LMFDB - Embedded newform 1380.2.r.c.737.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (of order $4$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.1
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72892 - 0.104128i) q^{3} +(1.51193 + 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(2.97831 + 0.360057i) q^{9} +O(q^{10})$	\(q+(-1.72892 - 0.104128i) q^{3} +(1.51193 + 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(2.97831 + 0.360057i) q^{9} -1.70534i q^{11} +(3.68884 - 3.68884i) q^{13} +(-2.44246 - 3.00573i) q^{15} +(4.61681 - 4.61681i) q^{17} +1.98235i q^{19} +(-5.31904 - 6.00081i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(-0.428136 + 4.98164i) q^{25} +(-5.11177 - 0.932633i) q^{27} -1.64979 q^{29} +9.87466 q^{31} +(-0.177573 + 2.94839i) q^{33} +(-0.443627 + 10.3428i) q^{35} +(-6.78052 - 6.78052i) q^{37} +(-6.76181 + 5.99359i) q^{39} -11.3456i q^{41} +(-5.37542 + 5.37542i) q^{43} +(3.90983 + 5.45098i) q^{45} +(0.169299 - 0.169299i) q^{47} +14.4340i q^{49} +(-8.46283 + 7.50135i) q^{51} +(0.593798 + 0.593798i) q^{53} +(2.80945 - 2.57835i) q^{55} +(0.206417 - 3.42731i) q^{57} +9.69856 q^{59} -1.66086 q^{61} +(8.57134 + 10.9288i) q^{63} +(11.6544 + 0.499886i) q^{65} +(3.54310 + 3.54310i) q^{67} +(1.14890 + 1.29616i) q^{69} -1.94914i q^{71} +(-2.66633 + 2.66633i) q^{73} +(1.25894 - 8.56826i) q^{75} +(5.58274 - 5.58274i) q^{77} +3.69783i q^{79} +(8.74072 + 2.14472i) q^{81} +(-10.4675 - 10.4675i) q^{83} +(14.5862 + 0.625639i) q^{85} +(2.85236 + 0.171789i) q^{87} +8.35452 q^{89} +24.1522 q^{91} +(-17.0725 - 1.02823i) q^{93} +(-3.26580 + 2.99717i) q^{95} +(-5.87875 - 5.87875i) q^{97} +(0.614019 - 5.07904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72892	−	0.104128i	−0.998191	−	0.0601182i
$3$	−1.72892	−	0.104128i	−0.998191	−	0.0601182i
$4$		0			0
$5$	1.51193	+	1.64744i	0.676156	+	0.736759i
$5$	1.51193	+	1.64744i	0.676156	+	0.736759i
$6$		0			0
$7$	3.27368	+	3.27368i	1.23734	+	1.23734i	0.961086	+	0.276249i	$0.0890914\pi$
$7$	3.27368	+	3.27368i	1.23734	+	1.23734i	0.276249	+	0.961086i	$0.410909\pi$
$8$		0			0
$9$	2.97831	+	0.360057i	0.992772	+	0.120019i
$10$		0			0
$11$		−	1.70534i		−	0.514179i	−0.966388	−	0.257090i	$-0.917236\pi$
$11$		−	1.70534i		−	0.514179i	0.966388	−	0.257090i	$-0.0827636\pi$
$12$		0			0
$13$	3.68884	−	3.68884i	1.02310	−	1.02310i	0.0233734	−	0.999727i	$-0.492559\pi$
$13$	3.68884	−	3.68884i	1.02310	−	1.02310i	0.999727	−	0.0233734i	$-0.00744066\pi$
$14$		0			0
$15$	−2.44246	−	3.00573i	−0.630640	−	0.776076i
$16$		0			0
$17$	4.61681	−	4.61681i	1.11974	−	1.11974i	0.127963	−	0.991779i	$-0.459156\pi$
$17$	4.61681	−	4.61681i	1.11974	−	1.11974i	0.991779	−	0.127963i	$-0.0408437\pi$
$18$		0			0
$19$			1.98235i			0.454781i	0.973804	+	0.227391i	$0.0730195\pi$
$19$			1.98235i			0.454781i	−0.973804	+	0.227391i	$0.926981\pi$
$20$		0			0
$21$	−5.31904	−	6.00081i	−1.16071	−	1.30948i
$22$		0			0
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	−0.428136	+	4.98164i	−0.0856273	+	0.996327i
$26$		0			0
$27$	−5.11177	−	0.932633i	−0.983761	−	0.179485i
$28$		0			0
$29$	−1.64979			−0.306359			−0.153179	−	0.988198i	$-0.548951\pi$
$29$	−1.64979			−0.306359			−0.153179	+	0.988198i	$0.548951\pi$
$30$		0			0
$31$	9.87466			1.77354			0.886770	−	0.462210i	$-0.152944\pi$
$31$	9.87466			1.77354			0.886770	+	0.462210i	$0.152944\pi$
$32$		0			0
$33$	−0.177573	+	2.94839i	−0.0309115	+	0.513249i
$34$		0			0
$35$	−0.443627	+	10.3428i	−0.0749866	+	1.74825i
$36$		0			0
$37$	−6.78052	−	6.78052i	−1.11471	−	1.11471i	−0.992505	−	0.122206i	$-0.961003\pi$
$37$	−6.78052	−	6.78052i	−1.11471	−	1.11471i	−0.122206	−	0.992505i	$-0.538997\pi$
$38$		0			0
$39$	−6.76181	+	5.99359i	−1.08276	+	0.959743i
$40$		0			0
$41$		−	11.3456i		−	1.77189i	−0.463791	−	0.885945i	$-0.653511\pi$
$41$		−	11.3456i		−	1.77189i	0.463791	−	0.885945i	$-0.346489\pi$
$42$		0			0
$43$	−5.37542	+	5.37542i	−0.819744	+	0.819744i	−0.986071	−	0.166327i	$-0.946809\pi$
$43$	−5.37542	+	5.37542i	−0.819744	+	0.819744i	0.166327	+	0.986071i	$0.446809\pi$
$44$		0			0
$45$	3.90983	+	5.45098i	0.582843	+	0.812585i
$46$		0			0
$47$	0.169299	−	0.169299i	0.0246948	−	0.0246948i	−0.694652	−	0.719346i	$-0.744441\pi$
$47$	0.169299	−	0.169299i	0.0246948	−	0.0246948i	0.719346	+	0.694652i	$0.244441\pi$
$48$		0			0
$49$			14.4340i			2.06200i
$50$		0			0
$51$	−8.46283	+	7.50135i	−1.18503	+	1.05040i
$52$		0			0
$53$	0.593798	+	0.593798i	0.0815644	+	0.0815644i	0.746712	−	0.665148i	$-0.231631\pi$
$53$	0.593798	+	0.593798i	0.0815644	+	0.0815644i	−0.665148	+	0.746712i	$0.731631\pi$
$54$		0			0
$55$	2.80945	−	2.57835i	0.378826	−	0.347665i
$56$		0			0
$57$	0.206417	−	3.42731i	0.0273406	−	0.453959i
$58$		0			0
$59$	9.69856			1.26264			0.631322	−	0.775521i	$-0.282512\pi$
$59$	9.69856			1.26264			0.631322	+	0.775521i	$0.282512\pi$
$60$		0			0
$61$	−1.66086			−0.212652			−0.106326	−	0.994331i	$-0.533909\pi$
$61$	−1.66086			−0.212652			−0.106326	+	0.994331i	$0.533909\pi$
$62$		0			0
$63$	8.57134	+	10.9288i	1.07989	+	1.37689i
$64$		0			0
$65$	11.6544	+	0.499886i	1.44555	+	0.0620032i
$66$		0			0
$67$	3.54310	+	3.54310i	0.432859	+	0.432859i	0.889600	−	0.456741i	$-0.150983\pi$
$67$	3.54310	+	3.54310i	0.432859	+	0.432859i	−0.456741	+	0.889600i	$0.650983\pi$
$68$		0			0
$69$	1.14890	+	1.29616i	0.138311	+	0.156039i
$70$		0			0
$71$		−	1.94914i		−	0.231320i	−0.993289	−	0.115660i	$-0.963102\pi$
$71$		−	1.94914i		−	0.231320i	0.993289	−	0.115660i	$-0.0368983\pi$
$72$		0			0
$73$	−2.66633	+	2.66633i	−0.312070	+	0.312070i	−0.845711	−	0.533641i	$-0.820823\pi$
$73$	−2.66633	+	2.66633i	−0.312070	+	0.312070i	0.533641	+	0.845711i	$0.320823\pi$
$74$		0			0
$75$	1.25894	−	8.56826i	0.145370	−	0.989377i
$76$		0			0
$77$	5.58274	−	5.58274i	0.636212	−	0.636212i
$78$		0			0
$79$			3.69783i			0.416039i	0.978125	+	0.208019i	$0.0667017\pi$
$79$			3.69783i			0.416039i	−0.978125	+	0.208019i	$0.933298\pi$
$80$		0			0
$81$	8.74072	+	2.14472i	0.971191	+	0.238303i
$82$		0			0
$83$	−10.4675	−	10.4675i	−1.14896	−	1.14896i	−0.986758	−	0.162202i	$-0.948140\pi$
$83$	−10.4675	−	10.4675i	−1.14896	−	1.14896i	−0.162202	−	0.986758i	$-0.551860\pi$
$84$		0			0
$85$	14.5862	+	0.625639i	1.58210	+	0.0678600i
$86$		0			0
$87$	2.85236	+	0.171789i	0.305805	+	0.0184177i
$88$		0			0
$89$	8.35452			0.885577			0.442789	−	0.896626i	$-0.353989\pi$
$89$	8.35452			0.885577			0.442789	+	0.896626i	$0.353989\pi$
$90$		0			0
$91$	24.1522			2.53184
$92$		0			0
$93$	−17.0725	−	1.02823i	−1.77033	−	0.106622i
$94$		0			0
$95$	−3.26580	+	2.99717i	−0.335064	+	0.307503i
$96$		0			0
$97$	−5.87875	−	5.87875i	−0.596897	−	0.596897i	0.342588	−	0.939486i	$-0.388696\pi$
$97$	−5.87875	−	5.87875i	−0.596897	−	0.596897i	−0.939486	+	0.342588i	$0.888696\pi$
$98$		0			0
$99$	0.614019	−	5.07904i	0.0617112	−	0.510463i
$100$		0			0
$101$			11.2036i			1.11480i	0.830243	+	0.557401i	$0.188201\pi$
$101$			11.2036i			1.11480i	−0.830243	+	0.557401i	$0.811799\pi$
$102$		0			0
$103$	−6.48391	+	6.48391i	−0.638879	+	0.638879i	−0.950279	−	0.311400i	$-0.899202\pi$
$103$	−6.48391	+	6.48391i	−0.638879	+	0.638879i	0.311400	+	0.950279i	$0.399202\pi$
$104$		0			0
$105$	1.84396	−	17.8356i	0.179952	−	1.74058i
$106$		0			0
$107$	2.33084	−	2.33084i	0.225331	−	0.225331i	−0.585408	−	0.810739i	$-0.699066\pi$
$107$	2.33084	−	2.33084i	0.225331	−	0.225331i	0.810739	+	0.585408i	$0.199066\pi$
$108$		0			0
$109$		−	0.136651i		−	0.0130887i	−0.999979	−	0.00654437i	$-0.997917\pi$
$109$		−	0.136651i		−	0.0130887i	0.999979	−	0.00654437i	$-0.00208315\pi$
$110$		0			0
$111$	11.0169	+	12.4290i	1.04568	+	1.17971i
$112$		0			0
$113$	3.85736	+	3.85736i	0.362870	+	0.362870i	0.864868	−	0.501999i	$-0.167402\pi$
$113$	3.85736	+	3.85736i	0.362870	+	0.362870i	−0.501999	+	0.864868i	$0.667402\pi$
$114$		0			0
$115$	0.0958222	−	2.23401i	0.00893547	−	0.208323i
$116$		0			0
$117$	12.3147	−	9.65834i	1.13850	−	0.892914i
$118$		0			0
$119$	30.2279			2.77099
$120$		0			0
$121$	8.09181			0.735619
$122$		0			0
$123$	−1.18139	+	19.6157i	−0.106523	+	1.76868i
$124$		0			0
$125$	−8.85427	+	6.82655i	−0.791950	+	0.610586i
$126$		0			0
$127$	−3.91521	−	3.91521i	−0.347418	−	0.347418i	0.511729	−	0.859147i	$-0.329005\pi$
$127$	−3.91521	−	3.91521i	−0.347418	−	0.347418i	−0.859147	+	0.511729i	$0.829005\pi$
$128$		0			0
$129$	9.85339	−	8.73393i	0.867542	−	0.768980i
$130$		0			0
$131$			5.23508i			0.457391i	0.973498	+	0.228696i	$0.0734460\pi$
$131$			5.23508i			0.457391i	−0.973498	+	0.228696i	$0.926554\pi$
$132$		0			0
$133$	−6.48957	+	6.48957i	−0.562717	+	0.562717i
$134$		0			0
$135$	−6.19218	−	9.83143i	−0.532938	−	0.846154i
$136$		0			0
$137$	0.0118511	−	0.0118511i	0.00101251	−	0.00101251i	−0.706600	−	0.707613i	$-0.749772\pi$
$137$	0.0118511	−	0.0118511i	0.00101251	−	0.00101251i	0.707613	+	0.706600i	$0.249772\pi$
$138$		0			0
$139$			6.71837i			0.569845i	0.958551	+	0.284922i	$0.0919678\pi$
$139$			6.71837i			0.569845i	−0.958551	+	0.284922i	$0.908032\pi$
$140$		0			0
$141$	−0.310332	+	0.275075i	−0.0261347	+	0.0231655i
$142$		0			0
$143$	−6.29073	−	6.29073i	−0.526057	−	0.526057i
$144$		0			0
$145$	−2.49437	−	2.71794i	−0.207146	−	0.225713i
$146$		0			0
$147$	1.50298	−	24.9552i	0.123963	−	2.05827i
$148$		0			0
$149$	−11.5341			−0.944910			−0.472455	−	0.881355i	$-0.656632\pi$
$149$	−11.5341			−0.944910			−0.472455	+	0.881355i	$0.656632\pi$
$150$		0			0
$151$	−11.0884			−0.902360			−0.451180	−	0.892433i	$-0.648997\pi$
$151$	−11.0884			−0.902360			−0.451180	+	0.892433i	$0.648997\pi$
$152$		0			0
$153$	15.4126	−	12.0880i	1.24604	−	0.977258i
$154$		0			0
$155$	14.9298	+	16.2679i	1.19919	+	1.30667i
$156$		0			0
$157$	13.4745	+	13.4745i	1.07538	+	1.07538i	0.996917	+	0.0784646i	$0.0250018\pi$
$157$	13.4745	+	13.4745i	1.07538	+	1.07538i	0.0784646	+	0.996917i	$0.474998\pi$
$158$		0			0
$159$	−0.964797	−	1.08846i	−0.0765134	−	0.0863204i
$160$		0			0
$161$		−	4.62968i		−	0.364870i
$162$		0			0
$163$	−11.5598	+	11.5598i	−0.905437	+	0.905437i	−0.995900	−	0.0904633i	$-0.971165\pi$
$163$	−11.5598	+	11.5598i	−0.905437	+	0.905437i	0.0904633	+	0.995900i	$0.471165\pi$
$164$		0			0
$165$	−5.12579	+	4.16522i	−0.399042	+	0.324262i
$166$		0			0
$167$	−15.8217	+	15.8217i	−1.22432	+	1.22432i	−0.258237	+	0.966082i	$0.583142\pi$
$167$	−15.8217	+	15.8217i	−1.22432	+	1.22432i	−0.966082	+	0.258237i	$0.916858\pi$
$168$		0			0
$169$		−	14.2151i		−	1.09347i
$170$		0			0
$171$	−0.713757	+	5.90405i	−0.0545824	+	0.451494i
$172$		0			0
$173$	−4.31076	−	4.31076i	−0.327741	−	0.327741i	0.523986	−	0.851727i	$-0.324444\pi$
$173$	−4.31076	−	4.31076i	−0.327741	−	0.327741i	−0.851727	+	0.523986i	$0.824444\pi$
$174$		0			0
$175$	−17.7099	+	14.9067i	−1.33874	+	1.12684i
$176$		0			0
$177$	−16.7680	−	1.00989i	−1.26036	−	0.0759079i
$178$		0			0
$179$	−18.7234			−1.39945			−0.699727	−	0.714410i	$-0.746695\pi$
$179$	−18.7234			−1.39945			−0.699727	+	0.714410i	$0.746695\pi$
$180$		0			0
$181$	−1.55267			−0.115409			−0.0577044	−	0.998334i	$-0.518378\pi$
$181$	−1.55267			−0.115409			−0.0577044	+	0.998334i	$0.518378\pi$
$182$		0			0
$183$	2.87149	+	0.172942i	0.212267	+	0.0127842i
$184$		0			0
$185$	0.918849	−	21.4222i	0.0675551	−	1.57499i
$186$		0			0
$187$	−7.87324	−	7.87324i	−0.575748	−	0.575748i
$188$		0			0
$189$	−13.6812	−	19.7874i	−0.995158	−	1.43933i
$190$		0			0
$191$			17.6143i			1.27452i	0.770648	+	0.637261i	$0.219933\pi$
$191$			17.6143i			1.27452i	−0.770648	+	0.637261i	$0.780067\pi$
$192$		0			0
$193$	0.448629	−	0.448629i	0.0322931	−	0.0322931i	−0.690776	−	0.723069i	$-0.742731\pi$
$193$	0.448629	−	0.448629i	0.0322931	−	0.0322931i	0.723069	+	0.690776i	$0.242731\pi$
$194$		0			0
$195$	−20.0975	−	2.07781i	−1.43921	−	0.148795i
$196$		0			0
$197$	−11.9864	+	11.9864i	−0.853993	+	0.853993i	−0.990622	−	0.136629i	$-0.956373\pi$
$197$	−11.9864	+	11.9864i	−0.853993	+	0.853993i	0.136629	+	0.990622i	$0.456373\pi$
$198$		0			0
$199$		−	3.21402i		−	0.227836i	−0.993490	−	0.113918i	$-0.963660\pi$
$199$		−	3.21402i		−	0.227836i	0.993490	−	0.113918i	$-0.0363401\pi$
$200$		0			0
$201$	−5.75680	−	6.49467i	−0.406053	−	0.458098i
$202$		0			0
$203$	−5.40089	−	5.40089i	−0.379068	−	0.379068i
$204$		0			0
$205$	18.6913	−	17.1538i	1.30546	−	1.19807i
$206$		0			0
$207$	−1.85139	−	2.36059i	−0.128680	−	0.164072i
$208$		0			0
$209$	3.38058			0.233839
$210$		0			0
$211$	23.9426			1.64828			0.824138	−	0.566389i	$-0.191660\pi$
$211$	23.9426			1.64828			0.824138	+	0.566389i	$0.191660\pi$
$212$		0			0
$213$	−0.202959	+	3.36990i	−0.0139065	+	0.230902i
$214$		0			0
$215$	−16.9830	−	0.728440i	−1.15823	−	0.0496792i
$216$		0			0
$217$	32.3265	+	32.3265i	2.19446	+	2.19446i
$218$		0			0
$219$	4.88751	−	4.33223i	0.330267	−	0.292745i
$220$		0			0
$221$		−	34.0614i		−	2.29122i
$222$		0			0
$223$	−4.21684	+	4.21684i	−0.282380	+	0.282380i	−0.834058	−	0.551677i	$-0.813988\pi$
$223$	−4.21684	+	4.21684i	−0.282380	+	0.282380i	0.551677	+	0.834058i	$0.313988\pi$
$224$		0			0
$225$	−3.06880	+	14.6827i	−0.204586	+	0.978849i
$226$		0			0
$227$	−0.573225	+	0.573225i	−0.0380462	+	0.0380462i	−0.725874	−	0.687828i	$-0.758564\pi$
$227$	−0.573225	+	0.573225i	−0.0380462	+	0.0380462i	0.687828	+	0.725874i	$0.258564\pi$
$228$		0			0
$229$		−	15.6796i		−	1.03614i	−0.855339	−	0.518068i	$-0.826651\pi$
$229$		−	15.6796i		−	1.03614i	0.855339	−	0.518068i	$-0.173349\pi$
$230$		0			0
$231$	−10.2334	+	9.07078i	−0.673309	+	0.596814i
$232$		0			0
$233$	−9.16034	−	9.16034i	−0.600114	−	0.600114i	0.340229	−	0.940343i	$-0.389495\pi$
$233$	−9.16034	−	9.16034i	−0.600114	−	0.600114i	−0.940343	+	0.340229i	$0.889495\pi$
$234$		0			0
$235$	0.534878	+	0.0229422i	0.0348916	+	0.00149658i
$236$		0			0
$237$	0.385047	−	6.39325i	0.0250115	−	0.415286i
$238$		0			0
$239$	−21.6009			−1.39725			−0.698623	−	0.715490i	$-0.746203\pi$
$239$	−21.6009			−1.39725			−0.698623	+	0.715490i	$0.746203\pi$
$240$		0			0
$241$	14.4150			0.928553			0.464277	−	0.885690i	$-0.346314\pi$
$241$	14.4150			0.928553			0.464277	+	0.885690i	$0.346314\pi$
$242$		0			0
$243$	−14.8887	−	4.61820i	−0.955108	−	0.296258i
$244$		0			0
$245$	−23.7791	+	21.8232i	−1.51919	+	1.39423i
$246$		0			0
$247$	7.31256	+	7.31256i	0.465287	+	0.465287i
$248$		0			0
$249$	17.0075	+	19.1874i	1.07781	+	1.21595i
$250$		0			0
$251$			8.43565i			0.532454i	0.963910	+	0.266227i	$0.0857770\pi$
$251$			8.43565i			0.532454i	−0.963910	+	0.266227i	$0.914223\pi$
$252$		0			0
$253$	−1.20586	+	1.20586i	−0.0758116	+	0.0758116i
$254$		0			0
$255$	−25.1533	−	2.60051i	−1.57516	−	0.162850i
$256$		0			0
$257$	−9.05154	+	9.05154i	−0.564620	+	0.564620i	−0.930616	−	0.365997i	$-0.880728\pi$
$257$	−9.05154	+	9.05154i	−0.564620	+	0.564620i	0.365997	+	0.930616i	$0.380728\pi$
$258$		0			0
$259$		−	44.3945i		−	2.75854i
$260$		0			0
$261$	−4.91360	−	0.594019i	−0.304144	−	0.0367688i
$262$		0			0
$263$	−8.82798	−	8.82798i	−0.544356	−	0.544356i	0.380447	−	0.924803i	$-0.375770\pi$
$263$	−8.82798	−	8.82798i	−0.544356	−	0.544356i	−0.924803	+	0.380447i	$0.875770\pi$
$264$		0			0
$265$	−0.0804674	+	1.87603i	−0.00494307	+	0.115244i
$266$		0			0
$267$	−14.4443	−	0.869937i	−0.883975	−	0.0532393i
$268$		0			0
$269$	−17.6986			−1.07910			−0.539551	−	0.841953i	$-0.681406\pi$
$269$	−17.6986			−1.07910			−0.539551	+	0.841953i	$0.681406\pi$
$270$		0			0
$271$	−1.36469			−0.0828991			−0.0414496	−	0.999141i	$-0.513198\pi$
$271$	−1.36469			−0.0828991			−0.0414496	+	0.999141i	$0.513198\pi$
$272$		0			0
$273$	−41.7571	−	2.51491i	−2.52726	−	0.152209i
$274$		0			0
$275$	8.49539	+	0.730118i	0.512291	+	0.0440278i
$276$		0			0
$277$	−9.91102	−	9.91102i	−0.595495	−	0.595495i	0.343615	−	0.939111i	$-0.388348\pi$
$277$	−9.91102	−	9.91102i	−0.595495	−	0.595495i	−0.939111	+	0.343615i	$0.888348\pi$
$278$		0			0
$279$	29.4098	+	3.55544i	1.76072	+	0.212858i
$280$		0			0
$281$		−	2.54532i		−	0.151841i	−0.997114	−	0.0759204i	$-0.975811\pi$
$281$		−	2.54532i		−	0.151841i	0.997114	−	0.0759204i	$-0.0241895\pi$
$282$		0			0
$283$	0.951249	−	0.951249i	0.0565459	−	0.0565459i	−0.678268	−	0.734814i	$-0.737269\pi$
$283$	0.951249	−	0.951249i	0.0565459	−	0.0565459i	0.734814	+	0.678268i	$0.237269\pi$
$284$		0			0
$285$	5.95839	−	4.84180i	0.352945	−	0.286803i
$286$		0			0
$287$	37.1420	−	37.1420i	2.19242	−	2.19242i
$288$		0			0
$289$		−	25.6299i		−	1.50764i
$290$		0			0
$291$	9.55174	+	10.7760i	0.559933	+	0.631702i
$292$		0			0
$293$	−0.913466	−	0.913466i	−0.0533653	−	0.0533653i	0.679921	−	0.733286i	$-0.262014\pi$
$293$	−0.913466	−	0.913466i	−0.0533653	−	0.0533653i	−0.733286	+	0.679921i	$0.762014\pi$
$294$		0			0
$295$	14.6635	+	15.9778i	0.853744	+	0.930265i
$296$		0			0
$297$	−1.59046	+	8.71731i	−0.0922877	+	0.505830i
$298$		0			0
$299$	−5.21681			−0.301696
$300$		0			0
$301$	−35.1948			−2.02860
$302$		0			0
$303$	1.16661	−	19.3701i	0.0670199	−	1.11279i
$304$		0			0
$305$	−2.51111	−	2.73617i	−0.143786	−	0.156673i
$306$		0			0
$307$	−20.8173	−	20.8173i	−1.18811	−	1.18811i	−0.977590	−	0.210516i	$-0.932486\pi$
$307$	−20.8173	−	20.8173i	−1.18811	−	1.18811i	−0.210516	−	0.977590i	$-0.567514\pi$
$308$		0			0
$309$	11.8853	−	10.5350i	0.676132	−	0.599315i
$310$		0			0
$311$			7.73707i			0.438729i	0.975643	+	0.219364i	$0.0703983\pi$
$311$			7.73707i			0.438729i	−0.975643	+	0.219364i	$0.929602\pi$
$312$		0			0
$313$	11.7538	−	11.7538i	0.664365	−	0.664365i	−0.292041	−	0.956406i	$-0.594334\pi$
$313$	11.7538	−	11.7538i	0.664365	−	0.664365i	0.956406	+	0.292041i	$0.0943343\pi$
$314$		0			0
$315$	−5.04525	+	30.6443i	−0.284267	+	1.72661i
$316$		0			0
$317$	−6.05100	+	6.05100i	−0.339858	+	0.339858i	−0.856314	−	0.516456i	$-0.827251\pi$
$317$	−6.05100	+	6.05100i	−0.339858	+	0.339858i	0.516456	+	0.856314i	$0.327251\pi$
$318$		0			0
$319$			2.81346i			0.157523i
$320$		0			0
$321$	−4.27253	+	3.78712i	−0.238470	+	0.211377i
$322$		0			0
$323$	9.15212	+	9.15212i	0.509238	+	0.509238i
$324$		0			0
$325$	16.7971	+	19.9558i	0.931737	+	1.10695i
$326$		0			0
$327$	−0.0142291	+	0.236258i	−0.000786871	+	0.0130651i
$328$		0			0
$329$	1.10846			0.0611114
$330$		0			0
$331$	21.2465			1.16782			0.583908	−	0.811820i	$-0.301523\pi$
$331$	21.2465			1.16782			0.583908	+	0.811820i	$0.301523\pi$
$332$		0			0
$333$	−17.7532	−	22.6359i	−0.972867	−	1.24044i
$334$		0			0
$335$	−0.480137	+	11.1940i	−0.0262327	+	0.611592i
$336$		0			0
$337$	10.8609	+	10.8609i	0.591633	+	0.591633i	0.938072	−	0.346439i	$-0.112609\pi$
$337$	10.8609	+	10.8609i	0.591633	+	0.591633i	−0.346439	+	0.938072i	$0.612609\pi$
$338$		0			0
$339$	−6.26740	−	7.07071i	−0.340398	−	0.384028i
$340$		0			0
$341$		−	16.8396i		−	0.911918i
$342$		0			0
$343$	−24.3365	+	24.3365i	−1.31405	+	1.31405i
$344$		0			0
$345$	−0.398292	+	3.85245i	−0.0214433	+	0.207409i
$346$		0			0
$347$	12.4888	−	12.4888i	0.670435	−	0.670435i	−0.287381	−	0.957816i	$-0.592785\pi$
$347$	12.4888	−	12.4888i	0.670435	−	0.670435i	0.957816	+	0.287381i	$0.0927847\pi$
$348$		0			0
$349$			32.8573i			1.75881i	0.476072	+	0.879406i	$0.342060\pi$
$349$			32.8573i			1.75881i	−0.476072	+	0.879406i	$0.657940\pi$
$350$		0			0
$351$	−22.2968	+	15.4162i	−1.19012	+	0.822854i
$352$		0			0
$353$	9.96694	+	9.96694i	0.530486	+	0.530486i	0.920717	−	0.390231i	$-0.127605\pi$
$353$	9.96694	+	9.96694i	0.530486	+	0.530486i	−0.390231	+	0.920717i	$0.627605\pi$
$354$		0			0
$355$	3.21109	−	2.94696i	0.170427	−	0.156408i
$356$		0			0
$357$	−52.2616	−	3.14757i	−2.76598	−	0.166587i
$358$		0			0
$359$	7.70121			0.406455			0.203227	−	0.979132i	$-0.434857\pi$
$359$	7.70121			0.406455			0.203227	+	0.979132i	$0.434857\pi$
$360$		0			0
$361$	15.0703			0.793174
$362$		0			0
$363$	−13.9901	−	0.842582i	−0.734289	−	0.0442241i
$364$		0			0
$365$	−8.42393	−	0.361323i	−0.440929	−	0.0189125i
$366$		0			0
$367$	−11.8418	−	11.8418i	−0.618136	−	0.618136i	0.326917	−	0.945053i	$-0.393990\pi$
$367$	−11.8418	−	11.8418i	−0.618136	−	0.618136i	−0.945053	+	0.326917i	$0.893990\pi$
$368$		0			0
$369$	4.08507	−	33.7908i	0.212660	−	1.75908i
$370$		0			0
$371$			3.88781i			0.201845i
$372$		0			0
$373$	12.9467	−	12.9467i	0.670353	−	0.670353i	−0.287444	−	0.957797i	$-0.592806\pi$
$373$	12.9467	−	12.9467i	0.670353	−	0.670353i	0.957797	+	0.287444i	$0.0928056\pi$
$374$		0			0
$375$	16.0191	−	10.8806i	0.827225	−	0.561871i
$376$		0			0
$377$	−6.08582	+	6.08582i	−0.313436	+	0.313436i
$378$		0			0
$379$		−	27.0535i		−	1.38964i	−0.719183	−	0.694821i	$-0.755483\pi$
$379$		−	27.0535i		−	1.38964i	0.719183	−	0.694821i	$-0.244517\pi$
$380$		0			0
$381$	6.36139	+	7.17675i	0.325904	+	0.367676i
$382$		0			0
$383$	0.00486119	+	0.00486119i	0.000248395	+	0.000248395i	0.707231	−	0.706983i	$-0.249944\pi$
$383$	0.00486119	+	0.00486119i	0.000248395	+	0.000248395i	−0.706983	+	0.707231i	$0.749944\pi$
$384$		0			0
$385$	17.6380	+	0.756534i	0.898914	+	0.0385566i
$386$		0			0
$387$	−17.9451	+	14.0742i	−0.912203	+	0.715434i
$388$		0			0
$389$	26.2299			1.32991			0.664953	−	0.746885i	$-0.268451\pi$
$389$	26.2299			1.32991			0.664953	+	0.746885i	$0.268451\pi$
$390$		0			0
$391$	−6.52916			−0.330194
$392$		0			0
$393$	0.545117	−	9.05103i	0.0274975	−	0.456564i
$394$		0			0
$395$	−6.09197	+	5.59086i	−0.306520	+	0.281307i
$396$		0			0
$397$	−26.9193	−	26.9193i	−1.35104	−	1.35104i	−0.884497	−	0.466546i	$-0.845498\pi$
$397$	−26.9193	−	26.9193i	−1.35104	−	1.35104i	−0.466546	−	0.884497i	$-0.654502\pi$
$398$		0			0
$399$	11.8957	−	10.5442i	0.595529	−	0.527870i
$400$		0			0
$401$			10.3412i			0.516414i	0.966090	+	0.258207i	$0.0831316\pi$
$401$			10.3412i			0.516414i	−0.966090	+	0.258207i	$0.916868\pi$
$402$		0			0
$403$	36.4260	−	36.4260i	1.81451	−	1.81451i
$404$		0			0
$405$	9.68204	+	17.6425i	0.481105	+	0.876663i
$406$		0			0
$407$	−11.5631	+	11.5631i	−0.573161	+	0.573161i
$408$		0			0
$409$			14.9541i			0.739435i	0.929144	+	0.369717i	$0.120546\pi$
$409$			14.9541i			0.739435i	−0.929144	+	0.369717i	$0.879454\pi$
$410$		0			0
$411$	−0.0217237	+	0.0192556i	−0.00107155	+	0.000949808i
$412$		0			0
$413$	31.7500	+	31.7500i	1.56231	+	1.56231i
$414$		0			0
$415$	1.41849	−	33.0708i	0.0696308	−	1.62338i
$416$		0			0
$417$	0.699569	−	11.6155i	0.0342580	−	0.568814i
$418$		0			0
$419$	−31.6533			−1.54636			−0.773182	−	0.634184i	$-0.781336\pi$
$419$	−31.6533			−1.54636			−0.773182	+	0.634184i	$0.781336\pi$
$420$		0			0
$421$	11.0493			0.538511			0.269255	−	0.963069i	$-0.413222\pi$
$421$	11.0493			0.538511			0.269255	+	0.963069i	$0.413222\pi$
$422$		0			0
$423$	0.565182	−	0.443268i	0.0274801	−	0.0215524i
$424$		0			0
$425$	21.0227	+	24.9759i	1.01975	+	1.21151i
$426$		0			0
$427$	−5.43713	−	5.43713i	−0.263121	−	0.263121i
$428$		0			0
$429$	10.2211	+	11.5312i	0.493480	+	0.556731i
$430$		0			0
$431$		−	37.5287i		−	1.80769i	−0.427858	−	0.903846i	$-0.640732\pi$
$431$		−	37.5287i		−	1.80769i	0.427858	−	0.903846i	$-0.359268\pi$
$432$		0			0
$433$	−13.2533	+	13.2533i	−0.636914	+	0.636914i	−0.949793	−	0.312879i	$-0.898707\pi$
$433$	−13.2533	+	13.2533i	−0.636914	+	0.636914i	0.312879	+	0.949793i	$0.398707\pi$
$434$		0			0
$435$	4.02955	+	4.95883i	0.193202	+	0.237758i
$436$		0			0
$437$	1.40173	−	1.40173i	0.0670539	−	0.0670539i
$438$		0			0
$439$			15.9540i			0.761443i	0.924690	+	0.380722i	$0.124324\pi$
$439$			15.9540i			0.761443i	−0.924690	+	0.380722i	$0.875676\pi$
$440$		0			0
$441$	−5.19705	+	42.9889i	−0.247478	+	2.04709i
$442$		0			0
$443$	−28.3577	−	28.3577i	−1.34732	−	1.34732i	−0.888565	−	0.458750i	$-0.848297\pi$
$443$	−28.3577	−	28.3577i	−1.34732	−	1.34732i	−0.458750	−	0.888565i	$-0.651703\pi$
$444$		0			0
$445$	12.6314	+	13.7636i	0.598788	+	0.652457i
$446$		0			0
$447$	19.9415	+	1.20102i	0.943201	+	0.0568063i
$448$		0			0
$449$	21.7135			1.02472			0.512362	−	0.858769i	$-0.328770\pi$
$449$	21.7135			1.02472			0.512362	+	0.858769i	$0.328770\pi$
$450$		0			0
$451$	−19.3482			−0.911069
$452$		0			0
$453$	19.1709	+	1.15461i	0.900728	+	0.0542482i
$454$		0			0
$455$	36.5164	+	39.7893i	1.71191	+	1.86535i
$456$		0			0
$457$	10.6225	+	10.6225i	0.496900	+	0.496900i	0.910472	−	0.413571i	$-0.135719\pi$
$457$	10.6225	+	10.6225i	0.496900	+	0.496900i	−0.413571	+	0.910472i	$0.635719\pi$
$458$		0			0
$459$	−27.9059	+	19.2943i	−1.30253	+	0.900580i
$460$		0			0
$461$			20.1686i			0.939345i	0.882841	+	0.469673i	$0.155628\pi$
$461$			20.1686i			0.939345i	−0.882841	+	0.469673i	$0.844372\pi$
$462$		0			0
$463$	21.5473	−	21.5473i	1.00139	−	1.00139i	0.00138835	−	0.999999i	$-0.499558\pi$
$463$	21.5473	−	21.5473i	1.00139	−	1.00139i	0.999999	−	0.00138835i	$-0.000441925\pi$
$464$		0			0
$465$	−24.1184	−	29.6805i	−1.11847	−	1.37640i
$466$		0			0
$467$	11.2064	−	11.2064i	0.518571	−	0.518571i	−0.398568	−	0.917139i	$-0.630493\pi$
$467$	11.2064	−	11.2064i	0.518571	−	0.518571i	0.917139	+	0.398568i	$0.130493\pi$
$468$		0			0
$469$			23.1980i			1.07118i
$470$		0			0
$471$	−21.8932	−	24.6994i	−1.00879	−	1.13809i
$472$		0			0
$473$	9.16692	+	9.16692i	0.421495	+	0.421495i
$474$		0			0
$475$	−9.87533	−	0.848715i	−0.453111	−	0.0389417i
$476$		0			0
$477$	1.55472	+	1.98232i	0.0711856	+	0.0907641i
$478$		0			0
$479$	−19.3784			−0.885420			−0.442710	−	0.896665i	$-0.645983\pi$
$479$	−19.3784			−0.885420			−0.442710	+	0.896665i	$0.645983\pi$
$480$		0			0
$481$	−50.0245			−2.28092
$482$		0			0
$483$	−0.482078	+	8.00434i	−0.0219353	+	0.364210i
$484$		0			0
$485$	0.796648	−	18.5732i	0.0361739	−	0.843365i
$486$		0			0
$487$	4.13501	+	4.13501i	0.187375	+	0.187375i	0.794560	−	0.607185i	$-0.207701\pi$
$487$	4.13501	+	4.13501i	0.187375	+	0.187375i	−0.607185	+	0.794560i	$0.707701\pi$
$488$		0			0
$489$	21.1897	−	18.7823i	0.958232	−	0.849366i
$490$		0			0
$491$			18.6858i			0.843278i	0.906764	+	0.421639i	$0.138545\pi$
$491$			18.6858i			0.843278i	−0.906764	+	0.421639i	$0.861455\pi$
$492$		0			0
$493$	−7.61678	+	7.61678i	−0.343043	+	0.343043i
$494$		0			0
$495$	9.29578	−	6.66759i	0.417814	−	0.299686i
$496$		0			0
$497$	6.38085	−	6.38085i	0.286220	−	0.286220i
$498$		0			0
$499$		−	8.22016i		−	0.367985i	−0.982928	−	0.183992i	$-0.941098\pi$
$499$		−	8.22016i		−	0.367985i	0.982928	−	0.183992i	$-0.0589022\pi$
$500$		0			0
$501$	29.0019	−	25.7069i	1.29571	−	1.14850i
$502$		0			0
$503$	31.0631	+	31.0631i	1.38503	+	1.38503i	0.835416	+	0.549618i	$0.185227\pi$
$503$	31.0631	+	31.0631i	1.38503	+	1.38503i	0.549618	+	0.835416i	$0.314773\pi$
$504$		0			0
$505$	−18.4573	+	16.9391i	−0.821341	+	0.753780i
$506$		0			0
$507$	−1.48018	+	24.5767i	−0.0657373	+	1.09149i
$508$		0			0
$509$	−31.7775			−1.40851			−0.704256	−	0.709946i	$-0.748719\pi$
$509$	−31.7775			−1.40851			−0.704256	+	0.709946i	$0.748719\pi$
$510$		0			0
$511$	−17.4574			−0.772271
$512$		0			0
$513$	1.84880	−	10.1333i	0.0816266	−	0.447396i
$514$		0			0
$515$	−20.4851	−	0.878655i	−0.902681	−	0.0387182i
$516$		0			0
$517$	−0.288712	−	0.288712i	−0.0126975	−	0.0126975i
$518$		0			0
$519$	7.00408	+	7.90182i	0.307445	+	0.346851i
$520$		0			0
$521$			36.7769i			1.61122i	0.592444	+	0.805612i	$0.298163\pi$
$521$			36.7769i			1.61122i	−0.592444	+	0.805612i	$0.701837\pi$
$522$		0			0
$523$	−6.54332	+	6.54332i	−0.286120	+	0.286120i	−0.835544	−	0.549424i	$-0.814847\pi$
$523$	−6.54332	+	6.54332i	−0.286120	+	0.286120i	0.549424	+	0.835544i	$0.314847\pi$
$524$		0			0
$525$	32.1711	−	23.9284i	1.40406	−	1.04432i
$526$		0			0
$527$	45.5894	−	45.5894i	1.98591	−	1.98591i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	28.8854	+	3.49203i	1.25352	+	0.151541i
$532$		0			0
$533$	−41.8522	−	41.8522i	−1.81282	−	1.81282i
$534$		0			0
$535$	7.36399	+	0.315859i	0.318373	+	0.0136558i
$536$		0			0
$537$	32.3713	+	1.94963i	1.39692	+	0.0841327i
$538$		0			0
$539$	24.6148			1.06024
$540$		0			0
$541$	−31.9301			−1.37278			−0.686390	−	0.727233i	$-0.740806\pi$
$541$	−31.9301			−1.37278			−0.686390	+	0.727233i	$0.740806\pi$
$542$		0			0
$543$	2.68444	+	0.161676i	0.115200	+	0.00693817i
$544$		0			0
$545$	0.225124	−	0.206606i	0.00964325	−	0.00885003i
$546$		0			0
$547$	−25.5680	−	25.5680i	−1.09321	−	1.09321i	−0.995184	−	0.0980233i	$-0.968748\pi$
$547$	−25.5680	−	25.5680i	−1.09321	−	1.09321i	−0.0980233	−	0.995184i	$-0.531252\pi$
$548$		0			0
$549$	−4.94657	−	0.598004i	−0.211114	−	0.0255222i
$550$		0			0
$551$		−	3.27046i		−	0.139326i
$552$		0			0
$553$	−12.1055	+	12.1055i	−0.514779	+	0.514779i
$554$		0			0
$555$	−3.81926	+	36.9415i	−0.162119	+	1.56808i
$556$		0			0
$557$	24.0438	−	24.0438i	1.01877	−	1.01877i	0.0189465	−	0.999820i	$-0.493969\pi$
$557$	24.0438	−	24.0438i	1.01877	−	1.01877i	0.999820	−	0.0189465i	$-0.00603123\pi$
$558$		0			0
$559$			39.6581i			1.67736i
$560$		0			0
$561$	12.7924	+	14.4320i	0.540094	+	0.609320i
$562$		0			0
$563$	2.14476	+	2.14476i	0.0903910	+	0.0903910i	0.750856	−	0.660465i	$-0.229641\pi$
$563$	2.14476	+	2.14476i	0.0903910	+	0.0903910i	−0.660465	+	0.750856i	$0.729641\pi$
$564$		0			0
$565$	−0.522722	+	12.1868i	−0.0219911	+	0.512704i
$566$		0			0
$567$	21.5932	+	35.6355i	0.906828	+	1.49655i
$568$		0			0
$569$	−3.88901			−0.163036			−0.0815178	−	0.996672i	$-0.525977\pi$
$569$	−3.88901			−0.163036			−0.0815178	+	0.996672i	$0.525977\pi$
$570$		0			0
$571$	19.6849			0.823786			0.411893	−	0.911232i	$-0.364868\pi$
$571$	19.6849			0.823786			0.411893	+	0.911232i	$0.364868\pi$
$572$		0			0
$573$	1.83413	−	30.4536i	0.0766220	−	1.27222i
$574$		0			0
$575$	3.82529	−	3.21981i	0.159525	−	0.134275i
$576$		0			0
$577$	−23.8776	−	23.8776i	−0.994038	−	0.994038i	0.00594423	−	0.999982i	$-0.498108\pi$
$577$	−23.8776	−	23.8776i	−0.994038	−	0.994038i	−0.999982	+	0.00594423i	$0.998108\pi$
$578$		0			0
$579$	−0.822358	+	0.728929i	−0.0341760	+	0.0302932i
$580$		0			0
$581$		−	68.5347i		−	2.84330i
$582$		0			0
$583$	1.01263	−	1.01263i	0.0419387	−	0.0419387i
$584$		0			0
$585$	34.5305	+	5.68507i	1.42766	+	0.235049i
$586$		0			0
$587$	15.9188	−	15.9188i	0.657038	−	0.657038i	−0.297640	−	0.954678i	$-0.596199\pi$
$587$	15.9188	−	15.9188i	0.657038	−	0.657038i	0.954678	+	0.297640i	$0.0961995\pi$
$588$		0			0
$589$			19.5750i			0.806573i
$590$		0			0
$591$	21.9716	−	19.4753i	0.903789	−	0.801108i
$592$		0			0
$593$	−24.0703	−	24.0703i	−0.988447	−	0.988447i	0.0114865	−	0.999934i	$-0.496344\pi$
$593$	−24.0703	−	24.0703i	−0.988447	−	0.988447i	−0.999934	+	0.0114865i	$0.996344\pi$
$594$		0			0
$595$	45.7025	+	49.7988i	1.87362	+	2.04155i
$596$		0			0
$597$	−0.334669	+	5.55678i	−0.0136971	+	0.227424i
$598$		0			0
$599$	−1.97373			−0.0806445			−0.0403222	−	0.999187i	$-0.512838\pi$
$599$	−1.97373			−0.0806445			−0.0403222	+	0.999187i	$0.512838\pi$
$600$		0			0
$601$	29.9014			1.21970			0.609851	−	0.792516i	$-0.291229\pi$
$601$	29.9014			1.21970			0.609851	+	0.792516i	$0.291229\pi$
$602$		0			0
$603$	9.27675	+	11.8282i	0.377779	+	0.481681i
$604$		0			0
$605$	12.2343	+	13.3308i	0.497393	+	0.541974i
$606$		0			0
$607$	14.9074	+	14.9074i	0.605072	+	0.605072i	0.941654	−	0.336582i	$-0.109271\pi$
$607$	14.9074	+	14.9074i	0.605072	+	0.605072i	−0.336582	+	0.941654i	$0.609271\pi$
$608$		0			0
$609$	8.77532	+	9.90009i	0.355594	+	0.401172i
$610$		0			0
$611$		−	1.24903i		−	0.0505304i
$612$		0			0
$613$	−17.1424	+	17.1424i	−0.692376	+	0.692376i	−0.962754	−	0.270378i	$-0.912851\pi$
$613$	−17.1424	+	17.1424i	−0.692376	+	0.692376i	0.270378	+	0.962754i	$0.412851\pi$
$614$		0			0
$615$	−34.1019	+	27.7112i	−1.37512	+	1.11742i
$616$		0			0
$617$	0.724956	−	0.724956i	0.0291856	−	0.0291856i	−0.692363	−	0.721549i	$-0.743430\pi$
$617$	0.724956	−	0.724956i	0.0291856	−	0.0291856i	0.721549	+	0.692363i	$0.243430\pi$
$618$		0			0
$619$		−	40.1281i		−	1.61288i	−0.591314	−	0.806441i	$-0.701391\pi$
$619$		−	40.1281i		−	1.61288i	0.591314	−	0.806441i	$-0.298609\pi$
$620$		0			0
$621$	2.95510	+	4.27404i	0.118584	+	0.171511i
$622$		0			0
$623$	27.3500	+	27.3500i	1.09576	+	1.09576i
$624$		0			0
$625$	−24.6334	−	4.26564i	−0.985336	−	0.170626i
$626$		0			0
$627$	−5.84474	−	0.352012i	−0.233416	−	0.0140580i
$628$		0			0
$629$	−62.6088			−2.49638
$630$		0			0
$631$	−26.6415			−1.06058			−0.530292	−	0.847815i	$-0.677918\pi$
$631$	−26.6415			−1.06058			−0.530292	+	0.847815i	$0.677918\pi$
$632$		0			0
$633$	−41.3948	−	2.49309i	−1.64529	−	0.0990913i
$634$		0			0
$635$	0.530562	−	12.3696i	0.0210547	−	0.490873i
$636$		0			0
$637$	53.2446	+	53.2446i	2.10963	+	2.10963i
$638$		0			0
$639$	0.701800	−	5.80514i	0.0277628	−	0.229648i
$640$		0			0
$641$		−	23.8178i		−	0.940748i	−0.882467	−	0.470374i	$-0.844119\pi$
$641$		−	23.8178i		−	0.940748i	0.882467	−	0.470374i	$-0.155881\pi$
$642$		0			0
$643$	−15.0850	+	15.0850i	−0.594896	+	0.594896i	−0.938950	−	0.344054i	$-0.888200\pi$
$643$	−15.0850	+	15.0850i	−0.594896	+	0.594896i	0.344054	+	0.938950i	$0.388200\pi$
$644$		0			0
$645$	29.2863	+	3.02781i	1.15315	+	0.119220i
$646$		0			0
$647$	−0.716126	+	0.716126i	−0.0281538	+	0.0281538i	−0.721044	−	0.692890i	$-0.756337\pi$
$647$	−0.716126	+	0.716126i	−0.0281538	+	0.0281538i	0.692890	+	0.721044i	$0.256337\pi$
$648$		0			0
$649$		−	16.5393i		−	0.649226i
$650$		0			0
$651$	−52.5237	−	59.2559i	−2.05857	−	2.32242i
$652$		0			0
$653$	−0.900209	−	0.900209i	−0.0352279	−	0.0352279i	0.689273	−	0.724501i	$-0.257930\pi$
$653$	−0.900209	−	0.900209i	−0.0352279	−	0.0352279i	−0.724501	+	0.689273i	$0.757930\pi$
$654$		0			0
$655$	−8.62450	+	7.91508i	−0.336987	+	0.309268i
$656$		0			0
$657$	−8.90120	+	6.98114i	−0.347269	+	0.272360i
$658$		0			0
$659$	−45.0775			−1.75597			−0.877986	−	0.478686i	$-0.841113\pi$
$659$	−45.0775			−1.75597			−0.877986	+	0.478686i	$0.841113\pi$
$660$		0			0
$661$	5.41994			0.210811			0.105406	−	0.994429i	$-0.466386\pi$
$661$	5.41994			0.210811			0.105406	+	0.994429i	$0.466386\pi$
$662$		0			0
$663$	−3.54673	+	58.8893i	−0.137744	+	2.28707i
$664$		0			0
$665$	−20.5030	−	0.879422i	−0.795071	−	0.0341025i
$666$		0			0
$667$	1.16658	+	1.16658i	0.0451701	+	0.0451701i
$668$		0			0
$669$	7.72965	−	6.85148i	0.298846	−	0.264893i
$670$		0			0
$671$			2.83233i			0.109341i
$672$		0			0
$673$	−33.3031	+	33.3031i	−1.28374	+	1.28374i	−0.345216	+	0.938523i	$0.612194\pi$
$673$	−33.3031	+	33.3031i	−1.28374	+	1.28374i	−0.938523	+	0.345216i	$0.887806\pi$
$674$		0			0
$675$	6.83458	−	25.0657i	0.263063	−	0.964779i
$676$		0			0
$677$	30.1261	−	30.1261i	1.15784	−	1.15784i	0.172903	−	0.984939i	$-0.444685\pi$
$677$	30.1261	−	30.1261i	1.15784	−	1.15784i	0.984939	−	0.172903i	$-0.0553146\pi$
$678$		0			0
$679$		−	38.4903i		−	1.47712i
$680$		0			0
$681$	1.05075	−	0.931370i	0.0402647	−	0.0356902i
$682$		0			0
$683$	32.8229	+	32.8229i	1.25593	+	1.25593i	0.953017	+	0.302917i	$0.0979604\pi$
$683$	32.8229	+	32.8229i	1.25593	+	1.25593i	0.302917	+	0.953017i	$0.402040\pi$
$684$		0			0
$685$	0.0374421	+	0.00160598i	0.00143059	+	6.13614e-5i
$686$		0			0
$687$	−1.63268	+	27.1087i	−0.0622906	+	1.03426i
$688$		0			0
$689$	4.38085			0.166897
$690$		0			0
$691$	14.9225			0.567678			0.283839	−	0.958872i	$-0.408392\pi$
$691$	14.9225			0.567678			0.283839	+	0.958872i	$0.408392\pi$
$692$		0			0
$693$	18.6373	−	14.6171i	0.707971	−	0.555256i
$694$		0			0
$695$	−11.0681	+	10.1577i	−0.419838	+	0.385304i
$696$		0			0
$697$	−52.3806	−	52.3806i	−1.98406	−	1.98406i
$698$		0			0
$699$	14.8836	+	16.7913i	0.562951	+	0.635106i
$700$		0			0
$701$			48.3253i			1.82522i	0.408830	+	0.912611i	$0.365937\pi$
$701$			48.3253i			1.82522i	−0.408830	+	0.912611i	$0.634063\pi$
$702$		0			0
$703$	13.4413	−	13.4413i	0.506950	−	0.506950i
$704$		0			0
$705$	−0.922371	−	0.0953608i	−0.0347385	−	0.00359150i
$706$		0			0
$707$	−36.6771	+	36.6771i	−1.37938	+	1.37938i
$708$		0			0
$709$		−	8.91090i		−	0.334656i	−0.985901	−	0.167328i	$-0.946486\pi$
$709$		−	8.91090i		−	0.334656i	0.985901	−	0.167328i	$-0.0535139\pi$
$710$		0			0
$711$	−1.33143	+	11.0133i	−0.0499325	+	0.413031i
$712$		0			0
$713$	−6.98244	−	6.98244i	−0.261494	−	0.261494i
$714$		0			0
$715$	0.852476	−	19.8748i	0.0318808	−	0.743274i
$716$		0			0
$717$	37.3462	+	2.24925i	1.39472	+	0.0839998i
$718$		0			0
$719$	−0.987771			−0.0368376			−0.0184188	−	0.999830i	$-0.505863\pi$
$719$	−0.987771			−0.0368376			−0.0184188	+	0.999830i	$0.505863\pi$
$720$		0			0
$721$	−42.4525			−1.58101
$722$		0			0
$723$	−24.9224	−	1.50100i	−0.926874	−	0.0558229i
$724$		0			0
$725$	0.706336	−	8.21867i	0.0262327	−	0.305234i
$726$		0			0
$727$	−36.6670	−	36.6670i	−1.35990	−	1.35990i	−0.874030	−	0.485872i	$-0.838502\pi$
$727$	−36.6670	−	36.6670i	−1.35990	−	1.35990i	−0.485872	−	0.874030i	$-0.661498\pi$
$728$		0			0
$729$	25.2604	+	9.53482i	0.935570	+	0.353141i
$730$		0			0
$731$			49.6346i			1.83580i
$732$		0			0
$733$	23.7739	−	23.7739i	0.878109	−	0.878109i	−0.115230	−	0.993339i	$-0.536761\pi$
$733$	23.7739	−	23.7739i	0.878109	−	0.878109i	0.993339	+	0.115230i	$0.0367606\pi$
$734$		0			0
$735$	43.3846	−	35.2544i	1.60026	−	1.30038i
$736$		0			0
$737$	6.04219	−	6.04219i	0.222567	−	0.222567i
$738$		0			0
$739$		−	7.63599i		−	0.280894i	−0.990088	−	0.140447i	$-0.955146\pi$
$739$		−	7.63599i		−	0.280894i	0.990088	−	0.140447i	$-0.0448540\pi$
$740$		0			0
$741$	−11.8814	−	13.4043i	−0.436473	−	0.492418i
$742$		0			0
$743$	1.43310	+	1.43310i	0.0525752	+	0.0525752i	0.732906	−	0.680330i	$-0.238164\pi$
$743$	1.43310	+	1.43310i	0.0525752	+	0.0525752i	−0.680330	+	0.732906i	$0.738164\pi$
$744$		0			0
$745$	−17.4388	−	19.0018i	−0.638906	−	0.696171i
$746$		0			0
$747$	−27.4067	−	34.9445i	−1.00276	−	1.27855i
$748$		0			0
$749$	15.2608			0.557619
$750$		0			0
$751$	23.1874			0.846119			0.423059	−	0.906102i	$-0.360956\pi$
$751$	23.1874			0.846119			0.423059	+	0.906102i	$0.360956\pi$
$752$		0			0
$753$	0.878386	−	14.5846i	0.0320101	−	0.531491i
$754$		0			0
$755$	−16.7649	−	18.2675i	−0.610136	−	0.664822i
$756$		0			0
$757$	23.4585	+	23.4585i	0.852613	+	0.852613i	0.990454	−	0.137841i	$-0.0440164\pi$
$757$	23.4585	+	23.4585i	0.852613	+	0.852613i	−0.137841	+	0.990454i	$0.544016\pi$
$758$		0			0
$759$	2.21039	−	1.95927i	0.0802322	−	0.0711168i
$760$		0			0
$761$		−	14.9443i		−	0.541729i	−0.962617	−	0.270865i	$-0.912690\pi$
$761$		−	14.9443i		−	0.541729i	0.962617	−	0.270865i	$-0.0873096\pi$
$762$		0			0
$763$	0.447350	−	0.447350i	0.0161952	−	0.0161952i
$764$		0			0
$765$	43.2171	+	7.11522i	1.56252	+	0.257251i
$766$		0			0
$767$	35.7764	−	35.7764i	1.29181	−	1.29181i
$768$		0			0
$769$			22.4564i			0.809797i	0.914362	+	0.404899i	$0.132693\pi$
$769$			22.4564i			0.809797i	−0.914362	+	0.404899i	$0.867307\pi$
$770$		0			0
$771$	16.5919	−	14.7069i	0.597542	−	0.529654i
$772$		0			0
$773$	−4.77906	−	4.77906i	−0.171891	−	0.171891i	0.615919	−	0.787810i	$-0.288785\pi$
$773$	−4.77906	−	4.77906i	−0.171891	−	0.171891i	−0.787810	+	0.615919i	$0.788785\pi$
$774$		0			0
$775$	−4.22770	+	49.1919i	−0.151863	+	1.76703i
$776$		0			0
$777$	−4.62270	+	76.7545i	−0.165838	+	2.75355i
$778$		0			0
$779$	22.4910			0.805822
$780$		0			0
$781$	−3.32394			−0.118940
$782$		0			0
$783$	8.43336	+	1.53865i	0.301384	+	0.0549869i
$784$		0			0
$785$	−1.82597	+	42.5709i	−0.0651717	+	1.51942i
$786$		0			0
$787$	23.5552	+	23.5552i	0.839653	+	0.839653i	0.988813	−	0.149160i	$-0.0476569\pi$
$787$	23.5552	+	23.5552i	0.839653	+	0.839653i	−0.149160	+	0.988813i	$0.547657\pi$
$788$		0			0
$789$	14.3436	+	16.1821i	0.510646	+	0.576098i
$790$		0			0
$791$			25.2555i			0.897983i
$792$		0			0
$793$	−6.12665	+	6.12665i	−0.217564	+	0.217564i
$794$		0			0
$795$	0.334468	−	3.23512i	0.0118624	−	0.114738i
$796$		0			0
$797$	7.19505	−	7.19505i	0.254862	−	0.254862i	−0.568099	−	0.822960i	$-0.692321\pi$
$797$	7.19505	−	7.19505i	0.254862	−	0.254862i	0.822960	+	0.568099i	$0.192321\pi$
$798$		0			0
$799$		−	1.56324i		−	0.0553035i
$800$		0			0
$801$	24.8824	+	3.00810i	0.879176	+	0.106286i
$802$		0			0
$803$	4.54700	+	4.54700i	0.160460	+	0.160460i
$804$		0			0
$805$	7.62714	−	6.99976i	0.268821	−	0.246709i
$806$		0			0
$807$	30.5994	+	1.84291i	1.07715	+	0.0648736i
$808$		0			0
$809$	2.45544			0.0863287			0.0431643	−	0.999068i	$-0.486256\pi$
$809$	2.45544			0.0863287			0.0431643	+	0.999068i	$0.486256\pi$
$810$		0			0
$811$	12.7033			0.446074			0.223037	−	0.974810i	$-0.428403\pi$
$811$	12.7033			0.446074			0.223037	+	0.974810i	$0.428403\pi$
$812$		0			0
$813$	2.35944	+	0.142102i	0.0827492	+	0.00498374i
$814$		0			0
$815$	−36.5218	−	1.56651i	−1.27930	−	0.0548724i
$816$		0			0
$817$	−10.6559	−	10.6559i	−0.372804	−	0.372804i
$818$		0			0
$819$	71.9328	+	8.69615i	2.51353	+	0.303868i
$820$		0			0
$821$			14.7177i			0.513653i	0.966458	+	0.256826i	$0.0826768\pi$
$821$			14.7177i			0.513653i	−0.966458	+	0.256826i	$0.917323\pi$
$822$		0			0
$823$	28.8659	−	28.8659i	1.00620	−	1.00620i	0.00622129	−	0.999981i	$-0.498020\pi$
$823$	28.8659	−	28.8659i	1.00620	−	1.00620i	0.999981	−	0.00622129i	$-0.00198031\pi$
$824$		0			0
$825$	−14.6118	−	2.14692i	−0.508718	−	0.0747461i
$826$		0			0
$827$	26.1066	−	26.1066i	0.907816	−	0.907816i	−0.0882801	−	0.996096i	$-0.528137\pi$
$827$	26.1066	−	26.1066i	0.907816	−	0.907816i	0.996096	+	0.0882801i	$0.0281371\pi$
$828$		0			0
$829$		−	3.64363i		−	0.126548i	−0.997996	−	0.0632742i	$-0.979846\pi$
$829$		−	3.64363i		−	0.126548i	0.997996	−	0.0632742i	$-0.0201543\pi$
$830$		0			0
$831$	16.1033	+	18.1673i	0.558618	+	0.630218i
$832$		0			0
$833$	66.6390	+	66.6390i	2.30890	+	2.30890i
$834$		0			0
$835$	−49.9866	−	2.14405i	−1.72986	−	0.0741977i
$836$		0			0
$837$	−50.4770	−	9.20943i	−1.74474	−	0.318325i
$838$		0			0
$839$	37.6219			1.29885			0.649427	−	0.760424i	$-0.275009\pi$
$839$	37.6219			1.29885			0.649427	+	0.760424i	$0.275009\pi$
$840$		0			0
$841$	−26.2782			−0.906144
$842$		0			0
$843$	−0.265038	+	4.40064i	−0.00912839	+	0.151566i
$844$		0			0
$845$	23.4185	−	21.4922i	0.805622	−	0.739355i
$846$		0			0
$847$	26.4900	+	26.4900i	0.910208	+	0.910208i
$848$		0			0
$849$	−1.74368	+	1.54558i	−0.0598430	+	0.0530442i
$850$		0			0
$851$			9.58910i			0.328710i
$852$		0			0
$853$	18.8882	−	18.8882i	0.646721	−	0.646721i	−0.305478	−	0.952199i	$-0.598816\pi$
$853$	18.8882	−	18.8882i	0.646721	−	0.646721i	0.952199	+	0.305478i	$0.0988164\pi$
$854$		0			0
$855$	−10.8057	+	7.75064i	−0.369548	+	0.265066i
$856$		0			0
$857$	−10.0141	+	10.0141i	−0.342074	+	0.342074i	−0.857147	−	0.515072i	$-0.827765\pi$
$857$	−10.0141	+	10.0141i	−0.342074	+	0.342074i	0.515072	+	0.857147i	$0.327765\pi$
$858$		0			0
$859$		−	28.7538i		−	0.981067i	−0.871422	−	0.490533i	$-0.836802\pi$
$859$		−	28.7538i		−	0.981067i	0.871422	−	0.490533i	$-0.163198\pi$
$860$		0			0
$861$	−68.0829	+	60.3479i	−2.32026	+	2.05665i
$862$		0			0
$863$	−32.1063	−	32.1063i	−1.09291	−	1.09291i	−0.995216	−	0.0976959i	$-0.968853\pi$
$863$	−32.1063	−	32.1063i	−1.09291	−	1.09291i	−0.0976959	−	0.995216i	$-0.531147\pi$
$864$		0			0
$865$	0.584164	−	13.6193i	0.0198622	−	0.463070i
$866$		0			0
$867$	−2.66879	+	44.3120i	−0.0906367	+	1.50492i
$868$		0			0
$869$	6.30606			0.213919
$870$		0			0
$871$	26.1399			0.885716
$872$		0			0
$873$	−15.3921	−	19.6255i	−0.520944	−	0.664221i
$874$		0			0
$875$	−51.3340	−	6.63811i	−1.73541	−	0.224409i
$876$		0			0
$877$	14.4671	+	14.4671i	0.488521	+	0.488521i	0.907839	−	0.419319i	$-0.137731\pi$
$877$	14.4671	+	14.4671i	0.488521	+	0.488521i	−0.419319	+	0.907839i	$0.637731\pi$
$878$		0			0
$879$	1.48419	+	1.67443i	0.0500605	+	0.0564770i
$880$		0			0
$881$		−	49.7715i		−	1.67685i	−0.545020	−	0.838423i	$-0.683478\pi$
$881$		−	49.7715i		−	1.67685i	0.545020	−	0.838423i	$-0.316522\pi$
$882$		0			0
$883$	−1.06170	+	1.06170i	−0.0357291	+	0.0357291i	−0.724746	−	0.689017i	$-0.758043\pi$
$883$	−1.06170	+	1.06170i	−0.0357291	+	0.0357291i	0.689017	+	0.724746i	$0.258043\pi$
$884$		0			0
$885$	−23.6883	−	29.1512i	−0.796274	−	0.979908i
$886$		0			0
$887$	−20.1303	+	20.1303i	−0.675908	+	0.675908i	−0.959072	−	0.283164i	$-0.908616\pi$
$887$	−20.1303	+	20.1303i	−0.675908	+	0.675908i	0.283164	+	0.959072i	$0.408616\pi$
$888$		0			0
$889$		−	25.6343i		−	0.859746i
$890$		0			0
$891$	3.65748	−	14.9059i	0.122530	−	0.499366i
$892$		0			0
$893$	0.335609	+	0.335609i	0.0112307	+	0.0112307i
$894$		0			0
$895$	−28.3085	−	30.8458i	−0.946249	−	1.03106i
$896$		0			0
$897$	9.01943	+	0.543214i	0.301150	+	0.0181374i
$898$		0			0
$899$	−16.2911			−0.543340
$900$		0			0
$901$	5.48291			0.182662
$902$		0			0
$903$	60.8489	+	3.66476i	2.02493	+	0.121955i
$904$		0			0
$905$	−2.34752	−	2.55793i	−0.0780344	−	0.0850285i
$906$		0			0
$907$	6.07001	+	6.07001i	0.201551	+	0.201551i	0.800664	−	0.599113i	$-0.204480\pi$
$907$	6.07001	+	6.07001i	0.201551	+	0.201551i	−0.599113	+	0.800664i	$0.704480\pi$
$908$		0			0
$909$	−4.03394	+	33.3679i	−0.133797	+	1.10674i
$910$		0			0
$911$		−	30.1436i		−	0.998703i	−0.866400	−	0.499351i	$-0.833572\pi$
$911$		−	30.1436i		−	0.998703i	0.866400	−	0.499351i	$-0.166428\pi$
$912$		0			0
$913$	−17.8507	+	17.8507i	−0.590772	+	0.590772i
$914$		0			0
$915$	4.05659	+	4.99210i	0.134107	+	0.165034i
$916$		0			0
$917$	−17.1380	+	17.1380i	−0.565946	+	0.565946i
$918$		0			0
$919$			30.0365i			0.990813i	0.868661	+	0.495406i	$0.164981\pi$
$919$			30.0365i			0.990813i	−0.868661	+	0.495406i	$0.835019\pi$
$920$		0			0
$921$	33.8238	+	38.1591i	1.11453	+	1.25738i
$922$		0			0
$923$	−7.19006	−	7.19006i	−0.236664	−	0.236664i
$924$		0			0
$925$	36.6811	−	30.8751i	1.20607	−	1.01517i
$926$		0			0
$927$	−21.6457	+	16.9766i	−0.710938	+	0.557583i
$928$		0			0
$929$	44.4530			1.45846			0.729228	−	0.684270i	$-0.239879\pi$
$929$	44.4530			1.45846			0.729228	+	0.684270i	$0.239879\pi$
$930$		0			0
$931$	−28.6131			−0.937758
$932$		0			0
$933$	0.805643	−	13.3768i	0.0263756	−	0.437935i
$934$		0			0
$935$	1.06693	−	24.8745i	0.0348922	−	0.813483i
$936$		0			0
$937$	−2.75604	−	2.75604i	−0.0900360	−	0.0900360i	0.660654	−	0.750690i	$-0.270279\pi$
$937$	−2.75604	−	2.75604i	−0.0900360	−	0.0900360i	−0.750690	+	0.660654i	$0.770279\pi$
$938$		0			0
$939$	−21.5453	+	19.0975i	−0.703104	+	0.623223i
$940$		0			0
$941$		−	44.6684i		−	1.45615i	−0.685498	−	0.728075i	$-0.740415\pi$
$941$		−	44.6684i		−	1.45615i	0.685498	−	0.728075i	$-0.259585\pi$
$942$		0			0
$943$	−8.02257	+	8.02257i	−0.261251	+	0.261251i
$944$		0			0
$945$	11.9137	−	52.4562i	0.387554	−	1.70640i
$946$		0			0
$947$	24.5300	−	24.5300i	0.797118	−	0.797118i	−0.185522	−	0.982640i	$-0.559398\pi$
$947$	24.5300	−	24.5300i	0.797118	−	0.797118i	0.982640	+	0.185522i	$0.0593976\pi$
$948$		0			0
$949$			19.6713i			0.638559i
$950$		0			0
$951$	11.0918	−	9.83160i	0.359675	−	0.318812i
$952$		0			0
$953$	−14.1644	−	14.1644i	−0.458830	−	0.458830i	0.439441	−	0.898271i	$-0.355177\pi$
$953$	−14.1644	−	14.1644i	−0.458830	−	0.458830i	−0.898271	+	0.439441i	$0.855177\pi$
$954$		0			0
$955$	−29.0185	+	26.6315i	−0.939016	+	0.861776i
$956$		0			0
$957$	0.292959	−	4.86424i	0.00947002	−	0.157238i
$958$		0			0
$959$	0.0775936			0.00250563
$960$		0			0
$961$	66.5088			2.14545
$962$		0			0
$963$	7.78121	−	6.10274i	0.250746	−	0.196658i
$964$		0			0
$965$	1.41739	+	0.0607952i	0.0456273	+	0.00195707i
$966$		0			0
$967$	20.7364	+	20.7364i	0.666837	+	0.666837i	0.956983	−	0.290146i	$-0.0937037\pi$
$967$	20.7364	+	20.7364i	0.666837	+	0.666837i	−0.290146	+	0.956983i	$0.593704\pi$
$968$		0			0
$969$	−14.8703	−	16.7763i	−0.477702	−	0.538931i
$970$		0			0
$971$			35.6655i			1.14456i	0.820058	+	0.572280i	$0.193941\pi$
$971$			35.6655i			1.14456i	−0.820058	+	0.572280i	$0.806059\pi$
$972$		0			0
$973$	−21.9938	+	21.9938i	−0.705089	+	0.705089i
$974$		0			0
$975$	−26.9629	−	36.2510i	−0.863504	−	1.16096i
$976$		0			0
$977$	−1.05368	+	1.05368i	−0.0337102	+	0.0337102i	−0.723761	−	0.690051i	$-0.757588\pi$
$977$	−1.05368	+	1.05368i	−0.0337102	+	0.0337102i	0.690051	+	0.723761i	$0.257588\pi$
$978$		0			0
$979$		−	14.2473i		−	0.455346i
$980$		0			0
$981$	0.0492019	−	0.406988i	0.00157090	−	0.0129941i
$982$		0			0
$983$	12.0419	+	12.0419i	0.384077	+	0.384077i	0.872569	−	0.488492i	$-0.162453\pi$
$983$	12.0419	+	12.0419i	0.384077	+	0.384077i	−0.488492	+	0.872569i	$0.662453\pi$
$984$		0			0
$985$	−37.8694	−	1.62431i	−1.20662	−	0.0517548i
$986$		0			0
$987$	−1.91644	−	0.115421i	−0.0610009	−	0.00367391i
$988$		0			0
$989$	7.60199			0.241729
$990$		0			0
$991$	−17.4612			−0.554675			−0.277337	−	0.960773i	$-0.589452\pi$
$991$	−17.4612			−0.554675			−0.277337	+	0.960773i	$0.589452\pi$
$992$		0			0
$993$	−36.7335	−	2.21235i	−1.16570	−	0.0702069i
$994$		0			0
$995$	5.29492	−	4.85938i	0.167860	−	0.154053i
$996$		0			0
$997$	20.8569	+	20.8569i	0.660544	+	0.660544i	0.955508	−	0.294964i	$-0.0953077\pi$
$997$	20.8569	+	20.8569i	0.660544	+	0.660544i	−0.294964	+	0.955508i	$0.595308\pi$
$998$		0			0
$999$	28.3367	+	40.9842i	0.896534	+	1.29668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.1	✓	80
3.2	odd	2	inner	1380.2.r.c.737.19	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.19	yes	80
15.8	even	4	inner	1380.2.r.c.1013.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.1	✓	80	1.1	even	1	trivial
1380.2.r.c.737.19	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.1	yes	80	15.8	even	4	inner
1380.2.r.c.1013.19	yes	80	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72892 - 0.104128i) q^{3} +(1.51193 + 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(2.97831 + 0.360057i) q^{9} +O(q^{10})\)	\(q+(-1.72892 - 0.104128i) q^{3} +(1.51193 + 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(2.97831 + 0.360057i) q^{9} -1.70534i q^{11} +(3.68884 - 3.68884i) q^{13} +(-2.44246 - 3.00573i) q^{15} +(4.61681 - 4.61681i) q^{17} +1.98235i q^{19} +(-5.31904 - 6.00081i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(-0.428136 + 4.98164i) q^{25} +(-5.11177 - 0.932633i) q^{27} -1.64979 q^{29} +9.87466 q^{31} +(-0.177573 + 2.94839i) q^{33} +(-0.443627 + 10.3428i) q^{35} +(-6.78052 - 6.78052i) q^{37} +(-6.76181 + 5.99359i) q^{39} -11.3456i q^{41} +(-5.37542 + 5.37542i) q^{43} +(3.90983 + 5.45098i) q^{45} +(0.169299 - 0.169299i) q^{47} +14.4340i q^{49} +(-8.46283 + 7.50135i) q^{51} +(0.593798 + 0.593798i) q^{53} +(2.80945 - 2.57835i) q^{55} +(0.206417 - 3.42731i) q^{57} +9.69856 q^{59} -1.66086 q^{61} +(8.57134 + 10.9288i) q^{63} +(11.6544 + 0.499886i) q^{65} +(3.54310 + 3.54310i) q^{67} +(1.14890 + 1.29616i) q^{69} -1.94914i q^{71} +(-2.66633 + 2.66633i) q^{73} +(1.25894 - 8.56826i) q^{75} +(5.58274 - 5.58274i) q^{77} +3.69783i q^{79} +(8.74072 + 2.14472i) q^{81} +(-10.4675 - 10.4675i) q^{83} +(14.5862 + 0.625639i) q^{85} +(2.85236 + 0.171789i) q^{87} +8.35452 q^{89} +24.1522 q^{91} +(-17.0725 - 1.02823i) q^{93} +(-3.26580 + 2.99717i) q^{95} +(-5.87875 - 5.87875i) q^{97} +(0.614019 - 5.07904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more