LMFDB - Embedded newform 1344.2.s.c.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.3
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61364 - 0.629429i) q^{3} +(-3.08691 - 3.08691i) q^{5} +1.00000 q^{7} +(2.20764 + 2.03134i) q^{9} +O(q^{10})$	\(q+(-1.61364 - 0.629429i) q^{3} +(-3.08691 - 3.08691i) q^{5} +1.00000 q^{7} +(2.20764 + 2.03134i) q^{9} +(-1.97950 + 1.97950i) q^{11} +(3.27530 + 3.27530i) q^{13} +(3.03816 + 6.92415i) q^{15} +2.57205i q^{17} +(1.18763 - 1.18763i) q^{19} +(-1.61364 - 0.629429i) q^{21} +1.21005i q^{23} +14.0581i q^{25} +(-2.28374 - 4.66739i) q^{27} +(-1.33641 + 1.33641i) q^{29} -5.84687i q^{31} +(4.44015 - 1.94824i) q^{33} +(-3.08691 - 3.08691i) q^{35} +(5.18528 - 5.18528i) q^{37} +(-3.22357 - 7.34670i) q^{39} -0.688196 q^{41} +(-0.649101 - 0.649101i) q^{43} +(-0.544230 - 13.0854i) q^{45} +10.5648 q^{47} +1.00000 q^{49} +(1.61892 - 4.15035i) q^{51} +(3.84828 + 3.84828i) q^{53} +12.2211 q^{55} +(-2.66394 + 1.16888i) q^{57} +(1.99283 - 1.99283i) q^{59} +(-6.62710 - 6.62710i) q^{61} +(2.20764 + 2.03134i) q^{63} -20.2211i q^{65} +(-4.50400 + 4.50400i) q^{67} +(0.761640 - 1.95258i) q^{69} +3.91342i q^{71} -9.83194i q^{73} +(8.84856 - 22.6846i) q^{75} +(-1.97950 + 1.97950i) q^{77} -3.86630i q^{79} +(0.747340 + 8.96892i) q^{81} +(2.99861 + 2.99861i) q^{83} +(7.93969 - 7.93969i) q^{85} +(2.99765 - 1.31530i) q^{87} +10.8761 q^{89} +(3.27530 + 3.27530i) q^{91} +(-3.68019 + 9.43472i) q^{93} -7.33224 q^{95} -10.1652 q^{97} +(-8.39105 + 0.348990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.61364	−	0.629429i	−0.931633	−	0.363401i
$3$	−1.61364	−	0.629429i	−0.931633	−	0.363401i
$4$		0			0
$5$	−3.08691	−	3.08691i	−1.38051	−	1.38051i	−0.843708	−	0.536802i	$-0.819632\pi$
$5$	−3.08691	−	3.08691i	−1.38051	−	1.38051i	−0.536802	−	0.843708i	$-0.680368\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	2.20764	+	2.03134i	0.735880	+	0.677112i
$10$		0			0
$11$	−1.97950	+	1.97950i	−0.596842	+	0.596842i	−0.939471	−	0.342629i	$-0.888683\pi$
$11$	−1.97950	+	1.97950i	−0.596842	+	0.596842i	0.342629	+	0.939471i	$0.388683\pi$
$12$		0			0
$13$	3.27530	+	3.27530i	0.908404	+	0.908404i	0.996143	−	0.0877398i	$-0.0279644\pi$
$13$	3.27530	+	3.27530i	0.908404	+	0.908404i	−0.0877398	+	0.996143i	$0.527964\pi$
$14$		0			0
$15$	3.03816	+	6.92415i	0.784450	+	1.78781i
$16$		0			0
$17$			2.57205i			0.623813i	0.950113	+	0.311907i	$0.100968\pi$
$17$			2.57205i			0.623813i	−0.950113	+	0.311907i	$0.899032\pi$
$18$		0			0
$19$	1.18763	−	1.18763i	0.272462	−	0.272462i	−0.557629	−	0.830090i	$-0.688289\pi$
$19$	1.18763	−	1.18763i	0.272462	−	0.272462i	0.830090	+	0.557629i	$0.188289\pi$
$20$		0			0
$21$	−1.61364	−	0.629429i	−0.352124	−	0.137353i
$22$		0			0
$23$			1.21005i			0.252313i	0.992010	+	0.126156i	$0.0402641\pi$
$23$			1.21005i			0.252313i	−0.992010	+	0.126156i	$0.959736\pi$
$24$		0			0
$25$			14.0581i			2.81162i
$26$		0			0
$27$	−2.28374	−	4.66739i	−0.439507	−	0.898239i
$28$		0			0
$29$	−1.33641	+	1.33641i	−0.248165	+	0.248165i	−0.820217	−	0.572052i	$-0.806147\pi$
$29$	−1.33641	+	1.33641i	−0.248165	+	0.248165i	0.572052	+	0.820217i	$0.306147\pi$
$30$		0			0
$31$		−	5.84687i		−	1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$31$		−	5.84687i		−	1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$32$		0			0
$33$	4.44015	−	1.94824i	0.772930	−	0.339145i
$34$		0			0
$35$	−3.08691	−	3.08691i	−0.521784	−	0.521784i
$36$		0			0
$37$	5.18528	−	5.18528i	0.852455	−	0.852455i	−0.137980	−	0.990435i	$-0.544061\pi$
$37$	5.18528	−	5.18528i	0.852455	−	0.852455i	0.990435	+	0.137980i	$0.0440608\pi$
$38$		0			0
$39$	−3.22357	−	7.34670i	−0.516184	−	1.17641i
$40$		0			0
$41$	−0.688196			−0.107478			−0.0537391	−	0.998555i	$-0.517114\pi$
$41$	−0.688196			−0.107478			−0.0537391	+	0.998555i	$0.517114\pi$
$42$		0			0
$43$	−0.649101	−	0.649101i	−0.0989870	−	0.0989870i	0.655879	−	0.754866i	$-0.272298\pi$
$43$	−0.649101	−	0.649101i	−0.0989870	−	0.0989870i	−0.754866	+	0.655879i	$0.772298\pi$
$44$		0			0
$45$	−0.544230	−	13.0854i	−0.0811290	−	1.95065i
$46$		0			0
$47$	10.5648			1.54104			0.770519	−	0.637417i	$-0.219997\pi$
$47$	10.5648			1.54104			0.770519	+	0.637417i	$0.219997\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	1.61892	−	4.15035i	0.226694	−	0.581165i
$52$		0			0
$53$	3.84828	+	3.84828i	0.528602	+	0.528602i	0.920155	−	0.391554i	$-0.128062\pi$
$53$	3.84828	+	3.84828i	0.528602	+	0.528602i	−0.391554	+	0.920155i	$0.628062\pi$
$54$		0			0
$55$	12.2211			1.64789
$56$		0			0
$57$	−2.66394	+	1.16888i	−0.352847	+	0.154822i
$58$		0			0
$59$	1.99283	−	1.99283i	0.259444	−	0.259444i	−0.565384	−	0.824828i	$-0.691272\pi$
$59$	1.99283	−	1.99283i	0.259444	−	0.259444i	0.824828	+	0.565384i	$0.191272\pi$
$60$		0			0
$61$	−6.62710	−	6.62710i	−0.848513	−	0.848513i	0.141435	−	0.989948i	$-0.454828\pi$
$61$	−6.62710	−	6.62710i	−0.848513	−	0.848513i	−0.989948	+	0.141435i	$0.954828\pi$
$62$		0			0
$63$	2.20764	+	2.03134i	0.278136	+	0.255924i
$64$		0			0
$65$		−	20.2211i		−	2.50812i
$66$		0			0
$67$	−4.50400	+	4.50400i	−0.550251	+	0.550251i	−0.926513	−	0.376262i	$-0.877209\pi$
$67$	−4.50400	+	4.50400i	−0.550251	+	0.550251i	0.376262	+	0.926513i	$0.377209\pi$
$68$		0			0
$69$	0.761640	−	1.95258i	0.0916907	−	0.235063i
$70$		0			0
$71$			3.91342i			0.464438i	0.972664	+	0.232219i	$0.0745986\pi$
$71$			3.91342i			0.464438i	−0.972664	+	0.232219i	$0.925401\pi$
$72$		0			0
$73$		−	9.83194i		−	1.15074i	−0.817893	−	0.575371i	$-0.804858\pi$
$73$		−	9.83194i		−	1.15074i	0.817893	−	0.575371i	$-0.195142\pi$
$74$		0			0
$75$	8.84856	−	22.6846i	1.02174	−	2.61939i
$76$		0			0
$77$	−1.97950	+	1.97950i	−0.225585	+	0.225585i
$78$		0			0
$79$		−	3.86630i		−	0.434992i	−0.976061	−	0.217496i	$-0.930211\pi$
$79$		−	3.86630i		−	0.434992i	0.976061	−	0.217496i	$-0.0697890\pi$
$80$		0			0
$81$	0.747340	+	8.96892i	0.0830378	+	0.996546i
$82$		0			0
$83$	2.99861	+	2.99861i	0.329140	+	0.329140i	0.852260	−	0.523119i	$-0.175232\pi$
$83$	2.99861	+	2.99861i	0.329140	+	0.329140i	−0.523119	+	0.852260i	$0.675232\pi$
$84$		0			0
$85$	7.93969	−	7.93969i	0.861180	−	0.861180i
$86$		0			0
$87$	2.99765	−	1.31530i	0.321382	−	0.141015i
$88$		0			0
$89$	10.8761			1.15286			0.576432	−	0.817145i	$-0.304444\pi$
$89$	10.8761			1.15286			0.576432	+	0.817145i	$0.304444\pi$
$90$		0			0
$91$	3.27530	+	3.27530i	0.343344	+	0.343344i
$92$		0			0
$93$	−3.68019	+	9.43472i	−0.381618	+	0.978335i
$94$		0			0
$95$	−7.33224			−0.752272
$96$		0			0
$97$	−10.1652			−1.03212			−0.516061	−	0.856552i	$-0.672602\pi$
$97$	−10.1652			−1.03212			−0.516061	+	0.856552i	$0.672602\pi$
$98$		0			0
$99$	−8.39105	+	0.348990i	−0.843332	+	0.0350748i
$100$		0			0
$101$	11.5965	+	11.5965i	1.15389	+	1.15389i	0.985765	+	0.168129i	$0.0537726\pi$
$101$	11.5965	+	11.5965i	1.15389	+	1.15389i	0.168129	+	0.985765i	$0.446227\pi$
$102$		0			0
$103$	6.00387			0.591579			0.295790	−	0.955253i	$-0.404417\pi$
$103$	6.00387			0.591579			0.295790	+	0.955253i	$0.404417\pi$
$104$		0			0
$105$	3.03816	+	6.92415i	0.296494	+	0.675728i
$106$		0			0
$107$	8.85702	−	8.85702i	0.856241	−	0.856241i	−0.134652	−	0.990893i	$-0.542992\pi$
$107$	8.85702	−	8.85702i	0.856241	−	0.856241i	0.990893	+	0.134652i	$0.0429917\pi$
$108$		0			0
$109$	9.12079	+	9.12079i	0.873613	+	0.873613i	0.992864	−	0.119251i	$-0.0380494\pi$
$109$	9.12079	+	9.12079i	0.873613	+	0.873613i	−0.119251	+	0.992864i	$0.538049\pi$
$110$		0			0
$111$	−11.6309	+	5.10339i	−1.10396	+	0.484393i
$112$		0			0
$113$		−	8.96882i		−	0.843715i	−0.906662	−	0.421858i	$-0.861378\pi$
$113$		−	8.96882i		−	0.843715i	0.906662	−	0.421858i	$-0.138622\pi$
$114$		0			0
$115$	3.73532	−	3.73532i	0.348320	−	0.348320i
$116$		0			0
$117$	0.577442	+	13.8839i	0.0533845	+	1.28357i
$118$		0			0
$119$			2.57205i			0.235779i
$120$		0			0
$121$			3.16316i			0.287560i
$122$		0			0
$123$	1.11050	+	0.433170i	0.100130	+	0.0390577i
$124$		0			0
$125$	27.9615	−	27.9615i	2.50096	−	2.50096i
$126$		0			0
$127$		−	0.567572i		−	0.0503638i	−0.999683	−	0.0251819i	$-0.991983\pi$
$127$		−	0.567572i		−	0.0503638i	0.999683	−	0.0251819i	$-0.00801650\pi$
$128$		0			0
$129$	0.638850	+	1.45598i	0.0562476	+	0.128191i
$130$		0			0
$131$	−3.91258	−	3.91258i	−0.341844	−	0.341844i	0.515216	−	0.857060i	$-0.327712\pi$
$131$	−3.91258	−	3.91258i	−0.341844	−	0.341844i	−0.857060	+	0.515216i	$0.827712\pi$
$132$		0			0
$133$	1.18763	−	1.18763i	0.102981	−	0.102981i
$134$		0			0
$135$	−7.35811	+	21.4576i	−0.633285	+	1.84677i
$136$		0			0
$137$	−18.8206			−1.60795			−0.803974	−	0.594664i	$-0.797285\pi$
$137$	−18.8206			−1.60795			−0.803974	+	0.594664i	$0.797285\pi$
$138$		0			0
$139$	10.0264	+	10.0264i	0.850426	+	0.850426i	0.990186	−	0.139759i	$-0.0446329\pi$
$139$	10.0264	+	10.0264i	0.850426	+	0.850426i	−0.139759	+	0.990186i	$0.544633\pi$
$140$		0			0
$141$	−17.0478	−	6.64980i	−1.43568	−	0.560015i
$142$		0			0
$143$	−12.9669			−1.08435
$144$		0			0
$145$	8.25076			0.685188
$146$		0			0
$147$	−1.61364	−	0.629429i	−0.133090	−	0.0519144i
$148$		0			0
$149$	−0.117671	−	0.117671i	−0.00963996	−	0.00963996i	0.702270	−	0.711910i	$-0.252170\pi$
$149$	−0.117671	−	0.117671i	−0.00963996	−	0.00963996i	−0.711910	+	0.702270i	$0.752170\pi$
$150$		0			0
$151$	24.0766			1.95933			0.979663	−	0.200650i	$-0.0643055\pi$
$151$	24.0766			1.95933			0.979663	+	0.200650i	$0.0643055\pi$
$152$		0			0
$153$	−5.22470	+	5.67815i	−0.422392	+	0.459051i
$154$		0			0
$155$	−18.0488	+	18.0488i	−1.44971	+	1.44971i
$156$		0			0
$157$	−5.29589	−	5.29589i	−0.422658	−	0.422658i	0.463460	−	0.886118i	$-0.346608\pi$
$157$	−5.29589	−	5.29589i	−0.422658	−	0.422658i	−0.886118	+	0.463460i	$0.846608\pi$
$158$		0			0
$159$	−3.78750	−	8.63194i	−0.300368	−	0.684557i
$160$		0			0
$161$			1.21005i			0.0953653i
$162$		0			0
$163$	−15.9523	+	15.9523i	−1.24948	+	1.24948i	−0.293529	+	0.955950i	$0.594830\pi$
$163$	−15.9523	+	15.9523i	−1.24948	+	1.24948i	−0.955950	+	0.293529i	$0.905170\pi$
$164$		0			0
$165$	−19.7204	−	7.69231i	−1.53523	−	0.598845i
$166$		0			0
$167$		−	16.5911i		−	1.28386i	−0.766765	−	0.641928i	$-0.778135\pi$
$167$		−	16.5911i		−	1.28386i	0.766765	−	0.641928i	$-0.221865\pi$
$168$		0			0
$169$			8.45513i			0.650394i
$170$		0			0
$171$	5.03435	−	0.209382i	0.384986	−	0.0160119i
$172$		0			0
$173$	2.74985	−	2.74985i	0.209067	−	0.209067i	−0.594804	−	0.803871i	$-0.702770\pi$
$173$	2.74985	−	2.74985i	0.209067	−	0.209067i	0.803871	+	0.594804i	$0.202770\pi$
$174$		0			0
$175$			14.0581i			1.06269i
$176$		0			0
$177$	−4.47004	+	1.96135i	−0.335989	+	0.147424i
$178$		0			0
$179$	5.58232	+	5.58232i	0.417242	+	0.417242i	0.884252	−	0.467010i	$-0.154669\pi$
$179$	5.58232	+	5.58232i	0.417242	+	0.417242i	−0.467010	+	0.884252i	$0.654669\pi$
$180$		0			0
$181$	6.74062	−	6.74062i	0.501026	−	0.501026i	−0.410731	−	0.911757i	$-0.634726\pi$
$181$	6.74062	−	6.74062i	0.501026	−	0.501026i	0.911757	+	0.410731i	$0.134726\pi$
$182$		0			0
$183$	6.52243	+	14.8650i	0.482152	+	1.09885i
$184$		0			0
$185$	−32.0131			−2.35365
$186$		0			0
$187$	−5.09137	−	5.09137i	−0.372318	−	0.372318i
$188$		0			0
$189$	−2.28374	−	4.66739i	−0.166118	−	0.339503i
$190$		0			0
$191$	24.3853			1.76446			0.882230	−	0.470819i	$-0.156042\pi$
$191$	24.3853			1.76446			0.882230	+	0.470819i	$0.156042\pi$
$192$		0			0
$193$	4.04091			0.290871			0.145435	−	0.989368i	$-0.453542\pi$
$193$	4.04091			0.290871			0.145435	+	0.989368i	$0.453542\pi$
$194$		0			0
$195$	−12.7278	+	32.6295i	−0.911453	+	2.33665i
$196$		0			0
$197$	5.19081	+	5.19081i	0.369830	+	0.369830i	0.867415	−	0.497585i	$-0.165780\pi$
$197$	5.19081	+	5.19081i	0.369830	+	0.369830i	−0.497585	+	0.867415i	$0.665780\pi$
$198$		0			0
$199$	−9.79611			−0.694428			−0.347214	−	0.937786i	$-0.612872\pi$
$199$	−9.79611			−0.694428			−0.347214	+	0.937786i	$0.612872\pi$
$200$		0			0
$201$	10.1028	−	4.43286i	0.712593	−	0.312670i
$202$		0			0
$203$	−1.33641	+	1.33641i	−0.0937975	+	0.0937975i
$204$		0			0
$205$	2.12440	+	2.12440i	0.148375	+	0.148375i
$206$		0			0
$207$	−2.45802	+	2.67135i	−0.170844	+	0.185672i
$208$		0			0
$209$			4.70184i			0.325233i
$210$		0			0
$211$	5.97473	−	5.97473i	0.411317	−	0.411317i	−0.470880	−	0.882197i	$-0.656064\pi$
$211$	5.97473	−	5.97473i	0.411317	−	0.411317i	0.882197	+	0.470880i	$0.156064\pi$
$212$		0			0
$213$	2.46322	−	6.31484i	0.168777	−	0.432685i
$214$		0			0
$215$			4.00744i			0.273305i
$216$		0			0
$217$		−	5.84687i		−	0.396912i
$218$		0			0
$219$	−6.18851	+	15.8652i	−0.418180	+	1.07207i
$220$		0			0
$221$	−8.42422	+	8.42422i	−0.566674	+	0.566674i
$222$		0			0
$223$		−	10.9984i		−	0.736505i	−0.929726	−	0.368253i	$-0.879956\pi$
$223$		−	10.9984i		−	0.736505i	0.929726	−	0.368253i	$-0.120044\pi$
$224$		0			0
$225$	−28.5567	+	31.0352i	−1.90378	+	2.06901i
$226$		0			0
$227$	12.2151	+	12.2151i	0.810742	+	0.810742i	0.984745	−	0.174003i	$-0.0556704\pi$
$227$	12.2151	+	12.2151i	0.810742	+	0.810742i	−0.174003	+	0.984745i	$0.555670\pi$
$228$		0			0
$229$	13.1881	−	13.1881i	0.871496	−	0.871496i	−0.121140	−	0.992635i	$-0.538655\pi$
$229$	13.1881	−	13.1881i	0.871496	−	0.871496i	0.992635	+	0.121140i	$0.0386549\pi$
$230$		0			0
$231$	4.44015	−	1.94824i	0.292140	−	0.128185i
$232$		0			0
$233$	3.56286			0.233411			0.116705	−	0.993167i	$-0.462767\pi$
$233$	3.56286			0.233411			0.116705	+	0.993167i	$0.462767\pi$
$234$		0			0
$235$	−32.6127	−	32.6127i	−2.12742	−	2.12742i
$236$		0			0
$237$	−2.43356	+	6.23879i	−0.158077	+	0.405253i
$238$		0			0
$239$	−1.40979			−0.0911918			−0.0455959	−	0.998960i	$-0.514519\pi$
$239$	−1.40979			−0.0911918			−0.0455959	+	0.998960i	$0.514519\pi$
$240$		0			0
$241$	8.32598			0.536324			0.268162	−	0.963374i	$-0.413584\pi$
$241$	8.32598			0.536324			0.268162	+	0.963374i	$0.413584\pi$
$242$		0			0
$243$	4.43936	−	14.9430i	0.284785	−	0.958591i
$244$		0			0
$245$	−3.08691	−	3.08691i	−0.197216	−	0.197216i
$246$		0			0
$247$	7.77970			0.495011
$248$		0			0
$249$	−2.95125	−	6.72608i	−0.187028	−	0.426248i
$250$		0			0
$251$	−7.86006	+	7.86006i	−0.496123	+	0.496123i	−0.910229	−	0.414106i	$-0.864094\pi$
$251$	−7.86006	+	7.86006i	−0.496123	+	0.496123i	0.414106	+	0.910229i	$0.364094\pi$
$252$		0			0
$253$	−2.39529	−	2.39529i	−0.150591	−	0.150591i
$254$		0			0
$255$	−17.8092	+	7.81430i	−1.11526	+	0.489350i
$256$		0			0
$257$		−	13.3701i		−	0.834004i	−0.908906	−	0.417002i	$-0.863081\pi$
$257$		−	13.3701i		−	0.834004i	0.908906	−	0.417002i	$-0.136919\pi$
$258$		0			0
$259$	5.18528	−	5.18528i	0.322198	−	0.322198i
$260$		0			0
$261$	−5.66501	+	0.235612i	−0.350655	+	0.0145840i
$262$		0			0
$263$		−	11.7128i		−	0.722240i	−0.932519	−	0.361120i	$-0.882395\pi$
$263$		−	11.7128i		−	0.722240i	0.932519	−	0.361120i	$-0.117605\pi$
$264$		0			0
$265$		−	23.7586i		−	1.45948i
$266$		0			0
$267$	−17.5501	−	6.84573i	−1.07405	−	0.418952i
$268$		0			0
$269$	−17.7527	+	17.7527i	−1.08240	+	1.08240i	−0.0861135	+	0.996285i	$0.527445\pi$
$269$	−17.7527	+	17.7527i	−1.08240	+	1.08240i	−0.996285	+	0.0861135i	$0.972555\pi$
$270$		0			0
$271$			8.40389i			0.510500i	0.966875	+	0.255250i	$0.0821577\pi$
$271$			8.40389i			0.510500i	−0.966875	+	0.255250i	$0.917842\pi$
$272$		0			0
$273$	−3.22357	−	7.34670i	−0.195099	−	0.444642i
$274$		0			0
$275$	−27.8280	−	27.8280i	−1.67809	−	1.67809i
$276$		0			0
$277$	13.3603	−	13.3603i	0.802743	−	0.802743i	−0.180781	−	0.983523i	$-0.557862\pi$
$277$	13.3603	−	13.3603i	0.802743	−	0.802743i	0.983523	+	0.180781i	$0.0578624\pi$
$278$		0			0
$279$	11.8770	−	12.9078i	0.711056	−	0.772769i
$280$		0			0
$281$	14.3212			0.854330			0.427165	−	0.904174i	$-0.359512\pi$
$281$	14.3212			0.854330			0.427165	+	0.904174i	$0.359512\pi$
$282$		0			0
$283$	5.80753	+	5.80753i	0.345222	+	0.345222i	0.858326	−	0.513104i	$-0.171505\pi$
$283$	5.80753	+	5.80753i	0.345222	+	0.345222i	−0.513104	+	0.858326i	$0.671505\pi$
$284$		0			0
$285$	11.8316	+	4.61513i	0.700842	+	0.273376i
$286$		0			0
$287$	−0.688196			−0.0406229
$288$		0			0
$289$	10.3846			0.610857
$290$		0			0
$291$	16.4030	+	6.39829i	0.961560	+	0.375074i
$292$		0			0
$293$	−1.00713	−	1.00713i	−0.0588371	−	0.0588371i	0.677076	−	0.735913i	$-0.263247\pi$
$293$	−1.00713	−	1.00713i	−0.0588371	−	0.0588371i	−0.735913	+	0.677076i	$0.763247\pi$
$294$		0			0
$295$	−12.3034			−0.716330
$296$		0			0
$297$	13.7598	+	4.71843i	0.798422	+	0.273791i
$298$		0			0
$299$	−3.96327	+	3.96327i	−0.229202	+	0.229202i
$300$		0			0
$301$	−0.649101	−	0.649101i	−0.0374136	−	0.0374136i
$302$		0			0
$303$	−11.4133	−	26.0117i	−0.655680	−	1.49433i
$304$		0			0
$305$			40.9146i			2.34276i
$306$		0			0
$307$	3.43988	−	3.43988i	0.196324	−	0.196324i	−0.602098	−	0.798422i	$-0.705668\pi$
$307$	3.43988	−	3.43988i	0.196324	−	0.196324i	0.798422	+	0.602098i	$0.205668\pi$
$308$		0			0
$309$	−9.68806	−	3.77901i	−0.551135	−	0.214980i
$310$		0			0
$311$			26.3610i			1.49480i	0.664377	+	0.747398i	$0.268697\pi$
$311$			26.3610i			1.49480i	−0.664377	+	0.747398i	$0.731303\pi$
$312$		0			0
$313$			26.3343i			1.48850i	0.667900	+	0.744251i	$0.267193\pi$
$313$			26.3343i			1.48850i	−0.667900	+	0.744251i	$0.732807\pi$
$314$		0			0
$315$	−0.544230	−	13.0854i	−0.0306639	−	0.737276i
$316$		0			0
$317$	−6.78539	+	6.78539i	−0.381105	+	0.381105i	−0.871500	−	0.490395i	$-0.836853\pi$
$317$	−6.78539	+	6.78539i	−0.381105	+	0.381105i	0.490395	+	0.871500i	$0.336853\pi$
$318$		0			0
$319$		−	5.29084i		−	0.296230i
$320$		0			0
$321$	−19.8669	+	8.71714i	−1.10886	+	0.486543i
$322$		0			0
$323$	3.05465	+	3.05465i	0.169965	+	0.169965i
$324$		0			0
$325$	−46.0444	+	46.0444i	−2.55408	+	2.55408i
$326$		0			0
$327$	−8.97674	−	20.4585i	−0.496415	−	1.13136i
$328$		0			0
$329$	10.5648			0.582458
$330$		0			0
$331$	16.6074	+	16.6074i	0.912823	+	0.912823i	0.996494	−	0.0836701i	$-0.0266642\pi$
$331$	16.6074	+	16.6074i	0.912823	+	0.912823i	−0.0836701	+	0.996494i	$0.526664\pi$
$332$		0			0
$333$	21.9803	−	0.914177i	1.20451	−	0.0500966i
$334$		0			0
$335$	27.8069			1.51925
$336$		0			0
$337$	−5.72436			−0.311826			−0.155913	−	0.987771i	$-0.549832\pi$
$337$	−5.72436			−0.311826			−0.155913	+	0.987771i	$0.549832\pi$
$338$		0			0
$339$	−5.64523	+	14.4724i	−0.306607	+	0.786033i
$340$		0			0
$341$	11.5739	+	11.5739i	0.626761	+	0.626761i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−8.37856	+	3.67633i	−0.451087	+	0.197927i
$346$		0			0
$347$	−8.46543	+	8.46543i	−0.454448	+	0.454448i	−0.896828	−	0.442380i	$-0.854134\pi$
$347$	−8.46543	+	8.46543i	−0.454448	+	0.454448i	0.442380	+	0.896828i	$0.354134\pi$
$348$		0			0
$349$	3.18646	+	3.18646i	0.170567	+	0.170567i	0.787229	−	0.616661i	$-0.211515\pi$
$349$	3.18646	+	3.18646i	0.170567	+	0.170567i	−0.616661	+	0.787229i	$0.711515\pi$
$350$		0			0
$351$	7.80715	−	22.7670i	0.416715	−	1.21521i
$352$		0			0
$353$			9.14533i			0.486757i	0.969931	+	0.243378i	$0.0782557\pi$
$353$			9.14533i			0.486757i	−0.969931	+	0.243378i	$0.921744\pi$
$354$		0			0
$355$	12.0804	−	12.0804i	0.641161	−	0.641161i
$356$		0			0
$357$	1.61892	−	4.15035i	0.0856824	−	0.219660i
$358$		0			0
$359$		−	32.5834i		−	1.71969i	−0.510557	−	0.859844i	$-0.670561\pi$
$359$		−	32.5834i		−	1.71969i	0.510557	−	0.859844i	$-0.329439\pi$
$360$		0			0
$361$			16.1791i			0.851529i
$362$		0			0
$363$	1.99098	−	5.10419i	0.104500	−	0.267900i
$364$		0			0
$365$	−30.3504	+	30.3504i	−1.58861	+	1.58861i
$366$		0			0
$367$			34.9220i			1.82292i	0.411394	+	0.911458i	$0.365042\pi$
$367$			34.9220i			1.82292i	−0.411394	+	0.911458i	$0.634958\pi$
$368$		0			0
$369$	−1.51929	−	1.39796i	−0.0790910	−	0.0727748i
$370$		0			0
$371$	3.84828	+	3.84828i	0.199793	+	0.199793i
$372$		0			0
$373$	−3.26165	+	3.26165i	−0.168882	+	0.168882i	−0.786488	−	0.617606i	$-0.788103\pi$
$373$	−3.26165	+	3.26165i	−0.168882	+	0.168882i	0.617606	+	0.786488i	$0.288103\pi$
$374$		0			0
$375$	−62.7195	+	27.5199i	−3.23882	+	1.42112i
$376$		0			0
$377$	−8.75427			−0.450868
$378$		0			0
$379$	−5.59162	−	5.59162i	−0.287222	−	0.287222i	0.548759	−	0.835981i	$-0.315101\pi$
$379$	−5.59162	−	5.59162i	−0.287222	−	0.287222i	−0.835981	+	0.548759i	$0.815101\pi$
$380$		0			0
$381$	−0.357246	+	0.915854i	−0.0183023	+	0.0469206i
$382$		0			0
$383$	−12.0233			−0.614362			−0.307181	−	0.951651i	$-0.599386\pi$
$383$	−12.0233			−0.614362			−0.307181	+	0.951651i	$0.599386\pi$
$384$		0			0
$385$	12.2211			0.622845
$386$		0			0
$387$	−0.114438	−	2.75152i	−0.00581721	−	0.139868i
$388$		0			0
$389$	−0.0179418	−	0.0179418i	−0.000909686	−	0.000909686i	0.706652	−	0.707561i	$-0.250205\pi$
$389$	−0.0179418	−	0.0179418i	−0.000909686	−	0.000909686i	−0.707561	+	0.706652i	$0.750205\pi$
$390$		0			0
$391$	−3.11231			−0.157396
$392$		0			0
$393$	3.85079	+	8.77618i	0.194247	+	0.442699i
$394$		0			0
$395$	−11.9349	+	11.9349i	−0.600511	+	0.600511i
$396$		0			0
$397$	−1.15667	−	1.15667i	−0.0580514	−	0.0580514i	0.677485	−	0.735537i	$-0.263070\pi$
$397$	−1.15667	−	1.15667i	−0.0580514	−	0.0580514i	−0.735537	+	0.677485i	$0.763070\pi$
$398$		0			0
$399$	−2.66394	+	1.16888i	−0.133364	+	0.0585170i
$400$		0			0
$401$		−	7.84082i		−	0.391552i	−0.980649	−	0.195776i	$-0.937278\pi$
$401$		−	7.84082i		−	0.391552i	0.980649	−	0.195776i	$-0.0627225\pi$
$402$		0			0
$403$	19.1502	−	19.1502i	0.953942	−	0.953942i
$404$		0			0
$405$	25.3793	−	29.9933i	1.26111	−	1.49038i
$406$		0			0
$407$			20.5285i			1.01756i
$408$		0			0
$409$		−	16.1657i		−	0.799344i	−0.916658	−	0.399672i	$-0.869124\pi$
$409$		−	16.1657i		−	0.799344i	0.916658	−	0.399672i	$-0.130876\pi$
$410$		0			0
$411$	30.3695	+	11.8462i	1.49802	+	0.584330i
$412$		0			0
$413$	1.99283	−	1.99283i	0.0980606	−	0.0980606i
$414$		0			0
$415$		−	18.5129i		−	0.908763i
$416$		0			0
$417$	−9.86803	−	22.4898i	−0.483239	−	1.10133i
$418$		0			0
$419$	−5.12464	−	5.12464i	−0.250355	−	0.250355i	0.570761	−	0.821116i	$-0.306648\pi$
$419$	−5.12464	−	5.12464i	−0.250355	−	0.250355i	−0.821116	+	0.570761i	$0.806648\pi$
$420$		0			0
$421$	8.36782	−	8.36782i	0.407823	−	0.407823i	−0.473156	−	0.880979i	$-0.656885\pi$
$421$	8.36782	−	8.36782i	0.407823	−	0.407823i	0.880979	+	0.473156i	$0.156885\pi$
$422$		0			0
$423$	23.3233	+	21.4607i	1.13402	+	1.04346i
$424$		0			0
$425$	−36.1581			−1.75392
$426$		0			0
$427$	−6.62710	−	6.62710i	−0.320708	−	0.320708i
$428$		0			0
$429$	20.9238	+	8.16174i	1.01021	+	0.394052i
$430$		0			0
$431$	27.9027			1.34403			0.672014	−	0.740539i	$-0.265430\pi$
$431$	27.9027			1.34403			0.672014	+	0.740539i	$0.265430\pi$
$432$		0			0
$433$	3.68845			0.177256			0.0886278	−	0.996065i	$-0.471752\pi$
$433$	3.68845			0.177256			0.0886278	+	0.996065i	$0.471752\pi$
$434$		0			0
$435$	−13.3137	−	5.19327i	−0.638344	−	0.248998i
$436$		0			0
$437$	1.43710	+	1.43710i	0.0687456	+	0.0687456i
$438$		0			0
$439$	−33.8702			−1.61654			−0.808268	−	0.588814i	$-0.799595\pi$
$439$	−33.8702			−1.61654			−0.808268	+	0.588814i	$0.799595\pi$
$440$		0			0
$441$	2.20764	+	2.03134i	0.105126	+	0.0967303i
$442$		0			0
$443$	2.28546	−	2.28546i	0.108586	−	0.108586i	−0.650727	−	0.759312i	$-0.725536\pi$
$443$	2.28546	−	2.28546i	0.108586	−	0.108586i	0.759312	+	0.650727i	$0.225536\pi$
$444$		0			0
$445$	−33.5736	−	33.5736i	−1.59154	−	1.59154i
$446$		0			0
$447$	0.115812	+	0.263943i	0.00547773	+	0.0124841i
$448$		0			0
$449$			0.726262i			0.0342744i	0.999853	+	0.0171372i	$0.00545521\pi$
$449$			0.726262i			0.0342744i	−0.999853	+	0.0171372i	$0.994545\pi$
$450$		0			0
$451$	1.36228	−	1.36228i	0.0641475	−	0.0641475i
$452$		0			0
$453$	−38.8509	−	15.1545i	−1.82537	−	0.712021i
$454$		0			0
$455$		−	20.2211i		−	0.947981i
$456$		0			0
$457$			5.34320i			0.249944i	0.992160	+	0.124972i	$0.0398842\pi$
$457$			5.34320i			0.249944i	−0.992160	+	0.124972i	$0.960116\pi$
$458$		0			0
$459$	12.0047	−	5.87390i	0.560334	−	0.274170i
$460$		0			0
$461$	−9.51942	+	9.51942i	−0.443364	+	0.443364i	−0.893141	−	0.449777i	$-0.851503\pi$
$461$	−9.51942	+	9.51942i	−0.443364	+	0.443364i	0.449777	+	0.893141i	$0.351503\pi$
$462$		0			0
$463$		−	10.7468i		−	0.499448i	−0.968317	−	0.249724i	$-0.919660\pi$
$463$		−	10.7468i		−	0.499448i	0.968317	−	0.249724i	$-0.0803399\pi$
$464$		0			0
$465$	40.4846	−	17.7638i	1.87743	−	0.823774i
$466$		0			0
$467$	23.0136	+	23.0136i	1.06494	+	1.06494i	0.997739	+	0.0672049i	$0.0214081\pi$
$467$	23.0136	+	23.0136i	1.06494	+	1.06494i	0.0672049	+	0.997739i	$0.478592\pi$
$468$		0			0
$469$	−4.50400	+	4.50400i	−0.207975	+	0.207975i
$470$		0			0
$471$	5.21226	+	11.8790i	0.240168	+	0.547357i
$472$		0			0
$473$	2.56979			0.118159
$474$		0			0
$475$	16.6958	+	16.6958i	0.766058	+	0.766058i
$476$		0			0
$477$	0.678460	+	16.3128i	0.0310645	+	0.746910i
$478$		0			0
$479$	−36.4521			−1.66554			−0.832769	−	0.553620i	$-0.813246\pi$
$479$	−36.4521			−1.66554			−0.832769	+	0.553620i	$0.813246\pi$
$480$		0			0
$481$	33.9667			1.54875
$482$		0			0
$483$	0.761640	−	1.95258i	0.0346558	−	0.0888454i
$484$		0			0
$485$	31.3792	+	31.3792i	1.42486	+	1.42486i
$486$		0			0
$487$	24.5053			1.11044			0.555221	−	0.831703i	$-0.312634\pi$
$487$	24.5053			1.11044			0.555221	+	0.831703i	$0.312634\pi$
$488$		0			0
$489$	35.7820	−	15.7003i	1.61812	−	0.709994i
$490$		0			0
$491$	−4.59091	+	4.59091i	−0.207185	+	0.207185i	−0.803070	−	0.595885i	$-0.796801\pi$
$491$	−4.59091	+	4.59091i	−0.207185	+	0.207185i	0.595885	+	0.803070i	$0.296801\pi$
$492$		0			0
$493$	−3.43731	−	3.43731i	−0.154809	−	0.154809i
$494$		0			0
$495$	26.9798	+	24.8252i	1.21265	+	1.11581i
$496$		0			0
$497$			3.91342i			0.175541i
$498$		0			0
$499$	−0.0693040	+	0.0693040i	−0.00310247	+	0.00310247i	−0.708656	−	0.705554i	$-0.750698\pi$
$499$	−0.0693040	+	0.0693040i	−0.00310247	+	0.00310247i	0.705554	+	0.708656i	$0.250698\pi$
$500$		0			0
$501$	−10.4429	+	26.7719i	−0.466554	+	1.19608i
$502$		0			0
$503$		−	2.99458i		−	0.133522i	−0.997769	−	0.0667609i	$-0.978734\pi$
$503$		−	2.99458i		−	0.133522i	0.997769	−	0.0667609i	$-0.0212665\pi$
$504$		0			0
$505$		−	71.5948i		−	3.18593i
$506$		0			0
$507$	5.32190	−	13.6435i	0.236354	−	0.605929i
$508$		0			0
$509$	16.5223	−	16.5223i	0.732339	−	0.732339i	−0.238744	−	0.971083i	$-0.576736\pi$
$509$	16.5223	−	16.5223i	0.732339	−	0.732339i	0.971083	+	0.238744i	$0.0767356\pi$
$510$		0			0
$511$		−	9.83194i		−	0.434939i
$512$		0			0
$513$	−8.25540	−	2.83090i	−0.364485	−	0.124987i
$514$		0			0
$515$	−18.5334	−	18.5334i	−0.816681	−	0.816681i
$516$		0			0
$517$	−20.9131	+	20.9131i	−0.919756	+	0.919756i
$518$		0			0
$519$	−6.16808	+	2.70642i	−0.270749	+	0.118798i
$520$		0			0
$521$	10.8943			0.477289			0.238645	−	0.971107i	$-0.423297\pi$
$521$	10.8943			0.477289			0.238645	+	0.971107i	$0.423297\pi$
$522$		0			0
$523$	0.249542	+	0.249542i	0.0109117	+	0.0109117i	0.712542	−	0.701630i	$-0.247544\pi$
$523$	0.249542	+	0.249542i	0.0109117	+	0.0109117i	−0.701630	+	0.712542i	$0.747544\pi$
$524$		0			0
$525$	8.84856	−	22.6846i	0.386183	−	0.990038i
$526$		0			0
$527$	15.0384			0.655085
$528$		0			0
$529$	21.5358			0.936338
$530$		0			0
$531$	8.44755	−	0.351340i	0.366592	−	0.0152468i
$532$		0			0
$533$	−2.25405	−	2.25405i	−0.0976336	−	0.0976336i
$534$		0			0
$535$	−54.6817			−2.36410
$536$		0			0
$537$	−5.49416	−	12.5215i	−0.237090	−	0.540343i
$538$		0			0
$539$	−1.97950	+	1.97950i	−0.0852631	+	0.0852631i
$540$		0			0
$541$	31.1489	+	31.1489i	1.33920	+	1.33920i	0.896839	+	0.442356i	$0.145857\pi$
$541$	31.1489	+	31.1489i	1.33920	+	1.33920i	0.442356	+	0.896839i	$0.354143\pi$
$542$		0			0
$543$	−15.1196	+	6.63416i	−0.648846	+	0.284699i
$544$		0			0
$545$		−	56.3102i		−	2.41206i
$546$		0			0
$547$	−0.0905284	+	0.0905284i	−0.00387072	+	0.00387072i	−0.709039	−	0.705169i	$-0.750871\pi$
$547$	−0.0905284	+	0.0905284i	−0.00387072	+	0.00387072i	0.705169	+	0.709039i	$0.250871\pi$
$548$		0			0
$549$	−1.16837	−	28.0921i	−0.0498649	−	1.19894i
$550$		0			0
$551$			3.17433i			0.135231i
$552$		0			0
$553$		−	3.86630i		−	0.164412i
$554$		0			0
$555$	51.6574	+	20.1499i	2.19273	+	0.855317i
$556$		0			0
$557$	3.38154	−	3.38154i	0.143280	−	0.143280i	−0.631828	−	0.775109i	$-0.717695\pi$
$557$	3.38154	−	3.38154i	0.143280	−	0.143280i	0.775109	+	0.631828i	$0.217695\pi$
$558$		0			0
$559$		−	4.25200i		−	0.179840i
$560$		0			0
$561$	5.01096	+	11.4203i	0.211563	+	0.482164i
$562$		0			0
$563$	−19.9160	−	19.9160i	−0.839359	−	0.839359i	0.149415	−	0.988775i	$-0.452261\pi$
$563$	−19.9160	−	19.9160i	−0.839359	−	0.839359i	−0.988775	+	0.149415i	$0.952261\pi$
$564$		0			0
$565$	−27.6860	+	27.6860i	−1.16476	+	1.16476i
$566$		0			0
$567$	0.747340	+	8.96892i	0.0313854	+	0.376659i
$568$		0			0
$569$	28.9671			1.21436			0.607182	−	0.794563i	$-0.292300\pi$
$569$	28.9671			1.21436			0.607182	+	0.794563i	$0.292300\pi$
$570$		0			0
$571$	−2.01378	−	2.01378i	−0.0842740	−	0.0842740i	0.663713	−	0.747987i	$-0.268980\pi$
$571$	−2.01378	−	2.01378i	−0.0842740	−	0.0842740i	−0.747987	+	0.663713i	$0.768980\pi$
$572$		0			0
$573$	−39.3490	−	15.3488i	−1.64383	−	0.641206i
$574$		0			0
$575$	−17.0110			−0.709407
$576$		0			0
$577$	1.36897			0.0569909			0.0284954	−	0.999594i	$-0.490928\pi$
$577$	1.36897			0.0569909			0.0284954	+	0.999594i	$0.490928\pi$
$578$		0			0
$579$	−6.52055	−	2.54346i	−0.270985	−	0.105703i
$580$		0			0
$581$	2.99861	+	2.99861i	0.124403	+	0.124403i
$582$		0			0
$583$	−15.2353			−0.630983
$584$		0			0
$585$	41.0759	−	44.6409i	1.69828	−	1.84568i
$586$		0			0
$587$	17.6935	−	17.6935i	0.730291	−	0.730291i	−0.240386	−	0.970677i	$-0.577274\pi$
$587$	17.6935	−	17.6935i	0.730291	−	0.730291i	0.970677	+	0.240386i	$0.0772742\pi$
$588$		0			0
$589$	−6.94394	−	6.94394i	−0.286120	−	0.286120i
$590$		0			0
$591$	−5.10883	−	11.6433i	−0.210149	−	0.478942i
$592$		0			0
$593$		−	35.7646i		−	1.46868i	−0.678784	−	0.734338i	$-0.737493\pi$
$593$		−	35.7646i		−	1.46868i	0.678784	−	0.734338i	$-0.262507\pi$
$594$		0			0
$595$	7.93969	−	7.93969i	0.325496	−	0.325496i
$596$		0			0
$597$	15.8074	+	6.16595i	0.646952	+	0.252356i
$598$		0			0
$599$		−	2.49924i		−	0.102116i	−0.998696	−	0.0510580i	$-0.983741\pi$
$599$		−	2.49924i		−	0.102116i	0.998696	−	0.0510580i	$-0.0162593\pi$
$600$		0			0
$601$			38.0455i			1.55191i	0.630788	+	0.775955i	$0.282732\pi$
$601$			38.0455i			1.55191i	−0.630788	+	0.775955i	$0.717268\pi$
$602$		0			0
$603$	−19.0923	+	0.794064i	−0.777500	+	0.0323368i
$604$		0			0
$605$	9.76441	−	9.76441i	0.396980	−	0.396980i
$606$		0			0
$607$			29.7645i			1.20810i	0.796945	+	0.604052i	$0.206448\pi$
$607$			29.7645i			1.20810i	−0.796945	+	0.604052i	$0.793552\pi$
$608$		0			0
$609$	2.99765	−	1.31530i	0.121471	−	0.0532988i
$610$		0			0
$611$	34.6029	+	34.6029i	1.39988	+	1.39988i
$612$		0			0
$613$	1.99144	−	1.99144i	0.0804334	−	0.0804334i	−0.665745	−	0.746179i	$-0.731886\pi$
$613$	1.99144	−	1.99144i	0.0804334	−	0.0804334i	0.746179	+	0.665745i	$0.231886\pi$
$614$		0			0
$615$	−2.09085	−	4.76517i	−0.0843113	−	0.192150i
$616$		0			0
$617$	−21.1861			−0.852919			−0.426459	−	0.904507i	$-0.640239\pi$
$617$	−21.1861			−0.852919			−0.426459	+	0.904507i	$0.640239\pi$
$618$		0			0
$619$	11.4071	+	11.4071i	0.458490	+	0.458490i	0.898160	−	0.439669i	$-0.144904\pi$
$619$	11.4071	+	11.4071i	0.458490	+	0.458490i	−0.439669	+	0.898160i	$0.644904\pi$
$620$		0			0
$621$	5.64777	−	2.76344i	0.226637	−	0.110893i
$622$		0			0
$623$	10.8761			0.435742
$624$		0			0
$625$	−102.339			−4.09357
$626$		0			0
$627$	2.95947	−	7.58706i	0.118190	−	0.302998i
$628$		0			0
$629$	13.3368	+	13.3368i	0.531773	+	0.531773i
$630$		0			0
$631$	7.58954			0.302135			0.151067	−	0.988523i	$-0.451729\pi$
$631$	7.58954			0.302135			0.151067	+	0.988523i	$0.451729\pi$
$632$		0			0
$633$	−13.4017	+	5.88037i	−0.532669	+	0.233724i
$634$		0			0
$635$	−1.75205	+	1.75205i	−0.0695278	+	0.0695278i
$636$		0			0
$637$	3.27530	+	3.27530i	0.129772	+	0.129772i
$638$		0			0
$639$	−7.94948	+	8.63942i	−0.314476	+	0.341770i
$640$		0			0
$641$		−	8.43526i		−	0.333173i	−0.986027	−	0.166586i	$-0.946726\pi$
$641$		−	8.43526i		−	0.333173i	0.986027	−	0.166586i	$-0.0532745\pi$
$642$		0			0
$643$	32.7140	−	32.7140i	1.29011	−	1.29011i	0.355400	−	0.934714i	$-0.384345\pi$
$643$	32.7140	−	32.7140i	1.29011	−	1.29011i	0.934714	−	0.355400i	$-0.115655\pi$
$644$		0			0
$645$	2.52240	−	6.46655i	0.0993193	−	0.254620i
$646$		0			0
$647$		−	27.3057i		−	1.07350i	−0.843742	−	0.536749i	$-0.819652\pi$
$647$		−	27.3057i		−	1.07350i	0.843742	−	0.536749i	$-0.180348\pi$
$648$		0			0
$649$			7.88960i			0.309694i
$650$		0			0
$651$	−3.68019	+	9.43472i	−0.144238	+	0.369776i
$652$		0			0
$653$	−8.02481	+	8.02481i	−0.314035	+	0.314035i	−0.846471	−	0.532435i	$-0.821277\pi$
$653$	−8.02481	+	8.02481i	−0.314035	+	0.314035i	0.532435	+	0.846471i	$0.321277\pi$
$654$		0			0
$655$			24.1556i			0.943838i
$656$		0			0
$657$	19.9720	−	21.7054i	0.779181	−	0.846807i
$658$		0			0
$659$	12.8214	+	12.8214i	0.499453	+	0.499453i	0.911268	−	0.411815i	$-0.135105\pi$
$659$	12.8214	+	12.8214i	0.499453	+	0.499453i	−0.411815	+	0.911268i	$0.635105\pi$
$660$		0			0
$661$	−3.38516	+	3.38516i	−0.131667	+	0.131667i	−0.769869	−	0.638202i	$-0.779679\pi$
$661$	−3.38516	+	3.38516i	−0.131667	+	0.131667i	0.638202	+	0.769869i	$0.279679\pi$
$662$		0			0
$663$	18.8961	−	8.29117i	0.733862	−	0.322002i
$664$		0			0
$665$	−7.33224			−0.284332
$666$		0			0
$667$	−1.61712	−	1.61712i	−0.0626152	−	0.0626152i
$668$		0			0
$669$	−6.92269	+	17.7474i	−0.267647	+	0.686153i
$670$		0			0
$671$	26.2367			1.01286
$672$		0			0
$673$	−17.9865			−0.693330			−0.346665	−	0.937989i	$-0.612686\pi$
$673$	−17.9865			−0.693330			−0.346665	+	0.937989i	$0.612686\pi$
$674$		0			0
$675$	65.6145	−	32.1051i	2.52550	−	1.23572i
$676$		0			0
$677$	−20.9528	−	20.9528i	−0.805282	−	0.805282i	0.178634	−	0.983916i	$-0.442832\pi$
$677$	−20.9528	−	20.9528i	−0.805282	−	0.805282i	−0.983916	+	0.178634i	$0.942832\pi$
$678$		0			0
$679$	−10.1652			−0.390106
$680$		0			0
$681$	−12.0221	−	27.3991i	−0.460689	−	1.04994i
$682$		0			0
$683$	5.56984	−	5.56984i	0.213124	−	0.213124i	−0.592469	−	0.805593i	$-0.701847\pi$
$683$	5.56984	−	5.56984i	0.213124	−	0.213124i	0.805593	+	0.592469i	$0.201847\pi$
$684$		0			0
$685$	58.0975	+	58.0975i	2.21979	+	2.21979i
$686$		0			0
$687$	−29.5818	+	12.9798i	−1.12862	+	0.495212i
$688$		0			0
$689$			25.2085i			0.960367i
$690$		0			0
$691$	−29.9017	+	29.9017i	−1.13751	+	1.13751i	−0.148621	+	0.988894i	$0.547483\pi$
$691$	−29.9017	+	29.9017i	−1.13751	+	1.13751i	−0.988894	+	0.148621i	$0.952517\pi$
$692$		0			0
$693$	−8.39105	+	0.348990i	−0.318750	+	0.0132570i
$694$		0			0
$695$		−	61.9011i		−	2.34804i
$696$		0			0
$697$		−	1.77007i		−	0.0670463i
$698$		0			0
$699$	−5.74915	−	2.24256i	−0.217453	−	0.0848216i
$700$		0			0
$701$	7.62355	−	7.62355i	0.287938	−	0.287938i	−0.548327	−	0.836264i	$-0.684735\pi$
$701$	7.62355	−	7.62355i	0.287938	−	0.287938i	0.836264	+	0.548327i	$0.184735\pi$
$702$		0			0
$703$		−	12.3164i		−	0.464523i
$704$		0			0
$705$	32.0977	+	73.1524i	1.20887	+	2.75508i
$706$		0			0
$707$	11.5965	+	11.5965i	0.436131	+	0.436131i
$708$		0			0
$709$	28.7112	−	28.7112i	1.07827	−	1.07827i	0.0816082	−	0.996664i	$-0.473994\pi$
$709$	28.7112	−	28.7112i	1.07827	−	1.07827i	0.996664	−	0.0816082i	$-0.0260056\pi$
$710$		0			0
$711$	7.85375	−	8.53539i	0.294539	−	0.320102i
$712$		0			0
$713$	7.07501			0.264961
$714$		0			0
$715$	40.0277	+	40.0277i	1.49695	+	1.49695i
$716$		0			0
$717$	2.27489	+	0.887363i	0.0849573	+	0.0331392i
$718$		0			0
$719$	−34.9223			−1.30238			−0.651191	−	0.758913i	$-0.725731\pi$
$719$	−34.9223			−1.30238			−0.651191	+	0.758913i	$0.725731\pi$
$720$		0			0
$721$	6.00387			0.223596
$722$		0			0
$723$	−13.4351	−	5.24061i	−0.499657	−	0.194900i
$724$		0			0
$725$	−18.7873	−	18.7873i	−0.697745	−	0.697745i
$726$		0			0
$727$	−33.6565			−1.24825			−0.624126	−	0.781324i	$-0.714545\pi$
$727$	−33.6565			−1.24825			−0.624126	+	0.781324i	$0.714545\pi$
$728$		0			0
$729$	−16.5690	+	21.3182i	−0.613668	+	0.789564i
$730$		0			0
$731$	1.66952	−	1.66952i	0.0617494	−	0.0617494i
$732$		0			0
$733$	1.66624	+	1.66624i	0.0615441	+	0.0615441i	0.737209	−	0.675665i	$-0.236143\pi$
$733$	1.66624	+	1.66624i	0.0615441	+	0.0615441i	−0.675665	+	0.737209i	$0.736143\pi$
$734$		0			0
$735$	3.03816	+	6.92415i	0.112064	+	0.255401i
$736$		0			0
$737$		−	17.8313i		−	0.656825i
$738$		0			0
$739$	−16.9821	+	16.9821i	−0.624695	+	0.624695i	−0.946728	−	0.322033i	$-0.895634\pi$
$739$	−16.9821	+	16.9821i	−0.624695	+	0.624695i	0.322033	+	0.946728i	$0.395634\pi$
$740$		0			0
$741$	−12.5536	−	4.89677i	−0.461168	−	0.179887i
$742$		0			0
$743$		−	28.1960i		−	1.03441i	−0.855861	−	0.517206i	$-0.826972\pi$
$743$		−	28.1960i		−	1.03441i	0.855861	−	0.517206i	$-0.173028\pi$
$744$		0			0
$745$			0.726479i			0.0266161i
$746$		0			0
$747$	0.528661	+	12.7110i	0.0193427	+	0.465073i
$748$		0			0
$749$	8.85702	−	8.85702i	0.323629	−	0.323629i
$750$		0			0
$751$		−	45.6010i		−	1.66400i	−0.554773	−	0.832002i	$-0.687195\pi$
$751$		−	45.6010i		−	1.66400i	0.554773	−	0.832002i	$-0.312805\pi$
$752$		0			0
$753$	17.6306	−	7.73593i	0.642496	−	0.281913i
$754$		0			0
$755$	−74.3224	−	74.3224i	−2.70487	−	2.70487i
$756$		0			0
$757$	−10.3540	+	10.3540i	−0.376321	+	0.376321i	−0.869773	−	0.493452i	$-0.835735\pi$
$757$	−10.3540	+	10.3540i	−0.376321	+	0.376321i	0.493452	+	0.869773i	$0.335735\pi$
$758$		0			0
$759$	2.35746	+	5.37280i	0.0855705	+	0.195020i
$760$		0			0
$761$	43.0264			1.55971			0.779854	−	0.625962i	$-0.215294\pi$
$761$	43.0264			1.55971			0.779854	+	0.625962i	$0.215294\pi$
$762$		0			0
$763$	9.12079	+	9.12079i	0.330195	+	0.330195i
$764$		0			0
$765$	33.6562	−	1.39978i	1.21684	−	0.0506093i
$766$		0			0
$767$	13.0542			0.471360
$768$		0			0
$769$	−26.0310			−0.938702			−0.469351	−	0.883012i	$-0.655512\pi$
$769$	−26.0310			−0.938702			−0.469351	+	0.883012i	$0.655512\pi$
$770$		0			0
$771$	−8.41553	+	21.5745i	−0.303078	+	0.776986i
$772$		0			0
$773$	−14.6325	−	14.6325i	−0.526293	−	0.526293i	0.393172	−	0.919465i	$-0.371378\pi$
$773$	−14.6325	−	14.6325i	−0.526293	−	0.526293i	−0.919465	+	0.393172i	$0.871378\pi$
$774$		0			0
$775$	82.1959			2.95256
$776$		0			0
$777$	−11.6309	+	5.10339i	−0.417257	+	0.183083i
$778$		0			0
$779$	−0.817325	+	0.817325i	−0.0292837	+	0.0292837i
$780$		0			0
$781$	−7.74662	−	7.74662i	−0.277196	−	0.277196i
$782$		0			0
$783$	9.28955	+	3.18553i	0.331982	+	0.113841i
$784$		0			0
$785$			32.6960i			1.16697i
$786$		0			0
$787$	−8.57358	+	8.57358i	−0.305615	+	0.305615i	−0.843206	−	0.537591i	$-0.819335\pi$
$787$	−8.57358	+	8.57358i	−0.305615	+	0.305615i	0.537591	+	0.843206i	$0.319335\pi$
$788$		0			0
$789$	−7.37235	+	18.9001i	−0.262463	+	0.672862i
$790$		0			0
$791$		−	8.96882i		−	0.318894i
$792$		0			0
$793$		−	43.4114i		−	1.54158i
$794$		0			0
$795$	−14.9544	+	38.3377i	−0.530376	+	1.35970i
$796$		0			0
$797$	−11.4463	+	11.4463i	−0.405448	+	0.405448i	−0.880148	−	0.474700i	$-0.842557\pi$
$797$	−11.4463	+	11.4463i	−0.405448	+	0.405448i	0.474700	+	0.880148i	$0.342557\pi$
$798$		0			0
$799$			27.1732i			0.961320i
$800$		0			0
$801$	24.0105	+	22.0930i	0.848370	+	0.780619i
$802$		0			0
$803$	19.4623	+	19.4623i	0.686811	+	0.686811i
$804$		0			0
$805$	3.73532	−	3.73532i	0.131653	−	0.131653i
$806$		0			0
$807$	39.8204	−	17.4723i	1.40174	−	0.615054i
$808$		0			0
$809$	38.0993			1.33950			0.669749	−	0.742587i	$-0.266402\pi$
$809$	38.0993			1.33950			0.669749	+	0.742587i	$0.266402\pi$
$810$		0			0
$811$	16.3455	+	16.3455i	0.573968	+	0.573968i	0.933235	−	0.359267i	$-0.116973\pi$
$811$	16.3455	+	16.3455i	0.573968	+	0.573968i	−0.359267	+	0.933235i	$0.616973\pi$
$812$		0			0
$813$	5.28965	−	13.5608i	0.185516	−	0.475598i
$814$		0			0
$815$	98.4866			3.44984
$816$		0			0
$817$	−1.54179			−0.0539403
$818$		0			0
$819$	0.577442	+	13.8839i	0.0201774	+	0.485143i
$820$		0			0
$821$	−21.2492	−	21.2492i	−0.741602	−	0.741602i	0.231285	−	0.972886i	$-0.425707\pi$
$821$	−21.2492	−	21.2492i	−0.741602	−	0.741602i	−0.972886	+	0.231285i	$0.925707\pi$
$822$		0			0
$823$	8.76959			0.305689			0.152844	−	0.988250i	$-0.451157\pi$
$823$	8.76959			0.305689			0.152844	+	0.988250i	$0.451157\pi$
$824$		0			0
$825$	27.3885	+	62.4199i	0.953545	+	2.17318i
$826$		0			0
$827$	−29.9690	+	29.9690i	−1.04212	+	1.04212i	−0.0430513	+	0.999073i	$0.513708\pi$
$827$	−29.9690	+	29.9690i	−1.04212	+	1.04212i	−0.999073	+	0.0430513i	$0.986292\pi$
$828$		0			0
$829$	−33.5844	−	33.5844i	−1.16644	−	1.16644i	−0.983039	−	0.183397i	$-0.941291\pi$
$829$	−33.5844	−	33.5844i	−1.16644	−	1.16644i	−0.183397	−	0.983039i	$-0.558709\pi$
$830$		0			0
$831$	−29.9680	+	13.1493i	−1.03958	+	0.456144i
$832$		0			0
$833$			2.57205i			0.0891162i
$834$		0			0
$835$	−51.2152	+	51.2152i	−1.77237	+	1.77237i
$836$		0			0
$837$	−27.2896	+	13.3528i	−0.943268	+	0.461539i
$838$		0			0
$839$			30.1442i			1.04069i	0.853955	+	0.520346i	$0.174197\pi$
$839$			30.1442i			1.04069i	−0.853955	+	0.520346i	$0.825803\pi$
$840$		0			0
$841$			25.4280i			0.876828i
$842$		0			0
$843$	−23.1092	−	9.01416i	−0.795922	−	0.310464i
$844$		0			0
$845$	26.1003	−	26.1003i	0.897876	−	0.897876i
$846$		0			0
$847$			3.16316i			0.108688i
$848$		0			0
$849$	−5.71581	−	13.0267i	−0.196166	−	0.447074i
$850$		0			0
$851$	6.27445	+	6.27445i	0.215085	+	0.215085i
$852$		0			0
$853$	10.2839	−	10.2839i	0.352114	−	0.352114i	−0.508782	−	0.860896i	$-0.669904\pi$
$853$	10.2839	−	10.2839i	0.352114	−	0.352114i	0.860896	+	0.508782i	$0.169904\pi$
$854$		0			0
$855$	−16.1870	−	14.8943i	−0.553582	−	0.509373i
$856$		0			0
$857$	26.6729			0.911130			0.455565	−	0.890203i	$-0.349437\pi$
$857$	26.6729			0.911130			0.455565	+	0.890203i	$0.349437\pi$
$858$		0			0
$859$	−28.1639	−	28.1639i	−0.960940	−	0.960940i	0.0383253	−	0.999265i	$-0.487798\pi$
$859$	−28.1639	−	28.1639i	−0.960940	−	0.960940i	−0.999265	+	0.0383253i	$0.987798\pi$
$860$		0			0
$861$	1.11050	+	0.433170i	0.0378457	+	0.0147624i
$862$		0			0
$863$	−26.6348			−0.906660			−0.453330	−	0.891343i	$-0.649764\pi$
$863$	−26.6348			−0.906660			−0.453330	+	0.891343i	$0.649764\pi$
$864$		0			0
$865$	−16.9771			−0.577238
$866$		0			0
$867$	−16.7569	−	6.53635i	−0.569095	−	0.221986i
$868$		0			0
$869$	7.65333	+	7.65333i	0.259622	+	0.259622i
$870$		0			0
$871$	−29.5038			−0.999699
$872$		0			0
$873$	−22.4412	−	20.6490i	−0.759518	−	0.698863i
$874$		0			0
$875$	27.9615	−	27.9615i	0.945272	−	0.945272i
$876$		0			0
$877$	−4.02186	−	4.02186i	−0.135809	−	0.135809i	0.635934	−	0.771743i	$-0.280615\pi$
$877$	−4.02186	−	4.02186i	−0.135809	−	0.135809i	−0.771743	+	0.635934i	$0.780615\pi$
$878$		0			0
$879$	0.991223	+	2.25905i	0.0334331	+	0.0761960i
$880$		0			0
$881$			29.0328i			0.978139i	0.872245	+	0.489070i	$0.162664\pi$
$881$			29.0328i			0.978139i	−0.872245	+	0.489070i	$0.837336\pi$
$882$		0			0
$883$	−15.0006	+	15.0006i	−0.504809	+	0.504809i	−0.912929	−	0.408119i	$-0.866185\pi$
$883$	−15.0006	+	15.0006i	−0.504809	+	0.504809i	0.408119	+	0.912929i	$0.366185\pi$
$884$		0			0
$885$	19.8532	+	7.74410i	0.667357	+	0.260315i
$886$		0			0
$887$		−	18.7872i		−	0.630811i	−0.948957	−	0.315405i	$-0.897859\pi$
$887$		−	18.7872i		−	0.630811i	0.948957	−	0.315405i	$-0.102141\pi$
$888$		0			0
$889$		−	0.567572i		−	0.0190357i
$890$		0			0
$891$	−19.2333	−	16.2746i	−0.644341	−	0.545220i
$892$		0			0
$893$	12.5471	−	12.5471i	0.419874	−	0.419874i
$894$		0			0
$895$		−	34.4643i		−	1.15201i
$896$		0			0
$897$	8.88987	−	3.90068i	0.296824	−	0.130240i
$898$		0			0
$899$	7.81382	+	7.81382i	0.260605	+	0.260605i
$900$		0			0
$901$	−9.89796	+	9.89796i	−0.329749	+	0.329749i
$902$		0			0
$903$	0.638850	+	1.45598i	0.0212596	+	0.0484518i
$904$		0			0
$905$	−41.6154			−1.38334
$906$		0			0
$907$	26.4990	+	26.4990i	0.879884	+	0.879884i	0.993522	−	0.113638i	$-0.0362504\pi$
$907$	26.4990	+	26.4990i	0.879884	+	0.879884i	−0.113638	+	0.993522i	$0.536250\pi$
$908$		0			0
$909$	2.04449	+	49.1573i	0.0678113	+	1.63044i
$910$		0			0
$911$	5.12785			0.169893			0.0849466	−	0.996386i	$-0.472928\pi$
$911$	5.12785			0.169893			0.0849466	+	0.996386i	$0.472928\pi$
$912$		0			0
$913$	−11.8715			−0.392889
$914$		0			0
$915$	25.7528	−	66.0212i	0.851361	−	2.18259i
$916$		0			0
$917$	−3.91258	−	3.91258i	−0.129205	−	0.129205i
$918$		0			0
$919$	−24.4708			−0.807217			−0.403609	−	0.914932i	$-0.632244\pi$
$919$	−24.4708			−0.807217			−0.403609	+	0.914932i	$0.632244\pi$
$920$		0			0
$921$	−7.71588	+	3.38556i	−0.254247	+	0.111558i
$922$		0			0
$923$	−12.8176	+	12.8176i	−0.421897	+	0.421897i
$924$		0			0
$925$	72.8952	+	72.8952i	2.39678	+	2.39678i
$926$		0			0
$927$	13.2544	+	12.1959i	0.435331	+	0.400566i
$928$		0			0
$929$		−	2.48396i		−	0.0814959i	−0.999169	−	0.0407480i	$-0.987026\pi$
$929$		−	2.48396i		−	0.0814959i	0.999169	−	0.0407480i	$-0.0129741\pi$
$930$		0			0
$931$	1.18763	−	1.18763i	0.0389231	−	0.0389231i
$932$		0			0
$933$	16.5924	−	42.5371i	0.543210	−	1.39260i
$934$		0			0
$935$			31.4332i			1.02798i
$936$		0			0
$937$		−	38.5530i		−	1.25947i	−0.776809	−	0.629737i	$-0.783163\pi$
$937$		−	38.5530i		−	1.25947i	0.776809	−	0.629737i	$-0.216837\pi$
$938$		0			0
$939$	16.5756	−	42.4939i	0.540923	−	1.38674i
$940$		0			0
$941$	26.7665	−	26.7665i	0.872561	−	0.872561i	−0.120190	−	0.992751i	$-0.538350\pi$
$941$	26.7665	−	26.7665i	0.872561	−	0.872561i	0.992751	+	0.120190i	$0.0383503\pi$
$942$		0			0
$943$		−	0.832752i		−	0.0271181i
$944$		0			0
$945$	−7.35811	+	21.4576i	−0.239359	+	0.698014i
$946$		0			0
$947$	23.3797	+	23.3797i	0.759740	+	0.759740i	0.976275	−	0.216535i	$-0.0694756\pi$
$947$	23.3797	+	23.3797i	0.759740	+	0.759740i	−0.216535	+	0.976275i	$0.569476\pi$
$948$		0			0
$949$	32.2025	−	32.2025i	1.04534	−	1.04534i
$950$		0			0
$951$	15.2201	−	6.67822i	0.493544	−	0.216556i
$952$		0			0
$953$	−35.9288			−1.16385			−0.581924	−	0.813243i	$-0.697700\pi$
$953$	−35.9288			−1.16385			−0.581924	+	0.813243i	$0.697700\pi$
$954$		0			0
$955$	−75.2754	−	75.2754i	−2.43585	−	2.43585i
$956$		0			0
$957$	−3.33021	+	8.53749i	−0.107650	+	0.275978i
$958$		0			0
$959$	−18.8206			−0.607748
$960$		0			0
$961$	−3.18594			−0.102772
$962$		0			0
$963$	37.5447	−	1.56151i	1.20986	−	0.0503190i
$964$		0			0
$965$	−12.4739	−	12.4739i	−0.401550	−	0.401550i
$966$		0			0
$967$	2.08883			0.0671722			0.0335861	−	0.999436i	$-0.489307\pi$
$967$	2.08883			0.0671722			0.0335861	+	0.999436i	$0.489307\pi$
$968$		0			0
$969$	−3.00641	−	6.85177i	−0.0965797	−	0.220111i
$970$		0			0
$971$	−1.66314	+	1.66314i	−0.0533728	+	0.0533728i	−0.733289	−	0.679917i	$-0.762016\pi$
$971$	−1.66314	+	1.66314i	−0.0533728	+	0.0533728i	0.679917	+	0.733289i	$0.262016\pi$
$972$		0			0
$973$	10.0264	+	10.0264i	0.321431	+	0.321431i
$974$		0			0
$975$	103.281	−	45.3172i	3.30762	−	1.45131i
$976$		0			0
$977$		−	41.6292i		−	1.33184i	−0.746025	−	0.665918i	$-0.768040\pi$
$977$		−	41.6292i		−	1.33184i	0.746025	−	0.665918i	$-0.231960\pi$
$978$		0			0
$979$	−21.5292	+	21.5292i	−0.688078	+	0.688078i
$980$		0			0
$981$	1.60801	+	38.6628i	0.0513399	+	1.23441i
$982$		0			0
$983$		−	4.18786i		−	0.133572i	−0.997767	−	0.0667861i	$-0.978726\pi$
$983$		−	4.18786i		−	0.133572i	0.997767	−	0.0667861i	$-0.0212745\pi$
$984$		0			0
$985$		−	32.0472i		−	1.02111i
$986$		0			0
$987$	−17.0478	−	6.64980i	−0.542637	−	0.211666i
$988$		0			0
$989$	0.785445	−	0.785445i	0.0249757	−	0.0249757i
$990$		0			0
$991$			6.94973i			0.220766i	0.993889	+	0.110383i	$0.0352077\pi$
$991$			6.94973i			0.220766i	−0.993889	+	0.110383i	$0.964792\pi$
$992$		0			0
$993$	−16.3451	−	37.2514i	−0.518696	−	1.18214i
$994$		0			0
$995$	30.2398	+	30.2398i	0.958665	+	0.958665i
$996$		0			0
$997$	−7.18530	+	7.18530i	−0.227561	+	0.227561i	−0.811673	−	0.584112i	$-0.801443\pi$
$997$	−7.18530	+	7.18530i	−0.227561	+	0.227561i	0.584112	+	0.811673i	$0.301443\pi$
$998$		0			0
$999$	−36.0436	−	12.3599i	−1.14037	−	0.391049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.3		40
3.2	odd	2	inner	1344.2.s.c.239.14		40
4.3	odd	2		336.2.s.c.323.17	yes	40
12.11	even	2		336.2.s.c.323.4	yes	40
16.5	even	4		336.2.s.c.155.4	✓	40
16.11	odd	4	inner	1344.2.s.c.911.14		40
48.5	odd	4		336.2.s.c.155.17	yes	40
48.11	even	4	inner	1344.2.s.c.911.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.4	✓	40	16.5	even	4
336.2.s.c.155.17	yes	40	48.5	odd	4
336.2.s.c.323.4	yes	40	12.11	even	2
336.2.s.c.323.17	yes	40	4.3	odd	2
1344.2.s.c.239.3		40	1.1	even	1	trivial
1344.2.s.c.239.14		40	3.2	odd	2	inner
1344.2.s.c.911.3		40	48.11	even	4	inner
1344.2.s.c.911.14		40	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61364 - 0.629429i) q^{3} +(-3.08691 - 3.08691i) q^{5} +1.00000 q^{7} +(2.20764 + 2.03134i) q^{9} +O(q^{10})\)	\(q+(-1.61364 - 0.629429i) q^{3} +(-3.08691 - 3.08691i) q^{5} +1.00000 q^{7} +(2.20764 + 2.03134i) q^{9} +(-1.97950 + 1.97950i) q^{11} +(3.27530 + 3.27530i) q^{13} +(3.03816 + 6.92415i) q^{15} +2.57205i q^{17} +(1.18763 - 1.18763i) q^{19} +(-1.61364 - 0.629429i) q^{21} +1.21005i q^{23} +14.0581i q^{25} +(-2.28374 - 4.66739i) q^{27} +(-1.33641 + 1.33641i) q^{29} -5.84687i q^{31} +(4.44015 - 1.94824i) q^{33} +(-3.08691 - 3.08691i) q^{35} +(5.18528 - 5.18528i) q^{37} +(-3.22357 - 7.34670i) q^{39} -0.688196 q^{41} +(-0.649101 - 0.649101i) q^{43} +(-0.544230 - 13.0854i) q^{45} +10.5648 q^{47} +1.00000 q^{49} +(1.61892 - 4.15035i) q^{51} +(3.84828 + 3.84828i) q^{53} +12.2211 q^{55} +(-2.66394 + 1.16888i) q^{57} +(1.99283 - 1.99283i) q^{59} +(-6.62710 - 6.62710i) q^{61} +(2.20764 + 2.03134i) q^{63} -20.2211i q^{65} +(-4.50400 + 4.50400i) q^{67} +(0.761640 - 1.95258i) q^{69} +3.91342i q^{71} -9.83194i q^{73} +(8.84856 - 22.6846i) q^{75} +(-1.97950 + 1.97950i) q^{77} -3.86630i q^{79} +(0.747340 + 8.96892i) q^{81} +(2.99861 + 2.99861i) q^{83} +(7.93969 - 7.93969i) q^{85} +(2.99765 - 1.31530i) q^{87} +10.8761 q^{89} +(3.27530 + 3.27530i) q^{91} +(-3.68019 + 9.43472i) q^{93} -7.33224 q^{95} -10.1652 q^{97} +(-8.39105 + 0.348990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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