LMFDB - Embedded newform 684.2.f.b.379.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(379,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.f (of order $2$, degree $1$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14453810176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 6x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.7
Root			$1.06789 - 0.927153i$ of defining polynomial
Character	$\chi$	$=$	684.379
Dual form			684.2.f.b.379.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} -1.56155 q^{5} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} +O(q^{10})$	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} -1.56155 q^{5} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} +(-1.66757 + 1.44780i) q^{10} -3.09218i q^{11} -4.74990i q^{13} +(0.804963 + 0.927153i) q^{14} +(-3.84233 - 1.11198i) q^{16} +1.00000 q^{17} +(-3.07221 - 3.09218i) q^{19} +(-0.438447 + 3.09218i) q^{20} +(-2.86692 - 3.30210i) q^{22} +3.96039i q^{23} -2.56155 q^{25} +(-4.40388 - 5.07237i) q^{26} +(1.71922 + 0.243773i) q^{28} -8.45851i q^{29} +4.27156 q^{31} +(-5.13416 + 2.37495i) q^{32} +(1.06789 - 0.927153i) q^{34} -1.35576i q^{35} -3.70861i q^{37} +(-6.14770 - 0.453700i) q^{38} +(2.39871 + 3.70861i) q^{40} -3.70861i q^{41} +11.0129i q^{43} +(-6.12311 - 0.868210i) q^{44} +(3.67188 + 4.22926i) q^{46} +9.27653i q^{47} +6.24621 q^{49} +(-2.73546 + 2.37495i) q^{50} +(-9.40572 - 1.33366i) q^{52} +1.04129i q^{53} +4.82860i q^{55} +(2.06196 - 1.33366i) q^{56} +(-7.84233 - 9.03276i) q^{58} +11.6153 q^{59} -0.684658 q^{61} +(4.56155 - 3.96039i) q^{62} +(-3.28078 + 7.29634i) q^{64} +7.41722i q^{65} +9.74247 q^{67} +(0.280776 - 1.98019i) q^{68} +(-1.25699 - 1.44780i) q^{70} -10.9418 q^{71} +8.12311 q^{73} +(-3.43845 - 3.96039i) q^{74} +(-6.98571 + 5.21535i) q^{76} +2.68466 q^{77} +8.01726 q^{79} +(6.00000 + 1.73642i) q^{80} +(-3.43845 - 3.96039i) q^{82} -9.65719i q^{83} -1.56155 q^{85} +(10.2107 + 11.7606i) q^{86} +(-7.34376 + 4.74990i) q^{88} -5.79119i q^{89} +4.12391 q^{91} +(7.84233 + 1.11198i) q^{92} +(8.60076 + 9.90631i) q^{94} +(4.79741 + 4.82860i) q^{95} -16.9170i q^{97} +(6.67026 - 5.79119i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} + 4 q^{5}+O(q^{10}) $ 8 * q - 6 * q^4 + 4 * q^5	$ 8 q - 6 q^{4} + 4 q^{5} - 6 q^{16} + 8 q^{17} - 20 q^{20} - 4 q^{25} + 6 q^{26} + 22 q^{28} - 18 q^{38} - 16 q^{44} - 16 q^{49} - 38 q^{58} + 44 q^{61} + 20 q^{62} - 18 q^{64} - 6 q^{68} + 32 q^{73} - 44 q^{74} - 16 q^{76} - 28 q^{77} + 48 q^{80} - 44 q^{82} + 4 q^{85} + 38 q^{92}+O(q^{100}) $ 8 * q - 6 * q^4 + 4 * q^5 - 6 * q^16 + 8 * q^17 - 20 * q^20 - 4 * q^25 + 6 * q^26 + 22 * q^28 - 18 * q^38 - 16 * q^44 - 16 * q^49 - 38 * q^58 + 44 * q^61 + 20 * q^62 - 18 * q^64 - 6 * q^68 + 32 * q^73 - 44 * q^74 - 16 * q^76 - 28 * q^77 + 48 * q^80 - 44 * q^82 + 4 * q^85 + 38 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.06789	−	0.927153i	0.755112	−	0.655596i
$2$	1.06789	−	0.927153i	0.755112	−	0.655596i
$3$		0			0
$3$		0			0
$4$	0.280776	−	1.98019i	0.140388	−	0.990097i
$5$	−1.56155			−0.698348			−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155			−0.698348			−0.349174	+	0.937058i	$0.613538\pi$
$6$		0			0
$7$			0.868210i			0.328153i	0.986448	+	0.164076i	$0.0524643\pi$
$7$			0.868210i			0.328153i	−0.986448	+	0.164076i	$0.947536\pi$
$8$	−1.53610	−	2.37495i	−0.543094	−	0.839672i
$9$		0			0
$10$	−1.66757	+	1.44780i	−0.527331	+	0.457834i
$11$		−	3.09218i		−	0.932326i	−0.884699	−	0.466163i	$-0.845636\pi$
$11$		−	3.09218i		−	0.932326i	0.884699	−	0.466163i	$-0.154364\pi$
$12$		0			0
$13$		−	4.74990i		−	1.31739i	−0.752412	−	0.658693i	$-0.771110\pi$
$13$		−	4.74990i		−	1.31739i	0.752412	−	0.658693i	$-0.228890\pi$
$14$	0.804963	+	0.927153i	0.215135	+	0.247792i
$15$		0			0
$16$	−3.84233	−	1.11198i	−0.960582	−	0.277996i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$		0			0
$19$	−3.07221	−	3.09218i	−0.704812	−	0.709394i
$19$	−3.07221	−	3.09218i	−0.704812	−	0.709394i
$20$	−0.438447	+	3.09218i	−0.0980398	+	0.691432i
$21$		0			0
$22$	−2.86692	−	3.30210i	−0.611229	−	0.704011i
$23$			3.96039i			0.825798i	0.910777	+	0.412899i	$0.135484\pi$
$23$			3.96039i			0.825798i	−0.910777	+	0.412899i	$0.864516\pi$
$24$		0			0
$25$	−2.56155			−0.512311
$26$	−4.40388	−	5.07237i	−0.863672	−	0.994773i
$27$		0			0
$28$	1.71922	+	0.243773i	0.324903	+	0.0460687i
$29$		−	8.45851i		−	1.57071i	−0.619048	−	0.785353i	$-0.712481\pi$
$29$		−	8.45851i		−	1.57071i	0.619048	−	0.785353i	$-0.287519\pi$
$30$		0			0
$31$	4.27156			0.767195			0.383597	−	0.923500i	$-0.374685\pi$
$31$	4.27156			0.767195			0.383597	+	0.923500i	$0.374685\pi$
$32$	−5.13416	+	2.37495i	−0.907600	+	0.419836i
$33$		0			0
$34$	1.06789	−	0.927153i	0.183142	−	0.159005i
$35$		−	1.35576i		−	0.229165i
$36$		0			0
$37$		−	3.70861i		−	0.609692i	−0.952402	−	0.304846i	$-0.901395\pi$
$37$		−	3.70861i		−	0.609692i	0.952402	−	0.304846i	$-0.0986050\pi$
$38$	−6.14770	−	0.453700i	−0.997288	−	0.0735998i
$39$		0			0
$40$	2.39871	+	3.70861i	0.379269	+	0.586383i
$41$		−	3.70861i		−	0.579188i	−0.957150	−	0.289594i	$-0.906480\pi$
$41$		−	3.70861i		−	0.579188i	0.957150	−	0.289594i	$-0.0935202\pi$
$42$		0			0
$43$			11.0129i			1.67946i	0.543005	+	0.839729i	$0.317286\pi$
$43$			11.0129i			1.67946i	−0.543005	+	0.839729i	$0.682714\pi$
$44$	−6.12311	−	0.868210i	−0.923093	−	0.130888i
$45$		0			0
$46$	3.67188	+	4.22926i	0.541389	+	0.623570i
$47$			9.27653i			1.35312i	0.736387	+	0.676560i	$0.236530\pi$
$47$			9.27653i			1.35312i	−0.736387	+	0.676560i	$0.763470\pi$
$48$		0			0
$49$	6.24621			0.892316
$50$	−2.73546	+	2.37495i	−0.386852	+	0.335869i
$51$		0			0
$52$	−9.40572	−	1.33366i	−1.30434	−	0.184945i
$53$			1.04129i			0.143032i	0.997439	+	0.0715161i	$0.0227837\pi$
$53$			1.04129i			0.143032i	−0.997439	+	0.0715161i	$0.977216\pi$
$54$		0			0
$55$			4.82860i			0.651088i
$56$	2.06196	−	1.33366i	0.275540	−	0.178218i
$57$		0			0
$58$	−7.84233	−	9.03276i	−1.02975	−	1.18606i
$59$	11.6153			1.51219			0.756093	−	0.654464i	$-0.227106\pi$
$59$	11.6153			1.51219			0.756093	+	0.654464i	$0.227106\pi$
$60$		0			0
$61$	−0.684658			−0.0876615			−0.0438308	−	0.999039i	$-0.513956\pi$
$61$	−0.684658			−0.0876615			−0.0438308	+	0.999039i	$0.513956\pi$
$62$	4.56155	−	3.96039i	0.579318	−	0.502970i
$63$		0			0
$64$	−3.28078	+	7.29634i	−0.410097	+	0.912042i
$65$			7.41722i			0.919993i
$66$		0			0
$67$	9.74247			1.19023			0.595116	−	0.803640i	$-0.297106\pi$
$67$	9.74247			1.19023			0.595116	+	0.803640i	$0.297106\pi$
$68$	0.280776	−	1.98019i	0.0340491	−	0.240134i
$69$		0			0
$70$	−1.25699	−	1.44780i	−0.150239	−	0.173045i
$71$	−10.9418			−1.29856			−0.649278	−	0.760551i	$-0.724929\pi$
$71$	−10.9418			−1.29856			−0.649278	+	0.760551i	$0.724929\pi$
$72$		0			0
$73$	8.12311			0.950738			0.475369	−	0.879787i	$-0.342315\pi$
$73$	8.12311			0.950738			0.475369	+	0.879787i	$0.342315\pi$
$74$	−3.43845	−	3.96039i	−0.399711	−	0.460386i
$75$		0			0
$76$	−6.98571	+	5.21535i	−0.801316	+	0.598242i
$77$	2.68466			0.305945
$78$		0			0
$79$	8.01726			0.902013			0.451006	−	0.892521i	$-0.351065\pi$
$79$	8.01726			0.902013			0.451006	+	0.892521i	$0.351065\pi$
$80$	6.00000	+	1.73642i	0.670820	+	0.194138i
$81$		0			0
$82$	−3.43845	−	3.96039i	−0.379713	−	0.437351i
$83$		−	9.65719i		−	1.06001i	−0.847993	−	0.530007i	$-0.822189\pi$
$83$		−	9.65719i		−	1.06001i	0.847993	−	0.530007i	$-0.177811\pi$
$84$		0			0
$85$	−1.56155			−0.169374
$86$	10.2107	+	11.7606i	1.10105	+	1.26818i
$87$		0			0
$88$	−7.34376	+	4.74990i	−0.782848	+	0.506341i
$89$		−	5.79119i		−	0.613865i	−0.951731	−	0.306932i	$-0.900697\pi$
$89$		−	5.79119i		−	0.613865i	0.951731	−	0.306932i	$-0.0993026\pi$
$90$		0			0
$91$	4.12391			0.432303
$92$	7.84233	+	1.11198i	0.817619	+	0.115932i
$93$		0			0
$94$	8.60076	+	9.90631i	0.887100	+	1.02176i
$95$	4.79741	+	4.82860i	0.492204	+	0.495404i
$96$		0			0
$97$		−	16.9170i		−	1.71766i	−0.512258	−	0.858832i	$-0.671191\pi$
$97$		−	16.9170i		−	1.71766i	0.512258	−	0.858832i	$-0.328809\pi$
$98$	6.67026	−	5.79119i	0.673798	−	0.584999i
$99$		0			0
$100$	−0.719224	+	5.07237i	−0.0719224	+	0.507237i
$101$	−8.24621			−0.820529			−0.410264	−	0.911967i	$-0.634564\pi$
$101$	−8.24621			−0.820529			−0.410264	+	0.911967i	$0.634564\pi$
$102$		0			0
$103$	−3.74571			−0.369075			−0.184538	−	0.982825i	$-0.559079\pi$
$103$	−3.74571			−0.369075			−0.184538	+	0.982825i	$0.559079\pi$
$104$	−11.2808	+	7.29634i	−1.10617	+	0.715465i
$105$		0			0
$106$	0.965435	+	1.11198i	0.0937713	+	0.108005i
$107$	7.86962			0.760785			0.380392	−	0.924825i	$-0.375789\pi$
$107$	7.86962			0.760785			0.380392	+	0.924825i	$0.375789\pi$
$108$		0			0
$109$			15.8757i			1.52062i	0.649561	+	0.760310i	$0.274953\pi$
$109$			15.8757i			1.52062i	−0.649561	+	0.760310i	$0.725047\pi$
$110$	4.47685	+	5.15641i	0.426850	+	0.491644i
$111$		0			0
$112$	0.965435	−	3.33595i	0.0912250	−	0.315218i
$113$			3.70861i			0.348877i	0.984668	+	0.174438i	$0.0558110\pi$
$113$			3.70861i			0.348877i	−0.984668	+	0.174438i	$0.944189\pi$
$114$		0			0
$115$		−	6.18435i		−	0.576694i
$116$	−16.7495	−	2.37495i	−1.55515	−	0.220509i
$117$		0			0
$118$	12.4039	−	10.7692i	1.14187	−	0.991383i
$119$			0.868210i			0.0795887i
$120$		0			0
$121$	1.43845			0.130768
$122$	−0.731140	+	0.634783i	−0.0661943	+	0.0574705i
$123$		0			0
$124$	1.19935	−	8.45851i	0.107705	−	0.759597i
$125$	11.8078			1.05612
$126$		0			0
$127$	−1.87285			−0.166189			−0.0830944	−	0.996542i	$-0.526480\pi$
$127$	−1.87285			−0.166189			−0.0830944	+	0.996542i	$0.526480\pi$
$128$	3.26131	+	10.8335i	0.288262	+	0.957552i
$129$		0			0
$130$	6.87689	+	7.92077i	0.603144	+	0.694698i
$131$			4.82860i			0.421876i	0.977499	+	0.210938i	$0.0676519\pi$
$131$			4.82860i			0.421876i	−0.977499	+	0.210938i	$0.932348\pi$
$132$		0			0
$133$	2.68466	−	2.66732i	0.232789	−	0.231286i
$134$	10.4039	−	9.03276i	0.898759	−	0.780311i
$135$		0			0
$136$	−1.53610	−	2.37495i	−0.131720	−	0.203650i
$137$	3.87689			0.331225			0.165613	−	0.986191i	$-0.447040\pi$
$137$	3.87689			0.331225			0.165613	+	0.986191i	$0.447040\pi$
$138$		0			0
$139$		−	0.380664i		−	0.0322875i	−0.999870	−	0.0161438i	$-0.994861\pi$
$139$		−	0.380664i		−	0.0322875i	0.999870	−	0.0161438i	$-0.00513894\pi$
$140$	−2.68466	−	0.380664i	−0.226895	−	0.0321720i
$141$		0			0
$142$	−11.6847	+	10.1447i	−0.980555	+	0.851328i
$143$	−14.6875			−1.22823
$144$		0			0
$145$			13.2084i			1.09690i
$146$	8.67458	−	7.53136i	0.717913	−	0.623300i
$147$		0			0
$148$	−7.34376	−	1.04129i	−0.603654	−	0.0855935i
$149$	17.8078			1.45887			0.729434	−	0.684051i	$-0.239783\pi$
$149$	17.8078			1.45887			0.729434	+	0.684051i	$0.239783\pi$
$150$		0			0
$151$	−24.2824			−1.97607			−0.988035	−	0.154231i	$-0.950710\pi$
$151$	−24.2824			−1.97607			−0.988035	+	0.154231i	$0.950710\pi$
$152$	−2.62454	+	12.0462i	−0.212878	+	0.977079i
$153$		0			0
$154$	2.86692	−	2.48909i	0.231023	−	0.200576i
$155$	−6.67026			−0.535769
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	8.56155	−	7.43323i	0.681121	−	0.591356i
$159$		0			0
$160$	8.01726	−	3.70861i	0.633820	−	0.293191i
$161$	−3.43845			−0.270988
$162$		0			0
$163$		−	10.6323i		−	0.832785i	−0.909185	−	0.416392i	$-0.863294\pi$
$163$		−	10.6323i		−	0.832785i	0.909185	−	0.416392i	$-0.136706\pi$
$164$	−7.34376	−	1.04129i	−0.573452	−	0.0813111i
$165$		0			0
$166$	−8.95369	−	10.3128i	−0.694941	−	0.800430i
$167$	0.525853			0.0406917			0.0203459	−	0.999793i	$-0.493523\pi$
$167$	0.525853			0.0406917			0.0203459	+	0.999793i	$0.493523\pi$
$168$		0			0
$169$	−9.56155			−0.735504
$170$	−1.66757	+	1.44780i	−0.127896	+	0.111041i
$171$		0			0
$172$	21.8078	+	3.09218i	1.66283	+	0.235776i
$173$			16.9170i			1.28618i	0.765792	+	0.643089i	$0.222347\pi$
$173$			16.9170i			1.28618i	−0.765792	+	0.643089i	$0.777653\pi$
$174$		0			0
$175$		−	2.22397i		−	0.168116i
$176$	−3.43845	+	11.8812i	−0.259183	+	0.895576i
$177$		0			0
$178$	−5.36932	−	6.18435i	−0.402447	−	0.463537i
$179$	9.06897			0.677847			0.338923	−	0.940814i	$-0.389937\pi$
$179$	9.06897			0.677847			0.338923	+	0.940814i	$0.389937\pi$
$180$		0			0
$181$		−	2.08258i		−	0.154797i	−0.997000	−	0.0773985i	$-0.975339\pi$
$181$		−	2.08258i		−	0.154797i	0.997000	−	0.0773985i	$-0.0246614\pi$
$182$	4.40388	−	3.82349i	0.326437	−	0.283416i
$183$		0			0
$184$	9.40572	−	6.08356i	0.693399	−	0.448486i
$185$			5.79119i			0.425777i
$186$		0			0
$187$		−	3.09218i		−	0.226122i
$188$	18.3693	+	2.60463i	1.33972	+	0.189962i
$189$		0			0
$190$	9.59995	+	0.708476i	0.696454	+	0.0513982i
$191$		−	8.78898i		−	0.635948i	−0.948099	−	0.317974i	$-0.896997\pi$
$191$		−	8.78898i		−	0.635948i	0.948099	−	0.317974i	$-0.103003\pi$
$192$		0			0
$193$			3.70861i			0.266952i	0.991052	+	0.133476i	$0.0426138\pi$
$193$			3.70861i			0.266952i	−0.991052	+	0.133476i	$0.957386\pi$
$194$	−15.6847	−	18.0655i	−1.12609	−	1.29703i
$195$		0			0
$196$	1.75379	−	12.3687i	0.125271	−	0.883479i
$197$	−10.4924			−0.747554			−0.373777	−	0.927519i	$-0.621937\pi$
$197$	−10.4924			−0.747554			−0.373777	+	0.927519i	$0.621937\pi$
$198$		0			0
$199$			13.2369i			0.938340i	0.883108	+	0.469170i	$0.155447\pi$
$199$			13.2369i			0.938340i	−0.883108	+	0.469170i	$0.844553\pi$
$200$	3.93481	+	6.08356i	0.278233	+	0.430173i
$201$		0			0
$202$	−8.80604	+	7.64550i	−0.619591	+	0.537935i
$203$	7.34376			0.515431
$204$		0			0
$205$			5.79119i			0.404474i
$206$	−4.00000	+	3.47284i	−0.278693	+	0.241964i
$207$		0			0
$208$	−5.28181	+	18.2507i	−0.366228	+	1.26546i
$209$	−9.56155	+	9.49980i	−0.661386	+	0.657115i
$210$		0			0
$211$	2.02050			0.139097			0.0695485	−	0.997579i	$-0.477844\pi$
$211$	2.02050			0.139097			0.0695485	+	0.997579i	$0.477844\pi$
$212$	2.06196	+	0.292370i	0.141616	+	0.0200800i
$213$		0			0
$214$	8.40388	−	7.29634i	0.574478	−	0.498767i
$215$		−	17.1973i		−	1.17285i
$216$		0			0
$217$			3.70861i			0.251757i
$218$	14.7192	+	16.9535i	0.996912	+	1.14824i
$219$		0			0
$220$	9.56155	+	1.35576i	0.644640	+	0.0914050i
$221$		−	4.74990i		−	0.319513i
$222$		0			0
$223$	16.2651			1.08919			0.544595	−	0.838699i	$-0.316683\pi$
$223$	16.2651			1.08919			0.544595	+	0.838699i	$0.316683\pi$
$224$	−2.06196	−	4.45753i	−0.137770	−	0.297831i
$225$		0			0
$226$	3.43845	+	3.96039i	0.228722	+	0.263441i
$227$	−17.4644			−1.15916			−0.579578	−	0.814917i	$-0.696783\pi$
$227$	−17.4644			−1.15916			−0.579578	+	0.814917i	$0.696783\pi$
$228$		0			0
$229$	−2.43845			−0.161137			−0.0805686	−	0.996749i	$-0.525674\pi$
$229$	−2.43845			−0.161137			−0.0805686	+	0.996749i	$0.525674\pi$
$230$	−5.73384	−	6.60421i	−0.378078	−	0.435468i
$231$		0			0
$232$	−20.0885	+	12.9931i	−1.31888	+	0.853042i
$233$	9.80776			0.642528			0.321264	−	0.946990i	$-0.395892\pi$
$233$	9.80776			0.642528			0.321264	+	0.946990i	$0.395892\pi$
$234$		0			0
$235$		−	14.4858i		−	0.944949i
$236$	3.26131	−	23.0006i	0.212293	−	1.49721i
$237$		0			0
$238$	0.804963	+	0.927153i	0.0521780	+	0.0600984i
$239$			19.4213i			1.25626i	0.778110	+	0.628129i	$0.216179\pi$
$239$			19.4213i			1.25626i	−0.778110	+	0.628129i	$0.783821\pi$
$240$		0			0
$241$		−	15.2910i		−	0.984979i	−0.870318	−	0.492490i	$-0.836087\pi$
$241$		−	15.2910i		−	0.984979i	0.870318	−	0.492490i	$-0.163913\pi$
$242$	1.53610	−	1.33366i	0.0987444	−	0.0857309i
$243$		0			0
$244$	−0.192236	+	1.35576i	−0.0123066	+	0.0867934i
$245$	−9.75379			−0.623147
$246$		0			0
$247$	−14.6875	+	14.5927i	−0.934545	+	0.928509i
$248$	−6.56155	−	10.1447i	−0.416659	−	0.644192i
$249$		0			0
$250$	12.6094	−	10.9476i	0.797488	−	0.692387i
$251$		−	22.4066i		−	1.41429i	−0.707069	−	0.707145i	$-0.749983\pi$
$251$		−	22.4066i		−	1.41429i	0.707069	−	0.707145i	$-0.250017\pi$
$252$		0			0
$253$	12.2462			0.769913
$254$	−2.00000	+	1.73642i	−0.125491	+	0.108953i
$255$		0			0
$256$	13.5270	+	8.54521i	0.845437	+	0.534076i
$257$		−	18.9996i		−	1.18516i	−0.805511	−	0.592581i	$-0.798109\pi$
$257$		−	18.9996i		−	1.18516i	0.805511	−	0.592581i	$-0.201891\pi$
$258$		0			0
$259$	3.21985			0.200072
$260$	14.6875	+	2.08258i	0.910882	+	0.129156i
$261$		0			0
$262$	4.47685	+	5.15641i	0.276580	+	0.318564i
$263$		−	6.56502i		−	0.404816i	−0.979301	−	0.202408i	$-0.935123\pi$
$263$		−	6.56502i		−	0.404816i	0.979301	−	0.202408i	$-0.0648768\pi$
$264$		0			0
$265$		−	1.62603i		−	0.0998862i
$266$	0.393906	−	5.33749i	0.0241520	−	0.327263i
$267$		0			0
$268$	2.73546	−	19.2920i	0.167095	−	1.17844i
$269$		−	3.70861i		−	0.226118i	−0.993588	−	0.113059i	$-0.963935\pi$
$269$		−	3.70861i		−	0.226118i	0.993588	−	0.113059i	$-0.0360649\pi$
$270$		0			0
$271$		−	15.3540i		−	0.932689i	−0.884603	−	0.466345i	$-0.845571\pi$
$271$		−	15.3540i		−	0.932689i	0.884603	−	0.466345i	$-0.154429\pi$
$272$	−3.84233	−	1.11198i	−0.232975	−	0.0674239i
$273$		0			0
$274$	4.14010	−	3.59447i	0.250112	−	0.217150i
$275$			7.92077i			0.477641i
$276$		0			0
$277$	−24.0540			−1.44526			−0.722632	−	0.691233i	$-0.757068\pi$
$277$	−24.0540			−1.44526			−0.722632	+	0.691233i	$0.757068\pi$
$278$	−0.352934	−	0.406507i	−0.0211676	−	0.0243807i
$279$		0			0
$280$	−3.21985	+	2.08258i	−0.192423	+	0.124458i
$281$			11.5824i			0.690947i	0.938429	+	0.345473i	$0.112282\pi$
$281$			11.5824i			0.690947i	−0.938429	+	0.345473i	$0.887718\pi$
$282$		0			0
$283$		−	4.82860i		−	0.287030i	−0.989648	−	0.143515i	$-0.954159\pi$
$283$		−	4.82860i		−	0.287030i	0.989648	−	0.143515i	$-0.0458406\pi$
$284$	−3.07221	+	21.6669i	−0.182302	+	1.28570i
$285$		0			0
$286$	−15.6847	+	13.6176i	−0.927453	+	0.805224i
$287$	3.21985			0.190062
$288$		0			0
$289$	−16.0000			−0.941176
$290$	12.2462	+	14.1051i	0.719122	+	0.828281i
$291$		0			0
$292$	2.28078	−	16.0853i	0.133472	−	0.941322i
$293$		−	4.74990i		−	0.277492i	−0.990328	−	0.138746i	$-0.955693\pi$
$293$		−	4.74990i		−	0.277492i	0.990328	−	0.138746i	$-0.0443072\pi$
$294$		0			0
$295$	−18.1379			−1.05603
$296$	−8.80776	+	5.69681i	−0.511941	+	0.331120i
$297$		0			0
$298$	19.0167	−	16.5105i	1.10161	−	0.956428i
$299$	18.8114			1.08789
$300$		0			0
$301$	−9.56155			−0.551119
$302$	−25.9309	+	22.5134i	−1.49215	+	1.29550i
$303$		0			0
$304$	8.36598	+	15.2974i	0.479822	+	0.877366i
$305$	1.06913			0.0612182
$306$		0			0
$307$	8.01726			0.457569			0.228785	−	0.973477i	$-0.426525\pi$
$307$	8.01726			0.457569			0.228785	+	0.973477i	$0.426525\pi$
$308$	0.753789	−	5.31614i	0.0429511	−	0.302915i
$309$		0			0
$310$	−7.12311	+	6.18435i	−0.404565	+	0.351248i
$311$		−	0.868210i		−	0.0492317i	−0.999697	−	0.0246158i	$-0.992164\pi$
$311$		−	0.868210i		−	0.0492317i	0.999697	−	0.0246158i	$-0.00783626\pi$
$312$		0			0
$313$	−4.56155			−0.257834			−0.128917	−	0.991655i	$-0.541150\pi$
$313$	−4.56155			−0.257834			−0.128917	+	0.991655i	$0.541150\pi$
$314$	6.40734	−	5.56292i	0.361587	−	0.313933i
$315$		0			0
$316$	2.25106	−	15.8757i	0.126632	−	0.893080i
$317$			4.74990i			0.266781i	0.991064	+	0.133390i	$0.0425864\pi$
$317$			4.74990i			0.266781i	−0.991064	+	0.133390i	$0.957414\pi$
$318$		0			0
$319$	−26.1552			−1.46441
$320$	5.12311	−	11.3936i	0.286390	−	0.636922i
$321$		0			0
$322$	−3.67188	+	3.18796i	−0.204626	+	0.177658i
$323$	−3.07221	−	3.09218i	−0.170942	−	0.172053i
$324$		0			0
$325$			12.1671i			0.674910i
$326$	−9.85775	−	11.3541i	−0.545970	−	0.628846i
$327$		0			0
$328$	−8.80776	+	5.69681i	−0.486327	+	0.314554i
$329$	−8.05398			−0.444030
$330$		0			0
$331$	−2.25106			−0.123729			−0.0618647	−	0.998085i	$-0.519705\pi$
$331$	−2.25106			−0.123729			−0.0618647	+	0.998085i	$0.519705\pi$
$332$	−19.1231	−	2.71151i	−1.04952	−	0.148814i
$333$		0			0
$334$	0.561553	−	0.487546i	0.0307268	−	0.0266773i
$335$	−15.2134			−0.831196
$336$		0			0
$337$			26.4168i			1.43902i	0.694484	+	0.719508i	$0.255633\pi$
$337$			26.4168i			1.43902i	−0.694484	+	0.719508i	$0.744367\pi$
$338$	−10.2107	+	8.86502i	−0.555388	+	0.482193i
$339$		0			0
$340$	−0.438447	+	3.09218i	−0.0237781	+	0.167697i
$341$		−	13.2084i		−	0.715276i
$342$		0			0
$343$			11.5005i			0.620968i
$344$	26.1552	−	16.9170i	1.41019	−	0.912105i
$345$		0			0
$346$	15.6847	+	18.0655i	0.843212	+	0.971208i
$347$			24.1430i			1.29606i	0.761613	+	0.648032i	$0.224408\pi$
$347$			24.1430i			1.29606i	−0.761613	+	0.648032i	$0.775592\pi$
$348$		0			0
$349$	−28.0540			−1.50169			−0.750847	−	0.660476i	$-0.770355\pi$
$349$	−28.0540			−1.50169			−0.750847	+	0.660476i	$0.770355\pi$
$350$	−2.06196	−	2.37495i	−0.110216	−	0.126946i
$351$		0			0
$352$	7.34376	+	15.8757i	0.391424	+	0.846179i
$353$	−6.31534			−0.336132			−0.168066	−	0.985776i	$-0.553752\pi$
$353$	−6.31534			−0.336132			−0.168066	+	0.985776i	$0.553752\pi$
$354$		0			0
$355$	17.0862			0.906843
$356$	−11.4677	−	1.62603i	−0.607786	−	0.0861794i
$357$		0			0
$358$	9.68466	−	8.40832i	0.511850	−	0.444393i
$359$			27.3420i			1.44306i	0.692384	+	0.721529i	$0.256560\pi$
$359$			27.3420i			1.44306i	−0.692384	+	0.721529i	$0.743440\pi$
$360$		0			0
$361$	−0.123106	+	18.9996i	−0.00647924	+	0.999979i
$362$	−1.93087	−	2.22397i	−0.101484	−	0.116889i
$363$		0			0
$364$	1.15790	−	8.16614i	0.0606903	−	0.428022i
$365$	−12.6847			−0.663945
$366$		0			0
$367$		−	14.1051i		−	0.736282i	−0.929770	−	0.368141i	$-0.879994\pi$
$367$		−	14.1051i		−	0.736282i	0.929770	−	0.368141i	$-0.120006\pi$
$368$	4.40388	−	15.2171i	0.229568	−	0.793247i
$369$		0			0
$370$	5.36932	+	6.18435i	0.279137	+	0.321509i
$371$	−0.904059			−0.0469364
$372$		0			0
$373$			12.1671i			0.629990i	0.949093	+	0.314995i	$0.102003\pi$
$373$			12.1671i			0.629990i	−0.949093	+	0.314995i	$0.897997\pi$
$374$	−2.86692	−	3.30210i	−0.148245	−	0.170748i
$375$		0			0
$376$	22.0313	−	14.2497i	1.13618	−	0.734872i
$377$	−40.1771			−2.06922
$378$		0			0
$379$	−6.81791			−0.350213			−0.175106	−	0.984550i	$-0.556027\pi$
$379$	−6.81791			−0.350213			−0.175106	+	0.984550i	$0.556027\pi$
$380$	10.9086	−	8.14404i	0.559597	−	0.417781i
$381$		0			0
$382$	−8.14873	−	9.38566i	−0.416925	−	0.480212i
$383$	16.2651			0.831107			0.415554	−	0.909569i	$-0.363588\pi$
$383$	16.2651			0.831107			0.415554	+	0.909569i	$0.363588\pi$
$384$		0			0
$385$	−4.19224			−0.213656
$386$	3.43845	+	3.96039i	0.175012	+	0.201578i
$387$		0			0
$388$	−33.4990	−	4.74990i	−1.70065	−	0.241140i
$389$	5.80776			0.294465			0.147233	−	0.989102i	$-0.452963\pi$
$389$	5.80776			0.294465			0.147233	+	0.989102i	$0.452963\pi$
$390$		0			0
$391$			3.96039i			0.200285i
$392$	−9.59482	−	14.8344i	−0.484612	−	0.749252i
$393$		0			0
$394$	−11.2047	+	9.72808i	−0.564487	+	0.490093i
$395$	−12.5194			−0.629918
$396$		0			0
$397$	24.9309			1.25124			0.625622	−	0.780126i	$-0.284845\pi$
$397$	24.9309			1.25124			0.625622	+	0.780126i	$0.284845\pi$
$398$	12.2726	+	14.1356i	0.615172	+	0.708552i
$399$		0			0
$400$	9.84233	+	2.84840i	0.492116	+	0.142420i
$401$		−	20.6256i		−	1.02999i	−0.857192	−	0.514997i	$-0.827793\pi$
$401$		−	20.6256i		−	1.02999i	0.857192	−	0.514997i	$-0.172207\pi$
$402$		0			0
$403$		−	20.2895i		−	1.01069i
$404$	−2.31534	+	16.3291i	−0.115193	+	0.812403i
$405$		0			0
$406$	7.84233	−	6.80879i	0.389208	−	0.337915i
$407$	−11.4677			−0.568432
$408$		0			0
$409$		−	18.5431i		−	0.916895i	−0.888722	−	0.458447i	$-0.848406\pi$
$409$		−	18.5431i		−	0.916895i	0.888722	−	0.458447i	$-0.151594\pi$
$410$	5.36932	+	6.18435i	0.265172	+	0.305423i
$411$		0			0
$412$	−1.05171	+	7.41722i	−0.0518138	+	0.365420i
$413$			10.0845i			0.496228i
$414$		0			0
$415$			15.0802i			0.740259i
$416$	11.2808	+	24.3868i	0.553086	+	1.19566i
$417$		0			0
$418$	−1.40292	+	19.0098i	−0.0686190	+	0.929798i
$419$		−	27.4489i		−	1.34097i	−0.741924	−	0.670484i	$-0.766087\pi$
$419$		−	27.4489i		−	1.34097i	0.741924	−	0.670484i	$-0.233913\pi$
$420$		0			0
$421$		−	23.2930i		−	1.13523i	−0.823294	−	0.567614i	$-0.807866\pi$
$421$		−	23.2930i		−	1.13523i	0.823294	−	0.567614i	$-0.192134\pi$
$422$	2.15767	−	1.87331i	0.105034	−	0.0911914i
$423$		0			0
$424$	2.47301	−	1.59953i	0.120100	−	0.0776800i
$425$	−2.56155			−0.124254
$426$		0			0
$427$		−	0.594427i		−	0.0287664i
$428$	2.20960	−	15.5834i	0.106805	−	0.753250i
$429$		0			0
$430$	−15.9445	−	18.3648i	−0.768913	−	0.885630i
$431$	−17.0862			−0.823015			−0.411507	−	0.911406i	$-0.634998\pi$
$431$	−17.0862			−0.823015			−0.411507	+	0.911406i	$0.634998\pi$
$432$		0			0
$433$		−	28.0429i		−	1.34765i	−0.738889	−	0.673827i	$-0.764649\pi$
$433$		−	28.0429i		−	1.34765i	0.738889	−	0.673827i	$-0.235351\pi$
$434$	3.43845	+	3.96039i	0.165051	+	0.190105i
$435$		0			0
$436$	31.4370	+	4.45753i	1.50556	+	0.213477i
$437$	12.2462	−	12.1671i	0.585816	−	0.582032i
$438$		0			0
$439$	24.8082			1.18403			0.592015	−	0.805927i	$-0.298332\pi$
$439$	24.8082			1.18403			0.592015	+	0.805927i	$0.298332\pi$
$440$	11.4677	−	7.41722i	0.546700	−	0.353602i
$441$		0			0
$442$	−4.40388	−	5.07237i	−0.209471	−	0.241268i
$443$		−	34.7753i		−	1.65222i	−0.563507	−	0.826111i	$-0.690548\pi$
$443$		−	34.7753i		−	1.65222i	0.563507	−	0.826111i	$-0.309452\pi$
$444$		0			0
$445$			9.04325i			0.428691i
$446$	17.3693	−	15.0802i	0.822461	−	0.714069i
$447$		0			0
$448$	−6.33475	−	2.84840i	−0.299289	−	0.134574i
$449$			35.9166i			1.69501i	0.530787	+	0.847505i	$0.321896\pi$
$449$			35.9166i			1.69501i	−0.530787	+	0.847505i	$0.678104\pi$
$450$		0			0
$451$	−11.4677			−0.539992
$452$	7.34376	+	1.04129i	0.345422	+	0.0489782i
$453$		0			0
$454$	−18.6501	+	16.1922i	−0.875292	+	0.759938i
$455$	−6.43971			−0.301898
$456$		0			0
$457$	12.1231			0.567095			0.283547	−	0.958958i	$-0.408489\pi$
$457$	12.1231			0.567095			0.283547	+	0.958958i	$0.408489\pi$
$458$	−2.60399	+	2.26081i	−0.121677	+	0.105641i
$459$		0			0
$460$	−12.2462	−	1.73642i	−0.570983	−	0.0809610i
$461$	−19.3153			−0.899605			−0.449803	−	0.893128i	$-0.648506\pi$
$461$	−19.3153			−0.899605			−0.449803	+	0.893128i	$0.648506\pi$
$462$		0			0
$463$		−	21.6452i		−	1.00594i	−0.864304	−	0.502970i	$-0.832241\pi$
$463$		−	21.6452i		−	1.00594i	0.864304	−	0.502970i	$-0.167759\pi$
$464$	−9.40572	+	32.5004i	−0.436650	+	1.50879i
$465$		0			0
$466$	10.4736	−	9.09329i	0.485181	−	0.421239i
$467$		−	3.09218i		−	0.143089i	−0.997437	−	0.0715444i	$-0.977207\pi$
$467$		−	3.09218i		−	0.143089i	0.997437	−	0.0715444i	$-0.0227928\pi$
$468$		0			0
$469$			8.45851i			0.390578i
$470$	−13.4305	−	15.4692i	−0.619504	−	0.713542i
$471$		0			0
$472$	−17.8423	−	27.5858i	−0.821260	−	1.26974i
$473$	34.0540			1.56580
$474$		0			0
$475$	7.86962	+	7.92077i	0.361083	+	0.363430i
$476$	1.71922	+	0.243773i	0.0788005	+	0.0111733i
$477$		0			0
$478$	18.0065	+	20.7398i	0.823597	+	0.948615i
$479$		−	8.68210i		−	0.396695i	−0.980132	−	0.198348i	$-0.936442\pi$
$479$		−	8.68210i		−	0.396695i	0.980132	−	0.198348i	$-0.0635575\pi$
$480$		0			0
$481$	−17.6155			−0.803199
$482$	−14.1771	−	16.3291i	−0.645748	−	0.743770i
$483$		0			0
$484$	0.403882	−	2.84840i	0.0183583	−	0.129473i
$485$			26.4168i			1.19953i
$486$		0			0
$487$	9.59482			0.434783			0.217391	−	0.976085i	$-0.430245\pi$
$487$	9.59482			0.434783			0.217391	+	0.976085i	$0.430245\pi$
$488$	1.05171	+	1.62603i	0.0476085	+	0.0736069i
$489$		0			0
$490$	−10.4160	+	9.04325i	−0.470546	+	0.408532i
$491$		−	2.71151i		−	0.122369i	−0.998126	−	0.0611844i	$-0.980512\pi$
$491$		−	2.71151i		−	0.122369i	0.998126	−	0.0611844i	$-0.0194878\pi$
$492$		0			0
$493$		−	8.45851i		−	0.380952i
$494$	−2.15503	+	29.2009i	−0.0969593	+	1.31381i
$495$		0			0
$496$	−16.4127	−	4.74990i	−0.736953	−	0.213277i
$497$		−	9.49980i		−	0.426124i
$498$		0			0
$499$			11.0129i			0.493007i	0.969142	+	0.246504i	$0.0792817\pi$
$499$			11.0129i			0.493007i	−0.969142	+	0.246504i	$0.920718\pi$
$500$	3.31534	−	23.3817i	0.148267	−	1.04566i
$501$		0			0
$502$	−20.7743	−	23.9277i	−0.927202	−	1.06795i
$503$			35.6435i			1.58926i	0.607091	+	0.794632i	$0.292336\pi$
$503$			35.6435i			1.58926i	−0.607091	+	0.794632i	$0.707664\pi$
$504$		0			0
$505$	12.8769			0.573014
$506$	13.0776	−	11.3541i	0.581370	−	0.504752i
$507$		0			0
$508$	−0.525853	+	3.70861i	−0.0233309	+	0.164543i
$509$		−	9.49980i		−	0.421071i	−0.977586	−	0.210536i	$-0.932479\pi$
$509$		−	9.49980i		−	0.421071i	0.977586	−	0.210536i	$-0.0675208\pi$
$510$		0			0
$511$			7.05256i			0.311987i
$512$	22.3680	−	3.41624i	0.988537	−	0.150978i
$513$		0			0
$514$	−17.6155	−	20.2895i	−0.776988	−	0.894930i
$515$	5.84912			0.257743
$516$		0			0
$517$	28.6847			1.26155
$518$	3.43845	−	2.98529i	0.151077	−	0.131166i
$519$		0			0
$520$	17.6155	−	11.3936i	0.772492	−	0.499643i
$521$		−	15.2910i		−	0.669910i	−0.942234	−	0.334955i	$-0.891279\pi$
$521$		−	15.2910i		−	0.669910i	0.942234	−	0.334955i	$-0.108721\pi$
$522$		0			0
$523$	−33.4990			−1.46481			−0.732404	−	0.680871i	$-0.761602\pi$
$523$	−33.4990			−1.46481			−0.732404	+	0.680871i	$0.761602\pi$
$524$	9.56155	+	1.35576i	0.417698	+	0.0592265i
$525$		0			0
$526$	−6.08677	−	7.01071i	−0.265396	−	0.305682i
$527$	4.27156			0.186072
$528$		0			0
$529$	7.31534			0.318058
$530$	−1.50758	−	1.73642i	−0.0654850	−	0.0754253i
$531$		0			0
$532$	−4.52802	−	6.06506i	−0.196315	−	0.262954i
$533$	−17.6155			−0.763013
$534$		0			0
$535$	−12.2888			−0.531292
$536$	−14.9654	−	23.1379i	−0.646408	−	0.999404i
$537$		0			0
$538$	−3.43845	−	3.96039i	−0.148242	−	0.170744i
$539$		−	19.3144i		−	0.831929i
$540$		0			0
$541$	−12.1922			−0.524185			−0.262093	−	0.965043i	$-0.584413\pi$
$541$	−12.1922			−0.524185			−0.262093	+	0.965043i	$0.584413\pi$
$542$	−14.2355	−	16.3964i	−0.611467	−	0.704285i
$543$		0			0
$544$	−5.13416	+	2.37495i	−0.220125	+	0.101825i
$545$		−	24.7908i		−	1.06192i
$546$		0			0
$547$	−19.4849			−0.833116			−0.416558	−	0.909109i	$-0.636764\pi$
$547$	−19.4849			−0.833116			−0.416558	+	0.909109i	$0.636764\pi$
$548$	1.08854	−	7.67700i	0.0465001	−	0.327945i
$549$		0			0
$550$	7.34376	+	8.45851i	0.313139	+	0.360672i
$551$	−26.1552	+	25.9863i	−1.11425	+	1.10705i
$552$		0			0
$553$			6.96067i			0.295998i
$554$	−25.6870	+	22.3017i	−1.09134	+	0.947509i
$555$		0			0
$556$	−0.753789	−	0.106882i	−0.0319678	−	0.00453279i
$557$	18.9309			0.802127			0.401063	−	0.916050i	$-0.368641\pi$
$557$	18.9309			0.802127			0.401063	+	0.916050i	$0.368641\pi$
$558$		0			0
$559$	52.3104			2.21249
$560$	−1.50758	+	5.20926i	−0.0637068	+	0.220131i
$561$		0			0
$562$	10.7386	+	12.3687i	0.452982	+	0.521742i
$563$	33.6466			1.41804			0.709018	−	0.705191i	$-0.249139\pi$
$563$	33.6466			1.41804			0.709018	+	0.705191i	$0.249139\pi$
$564$		0			0
$565$		−	5.79119i		−	0.243637i
$566$	−4.47685	−	5.15641i	−0.188176	−	0.216740i
$567$		0			0
$568$	16.8078	+	25.9863i	0.705238	+	1.09036i
$569$		−	12.7519i		−	0.534586i	−0.963615	−	0.267293i	$-0.913871\pi$
$569$		−	12.7519i		−	0.534586i	0.963615	−	0.267293i	$-0.0861291\pi$
$570$		0			0
$571$		−	17.5780i		−	0.735615i	−0.929902	−	0.367807i	$-0.880109\pi$
$571$		−	17.5780i		−	0.735615i	0.929902	−	0.367807i	$-0.119891\pi$
$572$	−4.12391	+	29.0841i	−0.172429	+	1.21607i
$573$		0			0
$574$	3.43845	−	2.98529i	0.143518	−	0.124604i
$575$		−	10.1447i		−	0.423065i
$576$		0			0
$577$	27.0000			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$578$	−17.0862	+	14.8344i	−0.710694	+	0.617031i
$579$		0			0
$580$	26.1552	+	3.70861i	1.08604	+	0.153992i
$581$	8.38447			0.347847
$582$		0			0
$583$	3.21985			0.133353
$584$	−12.4779	−	19.2920i	−0.516340	−	0.798307i
$585$		0			0
$586$	−4.40388	−	5.07237i	−0.181923	−	0.209538i
$587$			4.82860i			0.199297i	0.995023	+	0.0996487i	$0.0317719\pi$
$587$			4.82860i			0.199297i	−0.995023	+	0.0996487i	$0.968228\pi$
$588$		0			0
$589$	−13.1231	−	13.2084i	−0.540728	−	0.544243i
$590$	−19.3693	+	16.8166i	−0.797422	+	0.692330i
$591$		0			0
$592$	−4.12391	+	14.2497i	−0.169492	+	0.585659i
$593$	36.7386			1.50867			0.754337	−	0.656487i	$-0.227958\pi$
$593$	36.7386			1.50867			0.754337	+	0.656487i	$0.227958\pi$
$594$		0			0
$595$		−	1.35576i		−	0.0555806i
$596$	5.00000	−	35.2628i	0.204808	−	1.44442i
$597$		0			0
$598$	20.0885	−	17.4411i	0.821482	−	0.713219i
$599$	7.72197			0.315511			0.157756	−	0.987478i	$-0.449574\pi$
$599$	7.72197			0.315511			0.157756	+	0.987478i	$0.449574\pi$
$600$		0			0
$601$			39.1687i			1.59772i	0.601514	+	0.798862i	$0.294564\pi$
$601$			39.1687i			1.59772i	−0.601514	+	0.798862i	$0.705436\pi$
$602$	−10.2107	+	8.86502i	−0.416156	+	0.361311i
$603$		0			0
$604$	−6.81791	+	48.0837i	−0.277417	+	1.95650i
$605$	−2.24621			−0.0913215
$606$		0			0
$607$	−13.6358			−0.553461			−0.276730	−	0.960948i	$-0.589251\pi$
$607$	−13.6358			−0.553461			−0.276730	+	0.960948i	$0.589251\pi$
$608$	23.1170	+	8.57940i	0.937517	+	0.347940i
$609$		0			0
$610$	1.14171	−	0.991247i	0.0462266	−	0.0401344i
$611$	44.0626			1.78258
$612$		0			0
$613$	24.3002			0.981475			0.490738	−	0.871307i	$-0.336727\pi$
$613$	24.3002			0.981475			0.490738	+	0.871307i	$0.336727\pi$
$614$	8.56155	−	7.43323i	0.345516	−	0.299981i
$615$		0			0
$616$	−4.12391	−	6.37593i	−0.166157	−	0.256894i
$617$	28.5464			1.14923			0.574617	−	0.818422i	$-0.305151\pi$
$617$	28.5464			1.14923			0.574617	+	0.818422i	$0.305151\pi$
$618$		0			0
$619$			34.3946i			1.38244i	0.722646	+	0.691218i	$0.242926\pi$
$619$			34.3946i			1.38244i	−0.722646	+	0.691218i	$0.757074\pi$
$620$	−1.87285	+	13.2084i	−0.0752156	+	0.530463i
$621$		0			0
$622$	−0.804963	−	0.927153i	−0.0322761	−	0.0371754i
$623$	5.02797			0.201441
$624$		0			0
$625$	−5.63068			−0.225227
$626$	−4.87123	+	4.22926i	−0.194694	+	0.169035i
$627$		0			0
$628$	1.68466	−	11.8812i	0.0672252	−	0.474110i
$629$		−	3.70861i		−	0.147872i
$630$		0			0
$631$		−	12.7494i		−	0.507544i	−0.967264	−	0.253772i	$-0.918329\pi$
$631$		−	12.7494i		−	0.507544i	0.967264	−	0.253772i	$-0.0816713\pi$
$632$	−12.3153	−	19.0406i	−0.489878	−	0.757394i
$633$		0			0
$634$	4.40388	+	5.07237i	0.174900	+	0.201450i
$635$	2.92456			0.116058
$636$		0			0
$637$		−	29.6689i		−	1.17552i
$638$	−27.9309	+	24.2499i	−1.10579	+	0.960061i
$639$		0			0
$640$	−5.09271	−	16.9170i	−0.201307	−	0.668704i
$641$			48.6685i			1.92229i	0.276045	+	0.961145i	$0.410976\pi$
$641$			48.6685i			1.92229i	−0.276045	+	0.961145i	$0.589024\pi$
$642$		0			0
$643$			6.56502i			0.258899i	0.991586	+	0.129449i	$0.0413210\pi$
$643$			6.56502i			0.258899i	−0.991586	+	0.129449i	$0.958679\pi$
$644$	−0.965435	+	6.80879i	−0.0380435	+	0.268304i
$645$		0			0
$646$	−6.14770	−	0.453700i	−0.241878	−	0.0178506i
$647$			36.2379i			1.42466i	0.701845	+	0.712329i	$0.252360\pi$
$647$			36.2379i			1.42466i	−0.701845	+	0.712329i	$0.747640\pi$
$648$		0			0
$649$		−	35.9166i		−	1.40985i
$650$	11.2808	+	12.9931i	0.442468	+	0.509633i
$651$		0			0
$652$	−21.0540	−	2.98529i	−0.824537	−	0.116913i
$653$	45.8078			1.79260			0.896298	−	0.443452i	$-0.146246\pi$
$653$	45.8078			1.79260			0.896298	+	0.443452i	$0.146246\pi$
$654$		0			0
$655$		−	7.54011i		−	0.294616i
$656$	−4.12391	+	14.2497i	−0.161012	+	0.556357i
$657$		0			0
$658$	−8.60076	+	7.46726i	−0.335292	+	0.291104i
$659$	3.36750			0.131179			0.0655896	−	0.997847i	$-0.479107\pi$
$659$	3.36750			0.131179			0.0655896	+	0.997847i	$0.479107\pi$
$660$		0			0
$661$		−	17.5018i		−	0.680740i	−0.940292	−	0.340370i	$-0.889448\pi$
$661$		−	17.5018i		−	0.680740i	0.940292	−	0.340370i	$-0.110552\pi$
$662$	−2.40388	+	2.08707i	−0.0934295	+	0.0811165i
$663$		0			0
$664$	−22.9354	+	14.8344i	−0.890064	+	0.575688i
$665$	−4.19224	+	4.16516i	−0.162568	+	0.161518i
$666$		0			0
$667$	33.4990			1.29709
$668$	0.147647	−	1.04129i	0.00571264	−	0.0402887i
$669$		0			0
$670$	−16.2462	+	14.1051i	−0.627646	+	0.544928i
$671$			2.11708i			0.0817291i
$672$		0			0
$673$			31.7515i			1.22393i	0.790885	+	0.611964i	$0.209620\pi$
$673$			31.7515i			1.22393i	−0.790885	+	0.611964i	$0.790380\pi$
$674$	24.4924	+	28.2102i	0.943413	+	1.08662i
$675$		0			0
$676$	−2.68466	+	18.9337i	−0.103256	+	0.728220i
$677$			4.29335i			0.165007i	0.996591	+	0.0825034i	$0.0262915\pi$
$677$			4.29335i			0.165007i	−0.996591	+	0.0825034i	$0.973708\pi$
$678$		0			0
$679$	14.6875			0.563656
$680$	2.39871	+	3.70861i	0.0919862	+	0.142219i
$681$		0			0
$682$	−12.2462	−	14.1051i	−0.468932	−	0.540113i
$683$	−13.6358			−0.521760			−0.260880	−	0.965371i	$-0.584013\pi$
$683$	−13.6358			−0.521760			−0.260880	+	0.965371i	$0.584013\pi$
$684$		0			0
$685$	−6.05398			−0.231311
$686$	10.6627	+	12.2813i	0.407104	+	0.468901i
$687$		0			0
$688$	12.2462	−	42.3154i	0.466882	−	1.61326i
$689$	4.94602			0.188429
$690$		0			0
$691$			23.3817i			0.889480i	0.895660	+	0.444740i	$0.146704\pi$
$691$			23.3817i			0.889480i	−0.895660	+	0.444740i	$0.853296\pi$
$692$	33.4990	+	4.74990i	1.27344	+	0.180564i
$693$		0			0
$694$	22.3842	+	25.7820i	0.849694	+	0.978673i
$695$			0.594427i			0.0225479i
$696$		0			0
$697$		−	3.70861i		−	0.140474i
$698$	−29.9585	+	26.0103i	−1.13395	+	0.984505i
$699$		0			0
$700$	−4.40388	−	0.624437i	−0.166451	−	0.0236015i
$701$	−29.3693			−1.10926			−0.554632	−	0.832096i	$-0.687141\pi$
$701$	−29.3693			−1.10926			−0.554632	+	0.832096i	$0.687141\pi$
$702$		0			0
$703$	−11.4677	+	11.3936i	−0.432512	+	0.429718i
$704$	22.5616	+	10.1447i	0.850321	+	0.382344i
$705$		0			0
$706$	−6.74409	+	5.85528i	−0.253817	+	0.220367i
$707$		−	7.15944i		−	0.269259i
$708$		0			0
$709$	37.3693			1.40343			0.701717	−	0.712456i	$-0.252417\pi$
$709$	37.3693			1.40343			0.701717	+	0.712456i	$0.252417\pi$
$710$	18.2462	−	15.8415i	0.684768	−	0.594523i
$711$		0			0
$712$	−13.7538	+	8.89586i	−0.515445	+	0.333387i
$713$			16.9170i			0.633547i
$714$		0			0
$715$	22.9354			0.857733
$716$	2.54635	−	17.9583i	0.0951617	−	0.671134i
$717$		0			0
$718$	25.3502	+	29.1983i	0.946063	+	1.08967i
$719$			15.9484i			0.594776i	0.954757	+	0.297388i	$0.0961155\pi$
$719$			15.9484i			0.594776i	−0.954757	+	0.297388i	$0.903885\pi$
$720$		0			0
$721$		−	3.25206i		−	0.121113i
$722$	17.4841	+	20.4036i	0.650690	+	0.759344i
$723$		0			0
$724$	−4.12391	−	0.584739i	−0.153264	−	0.0217317i
$725$			21.6669i			0.804689i
$726$		0			0
$727$			23.6554i			0.877332i	0.898650	+	0.438666i	$0.144549\pi$
$727$			23.6554i			0.877332i	−0.898650	+	0.438666i	$0.855451\pi$
$728$	−6.33475	−	9.79408i	−0.234782	−	0.362993i
$729$		0			0
$730$	−13.5458	+	11.7606i	−0.501353	+	0.435280i
$731$			11.0129i			0.407329i
$732$		0			0
$733$	3.12311			0.115355			0.0576773	−	0.998335i	$-0.481631\pi$
$733$	3.12311			0.115355			0.0576773	+	0.998335i	$0.481631\pi$
$734$	−13.0776	−	15.0627i	−0.482703	−	0.555975i
$735$		0			0
$736$	−9.40572	−	20.3333i	−0.346699	−	0.749494i
$737$		−	30.1254i		−	1.10968i
$738$		0			0
$739$			30.3273i			1.11561i	0.829972	+	0.557804i	$0.188356\pi$
$739$			30.3273i			1.11561i	−0.829972	+	0.557804i	$0.811644\pi$
$740$	11.4677	+	1.62603i	0.421560	+	0.0597740i
$741$		0			0
$742$	−0.965435	+	0.838200i	−0.0354422	+	0.0307713i
$743$	−38.4440			−1.41037			−0.705187	−	0.709021i	$-0.749137\pi$
$743$	−38.4440			−1.41037			−0.705187	+	0.709021i	$0.749137\pi$
$744$		0			0
$745$	−27.8078			−1.01880
$746$	11.2808	+	12.9931i	0.413019	+	0.475713i
$747$		0			0
$748$	−6.12311	−	0.868210i	−0.223883	−	0.0317449i
$749$			6.83248i			0.249653i
$750$		0			0
$751$	8.24782			0.300967			0.150484	−	0.988612i	$-0.451917\pi$
$751$	8.24782			0.300967			0.150484	+	0.988612i	$0.451917\pi$
$752$	10.3153	−	35.6435i	0.376162	−	1.29978i
$753$		0			0
$754$	−42.9047	+	37.2503i	−1.56250	+	1.35658i
$755$	37.9182			1.37998
$756$		0			0
$757$	−24.1922			−0.879282			−0.439641	−	0.898174i	$-0.644894\pi$
$757$	−24.1922			−0.879282			−0.439641	+	0.898174i	$0.644894\pi$
$758$	−7.28078	+	6.32124i	−0.264450	+	0.229598i
$759$		0			0
$760$	4.09836	−	18.8108i	0.148663	−	0.682341i
$761$	10.6155			0.384813			0.192406	−	0.981315i	$-0.438371\pi$
$761$	10.6155			0.384813			0.192406	+	0.981315i	$0.438371\pi$
$762$		0			0
$763$	−13.7835			−0.498995
$764$	−17.4039	−	2.46774i	−0.629650	−	0.0892797i
$765$		0			0
$766$	17.3693	−	15.0802i	0.627579	−	0.544870i
$767$		−	55.1716i		−	1.99213i
$768$		0			0
$769$	54.2311			1.95562			0.977811	−	0.209489i	$-0.0671801\pi$
$769$	54.2311			1.95562			0.977811	+	0.209489i	$0.0671801\pi$
$770$	−4.47685	+	3.88684i	−0.161334	+	0.140072i
$771$		0			0
$772$	7.34376	+	1.04129i	0.264308	+	0.0374769i
$773$			25.8321i			0.929115i	0.885543	+	0.464558i	$0.153787\pi$
$773$			25.8321i			0.929115i	−0.885543	+	0.464558i	$0.846213\pi$
$774$		0			0
$775$	−10.9418			−0.393042
$776$	−40.1771	+	25.9863i	−1.44227	+	0.932853i
$777$		0			0
$778$	6.20205	−	5.38468i	0.222354	−	0.193050i
$779$	−11.4677	+	11.3936i	−0.410872	+	0.408219i
$780$		0			0
$781$			33.8340i			1.21068i
$782$	3.67188	+	4.22926i	0.131306	+	0.151238i
$783$		0			0
$784$	−24.0000	−	6.94568i	−0.857143	−	0.248060i
$785$	−9.36932			−0.334405
$786$		0			0
$787$	40.9904			1.46115			0.730575	−	0.682833i	$-0.239252\pi$
$787$	40.9904			1.46115			0.730575	+	0.682833i	$0.239252\pi$
$788$	−2.94602	+	20.7770i	−0.104948	+	0.740151i
$789$		0			0
$790$	−13.3693	+	11.6074i	−0.475659	+	0.412972i
$791$	−3.21985			−0.114485
$792$		0			0
$793$			3.25206i			0.115484i
$794$	26.6234	−	23.1147i	0.944830	−	0.820311i
$795$		0			0
$796$	26.2116	+	3.71661i	0.929047	+	0.131732i
$797$		−	23.2930i		−	0.825079i	−0.910940	−	0.412539i	$-0.864642\pi$
$797$		−	23.2930i		−	0.825079i	0.910940	−	0.412539i	$-0.135358\pi$
$798$		0			0
$799$			9.27653i			0.328180i
$800$	13.1514	−	6.08356i	0.464973	−	0.215086i
$801$		0			0
$802$	−19.1231	−	22.0259i	−0.675260	−	0.777761i
$803$		−	25.1181i		−	0.886398i
$804$		0			0
$805$	5.36932			0.189244
$806$	−18.8114	−	21.6669i	−0.662605	−	0.763185i
$807$		0			0
$808$	12.6670	+	19.5843i	0.445624	+	0.688975i
$809$	−19.6307			−0.690178			−0.345089	−	0.938570i	$-0.612151\pi$
$809$	−19.6307			−0.690178			−0.345089	+	0.938570i	$0.612151\pi$
$810$		0			0
$811$	−0.378206			−0.0132806			−0.00664030	−	0.999978i	$-0.502114\pi$
$811$	−0.378206			−0.0132806			−0.00664030	+	0.999978i	$0.502114\pi$
$812$	2.06196	−	14.5421i	0.0723605	−	0.510327i
$813$		0			0
$814$	−12.2462	+	10.6323i	−0.429229	+	0.372661i
$815$			16.6029i			0.581573i
$816$		0			0
$817$	34.0540	−	33.8340i	1.19140	−	1.18370i
$818$	−17.1922	−	19.8019i	−0.601112	−	0.692358i
$819$		0			0
$820$	11.4677	+	1.62603i	0.400469	+	0.0567834i
$821$	−33.4233			−1.16648			−0.583240	−	0.812300i	$-0.698215\pi$
$821$	−33.4233			−1.16648			−0.583240	+	0.812300i	$0.698215\pi$
$822$		0			0
$823$			22.1328i			0.771500i	0.922603	+	0.385750i	$0.126057\pi$
$823$			22.1328i			0.771500i	−0.922603	+	0.385750i	$0.873943\pi$
$824$	5.75379	+	8.89586i	0.200443	+	0.309902i
$825$		0			0
$826$	9.34991	+	10.7692i	0.325325	+	0.374708i
$827$	25.1864			0.875817			0.437909	−	0.899019i	$-0.355719\pi$
$827$	25.1864			0.875817			0.437909	+	0.899019i	$0.355719\pi$
$828$		0			0
$829$		−	8.91506i		−	0.309633i	−0.987943	−	0.154816i	$-0.950521\pi$
$829$		−	8.91506i		−	0.309633i	0.987943	−	0.154816i	$-0.0494786\pi$
$830$	13.9817	+	16.1040i	0.485311	+	0.558978i
$831$		0			0
$832$	34.6569	+	15.5834i	1.20151	+	0.540256i
$833$	6.24621			0.216418
$834$		0			0
$835$	−0.821147			−0.0284170
$836$	16.1268	+	21.6010i	0.557756	+	0.747088i
$837$		0			0
$838$	−25.4493	−	29.3124i	−0.879133	−	1.01258i
$839$	−51.2587			−1.76965			−0.884823	−	0.465926i	$-0.845721\pi$
$839$	−51.2587			−1.76965			−0.884823	+	0.465926i	$0.845721\pi$
$840$		0			0
$841$	−42.5464			−1.46712
$842$	−21.5961	−	24.8743i	−0.744251	−	0.857225i
$843$		0			0
$844$	0.567309	−	4.00098i	0.0195276	−	0.137719i
$845$	14.9309			0.513638
$846$		0			0
$847$			1.24887i			0.0429118i
$848$	1.15790	−	4.00098i	0.0397623	−	0.137394i
$849$		0			0
$850$	−2.73546	+	2.37495i	−0.0938254	+	0.0814601i
$851$	14.6875			0.503482
$852$		0			0
$853$	6.63068			0.227030			0.113515	−	0.993536i	$-0.463789\pi$
$853$	6.63068			0.227030			0.113515	+	0.993536i	$0.463789\pi$
$854$	−0.551125	−	0.634783i	−0.0188591	−	0.0217218i
$855$		0			0
$856$	−12.0885	−	18.6899i	−0.413178	−	0.638809i
$857$		−	4.16516i		−	0.142279i	−0.997466	−	0.0711396i	$-0.977336\pi$
$857$		−	4.16516i		−	0.142279i	0.997466	−	0.0711396i	$-0.0226636\pi$
$858$		0			0
$859$		−	22.6203i		−	0.771795i	−0.922542	−	0.385898i	$-0.873892\pi$
$859$		−	22.6203i		−	0.771795i	0.922542	−	0.385898i	$-0.126108\pi$
$860$	−34.0540	−	4.82860i	−1.16123	−	0.164654i
$861$		0			0
$862$	−18.2462	+	15.8415i	−0.621468	+	0.539565i
$863$	22.7048			0.772880			0.386440	−	0.922315i	$-0.373705\pi$
$863$	22.7048			0.772880			0.386440	+	0.922315i	$0.373705\pi$
$864$		0			0
$865$		−	26.4168i		−	0.898199i
$866$	−26.0000	−	29.9467i	−0.883516	−	1.01763i
$867$		0			0
$868$	7.34376	+	1.04129i	0.249264	+	0.0353437i
$869$		−	24.7908i		−	0.840970i
$870$		0			0
$871$		−	46.2758i		−	1.56799i
$872$	37.7041	−	24.3868i	1.27682	−	0.825840i
$873$		0			0
$874$	1.79683	−	24.3472i	0.0607785	−	0.823558i
$875$			10.2516i			0.346568i
$876$		0			0
$877$			14.2497i			0.481178i	0.970627	+	0.240589i	$0.0773406\pi$
$877$			14.2497i			0.481178i	−0.970627	+	0.240589i	$0.922659\pi$
$878$	26.4924	−	23.0010i	0.894076	−	0.776246i
$879$		0			0
$880$	5.36932	−	18.5531i	0.181000	−	0.625423i
$881$	−35.1771			−1.18515			−0.592573	−	0.805517i	$-0.701888\pi$
$881$	−35.1771			−1.18515			−0.592573	+	0.805517i	$0.701888\pi$
$882$		0			0
$883$			0.594427i			0.0200041i	0.999950	+	0.0100020i	$0.00318380\pi$
$883$			0.594427i			0.0200041i	−0.999950	+	0.0100020i	$0.996816\pi$
$884$	−9.40572	−	1.33366i	−0.316349	−	0.0448558i
$885$		0			0
$886$	−32.2420	−	37.1361i	−1.08319	−	1.24761i
$887$	31.4785			1.05694			0.528472	−	0.848951i	$-0.322765\pi$
$887$	31.4785			1.05694			0.528472	+	0.848951i	$0.322765\pi$
$888$		0			0
$889$		−	1.62603i		−	0.0545353i
$890$	8.38447	+	9.65719i	0.281048	+	0.323710i
$891$		0			0
$892$	4.56685	−	32.2080i	0.152910	−	1.07840i
$893$	28.6847	−	28.4994i	0.959895	−	0.953696i
$894$		0			0
$895$	−14.1617			−0.473373
$896$	−9.40572	+	2.83150i	−0.314223	+	0.0945938i
$897$		0			0
$898$	33.3002	+	38.3550i	1.11124	+	1.27992i
$899$		−	36.1310i		−	1.20504i
$900$		0			0
$901$			1.04129i			0.0346904i
$902$	−12.2462	+	10.6323i	−0.407754	+	0.354016i
$903$		0			0
$904$	8.80776	−	5.69681i	0.292942	−	0.189473i
$905$			3.25206i			0.108102i
$906$		0			0
$907$	36.7188			1.21923			0.609614	−	0.792698i	$-0.291324\pi$
$907$	36.7188			1.21923			0.609614	+	0.792698i	$0.291324\pi$
$908$	−4.90360	+	34.5830i	−0.162732	+	1.14768i
$909$		0			0
$910$	−6.87689	+	5.97059i	−0.227967	+	0.197923i
$911$	−10.6465			−0.352735			−0.176368	−	0.984324i	$-0.556435\pi$
$911$	−10.6465			−0.352735			−0.176368	+	0.984324i	$0.556435\pi$
$912$		0			0
$913$	−29.8617			−0.988279
$914$	12.9461	−	11.2400i	0.428220	−	0.371785i
$915$		0			0
$916$	−0.684658	+	4.82860i	−0.0226218	+	0.159541i
$917$	−4.19224			−0.138440
$918$		0			0
$919$		−	12.8563i		−	0.424089i	−0.977260	−	0.212044i	$-0.931988\pi$
$919$		−	12.8563i		−	0.424089i	0.977260	−	0.212044i	$-0.0680121\pi$
$920$	−14.6875	+	9.49980i	−0.484233	+	0.313199i
$921$		0			0
$922$	−20.6267	+	17.9083i	−0.679303	+	0.589777i
$923$			51.9726i			1.71070i
$924$		0			0
$925$			9.49980i			0.312352i
$926$	−20.0684	−	23.1147i	−0.659490	−	0.759597i
$927$		0			0
$928$	20.0885	+	43.4274i	0.659439	+	1.42557i
$929$	25.6847			0.842686			0.421343	−	0.906901i	$-0.361559\pi$
$929$	25.6847			0.842686			0.421343	+	0.906901i	$0.361559\pi$
$930$		0			0
$931$	−19.1896	−	19.3144i	−0.628915	−	0.633003i
$932$	2.75379	−	19.4213i	0.0902033	−	0.636165i
$933$		0			0
$934$	−2.86692	−	3.30210i	−0.0938084	−	0.108048i
$935$			4.82860i			0.157912i
$936$		0			0
$937$	−22.1231			−0.722730			−0.361365	−	0.932424i	$-0.617689\pi$
$937$	−22.1231			−0.722730			−0.361365	+	0.932424i	$0.617689\pi$
$938$	7.84233	+	9.03276i	0.256061	+	0.294930i
$939$		0			0
$940$	−28.6847	−	4.06727i	−0.935590	−	0.132660i
$941$		−	24.9190i		−	0.812336i	−0.913799	−	0.406168i	$-0.866865\pi$
$941$		−	24.9190i		−	0.812336i	0.913799	−	0.406168i	$-0.133135\pi$
$942$		0			0
$943$	14.6875			0.478292
$944$	−44.6299	−	12.9160i	−1.45258	−	0.420381i
$945$		0			0
$946$	36.3659	−	31.5732i	1.18236	−	1.02653i
$947$		−	2.71151i		−	0.0881123i	−0.999029	−	0.0440561i	$-0.985972\pi$
$947$		−	2.71151i		−	0.0881123i	0.999029	−	0.0440561i	$-0.0140280\pi$
$948$		0			0
$949$		−	38.5839i		−	1.25249i
$950$	15.7476	+	1.16218i	0.510921	+	0.0377059i
$951$		0			0
$952$	2.06196	−	1.33366i	0.0668284	−	0.0432242i
$953$		−	24.7908i		−	0.803053i	−0.915848	−	0.401526i	$-0.868480\pi$
$953$		−	24.7908i		−	0.803053i	0.915848	−	0.401526i	$-0.131520\pi$
$954$		0			0
$955$			13.7245i			0.444113i
$956$	38.4579	+	5.45303i	1.24382	+	0.176364i
$957$		0			0
$958$	−8.04963	−	9.27153i	−0.260072	−	0.299549i
$959$			3.36596i			0.108692i
$960$		0			0
$961$	−12.7538			−0.411413
$962$	−18.8114	+	16.3323i	−0.606505	+	0.526574i
$963$		0			0
$964$	−30.2791	−	4.29335i	−0.975225	−	0.138279i
$965$		−	5.79119i		−	0.186425i
$966$		0			0
$967$			26.4738i			0.851341i	0.904878	+	0.425670i	$0.139962\pi$
$967$			26.4738i			0.851341i	−0.904878	+	0.425670i	$0.860038\pi$
$968$	−2.20960	−	3.41624i	−0.0710193	−	0.109802i
$969$		0			0
$970$	24.4924	+	28.2102i	0.786404	+	0.905777i
$971$	−19.4849			−0.625301			−0.312651	−	0.949868i	$-0.601217\pi$
$971$	−19.4849			−0.625301			−0.312651	+	0.949868i	$0.601217\pi$
$972$		0			0
$973$	0.330497			0.0105952
$974$	10.2462	−	8.89586i	0.328310	−	0.285042i
$975$		0			0
$976$	2.63068	+	0.761329i	0.0842061	+	0.0243695i
$977$			26.8734i			0.859755i	0.902887	+	0.429878i	$0.141443\pi$
$977$			26.8734i			0.859755i	−0.902887	+	0.429878i	$0.858557\pi$
$978$		0			0
$979$	−17.9074			−0.572322
$980$	−2.73863	+	19.3144i	−0.0874824	+	0.616975i
$981$		0			0
$982$	−2.51398	−	2.89560i	−0.0802245	−	0.0924022i
$983$	13.3405			0.425497			0.212748	−	0.977107i	$-0.431759\pi$
$983$	13.3405			0.425497			0.212748	+	0.977107i	$0.431759\pi$
$984$		0			0
$985$	16.3845			0.522053
$986$	−7.84233	−	9.03276i	−0.249751	−	0.287662i
$987$		0			0
$988$	24.7724	+	33.1814i	0.788115	+	1.05564i
$989$	−43.6155			−1.38689
$990$		0			0
$991$	−54.1833			−1.72119			−0.860594	−	0.509292i	$-0.829907\pi$
$991$	−54.1833			−1.72119			−0.860594	+	0.509292i	$0.829907\pi$
$992$	−21.9309	+	10.1447i	−0.696306	+	0.322096i
$993$		0			0
$994$	−8.80776	−	10.1447i	−0.279365	−	0.321772i
$995$		−	20.6701i		−	0.655288i
$996$		0			0
$997$	−28.5464			−0.904073			−0.452037	−	0.891999i	$-0.649302\pi$
$997$	−28.5464			−0.904073			−0.452037	+	0.891999i	$0.649302\pi$
$998$	10.2107	+	11.7606i	0.323214	+	0.372276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.f.b.379.7		8
3.2	odd	2		76.2.d.a.75.2	yes	8
4.3	odd	2	inner	684.2.f.b.379.1		8
12.11	even	2		76.2.d.a.75.8	yes	8
19.18	odd	2	inner	684.2.f.b.379.2		8
24.5	odd	2		1216.2.h.d.1215.4		8
24.11	even	2		1216.2.h.d.1215.5		8
57.56	even	2		76.2.d.a.75.7	yes	8
76.75	even	2	inner	684.2.f.b.379.8		8
228.227	odd	2		76.2.d.a.75.1	✓	8
456.227	odd	2		1216.2.h.d.1215.3		8
456.341	even	2		1216.2.h.d.1215.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.d.a.75.1	✓	8	228.227	odd	2
76.2.d.a.75.2	yes	8	3.2	odd	2
76.2.d.a.75.7	yes	8	57.56	even	2
76.2.d.a.75.8	yes	8	12.11	even	2
684.2.f.b.379.1		8	4.3	odd	2	inner
684.2.f.b.379.2		8	19.18	odd	2	inner
684.2.f.b.379.7		8	1.1	even	1	trivial
684.2.f.b.379.8		8	76.75	even	2	inner
1216.2.h.d.1215.3		8	456.227	odd	2
1216.2.h.d.1215.4		8	24.5	odd	2
1216.2.h.d.1215.5		8	24.11	even	2
1216.2.h.d.1215.6		8	456.341	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} -1.56155 q^{5} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} +O(q^{10})\)	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} -1.56155 q^{5} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} +(-1.66757 + 1.44780i) q^{10} -3.09218i q^{11} -4.74990i q^{13} +(0.804963 + 0.927153i) q^{14} +(-3.84233 - 1.11198i) q^{16} +1.00000 q^{17} +(-3.07221 - 3.09218i) q^{19} +(-0.438447 + 3.09218i) q^{20} +(-2.86692 - 3.30210i) q^{22} +3.96039i q^{23} -2.56155 q^{25} +(-4.40388 - 5.07237i) q^{26} +(1.71922 + 0.243773i) q^{28} -8.45851i q^{29} +4.27156 q^{31} +(-5.13416 + 2.37495i) q^{32} +(1.06789 - 0.927153i) q^{34} -1.35576i q^{35} -3.70861i q^{37} +(-6.14770 - 0.453700i) q^{38} +(2.39871 + 3.70861i) q^{40} -3.70861i q^{41} +11.0129i q^{43} +(-6.12311 - 0.868210i) q^{44} +(3.67188 + 4.22926i) q^{46} +9.27653i q^{47} +6.24621 q^{49} +(-2.73546 + 2.37495i) q^{50} +(-9.40572 - 1.33366i) q^{52} +1.04129i q^{53} +4.82860i q^{55} +(2.06196 - 1.33366i) q^{56} +(-7.84233 - 9.03276i) q^{58} +11.6153 q^{59} -0.684658 q^{61} +(4.56155 - 3.96039i) q^{62} +(-3.28078 + 7.29634i) q^{64} +7.41722i q^{65} +9.74247 q^{67} +(0.280776 - 1.98019i) q^{68} +(-1.25699 - 1.44780i) q^{70} -10.9418 q^{71} +8.12311 q^{73} +(-3.43845 - 3.96039i) q^{74} +(-6.98571 + 5.21535i) q^{76} +2.68466 q^{77} +8.01726 q^{79} +(6.00000 + 1.73642i) q^{80} +(-3.43845 - 3.96039i) q^{82} -9.65719i q^{83} -1.56155 q^{85} +(10.2107 + 11.7606i) q^{86} +(-7.34376 + 4.74990i) q^{88} -5.79119i q^{89} +4.12391 q^{91} +(7.84233 + 1.11198i) q^{92} +(8.60076 + 9.90631i) q^{94} +(4.79741 + 4.82860i) q^{95} -16.9170i q^{97} +(6.67026 - 5.79119i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} + 4 q^{5}+O(q^{10}) \) 8 * q - 6 * q^4 + 4 * q^5	\( 8 q - 6 q^{4} + 4 q^{5} - 6 q^{16} + 8 q^{17} - 20 q^{20} - 4 q^{25} + 6 q^{26} + 22 q^{28} - 18 q^{38} - 16 q^{44} - 16 q^{49} - 38 q^{58} + 44 q^{61} + 20 q^{62} - 18 q^{64} - 6 q^{68} + 32 q^{73} - 44 q^{74} - 16 q^{76} - 28 q^{77} + 48 q^{80} - 44 q^{82} + 4 q^{85} + 38 q^{92}+O(q^{100}) \) 8 * q - 6 * q^4 + 4 * q^5 - 6 * q^16 + 8 * q^17 - 20 * q^20 - 4 * q^25 + 6 * q^26 + 22 * q^28 - 18 * q^38 - 16 * q^44 - 16 * q^49 - 38 * q^58 + 44 * q^61 + 20 * q^62 - 18 * q^64 - 6 * q^68 + 32 * q^73 - 44 * q^74 - 16 * q^76 - 28 * q^77 + 48 * q^80 - 44 * q^82 + 4 * q^85 + 38 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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