LMFDB - Embedded newform 605.2.e.a.483.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 $ x^20 + 67x^16 + 1315x^12 + 9193x^8 + 16040x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.1
Root			$-1.76854 - 1.76854i$ of defining polynomial
Character	$\chi$	$=$	605.483
Dual form			605.2.e.a.362.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76854 - 1.76854i) q^{2} +(1.85563 + 1.85563i) q^{3} +4.25546i q^{4} +(-2.19774 - 0.412263i) q^{5} -6.56351i q^{6} +(0.260724 + 0.260724i) q^{7} +(3.98886 - 3.98886i) q^{8} +3.88674i q^{9} +O(q^{10})$	\(q+(-1.76854 - 1.76854i) q^{2} +(1.85563 + 1.85563i) q^{3} +4.25546i q^{4} +(-2.19774 - 0.412263i) q^{5} -6.56351i q^{6} +(0.260724 + 0.260724i) q^{7} +(3.98886 - 3.98886i) q^{8} +3.88674i q^{9} +(3.15768 + 4.61588i) q^{10} +(-7.89656 + 7.89656i) q^{12} +(-3.13314 + 3.13314i) q^{13} -0.922200i q^{14} +(-3.31318 - 4.84319i) q^{15} -5.59800 q^{16} +(0.608103 + 0.608103i) q^{17} +(6.87385 - 6.87385i) q^{18} -4.44065 q^{19} +(1.75437 - 9.35237i) q^{20} +0.967614i q^{21} +(-2.17112 - 2.17112i) q^{23} +14.8037 q^{24} +(4.66008 + 1.81209i) q^{25} +11.0822 q^{26} +(-1.64546 + 1.64546i) q^{27} +(-1.10950 + 1.10950i) q^{28} -0.769606 q^{29} +(-2.70589 + 14.4249i) q^{30} -4.53579 q^{31} +(1.92256 + 1.92256i) q^{32} -2.15091i q^{34} +(-0.465515 - 0.680488i) q^{35} -16.5398 q^{36} +(-7.75001 + 7.75001i) q^{37} +(7.85346 + 7.85346i) q^{38} -11.6279 q^{39} +(-10.4109 + 7.12201i) q^{40} -5.01533i q^{41} +(1.71126 - 1.71126i) q^{42} +(-4.69057 + 4.69057i) q^{43} +(1.60236 - 8.54202i) q^{45} +7.67942i q^{46} +(-7.64329 + 7.64329i) q^{47} +(-10.3878 - 10.3878i) q^{48} -6.86405i q^{49} +(-5.03678 - 11.4463i) q^{50} +2.25683i q^{51} +(-13.3330 - 13.3330i) q^{52} +(0.711263 + 0.711263i) q^{53} +5.82012 q^{54} +2.07998 q^{56} +(-8.24021 - 8.24021i) q^{57} +(1.36108 + 1.36108i) q^{58} +1.09798i q^{59} +(20.6100 - 14.0991i) q^{60} +11.3546i q^{61} +(8.02172 + 8.02172i) q^{62} +(-1.01336 + 1.01336i) q^{63} +4.39578i q^{64} +(8.17749 - 5.59414i) q^{65} +(4.17112 - 4.17112i) q^{67} +(-2.58775 + 2.58775i) q^{68} -8.05760i q^{69} +(-0.380189 + 2.02675i) q^{70} +1.94677 q^{71} +(15.5037 + 15.5037i) q^{72} +(-9.10112 + 9.10112i) q^{73} +27.4124 q^{74} +(5.28482 + 12.0100i) q^{75} -18.8970i q^{76} +(20.5644 + 20.5644i) q^{78} +12.3728 q^{79} +(12.3029 + 2.30785i) q^{80} +5.55348 q^{81} +(-8.86981 + 8.86981i) q^{82} +(-5.04875 + 5.04875i) q^{83} -4.11764 q^{84} +(-1.08575 - 1.58715i) q^{85} +16.5909 q^{86} +(-1.42811 - 1.42811i) q^{87} -8.87803i q^{89} +(-17.9407 + 12.2731i) q^{90} -1.63377 q^{91} +(9.23911 - 9.23911i) q^{92} +(-8.41675 - 8.41675i) q^{93} +27.0349 q^{94} +(9.75937 + 1.83071i) q^{95} +7.13511i q^{96} +(5.07639 - 5.07639i) q^{97} +(-12.1393 + 12.1393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^3 + 4 * q^5	$ 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.76854	−	1.76854i	−1.25055	−	1.25055i	−0.955476	−	0.295070i	$-0.904657\pi$
$2$	−1.76854	−	1.76854i	−1.25055	−	1.25055i	−0.295070	−	0.955476i	$-0.595343\pi$
$3$	1.85563	+	1.85563i	1.07135	+	1.07135i	0.997251	+	0.0740986i	$0.0236079\pi$
$3$	1.85563	+	1.85563i	1.07135	+	1.07135i	0.0740986	+	0.997251i	$0.476392\pi$
$4$			4.25546i			2.12773i
$5$	−2.19774	−	0.412263i	−0.982857	−	0.184369i
$5$	−2.19774	−	0.412263i	−0.982857	−	0.184369i
$6$		−	6.56351i		−	2.67954i
$7$	0.260724	+	0.260724i	0.0985443	+	0.0985443i	0.754660	−	0.656116i	$-0.227802\pi$
$7$	0.260724	+	0.260724i	0.0985443	+	0.0985443i	−0.656116	+	0.754660i	$0.727802\pi$
$8$	3.98886	−	3.98886i	1.41028	−	1.41028i
$9$			3.88674i			1.29558i
$10$	3.15768	+	4.61588i	0.998545	+	1.45967i
$11$		0			0
$11$		0			0
$12$	−7.89656	+	7.89656i	−2.27954	+	2.27954i
$13$	−3.13314	+	3.13314i	−0.868977	+	0.868977i	−0.992359	−	0.123382i	$-0.960626\pi$
$13$	−3.13314	+	3.13314i	−0.868977	+	0.868977i	0.123382	+	0.992359i	$0.460626\pi$
$14$		−	0.922200i		−	0.246468i
$15$	−3.31318	−	4.84319i	−0.855459	−	1.25051i
$16$	−5.59800			−1.39950
$17$	0.608103	+	0.608103i	0.147487	+	0.147487i	0.776994	−	0.629508i	$-0.216743\pi$
$17$	0.608103	+	0.608103i	0.147487	+	0.147487i	−0.629508	+	0.776994i	$0.716743\pi$
$18$	6.87385	−	6.87385i	1.62018	−	1.62018i
$19$	−4.44065			−1.01875			−0.509377	−	0.860543i	$-0.670124\pi$
$19$	−4.44065			−1.01875			−0.509377	+	0.860543i	$0.670124\pi$
$20$	1.75437	−	9.35237i	0.392288	−	2.09125i
$21$			0.967614i			0.211151i
$22$		0			0
$23$	−2.17112	−	2.17112i	−0.452710	−	0.452710i	0.443543	−	0.896253i	$-0.353721\pi$
$23$	−2.17112	−	2.17112i	−0.452710	−	0.452710i	−0.896253	+	0.443543i	$0.853721\pi$
$24$	14.8037			3.02180
$25$	4.66008	+	1.81209i	0.932016	+	0.362418i
$26$	11.0822			2.17339
$27$	−1.64546	+	1.64546i	−0.316669	+	0.316669i
$28$	−1.10950	+	1.10950i	−0.209676	+	0.209676i
$29$	−0.769606			−0.142912			−0.0714561	−	0.997444i	$-0.522765\pi$
$29$	−0.769606			−0.142912			−0.0714561	+	0.997444i	$0.522765\pi$
$30$	−2.70589	+	14.4249i	−0.494026	+	2.63361i
$31$	−4.53579			−0.814652			−0.407326	−	0.913283i	$-0.633539\pi$
$31$	−4.53579			−0.814652			−0.407326	+	0.913283i	$0.633539\pi$
$32$	1.92256	+	1.92256i	0.339863	+	0.339863i
$33$		0			0
$34$		−	2.15091i		−	0.368877i
$35$	−0.465515	−	0.680488i	−0.0786864	−	0.115024i
$36$	−16.5398			−2.75664
$37$	−7.75001	+	7.75001i	−1.27409	+	1.27409i	−0.330174	+	0.943920i	$0.607107\pi$
$37$	−7.75001	+	7.75001i	−1.27409	+	1.27409i	−0.943920	+	0.330174i	$0.892893\pi$
$38$	7.85346	+	7.85346i	1.27400	+	1.27400i
$39$	−11.6279			−1.86196
$40$	−10.4109	+	7.12201i	−1.64611	+	1.12609i
$41$		−	5.01533i		−	0.783263i	−0.920122	−	0.391632i	$-0.871911\pi$
$41$		−	5.01533i		−	0.783263i	0.920122	−	0.391632i	$-0.128089\pi$
$42$	1.71126	−	1.71126i	0.264054	−	0.264054i
$43$	−4.69057	+	4.69057i	−0.715305	+	0.715305i	−0.967640	−	0.252335i	$-0.918801\pi$
$43$	−4.69057	+	4.69057i	−0.715305	+	0.715305i	0.252335	+	0.967640i	$0.418801\pi$
$44$		0			0
$45$	1.60236	−	8.54202i	0.238865	−	1.27337i
$46$			7.67942i			1.13227i
$47$	−7.64329	+	7.64329i	−1.11489	+	1.11489i	−0.122408	+	0.992480i	$0.539062\pi$
$47$	−7.64329	+	7.64329i	−1.11489	+	1.11489i	−0.992480	+	0.122408i	$0.960938\pi$
$48$	−10.3878	−	10.3878i	−1.49935	−	1.49935i
$49$		−	6.86405i		−	0.980578i
$50$	−5.03678	−	11.4463i	−0.712309	−	1.61875i
$51$			2.25683i			0.316019i
$52$	−13.3330	−	13.3330i	−1.84895	−	1.84895i
$53$	0.711263	+	0.711263i	0.0976995	+	0.0976995i	0.754267	−	0.656568i	$-0.227992\pi$
$53$	0.711263	+	0.711263i	0.0976995	+	0.0976995i	−0.656568	+	0.754267i	$0.727992\pi$
$54$	5.82012			0.792018
$55$		0			0
$56$	2.07998			0.277949
$57$	−8.24021	−	8.24021i	−1.09144	−	1.09144i
$58$	1.36108	+	1.36108i	0.178718	+	0.178718i
$59$			1.09798i			0.142945i	0.997443	+	0.0714724i	$0.0227698\pi$
$59$			1.09798i			0.142945i	−0.997443	+	0.0714724i	$0.977230\pi$
$60$	20.6100	−	14.0991i	2.66074	−	1.82019i
$61$			11.3546i			1.45381i	0.686738	+	0.726905i	$0.259042\pi$
$61$			11.3546i			1.45381i	−0.686738	+	0.726905i	$0.740958\pi$
$62$	8.02172	+	8.02172i	1.01876	+	1.01876i
$63$	−1.01336	+	1.01336i	−0.127672	+	0.127672i
$64$			4.39578i			0.549472i
$65$	8.17749	−	5.59414i	1.01429	−	0.693868i
$66$		0			0
$67$	4.17112	−	4.17112i	0.509583	−	0.509583i	−0.404815	−	0.914399i	$-0.632664\pi$
$67$	4.17112	−	4.17112i	0.509583	−	0.509583i	0.914399	+	0.404815i	$0.132664\pi$
$68$	−2.58775	+	2.58775i	−0.313811	+	0.313811i
$69$		−	8.05760i		−	0.970021i
$70$	−0.380189	+	2.02675i	−0.0454412	+	0.242243i
$71$	1.94677			0.231039			0.115519	−	0.993305i	$-0.463147\pi$
$71$	1.94677			0.231039			0.115519	+	0.993305i	$0.463147\pi$
$72$	15.5037	+	15.5037i	1.82712	+	1.82712i
$73$	−9.10112	+	9.10112i	−1.06521	+	1.06521i	−0.0674849	+	0.997720i	$0.521497\pi$
$73$	−9.10112	+	9.10112i	−1.06521	+	1.06521i	−0.997720	+	0.0674849i	$0.978503\pi$
$74$	27.4124			3.18663
$75$	5.28482	+	12.0100i	0.610239	+	1.38679i
$76$		−	18.8970i		−	2.16763i
$77$		0			0
$78$	20.5644	+	20.5644i	2.32846	+	2.32846i
$79$	12.3728			1.39205			0.696026	−	0.718017i	$-0.254950\pi$
$79$	12.3728			1.39205			0.696026	+	0.718017i	$0.254950\pi$
$80$	12.3029	+	2.30785i	1.37551	+	0.258025i
$81$	5.55348			0.617053
$82$	−8.86981	+	8.86981i	−0.979507	+	0.979507i
$83$	−5.04875	+	5.04875i	−0.554172	+	0.554172i	−0.927642	−	0.373470i	$-0.878168\pi$
$83$	−5.04875	+	5.04875i	−0.554172	+	0.554172i	0.373470	+	0.927642i	$0.378168\pi$
$84$	−4.11764			−0.449272
$85$	−1.08575	−	1.58715i	−0.117766	−	0.172150i
$86$	16.5909			1.78904
$87$	−1.42811	−	1.42811i	−0.153109	−	0.153109i
$88$		0			0
$89$		−	8.87803i		−	0.941069i	−0.882382	−	0.470535i	$-0.844061\pi$
$89$		−	8.87803i		−	0.941069i	0.882382	−	0.470535i	$-0.155939\pi$
$90$	−17.9407	+	12.2731i	−1.89112	+	1.29369i
$91$	−1.63377			−0.171266
$92$	9.23911	−	9.23911i	0.963243	−	0.963243i
$93$	−8.41675	−	8.41675i	−0.872777	−	0.872777i
$94$	27.0349			2.78844
$95$	9.75937	+	1.83071i	1.00129	+	0.187827i
$96$			7.13511i			0.728224i
$97$	5.07639	−	5.07639i	0.515429	−	0.515429i	−0.400756	−	0.916185i	$-0.631252\pi$
$97$	5.07639	−	5.07639i	0.515429	−	0.515429i	0.916185	+	0.400756i	$0.131252\pi$
$98$	−12.1393	+	12.1393i	−1.22626	+	1.22626i
$99$		0			0
$100$	−7.71126	+	19.8308i	−0.771126	+	1.98308i
$101$		−	2.04877i		−	0.203861i	−0.994792	−	0.101930i	$-0.967498\pi$
$101$		−	2.04877i		−	0.203861i	0.994792	−	0.101930i	$-0.0325019\pi$
$102$	3.99129	−	3.99129i	0.395197	−	0.395197i
$103$	3.07204	+	3.07204i	0.302697	+	0.302697i	0.842068	−	0.539371i	$-0.181338\pi$
$103$	3.07204	+	3.07204i	0.302697	+	0.302697i	−0.539371	+	0.842068i	$0.681338\pi$
$104$			24.9953i			2.45100i
$105$	0.398911	−	2.12656i	0.0389298	−	0.207531i
$106$		−	2.51579i		−	0.244355i
$107$	8.89695	+	8.89695i	0.860101	+	0.860101i	0.991349	−	0.131249i	$-0.0418987\pi$
$107$	8.89695	+	8.89695i	0.860101	+	0.860101i	−0.131249	+	0.991349i	$0.541899\pi$
$108$	−7.00218	−	7.00218i	−0.673785	−	0.673785i
$109$	4.04420			0.387364			0.193682	−	0.981064i	$-0.437957\pi$
$109$	4.04420			0.387364			0.193682	+	0.981064i	$0.437957\pi$
$110$		0			0
$111$	−28.7623			−2.73000
$112$	−1.45953	−	1.45953i	−0.137913	−	0.137913i
$113$	−2.21453	−	2.21453i	−0.208325	−	0.208325i	0.595230	−	0.803555i	$-0.297061\pi$
$113$	−2.21453	−	2.21453i	−0.208325	−	0.208325i	−0.803555	+	0.595230i	$0.797061\pi$
$114$			29.1463i			2.72980i
$115$	3.87647	+	5.66662i	0.361483	+	0.528415i
$116$		−	3.27503i		−	0.304079i
$117$	−12.1777	−	12.1777i	−1.12583	−	1.12583i
$118$	1.94182	−	1.94182i	0.178759	−	0.178759i
$119$			0.317094i			0.0290679i
$120$	−32.5347	−	6.10302i	−2.96999	−	0.557127i
$121$		0			0
$122$	20.0811	−	20.0811i	1.81806	−	1.81806i
$123$	9.30661	−	9.30661i	0.839149	−	0.839149i
$124$		−	19.3019i		−	1.73336i
$125$	−9.49456	−	5.90367i	−0.849220	−	0.528040i
$126$	3.58435			0.319319
$127$	−10.4053	−	10.4053i	−0.923321	−	0.923321i	0.0739411	−	0.997263i	$-0.476442\pi$
$127$	−10.4053	−	10.4053i	−0.923321	−	0.923321i	−0.997263	+	0.0739411i	$0.976442\pi$
$128$	11.6192	−	11.6192i	1.02700	−	1.02700i
$129$	−17.4079			−1.53268
$130$	−24.3557	−	4.56876i	−2.13613	−	0.400707i
$131$		−	9.05953i		−	0.791535i	−0.918351	−	0.395768i	$-0.870479\pi$
$131$		−	9.05953i		−	0.791535i	0.918351	−	0.395768i	$-0.129521\pi$
$132$		0			0
$133$	−1.15778	−	1.15778i	−0.100392	−	0.100392i
$134$	−14.7536			−1.27451
$135$	4.29465	−	2.93792i	0.369624	−	0.252856i
$136$	4.85128			0.415994
$137$	0.127440	−	0.127440i	0.0108880	−	0.0108880i	−0.701642	−	0.712530i	$-0.747549\pi$
$137$	0.127440	−	0.127440i	0.0108880	−	0.0108880i	0.712530	+	0.701642i	$0.247549\pi$
$138$	−14.2502	+	14.2502i	−1.21305	+	1.21305i
$139$	19.1456			1.62391			0.811954	−	0.583722i	$-0.198404\pi$
$139$	19.1456			1.62391			0.811954	+	0.583722i	$0.198404\pi$
$140$	2.89579	−	1.98098i	0.244739	−	0.167423i
$141$	−28.3663			−2.38887
$142$	−3.44294	−	3.44294i	−0.288925	−	0.288925i
$143$		0			0
$144$		−	21.7580i		−	1.81316i
$145$	1.69139	+	0.317280i	0.140462	+	0.0263487i
$146$	32.1914			2.66418
$147$	12.7371	−	12.7371i	1.05054	−	1.05054i
$148$	−32.9798	−	32.9798i	−2.71093	−	2.71093i
$149$	8.70842			0.713422			0.356711	−	0.934215i	$-0.383898\pi$
$149$	8.70842			0.713422			0.356711	+	0.934215i	$0.383898\pi$
$150$	11.8937	−	30.5865i	0.971114	−	2.49738i
$151$			5.32028i			0.432958i	0.976287	+	0.216479i	$0.0694573\pi$
$151$			5.32028i			0.432958i	−0.976287	+	0.216479i	$0.930543\pi$
$152$	−17.7131	+	17.7131i	−1.43673	+	1.43673i
$153$	−2.36354	+	2.36354i	−0.191081	+	0.191081i
$154$		0			0
$155$	9.96846	+	1.86994i	0.800686	+	0.150197i
$156$		−	49.4821i		−	3.96174i
$157$	−3.92579	+	3.92579i	−0.313312	+	0.313312i	−0.846191	−	0.532879i	$-0.821110\pi$
$157$	−3.92579	+	3.92579i	−0.313312	+	0.313312i	0.532879	+	0.846191i	$0.321110\pi$
$158$	−21.8818	−	21.8818i	−1.74082	−	1.74082i
$159$			2.63969i			0.209341i
$160$	−3.43267	−	5.01787i	−0.271376	−	0.396697i
$161$		−	1.13212i		−	0.0892239i
$162$	−9.82155	−	9.82155i	−0.771653	−	0.771653i
$163$	2.79201	+	2.79201i	0.218687	+	0.218687i	0.807945	−	0.589258i	$-0.200580\pi$
$163$	2.79201	+	2.79201i	0.218687	+	0.218687i	−0.589258	+	0.807945i	$0.700580\pi$
$164$	21.3425			1.66657
$165$		0			0
$166$	17.8578			1.38604
$167$	1.88219	+	1.88219i	0.145648	+	0.145648i	0.776171	−	0.630523i	$-0.217159\pi$
$167$	1.88219	+	1.88219i	0.145648	+	0.145648i	−0.630523	+	0.776171i	$0.717159\pi$
$168$	3.85968	+	3.85968i	0.297781	+	0.297781i
$169$		−	6.63316i		−	0.510243i
$170$	−0.886738	+	4.72712i	−0.0680097	+	0.362554i
$171$		−	17.2596i		−	1.31988i
$172$	−19.9605	−	19.9605i	−1.52197	−	1.52197i
$173$	−14.9413	+	14.9413i	−1.13596	+	1.13596i	−0.146798	+	0.989166i	$0.546897\pi$
$173$	−14.9413	+	14.9413i	−1.13596	+	1.13596i	−0.989166	+	0.146798i	$0.953103\pi$
$174$			5.05132i			0.382940i
$175$	0.742539	+	1.68745i	0.0561307	+	0.127559i
$176$		0			0
$177$	−2.03745	+	2.03745i	−0.153144	+	0.153144i
$178$	−15.7011	+	15.7011i	−1.17685	+	1.17685i
$179$			3.00130i			0.224328i	0.993690	+	0.112164i	$0.0357782\pi$
$179$			3.00130i			0.224328i	−0.993690	+	0.112164i	$0.964222\pi$
$180$	36.3502	+	6.81876i	2.70938	+	0.508240i
$181$	10.2448			0.761493			0.380747	−	0.924679i	$-0.375667\pi$
$181$	10.2448			0.761493			0.380747	+	0.924679i	$0.375667\pi$
$182$	2.88938	+	2.88938i	0.214175	+	0.214175i
$183$	−21.0700	+	21.0700i	−1.55754	+	1.55754i
$184$	−17.3206			−1.27689
$185$	20.2275	−	13.8374i	1.48716	−	1.01735i
$186$			29.7707i			2.18289i
$187$		0			0
$188$	−32.5257	−	32.5257i	−2.37218	−	2.37218i
$189$	−0.858021			−0.0624118
$190$	−14.0221	−	20.4975i	−1.01727	−	1.48705i
$191$	−13.8027			−0.998729			−0.499365	−	0.866392i	$-0.666433\pi$
$191$	−13.8027			−0.998729			−0.499365	+	0.866392i	$0.666433\pi$
$192$	−8.15694	+	8.15694i	−0.588677	+	0.588677i
$193$	9.55080	−	9.55080i	0.687482	−	0.687482i	−0.274193	−	0.961675i	$-0.588411\pi$
$193$	9.55080	−	9.55080i	0.687482	−	0.687482i	0.961675	+	0.274193i	$0.0884107\pi$
$194$	−17.9556			−1.28914
$195$	25.5551	+	4.79376i	1.83004	+	0.343288i
$196$	29.2097			2.08640
$197$	10.9820	+	10.9820i	0.782434	+	0.782434i	0.980241	−	0.197807i	$-0.0633820\pi$
$197$	10.9820	+	10.9820i	0.782434	+	0.782434i	−0.197807	+	0.980241i	$0.563382\pi$
$198$		0			0
$199$			16.1982i			1.14826i	0.818765	+	0.574129i	$0.194659\pi$
$199$			16.1982i			1.14826i	−0.818765	+	0.574129i	$0.805341\pi$
$200$	25.8166	−	11.3602i	1.82551	−	0.803291i
$201$	15.4801			1.09188
$202$	−3.62333	+	3.62333i	−0.254937	+	0.254937i
$203$	−0.200655	−	0.200655i	−0.0140832	−	0.0140832i
$204$	−9.60384			−0.672403
$205$	−2.06763	+	11.0224i	−0.144410	+	0.769836i
$206$		−	10.8660i		−	0.757072i
$207$	8.43857	−	8.43857i	0.586521	−	0.586521i
$208$	17.5393	−	17.5393i	1.21613	−	1.21613i
$209$		0			0
$210$	−4.46639	+	3.05541i	−0.308210	+	0.210844i
$211$			3.67640i			0.253094i	0.991961	+	0.126547i	$0.0403894\pi$
$211$			3.67640i			0.253094i	−0.991961	+	0.126547i	$0.959611\pi$
$212$	−3.02675	+	3.02675i	−0.207878	+	0.207878i
$213$	3.61249	+	3.61249i	0.247523	+	0.247523i
$214$		−	31.4692i		−	2.15119i
$215$	12.2424	−	8.37488i	0.834923	−	0.571162i
$216$			13.1270i			0.893181i
$217$	−1.18259	−	1.18259i	−0.0802793	−	0.0802793i
$218$	−7.15232	−	7.15232i	−0.484417	−	0.484417i
$219$	−33.7766			−2.28241
$220$		0			0
$221$	−3.81054			−0.256325
$222$	50.8673	+	50.8673i	3.41399	+	3.41399i
$223$	16.8846	+	16.8846i	1.13067	+	1.13067i	0.990065	+	0.140609i	$0.0449060\pi$
$223$	16.8846	+	16.8846i	1.13067	+	1.13067i	0.140609	+	0.990065i	$0.455094\pi$
$224$			1.00251i			0.0669831i
$225$	−7.04311	+	18.1125i	−0.469541	+	1.20750i
$226$			7.83295i			0.521040i
$227$	−13.1257	−	13.1257i	−0.871183	−	0.871183i	0.121418	−	0.992601i	$-0.461256\pi$
$227$	−13.1257	−	13.1257i	−0.871183	−	0.871183i	−0.992601	+	0.121418i	$0.961256\pi$
$228$	35.0659	−	35.0659i	2.32229	−	2.32229i
$229$		−	16.0685i		−	1.06184i	−0.847422	−	0.530919i	$-0.821847\pi$
$229$		−	16.0685i		−	1.06184i	0.847422	−	0.530919i	$-0.178153\pi$
$230$	3.16594	−	16.8773i	0.208756	−	1.11286i
$231$		0			0
$232$	−3.06985	+	3.06985i	−0.201546	+	0.201546i
$233$	−2.36045	+	2.36045i	−0.154638	+	0.154638i	−0.780186	−	0.625548i	$-0.784876\pi$
$233$	−2.36045	+	2.36045i	−0.154638	+	0.154638i	0.625548	+	0.780186i	$0.284876\pi$
$234$			43.0735i			2.81580i
$235$	19.9490	−	13.6469i	1.30133	−	0.890224i
$236$	−4.67241			−0.304148
$237$	22.9594	+	22.9594i	1.49137	+	1.49137i
$238$	0.560792	−	0.560792i	0.0363508	−	0.0363508i
$239$	0.467778			0.0302581			0.0151290	−	0.999886i	$-0.495184\pi$
$239$	0.467778			0.0302581			0.0151290	+	0.999886i	$0.495184\pi$
$240$	18.5472	+	27.1122i	1.19722	+	1.75009i
$241$		−	16.5275i		−	1.06463i	−0.846547	−	0.532314i	$-0.821322\pi$
$241$		−	16.5275i		−	1.06463i	0.846547	−	0.532314i	$-0.178678\pi$
$242$		0			0
$243$	15.2416	+	15.2416i	0.977749	+	0.977749i
$244$	−48.3191			−3.09332
$245$	−2.82979	+	15.0854i	−0.180789	+	0.963768i
$246$	−32.9182			−2.09879
$247$	13.9132	−	13.9132i	0.885275	−	0.885275i
$248$	−18.0926	+	18.0926i	−1.14888	+	1.14888i
$249$	−18.7372			−1.18742
$250$	6.35064	+	27.2324i	0.401650	+	1.72233i
$251$	6.54236			0.412950			0.206475	−	0.978452i	$-0.433801\pi$
$251$	6.54236			0.412950			0.206475	+	0.978452i	$0.433801\pi$
$252$	−4.31233	−	4.31233i	−0.271651	−	0.271651i
$253$		0			0
$254$			36.8044i			2.30931i
$255$	0.930406	−	4.95991i	0.0582643	−	0.310602i
$256$	−32.3065			−2.01916
$257$	−16.0840	+	16.0840i	−1.00329	+	1.00329i	−0.00330040	+	0.999995i	$0.501051\pi$
$257$	−16.0840	+	16.0840i	−1.00329	+	1.00329i	−0.999995	+	0.00330040i	$0.998949\pi$
$258$	30.7866	+	30.7866i	1.91669	+	1.91669i
$259$	−4.04122			−0.251109
$260$	23.8056	+	34.7990i	1.47636	+	2.15814i
$261$		−	2.99126i		−	0.185154i
$262$	−16.0221	+	16.0221i	−0.989851	+	0.989851i
$263$	17.4444	−	17.4444i	1.07567	−	1.07567i	0.0787777	−	0.996892i	$-0.474898\pi$
$263$	17.4444	−	17.4444i	1.07567	−	1.07567i	0.996892	−	0.0787777i	$-0.0251017\pi$
$264$		0			0
$265$	−1.26994	−	1.85640i	−0.0780119	−	0.114037i
$266$			4.09517i			0.251091i
$267$	16.4743	−	16.4743i	1.00821	−	1.00821i
$268$	17.7500	+	17.7500i	1.08426	+	1.08426i
$269$			6.15996i			0.375580i	0.982209	+	0.187790i	$0.0601324\pi$
$269$			6.15996i			0.375580i	−0.982209	+	0.187790i	$0.939868\pi$
$270$	−12.7911	−	2.39942i	−0.778440	−	0.146024i
$271$			6.98883i			0.424541i	0.977211	+	0.212270i	$0.0680858\pi$
$271$			6.98883i			0.424541i	−0.977211	+	0.212270i	$0.931914\pi$
$272$	−3.40416	−	3.40416i	−0.206407	−	0.206407i
$273$	−3.03167	−	3.03167i	−0.183485	−	0.183485i
$274$	−0.450766			−0.0272318
$275$		0			0
$276$	34.2888			2.06394
$277$	−0.619989	−	0.619989i	−0.0372515	−	0.0372515i	0.688236	−	0.725487i	$-0.258386\pi$
$277$	−0.619989	−	0.619989i	−0.0372515	−	0.0372515i	−0.725487	+	0.688236i	$0.758386\pi$
$278$	−33.8597	−	33.8597i	−2.03077	−	2.03077i
$279$		−	17.6294i		−	1.05545i
$280$	−4.57125	−	0.857499i	−0.273184	−	0.0512454i
$281$			8.17465i			0.487659i	0.969818	+	0.243829i	$0.0784037\pi$
$281$			8.17465i			0.487659i	−0.969818	+	0.243829i	$0.921596\pi$
$282$	50.1668	+	50.1668i	2.98739	+	2.98739i
$283$	5.06880	−	5.06880i	0.301309	−	0.301309i	−0.540217	−	0.841526i	$-0.681658\pi$
$283$	5.06880	−	5.06880i	0.301309	−	0.301309i	0.841526	+	0.540217i	$0.181658\pi$
$284$			8.28439i			0.491588i
$285$	14.7127	+	21.5069i	0.871503	+	1.27396i
$286$		0			0
$287$	1.30762	−	1.30762i	0.0771862	−	0.0771862i
$288$	−7.47247	+	7.47247i	−0.440320	+	0.440320i
$289$		−	16.2604i		−	0.956495i
$290$	−2.43017	−	3.55241i	−0.142704	−	0.208605i
$291$	18.8398			1.10441
$292$	−38.7294	−	38.7294i	−2.26647	−	2.26647i
$293$	16.4952	−	16.4952i	0.963659	−	0.963659i	−0.0357031	−	0.999362i	$-0.511367\pi$
$293$	16.4952	−	16.4952i	0.963659	−	0.963659i	0.999362	+	0.0357031i	$0.0113671\pi$
$294$	−45.0523			−2.62750
$295$	0.452656	−	2.41307i	0.0263547	−	0.140494i
$296$			61.8275i			3.59365i
$297$		0			0
$298$	−15.4012	−	15.4012i	−0.892166	−	0.892166i
$299$	13.6049			0.786789
$300$	−51.1079	+	22.4893i	−2.95071	+	1.29842i
$301$	−2.44588			−0.140978
$302$	9.40912	−	9.40912i	0.541434	−	0.541434i
$303$	3.80177	−	3.80177i	0.218406	−	0.218406i
$304$	24.8588			1.42575
$305$	4.68109	−	24.9545i	0.268038	−	1.42889i
$306$	8.36001			0.477910
$307$	4.25013	+	4.25013i	0.242568	+	0.242568i	0.817912	−	0.575344i	$-0.195132\pi$
$307$	4.25013	+	4.25013i	0.242568	+	0.242568i	−0.575344	+	0.817912i	$0.695132\pi$
$308$		0			0
$309$			11.4011i			0.648588i
$310$	−14.3226	−	20.9367i	−0.813466	−	1.18912i
$311$	−29.2801			−1.66032			−0.830160	−	0.557525i	$-0.811751\pi$
$311$	−29.2801			−1.66032			−0.830160	+	0.557525i	$0.811751\pi$
$312$	−46.3822	+	46.3822i	−2.62587	+	2.62587i
$313$	−9.85366	−	9.85366i	−0.556962	−	0.556962i	0.371480	−	0.928441i	$-0.378851\pi$
$313$	−9.85366	−	9.85366i	−0.556962	−	0.556962i	−0.928441	+	0.371480i	$0.878851\pi$
$314$	13.8858			0.783622
$315$	2.64488	−	1.80934i	0.149022	−	0.101944i
$316$			52.6520i			2.96191i
$317$	−5.09167	+	5.09167i	−0.285977	+	0.285977i	−0.835487	−	0.549510i	$-0.814814\pi$
$317$	−5.09167	+	5.09167i	−0.285977	+	0.285977i	0.549510	+	0.835487i	$0.314814\pi$
$318$	4.66839	−	4.66839i	0.261790	−	0.261790i
$319$		0			0
$320$	1.81221	−	9.66075i	0.101306	−	0.540052i
$321$			33.0189i			1.84294i
$322$	−2.00221	+	2.00221i	−0.111579	+	0.111579i
$323$	−2.70037	−	2.70037i	−0.150253	−	0.150253i
$324$			23.6326i			1.31292i
$325$	−20.2782	+	8.92316i	−1.12483	+	0.494968i
$326$		−	9.87556i		−	0.546956i
$327$	7.50455	+	7.50455i	0.415002	+	0.415002i
$328$	−20.0055	−	20.0055i	−1.10462	−	1.10462i
$329$	−3.98557			−0.219732
$330$		0			0
$331$	−13.2203			−0.726652			−0.363326	−	0.931662i	$-0.618359\pi$
$331$	−13.2203			−0.726652			−0.363326	+	0.931662i	$0.618359\pi$
$332$	−21.4847	−	21.4847i	−1.17913	−	1.17913i
$333$	−30.1223	−	30.1223i	−1.65069	−	1.65069i
$334$		−	6.65746i		−	0.364280i
$335$	−10.8866	+	7.44742i	−0.594799	+	0.406896i
$336$		−	5.41671i		−	0.295506i
$337$	23.3891	+	23.3891i	1.27409	+	1.27409i	0.943924	+	0.330162i	$0.107103\pi$
$337$	23.3891	+	23.3891i	1.27409	+	1.27409i	0.330162	+	0.943924i	$0.392897\pi$
$338$	−11.7310	+	11.7310i	−0.638082	+	0.638082i
$339$		−	8.21870i		−	0.446378i
$340$	6.75403	−	4.62036i	0.366289	−	0.250574i
$341$		0			0
$342$	−30.5243	+	30.5243i	−1.65057	+	1.65057i
$343$	3.61469	−	3.61469i	0.195175	−	0.195175i
$344$			37.4201i			2.01755i
$345$	−3.32185	+	17.7085i	−0.178842	+	0.953392i
$346$	52.8485			2.84115
$347$	9.74724	+	9.74724i	0.523259	+	0.523259i	0.918554	−	0.395295i	$-0.129358\pi$
$347$	9.74724	+	9.74724i	0.523259	+	0.523259i	−0.395295	+	0.918554i	$0.629358\pi$
$348$	6.07724	−	6.07724i	0.325774	−	0.325774i
$349$	−8.23325			−0.440716			−0.220358	−	0.975419i	$-0.570723\pi$
$349$	−8.23325			−0.440716			−0.220358	+	0.975419i	$0.570723\pi$
$350$	1.67111	−	4.29752i	0.0893245	−	0.229712i
$351$		−	10.3109i		−	0.550356i
$352$		0			0
$353$	18.2121	+	18.2121i	0.969330	+	0.969330i	0.999543	−	0.0302134i	$-0.00961869\pi$
$353$	18.2121	+	18.2121i	0.969330	+	0.969330i	−0.0302134	+	0.999543i	$0.509619\pi$
$354$	7.20661			0.383027
$355$	−4.27848	−	0.802580i	−0.227078	−	0.0425965i
$356$	37.7801			2.00234
$357$	−0.588409	+	0.588409i	−0.0311419	+	0.0311419i
$358$	5.30792	−	5.30792i	0.280532	−	0.280532i
$359$	−8.87466			−0.468387			−0.234193	−	0.972190i	$-0.575245\pi$
$359$	−8.87466			−0.468387			−0.234193	+	0.972190i	$0.575245\pi$
$360$	−27.6814	−	40.4645i	−1.45894	−	2.13267i
$361$	0.719363			0.0378612
$362$	−18.1184	−	18.1184i	−0.952282	−	0.952282i
$363$		0			0
$364$		−	6.95243i		−	0.364407i
$365$	23.7539	−	16.2498i	1.24334	−	0.850553i
$366$	74.5262			3.89555
$367$	16.6120	−	16.6120i	0.867139	−	0.867139i	−0.125016	−	0.992155i	$-0.539898\pi$
$367$	16.6120	−	16.6120i	0.867139	−	0.867139i	0.992155	+	0.125016i	$0.0398982\pi$
$368$	12.1539	+	12.1539i	0.633567	+	0.633567i
$369$	19.4933			1.01478
$370$	−60.2452	−	11.3011i	−3.13200	−	0.587516i
$371$			0.370887i			0.0192555i
$372$	35.8171	−	35.8171i	1.85703	−	1.85703i
$373$	−9.04941	+	9.04941i	−0.468560	+	0.468560i	−0.901448	−	0.432887i	$-0.857495\pi$
$373$	−9.04941	+	9.04941i	−0.468560	+	0.468560i	0.432887	+	0.901448i	$0.357495\pi$
$374$		0			0
$375$	−6.66338	−	28.5734i	−0.344096	−	1.47553i
$376$			60.9760i			3.14460i
$377$	2.41129	−	2.41129i	0.124188	−	0.124188i
$378$	1.51744	+	1.51744i	0.0780488	+	0.0780488i
$379$			9.83221i			0.505047i	0.967591	+	0.252523i	$0.0812604\pi$
$379$			9.83221i			0.505047i	−0.967591	+	0.252523i	$0.918740\pi$
$380$	−7.79052	+	41.5306i	−0.399645	+	2.13047i
$381$		−	38.6168i		−	1.97840i
$382$	24.4106	+	24.4106i	1.24896	+	1.24896i
$383$	−1.11269	−	1.11269i	−0.0568560	−	0.0568560i	0.678107	−	0.734963i	$-0.262801\pi$
$383$	−1.11269	−	1.11269i	−0.0568560	−	0.0568560i	−0.734963	+	0.678107i	$0.762801\pi$
$384$	43.1219			2.20056
$385$		0			0
$386$	−33.7819			−1.71945
$387$	−18.2310	−	18.2310i	−0.926734	−	0.926734i
$388$	21.6024	+	21.6024i	1.09669	+	1.09669i
$389$			20.4119i			1.03492i	0.855706	+	0.517462i	$0.173123\pi$
$389$			20.4119i			1.03492i	−0.855706	+	0.517462i	$0.826877\pi$
$390$	−36.7172	−	53.6731i	−1.85925	−	2.71784i
$391$		−	2.64053i		−	0.133537i
$392$	−27.3797	−	27.3797i	−1.38289	−	1.38289i
$393$	16.8112	−	16.8112i	0.848011	−	0.848011i
$394$		−	38.8441i		−	1.95694i
$395$	−27.1922	−	5.10085i	−1.36819	−	0.256652i
$396$		0			0
$397$	−0.702204	+	0.702204i	−0.0352426	+	0.0352426i	−0.724508	−	0.689266i	$-0.757933\pi$
$397$	−0.702204	+	0.702204i	−0.0352426	+	0.0352426i	0.689266	+	0.724508i	$0.257933\pi$
$398$	28.6471	−	28.6471i	1.43595	−	1.43595i
$399$		−	4.29684i		−	0.215111i
$400$	−26.0871	−	10.1441i	−1.30436	−	0.507204i
$401$	−28.0917			−1.40283			−0.701417	−	0.712751i	$-0.747449\pi$
$401$	−28.0917			−1.40283			−0.701417	+	0.712751i	$0.747449\pi$
$402$	−27.3772	−	27.3772i	−1.36545	−	1.36545i
$403$	14.2113	−	14.2113i	0.707914	−	0.707914i
$404$	8.71847			0.433760
$405$	−12.2051	−	2.28949i	−0.606475	−	0.113766i
$406$			0.709731i			0.0352233i
$407$		0			0
$408$	9.00218	+	9.00218i	0.445674	+	0.445674i
$409$	19.2579			0.952241			0.476120	−	0.879380i	$-0.342043\pi$
$409$	19.2579			0.952241			0.476120	+	0.879380i	$0.342043\pi$
$410$	23.1502	−	15.8368i	1.14331	−	0.782124i
$411$	0.472965			0.0233296
$412$	−13.0729	+	13.0729i	−0.644056	+	0.644056i
$413$	−0.286269	+	0.286269i	−0.0140864	+	0.0140864i
$414$	−29.8479			−1.46694
$415$	13.1772	−	9.01441i	0.646845	−	0.442500i
$416$	−12.0473			−0.590666
$417$	35.5271	+	35.5271i	1.73977	+	1.73977i
$418$		0			0
$419$			12.3724i			0.604429i	0.953240	+	0.302215i	$0.0977259\pi$
$419$			12.3724i			0.604429i	−0.953240	+	0.302215i	$0.902274\pi$
$420$	9.04949	+	1.69755i	0.441570	+	0.0828320i
$421$	−9.16536			−0.446692			−0.223346	−	0.974739i	$-0.571698\pi$
$421$	−9.16536			−0.446692			−0.223346	+	0.974739i	$0.571698\pi$
$422$	6.50186	−	6.50186i	0.316505	−	0.316505i
$423$	−29.7075	−	29.7075i	−1.44443	−	1.44443i
$424$	5.67426			0.275567
$425$	1.73187	+	3.93574i	0.0840081	+	0.190912i
$426$		−	12.7776i		−	0.619079i
$427$	−2.96042	+	2.96042i	−0.143265	+	0.143265i
$428$	−37.8606	+	37.8606i	−1.83006	+	1.83006i
$429$		0			0
$430$	−36.4624	−	6.83981i	−1.75837	−	0.329845i
$431$			21.5882i			1.03986i	0.854207	+	0.519932i	$0.174043\pi$
$431$			21.5882i			1.03986i	−0.854207	+	0.519932i	$0.825957\pi$
$432$	9.21128	−	9.21128i	0.443178	−	0.443178i
$433$	5.16978	+	5.16978i	0.248444	+	0.248444i	0.820332	−	0.571888i	$-0.193789\pi$
$433$	5.16978	+	5.16978i	0.248444	+	0.248444i	−0.571888	+	0.820332i	$0.693789\pi$
$434$			4.18290i			0.200786i
$435$	2.54984	+	3.72735i	0.122256	+	0.178713i
$436$			17.2099i			0.824206i
$437$	9.64118	+	9.64118i	0.461200	+	0.461200i
$438$	59.7353	+	59.7353i	2.85426	+	2.85426i
$439$	−2.54287			−0.121365			−0.0606823	−	0.998157i	$-0.519328\pi$
$439$	−2.54287			−0.121365			−0.0606823	+	0.998157i	$0.519328\pi$
$440$		0			0
$441$	26.6788			1.27042
$442$	6.73909	+	6.73909i	0.320546	+	0.320546i
$443$	−4.84165	−	4.84165i	−0.230034	−	0.230034i	0.582673	−	0.812707i	$-0.302007\pi$
$443$	−4.84165	−	4.84165i	−0.230034	−	0.230034i	−0.812707	+	0.582673i	$0.802007\pi$
$444$		−	122.397i		−	5.80870i
$445$	−3.66008	+	19.5116i	−0.173504	+	0.924936i
$446$		−	59.7220i		−	2.82792i
$447$	16.1596	+	16.1596i	0.764324	+	0.764324i
$448$	−1.14608	+	1.14608i	−0.0541473	+	0.0541473i
$449$			40.4649i			1.90966i	0.297159	+	0.954828i	$0.403961\pi$
$449$			40.4649i			1.90966i	−0.297159	+	0.954828i	$0.596039\pi$
$450$	44.4887	−	19.5767i	2.09722	−	0.922852i
$451$		0			0
$452$	9.42383	−	9.42383i	0.443260	−	0.443260i
$453$	−9.87248	+	9.87248i	−0.463850	+	0.463850i
$454$			46.4266i			2.17891i
$455$	3.59059	+	0.673542i	0.168330	+	0.0315761i
$456$	−65.7381			−3.07847
$457$	−3.38525	−	3.38525i	−0.158355	−	0.158355i	0.623482	−	0.781838i	$-0.285717\pi$
$457$	−3.38525	−	3.38525i	−0.158355	−	0.158355i	−0.781838	+	0.623482i	$0.785717\pi$
$458$	−28.4178	+	28.4178i	−1.32788	+	1.32788i
$459$	−2.00122			−0.0934088
$460$	−24.1140	+	16.4962i	−1.12432	+	0.769138i
$461$		−	23.9704i		−	1.11641i	−0.829703	−	0.558206i	$-0.811490\pi$
$461$		−	23.9704i		−	1.11641i	0.829703	−	0.558206i	$-0.188510\pi$
$462$		0			0
$463$	12.0906	+	12.0906i	0.561898	+	0.561898i	0.929846	−	0.367948i	$-0.119940\pi$
$463$	12.0906	+	12.0906i	0.561898	+	0.561898i	−0.367948	+	0.929846i	$0.619940\pi$
$464$	4.30826			0.200006
$465$	15.0279	+	21.9677i	0.696901	+	1.01873i
$466$	8.34909			0.386764
$467$	11.2586	−	11.2586i	0.520985	−	0.520985i	−0.396884	−	0.917869i	$-0.629908\pi$
$467$	11.2586	−	11.2586i	0.520985	−	0.520985i	0.917869	+	0.396884i	$0.129908\pi$
$468$	51.8217	−	51.8217i	2.39546	−	2.39546i
$469$	2.17502			0.100433
$470$	−59.4155	−	11.1455i	−2.74063	−	0.514103i
$471$	−14.5696			−0.671334
$472$	4.37969	+	4.37969i	0.201592	+	0.201592i
$473$		0			0
$474$		−	81.2092i		−	3.73006i
$475$	−20.6938	−	8.04685i	−0.949496	−	0.369215i
$476$	−1.34938			−0.0618486
$477$	−2.76449	+	2.76449i	−0.126578	+	0.126578i
$478$	−0.827284	−	0.827284i	−0.0378391	−	0.0378391i
$479$	−37.9796			−1.73533			−0.867666	−	0.497147i	$-0.834381\pi$
$479$	−37.9796			−1.73533			−0.867666	+	0.497147i	$0.834381\pi$
$480$	2.94154	−	15.6811i	0.134262	−	0.715740i
$481$		−	48.5638i		−	2.21432i
$482$	−29.2295	+	29.2295i	−1.33137	+	1.33137i
$483$	2.10081	−	2.10081i	0.0955900	−	0.0955900i
$484$		0			0
$485$	−13.2494	+	9.06376i	−0.601623	+	0.411564i
$486$		−	53.9107i		−	2.44544i
$487$	24.8084	−	24.8084i	1.12418	−	1.12418i	0.133070	−	0.991107i	$-0.457517\pi$
$487$	24.8084	−	24.8084i	1.12418	−	1.12418i	0.991107	−	0.133070i	$-0.0424835\pi$
$488$	45.2921	+	45.2921i	2.05027	+	2.05027i
$489$			10.3619i			0.468581i
$490$	31.6836	−	21.6744i	1.43132	−	0.979151i
$491$		−	29.4368i		−	1.32846i	−0.747527	−	0.664232i	$-0.768759\pi$
$491$		−	29.4368i		−	1.32846i	0.747527	−	0.664232i	$-0.231241\pi$
$492$	39.6039	+	39.6039i	1.78548	+	1.78548i
$493$	−0.468000	−	0.468000i	−0.0210776	−	0.0210776i
$494$	−49.2120			−2.21415
$495$		0			0
$496$	25.3914			1.14011
$497$	0.507569	+	0.507569i	0.0227676	+	0.0227676i
$498$	33.1375	+	33.1375i	1.48493	+	1.48493i
$499$			28.2019i			1.26249i	0.775583	+	0.631246i	$0.217456\pi$
$499$			28.2019i			1.26249i	−0.775583	+	0.631246i	$0.782544\pi$
$500$	25.1228	−	40.4037i	1.12353	−	1.80691i
$501$			6.98531i			0.312081i
$502$	−11.5704	−	11.5704i	−0.516413	−	0.516413i
$503$	−25.4869	+	25.4869i	−1.13640	+	1.13640i	−0.147313	+	0.989090i	$0.547062\pi$
$503$	−25.4869	+	25.4869i	−1.13640	+	1.13640i	−0.989090	+	0.147313i	$0.952938\pi$
$504$			8.08435i			0.360105i
$505$	−0.844633	+	4.50266i	−0.0375857	+	0.200366i
$506$		0			0
$507$	12.3087	−	12.3087i	0.546648	−	0.546648i
$508$	44.2793	−	44.2793i	1.96458	−	1.96458i
$509$			31.3435i			1.38928i	0.719359	+	0.694639i	$0.244436\pi$
$509$			31.3435i			1.38928i	−0.719359	+	0.694639i	$0.755564\pi$
$510$	−10.4173	+	7.12634i	−0.461284	+	0.315560i
$511$	−4.74575			−0.209940
$512$	33.8969	+	33.8969i	1.49804	+	1.49804i
$513$	7.30691	−	7.30691i	0.322608	−	0.322608i
$514$	56.8905			2.50933
$515$	−5.48504	−	8.01801i	−0.241700	−	0.353316i
$516$		−	74.0787i		−	3.26113i
$517$		0			0
$518$	7.14706	+	7.14706i	0.314024	+	0.314024i
$519$	−55.4510			−2.43403
$520$	10.3046	−	54.9332i	0.451889	−	2.40898i
$521$	−35.6967			−1.56390			−0.781951	−	0.623340i	$-0.785775\pi$
$521$	−35.6967			−1.56390			−0.781951	+	0.623340i	$0.785775\pi$
$522$	−5.29015	+	5.29015i	−0.231544	+	0.231544i
$523$	−7.14276	+	7.14276i	−0.312331	+	0.312331i	−0.845812	−	0.533481i	$-0.820884\pi$
$523$	−7.14276	+	7.14276i	−0.312331	+	0.312331i	0.533481	+	0.845812i	$0.320884\pi$
$524$	38.5525			1.68417
$525$	−1.75340	+	4.50916i	−0.0765248	+	0.196796i
$526$	−61.7023			−2.69035
$527$	−2.75823	−	2.75823i	−0.120150	−	0.120150i
$528$		0			0
$529$		−	13.5725i		−	0.590108i
$530$	−1.03717	+	5.52905i	−0.0450517	+	0.240166i
$531$	−4.26756			−0.185196
$532$	4.92689	−	4.92689i	0.213608	−	0.213608i
$533$	15.7138	+	15.7138i	0.680638	+	0.680638i
$534$	−58.2710			−2.52163
$535$	−15.8853	−	23.2210i	−0.686780	−	1.00393i
$536$		−	33.2760i		−	1.43731i
$537$	−5.56931	+	5.56931i	−0.240333	+	0.240333i
$538$	10.8941	−	10.8941i	0.469680	−	0.469680i
$539$		0			0
$540$	12.5022	+	18.2757i	0.538009	+	0.786460i
$541$			2.41825i			0.103969i	0.998648	+	0.0519844i	$0.0165546\pi$
$541$			2.41825i			0.103969i	−0.998648	+	0.0519844i	$0.983445\pi$
$542$	12.3600	−	12.3600i	0.530908	−	0.530908i
$543$	19.0107	+	19.0107i	0.815826	+	0.815826i
$544$			2.33822i			0.100250i
$545$	−8.88808	−	1.66727i	−0.380724	−	0.0714181i
$546$			10.7233i			0.458913i
$547$	−22.6752	−	22.6752i	−0.969520	−	0.969520i	0.0300287	−	0.999549i	$-0.490440\pi$
$547$	−22.6752	−	22.6752i	−0.969520	−	0.969520i	−0.999549	+	0.0300287i	$0.990440\pi$
$548$	0.542317	+	0.542317i	0.0231666	+	0.0231666i
$549$	−44.1325			−1.88353
$550$		0			0
$551$	3.41755			0.145593
$552$	−32.1406	−	32.1406i	−1.36800	−	1.36800i
$553$	3.22589	+	3.22589i	0.137179	+	0.137179i
$554$			2.19295i			0.0931695i
$555$	63.2120	+	11.8576i	2.68320	+	0.503329i
$556$			81.4732i			3.45523i
$557$	−15.0583	−	15.0583i	−0.638039	−	0.638039i	0.312032	−	0.950072i	$-0.398990\pi$
$557$	−15.0583	−	15.0583i	−0.638039	−	0.638039i	−0.950072	+	0.312032i	$0.898990\pi$
$558$	−31.1783	+	31.1783i	−1.31988	+	1.31988i
$559$		−	29.3924i		−	1.24317i
$560$	2.60595	+	3.80937i	0.110122	+	0.160975i
$561$		0			0
$562$	14.4572	−	14.4572i	0.609840	−	0.609840i
$563$	−27.3299	+	27.3299i	−1.15182	+	1.15182i	−0.165629	+	0.986188i	$0.552965\pi$
$563$	−27.3299	+	27.3299i	−1.15182	+	1.15182i	−0.986188	+	0.165629i	$0.947035\pi$
$564$		−	120.711i		−	5.08287i
$565$	3.95398	+	5.77991i	0.166345	+	0.243163i
$566$	−17.9287			−0.753601
$567$	1.44792	+	1.44792i	0.0608071	+	0.0608071i
$568$	7.76539	−	7.76539i	0.325829	−	0.325829i
$569$	9.21053			0.386125			0.193063	−	0.981186i	$-0.438158\pi$
$569$	9.21053			0.386125			0.193063	+	0.981186i	$0.438158\pi$
$570$	12.0159	−	64.0557i	0.503291	−	2.68300i
$571$			24.7774i			1.03690i	0.855107	+	0.518451i	$0.173491\pi$
$571$			24.7774i			1.03690i	−0.855107	+	0.518451i	$0.826509\pi$
$572$		0			0
$573$	−25.6128	−	25.6128i	−1.06999	−	1.06999i
$574$	−4.62514			−0.193050
$575$	−6.18333	−	14.0518i	−0.257863	−	0.586003i
$576$	−17.0852			−0.711885
$577$	−20.6537	+	20.6537i	−0.859823	+	0.859823i	−0.991317	−	0.131494i	$-0.958023\pi$
$577$	−20.6537	+	20.6537i	−0.859823	+	0.859823i	0.131494	+	0.991317i	$0.458023\pi$
$578$	−28.7572	+	28.7572i	−1.19614	+	1.19614i
$579$	35.4455			1.47307
$580$	−1.35017	+	7.19764i	−0.0560628	+	0.298866i
$581$	−2.63266			−0.109221
$582$	−33.3190	−	33.3190i	−1.38112	−	1.38112i
$583$		0			0
$584$			72.6062i			3.00447i
$585$	21.7430	+	31.7838i	0.898960	+	1.31410i
$586$	−58.3448			−2.41020
$587$	2.60288	−	2.60288i	0.107432	−	0.107432i	−0.651347	−	0.758780i	$-0.725796\pi$
$587$	2.60288	−	2.60288i	0.107432	−	0.107432i	0.758780	+	0.651347i	$0.225796\pi$
$588$	54.2024	+	54.2024i	2.23527	+	2.23527i
$589$	20.1418			0.829930
$590$	−5.06815	+	3.46707i	−0.208652	+	0.142737i
$591$			40.7570i			1.67652i
$592$	43.3846	−	43.3846i	1.78309	−	1.78309i
$593$	−12.2260	+	12.2260i	−0.502062	+	0.502062i	−0.912078	−	0.410016i	$-0.865523\pi$
$593$	−12.2260	+	12.2260i	−0.502062	+	0.502062i	0.410016	+	0.912078i	$0.365523\pi$
$594$		0			0
$595$	0.130726	−	0.696888i	0.00535924	−	0.0285696i
$596$			37.0583i			1.51797i
$597$	−30.0579	+	30.0579i	−1.23019	+	1.23019i
$598$	−24.0607	−	24.0607i	−0.983915	−	0.983915i
$599$		−	42.4110i		−	1.73287i	−0.499291	−	0.866434i	$-0.666406\pi$
$599$		−	42.4110i		−	1.73287i	0.499291	−	0.866434i	$-0.333594\pi$
$600$	68.9865	+	26.8256i	2.81636	+	1.09515i
$601$			38.0290i			1.55123i	0.631204	+	0.775617i	$0.282561\pi$
$601$			38.0290i			1.55123i	−0.631204	+	0.775617i	$0.717439\pi$
$602$	4.32564	+	4.32564i	0.176300	+	0.176300i
$603$	16.2120	+	16.2120i	0.660206	+	0.660206i
$604$	−22.6402			−0.921218
$605$		0			0
$606$	−13.4471			−0.546253
$607$	−20.2562	−	20.2562i	−0.822173	−	0.822173i	0.164247	−	0.986419i	$-0.447481\pi$
$607$	−20.2562	−	20.2562i	−0.822173	−	0.822173i	−0.986419	+	0.164247i	$0.947481\pi$
$608$	−8.53739	−	8.53739i	−0.346237	−	0.346237i
$609$		−	0.744682i		−	0.0301760i
$610$	−52.4116	+	35.8542i	−2.12208	+	1.45170i
$611$		−	47.8950i		−	1.93762i
$612$	−10.0579	−	10.0579i	−0.406568	−	0.406568i
$613$	−25.0196	+	25.0196i	−1.01053	+	1.01053i	−0.0105882	+	0.999944i	$0.503370\pi$
$613$	−25.0196	+	25.0196i	−1.01053	+	1.01053i	−0.999944	+	0.0105882i	$0.996630\pi$
$614$		−	15.0330i		−	0.606684i
$615$	−24.2902	+	16.6167i	−0.979477	+	0.670050i
$616$		0			0
$617$	−6.86653	+	6.86653i	−0.276436	+	0.276436i	−0.831685	−	0.555248i	$-0.812623\pi$
$617$	−6.86653	+	6.86653i	−0.276436	+	0.276436i	0.555248	+	0.831685i	$0.312623\pi$
$618$	20.1633	−	20.1633i	0.811089	−	0.811089i
$619$			13.1057i			0.526763i	0.964692	+	0.263381i	$0.0848378\pi$
$619$			13.1057i			0.526763i	−0.964692	+	0.263381i	$0.915162\pi$
$620$	−7.95743	+	42.4204i	−0.319578	+	1.70364i
$621$	7.14498			0.286718
$622$	51.7829	+	51.7829i	2.07631	+	2.07631i
$623$	2.31471	−	2.31471i	0.0927370	−	0.0927370i
$624$	65.0931			2.60581
$625$	18.4327	+	16.8889i	0.737307	+	0.675558i
$626$			34.8531i			1.39301i
$627$		0			0
$628$	−16.7060	−	16.7060i	−0.666643	−	0.666643i
$629$	−9.42560			−0.375823
$630$	−7.87745	−	1.47769i	−0.313845	−	0.0588727i
$631$	23.3545			0.929727			0.464863	−	0.885382i	$-0.346103\pi$
$631$	23.3545			0.929727			0.464863	+	0.885382i	$0.346103\pi$
$632$	49.3535	−	49.3535i	1.96318	−	1.96318i
$633$	−6.82204	+	6.82204i	−0.271152	+	0.271152i
$634$	18.0096			0.715254
$635$	18.5784	+	27.1578i	0.737261	+	1.07773i
$636$	−11.2331			−0.445420
$637$	21.5060	+	21.5060i	0.852100	+	0.852100i
$638$		0			0
$639$			7.56658i			0.299329i
$640$	−30.3261	+	20.7458i	−1.19874	+	0.820049i
$641$	37.2830			1.47259			0.736296	−	0.676660i	$-0.236573\pi$
$641$	37.2830			1.47259			0.736296	+	0.676660i	$0.236573\pi$
$642$	58.3952	−	58.3952i	2.30468	−	2.30468i
$643$	4.39799	+	4.39799i	0.173440	+	0.173440i	0.788489	−	0.615049i	$-0.210864\pi$
$643$	4.39799	+	4.39799i	0.173440	+	0.173440i	−0.615049	+	0.788489i	$0.710864\pi$
$644$	4.81771			0.189844
$645$	38.2580	+	7.17664i	1.50641	+	0.282580i
$646$			9.55142i			0.375796i
$647$	25.0575	−	25.0575i	0.985113	−	0.985113i	−0.0147777	−	0.999891i	$-0.504704\pi$
$647$	25.0575	−	25.0575i	0.985113	−	0.985113i	0.999891	+	0.0147777i	$0.00470406\pi$
$648$	22.1521	−	22.1521i	0.870216	−	0.870216i
$649$		0			0
$650$	51.6438	+	20.0819i	2.02564	+	0.787675i
$651$		−	4.38889i		−	0.172014i
$652$	−11.8813	+	11.8813i	−0.465307	+	0.465307i
$653$	−23.8281	−	23.8281i	−0.932467	−	0.932467i	0.0653926	−	0.997860i	$-0.479170\pi$
$653$	−23.8281	−	23.8281i	−0.932467	−	0.932467i	−0.997860	+	0.0653926i	$0.979170\pi$
$654$		−	26.5442i		−	1.03796i
$655$	−3.73491	+	19.9105i	−0.145935	+	0.777966i
$656$			28.0758i			1.09618i
$657$	−35.3737	−	35.3737i	−1.38006	−	1.38006i
$658$	7.04864	+	7.04864i	0.274785	+	0.274785i
$659$	50.1826			1.95484			0.977419	−	0.211310i	$-0.0677729\pi$
$659$	50.1826			1.95484			0.977419	+	0.211310i	$0.0677729\pi$
$660$		0			0
$661$	28.3220			1.10160			0.550798	−	0.834638i	$-0.314323\pi$
$661$	28.3220			1.10160			0.550798	+	0.834638i	$0.314323\pi$
$662$	23.3806	+	23.3806i	0.908711	+	0.908711i
$663$	−7.07097	−	7.07097i	−0.274614	−	0.274614i
$664$			40.2776i			1.56307i
$665$	2.06719	+	3.02181i	0.0801621	+	0.117181i
$666$			106.545i			4.12853i
$667$	1.67091	+	1.67091i	0.0646978	+	0.0646978i
$668$	−8.00958	+	8.00958i	−0.309900	+	0.309900i
$669$			62.6631i			2.42269i
$670$	32.4244	+	6.08235i	1.25267	+	0.234982i
$671$		0			0
$672$	−1.86029	+	1.86029i	−0.0717623	+	0.0717623i
$673$	−20.7252	+	20.7252i	−0.798898	+	0.798898i	−0.982922	−	0.184024i	$-0.941088\pi$
$673$	−20.7252	+	20.7252i	−0.798898	+	0.798898i	0.184024	+	0.982922i	$0.441088\pi$
$674$		−	82.7291i		−	3.18661i
$675$	−10.6497	+	4.68625i	−0.409907	+	0.180374i
$676$	28.2271			1.08566
$677$	−20.1880	−	20.1880i	−0.775887	−	0.775887i	0.203242	−	0.979129i	$-0.434852\pi$
$677$	−20.1880	−	20.1880i	−0.775887	−	0.775887i	−0.979129	+	0.203242i	$0.934852\pi$
$678$	−14.5351	+	14.5351i	−0.558216	+	0.558216i
$679$	2.64707			0.101585
$680$	−10.6618	−	2.00000i	−0.408862	−	0.0766965i
$681$		−	48.7129i		−	1.86668i
$682$		0			0
$683$	11.2345	+	11.2345i	0.429876	+	0.429876i	0.888586	−	0.458710i	$-0.151688\pi$
$683$	11.2345	+	11.2345i	0.429876	+	0.429876i	−0.458710	+	0.888586i	$0.651688\pi$
$684$	73.4477			2.80834
$685$	−0.332619	+	0.227541i	−0.0127087	+	0.00869390i
$686$	−12.7854			−0.488150
$687$	29.8173	−	29.8173i	1.13760	−	1.13760i
$688$	26.2578	−	26.2578i	1.00107	−	1.00107i
$689$	−4.45698			−0.169797
$690$	37.1929	−	25.4433i	1.41591	−	0.968609i
$691$	9.97362			0.379414			0.189707	−	0.981841i	$-0.439246\pi$
$691$	9.97362			0.379414			0.189707	+	0.981841i	$0.439246\pi$
$692$	−63.5820	−	63.5820i	−2.41702	−	2.41702i
$693$		0			0
$694$		−	34.4767i		−	1.30872i
$695$	−42.0769	−	7.89301i	−1.59607	−	0.299399i
$696$	−11.3930			−0.431852
$697$	3.04984	−	3.04984i	0.115521	−	0.115521i
$698$	14.5608	+	14.5608i	0.551135	+	0.551135i
$699$	−8.76025			−0.331343
$700$	−7.18086	+	3.15984i	−0.271411	+	0.119431i
$701$			23.9400i			0.904201i	0.891967	+	0.452101i	$0.149325\pi$
$701$			23.9400i			0.904201i	−0.891967	+	0.452101i	$0.850675\pi$
$702$	−18.2353	+	18.2353i	−0.688245	+	0.688245i
$703$	34.4151	−	34.4151i	1.29799	−	1.29799i
$704$		0			0
$705$	62.3415	+	11.6943i	2.34792	+	0.440435i
$706$		−	64.4175i		−	2.42438i
$707$	0.534164	−	0.534164i	0.0200893	−	0.0200893i
$708$	−8.67027	−	8.67027i	−0.325849	−	0.325849i
$709$			21.1788i			0.795385i	0.917519	+	0.397693i	$0.130189\pi$
$709$			21.1788i			0.795385i	−0.917519	+	0.397693i	$0.869811\pi$
$710$	6.14727	+	8.98605i	0.230703	+	0.337241i
$711$			48.0899i			1.80351i
$712$	−35.4132	−	35.4132i	−1.32717	−	1.32717i
$713$	9.84774	+	9.84774i	0.368801	+	0.368801i
$714$	2.08125			0.0778887
$715$		0			0
$716$	−12.7719			−0.477309
$717$	0.868025	+	0.868025i	0.0324170	+	0.0324170i
$718$	15.6952	+	15.6952i	0.585739	+	0.585739i
$719$			11.6286i			0.433672i	0.976208	+	0.216836i	$0.0695737\pi$
$719$			11.6286i			0.433672i	−0.976208	+	0.216836i	$0.930426\pi$
$720$	−8.97000	+	47.8182i	−0.334292	+	1.78208i
$721$			1.60191i			0.0596581i
$722$	−1.27222	−	1.27222i	−0.0473472	−	0.0473472i
$723$	30.6689	−	30.6689i	1.14059	−	1.14059i
$724$			43.5965i			1.62025i
$725$	−3.58643	−	1.39459i	−0.133197	−	0.0517939i
$726$		0			0
$727$	9.80845	−	9.80845i	0.363775	−	0.363775i	−0.501426	−	0.865201i	$-0.667191\pi$
$727$	9.80845	−	9.80845i	0.363775	−	0.363775i	0.865201	+	0.501426i	$0.167191\pi$
$728$	−6.51688	+	6.51688i	−0.241532	+	0.241532i
$729$			39.9051i			1.47797i
$730$	−70.7481	−	13.2713i	−2.61850	−	0.491193i
$731$	−5.70469			−0.210996
$732$	−89.6625	−	89.6625i	−3.31402	−	3.31402i
$733$	−9.10112	+	9.10112i	−0.336157	+	0.336157i	−0.854919	−	0.518762i	$-0.826393\pi$
$733$	−9.10112	+	9.10112i	−0.336157	+	0.336157i	0.518762	+	0.854919i	$0.326393\pi$
$734$	−58.7579			−2.16879
$735$	−33.2439	+	22.7418i	−1.22622	+	0.838845i
$736$		−	8.34820i		−	0.307719i
$737$		0			0
$738$	−34.4746	−	34.4746i	−1.26903	−	1.26903i
$739$	36.2156			1.33221			0.666106	−	0.745857i	$-0.267960\pi$
$739$	36.2156			1.33221			0.666106	+	0.745857i	$0.267960\pi$
$740$	58.8846	+	86.0773i	2.16464	+	3.16426i
$741$	51.6355			1.89688
$742$	0.655927	−	0.655927i	0.0240798	−	0.0240798i
$743$	28.8534	−	28.8534i	1.05853	−	1.05853i	0.0603500	−	0.998177i	$-0.480778\pi$
$743$	28.8534	−	28.8534i	1.05853	−	1.05853i	0.998177	−	0.0603500i	$-0.0192217\pi$
$744$	−67.1466			−2.46171
$745$	−19.1388	−	3.59016i	−0.701191	−	0.131533i
$746$	32.0084			1.17191
$747$	−19.6232	−	19.6232i	−0.717974	−	0.717974i
$748$		0			0
$749$			4.63929i			0.169516i
$750$	−38.7488	+	62.3177i	−1.41491	+	2.27552i
$751$	−9.16953			−0.334601			−0.167301	−	0.985906i	$-0.553505\pi$
$751$	−9.16953			−0.334601			−0.167301	+	0.985906i	$0.553505\pi$
$752$	42.7871	−	42.7871i	1.56029	−	1.56029i
$753$	12.1402	+	12.1402i	0.442414	+	0.442414i
$754$	−8.52890			−0.310604
$755$	2.19335	−	11.6926i	0.0798243	−	0.425536i
$756$		−	3.65127i		−	0.132795i
$757$	−14.7393	+	14.7393i	−0.535709	+	0.535709i	−0.922266	−	0.386557i	$-0.873664\pi$
$757$	−14.7393	+	14.7393i	−0.535709	+	0.535709i	0.386557	+	0.922266i	$0.373664\pi$
$758$	17.3886	−	17.3886i	0.631584	−	0.631584i
$759$		0			0
$760$	46.2313	−	31.6263i	1.67698	−	1.14721i
$761$		−	43.2073i		−	1.56626i	−0.621855	−	0.783132i	$-0.713621\pi$
$761$		−	43.2073i		−	1.56626i	0.621855	−	0.783132i	$-0.286379\pi$
$762$	−68.2953	+	68.2953i	−2.47408	+	2.47408i
$763$	1.05442	+	1.05442i	0.0381725	+	0.0381725i
$764$		−	58.7369i		−	2.12503i
$765$	6.16882	−	4.22003i	0.223034	−	0.152575i
$766$			3.93569i			0.142202i
$767$	−3.44013	−	3.44013i	−0.124216	−	0.124216i
$768$	−59.9489	−	59.9489i	−2.16322	−	2.16322i
$769$	−17.6513			−0.636523			−0.318261	−	0.948003i	$-0.603099\pi$
$769$	−17.6513			−0.636523			−0.318261	+	0.948003i	$0.603099\pi$
$770$		0			0
$771$	−59.6921			−2.14976
$772$	40.6430	+	40.6430i	1.46277	+	1.46277i
$773$	−13.3581	−	13.3581i	−0.480459	−	0.480459i	0.424819	−	0.905278i	$-0.360338\pi$
$773$	−13.3581	−	13.3581i	−0.480459	−	0.480459i	−0.905278	+	0.424819i	$0.860338\pi$
$774$			64.4845i			2.31785i
$775$	−21.1371	−	8.21925i	−0.759268	−	0.295244i
$776$		−	40.4981i		−	1.45380i
$777$	−7.49902	−	7.49902i	−0.269026	−	0.269026i
$778$	36.0992	−	36.0992i	1.29422	−	1.29422i
$779$			22.2713i			0.797953i
$780$	−20.3996	+	108.749i	−0.730424	+	3.89382i
$781$		0			0
$782$	−4.66987	+	4.66987i	−0.166994	+	0.166994i
$783$	1.26636	−	1.26636i	0.0452559	−	0.0452559i
$784$			38.4249i			1.37232i
$785$	10.2463	−	7.00939i	0.365706	−	0.250176i
$786$	−59.4624			−2.12095
$787$	−32.6528	−	32.6528i	−1.16395	−	1.16395i	−0.983604	−	0.180344i	$-0.942279\pi$
$787$	−32.6528	−	32.6528i	−1.16395	−	1.16395i	−0.180344	−	0.983604i	$-0.557721\pi$
$788$	−46.7333	+	46.7333i	−1.66481	+	1.66481i
$789$	64.7409			2.30484
$790$	39.0694	+	57.1115i	1.39003	+	2.03194i
$791$		−	1.15476i		−	0.0410585i
$792$		0			0
$793$	−35.5757	−	35.5757i	−1.26333	−	1.26333i
$794$	2.48375			0.0881450
$795$	1.08824	−	5.80133i	0.0385960	−	0.205752i
$796$	−68.9307			−2.44318
$797$	6.66696	−	6.66696i	0.236156	−	0.236156i	−0.579100	−	0.815256i	$-0.696596\pi$
$797$	6.66696	−	6.66696i	0.236156	−	0.236156i	0.815256	+	0.579100i	$0.196596\pi$
$798$	−7.59912	+	7.59912i	−0.269006	+	0.269006i
$799$	−9.29581			−0.328862
$800$	5.47542	+	12.4431i	0.193585	+	0.439930i
$801$	34.5066			1.21923
$802$	49.6813	+	49.6813i	1.75431	+	1.75431i
$803$		0			0
$804$			65.8750i			2.32323i
$805$	−0.466733	+	2.48811i	−0.0164502	+	0.0876944i
$806$	−50.2664			−1.77056
$807$	−11.4306	+	11.4306i	−0.402377	+	0.402377i
$808$	−8.17228	−	8.17228i	−0.287500	−	0.287500i
$809$	−1.81466			−0.0638001			−0.0319001	−	0.999491i	$-0.510156\pi$
$809$	−1.81466			−0.0638001			−0.0319001	+	0.999491i	$0.510156\pi$
$810$	17.5361	+	25.6342i	0.616156	+	0.900694i
$811$		−	30.4408i		−	1.06892i	−0.845193	−	0.534461i	$-0.820515\pi$
$811$		−	30.4408i		−	1.06892i	0.845193	−	0.534461i	$-0.179485\pi$
$812$	0.853877	−	0.853877i	0.0299652	−	0.0299652i
$813$	−12.9687	+	12.9687i	−0.454832	+	0.454832i
$814$		0			0
$815$	−4.98506	−	7.28714i	−0.174619	−	0.255257i
$816$		−	12.6337i		−	0.442269i
$817$	20.8292	−	20.8292i	0.728720	−	0.728720i
$818$	−34.0583	−	34.0583i	−1.19082	−	1.19082i
$819$		−	6.35003i		−	0.221888i
$820$	−46.9052	−	8.79873i	−1.63800	−	0.307265i
$821$		−	28.6807i		−	1.00096i	−0.865747	−	0.500482i	$-0.833156\pi$
$821$		−	28.6807i		−	1.00096i	0.865747	−	0.500482i	$-0.166844\pi$
$822$	−0.836456	−	0.836456i	−0.0291748	−	0.0291748i
$823$	−23.4705	−	23.4705i	−0.818128	−	0.818128i	0.167708	−	0.985837i	$-0.446363\pi$
$823$	−23.4705	−	23.4705i	−0.818128	−	0.818128i	−0.985837	+	0.167708i	$0.946363\pi$
$824$	24.5079			0.853772
$825$		0			0
$826$	1.01256			0.0352314
$827$	0.278504	+	0.278504i	0.00968454	+	0.00968454i	0.711932	−	0.702248i	$-0.247820\pi$
$827$	0.278504	+	0.278504i	0.00968454	+	0.00968454i	−0.702248	+	0.711932i	$0.747820\pi$
$828$	35.9100	+	35.9100i	1.24796	+	1.24796i
$829$			25.7237i			0.893421i	0.894679	+	0.446710i	$0.147405\pi$
$829$			25.7237i			0.893421i	−0.894679	+	0.446710i	$0.852595\pi$
$830$	−39.2468	−	7.36211i	−1.36228	−	0.255543i
$831$		−	2.30094i		−	0.0798188i
$832$	−13.7726	−	13.7726i	−0.477479	−	0.477479i
$833$	4.17404	−	4.17404i	0.144622	−	0.144622i
$834$		−	125.662i		−	4.35133i
$835$	−3.36060	−	4.91251i	−0.116298	−	0.170005i
$836$		0			0
$837$	7.46346	−	7.46346i	0.257975	−	0.257975i
$838$	21.8810	−	21.8810i	0.755866	−	0.755866i
$839$		−	41.2331i		−	1.42353i	−0.702420	−	0.711763i	$-0.747897\pi$
$839$		−	41.2331i		−	1.42353i	0.702420	−	0.711763i	$-0.252103\pi$
$840$	−6.89135	−	10.0738i	−0.237774	−	0.347578i
$841$	−28.4077			−0.979576
$842$	16.2093	+	16.2093i	0.558609	+	0.558609i
$843$	−15.1691	+	15.1691i	−0.522453	+	0.522453i
$844$	−15.6448			−0.538515
$845$	−2.73460	+	14.5779i	−0.0940732	+	0.501496i
$846$			105.078i			3.61264i
$847$		0			0
$848$	−3.98165	−	3.98165i	−0.136731	−	0.136731i
$849$	18.8117			0.645615
$850$	3.89763	−	10.0234i	0.133688	−	0.343800i
$851$	33.6524			1.15359
$852$	−15.3728	+	15.3728i	−0.526663	+	0.526663i
$853$	4.69322	−	4.69322i	0.160693	−	0.160693i	−0.622181	−	0.782874i	$-0.713753\pi$
$853$	4.69322	−	4.69322i	0.160693	−	0.160693i	0.782874	+	0.622181i	$0.213753\pi$
$854$	10.4712			0.358318
$855$	−7.11550	+	37.9321i	−0.243345	+	1.29725i
$856$	70.9774			2.42596
$857$	−28.1873	−	28.1873i	−0.962858	−	0.962858i	0.0364762	−	0.999335i	$-0.488387\pi$
$857$	−28.1873	−	28.1873i	−0.962858	−	0.962858i	−0.999335	+	0.0364762i	$0.988387\pi$
$858$		0			0
$859$		−	3.38503i		−	0.115496i	−0.998331	−	0.0577479i	$-0.981608\pi$
$859$		−	3.38503i		−	0.115496i	0.998331	−	0.0577479i	$-0.0183920\pi$
$860$	35.6389	+	52.0969i	1.21528	+	1.77649i
$861$	4.85291			0.165387
$862$	38.1795	−	38.1795i	1.30040	−	1.30040i
$863$	−4.82257	−	4.82257i	−0.164162	−	0.164162i	0.620245	−	0.784408i	$-0.287033\pi$
$863$	−4.82257	−	4.82257i	−0.164162	−	0.164162i	−0.784408	+	0.620245i	$0.787033\pi$
$864$	−6.32697			−0.215248
$865$	38.9967	−	26.6773i	1.32593	−	0.907054i
$866$		−	18.2859i		−	0.621380i
$867$	30.1734	−	30.1734i	1.02474	−	1.02474i
$868$	5.03245	−	5.03245i	0.170813	−	0.170813i
$869$		0			0
$870$	2.08247	−	11.1015i	0.0706024	−	0.376375i
$871$			26.1374i			0.885633i
$872$	16.1318	−	16.1318i	0.546290	−	0.546290i
$873$	19.7306	+	19.7306i	0.667780	+	0.667780i
$874$		−	34.1016i		−	1.15350i
$875$	−0.936232	−	4.01468i	−0.0316504	−	0.135721i
$876$		−	143.735i		−	4.85636i
$877$	−2.93904	−	2.93904i	−0.0992442	−	0.0992442i	0.655741	−	0.754986i	$-0.272356\pi$
$877$	−2.93904	−	2.93904i	−0.0992442	−	0.0992442i	−0.754986	+	0.655741i	$0.772356\pi$
$878$	4.49716	+	4.49716i	0.151772	+	0.151772i
$879$	61.2180			2.06483
$880$		0			0
$881$	−7.19015			−0.242242			−0.121121	−	0.992638i	$-0.538649\pi$
$881$	−7.19015			−0.242242			−0.121121	+	0.992638i	$0.538649\pi$
$882$	−47.1824	−	47.1824i	−1.58871	−	1.58871i
$883$	31.6567	+	31.6567i	1.06533	+	1.06533i	0.997711	+	0.0676221i	$0.0215412\pi$
$883$	31.6567	+	31.6567i	1.06533	+	1.06533i	0.0676221	+	0.997711i	$0.478459\pi$
$884$		−	16.2156i		−	0.545390i
$885$	5.31773	−	3.63781i	0.178754	−	0.122283i
$886$			17.1253i			0.575335i
$887$	−10.5828	−	10.5828i	−0.355337	−	0.355337i	0.506754	−	0.862091i	$-0.330845\pi$
$887$	−10.5828	−	10.5828i	−0.355337	−	0.355337i	−0.862091	+	0.506754i	$0.830845\pi$
$888$	−114.729	+	114.729i	−3.85005	+	3.85005i
$889$		−	5.42582i		−	0.181976i
$890$	40.9799	−	28.0339i	1.37365	−	0.939700i
$891$		0			0
$892$	−71.8515	+	71.8515i	−2.40577	+	2.40577i
$893$	33.9412	−	33.9412i	1.13580	−	1.13580i
$894$		−	57.1578i		−	1.91164i
$895$	1.23732	−	6.59606i	0.0413592	−	0.220482i
$896$	6.05881			0.202411
$897$	25.2456	+	25.2456i	0.842926	+	0.842926i
$898$	71.5637	−	71.5637i	2.38811	−	2.38811i
$899$	3.49077			0.116424
$900$	−77.0770	−	29.9717i	−2.56923	−	0.999055i
$901$			0.865042i			0.0288187i
$902$		0			0
$903$	−4.53866	−	4.53866i	−0.151037	−	0.151037i
$904$	−17.6669			−0.587592
$905$	−22.5155	−	4.22357i	−0.748439	−	0.140396i
$906$	34.9197			1.16013
$907$	−7.39651	+	7.39651i	−0.245597	+	0.245597i	−0.819161	−	0.573564i	$-0.805560\pi$
$907$	−7.39651	+	7.39651i	−0.245597	+	0.245597i	0.573564	+	0.819161i	$0.305560\pi$
$908$	55.8558	−	55.8558i	1.85364	−	1.85364i
$909$	7.96305			0.264118
$910$	−5.15891	−	7.54128i	−0.171016	−	0.249991i
$911$	−1.97645			−0.0654827			−0.0327414	−	0.999464i	$-0.510424\pi$
$911$	−1.97645			−0.0654827			−0.0327414	+	0.999464i	$0.510424\pi$
$912$	46.1287	+	46.1287i	1.52747	+	1.52747i
$913$		0			0
$914$			11.9739i			0.396061i
$915$	54.9927	−	37.6199i	1.81800	−	1.24368i
$916$	68.3790			2.25930
$917$	2.36204	−	2.36204i	0.0780013	−	0.0780013i
$918$	3.53923	+	3.53923i	0.116812	+	0.116812i
$919$	9.38958			0.309734			0.154867	−	0.987935i	$-0.450505\pi$
$919$	9.38958			0.309734			0.154867	+	0.987935i	$0.450505\pi$
$920$	38.0661	+	7.14063i	1.25500	+	0.235420i
$921$			15.7733i			0.519749i
$922$	−42.3925	+	42.3925i	−1.39612	+	1.39612i
$923$	−6.09950	+	6.09950i	−0.200768	+	0.200768i
$924$		0			0
$925$	−50.1594	+	22.0720i	−1.64923	+	0.725722i
$926$		−	42.7654i		−	1.40536i
$927$	−11.9402	+	11.9402i	−0.392168	+	0.392168i
$928$	−1.47961	−	1.47961i	−0.0485706	−	0.0485706i
$929$			16.3765i			0.537295i	0.963239	+	0.268648i	$0.0865767\pi$
$929$			16.3765i			0.537295i	−0.963239	+	0.268648i	$0.913423\pi$
$930$	12.2733	−	65.4281i	0.402459	−	2.14547i
$931$			30.4808i			0.998969i
$932$	−10.0448	−	10.0448i	−0.329028	−	0.329028i
$933$	−54.3330	−	54.3330i	−1.77878	−	1.77878i
$934$	−39.8225			−1.30303
$935$		0			0
$936$	−97.1504			−3.17546
$937$	5.42428	+	5.42428i	0.177204	+	0.177204i	0.790136	−	0.612932i	$-0.210010\pi$
$937$	5.42428	+	5.42428i	0.177204	+	0.177204i	−0.612932	+	0.790136i	$0.710010\pi$
$938$	−3.84661	−	3.84661i	−0.125596	−	0.125596i
$939$		−	36.5695i		−	1.19340i
$940$	58.0737	+	84.8919i	1.89416	+	2.76887i
$941$			52.3639i			1.70701i	0.521082	+	0.853507i	$0.325529\pi$
$941$			52.3639i			1.70701i	−0.521082	+	0.853507i	$0.674471\pi$
$942$	25.7670	+	25.7670i	0.839534	+	0.839534i
$943$	−10.8889	+	10.8889i	−0.354591	+	0.354591i
$944$		−	6.14650i		−	0.200051i
$945$	1.88570	+	0.353730i	0.0613419	+	0.0115068i
$946$		0			0
$947$	−18.6613	+	18.6613i	−0.606410	+	0.606410i	−0.942006	−	0.335596i	$-0.891062\pi$
$947$	−18.6613	+	18.6613i	−0.606410	+	0.606410i	0.335596	+	0.942006i	$0.391062\pi$
$948$	−97.7028	+	97.7028i	−3.17324	+	3.17324i
$949$		−	57.0302i		−	1.85128i
$950$	22.3666	+	50.8289i	0.725668	+	1.64911i
$951$	−18.8965			−0.612762
$952$	1.26484	+	1.26484i	0.0409938	+	0.0409938i
$953$	−0.972028	+	0.972028i	−0.0314871	+	0.0314871i	−0.722675	−	0.691188i	$-0.757088\pi$
$953$	−0.972028	+	0.972028i	−0.0314871	+	0.0314871i	0.691188	+	0.722675i	$0.257088\pi$
$954$	9.77823			0.316582
$955$	30.3347	+	5.69034i	0.981608	+	0.184135i
$956$			1.99061i			0.0643810i
$957$		0			0
$958$	67.1684	+	67.1684i	2.17011	+	2.17011i
$959$	0.0664534			0.00214589
$960$	21.2896	−	14.5640i	0.687119	−	0.470051i
$961$	−10.4266			−0.336343
$962$	−85.8869	+	85.8869i	−2.76910	+	2.76910i
$963$	−34.5801	+	34.5801i	−1.11433	+	1.11433i
$964$	70.3320			2.26524
$965$	−24.9276	+	17.0527i	−0.802447	+	0.548946i
$966$	−7.43071			−0.239079
$967$	−13.4951	−	13.4951i	−0.433974	−	0.433974i	0.456004	−	0.889978i	$-0.349280\pi$
$967$	−13.4951	−	13.4951i	−0.433974	−	0.433974i	−0.889978	+	0.456004i	$0.849280\pi$
$968$		0			0
$969$		−	10.0218i		−	0.321946i
$970$	39.4616	+	7.40242i	1.26704	+	0.237677i
$971$	−36.7311			−1.17876			−0.589379	−	0.807857i	$-0.700628\pi$
$971$	−36.7311			−1.17876			−0.589379	+	0.807857i	$0.700628\pi$
$972$	−64.8599	+	64.8599i	−2.08038	+	2.08038i
$973$	4.99171	+	4.99171i	0.160027	+	0.160027i
$974$	−87.7493			−2.81167
$975$	−54.1870	−	21.0708i	−1.73537	−	0.674806i
$976$		−	63.5632i		−	2.03461i
$977$	25.5024	−	25.5024i	0.815895	−	0.815895i	−0.169615	−	0.985510i	$-0.554252\pi$
$977$	25.5024	−	25.5024i	0.815895	−	0.815895i	0.985510	+	0.169615i	$0.0542524\pi$
$978$	18.3254	−	18.3254i	0.585981	−	0.585981i
$979$		0			0
$980$	−64.1951	−	12.0420i	−2.05064	−	0.384669i
$981$			15.7187i			0.501861i
$982$	−52.0601	+	52.0601i	−1.66130	+	1.66130i
$983$	20.0309	+	20.0309i	0.638886	+	0.638886i	0.950281	−	0.311395i	$-0.100796\pi$
$983$	20.0309	+	20.0309i	0.638886	+	0.638886i	−0.311395	+	0.950281i	$0.600796\pi$
$984$		−	74.2456i		−	2.36686i
$985$	−19.6080	−	28.6629i	−0.624764	−	0.913277i
$986$			1.65535i			0.0527171i
$987$	−7.39575	−	7.39575i	−0.235409	−	0.235409i
$988$	59.2070	+	59.2070i	1.88362	+	1.88362i
$989$	20.3676			0.647651
$990$		0			0
$991$	57.3361			1.82134			0.910671	−	0.413132i	$-0.135565\pi$
$991$	57.3361			1.82134			0.910671	+	0.413132i	$0.135565\pi$
$992$	−8.72031	−	8.72031i	−0.276870	−	0.276870i
$993$	−24.5319	−	24.5319i	−0.778498	−	0.778498i
$994$		−	1.79531i		−	0.0569438i
$995$	6.67791	−	35.5993i	0.211704	−	1.12857i
$996$		−	79.7356i		−	2.52652i
$997$	−10.8951	−	10.8951i	−0.345052	−	0.345052i	0.513210	−	0.858263i	$-0.328456\pi$
$997$	−10.8951	−	10.8951i	−0.345052	−	0.345052i	−0.858263	+	0.513210i	$0.828456\pi$
$998$	49.8762	−	49.8762i	1.57880	−	1.57880i
$999$		−	25.5047i		−	0.806932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.a.483.1	yes	20
5.2	odd	4	inner	605.2.e.a.362.10	yes	20
11.2	odd	10		605.2.m.f.403.1		80
11.3	even	5		605.2.m.f.233.1		80
11.4	even	5		605.2.m.f.578.10		80
11.5	even	5		605.2.m.f.118.10		80
11.6	odd	10		605.2.m.f.118.1		80
11.7	odd	10		605.2.m.f.578.1		80
11.8	odd	10		605.2.m.f.233.10		80
11.9	even	5		605.2.m.f.403.10		80
11.10	odd	2	inner	605.2.e.a.483.10	yes	20
55.2	even	20		605.2.m.f.282.10		80
55.7	even	20		605.2.m.f.457.1		80
55.17	even	20		605.2.m.f.602.10		80
55.27	odd	20		605.2.m.f.602.1		80
55.32	even	4	inner	605.2.e.a.362.1	✓	20
55.37	odd	20		605.2.m.f.457.10		80
55.42	odd	20		605.2.m.f.282.1		80
55.47	odd	20		605.2.m.f.112.1		80
55.52	even	20		605.2.m.f.112.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.1	✓	20	55.32	even	4	inner
605.2.e.a.362.10	yes	20	5.2	odd	4	inner
605.2.e.a.483.1	yes	20	1.1	even	1	trivial
605.2.e.a.483.10	yes	20	11.10	odd	2	inner
605.2.m.f.112.1		80	55.47	odd	20
605.2.m.f.112.10		80	55.52	even	20
605.2.m.f.118.1		80	11.6	odd	10
605.2.m.f.118.10		80	11.5	even	5
605.2.m.f.233.1		80	11.3	even	5
605.2.m.f.233.10		80	11.8	odd	10
605.2.m.f.282.1		80	55.42	odd	20
605.2.m.f.282.10		80	55.2	even	20
605.2.m.f.403.1		80	11.2	odd	10
605.2.m.f.403.10		80	11.9	even	5
605.2.m.f.457.1		80	55.7	even	20
605.2.m.f.457.10		80	55.37	odd	20
605.2.m.f.578.1		80	11.7	odd	10
605.2.m.f.578.10		80	11.4	even	5
605.2.m.f.602.1		80	55.27	odd	20
605.2.m.f.602.10		80	55.17	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76854 - 1.76854i) q^{2} +(1.85563 + 1.85563i) q^{3} +4.25546i q^{4} +(-2.19774 - 0.412263i) q^{5} -6.56351i q^{6} +(0.260724 + 0.260724i) q^{7} +(3.98886 - 3.98886i) q^{8} +3.88674i q^{9} +O(q^{10})\)	\(q+(-1.76854 - 1.76854i) q^{2} +(1.85563 + 1.85563i) q^{3} +4.25546i q^{4} +(-2.19774 - 0.412263i) q^{5} -6.56351i q^{6} +(0.260724 + 0.260724i) q^{7} +(3.98886 - 3.98886i) q^{8} +3.88674i q^{9} +(3.15768 + 4.61588i) q^{10} +(-7.89656 + 7.89656i) q^{12} +(-3.13314 + 3.13314i) q^{13} -0.922200i q^{14} +(-3.31318 - 4.84319i) q^{15} -5.59800 q^{16} +(0.608103 + 0.608103i) q^{17} +(6.87385 - 6.87385i) q^{18} -4.44065 q^{19} +(1.75437 - 9.35237i) q^{20} +0.967614i q^{21} +(-2.17112 - 2.17112i) q^{23} +14.8037 q^{24} +(4.66008 + 1.81209i) q^{25} +11.0822 q^{26} +(-1.64546 + 1.64546i) q^{27} +(-1.10950 + 1.10950i) q^{28} -0.769606 q^{29} +(-2.70589 + 14.4249i) q^{30} -4.53579 q^{31} +(1.92256 + 1.92256i) q^{32} -2.15091i q^{34} +(-0.465515 - 0.680488i) q^{35} -16.5398 q^{36} +(-7.75001 + 7.75001i) q^{37} +(7.85346 + 7.85346i) q^{38} -11.6279 q^{39} +(-10.4109 + 7.12201i) q^{40} -5.01533i q^{41} +(1.71126 - 1.71126i) q^{42} +(-4.69057 + 4.69057i) q^{43} +(1.60236 - 8.54202i) q^{45} +7.67942i q^{46} +(-7.64329 + 7.64329i) q^{47} +(-10.3878 - 10.3878i) q^{48} -6.86405i q^{49} +(-5.03678 - 11.4463i) q^{50} +2.25683i q^{51} +(-13.3330 - 13.3330i) q^{52} +(0.711263 + 0.711263i) q^{53} +5.82012 q^{54} +2.07998 q^{56} +(-8.24021 - 8.24021i) q^{57} +(1.36108 + 1.36108i) q^{58} +1.09798i q^{59} +(20.6100 - 14.0991i) q^{60} +11.3546i q^{61} +(8.02172 + 8.02172i) q^{62} +(-1.01336 + 1.01336i) q^{63} +4.39578i q^{64} +(8.17749 - 5.59414i) q^{65} +(4.17112 - 4.17112i) q^{67} +(-2.58775 + 2.58775i) q^{68} -8.05760i q^{69} +(-0.380189 + 2.02675i) q^{70} +1.94677 q^{71} +(15.5037 + 15.5037i) q^{72} +(-9.10112 + 9.10112i) q^{73} +27.4124 q^{74} +(5.28482 + 12.0100i) q^{75} -18.8970i q^{76} +(20.5644 + 20.5644i) q^{78} +12.3728 q^{79} +(12.3029 + 2.30785i) q^{80} +5.55348 q^{81} +(-8.86981 + 8.86981i) q^{82} +(-5.04875 + 5.04875i) q^{83} -4.11764 q^{84} +(-1.08575 - 1.58715i) q^{85} +16.5909 q^{86} +(-1.42811 - 1.42811i) q^{87} -8.87803i q^{89} +(-17.9407 + 12.2731i) q^{90} -1.63377 q^{91} +(9.23911 - 9.23911i) q^{92} +(-8.41675 - 8.41675i) q^{93} +27.0349 q^{94} +(9.75937 + 1.83071i) q^{95} +7.13511i q^{96} +(5.07639 - 5.07639i) q^{97} +(-12.1393 + 12.1393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^3 + 4 * q^5	\( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

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