LMFDB - Embedded newform 475.2.e.f.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.3
Root			$-0.0149173 + 0.0258375i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.f.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} +O(q^{10})$	\(q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} -5.16792 q^{11} -1.95999 q^{12} +(-1.76735 + 3.06115i) q^{13} +(0.510276 + 0.883825i) q^{14} +(-1.71432 - 2.96929i) q^{16} +(0.504641 + 0.874064i) q^{17} -0.603375 q^{18} +(2.42346 + 3.62310i) q^{19} +(1.68913 + 2.92565i) q^{21} +(0.803890 + 1.39238i) q^{22} +(3.83176 - 6.63680i) q^{23} +(0.625274 + 1.08301i) q^{24} +1.09968 q^{26} -5.08681 q^{27} +(-3.12163 + 5.40683i) q^{28} +(2.01303 - 3.48667i) q^{29} -4.60077 q^{31} +(-1.74766 + 3.02703i) q^{32} +(2.66105 + 4.60908i) q^{33} +(0.156998 - 0.271928i) q^{34} +(-1.84558 - 3.19664i) q^{36} -6.48831 q^{37} +(0.599183 - 1.21653i) q^{38} +3.64017 q^{39} +(3.40277 + 5.89377i) q^{41} +(0.525500 - 0.910193i) q^{42} +(-3.15511 - 5.46481i) q^{43} +(-4.91782 + 8.51792i) q^{44} -2.38418 q^{46} +(1.92079 - 3.32690i) q^{47} +(-1.76547 + 3.05788i) q^{48} +3.76091 q^{49} +(0.519697 - 0.900141i) q^{51} +(3.36365 + 5.82601i) q^{52} +(3.55946 - 6.16516i) q^{53} +(0.791273 + 1.37052i) q^{54} +3.98343 q^{56} +(1.98343 - 4.02699i) q^{57} -1.25254 q^{58} +(-6.73649 - 11.6679i) q^{59} +(-3.06850 + 5.31480i) q^{61} +(0.715668 + 1.23957i) q^{62} +(-3.18105 + 5.50975i) q^{63} -5.76986 q^{64} +(0.827874 - 1.43392i) q^{66} +(5.59897 - 9.69770i) q^{67} +1.92088 q^{68} -7.89215 q^{69} +(0.227702 + 0.394391i) q^{71} +(-1.17755 + 2.03958i) q^{72} +(-2.06691 - 3.57999i) q^{73} +(1.00928 + 1.74813i) q^{74} +(8.27788 - 0.546653i) q^{76} +16.9528 q^{77} +(-0.566242 - 0.980760i) q^{78} +(-1.44414 - 2.50132i) q^{79} +(-0.289876 - 0.502080i) q^{81} +(1.05863 - 1.83360i) q^{82} -5.50061 q^{83} +6.42953 q^{84} +(-0.981579 + 1.70014i) q^{86} -4.14617 q^{87} +6.27551 q^{88} +(3.56433 - 6.17360i) q^{89} +(5.79760 - 10.0417i) q^{91} +(-7.29264 - 12.6312i) q^{92} +(2.36902 + 4.10326i) q^{93} -1.19514 q^{94} +3.59960 q^{96} +(5.41252 + 9.37476i) q^{97} +(-0.585025 - 1.01329i) q^{98} +(-5.01144 + 8.68006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.155554	−	0.269427i	−0.109993	−	0.190514i	0.805774	−	0.592223i	$-0.201750\pi$
$2$	−0.155554	−	0.269427i	−0.109993	−	0.190514i	−0.915767	+	0.401709i	$0.868416\pi$
$3$	−0.514917	−	0.891863i	−0.297288	−	0.514917i	0.678227	−	0.734853i	$-0.262749\pi$
$3$	−0.514917	−	0.891863i	−0.297288	−	0.514917i	−0.975514	+	0.219935i	$0.929415\pi$
$4$	0.951606	−	1.64823i	0.475803	−	0.824115i
$5$		0			0
$5$		0			0
$6$	−0.160195	+	0.277466i	−0.0653993	+	0.113275i
$7$	−3.28038			−1.23987			−0.619934	−	0.784654i	$-0.712841\pi$
$7$	−3.28038			−1.23987			−0.619934	+	0.784654i	$0.712841\pi$
$8$	−1.21432			−0.429327
$9$	0.969720	−	1.67960i	0.323240	−	0.559868i
$10$		0			0
$11$	−5.16792			−1.55819			−0.779093	−	0.626908i	$-0.784320\pi$
$11$	−5.16792			−1.55819			−0.779093	+	0.626908i	$0.784320\pi$
$12$	−1.95999			−0.565801
$13$	−1.76735	+	3.06115i	−0.490176	+	0.849010i	−0.999936	−	0.0113069i	$-0.996401\pi$
$13$	−1.76735	+	3.06115i	−0.490176	+	0.849010i	0.509760	+	0.860317i	$0.329734\pi$
$14$	0.510276	+	0.883825i	0.136377	+	0.236212i
$15$		0			0
$16$	−1.71432	−	2.96929i	−0.428580	−	0.742322i
$17$	0.504641	+	0.874064i	0.122393	+	0.211992i	0.920711	−	0.390245i	$-0.127610\pi$
$17$	0.504641	+	0.874064i	0.122393	+	0.211992i	−0.798318	+	0.602237i	$0.794276\pi$
$18$	−0.603375			−0.142217
$19$	2.42346	+	3.62310i	0.555979	+	0.831196i
$19$	2.42346	+	3.62310i	0.555979	+	0.831196i
$20$		0			0
$21$	1.68913	+	2.92565i	0.368598	+	0.638430i
$22$	0.803890	+	1.39238i	0.171390	+	0.296856i
$23$	3.83176	−	6.63680i	0.798976	−	1.38387i	−0.121307	−	0.992615i	$-0.538709\pi$
$23$	3.83176	−	6.63680i	0.798976	−	1.38387i	0.920283	−	0.391253i	$-0.127958\pi$
$24$	0.625274	+	1.08301i	0.127634	+	0.221068i
$25$		0			0
$26$	1.09968			0.215664
$27$	−5.08681			−0.978956
$28$	−3.12163	+	5.40683i	−0.589933	+	1.02179i
$29$	2.01303	−	3.48667i	0.373810	−	0.647458i	−0.616338	−	0.787482i	$-0.711385\pi$
$29$	2.01303	−	3.48667i	0.373810	−	0.647458i	0.990148	+	0.140024i	$0.0447179\pi$
$30$		0			0
$31$	−4.60077			−0.826323			−0.413162	−	0.910658i	$-0.635576\pi$
$31$	−4.60077			−0.826323			−0.413162	+	0.910658i	$0.635576\pi$
$32$	−1.74766	+	3.02703i	−0.308945	+	0.535109i
$33$	2.66105	+	4.60908i	0.463230	+	0.802337i
$34$	0.156998	−	0.271928i	0.0269249	−	0.0466353i
$35$		0			0
$36$	−1.84558	−	3.19664i	−0.307597	−	0.532774i
$37$	−6.48831			−1.06667			−0.533336	−	0.845904i	$-0.679062\pi$
$37$	−6.48831			−1.06667			−0.533336	+	0.845904i	$0.679062\pi$
$38$	0.599183	−	1.21653i	0.0972004	−	0.197348i
$39$	3.64017			0.582893
$40$		0			0
$41$	3.40277	+	5.89377i	0.531423	+	0.920451i	0.999327	+	0.0366724i	$0.0116758\pi$
$41$	3.40277	+	5.89377i	0.531423	+	0.920451i	−0.467904	+	0.883779i	$0.654991\pi$
$42$	0.525500	−	0.910193i	0.0810865	−	0.140446i
$43$	−3.15511	−	5.46481i	−0.481150	−	0.833376i	0.518616	−	0.855007i	$-0.326447\pi$
$43$	−3.15511	−	5.46481i	−0.481150	−	0.833376i	−0.999766	+	0.0216315i	$0.993114\pi$
$44$	−4.91782	+	8.51792i	−0.741390	+	1.28412i
$45$		0			0
$46$	−2.38418			−0.351528
$47$	1.92079	−	3.32690i	0.280175	−	0.485278i	−0.691252	−	0.722613i	$-0.742941\pi$
$47$	1.92079	−	3.32690i	0.280175	−	0.485278i	0.971428	+	0.237335i	$0.0762740\pi$
$48$	−1.76547	+	3.05788i	−0.254823	+	0.441366i
$49$	3.76091			0.537273
$50$		0			0
$51$	0.519697	−	0.900141i	0.0727721	−	0.126045i
$52$	3.36365	+	5.82601i	0.466454	+	0.807923i
$53$	3.55946	−	6.16516i	0.488929	−	0.846850i	−0.510990	−	0.859587i	$-0.670721\pi$
$53$	3.55946	−	6.16516i	0.488929	−	0.846850i	0.999919	+	0.0127367i	$0.00405432\pi$
$54$	0.791273	+	1.37052i	0.107679	+	0.186505i
$55$		0			0
$56$	3.98343			0.532309
$57$	1.98343	−	4.02699i	0.262711	−	0.533388i
$58$	−1.25254			−0.164466
$59$	−6.73649	−	11.6679i	−0.877016	−	1.51904i	−0.854599	−	0.519288i	$-0.826197\pi$
$59$	−6.73649	−	11.6679i	−0.877016	−	1.51904i	−0.0224174	−	0.999749i	$-0.507136\pi$
$60$		0			0
$61$	−3.06850	+	5.31480i	−0.392881	+	0.680491i	−0.992828	−	0.119549i	$-0.961855\pi$
$61$	−3.06850	+	5.31480i	−0.392881	+	0.680491i	0.599947	+	0.800040i	$0.295188\pi$
$62$	0.715668	+	1.23957i	0.0908899	+	0.157426i
$63$	−3.18105	+	5.50975i	−0.400775	+	0.694163i
$64$	−5.76986			−0.721232
$65$		0			0
$66$	0.827874	−	1.43392i	0.101904	−	0.176503i
$67$	5.59897	−	9.69770i	0.684023	−	1.18476i	−0.289719	−	0.957112i	$-0.593562\pi$
$67$	5.59897	−	9.69770i	0.684023	−	1.18476i	0.973743	−	0.227652i	$-0.0731047\pi$
$68$	1.92088			0.232941
$69$	−7.89215			−0.950103
$70$		0			0
$71$	0.227702	+	0.394391i	0.0270233	+	0.0468056i	0.879221	−	0.476415i	$-0.158064\pi$
$71$	0.227702	+	0.394391i	0.0270233	+	0.0468056i	−0.852198	+	0.523220i	$0.824731\pi$
$72$	−1.17755	+	2.03958i	−0.138776	+	0.240367i
$73$	−2.06691	−	3.57999i	−0.241914	−	0.419007i	0.719346	−	0.694652i	$-0.244442\pi$
$73$	−2.06691	−	3.57999i	−0.241914	−	0.419007i	−0.961259	+	0.275646i	$0.911108\pi$
$74$	1.00928	+	1.74813i	0.117327	+	0.203216i
$75$		0			0
$76$	8.27788	−	0.546653i	0.949538	−	0.0627054i
$77$	16.9528			1.93195
$78$	−0.566242	−	0.980760i	−0.0641143	−	0.111049i
$79$	−1.44414	−	2.50132i	−0.162478	−	0.281421i	0.773278	−	0.634067i	$-0.218615\pi$
$79$	−1.44414	−	2.50132i	−0.162478	−	0.281421i	−0.935757	+	0.352646i	$0.885282\pi$
$80$		0			0
$81$	−0.289876	−	0.502080i	−0.0322085	−	0.0557867i
$82$	1.05863	−	1.83360i	0.116906	−	0.202487i
$83$	−5.50061			−0.603770			−0.301885	−	0.953344i	$-0.597616\pi$
$83$	−5.50061			−0.603770			−0.301885	+	0.953344i	$0.597616\pi$
$84$	6.42953			0.701519
$85$		0			0
$86$	−0.981579	+	1.70014i	−0.105846	+	0.183331i
$87$	−4.14617			−0.444516
$88$	6.27551			0.668971
$89$	3.56433	−	6.17360i	0.377818	−	0.654400i	−0.612926	−	0.790140i	$-0.710008\pi$
$89$	3.56433	−	6.17360i	0.377818	−	0.654400i	0.990745	+	0.135740i	$0.0433411\pi$
$90$		0			0
$91$	5.79760	−	10.0417i	0.607754	−	1.05266i
$92$	−7.29264	−	12.6312i	−0.760311	−	1.31690i
$93$	2.36902	+	4.10326i	0.245656	+	0.425488i
$94$	−1.19514			−0.123270
$95$		0			0
$96$	3.59960			0.367382
$97$	5.41252	+	9.37476i	0.549558	+	0.951862i	0.998305	+	0.0582034i	$0.0185372\pi$
$97$	5.41252	+	9.37476i	0.549558	+	0.951862i	−0.448747	+	0.893659i	$0.648129\pi$
$98$	−0.585025	−	1.01329i	−0.0590964	−	0.102358i
$99$	−5.01144	+	8.68006i	−0.503668	+	0.872379i
$100$		0			0
$101$	3.09011	−	5.35223i	0.307478	−	0.532567i	−0.670332	−	0.742061i	$-0.733848\pi$
$101$	3.09011	−	5.35223i	0.307478	−	0.532567i	0.977810	+	0.209494i	$0.0671818\pi$
$102$	−0.323363			−0.0320177
$103$	18.3217			1.80529			0.902644	−	0.430387i	$-0.141623\pi$
$103$	18.3217			1.80529			0.902644	+	0.430387i	$0.141623\pi$
$104$	2.14613	−	3.71721i	0.210446	−	0.364503i
$105$		0			0
$106$	−2.21475			−0.215116
$107$	8.73445			0.844391			0.422196	−	0.906505i	$-0.361260\pi$
$107$	8.73445			0.844391			0.422196	+	0.906505i	$0.361260\pi$
$108$	−4.84064	+	8.38423i	−0.465790	+	0.806773i
$109$	3.04839	+	5.27997i	0.291983	+	0.505730i	0.974279	−	0.225347i	$-0.0723515\pi$
$109$	3.04839	+	5.27997i	0.291983	+	0.505730i	−0.682295	+	0.731077i	$0.739018\pi$
$110$		0			0
$111$	3.34094	+	5.78668i	0.317108	+	0.549248i
$112$	5.62363	+	9.74041i	0.531383	+	0.920382i
$113$	10.3443			0.973111			0.486556	−	0.873650i	$-0.338253\pi$
$113$	10.3443			0.973111			0.486556	+	0.873650i	$0.338253\pi$
$114$	−1.39351	+	0.0920244i	−0.130514	+	0.00861887i
$115$		0			0
$116$	−3.83122	−	6.63587i	−0.355720	−	0.616125i
$117$	3.42768	+	5.93692i	0.316889	+	0.548868i
$118$	−2.09578	+	3.62999i	−0.192932	+	0.334168i
$119$	−1.65542	−	2.86726i	−0.151752	−	0.262842i
$120$		0			0
$121$	15.7074			1.42794
$122$	1.90927			0.172857
$123$	3.50429	−	6.06960i	0.315971	−	0.547278i
$124$	−4.37812	+	7.58313i	−0.393167	+	0.680985i
$125$		0			0
$126$	1.97930			0.176330
$127$	−1.68356	+	2.91602i	−0.149392	+	0.258755i	−0.931003	−	0.365012i	$-0.881065\pi$
$127$	−1.68356	+	2.91602i	−0.149392	+	0.258755i	0.781611	+	0.623766i	$0.214398\pi$
$128$	4.39284	+	7.60862i	0.388276	+	0.672514i
$129$	−3.24924	+	5.62785i	−0.286080	+	0.495504i
$130$		0			0
$131$	−1.21089	−	2.09732i	−0.105796	−	0.183244i	0.808267	−	0.588816i	$-0.200406\pi$
$131$	−1.21089	−	2.09732i	−0.105796	−	0.183244i	−0.914063	+	0.405572i	$0.867072\pi$
$132$	10.1291			0.881624
$133$	−7.94987	−	11.8852i	−0.689341	−	1.03057i
$134$	−3.48377			−0.300952
$135$		0			0
$136$	−0.612795	−	1.06139i	−0.0525468	−	0.0910137i
$137$	5.75955	−	9.97584i	0.492072	−	0.852293i	−0.507886	−	0.861424i	$-0.669573\pi$
$137$	5.75955	−	9.97584i	0.492072	−	0.852293i	0.999958	+	0.00913057i	$0.00290639\pi$
$138$	1.22765	+	2.12636i	0.104505	+	0.181008i
$139$	−3.53776	+	6.12759i	−0.300069	+	0.519735i	−0.976151	−	0.217091i	$-0.930343\pi$
$139$	−3.53776	+	6.12759i	−0.300069	+	0.519735i	0.676082	+	0.736826i	$0.263676\pi$
$140$		0			0
$141$	−3.95618			−0.333171
$142$	0.0708399	−	0.122698i	0.00594475	−	0.0102966i
$143$	9.13355	−	15.8198i	0.763785	−	1.32292i
$144$	−6.64964			−0.554137
$145$		0			0
$146$	−0.643032	+	1.11376i	−0.0532177	+	0.0921758i
$147$	−1.93656	−	3.35422i	−0.159725	−	0.276651i
$148$	−6.17431	+	10.6942i	−0.507525	+	0.879060i
$149$	−6.37476	−	11.0414i	−0.522240	−	0.904547i	−0.999665	−	0.0258744i	$-0.991763\pi$
$149$	−6.37476	−	11.0414i	−0.522240	−	0.904547i	0.477425	−	0.878673i	$-0.341570\pi$
$150$		0			0
$151$	−19.6361			−1.59797			−0.798983	−	0.601353i	$-0.794628\pi$
$151$	−19.6361			−1.59797			−0.798983	+	0.601353i	$0.794628\pi$
$152$	−2.94285	−	4.39960i	−0.238697	−	0.356855i
$153$	1.95744			0.158250
$154$	−2.63707	−	4.56753i	−0.212501	−	0.368062i
$155$		0			0
$156$	3.46400	−	5.99983i	0.277342	−	0.480371i
$157$	−1.54244	−	2.67159i	−0.123101	−	0.213216i	0.797888	−	0.602805i	$-0.205950\pi$
$157$	−1.54244	−	2.67159i	−0.123101	−	0.213216i	−0.920989	+	0.389589i	$0.872617\pi$
$158$	−0.449283	+	0.778182i	−0.0357431	+	0.0619088i
$159$	−7.33131			−0.581410
$160$		0			0
$161$	−12.5696	+	21.7712i	−0.990625	+	1.71581i
$162$	−0.0901827	+	0.156201i	−0.00708542	+	0.0122723i
$163$	−22.4721			−1.76015			−0.880077	−	0.474831i	$-0.842509\pi$
$163$	−22.4721			−1.76015			−0.880077	+	0.474831i	$0.842509\pi$
$164$	12.9524			1.01141
$165$		0			0
$166$	0.855642	+	1.48201i	0.0664107	+	0.115027i
$167$	−5.26987	+	9.12769i	−0.407795	+	0.706322i	−0.994642	−	0.103376i	$-0.967036\pi$
$167$	−5.26987	+	9.12769i	−0.407795	+	0.706322i	0.586847	+	0.809698i	$0.300369\pi$
$168$	−2.05114	−	3.55268i	−0.158249	−	0.274095i
$169$	0.252915	+	0.438062i	0.0194550	+	0.0336970i
$170$		0			0
$171$	8.43545	−	0.557059i	0.645075	−	0.0425994i
$172$	−12.0097			−0.915730
$173$	−11.4691	−	19.8650i	−0.871977	−	1.51031i	−0.859949	−	0.510380i	$-0.829505\pi$
$173$	−11.4691	−	19.8650i	−0.871977	−	1.51031i	−0.0120281	−	0.999928i	$-0.503829\pi$
$174$	0.644953	+	1.11709i	0.0488938	+	0.0846865i
$175$		0			0
$176$	8.85947	+	15.3450i	0.667807	+	1.15668i
$177$	−6.93747	+	12.0161i	−0.521452	+	0.903182i
$178$	−2.21778			−0.166230
$179$	23.2705			1.73932			0.869661	−	0.493649i	$-0.164337\pi$
$179$	23.2705			1.73932			0.869661	+	0.493649i	$0.164337\pi$
$180$		0			0
$181$	7.98346	−	13.8278i	0.593406	−	1.02781i	−0.400364	−	0.916356i	$-0.631116\pi$
$181$	7.98346	−	13.8278i	0.593406	−	1.02781i	0.993770	−	0.111453i	$-0.0355503\pi$
$182$	−3.60736			−0.267395
$183$	6.32010			0.467195
$184$	−4.65298	+	8.05919i	−0.343022	+	0.594132i
$185$		0			0
$186$	0.737020	−	1.27656i	0.0540409	−	0.0936016i
$187$	−2.60794	−	4.51709i	−0.190712	−	0.330322i
$188$	−3.65566	−	6.33179i	−0.266617	−	0.461793i
$189$	16.6867			1.21378
$190$		0			0
$191$	−2.44600			−0.176986			−0.0884930	−	0.996077i	$-0.528205\pi$
$191$	−2.44600			−0.176986			−0.0884930	+	0.996077i	$0.528205\pi$
$192$	2.97100	+	5.14592i	0.214413	+	0.371375i
$193$	9.52280	+	16.4940i	0.685466	+	1.18726i	0.973290	+	0.229579i	$0.0737350\pi$
$193$	9.52280	+	16.4940i	0.685466	+	1.18726i	−0.287824	+	0.957683i	$0.592932\pi$
$194$	1.68388	−	2.91656i	0.120895	−	0.209397i
$195$		0			0
$196$	3.57891	−	6.19885i	0.255636	−	0.442775i
$197$	−6.18524			−0.440680			−0.220340	−	0.975423i	$-0.570717\pi$
$197$	−6.18524			−0.440680			−0.220340	+	0.975423i	$0.570717\pi$
$198$	3.11819			0.221600
$199$	−3.60525	+	6.24447i	−0.255569	+	0.442659i	−0.965050	−	0.262066i	$-0.915596\pi$
$199$	−3.60525	+	6.24447i	−0.255569	+	0.442659i	0.709481	+	0.704725i	$0.248930\pi$
$200$		0			0
$201$	−11.5320			−0.813407
$202$	−1.92272			−0.135282
$203$	−6.60350	+	11.4376i	−0.463475	+	0.802763i
$204$	−0.989093	−	1.71316i	−0.0692504	−	0.119945i
$205$		0			0
$206$	−2.85001	−	4.93636i	−0.198570	−	0.343933i
$207$	−7.43146	−	12.8717i	−0.516522	−	0.894643i
$208$	12.1192			0.840318
$209$	−12.5242	−	18.7239i	−0.866320	−	1.29516i
$210$		0			0
$211$	9.82333	+	17.0145i	0.676266	+	1.17133i	0.976097	+	0.217335i	$0.0697362\pi$
$211$	9.82333	+	17.0145i	0.676266	+	1.17133i	−0.299831	+	0.953992i	$0.596930\pi$
$212$	−6.77440	−	11.7336i	−0.465268	−	0.805868i
$213$	0.234495	−	0.406158i	0.0160674	−	0.0278295i
$214$	−1.35868	−	2.35330i	−0.0928773	−	0.160868i
$215$		0			0
$216$	6.17701			0.420292
$217$	15.0923			1.02453
$218$	0.948379	−	1.64264i	0.0642323	−	0.111254i
$219$	−2.12858	+	3.68680i	−0.143836	+	0.249131i
$220$		0			0
$221$	−3.56752			−0.239977
$222$	1.03939	−	1.80028i	0.0697595	−	0.120827i
$223$	5.66690	+	9.81536i	0.379484	+	0.657285i	0.990987	−	0.133957i	$-0.0427683\pi$
$223$	5.66690	+	9.81536i	0.379484	+	0.657285i	−0.611504	+	0.791242i	$0.709435\pi$
$224$	5.73299	−	9.92983i	0.383051	−	0.663464i
$225$		0			0
$226$	−1.60910	−	2.78704i	−0.107036	−	0.185391i
$227$	−11.1369			−0.739180			−0.369590	−	0.929195i	$-0.620502\pi$
$227$	−11.1369			−0.739180			−0.369590	+	0.929195i	$0.620502\pi$
$228$	−4.74996	−	7.10125i	−0.314574	−	0.470292i
$229$	3.51221			0.232093			0.116047	−	0.993244i	$-0.462978\pi$
$229$	3.51221			0.232093			0.116047	+	0.993244i	$0.462978\pi$
$230$		0			0
$231$	−8.72927	−	15.1195i	−0.574344	−	0.994792i
$232$	−2.44446	+	4.23393i	−0.160487	+	0.277971i
$233$	−3.09499	−	5.36068i	−0.202759	−	0.351190i	0.746657	−	0.665209i	$-0.231658\pi$
$233$	−3.09499	−	5.36068i	−0.202759	−	0.351190i	−0.949417	+	0.314020i	$0.898324\pi$
$234$	1.06638	−	1.84702i	0.0697113	−	0.120744i
$235$		0			0
$236$	−25.6419			−1.66915
$237$	−1.48723	+	2.57595i	−0.0966057	+	0.167326i
$238$	−0.515013	+	0.892028i	−0.0333833	+	0.0578216i
$239$	12.1221			0.784116			0.392058	−	0.919940i	$-0.371763\pi$
$239$	12.1221			0.784116			0.392058	+	0.919940i	$0.371763\pi$
$240$		0			0
$241$	2.55102	−	4.41849i	0.164326	−	0.284620i	−0.772090	−	0.635513i	$-0.780789\pi$
$241$	2.55102	−	4.41849i	0.164326	−	0.284620i	0.936416	+	0.350893i	$0.114122\pi$
$242$	−2.44335	−	4.23200i	−0.157064	−	0.272043i
$243$	−7.92873	+	13.7330i	−0.508629	+	0.880971i
$244$	5.84001	+	10.1152i	0.373868	+	0.647559i
$245$		0			0
$246$	−2.18042			−0.139019
$247$	−15.3740	+	1.01526i	−0.978221	+	0.0645996i
$248$	5.58681			0.354763
$249$	2.83236	+	4.90579i	0.179494	+	0.310892i
$250$		0			0
$251$	−12.7122	+	22.0181i	−0.802385	+	1.38977i	0.115657	+	0.993289i	$0.463103\pi$
$251$	−12.7122	+	22.0181i	−0.802385	+	1.38977i	−0.918042	+	0.396483i	$0.870231\pi$
$252$	6.05422	+	10.4862i	0.381380	+	0.660570i
$253$	−19.8022	+	34.2984i	−1.24495	+	2.15632i
$254$	1.04754			0.0657285
$255$		0			0
$256$	−4.40321	+	7.62659i	−0.275201	+	0.476662i
$257$	−9.22493	+	15.9781i	−0.575436	+	0.996684i	0.420559	+	0.907265i	$0.361834\pi$
$257$	−9.22493	+	15.9781i	−0.575436	+	0.996684i	−0.995994	+	0.0894183i	$0.971499\pi$
$258$	2.02173			0.125867
$259$	21.2841			1.32253
$260$		0			0
$261$	−3.90415	−	6.76218i	−0.241661	−	0.418569i
$262$	−0.376717	+	0.652493i	−0.0232737	+	0.0403111i
$263$	−6.47530	−	11.2155i	−0.399284	−	0.691580i	0.594354	−	0.804204i	$-0.297408\pi$
$263$	−6.47530	−	11.2155i	−0.399284	−	0.691580i	−0.993638	+	0.112624i	$0.964075\pi$
$264$	−3.23137	−	5.59689i	−0.198877	−	0.344465i
$265$		0			0
$266$	−1.96555	+	3.99069i	−0.120516	+	0.244685i
$267$	−7.34134			−0.449283
$268$	−10.6560	−	18.4568i	−0.650921	−	1.12743i
$269$	−0.0782471	−	0.135528i	−0.00477081	−	0.00826329i	0.863630	−	0.504126i	$-0.168185\pi$
$269$	−0.0782471	−	0.135528i	−0.00477081	−	0.00826329i	−0.868401	+	0.495863i	$0.834852\pi$
$270$		0			0
$271$	−13.9095	−	24.0920i	−0.844944	−	1.46349i	−0.885670	−	0.464315i	$-0.846301\pi$
$271$	−13.9095	−	24.0920i	−0.844944	−	1.46349i	0.0407264	−	0.999170i	$-0.487033\pi$
$272$	1.73023	−	2.99685i	0.104911	−	0.181711i
$273$	−11.9411			−0.722711
$274$	−3.58368			−0.216498
$275$		0			0
$276$	−7.51022	+	13.0081i	−0.452062	+	0.782994i
$277$	−0.524062			−0.0314878			−0.0157439	−	0.999876i	$-0.505012\pi$
$277$	−0.524062			−0.0314878			−0.0157439	+	0.999876i	$0.505012\pi$
$278$	2.20125			0.132022
$279$	−4.46146	+	7.72748i	−0.267101	+	0.462632i
$280$		0			0
$281$	2.44413	−	4.23336i	0.145804	−	0.252541i	−0.783868	−	0.620927i	$-0.786756\pi$
$281$	2.44413	−	4.23336i	0.145804	−	0.252541i	0.929673	+	0.368386i	$0.120090\pi$
$282$	0.615400	+	1.06590i	0.0366465	+	0.0634736i
$283$	8.93931	+	15.4833i	0.531387	+	0.920389i	0.999329	+	0.0366299i	$0.0116623\pi$
$283$	8.93931	+	15.4833i	0.531387	+	0.920389i	−0.467942	+	0.883759i	$0.655004\pi$
$284$	0.866730			0.0514310
$285$		0			0
$286$	−5.68304			−0.336045
$287$	−11.1624	−	19.3338i	−0.658894	−	1.14124i
$288$	3.38948	+	5.87075i	0.199727	+	0.345937i
$289$	7.99068	−	13.8403i	0.470040	−	0.814133i
$290$		0			0
$291$	5.57400	−	9.65445i	0.326754	−	0.565954i
$292$	−7.86754			−0.460413
$293$	7.25399			0.423783			0.211891	−	0.977293i	$-0.432038\pi$
$293$	7.25399			0.423783			0.211891	+	0.977293i	$0.432038\pi$
$294$	−0.602479	+	1.04352i	−0.0351373	+	0.0608595i
$295$		0			0
$296$	7.87888			0.457951
$297$	26.2882			1.52540
$298$	−1.98324	+	3.43507i	−0.114886	+	0.198988i
$299$	13.5441	+	23.4591i	0.783278	+	1.35668i
$300$		0			0
$301$	10.3500	+	17.9267i	0.596562	+	1.03328i
$302$	3.05448	+	5.29051i	0.175766	+	0.304435i
$303$	−6.36461			−0.365637
$304$	6.60345	−	13.4071i	0.378734	−	0.768950i
$305$		0			0
$306$	−0.304488	−	0.527388i	−0.0174064	−	0.0301488i
$307$	−7.19015	−	12.4537i	−0.410364	−	0.710771i	0.584566	−	0.811346i	$-0.301265\pi$
$307$	−7.19015	−	12.4537i	−0.410364	−	0.710771i	−0.994929	+	0.100576i	$0.967932\pi$
$308$	16.1323	−	27.9420i	0.919226	−	1.59215i
$309$	−9.43415	−	16.3404i	−0.536690	−	0.929574i
$310$		0			0
$311$	8.52590			0.483459			0.241730	−	0.970344i	$-0.422285\pi$
$311$	8.52590			0.483459			0.241730	+	0.970344i	$0.422285\pi$
$312$	−4.42033			−0.250252
$313$	10.6809	−	18.4999i	0.603722	−	1.04568i	−0.388530	−	0.921436i	$-0.627017\pi$
$313$	10.6809	−	18.4999i	0.603722	−	1.04568i	0.992252	−	0.124241i	$-0.0396495\pi$
$314$	−0.479867	+	0.831153i	−0.0270804	+	0.0469047i
$315$		0			0
$316$	−5.49701			−0.309231
$317$	−14.0464	+	24.3291i	−0.788924	+	1.36646i	0.137702	+	0.990474i	$0.456028\pi$
$317$	−14.0464	+	24.3291i	−0.788924	+	1.36646i	−0.926626	+	0.375983i	$0.877305\pi$
$318$	1.14041	+	1.97525i	0.0639512	+	0.110767i
$319$	−10.4032	+	18.0188i	−0.582466	+	1.00886i
$320$		0			0
$321$	−4.49752	−	7.78993i	−0.251027	−	0.434792i
$322$	7.82102			0.435848
$323$	−1.94384	+	3.94662i	−0.108158	+	0.219596i
$324$	−1.10339			−0.0612995
$325$		0			0
$326$	3.49563	+	6.05461i	0.193605	+	0.335334i
$327$	3.13934	−	5.43750i	0.173606	−	0.300694i
$328$	−4.13205	−	7.15692i	−0.228154	−	0.395175i
$329$	−6.30091	+	10.9135i	−0.347381	+	0.601681i
$330$		0			0
$331$	15.1725			0.833957			0.416979	−	0.908916i	$-0.363089\pi$
$331$	15.1725			0.833957			0.416979	+	0.908916i	$0.363089\pi$
$332$	−5.23441	+	9.06627i	−0.287276	+	0.497576i
$333$	−6.29184	+	10.8978i	−0.344791	+	0.597195i
$334$	3.27900			0.179419
$335$		0			0
$336$	5.79140	−	10.0310i	0.315947	−	0.547236i
$337$	8.75041	+	15.1562i	0.476665	+	0.825608i	0.999642	−	0.0267383i	$-0.00851209\pi$
$337$	8.75041	+	15.1562i	0.476665	+	0.825608i	−0.522977	+	0.852347i	$0.675179\pi$
$338$	0.0786838	−	0.136284i	0.00427984	−	0.00741289i
$339$	−5.32647	−	9.22571i	−0.289294	−	0.501072i
$340$		0			0
$341$	23.7764			1.28757
$342$	−1.46225	−	2.18609i	−0.0790697	−	0.118210i
$343$	10.6254			0.573720
$344$	3.83131	+	6.63603i	0.206570	+	0.357791i
$345$		0			0
$346$	−3.56812	+	6.18016i	−0.191823	+	0.332247i
$347$	−8.68435	−	15.0417i	−0.466201	−	0.807483i	0.533054	−	0.846081i	$-0.321044\pi$
$347$	−8.68435	−	15.0417i	−0.466201	−	0.807483i	−0.999255	+	0.0385980i	$0.987711\pi$
$348$	−3.94552	+	6.83385i	−0.211502	+	0.366333i
$349$	−34.2563			−1.83370			−0.916850	−	0.399232i	$-0.869277\pi$
$349$	−34.2563			−1.83370			−0.916850	+	0.399232i	$0.869277\pi$
$350$		0			0
$351$	8.99019	−	15.5715i	0.479861	−	0.831144i
$352$	9.03176	−	15.6435i	0.481394	−	0.833799i
$353$	34.9287			1.85907			0.929534	−	0.368736i	$-0.120209\pi$
$353$	34.9287			1.85907			0.929534	+	0.368736i	$0.120209\pi$
$354$	4.31660			0.229425
$355$		0			0
$356$	−6.78367	−	11.7497i	−0.359534	−	0.622731i
$357$	−1.70480	+	2.95281i	−0.0902278	+	0.156279i
$358$	−3.61982	−	6.26972i	−0.191314	−	0.331365i
$359$	0.488273	+	0.845713i	0.0257701	+	0.0446350i	0.878623	−	0.477516i	$-0.158463\pi$
$359$	0.488273	+	0.845713i	0.0257701	+	0.0446350i	−0.852853	+	0.522151i	$0.825130\pi$
$360$		0			0
$361$	−7.25370	+	17.5609i	−0.381774	+	0.924256i
$362$	−4.96743			−0.261082
$363$	−8.08801	−	14.0088i	−0.424510	−	0.735273i
$364$	−11.0341	−	19.1116i	−0.578342	−	1.00172i
$365$		0			0
$366$	−0.983116	−	1.70281i	−0.0513883	−	0.0890071i
$367$	−4.93318	+	8.54451i	−0.257510	+	0.446020i	−0.965574	−	0.260128i	$-0.916235\pi$
$367$	−4.93318	+	8.54451i	−0.257510	+	0.446020i	0.708064	+	0.706148i	$0.249569\pi$
$368$	−26.2754			−1.36970
$369$	13.1989			0.687109
$370$		0			0
$371$	−11.6764	+	20.2241i	−0.606208	+	1.04998i
$372$	9.01748			0.467535
$373$	−12.9521			−0.670634			−0.335317	−	0.942105i	$-0.608843\pi$
$373$	−12.9521			−0.670634			−0.335317	+	0.942105i	$0.608843\pi$
$374$	−0.811352	+	1.40530i	−0.0419540	+	0.0726664i
$375$		0			0
$376$	−2.33245	+	4.03992i	−0.120287	+	0.208343i
$377$	7.11547	+	12.3244i	0.366465	+	0.634737i
$378$	−2.59568	−	4.49585i	−0.133507	−	0.231241i
$379$	5.21597			0.267926			0.133963	−	0.990986i	$-0.457230\pi$
$379$	5.21597			0.267926			0.133963	+	0.990986i	$0.457230\pi$
$380$		0			0
$381$	3.46758			0.177650
$382$	0.380484	+	0.659018i	0.0194673	+	0.0337183i
$383$	−16.7657	−	29.0390i	−0.856686	−	1.48382i	−0.875072	−	0.483993i	$-0.839186\pi$
$383$	−16.7657	−	29.0390i	−0.856686	−	1.48382i	0.0183857	−	0.999831i	$-0.494147\pi$
$384$	4.52390	−	7.83562i	0.230859	−	0.399860i
$385$		0			0
$386$	2.96262	−	5.13141i	0.150793	−	0.261182i
$387$	−12.2383			−0.622107
$388$	20.6023			1.04593
$389$	−13.8703	+	24.0241i	−0.703253	+	1.21807i	0.264066	+	0.964505i	$0.414936\pi$
$389$	−13.8703	+	24.0241i	−0.703253	+	1.21807i	−0.967318	+	0.253565i	$0.918397\pi$
$390$		0			0
$391$	7.73464			0.391158
$392$	−4.56695			−0.230666
$393$	−1.24702	+	2.15989i	−0.0629036	+	0.108952i
$394$	0.962139	+	1.66647i	0.0484718	+	0.0839557i
$395$		0			0
$396$	9.53783	+	16.5200i	0.479294	+	0.830161i
$397$	2.74971	+	4.76264i	0.138004	+	0.239030i	0.926741	−	0.375701i	$-0.122598\pi$
$397$	2.74971	+	4.76264i	0.138004	+	0.239030i	−0.788737	+	0.614731i	$0.789265\pi$
$398$	2.24324			0.112444
$399$	−6.50640	+	13.2101i	−0.325728	+	0.661331i
$400$		0			0
$401$	4.25655	+	7.37256i	0.212562	+	0.368168i	0.952516	−	0.304490i	$-0.0984860\pi$
$401$	4.25655	+	7.37256i	0.212562	+	0.368168i	−0.739954	+	0.672658i	$0.765153\pi$
$402$	1.79385	+	3.10704i	0.0894692	+	0.154965i
$403$	8.13120	−	14.0836i	0.405044	−	0.701556i
$404$	−5.88114	−	10.1864i	−0.292597	−	0.506794i
$405$		0			0
$406$	4.10880			0.203917
$407$	33.5311			1.66207
$408$	−0.631078	+	1.09306i	−0.0312430	+	0.0541145i
$409$	10.7353	−	18.5941i	0.530826	−	0.919418i	−0.468527	−	0.883449i	$-0.655215\pi$
$409$	10.7353	−	18.5941i	0.530826	−	0.919418i	0.999353	−	0.0359683i	$-0.0114515\pi$
$410$		0			0
$411$	−11.8628			−0.585148
$412$	17.4350	−	30.1983i	0.858962	−	1.48777i
$413$	22.0983	+	38.2753i	1.08738	+	1.88341i
$414$	−2.31199	+	4.00448i	−0.113628	+	0.196809i
$415$		0			0
$416$	−6.17746	−	10.6997i	−0.302875	−	0.524595i
$417$	7.28662			0.356827
$418$	−3.09653	+	6.28694i	−0.151456	+	0.307504i
$419$	−5.09378			−0.248848			−0.124424	−	0.992229i	$-0.539708\pi$
$419$	−5.09378			−0.248848			−0.124424	+	0.992229i	$0.539708\pi$
$420$		0			0
$421$	−2.82911	−	4.90017i	−0.137883	−	0.238820i	0.788812	−	0.614634i	$-0.210696\pi$
$421$	−2.82911	−	4.90017i	−0.137883	−	0.238820i	−0.926695	+	0.375815i	$0.877363\pi$
$422$	3.05611	−	5.29335i	0.148769	−	0.257676i
$423$	−3.72525	−	6.45232i	−0.181128	−	0.313723i
$424$	−4.32232	+	7.48648i	−0.209910	+	0.363576i
$425$		0			0
$426$	−0.145907			−0.00706920
$427$	10.0659	−	17.4346i	0.487121	−	0.843719i
$428$	8.31176	−	14.3964i	0.401764	−	0.695876i
$429$	−18.8121			−0.908256
$430$		0			0
$431$	19.1834	−	33.2267i	0.924033	−	1.60047i	0.130923	−	0.991392i	$-0.458206\pi$
$431$	19.1834	−	33.2267i	0.924033	−	1.60047i	0.793109	−	0.609079i	$-0.208461\pi$
$432$	8.72041	+	15.1042i	0.419561	+	0.726701i
$433$	−3.48125	+	6.02970i	−0.167298	+	0.289769i	−0.937469	−	0.348069i	$-0.886838\pi$
$433$	−3.48125	+	6.02970i	−0.167298	+	0.289769i	0.770171	+	0.637838i	$0.220171\pi$
$434$	−2.34767	−	4.06628i	−0.112692	−	0.195188i
$435$		0			0
$436$	11.6035			0.555706
$437$	33.3319	−	2.20116i	1.59448	−	0.105296i
$438$	1.32443			0.0632839
$439$	−4.76346	−	8.25055i	−0.227347	−	0.393777i	0.729674	−	0.683796i	$-0.239672\pi$
$439$	−4.76346	−	8.25055i	−0.227347	−	0.393777i	−0.957021	+	0.290018i	$0.906339\pi$
$440$		0			0
$441$	3.64703	−	6.31685i	0.173668	−	0.300802i
$442$	0.554941	+	0.961187i	0.0263959	+	0.0457190i
$443$	−17.3519	+	30.0544i	−0.824414	+	1.42793i	0.0779516	+	0.996957i	$0.475162\pi$
$443$	−17.3519	+	30.0544i	−0.824414	+	1.42793i	−0.902366	+	0.430971i	$0.858171\pi$
$444$	12.7170			0.603524
$445$		0			0
$446$	1.76302	−	3.05363i	0.0834813	−	0.144594i
$447$	−6.56495	+	11.3708i	−0.310511	+	0.537821i
$448$	18.9273			0.894233
$449$	−8.84228			−0.417293			−0.208646	−	0.977991i	$-0.566906\pi$
$449$	−8.84228			−0.417293			−0.208646	+	0.977991i	$0.566906\pi$
$450$		0			0
$451$	−17.5852	−	30.4585i	−0.828056	−	1.43423i
$452$	9.84371	−	17.0498i	0.463009	−	0.801956i
$453$	10.1110	+	17.5127i	0.475056	+	0.822821i
$454$	1.73238	+	3.00058i	0.0813048	+	0.140824i
$455$		0			0
$456$	−2.40852	+	4.89005i	−0.112789	+	0.228998i
$457$	0.664998			0.0311073			0.0155536	−	0.999879i	$-0.495049\pi$
$457$	0.664998			0.0311073			0.0155536	+	0.999879i	$0.495049\pi$
$458$	−0.546338	−	0.946285i	−0.0255287	−	0.0442170i
$459$	−2.56701	−	4.44619i	−0.119818	−	0.207531i
$460$		0			0
$461$	19.7696	+	34.2420i	0.920762	+	1.59481i	0.798238	+	0.602342i	$0.205766\pi$
$461$	19.7696	+	34.2420i	0.920762	+	1.59481i	0.122524	+	0.992466i	$0.460901\pi$
$462$	−2.71574	+	4.70381i	−0.126348	+	0.218841i
$463$	−15.5782			−0.723981			−0.361991	−	0.932182i	$-0.617903\pi$
$463$	−15.5782			−0.723981			−0.361991	+	0.932182i	$0.617903\pi$
$464$	−13.8039			−0.640830
$465$		0			0
$466$	−0.962875	+	1.66775i	−0.0446043	+	0.0772569i
$467$	41.0358			1.89891			0.949456	−	0.313901i	$-0.101636\pi$
$467$	41.0358			1.89891			0.949456	+	0.313901i	$0.101636\pi$
$468$	13.0472			0.603107
$469$	−18.3668	+	31.8122i	−0.848099	+	1.46895i
$470$		0			0
$471$	−1.58846	+	2.75130i	−0.0731925	+	0.126773i
$472$	8.18025	+	14.1686i	0.376527	+	0.652163i
$473$	16.3053	+	28.2417i	0.749721	+	1.29855i
$474$	0.925375			0.0425039
$475$		0			0
$476$	−6.30121			−0.288816
$477$	−6.90336	−	11.9570i	−0.316083	−	0.547472i
$478$	−1.88565	−	3.26604i	−0.0862475	−	0.149385i
$479$	11.7794	−	20.4024i	0.538213	−	0.932211i	−0.460788	−	0.887510i	$-0.652433\pi$
$479$	11.7794	−	20.4024i	0.538213	−	0.932211i	0.999000	−	0.0447012i	$-0.0142336\pi$
$480$		0			0
$481$	11.4671	−	19.8617i	0.522857	−	0.905614i
$482$	−1.58728			−0.0722988
$483$	25.8893			1.17800
$484$	14.9472	−	25.8894i	0.679420	−	1.17679i
$485$		0			0
$486$	4.93338			0.223783
$487$	−23.9166			−1.08377			−0.541883	−	0.840454i	$-0.682288\pi$
$487$	−23.9166			−1.08377			−0.541883	+	0.840454i	$0.682288\pi$
$488$	3.72614	−	6.45387i	0.168675	−	0.292153i
$489$	11.5713	+	20.0421i	0.523272	+	0.906334i
$490$		0			0
$491$	−8.17373	−	14.1573i	−0.368875	−	0.638911i	0.620515	−	0.784195i	$-0.286924\pi$
$491$	−8.17373	−	14.1573i	−0.368875	−	0.638911i	−0.989390	+	0.145284i	$0.953590\pi$
$492$	−6.66940	−	11.5517i	−0.300680	−	0.520793i
$493$	4.06343			0.183007
$494$	2.66502	+	3.98423i	0.119905	+	0.179259i
$495$		0			0
$496$	7.88720	+	13.6610i	0.354146	+	0.613398i
$497$	−0.746950	−	1.29375i	−0.0335053	−	0.0580328i
$498$	0.881169	−	1.52623i	0.0394861	−	0.0683920i
$499$	16.0354	+	27.7742i	0.717844	+	1.24334i	0.961852	+	0.273569i	$0.0882041\pi$
$499$	16.0354	+	27.7742i	0.717844	+	1.24334i	−0.244009	+	0.969773i	$0.578463\pi$
$500$		0			0
$501$	10.8542			0.484930
$502$	7.90972			0.353028
$503$	−7.36269	+	12.7525i	−0.328286	+	0.568608i	−0.982172	−	0.187985i	$-0.939804\pi$
$503$	−7.36269	+	12.7525i	−0.328286	+	0.568608i	0.653886	+	0.756593i	$0.273138\pi$
$504$	3.86282	−	6.69060i	0.172064	−	0.298023i
$505$		0			0
$506$	12.3212			0.547746
$507$	0.260461	−	0.451131i	0.0115675	−	0.0200354i
$508$	3.20418	+	5.54980i	0.142162	+	0.246232i
$509$	11.0332	−	19.1100i	0.489037	−	0.847036i	−0.510884	−	0.859650i	$-0.670682\pi$
$509$	11.0332	−	19.1100i	0.489037	−	0.847036i	0.999920	+	0.0126136i	$0.00401513\pi$
$510$		0			0
$511$	6.78026	+	11.7438i	0.299941	+	0.519513i
$512$	20.3111			0.897633
$513$	−12.3277	−	18.4300i	−0.544280	−	0.813705i
$514$	5.73990			0.253176
$515$		0			0
$516$	6.18399	+	10.7110i	0.272235	+	0.471525i
$517$	−9.92647	+	17.1931i	−0.436565	+	0.756154i
$518$	−3.31083	−	5.73453i	−0.145470	−	0.251961i
$519$	−11.8112	+	20.4577i	−0.518456	+	0.897992i
$520$		0			0
$521$	−14.7781			−0.647442			−0.323721	−	0.946153i	$-0.604934\pi$
$521$	−14.7781			−0.647442			−0.323721	+	0.946153i	$0.604934\pi$
$522$	−1.21461	+	2.10377i	−0.0531621	+	0.0920794i
$523$	6.35498	−	11.0072i	0.277884	−	0.481309i	−0.692975	−	0.720962i	$-0.743700\pi$
$523$	6.35498	−	11.0072i	0.277884	−	0.481309i	0.970859	+	0.239653i	$0.0770336\pi$
$524$	−4.60916			−0.201352
$525$		0			0
$526$	−2.01452	+	3.48924i	−0.0878371	+	0.152138i
$527$	−2.32174	−	4.02137i	−0.101136	−	0.175174i
$528$	9.12378	−	15.8029i	0.397062	−	0.687731i
$529$	−17.8647	−	30.9426i	−0.776726	−	1.34533i
$530$		0			0
$531$	−26.1301			−1.13395
$532$	−27.1546	+	1.79323i	−1.17730	+	0.0777464i
$533$	−24.0556			−1.04196
$534$	1.14197	+	1.97796i	0.0494180	+	0.0855946i
$535$		0			0
$536$	−6.79894	+	11.7761i	−0.293670	+	0.508651i
$537$	−11.9824	−	20.7541i	−0.517079	−	0.895607i
$538$	−0.0243433	+	0.0421638i	−0.00104951	+	0.00181781i
$539$	−19.4361			−0.837172
$540$		0			0
$541$	15.1172	−	26.1838i	0.649941	−	1.12573i	−0.333196	−	0.942858i	$-0.608127\pi$
$541$	15.1172	−	26.1838i	0.649941	−	1.12573i	0.983137	−	0.182873i	$-0.0585396\pi$
$542$	−4.32736	+	7.49521i	−0.185876	+	0.321947i
$543$	−16.4433			−0.705649
$544$	−3.52776			−0.151251
$545$		0			0
$546$	1.85749	+	3.21727i	0.0794933	+	0.137686i
$547$	3.90372	−	6.76144i	0.166911	−	0.289098i	−0.770421	−	0.637535i	$-0.779954\pi$
$547$	3.90372	−	6.76144i	0.166911	−	0.289098i	0.937332	+	0.348437i	$0.113287\pi$
$548$	−10.9617	−	18.9861i	−0.468259	−	0.811048i
$549$	5.95118	+	10.3077i	0.253990	+	0.439924i
$550$		0			0
$551$	17.5110	−	1.15639i	0.745995	−	0.0492639i
$552$	9.58359			0.407905
$553$	4.73733	+	8.20530i	0.201452	+	0.348925i
$554$	0.0815198	+	0.141196i	0.00346345	+	0.00599886i
$555$		0			0
$556$	6.73311	+	11.6621i	0.285548	+	0.494583i
$557$	−1.20747	+	2.09141i	−0.0511623	+	0.0886157i	−0.890472	−	0.455037i	$-0.849626\pi$
$557$	−1.20747	+	2.09141i	−0.0511623	+	0.0886157i	0.839310	+	0.543653i	$0.182959\pi$
$558$	2.77599			0.117517
$559$	22.3048			0.943392
$560$		0			0
$561$	−2.68575	+	4.65186i	−0.113392	+	0.196402i
$562$	−1.52078			−0.0641500
$563$	25.3392			1.06792			0.533960	−	0.845510i	$-0.320703\pi$
$563$	25.3392			1.06792			0.533960	+	0.845510i	$0.320703\pi$
$564$	−3.76473	+	6.52070i	−0.158524	+	0.274571i
$565$		0			0
$566$	2.78109	−	4.81699i	0.116898	−	0.202473i
$567$	0.950905	+	1.64702i	0.0399342	+	0.0691681i
$568$	−0.276503	−	0.478917i	−0.0116018	−	0.0200949i
$569$	−45.1046			−1.89088			−0.945441	−	0.325793i	$-0.894369\pi$
$569$	−45.1046			−1.89088			−0.945441	+	0.325793i	$0.894369\pi$
$570$		0			0
$571$	−9.73299			−0.407313			−0.203656	−	0.979042i	$-0.565283\pi$
$571$	−9.73299			−0.407313			−0.203656	+	0.979042i	$0.565283\pi$
$572$	−17.3831	−	30.1084i	−0.726823	−	1.25889i
$573$	1.25949	+	2.18149i	0.0526158	+	0.0911332i
$574$	−3.47270	+	6.01490i	−0.144948	+	0.251057i
$575$		0			0
$576$	−5.59515	+	9.69108i	−0.233131	+	0.403795i
$577$	−8.83145			−0.367658			−0.183829	−	0.982958i	$-0.558849\pi$
$577$	−8.83145			−0.367658			−0.183829	+	0.982958i	$0.558849\pi$
$578$	−4.97192			−0.206805
$579$	9.80691	−	16.9861i	0.407561	−	0.705917i
$580$		0			0
$581$	18.0441			0.748596
$582$	−3.46823			−0.143763
$583$	−18.3950	+	31.8611i	−0.761843	+	1.31955i
$584$	2.50989	+	4.34726i	0.103860	+	0.179891i
$585$		0			0
$586$	−1.12839	−	1.95442i	−0.0466132	−	0.0807365i
$587$	13.4966	+	23.3768i	0.557065	+	0.964865i	0.997740	+	0.0671982i	$0.0214060\pi$
$587$	13.4966	+	23.3768i	0.557065	+	0.964865i	−0.440674	+	0.897667i	$0.645261\pi$
$588$	−7.37137			−0.303990
$589$	−11.1498	−	16.6691i	−0.459419	−	0.686837i
$590$		0			0
$591$	3.18489	+	5.51639i	0.131009	+	0.226914i
$592$	11.1230	+	19.2657i	0.457154	+	0.791814i
$593$	10.6170	−	18.3891i	0.435987	−	0.755151i	−0.561389	−	0.827552i	$-0.689733\pi$
$593$	10.6170	−	18.3891i	0.435987	−	0.755151i	0.997376	+	0.0724009i	$0.0230661\pi$
$594$	−4.08923	−	7.08276i	−0.167783	−	0.290609i
$595$		0			0
$596$	−24.2650			−0.993934
$597$	7.42562			0.303910
$598$	4.21369	−	7.29832i	0.172311	−	0.298451i
$599$	15.1647	−	26.2660i	0.619612	−	1.07320i	−0.369945	−	0.929054i	$-0.620623\pi$
$599$	15.1647	−	26.2660i	0.619612	−	1.07320i	0.989556	−	0.144146i	$-0.0460434\pi$
$600$		0			0
$601$	−10.7285			−0.437624			−0.218812	−	0.975767i	$-0.570218\pi$
$601$	−10.7285			−0.437624			−0.218812	+	0.975767i	$0.570218\pi$
$602$	3.21996	−	5.57713i	0.131236	−	0.227307i
$603$	−10.8589	−	18.8081i	−0.442208	−	0.765926i
$604$	−18.6859	+	32.3649i	−0.760317	+	1.31691i
$605$		0			0
$606$	0.990039	+	1.71480i	0.0402176	+	0.0696589i
$607$	8.81498			0.357789			0.178894	−	0.983868i	$-0.442748\pi$
$607$	8.81498			0.357789			0.178894	+	0.983868i	$0.442748\pi$
$608$	−15.2026	+	1.00395i	−0.616548	+	0.0407154i
$609$	13.6010			0.551142
$610$		0			0
$611$	6.78942	+	11.7596i	0.274671	+	0.475743i
$612$	1.86271	−	3.22631i	0.0752957	−	0.130416i
$613$	−12.0654	−	20.8978i	−0.487315	−	0.844055i	0.512578	−	0.858640i	$-0.328690\pi$
$613$	−12.0654	−	20.8978i	−0.487315	−	0.844055i	−0.999894	+	0.0145856i	$0.995357\pi$
$614$	−2.23691	+	3.87445i	−0.0902744	+	0.156360i
$615$		0			0
$616$	−20.5861			−0.829436
$617$	7.73248	−	13.3930i	0.311298	−	0.539183i	−0.667346	−	0.744748i	$-0.732570\pi$
$617$	7.73248	−	13.3930i	0.311298	−	0.539183i	0.978644	+	0.205564i	$0.0659030\pi$
$618$	−2.93504	+	5.08363i	−0.118065	+	0.204494i
$619$	0.0390990			0.00157152			0.000785761	−	1.00000i	$-0.499750\pi$
$619$	0.0390990			0.00157152			0.000785761		1.00000i	$0.499750\pi$
$620$		0			0
$621$	−19.4914	+	33.7601i	−0.782163	+	1.35475i
$622$	−1.32624	−	2.29711i	−0.0531772	−	0.0921057i
$623$	−11.6924	+	20.2518i	−0.468445	+	0.811370i
$624$	−6.24041	−	10.8087i	−0.249816	−	0.432694i
$625$		0			0
$626$	−6.64584			−0.265621
$627$	−10.2502	+	20.8112i	−0.409353	+	0.831117i
$628$	−5.87120			−0.234286
$629$	−3.27427	−	5.67119i	−0.130554	−	0.226125i
$630$		0			0
$631$	−3.36758	+	5.83282i	−0.134061	+	0.232201i	−0.925238	−	0.379386i	$-0.876135\pi$
$631$	−3.36758	+	5.83282i	−0.134061	+	0.232201i	0.791177	+	0.611587i	$0.209469\pi$
$632$	1.75365	+	3.03741i	0.0697564	+	0.120822i
$633$	10.1164	−	17.5221i	0.402091	−	0.696442i
$634$	8.73989			0.347105
$635$		0			0
$636$	−6.97651	+	12.0837i	−0.276637	+	0.479149i
$637$	−6.64687	+	11.5127i	−0.263358	+	0.456150i
$638$	6.47301			0.256269
$639$	0.883229			0.0349400
$640$		0			0
$641$	−13.7894	−	23.8840i	−0.544649	−	0.943360i	−0.998629	−	0.0523477i	$-0.983330\pi$
$641$	−13.7894	−	23.8840i	−0.544649	−	0.943360i	0.453980	−	0.891012i	$-0.350004\pi$
$642$	−1.39921	+	2.42351i	−0.0552226	+	0.0956483i
$643$	−5.95407	−	10.3128i	−0.234806	−	0.406695i	0.724410	−	0.689369i	$-0.242112\pi$
$643$	−5.95407	−	10.3128i	−0.234806	−	0.406695i	−0.959216	+	0.282673i	$0.908779\pi$
$644$	23.9227	+	41.4353i	0.942685	+	1.63278i
$645$		0			0
$646$	1.36570	−	0.0901878i	0.0537327	−	0.00354839i
$647$	−11.6648			−0.458590			−0.229295	−	0.973357i	$-0.573642\pi$
$647$	−11.6648			−0.458590			−0.229295	+	0.973357i	$0.573642\pi$
$648$	0.352002	+	0.609686i	0.0138280	+	0.0239507i
$649$	34.8136	+	60.2990i	1.36656	+	2.36694i
$650$		0			0
$651$	−7.77128	−	13.4603i	−0.304581	−	0.527549i
$652$	−21.3846	+	37.0393i	−0.837487	+	1.45057i
$653$	−40.7527			−1.59477			−0.797387	−	0.603468i	$-0.793785\pi$
$653$	−40.7527			−1.59477			−0.797387	+	0.603468i	$0.793785\pi$
$654$	−1.95335			−0.0763819
$655$		0			0
$656$	11.6669	−	20.2076i	0.455514	−	0.788974i
$657$	−8.01730			−0.312785
$658$	3.92053			0.152838
$659$	11.5723	−	20.0438i	0.450793	−	0.780796i	−0.547643	−	0.836712i	$-0.684475\pi$
$659$	11.5723	−	20.0438i	0.450793	−	0.780796i	0.998435	+	0.0559165i	$0.0178081\pi$
$660$		0			0
$661$	−2.44485	+	4.23460i	−0.0950936	+	0.164707i	−0.909648	−	0.415381i	$-0.863648\pi$
$661$	−2.44485	+	4.23460i	−0.0950936	+	0.164707i	0.814554	+	0.580088i	$0.196982\pi$
$662$	−2.36015	−	4.08789i	−0.0917297	−	0.158880i
$663$	1.83698	+	3.18174i	0.0713423	+	0.123568i
$664$	6.67950			0.259215
$665$		0			0
$666$	3.91488			0.151699
$667$	−15.4269	−	26.7201i	−0.597331	−	1.03461i
$668$	10.0297	+	17.3719i	0.388060	+	0.672140i
$669$	5.83597	−	10.1082i	0.225632	−	0.390805i
$670$		0			0
$671$	15.8578	−	27.4665i	0.612182	−	1.06033i
$672$	−11.8081			−0.455506
$673$	29.5149			1.13771			0.568857	−	0.822436i	$-0.307386\pi$
$673$	29.5149			1.13771			0.568857	+	0.822436i	$0.307386\pi$
$674$	2.72232	−	4.71520i	0.104860	−	0.181623i
$675$		0			0
$676$	0.962701			0.0370270
$677$	−29.4248			−1.13089			−0.565443	−	0.824788i	$-0.691295\pi$
$677$	−29.4248			−1.13089			−0.565443	+	0.824788i	$0.691295\pi$
$678$	−1.65711	+	2.87019i	−0.0636408	+	0.110229i
$679$	−17.7551	−	30.7528i	−0.681380	−	1.18018i
$680$		0			0
$681$	5.73457	+	9.93256i	0.219749	+	0.380616i
$682$	−3.69852	−	6.40602i	−0.141623	−	0.245299i
$683$	29.9433			1.14575			0.572875	−	0.819643i	$-0.305828\pi$
$683$	29.9433			1.14575			0.572875	+	0.819643i	$0.305828\pi$
$684$	7.10907	−	14.4337i	0.271822	−	0.551885i
$685$		0			0
$686$	−1.65283	−	2.86278i	−0.0631053	−	0.109302i
$687$	−1.80850	−	3.13241i	−0.0689985	−	0.119509i
$688$	−10.8177	+	18.7369i	−0.412422	+	0.714336i
$689$	12.5816	+	21.7921i	0.479323	+	0.830211i
$690$		0			0
$691$	−24.2225			−0.921467			−0.460733	−	0.887539i	$-0.652414\pi$
$691$	−24.2225			−0.921467			−0.460733	+	0.887539i	$0.652414\pi$
$692$	−43.6561			−1.65956
$693$	16.4394	−	28.4739i	0.624482	−	1.08164i
$694$	−2.70177	+	4.67960i	−0.102558	+	0.177635i
$695$		0			0
$696$	5.03478			0.190843
$697$	−3.43435	+	5.94847i	−0.130085	+	0.225314i
$698$	5.32871	+	9.22959i	0.201695	+	0.349345i
$699$	−3.18733	+	5.52061i	−0.120556	+	0.208809i
$700$		0			0
$701$	7.42695	+	12.8639i	0.280512	+	0.485861i	0.971511	−	0.236995i	$-0.0761624\pi$
$701$	7.42695	+	12.8639i	0.280512	+	0.485861i	−0.690999	+	0.722856i	$0.742829\pi$
$702$	−5.59384			−0.211126
$703$	−15.7241	−	23.5078i	−0.593047	−	0.886613i
$704$	29.8182			1.12381
$705$		0			0
$706$	−5.43330	−	9.41075i	−0.204485	−	0.354178i
$707$	−10.1367	+	17.5574i	−0.381232	+	0.660313i
$708$	13.2035	+	22.8691i	0.496217	+	0.859473i
$709$	14.9004	−	25.8083i	0.559598	−	0.969252i	−0.437932	−	0.899008i	$-0.644289\pi$
$709$	14.9004	−	25.8083i	0.559598	−	0.969252i	0.997530	−	0.0702441i	$-0.0223778\pi$
$710$		0			0
$711$	−5.60165			−0.210078
$712$	−4.32823	+	7.49672i	−0.162207	+	0.280952i
$713$	−17.6290	+	30.5344i	−0.660213	+	1.14352i
$714$	1.06076			0.0396978
$715$		0			0
$716$	22.1444	−	38.3552i	0.827575	−	1.43340i
$717$	−6.24190	−	10.8113i	−0.233108	−	0.403755i
$718$	0.151905	−	0.263108i	0.00566906	−	0.00981910i
$719$	12.9463	+	22.4236i	0.482814	+	0.836258i	0.999805	−	0.0197322i	$-0.00628136\pi$
$719$	12.9463	+	22.4236i	0.482814	+	0.836258i	−0.516991	+	0.855991i	$0.672948\pi$
$720$		0			0
$721$	−60.1021			−2.23832
$722$	5.85972	−	0.777316i	0.218076	−	0.0289287i
$723$	−5.25426			−0.195408
$724$	−15.1942	−	26.3171i	−0.564688	−	0.978069i
$725$		0			0
$726$	−2.51624	+	4.35826i	−0.0933865	+	0.161750i
$727$	−4.67442	−	8.09634i	−0.173365	−	0.300277i	0.766229	−	0.642567i	$-0.222131\pi$
$727$	−4.67442	−	8.09634i	−0.173365	−	0.300277i	−0.939594	+	0.342291i	$0.888797\pi$
$728$	−7.04014	+	12.1939i	−0.260925	+	0.451935i
$729$	14.5913			0.540419
$730$		0			0
$731$	3.18439	−	5.51553i	0.117779	−	0.203999i
$732$	6.01424	−	10.4170i	0.222293	−	0.385022i
$733$	7.20434			0.266098			0.133049	−	0.991109i	$-0.457523\pi$
$733$	7.20434			0.266098			0.133049	+	0.991109i	$0.457523\pi$
$734$	3.06950			0.113297
$735$		0			0
$736$	13.3932	+	23.1977i	0.493680	+	0.855079i
$737$	−28.9350	+	50.1170i	−1.06584	+	1.84608i
$738$	−2.05314	−	3.55615i	−0.0755773	−	0.130904i
$739$	−6.48702	−	11.2359i	−0.238629	−	0.413318i	0.721692	−	0.692214i	$-0.243365\pi$
$739$	−6.48702	−	11.2359i	−0.238629	−	0.413318i	−0.960321	+	0.278897i	$0.910031\pi$
$740$		0			0
$741$	8.82179	+	13.1887i	0.324077	+	0.484498i
$742$	7.26523			0.266715
$743$	−4.61550	−	7.99428i	−0.169326	−	0.293282i	0.768857	−	0.639421i	$-0.220826\pi$
$743$	−4.61550	−	7.99428i	−0.169326	−	0.293282i	−0.938183	+	0.346139i	$0.887492\pi$
$744$	−2.87674	−	4.98267i	−0.105467	−	0.182673i
$745$		0			0
$746$	2.01475	+	3.48965i	0.0737652	+	0.127765i
$747$	−5.33405	+	9.23885i	−0.195163	+	0.338032i
$748$	−9.92694			−0.362965
$749$	−28.6523			−1.04693
$750$		0			0
$751$	−7.46131	+	12.9234i	−0.272267	+	0.471580i	−0.969442	−	0.245321i	$-0.921107\pi$
$751$	−7.46131	+	12.9234i	−0.272267	+	0.471580i	0.697175	+	0.716901i	$0.254440\pi$
$752$	−13.1714			−0.480310
$753$	26.1829			0.954157
$754$	2.21368	−	3.83420i	0.0806174	−	0.139633i
$755$		0			0
$756$	15.8791	−	27.5035i	0.577519	−	1.00029i
$757$	−12.2488	−	21.2156i	−0.445191	−	0.771093i	0.552874	−	0.833265i	$-0.313531\pi$
$757$	−12.2488	−	21.2156i	−0.445191	−	0.771093i	−0.998066	+	0.0621711i	$0.980198\pi$
$758$	−0.811365	−	1.40532i	−0.0294701	−	0.0510437i
$759$	40.7860			1.48044
$760$		0			0
$761$	−15.8968			−0.576260			−0.288130	−	0.957591i	$-0.593034\pi$
$761$	−15.8968			−0.576260			−0.288130	+	0.957591i	$0.593034\pi$
$762$	−0.539396	−	0.934262i	−0.0195403	−	0.0338447i
$763$	−9.99990	−	17.3203i	−0.362021	−	0.627038i
$764$	−2.32762	+	4.03156i	−0.0842105	+	0.145857i
$765$		0			0
$766$	−5.21593	+	9.03426i	−0.188459	+	0.326421i
$767$	47.6231			1.71957
$768$	9.06916			0.327255
$769$	14.7925	−	25.6214i	0.533432	−	0.923931i	−0.465806	−	0.884887i	$-0.654235\pi$
$769$	14.7925	−	25.6214i	0.533432	−	0.923931i	0.999238	−	0.0390437i	$-0.0124312\pi$
$770$		0			0
$771$	19.0003			0.684280
$772$	36.2478			1.30459
$773$	−7.06551	+	12.2378i	−0.254129	+	0.440164i	−0.964658	−	0.263503i	$-0.915122\pi$
$773$	−7.06551	+	12.2378i	−0.254129	+	0.440164i	0.710530	+	0.703667i	$0.248455\pi$
$774$	1.90371	+	3.29733i	0.0684276	+	0.118520i
$775$		0			0
$776$	−6.57253	−	11.3840i	−0.235940	−	0.408660i
$777$	−10.9596	−	18.9825i	−0.393172	−	0.680995i

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} +O(q^{10})\)	\(q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} -5.16792 q^{11} -1.95999 q^{12} +(-1.76735 + 3.06115i) q^{13} +(0.510276 + 0.883825i) q^{14} +(-1.71432 - 2.96929i) q^{16} +(0.504641 + 0.874064i) q^{17} -0.603375 q^{18} +(2.42346 + 3.62310i) q^{19} +(1.68913 + 2.92565i) q^{21} +(0.803890 + 1.39238i) q^{22} +(3.83176 - 6.63680i) q^{23} +(0.625274 + 1.08301i) q^{24} +1.09968 q^{26} -5.08681 q^{27} +(-3.12163 + 5.40683i) q^{28} +(2.01303 - 3.48667i) q^{29} -4.60077 q^{31} +(-1.74766 + 3.02703i) q^{32} +(2.66105 + 4.60908i) q^{33} +(0.156998 - 0.271928i) q^{34} +(-1.84558 - 3.19664i) q^{36} -6.48831 q^{37} +(0.599183 - 1.21653i) q^{38} +3.64017 q^{39} +(3.40277 + 5.89377i) q^{41} +(0.525500 - 0.910193i) q^{42} +(-3.15511 - 5.46481i) q^{43} +(-4.91782 + 8.51792i) q^{44} -2.38418 q^{46} +(1.92079 - 3.32690i) q^{47} +(-1.76547 + 3.05788i) q^{48} +3.76091 q^{49} +(0.519697 - 0.900141i) q^{51} +(3.36365 + 5.82601i) q^{52} +(3.55946 - 6.16516i) q^{53} +(0.791273 + 1.37052i) q^{54} +3.98343 q^{56} +(1.98343 - 4.02699i) q^{57} -1.25254 q^{58} +(-6.73649 - 11.6679i) q^{59} +(-3.06850 + 5.31480i) q^{61} +(0.715668 + 1.23957i) q^{62} +(-3.18105 + 5.50975i) q^{63} -5.76986 q^{64} +(0.827874 - 1.43392i) q^{66} +(5.59897 - 9.69770i) q^{67} +1.92088 q^{68} -7.89215 q^{69} +(0.227702 + 0.394391i) q^{71} +(-1.17755 + 2.03958i) q^{72} +(-2.06691 - 3.57999i) q^{73} +(1.00928 + 1.74813i) q^{74} +(8.27788 - 0.546653i) q^{76} +16.9528 q^{77} +(-0.566242 - 0.980760i) q^{78} +(-1.44414 - 2.50132i) q^{79} +(-0.289876 - 0.502080i) q^{81} +(1.05863 - 1.83360i) q^{82} -5.50061 q^{83} +6.42953 q^{84} +(-0.981579 + 1.70014i) q^{86} -4.14617 q^{87} +6.27551 q^{88} +(3.56433 - 6.17360i) q^{89} +(5.79760 - 10.0417i) q^{91} +(-7.29264 - 12.6312i) q^{92} +(2.36902 + 4.10326i) q^{93} -1.19514 q^{94} +3.59960 q^{96} +(5.41252 + 9.37476i) q^{97} +(-0.585025 - 1.01329i) q^{98} +(-5.01144 + 8.68006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

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