LMFDB - Embedded newform 225.2.u.a.79.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(4,225)]

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([10, 3]))

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

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

chi := DirichletCharacter("225.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.u (of order $30$, 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 $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			79.16
Character	$\chi$	$=$	225.79
Dual form			225.2.u.a.94.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.299541 - 0.269708i) q^{2} +(-1.24716 + 1.20191i) q^{3} +(-0.192074 + 1.82747i) q^{4} +(-1.79768 - 1.32979i) q^{5} +(-0.0494088 + 0.696391i) q^{6} +(-4.03987 - 2.33242i) q^{7} +(0.909187 + 1.25139i) q^{8} +(0.110803 - 2.99795i) q^{9} +O(q^{10})$	\(q+(0.299541 - 0.269708i) q^{2} +(-1.24716 + 1.20191i) q^{3} +(-0.192074 + 1.82747i) q^{4} +(-1.79768 - 1.32979i) q^{5} +(-0.0494088 + 0.696391i) q^{6} +(-4.03987 - 2.33242i) q^{7} +(0.909187 + 1.25139i) q^{8} +(0.110803 - 2.99795i) q^{9} +(-0.897134 + 0.0865220i) q^{10} +(1.78814 + 1.98593i) q^{11} +(-1.95691 - 2.51000i) q^{12} +(-3.63309 - 3.27125i) q^{13} +(-1.83918 + 0.390930i) q^{14} +(3.84029 - 0.502201i) q^{15} +(-2.98491 - 0.634462i) q^{16} +(0.388104 + 0.534179i) q^{17} +(-0.775381 - 0.927894i) q^{18} +(-3.29002 + 2.39034i) q^{19} +(2.77544 - 3.02978i) q^{20} +(7.84173 - 1.94669i) q^{21} +(1.07124 + 0.112592i) q^{22} +(0.898733 + 4.22821i) q^{23} +(-2.63796 - 0.467913i) q^{24} +(1.46331 + 4.78108i) q^{25} -1.97054 q^{26} +(3.46510 + 3.87209i) q^{27} +(5.03838 - 6.93474i) q^{28} +(-8.03092 + 3.57559i) q^{29} +(1.01487 - 1.18618i) q^{30} +(1.01176 + 0.450465i) q^{31} +(-3.74436 + 2.16181i) q^{32} +(-4.61701 - 0.327576i) q^{33} +(0.260325 + 0.0553338i) q^{34} +(4.16077 + 9.56514i) q^{35} +(5.45738 + 0.778318i) q^{36} +(-3.15275 + 1.02439i) q^{37} +(-0.340802 + 1.60335i) q^{38} +(8.46281 - 0.286902i) q^{39} +(0.0296563 - 3.45863i) q^{40} +(4.70059 - 5.22054i) q^{41} +(1.82388 - 2.69809i) q^{42} +(-1.95550 - 1.12901i) q^{43} +(-3.97268 + 2.88632i) q^{44} +(-4.18584 + 5.24202i) q^{45} +(1.40959 + 1.02413i) q^{46} +(-0.656473 - 1.47446i) q^{47} +(4.48522 - 2.79633i) q^{48} +(7.38039 + 12.7832i) q^{49} +(1.72782 + 1.03746i) q^{50} +(-1.12606 - 0.199738i) q^{51} +(6.67593 - 6.01104i) q^{52} +(4.22318 - 5.81270i) q^{53} +(2.08227 + 0.225287i) q^{54} +(-0.573634 - 5.94792i) q^{55} +(-0.754235 - 7.17606i) q^{56} +(1.23019 - 6.93545i) q^{57} +(-1.44122 + 3.23704i) q^{58} +(3.58259 - 3.97887i) q^{59} +(0.180135 + 7.11445i) q^{60} +(-6.67168 - 7.40965i) q^{61} +(0.424558 - 0.137947i) q^{62} +(-7.44012 + 11.8529i) q^{63} +(1.34746 - 4.14704i) q^{64} +(2.18106 + 10.7119i) q^{65} +(-1.47133 + 1.14712i) q^{66} +(1.07897 - 2.42340i) q^{67} +(-1.05074 + 0.606644i) q^{68} +(-6.20280 - 4.19304i) q^{69} +(3.82611 + 1.74296i) q^{70} +(8.66423 + 6.29493i) q^{71} +(3.85235 - 2.58704i) q^{72} +(-9.14313 - 2.97078i) q^{73} +(-0.668091 + 1.15717i) q^{74} +(-7.57143 - 4.20398i) q^{75} +(-3.73634 - 6.47152i) q^{76} +(-2.59183 - 12.1936i) q^{77} +(2.45758 - 2.36842i) q^{78} +(-3.11470 + 1.38675i) q^{79} +(4.52221 + 5.10986i) q^{80} +(-8.97545 - 0.664362i) q^{81} -2.83155i q^{82} +(-1.35856 + 0.142791i) q^{83} +(2.05131 + 14.7044i) q^{84} +(0.0126593 - 1.47638i) q^{85} +(-0.890256 + 0.189230i) q^{86} +(5.71826 - 14.1118i) q^{87} +(-0.859418 + 4.04324i) q^{88} +(1.57433 - 4.84528i) q^{89} +(0.159984 + 2.69915i) q^{90} +(7.04730 + 21.6894i) q^{91} +(-7.89953 + 0.830274i) q^{92} +(-1.80325 + 0.654250i) q^{93} +(-0.594314 - 0.264606i) q^{94} +(9.09306 + 0.0779692i) q^{95} +(2.07150 - 7.19652i) q^{96} +(6.03575 + 13.5565i) q^{97} +(5.65846 + 1.83854i) q^{98} +(6.15186 - 5.14071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.299541	−	0.269708i	0.211807	−	0.190712i	−0.556398	−	0.830916i	$-0.687817\pi$
$2$	0.299541	−	0.269708i	0.211807	−	0.190712i	0.768205	+	0.640204i	$0.221150\pi$
$3$	−1.24716	+	1.20191i	−0.720047	+	0.693926i
$3$	−1.24716	+	1.20191i	−0.720047	+	0.693926i
$4$	−0.192074	+	1.82747i	−0.0960372	+	0.913733i
$5$	−1.79768	−	1.32979i	−0.803947	−	0.594700i
$5$	−1.79768	−	1.32979i	−0.803947	−	0.594700i
$6$	−0.0494088	+	0.696391i	−0.0201711	+	0.284300i
$7$	−4.03987	−	2.33242i	−1.52693	−	0.881573i	−0.999488	−	0.0319808i	$-0.989818\pi$
$7$	−4.03987	−	2.33242i	−1.52693	−	0.881573i	−0.527440	−	0.849592i	$-0.676848\pi$
$8$	0.909187	+	1.25139i	0.321446	+	0.442433i
$9$	0.110803	−	2.99795i	0.0369342	−	0.999318i
$10$	−0.897134	+	0.0865220i	−0.283699	+	0.0273607i
$11$	1.78814	+	1.98593i	0.539144	+	0.598781i	0.949741	−	0.313037i	$-0.101346\pi$
$11$	1.78814	+	1.98593i	0.539144	+	0.598781i	−0.410597	+	0.911817i	$0.634680\pi$
$12$	−1.95691	−	2.51000i	−0.564912	−	0.724573i
$13$	−3.63309	−	3.27125i	−1.00764	−	0.907282i	−0.0119401	−	0.999929i	$-0.503801\pi$
$13$	−3.63309	−	3.27125i	−1.00764	−	0.907282i	−0.995699	+	0.0926463i	$0.970467\pi$
$14$	−1.83918	+	0.390930i	−0.491542	+	0.104480i
$15$	3.84029	−	0.502201i	0.991557	−	0.129668i
$16$	−2.98491	−	0.634462i	−0.746227	−	0.158615i
$17$	0.388104	+	0.534179i	0.0941289	+	0.129557i	0.853484	−	0.521119i	$-0.174485\pi$
$17$	0.388104	+	0.534179i	0.0941289	+	0.129557i	−0.759355	+	0.650677i	$0.774485\pi$
$18$	−0.775381	−	0.927894i	−0.182759	−	0.218707i
$19$	−3.29002	+	2.39034i	−0.754782	+	0.548381i	−0.897306	−	0.441410i	$-0.854478\pi$
$19$	−3.29002	+	2.39034i	−0.754782	+	0.548381i	0.142523	+	0.989791i	$0.454478\pi$
$20$	2.77544	−	3.02978i	0.620606	−	0.677480i
$21$	7.84173	−	1.94669i	1.71121	−	0.424802i
$22$	1.07124	+	0.112592i	0.228390	+	0.0240047i
$23$	0.898733	+	4.22821i	0.187399	+	0.881642i	0.966883	+	0.255220i	$0.0821479\pi$
$23$	0.898733	+	4.22821i	0.187399	+	0.881642i	−0.779484	+	0.626422i	$0.784519\pi$
$24$	−2.63796	−	0.467913i	−0.538472	−	0.0955124i
$25$	1.46331	+	4.78108i	0.292663	+	0.956216i
$26$	−1.97054			−0.386455
$27$	3.46510	+	3.87209i	0.666858	+	0.745185i
$28$	5.03838	−	6.93474i	0.952165	−	1.31054i
$29$	−8.03092	+	3.57559i	−1.49130	+	0.663971i	−0.980642	−	0.195810i	$-0.937266\pi$
$29$	−8.03092	+	3.57559i	−1.49130	+	0.663971i	−0.510662	+	0.859782i	$0.670600\pi$
$30$	1.01487	−	1.18618i	0.185290	−	0.216567i
$31$	1.01176	+	0.450465i	0.181718	+	0.0809060i	0.495579	−	0.868563i	$-0.334956\pi$
$31$	1.01176	+	0.450465i	0.181718	+	0.0809060i	−0.313861	+	0.949469i	$0.601623\pi$
$32$	−3.74436	+	2.16181i	−0.661916	+	0.382157i
$33$	−4.61701	−	0.327576i	−0.803718	−	0.0570237i
$34$	0.260325	+	0.0553338i	0.0446454	+	0.00948967i
$35$	4.16077	+	9.56514i	0.703299	+	1.61680i
$36$	5.45738	+	0.778318i	0.909563	+	0.129720i
$37$	−3.15275	+	1.02439i	−0.518308	+	0.168409i	−0.556478	−	0.830863i	$-0.687847\pi$
$37$	−3.15275	+	1.02439i	−0.518308	+	0.168409i	0.0381690	+	0.999271i	$0.487847\pi$
$38$	−0.340802	+	1.60335i	−0.0552854	+	0.260097i
$39$	8.46281	−	0.286902i	1.35513	−	0.0459411i
$40$	0.0296563	−	3.45863i	0.00468907	−	0.546857i
$41$	4.70059	−	5.22054i	0.734109	−	0.815311i	−0.254300	−	0.967125i	$-0.581845\pi$
$41$	4.70059	−	5.22054i	0.734109	−	0.815311i	0.988409	+	0.151814i	$0.0485116\pi$
$42$	1.82388	−	2.69809i	0.281431	−	0.416324i
$43$	−1.95550	−	1.12901i	−0.298211	−	0.172172i	0.343428	−	0.939179i	$-0.388412\pi$
$43$	−1.95550	−	1.12901i	−0.298211	−	0.172172i	−0.641639	+	0.767007i	$0.721745\pi$
$44$	−3.97268	+	2.88632i	−0.598904	+	0.435129i
$45$	−4.18584	+	5.24202i	−0.623988	+	0.781434i
$46$	1.40959	+	1.02413i	0.207832	+	0.150999i
$47$	−0.656473	−	1.47446i	−0.0957564	−	0.215072i	0.859316	−	0.511445i	$-0.170890\pi$
$47$	−0.656473	−	1.47446i	−0.0957564	−	0.215072i	−0.955072	+	0.296373i	$0.904223\pi$
$48$	4.48522	−	2.79633i	0.647386	−	0.403616i
$49$	7.38039	+	12.7832i	1.05434	+	1.82617i
$50$	1.72782	+	1.03746i	0.244350	+	0.146719i
$51$	−1.12606	−	0.199738i	−0.157680	−	0.0279688i
$52$	6.67593	−	6.01104i	0.925785	−	0.833581i
$53$	4.22318	−	5.81270i	0.580098	−	0.798436i	−0.413608	−	0.910455i	$-0.635732\pi$
$53$	4.22318	−	5.81270i	0.580098	−	0.798436i	0.993706	+	0.112019i	$0.0357316\pi$
$54$	2.08227	+	0.225287i	0.283361	+	0.0306577i
$55$	−0.573634	−	5.94792i	−0.0773488	−	0.802017i
$56$	−0.754235	−	7.17606i	−0.100789	−	0.958942i
$57$	1.23019	−	6.93545i	0.162942	−	0.918623i
$58$	−1.44122	+	3.23704i	−0.189242	+	0.425044i
$59$	3.58259	−	3.97887i	0.466414	−	0.518005i	−0.463343	−	0.886179i	$-0.653350\pi$
$59$	3.58259	−	3.97887i	0.466414	−	0.518005i	0.929757	+	0.368174i	$0.120017\pi$
$60$	0.180135	+	7.11445i	0.0232554	+	0.918472i
$61$	−6.67168	−	7.40965i	−0.854221	−	0.948708i	0.144950	−	0.989439i	$-0.453698\pi$
$61$	−6.67168	−	7.40965i	−0.854221	−	0.948708i	−0.999170	+	0.0407310i	$0.987031\pi$
$62$	0.424558	−	0.137947i	0.0539189	−	0.0175193i
$63$	−7.44012	+	11.8529i	−0.937367	+	1.49333i
$64$	1.34746	−	4.14704i	0.168432	−	0.518380i
$65$	2.18106	+	10.7119i	0.270528	+	1.32865i
$66$	−1.47133	+	1.14712i	−0.181109	+	0.141201i
$67$	1.07897	−	2.42340i	0.131817	−	0.296066i	−0.835563	−	0.549394i	$-0.814859\pi$
$67$	1.07897	−	2.42340i	0.131817	−	0.296066i	0.967380	+	0.253328i	$0.0815253\pi$
$68$	−1.05074	+	0.606644i	−0.127421	+	0.0735664i
$69$	−6.20280	−	4.19304i	−0.746730	−	0.504782i
$70$	3.82611	+	1.74296i	0.457308	+	0.208323i
$71$	8.66423	+	6.29493i	1.02826	+	0.747071i	0.967959	−	0.251109i	$-0.0807954\pi$
$71$	8.66423	+	6.29493i	1.02826	+	0.747071i	0.0602966	+	0.998181i	$0.480795\pi$
$72$	3.85235	−	2.58704i	0.454003	−	0.304886i
$73$	−9.14313	−	2.97078i	−1.07012	−	0.347704i	−0.279587	−	0.960120i	$-0.590198\pi$
$73$	−9.14313	−	2.97078i	−1.07012	−	0.347704i	−0.790535	+	0.612416i	$0.790198\pi$
$74$	−0.668091	+	1.15717i	−0.0776640	+	0.134518i
$75$	−7.57143	−	4.20398i	−0.874274	−	0.485434i
$76$	−3.73634	−	6.47152i	−0.428587	−	0.742335i
$77$	−2.59183	−	12.1936i	−0.295367	−	1.38959i
$78$	2.45758	−	2.36842i	0.278266	−	0.268171i
$79$	−3.11470	+	1.38675i	−0.350431	+	0.156022i	−0.574401	−	0.818574i	$-0.694765\pi$
$79$	−3.11470	+	1.38675i	−0.350431	+	0.156022i	0.223970	+	0.974596i	$0.428098\pi$
$80$	4.52221	+	5.10986i	0.505599	+	0.571300i
$81$	−8.97545	−	0.664362i	−0.997272	−	0.0738180i
$82$		−	2.83155i		−	0.312693i
$83$	−1.35856	+	0.142791i	−0.149122	+	0.0156733i	−0.178795	−	0.983886i	$-0.557220\pi$
$83$	−1.35856	+	0.142791i	−0.149122	+	0.0156733i	0.0296735	+	0.999560i	$0.490553\pi$
$84$	2.05131	+	14.7044i	0.223816	+	1.60438i
$85$	0.0126593	−	1.47638i	0.00137310	−	0.160136i
$86$	−0.890256	+	0.189230i	−0.0959987	+	0.0204052i
$87$	5.71826	−	14.1118i	0.613061	−	1.51294i
$88$	−0.859418	+	4.04324i	−0.0916142	+	0.431011i
$89$	1.57433	−	4.84528i	0.166878	−	0.513599i	−0.832291	−	0.554338i	$-0.812971\pi$
$89$	1.57433	−	4.84528i	0.166878	−	0.513599i	0.999170	+	0.0407393i	$0.0129713\pi$
$90$	0.159984	+	2.69915i	0.0168638	+	0.284516i
$91$	7.04730	+	21.6894i	0.738758	+	2.27366i
$92$	−7.89953	+	0.830274i	−0.823583	+	0.0865620i
$93$	−1.80325	+	0.654250i	−0.186988	+	0.0678426i
$94$	−0.594314	−	0.264606i	−0.0612988	−	0.0272920i
$95$	9.09306	+	0.0779692i	0.932928	+	0.00799947i
$96$	2.07150	−	7.19652i	0.211421	−	0.734491i
$97$	6.03575	+	13.5565i	0.612837	+	1.37646i	0.907175	+	0.420754i	$0.138234\pi$
$97$	6.03575	+	13.5565i	0.612837	+	1.37646i	−0.294338	+	0.955702i	$0.595099\pi$
$98$	5.65846	+	1.83854i	0.571591	+	0.185721i
$99$	6.15186	−	5.14071i	0.618285	−	0.516661i
$100$	−9.01833	+	1.75584i	−0.901833	+	0.175584i
$101$	−5.14470	+	8.91088i	−0.511916	+	0.886665i	0.487988	+	0.872850i	$0.337731\pi$
$101$	−5.14470	+	8.91088i	−0.511916	+	0.886665i	−0.999905	+	0.0138151i	$0.995602\pi$
$102$	−0.391173	+	0.243879i	−0.0387319	+	0.0241476i
$103$	−12.4178	−	1.30516i	−1.22356	−	0.128601i	−0.529369	−	0.848392i	$-0.677571\pi$
$103$	−12.4178	−	1.30516i	−1.22356	−	0.128601i	−0.694191	+	0.719791i	$0.744238\pi$
$104$	0.790447	−	7.52060i	0.0775097	−	0.737455i
$105$	−16.6856	−	6.92834i	−1.62835	−	0.676137i
$106$	−0.302718	−	2.88017i	−0.0294025	−	0.279747i
$107$			17.3230i			1.67468i	0.546685	+	0.837338i	$0.315889\pi$
$107$			17.3230i			1.67468i	−0.546685	+	0.837338i	$0.684111\pi$
$108$	−7.74168	+	5.58862i	−0.744944	+	0.537765i
$109$	−0.109625	−	0.337390i	−0.0105001	−	0.0323161i	0.945669	−	0.325130i	$-0.105408\pi$
$109$	−0.109625	−	0.337390i	−0.0105001	−	0.0323161i	−0.956169	+	0.292814i	$0.905408\pi$
$110$	−1.77603	−	1.62693i	−0.169338	−	0.155122i
$111$	2.70074	−	5.06691i	0.256343	−	0.480930i
$112$	10.5788	+	9.52521i	0.999605	+	0.900048i
$113$	−7.94819	−	7.15658i	−0.747703	−	0.673235i	0.204443	−	0.978878i	$-0.434462\pi$
$113$	−7.94819	−	7.15658i	−0.747703	−	0.673235i	−0.952146	+	0.305644i	$0.901128\pi$
$114$	−1.50205	−	2.40924i	−0.140680	−	0.225646i
$115$	4.00699	−	8.79609i	0.373654	−	0.820240i
$116$	−4.99175	−	15.3630i	−0.463472	−	1.42642i
$117$	−10.2096	+	10.5294i	−0.943880	+	0.973442i
$118$		−	2.15809i		−	0.198668i
$119$	−0.321959	−	3.06324i	−0.0295139	−	0.280806i
$120$	4.11999	+	4.34910i	0.376102	+	0.397016i
$121$	0.403337	−	3.83750i	0.0366670	−	0.348863i
$122$	−3.99688	−	0.420089i	−0.361860	−	0.0380331i
$123$	0.412261	+	12.1605i	0.0371724	+	1.09648i
$124$	−1.01754	+	1.76244i	−0.0913782	+	0.158272i
$125$	3.72726	−	10.5408i	0.333376	−	0.942794i
$126$	0.968203	+	5.55709i	0.0862544	+	0.495065i
$127$	3.59630	+	1.16851i	0.319120	+	0.103688i	0.464197	−	0.885732i	$-0.346343\pi$
$127$	3.59630	+	1.16851i	0.319120	+	0.103688i	−0.145077	+	0.989420i	$0.546343\pi$
$128$	−4.23202	−	9.50527i	−0.374061	−	0.840155i
$129$	3.79579	−	0.942294i	0.334201	−	0.0829644i
$130$	3.54241	+	2.62041i	0.310690	+	0.229825i
$131$	4.88186	+	2.17355i	0.426530	+	0.189904i	0.608763	−	0.793352i	$-0.291666\pi$
$131$	4.88186	+	2.17355i	0.426530	+	0.189904i	−0.182233	+	0.983255i	$0.558333\pi$
$132$	1.48544	−	8.37451i	0.129291	−	0.728908i
$133$	18.8665	−	1.98295i	1.63594	−	0.171944i
$134$	−0.330416	−	1.01691i	−0.0285436	−	0.0878480i
$135$	−1.08006	−	11.5686i	−0.0929569	−	0.995670i
$136$	−0.315607	+	0.971337i	−0.0270630	+	0.0832915i
$137$	−1.84446	+	8.67752i	−0.157583	+	0.741370i	0.826396	+	0.563089i	$0.190387\pi$
$137$	−1.84446	+	8.67752i	−0.157583	+	0.741370i	−0.983980	+	0.178281i	$0.942946\pi$
$138$	−2.98889	+	0.416958i	−0.254431	+	0.0354939i
$139$	−9.19131	+	1.95367i	−0.779597	+	0.165708i	−0.580488	−	0.814269i	$-0.697138\pi$
$139$	−9.19131	+	1.95367i	−0.779597	+	0.165708i	−0.199109	+	0.979977i	$0.563805\pi$
$140$	−18.2791	+	5.76645i	−1.54487	+	0.487354i
$141$	2.59090	+	1.04986i	0.218193	+	0.0884143i
$142$	4.29308	−	0.451221i	0.360268	−	0.0378657i
$143$		−	13.0645i		−	1.09251i
$144$	−2.23282	+	8.87832i	−0.186069	+	0.739860i
$145$	19.1918	+	4.25166i	1.59379	+	0.353081i
$146$	−3.53998	+	1.57610i	−0.292971	+	0.130439i
$147$	−24.5688	−	7.07207i	−2.02640	−	0.583295i
$148$	−1.26648	−	5.95830i	−0.104104	−	0.489769i
$149$	−9.05535	−	15.6843i	−0.741843	−	1.28491i	−0.951655	−	0.307168i	$-0.900619\pi$
$149$	−9.05535	−	15.6843i	−0.741843	−	1.28491i	0.209812	−	0.977742i	$-0.432715\pi$
$150$	−3.40180	+	0.782811i	−0.277756	+	0.0639163i
$151$	−0.803549	+	1.39179i	−0.0653919	+	0.113262i	−0.896868	−	0.442299i	$-0.854163\pi$
$151$	−0.803549	+	1.39179i	−0.0653919	+	0.113262i	0.831476	+	0.555561i	$0.187496\pi$
$152$	−5.98249	−	1.94383i	−0.485244	−	0.157665i
$153$	1.64445	−	1.10433i	0.132946	−	0.0892796i
$154$	−4.06507	−	2.95345i	−0.327573	−	0.237995i
$155$	−1.21980	−	2.15522i	−0.0979767	−	0.173112i
$156$	−1.10119	+	15.5206i	−0.0881654	+	1.24264i
$157$	5.96877	−	3.44607i	0.476359	−	0.275026i	−0.242539	−	0.970142i	$-0.577980\pi$
$157$	5.96877	−	3.44607i	0.476359	−	0.275026i	0.718898	+	0.695116i	$0.244647\pi$
$158$	−0.558962	+	1.25545i	−0.0444686	+	0.0998782i
$159$	1.71941	+	12.3253i	0.136358	+	0.977456i
$160$	9.60592	+	1.09297i	0.759415	+	0.0864072i
$161$	6.23119	−	19.1776i	0.491087	−	1.51141i
$162$	−2.86770	+	2.22174i	−0.225308	+	0.174557i
$163$	−9.77187	+	3.17507i	−0.765392	+	0.248691i	−0.665591	−	0.746317i	$-0.731820\pi$
$163$	−9.77187	+	3.17507i	−0.765392	+	0.248691i	−0.0998006	+	0.995007i	$0.531820\pi$
$164$	8.63750	+	9.59291i	0.674475	+	0.749081i
$165$	7.86430	+	6.72853i	0.612235	+	0.523816i
$166$	−0.368433	+	0.409187i	−0.0285960	+	0.0317590i
$167$	−0.286808	+	0.644182i	−0.0221939	+	0.0498483i	−0.924302	−	0.381661i	$-0.875352\pi$
$167$	−0.286808	+	0.644182i	−0.0221939	+	0.0498483i	0.902108	+	0.431509i	$0.142019\pi$
$168$	9.56567	+	8.04316i	0.738007	+	0.620543i
$169$	1.13941	+	10.8408i	0.0876469	+	0.833905i
$170$	−0.394399	−	0.445650i	−0.0302490	−	0.0341798i
$171$	6.80158	+	10.1282i	0.520130	+	0.774521i
$172$	2.43883	−	3.35676i	0.185959	−	0.255951i
$173$	0.283469	−	0.255237i	0.0215518	−	0.0194053i	−0.658284	−	0.752769i	$-0.728718\pi$
$173$	0.283469	−	0.255237i	0.0215518	−	0.0194053i	0.679836	+	0.733364i	$0.262051\pi$
$174$	−2.09321	−	5.76932i	−0.158686	−	0.437371i
$175$	5.23989	−	22.7280i	0.396098	−	1.71808i
$176$	−4.07744	−	7.06233i	−0.307348	−	0.532343i
$177$	0.314208	+	9.26825i	0.0236173	+	0.696644i
$178$	−0.835235	−	1.87597i	−0.0626035	−	0.140610i
$179$	−10.4612	−	7.60049i	−0.781905	−	0.568087i	0.123645	−	0.992326i	$-0.460541\pi$
$179$	−10.4612	−	7.60049i	−0.781905	−	0.568087i	−0.905550	+	0.424240i	$0.860541\pi$
$180$	−8.77562	−	8.65634i	−0.654096	−	0.645205i
$181$	−6.07632	+	4.41471i	−0.451649	+	0.328143i	−0.790247	−	0.612789i	$-0.790048\pi$
$181$	−6.07632	+	4.41471i	−0.451649	+	0.328143i	0.338597	+	0.940931i	$0.390048\pi$
$182$	7.96075	+	4.59614i	0.590090	+	0.340688i
$183$	17.2264	+	1.22221i	1.27341	+	0.0903484i
$184$	−4.47401	+	4.96890i	−0.329829	+	0.366312i
$185$	7.02986	+	2.35097i	0.516845	+	0.172847i
$186$	−0.363690	+	0.682324i	−0.0266670	+	0.0500305i
$187$	−0.366858	+	1.72593i	−0.0268273	+	0.126213i
$188$	2.82062	−	0.916476i	0.205715	−	0.0668409i
$189$	−4.96719	−	23.7248i	−0.361310	−	1.72573i
$190$	2.74477	−	2.42911i	0.199127	−	0.176226i
$191$	−1.09822	−	0.233434i	−0.0794646	−	0.0168907i	0.168008	−	0.985786i	$-0.446267\pi$
$191$	−1.09822	−	0.233434i	−0.0794646	−	0.0168907i	−0.247472	+	0.968895i	$0.579600\pi$
$192$	3.30390	+	6.79154i	0.238439	+	0.490137i
$193$	2.46433	−	1.42278i	0.177386	−	0.102414i	−0.408678	−	0.912679i	$-0.634010\pi$
$193$	2.46433	−	1.42278i	0.177386	−	0.102414i	0.586064	+	0.810265i	$0.300677\pi$
$194$	5.46425	+	2.43284i	0.392310	+	0.174668i
$195$	−15.5949	−	10.7380i	−1.11678	−	0.768964i
$196$	−24.7785	+	11.0321i	−1.76989	+	0.788006i
$197$	−0.907927	+	1.24965i	−0.0646872	+	0.0890342i	−0.840135	−	0.542378i	$-0.817524\pi$
$197$	−0.907927	+	1.24965i	−0.0646872	+	0.0890342i	0.775448	+	0.631412i	$0.217524\pi$
$198$	0.456242	−	3.19906i	0.0324237	−	0.227347i
$199$	12.0990			0.857678			0.428839	−	0.903381i	$-0.358923\pi$
$199$	12.0990			0.857678			0.428839	+	0.903381i	$0.358923\pi$
$200$	−4.65256	+	6.17807i	−0.328986	+	0.436856i
$201$	1.56708	+	4.31919i	0.110533	+	0.304652i
$202$	0.862286	+	4.05674i	0.0606702	+	0.285431i
$203$	40.7837	+	4.28654i	2.86245	+	0.300856i
$204$	0.581302	−	2.01948i	0.0406993	−	0.141392i
$205$	−15.3924	+	3.13406i	−1.07505	+	0.218892i
$206$	−4.07164	+	2.95822i	−0.283685	+	0.206109i
$207$	12.7755	−	2.22586i	0.887962	−	0.154708i
$208$	8.76897	+	12.0695i	0.608019	+	0.836866i
$209$	−10.6301	−	2.25949i	−0.735297	−	0.156292i
$210$	−6.86665	+	2.42492i	−0.473844	+	0.167335i
$211$	−6.46784	+	1.37478i	−0.445264	+	0.0946439i	−0.425087	−	0.905153i	$-0.639756\pi$
$211$	−6.46784	+	1.37478i	−0.445264	+	0.0946439i	−0.0201775	+	0.999796i	$0.506423\pi$
$212$	9.81136	+	8.83419i	0.673847	+	0.606735i
$213$	−18.3716	+	2.56290i	−1.25880	+	0.175607i
$214$	4.67215	+	5.18894i	0.319381	+	0.354709i
$215$	2.01402	+	4.63001i	0.137355	+	0.315764i
$216$	−1.69508	+	7.85664i	−0.115335	+	0.534577i
$217$	−3.03671	−	4.17968i	−0.206146	−	0.283735i
$218$	−0.123834	−	0.0714954i	−0.00838708	−	0.00484228i
$219$	14.9735	−	7.28423i	1.01182	−	0.492223i
$220$	10.9798	+	0.0941473i	0.740259	+	0.00634741i
$221$	0.337417	−	3.21031i	0.0226971	−	0.215949i
$222$	−0.557602	−	2.24616i	−0.0374238	−	0.150752i
$223$	15.1431	−	13.6349i	1.01406	−	0.913063i	0.0178318	−	0.999841i	$-0.494324\pi$
$223$	15.1431	−	13.6349i	1.01406	−	0.913063i	0.996228	+	0.0867777i	$0.0276570\pi$
$224$	20.1690			1.34760
$225$	14.4956	−	3.85719i	0.966373	−	0.257146i
$226$	−4.31100			−0.286763
$227$	−5.89468	+	5.30759i	−0.391243	+	0.352277i	−0.841153	−	0.540797i	$-0.818123\pi$
$227$	−5.89468	+	5.30759i	−0.391243	+	0.352277i	0.449910	+	0.893074i	$0.351456\pi$
$228$	12.4380	+	3.58025i	0.823728	+	0.237108i
$229$	0.0671773	−	0.639150i	0.00443920	−	0.0422362i	−0.992078	−	0.125623i	$-0.959907\pi$
$229$	0.0671773	−	0.639150i	0.00443920	−	0.0422362i	0.996517	+	0.0833868i	$0.0265737\pi$
$230$	−1.17212	−	3.71551i	−0.0772871	−	0.244993i
$231$	17.8881	+	12.0922i	1.17695	+	0.795607i
$232$	−11.7761	−	6.79892i	−0.773137	−	0.446371i
$233$	14.5616	+	20.0423i	0.953960	+	1.31301i	0.949746	+	0.313022i	$0.101341\pi$
$233$	14.5616	+	20.0423i	0.953960	+	1.31301i	0.00421421	+	0.999991i	$0.498659\pi$
$234$	−0.218341	+	5.90760i	−0.0142734	+	0.386192i
$235$	−0.780597	+	3.52358i	−0.0509205	+	0.229853i
$236$	6.58313	+	7.31131i	0.428525	+	0.475925i
$237$	2.21776	−	5.47311i	0.144059	−	0.355517i
$238$	−0.922619	−	0.830730i	−0.0598045	−	0.0538482i
$239$	4.70676	−	1.00045i	0.304455	−	0.0647139i	−0.0531508	−	0.998586i	$-0.516926\pi$
$239$	4.70676	−	1.00045i	0.304455	−	0.0647139i	0.357606	+	0.933873i	$0.383593\pi$
$240$	−11.7815	−	0.937490i	−0.760494	−	0.0605147i
$241$	−9.29500	−	1.97571i	−0.598743	−	0.127267i	−0.101437	−	0.994842i	$-0.532344\pi$
$241$	−9.29500	−	1.97571i	−0.598743	−	0.127267i	−0.497306	+	0.867575i	$0.665677\pi$
$242$	−0.914187	−	1.25827i	−0.0587662	−	0.0808847i
$243$	11.9923	−	9.95915i	0.769306	−	0.638880i
$244$	14.8223	−	10.7691i	0.948903	−	0.689419i
$245$	3.73140	−	32.7945i	0.238391	−	2.09516i
$246$	3.40328	+	3.53139i	0.216985	+	0.225153i
$247$	19.7724	+	2.07816i	1.25808	+	0.132230i
$248$	0.356174	+	1.67567i	0.0226170	+	0.106405i
$249$	1.52272	−	1.81096i	0.0964984	−	0.114765i
$250$	−1.72646	−	4.16266i	−0.109191	−	0.263270i
$251$	7.03498			0.444044			0.222022	−	0.975042i	$-0.428734\pi$
$251$	7.03498			0.444044			0.222022	+	0.975042i	$0.428734\pi$
$252$	−20.2317	−	15.8732i	−1.27448	−	0.999919i
$253$	−6.78986	+	9.34544i	−0.426875	+	0.587543i
$254$	1.39239	−	0.619933i	0.0873665	−	0.0388981i
$255$	1.75869	+	1.85649i	0.110134	+	0.116258i
$256$	4.13565	+	1.84131i	0.258478	+	0.115082i
$257$	7.02533	−	4.05608i	0.438228	−	0.253011i	−0.264618	−	0.964353i	$-0.585246\pi$
$257$	7.02533	−	4.05608i	0.438228	−	0.253011i	0.702846	+	0.711342i	$0.251912\pi$
$258$	0.882851	−	1.30601i	0.0549639	−	0.0813087i
$259$	15.1260	+	3.21513i	0.939885	+	0.199779i
$260$	−19.9946	+	1.92834i	−1.24001	+	0.119590i
$261$	9.82962	+	24.4725i	0.608438	+	1.51481i
$262$	2.04854	−	0.665611i	0.126559	−	0.0411216i
$263$	−1.25210	+	5.89069i	−0.0772080	+	0.363235i	−0.999743	−	0.0226787i	$-0.992781\pi$
$263$	−1.25210	+	5.89069i	−0.0772080	+	0.363235i	0.922535	+	0.385914i	$0.126114\pi$
$264$	−3.78780	−	6.07551i	−0.233123	−	0.373921i
$265$	−15.3216	+	4.83345i	−0.941199	+	0.296916i
$266$	5.11648	−	5.68243i	0.313712	−	0.348412i
$267$	3.86018	+	7.93504i	0.236239	+	0.485617i
$268$	4.22145	+	2.43725i	0.257866	+	0.148879i
$269$	−24.6282	+	17.8934i	−1.50161	+	1.09098i	−0.531872	+	0.846825i	$0.678511\pi$
$269$	−24.6282	+	17.8934i	−1.50161	+	1.09098i	−0.969736	+	0.244157i	$0.921489\pi$
$270$	−3.44368	−	3.17398i	−0.209575	−	0.193162i
$271$	−6.18082	−	4.49063i	−0.375458	−	0.272786i	0.384012	−	0.923328i	$-0.374542\pi$
$271$	−6.18082	−	4.49063i	−0.375458	−	0.272786i	−0.759471	+	0.650542i	$0.774542\pi$
$272$	−0.819538	−	1.84071i	−0.0496918	−	0.111610i
$273$	−34.8579	−	18.5798i	−2.10969	−	1.12450i
$274$	1.78790	+	3.09674i	0.108011	+	0.187081i
$275$	−6.87828	+	11.4553i	−0.414776	+	0.690779i
$276$	8.85404	−	10.5300i	0.532950	−	0.633834i
$277$	−16.6810	+	15.0196i	−1.00226	+	0.902442i	−0.995232	−	0.0975334i	$-0.968905\pi$
$277$	−16.6810	+	15.0196i	−1.00226	+	0.902442i	−0.00703103	+	0.999975i	$0.502238\pi$
$278$	−2.22625	+	3.06417i	−0.133522	+	0.183777i
$279$	1.46258	−	2.98330i	0.0875624	−	0.178606i
$280$	−8.18679	+	13.9032i	−0.489254	+	0.830878i
$281$	−2.93992	−	27.9714i	−0.175381	−	1.66864i	−0.628973	−	0.777427i	$-0.716525\pi$
$281$	−2.93992	−	27.9714i	−0.175381	−	1.66864i	0.453593	−	0.891209i	$-0.350142\pi$
$282$	1.05924	−	0.384310i	0.0630767	−	0.0228853i
$283$	−7.75514	+	17.4183i	−0.460995	+	1.03541i	0.522195	+	0.852826i	$0.325113\pi$
$283$	−7.75514	+	17.4183i	−0.460995	+	1.03541i	−0.983190	+	0.182586i	$0.941553\pi$
$284$	−13.1680	+	14.6245i	−0.781375	+	0.867805i
$285$	−11.4342	+	10.8318i	−0.677303	+	0.641623i
$286$	−3.52361	−	3.91336i	−0.208355	−	0.231402i
$287$	−31.1663	+	10.1265i	−1.83969	+	0.597751i
$288$	6.06611	+	11.4650i	0.357449	+	0.675579i
$289$	5.11857	−	15.7533i	0.301092	−	0.926666i
$290$	6.89544	−	3.90264i	0.404914	−	0.229171i
$291$	−23.8213	−	9.65265i	−1.39643	−	0.565848i
$292$	7.18517	−	16.1382i	0.420480	−	0.944414i
$293$	−23.3812	+	13.4992i	−1.36595	+	0.788629i	−0.990407	−	0.138178i	$-0.955875\pi$
$293$	−23.3812	+	13.4992i	−1.36595	+	0.788629i	−0.375538	+	0.926807i	$0.622542\pi$
$294$	−9.26676	+	4.50803i	−0.540449	+	0.262914i
$295$	−11.7314	+	2.38864i	−0.683030	+	0.139072i
$296$	−4.14835	−	3.01395i	−0.241118	−	0.175182i
$297$	−1.49364	+	13.8053i	−0.0866695	+	0.801064i
$298$	−6.94263	−	2.25580i	−0.402176	−	0.130675i
$299$	10.5663	−	18.3015i	0.611068	−	1.05840i
$300$	9.13691	−	13.0291i	0.527520	−	0.752233i
$301$	5.26666	+	9.12211i	0.303565	+	0.525790i
$302$	0.134680	+	0.633620i	0.00774997	+	0.0364608i
$303$	−4.29387	−	17.2968i	−0.246676	−	0.993672i
$304$	11.3370	−	5.04755i	0.650221	−	0.289497i
$305$	2.14027	+	22.1921i	0.122551	+	1.27072i
$306$	0.194733	−	0.774311i	0.0111321	−	0.0442644i
$307$			28.7446i			1.64054i	0.571975	+	0.820271i	$0.306177\pi$
$307$			28.7446i			1.64054i	−0.571975	+	0.820271i	$0.693823\pi$
$308$	22.7812	−	2.39440i	1.29808	−	0.136434i
$309$	17.0556	−	13.2974i	0.970260	−	0.756461i
$310$	−0.946661	−	0.316588i	−0.0537667	−	0.0179810i
$311$	−20.3634	+	4.32838i	−1.15470	+	0.245440i	−0.745182	−	0.666861i	$-0.767637\pi$
$311$	−20.3634	+	4.32838i	−1.15470	+	0.245440i	−0.409521	+	0.912301i	$0.634304\pi$
$312$	8.05330	+	10.3294i	0.455929	+	0.584788i
$313$	5.22914	−	24.6012i	0.295568	−	1.39054i	−0.540236	−	0.841513i	$-0.681665\pi$
$313$	5.22914	−	24.6012i	0.295568	−	1.39054i	0.835805	−	0.549027i	$-0.185002\pi$
$314$	0.858458	−	2.64206i	0.0484456	−	0.149100i
$315$	29.1369	−	11.4140i	1.64168	−	0.643104i
$316$	−1.93599	−	5.95838i	−0.108908	−	0.335185i
$317$	23.8105	−	2.50258i	1.33733	−	0.140559i	0.591290	−	0.806459i	$-0.298619\pi$
$317$	23.8105	−	2.50258i	1.33733	−	0.140559i	0.746041	+	0.665900i	$0.231952\pi$
$318$	3.83925	+	3.22818i	0.215294	+	0.181027i
$319$	−21.4613	−	9.55518i	−1.20160	−	0.534987i
$320$	−7.93699	+	5.66323i	−0.443691	+	0.316584i
$321$	−20.8208	−	21.6045i	−1.16210	−	1.20585i
$322$	−3.30586	−	7.42509i	−0.184229	−	0.413784i
$323$	−2.55374	−	0.829759i	−0.142094	−	0.0461690i
$324$	2.93805	−	16.2747i	0.163225	−	0.904151i
$325$	10.3238	−	22.1570i	0.572659	−	1.22905i
$326$	−2.07073	+	3.58661i	−0.114687	+	0.198644i
$327$	0.542233	+	0.289019i	0.0299855	+	0.0159828i
$328$	10.8066	+	1.13582i	0.596697	+	0.0627154i
$329$	−0.787001	+	7.48781i	−0.0433888	+	0.412816i
$330$	4.17042	−	0.105593i	0.229574	−	0.00581272i
$331$	−0.998767	−	9.50263i	−0.0548972	−	0.522312i	−0.987069	−	0.160296i	$-0.948755\pi$
$331$	−0.998767	−	9.50263i	−0.0548972	−	0.522312i	0.932172	−	0.362016i	$-0.117911\pi$
$332$		−	2.51015i		−	0.137763i
$333$	2.72174	+	9.56529i	0.149150	+	0.524175i
$334$	0.0878301	+	0.270313i	0.00480585	+	0.0147909i
$335$	−5.16226	+	2.92170i	−0.282044	+	0.159630i
$336$	−24.6419	+	0.835400i	−1.34433	+	0.0455748i
$337$	−10.3602	−	9.32841i	−0.564359	−	0.508151i	0.336837	−	0.941563i	$-0.390643\pi$
$337$	−10.3602	−	9.32841i	−0.564359	−	0.508151i	−0.901196	+	0.433412i	$0.857309\pi$
$338$	3.26514	+	2.93994i	0.177600	+	0.159912i
$339$	18.5142	−	0.627662i	1.00556	−	0.0340899i
$340$	2.69560	+	0.306709i	0.146190	+	0.0166336i
$341$	0.914579	+	2.81478i	0.0495272	+	0.152429i
$342$	4.76900	+	1.19936i	0.257878	+	0.0648542i
$343$		−	36.2028i		−	1.95477i
$344$	−0.365088	−	3.47358i	−0.0196842	−	0.187283i
$345$	5.57480	+	15.7862i	0.300137	+	0.849899i
$346$	0.0160712	−	0.152908i	0.000863996	−	0.00822037i
$347$	−3.92771	−	0.412818i	−0.210850	−	0.0221613i	−0.00148564	−	0.999999i	$-0.500473\pi$
$347$	−3.92771	−	0.412818i	−0.210850	−	0.0221613i	−0.209365	+	0.977838i	$0.567140\pi$
$348$	24.6905	+	13.1604i	1.32355	+	0.705474i
$349$	−9.65976	+	16.7312i	−0.517075	+	0.895600i	0.482728	+	0.875770i	$0.339646\pi$
$349$	−9.65976	+	16.7312i	−0.517075	+	0.895600i	−0.999803	+	0.0198299i	$0.993688\pi$
$350$	−4.56036	−	8.22121i	−0.243762	−	0.439442i
$351$	0.0775817	−	25.4029i	0.00414100	−	1.35591i
$352$	−10.9886	−	3.57043i	−0.585697	−	0.190304i
$353$	−1.15180	−	2.58699i	−0.0613042	−	0.137691i	0.880296	−	0.474426i	$-0.157344\pi$
$353$	−1.15180	−	2.58699i	−0.0613042	−	0.137691i	−0.941600	+	0.336734i	$0.890678\pi$
$354$	2.59384	+	2.69147i	0.137861	+	0.143050i
$355$	−7.20459	−	22.8379i	−0.382380	−	1.21211i
$356$	8.55221	+	3.80769i	0.453266	+	0.201807i
$357$	4.08328	+	3.43337i	0.216110	+	0.181713i
$358$	−5.18346	+	0.544803i	−0.273954	+	0.0287938i
$359$	−2.23700	−	6.88478i	−0.118064	−	0.363365i	0.874509	−	0.485008i	$-0.161183\pi$
$359$	−2.23700	−	6.88478i	−0.118064	−	0.363365i	−0.992574	+	0.121644i	$0.961183\pi$
$360$	−10.3655	−	0.472133i	−0.546311	−	0.0248836i
$361$	−0.760815	+	2.34155i	−0.0400429	+	0.123239i
$362$	−0.629426	+	2.96122i	−0.0330819	+	0.155638i
$363$	4.10932	+	5.27074i	0.215683	+	0.276642i
$364$	−40.9902	+	8.71273i	−2.14847	+	0.456671i
$365$	12.4859	+	17.4990i	0.653543	+	0.915938i
$366$	5.48965	−	4.27999i	0.286949	−	0.223719i
$367$	0.706596	−	0.0742663i	0.0368840	−	0.00387667i	−0.0860685	−	0.996289i	$-0.527430\pi$
$367$	0.706596	−	0.0742663i	0.0368840	−	0.00387667i	0.122953	+	0.992413i	$0.460764\pi$
$368$		−	13.1910i		−	0.687629i
$369$	−15.1301	−	14.6706i	−0.787641	−	0.763721i
$370$	2.73980	−	1.19180i	0.142436	−	0.0619586i
$371$	−30.6188	+	13.6324i	−1.58965	+	0.707757i
$372$	−0.849262	−	3.42104i	−0.0440322	−	0.177373i
$373$	4.21391	+	19.8249i	0.218188	+	1.02649i	0.941771	+	0.336256i	$0.109161\pi$
$373$	4.21391	+	19.8249i	0.218188	+	1.02649i	−0.723583	+	0.690238i	$0.757506\pi$
$374$	0.355608	+	0.615932i	0.0183881	+	0.0318491i
$375$	8.02061	+	17.6258i	0.414183	+	0.910194i
$376$	1.24827	−	2.16207i	0.0643746	−	0.111500i
$377$	40.8738	+	13.2807i	2.10511	+	0.683990i
$378$	−7.88665	−	5.76687i	−0.405646	−	0.296616i
$379$	−14.6035	−	10.6101i	−0.750134	−	0.545004i	0.145735	−	0.989324i	$-0.453445\pi$
$379$	−14.6035	−	10.6101i	−0.750134	−	0.545004i	−0.895868	+	0.444320i	$0.853445\pi$
$380$	−1.88903	+	16.6023i	−0.0969052	+	0.851679i
$381$	−5.88959	+	2.86513i	−0.301733	+	0.146785i
$382$	−0.391922	+	0.226276i	−0.0200524	+	0.0115773i
$383$	1.64122	−	3.68625i	0.0838626	−	0.188358i	−0.866747	−	0.498749i	$-0.833793\pi$
$383$	1.64122	−	3.68625i	0.0838626	−	0.188358i	0.950609	+	0.310390i	$0.100460\pi$
$384$	16.7025	+	6.76804i	0.852346	+	0.345380i
$385$	−11.5557	+	25.3668i	−0.588931	+	1.29281i
$386$	0.354432	−	1.09083i	0.0180401	−	0.0555217i
$387$	−3.60139	+	5.73741i	−0.183069	+	0.291649i
$388$	−25.9334	+	8.42627i	−1.31657	+	0.427779i
$389$	12.2881	+	13.6473i	0.623030	+	0.691944i	0.969213	−	0.246222i	$-0.0791893\pi$
$389$	12.2881	+	13.6473i	0.623030	+	0.691944i	−0.346184	+	0.938167i	$0.612523\pi$
$390$	−7.56745	+	0.989609i	−0.383193	+	0.0501108i
$391$	−1.90982	+	2.12107i	−0.0965835	+	0.107267i
$392$	−9.28661	+	20.8581i	−0.469045	+	1.05349i
$393$	−8.70087	+	3.15683i	−0.438901	+	0.159241i
$394$	0.0650803	+	0.619198i	0.00327870	+	0.0311947i
$395$	7.44334	+	1.64896i	0.374515	+	0.0829681i
$396$	8.21287	+	12.2297i	0.412712	+	0.614566i
$397$	−1.68812	+	2.32349i	−0.0847241	+	0.116613i	−0.849275	−	0.527950i	$-0.822961\pi$
$397$	−1.68812	+	2.32349i	−0.0847241	+	0.116613i	0.764551	+	0.644563i	$0.222961\pi$
$398$	3.62416	−	3.26320i	0.181663	−	0.163570i
$399$	−21.1462	+	25.1490i	−1.05863	+	1.25903i
$400$	−1.33445	−	15.1995i	−0.0667224	−	0.759975i
$401$	12.3674	+	21.4210i	0.617601	+	1.06972i	0.989922	+	0.141612i	$0.0452285\pi$
$401$	12.3674	+	21.4210i	0.617601	+	1.06972i	−0.372322	+	0.928104i	$0.621438\pi$
$402$	1.63432	+	0.871121i	0.0815127	+	0.0434476i
$403$	−2.20224	−	4.94631i	−0.109701	−	0.246393i
$404$	−15.2962	−	11.1133i	−0.761013	−	0.552908i
$405$	15.2515	+	13.1298i	0.757854	+	0.652424i
$406$	13.3725	−	9.71569i	0.663666	−	0.482181i
$407$	−7.67192	−	4.42938i	−0.380283	−	0.219556i
$408$	−0.773853	−	1.59074i	−0.0383114	−	0.0787535i
$409$	16.7752	−	18.6307i	0.829480	−	0.921231i	−0.168439	−	0.985712i	$-0.553873\pi$
$409$	16.7752	−	18.6307i	0.829480	−	0.921231i	0.997919	+	0.0644814i	$0.0205393\pi$
$410$	−3.76537	+	5.09023i	−0.185958	+	0.251388i
$411$	−8.12930	−	13.0391i	−0.400989	−	0.643172i
$412$	4.77028	−	22.4424i	0.235015	−	1.10566i
$413$	−23.7536	+	7.71802i	−1.16884	+	0.379779i
$414$	3.22646	−	4.11240i	0.158572	−	0.202113i
$415$	2.63214	+	1.54991i	0.129207	+	0.0760822i
$416$	20.6754	+	4.39470i	1.01370	+	0.215468i
$417$	9.11486	−	13.4837i	0.446357	−	0.660300i
$418$	−3.79354	+	2.19020i	−0.185548	+	0.107126i
$419$	−12.4533	−	5.54457i	−0.608384	−	0.270870i	0.0793340	−	0.996848i	$-0.474721\pi$
$419$	−12.4533	−	5.54457i	−0.608384	−	0.270870i	−0.687718	+	0.725978i	$0.741387\pi$
$420$	15.8662	−	29.1617i	0.774191	−	1.42294i
$421$	23.3855	−	10.4119i	1.13974	−	0.507445i	0.251971	−	0.967735i	$-0.418921\pi$
$421$	23.3855	−	10.4119i	1.13974	−	0.507445i	0.887769	+	0.460290i	$0.152255\pi$
$422$	−1.56659	+	2.15623i	−0.0762605	+	0.104964i
$423$	−4.49311	+	1.80470i	−0.218462	+	0.0877475i
$424$	11.1136			0.539725
$425$	−1.98603	+	2.63722i	−0.0963367	+	0.127924i
$426$	−4.81182	+	5.72267i	−0.233134	+	0.277264i
$427$	9.67030	+	45.4952i	0.467979	+	2.20167i
$428$	−31.6572	−	3.32730i	−1.53021	−	0.160831i
$429$	15.7025	+	16.2935i	0.758121	+	0.786659i
$430$	1.85203	+	0.843679i	0.0893129	+	0.0406858i
$431$	−19.3152	+	14.0333i	−0.930380	+	0.675961i	−0.946086	−	0.323916i	$-0.895001\pi$
$431$	−19.3152	+	14.0333i	−0.930380	+	0.675961i	0.0157056	+	0.999877i	$0.495001\pi$
$432$	−7.88630	−	13.7563i	−0.379430	−	0.661851i
$433$	−10.1886	−	14.0235i	−0.489635	−	0.673924i	0.490686	−	0.871337i	$-0.336746\pi$
$433$	−10.1886	−	14.0235i	−0.489635	−	0.673924i	−0.980321	+	0.197412i	$0.936746\pi$
$434$	−2.03691	−	0.432959i	−0.0977749	−	0.0207827i
$435$	−29.0453	+	17.7644i	−1.39262	+	0.851740i
$436$	0.637625	−	0.135531i	0.0305367	−	0.00649077i
$437$	−13.0637	−	11.7626i	−0.624921	−	0.562682i
$438$	2.52058	−	6.22041i	0.120438	−	0.297223i
$439$	−14.6885	−	16.3133i	−0.701046	−	0.778591i	0.282496	−	0.959268i	$-0.408838\pi$
$439$	−14.6885	−	16.3133i	−0.701046	−	0.778591i	−0.983542	+	0.180678i	$0.942171\pi$
$440$	6.92162	−	6.12561i	0.329975	−	0.292027i
$441$	39.1412	−	20.7096i	1.86387	−	0.986174i
$442$	−0.764775	−	1.05262i	−0.0363766	−	0.0500681i
$443$	31.3345	+	18.0910i	1.48875	+	0.859527i	0.999917	−	0.0128529i	$-0.00409132\pi$
$443$	31.3345	+	18.0910i	1.48875	+	0.859527i	0.488828	+	0.872380i	$0.337425\pi$
$444$	8.74086	+	5.90874i	0.414823	+	0.280416i
$445$	−9.27335	+	6.61675i	−0.439599	+	0.313664i
$446$	0.858538	−	8.16845i	0.0406530	−	0.386787i
$447$	30.1447	+	8.67706i	1.42579	+	0.410411i
$448$	−15.1162	+	13.6107i	−0.714174	+	0.643045i
$449$	34.7150			1.63830			0.819151	−	0.573578i	$-0.194445\pi$
$449$	34.7150			1.63830			0.819151	+	0.573578i	$0.194445\pi$
$450$	3.30171	−	5.06496i	0.155644	−	0.238765i
$451$	18.7729			0.883983
$452$	14.6051	−	13.1505i	0.686964	−	0.618546i
$453$	−0.670658	−	2.70157i	−0.0315102	−	0.126931i
$454$	−0.334198	+	3.17968i	−0.0156847	+	0.149230i
$455$	16.1735	−	48.3620i	0.758226	−	2.26725i
$456$	9.79742	−	4.76618i	0.458806	−	0.223197i
$457$	10.3841	+	5.99527i	0.485748	+	0.280447i	0.722809	−	0.691048i	$-0.242851\pi$
$457$	10.3841	+	5.99527i	0.485748	+	0.280447i	−0.237061	+	0.971495i	$0.576184\pi$
$458$	−0.152261	−	0.209570i	−0.00711470	−	0.00979255i
$459$	−0.723575	+	3.35375i	−0.0337736	+	0.156540i
$460$	15.3049	+	9.01215i	0.713596	+	0.420194i
$461$	19.2452	+	21.3740i	0.896338	+	0.995484i	1.00000		0.000871824i	$0.000277510\pi$
$461$	19.2452	+	21.3740i	0.896338	+	0.995484i	−0.103661	+	0.994613i	$0.533056\pi$
$462$	8.61957	−	1.20246i	0.401019	−	0.0559433i
$463$	17.4369	+	15.7003i	0.810362	+	0.729654i	0.966106	−	0.258144i	$-0.0831108\pi$
$463$	17.4369	+	15.7003i	0.810362	+	0.729654i	−0.155744	+	0.987797i	$0.549778\pi$
$464$	26.2401	−	5.57751i	1.21817	−	0.258929i
$465$	4.11168	+	1.22181i	0.190675	+	0.0566600i
$466$	9.76734	+	2.07611i	0.452463	+	0.0961741i
$467$	−21.1565	−	29.1194i	−0.979005	−	1.34748i	−0.937364	−	0.348352i	$-0.886741\pi$
$467$	−21.1565	−	29.1194i	−0.979005	−	1.34748i	−0.0416409	−	0.999133i	$-0.513259\pi$
$468$	−17.2811	−	20.6802i	−0.798819	−	0.955941i
$469$	−10.0113	+	7.27363i	−0.462279	+	0.335865i
$470$	0.716517	+	1.26599i	0.0330505	+	0.0583958i
$471$	−3.30211	+	11.4717i	−0.152153	+	0.528590i
$472$	8.23636	+	0.865677i	0.379109	+	0.0398460i
$473$	−1.25458	−	5.90232i	−0.0576855	−	0.271389i
$474$	−0.811829	−	2.23757i	−0.0372886	−	0.102775i
$475$	−16.2427	−	12.2320i	−0.745268	−	0.561244i
$476$	5.65980			0.259417
$477$	−16.9583	−	13.3049i	−0.776466	−	0.609192i
$478$	1.14004	−	1.56913i	0.0521441	−	0.0717702i
$479$	−14.5503	+	6.47820i	−0.664819	+	0.295996i	−0.711265	−	0.702924i	$-0.751877\pi$
$479$	−14.5503	+	6.47820i	−0.664819	+	0.295996i	0.0464457	+	0.998921i	$0.485211\pi$
$480$	−13.2938	+	10.1824i	−0.606774	+	0.464760i
$481$	14.8053	+	6.59173i	0.675062	+	0.300557i
$482$	−3.31710	+	1.91513i	−0.151090	+	0.0872316i
$483$	15.2786	+	31.4069i	0.695201	+	1.42906i
$484$	6.93543	+	1.47417i	0.315247	+	0.0670078i
$485$	7.17697	−	32.3966i	0.325889	−	1.47105i
$486$	0.906122	−	6.21759i	0.0411025	−	0.282036i
$487$	−17.7128	+	5.75525i	−0.802645	+	0.260795i	−0.681480	−	0.731837i	$-0.738663\pi$
$487$	−17.7128	+	5.75525i	−0.802645	+	0.260795i	−0.121166	+	0.992632i	$0.538663\pi$
$488$	3.20655	−	15.0856i	0.145154	−	0.682894i
$489$	8.37089	−	15.7048i	0.378545	−	0.710194i
$490$	−7.72723	−	10.8297i	−0.349080	−	0.489235i
$491$	−26.3377	+	29.2510i	−1.18860	+	1.32008i	−0.252818	+	0.967514i	$0.581357\pi$
$491$	−26.3377	+	29.2510i	−1.18860	+	1.32008i	−0.935787	+	0.352565i	$0.885309\pi$
$492$	−22.3022	−	1.58234i	−1.00546	−	0.0713372i
$493$	−5.02683	−	2.90224i	−0.226397	−	0.130710i
$494$	6.48312	−	4.71027i	0.291690	−	0.211925i
$495$	−17.8951	+	1.06068i	−0.804327	+	0.0476741i
$496$	−2.73421	−	1.98652i	−0.122770	−	0.0891975i
$497$	−20.3200	−	45.6394i	−0.911475	−	2.04721i
$498$	−0.0323131	−	0.953145i	−0.00144798	−	0.0427115i
$499$	12.0416	+	20.8566i	0.539054	+	0.933669i	0.998955	+	0.0456988i	$0.0145515\pi$
$499$	12.0416	+	20.8566i	0.539054	+	0.933669i	−0.459901	+	0.887970i	$0.652115\pi$
$500$	18.5470	+	8.83605i	0.829446	+	0.395160i
$501$	−0.416557	−	1.14812i	−0.0186104	−	0.0512940i
$502$	2.10726	−	1.89739i	0.0940518	−	0.0846846i
$503$	−5.34452	+	7.35611i	−0.238301	+	0.327993i	−0.911371	−	0.411586i	$-0.864975\pi$
$503$	−5.34452	+	7.35611i	−0.238301	+	0.327993i	0.673070	+	0.739578i	$0.264975\pi$
$504$	−21.5971	+	1.46603i	−0.962010	+	0.0653023i
$505$	21.0981	−	9.17755i	0.938854	−	0.408395i
$506$	0.486698	+	4.63062i	0.0216364	+	0.205856i
$507$	−14.4507	−	12.1507i	−0.641778	−	0.539630i
$508$	−2.82616	+	6.34767i	−0.125391	+	0.281632i
$509$	−1.35791	+	1.50811i	−0.0601884	+	0.0668460i	−0.772487	−	0.635031i	$-0.780988\pi$
$509$	−1.35791	+	1.50811i	−0.0601884	+	0.0668460i	0.712299	+	0.701877i	$0.247654\pi$
$510$	1.02751	+	0.0817620i	0.0454990	+	0.00362048i
$511$	30.0080	+	33.3272i	1.32747	+	1.47431i
$512$	21.5265	−	6.99440i	0.951347	−	0.309112i
$513$	−20.6558	−	4.45651i	−0.911978	−	0.196760i
$514$	1.01042	−	3.10975i	0.0445676	−	0.137165i
$515$	20.5876	+	18.8593i	0.907199	+	0.831040i
$516$	0.992936	+	7.11767i	0.0437116	+	0.313338i
$517$	1.75431	−	3.94025i	0.0771546	−	0.173292i
$518$	5.39801	−	3.11654i	0.237175	−	0.136933i
$519$	−0.0467578	+	0.659026i	−0.00205244	+	0.0289280i
$520$	−11.4218	+	12.4685i	−0.500879	+	0.546780i
$521$	−1.22226	−	0.888024i	−0.0535482	−	0.0389050i	0.560689	−	0.828026i	$-0.310536\pi$
$521$	−1.22226	−	0.888024i	−0.0535482	−	0.0389050i	−0.614237	+	0.789121i	$0.710536\pi$
$522$	9.54480	+	4.67939i	0.417764	+	0.204811i
$523$	0.0869563	+	0.0282538i	0.00380233	+	0.00123545i	0.310918	−	0.950437i	$-0.399364\pi$
$523$	0.0869563	+	0.0282538i	0.00380233	+	0.00123545i	−0.307115	+	0.951672i	$0.599364\pi$
$524$	−4.90976	+	8.50396i	−0.214484	+	0.371497i
$525$	20.7822	+	34.6433i	0.907009	+	1.51196i
$526$	1.21371	+	2.10220i	0.0529202	+	0.0916604i
$527$	0.152039	+	0.715289i	0.00662294	+	0.0311585i
$528$	13.5735	+	3.90710i	0.590712	+	0.170035i
$529$	3.94155	−	1.75489i	0.171372	−	0.0762996i
$530$	−3.28583	+	5.58017i	−0.142727	+	0.242387i
$531$	−11.5315	−	11.1813i	−0.500425	−	0.485227i
$532$			34.8589i			1.51132i
$533$	−34.1554	+	3.58988i	−1.47943	+	0.155495i
$534$	3.29643	+	1.33575i	0.142650	+	0.0578034i
$535$	23.0359	−	31.1412i	0.995931	−	1.34635i
$536$	4.01360	−	0.853118i	0.173361	−	0.0368491i
$537$	22.1819	−	3.09443i	0.957218	−	0.133535i
$538$	−2.55115	+	12.0022i	−0.109988	+	0.517453i
$539$	−12.1894	+	37.5151i	−0.525034	+	1.61589i
$540$	21.3488	+	0.248263i	0.918704	+	0.0106836i
$541$	1.62629	+	5.00522i	0.0699198	+	0.215191i	0.979911	−	0.199438i	$-0.0639115\pi$
$541$	1.62629	+	5.00522i	0.0699198	+	0.215191i	−0.909991	+	0.414629i	$0.863911\pi$
$542$	−3.06257	+	0.321889i	−0.131549	+	0.0138263i
$543$	2.27203	−	12.8091i	0.0975021	−	0.549689i
$544$	−2.60799	−	1.16115i	−0.111817	−	0.0497840i
$545$	−0.251588	+	0.752297i	−0.0107768	+	0.0322249i
$546$	−15.4525	+	3.83603i	−0.661305	+	0.164167i
$547$	−13.8432	−	31.0923i	−0.591891	−	1.32941i	−0.922630	−	0.385687i	$-0.873964\pi$
$547$	−13.8432	−	31.0923i	−0.591891	−	1.32941i	0.330739	−	0.943722i	$-0.392702\pi$
$548$	−15.5036	−	5.03742i	−0.662281	−	0.215188i
$549$	−22.9530	+	19.1804i	−0.979611	+	0.818598i
$550$	1.02925	+	5.28645i	0.0438875	+	0.225415i
$551$	17.8750	−	30.9604i	0.761500	−	1.31896i
$552$	−0.392389	−	11.5744i	−0.0167012	−	0.492638i
$553$	15.8175	+	1.66249i	0.672629	+	0.0706961i
$554$	−0.945726	+	8.99798i	−0.0401801	+	0.382288i
$555$	−11.5930	+	5.51726i	−0.492095	+	0.234195i
$556$	−1.80486	−	17.1721i	−0.0765430	−	0.728258i
$557$		−	40.7325i		−	1.72589i	−0.505297	−	0.862946i	$-0.668617\pi$
$557$		−	40.7325i		−	1.72589i	0.505297	−	0.862946i	$-0.331383\pi$
$558$	−0.366517	−	1.28809i	−0.0155159	−	0.0545292i
$559$	3.41125	+	10.4987i	0.144280	+	0.444049i
$560$	−6.35081	−	31.1909i	−0.268371	−	1.31806i
$561$	−1.61689	−	2.59344i	−0.0682653	−	0.109495i
$562$	−8.42474	−	7.58567i	−0.355376	−	0.319982i
$563$	9.48718	+	8.54229i	0.399837	+	0.360015i	0.844382	−	0.535742i	$-0.179968\pi$
$563$	9.48718	+	8.54229i	0.399837	+	0.360015i	−0.444545	+	0.895757i	$0.646635\pi$
$564$	−2.41623	+	4.53314i	−0.101742	+	0.190879i
$565$	4.77156	+	23.4347i	0.200741	+	0.985905i
$566$	2.37488	+	7.30912i	0.0998236	+	0.307225i
$567$	34.7101	+	23.6185i	1.45769	+	0.991882i
$568$			16.5656i			0.695077i
$569$	1.67690	+	15.9546i	0.0702991	+	0.668852i	0.971757	+	0.235984i	$0.0758314\pi$
$569$	1.67690	+	15.9546i	0.0702991	+	0.668852i	−0.901458	+	0.432867i	$0.857502\pi$
$570$	−0.503574	+	6.32847i	−0.0210924	+	0.265070i
$571$	4.80603	−	45.7263i	0.201126	−	1.91359i	−0.170765	−	0.985312i	$-0.554624\pi$
$571$	4.80603	−	45.7263i	0.201126	−	1.91359i	0.371892	−	0.928276i	$-0.378709\pi$
$572$	23.8750	+	2.50936i	0.998264	+	0.104922i
$573$	1.65022	−	1.02884i	0.0689391	−	0.0429804i
$574$	−6.60437	+	11.4391i	−0.275661	+	0.477459i
$575$	−18.9003	+	10.4841i	−0.788195	+	0.437217i
$576$	−12.2833	−	4.49911i	−0.511806	−	0.187463i
$577$	−21.5727	−	7.00940i	−0.898084	−	0.291805i	−0.176638	−	0.984276i	$-0.556522\pi$
$577$	−21.5727	−	7.00940i	−0.898084	−	0.291805i	−0.721446	+	0.692471i	$0.756522\pi$
$578$	−2.71558	−	6.09928i	−0.112953	−	0.253697i
$579$	−1.36334	+	4.73634i	−0.0566586	+	0.196835i
$580$	−11.4560	+	34.2558i	−0.475685	+	1.42239i
$581$	5.82147	+	2.59189i	0.241515	+	0.107530i
$582$	−9.73885	+	3.53343i	−0.403688	+	0.146465i
$583$	19.0953	−	2.00699i	0.790845	−	0.0831211i
$584$	−4.59521	−	14.1426i	−0.190151	−	0.585226i
$585$	32.3555	−	5.35182i	1.33774	−	0.221270i
$586$	−3.36280	+	10.3496i	−0.138916	+	0.427540i
$587$	−3.19660	+	15.0388i	−0.131938	+	0.620718i	0.861636	+	0.507528i	$0.169440\pi$
$587$	−3.19660	+	15.0388i	−0.131938	+	0.620718i	−0.993573	+	0.113191i	$0.963893\pi$
$588$	17.6430	−	43.5404i	0.727586	−	1.79557i
$589$	−4.40548	+	0.936414i	−0.181525	+	0.0385843i
$590$	−2.86980	+	3.87955i	−0.118148	+	0.159719i
$591$	−0.369650	−	2.64977i	−0.0152054	−	0.108997i
$592$	10.0606	−	1.05741i	0.413488	−	0.0434593i
$593$		−	32.8164i		−	1.34761i	−0.738909	−	0.673805i	$-0.764659\pi$
$593$		−	32.8164i		−	1.34761i	0.738909	−	0.673805i	$-0.235341\pi$
$594$	3.27599	+	4.53809i	0.134415	+	0.186200i
$595$	−3.49468	+	5.93486i	−0.143268	+	0.243306i
$596$	30.4019	−	13.5358i	1.24531	−	0.554448i
$597$	−15.0894	+	14.5420i	−0.617568	+	0.595165i
$598$	−1.77099	−	8.33186i	−0.0724212	−	0.340715i
$599$	6.66854	+	11.5503i	0.272469	+	0.471931i	0.969494	−	0.245117i	$-0.0788264\pi$
$599$	6.66854	+	11.5503i	0.272469	+	0.471931i	−0.697024	+	0.717048i	$0.745493\pi$
$600$	−1.62304	−	13.2970i	−0.0662603	−	0.542848i
$601$	−3.22848	+	5.59189i	−0.131692	+	0.228098i	−0.924329	−	0.381596i	$-0.875374\pi$
$601$	−3.22848	+	5.59189i	−0.131692	+	0.228098i	0.792637	+	0.609694i	$0.208708\pi$
$602$	4.03788	+	1.31199i	0.164572	+	0.0534726i
$603$	−7.14569	−	3.50322i	−0.290995	−	0.142662i
$604$	−2.38910	−	1.73579i	−0.0972112	−	0.0706281i
$605$	−5.82814	+	6.36224i	−0.236948	+	0.258662i
$606$	−5.95126	−	4.02299i	−0.241753	−	0.163423i
$607$	−31.8170	+	18.3695i	−1.29141	+	0.745596i	−0.978904	−	0.204320i	$-0.934502\pi$
$607$	−31.8170	+	18.3695i	−1.29141	+	0.745596i	−0.312506	+	0.949916i	$0.601168\pi$
$608$	7.15157	−	16.0627i	0.290034	−	0.651428i
$609$	−56.0157	+	43.6725i	−2.26987	+	1.76970i
$610$	6.62648	+	6.07020i	0.268299	+	0.245775i
$611$	−2.43831	+	7.50435i	−0.0986435	+	0.303593i
$612$	1.70227	+	3.21728i	0.0688100	+	0.130051i
$613$	27.5726	−	8.95887i	1.11365	−	0.361846i	0.306307	−	0.951933i	$-0.400907\pi$
$613$	27.5726	−	8.95887i	1.11365	−	0.361846i	0.807339	+	0.590087i	$0.200907\pi$
$614$	7.75265	+	8.61019i	0.312871	+	0.347479i
$615$	15.4299	−	22.4090i	0.622192	−	0.903618i
$616$	12.9025	−	14.3297i	0.519856	−	0.577359i
$617$	−4.61883	+	10.3741i	−0.185947	+	0.417644i	−0.982332	−	0.187146i	$-0.940076\pi$
$617$	−4.61883	+	10.3741i	−0.185947	+	0.417644i	0.796385	+	0.604790i	$0.206743\pi$
$618$	1.52245	−	8.58314i	0.0612419	−	0.345264i
$619$	2.69301	+	25.6223i	0.108241	+	1.02985i	0.904960	+	0.425497i	$0.139901\pi$
$619$	2.69301	+	25.6223i	0.108241	+	1.02985i	−0.796719	+	0.604350i	$0.793433\pi$
$620$	4.17289	−	1.81518i	0.167587	−	0.0728994i
$621$	−13.2578	+	18.1311i	−0.532018	+	0.727576i
$622$	−4.93228	+	6.78870i	−0.197766	+	0.272202i
$623$	−17.6613	+	15.9023i	−0.707587	+	0.637114i
$624$	−25.4427	−	4.51295i	−1.01852	−	0.180663i
$625$	−20.7174	+	13.9924i	−0.828697	+	0.559698i
$626$	−5.06879	−	8.77940i	−0.202589	−	0.350895i
$627$	15.9731	−	9.95849i	0.637903	−	0.397704i
$628$	5.15113	+	11.5696i	0.205552	+	0.461678i
$629$	−1.77080	−	1.28656i	−0.0706064	−	0.0512986i
$630$	5.64925	−	11.2774i	0.225071	−	0.449302i
$631$	−13.7657	+	10.0014i	−0.548004	+	0.398148i	−0.827049	−	0.562130i	$-0.809982\pi$
$631$	−13.7657	+	10.0014i	−0.548004	+	0.398148i	0.279045	+	0.960278i	$0.409982\pi$
$632$	−4.56722	−	2.63688i	−0.181674	−	0.104890i
$633$	6.41404	−	9.48836i	0.254935	−	0.377128i
$634$	6.45725	−	7.17150i	0.256450	−	0.284817i
$635$	−4.91112	−	6.88292i	−0.194892	−	0.273140i
$636$	−22.8542	+	0.774794i	−0.906230	+	0.0307226i
$637$	15.0035	−	70.5857i	0.594459	−	2.79671i
$638$	−9.00564	+	2.92611i	−0.356537	+	0.115846i
$639$	19.8319	−	25.2775i	0.784539	−	0.999961i
$640$	−5.03220	+	22.7151i	−0.198915	+	0.897895i
$641$	−23.3227	−	4.95739i	−0.921190	−	0.195805i	−0.277177	−	0.960819i	$-0.589399\pi$
$641$	−23.3227	−	4.95739i	−0.921190	−	0.195805i	−0.644014	+	0.765014i	$0.722732\pi$
$642$	−12.0636	−	0.855908i	−0.476111	−	0.0337800i
$643$	−8.90132	+	5.13918i	−0.351034	+	0.202670i	−0.665141	−	0.746718i	$-0.731628\pi$
$643$	−8.90132	+	5.13918i	−0.351034	+	0.202670i	0.314107	+	0.949388i	$0.398295\pi$
$644$	33.8496	+	15.0708i	1.33386	+	0.593874i
$645$	−8.07668	−	3.35366i	−0.318019	−	0.132050i
$646$	−0.988741	+	0.440216i	−0.0389015	+	0.0173201i
$647$	−3.54997	+	4.88611i	−0.139564	+	0.192093i	−0.873077	−	0.487582i	$-0.837879\pi$
$647$	−3.54997	+	4.88611i	−0.139564	+	0.192093i	0.733514	+	0.679675i	$0.237879\pi$
$648$	−7.32899	−	11.8358i	−0.287910	−	0.464954i
$649$	14.3079			0.561635
$650$	−2.88352	−	9.42132i	−0.113101	−	0.369535i
$651$	8.81088	+	1.56285i	0.345326	+	0.0612527i
$652$	−3.92541	−	18.4676i	−0.153731	−	0.723248i
$653$	−0.920513	−	0.0967498i	−0.0360225	−	0.00378611i	0.0865001	−	0.996252i	$-0.472432\pi$
$653$	−0.920513	−	0.0967498i	−0.0360225	−	0.00378611i	−0.122523	+	0.992466i	$0.539098\pi$
$654$	0.240371	−	0.0596715i	0.00939927	−	0.00233334i
$655$	−5.88567	−	10.3992i	−0.229972	−	0.406330i
$656$	−17.3431	+	12.6005i	−0.677133	+	0.491966i
$657$	−9.91935	+	27.0815i	−0.386991	+	1.05655i
$658$	1.78378	+	2.45517i	0.0695391	+	0.0957123i
$659$	−42.6826	−	9.07246i	−1.66268	−	0.353413i	−0.721785	−	0.692117i	$-0.756678\pi$
$659$	−42.6826	−	9.07246i	−1.66268	−	0.353413i	−0.940893	+	0.338704i	$0.890011\pi$
$660$	−13.8067	+	13.0794i	−0.537425	+	0.509114i
$661$	39.8160	−	8.46316i	1.54866	−	0.329179i	0.647298	−	0.762237i	$-0.275899\pi$
$661$	39.8160	−	8.46316i	1.54866	−	0.329179i	0.901366	+	0.433058i	$0.142565\pi$
$662$	−2.86211	−	2.57705i	−0.111239	−	0.100160i
$663$	3.43770	+	4.40930i	0.133509	+	0.171243i
$664$	−1.41387	−	1.57027i	−0.0548690	−	0.0609382i
$665$	−36.5529	−	21.5238i	−1.41746	−	0.834658i
$666$	3.39511	+	2.13112i	0.131558	+	0.0825793i
$667$	−22.3360	−	30.7429i	−0.864853	−	1.19037i
$668$	−1.12213	−	0.647863i	−0.0434166	−	0.0250666i
$669$	−2.49784	+	35.2057i	−0.0965720	+	1.36113i
$670$	−0.758301	+	2.26747i	−0.0292957	+	0.0876001i
$671$	2.78515	−	26.4990i	0.107520	−	1.02298i
$672$	−25.1539	+	24.2414i	−0.970333	+	0.935133i
$673$	0.570787	−	0.513939i	0.0220022	−	0.0198109i	−0.658056	−	0.752969i	$-0.728621\pi$
$673$	0.570787	−	0.513939i	0.0220022	−	0.0198109i	0.680058	+	0.733158i	$0.261954\pi$
$674$	−5.61926			−0.216446
$675$	−13.4423	+	22.2330i	−0.517393	+	0.855748i
$676$	−20.0300			−0.770384
$677$	20.3123	−	18.2893i	0.780664	−	0.702913i	−0.179066	−	0.983837i	$-0.557307\pi$
$677$	20.3123	−	18.2893i	0.780664	−	0.702913i	0.959730	+	0.280924i	$0.0906408\pi$
$678$	5.37649	−	5.18145i	0.206483	−	0.198992i
$679$	7.23585	−	68.8445i	0.277686	−	2.64201i
$680$	1.85903	−	1.32646i	0.0712907	−	0.0508676i
$681$	0.972318	−	13.7043i	0.0372593	−	0.525150i
$682$	1.03312	+	0.596474i	0.0395603	+	0.0228402i
$683$	−1.63289	−	2.24748i	−0.0624809	−	0.0859975i	0.776633	−	0.629953i	$-0.216926\pi$
$683$	−1.63289	−	2.24748i	−0.0624809	−	0.0859975i	−0.839114	+	0.543956i	$0.816926\pi$
$684$	−19.8153	+	10.4843i	−0.757658	+	0.400877i
$685$	14.8550	−	13.1467i	0.567582	−	0.502308i
$686$	−9.76418	−	10.8442i	−0.372798	−	0.414034i
$687$	0.684423	+	0.877862i	0.0261124	+	0.0334925i
$688$	5.12068	+	4.61068i	0.195224	+	0.175781i
$689$	−34.3580	+	7.30302i	−1.30894	+	0.278223i
$690$	5.92753	+	3.22504i	0.225657	+	0.122775i
$691$	−33.1731	−	7.05117i	−1.26197	−	0.268239i	−0.472114	−	0.881537i	$-0.656509\pi$
$691$	−33.1731	−	7.05117i	−1.26197	−	0.268239i	−0.789851	+	0.613298i	$0.789842\pi$
$692$	0.411990	+	0.567055i	0.0156615	+	0.0215562i
$693$	−36.8430	+	6.41910i	−1.39955	+	0.243842i
$694$	−1.28785	+	0.935677i	−0.0488861	+	0.0355178i
$695$	19.1210	+	8.71043i	0.725301	+	0.330406i
$696$	22.8583	−	5.67451i	0.866443	−	0.215092i
$697$	4.61302	+	0.484848i	0.174730	+	0.0183649i
$698$	1.61904	+	7.61699i	0.0612816	+	0.288307i
$699$	−42.2497	−	7.49411i	−1.59803	−	0.283453i
$700$	40.5283	+	13.9412i	1.53182	+	0.526928i
$701$	−2.42588			−0.0916243			−0.0458121	−	0.998950i	$-0.514588\pi$
$701$	−2.42588			−0.0916243			−0.0458121	+	0.998950i	$0.514588\pi$
$702$	−6.82812	−	7.63013i	−0.257711	−	0.287981i
$703$	7.92396	−	10.9064i	0.298858	−	0.411343i
$704$	10.6452	−	4.73954i	0.401205	−	0.178628i
$705$	−3.26152	−	5.33267i	−0.122836	−	0.200840i
$706$	−1.04274	−	0.464259i	−0.0392441	−	0.0174726i
$707$	41.5679	−	23.9992i	1.56332	−	0.902583i
$708$	−16.9978	−	1.20599i	−0.638815	−	0.0453238i
$709$	28.2910	+	6.01343i	1.06249	+	0.225839i	0.705820	−	0.708391i	$-0.250579\pi$
$709$	28.2910	+	6.01343i	1.06249	+	0.225839i	0.356670	+	0.934231i	$0.383912\pi$
$710$	−8.31763	−	4.89775i	−0.312155	−	0.183809i
$711$	3.81231	+	9.49139i	0.142973	+	0.355955i
$712$	7.49470	−	2.43517i	0.280876	−	0.0912620i
$713$	−0.995356	+	4.68278i	−0.0372764	+	0.175372i
$714$	2.14912	−	0.0728584i	0.0804287	−	0.00272666i
$715$	−17.3731	+	23.4859i	−0.649717	+	0.878321i
$716$	15.8990	−	17.6576i	0.594172	−	0.659895i
$717$	−4.66761	+	6.90485i	−0.174315	+	0.257866i
$718$	−2.52695	−	1.45894i	−0.0943050	−	0.0544470i
$719$	41.6638	−	30.2705i	1.55380	−	1.12890i	0.612926	−	0.790140i	$-0.289992\pi$
$719$	41.6638	−	30.2705i	1.55380	−	1.12890i	0.940873	−	0.338761i	$-0.110008\pi$
$720$	15.8202	−	12.9912i	0.589584	−	0.484153i
$721$	47.1221	+	34.2362i	1.75492	+	1.27502i
$722$	0.403639	+	0.906588i	0.0150219	+	0.0337397i
$723$	13.9670	−	8.70777i	0.519437	−	0.323845i
$724$	−6.90062	−	11.9522i	−0.256460	−	0.444201i
$725$	−28.8470	−	33.1642i	−1.07135	−	1.23169i
$726$	2.65247	+	0.470487i	0.0984424	+	0.0174614i
$727$	6.05582	−	5.45269i	0.224598	−	0.202229i	−0.549148	−	0.835725i	$-0.685048\pi$
$727$	6.05582	−	5.45269i	0.224598	−	0.202229i	0.773746	+	0.633496i	$0.218381\pi$
$728$	−20.7345	+	28.5386i	−0.768472	+	1.05771i
$729$	−2.98623	+	26.8344i	−0.110601	+	0.993865i
$730$	8.45965	+	1.87411i	0.313106	+	0.0693638i
$731$	−0.155844	−	1.48276i	−0.00576411	−	0.0548419i
$732$	−5.54230	+	31.2459i	−0.204849	+	1.15488i
$733$	−1.08878	+	2.44543i	−0.0402149	+	0.0903241i	−0.932536	−	0.361077i	$-0.882409\pi$
$733$	−1.08878	+	2.44543i	−0.0402149	+	0.0903241i	0.892321	+	0.451401i	$0.149076\pi$
$734$	0.191624	−	0.212820i	0.00707298	−	0.00785534i
$735$	34.7625	+	45.3847i	1.28224	+	1.67404i
$736$	−12.5057	−	13.8890i	−0.460968	−	0.511957i
$737$	6.74206	−	2.19063i	0.248347	−	0.0806928i
$738$	−8.48886	−	0.313743i	−0.312479	−	0.0115491i
$739$	−13.1689	+	40.5297i	−0.484426	+	1.49091i	0.348385	+	0.937351i	$0.386730\pi$
$739$	−13.1689	+	40.5297i	−0.484426	+	1.49091i	−0.832811	+	0.553557i	$0.813270\pi$
$740$	−5.64657	+	12.3953i	−0.207572	+	0.455659i
$741$	−27.1570	+	21.1729i	−0.997638	+	0.777806i
$742$	−5.49482	+	12.3416i	−0.201721	+	0.453074i
$743$	−18.4359	+	10.6440i	−0.676347	+	0.390489i	−0.798477	−	0.602025i	$-0.794361\pi$
$743$	−18.4359	+	10.6440i	−0.676347	+	0.390489i	0.122130	+	0.992514i	$0.461027\pi$
$744$	−2.45821	−	1.66173i	−0.0901224	−	0.0609219i
$745$	−4.57823	+	40.2371i	−0.167734	+	1.47417i
$746$	6.60917	+	4.80184i	0.241979	+	0.175808i
$747$	0.277547	+	4.08873i	0.0101549	+	0.149599i
$748$	−3.08362	−	1.00193i	−0.112748	−	0.0366342i
$749$	40.4045	−	69.9827i	1.47635	−	2.55711i
$750$	7.15632	+	3.11643i	0.261312	+	0.113796i
$751$	−7.90783	−	13.6968i	−0.288561	−	0.499802i	0.684906	−	0.728632i	$-0.259843\pi$
$751$	−7.90783	−	13.6968i	−0.288561	−	0.499802i	−0.973466	+	0.228830i	$0.926510\pi$
$752$	1.02402	+	4.81764i	0.0373422	+	0.175681i
$753$	−8.77373	+	8.45545i	−0.319732	+	0.308134i
$754$	15.8253	−	7.04586i	0.576322	−	0.256595i
$755$	3.29531	−	1.43344i	0.119929	−	0.0521681i
$756$	44.3104	−	4.52044i	1.61155	−	0.164407i
$757$		−	50.3254i		−	1.82911i	−0.404464	−	0.914554i	$-0.632542\pi$
$757$		−	50.3254i		−	1.82911i	0.404464	−	0.914554i	$-0.367458\pi$
$758$	−7.23599	+	0.760533i	−0.262823	+	0.0276238i
$759$	−2.76440	−	19.8161i	−0.100341	−	0.719278i
$760$	8.16972	+	11.4498i	0.296347	+	0.415329i
$761$	−13.6288	+	2.89690i	−0.494045	+	0.105013i	−0.448195	−	0.893936i	$-0.647933\pi$
$761$	−13.6288	+	2.89690i	−0.494045	+	0.105013i	−0.0458502	+	0.998948i	$0.514600\pi$
$762$	−0.991426	+	2.44669i	−0.0359156	+	0.0886343i
$763$	−0.344066	+	1.61870i	−0.0124560	+	0.0586010i
$764$	0.637534	−	1.96213i	0.0230652	−	0.0709873i
$765$	−4.42471	−	0.201539i	−0.159976	−	0.00728665i
$766$	−0.502596	−	1.54683i	−0.0181595	−	0.0558893i
$767$	−26.0318	+	2.73605i	−0.939953	+	0.0987931i
$768$	−7.37090	+	2.67429i	−0.265974	+	0.0965002i
$769$	−2.54315	−	1.13228i	−0.0917084	−	0.0408312i	0.360370	−	0.932810i	$-0.382651\pi$
$769$	−2.54315	−	1.13228i	−0.0917084	−	0.0408312i	−0.452078	+	0.891978i	$0.649317\pi$
$770$	3.38024	+	10.7150i	0.121815	+	0.386143i
$771$	−3.88663	+	13.5024i	−0.139974	+	0.486278i
$772$	2.12675	+	4.77675i	0.0765433	+	0.171919i
$773$	11.4468	+	3.71930i	0.411713	+	0.133774i	0.507548	−	0.861623i	$-0.330552\pi$
$773$	11.4468	+	3.71930i	0.411713	+	0.133774i	−0.0958346	+	0.995397i	$0.530552\pi$
$774$	0.468659	+	2.68991i	0.0168456	+	0.0966869i
$775$	−0.673184	+	5.49648i	−0.0241815	+	0.197440i
$776$	−11.4768	+	19.8785i	−0.411995	+	0.713596i
$777$	−22.7288	+	14.1704i	−0.815392	+	0.508360i
$778$	7.36156	+	0.773731i	0.263925	+	0.0277396i
$779$	−2.98619	+	28.4117i	−0.106991	+	1.01795i
$780$	22.6187	−	26.4368i	0.809881	−	0.946588i
$781$	2.99156	+	28.4628i	0.107046	+	1.01848i
$782$			1.15044i			0.0411396i
$783$	−41.6729	−	18.7067i	−1.48927	−	0.668523i
$784$	−13.9193	−	42.8393i	−0.497119	−	1.52997i
$785$	−15.3125	−	1.74228i	−0.546526	−	0.0621845i
$786$	−1.75484	+	3.29229i	−0.0625932	+	0.117432i
$787$	12.1157	+	10.9090i	0.431876	+	0.388863i	0.856198	−	0.516649i	$-0.172821\pi$
$787$	12.1157	+	10.9090i	0.431876	+	0.388863i	−0.424321	+	0.905512i	$0.639487\pi$
$788$	−2.10931	−	1.89923i	−0.0751412	−	0.0676574i
$789$	−5.51853	−	8.85153i	−0.196465	−	0.315123i
$790$	2.67432	−	1.51360i	0.0951480	−	0.0538513i
$791$	15.4175	+	47.4502i	0.548184	+	1.68714i
$792$	12.0262	+	3.02450i	0.427333	+	0.107471i
$793$			48.7447i			1.73097i
$794$	0.121004	+	1.15128i	0.00429428	+	0.0408574i
$795$	13.2991	−	24.4433i	0.471669	−	0.866916i
$796$	−2.32392	+	22.1106i	−0.0823690	+	0.783689i
$797$	25.7831	+	2.70991i	0.913284	+	0.0959900i	0.549500	−	0.835494i	$-0.314818\pi$
$797$	25.7831	+	2.70991i	0.913284	+	0.0959900i	0.363783	+	0.931484i	$0.381485\pi$
$798$	0.448737	+	13.2365i	0.0158851	+	0.468566i
$799$	0.532847	−	0.922918i	0.0188508	−	0.0326505i
$800$	−15.8150	−	14.7387i	−0.559143	−	0.521091i
$801$	−14.3515	−	5.25663i	−0.507085	−	0.185734i
$802$	9.48198	+	3.08088i	0.334820	+	0.108790i
$803$	−10.4494	−	23.4698i	−0.368752	−	0.828231i
$804$	−8.19418	+	2.03418i	−0.288986	+	0.0717400i
$805$	−36.7039	+	26.1891i	−1.29364	+	0.923045i
$806$	−1.99372	−	0.887661i	−0.0702258	−	0.0312665i
$807$	9.20886	−	51.9169i	0.324167	−	1.82756i
$808$	−15.8285	+	1.66364i	−0.556844	+	0.0585266i
$809$	15.8564	+	48.8010i	0.557482	+	1.71575i	0.689298	+	0.724478i	$0.257919\pi$
$809$	15.8564	+	48.8010i	0.557482	+	1.71575i	−0.131817	+	0.991274i	$0.542081\pi$
$810$	8.10966	−	0.180552i	0.284944	−	0.00634395i
$811$	6.90998	−	21.2667i	0.242642	−	0.746776i	−0.753373	−	0.657593i	$-0.771575\pi$
$811$	6.90998	−	21.2667i	0.242642	−	0.746776i	0.996015	−	0.0891825i	$-0.0284254\pi$
$812$	−15.6670	+	73.7075i	−0.549804	+	2.58663i
$813$	13.1058	−	1.82830i	0.459641	−	0.0641212i
$814$	−3.49269	+	0.742395i	−0.122419	+	0.0260209i
$815$	21.7889	+	7.28677i	0.763231	+	0.255244i
$816$	3.23447	+	1.31064i	0.113229	+	0.0458817i
$817$	9.13236	−	0.959849i	0.319501	−	0.0335809i
$818$		−	10.1051i		−	0.353315i
$819$	65.8045	−	18.7242i	2.29940	−	0.654278i
$820$	−2.77090	−	28.7311i	−0.0967641	−	1.00333i
$821$	37.7932	−	16.8266i	1.31899	−	0.587253i	0.378039	−	0.925790i	$-0.376599\pi$
$821$	37.7932	−	16.8266i	1.31899	−	0.587253i	0.940953	+	0.338537i	$0.109932\pi$
$822$	−5.95181	−	1.71321i	−0.207593	−	0.0597551i
$823$	4.31924	+	20.3204i	0.150559	+	0.708325i	0.987059	+	0.160358i	$0.0512648\pi$
$823$	4.31924	+	20.3204i	0.150559	+	0.708325i	−0.836500	+	0.547967i	$0.815402\pi$
$824$	−9.65682	−	16.7261i	−0.336411	−	0.582682i
$825$	−5.18997	−	22.5536i	−0.180692	−	0.785217i
$826$	−5.03357	+	8.71840i	−0.175140	+	0.303352i
$827$	35.1321	+	11.4151i	1.22166	+	0.396942i	0.847687	−	0.530497i	$-0.177995\pi$
$827$	35.1321	+	11.4151i	1.22166	+	0.396942i	0.373975	+	0.927439i	$0.377995\pi$
$828$	1.61383	+	23.7744i	0.0560846	+	0.826218i
$829$	0.494171	+	0.359036i	0.0171633	+	0.0124698i	0.596334	−	0.802737i	$-0.296623\pi$
$829$	0.494171	+	0.359036i	0.0171633	+	0.0124698i	−0.579171	+	0.815206i	$0.696623\pi$
$830$	1.20646	−	0.245648i	0.0418768	−	0.00852656i
$831$	2.75150	−	38.7810i	0.0954486	−	1.34530i
$832$	−18.4615	+	10.6587i	−0.640036	+	0.369525i
$833$	−3.96416	+	8.90365i	−0.137350	+	0.308493i
$834$	−0.906388	−	6.49727i	−0.0313856	−	0.224982i
$835$	1.37222	−	0.776639i	0.0474875	−	0.0268767i
$836$	6.17091	−	18.9921i	0.213425	−	0.656855i
$837$	1.76161	+	5.47854i	0.0608900	+	0.189366i
$838$	−5.22569	+	1.69793i	−0.180518	+	0.0586540i
$839$	15.6554	+	17.3871i	0.540486	+	0.600270i	0.950083	−	0.311996i	$-0.100998\pi$
$839$	15.6554	+	17.3871i	0.540486	+	0.600270i	−0.409598	+	0.912266i	$0.634331\pi$
$840$	−6.50031	−	27.1794i	−0.224282	−	0.937777i
$841$	32.3060	−	35.8794i	1.11400	−	1.23722i
$842$	4.19674	−	9.42604i	0.144629	−	0.324843i
$843$	37.2858	+	31.3512i	1.28419	+	1.07979i
$844$	−1.27006	−	12.0838i	−0.0437173	−	0.415942i
$845$	12.3676	−	21.0034i	0.425460	−	0.722539i
$846$	−0.859127	+	1.75241i	−0.0295374	+	0.0602490i
$847$	−10.5801	+	14.5623i	−0.363537	+	0.500365i
$848$	−16.2937	+	14.6709i	−0.559529	+	0.503802i
$849$	−11.2635	−	31.0444i	−0.386561	−	1.06544i
$850$	0.116382	+	1.32561i	0.00399188	+	0.0454679i
$851$	−7.16481	−	12.4098i	−0.245606	−	0.425403i
$852$	−1.15488	−	34.0658i	−0.0395657	−	1.16708i
$853$	0.194310	+	0.436426i	0.00665303	+	0.0149430i	0.916841	−	0.399252i	$-0.130730\pi$
$853$	0.194310	+	0.436426i	0.00665303	+	0.0149430i	−0.910188	+	0.414195i	$0.864063\pi$
$854$	15.1671	+	11.0195i	0.519006	+	0.377080i
$855$	1.24128	−	27.2519i	0.0424510	−	0.931996i
$856$	−21.6778	+	15.7498i	−0.740932	+	0.538319i
$857$	40.5723	+	23.4244i	1.38592	+	0.800163i	0.992853	−	0.119346i	$-0.0380798\pi$
$857$	40.5723	+	23.4244i	1.38592	+	0.800163i	0.393070	+	0.919509i	$0.371413\pi$
$858$	9.09802	+	0.645503i	0.310601	+	0.0220371i
$859$	8.78606	−	9.75790i	0.299776	−	0.332935i	−0.574372	−	0.818594i	$-0.694754\pi$
$859$	8.78606	−	9.75790i	0.299776	−	0.332935i	0.874148	+	0.485659i	$0.161420\pi$
$860$	−8.84803	+	2.79125i	−0.301715	+	0.0951810i
$861$	26.6980	−	50.0886i	0.909867	−	1.70702i
$862$	−2.00080	+	9.41301i	−0.0681474	+	0.320608i
$863$	4.35551	−	1.41519i	0.148263	−	0.0481737i	−0.233945	−	0.972250i	$-0.575164\pi$
$863$	4.35551	−	1.41519i	0.148263	−	0.0481737i	0.382209	+	0.924076i	$0.375164\pi$
$864$	−21.3453	−	7.00765i	−0.726182	−	0.238405i
$865$	−0.848999	+	0.0818797i	−0.0288668	+	0.00278399i
$866$	−6.83415	−	1.45264i	−0.232234	−	0.0493628i
$867$	12.5505	+	25.7990i	0.426237	+	0.876179i
$868$	8.22150	−	4.74669i	0.279056	−	0.161113i
$869$	−8.32352	−	3.70587i	−0.282356	−	0.125713i
$870$	−3.90906	+	13.1549i	−0.132530	+	0.445994i
$871$	−11.8476	+	5.27487i	−0.401439	+	0.178732i
$872$	0.322537	−	0.443934i	0.0109225	−	0.0150335i
$873$	41.3106	−	16.5928i	1.39815	−	0.561581i
$874$	−7.08558			−0.239673
$875$	−39.6432	+	33.8898i	−1.34018	+	1.14568i
$876$	10.4356	+	28.7628i	0.352588	+	0.971804i
$877$	2.45032	+	11.5278i	0.0827414	+	0.389268i	0.999958	−	0.00912022i	$-0.00290310\pi$
$877$	2.45032	+	11.5278i	0.0827414	+	0.389268i	−0.917217	+	0.398388i	$0.869570\pi$
$878$	−8.79964	−	0.924879i	−0.296973	−	0.0312132i
$879$	12.9352	−	44.9378i	0.436294	−	1.51571i
$880$	−2.06148	+	18.1179i	−0.0694926	+	0.610756i
$881$	12.4003	−	9.00931i	0.417775	−	0.303532i	−0.358967	−	0.933350i	$-0.616871\pi$
$881$	12.4003	−	9.00931i	0.417775	−	0.303532i	0.776742	+	0.629819i	$0.216871\pi$
$882$	6.13884	−	16.7601i	0.206706	−	0.564341i
$883$	−22.0819	−	30.3931i	−0.743115	−	1.02281i	−0.998433	−	0.0559529i	$-0.982180\pi$
$883$	−22.0819	−	30.3931i	−0.743115	−	1.02281i	0.255319	−	0.966857i	$-0.417820\pi$
$884$	5.80192	+	1.23324i	0.195140	+	0.0414782i
$885$	11.7600	−	17.0792i	0.395307	−	0.574110i
$886$	14.2652	−	3.03217i	0.479250	−	0.101868i
$887$	−1.03945	−	0.935926i	−0.0349013	−	0.0314253i	0.651495	−	0.758653i	$-0.274142\pi$
$887$	−1.03945	−	0.935926i	−0.0349013	−	0.0314253i	−0.686397	+	0.727227i	$0.740809\pi$
$888$	8.79616	−	1.22709i	0.295180	−	0.0411784i
$889$	−11.8031	−	13.1087i	−0.395864	−	0.439652i
$890$	−0.993159	+	4.48308i	−0.0332908	+	0.150273i
$891$	−14.7300	−	19.0126i	−0.493473	−	0.636945i
$892$	22.0088	+	30.2925i	0.736909	+	1.01427i
$893$	5.68427	+	3.28182i	0.190217	+	0.109822i
$894$	11.3698	−	5.53112i	0.380264	−	0.184988i
$895$	8.69880	+	27.5744i	0.290769	+	0.921711i
$896$	−5.07348	+	48.2709i	−0.169493	+	1.61262i
$897$	8.81888	+	35.5246i	0.294454	+	1.18613i
$898$	10.3986	−	9.36291i	0.347004	−	0.312444i
$899$	−9.73605			−0.324716
$900$	4.26466	+	27.2311i	0.142155	+	0.907702i
$901$	4.74405			0.158047
$902$	5.62326	−	5.06321i	0.187234	−	0.168586i
$903$	−17.5324	−	5.04664i	−0.583440	−	0.167942i
$904$	1.72928	−	16.4530i	0.0575149	−	0.547217i
$905$	16.7939	+	0.144001i	0.558249	+	0.00478675i
$906$	−0.929525	−	0.628350i	−0.0308814	−	0.0208755i
$907$	−32.2735	−	18.6331i	−1.07163	−	0.618703i	−0.143000	−	0.989723i	$-0.545675\pi$
$907$	−32.2735	−	18.6331i	−1.07163	−	0.618703i	−0.928625	+	0.371020i	$0.879008\pi$
$908$	−8.56723	−	11.7918i	−0.284314	−	0.391324i
$909$	26.1443	+	16.4109i	0.867153	+	0.544315i
$910$	−8.19898	−	18.8485i	−0.271794	−	0.624822i
$911$	10.6528	+	11.8312i	0.352945	+	0.391985i	0.893306	−	0.449448i	$-0.148379\pi$
$911$	10.6528	+	11.8312i	0.352945	+	0.391985i	−0.540362	+	0.841433i	$0.681713\pi$
$912$	−8.07228	+	19.9212i	−0.267300	+	0.659656i
$913$	−2.71287	−	2.44268i	−0.0897830	−	0.0808409i
$914$	4.72744	−	1.00485i	0.156370	−	0.0332374i
$915$	−29.3423	−	25.1046i	−0.970026	−	0.829934i
$916$	1.15512	+	0.245529i	0.0381663	+	0.00811250i
$917$	−14.6525	−	20.1674i	−0.483868	−	0.665987i
$918$	0.687793	+	1.19974i	0.0227006	+	0.0395973i
$919$	15.8659	−	11.5272i	0.523367	−	0.380248i	−0.294504	−	0.955650i	$-0.595154\pi$
$919$	15.8659	−	11.5272i	0.523367	−	0.380248i	0.817871	+	0.575402i	$0.195154\pi$
$920$	14.6504	−	2.98299i	0.483011	−	0.0983462i
$921$	−34.5486	−	35.8491i	−1.13841	−	1.18127i
$922$	11.5294	+	1.21179i	0.379702	+	0.0399083i
$923$	−10.8857	−	51.2130i	−0.358306	−	1.68570i
$924$	−25.5339	+	30.3673i	−0.840004	+	0.999011i
$925$	−9.51115	−	13.5745i	−0.312725	−	0.446328i
$926$	9.45756			0.310795
$927$	−5.28873	+	37.0833i	−0.173705	+	1.21798i
$928$	22.3409	−	30.7496i	0.733376	−	1.00941i
$929$	12.2677	−	5.46193i	0.402490	−	0.179200i	−0.195500	−	0.980704i	$-0.562633\pi$
$929$	12.2677	−	5.46193i	0.402490	−	0.179200i	0.597990	+	0.801504i	$0.295966\pi$
$930$	1.56115	−	0.742970i	0.0511920	−	0.0243630i
$931$	−54.8378	−	24.4154i	−1.79724	−	0.800182i
$932$	−39.4235	+	22.7612i	−1.29136	+	0.745567i
$933$	20.1940	−	29.8732i	0.661123	−	0.978006i
$934$	−14.1910	−	3.01638i	−0.464342	−	0.0986990i
$935$	2.95462	−	2.61483i	0.0966265	−	0.0855141i
$936$	−22.4588	−	3.20302i	−0.734089	−	0.104694i
$937$	−40.7258	+	13.2326i	−1.33045	+	0.432290i	−0.886072	−	0.463548i	$-0.846576\pi$
$937$	−40.7258	+	13.2326i	−1.33045	+	0.432290i	−0.444381	+	0.895838i	$0.646576\pi$
$938$	−1.03704	+	4.87887i	−0.0338605	+	0.159301i
$939$	23.0469	+	36.9665i	0.752109	+	1.20636i
$940$	−6.28930	−	2.10331i	−0.205134	−	0.0686023i
$941$	−17.2149	+	19.1191i	−0.561191	+	0.623265i	−0.955243	−	0.295823i	$-0.904406\pi$
$941$	−17.2149	+	19.1191i	−0.561191	+	0.623265i	0.394052	+	0.919088i	$0.371073\pi$
$942$	2.10490	+	4.32686i	0.0685814	+	0.140977i
$943$	26.2981	+	15.1832i	0.856383	+	0.494433i
$944$	−13.2181	+	9.60355i	−0.430214	+	0.312569i
$945$	−22.6196	+	49.2550i	−0.735817	+	1.60227i
$946$	−1.96770	−	1.42962i	−0.0639754	−	0.0464808i
$947$	−16.2810	−	36.5677i	−0.529062	−	1.18829i	−0.958473	−	0.285183i	$-0.907946\pi$
$947$	−16.2810	−	36.5677i	−0.529062	−	1.18829i	0.429411	−	0.903109i	$-0.358721\pi$
$948$	9.57595	+	5.10413i	0.311012	+	0.165775i
$949$	23.4997	+	40.7026i	0.762832	+	1.32126i
$950$	−8.16443	+	0.716801i	−0.264889	+	0.0232561i
$951$	−26.6875	+	31.7393i	−0.865403	+	1.02922i
$952$	3.54058	−	3.18795i	0.114751	−	0.103322i
$953$	−3.27273	+	4.50452i	−0.106014	+	0.145916i	−0.858728	−	0.512432i	$-0.828745\pi$
$953$	−3.27273	+	4.50452i	−0.106014	+	0.145916i	0.752714	+	0.658348i	$0.228745\pi$
$954$	−8.66815	+	0.588403i	−0.280642	+	0.0190503i
$955$	1.66383	+	1.88005i	0.0538404	+	0.0608369i
$956$	0.924246	+	8.79361i	0.0298923	+	0.284406i
$957$	38.2501	−	13.8778i	1.23645	−	0.448606i
$958$	−2.61118	+	5.86481i	−0.0843634	+	0.189483i
$959$	27.6910	−	30.7540i	0.894190	−	0.993099i
$960$	3.09196	−	16.6025i	0.0997927	−	0.535844i
$961$	−19.9223	−	22.1260i	−0.642655	−	0.713741i
$962$	6.21262	−	2.01860i	0.200303	−	0.0650824i
$963$	51.9335	+	1.91943i	1.67353	+	0.0618528i
$964$	5.39588	−	16.6068i	0.173790	−	0.534870i
$965$	−6.32207	−	0.719334i	−0.203515	−	0.0231562i
$966$	13.0473	+	5.28689i	0.419789	+	0.170103i
$967$	6.01720	−	13.5148i	0.193500	−	0.434608i	−0.790574	−	0.612366i	$-0.790218\pi$
$967$	6.01720	−	13.5148i	0.193500	−	0.434608i	0.984074	+	0.177758i	$0.0568845\pi$
$968$	5.16891	−	2.98427i	0.166135	−	0.0959182i
$969$	4.18221	−	2.03453i	0.134352	−	0.0653586i
$970$	−6.58781	−	11.6398i	−0.211522	−	0.373731i
$971$	−12.3168	−	8.94868i	−0.395265	−	0.287177i	0.372345	−	0.928095i	$-0.378554\pi$
$971$	−12.3168	−	8.94868i	−0.395265	−	0.287177i	−0.767610	+	0.640918i	$0.778554\pi$
$972$	15.8966	+	23.8284i	0.509884	+	0.764297i
$973$	41.6885	+	13.5454i	1.33647	+	0.434246i
$974$	−3.75348	+	6.50122i	−0.120269	+	0.208313i
$975$	13.7555	+	40.0415i	0.440527	+	1.28235i
$976$	15.2132	+	26.3500i	0.486963	+	0.843444i
$977$	−9.34769	−	43.9774i	−0.299059	−	1.40696i	−0.829152	−	0.559023i	$-0.811177\pi$
$977$	−9.34769	−	43.9774i	−0.299059	−	1.40696i	0.530093	−	0.847939i	$-0.322157\pi$
$978$	−1.72827	−	6.96191i	−0.0552641	−	0.222617i
$979$	12.4375	−	5.53754i	0.397505	−	0.176981i
$980$	59.2142	+	13.1180i	1.89153	+	0.419039i
$981$	−1.02363	+	0.291266i	−0.0326818	+	0.00929940i
$982$			15.8654i			0.506284i
$983$	−7.63074	+	0.802023i	−0.243383	+	0.0255806i	−0.225434	−	0.974258i	$-0.572380\pi$
$983$	−7.63074	+	0.802023i	−0.243383	+	0.0255806i	−0.0179485	+	0.999839i	$0.505713\pi$
$984$	−14.8428	+	11.5721i	−0.473170	+	0.368906i
$985$	3.29394	−	1.03913i	0.104954	−	0.0331094i
$986$	−2.28850	+	0.486436i	−0.0728807	+	0.0154913i
$987$	−8.01820	−	10.2844i	−0.255222	−	0.327356i
$988$	−7.59553	+	35.7342i	−0.241646	+	1.13686i
$989$	3.01621	−	9.28294i	0.0959099	−	0.295180i
$990$	−5.07425	+	5.14418i	−0.161270	+	0.163493i
$991$	−14.3742	−	44.2393i	−0.456612	−	1.40531i	−0.869232	−	0.494404i	$-0.835386\pi$
$991$	−14.3742	−	44.2393i	−0.456612	−	1.40531i	0.412620	−	0.910903i	$-0.364614\pi$
$992$	−4.76222	+	0.500530i	−0.151201	+	0.0158918i
$993$	12.6670	+	10.6508i	0.401974	+	0.337994i
$994$	−18.3960	−	8.19041i	−0.583484	−	0.259784i
$995$	−21.7502	−	16.0892i	−0.689528	−	0.510061i
$996$	3.01699	+	3.13056i	0.0955970	+	0.0991955i
$997$	12.7151	+	28.5586i	0.402691	+	0.904459i	0.995105	+	0.0988249i	$0.0315084\pi$
$997$	12.7151	+	28.5586i	0.402691	+	0.904459i	−0.592414	+	0.805634i	$0.701825\pi$
$998$	9.23212	+	2.99970i	0.292238	+	0.0949538i
$999$	−14.8911	−	8.65813i	−0.471134	−	0.273931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.u.a.79.16	yes	224
3.2	odd	2		675.2.y.a.154.13		224
9.4	even	3	inner	225.2.u.a.4.16	✓	224
9.5	odd	6		675.2.y.a.604.13		224
25.19	even	10	inner	225.2.u.a.169.16	yes	224
75.44	odd	10		675.2.y.a.19.13		224
225.94	even	30	inner	225.2.u.a.94.16	yes	224
225.194	odd	30		675.2.y.a.469.13		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.16	✓	224	9.4	even	3	inner
225.2.u.a.79.16	yes	224	1.1	even	1	trivial
225.2.u.a.94.16	yes	224	225.94	even	30	inner
225.2.u.a.169.16	yes	224	25.19	even	10	inner
675.2.y.a.19.13		224	75.44	odd	10
675.2.y.a.154.13		224	3.2	odd	2
675.2.y.a.469.13		224	225.194	odd	30
675.2.y.a.604.13		224	9.5	odd	6

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.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.299541 - 0.269708i) q^{2} +(-1.24716 + 1.20191i) q^{3} +(-0.192074 + 1.82747i) q^{4} +(-1.79768 - 1.32979i) q^{5} +(-0.0494088 + 0.696391i) q^{6} +(-4.03987 - 2.33242i) q^{7} +(0.909187 + 1.25139i) q^{8} +(0.110803 - 2.99795i) q^{9} +O(q^{10})\)	\(q+(0.299541 - 0.269708i) q^{2} +(-1.24716 + 1.20191i) q^{3} +(-0.192074 + 1.82747i) q^{4} +(-1.79768 - 1.32979i) q^{5} +(-0.0494088 + 0.696391i) q^{6} +(-4.03987 - 2.33242i) q^{7} +(0.909187 + 1.25139i) q^{8} +(0.110803 - 2.99795i) q^{9} +(-0.897134 + 0.0865220i) q^{10} +(1.78814 + 1.98593i) q^{11} +(-1.95691 - 2.51000i) q^{12} +(-3.63309 - 3.27125i) q^{13} +(-1.83918 + 0.390930i) q^{14} +(3.84029 - 0.502201i) q^{15} +(-2.98491 - 0.634462i) q^{16} +(0.388104 + 0.534179i) q^{17} +(-0.775381 - 0.927894i) q^{18} +(-3.29002 + 2.39034i) q^{19} +(2.77544 - 3.02978i) q^{20} +(7.84173 - 1.94669i) q^{21} +(1.07124 + 0.112592i) q^{22} +(0.898733 + 4.22821i) q^{23} +(-2.63796 - 0.467913i) q^{24} +(1.46331 + 4.78108i) q^{25} -1.97054 q^{26} +(3.46510 + 3.87209i) q^{27} +(5.03838 - 6.93474i) q^{28} +(-8.03092 + 3.57559i) q^{29} +(1.01487 - 1.18618i) q^{30} +(1.01176 + 0.450465i) q^{31} +(-3.74436 + 2.16181i) q^{32} +(-4.61701 - 0.327576i) q^{33} +(0.260325 + 0.0553338i) q^{34} +(4.16077 + 9.56514i) q^{35} +(5.45738 + 0.778318i) q^{36} +(-3.15275 + 1.02439i) q^{37} +(-0.340802 + 1.60335i) q^{38} +(8.46281 - 0.286902i) q^{39} +(0.0296563 - 3.45863i) q^{40} +(4.70059 - 5.22054i) q^{41} +(1.82388 - 2.69809i) q^{42} +(-1.95550 - 1.12901i) q^{43} +(-3.97268 + 2.88632i) q^{44} +(-4.18584 + 5.24202i) q^{45} +(1.40959 + 1.02413i) q^{46} +(-0.656473 - 1.47446i) q^{47} +(4.48522 - 2.79633i) q^{48} +(7.38039 + 12.7832i) q^{49} +(1.72782 + 1.03746i) q^{50} +(-1.12606 - 0.199738i) q^{51} +(6.67593 - 6.01104i) q^{52} +(4.22318 - 5.81270i) q^{53} +(2.08227 + 0.225287i) q^{54} +(-0.573634 - 5.94792i) q^{55} +(-0.754235 - 7.17606i) q^{56} +(1.23019 - 6.93545i) q^{57} +(-1.44122 + 3.23704i) q^{58} +(3.58259 - 3.97887i) q^{59} +(0.180135 + 7.11445i) q^{60} +(-6.67168 - 7.40965i) q^{61} +(0.424558 - 0.137947i) q^{62} +(-7.44012 + 11.8529i) q^{63} +(1.34746 - 4.14704i) q^{64} +(2.18106 + 10.7119i) q^{65} +(-1.47133 + 1.14712i) q^{66} +(1.07897 - 2.42340i) q^{67} +(-1.05074 + 0.606644i) q^{68} +(-6.20280 - 4.19304i) q^{69} +(3.82611 + 1.74296i) q^{70} +(8.66423 + 6.29493i) q^{71} +(3.85235 - 2.58704i) q^{72} +(-9.14313 - 2.97078i) q^{73} +(-0.668091 + 1.15717i) q^{74} +(-7.57143 - 4.20398i) q^{75} +(-3.73634 - 6.47152i) q^{76} +(-2.59183 - 12.1936i) q^{77} +(2.45758 - 2.36842i) q^{78} +(-3.11470 + 1.38675i) q^{79} +(4.52221 + 5.10986i) q^{80} +(-8.97545 - 0.664362i) q^{81} -2.83155i q^{82} +(-1.35856 + 0.142791i) q^{83} +(2.05131 + 14.7044i) q^{84} +(0.0126593 - 1.47638i) q^{85} +(-0.890256 + 0.189230i) q^{86} +(5.71826 - 14.1118i) q^{87} +(-0.859418 + 4.04324i) q^{88} +(1.57433 - 4.84528i) q^{89} +(0.159984 + 2.69915i) q^{90} +(7.04730 + 21.6894i) q^{91} +(-7.89953 + 0.830274i) q^{92} +(-1.80325 + 0.654250i) q^{93} +(-0.594314 - 0.264606i) q^{94} +(9.09306 + 0.0779692i) q^{95} +(2.07150 - 7.19652i) q^{96} +(6.03575 + 13.5565i) q^{97} +(5.65846 + 1.83854i) q^{98} +(6.15186 - 5.14071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more