LMFDB - Embedded newform 475.2.e.f.201.3

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} + \cdots + 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			201.3
Root			$-0.0149173 - 0.0258375i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.f.26.3

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.915767	−	0.401709i	$-0.868416\pi$
$2$	−0.155554	+	0.269427i	−0.109993	+	0.190514i	0.805774	+	0.592223i	$0.201750\pi$
$3$	−0.514917	+	0.891863i	−0.297288	+	0.514917i	−0.975514	−	0.219935i	$-0.929415\pi$
$3$	−0.514917	+	0.891863i	−0.297288	+	0.514917i	0.678227	+	0.734853i	$0.262749\pi$
$4$	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	0.509760	−	0.860317i	$-0.329734\pi$
$13$	−1.76735	−	3.06115i	−0.490176	−	0.849010i	−0.999936	+	0.0113069i	$0.996401\pi$
$14$	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	−0.798318	−	0.602237i	$-0.794276\pi$
$17$	0.504641	−	0.874064i	0.122393	−	0.211992i	0.920711	+	0.390245i	$0.127610\pi$
$18$	−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	0.920283	+	0.391253i	$0.127958\pi$
$23$	3.83176	+	6.63680i	0.798976	+	1.38387i	−0.121307	+	0.992615i	$0.538709\pi$
$24$	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	0.990148	−	0.140024i	$-0.0447179\pi$
$29$	2.01303	+	3.48667i	0.373810	+	0.647458i	−0.616338	+	0.787482i	$0.711385\pi$
$30$		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	−0.467904	−	0.883779i	$-0.654991\pi$
$41$	3.40277	−	5.89377i	0.531423	−	0.920451i	0.999327	−	0.0366724i	$-0.0116758\pi$
$42$	0.525500	+	0.910193i	0.0810865	+	0.140446i
$43$	−3.15511	+	5.46481i	−0.481150	+	0.833376i	−0.999766	−	0.0216315i	$-0.993114\pi$
$43$	−3.15511	+	5.46481i	−0.481150	+	0.833376i	0.518616	+	0.855007i	$0.326447\pi$
$44$	−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	0.971428	−	0.237335i	$-0.0762740\pi$
$47$	1.92079	+	3.32690i	0.280175	+	0.485278i	−0.691252	+	0.722613i	$0.742941\pi$
$48$	−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	0.999919	−	0.0127367i	$-0.00405432\pi$
$53$	3.55946	+	6.16516i	0.488929	+	0.846850i	−0.510990	+	0.859587i	$0.670721\pi$
$54$	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	−0.0224174	+	0.999749i	$0.507136\pi$
$59$	−6.73649	+	11.6679i	−0.877016	+	1.51904i	−0.854599	+	0.519288i	$0.826197\pi$
$60$		0			0
$61$	−3.06850	−	5.31480i	−0.392881	−	0.680491i	0.599947	−	0.800040i	$-0.295188\pi$
$61$	−3.06850	−	5.31480i	−0.392881	−	0.680491i	−0.992828	+	0.119549i	$0.961855\pi$
$62$	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	0.973743	+	0.227652i	$0.0731047\pi$
$67$	5.59897	+	9.69770i	0.684023	+	1.18476i	−0.289719	+	0.957112i	$0.593562\pi$
$68$	1.92088			0.232941
$69$	−7.89215			−0.950103
$70$		0			0
$71$	0.227702	−	0.394391i	0.0270233	−	0.0468056i	−0.852198	−	0.523220i	$-0.824731\pi$
$71$	0.227702	−	0.394391i	0.0270233	−	0.0468056i	0.879221	+	0.476415i	$0.158064\pi$
$72$	−1.17755	−	2.03958i	−0.138776	−	0.240367i
$73$	−2.06691	+	3.57999i	−0.241914	+	0.419007i	−0.961259	−	0.275646i	$-0.911108\pi$
$73$	−2.06691	+	3.57999i	−0.241914	+	0.419007i	0.719346	+	0.694652i	$0.244442\pi$
$74$	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	−0.935757	−	0.352646i	$-0.885282\pi$
$79$	−1.44414	+	2.50132i	−0.162478	+	0.281421i	0.773278	+	0.634067i	$0.218615\pi$
$80$		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	0.990745	−	0.135740i	$-0.0433411\pi$
$89$	3.56433	+	6.17360i	0.377818	+	0.654400i	−0.612926	+	0.790140i	$0.710008\pi$
$90$		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	−0.448747	−	0.893659i	$-0.648129\pi$
$97$	5.41252	−	9.37476i	0.549558	−	0.951862i	0.998305	−	0.0582034i	$-0.0185372\pi$
$98$	−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	0.977810	−	0.209494i	$-0.0671818\pi$
$101$	3.09011	+	5.35223i	0.307478	+	0.532567i	−0.670332	+	0.742061i	$0.733848\pi$
$102$	−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	−0.682295	−	0.731077i	$-0.739018\pi$
$109$	3.04839	−	5.27997i	0.291983	−	0.505730i	0.974279	+	0.225347i	$0.0723515\pi$
$110$		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	0.781611	−	0.623766i	$-0.214398\pi$
$127$	−1.68356	−	2.91602i	−0.149392	−	0.258755i	−0.931003	+	0.365012i	$0.881065\pi$
$128$	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	−0.914063	−	0.405572i	$-0.867072\pi$
$131$	−1.21089	+	2.09732i	−0.105796	+	0.183244i	0.808267	+	0.588816i	$0.200406\pi$
$132$	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	0.999958	−	0.00913057i	$-0.00290639\pi$
$137$	5.75955	+	9.97584i	0.492072	+	0.852293i	−0.507886	+	0.861424i	$0.669573\pi$
$138$	1.22765	−	2.12636i	0.104505	−	0.181008i
$139$	−3.53776	−	6.12759i	−0.300069	−	0.519735i	0.676082	−	0.736826i	$-0.263676\pi$
$139$	−3.53776	−	6.12759i	−0.300069	−	0.519735i	−0.976151	+	0.217091i	$0.930343\pi$
$140$		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	0.477425	+	0.878673i	$0.341570\pi$
$149$	−6.37476	+	11.0414i	−0.522240	+	0.904547i	−0.999665	+	0.0258744i	$0.991763\pi$
$150$		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	−0.920989	−	0.389589i	$-0.872617\pi$
$157$	−1.54244	+	2.67159i	−0.123101	+	0.213216i	0.797888	+	0.602805i	$0.205950\pi$
$158$	−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	0.586847	−	0.809698i	$-0.300369\pi$
$167$	−5.26987	−	9.12769i	−0.407795	−	0.706322i	−0.994642	+	0.103376i	$0.967036\pi$
$168$	−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	−0.0120281	+	0.999928i	$0.503829\pi$
$173$	−11.4691	+	19.8650i	−0.871977	+	1.51031i	−0.859949	+	0.510380i	$0.829505\pi$
$174$	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	0.993770	+	0.111453i	$0.0355503\pi$
$181$	7.98346	+	13.8278i	0.593406	+	1.02781i	−0.400364	+	0.916356i	$0.631116\pi$
$182$	−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	−0.287824	−	0.957683i	$-0.592932\pi$
$193$	9.52280	−	16.4940i	0.685466	−	1.18726i	0.973290	−	0.229579i	$-0.0737350\pi$
$194$	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	0.709481	−	0.704725i	$-0.248930\pi$
$199$	−3.60525	−	6.24447i	−0.255569	−	0.442659i	−0.965050	+	0.262066i	$0.915596\pi$
$200$		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	−0.299831	−	0.953992i	$-0.596930\pi$
$211$	9.82333	−	17.0145i	0.676266	−	1.17133i	0.976097	−	0.217335i	$-0.0697362\pi$
$212$	−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	−0.611504	−	0.791242i	$-0.709435\pi$
$223$	5.66690	−	9.81536i	0.379484	−	0.657285i	0.990987	+	0.133957i	$0.0427683\pi$
$224$	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	−0.949417	−	0.314020i	$-0.898324\pi$
$233$	−3.09499	+	5.36068i	−0.202759	+	0.351190i	0.746657	+	0.665209i	$0.231658\pi$
$234$	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	0.936416	−	0.350893i	$-0.114122\pi$
$241$	2.55102	+	4.41849i	0.164326	+	0.284620i	−0.772090	+	0.635513i	$0.780789\pi$
$242$	−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	−0.918042	−	0.396483i	$-0.870231\pi$
$251$	−12.7122	−	22.0181i	−0.802385	−	1.38977i	0.115657	−	0.993289i	$-0.463103\pi$
$252$	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	−0.995994	−	0.0894183i	$-0.971499\pi$
$257$	−9.22493	−	15.9781i	−0.575436	−	0.996684i	0.420559	−	0.907265i	$-0.361834\pi$
$258$	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	−0.993638	−	0.112624i	$-0.964075\pi$
$263$	−6.47530	+	11.2155i	−0.399284	+	0.691580i	0.594354	+	0.804204i	$0.297408\pi$
$264$	−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	−0.868401	−	0.495863i	$-0.834852\pi$
$269$	−0.0782471	+	0.135528i	−0.00477081	+	0.00826329i	0.863630	+	0.504126i	$0.168185\pi$
$270$		0			0
$271$	−13.9095	+	24.0920i	−0.844944	+	1.46349i	0.0407264	+	0.999170i	$0.487033\pi$
$271$	−13.9095	+	24.0920i	−0.844944	+	1.46349i	−0.885670	+	0.464315i	$0.846301\pi$
$272$	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	0.929673	−	0.368386i	$-0.120090\pi$
$281$	2.44413	+	4.23336i	0.145804	+	0.252541i	−0.783868	+	0.620927i	$0.786756\pi$
$282$	0.615400	−	1.06590i	0.0366465	−	0.0634736i
$283$	8.93931	−	15.4833i	0.531387	−	0.920389i	−0.467942	−	0.883759i	$-0.655004\pi$
$283$	8.93931	−	15.4833i	0.531387	−	0.920389i	0.999329	−	0.0366299i	$-0.0116623\pi$
$284$	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	−0.994929	−	0.100576i	$-0.967932\pi$
$307$	−7.19015	+	12.4537i	−0.410364	+	0.710771i	0.584566	+	0.811346i	$0.301265\pi$
$308$	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	0.992252	+	0.124241i	$0.0396495\pi$
$313$	10.6809	+	18.4999i	0.603722	+	1.04568i	−0.388530	+	0.921436i	$0.627017\pi$
$314$	−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	−0.926626	−	0.375983i	$-0.877305\pi$
$317$	−14.0464	−	24.3291i	−0.788924	−	1.36646i	0.137702	−	0.990474i	$-0.456028\pi$
$318$	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	−0.522977	−	0.852347i	$-0.675179\pi$
$337$	8.75041	−	15.1562i	0.476665	−	0.825608i	0.999642	+	0.0267383i	$0.00851209\pi$
$338$	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	−0.999255	−	0.0385980i	$-0.987711\pi$
$347$	−8.68435	+	15.0417i	−0.466201	+	0.807483i	0.533054	+	0.846081i	$0.321044\pi$
$348$	−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	−0.852853	−	0.522151i	$-0.825130\pi$
$359$	0.488273	−	0.845713i	0.0257701	−	0.0446350i	0.878623	+	0.477516i	$0.158463\pi$
$360$		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	0.708064	−	0.706148i	$-0.249569\pi$
$367$	−4.93318	−	8.54451i	−0.257510	−	0.446020i	−0.965574	+	0.260128i	$0.916235\pi$
$368$	−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	0.0183857	+	0.999831i	$0.494147\pi$
$383$	−16.7657	+	29.0390i	−0.856686	+	1.48382i	−0.875072	+	0.483993i	$0.839186\pi$
$384$	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	−0.967318	−	0.253565i	$-0.918397\pi$
$389$	−13.8703	−	24.0241i	−0.703253	−	1.21807i	0.264066	−	0.964505i	$-0.414936\pi$
$390$		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	−0.788737	−	0.614731i	$-0.789265\pi$
$397$	2.74971	−	4.76264i	0.138004	−	0.239030i	0.926741	+	0.375701i	$0.122598\pi$
$398$	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	−0.739954	−	0.672658i	$-0.765153\pi$
$401$	4.25655	−	7.37256i	0.212562	−	0.368168i	0.952516	+	0.304490i	$0.0984860\pi$
$402$	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	0.999353	+	0.0359683i	$0.0114515\pi$
$409$	10.7353	+	18.5941i	0.530826	+	0.919418i	−0.468527	+	0.883449i	$0.655215\pi$
$410$		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	−0.926695	−	0.375815i	$-0.877363\pi$
$421$	−2.82911	+	4.90017i	−0.137883	+	0.238820i	0.788812	+	0.614634i	$0.210696\pi$
$422$	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	0.793109	+	0.609079i	$0.208461\pi$
$431$	19.1834	+	33.2267i	0.924033	+	1.60047i	0.130923	+	0.991392i	$0.458206\pi$
$432$	8.72041	−	15.1042i	0.419561	−	0.726701i
$433$	−3.48125	−	6.02970i	−0.167298	−	0.289769i	0.770171	−	0.637838i	$-0.220171\pi$
$433$	−3.48125	−	6.02970i	−0.167298	−	0.289769i	−0.937469	+	0.348069i	$0.886838\pi$
$434$	−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	−0.957021	−	0.290018i	$-0.906339\pi$
$439$	−4.76346	+	8.25055i	−0.227347	+	0.393777i	0.729674	+	0.683796i	$0.239672\pi$
$440$		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	−0.902366	−	0.430971i	$-0.858171\pi$
$443$	−17.3519	−	30.0544i	−0.824414	−	1.42793i	0.0779516	−	0.996957i	$-0.475162\pi$
$444$	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	0.122524	−	0.992466i	$-0.460901\pi$
$461$	19.7696	−	34.2420i	0.920762	−	1.59481i	0.798238	−	0.602342i	$-0.205766\pi$
$462$	−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	0.999000	+	0.0447012i	$0.0142336\pi$
$479$	11.7794	+	20.4024i	0.538213	+	0.932211i	−0.460788	+	0.887510i	$0.652433\pi$
$480$		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	−0.989390	−	0.145284i	$-0.953590\pi$
$491$	−8.17373	+	14.1573i	−0.368875	+	0.638911i	0.620515	+	0.784195i	$0.286924\pi$
$492$	−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	−0.244009	−	0.969773i	$-0.578463\pi$
$499$	16.0354	−	27.7742i	0.717844	−	1.24334i	0.961852	−	0.273569i	$-0.0882041\pi$
$500$		0			0
$501$	10.8542			0.484930
$502$	7.90972			0.353028
$503$	−7.36269	−	12.7525i	−0.328286	−	0.568608i	0.653886	−	0.756593i	$-0.273138\pi$
$503$	−7.36269	−	12.7525i	−0.328286	−	0.568608i	−0.982172	+	0.187985i	$0.939804\pi$
$504$	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	0.999920	−	0.0126136i	$-0.00401513\pi$
$509$	11.0332	+	19.1100i	0.489037	+	0.847036i	−0.510884	+	0.859650i	$0.670682\pi$
$510$		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	0.970859	−	0.239653i	$-0.0770336\pi$
$523$	6.35498	+	11.0072i	0.277884	+	0.481309i	−0.692975	+	0.720962i	$0.743700\pi$
$524$	−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	0.983137	+	0.182873i	$0.0585396\pi$
$541$	15.1172	+	26.1838i	0.649941	+	1.12573i	−0.333196	+	0.942858i	$0.608127\pi$
$542$	−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	0.937332	−	0.348437i	$-0.113287\pi$
$547$	3.90372	+	6.76144i	0.166911	+	0.289098i	−0.770421	+	0.637535i	$0.779954\pi$
$548$	−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	0.839310	−	0.543653i	$-0.182959\pi$
$557$	−1.20747	−	2.09141i	−0.0511623	−	0.0886157i	−0.890472	+	0.455037i	$0.849626\pi$
$558$	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	−0.440674	−	0.897667i	$-0.645261\pi$
$587$	13.4966	−	23.3768i	0.557065	−	0.964865i	0.997740	−	0.0671982i	$-0.0214060\pi$
$588$	−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	0.997376	−	0.0724009i	$-0.0230661\pi$
$593$	10.6170	+	18.3891i	0.435987	+	0.755151i	−0.561389	+	0.827552i	$0.689733\pi$
$594$	−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	0.989556	+	0.144146i	$0.0460434\pi$
$599$	15.1647	+	26.2660i	0.619612	+	1.07320i	−0.369945	+	0.929054i	$0.620623\pi$
$600$		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	−0.999894	−	0.0145856i	$-0.995357\pi$
$613$	−12.0654	+	20.8978i	−0.487315	+	0.844055i	0.512578	+	0.858640i	$0.328690\pi$
$614$	−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	0.978644	−	0.205564i	$-0.0659030\pi$
$617$	7.73248	+	13.3930i	0.311298	+	0.539183i	−0.667346	+	0.744748i	$0.732570\pi$
$618$	−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	0.791177	−	0.611587i	$-0.209469\pi$
$631$	−3.36758	−	5.83282i	−0.134061	−	0.232201i	−0.925238	+	0.379386i	$0.876135\pi$
$632$	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	0.453980	+	0.891012i	$0.350004\pi$
$641$	−13.7894	+	23.8840i	−0.544649	+	0.943360i	−0.998629	+	0.0523477i	$0.983330\pi$
$642$	−1.39921	−	2.42351i	−0.0552226	−	0.0956483i
$643$	−5.95407	+	10.3128i	−0.234806	+	0.406695i	−0.959216	−	0.282673i	$-0.908779\pi$
$643$	−5.95407	+	10.3128i	−0.234806	+	0.406695i	0.724410	+	0.689369i	$0.242112\pi$
$644$	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	0.998435	−	0.0559165i	$-0.0178081\pi$
$659$	11.5723	+	20.0438i	0.450793	+	0.780796i	−0.547643	+	0.836712i	$0.684475\pi$
$660$		0			0
$661$	−2.44485	−	4.23460i	−0.0950936	−	0.164707i	0.814554	−	0.580088i	$-0.196982\pi$
$661$	−2.44485	−	4.23460i	−0.0950936	−	0.164707i	−0.909648	+	0.415381i	$0.863648\pi$
$662$	−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	−0.690999	−	0.722856i	$-0.742829\pi$
$701$	7.42695	−	12.8639i	0.280512	−	0.485861i	0.971511	+	0.236995i	$0.0761624\pi$
$702$	−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	0.997530	+	0.0702441i	$0.0223778\pi$
$709$	14.9004	+	25.8083i	0.559598	+	0.969252i	−0.437932	+	0.899008i	$0.644289\pi$
$710$		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	−0.516991	−	0.855991i	$-0.672948\pi$
$719$	12.9463	−	22.4236i	0.482814	−	0.836258i	0.999805	+	0.0197322i	$0.00628136\pi$
$720$		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	−0.939594	−	0.342291i	$-0.888797\pi$
$727$	−4.67442	+	8.09634i	−0.173365	+	0.300277i	0.766229	+	0.642567i	$0.222131\pi$
$728$	−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	−0.960321	−	0.278897i	$-0.910031\pi$
$739$	−6.48702	+	11.2359i	−0.238629	+	0.413318i	0.721692	+	0.692214i	$0.243365\pi$
$740$		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	−0.938183	−	0.346139i	$-0.887492\pi$
$743$	−4.61550	+	7.99428i	−0.169326	+	0.293282i	0.768857	+	0.639421i	$0.220826\pi$
$744$	−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	0.697175	−	0.716901i	$-0.254440\pi$
$751$	−7.46131	−	12.9234i	−0.272267	−	0.471580i	−0.969442	+	0.245321i	$0.921107\pi$
$752$	−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	−0.998066	−	0.0621711i	$-0.980198\pi$
$757$	−12.2488	+	21.2156i	−0.445191	+	0.771093i	0.552874	+	0.833265i	$0.313531\pi$
$758$	−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	0.999238	+	0.0390437i	$0.0124312\pi$
$769$	14.7925	+	25.6214i	0.533432	+	0.923931i	−0.465806	+	0.884887i	$0.654235\pi$
$770$		0			0
$771$	19.0003			0.684280
$772$	36.2478			1.30459
$773$	−7.06551	−	12.2378i	−0.254129	−	0.440164i	0.710530	−	0.703667i	$-0.248455\pi$
$773$	−7.06551	−	12.2378i	−0.254129	−	0.440164i	−0.964658	+	0.263503i	$0.915122\pi$
$774$	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
$778$	8.63032			0.309412
$779$	−13.1072	−	26.6119i	−0.469615	−	0.953469i
$780$		0			0
$781$	−1.17675	+	2.03818i	−0.0421073	+	0.0729319i
$782$	−1.20315	+	2.08392i	−0.0430247	+	0.0745210i
$783$	−10.2399	−	17.7360i	−0.365944	−	0.633833i
$784$	−6.44741	+	11.1672i	−0.230265	+	0.398830i
$785$		0			0
$786$	0.775912			0.0276759
$787$	24.2465			0.864293			0.432146	−	0.901803i	$-0.357756\pi$
$787$	24.2465			0.864293			0.432146	+	0.901803i	$0.357756\pi$
$788$	−5.88591	−	10.1947i	−0.209677	−	0.363171i
$789$	−6.66849	−	11.5502i	−0.237404	−	0.411196i
$790$		0			0
$791$	−33.9333			−1.20653
$792$	6.08549	+	10.5404i	0.216238	+	0.374536i
$793$	−10.8463	+	18.7863i	−0.385162	+	0.667120i
$794$	0.855456	+	1.48169i	0.0303590	+	0.0525833i
$795$		0			0
$796$	6.86155	−	11.8846i	0.243201	−	0.421237i
$797$	−27.9258			−0.989184			−0.494592	−	0.869125i	$-0.664682\pi$
$797$	−27.9258			−0.989184			−0.494592	+	0.869125i	$0.664682\pi$
$798$	4.57125	+	0.301875i	0.161820	+	0.0106863i
$799$	3.87723			0.137166
$800$		0			0
$801$	−6.91280	+	11.9733i	−0.244252	+	0.423057i
$802$	1.32425	+	2.29366i	0.0467607	+	0.0809919i
$803$	10.6816	−	18.5011i	0.376946	−	0.652890i
$804$	−10.9739	−	19.0074i	−0.387021	−	0.670341i
$805$		0			0
$806$	−5.05936			−0.178208
$807$	−0.0805816	−	0.139571i	−0.00283661	−	0.00491315i
$808$	−3.75238	−	6.49932i	−0.132008	−	0.228645i
$809$	8.78914			0.309010			0.154505	−	0.987992i	$-0.450622\pi$
$809$	8.78914			0.309010			0.154505	+	0.987992i	$0.450622\pi$
$810$		0			0
$811$	7.04963	+	12.2103i	0.247546	+	0.428762i	0.962844	−	0.270057i	$-0.0870425\pi$
$811$	7.04963	+	12.2103i	0.247546	+	0.428762i	−0.715298	+	0.698819i	$0.753709\pi$
$812$	12.5679	−	21.7682i	0.441046	−	0.763914i
$813$	−14.3245	−	24.8108i	−0.502383	−	0.870152i
$814$	−5.21589	+	9.03418i	−0.182817	+	0.316648i
$815$		0			0
$816$	−3.56370			−0.124755
$817$	12.1533	+	24.6750i	0.425189	+	0.863269i
$818$	−6.67967			−0.233549
$819$	−11.2441	+	19.4754i	−0.392901	+	0.680524i
$820$		0			0
$821$	15.2663	+	26.4420i	0.532797	+	0.922832i	0.999267	+	0.0382943i	$0.0121924\pi$
$821$	15.2663	+	26.4420i	0.532797	+	0.922832i	−0.466469	+	0.884537i	$0.654474\pi$
$822$	1.84530	−	3.19616i	0.0643623	−	0.111479i
$823$	7.17914	+	12.4346i	0.250249	+	0.433444i	0.963594	−	0.267369i	$-0.0861542\pi$
$823$	7.17914	+	12.4346i	0.250249	+	0.433444i	−0.713345	+	0.700813i	$0.752821\pi$
$824$	−22.2484			−0.775059
$825$		0			0
$826$	6.87495	+	11.9078i	0.239210	+	0.414324i
$827$	4.13682	+	7.16518i	0.143851	+	0.249158i	0.928944	−	0.370221i	$-0.120718\pi$
$827$	4.13682	+	7.16518i	0.143851	+	0.249158i	−0.785092	+	0.619379i	$0.787385\pi$
$828$	−28.2873			−0.983052
$829$	13.1498			0.456710			0.228355	−	0.973578i	$-0.426665\pi$
$829$	13.1498			0.456710			0.228355	+	0.973578i	$0.426665\pi$
$830$		0			0
$831$	0.269848	−	0.467391i	0.00936094	−	0.0162136i
$832$	10.1974	+	17.6624i	0.353531	+	0.612333i
$833$	1.89791	−	3.28728i	0.0657587	−	0.113897i
$834$	−1.13346	+	1.96322i	−0.0392486	+	0.0679806i
$835$		0			0
$836$	−42.7794	−	2.82506i	−1.47956	−	0.0977067i
$837$	23.4032			0.808934
$838$	0.792358	−	1.37240i	0.0273715	−	0.0474089i
$839$	4.20767	−	7.28790i	0.145265	−	0.251606i	−0.784207	−	0.620500i	$-0.786930\pi$
$839$	4.20767	−	7.28790i	0.145265	−	0.251606i	0.929472	+	0.368893i	$0.120263\pi$
$840$		0			0
$841$	6.39543	−	11.0772i	0.220532	−	0.381973i
$842$	−0.880159	−	1.52448i	−0.0303323	−	0.0525371i
$843$	−5.03410			−0.173384
$844$	37.3918			1.28708
$845$		0			0
$846$	−1.15895	−	2.00737i	−0.0398457	−	0.0690147i
$847$	−51.5262			−1.77046
$848$	−24.4082			−0.838181
$849$	9.20601	+	15.9453i	0.315950	+	0.547241i
$850$		0			0
$851$	−24.8616	−	43.0616i	−0.852245	−	1.47613i
$852$	−0.446294	+	0.773005i	−0.0152898	+	0.0264827i
$853$	−26.0182	+	45.0648i	−0.890845	+	1.54299i	−0.0519802	+	0.998648i	$0.516553\pi$
$853$	−26.0182	+	45.0648i	−0.890845	+	1.54299i	−0.838865	+	0.544340i	$0.816780\pi$
$854$	−6.26314			−0.214320
$855$		0			0
$856$	−10.6064			−0.362520
$857$	10.7298	−	18.5845i	0.366522	−	0.634834i	−0.622497	−	0.782622i	$-0.713882\pi$
$857$	10.7298	−	18.5845i	0.366522	−	0.634834i	0.989019	+	0.147788i	$0.0472152\pi$
$858$	2.92629	−	5.06849i	0.0999020	−	0.173035i
$859$	−9.07396	−	15.7166i	−0.309599	−	0.536242i	0.668675	−	0.743554i	$-0.266862\pi$
$859$	−9.07396	−	15.7166i	−0.309599	−	0.536242i	−0.978275	+	0.207313i	$0.933528\pi$
$860$		0			0
$861$	−11.4954	−	19.9106i	−0.391762	−	0.678552i
$862$	−11.9362			−0.406549
$863$	−13.7867			−0.469303			−0.234652	−	0.972080i	$-0.575395\pi$
$863$	−13.7867			−0.469303			−0.234652	+	0.972080i	$0.575395\pi$
$864$	8.89000	+	15.3979i	0.302444	+	0.523848i
$865$		0			0
$866$	2.16609			0.0736066
$867$	−16.4581			−0.558948
$868$	14.3619	+	24.8756i	0.487475	+	0.844332i
$869$	7.46320	−	12.9266i	0.253172	−	0.438506i
$870$		0			0
$871$	19.7907	−	34.2786i	0.670584	−	1.16148i
$872$	−3.70173	+	6.41158i	−0.125356	+	0.217123i
$873$	20.9945			0.710557
$874$	−5.77796	+	8.63812i	−0.195442	+	0.292189i
$875$		0			0
$876$	4.05113	−	7.01676i	0.136875	−	0.237075i
$877$	10.5968	−	18.3543i	0.357830	−	0.619780i	−0.629768	−	0.776783i	$-0.716850\pi$
$877$	10.5968	−	18.3543i	0.357830	−	0.619780i	0.987598	+	0.157003i	$0.0501834\pi$
$878$	−1.48195	−	2.56681i	−0.0500134	−	0.0866257i
$879$	−3.73521	+	6.46957i	−0.125985	+	0.218213i
$880$		0			0
$881$	44.5944			1.50242			0.751212	−	0.660061i	$-0.229469\pi$
$881$	44.5944			1.50242			0.751212	+	0.660061i	$0.229469\pi$
$882$	−2.26924			−0.0764093
$883$	−0.846773	−	1.46665i	−0.0284962	−	0.0493568i	0.851426	−	0.524475i	$-0.175739\pi$
$883$	−0.846773	−	1.46665i	−0.0284962	−	0.0493568i	−0.879922	+	0.475119i	$0.842405\pi$
$884$	−3.39487	−	5.88009i	−0.114182	−	0.197769i
$885$		0			0
$886$	10.7966			0.362720
$887$	−24.2177	−	41.9463i	−0.813151	−	1.40842i	−0.910648	−	0.413183i	$-0.864417\pi$
$887$	−24.2177	−	41.9463i	−0.813151	−	1.40842i	0.0974969	−	0.995236i	$-0.468916\pi$
$888$	−4.05697	+	7.02688i	−0.136143	+	0.235807i
$889$	5.52273	+	9.56565i	0.185227	+	0.320822i
$890$		0			0
$891$	1.49806	−	2.59471i	0.0501868	−	0.0869260i
$892$	21.5706			0.722238
$893$	16.7086	+	1.10340i	0.559133	+	0.0369239i
$894$	4.08481			0.136617
$895$		0			0
$896$	−14.4102	+	24.9592i	−0.481411	+	0.833828i
$897$	13.9482	+	24.1590i	0.465718	+	0.806647i
$898$	1.37545	−	2.38235i	0.0458994	−	0.0795001i
$899$	−9.26149	−	16.0414i	−0.308888	−	0.535009i
$900$		0			0
$901$	7.18499			0.239367
$902$	−5.47090	−	9.47588i	−0.182161	−	0.315512i
$903$	10.6588	+	18.4615i	0.354701	+	0.614360i
$904$	−12.5613			−0.417783
$905$		0			0
$906$	3.14561	+	5.44835i	0.104506	+	0.181009i
$907$	−13.9694	+	24.1957i	−0.463846	+	0.803404i	−0.999149	−	0.0412557i	$-0.986864\pi$
$907$	−13.9694	+	24.1957i	−0.463846	+	0.803404i	0.535303	+	0.844660i	$0.320197\pi$
$908$	−10.5979	−	18.3561i	−0.351704	−	0.609169i
$909$	−5.99309	+	10.3803i	−0.198778	+	0.344294i
$910$		0			0
$911$	45.0862			1.49377			0.746887	−	0.664951i	$-0.231548\pi$
$911$	45.0862			1.49377			0.746887	+	0.664951i	$0.231548\pi$
$912$	−15.3575	−	1.01418i	−0.508538	−	0.0335828i
$913$	28.4267			0.940787
$914$	−0.103443	+	0.179169i	−0.00342159	+	0.00592637i
$915$		0			0
$916$	3.34224	+	5.78893i	0.110431	+	0.191272i
$917$	3.97218	−	6.88002i	0.131173	−	0.227198i
$918$	−0.798617	−	1.38325i	−0.0263583	−	0.0456539i
$919$	−5.86849			−0.193584			−0.0967918	−	0.995305i	$-0.530858\pi$
$919$	−5.86849			−0.193584			−0.0967918	+	0.995305i	$0.530858\pi$
$920$		0			0
$921$	−7.40467	−	12.8253i	−0.243992	−	0.422607i
$922$	6.15048	+	10.6529i	0.202555	+	0.350836i
$923$	−1.60972			−0.0529846
$924$	−33.2273			−1.09310
$925$		0			0
$926$	2.42325	−	4.19720i	0.0796330	−	0.137928i
$927$	17.7669	+	30.7732i	0.583542	+	1.01072i
$928$	7.03617	−	12.1870i	0.230974	−	0.400058i
$929$	−23.3157	+	40.3839i	−0.764963	+	1.32495i	0.175304	+	0.984514i	$0.443909\pi$
$929$	−23.3157	+	40.3839i	−0.764963	+	1.32495i	−0.940266	+	0.340440i	$0.889424\pi$
$930$		0			0
$931$	9.11442	−	13.6262i	0.298713	−	0.446579i
$932$	−11.7808			−0.385894
$933$	−4.39013	+	7.60393i	−0.143726	+	0.248942i
$934$	−6.38328	+	11.0562i	−0.208867	+	0.361769i
$935$		0			0
$936$	−4.16230	+	7.20931i	−0.136049	+	0.235644i
$937$	25.6470	+	44.4219i	0.837850	+	1.45120i	0.891689	+	0.452649i	$0.149521\pi$
$937$	25.6470	+	44.4219i	0.837850	+	1.45120i	−0.0538383	+	0.998550i	$0.517146\pi$
$938$	11.4281			0.373140
$939$	−21.9992			−0.717916
$940$		0			0
$941$	5.67430	+	9.82817i	0.184977	+	0.320389i	0.943569	−	0.331177i	$-0.107446\pi$
$941$	5.67430	+	9.82817i	0.184977	+	0.320389i	−0.758592	+	0.651566i	$0.774112\pi$
$942$	0.988367			0.0322027
$943$	52.1543			1.69838
$944$	−23.0970	−	40.0052i	−0.751743	−	1.30206i
$945$		0			0
$946$	5.07272	+	8.78621i	0.164928	+	0.285664i
$947$	3.60467	−	6.24348i	0.117136	−	0.202886i	−0.801495	−	0.598001i	$-0.795962\pi$
$947$	3.60467	−	6.24348i	0.117136	−	0.202886i	0.918632	+	0.395115i	$0.129295\pi$
$948$	2.83051	−	4.90258i	0.0919305	−	0.159228i
$949$	14.6119			0.474321
$950$		0			0
$951$	28.9309			0.938150
$952$	2.01020	−	3.48177i	0.0651511	−	0.112845i
$953$	−10.2697	+	17.7877i	−0.332669	+	0.576199i	−0.983034	−	0.183422i	$-0.941282\pi$
$953$	−10.2697	+	17.7877i	−0.332669	+	0.576199i	0.650365	+	0.759622i	$0.274616\pi$
$954$	−2.14769	−	3.71991i	−0.0695340	−	0.120436i
$955$		0			0
$956$	11.5355	+	19.9801i	0.373085	+	0.646202i
$957$	21.4271			0.692639
$958$	−7.32930			−0.236799
$959$	−18.8935	−	32.7246i	−0.610104	−	1.05673i
$960$		0			0
$961$	−9.83289			−0.317190
$962$	−7.13504			−0.230043
$963$	8.46998	+	14.6704i	0.272941	+	0.472748i
$964$	−4.85513	+	8.40933i	−0.156373	+	0.270846i
$965$		0			0
$966$	−4.02718	+	6.97528i	−0.129572	+	0.224426i
$967$	8.53345	−	14.7804i	0.274417	−	0.475305i	−0.695571	−	0.718458i	$-0.744848\pi$
$967$	8.53345	−	14.7804i	0.274417	−	0.475305i	0.969988	+	0.243153i	$0.0781817\pi$
$968$	−19.0738			−0.613055
$969$	4.52076	+	0.298541i	0.145228	+	0.00959053i
$970$		0			0
$971$	1.74085	−	3.01525i	0.0558667	−	0.0967639i	−0.836740	−	0.547601i	$-0.815541\pi$
$971$	1.74085	−	3.01525i	0.0558667	−	0.0967639i	0.892606	+	0.450837i	$0.148874\pi$
$972$	15.0901	−	26.1368i	0.484014	−	0.838337i
$973$	11.6052	+	20.1008i	0.372046	+	0.644403i
$974$	3.72032	−	6.44379i	0.119207	−	0.206472i
$975$		0			0
$976$	21.0416			0.673524
$977$	21.9600			0.702562			0.351281	−	0.936270i	$-0.385746\pi$
$977$	21.9600			0.702562			0.351281	+	0.936270i	$0.385746\pi$
$978$	3.59992	+	6.23524i	0.115113	+	0.199381i
$979$	−18.4202	−	31.9047i	−0.588711	−	1.01968i
$980$		0			0
$981$	11.8244			0.377523
$982$	−2.54291	−	4.40445i	−0.0811476	−	0.140552i
$983$	2.74852	−	4.76057i	0.0876641	−	0.151839i	−0.818859	−	0.573994i	$-0.805393\pi$
$983$	2.74852	−	4.76057i	0.0876641	−	0.151839i	0.906523	+	0.422156i	$0.138726\pi$
$984$	−4.25533	−	7.37044i	−0.135655	−	0.234961i
$985$		0			0
$986$	−0.632082	+	1.09480i	−0.0201296	+	0.0348655i
$987$	12.9778			0.413088
$988$	−12.9566	−	26.3059i	−0.412203	−	0.836903i
$989$	−48.3584			−1.53771
$990$		0			0
$991$	14.7485	−	25.5452i	0.468502	−	0.811469i	−0.530850	−	0.847466i	$-0.678127\pi$
$991$	14.7485	−	25.5452i	0.468502	−	0.811469i	0.999352	+	0.0359970i	$0.0114607\pi$
$992$	8.04058	+	13.9267i	0.255289	+	0.442173i
$993$	−7.81259	+	13.5318i	−0.247925	+	0.429419i
$994$	−0.232382	−	0.402497i	−0.00737071	−	0.0127664i
$995$		0			0
$996$	10.7812			0.341614
$997$	3.63224	+	6.29123i	0.115034	+	0.199245i	0.917793	−	0.397058i	$-0.129969\pi$
$997$	3.63224	+	6.29123i	0.115034	+	0.199245i	−0.802759	+	0.596303i	$0.796636\pi$
$998$	4.98874	+	8.64076i	0.157916	+	0.273518i
$999$	33.0048			1.04422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.f.201.3	yes	12
5.2	odd	4		475.2.j.d.49.6		24
5.3	odd	4		475.2.j.d.49.7		24
5.4	even	2		475.2.e.h.201.4	yes	12
19.7	even	3	inner	475.2.e.f.26.3	✓	12
19.8	odd	6		9025.2.a.bs.1.3		6
19.11	even	3		9025.2.a.bz.1.4		6
95.7	odd	12		475.2.j.d.349.7		24
95.49	even	6		9025.2.a.br.1.3		6
95.64	even	6		475.2.e.h.26.4	yes	12
95.83	odd	12		475.2.j.d.349.6		24
95.84	odd	6		9025.2.a.by.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.3	✓	12	19.7	even	3	inner
475.2.e.f.201.3	yes	12	1.1	even	1	trivial
475.2.e.h.26.4	yes	12	95.64	even	6
475.2.e.h.201.4	yes	12	5.4	even	2
475.2.j.d.49.6		24	5.2	odd	4
475.2.j.d.49.7		24	5.3	odd	4
475.2.j.d.349.6		24	95.83	odd	12
475.2.j.d.349.7		24	95.7	odd	12
9025.2.a.br.1.3		6	95.49	even	6
9025.2.a.bs.1.3		6	19.8	odd	6
9025.2.a.by.1.4		6	95.84	odd	6
9025.2.a.bz.1.4		6	19.11	even	3

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more