LMFDB - Embedded newform 1380.2.r.c.737.19

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			737.19
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104128 + 1.72892i) q^{3} +(-1.51193 - 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(-2.97831 + 0.360057i) q^{9} +O(q^{10})$	\(q+(0.104128 + 1.72892i) q^{3} +(-1.51193 - 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(-2.97831 + 0.360057i) q^{9} +1.70534i q^{11} +(3.68884 - 3.68884i) q^{13} +(2.69086 - 2.78555i) q^{15} +(-4.61681 + 4.61681i) q^{17} +1.98235i q^{19} +(-5.31904 + 6.00081i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-0.428136 + 4.98164i) q^{25} +(-0.932633 - 5.11177i) q^{27} +1.64979 q^{29} +9.87466 q^{31} +(-2.94839 + 0.177573i) q^{33} +(0.443627 - 10.3428i) q^{35} +(-6.78052 - 6.78052i) q^{37} +(6.76181 + 5.99359i) q^{39} +11.3456i q^{41} +(-5.37542 + 5.37542i) q^{43} +(5.09618 + 4.36222i) q^{45} +(-0.169299 + 0.169299i) q^{47} +14.4340i q^{49} +(-8.46283 - 7.50135i) q^{51} +(-0.593798 - 0.593798i) q^{53} +(2.80945 - 2.57835i) q^{55} +(-3.42731 + 0.206417i) q^{57} -9.69856 q^{59} -1.66086 q^{61} +(-10.9288 - 8.57134i) q^{63} +(-11.6544 - 0.499886i) q^{65} +(3.54310 + 3.54310i) q^{67} +(-1.14890 + 1.29616i) q^{69} +1.94914i q^{71} +(-2.66633 + 2.66633i) q^{73} +(-8.65742 - 0.221486i) q^{75} +(-5.58274 + 5.58274i) q^{77} +3.69783i q^{79} +(8.74072 - 2.14472i) q^{81} +(10.4675 + 10.4675i) q^{83} +(14.5862 + 0.625639i) q^{85} +(0.171789 + 2.85236i) q^{87} -8.35452 q^{89} +24.1522 q^{91} +(1.02823 + 17.0725i) q^{93} +(3.26580 - 2.99717i) q^{95} +(-5.87875 - 5.87875i) q^{97} +(-0.614019 - 5.07904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.104128	+	1.72892i	0.0601182	+	0.998191i
$3$	0.104128	+	1.72892i	0.0601182	+	0.998191i
$4$		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	$0.0827636\pi$
$11$			1.70534i			0.514179i	−0.966388	+	0.257090i	$0.917236\pi$
$12$		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
$15$	2.69086	−	2.78555i	0.694777	−	0.719225i
$16$		0			0
$17$	−4.61681	+	4.61681i	−1.11974	+	1.11974i	−0.127963	+	0.991779i	$0.540844\pi$
$17$	−4.61681	+	4.61681i	−1.11974	+	1.11974i	−0.991779	+	0.127963i	$0.959156\pi$
$18$		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
$27$	−0.932633	−	5.11177i	−0.179485	−	0.983761i
$28$		0			0
$29$	1.64979			0.306359			0.153179	−	0.988198i	$-0.451049\pi$
$29$	1.64979			0.306359			0.153179	+	0.988198i	$0.451049\pi$
$30$		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
$33$	−2.94839	+	0.177573i	−0.513249	+	0.0309115i
$34$		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	$0.346489\pi$
$41$			11.3456i			1.77189i	−0.463791	+	0.885945i	$0.653511\pi$
$42$		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
$45$	5.09618	+	4.36222i	0.759693	+	0.650282i
$46$		0			0
$47$	−0.169299	+	0.169299i	−0.0246948	+	0.0246948i	−0.719346	−	0.694652i	$-0.755559\pi$
$47$	−0.169299	+	0.169299i	−0.0246948	+	0.0246948i	0.694652	+	0.719346i	$0.255559\pi$
$48$		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	0.665148	−	0.746712i	$-0.268369\pi$
$53$	−0.593798	−	0.593798i	−0.0815644	−	0.0815644i	−0.746712	+	0.665148i	$0.768369\pi$
$54$		0			0
$55$	2.80945	−	2.57835i	0.378826	−	0.347665i
$56$		0			0
$57$	−3.42731	+	0.206417i	−0.453959	+	0.0273406i
$58$		0			0
$59$	−9.69856			−1.26264			−0.631322	−	0.775521i	$-0.717488\pi$
$59$	−9.69856			−1.26264			−0.631322	+	0.775521i	$0.717488\pi$
$60$		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
$63$	−10.9288	−	8.57134i	−1.37689	−	1.07989i
$64$		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	$0.0368983\pi$
$71$			1.94914i			0.231320i	−0.993289	+	0.115660i	$0.963102\pi$
$72$		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
$75$	−8.65742	−	0.221486i	−0.999673	−	0.0255750i
$76$		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	$0.0518597\pi$
$83$	10.4675	+	10.4675i	1.14896	+	1.14896i	0.162202	+	0.986758i	$0.448140\pi$
$84$		0			0
$85$	14.5862	+	0.625639i	1.58210	+	0.0678600i
$86$		0			0
$87$	0.171789	+	2.85236i	0.0184177	+	0.305805i
$88$		0			0
$89$	−8.35452			−0.885577			−0.442789	−	0.896626i	$-0.646011\pi$
$89$	−8.35452			−0.885577			−0.442789	+	0.896626i	$0.646011\pi$
$90$		0			0
$91$	24.1522			2.53184
$92$		0			0
$93$	1.02823	+	17.0725i	0.106622	+	1.77033i
$94$		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	$-0.811799\pi$
$101$		−	11.2036i		−	1.11480i	0.830243	−	0.557401i	$-0.188201\pi$
$102$		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
$105$	17.9280	−	0.309976i	1.74959	−	0.0302505i
$106$		0			0
$107$	−2.33084	+	2.33084i	−0.225331	+	0.225331i	−0.810739	−	0.585408i	$-0.800934\pi$
$107$	−2.33084	+	2.33084i	−0.225331	+	0.225331i	0.585408	+	0.810739i	$0.300934\pi$
$108$		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	0.501999	−	0.864868i	$-0.332598\pi$
$113$	−3.85736	−	3.85736i	−0.362870	−	0.362870i	−0.864868	+	0.501999i	$0.832598\pi$
$114$		0			0
$115$	0.0958222	−	2.23401i	0.00893547	−	0.208323i
$116$		0			0
$117$	−9.65834	+	12.3147i	−0.892914	+	1.13850i
$118$		0			0
$119$	−30.2279			−2.77099
$120$		0			0
$121$	8.09181			0.735619
$122$		0			0
$123$	−19.6157	+	1.18139i	−1.76868	+	0.106523i
$124$		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	$-0.926554\pi$
$131$		−	5.23508i		−	0.457391i	0.973498	−	0.228696i	$-0.0734460\pi$
$132$		0			0
$133$	−6.48957	+	6.48957i	−0.562717	+	0.562717i
$134$		0			0
$135$	−7.01127	+	9.26510i	−0.603434	+	0.797413i
$136$		0			0
$137$	−0.0118511	+	0.0118511i	−0.00101251	+	0.00101251i	−0.707613	−	0.706600i	$-0.750228\pi$
$137$	−0.0118511	+	0.0118511i	−0.00101251	+	0.00101251i	0.706600	+	0.707613i	$0.250228\pi$
$138$		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
$147$	−24.9552	+	1.50298i	−2.05827	+	0.123963i
$148$		0			0
$149$	11.5341			0.944910			0.472455	−	0.881355i	$-0.343368\pi$
$149$	11.5341			0.944910			0.472455	+	0.881355i	$0.343368\pi$
$150$		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
$153$	12.0880	−	15.4126i	0.977258	−	1.24604i
$154$		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
$165$	4.75031	+	4.58883i	0.369811	+	0.357240i
$166$		0			0
$167$	15.8217	−	15.8217i	1.22432	−	1.22432i	0.258237	−	0.966082i	$-0.416858\pi$
$167$	15.8217	−	15.8217i	1.22432	−	1.22432i	0.966082	−	0.258237i	$-0.0831415\pi$
$168$		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	0.851727	−	0.523986i	$-0.175556\pi$
$173$	4.31076	+	4.31076i	0.327741	+	0.327741i	−0.523986	+	0.851727i	$0.675556\pi$
$174$		0			0
$175$	−17.7099	+	14.9067i	−1.33874	+	1.12684i
$176$		0			0
$177$	−1.00989	−	16.7680i	−0.0759079	−	1.26036i
$178$		0			0
$179$	18.7234			1.39945			0.699727	−	0.714410i	$-0.253305\pi$
$179$	18.7234			1.39945			0.699727	+	0.714410i	$0.253305\pi$
$180$		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
$183$	−0.172942	−	2.87149i	−0.0127842	−	0.212267i
$184$		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	$-0.780067\pi$
$191$		−	17.6143i		−	1.27452i	0.770648	−	0.637261i	$-0.219933\pi$
$192$		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
$195$	−0.349286	−	20.2016i	−0.0250129	−	1.44667i
$196$		0			0
$197$	11.9864	−	11.9864i	0.853993	−	0.853993i	−0.136629	−	0.990622i	$-0.543627\pi$
$197$	11.9864	−	11.9864i	0.853993	−	0.853993i	0.990622	+	0.136629i	$0.0436268\pi$
$198$		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
$207$	−2.36059	−	1.85139i	−0.164072	−	0.128680i
$208$		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
$213$	−3.36990	+	0.202959i	−0.230902	+	0.0139065i
$214$		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
$225$	−0.518546	−	14.9910i	−0.0345697	−	0.999402i
$226$		0			0
$227$	0.573225	−	0.573225i	0.0380462	−	0.0380462i	−0.687828	−	0.725874i	$-0.741436\pi$
$227$	0.573225	−	0.573225i	0.0380462	−	0.0380462i	0.725874	+	0.687828i	$0.241436\pi$
$228$		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	0.940343	−	0.340229i	$-0.110505\pi$
$233$	9.16034	+	9.16034i	0.600114	+	0.600114i	−0.340229	+	0.940343i	$0.610505\pi$
$234$		0			0
$235$	0.534878	+	0.0229422i	0.0348916	+	0.00149658i
$236$		0			0
$237$	−6.39325	+	0.385047i	−0.415286	+	0.0250115i
$238$		0			0
$239$	21.6009			1.39725			0.698623	−	0.715490i	$-0.253797\pi$
$239$	21.6009			1.39725			0.698623	+	0.715490i	$0.253797\pi$
$240$		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
$243$	4.61820	+	14.8887i	0.296258	+	0.955108i
$244$		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	$-0.914223\pi$
$251$		−	8.43565i		−	0.532454i	0.963910	−	0.266227i	$-0.0857770\pi$
$252$		0			0
$253$	−1.20586	+	1.20586i	−0.0758116	+	0.0758116i
$254$		0			0
$255$	0.437153	+	25.2835i	0.0273756	+	1.58332i
$256$		0			0
$257$	9.05154	−	9.05154i	0.564620	−	0.564620i	−0.365997	−	0.930616i	$-0.619272\pi$
$257$	9.05154	−	9.05154i	0.564620	−	0.564620i	0.930616	+	0.365997i	$0.119272\pi$
$258$		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	0.924803	−	0.380447i	$-0.124230\pi$
$263$	8.82798	+	8.82798i	0.544356	+	0.544356i	−0.380447	+	0.924803i	$0.624230\pi$
$264$		0			0
$265$	−0.0804674	+	1.87603i	−0.00494307	+	0.115244i
$266$		0			0
$267$	−0.869937	−	14.4443i	−0.0532393	−	0.883975i
$268$		0			0
$269$	17.6986			1.07910			0.539551	−	0.841953i	$-0.318594\pi$
$269$	17.6986			1.07910			0.539551	+	0.841953i	$0.318594\pi$
$270$		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
$273$	2.51491	+	41.7571i	0.152209	+	2.52726i
$274$		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	$0.0241895\pi$
$281$			2.54532i			0.151841i	−0.997114	+	0.0759204i	$0.975811\pi$
$282$		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
$285$	5.52192	+	5.33422i	0.327090	+	0.315972i
$286$		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	0.733286	−	0.679921i	$-0.237986\pi$
$293$	0.913466	+	0.913466i	0.0533653	+	0.0533653i	−0.679921	+	0.733286i	$0.737986\pi$
$294$		0			0
$295$	14.6635	+	15.9778i	0.853744	+	0.930265i
$296$		0			0
$297$	8.71731	−	1.59046i	0.505830	−	0.0922877i
$298$		0			0
$299$	5.21681			0.301696
$300$		0			0
$301$	−35.1948			−2.02860
$302$		0			0
$303$	19.3701	−	1.16661i	1.11279	−	0.0670199i
$304$		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	$-0.929602\pi$
$311$		−	7.73707i		−	0.438729i	0.975643	−	0.219364i	$-0.0703983\pi$
$312$		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
$315$	2.40273	+	30.9638i	0.135378	+	1.74461i
$316$		0			0
$317$	6.05100	−	6.05100i	0.339858	−	0.339858i	−0.516456	−	0.856314i	$-0.672749\pi$
$317$	6.05100	−	6.05100i	0.339858	−	0.339858i	0.856314	+	0.516456i	$0.172749\pi$
$318$		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
$327$	0.236258	−	0.0142291i	0.0130651	−	0.000786871i
$328$		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
$333$	22.6359	+	17.7532i	1.24044	+	0.972867i
$334$		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
$345$	3.87240	−	0.0669540i	0.208483	−	0.00360468i
$346$		0			0
$347$	−12.4888	+	12.4888i	−0.670435	+	0.670435i	−0.957816	−	0.287381i	$-0.907215\pi$
$347$	−12.4888	+	12.4888i	−0.670435	+	0.670435i	0.287381	+	0.957816i	$0.407215\pi$
$348$		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	0.390231	−	0.920717i	$-0.372395\pi$
$353$	−9.96694	−	9.96694i	−0.530486	−	0.530486i	−0.920717	+	0.390231i	$0.872395\pi$
$354$		0			0
$355$	3.21109	−	2.94696i	0.170427	−	0.156408i
$356$		0			0
$357$	−3.14757	−	52.2616i	−0.166587	−	2.76598i
$358$		0			0
$359$	−7.70121			−0.406455			−0.203227	−	0.979132i	$-0.565143\pi$
$359$	−7.70121			−0.406455			−0.203227	+	0.979132i	$0.565143\pi$
$360$		0			0
$361$	15.0703			0.793174
$362$		0			0
$363$	0.842582	+	13.9901i	0.0442241	+	0.734289i
$364$		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
$375$	12.7245	+	14.5975i	0.657092	+	0.753811i
$376$		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	0.706983	−	0.707231i	$-0.250056\pi$
$383$	−0.00486119	−	0.00486119i	−0.000248395	−	0.000248395i	−0.707231	+	0.706983i	$0.750056\pi$
$384$		0			0
$385$	17.6380	+	0.756534i	0.898914	+	0.0385566i
$386$		0			0
$387$	14.0742	−	17.9451i	0.715434	−	0.912203i
$388$		0			0
$389$	−26.2299			−1.32991			−0.664953	−	0.746885i	$-0.731549\pi$
$389$	−26.2299			−1.32991			−0.664953	+	0.746885i	$0.731549\pi$
$390$		0			0
$391$	−6.52916			−0.330194
$392$		0			0
$393$	9.05103	−	0.545117i	0.456564	−	0.0274975i
$394$		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	$-0.916868\pi$
$401$		−	10.3412i		−	0.516414i	0.966090	−	0.258207i	$-0.0831316\pi$
$402$		0			0
$403$	36.4260	−	36.4260i	1.81451	−	1.81451i
$404$		0			0
$405$	−16.7487	−	11.1572i	−0.832248	−	0.554404i
$406$		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
$417$	−11.6155	+	0.699569i	−0.568814	+	0.0342580i
$418$		0			0
$419$	31.6533			1.54636			0.773182	−	0.634184i	$-0.218664\pi$
$419$	31.6533			1.54636			0.773182	+	0.634184i	$0.218664\pi$
$420$		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
$423$	0.443268	−	0.565182i	0.0215524	−	0.0274801i
$424$		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	$0.359268\pi$
$431$			37.5287i			1.80769i	−0.427858	+	0.903846i	$0.640732\pi$
$432$		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
$435$	4.43936	−	4.59557i	0.212851	−	0.220341i
$436$		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	$0.151703\pi$
$443$	28.3577	+	28.3577i	1.34732	+	1.34732i	0.458750	+	0.888565i	$0.348297\pi$
$444$		0			0
$445$	12.6314	+	13.7636i	0.598788	+	0.652457i
$446$		0			0
$447$	1.20102	+	19.9415i	0.0568063	+	0.943201i
$448$		0			0
$449$	−21.7135			−1.02472			−0.512362	−	0.858769i	$-0.671230\pi$
$449$	−21.7135			−1.02472			−0.512362	+	0.858769i	$0.671230\pi$
$450$		0			0
$451$	−19.3482			−0.911069
$452$		0			0
$453$	−1.15461	−	19.1709i	−0.0542482	−	0.900728i
$454$		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	$-0.844372\pi$
$461$		−	20.1686i		−	0.939345i	0.882841	−	0.469673i	$-0.155628\pi$
$462$		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
$465$	26.5713	−	27.5063i	1.23222	−	1.27558i
$466$		0			0
$467$	−11.2064	+	11.2064i	−0.518571	+	0.518571i	−0.917139	−	0.398568i	$-0.869507\pi$
$467$	−11.2064	+	11.2064i	−0.518571	+	0.518571i	0.398568	+	0.917139i	$0.369507\pi$
$468$		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
$477$	1.98232	+	1.55472i	0.0907641	+	0.0711856i
$478$		0			0
$479$	19.3784			0.885420			0.442710	−	0.896665i	$-0.354017\pi$
$479$	19.3784			0.885420			0.442710	+	0.896665i	$0.354017\pi$
$480$		0			0
$481$	−50.0245			−2.28092
$482$		0			0
$483$	−8.00434	+	0.482078i	−0.364210	+	0.0219353i
$484$		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	$-0.861455\pi$
$491$		−	18.6858i		−	0.843278i	0.906764	−	0.421639i	$-0.138545\pi$
$492$		0			0
$493$	−7.61678	+	7.61678i	−0.343043	+	0.343043i
$494$		0			0
$495$	−7.43908	+	8.69071i	−0.334362	+	0.390619i
$496$		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	$-0.814773\pi$
$503$	−31.0631	−	31.0631i	−1.38503	−	1.38503i	−0.549618	−	0.835416i	$-0.685227\pi$
$504$		0			0
$505$	−18.4573	+	16.9391i	−0.821341	+	0.753780i
$506$		0			0
$507$	24.5767	−	1.48018i	1.09149	−	0.0657373i
$508$		0			0
$509$	31.7775			1.40851			0.704256	−	0.709946i	$-0.251281\pi$
$509$	31.7775			1.40851			0.704256	+	0.709946i	$0.251281\pi$
$510$		0			0
$511$	−17.4574			−0.772271
$512$		0			0
$513$	10.1333	−	1.84880i	0.447396	−	0.0816266i
$514$		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	$-0.701837\pi$
$521$		−	36.7769i		−	1.61122i	0.592444	−	0.805612i	$-0.298163\pi$
$522$		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
$525$	−27.6166	−	29.0667i	−1.20529	−	1.26858i
$526$		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
$537$	1.94963	+	32.3713i	0.0841327	+	1.39692i
$538$		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
$543$	−0.161676	−	2.68444i	−0.00693817	−	0.115200i
$544$		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
$555$	−37.1329	+	0.642029i	−1.57620	+	0.0272526i
$556$		0			0
$557$	−24.0438	+	24.0438i	−1.01877	+	1.01877i	−0.0189465	+	0.999820i	$0.506031\pi$
$557$	−24.0438	+	24.0438i	−1.01877	+	1.01877i	−0.999820	+	0.0189465i	$0.993969\pi$
$558$		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	0.660465	−	0.750856i	$-0.270359\pi$
$563$	−2.14476	−	2.14476i	−0.0903910	−	0.0903910i	−0.750856	+	0.660465i	$0.770359\pi$
$564$		0			0
$565$	−0.522722	+	12.1868i	−0.0219911	+	0.512704i
$566$		0			0
$567$	35.6355	+	21.5932i	1.49655	+	0.906828i
$568$		0			0
$569$	3.88901			0.163036			0.0815178	−	0.996672i	$-0.474023\pi$
$569$	3.88901			0.163036			0.0815178	+	0.996672i	$0.474023\pi$
$570$		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
$573$	30.4536	−	1.83413i	1.27222	−	0.0766220i
$574$		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
$585$	34.8905	−	2.70743i	1.44255	−	0.111939i
$586$		0			0
$587$	−15.9188	+	15.9188i	−0.657038	+	0.657038i	−0.954678	−	0.297640i	$-0.903801\pi$
$587$	−15.9188	+	15.9188i	−0.657038	+	0.657038i	0.297640	+	0.954678i	$0.403801\pi$
$588$		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	0.999934	−	0.0114865i	$-0.00365636\pi$
$593$	24.0703	+	24.0703i	0.988447	+	0.988447i	−0.0114865	+	0.999934i	$0.503656\pi$
$594$		0			0
$595$	45.7025	+	49.7988i	1.87362	+	2.04155i
$596$		0			0
$597$	5.55678	−	0.334669i	0.227424	−	0.0136971i
$598$		0			0
$599$	1.97373			0.0806445			0.0403222	−	0.999187i	$-0.487162\pi$
$599$	1.97373			0.0806445			0.0403222	+	0.999187i	$0.487162\pi$
$600$		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
$603$	−11.8282	−	9.27675i	−0.481681	−	0.377779i
$604$		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
$615$	31.6038	+	30.5295i	1.27439	+	1.23107i
$616$		0			0
$617$	−0.724956	+	0.724956i	−0.0291856	+	0.0291856i	−0.721549	−	0.692363i	$-0.756570\pi$
$617$	−0.724956	+	0.724956i	−0.0291856	+	0.0291856i	0.692363	+	0.721549i	$0.256570\pi$
$618$		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
$627$	−0.352012	−	5.84474i	−0.0140580	−	0.233416i
$628$		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
$633$	2.49309	+	41.3948i	0.0990913	+	1.64529i
$634$		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	$0.155881\pi$
$641$			23.8178i			0.940748i	−0.882467	+	0.470374i	$0.844119\pi$
$642$		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
$645$	0.508984	+	29.4380i	0.0200412	+	1.15912i
$646$		0			0
$647$	0.716126	−	0.716126i	0.0281538	−	0.0281538i	−0.692890	−	0.721044i	$-0.743663\pi$
$647$	0.716126	−	0.716126i	0.0281538	−	0.0281538i	0.721044	+	0.692890i	$0.243663\pi$
$648$		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	0.724501	−	0.689273i	$-0.242070\pi$
$653$	0.900209	+	0.900209i	0.0352279	+	0.0352279i	−0.689273	+	0.724501i	$0.742070\pi$
$654$		0			0
$655$	−8.62450	+	7.91508i	−0.336987	+	0.309268i
$656$		0			0
$657$	6.98114	−	8.90120i	0.272360	−	0.347269i
$658$		0			0
$659$	45.0775			1.75597			0.877986	−	0.478686i	$-0.158887\pi$
$659$	45.0775			1.75597			0.877986	+	0.478686i	$0.158887\pi$
$660$		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
$663$	−58.8893	+	3.54673i	−2.28707	+	0.137744i
$664$		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
$675$	25.8643	−	2.45751i	0.995516	−	0.0945894i
$676$		0			0
$677$	−30.1261	+	30.1261i	−1.15784	+	1.15784i	−0.172903	+	0.984939i	$0.555315\pi$
$677$	−30.1261	+	30.1261i	−1.15784	+	1.15784i	−0.984939	+	0.172903i	$0.944685\pi$
$678$		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	$-0.902040\pi$
$683$	−32.8229	−	32.8229i	−1.25593	−	1.25593i	−0.302917	−	0.953017i	$-0.597960\pi$
$684$		0			0
$685$	0.0374421	+	0.00160598i	0.00143059	+	6.13614e-5i
$686$		0			0
$687$	27.1087	−	1.63268i	1.03426	−	0.0622906i
$688$		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
$693$	14.6171	−	18.6373i	0.555256	−	0.707971i
$694$		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	$-0.634063\pi$
$701$		−	48.3253i		−	1.82522i	0.408830	−	0.912611i	$-0.365937\pi$
$702$		0			0
$703$	13.4413	−	13.4413i	0.506950	−	0.506950i
$704$		0			0
$705$	0.0160304	+	0.927149i	0.000603741	+	0.0349185i
$706$		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
$717$	2.24925	+	37.3462i	0.0839998	+	1.39472i
$718$		0			0
$719$	0.987771			0.0368376			0.0184188	−	0.999830i	$-0.494137\pi$
$719$	0.987771			0.0368376			0.0184188	+	0.999830i	$0.494137\pi$
$720$		0			0
$721$	−42.4525			−1.58101
$722$		0			0
$723$	1.50100	+	24.9224i	0.0558229	+	0.926874i
$724$		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
$735$	40.2065	+	38.8398i	1.48304	+	1.43263i
$736$		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	0.680330	−	0.732906i	$-0.261836\pi$
$743$	−1.43310	−	1.43310i	−0.0525752	−	0.0525752i	−0.732906	+	0.680330i	$0.761836\pi$
$744$		0			0
$745$	−17.4388	−	19.0018i	−0.638906	−	0.696171i
$746$		0			0
$747$	−34.9445	−	27.4067i	−1.27855	−	1.00276i
$748$		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
$753$	14.5846	−	0.878386i	0.531491	−	0.0320101i
$754$		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	$0.0873096\pi$
$761$			14.9443i			0.541729i	−0.962617	+	0.270865i	$0.912690\pi$
$762$		0			0
$763$	0.447350	−	0.447350i	0.0161952	−	0.0161952i
$764$		0			0
$765$	−43.6677	+	3.38852i	−1.57881	+	0.122512i
$766$		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	0.787810	−	0.615919i	$-0.211215\pi$
$773$	4.77906	+	4.77906i	0.171891	+	0.171891i	−0.615919	+	0.787810i	$0.711215\pi$
$774$		0			0
$775$	−4.22770	+	49.1919i	−0.151863	+	1.76703i
$776$		0			0
$777$	76.7545	−	4.62270i	2.75355	−	0.165838i
$778$		0			0
$779$	−22.4910			−0.805822
$780$		0			0
$781$	−3.32394			−0.118940
$782$		0			0
$783$	−1.53865	−	8.43336i	−0.0549869	−	0.301384i
$784$		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
$795$	−3.25188	+	0.0562251i	−0.115332	+	0.00199410i
$796$		0			0
$797$	−7.19505	+	7.19505i	−0.254862	+	0.254862i	−0.822960	−	0.568099i	$-0.807679\pi$
$797$	−7.19505	+	7.19505i	−0.254862	+	0.254862i	0.568099	+	0.822960i	$0.307679\pi$
$798$		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
$807$	1.84291	+	30.5994i	0.0648736	+	1.07715i
$808$		0			0
$809$	−2.45544			−0.0863287			−0.0431643	−	0.999068i	$-0.513744\pi$
$809$	−2.45544			−0.0863287			−0.0431643	+	0.999068i	$0.513744\pi$
$810$		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
$813$	−0.142102	−	2.35944i	−0.00498374	−	0.0827492i
$814$		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	$-0.917323\pi$
$821$		−	14.7177i		−	0.513653i	0.966458	−	0.256826i	$-0.0826768\pi$
$822$		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
$825$	0.377709	−	14.7638i	0.0131502	−	0.514011i
$826$		0			0
$827$	−26.1066	+	26.1066i	−0.907816	+	0.907816i	−0.996096	−	0.0882801i	$-0.971863\pi$
$827$	−26.1066	+	26.1066i	−0.907816	+	0.907816i	0.0882801	+	0.996096i	$0.471863\pi$
$828$		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
$837$	−9.20943	−	50.4770i	−0.318325	−	1.74474i
$838$		0			0
$839$	−37.6219			−1.29885			−0.649427	−	0.760424i	$-0.724991\pi$
$839$	−37.6219			−1.29885			−0.649427	+	0.760424i	$0.724991\pi$
$840$		0			0
$841$	−26.2782			−0.906144
$842$		0			0
$843$	−4.40064	+	0.265038i	−0.151566	+	0.00912839i
$844$		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
$855$	−8.64744	+	10.1024i	−0.295736	+	0.345494i
$856$		0			0
$857$	10.0141	−	10.0141i	0.342074	−	0.342074i	−0.515072	−	0.857147i	$-0.672235\pi$
$857$	10.0141	−	10.0141i	0.342074	−	0.342074i	0.857147	+	0.515072i	$0.172235\pi$
$858$		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	$0.0311472\pi$
$863$	32.1063	+	32.1063i	1.09291	+	1.09291i	0.0976959	+	0.995216i	$0.468853\pi$
$864$		0			0
$865$	0.584164	−	13.6193i	0.0198622	−	0.463070i
$866$		0			0
$867$	44.3120	−	2.66879i	1.50492	−	0.0906367i
$868$		0			0
$869$	−6.30606			−0.213919
$870$		0			0
$871$	26.1399			0.885716
$872$		0			0
$873$	19.6255	+	15.3921i	0.664221	+	0.520944i
$874$		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	$0.316522\pi$
$881$			49.7715i			1.67685i	−0.545020	+	0.838423i	$0.683478\pi$
$882$		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
$885$	−26.0975	+	27.0158i	−0.877257	+	0.908126i
$886$		0			0
$887$	20.1303	−	20.1303i	0.675908	−	0.675908i	−0.283164	−	0.959072i	$-0.591384\pi$
$887$	20.1303	−	20.1303i	0.675908	−	0.675908i	0.959072	+	0.283164i	$0.0913839\pi$
$888$		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
$897$	0.543214	+	9.01943i	0.0181374	+	0.301150i
$898$		0			0
$899$	16.2911			0.543340
$900$		0			0
$901$	5.48291			0.182662
$902$		0			0
$903$	−3.66476	−	60.8489i	−0.121955	−	2.02493i
$904$		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	$0.166428\pi$
$911$			30.1436i			0.998703i	−0.866400	+	0.499351i	$0.833572\pi$
$912$		0			0
$913$	−17.8507	+	17.8507i	−0.590772	+	0.590772i
$914$		0			0
$915$	−4.46915	+	4.62641i	−0.147745	+	0.152944i
$916$		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
$927$	16.9766	−	21.6457i	0.557583	−	0.710938i
$928$		0			0
$929$	−44.4530			−1.45846			−0.729228	−	0.684270i	$-0.760121\pi$
$929$	−44.4530			−1.45846			−0.729228	+	0.684270i	$0.760121\pi$
$930$		0			0
$931$	−28.6131			−0.937758
$932$		0			0
$933$	13.3768	−	0.805643i	0.437935	−	0.0263756i
$934$		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	$0.259585\pi$
$941$			44.6684i			1.45615i	−0.685498	+	0.728075i	$0.740415\pi$
$942$		0			0
$943$	−8.02257	+	8.02257i	−0.261251	+	0.261251i
$944$		0			0
$945$	−53.2836	+	7.37830i	−1.73332	+	0.240016i
$946$		0			0
$947$	−24.5300	+	24.5300i	−0.797118	+	0.797118i	−0.982640	−	0.185522i	$-0.940602\pi$
$947$	−24.5300	+	24.5300i	−0.797118	+	0.797118i	0.185522	+	0.982640i	$0.440602\pi$
$948$		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	0.898271	−	0.439441i	$-0.144823\pi$
$953$	14.1644	+	14.1644i	0.458830	+	0.458830i	−0.439441	+	0.898271i	$0.644823\pi$
$954$		0			0
$955$	−29.0185	+	26.6315i	−0.939016	+	0.861776i
$956$		0			0
$957$	−4.86424	+	0.292959i	−0.157238	+	0.00947002i
$958$		0			0
$959$	−0.0775936			−0.00250563
$960$		0			0
$961$	66.5088			2.14545
$962$		0			0
$963$	6.10274	−	7.78121i	0.196658	−	0.250746i
$964$		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	$-0.806059\pi$
$971$		−	35.6655i		−	1.14456i	0.820058	−	0.572280i	$-0.193941\pi$
$972$		0			0
$973$	−21.9938	+	21.9938i	−0.705089	+	0.705089i
$974$		0			0
$975$	−32.7529	+	31.1188i	−1.04893	+	0.996600i
$976$		0			0
$977$	1.05368	−	1.05368i	0.0337102	−	0.0337102i	−0.690051	−	0.723761i	$-0.742412\pi$
$977$	1.05368	−	1.05368i	0.0337102	−	0.0337102i	0.723761	+	0.690051i	$0.242412\pi$
$978$		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	0.488492	−	0.872569i	$-0.337547\pi$
$983$	−12.0419	−	12.0419i	−0.384077	−	0.384077i	−0.872569	+	0.488492i	$0.837547\pi$
$984$		0			0
$985$	−37.8694	−	1.62431i	−1.20662	−	0.0517548i
$986$		0			0
$987$	−0.115421	−	1.91644i	−0.00367391	−	0.0610009i
$988$		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
$993$	2.21235	+	36.7335i	0.0702069	+	1.16570i
$994$		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.737.19	yes	80
3.2	odd	2	inner	1380.2.r.c.737.1	✓	80
5.3	odd	4	inner	1380.2.r.c.1013.1	yes	80
15.8	even	4	inner	1380.2.r.c.1013.19	yes	80

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

\(f(q)\)	\(=\)	\(q+(0.104128 + 1.72892i) q^{3} +(-1.51193 - 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(-2.97831 + 0.360057i) q^{9} +O(q^{10})\)	\(q+(0.104128 + 1.72892i) q^{3} +(-1.51193 - 1.64744i) q^{5} +(3.27368 + 3.27368i) q^{7} +(-2.97831 + 0.360057i) q^{9} +1.70534i q^{11} +(3.68884 - 3.68884i) q^{13} +(2.69086 - 2.78555i) q^{15} +(-4.61681 + 4.61681i) q^{17} +1.98235i q^{19} +(-5.31904 + 6.00081i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-0.428136 + 4.98164i) q^{25} +(-0.932633 - 5.11177i) q^{27} +1.64979 q^{29} +9.87466 q^{31} +(-2.94839 + 0.177573i) q^{33} +(0.443627 - 10.3428i) q^{35} +(-6.78052 - 6.78052i) q^{37} +(6.76181 + 5.99359i) q^{39} +11.3456i q^{41} +(-5.37542 + 5.37542i) q^{43} +(5.09618 + 4.36222i) q^{45} +(-0.169299 + 0.169299i) q^{47} +14.4340i q^{49} +(-8.46283 - 7.50135i) q^{51} +(-0.593798 - 0.593798i) q^{53} +(2.80945 - 2.57835i) q^{55} +(-3.42731 + 0.206417i) q^{57} -9.69856 q^{59} -1.66086 q^{61} +(-10.9288 - 8.57134i) q^{63} +(-11.6544 - 0.499886i) q^{65} +(3.54310 + 3.54310i) q^{67} +(-1.14890 + 1.29616i) q^{69} +1.94914i q^{71} +(-2.66633 + 2.66633i) q^{73} +(-8.65742 - 0.221486i) q^{75} +(-5.58274 + 5.58274i) q^{77} +3.69783i q^{79} +(8.74072 - 2.14472i) q^{81} +(10.4675 + 10.4675i) q^{83} +(14.5862 + 0.625639i) q^{85} +(0.171789 + 2.85236i) q^{87} -8.35452 q^{89} +24.1522 q^{91} +(1.02823 + 17.0725i) q^{93} +(3.26580 - 2.99717i) q^{95} +(-5.87875 - 5.87875i) q^{97} +(-0.614019 - 5.07904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 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

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