LMFDB - Embedded newform 985.2.b.a.789.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [985,2,Mod(789,985)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(985, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("985.789");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 985 = 5 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	985.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:	$7.86526459910$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			789.68
Character	$\chi$	$=$	985.789
Dual form			985.2.b.a.789.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.27373i q^{2} -3.21433i q^{3} +0.377621 q^{4} +(-1.42261 + 1.72516i) q^{5} +4.09418 q^{6} -0.234977i q^{7} +3.02844i q^{8} -7.33194 q^{9} +(-2.19739 - 1.81201i) q^{10} -0.577101 q^{11} -1.21380i q^{12} +3.89397i q^{13} +0.299296 q^{14} +(5.54525 + 4.57273i) q^{15} -3.10216 q^{16} +3.49246i q^{17} -9.33888i q^{18} -7.16189 q^{19} +(-0.537206 + 0.651458i) q^{20} -0.755293 q^{21} -0.735069i q^{22} -4.85751i q^{23} +9.73441 q^{24} +(-0.952375 - 4.90846i) q^{25} -4.95986 q^{26} +13.9243i q^{27} -0.0887321i q^{28} -8.44483 q^{29} +(-5.82441 + 7.06313i) q^{30} -5.57555 q^{31} +2.10557i q^{32} +1.85499i q^{33} -4.44844 q^{34} +(0.405373 + 0.334280i) q^{35} -2.76869 q^{36} +5.18286i q^{37} -9.12229i q^{38} +12.5165 q^{39} +(-5.22455 - 4.30828i) q^{40} +4.90259 q^{41} -0.962037i q^{42} -3.12584i q^{43} -0.217925 q^{44} +(10.4305 - 12.6488i) q^{45} +6.18714 q^{46} +6.99306i q^{47} +9.97138i q^{48} +6.94479 q^{49} +(6.25204 - 1.21307i) q^{50} +11.2259 q^{51} +1.47045i q^{52} +12.1609i q^{53} -17.7357 q^{54} +(0.820988 - 0.995593i) q^{55} +0.711612 q^{56} +23.0207i q^{57} -10.7564i q^{58} +14.3710 q^{59} +(2.09400 + 1.72676i) q^{60} -7.71724 q^{61} -7.10173i q^{62} +1.72283i q^{63} -8.88625 q^{64} +(-6.71774 - 5.53960i) q^{65} -2.36276 q^{66} +2.57664i q^{67} +1.31883i q^{68} -15.6136 q^{69} +(-0.425781 + 0.516334i) q^{70} +7.82253 q^{71} -22.2043i q^{72} -8.14734i q^{73} -6.60155 q^{74} +(-15.7774 + 3.06125i) q^{75} -2.70448 q^{76} +0.135605i q^{77} +15.9426i q^{78} +0.388882 q^{79} +(4.41316 - 5.35173i) q^{80} +22.7615 q^{81} +6.24456i q^{82} +5.26069i q^{83} -0.285214 q^{84} +(-6.02507 - 4.96840i) q^{85} +3.98147 q^{86} +27.1445i q^{87} -1.74771i q^{88} -8.36693 q^{89} +(16.1111 + 13.2856i) q^{90} +0.914993 q^{91} -1.83430i q^{92} +17.9217i q^{93} -8.90725 q^{94} +(10.1886 - 12.3554i) q^{95} +6.76801 q^{96} -8.83287i q^{97} +8.84576i q^{98} +4.23127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) $ 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/985\mathbb{Z}\right)^\times$.

$n$	$396$	$592$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.27373i			0.900661i	0.892862	+	0.450330i	$0.148694\pi$
$2$			1.27373i			0.900661i	−0.892862	+	0.450330i	$0.851306\pi$
$3$		−	3.21433i		−	1.85580i	−0.372834	−	0.927898i	$-0.621614\pi$
$3$		−	3.21433i		−	1.85580i	0.372834	−	0.927898i	$-0.378386\pi$
$4$	0.377621			0.188810
$5$	−1.42261	+	1.72516i	−0.636209	+	0.771516i
$5$	−1.42261	+	1.72516i	−0.636209	+	0.771516i
$6$	4.09418			1.67144
$7$		−	0.234977i		−	0.0888128i	−0.999014	−	0.0444064i	$-0.985860\pi$
$7$		−	0.234977i		−	0.0888128i	0.999014	−	0.0444064i	$-0.0141396\pi$
$8$			3.02844i			1.07071i
$9$	−7.33194			−2.44398
$10$	−2.19739	−	1.81201i	−0.694874	−	0.573009i
$11$	−0.577101			−0.174002			−0.0870012	−	0.996208i	$-0.527728\pi$
$11$	−0.577101			−0.174002			−0.0870012	+	0.996208i	$0.527728\pi$
$12$		−	1.21380i		−	0.350394i
$13$			3.89397i			1.07999i	0.841667	+	0.539997i	$0.181575\pi$
$13$			3.89397i			1.07999i	−0.841667	+	0.539997i	$0.818425\pi$
$14$	0.299296			0.0799902
$15$	5.54525	+	4.57273i	1.43178	+	1.18068i
$16$	−3.10216			−0.775540
$17$			3.49246i			0.847047i	0.905885	+	0.423523i	$0.139207\pi$
$17$			3.49246i			0.847047i	−0.905885	+	0.423523i	$0.860793\pi$
$18$		−	9.33888i		−	2.20120i
$19$	−7.16189			−1.64305			−0.821525	−	0.570173i	$-0.806876\pi$
$19$	−7.16189			−1.64305			−0.821525	+	0.570173i	$0.806876\pi$
$20$	−0.537206	+	0.651458i	−0.120123	+	0.145670i
$21$	−0.755293			−0.164818
$22$		−	0.735069i		−	0.156717i
$23$		−	4.85751i		−	1.01286i	−0.862281	−	0.506430i	$-0.830965\pi$
$23$		−	4.85751i		−	1.01286i	0.862281	−	0.506430i	$-0.169035\pi$
$24$	9.73441			1.98703
$25$	−0.952375	−	4.90846i	−0.190475	−	0.981692i
$26$	−4.95986			−0.972708
$27$			13.9243i			2.67973i
$28$		−	0.0887321i		−	0.0167688i
$29$	−8.44483			−1.56817			−0.784083	−	0.620656i	$-0.786866\pi$
$29$	−8.44483			−1.56817			−0.784083	+	0.620656i	$0.786866\pi$
$30$	−5.82441	+	7.06313i	−1.06339	+	1.28955i
$31$	−5.57555			−1.00140			−0.500699	−	0.865621i	$-0.666924\pi$
$31$	−5.57555			−1.00140			−0.500699	+	0.865621i	$0.666924\pi$
$32$			2.10557i			0.372216i
$33$			1.85499i			0.322913i
$34$	−4.44844			−0.762901
$35$	0.405373	+	0.334280i	0.0685205	+	0.0565036i
$36$	−2.76869			−0.461449
$37$			5.18286i			0.852057i	0.904710	+	0.426028i	$0.140088\pi$
$37$			5.18286i			0.852057i	−0.904710	+	0.426028i	$0.859912\pi$
$38$		−	9.12229i		−	1.47983i
$39$	12.5165			2.00425
$40$	−5.22455	−	4.30828i	−0.826074	−	0.681199i
$41$	4.90259			0.765656			0.382828	−	0.923820i	$-0.374950\pi$
$41$	4.90259			0.765656			0.382828	+	0.923820i	$0.374950\pi$
$42$		−	0.962037i		−	0.148446i
$43$		−	3.12584i		−	0.476686i	−0.971181	−	0.238343i	$-0.923396\pi$
$43$		−	3.12584i		−	0.476686i	0.971181	−	0.238343i	$-0.0766043\pi$
$44$	−0.217925			−0.0328535
$45$	10.4305	−	12.6488i	1.55488	−	1.88557i
$46$	6.18714			0.912243
$47$			6.99306i			1.02004i	0.860162	+	0.510021i	$0.170363\pi$
$47$			6.99306i			1.02004i	−0.860162	+	0.510021i	$0.829637\pi$
$48$			9.97138i			1.43924i
$49$	6.94479			0.992112
$50$	6.25204	−	1.21307i	0.884171	−	0.171553i
$51$	11.2259			1.57195
$52$			1.47045i			0.203914i
$53$			12.1609i			1.67042i	0.549929	+	0.835212i	$0.314655\pi$
$53$			12.1609i			1.67042i	−0.549929	+	0.835212i	$0.685345\pi$
$54$	−17.7357			−2.41353
$55$	0.820988	−	0.995593i	0.110702	−	0.134246i
$56$	0.711612			0.0950932
$57$			23.0207i			3.04917i
$58$		−	10.7564i		−	1.41239i
$59$	14.3710			1.87095			0.935475	−	0.353393i	$-0.114972\pi$
$59$	14.3710			1.87095			0.935475	+	0.353393i	$0.114972\pi$
$60$	2.09400	+	1.72676i	0.270334	+	0.222924i
$61$	−7.71724			−0.988092			−0.494046	−	0.869436i	$-0.664482\pi$
$61$	−7.71724			−0.988092			−0.494046	+	0.869436i	$0.664482\pi$
$62$		−	7.10173i		−	0.901920i
$63$			1.72283i			0.217057i
$64$	−8.88625			−1.11078
$65$	−6.71774	−	5.53960i	−0.833233	−	0.687102i
$66$	−2.36276			−0.290835
$67$			2.57664i			0.314787i	0.987536	+	0.157393i	$0.0503090\pi$
$67$			2.57664i			0.314787i	−0.987536	+	0.157393i	$0.949691\pi$
$68$			1.31883i			0.159931i
$69$	−15.6136			−1.87966
$70$	−0.425781	+	0.516334i	−0.0508905	+	0.0617138i
$71$	7.82253			0.928363			0.464182	−	0.885740i	$-0.346348\pi$
$71$	7.82253			0.928363			0.464182	+	0.885740i	$0.346348\pi$
$72$		−	22.2043i		−	2.61680i
$73$		−	8.14734i		−	0.953574i	−0.879019	−	0.476787i	$-0.841801\pi$
$73$		−	8.14734i		−	0.953574i	0.879019	−	0.476787i	$-0.158199\pi$
$74$	−6.60155			−0.767414
$75$	−15.7774	+	3.06125i	−1.82182	+	0.353483i
$76$	−2.70448			−0.310225
$77$			0.135605i			0.0154537i
$78$			15.9426i			1.80515i
$79$	0.388882			0.0437526			0.0218763	−	0.999761i	$-0.493036\pi$
$79$	0.388882			0.0437526			0.0218763	+	0.999761i	$0.493036\pi$
$80$	4.41316	−	5.35173i	0.493406	−	0.598342i
$81$	22.7615			2.52906
$82$			6.24456i			0.689597i
$83$			5.26069i			0.577436i	0.957414	+	0.288718i	$0.0932289\pi$
$83$			5.26069i			0.577436i	−0.957414	+	0.288718i	$0.906771\pi$
$84$	−0.285214			−0.0311195
$85$	−6.02507	−	4.96840i	−0.653510	−	0.538899i
$86$	3.98147			0.429333
$87$			27.1445i			2.91020i
$88$		−	1.74771i		−	0.186307i
$89$	−8.36693			−0.886893			−0.443446	−	0.896301i	$-0.646244\pi$
$89$	−8.36693			−0.886893			−0.443446	+	0.896301i	$0.646244\pi$
$90$	16.1111	+	13.2856i	1.69826	+	1.40042i
$91$	0.914993			0.0959173
$92$		−	1.83430i		−	0.191239i
$93$			17.9217i			1.85839i
$94$	−8.90725			−0.918712
$95$	10.1886	−	12.3554i	1.04532	−	1.26764i
$96$	6.76801			0.690757
$97$		−	8.83287i		−	0.896842i	−0.893822	−	0.448421i	$-0.851987\pi$
$97$		−	8.83287i		−	0.896842i	0.893822	−	0.448421i	$-0.148013\pi$
$98$			8.84576i			0.893556i
$99$	4.23127			0.425258
$100$	−0.359637	−	1.85354i	−0.0359637	−	0.185354i
$101$	1.70238			0.169393			0.0846967	−	0.996407i	$-0.473008\pi$
$101$	1.70238			0.169393			0.0846967	+	0.996407i	$0.473008\pi$
$102$			14.2988i			1.41579i
$103$		−	2.80970i		−	0.276848i	−0.990373	−	0.138424i	$-0.955796\pi$
$103$		−	2.80970i		−	0.276848i	0.990373	−	0.138424i	$-0.0442036\pi$
$104$	−11.7927			−1.15637
$105$	1.07449	−	1.30300i	0.104859	−	0.127160i
$106$	−15.4896			−1.50448
$107$			6.50076i			0.628452i	0.949348	+	0.314226i	$0.101745\pi$
$107$			6.50076i			0.628452i	−0.949348	+	0.314226i	$0.898255\pi$
$108$			5.25810i			0.505961i
$109$	−11.9904			−1.14847			−0.574236	−	0.818690i	$-0.694701\pi$
$109$	−11.9904			−1.14847			−0.574236	+	0.818690i	$0.694701\pi$
$110$	1.26811	+	1.04571i	0.120910	+	0.0997050i
$111$	16.6594			1.58124
$112$			0.728935i			0.0688779i
$113$		−	9.74277i		−	0.916522i	−0.888818	−	0.458261i	$-0.848472\pi$
$113$		−	9.74277i		−	0.916522i	0.888818	−	0.458261i	$-0.151528\pi$
$114$	−29.3221			−2.74626
$115$	8.37999	+	6.91033i	0.781438	+	0.644391i
$116$	−3.18895			−0.296086
$117$		−	28.5504i		−	2.63948i
$118$			18.3048i			1.68509i
$119$	0.820647			0.0752286
$120$	−13.8482	+	16.7934i	−1.26417	+	1.53302i
$121$	−10.6670			−0.969723
$122$		−	9.82965i		−	0.889935i
$123$		−	15.7586i		−	1.42090i
$124$	−2.10544			−0.189075
$125$	9.82275	+	5.33981i	0.878573	+	0.477607i
$126$	−2.19442			−0.195494
$127$		−	10.3084i		−	0.914723i	−0.889281	−	0.457361i	$-0.848795\pi$
$127$		−	10.3084i		−	0.914723i	0.889281	−	0.457361i	$-0.151205\pi$
$128$		−	7.10750i		−	0.628220i
$129$	−10.0475			−0.884633
$130$	7.05593	−	8.55656i	0.618846	−	0.750460i
$131$	19.5189			1.70537			0.852686	−	0.522423i	$-0.174972\pi$
$131$	19.5189			1.70537			0.852686	+	0.522423i	$0.174972\pi$
$132$			0.700485i			0.0609694i
$133$			1.68288i			0.145924i
$134$	−3.28193			−0.283516
$135$	−24.0217	−	19.8088i	−2.06746	−	1.70487i
$136$	−10.5767			−0.906945
$137$		−	3.03314i		−	0.259139i	−0.991570	−	0.129569i	$-0.958641\pi$
$137$		−	3.03314i		−	0.259139i	0.991570	−	0.129569i	$-0.0413595\pi$
$138$		−	19.8875i		−	1.69294i
$139$	−2.29531			−0.194686			−0.0973428	−	0.995251i	$-0.531034\pi$
$139$	−2.29531			−0.194686			−0.0973428	+	0.995251i	$0.531034\pi$
$140$	0.153077	+	0.126231i	0.0129374	+	0.0106685i
$141$	22.4780			1.89299
$142$			9.96376i			0.836140i
$143$		−	2.24722i		−	0.187922i
$144$	22.7448			1.89540
$145$	12.0137	−	14.5687i	0.997682	−	1.20987i
$146$	10.3775			0.858847
$147$		−	22.3229i		−	1.84116i
$148$			1.95716i			0.160877i
$149$	−12.8336			−1.05137			−0.525685	−	0.850679i	$-0.676191\pi$
$149$	−12.8336			−1.05137			−0.525685	+	0.850679i	$0.676191\pi$
$150$	−3.89920	−	20.0961i	−0.318368	−	1.64084i
$151$	−4.69271			−0.381887			−0.190944	−	0.981601i	$-0.561155\pi$
$151$	−4.69271			−0.381887			−0.190944	+	0.981601i	$0.561155\pi$
$152$		−	21.6893i		−	1.75924i
$153$		−	25.6065i		−	2.07016i
$154$	−0.172724			−0.0139185
$155$	7.93182	−	9.61874i	0.637099	−	0.772595i
$156$	4.72650			0.378423
$157$		−	3.54513i		−	0.282933i	−0.989943	−	0.141466i	$-0.954818\pi$
$157$		−	3.54513i		−	0.282933i	0.989943	−	0.141466i	$-0.0451817\pi$
$158$			0.495329i			0.0394063i
$159$	39.0891			3.09997
$160$	−3.63246	−	2.99540i	−0.287171	−	0.236807i
$161$	−1.14140			−0.0899550
$162$			28.9919i			2.27782i
$163$			2.45347i			0.192171i	0.995373	+	0.0960853i	$0.0306322\pi$
$163$			2.45347i			0.192171i	−0.995373	+	0.0960853i	$0.969368\pi$
$164$	1.85132			0.144564
$165$	−3.20017	−	2.63893i	−0.249133	−	0.205440i
$166$	−6.70068			−0.520074
$167$			6.34224i			0.490777i	0.969425	+	0.245389i	$0.0789156\pi$
$167$			6.34224i			0.490777i	−0.969425	+	0.245389i	$0.921084\pi$
$168$		−	2.28736i		−	0.176474i
$169$	−2.16303			−0.166387
$170$	6.32839	−	7.67429i	0.485365	−	0.588591i
$171$	52.5105			4.01558
$172$		−	1.18038i		−	0.0900034i
$173$		−	7.16447i		−	0.544705i	−0.962198	−	0.272352i	$-0.912198\pi$
$173$		−	7.16447i		−	0.544705i	0.962198	−	0.272352i	$-0.0878017\pi$
$174$	−34.5747			−2.62110
$175$	−1.15337	+	0.223786i	−0.0871868	+	0.0169166i
$176$	1.79026			0.134946
$177$		−	46.1933i		−	3.47210i
$178$		−	10.6572i		−	0.798790i
$179$	7.39749			0.552914			0.276457	−	0.961026i	$-0.410840\pi$
$179$	7.39749			0.552914			0.276457	+	0.961026i	$0.410840\pi$
$180$	3.93876	−	4.77645i	0.293578	−	0.356015i
$181$	−20.1924			−1.50089			−0.750445	−	0.660933i	$-0.770161\pi$
$181$	−20.1924			−1.50089			−0.750445	+	0.660933i	$0.770161\pi$
$182$			1.16545i			0.0863889i
$183$			24.8058i			1.83370i
$184$	14.7107			1.08448
$185$	−8.94128	−	7.37318i	−0.657376	−	0.542087i
$186$	−22.8273			−1.67378
$187$		−	2.01550i		−	0.147388i
$188$			2.64073i			0.192595i
$189$	3.27188			0.237994
$190$	15.7374	+	12.9774i	1.14171	+	0.941482i
$191$	−20.5634			−1.48791			−0.743957	−	0.668227i	$-0.767053\pi$
$191$	−20.5634			−1.48791			−0.743957	+	0.668227i	$0.767053\pi$
$192$			28.5634i			2.06138i
$193$		−	2.68844i		−	0.193518i	−0.995308	−	0.0967591i	$-0.969152\pi$
$193$		−	2.68844i		−	0.193518i	0.995308	−	0.0967591i	$-0.0308476\pi$
$194$	11.2507			0.807750
$195$	−17.8061	+	21.5931i	−1.27512	+	1.54631i
$196$	2.62250			0.187321
$197$		−	1.00000i		−	0.0712470i
$197$		−	1.00000i		−	0.0712470i
$198$			5.38948i			0.383014i
$199$	5.33760			0.378373			0.189186	−	0.981941i	$-0.439415\pi$
$199$	5.33760			0.378373			0.189186	+	0.981941i	$0.439415\pi$
$200$	14.8650	−	2.88421i	1.05111	−	0.203944i
$201$	8.28218			0.584180
$202$			2.16837i			0.152566i
$203$			1.98434i			0.139273i
$204$	4.23915			0.296800
$205$	−6.97447	+	8.45777i	−0.487118	+	0.590717i
$206$	3.57878			0.249346
$207$			35.6149i			2.47541i
$208$		−	12.0797i		−	0.837579i
$209$	4.13313			0.285895
$210$	1.65967	+	1.36860i	0.114528	+	0.0944425i
$211$	−27.4653			−1.89079			−0.945395	−	0.325927i	$-0.894324\pi$
$211$	−27.4653			−1.89079			−0.945395	+	0.325927i	$0.894324\pi$
$212$			4.59220i			0.315393i
$213$		−	25.1442i		−	1.72285i
$214$	−8.28019			−0.566022
$215$	5.39259	+	4.44685i	0.367771	+	0.303272i
$216$	−42.1689			−2.86923
$217$			1.31012i			0.0889370i
$218$		−	15.2725i		−	1.03438i
$219$	−26.1883			−1.76964
$220$	0.310022	−	0.375957i	0.0209017	−	0.0253470i
$221$	−13.5996			−0.914805
$222$			21.2196i			1.42416i
$223$			24.1738i			1.61880i	0.587260	+	0.809399i	$0.300207\pi$
$223$			24.1738i			1.61880i	−0.587260	+	0.809399i	$0.699793\pi$
$224$	0.494760			0.0330576
$225$	6.98275	+	35.9885i	0.465517	+	2.39923i
$226$	12.4096			0.825476
$227$		−	17.8340i		−	1.18368i	−0.806054	−	0.591842i	$-0.798401\pi$
$227$		−	17.8340i		−	1.18368i	0.806054	−	0.591842i	$-0.201599\pi$
$228$			8.69309i			0.575714i
$229$	26.4544			1.74816			0.874079	−	0.485784i	$-0.161466\pi$
$229$	26.4544			1.74816			0.874079	+	0.485784i	$0.161466\pi$
$230$	−8.80187	+	10.6738i	−0.580378	+	0.703811i
$231$	0.435880			0.0286788
$232$		−	25.5747i		−	1.67906i
$233$			30.1629i			1.97604i	0.154335	+	0.988019i	$0.450676\pi$
$233$			30.1629i			1.97604i	−0.154335	+	0.988019i	$0.549324\pi$
$234$	36.3654			2.37728
$235$	−12.0642	−	9.94838i	−0.786980	−	0.648961i
$236$	5.42680			0.353255
$237$		−	1.25000i		−	0.0811959i
$238$			1.04528i			0.0677554i
$239$	−4.58904			−0.296840			−0.148420	−	0.988924i	$-0.547419\pi$
$239$	−4.58904			−0.296840			−0.148420	+	0.988924i	$0.547419\pi$
$240$	−17.2023	−	14.1854i	−1.11040	−	0.915661i
$241$	23.5615			1.51773			0.758864	−	0.651249i	$-0.225755\pi$
$241$	23.5615			1.51773			0.758864	+	0.651249i	$0.225755\pi$
$242$		−	13.5868i		−	0.873391i
$243$		−	31.3902i		−	2.01368i
$244$	−2.91419			−0.186562
$245$	−9.87971	+	11.9809i	−0.631191	+	0.765431i
$246$	20.0721			1.27975
$247$		−	27.8882i		−	1.77448i
$248$		−	16.8852i		−	1.07221i
$249$	16.9096			1.07160
$250$	−6.80146	+	12.5115i	−0.430162	+	0.791297i
$251$	12.0057			0.757794			0.378897	−	0.925439i	$-0.376304\pi$
$251$	12.0057			0.757794			0.378897	+	0.925439i	$0.376304\pi$
$252$			0.650578i			0.0409826i
$253$			2.80327i			0.176240i
$254$	13.1301			0.823855
$255$	−15.9701	+	19.3666i	−1.00009	+	1.21278i
$256$	−8.71948			−0.544967
$257$			14.1205i			0.880812i	0.897799	+	0.440406i	$0.145165\pi$
$257$			14.1205i			0.880812i	−0.897799	+	0.440406i	$0.854835\pi$
$258$		−	12.7978i		−	0.796754i
$259$	1.21785			0.0756736
$260$	−2.53676	−	2.09187i	−0.157323	−	0.129732i
$261$	61.9170			3.83257
$262$			24.8617i			1.53596i
$263$			10.3347i			0.637268i	0.947878	+	0.318634i	$0.103224\pi$
$263$			10.3347i			0.637268i	−0.947878	+	0.318634i	$0.896776\pi$
$264$	−5.61774			−0.345748
$265$	−20.9795	−	17.3001i	−1.28876	−	1.06274i
$266$	−2.14352			−0.131428
$267$			26.8941i			1.64589i
$268$			0.972993i			0.0594350i
$269$	15.0254			0.916112			0.458056	−	0.888923i	$-0.348546\pi$
$269$	15.0254			0.916112			0.458056	+	0.888923i	$0.348546\pi$
$270$	25.2310	−	30.5970i	1.53551	−	1.86208i
$271$	−3.06893			−0.186424			−0.0932120	−	0.995646i	$-0.529713\pi$
$271$	−3.06893			−0.186424			−0.0932120	+	0.995646i	$0.529713\pi$
$272$		−	10.8342i		−	0.656919i
$273$		−	2.94109i		−	0.178003i
$274$	3.86339			0.233396
$275$	0.549616	+	2.83268i	0.0331431	+	0.170817i
$276$	−5.89604			−0.354900
$277$			32.3023i			1.94086i	0.241385	+	0.970429i	$0.422398\pi$
$277$			32.3023i			1.94086i	−0.241385	+	0.970429i	$0.577602\pi$
$278$		−	2.92360i		−	0.175346i
$279$	40.8796			2.44740
$280$	−1.01235	+	1.22765i	−0.0604992	+	0.0733660i
$281$	−29.3552			−1.75118			−0.875592	−	0.483052i	$-0.839528\pi$
$281$	−29.3552			−1.75118			−0.875592	+	0.483052i	$0.839528\pi$
$282$			28.6309i			1.70494i
$283$		−	15.3472i		−	0.912298i	−0.889903	−	0.456149i	$-0.849228\pi$
$283$		−	15.3472i		−	0.912298i	0.889903	−	0.456149i	$-0.150772\pi$
$284$	2.95395			0.175285
$285$	−39.7144	−	32.7494i	−2.35248	−	1.93991i
$286$	2.86234			0.169254
$287$		−	1.15200i		−	0.0680001i
$288$		−	15.4379i		−	0.909689i
$289$	4.80271			0.282512
$290$	18.5566	+	15.3021i	1.08968	+	0.898573i
$291$	−28.3918			−1.66436
$292$		−	3.07661i		−	0.180045i
$293$			25.7169i			1.50240i	0.660075	+	0.751199i	$0.270524\pi$
$293$			25.7169i			1.50240i	−0.660075	+	0.751199i	$0.729476\pi$
$294$	28.4332			1.65826
$295$	−20.4443	+	24.7924i	−1.19032	+	1.44347i
$296$	−15.6960			−0.912310
$297$		−	8.03572i		−	0.466280i
$298$		−	16.3465i		−	0.946928i
$299$	18.9150			1.09388
$300$	−5.95789	+	1.15599i	−0.343979	+	0.0667412i
$301$	−0.734500			−0.0423359
$302$		−	5.97723i		−	0.343951i
$303$		−	5.47202i		−	0.314360i
$304$	22.2173			1.27425
$305$	10.9786	−	13.3135i	0.628633	−	0.762329i
$306$	32.6157			1.86452
$307$		−	2.60692i		−	0.148785i	−0.997229	−	0.0743924i	$-0.976298\pi$
$307$		−	2.60692i		−	0.148785i	0.997229	−	0.0743924i	$-0.0237017\pi$
$308$			0.0512074i			0.00291781i
$309$	−9.03130			−0.513773
$310$	12.2516	+	10.1030i	0.695846	+	0.573810i
$311$	−19.8431			−1.12520			−0.562599	−	0.826730i	$-0.690199\pi$
$311$	−19.8431			−1.12520			−0.562599	+	0.826730i	$0.690199\pi$
$312$			37.9055i			2.14598i
$313$		−	18.1393i		−	1.02529i	−0.858599	−	0.512647i	$-0.828665\pi$
$313$		−	18.1393i		−	1.02529i	0.858599	−	0.512647i	$-0.171335\pi$
$314$	4.51553			0.254826
$315$	−2.97217	−	2.45092i	−0.167463	−	0.138094i
$316$	0.146850			0.00826095
$317$		−	5.29542i		−	0.297420i	−0.988881	−	0.148710i	$-0.952488\pi$
$317$		−	5.29542i		−	0.297420i	0.988881	−	0.148710i	$-0.0475122\pi$
$318$			49.7888i			2.79202i
$319$	4.87352			0.272865
$320$	12.6416	−	15.3302i	0.706689	−	0.856985i
$321$	20.8956			1.16628
$322$		−	1.45383i		−	0.0810189i
$323$		−	25.0126i		−	1.39174i
$324$	8.59522			0.477512
$325$	19.1134	−	3.70852i	1.06022	−	0.205712i
$326$	−3.12505			−0.173081
$327$			38.5412i			2.13133i
$328$			14.8472i			0.819800i
$329$	1.64321			0.0905929
$330$	3.36127	−	4.07614i	0.185032	−	0.224384i
$331$	29.2462			1.60752			0.803760	−	0.594954i	$-0.202830\pi$
$331$	29.2462			1.60752			0.803760	+	0.594954i	$0.202830\pi$
$332$			1.98655i			0.109026i
$333$		−	38.0004i		−	2.08241i
$334$	−8.07828			−0.442024
$335$	−4.44512	−	3.66555i	−0.242863	−	0.200270i
$336$	2.34304			0.127823
$337$		−	23.6870i		−	1.29031i	−0.764051	−	0.645156i	$-0.776793\pi$
$337$		−	23.6870i		−	1.29031i	0.764051	−	0.645156i	$-0.223207\pi$
$338$		−	2.75511i		−	0.149858i
$339$	−31.3165			−1.70088
$340$	−2.27519	−	1.87617i	−0.123390	−	0.101750i
$341$	3.21766			0.174246
$342$			66.8840i			3.61667i
$343$		−	3.27670i		−	0.176925i
$344$	9.46642			0.510395
$345$	22.2121	−	26.9361i	1.19586	−	1.45019i
$346$	9.12558			0.490594
$347$			7.92141i			0.425244i	0.977135	+	0.212622i	$0.0682002\pi$
$347$			7.92141i			0.425244i	−0.977135	+	0.212622i	$0.931800\pi$
$348$			10.2503i			0.549475i
$349$	25.6673			1.37394			0.686969	−	0.726687i	$-0.258941\pi$
$349$	25.6673			1.37394			0.686969	+	0.726687i	$0.258941\pi$
$350$	−0.285042	−	1.46908i	−0.0152361	−	0.0785258i
$351$	−54.2208			−2.89409
$352$		−	1.21513i		−	0.0647665i
$353$		−	13.2644i		−	0.705995i	−0.935624	−	0.352997i	$-0.885162\pi$
$353$		−	13.2644i		−	0.705995i	0.935624	−	0.352997i	$-0.114838\pi$
$354$	58.8376			3.12718
$355$	−11.1284	+	13.4951i	−0.590634	+	0.716247i
$356$	−3.15953			−0.167455
$357$		−	2.63783i		−	0.139609i
$358$			9.42238i			0.497988i
$359$	5.67509			0.299520			0.149760	−	0.988722i	$-0.452150\pi$
$359$	5.67509			0.299520			0.149760	+	0.988722i	$0.452150\pi$
$360$	38.3061	+	31.5880i	2.01891	+	1.66484i
$361$	32.2926			1.69961
$362$		−	25.7196i		−	1.35179i
$363$			34.2871i			1.79961i
$364$	0.345520			0.0181102
$365$	14.0555	+	11.5905i	0.735698	+	0.606673i
$366$	−31.5958			−1.65154
$367$			18.8576i			0.984361i	0.870493	+	0.492180i	$0.163800\pi$
$367$			18.8576i			0.984361i	−0.870493	+	0.492180i	$0.836200\pi$
$368$			15.0688i			0.785514i
$369$	−35.9455			−1.87125
$370$	9.39141	−	11.3887i	0.488236	−	0.592073i
$371$	2.85752			0.148355
$372$			6.76760i			0.350884i
$373$			22.6052i			1.17045i	0.810870	+	0.585226i	$0.198994\pi$
$373$			22.6052i			1.17045i	−0.810870	+	0.585226i	$0.801006\pi$
$374$	2.56720			0.132747
$375$	17.1639	−	31.5736i	0.886342	−	1.63045i
$376$	−21.1781			−1.09217
$377$		−	32.8840i		−	1.69361i
$378$			4.16748i			0.214352i
$379$	13.2151			0.678815			0.339408	−	0.940639i	$-0.389773\pi$
$379$	13.2151			0.678815			0.339408	+	0.940639i	$0.389773\pi$
$380$	3.84741	−	4.66567i	0.197368	−	0.239344i
$381$	−33.1346			−1.69754
$382$		−	26.1921i		−	1.34011i
$383$		−	9.06658i		−	0.463281i	−0.972801	−	0.231640i	$-0.925591\pi$
$383$		−	9.06658i		−	0.463281i	0.972801	−	0.231640i	$-0.0744092\pi$
$384$	−22.8459			−1.16585
$385$	−0.233941	−	0.192913i	−0.0119227	−	0.00983176i
$386$	3.42434			0.174294
$387$			22.9185i			1.16501i
$388$		−	3.33548i		−	0.169333i
$389$	−24.1714			−1.22554			−0.612768	−	0.790263i	$-0.709944\pi$
$389$	−24.1714			−1.22554			−0.612768	+	0.790263i	$0.709944\pi$
$390$	−27.5036	−	22.6801i	−1.39270	−	1.14845i
$391$	16.9647			0.857940
$392$			21.0319i			1.06227i
$393$		−	62.7402i		−	3.16482i
$394$	1.27373			0.0641694
$395$	−0.553226	+	0.670884i	−0.0278358	+	0.0337559i
$396$	1.59782			0.0802932
$397$			10.7768i			0.540870i	0.962738	+	0.270435i	$0.0871675\pi$
$397$			10.7768i			0.540870i	−0.962738	+	0.270435i	$0.912833\pi$
$398$			6.79865i			0.340785i
$399$	5.40933			0.270805
$400$	2.95442	+	15.2268i	0.147721	+	0.761342i
$401$	0.512588			0.0255974			0.0127987	−	0.999918i	$-0.495926\pi$
$401$	0.512588			0.0255974			0.0127987	+	0.999918i	$0.495926\pi$
$402$			10.5492i			0.526148i
$403$		−	21.7111i		−	1.08150i
$404$	0.642855			0.0319832
$405$	−32.3807	+	39.2673i	−1.60901	+	1.95121i
$406$	−2.52750			−0.125438
$407$		−	2.99103i		−	0.148260i
$408$			33.9971i			1.68311i
$409$	−29.1701			−1.44237			−0.721183	−	0.692744i	$-0.756402\pi$
$409$	−29.1701			−1.44237			−0.721183	+	0.692744i	$0.756402\pi$
$410$	−10.7729	−	8.88356i	−0.532035	−	0.438728i
$411$	−9.74953			−0.480909
$412$		−	1.06100i		−	0.0522717i
$413$		−	3.37686i		−	0.166164i
$414$	−45.3637			−2.22950
$415$	−9.07555	−	7.48390i	−0.445501	−	0.367370i
$416$	−8.19905			−0.401991
$417$			7.37789i			0.361297i
$418$			5.26448i			0.257494i
$419$	7.18784			0.351149			0.175574	−	0.984466i	$-0.443822\pi$
$419$	7.18784			0.351149			0.175574	+	0.984466i	$0.443822\pi$
$420$	0.405748	−	0.492041i	0.0197985	−	0.0240092i
$421$	16.3859			0.798598			0.399299	−	0.916821i	$-0.369254\pi$
$421$	16.3859			0.798598			0.399299	+	0.916821i	$0.369254\pi$
$422$		−	34.9833i		−	1.70296i
$423$		−	51.2727i		−	2.49296i
$424$	−36.8284			−1.78855
$425$	17.1426	−	3.32613i	0.831539	−	0.161341i
$426$	32.0268			1.55171
$427$			1.81337i			0.0877552i
$428$			2.45482i			0.118658i
$429$	−7.22330			−0.348744
$430$	−5.66407	+	6.86868i	−0.273145	+	0.331237i
$431$	−24.6531			−1.18750			−0.593750	−	0.804650i	$-0.702353\pi$
$431$	−24.6531			−1.18750			−0.593750	+	0.804650i	$0.702353\pi$
$432$		−	43.1954i		−	2.07824i
$433$			16.5810i			0.796831i	0.917205	+	0.398415i	$0.130440\pi$
$433$			16.5810i			0.796831i	−0.917205	+	0.398415i	$0.869560\pi$
$434$	−1.66874			−0.0801021
$435$	−46.8287	−	38.6160i	−2.24526	−	1.85149i
$436$	−4.52783			−0.216844
$437$			34.7889i			1.66418i
$438$		−	33.3567i		−	1.59384i
$439$	−14.3127			−0.683110			−0.341555	−	0.939862i	$-0.610954\pi$
$439$	−14.3127			−0.683110			−0.341555	+	0.939862i	$0.610954\pi$
$440$	3.01509	+	2.48631i	0.143739	+	0.118530i
$441$	−50.9187			−2.42470
$442$		−	17.3221i		−	0.823929i
$443$		−	1.91828i		−	0.0911403i	−0.998961	−	0.0455702i	$-0.985490\pi$
$443$		−	1.91828i		−	0.0911403i	0.998961	−	0.0455702i	$-0.0145105\pi$
$444$	6.29095			0.298555
$445$	11.9029	−	14.4343i	0.564250	−	0.684252i
$446$	−30.7908			−1.45799
$447$			41.2515i			1.95113i
$448$			2.08806i			0.0986516i
$449$	−21.6287			−1.02072			−0.510360	−	0.859961i	$-0.670488\pi$
$449$	−21.6287			−1.02072			−0.510360	+	0.859961i	$0.670488\pi$
$450$	−45.8395	+	8.89412i	−2.16090	+	0.419273i
$451$	−2.82929			−0.133226
$452$		−	3.67907i		−	0.173049i
$453$			15.0839i			0.708705i
$454$	22.7157			1.06610
$455$	−1.30168	+	1.57851i	−0.0610235	+	0.0740018i
$456$	−69.7168			−3.26479
$457$			19.6638i			0.919835i	0.887962	+	0.459917i	$0.152121\pi$
$457$			19.6638i			0.919835i	−0.887962	+	0.459917i	$0.847879\pi$
$458$			33.6957i			1.57450i
$459$	−48.6301			−2.26986
$460$	3.16446	+	2.60948i	0.147544	+	0.121668i
$461$	10.3420			0.481676			0.240838	−	0.970565i	$-0.422578\pi$
$461$	10.3420			0.481676			0.240838	+	0.970565i	$0.422578\pi$
$462$			0.555192i			0.0258299i
$463$			10.9518i			0.508973i	0.967076	+	0.254486i	$0.0819064\pi$
$463$			10.9518i			0.508973i	−0.967076	+	0.254486i	$0.918094\pi$
$464$	26.1972			1.21618
$465$	−30.9178	−	25.4955i	−1.43378	−	1.18233i
$466$	−38.4193			−1.77974
$467$			20.9307i			0.968556i	0.874914	+	0.484278i	$0.160918\pi$
$467$			20.9307i			0.968556i	−0.874914	+	0.484278i	$0.839082\pi$
$468$		−	10.7812i		−	0.498362i
$469$	0.605450			0.0279571
$470$	12.6715	−	15.3665i	0.584494	−	0.708802i
$471$	−11.3952			−0.525065
$472$			43.5218i			2.00325i
$473$			1.80393i			0.0829446i
$474$	1.59215			0.0731300
$475$	6.82080	+	35.1538i	0.312960	+	1.61297i
$476$	0.309893			0.0142039
$477$		−	89.1627i		−	4.08248i
$478$		−	5.84518i		−	0.267352i
$479$	20.8556			0.952916			0.476458	−	0.879197i	$-0.341920\pi$
$479$	20.8556			0.952916			0.476458	+	0.879197i	$0.341920\pi$
$480$	−9.62823	+	11.6759i	−0.439466	+	0.532931i
$481$	−20.1819			−0.920216
$482$			30.0109i			1.36696i
$483$			3.66884i			0.166938i
$484$	−4.02806			−0.183094
$485$	15.2381	+	12.5657i	0.691928	+	0.570579i
$486$	39.9825			1.81364
$487$		−	27.2853i		−	1.23642i	−0.786015	−	0.618208i	$-0.787859\pi$
$487$		−	27.2853i		−	1.23642i	0.786015	−	0.618208i	$-0.212141\pi$
$488$		−	23.3712i		−	1.05796i
$489$	7.88627			0.356630
$490$	−15.2604	−	12.5840i	−0.689393	−	0.568489i
$491$	15.6305			0.705395			0.352697	−	0.935737i	$-0.385265\pi$
$491$	15.6305			0.705395			0.352697	+	0.935737i	$0.385265\pi$
$492$		−	5.95076i		−	0.268281i
$493$		−	29.4933i		−	1.32831i
$494$	35.5219			1.59821
$495$	−6.01943	+	7.29963i	−0.270553	+	0.328094i
$496$	17.2963			0.776625
$497$		−	1.83811i		−	0.0824506i
$498$			21.5382i			0.965150i
$499$	22.7946			1.02042			0.510212	−	0.860048i	$-0.329567\pi$
$499$	22.7946			1.02042			0.510212	+	0.860048i	$0.329567\pi$
$500$	3.70928	+	2.01642i	0.165884	+	0.0901772i
$501$	20.3861			0.910783
$502$			15.2920i			0.682515i
$503$			21.7516i			0.969858i	0.874554	+	0.484929i	$0.161155\pi$
$503$			21.7516i			0.969858i	−0.874554	+	0.484929i	$0.838845\pi$
$504$	−5.21750			−0.232406
$505$	−2.42182	+	2.93689i	−0.107770	+	0.130690i
$506$	−3.57060			−0.158733
$507$			6.95270i			0.308780i
$508$		−	3.89267i		−	0.172709i
$509$	36.9506			1.63781			0.818904	−	0.573930i	$-0.194582\pi$
$509$	36.9506			1.63781			0.818904	+	0.573930i	$0.194582\pi$
$510$	−24.6677	−	20.3415i	−1.09230	−	0.900739i
$511$	−1.91444			−0.0846896
$512$		−	25.3212i		−	1.11905i
$513$		−	99.7242i		−	4.40293i
$514$	−17.9856			−0.793312
$515$	4.84718	+	3.99709i	0.213592	+	0.176133i
$516$	−3.79414			−0.167028
$517$		−	4.03570i		−	0.177490i
$518$			1.55121i			0.0681562i
$519$	−23.0290			−1.01086
$520$	16.7763	−	20.3443i	0.735691	−	0.892155i
$521$	0.0246447			0.00107970			0.000539852	−	1.00000i	$-0.499828\pi$
$521$	0.0246447			0.00107970			0.000539852		1.00000i	$0.499828\pi$
$522$			78.8653i			3.45184i
$523$			21.2265i			0.928168i	0.885791	+	0.464084i	$0.153616\pi$
$523$			21.2265i			0.928168i	−0.885791	+	0.464084i	$0.846384\pi$
$524$	7.37074			0.321992
$525$	0.719322	+	3.70733i	0.0313938	+	0.161801i
$526$	−13.1636			−0.573962
$527$		−	19.4724i		−	0.848231i
$528$		−	5.75449i		−	0.250432i
$529$	−0.595377			−0.0258860
$530$	22.0356	−	26.7221i	0.957167	−	1.16073i
$531$	−105.368			−4.57256
$532$			0.635489i			0.0275520i
$533$			19.0906i			0.826904i
$534$	−34.2557			−1.48239
$535$	−11.2149	−	9.24804i	−0.484861	−	0.399827i
$536$	−7.80319			−0.337047
$537$		−	23.7780i		−	1.02610i
$538$			19.1382i			0.825106i
$539$	−4.00784			−0.172630
$540$	−9.07108	−	7.48022i	−0.390357	−	0.321897i
$541$	−25.2530			−1.08571			−0.542855	−	0.839827i	$-0.682657\pi$
$541$	−25.2530			−1.08571			−0.542855	+	0.839827i	$0.682657\pi$
$542$		−	3.90897i		−	0.167905i
$543$			64.9051i			2.78535i
$544$	−7.35363			−0.315284
$545$	17.0576	−	20.6854i	0.730669	−	0.886065i
$546$	3.74615			0.160320
$547$		−	12.9296i		−	0.552830i	−0.961038	−	0.276415i	$-0.910854\pi$
$547$		−	12.9296i		−	0.552830i	0.961038	−	0.276415i	$-0.0891464\pi$
$548$		−	1.14538i		−	0.0489281i
$549$	56.5823			2.41488
$550$	−3.60806	+	0.700061i	−0.153848	+	0.0298507i
$551$	60.4809			2.57657
$552$		−	47.2850i		−	2.01258i
$553$		−	0.0913781i		−	0.00388579i
$554$	−41.1443			−1.74806
$555$	−23.6998	+	28.7402i	−1.00600	+	1.21996i
$556$	−0.866757			−0.0367587
$557$		−	9.53791i		−	0.404134i	−0.979372	−	0.202067i	$-0.935234\pi$
$557$		−	9.53791i		−	0.404134i	0.979372	−	0.202067i	$-0.0647659\pi$
$558$			52.0694i			2.20427i
$559$	12.1719			0.514818
$560$	−1.25753	−	1.03699i	−0.0531404	−	0.0438208i
$561$	−6.47850			−0.273522
$562$		−	37.3905i		−	1.57722i
$563$		−	16.4517i		−	0.693356i	−0.937984	−	0.346678i	$-0.887310\pi$
$563$		−	16.4517i		−	0.693356i	0.937984	−	0.346678i	$-0.112690\pi$
$564$	8.48817			0.357417
$565$	16.8079	+	13.8601i	0.707112	+	0.583100i
$566$	19.5482			0.821671
$567$		−	5.34842i		−	0.224613i
$568$			23.6900i			0.994012i
$569$	−33.1531			−1.38985			−0.694926	−	0.719082i	$-0.744563\pi$
$569$	−33.1531			−1.38985			−0.694926	+	0.719082i	$0.744563\pi$
$570$	41.7138	−	50.5853i	1.74720	−	2.11879i
$571$	−21.2096			−0.887595			−0.443798	−	0.896127i	$-0.646369\pi$
$571$	−21.2096			−0.887595			−0.443798	+	0.896127i	$0.646369\pi$
$572$		−	0.848596i		−	0.0354816i
$573$			66.0976i			2.76127i
$574$	1.46733			0.0612450
$575$	−23.8429	+	4.62617i	−0.994317	+	0.192925i
$576$	65.1534			2.71472
$577$			3.39956i			0.141526i	0.997493	+	0.0707628i	$0.0225433\pi$
$577$			3.39956i			0.141526i	−0.997493	+	0.0707628i	$0.977457\pi$
$578$			6.11733i			0.254448i
$579$	−8.64155			−0.359130
$580$	4.53662	−	5.50145i	0.188373	−	0.228435i
$581$	1.23614			0.0512837
$582$		−	36.1634i		−	1.49902i
$583$		−	7.01805i		−	0.290658i
$584$	24.6737			1.02101
$585$	49.2540	+	40.6160i	2.03640	+	1.67926i
$586$	−32.7563			−1.35315
$587$			37.5978i			1.55183i	0.630839	+	0.775914i	$0.282711\pi$
$587$			37.5978i			1.55183i	−0.630839	+	0.775914i	$0.717289\pi$
$588$		−	8.42958i		−	0.347630i
$589$	39.9315			1.64535
$590$	−31.5787	−	26.0405i	−1.30008	−	1.07207i
$591$	−3.21433			−0.132220
$592$		−	16.0781i		−	0.660804i
$593$			17.6880i			0.726360i	0.931719	+	0.363180i	$0.118309\pi$
$593$			17.6880i			0.726360i	−0.931719	+	0.363180i	$0.881691\pi$
$594$	10.2353			0.419960
$595$	−1.16746	+	1.41575i	−0.0478611	+	0.0580401i
$596$	−4.84624			−0.198510
$597$		−	17.1568i		−	0.702183i
$598$			24.0925i			0.985217i
$599$	−2.70489			−0.110519			−0.0552595	−	0.998472i	$-0.517599\pi$
$599$	−2.70489			−0.110519			−0.0552595	+	0.998472i	$0.517599\pi$
$600$	−9.27081	−	47.7810i	−0.378479	−	1.95065i
$601$	−26.9989			−1.10131			−0.550654	−	0.834733i	$-0.685622\pi$
$601$	−26.9989			−1.10131			−0.550654	+	0.834733i	$0.685622\pi$
$602$		−	0.935552i		−	0.0381302i
$603$		−	18.8918i		−	0.769332i
$604$	−1.77206			−0.0721043
$605$	15.1749	−	18.4022i	0.616947	−	0.748157i
$606$	6.96986			0.283131
$607$			6.45409i			0.261964i	0.991385	+	0.130982i	$0.0418129\pi$
$607$			6.45409i			0.261964i	−0.991385	+	0.130982i	$0.958187\pi$
$608$		−	15.0799i		−	0.611570i
$609$	6.37833			0.258463
$610$	16.9578	+	13.9837i	0.686600	+	0.566185i
$611$	−27.2308			−1.10164
$612$		−	9.66956i		−	0.390869i
$613$			9.63640i			0.389211i	0.980882	+	0.194605i	$0.0623426\pi$
$613$			9.63640i			0.389211i	−0.980882	+	0.194605i	$0.937657\pi$
$614$	3.32050			0.134005
$615$	27.1861	+	22.4183i	1.09625	+	0.903992i
$616$	−0.410672			−0.0165465
$617$		−	8.69198i		−	0.349926i	−0.984575	−	0.174963i	$-0.944019\pi$
$617$		−	8.69198i		−	0.349926i	0.984575	−	0.174963i	$-0.0559806\pi$
$618$		−	11.5034i		−	0.462735i
$619$	22.1646			0.890870			0.445435	−	0.895314i	$-0.353049\pi$
$619$	22.1646			0.890870			0.445435	+	0.895314i	$0.353049\pi$
$620$	2.99522	−	3.63224i	0.120291	−	0.145874i
$621$	67.6373			2.71419
$622$		−	25.2747i		−	1.01342i
$623$			1.96603i			0.0787675i
$624$	−38.8283			−1.55438
$625$	−23.1860	+	9.34939i	−0.927439	+	0.373976i
$626$	23.1045			0.923443
$627$		−	13.2853i		−	0.530562i
$628$		−	1.33872i		−	0.0534206i
$629$	−18.1009			−0.721732
$630$	3.12180	−	3.78573i	0.124375	−	0.150827i
$631$	−2.65768			−0.105800			−0.0529002	−	0.998600i	$-0.516847\pi$
$631$	−2.65768			−0.105800			−0.0529002	+	0.998600i	$0.516847\pi$
$632$			1.17770i			0.0468466i
$633$			88.2827i			3.50892i
$634$	6.74492			0.267875
$635$	17.7837	+	14.6648i	0.705723	+	0.581955i
$636$	14.7608			0.585306
$637$			27.0428i			1.07148i
$638$			6.20753i			0.245759i
$639$	−57.3543			−2.26890
$640$	12.2616	+	10.1112i	0.484682	+	0.399680i
$641$	27.4000			1.08224			0.541118	−	0.840946i	$-0.318001\pi$
$641$	27.4000			1.08224			0.541118	+	0.840946i	$0.318001\pi$
$642$			26.6153i			1.05042i
$643$		−	26.5633i		−	1.04755i	−0.851856	−	0.523777i	$-0.824523\pi$
$643$		−	26.5633i		−	1.04755i	0.851856	−	0.523777i	$-0.175477\pi$
$644$	−0.431017			−0.0169844
$645$	14.2936	−	17.3336i	0.562812	−	0.682509i
$646$	31.8592			1.25349
$647$			25.6395i			1.00799i	0.863706	+	0.503996i	$0.168137\pi$
$647$			25.6395i			1.00799i	−0.863706	+	0.503996i	$0.831863\pi$
$648$			68.9318i			2.70790i
$649$	−8.29354			−0.325550
$650$	4.72364	+	24.3453i	0.185277	+	0.954900i
$651$	4.21118			0.165049
$652$			0.926482i			0.0362838i
$653$			17.4067i			0.681179i	0.940212	+	0.340589i	$0.110627\pi$
$653$			17.4067i			0.681179i	−0.940212	+	0.340589i	$0.889373\pi$
$654$	−49.0909			−1.91961
$655$	−27.7677	+	33.6733i	−1.08497	+	1.31572i
$656$	−15.2086			−0.593797
$657$			59.7358i			2.33052i
$658$			2.09299i			0.0815934i
$659$	−18.2733			−0.711827			−0.355913	−	0.934519i	$-0.615830\pi$
$659$	−18.2733			−0.711827			−0.355913	+	0.934519i	$0.615830\pi$
$660$	−1.20845	−	0.996515i	−0.0470389	−	0.0387893i
$661$	13.4912			0.524748			0.262374	−	0.964966i	$-0.415495\pi$
$661$	13.4912			0.524748			0.262374	+	0.964966i	$0.415495\pi$
$662$			37.2517i			1.44783i
$663$			43.7135i			1.69769i
$664$	−15.9317			−0.618269
$665$	−2.90324	−	2.39407i	−0.112583	−	0.0928382i
$666$	48.4021			1.87554
$667$			41.0208i			1.58833i
$668$			2.39496i			0.0926639i
$669$	77.7026			3.00416
$670$	4.66890	−	5.66187i	0.180375	−	0.218737i
$671$	4.45363			0.171930
$672$		−	1.59033i		−	0.0613481i
$673$		−	24.5543i		−	0.946497i	−0.880929	−	0.473249i	$-0.843081\pi$
$673$		−	24.5543i		−	0.946497i	0.880929	−	0.473249i	$-0.156919\pi$
$674$	30.1707			1.16213
$675$	68.3468	−	13.2611i	2.63067	−	0.510422i
$676$	−0.816805			−0.0314156
$677$		−	21.6592i		−	0.832429i	−0.909266	−	0.416215i	$-0.863356\pi$
$677$		−	21.6592i		−	0.832429i	0.909266	−	0.416215i	$-0.136644\pi$
$678$		−	39.8887i		−	1.53191i
$679$	−2.07552			−0.0796511
$680$	15.0465	−	18.2465i	0.577007	−	0.699723i
$681$	−57.3245			−2.19668
$682$			4.09841i			0.156936i
$683$			21.0697i			0.806209i	0.915154	+	0.403105i	$0.132069\pi$
$683$			21.0697i			0.806209i	−0.915154	+	0.403105i	$0.867931\pi$
$684$	19.8291			0.758183
$685$	5.23266	+	4.31497i	0.199930	+	0.164867i
$686$	4.17362			0.159349
$687$		−	85.0334i		−	3.24423i
$688$			9.69686i			0.369689i
$689$	−47.3541			−1.80405
$690$	34.3092	+	28.2921i	1.30613	+	1.07706i
$691$	22.7420			0.865146			0.432573	−	0.901599i	$-0.357606\pi$
$691$	22.7420			0.865146			0.432573	+	0.901599i	$0.357606\pi$
$692$		−	2.70545i		−	0.102846i
$693$		−	0.994249i		−	0.0377684i
$694$	−10.0897			−0.383000
$695$	3.26533	−	3.95978i	0.123861	−	0.150203i
$696$	−82.2055			−3.11599
$697$			17.1221i			0.648547i
$698$			32.6931i			1.23745i
$699$	96.9536			3.66712
$700$	−0.435538	+	0.0845062i	−0.0164618	+	0.00319403i
$701$	−35.8276			−1.35319			−0.676596	−	0.736355i	$-0.736545\pi$
$701$	−35.8276			−1.35319			−0.676596	+	0.736355i	$0.736545\pi$
$702$		−	69.0625i		−	2.60660i
$703$		−	37.1191i		−	1.39997i
$704$	5.12826			0.193279
$705$	−31.9774	+	38.7783i	−1.20434	+	1.46047i
$706$	16.8953			0.635862
$707$		−	0.400020i		−	0.0150443i
$708$		−	17.4436i		−	0.655569i
$709$	18.4033			0.691152			0.345576	−	0.938391i	$-0.387684\pi$
$709$	18.4033			0.691152			0.345576	+	0.938391i	$0.387684\pi$
$710$	−17.1891	−	14.1745i	−0.645096	−	0.531960i
$711$	−2.85126			−0.106930
$712$		−	25.3387i		−	0.949609i
$713$			27.0833i			1.01428i
$714$	3.35988			0.125740
$715$	3.87681	+	3.19691i	0.144985	+	0.119558i
$716$	2.79345			0.104396
$717$			14.7507i			0.550875i
$718$			7.22852i			0.269766i
$719$	−22.9617			−0.856326			−0.428163	−	0.903702i	$-0.640839\pi$
$719$	−22.9617			−0.856326			−0.428163	+	0.903702i	$0.640839\pi$
$720$	−32.3570	+	39.2386i	−1.20587	+	1.46234i
$721$	−0.660213			−0.0245876
$722$			41.1320i			1.53077i
$723$		−	75.7345i		−	2.81659i
$724$	−7.62507			−0.283384
$725$	8.04265	+	41.4511i	0.298696	+	1.53946i
$726$	−43.6724			−1.62084
$727$		−	19.2162i		−	0.712691i	−0.934354	−	0.356345i	$-0.884023\pi$
$727$		−	19.2162i		−	0.712691i	0.934354	−	0.356345i	$-0.115977\pi$
$728$			2.77100i			0.102700i
$729$	−32.6140			−1.20792
$730$	−14.7631	+	17.9029i	−0.546406	+	0.662614i
$731$	10.9169			0.403776
$732$			9.36718i			0.346221i
$733$			0.407800i			0.0150624i	0.999972	+	0.00753122i	$0.00239728\pi$
$733$			0.407800i			0.0150624i	−0.999972	+	0.00753122i	$0.997603\pi$
$734$	−24.0195			−0.886575
$735$	38.5106	+	31.7567i	1.42048	+	1.17136i
$736$	10.2278			0.377003
$737$		−	1.48698i		−	0.0547736i
$738$		−	45.7847i		−	1.68536i
$739$	23.3824			0.860135			0.430068	−	0.902797i	$-0.358490\pi$
$739$	23.3824			0.860135			0.430068	+	0.902797i	$0.358490\pi$
$740$	−3.37641	−	2.78427i	−0.124119	−	0.102352i
$741$	−89.6420			−3.29308
$742$			3.63970i			0.133618i
$743$		−	49.3094i		−	1.80899i	−0.426488	−	0.904493i	$-0.640249\pi$
$743$		−	49.3094i		−	1.80899i	0.426488	−	0.904493i	$-0.359751\pi$
$744$	−54.2747			−1.98981
$745$	18.2572	−	22.1401i	0.668892	−	0.811149i
$746$	−28.7928			−1.05418
$747$		−	38.5710i		−	1.41124i
$748$		−	0.761096i		−	0.0278284i
$749$	1.52753			0.0558146
$750$	40.2161	+	21.8622i	1.46849	+	0.798293i
$751$	0.947118			0.0345608			0.0172804	−	0.999851i	$-0.494499\pi$
$751$	0.947118			0.0345608			0.0172804	+	0.999851i	$0.494499\pi$
$752$		−	21.6936i		−	0.791084i
$753$		−	38.5903i		−	1.40631i
$754$	41.8852			1.52537
$755$	6.67588	−	8.09569i	0.242960	−	0.294632i
$756$	1.23553			0.0449358
$757$			42.8580i			1.55770i	0.627210	+	0.778850i	$0.284197\pi$
$757$			42.8580i			1.55770i	−0.627210	+	0.778850i	$0.715803\pi$
$758$			16.8325i			0.611382i
$759$	9.01065			0.327066
$760$	37.4176	+	30.8554i	1.35728	+	1.11924i
$761$	−14.6514			−0.531113			−0.265556	−	0.964095i	$-0.585556\pi$
$761$	−14.6514			−0.531113			−0.265556	+	0.964095i	$0.585556\pi$
$762$		−	42.2045i		−	1.52891i
$763$			2.81747i			0.101999i
$764$	−7.76517			−0.280934
$765$	44.1754	+	36.4280i	1.59717	+	1.31706i
$766$	11.5483			0.417259
$767$			55.9604i			2.02061i
$768$			28.0273i			1.01135i
$769$	0.134376			0.00484571			0.00242285	−	0.999997i	$-0.499229\pi$
$769$	0.134376			0.00484571			0.00242285	+	0.999997i	$0.499229\pi$
$770$	0.245718	−	0.297977i	0.00885508	−	0.0107383i
$771$	45.3879			1.63461
$772$		−	1.01521i		−	0.0365383i
$773$		−	15.4519i		−	0.555767i	−0.960615	−	0.277884i	$-0.910367\pi$
$773$		−	15.4519i		−	0.555767i	0.960615	−	0.277884i	$-0.0896329\pi$
$774$	−29.1919			−1.04928
$775$	5.31002	+	27.3674i	0.190741	+	0.983065i
$776$	26.7498			0.960262
$777$		−	3.91458i		−	0.140435i
$778$		−	30.7877i		−	1.10379i
$779$	−35.1118			−1.25801
$780$	−6.72396	+	8.15399i	−0.240756	+	0.291960i
$781$	−4.51439			−0.161538
$782$			21.6083i			0.772713i
$783$		−	117.588i		−	4.20226i
$784$	−21.5438			−0.769423
$785$	6.11594	+	5.04334i	0.218287	+	0.180004i
$786$	79.9139			2.85043
$787$			42.6277i			1.51951i	0.650207	+	0.759757i	$0.274682\pi$
$787$			42.6277i			1.51951i	−0.650207	+	0.759757i	$0.725318\pi$
$788$		−	0.377621i		−	0.0134522i
$789$	33.2193			1.18264
$790$	−0.854523	−	0.704659i	−0.0304026	−	0.0250706i
$791$	−2.28932			−0.0813989
$792$			12.8141i			0.455330i
$793$		−	30.0507i		−	1.06713i
$794$	−13.7266			−0.487140
$795$	−55.6084	+	67.4350i	−1.97223	+	2.39167i
$796$	2.01559			0.0714407
$797$		−	11.6332i		−	0.412069i	−0.978545	−	0.206035i	$-0.933944\pi$
$797$		−	11.6332i		−	0.412069i	0.978545	−	0.206035i	$-0.0660559\pi$
$798$			6.89000i			0.243903i
$799$	−24.4230			−0.864024
$800$	10.3351	−	2.00530i	0.365402	−	0.0708979i
$801$	61.3458			2.16755
$802$			0.652897i			0.0230546i
$803$			4.70184i			0.165924i
$804$	3.12752			0.110299
$805$	1.62377	−	1.96910i	0.0572302	−	0.0694017i
$806$	27.6539			0.974069
$807$		−	48.2965i		−	1.70012i
$808$			5.15556i			0.181372i
$809$	37.3413			1.31285			0.656425	−	0.754391i	$-0.272068\pi$
$809$	37.3413			1.31285			0.656425	+	0.754391i	$0.272068\pi$
$810$	−50.0158	−	41.2441i	−1.75738	−	1.44917i
$811$	−9.00258			−0.316123			−0.158062	−	0.987429i	$-0.550524\pi$
$811$	−9.00258			−0.316123			−0.158062	+	0.987429i	$0.550524\pi$
$812$			0.749328i			0.0262962i
$813$			9.86455i			0.345965i
$814$	3.80976			0.133532
$815$	−4.23264	−	3.49033i	−0.148263	−	0.122261i
$816$	−34.8247			−1.21911
$817$			22.3869i			0.783219i
$818$		−	37.1547i		−	1.29908i
$819$	−6.70867			−0.234420
$820$	−2.63370	+	3.19383i	−0.0919729	+	0.111533i
$821$	8.55499			0.298571			0.149286	−	0.988794i	$-0.452303\pi$
$821$	8.55499			0.298571			0.149286	+	0.988794i	$0.452303\pi$
$822$		−	12.4182i		−	0.433136i
$823$			27.1990i			0.948097i	0.880499	+	0.474049i	$0.157208\pi$
$823$			27.1990i			0.948097i	−0.880499	+	0.474049i	$0.842792\pi$
$824$	8.50899			0.296425
$825$	9.10517	−	1.76665i	0.317001	−	0.0615069i
$826$	4.30119			0.149658
$827$			8.38311i			0.291509i	0.989321	+	0.145755i	$0.0465610\pi$
$827$			8.38311i			0.291509i	−0.989321	+	0.145755i	$0.953439\pi$
$828$			13.4489i			0.467383i
$829$	−37.2591			−1.29406			−0.647030	−	0.762464i	$-0.723989\pi$
$829$	−37.2591			−1.29406			−0.647030	+	0.762464i	$0.723989\pi$
$830$	9.53244	−	11.5598i	0.330876	−	0.401245i
$831$	103.830			3.60184
$832$		−	34.6028i		−	1.19964i
$833$			24.2544i			0.840365i
$834$	−9.39741			−0.325406
$835$	−10.9414	−	9.02252i	−0.378643	−	0.312237i
$836$	1.56076			0.0539799
$837$		−	77.6356i		−	2.68348i
$838$			9.15534i			0.316266i
$839$	12.5348			0.432750			0.216375	−	0.976310i	$-0.430577\pi$
$839$	12.5348			0.432750			0.216375	+	0.976310i	$0.430577\pi$
$840$	3.94607	+	3.25401i	0.136152	+	0.112274i
$841$	42.3152			1.45914
$842$			20.8711i			0.719265i
$843$			94.3573i			3.24984i
$844$	−10.3715			−0.357001
$845$	3.07714	−	3.73158i	0.105857	−	0.128370i
$846$	65.3074			2.24531
$847$			2.50649i			0.0861239i
$848$		−	37.7250i		−	1.29548i
$849$	−49.3311			−1.69304
$850$	4.23658	+	21.8350i	0.145314	+	0.748934i
$851$	25.1758			0.863015
$852$		−	9.49498i		−	0.325293i
$853$			20.8885i			0.715210i	0.933873	+	0.357605i	$0.116407\pi$
$853$			20.8885i			0.715210i	−0.933873	+	0.357605i	$0.883593\pi$
$854$	−2.30974			−0.0790377
$855$	−74.7019	+	90.5892i	−2.55475	+	3.09809i
$856$	−19.6872			−0.672893
$857$			30.0053i			1.02496i	0.858699	+	0.512481i	$0.171273\pi$
$857$			30.0053i			1.02496i	−0.858699	+	0.512481i	$0.828727\pi$
$858$		−	9.20051i		−	0.314100i
$859$	−44.8428			−1.53002			−0.765008	−	0.644020i	$-0.777265\pi$
$859$	−44.8428			−1.53002			−0.765008	+	0.644020i	$0.777265\pi$
$860$	2.03635	+	1.67922i	0.0694391	+	0.0572610i
$861$	−3.70290			−0.126194
$862$		−	31.4013i		−	1.06953i
$863$		−	10.1816i		−	0.346586i	−0.984870	−	0.173293i	$-0.944559\pi$
$863$		−	10.1816i		−	0.346586i	0.984870	−	0.173293i	$-0.0554407\pi$
$864$	−29.3186			−0.997439
$865$	12.3599	+	10.1922i	0.420249	+	0.346546i
$866$	−21.1196			−0.717674
$867$		−	15.4375i		−	0.524285i
$868$			0.494730i			0.0167922i
$869$	−0.224424			−0.00761306
$870$	49.1862	−	59.6470i	1.66757	−	2.02222i
$871$	−10.0334			−0.339968
$872$		−	36.3122i		−	1.22969i
$873$			64.7620i			2.19186i
$874$	−44.3116			−1.49886
$875$	1.25473	−	2.30812i	0.0424176	−	0.0780286i
$876$	−9.88924			−0.334126
$877$			35.3951i			1.19521i	0.801792	+	0.597604i	$0.203880\pi$
$877$			35.3951i			1.19521i	−0.801792	+	0.597604i	$0.796120\pi$
$878$		−	18.2305i		−	0.615250i
$879$	82.6628			2.78815
$880$	−2.54684	+	3.08849i	−0.0858539	+	0.104113i
$881$	46.3047			1.56005			0.780023	−	0.625750i	$-0.215207\pi$
$881$	46.3047			1.56005			0.780023	+	0.625750i	$0.215207\pi$
$882$		−	64.8565i		−	2.18383i
$883$		−	36.2361i		−	1.21944i	−0.792616	−	0.609722i	$-0.791281\pi$
$883$		−	36.2361i		−	1.21944i	0.792616	−	0.609722i	$-0.208719\pi$
$884$	−5.13548			−0.172725
$885$	79.6910	+	65.7149i	2.67878	+	2.20898i
$886$	2.44337			0.0820865
$887$		−	26.9498i		−	0.904887i	−0.891793	−	0.452443i	$-0.850552\pi$
$887$		−	26.9498i		−	0.904887i	0.891793	−	0.452443i	$-0.149448\pi$
$888$			50.4521i			1.69306i
$889$	−2.42223			−0.0812391
$890$	18.3854	+	15.1610i	0.616279	+	0.508198i
$891$	−13.1357			−0.440062
$892$			9.12853i			0.305646i
$893$		−	50.0835i		−	1.67598i
$894$	−52.5431			−1.75731
$895$	−10.5237	+	12.7619i	−0.351769	+	0.426582i
$896$	−1.67010			−0.0557940
$897$		−	60.7991i		−	2.03002i
$898$		−	27.5490i		−	0.919322i
$899$	47.0846			1.57036
$900$	2.63683	+	13.5900i	0.0878945	+	0.453001i
$901$	−42.4714			−1.41493
$902$		−	3.60374i		−	0.119992i
$903$			2.36093i			0.0785667i
$904$	29.5054			0.981334
$905$	28.7259	−	34.8352i	0.954880	−	1.15796i
$906$	−19.2128			−0.638303
$907$			5.26836i			0.174933i	0.996167	+	0.0874664i	$0.0278771\pi$
$907$			5.26836i			0.174933i	−0.996167	+	0.0874664i	$0.972123\pi$
$908$		−	6.73449i		−	0.223492i
$909$	−12.4818			−0.413994
$910$	−2.01059	−	1.65798i	−0.0666505	−	0.0549615i
$911$	20.8539			0.690919			0.345459	−	0.938434i	$-0.387723\pi$
$911$	20.8539			0.690919			0.345459	+	0.938434i	$0.387723\pi$
$912$		−	71.4139i		−	2.36475i
$913$		−	3.03595i		−	0.100475i
$914$	−25.0463			−0.828459
$915$	−42.7940	−	35.2889i	−1.41473	−	1.16662i
$916$	9.98975			0.330070
$917$		−	4.58648i		−	0.151459i
$918$		−	61.9414i		−	2.04437i
$919$	9.82871			0.324219			0.162110	−	0.986773i	$-0.448170\pi$
$919$	9.82871			0.324219			0.162110	+	0.986773i	$0.448170\pi$
$920$	−20.9275	+	25.3783i	−0.689959	+	0.836698i
$921$	−8.37951			−0.276114
$922$			13.1729i			0.433827i
$923$			30.4607i			1.00263i
$924$	0.164598			0.00541486
$925$	25.4399	−	4.93603i	0.836457	−	0.162296i
$926$	−13.9496			−0.458412
$927$			20.6005i			0.676610i
$928$		−	17.7812i		−	0.583697i
$929$	−14.8642			−0.487677			−0.243839	−	0.969816i	$-0.578407\pi$
$929$	−14.8642			−0.487677			−0.243839	+	0.969816i	$0.578407\pi$
$930$	32.4743	−	39.3809i	1.06487	−	1.29135i
$931$	−49.7378			−1.63009
$932$			11.3901i			0.373096i
$933$			63.7823i			2.08814i
$934$	−26.6599			−0.872340
$935$	3.47707	+	2.86727i	0.113712	+	0.0937698i
$936$	86.4630			2.82613
$937$			56.7633i			1.85438i	0.374594	+	0.927189i	$0.377782\pi$
$937$			56.7633i			1.85438i	−0.374594	+	0.927189i	$0.622218\pi$
$938$			0.771178i			0.0251798i
$939$	−58.3058			−1.90274
$940$	−4.55568	−	3.75672i	−0.148590	−	0.122531i
$941$	−10.6242			−0.346341			−0.173170	−	0.984892i	$-0.555401\pi$
$941$	−10.6242			−0.346341			−0.173170	+	0.984892i	$0.555401\pi$
$942$		−	14.5144i		−	0.472905i
$943$		−	23.8144i		−	0.775503i
$944$	−44.5813			−1.45100
$945$	−4.65461	+	5.64453i	−0.151414	+	0.183617i
$946$	−2.29771			−0.0747049
$947$			35.9492i			1.16819i	0.811685	+	0.584095i	$0.198551\pi$
$947$			35.9492i			1.16819i	−0.811685	+	0.584095i	$0.801449\pi$
$948$		−	0.472024i		−	0.0153306i
$949$	31.7255			1.02985
$950$	−44.7764	+	8.68784i	−1.45274	+	0.281871i
$951$	−17.0212			−0.551952
$952$			2.48528i			0.0805484i
$953$			54.1752i			1.75491i	0.479661	+	0.877454i	$0.340760\pi$
$953$			54.1752i			1.75491i	−0.479661	+	0.877454i	$0.659240\pi$
$954$	113.569			3.67693
$955$	29.2536	−	35.4752i	0.946626	−	1.14795i
$956$	−1.73292			−0.0560466
$957$		−	15.6651i		−	0.506381i
$958$			26.5643i			0.858254i
$959$	−0.712717			−0.0230148
$960$	−49.2764	−	40.6344i	−1.59039	−	1.31147i
$961$	0.0867807			0.00279938
$962$		−	25.7062i		−	0.828803i
$963$		−	47.6632i		−	1.53592i
$964$	8.89731			0.286563
$965$	4.63800	+	3.82460i	0.149302	+	0.123118i
$966$	−4.67310			−0.150355
$967$		−	5.91237i		−	0.190129i	−0.995471	−	0.0950645i	$-0.969694\pi$
$967$		−	5.91237i		−	0.190129i	0.995471	−	0.0950645i	$-0.0303057\pi$
$968$		−	32.3042i		−	1.03830i
$969$	−80.3989			−2.58279
$970$	−16.0053	+	19.4092i	−0.513898	+	0.623192i
$971$	−25.0906			−0.805195			−0.402597	−	0.915377i	$-0.631893\pi$
$971$	−25.0906			−0.805195			−0.402597	+	0.915377i	$0.631893\pi$
$972$		−	11.8536i		−	0.380204i
$973$			0.539344i			0.0172906i
$974$	34.7540			1.11359
$975$	−11.9204	−	61.4369i	−0.381759	−	1.96755i
$976$	23.9401			0.766305
$977$		−	49.9680i		−	1.59862i	−0.600920	−	0.799309i	$-0.705199\pi$
$977$		−	49.9680i		−	1.59862i	0.600920	−	0.799309i	$-0.294801\pi$
$978$			10.0450i			0.321202i
$979$	4.82856			0.154322
$980$	−3.73078	+	4.52423i	−0.119175	+	0.144521i
$981$	87.9129			2.80684
$982$			19.9090i			0.635321i
$983$		−	43.1014i		−	1.37472i	−0.726316	−	0.687361i	$-0.758769\pi$
$983$		−	43.1014i		−	1.37472i	0.726316	−	0.687361i	$-0.241231\pi$
$984$	47.7239			1.52138
$985$	1.72516	+	1.42261i	0.0549683	+	0.0453280i
$986$	37.5663			1.19636
$987$		−	5.28181i		−	0.168122i
$988$		−	10.5312i		−	0.335041i
$989$	−15.1838			−0.482817
$990$	−9.29773	−	7.66711i	−0.295501	−	0.243677i
$991$	−39.3870			−1.25117			−0.625585	−	0.780156i	$-0.715140\pi$
$991$	−39.3870			−1.25117			−0.625585	+	0.780156i	$0.715140\pi$
$992$		−	11.7397i		−	0.372737i
$993$		−	94.0072i		−	2.98323i
$994$	2.34125			0.0742600
$995$	−7.59332	+	9.20824i	−0.240724	+	0.291921i
$996$	6.38542			0.202330
$997$		−	53.8563i		−	1.70565i	−0.522200	−	0.852823i	$-0.674888\pi$
$997$		−	53.8563i		−	1.70565i	0.522200	−	0.852823i	$-0.325112\pi$
$998$			29.0340i			0.919056i
$999$	−72.1676			−2.28328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	985.2.b.a.789.68	yes	98
5.2	odd	4		4925.2.a.r.1.17		49
5.3	odd	4		4925.2.a.s.1.33		49
5.4	even	2	inner	985.2.b.a.789.31	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
985.2.b.a.789.31	✓	98	5.4	even	2	inner
985.2.b.a.789.68	yes	98	1.1	even	1	trivial
4925.2.a.r.1.17		49	5.2	odd	4
4925.2.a.s.1.33		49	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.27373i q^{2} -3.21433i q^{3} +0.377621 q^{4} +(-1.42261 + 1.72516i) q^{5} +4.09418 q^{6} -0.234977i q^{7} +3.02844i q^{8} -7.33194 q^{9} +(-2.19739 - 1.81201i) q^{10} -0.577101 q^{11} -1.21380i q^{12} +3.89397i q^{13} +0.299296 q^{14} +(5.54525 + 4.57273i) q^{15} -3.10216 q^{16} +3.49246i q^{17} -9.33888i q^{18} -7.16189 q^{19} +(-0.537206 + 0.651458i) q^{20} -0.755293 q^{21} -0.735069i q^{22} -4.85751i q^{23} +9.73441 q^{24} +(-0.952375 - 4.90846i) q^{25} -4.95986 q^{26} +13.9243i q^{27} -0.0887321i q^{28} -8.44483 q^{29} +(-5.82441 + 7.06313i) q^{30} -5.57555 q^{31} +2.10557i q^{32} +1.85499i q^{33} -4.44844 q^{34} +(0.405373 + 0.334280i) q^{35} -2.76869 q^{36} +5.18286i q^{37} -9.12229i q^{38} +12.5165 q^{39} +(-5.22455 - 4.30828i) q^{40} +4.90259 q^{41} -0.962037i q^{42} -3.12584i q^{43} -0.217925 q^{44} +(10.4305 - 12.6488i) q^{45} +6.18714 q^{46} +6.99306i q^{47} +9.97138i q^{48} +6.94479 q^{49} +(6.25204 - 1.21307i) q^{50} +11.2259 q^{51} +1.47045i q^{52} +12.1609i q^{53} -17.7357 q^{54} +(0.820988 - 0.995593i) q^{55} +0.711612 q^{56} +23.0207i q^{57} -10.7564i q^{58} +14.3710 q^{59} +(2.09400 + 1.72676i) q^{60} -7.71724 q^{61} -7.10173i q^{62} +1.72283i q^{63} -8.88625 q^{64} +(-6.71774 - 5.53960i) q^{65} -2.36276 q^{66} +2.57664i q^{67} +1.31883i q^{68} -15.6136 q^{69} +(-0.425781 + 0.516334i) q^{70} +7.82253 q^{71} -22.2043i q^{72} -8.14734i q^{73} -6.60155 q^{74} +(-15.7774 + 3.06125i) q^{75} -2.70448 q^{76} +0.135605i q^{77} +15.9426i q^{78} +0.388882 q^{79} +(4.41316 - 5.35173i) q^{80} +22.7615 q^{81} +6.24456i q^{82} +5.26069i q^{83} -0.285214 q^{84} +(-6.02507 - 4.96840i) q^{85} +3.98147 q^{86} +27.1445i q^{87} -1.74771i q^{88} -8.36693 q^{89} +(16.1111 + 13.2856i) q^{90} +0.914993 q^{91} -1.83430i q^{92} +17.9217i q^{93} -8.90725 q^{94} +(10.1886 - 12.3554i) q^{95} +6.76801 q^{96} -8.83287i q^{97} +8.84576i q^{98} +4.23127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) \) 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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