LMFDB - Embedded newform 260.2.z.a.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(49,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, 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("260.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.z (of order $6$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 $ x^16 - 7x^14 + 21x^12 - 22x^10 - 26x^8 - 198x^6 + 1701x^4 - 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.6
Root			$1.56631 + 0.739379i$ of defining polynomial
Character	$\chi$	$=$	260.49
Dual form			260.2.z.a.69.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28064 - 0.739379i) q^{3} +(0.494086 - 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +O(q^{10})$	\(q+(1.28064 - 0.739379i) q^{3} +(0.494086 - 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +(-4.01176 + 2.31619i) q^{11} +(-2.44512 - 2.64979i) q^{13} +(-0.979690 - 3.15814i) q^{15} +(5.87021 + 3.38917i) q^{17} +(1.45442 + 0.839708i) q^{19} -4.63238i q^{21} +(4.79118 - 2.76619i) q^{23} +(-4.51176 - 2.15500i) q^{25} +5.63891i q^{27} +(3.87062 + 6.70410i) q^{29} -1.46127i q^{31} +(-3.42509 + 5.93242i) q^{33} +(-5.14245 - 4.75622i) q^{35} +(3.72577 + 6.45322i) q^{37} +(-5.09053 - 1.58556i) q^{39} +(4.78901 - 2.76494i) q^{41} +(-10.7707 - 6.21849i) q^{43} +(1.33506 + 1.23478i) q^{45} -1.97634 q^{47} +(-1.40664 - 2.43637i) q^{49} +10.0235 q^{51} +5.65865i q^{53} +(3.06899 + 9.89323i) q^{55} +2.48345 q^{57} +(2.27725 + 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(1.27384 + 2.20635i) q^{63} +(-6.98675 + 4.02310i) q^{65} +(-0.317776 - 0.550404i) q^{67} +(4.09053 - 7.08500i) q^{69} +(-12.0089 - 6.93335i) q^{71} -4.89025 q^{73} +(-7.37131 + 0.576115i) q^{75} +14.5115i q^{77} -6.21024 q^{79} +(2.94938 + 5.10848i) q^{81} +3.33075 q^{83} +(10.2915 - 11.1272i) q^{85} +(9.91375 + 5.72371i) q^{87} +(-2.27725 + 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(-1.08043 - 1.87136i) q^{93} +(2.54984 - 2.75690i) q^{95} +(3.13942 - 5.43764i) q^{97} -3.76739i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	1.28064	−	0.739379i	0.739379	−	0.426881i	−0.0824643	−	0.996594i	$-0.526279\pi$
$3$	1.28064	−	0.739379i	0.739379	−	0.426881i	0.821844	+	0.569713i	$0.192946\pi$
$4$		0			0
$5$	0.494086	−	2.18080i	0.220962	−	0.975282i
$5$	0.494086	−	2.18080i	0.220962	−	0.975282i
$6$		0			0
$7$	1.56631	−	2.71292i	0.592008	−	1.02539i	−0.401953	−	0.915660i	$-0.631669\pi$
$7$	1.56631	−	2.71292i	0.592008	−	1.02539i	0.993962	−	0.109729i	$-0.0349981\pi$
$8$		0			0
$9$	−0.406637	+	0.704315i	−0.135546	+	0.234772i
$10$		0			0
$11$	−4.01176	+	2.31619i	−1.20959	+	0.698358i	−0.962670	−	0.270678i	$-0.912752\pi$
$11$	−4.01176	+	2.31619i	−1.20959	+	0.698358i	−0.246921	+	0.969036i	$0.579419\pi$
$12$		0			0
$13$	−2.44512	−	2.64979i	−0.678155	−	0.734919i
$13$	−2.44512	−	2.64979i	−0.678155	−	0.734919i
$14$		0			0
$15$	−0.979690	−	3.15814i	−0.252955	−	0.815428i
$16$		0			0
$17$	5.87021	+	3.38917i	1.42373	+	0.821994i	0.996616	−	0.0822017i	$-0.0261952\pi$
$17$	5.87021	+	3.38917i	1.42373	+	0.821994i	0.427119	+	0.904195i	$0.359529\pi$
$18$		0			0
$19$	1.45442	+	0.839708i	0.333666	+	0.192642i	0.657468	−	0.753483i	$-0.271628\pi$
$19$	1.45442	+	0.839708i	0.333666	+	0.192642i	−0.323802	+	0.946125i	$0.604961\pi$
$20$		0			0
$21$		−	4.63238i		−	1.01087i
$22$		0			0
$23$	4.79118	−	2.76619i	0.999030	−	0.576790i	0.0910690	−	0.995845i	$-0.470972\pi$
$23$	4.79118	−	2.76619i	0.999030	−	0.576790i	0.907961	+	0.419054i	$0.137638\pi$
$24$		0			0
$25$	−4.51176	−	2.15500i	−0.902352	−	0.431000i
$26$		0			0
$27$			5.63891i			1.08521i
$28$		0			0
$29$	3.87062	+	6.70410i	0.718755	+	1.24492i	0.961493	+	0.274829i	$0.0886212\pi$
$29$	3.87062	+	6.70410i	0.718755	+	1.24492i	−0.242738	+	0.970092i	$0.578045\pi$
$30$		0			0
$31$		−	1.46127i		−	0.262451i	−0.991353	−	0.131226i	$-0.958109\pi$
$31$		−	1.46127i		−	0.262451i	0.991353	−	0.131226i	$-0.0418912\pi$
$32$		0			0
$33$	−3.42509	+	5.93242i	−0.596231	+	1.03270i
$34$		0			0
$35$	−5.14245	−	4.75622i	−0.869232	−	0.803947i
$36$		0			0
$37$	3.72577	+	6.45322i	0.612512	+	1.06090i	0.990816	+	0.135220i	$0.0431742\pi$
$37$	3.72577	+	6.45322i	0.612512	+	1.06090i	−0.378303	+	0.925682i	$0.623492\pi$
$38$		0			0
$39$	−5.09053	−	1.58556i	−0.815137	−	0.253892i
$40$		0			0
$41$	4.78901	−	2.76494i	0.747918	−	0.431811i	−0.0770232	−	0.997029i	$-0.524542\pi$
$41$	4.78901	−	2.76494i	0.747918	−	0.431811i	0.824941	+	0.565219i	$0.191208\pi$
$42$		0			0
$43$	−10.7707	−	6.21849i	−1.64252	−	0.948311i	−0.979933	−	0.199329i	$-0.936124\pi$
$43$	−10.7707	−	6.21849i	−1.64252	−	0.948311i	−0.662591	−	0.748982i	$-0.730543\pi$
$44$		0			0
$45$	1.33506	+	1.23478i	0.199018	+	0.184071i
$46$		0			0
$47$	−1.97634			−0.288279			−0.144140	−	0.989557i	$-0.546041\pi$
$47$	−1.97634			−0.288279			−0.144140	+	0.989557i	$0.546041\pi$
$48$		0			0
$49$	−1.40664	−	2.43637i	−0.200948	−	0.348052i
$50$		0			0
$51$	10.0235			1.40357
$52$		0			0
$53$			5.65865i			0.777276i	0.921391	+	0.388638i	$0.127054\pi$
$53$			5.65865i			0.777276i	−0.921391	+	0.388638i	$0.872946\pi$
$54$		0			0
$55$	3.06899	+	9.89323i	0.413823	+	1.33400i
$56$		0			0
$57$	2.48345			0.328941
$58$		0			0
$59$	2.27725	+	1.31477i	0.296473	+	0.171169i	0.640857	−	0.767660i	$-0.278579\pi$
$59$	2.27725	+	1.31477i	0.296473	+	0.171169i	−0.344384	+	0.938829i	$0.611912\pi$
$60$		0			0
$61$	−4.87062	+	8.43615i	−0.623618	+	1.08014i	0.365188	+	0.930934i	$0.381005\pi$
$61$	−4.87062	+	8.43615i	−0.623618	+	1.08014i	−0.988806	+	0.149205i	$0.952329\pi$
$62$		0			0
$63$	1.27384	+	2.20635i	0.160488	+	0.277974i
$64$		0			0
$65$	−6.98675	+	4.02310i	−0.866600	+	0.499004i
$66$		0			0
$67$	−0.317776	−	0.550404i	−0.0388225	−	0.0672426i	0.845961	−	0.533244i	$-0.179027\pi$
$67$	−0.317776	−	0.550404i	−0.0388225	−	0.0672426i	−0.884784	+	0.466002i	$0.845694\pi$
$68$		0			0
$69$	4.09053	−	7.08500i	0.492441	−	0.852934i
$70$		0			0
$71$	−12.0089	−	6.93335i	−1.42520	−	0.822838i	−0.428460	−	0.903561i	$-0.640944\pi$
$71$	−12.0089	−	6.93335i	−1.42520	−	0.822838i	−0.996737	+	0.0807229i	$0.974277\pi$
$72$		0			0
$73$	−4.89025			−0.572360			−0.286180	−	0.958176i	$-0.592386\pi$
$73$	−4.89025			−0.572360			−0.286180	+	0.958176i	$0.592386\pi$
$74$		0			0
$75$	−7.37131	+	0.576115i	−0.851166	+	0.0665240i
$76$		0			0
$77$			14.5115i			1.65373i
$78$		0			0
$79$	−6.21024			−0.698707			−0.349354	−	0.936991i	$-0.613599\pi$
$79$	−6.21024			−0.698707			−0.349354	+	0.936991i	$0.613599\pi$
$80$		0			0
$81$	2.94938	+	5.10848i	0.327709	+	0.567609i
$82$		0			0
$83$	3.33075			0.365597			0.182798	−	0.983150i	$-0.441484\pi$
$83$	3.33075			0.365597			0.182798	+	0.983150i	$0.441484\pi$
$84$		0			0
$85$	10.2915	−	11.1272i	1.11627	−	1.20691i
$86$		0			0
$87$	9.91375	+	5.72371i	1.06287	+	0.613646i
$88$		0			0
$89$	−2.27725	+	1.31477i	−0.241388	+	0.139366i	−0.615815	−	0.787891i	$-0.711173\pi$
$89$	−2.27725	+	1.31477i	−0.241388	+	0.139366i	0.374426	+	0.927257i	$0.377840\pi$
$90$		0			0
$91$	−11.0185	+	2.48305i	−1.15505	+	0.260294i
$92$		0			0
$93$	−1.08043	−	1.87136i	−0.112035	−	0.194051i
$94$		0			0
$95$	2.54984	−	2.75690i	0.261608	−	0.282852i
$96$		0			0
$97$	3.13942	−	5.43764i	0.318760	−	0.552108i	−0.661470	−	0.749972i	$-0.730067\pi$
$97$	3.13942	−	5.43764i	0.318760	−	0.552108i	0.980230	+	0.197864i	$0.0634003\pi$
$98$		0			0
$99$		−	3.76739i		−	0.378637i
$100$		0			0
$101$	8.41840	+	14.5811i	0.837662	+	1.45087i	0.891845	+	0.452342i	$0.149411\pi$
$101$	8.41840	+	14.5811i	0.837662	+	1.45087i	−0.0541831	+	0.998531i	$0.517255\pi$
$102$		0			0
$103$		−	9.86212i		−	0.971744i	−0.874030	−	0.485872i	$-0.838502\pi$
$103$		−	9.86212i		−	0.971744i	0.874030	−	0.485872i	$-0.161498\pi$
$104$		0			0
$105$	−10.1023	−	2.28879i	−0.985882	−	0.223363i
$106$		0			0
$107$	−3.53096	+	2.03860i	−0.341351	+	0.197079i	−0.660869	−	0.750501i	$-0.729812\pi$
$107$	−3.53096	+	2.03860i	−0.341351	+	0.197079i	0.319519	+	0.947580i	$0.396479\pi$
$108$		0			0
$109$		−	11.6762i		−	1.11837i	−0.829042	−	0.559186i	$-0.811114\pi$
$109$		−	11.6762i		−	1.11837i	0.829042	−	0.559186i	$-0.188886\pi$
$110$		0			0
$111$	9.54275	+	5.50951i	0.905757	+	0.522939i
$112$		0			0
$113$	−3.30892	−	1.91041i	−0.311277	−	0.179716i	0.336221	−	0.941783i	$-0.390851\pi$
$113$	−3.30892	−	1.91041i	−0.311277	−	0.179716i	−0.647498	+	0.762067i	$0.724185\pi$
$114$		0			0
$115$	−3.66525	−	11.8153i	−0.341786	−	1.10179i
$116$		0			0
$117$	2.86056	−	0.644637i	0.264459	−	0.0595967i
$118$		0			0
$119$	18.3891	−	10.6170i	1.68573	−	0.973254i
$120$		0			0
$121$	5.22947	−	9.05771i	0.475407	−	0.823428i
$122$		0			0
$123$	4.08867	−	7.08179i	0.368663	−	0.638544i
$124$		0			0
$125$	−6.92882	+	8.77448i	−0.619732	+	0.784813i
$126$		0			0
$127$	9.91375	−	5.72371i	0.879703	−	0.507897i	0.00914258	−	0.999958i	$-0.497090\pi$
$127$	9.91375	−	5.72371i	0.879703	−	0.507897i	0.870561	+	0.492061i	$0.163756\pi$
$128$		0			0
$129$	−18.3913			−1.61926
$130$		0			0
$131$	−4.36778			−0.381615			−0.190807	−	0.981628i	$-0.561111\pi$
$131$	−4.36778			−0.381615			−0.190807	+	0.981628i	$0.561111\pi$
$132$		0			0
$133$	4.55613	−	2.63048i	0.395066	−	0.228092i
$134$		0			0
$135$	12.2973	+	2.78610i	1.05839	+	0.239790i
$136$		0			0
$137$	2.76290	−	4.78548i	0.236050	−	0.408851i	−0.723527	−	0.690296i	$-0.757480\pi$
$137$	2.76290	−	4.78548i	0.236050	−	0.408851i	0.959577	+	0.281445i	$0.0908136\pi$
$138$		0			0
$139$	−5.64787	+	9.78240i	−0.479046	+	0.829732i	−0.999711	−	0.0240289i	$-0.992351\pi$
$139$	−5.64787	+	9.78240i	−0.479046	+	0.829732i	0.520665	+	0.853761i	$0.325684\pi$
$140$		0			0
$141$	−2.53099	+	1.46127i	−0.213148	+	0.123061i
$142$		0			0
$143$	15.9467	+	4.96694i	1.33353	+	0.415356i
$144$		0			0
$145$	16.5327	−	5.12863i	1.37297	−	0.425910i
$146$		0			0
$147$	−3.60280	−	2.08008i	−0.297154	−	0.171562i
$148$		0			0
$149$	−5.25802	−	3.03572i	−0.430754	−	0.248696i	0.268914	−	0.963164i	$-0.413335\pi$
$149$	−5.25802	−	3.03572i	−0.430754	−	0.248696i	−0.699668	+	0.714468i	$0.746669\pi$
$150$		0			0
$151$		−	15.1403i		−	1.23210i	−0.787708	−	0.616048i	$-0.788733\pi$
$151$		−	15.1403i		−	1.23210i	0.787708	−	0.616048i	$-0.211267\pi$
$152$		0			0
$153$	−4.77408	+	2.75632i	−0.385962	+	0.222835i
$154$		0			0
$155$	−3.18673	−	0.721991i	−0.255964	−	0.0579917i
$156$		0			0
$157$		−	19.3218i		−	1.54205i	−0.636804	−	0.771026i	$-0.719744\pi$
$157$		−	19.3218i		−	1.54205i	0.636804	−	0.771026i	$-0.280256\pi$
$158$		0			0
$159$	4.18389	+	7.24671i	0.331804	+	0.574701i
$160$		0			0
$161$		−	17.3308i		−	1.36586i
$162$		0			0
$163$	−0.278858	+	0.482997i	−0.0218419	+	0.0378312i	−0.876740	−	0.480965i	$-0.840286\pi$
$163$	−0.278858	+	0.482997i	−0.0218419	+	0.0378312i	0.854898	+	0.518796i	$0.173620\pi$
$164$		0			0
$165$	11.2451	+	10.4005i	0.875432	+	0.809681i
$166$		0			0
$167$	3.16473	+	5.48147i	0.244894	+	0.424169i	0.962102	−	0.272691i	$-0.0879136\pi$
$167$	3.16473	+	5.48147i	0.244894	+	0.424169i	−0.717208	+	0.696859i	$0.754580\pi$
$168$		0			0
$169$	−1.04275	+	12.9581i	−0.0802113	+	0.996778i
$170$		0			0
$171$	−1.18284	+	0.682912i	−0.0904539	+	0.0522236i
$172$		0			0
$173$	−6.62192	−	3.82317i	−0.503455	−	0.290670i	0.226684	−	0.973968i	$-0.427212\pi$
$173$	−6.62192	−	3.82317i	−0.503455	−	0.290670i	−0.730139	+	0.683298i	$0.760545\pi$
$174$		0			0
$175$	−12.9132	+	8.86466i	−0.976143	+	0.670106i
$176$		0			0
$177$	3.88846			0.292275
$178$		0			0
$179$	2.27725	+	3.94432i	0.170210	+	0.294812i	0.938493	−	0.345298i	$-0.112222\pi$
$179$	2.27725	+	3.94432i	0.170210	+	0.294812i	−0.768283	+	0.640110i	$0.778889\pi$
$180$		0			0
$181$	−7.76475			−0.577149			−0.288575	−	0.957457i	$-0.593181\pi$
$181$	−7.76475			−0.577149			−0.288575	+	0.957457i	$0.593181\pi$
$182$		0			0
$183$			14.4049i			1.06484i
$184$		0			0
$185$	15.9140	−	4.93670i	1.17002	−	0.362953i
$186$		0			0
$187$	−31.3998			−2.29618
$188$		0			0
$189$	15.2979	+	8.83227i	1.11276	+	0.642453i
$190$		0			0
$191$	−5.71991	+	9.90717i	−0.413878	+	0.716858i	−0.995310	−	0.0967371i	$-0.969159\pi$
$191$	−5.71991	+	9.90717i	−0.413878	+	0.716858i	0.581432	+	0.813595i	$0.302493\pi$
$192$		0			0
$193$	−1.58132	−	2.73893i	−0.113826	−	0.197153i	0.803484	−	0.595327i	$-0.202977\pi$
$193$	−1.58132	−	2.73893i	−0.113826	−	0.197153i	−0.917310	+	0.398174i	$0.869644\pi$
$194$		0			0
$195$	−5.97293	+	10.3180i	−0.427731	+	0.738888i
$196$		0			0
$197$	−11.5791	−	20.0556i	−0.824978	−	1.42890i	−0.901936	−	0.431870i	$-0.857854\pi$
$197$	−11.5791	−	20.0556i	−0.824978	−	1.42890i	0.0769575	−	0.997034i	$-0.475479\pi$
$198$		0			0
$199$	3.01176	−	5.21652i	0.213498	−	0.369789i	−0.739309	−	0.673366i	$-0.764848\pi$
$199$	3.01176	−	5.21652i	0.213498	−	0.369789i	0.952807	+	0.303577i	$0.0981810\pi$
$200$		0			0
$201$	−0.813915	−	0.469914i	−0.0574091	−	0.0331452i
$202$		0			0
$203$	24.2503			1.70204
$204$		0			0
$205$	−3.66359	−	11.8100i	−0.255876	−	0.824845i
$206$		0			0
$207$			4.49934i			0.312725i
$208$		0			0
$209$	−7.77969			−0.538132
$210$		0			0
$211$	2.56910	+	4.44981i	0.176864	+	0.306338i	0.940805	−	0.338949i	$-0.110071\pi$
$211$	2.56910	+	4.44981i	0.176864	+	0.306338i	−0.763941	+	0.645287i	$0.776738\pi$
$212$		0			0
$213$	−20.5055			−1.40501
$214$		0			0
$215$	−18.8829	+	20.4164i	−1.28781	+	1.39238i
$216$		0			0
$217$	−3.96430	−	2.28879i	−0.269115	−	0.155373i
$218$		0			0
$219$	−6.26266	+	3.61575i	−0.423191	+	0.244330i
$220$		0			0
$221$	−5.37281	−	23.8417i	−0.361414	−	1.60377i
$222$		0			0
$223$	8.31533	+	14.4026i	0.556836	+	0.964468i	0.997758	+	0.0669227i	$0.0213181\pi$
$223$	8.31533	+	14.4026i	0.556836	+	0.964468i	−0.440922	+	0.897545i	$0.645349\pi$
$224$		0			0
$225$	3.35245	−	2.30140i	0.223496	−	0.153427i
$226$		0			0
$227$	−7.22129	+	12.5076i	−0.479294	+	0.830161i	−0.999718	−	0.0237467i	$-0.992440\pi$
$227$	−7.22129	+	12.5076i	−0.479294	+	0.830161i	0.520424	+	0.853908i	$0.325774\pi$
$228$		0			0
$229$		−	4.00567i		−	0.264702i	−0.991203	−	0.132351i	$-0.957747\pi$
$229$		−	4.00567i		−	0.264702i	0.991203	−	0.132351i	$-0.0422526\pi$
$230$		0			0
$231$	10.7295	+	18.5840i	0.705948	+	1.22274i
$232$		0			0
$233$		−	3.48148i		−	0.228079i	−0.993476	−	0.114040i	$-0.963621\pi$
$233$		−	3.48148i		−	0.228079i	0.993476	−	0.114040i	$-0.0363791\pi$
$234$		0			0
$235$	−0.976482	+	4.31000i	−0.0636987	+	0.281154i
$236$		0			0
$237$	−7.95310	+	4.59173i	−0.516610	+	0.298265i
$238$		0			0
$239$			19.1155i			1.23648i	0.785990	+	0.618239i	$0.212154\pi$
$239$			19.1155i			1.23648i	−0.785990	+	0.618239i	$0.787846\pi$
$240$		0			0
$241$	19.3464	+	11.1696i	1.24621	+	0.719499i	0.970351	−	0.241700i	$-0.0777050\pi$
$241$	19.3464	+	11.1696i	1.24621	+	0.719499i	0.275857	+	0.961199i	$0.411038\pi$
$242$		0			0
$243$	−7.09611	−	4.09694i	−0.455216	−	0.262819i
$244$		0			0
$245$	−6.00822	+	1.86382i	−0.383851	+	0.119075i
$246$		0			0
$247$	−1.33118	−	5.90708i	−0.0847010	−	0.375859i
$248$		0			0
$249$	4.26549	−	2.46268i	0.270315	−	0.156066i
$250$		0			0
$251$	8.37281	−	14.5021i	0.528487	−	0.915367i	−0.470961	−	0.882154i	$-0.656093\pi$
$251$	8.37281	−	14.5021i	0.528487	−	0.915367i	0.999448	−	0.0332127i	$-0.0105739\pi$
$252$		0			0
$253$	−12.8140	+	22.1946i	−0.805612	+	1.39536i
$254$		0			0
$255$	4.95248	−	21.8593i	0.310136	−	1.36888i
$256$		0			0
$257$	−13.6560	+	7.88431i	−0.851839	+	0.491810i	−0.861271	−	0.508146i	$-0.830331\pi$
$257$	−13.6560	+	7.88431i	−0.851839	+	0.491810i	0.00943181	+	0.999956i	$0.496998\pi$
$258$		0			0
$259$	23.3428			1.45045
$260$		0			0
$261$	−6.29574			−0.389696
$262$		0			0
$263$	10.6443	−	6.14549i	0.656355	−	0.378947i	−0.134532	−	0.990909i	$-0.542953\pi$
$263$	10.6443	−	6.14549i	0.656355	−	0.378947i	0.790887	+	0.611962i	$0.209620\pi$
$264$		0			0
$265$	12.3404	+	2.79586i	0.758063	+	0.171748i
$266$		0			0
$267$	−1.94423	+	3.36751i	−0.118985	+	0.206088i
$268$		0			0
$269$	6.82503	−	11.8213i	0.416130	−	0.720758i	−0.579417	−	0.815031i	$-0.696720\pi$
$269$	6.82503	−	11.8213i	0.416130	−	0.720758i	0.995546	+	0.0942739i	$0.0300529\pi$
$270$		0			0
$271$	−1.54558	+	0.892343i	−0.0938875	+	0.0542060i	−0.546209	−	0.837649i	$-0.683929\pi$
$271$	−1.54558	+	0.892343i	−0.0938875	+	0.0542060i	0.452321	+	0.891855i	$0.350596\pi$
$272$		0			0
$273$	−12.2748	+	11.3267i	−0.742906	+	0.685525i
$274$		0			0
$275$	23.0915	−	1.80475i	1.39247	−	0.108830i
$276$		0			0
$277$	16.9723	+	9.79899i	1.01977	+	0.588764i	0.914037	−	0.405631i	$-0.132948\pi$
$277$	16.9723	+	9.79899i	1.01977	+	0.588764i	0.105732	+	0.994395i	$0.466281\pi$
$278$		0			0
$279$	1.02919	+	0.594204i	0.0616161	+	0.0355741i
$280$		0			0
$281$			18.0710i			1.07803i	0.842297	+	0.539013i	$0.181203\pi$
$281$			18.0710i			1.07803i	−0.842297	+	0.539013i	$0.818797\pi$
$282$		0			0
$283$	−6.31095	+	3.64363i	−0.375147	+	0.216591i	−0.675705	−	0.737172i	$-0.736161\pi$
$283$	−6.31095	+	3.64363i	−0.375147	+	0.216591i	0.300558	+	0.953764i	$0.402827\pi$
$284$		0			0
$285$	1.22704	−	5.41590i	0.0726834	−	0.320810i
$286$		0			0
$287$		−	17.3230i		−	1.02254i
$288$		0			0
$289$	14.4729	+	25.0678i	0.851347	+	1.47458i
$290$		0			0
$291$		−	9.28489i		−	0.544290i
$292$		0			0
$293$	6.14226	−	10.6387i	0.358835	−	0.621520i	−0.628932	−	0.777461i	$-0.716508\pi$
$293$	6.14226	−	10.6387i	0.358835	−	0.621520i	0.987766	+	0.155941i	$0.0498408\pi$
$294$		0			0
$295$	3.99241	−	4.31662i	0.232447	−	0.251323i
$296$		0			0
$297$	−13.0608	−	22.6219i	−0.757864	−	1.31266i
$298$		0			0
$299$	−19.0448	−	5.93194i	−1.10139	−	0.343053i
$300$		0			0
$301$	−33.7406	+	19.4801i	−1.94478	+	1.12282i
$302$		0			0
$303$	21.5619	+	12.4488i	1.23870	+	0.715163i
$304$		0			0
$305$	15.9910	+	14.7900i	0.915645	+	0.846874i
$306$		0			0
$307$	−31.1511			−1.77789			−0.888943	−	0.458018i	$-0.848560\pi$
$307$	−31.1511			−1.77789			−0.888943	+	0.458018i	$0.848560\pi$
$308$		0			0
$309$	−7.29185	−	12.6299i	−0.414819	−	0.718487i
$310$		0			0
$311$	0.694196			0.0393643			0.0196821	−	0.999806i	$-0.493735\pi$
$311$	0.694196			0.0393643			0.0196821	+	0.999806i	$0.493735\pi$
$312$		0			0
$313$		−	14.5944i		−	0.824925i	−0.910975	−	0.412463i	$-0.864669\pi$
$313$		−	14.5944i		−	0.824925i	0.910975	−	0.412463i	$-0.135331\pi$
$314$		0			0
$315$	5.44098	−	1.68785i	0.306565	−	0.0950998i
$316$		0			0
$317$	−14.5641			−0.817999			−0.408999	−	0.912535i	$-0.634122\pi$
$317$	−14.5641			−0.817999			−0.408999	+	0.912535i	$0.634122\pi$
$318$		0			0
$319$	−31.0560	−	17.9302i	−1.73880	−	1.00390i
$320$		0			0
$321$	−3.01460	+	5.22143i	−0.168258	+	0.291432i
$322$		0			0
$323$	5.69182	+	9.85852i	0.316701	+	0.548543i
$324$		0			0
$325$	5.32151	+	17.2244i	0.295184	+	0.955440i
$326$		0			0
$327$	−8.63311	−	14.9530i	−0.477412	−	0.826902i
$328$		0			0
$329$	−3.09556	+	5.36167i	−0.170664	+	0.295598i
$330$		0			0
$331$	−8.71991	−	5.03444i	−0.479290	−	0.276718i	0.240831	−	0.970567i	$-0.422580\pi$
$331$	−8.71991	−	5.03444i	−0.479290	−	0.276718i	−0.720120	+	0.693849i	$0.755913\pi$
$332$		0			0
$333$	−6.06013			−0.332093
$334$		0			0
$335$	−1.35733	+	0.421058i	−0.0741588	+	0.0230049i
$336$		0			0
$337$			0.974536i			0.0530863i	0.999648	+	0.0265432i	$0.00844995\pi$
$337$			0.974536i			0.0530863i	−0.999648	+	0.0265432i	$0.991550\pi$
$338$		0			0
$339$	−5.65006			−0.306869
$340$		0			0
$341$	3.38457	+	5.86225i	0.183285	+	0.317459i
$342$		0			0
$343$	13.1154			0.708165
$344$		0			0
$345$	−13.4299	−	12.4212i	−0.723040	−	0.668735i
$346$		0			0
$347$	7.29440	+	4.21142i	0.391584	+	0.226081i	0.682846	−	0.730562i	$-0.260742\pi$
$347$	7.29440	+	4.21142i	0.391584	+	0.226081i	−0.291262	+	0.956643i	$0.594075\pi$
$348$		0			0
$349$	3.51639	−	2.03019i	0.188228	−	0.108674i	−0.402925	−	0.915233i	$-0.632006\pi$
$349$	3.51639	−	2.03019i	0.188228	−	0.108674i	0.591153	+	0.806560i	$0.298673\pi$
$350$		0			0
$351$	14.9419	−	13.7878i	0.797540	−	0.735940i
$352$		0			0
$353$	1.95925	+	3.39351i	0.104280	+	0.180618i	0.913444	−	0.406965i	$-0.133413\pi$
$353$	1.95925	+	3.39351i	0.104280	+	0.180618i	−0.809164	+	0.587583i	$0.800079\pi$
$354$		0			0
$355$	−21.0537	+	22.7634i	−1.11741	+	1.20815i
$356$		0			0
$357$	15.6999	−	27.1930i	0.830927	−	1.43921i
$358$		0			0
$359$		−	4.23682i		−	0.223611i	−0.993730	−	0.111805i	$-0.964337\pi$
$359$		−	4.23682i		−	0.223611i	0.993730	−	0.111805i	$-0.0356633\pi$
$360$		0			0
$361$	−8.08978	−	14.0119i	−0.425778	−	0.737469i
$362$		0			0
$363$		−	15.4663i		−	0.811768i
$364$		0			0
$365$	−2.41620	+	10.6646i	−0.126470	+	0.558213i
$366$		0			0
$367$	19.9499	−	11.5181i	1.04138	−	0.601238i	0.121153	−	0.992634i	$-0.461341\pi$
$367$	19.9499	−	11.5181i	1.04138	−	0.601238i	0.920222	+	0.391396i	$0.128008\pi$
$368$		0			0
$369$			4.49730i			0.234120i
$370$		0			0
$371$	15.3515	+	8.86319i	0.797010	+	0.460154i
$372$		0			0
$373$	20.2984	+	11.7193i	1.05101	+	0.606801i	0.922932	−	0.384964i	$-0.125786\pi$
$373$	20.2984	+	11.7193i	1.05101	+	0.606801i	0.128078	+	0.991764i	$0.459119\pi$
$374$		0			0
$375$	−2.38567	+	16.3600i	−0.123195	+	0.844826i
$376$		0			0
$377$	8.30032	−	26.6487i	0.427488	−	1.37248i
$378$		0			0
$379$	18.8942	−	10.9086i	0.970532	−	0.560337i	0.0711334	−	0.997467i	$-0.477338\pi$
$379$	18.8942	−	10.9086i	0.970532	−	0.560337i	0.899398	+	0.437130i	$0.144005\pi$
$380$		0			0
$381$	8.46398	−	14.6600i	0.433623	−	0.751057i
$382$		0			0
$383$	6.94924	−	12.0364i	0.355089	−	0.615033i	−0.632044	−	0.774933i	$-0.717784\pi$
$383$	6.94924	−	12.0364i	0.355089	−	0.615033i	0.987133	+	0.159900i	$0.0511171\pi$
$384$		0			0
$385$	31.6466	+	7.16990i	1.61286	+	0.365412i
$386$		0			0
$387$	8.75956	−	5.05733i	0.445273	−	0.257079i
$388$		0			0
$389$	−6.66919			−0.338141			−0.169071	−	0.985604i	$-0.554077\pi$
$389$	−6.66919			−0.338141			−0.169071	+	0.985604i	$0.554077\pi$
$390$		0			0
$391$	37.5003			1.89647
$392$		0			0
$393$	−5.59356	+	3.22945i	−0.282158	+	0.162904i
$394$		0			0
$395$	−3.06839	+	13.5433i	−0.154388	+	0.681437i
$396$		0			0
$397$	−1.66745	+	2.88812i	−0.0836871	+	0.144950i	−0.904831	−	0.425771i	$-0.860003\pi$
$397$	−1.66745	+	2.88812i	−0.0836871	+	0.144950i	0.821144	+	0.570721i	$0.193336\pi$
$398$		0			0
$399$	3.88984	−	6.73741i	0.194736	−	0.337292i
$400$		0			0
$401$	−17.1405	+	9.89607i	−0.855956	+	0.494186i	−0.862656	−	0.505791i	$-0.831201\pi$
$401$	−17.1405	+	9.89607i	−0.855956	+	0.494186i	0.00670012	+	0.999978i	$0.497867\pi$
$402$		0			0
$403$	−3.87205	+	3.57298i	−0.192880	+	0.177983i
$404$		0			0
$405$	12.5978	−	3.90798i	0.625990	−	0.194189i
$406$		0			0
$407$	−29.8937	−	17.2592i	−1.48178	−	0.855505i
$408$		0			0
$409$	5.06018	+	2.92150i	0.250210	+	0.144459i	0.619860	−	0.784712i	$-0.287189\pi$
$409$	5.06018	+	2.92150i	0.250210	+	0.144459i	−0.369651	+	0.929171i	$0.620523\pi$
$410$		0			0
$411$		−	8.17132i		−	0.403062i
$412$		0			0
$413$	7.13375	−	4.11868i	0.351029	−	0.202667i
$414$		0			0
$415$	1.64567	−	7.26368i	0.0807829	−	0.356560i
$416$		0			0
$417$			16.7037i			0.817982i
$418$		0			0
$419$	−17.8553	−	30.9262i	−0.872287	−	1.51085i	−0.859625	−	0.510926i	$-0.829303\pi$
$419$	−17.8553	−	30.9262i	−0.872287	−	1.51085i	−0.0126627	−	0.999920i	$-0.504031\pi$
$420$		0			0
$421$		−	24.9384i		−	1.21542i	−0.794159	−	0.607711i	$-0.792088\pi$
$421$		−	24.9384i		−	1.21542i	0.794159	−	0.607711i	$-0.207912\pi$
$422$		0			0
$423$	0.803653	−	1.39197i	0.0390750	−	0.0676798i
$424$		0			0
$425$	−19.1813	−	27.9414i	−0.930430	−	1.35536i
$426$		0			0
$427$	15.2578	+	26.4272i	0.738375	+	1.27890i
$428$		0			0
$429$	24.0944	−	5.42975i	1.16329	−	0.262151i
$430$		0			0
$431$	−26.2773	+	15.1712i	−1.26573	+	0.730770i	−0.974177	−	0.225785i	$-0.927505\pi$
$431$	−26.2773	+	15.1712i	−1.26573	+	0.730770i	−0.291553	+	0.956555i	$0.594172\pi$
$432$		0			0
$433$	−10.1016	−	5.83216i	−0.485452	−	0.280276i	0.237234	−	0.971453i	$-0.423759\pi$
$433$	−10.1016	−	5.83216i	−0.485452	−	0.280276i	−0.722686	+	0.691177i	$0.757093\pi$
$434$		0			0
$435$	17.3805	−	18.7919i	0.833331	−	0.901002i
$436$		0			0
$437$	9.29116			0.444457
$438$		0			0
$439$	1.74627	+	3.02462i	0.0833447	+	0.144357i	0.904685	−	0.426082i	$-0.140106\pi$
$439$	1.74627	+	3.02462i	0.0833447	+	0.144357i	−0.821340	+	0.570439i	$0.806773\pi$
$440$		0			0
$441$	2.28796			0.108950
$442$		0			0
$443$		−	27.7833i		−	1.32002i	−0.751255	−	0.660012i	$-0.770551\pi$
$443$		−	27.7833i		−	1.32002i	0.751255	−	0.660012i	$-0.229449\pi$
$444$		0			0
$445$	1.74210	+	5.61584i	0.0825832	+	0.266216i
$446$		0			0
$447$	−8.97820			−0.424654
$448$		0			0
$449$	−3.16257	−	1.82591i	−0.149251	−	0.0861700i	0.423515	−	0.905889i	$-0.360796\pi$
$449$	−3.16257	−	1.82591i	−0.149251	−	0.0861700i	−0.572766	+	0.819719i	$0.694129\pi$
$450$		0			0
$451$	−12.8082	+	22.1845i	−0.603116	+	1.04463i
$452$		0			0
$453$	−11.1944	−	19.3893i	−0.525958	−	0.910987i
$454$		0			0
$455$	−0.0290415	+	25.2559i	−0.00136149	+	1.18402i
$456$		0			0
$457$	21.1718	+	36.6706i	0.990374	+	1.71538i	0.615061	+	0.788480i	$0.289131\pi$
$457$	21.1718	+	36.6706i	0.990374	+	1.71538i	0.375313	+	0.926898i	$0.377535\pi$
$458$		0			0
$459$	−19.1112	+	33.1016i	−0.892035	+	1.54505i
$460$		0			0
$461$	2.87450	+	1.65960i	0.133879	+	0.0772951i	0.565444	−	0.824787i	$-0.308705\pi$
$461$	2.87450	+	1.65960i	0.133879	+	0.0772951i	−0.431565	+	0.902082i	$0.642038\pi$
$462$		0			0
$463$	−26.2130			−1.21822			−0.609111	−	0.793085i	$-0.708474\pi$
$463$	−26.2130			−1.21822			−0.609111	+	0.793085i	$0.708474\pi$
$464$		0			0
$465$	−4.61488	+	1.43159i	−0.214010	+	0.0663883i
$466$		0			0
$467$			2.45243i			0.113485i	0.998389	+	0.0567424i	$0.0180714\pi$
$467$			2.45243i			0.113485i	−0.998389	+	0.0567424i	$0.981929\pi$
$468$		0			0
$469$	−1.99094			−0.0919330
$470$		0			0
$471$	−14.2862	−	24.7444i	−0.658272	−	1.14016i
$472$		0			0
$473$	57.6128			2.64904
$474$		0			0
$475$	−4.75240	−	6.92283i	−0.218055	−	0.317641i
$476$		0			0
$477$	−3.98548	−	2.30102i	−0.182482	−	0.105356i
$478$		0			0
$479$	1.89707	−	1.09528i	0.0866795	−	0.0500444i	−0.456034	−	0.889962i	$-0.650730\pi$
$479$	1.89707	−	1.09528i	0.0866795	−	0.0500444i	0.542713	+	0.839918i	$0.317397\pi$
$480$		0			0
$481$	7.98969	−	25.6514i	0.364299	−	1.16960i
$482$		0			0
$483$	−12.8140	−	22.1946i	−0.583059	−	1.00989i
$484$		0			0
$485$	−10.3072	−	9.53310i	−0.468028	−	0.432876i
$486$		0			0
$487$	9.75727	−	16.9001i	0.442144	−	0.765816i	−0.555704	−	0.831380i	$-0.687551\pi$
$487$	9.75727	−	16.9001i	0.442144	−	0.765816i	0.997848	+	0.0655640i	$0.0208847\pi$
$488$		0			0
$489$			0.824728i			0.0372955i
$490$		0			0
$491$	15.6383	+	27.0863i	0.705747	+	1.22239i	0.966421	+	0.256963i	$0.0827217\pi$
$491$	15.6383	+	27.0863i	0.705747	+	1.22239i	−0.260674	+	0.965427i	$0.583945\pi$
$492$		0			0
$493$			52.4727i			2.36325i
$494$		0			0
$495$	−8.21592	−	1.86141i	−0.369278	−	0.0836643i
$496$		0			0
$497$	−37.6193	+	21.7195i	−1.68746	+	0.974254i
$498$		0			0
$499$		−	31.5312i		−	1.41153i	−0.708445	−	0.705766i	$-0.750603\pi$
$499$		−	31.5312i		−	1.41153i	0.708445	−	0.705766i	$-0.249397\pi$
$500$		0			0
$501$	8.10576	+	4.67986i	0.362139	+	0.209081i
$502$		0			0
$503$	−4.86709	−	2.81002i	−0.217013	−	0.125293i	0.387553	−	0.921847i	$-0.373320\pi$
$503$	−4.86709	−	2.81002i	−0.217013	−	0.125293i	−0.604566	+	0.796555i	$0.706654\pi$
$504$		0			0
$505$	35.9578	−	11.1545i	1.60010	−	0.496369i
$506$		0			0
$507$	8.24557	+	17.3657i	0.366199	+	0.771238i
$508$		0			0
$509$	−13.7002	+	7.90980i	−0.607250	+	0.350596i	−0.771888	−	0.635758i	$-0.780688\pi$
$509$	−13.7002	+	7.90980i	−0.607250	+	0.350596i	0.164639	+	0.986354i	$0.447354\pi$
$510$		0			0
$511$	−7.65963	+	13.2669i	−0.338842	+	0.586892i
$512$		0			0
$513$	−4.73504	+	8.20132i	−0.209057	+	0.362097i
$514$		0			0
$515$	−21.5073	−	4.87273i	−0.947725	−	0.214718i
$516$		0			0
$517$	7.92861	−	4.57758i	0.348700	−	0.201322i
$518$		0			0
$519$	−11.3071			−0.496326
$520$		0			0
$521$	12.6030			0.552149			0.276074	−	0.961136i	$-0.410966\pi$
$521$	12.6030			0.552149			0.276074	+	0.961136i	$0.410966\pi$
$522$		0			0
$523$	−23.8881	+	13.7918i	−1.04456	+	0.603074i	−0.921120	−	0.389278i	$-0.872724\pi$
$523$	−23.8881	+	13.7918i	−1.04456	+	0.603074i	−0.123435	+	0.992353i	$0.539391\pi$
$524$		0			0
$525$	−9.98279	+	20.9002i	−0.435685	+	0.912159i
$526$		0			0
$527$	4.95248	−	8.57794i	0.215733	−	0.373661i
$528$		0			0
$529$	3.80361	−	6.58804i	0.165374	−	0.286437i
$530$		0			0
$531$	−1.85203	+	1.06927i	−0.0803712	+	0.0464023i
$532$		0			0
$533$	−19.0362	−	5.92925i	−0.824550	−	0.256824i
$534$		0			0
$535$	2.70118	+	8.70755i	0.116782	+	0.376460i
$536$		0			0
$537$	5.83269	+	3.36751i	0.251699	+	0.145319i
$538$		0			0
$539$	11.2862	+	6.51608i	0.486130	+	0.280667i
$540$		0			0
$541$			27.6835i			1.19021i	0.803650	+	0.595103i	$0.202889\pi$
$541$			27.6835i			1.19021i	−0.803650	+	0.595103i	$0.797111\pi$
$542$		0			0
$543$	−9.94387	+	5.74110i	−0.426732	+	0.246374i
$544$		0			0
$545$	−25.4633	−	5.76902i	−1.09073	−	0.247118i
$546$		0			0
$547$			24.7863i			1.05979i	0.848064	+	0.529893i	$0.177768\pi$
$547$			24.7863i			1.05979i	−0.848064	+	0.529893i	$0.822232\pi$
$548$		0			0
$549$	−3.96114	−	6.86090i	−0.169057	−	0.292816i
$550$		0			0
$551$			13.0007i			0.553850i
$552$		0			0
$553$	−9.72715	+	16.8479i	−0.413641	+	0.716446i
$554$		0			0
$555$	16.7301	−	18.0886i	0.710151	−	0.767820i
$556$		0			0
$557$	16.3096	+	28.2490i	0.691058	+	1.19695i	0.971491	+	0.237075i	$0.0761886\pi$
$557$	16.3096	+	28.2490i	0.691058	+	1.19695i	−0.280433	+	0.959874i	$0.590478\pi$
$558$		0			0
$559$	9.85811	+	43.7452i	0.416954	+	1.85022i
$560$		0			0
$561$	−40.2119	+	23.2164i	−1.69775	+	0.980196i
$562$		0			0
$563$	29.6082	+	17.0943i	1.24783	+	0.720438i	0.970677	−	0.240387i	$-0.0772742\pi$
$563$	29.6082	+	17.0943i	1.24783	+	0.720438i	0.277158	+	0.960824i	$0.410608\pi$
$564$		0			0
$565$	−5.80111	+	6.27219i	−0.244054	+	0.263873i
$566$		0			0
$567$	18.4786			0.776027
$568$		0			0
$569$	−10.1721	−	17.6186i	−0.426438	−	0.738612i	0.570116	−	0.821564i	$-0.306898\pi$
$569$	−10.1721	−	17.6186i	−0.426438	−	0.738612i	−0.996554	+	0.0829524i	$0.973565\pi$
$570$		0			0
$571$	46.7490			1.95639			0.978193	−	0.207700i	$-0.0665978\pi$
$571$	46.7490			1.95639			0.978193	+	0.207700i	$0.0665978\pi$
$572$		0			0
$573$			16.9167i			0.706707i
$574$		0			0
$575$	−27.5778	+	2.15538i	−1.15007	+	0.0898855i
$576$		0			0
$577$	11.8607			0.493768			0.246884	−	0.969045i	$-0.420593\pi$
$577$	11.8607			0.493768			0.246884	+	0.969045i	$0.420593\pi$
$578$		0			0
$579$	−4.05022	−	2.33839i	−0.168321	−	0.0971803i
$580$		0			0
$581$	5.21697	−	9.03606i	0.216436	−	0.374879i
$582$		0			0
$583$	−13.1065	−	22.7011i	−0.542816	−	0.940185i
$584$		0			0
$585$	0.00753961	−	6.55681i	0.000311725	−	0.271091i
$586$		0			0
$587$	−5.59483	−	9.69054i	−0.230924	−	0.399971i	0.727157	−	0.686472i	$-0.240841\pi$
$587$	−5.59483	−	9.69054i	−0.230924	−	0.399971i	−0.958080	+	0.286500i	$0.907508\pi$
$588$		0			0
$589$	1.22704	−	2.12529i	0.0505592	−	0.0875710i
$590$		0			0
$591$	−29.6574	−	17.1227i	−1.21994	−	0.704335i
$592$		0			0
$593$	−27.6058			−1.13363			−0.566817	−	0.823844i	$-0.691825\pi$
$593$	−27.6058			−1.13363			−0.566817	+	0.823844i	$0.691825\pi$
$594$		0			0
$595$	−14.0676	−	45.3486i	−0.576717	−	1.85911i
$596$		0			0
$597$		−	8.90733i		−	0.364553i
$598$		0			0
$599$	29.3193			1.19795			0.598976	−	0.800767i	$-0.295574\pi$
$599$	29.3193			1.19795			0.598976	+	0.800767i	$0.295574\pi$
$600$		0			0
$601$	−16.1764	−	28.0184i	−0.659850	−	1.14289i	−0.980654	−	0.195748i	$-0.937287\pi$
$601$	−16.1764	−	28.0184i	−0.659850	−	1.14289i	0.320804	−	0.947146i	$-0.396047\pi$
$602$		0			0
$603$	0.516878			0.0210489
$604$		0			0
$605$	−17.1692	−	15.8797i	−0.698029	−	0.645602i
$606$		0			0
$607$	−15.4492	−	8.91963i	−0.627066	−	0.362036i	0.152549	−	0.988296i	$-0.451252\pi$
$607$	−15.4492	−	8.91963i	−0.627066	−	0.362036i	−0.779615	+	0.626259i	$0.784585\pi$
$608$		0			0
$609$	31.0560	−	17.9302i	1.25845	−	0.726567i
$610$		0			0
$611$	4.83240	+	5.23689i	0.195498	+	0.211862i
$612$		0			0
$613$	−13.8288	−	23.9523i	−0.558542	−	0.967423i	−0.997619	−	0.0689733i	$-0.978028\pi$
$613$	−13.8288	−	23.9523i	−0.558542	−	0.967423i	0.439077	−	0.898450i	$-0.355306\pi$
$614$		0			0
$615$	−13.4238	−	12.4156i	−0.541300	−	0.500645i
$616$		0			0
$617$	−15.8577	+	27.4664i	−0.638408	+	1.10575i	0.347374	+	0.937727i	$0.387073\pi$
$617$	−15.8577	+	27.4664i	−0.638408	+	1.10575i	−0.985782	+	0.168028i	$0.946260\pi$
$618$		0			0
$619$			47.4958i			1.90902i	0.298186	+	0.954508i	$0.403618\pi$
$619$			47.4958i			1.90902i	−0.298186	+	0.954508i	$0.596382\pi$
$620$		0			0
$621$	15.5983	+	27.0170i	0.625938	+	1.08416i
$622$		0			0
$623$			8.23735i			0.330022i
$624$		0			0
$625$	15.7119	+	19.4457i	0.628478	+	0.777828i
$626$		0			0
$627$	−9.96300	+	5.75214i	−0.397884	+	0.229718i
$628$		0			0
$629$			50.5090i			2.01392i
$630$		0			0
$631$	−7.47459	−	4.31546i	−0.297559	−	0.171796i	0.343787	−	0.939048i	$-0.388290\pi$
$631$	−7.47459	−	4.31546i	−0.297559	−	0.171796i	−0.641346	+	0.767252i	$0.721624\pi$
$632$		0			0
$633$	6.58020	+	3.79908i	0.261540	+	0.151000i
$634$		0			0
$635$	−7.58401	−	24.4479i	−0.300962	−	0.970185i
$636$		0			0
$637$	−3.01645	+	9.68450i	−0.119516	+	0.383714i
$638$		0			0
$639$	9.76654	−	5.63871i	0.386358	−	0.223064i
$640$		0			0
$641$	7.59556	−	13.1559i	0.300007	−	0.519627i	−0.676131	−	0.736782i	$-0.736344\pi$
$641$	7.59556	−	13.1559i	0.300007	−	0.519627i	0.976137	+	0.217155i	$0.0696778\pi$
$642$		0			0
$643$	−6.80445	+	11.7856i	−0.268341	+	0.464781i	−0.968434	−	0.249272i	$-0.919809\pi$
$643$	−6.80445	+	11.7856i	−0.268341	+	0.464781i	0.700092	+	0.714052i	$0.253142\pi$
$644$		0			0
$645$	−9.08687	+	40.1077i	−0.357795	+	1.57924i
$646$		0			0
$647$	6.95677	−	4.01649i	0.273499	−	0.157905i	−0.356978	−	0.934113i	$-0.616193\pi$
$647$	6.95677	−	4.01649i	0.273499	−	0.157905i	0.630477	+	0.776208i	$0.282860\pi$
$648$		0			0
$649$	−12.1811			−0.478148
$650$		0			0
$651$	−6.76914			−0.265304
$652$		0			0
$653$	32.3286	−	18.6649i	1.26512	−	0.730415i	0.291055	−	0.956706i	$-0.405994\pi$
$653$	32.3286	−	18.6649i	1.26512	−	0.730415i	0.974060	+	0.226292i	$0.0726602\pi$
$654$		0			0
$655$	−2.15806	+	9.52524i	−0.0843222	+	0.372182i
$656$		0			0
$657$	1.98855	−	3.44428i	0.0775809	−	0.134374i
$658$		0			0
$659$	3.72275	−	6.44799i	0.145018	−	0.251178i	−0.784362	−	0.620303i	$-0.787009\pi$
$659$	3.72275	−	6.44799i	0.145018	−	0.251178i	0.929380	+	0.369126i	$0.120343\pi$
$660$		0			0
$661$	43.5907	−	25.1671i	1.69548	−	0.978888i	0.745542	−	0.666459i	$-0.232191\pi$
$661$	43.5907	−	25.1671i	1.69548	−	0.978888i	0.949941	−	0.312429i	$-0.101142\pi$
$662$		0			0
$663$	−24.5087	−	26.5602i	−0.951840	−	1.03151i
$664$		0			0
$665$	−3.48543	−	11.2357i	−0.135159	−	0.435701i
$666$		0			0
$667$	37.0896	+	21.4137i	1.43612	+	0.829142i
$668$		0			0
$669$	21.2979	+	12.2964i	0.823426	+	0.475405i
$670$		0			0
$671$		−	45.1251i		−	1.74203i
$672$		0			0
$673$	−12.7485	+	7.36034i	−0.491418	+	0.283720i	−0.725163	−	0.688578i	$-0.758235\pi$
$673$	−12.7485	+	7.36034i	−0.491418	+	0.283720i	0.233744	+	0.972298i	$0.424902\pi$
$674$		0			0
$675$	12.1519	−	25.4414i	0.467725	−	0.979240i
$676$		0			0
$677$			22.0788i			0.848559i	0.905531	+	0.424279i	$0.139473\pi$
$677$			22.0788i			0.848559i	−0.905531	+	0.424279i	$0.860527\pi$
$678$		0			0
$679$	−9.83460	−	17.0340i	−0.377417	−	0.653706i
$680$		0			0
$681$			21.3571i			0.818405i
$682$		0			0
$683$	19.9013	−	34.4700i	0.761501	−	1.31896i	−0.180576	−	0.983561i	$-0.557796\pi$
$683$	19.9013	−	34.4700i	0.761501	−	1.31896i	0.942077	−	0.335397i	$-0.108870\pi$
$684$		0			0
$685$	−9.07106	−	8.38976i	−0.346587	−	0.320556i
$686$		0			0
$687$	−2.96171	−	5.12983i	−0.112996	−	0.195715i
$688$		0			0
$689$	14.9942	−	13.8361i	0.571234	−	0.527113i
$690$		0			0
$691$	−34.6907	+	20.0287i	−1.31970	+	0.761927i	−0.983680	−	0.179928i	$-0.942413\pi$
$691$	−34.6907	+	20.0287i	−1.31970	+	0.761927i	−0.336017	+	0.941856i	$0.609080\pi$
$692$		0			0
$693$	−10.2206	−	5.90089i	−0.388250	−	0.224156i
$694$		0			0
$695$	18.5429	+	17.1502i	0.703372	+	0.650544i
$696$		0			0
$697$	37.4833			1.41978
$698$		0			0
$699$	−2.57413	−	4.45853i	−0.0973627	−	0.168637i
$700$		0			0
$701$	12.1911			0.460452			0.230226	−	0.973137i	$-0.426053\pi$
$701$	12.1911			0.460452			0.230226	+	0.973137i	$0.426053\pi$
$702$		0			0
$703$			12.5142i			0.471983i
$704$		0			0
$705$	1.93620	+	6.24156i	0.0729216	+	0.235071i
$706$		0			0
$707$	52.7432			1.98361
$708$		0			0
$709$	−18.7237	−	10.8101i	−0.703183	−	0.405983i	0.105349	−	0.994435i	$-0.466404\pi$
$709$	−18.7237	−	10.8101i	−0.703183	−	0.405983i	−0.808532	+	0.588452i	$0.799737\pi$
$710$		0			0
$711$	2.52531	−	4.37397i	0.0947066	−	0.164037i
$712$		0			0
$713$	−4.04214	−	7.00119i	−0.151379	−	0.262197i
$714$		0			0
$715$	18.7109	−	32.3223i	0.699748	−	1.20879i
$716$		0			0
$717$	14.1336	+	24.4801i	0.527829	+	0.914227i
$718$		0			0
$719$	−1.39194	+	2.41091i	−0.0519105	+	0.0899117i	−0.890813	−	0.454370i	$-0.849864\pi$
$719$	−1.39194	+	2.41091i	−0.0519105	+	0.0899117i	0.838903	+	0.544282i	$0.183198\pi$
$720$		0			0
$721$	−26.7552	−	15.4471i	−0.996415	−	0.575281i
$722$		0			0
$723$	33.0343			1.22856
$724$		0			0
$725$	−3.01593	−	38.5885i	−0.112009	−	1.43314i
$726$		0			0
$727$			22.5075i			0.834756i	0.908733	+	0.417378i	$0.137051\pi$
$727$			22.5075i			0.834756i	−0.908733	+	0.417378i	$0.862949\pi$
$728$		0			0
$729$	−29.8131			−1.10419
$730$		0			0
$731$	−42.1510	−	73.0077i	−1.55901	−	2.70029i
$732$		0			0
$733$	−8.58058			−0.316931			−0.158465	−	0.987365i	$-0.550655\pi$
$733$	−8.58058			−0.316931			−0.158465	+	0.987365i	$0.550655\pi$
$734$		0			0
$735$	−6.31632	+	6.82924i	−0.232981	+	0.251900i
$736$		0			0
$737$	2.54968	+	1.47206i	0.0939187	+	0.0542240i
$738$		0			0
$739$	−4.98591	+	2.87861i	−0.183410	+	0.105892i	−0.588894	−	0.808211i	$-0.700436\pi$
$739$	−4.98591	+	2.87861i	−0.183410	+	0.105892i	0.405484	+	0.914102i	$0.367103\pi$
$740$		0			0
$741$	−6.07234	−	6.58061i	−0.223073	−	0.241745i
$742$		0			0
$743$	13.3320	+	23.0918i	0.489105	+	0.847154i	0.999921	−	0.0125354i	$-0.00399025\pi$
$743$	13.3320	+	23.0918i	0.489105	+	0.847154i	−0.510817	+	0.859690i	$0.670657\pi$
$744$		0			0
$745$	−9.21821	+	9.96678i	−0.337729	+	0.365155i
$746$		0			0
$747$	−1.35440	+	2.34590i	−0.0495550	+	0.0858318i
$748$		0			0
$749$			12.7723i			0.466689i
$750$		0			0
$751$	21.8390	+	37.8262i	0.796916	+	1.38030i	0.921615	+	0.388104i	$0.126870\pi$
$751$	21.8390	+	37.8262i	0.796916	+	1.38030i	−0.124699	+	0.992195i	$0.539797\pi$
$752$		0			0
$753$		−	24.7627i		−	0.902404i
$754$		0			0
$755$	−33.0178	−	7.48058i	−1.20164	−	0.272246i
$756$		0			0
$757$	27.9105	−	16.1141i	1.01442	−	0.585678i	0.101941	−	0.994790i	$-0.467495\pi$
$757$	27.9105	−	16.1141i	1.01442	−	0.585678i	0.912484	+	0.409112i	$0.134162\pi$
$758$		0			0
$759$			37.8977i			1.37560i
$760$		0			0
$761$	10.4017	+	6.00543i	0.377062	+	0.217697i	0.676539	−	0.736407i	$-0.263479\pi$
$761$	10.4017	+	6.00543i	0.377062	+	0.217697i	−0.299477	+	0.954103i	$0.596812\pi$
$762$		0			0
$763$	−31.6765	−	18.2884i	−1.14677	−	0.662086i
$764$		0			0
$765$	3.65217	+	11.7732i	0.132044	+	0.425660i
$766$		0			0
$767$	−2.08430	−	9.24902i	−0.0752596	−	0.333963i
$768$		0			0
$769$	−43.3628	+	25.0355i	−1.56370	+	0.902804i	−0.566826	+	0.823838i	$0.691829\pi$
$769$	−43.3628	+	25.0355i	−1.56370	+	0.902804i	−0.996877	+	0.0789667i	$0.974838\pi$
$770$		0			0
$771$	−11.6590	+	20.1940i	−0.419888	+	0.727268i
$772$		0			0
$773$	24.3030	−	42.0940i	0.874118	−	1.51402i	0.0164180	−	0.999865i	$-0.494774\pi$
$773$	24.3030	−	42.0940i	0.874118	−	1.51402i	0.857700	−	0.514151i	$-0.171893\pi$
$774$		0			0
$775$	−3.14903	+	6.59288i	−0.113117	+	0.236823i
$776$		0			0
$777$	29.8937	−	17.2592i	1.07243	−	0.619169i
$778$		0			0
$779$	9.28695			0.332740
$780$		0			0
$781$	64.2359			2.29854
$782$		0			0
$783$	−37.8038	+	21.8261i	−1.35100	+	0.780000i
$784$		0			0
$785$	−42.1370	−	9.54665i	−1.50394	−	0.340734i
$786$		0			0
$787$	−20.3298	+	35.2122i	−0.724679	+	1.25518i	0.234427	+	0.972134i	$0.424679\pi$
$787$	−20.3298	+	35.2122i	−0.724679	+	1.25518i	−0.959106	+	0.283047i	$0.908655\pi$
$788$		0			0
$789$	9.08769	−	15.7403i	0.323530	−	0.560371i
$790$		0			0
$791$	−10.3656	+	5.98457i	−0.368558	+	0.212787i
$792$		0			0
$793$	34.2633	−	7.72134i	1.21672	−	0.274193i
$794$		0			0
$795$	17.8708	−	5.54372i	0.633812	−	0.196616i
$796$		0			0
$797$	−17.2116	−	9.93712i	−0.609666	−	0.351991i	0.163169	−	0.986598i	$-0.447829\pi$
$797$	−17.2116	−	9.93712i	−0.609666	−	0.351991i	−0.772835	+	0.634607i	$0.781162\pi$
$798$		0			0
$799$	−11.6015	−	6.69815i	−0.410433	−	0.236964i
$800$		0			0
$801$		−	2.13854i		−	0.0755616i
$802$		0			0
$803$	19.6185	−	11.3267i	0.692321	−	0.399712i
$804$		0			0
$805$	−37.7950	−	8.56290i	−1.33210	−	0.301803i
$806$		0			0
$807$		−	20.1851i		−	0.710551i
$808$		0			0
$809$	2.94549	+	5.10175i	0.103558	+	0.179368i	0.913148	−	0.407628i	$-0.133644\pi$
$809$	2.94549	+	5.10175i	0.103558	+	0.179368i	−0.809590	+	0.586996i	$0.800311\pi$
$810$		0			0
$811$		−	36.4566i		−	1.28016i	−0.768306	−	0.640082i	$-0.778900\pi$
$811$		−	36.4566i		−	1.28016i	0.768306	−	0.640082i	$-0.221100\pi$
$812$		0			0
$813$	−1.31956	+	2.28555i	−0.0462790	+	0.0801576i
$814$		0			0
$815$	0.915538	+	0.846775i	0.0320699	+	0.0296612i
$816$		0			0
$817$	−10.4434	−	18.0886i	−0.365369	−	0.632838i
$818$		0			0
$819$	2.73167	−	8.77019i	0.0954522	−	0.306455i
$820$		0			0
$821$	−31.1856	+	18.0050i	−1.08838	+	0.628379i	−0.933146	−	0.359498i	$-0.882948\pi$
$821$	−31.1856	+	18.0050i	−1.08838	+	0.628379i	−0.155238	+	0.987877i	$0.549615\pi$
$822$		0			0
$823$	5.19441	+	2.99899i	0.181066	+	0.104538i	0.587793	−	0.809011i	$-0.299997\pi$
$823$	5.19441	+	2.99899i	0.181066	+	0.104538i	−0.406728	+	0.913549i	$0.633330\pi$
$824$		0			0
$825$	28.2375	−	19.3846i	0.983105	−	0.674885i
$826$		0			0
$827$	9.98279			0.347135			0.173568	−	0.984822i	$-0.444470\pi$
$827$	9.98279			0.347135			0.173568	+	0.984822i	$0.444470\pi$
$828$		0			0
$829$	−23.1400	−	40.0797i	−0.803685	−	1.39202i	−0.917175	−	0.398485i	$-0.869536\pi$
$829$	−23.1400	−	40.0797i	−0.803685	−	1.39202i	0.113490	−	0.993539i	$-0.463797\pi$
$830$		0			0
$831$	28.9807			1.00533
$832$		0			0
$833$		−	19.0693i		−	0.660712i
$834$		0			0
$835$	13.5176	−	4.19331i	0.467796	−	0.145116i
$836$		0			0
$837$	8.23995			0.284814
$838$		0			0
$839$	−12.3449	−	7.12733i	−0.426193	−	0.246063i	0.271530	−	0.962430i	$-0.412470\pi$
$839$	−12.3449	−	7.12733i	−0.426193	−	0.246063i	−0.697724	+	0.716367i	$0.745804\pi$
$840$		0			0
$841$	−15.4633	+	26.7833i	−0.533219	+	0.923562i
$842$		0			0
$843$	13.3613	+	23.1425i	0.460189	+	0.797071i
$844$		0			0
$845$	27.7438	+	8.67644i	0.954416	+	0.298478i
$846$		0			0
$847$	−16.3819	−	28.3743i	−0.562890	−	0.974953i
$848$		0			0
$849$	−5.38805	+	9.33238i	−0.184917	+	0.320286i
$850$		0			0
$851$	35.7016	+	20.6123i	1.22384	+	0.706582i
$852$		0			0
$853$	28.1321			0.963225			0.481613	−	0.876384i	$-0.340051\pi$
$853$	28.1321			0.963225			0.481613	+	0.876384i	$0.340051\pi$
$854$		0			0
$855$	0.904869	+	2.91695i	0.0309459	+	0.0997575i
$856$		0			0
$857$		−	25.1192i		−	0.858054i	−0.903292	−	0.429027i	$-0.858857\pi$
$857$		−	25.1192i		−	0.858054i	0.903292	−	0.429027i	$-0.141143\pi$
$858$		0			0
$859$	54.9680			1.87549			0.937743	−	0.347331i	$-0.112912\pi$
$859$	54.9680			1.87549			0.937743	+	0.347331i	$0.112912\pi$
$860$		0			0
$861$	−12.8082	−	22.1845i	−0.436504	−	0.756047i
$862$		0			0
$863$	−56.9445			−1.93841			−0.969206	−	0.246252i	$-0.920801\pi$
$863$	−56.9445			−1.93841			−0.969206	+	0.246252i	$0.920801\pi$
$864$		0			0
$865$	−11.6094	+	12.5521i	−0.394730	+	0.426784i
$866$		0			0
$867$	37.0692	+	21.4019i	1.25894	+	0.726847i
$868$		0			0
$869$	24.9140	−	14.3841i	0.845150	−	0.487947i
$870$		0			0
$871$	−0.681453	+	2.18784i	−0.0230901	+	0.0741323i
$872$		0			0
$873$	2.55321	+	4.42228i	0.0864130	+	0.149672i
$874$		0			0
$875$	12.9518	+	32.5409i	0.437852	+	1.10008i
$876$		0			0
$877$	−7.56089	+	13.0958i	−0.255313	+	0.442215i	−0.964980	−	0.262322i	$-0.915512\pi$
$877$	−7.56089	+	13.0958i	−0.255313	+	0.442215i	0.709667	+	0.704537i	$0.248845\pi$
$878$		0			0
$879$		−	18.1658i		−	0.612719i
$880$		0			0
$881$	15.8443	+	27.4431i	0.533807	+	0.924580i	0.999220	+	0.0394869i	$0.0125723\pi$
$881$	15.8443	+	27.4431i	0.533807	+	0.924580i	−0.465413	+	0.885093i	$0.654094\pi$
$882$		0			0
$883$		−	26.8901i		−	0.904924i	−0.891784	−	0.452462i	$-0.850546\pi$
$883$		−	26.8901i		−	0.904924i	0.891784	−	0.452462i	$-0.149454\pi$
$884$		0			0
$885$	1.92123	−	8.47995i	0.0645815	−	0.285050i
$886$		0			0
$887$	17.2524	−	9.96070i	0.579280	−	0.334448i	−0.181567	−	0.983379i	$-0.558117\pi$
$887$	17.2524	−	9.96070i	0.579280	−	0.334448i	0.760847	+	0.648931i	$0.224784\pi$
$888$		0			0
$889$		−	35.8603i		−	1.20272i
$890$		0			0
$891$	−23.6644	−	13.6627i	−0.792788	−	0.457716i
$892$		0			0
$893$	−2.87442	−	1.65955i	−0.0961889	−	0.0555347i
$894$		0			0
$895$	9.72692	−	3.01740i	0.325135	−	0.100860i
$896$		0			0
$897$	−28.7756	+	6.48467i	−0.960789	+	0.216517i
$898$		0			0
$899$	9.79648	−	5.65600i	0.326731	−	0.188638i
$900$		0			0
$901$	−19.1781	+	33.2175i	−0.638916	+	1.10663i
$902$		0			0
$903$	−28.8064	+	49.8942i	−0.958618	+	1.66037i
$904$		0			0
$905$	−3.83645	+	16.9334i	−0.127528	+	0.562884i
$906$		0			0
$907$	−39.4739	+	22.7903i	−1.31071	+	0.756739i	−0.982214	−	0.187766i	$-0.939875\pi$
$907$	−39.4739	+	22.7903i	−1.31071	+	0.756739i	−0.328497	+	0.944505i	$0.606542\pi$
$908$		0			0
$909$	−13.6929			−0.454165
$910$		0			0
$911$	7.88950			0.261391			0.130695	−	0.991423i	$-0.458279\pi$
$911$	7.88950			0.261391			0.130695	+	0.991423i	$0.458279\pi$
$912$		0			0
$913$	−13.3621	+	7.71464i	−0.442223	+	0.255317i
$914$		0			0
$915$	31.4142	+	7.11727i	1.03852	+	0.235290i
$916$		0			0
$917$	−6.84128	+	11.8495i	−0.225919	+	0.391303i
$918$		0			0
$919$	21.8457	−	37.8379i	0.720624	−	1.24816i	−0.240127	−	0.970742i	$-0.577189\pi$
$919$	21.8457	−	37.8379i	0.720624	−	1.24816i	0.960750	−	0.277415i	$-0.0894777\pi$
$920$		0			0
$921$	−39.8934	+	23.0325i	−1.31453	+	0.758945i
$922$		0			0
$923$	10.9914	+	48.7740i	0.361786	+	1.60542i
$924$		0			0
$925$	−2.90307	−	37.1444i	−0.0954523	−	1.22130i
$926$		0			0
$927$	6.94604	+	4.01030i	0.228138	+	0.131716i
$928$		0			0
$929$	24.8952	+	14.3732i	0.816785	+	0.471571i	0.849306	−	0.527900i	$-0.177021\pi$
$929$	24.8952	+	14.3732i	0.816785	+	0.471571i	−0.0325218	+	0.999471i	$0.510354\pi$
$930$		0			0
$931$		−	4.72465i		−	0.154844i
$932$		0			0
$933$	0.889017	−	0.513274i	0.0291051	−	0.0168038i
$934$		0			0
$935$	−15.5142	+	68.4767i	−0.507368	+	2.23943i
$936$		0			0
$937$		−	43.1084i		−	1.40829i	−0.710056	−	0.704145i	$-0.751330\pi$
$937$		−	43.1084i		−	1.40829i	0.710056	−	0.704145i	$-0.248670\pi$
$938$		0			0
$939$	−10.7908	−	18.6902i	−0.352145	−	0.609932i
$940$		0			0
$941$		−	16.8675i		−	0.549866i	−0.961463	−	0.274933i	$-0.911344\pi$
$941$		−	16.8675i		−	0.549866i	0.961463	−	0.274933i	$-0.0886557\pi$
$942$		0			0
$943$	15.2967	−	26.4946i	0.498128	−	0.862784i
$944$		0			0
$945$	26.8199	−	28.9978i	0.872451	−	0.943299i
$946$		0			0
$947$	−16.9396	−	29.3402i	−0.550461	−	0.953427i	−0.998241	−	0.0592833i	$-0.981118\pi$
$947$	−16.9396	−	29.3402i	−0.550461	−	0.953427i	0.447780	−	0.894144i	$-0.352215\pi$
$948$		0			0
$949$	11.9573	+	12.9581i	0.388149	+	0.420638i
$950$		0			0
$951$	−18.6513	+	10.7684i	−0.604811	+	0.349188i
$952$		0			0
$953$	18.3445	+	10.5912i	0.594236	+	0.343083i	0.766771	−	0.641921i	$-0.221862\pi$
$953$	18.3445	+	10.5912i	0.594236	+	0.343083i	−0.172534	+	0.985003i	$0.555196\pi$
$954$		0			0
$955$	18.7794	+	17.3690i	0.607688	+	0.562046i
$956$		0			0
$957$	−53.0288			−1.71418
$958$		0			0
$959$	−8.65510	−	14.9911i	−0.279488	−	0.484087i
$960$		0			0
$961$	28.8647			0.931119
$962$		0			0
$963$		−	3.31588i		−	0.106853i
$964$		0			0
$965$	−6.75436	+	2.09528i	−0.217431	+	0.0674494i
$966$		0			0
$967$	29.6488			0.953442			0.476721	−	0.879055i	$-0.341825\pi$
$967$	29.6488			0.953442			0.476721	+	0.879055i	$0.341825\pi$
$968$		0			0
$969$	14.5784	+	8.41682i	0.468325	+	0.270387i
$970$		0			0
$971$	−11.4640	+	19.8562i	−0.367897	+	0.637216i	−0.989236	−	0.146326i	$-0.953255\pi$
$971$	−11.4640	+	19.8562i	−0.367897	+	0.637216i	0.621340	+	0.783541i	$0.286589\pi$
$972$		0			0
$973$	17.6926	+	30.6445i	0.567199	+	0.982417i
$974$		0			0
$975$	19.5503	+	18.1237i	0.626112	+	0.580424i
$976$		0			0
$977$	27.3631	+	47.3942i	0.875423	+	1.51628i	0.856312	+	0.516459i	$0.172750\pi$
$977$	27.3631	+	47.3942i	0.875423	+	1.51628i	0.0191106	+	0.999817i	$0.493917\pi$
$978$		0			0
$979$	6.09053	−	10.5491i	0.194654	−	0.337151i
$980$		0			0
$981$	8.22370	+	4.74795i	0.262562	+	0.151590i
$982$		0			0
$983$	−36.1492			−1.15298			−0.576490	−	0.817104i	$-0.695578\pi$
$983$	−36.1492			−1.15298			−0.576490	+	0.817104i	$0.695578\pi$
$984$		0			0
$985$	−49.4584	+	15.3425i	−1.57587	+	0.488854i
$986$		0			0
$987$			9.15517i			0.291412i
$988$		0			0
$989$	−68.8061			−2.18791
$990$		0			0
$991$	16.0324	+	27.7690i	0.509287	+	0.882111i	0.999942	+	0.0107574i	$0.00342424\pi$
$991$	16.0324	+	27.7690i	0.509287	+	0.882111i	−0.490655	+	0.871354i	$0.663242\pi$
$992$		0			0
$993$	−14.8894			−0.472502
$994$		0			0
$995$	−9.88811	−	9.14544i	−0.313474	−	0.289930i
$996$		0			0
$997$	−25.8308	−	14.9134i	−0.818070	−	0.472313i	0.0316805	−	0.999498i	$-0.489914\pi$
$997$	−25.8308	−	14.9134i	−0.818070	−	0.472313i	−0.849750	+	0.527185i	$0.823247\pi$
$998$		0			0
$999$	−36.3891	+	21.0093i	−1.15130	+	0.664703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.z.a.49.6	yes	16
3.2	odd	2		2340.2.cr.a.829.4		16
4.3	odd	2		1040.2.df.d.49.3		16
5.2	odd	4		1300.2.y.e.101.3		16
5.3	odd	4		1300.2.y.e.101.6		16
5.4	even	2	inner	260.2.z.a.49.3	✓	16
13.2	odd	12		3380.2.c.e.2029.11		16
13.3	even	3		3380.2.d.d.1689.12		16
13.4	even	6	inner	260.2.z.a.69.3	yes	16
13.10	even	6		3380.2.d.d.1689.11		16
13.11	odd	12		3380.2.c.e.2029.12		16
15.14	odd	2		2340.2.cr.a.829.5		16
20.19	odd	2		1040.2.df.d.49.6		16
39.17	odd	6		2340.2.cr.a.1369.5		16
52.43	odd	6		1040.2.df.d.849.6		16
65.4	even	6	inner	260.2.z.a.69.6	yes	16
65.17	odd	12		1300.2.y.e.901.3		16
65.24	odd	12		3380.2.c.e.2029.6		16
65.29	even	6		3380.2.d.d.1689.5		16
65.43	odd	12		1300.2.y.e.901.6		16
65.49	even	6		3380.2.d.d.1689.6		16
65.54	odd	12		3380.2.c.e.2029.5		16
195.134	odd	6		2340.2.cr.a.1369.4		16
260.199	odd	6		1040.2.df.d.849.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.3	✓	16	5.4	even	2	inner
260.2.z.a.49.6	yes	16	1.1	even	1	trivial
260.2.z.a.69.3	yes	16	13.4	even	6	inner
260.2.z.a.69.6	yes	16	65.4	even	6	inner
1040.2.df.d.49.3		16	4.3	odd	2
1040.2.df.d.49.6		16	20.19	odd	2
1040.2.df.d.849.3		16	260.199	odd	6
1040.2.df.d.849.6		16	52.43	odd	6
1300.2.y.e.101.3		16	5.2	odd	4
1300.2.y.e.101.6		16	5.3	odd	4
1300.2.y.e.901.3		16	65.17	odd	12
1300.2.y.e.901.6		16	65.43	odd	12
2340.2.cr.a.829.4		16	3.2	odd	2
2340.2.cr.a.829.5		16	15.14	odd	2
2340.2.cr.a.1369.4		16	195.134	odd	6
2340.2.cr.a.1369.5		16	39.17	odd	6
3380.2.c.e.2029.5		16	65.54	odd	12
3380.2.c.e.2029.6		16	65.24	odd	12
3380.2.c.e.2029.11		16	13.2	odd	12
3380.2.c.e.2029.12		16	13.11	odd	12
3380.2.d.d.1689.5		16	65.29	even	6
3380.2.d.d.1689.6		16	65.49	even	6
3380.2.d.d.1689.11		16	13.10	even	6
3380.2.d.d.1689.12		16	13.3	even	3

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28064 - 0.739379i) q^{3} +(0.494086 - 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +O(q^{10})\)	\(q+(1.28064 - 0.739379i) q^{3} +(0.494086 - 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +(-4.01176 + 2.31619i) q^{11} +(-2.44512 - 2.64979i) q^{13} +(-0.979690 - 3.15814i) q^{15} +(5.87021 + 3.38917i) q^{17} +(1.45442 + 0.839708i) q^{19} -4.63238i q^{21} +(4.79118 - 2.76619i) q^{23} +(-4.51176 - 2.15500i) q^{25} +5.63891i q^{27} +(3.87062 + 6.70410i) q^{29} -1.46127i q^{31} +(-3.42509 + 5.93242i) q^{33} +(-5.14245 - 4.75622i) q^{35} +(3.72577 + 6.45322i) q^{37} +(-5.09053 - 1.58556i) q^{39} +(4.78901 - 2.76494i) q^{41} +(-10.7707 - 6.21849i) q^{43} +(1.33506 + 1.23478i) q^{45} -1.97634 q^{47} +(-1.40664 - 2.43637i) q^{49} +10.0235 q^{51} +5.65865i q^{53} +(3.06899 + 9.89323i) q^{55} +2.48345 q^{57} +(2.27725 + 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(1.27384 + 2.20635i) q^{63} +(-6.98675 + 4.02310i) q^{65} +(-0.317776 - 0.550404i) q^{67} +(4.09053 - 7.08500i) q^{69} +(-12.0089 - 6.93335i) q^{71} -4.89025 q^{73} +(-7.37131 + 0.576115i) q^{75} +14.5115i q^{77} -6.21024 q^{79} +(2.94938 + 5.10848i) q^{81} +3.33075 q^{83} +(10.2915 - 11.1272i) q^{85} +(9.91375 + 5.72371i) q^{87} +(-2.27725 + 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(-1.08043 - 1.87136i) q^{93} +(2.54984 - 2.75690i) q^{95} +(3.13942 - 5.43764i) q^{97} -3.76739i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more