1.85026	+	0.138658i	−0.557875	+	0.0418070i	−0.350685	−	0.936494i	$-0.614051\pi$
$11$	−1.85026	+	0.138658i	−0.557875	+	0.0418070i	−0.207191	+	0.978301i	$0.566432\pi$
$12$	−0.620690	+	1.59178i	−0.179178	+	0.459506i
$13$	0.132527	−	0.275195i	0.0367564	−	0.0763255i	−0.881782	−	0.471657i	$-0.843656\pi$
$13$	0.132527	−	0.275195i	0.0367564	−	0.0763255i	0.918538	+	0.395332i	$0.129370\pi$
$14$	−3.59231	−	1.04656i	−0.960086	−	0.279704i
$15$	−0.385702	+	0.185744i	−0.0995878	+	0.0479590i
$16$	−2.48018	+	3.13826i	−0.620046	+	0.784566i
$17$	5.30929	+	0.800247i	1.28769	+	0.194088i	0.756966	−	0.653455i	$-0.226681\pi$
$17$	5.30929	+	0.800247i	1.28769	+	0.194088i	0.530726	+	0.847543i	$0.321919\pi$
$18$	−1.90369	+	2.58535i	−0.448703	+	0.609373i
$19$	2.82642	+	1.63184i	0.648426	+	0.374369i	0.787853	−	0.615864i	$-0.211193\pi$
$19$	2.82642	+	1.63184i	0.648426	+	0.374369i	−0.139427	+	0.990232i	$0.544526\pi$
$20$	−0.990744	+	0.151559i	−0.221537	+	0.0338897i
$21$	1.93109	+	1.17438i	0.421398	+	0.256270i
$22$	2.32127	+	1.22356i	0.494896	+	0.260865i
$23$	1.54014	−	0.232139i	0.321142	−	0.0484044i	0.0135070	−	0.999909i	$-0.495700\pi$
$23$	1.54014	−	0.232139i	0.321142	−	0.0484044i	0.307635	+	0.951504i	$0.400462\pi$
$24$	1.93932	−	1.44119i	0.395863	−	0.294182i
$25$	3.92370	+	2.67513i	0.784739	+	0.535026i
$26$	−0.365501	+	0.230220i	−0.0716806	+	0.0451499i
$27$	3.51991	−	2.80704i	0.677407	−	0.540214i
$28$	3.51852	+	3.95222i	0.664938	+	0.746899i
$29$	−1.53472	−	1.22390i	−0.284991	−	0.227273i	0.470551	−	0.882373i	$-0.344055\pi$
$29$	−1.53472	−	1.22390i	−0.284991	−	0.227273i	−0.755542	+	0.655100i	$0.772627\pi$
$30$	0.601688	+	0.0671242i	0.109853	+	0.0122551i
$31$	1.25229	+	2.16902i	0.224917	+	0.389568i	0.956295	−	0.292405i	$-0.0944555\pi$
$31$	1.25229	+	2.16902i	0.224917	+	0.389568i	−0.731377	+	0.681973i	$0.761122\pi$
$32$	5.32906	−	1.89766i	0.942054	−	0.335462i
$33$	−1.16191	−	1.07809i	−0.202262	−	0.187672i
$34$	−5.76093	−	4.94667i	−0.987992	−	0.848347i
$35$	−0.0302091	+	1.32553i	−0.00510626	+	0.224056i
$36$	4.22297	−	1.66812i	0.703829	−	0.278020i
$37$	−7.96832	+	3.12733i	−1.30998	+	0.514131i	−0.914590	−	0.404382i	$-0.867487\pi$
$37$	−7.96832	+	3.12733i	−1.30998	+	0.514131i	−0.395393	+	0.918512i	$0.629392\pi$
$38$	−2.16118	−	4.07828i	−0.350589	−	0.661585i
$39$	0.249335	−	0.0769096i	0.0399255	−	0.0123154i
$40$	1.30102	+	0.562529i	0.205709	+	0.0889436i
$41$	−2.42235	−	10.6130i	−0.378307	−	1.65747i	−0.702653	−	0.711532i	$-0.748001\pi$
$41$	−2.42235	−	10.6130i	−0.378307	−	1.65747i	0.324346	−	0.945938i	$-0.394856\pi$
$42$	−1.43191	−	2.85765i	−0.220949	−	0.440944i
$43$	11.6561	+	2.66042i	1.77754	+	0.405711i	0.980230	−	0.197864i	$-0.0634004\pi$
$43$	11.6561	+	2.66042i	1.77754	+	0.405711i	0.797306	+	0.603575i	$0.206258\pi$
$44$	−1.86251	−	3.20965i	−0.280784	−	0.483873i
$45$	1.05906	+	0.415649i	0.157875	+	0.0619613i
$46$	−2.01987	−	0.878620i	−0.297814	−	0.129545i
$47$	−5.80626	+	3.95864i	−0.846930	+	0.577427i	−0.907173	−	0.420757i	$-0.861765\pi$
$47$	−5.80626	+	3.95864i	−0.846930	+	0.577427i	0.0602438	+	0.998184i	$0.480812\pi$
$48$	−3.40631	+	0.270336i	−0.491658	+	0.0390196i
$49$	5.95731	−	3.67566i	0.851044	−	0.525095i
$50$	−2.69240	−	6.15259i	−0.380763	−	0.870108i
$51$	2.58379	+	3.78972i	0.361803	+	0.530667i
$52$	0.610886	−	0.00134317i	0.0847147	−	0.000186264i
$53$	−8.58578	−	3.36967i	−1.17935	−	0.462860i	−0.306983	−	0.951715i	$-0.599319\pi$
$53$	−8.58578	−	3.36967i	−1.17935	−	0.462860i	−0.872365	+	0.488855i	$0.837415\pi$
$54$	−6.32616	+	0.719831i	−0.860881	+	0.0979566i
$55$	0.206907	−	0.906519i	0.0278993	−	0.122235i
$56$	−1.24769	−	7.37857i	−0.166729	−	0.986003i
$57$	0.620390	+	2.71811i	0.0821726	+	0.360022i
$58$	0.919762	+	2.61929i	0.120771	+	0.343929i
$59$	2.05306	+	6.65587i	0.267286	+	0.866520i	0.985350	+	0.170543i	$0.0545522\pi$
$59$	2.05306	+	6.65587i	0.267286	+	0.866520i	−0.718064	+	0.695977i	$0.754972\pi$
$60$	−0.670571	−	0.532355i	−0.0865704	−	0.0687267i
$61$	8.93192	−	3.50552i	1.14362	−	0.448836i	0.283518	−	0.958967i	$-0.408498\pi$
$61$	8.93192	−	3.50552i	1.14362	−	0.448836i	0.860097	+	0.510131i	$0.170403\pi$
$62$	0.128548	−	3.53967i	0.0163257	−	0.449538i
$63$	−1.20281	−	5.88485i	−0.151539	−	0.741421i
$64$	−7.81100	−	1.72868i	−0.976374	−	0.216085i
$65$	0.112207	+	0.104113i	0.0139176	+	0.0129136i
$66$	0.582541	+	2.16455i	0.0717058	+	0.266438i
$67$	1.84379	−	1.06451i	0.225254	−	0.130051i	−0.383127	−	0.923696i	$-0.625153\pi$
$67$	1.84379	−	1.06451i	0.225254	−	0.130051i	0.608381	+	0.793645i	$0.291819\pi$
$68$	3.18779	+	10.2545i	0.386576	+	1.24354i
$69$	1.04026	+	0.829576i	0.125232	+	0.0998692i
$70$	1.03179	−	1.56567i	0.123323	−	0.187133i
$71$	3.67997	+	4.61453i	0.436732	+	0.547644i	0.950679	−	0.310178i	$-0.100389\pi$
$71$	3.67997	+	4.61453i	0.436732	+	0.547644i	−0.513947	+	0.857822i	$0.671817\pi$
$72$	−6.31319	−	1.17297i	−0.744017	−	0.138235i
$73$	−9.40355	−	6.41123i	−1.10060	−	0.750378i	−0.130107	−	0.991500i	$-0.541532\pi$
$73$	−9.40355	−	6.41123i	−1.10060	−	0.750378i	−0.970495	+	0.241122i	$0.922484\pi$
$74$	11.8971	+	2.23752i	1.38302	+	0.260106i
$75$	0.604626	+	4.01143i	0.0698162	+	0.463200i
$76$	−0.473476	+	6.51015i	−0.0543114	+	0.746765i
$77$	−4.60939	+	1.68890i	−0.525289	+	0.192468i
$78$	−0.356538	−	0.0951140i	−0.0403699	−	0.0107695i
$79$	−3.32010	+	5.75059i	−0.373541	+	0.646991i	−0.990107	−	0.140311i	$-0.955190\pi$
$79$	−3.32010	+	5.75059i	−0.373541	+	0.646991i	0.616567	+	0.787303i	$0.288523\pi$
$80$	−1.13647	−	1.65125i	−0.127061	−	0.184615i
$81$	−2.93166	−	0.441877i	−0.325740	−	0.0490974i
$82$	−5.06868	+	14.5367i	−0.559742	+	1.60531i
$83$	0.776799	+	1.61304i	0.0852648	+	0.177054i	0.939241	−	0.343257i	$-0.111530\pi$
$83$	0.776799	+	1.61304i	0.0852648	+	0.177054i	−0.853977	+	0.520311i	$0.825816\pi$
$84$	−0.430525	+	4.49974i	−0.0469741	+	0.490962i
$85$	−1.16746	+	2.42426i	−0.126629	+	0.262948i
$86$	−11.9690	−	11.9427i	−1.29065	−	1.28781i
$87$	−0.125314	−	1.67220i	−0.0134351	−	0.179279i
$88$	−0.178932	+	5.24496i	−0.0190742	+	0.559114i
$89$	−0.590524	+	7.87999i	−0.0625954	+	0.835277i	0.874237	+	0.485499i	$0.161362\pi$
$89$	−0.590524	+	7.87999i	−0.0625954	+	0.835277i	−0.936833	+	0.349778i	$0.886257\pi$
$90$	−0.956851	−	1.29351i	−0.100861	−	0.136348i
$91$	0.138621	−	0.796151i	0.0145314	−	0.0834593i
$92$	1.76044	+	2.56994i	0.183539	+	0.267934i
$93$	−0.630642	+	2.04449i	−0.0653945	+	0.212004i
$94$	9.93079	−	0.382517i	1.02428	−	0.0394536i
$95$	−1.19894	+	1.11245i	−0.123008	+	0.114135i
$96$	4.28474	+	2.23451i	0.437310	+	0.228059i
$97$	−4.65673			−0.472819			−0.236410	−	0.971653i	$-0.575971\pi$
$97$	−4.65673			−0.472819			−0.236410	+	0.971653i	$0.575971\pi$
$98$	−9.89925	−	0.0700191i	−0.999975	−	0.00707300i
$99$			4.21234i			0.423356i
$100$	−1.39491	+	9.39474i	−0.139491	+	0.939474i
$101$	−11.1919	−	12.0620i	−1.11364	−	1.20022i	−0.977812	−	0.209485i	$-0.932821\pi$
$101$	−11.1919	−	12.0620i	−1.11364	−	1.20022i	−0.135827	−	0.990733i	$-0.543369\pi$
$102$	−0.249668	−	6.48179i	−0.0247208	−	0.641793i
$103$	−6.83786	−	2.10920i	−0.673754	−	0.207826i	−0.0610460	−	0.998135i	$-0.519444\pi$
$103$	−6.83786	−	2.10920i	−0.673754	−	0.207826i	−0.612708	+	0.790309i	$0.709920\pi$
$104$	−0.733019	−	0.457221i	−0.0718784	−	0.0448342i
$105$	−0.847620	+	0.751272i	−0.0827192	+	0.0733167i
$106$	7.75720	+	10.4865i	0.753446	+	1.01854i
$107$	−18.2950	−	1.37102i	−1.76864	−	0.132541i	−0.849784	−	0.527131i	$-0.823268\pi$
$107$	−18.2950	−	1.37102i	−1.76864	−	0.132541i	−0.918857	+	0.394590i	$0.870887\pi$
$108$	8.12114	+	3.88896i	0.781457	+	0.374215i
$109$	−3.12514	+	0.234197i	−0.299334	+	0.0224320i	−0.223551	−	0.974692i	$-0.571765\pi$
$109$	−3.12514	+	0.234197i	−0.299334	+	0.0224320i	−0.0757833	+	0.997124i	$0.524146\pi$
$110$	−0.928809	+	0.930853i	−0.0885584	+	0.0887534i
$111$	−6.58830	−	3.17276i	−0.625333	−	0.301145i
$112$	−4.04690	+	9.77868i	−0.382396	+	0.923999i
$113$	0.938166	−	0.451797i	0.0882552	−	0.0425015i	−0.389235	−	0.921138i	$-0.627261\pi$
$113$	0.938166	−	0.451797i	0.0882552	−	0.0425015i	0.477491	+	0.878637i	$0.341546\pi$
$114$	1.29814	−	3.72301i	0.121582	−	0.348692i
$115$	−0.116333	+	0.771820i	−0.0108481	+	0.0719726i
$116$	0.865194	−	3.82945i	0.0803312	−	0.355556i
$117$	−0.600531	−	0.346717i	−0.0555191	−	0.0320540i
$118$	2.53902	−	9.51760i	0.233736	−	0.876166i
$119$	14.0917	−	1.79665i	1.29178	−	0.164699i
$120$	0.403683	+	1.14157i	0.0368510	+	0.104210i
$121$	−7.47289	+	1.12636i	−0.679354	+	0.102396i
$122$	−13.3359	−	2.50810i	−1.20737	−	0.227073i
$123$	5.23851	−	7.68349i	0.472341	−	0.692797i
$124$	−2.81265	+	4.14494i	−0.252583	+	0.372227i
$125$	−3.81963	+	3.04606i	−0.341639	+	0.272448i
$126$	−2.97876	+	7.95509i	−0.265369	+	0.708695i
$127$	−7.40838	+	9.28982i	−0.657388	+	0.824338i	−0.993056	−	0.117642i	$-0.962466\pi$
$127$	−7.40838	+	9.28982i	−0.657388	+	0.824338i	0.335669	+	0.941980i	$0.391038\pi$
$128$	8.06133	+	7.93820i	0.712527	+	0.701644i
$129$	5.10667	+	8.84501i	0.449617	+	0.778759i
$130$	−0.0562568	−	0.209034i	−0.00493405	−	0.0183335i
$131$	3.68305	−	3.96938i	0.321789	−	0.346807i	−0.551353	−	0.834272i	$-0.685888\pi$
$131$	3.68305	−	3.96938i	0.321789	−	0.346807i	0.873142	+	0.487466i	$0.162079\pi$
$132$	0.927728	−	3.03127i	0.0807484	−	0.263838i
$133$	8.37240	+	2.11274i	0.725979	+	0.183198i
$134$	−3.00891	−	0.109273i	−0.259930	−	0.00943975i
$135$	0.824274	+	2.10022i	0.0709422	+	0.180758i
$136$	3.88217	−	14.6820i	0.332893	−	1.25897i
$137$	−5.50113	+	1.69687i	−0.469993	+	0.144974i	−0.520700	−	0.853740i	$-0.674329\pi$
$137$	−5.50113	+	1.69687i	−0.469993	+	0.144974i	0.0507066	+	0.998714i	$0.483853\pi$
$138$	−0.623426	−	1.77539i	−0.0530695	−	0.151131i
$139$	2.98905	−	0.682231i	0.253528	−	0.0578661i	−0.0938680	−	0.995585i	$-0.529923\pi$
$139$	2.98905	−	0.682231i	0.253528	−	0.0578661i	0.347396	+	0.937719i	$0.387066\pi$
$140$	−2.41233	+	1.10113i	−0.203879	+	0.0930622i
$141$	−5.85262	−	1.33582i	−0.492880	−	0.112497i
$142$	−0.943684	−	8.29347i	−0.0791922	−	0.695972i
$143$	−0.207052	+	0.527560i	−0.0173146	+	0.0441168i
$144$	6.68394	+	6.14731i	0.556995	+	0.512276i
$145$	0.812789	−	0.554150i	0.0674984	−	0.0460196i
$146$	6.45263	+	14.7453i	0.534023	+	1.22033i
$147$	5.76319	+	1.59483i	0.475340	+	0.131540i
$148$	−12.5755	−	11.6170i	−1.03370	−	0.954911i
$149$	4.81068	+	7.05597i	0.394106	+	0.578048i	0.971092	−	0.238707i	$-0.0767234\pi$
$149$	4.81068	+	7.05597i	0.394106	+	0.578048i	−0.576985	+	0.816754i	$0.695771\pi$
$150$	2.28844	−	5.26093i	0.186850	−	0.429553i
$151$	0.445602	−	1.13538i	0.0362626	−	0.0923956i	−0.911595	−	0.411089i	$-0.865149\pi$
$151$	0.445602	−	1.13538i	0.0362626	−	0.0923956i	0.947858	+	0.318693i	$0.103244\pi$
$152$	5.45706	−	7.44532i	0.442626	−	0.603895i
$153$	2.71243	−	11.8839i	0.219287	−	0.960759i
$154$	6.79184	+	1.43830i	0.547302	+	0.115902i
$155$	−1.22366	+	0.279292i	−0.0982868	+	0.0224333i
$156$	0.355791	+	0.381765i	0.0284861	+	0.0305656i
$157$	−4.67932	−	15.1700i	−0.373450	−	1.21070i	−0.926098	−	0.377282i	$-0.876859\pi$
$157$	−4.67932	−	15.1700i	−0.373450	−	1.21070i	0.552648	−	0.833415i	$-0.313617\pi$
$158$	8.29760	−	4.39709i	0.660122	−	0.349814i
$159$	−2.87856	−	7.33444i	−0.228284	−	0.581659i
$160$	0.121568	+	2.83224i	0.00961082	+	0.223908i
$161$	3.75254	−	1.70292i	0.295742	−	0.134209i
$162$	3.18105	+	2.73143i	0.249927	+	0.214601i
$163$	0.381857	−	0.411544i	0.0299093	−	0.0322346i	−0.717920	−	0.696126i	$-0.754906\pi$
$163$	0.381857	−	0.411544i	0.0299093	−	0.0322346i	0.747829	+	0.663891i	$0.231096\pi$
$164$	16.9920	−	13.6119i	1.32685	−	1.06291i
$165$	0.687895	−	0.397157i	0.0535526	−	0.0309186i
$166$	0.280719	−	2.51631i	0.0217880	−	0.195304i
$167$	0.783572	−	0.982569i	0.0606347	−	0.0760335i	−0.750589	−	0.660769i	$-0.770230\pi$
$167$	0.783572	−	0.982569i	0.0606347	−	0.0760335i	0.811224	+	0.584736i	$0.198802\pi$
$168$	3.89560	−	5.06857i	0.300552	−	0.391049i
$169$	8.04720	+	10.0909i	0.619015	+	0.776221i
$170$	3.21978	−	2.02806i	0.246946	−	0.155545i
$171$	4.17383	−	6.12189i	0.319181	−	0.468152i
$172$	5.37209	+	23.3004i	0.409618	+	1.77664i
$173$	−0.533886	−	3.54210i	−0.0405906	−	0.269301i	0.959325	−	0.282304i	$-0.0910988\pi$
$173$	−0.533886	−	3.54210i	−0.0405906	−	0.269301i	−0.999915	+	0.0130035i	$0.995861\pi$
$174$	−1.10581	+	2.09788i	−0.0838315	+	0.159040i
$175$	11.9186	+	3.97598i	0.900963	+	0.300556i
$176$	4.15385	−	6.15051i	0.313108	−	0.463612i
$177$	−2.97508	+	5.15299i	−0.223621	+	0.387322i
$178$	6.62619	−	8.99886i	0.496654	−	0.674493i
$179$	3.55669	−	23.5971i	0.265839	−	1.76373i	−0.314408	−	0.949288i	$-0.601806\pi$
$179$	3.55669	−	23.5971i	0.265839	−	1.76373i	0.580247	−	0.814441i	$-0.302956\pi$
$180$	0.175030	+	2.26866i	0.0130459	+	0.169096i
$181$	−6.57279	−	13.6485i	−0.488552	−	1.01449i	−0.988889	−	0.148658i	$-0.952505\pi$
$181$	−6.57279	−	13.6485i	−0.488552	−	1.01449i	0.500337	−	0.865831i	$-0.333210\pi$
$182$	−0.764087	+	0.849891i	−0.0566379	+	0.0629981i
$183$	7.38501	+	3.55644i	0.545916	+	0.262899i
$184$	−0.179241	−	4.40174i	−0.0132138	−	0.324501i
$185$	−0.320572	−	4.27774i	−0.0235689	−	0.314506i
$186$	2.29128	−	1.97619i	0.168005	−	0.144901i
$187$	−9.93455	−	0.744491i	−0.726486	−	0.0544426i
$188$	−12.1871	−	7.00056i	−0.888837	−	0.510568i
$189$	6.93250	−	9.68633i	0.504265	−	0.704577i
$190$	2.27220	−	0.432512i	0.164843	−	0.0313777i
$191$	−1.13436	−	0.349903i	−0.0820792	−	0.0253181i	0.253444	−	0.967350i	$-0.418437\pi$
$191$	−1.13436	−	0.349903i	−0.0820792	−	0.0253181i	−0.335523	+	0.942032i	$0.608913\pi$
$192$	−3.45598	−	5.89578i	−0.249414	−	0.425492i
$193$	−9.16433	+	8.50326i	−0.659663	+	0.612078i	−0.937265	−	0.348618i	$-0.886651\pi$
$193$	−9.16433	+	8.50326i	−0.659663	+	0.612078i	0.277602	+	0.960696i	$0.410460\pi$
$194$	5.58005	+	3.49762i	0.400624	+	0.251115i
$195$			0.130760i			0.00936389i
$196$	11.8094	+	7.51913i	0.843531	+	0.537081i
$197$			12.1515i			0.865757i	0.901452	+	0.432879i	$0.142502\pi$
$197$			12.1515i			0.865757i	−0.901452	+	0.432879i	$0.857498\pi$
$198$	3.16384	−	5.04754i	0.224845	−	0.358713i
$199$	−5.73858	+	5.32463i	−0.406797	+	0.377453i	−0.856864	−	0.515542i	$-0.827591\pi$
$199$	−5.73858	+	5.32463i	−0.406797	+	0.377453i	0.450067	+	0.892995i	$0.351400\pi$
$200$	8.72778	−	10.2098i	0.617147	−	0.721940i
$201$	1.73793	+	0.536079i	0.122584	+	0.0378121i
$202$	4.35134	+	22.8598i	0.306159	+	1.60841i
$203$	−4.79008	−	2.00709i	−0.336197	−	0.140870i
$204$	−4.56924	+	7.95449i	−0.319911	+	0.556926i
$205$	5.44006	+	0.407676i	0.379950	+	0.0284734i
$206$	6.60944	+	7.66325i	0.460501	+	0.533924i
$207$	−0.264246	−	3.52612i	−0.0183664	−	0.245082i
$208$	0.534944	+	1.09844i	0.0370917	+	0.0761631i
$209$	−5.45589	−	2.62742i	−0.377392	−	0.181742i
$210$	1.57995	−	0.263592i	0.109027	−	0.0181896i
$211$	3.91419	+	8.12789i	0.269464	+	0.559547i	0.991161	−	0.132661i	$-0.0423522\pi$
$211$	3.91419	+	8.12789i	0.269464	+	0.559547i	−0.721698	+	0.692208i	$0.756638\pi$
$212$	−1.41897	−	18.3921i	−0.0974550	−	1.26317i
$213$	−0.751470	+	4.98568i	−0.0514899	+	0.341613i
$214$	20.8927	+	15.3840i	1.42819	+	1.05163i
$215$	−2.99574	+	5.18878i	−0.204308	+	0.353872i
$216$	−6.81040	−	10.7598i	−0.463389	−	0.732108i
$217$	4.75360	+	4.61665i	0.322695	+	0.313399i
$218$	3.92068	+	2.06663i	0.265542	+	0.139970i
$219$	−1.44905	−	9.61381i	−0.0979176	−	0.649641i
$220$	1.81212	−	0.417799i	0.122173	−	0.0281680i
$221$	0.923849	−	1.35504i	0.0621448	−	0.0911497i
$222$	5.51157	+	8.75024i	0.369912	+	0.587278i
$223$	−0.134983	−	0.169263i	−0.00903912	−	0.0113347i	0.777291	−	0.629141i	$-0.216593\pi$
$223$	−0.134983	−	0.169263i	−0.00903912	−	0.0113347i	−0.786331	+	0.617806i	$0.788022\pi$
$224$	12.1940	−	8.67797i	0.814744	−	0.579821i
$225$	6.72191	−	8.42900i	0.448127	−	0.561934i
$226$	−1.46352	−	0.163270i	−0.0973520	−	0.0108606i
$227$	−21.5088	+	12.4181i	−1.42759	+	0.824217i	−0.996930	−	0.0782988i	$-0.975051\pi$
$227$	−21.5088	+	12.4181i	−1.42759	+	0.824217i	−0.430656	+	0.902516i	$0.641718\pi$
$228$	−4.35185	+	3.48616i	−0.288208	+	0.230877i
$229$	14.5553	−	15.6869i	0.961843	−	1.03662i	−0.0374605	−	0.999298i	$-0.511927\pi$
$229$	14.5553	−	15.6869i	0.961843	−	1.03662i	0.999303	−	0.0373219i	$-0.0118827\pi$
$230$	0.719105	−	0.837476i	0.0474164	−	0.0552215i
$231$	−3.73586	−	1.90514i	−0.245801	−	0.125349i
$232$	−3.91300	+	3.93890i	−0.256901	+	0.258601i
$233$	1.01721	+	2.59181i	0.0666396	+	0.169795i	0.960314	−	0.278921i	$-0.0899768\pi$
$233$	1.01721	+	2.59181i	0.0666396	+	0.169795i	−0.893674	+	0.448716i	$0.851882\pi$
$234$	0.459186	+	0.866515i	0.0300179	+	0.0566459i
$235$	−1.03802	−	3.36519i	−0.0677131	−	0.219521i
$236$	−10.1910	+	9.49767i	−0.663379	+	0.618246i
$237$	−5.53021	+	1.26223i	−0.359226	+	0.0819909i
$238$	−18.2351	−	8.43122i	−1.18201	−	0.546515i
$239$	1.42438	−	6.24064i	0.0921358	−	0.403673i	−0.907738	−	0.419537i	$-0.862193\pi$
$239$	1.42438	−	6.24064i	0.0921358	−	0.403673i	0.999874	+	0.0158634i	$0.00504969\pi$
$240$	0.373697	−	1.67111i	0.0241220	−	0.107870i
$241$	−2.30781	+	5.88020i	−0.148659	+	0.378777i	−0.985734	−	0.168311i	$-0.946169\pi$
$241$	−2.30781	+	5.88020i	−0.148659	+	0.378777i	0.837075	+	0.547088i	$0.184264\pi$
$242$	9.80058	+	4.26313i	0.630005	+	0.274044i
$243$	−9.03514	−	13.2521i	−0.579604	−	0.850123i
$244$	14.0962	+	13.0218i	0.902418	+	0.833637i
$245$	0.880201	+	3.39572i	0.0562340	+	0.216945i
$246$	−12.0482	+	5.27234i	−0.768163	+	0.336152i
$247$	0.823651	−	0.561556i	0.0524077	−	0.0357309i
$248$	6.48355	−	2.85423i	0.411706	−	0.181244i
$249$	−0.558755	+	1.42368i	−0.0354097	+	0.0902223i
$250$	6.86484	−	0.781125i	0.434170	−	0.0494027i
$251$	26.9465	+	6.15037i	1.70085	+	0.388208i	0.959233	−	0.282615i	$-0.0912018\pi$
$251$	26.9465	+	6.15037i	1.70085	+	0.388208i	0.741617	+	0.670823i	$0.234059\pi$
$252$	9.54436	−	7.29507i	0.601238	−	0.459546i
$253$	−2.81748	+	0.643072i	−0.177134	+	0.0404296i
$254$	15.8548	−	5.56740i	0.994817	−	0.349329i
$255$	−2.19645	+	0.677514i	−0.137547	+	0.0424276i
$256$	−3.69739	−	15.5669i	−0.231087	−	0.972933i
$257$	−3.94089	−	10.0412i	−0.245826	−	0.626354i	0.753697	−	0.657222i	$-0.228268\pi$
$257$	−3.94089	−	10.0412i	−0.245826	−	0.626354i	−0.999523	+	0.0308670i	$0.990173\pi$
$258$	0.524204	−	14.4343i	0.0326355	−	0.898642i
$259$	−18.0238	+	13.7135i	−1.11995	+	0.852118i
$260$	−0.0895921	+	0.292734i	−0.00555627	+	0.0181546i
$261$	−3.03117	+	3.26682i	−0.187625	+	0.202211i
$262$	−7.39467	+	1.99011i	−0.456844	+	0.122949i
$263$	10.0251	+	17.3640i	0.618173	+	1.07071i	0.989819	+	0.142333i	$0.0454603\pi$
$263$	10.0251	+	17.3640i	0.618173	+	1.07071i	−0.371646	+	0.928375i	$0.621206\pi$
$264$	−3.38843	+	2.93549i	−0.208543	+	0.180667i
$265$	2.88186	−	3.61374i	0.177031	−	0.221990i
$266$	−8.44558	−	8.82008i	−0.517832	−	0.540794i
$267$	−5.27767	+	4.20880i	−0.322988	+	0.257575i
$268$	3.52342	+	2.39090i	0.215227	+	0.146047i
$269$	1.51732	−	2.22550i	0.0925128	−	0.135691i	−0.777192	−	0.629263i	$-0.783357\pi$
$269$	1.51732	−	2.22550i	0.0925128	−	0.135691i	0.869705	+	0.493572i	$0.164309\pi$
$270$	0.589744	−	3.13574i	0.0358907	−	0.190835i
$271$	−26.0427	+	3.92530i	−1.58198	+	0.238445i	−0.880430	−	0.474176i	$-0.842746\pi$
$271$	−26.0427	+	3.92530i	−1.58198	+	0.238445i	−0.701549	+	0.712621i	$0.747508\pi$
$272$	−15.6794	+	14.6772i	−0.950703	+	0.889935i
$273$	0.579105	−	0.375790i	0.0350490	−	0.0227438i
$274$	7.86637	+	2.09852i	0.475225	+	0.126776i
$275$	−7.63080	−	4.40564i	−0.460154	−	0.265670i
$276$	−0.586439	+	2.59565i	−0.0352995	+	0.156240i
$277$	−1.25235	+	8.30879i	−0.0752464	+	0.499227i	0.919184	+	0.393829i	$0.128850\pi$
$277$	−1.25235	+	8.30879i	−0.0752464	+	0.499227i	−0.994430	+	0.105398i	$0.966388\pi$
$278$	−4.09412	−	1.42754i	−0.245549	−	0.0856185i
$279$	5.12291	−	2.46706i	0.306701	−	0.147699i
$280$	3.71768	+	0.492423i	0.222174	+	0.0294279i
$281$	13.8328	+	6.66154i	0.825198	+	0.397394i	0.798312	−	0.602244i	$-0.205727\pi$
$281$	13.8328	+	6.66154i	0.825198	+	0.397394i	0.0268857	+	0.999639i	$0.491441\pi$
$282$	6.00973	+	5.99653i	0.357874	+	0.357088i
$283$	−18.1641	+	1.36121i	−1.07974	+	0.0809156i	−0.602703	−	0.797966i	$-0.705910\pi$
$283$	−18.1641	+	1.36121i	−1.07974	+	0.0809156i	−0.477041	+	0.878881i	$0.658291\pi$
$284$	−5.09835	+	10.6467i	−0.302531	+	0.631763i
$285$	−1.39326	−	0.104410i	−0.0825296	−	0.00618474i
$286$	0.644350	−	0.476647i	0.0381012	−	0.0281847i
$287$	−13.8287	−	25.2644i	−0.816281	−	1.49131i
$288$	−3.39201	−	12.3864i	−0.199876	−	0.729876i
$289$	11.3034	+	3.48665i	0.664908	+	0.205097i
$290$	−1.39016	+	0.0535466i	−0.0816331	+	0.00314437i
$291$	−2.70575	−	2.91611i	−0.158614	−	0.170945i
$292$	3.34305	−	22.5155i	0.195637	−	1.31762i
$293$			30.1607i			1.76201i	0.473110	+	0.881003i	$0.343131\pi$
$293$			30.1607i			1.76201i	−0.473110	+	0.881003i	$0.656869\pi$
$294$	−5.70802	−	6.23972i	−0.332899	−	0.363908i
$295$	−3.49056			−0.203228
$296$	6.34348	+	23.3657i	0.368707	+	1.35810i
$297$	−6.12354	+	5.68182i	−0.355324	+	0.329693i
$298$	−0.464849	−	12.0683i	−0.0269280	−	0.699095i
$299$	0.140227	−	0.454605i	0.00810955	−	0.0262905i
$300$	−6.69361	+	4.58521i	−0.386456	+	0.264727i
$301$	31.5894	−	1.64456i	1.82078	−	0.0947911i
$302$	−1.38672	+	1.02581i	−0.0797970	+	0.0590285i
$303$	1.05043	−	14.0171i	0.0603459	−	0.805260i
$304$	−12.1312	+	4.82280i	−0.695770	+	0.276607i
$305$	0.359339	+	4.79504i	0.0205757	+	0.274563i
$306$	−12.1761	+	12.2029i	−0.696064	+	0.697596i
$307$	4.14567	−	8.60857i	0.236606	−	0.491317i	−0.748529	−	0.663102i	$-0.769239\pi$
$307$	4.14567	−	8.60857i	0.236606	−	0.491317i	0.985134	+	0.171786i	$0.0549537\pi$
$308$	−7.05820	−	6.82477i	−0.402178	−	0.388877i
$309$	−2.65227	−	5.50749i	−0.150882	−	0.313310i
$310$	1.67606	+	0.584410i	0.0951936	+	0.0331922i
$311$	18.7613	+	2.82782i	1.06386	+	0.160351i	0.657569	−	0.753394i	$-0.271585\pi$
$311$	18.7613	+	2.82782i	1.06386	+	0.160351i	0.406289	+	0.913745i	$0.366823\pi$
$312$	−0.139596	−	0.724690i	−0.00790307	−	0.0410275i
$313$	3.52247	−	6.10110i	0.199102	−	0.344854i	−0.749136	−	0.662417i	$-0.769531\pi$
$313$	3.52247	−	6.10110i	0.199102	−	0.344854i	0.948237	+	0.317562i	$0.102864\pi$
$314$	−5.78691	+	21.6924i	−0.326574	+	1.22417i
$315$	2.99575	+	0.293275i	0.168792	+	0.0165242i
$316$	−13.2454	−	0.963326i	−0.745113	−	0.0541913i
$317$	3.79967	+	25.2092i	0.213411	+	1.41589i	0.797069	+	0.603888i	$0.206383\pi$
$317$	3.79967	+	25.2092i	0.213411	+	1.41589i	−0.583658	+	0.811999i	$0.698379\pi$
$318$	−2.05952	+	10.9507i	−0.115492	+	0.614087i
$319$	3.00935	+	2.05174i	0.168491	+	0.114875i
$320$	1.98159	−	3.48511i	0.110775	−	0.194824i
$321$	−9.77158	−	12.2532i	−0.545396	−	0.683905i
$322$	−5.77563	−	0.777932i	−0.321863	−	0.0433525i
$323$	13.7004	+	10.9257i	0.762312	+	0.607923i
$324$	−1.76022	−	5.66226i	−0.0977900	−	0.314570i
$325$	1.25618	−	0.725256i	0.0696803	−	0.0402300i
$326$	−0.766676	+	0.206334i	−0.0424623	+	0.0114278i
$327$	−1.96249	−	1.82092i	−0.108526	−	0.100697i
$328$	−30.5849	+	3.54828i	−1.68877	+	0.195921i
$329$	−11.9205	+	14.2684i	−0.657197	+	0.786641i
$330$	−1.12259	−	0.0407685i	−0.0617965	−	0.00224423i
$331$	−11.2545	+	4.41706i	−0.618603	+	0.242784i	−0.653885	−	0.756594i	$-0.726862\pi$
$331$	−11.2545	+	4.41706i	−0.618603	+	0.242784i	0.0352825	+	0.999377i	$0.488767\pi$
$332$	−2.22636	+	2.80439i	−0.122187	+	0.153911i
$333$	5.72810	+	18.5700i	0.313898	+	1.01763i
$334$	−1.67693	+	0.588854i	−0.0917577	+	0.0322207i
$335$	0.237413	+	1.04018i	0.0129713	+	0.0568309i
$336$	−8.47495	+	3.14759i	−0.462347	+	0.171715i
$337$	1.39261	−	6.10142i	0.0758602	−	0.332365i	−0.922730	−	0.385447i	$-0.874047\pi$
$337$	1.39261	−	6.10142i	0.0758602	−	0.332365i	0.998590	+	0.0530817i	$0.0169044\pi$
$338$	−2.06361	−	18.1358i	−0.112245	−	0.986458i
$339$	0.828034	+	0.324979i	0.0449726	+	0.0176505i
$340$	−5.38143	+	0.0118323i	−0.291849	+	0.000641695i
$341$	−2.61781	−	3.83962i	−0.141762	−	0.207927i
$342$	−9.59949	+	4.20078i	−0.519081	+	0.227152i
$343$	12.5093	−	13.6572i	0.675437	−	0.737418i
$344$	11.0635	−	31.9552i	0.596502	−	1.72291i
$345$	−0.550918	+	0.375610i	−0.0296604	+	0.0202221i
$346$	−2.02069	+	4.64541i	−0.108633	+	0.249739i
$347$	−9.54654	−	3.74674i	−0.512485	−	0.201136i	0.0949840	−	0.995479i	$-0.469720\pi$
$347$	−9.54654	−	3.74674i	−0.512485	−	0.201136i	−0.607469	+	0.794343i	$0.707815\pi$
$348$	2.90077	−	1.68327i	0.155497	−	0.0902329i
$349$	23.1853	+	5.29189i	1.24108	+	0.283268i	0.792166	−	0.610306i	$-0.208954\pi$
$349$	23.1853	+	5.29189i	1.24108	+	0.283268i	0.448915	+	0.893575i	$0.351811\pi$
$350$	−11.2955	−	13.7163i	−0.603768	−	0.733166i
$351$	−0.306000	−	1.34067i	−0.0163331	−	0.0715598i
$352$	−9.59704	+	4.25009i	−0.511524	+	0.226531i
$353$	0.275361	−	0.0849376i	0.0146560	−	0.00452077i	−0.287419	−	0.957805i	$-0.592797\pi$
$353$	0.275361	−	0.0849376i	0.0146560	−	0.00452077i	0.302075	+	0.953284i	$0.402321\pi$
$354$	7.43532	−	3.94014i	0.395183	−	0.209416i
$355$	−2.75334	+	1.08061i	−0.146132	+	0.0573527i
$356$	−14.6990	+	5.80624i	−0.779043	+	0.307730i
$357$	9.31292	+	7.78045i	0.492892	+	0.411785i
$358$	−21.9854	+	25.6044i	−1.16197	+	1.35323i
$359$	21.7005	+	20.1351i	1.14531	+	1.06269i	0.997280	+	0.0737057i	$0.0234826\pi$
$359$	21.7005	+	20.1351i	1.14531	+	1.06269i	0.148026	+	0.988983i	$0.452708\pi$
$360$	1.49423	−	2.84994i	0.0787531	−	0.150205i
$361$	−4.17423	−	7.22997i	−0.219696	−	0.380525i
$362$	−2.37527	+	21.2915i	−0.124842	+	1.11906i
$363$	−5.04739	−	4.02516i	−0.264920	−	0.211266i
$364$	1.55393	−	0.444505i	0.0814481	−	0.0232984i
$365$	4.45917	−	3.55607i	0.233404	−	0.186133i
$366$	−6.17808	−	9.80840i	−0.322933	−	0.512693i
$367$	−28.3009	−	19.2952i	−1.47729	−	1.00720i	−0.991067	−	0.133368i	$-0.957421\pi$
$367$	−28.3009	−	19.2952i	−1.47729	−	1.00720i	−0.486226	−	0.873833i	$-0.661627\pi$
$368$	−3.09132	+	5.40912i	−0.161146	+	0.281970i
$369$	−24.4377	+	3.68339i	−1.27218	+	0.191750i
$370$	−2.82883	+	5.36669i	−0.147064	+	0.279001i
$371$	−24.2866	−	2.37758i	−1.26090	−	0.123438i
$372$	−4.22988	+	0.647067i	−0.219309	+	0.0335488i
$373$	31.8669	+	18.3984i	1.65001	+	0.952632i	0.977066	+	0.212936i	$0.0683027\pi$
$373$	31.8669	+	18.3984i	1.65001	+	0.952632i	0.672941	+	0.739696i	$0.265031\pi$
$374$	11.3451	+	8.35384i	0.586643	+	0.431967i
$375$	−4.12684	−	0.622022i	−0.213109	−	0.0321211i
$376$	9.34548	+	17.5422i	0.481956	+	0.904671i
$377$	−0.540205	+	0.260149i	−0.0278220	+	0.0133984i
$378$	−15.5824	+	6.39996i	−0.801470	+	0.329178i
$379$	−9.52896	+	19.7871i	−0.489470	+	1.01640i	0.499227	+	0.866471i	$0.333617\pi$
$379$	−9.52896	+	19.7871i	−0.489470	+	1.01640i	−0.988698	+	0.149924i	$0.952097\pi$
$380$	−3.04758	−	1.18836i	−0.156338	−	0.0609616i
$381$	−10.1220	+	0.758537i	−0.518565	+	0.0388610i
$382$	1.09646	+	1.27128i	0.0560999	+	0.0650445i
$383$	1.03641	−	13.8299i	0.0529581	−	0.706677i	−0.906027	−	0.423220i	$-0.860900\pi$
$383$	1.03641	−	13.8299i	0.0529581	−	0.706677i	0.958985	−	0.283457i	$-0.0914813\pi$
$384$	−0.287045	+	9.66053i	−0.0146482	+	0.492987i
$385$	−0.127901	−	2.45678i	−0.00651845	−	0.125209i
$386$	17.3681	−	3.30601i	0.884014	−	0.168271i
$387$	8.00046	−	25.9369i	0.406686	−	1.31844i
$388$	−4.05940	−	8.38223i	−0.206085	−	0.425543i
$389$	4.35630	+	4.69498i	0.220873	+	0.238045i	0.833761	−	0.552125i	$-0.186183\pi$
$389$	4.35630	+	4.69498i	0.220873	+	0.238045i	−0.612888	+	0.790170i	$0.709992\pi$
$390$	0.0982122	−	0.156686i	0.00497317	−	0.00793410i
$391$	8.36284			0.422927
$392$	−8.50341	−	17.8799i	−0.429487	−	0.903073i
$393$	4.62568			0.233335
$394$	9.12686	−	14.5608i	0.459804	−	0.733564i
$395$	−2.26337	−	2.43933i	−0.113882	−	0.122736i
$396$	−7.58231	+	3.67201i	−0.381026	+	0.184525i
$397$	8.36319	−	27.1128i	0.419736	−	1.36075i	−0.461107	−	0.887344i	$-0.652548\pi$
$397$	8.36319	−	27.1128i	0.419736	−	1.36075i	0.880844	−	0.473408i	$-0.156976\pi$
$398$	10.8757	−	2.07018i	0.545148	−	0.103769i
$399$	3.54168	+	6.47050i	0.177306	+	0.323930i
$400$	−18.1267	+	5.67877i	−0.906337	+	0.283939i
$401$	−1.67145	+	22.3040i	−0.0834683	+	1.11381i	0.785475	+	0.618894i	$0.212419\pi$
$401$	−1.67145	+	22.3040i	−0.0834683	+	1.11381i	−0.868943	+	0.494913i	$0.835200\pi$
$402$	−1.67987	−	1.94771i	−0.0837843	−	0.0971429i
$403$	0.762867	−	0.0571690i	0.0380011	−	0.00284779i
$404$	11.9557	−	30.6606i	0.594816	−	1.52542i
$405$	0.644644	−	1.33862i	0.0320326	−	0.0665164i
$406$	4.23233	+	6.00282i	0.210047	+	0.297915i
$407$	14.3099	−	6.89126i	0.709313	−	0.341587i
$408$	11.4497	−	6.09976i	0.566847	−	0.301983i
$409$	22.7502	+	3.42903i	1.12492	+	0.169555i	0.685043	−	0.728502i	$-0.259783\pi$
$409$	22.7502	+	3.42903i	1.12492	+	0.169555i	0.439879	+	0.898057i	$0.355021\pi$
$410$	−6.21249	−	4.57449i	−0.306813	−	0.225918i
$411$	−4.25898	−	2.45893i	−0.210080	−	0.121290i
$412$	−2.16413	−	14.1470i	−0.106619	−	0.696971i
$413$	10.0315	+	15.4589i	0.493619	+	0.760683i
$414$	−2.33179	+	4.42373i	−0.114601	+	0.217414i
$415$	−0.887181	+	0.133721i	−0.0435500	+	0.00656410i
$416$	0.184017	−	1.71802i	0.00902219	−	0.0842331i
$417$	2.16398	+	1.47538i	0.105971	+	0.0722496i
$418$	4.56423	+	7.24624i	0.223244	+	0.354425i
$419$	13.9141	−	11.0961i	0.679748	−	0.542081i	−0.221621	−	0.975133i	$-0.571135\pi$
$419$	13.9141	−	11.0961i	0.679748	−	0.542081i	0.901369	+	0.433052i	$0.142563\pi$
$420$	−2.09120	−	0.870832i	−0.102040	−	0.0424923i
$421$	−24.8950	−	19.8531i	−1.21331	−	0.967582i	−0.213353	−	0.976975i	$-0.568439\pi$
$421$	−24.8950	−	19.8531i	−1.21331	−	0.967582i	−0.999956	+	0.00939345i	$0.997010\pi$
$422$	1.41451	−	12.6794i	0.0688571	−	0.617222i
$423$	7.97690	+	13.8164i	0.387850	+	0.671776i
$424$	−12.1138	+	23.1045i	−0.588297	+	1.12205i
$425$	18.6913	+	17.3430i	0.906660	+	0.841257i
$426$	4.64516	−	5.40979i	0.225059	−	0.262105i
$427$	20.2035	−	15.3719i	0.977714	−	0.743899i
$428$	−13.4804	−	34.1266i	−0.651598	−	1.64957i
$429$	−0.450671	+	0.176875i	−0.0217586	+	0.00853962i
$430$	7.48697	−	3.96751i	0.361054	−	0.191331i
$431$	−29.7557	+	9.17840i	−1.43328	+	0.442108i	−0.911616	−	0.411043i	$-0.865165\pi$
$431$	−29.7557	+	9.17840i	−1.43328	+	0.442108i	−0.521664	+	0.853151i	$0.674688\pi$
$432$	0.0791911	+	18.0084i	0.00381008	+	0.866428i
$433$	1.27044	+	5.56615i	0.0610534	+	0.267492i	0.996237	−	0.0866709i	$-0.0276229\pi$
$433$	1.27044	+	5.56615i	0.0610534	+	0.267492i	−0.935184	+	0.354163i	$0.884766\pi$
$434$	−2.22860	−	9.10240i	−0.106976	−	0.436929i
$435$	0.819279	+	0.186995i	0.0392814	+	0.00896573i
$436$	−3.14583	−	5.42117i	−0.150658	−	0.259627i
$437$	4.73191	+	1.85714i	0.226358	+	0.0888389i
$438$	−5.48448	+	12.6084i	−0.262059	+	0.602451i
$439$	32.0494	−	21.8509i	1.52964	−	1.04289i	0.551685	−	0.834052i	$-0.313985\pi$
$439$	32.0494	−	21.8509i	1.52964	−	1.04289i	0.977951	−	0.208836i	$-0.0669674\pi$
$440$	−2.48523	−	0.860429i	−0.118479	−	0.0410194i
$441$	−7.31064	−	14.1103i	−0.348126	−	0.671921i
$442$	−2.12478	+	0.929815i	−0.101066	+	0.0442268i
$443$	4.41134	+	6.47024i	0.209589	+	0.307411i	0.916610	−	0.399781i	$-0.130914\pi$
$443$	4.41134	+	6.47024i	0.209589	+	0.307411i	−0.707022	+	0.707192i	$0.749962\pi$
$444$	−0.0321560	−	14.6249i	−0.00152606	−	0.694066i
$445$	−3.68627	−	1.44675i	−0.174746	−	0.0685827i
$446$	0.0346147	+	0.304208i	0.00163906	+	0.0144047i
$447$	−1.62334	+	7.11232i	−0.0767814	+	0.336401i
$448$	−21.1297	+	1.23983i	−0.998283	+	0.0585763i
$449$	−6.77245	−	29.6720i	−0.319611	−	1.40031i	−0.838236	−	0.545307i	$-0.816413\pi$
$449$	−6.77245	−	29.6720i	−0.319611	−	1.40031i	0.518625	−	0.855002i	$-0.326444\pi$
$450$	−14.3856	+	5.05151i	−0.678145	+	0.238130i
$451$	5.95355	+	19.3010i	0.280342	+	0.908846i
$452$	1.63107	+	1.29488i	0.0767191	+	0.0609060i
$453$	0.969901	−	0.380658i	0.0455699	−	0.0178849i
$454$	35.1005	+	1.27473i	1.64735	+	0.0598259i
$455$	0.360777	+	0.183983i	0.0169135	+	0.00862524i
$456$	7.83313	−	0.908754i	0.366820	−	0.0425563i
$457$	−9.27953	−	8.61015i	−0.434078	−	0.402766i	0.432638	−	0.901568i	$-0.357583\pi$
$457$	−9.27953	−	8.61015i	−0.434078	−	0.402766i	−0.866716	+	0.498802i	$0.833773\pi$
$458$	−29.2236	+	7.86487i	−1.36553	+	0.367501i
$459$	20.9346	−	12.0866i	0.977141	−	0.564153i
$460$	−1.49071	+	0.463414i	−0.0695045	+	0.0216068i
$461$	−19.7811	−	15.7749i	−0.921297	−	0.734710i	0.0431269	−	0.999070i	$-0.486268\pi$
$461$	−19.7811	−	15.7749i	−0.921297	−	0.734710i	−0.964424	+	0.264359i	$0.914839\pi$
$462$	3.04565	+	5.08885i	0.141697	+	0.236755i
$463$	−10.8471	−	13.6018i	−0.504108	−	0.632131i	0.463043	−	0.886336i	$-0.346758\pi$
$463$	−10.8471	−	13.6018i	−0.504108	−	0.632131i	−0.967150	+	0.254205i	$0.918186\pi$
$464$	7.64733	−	1.78087i	0.355018	−	0.0826747i
$465$	−0.885893	−	0.603992i	−0.0410823	−	0.0280094i
$466$	0.727783	−	3.86971i	0.0337139	−	0.179261i
$467$	4.13629	+	27.4425i	0.191405	+	1.26989i	0.853748	+	0.520687i	$0.174324\pi$
$467$	4.13629	+	27.4425i	0.191405	+	1.26989i	−0.662343	+	0.749200i	$0.730438\pi$
$468$	0.100600	−	1.38321i	0.00465022	−	0.0639391i
$469$	3.92440	−	4.04081i	0.181212	−	0.186587i
$470$	−1.28372	+	4.81207i	−0.0592137	+	0.221964i
$471$	6.78077	−	11.7446i	0.312441	−	0.541164i
$472$	19.3453	−	3.72645i	0.890437	−	0.171524i
$473$	−21.9357	−	3.30628i	−1.00861	−	0.152023i
$474$	7.57476	+	2.64118i	0.347920	+	0.121313i
$475$	6.72465	+	13.9639i	0.308548	+	0.640706i
$476$	15.5181	+	23.7991i	0.711271	+	1.09083i
$477$	−9.08523	+	18.8657i	−0.415984	+	0.863800i
$478$	−6.39409	+	6.40816i	−0.292459	+	0.293102i
$479$	2.01774	+	26.9249i	0.0921930	+	1.23023i	0.830984	+	0.556296i	$0.187778\pi$
$479$	2.01774	+	26.9249i	0.0921930	+	1.23023i	−0.738791	+	0.673934i	$0.764603\pi$
$480$	−1.70295	+	1.72177i	−0.0777286	+	0.0785879i
$481$	−0.195390	+	2.60730i	−0.00890903	+	0.118883i
$482$	7.18195	−	5.31273i	0.327129	−	0.241988i
$483$	3.24677	+	1.36043i	0.147733	+	0.0619016i
$484$	−8.54179	−	12.4695i	−0.388263	−	0.566796i
$485$	0.687856	−	2.22997i	0.0312339	−	0.101258i
$486$	0.873051	+	22.6659i	0.0396024	+	1.02815i
$487$	20.0500	−	18.6037i	0.908552	−	0.843013i	−0.0795476	−	0.996831i	$-0.525348\pi$
$487$	20.0500	−	18.6037i	0.908552	−	0.843013i	0.988099	+	0.153818i	$0.0491571\pi$
$488$	−7.11059	−	26.1913i	−0.321881	−	1.18562i
$489$	0.479589			0.0216878
$490$	1.49577	−	4.73012i	0.0675719	−	0.213685i
$491$		−	4.21972i		−	0.190433i	−0.995457	−	0.0952167i	$-0.969646\pi$
$491$		−	4.21972i		−	0.190433i	0.995457	−	0.0952167i	$-0.0303544\pi$
$492$	18.3970	+	2.73155i	0.829402	+	0.123148i
$493$	−7.16888	−	7.72621i	−0.322870	−	0.347971i
$494$	−1.40874	+	0.0542623i	−0.0633822	+	0.00244137i
$495$	−2.01717	−	0.622213i	−0.0906648	−	0.0279664i
$496$	−9.91287	−	1.44957i	−0.445101	−	0.0650877i
$497$	12.6986	+	9.08837i	0.569610	+	0.407669i
$498$	1.73886	−	1.28629i	0.0779201	−	0.0576401i
$499$	−24.5174	−	1.83732i	−1.09755	−	0.0822498i	−0.486377	−	0.873749i	$-0.661682\pi$
$499$	−24.5174	−	1.83732i	−1.09755	−	0.0822498i	−0.611170	+	0.791499i	$0.709301\pi$
$500$	−8.81266	−	4.22011i	−0.394114	−	0.188729i
$501$	1.07059	−	0.0802293i	0.0478302	−	0.00358438i
$502$	−27.6699	−	27.6091i	−1.23497	−	1.23226i
$503$	13.9385	+	6.71245i	0.621489	+	0.299293i	0.718005	−	0.696038i	$-0.245056\pi$
$503$	13.9385	+	6.71245i	0.621489	+	0.299293i	−0.0965157	+	0.995331i	$0.530770\pi$
$504$	−16.9160	+	1.57282i	−0.753500	+	0.0700590i
$505$	7.42934	−	3.57778i	0.330601	−	0.159209i
$506$	3.85913	+	1.34561i	0.171559	+	0.0598195i
$507$	−1.64328	+	10.9025i	−0.0729807	+	0.484196i
$508$	−23.1800	−	5.23709i	−1.02845	−	0.232358i
$509$	21.9084	+	12.6488i	0.971074	+	0.560650i	0.899563	−	0.436790i	$-0.143885\pi$
$509$	21.9084	+	12.6488i	0.971074	+	0.560650i	0.0715104	+	0.997440i	$0.477218\pi$
$510$	3.14082	+	0.837880i	0.139078	+	0.0371020i
$511$	−28.5642	−	9.52886i	−1.26361	−	0.421532i
$512$	−7.26168	+	21.4305i	−0.320924	+	0.947105i
$513$	14.5294	−	2.18995i	0.641487	−	0.0966887i
$514$	−2.81959	+	14.9921i	−0.124367	+	0.661274i
$515$	2.02007	−	2.96290i	0.0890149	−	0.130561i
$516$	−11.4696	+	16.9026i	−0.504922	+	0.744094i
$517$	10.1942	−	8.12961i	0.448341	−	0.357540i
$518$	31.8976	−	2.89506i	1.40150	−	0.127202i
$519$	1.90790	−	2.39243i	0.0837475	−	0.105016i
$520$	0.327226	−	0.283484i	0.0143498	−	0.0124316i
$521$	7.66670	+	13.2791i	0.335884	+	0.581768i	0.983654	−	0.180067i	$-0.0576316\pi$
$521$	7.66670	+	13.2791i	0.335884	+	0.581768i	−0.647770	+	0.761836i	$0.724298\pi$
$522$	6.08585	−	1.63787i	0.266370	−	0.0716877i
$523$	−25.1573	+	27.1132i	−1.10005	+	1.18558i	−0.118788	+	0.992920i	$0.537901\pi$
$523$	−25.1573	+	27.1132i	−1.10005	+	1.18558i	−0.981266	+	0.192657i	$0.938290\pi$
$524$	10.3556	+	3.16936i	0.452387	+	0.138454i
$525$	4.43539	+	9.77381i	0.193576	+	0.426564i
$526$	1.02908	−	28.3365i	0.0448702	−	1.23553i
$527$	4.91300	+	12.5181i	0.214014	+	0.545298i
$528$	6.26508	−	0.972505i	0.272653	−	0.0423228i
$529$	−19.6600	+	6.06431i	−0.854784	+	0.263666i
$530$	−6.16751	+	2.16572i	−0.267899	+	0.0940727i
$531$	15.4165	−	3.51872i	0.669021	−	0.152700i
$532$	3.49546	+	16.9123i	0.151547	+	0.733240i
$533$	−3.24167	−	0.739891i	−0.140412	−	0.0320482i
$534$	9.48529	−	1.07930i	0.410469	−	0.0467058i
$535$	3.35893	−	8.55841i	0.145219	−	0.370012i
$536$	−2.42625	−	5.51136i	−0.104798	−	0.238055i
$537$	16.8434	−	11.4836i	0.726846	−	0.495555i
$538$	−3.48973	+	1.52712i	−0.150453	+	0.0658388i
$539$	−10.5129	+	7.62697i	−0.452824	+	0.328517i
$540$	−3.06190	+	3.31453i	−0.131763	+	0.142635i
$541$	−7.11804	−	10.4402i	−0.306028	−	0.448861i	0.642160	−	0.766571i	$-0.278039\pi$
$541$	−7.11804	−	10.4402i	−0.306028	−	0.448861i	−0.948188	+	0.317710i	$0.897086\pi$
$542$	34.1545	+	14.8568i	1.46706	+	0.638154i
$543$	4.72784	−	12.0463i	0.202891	−	0.516958i
$544$	29.8121	−	5.81067i	1.27818	−	0.249131i
$545$	0.349471	−	1.53113i	0.0149697	−	0.0655864i
$546$	−0.976179	+	0.0153401i	−0.0417766	+	0.000656494i
$547$	14.1467	−	3.22888i	0.604867	−	0.138057i	0.0908903	−	0.995861i	$-0.471029\pi$
$547$	14.1467	−	3.22888i	0.604867	−	0.138057i	0.513977	+	0.857804i	$0.328172\pi$
$548$	−7.84990	−	8.42296i	−0.335331	−	0.359811i
$549$	−6.42080	−	20.8157i	−0.274033	−	0.888393i
$550$	5.83476	+	11.0106i	0.248795	+	0.469493i
$551$	−2.34057	−	5.96368i	−0.0997117	−	0.254061i
$552$	2.65228	−	2.66983i	0.112889	−	0.113636i
$553$	−4.29855	+	17.0343i	−0.182793	+	0.724374i
$554$	7.74131	−	9.01560i	0.328897	−	0.383036i
$555$	2.49251	−	2.68629i	0.105801	−	0.114027i
$556$	3.83367	+	4.78565i	0.162584	+	0.202957i
$557$	−9.13585	+	5.27458i	−0.387098	+	0.223491i	−0.680902	−	0.732374i	$-0.738412\pi$
$557$	−9.13585	+	5.27458i	−0.387098	+	0.223491i	0.293804	+	0.955866i	$0.405079\pi$
$558$	−7.99165	−	0.891546i	−0.338313	−	0.0377422i
$559$	2.27688	−	2.85512i	0.0963019	−	0.120759i
$560$	−4.08495	−	3.38237i	−0.172621	−	0.142931i
$561$	−5.30617	−	6.65372i	−0.224027	−	0.280920i
$562$	−11.5721	−	18.3721i	−0.488141	−	0.774979i
$563$	−7.34638	+	10.7752i	−0.309613	+	0.454119i	−0.949234	−	0.314572i	$-0.898139\pi$
$563$	−7.34638	+	10.7752i	−0.309613	+	0.454119i	0.639621	+	0.768691i	$0.279091\pi$
$564$	−2.69738	−	11.6993i	−0.113580	−	0.492631i
$565$	0.0777739	+	0.515996i	0.00327197	+	0.0217081i
$566$	22.7880	+	12.0118i	0.957851	+	0.504892i
$567$	−7.78107	+	0.992068i	−0.326774	+	0.0416629i
$568$	14.1058	−	8.92830i	0.591867	−	0.374623i
$569$	−0.159645	+	0.276514i	−0.00669268	+	0.0115921i	−0.869352	−	0.494193i	$-0.835464\pi$
$569$	−0.159645	+	0.276514i	−0.00669268	+	0.0115921i	0.862660	+	0.505785i	$0.168797\pi$
$570$	1.59109	+	1.17158i	0.0666433	+	0.0490719i
$571$	−1.02440	+	6.79645i	−0.0428698	+	0.284422i	−0.999986	−	0.00528163i	$-0.998319\pi$
$571$	−1.02440	+	6.79645i	−0.0428698	+	0.284422i	0.957116	+	0.289704i	$0.0935569\pi$
$572$	−1.13011	+	0.0871895i	−0.0472525	+	0.00364558i
$573$	−0.439994	−	0.913657i	−0.0183810	−	0.0381686i
$574$	−2.40528	+	40.6603i	−0.100395	+	1.69713i
$575$	6.66406	+	3.20924i	0.277910	+	0.133835i
$576$	−5.23875	+	17.3900i	−0.218281	+	0.724585i
$577$	−1.56274	−	20.8534i	−0.0650578	−	0.868137i	−0.930304	−	0.366789i	$-0.880457\pi$
$577$	−1.56274	−	20.8534i	−0.0650578	−	0.868137i	0.865246	−	0.501347i	$-0.167162\pi$
$578$	−10.9258	−	12.6679i	−0.454455	−	0.526913i
$579$	−10.6497	−	0.798085i	−0.442587	−	0.0331673i
$580$	1.70601	+	0.979973i	0.0708384	+	0.0406911i
$581$	3.14189	+	3.54482i	0.130347	+	0.147064i
$582$	1.05198	+	5.52656i	0.0436058	+	0.229083i
$583$	16.3532	+	5.04429i	0.677280	+	0.208913i
$584$	−20.9170	+	24.4688i	−0.865553	+	1.01253i
$585$	0.254738	−	0.236363i	0.0105321	−	0.00977239i
$586$	22.6534	−	36.1408i	0.935803	−	1.49296i
$587$		−	32.1050i		−	1.32511i	−0.749012	−	0.662557i	$-0.769471\pi$
$587$		−	32.1050i		−	1.32511i	0.749012	−	0.662557i	$-0.230529\pi$
$588$	2.15319	+	11.7641i	0.0887959	+	0.485145i
$589$			8.17410i			0.336808i
$590$	4.18266	+	2.62173i	0.172197	+	0.107935i
$591$	−7.60942	+	7.06051i	−0.313010	+	0.290430i
$592$	9.94849	−	32.7630i	0.408880	−	1.34655i
$593$	5.45201	+	1.68172i	0.223887	+	0.0690601i	0.404669	−	0.914463i	$-0.367387\pi$
$593$	5.45201	+	1.68172i	0.223887	+	0.0690601i	−0.180782	+	0.983523i	$0.557863\pi$
$594$	11.6052	−	2.20905i	0.476169	−	0.0906384i
$595$	−1.22114	+	7.01347i	−0.0500620	+	0.287524i
$596$	−8.50733	+	14.8102i	−0.348474	+	0.606651i
$597$	−6.66870	−	0.499750i	−0.272932	−	0.0204534i
$598$	−0.509480	+	0.439419i	−0.0208342	+	0.0179692i
$599$	0.0352571	+	0.470473i	0.00144057	+	0.0192230i	0.997878	−	0.0651151i	$-0.0207415\pi$
$599$	0.0352571	+	0.470473i	0.00144057	+	0.0192230i	−0.996437	+	0.0843381i	$0.973122\pi$
$600$	11.4647	−	0.466848i	0.468044	−	0.0190590i
$601$	37.2256	+	17.9269i	1.51846	+	0.731254i	0.992839	−	0.119462i	$-0.0381170\pi$
$601$	37.2256	+	17.9269i	1.51846	+	0.731254i	0.525626	+	0.850716i	$0.323831\pi$
$602$	−39.0880	−	21.7558i	−1.59311	−	0.886702i
$603$	−2.09714	−	4.35475i	−0.0854020	−	0.177339i
$604$	2.43215	−	0.187643i	0.0989628	−	0.00763509i
$605$	0.564457	−	3.74493i	0.0229484	−	0.152253i
$606$	−11.7868	+	16.0073i	−0.478806	+	0.650254i
$607$	8.16601	−	14.1439i	0.331448	−	0.574085i	−0.651348	−	0.758779i	$-0.725796\pi$
$607$	8.16601	−	14.1439i	0.331448	−	0.574085i	0.982796	+	0.184694i	$0.0591295\pi$
$608$	18.1588	+	3.33256i	0.736438	+	0.135153i
$609$	−1.52637	−	4.16581i	−0.0618515	−	0.168807i
$610$	3.17092	−	6.01568i	0.128387	−	0.243568i
$611$	0.319913	+	2.12248i	0.0129423	+	0.0858665i
$612$	23.7559	−	5.47711i	0.960275	−	0.221399i
$613$	−15.7267	+	23.0669i	−0.635197	+	0.931663i	0.364803	+	0.931085i	$0.381136\pi$
$613$	−15.7267	+	23.0669i	−0.635197	+	0.931663i	−1.00000		0.000577818i	$0.999816\pi$
$614$	−11.4335	+	7.20166i	−0.461417	+	0.290635i
$615$	2.90561	+	3.64352i	0.117165	+	0.146921i
$616$	3.33165	+	13.4793i	0.134236	+	0.543096i
$617$	−8.32162	+	10.4350i	−0.335016	+	0.420096i	−0.920595	−	0.390519i	$-0.872296\pi$
$617$	−8.32162	+	10.4350i	−0.335016	+	0.420096i	0.585579	+	0.810615i	$0.300867\pi$
$618$	−0.958474	+	8.59158i	−0.0385555	+	0.345604i
$619$	5.93268	−	3.42523i	0.238454	−	0.137672i	−0.376012	−	0.926615i	$-0.622705\pi$
$619$	5.93268	−	3.42523i	0.238454	−	0.137672i	0.614466	+	0.788943i	$0.289371\pi$
$620$	−1.56943	−	1.95915i	−0.0630299	−	0.0786815i
$621$	4.76955	−	5.14035i	0.191395	−	0.206275i
$622$	−20.3573	−	17.4800i	−0.816254	−	0.700883i
$623$	4.18662	+	20.4835i	0.167733	+	0.820653i
$624$	−0.377033	+	0.973228i	−0.0150934	+	0.0389603i
$625$	7.78031	+	19.8239i	0.311212	+	0.792956i
$626$	−8.80336	+	4.66510i	−0.351853	+	0.186455i
$627$	−1.52477	−	4.94319i	−0.0608935	−	0.197412i
$628$	23.2273	−	21.6470i	0.926869	−	0.863809i
$629$	−44.8087	+	10.2273i	−1.78664	+	0.407789i
$630$	−3.36946	−	2.60150i	−0.134243	−	0.103646i
$631$	−8.03193	+	35.1902i	−0.319746	+	1.40090i	0.518253	+	0.855228i	$0.326583\pi$
$631$	−8.03193	+	35.1902i	−0.319746	+	1.40090i	−0.837999	+	0.545672i	$0.816274\pi$
$632$	15.1481	+	11.1028i	0.602560	+	0.441647i
$633$	−2.81549	+	7.17375i	−0.111906	+	0.285131i
$634$	14.3813	−	33.0614i	0.571154	−	1.31304i
$635$	−3.35432	−	4.91988i	−0.133112	−	0.195239i
$636$	10.6929	−	11.5751i	0.424000	−	0.458983i
$637$	−0.222021	−	2.12655i	−0.00879678	−	0.0842569i
$638$	−2.06499	−	4.71884i	−0.0817536	−	0.186821i
$639$	11.0712	−	7.54820i	0.437969	−	0.298602i
$640$	−4.99213	+	2.68777i	−0.197331	+	0.106243i
$641$	7.33598	−	18.6918i	0.289754	−	0.738280i	−0.709677	−	0.704528i	$-0.751159\pi$
$641$	7.33598	−	18.6918i	0.289754	−	0.738280i	0.999430	−	0.0337526i	$-0.0107458\pi$
$642$	2.50580	+	22.0220i	0.0988962	+	0.869139i
$643$	3.88688	+	0.887155i	0.153284	+	0.0349860i	0.298474	−	0.954418i	$-0.403522\pi$
$643$	3.88688	+	0.887155i	0.153284	+	0.0349860i	−0.145191	+	0.989404i	$0.546380\pi$
$644$	6.33649	+	5.27019i	0.249693	+	0.207675i
$645$	−4.98993	+	1.13892i	−0.196478	+	0.0448449i
$646$	−8.21067	−	23.3823i	−0.323045	−	0.919963i
$647$	−39.3367	+	12.1338i	−1.54649	+	0.477028i	−0.946424	−	0.322925i	$-0.895334\pi$
$647$	−39.3367	+	12.1338i	−1.54649	+	0.477028i	−0.600062	+	0.799953i	$0.704857\pi$
$648$	−2.14364	+	8.10703i	−0.0842101	+	0.318474i
$649$	−4.72160	−	12.0304i	−0.185339	−	0.472236i
$650$	−2.04998	−	0.0744482i	−0.0804069	−	0.00292010i
$651$	−0.128974	+	5.65923i	−0.00505491	+	0.221803i
$652$	1.07366	+	0.328598i	0.0420480	+	0.0128689i
$653$	−16.7169	+	18.0166i	−0.654184	+	0.705043i	−0.969816	−	0.243839i	$-0.921593\pi$
$653$	−16.7169	+	18.0166i	−0.654184	+	0.705043i	0.315632	+	0.948882i	$0.397784\pi$
$654$	0.983924	+	3.65597i	0.0384745	+	0.142960i
$655$	1.35679	+	2.35003i	0.0530142	+	0.0918233i
$656$	39.3142	+	18.7202i	1.53496	+	0.730901i
$657$	−16.1098	+	20.2010i	−0.628501	+	0.788116i
$658$	25.0008	−	8.14409i	0.974634	−	0.317490i
$659$	29.4817	−	23.5108i	1.14844	−	0.915852i	0.151086	−	0.988521i	$-0.451723\pi$
$659$	29.4817	−	23.5108i	1.14844	−	0.915852i	0.997356	+	0.0726683i	$0.0231515\pi$
$660$	1.31455	+	0.892017i	0.0511688	+	0.0347217i
$661$	22.9122	−	33.6060i	0.891180	−	1.30712i	−0.0599095	−	0.998204i	$-0.519081\pi$
$661$	22.9122	−	33.6060i	0.891180	−	1.30712i	0.951089	−	0.308917i	$-0.0999664\pi$
$662$	16.8036	+	3.16028i	0.653090	+	0.122828i
$663$	1.38534	−	0.208806i	0.0538020	−	0.00810935i
$664$	4.77414	−	1.68824i	0.185272	−	0.0655163i
$665$	−2.24844	+	3.69722i	−0.0871906	+	0.143372i
$666$	7.08394	−	26.5543i	0.274497	−	1.02896i
$667$	−2.64781	−	1.52872i	−0.102524	−	0.0591921i
$668$	2.45171	+	0.553918i	0.0948595	+	0.0214317i
$669$	0.0275642	−	0.182877i	0.00106570	−	0.00707042i
$670$	0.496779	−	1.42474i	0.0191923	−	0.0550424i
$671$	−16.0403	+	7.72462i	−0.619230	+	0.298206i
$672$	12.5195	+	2.59377i	0.482948	+	0.100057i
$673$	−7.87328	−	3.79157i	−0.303493	−	0.146154i	0.275939	−	0.961175i	$-0.411011\pi$
$673$	−7.87328	−	3.79157i	−0.303493	−	0.146154i	−0.579432	+	0.815021i	$0.696725\pi$
$674$	−6.25144	+	6.26520i	−0.240797	+	0.241327i
$675$	21.3202	−	1.59773i	0.820617	−	0.0614967i
$676$	−11.1489	+	23.2816i	−0.428802	+	0.895448i
$677$	21.7610	+	1.63076i	0.836342	+	0.0626752i	0.486013	−	0.873951i	$-0.338451\pi$
$677$	21.7610	+	1.63076i	0.836342	+	0.0626752i	0.350329	+	0.936627i	$0.386070\pi$
$678$	−0.748124	−	1.01134i	−0.0287315	−	0.0388404i
$679$	−11.8529	+	3.36236i	−0.454871	+	0.129036i
$680$	6.45733	+	4.02776i	0.247627	+	0.154458i
$681$	−20.2738	−	6.25365i	−0.776895	−	0.239640i
$682$	0.252955	+	6.56714i	0.00968615	+	0.251469i
$683$	−12.5295	−	13.5036i	−0.479429	−	0.516702i	0.446303	−	0.894882i	$-0.352740\pi$
$683$	−12.5295	−	13.5036i	−0.479429	−	0.516702i	−0.925732	+	0.378180i	$0.876550\pi$
$684$	14.6580	+	2.17639i	0.560462	+	0.0832162i
$685$		−	2.88498i		−	0.110229i
$686$	−25.2473	+	6.96946i	−0.963947	+	0.266095i
$687$	18.2806			0.697448
$688$	−37.2583	+	29.9815i	−1.42046	+	1.14303i
$689$	−2.06517	+	1.91619i	−0.0786766	+	0.0730012i
$690$	0.942268	−	0.0362946i	0.0358715	−	0.00138171i
$691$	3.77660	−	12.2434i	0.143668	−	0.465762i	−0.854927	−	0.518749i	$-0.826398\pi$
$691$	3.77660	−	12.2434i	0.143668	−	0.465762i	0.998595	+	0.0529870i	$0.0168742\pi$
$692$	5.91047	−	4.04875i	0.224682	−	0.153911i
$693$	3.04149	+	10.7217i	0.115537	+	0.407285i
$694$	8.62525	+	11.6599i	0.327410	+	0.442605i
$695$	−0.114818	+	1.53214i	−0.00435530	+	0.0581175i
$696$	−4.74021	−	0.161712i	−0.179677	−	0.00612969i
$697$	−4.36793	−	58.2859i	−0.165447	−	2.20774i
$698$	−23.8077	−	23.7554i	−0.901134	−	0.899155i
$699$	−1.03198	+	2.14293i	−0.0390332	+	0.0810532i
$700$	3.23291	+	24.9198i	0.122193	+	0.941880i
$701$	−15.3222	−	31.8168i	−0.578711	−	1.20171i	−0.960713	−	0.277544i	$-0.910480\pi$
$701$	−15.3222	−	31.8168i	−0.578711	−	1.20171i	0.382002	−	0.924161i	$-0.375235\pi$
$702$	−0.640294	+	1.83633i	−0.0241663	+	0.0693077i
$703$	−27.6251	−	4.16382i	−1.04190	−	0.157041i
$704$	14.6921	+	2.11546i	0.553729	+	0.0797294i
$705$	1.50419	−	2.60533i	0.0566511	−	0.0981226i
$706$	−0.393754	−	0.105042i	−0.0148191	−	0.00395332i
$707$	−37.1964	−	22.6207i	−1.39891	−	0.850738i
$708$	−11.8690	−	0.863217i	−0.446063	−	0.0324417i
$709$	−5.83014	−	38.6804i	−0.218955	−	1.45267i	−0.780463	−	0.625202i	$-0.785017\pi$
$709$	−5.83014	−	38.6804i	−0.218955	−	1.45267i	0.561508	−	0.827472i	$-0.310222\pi$
$710$	4.11089	+	0.773143i	0.154279	+	0.0290155i
$711$	12.4555	+	8.49200i	0.467117	+	0.318475i
$712$	21.9744	+	4.08276i	0.823526	+	0.153008i
$713$	2.43222	+	3.04990i	0.0910872	+	0.114220i
$714$	−5.31562	−	16.3180i	−0.198932	−	0.610684i
$715$	−0.222049	−	0.177078i	−0.00830416	−	0.00662235i
$716$	45.5758	−	14.1681i	1.70325	−	0.529486i
$717$	4.73560	−	2.73410i	0.176854	−	0.102107i
$718$	−10.8799	−	40.4264i	−0.406033	−	1.50870i
$719$	11.4092	+	10.5862i	0.425491	+	0.394798i	0.863644	−	0.504102i	$-0.168177\pi$
$719$	11.4092	+	10.5862i	0.425491	+	0.394798i	−0.438152	+	0.898901i	$0.644367\pi$
$720$	−3.93107	+	2.29271i	−0.146502	+	0.0854443i
$721$	−18.9275	−	0.431359i	−0.704896	−	0.0160646i
$722$	−0.428488	+	11.7987i	−0.0159467	+	0.439103i
$723$	−5.02319	+	1.97146i	−0.186814	+	0.0733192i
$724$	18.8380	−	23.7290i	0.700110	−	0.881882i
$725$	−2.74770	−	8.90781i	−0.102047	−	0.330828i
$726$	3.02491	+	8.61430i	0.112265	+	0.319707i
$727$	8.16780	+	35.7855i	0.302927	+	1.32721i	0.865685	+	0.500588i	$0.166883\pi$
$727$	8.16780	+	35.7855i	0.302927	+	1.32721i	−0.562758	+	0.826621i	$0.690260\pi$
$728$	−2.19590	−	0.634503i	−0.0813855	−	0.0235162i
$729$	1.06969	−	4.68661i	0.0396181	−	0.173578i
$730$	−8.01424	+	0.911911i	−0.296620	+	0.0337514i
$731$	59.7565	+	23.4527i	2.21018	+	0.867430i
$732$	0.0360446	+	16.3935i	0.00133225	+	0.605919i
$733$	−12.7191	−	18.6555i	−0.469790	−	0.689055i	0.516085	−	0.856537i	$-0.327389\pi$
$733$	−12.7191	−	18.6555i	−0.469790	−	0.689055i	−0.985875	+	0.167482i	$0.946436\pi$
$734$	19.4198	+	44.3775i	0.716797	+	1.63800i
$735$	−1.61501	+	2.52425i	−0.0595706	+	0.0931082i
$736$	7.76700	−	4.15976i	0.286295	−	0.153331i
$737$	−3.26389	+	2.22528i	−0.120227	+	0.0819692i
$738$	32.0497	+	13.9412i	1.17977	+	0.513183i
$739$	−8.18678	−	3.21307i	−0.301155	−	0.118195i	0.209952	−	0.977712i	$-0.432669\pi$
$739$	−8.18678	−	3.21307i	−0.301155	−	0.118195i	−0.511107	+	0.859517i	$0.670765\pi$
$740$	7.42059	−	4.30606i	0.272786	−	0.158294i
$741$	0.830229	+	0.189494i	0.0304992	+	0.00696125i
$742$	27.3163	+	21.0904i	1.00281	+	0.774254i
$743$	−7.86004	−	34.4371i	−0.288357	−	1.26337i	−0.886779	−	0.462194i	$-0.847063\pi$
$743$	−7.86004	−	34.4371i	−0.288357	−	1.26337i	0.598422	−	0.801181i	$-0.295795\pi$
$744$	5.55457	+	2.40166i	0.203640	+	0.0880490i
$745$	−4.08950	+	1.26144i	−0.149828	+	0.0462157i
$746$	−24.3665	−	45.9813i	−0.892122	−	1.68349i
$747$	3.78355	−	1.48493i	0.138433	−	0.0543309i
$748$	−7.32011	−	18.5314i	−0.267650	−	0.677576i
$749$	−47.5565	+	9.72008i	−1.73768	+	0.355164i
$750$	4.47790	+	3.84499i	0.163510	+	0.140399i
$751$	−20.1955	−	18.7386i	−0.736943	−	0.683783i	0.219530	−	0.975606i	$-0.429548\pi$
$751$	−20.1955	−	18.7386i	−0.736943	−	0.683783i	−0.956472	+	0.291823i	$0.905738\pi$
$752$	1.97733	−	28.0397i	0.0721058	−	1.02250i
$753$	11.8056	+	20.4479i	0.430220	+	0.745163i
$754$	0.842710	+	0.0940125i	0.0306897	+	0.00342373i
$755$	0.477878	+	0.381095i	0.0173918	+	0.0138695i
$756$	23.4789	+	4.03483i	0.853919	+	0.146746i
$757$	17.3363	−	13.8252i	0.630098	−	0.502487i	−0.255579	−	0.966788i	$-0.582266\pi$
$757$	17.3363	−	13.8252i	0.630098	−	0.502487i	0.885677	+	0.464301i	$0.153695\pi$
$758$	26.2802	−	16.5533i	0.954540	−	0.601242i
$759$	−2.03977	−	1.39069i	−0.0740391	−	0.0504790i
$760$	2.75927	+	3.71299i	0.100089	+	0.134684i
$761$	−28.2726	+	4.26141i	−1.02488	+	0.154476i	−0.639908	−	0.768452i	$-0.721027\pi$
$761$	−28.2726	+	4.26141i	−1.02488	+	0.154476i	−0.384973	+	0.922928i	$0.625789\pi$
$762$	12.6986	+	6.69358i	0.460023	+	0.242483i
$763$	−7.78537	+	2.85259i	−0.281849	+	0.103271i
$764$	−0.359016	−	2.34689i	−0.0129887	−	0.0849075i
$765$	5.29021	+	3.05431i	0.191268	+	0.110429i
$766$	−11.6294	+	15.7936i	−0.420189	+	0.570648i
$767$	2.10375	+	0.317089i	0.0759621	+	0.0114494i
$768$	7.59988	−	11.3604i	0.274237	−	0.409932i
$769$	20.7707	−	10.0027i	0.749012	−	0.360705i	−0.0201178	−	0.999798i	$-0.506404\pi$
$769$	20.7707	−	10.0027i	0.749012	−	0.360705i	0.769130	+	0.639092i	$0.220690\pi$
$770$	−1.69200	+	3.03996i	−0.0609754	+	0.109553i
$771$	3.99813	−	8.30220i	0.143989	−	0.298996i
$772$	−23.2949	−	9.08351i	−0.838401	−	0.326923i
$773$	−14.2211	+	1.06572i	−0.511496	+	0.0383313i	−0.327979	−	0.944685i	$-0.606367\pi$
$773$	−14.2211	+	1.06572i	−0.511496	+	0.0383313i	−0.183517	+	0.983016i	$0.558748\pi$
$774$	−29.0677	+	25.0704i	−1.04482	+	0.901138i
$775$	−0.888830	+	11.8606i	−0.0319277	+	0.426046i
$776$	−1.43153	+	13.0932i	−0.0513891	+	0.470018i
$777$	−19.0602	−	3.31864i	−0.683780	−	0.119056i
$778$	−1.69370	−	8.89785i	−0.0607220	−	0.319003i
$779$	10.4721	−	33.9497i	0.375201	−	1.21637i
$780$	−0.235371	+	0.113987i	−0.00842762	+	0.00408138i
$781$	−7.44875	−	8.02785i	−0.266537	−	0.287259i
$782$	−10.0210	−	6.28125i	−0.358350	−	0.224617i
$783$	−8.83763			−0.315831
$784$	−3.24002	+	27.8119i	−0.115715	+	0.993282i
$785$	7.95566			0.283950
$786$	−5.54284	−	3.47430i	−0.197707	−	0.123924i
$787$	−6.69872	−	7.21951i	−0.238784	−	0.257348i	0.602279	−	0.798286i	$-0.294260\pi$
$787$	−6.69872	−	7.21951i	−0.238784	−	0.257348i	−0.841062	+	0.540938i	$0.818069\pi$
$788$	−21.8730	+	10.5928i	−0.779193	+	0.377352i
$789$	−5.04855	+	16.3670i	−0.179733	+	0.582681i
$790$	0.879981	+	4.62298i	0.0313083	+	0.164478i
$791$	2.06172	−	1.82736i	0.0733061	−	0.0649736i
$792$	11.8437	+	1.29492i	0.420848	+	0.0460131i
$793$	0.219019	−	2.92260i	0.00777758	−	0.103785i
$794$	−30.3856	+	26.2071i	−1.07834	+	0.930054i
$795$	3.93745	−	0.295071i	0.139647	−	0.0104651i
$796$	−14.5869	−	5.68797i	−0.517020	−	0.201605i
$797$	4.34906	−	9.03092i	0.154052	−	0.319892i	−0.809632	−	0.586938i	$-0.800333\pi$
$797$	4.34906	−	9.03092i	0.154052	−	0.319892i	0.963684	+	0.267046i	$0.0860476\pi$
$798$	0.616020	−	10.4136i	0.0218069	−	0.368636i
$799$	−33.9950	+	16.3711i	−1.20266	+	0.579169i
$800$	25.9861	+	6.81008i	0.918747	+	0.240773i
$801$	17.7393	+	2.67377i	0.626788	+	0.0944731i
$802$	18.7551	−	25.4709i	0.662267	−	0.899408i
$803$	18.2880	+	10.5586i	0.645370	+	0.372604i
$804$	0.550041	+	3.59562i	0.0193985	+	0.126808i
$805$	0.261182	+	2.04853i	0.00920547	+	0.0722010i
$806$	−0.957064	−	0.504478i	−0.0337111	−	0.0177695i
$807$	2.27527	−	0.342941i	0.0800932	−	0.0120721i
$808$	−37.3550	+	27.7600i	−1.31414	+	0.976594i
$809$	0.385496	+	0.262827i	0.0135533	+	0.00924049i	0.570078	−	0.821591i	$-0.306913\pi$
$809$	0.385496	+	0.262827i	0.0135533	+	0.00924049i	−0.556524	+	0.830831i	$0.687865\pi$
$810$	−1.77788	+	1.11985i	−0.0624684	+	0.0393474i
$811$	1.79360	−	1.43035i	0.0629818	−	0.0502263i	−0.591493	−	0.806310i	$-0.701461\pi$
$811$	1.79360	−	1.43035i	0.0629818	−	0.0502263i	0.654475	+	0.756084i	$0.272890\pi$
$812$	−0.562836	−	10.3719i	−0.0197517	−	0.363982i
$813$	−17.5899	−	14.0275i	−0.616906	−	0.491966i
$814$	−22.3231	−	2.49036i	−0.782424	−	0.0872871i
$815$	0.140672	+	0.243650i	0.00492751	+	0.00853469i
$816$	−18.3014	−	1.29060i	−0.640678	−	0.0451799i
$817$	28.6036	+	26.5403i	1.00071	+	0.928527i
$818$	−24.6854	−	21.1963i	−0.863106	−	0.741113i
$819$	−1.77889	−	0.448896i	−0.0621594	−	0.0156857i
$820$	4.00842	+	10.1476i	0.139980	+	0.354371i
$821$	−6.11752	+	2.40095i	−0.213503	+	0.0837937i	−0.469682	−	0.882836i	$-0.655631\pi$
$821$	−6.11752	+	2.40095i	−0.213503	+	0.0837937i	0.256179	+	0.966629i	$0.417536\pi$
$822$	3.25656	+	6.14535i	0.113586	+	0.214344i
$823$	−18.9786	+	5.85411i	−0.661552	+	0.204062i	−0.607308	−	0.794466i	$-0.707751\pi$
$823$	−18.9786	+	5.85411i	−0.661552	+	0.204062i	−0.0542431	+	0.998528i	$0.517275\pi$
$824$	−8.03242	+	18.5774i	−0.279822	+	0.647175i
$825$	−1.67493	−	7.33836i	−0.0583137	−	0.255489i
$826$	−0.409495	−	26.0586i	−0.0142482	−	0.906695i
$827$	17.0913	+	3.90098i	0.594324	+	0.135650i	0.509094	−	0.860711i	$-0.329981\pi$
$827$	17.0913	+	3.90098i	0.594324	+	0.135650i	0.0852295	+	0.996361i	$0.472838\pi$
$828$	6.11675	−	3.54946i	0.212572	−	0.123352i
$829$	20.8156	+	8.16951i	0.722955	+	0.283739i	0.698148	−	0.715953i	$-0.254008\pi$
$829$	20.8156	+	8.16951i	0.722955	+	0.283739i	0.0248068	+	0.999692i	$0.492103\pi$
$830$	1.16352	+	0.506118i	0.0403865	+	0.0175676i
$831$	−5.93074	+	4.04351i	−0.205735	+	0.140268i
$832$	−1.51089	+	1.92045i	−0.0523808	+	0.0665797i
$833$	34.5705	−	14.7478i	1.19780	−	0.510982i
$834$	−1.48490	−	3.39325i	−0.0514180	−	0.117499i
$835$	0.354780	+	0.520367i	0.0122777	+	0.0180081i
$836$	−0.0266290	−	12.1111i	−0.000920983	−	0.418872i
$837$	10.4965	+	4.11956i	0.362811	+	0.142393i
$838$	−25.0071	+	2.84547i	−0.863856	+	0.0982950i
$839$	4.74991	−	20.8107i	0.163985	−	0.718466i	−0.824339	−	0.566097i	$-0.808453\pi$
$839$	4.74991	−	20.8107i	0.163985	−	0.718466i	0.988324	−	0.152369i	$-0.0486902\pi$
$840$	1.85176	+	2.61418i	0.0638919	+	0.0901977i
$841$	−5.59566	−	24.5162i	−0.192954	−	0.845386i
$842$	14.9196	+	42.4879i	0.514164	+	1.46423i
$843$	3.86590	+	12.5329i	0.133149	+	0.431657i
$844$	−11.2183	+	14.1309i	−0.386150	+	0.486407i
$845$	−6.02089	+	2.36303i	−0.207125	+	0.0812906i
$846$	0.818836	−	22.5472i	0.0281522	−	0.775189i
$847$	−18.2076	+	8.26269i	−0.625621	+	0.283909i
$848$	31.8692	−	18.5870i	1.09439	−	0.638281i
$849$	−11.4065	−	10.5837i	−0.391470	−	0.363231i
$850$	−9.37116	−	34.8205i	−0.321428	−	1.19433i
$851$	−11.5464	+	6.66630i	−0.395805	+	0.228518i
$852$	−9.62942	+	2.99349i	−0.329899	+	0.102555i
$853$	−12.9605	−	10.3356i	−0.443758	−	0.353885i	0.375976	−	0.926629i	$-0.377307\pi$
$853$	−12.9605	−	10.3356i	−0.443758	−	0.353885i	−0.819734	+	0.572744i	$0.805879\pi$
$854$	−35.7550	+	3.24516i	−1.22351	+	0.111047i
$855$	2.31507	+	2.90300i	0.0791737	+	0.0992806i
$856$	−9.47895	+	51.0180i	−0.323984	+	1.74376i
$857$	8.19061	+	5.58426i	0.279786	+	0.190755i	0.695080	−	0.718932i	$-0.255369\pi$
$857$	8.19061	+	5.58426i	0.279786	+	0.190755i	−0.415294	+	0.909687i	$0.636321\pi$
$858$	0.672877	+	0.126549i	0.0229716	+	0.00432031i
$859$	6.14236	+	40.7519i	0.209574	+	1.39044i	0.807965	+	0.589231i	$0.200569\pi$
$859$	6.14236	+	40.7519i	0.209574	+	1.39044i	−0.598390	+	0.801205i	$0.704193\pi$
$860$	−11.9514	−	0.869213i	−0.407540	−	0.0296399i
$861$	7.78588	−	23.3394i	0.265342	−	0.795403i
$862$	42.5493	+	11.3509i	1.44923	+	0.386614i
$863$	−13.7440	+	23.8053i	−0.467852	+	0.810343i	−0.999325	−	0.0367318i	$-0.988305\pi$
$863$	−13.7440	+	23.8053i	−0.467852	+	0.810343i	0.531473	+	0.847075i	$0.321639\pi$
$864$	13.4310	−	21.6385i	0.456932	−	0.736155i
$865$	1.77507	+	0.267549i	0.0603542	+	0.00909693i
$866$	2.65835	−	7.62400i	0.0903344	−	0.259074i
$867$	4.38437	+	9.10424i	0.148901	+	0.309196i
$868$	−4.16625	+	12.5811i	−0.141412	+	0.427029i
$869$	5.34570	−	11.1005i	0.181340	−	0.376557i
$870$	−0.841272	−	0.839424i	−0.0285218	−	0.0284592i
$871$	−0.0485967	−	0.648478i	−0.00164664	−	0.0219728i
$872$	−0.302220	+	8.85885i	−0.0102345	+	0.299999i
$873$	−0.790042	+	10.5424i	−0.0267389	+	0.356805i
$874$	−4.27525	−	5.77945i	−0.144613	−	0.195493i
$875$	−7.52281	+	10.5111i	−0.254317	+	0.355341i
$876$	16.0419	−	10.9889i	0.542006	−	0.371282i
$877$	−5.94738	+	19.2809i	−0.200829	+	0.651071i	0.797999	+	0.602659i	$0.205892\pi$
$877$	−5.94738	+	19.2809i	−0.200829	+	0.651071i	−0.998827	+	0.0484118i	$0.984584\pi$
$878$	−54.8161	+	2.11142i	−1.84995	+	0.0712570i
$879$	−18.8870	+	17.5246i	−0.637044	+	0.591090i
$880$	2.33173	+	2.89766i	0.0786025	+	0.0976801i
$881$	−43.1236			−1.45287			−0.726436	−	0.687234i	$-0.758825\pi$
$881$	−43.1236			−1.45287			−0.726436	+	0.687234i	$0.758825\pi$
$882$	−1.83798	+	22.3990i	−0.0618881	+	0.754215i
$883$			56.1330i			1.88903i	0.328475	+	0.944513i	$0.393465\pi$
$883$			56.1330i			1.88903i	−0.328475	+	0.944513i	$0.606535\pi$
$884$	3.24445	+	0.481729i	0.109123	+	0.0162023i
$885$	−2.02816	−	2.18584i	−0.0681759	−	0.0734761i
$886$	−0.426261	−	11.0664i	−0.0143205	−	0.371785i
$887$	9.75959	+	3.01043i	0.327695	+	0.101080i	0.454237	−	0.890881i	$-0.349912\pi$
$887$	9.75959	+	3.01043i	0.327695	+	0.101080i	−0.126542	+	0.991961i	$0.540388\pi$
$888$	−10.9461	+	17.5488i	−0.367326	+	0.588899i
$889$	−12.1491	+	28.9947i	−0.407466	+	0.972452i
$890$	3.33052	+	4.50233i	0.111639	+	0.150918i
$891$	5.48561	+	0.411090i	0.183775	+	0.0137720i
$892$	0.187010	−	0.390524i	0.00626155	−	0.0130757i
$893$	−22.8708	+	1.71393i	−0.765341	+	0.0573544i
$894$	7.28720	−	7.30324i	0.243720	−	0.244257i
$895$	10.7746	+	5.18877i	0.360155	+	0.173441i
$896$	26.2504	+	14.3846i	0.876964	+	0.480557i
$897$	0.366158	−	0.176332i	0.0122256	−	0.00588756i
$898$	−14.1711	+	40.6420i	−0.472896	+	1.35624i
$899$	0.732758	−	4.86153i	0.0244388	−	0.162141i
$900$	21.0321	+	4.75181i	0.701070	+	0.158394i
$901$	−42.8878	−	24.7613i	−1.42880	−	0.824918i
$902$	7.36276	−	27.5995i	0.245153	−	0.918963i
$903$	19.3846	+	18.8261i	0.645078	+	0.626495i
$904$	−0.981901	−	2.77670i	−0.0326575	−	0.0923517i
$905$	7.50677	−	1.13146i	0.249534	−	0.0376111i
$906$	−1.44812	−	0.272350i	−0.0481105	−	0.00904822i
$907$	14.8737	−	21.8157i	0.493872	−	0.724378i	−0.495687	−	0.868501i	$-0.665084\pi$
$907$	14.8737	−	21.8157i	0.493872	−	0.724378i	0.989560	+	0.144123i	$0.0460362\pi$
$908$	−41.1026	−	27.8911i	−1.36404	−	0.925599i
$909$	−29.2060	+	23.2910i	−0.968703	+	0.772515i
$910$	−0.294123	−	0.491438i	−0.00975009	−	0.0162910i
$911$	−24.6067	+	30.8559i	−0.815257	+	1.02230i	0.183967	+	0.982932i	$0.441106\pi$
$911$	−24.6067	+	30.8559i	−0.815257	+	1.02230i	−0.999225	+	0.0393680i	$0.987466\pi$
$912$	−10.0688	−	4.79445i	−0.333412	−	0.158760i
$913$	−1.66094	−	2.87684i	−0.0549692	−	0.0952095i
$914$	4.65244	+	17.2871i	0.153889	+	0.571806i
$915$	−2.79393	+	3.01114i	−0.0923645	+	0.0995452i
$916$	40.9251	+	12.5252i	1.35220	+	0.413846i
$917$	6.50847	−	12.7627i	0.214929	−	0.421460i
$918$	−34.1635	−	1.24070i	−1.12756	−	0.0409491i
$919$	−19.4929	−	49.6670i	−0.643011	−	1.63836i	−0.763621	−	0.645664i	$-0.776580\pi$
$919$	−19.4929	−	49.6670i	−0.643011	−	1.63836i	0.120611	−	0.992700i	$-0.461515\pi$
$920$	2.13434	+	0.564357i	0.0703672	+	0.0186063i
$921$	7.79960	−	2.40586i	0.257006	−	0.0792757i
$922$	11.8548	+	33.7601i	0.390418	+	1.11183i
$923$	1.75759	−	0.401159i	0.0578519	−	0.0132043i
$924$	0.172658	−	8.38540i	0.00568005	−	0.275860i
$925$	−39.6313	−	9.04558i	−1.30307	−	0.297417i
$926$	2.78161	+	24.4459i	0.0914094	+	0.803342i
$927$	−5.93510	+	15.1224i	−0.194934	+	0.496684i
$928$	−10.5012	−	3.60986i	−0.344719	−	0.118499i
$929$	31.6118	−	21.5526i	1.03715	−	0.707117i	0.0800250	−	0.996793i	$-0.474500\pi$
$929$	31.6118	−	21.5526i	1.03715	−	0.707117i	0.957125	+	0.289676i	$0.0935476\pi$
$930$	0.607892	+	1.38913i	0.0199336	+	0.0455515i
$931$	22.8359	−	0.667627i	0.748418	−	0.0218806i
$932$	−3.77859	+	4.09035i	−0.123772	+	0.133984i
$933$	9.13029	+	13.3917i	0.298912	+	0.438424i
$934$	15.6554	−	35.9904i	0.512259	−	1.17764i
$935$	1.82397	−	4.64739i	0.0596501	−	0.151986i
$936$	−1.15946	+	1.58191i	−0.0378983	+	0.0517064i
$937$	−5.99593	+	26.2699i	−0.195879	+	0.858200i	0.777479	+	0.628909i	$0.216498\pi$
$937$	−5.99593	+	26.2699i	−0.195879	+	0.858200i	−0.973358	+	0.229292i	$0.926359\pi$
$938$	−7.73753	+	1.89443i	−0.252639	+	0.0618552i
$939$	5.86729	−	1.33917i	0.191472	−	0.0437022i
$940$	5.15255	−	4.80199i	0.168058	−	0.156624i
$941$	9.71680	+	31.5011i	0.316758	+	1.02691i	0.964286	+	0.264864i	$0.0853269\pi$
$941$	9.71680	+	31.5011i	0.316758	+	1.02691i	−0.647527	+	0.762042i	$0.724197\pi$
$942$	−16.9465	+	8.98034i	−0.552147	+	0.292595i
$943$	−6.19445	−	15.7832i	−0.201719	−	0.513972i
$944$	−25.9798	−	10.0647i	−0.845572	−	0.327579i
$945$	3.61449	+	4.75056i	0.117579	+	0.154536i
$946$	23.8017	+	20.4375i	0.773860	+	0.664481i
$947$	33.2623	−	35.8482i	1.08088	−	1.16491i	0.0953419	−	0.995445i	$-0.469606\pi$
$947$	33.2623	−	35.8482i	1.08088	−	1.16491i	0.985536	−	0.169465i	$-0.0542040\pi$
$948$	−7.09289	−	8.85419i	−0.230366	−	0.287571i
$949$	−3.01057	+	1.73815i	−0.0977271	+	0.0564228i
$950$	2.43015	−	21.7834i	0.0788444	−	0.706746i
$951$	−13.5785	+	17.0270i	−0.440314	+	0.552137i
$952$	−0.719656	−	40.1734i	−0.0233242	−	1.30203i
$953$	−29.1598	−	36.5652i	−0.944579	−	1.18446i	−0.982703	−	0.185191i	$-0.940710\pi$
$953$	−29.1598	−	36.5652i	−0.944579	−	1.18446i	0.0381239	−	0.999273i	$-0.487862\pi$
$954$	25.0564	−	15.7824i	0.811231	−	0.510975i
$955$	0.335116	−	0.491526i	0.0108441	−	0.0159054i
$956$	12.4750	−	2.87621i	0.403470	−	0.0930231i
$957$	0.463729	+	3.07664i	0.0149902	+	0.0994536i
$958$	17.8052	−	33.7789i	0.575260	−	1.09135i
$959$	−12.7769	+	8.29114i	−0.412588	+	0.267735i
$960$	3.33381	−	0.784092i	0.107598	−	0.0253064i
$961$	12.3636	−	21.4143i	0.398824	−	0.690784i
$962$	2.19245	−	2.97751i	0.0706874	−	0.0959987i
$963$	−6.20770	+	41.1854i	−0.200040	+	1.32718i
$964$	−12.5963	+	0.971817i	−0.405699	+	0.0313001i
$965$	−2.71828	−	5.64457i	−0.0875045	−	0.181705i
$966$	−2.86872	−	4.06878i	−0.0922997	−	0.130911i
$967$	13.1490	+	6.33222i	0.422843	+	0.203630i	0.633190	−	0.773996i	$-0.281745\pi$
$967$	13.1490	+	6.33222i	0.422843	+	0.203630i	−0.210347	+	0.977627i	$0.567459\pi$
$968$	0.869690	+	21.3576i	0.0279529	+	0.686458i
$969$	1.11867	+	14.9277i	0.0359370	+	0.479546i
$970$	−2.49915	+	2.15548i	−0.0802429	+	0.0692083i
$971$	−28.7866	−	2.15726i	−0.923805	−	0.0692296i	−0.395673	−	0.918392i	$-0.629488\pi$
$971$	−28.7866	−	2.15726i	−0.923805	−	0.0692296i	−0.528132	+	0.849162i	$0.677108\pi$
$972$	15.9780	−	27.8157i	0.512493	−	0.892189i
$973$	7.11549	−	3.89472i	0.228112	−	0.124859i
$974$	−37.9984	+	7.23297i	−1.21755	+	0.231759i
$975$	1.18406	+	0.365233i	0.0379202	+	0.0116968i
$976$	−11.1516	+	36.7250i	−0.356952	+	1.17554i
$977$	−27.3534	+	25.3802i	−0.875112	+	0.811985i	−0.983271	−	0.182148i	$-0.941695\pi$
$977$	−27.3534	+	25.3802i	−0.875112	+	0.811985i	0.108159	+	0.994134i	$0.465504\pi$
$978$	−0.574679	−	0.360214i	−0.0183762	−	0.0115184i
$979$		−	14.6619i		−	0.468597i
$980$	−5.34509	+	4.54453i	−0.170743	+	0.145170i
$981$			7.11473i			0.227156i
$982$	−3.16939	+	5.05639i	−0.101139	+	0.161356i
$983$	42.7548	−	39.6707i	1.36367	−	1.26530i	0.432054	−	0.901848i	$-0.357789\pi$
$983$	42.7548	−	39.6707i	1.36367	−	1.26530i	0.931613	−	0.363451i	$-0.118402\pi$
$984$	−19.9931	−	17.0910i	−0.637356	−	0.544840i
$985$	−5.81899	−	1.79492i	−0.185408	−	0.0571909i
$986$	2.78721	+	14.6426i	0.0887627	+	0.466315i
$987$	−15.8613	+	0.825750i	−0.504872	+	0.0262839i
$988$	1.72881	+	0.993069i	0.0550009	+	0.0315937i
$989$	18.5696	+	1.39160i	0.590480	+	0.0442503i
$990$	1.94978	+	2.26066i	0.0619681	+	0.0718483i
$991$	−2.01594	−	26.9009i	−0.0640385	−	0.854534i	−0.933051	−	0.359744i	$-0.882864\pi$
$991$	−2.01594	−	26.9009i	−0.0640385	−	0.854534i	0.869013	−	0.494790i	$-0.164755\pi$
$992$	10.7896	+	9.18244i	0.342570	+	0.291543i
$993$	−9.30534	−	4.48122i	−0.295296	−	0.142207i
$994$	−8.39022	−	20.4282i	−0.266122	−	0.647942i
$995$	−1.70215	−	3.53455i	−0.0539618	−	0.112053i
$996$	−3.04975	+	0.235291i	−0.0966350	+	0.00745550i
$997$	−3.15231	+	20.9142i	−0.0998347	+	0.662360i	0.881805	+	0.471615i	$0.156329\pi$
$997$	−3.15231	+	20.9142i	−0.0998347	+	0.662360i	−0.981640	+	0.190745i	$0.938909\pi$
$998$	27.9985	+	20.6164i	0.886279	+	0.652600i
$999$	−19.2692	+	33.3753i	−0.609652	+	1.05595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.37.11	✓	648
8.5	even	2	inner	392.2.z.a.37.31	yes	648
49.4	even	21	inner	392.2.z.a.53.31	yes	648
392.53	even	42	inner	392.2.z.a.53.11	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.37.11	✓	648	1.1	even	1	trivial
392.2.z.a.37.31	yes	648	8.5	even	2	inner
392.2.z.a.53.11	yes	648	392.53	even	42	inner
392.2.z.a.53.31	yes	648	49.4	even	21	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19828 - 0.751090i) q^{2} +(0.581041 + 0.626213i) q^{3} +(0.871727 + 1.80003i) q^{4} +(-0.147712 + 0.478871i) q^{5} +(-0.225904 - 1.18679i) q^{6} +(2.54532 - 0.722043i) q^{7} +(0.307412 - 2.81167i) q^{8} +(0.169656 - 2.26390i) q^{9} +O(q^{10})\)	\(q+(-1.19828 - 0.751090i) q^{2} +(0.581041 + 0.626213i) q^{3} +(0.871727 + 1.80003i) q^{4} +(-0.147712 + 0.478871i) q^{5} +(-0.225904 - 1.18679i) q^{6} +(2.54532 - 0.722043i) q^{7} +(0.307412 - 2.81167i) q^{8} +(0.169656 - 2.26390i) q^{9} +(0.536675 - 0.462874i) q^{10} +(-1.85026 + 0.138658i) q^{11} +(-0.620690 + 1.59178i) q^{12} +(0.132527 - 0.275195i) q^{13} +(-3.59231 - 1.04656i) q^{14} +(-0.385702 + 0.185744i) q^{15} +(-2.48018 + 3.13826i) q^{16} +(5.30929 + 0.800247i) q^{17} +(-1.90369 + 2.58535i) q^{18} +(2.82642 + 1.63184i) q^{19} +(-0.990744 + 0.151559i) q^{20} +(1.93109 + 1.17438i) q^{21} +(2.32127 + 1.22356i) q^{22} +(1.54014 - 0.232139i) q^{23} +(1.93932 - 1.44119i) q^{24} +(3.92370 + 2.67513i) q^{25} +(-0.365501 + 0.230220i) q^{26} +(3.51991 - 2.80704i) q^{27} +(3.51852 + 3.95222i) q^{28} +(-1.53472 - 1.22390i) q^{29} +(0.601688 + 0.0671242i) q^{30} +(1.25229 + 2.16902i) q^{31} +(5.32906 - 1.89766i) q^{32} +(-1.16191 - 1.07809i) q^{33} +(-5.76093 - 4.94667i) q^{34} +(-0.0302091 + 1.32553i) q^{35} +(4.22297 - 1.66812i) q^{36} +(-7.96832 + 3.12733i) q^{37} +(-2.16118 - 4.07828i) q^{38} +(0.249335 - 0.0769096i) q^{39} +(1.30102 + 0.562529i) q^{40} +(-2.42235 - 10.6130i) q^{41} +(-1.43191 - 2.85765i) q^{42} +(11.6561 + 2.66042i) q^{43} +(-1.86251 - 3.20965i) q^{44} +(1.05906 + 0.415649i) q^{45} +(-2.01987 - 0.878620i) q^{46} +(-5.80626 + 3.95864i) q^{47} +(-3.40631 + 0.270336i) q^{48} +(5.95731 - 3.67566i) q^{49} +(-2.69240 - 6.15259i) q^{50} +(2.58379 + 3.78972i) q^{51} +(0.610886 - 0.00134317i) q^{52} +(-8.58578 - 3.36967i) q^{53} +(-6.32616 + 0.719831i) q^{54} +(0.206907 - 0.906519i) q^{55} +(-1.24769 - 7.37857i) q^{56} +(0.620390 + 2.71811i) q^{57} +(0.919762 + 2.61929i) q^{58} +(2.05306 + 6.65587i) q^{59} +(-0.670571 - 0.532355i) q^{60} +(8.93192 - 3.50552i) q^{61} +(0.128548 - 3.53967i) q^{62} +(-1.20281 - 5.88485i) q^{63} +(-7.81100 - 1.72868i) q^{64} +(0.112207 + 0.104113i) q^{65} +(0.582541 + 2.16455i) q^{66} +(1.84379 - 1.06451i) q^{67} +(3.18779 + 10.2545i) q^{68} +(1.04026 + 0.829576i) q^{69} +(1.03179 - 1.56567i) q^{70} +(3.67997 + 4.61453i) q^{71} +(-6.31319 - 1.17297i) q^{72} +(-9.40355 - 6.41123i) q^{73} +(11.8971 + 2.23752i) q^{74} +(0.604626 + 4.01143i) q^{75} +(-0.473476 + 6.51015i) q^{76} +(-4.60939 + 1.68890i) q^{77} +(-0.356538 - 0.0951140i) q^{78} +(-3.32010 + 5.75059i) q^{79} +(-1.13647 - 1.65125i) q^{80} +(-2.93166 - 0.441877i) q^{81} +(-5.06868 + 14.5367i) q^{82} +(0.776799 + 1.61304i) q^{83} +(-0.430525 + 4.49974i) q^{84} +(-1.16746 + 2.42426i) q^{85} +(-11.9690 - 11.9427i) q^{86} +(-0.125314 - 1.67220i) q^{87} +(-0.178932 + 5.24496i) q^{88} +(-0.590524 + 7.87999i) q^{89} +(-0.956851 - 1.29351i) q^{90} +(0.138621 - 0.796151i) q^{91} +(1.76044 + 2.56994i) q^{92} +(-0.630642 + 2.04449i) q^{93} +(9.93079 - 0.382517i) q^{94} +(-1.19894 + 1.11245i) q^{95} +(4.28474 + 2.23451i) q^{96} -4.65673 q^{97} +(-9.89925 - 0.0700191i) q^{98} +4.21234i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

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