LMFDB - Embedded newform 300.2.r.a.59.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(59,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("300.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.r (of order $10$, degree $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.8
Character	$\chi$	$=$	300.59
Dual form			300.2.r.a.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29016 - 0.579209i) q^{2} +(-1.71582 - 0.236546i) q^{3} +(1.32903 + 1.49455i) q^{4} +(-0.101169 - 2.23378i) q^{5} +(2.07668 + 1.29900i) q^{6} -0.903444 q^{7} +(-0.849014 - 2.69799i) q^{8} +(2.88809 + 0.811741i) q^{9} +O(q^{10})$	\(q+(-1.29016 - 0.579209i) q^{2} +(-1.71582 - 0.236546i) q^{3} +(1.32903 + 1.49455i) q^{4} +(-0.101169 - 2.23378i) q^{5} +(2.07668 + 1.29900i) q^{6} -0.903444 q^{7} +(-0.849014 - 2.69799i) q^{8} +(2.88809 + 0.811741i) q^{9} +(-1.16330 + 2.94053i) q^{10} +(0.0159524 + 0.0115901i) q^{11} +(-1.92686 - 2.87875i) q^{12} +(-1.50613 - 2.07301i) q^{13} +(1.16559 + 0.523283i) q^{14} +(-0.354802 + 3.85670i) q^{15} +(-0.467337 + 3.97261i) q^{16} +(-0.0389111 + 0.119756i) q^{17} +(-3.25594 - 2.72009i) q^{18} +(-5.78437 - 1.87945i) q^{19} +(3.20403 - 3.11997i) q^{20} +(1.55015 + 0.213706i) q^{21} +(-0.0138681 - 0.0241929i) q^{22} +(-4.34613 + 5.98194i) q^{23} +(0.818558 + 4.83011i) q^{24} +(-4.97953 + 0.451980i) q^{25} +(0.742446 + 3.54689i) q^{26} +(-4.76344 - 2.07597i) q^{27} +(-1.20071 - 1.35024i) q^{28} +(-6.74343 + 2.19107i) q^{29} +(2.69159 - 4.77026i) q^{30} +(1.78347 + 0.579484i) q^{31} +(2.90391 - 4.85462i) q^{32} +(-0.0246299 - 0.0236600i) q^{33} +(0.119566 - 0.131967i) q^{34} +(0.0914009 + 2.01809i) q^{35} +(2.62519 + 5.39522i) q^{36} +(2.02683 + 2.78969i) q^{37} +(6.37417 + 5.77516i) q^{38} +(2.09389 + 3.91319i) q^{39} +(-5.94083 + 2.16946i) q^{40} +(-2.58437 - 3.55708i) q^{41} +(-1.87616 - 1.17358i) q^{42} -7.15556 q^{43} +(0.00387935 + 0.0392452i) q^{44} +(1.52106 - 6.53348i) q^{45} +(9.07201 - 5.20035i) q^{46} +(5.03956 - 1.63745i) q^{47} +(1.74157 - 6.70574i) q^{48} -6.18379 q^{49} +(6.68619 + 2.30106i) q^{50} +(0.0950924 - 0.196276i) q^{51} +(1.09651 - 5.00609i) q^{52} +(0.0726282 + 0.223527i) q^{53} +(4.94319 + 5.43736i) q^{54} +(0.0242758 - 0.0368067i) q^{55} +(0.767037 + 2.43749i) q^{56} +(9.48037 + 4.59308i) q^{57} +(9.96920 + 1.07902i) q^{58} +(12.0918 - 8.78519i) q^{59} +(-6.23556 + 4.59541i) q^{60} +(5.52424 + 4.01360i) q^{61} +(-1.96532 - 1.78063i) q^{62} +(-2.60923 - 0.733363i) q^{63} +(-6.55835 + 4.58127i) q^{64} +(-4.47828 + 3.57409i) q^{65} +(0.0180725 + 0.0447911i) q^{66} +(4.13519 - 12.7268i) q^{67} +(-0.230695 + 0.101006i) q^{68} +(8.87220 - 9.23589i) q^{69} +(1.05098 - 2.65661i) q^{70} +(-3.59697 - 11.0703i) q^{71} +(-0.261957 - 8.48124i) q^{72} +(-3.17175 + 4.36554i) q^{73} +(-0.999124 - 4.77311i) q^{74} +(8.65090 + 0.402370i) q^{75} +(-4.87869 - 11.1429i) q^{76} +(-0.0144121 - 0.0104710i) q^{77} +(-0.434904 - 6.26145i) q^{78} +(0.586897 - 0.190695i) q^{79} +(8.92120 + 0.642022i) q^{80} +(7.68215 + 4.68877i) q^{81} +(1.27396 + 6.08610i) q^{82} +(-11.0296 - 3.58375i) q^{83} +(1.74081 + 2.60079i) q^{84} +(0.271445 + 0.0748032i) q^{85} +(9.23183 + 4.14457i) q^{86} +(12.0888 - 2.16436i) q^{87} +(0.0177262 - 0.0528797i) q^{88} +(-5.84353 + 8.04293i) q^{89} +(-5.74667 + 7.54823i) q^{90} +(1.36071 + 1.87285i) q^{91} +(-14.7164 + 1.45470i) q^{92} +(-2.92304 - 1.41616i) q^{93} +(-7.45028 - 0.806381i) q^{94} +(-3.61308 + 13.1111i) q^{95} +(-6.13093 + 7.64275i) q^{96} +(12.3121 - 4.00046i) q^{97} +(7.97809 + 3.58171i) q^{98} +(0.0366638 + 0.0464225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9}+O(q^{10}) $ 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9	$ 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9} - 5 q^{12} - 20 q^{13} + 6 q^{16} - 24 q^{21} - 10 q^{22} - 28 q^{24} - 20 q^{25} - 50 q^{28} - 25 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 60 q^{37} - 20 q^{40} - 85 q^{42} - 30 q^{45} + 6 q^{46} - 70 q^{48} + 88 q^{49} + 40 q^{52} - 46 q^{54} + 50 q^{58} + 10 q^{60} - 28 q^{61} + 18 q^{64} + 64 q^{66} - 42 q^{69} - 40 q^{70} - 5 q^{72} - 20 q^{73} - 80 q^{76} - 85 q^{78} + 18 q^{81} - 48 q^{84} - 20 q^{85} + 50 q^{88} - 60 q^{90} + 60 q^{94} + 44 q^{96} - 120 q^{97}+O(q^{100}) $ 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9 - 5 * q^12 - 20 * q^13 + 6 * q^16 - 24 * q^21 - 10 * q^22 - 28 * q^24 - 20 * q^25 - 50 * q^28 - 25 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 60 * q^37 - 20 * q^40 - 85 * q^42 - 30 * q^45 + 6 * q^46 - 70 * q^48 + 88 * q^49 + 40 * q^52 - 46 * q^54 + 50 * q^58 + 10 * q^60 - 28 * q^61 + 18 * q^64 + 64 * q^66 - 42 * q^69 - 40 * q^70 - 5 * q^72 - 20 * q^73 - 80 * q^76 - 85 * q^78 + 18 * q^81 - 48 * q^84 - 20 * q^85 + 50 * q^88 - 60 * q^90 + 60 * q^94 + 44 * q^96 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−1.29016	−	0.579209i	−0.912282	−	0.409563i
$2$	−1.29016	−	0.579209i	−0.912282	−	0.409563i
$3$	−1.71582	−	0.236546i	−0.990630	−	0.136570i
$3$	−1.71582	−	0.236546i	−0.990630	−	0.136570i
$4$	1.32903	+	1.49455i	0.664517	+	0.747273i
$5$	−0.101169	−	2.23378i	−0.0452443	−	0.998976i
$5$	−0.101169	−	2.23378i	−0.0452443	−	0.998976i
$6$	2.07668	+	1.29900i	0.847800	+	0.530315i
$7$	−0.903444			−0.341470			−0.170735	−	0.985317i	$-0.554614\pi$
$7$	−0.903444			−0.341470			−0.170735	+	0.985317i	$0.554614\pi$
$8$	−0.849014	−	2.69799i	−0.300172	−	0.953885i
$9$	2.88809	+	0.811741i	0.962697	+	0.270580i
$10$	−1.16330	+	2.94053i	−0.367868	+	0.929878i
$11$	0.0159524	+	0.0115901i	0.00480983	+	0.00349455i	0.590188	−	0.807266i	$-0.299054\pi$
$11$	0.0159524	+	0.0115901i	0.00480983	+	0.00349455i	−0.585378	+	0.810761i	$0.699054\pi$
$12$	−1.92686	−	2.87875i	−0.556236	−	0.831025i
$13$	−1.50613	−	2.07301i	−0.417726	−	0.574950i	0.547356	−	0.836900i	$-0.315635\pi$
$13$	−1.50613	−	2.07301i	−0.417726	−	0.574950i	−0.965082	+	0.261950i	$0.915635\pi$
$14$	1.16559	+	0.523283i	0.311517	+	0.139853i
$15$	−0.354802	+	3.85670i	−0.0916096	+	0.995795i
$16$	−0.467337	+	3.97261i	−0.116834	+	0.993151i
$17$	−0.0389111	+	0.119756i	−0.00943734	+	0.0290451i	−0.955664	−	0.294458i	$-0.904861\pi$
$17$	−0.0389111	+	0.119756i	−0.00943734	+	0.0290451i	0.946227	+	0.323504i	$0.104861\pi$
$18$	−3.25594	−	2.72009i	−0.767432	−	0.641130i
$19$	−5.78437	−	1.87945i	−1.32702	−	0.431176i	−0.442123	−	0.896954i	$-0.645775\pi$
$19$	−5.78437	−	1.87945i	−1.32702	−	0.431176i	−0.884902	+	0.465778i	$0.845775\pi$
$20$	3.20403	−	3.11997i	0.716442	−	0.697646i
$21$	1.55015	+	0.213706i	0.338270	+	0.0466345i
$22$	−0.0138681	−	0.0241929i	−0.00295669	−	0.00515794i
$23$	−4.34613	+	5.98194i	−0.906232	+	1.24732i	0.0622055	+	0.998063i	$0.480187\pi$
$23$	−4.34613	+	5.98194i	−0.906232	+	1.24732i	−0.968437	+	0.249258i	$0.919813\pi$
$24$	0.818558	+	4.83011i	0.167087	+	0.985942i
$25$	−4.97953	+	0.451980i	−0.995906	+	0.0903959i
$26$	0.742446	+	3.54689i	0.145606	+	0.695602i
$27$	−4.76344	−	2.07597i	−0.916724	−	0.399521i
$28$	−1.20071	−	1.35024i	−0.226913	−	0.255171i
$29$	−6.74343	+	2.19107i	−1.25222	+	0.406872i	−0.858717	−	0.512450i	$-0.828738\pi$
$29$	−6.74343	+	2.19107i	−1.25222	+	0.406872i	−0.393506	+	0.919322i	$0.628738\pi$
$30$	2.69159	−	4.77026i	0.491414	−	0.870926i
$31$	1.78347	+	0.579484i	0.320321	+	0.104078i	0.464764	−	0.885435i	$-0.346139\pi$
$31$	1.78347	+	0.579484i	0.320321	+	0.104078i	−0.144443	+	0.989513i	$0.546139\pi$
$32$	2.90391	−	4.85462i	0.513344	−	0.858183i
$33$	−0.0246299	−	0.0236600i	−0.00428752	−	0.00411868i
$34$	0.119566	−	0.131967i	0.0205053	−	0.0226322i
$35$	0.0914009	+	2.01809i	0.0154496	+	0.341120i
$36$	2.62519	+	5.39522i	0.437531	+	0.899203i
$37$	2.02683	+	2.78969i	0.333209	+	0.458623i	0.942443	−	0.334368i	$-0.108523\pi$
$37$	2.02683	+	2.78969i	0.333209	+	0.458623i	−0.609234	+	0.792991i	$0.708523\pi$
$38$	6.37417	+	5.77516i	1.03403	+	0.936854i
$39$	2.09389	+	3.91319i	0.335291	+	0.626612i
$40$	−5.94083	+	2.16946i	−0.939327	+	0.343022i
$41$	−2.58437	−	3.55708i	−0.403611	−	0.555523i	0.558035	−	0.829818i	$-0.311556\pi$
$41$	−2.58437	−	3.55708i	−0.403611	−	0.555523i	−0.961646	+	0.274295i	$0.911556\pi$
$42$	−1.87616	−	1.17358i	−0.289498	−	0.181087i
$43$	−7.15556			−1.09121			−0.545607	−	0.838041i	$-0.683701\pi$
$43$	−7.15556			−1.09121			−0.545607	+	0.838041i	$0.683701\pi$
$44$	0.00387935	+	0.0392452i	0.000584833	+	0.00591644i
$45$	1.52106	−	6.53348i	0.226747	−	0.973954i
$46$	9.07201	−	5.20035i	1.33759	−	0.766750i
$47$	5.03956	−	1.63745i	0.735096	−	0.238847i	0.0825400	−	0.996588i	$-0.473697\pi$
$47$	5.03956	−	1.63745i	0.735096	−	0.238847i	0.652556	+	0.757741i	$0.273697\pi$
$48$	1.74157	−	6.70574i	0.251374	−	0.967890i
$49$	−6.18379			−0.883398
$50$	6.68619	+	2.30106i	0.945570	+	0.325419i
$51$	0.0950924	−	0.196276i	0.0133156	−	0.0274841i
$52$	1.09651	−	5.00609i	0.152059	−	0.694220i
$53$	0.0726282	+	0.223527i	0.00997625	+	0.0307037i	0.955921	−	0.293625i	$-0.0948616\pi$
$53$	0.0726282	+	0.223527i	0.00997625	+	0.0307037i	−0.945944	+	0.324329i	$0.894862\pi$
$54$	4.94319	+	5.43736i	0.672682	+	0.739931i
$55$	0.0242758	−	0.0368067i	0.00327335	−	0.00496301i
$56$	0.767037	+	2.43749i	0.102500	+	0.325723i
$57$	9.48037	+	4.59308i	1.25571	+	0.608368i
$58$	9.96920	+	1.07902i	1.30902	+	0.141682i
$59$	12.0918	−	8.78519i	1.57422	−	1.14373i	0.651243	−	0.758869i	$-0.274248\pi$
$59$	12.0918	−	8.78519i	1.57422	−	1.14373i	0.922972	−	0.384866i	$-0.125752\pi$
$60$	−6.23556	+	4.59541i	−0.805007	+	0.593265i
$61$	5.52424	+	4.01360i	0.707307	+	0.513889i	0.882304	−	0.470680i	$-0.155992\pi$
$61$	5.52424	+	4.01360i	0.707307	+	0.513889i	−0.174997	+	0.984569i	$0.555992\pi$
$62$	−1.96532	−	1.78063i	−0.249596	−	0.226140i
$63$	−2.60923	−	0.733363i	−0.328732	−	0.0923951i
$64$	−6.55835	+	4.58127i	−0.819794	+	0.572659i
$65$	−4.47828	+	3.57409i	−0.555462	+	0.443311i
$66$	0.0180725	+	0.0447911i	0.00222456	+	0.00551341i
$67$	4.13519	−	12.7268i	0.505194	−	1.55483i	−0.295250	−	0.955420i	$-0.595403\pi$
$67$	4.13519	−	12.7268i	0.505194	−	1.55483i	0.800444	−	0.599407i	$-0.204597\pi$
$68$	−0.230695	+	0.101006i	−0.0279759	+	0.0122487i
$69$	8.87220	−	9.23589i	1.06809	−	1.11187i
$70$	1.05098	−	2.65661i	0.125616	−	0.317525i
$71$	−3.59697	−	11.0703i	−0.426881	−	1.31381i	−0.901181	−	0.433443i	$-0.857299\pi$
$71$	−3.59697	−	11.0703i	−0.426881	−	1.31381i	0.474300	−	0.880363i	$-0.342701\pi$
$72$	−0.261957	−	8.48124i	−0.0308719	−	0.999523i
$73$	−3.17175	+	4.36554i	−0.371225	+	0.510948i	−0.953233	−	0.302235i	$-0.902267\pi$
$73$	−3.17175	+	4.36554i	−0.371225	+	0.510948i	0.582008	+	0.813183i	$0.302267\pi$
$74$	−0.999124	−	4.77311i	−0.116146	−	0.554863i
$75$	8.65090	+	0.402370i	0.998920	+	0.0464617i
$76$	−4.87869	−	11.1429i	−0.559624	−	1.27817i
$77$	−0.0144121	−	0.0104710i	−0.00164241	−	0.00119328i
$78$	−0.434904	−	6.26145i	−0.0492432	−	0.708970i
$79$	0.586897	−	0.190695i	0.0660311	−	0.0214548i	−0.275815	−	0.961211i	$-0.588948\pi$
$79$	0.586897	−	0.190695i	0.0660311	−	0.0214548i	0.341846	+	0.939756i	$0.388948\pi$
$80$	8.92120	+	0.642022i	0.997420	+	0.0717803i
$81$	7.68215	+	4.68877i	0.853572	+	0.520974i
$82$	1.27396	+	6.08610i	0.140686	+	0.672097i
$83$	−11.0296	−	3.58375i	−1.21066	−	0.393367i	−0.366988	−	0.930226i	$-0.619611\pi$
$83$	−11.0296	−	3.58375i	−1.21066	−	0.393367i	−0.843672	+	0.536858i	$0.819611\pi$
$84$	1.74081	+	2.60079i	0.189938	+	0.283770i
$85$	0.271445	+	0.0748032i	0.0294424	+	0.00811355i
$86$	9.23183	+	4.14457i	0.995494	+	0.446920i
$87$	12.0888	−	2.16436i	1.29606	−	0.232044i
$88$	0.0177262	−	0.0528797i	0.00188962	−	0.00563699i
$89$	−5.84353	+	8.04293i	−0.619413	+	0.852549i	−0.997310	−	0.0732989i	$-0.976647\pi$
$89$	−5.84353	+	8.04293i	−0.619413	+	0.852549i	0.377897	+	0.925848i	$0.376647\pi$
$90$	−5.74667	+	7.54823i	−0.605752	+	0.795654i
$91$	1.36071	+	1.87285i	0.142641	+	0.196328i
$92$	−14.7164	+	1.45470i	−1.53430	+	0.151663i
$93$	−2.92304	−	1.41616i	−0.303105	−	0.146849i
$94$	−7.45028	−	0.806381i	−0.768438	−	0.0831718i
$95$	−3.61308	+	13.1111i	−0.370695	+	1.34517i
$96$	−6.13093	+	7.64275i	−0.625736	+	0.780035i
$97$	12.3121	−	4.00046i	1.25011	−	0.406185i	0.392149	−	0.919902i	$-0.371732\pi$
$97$	12.3121	−	4.00046i	1.25011	−	0.406185i	0.857960	+	0.513717i	$0.171732\pi$
$98$	7.97809	+	3.58171i	0.805908	+	0.361807i
$99$	0.0366638	+	0.0464225i	0.00368486	+	0.00466564i
$100$	−7.29347	−	6.84144i	−0.729347	−	0.684144i
$101$		−	3.98290i		−	0.396314i	−0.980170	−	0.198157i	$-0.936504\pi$
$101$		−	3.98290i		−	0.396314i	0.980170	−	0.198157i	$-0.0634955\pi$
$102$	−0.236369	+	0.198149i	−0.0234041	+	0.0196197i
$103$	0.978409	+	3.01123i	0.0964055	+	0.296705i	0.987617	−	0.156882i	$-0.0501441\pi$
$103$	0.978409	+	3.01123i	0.0964055	+	0.296705i	−0.891212	+	0.453587i	$0.850144\pi$
$104$	−4.31425	+	5.82355i	−0.423047	+	0.571046i
$105$	0.320544	−	3.48431i	0.0312819	−	0.340034i
$106$	0.0357665	−	0.330452i	0.00347395	−	0.0320964i
$107$			8.63326i			0.834609i	0.908767	+	0.417304i	$0.137025\pi$
$107$			8.63326i			0.834609i	−0.908767	+	0.417304i	$0.862975\pi$
$108$	−3.22814	−	9.87821i	−0.310628	−	0.950532i
$109$	−9.01184	+	6.54748i	−0.863177	+	0.627135i	−0.928748	−	0.370713i	$-0.879113\pi$
$109$	−9.01184	+	6.54748i	−0.863177	+	0.627135i	0.0655701	+	0.997848i	$0.479113\pi$
$110$	−0.0526385	+	0.0334258i	−0.00501888	+	0.00318703i
$111$	−2.81779	−	5.26606i	−0.267453	−	0.499832i
$112$	0.422213	−	3.58903i	0.0398954	−	0.339131i
$113$	1.95622	−	1.42128i	0.184026	−	0.133703i	−0.491958	−	0.870619i	$-0.663719\pi$
$113$	1.95622	−	1.42128i	0.184026	−	0.133703i	0.675984	+	0.736916i	$0.263719\pi$
$114$	−9.57085	−	11.4169i	−0.896393	−	1.06929i
$115$	13.8020	+	9.10311i	1.28705	+	0.848870i
$116$	−12.2369	−	7.16636i	−1.13617	−	0.665380i
$117$	−2.66710	−	7.20964i	−0.246573	−	0.666532i
$118$	−20.6888	+	4.33065i	−1.90456	+	0.398669i
$119$	0.0351541	−	0.108193i	0.00322257	−	0.00991804i
$120$	10.7066	−	2.31714i	0.977373	−	0.211525i
$121$	−3.39907	−	10.4613i	−0.309006	−	0.951023i
$122$	−4.80246	−	8.37788i	−0.434794	−	0.758498i
$123$	3.59291	+	6.71464i	0.323962	+	0.605439i
$124$	1.50423	+	3.43563i	0.135083	+	0.308529i
$125$	1.51340	+	11.0774i	0.135362	+	0.990796i
$126$	2.94156	+	2.45745i	0.262055	+	0.218927i
$127$	10.5934	+	7.69654i	0.940011	+	0.682958i	0.948423	−	0.317007i	$-0.102678\pi$
$127$	10.5934	+	7.69654i	0.940011	+	0.682958i	−0.00841253	+	0.999965i	$0.502678\pi$
$128$	11.1148	−	2.11192i	0.982423	−	0.186669i
$129$	12.2777	+	1.69262i	1.08099	+	0.149027i
$130$	7.84785	−	2.01730i	0.688302	−	0.176929i
$131$	5.75685	−	17.7178i	0.502978	−	1.54801i	−0.301165	−	0.953572i	$-0.597375\pi$
$131$	5.75685	−	17.7178i	0.502978	−	1.54801i	0.804143	−	0.594436i	$-0.202625\pi$
$132$	0.00262703	−	0.0682555i	0.000228654	−	0.00594088i
$133$	5.22585	+	1.69798i	0.453139	+	0.147234i
$134$	−12.7065	+	14.0245i	−1.09768	+	1.21153i
$135$	−4.15534	+	10.8505i	−0.357635	+	0.933861i
$136$	0.356138	+	0.00330738i	0.0305385	+	0.000283605i
$137$	−15.8417	+	11.5097i	−1.35345	+	0.983338i	−0.354617	+	0.935012i	$0.615389\pi$
$137$	−15.8417	+	11.5097i	−1.35345	+	0.983338i	−0.998832	+	0.0483266i	$0.984611\pi$
$138$	−16.7961	+	6.77693i	−1.42978	+	0.576891i
$139$	−5.11629	+	7.04197i	−0.433958	+	0.597292i	−0.968856	−	0.247625i	$-0.920350\pi$
$139$	−5.11629	+	7.04197i	−0.433958	+	0.597292i	0.534898	+	0.844917i	$0.320350\pi$
$140$	−2.89466	+	2.81872i	−0.244643	+	0.238225i
$141$	−9.03433	+	1.61749i	−0.760828	+	0.136217i
$142$	−1.77136	+	16.3659i	−0.148649	+	1.37340i
$143$		−	0.0505258i		−	0.00422518i
$144$	−4.57444	+	11.0939i	−0.381203	+	0.924491i
$145$	5.57660	+	14.8417i	0.463111	+	1.23253i
$146$	6.62063	−	3.79515i	0.547927	−	0.314089i
$147$	10.6103	+	1.46275i	0.875121	+	0.120646i
$148$	−1.47560	+	6.73679i	−0.121293	+	0.553761i
$149$		−	20.0993i		−	1.64660i	−0.567606	−	0.823300i	$-0.692130\pi$
$149$		−	20.0993i		−	1.64660i	0.567606	−	0.823300i	$-0.307870\pi$
$150$	−10.9280	−	5.52980i	−0.892268	−	0.451506i
$151$			6.79426i			0.552909i	0.961027	+	0.276455i	$0.0891595\pi$
$151$			6.79426i			0.552909i	−0.961027	+	0.276455i	$0.910840\pi$
$152$	−0.159750	+	17.2019i	−0.0129575	+	1.39526i
$153$	−0.209590	+	0.314281i	−0.0169443	+	0.0254081i
$154$	0.0125290	+	0.0218569i	0.00100962	+	0.00176128i
$155$	1.11401	−	4.04250i	0.0894792	−	0.324702i
$156$	−3.06559	+	8.33018i	−0.245444	+	0.666948i
$157$		−	16.6707i		−	1.33046i	−0.746637	−	0.665232i	$-0.768333\pi$
$157$		−	16.6707i		−	1.33046i	0.746637	−	0.665232i	$-0.231667\pi$
$158$	−0.867645	−	0.0939095i	−0.0690261	−	0.00747104i
$159$	−0.0717428	−	0.400712i	−0.00568957	−	0.0317785i
$160$	−11.1379	−	5.99555i	−0.880530	−	0.473990i
$161$	3.92649	−	5.40435i	0.309451	−	0.425923i
$162$	−7.19544	−	10.4988i	−0.565327	−	0.824867i
$163$	−1.13970	+	0.828038i	−0.0892679	+	0.0648570i	−0.631524	−	0.775356i	$-0.717570\pi$
$163$	−1.13970	+	0.828038i	−0.0892679	+	0.0648570i	0.542256	+	0.840213i	$0.317570\pi$
$164$	1.88151	−	8.58994i	0.146921	−	0.670762i
$165$	−0.0503595	+	0.0574114i	−0.00392048	+	0.00446947i
$166$	12.1543	+	11.0121i	0.943355	+	0.854703i
$167$	0.226354	+	0.0735469i	0.0175158	+	0.00569123i	0.317762	−	0.948171i	$-0.397069\pi$
$167$	0.226354	+	0.0735469i	0.0175158	+	0.00569123i	−0.300246	+	0.953862i	$0.597069\pi$
$168$	−0.739521	−	4.36374i	−0.0570553	−	0.336670i
$169$	1.98827	−	6.11927i	0.152944	−	0.470713i
$170$	−0.306882	−	0.253732i	−0.0235367	−	0.0194603i
$171$	−15.1802	−	10.1234i	−1.16086	−	0.774159i
$172$	−9.50999	−	10.6943i	−0.725130	−	0.815434i
$173$	−1.78034	−	1.29349i	−0.135357	−	0.0983426i	0.518046	−	0.855352i	$-0.326659\pi$
$173$	−1.78034	−	1.29349i	−0.135357	−	0.0983426i	−0.653403	+	0.757010i	$0.726659\pi$
$174$	−16.8501	−	4.20957i	−1.27741	−	0.319127i
$175$	4.49873	−	0.408338i	0.340072	−	0.0308675i
$176$	−0.0534980	+	0.0579561i	−0.00403257	+	0.00436861i
$177$	−22.8254	+	12.2136i	−1.71567	+	0.918028i
$178$	12.1976	−	6.99205i	0.914251	−	0.524077i
$179$	−2.98700	−	9.19303i	−0.223259	−	0.687119i	−0.998464	−	0.0554096i	$-0.982354\pi$
$179$	−2.98700	−	9.19303i	−0.223259	−	0.687119i	0.775205	−	0.631710i	$-0.217646\pi$
$180$	11.7861	−	6.40992i	0.878487	−	0.477767i
$181$	−1.94585	+	5.98871i	−0.144634	+	0.445137i	−0.996964	−	0.0778674i	$-0.975189\pi$
$181$	−1.94585	+	5.98871i	−0.144634	+	0.445137i	0.852330	+	0.523005i	$0.175189\pi$
$182$	−0.670759	−	3.20442i	−0.0497200	−	0.237527i
$183$	−8.52922	−	8.19336i	−0.630498	−	0.605670i
$184$	19.8292	+	6.64710i	1.46183	+	0.490030i
$185$	6.02650	−	4.80972i	0.443077	−	0.353618i
$186$	2.95094	+	3.52013i	0.216374	+	0.258109i
$187$	−0.00200871	+	0.00145941i	−0.000146892	+	0.000106723i
$188$	9.14500	+	5.35563i	0.666968	+	0.390599i
$189$	4.30350	+	1.87552i	0.313034	+	0.136424i
$190$	12.2555	−	14.8228i	0.889111	−	1.07536i
$191$	−15.1282	+	10.9913i	−1.09464	+	0.795303i	−0.980177	−	0.198124i	$-0.936515\pi$
$191$	−15.1282	+	10.9913i	−1.09464	+	0.795303i	−0.114464	+	0.993427i	$0.536515\pi$
$192$	12.3366	−	6.30930i	0.890321	−	0.455334i
$193$		−	19.5438i		−	1.40679i	−0.710798	−	0.703396i	$-0.751666\pi$
$193$		−	19.5438i		−	1.40679i	0.710798	−	0.703396i	$-0.248334\pi$
$194$	−18.2017	−	1.97007i	−1.30681	−	0.141442i
$195$	8.52936	−	5.07319i	0.610800	−	0.363298i
$196$	−8.21846	−	9.24196i	−0.587033	−	0.660140i
$197$	1.38996	+	4.27787i	0.0990308	+	0.304785i	0.988283	−	0.152631i	$-0.0487747\pi$
$197$	1.38996	+	4.27787i	0.0990308	+	0.304785i	−0.889252	+	0.457417i	$0.848775\pi$
$198$	−0.0204140	−	0.0811286i	−0.00145076	−	0.00576556i
$199$		−	19.0412i		−	1.34979i	−0.737912	−	0.674897i	$-0.764188\pi$
$199$		−	19.0412i		−	1.34979i	0.737912	−	0.674897i	$-0.235812\pi$
$200$	5.44713	+	13.0510i	0.385170	+	0.922846i
$201$	−10.1057	+	20.8588i	−0.712803	+	1.47127i
$202$	−2.30693	+	5.13859i	−0.162315	+	0.361550i
$203$	6.09231	−	1.97951i	0.427597	−	0.138935i
$204$	0.419725	−	0.118737i	0.0293866	−	0.00831329i
$205$	−7.68427	+	6.13278i	−0.536693	+	0.428332i
$206$	0.481827	−	4.45168i	0.0335705	−	0.310163i
$207$	−17.4078	+	13.7485i	−1.20993	+	0.955584i
$208$	8.93913	−	5.01447i	0.619817	−	0.347691i
$209$	−0.0704915	−	0.0970232i	−0.00487600	−	0.00671123i
$210$	−2.43170	+	4.30966i	−0.167803	+	0.297395i
$211$	6.36569	−	8.76162i	0.438232	−	0.603175i	−0.531586	−	0.847004i	$-0.678404\pi$
$211$	6.36569	−	8.76162i	0.438232	−	0.603175i	0.969818	+	0.243829i	$0.0784037\pi$
$212$	−0.237545	+	0.405621i	−0.0163147	+	0.0278581i
$213$	3.55312	+	19.8456i	0.243456	+	1.35980i
$214$	5.00046	−	11.1383i	0.341825	−	0.761399i
$215$	0.723923	+	15.9839i	0.0493712	+	1.09010i
$216$	−1.55673	+	14.6143i	−0.105922	+	0.994374i
$217$	−1.61127	−	0.523532i	−0.109380	−	0.0355397i
$218$	15.4191	−	3.22757i	1.04431	−	0.218599i
$219$	6.47481	−	6.74023i	0.437527	−	0.455462i
$220$	0.0872727	−	0.0126360i	0.00588392	−	0.000851920i
$221$	0.306861	−	0.0997053i	0.0206417	−	0.00670691i
$222$	0.585259	+	8.42615i	0.0392800	+	0.565526i
$223$	14.2795	+	10.3746i	0.956224	+	0.694738i	0.952271	−	0.305254i	$-0.0987415\pi$
$223$	14.2795	+	10.3746i	0.956224	+	0.694738i	0.00395365	+	0.999992i	$0.498742\pi$
$224$	−2.62352	+	4.38588i	−0.175291	+	0.293044i
$225$	−14.7482	−	2.73673i	−0.983215	−	0.182449i
$226$	−3.34706	+	0.700617i	−0.222643	+	0.0466043i
$227$	1.59211	−	2.19135i	0.105672	−	0.145445i	−0.752906	−	0.658128i	$-0.771349\pi$
$227$	1.59211	−	2.19135i	0.105672	−	0.145445i	0.858578	+	0.512683i	$0.171349\pi$
$228$	5.73516	+	20.2732i	0.379820	+	1.34263i
$229$	2.95113	+	9.08265i	0.195016	+	0.600199i	0.999976	+	0.00686958i	$0.00218667\pi$
$229$	2.95113	+	9.08265i	0.195016	+	0.600199i	−0.804960	+	0.593329i	$0.797813\pi$
$230$	−12.5342	−	19.7387i	−0.826483	−	1.30153i
$231$	0.0222517	+	0.0213755i	0.00146406	+	0.00140641i
$232$	11.6368	+	16.3335i	0.763991	+	1.07235i
$233$	7.82413	−	24.0802i	0.512576	−	1.57755i	−0.275074	−	0.961423i	$-0.588702\pi$
$233$	7.82413	−	24.0802i	0.512576	−	1.57755i	0.787650	−	0.616123i	$-0.211298\pi$
$234$	−0.734902	+	10.8464i	−0.0480420	+	0.709052i
$235$	−4.16756	−	11.0916i	−0.271861	−	0.723537i
$236$	29.2003	+	6.39591i	1.90078	+	0.416338i
$237$	−1.05212	+	0.188370i	−0.0683425	+	0.0122359i
$238$	−0.108021	+	0.119225i	−0.00700195	+	0.00772821i
$239$	−2.53026	−	1.83834i	−0.163669	−	0.118912i	0.502936	−	0.864324i	$-0.332253\pi$
$239$	−2.53026	−	1.83834i	−0.163669	−	0.118912i	−0.666605	+	0.745411i	$0.732253\pi$
$240$	−15.1553	−	3.21187i	−0.978272	−	0.207325i
$241$	16.2078	−	11.7757i	1.04404	−	0.758539i	0.0729691	−	0.997334i	$-0.476753\pi$
$241$	16.2078	−	11.7757i	1.04404	−	0.758539i	0.971070	+	0.238795i	$0.0767525\pi$
$242$	−1.67391	+	15.4655i	−0.107603	+	0.994158i
$243$	−12.0721	−	9.86227i	−0.774426	−	0.632665i
$244$	1.34340	+	13.5904i	0.0860023	+	0.870039i
$245$	0.625610	+	13.8132i	0.0399687	+	0.882494i
$246$	−0.746252	−	10.7440i	−0.0475793	−	0.685013i
$247$	4.81589	+	14.8218i	0.306427	+	0.943087i
$248$	0.0492551	−	5.30378i	0.00312770	−	0.336790i
$249$	18.0772	+	8.75809i	1.14559	+	0.555021i
$250$	4.46362	−	15.1683i	0.282304	−	0.959325i
$251$	10.7667			0.679590			0.339795	−	0.940499i	$-0.389642\pi$
$251$	10.7667			0.679590			0.339795	+	0.940499i	$0.389642\pi$
$252$	−2.37171	−	4.87428i	−0.149404	−	0.307051i
$253$	−0.138663	+	0.0450542i	−0.00871764	+	0.00283253i
$254$	−9.20927	−	16.0656i	−0.577841	−	1.00804i
$255$	−0.448058	−	0.192558i	−0.0280585	−	0.0120585i
$256$	−15.5632	−	3.71309i	−0.972699	−	0.232068i
$257$	−10.3946			−0.648396			−0.324198	−	0.945989i	$-0.605094\pi$
$257$	−10.3946			−0.648396			−0.324198	+	0.945989i	$0.605094\pi$
$258$	−14.8598	−	9.29509i	−0.925131	−	0.578687i
$259$	−1.83113	−	2.52033i	−0.113781	−	0.156606i
$260$	−11.2934	−	1.94290i	−0.700388	−	0.120494i
$261$	−21.2542	+	0.854101i	−1.31560	+	0.0528675i
$262$	−17.6896	+	19.5244i	−1.09286	+	1.20622i
$263$	5.84833	+	8.04953i	0.360623	+	0.496355i	0.950322	−	0.311268i	$-0.100754\pi$
$263$	5.84833	+	8.04953i	0.360623	+	0.496355i	−0.589699	+	0.807623i	$0.700754\pi$
$264$	−0.0429235	+	0.0865390i	−0.00264176	+	0.00532611i
$265$	0.491961	−	0.184849i	0.0302209	−	0.0113552i
$266$	−5.75871	−	5.21753i	−0.353089	−	0.319907i
$267$	11.9290	−	12.4180i	0.730042	−	0.759968i
$268$	24.5166	−	10.7341i	1.49759	−	0.655691i
$269$	17.1210	+	5.56295i	1.04389	+	0.339179i	0.780266	−	0.625448i	$-0.215084\pi$
$269$	17.1210	+	5.56295i	1.04389	+	0.339179i	0.263619	+	0.964627i	$0.415084\pi$
$270$	11.6458	−	11.5921i	0.708739	−	0.705471i
$271$	−31.0279	+	10.0816i	−1.88481	+	0.612412i	−0.900819	+	0.434195i	$0.857033\pi$
$271$	−31.0279	+	10.0816i	−1.88481	+	0.612412i	−0.983991	+	0.178217i	$0.942967\pi$
$272$	−0.457559	−	0.210545i	−0.0277436	−	0.0127662i
$273$	−1.89172	−	3.53535i	−0.114492	−	0.213969i
$274$	27.1049	−	5.67368i	1.63747	−	0.342760i
$275$	−0.0846740	−	0.0505031i	−0.00510603	−	0.00304545i
$276$	25.5949	+	0.985102i	1.54063	+	0.0592962i
$277$	8.71863	−	12.0002i	0.523852	−	0.721020i	−0.462326	−	0.886710i	$-0.652985\pi$
$277$	8.71863	−	12.0002i	0.523852	−	0.721020i	0.986178	+	0.165690i	$0.0529851\pi$
$278$	10.6796	−	6.12188i	0.640521	−	0.367166i
$279$	4.68043	+	3.12132i	0.280210	+	0.186869i
$280$	5.36721	−	1.95999i	0.320752	−	0.117132i
$281$	3.16219	+	1.02746i	0.188640	+	0.0612929i	0.401814	−	0.915721i	$-0.368380\pi$
$281$	3.16219	+	1.02746i	0.188640	+	0.0612929i	−0.213173	+	0.977014i	$0.568380\pi$
$282$	12.5926	+	3.14594i	0.749879	+	0.187338i
$283$	−0.507133	+	1.56079i	−0.0301459	+	0.0927796i	−0.964997	−	0.262259i	$-0.915532\pi$
$283$	−0.507133	+	1.56079i	−0.0301459	+	0.0927796i	0.934852	+	0.355039i	$0.115532\pi$
$284$	11.7646	−	20.0887i	0.698102	−	1.19204i
$285$	9.30079	−	21.6417i	0.550931	−	1.28194i
$286$	−0.0292650	+	0.0651864i	−0.00173047	+	0.00385455i
$287$	2.33484	+	3.21362i	0.137821	+	0.189694i
$288$	12.3275	−	11.6634i	0.726402	−	0.687270i
$289$	13.7405	+	9.98303i	0.808262	+	0.587237i
$290$	1.40171	−	22.3782i	0.0823110	−	1.31409i
$291$	−22.0717	+	3.95169i	−1.29387	+	0.231652i
$292$	−10.7399	+	1.06162i	−0.628503	+	0.0621268i
$293$	16.5822			0.968744			0.484372	−	0.874862i	$-0.339048\pi$
$293$	16.5822			0.968744			0.484372	+	0.874862i	$0.339048\pi$
$294$	−12.8417	−	8.03275i	−0.748946	−	0.468480i
$295$	−20.8475	−	26.1216i	−1.21379	−	1.52086i
$296$	5.80577	−	7.83687i	0.337454	−	0.455509i
$297$	−0.0519276	−	0.0883254i	−0.00301314	−	0.00512516i
$298$	−11.6417	+	25.9314i	−0.674386	+	1.50216i
$299$	18.9465			1.09570
$300$	10.8960	+	13.4639i	0.629080	+	0.777341i
$301$	6.46465			0.372616
$302$	3.93530	−	8.76569i	0.226451	−	0.504409i
$303$	−0.942139	+	6.83395i	−0.0541245	+	0.392600i
$304$	10.1696	−	22.1007i	0.583265	−	1.26756i
$305$	8.40660	−	12.7460i	0.481361	−	0.729833i
$306$	0.452439	−	0.284077i	0.0258642	−	0.0162396i
$307$	−21.4016			−1.22146			−0.610728	−	0.791841i	$-0.709123\pi$
$307$	−21.4016			−1.22146			−0.610728	+	0.791841i	$0.709123\pi$
$308$	−0.00350477	−	0.0354559i	−0.000199703	−	0.00202029i
$309$	−0.966481	−	5.39818i	−0.0549812	−	0.307092i
$310$	−3.77870	+	4.57024i	−0.214616	+	0.259572i
$311$	16.3800	+	11.9008i	0.928824	+	0.674830i	0.945705	−	0.325027i	$-0.105373\pi$
$311$	16.3800	+	11.9008i	0.928824	+	0.674830i	−0.0168804	+	0.999858i	$0.505373\pi$
$312$	8.78002	−	8.97166i	0.497071	−	0.507920i
$313$	−15.2080	−	20.9320i	−0.859608	−	1.18315i	−0.981663	−	0.190626i	$-0.938948\pi$
$313$	−15.2080	−	20.9320i	−0.859608	−	1.18315i	0.122054	−	0.992523i	$-0.461052\pi$
$314$	−9.65579	+	21.5078i	−0.544908	+	1.21376i
$315$	−1.37420	+	5.90264i	−0.0774272	+	0.332576i
$316$	1.06501	+	0.623706i	0.0599114	+	0.0350862i
$317$	−3.37828	+	10.3973i	−0.189743	+	0.583969i	−0.999998	−	0.00210901i	$-0.999329\pi$
$317$	−3.37828	+	10.3973i	−0.189743	+	0.583969i	0.810255	+	0.586078i	$0.199329\pi$
$318$	−0.139536	+	0.558537i	−0.00782479	+	0.0313212i
$319$	−0.132969	−	0.0432041i	−0.00744482	−	0.00241897i
$320$	10.8970	+	14.1864i	0.609163	+	0.793045i
$321$	2.04216	−	14.8131i	0.113982	−	0.826789i
$322$	−8.19606	+	4.69823i	−0.456748	+	0.261822i
$323$	0.450153	−	0.619582i	0.0250472	−	0.0344745i
$324$	3.20226	+	17.7129i	0.177903	+	0.984048i
$325$	8.43679	+	9.64189i	0.467989	+	0.534836i
$326$	1.95000	−	0.408181i	0.108001	−	0.0226070i
$327$	17.0115	−	9.10260i	0.940738	−	0.503375i
$328$	−7.40282	+	9.99263i	−0.408752	+	0.551751i
$329$	−4.55297	+	1.47935i	−0.251013	+	0.0815591i
$330$	0.0982250	−	0.0449013i	0.00540711	−	0.00247174i
$331$	−4.95255	−	1.60918i	−0.272217	−	0.0884485i	0.169728	−	0.985491i	$-0.445711\pi$
$331$	−4.95255	−	1.60918i	−0.272217	−	0.0884485i	−0.441944	+	0.897042i	$0.645711\pi$
$332$	−9.30269	−	21.2472i	−0.510551	−	1.16609i
$333$	3.58916	+	9.70215i	0.196685	+	0.531675i
$334$	−0.249434	−	0.225994i	−0.0136484	−	0.0123658i
$335$	−28.8472	−	7.94954i	−1.57609	−	0.434330i
$336$	−1.57341	+	6.05826i	−0.0858367	+	0.330505i
$337$	1.67846	+	2.31020i	0.0914314	+	0.125845i	0.852282	−	0.523082i	$-0.175218\pi$
$337$	1.67846	+	2.31020i	0.0914314	+	0.125845i	−0.760851	+	0.648927i	$0.775218\pi$
$338$	−6.10953	+	6.74323i	−0.332315	+	0.366783i
$339$	−3.69272	+	1.97592i	−0.200561	+	0.107317i
$340$	0.248963	+	0.505104i	0.0135019	+	0.0273931i
$341$	0.0217343	+	0.0299148i	0.00117698	+	0.00161997i
$342$	13.7213	+	21.8534i	0.741961	+	1.18169i
$343$	11.9108			0.643124
$344$	6.07517	+	19.3057i	0.327551	+	1.04089i
$345$	−21.5285	−	18.8841i	−1.15906	−	1.01669i
$346$	1.54773	+	2.70001i	0.0832063	+	0.145153i
$347$	8.19771	−	2.66360i	0.440076	−	0.142989i	−0.0805945	−	0.996747i	$-0.525682\pi$
$347$	8.19771	−	2.66360i	0.440076	−	0.142989i	0.520671	+	0.853757i	$0.325682\pi$
$348$	19.3012	+	15.1908i	1.03465	+	0.814312i
$349$	−33.7741			−1.80789			−0.903944	−	0.427652i	$-0.859341\pi$
$349$	−33.7741			−1.80789			−0.903944	+	0.427652i	$0.859341\pi$
$350$	−6.04060	−	2.07888i	−0.322884	−	0.111121i
$351$	2.87086	+	13.0014i	0.153235	+	0.693961i
$352$	0.102590	−	0.0437862i	0.00546806	−	0.00233381i
$353$	3.85991	+	11.8796i	0.205442	+	0.632287i	0.999695	+	0.0246990i	$0.00786273\pi$
$353$	3.85991	+	11.8796i	0.205442	+	0.632287i	−0.794252	+	0.607588i	$0.792137\pi$
$354$	36.5227	−	2.53677i	1.94116	−	0.134828i
$355$	−24.3647	+	9.15480i	−1.29315	+	0.485887i
$356$	−19.7868	+	1.95590i	−1.04870	+	0.103662i
$357$	−0.0859107	+	0.177324i	−0.00454688	+	0.00938501i
$358$	−1.47098	+	13.5906i	−0.0777435	+	0.718285i
$359$	−16.0992	+	11.6967i	−0.849681	+	0.617329i	−0.925058	−	0.379826i	$-0.875984\pi$
$359$	−16.0992	+	11.6967i	−0.849681	+	0.617329i	0.0753771	+	0.997155i	$0.475984\pi$
$360$	−18.9187	+	1.44319i	−0.997103	+	0.0760631i
$361$	14.5552	+	10.5750i	0.766064	+	0.556578i
$362$	5.97917	−	6.59935i	0.314258	−	0.346854i
$363$	3.35763	+	18.7537i	0.176230	+	0.984313i
$364$	−0.990639	+	4.52272i	−0.0519236	+	0.237055i
$365$	10.0725	+	6.64333i	0.527220	+	0.347728i
$366$	6.25841	+	15.5110i	0.327132	+	0.810771i
$367$	1.36020	−	4.18628i	0.0710021	−	0.218522i	−0.909258	−	0.416232i	$-0.863350\pi$
$367$	1.36020	−	4.18628i	0.0710021	−	0.218522i	0.980261	+	0.197710i	$0.0633504\pi$
$368$	−21.7328	−	20.0611i	−1.13290	−	1.04576i
$369$	−4.57647	−	12.3710i	−0.238242	−	0.644009i
$370$	−10.5610	+	2.71471i	−0.549040	+	0.141131i
$371$	−0.0656155	−	0.201944i	−0.00340659	−	0.0104844i
$372$	−1.76830	−	6.25075i	−0.0916820	−	0.324086i
$373$	−14.4746	+	19.9225i	−0.749465	+	1.03155i	0.248553	+	0.968618i	$0.420045\pi$
$373$	−14.4746	+	19.9225i	−0.749465	+	1.03155i	−0.998018	+	0.0629317i	$0.979955\pi$
$374$	0.00343687		0.000719417i	0.000177716		3.72002e-5i
$375$	0.0236002	−	19.3649i	0.00121871	−	0.999999i
$376$	−8.69650	−	12.2065i	−0.448488	−	0.629502i
$377$	14.6986	+	10.6792i	0.757017	+	0.550005i
$378$	−4.46589	−	4.91236i	−0.229701	−	0.252664i
$379$	10.0824	−	3.27597i	0.517898	−	0.168275i	−0.0383930	−	0.999263i	$-0.512224\pi$
$379$	10.0824	−	3.27597i	0.517898	−	0.168275i	0.556291	+	0.830987i	$0.312224\pi$
$380$	−24.3971	+	12.0252i	−1.25155	+	0.616881i
$381$	−16.3558	−	15.7117i	−0.837932	−	0.804936i
$382$	25.8841	−	5.41815i	1.32435	−	0.277217i
$383$	−11.6263	−	3.77762i	−0.594077	−	0.193027i	−0.00347997	−	0.999994i	$-0.501108\pi$
$383$	−11.6263	−	3.77762i	−0.594077	−	0.193027i	−0.590597	+	0.806967i	$0.701108\pi$
$384$	−19.5707	+	0.994516i	−0.998711	+	0.0507512i
$385$	−0.0219319	+	0.0332528i	−0.00111775	+	0.00169472i
$386$	−11.3199	+	25.2146i	−0.576169	+	1.28339i
$387$	−20.6659	−	5.80847i	−1.05051	−	0.295261i
$388$	22.3421	+	13.0843i	1.13425	+	0.664256i
$389$	−5.49021	+	7.55662i	−0.278365	+	0.383136i	−0.925191	−	0.379501i	$-0.876096\pi$
$389$	−5.49021	+	7.55662i	−0.278365	+	0.383136i	0.646827	+	0.762637i	$0.276096\pi$
$390$	−13.9427	+	1.60495i	−0.706016	+	0.0812696i
$391$	−0.547261	−	0.753241i	−0.0276762	−	0.0380930i
$392$	5.25012	+	16.6838i	0.265171	+	0.842661i
$393$	−14.0688	+	29.0388i	−0.709677	+	1.46481i
$394$	0.684502	−	6.32422i	0.0344847	−	0.318610i
$395$	−0.485345	−	1.29171i	−0.0244204	−	0.0649928i
$396$	−0.0206531	+	0.116493i	−0.00103786	+	0.00585399i
$397$	−22.3012	+	7.24611i	−1.11927	+	0.363672i	−0.809488	−	0.587136i	$-0.800255\pi$
$397$	−22.3012	+	7.24611i	−1.11927	+	0.363672i	−0.309779	+	0.950808i	$0.600255\pi$
$398$	−11.0288	+	24.5662i	−0.552825	+	1.23139i
$399$	−8.56498	−	4.14959i	−0.428786	−	0.207739i
$400$	0.531583	−	19.9929i	0.0265792	−	0.999647i
$401$		−	16.8545i		−	0.841674i	−0.907136	−	0.420837i	$-0.861736\pi$
$401$		−	16.8545i		−	0.841674i	0.907136	−	0.420837i	$-0.138264\pi$
$402$	25.1196	−	21.0579i	1.25285	−	1.05027i
$403$	−1.48486	−	4.56994i	−0.0739662	−	0.227645i
$404$	5.95263	−	5.29341i	0.296155	−	0.263357i
$405$	9.69647	−	17.6346i	0.481821	−	0.876269i
$406$	−9.00662	−	0.974831i	−0.446991	−	0.0483801i
$407$			0.0679935i			0.00337031i
$408$	−0.610286	−	0.0899177i	−0.0302137	−	0.00445159i
$409$	−0.595598	+	0.432727i	−0.0294504	+	0.0213970i	−0.602413	−	0.798184i	$-0.705794\pi$
$409$	−0.595598	+	0.432727i	−0.0294504	+	0.0213970i	0.572963	+	0.819581i	$0.305794\pi$
$410$	13.4661	−	3.46148i	0.665044	−	0.170950i
$411$	29.9041	−	16.0013i	1.47506	−	0.789284i
$412$	−3.20009	+	5.46431i	−0.157657	+	0.269207i
$413$	−10.9243	+	7.93693i	−0.537547	+	0.390551i
$414$	30.4221	−	7.65497i	1.49517	−	0.376221i
$415$	−6.88943	+	25.0003i	−0.338189	+	1.22722i
$416$	−14.4374	+	1.29185i	−0.707850	+	0.0633383i
$417$	10.4444	−	10.8725i	0.511464	−	0.532430i
$418$	0.0347487	+	0.166005i	0.00169961	+	0.00811956i
$419$	−3.53463	+	10.8785i	−0.172678	+	0.531449i	−0.999520	−	0.0309860i	$-0.990135\pi$
$419$	−3.53463	+	10.8785i	−0.172678	+	0.531449i	0.826842	+	0.562435i	$0.190135\pi$
$420$	5.63348	−	4.15170i	0.274886	−	0.202582i
$421$	8.05515	+	24.7912i	0.392584	+	1.20825i	0.930827	+	0.365460i	$0.119088\pi$
$421$	8.05515	+	24.7912i	0.392584	+	1.20825i	−0.538243	+	0.842789i	$0.680912\pi$
$422$	−13.2876	+	7.61684i	−0.646829	+	0.370782i
$423$	15.8839	−	0.638295i	0.772302	−	0.0310349i
$424$	0.541411	−	0.385728i	0.0262932	−	0.0187326i
$425$	0.139632	−	0.613916i	0.00677314	−	0.0297793i
$426$	6.91063	−	27.6620i	0.334821	−	1.34023i
$427$	−4.99085	−	3.62606i	−0.241524	−	0.175477i
$428$	−12.9028	+	11.4739i	−0.623681	+	0.554612i
$429$	−0.0119517	+	0.0866932i	−0.000577032	+	0.00418559i
$430$	8.32406	−	21.0412i	0.401422	−	1.01470i
$431$	−4.88985	+	15.0494i	−0.235536	+	0.724905i	0.761514	+	0.648149i	$0.224456\pi$
$431$	−4.88985	+	15.0494i	−0.235536	+	0.724905i	−0.997050	+	0.0767566i	$0.975544\pi$
$432$	10.4731	−	17.9531i	0.503889	−	0.863768i
$433$	−16.6030	−	5.39465i	−0.797891	−	0.259251i	−0.118430	−	0.992962i	$-0.537786\pi$
$433$	−16.6030	−	5.39465i	−0.797891	−	0.259251i	−0.679461	+	0.733712i	$0.737786\pi$
$434$	1.77556	+	1.60870i	0.0852295	+	0.0772201i
$435$	−6.05772	−	26.7848i	−0.290446	−	1.28423i
$436$	−21.7626	−	4.76678i	−1.04224	−	0.228287i
$437$	36.3824	−	26.4334i	1.74041	−	1.26448i
$438$	−12.2576	+	4.94571i	−0.585688	+	0.236315i
$439$	13.5607	−	18.6647i	0.647217	−	0.890817i	−0.351758	−	0.936091i	$-0.614416\pi$
$439$	13.5607	−	18.6647i	0.647217	−	0.890817i	0.998975	+	0.0452738i	$0.0144160\pi$
$440$	−0.119915	−	0.0342466i	−0.00571671	−	0.00163264i
$441$	−17.8593	−	5.01964i	−0.850445	−	0.239030i
$442$	−0.453651	−	0.0491009i	−0.0215780	−	0.00233549i
$443$			1.64428i			0.0781221i	0.999237	+	0.0390611i	$0.0124367\pi$
$443$			1.64428i			0.0781221i	−0.999237	+	0.0390611i	$0.987563\pi$
$444$	4.12542	−	11.2101i	0.195784	−	0.532007i
$445$	18.5573	+	12.2395i	0.879701	+	0.580206i
$446$	−12.4137	−	21.6558i	−0.587808	−	1.02543i
$447$	−4.75441	+	34.4869i	−0.224876	+	1.63117i
$448$	5.92511	−	4.13892i	0.279935	−	0.195546i
$449$			2.49959i			0.117963i	0.998259	+	0.0589815i	$0.0187853\pi$
$449$			2.49959i			0.117963i	−0.998259	+	0.0589815i	$0.981215\pi$
$450$	17.4425	+	12.0731i	0.822246	+	0.569133i
$451$		−	0.0866971i		−	0.00408241i
$452$	4.72405	+	1.03474i	0.222201	+	0.0486699i
$453$	1.60715	−	11.6577i	0.0755107	−	0.547729i
$454$	−3.32332	+	1.90503i	−0.155971	+	0.0894074i
$455$	4.04587	−	3.22899i	0.189674	−	0.151377i
$456$	4.34313	−	29.4776i	0.203386	−	1.38041i
$457$		−	18.0114i		−	0.842540i	−0.906935	−	0.421270i	$-0.861585\pi$
$457$		−	18.0114i		−	0.842540i	0.906935	−	0.421270i	$-0.138415\pi$
$458$	1.45332	−	13.4274i	0.0679090	−	0.627422i
$459$	0.433961	−	0.489673i	0.0202556	−	0.0228560i
$460$	4.73834	+	32.7261i	0.220926	+	1.52586i
$461$	−5.38319	+	7.40933i	−0.250720	+	0.345087i	−0.915763	−	0.401718i	$-0.868413\pi$
$461$	−5.38319	+	7.40933i	−0.250720	+	0.345087i	0.665043	+	0.746805i	$0.268413\pi$
$462$	−0.0163275	−	0.0404663i	−0.000759622	−	0.00188266i
$463$	24.9238	−	18.1082i	1.15831	−	0.841560i	0.168745	−	0.985660i	$-0.446029\pi$
$463$	24.9238	−	18.1082i	1.15831	−	0.841560i	0.989563	+	0.144099i	$0.0460285\pi$
$464$	−5.55281	−	27.8130i	−0.257783	−	1.29118i
$465$	−2.86768	+	6.67270i	−0.132985	+	0.309439i
$466$	−24.0419	+	26.5355i	−1.11372	+	1.22924i
$467$	−29.8438	−	9.69684i	−1.38101	−	0.448716i	−0.478006	−	0.878356i	$-0.658640\pi$
$467$	−29.8438	−	9.69684i	−1.38101	−	0.448716i	−0.903000	+	0.429640i	$0.858640\pi$
$468$	7.23048	−	13.5680i	0.334229	−	0.627179i
$469$	−3.73592	+	11.4980i	−0.172509	+	0.530927i
$470$	−1.04754	+	16.7239i	−0.0483192	+	0.771414i
$471$	−3.94337	+	28.6039i	−0.181701	+	1.31800i
$472$	−33.9685	−	25.1648i	−1.56353	−	1.15830i
$473$	−0.114148	−	0.0829337i	−0.00524855	−	0.00381329i
$474$	1.46651	+	0.366370i	0.0673590	+	0.0168279i
$475$	29.6529	+	6.74438i	1.36057	+	0.309454i
$476$	0.208420	−	0.0912529i	0.00955294	−	0.00418257i
$477$	0.0283111	+	0.704521i	0.00129628	+	0.0322578i
$478$	2.19966	+	3.83731i	0.100610	+	0.175514i
$479$	−6.50371	−	20.0164i	−0.297162	−	0.914571i	−0.982487	−	0.186333i	$-0.940340\pi$
$479$	−6.50371	−	20.0164i	−0.297162	−	0.914571i	0.685324	−	0.728238i	$-0.259660\pi$
$480$	17.6925	+	12.9219i	0.807547	+	0.589803i
$481$	2.73040	−	8.40329i	0.124495	−	0.383157i
$482$	−27.7313	+	5.80481i	−1.26313	+	0.264402i
$483$	−8.01554	+	8.34411i	−0.364720	+	0.379670i
$484$	11.1174	−	18.9834i	0.505334	−	0.862883i
$485$	−10.1817	−	27.0979i	−0.462329	−	1.23045i
$486$	9.86264	+	19.7162i	0.447379	+	0.894345i
$487$	−0.303633	+	0.220602i	−0.0137589	+	0.00999644i	−0.594643	−	0.803990i	$-0.702707\pi$
$487$	−0.303633	+	0.220602i	−0.0137589	+	0.00999644i	0.580885	+	0.813986i	$0.302707\pi$
$488$	6.13851	−	18.3120i	0.277877	−	0.828945i
$489$	2.15139	−	1.15118i	0.0972890	−	0.0520580i
$490$	7.19360	−	18.1836i	0.324974	−	0.821453i
$491$	−24.7225	+	17.9619i	−1.11571	+	0.810611i	−0.983553	−	0.180618i	$-0.942190\pi$
$491$	−24.7225	+	17.9619i	−1.11571	+	0.810611i	−0.132157	+	0.991229i	$0.542190\pi$
$492$	−5.26024	+	14.2938i	−0.237150	+	0.644412i
$493$		−	0.892824i		−	0.0402108i
$494$	2.37163	−	21.9119i	0.106705	−	0.985862i
$495$	0.0999883	−	0.0865954i	0.00449414	−	0.00389218i
$496$	−3.13554	+	6.81421i	−0.140790	+	0.305967i
$497$	3.24966	+	10.0014i	0.145767	+	0.448625i
$498$	−18.2497	−	21.7698i	−0.817790	−	0.975529i
$499$			17.3077i			0.774800i	0.921912	+	0.387400i	$0.126627\pi$
$499$			17.3077i			0.774800i	−0.921912	+	0.387400i	$0.873373\pi$
$500$	−14.5444	+	16.9841i	−0.650445	+	0.759554i
$501$	−0.370986	−	0.179736i	−0.0165744	−	0.00803003i
$502$	−13.8908	−	6.23619i	−0.619978	−	0.278335i
$503$	16.2862	−	5.29171i	0.726167	−	0.235946i	0.0774719	−	0.996995i	$-0.475315\pi$
$503$	16.2862	−	5.29171i	0.726167	−	0.235946i	0.648695	+	0.761049i	$0.275315\pi$
$504$	0.236664	+	7.66233i	0.0105418	+	0.341307i
$505$	−8.89692	+	0.402948i	−0.395908	+	0.0179309i
$506$	0.204993	+	0.0221874i	0.00911305	+	0.000986350i
$507$	−4.85901	+	10.0293i	−0.215796	+	0.445415i
$508$	2.57613	+	26.0613i	0.114297	+	1.15628i
$509$	−9.86230	−	13.5743i	−0.437139	−	0.601670i	0.532435	−	0.846471i	$-0.321277\pi$
$509$	−9.86230	−	13.5743i	−0.437139	−	0.601670i	−0.969573	+	0.244801i	$0.921277\pi$
$510$	0.466535	+	0.507950i	0.0206585	+	0.0224924i
$511$	2.86550	−	3.94402i	0.126762	−	0.174473i
$512$	17.9284	+	13.8048i	0.792330	+	0.610093i
$513$	23.6518	+	20.9608i	1.04425	+	0.925443i
$514$	13.4107	+	6.02063i	0.591520	+	0.265559i
$515$	6.62744	−	2.49019i	0.292040	−	0.109731i
$516$	13.7877	+	20.5991i	0.606972	+	0.906825i
$517$	0.0993714	+	0.0322877i	0.00437035	+	0.00142001i
$518$	0.902653	+	4.31224i	0.0396603	+	0.189469i
$519$	2.74878	+	2.64054i	0.120658	+	0.115907i
$520$	13.4450	+	9.04791i	0.589602	+	0.396777i
$521$	−3.18214	+	1.03394i	−0.139412	+	0.0452978i	−0.377892	−	0.925850i	$-0.623351\pi$
$521$	−3.18214	+	1.03394i	−0.139412	+	0.0452978i	0.238480	+	0.971147i	$0.423351\pi$
$522$	27.9161	+	11.2087i	1.22185	+	0.490592i
$523$	−18.8424	−	13.6898i	−0.823922	−	0.598614i	0.0939114	−	0.995581i	$-0.470063\pi$
$523$	−18.8424	−	13.6898i	−0.823922	−	0.598614i	−0.917833	+	0.396966i	$0.870063\pi$
$524$	34.1311	−	14.9436i	1.49102	−	0.652815i
$525$	−7.81561	−	0.363519i	−0.341101	−	0.0158653i
$526$	−2.88293	−	13.7726i	−0.125702	−	0.600514i
$527$	−0.138794	+	0.191033i	−0.00604595	+	0.00832153i
$528$	0.105502	−	0.0867877i	0.00459140	−	0.00377695i
$529$	−9.78734	−	30.1223i	−0.425537	−	1.30967i
$530$	−0.741776	−	0.0464628i	−0.0322207	−	0.00201821i
$531$	42.0535	−	15.5571i	1.82497	−	0.675118i
$532$	4.40762	+	10.0670i	0.191095	+	0.436458i
$533$	−3.48147	+	10.7149i	−0.150799	+	0.464112i
$534$	−22.5829	+	9.11182i	−0.977258	+	0.394307i
$535$	19.2848	−	0.873421i	0.833754	−	0.0377613i
$536$	−37.8477	−	0.351484i	−1.63477	−	0.0151818i
$537$	2.95058	+	16.4802i	0.127327	+	0.711171i
$538$	−18.8667	−	17.0937i	−0.813403	−	0.736963i
$539$	−0.0986463	−	0.0716707i	−0.00424900	−	0.00308708i
$540$	−21.7392	+	8.21032i	−0.935504	+	0.353316i
$541$	−18.7572	+	13.6279i	−0.806435	+	0.585909i	−0.912795	−	0.408418i	$-0.866080\pi$
$541$	−18.7572	+	13.6279i	−0.806435	+	0.585909i	0.106360	+	0.994328i	$0.466080\pi$
$542$	45.8703	+	4.96477i	1.97030	+	0.213255i
$543$	4.75534	−	9.81528i	0.204071	−	0.421214i
$544$	0.468376	+	0.536660i	0.0200815	+	0.0230091i
$545$	15.5373	+	19.4680i	0.665547	+	0.833919i
$546$	0.392912	+	5.65687i	0.0168151	+	0.242092i
$547$	9.29791	+	28.6160i	0.397550	+	1.22353i	0.926958	+	0.375166i	$0.122414\pi$
$547$	9.29791	+	28.6160i	0.397550	+	1.22353i	−0.529408	+	0.848367i	$0.677586\pi$
$548$	−38.2559	−	8.37942i	−1.63421	−	0.357951i
$549$	12.6965	+	16.0759i	0.541874	+	0.686103i
$550$	0.0799912	+	0.114201i	0.00341084	+	0.00486955i
$551$	43.1245			1.83716
$552$	−32.4510	−	16.0957i	−1.38121	−	0.685080i
$553$	−0.530229	+	0.172282i	−0.0225476	+	0.00732617i
$554$	−18.1990	+	10.4322i	−0.773203	+	0.443223i
$555$	−11.4781	+	6.82708i	−0.487219	+	0.289794i
$556$	−17.3243	+	1.71248i	−0.734713	+	0.0726255i
$557$	0.414052			0.0175439			0.00877197	−	0.999962i	$-0.497208\pi$
$557$	0.414052			0.0175439			0.00877197	+	0.999962i	$0.497208\pi$
$558$	−4.23062	−	6.73796i	−0.179096	−	0.285240i
$559$	10.7772	+	14.8336i	0.455828	+	0.627393i
$560$	−8.05981	−	0.580031i	−0.340589	−	0.0245108i
$561$	0.00379181	−	0.00202894i	0.000160090	−	8.56621e-5i
$562$	−3.48462	−	3.15715i	−0.146990	−	0.133176i
$563$	9.46697	+	13.0302i	0.398985	+	0.549156i	0.960489	−	0.278318i	$-0.0897769\pi$
$563$	9.46697	+	13.0302i	0.398985	+	0.549156i	−0.561504	+	0.827474i	$0.689777\pi$
$564$	−14.4243	−	11.3525i	−0.607374	−	0.478027i
$565$	−3.37273	−	4.22597i	−0.141892	−	0.177788i
$566$	1.55831	−	1.71994i	0.0655006	−	0.0722945i
$567$	−6.94040	−	4.23604i	−0.291469	−	0.177897i
$568$	−26.8138	+	19.1035i	−1.12508	+	0.801563i
$569$	1.80110	+	0.585212i	0.0755060	+	0.0245334i	0.346526	−	0.938040i	$-0.387361\pi$
$569$	1.80110	+	0.585212i	0.0755060	+	0.0245334i	−0.271020	+	0.962574i	$0.587361\pi$
$570$	−24.5346	+	22.5342i	−1.02764	+	0.943854i
$571$	10.6321	−	3.45456i	0.444938	−	0.144569i	−0.0779750	−	0.996955i	$-0.524845\pi$
$571$	10.6321	−	3.45456i	0.444938	−	0.144569i	0.522913	+	0.852386i	$0.324845\pi$
$572$	0.0755131	−	0.0671504i	0.00315736	−	0.00280770i
$573$	28.5573	−	15.2806i	1.19300	−	0.638357i
$574$	−1.15095	−	5.49845i	−0.0480399	−	0.229501i
$575$	18.9380	−	31.7516i	0.789769	−	1.32413i
$576$	−22.6599	+	7.90745i	−0.944164	+	0.329477i
$577$	1.14715	−	1.57892i	0.0477566	−	0.0657313i	−0.784471	−	0.620166i	$-0.787065\pi$
$577$	1.14715	−	1.57892i	0.0477566	−	0.0657313i	0.832227	+	0.554434i	$0.187065\pi$
$578$	−11.9452	−	20.8383i	−0.496853	−	0.866760i
$579$	−4.62300	+	33.5337i	−0.192125	+	1.39361i
$580$	−14.7701	+	28.0596i	−0.613293	+	1.16511i
$581$	9.96467	+	3.23772i	0.413404	+	0.134323i
$582$	30.7650	+	7.68583i	1.27525	+	0.318588i
$583$	−0.00143210	+	0.00440755i	−5.93116e−5	+	0.000182542i
$584$	14.4711	+	4.85096i	0.598817	+	0.200734i
$585$	−15.8349	+	6.68710i	−0.654693	+	0.276478i
$586$	−21.3937	−	9.60457i	−0.883768	−	0.396761i
$587$	−9.14257	−	12.5837i	−0.377354	−	0.519384i	0.577527	−	0.816372i	$-0.304018\pi$
$587$	−9.14257	−	12.5837i	−0.377354	−	0.519384i	−0.954881	+	0.296988i	$0.904018\pi$
$588$	11.9153	+	17.8016i	0.491378	+	0.734126i
$589$	−9.22713	−	6.70390i	−0.380197	−	0.276229i
$590$	11.7668	+	45.7761i	0.484431	+	1.88457i
$591$	−1.37302	−	7.66885i	−0.0564784	−	0.315454i
$592$	−12.0296	+	6.74807i	−0.494412	+	0.277344i
$593$	23.6667			0.971874			0.485937	−	0.873994i	$-0.338478\pi$
$593$	23.6667			0.971874			0.485937	+	0.873994i	$0.338478\pi$
$594$	0.0158361	+	0.144031i	0.000649763	+	0.00590966i
$595$	−0.245236	−	0.0675805i	−0.0100537	−	0.00277053i
$596$	30.0394	−	26.7127i	1.23046	−	1.09419i
$597$	−4.50411	+	32.6713i	−0.184341	+	1.33715i
$598$	−24.4440	−	10.9740i	−0.999591	−	0.448759i
$599$	−6.90906			−0.282297			−0.141148	−	0.989988i	$-0.545079\pi$
$599$	−6.90906			−0.282297			−0.141148	+	0.989988i	$0.545079\pi$
$600$	−6.25914	−	23.6817i	−0.255528	−	0.966802i
$601$	12.8685			0.524917			0.262459	−	0.964943i	$-0.415467\pi$
$601$	12.8685			0.524917			0.262459	+	0.964943i	$0.415467\pi$
$602$	−8.34045	−	3.74439i	−0.339931	−	0.152610i
$603$	22.2737	−	33.3995i	0.907055	−	1.36013i
$604$	−10.1543	+	9.02980i	−0.413174	+	0.367417i
$605$	−23.0242	+	8.65112i	−0.936068	+	0.351718i
$606$	5.17380	−	8.27121i	0.210171	−	0.335995i
$607$	−23.5971			−0.957779			−0.478889	−	0.877875i	$-0.658961\pi$
$607$	−23.5971			−0.957779			−0.478889	+	0.877875i	$0.658961\pi$
$608$	−25.9213	+	22.6231i	−1.05125	+	0.917489i
$609$	−10.9216	+	1.95538i	−0.442565	+	0.0792360i
$610$	−18.2285	+	11.5752i	−0.738049	+	0.468666i
$611$	−10.9847	−	7.98086i	−0.444394	−	0.322871i
$612$	−0.748260	+	0.104448i	−0.0302466	+	0.00422207i
$613$	−17.5398	−	24.1415i	−0.708427	−	0.975066i	−0.999829	−	0.0184656i	$-0.994122\pi$
$613$	−17.5398	−	24.1415i	−0.708427	−	0.975066i	0.291403	−	0.956601i	$-0.405878\pi$
$614$	27.6115	+	12.3960i	1.11431	+	0.500262i
$615$	14.6355	−	8.70507i	0.590161	−	0.351022i
$616$	−0.0160146	+	0.0477738i	−0.000645249	+	0.00192486i
$617$	6.53889	−	20.1246i	0.263246	−	0.810187i	−0.728847	−	0.684677i	$-0.759943\pi$
$617$	6.53889	−	20.1246i	0.263246	−	0.810187i	0.992092	−	0.125510i	$-0.0400568\pi$
$618$	−1.87976	+	7.52432i	−0.0756149	+	0.302672i
$619$	19.8653	+	6.45463i	0.798455	+	0.259434i	0.679700	−	0.733490i	$-0.262110\pi$
$619$	19.8653	+	6.45463i	0.798455	+	0.259434i	0.118754	+	0.992924i	$0.462110\pi$
$620$	7.52226	−	3.70769i	0.302101	−	0.148904i
$621$	33.1209	−	19.4722i	1.32909	−	0.781391i
$622$	−14.2398	−	24.8413i	−0.570964	−	0.996047i
$623$	5.27930	−	7.26634i	0.211511	−	0.291120i
$624$	−16.5241	+	6.48943i	−0.661494	+	0.259785i
$625$	24.5914	−	4.50129i	0.983657	−	0.180052i
$626$	7.49678	+	35.8143i	0.299632	+	1.43143i
$627$	0.0980004	+	0.183149i	0.00391376	+	0.00731427i
$628$	24.9151	−	22.1559i	0.994219	−	0.884115i
$629$	−0.412949	+	0.134175i	−0.0164654	+	0.00534992i
$630$	5.19180	−	6.81941i	0.206846	−	0.271692i
$631$	34.1089	+	11.0827i	1.35786	+	0.441194i	0.895327	−	0.445410i	$-0.146942\pi$
$631$	34.1089	+	11.0827i	1.35786	+	0.441194i	0.462529	+	0.886604i	$0.346942\pi$
$632$	−1.01278	−	1.42154i	−0.0402861	−	0.0565460i
$633$	−12.9949	+	13.5276i	−0.516502	+	0.537674i
$634$	10.3807	−	11.4574i	0.412271	−	0.455033i
$635$	16.1206	−	24.4419i	0.639728	−	0.969948i
$636$	0.503534	−	0.639782i	0.0199664	−	0.0253690i
$637$	9.31360	+	12.8191i	0.369018	+	0.507910i
$638$	0.146527	+	0.132757i	0.00580105	+	0.00525590i
$639$	−1.40213	−	34.8919i	−0.0554675	−	1.38030i
$640$	−5.84205	−	24.6144i	−0.230927	−	0.972971i
$641$	6.26340	+	8.62083i	0.247390	+	0.340502i	0.914595	−	0.404371i	$-0.132510\pi$
$641$	6.26340	+	8.62083i	0.247390	+	0.340502i	−0.667205	+	0.744874i	$0.732510\pi$
$642$	−11.2146	+	17.9285i	−0.442606	+	0.707582i
$643$	−13.7687			−0.542983			−0.271491	−	0.962441i	$-0.587517\pi$
$643$	−13.7687			−0.542983			−0.271491	+	0.962441i	$0.587517\pi$
$644$	13.2955	−	1.31424i	0.523916	−	0.0517885i
$645$	2.53881	−	27.5968i	0.0999656	−	1.08662i
$646$	−0.939637	+	0.538628i	−0.0369695	+	0.0211920i
$647$	14.0477	−	4.56436i	0.552270	−	0.179444i	−0.0195699	−	0.999808i	$-0.506230\pi$
$647$	14.0477	−	4.56436i	0.552270	−	0.179444i	0.571840	+	0.820365i	$0.306230\pi$
$648$	6.12801	−	24.7072i	0.240731	−	0.970592i
$649$	0.294714			0.0115685
$650$	−5.30015	−	17.3263i	−0.207889	−	0.679592i
$651$	2.64081	+	1.27943i	0.103501	+	0.0501447i
$652$	−2.75224	−	0.602839i	−0.107786	−	0.0236090i
$653$	10.7453	+	33.0705i	0.420494	+	1.29415i	0.907243	+	0.420607i	$0.138183\pi$
$653$	10.7453	+	33.0705i	0.420494	+	1.29415i	−0.486749	+	0.873542i	$0.661817\pi$
$654$	−27.2199	+	1.89062i	−1.06438	+	0.0739292i
$655$	−40.1600	−	11.0670i	−1.56918	−	0.432425i
$656$	15.3387	−	8.60433i	0.598874	−	0.335943i
$657$	−12.7040	+	10.0334i	−0.495630	+	0.391442i
$658$	6.73091	+	0.728520i	0.262398	+	0.0284007i
$659$	−26.5251	+	19.2716i	−1.03327	+	0.750717i	−0.968961	−	0.247213i	$-0.920485\pi$
$659$	−26.5251	+	19.2716i	−1.03327	+	0.750717i	−0.0643116	+	0.997930i	$0.520485\pi$
$660$	−0.152733	+	0.00103716i	−0.00594514	+	4.03713e-5i
$661$	20.7897	+	15.1046i	0.808626	+	0.587501i	0.913432	−	0.406992i	$-0.133422\pi$
$661$	20.7897	+	15.1046i	0.808626	+	0.587501i	−0.104806	+	0.994493i	$0.533422\pi$
$662$	5.45753	+	4.94466i	0.212113	+	0.192180i
$663$	−0.550105	+	0.0984898i	−0.0213643	+	0.00382503i
$664$	−0.304612	+	32.8006i	−0.0118212	+	1.27291i
$665$	3.26422	−	11.8452i	0.126581	−	0.459336i
$666$	0.988971	−	14.5962i	0.0383219	−	0.565592i
$667$	16.2010	−	49.8615i	0.627305	−	1.93064i
$668$	0.190913	+	0.436043i	0.00738664	+	0.0168710i
$669$	−22.0470	−	21.1788i	−0.852385	−	0.818820i
$670$	32.6131	+	26.9648i	1.25996	+	1.04174i
$671$	0.0416070	+	0.128053i	0.00160622	+	0.00494343i
$672$	5.53896	−	6.90480i	0.213670	−	0.266359i
$673$	6.56396	−	9.03451i	0.253022	−	0.348255i	−0.663545	−	0.748137i	$-0.730949\pi$
$673$	6.56396	−	9.03451i	0.253022	−	0.348255i	0.916567	+	0.399882i	$0.130949\pi$
$674$	−0.827394	−	3.95271i	−0.0318700	−	0.152253i
$675$	24.6580	+	8.18438i	0.949086	+	0.315017i
$676$	11.7880	−	5.16116i	0.453385	−	0.198506i
$677$	−23.8114	−	17.3000i	−0.915145	−	0.664891i	0.0271662	−	0.999631i	$-0.491352\pi$
$677$	−23.8114	−	17.3000i	−0.915145	−	0.664891i	−0.942311	+	0.334739i	$0.891352\pi$
$678$	5.90868	−	0.410402i	0.226922	−	0.0157614i
$679$	−11.1233	+	3.61419i	−0.426874	+	0.138700i
$680$	−0.0286423	−	0.795867i	−0.00109838	−	0.0305201i
$681$	−3.25013	+	3.38336i	−0.124545	+	0.129650i
$682$	−0.0107139	−	0.0511836i	−0.000410257	−	0.00195992i
$683$	39.4244	+	12.8098i	1.50853	+	0.490152i	0.942493	−	0.334225i	$-0.108474\pi$
$683$	39.4244	+	12.8098i	1.50853	+	0.490152i	0.566041	+	0.824377i	$0.308474\pi$
$684$	−5.04498	−	36.1418i	−0.192900	−	1.38192i
$685$	27.3128	+	34.2224i	1.04357	+	1.30757i
$686$	−15.3669	−	6.89885i	−0.586710	−	0.263399i
$687$	−2.91516	−	16.2823i	−0.111220	−	0.621208i
$688$	3.34406	−	28.4262i	0.127491	−	1.08374i
$689$	0.353986	−	0.487220i	0.0134858	−	0.0185616i
$690$	16.8374	+	36.8331i	0.640989	+	1.40221i
$691$	−4.37169	−	6.01711i	−0.166307	−	0.228902i	0.717727	−	0.696325i	$-0.245183\pi$
$691$	−4.37169	−	6.01711i	−0.166307	−	0.228902i	−0.884034	+	0.467423i	$0.845183\pi$
$692$	−0.432948	−	4.37990i	−0.0164582	−	0.166499i
$693$	−0.0331237	−	0.0419401i	−0.00125827	−	0.00159317i
$694$	−12.1192	−	1.31172i	−0.460037	−	0.0497921i
$695$	16.2478	+	10.7162i	0.616315	+	0.406490i
$696$	−16.1030	−	30.7780i	−0.610383	−	1.16664i
$697$	0.526543	−	0.171084i	0.0199442	−	0.00648028i
$698$	43.5741	+	19.5623i	1.64930	+	0.740443i
$699$	−19.1209	+	39.4666i	−0.723219	+	1.49276i
$700$	6.58924	+	6.18086i	0.249050	+	0.233615i
$701$		−	4.41207i		−	0.166641i	−0.996523	−	0.0833207i	$-0.973447\pi$
$701$		−	4.41207i		−	0.166641i	0.996523	−	0.0833207i	$-0.0265526\pi$
$702$	3.82663	−	18.4367i	0.144427	−	0.695847i
$703$	−6.48083	−	19.9459i	−0.244429	−	0.752275i
$704$	−0.157719	−	0.00292966i	−0.00594425	−	0.000110416i
$705$	4.52711	+	20.0170i	0.170501	+	0.753885i
$706$	1.90085	−	17.5623i	0.0715396	−	0.660965i
$707$			3.59833i			0.135329i
$708$	−48.5895	−	17.8814i	−1.82611	−	0.672026i
$709$	2.55928	−	1.85943i	0.0961158	−	0.0698322i	−0.538689	−	0.842504i	$-0.681080\pi$
$709$	2.55928	−	1.85943i	0.0961158	−	0.0698322i	0.634805	+	0.772672i	$0.281080\pi$
$710$	36.7370	+	2.30110i	1.37872	+	0.0863589i
$711$	1.84981	−	0.0743345i	0.0693732	−	0.00278776i
$712$	26.6610	+	8.93725i	0.999164	+	0.334938i
$713$	−11.2176	+	8.15009i	−0.420104	+	0.305223i
$714$	0.213547	−	0.179017i	0.00799178	−	0.00669954i
$715$	−0.112863	+	0.00511166i	−0.00422085	+	0.000191165i
$716$	9.76959	−	16.6820i	0.365107	−	0.623437i
$717$	3.90662	+	3.75279i	0.145896	+	0.140150i
$718$	27.5454	−	5.76589i	1.02798	−	0.215181i
$719$	−8.16195	+	25.1199i	−0.304389	+	0.936814i	0.675515	+	0.737346i	$0.263921\pi$
$719$	−8.16195	+	25.1199i	−0.304389	+	0.936814i	−0.979904	+	0.199468i	$0.936079\pi$
$720$	25.2441	+	9.09593i	0.940792	+	0.338985i
$721$	−0.883938	−	2.72048i	−0.0329196	−	0.101316i
$722$	−12.6535	−	22.0739i	−0.470913	−	0.821507i
$723$	−30.5953	+	16.3711i	−1.13785	+	0.608847i
$724$	−11.5365	+	5.05103i	−0.428751	+	0.187720i
$725$	32.5888	−	13.9584i	1.21032	−	0.518402i
$726$	6.53042	−	26.1401i	0.242367	−	0.970148i
$727$	30.2425	+	21.9725i	1.12163	+	0.814914i	0.984456	−	0.175632i	$-0.0561970\pi$
$727$	30.2425	+	21.9725i	1.12163	+	0.814914i	0.137177	+	0.990547i	$0.456197\pi$
$728$	3.89769	−	5.26126i	0.144458	−	0.194995i
$729$	18.3807	+	19.7775i	0.680767	+	0.732500i
$730$	−9.14732	−	14.4051i	−0.338557	−	0.533155i
$731$	0.278431	−	0.856923i	0.0102981	−	0.0316944i
$732$	0.909729	−	23.6366i	0.0336245	−	0.873633i
$733$	15.3496	+	4.98739i	0.566950	+	0.184213i	0.578446	−	0.815721i	$-0.303659\pi$
$733$	15.3496	+	4.98739i	0.566950	+	0.184213i	−0.0114958	+	0.999934i	$0.503659\pi$
$734$	−4.17961	+	4.61313i	−0.154272	+	0.170274i
$735$	2.19402	−	23.8490i	0.0809277	−	0.879684i
$736$	16.4193	+	38.4698i	0.605222	+	1.41802i
$737$	0.213471	−	0.155096i	0.00786331	−	0.00571303i
$738$	−1.26102	+	18.6113i	−0.0464187	+	0.685093i
$739$	−29.9328	+	41.1990i	−1.10110	+	1.51553i	−0.267174	+	0.963648i	$0.586090\pi$
$739$	−29.9328	+	41.1990i	−1.10110	+	1.51553i	−0.833923	+	0.551881i	$0.813910\pi$
$740$	15.1978	+	2.61460i	0.558681	+	0.0961147i
$741$	−4.75718	−	26.5707i	−0.174759	−	0.976099i
$742$	−0.0323130	+	0.298545i	−0.00118625	+	0.0109599i
$743$		−	23.5056i		−	0.862336i	−0.902272	−	0.431168i	$-0.858102\pi$
$743$		−	23.5056i		−	0.862336i	0.902272	−	0.431168i	$-0.141898\pi$
$744$	−1.33910	+	9.08870i	−0.0490938	+	0.333208i
$745$	−44.8974	+	2.03343i	−1.64491	+	0.0744993i
$746$	30.2139	−	17.3195i	1.10621	−	0.634112i
$747$	−28.9455	−	19.3034i	−1.05906	−	0.706275i
$748$	−0.00485081	−	0.00106250i	−0.000177363	−	3.88489e-5i
$749$		−	7.79967i		−	0.284994i
$750$	−11.2468	+	24.9702i	−0.410674	+	0.911782i
$751$			30.7299i			1.12135i	0.828036	+	0.560675i	$0.189458\pi$
$751$			30.7299i			1.12135i	−0.828036	+	0.560675i	$0.810542\pi$
$752$	4.14978	+	20.7854i	0.151327	+	0.757967i
$753$	−18.4738	−	2.54683i	−0.673223	−	0.0928115i
$754$	−12.7781	−	22.2914i	−0.465352	−	0.811806i
$755$	15.1769	−	0.687371i	0.552343	−	0.0250160i
$756$	2.91644	+	8.92442i	0.106070	+	0.324578i
$757$		−	9.04077i		−	0.328592i	−0.986411	−	0.164296i	$-0.947465\pi$
$757$		−	9.04077i		−	0.328592i	0.986411	−	0.164296i	$-0.0525353\pi$
$758$	−14.9054	−	1.61329i	−0.541389	−	0.0585972i
$759$	0.248578	−	0.0445049i	0.00902280	−	0.00161543i
$760$	38.4413	−	1.38346i	1.39441	−	0.0501832i
$761$	−6.35636	+	8.74878i	−0.230418	+	0.317143i	−0.908533	−	0.417812i	$-0.862797\pi$
$761$	−6.35636	+	8.74878i	−0.230418	+	0.317143i	0.678115	+	0.734955i	$0.262797\pi$
$762$	12.0012	+	29.7441i	0.434759	+	1.07751i
$763$	8.14169	−	5.91529i	0.294749	−	0.214148i
$764$	−36.5330	−	8.00203i	−1.32172	−	0.289503i
$765$	0.723238	+	0.436382i	0.0261487	+	0.0157774i
$766$	12.8118	+	11.6078i	0.462909	+	0.419407i
$767$	−36.4236	−	11.8348i	−1.31518	−	0.427328i
$768$	25.8254	+	10.0524i	0.931892	+	0.362735i
$769$	−13.3618	+	41.1234i	−0.481839	+	1.48295i	0.354668	+	0.934992i	$0.384594\pi$
$769$	−13.3618	+	41.1234i	−0.481839	+	1.48295i	−0.836507	+	0.547956i	$0.815406\pi$
$770$	0.0475560	−	0.0301984i	0.00171380	−	0.00108827i
$771$	17.8352	+	2.45879i	0.642320	+	0.0885513i
$772$	29.2091	−	25.9743i	1.05126	−	0.934837i
$773$	−38.2541	−	27.7932i	−1.37590	−	0.999653i	−0.997250	−	0.0741149i	$-0.976387\pi$
$773$	−38.2541	−	27.7932i	−1.37590	−	0.999653i	−0.378655	−	0.925538i	$-0.623613\pi$
$774$	23.2981	+	19.4637i	0.837432	+	0.699610i
$775$	−9.14275	−	2.07947i	−0.328417	−	0.0746967i
$776$	−21.2464	−	29.8216i	−0.762701	−	1.07053i
$777$	2.54572	+	4.75759i	0.0913271	+	0.170678i
$778$	11.4601	−	6.56929i	0.410865	−	0.235520i
$779$	8.26357	+	25.4327i	0.296073	+	0.911220i
$780$	18.9179	+	6.00509i	0.677370	+	0.215017i
$781$	0.0709259	−	0.218288i	0.00253793	−	0.00781094i
$782$	0.269772	+	1.28878i	0.00964702	+	0.0460867i
$783$	36.6705	+	3.56211i	1.31050	+	0.127300i
$784$	2.88992	−	24.5658i	0.103211	−	0.877348i
$785$	−37.2385	+	1.68656i	−1.32910	+	0.0601959i
$786$	34.9705	−	29.3159i	1.24736	−	1.04566i
$787$	17.2169	−	12.5088i	0.613716	−	0.445891i	−0.237005	−	0.971508i	$-0.576166\pi$
$787$	17.2169	−	12.5088i	0.613716	−	0.445891i	0.850721	+	0.525618i	$0.176166\pi$
$788$	−4.54616	+	7.76280i	−0.161950	+	0.276538i
$789$	−8.13061	−	15.1950i	−0.289457	−	0.540955i
$790$	−0.121994	+	1.94763i	−0.00434035	+	0.0692934i
$791$	−1.76734	+	1.28404i	−0.0628392	+	0.0456554i
$792$	0.0941195	−	0.138332i	0.00334439	−	0.00491542i
$793$		−	17.4968i		−	0.621331i
$794$	32.9692	+	3.56842i	1.17003	+	0.126639i
$795$	−0.887843	+	0.200797i	−0.0314885	+	0.00712154i
$796$	28.4579	−	25.3064i	1.00866	−	0.896961i
$797$	−11.8944	−	36.6073i	−0.421323	−	1.29670i	−0.906471	−	0.422267i	$-0.861234\pi$
$797$	−11.8944	−	36.6073i	−0.421323	−	1.29670i	0.485149	−	0.874432i	$-0.338766\pi$
$798$	8.64673	+	10.3146i	0.306091	+	0.365131i
$799$			0.667234i			0.0236050i
$800$	−12.2659	+	25.4862i	−0.433666	+	0.901074i
$801$	−23.4054	+	18.4853i	−0.826990	+	0.653145i
$802$	−9.76228	+	21.7450i	−0.344718	+	0.767844i
$803$	−0.101194	+	0.0328800i	−0.00357106	+	0.00116031i
$804$	−44.6053	+	12.6186i	−1.57311	+	0.445022i
$805$	−12.4694	−	8.22416i	−0.439487	−	0.289863i
$806$	−0.731236	+	6.75600i	−0.0257567	+	0.237970i
$807$	−28.0607	−	13.5949i	−0.987783	−	0.478564i
$808$	−10.7458	+	3.38154i	−0.378038	+	0.118962i
$809$	14.8253	+	20.4052i	0.521229	+	0.717410i	0.985762	−	0.168146i	$-0.0537779\pi$
$809$	14.8253	+	20.4052i	0.521229	+	0.717410i	−0.464533	+	0.885556i	$0.653778\pi$
$810$	−22.7241	+	17.1352i	−0.798444	+	0.602069i
$811$	29.2100	−	40.2041i	1.02570	−	1.41176i	0.117575	−	0.993064i	$-0.462488\pi$
$811$	29.2100	−	40.2041i	1.02570	−	1.41176i	0.908127	−	0.418694i	$-0.137512\pi$
$812$	11.0554	+	6.47441i	0.387967	+	0.227207i
$813$	55.6231	−	9.95867i	1.95079	−	0.349266i
$814$	0.0393824	−	0.0877226i	0.00138035	−	0.00307467i
$815$	1.96496	+	2.46206i	0.0688294	+	0.0862421i
$816$	0.735287	+	0.469492i	0.0257402	+	0.0164355i
$817$	41.3904	+	13.4486i	1.44807	+	0.470505i
$818$	1.01906	−	0.213312i	0.0356305	−	0.00745830i
$819$	2.40957	+	6.51351i	0.0841974	+	0.227600i
$820$	−19.3784	−	3.33383i	−0.676722	−	0.116422i
$821$	−45.0060	+	14.6233i	−1.57072	+	0.510358i	−0.959645	−	0.281213i	$-0.909263\pi$
$821$	−45.0060	+	14.6233i	−1.57072	+	0.510358i	−0.611076	+	0.791572i	$0.709263\pi$
$822$	−47.8492	+	3.32349i	−1.66893	+	0.115920i
$823$	−38.4544	−	27.9387i	−1.34043	−	0.973883i	−0.999428	−	0.0338220i	$-0.989232\pi$
$823$	−38.4544	−	27.9387i	−1.34043	−	0.973883i	−0.341007	−	0.940061i	$-0.610768\pi$
$824$	7.29360	−	5.19632i	0.254085	−	0.181022i
$825$	0.133339	+	0.106684i	0.00464227	+	0.00371425i
$826$	18.6912	−	3.91250i	0.650350	−	0.136133i
$827$	−9.93542	+	13.6749i	−0.345488	+	0.475524i	−0.946034	−	0.324066i	$-0.894950\pi$
$827$	−9.93542	+	13.6749i	−0.345488	+	0.475524i	0.600546	+	0.799590i	$0.294950\pi$
$828$	−43.6833	−	7.74463i	−1.51810	−	0.269145i
$829$	−4.90001	−	15.0807i	−0.170184	−	0.523773i	0.829197	−	0.558957i	$-0.188798\pi$
$829$	−4.90001	−	15.0807i	−0.170184	−	0.523773i	−0.999381	+	0.0351838i	$0.988798\pi$
$830$	23.3689	−	28.2640i	0.811146	−	0.981059i
$831$	−17.7982	+	18.5278i	−0.617413	+	0.642722i
$832$	19.3748	+	6.69555i	0.671699	+	0.232126i
$833$	0.240618	−	0.740547i	0.00833693	−	0.0256584i
$834$	−19.7724	+	7.97784i	−0.684663	+	0.276250i
$835$	0.141387	−	0.513065i	0.00489291	−	0.0177554i
$836$	0.0513201	−	0.234300i	0.00177494	−	0.00810343i
$837$	−7.29246	−	6.46277i	−0.252064	−	0.223386i
$838$	10.8612	−	11.9877i	0.375193	−	0.414109i
$839$	−0.0181263	−	0.0131695i	−0.000625789	−	0.000454663i	0.587472	−	0.809244i	$-0.300123\pi$
$839$	−0.0181263	−	0.0131695i	−0.000625789	−	0.000454663i	−0.588098	+	0.808790i	$0.700123\pi$
$840$	−9.67280	+	2.09340i	−0.333743	+	0.0722293i
$841$	17.2116	−	12.5049i	0.593502	−	0.431204i
$842$	3.96684	−	36.6503i	0.136706	−	1.26305i
$843$	−5.18271	−	2.51093i	−0.178502	−	0.0864812i
$844$	21.5549	−	2.13067i	0.741949	−	0.0733408i
$845$	−13.8702	−	3.82228i	−0.477151	−	0.131490i
$846$	−20.8625	−	8.37660i	−0.717268	−	0.287993i
$847$	3.07087	+	9.45116i	0.105516	+	0.324746i
$848$	−0.921925	+	0.184061i	−0.0316590	+	0.00632067i
$849$	1.23935	−	2.55809i	0.0425344	−	0.0877933i
$850$	−0.535733	+	0.711175i	−0.0183755	+	0.0243931i
$851$	−25.4967			−0.874014
$852$	−24.9379	+	31.6857i	−0.854358	+	1.08553i
$853$	17.4315	−	5.66385i	0.596845	−	0.193927i	0.00501201	−	0.999987i	$-0.498405\pi$
$853$	17.4315	−	5.66385i	0.596845	−	0.193927i	0.591833	+	0.806061i	$0.298405\pi$
$854$	4.33875	+	7.56895i	0.148469	+	0.259004i
$855$	−21.0778	+	34.9333i	−0.720844	+	1.19469i
$856$	23.2925	−	7.32976i	0.796121	−	0.250526i
$857$	−24.3226			−0.830845			−0.415422	−	0.909629i	$-0.636366\pi$
$857$	−24.3226			−0.830845			−0.415422	+	0.909629i	$0.636366\pi$
$858$	0.0656331	−	0.104926i	0.00224068	−	0.00358211i
$859$	−1.21238	−	1.66870i	−0.0413659	−	0.0569352i	0.787833	−	0.615889i	$-0.211203\pi$
$859$	−1.21238	−	1.66870i	−0.0413659	−	0.0569352i	−0.829199	+	0.558954i	$0.811203\pi$
$860$	−22.9266	+	22.3251i	−0.781791	+	0.761281i
$861$	−3.24599	−	6.06630i	−0.110623	−	0.206739i
$862$	15.0255	−	16.5839i	0.511769	−	0.564851i
$863$	−24.4611	−	33.6678i	−0.832664	−	1.14606i	−0.987421	−	0.158111i	$-0.949460\pi$
$863$	−24.4611	−	33.6678i	−0.832664	−	1.14606i	0.154757	−	0.987953i	$-0.450540\pi$
$864$	−23.9106	+	17.0962i	−0.813456	+	0.581626i
$865$	−2.70926	+	4.10775i	−0.0921177	+	0.139668i
$866$	18.2960	+	16.5766i	0.621722	+	0.563296i
$867$	−21.2147	−	20.3794i	−0.720491	−	0.692119i
$868$	−1.35898	−	3.10390i	−0.0461269	−	0.105353i
$869$	0.0115726	+	0.00376016i	0.000392573	+	0.000127555i
$870$	−7.69854	+	38.0654i	−0.261005	+	1.29054i
$871$	−32.6110	+	10.5960i	−1.10498	+	0.359030i
$872$	25.3162	+	18.7550i	0.857316	+	0.635124i
$873$	38.8059	−	1.55942i	1.31338	−	0.0527782i
$874$	−62.2496	+	13.0303i	−2.10563	+	0.440757i
$875$	−1.36727	−	10.0078i	−0.0462222	−	0.338327i
$876$	18.6788	+	0.718914i	0.631099	+	0.0242899i
$877$	−1.99302	+	2.74315i	−0.0672994	+	0.0926296i	−0.841340	−	0.540506i	$-0.818233\pi$
$877$	−1.99302	+	2.74315i	−0.0672994	+	0.0926296i	0.774041	+	0.633136i	$0.218233\pi$
$878$	−28.3062	+	16.2260i	−0.955289	+	0.547601i
$879$	−28.4521	−	3.92246i	−0.959667	−	0.132301i
$880$	0.134873	+	0.113639i	0.00454658	+	0.00383078i
$881$	24.1860	+	7.85851i	0.814847	+	0.264760i	0.686649	−	0.726989i	$-0.259081\pi$
$881$	24.1860	+	7.85851i	0.814847	+	0.264760i	0.128198	+	0.991749i	$0.459081\pi$
$882$	20.1340	+	16.8204i	0.677948	+	0.566374i
$883$	−12.6959	+	39.0741i	−0.427252	+	1.31495i	0.473569	+	0.880757i	$0.342965\pi$
$883$	−12.6959	+	39.0741i	−0.427252	+	1.31495i	−0.900821	+	0.434190i	$0.857035\pi$
$884$	0.556843	+	0.326107i	0.0187287	+	0.0109682i
$885$	29.5916	+	49.7514i	0.994712	+	1.67237i
$886$	0.952382	−	2.12139i	0.0319959	−	0.0712694i
$887$	7.23246	+	9.95463i	0.242842	+	0.334244i	0.912988	−	0.407985i	$-0.133769\pi$
$887$	7.23246	+	9.95463i	0.242842	+	0.334244i	−0.670146	+	0.742229i	$0.733769\pi$
$888$	−11.8154	+	12.0733i	−0.396500	+	0.405155i
$889$	−9.57053	−	6.95340i	−0.320985	−	0.233210i
$890$	−16.8527	−	26.5394i	−0.564905	−	0.889604i
$891$	0.0682055	+	0.163834i	0.00228497	+	0.00548865i
$892$	3.47252	+	35.1296i	0.116269	+	1.17623i
$893$	−32.2282			−1.07848
$894$	26.1091	−	41.7398i	0.873218	−	1.39599i
$895$	−20.2330	+	7.60234i	−0.676314	+	0.254118i
$896$	−10.0416	+	1.90801i	−0.335468	+	0.0637420i
$897$	−32.5088	−	4.48171i	−1.08544	−	0.149640i
$898$	1.44779	−	3.22488i	0.0483132	−	0.107616i
$899$	−13.2964			−0.443460
$900$	−15.5107	−	25.6791i	−0.517024	−	0.855971i
$901$	−0.0295947			−0.000985943
$902$	−0.0502157	+	0.111853i	−0.00167200	+	0.00372431i
$903$	−11.0922	−	1.52919i	−0.369125	−	0.0508882i
$904$	−5.49546	−	4.07119i	−0.182776	−	0.135406i
$905$	13.5743	+	3.74072i	0.451225	+	0.124346i
$906$	−8.82576	+	14.1095i	−0.293216	+	0.468757i
$907$	−56.2150			−1.86659			−0.933294	−	0.359112i	$-0.883080\pi$
$907$	−56.2150			−1.86659			−0.933294	+	0.359112i	$0.883080\pi$
$908$	5.39103	−	0.532897i	0.178908	−	0.0176848i
$909$	3.23309	−	11.5030i	0.107235	−	0.381530i
$910$	−7.09009	+	1.82251i	−0.235034	+	0.0604158i
$911$	−9.76979	−	7.09817i	−0.323688	−	0.235173i	0.414060	−	0.910250i	$-0.364110\pi$
$911$	−9.76979	−	7.09817i	−0.323688	−	0.235173i	−0.737747	+	0.675077i	$0.764110\pi$
$912$	−22.6770	+	35.5152i	−0.750911	+	1.17603i
$913$	−0.134413	−	0.185004i	−0.00444843	−	0.00612274i
$914$	−10.4324	+	23.2377i	−0.345073	+	0.768634i
$915$	−17.4392	+	19.8813i	−0.576524	+	0.657256i
$916$	−9.65229	+	16.4818i	−0.318921	+	0.544573i
$917$	−5.20099	+	16.0070i	−0.171752	+	0.528598i
$918$	−0.843503	+	0.380403i	−0.0278397	+	0.0125552i
$919$	−29.4362	−	9.56441i	−0.971012	−	0.315501i	−0.219787	−	0.975548i	$-0.570536\pi$
$919$	−29.4362	−	9.56441i	−0.971012	−	0.315501i	−0.751224	+	0.660047i	$0.770536\pi$
$920$	12.8420	−	44.9665i	0.423389	−	1.48250i
$921$	36.7214	+	5.06246i	1.21001	+	0.166814i
$922$	11.2367	−	6.44124i	0.370062	−	0.212131i
$923$	−17.5314	+	24.1299i	−0.577054	+	0.794246i
$924$	−0.00237338	+	0.0616651i	−7.80784e−5	+	0.00202863i
$925$	−11.3535	−	12.9753i	−0.373302	−	0.426624i
$926$	−42.6442	+	8.92643i	−1.40138	+	0.293341i
$927$	0.381393	+	9.49093i	0.0125266	+	0.311723i
$928$	−8.94549	+	39.0994i	−0.293650	+	1.28350i
$929$	−28.4310	+	9.23780i	−0.932792	+	0.303082i	−0.735704	−	0.677303i	$-0.763148\pi$
$929$	−28.4310	+	9.23780i	−0.932792	+	0.303082i	−0.197088	+	0.980386i	$0.563148\pi$
$930$	7.56465	−	6.94788i	0.248055	−	0.227830i
$931$	35.7693	+	11.6221i	1.17229	+	0.380901i
$932$	46.3875	−	20.3099i	1.51947	−	0.665272i
$933$	−25.2901	−	24.2942i	−0.827960	−	0.795357i
$934$	32.8868	+	29.7963i	1.07609	+	0.974964i
$935$	0.00346323	+	0.00433937i	0.000113260	+	0.000141913i
$936$	−17.1872	+	13.3169i	−0.561780	+	0.435277i
$937$	−30.9151	−	42.5510i	−1.00995	−	1.39008i	−0.919014	−	0.394226i	$-0.871013\pi$
$937$	−30.9151	−	42.5510i	−1.00995	−	1.39008i	−0.0909402	−	0.995856i	$-0.528987\pi$
$938$	11.4797	−	12.6704i	0.374824	−	0.413702i
$939$	21.1429	+	39.5131i	0.689972	+	1.28946i
$940$	11.0381	−	20.9697i	0.360023	−	0.683957i
$941$	26.3527	+	36.2714i	0.859074	+	1.18241i	0.981790	+	0.189972i	$0.0608396\pi$
$941$	26.3527	+	36.2714i	0.859074	+	1.18241i	−0.122716	+	0.992442i	$0.539160\pi$
$942$	21.6552	−	34.6196i	0.705565	−	1.12797i
$943$	32.5103			1.05868
$944$	29.2492	+	52.1415i	0.951979	+	1.69706i
$945$	3.75412	−	9.80281i	0.122122	−	0.318886i
$946$	0.0992340	+	0.173114i	0.00322638	+	0.00562841i
$947$	−9.48870	+	3.08306i	−0.308341	+	0.100186i	−0.459100	−	0.888384i	$-0.651828\pi$
$947$	−9.48870	+	3.08306i	−0.308341	+	0.100186i	0.150759	+	0.988571i	$0.451828\pi$
$948$	−1.67983	−	1.32209i	−0.0545583	−	0.0429395i
$949$	13.8269			0.448840
$950$	−34.3506	−	25.8766i	−1.11448	−	0.839547i
$951$	8.25595	−	17.0407i	0.267718	−	0.552584i
$952$	−0.321751	−	0.00298803i	−0.0104280	−	9.68426e-5i
$953$	−10.3227	−	31.7700i	−0.334385	−	1.02913i	−0.967024	−	0.254684i	$-0.918029\pi$
$953$	−10.3227	−	31.7700i	−0.334385	−	1.02913i	0.632640	−	0.774446i	$-0.281971\pi$
$954$	0.371539	−	0.925343i	0.0120290	−	0.0299591i
$955$	26.0827	+	32.6812i	0.844015	+	1.05754i
$956$	−0.615315	−	6.22481i	−0.0199007	−	0.201325i
$957$	0.217931	+	0.105584i	0.00704470	+	0.00341304i
$958$	−3.20282	+	29.5914i	−0.103478	+	0.956054i
$959$	14.3121	−	10.3984i	0.462162	−	0.335780i
$960$	−15.3417	−	26.9190i	−0.495150	−	0.868808i
$961$	−22.2346	−	16.1544i	−0.717244	−	0.521108i
$962$	−8.38991	+	9.26014i	−0.270502	+	0.298559i
$963$	−7.00797	+	24.9337i	−0.225829	+	0.803476i
$964$	39.1401	+	8.57308i	1.26062	+	0.276120i
$965$	−43.6565	+	1.97723i	−1.40535	+	0.0636493i
$966$	15.1743	−	6.12258i	0.488226	−	0.196991i
$967$	−3.58857	+	11.0445i	−0.115401	+	0.355167i	−0.992030	−	0.125999i	$-0.959786\pi$
$967$	−3.58857	+	11.0445i	−0.115401	+	0.355167i	0.876630	+	0.481166i	$0.159786\pi$
$968$	−25.3385	+	18.0524i	−0.814412	+	0.580227i
$969$	−0.918941	+	0.956611i	−0.0295206	+	0.0307308i
$970$	−2.55923	+	40.8580i	−0.0821720	+	1.31187i
$971$	10.6117	+	32.6594i	0.340545	+	1.04809i	0.963926	+	0.266171i	$0.0857584\pi$
$971$	10.6117	+	32.6594i	0.340545	+	1.04809i	−0.623381	+	0.781918i	$0.714242\pi$
$972$	−1.30461	−	31.1496i	−0.0418453	−	0.999124i
$973$	4.62228	−	6.36203i	0.148184	−	0.203957i
$974$	0.519510	−	0.108746i	0.0166462	−	0.00348444i
$975$	−12.1953	−	18.5395i	−0.390562	−	0.593738i
$976$	−18.5261	+	20.0699i	−0.593007	+	0.642423i
$977$	30.3194	+	22.0283i	0.970003	+	0.704749i	0.955452	−	0.295146i	$-0.0953681\pi$
$977$	30.3194	+	22.0283i	0.970003	+	0.704749i	0.0145509	+	0.999894i	$0.495368\pi$
$978$	−3.44241	+	0.239101i	−0.110076	+	0.00764560i
$979$	−0.186437	+	0.0605770i	−0.00595854	+	0.00193605i
$980$	−19.8130	+	19.2932i	−0.632904	+	0.616300i
$981$	−31.3419	+	11.5945i	−1.00067	+	0.370182i
$982$	42.2997	−	8.85431i	1.34984	−	0.282553i
$983$	28.5156	+	9.26529i	0.909507	+	0.295517i	0.726156	−	0.687530i	$-0.241305\pi$
$983$	28.5156	+	9.26529i	0.909507	+	0.295517i	0.183352	+	0.983047i	$0.441305\pi$
$984$	15.0656	−	15.3945i	0.480275	−	0.490758i
$985$	9.41518	−	3.53766i	0.299993	−	0.112719i
$986$	−0.517132	+	1.15189i	−0.0164688	+	0.0366836i
$987$	8.16201	−	1.46131i	0.259800	−	0.0465141i
$988$	−15.7513	+	26.8962i	−0.501117	+	0.855682i
$989$	31.0990	−	42.8042i	0.988892	−	1.36109i
$990$	−0.179158	+	0.0538080i	−0.00569401	+	0.00171013i
$991$	−28.0040	−	38.5442i	−0.889576	−	1.22440i	−0.973675	−	0.227939i	$-0.926801\pi$
$991$	−28.0040	−	38.5442i	−0.889576	−	1.22440i	0.0840998	−	0.996457i	$-0.473199\pi$
$992$	7.99221	−	6.97529i	0.253753	−	0.221466i
$993$	8.11704	+	3.93257i	0.257587	+	0.124796i
$994$	1.60033	−	14.7857i	0.0507593	−	0.468973i
$995$	−42.5338	+	1.92638i	−1.34841	+	0.0610705i
$996$	10.9358	+	38.6570i	0.346515	+	1.22489i
$997$	38.2353	−	12.4234i	1.21092	−	0.393453i	0.367155	−	0.930160i	$-0.380332\pi$
$997$	38.2353	−	12.4234i	1.21092	−	0.393453i	0.843769	+	0.536707i	$0.180332\pi$
$998$	10.0248	−	22.3298i	0.317329	−	0.706836i
$999$	−3.86336	−	17.4962i	−0.122231	−	0.553554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.r.a.59.8	✓	224
3.2	odd	2	inner	300.2.r.a.59.49	yes	224
4.3	odd	2	inner	300.2.r.a.59.15	yes	224
12.11	even	2	inner	300.2.r.a.59.42	yes	224
25.14	even	10	inner	300.2.r.a.239.42	yes	224
75.14	odd	10	inner	300.2.r.a.239.15	yes	224
100.39	odd	10	inner	300.2.r.a.239.49	yes	224
300.239	even	10	inner	300.2.r.a.239.8	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.r.a.59.8	✓	224	1.1	even	1	trivial
300.2.r.a.59.15	yes	224	4.3	odd	2	inner
300.2.r.a.59.42	yes	224	12.11	even	2	inner
300.2.r.a.59.49	yes	224	3.2	odd	2	inner
300.2.r.a.239.8	yes	224	300.239	even	10	inner
300.2.r.a.239.15	yes	224	75.14	odd	10	inner
300.2.r.a.239.42	yes	224	25.14	even	10	inner
300.2.r.a.239.49	yes	224	100.39	odd	10	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29016 - 0.579209i) q^{2} +(-1.71582 - 0.236546i) q^{3} +(1.32903 + 1.49455i) q^{4} +(-0.101169 - 2.23378i) q^{5} +(2.07668 + 1.29900i) q^{6} -0.903444 q^{7} +(-0.849014 - 2.69799i) q^{8} +(2.88809 + 0.811741i) q^{9} +O(q^{10})\)	\(q+(-1.29016 - 0.579209i) q^{2} +(-1.71582 - 0.236546i) q^{3} +(1.32903 + 1.49455i) q^{4} +(-0.101169 - 2.23378i) q^{5} +(2.07668 + 1.29900i) q^{6} -0.903444 q^{7} +(-0.849014 - 2.69799i) q^{8} +(2.88809 + 0.811741i) q^{9} +(-1.16330 + 2.94053i) q^{10} +(0.0159524 + 0.0115901i) q^{11} +(-1.92686 - 2.87875i) q^{12} +(-1.50613 - 2.07301i) q^{13} +(1.16559 + 0.523283i) q^{14} +(-0.354802 + 3.85670i) q^{15} +(-0.467337 + 3.97261i) q^{16} +(-0.0389111 + 0.119756i) q^{17} +(-3.25594 - 2.72009i) q^{18} +(-5.78437 - 1.87945i) q^{19} +(3.20403 - 3.11997i) q^{20} +(1.55015 + 0.213706i) q^{21} +(-0.0138681 - 0.0241929i) q^{22} +(-4.34613 + 5.98194i) q^{23} +(0.818558 + 4.83011i) q^{24} +(-4.97953 + 0.451980i) q^{25} +(0.742446 + 3.54689i) q^{26} +(-4.76344 - 2.07597i) q^{27} +(-1.20071 - 1.35024i) q^{28} +(-6.74343 + 2.19107i) q^{29} +(2.69159 - 4.77026i) q^{30} +(1.78347 + 0.579484i) q^{31} +(2.90391 - 4.85462i) q^{32} +(-0.0246299 - 0.0236600i) q^{33} +(0.119566 - 0.131967i) q^{34} +(0.0914009 + 2.01809i) q^{35} +(2.62519 + 5.39522i) q^{36} +(2.02683 + 2.78969i) q^{37} +(6.37417 + 5.77516i) q^{38} +(2.09389 + 3.91319i) q^{39} +(-5.94083 + 2.16946i) q^{40} +(-2.58437 - 3.55708i) q^{41} +(-1.87616 - 1.17358i) q^{42} -7.15556 q^{43} +(0.00387935 + 0.0392452i) q^{44} +(1.52106 - 6.53348i) q^{45} +(9.07201 - 5.20035i) q^{46} +(5.03956 - 1.63745i) q^{47} +(1.74157 - 6.70574i) q^{48} -6.18379 q^{49} +(6.68619 + 2.30106i) q^{50} +(0.0950924 - 0.196276i) q^{51} +(1.09651 - 5.00609i) q^{52} +(0.0726282 + 0.223527i) q^{53} +(4.94319 + 5.43736i) q^{54} +(0.0242758 - 0.0368067i) q^{55} +(0.767037 + 2.43749i) q^{56} +(9.48037 + 4.59308i) q^{57} +(9.96920 + 1.07902i) q^{58} +(12.0918 - 8.78519i) q^{59} +(-6.23556 + 4.59541i) q^{60} +(5.52424 + 4.01360i) q^{61} +(-1.96532 - 1.78063i) q^{62} +(-2.60923 - 0.733363i) q^{63} +(-6.55835 + 4.58127i) q^{64} +(-4.47828 + 3.57409i) q^{65} +(0.0180725 + 0.0447911i) q^{66} +(4.13519 - 12.7268i) q^{67} +(-0.230695 + 0.101006i) q^{68} +(8.87220 - 9.23589i) q^{69} +(1.05098 - 2.65661i) q^{70} +(-3.59697 - 11.0703i) q^{71} +(-0.261957 - 8.48124i) q^{72} +(-3.17175 + 4.36554i) q^{73} +(-0.999124 - 4.77311i) q^{74} +(8.65090 + 0.402370i) q^{75} +(-4.87869 - 11.1429i) q^{76} +(-0.0144121 - 0.0104710i) q^{77} +(-0.434904 - 6.26145i) q^{78} +(0.586897 - 0.190695i) q^{79} +(8.92120 + 0.642022i) q^{80} +(7.68215 + 4.68877i) q^{81} +(1.27396 + 6.08610i) q^{82} +(-11.0296 - 3.58375i) q^{83} +(1.74081 + 2.60079i) q^{84} +(0.271445 + 0.0748032i) q^{85} +(9.23183 + 4.14457i) q^{86} +(12.0888 - 2.16436i) q^{87} +(0.0177262 - 0.0528797i) q^{88} +(-5.84353 + 8.04293i) q^{89} +(-5.74667 + 7.54823i) q^{90} +(1.36071 + 1.87285i) q^{91} +(-14.7164 + 1.45470i) q^{92} +(-2.92304 - 1.41616i) q^{93} +(-7.45028 - 0.806381i) q^{94} +(-3.61308 + 13.1111i) q^{95} +(-6.13093 + 7.64275i) q^{96} +(12.3121 - 4.00046i) q^{97} +(7.97809 + 3.58171i) q^{98} +(0.0366638 + 0.0464225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9}+O(q^{10}) \) 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9	\( 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9} - 5 q^{12} - 20 q^{13} + 6 q^{16} - 24 q^{21} - 10 q^{22} - 28 q^{24} - 20 q^{25} - 50 q^{28} - 25 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 60 q^{37} - 20 q^{40} - 85 q^{42} - 30 q^{45} + 6 q^{46} - 70 q^{48} + 88 q^{49} + 40 q^{52} - 46 q^{54} + 50 q^{58} + 10 q^{60} - 28 q^{61} + 18 q^{64} + 64 q^{66} - 42 q^{69} - 40 q^{70} - 5 q^{72} - 20 q^{73} - 80 q^{76} - 85 q^{78} + 18 q^{81} - 48 q^{84} - 20 q^{85} + 50 q^{88} - 60 q^{90} + 60 q^{94} + 44 q^{96} - 120 q^{97}+O(q^{100}) \) 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9 - 5 * q^12 - 20 * q^13 + 6 * q^16 - 24 * q^21 - 10 * q^22 - 28 * q^24 - 20 * q^25 - 50 * q^28 - 25 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 60 * q^37 - 20 * q^40 - 85 * q^42 - 30 * q^45 + 6 * q^46 - 70 * q^48 + 88 * q^49 + 40 * q^52 - 46 * q^54 + 50 * q^58 + 10 * q^60 - 28 * q^61 + 18 * q^64 + 64 * q^66 - 42 * q^69 - 40 * q^70 - 5 * q^72 - 20 * q^73 - 80 * q^76 - 85 * q^78 + 18 * q^81 - 48 * q^84 - 20 * q^85 + 50 * q^88 - 60 * q^90 + 60 * q^94 + 44 * q^96 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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