LMFDB - Embedded newform 650.2.o.g.549.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(399,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("650.399");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.o (of order $6$, degree $2$, not 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.4
Root			$2.15988 + 0.578737i$ of defining polynomial
Character	$\chi$	$=$	650.549
Dual form			650.2.o.g.399.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(2.73861 - 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(2.73861 - 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +(2.08114 + 3.60464i) q^{11} -3.16228i q^{12} +(-3.60464 - 0.0811388i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00656 - 0.581139i) q^{17} -7.00000i q^{18} +(-4.08114 + 7.06874i) q^{19} +3.16228 q^{21} +(3.60464 + 2.08114i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(-1.58114 - 2.73861i) q^{24} +(-3.16228 + 1.73205i) q^{26} -12.6491i q^{27} +(0.866025 - 0.500000i) q^{28} +(-1.16228 - 2.01312i) q^{29} +0.837722 q^{31} +(-0.866025 - 0.500000i) q^{32} +(11.3989 + 6.58114i) q^{33} -1.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(5.33669 - 3.08114i) q^{37} +8.16228i q^{38} +(-10.0000 + 5.47723i) q^{39} +(-1.16228 - 2.01312i) q^{41} +(2.73861 - 1.58114i) q^{42} +(1.73205 + 1.00000i) q^{43} +4.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} -3.00000i q^{47} +(-2.73861 - 1.58114i) q^{48} +(-3.00000 - 5.19615i) q^{49} -3.67544 q^{51} +(-1.87259 + 3.08114i) q^{52} -4.16228i q^{53} +(-6.32456 - 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} +25.8114i q^{57} +(-2.01312 - 1.16228i) q^{58} +(1.16228 - 2.01312i) q^{59} +(-5.74342 + 9.94789i) q^{61} +(0.725489 - 0.418861i) q^{62} +(6.06218 - 3.50000i) q^{63} -1.00000 q^{64} +13.1623 q^{66} +(8.94133 - 5.16228i) q^{67} +(-1.00656 + 0.581139i) q^{68} +(-9.48683 + 16.4317i) q^{69} +(-4.16228 + 7.20928i) q^{71} +(-6.06218 - 3.50000i) q^{72} -9.16228i q^{73} +(3.08114 - 5.33669i) q^{74} +(4.08114 + 7.06874i) q^{76} +4.16228i q^{77} +(-5.92164 + 9.74342i) q^{78} -5.48683 q^{79} +(-9.50000 - 16.4545i) q^{81} +(-2.01312 - 1.16228i) q^{82} +9.48683i q^{83} +(1.58114 - 2.73861i) q^{84} +2.00000 q^{86} +(-6.36606 - 3.67544i) q^{87} +(3.60464 - 2.08114i) q^{88} +(2.66228 + 4.61120i) q^{89} +(-3.08114 - 1.87259i) q^{91} +6.00000i q^{92} +(2.29420 - 1.32456i) q^{93} +(-1.50000 - 2.59808i) q^{94} -3.16228 q^{96} +(-9.94789 - 5.74342i) q^{97} +(-5.19615 - 3.00000i) q^{98} +29.1359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 28 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 28 * q^9	$ 8 q + 4 q^{4} + 28 q^{9} + 4 q^{11} + 8 q^{14} - 4 q^{16} - 20 q^{19} + 16 q^{29} + 32 q^{31} + 16 q^{34} - 28 q^{36} - 80 q^{39} + 16 q^{41} + 8 q^{44} - 24 q^{46} - 24 q^{49} - 80 q^{51} + 4 q^{56} - 16 q^{59} - 8 q^{61} - 8 q^{64} + 80 q^{66} - 8 q^{71} + 12 q^{74} + 20 q^{76} + 32 q^{79} - 76 q^{81} + 16 q^{86} - 4 q^{89} - 12 q^{91} - 12 q^{94} + 56 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 28 * q^9 + 4 * q^11 + 8 * q^14 - 4 * q^16 - 20 * q^19 + 16 * q^29 + 32 * q^31 + 16 * q^34 - 28 * q^36 - 80 * q^39 + 16 * q^41 + 8 * q^44 - 24 * q^46 - 24 * q^49 - 80 * q^51 + 4 * q^56 - 16 * q^59 - 8 * q^61 - 8 * q^64 + 80 * q^66 - 8 * q^71 + 12 * q^74 + 20 * q^76 + 32 * q^79 - 76 * q^81 + 16 * q^86 - 4 * q^89 - 12 * q^91 - 12 * q^94 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	2.73861	−	1.58114i	1.58114	−	0.912871i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	2.73861	−	1.58114i	1.58114	−	0.912871i	0.994694	−	0.102882i	$-0.0328064\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.58114	−	2.73861i	0.645497	−	1.11803i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$		−	1.00000i		−	0.353553i
$9$	3.50000	−	6.06218i	1.16667	−	2.02073i
$10$		0			0
$11$	2.08114	+	3.60464i	0.627487	+	1.08684i	0.988054	+	0.154106i	$0.0492498\pi$
$11$	2.08114	+	3.60464i	0.627487	+	1.08684i	−0.360567	+	0.932733i	$0.617417\pi$
$12$		−	3.16228i		−	0.912871i
$13$	−3.60464	−	0.0811388i	−0.999747	−	0.0225039i
$13$	−3.60464	−	0.0811388i	−0.999747	−	0.0225039i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00656	−	0.581139i	−0.244127	−	0.140947i	0.372945	−	0.927853i	$-0.378348\pi$
$17$	−1.00656	−	0.581139i	−0.244127	−	0.140947i	−0.617072	+	0.786907i	$0.711681\pi$
$18$		−	7.00000i		−	1.64992i
$19$	−4.08114	+	7.06874i	−0.936277	+	1.62168i	−0.163937	+	0.986471i	$0.552420\pi$
$19$	−4.08114	+	7.06874i	−0.936277	+	1.62168i	−0.772340	+	0.635209i	$0.780914\pi$
$20$		0			0
$21$	3.16228			0.690066
$22$	3.60464	+	2.08114i	0.768511	+	0.443700i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	−1.58114	−	2.73861i	−0.322749	−	0.559017i
$25$		0			0
$26$	−3.16228	+	1.73205i	−0.620174	+	0.339683i
$27$		−	12.6491i		−	2.43432i
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−1.16228	−	2.01312i	−0.215830	−	0.373828i	0.737699	−	0.675129i	$-0.235912\pi$
$29$	−1.16228	−	2.01312i	−0.215830	−	0.373828i	−0.953529	+	0.301302i	$0.902579\pi$
$30$		0			0
$31$	0.837722			0.150459			0.0752297	−	0.997166i	$-0.476031\pi$
$31$	0.837722			0.150459			0.0752297	+	0.997166i	$0.476031\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	11.3989	+	6.58114i	1.98429	+	1.14563i
$34$	−1.16228			−0.199329
$35$		0			0
$36$	−3.50000	−	6.06218i	−0.583333	−	1.01036i
$37$	5.33669	−	3.08114i	0.877346	−	0.506536i	0.00756376	−	0.999971i	$-0.497592\pi$
$37$	5.33669	−	3.08114i	0.877346	−	0.506536i	0.869783	+	0.493435i	$0.164259\pi$
$38$			8.16228i			1.32410i
$39$	−10.0000	+	5.47723i	−1.60128	+	0.877058i
$40$		0			0
$41$	−1.16228	−	2.01312i	−0.181517	−	0.314397i	0.760880	−	0.648892i	$-0.224767\pi$
$41$	−1.16228	−	2.01312i	−0.181517	−	0.314397i	−0.942397	+	0.334495i	$0.891434\pi$
$42$	2.73861	−	1.58114i	0.422577	−	0.243975i
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$	4.16228			0.627487
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	−2.73861	−	1.58114i	−0.395285	−	0.228218i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$		0			0
$51$	−3.67544			−0.514665
$52$	−1.87259	+	3.08114i	−0.259681	+	0.427277i
$53$		−	4.16228i		−	0.571733i	−0.958269	−	0.285866i	$-0.907719\pi$
$53$		−	4.16228i		−	0.571733i	0.958269	−	0.285866i	$-0.0922814\pi$
$54$	−6.32456	−	10.9545i	−0.860663	−	1.49071i
$55$		0			0
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$			25.8114i			3.41880i
$58$	−2.01312	−	1.16228i	−0.264336	−	0.152615i
$59$	1.16228	−	2.01312i	0.151316	−	0.262086i	−0.780396	−	0.625286i	$-0.784982\pi$
$59$	1.16228	−	2.01312i	0.151316	−	0.262086i	0.931711	+	0.363200i	$0.118316\pi$
$60$		0			0
$61$	−5.74342	+	9.94789i	−0.735369	+	1.27370i	0.219192	+	0.975682i	$0.429658\pi$
$61$	−5.74342	+	9.94789i	−0.735369	+	1.27370i	−0.954561	+	0.298015i	$0.903675\pi$
$62$	0.725489	−	0.418861i	0.0921372	−	0.0531954i
$63$	6.06218	−	3.50000i	0.763763	−	0.440959i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	13.1623			1.62016
$67$	8.94133	−	5.16228i	1.09236	−	0.630673i	0.158154	−	0.987414i	$-0.449446\pi$
$67$	8.94133	−	5.16228i	1.09236	−	0.630673i	0.934203	+	0.356742i	$0.116112\pi$
$68$	−1.00656	+	0.581139i	−0.122064	+	0.0704734i
$69$	−9.48683	+	16.4317i	−1.14208	+	1.97814i
$70$		0			0
$71$	−4.16228	+	7.20928i	−0.493971	+	0.855584i	−0.999976	−	0.00694720i	$-0.997789\pi$
$71$	−4.16228	+	7.20928i	−0.493971	+	0.855584i	0.506004	+	0.862531i	$0.331122\pi$
$72$	−6.06218	−	3.50000i	−0.714435	−	0.412479i
$73$		−	9.16228i		−	1.07236i	−0.844103	−	0.536182i	$-0.819866\pi$
$73$		−	9.16228i		−	1.07236i	0.844103	−	0.536182i	$-0.180134\pi$
$74$	3.08114	−	5.33669i	0.358175	−	0.620377i
$75$		0			0
$76$	4.08114	+	7.06874i	0.468139	+	0.810840i
$77$			4.16228i			0.474336i
$78$	−5.92164	+	9.74342i	−0.670494	+	1.10322i
$79$	−5.48683			−0.617317			−0.308658	−	0.951173i	$-0.599880\pi$
$79$	−5.48683			−0.617317			−0.308658	+	0.951173i	$0.599880\pi$
$80$		0			0
$81$	−9.50000	−	16.4545i	−1.05556	−	1.82828i
$82$	−2.01312	−	1.16228i	−0.222312	−	0.128352i
$83$			9.48683i			1.04132i	0.853766	+	0.520658i	$0.174313\pi$
$83$			9.48683i			1.04132i	−0.853766	+	0.520658i	$0.825687\pi$
$84$	1.58114	−	2.73861i	0.172516	−	0.298807i
$85$		0			0
$86$	2.00000			0.215666
$87$	−6.36606	−	3.67544i	−0.682513	−	0.394049i
$88$	3.60464	−	2.08114i	0.384256	−	0.221850i
$89$	2.66228	+	4.61120i	0.282201	+	0.488786i	0.971927	−	0.235285i	$-0.0756022\pi$
$89$	2.66228	+	4.61120i	0.282201	+	0.488786i	−0.689726	+	0.724071i	$0.742269\pi$
$90$		0			0
$91$	−3.08114	−	1.87259i	−0.322991	−	0.196300i
$92$			6.00000i			0.625543i
$93$	2.29420	−	1.32456i	0.237897	−	0.137350i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	−3.16228			−0.322749
$97$	−9.94789	−	5.74342i	−1.01006	−	0.583156i	−0.0988473	−	0.995103i	$-0.531516\pi$
$97$	−9.94789	−	5.74342i	−1.01006	−	0.583156i	−0.911208	+	0.411947i	$0.864849\pi$
$98$	−5.19615	−	3.00000i	−0.524891	−	0.303046i
$99$	29.1359			2.92827
$100$		0			0
$101$	2.41886	+	4.18959i	0.240686	+	0.416880i	0.960910	−	0.276862i	$-0.0892944\pi$
$101$	2.41886	+	4.18959i	0.240686	+	0.416880i	−0.720224	+	0.693741i	$0.755961\pi$
$102$	−3.18303	+	1.83772i	−0.315167	+	0.181962i
$103$		−	13.3246i		−	1.31291i	−0.754366	−	0.656454i	$-0.772056\pi$
$103$		−	13.3246i		−	1.31291i	0.754366	−	0.656454i	$-0.227944\pi$
$104$	−0.0811388	+	3.60464i	−0.00795632	+	0.353464i
$105$		0			0
$106$	−2.08114	−	3.60464i	−0.202138	−	0.350113i
$107$	13.4120	−	7.74342i	1.29659	−	0.748584i	0.316773	−	0.948501i	$-0.397401\pi$
$107$	13.4120	−	7.74342i	1.29659	−	0.748584i	0.979813	+	0.199917i	$0.0640672\pi$
$108$	−10.9545	−	6.32456i	−1.05409	−	0.608581i
$109$	14.6491			1.40313			0.701565	−	0.712605i	$-0.252485\pi$
$109$	14.6491			1.40313			0.701565	+	0.712605i	$0.252485\pi$
$110$		0			0
$111$	9.74342	−	16.8761i	0.924804	−	1.60181i
$112$		−	1.00000i		−	0.0944911i
$113$	14.4186	+	8.32456i	1.35638	+	0.783108i	0.989134	−	0.147014i	$-0.0469664\pi$
$113$	14.4186	+	8.32456i	1.35638	+	0.783108i	0.367249	+	0.930123i	$0.380300\pi$
$114$	12.9057	+	22.3533i	1.20873	+	2.09358i
$115$		0			0
$116$	−2.32456			−0.215830
$117$	−13.1081	+	21.5680i	−1.21185	+	1.99396i
$118$		−	2.32456i		−	0.213993i
$119$	−0.581139	−	1.00656i	−0.0532729	−	0.0922714i
$120$		0			0
$121$	−3.16228	+	5.47723i	−0.287480	+	0.497930i
$122$			11.4868i			1.03997i
$123$	−6.36606	−	3.67544i	−0.574008	−	0.331404i
$124$	0.418861	−	0.725489i	0.0376148	−	0.0651508i
$125$		0			0
$126$	3.50000	−	6.06218i	0.311805	−	0.540062i
$127$	−8.07530	+	4.66228i	−0.716567	+	0.413710i	−0.813488	−	0.581582i	$-0.802434\pi$
$127$	−8.07530	+	4.66228i	−0.716567	+	0.413710i	0.0969207	+	0.995292i	$0.469101\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	6.32456			0.556846
$130$		0			0
$131$	20.8114			1.81830			0.909150	−	0.416469i	$-0.136733\pi$
$131$	20.8114			1.81830			0.909150	+	0.416469i	$0.136733\pi$
$132$	11.3989	−	6.58114i	0.992144	−	0.572815i
$133$	−7.06874	+	4.08114i	−0.612937	+	0.353880i
$134$	5.16228	−	8.94133i	0.445953	−	0.772413i
$135$		0			0
$136$	−0.581139	+	1.00656i	−0.0498322	+	0.0863120i
$137$	3.01969	+	1.74342i	0.257989	+	0.148950i	0.623417	−	0.781890i	$-0.285744\pi$
$137$	3.01969	+	1.74342i	0.257989	+	0.148950i	−0.365428	+	0.930840i	$0.619077\pi$
$138$			18.9737i			1.61515i
$139$	−2.91886	+	5.05562i	−0.247575	+	0.428812i	−0.962852	−	0.270029i	$-0.912967\pi$
$139$	−2.91886	+	5.05562i	−0.247575	+	0.428812i	0.715278	+	0.698840i	$0.246300\pi$
$140$		0			0
$141$	−4.74342	−	8.21584i	−0.399468	−	0.691898i
$142$			8.32456i			0.698581i
$143$	−7.20928	−	13.1623i	−0.602870	−	1.10068i
$144$	−7.00000			−0.583333
$145$		0			0
$146$	−4.58114	−	7.93477i	−0.379138	−	0.656686i
$147$	−16.4317	−	9.48683i	−1.35526	−	0.782461i
$148$		−	6.16228i		−	0.506536i
$149$	1.83772	−	3.18303i	0.150552	−	0.260764i	−0.780878	−	0.624683i	$-0.785228\pi$
$149$	1.83772	−	3.18303i	0.150552	−	0.260764i	0.931431	+	0.363919i	$0.118562\pi$
$150$		0			0
$151$	−11.1623			−0.908373			−0.454187	−	0.890907i	$-0.650070\pi$
$151$	−11.1623			−0.908373			−0.454187	+	0.890907i	$0.650070\pi$
$152$	7.06874	+	4.08114i	0.573351	+	0.331024i
$153$	−7.04593	+	4.06797i	−0.569630	+	0.328876i
$154$	2.08114	+	3.60464i	0.167703	+	0.290470i
$155$		0			0
$156$	−0.256584	+	11.3989i	−0.0205431	+	0.912640i
$157$		−	5.83772i		−	0.465901i	−0.972489	−	0.232950i	$-0.925162\pi$
$157$		−	5.83772i		−	0.465901i	0.972489	−	0.232950i	$-0.0748380\pi$
$158$	−4.75174	+	2.74342i	−0.378028	+	0.218254i
$159$	−6.58114	−	11.3989i	−0.521918	−	0.903989i
$160$		0			0
$161$	−6.00000			−0.472866
$162$	−16.4545	−	9.50000i	−1.29279	−	0.746390i
$163$	−1.28764	−	0.743416i	−0.100855	−	0.0582289i	0.448724	−	0.893670i	$-0.351879\pi$
$163$	−1.28764	−	0.743416i	−0.100855	−	0.0582289i	−0.549579	+	0.835442i	$0.685212\pi$
$164$	−2.32456			−0.181517
$165$		0			0
$166$	4.74342	+	8.21584i	0.368161	+	0.637673i
$167$	0.584952	−	0.337722i	0.0452650	−	0.0261337i	−0.477197	−	0.878796i	$-0.658347\pi$
$167$	0.584952	−	0.337722i	0.0452650	−	0.0261337i	0.522462	+	0.852663i	$0.325014\pi$
$168$		−	3.16228i		−	0.243975i
$169$	12.9868	+	0.584952i	0.998987	+	0.0449963i
$170$		0			0
$171$	28.5680	+	49.4812i	2.18465	+	3.78392i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	−3.60464	−	2.08114i	−0.274056	−	0.158226i	0.356674	−	0.934229i	$-0.383911\pi$
$173$	−3.60464	−	2.08114i	−0.274056	−	0.158226i	−0.630729	+	0.776003i	$0.717244\pi$
$174$	−7.35089			−0.557269
$175$		0			0
$176$	2.08114	−	3.60464i	0.156872	−	0.271710i
$177$		−	7.35089i		−	0.552527i
$178$	4.61120	+	2.66228i	0.345624	+	0.199546i
$179$	4.83772	+	8.37918i	0.361588	+	0.626289i	0.988222	−	0.153024i	$-0.0489013\pi$
$179$	4.83772	+	8.37918i	0.361588	+	0.626289i	−0.626634	+	0.779314i	$0.715568\pi$
$180$		0			0
$181$	−21.8114			−1.62123			−0.810614	−	0.585581i	$-0.800866\pi$
$181$	−21.8114			−1.62123			−0.810614	+	0.585581i	$0.800866\pi$
$182$	−3.60464	−	0.0811388i	−0.267194	−	0.00601441i
$183$			36.3246i			2.68519i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	1.32456	−	2.29420i	0.0971211	−	0.168219i
$187$		−	4.83772i		−	0.353769i
$188$	−2.59808	−	1.50000i	−0.189484	−	0.109399i
$189$	6.32456	−	10.9545i	0.460044	−	0.796819i
$190$		0			0
$191$	4.74342	−	8.21584i	0.343222	−	0.594477i	−0.641807	−	0.766866i	$-0.721815\pi$
$191$	4.74342	−	8.21584i	0.343222	−	0.594477i	0.985029	+	0.172389i	$0.0551485\pi$
$192$	−2.73861	+	1.58114i	−0.197642	+	0.114109i
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	−11.4868			−0.824707
$195$		0			0
$196$	−6.00000			−0.428571
$197$	0.421610	−	0.243416i	0.0300384	−	0.0173427i	−0.484906	−	0.874567i	$-0.661146\pi$
$197$	0.421610	−	0.243416i	0.0300384	−	0.0173427i	0.514944	+	0.857224i	$0.327813\pi$
$198$	25.2325	−	14.5680i	1.79319	−	1.03530i
$199$	−13.3246	+	23.0788i	−0.944553	+	1.63601i	−0.187908	+	0.982187i	$0.560171\pi$
$199$	−13.3246	+	23.0788i	−0.944553	+	1.63601i	−0.756644	+	0.653827i	$0.773163\pi$
$200$		0			0
$201$	16.3246	−	28.2750i	1.15145	−	1.99436i
$202$	4.18959	+	2.41886i	0.294779	+	0.170190i
$203$		−	2.32456i		−	0.163152i
$204$	−1.83772	+	3.18303i	−0.128666	+	0.222857i
$205$		0			0
$206$	−6.66228	−	11.5394i	−0.464183	−	0.803988i
$207$			42.0000i			2.91920i
$208$	1.73205	+	3.16228i	0.120096	+	0.219265i
$209$	−33.9737			−2.35001
$210$		0			0
$211$	−9.08114	−	15.7290i	−0.625171	−	1.08283i	−0.988508	−	0.151171i	$-0.951696\pi$
$211$	−9.08114	−	15.7290i	−0.625171	−	1.08283i	0.363336	−	0.931658i	$-0.381638\pi$
$212$	−3.60464	−	2.08114i	−0.247568	−	0.142933i
$213$			26.3246i			1.80373i
$214$	7.74342	−	13.4120i	0.529329	−	0.916825i
$215$		0			0
$216$	−12.6491			−0.860663
$217$	0.725489	+	0.418861i	0.0492494	+	0.0284341i
$218$	12.6865	−	7.32456i	0.859238	−	0.496081i
$219$	−14.4868	−	25.0919i	−0.978929	−	1.69556i
$220$		0			0
$221$	3.58114	+	2.17647i	0.240893	+	0.146405i
$222$		−	19.4868i		−	1.30787i
$223$	8.07530	−	4.66228i	0.540762	−	0.312209i	−0.204626	−	0.978840i	$-0.565598\pi$
$223$	8.07530	−	4.66228i	0.540762	−	0.312209i	0.745388	+	0.666631i	$0.232264\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	16.6491			1.10748
$227$	2.01312	+	1.16228i	0.133616	+	0.0771431i	0.565318	−	0.824873i	$-0.308754\pi$
$227$	2.01312	+	1.16228i	0.133616	+	0.0771431i	−0.431702	+	0.902016i	$0.642087\pi$
$228$	22.3533	+	12.9057i	1.48038	+	0.854700i
$229$	−9.16228			−0.605460			−0.302730	−	0.953076i	$-0.597898\pi$
$229$	−9.16228			−0.605460			−0.302730	+	0.953076i	$0.597898\pi$
$230$		0			0
$231$	6.58114	+	11.3989i	0.433007	+	0.749990i
$232$	−2.01312	+	1.16228i	−0.132168	+	0.0763073i
$233$			9.48683i			0.621503i	0.950491	+	0.310752i	$0.100581\pi$
$233$			9.48683i			0.621503i	−0.950491	+	0.310752i	$0.899419\pi$
$234$	−0.567972	+	25.2325i	−0.0371295	+	1.64950i
$235$		0			0
$236$	−1.16228	−	2.01312i	−0.0756578	−	0.131043i
$237$	−15.0263	+	8.67544i	−0.976064	+	0.563531i
$238$	−1.00656	−	0.581139i	−0.0652457	−	0.0376696i
$239$	−4.83772			−0.312926			−0.156463	−	0.987684i	$-0.550009\pi$
$239$	−4.83772			−0.312926			−0.156463	+	0.987684i	$0.550009\pi$
$240$		0			0
$241$	−5.98683	+	10.3695i	−0.385646	+	0.667958i	−0.991859	−	0.127344i	$-0.959355\pi$
$241$	−5.98683	+	10.3695i	−0.385646	+	0.667958i	0.606213	+	0.795303i	$0.292688\pi$
$242$			6.32456i			0.406558i
$243$	−19.1703	−	11.0680i	−1.22977	−	0.710011i
$244$	5.74342	+	9.94789i	0.367685	+	0.636848i
$245$		0			0
$246$	−7.35089			−0.468676
$247$	15.2846	−	25.1491i	0.972534	−	1.60020i
$248$		−	0.837722i		−	0.0531954i
$249$	15.0000	+	25.9808i	0.950586	+	1.64646i
$250$		0			0
$251$	3.24342	−	5.61776i	0.204723	−	0.354590i	−0.745322	−	0.666705i	$-0.767704\pi$
$251$	3.24342	−	5.61776i	0.204723	−	0.354590i	0.950044	+	0.312115i	$0.101037\pi$
$252$		−	7.00000i		−	0.440959i
$253$	−21.6278	−	12.4868i	−1.35973	−	0.785040i
$254$	−4.66228	+	8.07530i	−0.292537	+	0.506689i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	5.47723	−	3.16228i	0.340997	−	0.196875i
$259$	6.16228			0.382905
$260$		0			0
$261$	−16.2719			−1.00720
$262$	18.0232	−	10.4057i	1.11348	−	0.642866i
$263$	−11.8205	+	6.82456i	−0.728882	+	0.420820i	−0.818013	−	0.575200i	$-0.804924\pi$
$263$	−11.8205	+	6.82456i	−0.728882	+	0.420820i	0.0891312	+	0.996020i	$0.471591\pi$
$264$	6.58114	−	11.3989i	0.405041	−	0.701552i
$265$		0			0
$266$	−4.08114	+	7.06874i	−0.250231	+	0.433412i
$267$	14.5819	+	8.41886i	0.892397	+	0.515226i
$268$		−	10.3246i		−	0.630673i
$269$	10.7434	−	18.6081i	0.655038	−	1.13456i	−0.326847	−	0.945077i	$-0.605986\pi$
$269$	10.7434	−	18.6081i	0.655038	−	1.13456i	0.981884	−	0.189481i	$-0.0606806\pi$
$270$		0			0
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	0.945944	−	0.324329i	$-0.105139\pi$
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	−0.753850	+	0.657047i	$0.771805\pi$
$272$			1.16228i			0.0704734i
$273$	−11.3989	−	0.256584i	−0.689891	−	0.0155291i
$274$	3.48683			0.210647
$275$		0			0
$276$	9.48683	+	16.4317i	0.571040	+	0.989071i
$277$	−17.7421	−	10.2434i	−1.06602	−	0.615467i	−0.138929	−	0.990302i	$-0.544366\pi$
$277$	−17.7421	−	10.2434i	−1.06602	−	0.615467i	−0.927092	+	0.374835i	$0.877699\pi$
$278$			5.83772i			0.350123i
$279$	2.93203	−	5.07842i	0.175536	−	0.304037i
$280$		0			0
$281$	18.9737			1.13187			0.565937	−	0.824448i	$-0.308515\pi$
$281$	18.9737			1.13187			0.565937	+	0.824448i	$0.308515\pi$
$282$	−8.21584	−	4.74342i	−0.489246	−	0.282466i
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.187980	−	0.982173i	$-0.439806\pi$
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.944577	+	0.328291i	$0.106473\pi$
$284$	4.16228	+	7.20928i	0.246986	+	0.427792i
$285$		0			0
$286$	−12.8246	−	7.79423i	−0.758332	−	0.460882i
$287$		−	2.32456i		−	0.137214i
$288$	−6.06218	+	3.50000i	−0.357217	+	0.206239i
$289$	−7.82456	−	13.5525i	−0.460268	−	0.797207i
$290$		0			0
$291$	−36.3246			−2.12938
$292$	−7.93477	−	4.58114i	−0.464347	−	0.268091i
$293$	−24.3892	−	14.0811i	−1.42484	−	0.822629i	−0.428128	−	0.903718i	$-0.640827\pi$
$293$	−24.3892	−	14.0811i	−1.42484	−	0.822629i	−0.996707	+	0.0810891i	$0.974160\pi$
$294$	−18.9737			−1.10657
$295$		0			0
$296$	−3.08114	−	5.33669i	−0.179088	−	0.310189i
$297$	45.5955	−	26.3246i	2.64572	−	1.52751i
$298$		−	3.67544i		−	0.212913i
$299$	18.9737	−	10.3923i	1.09728	−	0.601003i
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−9.66682	+	5.58114i	−0.556263	+	0.321158i
$303$	13.2486	+	7.64911i	0.761115	+	0.439430i
$304$	8.16228			0.468139
$305$		0			0
$306$	−4.06797	+	7.04593i	−0.232550	+	0.402789i
$307$			28.3246i			1.61657i	0.588793	+	0.808284i	$0.299603\pi$
$307$			28.3246i			1.61657i	−0.588793	+	0.808284i	$0.700397\pi$
$308$	3.60464	+	2.08114i	0.205393	+	0.118584i
$309$	−21.0680	−	36.4908i	−1.19852	−	2.07589i
$310$		0			0
$311$	15.4868			0.878178			0.439089	−	0.898444i	$-0.355301\pi$
$311$	15.4868			0.878178			0.439089	+	0.898444i	$0.355301\pi$
$312$	5.47723	+	10.0000i	0.310087	+	0.566139i
$313$		−	4.32456i		−	0.244438i	−0.992503	−	0.122219i	$-0.960999\pi$
$313$		−	4.32456i		−	0.244438i	0.992503	−	0.122219i	$-0.0390011\pi$
$314$	−2.91886	−	5.05562i	−0.164721	−	0.285305i
$315$		0			0
$316$	−2.74342	+	4.75174i	−0.154329	+	0.267306i
$317$		−	6.48683i		−	0.364337i	−0.983267	−	0.182168i	$-0.941688\pi$
$317$		−	6.48683i		−	0.364337i	0.983267	−	0.182168i	$-0.0583116\pi$
$318$	−11.3989	−	6.58114i	−0.639217	−	0.369052i
$319$	4.83772	−	8.37918i	0.270860	−	0.469144i
$320$		0			0
$321$	24.4868	−	42.4124i	1.36672	−	2.36723i
$322$	−5.19615	+	3.00000i	−0.289570	+	0.167183i
$323$	8.21584	−	4.74342i	0.457141	−	0.263931i
$324$	−19.0000			−1.05556
$325$		0			0
$326$	−1.48683			−0.0823481
$327$	40.1182	−	23.1623i	2.21854	−	1.28088i
$328$	−2.01312	+	1.16228i	−0.111156	+	0.0641760i
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$		0			0
$331$	−0.324555	+	0.562146i	−0.0178392	+	0.0308984i	−0.874807	−	0.484471i	$-0.839012\pi$
$331$	−0.324555	+	0.562146i	−0.0178392	+	0.0308984i	0.856968	+	0.515370i	$0.172345\pi$
$332$	8.21584	+	4.74342i	0.450903	+	0.260329i
$333$		−	43.1359i		−	2.36384i
$334$	0.337722	−	0.584952i	0.0184793	−	0.0320072i
$335$		0			0
$336$	−1.58114	−	2.73861i	−0.0862582	−	0.149404i
$337$		−	1.48683i		−	0.0809930i	−0.999180	−	0.0404965i	$-0.987106\pi$
$337$		−	1.48683i		−	0.0809930i	0.999180	−	0.0404965i	$-0.0128940\pi$
$338$	11.5394	−	5.98683i	0.627661	−	0.325641i
$339$	52.6491			2.85951
$340$		0			0
$341$	1.74342	+	3.01969i	0.0944113	+	0.163525i
$342$	49.4812	+	28.5680i	2.67564	+	1.54478i
$343$		−	13.0000i		−	0.701934i
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$		0			0
$346$	−4.16228			−0.223765
$347$	−18.6081	−	10.7434i	−0.998937	−	0.576737i	−0.0910037	−	0.995851i	$-0.529008\pi$
$347$	−18.6081	−	10.7434i	−0.998937	−	0.576737i	−0.907934	+	0.419114i	$0.862341\pi$
$348$	−6.36606	+	3.67544i	−0.341256	+	0.197025i
$349$	−0.743416	−	1.28764i	−0.0397942	−	0.0689255i	0.845442	−	0.534067i	$-0.179337\pi$
$349$	−0.743416	−	1.28764i	−0.0397942	−	0.0689255i	−0.885237	+	0.465141i	$0.846004\pi$
$350$		0			0
$351$	−1.02633	+	45.5955i	−0.0547817	+	2.43371i
$352$		−	4.16228i		−	0.221850i
$353$	1.00656	−	0.581139i	0.0535739	−	0.0309309i	−0.472974	−	0.881076i	$-0.656819\pi$
$353$	1.00656	−	0.581139i	0.0535739	−	0.0309309i	0.526548	+	0.850146i	$0.323486\pi$
$354$	−3.67544	−	6.36606i	−0.195348	−	0.338352i
$355$		0			0
$356$	5.32456			0.282201
$357$	−3.18303	−	1.83772i	−0.168464	−	0.0972626i
$358$	8.37918	+	4.83772i	0.442853	+	0.255682i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	−23.8114	−	41.2425i	−1.25323	−	2.17066i
$362$	−18.8892	+	10.9057i	−0.992795	+	0.573191i
$363$			20.0000i			1.04973i
$364$	−3.16228	+	1.73205i	−0.165748	+	0.0907841i
$365$		0			0
$366$	18.1623	+	31.4580i	0.949357	+	1.64434i
$367$	−17.8827	+	10.3246i	−0.933467	+	0.538937i	−0.887906	−	0.460024i	$-0.847841\pi$
$367$	−17.8827	+	10.3246i	−0.933467	+	0.538937i	−0.0455606	+	0.998962i	$0.514507\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$	−16.2719			−0.847081
$370$		0			0
$371$	2.08114	−	3.60464i	0.108047	−	0.187143i
$372$		−	2.64911i		−	0.137350i
$373$	−4.63401	−	2.67544i	−0.239940	−	0.138529i	0.375209	−	0.926940i	$-0.377571\pi$
$373$	−4.63401	−	2.67544i	−0.239940	−	0.138529i	−0.615149	+	0.788411i	$0.710904\pi$
$374$	−2.41886	−	4.18959i	−0.125076	−	0.216639i
$375$		0			0
$376$	−3.00000			−0.154713
$377$	4.02625	+	7.35089i	0.207362	+	0.378590i
$378$		−	12.6491i		−	0.650600i
$379$	−3.59431	−	6.22552i	−0.184627	−	0.319784i	0.758824	−	0.651296i	$-0.225774\pi$
$379$	−3.59431	−	6.22552i	−0.184627	−	0.319784i	−0.943451	+	0.331513i	$0.892441\pi$
$380$		0			0
$381$	−14.7434	+	25.5363i	−0.755328	+	1.30827i
$382$		−	9.48683i		−	0.485389i
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.984921	−	0.173005i	$-0.0553476\pi$
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.342634	+	0.939469i	$0.388681\pi$
$384$	−1.58114	+	2.73861i	−0.0806872	+	0.139754i
$385$		0			0
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$	12.1244	−	7.00000i	0.616316	−	0.355830i
$388$	−9.94789	+	5.74342i	−0.505028	+	0.291578i
$389$	−19.1623			−0.971566			−0.485783	−	0.874079i	$-0.661465\pi$
$389$	−19.1623			−0.971566			−0.485783	+	0.874079i	$0.661465\pi$
$390$		0			0
$391$	6.97367			0.352673
$392$	−5.19615	+	3.00000i	−0.262445	+	0.151523i
$393$	56.9943	−	32.9057i	2.87498	−	1.65987i
$394$	0.243416	−	0.421610i	0.0122631	−	0.0212404i
$395$		0			0
$396$	14.5680	−	25.2325i	0.732068	−	1.26798i
$397$	−16.8989	−	9.75658i	−0.848131	−	0.489669i	0.0118885	−	0.999929i	$-0.496216\pi$
$397$	−16.8989	−	9.75658i	−0.848131	−	0.489669i	−0.860020	+	0.510260i	$0.829549\pi$
$398$			26.6491i			1.33580i
$399$	−12.9057	+	22.3533i	−0.646093	+	1.11907i
$400$		0			0
$401$	7.98683	+	13.8336i	0.398843	+	0.690817i	0.993583	−	0.113101i	$-0.0360784\pi$
$401$	7.98683	+	13.8336i	0.398843	+	0.690817i	−0.594740	+	0.803918i	$0.702745\pi$
$402$		−	32.6491i		−	1.62839i
$403$	−3.01969	−	0.0679718i	−0.150421	−	0.00338592i
$404$	4.83772			0.240686
$405$		0			0
$406$	−1.16228	−	2.01312i	−0.0576829	−	0.0999097i
$407$	22.2128	+	12.8246i	1.10105	+	0.635690i
$408$			3.67544i			0.181962i
$409$	1.82456	−	3.16022i	0.0902185	−	0.156263i	−0.817385	−	0.576092i	$-0.804577\pi$
$409$	1.82456	−	3.16022i	0.0902185	−	0.156263i	0.907603	+	0.419830i	$0.137910\pi$
$410$		0			0
$411$	11.0263			0.543889
$412$	−11.5394	−	6.66228i	−0.568506	−	0.328227i
$413$	2.01312	−	1.16228i	0.0990594	−	0.0571919i
$414$	21.0000	+	36.3731i	1.03209	+	1.78764i
$415$		0			0
$416$	3.08114	+	1.87259i	0.151065	+	0.0918112i
$417$			18.4605i			0.904015i
$418$	−29.4221	+	16.9868i	−1.43908	+	0.830853i
$419$	−5.32456	−	9.22240i	−0.260122	−	0.450544i	0.706152	−	0.708060i	$-0.250429\pi$
$419$	−5.32456	−	9.22240i	−0.260122	−	0.450544i	−0.966274	+	0.257516i	$0.917096\pi$
$420$		0			0
$421$	3.16228			0.154120			0.0770600	−	0.997026i	$-0.475447\pi$
$421$	3.16228			0.154120			0.0770600	+	0.997026i	$0.475447\pi$
$422$	−15.7290	−	9.08114i	−0.765675	−	0.442063i
$423$	−18.1865	−	10.5000i	−0.884260	−	0.510527i
$424$	−4.16228			−0.202138
$425$		0			0
$426$	13.1623	+	22.7977i	0.637714	+	1.10455i
$427$	−9.94789	+	5.74342i	−0.481412	+	0.277943i
$428$		−	15.4868i		−	0.748584i
$429$	−40.5548	−	24.6475i	−1.95800	−	1.18999i
$430$		0			0
$431$	1.74342	+	3.01969i	0.0839774	+	0.145453i	0.904955	−	0.425507i	$-0.139904\pi$
$431$	1.74342	+	3.01969i	0.0839774	+	0.145453i	−0.820978	+	0.570960i	$0.806571\pi$
$432$	−10.9545	+	6.32456i	−0.527046	+	0.304290i
$433$	−5.47723	−	3.16228i	−0.263219	−	0.151969i	0.362583	−	0.931951i	$-0.381895\pi$
$433$	−5.47723	−	3.16228i	−0.263219	−	0.151969i	−0.625802	+	0.779982i	$0.715228\pi$
$434$	0.837722			0.0402120
$435$		0			0
$436$	7.32456	−	12.6865i	0.350783	−	0.607573i
$437$		−	48.9737i		−	2.34273i
$438$	−25.0919	−	14.4868i	−1.19894	−	0.692208i
$439$	−13.9057	−	24.0854i	−0.663683	−	1.14953i	−0.979641	−	0.200759i	$-0.935659\pi$
$439$	−13.9057	−	24.0854i	−0.663683	−	1.14953i	0.315958	−	0.948773i	$-0.397674\pi$
$440$		0			0
$441$	−42.0000			−2.00000
$442$	4.18959	+	0.0943058i	0.199278	+	0.00448567i
$443$		−	1.35089i		−	0.0641827i	−0.999485	−	0.0320913i	$-0.989783\pi$
$443$		−	1.35089i		−	0.0641827i	0.999485	−	0.0320913i	$-0.0102167\pi$
$444$	−9.74342	−	16.8761i	−0.462402	−	0.800904i
$445$		0			0
$446$	4.66228	−	8.07530i	0.220765	−	0.382377i
$447$		−	11.6228i		−	0.549738i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−19.9868	+	34.6182i	−0.943237	+	1.63373i	−0.183994	+	0.982927i	$0.558903\pi$
$449$	−19.9868	+	34.6182i	−0.943237	+	1.63373i	−0.759243	+	0.650807i	$0.774431\pi$
$450$		0			0
$451$	4.83772	−	8.37918i	0.227799	−	0.394560i
$452$	14.4186	−	8.32456i	0.678192	−	0.391554i
$453$	−30.5692	+	17.6491i	−1.43626	+	0.829228i
$454$	2.32456			0.109097
$455$		0			0
$456$	25.8114			1.20873
$457$	−28.1116	+	16.2302i	−1.31501	+	0.759219i	−0.982921	−	0.184030i	$-0.941086\pi$
$457$	−28.1116	+	16.2302i	−1.31501	+	0.759219i	−0.332085	+	0.943249i	$0.607752\pi$
$458$	−7.93477	+	4.58114i	−0.370767	+	0.214063i
$459$	−7.35089	+	12.7321i	−0.343110	+	0.594284i
$460$		0			0
$461$	−1.25658	+	2.17647i	−0.0585249	+	0.101368i	−0.893803	−	0.448459i	$-0.851973\pi$
$461$	−1.25658	+	2.17647i	−0.0585249	+	0.101368i	0.835279	+	0.549827i	$0.185306\pi$
$462$	11.3989	+	6.58114i	0.530323	+	0.306182i
$463$			0.324555i			0.0150834i	0.999972	+	0.00754168i	$0.00240061\pi$
$463$			0.324555i			0.0150834i	−0.999972	+	0.00754168i	$0.997599\pi$
$464$	−1.16228	+	2.01312i	−0.0539574	+	0.0934569i
$465$		0			0
$466$	4.74342	+	8.21584i	0.219735	+	0.380591i
$467$			7.35089i			0.340159i	0.985430	+	0.170079i	$0.0544024\pi$
$467$			7.35089i			0.340159i	−0.985430	+	0.170079i	$0.945598\pi$
$468$	12.1244	+	22.1359i	0.560449	+	1.02323i
$469$	10.3246			0.476744
$470$		0			0
$471$	−9.23025	−	15.9873i	−0.425307	−	0.736654i
$472$	−2.01312	−	1.16228i	−0.0926615	−	0.0534982i
$473$			8.32456i			0.382763i
$474$	−8.67544	+	15.0263i	−0.398476	+	0.690181i
$475$		0			0
$476$	−1.16228			−0.0532729
$477$	−25.2325	−	14.5680i	−1.15532	−	0.667022i
$478$	−4.18959	+	2.41886i	−0.191627	+	0.110636i
$479$	16.0680	+	27.8305i	0.734164	+	1.27161i	0.955089	+	0.296319i	$0.0957592\pi$
$479$	16.0680	+	27.8305i	0.734164	+	1.27161i	−0.220925	+	0.975291i	$0.570907\pi$
$480$		0			0
$481$	−19.4868	+	10.6734i	−0.888523	+	0.486664i
$482$			11.9737i			0.545386i
$483$	−16.4317	+	9.48683i	−0.747667	+	0.431666i
$484$	3.16228	+	5.47723i	0.143740	+	0.248965i
$485$		0			0
$486$	−22.1359			−1.00411
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	0.519493	−	0.854475i	$-0.326121\pi$
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	−0.480250	+	0.877132i	$0.659454\pi$
$488$	9.94789	+	5.74342i	0.450320	+	0.259992i
$489$	−4.70178			−0.212622
$490$		0			0
$491$	−18.2434	−	31.5985i	−0.823314	−	1.42602i	−0.903201	−	0.429218i	$-0.858789\pi$
$491$	−18.2434	−	31.5985i	−0.823314	−	1.42602i	0.0798873	−	0.996804i	$-0.474544\pi$
$492$	−6.36606	+	3.67544i	−0.287004	+	0.165702i
$493$			2.70178i			0.121682i
$494$	0.662278	−	29.4221i	0.0297973	−	1.32376i
$495$		0			0
$496$	−0.418861	−	0.725489i	−0.0188074	−	0.0325754i
$497$	−7.20928	+	4.16228i	−0.323380	+	0.186704i
$498$	25.9808	+	15.0000i	1.16423	+	0.672166i
$499$	22.0000			0.984855			0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000			0.984855			0.492428	+	0.870353i	$0.336110\pi$
$500$		0			0
$501$	1.06797	−	1.84978i	0.0477135	−	0.0826421i
$502$		−	6.48683i		−	0.289522i
$503$	31.4352	+	18.1491i	1.40163	+	0.809229i	0.994560	−	0.104170i	$-0.0332186\pi$
$503$	31.4352	+	18.1491i	1.40163	+	0.809229i	0.407066	+	0.913399i	$0.366552\pi$
$504$	−3.50000	−	6.06218i	−0.155902	−	0.270031i
$505$		0			0
$506$	−24.9737			−1.11021
$507$	36.4908	−	18.9320i	1.62061	−	0.840801i
$508$			9.32456i			0.413710i
$509$	18.4868	+	32.0201i	0.819414	+	1.41927i	0.906114	+	0.423033i	$0.139035\pi$
$509$	18.4868	+	32.0201i	0.819414	+	1.41927i	−0.0866998	+	0.996234i	$0.527632\pi$
$510$		0			0
$511$	4.58114	−	7.93477i	0.202658	−	0.351013i
$512$			1.00000i			0.0441942i
$513$	89.4133	+	51.6228i	3.94769	+	2.27920i
$514$		0			0
$515$		0			0
$516$	3.16228	−	5.47723i	0.139212	−	0.241121i
$517$	10.8139	−	6.24342i	0.475595	−	0.274585i
$518$	5.33669	−	3.08114i	0.234481	−	0.135377i
$519$	−13.1623			−0.577760
$520$		0			0
$521$	35.3246			1.54760			0.773798	−	0.633432i	$-0.218354\pi$
$521$	35.3246			1.54760			0.773798	+	0.633432i	$0.218354\pi$
$522$	−14.0919	+	8.13594i	−0.616784	+	0.356101i
$523$	−9.78455	+	5.64911i	−0.427848	+	0.247018i	−0.698430	−	0.715679i	$-0.746117\pi$
$523$	−9.78455	+	5.64911i	−0.427848	+	0.247018i	0.270581	+	0.962697i	$0.412784\pi$
$524$	10.4057	−	18.0232i	0.454575	−	0.787347i
$525$		0			0
$526$	−6.82456	+	11.8205i	−0.297565	+	0.515397i
$527$	−0.843219	−	0.486833i	−0.0367312	−	0.0212068i
$528$		−	13.1623i		−	0.572815i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	−8.13594	−	14.0919i	−0.353070	−	0.611535i
$532$			8.16228i			0.353880i
$533$	4.02625	+	7.35089i	0.174396	+	0.318402i
$534$	16.8377			0.728640
$535$		0			0
$536$	−5.16228	−	8.94133i	−0.222976	−	0.386207i
$537$	26.4973	+	15.2982i	1.14344	+	0.660167i
$538$		−	21.4868i		−	0.926363i
$539$	12.4868	−	21.6278i	0.537846	−	0.931577i
$540$		0			0
$541$	33.1623			1.42576			0.712879	−	0.701287i	$-0.247391\pi$
$541$	33.1623			1.42576			0.712879	+	0.701287i	$0.247391\pi$
$542$	5.47723	+	3.16228i	0.235267	+	0.135831i
$543$	−59.7329	+	34.4868i	−2.56339	+	1.47997i
$544$	0.581139	+	1.00656i	0.0249161	+	0.0431560i
$545$		0			0
$546$	−10.0000	+	5.47723i	−0.427960	+	0.234404i
$547$			18.6491i			0.797378i	0.917086	+	0.398689i	$0.130535\pi$
$547$			18.6491i			0.797378i	−0.917086	+	0.398689i	$0.869465\pi$
$548$	3.01969	−	1.74342i	0.128995	−	0.0744751i
$549$	40.2039	+	69.6352i	1.71586	+	2.97196i
$550$		0			0
$551$	18.9737			0.808305
$552$	16.4317	+	9.48683i	0.699379	+	0.403786i
$553$	−4.75174	−	2.74342i	−0.202064	−	0.116662i
$554$	−20.4868			−0.870402
$555$		0			0
$556$	2.91886	+	5.05562i	0.123787	+	0.214406i
$557$	19.1931	−	11.0811i	0.813238	−	0.469523i	−0.0348414	−	0.999393i	$-0.511093\pi$
$557$	19.1931	−	11.0811i	0.813238	−	0.469523i	0.848079	+	0.529870i	$0.177759\pi$
$558$		−	5.86406i		−	0.248245i
$559$	−6.16228	−	3.74517i	−0.260637	−	0.158404i
$560$		0			0
$561$	−7.64911	−	13.2486i	−0.322946	−	0.559358i
$562$	16.4317	−	9.48683i	0.693128	−	0.400178i
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.00664037	−	0.999978i	$-0.502114\pi$
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.869326	+	0.494238i	$0.835447\pi$
$564$	−9.48683			−0.399468
$565$		0			0
$566$	11.0000	−	19.0526i	0.462364	−	0.800839i
$567$		−	19.0000i		−	0.797925i
$568$	7.20928	+	4.16228i	0.302495	+	0.174645i
$569$	1.98683	+	3.44130i	0.0832924	+	0.144267i	0.904662	−	0.426129i	$-0.140123\pi$
$569$	1.98683	+	3.44130i	0.0832924	+	0.144267i	−0.821370	+	0.570396i	$0.806790\pi$
$570$		0			0
$571$	19.1359			0.800814			0.400407	−	0.916337i	$-0.368869\pi$
$571$	19.1359			0.800814			0.400407	+	0.916337i	$0.368869\pi$
$572$	−15.0035	−	0.337722i	−0.627328	−	0.0141209i
$573$		−	30.0000i		−	1.25327i
$574$	−1.16228	−	2.01312i	−0.0485125	−	0.0840262i
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$			0.837722i			0.0348748i	0.999848	+	0.0174374i	$0.00555078\pi$
$577$			0.837722i			0.0348748i	−0.999848	+	0.0174374i	$0.994449\pi$
$578$	−13.5525	−	7.82456i	−0.563711	−	0.325459i
$579$	6.32456	−	10.9545i	0.262840	−	0.455251i
$580$		0			0
$581$	−4.74342	+	8.21584i	−0.196790	+	0.340850i
$582$	−31.4580	+	18.1623i	−1.30398	+	0.752851i
$583$	15.0035	−	8.66228i	0.621382	−	0.358755i
$584$	−9.16228			−0.379138
$585$		0			0
$586$	−28.1623			−1.16337
$587$	−21.6278	+	12.4868i	−0.892676	+	0.515387i	−0.874817	−	0.484454i	$-0.839018\pi$
$587$	−21.6278	+	12.4868i	−0.892676	+	0.515387i	−0.0178592	+	0.999841i	$0.505685\pi$
$588$	−16.4317	+	9.48683i	−0.677631	+	0.391230i
$589$	−3.41886	+	5.92164i	−0.140872	+	0.243997i
$590$		0			0
$591$	0.769751	−	1.33325i	0.0316633	−	0.0548425i
$592$	−5.33669	−	3.08114i	−0.219337	−	0.126634i
$593$			28.6491i			1.17648i	0.808687	+	0.588239i	$0.200179\pi$
$593$			28.6491i			1.17648i	−0.808687	+	0.588239i	$0.799821\pi$
$594$	26.3246	−	45.5955i	1.08011	−	1.87080i
$595$		0			0
$596$	−1.83772	−	3.18303i	−0.0752760	−	0.130382i
$597$			84.2719i			3.44902i
$598$	11.2355	−	18.4868i	0.459455	−	0.755983i
$599$	31.9473			1.30533			0.652666	−	0.757646i	$-0.273650\pi$
$599$	31.9473			1.30533			0.652666	+	0.757646i	$0.273650\pi$
$600$		0			0
$601$	8.14911	+	14.1147i	0.332409	+	0.575750i	0.982984	−	0.183693i	$-0.0588052\pi$
$601$	8.14911	+	14.1147i	0.332409	+	0.575750i	−0.650575	+	0.759442i	$0.725472\pi$
$602$	1.73205	+	1.00000i	0.0705931	+	0.0407570i
$603$		−	72.2719i		−	2.94314i
$604$	−5.58114	+	9.66682i	−0.227093	+	0.393337i
$605$		0			0
$606$	15.2982			0.621448
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	0.409542	−	0.912291i	$-0.365689\pi$
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	−0.585296	+	0.810819i	$0.699022\pi$
$608$	7.06874	−	4.08114i	0.286675	−	0.165512i
$609$	−3.67544	−	6.36606i	−0.148937	−	0.257966i
$610$		0			0
$611$	−0.243416	+	10.8139i	−0.00984758	+	0.437484i
$612$			8.13594i			0.328876i
$613$	−1.31044	+	0.756584i	−0.0529282	+	0.0305581i	−0.526231	−	0.850342i	$-0.676395\pi$
$613$	−1.31044	+	0.756584i	−0.0529282	+	0.0305581i	0.473302	+	0.880900i	$0.343062\pi$
$614$	14.1623	+	24.5298i	0.571543	+	0.989942i
$615$		0			0
$616$	4.16228			0.167703
$617$	−38.0595	−	21.9737i	−1.53222	−	0.884626i	−0.999259	−	0.0384853i	$-0.987747\pi$
$617$	−38.0595	−	21.9737i	−1.53222	−	0.884626i	−0.532959	−	0.846141i	$-0.678920\pi$
$618$	−36.4908	−	21.0680i	−1.46788	−	0.847478i
$619$	−27.4605			−1.10373			−0.551865	−	0.833933i	$-0.686084\pi$
$619$	−27.4605			−1.10373			−0.551865	+	0.833933i	$0.686084\pi$
$620$		0			0
$621$	37.9473	+	65.7267i	1.52277	+	2.63752i
$622$	13.4120	−	7.74342i	0.537772	−	0.310483i
$623$			5.32456i			0.213324i
$624$	9.74342	+	5.92164i	0.390049	+	0.237055i
$625$		0			0
$626$	−2.16228	−	3.74517i	−0.0864220	−	0.149687i
$627$	−93.0407	+	53.7171i	−3.71569	+	2.14525i
$628$	−5.05562	−	2.91886i	−0.201741	−	0.116475i
$629$	−7.16228			−0.285579
$630$		0			0
$631$	0.837722	−	1.45098i	0.0333492	−	0.0577625i	−0.848869	−	0.528603i	$-0.822716\pi$
$631$	0.837722	−	1.45098i	0.0333492	−	0.0577625i	0.882218	+	0.470841i	$0.156049\pi$
$632$			5.48683i			0.218254i
$633$	−49.7394	−	28.7171i	−1.97697	−	1.14140i
$634$	−3.24342	−	5.61776i	−0.128813	−	0.223110i
$635$		0			0
$636$	−13.1623			−0.521918
$637$	10.3923	+	18.9737i	0.411758	+	0.751764i
$638$		−	9.67544i		−	0.383055i
$639$	29.1359	+	50.4649i	1.15260	+	1.99636i
$640$		0			0
$641$	−13.9868	+	24.2259i	−0.552447	+	0.956866i	0.445651	+	0.895207i	$0.352972\pi$
$641$	−13.9868	+	24.2259i	−0.552447	+	0.956866i	−0.998097	+	0.0616587i	$0.980361\pi$
$642$		−	48.9737i		−	1.93284i
$643$	−38.5039	−	22.2302i	−1.51845	−	0.876675i	−0.999764	−	0.0217083i	$-0.993089\pi$
$643$	−38.5039	−	22.2302i	−1.51845	−	0.876675i	−0.518682	−	0.854967i	$-0.673577\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$	4.74342	−	8.21584i	0.186627	−	0.323248i
$647$	19.0298	−	10.9868i	0.748137	−	0.431937i	−0.0768835	−	0.997040i	$-0.524497\pi$
$647$	19.0298	−	10.9868i	0.748137	−	0.431937i	0.825020	+	0.565103i	$0.191164\pi$
$648$	−16.4545	+	9.50000i	−0.646393	+	0.373195i
$649$	9.67544			0.379794
$650$		0			0
$651$	2.64911			0.103827
$652$	−1.28764	+	0.743416i	−0.0504277	+	0.0291144i
$653$	−31.5985	+	18.2434i	−1.23655	+	0.713920i	−0.968387	−	0.249455i	$-0.919749\pi$
$653$	−31.5985	+	18.2434i	−1.23655	+	0.713920i	−0.268159	+	0.963375i	$0.586415\pi$
$654$	23.1623	−	40.1182i	0.905717	−	1.56875i
$655$		0			0
$656$	−1.16228	+	2.01312i	−0.0453793	+	0.0785993i
$657$	−55.5434	−	32.0680i	−2.16695	−	1.25109i
$658$		−	3.00000i		−	0.116952i
$659$	−13.6491	+	23.6410i	−0.531694	+	0.920921i	0.467622	+	0.883929i	$0.345111\pi$
$659$	−13.6491	+	23.6410i	−0.531694	+	0.920921i	−0.999316	+	0.0369921i	$0.988222\pi$
$660$		0			0
$661$	8.58114	+	14.8630i	0.333768	+	0.578102i	0.983247	−	0.182276i	$-0.0583466\pi$
$661$	8.58114	+	14.8630i	0.333768	+	0.578102i	−0.649480	+	0.760379i	$0.725013\pi$
$662$			0.649111i			0.0252284i
$663$	13.2486	+	0.298221i	0.514535	+	0.0115820i
$664$	9.48683			0.368161
$665$		0			0
$666$	−21.5680	−	37.3568i	−0.835742	−	1.44755i
$667$	12.0787	+	6.97367i	0.467691	+	0.270021i
$668$		−	0.675445i		−	0.0261337i
$669$	14.7434	−	25.5363i	0.570013	−	0.987292i
$670$		0			0
$671$	−47.8114			−1.84574
$672$	−2.73861	−	1.58114i	−0.105644	−	0.0609938i
$673$	19.8958	−	11.4868i	0.766926	−	0.442785i	−0.0648510	−	0.997895i	$-0.520657\pi$
$673$	19.8958	−	11.4868i	0.766926	−	0.442785i	0.831777	+	0.555110i	$0.187324\pi$
$674$	−0.743416	−	1.28764i	−0.0286353	−	0.0495979i
$675$		0			0
$676$	7.00000	−	10.9545i	0.269231	−	0.421325i
$677$			24.9737i			0.959816i	0.877319	+	0.479908i	$0.159330\pi$
$677$			24.9737i			0.959816i	−0.877319	+	0.479908i	$0.840670\pi$
$678$	45.5955	−	26.3246i	1.75108	−	1.01099i
$679$	−5.74342	−	9.94789i	−0.220412	−	0.381765i
$680$		0			0
$681$	7.35089			0.281687
$682$	3.01969	+	1.74342i	0.115630	+	0.0667589i
$683$	27.9939	+	16.1623i	1.07116	+	0.618432i	0.928497	−	0.371340i	$-0.121101\pi$
$683$	27.9939	+	16.1623i	1.07116	+	0.618432i	0.142659	+	0.989772i	$0.454435\pi$
$684$	57.1359			2.18465
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	−25.0919	+	14.4868i	−0.957317	+	0.552707i
$688$		−	2.00000i		−	0.0762493i
$689$	−0.337722	+	15.0035i	−0.0128662	+	0.571588i
$690$		0			0
$691$	−3.56797	−	6.17991i	−0.135732	−	0.235095i	0.790145	−	0.612920i	$-0.210005\pi$
$691$	−3.56797	−	6.17991i	−0.135732	−	0.235095i	−0.925877	+	0.377825i	$0.876672\pi$
$692$	−3.60464	+	2.08114i	−0.137028	+	0.0791130i
$693$	25.2325	+	14.5680i	0.958502	+	0.553391i
$694$	−21.4868			−0.815629
$695$		0			0
$696$	−3.67544	+	6.36606i	−0.139317	+	0.241305i
$697$			2.70178i			0.102337i
$698$	−1.28764	−	0.743416i	−0.0487377	−	0.0281387i
$699$	15.0000	+	25.9808i	0.567352	+	0.982683i
$700$		0			0
$701$	−16.8377			−0.635952			−0.317976	−	0.948099i	$-0.603003\pi$
$701$	−16.8377			−0.635952			−0.317976	+	0.948099i	$0.603003\pi$
$702$	21.9089	+	40.0000i	0.826898	+	1.50970i
$703$			50.2982i			1.89703i
$704$	−2.08114	−	3.60464i	−0.0784359	−	0.135855i
$705$		0			0
$706$	0.581139	−	1.00656i	0.0218714	−	0.0378825i
$707$			4.83772i			0.181941i
$708$	−6.36606	−	3.67544i	−0.239251	−	0.138132i
$709$	11.2566	−	19.4970i	0.422750	−	0.732224i	−0.573457	−	0.819235i	$-0.694398\pi$
$709$	11.2566	−	19.4970i	0.422750	−	0.732224i	0.996207	+	0.0870111i	$0.0277316\pi$
$710$		0			0
$711$	−19.2039	+	33.2622i	−0.720203	+	1.24743i
$712$	4.61120	−	2.66228i	0.172812	−	0.0997731i
$713$	−4.35293	+	2.51317i	−0.163019	+	0.0941188i
$714$	−3.67544			−0.137550
$715$		0			0
$716$	9.67544			0.361588
$717$	−13.2486	+	7.64911i	−0.494780	+	0.285661i
$718$	5.19615	−	3.00000i	0.193919	−	0.111959i
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	−0.732185	−	0.681106i	$-0.761499\pi$
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	0.955947	+	0.293538i	$0.0948328\pi$
$720$		0			0
$721$	6.66228	−	11.5394i	0.248116	−	0.429750i
$722$	−41.2425	−	23.8114i	−1.53489	−	0.886168i
$723$			37.8641i			1.40818i
$724$	−10.9057	+	18.8892i	−0.405307	+	0.702012i
$725$		0			0
$726$	10.0000	+	17.3205i	0.371135	+	0.642824i
$727$		−	33.3246i		−	1.23594i	−0.786202	−	0.617970i	$-0.787955\pi$
$727$		−	33.3246i		−	1.23594i	0.786202	−	0.617970i	$-0.212045\pi$
$728$	−1.87259	+	3.08114i	−0.0694027	+	0.114195i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−1.16228	−	2.01312i	−0.0429884	−	0.0744581i
$732$	31.4580	+	18.1623i	1.16272	+	0.671297i
$733$			10.4868i			0.387340i	0.981067	+	0.193670i	$0.0620391\pi$
$733$			10.4868i			0.387340i	−0.981067	+	0.193670i	$0.937961\pi$
$734$	−10.3246	+	17.8827i	−0.381086	+	0.660061i
$735$		0			0
$736$	6.00000			0.221163
$737$	37.2163	+	21.4868i	1.37088	+	0.791478i
$738$	−14.0919	+	8.13594i	−0.518729	+	0.299488i
$739$	−6.59431	−	11.4217i	−0.242575	−	0.420153i	0.718872	−	0.695143i	$-0.244659\pi$
$739$	−6.59431	−	11.4217i	−0.242575	−	0.420153i	−0.961447	+	0.274990i	$0.911326\pi$
$740$		0			0
$741$	2.09431	−	93.0407i	0.0769362	−	3.41794i
$742$		−	4.16228i		−	0.152802i
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	−0.186017	−	0.982547i	$-0.559558\pi$
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	0.757902	+	0.652369i	$0.226225\pi$
$744$	−1.32456	−	2.29420i	−0.0485606	−	0.0841093i
$745$		0			0
$746$	−5.35089			−0.195910
$747$	57.5109	+	33.2039i	2.10421	+	1.21487i
$748$	−4.18959	−	2.41886i	−0.153187	−	0.0884423i
$749$	15.4868			0.565877
$750$		0			0
$751$	−1.48683	−	2.57527i	−0.0542553	−	0.0939729i	0.837622	−	0.546250i	$-0.183945\pi$
$751$	−1.48683	−	2.57527i	−0.0542553	−	0.0939729i	−0.891877	+	0.452277i	$0.850612\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$		−	20.5132i		−	0.747541i
$754$	7.16228	+	4.35293i	0.260835	+	0.158524i
$755$		0			0
$756$	−6.32456	−	10.9545i	−0.230022	−	0.398410i
$757$	24.1082	−	13.9189i	0.876227	−	0.505890i	0.00681414	−	0.999977i	$-0.497831\pi$
$757$	24.1082	−	13.9189i	0.876227	−	0.505890i	0.869412	+	0.494087i	$0.164498\pi$
$758$	−6.22552	−	3.59431i	−0.226121	−	0.130551i
$759$	−78.9737			−2.86656
$760$		0			0
$761$	−21.1491	+	36.6313i	−0.766655	+	1.32788i	0.172713	+	0.984972i	$0.444747\pi$
$761$	−21.1491	+	36.6313i	−0.766655	+	1.32788i	−0.939367	+	0.342913i	$0.888587\pi$
$762$			29.4868i			1.06820i
$763$	12.6865	+	7.32456i	0.459282	+	0.265167i
$764$	−4.74342	−	8.21584i	−0.171611	−	0.297239i
$765$		0			0
$766$	30.0000			1.08394
$767$	−4.35293	+	7.16228i	−0.157175	+	0.258615i
$768$			3.16228i			0.114109i
$769$	−3.16228	−	5.47723i	−0.114035	−	0.197514i	0.803359	−	0.595495i	$-0.203044\pi$
$769$	−3.16228	−	5.47723i	−0.114035	−	0.197514i	−0.917393	+	0.397981i	$0.869711\pi$
$770$		0			0
$771$		0			0
$772$		−	4.00000i		−	0.143963i
$773$	−18.8664	−	10.8925i	−0.678578	−	0.391777i	0.120741	−	0.992684i	$-0.461473\pi$
$773$	−18.8664	−	10.8925i	−0.678578	−	0.391777i	−0.799319	+	0.600907i	$0.794806\pi$
$774$	7.00000	−	12.1244i	0.251610	−	0.435801i
$775$		0			0
$776$	−5.74342	+	9.94789i	−0.206177	+	0.357108i
$777$	16.8761	−	9.74342i	0.605426	−	0.349543i
$778$	−16.5950	+	9.58114i	−0.594960	+	0.343500i
$779$	18.9737			0.679802
$780$		0			0
$781$	−34.6491			−1.23984
$782$	6.03937	−	3.48683i	0.215967	−	0.124689i
$783$	−25.4642	+	14.7018i	−0.910017	+	0.525399i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$		0			0
$786$	32.9057	−	56.9943i	1.17371	−	2.03292i
$787$	1.61432	+	0.932028i	0.0575443	+	0.0332232i	0.528496	−	0.848936i	$-0.322756\pi$
$787$	1.61432	+	0.932028i	0.0575443	+	0.0332232i	−0.470952	+	0.882159i	$0.656089\pi$
$788$		−	0.486833i		−	0.0173427i
$789$	−21.5811	+	37.3796i	−0.768309	+	1.33075i
$790$		0			0
$791$	8.32456	+	14.4186i	0.295987	+	0.512665i
$792$		−	29.1359i		−	1.03530i
$793$	21.5101	−	35.3925i	0.763846	−	1.25683i
$794$	−19.5132			−0.692496
$795$		0			0
$796$	13.3246	+	23.0788i	0.472276	+	0.818007i
$797$	22.7977	+	13.1623i	0.807537	+	0.466232i	0.846100	−	0.533024i	$-0.178945\pi$
$797$	22.7977	+	13.1623i	0.807537	+	0.466232i	−0.0385627	+	0.999256i	$0.512278\pi$
$798$			25.8114i			0.913713i
$799$	−1.74342	+	3.01969i	−0.0616776	+	0.106829i
$800$		0			0
$801$	37.2719			1.31694
$802$	13.8336	+	7.98683i	0.488481	+	0.282025i
$803$	33.0267	−	19.0680i	1.16549	−	0.672894i
$804$	−16.3246	−	28.2750i	−0.575723	−	0.997181i
$805$		0			0
$806$	−2.64911	+	1.45098i	−0.0933109	+	0.0511085i
$807$		−	67.9473i		−	2.39186i
$808$	4.18959	−	2.41886i	0.147389	−	0.0850952i
$809$	−1.16228	−	2.01312i	−0.0408635	−	0.0707777i	0.844870	−	0.534971i	$-0.179678\pi$
$809$	−1.16228	−	2.01312i	−0.0408635	−	0.0707777i	−0.885734	+	0.464194i	$0.846344\pi$
$810$		0			0
$811$	0.162278			0.00569834			0.00284917	−	0.999996i	$-0.499093\pi$
$811$	0.162278			0.00569834			0.00284917	+	0.999996i	$0.499093\pi$
$812$	−2.01312	−	1.16228i	−0.0706468	−	0.0407879i
$813$	17.3205	+	10.0000i	0.607457	+	0.350715i
$814$	25.6491			0.899001
$815$		0			0
$816$	1.83772	+	3.18303i	0.0643331	+	0.111428i
$817$	−14.1375	+	8.16228i	−0.494608	+	0.285562i
$818$		−	3.64911i		−	0.127588i
$819$	−22.1359	+	12.1244i	−0.773492	+	0.423659i
$820$		0			0
$821$	−0.581139	−	1.00656i	−0.0202819	−	0.0351293i	0.855706	−	0.517462i	$-0.173123\pi$
$821$	−0.581139	−	1.00656i	−0.0202819	−	0.0351293i	−0.875988	+	0.482333i	$0.839790\pi$
$822$	9.54909	−	5.51317i	0.333063	−	0.192294i
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.996196	−	0.0871445i	$-0.0277742\pi$
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.422628	+	0.906303i	$0.361108\pi$
$824$	−13.3246			−0.464183
$825$		0			0
$826$	1.16228	−	2.01312i	0.0404408	−	0.0700455i
$827$		−	32.5132i		−	1.13059i	−0.824888	−	0.565297i	$-0.808762\pi$
$827$		−	32.5132i		−	1.13059i	0.824888	−	0.565297i	$-0.191238\pi$
$828$	36.3731	+	21.0000i	1.26405	+	0.729800i
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	0.997848	+	0.0655624i	$0.0208842\pi$
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	−0.442145	+	0.896943i	$0.645783\pi$
$830$		0			0
$831$	−64.7851			−2.24737
$832$	3.60464	+	0.0811388i	0.124968	+	0.00281298i
$833$			6.97367i			0.241623i
$834$	9.23025	+	15.9873i	0.319617	+	0.553594i
$835$		0			0
$836$	−16.9868	+	29.4221i	−0.587502	+	1.01758i
$837$		−	10.5964i		−	0.366267i
$838$	−9.22240	−	5.32456i	−0.318583	−	0.183934i
$839$	−8.41886	+	14.5819i	−0.290651	+	0.503423i	−0.973964	−	0.226703i	$-0.927205\pi$
$839$	−8.41886	+	14.5819i	−0.290651	+	0.503423i	0.683313	+	0.730126i	$0.260539\pi$
$840$		0			0
$841$	11.7982	−	20.4351i	0.406835	−	0.704659i
$842$	2.73861	−	1.58114i	0.0943788	−	0.0544896i
$843$	51.9615	−	30.0000i	1.78965	−	1.03325i
$844$	−18.1623			−0.625171
$845$		0			0
$846$	−21.0000			−0.721995
$847$	−5.47723	+	3.16228i	−0.188200	+	0.108657i
$848$	−3.60464	+	2.08114i	−0.123784	+	0.0714666i
$849$	34.7851	−	60.2495i	1.19382	−	2.06776i
$850$		0			0
$851$	−18.4868	+	32.0201i	−0.633720	+	1.09764i
$852$	22.7977	+	13.1623i	0.781037	+	0.450932i
$853$			32.2719i			1.10497i	0.833523	+	0.552484i	$0.186320\pi$
$853$			32.2719i			1.10497i	−0.833523	+	0.552484i	$0.813680\pi$
$854$	−5.74342	+	9.94789i	−0.196536	+	0.340410i
$855$		0			0
$856$	−7.74342	−	13.4120i	−0.264665	−	0.458412i
$857$		−	14.1359i		−	0.482875i	−0.970416	−	0.241437i	$-0.922381\pi$
$857$		−	14.1359i		−	0.482875i	0.970416	−	0.241437i	$-0.0776188\pi$
$858$	−47.4452	−	1.06797i	−1.61975	−	0.0364600i
$859$	−2.86406			−0.0977203			−0.0488602	−	0.998806i	$-0.515559\pi$
$859$	−2.86406			−0.0977203			−0.0488602	+	0.998806i	$0.515559\pi$
$860$		0			0
$861$	−3.67544	−	6.36606i	−0.125259	−	0.216955i
$862$	3.01969	+	1.74342i	0.102851	+	0.0593810i
$863$			18.0000i			0.612727i	0.951915	+	0.306364i	$0.0991123\pi$
$863$			18.0000i			0.612727i	−0.951915	+	0.306364i	$0.900888\pi$
$864$	−6.32456	+	10.9545i	−0.215166	+	0.372678i
$865$		0			0
$866$	−6.32456			−0.214917
$867$	−42.8569	−	24.7434i	−1.45550	−	0.840330i
$868$	0.725489	−	0.418861i	0.0246247	−	0.0142171i
$869$	−11.4189	−	19.7780i	−0.387358	−	0.670924i
$870$		0			0
$871$	−32.6491	+	17.8827i	−1.10627	+	0.605931i
$872$		−	14.6491i		−	0.496081i
$873$	−69.6352	+	40.2039i	−2.35680	+	1.36070i
$874$	−24.4868	−	42.4124i	−0.828279	−	1.43462i
$875$		0			0
$876$	−28.9737			−0.978929
$877$	31.4580	+	18.1623i	1.06226	+	0.613297i	0.926057	−	0.377384i	$-0.123176\pi$
$877$	31.4580	+	18.1623i	1.06226	+	0.613297i	0.136204	+	0.990681i	$0.456510\pi$
$878$	−24.0854	−	13.9057i	−0.812842	−	0.469294i
$879$	−89.0569			−3.00382
$880$		0			0
$881$	10.0132	+	17.3433i	0.337352	+	0.584311i	0.983934	−	0.178534i	$-0.0571354\pi$
$881$	10.0132	+	17.3433i	0.337352	+	0.584311i	−0.646582	+	0.762845i	$0.723802\pi$
$882$	−36.3731	+	21.0000i	−1.22474	+	0.707107i
$883$		−	16.5132i		−	0.555712i	−0.960623	−	0.277856i	$-0.910376\pi$
$883$		−	16.5132i		−	0.555712i	0.960623	−	0.277856i	$-0.0896239\pi$
$884$	3.67544	−	2.01312i	0.123619	−	0.0677087i
$885$		0			0
$886$	−0.675445	−	1.16990i	−0.0226920	−	0.0393037i
$887$	−23.0560	+	13.3114i	−0.774145	+	0.446953i	−0.834351	−	0.551233i	$-0.814157\pi$
$887$	−23.0560	+	13.3114i	−0.774145	+	0.446953i	0.0602064	+	0.998186i	$0.480824\pi$
$888$	−16.8761	−	9.74342i	−0.566325	−	0.326968i
$889$	−9.32456			−0.312736
$890$		0			0
$891$	39.5416	−	68.4881i	1.32469	−	2.29444i
$892$		−	9.32456i		−	0.312209i
$893$	21.2062	+	12.2434i	0.709639	+	0.409710i
$894$	−5.81139	−	10.0656i	−0.194362	−	0.336645i
$895$		0			0
$896$	−1.00000			−0.0334077
$897$	35.5298	−	58.4605i	1.18631	−	1.95194i
$898$			39.9737i			1.33394i
$899$	−0.973666	−	1.68644i	−0.0324736	−	0.0562459i
$900$		0			0
$901$	−2.41886	+	4.18959i	−0.0805839	+	0.139575i
$902$		−	9.67544i		−	0.322157i
$903$	5.47723	+	3.16228i	0.182271	+	0.105234i
$904$	8.32456	−	14.4186i	0.276871	−	0.479554i
$905$		0			0
$906$	−17.6491	+	30.5692i	−0.586352	+	1.01559i
$907$	24.3664	−	14.0680i	0.809074	−	0.467119i	−0.0375599	−	0.999294i	$-0.511959\pi$
$907$	24.3664	−	14.0680i	0.809074	−	0.467119i	0.846634	+	0.532175i	$0.178625\pi$
$908$	2.01312	−	1.16228i	0.0668079	−	0.0385715i
$909$	33.8641			1.12320
$910$		0			0
$911$	33.2982			1.10322			0.551610	−	0.834102i	$-0.314014\pi$
$911$	33.2982			1.10322			0.551610	+	0.834102i	$0.314014\pi$
$912$	22.3533	−	12.9057i	0.740192	−	0.427350i
$913$	−34.1966	+	19.7434i	−1.13174	+	0.653412i
$914$	−16.2302	+	28.1116i	−0.536849	+	0.929850i
$915$		0			0
$916$	−4.58114	+	7.93477i	−0.151365	+	0.262172i
$917$	18.0232	+	10.4057i	0.595178	+	0.343626i
$918$			14.7018i			0.485231i
$919$	−12.1623	+	21.0657i	−0.401197	+	0.694893i	−0.993871	−	0.110550i	$-0.964739\pi$
$919$	−12.1623	+	21.0657i	−0.401197	+	0.694893i	0.592674	+	0.805442i	$0.298072\pi$
$920$		0			0
$921$	44.7851	+	77.5700i	1.47572	+	2.55602i
$922$			2.51317i			0.0827667i
$923$	15.5885	−	25.6491i	0.513100	−	0.844251i
$924$	13.1623			0.433007
$925$		0			0
$926$	0.162278	+	0.281073i	0.00533277	+	0.00923664i
$927$	−80.7758	−	46.6359i	−2.65303	−	1.53173i
$928$			2.32456i			0.0763073i
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$		0			0
$931$	48.9737			1.60505
$932$	8.21584	+	4.74342i	0.269119	+	0.155376i
$933$	42.4124	−	24.4868i	1.38852	−	0.801663i
$934$	3.67544	+	6.36606i	0.120264	+	0.208304i
$935$		0			0
$936$	21.5680	+	13.1081i	0.704971	+	0.428452i
$937$			40.3246i			1.31735i	0.752429	+	0.658673i	$0.228882\pi$
$937$			40.3246i			1.31735i	−0.752429	+	0.658673i	$0.771118\pi$
$938$	8.94133	−	5.16228i	0.291945	−	0.168554i
$939$	−6.83772	−	11.8433i	−0.223141	−	0.386491i
$940$		0			0
$941$	9.67544			0.315410			0.157705	−	0.987486i	$-0.449590\pi$
$941$	9.67544			0.315410			0.157705	+	0.987486i	$0.449590\pi$
$942$	−15.9873	−	9.23025i	−0.520893	−	0.300738i
$943$	12.0787	+	6.97367i	0.393338	+	0.227094i
$944$	−2.32456			−0.0756578
$945$		0			0
$946$	4.16228	+	7.20928i	0.135327	+	0.234394i
$947$	25.8174	−	14.9057i	0.838953	−	0.484370i	−0.0179549	−	0.999839i	$-0.505716\pi$
$947$	25.8174	−	14.9057i	0.838953	−	0.484370i	0.856908	+	0.515469i	$0.172382\pi$
$948$			17.3509i			0.563531i
$949$	−0.743416	+	33.0267i	−0.0241323	+	1.07209i
$950$		0			0
$951$	−10.2566	−	17.7649i	−0.332593	−	0.576067i
$952$	−1.00656	+	0.581139i	−0.0326229	+	0.0188348i
$953$	−18.6081	−	10.7434i	−0.602777	−	0.348013i	0.167356	−	0.985896i	$-0.446477\pi$
$953$	−18.6081	−	10.7434i	−0.602777	−	0.348013i	−0.770133	+	0.637883i	$0.779810\pi$
$954$	−29.1359			−0.943311
$955$		0			0
$956$	−2.41886	+	4.18959i	−0.0782316	+	0.135501i
$957$		−	30.5964i		−	0.989043i
$958$	27.8305	+	16.0680i	0.899164	+	0.519133i
$959$	1.74342	+	3.01969i	0.0562979	+	0.0975107i
$960$		0			0
$961$	−30.2982			−0.977362
$962$	−11.5394	+	18.9868i	−0.372045	+	0.612160i
$963$		−	108.408i		−	3.49339i
$964$	5.98683	+	10.3695i	0.192823	+	0.333979i
$965$		0			0
$966$	−9.48683	+	16.4317i	−0.305234	+	0.528681i
$967$			46.6228i			1.49929i	0.661842	+	0.749644i	$0.269775\pi$
$967$			46.6228i			1.49929i	−0.661842	+	0.749644i	$0.730225\pi$
$968$	5.47723	+	3.16228i	0.176045	+	0.101639i
$969$	15.0000	−	25.9808i	0.481869	−	0.834622i
$970$		0			0
$971$	4.89253	−	8.47411i	0.157009	−	0.271947i	−0.776780	−	0.629772i	$-0.783148\pi$
$971$	4.89253	−	8.47411i	0.157009	−	0.271947i	0.933789	+	0.357825i	$0.116482\pi$
$972$	−19.1703	+	11.0680i	−0.614887	+	0.355005i
$973$	−5.05562	+	2.91886i	−0.162076	+	0.0935744i
$974$	1.00000			0.0320421
$975$		0			0
$976$	11.4868			0.367685
$977$	−16.4317	+	9.48683i	−0.525696	+	0.303511i	−0.739262	−	0.673418i	$-0.764825\pi$
$977$	−16.4317	+	9.48683i	−0.525696	+	0.303511i	0.213566	+	0.976929i	$0.431492\pi$
$978$	−4.07186	+	2.35089i	−0.130204	+	0.0751732i
$979$	−11.0811	+	19.1931i	−0.354155	+	0.613414i
$980$		0			0
$981$	51.2719	−	88.8055i	1.63699	−	2.83534i
$982$	−31.5985	−	18.2434i	−1.00835	−	0.582171i
$983$		−	55.6491i		−	1.77493i	−0.460874	−	0.887465i	$-0.652464\pi$
$983$		−	55.6491i		−	1.77493i	0.460874	−	0.887465i	$-0.347536\pi$
$984$	−3.67544	+	6.36606i	−0.117169	+	0.202942i
$985$		0			0
$986$	1.35089	+	2.33981i	0.0430211	+	0.0745147i
$987$		−	9.48683i		−	0.301969i
$988$	−14.1375	−	25.8114i	−0.449773	−	0.821170i
$989$	−12.0000			−0.381578
$990$		0			0
$991$	−5.64911	−	9.78455i	−0.179450	−	0.310816i	0.762242	−	0.647292i	$-0.224098\pi$
$991$	−5.64911	−	9.78455i	−0.179450	−	0.310816i	−0.941692	+	0.336475i	$0.890765\pi$
$992$	−0.725489	−	0.418861i	−0.0230343	−	0.0132989i
$993$			2.05267i			0.0651395i
$994$	−4.16228	+	7.20928i	−0.132019	+	0.228664i
$995$		0			0
$996$	30.0000			0.950586
$997$	−15.7290	−	9.08114i	−0.498142	−	0.287603i	0.229804	−	0.973237i	$-0.426192\pi$
$997$	−15.7290	−	9.08114i	−0.498142	−	0.287603i	−0.727946	+	0.685634i	$0.759525\pi$
$998$	19.0526	−	11.0000i	0.603098	−	0.348199i
$999$	−38.9737	−	67.5044i	−1.23307	−	2.13574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.o.g.549.4		8
5.2	odd	4		650.2.e.h.601.1		4
5.3	odd	4		130.2.e.c.81.2	yes	4
5.4	even	2	inner	650.2.o.g.549.1		8
13.9	even	3	inner	650.2.o.g.399.1		8
15.8	even	4		1170.2.i.q.991.1		4
20.3	even	4		1040.2.q.m.81.1		4
65.3	odd	12		1690.2.a.n.1.1		2
65.8	even	4		1690.2.l.k.361.4		8
65.9	even	6	inner	650.2.o.g.399.4		8
65.18	even	4		1690.2.l.k.361.2		8
65.22	odd	12		650.2.e.h.451.1		4
65.23	odd	12		1690.2.a.k.1.1		2
65.28	even	12		1690.2.d.g.1351.1		4
65.33	even	12		1690.2.l.k.1161.2		8
65.38	odd	4		1690.2.e.m.991.2		4
65.42	odd	12		8450.2.a.bc.1.2		2
65.43	odd	12		1690.2.e.m.191.2		4
65.48	odd	12		130.2.e.c.61.2	✓	4
65.58	even	12		1690.2.l.k.1161.4		8
65.62	odd	12		8450.2.a.bj.1.2		2
65.63	even	12		1690.2.d.g.1351.3		4
195.113	even	12		1170.2.i.q.451.1		4
260.243	even	12		1040.2.q.m.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.c.61.2	✓	4	65.48	odd	12
130.2.e.c.81.2	yes	4	5.3	odd	4
650.2.e.h.451.1		4	65.22	odd	12
650.2.e.h.601.1		4	5.2	odd	4
650.2.o.g.399.1		8	13.9	even	3	inner
650.2.o.g.399.4		8	65.9	even	6	inner
650.2.o.g.549.1		8	5.4	even	2	inner
650.2.o.g.549.4		8	1.1	even	1	trivial
1040.2.q.m.81.1		4	20.3	even	4
1040.2.q.m.321.1		4	260.243	even	12
1170.2.i.q.451.1		4	195.113	even	12
1170.2.i.q.991.1		4	15.8	even	4
1690.2.a.k.1.1		2	65.23	odd	12
1690.2.a.n.1.1		2	65.3	odd	12
1690.2.d.g.1351.1		4	65.28	even	12
1690.2.d.g.1351.3		4	65.63	even	12
1690.2.e.m.191.2		4	65.43	odd	12
1690.2.e.m.991.2		4	65.38	odd	4
1690.2.l.k.361.2		8	65.18	even	4
1690.2.l.k.361.4		8	65.8	even	4
1690.2.l.k.1161.2		8	65.33	even	12
1690.2.l.k.1161.4		8	65.58	even	12
8450.2.a.bc.1.2		2	65.42	odd	12
8450.2.a.bj.1.2		2	65.62	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.73861 - 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.73861 - 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +(2.08114 + 3.60464i) q^{11} -3.16228i q^{12} +(-3.60464 - 0.0811388i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00656 - 0.581139i) q^{17} -7.00000i q^{18} +(-4.08114 + 7.06874i) q^{19} +3.16228 q^{21} +(3.60464 + 2.08114i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(-1.58114 - 2.73861i) q^{24} +(-3.16228 + 1.73205i) q^{26} -12.6491i q^{27} +(0.866025 - 0.500000i) q^{28} +(-1.16228 - 2.01312i) q^{29} +0.837722 q^{31} +(-0.866025 - 0.500000i) q^{32} +(11.3989 + 6.58114i) q^{33} -1.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(5.33669 - 3.08114i) q^{37} +8.16228i q^{38} +(-10.0000 + 5.47723i) q^{39} +(-1.16228 - 2.01312i) q^{41} +(2.73861 - 1.58114i) q^{42} +(1.73205 + 1.00000i) q^{43} +4.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} -3.00000i q^{47} +(-2.73861 - 1.58114i) q^{48} +(-3.00000 - 5.19615i) q^{49} -3.67544 q^{51} +(-1.87259 + 3.08114i) q^{52} -4.16228i q^{53} +(-6.32456 - 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} +25.8114i q^{57} +(-2.01312 - 1.16228i) q^{58} +(1.16228 - 2.01312i) q^{59} +(-5.74342 + 9.94789i) q^{61} +(0.725489 - 0.418861i) q^{62} +(6.06218 - 3.50000i) q^{63} -1.00000 q^{64} +13.1623 q^{66} +(8.94133 - 5.16228i) q^{67} +(-1.00656 + 0.581139i) q^{68} +(-9.48683 + 16.4317i) q^{69} +(-4.16228 + 7.20928i) q^{71} +(-6.06218 - 3.50000i) q^{72} -9.16228i q^{73} +(3.08114 - 5.33669i) q^{74} +(4.08114 + 7.06874i) q^{76} +4.16228i q^{77} +(-5.92164 + 9.74342i) q^{78} -5.48683 q^{79} +(-9.50000 - 16.4545i) q^{81} +(-2.01312 - 1.16228i) q^{82} +9.48683i q^{83} +(1.58114 - 2.73861i) q^{84} +2.00000 q^{86} +(-6.36606 - 3.67544i) q^{87} +(3.60464 - 2.08114i) q^{88} +(2.66228 + 4.61120i) q^{89} +(-3.08114 - 1.87259i) q^{91} +6.00000i q^{92} +(2.29420 - 1.32456i) q^{93} +(-1.50000 - 2.59808i) q^{94} -3.16228 q^{96} +(-9.94789 - 5.74342i) q^{97} +(-5.19615 - 3.00000i) q^{98} +29.1359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 28 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 28 * q^9	\( 8 q + 4 q^{4} + 28 q^{9} + 4 q^{11} + 8 q^{14} - 4 q^{16} - 20 q^{19} + 16 q^{29} + 32 q^{31} + 16 q^{34} - 28 q^{36} - 80 q^{39} + 16 q^{41} + 8 q^{44} - 24 q^{46} - 24 q^{49} - 80 q^{51} + 4 q^{56} - 16 q^{59} - 8 q^{61} - 8 q^{64} + 80 q^{66} - 8 q^{71} + 12 q^{74} + 20 q^{76} + 32 q^{79} - 76 q^{81} + 16 q^{86} - 4 q^{89} - 12 q^{91} - 12 q^{94} + 56 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 28 * q^9 + 4 * q^11 + 8 * q^14 - 4 * q^16 - 20 * q^19 + 16 * q^29 + 32 * q^31 + 16 * q^34 - 28 * q^36 - 80 * q^39 + 16 * q^41 + 8 * q^44 - 24 * q^46 - 24 * q^49 - 80 * q^51 + 4 * q^56 - 16 * q^59 - 8 * q^61 - 8 * q^64 + 80 * q^66 - 8 * q^71 + 12 * q^74 + 20 * q^76 + 32 * q^79 - 76 * q^81 + 16 * q^86 - 4 * q^89 - 12 * q^91 - 12 * q^94 + 56 * q^99

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