LMFDB - Embedded newform 1300.2.y.e.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(101,1300)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1300.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.y (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:	$10.3805522628$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$-0.739379 - 1.56631i$ of defining polynomial
Character	$\chi$	$=$	1300.101
Dual form			1300.2.y.e.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.739379 + 1.28064i) q^{3} +(-2.71292 - 1.56631i) q^{7} +(0.406637 - 0.704315i) q^{9} +O(q^{10})$	$q+(0.739379 + 1.28064i) q^{3} +(-2.71292 - 1.56631i) q^{7} +(0.406637 - 0.704315i) q^{9} +(-4.01176 + 2.31619i) q^{11} +(2.64979 - 2.44512i) q^{13} +(3.38917 - 5.87021i) q^{17} +(-1.45442 - 0.839708i) q^{19} -4.63238i q^{21} +(2.76619 + 4.79118i) q^{23} +5.63891 q^{27} +(-3.87062 - 6.70410i) q^{29} -1.46127i q^{31} +(-5.93242 - 3.42509i) q^{33} +(6.45322 - 3.72577i) q^{37} +(5.09053 + 1.58556i) q^{39} +(4.78901 - 2.76494i) q^{41} +(6.21849 - 10.7707i) q^{43} +1.97634i q^{47} +(1.40664 + 2.43637i) q^{49} +10.0235 q^{51} -5.65865 q^{53} -2.48345i q^{57} +(-2.27725 - 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(-2.20635 + 1.27384i) q^{63} +(-0.550404 + 0.317776i) q^{67} +(-4.09053 + 7.08500i) q^{69} +(-12.0089 - 6.93335i) q^{71} -4.89025i q^{73} +14.5115 q^{77} +6.21024 q^{79} +(2.94938 + 5.10848i) q^{81} +3.33075i q^{83} +(5.72371 - 9.91375i) q^{87} +(2.27725 - 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(1.87136 - 1.08043i) q^{93} +(-5.43764 - 3.13942i) q^{97} +3.76739i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{9}+O(q^{10}) $ 16 * q - 10 * q^9	$ 16 q - 10 q^{9} - 6 q^{11} + 18 q^{19} - 12 q^{29} - 18 q^{39} - 48 q^{41} + 6 q^{49} + 44 q^{51} + 30 q^{59} - 28 q^{61} + 34 q^{69} - 18 q^{71} + 16 q^{79} - 44 q^{81} - 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q - 10 * q^9 - 6 * q^11 + 18 * q^19 - 12 * q^29 - 18 * q^39 - 48 * q^41 + 6 * q^49 + 44 * q^51 + 30 * q^59 - 28 * q^61 + 34 * q^69 - 18 * q^71 + 16 * q^79 - 44 * q^81 - 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.739379	+	1.28064i	0.426881	+	0.739379i	0.996594	−	0.0824643i	$-0.0262791\pi$
$3$	0.739379	+	1.28064i	0.426881	+	0.739379i	−0.569713	+	0.821844i	$0.692946\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.71292	−	1.56631i	−1.02539	−	0.592008i	−0.109729	−	0.993962i	$-0.534998\pi$
$7$	−2.71292	−	1.56631i	−1.02539	−	0.592008i	−0.915660	+	0.401953i	$0.868331\pi$
$8$		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
$13$	2.64979	−	2.44512i	0.734919	−	0.678155i
$13$	2.64979	−	2.44512i	0.734919	−	0.678155i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.38917	−	5.87021i	0.821994	−	1.42373i	−0.0822017	−	0.996616i	$-0.526195\pi$
$17$	3.38917	−	5.87021i	0.821994	−	1.42373i	0.904195	−	0.427119i	$-0.140471\pi$
$18$		0			0
$19$	−1.45442	−	0.839708i	−0.333666	−	0.192642i	0.323802	−	0.946125i	$-0.395039\pi$
$19$	−1.45442	−	0.839708i	−0.333666	−	0.192642i	−0.657468	+	0.753483i	$0.728372\pi$
$20$		0			0
$21$		−	4.63238i		−	1.01087i
$22$		0			0
$23$	2.76619	+	4.79118i	0.576790	+	0.999030i	0.995845	+	0.0910690i	$0.0290284\pi$
$23$	2.76619	+	4.79118i	0.576790	+	0.999030i	−0.419054	+	0.907961i	$0.637638\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.63891			1.08521
$28$		0			0
$29$	−3.87062	−	6.70410i	−0.718755	−	1.24492i	−0.961493	−	0.274829i	$-0.911379\pi$
$29$	−3.87062	−	6.70410i	−0.718755	−	1.24492i	0.242738	−	0.970092i	$-0.421955\pi$
$30$		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
$33$	−5.93242	−	3.42509i	−1.03270	−	0.596231i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.45322	−	3.72577i	1.06090	−	0.612512i	0.135220	−	0.990816i	$-0.456826\pi$
$37$	6.45322	−	3.72577i	1.06090	−	0.612512i	0.925682	+	0.378303i	$0.123492\pi$
$38$		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
$43$	6.21849	−	10.7707i	0.948311	−	1.64252i	0.199329	−	0.979933i	$-0.436124\pi$
$43$	6.21849	−	10.7707i	0.948311	−	1.64252i	0.748982	−	0.662591i	$-0.230543\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			1.97634i			0.288279i	0.989557	+	0.144140i	$0.0460414\pi$
$47$			1.97634i			0.288279i	−0.989557	+	0.144140i	$0.953959\pi$
$48$		0			0
$49$	1.40664	+	2.43637i	0.200948	+	0.348052i
$50$		0			0
$51$	10.0235			1.40357
$52$		0			0
$53$	−5.65865			−0.777276			−0.388638	−	0.921391i	$-0.627054\pi$
$53$	−5.65865			−0.777276			−0.388638	+	0.921391i	$0.627054\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.48345i		−	0.328941i
$58$		0			0
$59$	−2.27725	−	1.31477i	−0.296473	−	0.171169i	0.344384	−	0.938829i	$-0.388088\pi$
$59$	−2.27725	−	1.31477i	−0.296473	−	0.171169i	−0.640857	+	0.767660i	$0.721421\pi$
$60$		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
$63$	−2.20635	+	1.27384i	−0.277974	+	0.160488i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.550404	+	0.317776i	−0.0672426	+	0.0388225i	−0.533244	−	0.845961i	$-0.679027\pi$
$67$	−0.550404	+	0.317776i	−0.0672426	+	0.0388225i	0.466002	+	0.884784i	$0.345694\pi$
$68$		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
$73$		−	4.89025i		−	0.572360i	−0.958176	−	0.286180i	$-0.907614\pi$
$73$		−	4.89025i		−	0.572360i	0.958176	−	0.286180i	$-0.0923855\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	14.5115			1.65373
$78$		0			0
$79$	6.21024			0.698707			0.349354	−	0.936991i	$-0.386401\pi$
$79$	6.21024			0.698707			0.349354	+	0.936991i	$0.386401\pi$
$80$		0			0
$81$	2.94938	+	5.10848i	0.327709	+	0.567609i
$82$		0			0
$83$			3.33075i			0.365597i	0.983150	+	0.182798i	$0.0585156\pi$
$83$			3.33075i			0.365597i	−0.983150	+	0.182798i	$0.941484\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.72371	−	9.91375i	0.613646	−	1.06287i
$88$		0			0
$89$	2.27725	−	1.31477i	0.241388	−	0.139366i	−0.374426	−	0.927257i	$-0.622160\pi$
$89$	2.27725	−	1.31477i	0.241388	−	0.139366i	0.615815	+	0.787891i	$0.288827\pi$
$90$		0			0
$91$	−11.0185	+	2.48305i	−1.15505	+	0.260294i
$92$		0			0
$93$	1.87136	−	1.08043i	0.194051	−	0.112035i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.43764	−	3.13942i	−0.552108	−	0.318760i	0.197864	−	0.980230i	$-0.436600\pi$
$97$	−5.43764	−	3.13942i	−0.552108	−	0.318760i	−0.749972	+	0.661470i	$0.769933\pi$
$98$		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
$103$	9.86212			0.971744			0.485872	−	0.874030i	$-0.338502\pi$
$103$	9.86212			0.971744			0.485872	+	0.874030i	$0.338502\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.03860	+	3.53096i	0.197079	+	0.341351i	0.947580	−	0.319519i	$-0.103521\pi$
$107$	2.03860	+	3.53096i	0.197079	+	0.341351i	−0.750501	+	0.660869i	$0.770188\pi$
$108$		0			0
$109$			11.6762i			1.11837i	0.829042	+	0.559186i	$0.188886\pi$
$109$			11.6762i			1.11837i	−0.829042	+	0.559186i	$0.811114\pi$
$110$		0			0
$111$	9.54275	+	5.50951i	0.905757	+	0.522939i
$112$		0			0
$113$	1.91041	−	3.30892i	0.179716	−	0.311277i	−0.762067	−	0.647498i	$-0.775815\pi$
$113$	1.91041	−	3.30892i	0.179716	−	0.311277i	0.941783	+	0.336221i	$0.109149\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.644637	−	2.86056i	−0.0595967	−	0.264459i
$118$		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
$123$	7.08179	+	4.08867i	0.638544	+	0.368663i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.72371	−	9.91375i	−0.507897	−	0.879703i	−0.999958	−	0.00914258i	$-0.997090\pi$
$127$	−5.72371	−	9.91375i	−0.507897	−	0.879703i	0.492061	−	0.870561i	$-0.336244\pi$
$128$		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
$133$	2.63048	+	4.55613i	0.228092	+	0.395066i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.78548	−	2.76290i	−0.408851	−	0.236050i	0.281445	−	0.959577i	$-0.409186\pi$
$137$	−4.78548	−	2.76290i	−0.408851	−	0.236050i	−0.690296	+	0.723527i	$0.742520\pi$
$138$		0			0
$139$	5.64787	−	9.78240i	0.479046	−	0.829732i	−0.520665	−	0.853761i	$-0.674316\pi$
$139$	5.64787	−	9.78240i	0.479046	−	0.829732i	0.999711	+	0.0240289i	$0.00764938\pi$
$140$		0			0
$141$	−2.53099	+	1.46127i	−0.213148	+	0.123061i
$142$		0			0
$143$	−4.96694	+	15.9467i	−0.415356	+	1.33353i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.08008	+	3.60280i	−0.171562	+	0.297154i
$148$		0			0
$149$	5.25802	+	3.03572i	0.430754	+	0.248696i	0.699668	−	0.714468i	$-0.253331\pi$
$149$	5.25802	+	3.03572i	0.430754	+	0.248696i	−0.268914	+	0.963164i	$0.586665\pi$
$150$		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
$153$	−2.75632	−	4.77408i	−0.222835	−	0.385962i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−19.3218			−1.54205			−0.771026	−	0.636804i	$-0.780256\pi$
$157$	−19.3218			−1.54205			−0.771026	+	0.636804i	$0.780256\pi$
$158$		0			0
$159$	−4.18389	−	7.24671i	−0.331804	−	0.574701i
$160$		0			0
$161$		−	17.3308i		−	1.36586i
$162$		0			0
$163$	−0.482997	−	0.278858i	−0.0378312	−	0.0218419i	0.480965	−	0.876740i	$-0.340286\pi$
$163$	−0.482997	−	0.278858i	−0.0378312	−	0.0218419i	−0.518796	+	0.854898i	$0.673620\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.48147	−	3.16473i	0.424169	−	0.244894i	−0.272691	−	0.962102i	$-0.587914\pi$
$167$	5.48147	−	3.16473i	0.424169	−	0.244894i	0.696859	+	0.717208i	$0.254580\pi$
$168$		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
$173$	3.82317	−	6.62192i	0.290670	−	0.503455i	−0.683298	−	0.730139i	$-0.739455\pi$
$173$	3.82317	−	6.62192i	0.290670	−	0.503455i	0.973968	+	0.226684i	$0.0727884\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	3.88846i		−	0.292275i
$178$		0			0
$179$	−2.27725	−	3.94432i	−0.170210	−	0.294812i	0.768283	−	0.640110i	$-0.221111\pi$
$179$	−2.27725	−	3.94432i	−0.170210	−	0.294812i	−0.938493	+	0.345298i	$0.887778\pi$
$180$		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
$183$	−14.4049			−1.06484
$184$		0			0
$185$		0			0
$186$		0			0
$187$			31.3998i			2.29618i
$188$		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
$193$	2.73893	−	1.58132i	0.197153	−	0.113826i	−0.398174	−	0.917310i	$-0.630356\pi$
$193$	2.73893	−	1.58132i	0.197153	−	0.113826i	0.595327	+	0.803484i	$0.297023\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−20.0556	+	11.5791i	−1.42890	+	0.824978i	−0.997034	−	0.0769575i	$-0.975479\pi$
$197$	−20.0556	+	11.5791i	−1.42890	+	0.824978i	−0.431870	+	0.901936i	$0.642146\pi$
$198$		0			0
$199$	−3.01176	+	5.21652i	−0.213498	+	0.369789i	−0.952807	−	0.303577i	$-0.901819\pi$
$199$	−3.01176	+	5.21652i	−0.213498	+	0.369789i	0.739309	+	0.673366i	$0.235152\pi$
$200$		0			0
$201$	−0.813915	−	0.469914i	−0.0574091	−	0.0331452i
$202$		0			0
$203$			24.2503i			1.70204i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.49934			0.312725
$208$		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
$213$		−	20.5055i		−	1.40501i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.28879	+	3.96430i	−0.155373	+	0.269115i
$218$		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
$223$	−14.4026	+	8.31533i	−0.964468	+	0.556836i	−0.897545	−	0.440922i	$-0.854651\pi$
$223$	−14.4026	+	8.31533i	−0.964468	+	0.556836i	−0.0669227	+	0.997758i	$0.521318\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.5076	+	7.22129i	0.830161	+	0.479294i	0.853908	−	0.520424i	$-0.174226\pi$
$227$	12.5076	+	7.22129i	0.830161	+	0.479294i	−0.0237467	+	0.999718i	$0.507560\pi$
$228$		0			0
$229$			4.00567i			0.264702i	0.991203	+	0.132351i	$0.0422526\pi$
$229$			4.00567i			0.264702i	−0.991203	+	0.132351i	$0.957747\pi$
$230$		0			0
$231$	10.7295	+	18.5840i	0.705948	+	1.22274i
$232$		0			0
$233$	3.48148			0.228079			0.114040	−	0.993476i	$-0.463621\pi$
$233$	3.48148			0.228079			0.114040	+	0.993476i	$0.463621\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.59173	+	7.95310i	0.298265	+	0.516610i
$238$		0			0
$239$		−	19.1155i		−	1.23648i	−0.785990	−	0.618239i	$-0.787846\pi$
$239$		−	19.1155i		−	1.23648i	0.785990	−	0.618239i	$-0.212154\pi$
$240$		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
$243$	4.09694	−	7.09611i	0.262819	−	0.455216i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.90708	+	1.33118i	−0.375859	+	0.0847010i
$248$		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
$253$	−22.1946	−	12.8140i	−1.39536	−	0.805612i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.88431	+	13.6560i	0.491810	+	0.851839i	0.999956	−	0.00943181i	$-0.00300228\pi$
$257$	7.88431	+	13.6560i	0.491810	+	0.851839i	−0.508146	+	0.861271i	$0.669669\pi$
$258$		0			0
$259$	−23.3428			−1.45045
$260$		0			0
$261$	−6.29574			−0.389696
$262$		0			0
$263$	6.14549	+	10.6443i	0.378947	+	0.656355i	0.990909	−	0.134532i	$-0.0429530\pi$
$263$	6.14549	+	10.6443i	0.378947	+	0.656355i	−0.611962	+	0.790887i	$0.709620\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.36751	+	1.94423i	0.206088	+	0.118985i
$268$		0			0
$269$	−6.82503	+	11.8213i	−0.416130	+	0.720758i	−0.995546	−	0.0942739i	$-0.969947\pi$
$269$	−6.82503	+	11.8213i	−0.416130	+	0.720758i	0.579417	+	0.815031i	$0.303280\pi$
$270$		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
$273$	−11.3267	−	12.2748i	−0.685525	−	0.742906i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.79899	−	16.9723i	0.588764	−	1.01977i	−0.405631	−	0.914037i	$-0.632948\pi$
$277$	9.79899	−	16.9723i	0.588764	−	1.01977i	0.994395	−	0.105732i	$-0.0337186\pi$
$278$		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
$283$	−3.64363	−	6.31095i	−0.216591	−	0.375147i	0.737172	−	0.675705i	$-0.236161\pi$
$283$	−3.64363	−	6.31095i	−0.216591	−	0.375147i	−0.953764	+	0.300558i	$0.902827\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−17.3230			−1.02254
$288$		0			0
$289$	−14.4729	−	25.0678i	−0.851347	−	1.47458i
$290$		0			0
$291$		−	9.28489i		−	0.544290i
$292$		0			0
$293$	10.6387	+	6.14226i	0.621520	+	0.358835i	0.777461	−	0.628932i	$-0.216508\pi$
$293$	10.6387	+	6.14226i	0.621520	+	0.358835i	−0.155941	+	0.987766i	$0.549841\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−22.6219	+	13.0608i	−1.31266	+	0.757864i
$298$		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
$303$	−12.4488	+	21.5619i	−0.715163	+	1.23870i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			31.1511i			1.77789i	0.458018	+	0.888943i	$0.348560\pi$
$307$			31.1511i			1.77789i	−0.458018	+	0.888943i	$0.651440\pi$
$308$		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
$313$	14.5944			0.824925			0.412463	−	0.910975i	$-0.364669\pi$
$313$	14.5944			0.824925			0.412463	+	0.910975i	$0.364669\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			14.5641i			0.817999i	0.912535	+	0.408999i	$0.134122\pi$
$317$			14.5641i			0.817999i	−0.912535	+	0.408999i	$0.865878\pi$
$318$		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
$323$	−9.85852	+	5.69182i	−0.548543	+	0.316701i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−14.9530	+	8.63311i	−0.826902	+	0.477412i
$328$		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
$333$		−	6.06013i		−	0.332093i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.974536			0.0530863			0.0265432	−	0.999648i	$-0.491550\pi$
$337$	0.974536			0.0530863			0.0265432	+	0.999648i	$0.491550\pi$
$338$		0			0
$339$	5.65006			0.306869
$340$		0			0
$341$	3.38457	+	5.86225i	0.183285	+	0.317459i
$342$		0			0
$343$			13.1154i			0.708165i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.21142	−	7.29440i	0.226081	−	0.391584i	−0.730562	−	0.682846i	$-0.760742\pi$
$347$	4.21142	−	7.29440i	0.226081	−	0.391584i	0.956643	+	0.291262i	$0.0940752\pi$
$348$		0			0
$349$	−3.51639	+	2.03019i	−0.188228	+	0.108674i	−0.591153	−	0.806560i	$-0.701327\pi$
$349$	−3.51639	+	2.03019i	−0.188228	+	0.108674i	0.402925	+	0.915233i	$0.367994\pi$
$350$		0			0
$351$	14.9419	−	13.7878i	0.797540	−	0.735940i
$352$		0			0
$353$	−3.39351	+	1.95925i	−0.180618	+	0.104280i	−0.587583	−	0.809164i	$-0.699921\pi$
$353$	−3.39351	+	1.95925i	−0.180618	+	0.104280i	0.406965	+	0.913444i	$0.366587\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−27.1930	−	15.6999i	−1.43921	−	0.830927i
$358$		0			0
$359$			4.23682i			0.223611i	0.993730	+	0.111805i	$0.0356633\pi$
$359$			4.23682i			0.223611i	−0.993730	+	0.111805i	$0.964337\pi$
$360$		0			0
$361$	−8.08978	−	14.0119i	−0.425778	−	0.737469i
$362$		0			0
$363$	15.4663			0.811768
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.5181	−	19.9499i	−0.601238	−	1.04138i	−0.992634	−	0.121153i	$-0.961341\pi$
$367$	−11.5181	−	19.9499i	−0.601238	−	1.04138i	0.391396	−	0.920222i	$-0.371992\pi$
$368$		0			0
$369$		−	4.49730i		−	0.234120i
$370$		0			0
$371$	15.3515	+	8.86319i	0.797010	+	0.460154i
$372$		0			0
$373$	−11.7193	+	20.2984i	−0.606801	+	1.05101i	0.384964	+	0.922932i	$0.374214\pi$
$373$	−11.7193	+	20.2984i	−0.606801	+	1.05101i	−0.991764	+	0.128078i	$0.959119\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.6487	−	8.30032i	−1.37248	−	0.427488i
$378$		0			0
$379$	−18.8942	+	10.9086i	−0.970532	+	0.560337i	−0.899398	−	0.437130i	$-0.855995\pi$
$379$	−18.8942	+	10.9086i	−0.970532	+	0.560337i	−0.0711334	+	0.997467i	$0.522662\pi$
$380$		0			0
$381$	8.46398	−	14.6600i	0.433623	−	0.751057i
$382$		0			0
$383$	12.0364	+	6.94924i	0.615033	+	0.355089i	0.774933	−	0.632044i	$-0.217784\pi$
$383$	12.0364	+	6.94924i	0.615033	+	0.355089i	−0.159900	+	0.987133i	$0.551117\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.05733	−	8.75956i	−0.257079	−	0.445273i
$388$		0			0
$389$	6.66919			0.338141			0.169071	−	0.985604i	$-0.445923\pi$
$389$	6.66919			0.338141			0.169071	+	0.985604i	$0.445923\pi$
$390$		0			0
$391$	37.5003			1.89647
$392$		0			0
$393$	−3.22945	−	5.59356i	−0.162904	−	0.282158i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.88812	+	1.66745i	0.144950	+	0.0836871i	0.570721	−	0.821144i	$-0.306664\pi$
$397$	2.88812	+	1.66745i	0.144950	+	0.0836871i	−0.425771	+	0.904831i	$0.639997\pi$
$398$		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
$403$	−3.57298	−	3.87205i	−0.177983	−	0.192880i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.2592	+	29.8937i	−0.855505	+	1.48178i
$408$		0			0
$409$	−5.06018	−	2.92150i	−0.250210	−	0.144459i	0.369651	−	0.929171i	$-0.379477\pi$
$409$	−5.06018	−	2.92150i	−0.250210	−	0.144459i	−0.619860	+	0.784712i	$0.712811\pi$
$410$		0			0
$411$		−	8.17132i		−	0.403062i
$412$		0			0
$413$	4.11868	+	7.13375i	0.202667	+	0.351029i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	16.7037			0.817982
$418$		0			0
$419$	17.8553	+	30.9262i	0.872287	+	1.51085i	0.859625	+	0.510926i	$0.170697\pi$
$419$	17.8553	+	30.9262i	0.872287	+	1.51085i	0.0126627	+	0.999920i	$0.495969\pi$
$420$		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
$423$	1.39197	+	0.803653i	0.0676798	+	0.0390750i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	26.4272	−	15.2578i	1.27890	−	0.738375i
$428$		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
$433$	5.83216	−	10.1016i	0.280276	−	0.485452i	−0.691177	−	0.722686i	$-0.742907\pi$
$433$	5.83216	−	10.1016i	0.280276	−	0.485452i	0.971453	+	0.237234i	$0.0762408\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	9.29116i		−	0.444457i
$438$		0			0
$439$	−1.74627	−	3.02462i	−0.0833447	−	0.144357i	0.821340	−	0.570439i	$-0.193227\pi$
$439$	−1.74627	−	3.02462i	−0.0833447	−	0.144357i	−0.904685	+	0.426082i	$0.859894\pi$
$440$		0			0
$441$	2.28796			0.108950
$442$		0			0
$443$	27.7833			1.32002			0.660012	−	0.751255i	$-0.270551\pi$
$443$	27.7833			1.32002			0.660012	+	0.751255i	$0.270551\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			8.97820i			0.424654i
$448$		0			0
$449$	3.16257	+	1.82591i	0.149251	+	0.0861700i	0.572766	−	0.819719i	$-0.305871\pi$
$449$	3.16257	+	1.82591i	0.149251	+	0.0861700i	−0.423515	+	0.905889i	$0.639204\pi$
$450$		0			0
$451$	−12.8082	+	22.1845i	−0.603116	+	1.04463i
$452$		0			0
$453$	19.3893	−	11.1944i	0.910987	−	0.525958i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	36.6706	−	21.1718i	1.71538	−	0.990374i	0.788480	−	0.615061i	$-0.210869\pi$
$457$	36.6706	−	21.1718i	1.71538	−	0.990374i	0.926898	−	0.375313i	$-0.122465\pi$
$458$		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
$463$		−	26.2130i		−	1.21822i	−0.793085	−	0.609111i	$-0.791526\pi$
$463$		−	26.2130i		−	1.21822i	0.793085	−	0.609111i	$-0.208474\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.45243			0.113485			0.0567424	−	0.998389i	$-0.481929\pi$
$467$	2.45243			0.113485			0.0567424	+	0.998389i	$0.481929\pi$
$468$		0			0
$469$	1.99094			0.0919330
$470$		0			0
$471$	−14.2862	−	24.7444i	−0.658272	−	1.14016i
$472$		0			0
$473$			57.6128i			2.64904i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.30102	+	3.98548i	−0.105356	+	0.182482i
$478$		0			0
$479$	−1.89707	+	1.09528i	−0.0866795	+	0.0500444i	−0.542713	−	0.839918i	$-0.682603\pi$
$479$	−1.89707	+	1.09528i	−0.0866795	+	0.0500444i	0.456034	+	0.889962i	$0.349270\pi$
$480$		0			0
$481$	7.98969	−	25.6514i	0.364299	−	1.16960i
$482$		0			0
$483$	22.1946	−	12.8140i	1.00989	−	0.583059i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−16.9001	−	9.75727i	−0.765816	−	0.442144i	0.0655640	−	0.997848i	$-0.479115\pi$
$487$	−16.9001	−	9.75727i	−0.765816	−	0.442144i	−0.831380	+	0.555704i	$0.812449\pi$
$488$		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
$493$	−52.4727			−2.36325
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.7195	+	37.6193i	0.974254	+	1.68746i
$498$		0			0
$499$			31.5312i			1.41153i	0.708445	+	0.705766i	$0.249397\pi$
$499$			31.5312i			1.41153i	−0.708445	+	0.705766i	$0.750603\pi$
$500$		0			0
$501$	8.10576	+	4.67986i	0.362139	+	0.209081i
$502$		0			0
$503$	2.81002	−	4.86709i	0.125293	−	0.217013i	−0.796555	−	0.604566i	$-0.793346\pi$
$503$	2.81002	−	4.86709i	0.125293	−	0.217013i	0.921847	+	0.387553i	$0.126680\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	17.3657	−	8.24557i	0.771238	−	0.366199i
$508$		0			0
$509$	13.7002	−	7.90980i	0.607250	−	0.350596i	−0.164639	−	0.986354i	$-0.552646\pi$
$509$	13.7002	−	7.90980i	0.607250	−	0.350596i	0.771888	+	0.635758i	$0.219312\pi$
$510$		0			0
$511$	−7.65963	+	13.2669i	−0.338842	+	0.586892i
$512$		0			0
$513$	−8.20132	−	4.73504i	−0.362097	−	0.209057i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.57758	−	7.92861i	−0.201322	−	0.348700i
$518$		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
$523$	−13.7918	−	23.8881i	−0.603074	−	1.04456i	−0.992353	−	0.123435i	$-0.960609\pi$
$523$	−13.7918	−	23.8881i	−0.603074	−	1.04456i	0.389278	−	0.921120i	$-0.372724\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.57794	−	4.95248i	−0.373661	−	0.215733i
$528$		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
$533$	5.92925	−	19.0362i	0.256824	−	0.824550i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.36751	−	5.83269i	0.145319	−	0.251699i
$538$		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
$543$	−5.74110	−	9.94387i	−0.246374	−	0.426732i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	24.7863			1.05979			0.529893	−	0.848064i	$-0.322232\pi$
$547$	24.7863			1.05979			0.529893	+	0.848064i	$0.322232\pi$
$548$		0			0
$549$	3.96114	+	6.86090i	0.169057	+	0.292816i
$550$		0			0
$551$			13.0007i			0.553850i
$552$		0			0
$553$	−16.8479	−	9.72715i	−0.716446	−	0.413641i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	28.2490	−	16.3096i	1.19695	−	0.691058i	0.237075	−	0.971491i	$-0.423811\pi$
$557$	28.2490	−	16.3096i	1.19695	−	0.691058i	0.959874	+	0.280433i	$0.0904780\pi$
$558$		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
$563$	−17.0943	+	29.6082i	−0.720438	+	1.24783i	0.240387	+	0.970677i	$0.422726\pi$
$563$	−17.0943	+	29.6082i	−0.720438	+	1.24783i	−0.960824	+	0.277158i	$0.910608\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	18.4786i		−	0.776027i
$568$		0			0
$569$	10.1721	+	17.6186i	0.426438	+	0.738612i	0.996554	−	0.0829524i	$-0.0264349\pi$
$569$	10.1721	+	17.6186i	0.426438	+	0.738612i	−0.570116	+	0.821564i	$0.693102\pi$
$570$		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
$573$	−16.9167			−0.706707
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	11.8607i		−	0.493768i	−0.969045	−	0.246884i	$-0.920593\pi$
$577$		−	11.8607i		−	0.493768i	0.969045	−	0.246884i	$-0.0794067\pi$
$578$		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
$583$	22.7011	−	13.1065i	0.940185	−	0.542816i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.69054	+	5.59483i	−0.399971	+	0.230924i	−0.686472	−	0.727157i	$-0.740841\pi$
$587$	−9.69054	+	5.59483i	−0.399971	+	0.230924i	0.286500	+	0.958080i	$0.407508\pi$
$588$		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
$593$		−	27.6058i		−	1.13363i	−0.823844	−	0.566817i	$-0.808175\pi$
$593$		−	27.6058i		−	1.13363i	0.823844	−	0.566817i	$-0.191825\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.90733			−0.364553
$598$		0			0
$599$	−29.3193			−1.19795			−0.598976	−	0.800767i	$-0.704426\pi$
$599$	−29.3193			−1.19795			−0.598976	+	0.800767i	$0.704426\pi$
$600$		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
$603$			0.516878i			0.0210489i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−8.91963	+	15.4492i	−0.362036	+	0.627066i	−0.988296	−	0.152549i	$-0.951252\pi$
$607$	−8.91963	+	15.4492i	−0.362036	+	0.627066i	0.626259	+	0.779615i	$0.284585\pi$
$608$		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
$613$	23.9523	−	13.8288i	0.967423	−	0.558542i	0.0689733	−	0.997619i	$-0.478028\pi$
$613$	23.9523	−	13.8288i	0.967423	−	0.558542i	0.898450	+	0.439077i	$0.144694\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.4664	+	15.8577i	1.10575	+	0.638408i	0.937727	−	0.347374i	$-0.112927\pi$
$617$	27.4664	+	15.8577i	1.10575	+	0.638408i	0.168028	+	0.985782i	$0.446260\pi$
$618$		0			0
$619$		−	47.4958i		−	1.90902i	−0.298186	−	0.954508i	$-0.596382\pi$
$619$		−	47.4958i		−	1.90902i	0.298186	−	0.954508i	$-0.403618\pi$
$620$		0			0
$621$	15.5983	+	27.0170i	0.625938	+	1.08416i
$622$		0			0
$623$	−8.23735			−0.330022
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.75214	+	9.96300i	0.229718	+	0.397884i
$628$		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
$633$	−3.79908	+	6.58020i	−0.151000	+	0.261540i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.68450	+	3.01645i	0.383714	+	0.119516i
$638$		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
$643$	−11.7856	−	6.80445i	−0.464781	−	0.268341i	0.249272	−	0.968434i	$-0.419809\pi$
$643$	−11.7856	−	6.80445i	−0.464781	−	0.268341i	−0.714052	+	0.700092i	$0.753142\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.01649	−	6.95677i	−0.157905	−	0.273499i	0.776208	−	0.630477i	$-0.217140\pi$
$647$	−4.01649	−	6.95677i	−0.157905	−	0.273499i	−0.934113	+	0.356978i	$0.883807\pi$
$648$		0			0
$649$	12.1811			0.478148
$650$		0			0
$651$	−6.76914			−0.265304
$652$		0			0
$653$	18.6649	+	32.3286i	0.730415	+	1.26512i	0.956706	+	0.291055i	$0.0940064\pi$
$653$	18.6649	+	32.3286i	0.730415	+	1.26512i	−0.226292	+	0.974060i	$0.572660\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.44428	−	1.98855i	−0.134374	−	0.0775809i
$658$		0			0
$659$	−3.72275	+	6.44799i	−0.145018	+	0.251178i	−0.929380	−	0.369126i	$-0.879657\pi$
$659$	−3.72275	+	6.44799i	−0.145018	+	0.251178i	0.784362	+	0.620303i	$0.212991\pi$
$660$		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
$663$	26.5602	−	24.5087i	1.03151	−	0.951840i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.4137	−	37.0896i	0.829142	−	1.43612i
$668$		0			0
$669$	−21.2979	−	12.2964i	−0.823426	−	0.475405i
$670$		0			0
$671$		−	45.1251i		−	1.74203i
$672$		0			0
$673$	−7.36034	−	12.7485i	−0.283720	−	0.491418i	0.688578	−	0.725163i	$-0.258235\pi$
$673$	−7.36034	−	12.7485i	−0.283720	−	0.491418i	−0.972298	+	0.233744i	$0.924902\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.0788			0.848559			0.424279	−	0.905531i	$-0.360527\pi$
$677$	22.0788			0.848559			0.424279	+	0.905531i	$0.360527\pi$
$678$		0			0
$679$	9.83460	+	17.0340i	0.377417	+	0.653706i
$680$		0			0
$681$			21.3571i			0.818405i
$682$		0			0
$683$	34.4700	+	19.9013i	1.31896	+	0.761501i	0.983561	−	0.180576i	$-0.0577963\pi$
$683$	34.4700	+	19.9013i	1.31896	+	0.761501i	0.335397	+	0.942077i	$0.391130\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.12983	+	2.96171i	−0.195715	+	0.112996i
$688$		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
$693$	5.90089	−	10.2206i	0.224156	−	0.388250i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	37.4833i		−	1.41978i
$698$		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
$703$	−12.5142			−0.471983
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	52.7432i		−	1.98361i
$708$		0			0
$709$	18.7237	+	10.8101i	0.703183	+	0.405983i	0.808532	−	0.588452i	$-0.200263\pi$
$709$	18.7237	+	10.8101i	0.703183	+	0.405983i	−0.105349	+	0.994435i	$0.533596\pi$
$710$		0			0
$711$	2.52531	−	4.37397i	0.0947066	−	0.164037i
$712$		0			0
$713$	7.00119	−	4.04214i	0.262197	−	0.151379i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.4801	−	14.1336i	0.914227	−	0.527829i
$718$		0			0
$719$	1.39194	−	2.41091i	0.0519105	−	0.0899117i	−0.838903	−	0.544282i	$-0.816802\pi$
$719$	1.39194	−	2.41091i	0.0519105	−	0.0899117i	0.890813	+	0.454370i	$0.150136\pi$
$720$		0			0
$721$	−26.7552	−	15.4471i	−0.996415	−	0.575281i
$722$		0			0
$723$			33.0343i			1.22856i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	22.5075			0.834756			0.417378	−	0.908733i	$-0.362949\pi$
$727$	22.5075			0.834756			0.417378	+	0.908733i	$0.362949\pi$
$728$		0			0
$729$	29.8131			1.10419
$730$		0			0
$731$	−42.1510	−	73.0077i	−1.55901	−	2.70029i
$732$		0			0
$733$		−	8.58058i		−	0.316931i	−0.987365	−	0.158465i	$-0.949345\pi$
$733$		−	8.58058i		−	0.316931i	0.987365	−	0.158465i	$-0.0506546\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.47206	−	2.54968i	0.0542240	−	0.0939187i
$738$		0			0
$739$	4.98591	−	2.87861i	0.183410	−	0.105892i	−0.405484	−	0.914102i	$-0.632897\pi$
$739$	4.98591	−	2.87861i	0.183410	−	0.105892i	0.588894	+	0.808211i	$0.299564\pi$
$740$		0			0
$741$	−6.07234	−	6.58061i	−0.223073	−	0.241745i
$742$		0			0
$743$	−23.0918	+	13.3320i	−0.847154	+	0.489105i	−0.859690	−	0.510817i	$-0.829343\pi$
$743$	−23.0918	+	13.3320i	−0.847154	+	0.489105i	0.0125354	+	0.999921i	$0.496010\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.34590	+	1.35440i	0.0858318	+	0.0495550i
$748$		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
$753$	24.7627			0.902404
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−16.1141	−	27.9105i	−0.585678	−	1.01442i	−0.994790	−	0.101941i	$-0.967495\pi$
$757$	−16.1141	−	27.9105i	−0.585678	−	1.01442i	0.409112	−	0.912484i	$-0.365838\pi$
$758$		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
$763$	18.2884	−	31.6765i	0.662086	−	1.14677i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.24902	+	2.08430i	−0.333963	+	0.0752596i
$768$		0			0
$769$	43.3628	−	25.0355i	1.56370	−	0.902804i	0.566826	−	0.823838i	$-0.308171\pi$
$769$	43.3628	−	25.0355i	1.56370	−	0.902804i	0.996877	−	0.0789667i	$-0.0251621\pi$
$770$		0			0
$771$	−11.6590	+	20.1940i	−0.419888	+	0.727268i
$772$		0			0
$773$	42.0940	+	24.3030i	1.51402	+	0.874118i	0.999865	+	0.0164180i	$0.00522625\pi$
$773$	42.0940	+	24.3030i	1.51402	+	0.874118i	0.514151	+	0.857700i	$0.328107\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−17.2592	−	29.8937i	−0.619169	−	1.07243i
$778$		0			0
$779$	−9.28695			−0.332740
$780$		0			0
$781$	64.2359			2.29854
$782$		0			0
$783$	−21.8261	−	37.8038i	−0.780000	−	1.35100i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	35.2122	+	20.3298i	1.25518	+	0.724679i	0.972134	−	0.234427i	$-0.0753214\pi$
$787$	35.2122	+	20.3298i	1.25518	+	0.724679i	0.283047	+	0.959106i	$0.408655\pi$
$788$		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
$793$	7.72134	+	34.2633i	0.274193	+	1.21672i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.93712	+	17.2116i	−0.351991	+	0.609666i	−0.986598	−	0.163169i	$-0.947829\pi$
$797$	−9.93712	+	17.2116i	−0.351991	+	0.609666i	0.634607	+	0.772835i	$0.281162\pi$
$798$		0			0
$799$	11.6015	+	6.69815i	0.410433	+	0.236964i
$800$		0			0
$801$		−	2.13854i		−	0.0755616i
$802$		0			0
$803$	11.3267	+	19.6185i	0.399712	+	0.692321i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−20.1851			−0.710551
$808$		0			0
$809$	−2.94549	−	5.10175i	−0.103558	−	0.179368i	0.809590	−	0.586996i	$-0.199689\pi$
$809$	−2.94549	−	5.10175i	−0.103558	−	0.179368i	−0.913148	+	0.407628i	$0.866356\pi$
$810$		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
$813$	−2.28555	−	1.31956i	−0.0801576	−	0.0462790i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−18.0886	+	10.4434i	−0.632838	+	0.365369i
$818$		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
$823$	−2.99899	+	5.19441i	−0.104538	+	0.181066i	−0.913549	−	0.406728i	$-0.866670\pi$
$823$	−2.99899	+	5.19441i	−0.104538	+	0.181066i	0.809011	+	0.587793i	$0.200003\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	9.98279i		−	0.347135i	−0.984822	−	0.173568i	$-0.944470\pi$
$827$		−	9.98279i		−	0.347135i	0.984822	−	0.173568i	$-0.0555296\pi$
$828$		0			0
$829$	23.1400	+	40.0797i	0.803685	+	1.39202i	0.917175	+	0.398485i	$0.130464\pi$
$829$	23.1400	+	40.0797i	0.803685	+	1.39202i	−0.113490	+	0.993539i	$0.536203\pi$
$830$		0			0
$831$	28.9807			1.00533
$832$		0			0
$833$	19.0693			0.660712
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	8.23995i		−	0.284814i
$838$		0			0
$839$	12.3449	+	7.12733i	0.426193	+	0.246063i	0.697724	−	0.716367i	$-0.254196\pi$
$839$	12.3449	+	7.12733i	0.426193	+	0.246063i	−0.271530	+	0.962430i	$0.587530\pi$
$840$		0			0
$841$	−15.4633	+	26.7833i	−0.533219	+	0.923562i
$842$		0			0
$843$	−23.1425	+	13.3613i	−0.797071	+	0.460189i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−28.3743	+	16.3819i	−0.974953	+	0.562890i
$848$		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
$853$			28.1321i			0.963225i	0.876384	+	0.481613i	$0.159949\pi$
$853$			28.1321i			0.963225i	−0.876384	+	0.481613i	$0.840051\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.1192			−0.858054			−0.429027	−	0.903292i	$-0.641143\pi$
$857$	−25.1192			−0.858054			−0.429027	+	0.903292i	$0.641143\pi$
$858$		0			0
$859$	−54.9680			−1.87549			−0.937743	−	0.347331i	$-0.887088\pi$
$859$	−54.9680			−1.87549			−0.937743	+	0.347331i	$0.887088\pi$
$860$		0			0
$861$	−12.8082	−	22.1845i	−0.436504	−	0.756047i
$862$		0			0
$863$		−	56.9445i		−	1.93841i	−0.246252	−	0.969206i	$-0.579199\pi$
$863$		−	56.9445i		−	1.93841i	0.246252	−	0.969206i	$-0.420801\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	21.4019	−	37.0692i	0.726847	−	1.25894i
$868$		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
$873$	−4.42228	+	2.55321i	−0.149672	+	0.0864130i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	13.0958	+	7.56089i	0.442215	+	0.255313i	0.704537	−	0.709667i	$-0.251155\pi$
$877$	13.0958	+	7.56089i	0.442215	+	0.255313i	−0.262322	+	0.964980i	$0.584488\pi$
$878$		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
$883$	26.8901			0.904924			0.452462	−	0.891784i	$-0.350546\pi$
$883$	26.8901			0.904924			0.452462	+	0.891784i	$0.350546\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.96070	−	17.2524i	−0.334448	−	0.579280i	0.648931	−	0.760847i	$-0.275216\pi$
$887$	−9.96070	−	17.2524i	−0.334448	−	0.579280i	−0.983379	+	0.181567i	$0.941883\pi$
$888$		0			0
$889$			35.8603i			1.20272i
$890$		0			0
$891$	−23.6644	−	13.6627i	−0.792788	−	0.457716i
$892$		0			0
$893$	1.65955	−	2.87442i	0.0555347	−	0.0961889i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.48467	+	28.7756i	0.216517	+	0.960789i
$898$		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
$903$	−49.8942	−	28.8064i	−1.66037	−	0.958618i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	22.7903	+	39.4739i	0.756739	+	1.31071i	0.944505	+	0.328497i	$0.106542\pi$
$907$	22.7903	+	39.4739i	0.756739	+	1.31071i	−0.187766	+	0.982214i	$0.560125\pi$
$908$		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
$913$	−7.71464	−	13.3621i	−0.255317	−	0.442223i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.8495	+	6.84128i	0.391303	+	0.225919i
$918$		0			0
$919$	−21.8457	+	37.8379i	−0.720624	+	1.24816i	0.240127	+	0.970742i	$0.422811\pi$
$919$	−21.8457	+	37.8379i	−0.720624	+	1.24816i	−0.960750	+	0.277415i	$0.910522\pi$
$920$		0			0
$921$	−39.8934	+	23.0325i	−1.31453	+	0.758945i
$922$		0			0
$923$	−48.7740	+	10.9914i	−1.60542	+	0.361786i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.01030	−	6.94604i	0.131716	−	0.228138i
$928$		0			0
$929$	−24.8952	−	14.3732i	−0.816785	−	0.471571i	0.0325218	−	0.999471i	$-0.489646\pi$
$929$	−24.8952	−	14.3732i	−0.816785	−	0.471571i	−0.849306	+	0.527900i	$0.822979\pi$
$930$		0			0
$931$		−	4.72465i		−	0.154844i
$932$		0			0
$933$	0.513274	+	0.889017i	0.0168038	+	0.0291051i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−43.1084			−1.40829			−0.704145	−	0.710056i	$-0.748670\pi$
$937$	−43.1084			−1.40829			−0.704145	+	0.710056i	$0.748670\pi$
$938$		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
$943$	26.4946	+	15.2967i	0.862784	+	0.498128i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.3402	+	16.9396i	−0.953427	+	0.550461i	−0.894144	−	0.447780i	$-0.852215\pi$
$947$	−29.3402	+	16.9396i	−0.953427	+	0.550461i	−0.0592833	+	0.998241i	$0.518882\pi$
$948$		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
$953$	−10.5912	+	18.3445i	−0.343083	+	0.594236i	−0.985003	−	0.172534i	$-0.944804\pi$
$953$	−10.5912	+	18.3445i	−0.343083	+	0.594236i	0.641921	+	0.766771i	$0.278138\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			53.0288i			1.71418i
$958$		0			0
$959$	8.65510	+	14.9911i	0.279488	+	0.484087i
$960$		0			0
$961$	28.8647			0.931119
$962$		0			0
$963$	3.31588			0.106853
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	29.6488i		−	0.953442i	−0.879055	−	0.476721i	$-0.841825\pi$
$967$		−	29.6488i		−	0.953442i	0.879055	−	0.476721i	$-0.158175\pi$
$968$		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
$973$	−30.6445	+	17.6926i	−0.982417	+	0.567199i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	47.3942	−	27.3631i	1.51628	−	0.875423i	0.516459	−	0.856312i	$-0.327250\pi$
$977$	47.3942	−	27.3631i	1.51628	−	0.875423i	0.999817	−	0.0191106i	$-0.00608347\pi$
$978$		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
$983$		−	36.1492i		−	1.15298i	−0.817104	−	0.576490i	$-0.804422\pi$
$983$		−	36.1492i		−	1.15298i	0.817104	−	0.576490i	$-0.195578\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	9.15517			0.291412
$988$		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
$993$		−	14.8894i		−	0.472502i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−14.9134	+	25.8308i	−0.472313	+	0.818070i	−0.999498	−	0.0316805i	$-0.989914\pi$
$997$	−14.9134	+	25.8308i	−0.472313	+	0.818070i	0.527185	+	0.849750i	$0.323247\pi$
$998$		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	1300.2.y.e.101.6		16
5.2	odd	4		260.2.z.a.49.6	yes	16
5.3	odd	4		260.2.z.a.49.3	✓	16
5.4	even	2	inner	1300.2.y.e.101.3		16
13.4	even	6	inner	1300.2.y.e.901.6		16
15.2	even	4		2340.2.cr.a.829.4		16
15.8	even	4		2340.2.cr.a.829.5		16
20.3	even	4		1040.2.df.d.49.6		16
20.7	even	4		1040.2.df.d.49.3		16
65.2	even	12		3380.2.c.e.2029.11		16
65.3	odd	12		3380.2.d.d.1689.5		16
65.4	even	6	inner	1300.2.y.e.901.3		16
65.17	odd	12		260.2.z.a.69.3	yes	16
65.23	odd	12		3380.2.d.d.1689.6		16
65.28	even	12		3380.2.c.e.2029.5		16
65.37	even	12		3380.2.c.e.2029.12		16
65.42	odd	12		3380.2.d.d.1689.12		16
65.43	odd	12		260.2.z.a.69.6	yes	16
65.62	odd	12		3380.2.d.d.1689.11		16
65.63	even	12		3380.2.c.e.2029.6		16
195.17	even	12		2340.2.cr.a.1369.5		16
195.173	even	12		2340.2.cr.a.1369.4		16
260.43	even	12		1040.2.df.d.849.3		16
260.147	even	12		1040.2.df.d.849.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.3	✓	16	5.3	odd	4
260.2.z.a.49.6	yes	16	5.2	odd	4
260.2.z.a.69.3	yes	16	65.17	odd	12
260.2.z.a.69.6	yes	16	65.43	odd	12
1040.2.df.d.49.3		16	20.7	even	4
1040.2.df.d.49.6		16	20.3	even	4
1040.2.df.d.849.3		16	260.43	even	12
1040.2.df.d.849.6		16	260.147	even	12
1300.2.y.e.101.3		16	5.4	even	2	inner
1300.2.y.e.101.6		16	1.1	even	1	trivial
1300.2.y.e.901.3		16	65.4	even	6	inner
1300.2.y.e.901.6		16	13.4	even	6	inner
2340.2.cr.a.829.4		16	15.2	even	4
2340.2.cr.a.829.5		16	15.8	even	4
2340.2.cr.a.1369.4		16	195.173	even	12
2340.2.cr.a.1369.5		16	195.17	even	12
3380.2.c.e.2029.5		16	65.28	even	12
3380.2.c.e.2029.6		16	65.63	even	12
3380.2.c.e.2029.11		16	65.2	even	12
3380.2.c.e.2029.12		16	65.37	even	12
3380.2.d.d.1689.5		16	65.3	odd	12
3380.2.d.d.1689.6		16	65.23	odd	12
3380.2.d.d.1689.11		16	65.62	odd	12
3380.2.d.d.1689.12		16	65.42	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.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.739379 + 1.28064i) q^{3} +(-2.71292 - 1.56631i) q^{7} +(0.406637 - 0.704315i) q^{9} +O(q^{10})\)	\(q+(0.739379 + 1.28064i) q^{3} +(-2.71292 - 1.56631i) q^{7} +(0.406637 - 0.704315i) q^{9} +(-4.01176 + 2.31619i) q^{11} +(2.64979 - 2.44512i) q^{13} +(3.38917 - 5.87021i) q^{17} +(-1.45442 - 0.839708i) q^{19} -4.63238i q^{21} +(2.76619 + 4.79118i) q^{23} +5.63891 q^{27} +(-3.87062 - 6.70410i) q^{29} -1.46127i q^{31} +(-5.93242 - 3.42509i) q^{33} +(6.45322 - 3.72577i) q^{37} +(5.09053 + 1.58556i) q^{39} +(4.78901 - 2.76494i) q^{41} +(6.21849 - 10.7707i) q^{43} +1.97634i q^{47} +(1.40664 + 2.43637i) q^{49} +10.0235 q^{51} -5.65865 q^{53} -2.48345i q^{57} +(-2.27725 - 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(-2.20635 + 1.27384i) q^{63} +(-0.550404 + 0.317776i) q^{67} +(-4.09053 + 7.08500i) q^{69} +(-12.0089 - 6.93335i) q^{71} -4.89025i q^{73} +14.5115 q^{77} +6.21024 q^{79} +(2.94938 + 5.10848i) q^{81} +3.33075i q^{83} +(5.72371 - 9.91375i) q^{87} +(2.27725 - 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(1.87136 - 1.08043i) q^{93} +(-5.43764 - 3.13942i) q^{97} +3.76739i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{9}+O(q^{10}) \) 16 * q - 10 * q^9	\( 16 q - 10 q^{9} - 6 q^{11} + 18 q^{19} - 12 q^{29} - 18 q^{39} - 48 q^{41} + 6 q^{49} + 44 q^{51} + 30 q^{59} - 28 q^{61} + 34 q^{69} - 18 q^{71} + 16 q^{79} - 44 q^{81} - 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q - 10 * q^9 - 6 * q^11 + 18 * q^19 - 12 * q^29 - 18 * q^39 - 48 * q^41 + 6 * q^49 + 44 * q^51 + 30 * q^59 - 28 * q^61 + 34 * q^69 - 18 * q^71 + 16 * q^79 - 44 * q^81 - 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more