LMFDB - Embedded newform 380.2.bb.a.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.2
Character	$\chi$	$=$	380.319
Dual form			380.2.bb.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41388 + 0.0306836i) q^{2} +(0.151290 - 0.0266765i) q^{3} +(1.99812 - 0.0867660i) q^{4} +(-0.376017 - 2.20423i) q^{5} +(-0.213088 + 0.0423596i) q^{6} +(-1.14368 + 1.98092i) q^{7} +(-2.82244 + 0.183986i) q^{8} +(-2.79690 + 1.01799i) q^{9} +O(q^{10})$	\(q+(-1.41388 + 0.0306836i) q^{2} +(0.151290 - 0.0266765i) q^{3} +(1.99812 - 0.0867660i) q^{4} +(-0.376017 - 2.20423i) q^{5} +(-0.213088 + 0.0423596i) q^{6} +(-1.14368 + 1.98092i) q^{7} +(-2.82244 + 0.183986i) q^{8} +(-2.79690 + 1.01799i) q^{9} +(0.599277 + 3.10497i) q^{10} +(-2.70356 + 1.56090i) q^{11} +(0.299981 - 0.0664297i) q^{12} +(-0.571033 + 3.23849i) q^{13} +(1.55625 - 2.83587i) q^{14} +(-0.115689 - 0.323447i) q^{15} +(3.98494 - 0.346737i) q^{16} +(0.657317 - 1.80596i) q^{17} +(3.92325 - 1.52513i) q^{18} +(1.01826 + 4.23829i) q^{19} +(-0.942578 - 4.37168i) q^{20} +(-0.120184 + 0.330203i) q^{21} +(3.77462 - 2.28989i) q^{22} +(6.01752 + 5.04930i) q^{23} +(-0.422099 + 0.103128i) q^{24} +(-4.71722 + 1.65765i) q^{25} +(0.708003 - 4.59636i) q^{26} +(-0.795114 + 0.459059i) q^{27} +(-2.11334 + 4.05734i) q^{28} +(-1.63276 - 4.48597i) q^{29} +(0.173495 + 0.453765i) q^{30} +(-2.75076 + 4.76446i) q^{31} +(-5.62360 + 0.612518i) q^{32} +(-0.367383 + 0.308271i) q^{33} +(-0.873955 + 2.57359i) q^{34} +(4.79644 + 1.77608i) q^{35} +(-5.50021 + 2.27674i) q^{36} -5.87587 q^{37} +(-1.56975 - 5.96120i) q^{38} +0.505184i q^{39} +(1.46683 + 6.15211i) q^{40} +(-2.91951 + 0.514788i) q^{41} +(0.159794 - 0.470555i) q^{42} +(3.18112 - 2.66928i) q^{43} +(-5.26660 + 3.35344i) q^{44} +(3.29556 + 5.78222i) q^{45} +(-8.66299 - 6.95447i) q^{46} +(-5.85679 + 2.13170i) q^{47} +(0.593633 - 0.158762i) q^{48} +(0.883975 + 1.53109i) q^{49} +(6.61873 - 2.48846i) q^{50} +(0.0512688 - 0.290760i) q^{51} +(-0.859999 + 6.52042i) q^{52} +(5.37638 + 4.51132i) q^{53} +(1.11011 - 0.673452i) q^{54} +(4.45717 + 5.37234i) q^{55} +(2.86351 - 5.80144i) q^{56} +(0.267116 + 0.614049i) q^{57} +(2.44617 + 6.29253i) q^{58} +(-5.48925 - 1.99792i) q^{59} +(-0.259224 - 0.636247i) q^{60} +(-8.49907 - 7.13157i) q^{61} +(3.74306 - 6.82079i) q^{62} +(1.18222 - 6.70469i) q^{63} +(7.93230 - 1.03858i) q^{64} +(7.35307 + 0.0409589i) q^{65} +(0.509977 - 0.447131i) q^{66} +(-1.09648 - 3.01256i) q^{67} +(1.15670 - 3.66556i) q^{68} +(1.04509 + 0.603383i) q^{69} +(-6.83608 - 2.36399i) q^{70} +(-9.98926 + 8.38198i) q^{71} +(7.70678 - 3.38780i) q^{72} +(6.42811 - 1.13345i) q^{73} +(8.30778 - 0.180293i) q^{74} +(-0.669449 + 0.376626i) q^{75} +(2.40235 + 8.38026i) q^{76} -7.14072i q^{77} +(-0.0155009 - 0.714270i) q^{78} +(-0.838432 - 4.75499i) q^{79} +(-2.26269 - 8.65334i) q^{80} +(6.73212 - 5.64892i) q^{81} +(4.11204 - 0.817429i) q^{82} +(3.97221 - 6.88007i) q^{83} +(-0.211491 + 0.670212i) q^{84} +(-4.22792 - 0.769803i) q^{85} +(-4.41583 + 3.87165i) q^{86} +(-0.366691 - 0.635127i) q^{87} +(7.34345 - 4.90297i) q^{88} +(1.58191 + 0.278934i) q^{89} +(-4.83695 - 8.07425i) q^{90} +(-5.76210 - 4.83497i) q^{91} +(12.4618 + 9.56698i) q^{92} +(-0.289064 + 0.794197i) q^{93} +(8.21540 - 3.19368i) q^{94} +(8.95928 - 3.83815i) q^{95} +(-0.834455 + 0.242686i) q^{96} +(4.18121 + 1.52184i) q^{97} +(-1.29681 - 2.13765i) q^{98} +(5.97262 - 7.11789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$-1$

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 $

$2$	−1.41388	+	0.0306836i	−0.999765	+	0.0216966i
$2$	−1.41388	+	0.0306836i	−0.999765	+	0.0216966i
$3$	0.151290	−	0.0266765i	0.0873474	−	0.0154017i	−0.129804	−	0.991540i	$-0.541435\pi$
$3$	0.151290	−	0.0266765i	0.0873474	−	0.0154017i	0.217151	+	0.976138i	$0.430324\pi$
$4$	1.99812	−	0.0867660i	0.999059	−	0.0433830i
$5$	−0.376017	−	2.20423i	−0.168160	−	0.985760i
$5$	−0.376017	−	2.20423i	−0.168160	−	0.985760i
$6$	−0.213088	+	0.0423596i	−0.0869927	+	0.0172932i
$7$	−1.14368	+	1.98092i	−0.432272	+	0.748717i	−0.997069	−	0.0765133i	$-0.975621\pi$
$7$	−1.14368	+	1.98092i	−0.432272	+	0.748717i	0.564797	+	0.825230i	$0.308955\pi$
$8$	−2.82244	+	0.183986i	−0.997882	+	0.0650490i
$9$	−2.79690	+	1.01799i	−0.932300	+	0.339330i
$10$	0.599277	+	3.10497i	0.189508	+	0.981879i
$11$	−2.70356	+	1.56090i	−0.815155	+	0.470630i	−0.848743	−	0.528806i	$-0.822640\pi$
$11$	−2.70356	+	1.56090i	−0.815155	+	0.470630i	0.0335878	+	0.999436i	$0.489307\pi$
$12$	0.299981	−	0.0664297i	0.0865970	−	0.0191766i
$13$	−0.571033	+	3.23849i	−0.158376	+	0.898195i	0.797258	+	0.603638i	$0.206283\pi$
$13$	−0.571033	+	3.23849i	−0.158376	+	0.898195i	−0.955634	+	0.294556i	$0.904828\pi$
$14$	1.55625	−	2.83587i	0.415925	−	0.757919i
$15$	−0.115689	−	0.323447i	−0.0298707	−	0.0835136i
$16$	3.98494	−	0.346737i	0.996236	−	0.0866843i
$17$	0.657317	−	1.80596i	0.159423	−	0.438011i	−0.834104	−	0.551607i	$-0.814015\pi$
$17$	0.657317	−	1.80596i	0.159423	−	0.438011i	0.993527	+	0.113596i	$0.0362370\pi$
$18$	3.92325	−	1.52513i	0.924718	−	0.359477i
$19$	1.01826	+	4.23829i	0.233605	+	0.972332i
$19$	1.01826	+	4.23829i	0.233605	+	0.972332i
$20$	−0.942578	−	4.37168i	−0.210767	−	0.977536i
$21$	−0.120184	+	0.330203i	−0.0262263	+	0.0720562i
$22$	3.77462	−	2.28989i	0.804752	−	0.488205i
$23$	6.01752	+	5.04930i	1.25474	+	1.05285i	0.996222	+	0.0868461i	$0.0276789\pi$
$23$	6.01752	+	5.04930i	1.25474	+	1.05285i	0.258519	+	0.966006i	$0.416766\pi$
$24$	−0.422099	+	0.103128i	−0.0861605	+	0.0210509i
$25$	−4.71722	+	1.65765i	−0.943445	+	0.331530i
$26$	0.708003	−	4.59636i	0.138851	−	0.901419i
$27$	−0.795114	+	0.459059i	−0.153020	+	0.0883460i
$28$	−2.11334	+	4.05734i	−0.399383	+	0.766765i
$29$	−1.63276	−	4.48597i	−0.303196	−	0.833024i	−0.993940	−	0.109925i	$-0.964939\pi$
$29$	−1.63276	−	4.48597i	−0.303196	−	0.833024i	0.690744	−	0.723099i	$-0.257283\pi$
$30$	0.173495	+	0.453765i	0.0316756	+	0.0828459i
$31$	−2.75076	+	4.76446i	−0.494052	+	0.855723i	−0.999977	−	0.00685468i	$-0.997818\pi$
$31$	−2.75076	+	4.76446i	−0.494052	+	0.855723i	0.505925	+	0.862578i	$0.331151\pi$
$32$	−5.62360	+	0.612518i	−0.994121	+	0.108279i
$33$	−0.367383	+	0.308271i	−0.0639532	+	0.0536631i
$34$	−0.873955	+	2.57359i	−0.149882	+	0.441367i
$35$	4.79644	+	1.77608i	0.810746	+	0.300212i
$36$	−5.50021	+	2.27674i	−0.916701	+	0.379456i
$37$	−5.87587			−0.965987			−0.482994	−	0.875624i	$-0.660451\pi$
$37$	−5.87587			−0.965987			−0.482994	+	0.875624i	$0.660451\pi$
$38$	−1.56975	−	5.96120i	−0.254647	−	0.967034i
$39$			0.505184i			0.0808942i
$40$	1.46683	+	6.15211i	0.231926	+	0.972733i
$41$	−2.91951	+	0.514788i	−0.455950	+	0.0803963i	−0.396906	−	0.917859i	$-0.629916\pi$
$41$	−2.91951	+	0.514788i	−0.455950	+	0.0803963i	−0.0590437	+	0.998255i	$0.518805\pi$
$42$	0.159794	−	0.470555i	0.0246568	−	0.0726082i
$43$	3.18112	−	2.66928i	0.485117	−	0.407061i	−0.367156	−	0.930160i	$-0.619668\pi$
$43$	3.18112	−	2.66928i	0.485117	−	0.407061i	0.852272	+	0.523098i	$0.175224\pi$
$44$	−5.26660	+	3.35344i	−0.793970	+	0.505551i
$45$	3.29556	+	5.78222i	0.491273	+	0.861962i
$46$	−8.66299	−	6.95447i	−1.27729	−	1.02538i
$47$	−5.85679	+	2.13170i	−0.854301	+	0.310940i	−0.731793	−	0.681527i	$-0.761316\pi$
$47$	−5.85679	+	2.13170i	−0.854301	+	0.310940i	−0.122508	+	0.992467i	$0.539094\pi$
$48$	0.593633	−	0.158762i	0.0856835	−	0.0229154i
$49$	0.883975	+	1.53109i	0.126282	+	0.218727i
$50$	6.61873	−	2.48846i	0.936029	−	0.351922i
$51$	0.0512688	−	0.290760i	0.00717906	−	0.0407145i
$52$	−0.859999	+	6.52042i	−0.119260	+	0.904220i
$53$	5.37638	+	4.51132i	0.738502	+	0.619677i	0.932435	−	0.361338i	$-0.117680\pi$
$53$	5.37638	+	4.51132i	0.738502	+	0.619677i	−0.193933	+	0.981015i	$0.562124\pi$
$54$	1.11011	−	0.673452i	0.151067	−	0.0916452i
$55$	4.45717	+	5.37234i	0.601004	+	0.724406i
$56$	2.86351	−	5.80144i	0.382653	−	0.775250i
$57$	0.267116	+	0.614049i	0.0353804	+	0.0813327i
$58$	2.44617	+	6.29253i	0.321198	+	0.826250i
$59$	−5.48925	−	1.99792i	−0.714639	−	0.260107i	−0.0409910	−	0.999160i	$-0.513051\pi$
$59$	−5.48925	−	1.99792i	−0.714639	−	0.260107i	−0.673648	+	0.739052i	$0.735274\pi$
$60$	−0.259224	−	0.636247i	−0.0334657	−	0.0821391i
$61$	−8.49907	−	7.13157i	−1.08819	−	0.913104i	−0.0916195	−	0.995794i	$-0.529204\pi$
$61$	−8.49907	−	7.13157i	−1.08819	−	0.913104i	−0.996575	+	0.0826902i	$0.973649\pi$
$62$	3.74306	−	6.82079i	0.475369	−	0.866241i
$63$	1.18222	−	6.70469i	0.148945	−	0.844711i
$64$	7.93230	−	1.03858i	0.991537	−	0.129822i
$65$	7.35307	+	0.0409589i	0.912037	+	0.00508032i
$66$	0.509977	−	0.447131i	0.0627738	−	0.0550380i
$67$	−1.09648	−	3.01256i	−0.133957	−	0.368043i	0.854520	−	0.519419i	$-0.173852\pi$
$67$	−1.09648	−	3.01256i	−0.133957	−	0.368043i	−0.988476	+	0.151377i	$0.951629\pi$
$68$	1.15670	−	3.66556i	0.140271	−	0.444515i
$69$	1.04509	+	0.603383i	0.125814	+	0.0726388i
$70$	−6.83608	−	2.36399i	−0.817068	−	0.282551i
$71$	−9.98926	+	8.38198i	−1.18551	+	0.994759i	−0.185581	+	0.982629i	$0.559417\pi$
$71$	−9.98926	+	8.38198i	−1.18551	+	0.994759i	−0.999926	+	0.0121295i	$0.996139\pi$
$72$	7.70678	−	3.38780i	0.908253	−	0.399256i
$73$	6.42811	−	1.13345i	0.752353	−	0.132660i	0.215696	−	0.976461i	$-0.430798\pi$
$73$	6.42811	−	1.13345i	0.752353	−	0.132660i	0.536657	+	0.843801i	$0.319687\pi$
$74$	8.30778	−	0.180293i	0.965760	−	0.0209587i
$75$	−0.669449	+	0.376626i	−0.0773013	+	0.0434890i
$76$	2.40235	+	8.38026i	0.275568	+	0.961282i
$77$		−	7.14072i		−	0.813760i
$78$	−0.0155009	−	0.714270i	−0.00175513	−	0.0808752i
$79$	−0.838432	−	4.75499i	−0.0943310	−	0.534978i	−0.994950	−	0.100369i	$-0.967998\pi$
$79$	−0.838432	−	4.75499i	−0.0943310	−	0.534978i	0.900619	−	0.434609i	$-0.143113\pi$
$80$	−2.26269	−	8.65334i	−0.252977	−	0.967472i
$81$	6.73212	−	5.64892i	0.748013	−	0.627657i
$82$	4.11204	−	0.817429i	0.454098	−	0.0902700i
$83$	3.97221	−	6.88007i	0.436006	−	0.755185i	−0.561371	−	0.827564i	$-0.689726\pi$
$83$	3.97221	−	6.88007i	0.436006	−	0.755185i	0.997377	+	0.0723791i	$0.0230591\pi$
$84$	−0.211491	+	0.670212i	−0.0230756	+	0.0731261i
$85$	−4.22792	−	0.769803i	−0.458582	−	0.0834968i
$86$	−4.41583	+	3.87165i	−0.476171	+	0.417491i
$87$	−0.366691	−	0.635127i	−0.0393134	−	0.0680928i
$88$	7.34345	−	4.90297i	0.782815	−	0.522658i
$89$	1.58191	+	0.278934i	0.167682	+	0.0295669i	0.256859	−	0.966449i	$-0.417312\pi$
$89$	1.58191	+	0.278934i	0.167682	+	0.0295669i	−0.0891766	+	0.996016i	$0.528424\pi$
$90$	−4.83695	−	8.07425i	−0.509859	−	0.851101i
$91$	−5.76210	−	4.83497i	−0.604032	−	0.506843i
$92$	12.4618	+	9.56698i	1.29924	+	0.997427i
$93$	−0.289064	+	0.794197i	−0.0299746	+	0.0823544i
$94$	8.21540	−	3.19368i	0.847354	−	0.329402i
$95$	8.95928	−	3.83815i	0.919202	−	0.393786i
$96$	−0.834455	+	0.242686i	−0.0851662	+	0.0247690i
$97$	4.18121	+	1.52184i	0.424538	+	0.154519i	0.545449	−	0.838144i	$-0.316359\pi$
$97$	4.18121	+	1.52184i	0.424538	+	0.154519i	−0.120911	+	0.992663i	$0.538582\pi$
$98$	−1.29681	−	2.13765i	−0.130998	−	0.215936i
$99$	5.97262	−	7.11789i	0.600271	−	0.715375i
$100$	−9.28173	+	3.72148i	−0.928173	+	0.372148i
$101$	2.19281	−	12.4360i	0.218193	−	1.23743i	−0.657087	−	0.753815i	$-0.728212\pi$
$101$	2.19281	−	12.4360i	0.218193	−	1.23743i	0.875280	−	0.483617i	$-0.160677\pi$
$102$	−0.0635664	+	0.412673i	−0.00629401	+	0.0408607i
$103$	−11.9129	+	6.87794i	−1.17382	+	0.677704i	−0.954576	−	0.297967i	$-0.903691\pi$
$103$	−11.9129	+	6.87794i	−1.17382	+	0.677704i	−0.219241	+	0.975671i	$0.570358\pi$
$104$	1.01587	−	9.24549i	0.0996139	−	0.906595i
$105$	0.773033	+	0.140751i	0.0754403	+	0.0137359i
$106$	−7.73998	−	6.21349i	−0.751773	−	0.603508i
$107$	−4.51393	−	2.60612i	−0.436378	−	0.251943i	0.265682	−	0.964061i	$-0.414403\pi$
$107$	−4.51393	−	2.60612i	−0.436378	−	0.251943i	−0.702060	+	0.712118i	$0.747736\pi$
$108$	−1.54890	+	0.986243i	−0.149043	+	0.0949013i
$109$	12.8126	+	15.2694i	1.22722	+	1.46255i	0.841787	+	0.539810i	$0.181504\pi$
$109$	12.8126	+	15.2694i	1.22722	+	1.46255i	0.385434	+	0.922735i	$0.374052\pi$
$110$	−6.46675	−	7.45908i	−0.616580	−	0.711196i
$111$	−0.888962	+	0.156748i	−0.0843765	+	0.0148779i
$112$	−3.87066	+	8.29041i	−0.365743	+	0.783370i
$113$	−1.82511			−0.171692			−0.0858460	−	0.996308i	$-0.527359\pi$
$113$	−1.82511			−0.171692			−0.0858460	+	0.996308i	$0.527359\pi$
$114$	−0.396511	−	0.859995i	−0.0371367	−	0.0805459i
$115$	8.86711	−	15.1626i	0.826862	−	1.41392i
$116$	−3.65168	−	8.82183i	−0.339050	−	0.819086i
$117$	−1.69962	−	9.63903i	−0.157130	−	0.891129i
$118$	7.82245	+	2.65639i	0.720114	+	0.244541i
$119$	2.82571	+	3.36754i	0.259032	+	0.308702i
$120$	0.386034	+	0.891623i	0.0352399	+	0.0813937i
$121$	−0.627163	+	1.08628i	−0.0570148	+	0.0987526i
$122$	12.2355	+	9.82241i	1.10775	+	0.889279i
$123$	−0.427960	+	0.155765i	−0.0385878	+	0.0140448i
$124$	−5.08296	+	9.75863i	−0.456463	+	0.876351i
$125$	5.42760	+	9.77452i	0.485459	+	0.874259i
$126$	−1.46579	+	9.51591i	−0.130583	+	0.847744i
$127$	−20.9092	−	3.68685i	−1.85539	−	0.327155i	−0.869418	−	0.494078i	$-0.835506\pi$
$127$	−20.9092	−	3.68685i	−1.85539	−	0.327155i	−0.985970	+	0.166923i	$0.946617\pi$
$128$	−11.1835	+	1.71182i	−0.988487	+	0.151305i
$129$	0.410066	−	0.488697i	0.0361043	−	0.0430274i
$130$	−10.3976	+	0.167708i	−0.911932	+	0.0147090i
$131$	4.90471	−	13.4756i	0.428526	−	1.17737i	−0.518181	−	0.855271i	$-0.673391\pi$
$131$	4.90471	−	13.4756i	0.428526	−	1.17737i	0.946707	−	0.322095i	$-0.104387\pi$
$132$	−0.707327	+	0.647838i	−0.0615649	+	0.0563870i
$133$	−9.56029	−	2.83018i	−0.828982	−	0.245407i
$134$	1.64273	+	4.22575i	0.141910	+	0.365050i
$135$	1.31085	+	1.58000i	0.112820	+	0.135984i
$136$	−1.52296	+	5.21816i	−0.130593	+	0.447453i
$137$	3.41698	−	4.07220i	0.291932	−	0.347911i	−0.600066	−	0.799951i	$-0.704859\pi$
$137$	3.41698	−	4.07220i	0.291932	−	0.347911i	0.891998	+	0.452039i	$0.149303\pi$
$138$	−1.49615	−	0.821044i	−0.127360	−	0.0698919i
$139$	11.3456	+	2.00054i	0.962324	+	0.169684i	0.632673	−	0.774419i	$-0.281958\pi$
$139$	11.3456	+	2.00054i	0.962324	+	0.169684i	0.329651	+	0.944103i	$0.393069\pi$
$140$	9.73794	+	3.13264i	0.823006	+	0.264757i
$141$	−0.829209	+	0.478744i	−0.0698320	+	0.0403175i
$142$	13.8664	−	12.1576i	1.16365	−	1.02025i
$143$	−3.51114	−	9.64678i	−0.293616	−	0.806704i
$144$	−10.7925	+	5.02642i	−0.899376	+	0.418868i
$145$	−9.27415	+	5.28577i	−0.770176	+	0.438960i
$146$	−9.05380	+	1.79980i	−0.749297	+	0.148952i
$147$	0.174581	+	0.208057i	0.0143992	+	0.0171603i
$148$	−11.7407	+	0.509826i	−0.965078	+	0.0419075i
$149$	0.0359967	+	0.204147i	0.00294896	+	0.0167244i	0.986247	−	0.165280i	$-0.0528527\pi$
$149$	0.0359967	+	0.204147i	0.00294896	+	0.0167244i	−0.983298	+	0.182004i	$0.941742\pi$
$150$	0.934964	−	0.553045i	0.0763395	−	0.0451559i
$151$	19.5350			1.58974			0.794869	−	0.606782i	$-0.207540\pi$
$151$	19.5350			1.58974			0.794869	+	0.606782i	$0.207540\pi$
$152$	−3.65377	−	11.7750i	−0.296360	−	0.955076i
$153$			5.72025i			0.462454i
$154$	0.219103	+	10.0961i	0.0176558	+	0.813569i
$155$	11.5363	+	4.27179i	0.926617	+	0.343118i
$156$	0.0438328	+	1.00942i	0.00350944	+	0.0808181i
$157$	8.13938	+	9.70014i	0.649593	+	0.774155i	0.985853	−	0.167614i	$-0.0536063\pi$
$157$	8.13938	+	9.70014i	0.649593	+	0.774155i	−0.336259	+	0.941769i	$0.609162\pi$
$158$	1.33134	+	6.69726i	0.105916	+	0.532805i
$159$	0.933739	+	0.539094i	0.0740503	+	0.0427530i
$160$	3.46469	+	12.1654i	0.273908	+	0.961756i
$161$	−16.8844	+	6.14542i	−1.33068	+	0.484327i
$162$	−9.34508	+	8.19346i	−0.734219	+	0.643739i
$163$	12.2028	+	21.1358i	0.955794	+	1.65548i	0.732540	+	0.680724i	$0.238335\pi$
$163$	12.2028	+	21.1358i	0.955794	+	1.65548i	0.223254	+	0.974760i	$0.428332\pi$
$164$	−5.78885	+	1.28192i	−0.452033	+	0.100101i
$165$	0.817641	+	0.693880i	0.0636533	+	0.0540185i
$166$	−5.40512	+	9.84947i	−0.419519	+	0.764467i
$167$	−8.60781	+	10.2584i	−0.666093	+	0.793818i	−0.988246	−	0.152869i	$-0.951149\pi$
$167$	−8.60781	+	10.2584i	−0.666093	+	0.793818i	0.322154	+	0.946687i	$0.395593\pi$
$168$	0.278459	−	0.954089i	0.0214836	−	0.0736096i
$169$	2.05428	+	0.747699i	0.158022	+	0.0575153i
$170$	6.00139	+	0.958681i	0.460286	+	0.0735275i
$171$	−7.16251	−	10.8175i	−0.547731	−	0.827236i
$172$	6.12466	−	5.60955i	0.467001	−	0.427724i
$173$	−0.0360467	−	0.0131199i	−0.00274058	−	0.000997489i	0.340649	−	0.940190i	$-0.389353\pi$
$173$	−0.0360467	−	0.0131199i	−0.00274058	−	0.000997489i	−0.343390	+	0.939193i	$0.611575\pi$
$174$	0.537945	+	0.886742i	0.0407815	+	0.0672238i
$175$	2.11134	−	11.2403i	0.159602	−	0.849684i
$176$	−10.2323	+	7.15754i	−0.771290	+	0.539520i
$177$	−0.883767	−	0.155832i	−0.0664280	−	0.0117130i
$178$	−2.24519	−	0.345840i	−0.168284	−	0.0259218i
$179$	4.96725	+	8.60354i	0.371270	+	0.643059i	0.989761	−	0.142733i	$-0.0455891\pi$
$179$	4.96725	+	8.60354i	0.371270	+	0.643059i	−0.618491	+	0.785792i	$0.712256\pi$
$180$	7.08661	+	11.2676i	0.528205	+	0.839838i
$181$	1.28316	+	3.52546i	0.0953767	+	0.262045i	0.978202	−	0.207656i	$-0.0665836\pi$
$181$	1.28316	+	3.52546i	0.0953767	+	0.262045i	−0.882825	+	0.469702i	$0.844361\pi$
$182$	8.29527	+	6.65927i	0.614887	+	0.493618i
$183$	−1.47607	−	0.852210i	−0.109114	−	0.0629972i
$184$	−17.9131	−	13.1442i	−1.32057	−	0.969003i
$185$	2.20943	+	12.9517i	0.162440	+	0.952232i
$186$	0.384333	−	1.13177i	0.0281807	−	0.0829854i
$187$	1.04184	+	5.90855i	0.0761866	+	0.432076i
$188$	−11.5176	+	4.76755i	−0.840007	+	0.347710i
$189$		−	2.10007i		−	0.152758i
$190$	−12.5496	+	5.70159i	−0.910442	+	0.413637i
$191$			13.1089i			0.948525i	0.880384	+	0.474262i	$0.157285\pi$
$191$			13.1089i			0.948525i	−0.880384	+	0.474262i	$0.842715\pi$
$192$	1.17237	−	0.368733i	0.0846087	−	0.0266110i
$193$	−3.92601	−	22.2655i	−0.282600	−	1.60271i	−0.713733	−	0.700418i	$-0.752997\pi$
$193$	−3.92601	−	22.2655i	−0.282600	−	1.60271i	0.431132	−	0.902289i	$-0.358114\pi$
$194$	−5.95843	−	2.02340i	−0.427790	−	0.145272i
$195$	1.11354	−	0.189958i	0.0797423	−	0.0136032i
$196$	1.89913	+	2.98260i	0.135652	+	0.213043i
$197$	2.01367	+	1.16259i	0.143468	+	0.0828313i	0.570016	−	0.821634i	$-0.306937\pi$
$197$	2.01367	+	1.16259i	0.143468	+	0.0828313i	−0.426548	+	0.904465i	$0.640270\pi$
$198$	−8.22616	+	10.2471i	−0.584608	+	0.728230i
$199$	−6.35460	−	17.4591i	−0.450466	−	1.23764i	−0.932397	−	0.361435i	$-0.882287\pi$
$199$	−6.35460	−	17.4591i	−0.450466	−	1.23764i	0.481932	−	0.876209i	$-0.339935\pi$
$200$	13.0091	−	5.54652i	0.919881	−	0.392198i
$201$	−0.246251	−	0.426520i	−0.0173692	−	0.0300844i
$202$	−2.71879	+	17.6504i	−0.191293	+	1.24187i
$203$	10.7537	+	1.89617i	0.754762	+	0.133085i
$204$	0.0772129	−	0.585420i	0.00540599	−	0.0409876i
$205$	2.23249	+	6.24168i	0.155924	+	0.435938i
$206$	16.6324	−	10.0901i	1.15884	−	0.703012i
$207$	−21.9706	−	7.99663i	−1.52706	−	0.555804i
$208$	−1.15263	+	13.1032i	−0.0799204	+	0.908542i
$209$	−9.36850	−	9.86909i	−0.648033	−	0.682659i
$210$	−1.09730	−	0.175285i	−0.0757206	−	0.0120958i
$211$	0.643731	+	0.234299i	0.0443163	+	0.0161298i	0.364083	−	0.931366i	$-0.381382\pi$
$211$	0.643731	+	0.234299i	0.0443163	+	0.0161298i	−0.319767	+	0.947496i	$0.603605\pi$
$212$	11.1341	+	8.54765i	0.764690	+	0.587055i
$213$	−1.28767	+	1.53459i	−0.0882300	+	0.105148i
$214$	6.46213	+	3.54624i	0.441742	+	0.242416i
$215$	−7.07985	−	6.00822i	−0.482842	−	0.409757i
$216$	2.15970	−	1.44196i	0.146949	−	0.0981127i
$217$	−6.29201	−	10.8981i	−0.427129	−	0.739810i
$218$	−18.5840	−	21.1960i	−1.25866	−	1.43557i
$219$	0.942272	−	0.342959i	0.0636729	−	0.0231750i
$220$	9.37208	+	10.3478i	0.631866	+	0.697651i
$221$	5.47324	+	3.15998i	0.368170	+	0.212563i
$222$	1.25208	−	0.248899i	0.0840338	−	0.0167050i
$223$	−9.18731	−	10.9490i	−0.615228	−	0.733200i	0.365014	−	0.931002i	$-0.381064\pi$
$223$	−9.18731	−	10.9490i	−0.615228	−	0.733200i	−0.980242	+	0.197802i	$0.936620\pi$
$224$	5.21827	−	11.8404i	0.348660	−	0.791121i
$225$	11.5061	−	9.43837i	0.767075	−	0.629225i
$226$	2.58049	−	0.0560011i	0.171652	−	0.00372514i
$227$		−	1.48043i		−	0.0982597i	−0.998792	−	0.0491299i	$-0.984355\pi$
$227$		−	1.48043i		−	0.0982597i	0.998792	−	0.0491299i	$-0.0156448\pi$
$228$	0.587007	+	1.20376i	0.0388755	+	0.0797212i
$229$	−17.3105			−1.14391			−0.571955	−	0.820285i	$-0.693815\pi$
$229$	−17.3105			−1.14391			−0.571955	+	0.820285i	$0.693815\pi$
$230$	−12.0718	+	21.7102i	−0.795990	+	1.43153i
$231$	−0.190490	−	1.08032i	−0.0125333	−	0.0710799i
$232$	5.43372	+	12.3610i	0.356741	+	0.811537i
$233$	−0.819376	−	0.976494i	−0.0536791	−	0.0639723i	0.738537	−	0.674213i	$-0.235517\pi$
$233$	−0.819376	−	0.976494i	−0.0536791	−	0.0639723i	−0.792216	+	0.610241i	$0.791073\pi$
$234$	2.69882	+	13.5763i	0.176428	+	0.887510i
$235$	6.90100	+	12.1081i	0.450172	+	0.789848i
$236$	−11.1415	−	3.51580i	−0.725251	−	0.228859i
$237$	−0.253693	−	0.697016i	−0.0164791	−	0.0452761i
$238$	−4.09854	−	4.67460i	−0.265669	−	0.303010i
$239$	−10.7325	+	6.19641i	−0.694228	+	0.400813i	−0.805194	−	0.593012i	$-0.797939\pi$
$239$	−10.7325	+	6.19641i	−0.694228	+	0.400813i	0.110966	+	0.993824i	$0.464605\pi$
$240$	−0.573164	−	1.24880i	−0.0369976	−	0.0806099i
$241$	26.5697	+	4.68495i	1.71150	+	0.301784i	0.941690	−	0.336483i	$-0.109237\pi$
$241$	26.5697	+	4.68495i	1.71150	+	0.301784i	0.769815	+	0.638267i	$0.220349\pi$
$242$	0.853403	−	1.55511i	0.0548588	−	0.0999664i
$243$	2.63828	−	3.14417i	0.169245	−	0.201699i
$244$	−17.6009	−	13.5123i	−1.12678	−	0.865035i
$245$	3.04248	−	2.52420i	0.194377	−	0.161265i
$246$	0.600304	−	0.233364i	0.0382740	−	0.0148787i
$247$	−14.3071	+	0.877422i	−0.910340	+	0.0558290i
$248$	6.88726	−	13.9535i	0.437342	−	0.886048i
$249$	0.417420	−	1.14685i	0.0264529	−	0.0726787i
$250$	−7.97389	−	13.6535i	−0.504313	−	0.863521i
$251$	0.660711	−	0.787405i	0.0417037	−	0.0497006i	−0.744789	−	0.667300i	$-0.767450\pi$
$251$	0.660711	−	0.787405i	0.0417037	−	0.0497006i	0.786493	+	0.617599i	$0.211895\pi$
$252$	1.78047	−	13.4993i	0.112159	−	0.850378i
$253$	−24.1502	−	4.25834i	−1.51831	−	0.267719i
$254$	29.6762	+	4.57119i	1.86205	+	0.286822i
$255$	−0.660178	−	0.00367739i	−0.0413419	−	0.000230287i
$256$	15.7595	−	2.76346i	0.984972	−	0.172716i
$257$	−27.7385	+	10.0960i	−1.73028	+	0.629770i	−0.998651	−	0.0519329i	$-0.983462\pi$
$257$	−27.7385	+	10.0960i	−1.73028	+	0.629770i	−0.731629	+	0.681703i	$0.761240\pi$
$258$	−0.564789	+	0.703542i	−0.0351622	+	0.0438006i
$259$	6.72014	−	11.6396i	0.417569	−	0.723251i
$260$	14.6959	−	0.556156i	0.911398	−	0.0344914i
$261$	9.13334	+	10.8847i	0.565339	+	0.673745i
$262$	−6.52119	+	19.2033i	−0.402880	+	1.18639i
$263$	2.01885	+	11.4495i	0.124488	+	0.706005i	0.981611	+	0.190894i	$0.0611385\pi$
$263$	2.01885	+	11.4495i	0.124488	+	0.706005i	−0.857123	+	0.515112i	$0.827750\pi$
$264$	0.980198	−	0.937669i	0.0603270	−	0.0577095i
$265$	7.92235	−	13.5471i	0.486666	−	0.832190i
$266$	13.6039	+	3.70819i	0.834111	+	0.227364i
$267$	0.246768			0.0151020
$268$	−2.45229	−	5.92431i	−0.149797	−	0.361885i
$269$	−3.27256	+	0.577041i	−0.199532	+	0.0351828i	−0.272521	−	0.962150i	$-0.587857\pi$
$269$	−3.27256	+	0.577041i	−0.199532	+	0.0351828i	0.0729891	+	0.997333i	$0.476746\pi$
$270$	−1.90186	−	2.19371i	−0.115744	−	0.133505i
$271$	5.52013	+	6.57864i	0.335324	+	0.399624i	0.907188	−	0.420724i	$-0.138224\pi$
$271$	5.52013	+	6.57864i	0.335324	+	0.399624i	−0.571864	+	0.820348i	$0.693780\pi$
$272$	1.99318	−	7.42458i	0.120854	−	0.450182i
$273$	−1.00073	−	0.577771i	−0.0605669	−	0.0349683i
$274$	−4.70625	+	5.86245i	−0.284315	+	0.354163i
$275$	10.1659	−	11.8447i	0.613025	−	0.714262i
$276$	2.14057	+	1.11495i	0.128847	+	0.0671122i
$277$	24.8389	−	14.3407i	1.49242	−	0.861652i	0.492462	−	0.870334i	$-0.336097\pi$
$277$	24.8389	−	14.3407i	1.49242	−	0.861652i	0.999962	+	0.00868205i	$0.00276362\pi$
$278$	−16.1028	−	2.48040i	−0.965779	−	0.148765i
$279$	2.84345	−	16.1260i	0.170233	−	0.965437i
$280$	−13.8644	−	4.13039i	−0.828557	−	0.246838i
$281$	−5.12580	+	6.10870i	−0.305780	+	0.364414i	−0.896950	−	0.442133i	$-0.854222\pi$
$281$	−5.12580	+	6.10870i	−0.305780	+	0.364414i	0.591170	+	0.806547i	$0.298666\pi$
$282$	1.15771	−	0.702330i	0.0689408	−	0.0418231i
$283$	8.69829	+	3.16592i	0.517059	+	0.188194i	0.587351	−	0.809332i	$-0.300171\pi$
$283$	8.69829	+	3.16592i	0.517059	+	0.188194i	−0.0702917	+	0.997526i	$0.522393\pi$
$284$	−19.2324	+	17.6149i	−1.14124	+	1.04525i
$285$	1.25306	−	0.819676i	0.0742250	−	0.0485534i
$286$	5.26033	+	13.5317i	0.311050	+	0.800144i
$287$	2.31924	−	6.37206i	0.136900	−	0.376131i
$288$	15.1051	−	7.43791i	0.890077	−	0.438283i
$289$	10.1933	+	8.55320i	0.599607	+	0.503130i
$290$	12.9504	−	7.75802i	0.760471	−	0.455567i
$291$	0.673174	+	0.118699i	0.0394621	+	0.00695824i
$292$	12.7458	−	2.82250i	0.745889	−	0.165175i
$293$	11.6529	+	20.1833i	0.680767	+	1.17912i	0.974747	+	0.223311i	$0.0716867\pi$
$293$	11.6529	+	20.1833i	0.680767	+	1.17912i	−0.293980	+	0.955812i	$0.594980\pi$
$294$	−0.253220	−	0.288811i	−0.0147681	−	0.0168438i
$295$	−2.33982	+	12.8508i	−0.136230	+	0.748202i
$296$	16.5843	−	1.08108i	0.963942	−	0.0628365i
$297$	1.43309	−	2.48219i	0.0831566	−	0.144031i
$298$	−0.0571590	−	0.287536i	−0.00331113	−	0.0166565i
$299$	−19.7883	+	16.6044i	−1.14439	+	0.960255i
$300$	−1.30496	+	0.810627i	−0.0753418	+	0.0468016i
$301$	1.64943	+	9.35436i	0.0950713	+	0.539176i
$302$	−27.6202	+	0.599406i	−1.58936	+	0.0344919i
$303$		−	1.93995i		−	0.111447i
$304$	5.52729	+	16.5363i	0.317012	+	0.948422i
$305$	−12.5238	+	21.4155i	−0.717110	+	1.22625i
$306$	−0.175518	−	8.08775i	−0.0100337	−	0.462346i
$307$	20.9191	−	3.68859i	1.19391	−	0.210519i	0.458848	−	0.888515i	$-0.348262\pi$
$307$	20.9191	−	3.68859i	1.19391	−	0.210519i	0.735066	+	0.677996i	$0.237151\pi$
$308$	−0.619572	−	14.2680i	−0.0353034	−	0.812994i
$309$	−1.61883	+	1.35836i	−0.0920921	+	0.0772745i
$310$	−16.4420	−	5.68582i	−0.933843	−	0.322933i
$311$	12.1565	+	7.01855i	0.689331	+	0.397985i	0.803361	−	0.595492i	$-0.203043\pi$
$311$	12.1565	+	7.01855i	0.689331	+	0.397985i	−0.114031	+	0.993477i	$0.536376\pi$
$312$	−0.0929470	−	1.42585i	−0.00526209	−	0.0807229i
$313$	1.85628	+	5.10009i	0.104923	+	0.288274i	0.981034	−	0.193836i	$-0.0620929\pi$
$313$	1.85628	+	5.10009i	0.104923	+	0.288274i	−0.876111	+	0.482110i	$0.839871\pi$
$314$	−11.8057	−	13.4651i	−0.666237	−	0.759879i
$315$	−15.2232	−	0.0847978i	−0.857729	−	0.00477782i
$316$	−2.08786	−	9.42827i	−0.117451	−	0.530382i
$317$	1.32909	−	7.53762i	0.0746489	−	0.423355i	−0.924465	−	0.381267i	$-0.875488\pi$
$317$	1.32909	−	7.53762i	0.0746489	−	0.423355i	0.999114	−	0.0420880i	$-0.0134010\pi$
$318$	−1.33674	−	0.733565i	−0.0749605	−	0.0411363i
$319$	11.4164	+	9.57953i	0.639198	+	0.536351i
$320$	−5.27194	−	17.0941i	−0.294711	−	0.955587i
$321$	−0.752436	−	0.273864i	−0.0419969	−	0.0152856i
$322$	23.6840	−	9.20696i	1.31986	−	0.513084i
$323$	8.32353	+	0.946961i	0.463134	+	0.0526903i
$324$	12.9614	−	11.8713i	0.720079	−	0.659518i
$325$	−2.67460	−	16.2232i	−0.148360	−	0.899903i
$326$	−17.9018	−	29.5091i	−0.991488	−	1.63436i
$327$	2.34575	+	1.96832i	0.129720	+	0.108848i
$328$	8.14541	−	1.99010i	0.449755	−	0.109885i
$329$	2.47560	−	14.0398i	0.136484	−	0.774040i
$330$	−1.17734	−	0.955975i	−0.0648103	−	0.0526247i
$331$	−11.1928	−	19.3866i	−0.615214	−	1.06558i	−0.990347	−	0.138611i	$-0.955736\pi$
$331$	−11.1928	−	19.3866i	−0.615214	−	1.06558i	0.375132	−	0.926971i	$-0.377597\pi$
$332$	7.33998	−	14.0918i	0.402834	−	0.773390i
$333$	16.4342	−	5.98157i	0.900590	−	0.327788i
$334$	11.8557	−	14.7683i	0.648713	−	0.808083i
$335$	−6.22806	+	3.54967i	−0.340275	+	0.193939i
$336$	−0.364433	+	1.35751i	−0.0198814	+	0.0740584i
$337$	−3.20907	+	2.69273i	−0.174809	+	0.146682i	−0.725994	−	0.687701i	$-0.758620\pi$
$337$	−3.20907	+	2.69273i	−0.174809	+	0.146682i	0.551185	+	0.834383i	$0.314176\pi$
$338$	−2.92746	−	0.994124i	−0.159233	−	0.0540732i
$339$	−0.276121	+	0.0486877i	−0.0149969	+	0.00264435i
$340$	−8.51467	−	1.17132i	−0.461773	−	0.0635235i
$341$		−	17.1747i		−	0.930063i
$342$	10.4589	+	15.0749i	0.565550	+	0.815157i
$343$	−20.0555			−1.08290
$344$	−8.48741	+	8.11916i	−0.457611	+	0.437756i
$345$	0.937021	−	2.53050i	0.0504475	−	0.136237i
$346$	0.0513683	+	0.0174439i	0.00276157	+	0.000937792i
$347$	−12.9821	+	10.8933i	−0.696917	+	0.584783i	−0.920895	−	0.389811i	$-0.872540\pi$
$347$	−12.9821	+	10.8933i	−0.696917	+	0.584783i	0.223977	+	0.974594i	$0.428096\pi$
$348$	−0.787798	−	1.23724i	−0.0422304	−	0.0663231i
$349$	16.2865	−	28.2090i	0.871796	−	1.51000i	0.0116594	−	0.999932i	$-0.496289\pi$
$349$	16.2865	−	28.2090i	0.871796	−	1.51000i	0.860137	−	0.510063i	$-0.170378\pi$
$350$	−2.64029	+	15.9572i	−0.141129	+	0.852947i
$351$	−1.03262	−	2.83710i	−0.0551173	−	0.151433i
$352$	14.2477	−	10.4339i	0.759403	−	0.556127i
$353$	9.64584	−	5.56903i	0.513396	−	0.296409i	−0.220832	−	0.975312i	$-0.570877\pi$
$353$	9.64584	−	5.56903i	0.513396	−	0.296409i	0.734229	+	0.678902i	$0.237544\pi$
$354$	1.25432	+	0.193211i	0.0666665	+	0.0102690i
$355$	22.2319	+	18.8668i	1.17995	+	1.00135i
$356$	3.18504	+	0.420086i	0.168807	+	0.0222645i
$357$	0.517336	+	0.434096i	0.0273803	+	0.0229748i
$358$	−7.28709	−	12.0120i	−0.385135	−	0.634852i
$359$	−10.1160	+	27.7934i	−0.533901	+	1.46688i	0.320492	+	0.947251i	$0.396152\pi$
$359$	−10.1160	+	27.7934i	−0.533901	+	1.46688i	−0.854392	+	0.519629i	$0.826070\pi$
$360$	−10.3654	−	15.7136i	−0.546302	−	0.828180i
$361$	−16.9263	+	8.63138i	−0.890857	+	0.454283i
$362$	−1.92241	−	4.94521i	−0.101040	−	0.259914i
$363$	−0.0659055	+	0.181074i	−0.00345914	+	0.00950391i
$364$	−11.9329	−	9.16089i	−0.625452	−	0.480161i
$365$	−4.91545	−	13.7428i	−0.257287	−	0.719331i
$366$	2.11314	+	1.15963i	0.110455	+	0.0606150i
$367$	1.15830	−	6.56904i	0.0604627	−	0.342901i	−0.939537	−	0.342447i	$-0.888744\pi$
$367$	1.15830	−	6.56904i	0.0604627	−	0.342901i	1.00000		0.000454162i	$-0.000144564\pi$
$368$	25.7303	+	18.0347i	1.34128	+	0.940123i
$369$	7.64152	−	4.41183i	0.397802	−	0.229671i
$370$	−3.52127	−	18.2444i	−0.183062	−	0.948483i
$371$	−15.0854	+	5.49064i	−0.783196	+	0.285060i
$372$	−0.508675	+	1.61198i	−0.0263736	+	0.0835773i
$373$	−9.53959	+	16.5231i	−0.493941	+	0.855531i	−0.999976	−	0.00698201i	$-0.997778\pi$
$373$	−9.53959	+	16.5231i	−0.493941	+	0.855531i	0.506034	+	0.862513i	$0.331111\pi$
$374$	−1.65433	−	8.32202i	−0.0855433	−	0.430321i
$375$	1.08189	+	1.33400i	0.0558687	+	0.0688874i
$376$	16.1382	−	7.09415i	0.832265	−	0.365853i
$377$	15.4601	−	2.72604i	0.796237	−	0.140398i
$378$	0.0644380	+	2.96926i	0.00331433	+	0.152722i
$379$	−6.19766			−0.318352			−0.159176	−	0.987250i	$-0.550884\pi$
$379$	−6.19766			−0.318352			−0.159176	+	0.987250i	$0.550884\pi$
$380$	17.5687	−	8.44643i	0.901253	−	0.433293i
$381$	−3.26170			−0.167102
$382$	−0.402228	−	18.5344i	−0.0205798	−	0.948301i
$383$	20.5443	−	3.62251i	1.04976	−	0.185102i	0.377953	−	0.925825i	$-0.376628\pi$
$383$	20.5443	−	3.62251i	1.04976	−	0.185102i	0.671811	+	0.740723i	$0.265517\pi$
$384$	−1.64628	+	0.557317i	−0.0840114	+	0.0284405i
$385$	−15.7398	+	2.68503i	−0.802172	+	0.136842i
$386$	6.23410	+	31.3603i	0.317307	+	1.59620i
$387$	−6.17999	+	10.7041i	−0.314147	+	0.544118i
$388$	8.48660	+	2.67802i	0.430842	+	0.135956i
$389$	−28.0699	+	10.2166i	−1.42320	+	0.518003i	−0.934975	−	0.354714i	$-0.884578\pi$
$389$	−28.0699	+	10.2166i	−1.42320	+	0.518003i	−0.488226	+	0.872717i	$0.662356\pi$
$390$	−1.56858	+	0.302745i	−0.0794284	+	0.0153301i
$391$	13.0743	−	7.54844i	0.661195	−	0.381741i
$392$	−2.77666	−	4.15876i	−0.140243	−	0.210049i
$393$	0.382552	−	2.16956i	0.0192972	−	0.109440i
$394$	−2.88276	−	1.58198i	−0.145231	−	0.0796990i
$395$	−10.1658	+	3.63605i	−0.511497	+	0.182950i
$396$	11.3164	−	14.7406i	0.568670	−	0.740743i
$397$	−6.74781	+	18.5394i	−0.338663	+	0.930468i	0.647112	+	0.762395i	$0.275977\pi$
$397$	−6.74781	+	18.5394i	−0.338663	+	0.930468i	−0.985775	+	0.168073i	$0.946246\pi$
$398$	9.52035	+	24.4901i	0.477212	+	1.22758i
$399$	−1.52188	−	0.173142i	−0.0761891	−	0.00866797i
$400$	−18.2231	+	8.24129i	−0.911155	+	0.412064i
$401$	−4.34695	+	11.9431i	−0.217076	+	0.596412i	−0.999658	−	0.0261351i	$-0.991680\pi$
$401$	−4.34695	+	11.9431i	−0.217076	+	0.596412i	0.782582	+	0.622547i	$0.213902\pi$
$402$	0.361257	+	0.595492i	0.0180179	+	0.0297005i
$403$	−13.8589	−	11.6290i	−0.690360	−	0.579281i
$404$	3.30246	−	25.0389i	0.164304	−	1.24573i
$405$	−14.9829	−	12.7150i	−0.744505	−	0.631814i
$406$	−15.2626	−	2.35099i	−0.757472	−	0.116678i
$407$	15.8858	−	9.17167i	0.787430	−	0.454623i
$408$	−0.0912070	+	0.830083i	−0.00451542	+	0.0410953i
$409$	5.00258	+	13.7445i	0.247361	+	0.679620i	0.999781	+	0.0209356i	$0.00666451\pi$
$409$	5.00258	+	13.7445i	0.247361	+	0.679620i	−0.752419	+	0.658684i	$0.771113\pi$
$410$	−3.34799	−	8.75649i	−0.165346	−	0.432452i
$411$	0.408323	−	0.707237i	0.0201411	−	0.0348854i
$412$	−23.2067	+	14.7766i	−1.14331	+	0.727989i
$413$	10.2357	−	8.58876i	0.503665	−	0.422625i
$414$	31.3091	+	10.6321i	1.53876	+	0.522541i
$415$	−16.6588	−	6.16862i	−0.817750	−	0.302806i
$416$	1.22763	−	18.5617i	0.0601893	−	0.910063i
$417$	1.76985			0.0866699
$418$	13.5488	+	13.6663i	0.662692	+	0.668439i
$419$			8.44375i			0.412504i	0.978499	+	0.206252i	$0.0661267\pi$
$419$			8.44375i			0.412504i	−0.978499	+	0.206252i	$0.933873\pi$
$420$	1.55682	+	0.214164i	0.0759652	+	0.0104501i
$421$	16.1104	−	2.84070i	0.785173	−	0.138447i	0.233333	−	0.972397i	$-0.425037\pi$
$421$	16.1104	−	2.84070i	0.785173	−	0.138447i	0.551840	+	0.833950i	$0.313926\pi$
$422$	−0.917348	−	0.311519i	−0.0446558	−	0.0151645i
$423$	14.2108	−	11.9243i	0.690954	−	0.579779i
$424$	−16.0045	−	11.7437i	−0.777247	−	0.570326i
$425$	−0.107051	+	9.60874i	−0.00519272	+	0.466092i
$426$	1.77353	−	2.20924i	0.0859278	−	0.107038i
$427$	23.8473	−	8.67971i	1.15405	−	0.420041i
$428$	−9.24549	−	4.81568i	−0.446897	−	0.232774i
$429$	−0.788544	−	1.36580i	−0.0380712	−	0.0659413i
$430$	10.1944	+	8.27767i	0.491619	+	0.399185i
$431$	−5.59722	+	31.7434i	−0.269609	+	1.52903i	0.485974	+	0.873973i	$0.338465\pi$
$431$	−5.59722	+	31.7434i	−0.269609	+	1.52903i	−0.755583	+	0.655053i	$0.772646\pi$
$432$	−3.00931	+	2.10502i	−0.144786	+	0.101278i
$433$	16.2724	+	13.6542i	0.782003	+	0.656178i	0.943752	−	0.330654i	$-0.107269\pi$
$433$	16.2724	+	13.6542i	0.782003	+	0.656178i	−0.161750	+	0.986832i	$0.551714\pi$
$434$	9.23054	+	15.2155i	0.443080	+	0.730369i
$435$	−1.26208	+	1.04709i	−0.0605122	+	0.0502040i
$436$	26.9259	+	29.3984i	1.28952	+	1.40793i
$437$	−15.2730	+	30.6456i	−0.730608	+	1.46598i
$438$	−1.32174	+	0.513816i	−0.0631551	+	0.0245511i
$439$	−16.2767	−	5.92425i	−0.776846	−	0.282749i	−0.0769891	−	0.997032i	$-0.524531\pi$
$439$	−16.2767	−	5.92425i	−0.776846	−	0.282749i	−0.699857	+	0.714283i	$0.746753\pi$
$440$	−13.5685	−	14.3430i	−0.646853	−	0.683777i
$441$	−4.03102	−	3.38243i	−0.191953	−	0.161068i
$442$	−7.83547	−	4.29989i	−0.372695	−	0.204525i
$443$	1.90194	−	10.7864i	0.0903637	−	0.512478i	−0.905706	−	0.423906i	$-0.860659\pi$
$443$	1.90194	−	10.7864i	0.0903637	−	0.512478i	0.996070	−	0.0885718i	$-0.0282303\pi$
$444$	−1.76265	+	0.390332i	−0.0836516	+	0.0185244i
$445$	0.0200073	−	3.59177i	0.000948436	−	0.170266i
$446$	13.3257	+	15.1987i	0.630991	+	0.719679i
$447$	0.0108919	+	0.0299252i	0.000515169	+	0.00141541i
$448$	−7.01470	+	16.9010i	−0.331413	+	0.798499i
$449$	−20.3944	−	11.7747i	−0.962469	−	0.555682i	−0.0655371	−	0.997850i	$-0.520876\pi$
$449$	−20.3944	−	11.7747i	−0.962469	−	0.555682i	−0.896932	+	0.442168i	$0.854209\pi$
$450$	−15.9787	+	13.6978i	−0.753243	+	0.645719i
$451$	7.08953	−	5.94883i	0.333833	−	0.280119i
$452$	−3.64679	+	0.158358i	−0.171530	+	0.00744852i
$453$	2.95546	−	0.521127i	0.138859	−	0.0244847i
$454$	0.0454251	+	2.09315i	0.00213190	+	0.0982366i
$455$	−8.49073	+	14.5190i	−0.398051	+	0.680661i
$456$	−0.866894	−	1.68397i	−0.0405960	−	0.0788590i
$457$			2.91065i			0.136155i	0.997680	+	0.0680773i	$0.0216864\pi$
$457$			2.91065i			0.136155i	−0.997680	+	0.0680773i	$0.978314\pi$
$458$	24.4750	−	0.531149i	1.14364	−	0.0248190i
$459$	0.306403	+	1.73770i	0.0143017	+	0.0811087i
$460$	16.4019	−	31.0660i	0.764744	−	1.44846i
$461$	−22.8012	+	19.1325i	−1.06196	+	0.891089i	−0.994300	−	0.106620i	$-0.965997\pi$
$461$	−22.8012	+	19.1325i	−1.06196	+	0.891089i	−0.0676581	+	0.997709i	$0.521553\pi$
$462$	0.302478	+	1.52160i	0.0140725	+	0.0707912i
$463$	−16.4781	+	28.5409i	−0.765802	+	1.32641i	0.174020	+	0.984742i	$0.444324\pi$
$463$	−16.4781	+	28.5409i	−0.765802	+	1.32641i	−0.939822	+	0.341665i	$0.889009\pi$
$464$	−8.06191	−	17.3102i	−0.374265	−	0.803606i
$465$	1.85928	+	0.338531i	0.0862222	+	0.0156990i
$466$	1.18846	+	1.35551i	0.0550545	+	0.0627926i
$467$	6.66433	+	11.5430i	0.308389	+	0.534145i	0.978010	−	0.208558i	$-0.0668770\pi$
$467$	6.66433	+	11.5430i	0.308389	+	0.534145i	−0.669621	+	0.742703i	$0.733544\pi$
$468$	−4.23238	−	19.1124i	−0.195642	−	0.883473i
$469$	7.22166	+	1.27337i	0.333465	+	0.0587989i
$470$	−10.1287	−	16.9077i	−0.467203	−	0.779895i
$471$	1.49017	+	1.25040i	0.0686636	+	0.0576156i
$472$	15.8606	+	4.62906i	0.730045	+	0.213070i
$473$	−4.43388	+	12.1820i	−0.203870	+	0.560129i
$474$	0.380079	+	0.977713i	0.0174576	+	0.0449079i
$475$	−11.8290	−	18.3051i	−0.542751	−	0.839894i
$476$	5.93828	+	6.48357i	0.272181	+	0.297174i
$477$	−19.6297	−	7.14461i	−0.898780	−	0.327129i
$478$	14.9843	−	9.09030i	0.685368	−	0.415781i
$479$	−16.4832	+	19.6440i	−0.753139	+	0.897556i	−0.997393	−	0.0721554i	$-0.977012\pi$
$479$	−16.4832	+	19.6440i	−0.753139	+	0.897556i	0.244255	+	0.969711i	$0.421457\pi$
$480$	0.848704	+	1.74807i	0.0387378	+	0.0797882i
$481$	3.35531	−	19.0289i	0.152989	−	0.867645i
$482$	−37.7101	−	5.80871i	−1.71765	−	0.264580i
$483$	−2.39050	+	1.38016i	−0.108772	+	0.0627994i
$484$	−1.15889	+	2.22493i	−0.0526770	+	0.101133i
$485$	1.78227	−	9.78857i	0.0809285	−	0.444476i
$486$	−3.63373	+	4.52644i	−0.164829	+	0.205323i
$487$	3.49851	+	2.01987i	0.158533	+	0.0915288i	0.577168	−	0.816626i	$-0.304158\pi$
$487$	3.49851	+	2.01987i	0.158533	+	0.0915288i	−0.418635	+	0.908155i	$0.637491\pi$
$488$	25.3002	+	18.5647i	1.14529	+	0.840384i
$489$	2.40999	+	2.87211i	0.108983	+	0.129881i
$490$	−4.22425	+	3.66227i	−0.190832	+	0.165444i
$491$	23.9074	−	4.21551i	1.07892	−	0.190244i	0.394185	−	0.919031i	$-0.371027\pi$
$491$	23.9074	−	4.21551i	1.07892	−	0.190244i	0.684740	+	0.728788i	$0.259916\pi$
$492$	−0.841598	+	0.348368i	−0.0379422	+	0.0157057i
$493$	−9.17475			−0.413210
$494$	20.2016	−	1.67956i	0.908915	−	0.0755672i
$495$	−17.9352	−	10.4886i	−0.806129	−	0.471425i
$496$	−9.30962	+	19.9399i	−0.418014	+	0.895329i
$497$	−5.17947	−	29.3742i	−0.232331	−	1.31762i
$498$	−0.554992	+	1.63432i	−0.0248698	+	0.0732356i
$499$	−8.51458	−	10.1473i	−0.381165	−	0.454255i	0.541017	−	0.841012i	$-0.318040\pi$
$499$	−8.51458	−	10.1473i	−0.381165	−	0.454255i	−0.922182	+	0.386757i	$0.873595\pi$
$500$	11.6931	+	19.0597i	0.522930	+	0.852376i
$501$	−1.02862	+	1.78162i	−0.0459553	+	0.0795969i
$502$	−0.910006	+	1.13357i	−0.0406156	+	0.0505937i
$503$	6.85460	−	2.49487i	0.305631	−	0.111241i	−0.184652	−	0.982804i	$-0.559116\pi$
$503$	6.85460	−	2.49487i	0.305631	−	0.111241i	0.490283	+	0.871563i	$0.336893\pi$
$504$	−2.10316	+	19.1411i	−0.0936823	+	0.852611i
$505$	−28.2364	−	0.157285i	−1.25650	−	0.00699910i
$506$	34.2762	+	5.27976i	1.52376	+	0.234714i
$507$	0.330739	+	0.0583182i	0.0146886	+	0.00259000i
$508$	−42.0988	−	5.55255i	−1.86783	−	0.246355i
$509$	1.48698	−	1.77211i	0.0659091	−	0.0785475i	−0.732082	−	0.681216i	$-0.761451\pi$
$509$	1.48698	−	1.77211i	0.0659091	−	0.0785475i	0.797992	+	0.602669i	$0.205896\pi$
$510$	0.933525	−	0.0150573i	0.0413372	−	0.000666747i
$511$	−5.10645	+	14.0299i	−0.225896	+	0.620644i
$512$	−22.1973	+	4.39076i	−0.980992	+	0.194046i
$513$	−2.75526	−	2.90249i	−0.121648	−	0.128148i
$514$	38.9091	−	15.1256i	1.71621	−	0.667163i
$515$	19.6400	+	23.6726i	0.865442	+	1.04314i
$516$	0.776957	−	1.01205i	0.0342036	−	0.0445532i
$517$	12.5068	−	14.9051i	0.550050	−	0.655524i
$518$	−9.14433	+	16.6632i	−0.401779	+	0.732141i
$519$	−0.00580350	−	0.00102331i	−0.000254745	−	4.49185e-5i
$520$	−20.7611	+	1.23726i	−0.910435	+	0.0542575i
$521$	29.2942	−	16.9130i	1.28340	−	0.740971i	0.305932	−	0.952053i	$-0.401032\pi$
$521$	29.2942	−	16.9130i	1.28340	−	0.740971i	0.977468	+	0.211082i	$0.0676987\pi$
$522$	−13.2474	−	15.1094i	−0.579824	−	0.661321i
$523$	1.38633	+	3.80890i	0.0606198	+	0.166551i	0.966305	−	0.257399i	$-0.0828654\pi$
$523$	1.38633	+	3.80890i	0.0606198	+	0.166551i	−0.905686	+	0.423950i	$0.860643\pi$
$524$	8.63095	−	27.3513i	0.377045	−	1.19485i
$525$	0.0195732	−	1.75686i	0.000854242	−	0.0766758i
$526$	−3.20573	−	16.1263i	−0.139776	−	0.703138i
$527$	6.79633	+	8.09955i	0.296053	+	0.352822i
$528$	−1.35711	+	1.35583i	−0.0590607	+	0.0590048i
$529$	6.72124	+	38.1180i	0.292228	+	1.65731i
$530$	−10.7856	+	19.3970i	−0.468496	+	0.842553i
$531$	17.3867			0.754520
$532$	−19.3481	−	4.82552i	−0.838848	−	0.209213i
$533$		−	9.74874i		−	0.422265i
$534$	−0.348901	+	0.00757176i	−0.0150984	+	0.000327662i
$535$	−4.04716	+	10.9297i	−0.174974	+	0.472531i
$536$	3.64902	+	8.30102i	0.157614	+	0.358549i
$537$	0.981009	+	1.16912i	0.0423337	+	0.0504513i
$538$	4.60930	−	0.916281i	0.198721	−	0.0395037i
$539$	−4.77976	−	2.75960i	−0.205879	−	0.118864i
$540$	2.75632	+	3.04328i	0.118613	+	0.130962i
$541$	−8.11154	+	2.95236i	−0.348742	+	0.126932i	−0.510451	−	0.859907i	$-0.670522\pi$
$541$	−8.11154	+	2.95236i	−0.348742	+	0.126932i	0.161709	+	0.986838i	$0.448299\pi$
$542$	−8.00666	−	9.13203i	−0.343916	−	0.392254i
$543$	0.288177	+	0.499137i	0.0123669	+	0.0214200i
$544$	−2.59030	+	10.5586i	−0.111058	+	0.452698i
$545$	28.8395	−	33.9833i	1.23535	−	1.45569i
$546$	1.43264	+	0.786193i	0.0613113	+	0.0336460i
$547$	−9.82031	+	11.7034i	−0.419886	+	0.500401i	−0.933976	−	0.357335i	$-0.883685\pi$
$547$	−9.82031	+	11.7034i	−0.419886	+	0.500401i	0.514090	+	0.857736i	$0.328130\pi$
$548$	6.47420	−	8.43321i	0.276564	−	0.360249i
$549$	31.0309	+	11.2943i	1.32437	+	0.482030i
$550$	−14.0099	+	17.0589i	−0.597384	+	0.727394i
$551$	17.3503	−	11.4880i	0.739147	−	0.489406i
$552$	−3.06071	−	1.51073i	−0.130273	−	0.0643009i
$553$	10.3781	+	3.77733i	0.441324	+	0.160629i
$554$	−34.6792	+	21.0382i	−1.47338	+	0.893829i
$555$	0.679772	+	1.90053i	0.0288547	+	0.0806731i
$556$	22.8435	+	3.01290i	0.968780	+	0.127775i
$557$	−10.1981	−	1.79821i	−0.432109	−	0.0761924i	−0.0466366	−	0.998912i	$-0.514850\pi$
$557$	−10.1981	−	1.79821i	−0.432109	−	0.0761924i	−0.385472	+	0.922719i	$0.625961\pi$
$558$	−3.52549	+	22.8875i	−0.149246	+	0.968903i
$559$	6.82790	+	11.8263i	0.288790	+	0.500198i
$560$	19.7294	+	5.41447i	0.833718	+	0.228803i
$561$	0.315239	+	0.866113i	0.0133094	+	0.0365673i
$562$	7.05984	−	8.79425i	0.297801	−	0.370963i
$563$	12.0960	+	6.98361i	0.509784	+	0.294324i	0.732745	−	0.680503i	$-0.238239\pi$
$563$	12.0960	+	6.98361i	0.509784	+	0.294324i	−0.222961	+	0.974827i	$0.571572\pi$
$564$	−1.61532	+	1.02853i	−0.0680171	+	0.0433091i
$565$	0.686273	+	4.02296i	0.0288717	+	0.169247i
$566$	−12.3955	−	4.20933i	−0.521021	−	0.176932i
$567$	3.49063	+	19.7963i	0.146593	+	0.831368i
$568$	26.6519	−	25.4955i	1.11829	−	1.06977i
$569$		−	30.6059i		−	1.28307i	−0.767095	−	0.641533i	$-0.778299\pi$
$569$		−	30.6059i		−	1.28307i	0.767095	−	0.641533i	$-0.221701\pi$
$570$	−1.74653	+	1.19737i	−0.0731540	+	0.0501524i
$571$		−	28.6343i		−	1.19831i	−0.800634	−	0.599154i	$-0.795504\pi$
$571$		−	28.6343i		−	1.19831i	0.800634	−	0.599154i	$-0.204496\pi$
$572$	−7.85268	−	18.9708i	−0.328337	−	0.793207i
$573$	0.349699	+	1.98324i	0.0146089	+	0.0828512i
$574$	−3.08361	+	9.08049i	−0.128707	+	0.379012i
$575$	−36.7560	−	13.8437i	−1.53283	−	0.577323i
$576$	−21.1286	+	10.9798i	−0.880358	+	0.457491i
$577$	29.4687	+	17.0138i	1.22680	+	0.708293i	0.966359	−	0.257197i	$-0.0827990\pi$
$577$	29.4687	+	17.0138i	1.22680	+	0.708293i	0.260440	+	0.965490i	$0.416132\pi$
$578$	−14.6746	−	11.7804i	−0.610382	−	0.490002i
$579$	−1.18793	−	3.26382i	−0.0493688	−	0.135640i
$580$	−18.0722	+	11.3663i	−0.750408	+	0.471959i
$581$	9.08590	+	15.7372i	0.376947	+	0.652891i
$582$	−0.955429	−	0.147170i	−0.0396038	−	0.00610041i
$583$	−21.5771	−	3.80462i	−0.893632	−	0.157571i
$584$	−17.9344	+	4.38177i	−0.742130	+	0.181319i
$585$	−20.6075	+	7.37079i	−0.852016	+	0.304745i
$586$	−17.0950	−	28.1793i	−0.706190	−	1.16408i
$587$	−20.4108	−	7.42891i	−0.842442	−	0.306624i	−0.115487	−	0.993309i	$-0.536843\pi$
$587$	−20.4108	−	7.42891i	−0.842442	−	0.306624i	−0.726955	+	0.686685i	$0.759065\pi$
$588$	0.366885	+	0.400575i	0.0151301	+	0.0165194i
$589$	−22.9942	−	6.80708i	−0.947460	−	0.280481i
$590$	2.91392	−	18.2413i	0.119964	−	0.750982i
$591$	0.335662	+	0.122171i	0.0138073	+	0.00502545i
$592$	−23.4150	+	2.03738i	−0.962351	+	0.0837360i
$593$	−10.6247	+	12.6620i	−0.436303	+	0.519965i	−0.938730	−	0.344654i	$-0.887996\pi$
$593$	−10.6247	+	12.6620i	−0.436303	+	0.519965i	0.502427	+	0.864620i	$0.332441\pi$
$594$	−1.95006	+	3.55350i	−0.0800120	+	0.145802i
$595$	6.36032	−	7.49475i	0.260748	−	0.307255i
$596$	0.0896387	+	0.404787i	0.00367174	+	0.0165807i
$597$	−1.42714	−	2.47187i	−0.0584088	−	0.101167i
$598$	27.4688	−	24.0838i	1.12328	−	0.984858i
$599$	40.3682	−	14.6928i	1.64940	−	0.600333i	0.660756	−	0.750601i	$-0.270236\pi$
$599$	40.3682	−	14.6928i	1.64940	−	0.600333i	0.988645	+	0.150268i	$0.0480137\pi$
$600$	1.82018	−	1.18617i	0.0743087	−	0.0484252i
$601$	−3.91491	−	2.26027i	−0.159692	−	0.0921984i	0.418024	−	0.908436i	$-0.362723\pi$
$601$	−3.91491	−	2.26027i	−0.159692	−	0.0921984i	−0.577717	+	0.816237i	$0.696056\pi$
$602$	−2.61912	−	13.1753i	−0.106747	−	0.536987i
$603$	6.13350	+	7.30962i	0.249775	+	0.297671i
$604$	39.0333	−	1.69498i	1.58824	−	0.0689676i
$605$	2.63023	+	0.973950i	0.106934	+	0.0395967i
$606$	0.0595246	+	2.74285i	0.00241802	+	0.111421i
$607$		−	8.06467i		−	0.327335i	−0.986516	−	0.163667i	$-0.947668\pi$
$607$		−	8.06467i		−	0.327335i	0.986516	−	0.163667i	$-0.0523324\pi$
$608$	−8.32232	−	23.2108i	−0.337515	−	0.941320i
$609$	1.67751			0.0679763
$610$	17.0500	−	30.6632i	0.690336	−	1.24152i
$611$	−3.55906	−	20.1844i	−0.143984	−	0.816574i
$612$	0.496323	+	11.4297i	0.0200627	+	0.462019i
$613$	−18.7430	−	22.3370i	−0.757023	−	0.902185i	0.240633	−	0.970616i	$-0.422645\pi$
$613$	−18.7430	−	22.3370i	−0.757023	−	0.902185i	−0.997656	+	0.0684313i	$0.978201\pi$
$614$	−29.4639	+	5.85710i	−1.18906	+	0.236373i
$615$	0.504260	+	0.884750i	0.0203337	+	0.0356765i
$616$	1.31379	+	20.1542i	0.0529343	+	0.812037i
$617$	4.39846	+	12.0847i	0.177075	+	0.486511i	0.996199	−	0.0871063i	$-0.0277620\pi$
$617$	4.39846	+	12.0847i	0.177075	+	0.486511i	−0.819124	+	0.573617i	$0.805540\pi$
$618$	2.24716	−	1.97023i	0.0903938	−	0.0792544i
$619$	33.5791	−	19.3869i	1.34966	−	0.779226i	0.361459	−	0.932388i	$-0.382279\pi$
$619$	33.5791	−	19.3869i	1.34966	−	0.779226i	0.988201	+	0.153162i	$0.0489455\pi$
$620$	23.4215	+	7.53457i	0.940630	+	0.302596i
$621$	−7.10255	−	1.25237i	−0.285015	−	0.0502559i
$622$	−17.4032	−	9.55038i	−0.697803	−	0.382935i
$623$	−2.36175	+	2.81462i	−0.0946215	+	0.112766i
$624$	0.175166	+	2.01313i	0.00701226	+	0.0805897i
$625$	19.5044	−	15.6390i	0.780175	−	0.625561i
$626$	−2.78105	−	7.15396i	−0.111153	−	0.285930i
$627$	−1.68064	−	1.24318i	−0.0671181	−	0.0496477i
$628$	17.1051	+	18.6758i	0.682567	+	0.745245i
$629$	−3.86231	+	10.6116i	−0.154001	+	0.423113i
$630$	21.5264	−	0.347209i	0.857631	−	0.0138331i
$631$	−10.6132	+	12.6483i	−0.422505	+	0.503522i	−0.934744	−	0.355321i	$-0.884372\pi$
$631$	−10.6132	+	12.6483i	−0.422505	+	0.503522i	0.512239	+	0.858843i	$0.328816\pi$
$632$	3.24128	+	13.2664i	0.128931	+	0.527709i
$633$	0.103640	+	0.0182746i	0.00411934	+	0.000726350i
$634$	−1.64789	+	10.6981i	−0.0654459	+	0.424875i
$635$	−0.264449	+	47.4748i	−0.0104944	+	1.88398i
$636$	1.91249	+	0.996157i	0.0758353	+	0.0395002i
$637$	−5.46319	+	1.98844i	−0.216460	+	0.0787848i
$638$	−16.4354	−	13.1940i	−0.650684	−	0.522356i
$639$	19.4062	−	33.6125i	0.767698	−	1.32969i
$640$	7.97841	+	24.0072i	0.315374	+	0.948967i
$641$	4.19482	+	4.99919i	0.165685	+	0.197456i	0.842498	−	0.538699i	$-0.181084\pi$
$641$	4.19482	+	4.99919i	0.165685	+	0.197456i	−0.676813	+	0.736155i	$0.736639\pi$
$642$	1.07226	+	0.364124i	0.0423186	+	0.0143708i
$643$	−1.17418	−	6.65909i	−0.0463051	−	0.262609i	0.952863	−	0.303402i	$-0.0981226\pi$
$643$	−1.17418	−	6.65909i	−0.0463051	−	0.262609i	−0.999168	+	0.0407933i	$0.987011\pi$
$644$	−33.2038	+	13.7443i	−1.30841	+	0.541600i
$645$	−1.23139	−	0.720119i	−0.0484860	−	0.0283546i
$646$	−11.7975	−	1.08349i	−0.464168	−	0.0426295i
$647$	33.6860			1.32433			0.662166	−	0.749357i	$-0.269637\pi$
$647$	33.6860			1.32433			0.662166	+	0.749357i	$0.269637\pi$
$648$	−17.9616	+	17.1823i	−0.705600	+	0.674986i
$649$	17.9591	−	3.16667i	0.704956	−	0.124303i
$650$	4.27935	+	22.8557i	0.167850	+	0.896473i
$651$	−1.24264	−	1.48092i	−0.0487030	−	0.0580420i
$652$	26.2164	+	41.1730i	1.02671	+	1.61246i
$653$	7.68324	+	4.43592i	0.300669	+	0.173591i	0.642743	−	0.766082i	$-0.277796\pi$
$653$	7.68324	+	4.43592i	0.300669	+	0.173591i	−0.342075	+	0.939673i	$0.611130\pi$
$654$	−3.37701	−	2.71099i	−0.132051	−	0.106008i
$655$	−31.5474	−	5.74404i	−1.23266	−	0.224438i
$656$	−11.4556	+	3.06370i	−0.447265	+	0.119617i
$657$	−16.8249	+	9.71388i	−0.656403	+	0.378975i
$658$	−3.06941	+	19.9266i	−0.119658	+	0.776819i
$659$	1.04765	−	5.94152i	0.0408107	−	0.231449i	−0.957579	−	0.288169i	$-0.906953\pi$
$659$	1.04765	−	5.94152i	0.0408107	−	0.231449i	0.998390	+	0.0567207i	$0.0180645\pi$
$660$	1.69395	+	1.31551i	0.0659368	+	0.0512062i
$661$	−26.1357	+	31.1473i	−1.01656	+	1.21149i	−0.0393496	+	0.999226i	$0.512529\pi$
$661$	−26.1357	+	31.1473i	−1.01656	+	1.21149i	−0.977212	+	0.212266i	$0.931916\pi$
$662$	16.4202	+	27.0669i	0.638189	+	1.05198i
$663$	0.912345	+	0.332066i	0.0354325	+	0.0128964i
$664$	−9.94547	+	20.1494i	−0.385959	+	0.781948i
$665$	−2.64352	+	22.1372i	−0.102511	+	0.858445i
$666$	−23.0525	+	8.96149i	−0.893266	+	0.347251i
$667$	12.8259	−	35.2387i	0.496619	−	1.36445i
$668$	−16.3093	+	21.2443i	−0.631027	+	0.821968i
$669$	−1.68203	−	1.41139i	−0.0650311	−	0.0545675i
$670$	8.69682	−	5.20990i	0.335987	−	0.201276i
$671$	34.1095	+	6.01442i	1.31678	+	0.232184i
$672$	0.473611	−	1.93054i	0.0182699	−	0.0744723i
$673$	−7.84313	−	13.5847i	−0.302330	−	0.523651i	0.674333	−	0.738427i	$-0.264431\pi$
$673$	−7.84313	−	13.5847i	−0.302330	−	0.523651i	−0.976663	+	0.214776i	$0.931098\pi$
$674$	4.45462	−	3.90566i	0.171585	−	0.150440i
$675$	2.98977	−	3.48351i	0.115076	−	0.134080i
$676$	4.16958	+	1.31575i	0.160368	+	0.0506057i
$677$	2.80747	−	4.86268i	0.107900	−	0.186888i	−0.807019	−	0.590525i	$-0.798921\pi$
$677$	2.80747	−	4.86268i	0.107900	−	0.186888i	0.914919	+	0.403637i	$0.132254\pi$
$678$	0.388909	−	0.0773109i	0.0149360	−	0.00296911i
$679$	−7.79662	+	6.54214i	−0.299207	+	0.251064i
$680$	12.0747	+	1.39484i	0.463042	+	0.0534897i
$681$	−0.0394928	−	0.223975i	−0.00151337	−	0.00858273i
$682$	0.526983	+	24.2830i	0.0201792	+	0.929844i
$683$		−	24.1656i		−	0.924669i	−0.886705	−	0.462335i	$-0.847012\pi$
$683$		−	24.1656i		−	0.924669i	0.886705	−	0.462335i	$-0.152988\pi$
$684$	−15.2501	−	20.9932i	−0.583103	−	0.802695i
$685$	−10.2609	−	6.00058i	−0.392048	−	0.229270i
$686$	28.3561	−	0.615377i	1.08264	−	0.0234952i
$687$	−2.61891	+	0.461784i	−0.0999175	+	0.0176182i
$688$	11.7511	−	11.7399i	0.448005	−	0.447581i
$689$	−17.6799	+	14.8352i	−0.673551	+	0.565177i
$690$	−1.24719	+	3.60657i	−0.0474797	+	0.137300i
$691$	−36.2646	−	20.9374i	−1.37957	−	0.796494i	−0.387461	−	0.921886i	$-0.626648\pi$
$691$	−36.2646	−	20.9374i	−1.37957	−	0.796494i	−0.992107	+	0.125392i	$0.959981\pi$
$692$	−0.0731638	−	0.0230875i	−0.00278127	−	0.000877655i
$693$	7.26917	+	19.9719i	0.276133	+	0.758669i
$694$	18.0209	−	15.8002i	0.684066	−	0.599766i
$695$	0.143494	−	25.7606i	0.00544305	−	0.977154i
$696$	1.15182	+	1.72514i	0.0436595	+	0.0653912i
$697$	−0.989354	+	5.61090i	−0.0374744	+	0.212528i
$698$	−22.1616	+	40.3839i	−0.838829	+	1.52855i
$699$	−0.150013	−	0.125876i	−0.00567401	−	0.00476106i
$700$	3.24342	−	22.6426i	0.122590	−	0.855808i
$701$	40.3974	+	14.7035i	1.52579	+	0.555342i	0.962586	−	0.270976i	$-0.0873463\pi$
$701$	40.3974	+	14.7035i	1.52579	+	0.555342i	0.563204	+	0.826318i	$0.309569\pi$
$702$	1.54706	+	3.97964i	0.0583899	+	0.150202i
$703$	−5.98317	−	24.9037i	−0.225660	−	0.939260i
$704$	−19.8243	+	15.1894i	−0.747158	+	0.572473i
$705$	1.36706	+	1.64775i	0.0514863	+	0.0620578i
$706$	−13.4672	+	8.16991i	−0.506844	+	0.307479i
$707$	22.1269	+	18.5667i	0.832168	+	0.698272i
$708$	−1.77939	−	0.234689i	−0.0668736	−	0.00882017i
$709$	6.84302	−	38.8087i	0.256995	−	1.45749i	−0.533904	−	0.845545i	$-0.679276\pi$
$709$	6.84302	−	38.8087i	0.256995	−	1.45749i	0.790899	−	0.611947i	$-0.209613\pi$
$710$	−32.0122	−	25.9933i	−1.20140	−	0.975510i
$711$	7.18553	+	12.4457i	0.269479	+	0.466751i
$712$	−4.51616	−	0.496222i	−0.169250	−	0.0185967i
$713$	−40.6100	+	14.7808i	−1.52086	+	0.553547i
$714$	−0.744771	−	0.597887i	−0.0278723	−	0.0223753i
$715$	−19.9434	+	11.3667i	−0.745842	+	0.425091i
$716$	10.6717	+	16.7599i	0.398818	+	0.626346i
$717$	−1.45842	+	1.22376i	−0.0544658	+	0.0457022i
$718$	13.4500	−	39.6070i	0.501949	−	1.47812i
$719$	−39.1944	+	6.91103i	−1.46170	+	0.257738i	−0.847241	−	0.531208i	$-0.821738\pi$
$719$	−39.1944	+	6.91103i	−1.46170	+	0.257738i	−0.614462	+	0.788946i	$0.710627\pi$
$720$	15.1375	+	21.8991i	0.564142	+	0.816132i
$721$		−	31.4648i		−	1.17181i
$722$	23.6669	−	12.7231i	0.880791	−	0.473505i
$723$	4.14471			0.154143
$724$	2.86980	+	6.93295i	0.106655	+	0.257661i
$725$	15.1383	+	18.4548i	0.562221	+	0.685393i
$726$	0.0876265	−	0.258039i	0.00325212	−	0.00957672i
$727$	12.3945	−	10.4002i	0.459687	−	0.385723i	−0.383329	−	0.923612i	$-0.625222\pi$
$727$	12.3945	−	10.4002i	0.459687	−	0.385723i	0.843016	+	0.537889i	$0.180778\pi$
$728$	17.1527	+	12.5863i	0.635722	+	0.466478i
$729$	−12.8670	+	22.2862i	−0.476554	+	0.825416i
$730$	7.37154	+	19.2799i	0.272833	+	0.713579i
$731$	−2.72962	−	7.49956i	−0.100959	−	0.277381i
$732$	−3.02331	−	1.57474i	−0.111745	−	0.0582042i
$733$	42.5312	−	24.5554i	1.57093	−	0.906974i	0.574869	−	0.818245i	$-0.305053\pi$
$733$	42.5312	−	24.5554i	1.57093	−	0.906974i	0.996056	−	0.0887290i	$-0.0282805\pi$
$734$	−1.43613	+	9.32338i	−0.0530087	+	0.344132i
$735$	0.392960	−	0.463049i	0.0144945	−	0.0170798i
$736$	−36.9329	−	24.7094i	−1.36137	−	0.910800i
$737$	7.66672	+	6.43314i	0.282407	+	0.236968i
$738$	−10.6688	+	6.47228i	−0.392725	+	0.238248i
$739$	−4.24516	+	11.6635i	−0.156161	+	0.429049i	−0.992958	−	0.118464i	$-0.962203\pi$
$739$	−4.24516	+	11.6635i	−0.156161	+	0.429049i	0.836797	+	0.547513i	$0.184425\pi$
$740$	5.53847	+	25.6874i	0.203598	+	0.944288i
$741$	−2.14112	+	0.514410i	−0.0786560	+	0.0188973i
$742$	21.1605	−	8.22599i	0.776827	−	0.301986i
$743$	−9.27018	+	25.4696i	−0.340090	+	0.934389i	0.645278	+	0.763948i	$0.276742\pi$
$743$	−9.27018	+	25.4696i	−0.340090	+	0.934389i	−0.985368	+	0.170441i	$0.945481\pi$
$744$	0.669744	−	2.29476i	0.0245540	−	0.0841298i
$745$	0.436452	−	0.156108i	0.0159904	−	0.00571935i
$746$	12.9809	−	23.6543i	0.475263	−	0.866047i
$747$	−4.10604	+	23.2865i	−0.150232	+	0.852009i
$748$	2.59437	+	11.7156i	0.0948597	+	0.428364i
$749$	10.3250	−	5.96115i	0.377268	−	0.217816i
$750$	−1.57060	−	1.85292i	−0.0573501	−	0.0676590i
$751$	−13.4947	+	4.91168i	−0.492430	+	0.179230i	−0.576286	−	0.817248i	$-0.695499\pi$
$751$	−13.4947	+	4.91168i	−0.492430	+	0.179230i	0.0838560	+	0.996478i	$0.473276\pi$
$752$	−22.5999	+	10.5255i	−0.824132	+	0.383824i
$753$	0.0789538	−	0.136752i	0.00287724	−	0.00498352i
$754$	−21.7751	+	4.32866i	−0.793003	+	0.157641i
$755$	−7.34550	−	43.0596i	−0.267330	−	1.56710i
$756$	−0.182215	−	4.19620i	−0.00662710	−	0.152614i
$757$	16.7807	−	2.95889i	0.609904	−	0.107543i	0.139839	−	0.990174i	$-0.455342\pi$
$757$	16.7807	−	2.95889i	0.609904	−	0.107543i	0.470065	+	0.882632i	$0.344230\pi$
$758$	8.76275	−	0.190167i	0.318277	−	0.00690717i
$759$	−3.76729			−0.136744
$760$	−24.5808	+	12.4813i	−0.891640	+	0.452745i
$761$	−8.81354			−0.319491			−0.159745	−	0.987158i	$-0.551067\pi$
$761$	−8.81354			−0.319491			−0.159745	+	0.987158i	$0.551067\pi$
$762$	4.61166	−	0.100081i	0.167063	−	0.00362555i
$763$	−44.9010	+	7.91726i	−1.62553	+	0.286624i
$764$	1.13740	+	26.1931i	0.0411499	+	0.947631i
$765$	12.6087	−	2.15091i	0.455869	−	0.0777663i
$766$	−28.9360	+	5.75217i	−1.04550	+	0.207834i
$767$	9.60479	−	16.6360i	0.346809	−	0.600690i
$768$	2.31054	−	0.838494i	0.0833746	−	0.0302565i
$769$	−34.7585	+	12.6511i	−1.25342	+	0.456209i	−0.881557	−	0.472077i	$-0.843504\pi$
$769$	−34.7585	+	12.6511i	−1.25342	+	0.456209i	−0.371867	+	0.928286i	$0.621282\pi$
$770$	22.1717	−	4.27927i	0.799014	−	0.154214i
$771$	−3.92723	+	2.26739i	−0.141436	+	0.0816580i
$772$	−9.77652	−	44.1485i	−0.351865	−	1.58894i
$773$	−0.438918	+	2.48923i	−0.0157868	+	0.0895313i	−0.991683	−	0.128703i	$-0.958919\pi$
$773$	−0.438918	+	2.48923i	−0.0157868	+	0.0895313i	0.975896	+	0.218234i	$0.0700297\pi$
$774$	8.40933	−	15.3239i	0.302267	−	0.550806i
$775$	5.07814	−	27.0348i	0.182412	−	0.971120i
$776$	−12.0812	−	3.52600i	−0.433690	−	0.126576i
$777$	0.706186	−	1.94023i	0.0253343	−	0.0696054i
$778$	39.3740	−	15.3064i	1.41163	−	0.548760i
$779$	−5.15464	−	11.8495i	−0.184684	−	0.424554i
$780$	2.20850	−	0.476175i	0.0790771	−	0.0170498i
$781$	13.9231	−	38.2535i	0.498209	−	1.36882i
$782$	−18.2539	+	11.0738i	−0.652757	+	0.395997i
$783$	3.35756	+	2.81733i	0.119989	+	0.100683i
$784$	4.05348	+	5.79480i	0.144767	+	0.206957i
$785$	18.3207	−	21.5884i	0.653895	−	0.770525i
$786$	−0.474313	+	3.07924i	−0.0169182	+	0.109833i
$787$	43.0549	−	24.8578i	1.53474	−	0.886084i	0.535608	−	0.844467i	$-0.320082\pi$
$787$	43.0549	−	24.8578i	1.53474	−	0.886084i	0.999134	−	0.0416169i	$-0.0132509\pi$
$788$	4.12442	+	2.14828i	0.146926	+	0.0765292i
$789$	0.610865	+	1.67834i	0.0217474	+	0.0597504i
$790$	14.2617	−	5.45286i	0.507407	−	0.194004i
$791$	2.08735	−	3.61540i	0.0742176	−	0.128549i
$792$	−15.5477	+	21.1887i	−0.552465	+	0.752907i
$793$	27.9487	−	23.4518i	0.992489	−	0.832797i
$794$	8.97174	−	26.4196i	0.318395	−	0.937597i
$795$	0.837184	−	2.26088i	0.0296919	−	0.0801852i
$796$	−14.2121	−	34.3340i	−0.503734	−	1.21694i
$797$	−19.1523			−0.678409			−0.339205	−	0.940713i	$-0.610158\pi$
$797$	−19.1523			−0.678409			−0.339205	+	0.940713i	$0.610158\pi$
$798$	2.15706	+	0.198106i	0.0763592	+	0.00701288i
$799$			11.9784i			0.423764i
$800$	25.5124	−	12.2113i	0.902000	−	0.431736i
$801$	−4.70840	+	0.830218i	−0.166363	+	0.0293343i
$802$	5.77961	−	17.0196i	0.204085	−	0.600982i
$803$	−15.6096	+	13.0980i	−0.550850	+	0.462218i
$804$	−0.529047	−	0.830871i	−0.0186580	−	0.0293025i
$805$	19.8947	+	34.9063i	0.701197	+	1.23028i
$806$	19.9516	+	16.0167i	0.702766	+	0.564166i
$807$	−0.479713	+	0.174601i	−0.0168867	+	0.00614625i
$808$	−3.90100	+	35.5034i	−0.137237	+	1.24900i
$809$	−11.8414	−	20.5099i	−0.416321	−	0.721089i	0.579245	−	0.815154i	$-0.303347\pi$
$809$	−11.8414	−	20.5099i	−0.416321	−	0.721089i	−0.995566	+	0.0940641i	$0.970014\pi$
$810$	21.5741	+	17.5178i	0.758038	+	0.615512i
$811$	−4.44206	+	25.1922i	−0.155982	+	0.884616i	0.801901	+	0.597457i	$0.203822\pi$
$811$	−4.44206	+	25.1922i	−0.155982	+	0.884616i	−0.957883	+	0.287159i	$0.907289\pi$
$812$	21.6517	+	2.85571i	0.759825	+	0.100216i
$813$	1.01064	+	0.848025i	0.0354446	+	0.0297415i
$814$	−22.1792	+	13.4551i	−0.777380	+	0.471600i
$815$	41.9996	−	34.8451i	1.47118	−	1.22057i
$816$	0.103486	−	1.17644i	0.00362273	−	0.0411835i
$817$	14.5524	+	10.7645i	0.509125	+	0.376603i
$818$	−7.49478	−	19.2795i	−0.262049	−	0.674093i
$819$	21.0380	+	7.65719i	0.735126	+	0.267564i
$820$	5.00235	+	12.2779i	0.174689	+	0.428763i
$821$	18.2344	+	15.3005i	0.636386	+	0.533991i	0.902906	−	0.429838i	$-0.141429\pi$
$821$	18.2344	+	15.3005i	0.636386	+	0.533991i	−0.266520	+	0.963829i	$0.585874\pi$
$822$	−0.555620	+	1.01248i	−0.0193795	+	0.0353142i
$823$	2.43641	−	13.8176i	0.0849280	−	0.481651i	−0.912444	−	0.409201i	$-0.865807\pi$
$823$	2.43641	−	13.8176i	0.0849280	−	0.481651i	0.997372	−	0.0724493i	$-0.0230815\pi$
$824$	32.3581	−	21.6044i	1.12725	−	0.752624i
$825$	1.22202	−	2.06318i	0.0425453	−	0.0718306i
$826$	−14.2085	+	12.4576i	−0.494377	+	0.433454i
$827$	−18.8260	−	51.7241i	−0.654645	−	1.79862i	−0.599833	−	0.800125i	$-0.704766\pi$
$827$	−18.8260	−	51.7241i	−0.654645	−	1.79862i	−0.0548122	−	0.998497i	$-0.517456\pi$
$828$	−44.5936	−	14.0719i	−1.54973	−	0.489032i
$829$	−15.3447	−	8.85926i	−0.532943	−	0.307695i	0.209271	−	0.977858i	$-0.432891\pi$
$829$	−15.3447	−	8.85926i	−0.532943	−	0.307695i	−0.742214	+	0.670163i	$0.766224\pi$
$830$	23.7429	+	8.21054i	0.824128	+	0.284992i
$831$	3.37532	−	2.83223i	0.117089	−	0.0982489i
$832$	−1.16617	+	26.2817i	−0.0404298	+	0.911154i
$833$	3.34615	−	0.590016i	0.115937	−	0.0204428i
$834$	−2.50236	+	0.0543055i	−0.0866495	+	0.00188044i
$835$	25.8485	+	15.1162i	0.894524	+	0.523119i
$836$	−19.5757	−	18.9067i	−0.677039	−	0.653903i
$837$		−	5.05106i		−	0.174590i
$838$	−0.259085	−	11.9384i	−0.00894994	−	0.412407i
$839$	−6.20712	−	35.2023i	−0.214293	−	1.21532i	−0.882128	−	0.471009i	$-0.843890\pi$
$839$	−6.20712	−	35.2023i	−0.214293	−	1.21532i	0.667835	−	0.744309i	$-0.267221\pi$
$840$	−2.20773	−	0.255033i	−0.0761740	−	0.00879947i
$841$	4.75725	−	3.99181i	0.164043	−	0.137649i
$842$	−22.6910	+	4.51074i	−0.781985	+	0.155450i
$843$	−0.612525	+	1.06092i	−0.0210965	+	0.0365402i
$844$	1.30658	+	0.412303i	0.0449743	+	0.0141920i
$845$	0.875650	−	4.80925i	0.0301233	−	0.165443i
$846$	−19.7265	+	17.2956i	−0.678212	+	0.594634i
$847$	−1.43455	−	2.48472i	−0.0492918	−	0.0853759i
$848$	22.9888	+	16.1131i	0.789438	+	0.553328i
$849$	1.40042	+	0.246932i	0.0480623	+	0.00847468i
$850$	−0.143474	−	13.5889i	−0.00492113	−	0.466095i
$851$	−35.3582	−	29.6691i	−1.21206	−	1.01704i
$852$	−2.43977	+	3.17802i	−0.0835853	+	0.108877i
$853$	13.9882	−	38.4323i	0.478948	−	1.31590i	−0.431440	−	0.902142i	$-0.641994\pi$
$853$	13.9882	−	38.4323i	0.478948	−	1.31590i	0.910388	−	0.413756i	$-0.135783\pi$
$854$	−33.4509	+	13.0038i	−1.14467	+	0.444981i
$855$	−21.1510	+	19.8554i	−0.723349	+	0.679039i
$856$	13.2198	+	6.52511i	0.451843	+	0.223024i
$857$	4.28639	+	1.56012i	0.146420	+	0.0532927i	0.414191	−	0.910190i	$-0.364065\pi$
$857$	4.28639	+	1.56012i	0.146420	+	0.0532927i	−0.267770	+	0.963483i	$0.586287\pi$
$858$	1.15681	+	1.90688i	0.0394930	+	0.0650998i
$859$	6.94546	−	8.27727i	0.236976	−	0.282417i	−0.634429	−	0.772981i	$-0.718765\pi$
$859$	6.94546	−	8.27727i	0.236976	−	0.282417i	0.871405	+	0.490564i	$0.163209\pi$
$860$	−14.6677	−	11.3908i	−0.500164	−	0.388424i
$861$	0.180894	−	1.02590i	0.00616484	−	0.0349625i
$862$	6.93980	−	45.0531i	0.236370	−	1.53452i
$863$	−7.31900	+	4.22563i	−0.249142	+	0.143842i	−0.619371	−	0.785098i	$-0.712612\pi$
$863$	−7.31900	+	4.22563i	−0.249142	+	0.143842i	0.370230	+	0.928940i	$0.379279\pi$
$864$	4.19022	−	3.06859i	0.142554	−	0.104395i
$865$	−0.0153651	+	0.0843883i	−0.000522429	+	0.00286929i
$866$	−23.4262	−	18.8061i	−0.796055	−	0.639057i
$867$	1.77032	+	1.02209i	0.0601231	+	0.0347121i
$868$	−13.5178	−	21.2297i	−0.458823	−	0.720583i
$869$	9.68883	+	11.5467i	0.328671	+	0.391695i
$870$	1.75230	−	1.51918i	0.0594087	−	0.0515051i
$871$	10.3823	−	1.83067i	0.351789	−	0.0620300i
$872$	−38.9720	−	40.7396i	−1.31976	−	1.37962i
$873$	−13.2436			−0.448230
$874$	20.6539	−	43.7978i	0.698629	−	1.48148i
$875$	−25.5700	−	0.427333i	−0.864423	−	0.0144465i
$876$	1.85301	−	0.767030i	0.0626075	−	0.0259155i
$877$	7.40388	+	41.9895i	0.250011	+	1.41788i	0.808561	+	0.588413i	$0.200247\pi$
$877$	7.40388	+	41.9895i	0.250011	+	1.41788i	−0.558549	+	0.829471i	$0.688642\pi$
$878$	23.1951	+	7.87675i	0.782798	+	0.265827i
$879$	2.30138	+	2.74268i	0.0776237	+	0.0925084i
$880$	19.6244	+	19.8630i	0.661537	+	0.669581i
$881$	−14.7789	+	25.5978i	−0.497914	+	0.862412i	−0.999997	−	0.00240696i	$-0.999234\pi$
$881$	−14.7789	+	25.5978i	−0.497914	+	0.862412i	0.502083	+	0.864819i	$0.332567\pi$
$882$	5.80317	+	4.65866i	0.195403	+	0.156865i
$883$	−26.3646	+	9.59592i	−0.887238	+	0.322928i	−0.745127	−	0.666922i	$-0.767611\pi$
$883$	−26.3646	+	9.59592i	−0.887238	+	0.322928i	−0.142111	+	0.989851i	$0.545389\pi$
$884$	11.2104	+	5.83912i	0.377045	+	0.196391i
$885$	−0.0111775	+	2.00662i	−0.000375727	+	0.0674517i
$886$	−2.35814	+	15.3091i	−0.0792234	+	0.514318i
$887$	35.3649	+	6.23578i	1.18744	+	0.209377i	0.732260	−	0.681025i	$-0.238465\pi$
$887$	35.3649	+	6.23578i	1.18744	+	0.209377i	0.455176	+	0.890402i	$0.349577\pi$
$888$	2.48020	−	0.605968i	0.0832300	−	0.0203349i
$889$	31.2168	−	37.2027i	1.04698	−	1.24774i
$890$	0.0819208	+	5.07895i	0.00274599	+	0.170247i
$891$	−9.38329	+	25.7804i	−0.314352	+	0.863675i
$892$	−19.3073	−	21.0803i	−0.646457	−	0.705819i
$893$	−14.9985	−	22.6522i	−0.501906	−	0.758027i
$894$	−0.0163181	−	0.0419765i	−0.000545757	−	0.00140390i
$895$	17.0964	−	14.1840i	0.571469	−	0.474120i
$896$	9.39936	−	24.1113i	0.314011	−	0.805502i
$897$	−2.55083	+	3.03996i	−0.0851697	+	0.101501i
$898$	29.1965	+	16.0222i	0.974299	+	0.534669i
$899$	25.8646	+	4.56063i	0.862632	+	0.152105i
$900$	22.1717	−	19.8573i	0.739056	−	0.661910i
$901$	11.6813	−	6.74418i	0.389159	−	0.224681i
$902$	−9.84122	+	8.62846i	−0.327677	+	0.287296i
$903$	0.499084	+	1.37122i	0.0166085	+	0.0456314i
$904$	5.15126	−	0.335796i	0.171328	−	0.0111684i
$905$	7.28842	−	4.15401i	0.242275	−	0.138084i
$906$	−4.16267	+	0.827495i	−0.138296	+	0.0274917i
$907$	5.37377	+	6.40421i	0.178433	+	0.212648i	0.847846	−	0.530242i	$-0.177899\pi$
$907$	5.37377	+	6.40421i	0.178433	+	0.212648i	−0.669413	+	0.742890i	$0.733454\pi$
$908$	−0.128451	−	2.95808i	−0.00426280	−	0.0981672i
$909$	6.52668	+	37.0146i	0.216476	+	1.22770i
$910$	11.5594	−	20.7887i	0.383190	−	0.689137i
$911$	−11.5235			−0.381790			−0.190895	−	0.981610i	$-0.561139\pi$
$911$	−11.5235			−0.381790			−0.190895	+	0.981610i	$0.561139\pi$
$912$	1.27736	+	2.35433i	0.0422975	+	0.0779596i
$913$			24.8009i			0.820791i
$914$	−0.0893094	−	4.11531i	−0.00295409	−	0.136123i
$915$	−1.32344	+	3.57404i	−0.0437514	+	0.118154i
$916$	−34.5884	+	1.50196i	−1.14283	+	0.0496263i
$917$	21.0846	+	25.1276i	0.696274	+	0.829787i
$918$	−0.486536	−	2.44749i	−0.0160581	−	0.0807793i
$919$	3.21630	+	1.85693i	0.106096	+	0.0612544i	0.552109	−	0.833772i	$-0.313823\pi$
$919$	3.21630	+	1.85693i	0.106096	+	0.0612544i	−0.446013	+	0.895026i	$0.647157\pi$
$920$	−22.2371	+	44.4269i	−0.733137	+	1.46471i
$921$	3.06645	−	1.11610i	0.101043	−	0.0367766i
$922$	31.6511	−	27.7507i	1.04237	−	0.913920i
$923$	−21.4408	−	37.1365i	−0.705731	−	1.22236i
$924$	−0.474356	−	2.14208i	−0.0156052	−	0.0704692i
$925$	27.7178	−	9.74015i	0.911356	−	0.320254i
$926$	22.4223	−	40.8590i	0.736843	−	1.34271i
$927$	26.3177	−	31.3642i	0.864385	−	1.03013i
$928$	11.9297	+	24.2272i	0.391612	+	0.795297i
$929$	13.3721	+	4.86704i	0.438724	+	0.159682i	0.551932	−	0.833889i	$-0.313891\pi$
$929$	13.3721	+	4.86704i	0.438724	+	0.159682i	−0.113209	+	0.993571i	$0.536113\pi$
$930$	−2.63919	−	0.421593i	−0.0865425	−	0.0138246i
$931$	−5.58909	+	5.30559i	−0.183175	+	0.173884i
$932$	−1.72194	−	1.88006i	−0.0564039	−	0.0615833i
$933$	2.02639	+	0.737544i	0.0663409	+	0.0241461i
$934$	−9.77675	−	16.1159i	−0.319905	−	0.527328i
$935$	12.6320	−	4.51816i	0.413111	−	0.147760i
$936$	6.57052	+	26.8928i	0.214764	+	0.879020i
$937$	0.232559	+	0.0410063i	0.00759736	+	0.00133962i	0.177446	−	0.984131i	$-0.443217\pi$
$937$	0.232559	+	0.0410063i	0.00759736	+	0.00133962i	−0.169848	+	0.985470i	$0.554328\pi$
$938$	−10.2496	−	1.57881i	−0.334663	−	0.0515500i
$939$	0.416890	+	0.722074i	0.0136047	+	0.0235640i
$940$	14.8396	+	23.5947i	0.484014	+	0.769575i
$941$	−11.5277	−	31.6721i	−0.375793	−	1.03248i	−0.973083	−	0.230457i	$-0.925978\pi$
$941$	−11.5277	−	31.6721i	−0.375793	−	1.03248i	0.597290	−	0.802025i	$-0.296244\pi$
$942$	−2.14530	−	1.72220i	−0.0698975	−	0.0561123i
$943$	−20.1675	−	11.6437i	−0.656745	−	0.379172i
$944$	−22.5671	−	6.05828i	−0.734496	−	0.197180i
$945$	−4.62904	+	0.789664i	−0.150583	+	0.0256878i
$946$	5.89519	−	17.3599i	0.191669	−	0.564420i
$947$	9.11458	+	51.6914i	0.296184	+	1.67974i	0.662350	+	0.749194i	$0.269559\pi$
$947$	9.11458	+	51.6914i	0.296184	+	1.67974i	−0.366166	+	0.930549i	$0.619330\pi$
$948$	−0.567386	−	1.37071i	−0.0184278	−	0.0445185i
$949$			21.4646i			0.696769i
$950$	17.2864	+	25.5182i	0.560846	+	0.827920i
$951$		−	1.17582i		−	0.0381287i
$952$	−8.59496	−	8.98479i	−0.278564	−	0.291199i
$953$	−5.08698	−	28.8497i	−0.164783	−	0.934533i	−0.949287	−	0.314409i	$-0.898194\pi$
$953$	−5.08698	−	28.8497i	−0.164783	−	0.934533i	0.784504	−	0.620124i	$-0.212918\pi$
$954$	27.9732	+	9.49932i	0.905666	+	0.307552i
$955$	28.8949	−	4.92916i	0.935017	−	0.159504i
$956$	−20.9072	+	13.3124i	−0.676186	+	0.430553i
$957$	1.98274	+	1.14474i	0.0640930	+	0.0370041i
$958$	22.7026	−	28.2800i	0.733487	−	0.913685i
$959$	4.15875	+	11.4261i	0.134293	+	0.368967i
$960$	−1.25360	−	2.44552i	−0.0404599	−	0.0789290i
$961$	0.366587	+	0.634947i	0.0118254	+	0.0204822i
$962$	−4.16014	+	27.0076i	−0.134128	+	0.870760i
$963$	15.2780	+	2.69393i	0.492327	+	0.0868106i
$964$	53.4959	+	7.05574i	1.72299	+	0.227250i
$965$	−47.6020	+	17.0260i	−1.53236	+	0.548087i
$966$	3.33754	−	2.02473i	0.107384	−	0.0651446i
$967$	26.2363	+	9.54922i	0.843701	+	0.307082i	0.727469	−	0.686140i	$-0.240696\pi$
$967$	26.2363	+	9.54922i	0.843701	+	0.307082i	0.116232	+	0.993222i	$0.462919\pi$
$968$	1.57027	−	3.18134i	0.0504703	−	0.102252i
$969$	1.28453	−	0.0787772i	0.0412650	−	0.00253069i
$970$	−2.21956	+	13.8946i	−0.0712658	+	0.446127i
$971$	−8.80099	−	3.20330i	−0.282437	−	0.102799i	0.196917	−	0.980420i	$-0.436907\pi$
$971$	−8.80099	−	3.20330i	−0.282437	−	0.102799i	−0.479355	+	0.877621i	$0.659129\pi$
$972$	4.99877	−	6.51134i	0.160336	−	0.208851i
$973$	−16.9387	+	20.1868i	−0.543031	+	0.647159i
$974$	−5.00845	−	2.74850i	−0.160481	−	0.0880677i
$975$	−0.837420	−	2.38307i	−0.0268189	−	0.0763192i
$976$	−36.3411	−	25.4720i	−1.16325	−	0.815337i
$977$	−23.2459	−	40.2631i	−0.743702	−	1.28813i	−0.950799	−	0.309809i	$-0.899735\pi$
$977$	−23.2459	−	40.2631i	−0.743702	−	1.28813i	0.207097	−	0.978320i	$-0.433598\pi$
$978$	−3.49556	−	3.98688i	−0.111776	−	0.127486i
$979$	−4.71218	+	1.71509i	−0.150602	+	0.0548147i
$980$	5.86021	−	5.30762i	0.187198	−	0.169546i
$981$	−51.3796	−	29.6640i	−1.64042	−	0.947099i
$982$	−33.6728	+	6.69380i	−1.07454	+	0.213608i
$983$	15.3019	+	18.2361i	0.488056	+	0.581642i	0.952722	−	0.303844i	$-0.0982701\pi$
$983$	15.3019	+	18.2361i	0.488056	+	0.581642i	−0.464666	+	0.885486i	$0.653826\pi$
$984$	1.17923	−	0.518374i	0.0375925	−	0.0165252i
$985$	1.80544	−	4.87574i	0.0575262	−	0.155354i
$986$	12.9720	−	0.281515i	0.413113	−	0.00896526i
$987$		−	2.19013i		−	0.0697125i
$988$	−28.5112	+	2.99456i	−0.907061	+	0.0952698i
$989$	32.6205			1.03727
$990$	25.6801	+	14.2792i	0.816168	+	0.453824i
$991$	7.30134	+	41.4080i	0.231935	+	1.31537i	0.848974	+	0.528435i	$0.177221\pi$
$991$	7.30134	+	41.4080i	0.231935	+	1.31537i	−0.617039	+	0.786933i	$0.711668\pi$
$992$	12.5509	−	28.4783i	0.398490	−	0.904187i
$993$	−2.21053	−	2.63441i	−0.0701492	−	0.0836005i
$994$	8.22447	+	41.3728i	0.260864	+	1.31226i
$995$	−36.0944	+	20.5719i	−1.14427	+	0.652173i
$996$	0.734546	−	2.32776i	0.0232750	−	0.0737579i
$997$	1.99703	+	5.48680i	0.0632467	+	0.173769i	0.967291	−	0.253671i	$-0.0816379\pi$
$997$	1.99703	+	5.48680i	0.0632467	+	0.173769i	−0.904044	+	0.427439i	$0.859416\pi$
$998$	12.3500	+	14.0858i	0.390931	+	0.445878i
$999$	4.67199	−	2.69737i	0.147815	−	0.0853411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.319.2	yes	336
4.3	odd	2	inner	380.2.bb.a.319.13	yes	336
5.4	even	2	inner	380.2.bb.a.319.55	yes	336
19.14	odd	18	inner	380.2.bb.a.299.44	yes	336
20.19	odd	2	inner	380.2.bb.a.319.44	yes	336
76.71	even	18	inner	380.2.bb.a.299.55	yes	336
95.14	odd	18	inner	380.2.bb.a.299.13	yes	336
380.299	even	18	inner	380.2.bb.a.299.2	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.299.2	✓	336	380.299	even	18	inner
380.2.bb.a.299.13	yes	336	95.14	odd	18	inner
380.2.bb.a.299.44	yes	336	19.14	odd	18	inner
380.2.bb.a.299.55	yes	336	76.71	even	18	inner
380.2.bb.a.319.2	yes	336	1.1	even	1	trivial
380.2.bb.a.319.13	yes	336	4.3	odd	2	inner
380.2.bb.a.319.44	yes	336	20.19	odd	2	inner
380.2.bb.a.319.55	yes	336	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41388 + 0.0306836i) q^{2} +(0.151290 - 0.0266765i) q^{3} +(1.99812 - 0.0867660i) q^{4} +(-0.376017 - 2.20423i) q^{5} +(-0.213088 + 0.0423596i) q^{6} +(-1.14368 + 1.98092i) q^{7} +(-2.82244 + 0.183986i) q^{8} +(-2.79690 + 1.01799i) q^{9} +O(q^{10})\)	\(q+(-1.41388 + 0.0306836i) q^{2} +(0.151290 - 0.0266765i) q^{3} +(1.99812 - 0.0867660i) q^{4} +(-0.376017 - 2.20423i) q^{5} +(-0.213088 + 0.0423596i) q^{6} +(-1.14368 + 1.98092i) q^{7} +(-2.82244 + 0.183986i) q^{8} +(-2.79690 + 1.01799i) q^{9} +(0.599277 + 3.10497i) q^{10} +(-2.70356 + 1.56090i) q^{11} +(0.299981 - 0.0664297i) q^{12} +(-0.571033 + 3.23849i) q^{13} +(1.55625 - 2.83587i) q^{14} +(-0.115689 - 0.323447i) q^{15} +(3.98494 - 0.346737i) q^{16} +(0.657317 - 1.80596i) q^{17} +(3.92325 - 1.52513i) q^{18} +(1.01826 + 4.23829i) q^{19} +(-0.942578 - 4.37168i) q^{20} +(-0.120184 + 0.330203i) q^{21} +(3.77462 - 2.28989i) q^{22} +(6.01752 + 5.04930i) q^{23} +(-0.422099 + 0.103128i) q^{24} +(-4.71722 + 1.65765i) q^{25} +(0.708003 - 4.59636i) q^{26} +(-0.795114 + 0.459059i) q^{27} +(-2.11334 + 4.05734i) q^{28} +(-1.63276 - 4.48597i) q^{29} +(0.173495 + 0.453765i) q^{30} +(-2.75076 + 4.76446i) q^{31} +(-5.62360 + 0.612518i) q^{32} +(-0.367383 + 0.308271i) q^{33} +(-0.873955 + 2.57359i) q^{34} +(4.79644 + 1.77608i) q^{35} +(-5.50021 + 2.27674i) q^{36} -5.87587 q^{37} +(-1.56975 - 5.96120i) q^{38} +0.505184i q^{39} +(1.46683 + 6.15211i) q^{40} +(-2.91951 + 0.514788i) q^{41} +(0.159794 - 0.470555i) q^{42} +(3.18112 - 2.66928i) q^{43} +(-5.26660 + 3.35344i) q^{44} +(3.29556 + 5.78222i) q^{45} +(-8.66299 - 6.95447i) q^{46} +(-5.85679 + 2.13170i) q^{47} +(0.593633 - 0.158762i) q^{48} +(0.883975 + 1.53109i) q^{49} +(6.61873 - 2.48846i) q^{50} +(0.0512688 - 0.290760i) q^{51} +(-0.859999 + 6.52042i) q^{52} +(5.37638 + 4.51132i) q^{53} +(1.11011 - 0.673452i) q^{54} +(4.45717 + 5.37234i) q^{55} +(2.86351 - 5.80144i) q^{56} +(0.267116 + 0.614049i) q^{57} +(2.44617 + 6.29253i) q^{58} +(-5.48925 - 1.99792i) q^{59} +(-0.259224 - 0.636247i) q^{60} +(-8.49907 - 7.13157i) q^{61} +(3.74306 - 6.82079i) q^{62} +(1.18222 - 6.70469i) q^{63} +(7.93230 - 1.03858i) q^{64} +(7.35307 + 0.0409589i) q^{65} +(0.509977 - 0.447131i) q^{66} +(-1.09648 - 3.01256i) q^{67} +(1.15670 - 3.66556i) q^{68} +(1.04509 + 0.603383i) q^{69} +(-6.83608 - 2.36399i) q^{70} +(-9.98926 + 8.38198i) q^{71} +(7.70678 - 3.38780i) q^{72} +(6.42811 - 1.13345i) q^{73} +(8.30778 - 0.180293i) q^{74} +(-0.669449 + 0.376626i) q^{75} +(2.40235 + 8.38026i) q^{76} -7.14072i q^{77} +(-0.0155009 - 0.714270i) q^{78} +(-0.838432 - 4.75499i) q^{79} +(-2.26269 - 8.65334i) q^{80} +(6.73212 - 5.64892i) q^{81} +(4.11204 - 0.817429i) q^{82} +(3.97221 - 6.88007i) q^{83} +(-0.211491 + 0.670212i) q^{84} +(-4.22792 - 0.769803i) q^{85} +(-4.41583 + 3.87165i) q^{86} +(-0.366691 - 0.635127i) q^{87} +(7.34345 - 4.90297i) q^{88} +(1.58191 + 0.278934i) q^{89} +(-4.83695 - 8.07425i) q^{90} +(-5.76210 - 4.83497i) q^{91} +(12.4618 + 9.56698i) q^{92} +(-0.289064 + 0.794197i) q^{93} +(8.21540 - 3.19368i) q^{94} +(8.95928 - 3.83815i) q^{95} +(-0.834455 + 0.242686i) q^{96} +(4.18121 + 1.52184i) q^{97} +(-1.29681 - 2.13765i) q^{98} +(5.97262 - 7.11789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

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