LMFDB - Embedded newform 700.2.t.c.199.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(199,700)] 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("700.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,2,0,0,0,0,16,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	700.199
Dual form			700.2.t.c.299.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.942109 + 1.05472i) q^{2} +(-0.780530 - 0.450639i) q^{3} +(-0.224860 - 1.98732i) q^{4} +(1.21064 - 0.398687i) q^{6} +(1.30833 + 2.29962i) q^{7} +(2.30790 + 1.63511i) q^{8} +(-1.09385 - 1.89460i) q^{9} +(-3.24107 - 1.87123i) q^{11} +(-0.720054 + 1.65249i) q^{12} -2.41990 q^{13} +(-3.65805 - 0.786573i) q^{14} +(-3.89888 + 0.893735i) q^{16} +(0.291859 - 0.505515i) q^{17} +(3.02880 + 0.631220i) q^{18} +(3.07977 + 5.33433i) q^{19} +(0.0151060 - 2.38451i) q^{21} +(5.02706 - 1.65551i) q^{22} +(2.15605 + 3.73439i) q^{23} +(-1.06454 - 2.31628i) q^{24} +(2.27981 - 2.55232i) q^{26} +4.67556i q^{27} +(4.27589 - 3.11717i) q^{28} +0.435463 q^{29} +(-1.26933 + 2.19854i) q^{31} +(2.73053 - 4.95421i) q^{32} +(1.68650 + 2.92110i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-9.78676 + 5.65039i) q^{37} +(-8.52769 - 1.77723i) q^{38} +(1.88881 + 1.09050i) q^{39} -7.35068i q^{41} +(2.50075 + 2.26240i) q^{42} -5.80096 q^{43} +(-2.98995 + 6.86180i) q^{44} +(-5.96996 - 1.24418i) q^{46} +(-10.0256 + 5.78826i) q^{47} +(3.44594 + 1.05940i) q^{48} +(-3.57652 + 6.01735i) q^{49} +(-0.455610 + 0.263046i) q^{51} +(0.544138 + 4.80912i) q^{52} +(-2.69759 - 1.55746i) q^{53} +(-4.93139 - 4.40489i) q^{54} +(-0.740624 + 7.44657i) q^{56} -5.55147i q^{57} +(-0.410254 + 0.459290i) q^{58} +(1.73534 - 3.00569i) q^{59} +(-8.99597 + 5.19383i) q^{61} +(-1.12299 - 3.41004i) q^{62} +(2.92575 - 4.99421i) q^{63} +(2.65284 + 7.54735i) q^{64} +(-4.66981 - 0.973217i) q^{66} +(-4.92250 + 8.52602i) q^{67} +(-1.07025 - 0.466348i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(0.573383 - 6.16112i) q^{72} +(4.89946 - 8.48612i) q^{73} +(3.26063 - 15.6456i) q^{74} +(9.90849 - 7.31997i) q^{76} +(0.0627260 - 9.90142i) q^{77} +(-2.92964 + 0.964785i) q^{78} +(0.397549 - 0.229525i) q^{79} +(-1.17456 + 2.03439i) q^{81} +(7.75290 + 6.92515i) q^{82} +2.59747i q^{83} +(-4.74218 + 0.506159i) q^{84} +(5.46514 - 6.11837i) q^{86} +(-0.339892 - 0.196236i) q^{87} +(-4.42040 - 9.61812i) q^{88} +(8.55647 - 4.94008i) q^{89} +(-3.16604 - 5.56486i) q^{91} +(6.93662 - 5.12447i) q^{92} +(1.98149 - 1.14402i) q^{93} +(3.34020 - 16.0273i) q^{94} +(-4.36382 + 2.63643i) q^{96} +4.54044 q^{97} +(-2.97713 - 9.44122i) q^{98} +8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.942109	+	1.05472i	−0.666172	+	0.745798i
$2$	−0.942109	+	1.05472i	−0.666172	+	0.745798i
$3$	−0.780530	−	0.450639i	−0.450639	−	0.260177i	0.257461	−	0.966289i	$-0.417114\pi$
$3$	−0.780530	−	0.450639i	−0.450639	−	0.260177i	−0.708100	+	0.706112i	$0.750447\pi$
$4$	−0.224860	−	1.98732i	−0.112430	−	0.993660i
$5$		0			0
$5$		0			0
$6$	1.21064	−	0.398687i	0.494242	−	0.162763i
$7$	1.30833	+	2.29962i	0.494504	+	0.869175i
$7$	1.30833	+	2.29962i	0.494504	+	0.869175i
$8$	2.30790	+	1.63511i	0.815967	+	0.578098i
$9$	−1.09385	−	1.89460i	−0.364616	−	0.631534i
$10$		0			0
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.0757892	−	0.997124i	$-0.524148\pi$
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.901429	+	0.432927i	$0.857481\pi$
$12$	−0.720054	+	1.65249i	−0.207862	+	0.477033i
$13$	−2.41990			−0.671161			−0.335580	−	0.942012i	$-0.608932\pi$
$13$	−2.41990			−0.671161			−0.335580	+	0.942012i	$0.608932\pi$
$14$	−3.65805	−	0.786573i	−0.977654	−	0.210220i
$15$		0			0
$16$	−3.89888	+	0.893735i	−0.974719	+	0.223434i
$17$	0.291859	−	0.505515i	0.0707863	−	0.122605i	−0.828460	−	0.560048i	$-0.810782\pi$
$17$	0.291859	−	0.505515i	0.0707863	−	0.122605i	0.899246	+	0.437443i	$0.144116\pi$
$18$	3.02880	+	0.631220i	0.713894	+	0.148780i
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	0.966130	+	0.258057i	$0.0830822\pi$
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	−0.259581	+	0.965721i	$0.583584\pi$
$20$		0			0
$21$	0.0151060	−	2.38451i	0.00329639	−	0.520343i
$22$	5.02706	−	1.65551i	1.07177	−	0.352955i
$23$	2.15605	+	3.73439i	0.449568	+	0.778674i	0.998358	−	0.0572861i	$-0.0182447\pi$
$23$	2.15605	+	3.73439i	0.449568	+	0.778674i	−0.548790	+	0.835960i	$0.684911\pi$
$24$	−1.06454	−	2.31628i	−0.217299	−	0.472809i
$25$		0			0
$26$	2.27981	−	2.55232i	0.447108	−	0.500550i
$27$			4.67556i			0.899812i
$28$	4.27589	−	3.11717i	0.808068	−	0.589090i
$29$	0.435463			0.0808634			0.0404317	−	0.999182i	$-0.487127\pi$
$29$	0.435463			0.0808634			0.0404317	+	0.999182i	$0.487127\pi$
$30$		0			0
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	−0.957209	−	0.289399i	$-0.906545\pi$
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	0.729231	+	0.684268i	$0.239878\pi$
$32$	2.73053	−	4.95421i	0.482694	−	0.875789i
$33$	1.68650	+	2.92110i	0.293582	+	0.508499i
$34$	0.258212	+	0.784080i	0.0442831	+	0.134469i
$35$		0			0
$36$	−3.51922	+	2.59985i	−0.586536	+	0.433308i
$37$	−9.78676	+	5.65039i	−1.60893	+	0.928918i	−0.619324	+	0.785136i	$0.712593\pi$
$37$	−9.78676	+	5.65039i	−1.60893	+	0.928918i	−0.989609	+	0.143782i	$0.954073\pi$
$38$	−8.52769	−	1.77723i	−1.38337	−	0.288304i
$39$	1.88881	+	1.09050i	0.302451	+	0.174620i
$40$		0			0
$41$		−	7.35068i		−	1.14798i	−0.818861	−	0.573992i	$-0.805394\pi$
$41$		−	7.35068i		−	1.14798i	0.818861	−	0.573992i	$-0.194606\pi$
$42$	2.50075	+	2.26240i	0.385875	+	0.349096i
$43$	−5.80096			−0.884637			−0.442319	−	0.896858i	$-0.645844\pi$
$43$	−5.80096			−0.884637			−0.442319	+	0.896858i	$0.645844\pi$
$44$	−2.98995	+	6.86180i	−0.450752	+	1.03446i
$45$		0			0
$46$	−5.96996	−	1.24418i	−0.880223	−	0.183444i
$47$	−10.0256	+	5.78826i	−1.46238	+	0.844305i	−0.999121	−	0.0419181i	$-0.986653\pi$
$47$	−10.0256	+	5.78826i	−1.46238	+	0.844305i	−0.463258	+	0.886223i	$0.653320\pi$
$48$	3.44594	+	1.05940i	0.497379	+	0.152911i
$49$	−3.57652	+	6.01735i	−0.510932	+	0.859621i
$50$		0			0
$51$	−0.455610	+	0.263046i	−0.0637981	+	0.0368339i
$52$	0.544138	+	4.80912i	0.0754584	+	0.666905i
$53$	−2.69759	−	1.55746i	−0.370543	−	0.213933i	0.303153	−	0.952942i	$-0.401961\pi$
$53$	−2.69759	−	1.55746i	−0.370543	−	0.213933i	−0.673696	+	0.739009i	$0.735294\pi$
$54$	−4.93139	−	4.40489i	−0.671078	−	0.599429i
$55$		0			0
$56$	−0.740624	+	7.44657i	−0.0989701	+	0.995090i
$57$		−	5.55147i		−	0.735310i
$58$	−0.410254	+	0.459290i	−0.0538689	+	0.0603078i
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	−0.730674	−	0.682727i	$-0.760794\pi$
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	0.956596	+	0.291419i	$0.0941273\pi$
$60$		0			0
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.949329	−	0.314284i	$-0.898236\pi$
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.202487	+	0.979285i	$0.564902\pi$
$62$	−1.12299	−	3.41004i	−0.142620	−	0.433076i
$63$	2.92575	−	4.99421i	0.368610	−	0.629211i
$64$	2.65284	+	7.54735i	0.331605	+	0.943418i
$65$		0			0
$66$	−4.66981	−	0.973217i	−0.574813	−	0.119795i
$67$	−4.92250	+	8.52602i	−0.601379	+	1.04162i	0.391234	+	0.920291i	$0.372048\pi$
$67$	−4.92250	+	8.52602i	−0.601379	+	1.04162i	−0.992613	+	0.121327i	$0.961285\pi$
$68$	−1.07025	−	0.466348i	−0.129787	−	0.0565530i
$69$		−	3.88640i		−	0.467868i
$70$		0			0
$71$			9.96771i			1.18295i	0.806324	+	0.591475i	$0.201454\pi$
$71$			9.96771i			1.18295i	−0.806324	+	0.591475i	$0.798546\pi$
$72$	0.573383	−	6.16112i	0.0675738	−	0.726095i
$73$	4.89946	−	8.48612i	0.573439	−	0.993225i	−0.422771	−	0.906237i	$-0.638942\pi$
$73$	4.89946	−	8.48612i	0.573439	−	0.993225i	0.996209	−	0.0869881i	$-0.0277242\pi$
$74$	3.26063	−	15.6456i	0.379041	−	1.81876i
$75$		0			0
$76$	9.90849	−	7.31997i	1.13658	−	0.839658i
$77$	0.0627260	−	9.90142i	0.00714829	−	1.12837i
$78$	−2.92964	+	0.964785i	−0.331716	+	0.109240i
$79$	0.397549	−	0.229525i	0.0447278	−	0.0258236i	−0.477469	−	0.878648i	$-0.658446\pi$
$79$	0.397549	−	0.229525i	0.0447278	−	0.0258236i	0.522197	+	0.852825i	$0.325113\pi$
$80$		0			0
$81$	−1.17456	+	2.03439i	−0.130506	+	0.226044i
$82$	7.75290	+	6.92515i	0.856164	+	0.764755i
$83$			2.59747i			0.285109i	0.989787	+	0.142554i	$0.0455316\pi$
$83$			2.59747i			0.285109i	−0.989787	+	0.142554i	$0.954468\pi$
$84$	−4.74218	+	0.506159i	−0.517414	+	0.0552265i
$85$		0			0
$86$	5.46514	−	6.11837i	0.589321	−	0.659761i
$87$	−0.339892	−	0.196236i	−0.0364402	−	0.0210388i
$88$	−4.42040	−	9.61812i	−0.471217	−	1.02529i
$89$	8.55647	−	4.94008i	0.906984	−	0.523648i	0.0275247	−	0.999621i	$-0.491237\pi$
$89$	8.55647	−	4.94008i	0.906984	−	0.523648i	0.879460	+	0.475973i	$0.157904\pi$
$90$		0			0
$91$	−3.16604	−	5.56486i	−0.331891	−	0.583356i
$92$	6.93662	−	5.12447i	0.723192	−	0.534263i
$93$	1.98149	−	1.14402i	0.205471	−	0.118629i
$94$	3.34020	−	16.0273i	0.344515	−	1.65309i
$95$		0			0
$96$	−4.36382	+	2.63643i	−0.445381	+	0.269079i
$97$	4.54044			0.461011			0.230506	−	0.973071i	$-0.425962\pi$
$97$	4.54044			0.461011			0.230506	+	0.973071i	$0.425962\pi$
$98$	−2.97713	−	9.44122i	−0.300735	−	0.953708i
$99$			8.18738i			0.822862i
$100$		0			0
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	0.839258	−	0.543734i	$-0.182990\pi$
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	−0.0512584	+	0.998685i	$0.516323\pi$
$102$	0.151795	−	0.728358i	0.0150299	−	0.0721182i
$103$	−8.86113	+	5.11597i	−0.873113	+	0.504092i	−0.868381	−	0.495897i	$-0.834839\pi$
$103$	−8.86113	+	5.11597i	−0.873113	+	0.504092i	−0.00473128	+	0.999989i	$0.501506\pi$
$104$	−5.58490	−	3.95681i	−0.547645	−	0.387997i
$105$		0			0
$106$	4.18410	−	1.37790i	0.406396	−	0.133834i
$107$	−3.16601	−	5.48368i	−0.306069	−	0.530128i	0.671430	−	0.741068i	$-0.265681\pi$
$107$	−3.16601	−	5.48368i	−0.306069	−	0.530128i	−0.977499	+	0.210941i	$0.932347\pi$
$108$	9.29183	−	1.05134i	0.894107	−	0.101166i
$109$	−9.38027	+	16.2471i	−0.898467	+	1.55619i	−0.0690134	+	0.997616i	$0.521985\pi$
$109$	−9.38027	+	16.2471i	−0.898467	+	1.55619i	−0.829454	+	0.558575i	$0.811348\pi$
$110$		0			0
$111$	10.1851			0.966731
$112$	−7.15629	−	7.79664i	−0.676205	−	0.736713i
$113$		−	4.17847i		−	0.393077i	−0.980496	−	0.196539i	$-0.937030\pi$
$113$		−	4.17847i		−	0.393077i	0.980496	−	0.196539i	$-0.0629701\pi$
$114$	5.85523	+	5.23009i	0.548393	+	0.489843i
$115$		0			0
$116$	−0.0979179	−	0.865403i	−0.00909145	−	0.0803507i
$117$	2.64701	+	4.58475i	0.244716	+	0.423861i
$118$	1.53528	+	4.66198i	0.141334	+	0.429170i
$119$	1.54434	+	0.00978348i	0.141570	+	0.000896851i
$120$		0			0
$121$	1.50301	+	2.60329i	0.136637	+	0.236663i
$122$	2.99717	−	14.3814i	0.271351	−	1.30203i
$123$	−3.31250	+	5.73743i	−0.298678	+	0.517326i
$124$	4.65461	+	2.02819i	0.417997	+	0.182137i
$125$		0			0
$126$	2.51111	+	7.79093i	0.223707	+	0.694072i
$127$	4.91036			0.435724			0.217862	−	0.975980i	$-0.430092\pi$
$127$	4.91036			0.435724			0.217862	+	0.975980i	$0.430092\pi$
$128$	−10.4596	−	4.31243i	−0.924505	−	0.381169i
$129$	4.52782	+	2.61414i	0.398652	+	0.230162i
$130$		0			0
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	−0.970691	−	0.240332i	$-0.922744\pi$
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	0.277212	−	0.960809i	$-0.410590\pi$
$132$	5.42594	−	4.00845i	0.472267	−	0.348891i
$133$	−8.23756	+	14.0614i	−0.714287	+	1.21928i
$134$	−4.35501	−	13.2243i	−0.376216	−	1.14240i
$135$		0			0
$136$	1.50016	−	0.689459i	0.128637	−	0.0591206i
$137$	6.79155	+	3.92110i	0.580241	+	0.335002i	0.761229	−	0.648483i	$-0.224596\pi$
$137$	6.79155	+	3.92110i	0.580241	+	0.335002i	−0.180988	+	0.983485i	$0.557930\pi$
$138$	4.09906	+	3.66142i	0.348935	+	0.311680i
$139$	17.4044			1.47623			0.738113	−	0.674677i	$-0.235717\pi$
$139$	17.4044			1.47623			0.738113	+	0.674677i	$0.235717\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	−10.5131	−	9.39067i	−0.882242	−	0.788048i
$143$	7.84307	+	4.52820i	0.655871	+	0.378667i
$144$	5.95805	+	6.40921i	0.496505	+	0.534101i
$145$		0			0
$146$	4.33463	+	13.1624i	0.358736	+	1.08933i
$147$	5.50324	−	3.08500i	0.453899	−	0.254446i
$148$	13.4298	+	18.1789i	1.10392	+	1.49429i
$149$	0.825776	+	1.43029i	0.0676502	+	0.117174i	0.897867	−	0.440268i	$-0.145116\pi$
$149$	0.825776	+	1.43029i	0.0676502	+	0.117174i	−0.830216	+	0.557441i	$0.811783\pi$
$150$		0			0
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	0.736293	−	0.676663i	$-0.236575\pi$
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	−0.217861	+	0.975980i	$0.569908\pi$
$152$	−1.61438	+	17.3469i	−0.130944	+	1.40702i
$153$	−1.27700			−0.103239
$154$	10.3841	+	9.39438i	0.836776	+	0.757021i
$155$		0			0
$156$	1.74246	−	3.99887i	0.139509	−	0.320166i
$157$	1.54125	−	2.66953i	0.123005	−	0.213052i	−0.797946	−	0.602729i	$-0.794080\pi$
$157$	1.54125	−	2.66953i	0.123005	−	0.213052i	0.920952	+	0.389677i	$0.127413\pi$
$158$	−0.132451	+	0.635540i	−0.0105372	+	0.0505609i
$159$	1.40370	+	2.43128i	0.111321	+	0.192813i
$160$		0			0
$161$	−5.76685	+	9.84393i	−0.454491	+	0.775810i
$162$	−1.03915	−	3.15545i	−0.0816433	−	0.247915i
$163$	−2.25908	−	3.91284i	−0.176945	−	0.306477i	0.763888	−	0.645349i	$-0.223288\pi$
$163$	−2.25908	−	3.91284i	−0.176945	−	0.306477i	−0.940833	+	0.338872i	$0.889955\pi$
$164$	−14.6082	+	1.65287i	−1.14071	+	0.129068i
$165$		0			0
$166$	−2.73959	−	2.44710i	−0.212634	−	0.189932i
$167$		−	16.9358i		−	1.31053i	−0.755398	−	0.655266i	$-0.772556\pi$
$167$		−	16.9358i		−	1.31053i	0.755398	−	0.655266i	$-0.227444\pi$
$168$	3.93380	−	5.47852i	0.303499	−	0.422677i
$169$	−7.14406			−0.549543
$170$		0			0
$171$	6.73762	−	11.6699i	0.515238	−	0.892419i
$172$	1.30440	+	11.5284i	0.0994596	+	0.879029i
$173$	−0.0663486	−	0.114919i	−0.00504439	−	0.00873715i	0.863492	−	0.504362i	$-0.168272\pi$
$173$	−0.0663486	−	0.114919i	−0.00504439	−	0.00873715i	−0.868537	+	0.495625i	$0.834939\pi$
$174$	0.527189	−	0.173613i	0.0399661	−	0.0131616i
$175$		0			0
$176$	14.3089	+	4.39904i	1.07857	+	0.331590i
$177$	−2.70897	+	1.56402i	−0.203618	+	0.117559i
$178$	−2.85074	+	13.6788i	−0.213672	+	1.02527i
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.121664	−	0.992571i	$-0.538823\pi$
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.920424	+	0.390921i	$0.872157\pi$
$180$		0			0
$181$		−	3.99317i		−	0.296810i	−0.988927	−	0.148405i	$-0.952586\pi$
$181$		−	3.99317i		−	0.296810i	0.988927	−	0.148405i	$-0.0474139\pi$
$182$	8.85212	+	1.90343i	0.656163	+	0.141092i
$183$	9.36216			0.692071
$184$	−1.13018	+	12.1440i	−0.0833177	+	0.895267i
$185$		0			0
$186$	−0.660170	+	3.16770i	−0.0484060	+	0.232267i
$187$	−1.89187	+	1.09227i	−0.138347	+	0.0798749i
$188$	13.7575	+	18.6225i	1.00337	+	1.35818i
$189$	−10.7520	+	6.11719i	−0.782094	+	0.444960i
$190$		0			0
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.284030	−	0.958815i	$-0.408329\pi$
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.972373	+	0.233431i	$0.0749953\pi$
$192$	1.33051	−	7.08640i	0.0960214	−	0.511417i
$193$	16.7482	+	9.66959i	1.20556	+	0.696032i	0.961787	−	0.273799i	$-0.0882805\pi$
$193$	16.7482	+	9.66959i	1.20556	+	0.696032i	0.243776	+	0.969832i	$0.421614\pi$
$194$	−4.27759	+	4.78888i	−0.307113	+	0.343821i
$195$		0			0
$196$	12.7626	+	5.75464i	0.911615	+	0.411046i
$197$		−	1.63738i		−	0.116659i	−0.998297	−	0.0583293i	$-0.981423\pi$
$197$		−	1.63738i		−	0.116659i	0.998297	−	0.0583293i	$-0.0185773\pi$
$198$	−8.63537	−	7.71340i	−0.613689	−	0.548168i
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	−0.879573	−	0.475765i	$-0.842171\pi$
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	0.851811	+	0.523850i	$0.175505\pi$
$200$		0			0
$201$	7.68431	−	4.43654i	0.542009	−	0.312929i
$202$	−12.2832	+	4.04510i	−0.864245	+	0.284612i
$203$	0.569731	+	1.00140i	0.0399873	+	0.0702845i
$204$	0.625205	+	0.846294i	0.0437731	+	0.0592524i
$205$		0			0
$206$	2.95224	−	14.1658i	0.205692	−	0.986978i
$207$	4.71679	−	8.16972i	0.327839	−	0.567835i
$208$	9.43491	−	2.16275i	0.654193	−	0.149960i
$209$		−	23.0519i		−	1.59453i
$210$		0			0
$211$			9.22534i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$211$			9.22534i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$212$	−2.48858	+	5.71118i	−0.170916	+	0.392246i
$213$	4.49184	−	7.78009i	0.307776	−	0.533083i
$214$	8.76646	+	1.82699i	0.599263	+	0.124890i
$215$		0			0
$216$	−7.64505	+	10.7907i	−0.520180	+	0.734217i
$217$	−6.71651	−	0.0425494i	−0.455946	−	0.00288844i
$218$	−8.29887	−	25.2001i	−0.562071	−	1.70677i
$219$	−7.64835	+	4.41578i	−0.516828	+	0.298391i
$220$		0			0
$221$	−0.706272	+	1.22330i	−0.0475090	+	0.0822880i
$222$	−9.59552	+	10.7425i	−0.644009	+	0.720986i
$223$		−	24.2380i		−	1.62310i	−0.584284	−	0.811550i	$-0.698624\pi$
$223$		−	24.2380i		−	1.62310i	0.584284	−	0.811550i	$-0.301376\pi$
$224$	14.9653	−	0.202576i	0.999908	−	0.0135352i
$225$		0			0
$226$	4.40710	+	3.93657i	0.293156	+	0.261857i
$227$	9.20798	+	5.31623i	0.611155	+	0.352851i	0.773417	−	0.633897i	$-0.218546\pi$
$227$	9.20798	+	5.31623i	0.611155	+	0.352851i	−0.162262	+	0.986748i	$0.551879\pi$
$228$	−11.0325	+	1.24830i	−0.730648	+	0.0826707i
$229$	25.5589	−	14.7564i	1.68898	−	0.975132i	0.733676	−	0.679499i	$-0.237803\pi$
$229$	25.5589	−	14.7564i	1.68898	−	0.975132i	0.955302	−	0.295633i	$-0.0955304\pi$
$230$		0			0
$231$	−4.51093	+	7.70009i	−0.296797	+	0.506629i
$232$	1.00501	+	0.712029i	0.0659819	+	0.0467470i
$233$	−24.3096	+	14.0351i	−1.59257	+	0.919472i	−0.599709	+	0.800218i	$0.704717\pi$
$233$	−24.3096	+	14.0351i	−1.59257	+	0.919472i	−0.992864	+	0.119254i	$0.961950\pi$
$234$	−7.32940	−	1.52749i	−0.479138	−	0.0998553i
$235$		0			0
$236$	−6.36348	−	2.77281i	−0.414227	−	0.180495i
$237$	−0.413732			−0.0268748
$238$	−1.46526	+	1.61963i	−0.0949787	+	0.104985i
$239$		−	13.6279i		−	0.881512i	−0.897627	−	0.440756i	$-0.854710\pi$
$239$		−	13.6279i		−	0.881512i	0.897627	−	0.440756i	$-0.145290\pi$
$240$		0			0
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	0.378031	−	0.925793i	$-0.376601\pi$
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	−0.612744	+	0.790281i	$0.709934\pi$
$242$	−4.16174	−	0.867332i	−0.267527	−	0.0557542i
$243$	13.9810	−	8.07194i	0.896882	−	0.517815i
$244$	12.3446	+	16.7100i	0.790283	+	1.06975i
$245$		0			0
$246$	−2.93062	−	8.89904i	−0.186850	−	0.567382i
$247$	−7.45276	−	12.9086i	−0.474208	−	0.821352i
$248$	−6.52433	+	2.99852i	−0.414295	+	0.190406i
$249$	1.17052	−	2.02740i	0.0741787	−	0.128481i
$250$		0			0
$251$	−18.8826			−1.19186			−0.595928	−	0.803038i	$-0.703216\pi$
$251$	−18.8826			−1.19186			−0.595928	+	0.803038i	$0.703216\pi$
$252$	−10.5830	−	4.69140i	−0.666665	−	0.295531i
$253$		−	16.1379i		−	1.01458i
$254$	−4.62610	+	5.17905i	−0.290267	+	0.324962i
$255$		0			0
$256$	14.4025	−	6.96913i	0.900155	−	0.435570i
$257$	12.9173	+	22.3734i	0.805757	+	1.39561i	0.915779	+	0.401682i	$0.131574\pi$
$257$	12.9173	+	22.3734i	0.805757	+	1.39561i	−0.110022	+	0.993929i	$0.535092\pi$
$258$	−7.02288	+	2.31277i	−0.437225	+	0.143987i
$259$	−25.7981	−	15.1133i	−1.60302	−	0.939092i
$260$		0			0
$261$	−0.476330	−	0.825028i	−0.0294841	−	0.0510680i
$262$	21.9777	+	4.58029i	1.35779	+	0.282971i
$263$	−5.34857	+	9.26400i	−0.329807	+	0.571243i	−0.982473	−	0.186403i	$-0.940317\pi$
$263$	−5.34857	+	9.26400i	−0.329807	+	0.571243i	0.652666	+	0.757645i	$0.273650\pi$
$264$	−0.884043	+	9.49923i	−0.0544091	+	0.584637i
$265$		0			0
$266$	−7.07012	−	21.9357i	−0.433497	−	1.34496i
$267$	−8.90478			−0.544963
$268$	18.0508	+	7.86542i	1.10263	+	0.480457i
$269$	7.24441	+	4.18256i	0.441699	+	0.255015i	0.704318	−	0.709884i	$-0.251253\pi$
$269$	7.24441	+	4.18256i	0.441699	+	0.255015i	−0.262619	+	0.964900i	$0.584586\pi$
$270$		0			0
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	0.903100	+	0.429430i	$0.141286\pi$
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	−0.0796525	+	0.996823i	$0.525381\pi$
$272$	−0.686127	+	2.23179i	−0.0416025	+	0.135322i
$273$	−0.0365550	+	5.77028i	−0.00221241	+	0.349234i
$274$	−10.5340	+	3.46906i	−0.636385	+	0.209574i
$275$		0			0
$276$	−7.72352	+	0.873895i	−0.464901	+	0.0526023i
$277$	−2.90970	−	1.67991i	−0.174827	−	0.100936i	0.410033	−	0.912071i	$-0.365517\pi$
$277$	−2.90970	−	1.67991i	−0.174827	−	0.100936i	−0.584860	+	0.811134i	$0.698850\pi$
$278$	−16.3969	+	18.3568i	−0.983420	+	1.10097i
$279$	5.55380			0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	−9.82966	+	11.0046i	−0.585348	+	0.655313i
$283$	6.24027	+	3.60282i	0.370945	+	0.214165i	0.673871	−	0.738849i	$-0.264630\pi$
$283$	6.24027	+	3.60282i	0.370945	+	0.214165i	−0.302926	+	0.953014i	$0.597964\pi$
$284$	19.8090	−	2.24133i	1.17545	−	0.132999i
$285$		0			0
$286$	−12.1650	+	4.00617i	−0.719332	+	0.236890i
$287$	16.9038	−	9.61715i	0.997799	−	0.567682i
$288$	−12.3730	+	0.245892i	−0.729089	+	0.0144893i
$289$	8.32964	+	14.4274i	0.489979	+	0.848668i
$290$		0			0
$291$	−3.54395	−	2.04610i	−0.207750	−	0.119944i
$292$	−17.9663	−	7.82861i	−1.05140	−	0.458135i
$293$	−8.47879			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$293$	−8.47879			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$294$	−1.93085	+	8.71077i	−0.112609	+	0.508022i
$295$		0			0
$296$	−31.8259	−	2.96187i	−1.84984	−	0.172155i
$297$	8.74905	−	15.1538i	0.507671	−	0.879312i
$298$	−2.28652	−	0.476525i	−0.132455	−	0.0276044i
$299$	−5.21744	−	9.03686i	−0.301732	−	0.522615i
$300$		0			0
$301$	−7.58959	−	13.3400i	−0.437457	−	0.768905i
$302$	−9.88112	+	3.25404i	−0.568595	+	0.187249i
$303$	−4.12083	−	7.13749i	−0.236736	−	0.410038i
$304$	−16.7751	−	18.0454i	−0.962120	−	1.03497i
$305$		0			0
$306$	1.20307	−	1.34687i	0.0687752	−	0.0769957i
$307$			10.4271i			0.595104i	0.954706	+	0.297552i	$0.0961701\pi$
$307$			10.4271i			0.595104i	−0.954706	+	0.297552i	$0.903830\pi$
$308$	−19.6914	+	2.10177i	−1.12202	+	0.119760i
$309$	9.22183			0.524612
$310$		0			0
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	−0.956235	−	0.292600i	$-0.905480\pi$
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	0.731516	+	0.681824i	$0.238813\pi$
$312$	2.57609	+	5.60518i	0.145843	+	0.317331i
$313$	−7.23333	−	12.5285i	−0.408852	−	0.708152i	0.585910	−	0.810376i	$-0.300737\pi$
$313$	−7.23333	−	12.5285i	−0.408852	−	0.708152i	−0.994761	+	0.102224i	$0.967404\pi$
$314$	1.36357	+	4.14058i	0.0769507	+	0.233666i
$315$		0			0
$316$	−0.545533	−	0.738447i	−0.0306886	−	0.0415409i
$317$	3.06318	−	1.76853i	0.172046	−	0.0993305i	−0.411504	−	0.911408i	$-0.634997\pi$
$317$	3.06318	−	1.76853i	0.172046	−	0.0993305i	0.583550	+	0.812077i	$0.301663\pi$
$318$	−3.88675	−	0.810024i	−0.217958	−	0.0454239i
$319$	−1.41136	−	0.814851i	−0.0790212	−	0.0456229i
$320$		0			0
$321$			5.70690i			0.318528i
$322$	−4.94957	−	15.3565i	−0.275829	−	0.855782i
$323$	3.59544			0.200056
$324$	4.30710	+	1.87677i	0.239283	+	0.104265i
$325$		0			0
$326$	6.25524	+	1.30363i	0.346446	+	0.0722015i
$327$	14.6432	−	8.45423i	0.809769	−	0.467520i
$328$	12.0192	−	16.9647i	0.663648	−	0.936717i
$329$	−26.4276	−	15.4820i	−1.45700	−	0.853552i
$330$		0			0
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.941411	−	0.337261i	$-0.890499\pi$
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.178629	+	0.983917i	$0.557166\pi$
$332$	5.16199	−	0.584065i	0.283301	−	0.0320547i
$333$	21.4105	+	12.3613i	1.17329	+	0.677397i
$334$	17.8625	+	15.9554i	0.977393	+	0.873040i
$335$		0			0
$336$	2.07222	+	9.31041i	0.113049	+	0.507924i
$337$			5.10057i			0.277846i	0.990303	+	0.138923i	$0.0443640\pi$
$337$			5.10057i			0.277846i	−0.990303	+	0.138923i	$0.955636\pi$
$338$	6.73049	−	7.53497i	0.366090	−	0.409848i
$339$	−1.88298	+	3.26142i	−0.102269	+	0.177136i
$340$		0			0
$341$	8.22794	−	4.75040i	0.445568	−	0.257249i
$342$	5.96087	+	18.1006i	0.322327	+	0.978768i
$343$	−18.5169	−	0.351954i	−0.999819	−	0.0190037i
$344$	−13.3880	−	9.48520i	−0.721835	−	0.511407i
$345$		0			0
$346$	0.183715	+	0.0382874i	0.00987658	+	0.00205834i
$347$	0.833209	−	1.44316i	0.0447290	−	0.0774729i	−0.842794	−	0.538236i	$-0.819091\pi$
$347$	0.833209	−	1.44316i	0.0447290	−	0.0774729i	0.887523	+	0.460763i	$0.152424\pi$
$348$	−0.313557	+	0.719599i	−0.0168084	+	0.0385745i
$349$		−	27.6081i		−	1.47783i	−0.673801	−	0.738913i	$-0.735339\pi$
$349$		−	27.6081i		−	1.47783i	0.673801	−	0.738913i	$-0.264661\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	−18.1203	+	10.9475i	−0.965815	+	0.583503i
$353$	13.5789	−	23.5193i	0.722730	−	1.25180i	−0.237172	−	0.971468i	$-0.576221\pi$
$353$	13.5789	−	23.5193i	0.722730	−	1.25180i	0.959902	−	0.280337i	$-0.0904461\pi$
$354$	0.902540	−	4.33067i	0.0479695	−	0.230173i
$355$		0			0
$356$	−11.7415	−	15.8936i	−0.622300	−	0.842360i
$357$	−1.20100	−	0.703578i	−0.0635635	−	0.0372373i
$358$	21.6251	−	7.12154i	1.14292	−	0.376385i
$359$	−14.5102	+	8.37747i	−0.765819	+	0.442146i	−0.831381	−	0.555703i	$-0.812449\pi$
$359$	−14.5102	+	8.37747i	−0.765819	+	0.442146i	0.0655619	+	0.997849i	$0.479116\pi$
$360$		0			0
$361$	−9.47002	+	16.4026i	−0.498422	+	0.863293i
$362$	4.21166	+	3.76200i	0.221360	+	0.197726i
$363$		−	2.70926i		−	0.142199i
$364$	−10.3472	+	7.54325i	−0.542343	+	0.395374i
$365$		0			0
$366$	−8.82018	+	9.87444i	−0.461038	+	0.516145i
$367$	7.31294	+	4.22213i	0.381732	+	0.220393i	0.678572	−	0.734534i	$-0.262599\pi$
$367$	7.31294	+	4.22213i	0.381732	+	0.220393i	−0.296839	+	0.954927i	$0.595933\pi$
$368$	−11.7437	−	12.6330i	−0.612184	−	0.658540i
$369$	−13.9266	+	8.04054i	−0.724991	+	0.418574i
$370$		0			0
$371$	0.0522078	−	8.24111i	0.00271049	−	0.427857i
$372$	−2.71908	−	3.68062i	−0.140978	−	0.190831i
$373$	8.98694	−	5.18861i	0.465326	−	0.268656i	−0.248955	−	0.968515i	$-0.580087\pi$
$373$	8.98694	−	5.18861i	0.465326	−	0.268656i	0.714281	+	0.699859i	$0.246754\pi$
$374$	0.630311	−	3.02443i	0.0325926	−	0.156390i
$375$		0			0
$376$	−32.6025	−	3.03414i	−1.68134	−	0.156474i
$377$	−1.05378			−0.0542723
$378$	3.67767	−	17.1034i	0.189159	−	0.879704i
$379$		−	11.7976i		−	0.606002i	−0.952990	−	0.303001i	$-0.902011\pi$
$379$		−	11.7976i		−	0.606002i	0.952990	−	0.303001i	$-0.0979886\pi$
$380$		0			0
$381$	−3.83268	−	2.21280i	−0.196354	−	0.113365i
$382$	−5.78507	+	27.7586i	−0.295990	+	1.42025i
$383$	−0.828825	+	0.478522i	−0.0423510	+	0.0244514i	−0.521026	−	0.853541i	$-0.674451\pi$
$383$	−0.828825	+	0.478522i	−0.0423510	+	0.0244514i	0.478675	+	0.877992i	$0.341117\pi$
$384$	6.22067	+	8.07948i	0.317447	+	0.412304i
$385$		0			0
$386$	−25.9773	+	8.55483i	−1.32221	+	0.435430i
$387$	6.34537	+	10.9905i	0.322553	+	0.558679i
$388$	−1.02096	−	9.02330i	−0.0518314	−	0.458088i
$389$	−15.0820	+	26.1228i	−0.764689	+	1.32448i	0.175722	+	0.984440i	$0.443774\pi$
$389$	−15.0820	+	26.1228i	−0.764689	+	1.32448i	−0.940411	+	0.340041i	$0.889559\pi$
$390$		0			0
$391$	2.51705			0.127293
$392$	−18.0933	+	8.03945i	−0.913849	+	0.406054i
$393$			14.3073i			0.721708i
$394$	1.72697	+	1.54259i	0.0870037	+	0.0777147i
$395$		0			0
$396$	16.2709	−	1.84101i	0.817645	−	0.0925142i
$397$	−3.10349	−	5.37540i	−0.155760	−	0.269783i	0.777576	−	0.628789i	$-0.216449\pi$
$397$	−3.10349	−	5.37540i	−0.155760	−	0.269783i	−0.933335	+	0.359006i	$0.883116\pi$
$398$	−0.346483	−	1.05212i	−0.0173676	−	0.0527380i
$399$	12.7663	−	7.26317i	0.639113	−	0.363613i
$400$		0			0
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	−0.981387	−	0.192038i	$-0.938490\pi$
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	0.324384	−	0.945926i	$-0.394843\pi$
$402$	−2.56017	+	12.2845i	−0.127689	+	0.612694i
$403$	3.07165	−	5.32025i	0.153010	−	0.265020i
$404$	7.30571	−	16.7663i	0.363473	−	0.834153i
$405$		0			0
$406$	−1.59294	−	0.342523i	−0.0790564	−	0.0169991i
$407$	42.2927			2.09637
$408$	−1.48161	−	0.137886i	−0.0733508	−	0.00682637i
$409$	15.9374	+	9.20148i	0.788055	+	0.454984i	0.839277	−	0.543703i	$-0.182978\pi$
$409$	15.9374	+	9.20148i	0.788055	+	0.454984i	−0.0512223	+	0.998687i	$0.516312\pi$
$410$		0			0
$411$	−3.53400	−	6.12107i	−0.174320	−	0.301930i
$412$	12.1596	+	16.4595i	0.599060	+	0.810902i
$413$	9.18236	+	0.0581707i	0.451834	+	0.00286239i
$414$	4.17302	+	12.6716i	0.205093	+	0.622777i
$415$		0			0
$416$	−6.60762	+	11.9887i	−0.323965	+	0.587795i
$417$	−13.5847	−	7.84312i	−0.665245	−	0.384079i
$418$	24.3132	+	21.7174i	1.18920	+	1.06223i
$419$	−35.2426			−1.72171			−0.860856	−	0.508848i	$-0.830072\pi$
$419$	−35.2426			−1.72171			−0.860856	+	0.508848i	$0.830072\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−9.73014	−	8.69128i	−0.473656	−	0.423085i
$423$	21.9329	+	12.6630i	1.06641	+	0.615695i
$424$	−3.67917	−	8.00531i	−0.178676	−	0.388772i
$425$		0			0
$426$	3.97400	+	12.0673i	0.192541	+	0.584664i
$427$	−23.7136	−	13.8921i	−1.14758	−	0.672285i
$428$	−10.1859	+	7.52492i	−0.492355	+	0.363731i
$429$	−4.08117	−	7.06879i	−0.197041	−	0.341284i
$430$		0			0
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	0.457589	−	0.889164i	$-0.348713\pi$
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	−0.541244	+	0.840865i	$0.682047\pi$
$432$	−4.17871	−	18.2294i	−0.201048	−	0.877064i
$433$	−13.5978			−0.653469			−0.326734	−	0.945116i	$-0.605948\pi$
$433$	−13.5978			−0.653469			−0.326734	+	0.945116i	$0.605948\pi$
$434$	6.37256	−	7.04393i	0.305893	−	0.338120i
$435$		0			0
$436$	34.3974	+	14.9883i	1.64734	+	0.717809i
$437$	−13.2803	+	23.0022i	−0.635283	+	1.10034i
$438$	2.54818	−	12.2270i	0.121757	−	0.584228i
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	0.970776	+	0.239989i	$0.0771437\pi$
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	−0.277552	+	0.960711i	$0.589523\pi$
$440$		0			0
$441$	15.3127	+	0.194020i	0.729174	+	0.00923907i
$442$	−0.624849	−	1.89740i	−0.0297211	−	0.0902500i
$443$	−7.31831	−	12.6757i	−0.347703	−	0.602240i	0.638138	−	0.769922i	$-0.279705\pi$
$443$	−7.31831	−	12.6757i	−0.347703	−	0.602240i	−0.985841	+	0.167683i	$0.946372\pi$
$444$	−2.29023	−	20.2411i	−0.108689	−	0.960601i
$445$		0			0
$446$	25.5643	+	22.8349i	1.21050	+	1.08126i
$447$		−	1.48851i		−	0.0704040i
$448$	−13.8853	+	15.9750i	−0.656016	+	0.754747i
$449$	27.0699			1.27751			0.638754	−	0.769411i	$-0.279450\pi$
$449$	27.0699			1.27751			0.638754	+	0.769411i	$0.279450\pi$
$450$		0			0
$451$	−13.7548	+	23.8241i	−0.647689	+	1.12183i
$452$	−8.30395	+	0.939568i	−0.390585	+	0.0441936i
$453$	−3.31496	−	5.74168i	−0.155750	−	0.269768i
$454$	−14.2820	+	4.70335i	−0.670290	+	0.220739i
$455$		0			0
$456$	9.07725	−	12.8122i	0.425081	−	0.599989i
$457$	−6.58709	+	3.80306i	−0.308131	+	0.177900i	−0.646090	−	0.763261i	$-0.723597\pi$
$457$	−6.58709	+	3.80306i	−0.308131	+	0.177900i	0.337959	+	0.941161i	$0.390264\pi$
$458$	−8.51539	+	40.8596i	−0.397898	+	1.90924i
$459$	2.36357	+	1.36461i	0.110322	+	0.0636943i
$460$		0			0
$461$		−	12.7953i		−	0.595936i	−0.954576	−	0.297968i	$-0.903691\pi$
$461$		−	12.7953i		−	0.595936i	0.954576	−	0.297968i	$-0.0963089\pi$
$462$	−3.87163	−	12.0121i	−0.180125	−	0.558853i
$463$	−27.9178			−1.29745			−0.648724	−	0.761024i	$-0.724697\pi$
$463$	−27.9178			−1.29745			−0.648724	+	0.761024i	$0.724697\pi$
$464$	−1.69782	+	0.389188i	−0.0788191	+	0.0180676i
$465$		0			0
$466$	8.09917	−	38.8624i	0.375187	−	1.80026i
$467$	−19.5815	+	11.3054i	−0.906126	+	0.523152i	−0.879183	−	0.476485i	$-0.841911\pi$
$467$	−19.5815	+	11.3054i	−0.906126	+	0.523152i	−0.0269432	+	0.999637i	$0.508577\pi$
$468$	8.51617	−	6.29138i	0.393660	−	0.290819i
$469$	−26.0469	−	0.165008i	−1.20273	−	0.00761937i
$470$		0			0
$471$	−2.40599	+	1.38910i	−0.110862	+	0.0640062i
$472$	8.91963	−	4.09938i	0.410559	−	0.188689i
$473$	18.8013	+	10.8549i	0.864484	+	0.499110i
$474$	0.389781	−	0.436371i	0.0179032	−	0.0200432i
$475$		0			0
$476$	−0.327817	−	3.07130i	−0.0150255	−	0.140773i
$477$			6.81448i			0.312014i
$478$	14.3735	+	12.8389i	0.657430	+	0.587239i
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	0.497817	+	0.867282i	$0.334135\pi$
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	−0.999997	+	0.00251901i	$0.999198\pi$
$480$		0			0
$481$	23.6830	−	13.6734i	1.07985	−	0.623453i
$482$	5.65160	−	1.86118i	0.257423	−	0.0847744i
$483$	8.93726	−	5.08471i	0.406659	−	0.231362i
$484$	4.83560	−	3.57234i	0.219800	−	0.162379i
$485$		0			0
$486$	−4.65802	+	22.3507i	−0.211292	+	1.01385i
$487$	12.6914	−	21.9822i	0.575103	−	0.996108i	−0.420927	−	0.907095i	$-0.638295\pi$
$487$	12.6914	−	21.9822i	0.575103	−	0.996108i	0.996030	−	0.0890138i	$-0.0283715\pi$
$488$	−29.2543	−	2.72254i	−1.32428	−	0.123244i
$489$			4.07212i			0.184147i
$490$		0			0
$491$		−	36.4635i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$491$		−	36.4635i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$492$	12.1469	+	5.29289i	0.547627	+	0.238622i
$493$	0.127094	−	0.220133i	0.00572402	−	0.00991429i
$494$	20.6362	+	4.30072i	0.928467	+	0.193498i
$495$		0			0
$496$	2.98403	−	9.70626i	0.133987	−	0.435824i
$497$	−22.9220	+	13.0411i	−1.02819	+	0.584973i
$498$	1.03558	+	3.14460i	0.0464053	+	0.140913i
$499$	10.2874	−	5.93945i	0.460528	−	0.265886i	−0.251738	−	0.967795i	$-0.581002\pi$
$499$	10.2874	−	5.93945i	0.460528	−	0.265886i	0.712266	+	0.701909i	$0.247669\pi$
$500$		0			0
$501$	−7.63194	+	13.2189i	−0.340970	+	0.590577i
$502$	17.7894	−	19.9158i	0.793981	−	0.888884i
$503$			17.3055i			0.771614i	0.922580	+	0.385807i	$0.126077\pi$
$503$			17.3055i			0.771614i	−0.922580	+	0.385807i	$0.873923\pi$
$504$	14.9184	−	6.74224i	0.664520	−	0.300323i
$505$		0			0
$506$	17.0209	+	15.2036i	0.756672	+	0.675884i
$507$	5.57615	+	3.21939i	0.247646	+	0.142978i
$508$	−1.10414	−	9.75846i	−0.0489884	−	0.432962i
$509$	11.8717	−	6.85414i	0.526205	−	0.303805i	−0.213265	−	0.976994i	$-0.568410\pi$
$509$	11.8717	−	6.85414i	0.526205	−	0.303805i	0.739470	+	0.673190i	$0.235076\pi$
$510$		0			0
$511$	25.9250	+	0.164236i	1.14685	+	0.00726537i
$512$	−6.21824	+	21.7562i	−0.274810	+	0.961498i
$513$	−24.9410	+	14.3997i	−1.10117	+	0.635761i
$514$	−35.7671	−	7.45408i	−1.57762	−	0.328785i
$515$		0			0
$516$	4.17700	−	9.58603i	0.183882	−	0.422002i
$517$	43.3247			1.90542
$518$	40.2449	−	12.9714i	1.76826	−	0.569930i
$519$			0.119597i			0.00524973i
$520$		0			0
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.992068	−	0.125704i	$-0.0401190\pi$
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.387171	+	0.922008i	$0.373452\pi$
$522$	1.31893	+	0.274873i	0.0577279	+	0.0120309i
$523$	3.69292	−	2.13211i	0.161480	−	0.0932306i	−0.417082	−	0.908869i	$-0.636947\pi$
$523$	3.69292	−	2.13211i	0.161480	−	0.0932306i	0.578562	+	0.815638i	$0.303614\pi$
$524$	−25.5363	+	18.8651i	−1.11556	+	0.824126i
$525$		0			0
$526$	−4.73196	−	14.3689i	−0.206323	−	0.626515i
$527$	0.740929	+	1.28333i	0.0322754	+	0.0559026i
$528$	−9.18614	−	9.88173i	−0.399776	−	0.430047i
$529$	2.20289	−	3.81552i	0.0957778	−	0.165892i
$530$		0			0
$531$	−7.59279			−0.329499
$532$	29.7968	+	13.2088i	1.29185	+	0.572675i
$533$			17.7879i			0.770482i
$534$	8.38927	−	9.39203i	0.363039	−	0.406433i
$535$		0			0
$536$	−25.3016	+	11.6284i	−1.09286	+	0.502270i
$537$	7.25487	+	12.5658i	0.313071	+	0.542254i
$538$	−11.2364	+	3.70038i	−0.484438	+	0.159535i
$539$	22.8516	−	12.8101i	0.984288	−	0.551771i
$540$		0			0
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	0.928870	−	0.370405i	$-0.120781\pi$
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	−0.785215	+	0.619223i	$0.787448\pi$
$542$	−37.5347	−	7.82248i	−1.61225	−	0.336004i
$543$	−1.79948	+	3.11679i	−0.0772229	+	0.133754i
$544$	−1.70750	−	2.82626i	−0.0732084	−	0.121175i
$545$		0			0
$546$	−6.05158	−	5.47479i	−0.258984	−	0.234300i
$547$	−45.6888			−1.95351			−0.976756	−	0.214353i	$-0.931236\pi$
$547$	−45.6888			−1.95351			−0.976756	+	0.214353i	$0.931236\pi$
$548$	6.26534	−	14.3787i	0.267642	−	0.614226i
$549$	19.6805	+	11.3625i	0.839942	+	0.484941i
$550$		0			0
$551$	1.34113	+	2.32290i	0.0571339	+	0.0989589i
$552$	6.35469	−	8.96944i	0.270474	−	0.381765i
$553$	1.04795	+	0.613918i	0.0445633	+	0.0261064i
$554$	4.51309	−	1.48625i	0.191743	−	0.0631445i
$555$		0			0
$556$	−3.91355	−	34.5882i	−0.165972	−	1.46687i
$557$	−4.22972	−	2.44203i	−0.179219	−	0.103472i	0.407707	−	0.913113i	$-0.366329\pi$
$557$	−4.22972	−	2.44203i	−0.179219	−	0.103472i	−0.586926	+	0.809641i	$0.699662\pi$
$558$	−5.23229	+	5.85769i	−0.221500	+	0.247976i
$559$	14.0378			0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	6.91459	−	7.74107i	0.291674	−	0.326538i
$563$	−2.36931	−	1.36792i	−0.0998543	−	0.0576509i	0.449241	−	0.893410i	$-0.351694\pi$
$563$	−2.36931	−	1.36792i	−0.0998543	−	0.0576509i	−0.549096	+	0.835760i	$0.685028\pi$
$564$	−2.34611	−	20.7350i	−0.0987891	−	0.873103i
$565$		0			0
$566$	−9.67897	+	3.18747i	−0.406838	+	0.133979i
$567$	−6.21505	−	0.0393726i	−0.261008	−	0.00165349i
$568$	−16.2983	+	23.0045i	−0.683861	+	0.965248i
$569$	2.29674	+	3.97807i	0.0962843	+	0.166769i	0.910144	−	0.414292i	$-0.135971\pi$
$569$	2.29674	+	3.97807i	0.0962843	+	0.166769i	−0.813860	+	0.581062i	$0.802638\pi$
$570$		0			0
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	0.394720	−	0.918801i	$-0.370841\pi$
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	−0.598345	+	0.801239i	$0.704175\pi$
$572$	7.23539	−	16.6049i	0.302527	−	0.694286i
$573$	−18.0707			−0.754912
$574$	−5.78185	+	26.8891i	−0.241330	+	1.12233i
$575$		0			0
$576$	11.3974	−	13.2817i	0.474892	−	0.553405i
$577$	17.1731	−	29.7446i	0.714924	−	1.23828i	−0.248065	−	0.968743i	$-0.579795\pi$
$577$	17.1731	−	29.7446i	0.714924	−	1.23828i	0.962989	−	0.269541i	$-0.0868719\pi$
$578$	−23.0642	−	4.80673i	−0.959345	−	0.199934i
$579$	−8.71499	−	15.0948i	−0.362182	−	0.627318i
$580$		0			0
$581$	−5.97319	+	3.39835i	−0.247810	+	0.140987i
$582$	5.49684	−	1.81021i	0.227851	−	0.0750358i
$583$	5.82872	+	10.0956i	0.241401	+	0.418118i
$584$	25.1832	−	11.5740i	1.04209	−	0.478935i
$585$		0			0
$586$	7.98795	−	8.94273i	0.329979	−	0.369421i
$587$			40.1422i			1.65685i	0.560103	+	0.828423i	$0.310762\pi$
$587$			40.1422i			1.65685i	−0.560103	+	0.828423i	$0.689238\pi$
$588$	−7.36833	−	10.2430i	−0.303865	−	0.422414i
$589$	−15.6369			−0.644309
$590$		0			0
$591$	−0.737868	+	1.27802i	−0.0303518	+	0.0525709i
$592$	33.1074	−	30.7769i	1.36071	−	1.26492i
$593$	−5.46684	−	9.46884i	−0.224496	−	0.388839i	0.731672	−	0.681657i	$-0.238740\pi$
$593$	−5.46684	−	9.46884i	−0.224496	−	0.388839i	−0.956168	+	0.292818i	$0.905407\pi$
$594$	7.74042	+	23.5043i	0.317593	+	0.964394i
$595$		0			0
$596$	2.65675	−	1.96269i	0.108825	−	0.0803951i
$597$	0.611361	−	0.352969i	0.0250213	−	0.0144461i
$598$	14.4467	+	3.01079i	0.590771	+	0.123120i
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	0.589388	−	0.807850i	$-0.299369\pi$
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	−0.404924	+	0.914350i	$0.632702\pi$
$600$		0			0
$601$			16.1103i			0.657154i	0.944477	+	0.328577i	$0.106569\pi$
$601$			16.1103i			0.657154i	−0.944477	+	0.328577i	$0.893431\pi$
$602$	21.2202	+	4.56287i	0.864869	+	0.185969i
$603$	21.5379			0.877090
$604$	5.87700	−	13.4875i	0.239132	−	0.548797i
$605$		0			0
$606$	11.4103	+	2.37798i	0.463512	+	0.0965989i
$607$	8.36252	−	4.82810i	0.339424	−	0.195967i	−0.320593	−	0.947217i	$-0.603882\pi$
$607$	8.36252	−	4.82810i	0.339424	−	0.195967i	0.660017	+	0.751250i	$0.270549\pi$
$608$	34.8368	−	0.692317i	1.41282	−	0.0280772i
$609$	0.00657809	−	1.03837i	0.000266558	−	0.0420767i
$610$		0			0
$611$	24.2609	−	14.0070i	0.981491	−	0.566664i
$612$	0.287146	+	2.53781i	0.0116072	+	0.102585i
$613$	6.79635	+	3.92388i	0.274502	+	0.158484i	0.630932	−	0.775838i	$-0.282673\pi$
$613$	6.79635	+	3.92388i	0.274502	+	0.158484i	−0.356430	+	0.934322i	$0.616006\pi$
$614$	−10.9976	−	9.82343i	−0.443827	−	0.396441i
$615$		0			0
$616$	16.3347	−	22.7490i	0.658143	−	0.916582i
$617$		−	28.8434i		−	1.16119i	−0.814191	−	0.580597i	$-0.802819\pi$
$617$		−	28.8434i		−	1.16119i	0.814191	−	0.580597i	$-0.197181\pi$
$618$	−8.68797	+	9.72643i	−0.349481	+	0.391254i
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	−0.839968	−	0.542635i	$-0.817427\pi$
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	0.889920	+	0.456116i	$0.150760\pi$
$620$		0			0
$621$	−17.4604	+	10.0807i	−0.700660	+	0.404526i
$622$	−3.50609	−	10.6465i	−0.140581	−	0.426885i
$623$	22.5550	+	13.2134i	0.903649	+	0.529383i
$624$	−8.33885	−	2.56364i	−0.333821	−	0.102628i
$625$		0			0
$626$	20.0286	+	4.17409i	0.800504	+	0.166830i
$627$	−10.3881	+	17.9927i	−0.414860	+	0.718558i
$628$	−5.65177	−	2.46269i	−0.225530	−	0.0982722i
$629$			6.59647i			0.263019i
$630$		0			0
$631$			8.90728i			0.354593i	0.984157	+	0.177297i	$0.0567352\pi$
$631$			8.90728i			0.354593i	−0.984157	+	0.177297i	$0.943265\pi$
$632$	1.29280	+	0.120314i	0.0514250	+	0.00478585i
$633$	4.15730	−	7.20066i	0.165238	−	0.286200i
$634$	−1.02055	+	4.89694i	−0.0405314	+	0.194482i
$635$		0			0
$636$	4.51609	−	3.33630i	0.179075	−	0.132293i
$637$	8.65485	−	14.5614i	0.342917	−	0.576944i
$638$	2.18910	−	0.720911i	0.0866672	−	0.0285412i
$639$	18.8848	−	10.9032i	0.747073	−	0.431323i
$640$		0			0
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	−0.973568	−	0.228398i	$-0.926651\pi$
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	0.684583	+	0.728935i	$0.259984\pi$
$642$	−6.01917	−	5.37653i	−0.237558	−	0.212195i
$643$			24.2513i			0.956380i	0.878256	+	0.478190i	$0.158707\pi$
$643$			24.2513i			0.956380i	−0.878256	+	0.478190i	$0.841293\pi$
$644$	20.8598	+	9.24707i	0.821990	+	0.364386i
$645$		0			0
$646$	−3.38730	+	3.79218i	−0.133272	+	0.149201i
$647$	−25.9077	−	14.9578i	−1.01854	−	0.588053i	−0.104857	−	0.994487i	$-0.533439\pi$
$647$	−25.9077	−	14.9578i	−1.01854	−	0.588053i	−0.913680	+	0.406435i	$0.866772\pi$
$648$	−6.03722	+	2.77465i	−0.237164	+	0.108999i
$649$	−11.2487	+	6.49444i	−0.441550	+	0.254929i
$650$		0			0
$651$	5.22326	+	3.05993i	0.204716	+	0.119928i
$652$	−7.26808	+	5.36935i	−0.284640	+	0.210280i
$653$	13.4780	−	7.78155i	0.527436	−	0.304516i	−0.212535	−	0.977153i	$-0.568172\pi$
$653$	13.4780	−	7.78155i	0.527436	−	0.304516i	0.739972	+	0.672638i	$0.234839\pi$
$654$	−4.87863	+	23.4092i	−0.190770	+	0.915373i
$655$		0			0
$656$	6.56957	+	28.6594i	0.256498	+	1.11896i
$657$	−21.4371			−0.836340
$658$	41.2269	−	13.2879i	1.60719	−	0.518016i
$659$			30.2702i			1.17916i	0.807710	+	0.589580i	$0.200707\pi$
$659$			30.2702i			1.17916i	−0.807710	+	0.589580i	$0.799293\pi$
$660$		0			0
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	0.770493	−	0.637449i	$-0.220010\pi$
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	−0.166800	+	0.985991i	$0.553344\pi$
$662$	6.78907	−	32.5761i	0.263865	−	1.26611i
$663$	1.10253	−	0.636547i	0.0428188	−	0.0247214i
$664$	−4.24714	+	5.99470i	−0.164821	+	0.232640i
$665$		0			0
$666$	−33.2087	+	10.9363i	−1.28681	+	0.423772i
$667$	0.938880	+	1.62619i	0.0363536	+	0.0629662i
$668$	−33.6569	+	3.80818i	−1.30222	+	0.147343i
$669$	−10.9226	+	18.9185i	−0.422292	+	0.731432i
$670$		0			0
$671$	38.8754			1.50077
$672$	−11.7721	−	6.58581i	−0.454119	−	0.254053i
$673$		−	21.1876i		−	0.816723i	−0.912820	−	0.408362i	$-0.866100\pi$
$673$		−	21.1876i		−	0.816723i	0.912820	−	0.408362i	$-0.133900\pi$
$674$	−5.37966	−	4.80529i	−0.207217	−	0.185093i
$675$		0			0
$676$	1.60641	+	14.1975i	0.0617850	+	0.546059i
$677$	−12.6285	−	21.8732i	−0.485353	−	0.840657i	0.514505	−	0.857487i	$-0.327976\pi$
$677$	−12.6285	−	21.8732i	−0.485353	−	0.840657i	−0.999858	+	0.0168308i	$0.994642\pi$
$678$	−1.66590	−	5.05863i	−0.0639786	−	0.194275i
$679$	5.94041	+	10.4413i	0.227972	+	0.400700i
$680$		0			0
$681$	−4.79140	−	8.29895i	−0.183607	−	0.318016i
$682$	−2.74128	+	13.1536i	−0.104969	+	0.503676i
$683$	11.0499	−	19.1391i	0.422814	−	0.732336i	−0.573399	−	0.819276i	$-0.694376\pi$
$683$	11.0499	−	19.1391i	0.422814	−	0.732336i	0.996214	+	0.0869404i	$0.0277090\pi$
$684$	−24.7068	−	10.7657i	−0.944689	−	0.411637i
$685$		0			0
$686$	17.8162	−	19.1985i	0.680225	−	0.733004i
$687$	−26.5993			−1.01483
$688$	22.6172	−	5.18452i	0.862273	−	0.197658i
$689$	6.52791	+	3.76889i	0.248694	+	0.143583i
$690$		0			0
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	0.985258	−	0.171077i	$-0.0547248\pi$
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	−0.640786	+	0.767719i	$0.721391\pi$
$692$	−0.213462	+	0.157697i	−0.00811461	+	0.00599473i
$693$	−18.8279	+	10.7118i	−0.715212	+	0.406908i
$694$	0.737153	+	2.23841i	0.0279819	+	0.0849691i
$695$		0			0
$696$	−0.463569	−	1.00865i	−0.0175715	−	0.0382330i
$697$	−3.71588	−	2.14537i	−0.140749	−	0.0812615i
$698$	29.1187	+	26.0098i	1.10216	+	0.984486i
$699$	25.2991			0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	11.9335	+	10.6594i	0.450401	+	0.402313i
$703$	−60.2820	−	34.8038i	−2.27358	−	1.31265i
$704$	5.52481	−	29.4255i	0.208224	−	1.10902i
$705$		0			0
$706$	12.0134	+	36.4796i	0.452131	+	1.37293i
$707$	−0.153266	+	24.1934i	−0.00576416	+	0.909885i
$708$	3.71735	+	5.03189i	0.139706	+	0.189110i
$709$	−18.5131	−	32.0657i	−0.695275	−	1.20425i	−0.970088	−	0.242753i	$-0.921949\pi$
$709$	−18.5131	−	32.0657i	−0.695275	−	1.20425i	0.274814	−	0.961498i	$-0.411384\pi$
$710$		0			0
$711$	−0.869718	−	0.502132i	−0.0326170	−	0.0188314i
$712$	27.8251	+	2.58953i	1.04279	+	0.0970469i
$713$	−10.9469			−0.409965
$714$	1.87355	−	0.603866i	0.0701157	−	0.0225991i
$715$		0			0
$716$	−12.8620	+	29.5176i	−0.480674	+	1.10312i
$717$	−6.14124	+	10.6369i	−0.229349	+	0.397244i
$718$	4.83433	−	23.1967i	0.180416	−	0.865692i
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	0.990561	−	0.137072i	$-0.0437692\pi$
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	−0.613988	+	0.789315i	$0.710436\pi$
$720$		0			0
$721$	−23.3581	−	13.6838i	−0.869902	−	0.509613i
$722$	−8.37828	−	25.4412i	−0.311807	−	0.946824i
$723$	1.89602	+	3.28401i	0.0705138	+	0.122134i
$724$	−7.93570	+	0.897902i	−0.294928	+	0.0333703i
$725$		0			0
$726$	2.85750	+	2.55242i	0.106052	+	0.0947292i
$727$			10.7925i			0.400272i	0.979768	+	0.200136i	$0.0641385\pi$
$727$			10.7925i			0.400272i	−0.979768	+	0.200136i	$0.935862\pi$
$728$	1.79224	−	18.0200i	0.0664248	−	0.667865i
$729$	−7.50278			−0.277881
$730$		0			0
$731$	−1.69306	+	2.93247i	−0.0626202	+	0.108461i
$732$	−2.10517	−	18.6056i	−0.0778094	−	0.687683i
$733$	−3.61611	−	6.26329i	−0.133564	−	0.231340i	0.791484	−	0.611190i	$-0.209309\pi$
$733$	−3.61611	−	6.26329i	−0.133564	−	0.231340i	−0.925048	+	0.379850i	$0.875976\pi$
$734$	−11.3427	+	3.73538i	−0.418668	+	0.137875i
$735$		0			0
$736$	24.3881	−	0.484669i	0.898958	−	0.0178651i
$737$	31.9083	−	18.4223i	1.17536	−	0.678593i
$738$	4.63990	−	22.2637i	0.170797	−	0.819539i
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	0.468044	−	0.883705i	$-0.344959\pi$
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	−0.531289	+	0.847191i	$0.678292\pi$
$740$		0			0
$741$			13.4340i			0.493511i
$742$	8.64286	+	7.81909i	0.317289	+	0.287048i
$743$	19.8225			0.727216			0.363608	−	0.931552i	$-0.381545\pi$
$743$	19.8225			0.727216			0.363608	+	0.931552i	$0.381545\pi$
$744$	6.44368	+	0.599680i	0.236237	+	0.0219853i
$745$		0			0
$746$	−2.99416	+	14.3669i	−0.109624	+	0.526011i
$747$	4.92116	−	2.84124i	0.180056	−	0.103955i
$748$	2.59610	+	3.51414i	0.0949228	+	0.128490i
$749$	8.46821	−	14.4551i	0.309421	−	0.528178i
$750$		0			0
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	−0.829879	−	0.557944i	$-0.811590\pi$
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	0.0682545	+	0.997668i	$0.478257\pi$
$752$	33.9153	−	31.5279i	1.23676	−	1.14971i
$753$	14.7384	+	8.50921i	0.537097	+	0.310093i
$754$	0.992774	−	1.11144i	0.0361547	−	0.0404762i
$755$		0			0
$756$	14.5745	+	19.9922i	0.530070	+	0.727109i
$757$			34.8711i			1.26741i	0.773574	+	0.633706i	$0.218467\pi$
$757$			34.8711i			1.26741i	−0.773574	+	0.633706i	$0.781533\pi$
$758$	12.4431	+	11.1146i	0.451955	+	0.403702i
$759$	−7.27236	+	12.5961i	−0.263970	+	0.457209i
$760$		0			0
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	−0.352589	−	0.935778i	$-0.614699\pi$
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	0.634113	+	0.773240i	$0.281365\pi$
$762$	5.94469	−	1.95770i	0.215353	−	0.0709200i
$763$	−49.6347	−	0.314438i	−1.79690	−	0.0113834i
$764$	−23.8273	−	32.2533i	−0.862043	−	1.16688i
$765$		0			0
$766$	0.276138	−	1.32500i	0.00997727	−	0.0478741i
$767$	−4.19935	+	7.27349i	−0.151630	+	0.262631i
$768$	−14.3821	−	1.05071i	−0.518970	−	0.0379141i
$769$		−	0.573577i		−	0.0206837i	−0.999947	−	0.0103419i	$-0.996708\pi$
$769$		−	0.573577i		−	0.0206837i	0.999947	−	0.0103419i	$-0.00329197\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	15.4506	−	35.4584i	0.556078	−	1.27617i
$773$	−2.17425	+	3.76591i	−0.0782023	+	0.135450i	−0.902474	−	0.430744i	$-0.858251\pi$
$773$	−2.17425	+	3.76591i	−0.0782023	+	0.135450i	0.824272	+	0.566194i	$0.191585\pi$
$774$	−17.5699	−	3.66168i	−0.631537	−	0.131616i
$775$		0			0
$776$	10.4789	+	7.42411i	0.376170	+	0.266510i
$777$	13.3256	+	23.4220i	0.478052	+	0.840259i
$778$	−13.3433	−	40.5179i	−0.478381	−	1.45264i
$779$	39.2109	−	22.6384i	1.40488	−	0.811107i
$780$		0			0
$781$	18.6519	−	32.3060i	0.667417	−	1.15600i
$782$	−2.37134	+	2.65478i	−0.0847990	+	0.0949348i
$783$			2.03603i			0.0727618i
$784$	8.56651	−	26.6574i	0.305947	−	0.952049i
$785$		0			0
$786$	−15.0902	−	13.4790i	−0.538249	−	0.480782i
$787$	−18.2295	−	10.5248i	−0.649811	−	0.375168i	0.138573	−	0.990352i	$-0.455748\pi$
$787$	−18.2295	−	10.5248i	−0.649811	−	0.375168i	−0.788384	+	0.615184i	$0.789082\pi$
$788$	−3.25400	+	0.368181i	−0.115919	+	0.0131159i
$789$	8.34944	−	4.82055i	0.297248	−	0.171616i
$790$		0			0
$791$	9.60890	−	5.46683i	0.341653	−	0.194378i
$792$	−13.3873	+	18.8957i	−0.475695	+	0.671428i
$793$	21.7694	−	12.5686i	0.773054	−	0.446323i
$794$	8.59335	+	1.79091i	0.304967	+	0.0635570i
$795$		0			0
$796$	1.43611	+	0.625770i	0.0509017	+	0.0221798i
$797$	−14.7349			−0.521938			−0.260969	−	0.965347i	$-0.584042\pi$
$797$	−14.7349			−0.521938			−0.260969	+	0.965347i	$0.584042\pi$
$798$	−4.36663	+	20.3075i	−0.154577	+	0.718879i
$799$			6.75744i			0.239061i
$800$		0			0
$801$	−18.7190	−	10.8074i	−0.661403	−	0.381861i
$802$	36.4295	+	7.59213i	1.28637	+	0.268087i
$803$	−31.7590	+	18.3360i	−1.12075	+	0.647065i
$804$	−10.5447	−	14.2736i	−0.371883	−	0.503390i
$805$		0			0
$806$	2.71753	+	8.25198i	0.0957210	+	0.290663i
$807$	−3.76965	−	6.52923i	−0.132698	−	0.229840i
$808$	10.8009	+	23.5011i	0.379975	+	0.826767i
$809$	−7.23808	+	12.5367i	−0.254477	+	0.440768i	−0.964753	−	0.263156i	$-0.915237\pi$
$809$	−7.23808	+	12.5367i	−0.254477	+	0.440768i	0.710276	+	0.703923i	$0.248570\pi$
$810$		0			0
$811$	−18.5825			−0.652521			−0.326260	−	0.945280i	$-0.605789\pi$
$811$	−18.5825			−0.652521			−0.326260	+	0.945280i	$0.605789\pi$
$812$	1.86199	−	1.35741i	0.0653431	−	0.0476358i
$813$		−	24.4348i		−	0.856967i
$814$	−39.8444	+	44.6069i	−1.39654	+	1.56347i
$815$		0			0
$816$	1.54127	−	1.43278i	0.0539553	−	0.0501573i
$817$	−17.8656	−	30.9442i	−0.625040	−	1.08260i
$818$	−24.7198	+	8.14069i	−0.864306	+	0.284633i
$819$	−7.08003	+	12.0855i	−0.247396	+	0.422302i
$820$		0			0
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	0.972918	−	0.231149i	$-0.0742486\pi$
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	−0.686640	+	0.726997i	$0.740915\pi$
$822$	9.78542	+	2.03934i	0.341306	+	0.0711303i
$823$	−21.9486	+	38.0161i	−0.765081	+	1.32516i	0.175123	+	0.984547i	$0.443968\pi$
$823$	−21.9486	+	38.0161i	−0.765081	+	1.32516i	−0.940204	+	0.340612i	$0.889366\pi$
$824$	−28.8158	−	2.68173i	−1.00385	−	0.0934226i
$825$		0			0
$826$	−8.71214	+	9.63000i	−0.303134	+	0.335070i
$827$	8.10796			0.281941			0.140971	−	0.990014i	$-0.454978\pi$
$827$	8.10796			0.281941			0.140971	+	0.990014i	$0.454978\pi$
$828$	−17.2964	−	7.53673i	−0.601093	−	0.261919i
$829$	36.5657	+	21.1112i	1.26998	+	0.733223i	0.974984	−	0.222276i	$-0.0713486\pi$
$829$	36.5657	+	21.1112i	1.26998	+	0.733223i	0.294995	+	0.955499i	$0.404682\pi$
$830$		0			0
$831$	1.51407	+	2.62245i	0.0525225	+	0.0909716i
$832$	−6.41961	−	18.2639i	−0.222560	−	0.633185i
$833$	1.99802	+	3.56421i	0.0692273	+	0.123492i
$834$	21.0705	−	6.93893i	0.729613	−	0.240275i
$835$		0			0
$836$	−45.8114	+	5.18343i	−1.58442	+	0.179273i
$837$	−10.2794	−	5.93481i	−0.355308	−	0.205137i
$838$	33.2024	−	37.1710i	1.14696	−	1.28405i
$839$	31.8404			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$839$	31.8404			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	14.7599	−	16.5242i	0.508661	−	0.569460i
$843$	5.72868	+	3.30745i	0.197306	+	0.113915i
$844$	18.3337	−	2.07441i	0.631072	−	0.0714040i
$845$		0			0
$846$	−34.0191	+	11.2031i	−1.16960	+	0.385171i
$847$	−4.02014	+	6.86233i	−0.138134	+	0.235792i
$848$	11.9095	+	3.66139i	0.408975	+	0.125733i
$849$	−3.24714	−	5.62422i	−0.111442	−	0.193023i
$850$		0			0
$851$	−42.2015	−	24.3650i	−1.44665	−	0.835223i
$852$	−16.4716	−	7.17729i	−0.564306	−	0.245890i
$853$	−16.2023			−0.554755			−0.277378	−	0.960761i	$-0.589465\pi$
$853$	−16.2023			−0.554755			−0.277378	+	0.960761i	$0.589465\pi$
$854$	36.9930	−	11.9233i	1.26587	−	0.408006i
$855$		0			0
$856$	1.65958	−	17.8326i	0.0567234	−	0.609505i
$857$	−20.4762	+	35.4659i	−0.699455	+	1.21149i	0.269201	+	0.963084i	$0.413240\pi$
$857$	−20.4762	+	35.4659i	−0.699455	+	1.21149i	−0.968656	+	0.248407i	$0.920093\pi$
$858$	11.3005	+	2.35509i	0.385792	+	0.0804015i
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	0.950329	−	0.311246i	$-0.100746\pi$
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	−0.744711	+	0.667387i	$0.767413\pi$
$860$		0			0
$861$	−17.5278	−	0.111039i	−0.597345	−	0.00378421i
$862$	2.69376	−	0.887107i	0.0917499	−	0.0302150i
$863$	0.285426	+	0.494372i	0.00971602	+	0.0168286i	0.870843	−	0.491562i	$-0.163574\pi$
$863$	0.285426	+	0.494372i	0.00971602	+	0.0168286i	−0.861127	+	0.508391i	$0.830241\pi$
$864$	23.1637	+	12.7668i	0.788045	+	0.434334i
$865$		0			0
$866$	12.8106	−	14.3418i	0.435323	−	0.487356i
$867$		−	15.0146i		−	0.509924i
$868$	1.42571	+	13.3574i	0.0483918	+	0.453380i
$869$	−1.71798			−0.0582784
$870$		0			0
$871$	11.9120	−	20.6321i	0.403622	−	0.699093i
$872$	−48.2146	+	22.1590i	−1.63275	+	0.750398i
$873$	−4.96655	−	8.60232i	−0.168092	−	0.291144i
$874$	−11.7493	−	35.6775i	−0.397426	−	1.20681i
$875$		0			0
$876$	10.4954	+	14.2068i	0.354605	+	0.480003i
$877$	16.4059	−	9.47193i	0.553987	−	0.319844i	−0.196742	−	0.980455i	$-0.563036\pi$
$877$	16.4059	−	9.47193i	0.553987	−	0.319844i	0.750728	+	0.660611i	$0.229703\pi$
$878$	−40.2178	−	8.38165i	−1.35729	−	0.282867i
$879$	6.61794	+	3.82087i	0.223218	+	0.128875i
$880$		0			0
$881$		−	35.7695i		−	1.20511i	−0.798079	−	0.602553i	$-0.794150\pi$
$881$		−	35.7695i		−	1.20511i	0.798079	−	0.602553i	$-0.205850\pi$
$882$	−14.6308	+	15.9677i	−0.492646	+	0.537662i
$883$	25.4594			0.856776			0.428388	−	0.903595i	$-0.359082\pi$
$883$	25.4594			0.856776			0.428388	+	0.903595i	$0.359082\pi$
$884$	2.58990	+	1.12852i	0.0871076	+	0.0379561i
$885$		0			0
$886$	20.2639	+	4.22313i	0.680779	+	0.141879i
$887$	9.18408	−	5.30243i	0.308371	−	0.178038i	−0.337826	−	0.941209i	$-0.609692\pi$
$887$	9.18408	−	5.30243i	0.308371	−	0.178038i	0.646197	+	0.763170i	$0.276358\pi$
$888$	23.5063	+	16.6538i	0.788821	+	0.558865i
$889$	6.42439	+	11.2920i	0.215467	+	0.378721i
$890$		0			0
$891$	7.61364	−	4.39574i	0.255067	−	0.147263i
$892$	−48.1687	+	5.45015i	−1.61281	+	0.182485i
$893$	−61.7530	−	35.6531i	−2.06648	−	1.19309i
$894$	1.56996	+	1.40234i	0.0525072	+	0.0469012i
$895$		0			0
$896$	−3.76766	−	29.6952i	−0.125869	−	0.992047i
$897$			9.40472i			0.314014i
$898$	−25.5028	+	28.5511i	−0.851040	+	0.952763i
$899$	−0.552744	+	0.957381i	−0.0184350	+	0.0319304i
$900$		0			0
$901$	−1.57463	+	0.909116i	−0.0524587	+	0.0302870i
$902$	−12.1691	−	36.9523i	−0.405187	−	1.23038i
$903$	−0.0876291	+	13.8324i	−0.00291611	+	0.460315i
$904$	6.83225	−	9.64350i	0.227237	−	0.320738i
$905$		0			0
$906$	9.17891	+	1.91294i	0.304949	+	0.0635533i
$907$	−7.68190	+	13.3054i	−0.255073	+	0.441800i	−0.964915	−	0.262561i	$-0.915433\pi$
$907$	−7.68190	+	13.3054i	−0.255073	+	0.441800i	0.709842	+	0.704361i	$0.248766\pi$
$908$	8.49454	−	19.4946i	0.281901	−	0.646951i
$909$		−	20.0052i		−	0.663531i
$910$		0			0
$911$			22.0734i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$911$			22.0734i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$912$	4.96154	+	21.6445i	0.164293	+	0.716720i
$913$	4.86046	−	8.41856i	0.160858	−	0.278614i
$914$	2.19461	−	10.5304i	0.0725911	−	0.348315i
$915$		0			0
$916$	−35.0729	−	47.4755i	−1.15884	−	1.56864i
$917$	21.2299	−	36.2392i	0.701074	−	1.19672i
$918$	−3.66601	+	1.20729i	−0.120996	+	0.0398464i
$919$	−45.1598	+	26.0730i	−1.48968	+	0.860069i	−0.999930	−	0.0117923i	$-0.996246\pi$
$919$	−45.1598	+	26.0730i	−1.48968	+	0.860069i	−0.489753	+	0.871861i	$0.662913\pi$
$920$		0			0
$921$	4.69884	−	8.13863i	0.154832	−	0.268177i
$922$	13.4954	+	12.0546i	0.444448	+	0.396996i
$923$		−	24.1209i		−	0.793949i
$924$	16.3169	+	7.23322i	0.536785	+	0.237955i
$925$		0			0
$926$	26.3016	−	29.4454i	0.864323	−	0.967634i
$927$	19.3855	+	11.1922i	0.636702	+	0.367600i
$928$	1.18904	−	2.15737i	0.0390323	−	0.0708193i
$929$	−24.8707	+	14.3591i	−0.815982	+	0.471107i	−0.849029	−	0.528346i	$-0.822812\pi$
$929$	−24.8707	+	14.3591i	−0.815982	+	0.471107i	0.0330469	+	0.999454i	$0.489479\pi$
$930$		0			0
$931$	−43.1134	−	0.546272i	−1.41298	−	0.0179033i
$932$	33.3585	+	45.1549i	1.09270	+	1.47910i
$933$	6.18641	−	3.57173i	0.202534	−	0.116933i
$934$	6.52394	−	31.3039i	0.213470	−	1.02430i
$935$		0			0
$936$	−1.38753	+	14.9093i	−0.0453529	+	0.487326i
$937$	−44.9045			−1.46697			−0.733484	−	0.679707i	$-0.762107\pi$
$937$	−44.9045			−1.46697			−0.733484	+	0.679707i	$0.762107\pi$
$938$	24.7131	−	27.3167i	0.806910	−	0.891921i
$939$			13.0385i			0.425495i
$940$		0			0
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	0.729182	−	0.684320i	$-0.239901\pi$
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	−0.228048	+	0.973650i	$0.573234\pi$
$942$	0.801598	−	3.84632i	0.0261175	−	0.125320i
$943$	27.4503	−	15.8484i	0.893905	−	0.516096i
$944$	−4.07957	+	13.2698i	−0.132779	+	0.431894i
$945$		0			0
$946$	−29.1618	+	9.60352i	−0.948130	+	0.312237i
$947$	18.5387	+	32.1100i	0.602428	+	1.04344i	0.992452	+	0.122631i	$0.0391332\pi$
$947$	18.5387	+	32.1100i	0.602428	+	1.04344i	−0.390025	+	0.920804i	$0.627533\pi$
$948$	0.0930316	+	0.822218i	0.00302153	+	0.0267044i
$949$	−11.8562	+	20.5356i	−0.384869	+	0.666613i
$950$		0			0
$951$	−3.18787			−0.103374
$952$	3.54820	+	2.54775i	0.114998	+	0.0825730i
$953$			28.5420i			0.924567i	0.886732	+	0.462283i	$0.152970\pi$
$953$			28.5420i			0.924567i	−0.886732	+	0.462283i	$0.847030\pi$
$954$	−7.18736	−	6.41999i	−0.232699	−	0.207855i
$955$		0			0
$956$	−27.0829	+	3.06435i	−0.875923	+	0.0991082i
$957$	0.734408	+	1.27203i	0.0237400	+	0.0411189i
$958$	−9.72368	−	29.5266i	−0.314158	−	0.953962i
$959$	−0.131440	+	20.7481i	−0.00424442	+	0.669991i
$960$		0			0
$961$	12.2776	+	21.2655i	0.396052	+	0.685983i
$962$	−7.89042	+	37.8607i	−0.254397	+	1.22068i
$963$	−6.92626	+	11.9966i	−0.223196	+	0.386586i
$964$	−3.36141	+	7.71428i	−0.108264	+	0.248460i
$965$		0			0
$966$	−3.05694	+	14.2166i	−0.0983554	+	0.457413i
$967$	−5.33936			−0.171702			−0.0858510	−	0.996308i	$-0.527361\pi$
$967$	−5.33936			−0.171702			−0.0858510	+	0.996308i	$0.527361\pi$
$968$	−0.787860	+	8.46573i	−0.0253228	+	0.272099i
$969$	−2.80635	−	1.62025i	−0.0901530	−	0.0520498i
$970$		0			0
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	0.764197	−	0.644983i	$-0.223136\pi$
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	−0.940670	+	0.339323i	$0.889802\pi$
$972$	−19.1853	−	25.9697i	−0.615368	−	0.832978i
$973$	22.7708	+	40.0236i	0.729999	+	1.28310i
$974$	11.2283	+	34.0955i	0.359778	+	1.09249i
$975$		0			0
$976$	30.4323	−	28.2901i	0.974113	−	0.905544i
$977$	27.2684	+	15.7434i	0.872392	+	0.503676i	0.868142	−	0.496315i	$-0.165314\pi$
$977$	27.2684	+	15.7434i	0.872392	+	0.503676i	0.00424979	+	0.999991i	$0.498647\pi$
$978$	−4.29493	−	3.83638i	−0.137337	−	0.122674i
$979$	−36.9761			−1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	38.4587	+	34.3526i	1.22727	+	1.09624i
$983$	29.9232	+	17.2762i	0.954402	+	0.551025i	0.894446	−	0.447176i	$-0.147570\pi$
$983$	29.9232	+	17.2762i	0.954402	+	0.551025i	0.0599567	+	0.998201i	$0.480904\pi$
$984$	−17.0263	+	7.82512i	−0.542777	+	0.249456i
$985$		0			0
$986$	0.112442	+	0.341438i	0.00358088	+	0.0108736i
$987$	13.6507	+	23.9935i	0.434507	+	0.763722i
$988$	−23.9776	+	17.7136i	−0.762829	+	0.563545i
$989$	−12.5072	−	21.6630i	−0.397704	−	0.688844i
$990$		0			0
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.999707	+	0.0242247i	$0.00771173\pi$
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.520833	+	0.853659i	$0.325622\pi$
$992$	7.42608	+	12.2917i	0.235778	+	0.390261i
$993$	21.2068			0.672978
$994$	7.84033	−	36.4623i	0.248680	−	1.15652i
$995$		0			0
$996$	−4.29229	−	1.87032i	−0.136007	−	0.0592632i
$997$	−7.64087	+	13.2344i	−0.241989	+	0.419137i	−0.961281	−	0.275571i	$-0.911133\pi$
$997$	−7.64087	+	13.2344i	−0.241989	+	0.419137i	0.719292	+	0.694708i	$0.244466\pi$
$998$	−3.42744	+	16.4459i	−0.108494	+	0.520587i
$999$	−26.4187	−	45.7586i	−0.835851	−	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.c.199.6		32
4.3	odd	2	inner	700.2.t.c.199.1		32
5.2	odd	4		700.2.p.c.451.4		32
5.3	odd	4		140.2.o.a.31.13	yes	32
5.4	even	2		700.2.t.d.199.11		32
7.5	odd	6		700.2.t.d.299.16		32
20.3	even	4		140.2.o.a.31.9	✓	32
20.7	even	4		700.2.p.c.451.8		32
20.19	odd	2		700.2.t.d.199.16		32
28.19	even	6		700.2.t.d.299.11		32
35.3	even	12		980.2.g.a.391.8		32
35.12	even	12		700.2.p.c.551.8		32
35.13	even	4		980.2.o.f.31.13		32
35.18	odd	12		980.2.g.a.391.7		32
35.19	odd	6	inner	700.2.t.c.299.1		32
35.23	odd	12		980.2.o.f.411.9		32
35.33	even	12		140.2.o.a.131.9	yes	32
140.3	odd	12		980.2.g.a.391.5		32
140.19	even	6	inner	700.2.t.c.299.6		32
140.23	even	12		980.2.o.f.411.13		32
140.47	odd	12		700.2.p.c.551.4		32
140.83	odd	4		980.2.o.f.31.9		32
140.103	odd	12		140.2.o.a.131.13	yes	32
140.123	even	12		980.2.g.a.391.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	20.3	even	4
140.2.o.a.31.13	yes	32	5.3	odd	4
140.2.o.a.131.9	yes	32	35.33	even	12
140.2.o.a.131.13	yes	32	140.103	odd	12
700.2.p.c.451.4		32	5.2	odd	4
700.2.p.c.451.8		32	20.7	even	4
700.2.p.c.551.4		32	140.47	odd	12
700.2.p.c.551.8		32	35.12	even	12
700.2.t.c.199.1		32	4.3	odd	2	inner
700.2.t.c.199.6		32	1.1	even	1	trivial
700.2.t.c.299.1		32	35.19	odd	6	inner
700.2.t.c.299.6		32	140.19	even	6	inner
700.2.t.d.199.11		32	5.4	even	2
700.2.t.d.199.16		32	20.19	odd	2
700.2.t.d.299.11		32	28.19	even	6
700.2.t.d.299.16		32	7.5	odd	6
980.2.g.a.391.5		32	140.3	odd	12
980.2.g.a.391.6		32	140.123	even	12
980.2.g.a.391.7		32	35.18	odd	12
980.2.g.a.391.8		32	35.3	even	12
980.2.o.f.31.9		32	140.83	odd	4
980.2.o.f.31.13		32	35.13	even	4
980.2.o.f.411.9		32	35.23	odd	12
980.2.o.f.411.13		32	140.23	even	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.942109 + 1.05472i) q^{2} +(-0.780530 - 0.450639i) q^{3} +(-0.224860 - 1.98732i) q^{4} +(1.21064 - 0.398687i) q^{6} +(1.30833 + 2.29962i) q^{7} +(2.30790 + 1.63511i) q^{8} +(-1.09385 - 1.89460i) q^{9} +(-3.24107 - 1.87123i) q^{11} +(-0.720054 + 1.65249i) q^{12} -2.41990 q^{13} +(-3.65805 - 0.786573i) q^{14} +(-3.89888 + 0.893735i) q^{16} +(0.291859 - 0.505515i) q^{17} +(3.02880 + 0.631220i) q^{18} +(3.07977 + 5.33433i) q^{19} +(0.0151060 - 2.38451i) q^{21} +(5.02706 - 1.65551i) q^{22} +(2.15605 + 3.73439i) q^{23} +(-1.06454 - 2.31628i) q^{24} +(2.27981 - 2.55232i) q^{26} +4.67556i q^{27} +(4.27589 - 3.11717i) q^{28} +0.435463 q^{29} +(-1.26933 + 2.19854i) q^{31} +(2.73053 - 4.95421i) q^{32} +(1.68650 + 2.92110i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-9.78676 + 5.65039i) q^{37} +(-8.52769 - 1.77723i) q^{38} +(1.88881 + 1.09050i) q^{39} -7.35068i q^{41} +(2.50075 + 2.26240i) q^{42} -5.80096 q^{43} +(-2.98995 + 6.86180i) q^{44} +(-5.96996 - 1.24418i) q^{46} +(-10.0256 + 5.78826i) q^{47} +(3.44594 + 1.05940i) q^{48} +(-3.57652 + 6.01735i) q^{49} +(-0.455610 + 0.263046i) q^{51} +(0.544138 + 4.80912i) q^{52} +(-2.69759 - 1.55746i) q^{53} +(-4.93139 - 4.40489i) q^{54} +(-0.740624 + 7.44657i) q^{56} -5.55147i q^{57} +(-0.410254 + 0.459290i) q^{58} +(1.73534 - 3.00569i) q^{59} +(-8.99597 + 5.19383i) q^{61} +(-1.12299 - 3.41004i) q^{62} +(2.92575 - 4.99421i) q^{63} +(2.65284 + 7.54735i) q^{64} +(-4.66981 - 0.973217i) q^{66} +(-4.92250 + 8.52602i) q^{67} +(-1.07025 - 0.466348i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(0.573383 - 6.16112i) q^{72} +(4.89946 - 8.48612i) q^{73} +(3.26063 - 15.6456i) q^{74} +(9.90849 - 7.31997i) q^{76} +(0.0627260 - 9.90142i) q^{77} +(-2.92964 + 0.964785i) q^{78} +(0.397549 - 0.229525i) q^{79} +(-1.17456 + 2.03439i) q^{81} +(7.75290 + 6.92515i) q^{82} +2.59747i q^{83} +(-4.74218 + 0.506159i) q^{84} +(5.46514 - 6.11837i) q^{86} +(-0.339892 - 0.196236i) q^{87} +(-4.42040 - 9.61812i) q^{88} +(8.55647 - 4.94008i) q^{89} +(-3.16604 - 5.56486i) q^{91} +(6.93662 - 5.12447i) q^{92} +(1.98149 - 1.14402i) q^{93} +(3.34020 - 16.0273i) q^{94} +(-4.36382 + 2.63643i) q^{96} +4.54044 q^{97} +(-2.97713 - 9.44122i) q^{98} +8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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