LMFDB - Embedded newform 896.2.m.g.673.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(225,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("896.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.m (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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			673.6
Root			$-1.40471 - 0.163666i$ of defining polynomial
Character	$\chi$	$=$	896.673
Dual form			896.2.m.g.225.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05500 + 2.05500i) q^{3} +(-2.72766 + 2.72766i) q^{5} -1.00000i q^{7} +5.44602i q^{9} +O(q^{10})$	\(q+(2.05500 + 2.05500i) q^{3} +(-2.72766 + 2.72766i) q^{5} -1.00000i q^{7} +5.44602i q^{9} +(-0.919616 + 0.919616i) q^{11} +(1.12607 + 1.12607i) q^{13} -11.2107 q^{15} -1.50885 q^{17} +(-1.46271 - 1.46271i) q^{19} +(2.05500 - 2.05500i) q^{21} +4.77031i q^{23} -9.88030i q^{25} +(-5.02656 + 5.02656i) q^{27} +(-4.10069 - 4.10069i) q^{29} +4.10999 q^{31} -3.77961 q^{33} +(2.72766 + 2.72766i) q^{35} +(1.65467 - 1.65467i) q^{37} +4.62815i q^{39} +7.45533i q^{41} +(-5.68992 + 5.68992i) q^{43} +(-14.8549 - 14.8549i) q^{45} +3.59748 q^{47} -1.00000 q^{49} +(-3.10069 - 3.10069i) q^{51} +(0.675714 - 0.675714i) q^{53} -5.01680i q^{55} -6.01174i q^{57} +(-1.13843 + 1.13843i) q^{59} +(3.21881 + 3.21881i) q^{61} +5.44602 q^{63} -6.14310 q^{65} +(1.52640 + 1.52640i) q^{67} +(-9.80296 + 9.80296i) q^{69} +13.8202i q^{71} -14.4749i q^{73} +(20.3040 - 20.3040i) q^{75} +(0.919616 + 0.919616i) q^{77} -1.77961 q^{79} -4.32107 q^{81} +(7.16133 + 7.16133i) q^{83} +(4.11564 - 4.11564i) q^{85} -16.8538i q^{87} -8.45899i q^{89} +(1.12607 - 1.12607i) q^{91} +(8.44602 + 8.44602i) q^{93} +7.97958 q^{95} +16.2227 q^{97} +(-5.00824 - 5.00824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 12 * q - 4 * q^3 - 4 * q^5	$ 12 q - 4 q^{3} - 4 q^{5} - 24 q^{15} - 8 q^{17} - 4 q^{21} - 4 q^{27} + 4 q^{29} - 8 q^{31} + 4 q^{35} + 20 q^{37} - 16 q^{43} - 40 q^{45} + 16 q^{47} - 12 q^{49} + 16 q^{51} - 4 q^{53} + 16 q^{59} + 20 q^{61} + 12 q^{63} + 32 q^{65} - 24 q^{67} + 4 q^{69} + 40 q^{75} + 24 q^{79} - 44 q^{81} + 20 q^{83} + 8 q^{85} + 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - 4 * q^5 - 24 * q^15 - 8 * q^17 - 4 * q^21 - 4 * q^27 + 4 * q^29 - 8 * q^31 + 4 * q^35 + 20 * q^37 - 16 * q^43 - 40 * q^45 + 16 * q^47 - 12 * q^49 + 16 * q^51 - 4 * q^53 + 16 * q^59 + 20 * q^61 + 12 * q^63 + 32 * q^65 - 24 * q^67 + 4 * q^69 + 40 * q^75 + 24 * q^79 - 44 * q^81 + 20 * q^83 + 8 * q^85 + 48 * q^93 + 48 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.05500	+	2.05500i	1.18645	+	1.18645i	0.978041	+	0.208411i	$0.0668293\pi$
$3$	2.05500	+	2.05500i	1.18645	+	1.18645i	0.208411	+	0.978041i	$0.433171\pi$
$4$		0			0
$5$	−2.72766	+	2.72766i	−1.21985	+	1.21985i	−0.252164	+	0.967685i	$0.581142\pi$
$5$	−2.72766	+	2.72766i	−1.21985	+	1.21985i	−0.967685	+	0.252164i	$0.918858\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			5.44602i			1.81534i
$10$		0			0
$11$	−0.919616	+	0.919616i	−0.277275	+	0.277275i	−0.832020	−	0.554746i	$-0.812816\pi$
$11$	−0.919616	+	0.919616i	−0.277275	+	0.277275i	0.554746	+	0.832020i	$0.312816\pi$
$12$		0			0
$13$	1.12607	+	1.12607i	0.312316	+	0.312316i	0.845806	−	0.533490i	$-0.179120\pi$
$13$	1.12607	+	1.12607i	0.312316	+	0.312316i	−0.533490	+	0.845806i	$0.679120\pi$
$14$		0			0
$15$	−11.2107			−2.89458
$16$		0			0
$17$	−1.50885			−0.365950			−0.182975	−	0.983118i	$-0.558573\pi$
$17$	−1.50885			−0.365950			−0.182975	+	0.983118i	$0.558573\pi$
$18$		0			0
$19$	−1.46271	−	1.46271i	−0.335569	−	0.335569i	0.519127	−	0.854697i	$-0.326257\pi$
$19$	−1.46271	−	1.46271i	−0.335569	−	0.335569i	−0.854697	+	0.519127i	$0.826257\pi$
$20$		0			0
$21$	2.05500	−	2.05500i	0.448437	−	0.448437i
$22$		0			0
$23$			4.77031i			0.994677i	0.867556	+	0.497339i	$0.165689\pi$
$23$			4.77031i			0.994677i	−0.867556	+	0.497339i	$0.834311\pi$
$24$		0			0
$25$		−	9.88030i		−	1.97606i
$26$		0			0
$27$	−5.02656	+	5.02656i	−0.967362	+	0.967362i
$28$		0			0
$29$	−4.10069	−	4.10069i	−0.761478	−	0.761478i	0.215111	−	0.976590i	$-0.430989\pi$
$29$	−4.10069	−	4.10069i	−0.761478	−	0.761478i	−0.976590	+	0.215111i	$0.930989\pi$
$30$		0			0
$31$	4.10999			0.738176			0.369088	−	0.929394i	$-0.379670\pi$
$31$	4.10999			0.738176			0.369088	+	0.929394i	$0.379670\pi$
$32$		0			0
$33$	−3.77961			−0.657946
$34$		0			0
$35$	2.72766	+	2.72766i	0.461059	+	0.461059i
$36$		0			0
$37$	1.65467	−	1.65467i	0.272025	−	0.272025i	−0.557890	−	0.829915i	$-0.688389\pi$
$37$	1.65467	−	1.65467i	0.272025	−	0.272025i	0.829915	+	0.557890i	$0.188389\pi$
$38$		0			0
$39$			4.62815i			0.741097i
$40$		0			0
$41$			7.45533i			1.16433i	0.813072	+	0.582163i	$0.197794\pi$
$41$			7.45533i			1.16433i	−0.813072	+	0.582163i	$0.802206\pi$
$42$		0			0
$43$	−5.68992	+	5.68992i	−0.867705	+	0.867705i	−0.992218	−	0.124513i	$-0.960263\pi$
$43$	−5.68992	+	5.68992i	−0.867705	+	0.867705i	0.124513	+	0.992218i	$0.460263\pi$
$44$		0			0
$45$	−14.8549	−	14.8549i	−2.21444	−	2.21444i
$46$		0			0
$47$	3.59748			0.524747			0.262373	−	0.964966i	$-0.415495\pi$
$47$	3.59748			0.524747			0.262373	+	0.964966i	$0.415495\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−3.10069	−	3.10069i	−0.434183	−	0.434183i
$52$		0			0
$53$	0.675714	−	0.675714i	0.0928165	−	0.0928165i	−0.659174	−	0.751990i	$-0.729094\pi$
$53$	0.675714	−	0.675714i	0.0928165	−	0.0928165i	0.751990	+	0.659174i	$0.229094\pi$
$54$		0			0
$55$		−	5.01680i		−	0.676466i
$56$		0			0
$57$		−	6.01174i		−	0.796275i
$58$		0			0
$59$	−1.13843	+	1.13843i	−0.148211	+	0.148211i	−0.777318	−	0.629108i	$-0.783420\pi$
$59$	−1.13843	+	1.13843i	−0.148211	+	0.148211i	0.629108	+	0.777318i	$0.283420\pi$
$60$		0			0
$61$	3.21881	+	3.21881i	0.412127	+	0.412127i	0.882479	−	0.470352i	$-0.155873\pi$
$61$	3.21881	+	3.21881i	0.412127	+	0.412127i	−0.470352	+	0.882479i	$0.655873\pi$
$62$		0			0
$63$	5.44602			0.686134
$64$		0			0
$65$	−6.14310			−0.761957
$66$		0			0
$67$	1.52640	+	1.52640i	0.186480	+	0.186480i	0.794172	−	0.607692i	$-0.207905\pi$
$67$	1.52640	+	1.52640i	0.186480	+	0.186480i	−0.607692	+	0.794172i	$0.707905\pi$
$68$		0			0
$69$	−9.80296	+	9.80296i	−1.18014	+	1.18014i
$70$		0			0
$71$			13.8202i			1.64016i	0.572251	+	0.820079i	$0.306070\pi$
$71$			13.8202i			1.64016i	−0.572251	+	0.820079i	$0.693930\pi$
$72$		0			0
$73$		−	14.4749i		−	1.69416i	−0.531468	−	0.847078i	$-0.678359\pi$
$73$		−	14.4749i		−	1.69416i	0.531468	−	0.847078i	$-0.321641\pi$
$74$		0			0
$75$	20.3040	−	20.3040i	2.34450	−	2.34450i
$76$		0			0
$77$	0.919616	+	0.919616i	0.104800	+	0.104800i
$78$		0			0
$79$	−1.77961			−0.200222			−0.100111	−	0.994976i	$-0.531920\pi$
$79$	−1.77961			−0.200222			−0.100111	+	0.994976i	$0.531920\pi$
$80$		0			0
$81$	−4.32107			−0.480119
$82$		0			0
$83$	7.16133	+	7.16133i	0.786058	+	0.786058i	0.980845	−	0.194787i	$-0.0624017\pi$
$83$	7.16133	+	7.16133i	0.786058	+	0.786058i	−0.194787	+	0.980845i	$0.562402\pi$
$84$		0			0
$85$	4.11564	−	4.11564i	0.446404	−	0.446404i
$86$		0			0
$87$		−	16.8538i		−	1.80692i
$88$		0			0
$89$		−	8.45899i		−	0.896651i	−0.893870	−	0.448325i	$-0.852021\pi$
$89$		−	8.45899i		−	0.896651i	0.893870	−	0.448325i	$-0.147979\pi$
$90$		0			0
$91$	1.12607	−	1.12607i	0.118045	−	0.118045i
$92$		0			0
$93$	8.44602	+	8.44602i	0.875811	+	0.875811i
$94$		0			0
$95$	7.97958			0.818688
$96$		0			0
$97$	16.2227			1.64717			0.823585	−	0.567194i	$-0.191971\pi$
$97$	16.2227			1.64717			0.823585	+	0.567194i	$0.191971\pi$
$98$		0			0
$99$	−5.00824	−	5.00824i	−0.503348	−	0.503348i
$100$		0			0
$101$	11.5664	−	11.5664i	1.15090	−	1.15090i	0.164533	−	0.986372i	$-0.447388\pi$
$101$	11.5664	−	11.5664i	1.15090	−	1.15090i	0.986372	−	0.164533i	$-0.0526116\pi$
$102$		0			0
$103$			17.1875i			1.69354i	0.531963	+	0.846768i	$0.321455\pi$
$103$			17.1875i			1.69354i	−0.531963	+	0.846768i	$0.678545\pi$
$104$		0			0
$105$			11.2107i			1.09405i
$106$		0			0
$107$	−4.10143	+	4.10143i	−0.396501	+	0.396501i	−0.876997	−	0.480496i	$-0.840457\pi$
$107$	−4.10143	+	4.10143i	−0.396501	+	0.396501i	0.480496	+	0.876997i	$0.340457\pi$
$108$		0			0
$109$	3.27351	+	3.27351i	0.313545	+	0.313545i	0.846281	−	0.532736i	$-0.178836\pi$
$109$	3.27351	+	3.27351i	0.313545	+	0.313545i	−0.532736	+	0.846281i	$0.678836\pi$
$110$		0			0
$111$	6.80066			0.645490
$112$		0			0
$113$	−9.17193			−0.862822			−0.431411	−	0.902155i	$-0.641984\pi$
$113$	−9.17193			−0.862822			−0.431411	+	0.902155i	$0.641984\pi$
$114$		0			0
$115$	−13.0118	−	13.0118i	−1.21336	−	1.21336i
$116$		0			0
$117$	−6.13262	+	6.13262i	−0.566961	+	0.566961i
$118$		0			0
$119$			1.50885i			0.138316i
$120$		0			0
$121$			9.30861i			0.846238i
$122$		0			0
$123$	−15.3207	+	15.3207i	−1.38142	+	1.38142i
$124$		0			0
$125$	13.3118	+	13.3118i	1.19064	+	1.19064i
$126$		0			0
$127$	−12.9787			−1.15167			−0.575835	−	0.817566i	$-0.695323\pi$
$127$	−12.9787			−1.15167			−0.575835	+	0.817566i	$0.695323\pi$
$128$		0			0
$129$	−23.3855			−2.05898
$130$		0			0
$131$	6.81965	+	6.81965i	0.595836	+	0.595836i	0.939202	−	0.343366i	$-0.111567\pi$
$131$	6.81965	+	6.81965i	0.595836	+	0.595836i	−0.343366	+	0.939202i	$0.611567\pi$
$132$		0			0
$133$	−1.46271	+	1.46271i	−0.126833	+	0.126833i
$134$		0			0
$135$		−	27.4215i		−	2.36007i
$136$		0			0
$137$			22.6543i			1.93548i	0.251943	+	0.967742i	$0.418931\pi$
$137$			22.6543i			1.93548i	−0.251943	+	0.967742i	$0.581069\pi$
$138$		0			0
$139$	6.64728	−	6.64728i	0.563815	−	0.563815i	−0.366574	−	0.930389i	$-0.619469\pi$
$139$	6.64728	−	6.64728i	0.563815	−	0.563815i	0.930389	+	0.366574i	$0.119469\pi$
$140$		0			0
$141$	7.39281	+	7.39281i	0.622587	+	0.622587i
$142$		0			0
$143$	−2.07111			−0.173195
$144$		0			0
$145$	22.3706			1.85778
$146$		0			0
$147$	−2.05500	−	2.05500i	−0.169493	−	0.169493i
$148$		0			0
$149$	−7.77031	+	7.77031i	−0.636568	+	0.636568i	−0.949707	−	0.313139i	$-0.898619\pi$
$149$	−7.77031	+	7.77031i	−0.636568	+	0.636568i	0.313139	+	0.949707i	$0.398619\pi$
$150$		0			0
$151$		−	5.46829i		−	0.445004i	−0.974932	−	0.222502i	$-0.928578\pi$
$151$		−	5.46829i		−	0.445004i	0.974932	−	0.222502i	$-0.0714223\pi$
$152$		0			0
$153$		−	8.21724i		−	0.664324i
$154$		0			0
$155$	−11.2107	+	11.2107i	−0.900463	+	0.900463i
$156$		0			0
$157$	5.61722	+	5.61722i	0.448303	+	0.448303i	0.894790	−	0.446487i	$-0.147325\pi$
$157$	5.61722	+	5.61722i	0.448303	+	0.448303i	−0.446487	+	0.894790i	$0.647325\pi$
$158$		0			0
$159$	2.77718			0.220245
$160$		0			0
$161$	4.77031			0.375953
$162$		0			0
$163$	6.31758	+	6.31758i	0.494831	+	0.494831i	0.909824	−	0.414994i	$-0.136216\pi$
$163$	6.31758	+	6.31758i	0.494831	+	0.494831i	−0.414994	+	0.909824i	$0.636216\pi$
$164$		0			0
$165$	10.3095	−	10.3095i	0.802595	−	0.802595i
$166$		0			0
$167$			11.8175i			0.914463i	0.889348	+	0.457231i	$0.151159\pi$
$167$			11.8175i			0.914463i	−0.889348	+	0.457231i	$0.848841\pi$
$168$		0			0
$169$		−	10.4639i		−	0.804917i
$170$		0			0
$171$	7.96597	−	7.96597i	0.609173	−	0.609173i
$172$		0			0
$173$	−5.63858	−	5.63858i	−0.428694	−	0.428694i	0.459490	−	0.888183i	$-0.348032\pi$
$173$	−5.63858	−	5.63858i	−0.428694	−	0.428694i	−0.888183	+	0.459490i	$0.848032\pi$
$174$		0			0
$175$	−9.88030			−0.746880
$176$		0			0
$177$	−4.67893			−0.351690
$178$		0			0
$179$	−11.7278	−	11.7278i	−0.876575	−	0.876575i	0.116604	−	0.993179i	$-0.462799\pi$
$179$	−11.7278	−	11.7278i	−0.876575	−	0.876575i	−0.993179	+	0.116604i	$0.962799\pi$
$180$		0			0
$181$	4.18574	−	4.18574i	0.311124	−	0.311124i	−0.534221	−	0.845345i	$-0.679395\pi$
$181$	4.18574	−	4.18574i	0.311124	−	0.311124i	0.845345	+	0.534221i	$0.179395\pi$
$182$		0			0
$183$			13.2293i			0.977937i
$184$		0			0
$185$			9.02674i			0.663659i
$186$		0			0
$187$	1.38756	−	1.38756i	0.101469	−	0.101469i
$188$		0			0
$189$	5.02656	+	5.02656i	0.365629	+	0.365629i
$190$		0			0
$191$	12.3676			0.894891			0.447445	−	0.894311i	$-0.352334\pi$
$191$	12.3676			0.894891			0.447445	+	0.894311i	$0.352334\pi$
$192$		0			0
$193$	23.6837			1.70479			0.852395	−	0.522898i	$-0.175149\pi$
$193$	23.6837			1.70479			0.852395	+	0.522898i	$0.175149\pi$
$194$		0			0
$195$	−12.6240	−	12.6240i	−0.904026	−	0.904026i
$196$		0			0
$197$	11.4195	−	11.4195i	0.813606	−	0.813606i	−0.171566	−	0.985173i	$-0.554883\pi$
$197$	11.4195	−	11.4195i	0.813606	−	0.813606i	0.985173	+	0.171566i	$0.0548828\pi$
$198$		0			0
$199$		−	5.49683i		−	0.389660i	−0.980837	−	0.194830i	$-0.937585\pi$
$199$		−	5.49683i		−	0.389660i	0.980837	−	0.194830i	$-0.0624155\pi$
$200$		0			0
$201$			6.27351i			0.442499i
$202$		0			0
$203$	−4.10069	+	4.10069i	−0.287812	+	0.287812i
$204$		0			0
$205$	−20.3356	−	20.3356i	−1.42030	−	1.42030i
$206$		0			0
$207$	−25.9792			−1.80568
$208$		0			0
$209$	2.69027			0.186090
$210$		0			0
$211$	−0.907874	−	0.907874i	−0.0625007	−	0.0625007i	0.675166	−	0.737666i	$-0.264072\pi$
$211$	−0.907874	−	0.907874i	−0.0625007	−	0.0625007i	−0.737666	+	0.675166i	$0.764072\pi$
$212$		0			0
$213$	−28.4005	+	28.4005i	−1.94597	+	1.94597i
$214$		0			0
$215$		−	31.0404i		−	2.11694i
$216$		0			0
$217$		−	4.10999i		−	0.279004i
$218$		0			0
$219$	29.7458	−	29.7458i	2.01004	−	2.01004i
$220$		0			0
$221$	−1.69908	−	1.69908i	−0.114292	−	0.114292i
$222$		0			0
$223$	−3.20318			−0.214501			−0.107250	−	0.994232i	$-0.534205\pi$
$223$	−3.20318			−0.214501			−0.107250	+	0.994232i	$0.534205\pi$
$224$		0			0
$225$	53.8083			3.58722
$226$		0			0
$227$	13.7931	+	13.7931i	0.915480	+	0.915480i	0.996696	−	0.0812167i	$-0.0258806\pi$
$227$	13.7931	+	13.7931i	0.915480	+	0.915480i	−0.0812167	+	0.996696i	$0.525881\pi$
$228$		0			0
$229$	−7.02177	+	7.02177i	−0.464012	+	0.464012i	−0.899968	−	0.435956i	$-0.856410\pi$
$229$	−7.02177	+	7.02177i	−0.464012	+	0.464012i	0.435956	+	0.899968i	$0.356410\pi$
$230$		0			0
$231$			3.77961i			0.248680i
$232$		0			0
$233$		−	2.93857i		−	0.192512i	−0.995357	−	0.0962561i	$-0.969313\pi$
$233$		−	2.93857i		−	0.192512i	0.995357	−	0.0962561i	$-0.0306868\pi$
$234$		0			0
$235$	−9.81272	+	9.81272i	−0.640111	+	0.640111i
$236$		0			0
$237$	−3.65710	−	3.65710i	−0.237554	−	0.237554i
$238$		0			0
$239$	16.2109			1.04859			0.524297	−	0.851536i	$-0.324328\pi$
$239$	16.2109			1.04859			0.524297	+	0.851536i	$0.324328\pi$
$240$		0			0
$241$	−14.1166			−0.909329			−0.454665	−	0.890663i	$-0.650241\pi$
$241$	−14.1166			−0.909329			−0.454665	+	0.890663i	$0.650241\pi$
$242$		0			0
$243$	6.19990	+	6.19990i	0.397724	+	0.397724i
$244$		0			0
$245$	2.72766	−	2.72766i	0.174264	−	0.174264i
$246$		0			0
$247$		−	3.29424i		−	0.209608i
$248$		0			0
$249$			29.4330i			1.86524i
$250$		0			0
$251$	14.1967	−	14.1967i	0.896091	−	0.896091i	−0.0989969	−	0.995088i	$-0.531563\pi$
$251$	14.1967	−	14.1967i	0.896091	−	0.896091i	0.995088	+	0.0989969i	$0.0315634\pi$
$252$		0			0
$253$	−4.38685	−	4.38685i	−0.275799	−	0.275799i
$254$		0			0
$255$	16.9153			1.05927
$256$		0			0
$257$	−3.23679			−0.201905			−0.100953	−	0.994891i	$-0.532189\pi$
$257$	−3.23679			−0.201905			−0.100953	+	0.994891i	$0.532189\pi$
$258$		0			0
$259$	−1.65467	−	1.65467i	−0.102816	−	0.102816i
$260$		0			0
$261$	22.3324	−	22.3324i	1.38234	−	1.38234i
$262$		0			0
$263$		−	24.0161i		−	1.48090i	−0.672114	−	0.740448i	$-0.734614\pi$
$263$		−	24.0161i		−	1.48090i	0.672114	−	0.740448i	$-0.265386\pi$
$264$		0			0
$265$			3.68624i			0.226444i
$266$		0			0
$267$	17.3832	−	17.3832i	1.06383	−	1.06383i
$268$		0			0
$269$	0.0875040	+	0.0875040i	0.00533521	+	0.00533521i	0.709769	−	0.704434i	$-0.248799\pi$
$269$	0.0875040	+	0.0875040i	0.00533521	+	0.00533521i	−0.704434	+	0.709769i	$0.748799\pi$
$270$		0			0
$271$	−10.1138			−0.614372			−0.307186	−	0.951650i	$-0.599387\pi$
$271$	−10.1138			−0.614372			−0.307186	+	0.951650i	$0.599387\pi$
$272$		0			0
$273$	4.62815			0.280109
$274$		0			0
$275$	9.08608	+	9.08608i	0.547911	+	0.547911i
$276$		0			0
$277$	11.0080	−	11.0080i	0.661406	−	0.661406i	−0.294305	−	0.955711i	$-0.595088\pi$
$277$	11.0080	−	11.0080i	0.661406	−	0.661406i	0.955711	+	0.294305i	$0.0950882\pi$
$278$		0			0
$279$			22.3831i			1.34004i
$280$		0			0
$281$			4.21999i			0.251743i	0.992047	+	0.125872i	$0.0401727\pi$
$281$			4.21999i			0.251743i	−0.992047	+	0.125872i	$0.959827\pi$
$282$		0			0
$283$	16.5834	−	16.5834i	0.985781	−	0.985781i	−0.0141195	−	0.999900i	$-0.504495\pi$
$283$	16.5834	−	16.5834i	0.985781	−	0.985781i	0.999900	+	0.0141195i	$0.00449452\pi$
$284$		0			0
$285$	16.3980	+	16.3980i	0.971334	+	0.971334i
$286$		0			0
$287$	7.45533			0.440074
$288$		0			0
$289$	−14.7234			−0.866080
$290$		0			0
$291$	33.3377	+	33.3377i	1.95429	+	1.95429i
$292$		0			0
$293$	13.5242	−	13.5242i	0.790093	−	0.790093i	−0.191416	−	0.981509i	$-0.561308\pi$
$293$	13.5242	−	13.5242i	0.790093	−	0.790093i	0.981509	+	0.191416i	$0.0613079\pi$
$294$		0			0
$295$		−	6.21049i		−	0.361589i
$296$		0			0
$297$		−	9.24501i		−	0.536450i
$298$		0			0
$299$	−5.37171	+	5.37171i	−0.310654	+	0.310654i
$300$		0			0
$301$	5.68992	+	5.68992i	0.327962	+	0.327962i
$302$		0			0
$303$	47.5380			2.73099
$304$		0			0
$305$	−17.5597			−1.00546
$306$		0			0
$307$	8.93389	+	8.93389i	0.509884	+	0.509884i	0.914491	−	0.404607i	$-0.132592\pi$
$307$	8.93389	+	8.93389i	0.509884	+	0.509884i	−0.404607	+	0.914491i	$0.632592\pi$
$308$		0			0
$309$	−35.3203	+	35.3203i	−2.00930	+	2.00930i
$310$		0			0
$311$		−	19.7737i		−	1.12126i	−0.828066	−	0.560631i	$-0.810558\pi$
$311$		−	19.7737i		−	1.12126i	0.828066	−	0.560631i	$-0.189442\pi$
$312$		0			0
$313$		−	8.72743i		−	0.493303i	−0.969104	−	0.246652i	$-0.920670\pi$
$313$		−	8.72743i		−	0.493303i	0.969104	−	0.246652i	$-0.0793304\pi$
$314$		0			0
$315$	−14.8549	+	14.8549i	−0.836979	+	0.836979i
$316$		0			0
$317$	−19.0197	−	19.0197i	−1.06825	−	1.06825i	−0.997493	−	0.0707615i	$-0.977457\pi$
$317$	−19.0197	−	19.0197i	−1.06825	−	1.06825i	−0.0707615	−	0.997493i	$-0.522543\pi$
$318$		0			0
$319$	7.54211			0.422277
$320$		0			0
$321$	−16.8569			−0.940858
$322$		0			0
$323$	2.20702	+	2.20702i	0.122802	+	0.122802i
$324$		0			0
$325$	11.1259	−	11.1259i	0.617156	−	0.617156i
$326$		0			0
$327$			13.4541i			0.744013i
$328$		0			0
$329$		−	3.59748i		−	0.198336i
$330$		0			0
$331$	−22.3328	+	22.3328i	−1.22752	+	1.22752i	−0.262620	+	0.964899i	$0.584587\pi$
$331$	−22.3328	+	22.3328i	−1.22752	+	1.22752i	−0.964899	+	0.262620i	$0.915413\pi$
$332$		0			0
$333$	9.01134	+	9.01134i	0.493818	+	0.493818i
$334$		0			0
$335$	−8.32703			−0.454954
$336$		0			0
$337$	−23.4825			−1.27918			−0.639588	−	0.768718i	$-0.720895\pi$
$337$	−23.4825			−1.27918			−0.639588	+	0.768718i	$0.720895\pi$
$338$		0			0
$339$	−18.8483	−	18.8483i	−1.02370	−	1.02370i
$340$		0			0
$341$	−3.77961	+	3.77961i	−0.204678	+	0.204678i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	53.4784i		−	2.87918i
$346$		0			0
$347$	6.29716	−	6.29716i	0.338049	−	0.338049i	−0.517584	−	0.855633i	$-0.673168\pi$
$347$	6.29716	−	6.29716i	0.338049	−	0.338049i	0.855633	+	0.517584i	$0.173168\pi$
$348$		0			0
$349$	−6.94033	−	6.94033i	−0.371507	−	0.371507i	0.496519	−	0.868026i	$-0.334611\pi$
$349$	−6.94033	−	6.94033i	−0.371507	−	0.371507i	−0.868026	+	0.496519i	$0.834611\pi$
$350$		0			0
$351$	−11.3206			−0.604246
$352$		0			0
$353$	30.0934			1.60171			0.800856	−	0.598857i	$-0.204378\pi$
$353$	30.0934			1.60171			0.800856	+	0.598857i	$0.204378\pi$
$354$		0			0
$355$	−37.6969	−	37.6969i	−2.00074	−	2.00074i
$356$		0			0
$357$	−3.10069	+	3.10069i	−0.164106	+	0.164106i
$358$		0			0
$359$		−	10.3716i		−	0.547394i	−0.961816	−	0.273697i	$-0.911754\pi$
$359$		−	10.3716i		−	0.547394i	0.961816	−	0.273697i	$-0.0882465\pi$
$360$		0			0
$361$		−	14.7209i		−	0.774786i
$362$		0			0
$363$	−19.1292	+	19.1292i	−1.00402	+	1.00402i
$364$		0			0
$365$	39.4826	+	39.4826i	2.06661	+	2.06661i
$366$		0			0
$367$	−8.12973			−0.424368			−0.212184	−	0.977230i	$-0.568058\pi$
$367$	−8.12973			−0.424368			−0.212184	+	0.977230i	$0.568058\pi$
$368$		0			0
$369$	−40.6019			−2.11365
$370$		0			0
$371$	−0.675714	−	0.675714i	−0.0350813	−	0.0350813i
$372$		0			0
$373$	3.18688	−	3.18688i	0.165010	−	0.165010i	−0.619772	−	0.784782i	$-0.712775\pi$
$373$	3.18688	−	3.18688i	0.165010	−	0.165010i	0.784782	+	0.619772i	$0.212775\pi$
$374$		0			0
$375$			54.7115i			2.82529i
$376$		0			0
$377$		−	9.23534i		−	0.475644i
$378$		0			0
$379$	0.839080	−	0.839080i	0.0431006	−	0.0431006i	−0.685228	−	0.728329i	$-0.740297\pi$
$379$	0.839080	−	0.839080i	0.0431006	−	0.0431006i	0.728329	+	0.685228i	$0.240297\pi$
$380$		0			0
$381$	−26.6711	−	26.6711i	−1.36640	−	1.36640i
$382$		0			0
$383$	−34.3749			−1.75647			−0.878237	−	0.478225i	$-0.841280\pi$
$383$	−34.3749			−1.75647			−0.878237	+	0.478225i	$0.841280\pi$
$384$		0			0
$385$	−5.01680			−0.255680
$386$		0			0
$387$	−30.9874	−	30.9874i	−1.57518	−	1.57518i
$388$		0			0
$389$	−10.9633	+	10.9633i	−0.555860	+	0.555860i	−0.928126	−	0.372266i	$-0.878581\pi$
$389$	−10.9633	+	10.9633i	−0.555860	+	0.555860i	0.372266	+	0.928126i	$0.378581\pi$
$390$		0			0
$391$		−	7.19768i		−	0.364003i
$392$		0			0
$393$			28.0287i			1.41386i
$394$		0			0
$395$	4.85419	−	4.85419i	0.244241	−	0.244241i
$396$		0			0
$397$	−26.4375	−	26.4375i	−1.32686	−	1.32686i	−0.908095	−	0.418764i	$-0.862463\pi$
$397$	−26.4375	−	26.4375i	−1.32686	−	1.32686i	−0.418764	−	0.908095i	$-0.637537\pi$
$398$		0			0
$399$	−6.01174			−0.300963
$400$		0			0
$401$	4.97625			0.248502			0.124251	−	0.992251i	$-0.460347\pi$
$401$	4.97625			0.248502			0.124251	+	0.992251i	$0.460347\pi$
$402$		0			0
$403$	4.62815	+	4.62815i	0.230545	+	0.230545i
$404$		0			0
$405$	11.7864	−	11.7864i	0.585672	−	0.585672i
$406$		0			0
$407$			3.04331i			0.150851i
$408$		0			0
$409$		−	4.06359i		−	0.200932i	−0.994941	−	0.100466i	$-0.967967\pi$
$409$		−	4.06359i		−	0.200932i	0.994941	−	0.100466i	$-0.0320333\pi$
$410$		0			0
$411$	−46.5544	+	46.5544i	−2.29636	+	2.29636i
$412$		0			0
$413$	1.13843	+	1.13843i	0.0560184	+	0.0560184i
$414$		0			0
$415$	−39.0674			−1.91774
$416$		0			0
$417$	27.3203			1.33788
$418$		0			0
$419$	−0.552238	−	0.552238i	−0.0269786	−	0.0269786i	0.693489	−	0.720467i	$-0.256073\pi$
$419$	−0.552238	−	0.552238i	−0.0269786	−	0.0269786i	−0.720467	+	0.693489i	$0.756073\pi$
$420$		0			0
$421$	3.77763	−	3.77763i	0.184110	−	0.184110i	−0.609034	−	0.793144i	$-0.708443\pi$
$421$	3.77763	−	3.77763i	0.184110	−	0.184110i	0.793144	+	0.609034i	$0.208443\pi$
$422$		0			0
$423$			19.5920i			0.952593i
$424$		0			0
$425$			14.9079i			0.723140i
$426$		0			0
$427$	3.21881	−	3.21881i	0.155769	−	0.155769i
$428$		0			0
$429$	−4.25612	−	4.25612i	−0.205487	−	0.205487i
$430$		0			0
$431$	1.18186			0.0569283			0.0284641	−	0.999595i	$-0.490938\pi$
$431$	1.18186			0.0569283			0.0284641	+	0.999595i	$0.490938\pi$
$432$		0			0
$433$	−15.2584			−0.733273			−0.366637	−	0.930364i	$-0.619491\pi$
$433$	−15.2584			−0.733273			−0.366637	+	0.930364i	$0.619491\pi$
$434$		0			0
$435$	45.9715	+	45.9715i	2.20416	+	2.20416i
$436$		0			0
$437$	6.97759	−	6.97759i	0.333783	−	0.333783i
$438$		0			0
$439$		−	4.34502i		−	0.207376i	−0.994610	−	0.103688i	$-0.966936\pi$
$439$		−	4.34502i		−	0.207376i	0.994610	−	0.103688i	$-0.0330644\pi$
$440$		0			0
$441$		−	5.44602i		−	0.259334i
$442$		0			0
$443$	4.31392	−	4.31392i	0.204961	−	0.204961i	−0.597161	−	0.802121i	$-0.703705\pi$
$443$	4.31392	−	4.31392i	0.204961	−	0.204961i	0.802121	+	0.597161i	$0.203705\pi$
$444$		0			0
$445$	23.0733	+	23.0733i	1.09378	+	1.09378i
$446$		0			0
$447$	−31.9359			−1.51052
$448$		0			0
$449$	3.72499			0.175793			0.0878967	−	0.996130i	$-0.471985\pi$
$449$	3.72499			0.175793			0.0878967	+	0.996130i	$0.471985\pi$
$450$		0			0
$451$	−6.85604	−	6.85604i	−0.322838	−	0.322838i
$452$		0			0
$453$	11.2373	−	11.2373i	0.527976	−	0.527976i
$454$		0			0
$455$			6.14310i			0.287993i
$456$		0			0
$457$		−	10.7451i		−	0.502636i	−0.967905	−	0.251318i	$-0.919136\pi$
$457$		−	10.7451i		−	0.502636i	0.967905	−	0.251318i	$-0.0808640\pi$
$458$		0			0
$459$	7.58434	−	7.58434i	0.354007	−	0.354007i
$460$		0			0
$461$	−7.88785	−	7.88785i	−0.367374	−	0.367374i	0.499145	−	0.866519i	$-0.333648\pi$
$461$	−7.88785	−	7.88785i	−0.367374	−	0.367374i	−0.866519	+	0.499145i	$0.833648\pi$
$462$		0			0
$463$	27.3485			1.27099			0.635496	−	0.772104i	$-0.280796\pi$
$463$	27.3485			1.27099			0.635496	+	0.772104i	$0.280796\pi$
$464$		0			0
$465$	−46.0758			−2.13671
$466$		0			0
$467$	−11.3915	−	11.3915i	−0.527135	−	0.527135i	0.392582	−	0.919717i	$-0.371582\pi$
$467$	−11.3915	−	11.3915i	−0.527135	−	0.527135i	−0.919717	+	0.392582i	$0.871582\pi$
$468$		0			0
$469$	1.52640	−	1.52640i	0.0704828	−	0.0704828i
$470$		0			0
$471$			23.0867i			1.06378i
$472$		0			0
$473$		−	10.4651i		−	0.481185i
$474$		0			0
$475$	−14.4520	+	14.4520i	−0.663105	+	0.663105i
$476$		0			0
$477$	3.67995	+	3.67995i	0.168493	+	0.168493i
$478$		0			0
$479$	11.3880			0.520330			0.260165	−	0.965564i	$-0.416223\pi$
$479$	11.3880			0.520330			0.260165	+	0.965564i	$0.416223\pi$
$480$		0			0
$481$	3.72655			0.169916
$482$		0			0
$483$	9.80296	+	9.80296i	0.446050	+	0.446050i
$484$		0			0
$485$	−44.2502	+	44.2502i	−2.00930	+	2.00930i
$486$		0			0
$487$			31.3531i			1.42075i	0.703826	+	0.710373i	$0.251474\pi$
$487$			31.3531i			1.42075i	−0.703826	+	0.710373i	$0.748526\pi$
$488$		0			0
$489$			25.9652i			1.17419i
$490$		0			0
$491$	−20.2775	+	20.2775i	−0.915112	+	0.915112i	−0.996669	−	0.0815572i	$-0.974011\pi$
$491$	−20.2775	+	20.2775i	−0.915112	+	0.915112i	0.0815572	+	0.996669i	$0.474011\pi$
$492$		0			0
$493$	6.18733	+	6.18733i	0.278663	+	0.278663i
$494$		0			0
$495$	27.3216			1.22802
$496$		0			0
$497$	13.8202			0.619921
$498$		0			0
$499$	18.5167	+	18.5167i	0.828921	+	0.828921i	0.987368	−	0.158446i	$-0.0506485\pi$
$499$	18.5167	+	18.5167i	0.828921	+	0.828921i	−0.158446	+	0.987368i	$0.550649\pi$
$500$		0			0
$501$	−24.2848	+	24.2848i	−1.08497	+	1.08497i
$502$		0			0
$503$			31.9854i			1.42616i	0.701082	+	0.713080i	$0.252701\pi$
$503$			31.9854i			1.42616i	−0.701082	+	0.713080i	$0.747299\pi$
$504$		0			0
$505$			63.0987i			2.80786i
$506$		0			0
$507$	21.5033	−	21.5033i	0.954996	−	0.954996i
$508$		0			0
$509$	−12.1644	−	12.1644i	−0.539176	−	0.539176i	0.384111	−	0.923287i	$-0.374508\pi$
$509$	−12.1644	−	12.1644i	−0.539176	−	0.539176i	−0.923287	+	0.384111i	$0.874508\pi$
$510$		0			0
$511$	−14.4749			−0.640331
$512$		0			0
$513$	14.7048			0.649234
$514$		0			0
$515$	−46.8817	−	46.8817i	−2.06586	−	2.06586i
$516$		0			0
$517$	−3.30830	+	3.30830i	−0.145499	+	0.145499i
$518$		0			0
$519$		−	23.1745i		−	1.01725i
$520$		0			0
$521$			34.4322i			1.50850i	0.656586	+	0.754251i	$0.272000\pi$
$521$			34.4322i			1.50850i	−0.656586	+	0.754251i	$0.728000\pi$
$522$		0			0
$523$	15.4031	−	15.4031i	0.673530	−	0.673530i	−0.284998	−	0.958528i	$-0.591993\pi$
$523$	15.4031	−	15.4031i	0.673530	−	0.673530i	0.958528	+	0.284998i	$0.0919929\pi$
$524$		0			0
$525$	−20.3040	−	20.3040i	−0.886138	−	0.886138i
$526$		0			0
$527$	−6.20137			−0.270136
$528$		0			0
$529$	0.244184			0.0106167
$530$		0			0
$531$	−6.19990	−	6.19990i	−0.269053	−	0.269053i
$532$		0			0
$533$	−8.39524	+	8.39524i	−0.363638	+	0.363638i
$534$		0			0
$535$		−	22.3747i		−	0.967341i
$536$		0			0
$537$		−	48.2011i		−	2.08003i
$538$		0			0
$539$	0.919616	−	0.919616i	0.0396106	−	0.0396106i
$540$		0			0
$541$	23.7164	+	23.7164i	1.01965	+	1.01965i	0.999803	+	0.0198437i	$0.00631686\pi$
$541$	23.7164	+	23.7164i	1.01965	+	1.01965i	0.0198437	+	0.999803i	$0.493683\pi$
$542$		0			0
$543$	17.2034			0.738267
$544$		0			0
$545$	−17.8581			−0.764956
$546$		0			0
$547$	−27.8819	−	27.8819i	−1.19214	−	1.19214i	−0.976464	−	0.215680i	$-0.930803\pi$
$547$	−27.8819	−	27.8819i	−1.19214	−	1.19214i	−0.215680	−	0.976464i	$-0.569197\pi$
$548$		0			0
$549$	−17.5297	+	17.5297i	−0.748150	+	0.748150i
$550$		0			0
$551$			11.9963i			0.511058i
$552$		0			0
$553$			1.77961i			0.0756769i
$554$		0			0
$555$	−18.5499	+	18.5499i	−0.787400	+	0.787400i
$556$		0			0
$557$	−0.275943	−	0.275943i	−0.0116921	−	0.0116921i	0.701237	−	0.712929i	$-0.252632\pi$
$557$	−0.275943	−	0.275943i	−0.0116921	−	0.0116921i	−0.712929	+	0.701237i	$0.752632\pi$
$558$		0			0
$559$	−12.8145			−0.541997
$560$		0			0
$561$	5.70288			0.240776
$562$		0			0
$563$	13.8911	+	13.8911i	0.585438	+	0.585438i	0.936393	−	0.350954i	$-0.114143\pi$
$563$	13.8911	+	13.8911i	0.585438	+	0.585438i	−0.350954	+	0.936393i	$0.614143\pi$
$564$		0			0
$565$	25.0179	−	25.0179i	1.05251	−	1.05251i
$566$		0			0
$567$			4.32107i			0.181468i
$568$		0			0
$569$			8.08076i			0.338763i	0.985551	+	0.169381i	$0.0541770\pi$
$569$			8.08076i			0.338763i	−0.985551	+	0.169381i	$0.945823\pi$
$570$		0			0
$571$	7.55816	−	7.55816i	0.316299	−	0.316299i	−0.531045	−	0.847344i	$-0.678200\pi$
$571$	7.55816	−	7.55816i	0.316299	−	0.316299i	0.847344	+	0.531045i	$0.178200\pi$
$572$		0			0
$573$	25.4154	+	25.4154i	1.06175	+	1.06175i
$574$		0			0
$575$	47.1320			1.96554
$576$		0			0
$577$	1.95969			0.0815831			0.0407915	−	0.999168i	$-0.487012\pi$
$577$	1.95969			0.0815831			0.0407915	+	0.999168i	$0.487012\pi$
$578$		0			0
$579$	48.6699	+	48.6699i	2.02265	+	2.02265i
$580$		0			0
$581$	7.16133	−	7.16133i	0.297102	−	0.297102i
$582$		0			0
$583$			1.24279i			0.0514713i
$584$		0			0
$585$		−	33.4554i		−	1.38321i
$586$		0			0
$587$	−24.6131	+	24.6131i	−1.01589	+	1.01589i	−0.0160192	+	0.999872i	$0.505099\pi$
$587$	−24.6131	+	24.6131i	−1.01589	+	1.01589i	−0.999872	+	0.0160192i	$0.994901\pi$
$588$		0			0
$589$	−6.01174	−	6.01174i	−0.247709	−	0.247709i
$590$		0			0
$591$	46.9341			1.93061
$592$		0			0
$593$	16.5483			0.679558			0.339779	−	0.940505i	$-0.389648\pi$
$593$	16.5483			0.679558			0.339779	+	0.940505i	$0.389648\pi$
$594$		0			0
$595$	−4.11564	−	4.11564i	−0.168725	−	0.168725i
$596$		0			0
$597$	11.2960	−	11.2960i	0.462313	−	0.462313i
$598$		0			0
$599$		−	10.2649i		−	0.419412i	−0.977764	−	0.209706i	$-0.932749\pi$
$599$		−	10.2649i		−	0.419412i	0.977764	−	0.209706i	$-0.0672507\pi$
$600$		0			0
$601$		−	35.6586i		−	1.45455i	−0.686348	−	0.727273i	$-0.740787\pi$
$601$		−	35.6586i		−	1.45455i	0.686348	−	0.727273i	$-0.259213\pi$
$602$		0			0
$603$	−8.31283	+	8.31283i	−0.338524	+	0.338524i
$604$		0			0
$605$	−25.3908	−	25.3908i	−1.03228	−	1.03228i
$606$		0			0
$607$	23.1111			0.938052			0.469026	−	0.883184i	$-0.344605\pi$
$607$	23.1111			0.938052			0.469026	+	0.883184i	$0.344605\pi$
$608$		0			0
$609$	−16.8538			−0.682950
$610$		0			0
$611$	4.05103	+	4.05103i	0.163887	+	0.163887i
$612$		0			0
$613$	26.9200	−	26.9200i	1.08729	−	1.08729i	0.0914813	−	0.995807i	$-0.470840\pi$
$613$	26.9200	−	26.9200i	1.08729	−	1.08729i	0.995807	−	0.0914813i	$-0.0291602\pi$
$614$		0			0
$615$		−	83.5793i		−	3.37024i
$616$		0			0
$617$		−	47.9337i		−	1.92974i	−0.262732	−	0.964869i	$-0.584623\pi$
$617$		−	47.9337i		−	1.92974i	0.262732	−	0.964869i	$-0.415377\pi$
$618$		0			0
$619$	−4.05053	+	4.05053i	−0.162805	+	0.162805i	−0.783808	−	0.621003i	$-0.786725\pi$
$619$	−4.05053	+	4.05053i	−0.162805	+	0.162805i	0.621003	+	0.783808i	$0.286725\pi$
$620$		0			0
$621$	−23.9782	−	23.9782i	−0.962213	−	0.962213i
$622$		0			0
$623$	−8.45899			−0.338902
$624$		0			0
$625$	−23.2188			−0.928752
$626$		0			0
$627$	5.52849	+	5.52849i	0.220787	+	0.220787i
$628$		0			0
$629$	−2.49664	+	2.49664i	−0.0995477	+	0.0995477i
$630$		0			0
$631$		−	2.35784i		−	0.0938640i	−0.998898	−	0.0469320i	$-0.985056\pi$
$631$		−	2.35784i		−	0.0938640i	0.998898	−	0.0469320i	$-0.0149444\pi$
$632$		0			0
$633$		−	3.73136i		−	0.148308i
$634$		0			0
$635$	35.4014	−	35.4014i	1.40486	−	1.40486i
$636$		0			0
$637$	−1.12607	−	1.12607i	−0.0446166	−	0.0446166i
$638$		0			0
$639$	−75.2652			−2.97744
$640$		0			0
$641$	−49.8415			−1.96862			−0.984311	−	0.176440i	$-0.943542\pi$
$641$	−49.8415			−1.96862			−0.984311	+	0.176440i	$0.943542\pi$
$642$		0			0
$643$	6.07975	+	6.07975i	0.239762	+	0.239762i	0.816751	−	0.576990i	$-0.195773\pi$
$643$	6.07975	+	6.07975i	0.239762	+	0.239762i	−0.576990	+	0.816751i	$0.695773\pi$
$644$		0			0
$645$	63.7879	−	63.7879i	2.51165	−	2.51165i
$646$		0			0
$647$			0.463264i			0.0182128i	0.999959	+	0.00910640i	$0.00289870\pi$
$647$			0.463264i			0.0182128i	−0.999959	+	0.00910640i	$0.997101\pi$
$648$		0			0
$649$		−	2.09383i		−	0.0821901i
$650$		0			0
$651$	8.44602	−	8.44602i	0.331026	−	0.331026i
$652$		0			0
$653$	−6.63668	−	6.63668i	−0.259713	−	0.259713i	0.565224	−	0.824937i	$-0.308790\pi$
$653$	−6.63668	−	6.63668i	−0.259713	−	0.259713i	−0.824937	+	0.565224i	$0.808790\pi$
$654$		0			0
$655$	−37.2034			−1.45366
$656$		0			0
$657$	78.8305			3.07547
$658$		0			0
$659$	4.62922	+	4.62922i	0.180329	+	0.180329i	0.791499	−	0.611170i	$-0.209301\pi$
$659$	4.62922	+	4.62922i	0.180329	+	0.180329i	−0.611170	+	0.791499i	$0.709301\pi$
$660$		0			0
$661$	2.25711	−	2.25711i	0.0877916	−	0.0877916i	−0.661847	−	0.749639i	$-0.730227\pi$
$661$	2.25711	−	2.25711i	0.0877916	−	0.0877916i	0.749639	+	0.661847i	$0.230227\pi$
$662$		0			0
$663$		−	6.98320i		−	0.271205i
$664$		0			0
$665$		−	7.97958i		−	0.309435i
$666$		0			0
$667$	19.5615	−	19.5615i	0.757425	−	0.757425i
$668$		0			0
$669$	−6.58253	−	6.58253i	−0.254495	−	0.254495i
$670$		0			0
$671$	−5.92014			−0.228544
$672$		0			0
$673$	6.82222			0.262977			0.131489	−	0.991318i	$-0.458024\pi$
$673$	6.82222			0.262977			0.131489	+	0.991318i	$0.458024\pi$
$674$		0			0
$675$	49.6639	+	49.6639i	1.91157	+	1.91157i
$676$		0			0
$677$	−4.77844	+	4.77844i	−0.183650	+	0.183650i	−0.792944	−	0.609294i	$-0.791453\pi$
$677$	−4.77844	+	4.77844i	−0.183650	+	0.183650i	0.609294	+	0.792944i	$0.291453\pi$
$678$		0			0
$679$		−	16.2227i		−	0.622571i
$680$		0			0
$681$			56.6895i			2.17235i
$682$		0			0
$683$	29.2736	−	29.2736i	1.12012	−	1.12012i	0.128400	−	0.991723i	$-0.459016\pi$
$683$	29.2736	−	29.2736i	1.12012	−	1.12012i	0.991723	−	0.128400i	$-0.0409840\pi$
$684$		0			0
$685$	−61.7932	−	61.7932i	−2.36100	−	2.36100i
$686$		0			0
$687$	−28.8594			−1.10106
$688$		0			0
$689$	1.52181			0.0579762
$690$		0			0
$691$	4.65064	+	4.65064i	0.176919	+	0.176919i	0.790011	−	0.613092i	$-0.210075\pi$
$691$	4.65064	+	4.65064i	0.176919	+	0.176919i	−0.613092	+	0.790011i	$0.710075\pi$
$692$		0			0
$693$	−5.00824	+	5.00824i	−0.190247	+	0.190247i
$694$		0			0
$695$			36.2631i			1.37554i
$696$		0			0
$697$		−	11.2490i		−	0.426086i
$698$		0			0
$699$	6.03875	−	6.03875i	0.228407	−	0.228407i
$700$		0			0
$701$	4.01206	+	4.01206i	0.151533	+	0.151533i	0.778802	−	0.627269i	$-0.215827\pi$
$701$	4.01206	+	4.01206i	0.151533	+	0.151533i	−0.627269	+	0.778802i	$0.715827\pi$
$702$		0			0
$703$	−4.84060			−0.182567
$704$		0			0
$705$	−40.3302			−1.51892
$706$		0			0
$707$	−11.5664	−	11.5664i	−0.435001	−	0.435001i
$708$		0			0
$709$	−36.0117	+	36.0117i	−1.35245	+	1.35245i	−0.469533	+	0.882915i	$0.655578\pi$
$709$	−36.0117	+	36.0117i	−1.35245	+	1.35245i	−0.882915	+	0.469533i	$0.844422\pi$
$710$		0			0
$711$		−	9.69181i		−	0.363471i
$712$		0			0
$713$			19.6059i			0.734248i
$714$		0			0
$715$	5.64929	−	5.64929i	0.211271	−	0.211271i
$716$		0			0
$717$	33.3133	+	33.3133i	1.24411	+	1.24411i
$718$		0			0
$719$	7.62249			0.284271			0.142135	−	0.989847i	$-0.454603\pi$
$719$	7.62249			0.284271			0.142135	+	0.989847i	$0.454603\pi$
$720$		0			0
$721$	17.1875			0.640096
$722$		0			0
$723$	−29.0095	−	29.0095i	−1.07888	−	1.07888i
$724$		0			0
$725$	−40.5160	+	40.5160i	−1.50473	+	1.50473i
$726$		0			0
$727$			25.4856i			0.945207i	0.881275	+	0.472604i	$0.156686\pi$
$727$			25.4856i			0.945207i	−0.881275	+	0.472604i	$0.843314\pi$
$728$		0			0
$729$			38.4448i			1.42388i
$730$		0			0
$731$	8.58525	−	8.58525i	0.317537	−	0.317537i
$732$		0			0
$733$	14.9748	+	14.9748i	0.553106	+	0.553106i	0.927336	−	0.374230i	$-0.122093\pi$
$733$	14.9748	+	14.9748i	0.553106	+	0.553106i	−0.374230	+	0.927336i	$0.622093\pi$
$734$		0			0
$735$	11.2107			0.413512
$736$		0			0
$737$	−2.80741			−0.103412
$738$		0			0
$739$	12.3417	+	12.3417i	0.453996	+	0.453996i	0.896679	−	0.442682i	$-0.145973\pi$
$739$	12.3417	+	12.3417i	0.453996	+	0.453996i	−0.442682	+	0.896679i	$0.645973\pi$
$740$		0			0
$741$	6.76966	−	6.76966i	0.248690	−	0.248690i
$742$		0			0
$743$		−	10.6724i		−	0.391531i	−0.980651	−	0.195766i	$-0.937281\pi$
$743$		−	10.6724i		−	0.391531i	0.980651	−	0.195766i	$-0.0627192\pi$
$744$		0			0
$745$		−	42.3896i		−	1.55303i
$746$		0			0
$747$	−39.0007	+	39.0007i	−1.42696	+	1.42696i
$748$		0			0
$749$	4.10143	+	4.10143i	0.149863	+	0.149863i
$750$		0			0
$751$	−2.82952			−0.103251			−0.0516254	−	0.998667i	$-0.516440\pi$
$751$	−2.82952			−0.103251			−0.0516254	+	0.998667i	$0.516440\pi$
$752$		0			0
$753$	58.3485			2.12634
$754$		0			0
$755$	14.9157	+	14.9157i	0.542837	+	0.542837i
$756$		0			0
$757$	−15.6590	+	15.6590i	−0.569136	+	0.569136i	−0.931886	−	0.362750i	$-0.881838\pi$
$757$	−15.6590	+	15.6590i	−0.569136	+	0.569136i	0.362750	+	0.931886i	$0.381838\pi$
$758$		0			0
$759$		−	18.0299i		−	0.654444i
$760$		0			0
$761$		−	4.79367i		−	0.173770i	−0.996218	−	0.0868852i	$-0.972309\pi$
$761$		−	4.79367i		−	0.173770i	0.996218	−	0.0868852i	$-0.0276913\pi$
$762$		0			0
$763$	3.27351	−	3.27351i	0.118509	−	0.118509i
$764$		0			0
$765$	22.4139	+	22.4139i	0.810375	+	0.810375i
$766$		0			0
$767$	−2.56390			−0.0925772
$768$		0			0
$769$	13.5489			0.488585			0.244293	−	0.969702i	$-0.421444\pi$
$769$	13.5489			0.488585			0.244293	+	0.969702i	$0.421444\pi$
$770$		0			0
$771$	−6.65159	−	6.65159i	−0.239551	−	0.239551i
$772$		0			0
$773$	−18.7803	+	18.7803i	−0.675480	+	0.675480i	−0.958974	−	0.283494i	$-0.908506\pi$
$773$	−18.7803	+	18.7803i	−0.675480	+	0.675480i	0.283494	+	0.958974i	$0.408506\pi$
$774$		0			0
$775$		−	40.6080i		−	1.45868i
$776$		0			0
$777$		−	6.80066i		−	0.243972i
$778$		0			0
$779$	10.9050	−	10.9050i	0.390712	−	0.390712i
$780$		0			0
$781$	−12.7093	−	12.7093i	−0.454774	−	0.454774i
$782$		0			0
$783$	41.2247			1.47325
$784$		0			0
$785$	−30.6438			−1.09372
$786$		0			0
$787$	−24.4838	−	24.4838i	−0.872752	−	0.872752i	0.120020	−	0.992772i	$-0.461704\pi$
$787$	−24.4838	−	24.4838i	−0.872752	−	0.872752i	−0.992772	+	0.120020i	$0.961704\pi$
$788$		0			0
$789$	49.3530	−	49.3530i	1.75701	−	1.75701i
$790$		0			0
$791$			9.17193i			0.326116i
$792$		0			0
$793$			7.24923i			0.257428i
$794$		0			0
$795$	−7.57521	+	7.57521i	−0.268665	+	0.268665i
$796$		0			0
$797$	17.6690	+	17.6690i	0.625870	+	0.625870i	0.947026	−	0.321157i	$-0.104072\pi$
$797$	17.6690	+	17.6690i	0.625870	+	0.625870i	−0.321157	+	0.947026i	$0.604072\pi$
$798$		0			0
$799$	−5.42807			−0.192031
$800$		0			0
$801$	46.0678			1.62773
$802$		0			0
$803$	13.3113	+	13.3113i	0.469746	+	0.469746i
$804$		0			0
$805$	−13.0118	+	13.0118i	−0.458605	+	0.458605i
$806$		0			0
$807$			0.359641i			0.0126600i
$808$		0			0
$809$			2.99378i			0.105256i	0.998614	+	0.0526278i	$0.0167597\pi$
$809$			2.99378i			0.105256i	−0.998614	+	0.0526278i	$0.983240\pi$
$810$		0			0
$811$	2.28628	−	2.28628i	0.0802820	−	0.0802820i	−0.665825	−	0.746108i	$-0.731920\pi$
$811$	2.28628	−	2.28628i	0.0802820	−	0.0802820i	0.746108	+	0.665825i	$0.231920\pi$
$812$		0			0
$813$	−20.7839	−	20.7839i	−0.728923	−	0.728923i
$814$		0			0
$815$	−34.4644			−1.20724
$816$		0			0
$817$	16.6454			0.582351
$818$		0			0
$819$	6.13262	+	6.13262i	0.214291	+	0.214291i
$820$		0			0
$821$	28.6342	−	28.6342i	0.999339	−	0.999339i	−0.000660747	−	1.00000i	$-0.500210\pi$
$821$	28.6342	−	28.6342i	0.999339	−	0.999339i	1.00000		0.000660747i	$0.000210322\pi$
$822$		0			0
$823$		−	41.0492i		−	1.43088i	−0.698672	−	0.715442i	$-0.746225\pi$
$823$		−	41.0492i		−	1.43088i	0.698672	−	0.715442i	$-0.253775\pi$
$824$		0			0
$825$			37.3437i			1.30014i
$826$		0			0
$827$	20.3987	−	20.3987i	0.709331	−	0.709331i	−0.257064	−	0.966394i	$-0.582755\pi$
$827$	20.3987	−	20.3987i	0.709331	−	0.709331i	0.966394	+	0.257064i	$0.0827550\pi$
$828$		0			0
$829$	18.4892	+	18.4892i	0.642155	+	0.642155i	0.951085	−	0.308930i	$-0.0999708\pi$
$829$	18.4892	+	18.4892i	0.642155	+	0.642155i	−0.308930	+	0.951085i	$0.599971\pi$
$830$		0			0
$831$	45.2428			1.56945
$832$		0			0
$833$	1.50885			0.0522786
$834$		0			0
$835$	−32.2341	−	32.2341i	−1.11551	−	1.11551i
$836$		0			0
$837$	−20.6591	+	20.6591i	−0.714084	+	0.714084i
$838$		0			0
$839$			41.9862i			1.44953i	0.688999	+	0.724763i	$0.258051\pi$
$839$			41.9862i			1.44953i	−0.688999	+	0.724763i	$0.741949\pi$
$840$		0			0
$841$			4.63123i			0.159698i
$842$		0			0
$843$	−8.67205	+	8.67205i	−0.298681	+	0.298681i
$844$		0			0
$845$	28.5421	+	28.5421i	0.981876	+	0.981876i
$846$		0			0
$847$	9.30861			0.319848
$848$		0			0
$849$	68.1577			2.33916
$850$		0			0
$851$	7.89326	+	7.89326i	0.270577	+	0.270577i
$852$		0			0
$853$	−10.9845	+	10.9845i	−0.376104	+	0.376104i	−0.869694	−	0.493591i	$-0.835684\pi$
$853$	−10.9845	+	10.9845i	−0.376104	+	0.376104i	0.493591	+	0.869694i	$0.335684\pi$
$854$		0			0
$855$			43.4570i			1.48620i
$856$		0			0
$857$		−	47.3215i		−	1.61647i	−0.588858	−	0.808237i	$-0.700422\pi$
$857$		−	47.3215i		−	1.61647i	0.588858	−	0.808237i	$-0.299578\pi$
$858$		0			0
$859$	−5.11128	+	5.11128i	−0.174395	+	0.174395i	−0.788907	−	0.614512i	$-0.789353\pi$
$859$	−5.11128	+	5.11128i	−0.174395	+	0.174395i	0.614512	+	0.788907i	$0.289353\pi$
$860$		0			0
$861$	15.3207	+	15.3207i	0.522127	+	0.522127i
$862$		0			0
$863$	10.1105			0.344167			0.172084	−	0.985082i	$-0.444950\pi$
$863$	10.1105			0.344167			0.172084	+	0.985082i	$0.444950\pi$
$864$		0			0
$865$	30.7603			1.04588
$866$		0			0
$867$	−30.2565	−	30.2565i	−1.02756	−	1.02756i
$868$		0			0
$869$	1.63656	−	1.63656i	0.0555165	−	0.0555165i
$870$		0			0
$871$			3.43769i			0.116482i
$872$		0			0
$873$			88.3493i			2.99017i
$874$		0			0
$875$	13.3118	−	13.3118i	0.450021	−	0.450021i
$876$		0			0
$877$	38.0640	+	38.0640i	1.28533	+	1.28533i	0.937592	+	0.347738i	$0.113050\pi$
$877$	38.0640	+	38.0640i	1.28533	+	1.28533i	0.347738	+	0.937592i	$0.386950\pi$
$878$		0			0
$879$	55.5844			1.87482
$880$		0			0
$881$	−21.5769			−0.726946			−0.363473	−	0.931605i	$-0.618409\pi$
$881$	−21.5769			−0.726946			−0.363473	+	0.931605i	$0.618409\pi$
$882$		0			0
$883$	−21.5700	−	21.5700i	−0.725888	−	0.725888i	0.243910	−	0.969798i	$-0.421570\pi$
$883$	−21.5700	−	21.5700i	−0.725888	−	0.725888i	−0.969798	+	0.243910i	$0.921570\pi$
$884$		0			0
$885$	12.7625	−	12.7625i	0.429008	−	0.429008i
$886$		0			0
$887$		−	33.7110i		−	1.13191i	−0.824437	−	0.565953i	$-0.808508\pi$
$887$		−	33.7110i		−	1.13191i	0.824437	−	0.565953i	$-0.191492\pi$
$888$		0			0
$889$			12.9787i			0.435291i
$890$		0			0
$891$	3.97372	−	3.97372i	0.133125	−	0.133125i
$892$		0			0
$893$	−5.26208	−	5.26208i	−0.176089	−	0.176089i
$894$		0			0
$895$	63.9788			2.13858
$896$		0			0
$897$	−22.0777			−0.737153
$898$		0			0
$899$	−16.8538	−	16.8538i	−0.562105	−	0.562105i
$900$		0			0
$901$	−1.01955	+	1.01955i	−0.0339662	+	0.0339662i
$902$		0			0
$903$			23.3855i			0.778222i
$904$		0			0
$905$			22.8346i			0.759047i
$906$		0			0
$907$	−0.923962	+	0.923962i	−0.0306797	+	0.0306797i	−0.722280	−	0.691601i	$-0.756906\pi$
$907$	−0.923962	+	0.923962i	−0.0306797	+	0.0306797i	0.691601	+	0.722280i	$0.256906\pi$
$908$		0			0
$909$	62.9911	+	62.9911i	2.08928	+	2.08928i
$910$		0			0
$911$	−29.9873			−0.993522			−0.496761	−	0.867887i	$-0.665477\pi$
$911$	−29.9873			−0.993522			−0.496761	+	0.867887i	$0.665477\pi$
$912$		0			0
$913$	−13.1713			−0.435908
$914$		0			0
$915$	−36.0851	−	36.0851i	−1.19294	−	1.19294i
$916$		0			0
$917$	6.81965	−	6.81965i	0.225205	−	0.225205i
$918$		0			0
$919$		−	13.0725i		−	0.431220i	−0.976480	−	0.215610i	$-0.930826\pi$
$919$		−	13.0725i		−	0.431220i	0.976480	−	0.215610i	$-0.0691741\pi$
$920$		0			0
$921$			36.7182i			1.20991i
$922$		0			0
$923$	−15.5626	+	15.5626i	−0.512248	+	0.512248i
$924$		0			0
$925$	−16.3486	−	16.3486i	−0.537538	−	0.537538i
$926$		0			0
$927$	−93.6035			−3.07434
$928$		0			0
$929$	−20.7057			−0.679333			−0.339667	−	0.940546i	$-0.610314\pi$
$929$	−20.7057			−0.679333			−0.339667	+	0.940546i	$0.610314\pi$
$930$		0			0
$931$	1.46271	+	1.46271i	0.0479385	+	0.0479385i
$932$		0			0
$933$	40.6348	−	40.6348i	1.33033	−	1.33033i
$934$		0			0
$935$			7.56961i			0.247553i
$936$		0			0
$937$		−	5.93799i		−	0.193986i	−0.995285	−	0.0969929i	$-0.969078\pi$
$937$		−	5.93799i		−	0.193986i	0.995285	−	0.0969929i	$-0.0309224\pi$
$938$		0			0
$939$	17.9348	−	17.9348i	0.585281	−	0.585281i
$940$		0			0
$941$	13.9955	+	13.9955i	0.456241	+	0.456241i	0.897419	−	0.441178i	$-0.145439\pi$
$941$	13.9955	+	13.9955i	0.456241	+	0.456241i	−0.441178	+	0.897419i	$0.645439\pi$
$942$		0			0
$943$	−35.5642			−1.15813
$944$		0			0
$945$	−27.4215			−0.892023
$946$		0			0
$947$	30.2690	+	30.2690i	0.983611	+	0.983611i	0.999868	−	0.0162570i	$-0.00517500\pi$
$947$	30.2690	+	30.2690i	0.983611	+	0.983611i	−0.0162570	+	0.999868i	$0.505175\pi$
$948$		0			0
$949$	16.2998	−	16.2998i	0.529113	−	0.529113i
$950$		0			0
$951$		−	78.1710i		−	2.53487i
$952$		0			0
$953$			0.689500i			0.0223351i	0.999938	+	0.0111675i	$0.00355481\pi$
$953$			0.689500i			0.0223351i	−0.999938	+	0.0111675i	$0.996445\pi$
$954$		0			0
$955$	−33.7348	+	33.7348i	−1.09163	+	1.09163i
$956$		0			0
$957$	15.4990	+	15.4990i	0.501012	+	0.501012i
$958$		0			0
$959$	22.6543			0.731544
$960$		0			0
$961$	−14.1080			−0.455096
$962$		0			0
$963$	−22.3365	−	22.3365i	−0.719783	−	0.719783i
$964$		0			0
$965$	−64.6012	+	64.6012i	−2.07959	+	2.07959i
$966$		0			0
$967$		−	14.1022i		−	0.453497i	−0.973953	−	0.226749i	$-0.927190\pi$
$967$		−	14.1022i		−	0.453497i	0.973953	−	0.226749i	$-0.0728096\pi$
$968$		0			0
$969$			9.07083i			0.291397i
$970$		0			0
$971$	0.255230	−	0.255230i	0.00819071	−	0.00819071i	−0.703000	−	0.711190i	$-0.748156\pi$
$971$	0.255230	−	0.255230i	0.00819071	−	0.00819071i	0.711190	+	0.703000i	$0.248156\pi$
$972$		0			0
$973$	−6.64728	−	6.64728i	−0.213102	−	0.213102i
$974$		0			0
$975$	45.7275			1.46445
$976$		0			0
$977$	−9.83910			−0.314781			−0.157390	−	0.987536i	$-0.550308\pi$
$977$	−9.83910			−0.314781			−0.157390	+	0.987536i	$0.550308\pi$
$978$		0			0
$979$	7.77902	+	7.77902i	0.248618	+	0.248618i
$980$		0			0
$981$	−17.8276	+	17.8276i	−0.569191	+	0.569191i
$982$		0			0
$983$			26.6489i			0.849968i	0.905201	+	0.424984i	$0.139720\pi$
$983$			26.6489i			0.849968i	−0.905201	+	0.424984i	$0.860280\pi$
$984$		0			0
$985$			62.2971i			1.98495i
$986$		0			0
$987$	7.39281	−	7.39281i	0.235316	−	0.235316i
$988$		0			0
$989$	−27.1427	−	27.1427i	−0.863086	−	0.863086i
$990$		0			0
$991$	16.8287			0.534583			0.267291	−	0.963616i	$-0.413871\pi$
$991$	16.8287			0.534583			0.267291	+	0.963616i	$0.413871\pi$
$992$		0			0
$993$	−91.7875			−2.91279
$994$		0			0
$995$	14.9935	+	14.9935i	0.475326	+	0.475326i
$996$		0			0
$997$	25.7816	−	25.7816i	0.816511	−	0.816511i	−0.169089	−	0.985601i	$-0.554083\pi$
$997$	25.7816	−	25.7816i	0.816511	−	0.816511i	0.985601	+	0.169089i	$0.0540827\pi$
$998$		0			0
$999$			16.6346i			0.526294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.m.g.673.6		12
4.3	odd	2		896.2.m.h.673.1		12
8.3	odd	2		448.2.m.d.337.6		12
8.5	even	2		112.2.m.d.29.3	✓	12
16.3	odd	4		448.2.m.d.113.6		12
16.5	even	4	inner	896.2.m.g.225.6		12
16.11	odd	4		896.2.m.h.225.1		12
16.13	even	4		112.2.m.d.85.3	yes	12
32.5	even	8		7168.2.a.bj.1.2		12
32.11	odd	8		7168.2.a.bi.1.2		12
32.21	even	8		7168.2.a.bj.1.11		12
32.27	odd	8		7168.2.a.bi.1.11		12
56.5	odd	6		784.2.x.m.557.5		24
56.13	odd	2		784.2.m.h.589.3		12
56.37	even	6		784.2.x.l.557.5		24
56.45	odd	6		784.2.x.m.765.2		24
56.53	even	6		784.2.x.l.765.2		24
112.13	odd	4		784.2.m.h.197.3		12
112.45	odd	12		784.2.x.m.373.5		24
112.61	odd	12		784.2.x.m.165.2		24
112.93	even	12		784.2.x.l.165.2		24
112.109	even	12		784.2.x.l.373.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.3	✓	12	8.5	even	2
112.2.m.d.85.3	yes	12	16.13	even	4
448.2.m.d.113.6		12	16.3	odd	4
448.2.m.d.337.6		12	8.3	odd	2
784.2.m.h.197.3		12	112.13	odd	4
784.2.m.h.589.3		12	56.13	odd	2
784.2.x.l.165.2		24	112.93	even	12
784.2.x.l.373.5		24	112.109	even	12
784.2.x.l.557.5		24	56.37	even	6
784.2.x.l.765.2		24	56.53	even	6
784.2.x.m.165.2		24	112.61	odd	12
784.2.x.m.373.5		24	112.45	odd	12
784.2.x.m.557.5		24	56.5	odd	6
784.2.x.m.765.2		24	56.45	odd	6
896.2.m.g.225.6		12	16.5	even	4	inner
896.2.m.g.673.6		12	1.1	even	1	trivial
896.2.m.h.225.1		12	16.11	odd	4
896.2.m.h.673.1		12	4.3	odd	2
7168.2.a.bi.1.2		12	32.11	odd	8
7168.2.a.bi.1.11		12	32.27	odd	8
7168.2.a.bj.1.2		12	32.5	even	8
7168.2.a.bj.1.11		12	32.21	even	8

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05500 + 2.05500i) q^{3} +(-2.72766 + 2.72766i) q^{5} -1.00000i q^{7} +5.44602i q^{9} +O(q^{10})\)	\(q+(2.05500 + 2.05500i) q^{3} +(-2.72766 + 2.72766i) q^{5} -1.00000i q^{7} +5.44602i q^{9} +(-0.919616 + 0.919616i) q^{11} +(1.12607 + 1.12607i) q^{13} -11.2107 q^{15} -1.50885 q^{17} +(-1.46271 - 1.46271i) q^{19} +(2.05500 - 2.05500i) q^{21} +4.77031i q^{23} -9.88030i q^{25} +(-5.02656 + 5.02656i) q^{27} +(-4.10069 - 4.10069i) q^{29} +4.10999 q^{31} -3.77961 q^{33} +(2.72766 + 2.72766i) q^{35} +(1.65467 - 1.65467i) q^{37} +4.62815i q^{39} +7.45533i q^{41} +(-5.68992 + 5.68992i) q^{43} +(-14.8549 - 14.8549i) q^{45} +3.59748 q^{47} -1.00000 q^{49} +(-3.10069 - 3.10069i) q^{51} +(0.675714 - 0.675714i) q^{53} -5.01680i q^{55} -6.01174i q^{57} +(-1.13843 + 1.13843i) q^{59} +(3.21881 + 3.21881i) q^{61} +5.44602 q^{63} -6.14310 q^{65} +(1.52640 + 1.52640i) q^{67} +(-9.80296 + 9.80296i) q^{69} +13.8202i q^{71} -14.4749i q^{73} +(20.3040 - 20.3040i) q^{75} +(0.919616 + 0.919616i) q^{77} -1.77961 q^{79} -4.32107 q^{81} +(7.16133 + 7.16133i) q^{83} +(4.11564 - 4.11564i) q^{85} -16.8538i q^{87} -8.45899i q^{89} +(1.12607 - 1.12607i) q^{91} +(8.44602 + 8.44602i) q^{93} +7.97958 q^{95} +16.2227 q^{97} +(-5.00824 - 5.00824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 12 * q - 4 * q^3 - 4 * q^5	\( 12 q - 4 q^{3} - 4 q^{5} - 24 q^{15} - 8 q^{17} - 4 q^{21} - 4 q^{27} + 4 q^{29} - 8 q^{31} + 4 q^{35} + 20 q^{37} - 16 q^{43} - 40 q^{45} + 16 q^{47} - 12 q^{49} + 16 q^{51} - 4 q^{53} + 16 q^{59} + 20 q^{61} + 12 q^{63} + 32 q^{65} - 24 q^{67} + 4 q^{69} + 40 q^{75} + 24 q^{79} - 44 q^{81} + 20 q^{83} + 8 q^{85} + 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - 4 * q^5 - 24 * q^15 - 8 * q^17 - 4 * q^21 - 4 * q^27 + 4 * q^29 - 8 * q^31 + 4 * q^35 + 20 * q^37 - 16 * q^43 - 40 * q^45 + 16 * q^47 - 12 * q^49 + 16 * q^51 - 4 * q^53 + 16 * q^59 + 20 * q^61 + 12 * q^63 + 32 * q^65 - 24 * q^67 + 4 * q^69 + 40 * q^75 + 24 * q^79 - 44 * q^81 + 20 * q^83 + 8 * q^85 + 48 * q^93 + 48 * q^97 - 32 * q^99

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