LMFDB - Embedded newform 700.2.g.l.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 $ x^16 - 17x^12 - 104x^10 + 713x^8 + 238x^6 + 1004x^4 - 152x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.7
Root			$-0.645096 + 0.854135i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.l.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927153 + 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 - 1.98019i) q^{4} +(0.613917 - 0.707107i) q^{6} +(-2.35829 - 1.19935i) q^{7} +(2.37495 + 1.53610i) q^{8} -2.56155 q^{9} +O(q^{10})$	\(q+(-0.927153 + 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 - 1.98019i) q^{4} +(0.613917 - 0.707107i) q^{6} +(-2.35829 - 1.19935i) q^{7} +(2.37495 + 1.53610i) q^{8} -2.56155 q^{9} -3.09218i q^{11} +(0.185917 + 1.31119i) q^{12} +4.66988i q^{13} +(3.46728 - 1.40642i) q^{14} +(-3.84233 + 1.11198i) q^{16} +2.04750i q^{17} +(2.37495 - 2.73546i) q^{18} +5.60083 q^{19} +(1.56155 + 0.794156i) q^{21} +(3.30210 + 2.86692i) q^{22} +1.87285i q^{23} +(-1.57258 - 1.01714i) q^{24} +(-4.98691 - 4.32969i) q^{26} +3.68260 q^{27} +(-1.71280 + 5.00663i) q^{28} +3.56155 q^{29} +8.74599 q^{31} +(2.37495 - 5.13416i) q^{32} +2.04750i q^{33} +(-2.18650 - 1.89834i) q^{34} +(0.719224 + 5.07237i) q^{36} +3.70861 q^{37} +(-5.19283 + 5.98107i) q^{38} -3.09218i q^{39} +8.48528i q^{41} +(-2.29587 + 0.931263i) q^{42} -4.27156i q^{43} +(-6.12311 + 0.868210i) q^{44} +(-2.00000 - 1.73642i) q^{46} -0.290319 q^{47} +(2.54421 - 0.736303i) q^{48} +(4.12311 + 5.65685i) q^{49} -1.35576i q^{51} +(9.24726 - 1.31119i) q^{52} +9.49980 q^{53} +(-3.41433 + 3.93261i) q^{54} +(-3.75850 - 6.47099i) q^{56} -3.70861 q^{57} +(-3.30210 + 3.80335i) q^{58} -8.05650 q^{59} +6.45101i q^{61} +(-8.10887 + 9.33976i) q^{62} +(6.04090 + 3.07221i) q^{63} +(3.28078 + 7.29634i) q^{64} +(-2.18650 - 1.89834i) q^{66} +2.39871i q^{67} +(4.05444 - 0.574888i) q^{68} -1.24012i q^{69} +9.65719i q^{71} +(-6.08356 - 3.93481i) q^{72} -4.09499i q^{73} +(-3.43845 + 3.96039i) q^{74} +(-1.57258 - 11.0907i) q^{76} +(-3.70861 + 7.29226i) q^{77} +(3.30210 + 2.86692i) q^{78} -1.35576i q^{79} +5.24621 q^{81} +(-9.06134 - 7.86715i) q^{82} -12.4536 q^{83} +(1.13413 - 3.31516i) q^{84} +(4.56155 + 3.96039i) q^{86} -2.35829 q^{87} +(4.74990 - 7.34376i) q^{88} +2.82843i q^{89} +(5.60083 - 11.0129i) q^{91} +(3.70861 - 0.525853i) q^{92} -5.79119 q^{93} +(0.269170 - 0.310029i) q^{94} +(-1.57258 + 3.39960i) q^{96} -6.14249i q^{97} +(-9.86364 - 0.841745i) q^{98} +7.92077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^4 - 8 * q^9	$ 16 q + 12 q^{4} - 8 q^{9} + 4 q^{14} - 12 q^{16} - 8 q^{21} + 24 q^{29} + 28 q^{36} - 32 q^{44} - 32 q^{46} - 20 q^{56} + 36 q^{64} - 88 q^{74} - 48 q^{81} - 40 q^{84} + 40 q^{86}+O(q^{100}) $ 16 * q + 12 * q^4 - 8 * q^9 + 4 * q^14 - 12 * q^16 - 8 * q^21 + 24 * q^29 + 28 * q^36 - 32 * q^44 - 32 * q^46 - 20 * q^56 + 36 * q^64 - 88 * q^74 - 48 * q^81 - 40 * q^84 + 40 * q^86

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.927153	+	1.06789i	−0.655596	+	0.755112i
$2$	−0.927153	+	1.06789i	−0.655596	+	0.755112i
$3$	−0.662153			−0.382294			−0.191147	−	0.981561i	$-0.561221\pi$
$3$	−0.662153			−0.382294			−0.191147	+	0.981561i	$0.561221\pi$
$4$	−0.280776	−	1.98019i	−0.140388	−	0.990097i
$5$		0			0
$5$		0			0
$6$	0.613917	−	0.707107i	0.250631	−	0.288675i
$7$	−2.35829	−	1.19935i	−0.891352	−	0.453313i
$7$	−2.35829	−	1.19935i	−0.891352	−	0.453313i
$8$	2.37495	+	1.53610i	0.839672	+	0.543094i
$9$	−2.56155			−0.853851
$10$		0			0
$11$		−	3.09218i		−	0.932326i	−0.884699	−	0.466163i	$-0.845636\pi$
$11$		−	3.09218i		−	0.932326i	0.884699	−	0.466163i	$-0.154364\pi$
$12$	0.185917	+	1.31119i	0.0536696	+	0.378508i
$13$			4.66988i			1.29519i	0.761984	+	0.647596i	$0.224225\pi$
$13$			4.66988i			1.29519i	−0.761984	+	0.647596i	$0.775775\pi$
$14$	3.46728	−	1.40642i	0.926668	−	0.375880i
$15$		0			0
$16$	−3.84233	+	1.11198i	−0.960582	+	0.277996i
$17$			2.04750i			0.496590i	0.968684	+	0.248295i	$0.0798703\pi$
$17$			2.04750i			0.496590i	−0.968684	+	0.248295i	$0.920130\pi$
$18$	2.37495	−	2.73546i	0.559781	−	0.644753i
$19$	5.60083			1.28492			0.642459	−	0.766320i	$-0.277914\pi$
$19$	5.60083			1.28492			0.642459	+	0.766320i	$0.277914\pi$
$20$		0			0
$21$	1.56155	+	0.794156i	0.340759	+	0.173299i
$22$	3.30210	+	2.86692i	0.704011	+	0.611229i
$23$			1.87285i			0.390517i	0.980752	+	0.195258i	$0.0625545\pi$
$23$			1.87285i			0.390517i	−0.980752	+	0.195258i	$0.937445\pi$
$24$	−1.57258	−	1.01714i	−0.321002	−	0.207622i
$25$		0			0
$26$	−4.98691	−	4.32969i	−0.978014	−	0.849122i
$27$	3.68260			0.708717
$28$	−1.71280	+	5.00663i	−0.323688	+	0.946164i
$29$	3.56155			0.661364			0.330682	−	0.943742i	$-0.392721\pi$
$29$	3.56155			0.661364			0.330682	+	0.943742i	$0.392721\pi$
$30$		0			0
$31$	8.74599			1.57083			0.785414	−	0.618971i	$-0.212450\pi$
$31$	8.74599			1.57083			0.785414	+	0.618971i	$0.212450\pi$
$32$	2.37495	−	5.13416i	0.419836	−	0.907600i
$33$			2.04750i			0.356423i
$34$	−2.18650	−	1.89834i	−0.374981	−	0.325563i
$35$		0			0
$36$	0.719224	+	5.07237i	0.119871	+	0.845395i
$37$	3.70861			0.609692			0.304846	−	0.952402i	$-0.401395\pi$
$37$	3.70861			0.609692			0.304846	+	0.952402i	$0.401395\pi$
$38$	−5.19283	+	5.98107i	−0.842388	+	0.970258i
$39$		−	3.09218i		−	0.495144i
$40$		0			0
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	−2.29587	+	0.931263i	−0.354260	+	0.143697i
$43$		−	4.27156i		−	0.651407i	−0.945472	−	0.325703i	$-0.894399\pi$
$43$		−	4.27156i		−	0.651407i	0.945472	−	0.325703i	$-0.105601\pi$
$44$	−6.12311	+	0.868210i	−0.923093	+	0.130888i
$45$		0			0
$46$	−2.00000	−	1.73642i	−0.294884	−	0.256021i
$47$	−0.290319			−0.0423474			−0.0211737	−	0.999776i	$-0.506740\pi$
$47$	−0.290319			−0.0423474			−0.0211737	+	0.999776i	$0.506740\pi$
$48$	2.54421	−	0.736303i	0.367225	−	0.106276i
$49$	4.12311	+	5.65685i	0.589015	+	0.808122i
$50$		0			0
$51$		−	1.35576i		−	0.189844i
$52$	9.24726	−	1.31119i	1.28236	−	0.181830i
$53$	9.49980			1.30490			0.652449	−	0.757833i	$-0.273742\pi$
$53$	9.49980			1.30490			0.652449	+	0.757833i	$0.273742\pi$
$54$	−3.41433	+	3.93261i	−0.464632	+	0.535161i
$55$		0			0
$56$	−3.75850	−	6.47099i	−0.502251	−	0.864722i
$57$	−3.70861			−0.491217
$58$	−3.30210	+	3.80335i	−0.433587	+	0.499404i
$59$	−8.05650			−1.04887			−0.524434	−	0.851451i	$-0.675723\pi$
$59$	−8.05650			−1.04887			−0.524434	+	0.851451i	$0.675723\pi$
$60$		0			0
$61$			6.45101i			0.825967i	0.910738	+	0.412984i	$0.135513\pi$
$61$			6.45101i			0.825967i	−0.910738	+	0.412984i	$0.864487\pi$
$62$	−8.10887	+	9.33976i	−1.02983	+	1.18615i
$63$	6.04090	+	3.07221i	0.761081	+	0.387062i
$64$	3.28078	+	7.29634i	0.410097	+	0.912042i
$65$		0			0
$66$	−2.18650	−	1.89834i	−0.269139	−	0.233670i
$67$			2.39871i			0.293049i	0.989207	+	0.146524i	$0.0468086\pi$
$67$			2.39871i			0.293049i	−0.989207	+	0.146524i	$0.953191\pi$
$68$	4.05444	−	0.574888i	0.491673	−	0.0697154i
$69$		−	1.24012i		−	0.149292i
$70$		0			0
$71$			9.65719i			1.14610i	0.819521	+	0.573049i	$0.194240\pi$
$71$			9.65719i			1.14610i	−0.819521	+	0.573049i	$0.805760\pi$
$72$	−6.08356	−	3.93481i	−0.716954	−	0.463722i
$73$		−	4.09499i		−	0.479282i	−0.970862	−	0.239641i	$-0.922970\pi$
$73$		−	4.09499i		−	0.479282i	0.970862	−	0.239641i	$-0.0770298\pi$
$74$	−3.43845	+	3.96039i	−0.399711	+	0.460386i
$75$		0			0
$76$	−1.57258	−	11.0907i	−0.180387	−	1.27219i
$77$	−3.70861	+	7.29226i	−0.422635	+	0.831030i
$78$	3.30210	+	2.86692i	0.373890	+	0.324615i
$79$		−	1.35576i		−	0.152534i	−0.997087	−	0.0762672i	$-0.975700\pi$
$79$		−	1.35576i		−	0.152534i	0.997087	−	0.0762672i	$-0.0243002\pi$
$80$		0			0
$81$	5.24621			0.582912
$82$	−9.06134	−	7.86715i	−1.00066	−	0.868781i
$83$	−12.4536			−1.36696			−0.683482	−	0.729968i	$-0.739535\pi$
$83$	−12.4536			−1.36696			−0.683482	+	0.729968i	$0.739535\pi$
$84$	1.13413	−	3.31516i	0.123744	−	0.361713i
$85$		0			0
$86$	4.56155	+	3.96039i	0.491885	+	0.427059i
$87$	−2.35829			−0.252836
$88$	4.74990	−	7.34376i	0.506341	−	0.782848i
$89$			2.82843i			0.299813i	0.988700	+	0.149906i	$0.0478972\pi$
$89$			2.82843i			0.299813i	−0.988700	+	0.149906i	$0.952103\pi$
$90$		0			0
$91$	5.60083	−	11.0129i	0.587127	−	1.15447i
$92$	3.70861	−	0.525853i	0.386649	−	0.0548240i
$93$	−5.79119			−0.600518
$94$	0.269170	−	0.310029i	0.0277628	−	0.0319770i
$95$		0			0
$96$	−1.57258	+	3.39960i	−0.160501	+	0.346970i
$97$		−	6.14249i		−	0.623675i	−0.950135	−	0.311837i	$-0.899056\pi$
$97$		−	6.14249i		−	0.623675i	0.950135	−	0.311837i	$-0.100944\pi$
$98$	−9.86364	−	0.841745i	−0.996378	−	0.0850291i
$99$			7.92077i			0.796068i
$100$		0			0
$101$			2.38247i			0.237064i	0.992950	+	0.118532i	$0.0378189\pi$
$101$			2.38247i			0.237064i	−0.992950	+	0.118532i	$0.962181\pi$
$102$	1.44780	+	1.25699i	0.143353	+	0.124461i
$103$	1.03399			0.101882			0.0509409	−	0.998702i	$-0.483778\pi$
$103$	1.03399			0.101882			0.0509409	+	0.998702i	$0.483778\pi$
$104$	−7.17341	+	11.0907i	−0.703411	+	1.08754i
$105$		0			0
$106$	−8.80776	+	10.1447i	−0.855486	+	0.985344i
$107$			14.6875i			1.41990i	0.704254	+	0.709948i	$0.251282\pi$
$107$			14.6875i			1.41990i	−0.704254	+	0.709948i	$0.748718\pi$
$108$	−1.03399	−	7.29226i	−0.0994955	−	0.701698i
$109$	−0.438447			−0.0419956			−0.0209978	−	0.999780i	$-0.506684\pi$
$109$	−0.438447			−0.0419956			−0.0209978	+	0.999780i	$0.506684\pi$
$110$		0			0
$111$	−2.45567			−0.233082
$112$	10.3950	+	1.98593i	0.982236	+	0.187652i
$113$	−3.70861			−0.348877			−0.174438	−	0.984668i	$-0.555811\pi$
$113$	−3.70861			−0.348877			−0.174438	+	0.984668i	$0.555811\pi$
$114$	3.43845	−	3.96039i	0.322040	−	0.370924i
$115$		0			0
$116$	−1.00000	−	7.05256i	−0.0928477	−	0.654814i
$117$		−	11.9621i		−	1.10590i
$118$	7.46960	−	8.60345i	0.687633	−	0.792012i
$119$	2.45567	−	4.82860i	0.225111	−	0.442637i
$120$		0			0
$121$	1.43845			0.130768
$122$	−6.88897	−	5.98107i	−0.623698	−	0.541501i
$123$		−	5.61856i		−	0.506608i
$124$	−2.45567	−	17.3188i	−0.220526	−	1.55527i
$125$		0			0
$126$	−8.88161	+	3.60261i	−0.791237	+	0.320946i
$127$		−	17.0862i		−	1.51616i	−0.652163	−	0.758079i	$-0.726138\pi$
$127$		−	17.0862i		−	1.51616i	0.652163	−	0.758079i	$-0.273862\pi$
$128$	−10.8335	−	3.26131i	−0.957552	−	0.288262i
$129$			2.82843i			0.249029i
$130$		0			0
$131$	5.60083			0.489347			0.244673	−	0.969606i	$-0.421319\pi$
$131$	5.60083			0.489347			0.244673	+	0.969606i	$0.421319\pi$
$132$	4.05444	−	0.574888i	0.352893	−	0.0500376i
$133$	−13.2084	−	6.71737i	−1.14531	−	0.582470i
$134$	−2.56155	−	2.22397i	−0.221284	−	0.192121i
$135$		0			0
$136$	−3.14516	+	4.86270i	−0.269695	+	0.416973i
$137$	13.2084			1.12847			0.564235	−	0.825614i	$-0.309171\pi$
$137$	13.2084			1.12847			0.564235	+	0.825614i	$0.309171\pi$
$138$	1.32431	+	1.14978i	0.112732	+	0.0978755i
$139$	14.3468			1.21688			0.608441	−	0.793599i	$-0.291795\pi$
$139$	14.3468			1.21688			0.608441	+	0.793599i	$0.291795\pi$
$140$		0			0
$141$	0.192236			0.0161892
$142$	−10.3128	−	8.95369i	−0.865432	−	0.751377i
$143$	14.4401			1.20754
$144$	9.84233	−	2.84840i	0.820194	−	0.237367i
$145$		0			0
$146$	4.37300	+	3.79668i	0.361912	+	0.314216i
$147$	−2.73013	−	3.74571i	−0.225177	−	0.308941i
$148$	−1.04129	−	7.34376i	−0.0855935	−	0.603654i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$		−	18.9337i		−	1.54080i	−0.637558	−	0.770402i	$-0.720055\pi$
$151$		−	18.9337i		−	1.54080i	0.637558	−	0.770402i	$-0.279945\pi$
$152$	13.3017	+	8.60345i	1.07891	+	0.697832i
$153$		−	5.24477i		−	0.424014i
$154$	−4.34888	−	10.7214i	−0.350443	−	0.863957i
$155$		0			0
$156$	−6.12311	+	0.868210i	−0.490241	+	0.0695124i
$157$			2.62238i			0.209289i	0.994510	+	0.104644i	$0.0333705\pi$
$157$			2.62238i			0.209289i	−0.994510	+	0.104644i	$0.966630\pi$
$158$	1.44780	+	1.25699i	0.115181	+	0.100001i
$159$	−6.29033			−0.498855
$160$		0			0
$161$	2.24621	−	4.41674i	0.177026	−	0.348088i
$162$	−4.86404	+	5.60237i	−0.382155	+	0.440164i
$163$			15.7392i			1.23279i	0.787436	+	0.616396i	$0.211408\pi$
$163$			15.7392i			1.23279i	−0.787436	+	0.616396i	$0.788592\pi$
$164$	16.8025	−	2.38247i	1.31205	−	0.186039i
$165$		0			0
$166$	11.5464	−	13.2991i	0.896175	−	1.03221i
$167$	8.39919			0.649949			0.324974	−	0.945723i	$-0.394644\pi$
$167$	8.39919			0.649949			0.324974	+	0.945723i	$0.394644\pi$
$168$	2.48871	+	4.28479i	0.192008	+	0.330578i
$169$	−8.80776			−0.677520
$170$		0			0
$171$	−14.3468			−1.09713
$172$	−8.45851	+	1.19935i	−0.644955	+	0.0914498i
$173$		−	8.76487i		−	0.666381i	−0.942860	−	0.333190i	$-0.891875\pi$
$173$		−	8.76487i		−	0.666381i	0.942860	−	0.333190i	$-0.108125\pi$
$174$	2.18650	−	2.51840i	0.165758	−	0.190919i
$175$		0			0
$176$	3.43845	+	11.8812i	0.259183	+	0.895576i
$177$	5.33464			0.400976
$178$	−3.02045	−	2.62238i	−0.226392	−	0.196556i
$179$		−	1.73642i		−	0.129786i	−0.997892	−	0.0648931i	$-0.979329\pi$
$179$		−	1.73642i		−	0.129786i	0.997892	−	0.0648931i	$-0.0206706\pi$
$180$		0			0
$181$		−	9.27944i		−	0.689735i	−0.938651	−	0.344868i	$-0.887924\pi$
$181$		−	9.27944i		−	0.689735i	0.938651	−	0.344868i	$-0.112076\pi$
$182$	6.56779	+	16.1918i	0.486837	+	1.20021i
$183$		−	4.27156i		−	0.315763i
$184$	−2.87689	+	4.44793i	−0.212087	+	0.327906i
$185$		0			0
$186$	5.36932	−	6.18435i	0.393697	−	0.453459i
$187$	6.33122			0.462984
$188$	0.0815148	+	0.574888i	0.00594508	+	0.0419280i
$189$	−8.68466	−	4.41674i	−0.631716	−	0.321270i
$190$		0			0
$191$			13.7245i			0.993067i	0.868018	+	0.496534i	$0.165394\pi$
$191$			13.7245i			0.993067i	−0.868018	+	0.496534i	$0.834606\pi$
$192$	−2.17238	−	4.83129i	−0.156778	−	0.348669i
$193$	3.70861			0.266952			0.133476	−	0.991052i	$-0.457386\pi$
$193$	3.70861			0.266952			0.133476	+	0.991052i	$0.457386\pi$
$194$	6.55950	+	5.69502i	0.470944	+	0.408879i
$195$		0			0
$196$	10.0440	−	9.75286i	0.717428	−	0.696633i
$197$	−11.1258			−0.792683			−0.396341	−	0.918103i	$-0.629720\pi$
$197$	−11.1258			−0.792683			−0.396341	+	0.918103i	$0.629720\pi$
$198$	−8.45851	−	7.34376i	−0.601120	−	0.521899i
$199$	6.29033			0.445909			0.222955	−	0.974829i	$-0.428430\pi$
$199$	6.29033			0.445909			0.222955	+	0.974829i	$0.428430\pi$
$200$		0			0
$201$		−	1.58831i		−	0.112031i
$202$	−2.54421	−	2.20891i	−0.179010	−	0.155418i
$203$	−8.39919	−	4.27156i	−0.589508	−	0.299805i
$204$	−2.68466	+	0.380664i	−0.187964	+	0.0266518i
$205$		0			0
$206$	−0.958664	+	1.10418i	−0.0667933	+	0.0769322i
$207$		−	4.79741i		−	0.333443i
$208$	−5.19283	−	17.9432i	−0.360058	−	1.24414i
$209$		−	17.3188i		−	1.19796i
$210$		0			0
$211$			25.1181i			1.72920i	0.502461	+	0.864600i	$0.332428\pi$
$211$			25.1181i			1.72920i	−0.502461	+	0.864600i	$0.667572\pi$
$212$	−2.66732	−	18.8114i	−0.183192	−	1.29197i
$213$		−	6.39454i		−	0.438147i
$214$	−15.6847	−	13.6176i	−1.07218	−	0.930879i
$215$		0			0
$216$	8.74599	+	5.65685i	0.595090	+	0.384900i
$217$	−20.6256	−	10.4895i	−1.40016	−	0.712076i
$218$	0.406507	−	0.468213i	0.0275322	−	0.0317114i
$219$			2.71151i			0.183227i
$220$		0			0
$221$	−9.56155			−0.643180
$222$	2.27678	−	2.62238i	0.152807	−	0.176003i
$223$	19.1567			1.28283			0.641413	−	0.767196i	$-0.278349\pi$
$223$	19.1567			1.28283			0.641413	+	0.767196i	$0.278349\pi$
$224$	−11.7585	+	9.25946i	−0.785648	+	0.618674i
$225$		0			0
$226$	3.43845	−	3.96039i	0.228722	−	0.263441i
$227$	−14.0683			−0.933743			−0.466871	−	0.884325i	$-0.654619\pi$
$227$	−14.0683			−0.933743			−0.466871	+	0.884325i	$0.654619\pi$
$228$	1.04129	+	7.34376i	0.0689611	+	0.486353i
$229$			8.03932i			0.531253i	0.964076	+	0.265627i	$0.0855788\pi$
$229$			8.03932i			0.531253i	−0.964076	+	0.265627i	$0.914421\pi$
$230$		0			0
$231$	2.45567	−	4.82860i	0.161571	−	0.317698i
$232$	8.45851	+	5.47091i	0.555328	+	0.359183i
$233$	7.41722			0.485918			0.242959	−	0.970037i	$-0.421882\pi$
$233$	7.41722			0.485918			0.242959	+	0.970037i	$0.421882\pi$
$234$	12.7742	+	11.0907i	0.835079	+	0.725024i
$235$		0			0
$236$	2.26208	+	15.9534i	0.147249	+	1.03848i
$237$			0.897718i			0.0583131i
$238$	2.87963	+	7.09923i	0.186659	+	0.460175i
$239$			3.09218i			0.200016i	0.994987	+	0.100008i	$0.0318869\pi$
$239$			3.09218i			0.200016i	−0.994987	+	0.100008i	$0.968113\pi$
$240$		0			0
$241$		−	18.9071i		−	1.21791i	−0.793204	−	0.608956i	$-0.791589\pi$
$241$		−	18.9071i		−	1.21791i	0.793204	−	0.608956i	$-0.208411\pi$
$242$	−1.33366	+	1.53610i	−0.0857309	+	0.0987444i
$243$	−14.5216			−0.931561
$244$	12.7742	−	1.81129i	0.817787	−	0.115956i
$245$		0			0
$246$	6.00000	+	5.20926i	0.382546	+	0.332130i
$247$			26.1552i			1.66422i
$248$	20.7713	+	13.4347i	1.31898	+	0.853107i
$249$	8.24621			0.522582
$250$		0			0
$251$	−3.14516			−0.198521			−0.0992605	−	0.995061i	$-0.531648\pi$
$251$	−3.14516			−0.198521			−0.0992605	+	0.995061i	$0.531648\pi$
$252$	4.38742	−	12.8247i	0.276381	−	0.807883i
$253$	5.79119			0.364089
$254$	18.2462	+	15.8415i	1.14487	+	0.993987i
$255$		0			0
$256$	13.5270	−	8.54521i	0.845437	−	0.534076i
$257$			28.0193i			1.74779i	0.486111	+	0.873897i	$0.338415\pi$
$257$			28.0193i			1.74779i	−0.486111	+	0.873897i	$0.661585\pi$
$258$	−3.02045	−	2.62238i	−0.188045	−	0.163262i
$259$	−8.74599	−	4.44793i	−0.543450	−	0.276381i
$260$		0			0
$261$	−9.12311			−0.564706
$262$	−5.19283	+	5.98107i	−0.320814	+	0.369512i
$263$		−	11.9935i		−	0.739553i	−0.929121	−	0.369776i	$-0.879434\pi$
$263$		−	11.9935i		−	0.739553i	0.929121	−	0.369776i	$-0.120566\pi$
$264$	−3.14516	+	4.86270i	−0.193571	+	0.299278i
$265$		0			0
$266$	19.4196	−	7.87709i	1.19069	−	0.482976i
$267$		−	1.87285i		−	0.114617i
$268$	4.74990	−	0.673500i	0.290146	−	0.0411406i
$269$		−	16.5246i		−	1.00752i	−0.863843	−	0.503761i	$-0.831949\pi$
$269$		−	16.5246i		−	1.00752i	0.863843	−	0.503761i	$-0.168051\pi$
$270$		0			0
$271$	−8.74599			−0.531281			−0.265641	−	0.964072i	$-0.585583\pi$
$271$	−8.74599			−0.531281			−0.265641	+	0.964072i	$0.585583\pi$
$272$	−2.27678	−	7.86715i	−0.138050	−	0.477016i
$273$	−3.70861	+	7.29226i	−0.224455	+	0.441348i
$274$	−12.2462	+	14.1051i	−0.739821	+	0.852122i
$275$		0			0
$276$	−2.45567	+	0.348195i	−0.147814	+	0.0209589i
$277$	−2.08258			−0.125130			−0.0625651	−	0.998041i	$-0.519928\pi$
$277$	−2.08258			−0.125130			−0.0625651	+	0.998041i	$0.519928\pi$
$278$	−13.3017	+	15.3208i	−0.797783	+	0.918882i
$279$	−22.4033			−1.34125
$280$		0			0
$281$	−20.0540			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$281$	−20.0540			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$282$	−0.178232	+	0.205287i	−0.0106136	+	0.0122246i
$283$	−19.5285			−1.16085			−0.580425	−	0.814314i	$-0.697113\pi$
$283$	−19.5285			−1.16085			−0.580425	+	0.814314i	$0.697113\pi$
$284$	19.1231	−	2.71151i	1.13475	−	0.160899i
$285$		0			0
$286$	−13.3882	+	15.4204i	−0.791659	+	0.911828i
$287$	10.1768	−	20.0108i	0.600720	−	1.18120i
$288$	−6.08356	+	13.1514i	−0.358477	+	0.774955i
$289$	12.8078			0.753398
$290$		0			0
$291$			4.06727i			0.238427i
$292$	−8.10887	+	1.14978i	−0.474536	+	0.0672856i
$293$			15.1594i			0.885622i	0.896615	+	0.442811i	$0.146019\pi$
$293$			15.1594i			0.885622i	−0.896615	+	0.442811i	$0.853981\pi$
$294$	6.53125	+	0.557364i	0.380910	+	0.0325062i
$295$		0			0
$296$	8.80776	+	5.69681i	0.511941	+	0.331120i
$297$		−	11.3873i		−	0.660755i
$298$	−1.85431	+	2.13578i	−0.107417	+	0.123722i
$299$	−8.74599			−0.505794
$300$		0			0
$301$	−5.12311	+	10.0736i	−0.295291	+	0.580632i
$302$	20.2191	+	17.5544i	1.16348	+	1.01014i
$303$		−	1.57756i		−	0.0906284i
$304$	−21.5202	+	6.22803i	−1.23427	+	0.357202i
$305$		0			0
$306$	5.60083	+	4.86270i	0.320178	+	0.277982i
$307$	−26.1500			−1.49246			−0.746231	−	0.665687i	$-0.768139\pi$
$307$	−26.1500			−1.49246			−0.746231	+	0.665687i	$0.768139\pi$
$308$	15.4814	+	5.29627i	0.882133	+	0.301783i
$309$	−0.684658			−0.0389489
$310$		0			0
$311$	−19.9477			−1.13113			−0.565564	−	0.824704i	$-0.691341\pi$
$311$	−19.9477			−1.13113			−0.565564	+	0.824704i	$0.691341\pi$
$312$	4.74990	−	7.34376i	0.268910	−	0.415759i
$313$			11.3873i			0.643646i	0.946800	+	0.321823i	$0.104296\pi$
$313$			11.3873i			0.643646i	−0.946800	+	0.321823i	$0.895704\pi$
$314$	−2.80042	−	2.43135i	−0.158037	−	0.137209i
$315$		0			0
$316$	−2.68466	+	0.380664i	−0.151024	+	0.0214140i
$317$	31.7515			1.78334			0.891670	−	0.452686i	$-0.149534\pi$
$317$	31.7515			1.78334			0.891670	+	0.452686i	$0.149534\pi$
$318$	5.83209	−	6.71737i	0.327047	−	0.376692i
$319$		−	11.0129i		−	0.616607i
$320$		0			0
$321$		−	9.72540i		−	0.542819i
$322$	2.63401	+	6.49370i	0.146788	+	0.361880i
$323$			11.4677i			0.638079i
$324$	−1.47301	−	10.3885i	−0.0818340	−	0.577140i
$325$		0			0
$326$	−16.8078	−	14.5927i	−0.930896	−	0.808213i
$327$	0.290319			0.0160547
$328$	−13.0343	+	20.1521i	−0.719697	+	1.11271i
$329$	0.684658	+	0.348195i	0.0377464	+	0.0191966i
$330$		0			0
$331$			1.73642i			0.0954423i	0.998861	+	0.0477211i	$0.0151959\pi$
$331$			1.73642i			0.0954423i	−0.998861	+	0.0477211i	$0.984804\pi$
$332$	3.49668	+	24.6606i	0.191905	+	1.35343i
$333$	−9.49980			−0.520586
$334$	−7.78733	+	8.96941i	−0.426104	+	0.490784i
$335$		0			0
$336$	−6.88309	−	1.31499i	−0.375503	−	0.0717384i
$337$	−5.33464			−0.290596			−0.145298	−	0.989388i	$-0.546414\pi$
$337$	−5.33464			−0.290596			−0.145298	+	0.989388i	$0.546414\pi$
$338$	8.16614	−	9.40572i	0.444179	−	0.511604i
$339$	2.45567			0.133374
$340$		0			0
$341$		−	27.0442i		−	1.46452i
$342$	13.3017	−	15.3208i	0.719273	−	0.828455i
$343$	−2.93893	−	18.2856i	−0.158687	−	0.987329i
$344$	6.56155	−	10.1447i	0.353775	−	0.546968i
$345$		0			0
$346$	9.35991	+	8.12637i	0.503192	+	0.436876i
$347$			4.27156i			0.229309i	0.993405	+	0.114655i	$0.0365761\pi$
$347$			4.27156i			0.229309i	−0.993405	+	0.114655i	$0.963424\pi$
$348$	0.662153	+	4.66988i	0.0354952	+	0.250332i
$349$			36.3236i			1.94436i	0.234241	+	0.972179i	$0.424740\pi$
$349$			36.3236i			1.94436i	−0.234241	+	0.972179i	$0.575260\pi$
$350$		0			0
$351$			17.1973i			0.917924i
$352$	−15.8757	−	7.34376i	−0.846179	−	0.391424i
$353$			27.1216i			1.44353i	0.692136	+	0.721767i	$0.256670\pi$
$353$			27.1216i			1.44353i	−0.692136	+	0.721767i	$0.743330\pi$
$354$	−4.94602	+	5.69681i	−0.262878	+	0.302782i
$355$		0			0
$356$	5.60083	−	0.794156i	0.296843	−	0.0420902i
$357$	−1.62603	+	3.19727i	−0.0860586	+	0.169218i
$358$	1.85431	+	1.60993i	0.0980031	+	0.0850873i
$359$			26.4738i			1.39724i	0.715495	+	0.698618i	$0.246201\pi$
$359$			26.4738i			1.39724i	−0.715495	+	0.698618i	$0.753799\pi$
$360$		0			0
$361$	12.3693			0.651017
$362$	9.90941	+	8.60345i	0.520827	+	0.452187i
$363$	−0.952473			−0.0499919
$364$	−23.3803	−	7.99855i	−1.22546	−	0.419238i
$365$		0			0
$366$	4.56155	+	3.96039i	0.238436	+	0.207013i
$367$	31.8191			1.66094			0.830472	−	0.557061i	$-0.188071\pi$
$367$	31.8191			1.66094			0.830472	+	0.557061i	$0.188071\pi$
$368$	−2.08258	−	7.19612i	−0.108562	−	0.375124i
$369$		−	21.7355i		−	1.13150i
$370$		0			0
$371$	−22.4033	−	11.3936i	−1.16312	−	0.591527i
$372$	1.62603	+	11.4677i	0.0843057	+	0.594571i
$373$	22.7082			1.17579			0.587893	−	0.808938i	$-0.299957\pi$
$373$	22.7082			1.17579			0.587893	+	0.808938i	$0.299957\pi$
$374$	−5.87000	+	6.76104i	−0.303531	+	0.349605i
$375$		0			0
$376$	−0.689494	−	0.445960i	−0.0355579	−	0.0229986i
$377$			16.6320i			0.856593i
$378$	12.7686	−	5.17927i	0.656746	−	0.266393i
$379$			5.20926i			0.267582i	0.991010	+	0.133791i	$0.0427150\pi$
$379$			5.20926i			0.267582i	−0.991010	+	0.133791i	$0.957285\pi$
$380$		0			0
$381$			11.3137i			0.579619i
$382$	−14.6562	−	12.7247i	−0.749877	−	0.651051i
$383$	26.9752			1.37837			0.689185	−	0.724586i	$-0.257969\pi$
$383$	26.9752			1.37837			0.689185	+	0.724586i	$0.257969\pi$
$384$	7.17341	+	2.15949i	0.366067	+	0.110201i
$385$		0			0
$386$	−3.43845	+	3.96039i	−0.175012	+	0.201578i
$387$			10.9418i			0.556204i
$388$	−12.1633	+	1.72466i	−0.617498	+	0.0875566i
$389$	−16.9309			−0.858429			−0.429215	−	0.903203i	$-0.641210\pi$
$389$	−16.9309			−0.858429			−0.429215	+	0.903203i	$0.641210\pi$
$390$		0			0
$391$	−3.83466			−0.193927
$392$	1.10266	+	19.7683i	0.0556928	+	0.998448i
$393$	−3.70861			−0.187075
$394$	10.3153	−	11.8812i	0.519679	−	0.598564i
$395$		0			0
$396$	15.6847	−	2.22397i	0.788184	−	0.111758i
$397$		−	12.8599i		−	0.645418i	−0.946498	−	0.322709i	$-0.895407\pi$
$397$		−	12.8599i		−	0.645418i	0.946498	−	0.322709i	$-0.104593\pi$
$398$	−5.83209	+	6.71737i	−0.292336	+	0.336712i
$399$	8.74599	+	4.44793i	0.437847	+	0.222675i
$400$		0			0
$401$	17.5616			0.876982			0.438491	−	0.898736i	$-0.355513\pi$
$401$	17.5616			0.876982			0.438491	+	0.898736i	$0.355513\pi$
$402$	1.69614	+	1.47261i	0.0845958	+	0.0734469i
$403$			40.8427i			2.03452i
$404$	4.71774	−	0.668940i	0.234717	−	0.0332810i
$405$		0			0
$406$	12.3489	−	5.00902i	0.612865	−	0.248594i
$407$		−	11.4677i		−	0.568432i
$408$	2.08258	−	3.21985i	0.103103	−	0.159406i
$409$			4.76493i			0.235611i	0.993037	+	0.117805i	$0.0375859\pi$
$409$			4.76493i			0.235611i	−0.993037	+	0.117805i	$0.962414\pi$
$410$		0			0
$411$	−8.74599			−0.431408
$412$	−0.290319	−	2.04750i	−0.0143030	−	0.100873i
$413$	18.9996	+	9.66259i	0.934909	+	0.475465i
$414$	5.12311	+	4.44793i	0.251787	+	0.218604i
$415$		0			0
$416$	23.9759	+	11.0907i	1.17552	+	0.543768i
$417$	−9.49980			−0.465207
$418$	18.4945	+	16.0571i	0.904597	+	0.785380i
$419$	−20.6372			−1.00819			−0.504095	−	0.863648i	$-0.668174\pi$
$419$	−20.6372			−1.00819			−0.504095	+	0.863648i	$0.668174\pi$
$420$		0			0
$421$	8.43845			0.411265			0.205632	−	0.978629i	$-0.434075\pi$
$421$	8.43845			0.411265			0.205632	+	0.978629i	$0.434075\pi$
$422$	−26.8233	−	23.2883i	−1.30574	−	1.13366i
$423$	0.743668			0.0361584
$424$	22.5616	+	14.5927i	1.09569	+	0.708683i
$425$		0			0
$426$	6.82867	+	5.92872i	0.330850	+	0.287247i
$427$	7.73704	−	15.2134i	0.374421	−	0.736227i
$428$	29.0841	−	4.12391i	1.40584	−	0.199337i
$429$	−9.56155			−0.461636
$430$		0			0
$431$		−	15.4609i		−	0.744724i	−0.928087	−	0.372362i	$-0.878548\pi$
$431$		−	15.4609i		−	0.744724i	0.928087	−	0.372362i	$-0.121452\pi$
$432$	−14.1498	+	4.09499i	−0.680781	+	0.197020i
$433$		−	38.5088i		−	1.85062i	−0.379218	−	0.925308i	$-0.623807\pi$
$433$		−	38.5088i		−	1.85062i	0.379218	−	0.925308i	$-0.376193\pi$
$434$	30.3248	−	12.3005i	1.45564	−	0.590443i
$435$		0			0
$436$	0.123106	+	0.868210i	0.00589569	+	0.0415797i
$437$			10.4895i			0.501782i
$438$	−2.89560	−	2.51398i	−0.138357	−	0.120123i
$439$	23.7823			1.13507			0.567534	−	0.823350i	$-0.307898\pi$
$439$	23.7823			1.13507			0.567534	+	0.823350i	$0.307898\pi$
$440$		0			0
$441$	−10.5616	−	14.4903i	−0.502931	−	0.690016i
$442$	8.86502	−	10.2107i	0.421666	−	0.485673i
$443$			13.8664i			0.658812i	0.944188	+	0.329406i	$0.106848\pi$
$443$			13.8664i			0.658812i	−0.944188	+	0.329406i	$0.893152\pi$
$444$	0.689494	+	4.86270i	0.0327219	+	0.230773i
$445$		0			0
$446$	−17.7612	+	20.4572i	−0.841015	+	0.968677i
$447$	−1.32431			−0.0626376
$448$	1.01384	−	21.1417i	0.0478996	−	0.998852i
$449$	−18.6847			−0.881784			−0.440892	−	0.897560i	$-0.645338\pi$
$449$	−18.6847			−0.881784			−0.440892	+	0.897560i	$0.645338\pi$
$450$		0			0
$451$	26.2380			1.23550
$452$	1.04129	+	7.34376i	0.0489782	+	0.345422i
$453$			12.5370i			0.589041i
$454$	13.0434	−	15.0233i	0.612158	−	0.705080i
$455$		0			0
$456$	−8.80776	−	5.69681i	−0.412461	−	0.266777i
$457$	37.5427			1.75617			0.878086	−	0.478504i	$-0.158821\pi$
$457$	37.5427			1.75617			0.878086	+	0.478504i	$0.158821\pi$
$458$	−8.58511	−	7.45368i	−0.401156	−	0.348287i
$459$			7.54011i			0.351942i
$460$		0			0
$461$		−	19.7012i		−	0.917578i	−0.888545	−	0.458789i	$-0.848283\pi$
$461$		−	19.7012i		−	0.917578i	0.888545	−	0.458789i	$-0.151717\pi$
$462$	2.87963	+	7.09923i	0.133972	+	0.330286i
$463$		−	27.2069i		−	1.26441i	−0.774800	−	0.632206i	$-0.782150\pi$
$463$		−	27.2069i		−	1.26441i	0.774800	−	0.632206i	$-0.217850\pi$
$464$	−13.6847	+	3.96039i	−0.635294	+	0.183856i
$465$		0			0
$466$	−6.87689	+	7.92077i	−0.318566	+	0.366923i
$467$	−31.0297			−1.43588			−0.717941	−	0.696104i	$-0.754915\pi$
$467$	−31.0297			−1.43588			−0.717941	+	0.696104i	$0.754915\pi$
$468$	−23.6873	+	3.35869i	−1.09495	+	0.155255i
$469$	2.87689	−	5.65685i	0.132843	−	0.261209i
$470$		0			0
$471$		−	1.73642i		−	0.0800100i
$472$	−19.1338	−	12.3756i	−0.880704	−	0.569634i
$473$	−13.2084			−0.607323
$474$	−0.958664	−	0.832322i	−0.0440329	−	0.0382298i
$475$		0			0
$476$	−10.2510	−	3.50694i	−0.469856	−	0.160740i
$477$	−24.3342			−1.11419
$478$	−3.30210	−	2.86692i	−0.151035	−	0.131130i
$479$	−3.83466			−0.175210			−0.0876050	−	0.996155i	$-0.527921\pi$
$479$	−3.83466			−0.175210			−0.0876050	+	0.996155i	$0.527921\pi$
$480$		0			0
$481$			17.3188i			0.789667i
$482$	20.1907	+	17.5297i	0.919659	+	0.798458i
$483$	−1.48734	+	2.92456i	−0.0676762	+	0.133072i
$484$	−0.403882	−	2.84840i	−0.0183583	−	0.129473i
$485$		0			0
$486$	13.4637	−	15.5075i	0.610728	−	0.703433i
$487$			38.9699i			1.76589i	0.469473	+	0.882947i	$0.344444\pi$
$487$			38.9699i			1.76589i	−0.469473	+	0.882947i	$0.655556\pi$
$488$	−9.90941	+	15.3208i	−0.448578	+	0.693541i
$489$		−	10.4218i		−	0.471290i
$490$		0			0
$491$		−	6.56502i		−	0.296275i	−0.988967	−	0.148138i	$-0.952672\pi$
$491$		−	6.56502i		−	0.296275i	0.988967	−	0.148138i	$-0.0473278\pi$
$492$	−11.1258	+	1.57756i	−0.501591	+	0.0711218i
$493$			7.29226i			0.328427i
$494$	−27.9309	−	24.2499i	−1.25667	−	1.09105i
$495$		0			0
$496$	−33.6050	+	9.72540i	−1.50891	+	0.436683i
$497$	11.5824	−	22.7745i	0.519541	−	1.02158i
$498$	−7.64550	+	8.80604i	−0.342603	+	0.394608i
$499$		−	34.0139i		−	1.52267i	−0.648357	−	0.761336i	$-0.724544\pi$
$499$		−	34.0139i		−	1.52267i	0.648357	−	0.761336i	$-0.275456\pi$
$500$		0			0
$501$	−5.56155			−0.248472
$502$	2.91605	−	3.35869i	0.130149	−	0.149906i
$503$	7.81855			0.348612			0.174306	−	0.984692i	$-0.444232\pi$
$503$	7.81855			0.348612			0.174306	+	0.984692i	$0.444232\pi$
$504$	9.62760	+	16.5758i	0.428848	+	0.738344i
$505$		0			0
$506$	−5.36932	+	6.18435i	−0.238695	+	0.274928i
$507$	5.83209			0.259012
$508$	−33.8340	+	4.79741i	−1.50114	+	0.212851i
$509$		−	1.14235i		−	0.0506338i	−0.999679	−	0.0253169i	$-0.991941\pi$
$509$		−	1.14235i		−	0.0506338i	0.999679	−	0.0253169i	$-0.00805948\pi$
$510$		0			0
$511$	−4.91134	+	9.65719i	−0.217265	+	0.427209i
$512$	−3.41624	+	22.3680i	−0.150978	+	0.988537i
$513$	20.6256			0.910644
$514$	−29.9215	−	25.9781i	−1.31978	−	1.14585i
$515$		0			0
$516$	5.60083	−	0.794156i	0.246563	−	0.0349608i
$517$			0.897718i			0.0394816i
$518$	12.8588	−	5.21585i	0.564982	−	0.229171i
$519$			5.80369i			0.254754i
$520$		0			0
$521$			2.82843i			0.123916i	0.998079	+	0.0619578i	$0.0197344\pi$
$521$			2.82843i			0.123916i	−0.998079	+	0.0619578i	$0.980266\pi$
$522$	8.45851	−	9.74247i	0.370219	−	0.426416i
$523$	−7.15640			−0.312927			−0.156464	−	0.987684i	$-0.550009\pi$
$523$	−7.15640			−0.312927			−0.156464	+	0.987684i	$0.550009\pi$
$524$	−1.57258	−	11.0907i	−0.0686985	−	0.484501i
$525$		0			0
$526$	12.8078	+	11.1198i	0.558445	+	0.484848i
$527$			17.9074i			0.780058i
$528$	−2.27678	−	7.86715i	−0.0990841	−	0.342374i
$529$	19.4924			0.847497
$530$		0			0
$531$	20.6372			0.895576
$532$	−9.59309	+	28.0413i	−0.415913	+	1.21574i
$533$	−39.6252			−1.71636
$534$	2.00000	+	1.73642i	0.0865485	+	0.0751422i
$535$		0			0
$536$	−3.68466	+	5.69681i	−0.159153	+	0.246065i
$537$			1.14978i			0.0496165i
$538$	17.6465	+	15.3208i	0.760793	+	0.660528i
$539$	17.4920	−	12.7494i	0.753433	−	0.549154i
$540$		0			0
$541$	−23.5616			−1.01299			−0.506495	−	0.862243i	$-0.669059\pi$
$541$	−23.5616			−1.01299			−0.506495	+	0.862243i	$0.669059\pi$
$542$	8.10887	−	9.33976i	0.348306	−	0.401177i
$543$			6.14441i			0.263682i
$544$	10.5122	+	4.86270i	0.450706	+	0.208486i
$545$		0			0
$546$	−4.34888	−	10.7214i	−0.186115	−	0.458835i
$547$		−	37.3923i		−	1.59878i	−0.600812	−	0.799390i	$-0.705156\pi$
$547$		−	37.3923i		−	1.59878i	0.600812	−	0.799390i	$-0.294844\pi$
$548$	−3.70861	−	26.1552i	−0.158424	−	1.11729i
$549$		−	16.5246i		−	0.705253i
$550$		0			0
$551$	19.9477			0.849799
$552$	1.90495	−	2.94521i	0.0810799	−	0.125357i
$553$	−1.62603	+	3.19727i	−0.0691458	+	0.135962i
$554$	1.93087	−	2.22397i	0.0820348	−	0.0944873i
$555$		0			0
$556$	−4.02825	−	28.4095i	−0.170836	−	1.20483i
$557$	9.49980			0.402519			0.201260	−	0.979538i	$-0.435496\pi$
$557$	9.49980			0.402519			0.201260	+	0.979538i	$0.435496\pi$
$558$	20.7713	−	23.9243i	0.879319	−	1.01280i
$559$	19.9477			0.843696
$560$		0			0
$561$	−4.19224			−0.176996
$562$	18.5931	−	21.4154i	0.784302	−	0.903355i
$563$	−27.9277			−1.17701			−0.588506	−	0.808493i	$-0.700284\pi$
$563$	−27.9277			−1.17701			−0.588506	+	0.808493i	$0.700284\pi$
$564$	−0.0539753	−	0.380664i	−0.00227277	−	0.0160289i
$565$		0			0
$566$	18.1059	−	20.8543i	0.761048	−	0.876571i
$567$	−12.3721	−	6.29206i	−0.519580	−	0.264242i
$568$	−14.8344	+	22.9354i	−0.622439	+	0.962346i
$569$	−13.8617			−0.581114			−0.290557	−	0.956858i	$-0.593841\pi$
$569$	−13.8617			−0.581114			−0.290557	+	0.956858i	$0.593841\pi$
$570$		0			0
$571$			17.5780i			0.735615i	0.929902	+	0.367807i	$0.119891\pi$
$571$			17.5780i			0.735615i	−0.929902	+	0.367807i	$0.880109\pi$
$572$	−4.05444	−	28.5942i	−0.169524	−	1.19558i
$573$		−	9.08770i		−	0.379644i
$574$	11.9338	+	29.4208i	0.498108	+	1.22800i
$575$		0			0
$576$	−8.40388	−	18.6899i	−0.350162	−	0.778748i
$577$		−	18.9316i		−	0.788132i	−0.919082	−	0.394066i	$-0.871068\pi$
$577$		−	18.9316i		−	0.788132i	0.919082	−	0.394066i	$-0.128932\pi$
$578$	−11.8748	+	13.6773i	−0.493925	+	0.568900i
$579$	−2.45567			−0.102054
$580$		0			0
$581$	29.3693	+	14.9363i	1.21844	+	0.619662i
$582$	−4.34339	−	3.77098i	−0.180039	−	0.156312i
$583$		−	29.3751i		−	1.21659i
$584$	6.29033	−	9.72540i	0.260296	−	0.402440i
$585$		0			0
$586$	−16.1886	−	14.0551i	−0.668744	−	0.580610i
$587$	9.06134			0.374002			0.187001	−	0.982360i	$-0.440123\pi$
$587$	9.06134			0.374002			0.187001	+	0.982360i	$0.440123\pi$
$588$	−6.65066	+	6.45789i	−0.274269	+	0.266319i
$589$	48.9848			2.01839
$590$		0			0
$591$	7.36701			0.303038
$592$	−14.2497	+	4.12391i	−0.585659	+	0.169492i
$593$		−	31.2165i		−	1.28191i	−0.767579	−	0.640955i	$-0.778539\pi$
$593$		−	31.2165i		−	1.28191i	0.767579	−	0.640955i	$-0.221461\pi$
$594$	12.1603	+	10.5577i	0.498944	+	0.433188i
$595$		0			0
$596$	−0.561553	−	3.96039i	−0.0230021	−	0.162224i
$597$	−4.16516			−0.170469
$598$	8.10887	−	9.33976i	0.331596	−	0.381931i
$599$			14.4858i			0.591873i	0.955208	+	0.295937i	$0.0956317\pi$
$599$			14.4858i			0.591873i	−0.955208	+	0.295937i	$0.904368\pi$
$600$		0			0
$601$			39.4024i			1.60726i	0.595130	+	0.803630i	$0.297101\pi$
$601$			39.4024i			1.60726i	−0.595130	+	0.803630i	$0.702899\pi$
$602$	−6.00758	−	14.8107i	−0.244851	−	0.603638i
$603$		−	6.14441i		−	0.250220i
$604$	−37.4924	+	5.31614i	−1.52555	+	0.216311i
$605$		0			0
$606$	1.68466	+	1.46264i	0.0684346	+	0.0594156i
$607$	10.6302			0.431466			0.215733	−	0.976452i	$-0.430786\pi$
$607$	10.6302			0.431466			0.215733	+	0.976452i	$0.430786\pi$
$608$	13.3017	−	28.7556i	0.539455	−	1.16619i
$609$	5.56155	+	2.82843i	0.225365	+	0.114614i
$610$		0			0
$611$		−	1.35576i		−	0.0548480i
$612$	−10.3857	+	1.47261i	−0.419815	+	0.0595266i
$613$	−13.6650			−0.551923			−0.275961	−	0.961169i	$-0.588996\pi$
$613$	−13.6650			−0.551923			−0.275961	+	0.961169i	$0.588996\pi$
$614$	24.2451	−	27.9254i	0.978452	−	1.12698i
$615$		0			0
$616$	−20.0094	+	11.6220i	−0.806203	+	0.468262i
$617$	−35.9166			−1.44595			−0.722974	−	0.690875i	$-0.757226\pi$
$617$	−35.9166			−1.44595			−0.722974	+	0.690875i	$0.757226\pi$
$618$	0.634783	−	0.731140i	0.0255347	−	0.0294107i
$619$	10.5122			0.422520			0.211260	−	0.977430i	$-0.432243\pi$
$619$	10.5122			0.422520			0.211260	+	0.977430i	$0.432243\pi$
$620$		0			0
$621$			6.89697i			0.276766i
$622$	18.4945	−	21.3019i	0.741563	−	0.854128i
$623$	3.39228	−	6.67026i	0.135909	−	0.267238i
$624$	3.43845	+	11.8812i	0.137648	+	0.475627i
$625$		0			0
$626$	−12.1603	−	10.5577i	−0.486024	−	0.421971i
$627$			11.4677i			0.457975i
$628$	5.19283	−	0.736303i	0.207216	−	0.0293817i
$629$			7.59336i			0.302767i
$630$		0			0
$631$		−	32.2775i		−	1.28495i	−0.766308	−	0.642474i	$-0.777908\pi$
$631$		−	32.2775i		−	1.28495i	0.766308	−	0.642474i	$-0.222092\pi$
$632$	2.08258	−	3.21985i	0.0828406	−	0.128079i
$633$		−	16.6320i		−	0.661063i
$634$	−29.4384	+	33.9071i	−1.16915	+	1.34662i
$635$		0			0
$636$	1.76618	+	12.4561i	0.0700334	+	0.493915i
$637$	−26.4168	+	19.2544i	−1.04667	+	0.762887i
$638$	11.7606	+	10.2107i	0.465607	+	0.404245i
$639$		−	24.7374i		−	0.978597i
$640$		0			0
$641$	−17.8617			−0.705496			−0.352748	−	0.935718i	$-0.614753\pi$
$641$	−17.8617			−0.705496			−0.352748	+	0.935718i	$0.614753\pi$
$642$	10.3857	+	9.01693i	0.409889	+	0.355870i
$643$	0.499124			0.0196835			0.00984176	−	0.999952i	$-0.496867\pi$
$643$	0.499124			0.0196835			0.00984176	+	0.999952i	$0.496867\pi$
$644$	−9.37668	−	3.20782i	−0.369493	−	0.126406i
$645$		0			0
$646$	−12.2462	−	10.6323i	−0.481821	−	0.418322i
$647$	5.87787			0.231083			0.115541	−	0.993303i	$-0.463140\pi$
$647$	5.87787			0.231083			0.115541	+	0.993303i	$0.463140\pi$
$648$	12.4595	+	8.05872i	0.489455	+	0.316576i
$649$			24.9121i			0.977886i
$650$		0			0
$651$	13.6573	+	6.94568i	0.535273	+	0.272223i
$652$	31.1667	−	4.41921i	1.22058	−	0.173069i
$653$	11.1258			0.435387			0.217694	−	0.976017i	$-0.430147\pi$
$653$	11.1258			0.435387			0.217694	+	0.976017i	$0.430147\pi$
$654$	−0.269170	+	0.310029i	−0.0105254	+	0.0121231i
$655$		0			0
$656$	−9.43549	−	32.6032i	−0.368394	−	1.27294i
$657$			10.4895i			0.409236i
$658$	−1.00662	+	0.408309i	−0.0392420	+	0.0159176i
$659$		−	19.6950i		−	0.767210i	−0.923497	−	0.383605i	$-0.874682\pi$
$659$		−	19.6950i		−	0.767210i	0.923497	−	0.383605i	$-0.125318\pi$
$660$		0			0
$661$			42.3286i			1.64639i	0.567756	+	0.823197i	$0.307812\pi$
$661$			42.3286i			1.64639i	−0.567756	+	0.823197i	$0.692188\pi$
$662$	−1.85431	−	1.60993i	−0.0720696	−	0.0625716i
$663$	6.33122			0.245884
$664$	−29.5767	−	19.1300i	−1.14780	−	0.742390i
$665$		0			0
$666$	8.80776	−	10.1447i	0.341294	−	0.393101i
$667$			6.67026i			0.258274i
$668$	−2.35829	−	16.6320i	−0.0912452	−	0.643512i
$669$	−12.6847			−0.490417
$670$		0			0
$671$	19.9477			0.770071
$672$	7.78593	−	6.13118i	0.300349	−	0.236516i
$673$	−5.79119			−0.223234			−0.111617	−	0.993751i	$-0.535603\pi$
$673$	−5.79119			−0.223234			−0.111617	+	0.993751i	$0.535603\pi$
$674$	4.94602	−	5.69681i	0.190514	−	0.219433i
$675$		0			0
$676$	2.47301	+	17.4411i	0.0951159	+	0.670811i
$677$			6.46532i			0.248482i	0.992252	+	0.124241i	$0.0396496\pi$
$677$			6.46532i			0.248482i	−0.992252	+	0.124241i	$0.960350\pi$
$678$	−2.27678	+	2.62238i	−0.0874392	+	0.100712i
$679$	−7.36701	+	14.4858i	−0.282720	+	0.555914i
$680$		0			0
$681$	9.31534			0.356965
$682$	28.8802	+	25.0741i	1.10588	+	0.960135i
$683$			5.32326i			0.203689i	0.994800	+	0.101845i	$0.0324744\pi$
$683$			5.32326i			0.203689i	−0.994800	+	0.101845i	$0.967526\pi$
$684$	4.02825	+	28.4095i	0.154024	+	1.08626i
$685$		0			0
$686$	22.2518	+	13.8151i	0.849579	+	0.527462i
$687$		−	5.32326i		−	0.203095i
$688$	4.74990	+	16.4127i	0.181088	+	0.625730i
$689$			44.3629i			1.69009i
$690$		0			0
$691$	−12.9678			−0.493320			−0.246660	−	0.969102i	$-0.579333\pi$
$691$	−12.9678			−0.493320			−0.246660	+	0.969102i	$0.579333\pi$
$692$	−17.3561	+	2.46097i	−0.659781	+	0.0935520i
$693$	9.49980	−	18.6795i	0.360868	−	0.709576i
$694$	−4.56155	−	3.96039i	−0.173154	−	0.150334i
$695$		0			0
$696$	−5.60083	−	3.62258i	−0.212299	−	0.137314i
$697$	−17.3736			−0.658071
$698$	−38.7896	−	33.6775i	−1.46821	−	1.27471i
$699$	−4.91134			−0.185764
$700$		0			0
$701$	47.6695			1.80045			0.900226	−	0.435423i	$-0.143401\pi$
$701$	47.6695			1.80045			0.900226	+	0.435423i	$0.143401\pi$
$702$	−18.3648	−	15.9445i	−0.693135	−	0.601787i
$703$	20.7713			0.783404
$704$	22.5616	−	10.1447i	0.850321	−	0.382344i
$705$		0			0
$706$	−28.9628	−	25.1458i	−1.09003	−	0.946375i
$707$	2.85742	−	5.61856i	0.107464	−	0.211308i
$708$	−1.49784	−	10.5636i	−0.0562923	−	0.397005i
$709$	−10.1922			−0.382777			−0.191389	−	0.981514i	$-0.561299\pi$
$709$	−10.1922			−0.382777			−0.191389	+	0.981514i	$0.561299\pi$
$710$		0			0
$711$			3.47284i			0.130242i
$712$	−4.34475	+	6.71737i	−0.162827	+	0.251744i
$713$			16.3800i			0.613434i
$714$	−1.90676	−	4.70078i	−0.0713585	−	0.175922i
$715$		0			0
$716$	−3.43845	+	0.487546i	−0.128501	+	0.0182204i
$717$		−	2.04750i		−	0.0764651i
$718$	−28.2711	−	24.5453i	−1.05507	−	0.916022i
$719$	−36.0607			−1.34484			−0.672418	−	0.740172i	$-0.734744\pi$
$719$	−36.0607			−1.34484			−0.672418	+	0.740172i	$0.734744\pi$
$720$		0			0
$721$	−2.43845	−	1.24012i	−0.0908125	−	0.0461843i
$722$	−11.4682	+	13.2091i	−0.426804	+	0.491590i
$723$			12.5194i			0.465601i
$724$	−18.3751	+	2.60545i	−0.682904	+	0.0968307i
$725$		0			0
$726$	0.883088	−	1.01714i	0.0327745	−	0.0377494i
$727$	−6.20393			−0.230091			−0.115045	−	0.993360i	$-0.536701\pi$
$727$	−6.20393			−0.230091			−0.115045	+	0.993360i	$0.536701\pi$
$728$	30.2187	−	17.5517i	1.11998	−	0.650511i
$729$	−6.12311			−0.226782
$730$		0			0
$731$	8.74599			0.323482
$732$	−8.45851	+	1.19935i	−0.312636	+	0.0443294i
$733$		−	11.0644i		−	0.408674i	−0.978901	−	0.204337i	$-0.934496\pi$
$733$		−	11.0644i		−	0.408674i	0.978901	−	0.204337i	$-0.0655038\pi$
$734$	−29.5012	+	33.9793i	−1.08891	+	1.25420i
$735$		0			0
$736$	9.61553	+	4.44793i	0.354433	+	0.163953i
$737$	7.41722			0.273217
$738$	23.2111	+	20.1521i	0.854413	+	0.741810i
$739$		−	14.6996i		−	0.540732i	−0.962758	−	0.270366i	$-0.912855\pi$
$739$		−	14.6996i		−	0.540732i	0.962758	−	0.270366i	$-0.0871447\pi$
$740$		0			0
$741$		−	17.3188i		−	0.636220i
$742$	32.9384	−	13.3607i	1.20921	−	0.490485i
$743$		−	4.79741i		−	0.176000i	−0.996120	−	0.0880000i	$-0.971952\pi$
$743$		−	4.79741i		−	0.176000i	0.996120	−	0.0880000i	$-0.0280475\pi$
$744$	−13.7538	−	8.89586i	−0.504238	−	0.326138i
$745$		0			0
$746$	−21.0540	+	24.2499i	−0.770841	+	0.887851i
$747$	31.9006			1.16718
$748$	−1.77766	−	12.5370i	−0.0649975	−	0.458399i
$749$	17.6155	−	34.6375i	0.643657	−	1.26563i
$750$		0			0
$751$		−	24.3567i		−	0.888790i	−0.895831	−	0.444395i	$-0.853419\pi$
$751$		−	24.3567i		−	0.888790i	0.895831	−	0.444395i	$-0.146581\pi$
$752$	1.11550	−	0.322830i	0.0406782	−	0.0117724i
$753$	2.08258			0.0758934
$754$	−17.7612	−	15.4204i	−0.646823	−	0.561578i
$755$		0			0
$756$	−6.30755	+	18.4374i	−0.229403	+	0.670562i
$757$	28.4994			1.03583			0.517914	−	0.855433i	$-0.326709\pi$
$757$	28.4994			1.03583			0.517914	+	0.855433i	$0.326709\pi$
$758$	−5.56292	−	4.82978i	−0.202054	−	0.175425i
$759$	−3.83466			−0.139189
$760$		0			0
$761$			3.52482i			0.127775i	0.997957	+	0.0638873i	$0.0203498\pi$
$761$			3.52482i			0.127775i	−0.997957	+	0.0638873i	$0.979650\pi$
$762$	−12.0818	−	10.4895i	−0.437677	−	0.379996i
$763$	1.03399	+	0.525853i	0.0374329	+	0.0190372i
$764$	27.1771	−	3.85350i	0.983232	−	0.139415i
$765$		0			0
$766$	−25.0101	+	28.8066i	−0.903653	+	1.04082i
$767$		−	37.6229i		−	1.35848i
$768$	−8.95694	+	5.65824i	−0.323206	+	0.204174i
$769$		−	8.83348i		−	0.318543i	−0.987235	−	0.159272i	$-0.949085\pi$
$769$		−	8.83348i		−	0.318543i	0.987235	−	0.159272i	$-0.0509146\pi$
$770$		0			0
$771$		−	18.5531i		−	0.668172i
$772$	−1.04129	−	7.34376i	−0.0374769	−	0.264308i
$773$		−	48.4234i		−	1.74167i	−0.491575	−	0.870835i	$-0.663579\pi$
$773$		−	48.4234i		−	1.74167i	0.491575	−	0.870835i	$-0.336421\pi$
$774$	−11.6847	−	10.1447i	−0.419996	−	0.364645i
$775$		0			0
$776$	9.43549	−	14.5881i	0.338714	−	0.523682i
$777$	5.79119	+	2.94521i	0.207758	+	0.105659i
$778$	15.6975	−	18.0803i	0.562783	−	0.648210i
$779$			47.5246i			1.70275i
$780$		0			0
$781$	29.8617			1.06854
$782$	3.55531	−	4.09499i	0.127138	−	0.146437i
$783$	13.1158			0.468720
$784$	−22.1327	−	17.1507i	−0.790452	−	0.612524i
$785$		0			0
$786$	3.43845	−	3.96039i	0.122645	−	0.141262i
$787$	−37.4882			−1.33631			−0.668154	−	0.744023i	$-0.732915\pi$
$787$	−37.4882			−1.33631			−0.668154	+	0.744023i	$0.732915\pi$
$788$	3.12387	+	22.0313i	0.111283	+	0.784832i
$789$			7.94156i			0.282727i
$790$		0			0
$791$	8.74599	+	4.44793i	0.310972	+	0.158150i
$792$	−12.1671	+	18.8114i	−0.432340	+	0.668435i
$793$	−30.1254			−1.06979
$794$	13.7329	+	11.9231i	0.487363	+	0.423133i
$795$		0			0
$796$	−1.76618	−	12.4561i	−0.0626004	−	0.441493i
$797$		−	47.2737i		−	1.67452i	−0.546805	−	0.837260i	$-0.684156\pi$
$797$		−	47.2737i		−	1.67452i	0.546805	−	0.837260i	$-0.315844\pi$
$798$	−12.8588	+	5.21585i	−0.455196	+	0.184639i
$799$		−	0.594427i		−	0.0210293i
$800$		0			0
$801$		−	7.24517i		−	0.255995i
$802$	−16.2822	+	18.7538i	−0.574946	+	0.662220i
$803$	−12.6624			−0.446847
$804$	−3.14516	+	0.445960i	−0.110921	+	0.0157278i
$805$		0			0
$806$	−43.6155	−	37.8674i	−1.53629	−	1.33382i
$807$			10.9418i			0.385170i
$808$	−3.65971	+	5.65824i	−0.128748	+	0.199056i
$809$	−10.0540			−0.353479			−0.176739	−	0.984258i	$-0.556555\pi$
$809$	−10.0540			−0.353479			−0.176739	+	0.984258i	$0.556555\pi$
$810$		0			0
$811$	3.14516			0.110442			0.0552208	−	0.998474i	$-0.482414\pi$
$811$	3.14516			0.110442			0.0552208	+	0.998474i	$0.482414\pi$
$812$	−6.10022	+	17.8314i	−0.214076	+	0.625758i
$813$	5.79119			0.203106
$814$	12.2462	+	10.6323i	0.429229	+	0.372661i
$815$		0			0
$816$	1.50758	+	5.20926i	0.0527758	+	0.182361i
$817$		−	23.9243i		−	0.837005i
$818$	−5.08842	−	4.41782i	−0.177913	−	0.154465i
$819$	−14.3468	+	28.2102i	−0.501319	+	0.985746i
$820$		0			0
$821$	−7.06913			−0.246714			−0.123357	−	0.992362i	$-0.539366\pi$
$821$	−7.06913			−0.246714			−0.123357	+	0.992362i	$0.539366\pi$
$822$	8.10887	−	9.33976i	0.282829	−	0.325761i
$823$			3.21985i			0.112237i	0.998424	+	0.0561185i	$0.0178725\pi$
$823$			3.21985i			0.112237i	−0.998424	+	0.0561185i	$0.982128\pi$
$824$	2.45567	+	1.58831i	0.0855473	+	0.0553314i
$825$		0			0
$826$	−27.9341	+	11.3308i	−0.971952	+	0.394248i
$827$			2.39871i			0.0834112i	0.999130	+	0.0417056i	$0.0132792\pi$
$827$			2.39871i			0.0834112i	−0.999130	+	0.0417056i	$0.986721\pi$
$828$	−9.49980	+	1.34700i	−0.330141	+	0.0468115i
$829$			25.9018i			0.899607i	0.893128	+	0.449803i	$0.148506\pi$
$829$			25.9018i			0.899607i	−0.893128	+	0.449803i	$0.851494\pi$
$830$		0			0
$831$	1.37899			0.0478366
$832$	−34.0730	+	15.3208i	−1.18127	+	0.531154i
$833$	−11.5824	+	8.44204i	−0.401306	+	0.292499i
$834$	8.80776	−	10.1447i	0.304988	−	0.351284i
$835$		0			0
$836$	−34.2945	+	4.86270i	−1.18610	+	0.168180i
$837$	32.2080			1.11327
$838$	19.1338	−	22.0382i	0.660966	−	0.761297i
$839$	47.2623			1.63168			0.815838	−	0.578280i	$-0.196276\pi$
$839$	47.2623			1.63168			0.815838	+	0.578280i	$0.196276\pi$
$840$		0			0
$841$	−16.3153			−0.562598
$842$	−7.82373	+	9.01133i	−0.269623	+	0.310551i
$843$	13.2788			0.457346
$844$	49.7386	−	7.05256i	1.71207	−	0.242759i
$845$		0			0
$846$	−0.689494	+	0.794156i	−0.0237053	+	0.0273036i
$847$	−3.39228	−	1.72521i	−0.116560	−	0.0592788i
$848$	−36.5014	+	10.5636i	−1.25346	+	0.362756i
$849$	12.9309			0.443786
$850$		0			0
$851$			6.94568i			0.238095i
$852$	−12.6624	+	1.79544i	−0.433808	+	0.0615107i
$853$			45.2262i			1.54851i	0.632871	+	0.774257i	$0.281876\pi$
$853$			45.2262i			1.54851i	−0.632871	+	0.774257i	$0.718124\pi$
$854$	9.07280	+	22.3674i	0.310465	+	0.765398i
$855$		0			0
$856$	−22.5616	+	34.8821i	−0.771138	+	1.19225i
$857$			14.5845i			0.498198i	0.968478	+	0.249099i	$0.0801344\pi$
$857$			14.5845i			0.498198i	−0.968478	+	0.249099i	$0.919866\pi$
$858$	8.86502	−	10.2107i	0.302647	−	0.348587i
$859$	3.14516			0.107312			0.0536558	−	0.998559i	$-0.482913\pi$
$859$	3.14516			0.107312			0.0536558	+	0.998559i	$0.482913\pi$
$860$		0			0
$861$	−6.73863	+	13.2502i	−0.229652	+	0.451566i
$862$	16.5105	+	14.3346i	0.562350	+	0.488238i
$863$			28.8492i			0.982038i	0.871149	+	0.491019i	$0.163375\pi$
$863$			28.8492i			0.982038i	−0.871149	+	0.491019i	$0.836625\pi$
$864$	8.74599	−	18.9071i	0.297545	−	0.643232i
$865$		0			0
$866$	41.1232	+	35.7035i	1.39742	+	1.21326i
$867$	−8.48071			−0.288020
$868$	−14.9801	+	43.7879i	−0.508458	+	1.48626i
$869$	−4.19224			−0.142212
$870$		0			0
$871$	−11.2017			−0.379554
$872$	−1.04129	−	0.673500i	−0.0352625	−	0.0228076i
$873$			15.7343i			0.532525i
$874$	−11.2017	−	9.72540i	−0.378902	−	0.328966i
$875$		0			0
$876$	5.36932	−	0.761329i	0.181412	−	0.0257229i
$877$	−3.70861			−0.125231			−0.0626154	−	0.998038i	$-0.519944\pi$
$877$	−3.70861			−0.125231			−0.0626154	+	0.998038i	$0.519944\pi$
$878$	−22.0498	+	25.3969i	−0.744146	+	0.857103i
$879$		−	10.0379i		−	0.338569i
$880$		0			0
$881$			54.0883i			1.82228i	0.412095	+	0.911141i	$0.364797\pi$
$881$			54.0883i			1.82228i	−0.412095	+	0.911141i	$0.635203\pi$
$882$	25.2662	+	2.15617i	0.850759	+	0.0726022i
$883$			19.7155i			0.663479i	0.943371	+	0.331740i	$0.107636\pi$
$883$			19.7155i			0.663479i	−0.943371	+	0.331740i	$0.892364\pi$
$884$	2.68466	+	18.9337i	0.0902948	+	0.636810i
$885$		0			0
$886$	−14.8078	−	12.8563i	−0.497477	−	0.431914i
$887$	−15.3110			−0.514095			−0.257047	−	0.966399i	$-0.582750\pi$
$887$	−15.3110			−0.514095			−0.257047	+	0.966399i	$0.582750\pi$
$888$	−5.83209	−	3.77216i	−0.195712	−	0.126585i
$889$	−20.4924	+	40.2944i	−0.687294	+	1.35143i
$890$		0			0
$891$		−	16.2222i		−	0.543464i
$892$	−5.37874	−	37.9339i	−0.180094	−	1.27012i
$893$	−1.62603			−0.0544130
$894$	1.22783	−	1.41421i	0.0410649	−	0.0472984i
$895$		0			0
$896$	21.6370	+	20.6843i	0.722842	+	0.691013i
$897$	5.79119			0.193362
$898$	17.3235	−	19.9532i	0.578094	−	0.665845i
$899$	31.1493			1.03889
$900$		0			0
$901$			19.4508i			0.648000i
$902$	−24.3266	+	28.0193i	−0.809988	+	0.932940i
$903$	3.39228	−	6.67026i	0.112888	−	0.221972i
$904$	−8.80776	−	5.69681i	−0.292942	−	0.189473i
$905$		0			0
$906$	−13.3882	−	11.6237i	−0.444792	−	0.386173i
$907$		−	2.62926i		−	0.0873033i	−0.999047	−	0.0436516i	$-0.986101\pi$
$907$		−	2.62926i		−	0.0873033i	0.999047	−	0.0436516i	$-0.0138992\pi$
$908$	3.95003	+	27.8579i	0.131086	+	0.924495i
$909$		−	6.10281i		−	0.202418i
$910$		0			0
$911$		−	40.3652i		−	1.33736i	−0.743551	−	0.668679i	$-0.766860\pi$
$911$		−	40.3652i		−	1.33736i	0.743551	−	0.668679i	$-0.233140\pi$
$912$	14.2497	−	4.12391i	0.471855	−	0.136556i
$913$			38.5088i			1.27446i
$914$	−34.8078	+	40.0914i	−1.15134	+	1.32611i
$915$		0			0
$916$	15.9194	−	2.25725i	0.525992	−	0.0745817i
$917$	−13.2084	−	6.71737i	−0.436180	−	0.221827i
$918$	−8.05200	−	6.99083i	−0.265756	−	0.230732i
$919$		−	11.7743i		−	0.388398i	−0.980962	−	0.194199i	$-0.937789\pi$
$919$		−	11.7743i		−	0.388398i	0.980962	−	0.194199i	$-0.0622107\pi$
$920$		0			0
$921$	17.3153			0.570560
$922$	21.0387	+	18.2660i	0.692874	+	0.601560i
$923$	−45.0979			−1.48442
$924$	−10.2510	−	3.50694i	−0.337235	−	0.115370i
$925$		0			0
$926$	29.0540	+	25.2250i	0.954773	+	0.828943i
$927$	−2.64861			−0.0869919
$928$	8.45851	−	18.2856i	0.277664	−	0.600254i
$929$		−	17.6670i		−	0.579634i	−0.957082	−	0.289817i	$-0.906406\pi$
$929$		−	17.6670i		−	0.579634i	0.957082	−	0.289817i	$-0.0935944\pi$
$930$		0			0
$931$	23.0928	+	31.6831i	0.756837	+	1.03837i
$932$	−2.08258	−	14.6875i	−0.0682172	−	0.481106i
$933$	13.2084			0.432424
$934$	28.7692	−	33.1363i	0.941358	−	1.08425i
$935$		0			0
$936$	18.3751	−	28.4095i	0.600608	−	0.928593i
$937$			38.7609i			1.26626i	0.774045	+	0.633131i	$0.218231\pi$
$937$			38.7609i			1.26626i	−0.774045	+	0.633131i	$0.781769\pi$
$938$	3.37358	+	8.31697i	0.110151	+	0.271559i
$939$		−	7.54011i		−	0.246062i
$940$		0			0
$941$		−	37.9119i		−	1.23589i	−0.786220	−	0.617946i	$-0.787965\pi$
$941$		−	37.9119i		−	1.23589i	0.786220	−	0.617946i	$-0.212035\pi$
$942$	1.85431	+	1.60993i	0.0604165	+	0.0524542i
$943$	−15.8917			−0.517504
$944$	30.9557	−	8.95869i	1.00752	−	0.291581i
$945$		0			0
$946$	12.2462	−	14.1051i	0.398159	−	0.458597i
$947$			41.5991i			1.35179i	0.736998	+	0.675895i	$0.236243\pi$
$947$			41.5991i			1.35179i	−0.736998	+	0.675895i	$0.763757\pi$
$948$	1.77766	−	0.252058i	0.0577356	−	0.00818647i
$949$	19.1231			0.620762
$950$		0			0
$951$	−21.0243			−0.681761
$952$	13.2493	−	7.69552i	0.429413	−	0.249413i
$953$	24.7908			0.803053			0.401526	−	0.915848i	$-0.368480\pi$
$953$	24.7908			0.803053			0.401526	+	0.915848i	$0.368480\pi$
$954$	22.5616	−	25.9863i	0.730457	−	0.841337i
$955$		0			0
$956$	6.12311	−	0.868210i	0.198035	−	0.0280799i
$957$			7.29226i			0.235725i
$958$	3.55531	−	4.09499i	0.114867	−	0.132303i
$959$	−31.1493	−	15.8415i	−1.00586	−	0.511550i
$960$		0			0
$961$	45.4924			1.46750
$962$	−18.4945	−	16.0571i	−0.596287	−	0.517703i
$963$		−	37.6229i		−	1.21238i
$964$	−37.4396	+	5.30866i	−1.20585	+	0.170980i
$965$		0			0
$966$	−1.74412	−	4.29982i	−0.0561161	−	0.138345i
$967$			18.1379i			0.583277i	0.956529	+	0.291638i	$0.0942004\pi$
$967$			18.1379i			0.583277i	−0.956529	+	0.291638i	$0.905800\pi$
$968$	3.41624	+	2.20960i	0.109802	+	0.0710193i
$969$		−	7.59336i		−	0.243934i
$970$		0			0
$971$	32.9155			1.05631			0.528154	−	0.849148i	$-0.322884\pi$
$971$	32.9155			1.05631			0.528154	+	0.849148i	$0.322884\pi$
$972$	4.07732	+	28.7556i	0.130780	+	0.922335i
$973$	−33.8340	−	17.2069i	−1.08467	−	0.551628i
$974$	−41.6155	−	36.1310i	−1.33345	−	1.15771i
$975$		0			0
$976$	−7.17341	−	24.7869i	−0.229615	−	0.793409i
$977$	5.79119			0.185277			0.0926383	−	0.995700i	$-0.470470\pi$
$977$	5.79119			0.185277			0.0926383	+	0.995700i	$0.470470\pi$
$978$	11.1293	+	9.66259i	0.355876	+	0.308975i
$979$	8.74599			0.279523
$980$		0			0
$981$	1.12311			0.0358580
$982$	7.01071	+	6.08677i	0.223721	+	0.194237i
$983$	38.4406			1.22607			0.613033	−	0.790057i	$-0.289949\pi$
$983$	38.4406			1.22607			0.613033	+	0.790057i	$0.289949\pi$
$984$	8.63068	−	13.3438i	0.275136	−	0.425385i
$985$		0			0
$986$	−7.78733	−	6.76104i	−0.247999	−	0.215315i
$987$	−0.453349	−	0.230559i	−0.0144303	−	0.00733876i
$988$	51.7924	−	7.34376i	1.64773	−	0.233636i
$989$	8.00000			0.254385
$990$		0			0
$991$			50.2361i			1.59580i	0.602787	+	0.797902i	$0.294057\pi$
$991$			50.2361i			1.59580i	−0.602787	+	0.797902i	$0.705943\pi$
$992$	20.7713	−	44.9033i	0.659489	−	1.42568i
$993$		−	1.14978i		−	0.0364871i
$994$	13.5820	+	33.4841i	0.430796	+	1.06205i
$995$		0			0
$996$	−2.31534	−	16.3291i	−0.0733644	−	0.517407i
$997$			26.7987i			0.848724i	0.905493	+	0.424362i	$0.139502\pi$
$997$			26.7987i			0.848724i	−0.905493	+	0.424362i	$0.860498\pi$
$998$	36.3231	+	31.5361i	1.14979	+	0.998258i
$999$	13.6573			0.432099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.l.251.7		16
4.3	odd	2	inner	700.2.g.l.251.6		16
5.2	odd	4		140.2.c.b.139.2	yes	16
5.3	odd	4		140.2.c.b.139.15	yes	16
5.4	even	2	inner	700.2.g.l.251.10		16
7.6	odd	2	inner	700.2.g.l.251.8		16
20.3	even	4		140.2.c.b.139.4	yes	16
20.7	even	4		140.2.c.b.139.13	yes	16
20.19	odd	2	inner	700.2.g.l.251.11		16
28.27	even	2	inner	700.2.g.l.251.5		16
35.2	odd	12		980.2.s.f.619.7		32
35.3	even	12		980.2.s.f.19.4		32
35.12	even	12		980.2.s.f.619.8		32
35.13	even	4		140.2.c.b.139.16	yes	16
35.17	even	12		980.2.s.f.19.13		32
35.18	odd	12		980.2.s.f.19.3		32
35.23	odd	12		980.2.s.f.619.10		32
35.27	even	4		140.2.c.b.139.1	✓	16
35.32	odd	12		980.2.s.f.19.14		32
35.33	even	12		980.2.s.f.619.9		32
35.34	odd	2	inner	700.2.g.l.251.9		16
40.3	even	4		2240.2.e.f.2239.6		16
40.13	odd	4		2240.2.e.f.2239.10		16
40.27	even	4		2240.2.e.f.2239.12		16
40.37	odd	4		2240.2.e.f.2239.8		16
140.3	odd	12		980.2.s.f.19.7		32
140.23	even	12		980.2.s.f.619.13		32
140.27	odd	4		140.2.c.b.139.14	yes	16
140.47	odd	12		980.2.s.f.619.3		32
140.67	even	12		980.2.s.f.19.9		32
140.83	odd	4		140.2.c.b.139.3	yes	16
140.87	odd	12		980.2.s.f.19.10		32
140.103	odd	12		980.2.s.f.619.14		32
140.107	even	12		980.2.s.f.619.4		32
140.123	even	12		980.2.s.f.19.8		32
140.139	even	2	inner	700.2.g.l.251.12		16
280.13	even	4		2240.2.e.f.2239.7		16
280.27	odd	4		2240.2.e.f.2239.5		16
280.83	odd	4		2240.2.e.f.2239.11		16
280.237	even	4		2240.2.e.f.2239.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.1	✓	16	35.27	even	4
140.2.c.b.139.2	yes	16	5.2	odd	4
140.2.c.b.139.3	yes	16	140.83	odd	4
140.2.c.b.139.4	yes	16	20.3	even	4
140.2.c.b.139.13	yes	16	20.7	even	4
140.2.c.b.139.14	yes	16	140.27	odd	4
140.2.c.b.139.15	yes	16	5.3	odd	4
140.2.c.b.139.16	yes	16	35.13	even	4
700.2.g.l.251.5		16	28.27	even	2	inner
700.2.g.l.251.6		16	4.3	odd	2	inner
700.2.g.l.251.7		16	1.1	even	1	trivial
700.2.g.l.251.8		16	7.6	odd	2	inner
700.2.g.l.251.9		16	35.34	odd	2	inner
700.2.g.l.251.10		16	5.4	even	2	inner
700.2.g.l.251.11		16	20.19	odd	2	inner
700.2.g.l.251.12		16	140.139	even	2	inner
980.2.s.f.19.3		32	35.18	odd	12
980.2.s.f.19.4		32	35.3	even	12
980.2.s.f.19.7		32	140.3	odd	12
980.2.s.f.19.8		32	140.123	even	12
980.2.s.f.19.9		32	140.67	even	12
980.2.s.f.19.10		32	140.87	odd	12
980.2.s.f.19.13		32	35.17	even	12
980.2.s.f.19.14		32	35.32	odd	12
980.2.s.f.619.3		32	140.47	odd	12
980.2.s.f.619.4		32	140.107	even	12
980.2.s.f.619.7		32	35.2	odd	12
980.2.s.f.619.8		32	35.12	even	12
980.2.s.f.619.9		32	35.33	even	12
980.2.s.f.619.10		32	35.23	odd	12
980.2.s.f.619.13		32	140.23	even	12
980.2.s.f.619.14		32	140.103	odd	12
2240.2.e.f.2239.5		16	280.27	odd	4
2240.2.e.f.2239.6		16	40.3	even	4
2240.2.e.f.2239.7		16	280.13	even	4
2240.2.e.f.2239.8		16	40.37	odd	4
2240.2.e.f.2239.9		16	280.237	even	4
2240.2.e.f.2239.10		16	40.13	odd	4
2240.2.e.f.2239.11		16	280.83	odd	4
2240.2.e.f.2239.12		16	40.27	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927153 + 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 - 1.98019i) q^{4} +(0.613917 - 0.707107i) q^{6} +(-2.35829 - 1.19935i) q^{7} +(2.37495 + 1.53610i) q^{8} -2.56155 q^{9} +O(q^{10})\)	\(q+(-0.927153 + 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 - 1.98019i) q^{4} +(0.613917 - 0.707107i) q^{6} +(-2.35829 - 1.19935i) q^{7} +(2.37495 + 1.53610i) q^{8} -2.56155 q^{9} -3.09218i q^{11} +(0.185917 + 1.31119i) q^{12} +4.66988i q^{13} +(3.46728 - 1.40642i) q^{14} +(-3.84233 + 1.11198i) q^{16} +2.04750i q^{17} +(2.37495 - 2.73546i) q^{18} +5.60083 q^{19} +(1.56155 + 0.794156i) q^{21} +(3.30210 + 2.86692i) q^{22} +1.87285i q^{23} +(-1.57258 - 1.01714i) q^{24} +(-4.98691 - 4.32969i) q^{26} +3.68260 q^{27} +(-1.71280 + 5.00663i) q^{28} +3.56155 q^{29} +8.74599 q^{31} +(2.37495 - 5.13416i) q^{32} +2.04750i q^{33} +(-2.18650 - 1.89834i) q^{34} +(0.719224 + 5.07237i) q^{36} +3.70861 q^{37} +(-5.19283 + 5.98107i) q^{38} -3.09218i q^{39} +8.48528i q^{41} +(-2.29587 + 0.931263i) q^{42} -4.27156i q^{43} +(-6.12311 + 0.868210i) q^{44} +(-2.00000 - 1.73642i) q^{46} -0.290319 q^{47} +(2.54421 - 0.736303i) q^{48} +(4.12311 + 5.65685i) q^{49} -1.35576i q^{51} +(9.24726 - 1.31119i) q^{52} +9.49980 q^{53} +(-3.41433 + 3.93261i) q^{54} +(-3.75850 - 6.47099i) q^{56} -3.70861 q^{57} +(-3.30210 + 3.80335i) q^{58} -8.05650 q^{59} +6.45101i q^{61} +(-8.10887 + 9.33976i) q^{62} +(6.04090 + 3.07221i) q^{63} +(3.28078 + 7.29634i) q^{64} +(-2.18650 - 1.89834i) q^{66} +2.39871i q^{67} +(4.05444 - 0.574888i) q^{68} -1.24012i q^{69} +9.65719i q^{71} +(-6.08356 - 3.93481i) q^{72} -4.09499i q^{73} +(-3.43845 + 3.96039i) q^{74} +(-1.57258 - 11.0907i) q^{76} +(-3.70861 + 7.29226i) q^{77} +(3.30210 + 2.86692i) q^{78} -1.35576i q^{79} +5.24621 q^{81} +(-9.06134 - 7.86715i) q^{82} -12.4536 q^{83} +(1.13413 - 3.31516i) q^{84} +(4.56155 + 3.96039i) q^{86} -2.35829 q^{87} +(4.74990 - 7.34376i) q^{88} +2.82843i q^{89} +(5.60083 - 11.0129i) q^{91} +(3.70861 - 0.525853i) q^{92} -5.79119 q^{93} +(0.269170 - 0.310029i) q^{94} +(-1.57258 + 3.39960i) q^{96} -6.14249i q^{97} +(-9.86364 - 0.841745i) q^{98} +7.92077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^4 - 8 * q^9	\( 16 q + 12 q^{4} - 8 q^{9} + 4 q^{14} - 12 q^{16} - 8 q^{21} + 24 q^{29} + 28 q^{36} - 32 q^{44} - 32 q^{46} - 20 q^{56} + 36 q^{64} - 88 q^{74} - 48 q^{81} - 40 q^{84} + 40 q^{86}+O(q^{100}) \) 16 * q + 12 * q^4 - 8 * q^9 + 4 * q^14 - 12 * q^16 - 8 * q^21 + 24 * q^29 + 28 * q^36 - 32 * q^44 - 32 * q^46 - 20 * q^56 + 36 * q^64 - 88 * q^74 - 48 * q^81 - 40 * q^84 + 40 * q^86

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