LMFDB - Embedded newform 1088.2.m.i.353.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(225,1088)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1088, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1088.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.68772373992$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.8
Character	$\chi$	$=$	1088.353
Dual form			1088.2.m.i.225.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.514752 - 0.514752i) q^{3} +(1.38937 - 1.38937i) q^{5} +(-0.251879 + 0.251879i) q^{7} +2.47006i q^{9} +O(q^{10})$	\(q+(0.514752 - 0.514752i) q^{3} +(1.38937 - 1.38937i) q^{5} +(-0.251879 + 0.251879i) q^{7} +2.47006i q^{9} +(-2.30097 - 2.30097i) q^{11} +0.612098i q^{13} -1.43036i q^{15} +(4.09031 - 0.519042i) q^{17} +6.04990 q^{19} +0.259310i q^{21} +(4.27231 - 4.27231i) q^{23} +1.13929i q^{25} +(2.81572 + 2.81572i) q^{27} +(7.39969 - 7.39969i) q^{29} +(-6.55922 - 6.55922i) q^{31} -2.36886 q^{33} +0.699907i q^{35} +(2.81974 - 2.81974i) q^{37} +(0.315079 + 0.315079i) q^{39} +(-2.10978 + 2.10978i) q^{41} -3.01182 q^{43} +(3.43184 + 3.43184i) q^{45} -6.59564 q^{47} +6.87311i q^{49} +(1.83831 - 2.37267i) q^{51} +3.21352 q^{53} -6.39382 q^{55} +(3.11420 - 3.11420i) q^{57} -0.355861 q^{59} +(-1.74216 - 1.74216i) q^{61} +(-0.622156 - 0.622156i) q^{63} +(0.850433 + 0.850433i) q^{65} -5.91413i q^{67} -4.39836i q^{69} +(-3.03062 - 3.03062i) q^{71} +(-3.67364 - 3.67364i) q^{73} +(0.586450 + 0.586450i) q^{75} +1.15913 q^{77} +(-0.622156 + 0.622156i) q^{79} -4.51138 q^{81} +8.92184 q^{83} +(4.96182 - 6.40410i) q^{85} -7.61801i q^{87} +3.38978 q^{89} +(-0.154175 - 0.154175i) q^{91} -6.75274 q^{93} +(8.40557 - 8.40557i) q^{95} +(11.2113 + 11.2113i) q^{97} +(5.68354 - 5.68354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 4 q^{17} - 24 q^{19} + 16 q^{33} - 16 q^{41} + 32 q^{43} + 40 q^{51} - 48 q^{57} - 64 q^{59} - 16 q^{65} - 8 q^{73} + 32 q^{75} + 88 q^{81} - 144 q^{83} + 24 q^{89} + 48 q^{91} + 32 q^{97} + 40 q^{99}+O(q^{100}) $ 24 * q + 4 * q^17 - 24 * q^19 + 16 * q^33 - 16 * q^41 + 32 * q^43 + 40 * q^51 - 48 * q^57 - 64 * q^59 - 16 * q^65 - 8 * q^73 + 32 * q^75 + 88 * q^81 - 144 * q^83 + 24 * q^89 + 48 * q^91 + 32 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.514752	−	0.514752i	0.297192	−	0.297192i	−0.542721	−	0.839913i	$-0.682606\pi$
$3$	0.514752	−	0.514752i	0.297192	−	0.297192i	0.839913	+	0.542721i	$0.182606\pi$
$4$		0			0
$5$	1.38937	−	1.38937i	0.621346	−	0.621346i	−0.324529	−	0.945876i	$-0.605206\pi$
$5$	1.38937	−	1.38937i	0.621346	−	0.621346i	0.945876	+	0.324529i	$0.105206\pi$
$6$		0			0
$7$	−0.251879	+	0.251879i	−0.0952012	+	0.0952012i	−0.753103	−	0.657902i	$-0.771444\pi$
$7$	−0.251879	+	0.251879i	−0.0952012	+	0.0952012i	0.657902	+	0.753103i	$0.271444\pi$
$8$		0			0
$9$			2.47006i			0.823354i
$10$		0			0
$11$	−2.30097	−	2.30097i	−0.693769	−	0.693769i	0.269290	−	0.963059i	$-0.413211\pi$
$11$	−2.30097	−	2.30097i	−0.693769	−	0.693769i	−0.963059	+	0.269290i	$0.913211\pi$
$12$		0			0
$13$			0.612098i			0.169766i	0.996391	+	0.0848828i	$0.0270516\pi$
$13$			0.612098i			0.169766i	−0.996391	+	0.0848828i	$0.972948\pi$
$14$		0			0
$15$		−	1.43036i		−	0.369319i
$16$		0			0
$17$	4.09031	−	0.519042i	0.992045	−	0.125886i
$17$	4.09031	−	0.519042i	0.992045	−	0.125886i
$18$		0			0
$19$	6.04990			1.38794			0.693972	−	0.720002i	$-0.255859\pi$
$19$	6.04990			1.38794			0.693972	+	0.720002i	$0.255859\pi$
$20$		0			0
$21$			0.259310i			0.0565861i
$22$		0			0
$23$	4.27231	−	4.27231i	0.890838	−	0.890838i	−0.103764	−	0.994602i	$-0.533089\pi$
$23$	4.27231	−	4.27231i	0.890838	−	0.890838i	0.994602	+	0.103764i	$0.0330886\pi$
$24$		0			0
$25$			1.13929i			0.227857i
$26$		0			0
$27$	2.81572	+	2.81572i	0.541886	+	0.541886i
$28$		0			0
$29$	7.39969	−	7.39969i	1.37409	−	1.37409i	0.519802	−	0.854287i	$-0.326006\pi$
$29$	7.39969	−	7.39969i	1.37409	−	1.37409i	0.854287	−	0.519802i	$-0.173994\pi$
$30$		0			0
$31$	−6.55922	−	6.55922i	−1.17807	−	1.17807i	−0.980235	−	0.197836i	$-0.936609\pi$
$31$	−6.55922	−	6.55922i	−1.17807	−	1.17807i	−0.197836	−	0.980235i	$-0.563391\pi$
$32$		0			0
$33$	−2.36886			−0.412366
$34$		0			0
$35$			0.699907i			0.118306i
$36$		0			0
$37$	2.81974	−	2.81974i	0.463562	−	0.463562i	−0.436259	−	0.899821i	$-0.643697\pi$
$37$	2.81974	−	2.81974i	0.463562	−	0.463562i	0.899821	+	0.436259i	$0.143697\pi$
$38$		0			0
$39$	0.315079	+	0.315079i	0.0504530	+	0.0504530i
$40$		0			0
$41$	−2.10978	+	2.10978i	−0.329493	+	0.329493i	−0.852394	−	0.522901i	$-0.824850\pi$
$41$	−2.10978	+	2.10978i	−0.329493	+	0.329493i	0.522901	+	0.852394i	$0.324850\pi$
$42$		0			0
$43$	−3.01182			−0.459298			−0.229649	−	0.973273i	$-0.573758\pi$
$43$	−3.01182			−0.459298			−0.229649	+	0.973273i	$0.573758\pi$
$44$		0			0
$45$	3.43184	+	3.43184i	0.511588	+	0.511588i
$46$		0			0
$47$	−6.59564			−0.962072			−0.481036	−	0.876701i	$-0.659739\pi$
$47$	−6.59564			−0.962072			−0.481036	+	0.876701i	$0.659739\pi$
$48$		0			0
$49$			6.87311i			0.981873i
$50$		0			0
$51$	1.83831	−	2.37267i	0.257415	−	0.332240i
$52$		0			0
$53$	3.21352			0.441411			0.220705	−	0.975341i	$-0.429164\pi$
$53$	3.21352			0.441411			0.220705	+	0.975341i	$0.429164\pi$
$54$		0			0
$55$	−6.39382			−0.862142
$56$		0			0
$57$	3.11420	−	3.11420i	0.412486	−	0.412486i
$58$		0			0
$59$	−0.355861			−0.0463292			−0.0231646	−	0.999732i	$-0.507374\pi$
$59$	−0.355861			−0.0463292			−0.0231646	+	0.999732i	$0.507374\pi$
$60$		0			0
$61$	−1.74216	−	1.74216i	−0.223061	−	0.223061i	0.586725	−	0.809786i	$-0.300417\pi$
$61$	−1.74216	−	1.74216i	−0.223061	−	0.223061i	−0.809786	+	0.586725i	$0.800417\pi$
$62$		0			0
$63$	−0.622156	−	0.622156i	−0.0783843	−	0.0783843i
$64$		0			0
$65$	0.850433	+	0.850433i	0.105483	+	0.105483i
$66$		0			0
$67$		−	5.91413i		−	0.722526i	−0.932464	−	0.361263i	$-0.882346\pi$
$67$		−	5.91413i		−	0.722526i	0.932464	−	0.361263i	$-0.117654\pi$
$68$		0			0
$69$		−	4.39836i		−	0.529500i
$70$		0			0
$71$	−3.03062	−	3.03062i	−0.359669	−	0.359669i	0.504022	−	0.863691i	$-0.331853\pi$
$71$	−3.03062	−	3.03062i	−0.359669	−	0.359669i	−0.863691	+	0.504022i	$0.831853\pi$
$72$		0			0
$73$	−3.67364	−	3.67364i	−0.429967	−	0.429967i	0.458650	−	0.888617i	$-0.348333\pi$
$73$	−3.67364	−	3.67364i	−0.429967	−	0.429967i	−0.888617	+	0.458650i	$0.848333\pi$
$74$		0			0
$75$	0.586450	+	0.586450i	0.0677174	+	0.0677174i
$76$		0			0
$77$	1.15913			0.132095
$78$		0			0
$79$	−0.622156	+	0.622156i	−0.0699980	+	0.0699980i	−0.741239	−	0.671241i	$-0.765762\pi$
$79$	−0.622156	+	0.622156i	−0.0699980	+	0.0699980i	0.671241	+	0.741239i	$0.265762\pi$
$80$		0			0
$81$	−4.51138			−0.501265
$82$		0			0
$83$	8.92184			0.979299			0.489650	−	0.871919i	$-0.337125\pi$
$83$	8.92184			0.979299			0.489650	+	0.871919i	$0.337125\pi$
$84$		0			0
$85$	4.96182	−	6.40410i	0.538184	−	0.694622i
$86$		0			0
$87$		−	7.61801i		−	0.816737i
$88$		0			0
$89$	3.38978			0.359316			0.179658	−	0.983729i	$-0.442501\pi$
$89$	3.38978			0.359316			0.179658	+	0.983729i	$0.442501\pi$
$90$		0			0
$91$	−0.154175	−	0.154175i	−0.0161619	−	0.0161619i
$92$		0			0
$93$	−6.75274			−0.700227
$94$		0			0
$95$	8.40557	−	8.40557i	0.862394	−	0.862394i
$96$		0			0
$97$	11.2113	+	11.2113i	1.13833	+	1.13833i	0.988749	+	0.149585i	$0.0477939\pi$
$97$	11.2113	+	11.2113i	1.13833	+	1.13833i	0.149585	+	0.988749i	$0.452206\pi$
$98$		0			0
$99$	5.68354	−	5.68354i	0.571217	−	0.571217i
$100$		0			0
$101$			18.1902i			1.81000i	0.425416	+	0.904998i	$0.360128\pi$
$101$			18.1902i			1.81000i	−0.425416	+	0.904998i	$0.639872\pi$
$102$		0			0
$103$	−0.594039			−0.0585324			−0.0292662	−	0.999572i	$-0.509317\pi$
$103$	−0.594039			−0.0585324			−0.0292662	+	0.999572i	$0.509317\pi$
$104$		0			0
$105$	0.360278	+	0.360278i	0.0351596	+	0.0351596i
$106$		0			0
$107$	−8.43746	+	8.43746i	−0.815680	+	0.815680i	−0.985479	−	0.169798i	$-0.945688\pi$
$107$	−8.43746	+	8.43746i	−0.815680	+	0.815680i	0.169798	+	0.985479i	$0.445688\pi$
$108$		0			0
$109$	−1.64255	−	1.64255i	−0.157327	−	0.157327i	0.624054	−	0.781381i	$-0.285485\pi$
$109$	−1.64255	−	1.64255i	−0.157327	−	0.157327i	−0.781381	+	0.624054i	$0.785485\pi$
$110$		0			0
$111$		−	2.90293i		−	0.275534i
$112$		0			0
$113$	4.27117	−	4.27117i	0.401798	−	0.401798i	−0.477068	−	0.878866i	$-0.658301\pi$
$113$	4.27117	−	4.27117i	0.401798	−	0.401798i	0.878866	+	0.477068i	$0.158301\pi$
$114$		0			0
$115$		−	11.8717i		−	1.10704i
$116$		0			0
$117$	−1.51192			−0.139777
$118$		0			0
$119$	−0.899525	+	1.16100i	−0.0824593	+	0.106428i
$120$		0			0
$121$		−	0.411054i		−	0.0373685i
$122$		0			0
$123$			2.17203i			0.195845i
$124$		0			0
$125$	8.52976	+	8.52976i	0.762925	+	0.762925i
$126$		0			0
$127$			19.5280i			1.73283i	0.499323	+	0.866416i	$0.333582\pi$
$127$			19.5280i			1.73283i	−0.499323	+	0.866416i	$0.666418\pi$
$128$		0			0
$129$	−1.55034	+	1.55034i	−0.136500	+	0.136500i
$130$		0			0
$131$	7.52657	−	7.52657i	0.657600	−	0.657600i	−0.297212	−	0.954812i	$-0.596057\pi$
$131$	7.52657	−	7.52657i	0.657600	−	0.657600i	0.954812	+	0.297212i	$0.0960568\pi$
$132$		0			0
$133$	−1.52384	+	1.52384i	−0.132134	+	0.132134i
$134$		0			0
$135$	7.82418			0.673398
$136$		0			0
$137$	−15.7575			−1.34625			−0.673126	−	0.739528i	$-0.735049\pi$
$137$	−15.7575			−1.34625			−0.673126	+	0.739528i	$0.735049\pi$
$138$		0			0
$139$	−7.44350	+	7.44350i	−0.631349	+	0.631349i	−0.948406	−	0.317057i	$-0.897305\pi$
$139$	−7.44350	+	7.44350i	−0.631349	+	0.631349i	0.317057	+	0.948406i	$0.397305\pi$
$140$		0			0
$141$	−3.39512	+	3.39512i	−0.285920	+	0.285920i
$142$		0			0
$143$	1.40842	−	1.40842i	0.117778	−	0.117778i
$144$		0			0
$145$		−	20.5619i		−	1.70757i
$146$		0			0
$147$	3.53795	+	3.53795i	0.291805	+	0.291805i
$148$		0			0
$149$		−	3.36190i		−	0.275417i	−0.990473	−	0.137709i	$-0.956026\pi$
$149$		−	3.36190i		−	0.275417i	0.990473	−	0.137709i	$-0.0439738\pi$
$150$		0			0
$151$			19.0656i			1.55153i	0.631020	+	0.775767i	$0.282637\pi$
$151$			19.0656i			1.55153i	−0.631020	+	0.775767i	$0.717363\pi$
$152$		0			0
$153$	1.28207	+	10.1033i	0.103649	+	0.816804i
$154$		0			0
$155$	−18.2264			−1.46398
$156$		0			0
$157$		−	15.9979i		−	1.27677i	−0.769717	−	0.638385i	$-0.779603\pi$
$157$		−	15.9979i		−	1.27677i	0.769717	−	0.638385i	$-0.220397\pi$
$158$		0			0
$159$	1.65416	−	1.65416i	0.131184	−	0.131184i
$160$		0			0
$161$			2.15221i			0.169618i
$162$		0			0
$163$	3.46976	+	3.46976i	0.271773	+	0.271773i	0.829814	−	0.558041i	$-0.188447\pi$
$163$	3.46976	+	3.46976i	0.271773	+	0.271773i	−0.558041	+	0.829814i	$0.688447\pi$
$164$		0			0
$165$	−3.29123	+	3.29123i	−0.256222	+	0.256222i
$166$		0			0
$167$	3.85503	+	3.85503i	0.298311	+	0.298311i	0.840352	−	0.542041i	$-0.182348\pi$
$167$	3.85503	+	3.85503i	0.298311	+	0.298311i	−0.542041	+	0.840352i	$0.682348\pi$
$168$		0			0
$169$	12.6253			0.971180
$170$		0			0
$171$			14.9436i			1.14277i
$172$		0			0
$173$	−8.47727	+	8.47727i	−0.644515	+	0.644515i	−0.951662	−	0.307147i	$-0.900626\pi$
$173$	−8.47727	+	8.47727i	−0.644515	+	0.644515i	0.307147	+	0.951662i	$0.400626\pi$
$174$		0			0
$175$	−0.286962	−	0.286962i	−0.0216923	−	0.0216923i
$176$		0			0
$177$	−0.183180	+	0.183180i	−0.0137687	+	0.0137687i
$178$		0			0
$179$	−3.54618			−0.265054			−0.132527	−	0.991179i	$-0.542309\pi$
$179$	−3.54618			−0.265054			−0.132527	+	0.991179i	$0.542309\pi$
$180$		0			0
$181$	−10.6193	−	10.6193i	−0.789330	−	0.789330i	0.192054	−	0.981384i	$-0.438485\pi$
$181$	−10.6193	−	10.6193i	−0.789330	−	0.789330i	−0.981384	+	0.192054i	$0.938485\pi$
$182$		0			0
$183$	−1.79356			−0.132584
$184$		0			0
$185$		−	7.83533i		−	0.576065i
$186$		0			0
$187$	−10.6060	−	8.21738i	−0.775586	−	0.600914i
$188$		0			0
$189$	−1.41844			−0.103176
$190$		0			0
$191$	13.9186			1.00712			0.503559	−	0.863961i	$-0.332024\pi$
$191$	13.9186			1.00712			0.503559	+	0.863961i	$0.332024\pi$
$192$		0			0
$193$	−4.79760	+	4.79760i	−0.345339	+	0.345339i	−0.858370	−	0.513031i	$-0.828522\pi$
$193$	−4.79760	+	4.79760i	−0.345339	+	0.345339i	0.513031	+	0.858370i	$0.328522\pi$
$194$		0			0
$195$	0.875524			0.0626976
$196$		0			0
$197$	−6.64535	−	6.64535i	−0.473462	−	0.473462i	0.429571	−	0.903033i	$-0.358665\pi$
$197$	−6.64535	−	6.64535i	−0.473462	−	0.473462i	−0.903033	+	0.429571i	$0.858665\pi$
$198$		0			0
$199$	−12.0719	−	12.0719i	−0.855756	−	0.855756i	0.135079	−	0.990835i	$-0.456871\pi$
$199$	−12.0719	−	12.0719i	−0.855756	−	0.855756i	−0.990835	+	0.135079i	$0.956871\pi$
$200$		0			0
$201$	−3.04431	−	3.04431i	−0.214729	−	0.214729i
$202$		0			0
$203$			3.72765i			0.261630i
$204$		0			0
$205$			5.86255i			0.409458i
$206$		0			0
$207$	10.5529	+	10.5529i	0.733475	+	0.733475i
$208$		0			0
$209$	−13.9207	−	13.9207i	−0.962912	−	0.962912i
$210$		0			0
$211$	13.2560	+	13.2560i	0.912579	+	0.912579i	0.996475	−	0.0838951i	$-0.0267361\pi$
$211$	13.2560	+	13.2560i	0.912579	+	0.912579i	−0.0838951	+	0.996475i	$0.526736\pi$
$212$		0			0
$213$	−3.12004			−0.213782
$214$		0			0
$215$	−4.18454	+	4.18454i	−0.285383	+	0.285383i
$216$		0			0
$217$	3.30426			0.224308
$218$		0			0
$219$	−3.78203			−0.255566
$220$		0			0
$221$	0.317705	+	2.50367i	0.0213712	+	0.168415i
$222$		0			0
$223$			20.3081i			1.35993i	0.733244	+	0.679966i	$0.238005\pi$
$223$			20.3081i			1.35993i	−0.733244	+	0.679966i	$0.761995\pi$
$224$		0			0
$225$	−2.81411			−0.187607
$226$		0			0
$227$	−5.03362	−	5.03362i	−0.334093	−	0.334093i	0.520045	−	0.854139i	$-0.325915\pi$
$227$	−5.03362	−	5.03362i	−0.334093	−	0.334093i	−0.854139	+	0.520045i	$0.825915\pi$
$228$		0			0
$229$	−15.3175			−1.01221			−0.506104	−	0.862473i	$-0.668915\pi$
$229$	−15.3175			−1.01221			−0.506104	+	0.862473i	$0.668915\pi$
$230$		0			0
$231$	0.596665	−	0.596665i	0.0392577	−	0.0392577i
$232$		0			0
$233$	−8.15141	−	8.15141i	−0.534017	−	0.534017i	0.387748	−	0.921765i	$-0.373253\pi$
$233$	−8.15141	−	8.15141i	−0.534017	−	0.534017i	−0.921765	+	0.387748i	$0.873253\pi$
$234$		0			0
$235$	−9.16380	+	9.16380i	−0.597780	+	0.597780i
$236$		0			0
$237$			0.640512i			0.0416057i
$238$		0			0
$239$	6.00160			0.388211			0.194105	−	0.980981i	$-0.437820\pi$
$239$	6.00160			0.388211			0.194105	+	0.980981i	$0.437820\pi$
$240$		0			0
$241$	−14.4739	−	14.4739i	−0.932345	−	0.932345i	0.0655075	−	0.997852i	$-0.479133\pi$
$241$	−14.4739	−	14.4739i	−0.932345	−	0.932345i	−0.997852	+	0.0655075i	$0.979133\pi$
$242$		0			0
$243$	−10.7694	+	10.7694i	−0.690858	+	0.690858i
$244$		0			0
$245$	9.54932	+	9.54932i	0.610084	+	0.610084i
$246$		0			0
$247$			3.70314i			0.235625i
$248$		0			0
$249$	4.59253	−	4.59253i	0.291040	−	0.291040i
$250$		0			0
$251$			12.0432i			0.760158i	0.924954	+	0.380079i	$0.124103\pi$
$251$			12.0432i			0.760158i	−0.924954	+	0.380079i	$0.875897\pi$
$252$		0			0
$253$	−19.6609			−1.23607
$254$		0			0
$255$	−0.742420	−	5.85063i	−0.0464921	−	0.366380i
$256$		0			0
$257$			14.7478i			0.919940i	0.887934	+	0.459970i	$0.152140\pi$
$257$			14.7478i			0.919940i	−0.887934	+	0.459970i	$0.847860\pi$
$258$		0			0
$259$			1.42046i			0.0882633i
$260$		0			0
$261$	18.2777	+	18.2777i	1.13136	+	1.13136i
$262$		0			0
$263$			26.5614i			1.63784i	0.573905	+	0.818922i	$0.305428\pi$
$263$			26.5614i			1.63784i	−0.573905	+	0.818922i	$0.694572\pi$
$264$		0			0
$265$	4.46477	−	4.46477i	0.274269	−	0.274269i
$266$		0			0
$267$	1.74490	−	1.74490i	0.106786	−	0.106786i
$268$		0			0
$269$	−10.7067	+	10.7067i	−0.652798	+	0.652798i	−0.953666	−	0.300868i	$-0.902724\pi$
$269$	−10.7067	+	10.7067i	−0.652798	+	0.652798i	0.300868	+	0.953666i	$0.402724\pi$
$270$		0			0
$271$	18.3408			1.11412			0.557061	−	0.830471i	$-0.311929\pi$
$271$	18.3408			1.11412			0.557061	+	0.830471i	$0.311929\pi$
$272$		0			0
$273$	−0.158723			−0.00960637
$274$		0			0
$275$	2.62147	−	2.62147i	0.158080	−	0.158080i
$276$		0			0
$277$	−14.2578	+	14.2578i	−0.856670	+	0.856670i	−0.990944	−	0.134274i	$-0.957130\pi$
$277$	−14.2578	+	14.2578i	−0.856670	+	0.856670i	0.134274	+	0.990944i	$0.457130\pi$
$278$		0			0
$279$	16.2017	−	16.2017i	0.969969	−	0.969969i
$280$		0			0
$281$			23.0039i			1.37229i	0.727462	+	0.686147i	$0.240700\pi$
$281$			23.0039i			1.37229i	−0.727462	+	0.686147i	$0.759300\pi$
$282$		0			0
$283$	−22.1960	−	22.1960i	−1.31942	−	1.31942i	−0.914237	−	0.405179i	$-0.867209\pi$
$283$	−22.1960	−	22.1960i	−1.31942	−	1.31942i	−0.405179	−	0.914237i	$-0.632791\pi$
$284$		0			0
$285$		−	8.65357i		−	0.512593i
$286$		0			0
$287$		−	1.06282i		−	0.0627362i
$288$		0			0
$289$	16.4612	−	4.24608i	0.968305	−	0.249770i
$290$		0			0
$291$	11.5421			0.676608
$292$		0			0
$293$		−	13.7337i		−	0.802333i	−0.916005	−	0.401167i	$-0.868605\pi$
$293$		−	13.7337i		−	0.802333i	0.916005	−	0.401167i	$-0.131395\pi$
$294$		0			0
$295$	−0.494424	+	0.494424i	−0.0287865	+	0.0287865i
$296$		0			0
$297$		−	12.9578i		−	0.751888i
$298$		0			0
$299$	2.61507	+	2.61507i	0.151234	+	0.151234i
$300$		0			0
$301$	0.758614	−	0.758614i	0.0437258	−	0.0437258i
$302$		0			0
$303$	9.36346	+	9.36346i	0.537917	+	0.537917i
$304$		0			0
$305$	−4.84102			−0.277196
$306$		0			0
$307$		−	19.7931i		−	1.12965i	−0.825209	−	0.564827i	$-0.808943\pi$
$307$		−	19.7931i		−	1.12965i	0.825209	−	0.564827i	$-0.191057\pi$
$308$		0			0
$309$	−0.305783	+	0.305783i	−0.0173954	+	0.0173954i
$310$		0			0
$311$	8.97810	+	8.97810i	0.509101	+	0.509101i	0.914251	−	0.405149i	$-0.132780\pi$
$311$	8.97810	+	8.97810i	0.509101	+	0.509101i	−0.405149	+	0.914251i	$0.632780\pi$
$312$		0			0
$313$	−5.82211	+	5.82211i	−0.329085	+	0.329085i	−0.852238	−	0.523154i	$-0.824755\pi$
$313$	−5.82211	+	5.82211i	−0.329085	+	0.329085i	0.523154	+	0.852238i	$0.324755\pi$
$314$		0			0
$315$	−1.72881			−0.0974076
$316$		0			0
$317$	−1.48942	−	1.48942i	−0.0836539	−	0.0836539i	0.664042	−	0.747696i	$-0.268840\pi$
$317$	−1.48942	−	1.48942i	−0.0836539	−	0.0836539i	−0.747696	+	0.664042i	$0.768840\pi$
$318$		0			0
$319$	−34.0530			−1.90660
$320$		0			0
$321$			8.68640i			0.484828i
$322$		0			0
$323$	24.7460	−	3.14016i	1.37690	−	0.174723i
$324$		0			0
$325$	−0.697355			−0.0386823
$326$		0			0
$327$	−1.69101			−0.0935129
$328$		0			0
$329$	1.66130	−	1.66130i	0.0915905	−	0.0915905i
$330$		0			0
$331$	−23.6132			−1.29790			−0.648949	−	0.760832i	$-0.724791\pi$
$331$	−23.6132			−1.29790			−0.648949	+	0.760832i	$0.724791\pi$
$332$		0			0
$333$	6.96492	+	6.96492i	0.381675	+	0.381675i
$334$		0			0
$335$	−8.21693	−	8.21693i	−0.448939	−	0.448939i
$336$		0			0
$337$	−13.0741	−	13.0741i	−0.712190	−	0.712190i	0.254803	−	0.966993i	$-0.417989\pi$
$337$	−13.0741	−	13.0741i	−0.712190	−	0.712190i	−0.966993	+	0.254803i	$0.917989\pi$
$338$		0			0
$339$		−	4.39719i		−	0.238822i
$340$		0			0
$341$			30.1852i			1.63462i
$342$		0			0
$343$	−3.49434	−	3.49434i	−0.188677	−	0.188677i
$344$		0			0
$345$	−6.11096	−	6.11096i	−0.329003	−	0.329003i
$346$		0			0
$347$	12.7923	+	12.7923i	0.686725	+	0.686725i	0.961507	−	0.274782i	$-0.0886056\pi$
$347$	12.7923	+	12.7923i	0.686725	+	0.686725i	−0.274782	+	0.961507i	$0.588606\pi$
$348$		0			0
$349$	7.33456			0.392610			0.196305	−	0.980543i	$-0.437106\pi$
$349$	7.33456			0.392610			0.196305	+	0.980543i	$0.437106\pi$
$350$		0			0
$351$	−1.72350	+	1.72350i	−0.0919936	+	0.0919936i
$352$		0			0
$353$	23.9694			1.27576			0.637880	−	0.770136i	$-0.279812\pi$
$353$	23.9694			1.27576			0.637880	+	0.770136i	$0.279812\pi$
$354$		0			0
$355$	−8.42133			−0.446958
$356$		0			0
$357$	0.134593	+	1.06066i	0.00712341	+	0.0561360i
$358$		0			0
$359$			17.6475i			0.931398i	0.884943	+	0.465699i	$0.154197\pi$
$359$			17.6475i			0.931398i	−0.884943	+	0.465699i	$0.845803\pi$
$360$		0			0
$361$	17.6013			0.926387
$362$		0			0
$363$	−0.211591	−	0.211591i	−0.0111056	−	0.0111056i
$364$		0			0
$365$	−10.2081			−0.534317
$366$		0			0
$367$	−23.0347	+	23.0347i	−1.20240	+	1.20240i	−0.228969	+	0.973434i	$0.573535\pi$
$367$	−23.0347	+	23.0347i	−1.20240	+	1.20240i	−0.973434	+	0.228969i	$0.926465\pi$
$368$		0			0
$369$	−5.21129	−	5.21129i	−0.271289	−	0.271289i
$370$		0			0
$371$	−0.809417	+	0.809417i	−0.0420228	+	0.0420228i
$372$		0			0
$373$		−	23.4994i		−	1.21675i	−0.793649	−	0.608375i	$-0.791822\pi$
$373$		−	23.4994i		−	1.21675i	0.793649	−	0.608375i	$-0.208178\pi$
$374$		0			0
$375$	8.78142			0.453470
$376$		0			0
$377$	4.52934	+	4.52934i	0.233273	+	0.233273i
$378$		0			0
$379$	16.2546	−	16.2546i	0.834942	−	0.834942i	−0.153246	−	0.988188i	$-0.548973\pi$
$379$	16.2546	−	16.2546i	0.834942	−	0.834942i	0.988188	+	0.153246i	$0.0489726\pi$
$380$		0			0
$381$	10.0521	+	10.0521i	0.514984	+	0.514984i
$382$		0			0
$383$		−	20.1835i		−	1.03133i	−0.856791	−	0.515664i	$-0.827545\pi$
$383$		−	20.1835i		−	1.03133i	0.856791	−	0.515664i	$-0.172455\pi$
$384$		0			0
$385$	1.61047	−	1.61047i	0.0820770	−	0.0820770i
$386$		0			0
$387$		−	7.43938i		−	0.378165i
$388$		0			0
$389$	−30.4921			−1.54601			−0.773005	−	0.634400i	$-0.781247\pi$
$389$	−30.4921			−1.54601			−0.773005	+	0.634400i	$0.781247\pi$
$390$		0			0
$391$	15.2575	−	19.6926i	0.771607	−	0.995896i
$392$		0			0
$393$		−	7.74863i		−	0.390867i
$394$		0			0
$395$			1.72881i			0.0869860i
$396$		0			0
$397$	0.322205	+	0.322205i	0.0161710	+	0.0161710i	0.715146	−	0.698975i	$-0.246360\pi$
$397$	0.322205	+	0.322205i	0.0161710	+	0.0161710i	−0.698975	+	0.715146i	$0.746360\pi$
$398$		0			0
$399$			1.56880i			0.0785383i
$400$		0			0
$401$	−4.99142	+	4.99142i	−0.249260	+	0.249260i	−0.820667	−	0.571407i	$-0.806398\pi$
$401$	−4.99142	+	4.99142i	−0.249260	+	0.249260i	0.571407	+	0.820667i	$0.306398\pi$
$402$		0			0
$403$	4.01489	−	4.01489i	0.199996	−	0.199996i
$404$		0			0
$405$	−6.26800	+	6.26800i	−0.311459	+	0.311459i
$406$		0			0
$407$	−12.9763			−0.643210
$408$		0			0
$409$	0.839803			0.0415256			0.0207628	−	0.999784i	$-0.493391\pi$
$409$	0.839803			0.0415256			0.0207628	+	0.999784i	$0.493391\pi$
$410$		0			0
$411$	−8.11119	+	8.11119i	−0.400095	+	0.400095i
$412$		0			0
$413$	0.0896339	−	0.0896339i	0.00441060	−	0.00441060i
$414$		0			0
$415$	12.3958	−	12.3958i	0.608484	−	0.608484i
$416$		0			0
$417$			7.66311i			0.375264i
$418$		0			0
$419$	3.41355	+	3.41355i	0.166763	+	0.166763i	0.785555	−	0.618792i	$-0.212378\pi$
$419$	3.41355	+	3.41355i	0.166763	+	0.166763i	−0.618792	+	0.785555i	$0.712378\pi$
$420$		0			0
$421$		−	32.0466i		−	1.56186i	−0.624620	−	0.780929i	$-0.714746\pi$
$421$		−	32.0466i		−	1.56186i	0.624620	−	0.780929i	$-0.285254\pi$
$422$		0			0
$423$		−	16.2916i		−	0.792126i
$424$		0			0
$425$	0.591338	+	4.66003i	0.0286841	+	0.226045i
$426$		0			0
$427$	0.877627			0.0424713
$428$		0			0
$429$		−	1.44998i		−	0.0700055i
$430$		0			0
$431$	18.9251	−	18.9251i	0.911589	−	0.911589i	−0.0848083	−	0.996397i	$-0.527028\pi$
$431$	18.9251	−	18.9251i	0.911589	−	0.911589i	0.996397	+	0.0848083i	$0.0270278\pi$
$432$		0			0
$433$		−	2.03306i		−	0.0977025i	−0.998806	−	0.0488512i	$-0.984444\pi$
$433$		−	2.03306i		−	0.0977025i	0.998806	−	0.0488512i	$-0.0155560\pi$
$434$		0			0
$435$	−10.5843	−	10.5843i	−0.507476	−	0.507476i
$436$		0			0
$437$	25.8471	−	25.8471i	1.23643	−	1.23643i
$438$		0			0
$439$	−6.16323	−	6.16323i	−0.294155	−	0.294155i	0.544564	−	0.838719i	$-0.316695\pi$
$439$	−6.16323	−	6.16323i	−0.294155	−	0.294155i	−0.838719	+	0.544564i	$0.816695\pi$
$440$		0			0
$441$	−16.9770			−0.808429
$442$		0			0
$443$			26.1503i			1.24244i	0.783637	+	0.621219i	$0.213362\pi$
$443$			26.1503i			1.24244i	−0.783637	+	0.621219i	$0.786638\pi$
$444$		0			0
$445$	4.70967	−	4.70967i	0.223260	−	0.223260i
$446$		0			0
$447$	−1.73054	−	1.73054i	−0.0818519	−	0.0818519i
$448$		0			0
$449$	−24.1559	+	24.1559i	−1.13999	+	1.13999i	−0.151535	+	0.988452i	$0.548422\pi$
$449$	−24.1559	+	24.1559i	−1.13999	+	1.13999i	−0.988452	+	0.151535i	$0.951578\pi$
$450$		0			0
$451$	9.70910			0.457184
$452$		0			0
$453$	9.81403	+	9.81403i	0.461104	+	0.461104i
$454$		0			0
$455$	−0.428412			−0.0200843
$456$		0			0
$457$		−	18.9289i		−	0.885456i	−0.896656	−	0.442728i	$-0.854011\pi$
$457$		−	18.9289i		−	0.885456i	0.896656	−	0.442728i	$-0.145989\pi$
$458$		0			0
$459$	12.9787	+	10.0557i	0.605792	+	0.469359i
$460$		0			0
$461$	19.9098			0.927293			0.463647	−	0.886020i	$-0.346541\pi$
$461$	19.9098			0.927293			0.463647	+	0.886020i	$0.346541\pi$
$462$		0			0
$463$	−36.3136			−1.68764			−0.843818	−	0.536630i	$-0.819697\pi$
$463$	−36.3136			−1.68764			−0.843818	+	0.536630i	$0.819697\pi$
$464$		0			0
$465$	−9.38208	+	9.38208i	−0.435083	+	0.435083i
$466$		0			0
$467$	−16.2225			−0.750689			−0.375345	−	0.926885i	$-0.622476\pi$
$467$	−16.2225			−0.750689			−0.375345	+	0.926885i	$0.622476\pi$
$468$		0			0
$469$	1.48964	+	1.48964i	0.0687854	+	0.0687854i
$470$		0			0
$471$	−8.23494	−	8.23494i	−0.379446	−	0.379446i
$472$		0			0
$473$	6.93011	+	6.93011i	0.318647	+	0.318647i
$474$		0			0
$475$			6.89257i			0.316253i
$476$		0			0
$477$			7.93758i			0.363437i
$478$		0			0
$479$	10.7553	+	10.7553i	0.491424	+	0.491424i	0.908755	−	0.417331i	$-0.137034\pi$
$479$	10.7553	+	10.7553i	0.491424	+	0.491424i	−0.417331	+	0.908755i	$0.637034\pi$
$480$		0			0
$481$	1.72596	+	1.72596i	0.0786969	+	0.0786969i
$482$		0			0
$483$	1.10785	+	1.10785i	0.0504091	+	0.0504091i
$484$		0			0
$485$	31.1533			1.41460
$486$		0			0
$487$	−26.4840	+	26.4840i	−1.20010	+	1.20010i	−0.225968	+	0.974135i	$0.572554\pi$
$487$	−26.4840	+	26.4840i	−1.20010	+	1.20010i	−0.974135	+	0.225968i	$0.927446\pi$
$488$		0			0
$489$	3.57213			0.161537
$490$		0			0
$491$	10.1591			0.458473			0.229237	−	0.973371i	$-0.426377\pi$
$491$	10.1591			0.458473			0.229237	+	0.973371i	$0.426377\pi$
$492$		0			0
$493$	26.4263	−	34.1078i	1.19018	−	1.53614i
$494$		0			0
$495$		−	15.7931i		−	0.709848i
$496$		0			0
$497$	1.52670			0.0684819
$498$		0			0
$499$	11.9060	+	11.9060i	0.532985	+	0.532985i	0.921460	−	0.388474i	$-0.126998\pi$
$499$	11.9060	+	11.9060i	0.532985	+	0.532985i	−0.388474	+	0.921460i	$0.626998\pi$
$500$		0			0
$501$	3.96877			0.177311
$502$		0			0
$503$	19.2485	−	19.2485i	0.858246	−	0.858246i	−0.132885	−	0.991131i	$-0.542424\pi$
$503$	19.2485	−	19.2485i	0.858246	−	0.858246i	0.991131	+	0.132885i	$0.0424242\pi$
$504$		0			0
$505$	25.2730	+	25.2730i	1.12463	+	1.12463i
$506$		0			0
$507$	6.49891	−	6.49891i	0.288627	−	0.288627i
$508$		0			0
$509$			13.1191i			0.581496i	0.956800	+	0.290748i	$0.0939041\pi$
$509$			13.1191i			0.581496i	−0.956800	+	0.290748i	$0.906096\pi$
$510$		0			0
$511$	1.85063			0.0818668
$512$		0			0
$513$	17.0349	+	17.0349i	0.752108	+	0.752108i
$514$		0			0
$515$	−0.825342	+	0.825342i	−0.0363689	+	0.0363689i
$516$		0			0
$517$	15.1764	+	15.1764i	0.667456	+	0.667456i
$518$		0			0
$519$			8.72738i			0.383090i
$520$		0			0
$521$	−6.07083	+	6.07083i	−0.265968	+	0.265968i	−0.827473	−	0.561505i	$-0.810222\pi$
$521$	−6.07083	+	6.07083i	−0.265968	+	0.265968i	0.561505	+	0.827473i	$0.310222\pi$
$522$		0			0
$523$		−	30.0933i		−	1.31589i	−0.753066	−	0.657945i	$-0.771426\pi$
$523$		−	30.0933i		−	1.31589i	0.753066	−	0.657945i	$-0.228574\pi$
$524$		0			0
$525$	−0.295428			−0.0128936
$526$		0			0
$527$	−30.2337	−	23.4247i	−1.31700	−	1.02040i
$528$		0			0
$529$		−	13.5053i		−	0.587186i
$530$		0			0
$531$		−	0.878999i		−	0.0381453i
$532$		0			0
$533$	−1.29139	−	1.29139i	−0.0559365	−	0.0559365i
$534$		0			0
$535$			23.4456i			1.01364i
$536$		0			0
$537$	−1.82540	+	1.82540i	−0.0787719	+	0.0787719i
$538$		0			0
$539$	15.8148	−	15.8148i	0.681194	−	0.681194i
$540$		0			0
$541$	−3.53188	+	3.53188i	−0.151847	+	0.151847i	−0.778943	−	0.627095i	$-0.784244\pi$
$541$	−3.53188	+	3.53188i	−0.151847	+	0.151847i	0.627095	+	0.778943i	$0.284244\pi$
$542$		0			0
$543$	−10.9327			−0.469165
$544$		0			0
$545$	−4.56422			−0.195510
$546$		0			0
$547$	−11.1294	+	11.1294i	−0.475858	+	0.475858i	−0.903804	−	0.427946i	$-0.859237\pi$
$547$	−11.1294	+	11.1294i	−0.475858	+	0.475858i	0.427946	+	0.903804i	$0.359237\pi$
$548$		0			0
$549$	4.30324	−	4.30324i	0.183658	−	0.183658i
$550$		0			0
$551$	44.7674	−	44.7674i	1.90716	−	1.90716i
$552$		0			0
$553$		−	0.313416i		−	0.0133278i
$554$		0			0
$555$	−4.03325	−	4.03325i	−0.171202	−	0.171202i
$556$		0			0
$557$		−	34.0464i		−	1.44259i	−0.692627	−	0.721295i	$-0.743547\pi$
$557$		−	34.0464i		−	1.44259i	0.692627	−	0.721295i	$-0.256453\pi$
$558$		0			0
$559$		−	1.84353i		−	0.0779730i
$560$		0			0
$561$	−9.68936	+	1.22954i	−0.409085	+	0.0519112i
$562$		0			0
$563$	−10.5148			−0.443148			−0.221574	−	0.975144i	$-0.571119\pi$
$563$	−10.5148			−0.443148			−0.221574	+	0.975144i	$0.571119\pi$
$564$		0			0
$565$		−	11.8685i		−	0.499311i
$566$		0			0
$567$	1.13632	−	1.13632i	0.0477210	−	0.0477210i
$568$		0			0
$569$		−	6.51922i		−	0.273300i	−0.990619	−	0.136650i	$-0.956366\pi$
$569$		−	6.51922i		−	0.273300i	0.990619	−	0.136650i	$-0.0436336\pi$
$570$		0			0
$571$	3.23234	+	3.23234i	0.135269	+	0.135269i	0.771499	−	0.636230i	$-0.219507\pi$
$571$	3.23234	+	3.23234i	0.135269	+	0.135269i	−0.636230	+	0.771499i	$0.719507\pi$
$572$		0			0
$573$	7.16465	−	7.16465i	0.299308	−	0.299308i
$574$		0			0
$575$	4.86738	+	4.86738i	0.202984	+	0.202984i
$576$		0			0
$577$	38.0910			1.58575			0.792874	−	0.609386i	$-0.208584\pi$
$577$	38.0910			1.58575			0.792874	+	0.609386i	$0.208584\pi$
$578$		0			0
$579$			4.93914i			0.205264i
$580$		0			0
$581$	−2.24722	+	2.24722i	−0.0932305	+	0.0932305i
$582$		0			0
$583$	−7.39421	−	7.39421i	−0.306237	−	0.306237i
$584$		0			0
$585$	−2.10062	+	2.10062i	−0.0868500	+	0.0868500i
$586$		0			0
$587$	28.1221			1.16073			0.580363	−	0.814358i	$-0.302911\pi$
$587$	28.1221			1.16073			0.580363	+	0.814358i	$0.302911\pi$
$588$		0			0
$589$	−39.6827	−	39.6827i	−1.63510	−	1.63510i
$590$		0			0
$591$	−6.84142			−0.281418
$592$		0			0
$593$		−	37.0636i		−	1.52202i	−0.648740	−	0.761010i	$-0.724704\pi$
$593$		−	37.0636i		−	1.52202i	0.648740	−	0.761010i	$-0.275296\pi$
$594$		0			0
$595$	0.363281	+	2.86283i	0.0148931	+	0.117365i
$596$		0			0
$597$	−12.4281			−0.508648
$598$		0			0
$599$	−16.4294			−0.671285			−0.335643	−	0.941989i	$-0.608953\pi$
$599$	−16.4294			−0.671285			−0.335643	+	0.941989i	$0.608953\pi$
$600$		0			0
$601$	−17.7171	+	17.7171i	−0.722695	+	0.722695i	−0.969153	−	0.246459i	$-0.920733\pi$
$601$	−17.7171	+	17.7171i	−0.722695	+	0.722695i	0.246459	+	0.969153i	$0.420733\pi$
$602$		0			0
$603$	14.6083			0.594894
$604$		0			0
$605$	−0.571107	−	0.571107i	−0.0232188	−	0.0232188i
$606$		0			0
$607$	−7.27955	−	7.27955i	−0.295468	−	0.295468i	0.543768	−	0.839236i	$-0.316997\pi$
$607$	−7.27955	−	7.27955i	−0.295468	−	0.295468i	−0.839236	+	0.543768i	$0.816997\pi$
$608$		0			0
$609$	1.91882	+	1.91882i	0.0777543	+	0.0777543i
$610$		0			0
$611$		−	4.03718i		−	0.163327i
$612$		0			0
$613$		−	0.784441i		−	0.0316833i	−0.999875	−	0.0158416i	$-0.994957\pi$
$613$		−	0.784441i		−	0.0316833i	0.999875	−	0.0158416i	$-0.00504276\pi$
$614$		0			0
$615$	3.01776	+	3.01776i	0.121688	+	0.121688i
$616$		0			0
$617$	19.1414	+	19.1414i	0.770602	+	0.770602i	0.978212	−	0.207609i	$-0.0665683\pi$
$617$	19.1414	+	19.1414i	0.770602	+	0.770602i	−0.207609	+	0.978212i	$0.566568\pi$
$618$		0			0
$619$	−14.7781	−	14.7781i	−0.593982	−	0.593982i	0.344723	−	0.938705i	$-0.387973\pi$
$619$	−14.7781	−	14.7781i	−0.593982	−	0.593982i	−0.938705	+	0.344723i	$0.887973\pi$
$620$		0			0
$621$	24.0593			0.965466
$622$		0			0
$623$	−0.853814	+	0.853814i	−0.0342073	+	0.0342073i
$624$		0			0
$625$	18.0056			0.720224
$626$		0			0
$627$	−14.3314			−0.572340
$628$		0			0
$629$	10.0700	−	12.9971i	0.401518	−	0.518230i
$630$		0			0
$631$		−	22.2239i		−	0.884719i	−0.896838	−	0.442359i	$-0.854142\pi$
$631$		−	22.2239i		−	0.884719i	0.896838	−	0.442359i	$-0.145858\pi$
$632$		0			0
$633$	13.6471			0.542423
$634$		0			0
$635$	27.1317	+	27.1317i	1.07669	+	1.07669i
$636$		0			0
$637$	−4.20702			−0.166688
$638$		0			0
$639$	7.48583	−	7.48583i	0.296135	−	0.296135i
$640$		0			0
$641$	21.9684	+	21.9684i	0.867702	+	0.867702i	0.992218	−	0.124516i	$-0.0397378\pi$
$641$	21.9684	+	21.9684i	0.867702	+	0.867702i	−0.124516	+	0.992218i	$0.539738\pi$
$642$		0			0
$643$	3.13909	−	3.13909i	0.123794	−	0.123794i	−0.642496	−	0.766289i	$-0.722101\pi$
$643$	3.13909	−	3.13909i	0.123794	−	0.123794i	0.766289	+	0.642496i	$0.222101\pi$
$644$		0			0
$645$			4.30800i			0.169627i
$646$		0			0
$647$	−4.64834			−0.182745			−0.0913725	−	0.995817i	$-0.529125\pi$
$647$	−4.64834			−0.182745			−0.0913725	+	0.995817i	$0.529125\pi$
$648$		0			0
$649$	0.818827	+	0.818827i	0.0321418	+	0.0321418i
$650$		0			0
$651$	1.70087	−	1.70087i	0.0666624	−	0.0666624i
$652$		0			0
$653$	31.7229	+	31.7229i	1.24141	+	1.24141i	0.959415	+	0.281999i	$0.0909976\pi$
$653$	31.7229	+	31.7229i	1.24141	+	1.24141i	0.281999	+	0.959415i	$0.409002\pi$
$654$		0			0
$655$		−	20.9144i		−	0.817194i
$656$		0			0
$657$	9.07412	−	9.07412i	0.354015	−	0.354015i
$658$		0			0
$659$		−	30.8540i		−	1.20190i	−0.799286	−	0.600951i	$-0.794789\pi$
$659$		−	30.8540i		−	1.20190i	0.799286	−	0.600951i	$-0.205211\pi$
$660$		0			0
$661$	28.6647			1.11493			0.557464	−	0.830201i	$-0.311775\pi$
$661$	28.6647			1.11493			0.557464	+	0.830201i	$0.311775\pi$
$662$		0			0
$663$	1.45231	+	1.12523i	0.0564030	+	0.0437003i
$664$		0			0
$665$			4.23437i			0.164202i
$666$		0			0
$667$		−	63.2276i		−	2.44818i
$668$		0			0
$669$	10.4536	+	10.4536i	0.404161	+	0.404161i
$670$		0			0
$671$			8.01733i			0.309506i
$672$		0			0
$673$	5.86312	−	5.86312i	0.226007	−	0.226007i	−0.585015	−	0.811022i	$-0.698912\pi$
$673$	5.86312	−	5.86312i	0.226007	−	0.226007i	0.811022	+	0.585015i	$0.198912\pi$
$674$		0			0
$675$	−3.20792	+	3.20792i	−0.123473	+	0.123473i
$676$		0			0
$677$	−3.69061	+	3.69061i	−0.141842	+	0.141842i	−0.774462	−	0.632620i	$-0.781979\pi$
$677$	−3.69061	+	3.69061i	−0.141842	+	0.141842i	0.632620	+	0.774462i	$0.281979\pi$
$678$		0			0
$679$	−5.64777			−0.216742
$680$		0			0
$681$	−5.18213			−0.198580
$682$		0			0
$683$	25.3245	−	25.3245i	0.969016	−	0.969016i	−0.0305179	−	0.999534i	$-0.509716\pi$
$683$	25.3245	−	25.3245i	0.969016	−	0.969016i	0.999534	+	0.0305179i	$0.00971564\pi$
$684$		0			0
$685$	−21.8930	+	21.8930i	−0.836488	+	0.836488i
$686$		0			0
$687$	−7.88470	+	7.88470i	−0.300820	+	0.300820i
$688$		0			0
$689$			1.96699i			0.0749363i
$690$		0			0
$691$	34.1311	+	34.1311i	1.29841	+	1.29841i	0.929444	+	0.368964i	$0.120287\pi$
$691$	34.1311	+	34.1311i	1.29841	+	1.29841i	0.368964	+	0.929444i	$0.379713\pi$
$692$		0			0
$693$			2.86313i			0.108761i
$694$		0			0
$695$			20.6836i			0.784573i
$696$		0			0
$697$	−7.53459	+	9.72472i	−0.285393	+	0.368350i
$698$		0			0
$699$	−8.39191			−0.317411
$700$		0			0
$701$			7.74471i			0.292514i	0.989247	+	0.146257i	$0.0467226\pi$
$701$			7.74471i			0.292514i	−0.989247	+	0.146257i	$0.953277\pi$
$702$		0			0
$703$	17.0591	−	17.0591i	0.643398	−	0.643398i
$704$		0			0
$705$			9.43416i			0.355311i
$706$		0			0
$707$	−4.58173	−	4.58173i	−0.172314	−	0.172314i
$708$		0			0
$709$	20.3776	−	20.3776i	0.765296	−	0.765296i	−0.211978	−	0.977274i	$-0.567991\pi$
$709$	20.3776	−	20.3776i	0.765296	−	0.765296i	0.977274	+	0.211978i	$0.0679907\pi$
$710$		0			0
$711$	−1.53676	−	1.53676i	−0.0576331	−	0.0576331i
$712$		0			0
$713$	−56.0460			−2.09894
$714$		0			0
$715$		−	3.91364i		−	0.146362i
$716$		0			0
$717$	3.08933	−	3.08933i	0.115373	−	0.115373i
$718$		0			0
$719$	27.8007	+	27.8007i	1.03679	+	1.03679i	0.999297	+	0.0374924i	$0.0119370\pi$
$719$	27.8007	+	27.8007i	1.03679	+	1.03679i	0.0374924	+	0.999297i	$0.488063\pi$
$720$		0			0
$721$	0.149626	−	0.149626i	0.00557236	−	0.00557236i
$722$		0			0
$723$	−14.9009			−0.554171
$724$		0			0
$725$	8.43037	+	8.43037i	0.313096	+	0.313096i
$726$		0			0
$727$	−40.1362			−1.48857			−0.744284	−	0.667863i	$-0.767209\pi$
$727$	−40.1362			−1.48857			−0.744284	+	0.667863i	$0.767209\pi$
$728$		0			0
$729$		−	2.44700i		−	0.0906297i
$730$		0			0
$731$	−12.3193	+	1.56326i	−0.455644	+	0.0578193i
$732$		0			0
$733$	−8.80129			−0.325083			−0.162541	−	0.986702i	$-0.551969\pi$
$733$	−8.80129			−0.325083			−0.162541	+	0.986702i	$0.551969\pi$
$734$		0			0
$735$	9.83106			0.362624
$736$		0			0
$737$	−13.6082	+	13.6082i	−0.501266	+	0.501266i
$738$		0			0
$739$	−53.0181			−1.95030			−0.975151	−	0.221543i	$-0.928891\pi$
$739$	−53.0181			−1.95030			−0.975151	+	0.221543i	$0.928891\pi$
$740$		0			0
$741$	1.90620	+	1.90620i	0.0700259	+	0.0700259i
$742$		0			0
$743$	−35.7501	−	35.7501i	−1.31155	−	1.31155i	−0.920277	−	0.391268i	$-0.872036\pi$
$743$	−35.7501	−	35.7501i	−1.31155	−	1.31155i	−0.391268	−	0.920277i	$-0.627964\pi$
$744$		0			0
$745$	−4.67093	−	4.67093i	−0.171130	−	0.171130i
$746$		0			0
$747$			22.0375i			0.806310i
$748$		0			0
$749$		−	4.25044i		−	0.155308i
$750$		0			0
$751$	11.2657	+	11.2657i	0.411092	+	0.411092i	0.882119	−	0.471027i	$-0.156116\pi$
$751$	11.2657	+	11.2657i	0.411092	+	0.411092i	−0.471027	+	0.882119i	$0.656116\pi$
$752$		0			0
$753$	6.19924	+	6.19924i	0.225913	+	0.225913i
$754$		0			0
$755$	26.4892	+	26.4892i	0.964040	+	0.964040i
$756$		0			0
$757$	−32.2709			−1.17291			−0.586453	−	0.809983i	$-0.699476\pi$
$757$	−32.2709			−1.17291			−0.586453	+	0.809983i	$0.699476\pi$
$758$		0			0
$759$	−10.1205	+	10.1205i	−0.367351	+	0.367351i
$760$		0			0
$761$	6.30205			0.228449			0.114224	−	0.993455i	$-0.463562\pi$
$761$	6.30205			0.228449			0.114224	+	0.993455i	$0.463562\pi$
$762$		0			0
$763$	0.827445			0.0299555
$764$		0			0
$765$	15.8185	+	12.2560i	0.571920	+	0.443116i
$766$		0			0
$767$		−	0.217822i		−	0.00786510i
$768$		0			0
$769$	14.2638			0.514367			0.257183	−	0.966363i	$-0.417206\pi$
$769$	14.2638			0.514367			0.257183	+	0.966363i	$0.417206\pi$
$770$		0			0
$771$	7.59144	+	7.59144i	0.273399	+	0.273399i
$772$		0			0
$773$	−41.9941			−1.51042			−0.755212	−	0.655481i	$-0.772466\pi$
$773$	−41.9941			−1.51042			−0.755212	+	0.655481i	$0.772466\pi$
$774$		0			0
$775$	7.47283	−	7.47283i	0.268432	−	0.268432i
$776$		0			0
$777$	0.731186	+	0.731186i	0.0262312	+	0.0262312i
$778$		0			0
$779$	−12.7640	+	12.7640i	−0.457317	+	0.457317i
$780$		0			0
$781$			13.9468i			0.499054i
$782$		0			0
$783$	41.6710			1.48920
$784$		0			0
$785$	−22.2270	−	22.2270i	−0.793316	−	0.793316i
$786$		0			0
$787$	−22.8036	+	22.8036i	−0.812859	+	0.812859i	−0.985062	−	0.172203i	$-0.944912\pi$
$787$	−22.8036	+	22.8036i	−0.812859	+	0.812859i	0.172203	+	0.985062i	$0.444912\pi$
$788$		0			0
$789$	13.6725	+	13.6725i	0.486754	+	0.486754i
$790$		0			0
$791$			2.15163i			0.0765033i
$792$		0			0
$793$	1.06637	−	1.06637i	0.0378681	−	0.0378681i
$794$		0			0
$795$		−	4.59650i		−	0.163021i
$796$		0			0
$797$	−3.14834			−0.111520			−0.0557599	−	0.998444i	$-0.517758\pi$
$797$	−3.14834			−0.111520			−0.0557599	+	0.998444i	$0.517758\pi$
$798$		0			0
$799$	−26.9782	+	3.42341i	−0.954419	+	0.121112i
$800$		0			0
$801$			8.37297i			0.295844i
$802$		0			0
$803$			16.9059i			0.596596i
$804$		0			0
$805$	2.99022	+	2.99022i	0.105391	+	0.105391i
$806$		0			0
$807$			11.0226i			0.388013i
$808$		0			0
$809$	13.3467	−	13.3467i	0.469246	−	0.469246i	−0.432424	−	0.901670i	$-0.642342\pi$
$809$	13.3467	−	13.3467i	0.469246	−	0.469246i	0.901670	+	0.432424i	$0.142342\pi$
$810$		0			0
$811$	17.3804	−	17.3804i	0.610308	−	0.610308i	−0.332718	−	0.943026i	$-0.607966\pi$
$811$	17.3804	−	17.3804i	0.610308	−	0.610308i	0.943026	+	0.332718i	$0.107966\pi$
$812$		0			0
$813$	9.44095	−	9.44095i	0.331109	−	0.331109i
$814$		0			0
$815$	9.64159			0.337730
$816$		0			0
$817$	−18.2212			−0.637480
$818$		0			0
$819$	0.380821	−	0.380821i	0.0133070	−	0.0133070i
$820$		0			0
$821$	−22.9239	+	22.9239i	−0.800049	+	0.800049i	−0.983103	−	0.183054i	$-0.941402\pi$
$821$	−22.9239	+	22.9239i	−0.800049	+	0.800049i	0.183054	+	0.983103i	$0.441402\pi$
$822$		0			0
$823$	3.97749	−	3.97749i	0.138647	−	0.138647i	−0.634377	−	0.773024i	$-0.718743\pi$
$823$	3.97749	−	3.97749i	0.138647	−	0.138647i	0.773024	+	0.634377i	$0.218743\pi$
$824$		0			0
$825$		−	2.69881i		−	0.0939605i
$826$		0			0
$827$	−23.9589	−	23.9589i	−0.833131	−	0.833131i	0.154813	−	0.987944i	$-0.450523\pi$
$827$	−23.9589	−	23.9589i	−0.833131	−	0.833131i	−0.987944	+	0.154813i	$0.950523\pi$
$828$		0			0
$829$		−	9.98318i		−	0.346730i	−0.984858	−	0.173365i	$-0.944536\pi$
$829$		−	9.98318i		−	0.346730i	0.984858	−	0.173365i	$-0.0554640\pi$
$830$		0			0
$831$			14.6785i			0.509191i
$832$		0			0
$833$	3.56744	+	28.1131i	0.123604	+	0.974062i
$834$		0			0
$835$	10.7121			0.370709
$836$		0			0
$837$		−	36.9379i		−	1.27676i
$838$		0			0
$839$	−1.99542	+	1.99542i	−0.0688896	+	0.0688896i	−0.740712	−	0.671823i	$-0.765512\pi$
$839$	−1.99542	+	1.99542i	−0.0688896	+	0.0688896i	0.671823	+	0.740712i	$0.265512\pi$
$840$		0			0
$841$		−	80.5110i		−	2.77624i
$842$		0			0
$843$	11.8413	+	11.8413i	0.407835	+	0.407835i
$844$		0			0
$845$	17.5413	−	17.5413i	0.603439	−	0.603439i
$846$		0			0
$847$	0.103536	+	0.103536i	0.00355753	+	0.00355753i
$848$		0			0
$849$	−22.8509			−0.784240
$850$		0			0
$851$		−	24.0936i		−	0.825917i
$852$		0			0
$853$	−31.3759	+	31.3759i	−1.07429	+	1.07429i	−0.0772817	+	0.997009i	$0.524624\pi$
$853$	−31.3759	+	31.3759i	−1.07429	+	1.07429i	−0.997009	+	0.0772817i	$0.975376\pi$
$854$		0			0
$855$	20.7623	+	20.7623i	0.710055	+	0.710055i
$856$		0			0
$857$	25.8756	−	25.8756i	0.883895	−	0.883895i	−0.110033	−	0.993928i	$-0.535096\pi$
$857$	25.8756	−	25.8756i	0.883895	−	0.883895i	0.993928	+	0.110033i	$0.0350957\pi$
$858$		0			0
$859$	38.4115			1.31058			0.655291	−	0.755376i	$-0.272546\pi$
$859$	38.4115			1.31058			0.655291	+	0.755376i	$0.272546\pi$
$860$		0			0
$861$	−0.547088	−	0.547088i	−0.0186447	−	0.0186447i
$862$		0			0
$863$	−40.1320			−1.36611			−0.683055	−	0.730367i	$-0.739349\pi$
$863$	−40.1320			−1.36611			−0.683055	+	0.730367i	$0.739349\pi$
$864$		0			0
$865$			23.5562i			0.800934i
$866$		0			0
$867$	6.28775	−	10.6591i	0.213543	−	0.362002i
$868$		0			0
$869$	2.86313			0.0971249
$870$		0			0
$871$	3.62003			0.122660
$872$		0			0
$873$	−27.6926	+	27.6926i	−0.937252	+	0.937252i
$874$		0			0
$875$	−4.29693			−0.145263
$876$		0			0
$877$	−13.5639	−	13.5639i	−0.458021	−	0.458021i	0.439984	−	0.898005i	$-0.354984\pi$
$877$	−13.5639	−	13.5639i	−0.458021	−	0.458021i	−0.898005	+	0.439984i	$0.854984\pi$
$878$		0			0
$879$	−7.06947	−	7.06947i	−0.238447	−	0.238447i
$880$		0			0
$881$	−18.8555	−	18.8555i	−0.635257	−	0.635257i	0.314124	−	0.949382i	$-0.398289\pi$
$881$	−18.8555	−	18.8555i	−0.635257	−	0.635257i	−0.949382	+	0.314124i	$0.898289\pi$
$882$		0			0
$883$			29.2045i			0.982810i	0.870931	+	0.491405i	$0.163517\pi$
$883$			29.2045i			0.982810i	−0.870931	+	0.491405i	$0.836483\pi$
$884$		0			0
$885$			0.509011i			0.0171102i
$886$		0			0
$887$	−8.50013	−	8.50013i	−0.285406	−	0.285406i	0.549854	−	0.835261i	$-0.314683\pi$
$887$	−8.50013	−	8.50013i	−0.285406	−	0.285406i	−0.835261	+	0.549854i	$0.814683\pi$
$888$		0			0
$889$	−4.91869	−	4.91869i	−0.164968	−	0.164968i
$890$		0			0
$891$	10.3806	+	10.3806i	0.347762	+	0.347762i
$892$		0			0
$893$	−39.9030			−1.33530
$894$		0			0
$895$	−4.92696	+	4.92696i	−0.164690	+	0.164690i
$896$		0			0
$897$	2.69223			0.0898909
$898$		0			0
$899$	−97.0725			−3.23755
$900$		0			0
$901$	13.1443	−	1.66795i	0.437899	−	0.0555675i
$902$		0			0
$903$		−	0.780995i		−	0.0259899i
$904$		0			0
$905$	−29.5085			−0.980895
$906$		0			0
$907$	−3.26001	−	3.26001i	−0.108247	−	0.108247i	0.650909	−	0.759156i	$-0.274388\pi$
$907$	−3.26001	−	3.26001i	−0.108247	−	0.108247i	−0.759156	+	0.650909i	$0.774388\pi$
$908$		0			0
$909$	−44.9310			−1.49027
$910$		0			0
$911$	2.30760	−	2.30760i	0.0764541	−	0.0764541i	−0.667846	−	0.744300i	$-0.732783\pi$
$911$	2.30760	−	2.30760i	0.0764541	−	0.0764541i	0.744300	+	0.667846i	$0.232783\pi$
$912$		0			0
$913$	−20.5289	−	20.5289i	−0.679408	−	0.679408i
$914$		0			0
$915$	−2.49193	+	2.49193i	−0.0823805	+	0.0823805i
$916$		0			0
$917$			3.79157i			0.125209i
$918$		0			0
$919$	27.0170			0.891210			0.445605	−	0.895230i	$-0.352989\pi$
$919$	27.0170			0.891210			0.445605	+	0.895230i	$0.352989\pi$
$920$		0			0
$921$	−10.1886	−	10.1886i	−0.335724	−	0.335724i
$922$		0			0
$923$	1.85504	−	1.85504i	0.0610594	−	0.0610594i
$924$		0			0
$925$	3.21249	+	3.21249i	0.105626	+	0.105626i
$926$		0			0
$927$		−	1.46731i		−	0.0481929i
$928$		0			0
$929$	19.5296	−	19.5296i	0.640747	−	0.640747i	−0.309992	−	0.950739i	$-0.600326\pi$
$929$	19.5296	−	19.5296i	0.640747	−	0.640747i	0.950739	+	0.309992i	$0.100326\pi$
$930$		0			0
$931$			41.5817i			1.36278i
$932$		0			0
$933$	9.24298			0.302602
$934$		0			0
$935$	−26.1527	+	3.31866i	−0.855283	+	0.108532i
$936$		0			0
$937$			14.6044i			0.477105i	0.971130	+	0.238552i	$0.0766728\pi$
$937$			14.6044i			0.477105i	−0.971130	+	0.238552i	$0.923327\pi$
$938$		0			0
$939$			5.99388i			0.195603i
$940$		0			0
$941$	10.9025	+	10.9025i	0.355411	+	0.355411i	0.862118	−	0.506707i	$-0.169137\pi$
$941$	10.9025	+	10.9025i	0.355411	+	0.355411i	−0.506707	+	0.862118i	$0.669137\pi$
$942$		0			0
$943$			18.0273i			0.587049i
$944$		0			0
$945$	−1.97075	+	1.97075i	−0.0641083	+	0.0641083i
$946$		0			0
$947$	−19.3381	+	19.3381i	−0.628404	+	0.628404i	−0.947666	−	0.319262i	$-0.896565\pi$
$947$	−19.3381	+	19.3381i	−0.628404	+	0.628404i	0.319262	+	0.947666i	$0.396565\pi$
$948$		0			0
$949$	2.24863	−	2.24863i	0.0729936	−	0.0729936i
$950$		0			0
$951$	−1.53336			−0.0497226
$952$		0			0
$953$	47.3102			1.53253			0.766265	−	0.642525i	$-0.222113\pi$
$953$	47.3102			1.53253			0.766265	+	0.642525i	$0.222113\pi$
$954$		0			0
$955$	19.3382	−	19.3382i	0.625769	−	0.625769i
$956$		0			0
$957$	−17.5288	+	17.5288i	−0.566627	+	0.566627i
$958$		0			0
$959$	3.96897	−	3.96897i	0.128165	−	0.128165i
$960$		0			0
$961$			55.0467i			1.77570i
$962$		0			0
$963$	−20.8410	−	20.8410i	−0.671593	−	0.671593i
$964$		0			0
$965$			13.3313i			0.429150i
$966$		0			0
$967$			53.2830i			1.71346i	0.515762	+	0.856732i	$0.327509\pi$
$967$			53.2830i			1.71346i	−0.515762	+	0.856732i	$0.672491\pi$
$968$		0			0
$969$	11.1216	−	14.3544i	0.357278	−	0.461131i
$970$		0			0
$971$	29.8647			0.958403			0.479201	−	0.877705i	$-0.340926\pi$
$971$	29.8647			0.958403			0.479201	+	0.877705i	$0.340926\pi$
$972$		0			0
$973$		−	3.74972i		−	0.120210i
$974$		0			0
$975$	−0.358965	+	0.358965i	−0.0114961	+	0.0114961i
$976$		0			0
$977$		−	39.6384i		−	1.26814i	−0.773274	−	0.634072i	$-0.781382\pi$
$977$		−	39.6384i		−	1.26814i	0.773274	−	0.634072i	$-0.218618\pi$
$978$		0			0
$979$	−7.79979	−	7.79979i	−0.249283	−	0.249283i
$980$		0			0
$981$	4.05719	−	4.05719i	0.129536	−	0.129536i
$982$		0			0
$983$	22.5023	+	22.5023i	0.717712	+	0.717712i	0.968136	−	0.250424i	$-0.0805700\pi$
$983$	22.5023	+	22.5023i	0.717712	+	0.717712i	−0.250424	+	0.968136i	$0.580570\pi$
$984$		0			0
$985$	−18.4657			−0.588368
$986$		0			0
$987$		−	1.71032i		−	0.0544399i
$988$		0			0
$989$	−12.8674	+	12.8674i	−0.409160	+	0.409160i
$990$		0			0
$991$	35.2702	+	35.2702i	1.12039	+	1.12039i	0.991682	+	0.128712i	$0.0410843\pi$
$991$	35.2702	+	35.2702i	1.12039	+	1.12039i	0.128712	+	0.991682i	$0.458916\pi$
$992$		0			0
$993$	−12.1549	+	12.1549i	−0.385725	+	0.385725i
$994$		0			0
$995$	−33.5448			−1.06344
$996$		0			0
$997$	−33.5415	−	33.5415i	−1.06227	−	1.06227i	−0.997928	−	0.0643431i	$-0.979505\pi$
$997$	−33.5415	−	33.5415i	−1.06227	−	1.06227i	−0.0643431	−	0.997928i	$-0.520495\pi$
$998$		0			0
$999$	15.8792			0.502396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.m.i.353.8	yes	24
4.3	odd	2		1088.2.m.j.353.5	yes	24
8.3	odd	2	inner	1088.2.m.i.353.7	yes	24
8.5	even	2		1088.2.m.j.353.6	yes	24
17.4	even	4		1088.2.m.j.225.6	yes	24
68.55	odd	4	inner	1088.2.m.i.225.7	✓	24
136.21	even	4	inner	1088.2.m.i.225.8	yes	24
136.123	odd	4		1088.2.m.j.225.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1088.2.m.i.225.7	✓	24	68.55	odd	4	inner
1088.2.m.i.225.8	yes	24	136.21	even	4	inner
1088.2.m.i.353.7	yes	24	8.3	odd	2	inner
1088.2.m.i.353.8	yes	24	1.1	even	1	trivial
1088.2.m.j.225.5	yes	24	136.123	odd	4
1088.2.m.j.225.6	yes	24	17.4	even	4
1088.2.m.j.353.5	yes	24	4.3	odd	2
1088.2.m.j.353.6	yes	24	8.5	even	2

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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.514752 - 0.514752i) q^{3} +(1.38937 - 1.38937i) q^{5} +(-0.251879 + 0.251879i) q^{7} +2.47006i q^{9} +O(q^{10})\)	\(q+(0.514752 - 0.514752i) q^{3} +(1.38937 - 1.38937i) q^{5} +(-0.251879 + 0.251879i) q^{7} +2.47006i q^{9} +(-2.30097 - 2.30097i) q^{11} +0.612098i q^{13} -1.43036i q^{15} +(4.09031 - 0.519042i) q^{17} +6.04990 q^{19} +0.259310i q^{21} +(4.27231 - 4.27231i) q^{23} +1.13929i q^{25} +(2.81572 + 2.81572i) q^{27} +(7.39969 - 7.39969i) q^{29} +(-6.55922 - 6.55922i) q^{31} -2.36886 q^{33} +0.699907i q^{35} +(2.81974 - 2.81974i) q^{37} +(0.315079 + 0.315079i) q^{39} +(-2.10978 + 2.10978i) q^{41} -3.01182 q^{43} +(3.43184 + 3.43184i) q^{45} -6.59564 q^{47} +6.87311i q^{49} +(1.83831 - 2.37267i) q^{51} +3.21352 q^{53} -6.39382 q^{55} +(3.11420 - 3.11420i) q^{57} -0.355861 q^{59} +(-1.74216 - 1.74216i) q^{61} +(-0.622156 - 0.622156i) q^{63} +(0.850433 + 0.850433i) q^{65} -5.91413i q^{67} -4.39836i q^{69} +(-3.03062 - 3.03062i) q^{71} +(-3.67364 - 3.67364i) q^{73} +(0.586450 + 0.586450i) q^{75} +1.15913 q^{77} +(-0.622156 + 0.622156i) q^{79} -4.51138 q^{81} +8.92184 q^{83} +(4.96182 - 6.40410i) q^{85} -7.61801i q^{87} +3.38978 q^{89} +(-0.154175 - 0.154175i) q^{91} -6.75274 q^{93} +(8.40557 - 8.40557i) q^{95} +(11.2113 + 11.2113i) q^{97} +(5.68354 - 5.68354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 4 q^{17} - 24 q^{19} + 16 q^{33} - 16 q^{41} + 32 q^{43} + 40 q^{51} - 48 q^{57} - 64 q^{59} - 16 q^{65} - 8 q^{73} + 32 q^{75} + 88 q^{81} - 144 q^{83} + 24 q^{89} + 48 q^{91} + 32 q^{97} + 40 q^{99}+O(q^{100}) \) 24 * q + 4 * q^17 - 24 * q^19 + 16 * q^33 - 16 * q^41 + 32 * q^43 + 40 * q^51 - 48 * q^57 - 64 * q^59 - 16 * q^65 - 8 * q^73 + 32 * q^75 + 88 * q^81 - 144 * q^83 + 24 * q^89 + 48 * q^91 + 32 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

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