LMFDB - Embedded newform 1148.2.k.b.337.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.3
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +O(q^{10})$	\(q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +(-0.00674500 - 0.00674500i) q^{11} +(-3.61779 - 3.61779i) q^{13} +(-2.64249 + 2.64249i) q^{15} +(-2.98892 + 2.98892i) q^{17} +(3.03265 - 3.03265i) q^{19} +2.68164i q^{21} -6.42985 q^{23} +3.05797 q^{25} +(2.25878 - 2.25878i) q^{27} +(6.04055 + 6.04055i) q^{29} -9.06781 q^{31} +0.0255799i q^{33} +(-0.985400 + 0.985400i) q^{35} -2.92526 q^{37} +13.7202i q^{39} +(-3.12241 - 5.59022i) q^{41} -7.31038i q^{43} +5.84073 q^{45} +(3.23183 - 3.23183i) q^{47} +1.00000i q^{49} +11.3352 q^{51} +(9.80407 + 9.80407i) q^{53} +(-0.00939961 + 0.00939961i) q^{55} -11.5011 q^{57} +8.32596 q^{59} +12.1771i q^{61} +(2.96363 - 2.96363i) q^{63} +(-5.04163 + 5.04163i) q^{65} +(-7.17560 + 7.17560i) q^{67} +(12.1923 + 12.1923i) q^{69} +(-0.0715608 - 0.0715608i) q^{71} +15.1426i q^{73} +(-5.79855 - 5.79855i) q^{75} +0.00953888i q^{77} +(7.11491 + 7.11491i) q^{79} +4.00739 q^{81} +0.354618 q^{83} +(4.16525 + 4.16525i) q^{85} -22.9083i q^{87} +(-2.66353 - 2.66353i) q^{89} +5.11633i q^{91} +(17.1944 + 17.1944i) q^{93} +(-4.22621 - 4.22621i) q^{95} +(3.41973 - 3.41973i) q^{97} +(0.0282697 - 0.0282697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.89621	−	1.89621i	−1.09478	−	1.09478i	−0.995011	−	0.0997652i	$-0.968191\pi$
$3$	−1.89621	−	1.89621i	−1.09478	−	1.09478i	−0.0997652	−	0.995011i	$-0.531809\pi$
$4$		0			0
$5$		−	1.39357i		−	0.623222i	−0.950210	−	0.311611i	$-0.899131\pi$
$5$		−	1.39357i		−	0.623222i	0.950210	−	0.311611i	$-0.100869\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$			4.19121i			1.39707i
$10$		0			0
$11$	−0.00674500	−	0.00674500i	−0.00203370	−	0.00203370i	0.706089	−	0.708123i	$-0.250458\pi$
$11$	−0.00674500	−	0.00674500i	−0.00203370	−	0.00203370i	−0.708123	+	0.706089i	$0.750458\pi$
$12$		0			0
$13$	−3.61779	−	3.61779i	−1.00339	−	1.00339i	−0.999994	−	0.00340044i	$-0.998918\pi$
$13$	−3.61779	−	3.61779i	−1.00339	−	1.00339i	−0.00340044	−	0.999994i	$-0.501082\pi$
$14$		0			0
$15$	−2.64249	+	2.64249i	−0.682289	+	0.682289i
$16$		0			0
$17$	−2.98892	+	2.98892i	−0.724918	+	0.724918i	−0.969603	−	0.244684i	$-0.921316\pi$
$17$	−2.98892	+	2.98892i	−0.724918	+	0.724918i	0.244684	+	0.969603i	$0.421316\pi$
$18$		0			0
$19$	3.03265	−	3.03265i	0.695739	−	0.695739i	−0.267750	−	0.963488i	$-0.586280\pi$
$19$	3.03265	−	3.03265i	0.695739	−	0.695739i	0.963488	+	0.267750i	$0.0862801\pi$
$20$		0			0
$21$			2.68164i			0.585182i
$22$		0			0
$23$	−6.42985			−1.34072			−0.670359	−	0.742037i	$-0.733860\pi$
$23$	−6.42985			−1.34072			−0.670359	+	0.742037i	$0.733860\pi$
$24$		0			0
$25$	3.05797			0.611594
$26$		0			0
$27$	2.25878	−	2.25878i	0.434702	−	0.434702i
$28$		0			0
$29$	6.04055	+	6.04055i	1.12170	+	1.12170i	0.991486	+	0.130216i	$0.0415671\pi$
$29$	6.04055	+	6.04055i	1.12170	+	1.12170i	0.130216	+	0.991486i	$0.458433\pi$
$30$		0			0
$31$	−9.06781			−1.62863			−0.814313	−	0.580426i	$-0.802886\pi$
$31$	−9.06781			−1.62863			−0.814313	+	0.580426i	$0.802886\pi$
$32$		0			0
$33$			0.0255799i			0.00445288i
$34$		0			0
$35$	−0.985400	+	0.985400i	−0.166563	+	0.166563i
$36$		0			0
$37$	−2.92526			−0.480910			−0.240455	−	0.970660i	$-0.577297\pi$
$37$	−2.92526			−0.480910			−0.240455	+	0.970660i	$0.577297\pi$
$38$		0			0
$39$			13.7202i			2.19699i
$40$		0			0
$41$	−3.12241	−	5.59022i	−0.487639	−	0.873045i
$41$	−3.12241	−	5.59022i	−0.487639	−	0.873045i
$42$		0			0
$43$		−	7.31038i		−	1.11482i	−0.830236	−	0.557411i	$-0.811795\pi$
$43$		−	7.31038i		−	1.11482i	0.830236	−	0.557411i	$-0.188205\pi$
$44$		0			0
$45$	5.84073			0.870685
$46$		0			0
$47$	3.23183	−	3.23183i	0.471412	−	0.471412i	−0.430960	−	0.902371i	$-0.641825\pi$
$47$	3.23183	−	3.23183i	0.471412	−	0.471412i	0.902371	+	0.430960i	$0.141825\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	11.3352			1.58725
$52$		0			0
$53$	9.80407	+	9.80407i	1.34669	+	1.34669i	0.889228	+	0.457464i	$0.151242\pi$
$53$	9.80407	+	9.80407i	1.34669	+	1.34669i	0.457464	+	0.889228i	$0.348758\pi$
$54$		0			0
$55$	−0.00939961	+	0.00939961i	−0.00126744	+	0.00126744i
$56$		0			0
$57$	−11.5011			−1.52336
$58$		0			0
$59$	8.32596			1.08395			0.541974	−	0.840396i	$-0.317677\pi$
$59$	8.32596			1.08395			0.541974	+	0.840396i	$0.317677\pi$
$60$		0			0
$61$			12.1771i			1.55911i	0.626333	+	0.779556i	$0.284555\pi$
$61$			12.1771i			1.55911i	−0.626333	+	0.779556i	$0.715445\pi$
$62$		0			0
$63$	2.96363	−	2.96363i	0.373383	−	0.373383i
$64$		0			0
$65$	−5.04163	+	5.04163i	−0.625338	+	0.625338i
$66$		0			0
$67$	−7.17560	+	7.17560i	−0.876639	+	0.876639i	−0.993185	−	0.116546i	$-0.962818\pi$
$67$	−7.17560	+	7.17560i	−0.876639	+	0.876639i	0.116546	+	0.993185i	$0.462818\pi$
$68$		0			0
$69$	12.1923	+	12.1923i	1.46779	+	1.46779i
$70$		0			0
$71$	−0.0715608	−	0.0715608i	−0.00849271	−	0.00849271i	0.702848	−	0.711340i	$-0.251912\pi$
$71$	−0.0715608	−	0.0715608i	−0.00849271	−	0.00849271i	−0.711340	+	0.702848i	$0.751912\pi$
$72$		0			0
$73$			15.1426i			1.77230i	0.463394	+	0.886152i	$0.346632\pi$
$73$			15.1426i			1.77230i	−0.463394	+	0.886152i	$0.653368\pi$
$74$		0			0
$75$	−5.79855	−	5.79855i	−0.669559	−	0.669559i
$76$		0			0
$77$			0.00953888i			0.00108706i
$78$		0			0
$79$	7.11491	+	7.11491i	0.800490	+	0.800490i	0.983172	−	0.182682i	$-0.0584779\pi$
$79$	7.11491	+	7.11491i	0.800490	+	0.800490i	−0.182682	+	0.983172i	$0.558478\pi$
$80$		0			0
$81$	4.00739			0.445266
$82$		0			0
$83$	0.354618			0.0389243			0.0194622	−	0.999811i	$-0.493805\pi$
$83$	0.354618			0.0389243			0.0194622	+	0.999811i	$0.493805\pi$
$84$		0			0
$85$	4.16525	+	4.16525i	0.451785	+	0.451785i
$86$		0			0
$87$		−	22.9083i		−	2.45602i
$88$		0			0
$89$	−2.66353	−	2.66353i	−0.282333	−	0.282333i	0.551706	−	0.834039i	$-0.313977\pi$
$89$	−2.66353	−	2.66353i	−0.282333	−	0.282333i	−0.834039	+	0.551706i	$0.813977\pi$
$90$		0			0
$91$			5.11633i			0.536337i
$92$		0			0
$93$	17.1944	+	17.1944i	1.78298	+	1.78298i
$94$		0			0
$95$	−4.22621	−	4.22621i	−0.433600	−	0.433600i
$96$		0			0
$97$	3.41973	−	3.41973i	0.347221	−	0.347221i	−0.511853	−	0.859073i	$-0.671041\pi$
$97$	3.41973	−	3.41973i	0.347221	−	0.347221i	0.859073	+	0.511853i	$0.171041\pi$
$98$		0			0
$99$	0.0282697	−	0.0282697i	0.00284121	−	0.00284121i
$100$		0			0
$101$	−10.8891	+	10.8891i	−1.08351	+	1.08351i	−0.0873257	+	0.996180i	$0.527832\pi$
$101$	−10.8891	+	10.8891i	−1.08351	+	1.08351i	−0.996180	+	0.0873257i	$0.972168\pi$
$102$		0			0
$103$		−	12.7483i		−	1.25613i	−0.778163	−	0.628063i	$-0.783848\pi$
$103$		−	12.7483i		−	1.25613i	0.778163	−	0.628063i	$-0.216152\pi$
$104$		0			0
$105$	3.73705			0.364699
$106$		0			0
$107$	−11.9150			−1.15187			−0.575936	−	0.817495i	$-0.695362\pi$
$107$	−11.9150			−1.15187			−0.575936	+	0.817495i	$0.695362\pi$
$108$		0			0
$109$	−6.77678	+	6.77678i	−0.649098	+	0.649098i	−0.952775	−	0.303677i	$-0.901785\pi$
$109$	−6.77678	+	6.77678i	−0.649098	+	0.649098i	0.303677	+	0.952775i	$0.401785\pi$
$110$		0			0
$111$	5.54690	+	5.54690i	0.526489	+	0.526489i
$112$		0			0
$113$	−7.61496			−0.716355			−0.358177	−	0.933654i	$-0.616602\pi$
$113$	−7.61496			−0.716355			−0.358177	+	0.933654i	$0.616602\pi$
$114$		0			0
$115$			8.96043i			0.835565i
$116$		0			0
$117$	15.1629	−	15.1629i	1.40181	−	1.40181i
$118$		0			0
$119$	4.22696			0.387485
$120$		0			0
$121$		−	10.9999i		−	0.999992i
$122$		0			0
$123$	−4.67947	+	16.5210i	−0.421934	+	1.48964i
$124$		0			0
$125$		−	11.2293i		−	1.00438i
$126$		0			0
$127$	−17.1559			−1.52234			−0.761171	−	0.648551i	$-0.775375\pi$
$127$	−17.1559			−1.52234			−0.761171	+	0.648551i	$0.775375\pi$
$128$		0			0
$129$	−13.8620	+	13.8620i	−1.22048	+	1.22048i
$130$		0			0
$131$		−	18.2459i		−	1.59416i	−0.603877	−	0.797078i	$-0.706378\pi$
$131$		−	18.2459i		−	1.59416i	0.603877	−	0.797078i	$-0.293622\pi$
$132$		0			0
$133$	−4.28882			−0.371888
$134$		0			0
$135$	−3.14776	−	3.14776i	−0.270916	−	0.270916i
$136$		0			0
$137$	−3.70202	+	3.70202i	−0.316285	+	0.316285i	−0.847338	−	0.531054i	$-0.821796\pi$
$137$	−3.70202	+	3.70202i	−0.316285	+	0.316285i	0.531054	+	0.847338i	$0.321796\pi$
$138$		0			0
$139$	0.532554			0.0451707			0.0225853	−	0.999745i	$-0.492810\pi$
$139$	0.532554			0.0451707			0.0225853	+	0.999745i	$0.492810\pi$
$140$		0			0
$141$	−12.2565			−1.03218
$142$		0			0
$143$			0.0488040i			0.00408120i
$144$		0			0
$145$	8.41791	−	8.41791i	0.699069	−	0.699069i
$146$		0			0
$147$	1.89621	−	1.89621i	0.156397	−	0.156397i
$148$		0			0
$149$	13.3321	−	13.3321i	1.09221	−	1.09221i	0.0969123	−	0.995293i	$-0.469103\pi$
$149$	13.3321	−	13.3321i	1.09221	−	1.09221i	0.995293	−	0.0969123i	$-0.0308966\pi$
$150$		0			0
$151$	1.25214	+	1.25214i	0.101898	+	0.101898i	0.756218	−	0.654320i	$-0.227045\pi$
$151$	1.25214	+	1.25214i	0.101898	+	0.101898i	−0.654320	+	0.756218i	$0.727045\pi$
$152$		0			0
$153$	−12.5272	−	12.5272i	−1.01276	−	1.01276i
$154$		0			0
$155$			12.6366i			1.01500i
$156$		0			0
$157$	−1.93133	−	1.93133i	−0.154137	−	0.154137i	0.625826	−	0.779963i	$-0.284762\pi$
$157$	−1.93133	−	1.93133i	−0.154137	−	0.154137i	−0.779963	+	0.625826i	$0.784762\pi$
$158$		0			0
$159$		−	37.1811i		−	2.94865i
$160$		0			0
$161$	4.54659	+	4.54659i	0.358322	+	0.358322i
$162$		0			0
$163$	−3.13101			−0.245239			−0.122620	−	0.992454i	$-0.539130\pi$
$163$	−3.13101			−0.245239			−0.122620	+	0.992454i	$0.539130\pi$
$164$		0			0
$165$	0.0356472			0.00277513
$166$		0			0
$167$	11.0777	+	11.0777i	0.857217	+	0.857217i	0.991009	−	0.133792i	$-0.0427155\pi$
$167$	11.0777	+	11.0777i	0.857217	+	0.857217i	−0.133792	+	0.991009i	$0.542715\pi$
$168$		0			0
$169$			13.1768i			1.01360i
$170$		0			0
$171$	12.7105	+	12.7105i	0.971995	+	0.971995i
$172$		0			0
$173$			3.43858i			0.261430i	0.991420	+	0.130715i	$0.0417273\pi$
$173$			3.43858i			0.261430i	−0.991420	+	0.130715i	$0.958273\pi$
$174$		0			0
$175$	−2.16231	−	2.16231i	−0.163455	−	0.163455i
$176$		0			0
$177$	−15.7877	−	15.7877i	−1.18668	−	1.18668i
$178$		0			0
$179$	1.39953	−	1.39953i	0.104606	−	0.104606i	−0.652867	−	0.757473i	$-0.726434\pi$
$179$	1.39953	−	1.39953i	0.104606	−	0.104606i	0.757473	+	0.652867i	$0.226434\pi$
$180$		0			0
$181$	−10.6180	+	10.6180i	−0.789232	+	0.789232i	−0.981368	−	0.192136i	$-0.938459\pi$
$181$	−10.6180	+	10.6180i	−0.789232	+	0.789232i	0.192136	+	0.981368i	$0.438459\pi$
$182$		0			0
$183$	23.0902	−	23.0902i	1.70688	−	1.70688i
$184$		0			0
$185$			4.07654i			0.299714i
$186$		0			0
$187$	0.0403205			0.00294853
$188$		0			0
$189$	−3.19440			−0.232358
$190$		0			0
$191$	−5.08849	+	5.08849i	−0.368190	+	0.368190i	−0.866817	−	0.498627i	$-0.833838\pi$
$191$	−5.08849	+	5.08849i	−0.368190	+	0.368190i	0.498627	+	0.866817i	$0.333838\pi$
$192$		0			0
$193$	−18.5213	−	18.5213i	−1.33319	−	1.33319i	−0.902498	−	0.430694i	$-0.858269\pi$
$193$	−18.5213	−	18.5213i	−1.33319	−	1.33319i	−0.430694	−	0.902498i	$-0.641731\pi$
$194$		0			0
$195$	19.1200			1.36921
$196$		0			0
$197$		−	19.5976i		−	1.39627i	−0.715966	−	0.698135i	$-0.754014\pi$
$197$		−	19.5976i		−	1.39627i	0.715966	−	0.698135i	$-0.245986\pi$
$198$		0			0
$199$	−11.9830	+	11.9830i	−0.849450	+	0.849450i	−0.990064	−	0.140614i	$-0.955092\pi$
$199$	−11.9830	+	11.9830i	−0.849450	+	0.849450i	0.140614	+	0.990064i	$0.455092\pi$
$200$		0			0
$201$	27.2129			1.91945
$202$		0			0
$203$		−	8.54263i		−	0.599575i
$204$		0			0
$205$	−7.79034	+	4.35129i	−0.544101	+	0.303907i
$206$		0			0
$207$		−	26.9489i		−	1.87308i
$208$		0			0
$209$	−0.0409105			−0.00282984
$210$		0			0
$211$	−10.7095	+	10.7095i	−0.737271	+	0.737271i	−0.972049	−	0.234778i	$-0.924564\pi$
$211$	−10.7095	+	10.7095i	−0.737271	+	0.737271i	0.234778	+	0.972049i	$0.424564\pi$
$212$		0			0
$213$			0.271388i			0.0185952i
$214$		0			0
$215$	−10.1875			−0.694782
$216$		0			0
$217$	6.41191	+	6.41191i	0.435269	+	0.435269i
$218$		0			0
$219$	28.7135	−	28.7135i	1.94028	−	1.94028i
$220$		0			0
$221$	21.6265			1.45476
$222$		0			0
$223$	1.13400			0.0759381			0.0379691	−	0.999279i	$-0.487911\pi$
$223$	1.13400			0.0759381			0.0379691	+	0.999279i	$0.487911\pi$
$224$		0			0
$225$			12.8166i			0.854440i
$226$		0			0
$227$	0.320841	−	0.320841i	0.0212950	−	0.0212950i	−0.696379	−	0.717674i	$-0.745207\pi$
$227$	0.320841	−	0.320841i	0.0212950	−	0.0212950i	0.717674	+	0.696379i	$0.245207\pi$
$228$		0			0
$229$	−1.15816	+	1.15816i	−0.0765336	+	0.0765336i	−0.744337	−	0.667804i	$-0.767235\pi$
$229$	−1.15816	+	1.15816i	−0.0765336	+	0.0765336i	0.667804	+	0.744337i	$0.267235\pi$
$230$		0			0
$231$	0.0180877	−	0.0180877i	0.00119008	−	0.00119008i
$232$		0			0
$233$	7.26218	+	7.26218i	0.475762	+	0.475762i	0.903773	−	0.428012i	$-0.140786\pi$
$233$	7.26218	+	7.26218i	0.475762	+	0.475762i	−0.428012	+	0.903773i	$0.640786\pi$
$234$		0			0
$235$	−4.50378	−	4.50378i	−0.293794	−	0.293794i
$236$		0			0
$237$		−	26.9827i		−	1.75271i
$238$		0			0
$239$	−13.4710	−	13.4710i	−0.871364	−	0.871364i	0.121257	−	0.992621i	$-0.461307\pi$
$239$	−13.4710	−	13.4710i	−0.871364	−	0.871364i	−0.992621	+	0.121257i	$0.961307\pi$
$240$		0			0
$241$		−	26.7671i		−	1.72422i	−0.506718	−	0.862112i	$-0.669141\pi$
$241$		−	26.7671i		−	1.72422i	0.506718	−	0.862112i	$-0.330859\pi$
$242$		0			0
$243$	−14.3752	−	14.3752i	−0.922169	−	0.922169i
$244$		0			0
$245$	1.39357			0.0890317
$246$		0			0
$247$	−21.9430			−1.39620
$248$		0			0
$249$	−0.672429	−	0.672429i	−0.0426134	−	0.0426134i
$250$		0			0
$251$		−	4.39407i		−	0.277351i	−0.990338	−	0.138676i	$-0.955715\pi$
$251$		−	4.39407i		−	0.277351i	0.990338	−	0.138676i	$-0.0442845\pi$
$252$		0			0
$253$	0.0433694	+	0.0433694i	0.00272661	+	0.00272661i
$254$		0			0
$255$		−	15.7964i		−	0.989207i
$256$		0			0
$257$	−11.0972	−	11.0972i	−0.692225	−	0.692225i	0.270496	−	0.962721i	$-0.412812\pi$
$257$	−11.0972	−	11.0972i	−0.692225	−	0.692225i	−0.962721	+	0.270496i	$0.912812\pi$
$258$		0			0
$259$	2.06847	+	2.06847i	0.128529	+	0.128529i
$260$		0			0
$261$	−25.3172	+	25.3172i	−1.56710	+	1.56710i
$262$		0			0
$263$	−6.60565	+	6.60565i	−0.407322	+	0.407322i	−0.880804	−	0.473482i	$-0.842997\pi$
$263$	−6.60565	+	6.60565i	−0.407322	+	0.407322i	0.473482	+	0.880804i	$0.342997\pi$
$264$		0			0
$265$	13.6626	−	13.6626i	0.839288	−	0.839288i
$266$		0			0
$267$			10.1012i			0.618184i
$268$		0			0
$269$	18.7014			1.14025			0.570123	−	0.821560i	$-0.306896\pi$
$269$	18.7014			1.14025			0.570123	+	0.821560i	$0.306896\pi$
$270$		0			0
$271$	−15.7181			−0.954804			−0.477402	−	0.878685i	$-0.658421\pi$
$271$	−15.7181			−0.954804			−0.477402	+	0.878685i	$0.658421\pi$
$272$		0			0
$273$	9.70162	−	9.70162i	0.587169	−	0.587169i
$274$		0			0
$275$	−0.0206260	−	0.0206260i	−0.00124380	−	0.00124380i
$276$		0			0
$277$	−29.2099			−1.75505			−0.877526	−	0.479529i	$-0.840808\pi$
$277$	−29.2099			−1.75505			−0.877526	+	0.479529i	$0.840808\pi$
$278$		0			0
$279$		−	38.0051i		−	2.27530i
$280$		0			0
$281$	0.718430	−	0.718430i	0.0428579	−	0.0428579i	−0.685353	−	0.728211i	$-0.740352\pi$
$281$	0.718430	−	0.718430i	0.0428579	−	0.0428579i	0.728211	+	0.685353i	$0.240352\pi$
$282$		0			0
$283$	−12.0991			−0.719218			−0.359609	−	0.933103i	$-0.617090\pi$
$283$	−12.0991			−0.719218			−0.359609	+	0.933103i	$0.617090\pi$
$284$		0			0
$285$			16.0275i			0.949389i
$286$		0			0
$287$	−1.74500	+	6.16076i	−0.103004	+	0.363658i
$288$		0			0
$289$		−	0.867231i		−	0.0510136i
$290$		0			0
$291$	−12.9690			−0.760258
$292$		0			0
$293$	−0.807697	+	0.807697i	−0.0471861	+	0.0471861i	−0.730306	−	0.683120i	$-0.760623\pi$
$293$	−0.807697	+	0.807697i	−0.0471861	+	0.0471861i	0.683120	+	0.730306i	$0.260623\pi$
$294$		0			0
$295$		−	11.6028i		−	0.675540i
$296$		0			0
$297$	−0.0304710			−0.00176810
$298$		0			0
$299$	23.2619	+	23.2619i	1.34527	+	1.34527i
$300$		0			0
$301$	−5.16922	+	5.16922i	−0.297949	+	0.297949i
$302$		0			0
$303$	41.2960			2.37239
$304$		0			0
$305$	16.9695			0.971673
$306$		0			0
$307$			0.961340i			0.0548666i	0.999624	+	0.0274333i	$0.00873338\pi$
$307$			0.961340i			0.0548666i	−0.999624	+	0.0274333i	$0.991267\pi$
$308$		0			0
$309$	−24.1734	+	24.1734i	−1.37518	+	1.37518i
$310$		0			0
$311$	−23.9158	+	23.9158i	−1.35614	+	1.35614i	−0.477516	+	0.878623i	$0.658463\pi$
$311$	−23.9158	+	23.9158i	−1.35614	+	1.35614i	−0.878623	+	0.477516i	$0.841537\pi$
$312$		0			0
$313$	2.11859	−	2.11859i	0.119750	−	0.119750i	−0.644692	−	0.764442i	$-0.723015\pi$
$313$	2.11859	−	2.11859i	0.119750	−	0.119750i	0.764442	+	0.644692i	$0.223015\pi$
$314$		0			0
$315$	−4.13002	−	4.13002i	−0.232700	−	0.232700i
$316$		0			0
$317$	14.0222	+	14.0222i	0.787566	+	0.787566i	0.981095	−	0.193528i	$-0.0619931\pi$
$317$	14.0222	+	14.0222i	0.787566	+	0.787566i	−0.193528	+	0.981095i	$0.561993\pi$
$318$		0			0
$319$		−	0.0814871i		−	0.00456240i
$320$		0			0
$321$	22.5934	+	22.5934i	1.26104	+	1.26104i
$322$		0			0
$323$			18.1287i			1.00871i
$324$		0			0
$325$	−11.0631	−	11.0631i	−0.613671	−	0.613671i
$326$		0			0
$327$	25.7004			1.42123
$328$		0			0
$329$	−4.57050			−0.251980
$330$		0			0
$331$	−13.7087	−	13.7087i	−0.753498	−	0.753498i	0.221632	−	0.975130i	$-0.428862\pi$
$331$	−13.7087	−	13.7087i	−0.753498	−	0.753498i	−0.975130	+	0.221632i	$0.928862\pi$
$332$		0			0
$333$		−	12.2604i		−	0.671865i
$334$		0			0
$335$	9.99968	+	9.99968i	0.546341	+	0.546341i
$336$		0			0
$337$			13.5539i			0.738328i	0.929364	+	0.369164i	$0.120356\pi$
$337$			13.5539i			0.738328i	−0.929364	+	0.369164i	$0.879644\pi$
$338$		0			0
$339$	14.4395	+	14.4395i	0.784248	+	0.784248i
$340$		0			0
$341$	0.0611624	+	0.0611624i	0.00331213	+	0.00331213i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	16.9908	−	16.9908i	0.914756	−	0.914756i
$346$		0			0
$347$	10.3180	−	10.3180i	0.553901	−	0.553901i	−0.373663	−	0.927564i	$-0.621898\pi$
$347$	10.3180	−	10.3180i	0.553901	−	0.553901i	0.927564	+	0.373663i	$0.121898\pi$
$348$		0			0
$349$		−	9.62802i		−	0.515376i	−0.966228	−	0.257688i	$-0.917039\pi$
$349$		−	9.62802i		−	0.515376i	0.966228	−	0.257688i	$-0.0829607\pi$
$350$		0			0
$351$	−16.3436			−0.872356
$352$		0			0
$353$	−0.263588			−0.0140293			−0.00701467	−	0.999975i	$-0.502233\pi$
$353$	−0.263588			−0.0140293			−0.00701467	+	0.999975i	$0.502233\pi$
$354$		0			0
$355$	−0.0997248	+	0.0997248i	−0.00529284	+	0.00529284i
$356$		0			0
$357$	−8.01520	−	8.01520i	−0.424210	−	0.424210i
$358$		0			0
$359$	21.8699			1.15425			0.577125	−	0.816656i	$-0.304175\pi$
$359$	21.8699			1.15425			0.577125	+	0.816656i	$0.304175\pi$
$360$		0			0
$361$			0.606016i			0.0318956i
$362$		0			0
$363$	−20.8581	+	20.8581i	−1.09477	+	1.09477i
$364$		0			0
$365$	21.1022			1.10454
$366$		0			0
$367$		−	5.62891i		−	0.293827i	−0.989149	−	0.146913i	$-0.953066\pi$
$367$		−	5.62891i		−	0.293827i	0.989149	−	0.146913i	$-0.0469339\pi$
$368$		0			0
$369$	23.4298	−	13.0867i	1.21971	−	0.681265i
$370$		0			0
$371$		−	13.8650i		−	0.719837i
$372$		0			0
$373$	−26.6675			−1.38079			−0.690396	−	0.723432i	$-0.742564\pi$
$373$	−26.6675			−1.38079			−0.690396	+	0.723432i	$0.742564\pi$
$374$		0			0
$375$	−21.2931	+	21.2931i	−1.09957	+	1.09957i
$376$		0			0
$377$		−	43.7069i		−	2.25102i
$378$		0			0
$379$	26.5049			1.36147			0.680733	−	0.732531i	$-0.261661\pi$
$379$	26.5049			1.36147			0.680733	+	0.732531i	$0.261661\pi$
$380$		0			0
$381$	32.5312	+	32.5312i	1.66662	+	1.66662i
$382$		0			0
$383$	−9.81104	+	9.81104i	−0.501321	+	0.501321i	−0.911848	−	0.410528i	$-0.865345\pi$
$383$	−9.81104	+	9.81104i	−0.501321	+	0.501321i	0.410528	+	0.911848i	$0.365345\pi$
$384$		0			0
$385$	0.0132931			0.000677477
$386$		0			0
$387$	30.6393			1.55749
$388$		0			0
$389$		−	21.2251i		−	1.07616i	−0.842895	−	0.538078i	$-0.819151\pi$
$389$		−	21.2251i		−	1.07616i	0.842895	−	0.538078i	$-0.180849\pi$
$390$		0			0
$391$	19.2183	−	19.2183i	0.971911	−	0.971911i
$392$		0			0
$393$	−34.5981	+	34.5981i	−1.74524	+	1.74524i
$394$		0			0
$395$	9.91510	−	9.91510i	0.498883	−	0.498883i
$396$		0			0
$397$	17.9977	+	17.9977i	0.903280	+	0.903280i	0.995718	−	0.0924383i	$-0.0294661\pi$
$397$	17.9977	+	17.9977i	0.903280	+	0.903280i	−0.0924383	+	0.995718i	$0.529466\pi$
$398$		0			0
$399$	8.13250	+	8.13250i	0.407134	+	0.407134i
$400$		0			0
$401$		−	1.49738i		−	0.0747756i	−0.999301	−	0.0373878i	$-0.988096\pi$
$401$		−	1.49738i		−	0.0747756i	0.999301	−	0.0373878i	$-0.0119037\pi$
$402$		0			0
$403$	32.8054	+	32.8054i	1.63415	+	1.63415i
$404$		0			0
$405$		−	5.58457i		−	0.277499i
$406$		0			0
$407$	0.0197309	+	0.0197309i	0.000978024	+	0.000978024i
$408$		0			0
$409$	−1.12242			−0.0554999			−0.0277500	−	0.999615i	$-0.508834\pi$
$409$	−1.12242			−0.0554999			−0.0277500	+	0.999615i	$0.508834\pi$
$410$		0			0
$411$	14.0396			0.692522
$412$		0			0
$413$	−5.88734	−	5.88734i	−0.289697	−	0.289697i
$414$		0			0
$415$		−	0.494183i		−	0.0242585i
$416$		0			0
$417$	−1.00983	−	1.00983i	−0.0494518	−	0.0494518i
$418$		0			0
$419$			1.10985i			0.0542197i	0.999632	+	0.0271098i	$0.00863039\pi$
$419$			1.10985i			0.0542197i	−0.999632	+	0.0271098i	$0.991370\pi$
$420$		0			0
$421$	−17.8911	−	17.8911i	−0.871961	−	0.871961i	0.120725	−	0.992686i	$-0.461478\pi$
$421$	−17.8911	−	17.8911i	−0.871961	−	0.871961i	−0.992686	+	0.120725i	$0.961478\pi$
$422$		0			0
$423$	13.5453	+	13.5453i	0.658595	+	0.658595i
$424$		0			0
$425$	−9.14002	+	9.14002i	−0.443356	+	0.443356i
$426$		0			0
$427$	8.61048	−	8.61048i	0.416690	−	0.416690i
$428$		0			0
$429$	0.0925426	−	0.0925426i	0.00446800	−	0.00446800i
$430$		0			0
$431$			24.2929i			1.17015i	0.810980	+	0.585074i	$0.198934\pi$
$431$			24.2929i			1.17015i	−0.810980	+	0.585074i	$0.801066\pi$
$432$		0			0
$433$	−27.6018			−1.32646			−0.663229	−	0.748417i	$-0.730814\pi$
$433$	−27.6018			−1.32646			−0.663229	+	0.748417i	$0.730814\pi$
$434$		0			0
$435$	−31.9242			−1.53065
$436$		0			0
$437$	−19.4995	+	19.4995i	−0.932789	+	0.932789i
$438$		0			0
$439$	8.39852	+	8.39852i	0.400839	+	0.400839i	0.878529	−	0.477689i	$-0.158526\pi$
$439$	8.39852	+	8.39852i	0.400839	+	0.400839i	−0.477689	+	0.878529i	$0.658526\pi$
$440$		0			0
$441$	−4.19121			−0.199581
$442$		0			0
$443$			9.52893i			0.452733i	0.974042	+	0.226367i	$0.0726848\pi$
$443$			9.52893i			0.452733i	−0.974042	+	0.226367i	$0.927315\pi$
$444$		0			0
$445$	−3.71180	+	3.71180i	−0.175956	+	0.175956i
$446$		0			0
$447$	−50.5607			−2.39144
$448$		0			0
$449$			9.07784i			0.428410i	0.976789	+	0.214205i	$0.0687160\pi$
$449$			9.07784i			0.428410i	−0.976789	+	0.214205i	$0.931284\pi$
$450$		0			0
$451$	−0.0166454	+	0.0587667i	−0.000783800	+	0.00276722i
$452$		0			0
$453$		−	4.74863i		−	0.223110i
$454$		0			0
$455$	7.12995			0.334257
$456$		0			0
$457$	−8.30624	+	8.30624i	−0.388550	+	0.388550i	−0.874170	−	0.485620i	$-0.838594\pi$
$457$	−8.30624	+	8.30624i	−0.388550	+	0.388550i	0.485620	+	0.874170i	$0.338594\pi$
$458$		0			0
$459$			13.5026i			0.630248i
$460$		0			0
$461$	20.0754			0.935004			0.467502	−	0.883992i	$-0.345154\pi$
$461$	20.0754			0.935004			0.467502	+	0.883992i	$0.345154\pi$
$462$		0			0
$463$	−9.44582	−	9.44582i	−0.438985	−	0.438985i	0.452686	−	0.891670i	$-0.350466\pi$
$463$	−9.44582	−	9.44582i	−0.438985	−	0.438985i	−0.891670	+	0.452686i	$0.850466\pi$
$464$		0			0
$465$	23.9616	−	23.9616i	1.11119	−	1.11119i
$466$		0			0
$467$	−29.8969			−1.38346			−0.691731	−	0.722155i	$-0.743152\pi$
$467$	−29.8969			−1.38346			−0.691731	+	0.722155i	$0.743152\pi$
$468$		0			0
$469$	10.1478			0.468583
$470$		0			0
$471$			7.32440i			0.337491i
$472$		0			0
$473$	−0.0493086	+	0.0493086i	−0.00226721	+	0.00226721i
$474$		0			0
$475$	9.27377	−	9.27377i	0.425510	−	0.425510i
$476$		0			0
$477$	−41.0909	+	41.0909i	−1.88142	+	1.88142i
$478$		0			0
$479$	−14.1130	−	14.1130i	−0.644838	−	0.644838i	0.306903	−	0.951741i	$-0.400707\pi$
$479$	−14.1130	−	14.1130i	−0.644838	−	0.644838i	−0.951741	+	0.306903i	$0.900707\pi$
$480$		0			0
$481$	10.5830	+	10.5830i	0.482542	+	0.482542i
$482$		0			0
$483$		−	17.2426i		−	0.784564i
$484$		0			0
$485$	−4.76562	−	4.76562i	−0.216395	−	0.216395i
$486$		0			0
$487$		−	5.15444i		−	0.233570i	−0.993157	−	0.116785i	$-0.962741\pi$
$487$		−	5.15444i		−	0.233570i	0.993157	−	0.116785i	$-0.0372588\pi$
$488$		0			0
$489$	5.93704	+	5.93704i	0.268482	+	0.268482i
$490$		0			0
$491$	−14.9946			−0.676698			−0.338349	−	0.941021i	$-0.609868\pi$
$491$	−14.9946			−0.676698			−0.338349	+	0.941021i	$0.609868\pi$
$492$		0			0
$493$	−36.1094			−1.62628
$494$		0			0
$495$	−0.0393957	−	0.0393957i	−0.00177071	−	0.00177071i
$496$		0			0
$497$			0.101202i			0.00453954i
$498$		0			0
$499$	−13.6146	−	13.6146i	−0.609473	−	0.609473i	0.333335	−	0.942808i	$-0.391826\pi$
$499$	−13.6146	−	13.6146i	−0.609473	−	0.609473i	−0.942808	+	0.333335i	$0.891826\pi$
$500$		0			0
$501$		−	42.0112i		−	1.87692i
$502$		0			0
$503$	11.4796	+	11.4796i	0.511851	+	0.511851i	0.915093	−	0.403242i	$-0.132117\pi$
$503$	11.4796	+	11.4796i	0.511851	+	0.511851i	−0.403242	+	0.915093i	$0.632117\pi$
$504$		0			0
$505$	15.1747	+	15.1747i	0.675264	+	0.675264i
$506$		0			0
$507$	24.9860	−	24.9860i	1.10967	−	1.10967i
$508$		0			0
$509$	−26.6021	+	26.6021i	−1.17912	+	1.17912i	−0.199147	+	0.979970i	$0.563817\pi$
$509$	−26.6021	+	26.6021i	−1.17912	+	1.17912i	−0.979970	+	0.199147i	$0.936183\pi$
$510$		0			0
$511$	10.7074	−	10.7074i	0.473668	−	0.473668i
$512$		0			0
$513$		−	13.7002i		−	0.604879i
$514$		0			0
$515$	−17.7656			−0.782845
$516$		0			0
$517$	−0.0435975			−0.00191742
$518$		0			0
$519$	6.52026	−	6.52026i	0.286208	−	0.286208i
$520$		0			0
$521$	−12.6539	−	12.6539i	−0.554377	−	0.554377i	0.373324	−	0.927701i	$-0.378218\pi$
$521$	−12.6539	−	12.6539i	−0.554377	−	0.554377i	−0.927701	+	0.373324i	$0.878218\pi$
$522$		0			0
$523$	29.1074			1.27278			0.636389	−	0.771368i	$-0.280427\pi$
$523$	29.1074			1.27278			0.636389	+	0.771368i	$0.280427\pi$
$524$		0			0
$525$			8.20039i			0.357894i
$526$		0			0
$527$	27.1029	−	27.1029i	1.18062	−	1.18062i
$528$		0			0
$529$	18.3430			0.797523
$530$		0			0
$531$			34.8958i			1.51435i
$532$		0			0
$533$	−8.92801	+	31.5205i	−0.386715	+	1.36530i
$534$		0			0
$535$			16.6044i			0.717871i
$536$		0			0
$537$	−5.30760			−0.229040
$538$		0			0
$539$	0.00674500	−	0.00674500i	0.000290528	−	0.000290528i
$540$		0			0
$541$		−	36.5818i		−	1.57278i	−0.617733	−	0.786388i	$-0.711949\pi$
$541$		−	36.5818i		−	1.57278i	0.617733	−	0.786388i	$-0.288051\pi$
$542$		0			0
$543$	40.2680			1.72807
$544$		0			0
$545$	9.44389	+	9.44389i	0.404532	+	0.404532i
$546$		0			0
$547$	18.3817	−	18.3817i	0.785944	−	0.785944i	−0.194883	−	0.980827i	$-0.562433\pi$
$547$	18.3817	−	18.3817i	0.785944	−	0.785944i	0.980827	+	0.194883i	$0.0624327\pi$
$548$		0			0
$549$	−51.0366			−2.17819
$550$		0			0
$551$	36.6378			1.56082
$552$		0			0
$553$		−	10.0620i		−	0.427880i
$554$		0			0
$555$	7.72998	−	7.72998i	0.328119	−	0.328119i
$556$		0			0
$557$	13.9573	−	13.9573i	0.591390	−	0.591390i	−0.346617	−	0.938007i	$-0.612670\pi$
$557$	13.9573	−	13.9573i	0.591390	−	0.591390i	0.938007	+	0.346617i	$0.112670\pi$
$558$		0			0
$559$	−26.4474	+	26.4474i	−1.11861	+	1.11861i
$560$		0			0
$561$	−0.0764560	−	0.0764560i	−0.00322798	−	0.00322798i
$562$		0			0
$563$	1.09376	+	1.09376i	0.0460966	+	0.0460966i	0.729779	−	0.683683i	$-0.239623\pi$
$563$	1.09376	+	1.09376i	0.0460966	+	0.0460966i	−0.683683	+	0.729779i	$0.739623\pi$
$564$		0			0
$565$			10.6120i			0.446448i
$566$		0			0
$567$	−2.83365	−	2.83365i	−0.119002	−	0.119002i
$568$		0			0
$569$		−	1.32617i		−	0.0555959i	−0.999614	−	0.0277980i	$-0.991150\pi$
$569$		−	1.32617i		−	0.0555959i	0.999614	−	0.0277980i	$-0.00884951\pi$
$570$		0			0
$571$	16.4221	+	16.4221i	0.687244	+	0.687244i	0.961622	−	0.274378i	$-0.0884720\pi$
$571$	16.4221	+	16.4221i	0.687244	+	0.687244i	−0.274378	+	0.961622i	$0.588472\pi$
$572$		0			0
$573$	19.2977			0.806171
$574$		0			0
$575$	−19.6623			−0.819975
$576$		0			0
$577$	−29.2600	−	29.2600i	−1.21811	−	1.21811i	−0.968294	−	0.249815i	$-0.919630\pi$
$577$	−29.2600	−	29.2600i	−1.21811	−	1.21811i	−0.249815	−	0.968294i	$-0.580370\pi$
$578$		0			0
$579$			70.2405i			2.91909i
$580$		0			0
$581$	−0.250752	−	0.250752i	−0.0104030	−	0.0104030i
$582$		0			0
$583$		−	0.132257i		−	0.00547752i
$584$		0			0
$585$	−21.1305	−	21.1305i	−0.873640	−	0.873640i
$586$		0			0
$587$	18.1193	+	18.1193i	0.747863	+	0.747863i	0.974078	−	0.226214i	$-0.0726350\pi$
$587$	18.1193	+	18.1193i	0.747863	+	0.747863i	−0.226214	+	0.974078i	$0.572635\pi$
$588$		0			0
$589$	−27.4995	+	27.4995i	−1.13310	+	1.13310i
$590$		0			0
$591$	−37.1611	+	37.1611i	−1.52860	+	1.52860i
$592$		0			0
$593$	6.80967	−	6.80967i	0.279640	−	0.279640i	−0.553325	−	0.832965i	$-0.686641\pi$
$593$	6.80967	−	6.80967i	0.279640	−	0.279640i	0.832965	+	0.553325i	$0.186641\pi$
$594$		0			0
$595$		−	5.89056i		−	0.241489i
$596$		0			0
$597$	45.4444			1.85992
$598$		0			0
$599$	−35.5213			−1.45136			−0.725680	−	0.688032i	$-0.758475\pi$
$599$	−35.5213			−1.45136			−0.725680	+	0.688032i	$0.758475\pi$
$600$		0			0
$601$	−17.3178	+	17.3178i	−0.706408	+	0.706408i	−0.965778	−	0.259370i	$-0.916485\pi$
$601$	−17.3178	+	17.3178i	−0.706408	+	0.706408i	0.259370	+	0.965778i	$0.416485\pi$
$602$		0			0
$603$	−30.0744	−	30.0744i	−1.22473	−	1.22473i
$604$		0			0
$605$	−15.3291			−0.623217
$606$		0			0
$607$			1.58614i			0.0643795i	0.999482	+	0.0321897i	$0.0102481\pi$
$607$			1.58614i			0.0643795i	−0.999482	+	0.0321897i	$0.989752\pi$
$608$		0			0
$609$	−16.1986	+	16.1986i	−0.656400	+	0.656400i
$610$		0			0
$611$	−23.3842			−0.946024
$612$		0			0
$613$		−	5.57022i		−	0.224979i	−0.993653	−	0.112489i	$-0.964118\pi$
$613$		−	5.57022i		−	0.224979i	0.993653	−	0.112489i	$-0.0358825\pi$
$614$		0			0
$615$	23.0231	+	6.52116i	0.928379	+	0.262959i
$616$		0			0
$617$		−	17.3638i		−	0.699039i	−0.936929	−	0.349520i	$-0.886345\pi$
$617$		−	17.3638i		−	0.699039i	0.936929	−	0.349520i	$-0.113655\pi$
$618$		0			0
$619$	8.25046			0.331614			0.165807	−	0.986158i	$-0.446977\pi$
$619$	8.25046			0.331614			0.165807	+	0.986158i	$0.446977\pi$
$620$		0			0
$621$	−14.5236	+	14.5236i	−0.582813	+	0.582813i
$622$		0			0
$623$			3.76680i			0.150914i
$624$		0			0
$625$	−0.358948			−0.0143579
$626$		0			0
$627$	0.0775749	+	0.0775749i	0.00309804	+	0.00309804i
$628$		0			0
$629$	8.74336	−	8.74336i	0.348620	−	0.348620i
$630$		0			0
$631$	−8.58953			−0.341944			−0.170972	−	0.985276i	$-0.554691\pi$
$631$	−8.58953			−0.341944			−0.170972	+	0.985276i	$0.554691\pi$
$632$		0			0
$633$	40.6148			1.61429
$634$		0			0
$635$			23.9079i			0.948757i
$636$		0			0
$637$	3.61779	−	3.61779i	0.143342	−	0.143342i
$638$		0			0
$639$	0.299926	−	0.299926i	0.0118649	−	0.0118649i
$640$		0			0
$641$	12.8597	−	12.8597i	0.507928	−	0.507928i	−0.405962	−	0.913890i	$-0.633063\pi$
$641$	12.8597	−	12.8597i	0.507928	−	0.507928i	0.913890	+	0.405962i	$0.133063\pi$
$642$		0			0
$643$	11.1854	+	11.1854i	0.441109	+	0.441109i	0.892385	−	0.451276i	$-0.149031\pi$
$643$	11.1854	+	11.1854i	0.441109	+	0.441109i	−0.451276	+	0.892385i	$0.649031\pi$
$644$		0			0
$645$	19.3176	+	19.3176i	0.760631	+	0.760631i
$646$		0			0
$647$		−	16.0824i		−	0.632262i	−0.948715	−	0.316131i	$-0.897616\pi$
$647$		−	16.0824i		−	0.632262i	0.948715	−	0.316131i	$-0.102384\pi$
$648$		0			0
$649$	−0.0561586	−	0.0561586i	−0.00220442	−	0.00220442i
$650$		0			0
$651$		−	24.3166i		−	0.953043i
$652$		0			0
$653$	30.4749	+	30.4749i	1.19257	+	1.19257i	0.976342	+	0.216232i	$0.0693767\pi$
$653$	30.4749	+	30.4749i	1.19257	+	1.19257i	0.216232	+	0.976342i	$0.430623\pi$
$654$		0			0
$655$	−25.4269			−0.993513
$656$		0			0
$657$	−63.4657			−2.47603
$658$		0			0
$659$	28.5379	+	28.5379i	1.11168	+	1.11168i	0.992923	+	0.118757i	$0.0378910\pi$
$659$	28.5379	+	28.5379i	1.11168	+	1.11168i	0.118757	+	0.992923i	$0.462109\pi$
$660$		0			0
$661$			37.6558i			1.46464i	0.680960	+	0.732321i	$0.261563\pi$
$661$			37.6558i			1.46464i	−0.680960	+	0.732321i	$0.738437\pi$
$662$		0			0
$663$	−41.0084	−	41.0084i	−1.59264	−	1.59264i
$664$		0			0
$665$			5.97676i			0.231769i
$666$		0			0
$667$	−38.8399	−	38.8399i	−1.50389	−	1.50389i
$668$		0			0
$669$	−2.15030	−	2.15030i	−0.0831353	−	0.0831353i
$670$		0			0
$671$	0.0821343	−	0.0821343i	0.00317076	−	0.00317076i
$672$		0			0
$673$	11.5798	−	11.5798i	0.446367	−	0.446367i	−0.447778	−	0.894145i	$-0.647784\pi$
$673$	11.5798	−	11.5798i	0.446367	−	0.446367i	0.894145	+	0.447778i	$0.147784\pi$
$674$		0			0
$675$	6.90729	−	6.90729i	0.265862	−	0.265862i
$676$		0			0
$677$		−	28.7742i		−	1.10588i	−0.833220	−	0.552941i	$-0.813506\pi$
$677$		−	28.7742i		−	1.10588i	0.833220	−	0.552941i	$-0.186494\pi$
$678$		0			0
$679$	−4.83622			−0.185597
$680$		0			0
$681$	−1.21676			−0.0466264
$682$		0			0
$683$	13.3405	−	13.3405i	0.510461	−	0.510461i	−0.404207	−	0.914668i	$-0.632452\pi$
$683$	13.3405	−	13.3405i	0.510461	−	0.510461i	0.914668	+	0.404207i	$0.132452\pi$
$684$		0			0
$685$	5.15901	+	5.15901i	0.197116	+	0.197116i
$686$		0			0
$687$	4.39224			0.167574
$688$		0			0
$689$		−	70.9381i		−	2.70253i
$690$		0			0
$691$	−10.8623	+	10.8623i	−0.413223	+	0.413223i	−0.882860	−	0.469637i	$-0.844385\pi$
$691$	−10.8623	+	10.8623i	−0.413223	+	0.413223i	0.469637	+	0.882860i	$0.344385\pi$
$692$		0			0
$693$	−0.0399794			−0.00151869
$694$		0			0
$695$		−	0.742150i		−	0.0281514i
$696$		0			0
$697$	26.0413	+	7.37607i	0.986385	+	0.279388i
$698$		0			0
$699$		−	27.5412i		−	1.04170i
$700$		0			0
$701$	38.5490			1.45597			0.727987	−	0.685590i	$-0.240456\pi$
$701$	38.5490			1.45597			0.727987	+	0.685590i	$0.240456\pi$
$702$		0			0
$703$	−8.87130	+	8.87130i	−0.334588	+	0.334588i
$704$		0			0
$705$			17.0802i			0.643277i
$706$		0			0
$707$	15.3995			0.579158
$708$		0			0
$709$	−5.66884	−	5.66884i	−0.212898	−	0.212898i	0.592599	−	0.805497i	$-0.298102\pi$
$709$	−5.66884	−	5.66884i	−0.212898	−	0.212898i	−0.805497	+	0.592599i	$0.798102\pi$
$710$		0			0
$711$	−29.8201	+	29.8201i	−1.11834	+	1.11834i
$712$		0			0
$713$	58.3047			2.18353
$714$		0			0
$715$	0.0680117			0.00254349
$716$		0			0
$717$			51.0875i			1.90790i
$718$		0			0
$719$	−4.13342	+	4.13342i	−0.154151	+	0.154151i	−0.779969	−	0.625818i	$-0.784765\pi$
$719$	−4.13342	+	4.13342i	−0.154151	+	0.154151i	0.625818	+	0.779969i	$0.284765\pi$
$720$		0			0
$721$	−9.01439	+	9.01439i	−0.335714	+	0.335714i
$722$		0			0
$723$	−50.7561	+	50.7561i	−1.88764	+	1.88764i
$724$		0			0
$725$	18.4718	+	18.4718i	0.686027	+	0.686027i
$726$		0			0
$727$	−22.2792	−	22.2792i	−0.826290	−	0.826290i	0.160711	−	0.987001i	$-0.448621\pi$
$727$	−22.2792	−	22.2792i	−0.826290	−	0.826290i	−0.987001	+	0.160711i	$0.948621\pi$
$728$		0			0
$729$			42.4945i			1.57387i
$730$		0			0
$731$	21.8501	+	21.8501i	0.808156	+	0.808156i
$732$		0			0
$733$			2.65116i			0.0979227i	0.998801	+	0.0489613i	$0.0155911\pi$
$733$			2.65116i			0.0979227i	−0.998801	+	0.0489613i	$0.984409\pi$
$734$		0			0
$735$	−2.64249	−	2.64249i	−0.0974698	−	0.0974698i
$736$		0			0
$737$	0.0967989			0.00356563
$738$		0			0
$739$	−21.0698			−0.775063			−0.387532	−	0.921856i	$-0.626672\pi$
$739$	−21.0698			−0.775063			−0.387532	+	0.921856i	$0.626672\pi$
$740$		0			0
$741$	41.6085	+	41.6085i	1.52853	+	1.52853i
$742$		0			0
$743$		−	3.45220i		−	0.126649i	−0.997993	−	0.0633244i	$-0.979830\pi$
$743$		−	3.45220i		−	0.126649i	0.997993	−	0.0633244i	$-0.0201703\pi$
$744$		0			0
$745$	−18.5791	−	18.5791i	−0.680686	−	0.680686i
$746$		0			0
$747$			1.48628i			0.0543800i
$748$		0			0
$749$	8.42521	+	8.42521i	0.307851	+	0.307851i
$750$		0			0
$751$	−7.25122	−	7.25122i	−0.264601	−	0.264601i	0.562319	−	0.826920i	$-0.309909\pi$
$751$	−7.25122	−	7.25122i	−0.264601	−	0.264601i	−0.826920	+	0.562319i	$0.809909\pi$
$752$		0			0
$753$	−8.33206	+	8.33206i	−0.303637	+	0.303637i
$754$		0			0
$755$	1.74494	−	1.74494i	0.0635048	−	0.0635048i
$756$		0			0
$757$	30.8552	−	30.8552i	1.12145	−	1.12145i	0.129930	−	0.991523i	$-0.458525\pi$
$757$	30.8552	−	30.8552i	1.12145	−	1.12145i	0.991523	−	0.129930i	$-0.0414752\pi$
$758$		0			0
$759$		−	0.164475i		−	0.00597006i
$760$		0			0
$761$	37.6284			1.36403			0.682015	−	0.731338i	$-0.261104\pi$
$761$	37.6284			1.36403			0.682015	+	0.731338i	$0.261104\pi$
$762$		0			0
$763$	9.58381			0.346957
$764$		0			0
$765$	−17.4574	+	17.4574i	−0.631175	+	0.631175i
$766$		0			0
$767$	−30.1216	−	30.1216i	−1.08763	−	1.08763i
$768$		0			0
$769$	−41.8990			−1.51092			−0.755459	−	0.655196i	$-0.772586\pi$
$769$	−41.8990			−1.51092			−0.755459	+	0.655196i	$0.772586\pi$
$770$		0			0
$771$			42.0852i			1.51566i
$772$		0			0
$773$	35.1673	−	35.1673i	1.26488	−	1.26488i	0.316180	−	0.948699i	$-0.397600\pi$
$773$	35.1673	−	35.1673i	1.26488	−	1.26488i	0.948699	−	0.316180i	$-0.102400\pi$
$774$		0			0
$775$	−27.7291			−0.996059
$776$		0			0
$777$		−	7.84450i		−	0.281420i
$778$		0			0
$779$	−26.4224	−	7.48400i	−0.946681	−	0.268142i
$780$		0			0
$781$		0	0.000965356i		0	3.45432e-5i
$782$		0			0
$783$	27.2885			0.975213
$784$		0			0
$785$	−2.69144	+	2.69144i	−0.0960615	+	0.0960615i
$786$		0			0
$787$			37.5717i			1.33929i	0.742683	+	0.669643i	$0.233553\pi$
$787$			37.5717i			1.33929i	−0.742683	+	0.669643i	$0.766447\pi$
$788$		0			0
$789$	25.0514			0.891852
$790$		0			0
$791$	5.38459	+	5.38459i	0.191454	+	0.191454i
$792$		0			0
$793$	44.0540	−	44.0540i	1.56440	−	1.56440i
$794$		0			0
$795$	−51.8143			−1.83767
$796$		0			0
$797$	28.9887			1.02683			0.513417	−	0.858139i	$-0.328380\pi$
$797$	28.9887			1.02683			0.513417	+	0.858139i	$0.328380\pi$
$798$		0			0
$799$			19.3194i			0.683470i
$800$		0			0
$801$	11.1634	−	11.1634i	0.394439	−	0.394439i
$802$		0			0
$803$	0.102137	−	0.102137i	0.00360433	−	0.00360433i
$804$		0			0
$805$	6.33598	−	6.33598i	0.223314	−	0.223314i
$806$		0			0
$807$	−35.4618	−	35.4618i	−1.24831	−	1.24831i
$808$		0			0
$809$	−2.70444	−	2.70444i	−0.0950831	−	0.0950831i	0.657965	−	0.753048i	$-0.271417\pi$
$809$	−2.70444	−	2.70444i	−0.0950831	−	0.0950831i	−0.753048	+	0.657965i	$0.771417\pi$
$810$		0			0
$811$			5.27800i			0.185336i	0.995697	+	0.0926679i	$0.0295395\pi$
$811$			5.27800i			0.185336i	−0.995697	+	0.0926679i	$0.970461\pi$
$812$		0			0
$813$	29.8047	+	29.8047i	1.04530	+	1.04530i
$814$		0			0
$815$			4.36327i			0.152839i
$816$		0			0
$817$	−22.1699	−	22.1699i	−0.775625	−	0.775625i
$818$		0			0
$819$	−21.4436			−0.749300
$820$		0			0
$821$	−39.6474			−1.38370			−0.691852	−	0.722039i	$-0.743205\pi$
$821$	−39.6474			−1.38370			−0.691852	+	0.722039i	$0.743205\pi$
$822$		0			0
$823$	17.8686	+	17.8686i	0.622860	+	0.622860i	0.946262	−	0.323402i	$-0.104827\pi$
$823$	17.8686	+	17.8686i	0.622860	+	0.622860i	−0.323402	+	0.946262i	$0.604827\pi$
$824$		0			0
$825$			0.0782225i			0.00272336i
$826$		0			0
$827$	19.0540	+	19.0540i	0.662571	+	0.662571i	0.955985	−	0.293414i	$-0.0947915\pi$
$827$	19.0540	+	19.0540i	0.662571	+	0.662571i	−0.293414	+	0.955985i	$0.594792\pi$
$828$		0			0
$829$		−	9.21121i		−	0.319918i	−0.987124	−	0.159959i	$-0.948864\pi$
$829$		−	9.21121i		−	0.319918i	0.987124	−	0.159959i	$-0.0511363\pi$
$830$		0			0
$831$	55.3880	+	55.3880i	1.92139	+	1.92139i
$832$		0			0
$833$	−2.98892	−	2.98892i	−0.103560	−	0.103560i
$834$		0			0
$835$	15.4375	−	15.4375i	0.534237	−	0.534237i
$836$		0			0
$837$	−20.4822	+	20.4822i	−0.707968	+	0.707968i
$838$		0			0
$839$	2.90860	−	2.90860i	0.100416	−	0.100416i	−0.655114	−	0.755530i	$-0.727379\pi$
$839$	2.90860	−	2.90860i	0.100416	−	0.100416i	0.755530	+	0.655114i	$0.227379\pi$
$840$		0			0
$841$			43.9765i			1.51643i
$842$		0			0
$843$	−2.72458			−0.0938396
$844$		0			0
$845$	18.3628			0.631699
$846$		0			0
$847$	−7.77811	+	7.77811i	−0.267259	+	0.267259i
$848$		0			0
$849$	22.9424	+	22.9424i	0.787383	+	0.787383i
$850$		0			0
$851$	18.8090			0.644764
$852$		0			0
$853$			35.5187i			1.21614i	0.793884	+	0.608069i	$0.208056\pi$
$853$			35.5187i			1.21614i	−0.793884	+	0.608069i	$0.791944\pi$
$854$		0			0
$855$	17.7129	−	17.7129i	0.605769	−	0.605769i
$856$		0			0
$857$	−12.3846			−0.423049			−0.211524	−	0.977373i	$-0.567843\pi$
$857$	−12.3846			−0.423049			−0.211524	+	0.977373i	$0.567843\pi$
$858$		0			0
$859$		−	31.5344i		−	1.07594i	−0.842964	−	0.537970i	$-0.819191\pi$
$859$		−	31.5344i		−	1.07594i	0.842964	−	0.537970i	$-0.180809\pi$
$860$		0			0
$861$	14.9910	−	8.37319i	0.510891	−	0.285358i
$862$		0			0
$863$		−	14.7993i		−	0.503775i	−0.967757	−	0.251888i	$-0.918949\pi$
$863$		−	14.7993i		−	0.503775i	0.967757	−	0.251888i	$-0.0810513\pi$
$864$		0			0
$865$	4.79189			0.162929
$866$		0			0
$867$	−1.64445	+	1.64445i	−0.0558485	+	0.0558485i
$868$		0			0
$869$		−	0.0959802i		−	0.00325591i
$870$		0			0
$871$	51.9196			1.75923
$872$		0			0
$873$	14.3328	+	14.3328i	0.485091	+	0.485091i
$874$		0			0
$875$	−7.94033	+	7.94033i	−0.268432	+	0.268432i
$876$		0			0
$877$	−25.9737			−0.877071			−0.438535	−	0.898714i	$-0.644503\pi$
$877$	−25.9737			−0.877071			−0.438535	+	0.898714i	$0.644503\pi$
$878$		0			0
$879$	3.06312			0.103317
$880$		0			0
$881$		−	26.4635i		−	0.891578i	−0.895138	−	0.445789i	$-0.852923\pi$
$881$		−	26.4635i		−	0.891578i	0.895138	−	0.445789i	$-0.147077\pi$
$882$		0			0
$883$	6.14907	−	6.14907i	0.206933	−	0.206933i	−0.596030	−	0.802962i	$-0.703256\pi$
$883$	6.14907	−	6.14907i	0.206933	−	0.206933i	0.802962	+	0.596030i	$0.203256\pi$
$884$		0			0
$885$	−22.0013	+	22.0013i	−0.739565	+	0.739565i
$886$		0			0
$887$	−4.23258	+	4.23258i	−0.142116	+	0.142116i	−0.774585	−	0.632469i	$-0.782041\pi$
$887$	−4.23258	+	4.23258i	−0.142116	+	0.142116i	0.632469	+	0.774585i	$0.282041\pi$
$888$		0			0
$889$	12.1311	+	12.1311i	0.406863	+	0.406863i
$890$		0			0
$891$	−0.0270299	−	0.0270299i	−0.000905535	−	0.000905535i
$892$		0			0
$893$		−	19.6021i		−	0.655958i
$894$		0			0
$895$	−1.95034	−	1.95034i	−0.0651927	−	0.0651927i
$896$		0			0
$897$		−	88.2187i		−	2.94554i
$898$		0			0
$899$	−54.7745	−	54.7745i	−1.82683	−	1.82683i
$900$		0			0
$901$	−58.6071			−1.95248
$902$		0			0
$903$	19.6038			0.652375
$904$		0			0
$905$	14.7969	+	14.7969i	0.491867	+	0.491867i
$906$		0			0
$907$		−	4.40093i		−	0.146130i	−0.997327	−	0.0730652i	$-0.976722\pi$
$907$		−	4.40093i		−	0.146130i	0.997327	−	0.0730652i	$-0.0232781\pi$
$908$		0			0
$909$	−45.6385	−	45.6385i	−1.51373	−	1.51373i
$910$		0			0
$911$			40.4806i			1.34118i	0.741827	+	0.670591i	$0.233959\pi$
$911$			40.4806i			1.34118i	−0.741827	+	0.670591i	$0.766041\pi$
$912$		0			0
$913$	−0.00239190	−	0.00239190i	−7.91602e−5	−	7.91602e-5i
$914$		0			0
$915$	−32.1778	−	32.1778i	−1.06376	−	1.06376i
$916$		0			0
$917$	−12.9018	+	12.9018i	−0.426056	+	0.426056i
$918$		0			0
$919$	8.59250	−	8.59250i	0.283440	−	0.283440i	−0.551039	−	0.834479i	$-0.685768\pi$
$919$	8.59250	−	8.59250i	0.283440	−	0.283440i	0.834479	+	0.551039i	$0.185768\pi$
$920$		0			0
$921$	1.82290	−	1.82290i	0.0600666	−	0.0600666i
$922$		0			0
$923$			0.517784i			0.0170431i
$924$		0			0
$925$	−8.94536			−0.294122
$926$		0			0
$927$	53.4307			1.75489
$928$		0			0
$929$	8.35467	−	8.35467i	0.274108	−	0.274108i	−0.556644	−	0.830751i	$-0.687911\pi$
$929$	8.35467	−	8.35467i	0.274108	−	0.274108i	0.830751	+	0.556644i	$0.187911\pi$
$930$		0			0
$931$	3.03265	+	3.03265i	0.0993912	+	0.0993912i
$932$		0			0
$933$	90.6985			2.96934
$934$		0			0
$935$		−	0.0561893i		−	0.00183759i
$936$		0			0
$937$	36.6183	−	36.6183i	1.19627	−	1.19627i	0.220991	−	0.975276i	$-0.429071\pi$
$937$	36.6183	−	36.6183i	1.19627	−	1.19627i	0.975276	−	0.220991i	$-0.0709292\pi$
$938$		0			0
$939$	−8.03456			−0.262198
$940$		0			0
$941$			55.7058i			1.81596i	0.419018	+	0.907978i	$0.362375\pi$
$941$			55.7058i			1.81596i	−0.419018	+	0.907978i	$0.637625\pi$
$942$		0			0
$943$	20.0767	+	35.9443i	0.653786	+	1.17051i
$944$		0			0
$945$			4.45161i			0.144811i
$946$		0			0
$947$	13.2329			0.430011			0.215005	−	0.976613i	$-0.431023\pi$
$947$	13.2329			0.430011			0.215005	+	0.976613i	$0.431023\pi$
$948$		0			0
$949$	54.7827	−	54.7827i	1.77832	−	1.77832i
$950$		0			0
$951$		−	53.1781i		−	1.72442i
$952$		0			0
$953$	−14.5658			−0.471834			−0.235917	−	0.971773i	$-0.575809\pi$
$953$	−14.5658			−0.471834			−0.235917	+	0.971773i	$0.575809\pi$
$954$		0			0
$955$	7.09114	+	7.09114i	0.229464	+	0.229464i
$956$		0			0
$957$	−0.154516	+	0.154516i	−0.00499481	+	0.00499481i
$958$		0			0
$959$	5.23544			0.169061
$960$		0			0
$961$	51.2251			1.65242
$962$		0			0
$963$		−	49.9385i		−	1.60924i
$964$		0			0
$965$	−25.8107	+	25.8107i	−0.830875	+	0.830875i
$966$		0			0
$967$	−3.63097	+	3.63097i	−0.116764	+	0.116764i	−0.763075	−	0.646310i	$-0.776311\pi$
$967$	−3.63097	+	3.63097i	−0.116764	+	0.116764i	0.646310	+	0.763075i	$0.276311\pi$
$968$		0			0
$969$	34.3758	−	34.3758i	1.10431	−	1.10431i
$970$		0			0
$971$	−29.4424	−	29.4424i	−0.944852	−	0.944852i	0.0537049	−	0.998557i	$-0.482897\pi$
$971$	−29.4424	−	29.4424i	−0.944852	−	0.944852i	−0.998557	+	0.0537049i	$0.982897\pi$
$972$		0			0
$973$	−0.376573	−	0.376573i	−0.0120724	−	0.0120724i
$974$		0			0
$975$			41.9559i			1.34366i
$976$		0			0
$977$	4.87520	+	4.87520i	0.155972	+	0.155972i	0.780779	−	0.624807i	$-0.214823\pi$
$977$	4.87520	+	4.87520i	0.155972	+	0.155972i	−0.624807	+	0.780779i	$0.714823\pi$
$978$		0			0
$979$			0.0359310i			0.00114836i
$980$		0			0
$981$	−28.4029	−	28.4029i	−0.906834	−	0.906834i
$982$		0			0
$983$	−16.6753			−0.531859			−0.265929	−	0.963993i	$-0.585679\pi$
$983$	−16.6753			−0.531859			−0.265929	+	0.963993i	$0.585679\pi$
$984$		0			0
$985$	−27.3105			−0.870186
$986$		0			0
$987$	8.66663	+	8.66663i	0.275862	+	0.275862i
$988$		0			0
$989$			47.0047i			1.49466i
$990$		0			0
$991$	28.6884	+	28.6884i	0.911317	+	0.911317i	0.996376	−	0.0850587i	$-0.0271078\pi$
$991$	28.6884	+	28.6884i	0.911317	+	0.911317i	−0.0850587	+	0.996376i	$0.527108\pi$
$992$		0			0
$993$			51.9891i			1.64982i
$994$		0			0
$995$	16.6991	+	16.6991i	0.529396	+	0.529396i
$996$		0			0
$997$	30.0428	+	30.0428i	0.951464	+	0.951464i	0.998875	−	0.0474111i	$-0.0150971\pi$
$997$	30.0428	+	30.0428i	0.951464	+	0.951464i	−0.0474111	+	0.998875i	$0.515097\pi$
$998$		0			0
$999$	−6.60752	+	6.60752i	−0.209053	+	0.209053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.3	✓	36
41.32	even	4	inner	1148.2.k.b.729.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.3	✓	36	1.1	even	1	trivial
1148.2.k.b.729.3	yes	36	41.32	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +O(q^{10})\)	\(q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +(-0.00674500 - 0.00674500i) q^{11} +(-3.61779 - 3.61779i) q^{13} +(-2.64249 + 2.64249i) q^{15} +(-2.98892 + 2.98892i) q^{17} +(3.03265 - 3.03265i) q^{19} +2.68164i q^{21} -6.42985 q^{23} +3.05797 q^{25} +(2.25878 - 2.25878i) q^{27} +(6.04055 + 6.04055i) q^{29} -9.06781 q^{31} +0.0255799i q^{33} +(-0.985400 + 0.985400i) q^{35} -2.92526 q^{37} +13.7202i q^{39} +(-3.12241 - 5.59022i) q^{41} -7.31038i q^{43} +5.84073 q^{45} +(3.23183 - 3.23183i) q^{47} +1.00000i q^{49} +11.3352 q^{51} +(9.80407 + 9.80407i) q^{53} +(-0.00939961 + 0.00939961i) q^{55} -11.5011 q^{57} +8.32596 q^{59} +12.1771i q^{61} +(2.96363 - 2.96363i) q^{63} +(-5.04163 + 5.04163i) q^{65} +(-7.17560 + 7.17560i) q^{67} +(12.1923 + 12.1923i) q^{69} +(-0.0715608 - 0.0715608i) q^{71} +15.1426i q^{73} +(-5.79855 - 5.79855i) q^{75} +0.00953888i q^{77} +(7.11491 + 7.11491i) q^{79} +4.00739 q^{81} +0.354618 q^{83} +(4.16525 + 4.16525i) q^{85} -22.9083i q^{87} +(-2.66353 - 2.66353i) q^{89} +5.11633i q^{91} +(17.1944 + 17.1944i) q^{93} +(-4.22621 - 4.22621i) q^{95} +(3.41973 - 3.41973i) q^{97} +(0.0282697 - 0.0282697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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