LMFDB - Embedded newform 2340.2.cr.a.829.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2340,2,Mod(829,2340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2340, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2340.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.cr (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:	$18.6849940730$
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^{8} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.4
Root			$-1.56631 - 0.739379i$ of defining polynomial
Character	$\chi$	$=$	2340.829
Dual form			2340.2.cr.a.1369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.494086 + 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +O(q^{10})$	$q+(-0.494086 + 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(4.01176 - 2.31619i) q^{11} +(-2.44512 - 2.64979i) q^{13} +(-5.87021 - 3.38917i) q^{17} +(1.45442 + 0.839708i) q^{19} +(-4.79118 + 2.76619i) q^{23} +(-4.51176 - 2.15500i) q^{25} +(-3.87062 - 6.70410i) q^{29} -1.46127i q^{31} +(5.14245 + 4.75622i) q^{35} +(3.72577 + 6.45322i) q^{37} +(-4.78901 + 2.76494i) q^{41} +(-10.7707 - 6.21849i) q^{43} +1.97634 q^{47} +(-1.40664 - 2.43637i) q^{49} -5.65865i q^{53} +(3.06899 + 9.89323i) q^{55} +(-2.27725 - 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(6.98675 - 4.02310i) q^{65} +(-0.317776 - 0.550404i) q^{67} +(12.0089 + 6.93335i) q^{71} -4.89025 q^{73} -14.5115i q^{77} -6.21024 q^{79} -3.33075 q^{83} +(10.2915 - 11.1272i) q^{85} +(2.27725 - 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(-2.54984 + 2.75690i) q^{95} +(3.13942 - 5.43764i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 6 q^{11} - 18 q^{19} - 14 q^{25} - 12 q^{29} + 48 q^{41} - 6 q^{49} + 2 q^{55} + 30 q^{59} - 28 q^{61} + 15 q^{65} + 18 q^{71} - 16 q^{79} - 45 q^{85} - 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q + 6 * q^11 - 18 * q^19 - 14 * q^25 - 12 * q^29 + 48 * q^41 - 6 * q^49 + 2 * q^55 + 30 * q^59 - 28 * q^61 + 15 * q^65 + 18 * q^71 - 16 * q^79 - 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 $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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			0
$3$		0			0
$4$		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			0
$10$		0			0
$11$	4.01176	−	2.31619i	1.20959	−	0.698358i	0.246921	−	0.969036i	$-0.420581\pi$
$11$	4.01176	−	2.31619i	1.20959	−	0.698358i	0.962670	+	0.270678i	$0.0872479\pi$
$12$		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			0
$16$		0			0
$17$	−5.87021	−	3.38917i	−1.42373	−	0.821994i	−0.427119	−	0.904195i	$-0.640471\pi$
$17$	−5.87021	−	3.38917i	−1.42373	−	0.821994i	−0.996616	+	0.0822017i	$0.973805\pi$
$18$		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
$21$		0			0
$22$		0			0
$23$	−4.79118	+	2.76619i	−0.999030	+	0.576790i	−0.907961	−	0.419054i	$-0.862362\pi$
$23$	−4.79118	+	2.76619i	−0.999030	+	0.576790i	−0.0910690	+	0.995845i	$0.529028\pi$
$24$		0			0
$25$	−4.51176	−	2.15500i	−0.902352	−	0.431000i
$26$		0			0
$27$		0			0
$28$		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
$33$		0			0
$34$		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
$39$		0			0
$40$		0			0
$41$	−4.78901	+	2.76494i	−0.747918	+	0.431811i	−0.824941	−	0.565219i	$-0.808792\pi$
$41$	−4.78901	+	2.76494i	−0.747918	+	0.431811i	0.0770232	+	0.997029i	$0.475458\pi$
$42$		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
$45$		0			0
$46$		0			0
$47$	1.97634			0.288279			0.144140	−	0.989557i	$-0.453959\pi$
$47$	1.97634			0.288279			0.144140	+	0.989557i	$0.453959\pi$
$48$		0			0
$49$	−1.40664	−	2.43637i	−0.200948	−	0.348052i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	5.65865i		−	0.777276i	−0.921391	−	0.388638i	$-0.872946\pi$
$53$		−	5.65865i		−	0.777276i	0.921391	−	0.388638i	$-0.127054\pi$
$54$		0			0
$55$	3.06899	+	9.89323i	0.413823	+	1.33400i
$56$		0			0
$57$		0			0
$58$		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
$63$		0			0
$64$		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
$69$		0			0
$70$		0			0
$71$	12.0089	+	6.93335i	1.42520	+	0.822838i	0.996737	−	0.0807229i	$-0.0257229\pi$
$71$	12.0089	+	6.93335i	1.42520	+	0.822838i	0.428460	+	0.903561i	$0.359056\pi$
$72$		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
$75$		0			0
$76$		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
$81$		0			0
$82$		0			0
$83$	−3.33075			−0.365597			−0.182798	−	0.983150i	$-0.558516\pi$
$83$	−3.33075			−0.365597			−0.182798	+	0.983150i	$0.558516\pi$
$84$		0			0
$85$	10.2915	−	11.1272i	1.11627	−	1.20691i
$86$		0			0
$87$		0			0
$88$		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
$93$		0			0
$94$		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
$99$		0			0
$100$		0			0
$101$	−8.41840	−	14.5811i	−0.837662	−	1.45087i	−0.891845	−	0.452342i	$-0.850589\pi$
$101$	−8.41840	−	14.5811i	−0.837662	−	1.45087i	0.0541831	−	0.998531i	$-0.482745\pi$
$102$		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
$105$		0			0
$106$		0			0
$107$	3.53096	−	2.03860i	0.341351	−	0.197079i	−0.319519	−	0.947580i	$-0.603521\pi$
$107$	3.53096	−	2.03860i	0.341351	−	0.197079i	0.660869	+	0.750501i	$0.270188\pi$
$108$		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
$111$		0			0
$112$		0			0
$113$	3.30892	+	1.91041i	0.311277	+	0.179716i	0.647498	−	0.762067i	$-0.275815\pi$
$113$	3.30892	+	1.91041i	0.311277	+	0.179716i	−0.336221	+	0.941783i	$0.609149\pi$
$114$		0			0
$115$	−3.66525	−	11.8153i	−0.341786	−	1.10179i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		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
$129$		0			0
$130$		0			0
$131$	4.36778			0.381615			0.190807	−	0.981628i	$-0.438889\pi$
$131$	4.36778			0.381615			0.190807	+	0.981628i	$0.438889\pi$
$132$		0			0
$133$	4.55613	−	2.63048i	0.395066	−	0.228092i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.76290	+	4.78548i	−0.236050	+	0.408851i	−0.959577	−	0.281445i	$-0.909186\pi$
$137$	−2.76290	+	4.78548i	−0.236050	+	0.408851i	0.723527	+	0.690296i	$0.242520\pi$
$138$		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
$141$		0			0
$142$		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
$147$		0			0
$148$		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
$153$		0			0
$154$		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
$159$		0			0
$160$		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
$165$		0			0
$166$		0			0
$167$	−3.16473	−	5.48147i	−0.244894	−	0.424169i	0.717208	−	0.696859i	$-0.245420\pi$
$167$	−3.16473	−	5.48147i	−0.244894	−	0.424169i	−0.962102	+	0.272691i	$0.912086\pi$
$168$		0			0
$169$	−1.04275	+	12.9581i	−0.0802113	+	0.996778i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.62192	+	3.82317i	0.503455	+	0.290670i	0.730139	−	0.683298i	$-0.239455\pi$
$173$	6.62192	+	3.82317i	0.503455	+	0.290670i	−0.226684	+	0.973968i	$0.572788\pi$
$174$		0			0
$175$	−12.9132	+	8.86466i	−0.976143	+	0.670106i
$176$		0			0
$177$		0			0
$178$		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
$183$		0			0
$184$		0			0
$185$	−15.9140	+	4.93670i	−1.17002	+	0.362953i
$186$		0			0
$187$	−31.3998			−2.29618
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.71991	−	9.90717i	0.413878	−	0.716858i	−0.581432	−	0.813595i	$-0.697507\pi$
$191$	5.71991	−	9.90717i	0.413878	−	0.716858i	0.995310	+	0.0967371i	$0.0308406\pi$
$192$		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
$195$		0			0
$196$		0			0
$197$	11.5791	+	20.0556i	0.824978	+	1.42890i	0.901936	+	0.431870i	$0.142146\pi$
$197$	11.5791	+	20.0556i	0.824978	+	1.42890i	−0.0769575	+	0.997034i	$0.524521\pi$
$198$		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			0
$202$		0			0
$203$	−24.2503			−1.70204
$204$		0			0
$205$	−3.66359	−	11.8100i	−0.255876	−	0.824845i
$206$		0			0
$207$		0			0
$208$		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
$213$		0			0
$214$		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
$219$		0			0
$220$		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
$225$		0			0
$226$		0			0
$227$	7.22129	−	12.5076i	0.479294	−	0.830161i	−0.520424	−	0.853908i	$-0.674226\pi$
$227$	7.22129	−	12.5076i	0.479294	−	0.830161i	0.999718	+	0.0237467i	$0.00755951\pi$
$228$		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
$231$		0			0
$232$		0			0
$233$			3.48148i			0.228079i	0.993476	+	0.114040i	$0.0363791\pi$
$233$			3.48148i			0.228079i	−0.993476	+	0.114040i	$0.963621\pi$
$234$		0			0
$235$	−0.976482	+	4.31000i	−0.0636987	+	0.281154i
$236$		0			0
$237$		0			0
$238$		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
$243$		0			0
$244$		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
$249$		0			0
$250$		0			0
$251$	−8.37281	+	14.5021i	−0.528487	+	0.915367i	0.470961	+	0.882154i	$0.343907\pi$
$251$	−8.37281	+	14.5021i	−0.528487	+	0.915367i	−0.999448	+	0.0332127i	$0.989426\pi$
$252$		0			0
$253$	−12.8140	+	22.1946i	−0.805612	+	1.39536i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.6560	−	7.88431i	0.851839	−	0.491810i	−0.00943181	−	0.999956i	$-0.503002\pi$
$257$	13.6560	−	7.88431i	0.851839	−	0.491810i	0.861271	+	0.508146i	$0.169669\pi$
$258$		0			0
$259$	23.3428			1.45045
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.6443	+	6.14549i	−0.656355	+	0.378947i	−0.790887	−	0.611962i	$-0.790380\pi$
$263$	−10.6443	+	6.14549i	−0.656355	+	0.378947i	0.134532	+	0.990909i	$0.457047\pi$
$264$		0			0
$265$	12.3404	+	2.79586i	0.758063	+	0.171748i
$266$		0			0
$267$		0			0
$268$		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
$273$		0			0
$274$		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
$279$		0			0
$280$		0			0
$281$		−	18.0710i		−	1.07803i	−0.842297	−	0.539013i	$-0.818797\pi$
$281$		−	18.0710i		−	1.07803i	0.842297	−	0.539013i	$-0.181203\pi$
$282$		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
$285$		0			0
$286$		0			0
$287$			17.3230i			1.02254i
$288$		0			0
$289$	14.4729	+	25.0678i	0.851347	+	1.47458i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.14226	+	10.6387i	−0.358835	+	0.621520i	−0.987766	−	0.155941i	$-0.950159\pi$
$293$	−6.14226	+	10.6387i	−0.358835	+	0.621520i	0.628932	+	0.777461i	$0.283492\pi$
$294$		0			0
$295$	3.99241	−	4.31662i	0.232447	−	0.251323i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		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
$309$		0			0
$310$		0			0
$311$	−0.694196			−0.0393643			−0.0196821	−	0.999806i	$-0.506265\pi$
$311$	−0.694196			−0.0393643			−0.0196821	+	0.999806i	$0.506265\pi$
$312$		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
$315$		0			0
$316$		0			0
$317$	14.5641			0.817999			0.408999	−	0.912535i	$-0.365878\pi$
$317$	14.5641			0.817999			0.408999	+	0.912535i	$0.365878\pi$
$318$		0			0
$319$	−31.0560	−	17.9302i	−1.73880	−	1.00390i
$320$		0			0
$321$		0			0
$322$		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
$327$		0			0
$328$		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
$333$		0			0
$334$		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
$339$		0			0
$340$		0			0
$341$	−3.38457	−	5.86225i	−0.183285	−	0.317459i
$342$		0			0
$343$	13.1154			0.708165
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.29440	−	4.21142i	−0.391584	−	0.226081i	0.291262	−	0.956643i	$-0.405925\pi$
$347$	−7.29440	−	4.21142i	−0.391584	−	0.226081i	−0.682846	+	0.730562i	$0.739258\pi$
$348$		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
$351$		0			0
$352$		0			0
$353$	−1.95925	−	3.39351i	−0.104280	−	0.180618i	0.809164	−	0.587583i	$-0.199921\pi$
$353$	−1.95925	−	3.39351i	−0.104280	−	0.180618i	−0.913444	+	0.406965i	$0.866587\pi$
$354$		0			0
$355$	−21.0537	+	22.7634i	−1.11741	+	1.20815i
$356$		0			0
$357$		0			0
$358$		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
$363$		0			0
$364$		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
$369$		0			0
$370$		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
$375$		0			0
$376$		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
$381$		0			0
$382$		0			0
$383$	−6.94924	+	12.0364i	−0.355089	+	0.615033i	−0.987133	−	0.159900i	$-0.948883\pi$
$383$	−6.94924	+	12.0364i	−0.355089	+	0.615033i	0.632044	+	0.774933i	$0.282216\pi$
$384$		0			0
$385$	31.6466	+	7.16990i	1.61286	+	0.365412i
$386$		0			0
$387$		0			0
$388$		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
$393$		0			0
$394$		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
$399$		0			0
$400$		0			0
$401$	17.1405	−	9.89607i	0.855956	−	0.494186i	−0.00670012	−	0.999978i	$-0.502133\pi$
$401$	17.1405	−	9.89607i	0.855956	−	0.494186i	0.862656	+	0.505791i	$0.168799\pi$
$402$		0			0
$403$	−3.87205	+	3.57298i	−0.192880	+	0.177983i
$404$		0			0
$405$		0			0
$406$		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
$411$		0			0
$412$		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
$417$		0			0
$418$		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
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	26.2773	−	15.1712i	1.26573	−	0.730770i	0.291553	−	0.956555i	$-0.405828\pi$
$431$	26.2773	−	15.1712i	1.26573	−	0.730770i	0.974177	+	0.225785i	$0.0724945\pi$
$432$		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
$435$		0			0
$436$		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
$441$		0			0
$442$		0			0
$443$			27.7833i			1.32002i	0.751255	+	0.660012i	$0.229449\pi$
$443$			27.7833i			1.32002i	−0.751255	+	0.660012i	$0.770551\pi$
$444$		0			0
$445$	1.74210	+	5.61584i	0.0825832	+	0.266216i
$446$		0			0
$447$		0			0
$448$		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
$453$		0			0
$454$		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
$459$		0			0
$460$		0			0
$461$	−2.87450	−	1.65960i	−0.133879	−	0.0772951i	0.431565	−	0.902082i	$-0.357962\pi$
$461$	−2.87450	−	1.65960i	−0.133879	−	0.0772951i	−0.565444	+	0.824787i	$0.691295\pi$
$462$		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
$465$		0			0
$466$		0			0
$467$		−	2.45243i		−	0.113485i	−0.998389	−	0.0567424i	$-0.981929\pi$
$467$		−	2.45243i		−	0.113485i	0.998389	−	0.0567424i	$-0.0180714\pi$
$468$		0			0
$469$	−1.99094			−0.0919330
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−57.6128			−2.64904
$474$		0			0
$475$	−4.75240	−	6.92283i	−0.218055	−	0.317641i
$476$		0			0
$477$		0			0
$478$		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
$483$		0			0
$484$		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			0
$490$		0			0
$491$	−15.6383	−	27.0863i	−0.705747	−	1.22239i	−0.966421	−	0.256963i	$-0.917278\pi$
$491$	−15.6383	−	27.0863i	−0.705747	−	1.22239i	0.260674	−	0.965427i	$-0.416055\pi$
$492$		0			0
$493$			52.4727i			2.36325i
$494$		0			0
$495$		0			0
$496$		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
$501$		0			0
$502$		0			0
$503$	4.86709	+	2.81002i	0.217013	+	0.125293i	0.604566	−	0.796555i	$-0.293346\pi$
$503$	4.86709	+	2.81002i	0.217013	+	0.125293i	−0.387553	+	0.921847i	$0.626680\pi$
$504$		0			0
$505$	35.9578	−	11.1545i	1.60010	−	0.496369i
$506$		0			0
$507$		0			0
$508$		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
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$	−12.6030			−0.552149			−0.276074	−	0.961136i	$-0.589034\pi$
$521$	−12.6030			−0.552149			−0.276074	+	0.961136i	$0.589034\pi$
$522$		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
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		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
$543$		0			0
$544$		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
$549$		0			0
$550$		0			0
$551$		−	13.0007i		−	0.553850i
$552$		0			0
$553$	−9.72715	+	16.8479i	−0.413641	+	0.716446i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.3096	−	28.2490i	−0.691058	−	1.19695i	−0.971491	−	0.237075i	$-0.923811\pi$
$557$	−16.3096	−	28.2490i	−0.691058	−	1.19695i	0.280433	−	0.959874i	$-0.409522\pi$
$558$		0			0
$559$	9.85811	+	43.7452i	0.416954	+	1.85022i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−29.6082	−	17.0943i	−1.24783	−	0.720438i	−0.277158	−	0.960824i	$-0.589392\pi$
$563$	−29.6082	−	17.0943i	−1.24783	−	0.720438i	−0.970677	+	0.240387i	$0.922726\pi$
$564$		0			0
$565$	−5.80111	+	6.27219i	−0.244054	+	0.263873i
$566$		0			0
$567$		0			0
$568$		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
$573$		0			0
$574$		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
$579$		0			0
$580$		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			0
$586$		0			0
$587$	5.59483	+	9.69054i	0.230924	+	0.399971i	0.958080	−	0.286500i	$-0.0924920\pi$
$587$	5.59483	+	9.69054i	0.230924	+	0.399971i	−0.727157	+	0.686472i	$0.759159\pi$
$588$		0			0
$589$	1.22704	−	2.12529i	0.0505592	−	0.0875710i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	27.6058			1.13363			0.566817	−	0.823844i	$-0.308175\pi$
$593$	27.6058			1.13363			0.566817	+	0.823844i	$0.308175\pi$
$594$		0			0
$595$	−14.0676	−	45.3486i	−0.576717	−	1.85911i
$596$		0			0
$597$		0			0
$598$		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			0
$604$		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
$609$		0			0
$610$		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
$615$		0			0
$616$		0			0
$617$	15.8577	−	27.4664i	0.638408	−	1.10575i	−0.347374	−	0.937727i	$-0.612927\pi$
$617$	15.8577	−	27.4664i	0.638408	−	1.10575i	0.985782	−	0.168028i	$-0.0537400\pi$
$618$		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
$621$		0			0
$622$		0			0
$623$		−	8.23735i		−	0.330022i
$624$		0			0
$625$	15.7119	+	19.4457i	0.628478	+	0.777828i
$626$		0			0
$627$		0			0
$628$		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
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−7.59556	+	13.1559i	−0.300007	+	0.519627i	−0.976137	−	0.217155i	$-0.930322\pi$
$641$	−7.59556	+	13.1559i	−0.300007	+	0.519627i	0.676131	+	0.736782i	$0.263656\pi$
$642$		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
$645$		0			0
$646$		0			0
$647$	−6.95677	+	4.01649i	−0.273499	+	0.157905i	−0.630477	−	0.776208i	$-0.717140\pi$
$647$	−6.95677	+	4.01649i	−0.273499	+	0.157905i	0.356978	+	0.934113i	$0.383807\pi$
$648$		0			0
$649$	−12.1811			−0.478148
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−32.3286	+	18.6649i	−1.26512	+	0.730415i	−0.974060	−	0.226292i	$-0.927340\pi$
$653$	−32.3286	+	18.6649i	−1.26512	+	0.730415i	−0.291055	+	0.956706i	$0.594006\pi$
$654$		0			0
$655$	−2.15806	+	9.52524i	−0.0843222	+	0.372182i
$656$		0			0
$657$		0			0
$658$		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
$663$		0			0
$664$		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
$669$		0			0
$670$		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
$675$		0			0
$676$		0			0
$677$		−	22.0788i		−	0.848559i	−0.905531	−	0.424279i	$-0.860527\pi$
$677$		−	22.0788i		−	0.848559i	0.905531	−	0.424279i	$-0.139473\pi$
$678$		0			0
$679$	−9.83460	−	17.0340i	−0.377417	−	0.653706i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.9013	+	34.4700i	−0.761501	+	1.31896i	0.180576	+	0.983561i	$0.442204\pi$
$683$	−19.9013	+	34.4700i	−0.761501	+	1.31896i	−0.942077	+	0.335397i	$0.891130\pi$
$684$		0			0
$685$	−9.07106	−	8.38976i	−0.346587	−	0.320556i
$686$		0			0
$687$		0			0
$688$		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
$693$		0			0
$694$		0			0
$695$	−18.5429	−	17.1502i	−0.703372	−	0.650544i
$696$		0			0
$697$	37.4833			1.41978
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−12.1911			−0.460452			−0.230226	−	0.973137i	$-0.573947\pi$
$701$	−12.1911			−0.460452			−0.230226	+	0.973137i	$0.573947\pi$
$702$		0			0
$703$			12.5142i			0.471983i
$704$		0			0
$705$		0			0
$706$		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
$711$		0			0
$712$		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
$717$		0			0
$718$		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
$723$		0			0
$724$		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
$729$		0			0
$730$		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
$735$		0			0
$736$		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
$741$		0			0
$742$		0			0
$743$	−13.3320	−	23.0918i	−0.489105	−	0.847154i	0.510817	−	0.859690i	$-0.329343\pi$
$743$	−13.3320	−	23.0918i	−0.489105	−	0.847154i	−0.999921	+	0.0125354i	$0.996010\pi$
$744$		0			0
$745$	−9.21821	+	9.96678i	−0.337729	+	0.365155i
$746$		0			0
$747$		0			0
$748$		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
$753$		0			0
$754$		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
$759$		0			0
$760$		0			0
$761$	−10.4017	−	6.00543i	−0.377062	−	0.217697i	0.299477	−	0.954103i	$-0.403188\pi$
$761$	−10.4017	−	6.00543i	−0.377062	−	0.217697i	−0.676539	+	0.736407i	$0.736521\pi$
$762$		0			0
$763$	−31.6765	−	18.2884i	−1.14677	−	0.662086i
$764$		0			0
$765$		0			0
$766$		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
$771$		0			0
$772$		0			0
$773$	−24.3030	+	42.0940i	−0.874118	+	1.51402i	−0.0164180	+	0.999865i	$0.505226\pi$
$773$	−24.3030	+	42.0940i	−0.874118	+	1.51402i	−0.857700	+	0.514151i	$0.828107\pi$
$774$		0			0
$775$	−3.14903	+	6.59288i	−0.113117	+	0.236823i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.28695			−0.332740
$780$		0			0
$781$	64.2359			2.29854
$782$		0			0
$783$		0			0
$784$		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
$789$		0			0
$790$		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
$795$		0			0
$796$		0			0
$797$	17.2116	+	9.93712i	0.609666	+	0.351991i	0.772835	−	0.634607i	$-0.218838\pi$
$797$	17.2116	+	9.93712i	0.609666	+	0.351991i	−0.163169	+	0.986598i	$0.552171\pi$
$798$		0			0
$799$	−11.6015	−	6.69815i	−0.410433	−	0.236964i
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		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
$813$		0			0
$814$		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
$819$		0			0
$820$		0			0
$821$	31.1856	−	18.0050i	1.08838	−	0.628379i	0.155238	−	0.987877i	$-0.450385\pi$
$821$	31.1856	−	18.0050i	1.08838	−	0.628379i	0.933146	+	0.359498i	$0.117052\pi$
$822$		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
$825$		0			0
$826$		0			0
$827$	−9.98279			−0.347135			−0.173568	−	0.984822i	$-0.555530\pi$
$827$	−9.98279			−0.347135			−0.173568	+	0.984822i	$0.555530\pi$
$828$		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
$831$		0			0
$832$		0			0
$833$			19.0693i			0.660712i
$834$		0			0
$835$	13.5176	−	4.19331i	0.467796	−	0.145116i
$836$		0			0
$837$		0			0
$838$		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
$843$		0			0
$844$		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
$849$		0			0
$850$		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			0
$856$		0			0
$857$			25.1192i			0.858054i	0.903292	+	0.429027i	$0.141143\pi$
$857$			25.1192i			0.858054i	−0.903292	+	0.429027i	$0.858857\pi$
$858$		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
$861$		0			0
$862$		0			0
$863$	56.9445			1.93841			0.969206	−	0.246252i	$-0.0791990\pi$
$863$	56.9445			1.93841			0.969206	+	0.246252i	$0.0791990\pi$
$864$		0			0
$865$	−11.6094	+	12.5521i	−0.394730	+	0.426784i
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		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
$879$		0			0
$880$		0			0
$881$	−15.8443	−	27.4431i	−0.533807	−	0.924580i	−0.999220	−	0.0394869i	$-0.987428\pi$
$881$	−15.8443	−	27.4431i	−0.533807	−	0.924580i	0.465413	−	0.885093i	$-0.345906\pi$
$882$		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
$885$		0			0
$886$		0			0
$887$	−17.2524	+	9.96070i	−0.579280	+	0.334448i	−0.760847	−	0.648931i	$-0.775216\pi$
$887$	−17.2524	+	9.96070i	−0.579280	+	0.334448i	0.181567	+	0.983379i	$0.441883\pi$
$888$		0			0
$889$		−	35.8603i		−	1.20272i
$890$		0			0
$891$		0			0
$892$		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
$897$		0			0
$898$		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
$903$		0			0
$904$		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
$909$		0			0
$910$		0			0
$911$	−7.88950			−0.261391			−0.130695	−	0.991423i	$-0.541721\pi$
$911$	−7.88950			−0.261391			−0.130695	+	0.991423i	$0.541721\pi$
$912$		0			0
$913$	−13.3621	+	7.71464i	−0.442223	+	0.255317i
$914$		0			0
$915$		0			0
$916$		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
$921$		0			0
$922$		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
$927$		0			0
$928$		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			0
$934$		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
$939$		0			0
$940$		0			0
$941$			16.8675i			0.549866i	0.961463	+	0.274933i	$0.0886557\pi$
$941$			16.8675i			0.549866i	−0.961463	+	0.274933i	$0.911344\pi$
$942$		0			0
$943$	15.2967	−	26.4946i	0.498128	−	0.862784i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.9396	+	29.3402i	0.550461	+	0.953427i	0.998241	+	0.0592833i	$0.0188815\pi$
$947$	16.9396	+	29.3402i	0.550461	+	0.953427i	−0.447780	+	0.894144i	$0.647785\pi$
$948$		0			0
$949$	11.9573	+	12.9581i	0.388149	+	0.420638i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−18.3445	−	10.5912i	−0.594236	−	0.343083i	0.172534	−	0.985003i	$-0.444804\pi$
$953$	−18.3445	−	10.5912i	−0.594236	−	0.343083i	−0.766771	+	0.641921i	$0.778138\pi$
$954$		0			0
$955$	18.7794	+	17.3690i	0.607688	+	0.562046i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.65510	+	14.9911i	0.279488	+	0.484087i
$960$		0			0
$961$	28.8647			0.931119
$962$		0			0
$963$		0			0
$964$		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
$969$		0			0
$970$		0			0
$971$	11.4640	−	19.8562i	0.367897	−	0.637216i	−0.621340	−	0.783541i	$-0.713411\pi$
$971$	11.4640	−	19.8562i	0.367897	−	0.637216i	0.989236	+	0.146326i	$0.0467447\pi$
$972$		0			0
$973$	17.6926	+	30.6445i	0.567199	+	0.982417i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.3631	−	47.3942i	−0.875423	−	1.51628i	−0.856312	−	0.516459i	$-0.827250\pi$
$977$	−27.3631	−	47.3942i	−0.875423	−	1.51628i	−0.0191106	−	0.999817i	$-0.506083\pi$
$978$		0			0
$979$	6.09053	−	10.5491i	0.194654	−	0.337151i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	36.1492			1.15298			0.576490	−	0.817104i	$-0.304422\pi$
$983$	36.1492			1.15298			0.576490	+	0.817104i	$0.304422\pi$
$984$		0			0
$985$	−49.4584	+	15.3425i	−1.57587	+	0.488854i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.cr.a.829.4		16
3.2	odd	2		260.2.z.a.49.6	yes	16
5.4	even	2	inner	2340.2.cr.a.829.5		16
12.11	even	2		1040.2.df.d.49.3		16
13.4	even	6	inner	2340.2.cr.a.1369.5		16
15.2	even	4		1300.2.y.e.101.3		16
15.8	even	4		1300.2.y.e.101.6		16
15.14	odd	2		260.2.z.a.49.3	✓	16
39.2	even	12		3380.2.c.e.2029.11		16
39.11	even	12		3380.2.c.e.2029.12		16
39.17	odd	6		260.2.z.a.69.3	yes	16
39.23	odd	6		3380.2.d.d.1689.11		16
39.29	odd	6		3380.2.d.d.1689.12		16
60.59	even	2		1040.2.df.d.49.6		16
65.4	even	6	inner	2340.2.cr.a.1369.4		16
156.95	even	6		1040.2.df.d.849.6		16
195.17	even	12		1300.2.y.e.901.3		16
195.29	odd	6		3380.2.d.d.1689.5		16
195.89	even	12		3380.2.c.e.2029.6		16
195.119	even	12		3380.2.c.e.2029.5		16
195.134	odd	6		260.2.z.a.69.6	yes	16
195.173	even	12		1300.2.y.e.901.6		16
195.179	odd	6		3380.2.d.d.1689.6		16
780.719	even	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	15.14	odd	2
260.2.z.a.49.6	yes	16	3.2	odd	2
260.2.z.a.69.3	yes	16	39.17	odd	6
260.2.z.a.69.6	yes	16	195.134	odd	6
1040.2.df.d.49.3		16	12.11	even	2
1040.2.df.d.49.6		16	60.59	even	2
1040.2.df.d.849.3		16	780.719	even	6
1040.2.df.d.849.6		16	156.95	even	6
1300.2.y.e.101.3		16	15.2	even	4
1300.2.y.e.101.6		16	15.8	even	4
1300.2.y.e.901.3		16	195.17	even	12
1300.2.y.e.901.6		16	195.173	even	12
2340.2.cr.a.829.4		16	1.1	even	1	trivial
2340.2.cr.a.829.5		16	5.4	even	2	inner
2340.2.cr.a.1369.4		16	65.4	even	6	inner
2340.2.cr.a.1369.5		16	13.4	even	6	inner
3380.2.c.e.2029.5		16	195.119	even	12
3380.2.c.e.2029.6		16	195.89	even	12
3380.2.c.e.2029.11		16	39.2	even	12
3380.2.c.e.2029.12		16	39.11	even	12
3380.2.d.d.1689.5		16	195.29	odd	6
3380.2.d.d.1689.6		16	195.179	odd	6
3380.2.d.d.1689.11		16	39.23	odd	6
3380.2.d.d.1689.12		16	39.29	odd	6

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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.cr (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.494086 + 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +O(q^{10})\)	\(q+(-0.494086 + 2.18080i) q^{5} +(1.56631 - 2.71292i) q^{7} +(4.01176 - 2.31619i) q^{11} +(-2.44512 - 2.64979i) q^{13} +(-5.87021 - 3.38917i) q^{17} +(1.45442 + 0.839708i) q^{19} +(-4.79118 + 2.76619i) q^{23} +(-4.51176 - 2.15500i) q^{25} +(-3.87062 - 6.70410i) q^{29} -1.46127i q^{31} +(5.14245 + 4.75622i) q^{35} +(3.72577 + 6.45322i) q^{37} +(-4.78901 + 2.76494i) q^{41} +(-10.7707 - 6.21849i) q^{43} +1.97634 q^{47} +(-1.40664 - 2.43637i) q^{49} -5.65865i q^{53} +(3.06899 + 9.89323i) q^{55} +(-2.27725 - 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(6.98675 - 4.02310i) q^{65} +(-0.317776 - 0.550404i) q^{67} +(12.0089 + 6.93335i) q^{71} -4.89025 q^{73} -14.5115i q^{77} -6.21024 q^{79} -3.33075 q^{83} +(10.2915 - 11.1272i) q^{85} +(2.27725 - 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(-2.54984 + 2.75690i) q^{95} +(3.13942 - 5.43764i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 6 q^{11} - 18 q^{19} - 14 q^{25} - 12 q^{29} + 48 q^{41} - 6 q^{49} + 2 q^{55} + 30 q^{59} - 28 q^{61} + 15 q^{65} + 18 q^{71} - 16 q^{79} - 45 q^{85} - 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q + 6 * q^11 - 18 * q^19 - 14 * q^25 - 12 * q^29 + 48 * q^41 - 6 * q^49 + 2 * q^55 + 30 * q^59 - 28 * q^61 + 15 * q^65 + 18 * q^71 - 16 * q^79 - 45 * q^85 - 30 * q^89 - 10 * q^91

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