LMFDB - Embedded newform 400.2.l.h.101.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(101,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			101.5
Root			$1.32070 + 0.505727i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.h.301.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.257150 - 1.39064i) q^{2} +(1.66366 - 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-1.88574 - 2.74137i) q^{6} -2.89402i q^{7} +(-1.47488 + 2.41345i) q^{8} -2.53555i q^{9} +(1.84462 + 1.84462i) q^{11} +(-4.29717 + 1.91744i) q^{12} +(3.08011 - 3.08011i) q^{13} +(-4.02454 - 0.744198i) q^{14} +(2.97696 + 2.67165i) q^{16} -7.29875 q^{17} +(-3.52604 - 0.652018i) q^{18} +(-1.23593 + 1.23593i) q^{19} +(-4.81468 - 4.81468i) q^{21} +(3.03955 - 2.09086i) q^{22} +4.60490i q^{23} +(1.56145 + 6.46887i) q^{24} +(-3.49126 - 5.07536i) q^{26} +(0.772683 + 0.772683i) q^{27} +(-2.06982 + 5.40530i) q^{28} +(4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(4.48082 - 3.45286i) q^{32} +6.13767 q^{33} +(-1.87688 + 10.1499i) q^{34} +(-1.81344 + 4.73577i) q^{36} +(1.17899 + 1.17899i) q^{37} +(1.40091 + 2.03655i) q^{38} -10.2485i q^{39} +4.61484i q^{41} +(-7.93357 + 5.45738i) q^{42} +(-3.03019 - 3.03019i) q^{43} +(-2.12601 - 4.76458i) q^{44} +(6.40375 + 1.18415i) q^{46} +11.7111 q^{47} +(9.39739 - 0.507943i) q^{48} -1.37537 q^{49} +(-12.1427 + 12.1427i) q^{51} +(-7.95577 + 3.54995i) q^{52} +(-2.73048 - 2.73048i) q^{53} +(1.27322 - 0.875827i) q^{54} +(6.98457 + 4.26835i) q^{56} +4.11235i q^{57} +(-4.81369 - 6.99782i) q^{58} +(3.11306 + 3.11306i) q^{59} +(2.34962 - 2.34962i) q^{61} +(0.530498 - 2.86887i) q^{62} -7.33795 q^{63} +(-3.64944 - 7.11910i) q^{64} +(1.57830 - 8.53528i) q^{66} +(-8.24311 + 8.24311i) q^{67} +(13.6322 + 5.22011i) q^{68} +(7.66101 + 7.66101i) q^{69} -3.25937i q^{71} +(6.11942 + 3.73965i) q^{72} -12.6877i q^{73} +(1.94272 - 1.33637i) q^{74} +(3.19235 - 1.42446i) q^{76} +(5.33839 - 5.33839i) q^{77} +(-14.2520 - 2.63541i) q^{78} -0.113885 q^{79} +10.1776 q^{81} +(6.41758 + 1.18671i) q^{82} +(-9.76813 + 9.76813i) q^{83} +(5.54912 + 12.4361i) q^{84} +(-4.99310 + 3.43468i) q^{86} -14.1305i q^{87} +(-7.17251 + 1.73129i) q^{88} -3.74593i q^{89} +(-8.91390 - 8.91390i) q^{91} +(3.29345 - 8.60080i) q^{92} +(3.43212 - 3.43212i) q^{93} +(3.01150 - 16.2858i) q^{94} +(1.71017 - 13.1990i) q^{96} +13.9853 q^{97} +(-0.353676 + 1.91264i) q^{98} +(4.67714 - 4.67714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	0.257150	−	1.39064i	0.181833	−	0.983329i
$2$	0.257150	−	1.39064i	0.181833	−	0.983329i
$3$	1.66366	−	1.66366i	0.960517	−	0.960517i	−0.0387330	−	0.999250i	$-0.512332\pi$
$3$	1.66366	−	1.66366i	0.960517	−	0.960517i	0.999250	+	0.0387330i	$0.0123322\pi$
$4$	−1.86775	−	0.715205i	−0.933874	−	0.357603i
$5$		0			0
$5$		0			0
$6$	−1.88574	−	2.74137i	−0.769851	−	1.11916i
$7$		−	2.89402i		−	1.09384i	−0.837186	−	0.546919i	$-0.815801\pi$
$7$		−	2.89402i		−	1.09384i	0.837186	−	0.546919i	$-0.184199\pi$
$8$	−1.47488	+	2.41345i	−0.521450	+	0.853282i
$9$		−	2.53555i		−	0.845184i
$10$		0			0
$11$	1.84462	+	1.84462i	0.556175	+	0.556175i	0.928216	−	0.372041i	$-0.121342\pi$
$11$	1.84462	+	1.84462i	0.556175	+	0.556175i	−0.372041	+	0.928216i	$0.621342\pi$
$12$	−4.29717	+	1.91744i	−1.24048	+	0.553518i
$13$	3.08011	−	3.08011i	0.854268	−	0.854268i	−0.136388	−	0.990656i	$-0.543549\pi$
$13$	3.08011	−	3.08011i	0.854268	−	0.854268i	0.990656	+	0.136388i	$0.0435493\pi$
$14$	−4.02454	−	0.744198i	−1.07560	−	0.198895i
$15$		0			0
$16$	2.97696	+	2.67165i	0.744241	+	0.667912i
$17$	−7.29875			−1.77021			−0.885104	−	0.465393i	$-0.845913\pi$
$17$	−7.29875			−1.77021			−0.885104	+	0.465393i	$0.845913\pi$
$18$	−3.52604	−	0.652018i	−0.831095	−	0.153682i
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	−0.834520	−	0.550978i	$-0.814255\pi$
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	0.550978	+	0.834520i	$0.314255\pi$
$20$		0			0
$21$	−4.81468	−	4.81468i	−1.05065	−	1.05065i
$22$	3.03955	−	2.09086i	0.648034	−	0.445773i
$23$			4.60490i			0.960189i	0.877217	+	0.480094i	$0.159398\pi$
$23$			4.60490i			0.960189i	−0.877217	+	0.480094i	$0.840602\pi$
$24$	1.56145	+	6.46887i	0.318730	+	1.32045i
$25$		0			0
$26$	−3.49126	−	5.07536i	−0.684693	−	0.995360i
$27$	0.772683	+	0.772683i	0.148703	+	0.148703i
$28$	−2.06982	+	5.40530i	−0.391159	+	1.02151i
$29$	4.24680	−	4.24680i	0.788611	−	0.788611i	−0.192656	−	0.981266i	$-0.561710\pi$
$29$	4.24680	−	4.24680i	0.788611	−	0.788611i	0.981266	+	0.192656i	$0.0617101\pi$
$30$		0			0
$31$	2.06299			0.370524			0.185262	−	0.982689i	$-0.440687\pi$
$31$	2.06299			0.370524			0.185262	+	0.982689i	$0.440687\pi$
$32$	4.48082	−	3.45286i	0.792104	−	0.610386i
$33$	6.13767			1.06843
$34$	−1.87688	+	10.1499i	−0.321882	+	1.74070i
$35$		0			0
$36$	−1.81344	+	4.73577i	−0.302240	+	0.789296i
$37$	1.17899	+	1.17899i	0.193825	+	0.193825i	0.797346	−	0.603522i	$-0.206236\pi$
$37$	1.17899	+	1.17899i	0.193825	+	0.193825i	−0.603522	+	0.797346i	$0.706236\pi$
$38$	1.40091	+	2.03655i	0.227258	+	0.330373i
$39$		−	10.2485i		−	1.64108i
$40$		0			0
$41$			4.61484i			0.720717i	0.932814	+	0.360359i	$0.117346\pi$
$41$			4.61484i			0.720717i	−0.932814	+	0.360359i	$0.882654\pi$
$42$	−7.93357	+	5.45738i	−1.22418	+	0.842092i
$43$	−3.03019	−	3.03019i	−0.462099	−	0.462099i	0.437244	−	0.899343i	$-0.355955\pi$
$43$	−3.03019	−	3.03019i	−0.462099	−	0.462099i	−0.899343	+	0.437244i	$0.855955\pi$
$44$	−2.12601	−	4.76458i	−0.320508	−	0.718287i
$45$		0			0
$46$	6.40375	+	1.18415i	0.944182	+	0.174594i
$47$	11.7111			1.70823			0.854117	−	0.520081i	$-0.174098\pi$
$47$	11.7111			1.70823			0.854117	+	0.520081i	$0.174098\pi$
$48$	9.39739	−	0.507943i	1.35640	−	0.0733152i
$49$	−1.37537			−0.196481
$50$		0			0
$51$	−12.1427	+	12.1427i	−1.70031	+	1.70031i
$52$	−7.95577	+	3.54995i	−1.10327	+	0.492290i
$53$	−2.73048	−	2.73048i	−0.375061	−	0.375061i	0.494256	−	0.869316i	$-0.335441\pi$
$53$	−2.73048	−	2.73048i	−0.375061	−	0.375061i	−0.869316	+	0.494256i	$0.835441\pi$
$54$	1.27322	−	0.875827i	0.173263	−	0.119185i
$55$		0			0
$56$	6.98457	+	4.26835i	0.933352	+	0.570382i
$57$			4.11235i			0.544694i
$58$	−4.81369	−	6.99782i	−0.632069	−	0.918859i
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	0.880091	−	0.474805i	$-0.157482\pi$
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	−0.474805	+	0.880091i	$0.657482\pi$
$60$		0			0
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	−0.540503	−	0.841342i	$-0.681766\pi$
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	0.841342	+	0.540503i	$0.181766\pi$
$62$	0.530498	−	2.86887i	0.0673733	−	0.364347i
$63$	−7.33795			−0.924495
$64$	−3.64944	−	7.11910i	−0.456180	−	0.889888i
$65$		0			0
$66$	1.57830	−	8.53528i	0.194276	−	1.05062i
$67$	−8.24311	+	8.24311i	−1.00706	+	1.00706i	−0.00708173	+	0.999975i	$0.502254\pi$
$67$	−8.24311	+	8.24311i	−1.00706	+	1.00706i	−0.999975	+	0.00708173i	$0.997746\pi$
$68$	13.6322	+	5.22011i	1.65315	+	0.633031i
$69$	7.66101	+	7.66101i	0.922277	+	0.922277i
$70$		0			0
$71$		−	3.25937i		−	0.386816i	−0.981118	−	0.193408i	$-0.938046\pi$
$71$		−	3.25937i		−	0.386816i	0.981118	−	0.193408i	$-0.0619541\pi$
$72$	6.11942	+	3.73965i	0.721180	+	0.440721i
$73$		−	12.6877i		−	1.48499i	−0.669853	−	0.742494i	$-0.733643\pi$
$73$		−	12.6877i		−	1.48499i	0.669853	−	0.742494i	$-0.266357\pi$
$74$	1.94272	−	1.33637i	0.225837	−	0.155350i
$75$		0			0
$76$	3.19235	−	1.42446i	0.366188	−	0.163397i
$77$	5.33839	−	5.33839i	0.608365	−	0.608365i
$78$	−14.2520	−	2.63541i	−1.61372	−	0.298401i
$79$	−0.113885			−0.0128130			−0.00640652	−	0.999979i	$-0.502039\pi$
$79$	−0.113885			−0.0128130			−0.00640652	+	0.999979i	$0.502039\pi$
$80$		0			0
$81$	10.1776			1.13085
$82$	6.41758	+	1.18671i	0.708703	+	0.131050i
$83$	−9.76813	+	9.76813i	−1.07219	+	1.07219i	−0.0750089	+	0.997183i	$0.523899\pi$
$83$	−9.76813	+	9.76813i	−1.07219	+	1.07219i	−0.997183	+	0.0750089i	$0.976101\pi$
$84$	5.54912	+	12.4361i	0.605459	+	1.35689i
$85$		0			0
$86$	−4.99310	+	3.43468i	−0.538420	+	0.370371i
$87$		−	14.1305i		−	1.51495i
$88$	−7.17251	+	1.73129i	−0.764592	+	0.184557i
$89$		−	3.74593i		−	0.397068i	−0.980094	−	0.198534i	$-0.936382\pi$
$89$		−	3.74593i		−	0.397068i	0.980094	−	0.198534i	$-0.0636180\pi$
$90$		0			0
$91$	−8.91390	−	8.91390i	−0.934430	−	0.934430i
$92$	3.29345	−	8.60080i	0.343366	−	0.896695i
$93$	3.43212	−	3.43212i	0.355894	−	0.355894i
$94$	3.01150	−	16.2858i	0.310613	−	1.67976i
$95$		0			0
$96$	1.71017	−	13.1990i	0.174544	−	1.34711i
$97$	13.9853			1.41999			0.709995	−	0.704206i	$-0.248697\pi$
$97$	13.9853			1.41999			0.709995	+	0.704206i	$0.248697\pi$
$98$	−0.353676	+	1.91264i	−0.0357267	+	0.193206i
$99$	4.67714	−	4.67714i	0.470071	−	0.470071i
$100$		0			0
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	0.860288	−	0.509808i	$-0.170284\pi$
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	−0.509808	+	0.860288i	$0.670284\pi$
$102$	13.7636	+	20.0085i	1.36280	+	1.98114i
$103$		−	0.150216i		−	0.0148013i	−0.999973	−	0.00740063i	$-0.997644\pi$
$103$		−	0.150216i		−	0.0148013i	0.999973	−	0.00740063i	$-0.00235572\pi$
$104$	2.89087	+	11.9765i	0.283473	+	1.17439i
$105$		0			0
$106$	−4.49926	+	3.09497i	−0.437006	+	0.300610i
$107$	2.75062	+	2.75062i	0.265912	+	0.265912i	0.827451	−	0.561539i	$-0.189790\pi$
$107$	2.75062	+	2.75062i	0.265912	+	0.265912i	−0.561539	+	0.827451i	$0.689790\pi$
$108$	−0.890550	−	1.99580i	−0.0856932	−	0.192046i
$109$	−6.90778	+	6.90778i	−0.661646	+	0.661646i	−0.955768	−	0.294122i	$-0.904973\pi$
$109$	−6.90778	+	6.90778i	−0.661646	+	0.661646i	0.294122	+	0.955768i	$0.404973\pi$
$110$		0			0
$111$	3.92288			0.372344
$112$	7.73181	−	8.61540i	0.730587	−	0.814078i
$113$	3.49507			0.328788			0.164394	−	0.986395i	$-0.447433\pi$
$113$	3.49507			0.328788			0.164394	+	0.986395i	$0.447433\pi$
$114$	5.71879	+	1.05749i	0.535614	+	0.0990431i
$115$		0			0
$116$	−10.9693	+	4.89461i	−1.01847	+	0.454454i
$117$	−7.80977	−	7.80977i	−0.722014	−	0.722014i
$118$	5.12966	−	3.52861i	0.472223	−	0.324835i
$119$			21.1228i			1.93632i
$120$		0			0
$121$		−	4.19472i		−	0.381338i
$122$	−2.66327	−	3.87168i	−0.241121	−	0.350526i
$123$	7.67755	+	7.67755i	0.692261	+	0.692261i
$124$	−3.85314	−	1.47546i	−0.346022	−	0.132500i
$125$		0			0
$126$	−1.88695	+	10.2044i	−0.168103	+	0.909083i
$127$	−6.25357			−0.554915			−0.277458	−	0.960738i	$-0.589492\pi$
$127$	−6.25357			−0.554915			−0.277458	+	0.960738i	$0.589492\pi$
$128$	−10.8385	+	3.24437i	−0.958001	+	0.286764i
$129$	−10.0824			−0.887708
$130$		0			0
$131$	−5.16490	+	5.16490i	−0.451259	+	0.451259i	−0.895772	−	0.444513i	$-0.853377\pi$
$131$	−5.16490	+	5.16490i	−0.451259	+	0.451259i	0.444513	+	0.895772i	$0.353377\pi$
$132$	−11.4636	−	4.38969i	−0.997780	−	0.382074i
$133$	3.57681	+	3.57681i	0.310149	+	0.310149i
$134$	9.34347	+	13.5829i	0.807153	+	1.17338i
$135$		0			0
$136$	10.7648	−	17.6151i	0.923075	−	1.51049i
$137$			18.9408i			1.61823i	0.587654	+	0.809113i	$0.300052\pi$
$137$			18.9408i			1.61823i	−0.587654	+	0.809113i	$0.699948\pi$
$138$	12.6237	−	8.68366i	1.07460	−	0.739203i
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	0.815479	−	0.578786i	$-0.196473\pi$
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	−0.578786	+	0.815479i	$0.696473\pi$
$140$		0			0
$141$	19.4833	−	19.4833i	1.64079	−	1.64079i
$142$	−4.53260	−	0.838147i	−0.380367	−	0.0703357i
$143$	11.3633			0.950245
$144$	6.77410	−	7.54825i	0.564509	−	0.629021i
$145$		0			0
$146$	−17.6441	−	3.26265i	−1.46023	−	0.270019i
$147$	−2.28815	+	2.28815i	−0.188723	+	0.188723i
$148$	−1.35883	−	3.04527i	−0.111696	−	0.250320i
$149$	−1.60372	−	1.60372i	−0.131382	−	0.131382i	0.638358	−	0.769740i	$-0.279614\pi$
$149$	−1.60372	−	1.60372i	−0.131382	−	0.131382i	−0.769740	+	0.638358i	$0.779614\pi$
$150$		0			0
$151$			2.53754i			0.206502i	0.994655	+	0.103251i	$0.0329245\pi$
$151$			2.53754i			0.206502i	−0.994655	+	0.103251i	$0.967076\pi$
$152$	−1.16000	−	4.80571i	−0.0940883	−	0.389794i
$153$			18.5064i			1.49615i
$154$	−6.05099	−	8.79653i	−0.487603	−	0.708844i
$155$		0			0
$156$	−7.32980	+	19.1417i	−0.586854	+	1.53256i
$157$	−10.2405	+	10.2405i	−0.817278	+	0.817278i	−0.985713	−	0.168435i	$-0.946129\pi$
$157$	−10.2405	+	10.2405i	−0.817278	+	0.817278i	0.168435	+	0.985713i	$0.446129\pi$
$158$	−0.0292855	+	0.158373i	−0.00232983	+	0.0125994i
$159$	−9.08521			−0.720504
$160$		0			0
$161$	13.3267			1.05029
$162$	2.61718	−	14.1534i	0.205625	−	1.11200i
$163$	−8.02607	+	8.02607i	−0.628650	+	0.628650i	−0.947728	−	0.319078i	$-0.896627\pi$
$163$	−8.02607	+	8.02607i	−0.628650	+	0.628650i	0.319078	+	0.947728i	$0.396627\pi$
$164$	3.30056	−	8.61936i	0.257731	−	0.673059i
$165$		0			0
$166$	11.0721	+	16.0958i	0.859358	+	1.24928i
$167$			6.82611i			0.528221i	0.964492	+	0.264110i	$0.0850783\pi$
$167$			6.82611i			0.528221i	−0.964492	+	0.264110i	$0.914922\pi$
$168$	18.7211	−	4.51888i	1.44436	−	0.348639i
$169$		−	5.97411i		−	0.459547i
$170$		0			0
$171$	3.13377	+	3.13377i	0.239645	+	0.239645i
$172$	3.49242	+	7.82683i	0.266294	+	0.596790i
$173$	−5.08901	+	5.08901i	−0.386910	+	0.386910i	−0.873584	−	0.486674i	$-0.838210\pi$
$173$	−5.08901	+	5.08901i	−0.386910	+	0.386910i	0.486674	+	0.873584i	$0.338210\pi$
$174$	−19.6504	−	3.63366i	−1.48969	−	0.275467i
$175$		0			0
$176$	0.563193	+	10.4196i	0.0424523	+	0.785404i
$177$	10.3582			0.778567
$178$	−5.20924	−	0.963267i	−0.390449	−	0.0721999i
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	−0.643238	−	0.765666i	$-0.722410\pi$
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	0.765666	+	0.643238i	$0.222410\pi$
$180$		0			0
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.957071	−	0.289855i	$-0.906393\pi$
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.289855	−	0.957071i	$-0.593607\pi$
$182$	−14.6882	+	10.1038i	−1.08876	+	0.748943i
$183$		−	7.81797i		−	0.577921i
$184$	−11.1137	−	6.79170i	−0.819312	−	0.500691i
$185$		0			0
$186$	−3.89026	−	5.65540i	−0.285248	−	0.414674i
$187$	−13.4635	−	13.4635i	−0.984546	−	0.984546i
$188$	−21.8733	−	8.37582i	−1.59527	−	0.610869i
$189$	2.23616	−	2.23616i	0.162657	−	0.162657i
$190$		0			0
$191$	5.85815			0.423881			0.211940	−	0.977283i	$-0.432022\pi$
$191$	5.85815			0.423881			0.211940	+	0.977283i	$0.432022\pi$
$192$	−17.9152	−	5.77235i	−1.29292	−	0.416584i
$193$	0.0241155			0.00173587			0.000867935	−	1.00000i	$-0.499724\pi$
$193$	0.0241155			0.00173587			0.000867935		1.00000i	$0.499724\pi$
$194$	3.59632	−	19.4485i	0.258201	−	1.39632i
$195$		0			0
$196$	2.56884	+	0.983671i	0.183489	+	0.0702622i
$197$	−14.9086	−	14.9086i	−1.06219	−	1.06219i	−0.997933	−	0.0642576i	$-0.979532\pi$
$197$	−14.9086	−	14.9086i	−1.06219	−	1.06219i	−0.0642576	−	0.997933i	$-0.520468\pi$
$198$	−5.30149	−	7.70694i	−0.376760	−	0.547708i
$199$			13.6525i			0.967801i	0.875123	+	0.483900i	$0.160780\pi$
$199$			13.6525i			0.967801i	−0.875123	+	0.483900i	$0.839220\pi$
$200$		0			0
$201$			27.4275i			1.93459i
$202$	5.80397	−	3.99246i	0.408366	−	0.280909i
$203$	−12.2903	−	12.2903i	−0.862612	−	0.862612i
$204$	31.3640	−	13.9949i	2.19592	−	0.979842i
$205$		0			0
$206$	−0.208897	−	0.0386282i	−0.0145545	−	0.00269135i
$207$	11.6760			0.811537
$208$	17.3983	−	0.940405i	1.20636	−	0.0652053i
$209$	−4.55966			−0.315398
$210$		0			0
$211$	−2.45103	+	2.45103i	−0.168736	+	0.168736i	−0.786424	−	0.617688i	$-0.788070\pi$
$211$	−2.45103	+	2.45103i	−0.168736	+	0.168736i	0.617688	+	0.786424i	$0.288070\pi$
$212$	3.14700	+	7.05271i	0.216137	+	0.484382i
$213$	−5.42249	−	5.42249i	−0.371543	−	0.371543i
$214$	4.53243	−	3.11779i	0.309831	−	0.213128i
$215$		0			0
$216$	−3.00445	+	0.725211i	−0.204427	+	0.0493444i
$217$		−	5.97033i		−	0.405293i
$218$	7.82989	+	11.3826i	0.530307	+	0.770924i
$219$	−21.1081	−	21.1081i	−1.42636	−	1.42636i
$220$		0			0
$221$	−22.4809	+	22.4809i	−1.51223	+	1.51223i
$222$	1.00877	−	5.45531i	0.0677042	−	0.366136i
$223$	−13.9483			−0.934045			−0.467023	−	0.884245i	$-0.654673\pi$
$223$	−13.9483			−0.934045			−0.467023	+	0.884245i	$0.654673\pi$
$224$	−9.99266	−	12.9676i	−0.667663	−	0.866434i
$225$		0			0
$226$	0.898758	−	4.86038i	0.0597845	−	0.323307i
$227$	−4.43883	+	4.43883i	−0.294616	+	0.294616i	−0.838901	−	0.544285i	$-0.816801\pi$
$227$	−4.43883	+	4.43883i	−0.294616	+	0.294616i	0.544285	+	0.838901i	$0.316801\pi$
$228$	2.94117	−	7.68083i	0.194784	−	0.508675i
$229$	−5.35068	−	5.35068i	−0.353583	−	0.353583i	0.507858	−	0.861441i	$-0.330438\pi$
$229$	−5.35068	−	5.35068i	−0.353583	−	0.353583i	−0.861441	+	0.507858i	$0.830438\pi$
$230$		0			0
$231$		−	17.7626i		−	1.16869i
$232$	3.98588	+	16.5129i	0.261686	+	1.08413i
$233$			11.9370i			0.782019i	0.920387	+	0.391010i	$0.127874\pi$
$233$			11.9370i			0.782019i	−0.920387	+	0.391010i	$0.872126\pi$
$234$	−12.8689	+	8.85228i	−0.841263	+	0.578692i
$235$		0			0
$236$	−3.58793	−	8.04088i	−0.233554	−	0.523416i
$237$	−0.189466	+	0.189466i	−0.0123071	+	0.0123071i
$238$	29.3741	+	5.43172i	1.90404	+	0.352086i
$239$	−16.7720			−1.08489			−0.542445	−	0.840091i	$-0.682501\pi$
$239$	−16.7720			−1.08489			−0.542445	+	0.840091i	$0.682501\pi$
$240$		0			0
$241$	−22.0294			−1.41904			−0.709519	−	0.704686i	$-0.751088\pi$
$241$	−22.0294			−1.41904			−0.709519	+	0.704686i	$0.751088\pi$
$242$	−5.83334	−	1.07867i	−0.374981	−	0.0693397i
$243$	14.6141	−	14.6141i	0.937495	−	0.937495i
$244$	−6.06897	+	2.70804i	−0.388526	+	0.173365i
$245$		0			0
$246$	12.6510	−	8.70241i	0.806596	−	0.554845i
$247$			7.61360i			0.484442i
$248$	−3.04267	+	4.97891i	−0.193210	+	0.316161i
$249$			32.5018i			2.05972i
$250$		0			0
$251$	6.63925	+	6.63925i	0.419066	+	0.419066i	0.884882	−	0.465816i	$-0.154239\pi$
$251$	6.63925	+	6.63925i	0.419066	+	0.419066i	−0.465816	+	0.884882i	$0.654239\pi$
$252$	13.7054	+	5.24814i	0.863361	+	0.330602i
$253$	−8.49432	+	8.49432i	−0.534033	+	0.534033i
$254$	−1.60811	+	8.69646i	−0.100902	+	0.545664i
$255$		0			0
$256$	1.72461	+	15.9068i	0.107788	+	0.994174i
$257$	7.25821			0.452755			0.226377	−	0.974040i	$-0.427312\pi$
$257$	7.25821			0.452755			0.226377	+	0.974040i	$0.427312\pi$
$258$	−2.59270	+	14.0210i	−0.161414	+	0.872909i
$259$	3.41202	−	3.41202i	0.212013	−	0.212013i
$260$		0			0
$261$	−10.7680	−	10.7680i	−0.666521	−	0.666521i
$262$	5.85435	+	8.51066i	0.361683	+	0.525790i
$263$			9.27431i			0.571878i	0.958248	+	0.285939i	$0.0923055\pi$
$263$			9.27431i			0.571878i	−0.958248	+	0.285939i	$0.907694\pi$
$264$	−9.05235	+	14.8129i	−0.557133	+	0.911673i
$265$		0			0
$266$	5.89383	−	4.05428i	0.361374	−	0.248584i
$267$	−6.23197	−	6.23197i	−0.381390	−	0.381390i
$268$	21.2916	−	9.50054i	1.30059	−	0.580338i
$269$	−13.4195	+	13.4195i	−0.818199	+	0.818199i	−0.985847	−	0.167648i	$-0.946383\pi$
$269$	−13.4195	+	13.4195i	−0.818199	+	0.818199i	0.167648	+	0.985847i	$0.446383\pi$
$270$		0			0
$271$	22.5999			1.37285			0.686423	−	0.727202i	$-0.259180\pi$
$271$	22.5999			1.37285			0.686423	+	0.727202i	$0.259180\pi$
$272$	−21.7281	−	19.4997i	−1.31746	−	1.18234i
$273$	−29.6595			−1.79507
$274$	26.3399	+	4.87064i	1.59125	+	0.294246i
$275$		0			0
$276$	−8.82964	−	19.7880i	−0.531482	−	1.19110i
$277$	−16.2015	−	16.2015i	−0.973451	−	0.973451i	0.0262056	−	0.999657i	$-0.491658\pi$
$277$	−16.2015	−	16.2015i	−0.973451	−	0.973451i	−0.999657	+	0.0262056i	$0.991658\pi$
$278$	4.59827	−	3.16308i	0.275786	−	0.189709i
$279$		−	5.23082i		−	0.313161i
$280$		0			0
$281$		−	8.84793i		−	0.527824i	−0.964547	−	0.263912i	$-0.914987\pi$
$281$		−	8.84793i		−	0.527824i	0.964547	−	0.263912i	$-0.0850128\pi$
$282$	−22.0840	−	32.1043i	−1.31509	−	1.91178i
$283$	20.3062	+	20.3062i	1.20708	+	1.20708i	0.971969	+	0.235109i	$0.0755447\pi$
$283$	20.3062	+	20.3062i	1.20708	+	1.20708i	0.235109	+	0.971969i	$0.424455\pi$
$284$	−2.33112	+	6.08768i	−0.138326	+	0.361237i
$285$		0			0
$286$	2.92207	−	15.8022i	0.172786	−	0.934404i
$287$	13.3555			0.788348
$288$	−8.75492	−	11.3614i	−0.515888	−	0.669474i
$289$	36.2718			2.13364
$290$		0			0
$291$	23.2668	−	23.2668i	1.36392	−	1.36392i
$292$	−9.07434	+	23.6975i	−0.531036	+	1.38679i
$293$	7.16936	+	7.16936i	0.418839	+	0.418839i	0.884803	−	0.465965i	$-0.154293\pi$
$293$	7.16936	+	7.16936i	0.418839	+	0.418839i	−0.465965	+	0.884803i	$0.654293\pi$
$294$	2.59359	+	3.77039i	0.151261	+	0.219893i
$295$		0			0
$296$	−4.58430	+	1.10655i	−0.266457	+	0.0643172i
$297$			2.85062i			0.165410i
$298$	−2.64259	+	1.81779i	−0.153081	+	0.105302i
$299$	14.1836	+	14.1836i	0.820258	+	0.820258i
$300$		0			0
$301$	−8.76943	+	8.76943i	−0.505461	+	0.505461i
$302$	3.52880	+	0.652528i	0.203059	+	0.0375488i
$303$	11.7198			0.673284
$304$	−6.98129	+	0.377349i	−0.400405	+	0.0216425i
$305$		0			0
$306$	25.7357	+	4.75892i	1.47121	+	0.272049i
$307$	18.4308	−	18.4308i	1.05190	−	1.05190i	0.0533241	−	0.998577i	$-0.483018\pi$
$307$	18.4308	−	18.4308i	1.05190	−	1.05190i	0.998577	−	0.0533241i	$-0.0169816\pi$
$308$	−13.7888	+	6.15271i	−0.785690	+	0.350583i
$309$	−0.249910	−	0.249910i	−0.0142169	−	0.0142169i
$310$		0			0
$311$			7.08961i			0.402015i	0.979590	+	0.201007i	$0.0644215\pi$
$311$			7.08961i			0.402015i	−0.979590	+	0.201007i	$0.935578\pi$
$312$	24.7342	+	15.1154i	1.40030	+	0.855739i
$313$		−	22.0477i		−	1.24621i	−0.782139	−	0.623104i	$-0.785871\pi$
$313$		−	22.0477i		−	1.24621i	0.782139	−	0.623104i	$-0.214129\pi$
$314$	11.6074	+	16.8741i	0.655046	+	0.952262i
$315$		0			0
$316$	0.212708	+	0.0814510i	0.0119658	+	0.00458198i
$317$	6.19670	−	6.19670i	0.348042	−	0.348042i	−0.511338	−	0.859380i	$-0.670850\pi$
$317$	6.19670	−	6.19670i	0.348042	−	0.348042i	0.859380	+	0.511338i	$0.170850\pi$
$318$	−2.33626	+	12.6342i	−0.131011	+	0.708493i
$319$	15.6675			0.877211
$320$		0			0
$321$	9.15220			0.510826
$322$	3.42696	−	18.5326i	0.190977	−	1.03278i
$323$	9.02076	−	9.02076i	0.501929	−	0.501929i
$324$	−19.0092	−	7.27910i	−1.05607	−	0.404394i
$325$		0			0
$326$	9.09745	+	13.2253i	0.503861	+	0.732479i
$327$			22.9845i			1.27104i
$328$	−11.1377	−	6.80636i	−0.614975	−	0.375818i
$329$		−	33.8921i		−	1.86853i
$330$		0			0
$331$	−18.6174	−	18.6174i	−1.02330	−	1.02330i	−0.999722	−	0.0235823i	$-0.992493\pi$
$331$	−18.6174	−	18.6174i	−1.02330	−	1.02330i	−0.0235823	−	0.999722i	$-0.507507\pi$
$332$	25.2306	−	11.2582i	1.38471	−	0.617873i
$333$	2.98939	−	2.98939i	0.163818	−	0.163818i
$334$	9.49265	+	1.75534i	0.519415	+	0.0960477i
$335$		0			0
$336$	−1.47000	−	27.1962i	−0.0801949	−	1.48368i
$337$	−14.2577			−0.776666			−0.388333	−	0.921519i	$-0.626949\pi$
$337$	−14.2577			−0.776666			−0.388333	+	0.921519i	$0.626949\pi$
$338$	−8.30782	−	1.53624i	−0.451886	−	0.0835606i
$339$	5.81462	−	5.81462i	0.315807	−	0.315807i
$340$		0			0
$341$	3.80544	+	3.80544i	0.206076	+	0.206076i
$342$	5.16379	−	3.55209i	0.279226	−	0.192075i
$343$		−	16.2778i		−	0.878919i
$344$	11.7824	−	2.84402i	0.635262	−	0.153339i
$345$		0			0
$346$	5.76833	+	8.38561i	0.310107	+	0.450813i
$347$	23.5395	+	23.5395i	1.26367	+	1.26367i	0.949303	+	0.314363i	$0.101791\pi$
$347$	23.5395	+	23.5395i	1.26367	+	1.26367i	0.314363	+	0.949303i	$0.398209\pi$
$348$	−10.1062	+	26.3922i	−0.541749	+	1.41477i
$349$	−1.56682	+	1.56682i	−0.0838701	+	0.0838701i	−0.747797	−	0.663927i	$-0.768888\pi$
$349$	−1.56682	+	1.56682i	−0.0838701	+	0.0838701i	0.663927	+	0.747797i	$0.268888\pi$
$350$		0			0
$351$	4.75989			0.254064
$352$	14.6347	+	1.89619i	0.780030	+	0.101068i
$353$	−9.44678			−0.502801			−0.251401	−	0.967883i	$-0.580891\pi$
$353$	−9.44678			−0.502801			−0.251401	+	0.967883i	$0.580891\pi$
$354$	2.66360	−	14.4044i	0.141569	−	0.765588i
$355$		0			0
$356$	−2.67911	+	6.99646i	−0.141993	+	0.370811i
$357$	35.1412	+	35.1412i	1.85987	+	1.85987i
$358$	−1.85662	−	2.69903i	−0.0981256	−	0.142648i
$359$		−	18.0452i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$359$		−	18.0452i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$360$		0			0
$361$			15.9449i			0.839208i
$362$	−27.6427	+	19.0150i	−1.45287	+	0.999407i
$363$	−6.97860	−	6.97860i	−0.366282	−	0.366282i
$364$	10.2736	+	23.0242i	0.538485	+	1.20679i
$365$		0			0
$366$	−10.8720	−	2.01039i	−0.568286	−	0.105085i
$367$	−29.1329			−1.52073			−0.760363	−	0.649498i	$-0.774979\pi$
$367$	−29.1329			−1.52073			−0.760363	+	0.649498i	$0.774979\pi$
$368$	−12.3027	+	13.7086i	−0.641321	+	0.714612i
$369$	11.7012			0.609139
$370$		0			0
$371$	−7.90208	+	7.90208i	−0.410255	+	0.410255i
$372$	−8.86500	+	3.95566i	−0.459629	+	0.205091i
$373$	−3.35598	−	3.35598i	−0.173766	−	0.173766i	0.614866	−	0.788632i	$-0.289210\pi$
$373$	−3.35598	−	3.35598i	−0.173766	−	0.173766i	−0.788632	+	0.614866i	$0.789210\pi$
$374$	−22.1849	+	15.2607i	−1.14716	+	0.789110i
$375$		0			0
$376$	−17.2725	+	28.2640i	−0.890759	+	1.45760i
$377$		−	26.1612i		−	1.34737i
$378$	−2.53466	−	3.68472i	−0.130369	−	0.189522i
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	0.939902	−	0.341445i	$-0.110916\pi$
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	−0.341445	+	0.939902i	$0.610916\pi$
$380$		0			0
$381$	−10.4038	+	10.4038i	−0.533005	+	0.533005i
$382$	1.50642	−	8.14656i	0.0770753	−	0.416814i
$383$	21.8044			1.11415			0.557077	−	0.830461i	$-0.311923\pi$
$383$	21.8044			1.11415			0.557077	+	0.830461i	$0.311923\pi$
$384$	−12.6342	+	23.4292i	−0.644734	+	1.19562i
$385$		0			0
$386$	0.00620130	−	0.0335359i	0.000315638	−	0.00170693i
$387$	−7.68320	+	7.68320i	−0.390559	+	0.390559i
$388$	−26.1210	−	10.0024i	−1.32609	−	0.507793i
$389$	−11.8899	−	11.8899i	−0.602842	−	0.602842i	0.338224	−	0.941066i	$-0.390174\pi$
$389$	−11.8899	−	11.8899i	−0.602842	−	0.602842i	−0.941066	+	0.338224i	$0.890174\pi$
$390$		0			0
$391$		−	33.6101i		−	1.69973i
$392$	2.02851	−	3.31938i	0.102455	−	0.167654i
$393$			17.1853i			0.866884i
$394$	−24.5661	+	16.8987i	−1.23762	+	0.851343i
$395$		0			0
$396$	−12.0808	+	5.39061i	−0.607085	+	0.270888i
$397$	9.23905	−	9.23905i	0.463694	−	0.463694i	−0.436170	−	0.899864i	$-0.643665\pi$
$397$	9.23905	−	9.23905i	0.463694	−	0.463694i	0.899864	+	0.436170i	$0.143665\pi$
$398$	18.9857	+	3.51074i	0.951667	+	0.175978i
$399$	11.9012			0.595807
$400$		0			0
$401$	−14.4744			−0.722818			−0.361409	−	0.932407i	$-0.617704\pi$
$401$	−14.4744			−0.722818			−0.361409	+	0.932407i	$0.617704\pi$
$402$	38.1418	+	7.05300i	1.90234	+	0.351771i
$403$	6.35422	−	6.35422i	0.316526	−	0.316526i
$404$	−4.05958	−	9.09789i	−0.201972	−	0.452637i
$405$		0			0
$406$	−20.2519	+	13.9309i	−1.00508	+	0.691381i
$407$			4.34958i			0.215601i
$408$	−11.3967	−	47.2147i	−0.564218	−	2.33748i
$409$		−	9.54117i		−	0.471781i	−0.971780	−	0.235890i	$-0.924199\pi$
$409$		−	9.54117i		−	0.471781i	0.971780	−	0.235890i	$-0.0758006\pi$
$410$		0			0
$411$	31.5112	+	31.5112i	1.55433	+	1.55433i
$412$	−0.107436	+	0.280566i	−0.00529297	+	0.0138225i
$413$	9.00925	−	9.00925i	0.443316	−	0.443316i
$414$	3.00248	−	16.2371i	0.147564	−	0.798008i
$415$		0			0
$416$	3.16622	−	24.4366i	0.155237	−	1.19810i
$417$	9.28514			0.454695
$418$	−1.17252	+	6.34083i	−0.0573497	+	0.310140i
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	−0.686349	−	0.727272i	$-0.740788\pi$
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	0.727272	+	0.686349i	$0.240788\pi$
$420$		0			0
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	0.993087	−	0.117385i	$-0.0374511\pi$
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	−0.117385	+	0.993087i	$0.537451\pi$
$422$	2.77822	+	4.03878i	0.135241	+	0.196605i
$423$		−	29.6940i		−	1.44377i
$424$	10.6170	−	2.56273i	0.515608	−	0.124457i
$425$		0			0
$426$	−8.93512	+	6.14633i	−0.432908	+	0.297791i
$427$	−6.79986	−	6.79986i	−0.329068	−	0.329068i
$428$	−3.17020	−	7.10471i	−0.153237	−	0.343419i
$429$	18.9047	−	18.9047i	0.912726	−	0.912726i
$430$		0			0
$431$	−3.85473			−0.185676			−0.0928380	−	0.995681i	$-0.529594\pi$
$431$	−3.85473			−0.185676			−0.0928380	+	0.995681i	$0.529594\pi$
$432$	0.235912	+	4.36459i	0.0113503	+	0.209991i
$433$	25.5651			1.22858			0.614289	−	0.789081i	$-0.289443\pi$
$433$	25.5651			1.22858			0.614289	+	0.789081i	$0.289443\pi$
$434$	−8.30257	−	1.53527i	−0.398536	−	0.0736954i
$435$		0			0
$436$	17.8425	−	7.96151i	0.854500	−	0.381287i
$437$	−5.69135	−	5.69135i	−0.272254	−	0.272254i
$438$	−34.7817	+	23.9258i	−1.66194	+	1.14322i
$439$		−	30.1311i		−	1.43808i	−0.694970	−	0.719039i	$-0.744582\pi$
$439$		−	30.1311i		−	1.43808i	0.694970	−	0.719039i	$-0.255418\pi$
$440$		0			0
$441$			3.48732i			0.166063i
$442$	25.4819	+	37.0438i	1.21205	+	1.76199i
$443$	−20.1625	−	20.1625i	−0.957948	−	0.957948i	0.0412027	−	0.999151i	$-0.486881\pi$
$443$	−20.1625	−	20.1625i	−0.957948	−	0.957948i	−0.999151	+	0.0412027i	$0.986881\pi$
$444$	−7.32695	−	2.80567i	−0.347722	−	0.133151i
$445$		0			0
$446$	−3.58680	+	19.3970i	−0.169840	+	0.918474i
$447$	−5.33610			−0.252389
$448$	−20.6028	+	10.5616i	−0.973393	+	0.498987i
$449$	−36.5827			−1.72644			−0.863221	−	0.504826i	$-0.831557\pi$
$449$	−36.5827			−1.72644			−0.863221	+	0.504826i	$0.831557\pi$
$450$		0			0
$451$	−8.51265	+	8.51265i	−0.400845	+	0.400845i
$452$	−6.52791	−	2.49969i	−0.307047	−	0.117576i
$453$	4.22161	+	4.22161i	0.198349	+	0.198349i
$454$	5.03136	+	7.31426i	0.236134	+	0.343275i
$455$		0			0
$456$	−9.92493	−	6.06523i	−0.464777	−	0.284031i
$457$			16.7340i			0.782785i	0.920224	+	0.391392i	$0.128006\pi$
$457$			16.7340i			0.782785i	−0.920224	+	0.391392i	$0.871994\pi$
$458$	−8.81679	+	6.06493i	−0.411982	+	0.283396i
$459$	−5.63962	−	5.63962i	−0.263235	−	0.263235i
$460$		0			0
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	−0.375491	−	0.926826i	$-0.622526\pi$
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	0.926826	+	0.375491i	$0.122526\pi$
$462$	−24.7013	−	4.56764i	−1.14921	−	0.212506i
$463$	32.2711			1.49976			0.749882	−	0.661572i	$-0.230110\pi$
$463$	32.2711			1.49976			0.749882	+	0.661572i	$0.230110\pi$
$464$	23.9885	−	1.29661i	1.11364	−	0.0601938i
$465$		0			0
$466$	16.6000	+	3.06960i	0.768982	+	0.142197i
$467$	−1.22565	+	1.22565i	−0.0567163	+	0.0567163i	−0.734896	−	0.678180i	$-0.762769\pi$
$467$	−1.22565	+	1.22565i	−0.0567163	+	0.0567163i	0.678180	+	0.734896i	$0.262769\pi$
$468$	9.00109	+	20.1723i	0.416076	+	0.932464i
$469$	23.8558	+	23.8558i	1.10156	+	1.10156i
$470$		0			0
$471$			34.0734i			1.57002i
$472$	−12.1046	+	2.92180i	−0.557159	+	0.134487i
$473$		−	11.1791i		−	0.514016i
$474$	0.214757	+	0.312200i	0.00986413	+	0.0143398i
$475$		0			0
$476$	15.1071	−	39.4520i	0.692433	−	1.80828i
$477$	−6.92328	+	6.92328i	−0.316995	+	0.316995i
$478$	−4.31292	+	23.3238i	−0.197268	+	1.06680i
$479$	28.8399			1.31773			0.658865	−	0.752261i	$-0.271037\pi$
$479$	28.8399			1.31773			0.658865	+	0.752261i	$0.271037\pi$
$480$		0			0
$481$	7.26282			0.331156
$482$	−5.66486	+	30.6349i	−0.258027	+	1.39538i
$483$	22.1711	−	22.1711i	1.00882	−	1.00882i
$484$	−3.00009	+	7.83468i	−0.136368	+	0.356122i
$485$		0			0
$486$	−16.5649	−	24.0809i	−0.751399	−	1.09233i
$487$		−	32.1668i		−	1.45762i	−0.684718	−	0.728808i	$-0.740075\pi$
$487$		−	32.1668i		−	1.45762i	0.684718	−	0.728808i	$-0.259925\pi$
$488$	2.20527	+	9.13611i	0.0998278	+	0.413572i
$489$			26.7054i			1.20766i
$490$		0			0
$491$	−5.43607	−	5.43607i	−0.245326	−	0.245326i	0.573723	−	0.819049i	$-0.305499\pi$
$491$	−5.43607	−	5.43607i	−0.245326	−	0.245326i	−0.819049	+	0.573723i	$0.805499\pi$
$492$	−8.84870	−	19.8307i	−0.398930	−	0.894039i
$493$	−30.9963	+	30.9963i	−1.39600	+	1.39600i
$494$	10.5878	+	1.95784i	0.476366	+	0.0880873i
$495$		0			0
$496$	6.14144	+	5.51157i	0.275759	+	0.247477i
$497$	−9.43268			−0.423114
$498$	45.1982	+	8.35783i	2.02538	+	0.374524i
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	−0.977535	−	0.210773i	$-0.932402\pi$
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	0.210773	+	0.977535i	$0.432402\pi$
$500$		0			0
$501$	11.3564	+	11.3564i	0.507365	+	0.507365i
$502$	10.9401	−	7.52551i	0.488280	−	0.335880i
$503$			23.5180i			1.04862i	0.851529	+	0.524308i	$0.175676\pi$
$503$			23.5180i			1.04862i	−0.851529	+	0.524308i	$0.824324\pi$
$504$	10.8226	−	17.7097i	0.482078	−	0.788855i
$505$		0			0
$506$	9.62821	+	13.9968i	0.428026	+	0.622235i
$507$	−9.93890	−	9.93890i	−0.441402	−	0.441402i
$508$	11.6801	+	4.47259i	0.518221	+	0.198439i
$509$	20.3147	−	20.3147i	0.900434	−	0.900434i	−0.0950391	−	0.995474i	$-0.530298\pi$
$509$	20.3147	−	20.3147i	0.900434	−	0.900434i	0.995474	+	0.0950391i	$0.0302976\pi$
$510$		0			0
$511$	−36.7186			−1.62434
$512$	22.5641	+	1.69212i	0.997200	+	0.0747820i
$513$	−1.90997			−0.0843271
$514$	1.86645	−	10.0935i	0.0823256	−	0.445207i
$515$		0			0
$516$	18.8314	+	7.21100i	0.829007	+	0.317447i
$517$	21.6025	+	21.6025i	0.950077	+	0.950077i
$518$	−3.86748	−	5.62229i	−0.169928	−	0.247029i
$519$			16.9328i			0.743268i
$520$		0			0
$521$		−	35.5082i		−	1.55564i	−0.628487	−	0.777820i	$-0.716325\pi$
$521$		−	35.5082i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$522$	−17.7434	+	12.2054i	−0.776606	+	0.534215i
$523$	−0.677766	−	0.677766i	−0.0296366	−	0.0296366i	0.692133	−	0.721770i	$-0.256671\pi$
$523$	−0.677766	−	0.677766i	−0.0296366	−	0.0296366i	−0.721770	+	0.692133i	$0.756671\pi$
$524$	13.3407	−	5.95276i	0.582791	−	0.260048i
$525$		0			0
$526$	12.8972	+	2.38489i	0.562345	+	0.103986i
$527$	−15.0572			−0.655904
$528$	18.2716	+	16.3977i	0.795170	+	0.713618i
$529$	1.79485			0.0780371
$530$		0			0
$531$	7.89332	−	7.89332i	0.342541	−	0.342541i
$532$	−4.12243	−	9.23874i	−0.178730	−	0.400550i
$533$	14.2142	+	14.2142i	0.615686	+	0.615686i
$534$	−10.2690	+	7.06386i	−0.444382	+	0.305683i
$535$		0			0
$536$	−7.73667	−	32.0519i	−0.334173	−	1.38443i
$537$		−	5.45007i		−	0.235188i
$538$	15.2108	+	22.1124i	0.655784	+	0.953334i
$539$	−2.53704	−	2.53704i	−0.109278	−	0.109278i
$540$		0			0
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	−0.582158	−	0.813075i	$-0.697792\pi$
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	0.813075	+	0.582158i	$0.197792\pi$
$542$	5.81157	−	31.4283i	0.249628	−	1.34996i
$543$	−55.8181			−2.39539
$544$	−32.7044	+	25.2016i	−1.40219	+	1.08051i
$545$		0			0
$546$	−7.62693	+	41.2456i	−0.326403	+	1.76515i
$547$	−8.86782	+	8.86782i	−0.379161	+	0.379161i	−0.870799	−	0.491639i	$-0.836398\pi$
$547$	−8.86782	+	8.86782i	−0.379161	+	0.379161i	0.491639	+	0.870799i	$0.336398\pi$
$548$	13.5466	−	35.3767i	0.578682	−	1.51122i
$549$	−5.95760	−	5.95760i	−0.254264	−	0.254264i
$550$		0			0
$551$			10.4975i			0.447209i
$552$	−29.7885	+	7.19034i	−1.26788	+	0.306041i
$553$			0.329585i			0.0140154i
$554$	−26.6966	+	18.3641i	−1.13423	+	0.780218i
$555$		0			0
$556$	−3.21625	−	7.20791i	−0.136399	−	0.305684i
$557$	22.8089	−	22.8089i	0.966446	−	0.966446i	−0.0330091	−	0.999455i	$-0.510509\pi$
$557$	22.8089	−	22.8089i	0.966446	−	0.966446i	0.999455	+	0.0330091i	$0.0105090\pi$
$558$	−7.27417	−	1.34510i	−0.307940	−	0.0569428i
$559$	−18.6666			−0.789513
$560$		0			0
$561$	−44.7973			−1.89135
$562$	−12.3043	−	2.27525i	−0.519024	−	0.0959755i
$563$	−20.9711	+	20.9711i	−0.883826	+	0.883826i	−0.993921	−	0.110095i	$-0.964884\pi$
$563$	−20.9711	+	20.9711i	−0.883826	+	0.883826i	0.110095	+	0.993921i	$0.464884\pi$
$564$	−50.3244	+	22.4553i	−2.11904	+	0.945538i
$565$		0			0
$566$	33.4603	−	23.0168i	1.40644	−	0.967469i
$567$		−	29.4543i		−	1.23696i
$568$	7.86630	+	4.80719i	0.330063	+	0.201705i
$569$		−	8.05295i		−	0.337597i	−0.985651	−	0.168799i	$-0.946011\pi$
$569$		−	8.05295i		−	0.337597i	0.985651	−	0.168799i	$-0.0539888\pi$
$570$		0			0
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	0.0566333	−	0.998395i	$-0.481963\pi$
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	−0.998395	+	0.0566333i	$0.981963\pi$
$572$	−21.2237	−	8.12708i	−0.887409	−	0.339810i
$573$	9.74599	−	9.74599i	0.407144	−	0.407144i
$574$	3.43436	−	18.5726i	0.143347	−	0.775206i
$575$		0			0
$576$	−18.0509	+	9.25334i	−0.752119	+	0.385556i
$577$	−15.9819			−0.665334			−0.332667	−	0.943044i	$-0.607949\pi$
$577$	−15.9819			−0.665334			−0.332667	+	0.943044i	$0.607949\pi$
$578$	9.32730	−	50.4410i	0.387965	−	2.09807i
$579$	0.0401200	−	0.0401200i	0.00166733	−	0.00166733i
$580$		0			0
$581$	28.2692	+	28.2692i	1.17280	+	1.17280i
$582$	−26.3727	−	38.3388i	−1.09318	−	1.58919i
$583$		−	10.0734i		−	0.417199i
$584$	30.6212	+	18.7129i	1.26711	+	0.774347i
$585$		0			0
$586$	11.8136	−	8.12638i	0.488015	−	0.335698i
$587$	5.25752	+	5.25752i	0.217001	+	0.217001i	0.807233	−	0.590232i	$-0.200964\pi$
$587$	5.25752	+	5.25752i	0.217001	+	0.217001i	−0.590232	+	0.807233i	$0.700964\pi$
$588$	5.91018	−	2.63719i	0.243732	−	0.108756i
$589$	−2.54971	+	2.54971i	−0.105059	+	0.105059i
$590$		0			0
$591$	−49.6057			−2.04050
$592$	0.359964	+	6.65965i	0.0147944	+	0.273710i
$593$	−3.96571			−0.162852			−0.0814260	−	0.996679i	$-0.525947\pi$
$593$	−3.96571			−0.162852			−0.0814260	+	0.996679i	$0.525947\pi$
$594$	3.96418	+	0.733038i	0.162652	+	0.0300769i
$595$		0			0
$596$	1.84835	+	4.14233i	0.0757115	+	0.169676i
$597$	22.7132	+	22.7132i	0.929589	+	0.929589i
$598$	23.3716	−	16.0769i	0.955734	−	0.657435i
$599$			8.31600i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$599$			8.31600i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$600$		0			0
$601$		−	46.0550i		−	1.87862i	−0.343068	−	0.939310i	$-0.611466\pi$
$601$		−	46.0550i		−	1.87862i	0.343068	−	0.939310i	$-0.388534\pi$
$602$	9.94004	+	14.4502i	0.405126	+	0.588944i
$603$	20.9009	+	20.9009i	0.851149	+	0.851149i
$604$	1.81486	−	4.73948i	0.0738456	−	0.192847i
$605$		0			0
$606$	3.01374	−	16.2980i	0.122425	−	0.662060i
$607$	5.05760			0.205282			0.102641	−	0.994718i	$-0.467271\pi$
$607$	5.05760			0.205282			0.102641	+	0.994718i	$0.467271\pi$
$608$	−1.27048	+	9.80549i	−0.0515249	+	0.397665i
$609$	−40.8940			−1.65711
$610$		0			0
$611$	36.0713	−	36.0713i	1.45929	−	1.45929i
$612$	13.2359	−	34.5652i	0.535028	−	1.39722i
$613$	−31.2000	−	31.2000i	−1.26016	−	1.26016i	−0.951016	−	0.309141i	$-0.899958\pi$
$613$	−31.2000	−	31.2000i	−1.26016	−	1.26016i	−0.309141	−	0.951016i	$-0.600042\pi$
$614$	−20.8911	−	30.3701i	−0.843096	−	1.22564i
$615$		0			0
$616$	5.01041	+	20.7574i	0.201875	+	0.836339i
$617$		−	30.7412i		−	1.23759i	−0.785551	−	0.618796i	$-0.787621\pi$
$617$		−	30.7412i		−	1.23759i	0.785551	−	0.618796i	$-0.212379\pi$
$618$	−0.411798	+	0.283269i	−0.0165649	+	0.0113948i
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	0.281293	−	0.959622i	$-0.409237\pi$
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	−0.959622	+	0.281293i	$0.909237\pi$
$620$		0			0
$621$	−3.55813	+	3.55813i	−0.142783	+	0.142783i
$622$	9.85908	+	1.82309i	0.395313	+	0.0730994i
$623$	−10.8408			−0.434328
$624$	27.3804	−	30.5095i	1.09609	−	1.22136i
$625$		0			0
$626$	−30.6603	−	5.66956i	−1.22543	−	0.226601i
$627$	−7.58574	+	7.58574i	−0.302945	+	0.302945i
$628$	26.4506	−	11.8026i	1.05550	−	0.470974i
$629$	−8.60515	−	8.60515i	−0.343110	−	0.343110i
$630$		0			0
$631$			30.7318i			1.22342i	0.791084	+	0.611708i	$0.209517\pi$
$631$			30.7318i			1.22342i	−0.791084	+	0.611708i	$0.790483\pi$
$632$	0.167967	−	0.274855i	0.00668136	−	0.0109331i
$633$			8.15539i			0.324147i
$634$	−7.02389	−	10.2109i	−0.278954	−	0.405525i
$635$		0			0
$636$	16.9689	+	6.49779i	0.672860	+	0.257654i
$637$	−4.23628	+	4.23628i	−0.167848	+	0.167848i
$638$	4.02890	−	21.7878i	0.159506	−	0.862588i
$639$	−8.26430			−0.326931
$640$		0			0
$641$	22.1658			0.875496			0.437748	−	0.899098i	$-0.355776\pi$
$641$	22.1658			0.875496			0.437748	+	0.899098i	$0.355776\pi$
$642$	2.35349	−	12.7274i	0.0928848	−	0.502310i
$643$	−0.975773	+	0.975773i	−0.0384807	+	0.0384807i	−0.726085	−	0.687605i	$-0.758662\pi$
$643$	−0.975773	+	0.975773i	−0.0384807	+	0.0384807i	0.687605	+	0.726085i	$0.258662\pi$
$644$	−24.8909	−	9.53133i	−0.980839	−	0.375587i
$645$		0			0
$646$	−10.2249	−	14.8643i	−0.402294	−	0.584828i
$647$			23.2610i			0.914484i	0.889342	+	0.457242i	$0.151163\pi$
$647$			23.2610i			0.914484i	−0.889342	+	0.457242i	$0.848837\pi$
$648$	−15.0108	+	24.5632i	−0.589681	+	0.964932i
$649$			11.4848i			0.450819i
$650$		0			0
$651$	−9.93263	−	9.93263i	−0.389290	−	0.389290i
$652$	20.7310	−	9.25038i	0.811887	−	0.362273i
$653$	23.9372	−	23.9372i	0.936735	−	0.936735i	−0.0613792	−	0.998115i	$-0.519550\pi$
$653$	23.9372	−	23.9372i	0.936735	−	0.936735i	0.998115	+	0.0613792i	$0.0195499\pi$
$654$	31.9631	+	5.91046i	1.24985	+	0.231117i
$655$		0			0
$656$	−12.3292	+	13.7382i	−0.481376	+	0.536387i
$657$	−32.1704			−1.25509
$658$	−47.1316	−	8.71535i	−1.83738	−	0.339760i
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	−0.926299	−	0.376790i	$-0.877028\pi$
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	0.376790	+	0.926299i	$0.377028\pi$
$660$		0			0
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	0.645484	−	0.763774i	$-0.276656\pi$
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	−0.763774	+	0.645484i	$0.776656\pi$
$662$	−30.6775	+	21.1026i	−1.19232	+	0.820175i
$663$			74.8014i			2.90505i
$664$	−9.16800	−	37.9817i	−0.355787	−	1.47398i
$665$		0			0
$666$	−3.38844	−	4.92588i	−0.131299	−	0.190874i
$667$	19.5561	+	19.5561i	0.757215	+	0.757215i
$668$	4.88207	−	12.7495i	0.188893	−	0.493291i
$669$	−23.2052	+	23.2052i	−0.897166	+	0.897166i
$670$		0			0
$671$	8.66835			0.334638
$672$	−38.1981	−	4.94928i	−1.47353	−	0.190923i
$673$	25.3628			0.977662			0.488831	−	0.872378i	$-0.337423\pi$
$673$	25.3628			0.977662			0.488831	+	0.872378i	$0.337423\pi$
$674$	−3.66637	+	19.8273i	−0.141223	+	0.763719i
$675$		0			0
$676$	−4.27271	+	11.1581i	−0.164335	+	0.429159i
$677$	−9.36526	−	9.36526i	−0.359936	−	0.359936i	0.503853	−	0.863789i	$-0.331915\pi$
$677$	−9.36526	−	9.36526i	−0.359936	−	0.359936i	−0.863789	+	0.503853i	$0.831915\pi$
$678$	−6.59080	−	9.58126i	−0.253118	−	0.367966i
$679$		−	40.4737i		−	1.55324i
$680$		0			0
$681$			14.7695i			0.565967i
$682$	6.27056	−	4.31342i	0.240112	−	0.165169i
$683$	−4.20530	−	4.20530i	−0.160911	−	0.160911i	0.622059	−	0.782970i	$-0.286296\pi$
$683$	−4.20530	−	4.20530i	−0.160911	−	0.160911i	−0.782970	+	0.622059i	$0.786296\pi$
$684$	−3.61180	−	8.09438i	−0.138101	−	0.309496i
$685$		0			0
$686$	−22.6365	−	4.18584i	−0.864267	−	0.159816i
$687$	−17.8035			−0.679245
$688$	−0.925163	−	17.1163i	−0.0352715	−	0.652554i
$689$	−16.8204			−0.640804
$690$		0			0
$691$	5.79295	−	5.79295i	0.220374	−	0.220374i	−0.588282	−	0.808656i	$-0.700195\pi$
$691$	5.79295	−	5.79295i	0.220374	−	0.220374i	0.808656	+	0.588282i	$0.200195\pi$
$692$	13.1447	−	5.86530i	0.499686	−	0.222965i
$693$	−13.5358	−	13.5358i	−0.514181	−	0.514181i
$694$	38.7881	−	26.6817i	1.47238	−	1.01282i
$695$		0			0
$696$	34.1032	+	20.8408i	1.29268	+	0.789969i
$697$		−	33.6826i		−	1.27582i
$698$	1.77598	+	2.58179i	0.0672217	+	0.0977223i
$699$	19.8592	+	19.8592i	0.751142	+	0.751142i
$700$		0			0
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	−0.711981	−	0.702199i	$-0.752202\pi$
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	0.702199	+	0.711981i	$0.252202\pi$
$702$	1.22401	−	6.61929i	0.0461972	−	0.249829i
$703$	−2.91430			−0.109915
$704$	6.40023	−	19.8639i	0.241218	−	0.748649i
$705$		0			0
$706$	−2.42924	+	13.1370i	−0.0914257	+	0.494419i
$707$	10.1936	−	10.1936i	0.383368	−	0.383368i
$708$	−19.3464	−	7.40821i	−0.727083	−	0.278418i
$709$	−0.751674	−	0.751674i	−0.0282297	−	0.0282297i	0.692851	−	0.721081i	$-0.256354\pi$
$709$	−0.751674	−	0.751674i	−0.0282297	−	0.0282297i	−0.721081	+	0.692851i	$0.756354\pi$
$710$		0			0
$711$			0.288761i			0.0108294i
$712$	9.04060	+	5.52481i	0.338811	+	0.207051i
$713$			9.49986i			0.355773i
$714$	57.9052	−	39.8321i	2.16705	−	1.49068i
$715$		0			0
$716$	−4.23081	+	1.88783i	−0.158113	+	0.0705516i
$717$	−27.9029	+	27.9029i	−1.04205	+	1.04205i
$718$	−25.0944	−	4.64034i	−0.936515	−	0.173176i
$719$	39.6557			1.47891			0.739455	−	0.673206i	$-0.235083\pi$
$719$	39.6557			1.47891			0.739455	+	0.673206i	$0.235083\pi$
$720$		0			0
$721$	−0.434730			−0.0161902
$722$	22.1736	+	4.10025i	0.825218	+	0.152595i
$723$	−36.6495	+	36.6495i	−1.36301	+	1.36301i
$724$	19.3347	+	43.3308i	0.718567	+	1.61037i
$725$		0			0
$726$	−11.4993	+	7.91016i	−0.426778	+	0.293574i
$727$		−	22.2952i		−	0.826881i	−0.910531	−	0.413441i	$-0.864327\pi$
$727$		−	22.2952i		−	0.826881i	0.910531	−	0.413441i	$-0.135673\pi$
$728$	34.6602	−	8.36625i	1.28459	−	0.310074i
$729$		−	18.0930i		−	0.670112i
$730$		0			0
$731$	22.1166	+	22.1166i	0.818011	+	0.818011i
$732$	−5.59145	+	14.6020i	−0.206666	+	0.539705i
$733$	−28.2309	+	28.2309i	−1.04273	+	1.04273i	−0.0436851	+	0.999045i	$0.513910\pi$
$733$	−28.2309	+	28.2309i	−1.04273	+	1.04273i	−0.999045	+	0.0436851i	$0.986090\pi$
$734$	−7.49154	+	40.5134i	−0.276518	+	1.49538i
$735$		0			0
$736$	15.9001	+	20.6337i	0.586086	+	0.760570i
$737$	−30.4109			−1.12020
$738$	3.00896	−	16.2721i	0.110761	−	0.598985i
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	−0.800228	−	0.599695i	$-0.795288\pi$
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	0.599695	+	0.800228i	$0.295288\pi$
$740$		0			0
$741$	12.6665	+	12.6665i	0.465314	+	0.465314i
$742$	8.95691	+	13.0210i	0.328819	+	0.478014i
$743$		−	52.5667i		−	1.92849i	−0.265020	−	0.964243i	$-0.585379\pi$
$743$		−	52.5667i		−	1.92849i	0.265020	−	0.964243i	$-0.414621\pi$
$744$	3.22126	+	13.3452i	0.118097	+	0.489259i
$745$		0			0
$746$	−5.52994	+	3.80396i	−0.202466	+	0.139273i
$747$	24.7676	+	24.7676i	0.906200	+	0.906200i
$748$	15.5172	+	34.7755i	0.567365	+	1.27152i
$749$	7.96035	−	7.96035i	0.290865	−	0.290865i
$750$		0			0
$751$	31.0189			1.13190			0.565948	−	0.824441i	$-0.308510\pi$
$751$	31.0189			1.13190			0.565948	+	0.824441i	$0.308510\pi$
$752$	34.8634	+	31.2878i	1.27134	+	1.14095i
$753$	22.0910			0.805040
$754$	−36.3807	−	6.72735i	−1.32491	−	0.244996i
$755$		0			0
$756$	−5.77590	+	2.57727i	−0.210068	+	0.0937345i
$757$	2.47389	+	2.47389i	0.0899152	+	0.0899152i	0.750634	−	0.660719i	$-0.229748\pi$
$757$	2.47389	+	2.47389i	0.0899152	+	0.0899152i	−0.660719	+	0.750634i	$0.729748\pi$
$758$	19.1979	−	13.2059i	0.697300	−	0.479662i
$759$			28.2634i			1.02590i
$760$		0			0
$761$		−	2.48375i		−	0.0900358i	−0.998986	−	0.0450179i	$-0.985666\pi$
$761$		−	2.48375i		−	0.0900358i	0.998986	−	0.0450179i	$-0.0143345\pi$
$762$	11.7926	+	17.1433i	0.427202	+	0.621037i
$763$	19.9913	+	19.9913i	0.723733	+	0.723733i
$764$	−10.9415	−	4.18978i	−0.395851	−	0.151581i
$765$		0			0
$766$	5.60701	−	30.3221i	0.202590	−	1.09558i
$767$	19.1771			0.692444
$768$	29.3327	+	23.5944i	1.05845	+	0.851388i
$769$	43.4690			1.56753			0.783767	−	0.621055i	$-0.213296\pi$
$769$	43.4690			1.56753			0.783767	+	0.621055i	$0.213296\pi$
$770$		0			0
$771$	12.0752	−	12.0752i	0.434879	−	0.434879i
$772$	−0.0450416	−	0.0172475i	−0.00162108	−	0.000620752i
$773$	−0.297026	−	0.297026i	−0.0106833	−	0.0106833i	0.701745	−	0.712428i	$-0.252405\pi$
$773$	−0.297026	−	0.297026i	−0.0106833	−	0.0106833i	−0.712428	+	0.701745i	$0.752405\pi$
$774$	8.70881	+	12.6603i	0.313032	+	0.455064i
$775$		0			0
$776$	−20.6267	+	33.7527i	−0.740454	+	1.21165i
$777$		−	11.3529i		−	0.407283i
$778$	−19.5920	+	13.4771i	−0.702409	+	0.483176i
$779$	−5.70363	−	5.70363i	−0.204354	−	0.204354i
$780$		0			0
$781$	6.01231	−	6.01231i	0.215137	−	0.215137i
$782$	−46.7394	−	8.64283i	−1.67140	−	0.309067i
$783$	6.56286			0.234537
$784$	−4.09442	−	3.67450i	−0.146229	−	0.131232i
$785$		0			0
$786$	23.8985	+	4.41920i	0.852433	+	0.157628i
$787$	23.6931	−	23.6931i	0.844567	−	0.844567i	−0.144882	−	0.989449i	$-0.546280\pi$
$787$	23.6931	−	23.6931i	0.844567	−	0.844567i	0.989449	+	0.144882i	$0.0462802\pi$
$788$	17.1827	+	38.5081i	0.612110	+	1.37179i
$789$	15.4293	+	15.4293i	0.549299	+	0.549299i
$790$		0			0
$791$		−	10.1148i		−	0.359641i
$792$	4.38979	+	18.1863i	0.155984	+	0.646221i
$793$		−	14.4742i		−	0.513993i
$794$	−10.4723	−	15.2240i	−0.371650	−	0.540279i
$795$		0			0
$796$	9.76435	−	25.4994i	0.346088	−	0.903804i
$797$	−38.2292	+	38.2292i	−1.35415	+	1.35415i	−0.473186	+	0.880963i	$0.656896\pi$
$797$	−38.2292	+	38.2292i	−1.35415	+	1.35415i	−0.880963	+	0.473186i	$0.843104\pi$
$798$	3.06040	−	16.5503i	0.108337	−	0.585874i
$799$	−85.4762			−3.02393
$800$		0			0
$801$	−9.49801			−0.335596
$802$	−3.72210	+	20.1287i	−0.131432	+	0.710768i
$803$	23.4041	−	23.4041i	0.825913	−	0.825913i
$804$	19.6163	−	51.2277i	0.691814	−	1.80666i
$805$		0			0
$806$	−7.20243	−	10.4704i	−0.253695	−	0.368804i
$807$			44.6509i			1.57179i
$808$	−13.6958	+	3.30588i	−0.481816	+	0.116300i
$809$			53.8310i			1.89260i	0.323296	+	0.946298i	$0.395209\pi$
$809$			53.8310i			1.89260i	−0.323296	+	0.946298i	$0.604791\pi$
$810$		0			0
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	0.998809	−	0.0487847i	$-0.0155348\pi$
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	−0.0487847	+	0.998809i	$0.515535\pi$
$812$	14.1651	+	31.7454i	0.497098	+	1.11404i
$813$	37.5986	−	37.5986i	1.31864	−	1.31864i
$814$	6.04870	+	1.11850i	0.212007	+	0.0392033i
$815$		0			0
$816$	−68.5892	+	3.70735i	−2.40110	+	0.129783i
$817$	7.49020			0.262049
$818$	−13.2683	−	2.45351i	−0.463916	−	0.0857851i
$819$	−22.6017	+	22.6017i	−0.789766	+	0.789766i
$820$		0			0
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	0.144347	−	0.989527i	$-0.453892\pi$
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	−0.989527	+	0.144347i	$0.953892\pi$
$822$	51.9238	−	35.7175i	1.81105	−	1.24579i
$823$			41.3013i			1.43967i	0.694144	+	0.719836i	$0.255783\pi$
$823$			41.3013i			1.43967i	−0.694144	+	0.719836i	$0.744217\pi$
$824$	0.362539	+	0.221552i	0.0126296	+	0.00771812i
$825$		0			0
$826$	−10.2119	−	14.8453i	−0.355317	−	0.516535i
$827$	−15.7264	−	15.7264i	−0.546862	−	0.546862i	0.378670	−	0.925532i	$-0.376382\pi$
$827$	−15.7264	−	15.7264i	−0.546862	−	0.546862i	−0.925532	+	0.378670i	$0.876382\pi$
$828$	−21.8078	−	8.35072i	−0.757873	−	0.290208i
$829$	−20.7323	+	20.7323i	−0.720061	+	0.720061i	−0.968618	−	0.248556i	$-0.920044\pi$
$829$	−20.7323	+	20.7323i	−0.720061	+	0.720061i	0.248556	+	0.968618i	$0.420044\pi$
$830$		0			0
$831$	−53.9075			−1.87003
$832$	−33.1682	−	10.6869i	−1.14990	−	0.370503i
$833$	10.0385			0.347813
$834$	2.38767	−	12.9123i	0.0826784	−	0.447115i
$835$		0			0
$836$	8.51629	+	3.26109i	0.294542	+	0.112787i
$837$	1.59404	+	1.59404i	0.0550980	+	0.0550980i
$838$	−0.949485	−	1.38030i	−0.0327994	−	0.0476816i
$839$			43.6919i			1.50841i	0.656638	+	0.754206i	$0.271978\pi$
$839$			43.6919i			1.50841i	−0.656638	+	0.754206i	$0.728022\pi$
$840$		0			0
$841$		−	7.07060i		−	0.243814i
$842$	29.6073	−	20.3664i	1.02033	−	0.701872i
$843$	−14.7200	−	14.7200i	−0.506983	−	0.506983i
$844$	6.33090	−	2.82492i	0.217919	−	0.0972377i
$845$		0			0
$846$	−41.2936	−	7.63582i	−1.41970	−	0.262525i
$847$	−12.1396			−0.417122
$848$	−0.833659	−	15.4234i	−0.0286280	−	0.529643i
$849$	67.5654			2.31884
$850$		0			0
$851$	−5.42913	+	5.42913i	−0.186108	+	0.186108i
$852$	6.24965	+	14.0060i	0.214109	+	0.479839i
$853$	35.0610	+	35.0610i	1.20046	+	1.20046i	0.974025	+	0.226439i	$0.0727084\pi$
$853$	35.0610	+	35.0610i	1.20046	+	1.20046i	0.226439	+	0.974025i	$0.427292\pi$
$854$	−11.2047	+	7.70756i	−0.383418	+	0.263747i
$855$		0			0
$856$	−10.6953	+	2.58162i	−0.365558	+	0.0882381i
$857$			45.3397i			1.54878i	0.632711	+	0.774388i	$0.281942\pi$
$857$			45.3397i			1.54878i	−0.632711	+	0.774388i	$0.718058\pi$
$858$	−21.4282	−	31.1509i	−0.731547	−	1.06347i
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.994871	+	0.101147i	$0.0322514\pi$
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.101147	+	0.994871i	$0.467749\pi$
$860$		0			0
$861$	22.2190	−	22.2190i	0.757221	−	0.757221i
$862$	−0.991245	+	5.36054i	−0.0337619	+	0.182581i
$863$	−36.9142			−1.25657			−0.628287	−	0.777981i	$-0.716244\pi$
$863$	−36.9142			−1.25657			−0.628287	+	0.777981i	$0.716244\pi$
$864$	6.13022	+	0.794285i	0.208554	+	0.0270221i
$865$		0			0
$866$	6.57406	−	35.5517i	0.223396	−	1.20810i
$867$	60.3441	−	60.3441i	2.04939	−	2.04939i
$868$	−4.27002	+	11.1511i	−0.144934	+	0.378492i
$869$	−0.210075	−	0.210075i	−0.00712630	−	0.00712630i
$870$		0			0
$871$			50.7793i			1.72059i
$872$	−6.48338	−	26.8597i	−0.219555	−	0.909585i
$873$		−	35.4604i		−	1.20015i
$874$	−9.37813	+	6.45107i	−0.317220	+	0.218211i
$875$		0			0
$876$	24.3280	+	54.5213i	0.821967	+	1.84210i
$877$	15.7178	−	15.7178i	0.530753	−	0.530753i	−0.390044	−	0.920796i	$-0.627540\pi$
$877$	15.7178	−	15.7178i	0.530753	−	0.530753i	0.920796	+	0.390044i	$0.127540\pi$
$878$	−41.9014	−	7.74821i	−1.41410	−	0.261490i
$879$	23.8548			0.804603
$880$		0			0
$881$	1.16748			0.0393335			0.0196667	−	0.999807i	$-0.493739\pi$
$881$	1.16748			0.0393335			0.0196667	+	0.999807i	$0.493739\pi$
$882$	4.84960	+	0.896765i	0.163294	+	0.0301956i
$883$	−32.2410	+	32.2410i	−1.08500	+	1.08500i	−0.0889621	+	0.996035i	$0.528355\pi$
$883$	−32.2410	+	32.2410i	−1.08500	+	1.08500i	−0.996035	+	0.0889621i	$0.971645\pi$
$884$	58.0672	−	25.9102i	1.95301	−	0.871455i
$885$		0			0
$886$	−33.2235	+	22.8539i	−1.11616	+	0.767792i
$887$			42.7282i			1.43467i	0.696728	+	0.717336i	$0.254639\pi$
$887$			42.7282i			1.43467i	−0.696728	+	0.717336i	$0.745361\pi$
$888$	−5.78579	+	9.46766i	−0.194159	+	0.317714i
$889$			18.0980i			0.606987i
$890$		0			0
$891$	18.7739	+	18.7739i	0.628949	+	0.628949i
$892$	26.0518	+	9.97588i	0.872280	+	0.334017i
$893$	−14.4741	+	14.4741i	−0.484356	+	0.484356i
$894$	−1.37218	+	7.42058i	−0.0458925	+	0.248181i
$895$		0			0
$896$	9.38928	+	31.3670i	0.313674	+	1.04790i
$897$	47.1935			1.57574
$898$	−9.40724	+	50.8732i	−0.313924	+	1.69766i
$899$	8.76109	−	8.76109i	0.292199	−	0.292199i
$900$		0			0
$901$	19.9291	+	19.9291i	0.663935	+	0.663935i
$902$	9.64899	+	14.0270i	0.321276	+	0.467050i
$903$			29.1788i			0.971008i
$904$	−5.15482	+	8.43516i	−0.171447	+	0.280549i
$905$		0			0
$906$	6.95632	−	4.78514i	0.231108	−	0.158976i
$907$	−1.23335	−	1.23335i	−0.0409528	−	0.0409528i	0.686334	−	0.727287i	$-0.259219\pi$
$907$	−1.23335	−	1.23335i	−0.0409528	−	0.0409528i	−0.727287	+	0.686334i	$0.759219\pi$
$908$	11.4653	−	5.11594i	0.380489	−	0.169779i
$909$	8.93093	−	8.93093i	0.296220	−	0.296220i
$910$		0			0
$911$	23.9284			0.792785			0.396392	−	0.918081i	$-0.370262\pi$
$911$	23.9284			0.792785			0.396392	+	0.918081i	$0.370262\pi$
$912$	−10.9867	+	12.2423i	−0.363807	+	0.405383i
$913$	−36.0371			−1.19265
$914$	23.2710	+	4.30316i	0.769735	+	0.142336i
$915$		0			0
$916$	6.16689	+	13.8206i	0.203760	+	0.456644i
$917$	14.9473	+	14.9473i	0.493605	+	0.493605i
$918$	−9.29291	+	6.39245i	−0.306712	+	0.210982i
$919$		−	45.3844i		−	1.49709i	−0.663082	−	0.748546i	$-0.730752\pi$
$919$		−	45.3844i		−	1.49709i	0.663082	−	0.748546i	$-0.269248\pi$
$920$		0			0
$921$		−	61.3253i		−	2.02074i
$922$	−13.4179	−	19.5060i	−0.441893	−	0.642395i
$923$	−10.0392	−	10.0392i	−0.330444	−	0.330444i
$924$	−12.7039	+	33.1760i	−0.417927	+	1.09141i
$925$		0			0
$926$	8.29851	−	44.8774i	0.272706	−	1.47476i
$927$	−0.380882			−0.0125098
$928$	4.36553	−	33.6927i	0.143305	−	1.10602i
$929$	−6.51036			−0.213598			−0.106799	−	0.994281i	$-0.534060\pi$
$929$	−6.51036			−0.213598			−0.106799	+	0.994281i	$0.534060\pi$
$930$		0			0
$931$	1.69986	−	1.69986i	0.0557107	−	0.0557107i
$932$	8.53741	−	22.2953i	0.279652	−	0.730307i
$933$	11.7947	+	11.7947i	0.386142	+	0.386142i
$934$	1.38926	+	2.01961i	0.0454579	+	0.0660837i
$935$		0			0
$936$	30.3670	−	7.32996i	0.992575	−	0.239587i
$937$			40.2986i			1.31650i	0.752801	+	0.658248i	$0.228702\pi$
$937$			40.2986i			1.31650i	−0.752801	+	0.658248i	$0.771298\pi$
$938$	39.3092	−	27.0402i	1.28349	−	0.882894i
$939$	−36.6799	−	36.6799i	−1.19700	−	1.19700i
$940$		0			0
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	−0.688841	−	0.724912i	$-0.741880\pi$
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	0.724912	+	0.688841i	$0.241880\pi$
$942$	47.3837	+	8.76198i	1.54385	+	0.285481i
$943$	−21.2509			−0.692025
$944$	0.950465	+	17.5844i	0.0309350	+	0.572325i
$945$		0			0
$946$	−15.5461	−	2.87471i	−0.505447	−	0.0934649i
$947$	8.83833	−	8.83833i	0.287207	−	0.287207i	−0.548768	−	0.835975i	$-0.684903\pi$
$947$	8.83833	−	8.83833i	0.287207	−	0.287207i	0.835975	+	0.548768i	$0.184903\pi$
$948$	0.489382	−	0.218368i	0.0158944	−	0.00709225i
$949$	−39.0796	−	39.0796i	−1.26858	−	1.26858i
$950$		0			0
$951$		−	20.6185i		−	0.668600i
$952$	−50.9786	−	31.1536i	−1.65223	−	1.00969i
$953$		−	14.9610i		−	0.484636i	−0.970197	−	0.242318i	$-0.922092\pi$
$953$		−	14.9610i		−	0.484636i	0.970197	−	0.242318i	$-0.0779077\pi$
$954$	7.84746	+	11.4081i	0.254071	+	0.369351i
$955$		0			0
$956$	31.3258	+	11.9954i	1.01315	+	0.387959i
$957$	26.0654	−	26.0654i	0.842576	−	0.842576i
$958$	7.41620	−	40.1059i	0.239606	−	1.29576i
$959$	54.8152			1.77008
$960$		0			0
$961$	−26.7441			−0.862712
$962$	1.86764	−	10.1000i	0.0602150	−	0.325636i
$963$	6.97433	−	6.97433i	0.224745	−	0.224745i
$964$	41.1453	+	15.7555i	1.32520	+	0.507452i
$965$		0			0
$966$	−25.1307	−	36.5333i	−0.808568	−	1.17544i
$967$			3.95287i			0.127116i	0.997978	+	0.0635578i	$0.0202447\pi$
$967$			3.95287i			0.127116i	−0.997978	+	0.0635578i	$0.979755\pi$
$968$	10.1237	+	6.18672i	0.325389	+	0.198849i
$969$		−	30.0150i		−	0.964221i
$970$		0			0
$971$	−29.0538	−	29.0538i	−0.932380	−	0.932380i	0.0654740	−	0.997854i	$-0.479144\pi$
$971$	−29.0538	−	29.0538i	−0.932380	−	0.932380i	−0.997854	+	0.0654740i	$0.979144\pi$
$972$	−37.7475	+	16.8434i	−1.21075	+	0.540251i
$973$	8.07597	−	8.07597i	0.258904	−	0.258904i
$974$	−44.7323	−	8.27169i	−1.43332	−	0.265042i
$975$		0			0
$976$	13.2721	−	0.717377i	0.424830	−	0.0229627i
$977$	−25.8962			−0.828494			−0.414247	−	0.910164i	$-0.635955\pi$
$977$	−25.8962			−0.828494			−0.414247	+	0.910164i	$0.635955\pi$
$978$	37.1375	+	6.86729i	1.18753	+	0.219592i
$979$	6.90984	−	6.90984i	0.220839	−	0.220839i
$980$		0			0
$981$	17.5151	+	17.5151i	0.559213	+	0.559213i
$982$	−8.95749	+	6.16172i	−0.285845	+	0.196628i
$983$		−	22.0151i		−	0.702173i	−0.936343	−	0.351087i	$-0.885812\pi$
$983$		−	22.0151i		−	0.702173i	0.936343	−	0.351087i	$-0.114188\pi$
$984$	−29.8528	+	7.20585i	−0.951673	+	0.229714i
$985$		0			0
$986$	35.1340	+	51.0754i	1.11889	+	1.62657i
$987$	−56.3850	−	56.3850i	−1.79476	−	1.79476i
$988$	5.44529	−	14.2203i	0.173238	−	0.452407i
$989$	13.9537	−	13.9537i	0.443702	−	0.443702i
$990$		0			0
$991$	−54.3207			−1.72556			−0.862778	−	0.505583i	$-0.831277\pi$
$991$	−54.3207			−1.72556			−0.862778	+	0.505583i	$0.831277\pi$
$992$	9.24388	−	7.12321i	0.293493	−	0.226162i
$993$	−61.9461			−1.96580
$994$	−2.42562	+	13.1174i	−0.0769359	+	0.416060i
$995$		0			0
$996$	23.2454	−	60.7051i	0.736560	−	1.92351i
$997$	−8.14405	−	8.14405i	−0.257925	−	0.257925i	0.566285	−	0.824210i	$-0.308380\pi$
$997$	−8.14405	−	8.14405i	−0.257925	−	0.257925i	−0.824210	+	0.566285i	$0.808380\pi$
$998$	19.4146	+	28.2236i	0.614557	+	0.893402i
$999$			1.82197i			0.0576446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.h.101.5		16
4.3	odd	2		1600.2.l.i.1201.2		16
5.2	odd	4		400.2.q.h.149.7		16
5.3	odd	4		400.2.q.g.149.2		16
5.4	even	2		80.2.l.a.21.4	✓	16
15.14	odd	2		720.2.t.c.181.5		16
16.3	odd	4		1600.2.l.i.401.2		16
16.13	even	4	inner	400.2.l.h.301.5		16
20.3	even	4		1600.2.q.h.49.2		16
20.7	even	4		1600.2.q.g.49.7		16
20.19	odd	2		320.2.l.a.241.7		16
40.19	odd	2		640.2.l.a.481.2		16
40.29	even	2		640.2.l.b.481.7		16
60.59	even	2		2880.2.t.c.2161.6		16
80.3	even	4		1600.2.q.g.849.7		16
80.13	odd	4		400.2.q.h.349.7		16
80.19	odd	4		320.2.l.a.81.7		16
80.29	even	4		80.2.l.a.61.4	yes	16
80.59	odd	4		640.2.l.a.161.2		16
80.67	even	4		1600.2.q.h.849.2		16
80.69	even	4		640.2.l.b.161.7		16
80.77	odd	4		400.2.q.g.349.2		16
160.19	odd	8		5120.2.a.u.1.1		8
160.29	even	8		5120.2.a.v.1.1		8
160.99	odd	8		5120.2.a.t.1.8		8
160.109	even	8		5120.2.a.s.1.8		8
240.29	odd	4		720.2.t.c.541.5		16
240.179	even	4		2880.2.t.c.721.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	5.4	even	2
80.2.l.a.61.4	yes	16	80.29	even	4
320.2.l.a.81.7		16	80.19	odd	4
320.2.l.a.241.7		16	20.19	odd	2
400.2.l.h.101.5		16	1.1	even	1	trivial
400.2.l.h.301.5		16	16.13	even	4	inner
400.2.q.g.149.2		16	5.3	odd	4
400.2.q.g.349.2		16	80.77	odd	4
400.2.q.h.149.7		16	5.2	odd	4
400.2.q.h.349.7		16	80.13	odd	4
640.2.l.a.161.2		16	80.59	odd	4
640.2.l.a.481.2		16	40.19	odd	2
640.2.l.b.161.7		16	80.69	even	4
640.2.l.b.481.7		16	40.29	even	2
720.2.t.c.181.5		16	15.14	odd	2
720.2.t.c.541.5		16	240.29	odd	4
1600.2.l.i.401.2		16	16.3	odd	4
1600.2.l.i.1201.2		16	4.3	odd	2
1600.2.q.g.49.7		16	20.7	even	4
1600.2.q.g.849.7		16	80.3	even	4
1600.2.q.h.49.2		16	20.3	even	4
1600.2.q.h.849.2		16	80.67	even	4
2880.2.t.c.721.7		16	240.179	even	4
2880.2.t.c.2161.6		16	60.59	even	2
5120.2.a.s.1.8		8	160.109	even	8
5120.2.a.t.1.8		8	160.99	odd	8
5120.2.a.u.1.1		8	160.19	odd	8
5120.2.a.v.1.1		8	160.29	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.257150 - 1.39064i) q^{2} +(1.66366 - 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-1.88574 - 2.74137i) q^{6} -2.89402i q^{7} +(-1.47488 + 2.41345i) q^{8} -2.53555i q^{9} +(1.84462 + 1.84462i) q^{11} +(-4.29717 + 1.91744i) q^{12} +(3.08011 - 3.08011i) q^{13} +(-4.02454 - 0.744198i) q^{14} +(2.97696 + 2.67165i) q^{16} -7.29875 q^{17} +(-3.52604 - 0.652018i) q^{18} +(-1.23593 + 1.23593i) q^{19} +(-4.81468 - 4.81468i) q^{21} +(3.03955 - 2.09086i) q^{22} +4.60490i q^{23} +(1.56145 + 6.46887i) q^{24} +(-3.49126 - 5.07536i) q^{26} +(0.772683 + 0.772683i) q^{27} +(-2.06982 + 5.40530i) q^{28} +(4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(4.48082 - 3.45286i) q^{32} +6.13767 q^{33} +(-1.87688 + 10.1499i) q^{34} +(-1.81344 + 4.73577i) q^{36} +(1.17899 + 1.17899i) q^{37} +(1.40091 + 2.03655i) q^{38} -10.2485i q^{39} +4.61484i q^{41} +(-7.93357 + 5.45738i) q^{42} +(-3.03019 - 3.03019i) q^{43} +(-2.12601 - 4.76458i) q^{44} +(6.40375 + 1.18415i) q^{46} +11.7111 q^{47} +(9.39739 - 0.507943i) q^{48} -1.37537 q^{49} +(-12.1427 + 12.1427i) q^{51} +(-7.95577 + 3.54995i) q^{52} +(-2.73048 - 2.73048i) q^{53} +(1.27322 - 0.875827i) q^{54} +(6.98457 + 4.26835i) q^{56} +4.11235i q^{57} +(-4.81369 - 6.99782i) q^{58} +(3.11306 + 3.11306i) q^{59} +(2.34962 - 2.34962i) q^{61} +(0.530498 - 2.86887i) q^{62} -7.33795 q^{63} +(-3.64944 - 7.11910i) q^{64} +(1.57830 - 8.53528i) q^{66} +(-8.24311 + 8.24311i) q^{67} +(13.6322 + 5.22011i) q^{68} +(7.66101 + 7.66101i) q^{69} -3.25937i q^{71} +(6.11942 + 3.73965i) q^{72} -12.6877i q^{73} +(1.94272 - 1.33637i) q^{74} +(3.19235 - 1.42446i) q^{76} +(5.33839 - 5.33839i) q^{77} +(-14.2520 - 2.63541i) q^{78} -0.113885 q^{79} +10.1776 q^{81} +(6.41758 + 1.18671i) q^{82} +(-9.76813 + 9.76813i) q^{83} +(5.54912 + 12.4361i) q^{84} +(-4.99310 + 3.43468i) q^{86} -14.1305i q^{87} +(-7.17251 + 1.73129i) q^{88} -3.74593i q^{89} +(-8.91390 - 8.91390i) q^{91} +(3.29345 - 8.60080i) q^{92} +(3.43212 - 3.43212i) q^{93} +(3.01150 - 16.2858i) q^{94} +(1.71017 - 13.1990i) q^{96} +13.9853 q^{97} +(-0.353676 + 1.91264i) q^{98} +(4.67714 - 4.67714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more