LMFDB - Embedded newform 1300.2.ba.b.49.3

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			49.3
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1300.49
Dual form			1300.2.ba.b.849.3

$q$-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 $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0820885	−	0.0473938i	0.0473938	−	0.0273628i	−0.476116	−	0.879383i	$-0.657956\pi$
$3$	0.0820885	−	0.0473938i	0.0473938	−	0.0273628i	0.523510	+	0.852020i	$0.324622\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.413419	+	0.716063i	−0.156258	+	0.270646i	−0.933516	−	0.358535i	$-0.883276\pi$
$7$	−0.413419	+	0.716063i	−0.156258	+	0.270646i	0.777259	+	0.629181i	$0.216610\pi$
$8$		0			0
$9$	−1.49551	+	2.59030i	−0.498503	+	0.863432i
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		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	$-0.277770\pi$
$17$	1.24026	+	0.716063i	0.300807	+	0.173671i	−0.341999	+	0.939700i	$0.611104\pi$
$18$		0			0
$19$	0.926118	+	0.534695i	0.212466	+	0.122667i	0.602457	−	0.798151i	$-0.294189\pi$
$19$	0.926118	+	0.534695i	0.212466	+	0.122667i	−0.389991	+	0.920819i	$0.627522\pi$
$20$		0			0
$21$			0.0783740i			0.0171026i
$22$		0			0
$23$	2.67238	−	1.54290i	0.557231	−	0.321717i	−0.194803	−	0.980842i	$-0.562407\pi$
$23$	2.67238	−	1.54290i	0.557231	−	0.321717i	0.752033	+	0.659125i	$0.229073\pi$
$24$		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	0.971119	+	0.238597i	$0.0766874\pi$
$29$	3.72756	+	6.45632i	0.692190	+	1.19891i	−0.278928	+	0.960312i	$0.589979\pi$
$30$		0			0
$31$			5.84325i			1.04948i	0.851263	+	0.524740i	$0.175837\pi$
$31$			5.84325i			1.04948i	−0.851263	+	0.524740i	$0.824163\pi$
$32$		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	$-0.140903\pi$
$37$	0.491793	+	0.851811i	0.0808503	+	0.140037i	−0.822765	+	0.568382i	$0.807570\pi$
$38$		0			0
$39$	−0.0424756	−	0.339112i	−0.00680154	−	0.0543013i
$40$		0			0
$41$	−3.69615	+	2.13397i	−0.577242	+	0.333271i	−0.760037	−	0.649880i	$-0.774819\pi$
$41$	−3.69615	+	2.13397i	−0.577242	+	0.333271i	0.182795	+	0.983151i	$0.441486\pi$
$42$		0			0
$43$	8.26268	+	4.77046i	1.26005	+	0.727488i	0.973083	−	0.230453i	$-0.0740209\pi$
$43$	8.26268	+	4.77046i	1.26005	+	0.727488i	0.286963	+	0.957942i	$0.407354\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$		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	0.980292	−	0.197553i	$-0.0632995\pi$
$59$	9.98052	+	5.76225i	1.29935	+	0.750181i	0.319060	+	0.947734i	$0.396633\pi$
$60$		0			0
$61$	−1.35824	+	2.35255i	−0.173905	+	0.301213i	−0.939782	−	0.341775i	$-0.888972\pi$
$61$	−1.35824	+	2.35255i	−0.173905	+	0.301213i	0.765877	+	0.642988i	$0.222305\pi$
$62$		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	−0.889706	−	0.456534i	$-0.849091\pi$
$67$	−6.87752	−	11.9122i	−0.840223	−	1.45531i	0.0494832	−	0.998775i	$-0.484243\pi$
$68$		0			0
$69$	0.146248	−	0.253309i	0.0176062	−	0.0304948i
$70$		0			0
$71$	8.46704	+	4.88845i	1.00485	+	0.580152i	0.909680	−	0.415309i	$-0.136327\pi$
$71$	8.46704	+	4.88845i	1.00485	+	0.580152i	0.0951721	+	0.995461i	$0.469660\pi$
$72$		0			0
$73$	11.1806			1.30859			0.654295	−	0.756240i	$-0.272966\pi$
$73$	11.1806			1.30859			0.654295	+	0.756240i	$0.272966\pi$
$74$		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	$-0.399245\pi$
$83$	5.67165			0.622544			0.311272	+	0.950321i	$0.399245\pi$
$84$		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	−0.695904	−	0.718135i	$-0.744996\pi$
$89$	−3.98052	+	2.29815i	−0.421934	+	0.243604i	0.273971	+	0.961738i	$0.411663\pi$
$90$		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	$-0.994162\pi$
$97$	−4.76717	+	8.25698i	−0.484033	+	0.838370i	0.515799	+	0.856710i	$0.327495\pi$
$98$		0			0
$99$			5.18059i			0.520669i
$100$		0			0
$101$	−2.90072	−	5.02419i	−0.288632	−	0.499926i	0.684851	−	0.728683i	$-0.259867\pi$
$101$	−2.90072	−	5.02419i	−0.288632	−	0.499926i	−0.973484	+	0.228757i	$0.926534\pi$
$102$		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	$-0.378351\pi$
$107$	14.0985	−	8.13977i	1.36295	−	0.786902i	0.990016	+	0.140955i	$0.0450172\pi$
$108$		0			0
$109$		−	3.12979i		−	0.299780i	−0.988703	−	0.149890i	$-0.952108\pi$
$109$		−	3.12979i		−	0.299780i	0.988703	−	0.149890i	$-0.0478919\pi$
$110$		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	$-0.492114\pi$
$113$	−8.80813	−	5.08538i	−0.828599	−	0.478392i	−0.853373	+	0.521301i	$0.825447\pi$
$114$		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	$-0.751969\pi$
$127$	−5.16846	+	2.98401i	−0.458627	+	0.264788i	0.252840	+	0.967508i	$0.418635\pi$
$128$		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	$-0.827832\pi$
$137$	0.202274	−	0.350349i	0.0172815	−	0.0299324i	0.874537	+	0.484959i	$0.161166\pi$
$138$		0			0
$139$	−4.65817	+	8.06819i	−0.395101	+	0.684335i	−0.993114	−	0.117152i	$-0.962624\pi$
$139$	−4.65817	+	8.06819i	−0.395101	+	0.684335i	0.598013	+	0.801486i	$0.295957\pi$
$140$		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	0.0622030	−	0.998064i	$-0.480187\pi$
$149$	−9.41179	−	5.43390i	−0.771044	−	0.445162i	−0.833247	+	0.552901i	$0.813521\pi$
$150$		0			0
$151$		−	0.991015i		−	0.0806477i	−0.999187	−	0.0403238i	$-0.987161\pi$
$151$		−	0.991015i		−	0.0806477i	0.999187	−	0.0403238i	$-0.0128390\pi$
$152$		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	0.299122	+	0.954215i	$0.403306\pi$
$163$	−8.64098	+	14.9666i	−0.676814	+	1.17228i	−0.975935	+	0.218061i	$0.930027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.52978	−	2.64965i	−0.118378	−	0.205036i	0.800747	−	0.599002i	$-0.204436\pi$
$167$	−1.52978	−	2.64965i	−0.118378	−	0.205036i	−0.919125	+	0.393966i	$0.871103\pi$
$168$		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	$-0.291831\pi$
$173$	2.96190	+	1.71006i	0.225189	+	0.130013i	−0.383161	+	0.923681i	$0.625165\pi$
$174$		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	0.992180	−	0.124811i	$-0.0398326\pi$
$179$	5.19109	+	8.99123i	0.388000	+	0.672036i	−0.604180	+	0.796848i	$0.706499\pi$
$180$		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	−0.436427	−	0.899740i	$-0.643756\pi$
$191$	7.75296	−	13.4285i	0.560984	−	0.971653i	0.997411	−	0.0719134i	$-0.0229105\pi$
$192$		0			0
$193$	−2.78514	−	4.82401i	−0.200479	−	0.347239i	0.748204	−	0.663469i	$-0.230916\pi$
$193$	−2.78514	−	4.82401i	−0.200479	−	0.347239i	−0.948683	+	0.316229i	$0.897583\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.4364	−	21.5405i	−0.886058	−	1.53470i	−0.844497	−	0.535561i	$-0.820100\pi$
$197$	−12.4364	−	21.5405i	−0.886058	−	1.53470i	−0.0415608	−	0.999136i	$-0.513233\pi$
$198$		0			0
$199$	9.32443	−	16.1504i	0.660991	−	1.14487i	−0.319364	−	0.947632i	$-0.603469\pi$
$199$	9.32443	−	16.1504i	0.660991	−	1.14487i	0.980356	−	0.197239i	$-0.0631974\pi$
$200$		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	0.650917	−	0.759149i	$-0.274385\pi$
$211$	−4.82235	−	8.35255i	−0.331984	−	0.575013i	−0.982901	+	0.184136i	$0.941051\pi$
$212$		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	$-0.154288\pi$
$223$	0.580573	+	1.00558i	0.0388780	+	0.0673387i	−0.845932	+	0.533291i	$0.820955\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.6230	−	23.5957i	0.904191	−	1.56610i	0.0821911	−	0.996617i	$-0.473808\pi$
$227$	13.6230	−	23.5957i	0.904191	−	1.56610i	0.822000	−	0.569488i	$-0.192858\pi$
$228$		0			0
$229$		−	24.3432i		−	1.60864i	−0.594193	−	0.804322i	$-0.702529\pi$
$229$		−	24.3432i		−	1.60864i	0.594193	−	0.804322i	$-0.297471\pi$
$230$		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	$-0.721898\pi$
$239$		−	23.7057i		−	1.53340i	0.642008	−	0.766698i	$-0.278102\pi$
$240$		0			0
$241$	−9.37968	−	5.41536i	−0.604198	−	0.348834i	0.166493	−	0.986043i	$-0.446756\pi$
$241$	−9.37968	−	5.41536i	−0.604198	−	0.348834i	−0.770691	+	0.637209i	$0.780089\pi$
$242$		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	−0.883170	−	0.469054i	$-0.844595\pi$
$251$	−0.560405	+	0.970649i	−0.0353724	+	0.0612668i	0.847797	+	0.530321i	$0.177928\pi$
$252$		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	$-0.840249\pi$
$257$	−14.4026	+	8.31534i	−0.898409	+	0.518697i	−0.0217255	+	0.999764i	$0.506916\pi$
$258$		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	$-0.939237\pi$
$263$	−21.2193	+	12.2510i	−1.30844	+	0.755427i	−0.326603	+	0.945162i	$0.605904\pi$
$264$		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	−0.948256	−	0.317508i	$-0.897154\pi$
$269$	−3.26643	+	5.65763i	−0.199158	+	0.344952i	0.749098	+	0.662460i	$0.230487\pi$
$270$		0			0
$271$	4.89831	−	2.82804i	0.297551	−	0.171791i	−0.343791	−	0.939046i	$-0.611711\pi$
$271$	4.89831	−	2.82804i	0.297551	−	0.171791i	0.641342	+	0.767255i	$0.278378\pi$
$272$		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	$-0.297728\pi$
$277$	3.21784	+	1.85782i	0.193341	+	0.111626i	−0.400205	+	0.916426i	$0.631061\pi$
$278$		0			0
$279$	−15.1357	−	8.73863i	−0.906154	−	0.523168i
$280$		0			0
$281$			9.70447i			0.578920i	0.957190	+	0.289460i	$0.0934758\pi$
$281$			9.70447i			0.578920i	−0.957190	+	0.289460i	$0.906524\pi$
$282$		0			0
$283$	−20.9558	+	12.0988i	−1.24569	+	0.719200i	−0.970247	−	0.242117i	$-0.922158\pi$
$283$	−20.9558	+	12.0988i	−1.24569	+	0.719200i	−0.275444	+	0.961317i	$0.588825\pi$
$284$		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	$-0.867132\pi$
$293$	−1.81414	+	3.14218i	−0.105983	+	0.183568i	0.808156	+	0.588968i	$0.200466\pi$
$294$		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	$-0.413545\pi$
$307$	9.40129			0.536560			0.268280	+	0.963341i	$0.413545\pi$
$308$		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	$-0.369887\pi$
$317$	14.1536			0.794947			0.397474	+	0.917614i	$0.369887\pi$
$318$		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	−0.0124490	−	0.999923i	$-0.503963\pi$
$331$	−16.0945	−	9.29214i	−0.884632	−	0.510742i	−0.872183	+	0.489180i	$0.837296\pi$
$332$		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	$-0.515460\pi$
$347$	−17.4699	−	10.0862i	−0.937831	−	0.541457i	−0.889280	+	0.457364i	$0.848794\pi$
$348$		0			0
$349$	−24.7634	+	14.2972i	−1.32556	+	0.765310i	−0.984609	−	0.174773i	$-0.944081\pi$
$349$	−24.7634	+	14.2972i	−1.32556	+	0.765310i	−0.340947	+	0.940083i	$0.610748\pi$
$350$		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	$-0.262618\pi$
$353$	−5.57817	−	9.66167i	−0.296896	−	0.514239i	−0.975424	+	0.220336i	$0.929285\pi$
$354$		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	$-0.905822\pi$
$359$		−	11.0490i		−	0.583145i	0.956549	−	0.291572i	$-0.0941784\pi$
$360$		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	$-0.446854\pi$
$367$	21.1355	−	12.2026i	1.10326	−	0.636970i	0.937076	+	0.349124i	$0.113521\pi$
$368$		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	$-0.377242\pi$
$373$	−4.59974	−	2.65566i	−0.238165	−	0.137505i	−0.614333	+	0.789047i	$0.710575\pi$
$374$		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	−0.999958	−	0.00911888i	$-0.997097\pi$
$379$	−29.0469	+	16.7703i	−1.49204	+	0.861430i	−0.492082	+	0.870549i	$0.663764\pi$
$380$		0			0
$381$	−0.282847	+	0.489906i	−0.0144907	+	0.0250986i
$382$		0			0
$383$	11.9014	−	20.6138i	0.608131	−	1.05331i	−0.383417	−	0.923575i	$-0.625253\pi$
$383$	11.9014	−	20.6138i	0.608131	−	1.05331i	0.991548	−	0.129739i	$-0.0414139\pi$
$384$		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	0.0582340	+	0.998303i	$0.481453\pi$
$397$	−16.6460	+	28.8317i	−0.835439	+	1.44702i	−0.893673	+	0.448719i	$0.851880\pi$
$398$		0			0
$399$	−0.0419062	+	0.0725836i	−0.00209793	+	0.00363373i
$400$		0			0
$401$	12.2709	−	7.08460i	0.612779	−	0.353788i	−0.161273	−	0.986910i	$-0.551560\pi$
$401$	12.2709	−	7.08460i	0.612779	−	0.353788i	0.774052	+	0.633122i	$0.218227\pi$
$402$		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	0.346116	−	0.938192i	$-0.387501\pi$
$409$	−5.93213	−	3.42491i	−0.293325	−	0.169351i	−0.639440	+	0.768841i	$0.720834\pi$
$410$		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	0.593584	−	0.804772i	$-0.297712\pi$
$419$	−8.19109	−	14.1874i	−0.400161	−	0.693099i	−0.993745	+	0.111673i	$0.964379\pi$
$420$		0			0
$421$		−	21.7045i		−	1.05781i	−0.848681	−	0.528906i	$-0.822603\pi$
$421$		−	21.7045i		−	1.05781i	0.848681	−	0.528906i	$-0.177397\pi$
$422$		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	0.362693	−	0.931909i	$-0.381857\pi$
$431$	28.0495	−	16.1944i	1.35110	−	0.780056i	0.988403	+	0.151853i	$0.0485240\pi$
$432$		0			0
$433$	−24.9393	−	14.3987i	−1.19851	−	0.691959i	−0.238286	−	0.971195i	$-0.576586\pi$
$433$	−24.9393	−	14.3987i	−1.19851	−	0.691959i	−0.960223	+	0.279236i	$0.909919\pi$
$434$		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	0.995939	−	0.0900341i	$-0.0286976\pi$
$439$	8.79992	+	15.2419i	0.419997	+	0.727457i	−0.575941	+	0.817491i	$0.695364\pi$
$440$		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	0.559828	−	0.828609i	$-0.310867\pi$
$449$	2.58821	+	1.49430i	0.122145	+	0.0705206i	−0.437683	+	0.899130i	$0.644201\pi$
$450$		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	−0.988995	−	0.147950i	$-0.952733\pi$
$457$	−13.3102	−	23.0540i	−0.622626	−	1.07842i	0.366369	−	0.930470i	$-0.380601\pi$
$458$		0			0
$459$	−0.406634	+	0.704310i	−0.0189800	+	0.0328744i
$460$		0			0
$461$	7.26488	+	4.19438i	0.338359	+	0.195352i	0.659546	−	0.751664i	$-0.270748\pi$
$461$	7.26488	+	4.19438i	0.338359	+	0.195352i	−0.321187	+	0.947016i	$0.604082\pi$
$462$		0			0
$463$	−21.3014			−0.989960			−0.494980	−	0.868904i	$-0.664825\pi$
$463$	−21.3014			−0.989960			−0.494980	+	0.868904i	$0.664825\pi$
$464$		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	0.200862	−	0.979619i	$-0.435626\pi$
$479$	25.1617	−	14.5271i	1.14967	−	0.663762i	0.948806	+	0.315858i	$0.102292\pi$
$480$		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	−0.285881	−	0.958265i	$-0.592286\pi$
$487$	15.1595	−	26.2570i	0.686941	−	1.18982i	0.972822	−	0.231552i	$-0.0743805\pi$
$488$		0			0
$489$			1.63811i			0.0740781i
$490$		0			0
$491$	19.0759	+	33.0405i	0.860884	+	1.49110i	0.871076	+	0.491148i	$0.163422\pi$
$491$	19.0759	+	33.0405i	0.860884	+	1.49110i	−0.0101919	+	0.999948i	$0.503244\pi$
$492$		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	$0.120547\pi$
$499$			16.5179i			0.739444i	−0.929142	+	0.369722i	$0.879453\pi$
$500$		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	$-0.248881\pi$
$503$	10.1859	+	5.88081i	0.454165	+	0.262212i	−0.255423	+	0.966830i	$0.582215\pi$
$504$		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	−0.965565	−	0.260164i	$-0.916223\pi$
$509$	−27.5930	+	15.9308i	−1.22304	+	0.706122i	−0.257474	+	0.966285i	$0.582890\pi$
$510$		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	0.731340	−	0.682014i	$-0.238895\pi$
$523$	38.5952	−	22.2830i	1.68765	−	0.974365i	0.956311	−	0.292352i	$-0.0944378\pi$
$524$		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	$-0.974350\pi$
$541$		−	3.74450i		−	0.160989i	0.996755	−	0.0804943i	$-0.0256499\pi$
$542$		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	−0.997094	−	0.0761755i	$-0.975729\pi$
$557$	−13.3231	−	23.0763i	−0.564517	−	0.977772i	0.432577	−	0.901597i	$-0.357604\pi$
$558$		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	$-0.218912\pi$
$563$	14.4570	+	8.34675i	0.609290	+	0.351774i	−0.163398	+	0.986560i	$0.552245\pi$
$564$		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	0.798344	+	0.602202i	$0.205710\pi$
$569$	21.9620	+	38.0393i	0.920694	+	1.59469i	0.122350	+	0.992487i	$0.460957\pi$
$570$		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	$-0.115091\pi$
$577$	44.9354			1.87069			0.935343	+	0.353743i	$0.115091\pi$
$578$		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	−0.999975	−	0.00701059i	$-0.997768\pi$
$587$	−12.2608	−	21.2364i	−0.506059	−	0.876520i	0.493916	−	0.869509i	$-0.335565\pi$
$588$		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	$-0.374097\pi$
$593$	18.7655			0.770607			0.385303	+	0.922790i	$0.374097\pi$
$594$		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	0.912039	+	0.410103i	$0.134507\pi$
$601$	19.8863	+	34.4441i	0.811179	+	1.40500i	−0.100860	+	0.994901i	$0.532160\pi$
$602$		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	$-0.570953\pi$
$607$	−28.9783	−	16.7306i	−1.17619	−	0.679076i	−0.955131	+	0.296184i	$0.904286\pi$
$608$		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	$-0.297396\pi$
$613$	−9.88495	−	17.1212i	−0.399249	−	0.691520i	−0.993633	+	0.112661i	$0.964063\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.75436	−	16.8950i	0.392696	−	0.680169i	−0.600108	−	0.799919i	$-0.704876\pi$
$617$	9.75436	−	16.8950i	0.392696	−	0.680169i	0.992804	+	0.119750i	$0.0382092\pi$
$618$		0			0
$619$			40.4640i			1.62639i	0.581994	+	0.813193i	$0.302273\pi$
$619$			40.4640i			1.62639i	−0.581994	+	0.813193i	$0.697727\pi$
$620$		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	0.122599	−	0.992456i	$-0.460877\pi$
$631$	−16.9707	−	9.79806i	−0.675594	−	0.390054i	−0.798193	+	0.602402i	$0.794211\pi$
$632$		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	−0.377550	−	0.925989i	$-0.623233\pi$
$641$	15.5238	−	26.8881i	0.613155	−	1.06202i	0.990705	−	0.136026i	$-0.0434332\pi$
$642$		0			0
$643$	−2.97329	+	5.14990i	−0.117255	+	0.203092i	−0.918679	−	0.395005i	$-0.870743\pi$
$643$	−2.97329	+	5.14990i	−0.117255	+	0.203092i	0.801424	+	0.598097i	$0.204076\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−36.8078	+	21.2510i	−1.44706	+	0.835462i	−0.998305	−	0.0581916i	$-0.981467\pi$
$647$	−36.8078	+	21.2510i	−1.44706	+	0.835462i	−0.448757	+	0.893654i	$0.648133\pi$
$648$		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	$-0.462253\pi$
$653$	26.5097	−	15.3054i	1.03740	−	0.598945i	0.919097	+	0.394032i	$0.128920\pi$
$654$		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	−0.999986	−	0.00522582i	$-0.998337\pi$
$659$	−12.7191	+	22.0302i	−0.495467	+	0.858175i	0.504519	+	0.863401i	$0.331670\pi$
$660$		0			0
$661$	−0.288909	+	0.166802i	−0.0112373	+	0.00648784i	−0.505608	−	0.862763i	$-0.668732\pi$
$661$	−0.288909	+	0.166802i	−0.0112373	+	0.00648784i	0.494371	+	0.869251i	$0.335398\pi$
$662$		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	$-0.606092\pi$
$673$	8.49928	−	4.90706i	0.327623	−	0.189153i	0.654785	+	0.755815i	$0.272759\pi$
$674$		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	$-0.801203\pi$
$683$	2.63355	−	4.56144i	0.100770	−	0.174539i	0.912002	+	0.410186i	$0.134536\pi$
$684$		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	−0.137354	−	0.990522i	$-0.543860\pi$
$691$	17.1334	−	9.89199i	0.651787	−	0.376309i	0.789140	+	0.614213i	$0.210526\pi$
$692$		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	0.857068	−	0.515203i	$-0.172283\pi$
$709$	22.3514	+	12.9046i	0.839424	+	0.484642i	−0.0176445	+	0.999844i	$0.505617\pi$
$710$		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	−0.769509	−	0.638636i	$-0.779499\pi$
$719$	4.51338	−	7.81741i	0.168321	−	0.291540i	0.937830	+	0.347096i	$0.112832\pi$
$720$		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	$-0.578867\pi$
$733$	−13.2793			−0.490484			−0.245242	+	0.969462i	$0.578867\pi$
$734$		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	−0.778459	−	0.627695i	$-0.783998\pi$
$739$	−16.9656	+	9.79508i	−0.624089	+	0.360318i	0.154370	+	0.988013i	$0.450665\pi$
$740$		0			0
$741$	0.141984	−	0.336769i	0.00521590	−	0.0123715i
$742$		0			0
$743$	−25.6230	−	44.3804i	−0.940017	−	1.62816i	−0.765434	−	0.643515i	$-0.777475\pi$
$743$	−25.6230	−	44.3804i	−0.940017	−	1.62816i	−0.174583	−	0.984642i	$-0.555858\pi$
$744$		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	0.605242	−	0.796042i	$-0.293077\pi$
$751$	−10.5992	−	18.3584i	−0.386772	−	0.669908i	−0.992013	+	0.126134i	$0.959743\pi$
$752$		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	$-0.871016\pi$
$757$	−28.5350	+	16.4747i	−1.03712	+	0.598783i	−0.118106	+	0.993001i	$0.537682\pi$
$758$		0			0
$759$		−	0.506618i		−	0.0183891i
$760$		0			0
$761$	45.2367	+	26.1174i	1.63983	+	0.946756i	0.980891	+	0.194559i	$0.0623277\pi$
$761$	45.2367	+	26.1174i	1.63983	+	0.946756i	0.658939	+	0.752197i	$0.271006\pi$
$762$		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	−0.856992	−	0.515329i	$-0.827670\pi$
$769$	−23.2717	+	13.4359i	−0.839200	+	0.484513i	0.0177920	+	0.999842i	$0.494336\pi$
$770$		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	$-0.764360\pi$
$773$	5.97746	−	10.3533i	0.214994	−	0.372381i	0.953271	+	0.302117i	$0.0976933\pi$
$774$		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	0.375639	+	0.926766i	$0.377423\pi$
$787$	−17.2468	+	29.8724i	−0.614783	+	1.06484i	−0.990422	+	0.138070i	$0.955910\pi$
$788$		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	$-0.133214\pi$
$797$	28.7563	+	16.6025i	1.01860	+	0.588089i	0.104902	+	0.994483i	$0.466547\pi$
$798$		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	0.779338	−	0.626604i	$-0.215556\pi$
$809$	−4.35139	−	7.53682i	−0.152987	−	0.264980i	−0.932324	+	0.361624i	$0.882222\pi$
$810$		0			0
$811$		−	7.69132i		−	0.270079i	−0.990840	−	0.135039i	$-0.956884\pi$
$811$		−	7.69132i		−	0.270079i	0.990840	−	0.135039i	$-0.0431161\pi$
$812$		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	−0.509271	−	0.860606i	$-0.670085\pi$
$821$	−0.532962	+	0.307706i	−0.0186005	+	0.0107390i	0.490671	+	0.871345i	$0.336752\pi$
$822$		0			0
$823$	19.3449	+	11.1688i	0.674320	+	0.389319i	0.797712	−	0.603039i	$-0.206044\pi$
$823$	19.3449	+	11.1688i	0.674320	+	0.389319i	−0.123391	+	0.992358i	$0.539377\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.8701			1.17778			0.588890	−	0.808213i	$-0.299565\pi$
$827$	33.8701			1.17778			0.588890	+	0.808213i	$0.299565\pi$
$828$		0			0
$829$	17.2646	+	29.9033i	0.599626	+	1.03858i	0.992876	+	0.119151i	$0.0380173\pi$
$829$	17.2646	+	29.9033i	0.599626	+	1.03858i	−0.393250	+	0.919432i	$0.628649\pi$
$830$		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	0.875738	−	0.482787i	$-0.160376\pi$
$839$	25.9386	+	14.9757i	0.895501	+	0.517018i	0.0197630	+	0.999805i	$0.493709\pi$
$840$		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	$-0.123065\pi$
$853$	54.1009			1.85238			0.926189	+	0.377059i	$0.123065\pi$
$854$		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	$-0.898504\pi$
$863$	−55.7922			−1.89919			−0.949594	+	0.313482i	$0.898504\pi$
$864$		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	−0.329054	−	0.944311i	$-0.606730\pi$
$877$	19.3461	−	33.5084i	0.653271	−	1.13150i	0.982324	−	0.187187i	$-0.0599369\pi$
$878$		0			0
$879$			0.343916i			0.0116000i
$880$		0			0
$881$	−2.71058	−	4.69485i	−0.0913216	−	0.158174i	0.816746	−	0.576998i	$-0.195776\pi$
$881$	−2.71058	−	4.69485i	−0.0913216	−	0.158174i	−0.908067	+	0.418824i	$0.862442\pi$
$882$		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	$-0.663641\pi$
$887$	0.490318	−	0.283085i	0.0164633	−	0.00950507i	0.508209	+	0.861234i	$0.330308\pi$
$888$		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	$-0.877567\pi$
$907$	−32.0876	+	18.5258i	−1.06545	+	0.615139i	−0.138516	+	0.990360i	$0.544233\pi$
$908$		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	−0.382013	−	0.924157i	$-0.624769\pi$
$919$	18.4721	−	31.9945i	0.609337	−	1.05540i	0.991350	−	0.131246i	$-0.0418977\pi$
$920$		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	0.298541	−	0.954397i	$-0.403500\pi$
$929$	−11.5432	−	6.66449i	−0.378721	−	0.218655i	−0.677262	+	0.735742i	$0.736834\pi$
$930$		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	$0.247500\pi$
$941$			43.0399i			1.40306i	−0.712639	+	0.701531i	$0.752500\pi$
$942$		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	$-0.331135\pi$
$947$	−15.2023	−	26.3311i	−0.494008	−	0.855646i	−0.999976	+	0.00690573i	$0.997802\pi$
$948$		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	$-0.220655\pi$
$953$	18.5349	+	10.7011i	0.600404	+	0.346643i	−0.168796	+	0.985651i	$0.553988\pi$
$954$		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	$-0.264776\pi$
$967$	41.8892			1.34707			0.673533	+	0.739157i	$0.264776\pi$
$968$		0			0
$969$	0.125719	+	0.0725836i	0.00403866	+	0.00233172i
$970$		0			0
$971$	14.4126	−	24.9634i	0.462524	−	0.801114i	−0.536562	−	0.843861i	$-0.680277\pi$
$971$	14.4126	−	24.9634i	0.462524	−	0.801114i	0.999086	+	0.0427462i	$0.0136107\pi$
$972$		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	−0.860664	−	0.509174i	$-0.829951\pi$
$977$	−27.2339	−	47.1705i	−0.871289	−	1.50912i	−0.0106254	−	0.999944i	$-0.503382\pi$
$978$		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	$-0.858356\pi$
$983$	−56.5991			−1.80523			−0.902616	+	0.430447i	$0.858356\pi$
$984$		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	0.627606	−	0.778531i	$-0.284035\pi$
$991$	−11.3462	−	19.6522i	−0.360425	−	0.624274i	−0.988031	+	0.154257i	$0.950702\pi$
$992$		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	$-0.598443\pi$
$997$	−40.4631	−	23.3614i	−1.28148	−	0.739862i	−0.977119	+	0.212695i	$0.931776\pi$
$998$		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.b.49.3		8
5.2	odd	4		1300.2.y.b.101.2		8
5.3	odd	4		260.2.x.a.101.3	✓	8
5.4	even	2		1300.2.ba.c.49.2		8
13.4	even	6		1300.2.ba.c.849.2		8
15.8	even	4		2340.2.dj.d.361.4		8
20.3	even	4		1040.2.da.c.881.2		8
65.3	odd	12		3380.2.f.i.3041.3		8
65.4	even	6	inner	1300.2.ba.b.849.3		8
65.17	odd	12		1300.2.y.b.901.2		8
65.23	odd	12		3380.2.f.i.3041.4		8
65.28	even	12		3380.2.a.p.1.2		4
65.43	odd	12		260.2.x.a.121.3	yes	8
65.63	even	12		3380.2.a.q.1.2		4
195.173	even	12		2340.2.dj.d.901.2		8
260.43	even	12		1040.2.da.c.641.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.3	✓	8	5.3	odd	4
260.2.x.a.121.3	yes	8	65.43	odd	12
1040.2.da.c.641.2		8	260.43	even	12
1040.2.da.c.881.2		8	20.3	even	4
1300.2.y.b.101.2		8	5.2	odd	4
1300.2.y.b.901.2		8	65.17	odd	12
1300.2.ba.b.49.3		8	1.1	even	1	trivial
1300.2.ba.b.849.3		8	65.4	even	6	inner
1300.2.ba.c.49.2		8	5.4	even	2
1300.2.ba.c.849.2		8	13.4	even	6
2340.2.dj.d.361.4		8	15.8	even	4
2340.2.dj.d.901.2		8	195.173	even	12
3380.2.a.p.1.2		4	65.28	even	12
3380.2.a.q.1.2		4	65.63	even	12
3380.2.f.i.3041.3		8	65.3	odd	12
3380.2.f.i.3041.4		8	65.23	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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