LMFDB - Embedded newform 700.2.t.c.299.1

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			299.1
Character	$\chi$	$=$	700.299
Dual form			700.2.t.c.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38447 - 0.288532i) q^{2} +(0.780530 - 0.450639i) q^{3} +(1.83350 + 0.798926i) 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} +(1.79113 - 0.202661i) q^{12} -2.41990 q^{13} +(2.47486 - 2.80626i) q^{14} +(2.72344 + 2.92966i) q^{16} +(0.291859 + 0.505515i) q^{17} +(2.06105 - 2.30740i) 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} +(-2.53823 - 0.236220i) q^{24} +(3.35028 + 0.698219i) q^{26} +4.67556i q^{27} +(-4.23606 + 3.17109i) q^{28} +0.435463 q^{29} +(1.26933 + 2.19854i) q^{31} +(-2.92521 - 4.84181i) 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} +(5.80297 - 6.49659i) q^{38} +(-1.88881 + 1.09050i) q^{39} +7.35068i q^{41} +(0.667093 - 3.30563i) q^{42} +5.80096 q^{43} +(7.43747 - 0.841528i) q^{44} +(4.06247 - 4.54805i) 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} +(-4.43689 - 1.93332i) q^{52} +(-2.69759 + 1.55746i) q^{53} +(1.34905 - 6.47316i) q^{54} +(6.77964 - 3.16804i) q^{56} +5.55147i q^{57} +(-0.602884 - 0.125645i) 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} +(-3.17773 + 3.55756i) q^{66} +(4.92250 + 8.52602i) q^{67} +(0.131255 + 1.16004i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(5.62238 - 2.58400i) q^{72} +(4.89946 + 8.48612i) q^{73} +(11.9191 + 10.6466i) 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} +(2.12091 - 10.1768i) q^{82} +2.59747i q^{83} +(-1.87735 + 4.38406i) q^{84} +(-8.03123 - 1.67376i) q^{86} +(0.339892 - 0.196236i) q^{87} +(-10.5397 - 0.980878i) 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} +(-12.2100 - 10.9064i) q^{94} +(-4.46512 - 2.46097i) q^{96} +4.54044 q^{97} +(3.21538 + 9.36276i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.38447	−	0.288532i	−0.978966	−	0.204023i
$2$	−1.38447	−	0.288532i	−0.978966	−	0.204023i
$3$	0.780530	−	0.450639i	0.450639	−	0.260177i	−0.257461	−	0.966289i	$-0.582886\pi$
$3$	0.780530	−	0.450639i	0.450639	−	0.260177i	0.708100	+	0.706112i	$0.249553\pi$
$4$	1.83350	+	0.798926i	0.916749	+	0.399463i
$5$		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	$-0.475852\pi$
$11$	3.24107	−	1.87123i	0.977218	−	0.564197i	0.901429	+	0.432927i	$0.142519\pi$
$12$	1.79113	−	0.202661i	0.517054	−	0.0585032i
$13$	−2.41990			−0.671161			−0.335580	−	0.942012i	$-0.608932\pi$
$13$	−2.41990			−0.671161			−0.335580	+	0.942012i	$0.608932\pi$
$14$	2.47486	−	2.80626i	0.661434	−	0.750003i
$15$		0			0
$16$	2.72344	+	2.92966i	0.680859	+	0.732415i
$17$	0.291859	+	0.505515i	0.0707863	+	0.122605i	0.899246	−	0.437443i	$-0.144116\pi$
$17$	0.291859	+	0.505515i	0.0707863	+	0.122605i	−0.828460	+	0.560048i	$0.810782\pi$
$18$	2.06105	−	2.30740i	0.485794	−	0.543860i
$19$	−3.07977	+	5.33433i	−0.706549	+	1.22378i	0.259581	+	0.965721i	$0.416416\pi$
$19$	−3.07977	+	5.33433i	−0.706549	+	1.22378i	−0.966130	+	0.258057i	$0.916918\pi$
$20$		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	$-0.981755\pi$
$23$	−2.15605	+	3.73439i	−0.449568	+	0.778674i	0.548790	+	0.835960i	$0.315089\pi$
$24$	−2.53823	−	0.236220i	−0.518114	−	0.0482182i
$25$		0			0
$26$	3.35028	+	0.698219i	0.657043	+	0.136932i
$27$			4.67556i			0.899812i
$28$	−4.23606	+	3.17109i	−0.800539	+	0.599280i
$29$	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	$-0.0934554\pi$
$31$	1.26933	+	2.19854i	0.227978	+	0.394869i	−0.729231	+	0.684268i	$0.760122\pi$
$32$	−2.92521	−	4.84181i	−0.517109	−	0.855920i
$33$	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	−0.989609	−	0.143782i	$-0.954073\pi$
$37$	−9.78676	−	5.65039i	−1.60893	−	0.928918i	−0.619324	−	0.785136i	$-0.712593\pi$
$38$	5.80297	−	6.49659i	0.941366	−	1.05389i
$39$	−1.88881	+	1.09050i	−0.302451	+	0.174620i
$40$		0			0
$41$			7.35068i			1.14798i	0.818861	+	0.573992i	$0.194606\pi$
$41$			7.35068i			1.14798i	−0.818861	+	0.573992i	$0.805394\pi$
$42$	0.667093	−	3.30563i	0.102935	−	0.510070i
$43$	5.80096			0.884637			0.442319	−	0.896858i	$-0.354156\pi$
$43$	5.80096			0.884637			0.442319	+	0.896858i	$0.354156\pi$
$44$	7.43747	−	0.841528i	1.12124	−	0.126865i
$45$		0			0
$46$	4.06247	−	4.54805i	0.598979	−	0.670573i
$47$	10.0256	+	5.78826i	1.46238	+	0.844305i	0.999121	−	0.0419181i	$-0.0133469\pi$
$47$	10.0256	+	5.78826i	1.46238	+	0.844305i	0.463258	+	0.886223i	$0.346680\pi$
$48$	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
$52$	−4.43689	−	1.93332i	−0.615286	−	0.268104i
$53$	−2.69759	+	1.55746i	−0.370543	+	0.213933i	−0.673696	−	0.739009i	$-0.735294\pi$
$53$	−2.69759	+	1.55746i	−0.370543	+	0.213933i	0.303153	+	0.952942i	$0.401961\pi$
$54$	1.34905	−	6.47316i	0.183582	−	0.880885i
$55$		0			0
$56$	6.77964	−	3.16804i	0.905968	−	0.423347i
$57$			5.55147i			0.735310i
$58$	−0.602884	−	0.125645i	−0.0791625	−	0.0164980i
$59$	−1.73534	−	3.00569i	−0.225922	−	0.391308i	0.730674	−	0.682727i	$-0.239206\pi$
$59$	−1.73534	−	3.00569i	−0.225922	−	0.391308i	−0.956596	+	0.291419i	$0.905873\pi$
$60$		0			0
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.202487	−	0.979285i	$-0.564902\pi$
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.949329	+	0.314284i	$0.898236\pi$
$62$	−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
$66$	−3.17773	+	3.55756i	−0.391152	+	0.437906i
$67$	4.92250	+	8.52602i	0.601379	+	1.04162i	0.992613	+	0.121327i	$0.0387151\pi$
$67$	4.92250	+	8.52602i	0.601379	+	1.04162i	−0.391234	+	0.920291i	$0.627952\pi$
$68$	0.131255	+	1.16004i	0.0159170	+	0.140675i
$69$			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	$0.798546\pi$
$72$	5.62238	−	2.58400i	0.662604	−	0.304527i
$73$	4.89946	+	8.48612i	0.573439	+	0.993225i	0.996209	+	0.0869881i	$0.0277242\pi$
$73$	4.89946	+	8.48612i	0.573439	+	0.993225i	−0.422771	+	0.906237i	$0.638942\pi$
$74$	11.9191	+	10.6466i	1.38557	+	1.23764i
$75$		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	$-0.341554\pi$
$79$	−0.397549	−	0.229525i	−0.0447278	−	0.0258236i	−0.522197	+	0.852825i	$0.674887\pi$
$80$		0			0
$81$	−1.17456	−	2.03439i	−0.130506	−	0.226044i
$82$	2.12091	−	10.1768i	0.234215	−	1.12384i
$83$			2.59747i			0.285109i	0.989787	+	0.142554i	$0.0455316\pi$
$83$			2.59747i			0.285109i	−0.989787	+	0.142554i	$0.954468\pi$
$84$	−1.87735	+	4.38406i	−0.204836	+	0.478341i
$85$		0			0
$86$	−8.03123	−	1.67376i	−0.866030	−	0.180486i
$87$	0.339892	−	0.196236i	0.0364402	−	0.0210388i
$88$	−10.5397	−	0.980878i	−1.12354	−	0.104562i
$89$	8.55647	+	4.94008i	0.906984	+	0.523648i	0.879460	−	0.475973i	$-0.157904\pi$
$89$	8.55647	+	4.94008i	0.906984	+	0.523648i	0.0275247	+	0.999621i	$0.491237\pi$
$90$		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
$94$	−12.2100	−	10.9064i	−1.25936	−	1.12490i
$95$		0			0
$96$	−4.46512	−	2.46097i	−0.455720	−	0.251171i
$97$	4.54044			0.461011			0.230506	−	0.973071i	$-0.425962\pi$
$97$	4.54044			0.461011			0.230506	+	0.973071i	$0.425962\pi$
$98$	3.21538	+	9.36276i	0.324803	+	0.945782i
$99$			8.18738i			0.822862i
$100$		0			0
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	−0.0512584	−	0.998685i	$-0.516323\pi$
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	0.839258	+	0.543734i	$0.182990\pi$
$102$	−0.554880	−	0.495637i	−0.0549413	−	0.0490754i
$103$	8.86113	+	5.11597i	0.873113	+	0.504092i	0.868381	−	0.495897i	$-0.165161\pi$
$103$	8.86113	+	5.11597i	0.873113	+	0.504092i	0.00473128	+	0.999989i	$0.498494\pi$
$104$	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	$-0.734319\pi$
$107$	3.16601	−	5.48368i	0.306069	−	0.530128i	0.977499	+	0.210941i	$0.0676527\pi$
$108$	−3.73542	+	8.57263i	−0.359441	+	0.824902i
$109$	−9.38027	−	16.2471i	−0.898467	−	1.55619i	−0.829454	−	0.558575i	$-0.811348\pi$
$109$	−9.38027	−	16.2471i	−0.898467	−	1.55619i	−0.0690134	−	0.997616i	$-0.521985\pi$
$110$		0			0
$111$	−10.1851			−0.966731
$112$	−10.3003	+	2.42990i	−0.973284	+	0.229604i
$113$			4.17847i			0.393077i	0.980496	+	0.196539i	$0.0629701\pi$
$113$			4.17847i			0.393077i	−0.980496	+	0.196539i	$0.937030\pi$
$114$	1.60177	−	7.68582i	0.150020	−	0.719843i
$115$		0			0
$116$	0.798420	+	0.347902i	0.0741315	+	0.0323019i
$117$	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
$122$	10.9560	+	9.78631i	0.991913	+	0.886010i
$123$	3.31250	+	5.73743i	0.298678	+	0.517326i
$124$	0.570840	+	5.04511i	0.0512629	+	0.453064i
$125$		0			0
$126$	2.60961	+	7.75849i	0.232483	+	0.691182i
$127$	−4.91036			−0.435724			−0.217862	−	0.975980i	$-0.569908\pi$
$127$	−4.91036			−0.435724			−0.217862	+	0.975980i	$0.569908\pi$
$128$	−1.49512	−	11.2145i	−0.132151	−	0.991230i
$129$	4.52782	−	2.61414i	0.398652	−	0.230162i
$130$		0			0
$131$	7.93723	−	13.7477i	0.693479	−	1.20114i	−0.277212	−	0.960809i	$-0.589410\pi$
$131$	7.93723	−	13.7477i	0.693479	−	1.20114i	0.970691	−	0.240332i	$-0.0772564\pi$
$132$	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
$136$	0.152989	−	1.64390i	0.0131187	−	0.140963i
$137$	6.79155	−	3.92110i	0.580241	−	0.335002i	−0.180988	−	0.983485i	$-0.557930\pi$
$137$	6.79155	−	3.92110i	0.580241	−	0.335002i	0.761229	+	0.648483i	$0.224596\pi$
$138$	1.12135	−	5.38060i	0.0954557	−	0.458027i
$139$	−17.4044			−1.47623			−0.738113	−	0.674677i	$-0.764283\pi$
$139$	−17.4044			−1.47623			−0.738113	+	0.674677i	$0.764283\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	2.87600	−	13.8000i	0.241349	−	1.15807i
$143$	−7.84307	+	4.52820i	−0.655871	+	0.378667i
$144$	−8.52956	+	1.95522i	−0.710797	+	0.162935i
$145$		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	−0.830216	−	0.557441i	$-0.811783\pi$
$149$	0.825776	−	1.43029i	0.0676502	−	0.117174i	0.897867	+	0.440268i	$0.145116\pi$
$150$		0			0
$151$	−6.37060	+	3.67807i	−0.518432	+	0.299317i	−0.736293	−	0.676663i	$-0.763425\pi$
$151$	−6.37060	+	3.67807i	−0.518432	+	0.299317i	0.217861	+	0.975980i	$0.430092\pi$
$152$	15.8300	−	7.27534i	1.28398	−	0.590108i
$153$	−1.27700			−0.103239
$154$	2.77003	−	13.7263i	0.223216	−	1.10610i
$155$		0			0
$156$	−4.33436	+	0.490420i	−0.347026	+	0.0392650i
$157$	1.54125	+	2.66953i	0.123005	+	0.213052i	0.920952	−	0.389677i	$-0.127413\pi$
$157$	1.54125	+	2.66953i	0.123005	+	0.213052i	−0.797946	+	0.602729i	$0.794080\pi$
$158$	0.484169	+	0.432476i	0.0385184	+	0.0344059i
$159$	−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	$-0.776712\pi$
$163$	2.25908	−	3.91284i	0.176945	−	0.306477i	0.940833	+	0.338872i	$0.110045\pi$
$164$	−5.87265	+	13.4775i	−0.458577	+	1.05241i
$165$		0			0
$166$	0.749452	−	3.59611i	0.0581687	−	0.279112i
$167$		−	16.9358i		−	1.31053i	−0.755398	−	0.655266i	$-0.772556\pi$
$167$		−	16.9358i		−	1.31053i	0.755398	−	0.655266i	$-0.227444\pi$
$168$	3.86407	−	5.52792i	0.298119	−	0.426488i
$169$	−7.14406			−0.549543
$170$		0			0
$171$	−6.73762	−	11.6699i	−0.515238	−	0.892419i
$172$	10.6360	+	4.63453i	0.810991	+	0.353380i
$173$	−0.0663486	+	0.114919i	−0.00504439	+	0.00873715i	−0.868537	−	0.495625i	$-0.834939\pi$
$173$	−0.0663486	+	0.114919i	−0.00504439	+	0.00873715i	0.863492	+	0.504362i	$0.168272\pi$
$174$	−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
$178$	−10.4208	−	9.30820i	−0.781071	−	0.697679i
$179$	13.9422	−	8.04953i	1.04209	−	0.601650i	0.121664	−	0.992571i	$-0.461177\pi$
$179$	13.9422	−	8.04953i	1.04209	−	0.601650i	0.920424	+	0.390921i	$0.127843\pi$
$180$		0			0
$181$			3.99317i			0.296810i	0.988927	+	0.148405i	$0.0474139\pi$
$181$			3.99317i			0.296810i	−0.988927	+	0.148405i	$0.952586\pi$
$182$	−5.98892	+	6.79087i	−0.443928	+	0.503373i
$183$	−9.36216			−0.692071
$184$	11.0821	−	5.09323i	0.816983	−	0.375478i
$185$		0			0
$186$	−2.41323	−	2.15558i	−0.176946	−	0.158054i
$187$	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	$-0.591671\pi$
$191$	−17.3638	−	10.0250i	−1.25640	−	0.725385i	−0.972373	+	0.233431i	$0.925005\pi$
$192$	5.47175	+	4.69546i	0.394889	+	0.338865i
$193$	16.7482	−	9.66959i	1.20556	−	0.696032i	0.243776	−	0.969832i	$-0.421614\pi$
$193$	16.7482	−	9.66959i	1.20556	−	0.696032i	0.961787	+	0.273799i	$0.0882805\pi$
$194$	−6.28608	−	1.31006i	−0.451315	−	0.0940568i
$195$		0			0
$196$	−1.75014	−	13.8902i	−0.125010	−	0.992155i
$197$			1.63738i			0.116659i	0.998297	+	0.0583293i	$0.0185773\pi$
$197$			1.63738i			0.116659i	−0.998297	+	0.0583293i	$0.981423\pi$
$198$	2.36232	−	11.3352i	0.167883	−	0.805554i
$199$	0.391632	+	0.678326i	0.0277621	+	0.0480853i	0.879573	−	0.475765i	$-0.157829\pi$
$199$	0.391632	+	0.678326i	0.0277621	+	0.0480853i	−0.851811	+	0.523850i	$0.824495\pi$
$200$		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
$206$	−10.7918	−	9.63961i	−0.751901	−	0.671624i
$207$	−4.71679	−	8.16972i	−0.327839	−	0.567835i
$208$	−6.59045	−	7.08949i	−0.456966	−	0.491568i
$209$			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	$0.897140\pi$
$212$	−6.19032	+	0.700417i	−0.425153	+	0.0481048i
$213$	4.49184	+	7.78009i	0.307776	+	0.533083i
$214$	−5.96545	+	6.67849i	−0.407790	+	0.456532i
$215$		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
$222$	14.1010	+	2.93874i	0.946397	+	0.197235i
$223$		−	24.2380i		−	1.62310i	−0.584284	−	0.811550i	$-0.698624\pi$
$223$		−	24.2380i		−	1.62310i	0.584284	−	0.811550i	$-0.301376\pi$
$224$	14.9615	−	0.392163i	0.999657	−	0.0262025i
$225$		0			0
$226$	1.20562	−	5.78495i	0.0801967	−	0.384809i
$227$	−9.20798	+	5.31623i	−0.611155	+	0.352851i	−0.773417	−	0.633897i	$-0.781454\pi$
$227$	−9.20798	+	5.31623i	−0.611155	+	0.352851i	0.162262	+	0.986748i	$0.448121\pi$
$228$	−4.43521	+	10.1786i	−0.293729	+	0.674095i
$229$	25.5589	+	14.7564i	1.68898	+	0.975132i	0.955302	+	0.295633i	$0.0955304\pi$
$229$	25.5589	+	14.7564i	1.68898	+	0.975132i	0.733676	+	0.679499i	$0.237803\pi$
$230$		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	−0.992864	−	0.119254i	$-0.961950\pi$
$233$	−24.3096	−	14.0351i	−1.59257	−	0.919472i	−0.599709	−	0.800218i	$-0.704717\pi$
$234$	−4.98755	+	5.58370i	−0.326046	+	0.365018i
$235$		0			0
$236$	−0.780415	−	6.89734i	−0.0508007	−	0.448979i
$237$	−0.413732			−0.0268748
$238$	2.14092	+	0.432047i	0.138775	+	0.0280055i
$239$		−	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	−0.612744	−	0.790281i	$-0.709934\pi$
$241$	−3.64372	+	2.10370i	−0.234713	+	0.135512i	0.378031	+	0.925793i	$0.376601\pi$
$242$	−2.83200	+	3.17050i	−0.182048	+	0.203808i
$243$	−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
$248$	0.665366	−	7.14950i	0.0422508	−	0.453993i
$249$	1.17052	+	2.02740i	0.0741787	+	0.128481i
$250$		0			0
$251$	18.8826			1.19186			0.595928	−	0.803038i	$-0.296784\pi$
$251$	18.8826			1.19186			0.595928	+	0.803038i	$0.296784\pi$
$252$	−1.37435	−	11.4943i	−0.0865761	−	0.724075i
$253$			16.1379i			1.01458i
$254$	6.79824	+	1.41680i	0.426559	+	0.0888977i
$255$		0			0
$256$	−1.16580	+	15.9575i	−0.0728623	+	0.997342i
$257$	12.9173	−	22.3734i	0.805757	−	1.39561i	−0.110022	−	0.993929i	$-0.535092\pi$
$257$	12.9173	−	22.3734i	0.805757	−	1.39561i	0.915779	−	0.401682i	$-0.131574\pi$
$258$	−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
$262$	−14.9555	+	16.7431i	−0.923953	+	1.03439i
$263$	5.34857	+	9.26400i	0.329807	+	0.571243i	0.982473	−	0.186403i	$-0.0596830\pi$
$263$	5.34857	+	9.26400i	0.329807	+	0.571243i	−0.652666	+	0.757645i	$0.726350\pi$
$264$	−8.66860	+	3.98401i	−0.533515	+	0.245199i
$265$		0			0
$266$	7.34747	+	21.8443i	0.450502	+	1.33936i
$267$	8.90478			0.544963
$268$	2.21374	+	19.5651i	0.135226	+	1.19513i
$269$	7.24441	−	4.18256i	0.441699	−	0.255015i	−0.262619	−	0.964900i	$-0.584586\pi$
$269$	7.24441	−	4.18256i	0.441699	−	0.255015i	0.704318	+	0.709884i	$0.251253\pi$
$270$		0			0
$271$	−13.5557	+	23.4791i	−0.823448	+	1.42625i	0.0796525	+	0.996823i	$0.474619\pi$
$271$	−13.5557	+	23.4791i	−0.823448	+	1.42625i	−0.903100	+	0.429430i	$0.858714\pi$
$272$	−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
$276$	−3.10495	+	7.12571i	−0.186896	+	0.428918i
$277$	−2.90970	+	1.67991i	−0.174827	+	0.100936i	−0.584860	−	0.811134i	$-0.698850\pi$
$277$	−2.90970	+	1.67991i	−0.174827	+	0.100936i	0.410033	+	0.912071i	$0.365517\pi$
$278$	24.0959	+	5.02173i	1.44517	+	0.301184i
$279$	−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	$0.570253\pi$
$282$	−14.4451	−	3.01045i	−0.860192	−	0.179269i
$283$	−6.24027	+	3.60282i	−0.370945	+	0.214165i	−0.673871	−	0.738849i	$-0.735370\pi$
$283$	−6.24027	+	3.60282i	−0.370945	+	0.214165i	0.302926	+	0.953014i	$0.402036\pi$
$284$	−7.96346	+	18.2758i	−0.472544	+	1.08447i
$285$		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
$292$	2.20338	+	19.4736i	0.128943	+	1.13961i
$293$	−8.47879			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$293$	−8.47879			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$294$	6.72893	+	5.85894i	0.392439	+	0.341700i
$295$		0			0
$296$	13.3479	+	29.0430i	0.775831	+	1.68809i
$297$	8.74905	+	15.1538i	0.507671	+	0.879312i
$298$	−1.55594	+	1.74192i	−0.0901333	+	0.100907i
$299$	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
$304$	−24.0153	+	5.50501i	−1.37737	+	0.315734i
$305$		0			0
$306$	1.76796	+	0.368455i	0.101068	+	0.0210632i
$307$			10.4271i			0.595104i	0.954706	+	0.297552i	$0.0961701\pi$
$307$			10.4271i			0.595104i	−0.954706	+	0.297552i	$0.903830\pi$
$308$	−7.79549	+	18.2044i	−0.444189	+	1.03729i
$309$	9.22183			0.524612
$310$		0			0
$311$	3.96296	+	6.86404i	0.224719	+	0.389224i	0.956235	−	0.292600i	$-0.0945203\pi$
$311$	3.96296	+	6.86404i	0.224719	+	0.389224i	−0.731516	+	0.681824i	$0.761187\pi$
$312$	6.14228	+	0.571629i	0.347738	+	0.0323621i
$313$	−7.23333	+	12.5285i	−0.408852	+	0.708152i	−0.994761	−	0.102224i	$-0.967404\pi$
$313$	−7.23333	+	12.5285i	−0.408852	+	0.708152i	0.585910	+	0.810376i	$0.300737\pi$
$314$	−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	0.583550	−	0.812077i	$-0.301663\pi$
$317$	3.06318	+	1.76853i	0.172046	+	0.0993305i	−0.411504	+	0.911408i	$0.634997\pi$
$318$	2.64488	−	2.96101i	0.148317	−	0.166045i
$319$	1.41136	−	0.814851i	0.0790212	−	0.0456229i
$320$		0			0
$321$		−	5.70690i		−	0.318528i
$322$	5.14373	+	15.2925i	0.286649	+	0.852219i
$323$	−3.59544			−0.200056
$324$	−0.528221	−	4.66844i	−0.0293456	−	0.259358i
$325$		0			0
$326$	−4.25660	+	4.76538i	−0.235751	+	0.263930i
$327$	−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	$-0.109501\pi$
$331$	20.3773	+	11.7649i	1.12004	+	0.646655i	0.178629	+	0.983917i	$0.442834\pi$
$332$	−2.07518	+	4.76245i	−0.113890	+	0.261373i
$333$	21.4105	−	12.3613i	1.17329	−	0.677397i
$334$	−4.88652	+	23.4471i	−0.267378	+	1.28297i
$335$		0			0
$336$	−6.94466	+	6.53831i	−0.378862	+	0.356694i
$337$		−	5.10057i		−	0.277846i	−0.990303	−	0.138923i	$-0.955636\pi$
$337$		−	5.10057i		−	0.277846i	0.990303	−	0.138923i	$-0.0443640\pi$
$338$	9.89072	+	2.06129i	0.537984	+	0.112119i
$339$	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
$346$	0.125015	−	0.139958i	0.00672087	−	0.00752420i
$347$	−0.833209	−	1.44316i	−0.0447290	−	0.0774729i	0.842794	−	0.538236i	$-0.180909\pi$
$347$	−0.833209	−	1.44316i	−0.0447290	−	0.0774729i	−0.887523	+	0.460763i	$0.847576\pi$
$348$	0.779969	−	0.0882513i	0.0418107	−	0.00473077i
$349$			27.6081i			1.47783i	0.673801	+	0.738913i	$0.264661\pi$
$349$			27.6081i			1.47783i	−0.673801	+	0.738913i	$0.735339\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	−18.5409	−	10.2189i	−0.988236	−	0.544669i
$353$	13.5789	+	23.5193i	0.722730	+	1.25180i	0.959902	+	0.280337i	$0.0904461\pi$
$353$	13.5789	+	23.5193i	0.722730	+	1.25180i	−0.237172	+	0.971468i	$0.576221\pi$
$354$	3.29920	+	2.94696i	0.175351	+	0.156629i
$355$		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	$-0.187551\pi$
$359$	14.5102	+	8.37747i	0.765819	+	0.442146i	−0.0655619	+	0.997849i	$0.520884\pi$
$360$		0			0
$361$	−9.47002	−	16.4026i	−0.498422	−	0.863293i
$362$	1.15216	−	5.52841i	0.0605560	−	0.290567i
$363$		−	2.70926i		−	0.142199i
$364$	10.2508	−	7.67374i	0.537290	−	0.402213i
$365$		0			0
$366$	12.9616	+	2.70128i	0.677514	+	0.141198i
$367$	−7.31294	+	4.22213i	−0.381732	+	0.220393i	−0.678572	−	0.734534i	$-0.737401\pi$
$367$	−7.31294	+	4.22213i	−0.381732	+	0.220393i	0.296839	+	0.954927i	$0.404067\pi$
$368$	−16.8124	+	3.85388i	−0.876404	+	0.200897i
$369$	−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	0.714281	−	0.699859i	$-0.246754\pi$
$373$	8.98694	+	5.18861i	0.465326	+	0.268656i	−0.248955	+	0.968515i	$0.580087\pi$
$374$	−2.30408	−	2.05808i	−0.119141	−	0.106421i
$375$		0			0
$376$	−13.6736	−	29.7517i	−0.705162	−	1.53432i
$377$	−1.05378			−0.0542723
$378$	13.1208	+	11.5714i	0.674862	+	0.595166i
$379$		−	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
$382$	21.1471	+	18.8893i	1.08198	+	0.966462i
$383$	0.828825	+	0.478522i	0.0423510	+	0.0244514i	0.521026	−	0.853541i	$-0.325549\pi$
$383$	0.828825	+	0.478522i	0.0423510	+	0.0244514i	−0.478675	+	0.877992i	$0.658883\pi$
$384$	−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
$388$	8.32488	+	3.62747i	0.422632	+	0.184157i
$389$	−15.0820	−	26.1228i	−0.764689	−	1.32448i	−0.940411	−	0.340041i	$-0.889559\pi$
$389$	−15.0820	−	26.1228i	−0.764689	−	1.32448i	0.175722	−	0.984440i	$-0.443774\pi$
$390$		0			0
$391$	−2.51705			−0.127293
$392$	−1.58475	+	19.7355i	−0.0800418	+	0.996792i
$393$		−	14.3073i		−	0.721708i
$394$	0.472436	−	2.26690i	0.0238010	−	0.114205i
$395$		0			0
$396$	−6.54110	+	15.0115i	−0.328703	+	0.754358i
$397$	−3.10349	+	5.37540i	−0.155760	+	0.269783i	−0.933335	−	0.359006i	$-0.883116\pi$
$397$	−3.10349	+	5.37540i	−0.155760	+	0.269783i	0.777576	+	0.628789i	$0.216449\pi$
$398$	−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	0.324384	+	0.945926i	$0.394843\pi$
$401$	−13.1565	+	22.7877i	−0.657004	+	1.13796i	−0.981387	+	0.192038i	$0.938490\pi$
$402$	−9.35859	−	8.35941i	−0.466764	−	0.416930i
$403$	−3.07165	−	5.32025i	−0.153010	−	0.265020i
$404$	18.1729	−	2.05621i	0.904134	−	0.102300i
$405$		0			0
$406$	1.07771	−	1.22202i	0.0534858	−	0.0606478i
$407$	−42.2927			−2.09637
$408$	−0.621394	−	1.35206i	−0.0307636	−	0.0669368i
$409$	15.9374	−	9.20148i	0.788055	−	0.454984i	−0.0512223	−	0.998687i	$-0.516312\pi$
$409$	15.9374	−	9.20148i	0.788055	−	0.454984i	0.839277	+	0.543703i	$0.182978\pi$
$410$		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
$416$	7.07872	+	11.7167i	0.347063	+	0.574460i
$417$	−13.5847	+	7.84312i	−0.665245	+	0.384079i
$418$	6.65120	−	31.9146i	0.325321	−	1.56099i
$419$	35.2426			1.72171			0.860856	−	0.508848i	$-0.169928\pi$
$419$	35.2426			1.72171			0.860856	+	0.508848i	$0.169928\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	2.66181	−	12.7722i	0.129575	−	0.621740i
$423$	−21.9329	+	12.6630i	−1.06641	+	0.615695i
$424$	8.77239	+	0.816400i	0.426025	+	0.0396479i
$425$		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	$-0.651287\pi$
$431$	1.73673	−	1.00270i	0.0836555	−	0.0482985i	0.541244	+	0.840865i	$0.317953\pi$
$432$	−13.6978	+	12.7336i	−0.659035	+	0.612645i
$433$	−13.5978			−0.653469			−0.326734	−	0.945116i	$-0.605948\pi$
$433$	−13.5978			−0.653469			−0.326734	+	0.945116i	$0.605948\pi$
$434$	9.31106	+	1.87902i	0.446945	+	0.0901957i
$435$		0			0
$436$	−4.21849	−	37.2832i	−0.202029	−	1.78554i
$437$	−13.2803	−	23.0022i	−0.635283	−	1.10034i
$438$	−9.31480	−	8.32029i	−0.445078	−	0.397559i
$439$	−14.5247	+	25.1574i	−0.693224	+	1.20070i	0.277552	+	0.960711i	$0.410477\pi$
$439$	−14.5247	+	25.1574i	−0.693224	+	1.20070i	−0.970776	+	0.239989i	$0.922856\pi$
$440$		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	$-0.720295\pi$
$443$	7.31831	−	12.6757i	0.347703	−	0.602240i	0.985841	+	0.167683i	$0.0536283\pi$
$444$	−18.6744	−	8.13717i	−0.886250	−	0.386173i
$445$		0			0
$446$	−6.99345	+	33.5568i	−0.331149	+	1.58896i
$447$		−	1.48851i		−	0.0704040i
$448$	−20.8268	−	3.77393i	−0.983976	−	0.178301i
$449$	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
$452$	−3.33829	+	7.66122i	−0.157020	+	0.360353i
$453$	−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	0.337959	−	0.941161i	$-0.390264\pi$
$457$	−6.58709	−	3.80306i	−0.308131	−	0.177900i	−0.646090	+	0.763261i	$0.723597\pi$
$458$	−31.1277	−	27.8043i	−1.45450	−	1.29921i
$459$	−2.36357	+	1.36461i	−0.110322	+	0.0636943i
$460$		0			0
$461$			12.7953i			0.595936i	0.954576	+	0.297968i	$0.0963089\pi$
$461$			12.7953i			0.595936i	−0.954576	+	0.297968i	$0.903691\pi$
$462$	−4.02351	−	11.9621i	−0.187191	−	0.556526i
$463$	27.9178			1.29745			0.648724	−	0.761024i	$-0.275303\pi$
$463$	27.9178			1.29745			0.648724	+	0.761024i	$0.275303\pi$
$464$	1.18595	+	1.27576i	0.0550566	+	0.0592255i
$465$		0			0
$466$	29.6062	+	26.4453i	1.37148	+	1.22505i
$467$	19.5815	+	11.3054i	0.906126	+	0.523152i	0.879183	−	0.476485i	$-0.158089\pi$
$467$	19.5815	+	11.3054i	0.906126	+	0.523152i	0.0269432	+	0.999637i	$0.491423\pi$
$468$	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
$472$	−0.909644	+	9.77432i	−0.0418698	+	0.449899i
$473$	18.8013	−	10.8549i	0.864484	−	0.499110i
$474$	0.572798	+	0.119375i	0.0263095	+	0.00548307i
$475$		0			0
$476$	−2.83937	−	1.21588i	−0.130142	−	0.0557297i
$477$		−	6.81448i		−	0.312014i
$478$	−3.93207	+	18.8673i	−0.179849	+	0.862971i
$479$	10.9907	+	19.0365i	0.502180	+	0.869801i	0.999997	+	0.00251901i	$0.000801826\pi$
$479$	10.9907	+	19.0365i	0.502180	+	0.869801i	−0.497817	+	0.867282i	$0.665865\pi$
$480$		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
$486$	17.0272	+	15.2093i	0.772371	+	0.689908i
$487$	−12.6914	−	21.9822i	−0.575103	−	0.996108i	−0.996030	−	0.0890138i	$-0.971628\pi$
$487$	−12.6914	−	21.9822i	−0.575103	−	0.996108i	0.420927	−	0.907095i	$-0.361705\pi$
$488$	12.2694	+	26.6962i	0.555408	+	1.20848i
$489$		−	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	$-0.307582\pi$
$492$	1.48970	+	13.1660i	0.0671607	+	0.593570i
$493$	0.127094	+	0.220133i	0.00572402	+	0.00991429i
$494$	−14.0426	+	15.7211i	−0.631808	+	0.707326i
$495$		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	$-0.418998\pi$
$499$	−10.2874	−	5.93945i	−0.460528	−	0.265886i	−0.712266	+	0.701909i	$0.752331\pi$
$500$		0			0
$501$	−7.63194	−	13.2189i	−0.340970	−	0.590577i
$502$	−26.1423	−	5.44822i	−1.16679	−	0.243166i
$503$			17.3055i			0.771614i	0.922580	+	0.385807i	$0.126077\pi$
$503$			17.3055i			0.771614i	−0.922580	+	0.385807i	$0.873923\pi$
$504$	−1.41373	+	16.3101i	−0.0629727	+	0.726509i
$505$		0			0
$506$	4.65629	−	22.3424i	0.206997	−	0.993239i
$507$	−5.57615	+	3.21939i	−0.247646	+	0.142978i
$508$	−9.00314	−	3.92301i	−0.399450	−	0.174056i
$509$	11.8717	+	6.85414i	0.526205	+	0.303805i	0.739470	−	0.673190i	$-0.235076\pi$
$509$	11.8717	+	6.85414i	0.526205	+	0.303805i	−0.213265	+	0.976994i	$0.568410\pi$
$510$		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
$514$	−24.3389	+	27.2481i	−1.07355	+	1.20186i
$515$		0			0
$516$	10.3903	−	1.17563i	0.457405	−	0.0517541i
$517$	43.3247			1.90542
$518$	−40.0773	+	13.4802i	−1.76089	+	0.592287i
$519$			0.119597i			0.00524973i
$520$		0			0
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.387171	−	0.922008i	$-0.373452\pi$
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.992068	+	0.125704i	$0.0401190\pi$
$522$	0.897511	−	1.00479i	0.0392830	−	0.0439784i
$523$	−3.69292	−	2.13211i	−0.161480	−	0.0932306i	0.417082	−	0.908869i	$-0.363053\pi$
$523$	−3.69292	−	2.13211i	−0.161480	−	0.0932306i	−0.578562	+	0.815638i	$0.696386\pi$
$524$	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
$528$	13.1509	−	3.01457i	0.572320	−	0.131192i
$529$	2.20289	+	3.81552i	0.0957778	+	0.165892i
$530$		0			0
$531$	7.59279			0.329499
$532$	−3.86955	−	32.3628i	−0.167766	−	1.40310i
$533$		−	17.7879i		−	0.770482i
$534$	−12.3284	−	2.56931i	−0.533501	−	0.111185i
$535$		0			0
$536$	2.58032	−	27.7260i	0.111453	−	1.19758i
$537$	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	−0.785215	−	0.619223i	$-0.787448\pi$
$541$	3.34133	−	5.78736i	0.143655	−	0.248818i	0.928870	+	0.370405i	$0.120781\pi$
$542$	25.5418	−	28.5948i	1.09712	−	1.22825i
$543$	1.79948	+	3.11679i	0.0772229	+	0.133754i
$544$	1.59386	−	2.89187i	0.0683362	−	0.123988i
$545$		0			0
$546$	−1.61430	+	7.99932i	−0.0690857	+	0.342339i
$547$	45.6888			1.95351			0.976756	−	0.214353i	$-0.0687642\pi$
$547$	45.6888			1.95351			0.976756	+	0.214353i	$0.0687642\pi$
$548$	15.5850	−	1.76339i	0.665757	−	0.0753285i
$549$	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
$556$	−31.9110	−	13.9049i	−1.35333	−	0.589697i
$557$	−4.22972	+	2.44203i	−0.179219	+	0.103472i	−0.586926	−	0.809641i	$-0.699662\pi$
$557$	−4.22972	+	2.44203i	−0.179219	+	0.103472i	0.407707	+	0.913113i	$0.366329\pi$
$558$	7.68906	+	1.60245i	0.325504	+	0.0678371i
$559$	−14.0378			−0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	10.1613	+	2.11767i	0.428627	+	0.0893286i
$563$	2.36931	−	1.36792i	0.0998543	−	0.0576509i	−0.449241	−	0.893410i	$-0.648306\pi$
$563$	2.36931	−	1.36792i	0.0998543	−	0.0576509i	0.549096	+	0.835760i	$0.314972\pi$
$564$	19.1301	+	8.33573i	0.805524	+	0.350997i
$565$		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	−0.813860	−	0.581062i	$-0.802638\pi$
$569$	2.29674	−	3.97807i	0.0962843	−	0.166769i	0.910144	+	0.414292i	$0.135971\pi$
$570$		0			0
$571$	4.86573	−	2.80923i	0.203625	−	0.117563i	−0.394720	−	0.918801i	$-0.629159\pi$
$571$	4.86573	−	2.80923i	0.203625	−	0.117563i	0.598345	+	0.801239i	$0.295825\pi$
$572$	−17.9980	+	2.03642i	−0.752532	+	0.0851469i
$573$	−18.0707			−0.754912
$574$	20.6279	+	18.1919i	0.860992	+	0.759316i
$575$		0			0
$576$	−17.2010	−	3.22959i	−0.716709	−	0.134566i
$577$	17.1731	+	29.7446i	0.714924	+	1.23828i	0.962989	+	0.269541i	$0.0868719\pi$
$577$	17.1731	+	29.7446i	0.714924	+	1.23828i	−0.248065	+	0.968743i	$0.579795\pi$
$578$	−15.6949	+	17.5708i	−0.652820	+	0.730850i
$579$	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
$584$	2.56824	−	27.5963i	0.106275	−	1.14194i
$585$		0			0
$586$	11.7386	+	2.44640i	0.484917	+	0.101060i
$587$			40.1422i			1.65685i	0.560103	+	0.828423i	$0.310762\pi$
$587$			40.1422i			1.65685i	−0.560103	+	0.828423i	$0.689238\pi$
$588$	−7.62549	−	10.0530i	−0.314470	−	0.414579i
$589$	−15.6369			−0.644309
$590$		0			0
$591$	0.737868	+	1.27802i	0.0303518	+	0.0525709i
$592$	−10.0999	−	44.0603i	−0.415103	−	1.81087i
$593$	−5.46684	+	9.46884i	−0.224496	+	0.388839i	−0.956168	−	0.292818i	$-0.905407\pi$
$593$	−5.46684	+	9.46884i	−0.224496	+	0.388839i	0.731672	+	0.681657i	$0.238740\pi$
$594$	−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
$598$	−9.83079	+	11.0058i	−0.402011	+	0.450063i
$599$	−4.51466	+	2.60654i	−0.184464	+	0.106500i	−0.589388	−	0.807850i	$-0.700631\pi$
$599$	−4.51466	+	2.60654i	−0.184464	+	0.106500i	0.404924	+	0.914350i	$0.367298\pi$
$600$		0			0
$601$		−	16.1103i		−	0.657154i	−0.944477	−	0.328577i	$-0.893431\pi$
$601$		−	16.1103i		−	0.657154i	0.944477	−	0.328577i	$-0.106569\pi$
$602$	14.3566	−	16.2790i	0.585129	−	0.663481i
$603$	−21.5379			−0.877090
$604$	−14.6190	+	1.65410i	−0.594838	+	0.0673042i
$605$		0			0
$606$	−7.76455	+	8.69263i	−0.315413	+	0.353114i
$607$	−8.36252	−	4.82810i	−0.339424	−	0.195967i	0.320593	−	0.947217i	$-0.396118\pi$
$607$	−8.36252	−	4.82810i	−0.339424	−	0.195967i	−0.660017	+	0.751250i	$0.729451\pi$
$608$	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
$612$	−2.34138	−	1.02023i	−0.0946446	−	0.0412403i
$613$	6.79635	−	3.92388i	0.274502	−	0.158484i	−0.356430	−	0.934322i	$-0.616006\pi$
$613$	6.79635	−	3.92388i	0.274502	−	0.158484i	0.630932	+	0.775838i	$0.282673\pi$
$614$	3.00854	−	14.4359i	0.121415	−	0.582586i
$615$		0			0
$616$	16.0451	−	22.9541i	0.646477	−	0.924847i
$617$			28.8434i			1.16119i	0.814191	+	0.580597i	$0.197181\pi$
$617$			28.8434i			1.16119i	−0.814191	+	0.580597i	$0.802819\pi$
$618$	−12.7673	−	2.66079i	−0.513577	−	0.107033i
$619$	−1.24278	−	2.15256i	−0.0499517	−	0.0865189i	0.839968	−	0.542635i	$-0.182573\pi$
$619$	−1.24278	−	2.15256i	−0.0499517	−	0.0865189i	−0.889920	+	0.456116i	$0.849240\pi$
$620$		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
$626$	13.6292	−	15.2582i	0.544731	−	0.609842i
$627$	10.3881	+	17.9927i	0.414860	+	0.718558i
$628$	0.693131	+	6.12592i	0.0276589	+	0.244451i
$629$		−	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	$0.943265\pi$
$632$	0.542207	+	1.17976i	0.0215678	+	0.0469283i
$633$	4.15730	+	7.20066i	0.165238	+	0.286200i
$634$	−3.73060	−	3.33230i	−0.148161	−	0.132342i
$635$		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	0.684583	−	0.728935i	$-0.259984\pi$
$641$	−7.31652	−	12.6726i	−0.288985	−	0.500537i	−0.973568	+	0.228398i	$0.926651\pi$
$642$	−1.64662	+	7.90102i	−0.0649870	+	0.311828i
$643$			24.2513i			0.956380i	0.878256	+	0.478190i	$0.158707\pi$
$643$			24.2513i			0.956380i	−0.878256	+	0.478190i	$0.841293\pi$
$644$	−2.70894	−	22.6561i	−0.106747	−	0.892776i
$645$		0			0
$646$	4.97777	+	1.03740i	0.195848	+	0.0408160i
$647$	25.9077	−	14.9578i	1.01854	−	0.588053i	0.104857	−	0.994487i	$-0.466561\pi$
$647$	25.9077	−	14.9578i	1.01854	−	0.588053i	0.913680	+	0.406435i	$0.133228\pi$
$648$	−0.615690	+	6.61571i	−0.0241866	+	0.259890i
$649$	−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	0.739972	−	0.672638i	$-0.234839\pi$
$653$	13.4780	+	7.78155i	0.527436	+	0.304516i	−0.212535	+	0.977153i	$0.568172\pi$
$654$	17.8337	+	15.9296i	0.697351	+	0.622898i
$655$		0			0
$656$	−21.5350	+	20.0191i	−0.840800	+	0.781615i
$657$	−21.4371			−0.836340
$658$	41.0552	−	13.8092i	1.60050	−	0.538337i
$659$			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	−0.166800	−	0.985991i	$-0.553344\pi$
$661$	15.5209	−	8.96099i	0.603693	−	0.348542i	0.770493	+	0.637449i	$0.220010\pi$
$662$	−24.8172	−	22.1676i	−0.964549	−	0.861567i
$663$	−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
$668$	13.5305	−	31.0518i	0.523509	−	1.20143i
$669$	−10.9226	−	18.9185i	−0.422292	−	0.731432i
$670$		0			0
$671$	−38.8754			−1.50077
$672$	11.5012	−	7.04833i	0.443667	−	0.271895i
$673$			21.1876i			0.816723i	0.912820	+	0.408362i	$0.133900\pi$
$673$			21.1876i			0.816723i	−0.912820	+	0.408362i	$0.866100\pi$
$674$	−1.47168	+	7.06157i	−0.0566868	+	0.272001i
$675$		0			0
$676$	−13.0986	−	5.70758i	−0.503794	−	0.219522i
$677$	−12.6285	+	21.8732i	−0.485353	+	0.840657i	−0.999858	−	0.0168308i	$-0.994642\pi$
$677$	−12.6285	+	21.8732i	−0.485353	+	0.840657i	0.514505	+	0.857487i	$0.327976\pi$
$678$	−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
$682$	−10.0207	−	8.95080i	−0.383711	−	0.342744i
$683$	−11.0499	−	19.1391i	−0.422814	−	0.732336i	0.573399	−	0.819276i	$-0.305624\pi$
$683$	−11.0499	−	19.1391i	−0.422814	−	0.732336i	−0.996214	+	0.0869404i	$0.972291\pi$
$684$	−3.03003	−	26.7796i	−0.115856	−	1.02394i
$685$		0			0
$686$	−25.7376	−	4.85545i	−0.982667	−	0.185382i
$687$	26.5993			1.01483
$688$	15.7985	+	16.9948i	0.602313	+	0.647921i
$689$	6.52791	−	3.76889i	0.248694	−	0.143583i
$690$		0			0
$691$	−9.05508	+	15.6839i	−0.344471	+	0.596642i	−0.985258	−	0.171077i	$-0.945275\pi$
$691$	−9.05508	+	15.6839i	−0.344471	+	0.596642i	0.640786	+	0.767719i	$0.278609\pi$
$692$	−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
$696$	−1.10530	−	0.102865i	−0.0418965	−	0.00389908i
$697$	−3.71588	+	2.14537i	−0.140749	+	0.0812615i
$698$	7.96581	−	38.2225i	0.301510	−	1.44674i
$699$	−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	$0.412138\pi$
$702$	−3.26456	+	15.6644i	−0.123213	+	0.591215i
$703$	60.2820	−	34.8038i	2.27358	−	1.31265i
$704$	22.7209	+	19.4974i	0.856324	+	0.734835i
$705$		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	0.274814	+	0.961498i	$0.411384\pi$
$709$	−18.5131	+	32.0657i	−0.695275	+	1.20425i	−0.970088	+	0.242753i	$0.921949\pi$
$710$		0			0
$711$	0.869718	−	0.502132i	0.0326170	−	0.0188314i
$712$	−11.6699	−	25.3920i	−0.437350	−	0.951605i
$713$	−10.9469			−0.409965
$714$	1.86575	−	0.627554i	0.0698238	−	0.0234856i
$715$		0			0
$716$	31.9940	−	3.62003i	1.19567	−	0.135287i
$717$	−6.14124	−	10.6369i	−0.229349	−	0.397244i
$718$	−17.6717	−	15.7850i	−0.659503	−	0.589091i
$719$	−10.0975	+	17.4894i	−0.376573	+	0.652243i	−0.990561	−	0.137072i	$-0.956231\pi$
$719$	−10.0975	+	17.4894i	−0.376573	+	0.652243i	0.613988	+	0.789315i	$0.289564\pi$
$720$		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
$724$	−3.19024	+	7.32147i	−0.118564	+	0.272100i
$725$		0			0
$726$	−0.781708	+	3.75088i	−0.0290119	+	0.139208i
$727$			10.7925i			0.400272i	0.979768	+	0.200136i	$0.0641385\pi$
$727$			10.7925i			0.400272i	−0.979768	+	0.200136i	$0.935862\pi$
$728$	−16.4061	+	7.66635i	−0.608050	+	0.284134i
$729$	−7.50278			−0.277881
$730$		0			0
$731$	1.69306	+	2.93247i	0.0626202	+	0.108461i
$732$	−17.1655	−	7.47967i	−0.634456	−	0.276457i
$733$	−3.61611	+	6.26329i	−0.133564	+	0.231340i	−0.925048	−	0.379850i	$-0.875976\pi$
$733$	−3.61611	+	6.26329i	−0.133564	+	0.231340i	0.791484	+	0.611190i	$0.209309\pi$
$734$	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
$738$	16.9610	+	15.1501i	0.624343	+	0.557684i
$739$	1.71927	−	0.992622i	0.0632444	−	0.0365142i	−0.468044	−	0.883705i	$-0.655041\pi$
$739$	1.71927	−	0.992622i	0.0632444	−	0.0365142i	0.531289	+	0.847191i	$0.321708\pi$
$740$		0			0
$741$		−	13.4340i		−	0.493511i
$742$	−2.30554	+	11.4246i	−0.0846391	+	0.419411i
$743$	−19.8225			−0.727216			−0.363608	−	0.931552i	$-0.618455\pi$
$743$	−19.8225			−0.727216			−0.363608	+	0.931552i	$0.618455\pi$
$744$	−2.70250	−	5.88023i	−0.0990786	−	0.215580i
$745$		0			0
$746$	−10.9450	−	9.77648i	−0.400727	−	0.357942i
$747$	−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	$-0.188410\pi$
$751$	20.8718	+	12.0504i	0.761624	+	0.439724i	−0.0682545	+	0.997668i	$0.521743\pi$
$752$	10.3464	+	45.1355i	0.377293	+	1.64592i
$753$	14.7384	−	8.50921i	0.537097	−	0.310093i
$754$	1.45892	+	0.304048i	0.0531308	+	0.0110728i
$755$		0			0
$756$	−14.8266	−	19.8059i	−0.539239	−	0.720335i
$757$		−	34.8711i		−	1.26741i	−0.773574	−	0.633706i	$-0.781533\pi$
$757$		−	34.8711i		−	1.26741i	0.773574	−	0.633706i	$-0.218467\pi$
$758$	−3.40398	+	16.3334i	−0.123638	+	0.593256i
$759$	7.27236	+	12.5961i	0.263970	+	0.457209i
$760$		0			0
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	0.634113	−	0.773240i	$-0.281365\pi$
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	−0.352589	+	0.935778i	$0.614699\pi$
$762$	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
$766$	−1.00941	−	0.901641i	−0.0364715	−	0.0325776i
$767$	4.19935	+	7.27349i	0.151630	+	0.262631i
$768$	6.28112	+	12.9806i	0.226650	+	0.468398i
$769$			0.573577i			0.0206837i	0.999947	+	0.0103419i	$0.00329197\pi$
$769$			0.573577i			0.0206837i	−0.999947	+	0.0103419i	$0.996708\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	38.4331	−	4.34860i	1.38324	−	0.156509i
$773$	−2.17425	−	3.76591i	−0.0782023	−	0.135450i	0.824272	−	0.566194i	$-0.191585\pi$
$773$	−2.17425	−	3.76591i	−0.0782023	−	0.135450i	−0.902474	+	0.430744i	$0.858251\pi$
$774$	11.9561	−	13.3851i	0.429752	−	0.481119i
$775$		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
$782$	3.48478	+	0.726250i	0.124615	+	0.0259707i
$783$			2.03603i			0.0727618i
$784$	7.88834	−	26.8659i	0.281726	−	0.959495i
$785$		0			0
$786$	−4.12811	+	19.8080i	−0.147245	+	0.706528i
$787$	18.2295	−	10.5248i	0.649811	−	0.375168i	−0.138573	−	0.990352i	$-0.544252\pi$
$787$	18.2295	−	10.5248i	0.649811	−	0.375168i	0.788384	+	0.615184i	$0.210918\pi$
$788$	−1.30815	+	3.00214i	−0.0466008	+	0.106947i
$789$	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
$794$	5.84765	−	6.54661i	0.207525	−	0.232330i
$795$		0			0
$796$	0.176124	+	1.55660i	0.00624256	+	0.0551721i
$797$	−14.7349			−0.521938			−0.260969	−	0.965347i	$-0.584042\pi$
$797$	−14.7349			−0.521938			−0.260969	+	0.965347i	$0.584042\pi$
$798$	15.5788	+	13.7391i	0.551485	+	0.486359i
$799$			6.75744i			0.239061i
$800$		0			0
$801$	−18.7190	+	10.8074i	−0.661403	+	0.381861i
$802$	24.7897	−	27.7528i	0.875355	−	0.979984i
$803$	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
$808$	−25.7530	−	2.39670i	−0.905988	−	0.0843156i
$809$	−7.23808	−	12.5367i	−0.254477	−	0.440768i	0.710276	−	0.703923i	$-0.248570\pi$
$809$	−7.23808	−	12.5367i	−0.254477	−	0.440768i	−0.964753	+	0.263156i	$0.915237\pi$
$810$		0			0
$811$	18.5825			0.652521			0.326260	−	0.945280i	$-0.394211\pi$
$811$	18.5825			0.652521			0.326260	+	0.945280i	$0.394211\pi$
$812$	−1.84464	+	1.38089i	−0.0647343	+	0.0484598i
$813$			24.4348i			0.856967i
$814$	58.5529	+	12.2028i	2.05228	+	0.427708i
$815$		0			0
$816$	0.470188	+	2.05117i	0.0164599	+	0.0718054i
$817$	−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	−0.686640	−	0.726997i	$-0.740915\pi$
$821$	8.20275	−	14.2076i	0.286278	−	0.495848i	0.972918	+	0.231149i	$0.0742486\pi$
$822$	−6.65884	+	7.45475i	−0.232254	+	0.260014i
$823$	21.9486	+	38.0161i	0.765081	+	1.32516i	0.940204	+	0.340612i	$0.110634\pi$
$823$	21.9486	+	38.0161i	0.765081	+	1.32516i	−0.175123	+	0.984547i	$0.556032\pi$
$824$	−12.0854	−	26.2961i	−0.421017	−	0.916067i
$825$		0			0
$826$	−12.7295	−	2.56887i	−0.442915	−	0.0893823i
$827$	−8.10796			−0.281941			−0.140971	−	0.990014i	$-0.545022\pi$
$827$	−8.10796			−0.281941			−0.140971	+	0.990014i	$0.545022\pi$
$828$	−2.12123	−	18.7475i	−0.0737178	−	0.651522i
$829$	36.5657	−	21.1112i	1.26998	−	0.733223i	0.294995	−	0.955499i	$-0.404682\pi$
$829$	36.5657	−	21.1112i	1.26998	−	0.733223i	0.974984	+	0.222276i	$0.0713486\pi$
$830$		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
$836$	−18.4167	+	42.2656i	−0.636956	+	1.46179i
$837$	−10.2794	+	5.93481i	−0.355308	+	0.205137i
$838$	−48.7922	−	10.1686i	−1.68550	−	0.351269i
$839$	−31.8404			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$839$	−31.8404			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	21.6903	+	4.52040i	0.747497	+	0.155783i
$843$	−5.72868	+	3.30745i	−0.197306	+	0.113915i
$844$	−7.37036	+	16.9147i	−0.253698	+	0.582227i
$845$		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
$852$	2.02007	+	17.8534i	0.0692063	+	0.611649i
$853$	−16.2023			−0.554755			−0.277378	−	0.960761i	$-0.589465\pi$
$853$	−16.2023			−0.554755			−0.277378	+	0.960761i	$0.589465\pi$
$854$	−36.8390	+	12.3910i	−1.26060	+	0.424011i
$855$		0			0
$856$	−16.2733	+	7.47905i	−0.556208	+	0.255629i
$857$	−20.4762	−	35.4659i	−0.699455	−	1.21149i	−0.968656	−	0.248407i	$-0.920093\pi$
$857$	−20.4762	−	35.4659i	−0.699455	−	1.21149i	0.269201	−	0.963084i	$-0.413240\pi$
$858$	7.68981	−	8.60896i	0.262526	−	0.293905i
$859$	−6.02640	+	10.4380i	−0.205618	+	0.356141i	−0.950329	−	0.311246i	$-0.899254\pi$
$859$	−6.02640	+	10.4380i	−0.205618	+	0.356141i	0.744711	+	0.667387i	$0.232587\pi$
$860$		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	$-0.836426\pi$
$863$	−0.285426	+	0.494372i	−0.00971602	+	0.0168286i	0.861127	+	0.508391i	$0.169759\pi$
$864$	22.6382	−	13.6770i	0.770167	−	0.465300i
$865$		0			0
$866$	18.8257	+	3.92340i	0.639724	+	0.133323i
$867$		−	15.0146i		−	0.509924i
$868$	−12.3487	−	5.28797i	−0.419142	−	0.179486i
$869$	−1.71798			−0.0582784
$870$		0			0
$871$	−11.9120	−	20.6321i	−0.403622	−	0.699093i
$872$	−4.91703	+	52.8345i	−0.166512	+	1.78920i
$873$	−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	0.750728	−	0.660611i	$-0.229703\pi$
$877$	16.4059	+	9.47193i	0.553987	+	0.319844i	−0.196742	+	0.980455i	$0.563036\pi$
$878$	27.3676	−	30.6388i	0.923613	−	1.03401i
$879$	−6.61794	+	3.82087i	−0.223218	+	0.128875i
$880$		0			0
$881$			35.7695i			1.20511i	0.798079	+	0.602553i	$0.205850\pi$
$881$			35.7695i			1.20511i	−0.798079	+	0.602553i	$0.794150\pi$
$882$	−21.2559	−	4.14957i	−0.715722	−	0.139723i
$883$	−25.4594			−0.856776			−0.428388	−	0.903595i	$-0.640918\pi$
$883$	−25.4594			−0.856776			−0.428388	+	0.903595i	$0.640918\pi$
$884$	−0.317624	−	2.80717i	−0.0106828	−	0.0944155i
$885$		0			0
$886$	−13.7893	+	15.4375i	−0.463260	+	0.518633i
$887$	−9.18408	−	5.30243i	−0.308371	−	0.178038i	0.337826	−	0.941209i	$-0.390308\pi$
$887$	−9.18408	−	5.30243i	−0.308371	−	0.178038i	−0.646197	+	0.763170i	$0.723642\pi$
$888$	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
$892$	19.3644	−	44.4404i	0.648368	−	1.48798i
$893$	−61.7530	+	35.6531i	−2.06648	+	1.19309i
$894$	−0.429482	+	2.06079i	−0.0143640	+	0.0689231i
$895$		0			0
$896$	27.7452	+	11.2341i	0.926902	+	0.375305i
$897$		−	9.40472i		−	0.314014i
$898$	−37.4774	−	7.81053i	−1.25064	−	0.260641i
$899$	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
$906$	6.24611	−	6.99269i	0.207513	−	0.232317i
$907$	7.68190	+	13.3054i	0.255073	+	0.441800i	0.964915	−	0.262561i	$-0.0845671\pi$
$907$	7.68190	+	13.3054i	0.255073	+	0.441800i	−0.709842	+	0.704361i	$0.751234\pi$
$908$	−21.1301	+	2.39081i	−0.701227	+	0.0793418i
$909$			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	$0.880843\pi$
$912$	−16.2639	+	15.1191i	−0.538552	+	0.500642i
$913$	4.86046	+	8.41856i	0.160858	+	0.278614i
$914$	8.02231	+	7.16579i	0.265354	+	0.237023i
$915$		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	$-0.00375369\pi$
$919$	45.1598	+	26.0730i	1.48968	+	0.860069i	0.489753	+	0.871861i	$0.337087\pi$
$920$		0			0
$921$	4.69884	+	8.13863i	0.154832	+	0.268177i
$922$	3.69185	−	17.7147i	0.121585	−	0.583401i
$923$		−	24.1209i		−	0.793949i
$924$	2.11898	+	17.7220i	0.0697094	+	0.583011i
$925$		0			0
$926$	−38.6512	−	8.05516i	−1.27016	−	0.264709i
$927$	−19.3855	+	11.1922i	−0.636702	+	0.367600i
$928$	−1.27382	−	2.10843i	−0.0418152	−	0.0692126i
$929$	−24.8707	−	14.3591i	−0.815982	−	0.471107i	0.0330469	−	0.999454i	$-0.489479\pi$
$929$	−24.8707	−	14.3591i	−0.815982	−	0.471107i	−0.849029	+	0.528346i	$0.822812\pi$
$930$		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
$934$	−23.8480	−	21.3019i	−0.780332	−	0.697018i
$935$		0			0
$936$	−13.6056	+	6.25302i	−0.444713	+	0.204386i
$937$	−44.9045			−1.46697			−0.733484	−	0.679707i	$-0.762107\pi$
$937$	−44.9045			−1.46697			−0.733484	+	0.679707i	$0.762107\pi$
$938$	36.1087	+	7.28691i	1.17899	+	0.237926i
$939$			13.0385i			0.425495i
$940$		0			0
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	−0.228048	−	0.973650i	$-0.573234\pi$
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	0.729182	+	0.684320i	$0.239901\pi$
$942$	−2.93021	−	2.61736i	−0.0954715	−	0.0852783i
$943$	−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	0.390025	+	0.920804i	$0.372467\pi$
$947$	−18.5387	+	32.1100i	−0.602428	+	1.04344i	−0.992452	+	0.122631i	$0.960867\pi$
$948$	−0.758577	−	0.330541i	−0.0246374	−	0.0107355i
$949$	−11.8562	−	20.5356i	−0.384869	−	0.666613i
$950$		0			0
$951$	3.18787			0.103374
$952$	3.58019	+	2.50259i	0.116035	+	0.0811094i
$953$		−	28.5420i		−	0.924567i	−0.886732	−	0.462283i	$-0.847030\pi$
$953$		−	28.5420i		−	0.924567i	0.886732	−	0.462283i	$-0.152970\pi$
$954$	−1.96619	+	9.43443i	−0.0636579	+	0.305451i
$955$		0			0
$956$	10.8876	−	24.9866i	0.352131	−	0.808126i
$957$	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
$962$	−28.8431	−	25.7637i	−0.929940	−	0.830654i
$963$	6.92626	+	11.9966i	0.223196	+	0.386586i
$964$	−8.36146	+	0.946076i	−0.269305	+	0.0304711i
$965$		0			0
$966$	10.9062	+	9.61830i	0.350902	+	0.309464i
$967$	5.33936			0.171702			0.0858510	−	0.996308i	$-0.472639\pi$
$967$	5.33936			0.171702			0.0858510	+	0.996308i	$0.472639\pi$
$968$	−7.72546	+	3.55056i	−0.248306	+	0.114119i
$969$	−2.80635	+	1.62025i	−0.0901530	+	0.0520498i
$970$		0			0
$971$	5.49906	−	9.52465i	0.176473	−	0.305660i	−0.764197	−	0.644983i	$-0.776864\pi$
$971$	5.49906	−	9.52465i	0.176473	−	0.305660i	0.940670	+	0.339323i	$0.110198\pi$
$972$	−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
$976$	−9.28381	−	40.5002i	−0.297168	−	1.29638i
$977$	27.2684	−	15.7434i	0.872392	−	0.503676i	0.00424979	−	0.999991i	$-0.498647\pi$
$977$	27.2684	−	15.7434i	0.872392	−	0.503676i	0.868142	+	0.496315i	$0.165314\pi$
$978$	−1.17493	+	5.63771i	−0.0375703	+	0.180274i
$979$	36.9761			1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	−10.5209	+	50.4825i	−0.335735	+	1.61096i
$983$	−29.9232	+	17.2762i	−0.954402	+	0.551025i	−0.894446	−	0.447176i	$-0.852430\pi$
$983$	−29.9232	+	17.2762i	−0.954402	+	0.551025i	−0.0599567	+	0.998201i	$0.519096\pi$
$984$	1.73638	−	18.6577i	0.0553537	−	0.594787i
$985$		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	−0.520833	+	0.853659i	$0.674378\pi$
$991$	−47.8668	+	27.6359i	−1.52054	+	0.877884i	−0.999707	+	0.0242247i	$0.992288\pi$
$992$	6.93186	−	12.5770i	0.220087	−	0.399321i
$993$	21.2068			0.672978
$994$	27.9719	+	24.6687i	0.887216	+	0.782443i
$995$		0			0
$996$	0.526405	+	4.65239i	0.0166798	+	0.147417i
$997$	−7.64087	−	13.2344i	−0.241989	−	0.419137i	0.719292	−	0.694708i	$-0.244466\pi$
$997$	−7.64087	−	13.2344i	−0.241989	−	0.419137i	−0.961281	+	0.275571i	$0.911133\pi$
$998$	12.5289	+	11.1912i	0.396595	+	0.354252i
$999$	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.299.1		32
4.3	odd	2	inner	700.2.t.c.299.6		32
5.2	odd	4		140.2.o.a.131.9	yes	32
5.3	odd	4		700.2.p.c.551.8		32
5.4	even	2		700.2.t.d.299.16		32
7.3	odd	6		700.2.t.d.199.11		32
20.3	even	4		700.2.p.c.551.4		32
20.7	even	4		140.2.o.a.131.13	yes	32
20.19	odd	2		700.2.t.d.299.11		32
28.3	even	6		700.2.t.d.199.16		32
35.2	odd	12		980.2.g.a.391.8		32
35.3	even	12		700.2.p.c.451.4		32
35.12	even	12		980.2.g.a.391.7		32
35.17	even	12		140.2.o.a.31.13	yes	32
35.24	odd	6	inner	700.2.t.c.199.6		32
35.27	even	4		980.2.o.f.411.9		32
35.32	odd	12		980.2.o.f.31.13		32
140.3	odd	12		700.2.p.c.451.8		32
140.27	odd	4		980.2.o.f.411.13		32
140.47	odd	12		980.2.g.a.391.6		32
140.59	even	6	inner	700.2.t.c.199.1		32
140.67	even	12		980.2.o.f.31.9		32
140.87	odd	12		140.2.o.a.31.9	✓	32
140.107	even	12		980.2.g.a.391.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	140.87	odd	12
140.2.o.a.31.13	yes	32	35.17	even	12
140.2.o.a.131.9	yes	32	5.2	odd	4
140.2.o.a.131.13	yes	32	20.7	even	4
700.2.p.c.451.4		32	35.3	even	12
700.2.p.c.451.8		32	140.3	odd	12
700.2.p.c.551.4		32	20.3	even	4
700.2.p.c.551.8		32	5.3	odd	4
700.2.t.c.199.1		32	140.59	even	6	inner
700.2.t.c.199.6		32	35.24	odd	6	inner
700.2.t.c.299.1		32	1.1	even	1	trivial
700.2.t.c.299.6		32	4.3	odd	2	inner
700.2.t.d.199.11		32	7.3	odd	6
700.2.t.d.199.16		32	28.3	even	6
700.2.t.d.299.11		32	20.19	odd	2
700.2.t.d.299.16		32	5.4	even	2
980.2.g.a.391.5		32	140.107	even	12
980.2.g.a.391.6		32	140.47	odd	12
980.2.g.a.391.7		32	35.12	even	12
980.2.g.a.391.8		32	35.2	odd	12
980.2.o.f.31.9		32	140.67	even	12
980.2.o.f.31.13		32	35.32	odd	12
980.2.o.f.411.9		32	35.27	even	4
980.2.o.f.411.13		32	140.27	odd	4

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+(-1.38447 - 0.288532i) q^{2} +(0.780530 - 0.450639i) q^{3} +(1.83350 + 0.798926i) 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} +(1.79113 - 0.202661i) q^{12} -2.41990 q^{13} +(2.47486 - 2.80626i) q^{14} +(2.72344 + 2.92966i) q^{16} +(0.291859 + 0.505515i) q^{17} +(2.06105 - 2.30740i) 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} +(-2.53823 - 0.236220i) q^{24} +(3.35028 + 0.698219i) q^{26} +4.67556i q^{27} +(-4.23606 + 3.17109i) q^{28} +0.435463 q^{29} +(1.26933 + 2.19854i) q^{31} +(-2.92521 - 4.84181i) 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} +(5.80297 - 6.49659i) q^{38} +(-1.88881 + 1.09050i) q^{39} +7.35068i q^{41} +(0.667093 - 3.30563i) q^{42} +5.80096 q^{43} +(7.43747 - 0.841528i) q^{44} +(4.06247 - 4.54805i) 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} +(-4.43689 - 1.93332i) q^{52} +(-2.69759 + 1.55746i) q^{53} +(1.34905 - 6.47316i) q^{54} +(6.77964 - 3.16804i) q^{56} +5.55147i q^{57} +(-0.602884 - 0.125645i) 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} +(-3.17773 + 3.55756i) q^{66} +(4.92250 + 8.52602i) q^{67} +(0.131255 + 1.16004i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(5.62238 - 2.58400i) q^{72} +(4.89946 + 8.48612i) q^{73} +(11.9191 + 10.6466i) 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} +(2.12091 - 10.1768i) q^{82} +2.59747i q^{83} +(-1.87735 + 4.38406i) q^{84} +(-8.03123 - 1.67376i) q^{86} +(0.339892 - 0.196236i) q^{87} +(-10.5397 - 0.980878i) 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} +(-12.2100 - 10.9064i) q^{94} +(-4.46512 - 2.46097i) q^{96} +4.54044 q^{97} +(3.21538 + 9.36276i) 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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