LMFDB - Embedded newform 300.2.j.d.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(7,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("300.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.j (of order $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-0.394157 + 1.35818i$ of defining polynomial
Character	$\chi$	$=$	300.43
Dual form			300.2.j.d.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.394157 + 1.35818i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 - 2.47817i) q^{7} +(2.12000 - 1.87233i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.394157 + 1.35818i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 - 2.47817i) q^{7} +(2.12000 - 1.87233i) q^{8} -1.00000i q^{9} -3.02831i q^{11} +(1.95158 - 0.437425i) q^{12} +(-0.363328 - 0.363328i) q^{13} +(4.34258 - 2.38900i) q^{14} +(1.70734 + 3.61732i) q^{16} +(2.36333 - 2.36333i) q^{17} +(1.35818 + 0.394157i) q^{18} -4.95634 q^{19} +3.50466 q^{21} +(4.11297 + 1.19363i) q^{22} +(0.900390 - 0.900390i) q^{23} +(-0.175128 + 2.82300i) q^{24} +(0.636672 - 0.350255i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.53303 + 6.83963i) q^{28} -3.50466i q^{29} -3.85607i q^{31} +(-5.58591 + 0.893077i) q^{32} +(2.14134 + 2.14134i) q^{33} +(2.27829 + 4.14134i) q^{34} +(-1.07067 + 1.68928i) q^{36} +(0.363328 - 0.363328i) q^{37} +(1.95358 - 6.73158i) q^{38} +0.513824 q^{39} +2.72666 q^{41} +(-1.38139 + 4.75995i) q^{42} +(-3.92870 + 3.92870i) q^{43} +(-3.24231 + 5.11566i) q^{44} +(0.867993 + 1.57778i) q^{46} +(-5.85673 - 5.85673i) q^{47} +(-3.76510 - 1.35056i) q^{48} +5.28267i q^{49} +3.34225i q^{51} +(0.224760 + 1.00277i) q^{52} +(-3.14134 - 3.14134i) q^{53} +(-1.23909 + 0.681664i) q^{54} +(-9.89367 - 0.613763i) q^{56} +(3.50466 - 3.50466i) q^{57} +(4.75995 + 1.38139i) q^{58} +8.68516 q^{59} -15.2920 q^{61} +(5.23723 + 1.51990i) q^{62} +(-2.47817 + 2.47817i) q^{63} +(0.988770 - 7.93866i) q^{64} +(-3.75233 + 2.06429i) q^{66} +(3.92870 + 3.92870i) q^{67} +(-6.52267 + 1.46199i) q^{68} +1.27334i q^{69} +4.25583i q^{71} +(-1.87233 - 2.12000i) q^{72} +(-9.28267 - 9.28267i) q^{73} +(0.350255 + 0.636672i) q^{74} +(8.37266 + 5.30660i) q^{76} +(-7.50466 + 7.50466i) q^{77} +(-0.202527 + 0.697863i) q^{78} +0.399759 q^{79} -1.00000 q^{81} +(-1.07473 + 3.70328i) q^{82} +(0.199879 - 0.199879i) q^{83} +(-5.92036 - 3.75233i) q^{84} +(-3.78734 - 6.88438i) q^{86} +(2.47817 + 2.47817i) q^{87} +(-5.66999 - 6.42000i) q^{88} -4.28267i q^{89} +1.80078i q^{91} +(-2.48503 + 0.556993i) q^{92} +(2.72666 + 2.72666i) q^{93} +(10.2629 - 5.64600i) q^{94} +(3.31834 - 4.58134i) q^{96} +(-6.73599 + 6.73599i) q^{97} +(-7.17480 - 2.08220i) q^{98} -3.02831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 + 12 * q^8	$ 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.394157	+	1.35818i	−0.278711	+	0.960375i
$2$	−0.394157	+	1.35818i	−0.278711	+	0.960375i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.68928	−	1.07067i	−0.844640	−	0.535334i
$5$		0			0
$5$		0			0
$6$	−0.681664	−	1.23909i	−0.278288	−	0.505855i
$7$	−2.47817	−	2.47817i	−0.936661	−	0.936661i	0.0614493	−	0.998110i	$-0.480428\pi$
$7$	−2.47817	−	2.47817i	−0.936661	−	0.936661i	−0.998110	+	0.0614493i	$0.980428\pi$
$8$	2.12000	−	1.87233i	0.749532	−	0.661968i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	3.02831i		−	0.913069i	−0.889706	−	0.456534i	$-0.849091\pi$
$11$		−	3.02831i		−	0.913069i	0.889706	−	0.456534i	$-0.150909\pi$
$12$	1.95158	−	0.437425i	0.563372	−	0.126274i
$13$	−0.363328	−	0.363328i	−0.100769	−	0.100769i	0.654925	−	0.755694i	$-0.272700\pi$
$13$	−0.363328	−	0.363328i	−0.100769	−	0.100769i	−0.755694	+	0.654925i	$0.772700\pi$
$14$	4.34258	−	2.38900i	1.16060	−	0.638488i
$15$		0			0
$16$	1.70734	+	3.61732i	0.426835	+	0.904330i
$17$	2.36333	−	2.36333i	0.573191	−	0.573191i	−0.359828	−	0.933019i	$-0.617164\pi$
$17$	2.36333	−	2.36333i	0.573191	−	0.573191i	0.933019	+	0.359828i	$0.117164\pi$
$18$	1.35818	+	0.394157i	0.320125	+	0.0929036i
$19$	−4.95634			−1.13706			−0.568532	−	0.822661i	$-0.692488\pi$
$19$	−4.95634			−1.13706			−0.568532	+	0.822661i	$0.692488\pi$
$20$		0			0
$21$	3.50466			0.764780
$22$	4.11297	+	1.19363i	0.876888	+	0.254482i
$23$	0.900390	−	0.900390i	0.187744	−	0.187744i	−0.606976	−	0.794720i	$-0.707618\pi$
$23$	0.900390	−	0.900390i	0.187744	−	0.187744i	0.794720	+	0.606976i	$0.207618\pi$
$24$	−0.175128	+	2.82300i	−0.0357478	+	0.576243i
$25$		0			0
$26$	0.636672	−	0.350255i	0.124862	−	0.0686907i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.53303	+	6.83963i	0.289715	+	1.29257i
$29$		−	3.50466i		−	0.650800i	−0.945576	−	0.325400i	$-0.894501\pi$
$29$		−	3.50466i		−	0.650800i	0.945576	−	0.325400i	$-0.105499\pi$
$30$		0			0
$31$		−	3.85607i		−	0.692571i	−0.938129	−	0.346286i	$-0.887443\pi$
$31$		−	3.85607i		−	0.692571i	0.938129	−	0.346286i	$-0.112557\pi$
$32$	−5.58591	+	0.893077i	−0.987459	+	0.157875i
$33$	2.14134	+	2.14134i	0.372759	+	0.372759i
$34$	2.27829	+	4.14134i	0.390724	+	0.710233i
$35$		0			0
$36$	−1.07067	+	1.68928i	−0.178445	+	0.281547i
$37$	0.363328	−	0.363328i	0.0597308	−	0.0597308i	−0.676610	−	0.736341i	$-0.736552\pi$
$37$	0.363328	−	0.363328i	0.0597308	−	0.0597308i	0.736341	+	0.676610i	$0.236552\pi$
$38$	1.95358	−	6.73158i	0.316912	−	1.09201i
$39$	0.513824			0.0822776
$40$		0			0
$41$	2.72666			0.425832			0.212916	−	0.977070i	$-0.431704\pi$
$41$	2.72666			0.425832			0.212916	+	0.977070i	$0.431704\pi$
$42$	−1.38139	+	4.75995i	−0.213153	+	0.734476i
$43$	−3.92870	+	3.92870i	−0.599121	+	0.599121i	−0.940079	−	0.340958i	$-0.889249\pi$
$43$	−3.92870	+	3.92870i	−0.599121	+	0.599121i	0.340958	+	0.940079i	$0.389249\pi$
$44$	−3.24231	+	5.11566i	−0.488797	+	0.771215i
$45$		0			0
$46$	0.867993	+	1.57778i	0.127979	+	0.232631i
$47$	−5.85673	−	5.85673i	−0.854292	−	0.854292i	0.136366	−	0.990659i	$-0.456458\pi$
$47$	−5.85673	−	5.85673i	−0.854292	−	0.854292i	−0.990659	+	0.136366i	$0.956458\pi$
$48$	−3.76510	−	1.35056i	−0.543446	−	0.194936i
$49$			5.28267i			0.754667i
$50$		0			0
$51$			3.34225i			0.468009i
$52$	0.224760	+	1.00277i	0.0311685	+	0.139059i
$53$	−3.14134	−	3.14134i	−0.431496	−	0.431496i	0.457641	−	0.889137i	$-0.348694\pi$
$53$	−3.14134	−	3.14134i	−0.431496	−	0.431496i	−0.889137	+	0.457641i	$0.848694\pi$
$54$	−1.23909	+	0.681664i	−0.168618	+	0.0927627i
$55$		0			0
$56$	−9.89367	−	0.613763i	−1.32210	−	0.0820176i
$57$	3.50466	−	3.50466i	0.464204	−	0.464204i
$58$	4.75995	+	1.38139i	0.625012	+	0.181385i
$59$	8.68516			1.13071			0.565356	−	0.824847i	$-0.308739\pi$
$59$	8.68516			1.13071			0.565356	+	0.824847i	$0.308739\pi$
$60$		0			0
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	5.23723	+	1.51990i	0.665128	+	0.193027i
$63$	−2.47817	+	2.47817i	−0.312220	+	0.312220i
$64$	0.988770	−	7.93866i	0.123596	−	0.992333i
$65$		0			0
$66$	−3.75233	+	2.06429i	−0.461880	+	0.254096i
$67$	3.92870	+	3.92870i	0.479967	+	0.479967i	0.905121	−	0.425154i	$-0.139780\pi$
$67$	3.92870	+	3.92870i	0.479967	+	0.479967i	−0.425154	+	0.905121i	$0.639780\pi$
$68$	−6.52267	+	1.46199i	−0.790989	+	0.177292i
$69$			1.27334i			0.153293i
$70$		0			0
$71$			4.25583i			0.505075i	0.967587	+	0.252537i	$0.0812650\pi$
$71$			4.25583i			0.505075i	−0.967587	+	0.252537i	$0.918735\pi$
$72$	−1.87233	−	2.12000i	−0.220656	−	0.249844i
$73$	−9.28267	−	9.28267i	−1.08645	−	1.08645i	−0.995891	−	0.0905640i	$-0.971133\pi$
$73$	−9.28267	−	9.28267i	−1.08645	−	1.08645i	−0.0905640	−	0.995891i	$-0.528867\pi$
$74$	0.350255	+	0.636672i	0.0407163	+	0.0740116i
$75$		0			0
$76$	8.37266	+	5.30660i	0.960410	+	0.608709i
$77$	−7.50466	+	7.50466i	−0.855236	+	0.855236i
$78$	−0.202527	+	0.697863i	−0.0229317	+	0.0790174i
$79$	0.399759			0.0449764			0.0224882	−	0.999747i	$-0.492841\pi$
$79$	0.399759			0.0449764			0.0224882	+	0.999747i	$0.492841\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−1.07473	+	3.70328i	−0.118684	+	0.408959i
$83$	0.199879	−	0.199879i	0.0219396	−	0.0219396i	−0.696052	−	0.717991i	$-0.745062\pi$
$83$	0.199879	−	0.199879i	0.0219396	−	0.0219396i	0.717991	+	0.696052i	$0.245062\pi$
$84$	−5.92036	−	3.75233i	−0.645965	−	0.409413i
$85$		0			0
$86$	−3.78734	−	6.88438i	−0.408399	−	0.742362i
$87$	2.47817	+	2.47817i	0.265688	+	0.265688i
$88$	−5.66999	−	6.42000i	−0.604422	−	0.684374i
$89$		−	4.28267i		−	0.453962i	−0.973899	−	0.226981i	$-0.927114\pi$
$89$		−	4.28267i		−	0.453962i	0.973899	−	0.226981i	$-0.0728856\pi$
$90$		0			0
$91$			1.80078i			0.188773i
$92$	−2.48503	+	0.556993i	−0.259082	+	0.0580705i
$93$	2.72666	+	2.72666i	0.282741	+	0.282741i
$94$	10.2629	−	5.64600i	1.05854	−	0.582340i
$95$		0			0
$96$	3.31834	−	4.58134i	0.338676	−	0.467581i
$97$	−6.73599	+	6.73599i	−0.683936	+	0.683936i	−0.960885	−	0.276949i	$-0.910677\pi$
$97$	−6.73599	+	6.73599i	−0.683936	+	0.683936i	0.276949	+	0.960885i	$0.410677\pi$
$98$	−7.17480	−	2.08220i	−0.724764	−	0.210334i
$99$	−3.02831			−0.304356
$100$		0			0
$101$	5.78734			0.575862			0.287931	−	0.957651i	$-0.407033\pi$
$101$	5.78734			0.575862			0.287931	+	0.957651i	$0.407033\pi$
$102$	−4.53936	−	1.31737i	−0.449464	−	0.130439i
$103$	13.0914	−	13.0914i	1.28993	−	1.28993i	0.355104	−	0.934827i	$-0.384445\pi$
$103$	13.0914	−	13.0914i	1.28993	−	1.28993i	0.934827	−	0.355104i	$-0.115555\pi$
$104$	−1.45052	−	0.0899847i	−0.142236	−	0.00882373i
$105$		0			0
$106$	5.50466	−	3.02831i	0.534660	−	0.294135i
$107$	9.71281	+	9.71281i	0.938973	+	0.938973i	0.998242	−	0.0592694i	$-0.0188771\pi$
$107$	9.71281	+	9.71281i	0.938973	+	0.938973i	−0.0592694	+	0.998242i	$0.518877\pi$
$108$	−0.437425	−	1.95158i	−0.0420913	−	0.187791i
$109$			10.4626i			1.00214i	0.865407	+	0.501070i	$0.167060\pi$
$109$			10.4626i			1.00214i	−0.865407	+	0.501070i	$0.832940\pi$
$110$		0			0
$111$			0.513824i			0.0487700i
$112$	4.73325	−	13.1954i	0.447251	−	1.24685i
$113$	10.6460	+	10.6460i	1.00149	+	1.00149i	0.999999	+	0.00149259i	$0.000475108\pi$
$113$	10.6460	+	10.6460i	1.00149	+	1.00149i	0.00149259	+	0.999999i	$0.499525\pi$
$114$	3.37856	+	6.14134i	0.316431	+	0.575189i
$115$		0			0
$116$	−3.75233	+	5.92036i	−0.348395	+	0.549692i
$117$	−0.363328	+	0.363328i	−0.0335897	+	0.0335897i
$118$	−3.42331	+	11.7960i	−0.315142	+	1.08591i
$119$	−11.7135			−1.07377
$120$		0			0
$121$	1.82936			0.166305
$122$	6.02745	−	20.7692i	0.545699	−	1.88036i
$123$	−1.92804	+	1.92804i	−0.173845	+	0.173845i
$124$	−4.12858	+	6.51399i	−0.370757	+	0.584974i
$125$		0			0
$126$	−2.38900	−	4.34258i	−0.212829	−	0.386868i
$127$	1.77766	+	1.77766i	0.157742	+	0.157742i	0.781565	−	0.623823i	$-0.214422\pi$
$127$	1.77766	+	1.77766i	0.157742	+	0.157742i	−0.623823	+	0.781565i	$0.714422\pi$
$128$	10.3924	+	4.47200i	0.918564	+	0.395273i
$129$		−	5.55602i		−	0.489180i
$130$		0			0
$131$			18.1981i			1.58997i	0.606626	+	0.794987i	$0.292523\pi$
$131$			18.1981i			1.58997i	−0.606626	+	0.794987i	$0.707477\pi$
$132$	−1.32466	−	5.90998i	−0.115297	−	0.514398i
$133$	12.2827	+	12.2827i	1.06504	+	1.06504i
$134$	−6.88438	+	3.78734i	−0.594720	+	0.327176i
$135$		0			0
$136$	0.585320	−	9.43517i	0.0501908	−	0.809060i
$137$	5.91934	−	5.91934i	0.505724	−	0.505724i	−0.407487	−	0.913211i	$-0.633595\pi$
$137$	5.91934	−	5.91934i	0.505724	−	0.505724i	0.913211	+	0.407487i	$0.133595\pi$
$138$	−1.72942	−	0.501897i	−0.147218	−	0.0427243i
$139$	12.4140			1.05294			0.526470	−	0.850194i	$-0.323515\pi$
$139$	12.4140			1.05294			0.526470	+	0.850194i	$0.323515\pi$
$140$		0			0
$141$	8.28267			0.697527
$142$	−5.78017	−	1.67747i	−0.485061	−	0.140770i
$143$	−1.10027	+	1.10027i	−0.0920091	+	0.0920091i
$144$	3.61732	−	1.70734i	0.301443	−	0.142278i
$145$		0			0
$146$	16.2663	−	8.94867i	1.34621	−	0.740597i
$147$	−3.73541	−	3.73541i	−0.308092	−	0.308092i
$148$	−1.00277	+	0.224760i	−0.0824270	+	0.0184751i
$149$			5.78734i			0.474117i	0.971495	+	0.237059i	$0.0761833\pi$
$149$			5.78734i			0.474117i	−0.971495	+	0.237059i	$0.923817\pi$
$150$		0			0
$151$		−	18.0708i		−	1.47058i	−0.677751	−	0.735292i	$-0.737045\pi$
$151$		−	18.0708i		−	1.47058i	0.677751	−	0.735292i	$-0.262955\pi$
$152$	−10.5074	+	9.27990i	−0.852265	+	0.752700i
$153$	−2.36333	−	2.36333i	−0.191064	−	0.191064i
$154$	−7.23464	−	13.1507i	−0.582984	−	1.05971i
$155$		0			0
$156$	−0.867993	−	0.550135i	−0.0694950	−	0.0440460i
$157$	3.91934	−	3.91934i	0.312798	−	0.312798i	−0.533195	−	0.845992i	$-0.679009\pi$
$157$	3.91934	−	3.91934i	0.312798	−	0.312798i	0.845992	+	0.533195i	$0.179009\pi$
$158$	−0.157568	+	0.542943i	−0.0125354	+	0.0431942i
$159$	4.44252			0.352315
$160$		0			0
$161$	−4.46264			−0.351705
$162$	0.394157	−	1.35818i	0.0309679	−	0.106708i
$163$	3.22819	−	3.22819i	0.252851	−	0.252851i	−0.569287	−	0.822139i	$-0.692781\pi$
$163$	3.22819	−	3.22819i	0.252851	−	0.252851i	0.822139	+	0.569287i	$0.192781\pi$
$164$	−4.60609	−	2.91934i	−0.359675	−	0.227962i
$165$		0			0
$166$	0.192688	+	0.350255i	0.0149555	+	0.0271851i
$167$	6.95700	+	6.95700i	0.538349	+	0.538349i	0.923044	−	0.384695i	$-0.125693\pi$
$167$	6.95700	+	6.95700i	0.538349	+	0.538349i	−0.384695	+	0.923044i	$0.625693\pi$
$168$	7.42988	−	6.56188i	0.573227	−	0.506260i
$169$		−	12.7360i		−	0.979691i
$170$		0			0
$171$			4.95634i			0.379021i
$172$	10.8430	−	2.43034i	0.826771	−	0.185312i
$173$	−0.627343	−	0.627343i	−0.0476960	−	0.0476960i	0.682857	−	0.730553i	$-0.260737\pi$
$173$	−0.627343	−	0.627343i	−0.0476960	−	0.0476960i	−0.730553	+	0.682857i	$0.760737\pi$
$174$	−4.34258	+	2.38900i	−0.329210	+	0.181110i
$175$		0			0
$176$	10.9543	−	5.17035i	0.825715	−	0.389730i
$177$	−6.14134	+	6.14134i	−0.461611	+	0.461611i
$178$	5.81662	+	1.68804i	0.435974	+	0.126524i
$179$	8.93968			0.668183			0.334091	−	0.942541i	$-0.391571\pi$
$179$	8.93968			0.668183			0.334091	+	0.942541i	$0.391571\pi$
$180$		0			0
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	−2.44577	−	0.709789i	−0.181293	−	0.0526131i
$183$	10.8131	−	10.8131i	0.799326	−	0.799326i
$184$	0.222998	−	3.59465i	0.0164396	−	0.265001i
$185$		0			0
$186$	−4.77801	+	2.62855i	−0.350341	+	0.192734i
$187$	−7.15688	−	7.15688i	−0.523363	−	0.523363i
$188$	3.62305	+	16.1643i	0.264238	+	1.17890i
$189$		−	3.50466i		−	0.254927i
$190$		0			0
$191$		−	21.6262i		−	1.56481i	−0.622768	−	0.782407i	$-0.713992\pi$
$191$		−	21.6262i		−	1.56481i	0.622768	−	0.782407i	$-0.286008\pi$
$192$	4.91431	+	6.31265i	0.354660	+	0.455576i
$193$	−11.5653	−	11.5653i	−0.832492	−	0.832492i	0.155365	−	0.987857i	$-0.450345\pi$
$193$	−11.5653	−	11.5653i	−0.832492	−	0.832492i	−0.987857	+	0.155365i	$0.950345\pi$
$194$	−6.49362	−	11.8037i	−0.466214	−	0.847455i
$195$		0			0
$196$	5.65599	−	8.92392i	0.403999	−	0.637423i
$197$	9.42401	−	9.42401i	0.671433	−	0.671433i	−0.286614	−	0.958046i	$-0.592530\pi$
$197$	9.42401	−	9.42401i	0.671433	−	0.671433i	0.958046	+	0.286614i	$0.0925296\pi$
$198$	1.19363	−	4.11297i	0.0848274	−	0.292296i
$199$	−11.0130			−0.780688			−0.390344	−	0.920669i	$-0.627644\pi$
$199$	−11.0130			−0.780688			−0.390344	+	0.920669i	$0.627644\pi$
$200$		0			0
$201$	−5.55602			−0.391891
$202$	−2.28112	+	7.86022i	−0.160499	+	0.553043i
$203$	−8.68516	+	8.68516i	−0.609579	+	0.609579i
$204$	3.57844	−	5.64600i	0.250541	−	0.395299i
$205$		0			0
$206$	12.6203	+	22.9404i	0.879300	+	1.59834i
$207$	−0.900390	−	0.900390i	−0.0625814	−	0.0625814i
$208$	0.693949	−	1.93460i	0.0481167	−	0.134140i
$209$			15.0093i			1.03822i
$210$		0			0
$211$			27.9835i			1.92646i	0.268669	+	0.963232i	$0.413416\pi$
$211$			27.9835i			1.92646i	−0.268669	+	0.963232i	$0.586584\pi$
$212$	1.94327	+	8.66993i	0.133464	+	0.595453i
$213$	−3.00933	−	3.00933i	−0.206196	−	0.206196i
$214$	−17.0201	+	9.36333i	−1.16347	+	0.640064i
$215$		0			0
$216$	2.82300	+	0.175128i	0.192081	+	0.0119159i
$217$	−9.55602	+	9.55602i	−0.648705	+	0.648705i
$218$	−14.2101	−	4.12392i	−0.962430	−	0.279307i
$219$	13.1277			0.887086
$220$		0			0
$221$	−1.71733			−0.115520
$222$	−0.697863	−	0.202527i	−0.0468375	−	0.0135927i
$223$	−8.53479	+	8.53479i	−0.571531	+	0.571531i	−0.932556	−	0.361025i	$-0.882427\pi$
$223$	−8.53479	+	8.53479i	−0.571531	+	0.571531i	0.361025	+	0.932556i	$0.382427\pi$
$224$	16.0560	+	11.6297i	1.07279	+	0.777039i
$225$		0			0
$226$	−18.6553	+	10.2629i	−1.24093	+	0.682681i
$227$	−1.02765	−	1.02765i	−0.0682074	−	0.0682074i	0.672180	−	0.740388i	$-0.265358\pi$
$227$	−1.02765	−	1.02765i	−0.0682074	−	0.0682074i	−0.740388	+	0.672180i	$0.765358\pi$
$228$	−9.67269	+	2.16803i	−0.640590	+	0.143581i
$229$		−	8.84802i		−	0.584693i	−0.956312	−	0.292347i	$-0.905564\pi$
$229$		−	8.84802i		−	0.584693i	0.956312	−	0.292347i	$-0.0944361\pi$
$230$		0			0
$231$		−	10.6132i		−	0.698297i
$232$	−6.56188	−	7.42988i	−0.430809	−	0.487795i
$233$	4.91002	+	4.91002i	0.321666	+	0.321666i	0.849406	−	0.527740i	$-0.176960\pi$
$233$	4.91002	+	4.91002i	0.321666	+	0.321666i	−0.527740	+	0.849406i	$0.676960\pi$
$234$	−0.350255	−	0.636672i	−0.0228969	−	0.0416205i
$235$		0			0
$236$	−14.6717	−	9.29892i	−0.955045	−	0.605308i
$237$	−0.282672	+	0.282672i	−0.0183615	+	0.0183615i
$238$	4.61694	−	15.9089i	0.299272	−	1.03122i
$239$	−19.0259			−1.23068			−0.615340	−	0.788262i	$-0.710981\pi$
$239$	−19.0259			−1.23068			−0.615340	+	0.788262i	$0.710981\pi$
$240$		0			0
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	−0.721054	+	2.48459i	−0.0463511	+	0.159716i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	25.8325	+	16.3727i	1.65376	+	1.04815i
$245$		0			0
$246$	−1.85866	−	3.37856i	−0.118504	−	0.215409i
$247$	1.80078	+	1.80078i	0.114581	+	0.114581i
$248$	−7.21984	−	8.17486i	−0.458460	−	0.519104i
$249$			0.282672i			0.0179136i
$250$		0			0
$251$			2.77379i			0.175080i	0.996161	+	0.0875401i	$0.0279006\pi$
$251$			2.77379i			0.175080i	−0.996161	+	0.0875401i	$0.972099\pi$
$252$	6.83963	−	1.53303i	0.430856	−	0.0965717i
$253$	−2.72666	−	2.72666i	−0.171423	−	0.171423i
$254$	−3.11505	+	1.71370i	−0.195456	+	0.107527i
$255$		0			0
$256$	−10.1700	+	12.3520i	−0.635624	+	0.771999i
$257$	2.08066	−	2.08066i	0.129788	−	0.129788i	−0.639229	−	0.769017i	$-0.720746\pi$
$257$	2.08066	−	2.08066i	0.129788	−	0.129788i	0.769017	+	0.639229i	$0.220746\pi$
$258$	7.54604	+	2.18994i	0.469796	+	0.136340i
$259$	−1.80078			−0.111895
$260$		0			0
$261$	−3.50466			−0.216933
$262$	−24.7162	−	7.17290i	−1.52697	−	0.443143i
$263$	4.75646	−	4.75646i	0.293296	−	0.293296i	−0.545085	−	0.838381i	$-0.683503\pi$
$263$	4.75646	−	4.75646i	0.293296	−	0.293296i	0.838381	+	0.545085i	$0.183503\pi$
$264$	8.54891	+	0.530340i	0.526149	+	0.0326402i
$265$		0			0
$266$	−21.5233	+	11.8407i	−1.31968	+	0.726001i
$267$	3.02831	+	3.02831i	0.185329	+	0.185329i
$268$	−2.43034	−	10.8430i	−0.148457	−	0.662342i
$269$		−	21.6846i		−	1.32214i	−0.750326	−	0.661068i	$-0.770104\pi$
$269$		−	21.6846i		−	1.32214i	0.750326	−	0.661068i	$-0.229896\pi$
$270$		0			0
$271$			3.15556i			0.191687i	0.995396	+	0.0958434i	$0.0305548\pi$
$271$			3.15556i			0.191687i	−0.995396	+	0.0958434i	$0.969445\pi$
$272$	12.5839	+	4.51391i	0.763012	+	0.273696i
$273$	−1.27334	−	1.27334i	−0.0770663	−	0.0770663i
$274$	5.70636	+	10.3727i	0.344734	+	0.626635i
$275$		0			0
$276$	1.36333	−	2.15103i	0.0820627	−	0.129477i
$277$	3.53397	−	3.53397i	0.212336	−	0.212336i	−0.592923	−	0.805259i	$-0.702026\pi$
$277$	3.53397	−	3.53397i	0.212336	−	0.212336i	0.805259	+	0.592923i	$0.202026\pi$
$278$	−4.89305	+	16.8604i	−0.293466	+	1.01122i
$279$	−3.85607			−0.230857
$280$		0			0
$281$	0.179969			0.0107361			0.00536804	−	0.999986i	$-0.498291\pi$
$281$	0.179969			0.0107361			0.00536804	+	0.999986i	$0.498291\pi$
$282$	−3.26467	+	11.2493i	−0.194408	+	0.669887i
$283$	−9.84007	+	9.84007i	−0.584931	+	0.584931i	−0.936254	−	0.351323i	$-0.885732\pi$
$283$	−9.84007	+	9.84007i	−0.584931	+	0.584931i	0.351323	+	0.936254i	$0.385732\pi$
$284$	4.55658	−	7.18930i	0.270384	−	0.426606i
$285$		0			0
$286$	−1.06068	−	1.92804i	−0.0627193	−	0.114007i
$287$	−6.75712	−	6.75712i	−0.398860	−	0.398860i
$288$	0.893077	+	5.58591i	0.0526250	+	0.329153i
$289$			5.82936i			0.342903i
$290$		0			0
$291$		−	9.52612i		−	0.558431i
$292$	5.74238	+	25.6197i	0.336047	+	1.49928i
$293$	−15.8680	−	15.8680i	−0.927018	−	0.927018i	0.0704942	−	0.997512i	$-0.477542\pi$
$293$	−15.8680	−	15.8680i	−0.927018	−	0.927018i	−0.997512	+	0.0704942i	$0.977542\pi$
$294$	6.54569	−	3.60101i	0.381752	−	0.210015i
$295$		0			0
$296$	0.0899847	−	1.45052i	0.00523026	−	0.0843100i
$297$	2.14134	−	2.14134i	0.124253	−	0.124253i
$298$	−7.86022	−	2.28112i	−0.455330	−	0.132142i
$299$	−0.654274			−0.0378376
$300$		0			0
$301$	19.4720			1.12235
$302$	24.5434	+	7.12274i	1.41231	+	0.409868i
$303$	−4.09226	+	4.09226i	−0.235094	+	0.235094i
$304$	−8.46216	−	17.9287i	−0.485338	−	1.02828i
$305$		0			0
$306$	4.14134	−	2.27829i	0.236744	−	0.130241i
$307$	−7.78477	−	7.78477i	−0.444300	−	0.444300i	0.449154	−	0.893454i	$-0.351725\pi$
$307$	−7.78477	−	7.78477i	−0.444300	−	0.444300i	−0.893454	+	0.449154i	$0.851725\pi$
$308$	20.7125	−	4.64248i	1.18020	−	0.264530i
$309$			18.5140i			1.05322i
$310$		0			0
$311$		−	7.05788i		−	0.400215i	−0.979774	−	0.200108i	$-0.935871\pi$
$311$		−	7.05788i		−	0.400215i	0.979774	−	0.200108i	$-0.0641292\pi$
$312$	1.08930	−	0.962047i	0.0616697	−	0.0544652i
$313$	11.3013	+	11.3013i	0.638789	+	0.638789i	0.950257	−	0.311468i	$-0.100821\pi$
$313$	11.3013	+	11.3013i	0.638789	+	0.638789i	−0.311468	+	0.950257i	$0.600821\pi$
$314$	3.77832	+	6.86799i	0.213223	+	0.387583i
$315$		0			0
$316$	−0.675305	−	0.428009i	−0.0379889	−	0.0240774i
$317$	−19.4754	+	19.4754i	−1.09385	+	1.09385i	−0.0987310	+	0.995114i	$0.531478\pi$
$317$	−19.4754	+	19.4754i	−1.09385	+	1.09385i	−0.995114	+	0.0987310i	$0.968522\pi$
$318$	−1.75105	+	6.03372i	−0.0981940	+	0.338354i
$319$	−10.6132			−0.594225
$320$		0			0
$321$	−13.7360			−0.766668
$322$	1.75898	−	6.06105i	0.0980241	−	0.337769i
$323$	−11.7135	+	11.7135i	−0.651755	+	0.651755i
$324$	1.68928	+	1.07067i	0.0938489	+	0.0594816i
$325$		0			0
$326$	3.11203	+	5.65685i	0.172359	+	0.313304i
$327$	−7.39820	−	7.39820i	−0.409122	−	0.409122i
$328$	5.78050	−	5.10520i	0.319175	−	0.281887i
$329$			29.0280i			1.60036i
$330$		0			0
$331$		−	15.0143i		−	0.825259i	−0.910899	−	0.412630i	$-0.864610\pi$
$331$		−	15.0143i		−	0.825259i	0.910899	−	0.412630i	$-0.135390\pi$
$332$	−0.551657	+	0.123648i	−0.0302761	+	0.00678607i
$333$	−0.363328	−	0.363328i	−0.0199103	−	0.0199103i
$334$	−12.1910	+	6.70668i	−0.667061	+	0.366973i
$335$		0			0
$336$	5.98365	+	12.6775i	0.326435	+	0.691614i
$337$	21.5840	−	21.5840i	1.17576	−	1.17576i	0.194940	−	0.980815i	$-0.437549\pi$
$337$	21.5840	−	21.5840i	1.17576	−	1.17576i	0.980815	−	0.194940i	$-0.0624513\pi$
$338$	17.2977	+	5.01997i	0.940871	+	0.273051i
$339$	−15.0557			−0.817714
$340$		0			0
$341$	−11.6774			−0.632365
$342$	−6.73158	−	1.95358i	−0.364002	−	0.105637i
$343$	−4.25583	+	4.25583i	−0.229793	+	0.229793i
$344$	−0.973012	+	15.6846i	−0.0524613	+	0.845659i
$345$		0			0
$346$	1.09931	−	0.604770i	0.0590995	−	0.0325127i
$347$	−16.9969	−	16.9969i	−0.912444	−	0.912444i	0.0840201	−	0.996464i	$-0.473224\pi$
$347$	−16.9969	−	16.9969i	−0.912444	−	0.912444i	−0.996464	+	0.0840201i	$0.973224\pi$
$348$	−1.53303	−	6.83963i	−0.0821790	−	0.366643i
$349$			4.38538i			0.234744i	0.993088	+	0.117372i	$0.0374469\pi$
$349$			4.38538i			0.234744i	−0.993088	+	0.117372i	$0.962553\pi$
$350$		0			0
$351$		−	0.513824i		−	0.0274259i
$352$	2.70451	+	16.9159i	0.144151	+	0.901618i
$353$	2.62734	+	2.62734i	0.139839	+	0.139839i	0.773561	−	0.633722i	$-0.218474\pi$
$353$	2.62734	+	2.62734i	0.139839	+	0.139839i	−0.633722	+	0.773561i	$0.718474\pi$
$354$	−5.92036	−	10.7617i	−0.314664	−	0.571976i
$355$		0			0
$356$	−4.58532	+	7.23464i	−0.243021	+	0.383435i
$357$	8.28267	−	8.28267i	0.438366	−	0.438366i
$358$	−3.52363	+	12.1416i	−0.186230	+	0.641706i
$359$	34.9952			1.84697			0.923487	−	0.383630i	$-0.125326\pi$
$359$	34.9952			1.84697			0.923487	+	0.383630i	$0.125326\pi$
$360$		0			0
$361$	5.56534			0.292913
$362$	0.397834	−	1.37085i	0.0209097	−	0.0720500i
$363$	−1.29355	+	1.29355i	−0.0678939	+	0.0678939i
$364$	1.92804	−	3.04202i	0.101057	−	0.159445i
$365$		0			0
$366$	10.4240	+	18.9481i	0.544872	+	0.990433i
$367$	−9.93581	−	9.93581i	−0.518645	−	0.518645i	0.398516	−	0.917161i	$-0.369525\pi$
$367$	−9.93581	−	9.93581i	−0.518645	−	0.518645i	−0.917161	+	0.398516i	$0.869525\pi$
$368$	4.79427	+	1.71973i	0.249918	+	0.0896469i
$369$		−	2.72666i		−	0.141944i
$370$		0			0
$371$			15.5695i			0.808330i
$372$	−1.68674	−	7.52543i	−0.0874536	−	0.390176i
$373$	7.08998	+	7.08998i	0.367105	+	0.367105i	0.866421	−	0.499315i	$-0.166415\pi$
$373$	7.08998	+	7.08998i	0.367105	+	0.367105i	−0.499315	+	0.866421i	$0.666415\pi$
$374$	12.5412	−	6.89937i	0.648492	−	0.356758i
$375$		0			0
$376$	−23.3820	−	1.45052i	−1.20583	−	0.0748051i
$377$	−1.27334	+	1.27334i	−0.0655805	+	0.0655805i
$378$	4.75995	+	1.38139i	0.244825	+	0.0710509i
$379$	30.0388			1.54299			0.771495	−	0.636235i	$-0.219509\pi$
$379$	30.0388			1.54299			0.771495	+	0.636235i	$0.219509\pi$
$380$		0			0
$381$	−2.51399			−0.128796
$382$	29.3721	+	8.52410i	1.50281	+	0.436131i
$383$	11.9133	−	11.9133i	0.608744	−	0.608744i	−0.333874	−	0.942618i	$-0.608356\pi$
$383$	11.9133	−	11.9133i	0.608744	−	0.608744i	0.942618	+	0.333874i	$0.108356\pi$
$384$	−10.5107	+	4.18633i	−0.536372	+	0.213633i
$385$		0			0
$386$	20.2663	−	11.1492i	1.03153	−	0.567480i
$387$	3.92870	+	3.92870i	0.199707	+	0.199707i
$388$	18.5910	−	4.16697i	0.943814	−	0.211546i
$389$		−	16.3340i		−	0.828168i	−0.910239	−	0.414084i	$-0.864102\pi$
$389$		−	16.3340i		−	0.828168i	0.910239	−	0.414084i	$-0.135898\pi$
$390$		0			0
$391$		−	4.25583i		−	0.215227i
$392$	9.89090	+	11.1992i	0.499566	+	0.565647i
$393$	−12.8680	−	12.8680i	−0.649104	−	0.649104i
$394$	9.08492	+	16.5140i	0.457692	+	0.831963i
$395$		0			0
$396$	5.11566	+	3.24231i	0.257072	+	0.162932i
$397$	19.1927	−	19.1927i	0.963253	−	0.963253i	−0.0360950	−	0.999348i	$-0.511492\pi$
$397$	19.1927	−	19.1927i	0.963253	−	0.963253i	0.999348	+	0.0360950i	$0.0114919\pi$
$398$	4.34083	−	14.9575i	0.217586	−	0.749753i
$399$	−17.3703			−0.869604
$400$		0			0
$401$	26.5653			1.32661			0.663305	−	0.748349i	$-0.269153\pi$
$401$	26.5653			1.32661			0.663305	+	0.748349i	$0.269153\pi$
$402$	2.18994	−	7.54604i	0.109224	−	0.376362i
$403$	−1.40102	+	1.40102i	−0.0697898	+	0.0697898i
$404$	−9.77644	−	6.19632i	−0.486396	−	0.308278i
$405$		0			0
$406$	−8.37266	−	15.2193i	−0.415528	−	0.755321i
$407$	−1.10027	−	1.10027i	−0.0545383	−	0.0545383i
$408$	6.25779	+	7.08556i	0.309807	+	0.350787i
$409$		−	25.3947i		−	1.25569i	−0.778339	−	0.627844i	$-0.783938\pi$
$409$		−	25.3947i		−	1.25569i	0.778339	−	0.627844i	$-0.216062\pi$
$410$		0			0
$411$			8.37122i			0.412922i
$412$	−36.1315	+	8.09849i	−1.78007	+	0.398984i
$413$	−21.5233	−	21.5233i	−1.05909	−	1.05909i
$414$	1.57778	−	0.867993i	0.0775438	−	0.0426595i
$415$		0			0
$416$	2.35400	+	1.70504i	0.115414	+	0.0835964i
$417$	−8.77801	+	8.77801i	−0.429861	+	0.429861i
$418$	−20.3853	−	5.91603i	−0.997078	−	0.289362i
$419$	−40.0788			−1.95798			−0.978988	−	0.203919i	$-0.934632\pi$
$419$	−40.0788			−1.95798			−0.978988	+	0.203919i	$0.934632\pi$
$420$		0			0
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	−38.0065	−	11.0299i	−1.85013	−	0.536927i
$423$	−5.85673	+	5.85673i	−0.284764	+	0.284764i
$424$	−12.5412	−	0.778008i	−0.609056	−	0.0377834i
$425$		0			0
$426$	5.27334	−	2.90105i	0.255494	−	0.140556i
$427$	37.8962	+	37.8962i	1.83393	+	1.83393i
$428$	−6.00847	−	26.8069i	−0.290430	−	1.29576i
$429$		−	1.55602i		−	0.0751251i
$430$		0			0
$431$		−	15.8241i		−	0.762218i	−0.924530	−	0.381109i	$-0.875542\pi$
$431$		−	15.8241i		−	0.762218i	0.924530	−	0.381109i	$-0.124458\pi$
$432$	−1.35056	+	3.76510i	−0.0649788	+	0.181149i
$433$	21.1214	+	21.1214i	1.01503	+	1.01503i	0.999885	+	0.0151424i	$0.00482018\pi$
$433$	21.1214	+	21.1214i	1.01503	+	1.01503i	0.0151424	+	0.999885i	$0.495180\pi$
$434$	−9.21218	−	16.7453i	−0.442199	−	0.803801i
$435$		0			0
$436$	11.2020	−	17.6743i	0.536479	−	0.846447i
$437$	−4.46264	+	4.46264i	−0.213477	+	0.213477i
$438$	−5.17436	+	17.8297i	−0.247241	+	0.851936i
$439$	6.61188			0.315568			0.157784	−	0.987474i	$-0.449565\pi$
$439$	6.61188			0.315568			0.157784	+	0.987474i	$0.449565\pi$
$440$		0			0
$441$	5.28267			0.251556
$442$	0.676896	−	2.33243i	0.0321967	−	0.110942i
$443$	14.5419	−	14.5419i	0.690906	−	0.690906i	−0.271525	−	0.962431i	$-0.587528\pi$
$443$	14.5419	−	14.5419i	0.690906	−	0.690906i	0.962431	+	0.271525i	$0.0875280\pi$
$444$	0.550135	−	0.867993i	0.0261082	−	0.0411931i
$445$		0			0
$446$	−8.22769	−	14.9558i	−0.389593	−	0.708177i
$447$	−4.09226	−	4.09226i	−0.193557	−	0.193557i
$448$	−22.1237	+	17.2230i	−1.04525	+	0.813711i
$449$		−	33.6120i		−	1.58625i	−0.609060	−	0.793124i	$-0.708453\pi$
$449$		−	33.6120i		−	1.58625i	0.609060	−	0.793124i	$-0.291547\pi$
$450$		0			0
$451$		−	8.25715i		−	0.388814i
$452$	−6.58575	−	29.3824i	−0.309768	−	1.38203i
$453$	12.7780	+	12.7780i	0.600363	+	0.600363i
$454$	1.80078	−	0.990671i	0.0845148	−	0.0464945i
$455$		0			0
$456$	0.867993	−	13.9918i	0.0406475	−	0.655224i
$457$	−15.5653	+	15.5653i	−0.728116	+	0.728116i	−0.970244	−	0.242128i	$-0.922155\pi$
$457$	−15.5653	+	15.5653i	−0.728116	+	0.728116i	0.242128	+	0.970244i	$0.422155\pi$
$458$	12.0172	+	3.48751i	0.561525	+	0.162960i
$459$	3.34225			0.156003
$460$		0			0
$461$	−26.1473			−1.21780			−0.608900	−	0.793247i	$-0.708389\pi$
$461$	−26.1473			−1.21780			−0.608900	+	0.793247i	$0.708389\pi$
$462$	14.4146	+	4.18326i	0.670627	+	0.194623i
$463$	5.77898	−	5.77898i	0.268572	−	0.268572i	−0.559953	−	0.828525i	$-0.689181\pi$
$463$	5.77898	−	5.77898i	0.268572	−	0.268572i	0.828525	+	0.559953i	$0.189181\pi$
$464$	12.6775	−	5.98365i	0.588538	−	0.277784i
$465$		0			0
$466$	−8.60398	+	4.73335i	−0.398572	+	0.219268i
$467$	2.25517	+	2.25517i	0.104357	+	0.104357i	0.757357	−	0.653000i	$-0.226490\pi$
$467$	2.25517	+	2.25517i	0.104357	+	0.104357i	−0.653000	+	0.757357i	$0.726490\pi$
$468$	1.00277	−	0.224760i	0.0463529	−	0.0103895i
$469$		−	19.4720i		−	0.899132i
$470$		0			0
$471$			5.54279i			0.255398i
$472$	18.4125	−	16.2615i	0.847505	−	0.748495i
$473$	11.8973	+	11.8973i	0.547038	+	0.547038i
$474$	−0.272501	−	0.495336i	−0.0125164	−	0.0227515i
$475$		0			0
$476$	19.7873	+	12.5412i	0.906951	+	0.574827i
$477$	−3.14134	+	3.14134i	−0.143832	+	0.143832i
$478$	7.49917	−	25.8405i	0.343004	−	1.18191i
$479$	−1.40102			−0.0640143			−0.0320071	−	0.999488i	$-0.510190\pi$
$479$	−1.40102			−0.0640143			−0.0320071	+	0.999488i	$0.510190\pi$
$480$		0			0
$481$	−0.264015			−0.0120380
$482$	−1.14567	+	3.94771i	−0.0521837	+	0.179813i
$483$	3.15556	−	3.15556i	0.143583	−	0.143583i
$484$	−3.09030	−	1.95864i	−0.140468	−	0.0890289i
$485$		0			0
$486$	0.681664	+	1.23909i	0.0309209	+	0.0562061i
$487$	0.978144	+	0.978144i	0.0443239	+	0.0443239i	0.728921	−	0.684597i	$-0.240022\pi$
$487$	0.978144	+	0.978144i	0.0443239	+	0.0443239i	−0.684597	+	0.728921i	$0.740022\pi$
$488$	−32.4190	+	28.6317i	−1.46754	+	1.29609i
$489$			4.56534i			0.206452i
$490$		0			0
$491$		−	36.1134i		−	1.62978i	−0.579619	−	0.814888i	$-0.696799\pi$
$491$		−	36.1134i		−	1.62978i	0.579619	−	0.814888i	$-0.303201\pi$
$492$	5.32128	−	1.19271i	0.239902	−	0.0537715i
$493$	−8.28267	−	8.28267i	−0.373033	−	0.373033i
$494$	−3.15556	+	1.73599i	−0.141976	+	0.0781057i
$495$		0			0
$496$	13.9486	−	6.58363i	0.626313	−	0.295614i
$497$	10.5467	−	10.5467i	0.473084	−	0.473084i
$498$	−0.383918	−	0.111417i	−0.0172038	−	0.00499272i
$499$	−6.35736			−0.284595			−0.142297	−	0.989824i	$-0.545449\pi$
$499$	−6.35736			−0.284595			−0.142297	+	0.989824i	$0.545449\pi$
$500$		0			0
$501$	−9.83869			−0.439560
$502$	−3.76730	−	1.09331i	−0.168143	−	0.0487968i
$503$	17.1704	−	17.1704i	0.765592	−	0.765592i	−0.211735	−	0.977327i	$-0.567911\pi$
$503$	17.1704	−	17.1704i	0.765592	−	0.765592i	0.977327	+	0.211735i	$0.0679114\pi$
$504$	−0.613763	+	9.89367i	−0.0273392	+	0.440699i
$505$		0			0
$506$	4.77801	−	2.62855i	0.212408	−	0.116853i
$507$	9.00570	+	9.00570i	0.399957	+	0.399957i
$508$	−1.09968	−	4.90626i	−0.0487906	−	0.217680i
$509$			18.8739i			0.836572i	0.908315	+	0.418286i	$0.137369\pi$
$509$			18.8739i			0.836572i	−0.908315	+	0.418286i	$0.862631\pi$
$510$		0			0
$511$			46.0081i			2.03528i
$512$	−12.7676	−	18.6812i	−0.564253	−	0.825602i
$513$	−3.50466	−	3.50466i	−0.154735	−	0.154735i
$514$	2.00579	+	3.64600i	0.0884717	+	0.160818i
$515$		0			0
$516$	−5.94865	+	9.38567i	−0.261875	+	0.413181i
$517$	−17.7360	+	17.7360i	−0.780028	+	0.780028i
$518$	0.709789	−	2.44577i	0.0311864	−	0.107461i
$519$	0.887197			0.0389436
$520$		0			0
$521$	−33.9346			−1.48670			−0.743351	−	0.668901i	$-0.766765\pi$
$521$	−33.9346			−1.48670			−0.743351	+	0.668901i	$0.766765\pi$
$522$	1.38139	−	4.75995i	0.0604617	−	0.208337i
$523$	3.78345	−	3.78345i	0.165439	−	0.165439i	−0.619532	−	0.784971i	$-0.712678\pi$
$523$	3.78345	−	3.78345i	0.165439	−	0.165439i	0.784971	+	0.619532i	$0.212678\pi$
$524$	19.4841	−	30.7417i	0.851167	−	1.34296i
$525$		0			0
$526$	4.58532	+	8.33491i	0.199929	+	0.363419i
$527$	−9.11317	−	9.11317i	−0.396976	−	0.396976i
$528$	−4.08991	+	11.4019i	−0.177990	+	0.496203i
$529$			21.3786i			0.929504i
$530$		0			0
$531$		−	8.68516i		−	0.376904i
$532$	−7.59822	−	33.8995i	−0.329425	−	1.46973i
$533$	−0.990671	−	0.990671i	−0.0429107	−	0.0429107i
$534$	−5.30660	+	2.91934i	−0.229639	+	0.126332i
$535$		0			0
$536$	15.6846	+	0.973012i	0.677473	+	0.0420277i
$537$	−6.32131	+	6.32131i	−0.272784	+	0.272784i
$538$	29.4515	+	8.54715i	1.26975	+	0.368494i
$539$	15.9976			0.689063
$540$		0			0
$541$	28.4813			1.22451			0.612253	−	0.790662i	$-0.290263\pi$
$541$	28.4813			1.22451			0.612253	+	0.790662i	$0.290263\pi$
$542$	−4.28581	−	1.24379i	−0.184091	−	0.0534252i
$543$	0.713703	−	0.713703i	0.0306279	−	0.0306279i
$544$	−11.0907	+	15.3120i	−0.475510	+	0.656496i
$545$		0			0
$546$	2.23132	−	1.22753i	0.0954917	−	0.0525333i
$547$	0.726896	+	0.726896i	0.0310798	+	0.0310798i	0.722476	−	0.691396i	$-0.243004\pi$
$547$	0.726896	+	0.726896i	0.0310798	+	0.0310798i	−0.691396	+	0.722476i	$0.743004\pi$
$548$	−16.3371	+	3.66178i	−0.697886	+	0.156424i
$549$			15.2920i			0.652647i
$550$		0			0
$551$			17.3703i			0.740001i
$552$	2.38412	+	2.69948i	0.101475	+	0.114898i
$553$	−0.990671	−	0.990671i	−0.0421276	−	0.0421276i
$554$	3.40681	+	6.19269i	0.144742	+	0.263102i
$555$		0			0
$556$	−20.9707	−	13.2912i	−0.889356	−	0.563675i
$557$	11.4427	−	11.4427i	0.484841	−	0.484841i	−0.421832	−	0.906674i	$-0.638613\pi$
$557$	11.4427	−	11.4427i	0.484841	−	0.484841i	0.906674	+	0.421832i	$0.138613\pi$
$558$	1.51990	−	5.23723i	0.0643424	−	0.221709i
$559$	2.85481			0.120746
$560$		0			0
$561$	10.1214			0.427324
$562$	−0.0709362	+	0.244430i	−0.00299226	+	0.0103107i
$563$	−7.08426	+	7.08426i	−0.298566	+	0.298566i	−0.840452	−	0.541886i	$-0.817710\pi$
$563$	−7.08426	+	7.08426i	−0.298566	+	0.298566i	0.541886	+	0.840452i	$0.317710\pi$
$564$	−13.9918	−	8.86799i	−0.589159	−	0.373410i
$565$		0			0
$566$	−9.48601	−	17.2431i	−0.398727	−	0.724780i
$567$	2.47817	+	2.47817i	0.104073	+	0.104073i
$568$	7.96832	+	9.02235i	0.334343	+	0.378569i
$569$			46.2427i			1.93860i	0.245890	+	0.969298i	$0.420920\pi$
$569$			46.2427i			1.93860i	−0.245890	+	0.969298i	$0.579080\pi$
$570$		0			0
$571$			31.2381i			1.30727i	0.756808	+	0.653637i	$0.226758\pi$
$571$			31.2381i			1.30727i	−0.756808	+	0.653637i	$0.773242\pi$
$572$	3.03669	−	0.680641i	0.126970	−	0.0284590i
$573$	15.2920	+	15.2920i	0.638833	+	0.638833i
$574$	11.8407	−	6.51399i	0.494222	−	0.271889i
$575$		0			0
$576$	−7.93866	−	0.988770i	−0.330778	−	0.0411988i
$577$	−1.16131	+	1.16131i	−0.0483461	+	0.0483461i	−0.730866	−	0.682520i	$-0.760884\pi$
$577$	−1.16131	+	1.16131i	−0.0483461	+	0.0483461i	0.682520	+	0.730866i	$0.260884\pi$
$578$	−7.91729	−	2.29768i	−0.329316	−	0.0955709i
$579$	16.3559			0.679727
$580$		0			0
$581$	−0.990671			−0.0411000
$582$	12.9381	+	3.75479i	0.536303	+	0.155641i
$583$	−9.51293	+	9.51293i	−0.393985	+	0.393985i
$584$	−37.0594	−	2.29902i	−1.53353	−	0.0951341i
$585$		0			0
$586$	27.8060	−	15.2970i	1.14866	−	0.631915i
$587$	23.6268	+	23.6268i	0.975183	+	0.975183i	0.999699	−	0.0245164i	$-0.00780461\pi$
$587$	23.6268	+	23.6268i	0.975183	+	0.975183i	−0.0245164	+	0.999699i	$0.507805\pi$
$588$	2.31077	+	10.3096i	0.0952947	+	0.425159i
$589$			19.1120i			0.787498i
$590$		0			0
$591$			13.3276i			0.548223i
$592$	1.93460	+	0.693949i	0.0795115	+	0.0285211i
$593$	0.260625	+	0.260625i	0.0107026	+	0.0107026i	0.712438	−	0.701735i	$-0.247591\pi$
$593$	0.260625	+	0.260625i	0.0107026	+	0.0107026i	−0.701735	+	0.712438i	$0.747591\pi$
$594$	2.06429	+	3.75233i	0.0846988	+	0.153960i
$595$		0			0
$596$	6.19632	−	9.77644i	0.253811	−	0.400458i
$597$	7.78734	−	7.78734i	0.318714	−	0.318714i
$598$	0.257887	−	0.888619i	0.0105458	−	0.0363383i
$599$	33.0851			1.35182			0.675910	−	0.736984i	$-0.263751\pi$
$599$	33.0851			1.35182			0.675910	+	0.736984i	$0.263751\pi$
$600$		0			0
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	−7.67501	+	26.4464i	−0.312810	+	1.07787i
$603$	3.92870	−	3.92870i	0.159989	−	0.159989i
$604$	−19.3479	+	30.5267i	−0.787253	+	1.24211i
$605$		0			0
$606$	−3.94502	−	7.17101i	−0.160255	−	0.291302i
$607$	−4.53347	−	4.53347i	−0.184008	−	0.184008i	0.609092	−	0.793100i	$-0.291534\pi$
$607$	−4.53347	−	4.53347i	−0.184008	−	0.184008i	−0.793100	+	0.609092i	$0.791534\pi$
$608$	27.6857	−	4.42639i	1.12280	−	0.179514i
$609$		−	12.2827i		−	0.497719i
$610$		0			0
$611$			4.25583i			0.172173i
$612$	1.46199	+	6.52267i	0.0590972	+	0.263663i
$613$	20.2793	+	20.2793i	0.819073	+	0.819073i	0.985974	−	0.166901i	$-0.0533761\pi$
$613$	20.2793	+	20.2793i	0.819073	+	0.819073i	−0.166901	+	0.985974i	$0.553376\pi$
$614$	13.6415	−	7.50466i	0.550526	−	0.302864i
$615$		0			0
$616$	−1.85866	+	29.9611i	−0.0748877	+	1.20717i
$617$	−17.1086	+	17.1086i	−0.688768	+	0.688768i	−0.961960	−	0.273192i	$-0.911921\pi$
$617$	−17.1086	+	17.1086i	−0.688768	+	0.688768i	0.273192	+	0.961960i	$0.411921\pi$
$618$	−25.1453	−	7.29742i	−1.01149	−	0.293545i
$619$	−29.4373			−1.18319			−0.591593	−	0.806237i	$-0.701501\pi$
$619$	−29.4373			−1.18319			−0.591593	+	0.806237i	$0.701501\pi$
$620$		0			0
$621$	1.27334			0.0510975
$622$	9.58583	+	2.78191i	0.384357	+	0.111544i
$623$	−10.6132	+	10.6132i	−0.425209	+	0.425209i
$624$	0.877272	+	1.85866i	0.0351190	+	0.0744061i
$625$		0			0
$626$	−19.8037	+	10.8947i	−0.791514	+	0.435439i
$627$	−10.6132	−	10.6132i	−0.423850	−	0.423850i
$628$	−10.8172	+	2.42456i	−0.431653	+	0.0967503i
$629$		−	1.71733i		−	0.0684743i
$630$		0			0
$631$		−	5.25710i		−	0.209282i	−0.994510	−	0.104641i	$-0.966631\pi$
$631$		−	5.25710i		−	0.209282i	0.994510	−	0.104641i	$-0.0333693\pi$
$632$	0.847487	−	0.748480i	0.0337112	−	0.0297729i
$633$	−19.7873	−	19.7873i	−0.786476	−	0.786476i
$634$	−18.7746	−	34.1273i	−0.745635	−	1.35537i
$635$		0			0
$636$	−7.50466	−	4.75646i	−0.297579	−	0.188606i
$637$	1.91934	−	1.91934i	0.0760472	−	0.0760472i
$638$	4.18326	−	14.4146i	0.165617	−	0.570679i
$639$	4.25583			0.168358
$640$		0			0
$641$	20.0773			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$641$	20.0773			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$642$	5.41413	−	18.6559i	0.213679	−	0.736289i
$643$	−9.28480	+	9.28480i	−0.366157	+	0.366157i	−0.866073	−	0.499917i	$-0.833364\pi$
$643$	−9.28480	+	9.28480i	−0.366157	+	0.366157i	0.499917	+	0.866073i	$0.333364\pi$
$644$	7.53866	+	4.77801i	0.297065	+	0.188280i
$645$		0			0
$646$	−11.2920	−	20.5259i	−0.444278	−	0.807580i
$647$	28.7387	+	28.7387i	1.12983	+	1.12983i	0.990204	+	0.139630i	$0.0445912\pi$
$647$	28.7387	+	28.7387i	1.12983	+	1.12983i	0.139630	+	0.990204i	$0.455409\pi$
$648$	−2.12000	+	1.87233i	−0.0832813	+	0.0735520i
$649$		−	26.3013i		−	1.03242i
$650$		0			0
$651$		−	13.5142i		−	0.529665i
$652$	−8.90963	+	1.99700i	−0.348928	+	0.0782084i
$653$	11.9380	+	11.9380i	0.467170	+	0.467170i	0.900996	−	0.433826i	$-0.142837\pi$
$653$	11.9380	+	11.9380i	0.467170	+	0.467170i	−0.433826	+	0.900996i	$0.642837\pi$
$654$	12.9641	−	7.13201i	0.506937	−	0.278884i
$655$		0			0
$656$	4.65533	+	9.86318i	0.181760	+	0.385093i
$657$	−9.28267	+	9.28267i	−0.362152	+	0.362152i
$658$	−39.4251	−	11.4416i	−1.53695	−	0.446039i
$659$	17.9963			0.701038			0.350519	−	0.936556i	$-0.386005\pi$
$659$	17.9963			0.701038			0.350519	+	0.936556i	$0.386005\pi$
$660$		0			0
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	20.3920	+	5.91798i	0.792558	+	0.230009i
$663$	1.21433	−	1.21433i	0.0471608	−	0.0471608i
$664$	0.0495037	−	0.797984i	0.00192112	−	0.0309678i
$665$		0			0
$666$	0.636672	−	0.350255i	0.0246705	−	0.0135721i
$667$	−3.15556	−	3.15556i	−0.122184	−	0.122184i
$668$	−4.30369	−	19.2010i	−0.166515	−	0.742908i
$669$		−	12.0700i		−	0.466654i
$670$		0			0
$671$			46.3089i			1.78773i
$672$	−19.5767	+	3.12993i	−0.755189	+	0.120740i
$673$	−35.7640	−	35.7640i	−1.37860	−	1.37860i	−0.846988	−	0.531611i	$-0.821587\pi$
$673$	−35.7640	−	35.7640i	−1.37860	−	1.37860i	−0.531611	−	0.846988i	$-0.678413\pi$
$674$	20.8074	+	37.8223i	0.801470	+	1.45686i
$675$		0			0
$676$	−13.6360	+	21.5147i	−0.524462	+	0.827487i
$677$	−16.2020	+	16.2020i	−0.622694	+	0.622694i	−0.946219	−	0.323525i	$-0.895132\pi$
$677$	−16.2020	+	16.2020i	−0.622694	+	0.622694i	0.323525	+	0.946219i	$0.395132\pi$
$678$	5.93431	−	20.4483i	0.227906	−	0.785312i
$679$	33.3859			1.28123
$680$		0			0
$681$	1.45331			0.0556911
$682$	4.60272	−	15.8599i	0.176247	−	0.607308i
$683$	33.3943	−	33.3943i	1.27780	−	1.27780i	0.335897	−	0.941899i	$-0.390961\pi$
$683$	33.3943	−	33.3943i	1.27780	−	1.27780i	0.941899	−	0.335897i	$-0.109039\pi$
$684$	5.30660	−	8.37266i	0.202903	−	0.320137i
$685$		0			0
$686$	−4.10270	−	7.45763i	−0.156642	−	0.284734i
$687$	6.25649	+	6.25649i	0.238700	+	0.238700i
$688$	−20.9190	−	7.50373i	−0.797528	−	0.286077i
$689$			2.28267i			0.0869629i
$690$		0			0
$691$		−	24.6365i		−	0.937216i	−0.883406	−	0.468608i	$-0.844756\pi$
$691$		−	24.6365i		−	0.937216i	0.883406	−	0.468608i	$-0.155244\pi$
$692$	0.388082	+	1.73143i	0.0147527	+	0.0658193i
$693$	7.50466	+	7.50466i	0.285079	+	0.285079i
$694$	29.7843	−	16.3854i	1.13060	−	0.621980i
$695$		0			0
$696$	9.89367	+	0.613763i	0.375019	+	0.0232646i
$697$	6.44398	−	6.44398i	0.244083	−	0.244083i
$698$	−5.95611	−	1.72853i	−0.225442	−	0.0654256i
$699$	−6.94381			−0.262639
$700$		0			0
$701$	−23.0420			−0.870285			−0.435143	−	0.900362i	$-0.643302\pi$
$701$	−23.0420			−0.870285			−0.435143	+	0.900362i	$0.643302\pi$
$702$	0.697863	+	0.202527i	0.0263391	+	0.00764389i
$703$	−1.80078	+	1.80078i	−0.0679177	+	0.0679177i
$704$	−24.0407	−	2.99430i	−0.906068	−	0.112852i
$705$		0			0
$706$	−4.60398	+	2.53281i	−0.173273	+	0.0953235i
$707$	−14.3420	−	14.3420i	−0.539387	−	0.539387i
$708$	16.9498	−	3.79911i	0.637012	−	0.142779i
$709$			37.7360i			1.41720i	0.705608	+	0.708602i	$0.250674\pi$
$709$			37.7360i			1.41720i	−0.705608	+	0.708602i	$0.749326\pi$
$710$		0			0
$711$		−	0.399759i		−	0.0149921i
$712$	−8.01857	−	9.07925i	−0.300509	−	0.340259i
$713$	−3.47197	−	3.47197i	−0.130026	−	0.130026i
$714$	7.98465	+	14.5140i	0.298818	+	0.543173i
$715$		0			0
$716$	−15.1016	−	9.57143i	−0.564374	−	0.357701i
$717$	13.4533	−	13.4533i	0.502423	−	0.502423i
$718$	−13.7936	+	47.5296i	−0.514772	+	1.77379i
$719$	−41.3423			−1.54181			−0.770903	−	0.636953i	$-0.780195\pi$
$719$	−41.3423			−1.54181			−0.770903	+	0.636953i	$0.780195\pi$
$720$		0			0
$721$	−64.8853			−2.41646
$722$	−2.19362	+	7.55871i	−0.0816380	+	0.281306i
$723$	−2.05529	+	2.05529i	−0.0764372	+	0.0764372i
$724$	1.70504	+	1.08066i	0.0633673	+	0.0401623i
$725$		0			0
$726$	−1.24701	−	2.26673i	−0.0462808	−	0.0841264i
$727$	9.48981	+	9.48981i	0.351958	+	0.351958i	0.860838	−	0.508880i	$-0.169940\pi$
$727$	9.48981	+	9.48981i	0.351958	+	0.351958i	−0.508880	+	0.860838i	$0.669940\pi$
$728$	3.37165	+	3.81765i	0.124962	+	0.141491i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			18.5696i			0.686821i
$732$	−29.8435	+	6.68911i	−1.10305	+	0.247237i
$733$	−3.21134	−	3.21134i	−0.118614	−	0.118614i	0.645308	−	0.763922i	$-0.276729\pi$
$733$	−3.21134	−	3.21134i	−0.118614	−	0.118614i	−0.763922	+	0.645308i	$0.776729\pi$
$734$	17.4108	−	9.57830i	0.642646	−	0.353542i
$735$		0			0
$736$	−4.22538	+	5.83362i	−0.155750	+	0.215030i
$737$	11.8973	−	11.8973i	0.438243	−	0.438243i
$738$	3.70328	+	1.07473i	0.136320	+	0.0395614i
$739$	−25.3832			−0.933737			−0.466868	−	0.884327i	$-0.654618\pi$
$739$	−25.3832			−0.933737			−0.466868	+	0.884327i	$0.654618\pi$
$740$		0			0
$741$	−2.54669			−0.0935549
$742$	−21.1462	−	6.13684i	−0.776300	−	0.225290i
$743$	−32.7400	+	32.7400i	−1.20111	+	1.20111i	−0.227285	+	0.973828i	$0.572985\pi$
$743$	−32.7400	+	32.7400i	−1.20111	+	1.20111i	−0.973828	+	0.227285i	$0.927015\pi$
$744$	10.8857	+	0.675305i	0.399089	+	0.0247579i
$745$		0			0
$746$	−12.4240	+	6.83488i	−0.454875	+	0.250243i
$747$	−0.199879	−	0.199879i	−0.00731321	−	0.00731321i
$748$	4.42734	+	19.7526i	0.161880	+	0.722228i
$749$		−	48.1400i		−	1.75900i
$750$		0			0
$751$		−	24.4810i		−	0.893323i	−0.894703	−	0.446662i	$-0.852613\pi$
$751$		−	24.4810i		−	0.893323i	0.894703	−	0.446662i	$-0.147387\pi$
$752$	11.1862	−	31.1851i	0.407920	−	1.13720i
$753$	−1.96137	−	1.96137i	−0.0714762	−	0.0714762i
$754$	−1.22753	−	2.23132i	−0.0447039	−	0.0812599i
$755$		0			0
$756$	−3.75233	+	5.92036i	−0.136471	+	0.215322i
$757$	−22.9473	+	22.9473i	−0.834035	+	0.834035i	−0.988066	−	0.154031i	$-0.950774\pi$
$757$	−22.9473	+	22.9473i	−0.834035	+	0.834035i	0.154031	+	0.988066i	$0.450774\pi$
$758$	−11.8400	+	40.7980i	−0.430048	+	1.48185i
$759$	3.85607			0.139967
$760$		0			0
$761$	37.0466			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$761$	37.0466			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$762$	0.990907	−	3.41444i	0.0358968	−	0.123692i
$763$	25.9282	−	25.9282i	0.938665	−	0.938665i
$764$	−23.1544	+	36.5327i	−0.837698	+	1.32170i
$765$		0			0
$766$	11.4847	+	20.8761i	0.414959	+	0.754286i
$767$	−3.15556	−	3.15556i	−0.113941	−	0.113941i
$768$	−1.54291	−	15.9254i	−0.0556749	−	0.574660i
$769$		−	6.62395i		−	0.238866i	−0.992842	−	0.119433i	$-0.961892\pi$
$769$		−	6.62395i		−	0.238866i	0.992842	−	0.119433i	$-0.0381077\pi$
$770$		0			0
$771$			2.94249i			0.105971i
$772$	7.15447	+	31.9198i	0.257495	+	1.14882i
$773$	−16.2606	−	16.2606i	−0.584854	−	0.584854i	0.351379	−	0.936233i	$-0.385713\pi$
$773$	−16.2606	−	16.2606i	−0.584854	−	0.584854i	−0.936233	+	0.351379i	$0.885713\pi$
$774$	−6.88438	+	3.78734i	−0.247454	+	0.136133i
$775$		0			0
$776$	−1.66829	+	26.8922i	−0.0598880	+	0.965375i
$777$	1.27334	−	1.27334i	0.0456809	−	0.0456809i
$778$	22.1845	+	6.43817i	0.795352	+	0.230819i
$779$	−13.5142			−0.484198
$780$		0			0
$781$	12.8880			0.461168
$782$	5.78017	+	1.67747i	0.206698	+	0.0599860i
$783$	2.47817	−	2.47817i	0.0885626	−	0.0885626i
$784$	−19.1091	+	9.01932i	−0.682468	+	0.322118i
$785$		0			0
$786$	22.5490	−	12.4050i	0.804296	−	0.442471i
$787$	−31.2117	−	31.2117i	−1.11258	−	1.11258i	−0.992801	−	0.119776i	$-0.961782\pi$
$787$	−31.2117	−	31.2117i	−1.11258	−	1.11258i	−0.119776	−	0.992801i	$-0.538218\pi$
$788$	−26.0098	+	5.82981i	−0.926560	+	0.207678i
$789$			6.72666i			0.239475i
$790$		0			0
$791$		−	52.7652i		−	1.87612i
$792$	−6.42000	+	5.66999i	−0.228125	+	0.201474i
$793$	5.55602	+	5.55602i	0.197300	+	0.197300i
$794$	18.5021	+	33.6320i	0.656615	+	1.19355i
$795$		0			0
$796$	18.6040	+	11.7912i	0.659401	+	0.417929i
$797$	−17.3540	+	17.3540i	−0.614710	+	0.614710i	−0.944170	−	0.329460i	$-0.893133\pi$
$797$	−17.3540	+	17.3540i	−0.614710	+	0.614710i	0.329460	+	0.944170i	$0.393133\pi$
$798$	6.84663	−	23.5919i	0.242368	−	0.835146i
$799$	−27.6828			−0.979346
$800$		0			0
$801$	−4.28267			−0.151321
$802$	−10.4709	+	36.0804i	−0.369741	+	1.27404i
$803$	−28.1108	+	28.1108i	−0.992008	+	0.992008i
$804$	9.38567	+	5.94865i	0.331007	+	0.209793i
$805$		0			0
$806$	−1.35061	−	2.45505i	−0.0475732	−	0.0864756i
$807$	15.3334	+	15.3334i	0.539760	+	0.539760i
$808$	12.2691	−	10.8358i	0.431627	−	0.381202i
$809$		−	27.4320i		−	0.964458i	−0.876045	−	0.482229i	$-0.839827\pi$
$809$		−	27.4320i		−	0.964458i	0.876045	−	0.482229i	$-0.160173\pi$
$810$		0			0
$811$		−	27.1840i		−	0.954559i	−0.878751	−	0.477280i	$-0.841623\pi$
$811$		−	27.1840i		−	0.954559i	0.878751	−	0.477280i	$-0.158377\pi$
$812$	23.9706	−	5.37275i	0.841203	−	0.188547i
$813$	−2.23132	−	2.23132i	−0.0782558	−	0.0782558i
$814$	1.92804	−	1.06068i	0.0675777	−	0.0371768i
$815$		0			0
$816$	−12.0900	+	5.70636i	−0.423234	+	0.199762i
$817$	19.4720	−	19.4720i	0.681238	−	0.681238i
$818$	34.4905	+	10.0095i	1.20593	+	0.349974i
$819$	1.80078			0.0629243
$820$		0			0
$821$	23.6074			0.823903			0.411951	−	0.911206i	$-0.364847\pi$
$821$	23.6074			0.823903			0.411951	+	0.911206i	$0.364847\pi$
$822$	−11.3696	−	3.29957i	−0.396560	−	0.115086i
$823$	24.6596	−	24.6596i	0.859579	−	0.859579i	−0.131709	−	0.991288i	$-0.542046\pi$
$823$	24.6596	−	24.6596i	0.859579	−	0.859579i	0.991288	+	0.131709i	$0.0420465\pi$
$824$	3.24231	−	52.2650i	0.112951	−	1.82074i
$825$		0			0
$826$	37.7160	−	20.7489i	1.31231	−	0.721946i
$827$	−13.5406	−	13.5406i	−0.470854	−	0.470854i	0.431337	−	0.902191i	$-0.358042\pi$
$827$	−13.5406	−	13.5406i	−0.470854	−	0.470854i	−0.902191	+	0.431337i	$0.858042\pi$
$828$	0.556993	+	2.48503i	0.0193568	+	0.0863608i
$829$			9.00933i			0.312907i	0.987685	+	0.156453i	$0.0500061\pi$
$829$			9.00933i			0.312907i	−0.987685	+	0.156453i	$0.949994\pi$
$830$		0			0
$831$			4.99779i			0.173371i
$832$	−3.24359	+	2.52509i	−0.112451	+	0.0875418i
$833$	12.4847	+	12.4847i	0.432569	+	0.432569i
$834$	−8.46216	−	15.3820i	−0.293021	−	0.532635i
$835$		0			0
$836$	16.0700	−	25.3550i	0.555793	−	0.876920i
$837$	2.72666	−	2.72666i	0.0942470	−	0.0942470i
$838$	15.7973	−	54.4340i	0.545709	−	1.88039i
$839$	10.2597			0.354203			0.177102	−	0.984193i	$-0.443328\pi$
$839$	10.2597			0.354203			0.177102	+	0.984193i	$0.443328\pi$
$840$		0			0
$841$	16.7173			0.576460
$842$	−7.64455	+	26.3414i	−0.263449	+	0.907785i
$843$	−0.127258	+	0.127258i	−0.00438298	+	0.00438298i
$844$	29.9611	−	47.2720i	1.03130	−	1.62717i
$845$		0			0
$846$	−5.64600	−	10.2629i	−0.194113	−	0.352847i
$847$	−4.53347	−	4.53347i	−0.155772	−	0.155772i
$848$	5.99988	−	16.7265i	0.206037	−	0.574392i
$849$		−	13.9160i		−	0.477594i
$850$		0			0
$851$		−	0.654274i		−	0.0224282i
$852$	1.86161	+	8.30559i	0.0637777	+	0.284545i
$853$	−17.1086	−	17.1086i	−0.585789	−	0.585789i	0.350699	−	0.936488i	$-0.385944\pi$
$853$	−17.1086	−	17.1086i	−0.585789	−	0.585789i	−0.936488	+	0.350699i	$0.885944\pi$
$854$	−66.4067	+	36.5327i	−2.27239	+	1.25012i
$855$		0			0
$856$	38.7767	+	2.40555i	1.32536	+	0.0822200i
$857$	26.7674	−	26.7674i	0.914356	−	0.914356i	−0.0822556	−	0.996611i	$-0.526212\pi$
$857$	26.7674	−	26.7674i	0.914356	−	0.914356i	0.996611	+	0.0822556i	$0.0262124\pi$
$858$	2.11334	+	0.613314i	0.0721483	+	0.0209382i
$859$	28.6378			0.977109			0.488554	−	0.872533i	$-0.337524\pi$
$859$	28.6378			0.977109			0.488554	+	0.872533i	$0.337524\pi$
$860$		0			0
$861$	9.55602			0.325668
$862$	21.4918	+	6.23716i	0.732015	+	0.212438i
$863$	−15.8157	+	15.8157i	−0.538371	+	0.538371i	−0.923050	−	0.384679i	$-0.874312\pi$
$863$	−15.8157	+	15.8157i	−0.538371	+	0.538371i	0.384679	+	0.923050i	$0.374312\pi$
$864$	−4.58134	−	3.31834i	−0.155860	−	0.112892i
$865$		0			0
$866$	−37.0116	+	20.3614i	−1.25771	+	0.691908i
$867$	−4.12198	−	4.12198i	−0.139990	−	0.139990i
$868$	26.3741	−	5.91147i	0.895196	−	0.200648i
$869$		−	1.21059i		−	0.0410665i
$870$		0			0
$871$		−	2.85481i		−	0.0967316i
$872$	19.5895	+	22.1808i	0.663384	+	0.751135i
$873$	6.73599	+	6.73599i	0.227979	+	0.227979i
$874$	−4.30207	−	7.82003i	−0.145520	−	0.264516i
$875$		0			0
$876$	−22.1763	−	14.0554i	−0.749269	−	0.474888i
$877$	17.3727	−	17.3727i	0.586633	−	0.586633i	−0.350085	−	0.936718i	$-0.613847\pi$
$877$	17.3727	−	17.3727i	0.586633	−	0.586633i	0.936718	+	0.350085i	$0.113847\pi$
$878$	−2.60612	+	8.98009i	−0.0879522	+	0.303063i
$879$	22.4407			0.756907
$880$		0			0
$881$	56.5254			1.90439			0.952194	−	0.305493i	$-0.0988211\pi$
$881$	56.5254			1.90439			0.952194	+	0.305493i	$0.0988211\pi$
$882$	−2.08220	+	7.17480i	−0.0701114	+	0.241588i
$883$	−15.1962	+	15.1962i	−0.511392	+	0.511392i	−0.914953	−	0.403561i	$-0.867772\pi$
$883$	−15.1962	+	15.1962i	−0.511392	+	0.511392i	0.403561	+	0.914953i	$0.367772\pi$
$884$	2.90105	+	1.83869i	0.0975728	+	0.0618418i
$885$		0			0
$886$	14.0187	+	25.4822i	0.470966	+	0.856092i
$887$	−11.0676	−	11.0676i	−0.371613	−	0.371613i	0.496451	−	0.868065i	$-0.334636\pi$
$887$	−11.0676	−	11.0676i	−0.371613	−	0.371613i	−0.868065	+	0.496451i	$0.834636\pi$
$888$	0.962047	+	1.08930i	0.0322842	+	0.0365547i
$889$		−	8.81070i		−	0.295501i
$890$		0			0
$891$			3.02831i			0.101452i
$892$	23.5556	−	5.27973i	0.788699	−	0.176778i
$893$	29.0280	+	29.0280i	0.971385	+	0.971385i
$894$	7.17101	−	3.94502i	0.239834	−	0.131941i
$895$		0			0
$896$	−14.6717	−	36.8364i	−0.490146	−	1.23062i
$897$	0.462642	−	0.462642i	0.0154472	−	0.0154472i
$898$	45.6510	+	13.2484i	1.52339	+	0.442105i
$899$	−13.5142			−0.450725
$900$		0			0
$901$	−14.8480			−0.494659
$902$	11.2147	+	3.25461i	0.373407	+	0.108367i
$903$	−13.7688	+	13.7688i	−0.458196	+	0.458196i
$904$	42.5023	+	2.63667i	1.41361	+	0.0876944i
$905$		0			0
$906$	−22.3913	+	12.3182i	−0.743902	+	0.409246i
$907$	−28.1654	−	28.1654i	−0.935217	−	0.935217i	0.0628084	−	0.998026i	$-0.479994\pi$
$907$	−28.1654	−	28.1654i	−0.935217	−	0.935217i	−0.998026	+	0.0628084i	$0.979994\pi$
$908$	0.635716	+	2.83625i	0.0210970	+	0.0941244i
$909$		−	5.78734i		−	0.191954i
$910$		0			0
$911$			34.8499i			1.15463i	0.816522	+	0.577315i	$0.195899\pi$
$911$			34.8499i			1.15463i	−0.816522	+	0.577315i	$0.804101\pi$
$912$	18.6611	+	6.69383i	0.617932	+	0.221655i
$913$	−0.605296	−	0.605296i	−0.0200324	−	0.0200324i
$914$	−15.0053	−	27.2757i	−0.496331	−	0.902198i
$915$		0			0
$916$	−9.47329	+	14.9468i	−0.313006	+	0.493856i
$917$	45.0980	−	45.0980i	1.48927	−	1.48927i
$918$	−1.31737	+	4.53936i	−0.0434797	+	0.149821i
$919$	21.1171			0.696590			0.348295	−	0.937385i	$-0.386761\pi$
$919$	21.1171			0.696590			0.348295	+	0.937385i	$0.386761\pi$
$920$		0			0
$921$	11.0093			0.362770
$922$	10.3061	−	35.5126i	0.339414	−	1.16954i
$923$	1.54626	−	1.54626i	0.0508959	−	0.0508959i
$924$	−11.3632	+	17.9287i	−0.373822	+	0.589810i
$925$		0			0
$926$	5.57104	+	10.1267i	0.183076	+	0.332784i
$927$	−13.0914	−	13.0914i	−0.429977	−	0.429977i
$928$	3.12993	+	19.5767i	0.102745	+	0.642638i
$929$			39.0653i			1.28169i	0.767670	+	0.640845i	$0.221416\pi$
$929$			39.0653i			1.28169i	−0.767670	+	0.640845i	$0.778584\pi$
$930$		0			0
$931$		−	26.1827i		−	0.858105i
$932$	−3.03740	−	13.5514i	−0.0994933	−	0.443891i
$933$	4.99067	+	4.99067i	0.163387	+	0.163387i
$934$	−3.95181	+	2.17403i	−0.129307	+	0.0711364i
$935$		0			0
$936$	−0.0899847	+	1.45052i	−0.00294124	+	0.0474119i
$937$	−1.82936	+	1.82936i	−0.0597626	+	0.0597626i	−0.736356	−	0.676594i	$-0.763455\pi$
$937$	−1.82936	+	1.82936i	−0.0597626	+	0.0597626i	0.676594	+	0.736356i	$0.263455\pi$
$938$	26.4464	+	7.67501i	0.863504	+	0.250598i
$939$	−15.9825			−0.521569
$940$		0			0
$941$	1.58193			0.0515695			0.0257847	−	0.999668i	$-0.491792\pi$
$941$	1.58193			0.0515695			0.0257847	+	0.999668i	$0.491792\pi$
$942$	−7.52808	−	2.18473i	−0.245278	−	0.0711823i
$943$	2.45505	−	2.45505i	0.0799476	−	0.0799476i
$944$	14.8285	+	31.4170i	0.482627	+	1.02254i
$945$		0			0
$946$	−20.8480	+	11.4692i	−0.677827	+	0.372896i
$947$	−15.9429	−	15.9429i	−0.518075	−	0.518075i	0.398913	−	0.916989i	$-0.369387\pi$
$947$	−15.9429	−	15.9429i	−0.518075	−	0.518075i	−0.916989	+	0.398913i	$0.869387\pi$
$948$	0.780161	−	0.174865i	0.0253384	−	0.00567934i
$949$			6.74531i			0.218962i
$950$		0			0
$951$		−	27.5423i		−	0.893121i
$952$	−24.8325	+	21.9315i	−0.804826	+	0.710803i
$953$	27.2113	+	27.2113i	0.881462	+	0.881462i	0.993683	−	0.112221i	$-0.0357966\pi$
$953$	27.2113	+	27.2113i	0.881462	+	0.881462i	−0.112221	+	0.993683i	$0.535797\pi$
$954$	−3.02831	−	5.50466i	−0.0980450	−	0.178220i
$955$		0			0
$956$	32.1400	+	20.3704i	1.03948	+	0.658825i
$957$	7.50466	−	7.50466i	0.242591	−	0.242591i
$958$	0.552222	−	1.90283i	0.0178415	−	0.0614777i
$959$	−29.3383			−0.947383
$960$		0			0
$961$	16.1307			0.520345
$962$	0.104063	−	0.358578i	0.00335513	−	0.0115610i
$963$	9.71281	−	9.71281i	0.312991	−	0.312991i
$964$	−4.91011	−	3.11203i	−0.158144	−	0.100232i
$965$		0			0
$966$	3.04202	+	5.52960i	0.0978755	+	0.177912i
$967$	14.8921	+	14.8921i	0.478899	+	0.478899i	0.904780	−	0.425880i	$-0.140036\pi$
$967$	14.8921	+	14.8921i	0.478899	+	0.478899i	−0.425880	+	0.904780i	$0.640036\pi$
$968$	3.87824	−	3.42516i	0.124651	−	0.110089i
$969$		−	16.5653i		−	0.532156i
$970$		0			0
$971$		−	41.6250i		−	1.33581i	−0.744246	−	0.667905i	$-0.767191\pi$
$971$		−	41.6250i		−	1.33581i	0.744246	−	0.667905i	$-0.232809\pi$
$972$	−1.95158	+	0.437425i	−0.0625969	+	0.0140304i
$973$	−30.7640	−	30.7640i	−0.986248	−	0.986248i
$974$	−1.71403	+	0.942949i	−0.0549212	+	0.0302140i
$975$		0			0
$976$	−26.1086	−	55.3160i	−0.835717	−	1.77062i
$977$	12.0807	−	12.0807i	0.386494	−	0.386494i	−0.486941	−	0.873435i	$-0.661887\pi$
$977$	12.0807	−	12.0807i	0.386494	−	0.386494i	0.873435	+	0.486941i	$0.161887\pi$
$978$	−6.20054	−	1.79946i	−0.198271	−	0.0575404i
$979$	−12.9692			−0.414499
$980$		0			0
$981$	10.4626			0.334046
$982$	49.0484	+	14.2343i	1.56520	+	0.454236i
$983$	−22.2258	+	22.2258i	−0.708893	+	0.708893i	−0.966302	−	0.257410i	$-0.917131\pi$
$983$	−22.2258	+	22.2258i	−0.708893	+	0.708893i	0.257410	+	0.966302i	$0.417131\pi$
$984$	−0.477513	+	7.69735i	−0.0152226	+	0.245383i
$985$		0			0
$986$	14.5140	−	7.98465i	0.462220	−	0.254283i
$987$	−20.5259	−	20.5259i	−0.653346	−	0.653346i
$988$	−1.11399	−	4.97006i	−0.0354406	−	0.158119i
$989$			7.07472i			0.224963i
$990$		0			0
$991$		−	0.353523i		−	0.0112300i	−0.999984	−	0.00561501i	$-0.998213\pi$
$991$		−	0.353523i		−	0.0112300i	0.999984	−	0.00561501i	$-0.00178732\pi$
$992$	3.44377	+	21.5397i	0.109340	+	0.683886i
$993$	10.6167	+	10.6167i	0.336911	+	0.336911i
$994$	10.1672	+	18.4813i	0.322484	+	0.586191i
$995$		0			0
$996$	0.302648	−	0.477513i	0.00958977	−	0.0151306i
$997$	−27.9380	+	27.9380i	−0.884805	+	0.884805i	−0.994018	−	0.109213i	$-0.965167\pi$
$997$	−27.9380	+	27.9380i	−0.884805	+	0.884805i	0.109213	+	0.994018i	$0.465167\pi$
$998$	2.50580	−	8.63442i	0.0793197	−	0.273318i
$999$	0.513824			0.0162567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.j.d.43.3		12
3.2	odd	2		900.2.k.n.343.4		12
4.3	odd	2	inner	300.2.j.d.43.1		12
5.2	odd	4	inner	300.2.j.d.7.1		12
5.3	odd	4		60.2.j.a.7.6	yes	12
5.4	even	2		60.2.j.a.43.4	yes	12
12.11	even	2		900.2.k.n.343.6		12
15.2	even	4		900.2.k.n.307.6		12
15.8	even	4		180.2.k.e.127.1		12
15.14	odd	2		180.2.k.e.163.3		12
20.3	even	4		60.2.j.a.7.4	✓	12
20.7	even	4	inner	300.2.j.d.7.3		12
20.19	odd	2		60.2.j.a.43.6	yes	12
40.3	even	4		960.2.w.g.127.3		12
40.13	odd	4		960.2.w.g.127.6		12
40.19	odd	2		960.2.w.g.703.6		12
40.29	even	2		960.2.w.g.703.3		12
60.23	odd	4		180.2.k.e.127.3		12
60.47	odd	4		900.2.k.n.307.4		12
60.59	even	2		180.2.k.e.163.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	20.3	even	4
60.2.j.a.7.6	yes	12	5.3	odd	4
60.2.j.a.43.4	yes	12	5.4	even	2
60.2.j.a.43.6	yes	12	20.19	odd	2
180.2.k.e.127.1		12	15.8	even	4
180.2.k.e.127.3		12	60.23	odd	4
180.2.k.e.163.1		12	60.59	even	2
180.2.k.e.163.3		12	15.14	odd	2
300.2.j.d.7.1		12	5.2	odd	4	inner
300.2.j.d.7.3		12	20.7	even	4	inner
300.2.j.d.43.1		12	4.3	odd	2	inner
300.2.j.d.43.3		12	1.1	even	1	trivial
900.2.k.n.307.4		12	60.47	odd	4
900.2.k.n.307.6		12	15.2	even	4
900.2.k.n.343.4		12	3.2	odd	2
900.2.k.n.343.6		12	12.11	even	2
960.2.w.g.127.3		12	40.3	even	4
960.2.w.g.127.6		12	40.13	odd	4
960.2.w.g.703.3		12	40.29	even	2
960.2.w.g.703.6		12	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.394157 + 1.35818i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 - 2.47817i) q^{7} +(2.12000 - 1.87233i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.394157 + 1.35818i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 - 2.47817i) q^{7} +(2.12000 - 1.87233i) q^{8} -1.00000i q^{9} -3.02831i q^{11} +(1.95158 - 0.437425i) q^{12} +(-0.363328 - 0.363328i) q^{13} +(4.34258 - 2.38900i) q^{14} +(1.70734 + 3.61732i) q^{16} +(2.36333 - 2.36333i) q^{17} +(1.35818 + 0.394157i) q^{18} -4.95634 q^{19} +3.50466 q^{21} +(4.11297 + 1.19363i) q^{22} +(0.900390 - 0.900390i) q^{23} +(-0.175128 + 2.82300i) q^{24} +(0.636672 - 0.350255i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.53303 + 6.83963i) q^{28} -3.50466i q^{29} -3.85607i q^{31} +(-5.58591 + 0.893077i) q^{32} +(2.14134 + 2.14134i) q^{33} +(2.27829 + 4.14134i) q^{34} +(-1.07067 + 1.68928i) q^{36} +(0.363328 - 0.363328i) q^{37} +(1.95358 - 6.73158i) q^{38} +0.513824 q^{39} +2.72666 q^{41} +(-1.38139 + 4.75995i) q^{42} +(-3.92870 + 3.92870i) q^{43} +(-3.24231 + 5.11566i) q^{44} +(0.867993 + 1.57778i) q^{46} +(-5.85673 - 5.85673i) q^{47} +(-3.76510 - 1.35056i) q^{48} +5.28267i q^{49} +3.34225i q^{51} +(0.224760 + 1.00277i) q^{52} +(-3.14134 - 3.14134i) q^{53} +(-1.23909 + 0.681664i) q^{54} +(-9.89367 - 0.613763i) q^{56} +(3.50466 - 3.50466i) q^{57} +(4.75995 + 1.38139i) q^{58} +8.68516 q^{59} -15.2920 q^{61} +(5.23723 + 1.51990i) q^{62} +(-2.47817 + 2.47817i) q^{63} +(0.988770 - 7.93866i) q^{64} +(-3.75233 + 2.06429i) q^{66} +(3.92870 + 3.92870i) q^{67} +(-6.52267 + 1.46199i) q^{68} +1.27334i q^{69} +4.25583i q^{71} +(-1.87233 - 2.12000i) q^{72} +(-9.28267 - 9.28267i) q^{73} +(0.350255 + 0.636672i) q^{74} +(8.37266 + 5.30660i) q^{76} +(-7.50466 + 7.50466i) q^{77} +(-0.202527 + 0.697863i) q^{78} +0.399759 q^{79} -1.00000 q^{81} +(-1.07473 + 3.70328i) q^{82} +(0.199879 - 0.199879i) q^{83} +(-5.92036 - 3.75233i) q^{84} +(-3.78734 - 6.88438i) q^{86} +(2.47817 + 2.47817i) q^{87} +(-5.66999 - 6.42000i) q^{88} -4.28267i q^{89} +1.80078i q^{91} +(-2.48503 + 0.556993i) q^{92} +(2.72666 + 2.72666i) q^{93} +(10.2629 - 5.64600i) q^{94} +(3.31834 - 4.58134i) q^{96} +(-6.73599 + 6.73599i) q^{97} +(-7.17480 - 2.08220i) q^{98} -3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 + 12 * q^8	\( 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more