LMFDB - Embedded newform 1300.2.ba.c.849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(49,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1300.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.ba (of order $6$, degree $2$, not 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.2
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1300.849
Dual form			1300.2.ba.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0820885 - 0.0473938i) q^{3} +(0.413419 + 0.716063i) q^{7} +(-1.49551 - 2.59030i) q^{9} +O(q^{10})$	\(q+(-0.0820885 - 0.0473938i) q^{3} +(0.413419 + 0.716063i) q^{7} +(-1.49551 - 2.59030i) q^{9} +(1.50000 + 0.866025i) q^{11} +(-1.40072 - 3.32235i) q^{13} +(-1.24026 + 0.716063i) q^{17} +(0.926118 - 0.534695i) q^{19} -0.0783740i q^{21} +(-2.67238 - 1.54290i) q^{23} +0.567874i q^{27} +(3.72756 - 6.45632i) q^{29} -5.84325i q^{31} +(-0.0820885 - 0.142181i) q^{33} +(-0.491793 + 0.851811i) q^{37} +(-0.0424756 + 0.339112i) q^{39} +(-3.69615 - 2.13397i) q^{41} +(-8.26268 + 4.77046i) q^{43} +3.46410 q^{47} +(3.15817 - 5.47011i) q^{49} +0.135748 q^{51} -0.334308i q^{53} -0.101365 q^{57} +(9.98052 - 5.76225i) q^{59} +(-1.35824 - 2.35255i) q^{61} +(1.23654 - 2.14176i) q^{63} +(6.87752 - 11.9122i) q^{67} +(0.146248 + 0.253309i) q^{69} +(8.46704 - 4.88845i) q^{71} -11.1806 q^{73} +1.43213i q^{77} +0.252387 q^{79} +(-4.45961 + 7.72427i) q^{81} -5.67165 q^{83} +(-0.611979 + 0.353326i) q^{87} +(-3.98052 - 2.29815i) q^{89} +(1.79992 - 2.37653i) q^{91} +(-0.276934 + 0.479664i) q^{93} +(4.76717 + 8.25698i) q^{97} -5.18059i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9	$ 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9} + 12 q^{11} + 18 q^{17} + 6 q^{23} + 6 q^{33} - 18 q^{37} + 4 q^{39} + 12 q^{41} - 18 q^{43} + 4 q^{49} + 36 q^{57} + 24 q^{59} - 4 q^{61} + 12 q^{63} + 18 q^{67} + 24 q^{69} - 36 q^{71} - 48 q^{73} + 16 q^{79} + 8 q^{81} - 72 q^{83} - 18 q^{87} + 24 q^{89} - 48 q^{93} + 6 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9 + 12 * q^11 + 18 * q^17 + 6 * q^23 + 6 * q^33 - 18 * q^37 + 4 * q^39 + 12 * q^41 - 18 * q^43 + 4 * q^49 + 36 * q^57 + 24 * q^59 - 4 * q^61 + 12 * q^63 + 18 * q^67 + 24 * q^69 - 36 * q^71 - 48 * q^73 + 16 * q^79 + 8 * q^81 - 72 * q^83 - 18 * q^87 + 24 * q^89 - 48 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0820885	−	0.0473938i	−0.0473938	−	0.0273628i	0.476116	−	0.879383i	$-0.342044\pi$
$3$	−0.0820885	−	0.0473938i	−0.0473938	−	0.0273628i	−0.523510	+	0.852020i	$0.675378\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.413419	+	0.716063i	0.156258	+	0.270646i	0.933516	−	0.358535i	$-0.116724\pi$
$7$	0.413419	+	0.716063i	0.156258	+	0.270646i	−0.777259	+	0.629181i	$0.783390\pi$
$8$		0			0
$9$	−1.49551	−	2.59030i	−0.498503	−	0.863432i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	−1.40072	−	3.32235i	−0.388490	−	0.921453i
$13$	−1.40072	−	3.32235i	−0.388490	−	0.921453i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.24026	+	0.716063i	−0.300807	+	0.173671i	−0.642805	−	0.766030i	$-0.722230\pi$
$17$	−1.24026	+	0.716063i	−0.300807	+	0.173671i	0.341999	+	0.939700i	$0.388896\pi$
$18$		0			0
$19$	0.926118	−	0.534695i	0.212466	−	0.122667i	−0.389991	−	0.920819i	$-0.627522\pi$
$19$	0.926118	−	0.534695i	0.212466	−	0.122667i	0.602457	+	0.798151i	$0.294189\pi$
$20$		0			0
$21$		−	0.0783740i		−	0.0171026i
$22$		0			0
$23$	−2.67238	−	1.54290i	−0.557231	−	0.321717i	0.194803	−	0.980842i	$-0.437593\pi$
$23$	−2.67238	−	1.54290i	−0.557231	−	0.321717i	−0.752033	+	0.659125i	$0.770927\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			0.567874i			0.109287i
$28$		0			0
$29$	3.72756	−	6.45632i	0.692190	−	1.19891i	−0.278928	−	0.960312i	$-0.589979\pi$
$29$	3.72756	−	6.45632i	0.692190	−	1.19891i	0.971119	−	0.238597i	$-0.0766874\pi$
$30$		0			0
$31$		−	5.84325i		−	1.04948i	−0.851263	−	0.524740i	$-0.824163\pi$
$31$		−	5.84325i		−	1.04948i	0.851263	−	0.524740i	$-0.175837\pi$
$32$		0			0
$33$	−0.0820885	−	0.142181i	−0.0142898	−	0.0247506i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.491793	+	0.851811i	−0.0808503	+	0.140037i	−0.903615	−	0.428345i	$-0.859097\pi$
$37$	−0.491793	+	0.851811i	−0.0808503	+	0.140037i	0.822765	+	0.568382i	$0.192430\pi$
$38$		0			0
$39$	−0.0424756	+	0.339112i	−0.00680154	+	0.0543013i
$40$		0			0
$41$	−3.69615	−	2.13397i	−0.577242	−	0.333271i	0.182795	−	0.983151i	$-0.441486\pi$
$41$	−3.69615	−	2.13397i	−0.577242	−	0.333271i	−0.760037	+	0.649880i	$0.774819\pi$
$42$		0			0
$43$	−8.26268	+	4.77046i	−1.26005	+	0.727488i	−0.973083	−	0.230453i	$-0.925979\pi$
$43$	−8.26268	+	4.77046i	−1.26005	+	0.727488i	−0.286963	+	0.957942i	$0.592646\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$		0			0
$49$	3.15817	−	5.47011i	0.451167	−	0.781444i
$50$		0			0
$51$	0.135748			0.0190085
$52$		0			0
$53$		−	0.334308i		−	0.0459207i	−0.999736	−	0.0229603i	$-0.992691\pi$
$53$		−	0.334308i		−	0.0459207i	0.999736	−	0.0229603i	$-0.00730915\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.101365			−0.0134261
$58$		0			0
$59$	9.98052	−	5.76225i	1.29935	−	0.750181i	0.319060	−	0.947734i	$-0.396633\pi$
$59$	9.98052	−	5.76225i	1.29935	−	0.750181i	0.980292	+	0.197553i	$0.0632995\pi$
$60$		0			0
$61$	−1.35824	−	2.35255i	−0.173905	−	0.301213i	0.765877	−	0.642988i	$-0.222305\pi$
$61$	−1.35824	−	2.35255i	−0.173905	−	0.301213i	−0.939782	+	0.341775i	$0.888972\pi$
$62$		0			0
$63$	1.23654	−	2.14176i	0.155790	−	0.269836i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.87752	−	11.9122i	0.840223	−	1.45531i	−0.0494832	−	0.998775i	$-0.515757\pi$
$67$	6.87752	−	11.9122i	0.840223	−	1.45531i	0.889706	−	0.456534i	$-0.150909\pi$
$68$		0			0
$69$	0.146248	+	0.253309i	0.0176062	+	0.0304948i
$70$		0			0
$71$	8.46704	−	4.88845i	1.00485	−	0.580152i	0.0951721	−	0.995461i	$-0.469660\pi$
$71$	8.46704	−	4.88845i	1.00485	−	0.580152i	0.909680	+	0.415309i	$0.136327\pi$
$72$		0			0
$73$	−11.1806			−1.30859			−0.654295	−	0.756240i	$-0.727034\pi$
$73$	−11.1806			−1.30859			−0.654295	+	0.756240i	$0.727034\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			1.43213i			0.163206i
$78$		0			0
$79$	0.252387			0.0283958			0.0141979	−	0.999899i	$-0.495481\pi$
$79$	0.252387			0.0283958			0.0141979	+	0.999899i	$0.495481\pi$
$80$		0			0
$81$	−4.45961	+	7.72427i	−0.495512	+	0.858252i
$82$		0			0
$83$	−5.67165			−0.622544			−0.311272	−	0.950321i	$-0.600755\pi$
$83$	−5.67165			−0.622544			−0.311272	+	0.950321i	$0.600755\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.611979	+	0.353326i	−0.0656110	+	0.0378806i
$88$		0			0
$89$	−3.98052	−	2.29815i	−0.421934	−	0.243604i	0.273971	−	0.961738i	$-0.411663\pi$
$89$	−3.98052	−	2.29815i	−0.421934	−	0.243604i	−0.695904	+	0.718135i	$0.744996\pi$
$90$		0			0
$91$	1.79992	−	2.37653i	0.188683	−	0.249128i
$92$		0			0
$93$	−0.276934	+	0.479664i	−0.0287167	+	0.0497388i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.76717	+	8.25698i	0.484033	+	0.838370i	0.999832	−	0.0183401i	$-0.00583816\pi$
$97$	4.76717	+	8.25698i	0.484033	+	0.838370i	−0.515799	+	0.856710i	$0.672505\pi$
$98$		0			0
$99$		−	5.18059i		−	0.520669i
$100$		0			0
$101$	−2.90072	+	5.02419i	−0.288632	+	0.499926i	−0.973484	−	0.228757i	$-0.926534\pi$
$101$	−2.90072	+	5.02419i	−0.288632	+	0.499926i	0.684851	+	0.728683i	$0.259867\pi$
$102$		0			0
$103$		−	10.0760i		−	0.992814i	−0.868090	−	0.496407i	$-0.834652\pi$
$103$		−	10.0760i		−	0.992814i	0.868090	−	0.496407i	$-0.165348\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.0985	−	8.13977i	−1.36295	−	0.786902i	−0.372938	−	0.927856i	$-0.621649\pi$
$107$	−14.0985	−	8.13977i	−1.36295	−	0.786902i	−0.990016	+	0.140955i	$0.954983\pi$
$108$		0			0
$109$			3.12979i			0.299780i	0.988703	+	0.149890i	$0.0478919\pi$
$109$			3.12979i			0.299780i	−0.988703	+	0.149890i	$0.952108\pi$
$110$		0			0
$111$	0.0807411	−	0.0466159i	0.00766361	−	0.00442458i
$112$		0			0
$113$	8.80813	−	5.08538i	0.828599	−	0.478392i	−0.0247735	−	0.999693i	$-0.507886\pi$
$113$	8.80813	−	5.08538i	0.828599	−	0.478392i	0.853373	+	0.521301i	$0.174553\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.51107	+	8.59687i	−0.601949	+	0.794781i
$118$		0			0
$119$	−1.02549	−	0.592068i	−0.0940068	−	0.0542748i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	0.202274	+	0.350349i	0.0182385	+	0.0315899i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.16846	+	2.98401i	0.458627	+	0.264788i	0.711467	−	0.702720i	$-0.248031\pi$
$127$	5.16846	+	2.98401i	0.458627	+	0.264788i	−0.252840	+	0.967508i	$0.581365\pi$
$128$		0			0
$129$	0.904361			0.0796245
$130$		0			0
$131$	16.6267			1.45268			0.726342	−	0.687334i	$-0.241219\pi$
$131$	16.6267			1.45268			0.726342	+	0.687334i	$0.241219\pi$
$132$		0			0
$133$	0.765750	+	0.442106i	0.0663990	+	0.0383355i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.202274	−	0.350349i	−0.0172815	−	0.0299324i	0.857255	−	0.514892i	$-0.172168\pi$
$137$	−0.202274	−	0.350349i	−0.0172815	−	0.0299324i	−0.874537	+	0.484959i	$0.838834\pi$
$138$		0			0
$139$	−4.65817	−	8.06819i	−0.395101	−	0.684335i	0.598013	−	0.801486i	$-0.295957\pi$
$139$	−4.65817	−	8.06819i	−0.395101	−	0.684335i	−0.993114	+	0.117152i	$0.962624\pi$
$140$		0			0
$141$	−0.284363	−	0.164177i	−0.0239477	−	0.0138262i
$142$		0			0
$143$	0.776156	−	6.19658i	0.0649054	−	0.518184i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.518498	+	0.299355i	−0.0427650	+	0.0246904i
$148$		0			0
$149$	−9.41179	+	5.43390i	−0.771044	+	0.445162i	−0.833247	−	0.552901i	$-0.813521\pi$
$149$	−9.41179	+	5.43390i	−0.771044	+	0.445162i	0.0622030	+	0.998064i	$0.480187\pi$
$150$		0			0
$151$			0.991015i			0.0806477i	0.999187	+	0.0403238i	$0.0128390\pi$
$151$			0.991015i			0.0806477i	−0.999187	+	0.0403238i	$0.987161\pi$
$152$		0			0
$153$	3.70963	+	2.14176i	0.299906	+	0.173151i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			17.5729i			1.40247i	0.712930	+	0.701235i	$0.247368\pi$
$157$			17.5729i			1.40247i	−0.712930	+	0.701235i	$0.752632\pi$
$158$		0			0
$159$	−0.0158441	+	0.0274428i	−0.00125652	+	0.00217636i
$160$		0			0
$161$		−	2.55146i		−	0.201083i
$162$		0			0
$163$	8.64098	+	14.9666i	0.676814	+	1.17228i	0.975935	+	0.218061i	$0.0699730\pi$
$163$	8.64098	+	14.9666i	0.676814	+	1.17228i	−0.299122	+	0.954215i	$0.596694\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.52978	−	2.64965i	0.118378	−	0.205036i	−0.800747	−	0.599002i	$-0.795564\pi$
$167$	1.52978	−	2.64965i	0.118378	−	0.205036i	0.919125	+	0.393966i	$0.128897\pi$
$168$		0			0
$169$	−9.07597	+	9.30735i	−0.698151	+	0.715950i
$170$		0			0
$171$	−2.77003	−	1.59928i	−0.211830	−	0.122300i
$172$		0			0
$173$	−2.96190	+	1.71006i	−0.225189	+	0.130013i	−0.608351	−	0.793668i	$-0.708169\pi$
$173$	−2.96190	+	1.71006i	−0.225189	+	0.130013i	0.383161	+	0.923681i	$0.374835\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.09238			−0.0821083
$178$		0			0
$179$	5.19109	−	8.99123i	0.388000	−	0.672036i	−0.604180	−	0.796848i	$-0.706499\pi$
$179$	5.19109	−	8.99123i	0.388000	−	0.672036i	0.992180	+	0.124811i	$0.0398326\pi$
$180$		0			0
$181$	−10.3492			−0.769247			−0.384624	−	0.923073i	$-0.625669\pi$
$181$	−10.3492			−0.769247			−0.384624	+	0.923073i	$0.625669\pi$
$182$		0			0
$183$			0.257489i			0.0190342i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.48052			−0.181393
$188$		0			0
$189$	−0.406634	+	0.234770i	−0.0295782	+	0.0170770i
$190$		0			0
$191$	7.75296	+	13.4285i	0.560984	+	0.971653i	0.997411	+	0.0719134i	$0.0229105\pi$
$191$	7.75296	+	13.4285i	0.560984	+	0.971653i	−0.436427	+	0.899740i	$0.643756\pi$
$192$		0			0
$193$	2.78514	−	4.82401i	0.200479	−	0.347239i	−0.748204	−	0.663469i	$-0.769084\pi$
$193$	2.78514	−	4.82401i	0.200479	−	0.347239i	0.948683	+	0.316229i	$0.102417\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.4364	−	21.5405i	0.886058	−	1.53470i	0.0415608	−	0.999136i	$-0.486767\pi$
$197$	12.4364	−	21.5405i	0.886058	−	1.53470i	0.844497	−	0.535561i	$-0.179900\pi$
$198$		0			0
$199$	9.32443	+	16.1504i	0.660991	+	1.14487i	0.980356	+	0.197239i	$0.0631974\pi$
$199$	9.32443	+	16.1504i	0.660991	+	1.14487i	−0.319364	+	0.947632i	$0.603469\pi$
$200$		0			0
$201$	−1.12913	+	0.651904i	−0.0796427	+	0.0459817i
$202$		0			0
$203$	6.16418			0.432640
$204$		0			0
$205$		0			0
$206$		0			0
$207$			9.22968i			0.641507i
$208$		0			0
$209$	1.85224			0.128122
$210$		0			0
$211$	−4.82235	+	8.35255i	−0.331984	+	0.575013i	−0.982901	−	0.184136i	$-0.941051\pi$
$211$	−4.82235	+	8.35255i	−0.331984	+	0.575013i	0.650917	+	0.759149i	$0.274385\pi$
$212$		0			0
$213$	−0.926728			−0.0634984
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.18414	−	2.41571i	0.284038	−	0.163989i
$218$		0			0
$219$	0.917797	+	0.529891i	0.0620190	+	0.0358067i
$220$		0			0
$221$	4.11626	+	3.11756i	0.276890	+	0.209710i
$222$		0			0
$223$	−0.580573	+	1.00558i	−0.0388780	+	0.0673387i	−0.884810	−	0.465953i	$-0.845712\pi$
$223$	−0.580573	+	1.00558i	−0.0388780	+	0.0673387i	0.845932	+	0.533291i	$0.179045\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.6230	−	23.5957i	−0.904191	−	1.56610i	−0.822000	−	0.569488i	$-0.807142\pi$
$227$	−13.6230	−	23.5957i	−0.904191	−	1.56610i	−0.0821911	−	0.996617i	$-0.526192\pi$
$228$		0			0
$229$			24.3432i			1.60864i	0.594193	+	0.804322i	$0.297471\pi$
$229$			24.3432i			1.60864i	−0.594193	+	0.804322i	$0.702529\pi$
$230$		0			0
$231$	0.0678739	−	0.117561i	0.00446577	−	0.00773495i
$232$		0			0
$233$			23.0238i			1.50834i	0.656678	+	0.754171i	$0.271961\pi$
$233$			23.0238i			1.50834i	−0.656678	+	0.754171i	$0.728039\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.0207181	−	0.0119616i	−0.00134578	−	0.000776989i
$238$		0			0
$239$			23.7057i			1.53340i	0.642008	+	0.766698i	$0.278102\pi$
$239$			23.7057i			1.53340i	−0.642008	+	0.766698i	$0.721898\pi$
$240$		0			0
$241$	−9.37968	+	5.41536i	−0.604198	+	0.348834i	−0.770691	−	0.637209i	$-0.780089\pi$
$241$	−9.37968	+	5.41536i	−0.604198	+	0.348834i	0.166493	+	0.986043i	$0.446756\pi$
$242$		0			0
$243$	2.20754	−	1.27453i	0.141614	−	0.0817609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.07367	−	2.32793i	−0.195573	−	0.148123i
$248$		0			0
$249$	0.465577	+	0.268801i	0.0295047	+	0.0170346i
$250$		0			0
$251$	−0.560405	−	0.970649i	−0.0353724	−	0.0612668i	0.847797	−	0.530321i	$-0.177928\pi$
$251$	−0.560405	−	0.970649i	−0.0353724	−	0.0612668i	−0.883170	+	0.469054i	$0.844595\pi$
$252$		0			0
$253$	−2.67238	−	4.62870i	−0.168011	−	0.291004i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.4026	+	8.31534i	0.898409	+	0.518697i	0.876684	−	0.481067i	$-0.159751\pi$
$257$	14.4026	+	8.31534i	0.898409	+	0.518697i	0.0217255	+	0.999764i	$0.493084\pi$
$258$		0			0
$259$	−0.813267			−0.0505340
$260$		0			0
$261$	−22.2984			−1.38023
$262$		0			0
$263$	21.2193	+	12.2510i	1.30844	+	0.755427i	0.981836	−	0.189734i	$-0.0607626\pi$
$263$	21.2193	+	12.2510i	1.30844	+	0.755427i	0.326603	+	0.945162i	$0.394096\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.217836	+	0.377303i	0.0133314	+	0.0230906i
$268$		0			0
$269$	−3.26643	−	5.65763i	−0.199158	−	0.344952i	0.749098	−	0.662460i	$-0.230487\pi$
$269$	−3.26643	−	5.65763i	−0.199158	−	0.344952i	−0.948256	+	0.317508i	$0.897154\pi$
$270$		0			0
$271$	4.89831	+	2.82804i	0.297551	+	0.171791i	0.641342	−	0.767255i	$-0.278378\pi$
$271$	4.89831	+	2.82804i	0.297551	+	0.171791i	−0.343791	+	0.939046i	$0.611711\pi$
$272$		0			0
$273$	−0.260386	+	0.109780i	−0.0157593	+	0.00664419i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.21784	+	1.85782i	−0.193341	+	0.111626i	−0.593546	−	0.804800i	$-0.702272\pi$
$277$	−3.21784	+	1.85782i	−0.193341	+	0.111626i	0.400205	+	0.916426i	$0.368939\pi$
$278$		0			0
$279$	−15.1357	+	8.73863i	−0.906154	+	0.523168i
$280$		0			0
$281$		−	9.70447i		−	0.578920i	−0.957190	−	0.289460i	$-0.906524\pi$
$281$		−	9.70447i		−	0.578920i	0.957190	−	0.289460i	$-0.0934758\pi$
$282$		0			0
$283$	20.9558	+	12.0988i	1.24569	+	0.719200i	0.970247	−	0.242117i	$-0.0778419\pi$
$283$	20.9558	+	12.0988i	1.24569	+	0.719200i	0.275444	+	0.961317i	$0.411175\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	3.52890i		−	0.208305i
$288$		0			0
$289$	−7.47451	+	12.9462i	−0.439677	+	0.761543i
$290$		0			0
$291$		−	0.903737i		−	0.0529780i
$292$		0			0
$293$	1.81414	+	3.14218i	0.105983	+	0.183568i	0.914139	−	0.405400i	$-0.132868\pi$
$293$	1.81414	+	3.14218i	0.105983	+	0.183568i	−0.808156	+	0.588968i	$0.799534\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.491793	+	0.851811i	−0.0285367	+	0.0494271i
$298$		0			0
$299$	−1.38279	+	11.0398i	−0.0799689	+	0.638446i
$300$		0			0
$301$	−6.83190	−	3.94440i	−0.393784	−	0.227351i
$302$		0			0
$303$	0.476231	−	0.274952i	0.0273588	−	0.0157956i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−9.40129			−0.536560			−0.268280	−	0.963341i	$-0.586455\pi$
$307$	−9.40129			−0.536560			−0.268280	+	0.963341i	$0.586455\pi$
$308$		0			0
$309$	−0.477538	+	0.827121i	−0.0271662	+	0.0470532i
$310$		0			0
$311$	25.5370			1.44807			0.724034	−	0.689764i	$-0.242286\pi$
$311$	25.5370			1.44807			0.724034	+	0.689764i	$0.242286\pi$
$312$		0			0
$313$		−	5.25656i		−	0.297118i	−0.988904	−	0.148559i	$-0.952536\pi$
$313$		−	5.25656i		−	0.297118i	0.988904	−	0.148559i	$-0.0474635\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.1536			−0.794947			−0.397474	−	0.917614i	$-0.630113\pi$
$317$	−14.1536			−0.794947			−0.397474	+	0.917614i	$0.630113\pi$
$318$		0			0
$319$	11.1827	−	6.45632i	0.626110	−	0.361485i
$320$		0			0
$321$	0.771550	+	1.33636i	0.0430637	+	0.0745885i
$322$		0			0
$323$	−0.765750	+	1.32632i	−0.0426075	+	0.0737983i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.148333	−	0.256920i	0.00820282	−	0.0142077i
$328$		0			0
$329$	1.43213	+	2.48052i	0.0789557	+	0.136755i
$330$		0			0
$331$	−16.0945	+	9.29214i	−0.884632	+	0.510742i	−0.872183	−	0.489180i	$-0.837296\pi$
$331$	−16.0945	+	9.29214i	−0.884632	+	0.510742i	−0.0124490	+	0.999923i	$0.503963\pi$
$332$		0			0
$333$	2.94192			0.161216
$334$		0			0
$335$		0			0
$336$		0			0
$337$			22.4060i			1.22053i	0.792196	+	0.610267i	$0.208938\pi$
$337$			22.4060i			1.22053i	−0.792196	+	0.610267i	$0.791062\pi$
$338$		0			0
$339$	−0.964061			−0.0523606
$340$		0			0
$341$	5.06040	−	8.76488i	0.274036	−	0.474645i
$342$		0			0
$343$	11.0105			0.594509
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.4699	−	10.0862i	0.937831	−	0.541457i	0.0485514	−	0.998821i	$-0.484540\pi$
$347$	17.4699	−	10.0862i	0.937831	−	0.541457i	0.889280	+	0.457364i	$0.151206\pi$
$348$		0			0
$349$	−24.7634	−	14.2972i	−1.32556	−	0.765310i	−0.340947	−	0.940083i	$-0.610748\pi$
$349$	−24.7634	−	14.2972i	−1.32556	−	0.765310i	−0.984609	+	0.174773i	$0.944081\pi$
$350$		0			0
$351$	1.88667	−	0.795432i	0.100703	−	0.0424570i
$352$		0			0
$353$	5.57817	−	9.66167i	0.296896	−	0.514239i	−0.678528	−	0.734574i	$-0.737382\pi$
$353$	5.57817	−	9.66167i	0.296896	−	0.514239i	0.975424	+	0.220336i	$0.0707153\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.0561207	+	0.0972040i	0.00297022	+	0.00514458i
$358$		0			0
$359$			11.0490i			0.583145i	0.956549	+	0.291572i	$0.0941784\pi$
$359$			11.0490i			0.583145i	−0.956549	+	0.291572i	$0.905822\pi$
$360$		0			0
$361$	−8.92820	+	15.4641i	−0.469905	+	0.813900i
$362$		0			0
$363$			0.758301i			0.0398005i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−21.1355	−	12.2026i	−1.10326	−	0.636970i	−0.166188	−	0.986094i	$-0.553146\pi$
$367$	−21.1355	−	12.2026i	−1.10326	−	0.636970i	−0.937076	+	0.349124i	$0.886479\pi$
$368$		0			0
$369$			12.7655i			0.664545i
$370$		0			0
$371$	0.239385	−	0.138209i	0.0124283	−	0.00717546i
$372$		0			0
$373$	4.59974	−	2.65566i	0.238165	−	0.137505i	−0.376168	−	0.926552i	$-0.622758\pi$
$373$	4.59974	−	2.65566i	0.238165	−	0.137505i	0.614333	+	0.789047i	$0.289425\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.6714	−	3.34074i	−1.37365	−	0.172057i
$378$		0			0
$379$	−29.0469	−	16.7703i	−1.49204	−	0.861430i	−0.492082	−	0.870549i	$-0.663764\pi$
$379$	−29.0469	−	16.7703i	−1.49204	−	0.861430i	−0.999958	+	0.00911888i	$0.997097\pi$
$380$		0			0
$381$	−0.282847	−	0.489906i	−0.0144907	−	0.0250986i
$382$		0			0
$383$	−11.9014	−	20.6138i	−0.608131	−	1.05331i	−0.991548	−	0.129739i	$-0.958586\pi$
$383$	−11.9014	−	20.6138i	−0.608131	−	1.05331i	0.383417	−	0.923575i	$-0.374747\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	24.7138	+	14.2685i	1.25627	+	0.725310i
$388$		0			0
$389$	26.2787			1.33238			0.666191	−	0.745781i	$-0.267923\pi$
$389$	26.2787			1.33238			0.666191	+	0.745781i	$0.267923\pi$
$390$		0			0
$391$	4.41926			0.223492
$392$		0			0
$393$	−1.36486	−	0.788003i	−0.0688482	−	0.0397495i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	16.6460	+	28.8317i	0.835439	+	1.44702i	0.893673	+	0.448719i	$0.148120\pi$
$397$	16.6460	+	28.8317i	0.835439	+	1.44702i	−0.0582340	+	0.998303i	$0.518547\pi$
$398$		0			0
$399$	−0.0419062	−	0.0725836i	−0.00209793	−	0.00363373i
$400$		0			0
$401$	12.2709	+	7.08460i	0.612779	+	0.353788i	0.774052	−	0.633122i	$-0.218227\pi$
$401$	12.2709	+	7.08460i	0.612779	+	0.353788i	−0.161273	+	0.986910i	$0.551560\pi$
$402$		0			0
$403$	−19.4133	+	8.18476i	−0.967046	+	0.407712i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.47538	+	0.851811i	−0.0731319	+	0.0422227i
$408$		0			0
$409$	−5.93213	+	3.42491i	−0.293325	+	0.169351i	−0.639440	−	0.768841i	$-0.720834\pi$
$409$	−5.93213	+	3.42491i	−0.293325	+	0.169351i	0.346116	+	0.938192i	$0.387501\pi$
$410$		0			0
$411$			0.0383462i			0.00189148i
$412$		0			0
$413$	8.25227	+	4.76445i	0.406068	+	0.234443i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			0.883073i			0.0432443i
$418$		0			0
$419$	−8.19109	+	14.1874i	−0.400161	+	0.693099i	−0.993745	−	0.111673i	$-0.964379\pi$
$419$	−8.19109	+	14.1874i	−0.400161	+	0.693099i	0.593584	+	0.804772i	$0.297712\pi$
$420$		0			0
$421$			21.7045i			1.05781i	0.848681	+	0.528906i	$0.177397\pi$
$421$			21.7045i			1.05781i	−0.848681	+	0.528906i	$0.822603\pi$
$422$		0			0
$423$	−5.18059	−	8.97305i	−0.251889	−	0.436284i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.12305	−	1.94518i	0.0543481	−	0.0941337i
$428$		0			0
$429$	−0.357393	+	0.471883i	−0.0172551	+	0.0227827i
$430$		0			0
$431$	28.0495	+	16.1944i	1.35110	+	0.780056i	0.988403	−	0.151853i	$-0.0485240\pi$
$431$	28.0495	+	16.1944i	1.35110	+	0.780056i	0.362693	+	0.931909i	$0.381857\pi$
$432$		0			0
$433$	24.9393	−	14.3987i	1.19851	−	0.691959i	0.238286	−	0.971195i	$-0.423414\pi$
$433$	24.9393	−	14.3987i	1.19851	−	0.691959i	0.960223	+	0.279236i	$0.0900811\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.29992			−0.157857
$438$		0			0
$439$	8.79992	−	15.2419i	0.419997	−	0.727457i	−0.575941	−	0.817491i	$-0.695364\pi$
$439$	8.79992	−	15.2419i	0.419997	−	0.727457i	0.995939	+	0.0900341i	$0.0286976\pi$
$440$		0			0
$441$	−18.8923			−0.899632
$442$		0			0
$443$			14.4043i			0.684370i	0.939633	+	0.342185i	$0.111167\pi$
$443$			14.4043i			0.684370i	−0.939633	+	0.342185i	$0.888833\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.03013			0.0487236
$448$		0			0
$449$	2.58821	−	1.49430i	0.122145	−	0.0705206i	−0.437683	−	0.899130i	$-0.644201\pi$
$449$	2.58821	−	1.49430i	0.122145	−	0.0705206i	0.559828	+	0.828609i	$0.310867\pi$
$450$		0			0
$451$	−3.69615	−	6.40192i	−0.174045	−	0.301455i
$452$		0			0
$453$	0.0469680	−	0.0813509i	0.00220675	−	0.00382220i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.3102	−	23.0540i	0.622626	−	1.07842i	−0.366369	−	0.930470i	$-0.619399\pi$
$457$	13.3102	−	23.0540i	0.622626	−	1.07842i	0.988995	−	0.147950i	$-0.0472674\pi$
$458$		0			0
$459$	−0.406634	−	0.704310i	−0.0189800	−	0.0328744i
$460$		0			0
$461$	7.26488	−	4.19438i	0.338359	−	0.195352i	−0.321187	−	0.947016i	$-0.604082\pi$
$461$	7.26488	−	4.19438i	0.338359	−	0.195352i	0.659546	+	0.751664i	$0.270748\pi$
$462$		0			0
$463$	21.3014			0.989960			0.494980	−	0.868904i	$-0.335175\pi$
$463$	21.3014			0.989960			0.494980	+	0.868904i	$0.335175\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			2.12392i			0.0982833i	0.998792	+	0.0491417i	$0.0156486\pi$
$467$			2.12392i			0.0982833i	−0.998792	+	0.0491417i	$0.984351\pi$
$468$		0			0
$469$	11.3732			0.525165
$470$		0			0
$471$	0.832846	−	1.44253i	0.0383755	−	0.0664684i
$472$		0			0
$473$	−16.5254			−0.759837
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.865955	+	0.499960i	−0.0396494	+	0.0228916i
$478$		0			0
$479$	25.1617	+	14.5271i	1.14967	+	0.663762i	0.948806	−	0.315858i	$-0.102292\pi$
$479$	25.1617	+	14.5271i	1.14967	+	0.663762i	0.200862	+	0.979619i	$0.435626\pi$
$480$		0			0
$481$	3.51887	+	0.440759i	0.160447	+	0.0200969i
$482$		0			0
$483$	−0.120923	+	0.209445i	−0.00550220	+	0.00953010i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−15.1595	−	26.2570i	−0.686941	−	1.18982i	−0.972822	−	0.231552i	$-0.925620\pi$
$487$	−15.1595	−	26.2570i	−0.686941	−	1.18982i	0.285881	−	0.958265i	$-0.407714\pi$
$488$		0			0
$489$		−	1.63811i		−	0.0740781i
$490$		0			0
$491$	19.0759	−	33.0405i	0.860884	−	1.49110i	−0.0101919	−	0.999948i	$-0.503244\pi$
$491$	19.0759	−	33.0405i	0.860884	−	1.49110i	0.871076	−	0.491148i	$-0.163422\pi$
$492$		0			0
$493$			10.6767i			0.480853i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.00087	+	4.04196i	0.314032	+	0.181306i
$498$		0			0
$499$		−	16.5179i		−	0.739444i	−0.929142	−	0.369722i	$-0.879453\pi$
$499$		−	16.5179i		−	0.739444i	0.929142	−	0.369722i	$-0.120547\pi$
$500$		0			0
$501$	−0.251154	+	0.145004i	−0.0112207	+	0.00647829i
$502$		0			0
$503$	−10.1859	+	5.88081i	−0.454165	+	0.262212i	−0.709588	−	0.704617i	$-0.751119\pi$
$503$	−10.1859	+	5.88081i	−0.454165	+	0.262212i	0.255423	+	0.966830i	$0.417785\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.18614	−	0.333882i	0.0526785	−	0.0148282i
$508$		0			0
$509$	−27.5930	−	15.9308i	−1.22304	−	0.706122i	−0.257474	−	0.966285i	$-0.582890\pi$
$509$	−27.5930	−	15.9308i	−1.22304	−	0.706122i	−0.965565	+	0.260164i	$0.916223\pi$
$510$		0			0
$511$	−4.62227	−	8.00601i	−0.204477	−	0.354165i
$512$		0			0
$513$	0.303639	+	0.525918i	0.0134060	+	0.0232199i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.19615	+	3.00000i	0.228527	+	0.131940i
$518$		0			0
$519$	0.324184			0.0142301
$520$		0			0
$521$	−19.5013			−0.854367			−0.427183	−	0.904165i	$-0.640494\pi$
$521$	−19.5013			−0.854367			−0.427183	+	0.904165i	$0.640494\pi$
$522$		0			0
$523$	−38.5952	−	22.2830i	−1.68765	−	0.974365i	−0.956311	−	0.292352i	$-0.905562\pi$
$523$	−38.5952	−	22.2830i	−1.68765	−	0.974365i	−0.731340	−	0.682014i	$-0.761105\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.18414	+	7.24714i	0.182264	+	0.315690i
$528$		0			0
$529$	−6.73891	−	11.6721i	−0.292996	−	0.507484i
$530$		0			0
$531$	−29.8519	−	17.2350i	−1.29546	−	0.747935i
$532$		0			0
$533$	−1.91253	+	15.2690i	−0.0828407	+	0.661374i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.852257	+	0.492051i	−0.0367776	+	0.0212336i
$538$		0			0
$539$	9.47451	−	5.47011i	0.408096	−	0.235614i
$540$		0			0
$541$			3.74450i			0.160989i	0.996755	+	0.0804943i	$0.0256499\pi$
$541$			3.74450i			0.160989i	−0.996755	+	0.0804943i	$0.974350\pi$
$542$		0			0
$543$	0.849547	+	0.490486i	0.0364576	+	0.0210488i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			38.3803i			1.64102i	0.571630	+	0.820511i	$0.306311\pi$
$547$			38.3803i			1.64102i	−0.571630	+	0.820511i	$0.693689\pi$
$548$		0			0
$549$	−4.06253	+	7.03651i	−0.173385	+	0.300311i
$550$		0			0
$551$		−	7.97242i		−	0.339637i
$552$		0			0
$553$	0.104342	+	0.180725i	0.00443706	+	0.00768522i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.3231	−	23.0763i	0.564517	−	0.977772i	−0.432577	−	0.901597i	$-0.642396\pi$
$557$	13.3231	−	23.0763i	0.564517	−	0.977772i	0.997094	−	0.0761755i	$-0.0242709\pi$
$558$		0			0
$559$	27.4228	+	20.7694i	1.15986	+	0.878452i
$560$		0			0
$561$	0.203622	+	0.117561i	0.00859691	+	0.00496343i
$562$		0			0
$563$	−14.4570	+	8.34675i	−0.609290	+	0.351774i	−0.772687	−	0.634787i	$-0.781088\pi$
$563$	−14.4570	+	8.34675i	−0.609290	+	0.351774i	0.163398	+	0.986560i	$0.447755\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.37475			−0.309710
$568$		0			0
$569$	21.9620	−	38.0393i	0.920694	−	1.59469i	0.122350	−	0.992487i	$-0.460957\pi$
$569$	21.9620	−	38.0393i	0.920694	−	1.59469i	0.798344	−	0.602202i	$-0.205710\pi$
$570$		0			0
$571$	−11.4641			−0.479758			−0.239879	−	0.970803i	$-0.577108\pi$
$571$	−11.4641			−0.479758			−0.239879	+	0.970803i	$0.577108\pi$
$572$		0			0
$573$		−	1.46977i		−	0.0614004i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−44.9354			−1.87069			−0.935343	−	0.353743i	$-0.884909\pi$
$577$	−44.9354			−1.87069			−0.935343	+	0.353743i	$0.884909\pi$
$578$		0			0
$579$	−0.457256	+	0.263997i	−0.0190029	+	0.0109713i
$580$		0			0
$581$	−2.34477	−	4.06126i	−0.0972773	−	0.168489i
$582$		0			0
$583$	0.289519	−	0.501461i	0.0119906	−	0.0207684i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.2608	−	21.2364i	0.506059	−	0.876520i	−0.493916	−	0.869509i	$-0.664435\pi$
$587$	12.2608	−	21.2364i	0.506059	−	0.876520i	0.999975	−	0.00701059i	$-0.00223156\pi$
$588$		0			0
$589$	−3.12436	−	5.41154i	−0.128737	−	0.222979i
$590$		0			0
$591$	−2.04177	+	1.17882i	−0.0839873	+	0.0484901i
$592$		0			0
$593$	−18.7655			−0.770607			−0.385303	−	0.922790i	$-0.625903\pi$
$593$	−18.7655			−0.770607			−0.385303	+	0.922790i	$0.625903\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	1.76768i		−	0.0723464i
$598$		0			0
$599$	35.9293			1.46803			0.734015	−	0.679133i	$-0.237644\pi$
$599$	35.9293			1.46803			0.734015	+	0.679133i	$0.237644\pi$
$600$		0			0
$601$	19.8863	−	34.4441i	0.811179	−	1.40500i	−0.100860	−	0.994901i	$-0.532160\pi$
$601$	19.8863	−	34.4441i	0.811179	−	1.40500i	0.912039	−	0.410103i	$-0.134507\pi$
$602$		0			0
$603$	−41.1415			−1.67541
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.9783	−	16.7306i	1.17619	−	0.679076i	0.221063	−	0.975260i	$-0.429047\pi$
$607$	28.9783	−	16.7306i	1.17619	−	0.679076i	0.955131	+	0.296184i	$0.0957141\pi$
$608$		0			0
$609$	−0.506008	−	0.292144i	−0.0205045	−	0.0118383i
$610$		0			0
$611$	−4.85224	−	11.5089i	−0.196300	−	0.465602i
$612$		0			0
$613$	9.88495	−	17.1212i	0.399249	−	0.691520i	−0.594384	−	0.804181i	$-0.702604\pi$
$613$	9.88495	−	17.1212i	0.399249	−	0.691520i	0.993633	+	0.112661i	$0.0359374\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.75436	−	16.8950i	−0.392696	−	0.680169i	0.600108	−	0.799919i	$-0.295124\pi$
$617$	−9.75436	−	16.8950i	−0.392696	−	0.680169i	−0.992804	+	0.119750i	$0.961791\pi$
$618$		0			0
$619$		−	40.4640i		−	1.62639i	−0.581994	−	0.813193i	$-0.697727\pi$
$619$		−	40.4640i		−	1.62639i	0.581994	−	0.813193i	$-0.302273\pi$
$620$		0			0
$621$	0.876173	−	1.51758i	0.0351596	−	0.0608983i
$622$		0			0
$623$		−	3.80040i		−	0.152260i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.152047	−	0.0877845i	−0.00607218	−	0.00350578i
$628$		0			0
$629$		−	1.40862i		−	0.0561653i
$630$		0			0
$631$	−16.9707	+	9.79806i	−0.675594	+	0.390054i	−0.798193	−	0.602402i	$-0.794211\pi$
$631$	−16.9707	+	9.79806i	−0.675594	+	0.390054i	0.122599	+	0.992456i	$0.460877\pi$
$632$		0			0
$633$	0.791718	−	0.457099i	0.0314680	−	0.0181680i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−22.5973	−	2.83044i	−0.895338	−	0.112146i
$638$		0			0
$639$	−25.3250	−	14.6214i	−1.00184	−	0.578414i
$640$		0			0
$641$	15.5238	+	26.8881i	0.613155	+	1.06202i	0.990705	+	0.136026i	$0.0434332\pi$
$641$	15.5238	+	26.8881i	0.613155	+	1.06202i	−0.377550	+	0.925989i	$0.623233\pi$
$642$		0			0
$643$	2.97329	+	5.14990i	0.117255	+	0.203092i	0.918679	−	0.395005i	$-0.129257\pi$
$643$	2.97329	+	5.14990i	0.117255	+	0.203092i	−0.801424	+	0.598097i	$0.795924\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	36.8078	+	21.2510i	1.44706	+	0.835462i	0.998305	−	0.0581916i	$-0.0185334\pi$
$647$	36.8078	+	21.2510i	1.44706	+	0.835462i	0.448757	+	0.893654i	$0.351867\pi$
$648$		0			0
$649$	19.9610			0.783539
$650$		0			0
$651$	−0.457959			−0.0179488
$652$		0			0
$653$	−26.5097	−	15.3054i	−1.03740	−	0.598945i	−0.118307	−	0.992977i	$-0.537747\pi$
$653$	−26.5097	−	15.3054i	−1.03740	−	0.598945i	−0.919097	+	0.394032i	$0.871080\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.7207	+	28.9610i	0.652335	+	1.12988i
$658$		0			0
$659$	−12.7191	−	22.0302i	−0.495467	−	0.858175i	0.504519	−	0.863401i	$-0.331670\pi$
$659$	−12.7191	−	22.0302i	−0.495467	−	0.858175i	−0.999986	+	0.00522582i	$0.998337\pi$
$660$		0			0
$661$	−0.288909	−	0.166802i	−0.0112373	−	0.00648784i	0.494371	−	0.869251i	$-0.335398\pi$
$661$	−0.288909	−	0.166802i	−0.0112373	−	0.00648784i	−0.505608	+	0.862763i	$0.668732\pi$
$662$		0			0
$663$	−0.190145	−	0.451001i	−0.00738461	−	0.0175154i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−19.9229	+	11.5025i	−0.771419	+	0.445379i
$668$		0			0
$669$	0.0953167	−	0.0550311i	0.00368516	−	0.00212763i
$670$		0			0
$671$		−	4.70510i		−	0.181638i
$672$		0			0
$673$	−8.49928	−	4.90706i	−0.327623	−	0.189153i	0.327162	−	0.944968i	$-0.393908\pi$
$673$	−8.49928	−	4.90706i	−0.327623	−	0.189153i	−0.654785	+	0.755815i	$0.727241\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	23.2414i		−	0.893241i	−0.894724	−	0.446620i	$-0.852627\pi$
$677$		−	23.2414i		−	0.893241i	0.894724	−	0.446620i	$-0.147373\pi$
$678$		0			0
$679$	−3.94168	+	6.82719i	−0.151268	+	0.262004i
$680$		0			0
$681$			2.58258i			0.0989648i
$682$		0			0
$683$	−2.63355	−	4.56144i	−0.100770	−	0.174539i	0.811232	−	0.584724i	$-0.198797\pi$
$683$	−2.63355	−	4.56144i	−0.100770	−	0.174539i	−0.912002	+	0.410186i	$0.865464\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.15372	−	1.99830i	0.0440171	−	0.0762398i
$688$		0			0
$689$	−1.11069	+	0.468271i	−0.0423138	+	0.0178397i
$690$		0			0
$691$	17.1334	+	9.89199i	0.651787	+	0.376309i	0.789140	−	0.614213i	$-0.210526\pi$
$691$	17.1334	+	9.89199i	0.651787	+	0.376309i	−0.137354	+	0.990522i	$0.543860\pi$
$692$		0			0
$693$	3.70963	−	2.14176i	0.140917	−	0.0813586i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	6.11224			0.231518
$698$		0			0
$699$	1.09119	−	1.88999i	0.0412725	−	0.0714861i
$700$		0			0
$701$	18.1256			0.684595			0.342298	−	0.939592i	$-0.388795\pi$
$701$	18.1256			0.684595			0.342298	+	0.939592i	$0.388795\pi$
$702$		0			0
$703$			1.05184i			0.0396708i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.79685			−0.180404
$708$		0			0
$709$	22.3514	−	12.9046i	0.839424	−	0.484642i	−0.0176445	−	0.999844i	$-0.505617\pi$
$709$	22.3514	−	12.9046i	0.839424	−	0.484642i	0.857068	+	0.515203i	$0.172283\pi$
$710$		0			0
$711$	−0.377447	−	0.653758i	−0.0141554	−	0.0245178i
$712$		0			0
$713$	−9.01556	+	15.6154i	−0.337635	+	0.584802i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.12350	−	1.94597i	0.0419580	−	0.0726734i
$718$		0			0
$719$	4.51338	+	7.81741i	0.168321	+	0.291540i	0.937830	−	0.347096i	$-0.112832\pi$
$719$	4.51338	+	7.81741i	0.168321	+	0.291540i	−0.769509	+	0.638636i	$0.779499\pi$
$720$		0			0
$721$	7.21503	−	4.16560i	0.268702	−	0.155135i
$722$		0			0
$723$	1.02662			0.0381803
$724$		0			0
$725$		0			0
$726$		0			0
$727$			24.8934i			0.923245i	0.887076	+	0.461623i	$0.152733\pi$
$727$			24.8934i			0.923245i	−0.887076	+	0.461623i	$0.847267\pi$
$728$		0			0
$729$	26.5160			0.982075
$730$		0			0
$731$	6.83190	−	11.8332i	0.252687	−	0.437667i
$732$		0			0
$733$	13.2793			0.490484			0.245242	−	0.969462i	$-0.421133\pi$
$733$	13.2793			0.490484			0.245242	+	0.969462i	$0.421133\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.6326	−	11.9122i	0.760010	−	0.438792i
$738$		0			0
$739$	−16.9656	−	9.79508i	−0.624089	−	0.360318i	0.154370	−	0.988013i	$-0.450665\pi$
$739$	−16.9656	−	9.79508i	−0.624089	−	0.360318i	−0.778459	+	0.627695i	$0.783998\pi$
$740$		0			0
$741$	0.141984	+	0.336769i	0.00521590	+	0.0123715i
$742$		0			0
$743$	25.6230	−	44.3804i	0.940017	−	1.62816i	0.174583	−	0.984642i	$-0.444142\pi$
$743$	25.6230	−	44.3804i	0.940017	−	1.62816i	0.765434	−	0.643515i	$-0.222525\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.48199	+	14.6912i	0.310340	+	0.537524i
$748$		0			0
$749$		−	13.4606i		−	0.491838i
$750$		0			0
$751$	−10.5992	+	18.3584i	−0.386772	+	0.669908i	−0.992013	−	0.126134i	$-0.959743\pi$
$751$	−10.5992	+	18.3584i	−0.386772	+	0.669908i	0.605242	+	0.796042i	$0.293077\pi$
$752$		0			0
$753$			0.106239i			0.00387156i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	28.5350	+	16.4747i	1.03712	+	0.598783i	0.919017	−	0.394218i	$-0.128984\pi$
$757$	28.5350	+	16.4747i	1.03712	+	0.598783i	0.118106	+	0.993001i	$0.462318\pi$
$758$		0			0
$759$			0.506618i			0.0183891i
$760$		0			0
$761$	45.2367	−	26.1174i	1.63983	−	0.946756i	0.658939	−	0.752197i	$-0.271006\pi$
$761$	45.2367	−	26.1174i	1.63983	−	0.946756i	0.980891	−	0.194559i	$-0.0623277\pi$
$762$		0			0
$763$	−2.24113	+	1.29392i	−0.0811343	+	0.0468429i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−33.1241	−	25.0874i	−1.19604	−	0.905854i
$768$		0			0
$769$	−23.2717	−	13.4359i	−0.839200	−	0.484513i	0.0177920	−	0.999842i	$-0.494336\pi$
$769$	−23.2717	−	13.4359i	−0.839200	−	0.484513i	−0.856992	+	0.515329i	$0.827670\pi$
$770$		0			0
$771$	−0.788191	−	1.36519i	−0.0283860	−	0.0491660i
$772$		0			0
$773$	−5.97746	−	10.3533i	−0.214994	−	0.372381i	0.738276	−	0.674498i	$-0.235640\pi$
$773$	−5.97746	−	10.3533i	−0.214994	−	0.372381i	−0.953271	+	0.302117i	$0.902307\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0667598	+	0.0385438i	0.00239500	+	0.00138275i
$778$		0			0
$779$	−4.56410			−0.163526
$780$		0			0
$781$	16.9341			0.605949
$782$		0			0
$783$	3.66638	+	2.11678i	0.131026	+	0.0756477i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	17.2468	+	29.8724i	0.614783	+	1.06484i	0.990422	+	0.138070i	$0.0440899\pi$
$787$	17.2468	+	29.8724i	0.614783	+	1.06484i	−0.375639	+	0.926766i	$0.622577\pi$
$788$		0			0
$789$	−1.16124	−	2.01133i	−0.0413413	−	0.0716051i
$790$		0			0
$791$	7.28290	+	4.20479i	0.258950	+	0.149505i
$792$		0			0
$793$	−5.91346	+	7.80782i	−0.209993	+	0.277264i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.7563	+	16.6025i	−1.01860	+	0.588089i	−0.913698	−	0.406393i	$-0.866786\pi$
$797$	−28.7563	+	16.6025i	−1.01860	+	0.588089i	−0.104902	+	0.994483i	$0.533453\pi$
$798$		0			0
$799$	−4.29638	+	2.48052i	−0.151995	+	0.0877543i
$800$		0			0
$801$			13.7476i			0.485748i
$802$		0			0
$803$	−16.7709	−	9.68268i	−0.591832	−	0.341694i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			0.619235i			0.0217981i
$808$		0			0
$809$	−4.35139	+	7.53682i	−0.152987	+	0.264980i	−0.932324	−	0.361624i	$-0.882222\pi$
$809$	−4.35139	+	7.53682i	−0.152987	+	0.264980i	0.779338	+	0.626604i	$0.215556\pi$
$810$		0			0
$811$			7.69132i			0.270079i	0.990840	+	0.135039i	$0.0431161\pi$
$811$			7.69132i			0.270079i	−0.990840	+	0.135039i	$0.956884\pi$
$812$		0			0
$813$	−0.268063	−	0.464299i	−0.00940139	−	0.0162837i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.10148	+	8.83602i	−0.178478	+	0.309133i
$818$		0			0
$819$	−8.84770	−	1.10822i	−0.309164	−	0.0387245i
$820$		0			0
$821$	−0.532962	−	0.307706i	−0.0186005	−	0.0107390i	0.490671	−	0.871345i	$-0.336752\pi$
$821$	−0.532962	−	0.307706i	−0.0186005	−	0.0107390i	−0.509271	+	0.860606i	$0.670085\pi$
$822$		0			0
$823$	−19.3449	+	11.1688i	−0.674320	+	0.389319i	−0.797712	−	0.603039i	$-0.793956\pi$
$823$	−19.3449	+	11.1688i	−0.674320	+	0.389319i	0.123391	+	0.992358i	$0.460623\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−33.8701			−1.17778			−0.588890	−	0.808213i	$-0.700435\pi$
$827$	−33.8701			−1.17778			−0.588890	+	0.808213i	$0.700435\pi$
$828$		0			0
$829$	17.2646	−	29.9033i	0.599626	−	1.03858i	−0.393250	−	0.919432i	$-0.628649\pi$
$829$	17.2646	−	29.9033i	0.599626	−	1.03858i	0.992876	−	0.119151i	$-0.0380173\pi$
$830$		0			0
$831$	0.352196			0.0122176
$832$		0			0
$833$			9.04579i			0.313418i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.31823			0.114695
$838$		0			0
$839$	25.9386	−	14.9757i	0.895501	−	0.517018i	0.0197630	−	0.999805i	$-0.493709\pi$
$839$	25.9386	−	14.9757i	0.895501	−	0.517018i	0.875738	+	0.482787i	$0.160376\pi$
$840$		0			0
$841$	−13.2894	−	23.0179i	−0.458255	−	0.793720i
$842$		0			0
$843$	−0.459932	+	0.796625i	−0.0158409	+	0.0274372i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.30735	−	5.72850i	0.113642	−	0.196834i
$848$		0			0
$849$	−1.14682	−	1.98635i	−0.0393587	−	0.0681712i
$850$		0			0
$851$	2.62852	−	1.51758i	0.0901045	−	0.0520219i
$852$		0			0
$853$	−54.1009			−1.85238			−0.926189	−	0.377059i	$-0.876935\pi$
$853$	−54.1009			−1.85238			−0.926189	+	0.377059i	$0.876935\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	16.4383i		−	0.561521i	−0.959778	−	0.280761i	$-0.909413\pi$
$857$		−	16.4383i		−	0.561521i	0.959778	−	0.280761i	$-0.0905867\pi$
$858$		0			0
$859$	−32.7187			−1.11635			−0.558174	−	0.829724i	$-0.688498\pi$
$859$	−32.7187			−1.11635			−0.558174	+	0.829724i	$0.688498\pi$
$860$		0			0
$861$	−0.167248	+	0.289682i	−0.00569980	+	0.00987235i
$862$		0			0
$863$	55.7922			1.89919			0.949594	−	0.313482i	$-0.101496\pi$
$863$	55.7922			1.89919			0.949594	+	0.313482i	$0.101496\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.22714	−	0.708491i	0.0416759	−	0.0240616i
$868$		0			0
$869$	0.378581	+	0.218574i	0.0128425	+	0.00741461i
$870$		0			0
$871$	−49.2100	−	6.16382i	−1.66742	−	0.208853i
$872$		0			0
$873$	14.2587	−	24.6968i	0.482583	−	0.835859i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.3461	−	33.5084i	−0.653271	−	1.13150i	−0.982324	−	0.187187i	$-0.940063\pi$
$877$	−19.3461	−	33.5084i	−0.653271	−	1.13150i	0.329054	−	0.944311i	$-0.393270\pi$
$878$		0			0
$879$		−	0.343916i		−	0.0116000i
$880$		0			0
$881$	−2.71058	+	4.69485i	−0.0913216	+	0.158174i	−0.908067	−	0.418824i	$-0.862442\pi$
$881$	−2.71058	+	4.69485i	−0.0913216	+	0.158174i	0.816746	+	0.576998i	$0.195776\pi$
$882$		0			0
$883$		−	21.2583i		−	0.715397i	−0.933837	−	0.357699i	$-0.883561\pi$
$883$		−	21.2583i		−	0.715397i	0.933837	−	0.357699i	$-0.116439\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.490318	−	0.283085i	−0.0164633	−	0.00950507i	0.491746	−	0.870739i	$-0.336359\pi$
$887$	−0.490318	−	0.283085i	−0.0164633	−	0.00950507i	−0.508209	+	0.861234i	$0.669692\pi$
$888$		0			0
$889$			4.93459i			0.165501i
$890$		0			0
$891$	−13.3788	+	7.72427i	−0.448208	+	0.258773i
$892$		0			0
$893$	3.20817	−	1.85224i	0.107357	−	0.0619827i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.636727	−	0.840701i	0.0212597	−	0.0280702i
$898$		0			0
$899$	−37.7259	−	21.7811i	−1.25823	−	0.726439i
$900$		0			0
$901$	0.239385	+	0.414628i	0.00797508	+	0.0138132i
$902$		0			0
$903$	0.373880	+	0.647579i	0.0124420	+	0.0215501i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	32.0876	+	18.5258i	1.06545	+	0.615139i	0.926935	−	0.375222i	$-0.122433\pi$
$907$	32.0876	+	18.5258i	1.06545	+	0.615139i	0.138516	+	0.990360i	$0.455767\pi$
$908$		0			0
$909$	17.3522			0.575536
$910$		0			0
$911$	−27.9952			−0.927522			−0.463761	−	0.885960i	$-0.653500\pi$
$911$	−27.9952			−0.927522			−0.463761	+	0.885960i	$0.653500\pi$
$912$		0			0
$913$	−8.50747	−	4.91179i	−0.281556	−	0.162557i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.87381	+	11.9058i	0.226993	+	0.393164i
$918$		0			0
$919$	18.4721	+	31.9945i	0.609337	+	1.05540i	0.991350	+	0.131246i	$0.0418977\pi$
$919$	18.4721	+	31.9945i	0.609337	+	1.05540i	−0.382013	+	0.924157i	$0.624769\pi$
$920$		0			0
$921$	0.771737	+	0.445563i	0.0254296	+	0.0146818i
$922$		0			0
$923$	−28.1011	−	21.2831i	−0.924958	−	0.700541i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−26.0997	+	15.0687i	−0.857228	+	0.494921i
$928$		0			0
$929$	−11.5432	+	6.66449i	−0.378721	+	0.218655i	−0.677262	−	0.735742i	$-0.736834\pi$
$929$	−11.5432	+	6.66449i	−0.378721	+	0.218655i	0.298541	+	0.954397i	$0.403500\pi$
$930$		0			0
$931$		−	6.75462i		−	0.221374i
$932$		0			0
$933$	−2.09629	−	1.21029i	−0.0686294	−	0.0396232i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			13.0922i			0.427702i	0.976866	+	0.213851i	$0.0686007\pi$
$937$			13.0922i			0.427702i	−0.976866	+	0.213851i	$0.931399\pi$
$938$		0			0
$939$	−0.249128	+	0.431503i	−0.00812999	+	0.0140816i
$940$		0			0
$941$		−	43.0399i		−	1.40306i	−0.712639	−	0.701531i	$-0.752500\pi$
$941$		−	43.0399i		−	1.40306i	0.712639	−	0.701531i	$-0.247500\pi$
$942$		0			0
$943$	6.58502	+	11.4056i	0.214438	+	0.371417i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.2023	−	26.3311i	0.494008	−	0.855646i	−0.505969	−	0.862552i	$-0.668865\pi$
$947$	15.2023	−	26.3311i	0.494008	−	0.855646i	0.999976	+	0.00690573i	$0.00219818\pi$
$948$		0			0
$949$	15.6609	+	37.1458i	0.508374	+	1.20580i
$950$		0			0
$951$	1.16185	+	0.670795i	0.0376756	+	0.0217520i
$952$		0			0
$953$	−18.5349	+	10.7011i	−0.600404	+	0.346643i	−0.769201	−	0.639008i	$-0.779345\pi$
$953$	−18.5349	+	10.7011i	−0.600404	+	0.346643i	0.168796	+	0.985651i	$0.446012\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.22396			−0.0395649
$958$		0			0
$959$	0.167248	−	0.289682i	0.00540072	−	0.00935433i
$960$		0			0
$961$	−3.14359			−0.101406
$962$		0			0
$963$			48.6924i			1.56909i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−41.8892			−1.34707			−0.673533	−	0.739157i	$-0.735224\pi$
$967$	−41.8892			−1.34707			−0.673533	+	0.739157i	$0.735224\pi$
$968$		0			0
$969$	0.125719	−	0.0725836i	0.00403866	−	0.00233172i
$970$		0			0
$971$	14.4126	+	24.9634i	0.462524	+	0.801114i	0.999086	−	0.0427462i	$-0.0136107\pi$
$971$	14.4126	+	24.9634i	0.462524	+	0.801114i	−0.536562	+	0.843861i	$0.680277\pi$
$972$		0			0
$973$	3.85155	−	6.67109i	0.123475	−	0.213865i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.2339	−	47.1705i	0.871289	−	1.50912i	0.0106254	−	0.999944i	$-0.496618\pi$
$977$	27.2339	−	47.1705i	0.871289	−	1.50912i	0.860664	−	0.509174i	$-0.170049\pi$
$978$		0			0
$979$	−3.98052	−	6.89445i	−0.127218	−	0.220348i
$980$		0			0
$981$	8.10709	−	4.68063i	0.258839	−	0.149441i
$982$		0			0
$983$	56.5991			1.80523			0.902616	−	0.430447i	$-0.141644\pi$
$983$	56.5991			1.80523			0.902616	+	0.430447i	$0.141644\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	0.271496i		−	0.00864180i
$988$		0			0
$989$	29.4414			0.936182
$990$		0			0
$991$	−11.3462	+	19.6522i	−0.360425	+	0.624274i	−0.988031	−	0.154257i	$-0.950702\pi$
$991$	−11.3462	+	19.6522i	−0.360425	+	0.624274i	0.627606	+	0.778531i	$0.284035\pi$
$992$		0			0
$993$	1.76156			0.0559014
$994$		0			0
$995$		0			0
$996$		0			0
$997$	40.4631	−	23.3614i	1.28148	−	0.739862i	0.304360	−	0.952557i	$-0.401557\pi$
$997$	40.4631	−	23.3614i	1.28148	−	0.739862i	0.977119	+	0.212695i	$0.0682240\pi$
$998$		0			0
$999$	−0.483721	−	0.279277i	−0.0153043	−	0.00883592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.ba.c.849.2		8
5.2	odd	4		1300.2.y.b.901.2		8
5.3	odd	4		260.2.x.a.121.3	yes	8
5.4	even	2		1300.2.ba.b.849.3		8
13.10	even	6		1300.2.ba.b.49.3		8
15.8	even	4		2340.2.dj.d.901.2		8
20.3	even	4		1040.2.da.c.641.2		8
65.23	odd	12		260.2.x.a.101.3	✓	8
65.33	even	12		3380.2.a.p.1.2		4
65.43	odd	12		3380.2.f.i.3041.3		8
65.48	odd	12		3380.2.f.i.3041.4		8
65.49	even	6	inner	1300.2.ba.c.49.2		8
65.58	even	12		3380.2.a.q.1.2		4
65.62	odd	12		1300.2.y.b.101.2		8
195.23	even	12		2340.2.dj.d.361.4		8
260.23	even	12		1040.2.da.c.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.3	✓	8	65.23	odd	12
260.2.x.a.121.3	yes	8	5.3	odd	4
1040.2.da.c.641.2		8	20.3	even	4
1040.2.da.c.881.2		8	260.23	even	12
1300.2.y.b.101.2		8	65.62	odd	12
1300.2.y.b.901.2		8	5.2	odd	4
1300.2.ba.b.49.3		8	13.10	even	6
1300.2.ba.b.849.3		8	5.4	even	2
1300.2.ba.c.49.2		8	65.49	even	6	inner
1300.2.ba.c.849.2		8	1.1	even	1	trivial
2340.2.dj.d.361.4		8	195.23	even	12
2340.2.dj.d.901.2		8	15.8	even	4
3380.2.a.p.1.2		4	65.33	even	12
3380.2.a.q.1.2		4	65.58	even	12
3380.2.f.i.3041.3		8	65.43	odd	12
3380.2.f.i.3041.4		8	65.48	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0820885 - 0.0473938i) q^{3} +(0.413419 + 0.716063i) q^{7} +(-1.49551 - 2.59030i) q^{9} +O(q^{10})\)	\(q+(-0.0820885 - 0.0473938i) q^{3} +(0.413419 + 0.716063i) q^{7} +(-1.49551 - 2.59030i) q^{9} +(1.50000 + 0.866025i) q^{11} +(-1.40072 - 3.32235i) q^{13} +(-1.24026 + 0.716063i) q^{17} +(0.926118 - 0.534695i) q^{19} -0.0783740i q^{21} +(-2.67238 - 1.54290i) q^{23} +0.567874i q^{27} +(3.72756 - 6.45632i) q^{29} -5.84325i q^{31} +(-0.0820885 - 0.142181i) q^{33} +(-0.491793 + 0.851811i) q^{37} +(-0.0424756 + 0.339112i) q^{39} +(-3.69615 - 2.13397i) q^{41} +(-8.26268 + 4.77046i) q^{43} +3.46410 q^{47} +(3.15817 - 5.47011i) q^{49} +0.135748 q^{51} -0.334308i q^{53} -0.101365 q^{57} +(9.98052 - 5.76225i) q^{59} +(-1.35824 - 2.35255i) q^{61} +(1.23654 - 2.14176i) q^{63} +(6.87752 - 11.9122i) q^{67} +(0.146248 + 0.253309i) q^{69} +(8.46704 - 4.88845i) q^{71} -11.1806 q^{73} +1.43213i q^{77} +0.252387 q^{79} +(-4.45961 + 7.72427i) q^{81} -5.67165 q^{83} +(-0.611979 + 0.353326i) q^{87} +(-3.98052 - 2.29815i) q^{89} +(1.79992 - 2.37653i) q^{91} +(-0.276934 + 0.479664i) q^{93} +(4.76717 + 8.25698i) q^{97} -5.18059i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9	\( 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9} + 12 q^{11} + 18 q^{17} + 6 q^{23} + 6 q^{33} - 18 q^{37} + 4 q^{39} + 12 q^{41} - 18 q^{43} + 4 q^{49} + 36 q^{57} + 24 q^{59} - 4 q^{61} + 12 q^{63} + 18 q^{67} + 24 q^{69} - 36 q^{71} - 48 q^{73} + 16 q^{79} + 8 q^{81} - 72 q^{83} - 18 q^{87} + 24 q^{89} - 48 q^{93} + 6 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9 + 12 * q^11 + 18 * q^17 + 6 * q^23 + 6 * q^33 - 18 * q^37 + 4 * q^39 + 12 * q^41 - 18 * q^43 + 4 * q^49 + 36 * q^57 + 24 * q^59 - 4 * q^61 + 12 * q^63 + 18 * q^67 + 24 * q^69 - 36 * q^71 - 48 * q^73 + 16 * q^79 + 8 * q^81 - 72 * q^83 - 18 * q^87 + 24 * q^89 - 48 * q^93 + 6 * q^97

Introduction

L-functions

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