LMFDB - Embedded newform 845.2.f.a.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.a.408.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +2.00000 q^{7} -3.00000i q^{8} +1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(1.00000 - 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} -2.00000i q^{14} +(3.00000 - 1.00000i) q^{15} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +1.00000 q^{18} +(-5.00000 + 5.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +(2.00000 - 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 3.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +2.00000 q^{28} +(-1.00000 - 3.00000i) q^{30} +(-5.00000 - 5.00000i) q^{31} -5.00000i q^{32} -2.00000i q^{33} +(1.00000 + 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +1.00000i q^{36} +(5.00000 + 5.00000i) q^{38} +(3.00000 - 6.00000i) q^{40} +(7.00000 + 7.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.00000 + 1.00000i) q^{43} +(1.00000 - 1.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} +(-3.00000 + 3.00000i) q^{46} -6.00000 q^{47} +(-1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} +10.0000i q^{57} +(-7.00000 - 7.00000i) q^{59} +(3.00000 - 1.00000i) q^{60} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} +2.00000i q^{63} -7.00000 q^{64} -2.00000 q^{66} +4.00000i q^{67} +(-1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(2.00000 - 4.00000i) q^{70} +(-1.00000 - 1.00000i) q^{71} +3.00000 q^{72} -10.0000i q^{73} +(7.00000 + 1.00000i) q^{75} +(-5.00000 + 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-2.00000 - 1.00000i) q^{80} +5.00000 q^{81} +(7.00000 - 7.00000i) q^{82} -6.00000 q^{83} +(2.00000 - 2.00000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(1.00000 - 1.00000i) q^{86} +(-3.00000 - 3.00000i) q^{88} +(5.00000 + 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(-3.00000 - 3.00000i) q^{92} -10.0000 q^{93} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +(-5.00000 - 5.00000i) q^{96} -2.00000i q^{97} +3.00000i q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} - 10 q^{19} + 4 q^{20} + 4 q^{21} - 2 q^{22} - 6 q^{23} - 6 q^{24} + 6 q^{25}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 - 10 * q^19 + 4 * q^20 + 4 * q^21 - 2 * q^22 - 6 * q^23 - 6 * q^24 + 6 * q^25 + 8 * q^27 + 4 * q^28 - 2 * q^30 - 10 * q^31 + 2 * q^34 + 8 * q^35 + 10 * q^38 + 6 * q^40 + 14 * q^41 - 4 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 - 12 * q^47 - 2 * q^48 - 6 * q^49 + 8 * q^50 + 10 * q^53 + 8 * q^54 + 6 * q^55 - 14 * q^59 + 6 * q^60 - 28 * q^61 - 10 * q^62 - 14 * q^64 - 4 * q^66 - 2 * q^68 - 12 * q^69 + 4 * q^70 - 2 * q^71 + 6 * q^72 + 14 * q^75 - 10 * q^76 + 4 * q^77 - 4 * q^80 + 10 * q^81 + 14 * q^82 - 12 * q^83 + 4 * q^84 - 6 * q^85 + 2 * q^86 - 6 * q^88 + 10 * q^89 + 4 * q^90 - 6 * q^92 - 20 * q^93 - 30 * q^95 - 10 * q^96 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$	1.00000			0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		−	3.00000i		−	1.06066i
$9$			1.00000i			0.333333i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	1.00000	−	1.00000i	0.288675	−	0.288675i
$13$		0			0
$13$		0			0
$14$		−	2.00000i		−	0.534522i
$15$	3.00000	−	1.00000i	0.774597	−	0.258199i
$16$	−1.00000			−0.250000
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$	1.00000			0.235702
$19$	−5.00000	+	5.00000i	−1.14708	+	1.14708i	−0.159954	+	0.987124i	$0.551135\pi$
$19$	−5.00000	+	5.00000i	−1.14708	+	1.14708i	−0.987124	+	0.159954i	$0.948865\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$	2.00000	−	2.00000i	0.436436	−	0.436436i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	0.321400	−	0.946943i	$-0.395847\pi$
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	−0.946943	+	0.321400i	$0.895847\pi$
$24$	−3.00000	−	3.00000i	−0.612372	−	0.612372i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$	2.00000			0.377964
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−1.00000	−	3.00000i	−0.182574	−	0.547723i
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	0.0972349	−	0.995261i	$-0.469000\pi$
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	−0.995261	+	0.0972349i	$0.969000\pi$
$32$		−	5.00000i		−	0.883883i
$33$		−	2.00000i		−	0.348155i
$34$	1.00000	+	1.00000i	0.171499	+	0.171499i
$35$	4.00000	+	2.00000i	0.676123	+	0.338062i
$36$			1.00000i			0.166667i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	5.00000	+	5.00000i	0.811107	+	0.811107i
$39$		0			0
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	7.00000	+	7.00000i	1.09322	+	1.09322i	0.995183	+	0.0980332i	$0.0312551\pi$
$41$	7.00000	+	7.00000i	1.09322	+	1.09322i	0.0980332	+	0.995183i	$0.468745\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	0.779233	−	0.626734i	$-0.215609\pi$
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	−0.626734	+	0.779233i	$0.715609\pi$
$44$	1.00000	−	1.00000i	0.150756	−	0.150756i
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	−3.00000	+	3.00000i	−0.442326	+	0.442326i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$			2.00000i			0.280056i
$52$		0			0
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$	4.00000	−	4.00000i	0.544331	−	0.544331i
$55$	3.00000	−	1.00000i	0.404520	−	0.134840i
$56$		−	6.00000i		−	0.801784i
$57$			10.0000i			1.32453i
$58$		0			0
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	0.0850540	−	0.996376i	$-0.472894\pi$
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	−0.996376	+	0.0850540i	$0.972894\pi$
$60$	3.00000	−	1.00000i	0.387298	−	0.129099i
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	−5.00000	+	5.00000i	−0.635001	+	0.635001i
$63$			2.00000i			0.251976i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	−1.00000	+	1.00000i	−0.121268	+	0.121268i
$69$	−6.00000			−0.722315
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	0.645273	−	0.763952i	$-0.276743\pi$
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	−0.763952	+	0.645273i	$0.776743\pi$
$72$	3.00000			0.353553
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$		0			0
$75$	7.00000	+	1.00000i	0.808290	+	0.115470i
$76$	−5.00000	+	5.00000i	−0.573539	+	0.573539i
$77$	2.00000	−	2.00000i	0.227921	−	0.227921i
$78$		0			0
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	5.00000			0.555556
$82$	7.00000	−	7.00000i	0.773021	−	0.773021i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	2.00000	−	2.00000i	0.218218	−	0.218218i
$85$	−3.00000	+	1.00000i	−0.325396	+	0.108465i
$86$	1.00000	−	1.00000i	0.107833	−	0.107833i
$87$		0			0
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	5.00000	+	5.00000i	0.529999	+	0.529999i	0.920572	−	0.390573i	$-0.127723\pi$
$89$	5.00000	+	5.00000i	0.529999	+	0.529999i	−0.390573	+	0.920572i	$0.627723\pi$
$90$	2.00000	+	1.00000i	0.210819	+	0.105409i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	−10.0000			−1.03695
$94$			6.00000i			0.618853i
$95$	−15.0000	+	5.00000i	−1.53897	+	0.512989i
$96$	−5.00000	−	5.00000i	−0.510310	−	0.510310i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$			3.00000i			0.303046i
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	12.0000i		−	1.19404i	−0.802225	−	0.597022i	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$	2.00000			0.198030
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	0.272442	−	0.962172i	$-0.412169\pi$
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	−0.962172	+	0.272442i	$0.912169\pi$
$104$		0			0
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$	−5.00000	−	5.00000i	−0.485643	−	0.485643i
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	0.959256	−	0.282540i	$-0.0911770\pi$
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	−0.282540	+	0.959256i	$0.591177\pi$
$108$	4.00000	+	4.00000i	0.384900	+	0.384900i
$109$	9.00000	−	9.00000i	0.862044	−	0.862044i	−0.129532	−	0.991575i	$-0.541347\pi$
$109$	9.00000	−	9.00000i	0.862044	−	0.862044i	0.991575	+	0.129532i	$0.0413474\pi$
$110$	−1.00000	−	3.00000i	−0.0953463	−	0.286039i
$111$		0			0
$112$	−2.00000			−0.188982
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$	10.0000			0.936586
$115$	−3.00000	−	9.00000i	−0.279751	−	0.839254i
$116$		0			0
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−2.00000	+	2.00000i	−0.183340	+	0.183340i
$120$	−3.00000	−	9.00000i	−0.273861	−	0.821584i
$121$			9.00000i			0.818182i
$122$			14.0000i			1.26750i
$123$	14.0000			1.26234
$124$	−5.00000	−	5.00000i	−0.449013	−	0.449013i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	2.00000			0.178174
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$		−	3.00000i		−	0.265165i
$129$	2.00000			0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$		−	2.00000i		−	0.174078i
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$	4.00000			0.345547
$135$	4.00000	+	12.0000i	0.344265	+	1.03280i
$136$	3.00000	+	3.00000i	0.257248	+	0.257248i
$137$	16.0000			1.36697			0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000			1.36697			0.683486	+	0.729964i	$0.260463\pi$
$138$			6.00000i			0.510754i
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$	−6.00000	+	6.00000i	−0.505291	+	0.505291i
$142$	−1.00000	+	1.00000i	−0.0839181	+	0.0839181i
$143$		0			0
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−10.0000			−0.827606
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$		0			0
$149$	−3.00000	+	3.00000i	−0.245770	+	0.245770i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−3.00000	+	3.00000i	−0.245770	+	0.245770i	0.573462	+	0.819232i	$0.305600\pi$
$150$	1.00000	−	7.00000i	0.0816497	−	0.571548i
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	−0.932031	−	0.362379i	$-0.881965\pi$
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	0.362379	+	0.932031i	$0.381965\pi$
$152$	15.0000	+	15.0000i	1.21666	+	1.21666i
$153$	−1.00000	−	1.00000i	−0.0808452	−	0.0808452i
$154$	−2.00000	−	2.00000i	−0.161165	−	0.161165i
$155$	−5.00000	−	15.0000i	−0.401610	−	1.20483i
$156$		0			0
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$	−2.00000			−0.159111
$159$		−	10.0000i		−	0.793052i
$160$	5.00000	−	10.0000i	0.395285	−	0.790569i
$161$	−6.00000	−	6.00000i	−0.472866	−	0.472866i
$162$		−	5.00000i		−	0.392837i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	7.00000	+	7.00000i	0.546608	+	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$			6.00000i			0.465690i
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$	−6.00000	−	6.00000i	−0.462910	−	0.462910i
$169$		0			0
$170$	1.00000	+	3.00000i	0.0766965	+	0.230089i
$171$	−5.00000	−	5.00000i	−0.382360	−	0.382360i
$172$	1.00000	+	1.00000i	0.0762493	+	0.0762493i
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$	6.00000	+	8.00000i	0.453557	+	0.604743i
$176$	−1.00000	+	1.00000i	−0.0753778	+	0.0753778i
$177$	−14.0000			−1.05230
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	−1.00000	+	2.00000i	−0.0745356	+	0.149071i
$181$			8.00000i			0.594635i	0.954779	+	0.297318i	$0.0960920\pi$
$181$			8.00000i			0.594635i	−0.954779	+	0.297318i	$0.903908\pi$
$182$		0			0
$183$	−14.0000	+	14.0000i	−1.03491	+	1.03491i
$184$	−9.00000	+	9.00000i	−0.663489	+	0.663489i
$185$		0			0
$186$			10.0000i			0.733236i
$187$			2.00000i			0.146254i
$188$	−6.00000			−0.437595
$189$	8.00000	+	8.00000i	0.581914	+	0.581914i
$190$	5.00000	+	15.0000i	0.362738	+	1.08821i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	−7.00000	+	7.00000i	−0.505181	+	0.505181i
$193$			18.0000i			1.29567i	0.761781	+	0.647834i	$0.224325\pi$
$193$			18.0000i			1.29567i	−0.761781	+	0.647834i	$0.775675\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$	4.00000	+	4.00000i	0.282138	+	0.282138i
$202$	−12.0000			−0.844317
$203$		0			0
$204$			2.00000i			0.140028i
$205$	7.00000	+	21.0000i	0.488901	+	1.46670i
$206$	−7.00000	+	7.00000i	−0.487713	+	0.487713i
$207$	3.00000	−	3.00000i	0.208514	−	0.208514i
$208$		0			0
$209$			10.0000i			0.691714i
$210$	−2.00000	−	6.00000i	−0.138013	−	0.414039i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	5.00000	−	5.00000i	0.343401	−	0.343401i
$213$	−2.00000			−0.137038
$214$	7.00000	−	7.00000i	0.478510	−	0.478510i
$215$	1.00000	+	3.00000i	0.0681994	+	0.204598i
$216$	12.0000	−	12.0000i	0.816497	−	0.816497i
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$	−10.0000	−	10.0000i	−0.675737	−	0.675737i
$220$	3.00000	−	1.00000i	0.202260	−	0.0674200i
$221$		0			0
$222$		0			0
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$		−	10.0000i		−	0.668153i
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$	−5.00000	−	5.00000i	−0.332595	−	0.332595i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$			10.0000i			0.662266i
$229$	−3.00000	−	3.00000i	−0.198246	−	0.198246i	0.601002	−	0.799248i	$-0.294768\pi$
$229$	−3.00000	−	3.00000i	−0.198246	−	0.198246i	−0.799248	+	0.601002i	$0.794768\pi$
$230$	−9.00000	+	3.00000i	−0.593442	+	0.197814i
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$		0			0
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	−7.00000	−	7.00000i	−0.455661	−	0.455661i
$237$	−2.00000	−	2.00000i	−0.129914	−	0.129914i
$238$	2.00000	+	2.00000i	0.129641	+	0.129641i
$239$	3.00000	−	3.00000i	0.194054	−	0.194054i	−0.603391	−	0.797445i	$-0.706184\pi$
$239$	3.00000	−	3.00000i	0.194054	−	0.194054i	0.797445	+	0.603391i	$0.206184\pi$
$240$	−3.00000	+	1.00000i	−0.193649	+	0.0645497i
$241$	−17.0000	+	17.0000i	−1.09507	+	1.09507i	−0.100088	+	0.994979i	$0.531912\pi$
$241$	−17.0000	+	17.0000i	−1.09507	+	1.09507i	−0.994979	+	0.100088i	$0.968088\pi$
$242$	9.00000			0.578542
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	−14.0000			−0.896258
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		−	14.0000i		−	0.892607i
$247$		0			0
$248$	−15.0000	+	15.0000i	−0.952501	+	0.952501i
$249$	−6.00000	+	6.00000i	−0.380235	+	0.380235i
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$		−	2.00000i		−	0.126239i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$		−	2.00000i		−	0.126239i	0.998006	−	0.0631194i	$-0.0201049\pi$
$252$			2.00000i			0.125988i
$253$	−6.00000			−0.377217
$254$	9.00000	+	9.00000i	0.564710	+	0.564710i
$255$	−2.00000	+	4.00000i	−0.125245	+	0.250490i
$256$	−17.0000			−1.06250
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	−0.275220	−	0.961381i	$-0.588751\pi$
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	0.961381	+	0.275220i	$0.0887507\pi$
$258$		−	2.00000i		−	0.124515i
$259$		0			0
$260$		0			0
$261$		0			0
$262$			20.0000i			1.23560i
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	−0.675603	−	0.737266i	$-0.736117\pi$
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	0.737266	+	0.675603i	$0.236117\pi$
$264$	−6.00000			−0.369274
$265$	15.0000	−	5.00000i	0.921443	−	0.307148i
$266$	10.0000	+	10.0000i	0.613139	+	0.613139i
$267$	10.0000			0.611990
$268$			4.00000i			0.244339i
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$	12.0000	−	4.00000i	0.730297	−	0.243432i
$271$	9.00000	−	9.00000i	0.546711	−	0.546711i	−0.378777	−	0.925488i	$-0.623655\pi$
$271$	9.00000	−	9.00000i	0.546711	−	0.546711i	0.925488	+	0.378777i	$0.123655\pi$
$272$	1.00000	−	1.00000i	0.0606339	−	0.0606339i
$273$		0			0
$274$		−	16.0000i		−	0.966595i
$275$	7.00000	+	1.00000i	0.422116	+	0.0603023i
$276$	−6.00000			−0.361158
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	−0.0942828	−	0.995545i	$-0.530056\pi$
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	0.995545	+	0.0942828i	$0.0300558\pi$
$278$	−14.0000			−0.839664
$279$	5.00000	−	5.00000i	0.299342	−	0.299342i
$280$	6.00000	−	12.0000i	0.358569	−	0.717137i
$281$	−1.00000	+	1.00000i	−0.0596550	+	0.0596550i	−0.736305	−	0.676650i	$-0.763431\pi$
$281$	−1.00000	+	1.00000i	−0.0596550	+	0.0596550i	0.676650	+	0.736305i	$0.263431\pi$
$282$	6.00000	+	6.00000i	0.357295	+	0.357295i
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	0.922055	−	0.387060i	$-0.126509\pi$
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	−0.387060	+	0.922055i	$0.626509\pi$
$284$	−1.00000	−	1.00000i	−0.0593391	−	0.0593391i
$285$	−10.0000	+	20.0000i	−0.592349	+	1.18470i
$286$		0			0
$287$	14.0000	+	14.0000i	0.826394	+	0.826394i
$288$	5.00000			0.294628
$289$			15.0000i			0.882353i
$290$		0			0
$291$	−2.00000	−	2.00000i	−0.117242	−	0.117242i
$292$		−	10.0000i		−	0.585206i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	3.00000	+	3.00000i	0.174964	+	0.174964i
$295$	−7.00000	−	21.0000i	−0.407556	−	1.22267i
$296$		0			0
$297$	8.00000			0.464207
$298$	3.00000	+	3.00000i	0.173785	+	0.173785i
$299$		0			0
$300$	7.00000	+	1.00000i	0.404145	+	0.0577350i
$301$	2.00000	+	2.00000i	0.115278	+	0.115278i
$302$	7.00000	+	7.00000i	0.402805	+	0.402805i
$303$	−12.0000	−	12.0000i	−0.689382	−	0.689382i
$304$	5.00000	−	5.00000i	0.286770	−	0.286770i
$305$	−28.0000	−	14.0000i	−1.60328	−	0.801638i
$306$	−1.00000	+	1.00000i	−0.0571662	+	0.0571662i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	−14.0000			−0.796432
$310$	−15.0000	+	5.00000i	−0.851943	+	0.283981i
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	13.0000	−	13.0000i	0.733632	−	0.733632i
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$		−	2.00000i		−	0.112509i
$317$			14.0000i			0.786318i	0.919470	+	0.393159i	$0.128618\pi$
$317$			14.0000i			0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$	−10.0000			−0.560772
$319$		0			0
$320$	−14.0000	−	7.00000i	−0.782624	−	0.391312i
$321$	14.0000			0.781404
$322$	−6.00000	+	6.00000i	−0.334367	+	0.334367i
$323$		−	10.0000i		−	0.556415i
$324$	5.00000			0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$		−	18.0000i		−	0.995402i
$328$	21.0000	−	21.0000i	1.15953	−	1.15953i
$329$	−12.0000			−0.661581
$330$	−4.00000	−	2.00000i	−0.220193	−	0.110096i
$331$	3.00000	+	3.00000i	0.164895	+	0.164895i	0.784731	−	0.619836i	$-0.212801\pi$
$331$	3.00000	+	3.00000i	0.164895	+	0.164895i	−0.619836	+	0.784731i	$0.712801\pi$
$332$	−6.00000			−0.329293
$333$		0			0
$334$		−	18.0000i		−	0.984916i
$335$	−4.00000	+	8.00000i	−0.218543	+	0.437087i
$336$	−2.00000	+	2.00000i	−0.109109	+	0.109109i
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	−0.966147	−	0.257992i	$-0.916939\pi$
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	0.257992	+	0.966147i	$0.416939\pi$
$338$		0			0
$339$		−	10.0000i		−	0.543125i
$340$	−3.00000	+	1.00000i	−0.162698	+	0.0542326i
$341$	−10.0000			−0.541530
$342$	−5.00000	+	5.00000i	−0.270369	+	0.270369i
$343$	−20.0000			−1.07990
$344$	3.00000	−	3.00000i	0.161749	−	0.161749i
$345$	−12.0000	−	6.00000i	−0.646058	−	0.323029i
$346$	11.0000	−	11.0000i	0.591364	−	0.591364i
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	0.783031	−	0.621983i	$-0.213673\pi$
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	−0.621983	+	0.783031i	$0.713673\pi$
$348$		0			0
$349$	9.00000	+	9.00000i	0.481759	+	0.481759i	0.905693	−	0.423934i	$-0.139351\pi$
$349$	9.00000	+	9.00000i	0.481759	+	0.481759i	−0.423934	+	0.905693i	$0.639351\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$		0			0
$352$	−5.00000	−	5.00000i	−0.266501	−	0.266501i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$			14.0000i			0.744092i
$355$	−1.00000	−	3.00000i	−0.0530745	−	0.159223i
$356$	5.00000	+	5.00000i	0.264999	+	0.264999i
$357$			4.00000i			0.211702i
$358$		−	20.0000i		−	1.05703i
$359$	1.00000	+	1.00000i	0.0527780	+	0.0527780i	0.733003	−	0.680225i	$-0.238118\pi$
$359$	1.00000	+	1.00000i	0.0527780	+	0.0527780i	−0.680225	+	0.733003i	$0.738118\pi$
$360$	6.00000	+	3.00000i	0.316228	+	0.158114i
$361$		−	31.0000i		−	1.63158i
$362$	8.00000			0.420471
$363$	9.00000	+	9.00000i	0.472377	+	0.472377i
$364$		0			0
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$	14.0000	+	14.0000i	0.731792	+	0.731792i
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	0.680525	−	0.732725i	$-0.261752\pi$
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	−0.732725	+	0.680525i	$0.761752\pi$
$368$	3.00000	+	3.00000i	0.156386	+	0.156386i
$369$	−7.00000	+	7.00000i	−0.364405	+	0.364405i
$370$		0			0
$371$	10.0000	−	10.0000i	0.519174	−	0.519174i
$372$	−10.0000			−0.518476
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$	2.00000			0.103418
$375$	13.0000	+	9.00000i	0.671317	+	0.464758i
$376$			18.0000i			0.928279i
$377$		0			0
$378$	8.00000	−	8.00000i	0.411476	−	0.411476i
$379$	−1.00000	+	1.00000i	−0.0513665	+	0.0513665i	−0.732323	−	0.680957i	$-0.761564\pi$
$379$	−1.00000	+	1.00000i	−0.0513665	+	0.0513665i	0.680957	+	0.732323i	$0.261564\pi$
$380$	−15.0000	+	5.00000i	−0.769484	+	0.256495i
$381$			18.0000i			0.922168i
$382$		−	8.00000i		−	0.409316i
$383$	30.0000			1.53293			0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000			1.53293			0.766464	+	0.642287i	$0.222014\pi$
$384$	−3.00000	−	3.00000i	−0.153093	−	0.153093i
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$	18.0000			0.916176
$387$	−1.00000	+	1.00000i	−0.0508329	+	0.0508329i
$388$		−	2.00000i		−	0.101535i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$			9.00000i			0.454569i
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$	−6.00000			−0.302276
$395$	2.00000	−	4.00000i	0.100631	−	0.201262i
$396$	1.00000	+	1.00000i	0.0502519	+	0.0502519i
$397$	−16.0000			−0.803017			−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000			−0.803017			−0.401508	+	0.915855i	$0.631514\pi$
$398$		−	8.00000i		−	0.401004i
$399$			20.0000i			1.00125i
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	11.0000	−	11.0000i	0.549314	−	0.549314i	−0.376929	−	0.926242i	$-0.623020\pi$
$401$	11.0000	−	11.0000i	0.549314	−	0.549314i	0.926242	+	0.376929i	$0.123020\pi$
$402$	4.00000	−	4.00000i	0.199502	−	0.199502i
$403$		0			0
$404$		−	12.0000i		−	0.597022i
$405$	10.0000	+	5.00000i	0.496904	+	0.248452i
$406$		0			0
$407$		0			0
$408$	6.00000			0.297044
$409$	−7.00000	+	7.00000i	−0.346128	+	0.346128i	−0.858665	−	0.512537i	$-0.828706\pi$
$409$	−7.00000	+	7.00000i	−0.346128	+	0.346128i	0.512537	+	0.858665i	$0.328706\pi$
$410$	21.0000	−	7.00000i	1.03712	−	0.345705i
$411$	16.0000	−	16.0000i	0.789222	−	0.789222i
$412$	−7.00000	−	7.00000i	−0.344865	−	0.344865i
$413$	−14.0000	−	14.0000i	−0.688895	−	0.688895i
$414$	−3.00000	−	3.00000i	−0.147442	−	0.147442i
$415$	−12.0000	−	6.00000i	−0.589057	−	0.294528i
$416$		0			0
$417$	−14.0000	−	14.0000i	−0.685583	−	0.685583i
$418$	10.0000			0.489116
$419$		−	38.0000i		−	1.85642i	−0.372055	−	0.928211i	$-0.621347\pi$
$419$		−	38.0000i		−	1.85642i	0.372055	−	0.928211i	$-0.378653\pi$
$420$	6.00000	−	2.00000i	0.292770	−	0.0975900i
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	0.922383	−	0.386276i	$-0.126239\pi$
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	−0.386276	+	0.922383i	$0.626239\pi$
$422$		−	4.00000i		−	0.194717i
$423$		−	6.00000i		−	0.291730i
$424$	−15.0000	−	15.0000i	−0.728464	−	0.728464i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$			2.00000i			0.0969003i
$427$	−28.0000			−1.35501
$428$	7.00000	+	7.00000i	0.338358	+	0.338358i
$429$		0			0
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$	−13.0000	−	13.0000i	−0.626188	−	0.626188i	0.320919	−	0.947107i	$-0.396008\pi$
$431$	−13.0000	−	13.0000i	−0.626188	−	0.626188i	−0.947107	+	0.320919i	$0.896008\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	0.168700	−	0.985668i	$-0.446043\pi$
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	−0.985668	+	0.168700i	$0.946043\pi$
$434$	−10.0000	+	10.0000i	−0.480015	+	0.480015i
$435$		0			0
$436$	9.00000	−	9.00000i	0.431022	−	0.431022i
$437$	30.0000			1.43509
$438$	−10.0000	+	10.0000i	−0.477818	+	0.477818i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	−3.00000	−	9.00000i	−0.143019	−	0.429058i
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.210108	−	0.977678i	$-0.432619\pi$
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.977678	−	0.210108i	$-0.0673814\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$			2.00000i			0.0947027i
$447$			6.00000i			0.283790i
$448$	−14.0000			−0.661438
$449$	−3.00000	−	3.00000i	−0.141579	−	0.141579i	0.632765	−	0.774344i	$-0.281920\pi$
$449$	−3.00000	−	3.00000i	−0.141579	−	0.141579i	−0.774344	+	0.632765i	$0.781920\pi$
$450$	3.00000	+	4.00000i	0.141421	+	0.188562i
$451$	14.0000			0.659234
$452$	5.00000	−	5.00000i	0.235180	−	0.235180i
$453$			14.0000i			0.657777i
$454$	12.0000			0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$	−3.00000	+	3.00000i	−0.140181	+	0.140181i
$459$	−8.00000			−0.373408
$460$	−3.00000	−	9.00000i	−0.139876	−	0.419627i
$461$	−17.0000	−	17.0000i	−0.791769	−	0.791769i	0.190013	−	0.981782i	$-0.439147\pi$
$461$	−17.0000	−	17.0000i	−0.791769	−	0.791769i	−0.981782	+	0.190013i	$0.939147\pi$
$462$	−4.00000			−0.186097
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	−20.0000	−	10.0000i	−0.927478	−	0.463739i
$466$	−1.00000	+	1.00000i	−0.0463241	+	0.0463241i
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$	−6.00000	+	12.0000i	−0.276759	+	0.553519i
$471$	26.0000			1.19802
$472$	−21.0000	+	21.0000i	−0.966603	+	0.966603i
$473$	2.00000			0.0919601
$474$	−2.00000	+	2.00000i	−0.0918630	+	0.0918630i
$475$	−35.0000	−	5.00000i	−1.60591	−	0.229416i
$476$	−2.00000	+	2.00000i	−0.0916698	+	0.0916698i
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$	−3.00000	−	3.00000i	−0.137217	−	0.137217i
$479$	−7.00000	−	7.00000i	−0.319838	−	0.319838i	0.528867	−	0.848705i	$-0.322617\pi$
$479$	−7.00000	−	7.00000i	−0.319838	−	0.319838i	−0.848705	+	0.528867i	$0.822617\pi$
$480$	−5.00000	−	15.0000i	−0.228218	−	0.684653i
$481$		0			0
$482$	17.0000	+	17.0000i	0.774329	+	0.774329i
$483$	−12.0000			−0.546019
$484$			9.00000i			0.409091i
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$		−	16.0000i		−	0.725029i	−0.931978	−	0.362515i	$-0.881918\pi$
$487$		−	16.0000i		−	0.725029i	0.931978	−	0.362515i	$-0.118082\pi$
$488$			42.0000i			1.90125i
$489$	4.00000	+	4.00000i	0.180886	+	0.180886i
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$			22.0000i			0.992846i	0.868081	+	0.496423i	$0.165354\pi$
$491$			22.0000i			0.992846i	−0.868081	+	0.496423i	$0.834646\pi$
$492$	14.0000			0.631169
$493$		0			0
$494$		0			0
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$	5.00000	+	5.00000i	0.224507	+	0.224507i
$497$	−2.00000	−	2.00000i	−0.0897123	−	0.0897123i
$498$	6.00000	+	6.00000i	0.268866	+	0.268866i
$499$	3.00000	−	3.00000i	0.134298	−	0.134298i	−0.636762	−	0.771060i	$-0.719727\pi$
$499$	3.00000	−	3.00000i	0.134298	−	0.134298i	0.771060	+	0.636762i	$0.219727\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$	18.0000	−	18.0000i	0.804181	−	0.804181i
$502$	−2.00000			−0.0892644
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	−0.770818	−	0.637055i	$-0.780152\pi$
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	0.637055	+	0.770818i	$0.280152\pi$
$504$	6.00000			0.267261
$505$	12.0000	−	24.0000i	0.533993	−	1.06799i
$506$			6.00000i			0.266733i
$507$		0			0
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	13.0000	−	13.0000i	0.576215	−	0.576215i	−0.357643	−	0.933858i	$-0.616420\pi$
$509$	13.0000	−	13.0000i	0.576215	−	0.576215i	0.933858	+	0.357643i	$0.116420\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$		−	20.0000i		−	0.884748i
$512$			11.0000i			0.486136i
$513$	−40.0000			−1.76604
$514$	−11.0000	−	11.0000i	−0.485189	−	0.485189i
$515$	−7.00000	−	21.0000i	−0.308457	−	0.925371i
$516$	2.00000			0.0880451
$517$	−6.00000	+	6.00000i	−0.263880	+	0.263880i
$518$		0			0
$519$	22.0000			0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$	−20.0000			−0.873704
$525$	14.0000	+	2.00000i	0.611010	+	0.0872872i
$526$	−1.00000	−	1.00000i	−0.0436021	−	0.0436021i
$527$	10.0000			0.435607
$528$			2.00000i			0.0870388i
$529$		−	5.00000i		−	0.217391i
$530$	−5.00000	−	15.0000i	−0.217186	−	0.651558i
$531$	7.00000	−	7.00000i	0.303774	−	0.303774i
$532$	−10.0000	+	10.0000i	−0.433555	+	0.433555i
$533$		0			0
$534$		−	10.0000i		−	0.432742i
$535$	7.00000	+	21.0000i	0.302636	+	0.907909i
$536$	12.0000			0.518321
$537$	20.0000	−	20.0000i	0.863064	−	0.863064i
$538$	12.0000			0.517357
$539$	−3.00000	+	3.00000i	−0.129219	+	0.129219i
$540$	4.00000	+	12.0000i	0.172133	+	0.516398i
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	−9.00000	−	9.00000i	−0.386583	−	0.386583i
$543$	8.00000	+	8.00000i	0.343313	+	0.343313i
$544$	5.00000	+	5.00000i	0.214373	+	0.214373i
$545$	27.0000	−	9.00000i	1.15655	−	0.385518i
$546$		0			0
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$	16.0000			0.683486
$549$		−	14.0000i		−	0.597505i
$550$	1.00000	−	7.00000i	0.0426401	−	0.298481i
$551$		0			0
$552$			18.0000i			0.766131i
$553$		−	4.00000i		−	0.170097i
$554$	−15.0000	−	15.0000i	−0.637289	−	0.637289i
$555$		0			0
$556$		−	14.0000i		−	0.593732i
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	−5.00000	−	5.00000i	−0.211667	−	0.211667i
$559$		0			0
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$	2.00000	+	2.00000i	0.0844401	+	0.0844401i
$562$	1.00000	+	1.00000i	0.0421825	+	0.0421825i
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	0.316438	−	0.948613i	$-0.397513\pi$
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	−0.948613	+	0.316438i	$0.897513\pi$
$564$	−6.00000	+	6.00000i	−0.252646	+	0.252646i
$565$	15.0000	−	5.00000i	0.631055	−	0.210352i
$566$	9.00000	−	9.00000i	0.378298	−	0.378298i
$567$	10.0000			0.419961
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	20.0000	+	10.0000i	0.837708	+	0.418854i
$571$			6.00000i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$571$			6.00000i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$572$		0			0
$573$	8.00000	−	8.00000i	0.334205	−	0.334205i
$574$	14.0000	−	14.0000i	0.584349	−	0.584349i
$575$	3.00000	−	21.0000i	0.125109	−	0.875761i
$576$		−	7.00000i		−	0.291667i
$577$		−	46.0000i		−	1.91501i	−0.288425	−	0.957503i	$-0.593132\pi$
$577$		−	46.0000i		−	1.91501i	0.288425	−	0.957503i	$-0.406868\pi$
$578$	15.0000			0.623918
$579$	18.0000	+	18.0000i	0.748054	+	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	−2.00000	+	2.00000i	−0.0829027	+	0.0829027i
$583$		−	10.0000i		−	0.414158i
$584$	−30.0000			−1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$			4.00000i			0.165098i	0.996587	+	0.0825488i	$0.0263060\pi$
$587$			4.00000i			0.165098i	−0.996587	+	0.0825488i	$0.973694\pi$
$588$	−3.00000	+	3.00000i	−0.123718	+	0.123718i
$589$	50.0000			2.06021
$590$	−21.0000	+	7.00000i	−0.864556	+	0.288185i
$591$	−6.00000	−	6.00000i	−0.246807	−	0.246807i
$592$		0			0
$593$			10.0000i			0.410651i	0.978694	+	0.205325i	$0.0658253\pi$
$593$			10.0000i			0.410651i	−0.978694	+	0.205325i	$0.934175\pi$
$594$		−	8.00000i		−	0.328244i
$595$	−6.00000	+	2.00000i	−0.245976	+	0.0819920i
$596$	−3.00000	+	3.00000i	−0.122885	+	0.122885i
$597$	8.00000	−	8.00000i	0.327418	−	0.327418i
$598$		0			0
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	3.00000	−	21.0000i	0.122474	−	0.857321i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	2.00000	−	2.00000i	0.0815139	−	0.0815139i
$603$	−4.00000			−0.162893
$604$	−7.00000	+	7.00000i	−0.284826	+	0.284826i
$605$	−9.00000	+	18.0000i	−0.365902	+	0.731804i
$606$	−12.0000	+	12.0000i	−0.487467	+	0.487467i
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	0.392218	−	0.919872i	$-0.371708\pi$
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	−0.919872	+	0.392218i	$0.871708\pi$
$608$	25.0000	+	25.0000i	1.01388	+	1.01388i
$609$		0			0
$610$	−14.0000	+	28.0000i	−0.566843	+	1.13369i
$611$		0			0
$612$	−1.00000	−	1.00000i	−0.0404226	−	0.0404226i
$613$	20.0000			0.807792			0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000			0.807792			0.403896	+	0.914805i	$0.367656\pi$
$614$			18.0000i			0.726421i
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$	−6.00000	−	6.00000i	−0.241747	−	0.241747i
$617$			22.0000i			0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$			22.0000i			0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$			14.0000i			0.563163i
$619$	25.0000	+	25.0000i	1.00483	+	1.00483i	0.999988	+	0.00484658i	$0.00154272\pi$
$619$	25.0000	+	25.0000i	1.00483	+	1.00483i	0.00484658	+	0.999988i	$0.498457\pi$
$620$	−5.00000	−	15.0000i	−0.200805	−	0.602414i
$621$		−	24.0000i		−	0.963087i
$622$	−6.00000			−0.240578
$623$	10.0000	+	10.0000i	0.400642	+	0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−9.00000	−	9.00000i	−0.359712	−	0.359712i
$627$	10.0000	+	10.0000i	0.399362	+	0.399362i
$628$	13.0000	+	13.0000i	0.518756	+	0.518756i
$629$		0			0
$630$	4.00000	+	2.00000i	0.159364	+	0.0796819i
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	−0.891306	−	0.453403i	$-0.850210\pi$
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	0.453403	+	0.891306i	$0.350210\pi$
$632$	−6.00000			−0.238667
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$	14.0000			0.556011
$635$	−27.0000	+	9.00000i	−1.07146	+	0.357154i
$636$		−	10.0000i		−	0.396526i
$637$		0			0
$638$		0			0
$639$	1.00000	−	1.00000i	0.0395594	−	0.0395594i
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$		−	14.0000i		−	0.552536i
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$	−6.00000	−	6.00000i	−0.236433	−	0.236433i
$645$	4.00000	+	2.00000i	0.157500	+	0.0787499i
$646$	−10.0000			−0.393445
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	−0.726491	−	0.687176i	$-0.758850\pi$
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	0.687176	+	0.726491i	$0.258850\pi$
$648$		−	15.0000i		−	0.589256i
$649$	−14.0000			−0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$			4.00000i			0.156652i
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	−0.405407	−	0.914136i	$-0.632870\pi$
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	0.914136	+	0.405407i	$0.132870\pi$
$654$	−18.0000			−0.703856
$655$	−40.0000	−	20.0000i	−1.56293	−	0.781465i
$656$	−7.00000	−	7.00000i	−0.273304	−	0.273304i
$657$	10.0000			0.390137
$658$			12.0000i			0.467809i
$659$			26.0000i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$659$			26.0000i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$660$	2.00000	−	4.00000i	0.0778499	−	0.155700i
$661$	−17.0000	+	17.0000i	−0.661223	+	0.661223i	−0.955668	−	0.294445i	$-0.904865\pi$
$661$	−17.0000	+	17.0000i	−0.661223	+	0.661223i	0.294445	+	0.955668i	$0.404865\pi$
$662$	3.00000	−	3.00000i	0.116598	−	0.116598i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	−30.0000	+	10.0000i	−1.16335	+	0.387783i
$666$		0			0
$667$		0			0
$668$	18.0000			0.696441
$669$	−2.00000	+	2.00000i	−0.0773245	+	0.0773245i
$670$	8.00000	+	4.00000i	0.309067	+	0.154533i
$671$	−14.0000	+	14.0000i	−0.540464	+	0.540464i
$672$	−10.0000	−	10.0000i	−0.385758	−	0.385758i
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$	13.0000	+	13.0000i	0.500741	+	0.500741i
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$		0			0
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$	−10.0000			−0.384048
$679$		−	4.00000i		−	0.153506i
$680$	3.00000	+	9.00000i	0.115045	+	0.345134i
$681$	12.0000	+	12.0000i	0.459841	+	0.459841i
$682$			10.0000i			0.382920i
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$	−5.00000	−	5.00000i	−0.191180	−	0.191180i
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$			20.0000i			0.763604i
$687$	−6.00000			−0.228914
$688$	−1.00000	−	1.00000i	−0.0381246	−	0.0381246i
$689$		0			0
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	3.00000	+	3.00000i	0.114125	+	0.114125i	0.761863	−	0.647738i	$-0.224285\pi$
$691$	3.00000	+	3.00000i	0.114125	+	0.114125i	−0.647738	+	0.761863i	$0.724285\pi$
$692$	11.0000	+	11.0000i	0.418157	+	0.418157i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	3.00000	−	3.00000i	0.113878	−	0.113878i
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$		0			0
$697$	−14.0000			−0.530288
$698$	9.00000	−	9.00000i	0.340655	−	0.340655i
$699$	−2.00000			−0.0756469
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$		0			0
$704$	−7.00000	+	7.00000i	−0.263822	+	0.263822i
$705$	−18.0000	+	6.00000i	−0.677919	+	0.225973i
$706$		−	12.0000i		−	0.451626i
$707$		−	24.0000i		−	0.902613i
$708$	−14.0000			−0.526152
$709$	29.0000	+	29.0000i	1.08912	+	1.08912i	0.995619	+	0.0934984i	$0.0298050\pi$
$709$	29.0000	+	29.0000i	1.08912	+	1.08912i	0.0934984	+	0.995619i	$0.470195\pi$
$710$	−3.00000	+	1.00000i	−0.112588	+	0.0375293i
$711$	2.00000			0.0750059
$712$	15.0000	−	15.0000i	0.562149	−	0.562149i
$713$			30.0000i			1.12351i
$714$	4.00000			0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$		−	6.00000i		−	0.224074i
$718$	1.00000	−	1.00000i	0.0373197	−	0.0373197i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$	−14.0000	−	14.0000i	−0.521387	−	0.521387i
$722$	−31.0000			−1.15370
$723$			34.0000i			1.26447i
$724$			8.00000i			0.297318i
$725$		0			0
$726$	9.00000	−	9.00000i	0.334021	−	0.334021i
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.368418	−	0.929660i	$-0.379900\pi$
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.929660	−	0.368418i	$-0.120100\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$	−20.0000	−	10.0000i	−0.740233	−	0.370117i
$731$	−2.00000			−0.0739727
$732$	−14.0000	+	14.0000i	−0.517455	+	0.517455i
$733$	4.00000			0.147743			0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$734$	−1.00000	+	1.00000i	−0.0369107	+	0.0369107i
$735$	−9.00000	+	3.00000i	−0.331970	+	0.110657i
$736$	−15.0000	+	15.0000i	−0.552907	+	0.552907i
$737$	4.00000	+	4.00000i	0.147342	+	0.147342i
$738$	7.00000	+	7.00000i	0.257674	+	0.257674i
$739$	−3.00000	−	3.00000i	−0.110357	−	0.110357i	0.649772	−	0.760129i	$-0.274864\pi$
$739$	−3.00000	−	3.00000i	−0.110357	−	0.110357i	−0.760129	+	0.649772i	$0.774864\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$			30.0000i			1.09985i
$745$	−9.00000	+	3.00000i	−0.329734	+	0.109911i
$746$	15.0000	+	15.0000i	0.549189	+	0.549189i
$747$		−	6.00000i		−	0.219529i
$748$			2.00000i			0.0731272i
$749$	14.0000	+	14.0000i	0.511549	+	0.511549i
$750$	9.00000	−	13.0000i	0.328634	−	0.474693i
$751$			50.0000i			1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$			50.0000i			1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$	6.00000			0.218797
$753$	−2.00000	−	2.00000i	−0.0728841	−	0.0728841i
$754$		0			0
$755$	−21.0000	+	7.00000i	−0.764268	+	0.254756i
$756$	8.00000	+	8.00000i	0.290957	+	0.290957i
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$	1.00000	+	1.00000i	0.0363216	+	0.0363216i
$759$	−6.00000	+	6.00000i	−0.217786	+	0.217786i
$760$	15.0000	+	45.0000i	0.544107	+	1.63232i
$761$	7.00000	−	7.00000i	0.253750	−	0.253750i	−0.568756	−	0.822506i	$-0.692575\pi$
$761$	7.00000	−	7.00000i	0.253750	−	0.253750i	0.822506	+	0.568756i	$0.192575\pi$
$762$	18.0000			0.652071
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$	8.00000			0.289430
$765$	−1.00000	−	3.00000i	−0.0361551	−	0.108465i
$766$		−	30.0000i		−	1.08394i
$767$		0			0
$768$	−17.0000	+	17.0000i	−0.613435	+	0.613435i
$769$	−15.0000	+	15.0000i	−0.540914	+	0.540914i	−0.923797	−	0.382883i	$-0.874931\pi$
$769$	−15.0000	+	15.0000i	−0.540914	+	0.540914i	0.382883	+	0.923797i	$0.374931\pi$
$770$	−2.00000	−	6.00000i	−0.0720750	−	0.216225i
$771$		−	22.0000i		−	0.792311i
$772$			18.0000i			0.647834i
$773$	32.0000			1.15096			0.575480	−	0.817816i	$-0.304815\pi$
$773$	32.0000			1.15096			0.575480	+	0.817816i	$0.304815\pi$
$774$	1.00000	+	1.00000i	0.0359443	+	0.0359443i
$775$	5.00000	−	35.0000i	0.179605	−	1.25724i
$776$	−6.00000			−0.215387
$777$		0			0
$778$		−	18.0000i		−	0.645331i
$779$	−70.0000			−2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$		−	6.00000i		−	0.214560i
$783$		0			0
$784$	3.00000			0.107143
$785$	13.0000	+	39.0000i	0.463990	+	1.39197i
$786$	20.0000	+	20.0000i	0.713376	+	0.713376i
$787$	22.0000			0.784215			0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000			0.784215			0.392108	+	0.919919i	$0.371746\pi$
$788$		−	6.00000i		−	0.213741i
$789$		−	2.00000i		−	0.0712019i
$790$	−4.00000	−	2.00000i	−0.142314	−	0.0711568i
$791$	10.0000	−	10.0000i	0.355559	−	0.355559i
$792$	3.00000	−	3.00000i	0.106600	−	0.106600i
$793$		0			0
$794$			16.0000i			0.567819i
$795$	10.0000	−	20.0000i	0.354663	−	0.709327i
$796$	8.00000			0.283552
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	−0.940888	−	0.338717i	$-0.890007\pi$
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	0.338717	+	0.940888i	$0.390007\pi$
$798$	20.0000			0.707992
$799$	6.00000	−	6.00000i	0.212265	−	0.212265i
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$	−5.00000	+	5.00000i	−0.176666	+	0.176666i
$802$	−11.0000	−	11.0000i	−0.388424	−	0.388424i
$803$	−10.0000	−	10.0000i	−0.352892	−	0.352892i
$804$	4.00000	+	4.00000i	0.141069	+	0.141069i
$805$	−6.00000	−	18.0000i	−0.211472	−	0.634417i
$806$		0			0
$807$	12.0000	+	12.0000i	0.422420	+	0.422420i
$808$	−36.0000			−1.26648
$809$			28.0000i			0.984428i	0.870474	+	0.492214i	$0.163812\pi$
$809$			28.0000i			0.984428i	−0.870474	+	0.492214i	$0.836188\pi$
$810$	5.00000	−	10.0000i	0.175682	−	0.351364i
$811$	27.0000	+	27.0000i	0.948098	+	0.948098i	0.998718	−	0.0506198i	$-0.0161197\pi$
$811$	27.0000	+	27.0000i	0.948098	+	0.948098i	−0.0506198	+	0.998718i	$0.516120\pi$
$812$		0			0
$813$		−	18.0000i		−	0.631288i
$814$		0			0
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$		−	2.00000i		−	0.0700140i
$817$	−10.0000			−0.349856
$818$	7.00000	+	7.00000i	0.244749	+	0.244749i
$819$		0			0
$820$	7.00000	+	21.0000i	0.244451	+	0.733352i
$821$	−9.00000	−	9.00000i	−0.314102	−	0.314102i	0.532394	−	0.846496i	$-0.321292\pi$
$821$	−9.00000	−	9.00000i	−0.314102	−	0.314102i	−0.846496	+	0.532394i	$0.821292\pi$
$822$	−16.0000	−	16.0000i	−0.558064	−	0.558064i
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	0.846349	−	0.532629i	$-0.178796\pi$
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	−0.532629	+	0.846349i	$0.678796\pi$
$824$	−21.0000	+	21.0000i	−0.731570	+	0.731570i
$825$	8.00000	−	6.00000i	0.278524	−	0.208893i
$826$	−14.0000	+	14.0000i	−0.487122	+	0.487122i
$827$	46.0000			1.59958			0.799788	−	0.600282i	$-0.204945\pi$
$827$	46.0000			1.59958			0.799788	+	0.600282i	$0.204945\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	−6.00000	+	12.0000i	−0.208263	+	0.416526i
$831$		−	30.0000i		−	1.04069i
$832$		0			0
$833$	3.00000	−	3.00000i	0.103944	−	0.103944i
$834$	−14.0000	+	14.0000i	−0.484780	+	0.484780i
$835$	36.0000	+	18.0000i	1.24583	+	0.622916i
$836$			10.0000i			0.345857i
$837$		−	40.0000i		−	1.38260i
$838$	−38.0000			−1.31269
$839$	−35.0000	−	35.0000i	−1.20833	−	1.20833i	−0.971566	−	0.236768i	$-0.923912\pi$
$839$	−35.0000	−	35.0000i	−1.20833	−	1.20833i	−0.236768	−	0.971566i	$-0.576088\pi$
$840$	−6.00000	−	18.0000i	−0.207020	−	0.621059i
$841$	29.0000			1.00000
$842$	11.0000	−	11.0000i	0.379085	−	0.379085i
$843$			2.00000i			0.0688837i
$844$	4.00000			0.137686
$845$		0			0
$846$	−6.00000			−0.206284
$847$			18.0000i			0.618487i
$848$	−5.00000	+	5.00000i	−0.171701	+	0.171701i
$849$	18.0000			0.617758
$850$	−1.00000	+	7.00000i	−0.0342997	+	0.240098i
$851$		0			0
$852$	−2.00000			−0.0685189
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$			28.0000i			0.958140i
$855$	−5.00000	−	15.0000i	−0.170996	−	0.512989i
$856$	21.0000	−	21.0000i	0.717765	−	0.717765i
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	−0.654009	−	0.756487i	$-0.726914\pi$
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	0.756487	+	0.654009i	$0.226914\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	1.00000	+	3.00000i	0.0340997	+	0.102299i
$861$	28.0000			0.954237
$862$	−13.0000	+	13.0000i	−0.442782	+	0.442782i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	20.0000	−	20.0000i	0.680414	−	0.680414i
$865$	11.0000	+	33.0000i	0.374011	+	1.12203i
$866$	−17.0000	+	17.0000i	−0.577684	+	0.577684i
$867$	15.0000	+	15.0000i	0.509427	+	0.509427i
$868$	−10.0000	−	10.0000i	−0.339422	−	0.339422i
$869$	−2.00000	−	2.00000i	−0.0678454	−	0.0678454i
$870$		0			0
$871$		0			0
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$	2.00000			0.0676897
$874$		−	30.0000i		−	1.01477i
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$	−10.0000	−	10.0000i	−0.337869	−	0.337869i
$877$		−	38.0000i		−	1.28317i	−0.767052	−	0.641584i	$-0.778277\pi$
$877$		−	38.0000i		−	1.28317i	0.767052	−	0.641584i	$-0.221723\pi$
$878$		0			0
$879$	−6.00000	−	6.00000i	−0.202375	−	0.202375i
$880$	−3.00000	+	1.00000i	−0.101130	+	0.0337100i
$881$			52.0000i			1.75192i	0.482380	+	0.875962i	$0.339773\pi$
$881$			52.0000i			1.75192i	−0.482380	+	0.875962i	$0.660227\pi$
$882$	−3.00000			−0.101015
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.919601	−	0.392853i	$-0.871488\pi$
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.392853	−	0.919601i	$-0.628512\pi$
$884$		0			0
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$	−25.0000	−	25.0000i	−0.839891	−	0.839891i
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	0.690119	−	0.723696i	$-0.257558\pi$
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	−0.723696	+	0.690119i	$0.757558\pi$
$888$		0			0
$889$	−18.0000	+	18.0000i	−0.603701	+	0.603701i
$890$	15.0000	−	5.00000i	0.502801	−	0.167600i
$891$	5.00000	−	5.00000i	0.167506	−	0.167506i
$892$	−2.00000			−0.0669650
$893$	30.0000	−	30.0000i	1.00391	−	1.00391i
$894$	6.00000			0.200670
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$		−	6.00000i		−	0.200446i
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$			10.0000i			0.333148i
$902$		−	14.0000i		−	0.466149i
$903$	4.00000			0.133112
$904$	−15.0000	−	15.0000i	−0.498893	−	0.498893i
$905$	−8.00000	+	16.0000i	−0.265929	+	0.531858i
$906$	14.0000			0.465119
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.363303	−	0.931671i	$-0.381649\pi$
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.931671	−	0.363303i	$-0.118351\pi$
$908$			12.0000i			0.398234i
$909$	12.0000			0.398015
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		−	10.0000i		−	0.331133i
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	−2.00000			−0.0661541
$915$	−42.0000	+	14.0000i	−1.38848	+	0.462826i
$916$	−3.00000	−	3.00000i	−0.0991228	−	0.0991228i
$917$	−40.0000			−1.32092
$918$			8.00000i			0.264039i
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$	−27.0000	+	9.00000i	−0.890164	+	0.296721i
$921$	−18.0000	+	18.0000i	−0.593120	+	0.593120i
$922$	−17.0000	+	17.0000i	−0.559865	+	0.559865i
$923$		0			0
$924$		−	4.00000i		−	0.131590i
$925$		0			0
$926$	−24.0000			−0.788689
$927$	7.00000	−	7.00000i	0.229910	−	0.229910i
$928$		0			0
$929$	−19.0000	+	19.0000i	−0.623370	+	0.623370i	−0.946392	−	0.323022i	$-0.895301\pi$
$929$	−19.0000	+	19.0000i	−0.623370	+	0.623370i	0.323022	+	0.946392i	$0.395301\pi$
$930$	−10.0000	+	20.0000i	−0.327913	+	0.655826i
$931$	15.0000	−	15.0000i	0.491605	−	0.491605i
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$	−6.00000	−	6.00000i	−0.196431	−	0.196431i
$934$	9.00000	+	9.00000i	0.294489	+	0.294489i
$935$	−2.00000	+	4.00000i	−0.0654070	+	0.130814i
$936$		0			0
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$	8.00000			0.261209
$939$		−	18.0000i		−	0.587408i
$940$	−12.0000	−	6.00000i	−0.391397	−	0.195698i
$941$	−21.0000	−	21.0000i	−0.684580	−	0.684580i	0.276448	−	0.961029i	$-0.410843\pi$
$941$	−21.0000	−	21.0000i	−0.684580	−	0.684580i	−0.961029	+	0.276448i	$0.910843\pi$
$942$		−	26.0000i		−	0.847126i
$943$		−	42.0000i		−	1.36771i
$944$	7.00000	+	7.00000i	0.227831	+	0.227831i
$945$	8.00000	+	24.0000i	0.260240	+	0.780720i
$946$		−	2.00000i		−	0.0650256i
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$	−2.00000	−	2.00000i	−0.0649570	−	0.0649570i
$949$		0			0
$950$	−5.00000	+	35.0000i	−0.162221	+	1.13555i
$951$	14.0000	+	14.0000i	0.453981	+	0.453981i
$952$	6.00000	+	6.00000i	0.194461	+	0.194461i
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	0.464475	−	0.885586i	$-0.346243\pi$
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	−0.885586	+	0.464475i	$0.846243\pi$
$954$	5.00000	−	5.00000i	0.161881	−	0.161881i
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$	3.00000	−	3.00000i	0.0970269	−	0.0970269i
$957$		0			0
$958$	−7.00000	+	7.00000i	−0.226160	+	0.226160i
$959$	32.0000			1.03333
$960$	−21.0000	+	7.00000i	−0.677772	+	0.225924i
$961$			19.0000i			0.612903i
$962$		0			0
$963$	−7.00000	+	7.00000i	−0.225572	+	0.225572i
$964$	−17.0000	+	17.0000i	−0.547533	+	0.547533i
$965$	−18.0000	+	36.0000i	−0.579441	+	1.15888i
$966$			12.0000i			0.386094i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	27.0000			0.867813
$969$	−10.0000	−	10.0000i	−0.321246	−	0.321246i
$970$	−4.00000	−	2.00000i	−0.128432	−	0.0642161i
$971$	−60.0000			−1.92549			−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000			−1.92549			−0.962746	+	0.270408i	$0.912841\pi$
$972$	−7.00000	+	7.00000i	−0.224525	+	0.224525i
$973$		−	28.0000i		−	0.897639i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$		−	62.0000i		−	1.98356i	−0.127971	−	0.991778i	$-0.540847\pi$
$977$		−	62.0000i		−	1.98356i	0.127971	−	0.991778i	$-0.459153\pi$
$978$	4.00000	−	4.00000i	0.127906	−	0.127906i
$979$	10.0000			0.319601
$980$	−6.00000	−	3.00000i	−0.191663	−	0.0958315i
$981$	9.00000	+	9.00000i	0.287348	+	0.287348i
$982$	22.0000			0.702048
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		−	42.0000i		−	1.33891i
$985$	6.00000	−	12.0000i	0.191176	−	0.382352i
$986$		0			0
$987$	−12.0000	+	12.0000i	−0.381964	+	0.381964i
$988$		0			0
$989$		−	6.00000i		−	0.190789i
$990$	3.00000	−	1.00000i	0.0953463	−	0.0317821i
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$	−25.0000	+	25.0000i	−0.793751	+	0.793751i
$993$	6.00000			0.190404
$994$	−2.00000	+	2.00000i	−0.0634361	+	0.0634361i
$995$	16.0000	+	8.00000i	0.507234	+	0.253617i
$996$	−6.00000	+	6.00000i	−0.190117	+	0.190117i
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$	−3.00000	−	3.00000i	−0.0949633	−	0.0949633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.a.437.1		2
5.3	odd	4		845.2.k.a.268.1		2
13.2	odd	12		845.2.o.b.357.1		4
13.3	even	3		845.2.t.b.657.1		4
13.4	even	6		845.2.t.a.427.1		4
13.5	odd	4		845.2.k.a.577.1		2
13.6	odd	12		845.2.o.b.587.1		4
13.7	odd	12		845.2.o.a.587.1		4
13.8	odd	4		65.2.k.a.57.1	yes	2
13.9	even	3		845.2.t.b.427.1		4
13.10	even	6		845.2.t.a.657.1		4
13.11	odd	12		845.2.o.a.357.1		4
13.12	even	2		65.2.f.a.47.1	yes	2
39.8	even	4		585.2.w.b.577.1		2
39.38	odd	2		585.2.n.c.307.1		2
52.47	even	4		1040.2.bg.a.577.1		2
52.51	odd	2		1040.2.cd.b.177.1		2
65.3	odd	12		845.2.o.b.488.1		4
65.8	even	4		65.2.f.a.18.1	✓	2
65.12	odd	4		325.2.k.a.268.1		2
65.18	even	4	inner	845.2.f.a.408.1		2
65.23	odd	12		845.2.o.a.488.1		4
65.28	even	12		845.2.t.b.188.1		4
65.33	even	12		845.2.t.a.418.1		4
65.34	odd	4		325.2.k.a.57.1		2
65.38	odd	4		65.2.k.a.8.1	yes	2
65.43	odd	12		845.2.o.a.258.1		4
65.47	even	4		325.2.f.a.18.1		2
65.48	odd	12		845.2.o.b.258.1		4
65.58	even	12		845.2.t.b.418.1		4
65.63	even	12		845.2.t.a.188.1		4
65.64	even	2		325.2.f.a.307.1		2
195.8	odd	4		585.2.n.c.343.1		2
195.38	even	4		585.2.w.b.73.1		2
260.103	even	4		1040.2.bg.a.593.1		2
260.203	odd	4		1040.2.cd.b.993.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	65.8	even	4
65.2.f.a.47.1	yes	2	13.12	even	2
65.2.k.a.8.1	yes	2	65.38	odd	4
65.2.k.a.57.1	yes	2	13.8	odd	4
325.2.f.a.18.1		2	65.47	even	4
325.2.f.a.307.1		2	65.64	even	2
325.2.k.a.57.1		2	65.34	odd	4
325.2.k.a.268.1		2	65.12	odd	4
585.2.n.c.307.1		2	39.38	odd	2
585.2.n.c.343.1		2	195.8	odd	4
585.2.w.b.73.1		2	195.38	even	4
585.2.w.b.577.1		2	39.8	even	4
845.2.f.a.408.1		2	65.18	even	4	inner
845.2.f.a.437.1		2	1.1	even	1	trivial
845.2.k.a.268.1		2	5.3	odd	4
845.2.k.a.577.1		2	13.5	odd	4
845.2.o.a.258.1		4	65.43	odd	12
845.2.o.a.357.1		4	13.11	odd	12
845.2.o.a.488.1		4	65.23	odd	12
845.2.o.a.587.1		4	13.7	odd	12
845.2.o.b.258.1		4	65.48	odd	12
845.2.o.b.357.1		4	13.2	odd	12
845.2.o.b.488.1		4	65.3	odd	12
845.2.o.b.587.1		4	13.6	odd	12
845.2.t.a.188.1		4	65.63	even	12
845.2.t.a.418.1		4	65.33	even	12
845.2.t.a.427.1		4	13.4	even	6
845.2.t.a.657.1		4	13.10	even	6
845.2.t.b.188.1		4	65.28	even	12
845.2.t.b.418.1		4	65.58	even	12
845.2.t.b.427.1		4	13.9	even	3
845.2.t.b.657.1		4	13.3	even	3
1040.2.bg.a.577.1		2	52.47	even	4
1040.2.bg.a.593.1		2	260.103	even	4
1040.2.cd.b.177.1		2	52.51	odd	2
1040.2.cd.b.993.1		2	260.203	odd	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +2.00000 q^{7} -3.00000i q^{8} +1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(1.00000 - 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} -2.00000i q^{14} +(3.00000 - 1.00000i) q^{15} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +1.00000 q^{18} +(-5.00000 + 5.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +(2.00000 - 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 3.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +2.00000 q^{28} +(-1.00000 - 3.00000i) q^{30} +(-5.00000 - 5.00000i) q^{31} -5.00000i q^{32} -2.00000i q^{33} +(1.00000 + 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +1.00000i q^{36} +(5.00000 + 5.00000i) q^{38} +(3.00000 - 6.00000i) q^{40} +(7.00000 + 7.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.00000 + 1.00000i) q^{43} +(1.00000 - 1.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} +(-3.00000 + 3.00000i) q^{46} -6.00000 q^{47} +(-1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} +10.0000i q^{57} +(-7.00000 - 7.00000i) q^{59} +(3.00000 - 1.00000i) q^{60} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} +2.00000i q^{63} -7.00000 q^{64} -2.00000 q^{66} +4.00000i q^{67} +(-1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(2.00000 - 4.00000i) q^{70} +(-1.00000 - 1.00000i) q^{71} +3.00000 q^{72} -10.0000i q^{73} +(7.00000 + 1.00000i) q^{75} +(-5.00000 + 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-2.00000 - 1.00000i) q^{80} +5.00000 q^{81} +(7.00000 - 7.00000i) q^{82} -6.00000 q^{83} +(2.00000 - 2.00000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(1.00000 - 1.00000i) q^{86} +(-3.00000 - 3.00000i) q^{88} +(5.00000 + 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(-3.00000 - 3.00000i) q^{92} -10.0000 q^{93} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +(-5.00000 - 5.00000i) q^{96} -2.00000i q^{97} +3.00000i q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} - 10 q^{19} + 4 q^{20} + 4 q^{21} - 2 q^{22} - 6 q^{23} - 6 q^{24} + 6 q^{25}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 - 10 * q^19 + 4 * q^20 + 4 * q^21 - 2 * q^22 - 6 * q^23 - 6 * q^24 + 6 * q^25 + 8 * q^27 + 4 * q^28 - 2 * q^30 - 10 * q^31 + 2 * q^34 + 8 * q^35 + 10 * q^38 + 6 * q^40 + 14 * q^41 - 4 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 - 12 * q^47 - 2 * q^48 - 6 * q^49 + 8 * q^50 + 10 * q^53 + 8 * q^54 + 6 * q^55 - 14 * q^59 + 6 * q^60 - 28 * q^61 - 10 * q^62 - 14 * q^64 - 4 * q^66 - 2 * q^68 - 12 * q^69 + 4 * q^70 - 2 * q^71 + 6 * q^72 + 14 * q^75 - 10 * q^76 + 4 * q^77 - 4 * q^80 + 10 * q^81 + 14 * q^82 - 12 * q^83 + 4 * q^84 - 6 * q^85 + 2 * q^86 - 6 * q^88 + 10 * q^89 + 4 * q^90 - 6 * q^92 - 20 * q^93 - 30 * q^95 - 10 * q^96 + 2 * q^99

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