LMFDB - Embedded newform 225.2.q.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47708 + 0.526519i) q^{2} +(-1.29428 - 1.15102i) q^{3} +(4.03160 - 1.79498i) q^{4} +(1.67112 + 1.48572i) q^{5} +(3.81206 + 2.16971i) q^{6} +(-1.03406 - 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(0.350302 + 2.97948i) q^{9} +O(q^{10})$	\(q+(-2.47708 + 0.526519i) q^{2} +(-1.29428 - 1.15102i) q^{3} +(4.03160 - 1.79498i) q^{4} +(1.67112 + 1.48572i) q^{5} +(3.81206 + 2.16971i) q^{6} +(-1.03406 - 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(0.350302 + 2.97948i) q^{9} +(-4.92175 - 2.80036i) q^{10} +(-2.39587 + 0.509257i) q^{11} +(-7.28407 - 2.31725i) q^{12} +(1.74601 + 0.371125i) q^{13} +(3.50448 + 3.89212i) q^{14} +(-0.452799 - 3.84642i) q^{15} +(4.44939 - 4.94155i) q^{16} +(3.67466 - 2.66979i) q^{17} +(-2.43648 - 7.19596i) q^{18} +(5.85004 - 4.25031i) q^{19} +(9.40413 + 2.99019i) q^{20} +(-0.723173 + 3.50834i) q^{21} +(5.66661 - 2.52294i) q^{22} +(1.58401 + 1.75922i) q^{23} +(10.5333 + 1.04156i) q^{24} +(0.585285 + 4.96563i) q^{25} -4.52040 q^{26} +(2.97605 - 4.25947i) q^{27} +(-7.38384 - 5.36467i) q^{28} +(0.855066 - 8.13541i) q^{29} +(3.14683 + 9.28948i) q^{30} +(-0.709441 - 6.74988i) q^{31} +(-2.30859 + 3.99860i) q^{32} +(3.68708 + 2.09857i) q^{33} +(-7.69671 + 8.54806i) q^{34} +(0.932951 - 4.52939i) q^{35} +(6.76040 + 11.3833i) q^{36} +(1.53985 + 4.73917i) q^{37} +(-12.2531 + 13.6085i) q^{38} +(-1.83264 - 2.49003i) q^{39} +(-13.5986 - 1.34267i) q^{40} +(4.68289 + 0.995378i) q^{41} +(-0.0558547 - 9.07120i) q^{42} +(4.14034 + 7.17127i) q^{43} +(-8.74507 + 6.35367i) q^{44} +(-3.84127 + 5.49952i) q^{45} +(-4.84997 - 3.52371i) q^{46} +(1.05889 - 10.0746i) q^{47} +(-11.4466 + 1.27439i) q^{48} +(1.36143 - 2.35806i) q^{49} +(-4.06429 - 11.9921i) q^{50} +(-7.82901 - 0.774155i) q^{51} +(7.70536 - 1.63783i) q^{52} +(-2.52356 - 1.83348i) q^{53} +(-5.12922 + 12.1180i) q^{54} +(-4.76039 - 2.70855i) q^{55} +(11.5458 + 5.14053i) q^{56} +(-12.4638 - 1.23245i) q^{57} +(2.16538 + 20.6023i) q^{58} +(-10.2183 - 2.17198i) q^{59} +(-8.72978 - 14.6945i) q^{60} +(2.57932 - 0.548251i) q^{61} +(5.31128 + 16.3465i) q^{62} +(4.97416 - 3.70838i) q^{63} +(-0.496397 + 1.52775i) q^{64} +(2.36640 + 3.21427i) q^{65} +(-10.2381 - 3.25701i) q^{66} +(0.170417 + 1.62141i) q^{67} +(10.0225 - 17.3595i) q^{68} +(-0.0252460 - 4.10014i) q^{69} +(0.0738159 + 11.7109i) q^{70} +(8.24169 + 5.98794i) q^{71} +(-12.4342 - 13.4721i) q^{72} +(-0.608028 + 1.87132i) q^{73} +(-6.30959 - 10.9285i) q^{74} +(4.95802 - 7.10057i) q^{75} +(15.9558 - 27.6363i) q^{76} +(3.38958 + 3.76451i) q^{77} +(5.85064 + 5.20307i) q^{78} +(-1.55944 + 14.8370i) q^{79} +(14.7772 - 1.64738i) q^{80} +(-8.75458 + 2.08743i) q^{81} -12.1240 q^{82} +(3.70931 + 1.65149i) q^{83} +(3.38188 + 15.4423i) q^{84} +(10.1074 + 0.997956i) q^{85} +(-14.0318 - 15.5838i) q^{86} +(-10.4707 + 9.54527i) q^{87} +(10.0158 - 11.1237i) q^{88} +(0.105993 - 0.326212i) q^{89} +(6.61952 - 15.6452i) q^{90} +(-1.14078 - 3.51095i) q^{91} +(9.54385 + 4.24919i) q^{92} +(-6.85104 + 9.55279i) q^{93} +(2.68154 + 25.5132i) q^{94} +(16.0909 + 1.58874i) q^{95} +(7.59043 - 2.51805i) q^{96} +(1.15152 - 10.9560i) q^{97} +(-2.13079 + 6.55791i) q^{98} +(-2.35660 - 6.96004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−2.47708	+	0.526519i	−1.75156	+	0.372305i	−0.968378	−	0.249489i	$-0.919737\pi$
$2$	−2.47708	+	0.526519i	−1.75156	+	0.372305i	−0.783181	+	0.621794i	$0.786404\pi$
$3$	−1.29428	−	1.15102i	−0.747251	−	0.664542i
$3$	−1.29428	−	1.15102i	−0.747251	−	0.664542i
$4$	4.03160	−	1.79498i	2.01580	−	0.897492i
$5$	1.67112	+	1.48572i	0.747348	+	0.664433i
$5$	1.67112	+	1.48572i	0.747348	+	0.664433i
$6$	3.81206	+	2.16971i	1.55627	+	0.885779i
$7$	−1.03406	−	1.79105i	−0.390839	−	0.676953i	0.601721	−	0.798706i	$-0.294482\pi$
$7$	−1.03406	−	1.79105i	−0.390839	−	0.676953i	−0.992560	+	0.121753i	$0.961148\pi$
$8$	−4.94396	+	3.59200i	−1.74795	+	1.26996i
$9$	0.350302	+	2.97948i	0.116767	+	0.993159i
$10$	−4.92175	−	2.80036i	−1.55640	−	0.885552i
$11$	−2.39587	+	0.509257i	−0.722381	+	0.153547i	−0.554408	−	0.832245i	$-0.687055\pi$
$11$	−2.39587	+	0.509257i	−0.722381	+	0.153547i	−0.167973	+	0.985792i	$0.553722\pi$
$12$	−7.28407	−	2.31725i	−2.10273	−	0.668933i
$13$	1.74601	+	0.371125i	0.484255	+	0.102932i	0.443569	−	0.896240i	$-0.353712\pi$
$13$	1.74601	+	0.371125i	0.484255	+	0.102932i	0.0406862	+	0.999172i	$0.487046\pi$
$14$	3.50448	+	3.89212i	0.936611	+	1.04021i
$15$	−0.452799	−	3.84642i	−0.116912	−	0.993142i
$16$	4.44939	−	4.94155i	1.11235	−	1.23539i
$17$	3.67466	−	2.66979i	0.891235	−	0.647520i	−0.0449649	−	0.998989i	$-0.514318\pi$
$17$	3.67466	−	2.66979i	0.891235	−	0.647520i	0.936200	+	0.351469i	$0.114318\pi$
$18$	−2.43648	−	7.19596i	−0.574283	−	1.69610i
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.342728	−	0.939435i	$-0.388649\pi$
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.999364	−	0.0356524i	$-0.0113509\pi$
$20$	9.40413	+	2.99019i	2.10283	+	0.668626i
$21$	−0.723173	+	3.50834i	−0.157809	+	0.765583i
$22$	5.66661	−	2.52294i	1.20813	−	0.537892i
$23$	1.58401	+	1.75922i	0.330288	+	0.366822i	0.885300	−	0.465020i	$-0.153953\pi$
$23$	1.58401	+	1.75922i	0.330288	+	0.366822i	−0.555012	+	0.831842i	$0.687286\pi$
$24$	10.5333	+	1.04156i	2.15010	+	0.212608i
$25$	0.585285	+	4.96563i	0.117057	+	0.993125i
$26$	−4.52040			−0.886523
$27$	2.97605	−	4.25947i	0.572742	−	0.819736i
$28$	−7.38384	−	5.36467i	−1.39541	−	1.01383i
$29$	0.855066	−	8.13541i	0.158782	−	1.51071i	−0.567536	−	0.823349i	$-0.692103\pi$
$29$	0.855066	−	8.13541i	0.158782	−	1.51071i	0.726318	−	0.687359i	$-0.241230\pi$
$30$	3.14683	+	9.28948i	0.574531	+	1.69602i
$31$	−0.709441	−	6.74988i	−0.127419	−	1.21231i	−0.852156	−	0.523288i	$-0.824705\pi$
$31$	−0.709441	−	6.74988i	−0.127419	−	1.21231i	0.724736	−	0.689026i	$-0.241962\pi$
$32$	−2.30859	+	3.99860i	−0.408105	+	0.706859i
$33$	3.68708	+	2.09857i	0.641838	+	0.365315i
$34$	−7.69671	+	8.54806i	−1.31997	+	1.46598i
$35$	0.932951	−	4.52939i	0.157698	−	0.765606i
$36$	6.76040	+	11.3833i	1.12673	+	1.89721i
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	0.994189	+	0.107653i	$0.0343334\pi$
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	−0.741039	+	0.671462i	$0.765667\pi$
$38$	−12.2531	+	13.6085i	−1.98772	+	2.20759i
$39$	−1.83264	−	2.49003i	−0.293457	−	0.398723i
$40$	−13.5986	−	1.34267i	−2.15013	−	0.212295i
$41$	4.68289	+	0.995378i	0.731344	+	0.155452i	0.558508	−	0.829499i	$-0.311374\pi$
$41$	4.68289	+	0.995378i	0.731344	+	0.155452i	0.172835	+	0.984951i	$0.444707\pi$
$42$	−0.0558547	−	9.07120i	−0.00861857	−	1.39972i
$43$	4.14034	+	7.17127i	0.631395	+	1.09361i	0.987267	+	0.159074i	$0.0508508\pi$
$43$	4.14034	+	7.17127i	0.631395	+	1.09361i	−0.355871	+	0.934535i	$0.615816\pi$
$44$	−8.74507	+	6.35367i	−1.31837	+	0.957851i
$45$	−3.84127	+	5.49952i	−0.572622	+	0.819819i
$46$	−4.84997	−	3.52371i	−0.715088	−	0.519542i
$47$	1.05889	−	10.0746i	0.154455	−	1.46954i	−0.592988	−	0.805211i	$-0.702052\pi$
$47$	1.05889	−	10.0746i	0.154455	−	1.46954i	0.747443	−	0.664326i	$-0.231281\pi$
$48$	−11.4466	+	1.27439i	−1.65217	+	0.183942i
$49$	1.36143	−	2.35806i	0.194489	−	0.336866i
$50$	−4.06429	−	11.9921i	−0.574778	−	1.69594i
$51$	−7.82901	−	0.774155i	−1.09628	−	0.108403i
$52$	7.70536	−	1.63783i	1.06854	−	0.227125i
$53$	−2.52356	−	1.83348i	−0.346638	−	0.251847i	0.400819	−	0.916157i	$-0.368726\pi$
$53$	−2.52356	−	1.83348i	−0.346638	−	0.251847i	−0.747457	+	0.664310i	$0.768726\pi$
$54$	−5.12922	+	12.1180i	−0.697999	+	1.64905i
$55$	−4.76039	−	2.70855i	−0.641891	−	0.365221i
$56$	11.5458	+	5.14053i	1.54287	+	0.686932i
$57$	−12.4638	−	1.23245i	−1.65087	−	0.163242i
$58$	2.16538	+	20.6023i	0.284329	+	2.70521i
$59$	−10.2183	−	2.17198i	−1.33032	−	0.282767i	−0.512718	−	0.858557i	$-0.671361\pi$
$59$	−10.2183	−	2.17198i	−1.33032	−	0.282767i	−0.817598	+	0.575790i	$0.804695\pi$
$60$	−8.72978	−	14.6945i	−1.12701	−	1.89705i
$61$	2.57932	−	0.548251i	0.330248	−	0.0701964i	−0.0398037	−	0.999208i	$-0.512673\pi$
$61$	2.57932	−	0.548251i	0.330248	−	0.0701964i	0.370052	+	0.929011i	$0.379340\pi$
$62$	5.31128	+	16.3465i	0.674534	+	2.07600i
$63$	4.97416	−	3.70838i	0.626685	−	0.467212i
$64$	−0.496397	+	1.52775i	−0.0620496	+	0.190969i
$65$	2.36640	+	3.21427i	0.293516	+	0.398681i
$66$	−10.2381	−	3.25701i	−1.26023	−	0.400910i
$67$	0.170417	+	1.62141i	0.0208197	+	0.198086i	0.999988	−	0.00496571i	$-0.00158064\pi$
$67$	0.170417	+	1.62141i	0.0208197	+	0.198086i	−0.979168	+	0.203052i	$0.934914\pi$
$68$	10.0225	−	17.3595i	1.21541	−	2.10515i
$69$	−0.0252460	−	4.10014i	−0.00303927	−	0.493598i
$70$	0.0738159	+	11.7109i	0.00882269	+	1.39972i
$71$	8.24169	+	5.98794i	0.978109	+	0.710638i	0.957285	−	0.289145i	$-0.0933711\pi$
$71$	8.24169	+	5.98794i	0.978109	+	0.710638i	0.0208238	+	0.999783i	$0.493371\pi$
$72$	−12.4342	−	13.4721i	−1.46538	−	1.58771i
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	−0.980313	−	0.197451i	$-0.936734\pi$
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	0.909148	+	0.416472i	$0.136734\pi$
$74$	−6.30959	−	10.9285i	−0.733475	−	1.27042i
$75$	4.95802	−	7.10057i	0.572503	−	0.819903i
$76$	15.9558	−	27.6363i	1.83026	−	3.17010i
$77$	3.38958	+	3.76451i	0.386279	+	0.429006i
$78$	5.85064	+	5.20307i	0.662455	+	0.589132i
$79$	−1.55944	+	14.8370i	−0.175450	+	1.66930i	0.453048	+	0.891486i	$0.350336\pi$
$79$	−1.55944	+	14.8370i	−0.175450	+	1.66930i	−0.628499	+	0.777811i	$0.716330\pi$
$80$	14.7772	−	1.64738i	1.65214	−	0.184183i
$81$	−8.75458	+	2.08743i	−0.972731	+	0.231937i
$82$	−12.1240			−1.33887
$83$	3.70931	+	1.65149i	0.407150	+	0.181275i	0.600084	−	0.799937i	$-0.295134\pi$
$83$	3.70931	+	1.65149i	0.407150	+	0.181275i	−0.192934	+	0.981212i	$0.561800\pi$
$84$	3.38188	+	15.4423i	0.368993	+	1.68490i
$85$	10.1074	+	0.997956i	1.09630	+	0.108243i
$86$	−14.0318	−	15.5838i	−1.51308	−	1.68045i
$87$	−10.4707	+	9.54527i	−1.12258	+	1.02336i
$88$	10.0158	−	11.1237i	1.06769	−	1.18579i
$89$	0.105993	−	0.326212i	0.0112352	−	0.0345784i	−0.945282	−	0.326255i	$-0.894213\pi$
$89$	0.105993	−	0.326212i	0.0112352	−	0.0345784i	0.956517	+	0.291677i	$0.0942131\pi$
$90$	6.61952	−	15.6452i	0.697758	−	1.64915i
$91$	−1.14078	−	3.51095i	−0.119586	−	0.368048i
$92$	9.54385	+	4.24919i	0.995015	+	0.443009i
$93$	−6.85104	+	9.55279i	−0.710420	+	0.990579i
$94$	2.68154	+	25.5132i	0.276580	+	2.63148i
$95$	16.0909	+	1.58874i	1.65089	+	0.163002i
$96$	7.59043	−	2.51805i	0.774695	−	0.256998i
$97$	1.15152	−	10.9560i	0.116920	−	1.11242i	−0.765983	−	0.642860i	$-0.777748\pi$
$97$	1.15152	−	10.9560i	0.116920	−	1.11242i	0.882903	−	0.469555i	$-0.155586\pi$
$98$	−2.13079	+	6.55791i	−0.215243	+	0.662449i
$99$	−2.35660	−	6.96004i	−0.236847	−	0.699510i
$100$	11.2729	+	18.9688i	1.12729	+	1.89688i
$101$	6.38861	+	11.0654i	0.635691	+	1.10105i	0.986368	+	0.164553i	$0.0526180\pi$
$101$	6.38861	+	11.0654i	0.635691	+	1.10105i	−0.350677	+	0.936496i	$0.614049\pi$
$102$	19.8007	−	2.20448i	1.96056	−	0.218276i
$103$	−8.38725	+	3.73425i	−0.826421	+	0.367946i	−0.775962	−	0.630780i	$-0.782735\pi$
$103$	−8.38725	+	3.73425i	−0.826421	+	0.367946i	−0.0504589	+	0.998726i	$0.516068\pi$
$104$	−9.96526	+	4.43682i	−0.977174	+	0.435066i
$105$	−6.42092	+	4.78843i	−0.626617	+	0.467303i
$106$	7.21643	+	3.21296i	0.700921	+	0.312070i
$107$	0.980681			0.0948061			0.0474030	−	0.998876i	$-0.484905\pi$
$107$	0.980681			0.0948061			0.0474030	+	0.998876i	$0.484905\pi$
$108$	4.35257	−	22.5145i	0.418827	−	2.16646i
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	−0.992189	−	0.124741i	$-0.960190\pi$
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	0.729377	−	0.684112i	$-0.239810\pi$
$110$	13.2180	+	4.20286i	1.26028	+	0.400727i
$111$	3.46189	−	7.90619i	0.328588	−	0.750423i
$112$	−13.4515	−	2.85921i	−1.27105	−	0.270170i
$113$	−6.63465	−	1.41024i	−0.624135	−	0.132664i	−0.115021	−	0.993363i	$-0.536694\pi$
$113$	−6.63465	−	1.41024i	−0.624135	−	0.132664i	−0.509114	+	0.860699i	$0.670027\pi$
$114$	31.5226	−	3.50953i	2.95236	−	0.328698i
$115$	0.0333644	+	5.29325i	0.00311125	+	0.493598i
$116$	−11.1557	−	34.3336i	−1.03578	−	3.18779i
$117$	−0.494129	+	5.33219i	−0.0456823	+	0.492961i
$118$	26.4552			2.43540
$119$	−8.58156	−	3.82076i	−0.786670	−	0.350248i
$120$	16.0550	+	17.3901i	1.46561	+	1.58749i
$121$	−4.56817	+	2.03388i	−0.415288	+	0.184898i
$122$	−6.10051	+	2.71612i	−0.552314	+	0.245906i
$123$	−4.91525	−	6.67839i	−0.443193	−	0.602170i
$124$	−14.9761	−	25.9394i	−1.34490	−	2.32943i
$125$	−6.39944	+	9.16773i	−0.572383	+	0.819986i
$126$	−10.3689	+	11.8049i	−0.923731	+	1.05167i
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	−0.716141	−	0.697955i	$-0.754093\pi$
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	0.989618	−	0.143721i	$-0.0459067\pi$
$128$	1.39048	−	13.2295i	0.122902	−	1.16933i
$129$	2.89555	−	14.0472i	0.254939	−	1.23679i
$130$	−7.55412	−	6.71603i	−0.662541	−	0.589035i
$131$	1.43811	+	13.6827i	0.125648	+	1.19546i	0.857677	+	0.514189i	$0.171907\pi$
$131$	1.43811	+	13.6827i	0.125648	+	1.19546i	−0.732029	+	0.681274i	$0.761426\pi$
$132$	18.6317	+	1.84236i	1.62168	+	0.160357i
$133$	−13.6618	−	6.08264i	−1.18463	−	0.527432i
$134$	−1.27584	−	3.92662i	−0.110215	−	0.339208i
$135$	11.3017	−	2.69651i	0.972697	−	0.232079i
$136$	−8.57746	+	26.3987i	−0.735511	+	2.26367i
$137$	−5.70711	+	6.33838i	−0.487591	+	0.541525i	−0.935859	−	0.352374i	$-0.885374\pi$
$137$	−5.70711	+	6.33838i	−0.487591	+	0.541525i	0.448268	+	0.893899i	$0.352041\pi$
$138$	2.22134	+	10.1431i	0.189093	+	0.863435i
$139$	−6.24293	−	6.93348i	−0.529518	−	0.588090i	0.417738	−	0.908568i	$-0.362823\pi$
$139$	−6.24293	−	6.93348i	−0.529518	−	0.588090i	−0.947256	+	0.320478i	$0.896157\pi$
$140$	−4.36889	−	19.9353i	−0.369239	−	1.68484i
$141$	−12.9666	+	11.8206i	−1.09199	+	0.995471i
$142$	−23.5681	−	10.4932i	−1.97779	−	0.880569i
$143$	−4.37219			−0.365621
$144$	16.2819	+	11.5258i	1.35682	+	0.960485i
$145$	13.5158	−	12.3249i	1.12243	−	1.02352i
$146$	0.520848	−	4.95554i	0.0431057	−	0.410123i
$147$	−4.47624	+	1.48495i	−0.369194	+	0.122477i
$148$	14.7148	+	16.3424i	1.20955	+	1.34334i
$149$	−3.47298	+	6.01538i	−0.284518	+	0.492799i	−0.972492	−	0.232936i	$-0.925167\pi$
$149$	−3.47298	+	6.01538i	−0.284518	+	0.492799i	0.687974	+	0.725735i	$0.258500\pi$
$150$	−8.54281	+	20.1991i	−0.697518	+	1.64925i
$151$	0.394205	+	0.682783i	0.0320800	+	0.0555641i	0.881620	−	0.471961i	$-0.156454\pi$
$151$	0.394205	+	0.682783i	0.0320800	+	0.0555641i	−0.849540	+	0.527525i	$0.823120\pi$
$152$	−13.6553	+	42.0267i	−1.10759	+	3.40881i
$153$	9.24183	+	10.0133i	0.747158	+	0.809529i
$154$	−10.3783	−	7.54031i	−0.836311	−	0.607616i
$155$	8.84286	−	12.3339i	0.710276	−	0.990682i
$156$	−11.8580	−	6.74923i	−0.949403	−	0.540371i
$157$	−1.94393	+	3.36698i	−0.155142	+	0.268714i	−0.933111	−	0.359589i	$-0.882917\pi$
$157$	−1.94393	+	3.36698i	−0.155142	+	0.268714i	0.777969	+	0.628303i	$0.216250\pi$
$158$	−3.94914	−	37.5736i	−0.314177	−	2.98919i
$159$	1.15582	+	5.27770i	0.0916625	+	0.418549i
$160$	−9.79873	+	3.25222i	−0.774657	+	0.257111i
$161$	1.51288	−	4.65617i	0.119232	−	0.366958i
$162$	20.5867	−	9.78019i	1.61744	−	0.768404i
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	0.999784	+	0.0207767i	$0.00661392\pi$
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	−0.796630	+	0.604467i	$0.793386\pi$
$164$	20.6662	−	4.39274i	1.61376	−	0.343015i
$165$	3.04366	+	8.98493i	0.236949	+	0.699475i
$166$	−10.0578	−	2.13785i	−0.780637	−	0.165929i
$167$	−1.12972	−	10.7486i	−0.0874207	−	0.831753i	−0.947104	−	0.320926i	$-0.896006\pi$
$167$	−1.12972	−	10.7486i	−0.0874207	−	0.831753i	0.859684	−	0.510827i	$-0.170661\pi$
$168$	−9.02662	−	19.9427i	−0.696419	−	1.53862i
$169$	−8.96529	−	3.99160i	−0.689638	−	0.307046i
$170$	−25.5621	+	2.84970i	−1.96053	+	0.218562i
$171$	14.7130	+	15.9412i	1.12513	+	1.21905i
$172$	29.5645	+	21.4799i	2.25427	+	1.63783i
$173$	16.1013	−	3.42244i	1.22416	−	0.260203i	0.449904	−	0.893077i	$-0.351458\pi$
$173$	16.1013	−	3.42244i	1.22416	−	0.260203i	0.774255	+	0.632874i	$0.218125\pi$
$174$	20.9110	−	29.1574i	1.58526	−	2.21042i
$175$	8.28846	−	6.18305i	0.626549	−	0.467394i
$176$	−8.14362	+	14.1052i	−0.613849	+	1.06322i
$177$	10.7254	+	14.5727i	0.806168	+	1.09535i
$178$	−0.0907954	+	0.863860i	−0.00680540	+	0.0647491i
$179$	−0.422707	−	0.307115i	−0.0315946	−	0.0229548i	0.571876	−	0.820340i	$-0.306216\pi$
$179$	−0.422707	−	0.307115i	−0.0315946	−	0.0229548i	−0.603471	+	0.797385i	$0.706216\pi$
$180$	−5.61491	+	29.0669i	−0.418511	+	2.16652i
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.391756	+	0.920069i	$0.628132\pi$
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.996097	+	0.0882646i	$0.971868\pi$
$182$	4.67438	+	8.09626i	0.346488	+	0.600134i
$183$	−3.96940	−	2.25926i	−0.293427	−	0.167009i
$184$	−14.1504	−	3.00775i	−1.04318	−	0.221734i
$185$	−4.46780	+	10.2075i	−0.328479	+	0.750471i
$186$	11.9408	−	27.2702i	0.875545	−	1.99955i
$187$	−7.44437	+	8.26781i	−0.544386	+	0.604602i
$188$	−13.8148	−	42.5176i	−1.00755	−	3.10092i
$189$	−10.7064	−	0.925697i	−0.778773	−	0.0673346i
$190$	−40.6949	+	4.53672i	−2.95232	+	0.329128i
$191$	−0.671770	+	0.746076i	−0.0486076	+	0.0539842i	−0.766958	−	0.641697i	$-0.778231\pi$
$191$	−0.671770	+	0.746076i	−0.0486076	+	0.0539842i	0.718351	+	0.695681i	$0.244897\pi$
$192$	2.40095	−	1.40597i	0.173274	−	0.101467i
$193$	6.92614	−	11.9964i	0.498554	−	0.863521i	−0.501444	−	0.865190i	$-0.667198\pi$
$193$	6.92614	−	11.9964i	0.498554	−	0.863521i	0.999999	+	0.00166856i	$0.000531120\pi$
$194$	2.91614	+	27.7452i	0.209367	+	1.99199i
$195$	0.636914	−	6.88392i	0.0456104	−	0.492968i
$196$	1.25605	−	11.9505i	0.0897177	−	0.853607i
$197$	6.40803	+	4.65571i	0.456553	+	0.331705i	0.792178	−	0.610291i	$-0.208947\pi$
$197$	6.40803	+	4.65571i	0.456553	+	0.331705i	−0.335624	+	0.941996i	$0.608947\pi$
$198$	9.50207	+	15.9998i	0.675283	+	1.13705i
$199$	14.6161			1.03611			0.518053	−	0.855348i	$-0.326657\pi$
$199$	14.6161			1.03611			0.518053	+	0.855348i	$0.326657\pi$
$200$	−20.7301	−	22.4475i	−1.46584	−	1.58728i
$201$	1.64571	−	2.29470i	0.116079	−	0.161856i
$202$	−21.6512	−	24.0461i	−1.52338	−	1.69188i
$203$	−15.4551	+	6.88107i	−1.08474	+	0.482956i
$204$	−32.9530	+	10.9319i	−2.30717	+	0.765384i
$205$	6.34681	+	8.62084i	0.443281	+	0.602106i
$206$	18.8097	−	13.6661i	1.31054	−	0.952160i
$207$	−4.68667	+	5.33577i	−0.325746	+	0.370861i
$208$	9.60259	−	6.97669i	0.665820	−	0.483746i
$209$	−11.8514	+	13.1623i	−0.819780	+	0.910458i
$210$	13.3839	−	15.2421i	0.923577	−	1.05180i
$211$	8.91267	+	9.89852i	0.613574	+	0.681442i	0.967221	−	0.253936i	$-0.0817254\pi$
$211$	8.91267	+	9.89852i	0.613574	+	0.681442i	−0.353647	+	0.935379i	$0.615059\pi$
$212$	−13.4651	−	2.86209i	−0.924785	−	0.196569i
$213$	−3.77478	−	17.2364i	−0.258644	−	1.18102i
$214$	−2.42922	+	0.516348i	−0.166058	+	0.0352968i
$215$	−3.73549	+	18.1354i	−0.254758	+	1.23683i
$216$	0.586523	+	31.7486i	0.0399079	+	2.16022i
$217$	−11.3558	+	8.25045i	−0.770880	+	0.560077i
$218$	11.2430	+	19.4734i	0.761471	+	1.31891i
$219$	2.94088	−	1.72215i	0.198726	−	0.116372i
$220$	−24.0538	−	2.37497i	−1.62171	−	0.160120i
$221$	7.40679	−	3.29772i	0.498235	−	0.221828i
$222$	−4.41261	+	21.4070i	−0.296155	+	1.43674i
$223$	−3.56890	+	0.758594i	−0.238991	+	0.0507992i	−0.325850	−	0.945421i	$-0.605650\pi$
$223$	−3.56890	+	0.758594i	−0.238991	+	0.0507992i	0.0868587	+	0.996221i	$0.472317\pi$
$224$	9.54893			0.638014
$225$	−14.5899	+	3.48331i	−0.972663	+	0.232221i
$226$	17.1771			1.14260
$227$	−15.3712	+	3.26726i	−1.02023	+	0.216856i	−0.687513	−	0.726172i	$-0.741297\pi$
$227$	−15.3712	+	3.26726i	−1.02023	+	0.216856i	−0.332713	+	0.943028i	$0.607964\pi$
$228$	−52.4612	+	17.4035i	−3.47433	+	1.15258i
$229$	5.48833	−	2.44356i	0.362679	−	0.161475i	−0.217303	−	0.976104i	$-0.569726\pi$
$229$	5.48833	−	2.44356i	0.362679	−	0.161475i	0.579982	+	0.814629i	$0.303059\pi$
$230$	−2.86964	−	13.0942i	−0.189219	−	0.863407i
$231$	−0.0540235	−	8.77380i	−0.00355449	−	0.577274i
$232$	24.9950	+	43.2926i	1.64100	+	2.84230i
$233$	−0.484321	+	0.351880i	−0.0317289	+	0.0230524i	−0.603537	−	0.797335i	$-0.706242\pi$
$233$	−0.484321	+	0.351880i	−0.0317289	+	0.0230524i	0.571808	+	0.820388i	$0.306242\pi$
$234$	−1.58350	−	13.4684i	−0.103517	−	0.880458i
$235$	16.7376	−	15.2627i	1.09184	−	0.995630i
$236$	−45.0950	+	9.58523i	−2.93543	+	0.623945i
$237$	19.0961	−	17.4083i	1.24042	−	1.13079i
$238$	23.2689	+	4.94596i	1.50830	+	0.320599i
$239$	0.786263	+	0.873234i	0.0508592	+	0.0564848i	0.768038	−	0.640405i	$-0.221233\pi$
$239$	0.786263	+	0.873234i	0.0508592	+	0.0564848i	−0.717178	+	0.696890i	$0.754567\pi$
$240$	−21.0220	−	14.8767i	−1.35696	−	0.960287i
$241$	12.0251	−	13.3552i	0.774604	−	0.860284i	−0.218703	−	0.975791i	$-0.570183\pi$
$241$	12.0251	−	13.3552i	0.774604	−	0.860284i	0.993307	+	0.115507i	$0.0368493\pi$
$242$	10.2448	−	7.44331i	0.658563	−	0.478474i
$243$	13.7335	+	7.37498i	0.881006	+	0.473105i
$244$	9.41469	−	6.84017i	0.602714	−	0.437897i
$245$	5.77852	−	1.91790i	0.369176	−	0.122530i
$246$	15.6917	+	13.9549i	1.00047	+	0.889734i
$247$	11.7916	−	5.24996i	0.750282	−	0.334047i
$248$	27.7530	+	30.8228i	1.76232	+	1.95725i
$249$	−2.89997	−	6.40699i	−0.183778	−	0.406026i
$250$	11.0249	−	26.0786i	0.697277	−	1.64936i
$251$	0.313172			0.0197673			0.00988364	−	0.999951i	$-0.496854\pi$
$251$	0.313172			0.0197673			0.00988364	+	0.999951i	$0.496854\pi$
$252$	13.3974	−	23.8792i	0.843954	−	1.50425i
$253$	−4.69096	−	3.40818i	−0.294918	−	0.214270i
$254$	−2.64004	+	25.1183i	−0.165651	+	1.57606i
$255$	−11.9330	−	12.9254i	−0.747276	−	0.809420i
$256$	3.18545	+	30.3075i	0.199090	+	1.89422i
$257$	1.48530	−	2.57262i	0.0926507	−	0.160476i	−0.815975	−	0.578087i	$-0.803799\pi$
$257$	1.48530	−	2.57262i	0.0926507	−	0.160476i	0.908626	+	0.417611i	$0.137133\pi$
$258$	0.223639	+	36.3206i	0.0139232	+	2.26122i
$259$	6.89579	−	7.65855i	0.428484	−	0.475879i
$260$	15.3099	+	8.71099i	0.949482	+	0.540233i
$261$	24.5388	−	0.302200i	1.51891	−	0.0187057i
$262$	−10.7665	−	33.1359i	−0.665158	−	2.04714i
$263$	−5.43812	+	6.03964i	−0.335329	+	0.372420i	−0.887102	−	0.461574i	$-0.847285\pi$
$263$	−5.43812	+	6.03964i	−0.335329	+	0.372420i	0.551773	+	0.833994i	$0.313952\pi$
$264$	−25.7668	+	2.86872i	−1.58584	+	0.176557i
$265$	−1.49315	−	6.81327i	−0.0917235	−	0.418536i
$266$	37.0440	+	7.87395i	2.27132	+	0.482783i
$267$	−0.512661	+	0.300209i	−0.0313743	+	0.0183725i
$268$	3.59745	+	6.23097i	0.219749	+	0.380617i
$269$	18.6230	−	13.5304i	1.13547	−	0.824965i	0.148986	−	0.988839i	$-0.452399\pi$
$269$	18.6230	−	13.5304i	1.13547	−	0.824965i	0.986481	+	0.163874i	$0.0523992\pi$
$270$	−26.5755	+	12.6300i	−1.61733	+	0.768640i
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.128974	−	0.991648i	$-0.541169\pi$
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.982969	+	0.183774i	$0.941169\pi$
$272$	3.15706	−	30.0374i	0.191425	−	1.82129i
$273$	−2.56470	+	5.85720i	−0.155222	+	0.354494i
$274$	10.7997	−	18.7056i	0.652432	−	1.13005i
$275$	−3.93104	−	11.5989i	−0.237051	−	0.699441i
$276$	−7.46146	−	16.4848i	−0.449127	−	0.992268i
$277$	10.1292	−	2.15304i	0.608607	−	0.129363i	0.106709	−	0.994290i	$-0.465969\pi$
$277$	10.1292	−	2.15304i	0.608607	−	0.129363i	0.501898	+	0.864927i	$0.332635\pi$
$278$	19.1148	+	13.8877i	1.14643	+	0.832931i
$279$	19.8626	−	4.47826i	1.18914	−	0.268107i
$280$	11.6571	+	25.7443i	0.696643	+	1.53851i
$281$	−23.2406	−	10.3474i	−1.38642	−	0.617273i	−0.428297	−	0.903638i	$-0.640886\pi$
$281$	−23.2406	−	10.3474i	−1.38642	−	0.617273i	−0.958121	+	0.286365i	$0.907553\pi$
$282$	25.8956	−	36.1076i	1.54206	−	2.15018i
$283$	1.73208	+	16.4797i	0.102962	+	0.979614i	0.917023	+	0.398835i	$0.130585\pi$
$283$	1.73208	+	16.4797i	0.102962	+	0.979614i	−0.814061	+	0.580779i	$0.802748\pi$
$284$	43.9755	+	9.34728i	2.60946	+	0.554659i
$285$	−18.9974	−	20.5772i	−1.12531	−	1.21889i
$286$	10.8303	−	2.30204i	0.640407	−	0.136123i
$287$	−3.05963	−	9.41657i	−0.180604	−	0.555842i
$288$	−12.7224	−	5.47768i	−0.749677	−	0.322776i
$289$	1.12201	−	3.45318i	0.0660004	−	0.203128i
$290$	−26.9905	+	37.6460i	−1.58494	+	2.21065i
$291$	−14.1010	+	12.8547i	−0.826615	+	0.753555i
$292$	0.907660	+	8.63581i	0.0531168	+	0.505373i
$293$	−6.06420	+	10.5035i	−0.354274	+	0.613621i	−0.986993	−	0.160760i	$-0.948605\pi$
$293$	−6.06420	+	10.5035i	−0.354274	+	0.613621i	0.632719	+	0.774381i	$0.281939\pi$
$294$	10.3061	−	6.03516i	0.601066	−	0.351978i
$295$	−13.8491	−	18.8112i	−0.806328	−	1.09523i
$296$	−24.6360	−	17.8991i	−1.43194	−	1.04037i
$297$	−4.96106	+	11.7207i	−0.287870	+	0.680104i
$298$	5.43564	−	16.7292i	0.314878	−	0.969095i
$299$	2.11279	+	3.65946i	0.122186	+	0.211632i
$300$	7.24335	−	37.5262i	0.418195	−	2.16658i
$301$	8.56274	−	14.8311i	0.493548	−	0.854851i
$302$	−1.33598	−	1.48375i	−0.0768768	−	0.0853803i
$303$	4.46788	−	21.6751i	0.256673	−	1.24520i
$304$	5.02604	−	47.8195i	0.288263	−	2.74264i
$305$	5.12490	+	2.91595i	0.293451	+	0.166967i
$306$	−28.1649	−	19.9378i	−1.61008	−	1.13977i
$307$	−11.7705			−0.671776			−0.335888	−	0.941902i	$-0.609036\pi$
$307$	−11.7705			−0.671776			−0.335888	+	0.941902i	$0.609036\pi$
$308$	20.4227	+	9.09277i	1.16369	+	0.518109i
$309$	15.1536	+	4.82076i	0.862059	+	0.274243i
$310$	−15.4104	+	35.2080i	−0.875253	+	1.99968i
$311$	6.61932	+	7.35150i	0.375347	+	0.416865i	0.900990	−	0.433840i	$-0.142842\pi$
$311$	6.61932	+	7.35150i	0.375347	+	0.416865i	−0.525643	+	0.850705i	$0.676175\pi$
$312$	18.0047	+	5.72775i	1.01931	+	0.324270i
$313$	−23.0294	+	25.5767i	−1.30170	+	1.44568i	−0.478322	+	0.878185i	$0.658755\pi$
$313$	−23.0294	+	25.5767i	−1.30170	+	1.44568i	−0.823376	+	0.567497i	$0.807912\pi$
$314$	3.04248	−	9.36378i	0.171697	−	0.528429i
$315$	13.8220	+	1.19305i	0.778783	+	0.0672210i
$316$	20.3452	+	62.6162i	1.14451	+	3.52243i
$317$	20.3148	+	9.04473i	1.14099	+	0.508003i	0.888172	−	0.459510i	$-0.151975\pi$
$317$	20.3148	+	9.04473i	1.14099	+	0.508003i	0.252821	+	0.967513i	$0.418642\pi$
$318$	−5.64187	−	12.4647i	−0.316380	−	0.698987i
$319$	2.09439	+	19.9268i	0.117263	+	1.11569i
$320$	−3.09935	+	1.81555i	−0.173259	+	0.101492i
$321$	−1.26927	−	1.12878i	−0.0708439	−	0.0630026i
$322$	−1.29596	+	12.3303i	−0.0722212	+	0.687139i
$323$	10.1495	−	31.2368i	0.564731	−	1.73806i
$324$	−31.5481	+	24.1300i	−1.75267	+	1.34056i
$325$	−0.820957	+	8.88722i	−0.0455385	+	0.492974i
$326$	−10.6278	−	18.4078i	−0.588618	−	1.01952i
$327$	−6.16871	+	14.0880i	−0.341130	+	0.779066i
$328$	−26.7274	+	11.8998i	−1.47577	+	0.657057i
$329$	−19.1391	+	8.52130i	−1.05518	+	0.469794i
$330$	−12.2701	−	20.6538i	−0.675448	−	1.13695i
$331$	−11.9559	−	5.32309i	−0.657154	−	0.292584i	0.0509405	−	0.998702i	$-0.483778\pi$
$331$	−11.9559	−	5.32309i	−0.657154	−	0.292584i	−0.708094	+	0.706118i	$0.750445\pi$
$332$	17.9189			0.983426
$333$	−13.5808	+	6.24809i	−0.744225	+	0.342393i
$334$	8.45777	+	26.0303i	0.462788	+	1.42432i
$335$	−2.12416	+	2.96275i	−0.116056	+	0.161873i
$336$	14.1190	+	19.1836i	0.770253	+	1.04655i
$337$	−14.2119	−	3.02084i	−0.774174	−	0.164556i	−0.196148	−	0.980574i	$-0.562843\pi$
$337$	−14.2119	−	3.02084i	−0.774174	−	0.164556i	−0.578026	+	0.816019i	$0.696177\pi$
$338$	24.3094	+	5.16712i	1.32226	+	0.281054i
$339$	6.96385	+	9.46185i	0.378225	+	0.513897i
$340$	42.5401	−	14.1192i	2.30706	−	0.765720i
$341$	5.13715	+	15.8105i	0.278192	+	0.856188i
$342$	−44.8385	−	31.7409i	−2.42459	−	1.71635i
$343$	−20.1081			−1.08573
$344$	−46.2289	−	20.5824i	−2.49249	−	1.10973i
$345$	6.04945	−	6.88933i	0.325692	−	0.370909i
$346$	−38.0822	+	16.9553i	−2.04731	+	0.911522i
$347$	10.1994	−	4.54109i	0.547535	−	0.243778i	−0.114276	−	0.993449i	$-0.536455\pi$
$347$	10.1994	−	4.54109i	0.547535	−	0.243778i	0.661811	+	0.749671i	$0.269788\pi$
$348$	−25.0802	+	57.2775i	−1.34444	+	3.07040i
$349$	4.08628	+	7.07765i	0.218734	+	0.378858i	0.954421	−	0.298463i	$-0.0964740\pi$
$349$	4.08628	+	7.07765i	0.218734	+	0.378858i	−0.735687	+	0.677321i	$0.763141\pi$
$350$	−17.2757	+	19.6799i	−0.923424	+	1.05194i
$351$	6.77700	−	6.33257i	0.361730	−	0.338008i
$352$	3.49476	−	10.7558i	0.186272	−	0.573285i
$353$	2.35701	−	22.4255i	0.125451	−	1.19359i	−0.732832	−	0.680410i	$-0.761802\pi$
$353$	2.35701	−	22.4255i	0.125451	−	1.19359i	0.858283	−	0.513177i	$-0.171532\pi$
$354$	−34.2404	−	30.4505i	−1.81986	−	1.61843i
$355$	4.87647	+	22.2514i	0.258816	+	1.18098i
$356$	−0.158225	−	1.50541i	−0.00838592	−	0.0797867i
$357$	6.70914	+	14.8227i	0.355085	+	0.784499i
$358$	1.20878	+	0.538184i	0.0638861	+	0.0284439i
$359$	−7.75846	−	23.8781i	−0.409476	−	1.26024i	−0.917100	−	0.398658i	$-0.869476\pi$
$359$	−7.75846	−	23.8781i	−0.409476	−	1.26024i	0.507624	−	0.861579i	$-0.330524\pi$
$360$	−0.763175	−	40.9872i	−0.0402229	−	2.16022i
$361$	10.2866	−	31.6589i	0.541400	−	1.66626i
$362$	39.1085	−	43.4344i	2.05550	−	2.28286i
$363$	8.25351	+	2.62565i	0.433197	+	0.137811i
$364$	−10.9013	−	12.1071i	−0.571381	−	0.634583i
$365$	−3.79634	+	2.22384i	−0.198709	+	0.116401i
$366$	11.0221	+	3.50640i	0.576132	+	0.183283i
$367$	−5.89638	−	2.62524i	−0.307788	−	0.137036i	0.247030	−	0.969008i	$-0.420545\pi$
$367$	−5.89638	−	2.62524i	−0.307788	−	0.137036i	−0.554818	+	0.831972i	$0.687212\pi$
$368$	15.7411			0.820562
$369$	−1.32528	+	14.3012i	−0.0689914	+	0.744493i
$370$	5.69263	−	27.6372i	0.295946	−	1.43679i
$371$	−0.674324	+	6.41576i	−0.0350092	+	0.333090i
$372$	−10.4736	+	50.8106i	−0.543029	+	2.63441i
$373$	−16.1275	−	17.9114i	−0.835050	−	0.927417i	0.163198	−	0.986593i	$-0.447819\pi$
$373$	−16.1275	−	17.9114i	−0.835050	−	0.927417i	−0.998248	+	0.0591766i	$0.981152\pi$
$374$	14.0871	−	24.3996i	0.728428	−	1.26167i
$375$	18.8349	−	4.49968i	0.972629	−	0.232363i
$376$	30.9530	+	53.6121i	1.59628	+	2.76484i
$377$	4.51220	−	13.8871i	0.232390	−	0.715224i
$378$	27.0079	−	3.34408i	1.38914	−	0.172001i
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	0.578876	−	0.815415i	$-0.303491\pi$
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	−0.596623	+	0.802521i	$0.703491\pi$
$380$	67.7238	−	22.4777i	3.47416	−	1.15308i
$381$	−14.9065	+	8.72911i	−0.763685	+	0.447206i
$382$	1.27120	−	2.20179i	0.0650404	−	0.112653i
$383$	−2.38455	−	22.6874i	−0.121845	−	1.15927i	−0.869065	−	0.494698i	$-0.835279\pi$
$383$	−2.38455	−	22.6874i	−0.121845	−	1.15927i	0.747220	−	0.664576i	$-0.231388\pi$
$384$	−17.0271	+	15.5222i	−0.868911	+	0.792112i
$385$	0.0713958	+	11.3269i	0.00363867	+	0.577273i
$386$	−10.8402	+	33.3628i	−0.551753	+	1.69812i
$387$	−19.9163	+	14.8482i	−1.01240	+	0.754774i
$388$	−15.0234	−	46.2373i	−0.762698	−	2.34734i
$389$	−12.1318	+	2.57870i	−0.615108	+	0.130745i	−0.504921	−	0.863166i	$-0.668478\pi$
$389$	−12.1318	+	2.57870i	−0.615108	+	0.130745i	−0.110187	+	0.993911i	$0.535145\pi$
$390$	2.04683	+	17.3874i	0.103645	+	0.880443i
$391$	10.5174	+	2.23555i	0.531889	+	0.113056i
$392$	1.73931	+	16.5484i	0.0878482	+	0.835820i
$393$	13.8878	−	19.3645i	0.700545	−	0.976809i
$394$	−18.3245	−	8.15860i	−0.923175	−	0.411024i
$395$	−24.6496	+	22.4776i	−1.24026	+	1.13097i
$396$	−21.9940	−	23.8300i	−1.10524	−	1.19750i
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	0.529623	−	0.848233i	$-0.322333\pi$
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	−0.643055	+	0.765820i	$0.722333\pi$
$398$	−36.2052	+	7.69565i	−1.81480	+	0.385748i
$399$	10.6809	+	23.5977i	0.534716	+	1.18136i
$400$	27.1420	+	19.2018i	1.35710	+	0.960089i
$401$	−18.1027	+	31.3549i	−0.904008	+	1.56579i	−0.0817642	+	0.996652i	$0.526055\pi$
$401$	−18.1027	+	31.3549i	−0.904008	+	1.56579i	−0.822244	+	0.569136i	$0.807278\pi$
$402$	−2.86834	+	6.55065i	−0.143060	+	0.326717i
$403$	1.26636	−	12.0486i	0.0630820	−	0.600185i
$404$	45.6186	+	33.1438i	2.26961	+	1.64897i
$405$	−17.7313	−	9.51848i	−0.881075	−	0.472977i
$406$	34.6605	−	25.1824i	1.72017	−	1.24978i
$407$	−6.10273	−	10.5702i	−0.302501	−	0.523947i
$408$	41.4871	−	24.2944i	2.05392	−	1.20275i
$409$	21.7118	+	4.61499i	1.07358	+	0.228196i	0.710597	−	0.703599i	$-0.248425\pi$
$409$	21.7118	+	4.61499i	1.07358	+	0.228196i	0.362983	+	0.931796i	$0.381758\pi$
$410$	−20.2606	−	18.0128i	−1.00060	−	0.889588i
$411$	14.6822	−	1.63462i	0.724219	−	0.0806299i
$412$	−27.1112	+	30.1100i	−1.33567	+	1.48341i
$413$	6.67630	+	20.5475i	0.328519	+	1.01108i
$414$	8.79985	−	15.6847i	0.432489	−	0.770862i
$415$	3.74506	+	8.27084i	0.183838	+	0.405999i
$416$	−5.51480	+	6.12480i	−0.270385	+	0.300293i
$417$	0.0995004	+	16.1596i	0.00487256	+	0.791338i
$418$	22.4267	−	38.8441i	1.09692	−	1.89993i
$419$	3.34167	+	31.7939i	0.163251	+	1.55323i	0.702868	+	0.711320i	$0.251903\pi$
$419$	3.34167	+	31.7939i	0.163251	+	1.55323i	−0.539617	+	0.841911i	$0.681431\pi$
$420$	−17.2914	+	30.8305i	−0.843734	+	1.50437i
$421$	0.145994	−	1.38904i	0.00711533	−	0.0676978i	−0.990388	−	0.138317i	$-0.955831\pi$
$421$	0.145994	−	1.38904i	0.00711533	−	0.0676978i	0.997503	+	0.0706190i	$0.0224974\pi$
$422$	−27.2891	−	19.8267i	−1.32841	−	0.965150i
$423$	30.3881	−	0.374235i	1.47752	−	0.0181960i
$424$	19.0622			0.925745
$425$	15.4079	+	16.6844i	0.747394	+	0.809311i
$426$	18.4257	+	40.7084i	0.892730	+	1.97233i
$427$	−3.64913	−	4.05277i	−0.176594	−	0.196127i
$428$	3.95372	−	1.76031i	0.191110	−	0.0850877i
$429$	5.65883	+	5.03249i	0.273211	+	0.242971i
$430$	−0.295555	−	46.8897i	−0.0142529	−	2.26122i
$431$	−0.506575	+	0.368048i	−0.0244009	+	0.0177283i	−0.599919	−	0.800061i	$-0.704800\pi$
$431$	−0.506575	+	0.368048i	−0.0244009	+	0.0177283i	0.575518	+	0.817789i	$0.304800\pi$
$432$	−7.80676	−	33.6584i	−0.375603	−	1.61939i
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	−0.693724	−	0.720241i	$-0.744031\pi$
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	0.470617	+	0.882338i	$0.344031\pi$
$434$	23.7851	−	26.4160i	1.14172	−	1.26801i
$435$	−31.6794	+	0.394759i	−1.51891	+	0.0189272i
$436$	−26.2201	−	29.1204i	−1.25572	−	1.39461i
$437$	16.7437	+	3.55899i	0.800960	+	0.170249i
$438$	−6.37805	+	5.81433i	−0.304755	+	0.277819i
$439$	22.6653	−	4.81766i	1.08176	−	0.229934i	0.367644	−	0.929966i	$-0.380164\pi$
$439$	22.6653	−	4.81766i	1.08176	−	0.229934i	0.714111	+	0.700032i	$0.246831\pi$
$440$	33.2643	−	3.70835i	1.58581	−	0.176789i
$441$	7.50269	+	3.23031i	0.357271	+	0.153824i
$442$	−16.6109	+	12.0685i	−0.790100	+	0.574041i
$443$	10.9667	+	18.9950i	0.521046	+	0.902477i	0.999700	+	0.0244742i	$0.00779117\pi$
$443$	10.9667	+	18.9950i	0.521046	+	0.902477i	−0.478655	+	0.878003i	$0.658875\pi$
$444$	−0.234526	−	38.0887i	−0.0111301	−	1.80761i
$445$	0.661786	−	0.387664i	0.0313717	−	0.0183771i
$446$	8.44104	−	3.75819i	0.399695	−	0.177956i
$447$	11.4188	−	3.78809i	0.540092	−	0.179171i
$448$	3.24959	−	0.690721i	0.153529	−	0.0326335i
$449$	−12.6712			−0.597990			−0.298995	−	0.954255i	$-0.596651\pi$
$449$	−12.6712			−0.597990			−0.298995	+	0.954255i	$0.596651\pi$
$450$	34.3064	−	16.3103i	1.61722	−	0.768876i
$451$	−11.7265			−0.552178
$452$	−29.2796	+	6.22357i	−1.37720	+	0.292732i
$453$	0.275688	−	1.33745i	0.0129529	−	0.0628388i
$454$	36.3555	−	16.1865i	1.70625	−	0.759671i
$455$	3.30991	−	7.56209i	0.155171	−	0.354516i
$456$	66.0473	−	38.6766i	3.09295	−	1.81120i
$457$	0.0638731	+	0.110631i	0.00298786	+	0.00517512i	0.867515	−	0.497410i	$-0.165716\pi$
$457$	0.0638731	+	0.110631i	0.00298786	+	0.00517512i	−0.864528	+	0.502585i	$0.832382\pi$
$458$	−12.3084	+	8.94261i	−0.575136	+	0.417861i
$459$	−0.435940	−	23.5975i	−0.0203479	−	1.10144i
$460$	9.63581	+	21.2804i	0.449272	+	0.992203i
$461$	7.08732	−	1.50646i	0.330090	−	0.0701627i	−0.0398858	−	0.999204i	$-0.512699\pi$
$461$	7.08732	−	1.50646i	0.330090	−	0.0701627i	0.369975	+	0.929042i	$0.379366\pi$
$462$	4.75339	+	21.7049i	0.221148	+	1.00981i
$463$	−22.2769	−	4.73511i	−1.03530	−	0.220059i	−0.341238	−	0.939977i	$-0.610846\pi$
$463$	−22.2769	−	4.73511i	−1.03530	−	0.220059i	−0.694059	+	0.719918i	$0.744179\pi$
$464$	−36.3970	−	40.4230i	−1.68969	−	1.87659i
$465$	−25.6417	+	5.78515i	−1.18910	+	0.268280i
$466$	1.01443	−	1.12664i	0.0469925	−	0.0521905i
$467$	−7.87672	+	5.72277i	−0.364491	+	0.264818i	−0.754923	−	0.655814i	$-0.772326\pi$
$467$	−7.87672	+	5.72277i	−0.364491	+	0.264818i	0.390432	+	0.920632i	$0.372326\pi$
$468$	7.57907	+	22.3842i	0.350343	+	1.03471i
$469$	2.72780	−	1.98186i	0.125958	−	0.0915138i
$470$	−33.4242	+	46.6196i	−1.54174	+	2.15040i
$471$	6.39144	−	2.12030i	0.294502	−	0.0976983i
$472$	58.3208	−	25.9661i	2.68443	−	1.19519i
$473$	−13.5717	−	15.0729i	−0.624028	−	0.693053i
$474$	−38.1367	+	53.1761i	−1.75168	+	2.44246i
$475$	24.5294	+	26.5615i	1.12548	+	1.21872i
$476$	−41.4556			−1.90012
$477$	4.57879	−	8.16118i	0.209649	−	0.373675i
$478$	−2.40741	−	1.74909i	−0.110112	−	0.0800013i
$479$	1.17638	−	11.1925i	0.0537503	−	0.511400i	−0.934213	−	0.356715i	$-0.883897\pi$
$479$	1.17638	−	11.1925i	0.0537503	−	0.511400i	0.987964	−	0.154686i	$-0.0494365\pi$
$480$	16.4256	+	7.06926i	0.749724	+	0.322666i
$481$	0.929762	+	8.84609i	0.0423935	+	0.403347i
$482$	−22.7553	+	39.4133i	−1.03648	+	1.79523i
$483$	−7.31744	+	4.28502i	−0.332955	+	0.194975i
$484$	−14.7662	+	16.3996i	−0.671193	+	0.745436i
$485$	18.2019	−	16.5980i	0.826506	−	0.753676i
$486$	−37.9021	−	11.0374i	−1.71927	−	0.500669i
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	0.880047	−	0.474886i	$-0.157511\pi$
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	−0.991104	+	0.133088i	$0.957511\pi$
$488$	−10.7827	+	11.9754i	−0.488112	+	0.542103i
$489$	5.83115	−	13.3171i	0.263694	−	0.602218i
$490$	−13.3040	+	7.79330i	−0.601014	+	0.352065i
$491$	−14.3906	−	3.05881i	−0.649438	−	0.138042i	−0.128598	−	0.991697i	$-0.541048\pi$
$491$	−14.3906	−	3.05881i	−0.649438	−	0.138042i	−0.520840	+	0.853654i	$0.674381\pi$
$492$	−31.8039	−	18.1018i	−1.43383	−	0.816093i
$493$	−18.5778	−	32.1777i	−0.836702	−	1.44921i
$494$	−26.4445	+	19.2131i	−1.18980	+	0.864437i
$495$	6.40249	−	15.1323i	0.287771	−	0.680146i
$496$	−36.5114	−	26.5271i	−1.63941	−	1.19110i
$497$	2.20227	−	20.9532i	0.0987853	−	0.939879i
$498$	10.5569	+	14.3437i	0.473064	+	0.642757i
$499$	−11.7212	+	20.3017i	−0.524714	+	0.908831i	0.474872	+	0.880055i	$0.342494\pi$
$499$	−11.7212	+	20.3017i	−0.524714	+	0.908831i	−0.999586	+	0.0287762i	$0.990839\pi$
$500$	−9.34406	+	48.4475i	−0.417879	+	2.16664i
$501$	−10.9097	+	15.2120i	−0.487410	+	0.679623i
$502$	−0.775753	+	0.164891i	−0.0346235	+	0.00735946i
$503$	−11.6643	−	8.47463i	−0.520087	−	0.377865i	0.296550	−	0.955017i	$-0.404164\pi$
$503$	−11.6643	−	8.47463i	−0.520087	−	0.377865i	−0.816637	+	0.577152i	$0.804164\pi$
$504$	−11.2716	+	36.2012i	−0.502076	+	1.61253i
$505$	−5.76393	+	27.9833i	−0.256491	+	1.24524i
$506$	13.4143	+	5.97245i	0.596340	+	0.265508i
$507$	7.00914	+	15.4855i	0.311287	+	0.687734i
$508$	−4.60069	−	43.7726i	−0.204122	−	1.94209i
$509$	−0.377856	−	0.0803159i	−0.0167482	−	0.00355994i	0.199530	−	0.979892i	$-0.436058\pi$
$509$	−0.377856	−	0.0803159i	−0.0167482	−	0.00355994i	−0.216278	+	0.976332i	$0.569392\pi$
$510$	36.3645	+	25.7343i	1.61025	+	1.13953i
$511$	3.98037	−	0.846053i	0.176081	−	0.0374272i
$512$	−15.6267	−	48.0942i	−0.690611	−	2.12548i
$513$	−0.694016	−	37.5672i	−0.0306416	−	1.65863i
$514$	−2.32468	+	7.15462i	−0.102537	+	0.315577i
$515$	−19.5641	−	6.22072i	−0.862099	−	0.274118i
$516$	−13.5409	−	61.8303i	−0.596103	−	2.72193i
$517$	2.59363	+	24.6767i	0.114068	+	1.08528i
$518$	−13.0490	+	22.6016i	−0.573342	+	0.993057i
$519$	−24.7788	−	14.1034i	−1.08767	−	0.619068i
$520$	−23.2450	−	7.39111i	−1.01936	−	0.324121i
$521$	35.3256	+	25.6656i	1.54764	+	1.12443i	0.945304	+	0.326190i	$0.105765\pi$
$521$	35.3256	+	25.6656i	1.54764	+	1.12443i	0.602340	+	0.798240i	$0.294235\pi$
$522$	−60.6254	+	13.6687i	−2.65350	+	0.598264i
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	0.728052	+	0.685522i	$0.240426\pi$
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	−0.991946	+	0.126660i	$0.959574\pi$
$524$	30.3581	+	52.5818i	1.32620	+	2.29705i
$525$	−17.8444	−	1.53762i	−0.778793	−	0.0671074i
$526$	10.2907	−	17.8239i	0.448694	−	0.777161i
$527$	−20.6277	−	22.9094i	−0.898559	−	0.997950i
$528$	26.7754	−	8.88251i	1.16525	−	0.386561i
$529$	1.81839	−	17.3008i	0.0790603	−	0.752208i
$530$	7.28596	+	16.0908i	0.316482	+	0.698940i
$531$	2.89185	−	31.2062i	0.125496	−	1.35423i
$532$	−65.9973			−2.86135
$533$	7.80693	+	3.47587i	0.338156	+	0.150557i
$534$	1.11184	−	1.01357i	0.0481138	−	0.0438613i
$535$	1.63884	+	1.45702i	0.0708531	+	0.0629923i
$536$	−6.66662	−	7.40403i	−0.287954	−	0.319805i
$537$	0.193605	+	0.884037i	0.00835465	+	0.0381490i
$538$	−39.0067	+	43.3213i	−1.68170	+	1.86771i
$539$	−2.06094	+	6.34291i	−0.0887708	+	0.273208i
$540$	40.7238	−	31.1577i	1.75247	−	1.34081i
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	−0.995803	−	0.0915249i	$-0.970826\pi$
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	0.751824	−	0.659363i	$-0.229174\pi$
$542$	52.3450	+	23.3055i	2.24841	+	1.00106i
$543$	39.7807	+	3.93363i	1.70715	+	0.168808i
$544$	2.19215	+	20.8569i	0.0939878	+	0.894234i
$545$	7.96111	−	18.1886i	0.341017	−	0.779115i
$546$	3.26903	−	15.8591i	0.139901	−	0.678707i
$547$	−4.02229	+	38.2695i	−0.171981	+	1.63629i	0.479444	+	0.877572i	$0.340838\pi$
$547$	−4.02229	+	38.2695i	−0.171981	+	1.63629i	−0.651425	+	0.758713i	$0.725828\pi$
$548$	−11.6315	+	35.7980i	−0.496872	+	1.52922i
$549$	2.53704	+	7.49297i	0.108278	+	0.319792i
$550$	15.8446	+	26.6616i	0.675614	+	1.13686i
$551$	−29.5758	−	51.2268i	−1.25997	−	2.18234i
$552$	14.8525	+	20.1802i	0.632164	+	0.858927i
$553$	28.1864	−	12.5494i	1.19861	−	0.533655i
$554$	−23.9573	+	10.6665i	−1.01785	+	0.453175i
$555$	17.5316	−	8.06881i	0.744176	−	0.342502i
$556$	−37.6145	−	16.7471i	−1.59521	−	0.710233i
$557$	34.0992			1.44483			0.722414	−	0.691461i	$-0.243032\pi$
$557$	34.0992			1.44483			0.722414	+	0.691461i	$0.243032\pi$
$558$	−46.8433	+	21.5510i	−1.98304	+	0.912329i
$559$	4.56761	+	14.0577i	0.193189	+	0.594576i
$560$	−18.2311	−	24.7632i	−0.770405	−	1.04644i
$561$	19.1515	−	2.13221i	0.808577	−	0.0900218i
$562$	63.0169	+	13.3946i	2.65821	+	0.565019i
$563$	24.2833	+	5.16157i	1.02342	+	0.217534i	0.688901	−	0.724855i	$-0.258093\pi$
$563$	24.2833	+	5.16157i	1.02342	+	0.217534i	0.334518	+	0.942390i	$0.391427\pi$
$564$	−31.0585	+	70.9307i	−1.30780	+	2.98672i
$565$	−8.99208	−	12.2139i	−0.378300	−	0.513842i
$566$	−12.9674	−	39.9094i	−0.545058	−	1.67752i
$567$	12.7915	+	13.5213i	0.537192	+	0.567843i
$568$	−62.2553			−2.61217
$569$	−25.8779	−	11.5216i	−1.08486	−	0.483011i	−0.215153	−	0.976580i	$-0.569025\pi$
$569$	−25.8779	−	11.5216i	−1.08486	−	0.483011i	−0.869706	+	0.493570i	$0.835692\pi$
$570$	57.8923	+	40.9689i	2.42484	+	1.71600i
$571$	29.1809	−	12.9922i	1.22118	−	0.543706i	0.308052	−	0.951370i	$-0.400323\pi$
$571$	29.1809	−	12.9922i	1.22118	−	0.543706i	0.913132	+	0.407663i	$0.133656\pi$
$572$	−17.6269	+	7.84802i	−0.737020	+	0.328142i
$573$	1.72821	−	0.192407i	0.0721968	−	0.00803794i
$574$	12.5369	+	21.7146i	0.523282	+	0.906351i
$575$	−7.80852	+	8.89522i	−0.325638	+	0.370956i
$576$	−4.72579	−	0.943829i	−0.196908	−	0.0393262i
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	−0.999650	−	0.0264408i	$-0.991583\pi$
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	0.824276	+	0.566189i	$0.191583\pi$
$578$	−0.961131	+	9.14455i	−0.0399778	+	0.380363i
$579$	−22.7725	+	7.55456i	−0.946391	+	0.313957i
$580$	32.3676	−	73.9497i	1.34399	−	3.07059i
$581$	−0.877759	−	8.35132i	−0.0364156	−	0.346471i
$582$	28.1610	−	39.2665i	1.16731	−	1.62765i
$583$	6.97983	+	3.10762i	0.289075	+	0.128705i
$584$	−3.71570	−	11.4358i	−0.153757	−	0.473215i
$585$	−8.74788	+	8.17659i	−0.361680	+	0.338061i
$586$	9.49120	−	29.2109i	0.392078	−	1.20669i
$587$	−26.5805	+	29.5207i	−1.09710	+	1.21845i	−0.122978	+	0.992409i	$0.539244\pi$
$587$	−26.5805	+	29.5207i	−1.09710	+	1.21845i	−0.974118	+	0.226039i	$0.927422\pi$
$588$	−15.3809	+	14.0215i	−0.634299	+	0.578237i
$589$	−32.8393	−	36.4718i	−1.35312	−	1.50279i
$590$	44.2099	+	39.3050i	1.82009	+	1.61816i
$591$	−2.93495	−	13.4015i	−0.120728	−	0.551266i
$592$	30.2702	+	13.4772i	1.24410	+	0.553908i
$593$	16.9892			0.697663			0.348832	−	0.937185i	$-0.386579\pi$
$593$	16.9892			0.697663			0.348832	+	0.937185i	$0.386579\pi$
$594$	6.11776	−	31.6452i	0.251015	−	1.29842i
$595$	−8.66425	−	19.1347i	−0.355200	−	0.784447i
$596$	−3.20416	+	30.4856i	−0.131248	+	1.24874i
$597$	−18.9173	−	16.8234i	−0.774232	−	0.688537i
$598$	−7.16033	−	7.95235i	−0.292808	−	0.325196i
$599$	−7.81800	+	13.5412i	−0.319435	+	0.553277i	−0.980370	−	0.197166i	$-0.936826\pi$
$599$	−7.81800	+	13.5412i	−0.319435	+	0.553277i	0.660935	+	0.750443i	$0.270160\pi$
$600$	0.992972	+	52.9141i	0.0405379	+	2.16021i
$601$	−0.702116	−	1.21610i	−0.0286399	−	0.0496058i	0.851350	−	0.524598i	$-0.175784\pi$
$601$	−0.702116	−	1.21610i	−0.0286399	−	0.0496058i	−0.879990	+	0.474992i	$0.842451\pi$
$602$	−13.4017	+	41.2462i	−0.546213	+	1.68107i
$603$	−4.77124	+	1.07573i	−0.194300	+	0.0438073i
$604$	2.81486	+	2.04512i	0.114535	+	0.0832147i
$605$	−10.6557	−	3.38815i	−0.433217	−	0.137748i
$606$	0.345080	+	56.0434i	0.0140179	+	2.27661i
$607$	−3.79337	+	6.57031i	−0.153968	+	0.266681i	−0.932683	−	0.360698i	$-0.882539\pi$
$607$	−3.79337	+	6.57031i	−0.153968	+	0.266681i	0.778715	+	0.627378i	$0.215872\pi$
$608$	3.48990	+	33.2042i	0.141534	+	1.34661i
$609$	27.9235	+	8.88317i	1.13152	+	0.359964i
$610$	−14.2301	−	4.52467i	−0.576159	−	0.183199i
$611$	5.58777	−	17.1974i	0.226057	−	0.695732i
$612$	55.2331	+	23.7808i	2.23267	+	0.961281i
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	0.939037	+	0.343816i	$0.111720\pi$
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	−0.557607	+	0.830105i	$0.688280\pi$
$614$	29.1564	−	6.19737i	1.17665	−	0.250106i
$615$	1.70824	−	18.4631i	0.0688829	−	0.744503i
$616$	−30.2801	−	6.43623i	−1.22002	−	0.259323i
$617$	−0.105946	−	1.00801i	−0.00426524	−	0.0405811i	0.992182	−	0.124797i	$-0.0398280\pi$
$617$	−0.105946	−	1.00801i	−0.00426524	−	0.0405811i	−0.996448	+	0.0842162i	$0.973161\pi$
$618$	−40.0749	−	3.96272i	−1.61205	−	0.159404i
$619$	42.0648	+	18.7285i	1.69073	+	0.752761i	0.999548	+	0.0300796i	$0.00957609\pi$
$619$	42.0648	+	18.7285i	1.69073	+	0.752761i	0.691181	+	0.722681i	$0.257091\pi$
$620$	13.5117	−	65.5981i	0.542644	−	2.63448i
$621$	12.2074	−	1.51151i	0.489867	−	0.0606546i
$622$	−20.2673	−	14.7250i	−0.812644	−	0.590420i
$623$	−0.693866	+	0.147486i	−0.0277991	+	0.00590889i
$624$	−20.4587	−	2.02302i	−0.819004	−	0.0809855i
$625$	−24.3149	+	5.81261i	−0.972595	+	0.232505i
$626$	43.5789	−	75.4809i	1.74176	−	3.01682i
$627$	30.4891	−	3.39447i	1.21762	−	0.135562i
$628$	−1.79346	+	17.0636i	−0.0715668	+	0.680913i
$629$	18.3110	+	13.3037i	0.730108	+	0.530455i
$630$	−34.8664	+	4.32227i	−1.38911	+	0.172203i
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	−0.705120	−	0.709088i	$-0.749107\pi$
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	0.456488	+	0.889729i	$0.349107\pi$
$632$	−45.5848	−	78.9552i	−1.81327	−	3.14067i
$633$	−0.142051	−	23.0701i	−0.00564602	−	0.916954i
$634$	−55.0836	−	11.7084i	−2.18765	−	0.464999i
$635$	19.2426	−	11.2720i	0.763620	−	0.447317i
$636$	14.1332	+	19.2029i	0.560418	+	0.761445i
$637$	3.25219	−	3.61192i	0.128857	−	0.143110i
$638$	−15.6798	−	48.2575i	−0.620770	−	1.91053i
$639$	−14.9539	+	26.6535i	−0.591565	+	1.05440i
$640$	21.9790	−	20.0422i	0.868795	−	0.792239i
$641$	18.6755	−	20.7412i	0.737637	−	0.819229i	−0.251246	−	0.967923i	$-0.580840\pi$
$641$	18.6755	−	20.7412i	0.737637	−	0.819229i	0.988883	+	0.148694i	$0.0475070\pi$
$642$	3.73841	+	2.12779i	0.147543	+	0.0839772i
$643$	−3.87285	+	6.70797i	−0.152730	+	0.264537i	−0.932230	−	0.361866i	$-0.882140\pi$
$643$	−3.87285	+	6.70797i	−0.152730	+	0.264537i	0.779500	+	0.626402i	$0.215473\pi$
$644$	−2.25842	−	21.4874i	−0.0889943	−	0.846724i
$645$	25.7090	−	19.1726i	1.01229	−	0.754922i
$646$	−8.69421	+	82.7199i	−0.342069	+	3.25457i
$647$	−27.8778	−	20.2544i	−1.09599	−	0.796283i	−0.115588	−	0.993297i	$-0.536875\pi$
$647$	−27.8778	−	20.2544i	−1.09599	−	0.796283i	−0.980401	+	0.197015i	$0.936875\pi$
$648$	35.7842	−	41.7666i	1.40574	−	1.64075i
$649$	25.5879			1.00441
$650$	−2.64572	−	22.4466i	−0.103774	−	0.880428i
$651$	24.1939	+	2.39237i	0.948236	+	0.0937643i
$652$	24.7854	+	27.5269i	0.970670	+	1.07804i
$653$	−10.9336	+	4.86796i	−0.427866	+	0.190498i	−0.609360	−	0.792894i	$-0.708573\pi$
$653$	−10.9336	+	4.86796i	−0.427866	+	0.190498i	0.181494	+	0.983392i	$0.441907\pi$
$654$	7.86279	−	38.1449i	0.307459	−	1.49158i
$655$	−17.9254	+	25.0021i	−0.700403	+	0.976911i
$656$	25.7547	−	18.7119i	1.00555	−	0.730576i
$657$	−5.78855	−	1.15608i	−0.225833	−	0.0451030i
$658$	42.9225	−	31.1850i	1.67329	−	1.21572i
$659$	6.24538	−	6.93619i	0.243285	−	0.270196i	−0.609119	−	0.793079i	$-0.708477\pi$
$659$	6.24538	−	6.93619i	0.243285	−	0.270196i	0.852404	+	0.522883i	$0.175144\pi$
$660$	28.3986	+	30.7603i	1.10542	+	1.19734i
$661$	3.22292	+	3.57941i	0.125357	+	0.139223i	0.802556	−	0.596577i	$-0.203473\pi$
$661$	3.22292	+	3.57941i	0.125357	+	0.139223i	−0.677199	+	0.735800i	$0.736806\pi$
$662$	32.4183	+	6.89073i	1.25997	+	0.267816i
$663$	−13.3822	−	4.25722i	−0.519721	−	0.165337i
$664$	−24.2709	+	5.15893i	−0.941892	+	0.200205i
$665$	−13.7935	−	30.4624i	−0.534888	−	1.18128i
$666$	30.3511	−	22.6276i	1.17608	−	0.876801i
$667$	15.6664	−	11.3823i	0.606605	−	0.440724i
$668$	−23.8482	−	41.3063i	−0.922714	−	1.59819i
$669$	5.49230	+	3.12605i	0.212345	+	0.120860i
$670$	3.70177	−	8.45739i	0.143012	−	0.326737i
$671$	−5.90050	+	2.62707i	−0.227786	+	0.101417i
$672$	−12.3589	−	10.9910i	−0.476757	−	0.423987i
$673$	17.4410	−	3.70720i	0.672301	−	0.142902i	0.140902	−	0.990024i	$-0.455000\pi$
$673$	17.4410	−	3.70720i	0.672301	−	0.142902i	0.531399	+	0.847122i	$0.321666\pi$
$674$	36.7946			1.41728
$675$	22.8928	+	12.2850i	0.881144	+	0.472848i
$676$	−43.3093			−1.66574
$677$	−14.9861	+	3.18540i	−0.575963	+	0.122425i	−0.486678	−	0.873581i	$-0.661792\pi$
$677$	−14.9861	+	3.18540i	−0.575963	+	0.122425i	−0.0892851	+	0.996006i	$0.528458\pi$
$678$	−22.2319	−	19.7711i	−0.853809	−	0.759306i
$679$	−20.8135	+	9.26678i	−0.798750	+	0.355627i
$680$	−53.5550	+	31.3717i	−2.05374	+	1.20305i
$681$	23.6553	+	13.4639i	0.906474	+	0.515937i
$682$	−21.0497	−	36.4591i	−0.806034	−	1.39609i
$683$	−22.9889	+	16.7024i	−0.879645	+	0.639100i	−0.933158	−	0.359468i	$-0.882958\pi$
$683$	−22.9889	+	16.7024i	−0.879645	+	0.639100i	0.0535124	+	0.998567i	$0.482958\pi$
$684$	87.9310	+	37.8590i	3.36213	+	1.44757i
$685$	−18.9543	+	2.11305i	−0.724207	+	0.0807355i
$686$	49.8093	−	10.5873i	1.90173	−	0.404225i
$687$	−9.91601	−	3.15454i	−0.378319	−	0.120353i
$688$	53.8592	+	11.4481i	2.05336	+	0.436455i
$689$	−3.72571	−	4.13782i	−0.141938	−	0.157638i
$690$	−11.3576	+	20.2506i	−0.432377	+	0.770925i
$691$	14.7072	−	16.3340i	0.559488	−	0.621374i	−0.395340	−	0.918535i	$-0.629373\pi$
$691$	14.7072	−	16.3340i	0.559488	−	0.621374i	0.954827	+	0.297161i	$0.0960397\pi$
$692$	58.7708	−	42.6995i	2.23413	−	1.62319i
$693$	−10.0289	+	11.4179i	−0.380967	+	0.433730i
$694$	−22.8739	+	16.6188i	−0.868280	+	0.630842i
$695$	−0.131497	−	20.8619i	−0.00498796	−	0.791337i
$696$	17.4802	−	84.8022i	0.662587	−	3.21442i
$697$	19.8654	−	8.84466i	0.752457	−	0.335016i
$698$	−13.8486	−	15.3804i	−0.524176	−	0.582156i
$699$	1.03187	+	0.102034i	0.0390287	+	0.00385928i
$700$	22.3173	−	39.8052i	0.843515	−	1.50450i
$701$	6.44692			0.243497			0.121748	−	0.992561i	$-0.461150\pi$
$701$	6.44692			0.243497			0.121748	+	0.992561i	$0.461150\pi$
$702$	−13.4529	+	19.2545i	−0.507749	+	0.726714i
$703$	29.1511	+	21.1795i	1.09946	+	0.798801i
$704$	0.411282	−	3.91309i	0.0155008	−	0.147480i
$705$	−39.2308	+	0.488857i	−1.47752	+	0.0184114i
$706$	5.96893	+	56.7906i	0.224644	+	2.13734i
$707$	13.2125	−	22.8847i	0.496906	−	0.860666i
$708$	69.3981	+	39.4993i	2.60814	+	1.48447i
$709$	−3.28572	+	3.64916i	−0.123398	+	0.137047i	−0.801678	−	0.597756i	$-0.796059\pi$
$709$	−3.28572	+	3.64916i	−0.123398	+	0.137047i	0.678280	+	0.734804i	$0.262726\pi$
$710$	−23.7952	−	52.5509i	−0.893017	−	1.97220i
$711$	−44.7529	+	0.551141i	−1.67836	+	0.0206694i
$712$	0.647729	+	1.99351i	0.0242747	+	0.0747098i
$713$	10.7507	−	11.9399i	0.402619	−	0.447153i
$714$	−24.4235	−	33.1844i	−0.914026	−	1.24190i
$715$	−7.30646	−	6.49585i	−0.273246	−	0.242931i
$716$	−2.25545	−	0.479412i	−0.0842903	−	0.0179165i
$717$	−0.0125315	−	2.03521i	−0.000467999	−	0.0760064i
$718$	31.7906	+	55.0629i	1.18641	+	2.05493i
$719$	38.7957	−	28.1867i	1.44683	−	1.05119i	0.460277	−	0.887775i	$-0.347750\pi$
$719$	38.7957	−	28.1867i	1.44683	−	1.05119i	0.986558	−	0.163412i	$-0.0522498\pi$
$720$	10.0848	+	43.4513i	0.375839	+	1.61933i
$721$	15.3612	+	11.1605i	0.572080	+	0.415640i
$722$	−8.81169	+	83.8376i	−0.327937	+	3.12011i
$723$	−30.9359	+	3.44421i	−1.15052	+	0.128091i
$724$	−50.9263	+	88.2070i	−1.89266	+	3.27819i
$725$	40.8979	−	0.515595i	1.51891	−	0.0191487i
$726$	−21.8270	−	2.15832i	−0.810077	−	0.0801028i
$727$	−10.1485	+	2.15714i	−0.376389	+	0.0800039i	−0.392222	−	0.919871i	$-0.628293\pi$
$727$	−10.1485	+	2.15714i	−0.376389	+	0.0800039i	0.0158329	+	0.999875i	$0.494960\pi$
$728$	18.2513	+	13.2603i	0.676437	+	0.491461i
$729$	−9.28621	−	25.3528i	−0.343934	−	0.938994i
$730$	8.23293	−	7.50747i	0.304715	−	0.277864i
$731$	34.3601	+	15.2981i	1.27086	+	0.565821i
$732$	−20.0584	−	1.98343i	−0.741379	−	0.0733097i
$733$	1.00624	+	9.57373i	0.0371663	+	0.353614i	0.997262	+	0.0739435i	$0.0235584\pi$
$733$	1.00624	+	9.57373i	0.0371663	+	0.353614i	−0.960096	+	0.279670i	$0.909775\pi$
$734$	15.9880	+	3.39836i	0.590129	+	0.125436i
$735$	−9.68654	−	4.16889i	−0.357294	−	0.153772i
$736$	−10.6912	+	2.27249i	−0.394084	+	0.0837651i
$737$	−1.23401	−	3.79789i	−0.0454553	−	0.139897i
$738$	−4.24705	−	36.1231i	−0.156336	−	1.32971i
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	0.519056	+	0.854740i	$0.326284\pi$
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	−0.922329	+	0.386406i	$0.873716\pi$
$740$	0.309942	+	49.1722i	0.0113937	+	1.80761i
$741$	−21.3044	−	6.77748i	−0.782637	−	0.248977i
$742$	−1.70767	−	16.2474i	−0.0626905	−	0.596460i
$743$	1.41943	−	2.45852i	0.0520738	−	0.0901944i	−0.838814	−	0.544419i	$-0.816750\pi$
$743$	1.41943	−	2.45852i	0.0520738	−	0.0901944i	0.890887	+	0.454224i	$0.150084\pi$
$744$	−0.442330	−	71.8376i	−0.0162166	−	2.63369i
$745$	−14.7409	+	4.89255i	−0.540066	+	0.179249i
$746$	49.3797	+	35.8765i	1.80792	+	1.31353i
$747$	−3.62121	+	11.6303i	−0.132493	+	0.425532i
$748$	−15.1721	+	46.6951i	−0.554749	+	1.70734i
$749$	−1.01409	−	1.75645i	−0.0370539	−	0.0641793i
$750$	−44.2863	+	21.0630i	−1.61711	+	0.769112i
$751$	−19.4018	+	33.6049i	−0.707983	+	1.22626i	0.257622	+	0.966246i	$0.417061\pi$
$751$	−19.4018	+	33.6049i	−0.707983	+	1.22626i	−0.965604	+	0.260016i	$0.916272\pi$
$752$	−45.0729	−	50.0585i	−1.64364	−	1.82545i
$753$	−0.405332	−	0.360468i	−0.0147711	−	0.0131362i
$754$	−3.86524	+	36.7753i	−0.140764	+	1.33928i
$755$	−0.355659	+	1.72669i	−0.0129438	+	0.0628407i
$756$	−44.8254	+	15.4857i	−1.63028	+	0.563210i
$757$	32.7437			1.19009			0.595046	−	0.803692i	$-0.297134\pi$
$757$	32.7437			1.19009			0.595046	+	0.803692i	$0.297134\pi$
$758$	0.987987	+	0.439880i	0.0358853	+	0.0159772i
$759$	2.14851	+	9.81052i	0.0779859	+	0.356099i
$760$	−85.2594	+	49.9437i	−3.09269	+	1.81165i
$761$	−0.299221	−	0.332319i	−0.0108468	−	0.0120465i	0.737697	−	0.675132i	$-0.235913\pi$
$761$	−0.299221	−	0.332319i	−0.0108468	−	0.0120465i	−0.748544	+	0.663085i	$0.769247\pi$
$762$	32.3286	−	29.4713i	1.17114	−	1.06763i
$763$	−12.2875	+	13.6467i	−0.444838	+	0.494043i
$764$	−1.36911	+	4.21370i	−0.0495328	+	0.152446i
$765$	0.567239	+	30.4642i	0.0205086	+	1.10144i
$766$	17.8521	+	54.9431i	0.645022	+	1.98517i
$767$	−17.0352	−	7.58457i	−0.615106	−	0.273863i
$768$	30.7617	−	42.8928i	1.11002	−	1.54776i
$769$	0.783090	+	7.45061i	0.0282390	+	0.268676i	0.999527	+	0.0307674i	$0.00979512\pi$
$769$	0.783090	+	7.45061i	0.0282390	+	0.268676i	−0.971288	+	0.237908i	$0.923538\pi$
$770$	−6.14069	−	28.0201i	−0.221295	−	1.00977i
$771$	−4.88353	+	1.62007i	−0.175876	+	0.0583453i
$772$	6.39003	−	60.7971i	0.229982	−	2.18814i
$773$	−5.48853	+	16.8920i	−0.197409	+	0.607562i	0.802531	+	0.596610i	$0.203486\pi$
$773$	−5.48853	+	16.8920i	−0.197409	+	0.607562i	−0.999940	+	0.0109516i	$0.996514\pi$
$774$	41.5163	−	47.2663i	1.49227	−	1.69895i
$775$	33.1022	−	7.47343i	1.18906	−	0.268453i
$776$	33.6609	+	58.3024i	1.20836	+	2.09293i
$777$	−17.7402	+	1.97508i	−0.636426	+	0.0708557i
$778$	28.6937	−	12.7753i	1.02872	−	0.458016i
$779$	31.6257	−	14.0807i	1.13311	−	0.504493i
$780$	−9.78875	−	28.8965i	−0.350493	−	1.03466i
$781$	−22.7954	−	10.1492i	−0.815683	−	0.363166i
$782$	−27.2295			−0.973726
$783$	−32.1078	−	27.8536i	−1.14744	−	0.995405i
$784$	−5.59494	−	17.2195i	−0.199819	−	0.614981i
$785$	−8.25091	+	2.73850i	−0.294488	+	0.0977412i
$786$	−24.2053	+	55.2795i	−0.863374	+	1.97176i
$787$	−13.4663	−	2.86235i	−0.480022	−	0.102032i	−0.0384555	−	0.999260i	$-0.512244\pi$
$787$	−13.4663	−	2.86235i	−0.480022	−	0.102032i	−0.441567	+	0.897228i	$0.645577\pi$
$788$	34.1915	+	7.26764i	1.21802	+	0.258899i
$789$	13.9902	−	1.55758i	0.498064	−	0.0554513i
$790$	49.2242	−	68.6572i	1.75132	−	2.44272i
$791$	4.33484	+	13.3413i	0.154129	+	0.474361i
$792$	36.6514	+	25.9453i	1.30235	+	0.921925i
$793$	4.70698			0.167150
$794$	6.46308	+	2.87755i	0.229366	+	0.102120i
$795$	−5.90966	+	10.5369i	−0.209594	+	0.373705i
$796$	58.9262	−	26.2357i	2.08859	−	0.929898i
$797$	21.3588	−	9.50955i	0.756567	−	0.336846i	0.00805616	−	0.999968i	$-0.497436\pi$
$797$	21.3588	−	9.50955i	0.756567	−	0.336846i	0.748511	+	0.663122i	$0.230769\pi$
$798$	−38.8821	−	52.8295i	−1.37641	−	1.87015i
$799$	−23.0062	−	39.8478i	−0.813899	−	1.40972i
$800$	−21.2067	−	9.12329i	−0.749771	−	0.322557i
$801$	1.00907	+	0.201530i	0.0356538	+	0.00712072i
$802$	28.3330	−	87.1999i	1.00047	−	3.07914i
$803$	0.503772	−	4.79307i	0.0177777	−	0.169144i
$804$	2.51588	−	12.2053i	0.0887282	−	0.430449i
$805$	9.44597	−	5.53331i	0.332927	−	0.195024i
$806$	3.20696	+	30.5121i	0.112960	+	1.07474i
$807$	−39.6772	−	3.92339i	−1.39670	−	0.138110i
$808$	−71.3320	−	31.7590i	−2.50945	−	1.11728i
$809$	−3.98567	−	12.2666i	−0.140129	−	0.431272i	0.856224	−	0.516605i	$-0.172805\pi$
$809$	−3.98567	−	12.2666i	−0.140129	−	0.431272i	−0.996352	+	0.0853332i	$0.972805\pi$
$810$	48.9334	+	14.2421i	1.71935	+	0.500418i
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	0.798154	+	0.602454i	$0.205810\pi$
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	−0.999833	+	0.0182520i	$0.994190\pi$
$812$	−49.9575	+	55.4834i	−1.75316	+	1.94709i
$813$	8.38383	+	38.2823i	0.294034	+	1.34262i
$814$	20.6824	+	22.9701i	0.724917	+	0.805102i
$815$	−7.52548	+	17.1934i	−0.263606	+	0.602257i
$816$	−38.6598	+	35.2429i	−1.35336	+	1.23375i
$817$	54.7013	+	24.3546i	1.91375	+	0.852059i
$818$	−56.2117			−1.96540
$819$	10.0612	−	4.62881i	0.351566	−	0.161744i
$820$	41.0621	+	23.3634i	1.43395	+	0.815884i
$821$	−3.64312	+	34.6620i	−0.127146	+	1.20971i	0.725872	+	0.687830i	$0.241437\pi$
$821$	−3.64312	+	34.6620i	−0.127146	+	1.20971i	−0.853018	+	0.521882i	$0.825230\pi$
$822$	−35.5083	+	11.7795i	−1.23849	+	0.410859i
$823$	17.3963	+	19.3206i	0.606398	+	0.673473i	0.965674	−	0.259758i	$-0.0836429\pi$
$823$	17.3963	+	19.3206i	0.606398	+	0.673473i	−0.359276	+	0.933231i	$0.616976\pi$
$824$	28.0528	−	48.5890i	0.977267	−	1.69268i
$825$	−8.26274	+	19.5369i	−0.287672	+	0.680188i
$826$	−27.3564	−	47.3826i	−0.951850	−	1.64865i
$827$	−10.5951	+	32.6084i	−0.368428	+	1.13390i	0.579379	+	0.815058i	$0.303295\pi$
$827$	−10.5951	+	32.6084i	−0.368428	+	1.13390i	−0.947807	+	0.318846i	$0.896705\pi$
$828$	−9.31715	+	29.9242i	−0.323793	+	1.03994i
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	0.376168	−	0.926551i	$-0.377242\pi$
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	−0.764960	+	0.644077i	$0.777242\pi$
$830$	−13.6316	−	18.5157i	−0.473158	−	0.642688i
$831$	−15.5882	−	8.87235i	−0.540750	−	0.307778i
$832$	−1.43370	+	2.48324i	−0.0497046	+	0.0860908i
$833$	−1.29276	−	12.2998i	−0.0447914	−	0.426162i
$834$	−8.75480	−	39.9761i	−0.303154	−	1.38426i
$835$	14.0815	−	19.6407i	0.487310	−	0.679694i
$836$	−24.1540	+	74.3384i	−0.835384	+	2.57105i
$837$	−30.8623	−	17.0662i	−1.06676	−	0.589893i
$838$	−25.0176	−	76.9964i	−0.864220	−	2.65980i
$839$	−35.4174	+	7.52820i	−1.22274	+	0.259902i	−0.773668	−	0.633591i	$-0.781580\pi$
$839$	−35.4174	+	7.52820i	−1.22274	+	0.259902i	−0.449077	+	0.893493i	$0.648247\pi$
$840$	14.5447	−	46.7377i	0.501840	−	1.61260i
$841$	−37.0875	−	7.88319i	−1.27888	−	0.271834i
$842$	0.369719	+	3.51764i	0.0127413	+	0.121226i
$843$	18.1697	+	40.1428i	0.625798	+	1.38259i
$844$	53.7000	+	23.9088i	1.84843	+	0.822975i
$845$	−9.05168	−	19.9903i	−0.311387	−	0.687689i
$846$	−75.0766	+	16.9269i	−2.58119	+	0.581960i
$847$	8.36655	+	6.07866i	0.287478	+	0.208865i
$848$	−20.2885	+	4.31246i	−0.696711	+	0.148091i
$849$	16.7266	−	23.3229i	0.574056	−	0.800439i
$850$	−46.9513	−	33.2159i	−1.61041	−	1.13930i
$851$	−5.89809	+	10.2158i	−0.202184	+	0.350193i
$852$	−46.1575	−	62.7147i	−1.58133	−	2.14857i
$853$	3.27183	−	31.1294i	0.112025	−	1.06585i	−0.783669	−	0.621179i	$-0.786654\pi$
$853$	3.27183	−	31.1294i	0.112025	−	1.06585i	0.895694	−	0.444671i	$-0.146679\pi$
$854$	11.1730	+	8.11768i	0.382333	+	0.277781i
$855$	0.903043	+	48.4990i	0.0308834	+	1.65863i
$856$	−4.84845	+	3.52261i	−0.165717	+	0.120400i
$857$	6.62700	+	11.4783i	0.226374	+	0.392091i	0.956731	−	0.290975i	$-0.0939795\pi$
$857$	6.62700	+	11.4783i	0.226374	+	0.392091i	−0.730357	+	0.683066i	$0.760646\pi$
$858$	−16.6671	−	9.48638i	−0.569004	−	0.323860i
$859$	26.5737	+	5.64842i	0.906685	+	0.192722i	0.637575	−	0.770388i	$-0.279937\pi$
$859$	26.5737	+	5.64842i	0.906685	+	0.192722i	0.269109	+	0.963110i	$0.413271\pi$
$860$	17.4928	+	79.8200i	0.596500	+	2.72184i
$861$	−6.87866	+	15.7093i	−0.234424	+	0.535373i
$862$	1.06104	−	1.17841i	0.0361392	−	0.0401367i
$863$	17.1394	+	52.7496i	0.583431	+	1.79562i	0.605481	+	0.795859i	$0.292981\pi$
$863$	17.1394	+	52.7496i	0.583431	+	1.79562i	−0.0220503	+	0.999757i	$0.507019\pi$
$864$	10.1614	+	21.7334i	0.345699	+	0.739386i
$865$	31.9920	+	18.2027i	1.08776	+	0.618910i
$866$	9.72404	−	10.7996i	0.330436	−	0.366987i
$867$	−5.42687	+	3.17792i	−0.184306	+	0.107928i
$868$	−30.9725	+	53.6460i	−1.05128	+	1.82086i
$869$	−3.81967	−	36.3417i	−0.129573	−	1.23281i
$870$	78.2645	−	17.6577i	2.65342	−	0.598651i
$871$	−0.304196	+	2.89423i	−0.0103073	+	0.0980672i
$872$	43.8987	+	31.8943i	1.48660	+	1.08008i
$873$	33.0466	−	0.406976i	1.11846	−	0.0137740i
$874$	−43.3493			−1.46631
$875$	23.0373	+	1.98170i	0.778802	+	0.0669939i
$876$	8.76524	−	12.2219i	0.296150	−	0.412938i
$877$	−30.2841	−	33.6339i	−1.02262	−	1.13574i	−0.990675	−	0.136248i	$-0.956496\pi$
$877$	−30.2841	−	33.6339i	−1.02262	−	1.13574i	−0.0319477	−	0.999490i	$-0.510171\pi$
$878$	−53.6071	+	23.8674i	−1.80915	+	0.805487i
$879$	19.9385	−	6.61441i	0.672509	−	0.223099i
$880$	−34.5653	+	11.4723i	−1.16520	+	0.386731i
$881$	3.25840	−	2.36737i	0.109778	−	0.0797587i	−0.531542	−	0.847032i	$-0.678387\pi$
$881$	3.25840	−	2.36737i	0.109778	−	0.0797587i	0.641320	+	0.767273i	$0.278387\pi$
$882$	−20.2856	−	4.05141i	−0.683051	−	0.136418i
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	−0.908527	−	0.417827i	$-0.862792\pi$
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	0.116626	+	0.993176i	$0.462792\pi$
$884$	23.9419	−	26.5902i	0.805253	−	0.894324i
$885$	−3.72749	+	40.2876i	−0.125298	+	1.35425i
$886$	−37.1667	−	41.2778i	−1.24864	−	1.38675i
$887$	−12.3394	−	2.62282i	−0.414317	−	0.0880658i	−0.00396318	−	0.999992i	$-0.501262\pi$
$887$	−12.3394	−	2.62282i	−0.414317	−	0.0880658i	−0.410354	+	0.911926i	$0.634595\pi$
$888$	11.2836	+	51.5230i	0.378652	+	1.72900i
$889$	−20.1754	+	4.28841i	−0.676661	+	0.143829i
$890$	−1.43518	+	1.30872i	−0.0481074	+	0.0438683i
$891$	19.9118	−	9.45954i	0.667069	−	0.316907i
$892$	−13.0267	+	9.46448i	−0.436167	+	0.316894i
$893$	−36.6258	−	63.4377i	−1.22563	−	2.12286i
$894$	−26.2908	+	15.3956i	−0.879297	+	0.514907i
$895$	−0.250109	−	1.14125i	−0.00836022	−	0.0381478i
$896$	−25.1326	+	11.1897i	−0.839620	+	0.373823i
$897$	1.47758	−	7.16823i	0.0493350	−	0.239340i
$898$	31.3875	−	6.67162i	1.04741	−	0.222635i
$899$	−55.5197			−1.85169
$900$	−52.5684	+	40.2321i	−1.75228	+	1.34107i
$901$	−14.1682			−0.472012
$902$	29.0474	−	6.17421i	0.967172	−	0.205579i
$903$	−28.1535	+	9.33965i	−0.936889	+	0.310804i
$904$	37.8670	−	16.8595i	1.25944	−	0.560738i
$905$	−51.3574	−	5.07081i	−1.70718	−	0.168559i
$906$	0.0212929	+	3.45812i	0.000707409	+	0.114888i
$907$	3.40353	+	5.89509i	0.113012	+	0.195743i	0.916983	−	0.398925i	$-0.130617\pi$
$907$	3.40353	+	5.89509i	0.113012	+	0.195743i	−0.803971	+	0.594668i	$0.797283\pi$
$908$	−56.1061	+	40.7634i	−1.86195	+	1.35278i
$909$	−30.7312	+	22.9110i	−1.01929	+	0.759909i
$910$	−4.21731	+	20.4746i	−0.139802	+	0.678727i
$911$	25.3692	−	5.39238i	0.840518	−	0.178658i	0.232515	−	0.972593i	$-0.425304\pi$
$911$	25.3692	−	5.39238i	0.840518	−	0.178658i	0.608003	+	0.793935i	$0.291971\pi$
$912$	−61.5464	+	56.1066i	−2.03800	+	1.85788i
$913$	−9.72805	−	2.06776i	−0.321952	−	0.0684329i
$914$	−0.216468	−	0.240412i	−0.00716013	−	0.00795213i
$915$	−3.27672	−	9.67291i	−0.108325	−	0.319776i
$916$	17.7406	−	19.7029i	0.586166	−	0.651004i
$917$	23.0193	−	16.7245i	0.760165	−	0.552292i
$918$	13.5044	+	58.2234i	0.445712	+	1.92166i
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	−0.569930	−	0.821694i	$-0.693030\pi$
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	0.605359	+	0.795952i	$0.293030\pi$
$920$	−19.1783	−	26.0498i	−0.632289	−	0.858835i
$921$	15.2342	+	13.5480i	0.501985	+	0.446423i
$922$	−16.7627	+	7.46322i	−0.552049	+	0.245788i
$923$	12.1678	+	13.5137i	0.400507	+	0.444808i
$924$	−15.9666	−	35.2755i	−0.525264	−	1.16048i
$925$	−22.6317	+	10.4201i	−0.744126	+	0.342610i
$926$	57.6748			1.89531
$927$	−14.0642	−	23.6815i	−0.461928	−	0.777803i
$928$	30.5563	+	22.2004i	1.00306	+	0.728765i
$929$	−3.51432	+	33.4365i	−0.115301	+	1.09702i	0.771935	+	0.635702i	$0.219289\pi$
$929$	−3.51432	+	33.4365i	−0.115301	+	1.09702i	−0.887236	+	0.461316i	$0.847377\pi$
$930$	60.4704	−	27.8311i	1.98290	−	0.912618i
$931$	−2.05807	−	19.5812i	−0.0674505	−	0.641749i
$932$	−1.32097	+	2.28799i	−0.0432698	+	0.0749455i
$933$	−0.105499	−	17.1338i	−0.00345389	−	0.560937i
$934$	16.4981	−	18.3230i	0.539834	−	0.599547i
$935$	−24.7241	+	2.75627i	−0.808564	+	0.0901397i
$936$	−16.7103	−	28.1370i	−0.546192	−	0.919688i
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	0.999613	−	0.0278089i	$-0.00885300\pi$
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	−0.825050	+	0.565060i	$0.808853\pi$
$938$	−5.71348	+	6.34546i	−0.186552	+	0.207187i
$939$	59.2457	−	6.59604i	1.93341	−	0.215254i
$940$	40.0830	−	91.5770i	1.30736	−	2.98691i
$941$	−35.4844	−	7.54245i	−1.15676	−	0.245877i	−0.410709	−	0.911766i	$-0.634719\pi$
$941$	−35.4844	−	7.54245i	−1.15676	−	0.245877i	−0.746050	+	0.665889i	$0.768052\pi$
$942$	−14.7157	+	8.61736i	−0.479464	+	0.280769i
$943$	5.66663	+	9.81489i	0.184531	+	0.319617i
$944$	−56.1983	+	40.8305i	−1.82910	+	1.32892i
$945$	−16.5163	−	17.4536i	−0.537275	−	0.567765i
$946$	41.5544	+	30.1910i	1.35105	+	0.981595i
$947$	−1.22544	+	11.6593i	−0.0398216	+	0.378877i	0.956402	+	0.292053i	$0.0943384\pi$
$947$	−1.22544	+	11.6593i	−0.0398216	+	0.378877i	−0.996224	+	0.0868238i	$0.972328\pi$
$948$	45.7402	−	104.460i	1.48557	−	3.39272i
$949$	−1.75611	+	3.04168i	−0.0570059	+	0.0987370i
$950$	−74.7463	−	52.8797i	−2.42509	−	1.71564i
$951$	−15.8823	−	35.0891i	−0.515019	−	1.13784i
$952$	56.1510	−	11.9353i	1.81987	−	0.386824i
$953$	0.574496	+	0.417395i	0.0186097	+	0.0135208i	0.597051	−	0.802203i	$-0.296339\pi$
$953$	0.574496	+	0.417395i	0.0186097	+	0.0135208i	−0.578442	+	0.815724i	$0.696339\pi$
$954$	−7.04502	+	22.6267i	−0.228091	+	0.732566i
$955$	−2.23107	+	0.248722i	−0.0721957	+	0.00804847i
$956$	4.73734	+	2.10920i	0.153217	+	0.0682164i
$957$	20.2254	−	28.2015i	0.653796	−	0.911624i
$958$	2.97909	+	28.3442i	0.0962501	+	0.915759i
$959$	17.2539	+	3.66742i	0.557157	+	0.118427i
$960$	6.10115	+	1.21759i	0.196914	+	0.0392975i
$961$	−14.7350	+	3.13203i	−0.475324	+	0.101033i
$962$	−6.96073	−	21.4229i	−0.224423	−	0.690703i
$963$	0.343535	+	2.92192i	0.0110703	+	0.0941575i
$964$	24.5079	−	75.4277i	0.789348	−	2.42936i
$965$	29.3977	−	9.75718i	0.946346	−	0.314095i
$966$	15.8697	−	14.4671i	0.510600	−	0.465471i
$967$	−2.91903	−	27.7728i	−0.0938698	−	0.893112i	−0.935564	−	0.353157i	$-0.885108\pi$
$967$	−2.91903	−	27.7728i	−0.0938698	−	0.893112i	0.841694	−	0.539955i	$-0.181559\pi$
$968$	15.2792	−	26.4643i	0.491090	−	0.850594i
$969$	−49.0904	+	28.7468i	−1.57701	+	0.923481i
$970$	−36.3484	+	50.6982i	−1.16708	+	1.62782i
$971$	−24.9120	−	18.0996i	−0.799465	−	0.580845i	0.111292	−	0.993788i	$-0.464501\pi$
$971$	−24.9120	−	18.0996i	−0.799465	−	0.580845i	−0.910757	+	0.412942i	$0.864501\pi$
$972$	68.6061	+	5.08154i	2.20054	+	0.162990i
$973$	−5.96262	+	18.3511i	−0.191153	+	0.588308i
$974$	10.0423	+	17.3938i	0.321776	+	0.557333i
$975$	11.2919	−	10.5576i	0.361631	−	0.338113i
$976$	8.76719	−	15.1852i	0.280631	−	0.486067i
$977$	16.8170	+	18.6771i	0.538022	+	0.597534i	0.949454	−	0.313907i	$-0.101638\pi$
$977$	16.8170	+	18.6771i	0.538022	+	0.597534i	−0.411432	+	0.911441i	$0.634971\pi$
$978$	−7.43253	+	36.0576i	−0.237666	+	1.15300i
$979$	−0.0878186	+	0.835538i	−0.00280669	+	0.0267039i
$980$	19.8541	−	18.1046i	0.634215	−	0.578329i
$981$	24.1995	−	11.1334i	0.772632	−	0.355462i
$982$	37.2571			1.18892
$983$	43.2866	+	19.2725i	1.38063	+	0.614696i	0.956720	−	0.291009i	$-0.0939909\pi$
$983$	43.2866	+	19.2725i	1.38063	+	0.614696i	0.423909	+	0.905705i	$0.360658\pi$
$984$	48.2896	+	15.3622i	1.53941	+	0.489728i
$985$	3.79152	+	17.3008i	0.120808	+	0.551248i
$986$	62.9608	+	69.9251i	2.00508	+	2.22687i
$987$	34.5795	+	11.0006i	1.10068	+	0.350154i
$988$	38.1155	−	42.3315i	1.21261	−	1.34674i
$989$	−6.05751	+	18.6431i	−0.192617	+	0.592816i
$990$	−7.89203	+	40.8549i	−0.250825	+	1.29845i
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	0.872294	+	0.488982i	$0.162632\pi$
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	−0.418284	+	0.908316i	$0.637368\pi$
$992$	28.6279	+	12.7460i	0.908936	+	0.404685i
$993$	9.34720	+	20.6510i	0.296624	+	0.655340i
$994$	5.57707	+	53.0622i	0.176894	+	1.68303i
$995$	24.4252	+	21.7154i	0.774332	+	0.688424i
$996$	−23.1920	−	20.6250i	−0.734866	−	0.653528i
$997$	5.40789	−	51.4526i	0.171269	−	1.62952i	−0.484663	−	0.874701i	$-0.661058\pi$
$997$	5.40789	−	51.4526i	0.171269	−	1.62952i	0.655933	−	0.754819i	$-0.272275\pi$
$998$	18.3451	−	56.4605i	0.580705	−	1.78722i
$999$	24.7690	+	7.54508i	0.783658	+	0.238716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.2	yes	224
3.2	odd	2		675.2.r.a.496.27		224
9.2	odd	6		675.2.r.a.46.2		224
9.7	even	3	inner	225.2.q.a.196.27	yes	224
25.6	even	5	inner	225.2.q.a.31.27	✓	224
75.56	odd	10		675.2.r.a.631.2		224
225.56	odd	30		675.2.r.a.181.27		224
225.106	even	15	inner	225.2.q.a.106.2	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.27	✓	224	25.6	even	5	inner
225.2.q.a.106.2	yes	224	225.106	even	15	inner
225.2.q.a.121.2	yes	224	1.1	even	1	trivial
225.2.q.a.196.27	yes	224	9.7	even	3	inner
675.2.r.a.46.2		224	9.2	odd	6
675.2.r.a.181.27		224	225.56	odd	30
675.2.r.a.496.27		224	3.2	odd	2
675.2.r.a.631.2		224	75.56	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47708 + 0.526519i) q^{2} +(-1.29428 - 1.15102i) q^{3} +(4.03160 - 1.79498i) q^{4} +(1.67112 + 1.48572i) q^{5} +(3.81206 + 2.16971i) q^{6} +(-1.03406 - 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(0.350302 + 2.97948i) q^{9} +O(q^{10})\)	\(q+(-2.47708 + 0.526519i) q^{2} +(-1.29428 - 1.15102i) q^{3} +(4.03160 - 1.79498i) q^{4} +(1.67112 + 1.48572i) q^{5} +(3.81206 + 2.16971i) q^{6} +(-1.03406 - 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(0.350302 + 2.97948i) q^{9} +(-4.92175 - 2.80036i) q^{10} +(-2.39587 + 0.509257i) q^{11} +(-7.28407 - 2.31725i) q^{12} +(1.74601 + 0.371125i) q^{13} +(3.50448 + 3.89212i) q^{14} +(-0.452799 - 3.84642i) q^{15} +(4.44939 - 4.94155i) q^{16} +(3.67466 - 2.66979i) q^{17} +(-2.43648 - 7.19596i) q^{18} +(5.85004 - 4.25031i) q^{19} +(9.40413 + 2.99019i) q^{20} +(-0.723173 + 3.50834i) q^{21} +(5.66661 - 2.52294i) q^{22} +(1.58401 + 1.75922i) q^{23} +(10.5333 + 1.04156i) q^{24} +(0.585285 + 4.96563i) q^{25} -4.52040 q^{26} +(2.97605 - 4.25947i) q^{27} +(-7.38384 - 5.36467i) q^{28} +(0.855066 - 8.13541i) q^{29} +(3.14683 + 9.28948i) q^{30} +(-0.709441 - 6.74988i) q^{31} +(-2.30859 + 3.99860i) q^{32} +(3.68708 + 2.09857i) q^{33} +(-7.69671 + 8.54806i) q^{34} +(0.932951 - 4.52939i) q^{35} +(6.76040 + 11.3833i) q^{36} +(1.53985 + 4.73917i) q^{37} +(-12.2531 + 13.6085i) q^{38} +(-1.83264 - 2.49003i) q^{39} +(-13.5986 - 1.34267i) q^{40} +(4.68289 + 0.995378i) q^{41} +(-0.0558547 - 9.07120i) q^{42} +(4.14034 + 7.17127i) q^{43} +(-8.74507 + 6.35367i) q^{44} +(-3.84127 + 5.49952i) q^{45} +(-4.84997 - 3.52371i) q^{46} +(1.05889 - 10.0746i) q^{47} +(-11.4466 + 1.27439i) q^{48} +(1.36143 - 2.35806i) q^{49} +(-4.06429 - 11.9921i) q^{50} +(-7.82901 - 0.774155i) q^{51} +(7.70536 - 1.63783i) q^{52} +(-2.52356 - 1.83348i) q^{53} +(-5.12922 + 12.1180i) q^{54} +(-4.76039 - 2.70855i) q^{55} +(11.5458 + 5.14053i) q^{56} +(-12.4638 - 1.23245i) q^{57} +(2.16538 + 20.6023i) q^{58} +(-10.2183 - 2.17198i) q^{59} +(-8.72978 - 14.6945i) q^{60} +(2.57932 - 0.548251i) q^{61} +(5.31128 + 16.3465i) q^{62} +(4.97416 - 3.70838i) q^{63} +(-0.496397 + 1.52775i) q^{64} +(2.36640 + 3.21427i) q^{65} +(-10.2381 - 3.25701i) q^{66} +(0.170417 + 1.62141i) q^{67} +(10.0225 - 17.3595i) q^{68} +(-0.0252460 - 4.10014i) q^{69} +(0.0738159 + 11.7109i) q^{70} +(8.24169 + 5.98794i) q^{71} +(-12.4342 - 13.4721i) q^{72} +(-0.608028 + 1.87132i) q^{73} +(-6.30959 - 10.9285i) q^{74} +(4.95802 - 7.10057i) q^{75} +(15.9558 - 27.6363i) q^{76} +(3.38958 + 3.76451i) q^{77} +(5.85064 + 5.20307i) q^{78} +(-1.55944 + 14.8370i) q^{79} +(14.7772 - 1.64738i) q^{80} +(-8.75458 + 2.08743i) q^{81} -12.1240 q^{82} +(3.70931 + 1.65149i) q^{83} +(3.38188 + 15.4423i) q^{84} +(10.1074 + 0.997956i) q^{85} +(-14.0318 - 15.5838i) q^{86} +(-10.4707 + 9.54527i) q^{87} +(10.0158 - 11.1237i) q^{88} +(0.105993 - 0.326212i) q^{89} +(6.61952 - 15.6452i) q^{90} +(-1.14078 - 3.51095i) q^{91} +(9.54385 + 4.24919i) q^{92} +(-6.85104 + 9.55279i) q^{93} +(2.68154 + 25.5132i) q^{94} +(16.0909 + 1.58874i) q^{95} +(7.59043 - 2.51805i) q^{96} +(1.15152 - 10.9560i) q^{97} +(-2.13079 + 6.55791i) q^{98} +(-2.35660 - 6.96004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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