LMFDB - Embedded newform 7.11.b.b.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,11,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	7.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.44750076872$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.373770240.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 368x^{2} + 2760 $ x^4 + 368*x^2 + 2760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.1
Root			$-18.9826i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.11.b.b.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.1293 q^{2} -252.583i q^{3} +507.104 q^{4} +2873.50i q^{5} +9883.42i q^{6} +(-2763.01 + 16578.3i) q^{7} +20225.8 q^{8} -4749.36 q^{9} +O(q^{10})$	\(q-39.1293 q^{2} -252.583i q^{3} +507.104 q^{4} +2873.50i q^{5} +9883.42i q^{6} +(-2763.01 + 16578.3i) q^{7} +20225.8 q^{8} -4749.36 q^{9} -112438. i q^{10} -92553.7 q^{11} -128086. i q^{12} +412302. i q^{13} +(108115. - 648699. i) q^{14} +725798. q^{15} -1.31070e6 q^{16} -100846. i q^{17} +185839. q^{18} +2.99705e6i q^{19} +1.45716e6i q^{20} +(4.18741e6 + 697890. i) q^{21} +3.62156e6 q^{22} -1.19728e7 q^{23} -5.10870e6i q^{24} +1.50863e6 q^{25} -1.61331e7i q^{26} -1.37152e7i q^{27} +(-1.40113e6 + 8.40693e6i) q^{28} +2.10241e7 q^{29} -2.84000e7 q^{30} +5.15236e7i q^{31} +3.05754e7 q^{32} +2.33775e7i q^{33} +3.94603e6i q^{34} +(-4.76378e7 - 7.93951e6i) q^{35} -2.40842e6 q^{36} +1.98045e7 q^{37} -1.17273e8i q^{38} +1.04141e8 q^{39} +5.81188e7i q^{40} -4.41673e6i q^{41} +(-1.63851e8 - 2.73080e7i) q^{42} -1.13685e8 q^{43} -4.69343e7 q^{44} -1.36473e7i q^{45} +4.68488e8 q^{46} -2.89933e8i q^{47} +3.31060e8i q^{48} +(-2.67207e8 - 9.16122e7i) q^{49} -5.90315e7 q^{50} -2.54720e7 q^{51} +2.09080e8i q^{52} +1.00949e8 q^{53} +5.36666e8i q^{54} -2.65953e8i q^{55} +(-5.58841e7 + 3.35310e8i) q^{56} +7.57006e8 q^{57} -8.22657e8 q^{58} +1.51102e8i q^{59} +3.68055e8 q^{60} -4.24061e8i q^{61} -2.01608e9i q^{62} +(1.31225e7 - 7.87365e7i) q^{63} +1.45757e8 q^{64} -1.18475e9 q^{65} -9.14746e8i q^{66} -7.07000e8 q^{67} -5.11393e7i q^{68} +3.02413e9i q^{69} +(1.86404e9 + 3.10668e8i) q^{70} +1.42045e9 q^{71} -9.60596e7 q^{72} +2.72735e9i q^{73} -7.74937e8 q^{74} -3.81054e8i q^{75} +1.51982e9i q^{76} +(2.55727e8 - 1.53439e9i) q^{77} -4.07496e9 q^{78} +3.87959e9 q^{79} -3.76628e9i q^{80} -3.74467e9 q^{81} +1.72824e8i q^{82} -2.67518e9i q^{83} +(2.12345e9 + 3.53903e8i) q^{84} +2.89780e8 q^{85} +4.44843e9 q^{86} -5.31033e9i q^{87} -1.87197e9 q^{88} +6.01371e9i q^{89} +5.34009e8i q^{90} +(-6.83529e9 - 1.13920e9i) q^{91} -6.07145e9 q^{92} +1.30140e10 q^{93} +1.13449e10i q^{94} -8.61204e9 q^{95} -7.72284e9i q^{96} -7.10446e9i q^{97} +(1.04556e10 + 3.58472e9i) q^{98} +4.39571e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 48 q^{2} - 576 q^{4} + 4900 q^{7} - 14592 q^{8} - 28764 q^{9}+O(q^{10}) $ 4 * q - 48 * q^2 - 576 * q^4 + 4900 * q^7 - 14592 * q^8 - 28764 * q^9	\( 4 q - 48 q^{2} - 576 q^{4} + 4900 q^{7} - 14592 q^{8} - 28764 q^{9} + 85992 q^{11} + 373968 q^{14} + 529920 q^{15} - 1825792 q^{16} + 80208 q^{18} + 11344672 q^{22} - 19261752 q^{23} + 16364260 q^{25} - 11092032 q^{28} + 23044008 q^{29} - 70744320 q^{30} + 129552384 q^{32} - 151468800 q^{35} + 10501056 q^{36} - 174916888 q^{37} + 489646080 q^{39} - 454406400 q^{42} + 163158248 q^{43} - 309420672 q^{44} + 1007838880 q^{46} - 990662204 q^{49} + 83868240 q^{50} - 955445760 q^{51} + 1693931880 q^{53} - 398711040 q^{56} + 803623680 q^{57} - 1932834272 q^{58} + 1468938240 q^{60} - 74185020 q^{63} + 511688704 q^{64} - 481608960 q^{65} - 2064766168 q^{67} + 2877907200 q^{70} + 1129059912 q^{71} + 338095872 q^{72} - 4795503840 q^{74} + 1924696872 q^{77} - 3893057280 q^{78} + 10836295688 q^{79} - 15414934716 q^{81} + 10905753600 q^{84} - 5489441280 q^{85} + 14805307680 q^{86} - 11205085696 q^{88} + 3483782400 q^{91} - 15867056256 q^{92} + 27132433920 q^{93} - 21990620160 q^{95} + 14008509648 q^{98} - 1732260312 q^{99}+O(q^{100}) \) 4 * q - 48 * q^2 - 576 * q^4 + 4900 * q^7 - 14592 * q^8 - 28764 * q^9 + 85992 * q^11 + 373968 * q^14 + 529920 * q^15 - 1825792 * q^16 + 80208 * q^18 + 11344672 * q^22 - 19261752 * q^23 + 16364260 * q^25 - 11092032 * q^28 + 23044008 * q^29 - 70744320 * q^30 + 129552384 * q^32 - 151468800 * q^35 + 10501056 * q^36 - 174916888 * q^37 + 489646080 * q^39 - 454406400 * q^42 + 163158248 * q^43 - 309420672 * q^44 + 1007838880 * q^46 - 990662204 * q^49 + 83868240 * q^50 - 955445760 * q^51 + 1693931880 * q^53 - 398711040 * q^56 + 803623680 * q^57 - 1932834272 * q^58 + 1468938240 * q^60 - 74185020 * q^63 + 511688704 * q^64 - 481608960 * q^65 - 2064766168 * q^67 + 2877907200 * q^70 + 1129059912 * q^71 + 338095872 * q^72 - 4795503840 * q^74 + 1924696872 * q^77 - 3893057280 * q^78 + 10836295688 * q^79 - 15414934716 * q^81 + 10905753600 * q^84 - 5489441280 * q^85 + 14805307680 * q^86 - 11205085696 * q^88 + 3483782400 * q^91 - 15867056256 * q^92 + 27132433920 * q^93 - 21990620160 * q^95 + 14008509648 * q^98 - 1732260312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−39.1293			−1.22279			−0.611396	−	0.791325i	$-0.709392\pi$
$2$	−39.1293			−1.22279			−0.611396	+	0.791325i	$0.709392\pi$
$3$		−	252.583i		−	1.03944i	−0.854337	−	0.519719i	$-0.826037\pi$
$3$		−	252.583i		−	1.03944i	0.854337	−	0.519719i	$-0.173963\pi$
$4$	507.104			0.495218
$5$			2873.50i			0.919520i	0.888043	+	0.459760i	$0.152065\pi$
$5$			2873.50i			0.919520i	−0.888043	+	0.459760i	$0.847935\pi$
$6$			9883.42i			1.27102i
$7$	−2763.01	+	16578.3i	−0.164396	+	0.986394i
$7$	−2763.01	+	16578.3i	−0.164396	+	0.986394i
$8$	20225.8			0.617242
$9$	−4749.36			−0.0804308
$10$		−	112438.i		−	1.12438i
$11$	−92553.7			−0.574685			−0.287343	−	0.957828i	$-0.592772\pi$
$11$	−92553.7			−0.574685			−0.287343	+	0.957828i	$0.592772\pi$
$12$		−	128086.i		−	0.514749i
$13$			412302.i			1.11045i	0.831700	+	0.555225i	$0.187368\pi$
$13$			412302.i			1.11045i	−0.831700	+	0.555225i	$0.812632\pi$
$14$	108115.	−	648699.i	0.201022	−	1.20615i
$15$	725798.			0.955784
$16$	−1.31070e6			−1.24998
$17$		−	100846.i		−	0.0710253i	−0.999369	−	0.0355127i	$-0.988694\pi$
$17$		−	100846.i		−	0.0710253i	0.999369	−	0.0355127i	$-0.0113064\pi$
$18$	185839.			0.0983501
$19$			2.99705e6i			1.21039i	0.796076	+	0.605197i	$0.206906\pi$
$19$			2.99705e6i			1.21039i	−0.796076	+	0.605197i	$0.793094\pi$
$20$			1.45716e6i			0.455363i
$21$	4.18741e6	+	697890.i	1.02530	+	0.170880i
$22$	3.62156e6			0.702720
$23$	−1.19728e7			−1.86019			−0.930094	−	0.367322i	$-0.880275\pi$
$23$	−1.19728e7			−1.86019			−0.930094	+	0.367322i	$0.880275\pi$
$24$		−	5.10870e6i		−	0.641585i
$25$	1.50863e6			0.154483
$26$		−	1.61331e7i		−	1.35785i
$27$		−	1.37152e7i		−	0.955835i
$28$	−1.40113e6	+	8.40693e6i	−0.0814121	+	0.488481i
$29$	2.10241e7			1.02501			0.512503	−	0.858685i	$-0.328718\pi$
$29$	2.10241e7			1.02501			0.512503	+	0.858685i	$0.328718\pi$
$30$	−2.84000e7			−1.16872
$31$			5.15236e7i			1.79969i	0.436211	+	0.899844i	$0.356320\pi$
$31$			5.15236e7i			1.79969i	−0.436211	+	0.899844i	$0.643680\pi$
$32$	3.05754e7			0.911219
$33$			2.33775e7i			0.597350i
$34$			3.94603e6i			0.0868492i
$35$	−4.76378e7	−	7.93951e6i	−0.907009	−	0.151166i
$36$	−2.40842e6			−0.0398308
$37$	1.98045e7			0.285598			0.142799	−	0.989752i	$-0.454390\pi$
$37$	1.98045e7			0.285598			0.142799	+	0.989752i	$0.454390\pi$
$38$		−	1.17273e8i		−	1.48006i
$39$	1.04141e8			1.15424
$40$			5.81188e7i			0.567567i
$41$		−	4.41673e6i		−	0.0381225i	−0.999818	−	0.0190613i	$-0.993932\pi$
$41$		−	4.41673e6i		−	0.0381225i	0.999818	−	0.0190613i	$-0.00606775\pi$
$42$	−1.63851e8	−	2.73080e7i	−1.25372	−	0.208950i
$43$	−1.13685e8			−0.773326			−0.386663	−	0.922221i	$-0.626372\pi$
$43$	−1.13685e8			−0.773326			−0.386663	+	0.922221i	$0.626372\pi$
$44$	−4.69343e7			−0.284595
$45$		−	1.36473e7i		−	0.0739578i
$46$	4.68488e8			2.27462
$47$		−	2.89933e8i		−	1.26418i	−0.774895	−	0.632089i	$-0.782197\pi$
$47$		−	2.89933e8i		−	1.26418i	0.774895	−	0.632089i	$-0.217803\pi$
$48$			3.31060e8i			1.29927i
$49$	−2.67207e8	−	9.16122e7i	−0.945948	−	0.324319i
$50$	−5.90315e7			−0.188901
$51$	−2.54720e7			−0.0738264
$52$			2.09080e8i			0.549915i
$53$	1.00949e8			0.241391			0.120695	−	0.992690i	$-0.461488\pi$
$53$	1.00949e8			0.241391			0.120695	+	0.992690i	$0.461488\pi$
$54$			5.36666e8i			1.16879i
$55$		−	2.65953e8i		−	0.528435i
$56$	−5.58841e7	+	3.35310e8i	−0.101472	+	0.608844i
$57$	7.57006e8			1.25813
$58$	−8.22657e8			−1.25337
$59$			1.51102e8i			0.211354i	0.994400	+	0.105677i	$0.0337010\pi$
$59$			1.51102e8i			0.211354i	−0.994400	+	0.105677i	$0.966299\pi$
$60$	3.68055e8			0.473322
$61$		−	4.24061e8i		−	0.502087i	−0.967976	−	0.251044i	$-0.919226\pi$
$61$		−	4.24061e8i		−	0.502087i	0.967976	−	0.251044i	$-0.0807738\pi$
$62$		−	2.01608e9i		−	2.20064i
$63$	1.31225e7	−	7.87365e7i	0.0132225	−	0.0793365i
$64$	1.45757e8			0.135747
$65$	−1.18475e9			−1.02108
$66$		−	9.14746e8i		−	0.730434i
$67$	−7.07000e8			−0.523655			−0.261828	−	0.965115i	$-0.584325\pi$
$67$	−7.07000e8			−0.523655			−0.261828	+	0.965115i	$0.584325\pi$
$68$		−	5.11393e7i		−	0.0351731i
$69$			3.02413e9i			1.93355i
$70$	1.86404e9	+	3.10668e8i	1.10908	+	0.184844i
$71$	1.42045e9			0.787289			0.393645	−	0.919263i	$-0.371214\pi$
$71$	1.42045e9			0.787289			0.393645	+	0.919263i	$0.371214\pi$
$72$	−9.60596e7			−0.0496453
$73$			2.72735e9i			1.31561i	0.753190	+	0.657803i	$0.228514\pi$
$73$			2.72735e9i			1.31561i	−0.753190	+	0.657803i	$0.771486\pi$
$74$	−7.74937e8			−0.349227
$75$		−	3.81054e8i		−	0.160576i
$76$			1.51982e9i			0.599409i
$77$	2.55727e8	−	1.53439e9i	0.0944762	−	0.566866i
$78$	−4.07496e9			−1.41140
$79$	3.87959e9			1.26081			0.630407	−	0.776265i	$-0.282888\pi$
$79$	3.87959e9			1.26081			0.630407	+	0.776265i	$0.282888\pi$
$80$		−	3.76628e9i		−	1.14938i
$81$	−3.74467e9			−1.07396
$82$			1.72824e8i			0.0466159i
$83$		−	2.67518e9i		−	0.679144i	−0.940580	−	0.339572i	$-0.889718\pi$
$83$		−	2.67518e9i		−	0.679144i	0.940580	−	0.339572i	$-0.110282\pi$
$84$	2.12345e9	+	3.53903e8i	0.507745	+	0.0846228i
$85$	2.89780e8			0.0653092
$86$	4.44843e9			0.945616
$87$		−	5.31033e9i		−	1.06543i
$88$	−1.87197e9			−0.354720
$89$			6.01371e9i			1.07694i	0.842644	+	0.538472i	$0.180998\pi$
$89$			6.01371e9i			1.07694i	−0.842644	+	0.538472i	$0.819002\pi$
$90$			5.34009e8i			0.0904349i
$91$	−6.83529e9	−	1.13920e9i	−1.09534	−	0.182554i
$92$	−6.07145e9			−0.921199
$93$	1.30140e10			1.87066
$94$			1.13449e10i			1.54583i
$95$	−8.61204e9			−1.11298
$96$		−	7.72284e9i		−	0.947155i
$97$		−	7.10446e9i		−	0.827318i	−0.910432	−	0.413659i	$-0.864251\pi$
$97$		−	7.10446e9i		−	0.827318i	0.910432	−	0.413659i	$-0.135749\pi$
$98$	1.04556e10	+	3.58472e9i	1.15670	+	0.396575i
$99$	4.39571e8			0.0462224
$100$	7.65029e8			0.0765029
$101$			9.06520e9i			0.862523i	0.902227	+	0.431261i	$0.141931\pi$
$101$			9.06520e9i			0.862523i	−0.902227	+	0.431261i	$0.858069\pi$
$102$	9.96701e8			0.0902743
$103$		−	7.81587e9i		−	0.674204i	−0.941468	−	0.337102i	$-0.890553\pi$
$103$		−	7.81587e9i		−	0.674204i	0.941468	−	0.337102i	$-0.109447\pi$
$104$			8.33915e9i			0.685417i
$105$	−2.00539e9	+	1.20325e10i	−0.157127	+	0.942780i
$106$	−3.95005e9			−0.295171
$107$	−7.93293e9			−0.565607			−0.282803	−	0.959178i	$-0.591264\pi$
$107$	−7.93293e9			−0.565607			−0.282803	+	0.959178i	$0.591264\pi$
$108$		−	6.95502e9i		−	0.473347i
$109$	4.72557e9			0.307130			0.153565	−	0.988139i	$-0.450925\pi$
$109$	4.72557e9			0.307130			0.153565	+	0.988139i	$0.450925\pi$
$110$			1.04066e10i			0.646165i
$111$		−	5.00229e9i		−	0.296861i
$112$	3.62147e9	−	2.17292e10i	0.205492	−	1.23297i
$113$	1.61106e10			0.874416			0.437208	−	0.899360i	$-0.355967\pi$
$113$	1.61106e10			0.874416			0.437208	+	0.899360i	$0.355967\pi$
$114$	−2.96211e10			−1.53843
$115$		−	3.44038e10i		−	1.71048i
$116$	1.06614e10			0.507602
$117$		−	1.95817e9i		−	0.0893145i
$118$		−	5.91254e9i		−	0.258442i
$119$	1.67186e9	+	2.78638e8i	0.0700590	+	0.0116763i
$120$	1.46799e10			0.589950
$121$	−1.73712e10			−0.669737
$122$			1.65932e10i			0.613948i
$123$	−1.11559e9			−0.0396260
$124$			2.61278e10i			0.891239i
$125$			3.23966e10i			1.06157i
$126$	−5.13476e8	+	3.08090e9i	−0.0161684	+	0.0970120i
$127$	1.45906e10			0.441627			0.220814	−	0.975316i	$-0.429129\pi$
$127$	1.45906e10			0.441627			0.220814	+	0.975316i	$0.429129\pi$
$128$	−3.70126e10			−1.07721
$129$			2.87151e10i			0.803824i
$130$	4.63585e10			1.24857
$131$			1.08015e10i			0.279980i	0.990153	+	0.139990i	$0.0447070\pi$
$131$			1.08015e10i			0.279980i	−0.990153	+	0.139990i	$0.955293\pi$
$132$			1.18548e10i			0.295819i
$133$	−4.96862e10	−	8.28089e9i	−1.19393	−	0.198984i
$134$	2.76644e10			0.640321
$135$	3.94106e10			0.878909
$136$		−	2.03969e9i		−	0.0438399i
$137$	3.07627e10			0.637414			0.318707	−	0.947853i	$-0.396751\pi$
$137$	3.07627e10			0.637414			0.318707	+	0.947853i	$0.396751\pi$
$138$		−	1.18332e11i		−	2.36433i
$139$		−	1.41255e10i		−	0.272225i	−0.990693	−	0.136113i	$-0.956539\pi$
$139$		−	1.41255e10i		−	0.272225i	0.990693	−	0.136113i	$-0.0434609\pi$
$140$	−2.41573e10	−	4.02615e9i	−0.449168	−	0.0748601i
$141$	−7.32323e10			−1.31404
$142$	−5.55813e10			−0.962690
$143$		−	3.81601e10i		−	0.638160i
$144$	6.22497e9			0.100537
$145$			6.04126e10i			0.942514i
$146$		−	1.06719e11i		−	1.60871i
$147$	−2.31397e10	+	6.74920e10i	−0.337110	+	0.983254i
$148$	1.00429e10			0.141433
$149$	1.07315e11			1.46126			0.730632	−	0.682772i	$-0.239226\pi$
$149$	1.07315e11			1.46126			0.730632	+	0.682772i	$0.239226\pi$
$150$			1.49104e10i			0.196351i
$151$	1.21510e11			1.54785			0.773923	−	0.633279i	$-0.218292\pi$
$151$	1.21510e11			1.54785			0.773923	+	0.633279i	$0.218292\pi$
$152$			6.06178e10i			0.747106i
$153$			4.78953e8i			0.00571263i
$154$	−1.00064e10	+	6.00394e10i	−0.115525	+	0.693159i
$155$	−1.48053e11			−1.65485
$156$	5.28102e10			0.571603
$157$			6.25470e10i			0.655705i	0.944729	+	0.327852i	$0.106325\pi$
$157$			6.25470e10i			0.655705i	−0.944729	+	0.327852i	$0.893675\pi$
$158$	−1.51806e11			−1.54171
$159$		−	2.54979e10i		−	0.250911i
$160$			8.78585e10i			0.837884i
$161$	3.30810e10	−	1.98489e11i	0.305808	−	1.83488i
$162$	1.46527e11			1.31323
$163$	−3.16909e9			−0.0275420			−0.0137710	−	0.999905i	$-0.504384\pi$
$163$	−3.16909e9			−0.0275420			−0.0137710	+	0.999905i	$0.504384\pi$
$164$		−	2.23974e9i		−	0.0188790i
$165$	−6.71753e10			−0.549275
$166$			1.04678e11i			0.830451i
$167$			1.69209e10i			0.130269i	0.997877	+	0.0651344i	$0.0207476\pi$
$167$			1.69209e10i			0.130269i	−0.997877	+	0.0651344i	$0.979252\pi$
$168$	8.46937e10	+	1.41154e10i	0.632856	+	0.105474i
$169$	−3.21348e10			−0.233100
$170$	−1.13389e10			−0.0798595
$171$		−	1.42341e10i		−	0.0973530i
$172$	−5.76503e10			−0.382965
$173$		−	2.10975e11i		−	1.36145i	−0.732541	−	0.680723i	$-0.761666\pi$
$173$		−	2.10975e11i		−	1.36145i	0.732541	−	0.680723i	$-0.238334\pi$
$174$			2.07790e11i			1.30280i
$175$	−4.16835e9	+	2.50105e10i	−0.0253965	+	0.152381i
$176$	1.21310e11			0.718344
$177$	3.81660e10			0.219690
$178$		−	2.35313e11i		−	1.31688i
$179$	−1.38940e11			−0.756070			−0.378035	−	0.925791i	$-0.623400\pi$
$179$	−1.38940e11			−0.756070			−0.378035	+	0.925791i	$0.623400\pi$
$180$		−	6.92059e9i		−	0.0366252i
$181$		−	1.82283e11i		−	0.938327i	−0.883111	−	0.469163i	$-0.844556\pi$
$181$		−	1.82283e11i		−	0.938327i	0.883111	−	0.469163i	$-0.155444\pi$
$182$	2.67460e11	+	4.45760e10i	1.33937	+	0.223225i
$183$	−1.07111e11			−0.521888
$184$	−2.42160e11			−1.14819
$185$			5.69082e10i			0.262613i
$186$	−5.09229e11			−2.28743
$187$			9.33365e9i			0.0408172i
$188$		−	1.47026e11i		−	0.626045i
$189$	2.27375e11	+	3.78952e10i	0.942830	+	0.157136i
$190$	3.36983e11			1.36094
$191$	2.83910e11			1.11690			0.558449	−	0.829539i	$-0.311397\pi$
$191$	2.83910e11			1.11690			0.558449	+	0.829539i	$0.311397\pi$
$192$		−	3.68158e10i		−	0.141101i
$193$	2.83839e11			1.05995			0.529975	−	0.848014i	$-0.322201\pi$
$193$	2.83839e11			1.05995			0.529975	+	0.848014i	$0.322201\pi$
$194$			2.77993e11i			1.01164i
$195$			2.99248e11i			1.06135i
$196$	−1.35502e11	−	4.64569e10i	−0.468451	−	0.160609i
$197$	−4.44603e11			−1.49845			−0.749223	−	0.662318i	$-0.769573\pi$
$197$	−4.44603e11			−1.49845			−0.749223	+	0.662318i	$0.769573\pi$
$198$	−1.72001e10			−0.0565204
$199$			4.26575e11i			1.36688i	0.730007	+	0.683439i	$0.239517\pi$
$199$			4.26575e11i			1.36688i	−0.730007	+	0.683439i	$0.760483\pi$
$200$	3.05132e10			0.0953536
$201$			1.78576e11i			0.544307i
$202$		−	3.54715e11i		−	1.05468i
$203$	−5.80897e10	+	3.48544e11i	−0.168507	+	1.01106i
$204$	−1.29169e10			−0.0365602
$205$	1.26915e10			0.0350544
$206$			3.05830e11i			0.824411i
$207$	5.68632e10			0.149616
$208$		−	5.40403e11i		−	1.38804i
$209$		−	2.77388e11i		−	0.695596i
$210$	7.84695e10	−	4.70824e11i	0.192134	−	1.15282i
$211$	−3.36458e10			−0.0804487			−0.0402243	−	0.999191i	$-0.512807\pi$
$211$	−3.36458e10			−0.0804487			−0.0402243	+	0.999191i	$0.512807\pi$
$212$	5.11914e10			0.119541
$213$		−	3.58782e11i		−	0.818338i
$214$	3.10410e11			0.691619
$215$		−	3.26675e11i		−	0.711089i
$216$		−	2.77401e11i		−	0.589982i
$217$	−8.54175e11	−	1.42360e11i	−1.77520	−	0.295862i
$218$	−1.84908e11			−0.375556
$219$	6.88882e11			1.36749
$220$		−	1.34866e11i		−	0.261691i
$221$	4.15790e10			0.0788701
$222$			1.95736e11i			0.363000i
$223$			7.98327e11i			1.44763i	0.689996	+	0.723813i	$0.257612\pi$
$223$			7.98327e11i			1.44763i	−0.689996	+	0.723813i	$0.742388\pi$
$224$	−8.44802e10	+	5.06889e11i	−0.149801	+	0.898821i
$225$	−7.16501e9			−0.0124252
$226$	−6.30395e11			−1.06923
$227$		−	8.12638e11i		−	1.34824i	−0.738621	−	0.674121i	$-0.764523\pi$
$227$		−	8.12638e11i		−	1.34824i	0.738621	−	0.674121i	$-0.235477\pi$
$228$	3.83881e11			0.623049
$229$			6.75448e11i			1.07254i	0.844046	+	0.536271i	$0.180168\pi$
$229$			6.75448e11i			1.07254i	−0.844046	+	0.536271i	$0.819832\pi$
$230$			1.34620e12i			2.09156i
$231$	−3.87560e11	−	6.45923e10i	−0.589222	−	0.0982021i
$232$	4.25229e11			0.632678
$233$	3.10522e11			0.452182			0.226091	−	0.974106i	$-0.427405\pi$
$233$	3.10522e11			0.452182			0.226091	+	0.974106i	$0.427405\pi$
$234$			7.66220e10i			0.109213i
$235$	8.33123e11			1.16244
$236$			7.66246e10i			0.104667i
$237$		−	9.79921e11i		−	1.31054i
$238$	−6.54186e10	−	1.09029e10i	−0.0856675	−	0.0142777i
$239$	−9.22692e10			−0.118322			−0.0591612	−	0.998248i	$-0.518843\pi$
$239$	−9.22692e10			−0.118322			−0.0591612	+	0.998248i	$0.518843\pi$
$240$	−9.51301e11			−1.19471
$241$			3.28923e11i			0.404584i	0.979325	+	0.202292i	$0.0648390\pi$
$241$			3.28923e11i			0.404584i	−0.979325	+	0.202292i	$0.935161\pi$
$242$	6.79725e11			0.818948
$243$			1.35974e11i			0.160481i
$244$		−	2.15043e11i		−	0.248643i
$245$	2.63248e11	−	7.67819e11i	0.298218	−	0.869818i
$246$	4.36524e10			0.0484543
$247$	−1.23569e12			−1.34408
$248$			1.04211e12i			1.11084i
$249$	−6.75705e11			−0.705928
$250$		−	1.26766e12i		−	1.29808i
$251$		−	1.96182e11i		−	0.196920i	−0.995141	−	0.0984601i	$-0.968608\pi$
$251$		−	1.96182e11i		−	0.196920i	0.995141	−	0.0984601i	$-0.0313917\pi$
$252$	6.65448e9	−	3.99276e10i	0.00654805	−	0.0392889i
$253$	1.10813e12			1.06902
$254$	−5.70922e11			−0.540018
$255$		−	7.31937e10i		−	0.0678849i
$256$	1.29902e12			1.18145
$257$			7.42653e11i			0.662400i	0.943561	+	0.331200i	$0.107453\pi$
$257$			7.42653e11i			0.662400i	−0.943561	+	0.331200i	$0.892547\pi$
$258$		−	1.12360e12i		−	0.982909i
$259$	−5.47200e10	+	3.28326e11i	−0.0469513	+	0.281712i
$260$	−6.00792e11			−0.505658
$261$	−9.98509e10			−0.0824422
$262$		−	4.22654e11i		−	0.342357i
$263$	−1.25361e12			−0.996283			−0.498142	−	0.867096i	$-0.665984\pi$
$263$	−1.25361e12			−0.996283			−0.498142	+	0.867096i	$0.665984\pi$
$264$			4.72829e11i			0.368710i
$265$			2.90076e11i			0.221964i
$266$	1.94419e12	+	3.24026e11i	1.45992	+	0.243316i
$267$	1.51896e12			1.11942
$268$	−3.58522e11			−0.259324
$269$		−	9.46524e11i		−	0.672002i	−0.941862	−	0.336001i	$-0.890926\pi$
$269$		−	9.46524e11i		−	0.672002i	0.941862	−	0.336001i	$-0.109074\pi$
$270$	−1.54211e12			−1.07472
$271$		−	2.02084e12i		−	1.38256i	−0.722586	−	0.691281i	$-0.757047\pi$
$271$		−	2.02084e12i		−	1.38256i	0.722586	−	0.691281i	$-0.242953\pi$
$272$			1.32178e11i			0.0887800i
$273$	−2.87742e11	+	1.72648e12i	−0.189754	+	1.13854i
$274$	−1.20372e12			−0.779424
$275$	−1.39629e11			−0.0887792
$276$			1.53355e12i			0.957529i
$277$	−1.01987e11			−0.0625382			−0.0312691	−	0.999511i	$-0.509955\pi$
$277$	−1.01987e11			−0.0625382			−0.0312691	+	0.999511i	$0.509955\pi$
$278$			5.52719e11i			0.332875i
$279$		−	2.44704e11i		−	0.144750i
$280$	−9.63513e11	−	1.60583e11i	−0.559845	−	0.0933059i
$281$	1.42513e11			0.0813436			0.0406718	−	0.999173i	$-0.487050\pi$
$281$	1.42513e11			0.0813436			0.0406718	+	0.999173i	$0.487050\pi$
$282$	2.86553e12			1.60679
$283$			6.97041e11i			0.383996i	0.981395	+	0.191998i	$0.0614967\pi$
$283$			6.97041e11i			0.383996i	−0.981395	+	0.191998i	$0.938503\pi$
$284$	7.20316e11			0.389880
$285$			2.17526e12i			1.15687i
$286$			1.49318e12i			0.780336i
$287$	7.32220e10	+	1.22035e10i	0.0376038	+	0.00626720i
$288$	−1.45214e11			−0.0732901
$289$	2.00582e12			0.994955
$290$		−	2.36391e12i		−	1.15250i
$291$	−1.79447e12			−0.859946
$292$			1.38305e12i			0.651513i
$293$			5.89856e11i			0.273154i	0.990629	+	0.136577i	$0.0436101\pi$
$293$			5.89856e11i			0.273154i	−0.990629	+	0.136577i	$0.956390\pi$
$294$	9.05441e11	−	2.64092e12i	0.412215	−	1.20231i
$295$	−4.34193e11			−0.194345
$296$	4.00562e11			0.176283
$297$			1.26939e12i			0.549304i
$298$	−4.19916e12			−1.78682
$299$		−	4.93642e12i		−	2.06565i
$300$		−	1.93234e11i		−	0.0795200i
$301$	3.14114e11	−	1.88471e12i	0.127132	−	0.762804i
$302$	−4.75461e12			−1.89269
$303$	2.28972e12			0.896538
$304$		−	3.92823e12i		−	1.51296i
$305$	1.21854e12			0.461679
$306$		−	1.87411e10i		−	0.00698535i
$307$			6.78543e11i			0.248820i	0.992231	+	0.124410i	$0.0397038\pi$
$307$			6.78543e11i			0.248820i	−0.992231	+	0.124410i	$0.960296\pi$
$308$	1.29680e11	−	7.78092e11i	0.0467864	−	0.280723i
$309$	−1.97416e12			−0.700793
$310$	5.79321e12			2.02354
$311$			3.17213e12i			1.09031i	0.838336	+	0.545154i	$0.183529\pi$
$311$			3.17213e12i			1.09031i	−0.838336	+	0.545154i	$0.816471\pi$
$312$	2.10633e12			0.712448
$313$			4.52166e12i			1.50514i	0.658513	+	0.752569i	$0.271186\pi$
$313$			4.52166e12i			1.50514i	−0.658513	+	0.752569i	$0.728814\pi$
$314$		−	2.44742e12i		−	0.801790i
$315$	2.26249e11	+	3.77076e10i	0.0729515	+	0.0121584i
$316$	1.96736e12			0.624378
$317$	−3.31903e12			−1.03685			−0.518424	−	0.855124i	$-0.673481\pi$
$317$	−3.31903e12			−1.03685			−0.518424	+	0.855124i	$0.673481\pi$
$318$			9.97717e11i			0.306811i
$319$	−1.94585e12			−0.589056
$320$			4.18833e11i			0.124822i
$321$			2.00373e12i			0.587913i
$322$	−1.29444e12	+	7.76674e12i	−0.373939	+	2.24367i
$323$	3.02240e11			0.0859686
$324$	−1.89894e12			−0.531846
$325$			6.22010e11i			0.171546i
$326$	1.24004e11			0.0336782
$327$		−	1.19360e12i		−	0.319242i
$328$		−	8.93319e10i		−	0.0235308i
$329$	4.80661e12	+	8.01088e11i	1.24698	+	0.207826i
$330$	2.62852e12			0.671649
$331$	−3.06225e12			−0.770728			−0.385364	−	0.922765i	$-0.625924\pi$
$331$	−3.06225e12			−0.770728			−0.385364	+	0.922765i	$0.625924\pi$
$332$		−	1.35659e12i		−	0.336325i
$333$	−9.40587e10			−0.0229709
$334$		−	6.62102e11i		−	0.159291i
$335$		−	2.03156e12i		−	0.481511i
$336$	−5.48842e12	−	9.14722e11i	−1.28160	−	0.213596i
$337$	4.17504e12			0.960530			0.480265	−	0.877123i	$-0.340540\pi$
$337$	4.17504e12			0.960530			0.480265	+	0.877123i	$0.340540\pi$
$338$	1.25741e12			0.285032
$339$		−	4.06926e12i		−	0.908901i
$340$	1.46949e11			0.0323423
$341$		−	4.76869e12i		−	1.03425i
$342$			5.56971e11i			0.119042i
$343$	2.25707e12	−	4.17672e12i	0.475417	−	0.879761i
$344$	−2.29938e12			−0.477330
$345$	−8.68984e12			−1.77794
$346$			8.25530e12i			1.66476i
$347$	5.71594e12			1.13616			0.568081	−	0.822973i	$-0.307686\pi$
$347$	5.71594e12			1.13616			0.568081	+	0.822973i	$0.307686\pi$
$348$		−	2.69289e12i		−	0.527621i
$349$		−	7.35784e12i		−	1.42110i	−0.703649	−	0.710548i	$-0.748447\pi$
$349$		−	7.35784e12i		−	1.42110i	0.703649	−	0.710548i	$-0.251553\pi$
$350$	1.63105e11	−	9.78643e11i	0.0310546	−	0.186331i
$351$	5.65480e12			1.06141
$352$	−2.82987e12			−0.523664
$353$			2.11341e12i			0.385577i	0.981240	+	0.192788i	$0.0617530\pi$
$353$			2.11341e12i			0.385577i	−0.981240	+	0.192788i	$0.938247\pi$
$354$	−1.49341e12			−0.268635
$355$			4.08166e12i			0.723928i
$356$			3.04958e12i			0.533322i
$357$	7.03793e10	−	4.22283e11i	0.0121368	−	0.0728220i
$358$	5.43662e12			0.924516
$359$	−8.05546e12			−1.35088			−0.675442	−	0.737413i	$-0.736047\pi$
$359$	−8.05546e12			−1.35088			−0.675442	+	0.737413i	$0.736047\pi$
$360$		−	2.76027e11i		−	0.0456499i
$361$	−2.85127e12			−0.465053
$362$			7.13262e12i			1.14738i
$363$			4.38769e12i			0.696150i
$364$	−3.46620e12	−	5.77690e11i	−0.542434	−	0.0904041i
$365$	−7.83703e12			−1.20973
$366$	4.19117e12			0.638161
$367$		−	8.86542e12i		−	1.33159i	−0.746137	−	0.665793i	$-0.768094\pi$
$367$		−	8.86542e12i		−	1.33159i	0.746137	−	0.665793i	$-0.231906\pi$
$368$	1.56927e13			2.32519
$369$			2.09766e10i			0.00306623i
$370$		−	2.22678e12i		−	0.321121i
$371$	−2.78922e11	+	1.67356e12i	−0.0396838	+	0.238107i
$372$	6.59944e12			0.926388
$373$	8.44347e11			0.116944			0.0584718	−	0.998289i	$-0.481377\pi$
$373$	8.44347e11			0.116944			0.0584718	+	0.998289i	$0.481377\pi$
$374$		−	3.65219e11i		−	0.0499109i
$375$	8.18283e12			1.10344
$376$		−	5.86413e12i		−	0.780305i
$377$			8.66827e12i			1.13822i
$378$	−8.89702e12	−	1.48281e12i	−1.15288	−	0.192144i
$379$	−5.07585e12			−0.649102			−0.324551	−	0.945868i	$-0.605213\pi$
$379$	−5.07585e12			−0.649102			−0.324551	+	0.945868i	$0.605213\pi$
$380$	−4.36720e12			−0.551169
$381$		−	3.68535e12i		−	0.459044i
$382$	−1.11092e13			−1.36573
$383$			1.58935e13i			1.92853i	0.264948	+	0.964263i	$0.414645\pi$
$383$			1.58935e13i			1.92853i	−0.264948	+	0.964263i	$0.585355\pi$
$384$			9.34877e12i			1.11969i
$385$	4.40906e12	+	7.34831e11i	0.521245	+	0.0868727i
$386$	−1.11064e13			−1.29610
$387$	5.39933e11			0.0621993
$388$		−	3.60270e12i		−	0.409703i
$389$	1.47264e13			1.65329			0.826643	−	0.562727i	$-0.190248\pi$
$389$	1.47264e13			1.65329			0.826643	+	0.562727i	$0.190248\pi$
$390$		−	1.17094e13i		−	1.29781i
$391$			1.20741e12i			0.132120i
$392$	−5.40447e12	−	1.85293e12i	−0.583879	−	0.200184i
$393$	2.72827e12			0.291021
$394$	1.73970e13			1.83229
$395$			1.11480e13i			1.15934i
$396$	2.22908e11			0.0228902
$397$		−	1.36618e13i		−	1.38534i	−0.721256	−	0.692669i	$-0.756435\pi$
$397$		−	1.36618e13i		−	1.38534i	0.721256	−	0.692669i	$-0.243565\pi$
$398$		−	1.66916e13i		−	1.67141i
$399$	−2.09162e12	+	1.25499e13i	−0.206832	+	1.24101i
$400$	−1.97735e12			−0.193100
$401$	6.21273e12			0.599185			0.299592	−	0.954067i	$-0.403149\pi$
$401$	6.21273e12			0.599185			0.299592	+	0.954067i	$0.403149\pi$
$402$		−	6.98758e12i		−	0.665574i
$403$	−2.12433e13			−1.99846
$404$			4.59700e12i			0.427137i
$405$		−	1.07603e13i		−	0.987529i
$406$	2.27301e12	−	1.36383e13i	0.206049	−	1.23632i
$407$	−1.83298e12			−0.164129
$408$	−5.15191e11			−0.0455688
$409$			7.40856e12i			0.647317i	0.946174	+	0.323659i	$0.104913\pi$
$409$			7.40856e12i			0.647317i	−0.946174	+	0.323659i	$0.895087\pi$
$410$	−4.96609e11			−0.0428642
$411$		−	7.77014e12i		−	0.662552i
$412$		−	3.96346e12i		−	0.333878i
$413$	−2.50503e12	−	4.17498e11i	−0.208479	−	0.0347459i
$414$	−2.22502e12			−0.182950
$415$	7.68712e12			0.624486
$416$			1.26063e13i			1.01186i
$417$	−3.56786e12			−0.282961
$418$			1.08540e13i			0.850568i
$419$		−	2.63638e11i		−	0.0204145i	−0.999948	−	0.0102072i	$-0.996751\pi$
$419$		−	2.63638e11i		−	0.0204145i	0.999948	−	0.0102072i	$-0.00324912\pi$
$420$	−1.01694e12	+	6.10174e12i	−0.0778124	+	0.466882i
$421$	6.05447e12			0.457789			0.228894	−	0.973451i	$-0.426489\pi$
$421$	6.05447e12			0.457789			0.228894	+	0.973451i	$0.426489\pi$
$422$	1.31654e12			0.0983719
$423$			1.37700e12i			0.101679i
$424$	2.04177e12			0.148997
$425$		−	1.52139e11i		−	0.0109722i
$426$			1.40389e13i			1.00066i
$427$	7.03022e12	+	1.17168e12i	0.495256	+	0.0825413i
$428$	−4.02282e12			−0.280099
$429$	−9.63861e12			−0.663327
$430$			1.27826e13i			0.869513i
$431$	−4.25728e12			−0.286250			−0.143125	−	0.989705i	$-0.545715\pi$
$431$	−4.25728e12			−0.286250			−0.143125	+	0.989705i	$0.545715\pi$
$432$			1.79764e13i			1.19477i
$433$			4.98436e12i			0.327469i	0.986504	+	0.163734i	$0.0523540\pi$
$433$			4.98436e12i			0.327469i	−0.986504	+	0.163734i	$0.947646\pi$
$434$	3.34233e13	+	5.57045e12i	2.17070	+	0.361778i
$435$	1.52592e13			0.979685
$436$	2.39636e12			0.152096
$437$		−	3.58832e13i		−	2.25156i
$438$	−2.69555e13			−1.67216
$439$			2.46687e13i			1.51295i	0.654024	+	0.756474i	$0.273080\pi$
$439$			2.46687e13i			1.51295i	−0.654024	+	0.756474i	$0.726920\pi$
$440$		−	5.37911e12i		−	0.326172i
$441$	1.26906e12	+	4.35099e11i	0.0760834	+	0.0260853i
$442$	−1.62696e12			−0.0964417
$443$	−1.45874e12			−0.0854988			−0.0427494	−	0.999086i	$-0.513612\pi$
$443$	−1.45874e12			−0.0854988			−0.0427494	+	0.999086i	$0.513612\pi$
$444$		−	2.53668e12i		−	0.147011i
$445$	−1.72804e13			−0.990271
$446$		−	3.12380e13i		−	1.77015i
$447$		−	2.71059e13i		−	1.51889i
$448$	−4.02729e11	+	2.41641e12i	−0.0223163	+	0.133900i
$449$	−2.84201e13			−1.55738			−0.778688	−	0.627411i	$-0.784115\pi$
$449$	−2.84201e13			−1.55738			−0.778688	+	0.627411i	$0.784115\pi$
$450$	2.80362e11			0.0151934
$451$			4.08784e11i			0.0219084i
$452$	8.16972e12			0.433027
$453$		−	3.06914e13i		−	1.60889i
$454$			3.17980e13i			1.64862i
$455$	3.27348e12	−	1.96412e13i	0.167862	−	1.00719i
$456$	1.53111e13			0.776571
$457$	−1.12423e12			−0.0563993			−0.0281996	−	0.999602i	$-0.508977\pi$
$457$	−1.12423e12			−0.0563993			−0.0281996	+	0.999602i	$0.508977\pi$
$458$		−	2.64298e13i		−	1.31150i
$459$	−1.38312e12			−0.0678885
$460$		−	1.74463e13i		−	0.847061i
$461$			2.50668e13i			1.20391i	0.798530	+	0.601956i	$0.205612\pi$
$461$			2.50668e13i			1.20391i	−0.798530	+	0.601956i	$0.794388\pi$
$462$	1.51650e13	+	2.52745e12i	0.720496	+	0.120081i
$463$	4.13932e13			1.94547			0.972735	−	0.231921i	$-0.0745009\pi$
$463$	4.13932e13			1.94547			0.972735	+	0.231921i	$0.0745009\pi$
$464$	−2.75562e13			−1.28123
$465$			3.73957e13i			1.72011i
$466$	−1.21505e13			−0.552924
$467$			1.64639e13i			0.741224i	0.928788	+	0.370612i	$0.120852\pi$
$467$			1.64639e13i			0.741224i	−0.928788	+	0.370612i	$0.879148\pi$
$468$		−	9.92997e11i		−	0.0442302i
$469$	1.95345e12	−	1.17209e13i	0.0860870	−	0.516531i
$470$	−3.25995e13			−1.42142
$471$	1.57983e13			0.681564
$472$			3.05617e12i			0.130457i
$473$	1.05220e13			0.444419
$474$			3.83436e13i			1.60251i
$475$			4.52143e12i			0.186986i
$476$	8.47804e11	+	1.41298e11i	0.0346945	+	0.00578232i
$477$	−4.79441e11			−0.0194153
$478$	3.61043e12			0.144684
$479$			2.08003e12i			0.0824884i	0.999149	+	0.0412442i	$0.0131322\pi$
$479$			2.08003e12i			0.0824884i	−0.999149	+	0.0412442i	$0.986868\pi$
$480$	2.21916e13			0.870928
$481$			8.16544e12i			0.317142i
$482$		−	1.28705e13i		−	0.494722i
$483$	−5.01350e13	−	8.35570e12i	−1.90724	−	0.317868i
$484$	−8.80902e12			−0.331666
$485$	2.04147e13			0.760736
$486$		−	5.32058e12i		−	0.196235i
$487$	−1.70804e13			−0.623525			−0.311763	−	0.950160i	$-0.600919\pi$
$487$	−1.70804e13			−0.623525			−0.311763	+	0.950160i	$0.600919\pi$
$488$		−	8.57697e12i		−	0.309910i
$489$			8.00459e11i			0.0286282i
$490$	−1.03007e13	+	3.00442e13i	−0.364658	+	1.06361i
$491$	1.84220e12			0.0645550			0.0322775	−	0.999479i	$-0.489724\pi$
$491$	1.84220e12			0.0645550			0.0322775	+	0.999479i	$0.489724\pi$
$492$	−5.65721e11			−0.0196235
$493$		−	2.12019e12i		−	0.0728014i
$494$	4.83518e13			1.64353
$495$			1.26311e12i			0.0425024i
$496$		−	6.75317e13i		−	2.24957i
$497$	−3.92472e12	+	2.35487e13i	−0.129427	+	0.776578i
$498$	2.64399e13			0.863202
$499$	1.94695e13			0.629291			0.314646	−	0.949209i	$-0.398114\pi$
$499$	1.94695e13			0.629291			0.314646	+	0.949209i	$0.398114\pi$
$500$			1.64284e13i			0.525709i
$501$	4.27393e12			0.135406
$502$			7.67646e12i			0.240792i
$503$		−	1.10616e12i		−	0.0343541i	−0.999852	−	0.0171771i	$-0.994532\pi$
$503$		−	1.10616e12i		−	0.0343541i	0.999852	−	0.0171771i	$-0.00546790\pi$
$504$	2.65414e11	−	1.59251e12i	0.00816151	−	0.0489699i
$505$	−2.60488e13			−0.793107
$506$	−4.33602e13			−1.30719
$507$			8.11671e12i			0.242293i
$508$	7.39897e12			0.218702
$509$		−	2.73817e13i		−	0.801441i	−0.916200	−	0.400720i	$-0.868760\pi$
$509$		−	2.73817e13i		−	0.801441i	0.916200	−	0.400720i	$-0.131240\pi$
$510$			2.86402e12i			0.0830090i
$511$	−4.52148e13	−	7.53568e12i	−1.29771	−	0.216281i
$512$	−1.29290e13			−0.367463
$513$	4.11052e13			1.15694
$514$		−	2.90595e13i		−	0.809977i
$515$	2.24589e13			0.619944
$516$			1.45615e13i			0.398069i
$517$			2.68344e13i			0.726505i
$518$	2.14116e12	−	1.28472e13i	0.0574116	−	0.344475i
$519$	−5.32887e13			−1.41514
$520$	−2.39625e13			−0.630255
$521$			2.22738e13i			0.580238i	0.956991	+	0.290119i	$0.0936949\pi$
$521$			2.22738e13i			0.580238i	−0.956991	+	0.290119i	$0.906305\pi$
$522$	3.90710e12			0.100810
$523$		−	5.87184e13i		−	1.50060i	−0.661096	−	0.750301i	$-0.729908\pi$
$523$		−	5.87184e13i		−	1.50060i	0.661096	−	0.750301i	$-0.270092\pi$
$524$			5.47746e12i			0.138651i
$525$	6.31723e12	+	1.05285e12i	0.158391	+	0.0263981i
$526$	4.90528e13			1.21825
$527$	5.19594e12			0.127823
$528$		−	3.06408e13i		−	0.746673i
$529$	1.01922e14			2.46030
$530$		−	1.13505e13i		−	0.271415i
$531$		−	7.17640e11i		−	0.0169994i
$532$	−2.51960e13	−	4.19927e12i	−0.591254	−	0.0985407i
$533$	1.82103e12			0.0423332
$534$	−5.94360e13			−1.36881
$535$		−	2.27953e13i		−	0.520087i
$536$	−1.42996e13			−0.323222
$537$			3.50939e13i			0.785887i
$538$			3.70368e13i			0.821718i
$539$	2.47310e13	+	8.47904e12i	0.543622	+	0.186382i
$540$	1.99853e13			0.435252
$541$	−6.03856e13			−1.30301			−0.651504	−	0.758645i	$-0.725862\pi$
$541$	−6.03856e13			−1.30301			−0.651504	+	0.758645i	$0.725862\pi$
$542$			7.90739e13i			1.69058i
$543$	−4.60417e13			−0.975332
$544$		−	3.08340e12i		−	0.0647196i
$545$			1.35789e13i			0.282412i
$546$	1.12591e13	−	6.75560e13i	0.232029	−	1.39220i
$547$	4.76121e13			0.972256			0.486128	−	0.873888i	$-0.338409\pi$
$547$	4.76121e13			0.972256			0.486128	+	0.873888i	$0.338409\pi$
$548$	1.55999e13			0.315659
$549$			2.01402e12i			0.0403833i
$550$	5.46358e12			0.108558
$551$			6.30103e13i			1.24066i
$552$			6.11655e13i			1.19347i
$553$	−1.07194e13	+	6.43172e13i	−0.207273	+	1.24366i
$554$	3.99068e12			0.0764711
$555$	1.43741e13			0.272970
$556$		−	7.16307e12i		−	0.134811i
$557$	−3.92115e13			−0.731370			−0.365685	−	0.930739i	$-0.619165\pi$
$557$	−3.92115e13			−0.731370			−0.365685	+	0.930739i	$0.619165\pi$
$558$			9.57510e12i			0.177000i
$559$		−	4.68728e13i		−	0.858740i
$560$	6.24387e13	+	1.04063e13i	1.13374	+	0.188954i
$561$	2.35752e12			0.0424270
$562$	−5.57644e12			−0.0994663
$563$		−	4.59346e13i		−	0.812079i	−0.913855	−	0.406040i	$-0.866910\pi$
$563$		−	4.59346e13i		−	0.812079i	0.913855	−	0.406040i	$-0.133090\pi$
$564$	−3.71364e13			−0.650735
$565$			4.62937e13i			0.804043i
$566$		−	2.72748e13i		−	0.469547i
$567$	1.03466e13	−	6.20804e13i	0.176555	−	1.05935i
$568$	2.87297e13			0.485948
$569$	−2.24415e13			−0.376263			−0.188131	−	0.982144i	$-0.560243\pi$
$569$	−2.24415e13			−0.376263			−0.188131	+	0.982144i	$0.560243\pi$
$570$		−	8.51163e13i		−	1.41462i
$571$	5.80873e11			0.00956975			0.00478488	−	0.999989i	$-0.498477\pi$
$571$	5.80873e11			0.00956975			0.00478488	+	0.999989i	$0.498477\pi$
$572$		−	1.93511e13i		−	0.316028i
$573$		−	7.17109e13i		−	1.16095i
$574$	−2.86513e12	−	4.77513e11i	−0.0459816	−	0.00766348i
$575$	−1.80625e13			−0.287368
$576$	−6.92254e11			−0.0109182
$577$		−	7.12685e13i		−	1.11434i	−0.830398	−	0.557171i	$-0.811887\pi$
$577$		−	7.12685e13i		−	1.11434i	0.830398	−	0.557171i	$-0.188113\pi$
$578$	−7.84865e13			−1.21662
$579$		−	7.16929e13i		−	1.10175i
$580$			3.06355e13i			0.466750i
$581$	4.43499e13	+	7.39154e12i	0.669904	+	0.111649i
$582$	7.02164e13			1.05153
$583$	−9.34316e12			−0.138724
$584$			5.51628e13i			0.812048i
$585$	5.62681e12			0.0821264
$586$		−	2.30806e13i		−	0.334010i
$587$			5.71609e12i			0.0820179i	0.999159	+	0.0410089i	$0.0130572\pi$
$587$			5.71609e12i			0.0820179i	−0.999159	+	0.0410089i	$0.986943\pi$
$588$	−1.17342e13	+	3.42254e13i	−0.166943	+	0.486925i
$589$	−1.54419e14			−2.17833
$590$	1.69897e13			0.237643
$591$			1.12299e14i			1.55754i
$592$	−2.59577e13			−0.356991
$593$		−	2.76901e13i		−	0.377617i	−0.982014	−	0.188808i	$-0.939537\pi$
$593$		−	2.76901e13i		−	0.377617i	0.982014	−	0.188808i	$-0.0604625\pi$
$594$		−	4.96704e13i		−	0.671685i
$595$	−8.00666e11	+	4.80408e12i	−0.0107366	+	0.0644206i
$596$	5.44197e13			0.723644
$597$	1.07746e14			1.42079
$598$			1.93159e14i			2.52585i
$599$	1.85608e12			0.0240693			0.0120346	−	0.999928i	$-0.496169\pi$
$599$	1.85608e12			0.0240693			0.0120346	+	0.999928i	$0.496169\pi$
$600$		−	7.70711e12i		−	0.0991141i
$601$			1.54942e13i			0.197605i	0.995107	+	0.0988023i	$0.0315011\pi$
$601$			1.54942e13i			0.197605i	−0.995107	+	0.0988023i	$0.968499\pi$
$602$	−1.22911e13	+	7.37476e13i	−0.155456	+	0.932750i
$603$	3.35780e12			0.0421180
$604$	6.16183e13			0.766522
$605$		−	4.99163e13i		−	0.615836i
$606$	−8.95951e13			−1.09628
$607$		−	3.98863e13i		−	0.484039i	−0.970271	−	0.242019i	$-0.922190\pi$
$607$		−	3.98863e13i		−	0.484039i	0.970271	−	0.242019i	$-0.0778098\pi$
$608$			9.16362e13i			1.10293i
$609$	8.80364e13	+	1.46725e13i	1.05093	+	0.175153i
$610$	−4.76806e13			−0.564537
$611$	1.19540e14			1.40381
$612$			2.42879e11i			0.00282900i
$613$	8.01006e13			0.925408			0.462704	−	0.886513i	$-0.346879\pi$
$613$	8.01006e13			0.925408			0.462704	+	0.886513i	$0.346879\pi$
$614$		−	2.65509e13i		−	0.304255i
$615$		−	3.20565e12i		−	0.0364369i
$616$	5.17228e12	−	3.10342e13i	0.0583147	−	0.349894i
$617$	−1.66963e14			−1.86722			−0.933609	−	0.358293i	$-0.883359\pi$
$617$	−1.66963e14			−1.86722			−0.933609	+	0.358293i	$0.883359\pi$
$618$	7.72475e13			0.856924
$619$		−	3.06340e13i		−	0.337094i	−0.985694	−	0.168547i	$-0.946093\pi$
$619$		−	3.06340e13i		−	0.337094i	0.985694	−	0.168547i	$-0.0539075\pi$
$620$	−7.50782e13			−0.819512
$621$			1.64209e14i			1.77803i
$622$		−	1.24123e14i		−	1.33322i
$623$	−9.96973e13	−	1.66160e13i	−1.06229	−	0.177046i
$624$	−1.36497e14			−1.44278
$625$	−7.83588e13			−0.821652
$626$		−	1.76930e14i		−	1.84047i
$627$	−7.00637e13			−0.723028
$628$			3.17178e13i			0.324717i
$629$		−	1.99720e12i		−	0.0202847i
$630$	−8.85298e12	−	1.47547e12i	−0.0892045	−	0.0148672i
$631$	1.69166e14			1.69109			0.845543	−	0.533907i	$-0.179277\pi$
$631$	1.69166e14			1.69109			0.845543	+	0.533907i	$0.179277\pi$
$632$	7.84679e13			0.778228
$633$			8.49838e12i			0.0836214i
$634$	1.29871e14			1.26785
$635$			4.19262e13i			0.406085i
$636$		−	1.29301e13i		−	0.124256i
$637$	3.77719e13	−	1.10170e14i	0.360140	−	1.05043i
$638$	7.61400e13			0.720293
$639$	−6.74623e12			−0.0633223
$640$		−	1.06356e14i		−	0.990515i
$641$	−8.03538e12			−0.0742534			−0.0371267	−	0.999311i	$-0.511821\pi$
$641$	−8.03538e12			−0.0742534			−0.0371267	+	0.999311i	$0.511821\pi$
$642$		−	7.84044e13i		−	0.718895i
$643$			1.75906e14i			1.60039i	0.599739	+	0.800196i	$0.295271\pi$
$643$			1.75906e14i			1.60039i	−0.599739	+	0.800196i	$0.704729\pi$
$644$	1.67755e13	−	1.00655e14i	0.151442	−	0.908666i
$645$	−8.25127e13			−0.739132
$646$	−1.18265e13			−0.105122
$647$			4.95979e13i			0.437464i	0.975785	+	0.218732i	$0.0701920\pi$
$647$			4.95979e13i			0.437464i	−0.975785	+	0.218732i	$0.929808\pi$
$648$	−7.57390e13			−0.662895
$649$		−	1.39851e13i		−	0.121462i
$650$		−	2.43388e13i		−	0.209765i
$651$	−3.59578e13	+	2.15750e14i	−0.307530	+	1.84521i
$652$	−1.60706e12			−0.0136393
$653$	3.66721e13			0.308866			0.154433	−	0.988003i	$-0.450645\pi$
$653$	3.66721e13			0.308866			0.154433	+	0.988003i	$0.450645\pi$
$654$			4.67048e13i			0.390367i
$655$	−3.10380e13			−0.257447
$656$			5.78899e12i			0.0476523i
$657$		−	1.29532e13i		−	0.105815i
$658$	−1.88079e14	−	3.13460e13i	−1.52480	−	0.254128i
$659$	1.17411e14			0.944675			0.472338	−	0.881418i	$-0.343410\pi$
$659$	1.17411e14			0.944675			0.472338	+	0.881418i	$0.343410\pi$
$660$	−3.40648e13			−0.272011
$661$			1.15192e13i			0.0912884i	0.998958	+	0.0456442i	$0.0145341\pi$
$661$			1.15192e13i			0.0912884i	−0.998958	+	0.0456442i	$0.985466\pi$
$662$	1.19824e14			0.942439
$663$		−	1.05022e13i		−	0.0819806i
$664$		−	5.41076e13i		−	0.419197i
$665$	2.37951e13	−	1.42773e14i	0.182970	−	1.09784i
$666$	3.68045e12			0.0280886
$667$	−2.51717e14			−1.90670
$668$			8.58063e12i			0.0645115i
$669$	2.01644e14			1.50472
$670$			7.94937e13i			0.588788i
$671$			3.92484e13i			0.288542i
$672$	1.28032e14	+	2.13383e13i	0.934268	+	0.155709i
$673$	1.55036e14			1.12294			0.561472	−	0.827496i	$-0.310235\pi$
$673$	1.55036e14			1.12294			0.561472	+	0.827496i	$0.310235\pi$
$674$	−1.63366e14			−1.17453
$675$		−	2.06911e13i		−	0.147660i
$676$	−1.62957e13			−0.115435
$677$		−	1.63546e14i		−	1.15000i	−0.818153	−	0.575000i	$-0.805002\pi$
$677$		−	1.63546e14i		−	1.15000i	0.818153	−	0.575000i	$-0.194998\pi$
$678$			1.59227e14i			1.11140i
$679$	1.17780e14	+	1.96297e13i	0.816062	+	0.136008i
$680$	5.86104e12			0.0403116
$681$	−2.05259e14			−1.40141
$682$			1.86596e14i			1.26468i
$683$	−1.89282e14			−1.27352			−0.636762	−	0.771061i	$-0.719726\pi$
$683$	−1.89282e14			−1.27352			−0.636762	+	0.771061i	$0.719726\pi$
$684$		−	7.21816e12i		−	0.0482110i
$685$			8.83966e13i			0.586115i
$686$	−8.83177e13	+	1.63432e14i	−0.581336	+	1.07576i
$687$	1.70607e14			1.11484
$688$	1.49007e14			0.966640
$689$			4.16213e13i			0.268053i
$690$	3.40028e14			2.17405
$691$		−	1.16415e14i		−	0.738956i	−0.929240	−	0.369478i	$-0.879537\pi$
$691$		−	1.16415e14i		−	0.738956i	0.929240	−	0.369478i	$-0.120463\pi$
$692$		−	1.06986e14i		−	0.674213i
$693$	−1.21454e12	+	7.28735e12i	−0.00759880	+	0.0455936i
$694$	−2.23661e14			−1.38929
$695$	4.05895e13			0.250317
$696$		−	1.07406e14i		−	0.657629i
$697$	−4.45409e11			−0.00270766
$698$			2.87907e14i			1.73770i
$699$		−	7.84327e13i		−	0.470015i
$700$	−2.11378e12	+	1.26829e13i	−0.0125768	+	0.0754621i
$701$	6.04150e13			0.356907			0.178453	−	0.983948i	$-0.442891\pi$
$701$	6.04150e13			0.356907			0.178453	+	0.983948i	$0.442891\pi$
$702$	−2.21269e14			−1.29788
$703$			5.93552e13i			0.345686i
$704$	−1.34904e13			−0.0780118
$705$		−	2.10433e14i		−	1.20828i
$706$		−	8.26964e13i		−	0.471480i
$707$	−1.50286e14	−	2.50472e13i	−0.850787	−	0.141796i
$708$	1.93541e13			0.108794
$709$	−2.49142e14			−1.39065			−0.695323	−	0.718698i	$-0.744739\pi$
$709$	−2.49142e14			−1.39065			−0.695323	+	0.718698i	$0.744739\pi$
$710$		−	1.59713e14i		−	0.885213i
$711$	−1.84256e13			−0.101408
$712$			1.21632e14i			0.664735i
$713$		−	6.16881e14i		−	3.34776i
$714$	−2.75390e12	+	1.65236e13i	−0.0148408	+	0.0890460i
$715$	1.09653e14			0.586800
$716$	−7.04569e13			−0.374420
$717$			2.33057e13i			0.122989i
$718$	3.15205e14			1.65185
$719$			3.22257e13i			0.167709i	0.996478	+	0.0838547i	$0.0267232\pi$
$719$			3.22257e13i			0.167709i	−0.996478	+	0.0838547i	$0.973277\pi$
$720$			1.78874e13i			0.0924455i
$721$	1.29574e14	+	2.15953e13i	0.665031	+	0.110837i
$722$	1.11568e14			0.568663
$723$	8.30804e13			0.420540
$724$		−	9.24365e13i		−	0.464677i
$725$	3.17174e13			0.158346
$726$		−	1.71687e14i		−	0.851246i
$727$			1.14961e14i			0.566080i	0.959108	+	0.283040i	$0.0913429\pi$
$727$			1.14961e14i			0.566080i	−0.959108	+	0.283040i	$0.908657\pi$
$728$	−1.38249e14	−	2.30411e13i	−0.676092	−	0.112680i
$729$	−1.86774e14			−0.907151
$730$	3.06658e14			1.47924
$731$			1.14647e13i			0.0549257i
$732$	−5.43163e13			−0.258449
$733$			3.05572e14i			1.44409i	0.691847	+	0.722044i	$0.256797\pi$
$733$			3.05572e14i			1.44409i	−0.691847	+	0.722044i	$0.743203\pi$
$734$			3.46898e14i			1.62825i
$735$	−1.93938e14	−	6.64920e13i	−0.904121	−	0.309979i
$736$	−3.66074e14			−1.69504
$737$	6.54354e13			0.300937
$738$		−	8.20802e11i		−	0.00374935i
$739$	−1.84101e14			−0.835282			−0.417641	−	0.908612i	$-0.637143\pi$
$739$	−1.84101e14			−0.835282			−0.417641	+	0.908612i	$0.637143\pi$
$740$			2.88584e13i			0.130051i
$741$			3.12116e14i			1.39709i
$742$	1.09140e13	−	6.54852e13i	0.0485250	−	0.291155i
$743$	3.16811e14			1.39912			0.699562	−	0.714572i	$-0.253379\pi$
$743$	3.16811e14			1.39912			0.699562	+	0.714572i	$0.253379\pi$
$744$	2.63218e14			1.15465
$745$			3.08369e14i			1.34366i
$746$	−3.30387e13			−0.142998
$747$			1.27054e13i			0.0546241i
$748$			4.73313e12i			0.0202134i
$749$	2.19188e13	−	1.31515e14i	0.0929837	−	0.557911i
$750$	−3.20189e14			−1.34927
$751$	1.69321e14			0.708779			0.354389	−	0.935098i	$-0.384689\pi$
$751$	1.69321e14			0.708779			0.354389	+	0.935098i	$0.384689\pi$
$752$			3.80014e14i			1.58019i
$753$	−4.95523e13			−0.204686
$754$		−	3.39184e14i		−	1.39180i
$755$			3.49159e14i			1.42328i
$756$	1.15303e14	+	1.92168e13i	0.466907	+	0.0778165i
$757$	2.01381e13			0.0810101			0.0405051	−	0.999179i	$-0.487103\pi$
$757$	2.01381e13			0.0810101			0.0405051	+	0.999179i	$0.487103\pi$
$758$	1.98615e14			0.793716
$759$		−	2.79894e14i		−	1.11118i
$760$	−1.74185e14			−0.686979
$761$			1.69199e14i			0.662940i	0.943466	+	0.331470i	$0.107545\pi$
$761$			1.69199e14i			0.662940i	−0.943466	+	0.331470i	$0.892455\pi$
$762$			1.44205e14i			0.561315i
$763$	−1.30568e13	+	7.83421e13i	−0.0504910	+	0.302951i
$764$	1.43972e14			0.553109
$765$	−1.37627e12			−0.00525287
$766$		−	6.21901e14i		−	2.35818i
$767$	−6.22999e13			−0.234699
$768$		−	3.28112e14i		−	1.22805i
$769$		−	3.34843e14i		−	1.24512i	−0.782573	−	0.622558i	$-0.786093\pi$
$769$		−	3.34843e14i		−	1.24512i	0.782573	−	0.622558i	$-0.213907\pi$
$770$	−1.72523e14	−	2.87534e13i	−0.637374	−	0.106227i
$771$	1.87582e14			0.688523
$772$	1.43936e14			0.524906
$773$		−	1.20926e14i		−	0.438150i	−0.975708	−	0.219075i	$-0.929696\pi$
$773$		−	1.20926e14i		−	0.438150i	0.975708	−	0.219075i	$-0.0703040\pi$
$774$	−2.11272e13			−0.0760567
$775$			7.77297e13i			0.278022i
$776$		−	1.43693e14i		−	0.510656i
$777$	8.29296e13	+	1.38214e13i	0.292822	+	0.0488029i
$778$	−5.76233e14			−2.02162
$779$	1.32372e13			0.0461432
$780$			1.51750e14i			0.525600i
$781$	−1.31468e14			−0.452444
$782$		−	4.72450e13i		−	0.161556i
$783$		−	2.88349e14i		−	0.979737i
$784$	3.50227e14	+	1.20076e14i	1.18241	+	0.405392i
$785$	−1.79729e14			−0.602934
$786$	−1.06755e14			−0.355858
$787$		−	3.39922e14i		−	1.12592i	−0.826486	−	0.562958i	$-0.809663\pi$
$787$		−	3.39922e14i		−	1.12592i	0.826486	−	0.562958i	$-0.190337\pi$
$788$	−2.25460e14			−0.742058
$789$			3.16640e14i			1.03557i
$790$		−	4.36214e14i		−	1.41763i
$791$	−4.45136e13	+	2.67086e14i	−0.143751	+	0.862519i
$792$	8.89067e12			0.0285305
$793$	1.74841e14			0.557543
$794$			5.34577e14i			1.69398i
$795$	7.32683e13			0.230717
$796$			2.16318e14i			0.676903i
$797$			5.74563e14i			1.78668i	0.449385	+	0.893338i	$0.351643\pi$
$797$			5.74563e14i			1.78668i	−0.449385	+	0.893338i	$0.648357\pi$
$798$	8.18435e13	−	4.91069e14i	0.252912	−	1.51750i
$799$	−2.92385e13			−0.0897887
$800$	4.61268e13			0.140768
$801$		−	2.85613e13i		−	0.0866194i
$802$	−2.43100e14			−0.732678
$803$		−	2.52426e14i		−	0.756060i
$804$			9.05568e13i			0.269551i
$805$	5.70358e14	+	9.50582e13i	1.68721	+	0.281197i
$806$	8.31235e14			2.44371
$807$	−2.39076e14			−0.698504
$808$			1.83351e14i			0.532386i
$809$	−2.53422e13			−0.0731309			−0.0365655	−	0.999331i	$-0.511642\pi$
$809$	−2.53422e13			−0.0731309			−0.0365655	+	0.999331i	$0.511642\pi$
$810$			4.21044e14i			1.20754i
$811$		−	2.46698e14i		−	0.703172i	−0.936156	−	0.351586i	$-0.885642\pi$
$811$		−	2.46698e14i		−	0.703172i	0.936156	−	0.351586i	$-0.114358\pi$
$812$	−2.94575e13	+	1.76748e14i	−0.0834480	+	0.500696i
$813$	−5.10429e14			−1.43709
$814$	7.17232e13			0.200696
$815$		−	9.10637e12i		−	0.0253255i
$816$	3.33860e13			0.0922813
$817$		−	3.40721e14i		−	0.936029i
$818$		−	2.89892e14i		−	0.791534i
$819$	3.24632e13	+	5.41045e12i	0.0880993	+	0.0146830i
$820$	6.43589e12			0.0173596
$821$	−4.66576e14			−1.25085			−0.625427	−	0.780283i	$-0.715075\pi$
$821$	−4.66576e14			−1.25085			−0.625427	+	0.780283i	$0.715075\pi$
$822$			3.04040e14i			0.810163i
$823$	−6.03555e14			−1.59852			−0.799259	−	0.600987i	$-0.794774\pi$
$823$	−6.03555e14			−1.59852			−0.799259	+	0.600987i	$0.794774\pi$
$824$		−	1.58082e14i		−	0.416147i
$825$			3.52679e13i			0.0922805i
$826$	9.80200e13	+	1.63364e13i	0.254926	+	0.0424870i
$827$	5.44095e14			1.40653			0.703263	−	0.710930i	$-0.251726\pi$
$827$	5.44095e14			1.40653			0.703263	+	0.710930i	$0.251726\pi$
$828$	2.88355e13			0.0740928
$829$			3.69513e14i			0.943749i	0.881666	+	0.471875i	$0.156423\pi$
$829$			3.69513e14i			0.943749i	−0.881666	+	0.471875i	$0.843577\pi$
$830$	−3.00792e14			−0.763617
$831$			2.57602e13i			0.0650046i
$832$			6.00960e13i			0.150740i
$833$	−9.23871e12	+	2.69467e13i	−0.0230349	+	0.0671862i
$834$	1.39608e14			0.346003
$835$	−4.86221e13			−0.119785
$836$		−	1.40665e14i		−	0.344472i
$837$	7.06655e14			1.72021
$838$			1.03160e13i			0.0249626i
$839$		−	5.97115e13i		−	0.143631i	−0.997418	−	0.0718155i	$-0.977121\pi$
$839$		−	5.97115e13i		−	0.143631i	0.997418	−	0.0718155i	$-0.0228793\pi$
$840$	−4.05606e13	+	2.43367e14i	−0.0969857	+	0.581924i
$841$	2.13041e13			0.0506388
$842$	−2.36907e14			−0.559780
$843$		−	3.59965e13i		−	0.0845516i
$844$	−1.70619e13			−0.0398397
$845$		−	9.23393e13i		−	0.214340i
$846$		−	5.38810e13i		−	0.124332i
$847$	4.79969e13	−	2.87986e14i	0.110102	−	0.660624i
$848$	−1.32313e14			−0.301733
$849$	1.76061e14			0.399140
$850$			5.95308e12i			0.0134167i
$851$	−2.37115e14			−0.531266
$852$		−	1.81940e14i		−	0.405256i
$853$			7.17531e14i			1.58890i	0.607332	+	0.794448i	$0.292240\pi$
$853$			7.17531e14i			1.58890i	−0.607332	+	0.794448i	$0.707760\pi$
$854$	−2.75088e14	−	4.58472e13i	−0.605595	−	0.100931i
$855$	4.09017e13			0.0895180
$856$	−1.60450e14			−0.349116
$857$		−	4.56916e14i		−	0.988399i	−0.869349	−	0.494199i	$-0.835461\pi$
$857$		−	4.56916e14i		−	0.988399i	0.869349	−	0.494199i	$-0.164539\pi$
$858$	3.77152e14			0.811111
$859$		−	3.46558e13i		−	0.0740987i	−0.999313	−	0.0370494i	$-0.988204\pi$
$859$		−	3.46558e13i		−	0.0740987i	0.999313	−	0.0370494i	$-0.0117959\pi$
$860$		−	1.65658e14i		−	0.352144i
$861$	3.08239e12	−	1.84947e13i	0.00651437	−	0.0390868i
$862$	1.66584e14			0.350024
$863$	2.83175e14			0.591563			0.295782	−	0.955256i	$-0.404420\pi$
$863$	2.83175e14			0.591563			0.295782	+	0.955256i	$0.404420\pi$
$864$		−	4.19348e14i		−	0.870975i
$865$	6.06236e14			1.25188
$866$		−	1.95034e14i		−	0.400426i
$867$		−	5.06638e14i		−	1.03419i
$868$	−4.33155e14	−	7.21913e13i	−0.879113	−	0.146516i
$869$	−3.59071e14			−0.724571
$870$	−5.97083e14			−1.19795
$871$		−	2.91498e14i		−	0.581493i
$872$	9.55785e13			0.189574
$873$			3.37417e13i			0.0665419i
$874$			1.40408e15i			2.75319i
$875$	−5.37081e14	−	8.95120e13i	−1.04713	−	0.174518i
$876$	3.49335e14			0.677207
$877$	−1.37586e14			−0.265202			−0.132601	−	0.991169i	$-0.542333\pi$
$877$	−1.37586e14			−0.265202			−0.132601	+	0.991169i	$0.542333\pi$
$878$		−	9.65270e14i		−	1.85002i
$879$	1.48988e14			0.283927
$880$			3.48583e14i			0.660531i
$881$		−	4.33541e14i		−	0.816865i	−0.912788	−	0.408433i	$-0.866075\pi$
$881$		−	4.33541e14i		−	0.816865i	0.912788	−	0.408433i	$-0.133925\pi$
$882$	−4.96575e13	−	1.70251e13i	−0.0930341	−	0.0318969i
$883$	−7.15525e14			−1.33297			−0.666486	−	0.745517i	$-0.732202\pi$
$883$	−7.15525e14			−1.33297			−0.666486	+	0.745517i	$0.732202\pi$
$884$	2.10849e13			0.0390579
$885$			1.09670e14i			0.202009i
$886$	5.70796e13			0.104547
$887$			2.88088e14i			0.524694i	0.964974	+	0.262347i	$0.0844966\pi$
$887$			2.88088e14i			0.524694i	−0.964974	+	0.262347i	$0.915503\pi$
$888$		−	1.01175e14i		−	0.183235i
$889$	−4.03141e13	+	2.41888e14i	−0.0726019	+	0.435619i
$890$	6.76171e14			1.21089
$891$	3.46583e14			0.617190
$892$			4.04835e14i			0.716891i
$893$	8.68946e14			1.53015
$894$			1.06064e15i			1.85729i
$895$		−	3.99244e14i		−	0.695221i
$896$	1.02266e14	−	6.13607e14i	0.177089	−	1.06255i
$897$	−1.24686e15			−2.14711
$898$	1.11206e15			1.90435
$899$			1.08323e15i			1.84469i
$900$	−3.63340e12			−0.00615320
$901$		−	1.01802e13i		−	0.0171449i
$902$		−	1.59955e13i		−	0.0267895i
$903$	−4.76048e14	−	7.93400e13i	−0.792888	−	0.132146i
$904$	3.25849e14			0.539727
$905$	5.23791e14			0.862810
$906$			1.20094e15i			1.96734i
$907$	4.32873e14			0.705218			0.352609	−	0.935771i	$-0.385295\pi$
$907$	4.32873e14			0.705218			0.352609	+	0.935771i	$0.385295\pi$
$908$		−	4.12092e14i		−	0.667675i
$909$		−	4.30539e13i		−	0.0693734i
$910$	−1.28089e14	+	7.68546e14i	−0.205260	+	1.23158i
$911$	−2.60580e14			−0.415288			−0.207644	−	0.978205i	$-0.566579\pi$
$911$	−2.60580e14			−0.415288			−0.207644	+	0.978205i	$0.566579\pi$
$912$	−9.92205e14			−1.57263
$913$			2.47597e14i			0.390294i
$914$	4.39903e13			0.0689645
$915$		−	3.07783e14i		−	0.479887i
$916$			3.42522e14i			0.531143i
$917$	−1.79070e14	−	2.98446e13i	−0.276170	−	0.0460276i
$918$	5.41205e13			0.0830135
$919$	−4.26052e14			−0.649957			−0.324979	−	0.945721i	$-0.605357\pi$
$919$	−4.26052e14			−0.649957			−0.324979	+	0.945721i	$0.605357\pi$
$920$		−	6.95845e14i		−	1.05578i
$921$	1.71389e14			0.258633
$922$		−	9.80847e14i		−	1.47213i
$923$			5.85655e14i			0.874246i
$924$	−1.96533e14	−	3.27550e13i	−0.291794	−	0.0486315i
$925$	2.98776e13			0.0441201
$926$	−1.61969e15			−2.37890
$927$			3.71204e13i			0.0542268i
$928$	6.42820e14			0.934005
$929$		−	2.77657e14i		−	0.401264i	−0.979667	−	0.200632i	$-0.935700\pi$
$929$		−	2.77657e14i		−	0.401264i	0.979667	−	0.200632i	$-0.0642995\pi$
$930$		−	1.46327e15i		−	2.10334i
$931$	2.74567e14	−	8.00833e14i	0.392554	−	1.14497i
$932$	1.57467e14			0.223929
$933$	8.01227e14			1.13331
$934$		−	6.44223e14i		−	0.906362i
$935$	−2.68202e13			−0.0375322
$936$		−	3.96056e13i		−	0.0551287i
$937$		−	7.81344e14i		−	1.08179i	−0.841089	−	0.540897i	$-0.818085\pi$
$937$		−	7.81344e14i		−	1.08179i	0.841089	−	0.540897i	$-0.181915\pi$
$938$	−7.64371e13	+	4.58630e14i	−0.105266	+	0.631609i
$939$	1.14210e15			1.56450
$940$	4.22480e14			0.575661
$941$		−	5.27015e14i		−	0.714290i	−0.934049	−	0.357145i	$-0.883750\pi$
$941$		−	5.27015e14i		−	0.714290i	0.934049	−	0.357145i	$-0.116250\pi$
$942$	−6.18178e14			−0.833411
$943$			5.28806e13i			0.0709150i
$944$		−	1.98049e14i		−	0.264188i
$945$	−1.08892e14	+	6.53362e14i	−0.144489	+	0.866951i
$946$	−4.11719e14			−0.543432
$947$	9.48695e14			1.24559			0.622797	−	0.782383i	$-0.285996\pi$
$947$	9.48695e14			1.24559			0.622797	+	0.782383i	$0.285996\pi$
$948$		−	4.96921e14i		−	0.649002i
$949$	−1.12449e15			−1.46092
$950$		−	1.76921e14i		−	0.228644i
$951$			8.38332e14i			1.07774i
$952$	3.38146e13	+	5.63568e12i	0.0432434	+	0.00720711i
$953$	−2.67219e14			−0.339941			−0.169970	−	0.985449i	$-0.554367\pi$
$953$	−2.67219e14			−0.339941			−0.169970	+	0.985449i	$0.554367\pi$
$954$	1.87602e13			0.0237408
$955$			8.15815e14i			1.02701i
$956$	−4.67900e13			−0.0585955
$957$			4.91490e14i			0.612287i
$958$		−	8.13903e13i		−	0.100866i
$959$	−8.49976e13	+	5.09994e14i	−0.104789	+	0.628741i
$960$	1.05790e14			0.129745
$961$	−1.83505e15			−2.23888
$962$		−	3.19508e14i		−	0.387799i
$963$	3.76763e13			0.0454922
$964$			1.66798e14i			0.200357i
$965$			8.15610e14i			0.974644i
$966$	1.96175e15	+	3.26953e14i	2.33216	+	0.388687i
$967$	1.04224e15			1.23264			0.616321	−	0.787495i	$-0.288622\pi$
$967$	1.04224e15			1.23264			0.616321	+	0.787495i	$0.288622\pi$
$968$	−3.51347e14			−0.413390
$969$		−	7.63409e13i		−	0.0893590i
$970$	−7.98812e14			−0.930221
$971$			1.06619e15i			1.23520i	0.786491	+	0.617601i	$0.211895\pi$
$971$			1.06619e15i			1.23520i	−0.786491	+	0.617601i	$0.788105\pi$
$972$			6.89530e13i			0.0794734i
$973$	2.34176e14	+	3.90288e13i	0.268521	+	0.0447529i
$974$	6.68346e14			0.762441
$975$	1.57109e14			0.178311
$976$			5.55815e14i			0.627598i
$977$	−9.17302e14			−1.03048			−0.515240	−	0.857046i	$-0.672297\pi$
$977$	−9.17302e14			−1.03048			−0.515240	+	0.857046i	$0.672297\pi$
$978$		−	3.13214e13i		−	0.0350064i
$979$		−	5.56591e14i		−	0.618903i
$980$	1.33494e14	−	3.89364e14i	0.147683	−	0.430750i
$981$	−2.24435e13			−0.0247027
$982$	−7.20841e13			−0.0789373
$983$			1.22149e15i			1.33083i	0.746473	+	0.665415i	$0.231746\pi$
$983$			1.22149e15i			1.33083i	−0.746473	+	0.665415i	$0.768254\pi$
$984$	−2.25637e13			−0.0244588
$985$		−	1.27757e15i		−	1.37785i
$986$			8.29616e13i			0.0890210i
$987$	2.02342e14	−	1.21407e15i	0.216023	−	1.29616i
$988$	−6.26624e14			−0.665614
$989$	1.36113e15			1.43853
$990$		−	4.94245e13i		−	0.0519716i
$991$	6.39925e14			0.669516			0.334758	−	0.942304i	$-0.391345\pi$
$991$	6.39925e14			0.669516			0.334758	+	0.942304i	$0.391345\pi$
$992$			1.57535e15i			1.63991i
$993$			7.73474e14i			0.801124i
$994$	1.53572e14	−	9.21444e14i	0.158263	−	0.949592i
$995$	−1.22576e15			−1.25687
$996$	−3.42652e14			−0.349589
$997$		−	1.61426e15i		−	1.63870i	−0.573296	−	0.819348i	$-0.694335\pi$
$997$		−	1.61426e15i		−	1.63870i	0.573296	−	0.819348i	$-0.305665\pi$
$998$	−7.61827e14			−0.769492
$999$		−	2.71622e14i		−	0.272985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.11.b.b.6.1	✓	4
3.2	odd	2		63.11.d.c.55.3		4
4.3	odd	2		112.11.c.b.97.3		4
7.2	even	3		49.11.d.b.31.4		8
7.3	odd	6		49.11.d.b.19.4		8
7.4	even	3		49.11.d.b.19.3		8
7.5	odd	6		49.11.d.b.31.3		8
7.6	odd	2	inner	7.11.b.b.6.2	yes	4
21.20	even	2		63.11.d.c.55.4		4
28.27	even	2		112.11.c.b.97.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.11.b.b.6.1	✓	4	1.1	even	1	trivial
7.11.b.b.6.2	yes	4	7.6	odd	2	inner
49.11.d.b.19.3		8	7.4	even	3
49.11.d.b.19.4		8	7.3	odd	6
49.11.d.b.31.3		8	7.5	odd	6
49.11.d.b.31.4		8	7.2	even	3
63.11.d.c.55.3		4	3.2	odd	2
63.11.d.c.55.4		4	21.20	even	2
112.11.c.b.97.2		4	28.27	even	2
112.11.c.b.97.3		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-39.1293 q^{2} -252.583i q^{3} +507.104 q^{4} +2873.50i q^{5} +9883.42i q^{6} +(-2763.01 + 16578.3i) q^{7} +20225.8 q^{8} -4749.36 q^{9} +O(q^{10})\)	\(q-39.1293 q^{2} -252.583i q^{3} +507.104 q^{4} +2873.50i q^{5} +9883.42i q^{6} +(-2763.01 + 16578.3i) q^{7} +20225.8 q^{8} -4749.36 q^{9} -112438. i q^{10} -92553.7 q^{11} -128086. i q^{12} +412302. i q^{13} +(108115. - 648699. i) q^{14} +725798. q^{15} -1.31070e6 q^{16} -100846. i q^{17} +185839. q^{18} +2.99705e6i q^{19} +1.45716e6i q^{20} +(4.18741e6 + 697890. i) q^{21} +3.62156e6 q^{22} -1.19728e7 q^{23} -5.10870e6i q^{24} +1.50863e6 q^{25} -1.61331e7i q^{26} -1.37152e7i q^{27} +(-1.40113e6 + 8.40693e6i) q^{28} +2.10241e7 q^{29} -2.84000e7 q^{30} +5.15236e7i q^{31} +3.05754e7 q^{32} +2.33775e7i q^{33} +3.94603e6i q^{34} +(-4.76378e7 - 7.93951e6i) q^{35} -2.40842e6 q^{36} +1.98045e7 q^{37} -1.17273e8i q^{38} +1.04141e8 q^{39} +5.81188e7i q^{40} -4.41673e6i q^{41} +(-1.63851e8 - 2.73080e7i) q^{42} -1.13685e8 q^{43} -4.69343e7 q^{44} -1.36473e7i q^{45} +4.68488e8 q^{46} -2.89933e8i q^{47} +3.31060e8i q^{48} +(-2.67207e8 - 9.16122e7i) q^{49} -5.90315e7 q^{50} -2.54720e7 q^{51} +2.09080e8i q^{52} +1.00949e8 q^{53} +5.36666e8i q^{54} -2.65953e8i q^{55} +(-5.58841e7 + 3.35310e8i) q^{56} +7.57006e8 q^{57} -8.22657e8 q^{58} +1.51102e8i q^{59} +3.68055e8 q^{60} -4.24061e8i q^{61} -2.01608e9i q^{62} +(1.31225e7 - 7.87365e7i) q^{63} +1.45757e8 q^{64} -1.18475e9 q^{65} -9.14746e8i q^{66} -7.07000e8 q^{67} -5.11393e7i q^{68} +3.02413e9i q^{69} +(1.86404e9 + 3.10668e8i) q^{70} +1.42045e9 q^{71} -9.60596e7 q^{72} +2.72735e9i q^{73} -7.74937e8 q^{74} -3.81054e8i q^{75} +1.51982e9i q^{76} +(2.55727e8 - 1.53439e9i) q^{77} -4.07496e9 q^{78} +3.87959e9 q^{79} -3.76628e9i q^{80} -3.74467e9 q^{81} +1.72824e8i q^{82} -2.67518e9i q^{83} +(2.12345e9 + 3.53903e8i) q^{84} +2.89780e8 q^{85} +4.44843e9 q^{86} -5.31033e9i q^{87} -1.87197e9 q^{88} +6.01371e9i q^{89} +5.34009e8i q^{90} +(-6.83529e9 - 1.13920e9i) q^{91} -6.07145e9 q^{92} +1.30140e10 q^{93} +1.13449e10i q^{94} -8.61204e9 q^{95} -7.72284e9i q^{96} -7.10446e9i q^{97} +(1.04556e10 + 3.58472e9i) q^{98} +4.39571e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 48 q^{2} - 576 q^{4} + 4900 q^{7} - 14592 q^{8} - 28764 q^{9}+O(q^{10}) \) 4 * q - 48 * q^2 - 576 * q^4 + 4900 * q^7 - 14592 * q^8 - 28764 * q^9	\( 4 q - 48 q^{2} - 576 q^{4} + 4900 q^{7} - 14592 q^{8} - 28764 q^{9} + 85992 q^{11} + 373968 q^{14} + 529920 q^{15} - 1825792 q^{16} + 80208 q^{18} + 11344672 q^{22} - 19261752 q^{23} + 16364260 q^{25} - 11092032 q^{28} + 23044008 q^{29} - 70744320 q^{30} + 129552384 q^{32} - 151468800 q^{35} + 10501056 q^{36} - 174916888 q^{37} + 489646080 q^{39} - 454406400 q^{42} + 163158248 q^{43} - 309420672 q^{44} + 1007838880 q^{46} - 990662204 q^{49} + 83868240 q^{50} - 955445760 q^{51} + 1693931880 q^{53} - 398711040 q^{56} + 803623680 q^{57} - 1932834272 q^{58} + 1468938240 q^{60} - 74185020 q^{63} + 511688704 q^{64} - 481608960 q^{65} - 2064766168 q^{67} + 2877907200 q^{70} + 1129059912 q^{71} + 338095872 q^{72} - 4795503840 q^{74} + 1924696872 q^{77} - 3893057280 q^{78} + 10836295688 q^{79} - 15414934716 q^{81} + 10905753600 q^{84} - 5489441280 q^{85} + 14805307680 q^{86} - 11205085696 q^{88} + 3483782400 q^{91} - 15867056256 q^{92} + 27132433920 q^{93} - 21990620160 q^{95} + 14008509648 q^{98} - 1732260312 q^{99}+O(q^{100}) \) 4 * q - 48 * q^2 - 576 * q^4 + 4900 * q^7 - 14592 * q^8 - 28764 * q^9 + 85992 * q^11 + 373968 * q^14 + 529920 * q^15 - 1825792 * q^16 + 80208 * q^18 + 11344672 * q^22 - 19261752 * q^23 + 16364260 * q^25 - 11092032 * q^28 + 23044008 * q^29 - 70744320 * q^30 + 129552384 * q^32 - 151468800 * q^35 + 10501056 * q^36 - 174916888 * q^37 + 489646080 * q^39 - 454406400 * q^42 + 163158248 * q^43 - 309420672 * q^44 + 1007838880 * q^46 - 990662204 * q^49 + 83868240 * q^50 - 955445760 * q^51 + 1693931880 * q^53 - 398711040 * q^56 + 803623680 * q^57 - 1932834272 * q^58 + 1468938240 * q^60 - 74185020 * q^63 + 511688704 * q^64 - 481608960 * q^65 - 2064766168 * q^67 + 2877907200 * q^70 + 1129059912 * q^71 + 338095872 * q^72 - 4795503840 * q^74 + 1924696872 * q^77 - 3893057280 * q^78 + 10836295688 * q^79 - 15414934716 * q^81 + 10905753600 * q^84 - 5489441280 * q^85 + 14805307680 * q^86 - 11205085696 * q^88 + 3483782400 * q^91 - 15867056256 * q^92 + 27132433920 * q^93 - 21990620160 * q^95 + 14008509648 * q^98 - 1732260312 * q^99

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