LMFDB - Embedded newform 448.2.ba.c.81.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(81,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.5
Character	$\chi$	$=$	448.81
Dual form			448.2.ba.c.177.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831674 + 0.222846i) q^{3} +(-2.02749 - 0.543265i) q^{5} +(2.63544 + 0.233350i) q^{7} +(-1.95606 + 1.12933i) q^{9} +(-1.03385 - 3.85837i) q^{11} +(-0.990473 - 0.990473i) q^{13} +1.80728 q^{15} +(3.07828 - 5.33174i) q^{17} +(1.01626 - 3.79274i) q^{19} +(-2.24383 + 0.393227i) q^{21} +(-5.91462 + 3.41481i) q^{23} +(-0.514543 - 0.297072i) q^{25} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(2.05131 - 3.55296i) q^{31} +(1.71965 + 2.97851i) q^{33} +(-5.21656 - 1.90486i) q^{35} +(0.0740993 + 0.0198548i) q^{37} +(1.04447 + 0.603027i) q^{39} -8.68707i q^{41} +(-0.713530 + 0.713530i) q^{43} +(4.57941 - 1.22705i) q^{45} +(-1.95337 - 3.38334i) q^{47} +(6.89110 + 1.22996i) q^{49} +(-1.37197 + 5.12025i) q^{51} +(1.89324 + 7.06568i) q^{53} +8.38446i q^{55} +3.38079i q^{57} +(0.851626 + 3.17831i) q^{59} +(-2.37044 + 8.84662i) q^{61} +(-5.41860 + 2.51983i) q^{63} +(1.47009 + 2.54627i) q^{65} +(1.49739 - 0.401223i) q^{67} +(4.15805 - 4.15805i) q^{69} +2.86486i q^{71} +(8.95624 + 5.17089i) q^{73} +(0.494133 + 0.132403i) q^{75} +(-1.82429 - 10.4097i) q^{77} +(3.33631 + 5.77865i) q^{79} +(1.43876 - 2.49200i) q^{81} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(4.04486 + 2.33530i) q^{87} +(-1.16348 + 0.671733i) q^{89} +(-2.37921 - 2.84146i) q^{91} +(-0.914251 + 3.41203i) q^{93} +(-4.12092 + 7.13765i) q^{95} -18.7539 q^{97} +(6.37963 + 6.37963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.831674	+	0.222846i	−0.480167	+	0.128660i	−0.490780	−	0.871283i	$-0.663288\pi$
$3$	−0.831674	+	0.222846i	−0.480167	+	0.128660i	0.0106134	+	0.999944i	$0.496622\pi$
$4$		0			0
$5$	−2.02749	−	0.543265i	−0.906722	−	0.242955i	−0.224821	−	0.974400i	$-0.572180\pi$
$5$	−2.02749	−	0.543265i	−0.906722	−	0.242955i	−0.681901	+	0.731445i	$0.738846\pi$
$6$		0			0
$7$	2.63544	+	0.233350i	0.996103	+	0.0881982i
$7$	2.63544	+	0.233350i	0.996103	+	0.0881982i
$8$		0			0
$9$	−1.95606	+	1.12933i	−0.652019	+	0.376443i
$10$		0			0
$11$	−1.03385	−	3.85837i	−0.311716	−	1.16334i	−0.927008	−	0.375042i	$-0.877628\pi$
$11$	−1.03385	−	3.85837i	−0.311716	−	1.16334i	0.615291	−	0.788300i	$-0.289038\pi$
$12$		0			0
$13$	−0.990473	−	0.990473i	−0.274708	−	0.274708i	0.556284	−	0.830992i	$-0.312227\pi$
$13$	−0.990473	−	0.990473i	−0.274708	−	0.274708i	−0.830992	+	0.556284i	$0.812227\pi$
$14$		0			0
$15$	1.80728			0.466636
$16$		0			0
$17$	3.07828	−	5.33174i	0.746592	−	1.29314i	−0.202855	−	0.979209i	$-0.565022\pi$
$17$	3.07828	−	5.33174i	0.746592	−	1.29314i	0.949447	−	0.313927i	$-0.101645\pi$
$18$		0			0
$19$	1.01626	−	3.79274i	0.233146	−	0.870114i	−0.745829	−	0.666137i	$-0.767947\pi$
$19$	1.01626	−	3.79274i	0.233146	−	0.870114i	0.978976	−	0.203977i	$-0.0653867\pi$
$20$		0			0
$21$	−2.24383	+	0.393227i	−0.489643	+	0.0858091i
$22$		0			0
$23$	−5.91462	+	3.41481i	−1.23328	+	0.712036i	−0.967713	−	0.252055i	$-0.918894\pi$
$23$	−5.91462	+	3.41481i	−1.23328	+	0.712036i	−0.265570	+	0.964092i	$0.585560\pi$
$24$		0			0
$25$	−0.514543	−	0.297072i	−0.102909	−	0.0594143i
$26$		0			0
$27$	3.20161	−	3.20161i	0.616151	−	0.616151i
$28$		0			0
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	0.254732	−	0.967012i	$-0.418013\pi$
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	−0.967012	+	0.254732i	$0.918013\pi$
$30$		0			0
$31$	2.05131	−	3.55296i	0.368425	−	0.638131i	−0.620894	−	0.783894i	$-0.713230\pi$
$31$	2.05131	−	3.55296i	0.368425	−	0.638131i	0.989320	+	0.145763i	$0.0465637\pi$
$32$		0			0
$33$	1.71965	+	2.97851i	0.299352	+	0.518493i
$34$		0			0
$35$	−5.21656	−	1.90486i	−0.881760	−	0.321980i
$36$		0			0
$37$	0.0740993	+	0.0198548i	0.0121818	+	0.00326412i	0.264905	−	0.964275i	$-0.414659\pi$
$37$	0.0740993	+	0.0198548i	0.0121818	+	0.00326412i	−0.252723	+	0.967539i	$0.581326\pi$
$38$		0			0
$39$	1.04447	+	0.603027i	0.167250	+	0.0965616i
$40$		0			0
$41$		−	8.68707i		−	1.35669i	−0.734742	−	0.678346i	$-0.762697\pi$
$41$		−	8.68707i		−	1.35669i	0.734742	−	0.678346i	$-0.237303\pi$
$42$		0			0
$43$	−0.713530	+	0.713530i	−0.108812	+	0.108812i	−0.759417	−	0.650604i	$-0.774516\pi$
$43$	−0.713530	+	0.713530i	−0.108812	+	0.108812i	0.650604	+	0.759417i	$0.274516\pi$
$44$		0			0
$45$	4.57941	−	1.22705i	0.682658	−	0.182918i
$46$		0			0
$47$	−1.95337	−	3.38334i	−0.284929	−	0.493511i	0.687663	−	0.726030i	$-0.258637\pi$
$47$	−1.95337	−	3.38334i	−0.284929	−	0.493511i	−0.972592	+	0.232519i	$0.925303\pi$
$48$		0			0
$49$	6.89110	+	1.22996i	0.984442	+	0.175709i
$50$		0			0
$51$	−1.37197	+	5.12025i	−0.192114	+	0.716978i
$52$		0			0
$53$	1.89324	+	7.06568i	0.260057	+	0.970545i	0.965207	+	0.261487i	$0.0842129\pi$
$53$	1.89324	+	7.06568i	0.260057	+	0.970545i	−0.705150	+	0.709058i	$0.749120\pi$
$54$		0			0
$55$			8.38446i			1.13056i
$56$		0			0
$57$			3.38079i			0.447797i
$58$		0			0
$59$	0.851626	+	3.17831i	0.110872	+	0.413781i	0.998945	−	0.0459220i	$-0.0146226\pi$
$59$	0.851626	+	3.17831i	0.110872	+	0.413781i	−0.888073	+	0.459703i	$0.847956\pi$
$60$		0			0
$61$	−2.37044	+	8.84662i	−0.303504	+	1.13269i	0.630721	+	0.776010i	$0.282759\pi$
$61$	−2.37044	+	8.84662i	−0.303504	+	1.13269i	−0.934225	+	0.356684i	$0.883907\pi$
$62$		0			0
$63$	−5.41860	+	2.51983i	−0.682679	+	0.317469i
$64$		0			0
$65$	1.47009	+	2.54627i	0.182342	+	0.315825i
$66$		0			0
$67$	1.49739	−	0.401223i	0.182935	−	0.0490172i	−0.166189	−	0.986094i	$-0.553146\pi$
$67$	1.49739	−	0.401223i	0.182935	−	0.0490172i	0.349123	+	0.937077i	$0.386479\pi$
$68$		0			0
$69$	4.15805	−	4.15805i	0.500571	−	0.500571i
$70$		0			0
$71$			2.86486i			0.339997i	0.985444	+	0.169998i	$0.0543762\pi$
$71$			2.86486i			0.339997i	−0.985444	+	0.169998i	$0.945624\pi$
$72$		0			0
$73$	8.95624	+	5.17089i	1.04825	+	0.605207i	0.922159	−	0.386812i	$-0.126424\pi$
$73$	8.95624	+	5.17089i	1.04825	+	0.605207i	0.126090	+	0.992019i	$0.459757\pi$
$74$		0			0
$75$	0.494133	+	0.132403i	0.0570576	+	0.0152885i
$76$		0			0
$77$	−1.82429	−	10.4097i	−0.207897	−	1.18630i
$78$		0			0
$79$	3.33631	+	5.77865i	0.375364	+	0.650149i	0.990381	−	0.138364i	$-0.0441845\pi$
$79$	3.33631	+	5.77865i	0.375364	+	0.650149i	−0.615018	+	0.788513i	$0.710851\pi$
$80$		0			0
$81$	1.43876	−	2.49200i	0.159862	−	0.276889i
$82$		0			0
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.991674	−	0.128776i	$-0.958895\pi$
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.128776	−	0.991674i	$-0.541105\pi$
$84$		0			0
$85$	−9.13773	+	9.13773i	−0.991126	+	0.991126i
$86$		0			0
$87$	4.04486	+	2.33530i	0.433655	+	0.250371i
$88$		0			0
$89$	−1.16348	+	0.671733i	−0.123328	+	0.0712036i	−0.560395	−	0.828225i	$-0.689351\pi$
$89$	−1.16348	+	0.671733i	−0.123328	+	0.0712036i	0.437067	+	0.899429i	$0.356017\pi$
$90$		0			0
$91$	−2.37921	−	2.84146i	−0.249409	−	0.297866i
$92$		0			0
$93$	−0.914251	+	3.41203i	−0.0948034	+	0.353811i
$94$		0			0
$95$	−4.12092	+	7.13765i	−0.422798	+	0.732307i
$96$		0			0
$97$	−18.7539			−1.90417			−0.952086	−	0.305831i	$-0.901066\pi$
$97$	−18.7539			−1.90417			−0.952086	+	0.305831i	$0.901066\pi$
$98$		0			0
$99$	6.37963	+	6.37963i	0.641177	+	0.641177i
$100$		0			0
$101$	1.15143	+	4.29719i	0.114571	+	0.427587i	0.999254	−	0.0386065i	$-0.0122919\pi$
$101$	1.15143	+	4.29719i	0.114571	+	0.427587i	−0.884683	+	0.466193i	$0.845625\pi$
$102$		0			0
$103$	7.76159	−	4.48115i	0.764772	−	0.441541i	−0.0662345	−	0.997804i	$-0.521099\pi$
$103$	7.76159	−	4.48115i	0.764772	−	0.441541i	0.831006	+	0.556263i	$0.187765\pi$
$104$		0			0
$105$	4.76297	+	0.421728i	0.464818	+	0.0411565i
$106$		0			0
$107$	12.2706	+	3.28789i	1.18624	+	0.317852i	0.797399	−	0.603453i	$-0.206209\pi$
$107$	12.2706	+	3.28789i	1.18624	+	0.317852i	0.388841	+	0.921305i	$0.372875\pi$
$108$		0			0
$109$	−13.9805	+	3.74605i	−1.33909	+	0.358807i	−0.856095	−	0.516819i	$-0.827116\pi$
$109$	−13.9805	+	3.74605i	−1.33909	+	0.358807i	−0.482990	+	0.875626i	$0.660449\pi$
$110$		0			0
$111$	−0.0660510			−0.00626928
$112$		0			0
$113$	2.61081			0.245605			0.122802	−	0.992431i	$-0.460812\pi$
$113$	2.61081			0.245605			0.122802	+	0.992431i	$0.460812\pi$
$114$		0			0
$115$	13.8470	−	3.71029i	1.29124	−	0.345986i
$116$		0			0
$117$	3.05599	+	0.818851i	0.282527	+	0.0757028i
$118$		0			0
$119$	9.35678	−	13.3332i	0.857735	−	1.22225i
$120$		0			0
$121$	−4.29189	+	2.47792i	−0.390171	+	0.225266i
$122$		0			0
$123$	1.93588	+	7.22481i	0.174553	+	0.651439i
$124$		0			0
$125$	8.30298	+	8.30298i	0.742641	+	0.742641i
$126$		0			0
$127$	9.68594			0.859488			0.429744	−	0.902951i	$-0.358604\pi$
$127$	9.68594			0.859488			0.429744	+	0.902951i	$0.358604\pi$
$128$		0			0
$129$	0.434417	−	0.752432i	0.0382483	−	0.0662479i
$130$		0			0
$131$	−3.58278	+	13.3711i	−0.313029	+	1.16824i	0.612782	+	0.790252i	$0.290050\pi$
$131$	−3.58278	+	13.3711i	−0.313029	+	1.16824i	−0.925811	+	0.377987i	$0.876616\pi$
$132$		0			0
$133$	3.56333	−	9.75839i	0.308980	−	0.846160i
$134$		0			0
$135$	−8.23057	+	4.75192i	−0.708375	+	0.408980i
$136$		0			0
$137$	−9.80462	−	5.66070i	−0.837665	−	0.483626i	0.0188049	−	0.999823i	$-0.494014\pi$
$137$	−9.80462	−	5.66070i	−0.837665	−	0.483626i	−0.856470	+	0.516197i	$0.827347\pi$
$138$		0			0
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	−0.797624	−	0.603155i	$-0.793910\pi$
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	0.603155	+	0.797624i	$0.293910\pi$
$140$		0			0
$141$	2.37854	+	2.37854i	0.200309	+	0.200309i
$142$		0			0
$143$	−2.79761	+	4.84561i	−0.233948	+	0.405210i
$144$		0			0
$145$	5.69311	+	9.86075i	0.472787	+	0.818891i
$146$		0			0
$147$	−6.00523	+	0.512728i	−0.495303	+	0.0422891i
$148$		0			0
$149$	1.82301	+	0.488473i	0.149346	+	0.0400172i	0.332718	−	0.943026i	$-0.392034\pi$
$149$	1.82301	+	0.488473i	0.149346	+	0.0400172i	−0.183371	+	0.983044i	$0.558701\pi$
$150$		0			0
$151$	−12.3236	−	7.11503i	−1.00288	−	0.579013i	−0.0937803	−	0.995593i	$-0.529895\pi$
$151$	−12.3236	−	7.11503i	−1.00288	−	0.579013i	−0.909099	+	0.416580i	$0.863228\pi$
$152$		0			0
$153$			13.9056i			1.12420i
$154$		0			0
$155$	−6.08920	+	6.08920i	−0.489097	+	0.489097i
$156$		0			0
$157$	18.7320	−	5.01921i	1.49497	−	0.400577i	0.583560	−	0.812070i	$-0.301659\pi$
$157$	18.7320	−	5.01921i	1.49497	−	0.400577i	0.911413	+	0.411493i	$0.134993\pi$
$158$		0			0
$159$	−3.14912	−	5.45443i	−0.249741	−	0.432565i
$160$		0			0
$161$	−16.3845	+	7.61934i	−1.29128	+	0.600488i
$162$		0			0
$163$	1.09977	−	4.10438i	0.0861403	−	0.321480i	−0.909387	−	0.415950i	$-0.863449\pi$
$163$	1.09977	−	4.10438i	0.0861403	−	0.321480i	0.995528	+	0.0944702i	$0.0301157\pi$
$164$		0			0
$165$	−1.86845	−	6.97313i	−0.145458	−	0.542858i
$166$		0			0
$167$		−	12.2720i		−	0.949638i	−0.880084	−	0.474819i	$-0.842514\pi$
$167$		−	12.2720i		−	0.949638i	0.880084	−	0.474819i	$-0.157486\pi$
$168$		0			0
$169$		−	11.0379i		−	0.849071i
$170$		0			0
$171$	2.29539	+	8.56650i	0.175533	+	0.655097i
$172$		0			0
$173$	3.86401	−	14.4207i	0.293776	−	1.09639i	−0.648409	−	0.761292i	$-0.724565\pi$
$173$	3.86401	−	14.4207i	0.293776	−	1.09639i	0.942185	−	0.335093i	$-0.108768\pi$
$174$		0			0
$175$	−1.28673	−	0.902983i	−0.0972674	−	0.0682591i
$176$		0			0
$177$	−1.41655	−	2.45354i	−0.106474	−	0.184419i
$178$		0			0
$179$	6.59910	−	1.76822i	0.493240	−	0.132163i	−0.00362111	−	0.999993i	$-0.501153\pi$
$179$	6.59910	−	1.76822i	0.493240	−	0.132163i	0.496861	+	0.867830i	$0.334486\pi$
$180$		0			0
$181$	5.61848	−	5.61848i	0.417618	−	0.417618i	−0.466764	−	0.884382i	$-0.654580\pi$
$181$	5.61848	−	5.61848i	0.417618	−	0.417618i	0.884382	+	0.466764i	$0.154580\pi$
$182$		0			0
$183$		−	7.88574i		−	0.582931i
$184$		0			0
$185$	−0.139449	−	0.0805110i	−0.0102525	−	0.00591929i
$186$		0			0
$187$	−23.7543	−	6.36494i	−1.73708	−	0.465450i
$188$		0			0
$189$	9.18476	−	7.69057i	0.668093	−	0.559407i
$190$		0			0
$191$	−3.19941	−	5.54154i	−0.231501	−	0.400972i	0.726749	−	0.686903i	$-0.241030\pi$
$191$	−3.19941	−	5.54154i	−0.231501	−	0.400972i	−0.958250	+	0.285932i	$0.907697\pi$
$192$		0			0
$193$	4.90762	−	8.50025i	0.353258	−	0.611861i	−0.633560	−	0.773694i	$-0.718407\pi$
$193$	4.90762	−	8.50025i	0.353258	−	0.611861i	0.986818	+	0.161832i	$0.0517403\pi$
$194$		0			0
$195$	−1.79006	−	1.79006i	−0.128189	−	0.128189i
$196$		0			0
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.0565783	−	0.998398i	$-0.481981\pi$
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.998398	−	0.0565783i	$-0.0180191\pi$
$198$		0			0
$199$	−3.76329	−	2.17274i	−0.266772	−	0.154021i	0.360648	−	0.932702i	$-0.382556\pi$
$199$	−3.76329	−	2.17274i	−0.266772	−	0.154021i	−0.627420	+	0.778681i	$0.715889\pi$
$200$		0			0
$201$	−1.15593	+	0.667374i	−0.0815327	+	0.0470729i
$202$		0			0
$203$	−9.21380	−	11.0039i	−0.646682	−	0.772325i
$204$		0			0
$205$	−4.71938	+	17.6130i	−0.329616	+	1.23014i
$206$		0			0
$207$	7.71288	−	13.3591i	0.536082	−	0.928522i
$208$		0			0
$209$	−15.6844			−1.08492
$210$		0			0
$211$	14.5998	+	14.5998i	1.00509	+	1.00509i	0.999987	+	0.00510394i	$0.00162464\pi$
$211$	14.5998	+	14.5998i	1.00509	+	1.00509i	0.00510394	+	0.999987i	$0.498375\pi$
$212$		0			0
$213$	−0.638424	−	2.38263i	−0.0437441	−	0.163255i
$214$		0			0
$215$	1.83431	−	1.05904i	0.125099	−	0.0722260i
$216$		0			0
$217$	6.23518	−	8.88495i	0.423271	−	0.603150i
$218$		0			0
$219$	−8.60098	−	2.30463i	−0.581201	−	0.155732i
$220$		0			0
$221$	−8.32990	+	2.23199i	−0.560329	+	0.150140i
$222$		0			0
$223$	−0.272719			−0.0182626			−0.00913130	−	0.999958i	$-0.502907\pi$
$223$	−0.272719			−0.0182626			−0.00913130	+	0.999958i	$0.502907\pi$
$224$		0			0
$225$	1.34197			0.0894645
$226$		0			0
$227$	11.0202	−	2.95285i	0.731436	−	0.195988i	0.126167	−	0.992009i	$-0.459732\pi$
$227$	11.0202	−	2.95285i	0.731436	−	0.195988i	0.605268	+	0.796021i	$0.293066\pi$
$228$		0			0
$229$	−15.1779	−	4.06690i	−1.00298	−	0.268748i	−0.280288	−	0.959916i	$-0.590430\pi$
$229$	−15.1779	−	4.06690i	−1.00298	−	0.268748i	−0.722694	+	0.691168i	$0.757097\pi$
$230$		0			0
$231$	3.83699	+	8.25098i	0.252455	+	0.542874i
$232$		0			0
$233$	−4.95726	+	2.86207i	−0.324761	+	0.187501i	−0.653513	−	0.756916i	$-0.726705\pi$
$233$	−4.95726	+	2.86207i	−0.324761	+	0.187501i	0.328752	+	0.944416i	$0.393372\pi$
$234$		0			0
$235$	2.12240	+	7.92090i	0.138450	+	0.516703i
$236$		0			0
$237$	−4.06247	−	4.06247i	−0.263886	−	0.263886i
$238$		0			0
$239$	−14.5430			−0.940708			−0.470354	−	0.882478i	$-0.655874\pi$
$239$	−14.5430			−0.940708			−0.470354	+	0.882478i	$0.655874\pi$
$240$		0			0
$241$	1.50912	−	2.61387i	0.0972111	−	0.168374i	−0.813318	−	0.581819i	$-0.802341\pi$
$241$	1.50912	−	2.61387i	0.0972111	−	0.168374i	0.910529	+	0.413445i	$0.135674\pi$
$242$		0			0
$243$	−4.15686	+	15.5136i	−0.266663	+	0.995199i
$244$		0			0
$245$	−13.3034	−	6.23743i	−0.849926	−	0.398495i
$246$		0			0
$247$	−4.76319	+	2.75003i	−0.303074	+	0.174980i
$248$		0			0
$249$	10.7643	+	6.21478i	0.682160	+	0.393845i
$250$		0			0
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	−0.136819	−	0.990596i	$-0.543688\pi$
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	0.990596	+	0.136819i	$0.0436880\pi$
$252$		0			0
$253$	19.2904	+	19.2904i	1.21278	+	1.21278i
$254$		0			0
$255$	5.56330	−	9.63591i	0.348387	−	0.603424i
$256$		0			0
$257$	−1.52413	−	2.63988i	−0.0950728	−	0.164671i	0.814566	−	0.580071i	$-0.196975\pi$
$257$	−1.52413	−	2.63988i	−0.0950728	−	0.164671i	−0.909639	+	0.415400i	$0.863642\pi$
$258$		0			0
$259$	0.190651	+	0.0696174i	0.0118465	+	0.00432581i
$260$		0			0
$261$	11.8347	+	3.17111i	0.732552	+	0.196287i
$262$		0			0
$263$	−23.3754	−	13.4958i	−1.44139	−	0.832188i	−0.443449	−	0.896300i	$-0.646245\pi$
$263$	−23.3754	−	13.4958i	−1.44139	−	0.832188i	−0.997943	+	0.0641116i	$0.979579\pi$
$264$		0			0
$265$		−	15.3541i		−	0.943197i
$266$		0			0
$267$	0.817939	−	0.817939i	0.0500570	−	0.0500570i
$268$		0			0
$269$	−17.5785	+	4.71013i	−1.07178	+	0.287182i	−0.751223	−	0.660048i	$-0.770536\pi$
$269$	−17.5785	+	4.71013i	−1.07178	+	0.287182i	−0.320554	+	0.947230i	$0.603869\pi$
$270$		0			0
$271$	15.6541	+	27.1137i	0.950917	+	1.64704i	0.743446	+	0.668796i	$0.233190\pi$
$271$	15.6541	+	27.1137i	0.950917	+	1.64704i	0.207472	+	0.978241i	$0.433477\pi$
$272$		0			0
$273$	2.61193	+	1.83297i	0.158081	+	0.110936i
$274$		0			0
$275$	−0.614253	+	2.29242i	−0.0370408	+	0.138238i
$276$		0			0
$277$	4.26100	+	15.9023i	0.256019	+	0.955476i	0.967521	+	0.252792i	$0.0813487\pi$
$277$	4.26100	+	15.9023i	0.256019	+	0.955476i	−0.711502	+	0.702684i	$0.751985\pi$
$278$		0			0
$279$			9.26640i			0.554765i
$280$		0			0
$281$			25.4166i			1.51622i	0.652124	+	0.758112i	$0.273878\pi$
$281$			25.4166i			1.51622i	−0.652124	+	0.758112i	$0.726122\pi$
$282$		0			0
$283$	−1.61086	−	6.01181i	−0.0957556	−	0.357365i	0.901377	−	0.433035i	$-0.142557\pi$
$283$	−1.61086	−	6.01181i	−0.0957556	−	0.357365i	−0.997133	+	0.0756698i	$0.975891\pi$
$284$		0			0
$285$	1.83666	−	6.85452i	0.108795	−	0.406027i
$286$		0			0
$287$	2.02713	−	22.8943i	0.119658	−	1.35141i
$288$		0			0
$289$	−10.4516	−	18.1027i	−0.614800	−	1.06486i
$290$		0			0
$291$	15.5971	−	4.17924i	0.914320	−	0.244991i
$292$		0			0
$293$	18.5820	−	18.5820i	1.08557	−	1.08557i	0.0895915	−	0.995979i	$-0.471444\pi$
$293$	18.5820	−	18.5820i	1.08557	−	1.08557i	0.995979	−	0.0895915i	$-0.0285562\pi$
$294$		0			0
$295$		−	6.90666i		−	0.402121i
$296$		0			0
$297$	−15.6630	−	9.04303i	−0.908859	−	0.524730i
$298$		0			0
$299$	9.24055	+	2.47600i	0.534395	+	0.143191i
$300$		0			0
$301$	−2.04697	+	1.71396i	−0.117985	+	0.0987912i
$302$		0			0
$303$	−1.91523	−	3.31727i	−0.110027	−	0.190572i
$304$		0			0
$305$	9.61211	−	16.6487i	0.550388	−	0.953300i
$306$		0			0
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.995742	−	0.0921822i	$-0.970616\pi$
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.0921822	−	0.995742i	$-0.529384\pi$
$308$		0			0
$309$	−5.45650	+	5.45650i	−0.310409	+	0.310409i
$310$		0			0
$311$	5.95180	+	3.43627i	0.337496	+	0.194853i	0.659164	−	0.751999i	$-0.270910\pi$
$311$	5.95180	+	3.43627i	0.337496	+	0.194853i	−0.321668	+	0.946852i	$0.604244\pi$
$312$		0			0
$313$	6.94756	−	4.01118i	0.392699	−	0.226725i	−0.290630	−	0.956836i	$-0.593865\pi$
$313$	6.94756	−	4.01118i	0.392699	−	0.226725i	0.683329	+	0.730110i	$0.260531\pi$
$314$		0			0
$315$	12.3551	−	2.16521i	0.696131	−	0.121996i
$316$		0			0
$317$	0.719764	−	2.68620i	0.0404260	−	0.150872i	−0.942763	−	0.333464i	$-0.891782\pi$
$317$	0.719764	−	2.68620i	0.0404260	−	0.150872i	0.983189	+	0.182593i	$0.0584490\pi$
$318$		0			0
$319$	−10.8341	+	18.7653i	−0.606595	+	1.05065i
$320$		0			0
$321$	−10.9378			−0.610488
$322$		0			0
$323$	−17.0935	−	17.0935i	−0.951110	−	0.951110i
$324$		0			0
$325$	0.215400	+	0.803883i	0.0119482	+	0.0445914i
$326$		0			0
$327$	10.7924	−	6.23099i	0.596820	−	0.344574i
$328$		0			0
$329$	−4.35850	−	9.37242i	−0.240292	−	0.516718i
$330$		0			0
$331$	−10.3801	−	2.78135i	−0.570544	−	0.152877i	−0.0379979	−	0.999278i	$-0.512098\pi$
$331$	−10.3801	−	2.78135i	−0.570544	−	0.152877i	−0.532546	+	0.846401i	$0.678765\pi$
$332$		0			0
$333$	−0.167365	+	0.0448453i	−0.00917154	+	0.00245751i
$334$		0			0
$335$	−3.25391			−0.177780
$336$		0			0
$337$	16.4062			0.893704			0.446852	−	0.894608i	$-0.352545\pi$
$337$	16.4062			0.893704			0.446852	+	0.894608i	$0.352545\pi$
$338$		0			0
$339$	−2.17134	+	0.581810i	−0.117931	+	0.0315996i
$340$		0			0
$341$	−15.8294	−	4.24147i	−0.857209	−	0.229688i
$342$		0			0
$343$	17.8741	+	4.84953i	0.965109	+	0.261850i
$344$		0			0
$345$	−10.6893	+	6.17149i	−0.575495	+	0.332262i
$346$		0			0
$347$	9.39255	+	35.0535i	0.504219	+	1.88177i	0.470623	+	0.882334i	$0.344029\pi$
$347$	9.39255	+	35.0535i	0.504219	+	1.88177i	0.0335953	+	0.999436i	$0.489304\pi$
$348$		0			0
$349$	10.3424	+	10.3424i	0.553614	+	0.553614i	0.927482	−	0.373868i	$-0.121969\pi$
$349$	10.3424	+	10.3424i	0.553614	+	0.553614i	−0.373868	+	0.927482i	$0.621969\pi$
$350$		0			0
$351$	−6.34223			−0.338523
$352$		0			0
$353$	−4.57499	+	7.92412i	−0.243502	+	0.421758i	−0.961709	−	0.274071i	$-0.911630\pi$
$353$	−4.57499	+	7.92412i	−0.243502	+	0.421758i	0.718207	+	0.695829i	$0.244963\pi$
$354$		0			0
$355$	1.55638	−	5.80848i	0.0826040	−	0.308282i
$356$		0			0
$357$	−4.81055	+	13.1740i	−0.254601	+	0.697240i
$358$		0			0
$359$	7.29942	−	4.21432i	0.385248	−	0.222423i	−0.294851	−	0.955543i	$-0.595270\pi$
$359$	7.29942	−	4.21432i	0.385248	−	0.222423i	0.680099	+	0.733120i	$0.261937\pi$
$360$		0			0
$361$	3.10240	+	1.79117i	0.163284	+	0.0942723i
$362$		0			0
$363$	3.01725	−	3.01725i	0.158365	−	0.158365i
$364$		0			0
$365$	−15.3495	−	15.3495i	−0.803432	−	0.803432i
$366$		0			0
$367$	4.65182	−	8.05718i	0.242823	−	0.420582i	−0.718694	−	0.695326i	$-0.755260\pi$
$367$	4.65182	−	8.05718i	0.242823	−	0.420582i	0.961517	+	0.274745i	$0.0885933\pi$
$368$		0			0
$369$	9.81057	+	16.9924i	0.510718	+	0.884589i
$370$		0			0
$371$	3.34075	+	19.0630i	0.173443	+	0.989699i
$372$		0			0
$373$	−19.8310	−	5.31370i	−1.02681	−	0.275133i	−0.294172	−	0.955752i	$-0.595044\pi$
$373$	−19.8310	−	5.31370i	−1.02681	−	0.275133i	−0.732637	+	0.680620i	$0.761711\pi$
$374$		0			0
$375$	−8.75565	−	5.05508i	−0.452140	−	0.261043i
$376$		0			0
$377$			7.59840i			0.391337i
$378$		0			0
$379$	9.02290	−	9.02290i	0.463475	−	0.463475i	−0.436317	−	0.899793i	$-0.643718\pi$
$379$	9.02290	−	9.02290i	0.463475	−	0.463475i	0.899793	+	0.436317i	$0.143718\pi$
$380$		0			0
$381$	−8.05554	+	2.15847i	−0.412698	+	0.110582i
$382$		0			0
$383$	−0.562798	−	0.974794i	−0.0287576	−	0.0498097i	0.851288	−	0.524698i	$-0.175822\pi$
$383$	−0.562798	−	0.974794i	−0.0287576	−	0.0498097i	−0.880046	+	0.474888i	$0.842488\pi$
$384$		0			0
$385$	−1.95652	+	22.0967i	−0.0997133	+	1.12615i
$386$		0			0
$387$	0.589894	−	2.20152i	0.0299860	−	0.111909i
$388$		0			0
$389$	4.47334	+	16.6947i	0.226807	+	0.846457i	0.981672	+	0.190577i	$0.0610358\pi$
$389$	4.47334	+	16.6947i	0.226807	+	0.846457i	−0.754865	+	0.655880i	$0.772298\pi$
$390$		0			0
$391$			42.0469i			2.12640i
$392$		0			0
$393$		−	11.9188i		−	0.601224i
$394$		0			0
$395$	−3.62499	−	13.5287i	−0.182393	−	0.680701i
$396$		0			0
$397$	7.33912	−	27.3900i	0.368340	−	1.37466i	−0.494497	−	0.869179i	$-0.664648\pi$
$397$	7.33912	−	27.3900i	0.368340	−	1.37466i	0.862837	−	0.505483i	$-0.168686\pi$
$398$		0			0
$399$	−0.788909	+	8.90987i	−0.0394948	+	0.446052i
$400$		0			0
$401$	11.2636	+	19.5091i	0.562477	+	0.974238i	0.997280	+	0.0737127i	$0.0234848\pi$
$401$	11.2636	+	19.5091i	0.562477	+	0.974238i	−0.434803	+	0.900526i	$0.643182\pi$
$402$		0			0
$403$	−5.55088	+	1.48735i	−0.276509	+	0.0740904i
$404$		0			0
$405$	−4.27088	+	4.27088i	−0.212222	+	0.212222i
$406$		0			0
$407$		−	0.306429i		−	0.0151891i
$408$		0			0
$409$	26.7305	+	15.4328i	1.32174	+	0.763105i	0.984006	−	0.178138i	$-0.0570073\pi$
$409$	26.7305	+	15.4328i	1.32174	+	0.763105i	0.337731	+	0.941243i	$0.390341\pi$
$410$		0			0
$411$	9.41570	+	2.52293i	0.464442	+	0.124447i
$412$		0			0
$413$	1.50275	+	8.57498i	0.0739455	+	0.421947i
$414$		0			0
$415$	15.1507	+	26.2417i	0.743717	+	1.28816i
$416$		0			0
$417$	1.39589	−	2.41776i	0.0683572	−	0.118398i
$418$		0			0
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	0.870592	−	0.492006i	$-0.163736\pi$
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	−0.492006	+	0.870592i	$0.663736\pi$
$420$		0			0
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	−0.945953	−	0.324302i	$-0.894870\pi$
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	0.324302	+	0.945953i	$0.394870\pi$
$422$		0			0
$423$	7.64182	+	4.41201i	0.371558	+	0.214519i
$424$		0			0
$425$	−3.16781	+	1.82894i	−0.153662	+	0.0887165i
$426$		0			0
$427$	−8.31153	+	22.7616i	−0.402223	+	1.10151i
$428$		0			0
$429$	1.24688	−	4.65340i	0.0601997	−	0.224668i
$430$		0			0
$431$	4.92680	−	8.53348i	0.237316	−	0.411043i	−0.722627	−	0.691238i	$-0.757066\pi$
$431$	4.92680	−	8.53348i	0.237316	−	0.411043i	0.959943	+	0.280195i	$0.0903990\pi$
$432$		0			0
$433$	14.9150			0.716769			0.358385	−	0.933574i	$-0.383328\pi$
$433$	14.9150			0.716769			0.358385	+	0.933574i	$0.383328\pi$
$434$		0			0
$435$	−6.93224	−	6.93224i	−0.332375	−	0.332375i
$436$		0			0
$437$	6.94067	+	25.9029i	0.332017	+	1.23911i
$438$		0			0
$439$	8.04703	−	4.64596i	0.384064	−	0.221739i	−0.295521	−	0.955336i	$-0.595493\pi$
$439$	8.04703	−	4.64596i	0.384064	−	0.221739i	0.679585	+	0.733597i	$0.262160\pi$
$440$		0			0
$441$	−14.8684	+	5.37644i	−0.708019	+	0.256021i
$442$		0			0
$443$	9.83379	+	2.63496i	0.467217	+	0.125191i	0.484744	−	0.874656i	$-0.338913\pi$
$443$	9.83379	+	2.63496i	0.467217	+	0.125191i	−0.0175270	+	0.999846i	$0.505579\pi$
$444$		0			0
$445$	2.72387	−	0.729858i	0.129124	−	0.0345986i
$446$		0			0
$447$	−1.62500			−0.0768598
$448$		0			0
$449$	3.82136			0.180341			0.0901705	−	0.995926i	$-0.471259\pi$
$449$	3.82136			0.180341			0.0901705	+	0.995926i	$0.471259\pi$
$450$		0			0
$451$	−33.5179	+	8.98110i	−1.57830	+	0.422904i
$452$		0			0
$453$	11.8348	+	3.17111i	0.556045	+	0.148992i
$454$		0			0
$455$	3.28015	+	7.05358i	0.153776	+	0.330677i
$456$		0			0
$457$	21.7306	−	12.5462i	1.01651	−	0.586885i	0.103422	−	0.994638i	$-0.467021\pi$
$457$	21.7306	−	12.5462i	1.01651	−	0.586885i	0.913092	+	0.407753i	$0.133688\pi$
$458$		0			0
$459$	−7.21470	−	26.9256i	−0.336753	−	1.25678i
$460$		0			0
$461$	−7.13847	−	7.13847i	−0.332472	−	0.332472i	0.521053	−	0.853524i	$-0.325539\pi$
$461$	−7.13847	−	7.13847i	−0.332472	−	0.332472i	−0.853524	+	0.521053i	$0.825539\pi$
$462$		0			0
$463$	−3.67655			−0.170864			−0.0854320	−	0.996344i	$-0.527227\pi$
$463$	−3.67655			−0.170864			−0.0854320	+	0.996344i	$0.527227\pi$
$464$		0			0
$465$	3.70727	−	6.42118i	0.171921	−	0.297775i
$466$		0			0
$467$	−2.51848	+	9.39910i	−0.116541	+	0.434938i	−0.999398	−	0.0347050i	$-0.988951\pi$
$467$	−2.51848	+	9.39910i	−0.116541	+	0.434938i	0.882856	+	0.469643i	$0.155617\pi$
$468$		0			0
$469$	4.03990	−	0.707985i	0.186545	−	0.0326917i
$470$		0			0
$471$	−14.4604	+	8.34869i	−0.666298	+	0.384687i
$472$		0			0
$473$	3.49074	+	2.01538i	0.160505	+	0.0926673i
$474$		0			0
$475$	−1.64963	+	1.64963i	−0.0756900	+	0.0756900i
$476$		0			0
$477$	−11.6828	−	11.6828i	−0.534917	−	0.534917i
$478$		0			0
$479$	−8.06678	+	13.9721i	−0.368581	+	0.638400i	−0.989344	−	0.145598i	$-0.953490\pi$
$479$	−8.06678	+	13.9721i	−0.368581	+	0.638400i	0.620763	+	0.783998i	$0.286823\pi$
$480$		0			0
$481$	−0.0537277	−	0.0930591i	−0.00244977	−	0.00424313i
$482$		0			0
$483$	11.9286	−	9.98802i	0.542770	−	0.454471i
$484$		0			0
$485$	38.0234	+	10.1883i	1.72655	+	0.462629i
$486$		0			0
$487$	11.3224	+	6.53697i	0.513065	+	0.296218i	0.734093	−	0.679049i	$-0.237608\pi$
$487$	11.3224	+	6.53697i	0.513065	+	0.296218i	−0.221027	+	0.975268i	$0.570941\pi$
$488$		0			0
$489$			3.65859i			0.165447i
$490$		0			0
$491$	−10.1749	+	10.1749i	−0.459188	+	0.459188i	−0.898389	−	0.439201i	$-0.855262\pi$
$491$	−10.1749	+	10.1749i	−0.459188	+	0.459188i	0.439201	+	0.898389i	$0.355262\pi$
$492$		0			0
$493$	−32.2586	+	8.64368i	−1.45286	+	0.389292i
$494$		0			0
$495$	−9.46882	−	16.4005i	−0.425592	−	0.737146i
$496$		0			0
$497$	−0.668517	+	7.55018i	−0.0299871	+	0.338672i
$498$		0			0
$499$	10.7751	−	40.2131i	0.482358	−	1.80019i	−0.109313	−	0.994007i	$-0.534865\pi$
$499$	10.7751	−	40.2131i	0.482358	−	1.80019i	0.591672	−	0.806179i	$-0.298468\pi$
$500$		0			0
$501$	2.73477	+	10.2063i	0.122181	+	0.455985i
$502$		0			0
$503$			35.0535i			1.56296i	0.623930	+	0.781480i	$0.285535\pi$
$503$			35.0535i			1.56296i	−0.623930	+	0.781480i	$0.714465\pi$
$504$		0			0
$505$		−	9.33805i		−	0.415538i
$506$		0			0
$507$	2.45976	+	9.17995i	0.109242	+	0.407696i
$508$		0			0
$509$	0.769772	−	2.87283i	0.0341195	−	0.127336i	−0.946765	−	0.321924i	$-0.895670\pi$
$509$	0.769772	−	2.87283i	0.0341195	−	0.127336i	0.980885	+	0.194588i	$0.0623371\pi$
$510$		0			0
$511$	22.3970	+	15.7175i	0.990786	+	0.695302i
$512$		0			0
$513$	−8.88921	−	15.3966i	−0.392468	−	0.679775i
$514$		0			0
$515$	−18.1710	+	4.86891i	−0.800710	+	0.214550i
$516$		0			0
$517$	−11.0347	+	11.0347i	−0.485305	+	0.485305i
$518$		0			0
$519$			12.8544i			0.564245i
$520$		0			0
$521$	−21.8703	−	12.6268i	−0.958155	−	0.553191i	−0.0625503	−	0.998042i	$-0.519923\pi$
$521$	−21.8703	−	12.6268i	−0.958155	−	0.553191i	−0.895605	+	0.444851i	$0.853257\pi$
$522$		0			0
$523$	−0.671120	−	0.179826i	−0.0293460	−	0.00786324i	0.244116	−	0.969746i	$-0.421502\pi$
$523$	−0.671120	−	0.179826i	−0.0293460	−	0.00786324i	−0.273462	+	0.961883i	$0.588169\pi$
$524$		0			0
$525$	1.27136	+	0.464245i	0.0554868	+	0.0202613i
$526$		0			0
$527$	−12.6290	−	21.8740i	−0.550127	−	0.952848i
$528$		0			0
$529$	11.8218	−	20.4760i	0.513991	−	0.890259i
$530$		0			0
$531$	−5.25519	−	5.25519i	−0.228056	−	0.228056i
$532$		0			0
$533$	−8.60431	+	8.60431i	−0.372694	+	0.372694i
$534$		0			0
$535$	−23.0923	−	13.3323i	−0.998366	−	0.576407i
$536$		0			0
$537$	−5.09425	+	2.94117i	−0.219833	+	0.126921i
$538$		0			0
$539$	−2.37869	−	27.8600i	−0.102457	−	1.20001i
$540$		0			0
$541$	−3.00200	+	11.2036i	−0.129066	+	0.481681i	−0.999952	−	0.00980419i	$-0.996879\pi$
$541$	−3.00200	+	11.2036i	−0.129066	+	0.481681i	0.870886	+	0.491485i	$0.163546\pi$
$542$		0			0
$543$	−3.42068	+	5.92480i	−0.146796	+	0.254257i
$544$		0			0
$545$	30.3804			1.30135
$546$		0			0
$547$	−8.29783	−	8.29783i	−0.354790	−	0.354790i	0.507098	−	0.861888i	$-0.330718\pi$
$547$	−8.29783	−	8.29783i	−0.354790	−	0.354790i	−0.861888	+	0.507098i	$0.830718\pi$
$548$		0			0
$549$	−5.35402	−	19.9815i	−0.228504	−	0.852789i
$550$		0			0
$551$	−18.4461	+	10.6498i	−0.785829	+	0.453699i
$552$		0			0
$553$	7.44419	+	16.0078i	0.316559	+	0.680722i
$554$		0			0
$555$	0.133918	+	0.0358832i	0.00568449	+	0.00152316i
$556$		0			0
$557$	19.4942	−	5.22346i	0.825997	−	0.221325i	0.179030	−	0.983844i	$-0.442704\pi$
$557$	19.4942	−	5.22346i	0.825997	−	0.221325i	0.646967	+	0.762518i	$0.276037\pi$
$558$		0			0
$559$	1.41347			0.0597832
$560$		0			0
$561$	21.1742			0.893975
$562$		0			0
$563$	24.7408	−	6.62929i	1.04270	−	0.279391i	0.303469	−	0.952841i	$-0.401855\pi$
$563$	24.7408	−	6.62929i	1.04270	−	0.279391i	0.739233	+	0.673450i	$0.235188\pi$
$564$		0			0
$565$	−5.29340	−	1.41836i	−0.222695	−	0.0596709i
$566$		0			0
$567$	4.37327	−	6.23179i	0.183660	−	0.261710i
$568$		0			0
$569$	28.6248	−	16.5265i	1.20001	−	0.692828i	0.239455	−	0.970908i	$-0.423031\pi$
$569$	28.6248	−	16.5265i	1.20001	−	0.692828i	0.960558	+	0.278080i	$0.0896980\pi$
$570$		0			0
$571$	−3.86560	−	14.4266i	−0.161770	−	0.603735i	−0.998430	−	0.0560119i	$-0.982162\pi$
$571$	−3.86560	−	14.4266i	−0.161770	−	0.603735i	0.836660	−	0.547723i	$-0.184505\pi$
$572$		0			0
$573$	3.89577	+	3.89577i	0.162748	+	0.162748i
$574$		0			0
$575$	4.05777			0.169221
$576$		0			0
$577$	−0.666623	+	1.15463i	−0.0277519	+	0.0480677i	−0.879568	−	0.475774i	$-0.842168\pi$
$577$	−0.666623	+	1.15463i	−0.0277519	+	0.0480677i	0.851816	+	0.523841i	$0.175502\pi$
$578$		0			0
$579$	−2.18729	+	8.16308i	−0.0909007	+	0.339246i
$580$		0			0
$581$	−24.5200	−	29.2840i	−1.01726	−	1.21490i
$582$		0			0
$583$	25.3047	−	14.6097i	1.04801	−	0.605070i
$584$		0			0
$585$	−5.75114	−	3.32042i	−0.237781	−	0.137283i
$586$		0			0
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	−0.171058	−	0.985261i	$-0.554719\pi$
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	0.985261	+	0.171058i	$0.0547186\pi$
$588$		0			0
$589$	−11.3908	−	11.3908i	−0.469350	−	0.469350i
$590$		0			0
$591$	−9.01509	+	15.6146i	−0.370831	+	0.642298i
$592$		0			0
$593$	−9.40250	−	16.2856i	−0.386114	−	0.668769i	0.605809	−	0.795610i	$-0.292850\pi$
$593$	−9.40250	−	16.2856i	−0.386114	−	0.668769i	−0.991923	+	0.126841i	$0.959516\pi$
$594$		0			0
$595$	−26.2142	+	21.9496i	−1.07468	+	0.899848i
$596$		0			0
$597$	3.61401	+	0.968372i	0.147912	+	0.0396328i
$598$		0			0
$599$	24.0798	+	13.9025i	0.983873	+	0.568039i	0.903437	−	0.428720i	$-0.141035\pi$
$599$	24.0798	+	13.9025i	0.983873	+	0.568039i	0.0804358	+	0.996760i	$0.474369\pi$
$600$		0			0
$601$			13.6372i			0.556271i	0.960542	+	0.278136i	$0.0897165\pi$
$601$			13.6372i			0.556271i	−0.960542	+	0.278136i	$0.910284\pi$
$602$		0			0
$603$	−2.47586	+	2.47586i	−0.100825	+	0.100825i
$604$		0			0
$605$	10.0479	−	2.69233i	0.408506	−	0.109459i
$606$		0			0
$607$	−14.5489	−	25.1994i	−0.590522	−	1.02281i	−0.994162	−	0.107896i	$-0.965589\pi$
$607$	−14.5489	−	25.1994i	−0.590522	−	1.02281i	0.403640	−	0.914918i	$-0.367745\pi$
$608$		0			0
$609$	10.1151	+	7.09843i	0.409883	+	0.287643i
$610$		0			0
$611$	−1.41635	+	5.28588i	−0.0572993	+	0.213844i
$612$		0			0
$613$	−7.49934	−	27.9879i	−0.302895	−	1.13042i	−0.934742	−	0.355327i	$-0.884369\pi$
$613$	−7.49934	−	27.9879i	−0.302895	−	1.13042i	0.631846	−	0.775094i	$-0.282297\pi$
$614$		0			0
$615$		−	15.6999i		−	0.633082i
$616$		0			0
$617$		−	5.44754i		−	0.219310i	−0.993970	−	0.109655i	$-0.965025\pi$
$617$		−	5.44754i		−	0.219310i	0.993970	−	0.109655i	$-0.0349745\pi$
$618$		0			0
$619$	−1.57246	−	5.86850i	−0.0632025	−	0.235875i	0.927098	−	0.374820i	$-0.122295\pi$
$619$	−1.57246	−	5.86850i	−0.0632025	−	0.235875i	−0.990300	+	0.138945i	$0.955629\pi$
$620$		0			0
$621$	−8.00343	+	29.8692i	−0.321167	+	1.19861i
$622$		0			0
$623$	−3.22302	+	1.49882i	−0.129128	+	0.0600488i
$624$		0			0
$625$	−10.8381	−	18.7722i	−0.433526	−	0.750888i
$626$		0			0
$627$	13.0443	−	3.49522i	0.520941	−	0.139586i
$628$		0			0
$629$	0.333959	−	0.333959i	0.0133158	−	0.0133158i
$630$		0			0
$631$		−	31.5326i		−	1.25529i	−0.778499	−	0.627646i	$-0.784018\pi$
$631$		−	31.5326i		−	1.25529i	0.778499	−	0.627646i	$-0.215982\pi$
$632$		0			0
$633$	−15.3958	−	8.88875i	−0.611927	−	0.353296i
$634$		0			0
$635$	−19.6381	−	5.26203i	−0.779316	−	0.208817i
$636$		0			0
$637$	−5.60720	−	8.04369i	−0.222165	−	0.318703i
$638$		0			0
$639$	−3.23537	−	5.60383i	−0.127989	−	0.221684i
$640$		0			0
$641$	−13.6133	+	23.5789i	−0.537691	+	0.931309i	0.461337	+	0.887225i	$0.347370\pi$
$641$	−13.6133	+	23.5789i	−0.537691	+	0.931309i	−0.999028	+	0.0440835i	$0.985963\pi$
$642$		0			0
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	0.849143	−	0.528164i	$-0.177119\pi$
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	−0.528164	+	0.849143i	$0.677119\pi$
$644$		0			0
$645$	−1.28955	+	1.28955i	−0.0507758	+	0.0507758i
$646$		0			0
$647$	−6.70236	−	3.86961i	−0.263497	−	0.152130i	0.362432	−	0.932010i	$-0.381947\pi$
$647$	−6.70236	−	3.86961i	−0.263497	−	0.152130i	−0.625929	+	0.779880i	$0.715280\pi$
$648$		0			0
$649$	11.3826	−	6.57177i	0.446808	−	0.257965i
$650$		0			0
$651$	−3.20565	+	8.77887i	−0.125639	+	0.344071i
$652$		0			0
$653$	2.60819	−	9.73388i	0.102066	−	0.380916i	−0.895930	−	0.444196i	$-0.853489\pi$
$653$	2.60819	−	9.73388i	0.102066	−	0.380916i	0.997996	+	0.0632798i	$0.0201561\pi$
$654$		0			0
$655$	14.5281	−	25.1634i	0.567660	−	0.983216i
$656$		0			0
$657$	−23.3585			−0.911304
$658$		0			0
$659$	4.61254	+	4.61254i	0.179679	+	0.179679i	0.791216	−	0.611537i	$-0.209448\pi$
$659$	4.61254	+	4.61254i	0.179679	+	0.179679i	−0.611537	+	0.791216i	$0.709448\pi$
$660$		0			0
$661$	−5.03853	−	18.8040i	−0.195976	−	0.731393i	−0.992012	−	0.126143i	$-0.959740\pi$
$661$	−5.03853	−	18.8040i	−0.195976	−	0.731393i	0.796036	−	0.605249i	$-0.206927\pi$
$662$		0			0
$663$	6.43036	−	3.71257i	0.249735	−	0.144184i
$664$		0			0
$665$	−12.5260	+	17.8492i	−0.485738	+	0.692163i
$666$		0			0
$667$	35.7853	+	9.58863i	1.38561	+	0.371273i
$668$		0			0
$669$	0.226813	−	0.0607743i	0.00876910	−	0.00234967i
$670$		0			0
$671$	36.5842			1.41232
$672$		0			0
$673$	−28.4799			−1.09782			−0.548910	−	0.835881i	$-0.684957\pi$
$673$	−28.4799			−1.09782			−0.548910	+	0.835881i	$0.684957\pi$
$674$		0			0
$675$	−2.59848	+	0.696260i	−0.100015	+	0.0267991i
$676$		0			0
$677$	−10.0011	−	2.67980i	−0.384375	−	0.102993i	0.0614567	−	0.998110i	$-0.480425\pi$
$677$	−10.0011	−	2.67980i	−0.384375	−	0.102993i	−0.445832	+	0.895117i	$0.647092\pi$
$678$		0			0
$679$	−49.4248	−	4.37623i	−1.89675	−	0.167944i
$680$		0			0
$681$	−8.50717	+	4.91162i	−0.325995	+	0.188214i
$682$		0			0
$683$	2.41481	+	9.01220i	0.0924002	+	0.344842i	0.996612	−	0.0822411i	$-0.0262077\pi$
$683$	2.41481	+	9.01220i	0.0924002	+	0.344842i	−0.904212	+	0.427083i	$0.859541\pi$
$684$		0			0
$685$	16.8035	+	16.8035i	0.642029	+	0.642029i
$686$		0			0
$687$	13.5293			0.516176
$688$		0			0
$689$	5.12316	−	8.87357i	0.195177	−	0.338056i
$690$		0			0
$691$	6.68364	−	24.9437i	0.254258	−	0.948902i	−0.714244	−	0.699896i	$-0.753230\pi$
$691$	6.68364	−	24.9437i	0.254258	−	0.948902i	0.968502	−	0.249006i	$-0.0801038\pi$
$692$		0			0
$693$	15.3244	+	18.3018i	0.582128	+	0.695229i
$694$		0			0
$695$	5.89412	−	3.40297i	0.223577	−	0.129082i
$696$		0			0
$697$	−46.3172	−	26.7412i	−1.75439	−	1.01290i
$698$		0			0
$699$	3.48502	−	3.48502i	0.131815	−	0.131815i
$700$		0			0
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	0.769036	−	0.639206i	$-0.220737\pi$
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	−0.639206	+	0.769036i	$0.720737\pi$
$702$		0			0
$703$	0.150608	−	0.260861i	0.00568031	−	0.00983858i
$704$		0			0
$705$	−3.53029	−	6.11463i	−0.132958	−	0.230290i
$706$		0			0
$707$	2.03177	+	11.5937i	0.0764126	+	0.436025i
$708$		0			0
$709$	−28.9026	−	7.74444i	−1.08546	−	0.290849i	−0.328630	−	0.944459i	$-0.606587\pi$
$709$	−28.9026	−	7.74444i	−1.08546	−	0.290849i	−0.756831	+	0.653610i	$0.773254\pi$
$710$		0			0
$711$	−13.0520	−	7.53558i	−0.489488	−	0.282606i
$712$		0			0
$713$			28.0192i			1.04933i
$714$		0			0
$715$	8.30458	−	8.30458i	0.310574	−	0.310574i
$716$		0			0
$717$	12.0950	−	3.24085i	0.451697	−	0.121032i
$718$		0			0
$719$	2.49771	+	4.32616i	0.0931488	+	0.161339i	0.908835	−	0.417157i	$-0.136973\pi$
$719$	2.49771	+	4.32616i	0.0931488	+	0.161339i	−0.815686	+	0.578495i	$0.803640\pi$
$720$		0			0
$721$	21.5009	−	9.99865i	0.800735	−	0.372369i
$722$		0			0
$723$	−0.672604	+	2.51019i	−0.0250144	+	0.0933551i
$724$		0			0
$725$	0.834164	+	3.11314i	0.0309801	+	0.115619i
$726$		0			0
$727$		−	4.59798i		−	0.170530i	−0.996358	−	0.0852648i	$-0.972826\pi$
$727$		−	4.59798i		−	0.170530i	0.996358	−	0.0852648i	$-0.0271736\pi$
$728$		0			0
$729$		−	5.19606i		−	0.192447i
$730$		0			0
$731$	1.60791	+	6.00080i	0.0594707	+	0.221948i
$732$		0			0
$733$	−2.74210	+	10.2337i	−0.101282	+	0.377989i	−0.997897	−	0.0648221i	$-0.979352\pi$
$733$	−2.74210	+	10.2337i	−0.101282	+	0.377989i	0.896615	+	0.442811i	$0.146019\pi$
$734$		0			0
$735$	12.4541	+	2.22288i	0.459377	+	0.0819922i
$736$		0			0
$737$	−3.09614	−	5.36266i	−0.114048	−	0.197536i
$738$		0			0
$739$	45.8723	−	12.2915i	1.68744	−	0.452149i	0.717714	−	0.696338i	$-0.245189\pi$
$739$	45.8723	−	12.2915i	1.68744	−	0.452149i	0.969728	+	0.244190i	$0.0785219\pi$
$740$		0			0
$741$	3.34858	−	3.34858i	0.123013	−	0.123013i
$742$		0			0
$743$			17.5619i			0.644285i	0.946691	+	0.322142i	$0.104403\pi$
$743$			17.5619i			0.644285i	−0.946691	+	0.322142i	$0.895597\pi$
$744$		0			0
$745$	−3.43076	−	1.98075i	−0.125693	−	0.0725690i
$746$		0			0
$747$	31.4949	+	8.43904i	1.15234	+	0.308768i
$748$		0			0
$749$	31.5711	+	11.5284i	1.15358	+	0.421238i
$750$		0			0
$751$	−9.02361	−	15.6293i	−0.329276	−	0.570323i	0.653092	−	0.757278i	$-0.273471\pi$
$751$	−9.02361	−	15.6293i	−0.329276	−	0.570323i	−0.982368	+	0.186955i	$0.940138\pi$
$752$		0			0
$753$	−8.23522	+	14.2638i	−0.300108	+	0.519803i
$754$		0			0
$755$	21.1206	+	21.1206i	0.768658	+	0.768658i
$756$		0			0
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	−0.286448	−	0.958096i	$-0.592475\pi$
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	0.958096	+	0.286448i	$0.0924747\pi$
$758$		0			0
$759$	−20.3421	−	11.7445i	−0.738371	−	0.426299i
$760$		0			0
$761$	−5.61500	+	3.24182i	−0.203543	+	0.117516i	−0.598307	−	0.801267i	$-0.704160\pi$
$761$	−5.61500	+	3.24182i	−0.203543	+	0.117516i	0.394764	+	0.918783i	$0.370826\pi$
$762$		0			0
$763$	−37.7188	+	6.61015i	−1.36551	+	0.239304i
$764$		0			0
$765$	7.55440	−	28.1934i	0.273130	−	1.01933i
$766$		0			0
$767$	2.30452	−	3.99155i	0.0832114	−	0.144126i
$768$		0			0
$769$	−23.9598			−0.864014			−0.432007	−	0.901870i	$-0.642194\pi$
$769$	−23.9598			−0.864014			−0.432007	+	0.901870i	$0.642194\pi$
$770$		0			0
$771$	1.85587	+	1.85587i	0.0668374	+	0.0668374i
$772$		0			0
$773$	−0.711549	−	2.65554i	−0.0255926	−	0.0955130i	0.951948	−	0.306259i	$-0.0990774\pi$
$773$	−0.711549	−	2.65554i	−0.0255926	−	0.0955130i	−0.977541	+	0.210746i	$0.932411\pi$
$774$		0			0
$775$	−2.11097	+	1.21877i	−0.0758283	+	0.0437795i
$776$		0			0
$777$	−0.174073	−	0.0154130i	−0.00624485	−	0.000552939i
$778$		0			0
$779$	−32.9478	−	8.82834i	−1.18048	−	0.316308i
$780$		0			0
$781$	11.0537	−	2.96183i	0.395532	−	0.105983i
$782$		0			0
$783$	−24.5611			−0.877743
$784$		0			0
$785$	−40.7056			−1.45285
$786$		0			0
$787$	−47.5886	+	12.7513i	−1.69635	+	0.454536i	−0.972016	−	0.234913i	$-0.924519\pi$
$787$	−47.5886	+	12.7513i	−1.69635	+	0.454536i	−0.724334	+	0.689449i	$0.757853\pi$
$788$		0			0
$789$	22.4482	+	6.01499i	0.799178	+	0.214139i
$790$		0			0
$791$	6.88064	+	0.609234i	0.244647	+	0.0216619i
$792$		0			0
$793$	11.1102	−	6.41448i	0.394535	−	0.227785i
$794$		0			0
$795$	3.42161	+	12.7696i	0.121352	+	0.452892i
$796$		0			0
$797$	22.5200	+	22.5200i	0.797699	+	0.797699i	0.982732	−	0.185033i	$-0.0592394\pi$
$797$	22.5200	+	22.5200i	0.797699	+	0.797699i	−0.185033	+	0.982732i	$0.559239\pi$
$798$		0			0
$799$	−24.0521			−0.850903
$800$		0			0
$801$	1.51722	−	2.62789i	0.0536082	−	0.0928521i
$802$		0			0
$803$	10.6918	−	39.9024i	0.377306	−	1.40812i
$804$		0			0
$805$	37.3587	−	6.54704i	1.31672	−	0.230753i
$806$		0			0
$807$	13.5699	−	7.83459i	0.477683	−	0.275791i
$808$		0			0
$809$	41.1059	+	23.7325i	1.44521	+	0.834391i	0.998190	−	0.0601343i	$-0.0191529\pi$
$809$	41.1059	+	23.7325i	1.44521	+	0.834391i	0.447017	+	0.894525i	$0.352486\pi$
$810$		0			0
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.516058	+	0.856554i	$0.672601\pi$
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.856554	+	0.516058i	$0.827399\pi$
$812$		0			0
$813$	−19.0613	−	19.0613i	−0.668507	−	0.668507i
$814$		0			0
$815$	−4.45953	+	7.72414i	−0.156211	+	0.270565i
$816$		0			0
$817$	1.98110	+	3.43137i	0.0693099	+	0.120048i
$818$		0			0
$819$	7.86281	+	2.87115i	0.274749	+	0.100326i
$820$		0			0
$821$	−12.1621	−	3.25883i	−0.424461	−	0.113734i	0.0402639	−	0.999189i	$-0.487180\pi$
$821$	−12.1621	−	3.25883i	−0.424461	−	0.113734i	−0.464725	+	0.885455i	$0.653847\pi$
$822$		0			0
$823$	4.29959	+	2.48237i	0.149874	+	0.0865300i	0.573062	−	0.819512i	$-0.305755\pi$
$823$	4.29959	+	2.48237i	0.149874	+	0.0865300i	−0.423187	+	0.906042i	$0.639089\pi$
$824$		0			0
$825$		−	2.04343i		−	0.0711432i
$826$		0			0
$827$	−11.3168	+	11.3168i	−0.393524	+	0.393524i	−0.875942	−	0.482417i	$-0.839759\pi$
$827$	−11.3168	+	11.3168i	−0.393524	+	0.393524i	0.482417	+	0.875942i	$0.339759\pi$
$828$		0			0
$829$	−34.1690	+	9.15557i	−1.18674	+	0.317986i	−0.797597	−	0.603191i	$-0.793896\pi$
$829$	−34.1690	+	9.15557i	−1.18674	+	0.317986i	−0.389143	+	0.921177i	$0.627229\pi$
$830$		0			0
$831$	−7.08753	−	12.2760i	−0.245864	−	0.425848i
$832$		0			0
$833$	27.7705	−	32.9553i	0.962192	−	1.14183i
$834$		0			0
$835$	−6.66696	+	24.8814i	−0.230719	+	0.861057i
$836$		0			0
$837$	−4.80774	−	17.9427i	−0.166180	−	0.620191i
$838$		0			0
$839$		−	47.7342i		−	1.64797i	−0.566614	−	0.823983i	$-0.691747\pi$
$839$		−	47.7342i		−	1.64797i	0.566614	−	0.823983i	$-0.308253\pi$
$840$		0			0
$841$			0.425820i			0.0146834i
$842$		0			0
$843$	−5.66398	−	21.1383i	−0.195078	−	0.728041i
$844$		0			0
$845$	−5.99651	+	22.3793i	−0.206286	+	0.769871i
$846$		0			0
$847$	−11.8892	+	5.52890i	−0.408519	+	0.189975i
$848$		0			0
$849$	2.67942	+	4.64089i	0.0919573	+	0.159275i
$850$		0			0
$851$	−0.506069	+	0.135601i	−0.0173478	+	0.00464834i
$852$		0			0
$853$	3.65043	−	3.65043i	0.124988	−	0.124988i	−0.641846	−	0.766834i	$-0.721831\pi$
$853$	3.65043	−	3.65043i	0.124988	−	0.124988i	0.766834	+	0.641846i	$0.221831\pi$
$854$		0			0
$855$		−	18.6155i		−	0.636637i
$856$		0			0
$857$	−19.0400	−	10.9927i	−0.650394	−	0.375505i	0.138213	−	0.990402i	$-0.455864\pi$
$857$	−19.0400	−	10.9927i	−0.650394	−	0.375505i	−0.788607	+	0.614898i	$0.789197\pi$
$858$		0			0
$859$	−11.9718	−	3.20783i	−0.408472	−	0.109450i	0.0487316	−	0.998812i	$-0.484482\pi$
$859$	−11.9718	−	3.20783i	−0.408472	−	0.109450i	−0.457203	+	0.889362i	$0.651149\pi$
$860$		0			0
$861$	3.41599	+	19.4923i	0.116417	+	0.664296i
$862$		0			0
$863$	9.23283	+	15.9917i	0.314289	+	0.544365i	0.979286	−	0.202481i	$-0.0649005\pi$
$863$	9.23283	+	15.9917i	0.314289	+	0.544365i	−0.664997	+	0.746846i	$0.731567\pi$
$864$		0			0
$865$	−15.6685	+	27.1387i	−0.532745	+	0.922742i
$866$		0			0
$867$	12.7264	+	12.7264i	0.432213	+	0.432213i
$868$		0			0
$869$	18.8469	−	18.8469i	0.639338	−	0.639338i
$870$		0			0
$871$	−1.88052	−	1.08572i	−0.0637191	−	0.0367882i
$872$		0			0
$873$	36.6837	−	21.1793i	1.24156	−	0.716812i
$874$		0			0
$875$	19.9445	+	23.8195i	0.674247	+	0.805246i
$876$		0			0
$877$	5.01836	−	18.7288i	0.169458	−	0.632426i	−0.827971	−	0.560770i	$-0.810505\pi$
$877$	5.01836	−	18.7288i	0.169458	−	0.632426i	0.997429	−	0.0716557i	$-0.0228283\pi$
$878$		0			0
$879$	−11.3132	+	19.5951i	−0.381585	+	0.660925i
$880$		0			0
$881$	21.6393			0.729046			0.364523	−	0.931194i	$-0.381232\pi$
$881$	21.6393			0.729046			0.364523	+	0.931194i	$0.381232\pi$
$882$		0			0
$883$	34.6173	+	34.6173i	1.16496	+	1.16496i	0.983374	+	0.181589i	$0.0581241\pi$
$883$	34.6173	+	34.6173i	1.16496	+	1.16496i	0.181589	+	0.983374i	$0.441876\pi$
$884$		0			0
$885$	1.53912	+	5.74408i	0.0517370	+	0.193085i
$886$		0			0
$887$	−3.36305	+	1.94166i	−0.112920	+	0.0651945i	−0.555396	−	0.831586i	$-0.687433\pi$
$887$	−3.36305	+	1.94166i	−0.112920	+	0.0651945i	0.442476	+	0.896780i	$0.354100\pi$
$888$		0			0
$889$	25.5267	+	2.26022i	0.856138	+	0.0758052i
$890$		0			0
$891$	−11.1025	−	2.97491i	−0.371948	−	0.0996632i
$892$		0			0
$893$	−14.8173	+	3.97028i	−0.495841	+	0.132860i
$894$		0			0
$895$	−14.3402			−0.479341
$896$		0			0
$897$	−8.23688			−0.275022
$898$		0			0
$899$	−21.4965	+	5.75998i	−0.716949	+	0.192106i
$900$		0			0
$901$	43.5002	+	11.6559i	1.44920	+	0.388313i
$902$		0			0
$903$	1.32046	−	1.88162i	0.0439421	−	0.0626163i
$904$		0			0
$905$	−14.4437	+	8.33910i	−0.480126	+	0.277201i
$906$		0			0
$907$	−10.3652	−	38.6836i	−0.344172	−	1.28447i	−0.893577	−	0.448911i	$-0.851812\pi$
$907$	−10.3652	−	38.6836i	−0.344172	−	1.28447i	0.549404	−	0.835557i	$-0.314855\pi$
$908$		0			0
$909$	−7.10521	−	7.10521i	−0.235665	−	0.235665i
$910$		0			0
$911$	30.3771			1.00644			0.503218	−	0.864159i	$-0.332149\pi$
$911$	30.3771			1.00644			0.503218	+	0.864159i	$0.332149\pi$
$912$		0			0
$913$	−28.8321	+	49.9387i	−0.954203	+	1.65273i
$914$		0			0
$915$	−4.28404	+	15.9883i	−0.141626	+	0.528556i
$916$		0			0
$917$	−12.5624	+	34.4027i	−0.414845	+	1.13608i
$918$		0			0
$919$	9.74979	−	5.62904i	0.321616	−	0.185685i	−0.330497	−	0.943807i	$-0.607216\pi$
$919$	9.74979	−	5.62904i	0.321616	−	0.185685i	0.652113	+	0.758122i	$0.273883\pi$
$920$		0			0
$921$	20.1012	+	11.6054i	0.662358	+	0.382413i
$922$		0			0
$923$	2.83757	−	2.83757i	0.0933998	−	0.0933998i
$924$		0			0
$925$	−0.0322290	−	0.0322290i	−0.00105968	−	0.00105968i
$926$		0			0
$927$	−10.1214	+	17.5308i	−0.332430	+	0.575786i
$928$		0			0
$929$	12.8415	+	22.2420i	0.421314	+	0.729738i	0.996068	−	0.0885883i	$-0.0282356\pi$
$929$	12.8415	+	22.2420i	0.421314	+	0.729738i	−0.574754	+	0.818326i	$0.694902\pi$
$930$		0			0
$931$	11.6681	−	24.8862i	0.382406	−	0.815611i
$932$		0			0
$933$	−5.71572	−	1.53152i	−0.187124	−	0.0501398i
$934$		0			0
$935$	44.7037	+	25.8097i	1.46197	+	0.844068i
$936$		0			0
$937$		−	23.0570i		−	0.753238i	−0.926368	−	0.376619i	$-0.877087\pi$
$937$		−	23.0570i		−	0.753238i	0.926368	−	0.376619i	$-0.122913\pi$
$938$		0			0
$939$	−4.88423	+	4.88423i	−0.159391	+	0.159391i
$940$		0			0
$941$	30.8769	−	8.27344i	1.00656	−	0.269706i	0.282367	−	0.959306i	$-0.408880\pi$
$941$	30.8769	−	8.27344i	1.00656	−	0.269706i	0.724191	+	0.689600i	$0.242214\pi$
$942$		0			0
$943$	29.6647	+	51.3807i	0.966015	+	1.67319i
$944$		0			0
$945$	−22.8000	+	10.6028i	−0.741685	+	0.344909i
$946$		0			0
$947$	2.78357	−	10.3884i	0.0904539	−	0.337578i	−0.905837	−	0.423626i	$-0.860757\pi$
$947$	2.78357	−	10.3884i	0.0904539	−	0.337578i	0.996291	+	0.0860477i	$0.0274237\pi$
$948$		0			0
$949$	−3.74929	−	13.9925i	−0.121707	−	0.454217i
$950$		0			0
$951$			2.39443i			0.0776449i
$952$		0			0
$953$			2.60332i			0.0843297i	0.999111	+	0.0421649i	$0.0134255\pi$
$953$			2.60332i			0.0843297i	−0.999111	+	0.0421649i	$0.986575\pi$
$954$		0			0
$955$	3.47625	+	12.9735i	0.112489	+	0.419814i
$956$		0			0
$957$	4.82869	−	18.0209i	0.156089	−	0.582534i
$958$		0			0
$959$	−24.5186	−	17.2063i	−0.791745	−	0.555622i
$960$		0			0
$961$	7.08430	+	12.2704i	0.228526	+	0.395818i
$962$		0			0
$963$	−27.7150	+	7.42622i	−0.893104	+	0.239307i
$964$		0			0
$965$	−14.5680	+	14.5680i	−0.468962	+	0.468962i
$966$		0			0
$967$		−	10.6383i		−	0.342106i	−0.985262	−	0.171053i	$-0.945283\pi$
$967$		−	10.6383i		−	0.342106i	0.985262	−	0.171053i	$-0.0547169\pi$
$968$		0			0
$969$	18.0255	+	10.4070i	0.579062	+	0.334322i
$970$		0			0
$971$	−1.79607	−	0.481257i	−0.0576388	−	0.0154443i	0.229884	−	0.973218i	$-0.426165\pi$
$971$	−1.79607	−	0.481257i	−0.0576388	−	0.0154443i	−0.287523	+	0.957774i	$0.592832\pi$
$972$		0			0
$973$	−6.57744	+	5.50741i	−0.210863	+	0.176560i
$974$		0			0
$975$	−0.358285	−	0.620567i	−0.0114743	−	0.0198741i
$976$		0			0
$977$	−3.20547	+	5.55203i	−0.102552	+	0.177625i	−0.912735	−	0.408551i	$-0.866034\pi$
$977$	−3.20547	+	5.55203i	−0.102552	+	0.177625i	0.810183	+	0.586176i	$0.199367\pi$
$978$		0			0
$979$	3.79465	+	3.79465i	0.121278	+	0.121278i
$980$		0			0
$981$	23.1160	−	23.1160i	0.738038	−	0.738038i
$982$		0			0
$983$	−16.6011	−	9.58464i	−0.529492	−	0.305702i	0.211317	−	0.977417i	$-0.432225\pi$
$983$	−16.6011	−	9.58464i	−0.529492	−	0.305702i	−0.740810	+	0.671715i	$0.765558\pi$
$984$		0			0
$985$	−38.0660	+	21.9774i	−1.21288	+	0.700258i
$986$		0			0
$987$	5.71346	+	6.82352i	0.181861	+	0.217195i
$988$		0			0
$989$	1.78369	−	6.65683i	0.0567181	−	0.211675i
$990$		0			0
$991$	−8.09070	+	14.0135i	−0.257009	+	0.445153i	−0.965439	−	0.260628i	$-0.916070\pi$
$991$	−8.09070	+	14.0135i	−0.257009	+	0.445153i	0.708430	+	0.705781i	$0.249404\pi$
$992$		0			0
$993$	9.25270			0.293626
$994$		0			0
$995$	6.44966	+	6.44966i	0.204468	+	0.204468i
$996$		0			0
$997$	6.95744	+	25.9655i	0.220344	+	0.822336i	0.984217	+	0.176969i	$0.0566291\pi$
$997$	6.95744	+	25.9655i	0.220344	+	0.822336i	−0.763872	+	0.645368i	$0.776704\pi$
$998$		0			0
$999$	0.300805	−	0.173670i	0.00951705	−	0.00549467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.ba.c.81.5		48
4.3	odd	2		112.2.w.c.109.12	yes	48
7.2	even	3	inner	448.2.ba.c.401.8		48
8.3	odd	2		896.2.ba.f.417.5		48
8.5	even	2		896.2.ba.e.417.8		48
16.3	odd	4		896.2.ba.f.865.8		48
16.5	even	4	inner	448.2.ba.c.305.8		48
16.11	odd	4		112.2.w.c.53.4	yes	48
16.13	even	4		896.2.ba.e.865.5		48
28.3	even	6		784.2.m.k.589.4		24
28.11	odd	6		784.2.m.j.589.4		24
28.19	even	6		784.2.x.o.765.4		48
28.23	odd	6		112.2.w.c.93.4	yes	48
28.27	even	2		784.2.x.o.557.12		48
56.37	even	6		896.2.ba.e.289.5		48
56.51	odd	6		896.2.ba.f.289.8		48
112.11	odd	12		784.2.m.j.197.4		24
112.27	even	4		784.2.x.o.165.4		48
112.37	even	12	inner	448.2.ba.c.177.5		48
112.51	odd	12		896.2.ba.f.737.5		48
112.59	even	12		784.2.m.k.197.4		24
112.75	even	12		784.2.x.o.373.12		48
112.93	even	12		896.2.ba.e.737.8		48
112.107	odd	12		112.2.w.c.37.12	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.12	✓	48	112.107	odd	12
112.2.w.c.53.4	yes	48	16.11	odd	4
112.2.w.c.93.4	yes	48	28.23	odd	6
112.2.w.c.109.12	yes	48	4.3	odd	2
448.2.ba.c.81.5		48	1.1	even	1	trivial
448.2.ba.c.177.5		48	112.37	even	12	inner
448.2.ba.c.305.8		48	16.5	even	4	inner
448.2.ba.c.401.8		48	7.2	even	3	inner
784.2.m.j.197.4		24	112.11	odd	12
784.2.m.j.589.4		24	28.11	odd	6
784.2.m.k.197.4		24	112.59	even	12
784.2.m.k.589.4		24	28.3	even	6
784.2.x.o.165.4		48	112.27	even	4
784.2.x.o.373.12		48	112.75	even	12
784.2.x.o.557.12		48	28.27	even	2
784.2.x.o.765.4		48	28.19	even	6
896.2.ba.e.289.5		48	56.37	even	6
896.2.ba.e.417.8		48	8.5	even	2
896.2.ba.e.737.8		48	112.93	even	12
896.2.ba.e.865.5		48	16.13	even	4
896.2.ba.f.289.8		48	56.51	odd	6
896.2.ba.f.417.5		48	8.3	odd	2
896.2.ba.f.737.5		48	112.51	odd	12
896.2.ba.f.865.8		48	16.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.831674 + 0.222846i) q^{3} +(-2.02749 - 0.543265i) q^{5} +(2.63544 + 0.233350i) q^{7} +(-1.95606 + 1.12933i) q^{9} +(-1.03385 - 3.85837i) q^{11} +(-0.990473 - 0.990473i) q^{13} +1.80728 q^{15} +(3.07828 - 5.33174i) q^{17} +(1.01626 - 3.79274i) q^{19} +(-2.24383 + 0.393227i) q^{21} +(-5.91462 + 3.41481i) q^{23} +(-0.514543 - 0.297072i) q^{25} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(2.05131 - 3.55296i) q^{31} +(1.71965 + 2.97851i) q^{33} +(-5.21656 - 1.90486i) q^{35} +(0.0740993 + 0.0198548i) q^{37} +(1.04447 + 0.603027i) q^{39} -8.68707i q^{41} +(-0.713530 + 0.713530i) q^{43} +(4.57941 - 1.22705i) q^{45} +(-1.95337 - 3.38334i) q^{47} +(6.89110 + 1.22996i) q^{49} +(-1.37197 + 5.12025i) q^{51} +(1.89324 + 7.06568i) q^{53} +8.38446i q^{55} +3.38079i q^{57} +(0.851626 + 3.17831i) q^{59} +(-2.37044 + 8.84662i) q^{61} +(-5.41860 + 2.51983i) q^{63} +(1.47009 + 2.54627i) q^{65} +(1.49739 - 0.401223i) q^{67} +(4.15805 - 4.15805i) q^{69} +2.86486i q^{71} +(8.95624 + 5.17089i) q^{73} +(0.494133 + 0.132403i) q^{75} +(-1.82429 - 10.4097i) q^{77} +(3.33631 + 5.77865i) q^{79} +(1.43876 - 2.49200i) q^{81} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(4.04486 + 2.33530i) q^{87} +(-1.16348 + 0.671733i) q^{89} +(-2.37921 - 2.84146i) q^{91} +(-0.914251 + 3.41203i) q^{93} +(-4.12092 + 7.13765i) q^{95} -18.7539 q^{97} +(6.37963 + 6.37963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

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