LMFDB - Embedded newform 968.2.ba.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(19,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 55, 83]))

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

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

chi := DirichletCharacter("968.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.ba (of order $110$, degree $40$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$2$ over $\Q(\zeta_{110})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{110}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	968.107
Dual form			968.2.ba.a.579.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.320315 + 1.37746i) q^{2} +(0.484606 + 1.49147i) q^{3} +(-1.79480 - 0.882442i) q^{4} +(-2.20966 + 0.189788i) q^{6} +(1.79043 - 2.18960i) q^{8} +(0.437426 - 0.317808i) q^{9} +(2.13041 - 2.54192i) q^{11} +(0.446362 - 3.10451i) q^{12} +(2.44259 + 3.16761i) q^{16} +(8.01441 + 1.62393i) q^{17} +(0.297655 + 0.704335i) q^{18} +(-0.466385 + 4.06474i) q^{19} +(2.81900 + 3.74877i) q^{22} +(4.13337 + 1.60927i) q^{24} +(-3.68371 + 3.38087i) q^{25} +(4.49213 + 3.26372i) q^{27} +(-5.14566 + 2.34994i) q^{32} +(4.82360 + 1.94560i) q^{33} +(-4.80403 + 10.5194i) q^{34} +(-1.06554 + 0.184399i) q^{36} +(-5.44963 - 1.94442i) q^{38} +(1.84738 + 1.11401i) q^{41} +(-6.65305 - 10.3523i) q^{43} +(-6.06675 + 2.68227i) q^{44} +(-3.54068 + 5.17808i) q^{48} +(6.98858 + 0.399622i) q^{49} +(-3.47708 - 6.15710i) q^{50} +(1.46180 + 12.7402i) q^{51} +(-5.93454 + 5.14231i) q^{54} +(-6.28843 + 1.27420i) q^{57} +(0.441736 + 0.732536i) q^{59} +(-1.58872 - 7.84066i) q^{64} +(-4.22505 + 6.02111i) q^{66} +(2.45163 + 2.82933i) q^{67} +(-12.9512 - 9.98688i) q^{68} +(0.0873057 - 1.52680i) q^{72} +(8.57926 + 5.86635i) q^{73} +(-6.82760 - 3.85573i) q^{75} +(4.42396 - 6.88382i) q^{76} +(-2.18957 + 6.73880i) q^{81} +(-2.12625 + 2.18786i) q^{82} +(-2.78648 + 7.80967i) q^{83} +(16.3910 - 5.84830i) q^{86} +(-1.75146 - 9.21588i) q^{88} +(6.25292 + 13.6920i) q^{89} +(-5.99848 - 6.53577i) q^{96} +(5.82399 - 14.9588i) q^{97} +(-2.78901 + 9.49850i) q^{98} +(0.124051 - 1.78896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} - 4 q^{4} + 20 q^{6} - 64 q^{9} - 6 q^{11} + 36 q^{12} + 8 q^{16} - 40 q^{18} + 10 q^{19} + 4 q^{22} + 40 q^{24} + 10 q^{25} - 38 q^{27} + 38 q^{33} - 16 q^{34} - 24 q^{36} + 24 q^{38} - 48 q^{44}+ \cdots - 6 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 - 4 * q^4 + 20 * q^6 - 64 * q^9 - 6 * q^11 + 36 * q^12 + 8 * q^16 - 40 * q^18 + 10 * q^19 + 4 * q^22 + 40 * q^24 + 10 * q^25 - 38 * q^27 + 38 * q^33 - 16 * q^34 - 24 * q^36 + 24 * q^38 - 48 * q^44 + 16 * q^48 - 14 * q^49 + 48 * q^51 - 180 * q^57 + 18 * q^59 - 16 * q^64 - 168 * q^66 + 28 * q^67 - 30 * q^75 - 44 * q^76 - 190 * q^81 + 48 * q^82 - 90 * q^83 + 36 * q^86 + 80 * q^88 + 36 * q^89 - 30 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{63}{110}\right)$

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 $

$2$	−0.320315	+	1.37746i	−0.226497	+	0.974012i
$2$	−0.320315	+	1.37746i	−0.226497	+	0.974012i
$3$	0.484606	+	1.49147i	0.279788	+	0.861098i	0.987913	+	0.155011i	$0.0495413\pi$
$3$	0.484606	+	1.49147i	0.279788	+	0.861098i	−0.708125	+	0.706087i	$0.750459\pi$
$4$	−1.79480	−	0.882442i	−0.897398	−	0.441221i
$5$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$5$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$6$	−2.20966	+	0.189788i	−0.902091	+	0.0774806i
$7$		0			0		−0.999592	−	0.0285561i	$-0.990909\pi$
$7$		0			0		0.999592	+	0.0285561i	$0.00909091\pi$
$8$	1.79043	−	2.18960i	0.633012	−	0.774142i
$9$	0.437426	−	0.317808i	0.145809	−	0.105936i
$10$		0			0
$11$	2.13041	−	2.54192i	0.642342	−	0.766418i
$11$	2.13041	−	2.54192i	0.642342	−	0.766418i
$12$	0.446362	−	3.10451i	0.128854	−	0.896196i
$13$		0			0		0.884433	−	0.466667i	$-0.154545\pi$
$13$		0			0		−0.884433	+	0.466667i	$0.845455\pi$
$14$		0			0
$15$		0			0
$16$	2.44259	+	3.16761i	0.610648	+	0.791902i
$17$	8.01441	+	1.62393i	1.94378	+	0.393861i	0.997514	+	0.0704726i	$0.0224507\pi$
$17$	8.01441	+	1.62393i	1.94378	+	0.393861i	0.946266	+	0.323388i	$0.104822\pi$
$18$	0.297655	+	0.704335i	0.0701579	+	0.166013i
$19$	−0.466385	+	4.06474i	−0.106996	+	0.932515i	0.823776	+	0.566915i	$0.191863\pi$
$19$	−0.466385	+	4.06474i	−0.106996	+	0.932515i	−0.930772	+	0.365600i	$0.880864\pi$
$20$		0			0
$21$		0			0
$22$	2.81900	+	3.74877i	0.601012	+	0.799240i
$23$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$23$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$24$	4.13337	+	1.60927i	0.843721	+	0.328490i
$25$	−3.68371	+	3.38087i	−0.736741	+	0.676175i
$26$		0			0
$27$	4.49213	+	3.26372i	0.864510	+	0.628104i
$28$		0			0
$29$		0			0		0.676175	−	0.736741i	$-0.263636\pi$
$29$		0			0		−0.676175	+	0.736741i	$0.736364\pi$
$30$		0			0
$31$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$31$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$32$	−5.14566	+	2.34994i	−0.909632	+	0.415415i
$33$	4.82360	+	1.94560i	0.839680	+	0.338685i
$34$	−4.80403	+	10.5194i	−0.823885	+	1.80406i
$35$		0			0
$36$	−1.06554	+	0.184399i	−0.177590	+	0.0307331i
$37$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$37$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$38$	−5.44963	−	1.94442i	−0.884047	−	0.315427i
$39$		0			0
$40$		0			0
$41$	1.84738	+	1.11401i	0.288513	+	0.173980i	0.653274	−	0.757121i	$-0.273395\pi$
$41$	1.84738	+	1.11401i	0.288513	+	0.173980i	−0.364761	+	0.931101i	$0.618849\pi$
$42$		0			0
$43$	−6.65305	−	10.3523i	−1.01458	−	1.57872i	−0.798186	−	0.602412i	$-0.794207\pi$
$43$	−6.65305	−	10.3523i	−1.01458	−	1.57872i	−0.216395	−	0.976306i	$-0.569430\pi$
$44$	−6.06675	+	2.68227i	−0.914597	+	0.404368i
$45$		0			0
$46$		0			0
$47$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$47$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$48$	−3.54068	+	5.17808i	−0.511054	+	0.747392i
$49$	6.98858	+	0.399622i	0.998369	+	0.0570888i
$50$	−3.47708	−	6.15710i	−0.491733	−	0.870746i
$51$	1.46180	+	12.7402i	0.204693	+	1.78398i
$52$		0			0
$53$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$53$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$54$	−5.93454	+	5.14231i	−0.807589	+	0.699780i
$55$		0			0
$56$		0			0
$57$	−6.28843	+	1.27420i	−0.832923	+	0.168772i
$58$		0			0
$59$	0.441736	+	0.732536i	0.0575091	+	0.0953681i	0.883775	−	0.467912i	$-0.154994\pi$
$59$	0.441736	+	0.732536i	0.0575091	+	0.0953681i	−0.826266	+	0.563280i	$0.809539\pi$
$60$		0			0
$61$		0			0		−0.226497	−	0.974012i	$-0.572727\pi$
$61$		0			0		0.226497	+	0.974012i	$0.427273\pi$
$62$		0			0
$63$		0			0
$64$	−1.58872	−	7.84066i	−0.198590	−	0.980083i
$65$		0			0
$66$	−4.22505	+	6.02111i	−0.520068	+	0.741148i
$67$	2.45163	+	2.82933i	0.299514	+	0.345658i	0.885480	−	0.464678i	$-0.153830\pi$
$67$	2.45163	+	2.82933i	0.299514	+	0.345658i	−0.585965	+	0.810336i	$0.699285\pi$
$68$	−12.9512	−	9.98688i	−1.57057	−	1.21109i
$69$		0			0
$70$		0			0
$71$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$71$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$72$	0.0873057	−	1.52680i	0.0102891	−	0.179935i
$73$	8.57926	+	5.86635i	1.00413	+	0.686604i	0.950103	−	0.311936i	$-0.100977\pi$
$73$	8.57926	+	5.86635i	1.00413	+	0.686604i	0.0540233	+	0.998540i	$0.482795\pi$
$74$		0			0
$75$	−6.82760	−	3.85573i	−0.788384	−	0.445221i
$76$	4.42396	−	6.88382i	0.507463	−	0.789629i
$77$		0			0
$78$		0			0
$79$		0			0		−0.0570888	−	0.998369i	$-0.518182\pi$
$79$		0			0		0.0570888	+	0.998369i	$0.481818\pi$
$80$		0			0
$81$	−2.18957	+	6.73880i	−0.243285	+	0.748756i
$82$	−2.12625	+	2.18786i	−0.234805	+	0.241609i
$83$	−2.78648	+	7.80967i	−0.305856	+	0.857223i	0.685739	+	0.727847i	$0.259479\pi$
$83$	−2.78648	+	7.80967i	−0.305856	+	0.857223i	−0.991596	+	0.129375i	$0.958703\pi$
$84$		0			0
$85$		0			0
$86$	16.3910	−	5.84830i	1.76749	−	0.630639i
$87$		0			0
$88$	−1.75146	−	9.21588i	−0.186706	−	0.982416i
$89$	6.25292	+	13.6920i	0.662808	+	1.45135i	0.879882	+	0.475192i	$0.157621\pi$
$89$	6.25292	+	13.6920i	0.662808	+	1.45135i	−0.217074	+	0.976155i	$0.569651\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−5.99848	−	6.53577i	−0.612217	−	0.667054i
$97$	5.82399	−	14.9588i	0.591337	−	1.51884i	−0.244382	−	0.969679i	$-0.578585\pi$
$97$	5.82399	−	14.9588i	0.591337	−	1.51884i	0.835719	−	0.549157i	$-0.185051\pi$
$98$	−2.78901	+	9.49850i	−0.281733	+	0.959493i
$99$	0.124051	−	1.78896i	0.0124676	−	0.179798i
$100$	9.59493	−	2.81733i	0.959493	−	0.281733i
$101$		0			0		−0.996332	−	0.0855750i	$-0.972727\pi$
$101$		0			0		0.996332	+	0.0855750i	$0.0272727\pi$
$102$	−18.0173	−	2.06730i	−1.78398	−	0.204693i
$103$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$103$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.4486	−	5.11214i	−1.88017	−	0.494209i	−0.999802	−	0.0199092i	$-0.993662\pi$
$107$	−19.4486	−	5.11214i	−1.88017	−	0.494209i	−0.880364	−	0.474300i	$-0.842701\pi$
$108$	−5.18241	−	9.82176i	−0.498678	−	0.945099i
$109$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$109$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.304492	+	0.248982i	0.0286442	+	0.0234223i	0.647226	−	0.762298i	$-0.275929\pi$
$113$	0.304492	+	0.248982i	0.0286442	+	0.0234223i	−0.618582	+	0.785720i	$0.712293\pi$
$114$	0.259115	−	9.07021i	0.0242684	−	0.849503i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.15053	+	0.373831i	−0.105915	+	0.0344140i
$119$		0			0
$120$		0			0
$121$	−1.92273	−	10.8307i	−0.174794	−	0.984605i
$122$		0			0
$123$	−0.766258	+	3.29517i	−0.0690912	+	0.297115i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.996332	−	0.0855750i	$-0.0272727\pi$
$127$		0			0		−0.996332	+	0.0855750i	$0.972727\pi$
$128$	11.3091	+	0.323075i	0.999592	+	0.0285561i
$129$	12.2161	−	14.9396i	1.07556	−	1.31536i
$130$		0			0
$131$	−22.4860	+	3.23300i	−1.96461	+	0.282469i	−0.964802	+	0.262976i	$0.915296\pi$
$131$	−22.4860	+	3.23300i	−1.96461	+	0.282469i	−0.999810	+	0.0194927i	$0.993795\pi$
$132$	−6.94050	−	7.74850i	−0.604093	−	0.674420i
$133$		0			0
$134$	−4.68259	+	2.47075i	−0.404514	+	0.213440i
$135$		0			0
$136$	17.9050	−	14.6408i	1.53534	−	1.25544i
$137$	−2.86909	−	3.72071i	−0.245123	−	0.317881i	0.653226	−	0.757163i	$-0.273415\pi$
$137$	−2.86909	−	3.72071i	−0.245123	−	0.317881i	−0.898350	+	0.439281i	$0.855233\pi$
$138$		0			0
$139$	8.94685	+	21.1708i	0.758862	+	1.79568i	0.585221	+	0.810874i	$0.301008\pi$
$139$	8.94685	+	21.1708i	0.758862	+	1.79568i	0.173640	+	0.984809i	$0.444447\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.07514	+	0.609317i	0.172929	+	0.0507764i
$145$		0			0
$146$	−10.8287	+	9.93852i	−0.896192	+	0.822518i
$147$	2.79069	+	10.6169i	0.230172	+	0.875666i
$148$		0			0
$149$		0			0		−0.884433	−	0.466667i	$-0.845455\pi$
$149$		0			0		0.884433	+	0.466667i	$0.154545\pi$
$150$	7.49809	−	8.16971i	0.612217	−	0.667054i
$151$		0			0		−0.441221	−	0.897398i	$-0.645455\pi$
$151$		0			0		0.441221	+	0.897398i	$0.354545\pi$
$152$	8.06513	+	8.29883i	0.654169	+	0.673124i
$153$	4.02181	−	1.83670i	0.325144	−	0.148488i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$157$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−8.58108	−	5.17458i	−0.674193	−	0.406554i
$163$	2.36621	−	0.135305i	0.185336	−	0.0105979i	0.0358257	−	0.999358i	$-0.488594\pi$
$163$	2.36621	−	0.135305i	0.185336	−	0.0105979i	0.149510	+	0.988760i	$0.452230\pi$
$164$	−2.33263	−	3.62964i	−0.182147	−	0.283427i
$165$		0			0
$166$	−9.86496	−	6.33983i	−0.765669	−	0.492066i
$167$		0			0		0.491733	−	0.870746i	$-0.336364\pi$
$167$		0			0		−0.491733	+	0.870746i	$0.663636\pi$
$168$		0			0
$169$	7.33776	−	10.7311i	0.564443	−	0.825472i
$170$		0			0
$171$	1.08780	+	1.92624i	0.0831861	+	0.147303i
$172$	2.80552	+	24.4513i	0.213919	+	1.86439i
$173$		0			0		0.999592	−	0.0285561i	$-0.00909091\pi$
$173$		0			0		−0.999592	+	0.0285561i	$0.990909\pi$
$174$		0			0
$175$		0			0
$176$	13.2555	+	0.539421i	0.999173	+	0.0406604i
$177$	−0.878485	+	1.01383i	−0.0660310	+	0.0762038i
$178$	−20.8631	+	4.22740i	−1.56375	+	0.316857i
$179$	10.8807	+	15.9125i	0.813263	+	1.18936i	0.979135	+	0.203212i	$0.0651381\pi$
$179$	10.8807	+	15.9125i	0.813263	+	1.18936i	−0.165872	+	0.986147i	$0.553044\pi$
$180$		0			0
$181$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$181$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	21.2019	−	16.9124i	1.55043	−	1.23676i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$191$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$192$	10.9242	−	6.16916i	0.788384	−	0.445221i
$193$	−0.314738	+	5.50414i	−0.0226554	+	0.396197i	0.967191	+	0.254052i	$0.0817635\pi$
$193$	−0.314738	+	5.50414i	−0.0226554	+	0.396197i	−0.989846	+	0.142145i	$0.954600\pi$
$194$	18.7397	+	12.8138i	1.34543	+	0.919981i
$195$		0			0
$196$	−12.1904	−	6.88426i	−0.870746	−	0.491733i
$197$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$197$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$198$	2.42449	+	0.743906i	0.172301	+	0.0528671i
$199$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$199$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$200$	0.807358	+	14.1191i	0.0570888	+	0.998369i
$201$	−3.03178	+	5.02764i	−0.213845	+	0.354622i
$202$		0			0
$203$		0			0
$204$	8.61884	−	24.1560i	0.603440	−	1.69126i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.33866	+	9.84506i	0.645968	+	0.680997i
$210$		0			0
$211$	15.9789	−	15.5289i	1.10003	−	1.06906i	0.102801	−	0.994702i	$-0.467220\pi$
$211$	15.9789	−	15.5289i	1.10003	−	1.06906i	0.997232	−	0.0743540i	$-0.0236895\pi$
$212$		0			0
$213$		0			0
$214$	13.2714	−	25.1522i	0.907217	−	1.71937i
$215$		0			0
$216$	15.1891	−	3.99251i	1.03349	−	0.271656i
$217$		0			0
$218$		0			0
$219$	−4.59189	+	15.6385i	−0.310291	+	1.05675i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$223$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$224$		0			0
$225$	−0.536877	+	2.64959i	−0.0357918	+	0.176640i
$226$	−0.440497	+	0.339674i	−0.0293014	+	0.0225948i
$227$	−18.9315	−	23.1523i	−1.25653	−	1.53667i	−0.722908	−	0.690945i	$-0.757195\pi$
$227$	−18.9315	−	23.1523i	−1.25653	−	1.53667i	−0.533620	−	0.845724i	$-0.679169\pi$
$228$	12.4109	+	3.26224i	0.821930	+	0.216047i
$229$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$229$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.6384	−	24.2772i	−1.15553	−	1.59045i	−0.726506	−	0.687160i	$-0.758857\pi$
$233$	−17.6384	−	24.2772i	−1.15553	−	1.59045i	−0.429025	−	0.903293i	$-0.641143\pi$
$234$		0			0
$235$		0			0
$236$	−0.146405	−	1.70456i	−0.00953014	−	0.110957i
$237$		0			0
$238$		0			0
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$		0			0
$241$		−	21.1556i		−	1.36275i	−0.731934	−	0.681376i	$-0.761382\pi$
$241$		−	21.1556i		−	1.36275i	0.731934	−	0.681376i	$-0.238618\pi$
$242$	15.5347	+	0.820734i	0.998607	+	0.0527588i
$243$	5.54596			0.355774
$244$		0			0
$245$		0			0
$246$	−4.29352	−	2.11098i	−0.273745	−	0.134591i
$247$		0			0
$248$		0			0
$249$	−12.9982	−	0.371329i	−0.823727	−	0.0235320i
$250$		0			0
$251$	−2.43393	+	1.76835i	−0.153628	+	0.111617i	−0.661944	−	0.749553i	$-0.730268\pi$
$251$	−2.43393	+	1.76835i	−0.153628	+	0.111617i	0.508316	+	0.861171i	$0.330268\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−4.06749	+	15.4743i	−0.254218	+	0.967147i
$257$	20.6369	−	16.8747i	1.28730	−	1.05262i	0.291933	−	0.956439i	$-0.405702\pi$
$257$	20.6369	−	16.8747i	1.28730	−	1.05262i	0.995364	−	0.0961789i	$-0.0306621\pi$
$258$	16.6657	+	21.6125i	1.03756	+	1.34554i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	2.74927	−	32.0092i	0.169851	−	1.97753i
$263$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$263$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$264$	12.8964	−	7.07831i	0.793718	−	0.435640i
$265$		0			0
$266$		0			0
$267$	−17.3909	+	15.9612i	−1.06431	+	0.976811i
$268$	−1.90346	−	7.24150i	−0.116272	−	0.442345i
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$		0			0
$271$		0			0		0.676175	−	0.736741i	$-0.263636\pi$
$271$		0			0		−0.676175	+	0.736741i	$0.736364\pi$
$272$	14.4320	+	29.3531i	0.875066	+	1.77979i
$273$		0			0
$274$	6.04414	−	2.76027i	0.365140	−	0.166754i
$275$	0.746125	+	16.5663i	0.0449930	+	0.998987i
$276$		0			0
$277$		0			0		−0.336049	−	0.941844i	$-0.609091\pi$
$277$		0			0		0.336049	+	0.941844i	$0.390909\pi$
$278$	−32.0277	+	5.54262i	−1.92090	+	0.332424i
$279$		0			0
$280$		0			0
$281$	−23.4418	−	22.7817i	−1.39842	−	1.35904i	−0.854044	−	0.520200i	$-0.825857\pi$
$281$	−23.4418	−	22.7817i	−1.39842	−	1.35904i	−0.544376	−	0.838841i	$-0.683233\pi$
$282$		0			0
$283$	8.15306	+	4.91648i	0.484649	+	0.292254i	0.737616	−	0.675221i	$-0.235952\pi$
$283$	8.15306	+	4.91648i	0.484649	+	0.292254i	−0.252966	+	0.967475i	$0.581406\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.50401	+	2.66326i	−0.0886247	+	0.156934i
$289$	45.9345	+	19.4121i	2.70203	+	1.14189i
$290$		0			0
$291$	25.1329	+	1.43715i	1.47332	+	0.0842472i
$292$	−10.2213	−	18.0996i	−0.598157	−	1.05920i
$293$		0			0		−0.113991	−	0.993482i	$-0.536364\pi$
$293$		0			0		0.113991	+	0.993482i	$0.463636\pi$
$294$	−15.5182	+	0.443321i	−0.905043	+	0.0258550i
$295$		0			0
$296$		0			0
$297$	17.8662	−	4.46558i	1.03670	−	0.259119i
$298$		0			0
$299$		0			0
$300$	8.85171	+	12.9452i	0.511054	+	0.747392i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−14.0147	+	8.45117i	−0.803798	+	0.484708i
$305$		0			0
$306$	1.24173	+	6.12820i	0.0709853	+	0.350326i
$307$	−26.1500	−	22.6591i	−1.49246	−	1.29322i	−0.849844	−	0.527034i	$-0.823304\pi$
$307$	−26.1500	−	22.6591i	−1.49246	−	1.29322i	−0.642615	−	0.766189i	$-0.722151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$311$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$312$		0			0
$313$	13.5686	−	7.66254i	0.766942	−	0.433112i	−0.0580089	−	0.998316i	$-0.518475\pi$
$313$	13.5686	−	7.66254i	0.766942	−	0.433112i	0.824951	+	0.565204i	$0.191202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$317$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.80034	−	31.4843i	−0.100485	−	1.75728i
$322$		0			0
$323$	−10.3387	+	31.8191i	−0.575258	+	1.77046i
$324$	9.87643	−	10.1626i	0.548691	−	0.564589i
$325$		0			0
$326$	−0.571556	+	3.30271i	−0.0316556	+	0.182920i
$327$		0			0
$328$	5.74686	−	2.05047i	0.317317	−	0.113219i
$329$		0			0
$330$		0			0
$331$	−15.1110	−	33.0884i	−0.830573	−	1.81870i	−0.437893	−	0.899027i	$-0.644275\pi$
$331$	−15.1110	−	33.0884i	−0.830573	−	1.81870i	−0.392680	−	0.919675i	$-0.628452\pi$
$332$	11.8928	−	11.5579i	0.652700	−	0.634320i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−23.0212	+	6.05120i	−1.25404	+	0.329630i	−0.820575	−	0.571539i	$-0.806347\pi$
$337$	−23.0212	+	6.05120i	−1.25404	+	0.329630i	−0.433468	+	0.901169i	$0.642710\pi$
$338$	12.4313	+	13.5448i	0.676175	+	0.736741i
$339$	−0.223789	+	0.574798i	−0.0121546	+	0.0312187i
$340$		0			0
$341$		0			0
$342$	−3.00176	+	0.881397i	−0.162317	+	0.0476605i
$343$		0			0
$344$	−34.5793	−	3.96761i	−1.86439	−	0.213919i
$345$		0			0
$346$		0			0
$347$	−24.0339	+	18.5329i	−1.29021	+	0.994900i	−0.290937	+	0.956742i	$0.593967\pi$
$347$	−24.0339	+	18.5329i	−1.29021	+	0.994900i	−0.999272	+	0.0381574i	$0.987851\pi$
$348$		0			0
$349$		0			0		−0.967147	−	0.254218i	$-0.918182\pi$
$349$		0			0		0.967147	+	0.254218i	$0.0818182\pi$
$350$		0			0
$351$		0			0
$352$	−4.98897	+	18.0862i	−0.265913	+	0.963997i
$353$	−2.67915	−	18.6339i	−0.142597	−	0.991783i	−0.927942	−	0.372725i	$-0.878424\pi$
$353$	−2.67915	−	18.6339i	−0.142597	−	0.991783i	0.785345	−	0.619058i	$-0.212486\pi$
$354$	−1.11511	−	1.53482i	−0.0592676	−	0.0815748i
$355$		0			0
$356$	0.859664	−	30.0922i	0.0455621	−	1.59488i
$357$		0			0
$358$	−25.4042	+	9.89074i	−1.34265	+	0.522742i
$359$		0			0		0.441221	−	0.897398i	$-0.354545\pi$
$359$		0			0		−0.441221	+	0.897398i	$0.645455\pi$
$360$		0			0
$361$	2.20164	+	0.511969i	0.115876	+	0.0269458i
$362$		0			0
$363$	15.2218	−	8.11629i	0.798936	−	0.425995i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$367$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$368$		0			0
$369$	1.16214	−	0.0998159i	0.0604984	−	0.00519621i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$373$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$374$	16.5049	+	34.6220i	0.853446	+	1.79026i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−23.7752	−	30.8322i	−1.22125	−	1.58374i	−0.617582	−	0.786506i	$-0.711888\pi$
$379$	−23.7752	−	30.8322i	−1.22125	−	1.58374i	−0.603666	−	0.797237i	$-0.706294\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$383$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$384$	4.99861	+	17.0237i	0.255084	+	0.868736i
$385$		0			0
$386$	−7.48093	−	2.19660i	−0.380769	−	0.111804i
$387$	−6.20027	−	2.41399i	−0.315178	−	0.122710i
$388$	−23.6532	+	21.7087i	−1.20081	+	1.10209i
$389$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$389$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$390$		0			0
$391$		0			0
$392$	13.3876	−	14.5867i	0.676175	−	0.736741i
$393$	−15.7188	−	31.9704i	−0.792907	−	1.61269i
$394$		0			0
$395$		0			0
$396$	−1.80130	+	3.10136i	−0.0905188	+	0.155849i
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	−19.7071	−	3.41044i	−0.985354	−	0.170522i
$401$	32.9849	+	11.7690i	1.64719	+	0.587715i	0.986618	−	0.163049i	$-0.0521329\pi$
$401$	32.9849	+	11.7690i	1.64719	+	0.587715i	0.660570	+	0.750765i	$0.270315\pi$
$402$	−5.95425	−	5.78658i	−0.296971	−	0.288608i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	30.5132	+	19.6096i	1.51063	+	0.970822i
$409$	16.7738	−	29.7025i	0.829410	−	1.46869i	−0.0531978	−	0.998584i	$-0.516941\pi$
$409$	16.7738	−	29.7025i	0.829410	−	1.46869i	0.882608	−	0.470110i	$-0.155786\pi$
$410$		0			0
$411$	4.15892	−	6.08223i	0.205145	−	0.300014i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−27.2398	+	23.6034i	−1.33394	+	1.15586i
$418$	−16.5525	+	9.71011i	−0.809609	+	0.474937i
$419$	−25.9402	+	29.9366i	−1.26726	+	1.46250i	−0.442762	+	0.896639i	$0.646001\pi$
$419$	−25.9402	+	29.9366i	−1.26726	+	1.46250i	−0.824501	+	0.565860i	$0.808544\pi$
$420$		0			0
$421$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$421$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$422$	16.2722	+	26.9845i	0.792119	+	1.31358i
$423$		0			0
$424$		0			0
$425$	−35.0130	+	21.1136i	−1.69838	+	1.02416i
$426$		0			0
$427$		0			0
$428$	30.3951	+	26.3375i	1.46920	+	1.27307i
$429$		0			0
$430$		0			0
$431$		0			0		−0.791902	−	0.610648i	$-0.790909\pi$
$431$		0			0		0.791902	+	0.610648i	$0.209091\pi$
$432$	0.634239	+	22.2012i	0.0305148	+	1.06816i
$433$	−41.3376	+	4.74305i	−1.98656	+	0.227936i	−0.990979	+	0.134014i	$0.957213\pi$
$433$	−41.3376	+	4.74305i	−1.98656	+	0.227936i	−0.995580	+	0.0939225i	$0.970059\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−20.0706	−	11.3344i	−0.959012	−	0.541579i
$439$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$439$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$440$		0			0
$441$	3.18399	−	2.04623i	0.151618	−	0.0974393i
$442$		0			0
$443$	−0.400775	+	0.664611i	−0.0190414	+	0.0315766i	−0.865724	−	0.500521i	$-0.833142\pi$
$443$	−0.400775	+	0.664611i	−0.0190414	+	0.0315766i	0.846683	+	0.532098i	$0.178596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−25.5410	+	9.11302i	−1.20536	+	0.430070i	−0.860920	−	0.508740i	$-0.830112\pi$
$449$	−25.5410	+	9.11302i	−1.20536	+	0.430070i	−0.344436	+	0.938810i	$0.611930\pi$
$450$	−3.47774	−	1.58823i	−0.163942	−	0.0748699i
$451$	6.76741	−	2.32260i	0.318665	−	0.109367i
$452$	−0.326790	−	0.715569i	−0.0153709	−	0.0336575i
$453$		0			0
$454$	37.9554	−	18.6614i	1.78133	−	0.875823i
$455$		0			0
$456$	−8.46900	+	16.0505i	−0.396597	+	0.751635i
$457$	−25.1227	+	34.5785i	−1.17519	+	1.61751i	−0.567078	+	0.823664i	$0.691926\pi$
$457$	−25.1227	+	34.5785i	−1.17519	+	1.61751i	−0.608114	+	0.793849i	$0.708074\pi$
$458$		0			0
$459$	30.7017	+	33.4517i	1.43303	+	1.56139i
$460$		0			0
$461$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$461$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$462$		0			0
$463$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$463$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$464$		0			0
$465$		0			0
$466$	39.0907	−	16.5199i	1.81084	−	0.765269i
$467$	8.35240	−	41.2207i	0.386503	−	1.90747i	−0.0324796	−	0.999472i	$-0.510340\pi$
$467$	8.35240	−	41.2207i	0.386503	−	1.90747i	0.418982	−	0.907994i	$-0.362387\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	2.39486	+	0.344329i	0.110232	+	0.0158490i
$473$	−40.4885	−	5.14318i	−1.86167	−	0.236484i
$474$		0			0
$475$	−12.0243	−	16.5501i	−0.551715	−	0.759370i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.931864	−	0.362808i	$-0.118182\pi$
$479$		0			0		−0.931864	+	0.362808i	$0.881818\pi$
$480$		0			0
$481$		0			0
$482$	29.1410	+	6.77645i	1.32734	+	0.308659i
$483$		0			0
$484$	−6.10652	+	21.1355i	−0.277569	+	0.960706i
$485$		0			0
$486$	−1.77645	+	7.63934i	−0.0805816	+	0.346528i
$487$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$487$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$488$		0			0
$489$	1.34848	+	3.46356i	0.0609806	+	0.156627i
$490$		0			0
$491$	20.2551	+	0.578641i	0.914099	+	0.0261137i	0.482446	−	0.875926i	$-0.339749\pi$
$491$	20.2551	+	0.578641i	0.914099	+	0.0261137i	0.431653	+	0.902040i	$0.357930\pi$
$492$	4.28307	−	5.23798i	0.193096	−	0.236146i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	4.67501	−	17.7856i	0.209492	−	0.796990i
$499$	0.829529	−	0.678303i	0.0371348	−	0.0303650i	−0.614263	−	0.789101i	$-0.710547\pi$
$499$	0.829529	−	0.678303i	0.0371348	−	0.0303650i	0.651398	+	0.758736i	$0.274183\pi$
$500$		0			0
$501$		0			0
$502$	−1.65621	−	3.91907i	−0.0739204	−	0.174917i
$503$		0			0		0.113991	−	0.993482i	$-0.463636\pi$
$503$		0			0		−0.113991	+	0.993482i	$0.536364\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	19.5610	+	5.74364i	0.868736	+	0.255084i
$508$		0			0
$509$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$509$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$510$		0			0
$511$		0			0
$512$	−20.0124	−	10.5595i	−0.884433	−	0.466667i
$513$	−15.3612	+	16.7372i	−0.678215	+	0.738964i
$514$	16.6340	+	33.8318i	0.733693	+	1.49226i
$515$		0			0
$516$	−35.1087	+	16.0336i	−1.54557	+	0.705839i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	44.2365	+	7.65542i	1.93804	+	0.335390i	0.999940	−	0.0109857i	$-0.00349692\pi$
$521$	44.2365	+	7.65542i	1.93804	+	0.335390i	0.938096	+	0.346376i	$0.112588\pi$
$522$		0			0
$523$	−4.97709	−	4.83694i	−0.217633	−	0.211505i	0.580051	−	0.814580i	$-0.303033\pi$
$523$	−4.97709	−	4.83694i	−0.217633	−	0.211505i	−0.797684	+	0.603076i	$0.793942\pi$
$524$	43.2108	+	14.0400i	1.88767	+	0.613342i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	5.61919	+	20.0316i	0.244544	+	0.871762i
$529$	19.3488	+	12.4347i	0.841254	+	0.540641i
$530$		0			0
$531$	0.426033	+	0.180043i	0.0184882	+	0.00781320i
$532$		0			0
$533$		0			0
$534$	−16.4154	−	29.0679i	−0.710364	−	1.25789i
$535$		0			0
$536$	10.5846	−	0.302377i	0.457185	−	0.0130607i
$537$	−18.4601	+	23.9395i	−0.796614	+	1.03307i
$538$		0			0
$539$	15.9043	−	16.9131i	0.685048	−	0.728498i
$540$		0			0
$541$		0			0		0.980083	−	0.198590i	$-0.0636364\pi$
$541$		0			0		−0.980083	+	0.198590i	$0.936364\pi$
$542$		0			0
$543$		0			0
$544$	−45.0555	+	10.4772i	−1.93174	+	0.449207i
$545$		0			0
$546$		0			0
$547$	−2.63026	+	1.79852i	−0.112462	+	0.0768993i	−0.619363	−	0.785105i	$-0.712609\pi$
$547$	−2.63026	+	1.79852i	−0.112462	+	0.0768993i	0.506901	+	0.862004i	$0.330791\pi$
$548$	1.86613	+	9.20972i	0.0797172	+	0.393420i
$549$		0			0
$550$	−23.0585	−	4.27868i	−0.983216	−	0.182444i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	2.62422	−	45.8923i	0.111292	−	1.94627i
$557$		0			0		−0.825472	−	0.564443i	$-0.809091\pi$
$557$		0			0		0.825472	+	0.564443i	$0.190909\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	35.4988	+	23.4260i	1.49876	+	0.989046i
$562$	38.8896	−	24.9928i	1.64046	−	1.05426i
$563$	1.65666	+	28.9718i	0.0698201	+	1.22101i	0.824861	+	0.565336i	$0.191253\pi$
$563$	1.65666	+	28.9718i	0.0698201	+	1.22101i	−0.755041	+	0.655678i	$0.772383\pi$
$564$		0			0
$565$		0			0
$566$	−9.38380	+	9.65570i	−0.394430	+	0.405859i
$567$		0			0
$568$		0			0
$569$	−3.01693	−	17.4332i	−0.126476	−	0.730836i	−0.978329	−	0.207055i	$-0.933612\pi$
$569$	−3.01693	−	17.4332i	−0.126476	−	0.730836i	0.851853	−	0.523781i	$-0.175479\pi$
$570$		0			0
$571$	−42.6672	−	19.4854i	−1.78556	−	0.815440i	−0.972369	−	0.233451i	$-0.924998\pi$
$571$	−42.6672	−	19.4854i	−1.78556	−	0.815440i	−0.813196	−	0.581989i	$-0.802275\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−3.18678	−	2.92480i	−0.132782	−	0.121866i
$577$	−21.2273	+	40.2303i	−0.883706	+	1.67481i	−0.157290	+	0.987552i	$0.550276\pi$
$577$	−21.2273	+	40.2303i	−0.883706	+	1.67481i	−0.726415	+	0.687256i	$0.758815\pi$
$578$	−41.4529	+	57.0550i	−1.72421	+	2.37318i
$579$	−8.36176	+	2.19792i	−0.347503	+	0.0913425i
$580$		0			0
$581$		0			0
$582$	−10.0301	+	34.1592i	−0.415759	+	1.41595i
$583$		0			0
$584$	28.2055	−	8.28189i	1.16715	−	0.342707i
$585$		0			0
$586$		0			0
$587$	−34.0200	+	14.3770i	−1.40416	+	0.593401i	−0.954070	−	0.299585i	$-0.903152\pi$
$587$	−34.0200	+	14.3770i	−1.40416	+	0.593401i	−0.450085	+	0.892985i	$0.648606\pi$
$588$	4.36007	−	21.5178i	0.179806	−	0.887378i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−34.3255	−	4.93526i	−1.40958	−	0.202667i	−0.604864	−	0.796329i	$-0.706772\pi$
$593$	−34.3255	−	4.93526i	−1.40958	−	0.202667i	−0.804714	+	0.593662i	$0.797681\pi$
$594$	0.428358	+	26.0404i	0.0175757	+	1.06845i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$599$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$600$	−20.6669	+	8.04634i	−0.843721	+	0.328490i
$601$	−18.4049	+	37.4337i	−0.750752	+	1.52695i	0.0962457	+	0.995358i	$0.469317\pi$
$601$	−18.4049	+	37.4337i	−0.750752	+	1.52695i	−0.846998	+	0.531596i	$0.821593\pi$
$602$		0			0
$603$	1.97159	+	0.458474i	0.0802894	+	0.0186705i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.226497	−	0.974012i	$-0.427273\pi$
$607$		0			0		−0.226497	+	0.974012i	$0.572727\pi$
$608$	−7.15204	−	22.0117i	−0.290054	−	0.892693i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−8.83911	−	0.252513i	−0.357300	−	0.0102072i
$613$		0			0		0.633012	−	0.774142i	$-0.281818\pi$
$613$		0			0		−0.633012	+	0.774142i	$0.718182\pi$
$614$	39.5883	−	28.7626i	1.59765	−	1.16076i
$615$		0			0
$616$		0			0
$617$	−3.24596	+	22.5761i	−0.130677	+	0.908881i	0.813997	+	0.580870i	$0.197287\pi$
$617$	−3.24596	+	22.5761i	−0.130677	+	0.908881i	−0.944674	+	0.328011i	$0.893622\pi$
$618$		0			0
$619$	1.88983	−	7.18966i	0.0759587	−	0.288977i	−0.918314	−	0.395854i	$-0.870449\pi$
$619$	1.88983	−	7.18966i	0.0759587	−	0.288977i	0.994272	+	0.106877i	$0.0340851\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2.13938	−	24.9083i	0.0855750	−	0.996332i
$626$	6.20863	+	21.1446i	0.248147	+	0.845110i
$627$	−10.1580	+	18.6993i	−0.405671	+	0.746777i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$631$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$632$		0			0
$633$	30.9043	+	16.3065i	1.22834	+	0.648127i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−19.0963	+	3.30474i	−0.754258	+	0.130529i	−0.534667	−	0.845063i	$-0.679563\pi$
$641$	−19.0963	+	3.30474i	−0.754258	+	0.130529i	−0.219590	+	0.975592i	$0.570472\pi$
$642$	43.9450	+	7.60498i	1.73437	+	0.300145i
$643$	−24.5327	−	8.75325i	−0.967475	−	0.345195i	−0.195399	−	0.980724i	$-0.562600\pi$
$643$	−24.5327	−	8.75325i	−0.967475	−	0.345195i	−0.772077	+	0.635529i	$0.780782\pi$
$644$		0			0
$645$		0			0
$646$	−40.5180	−	24.4332i	−1.59416	−	0.961312i
$647$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$647$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$648$	10.8350	+	16.8596i	0.425640	+	0.662309i
$649$	2.80313	+	0.437743i	0.110032	+	0.0171829i
$650$		0			0
$651$		0			0
$652$	−4.36627	−	1.84520i	−0.170996	−	0.0722637i
$653$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$653$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$654$		0			0
$655$		0			0
$656$	0.983645	+	8.57287i	0.0384049	+	0.334714i
$657$	5.61716	−	0.160469i	0.219146	−	0.00626051i
$658$		0			0
$659$	−17.5740	+	15.2280i	−0.684587	+	0.593198i	−0.926136	−	0.377191i	$-0.876890\pi$
$659$	−17.5740	+	15.2280i	−0.684587	+	0.593198i	0.241549	+	0.970389i	$0.422345\pi$
$660$		0			0
$661$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$661$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$662$	50.4182	−	10.2161i	1.95956	−	0.397058i
$663$		0			0
$664$	12.1111	+	20.0840i	0.470001	+	0.779409i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−40.2197	−	31.0140i	−1.55035	−	1.19550i	−0.900017	−	0.435856i	$-0.856446\pi$
$673$	−40.2197	−	31.0140i	−1.55035	−	1.19550i	−0.650337	−	0.759646i	$-0.725372\pi$
$674$	−0.961276	−	33.6490i	−0.0370270	−	1.29611i
$675$	−27.5819	+	3.16473i	−1.06163	+	0.121810i
$676$	−22.6394	+	12.7851i	−0.870746	+	0.491733i
$677$		0			0		0.0570888	−	0.998369i	$-0.481818\pi$
$677$		0			0		−0.0570888	+	0.998369i	$0.518182\pi$
$678$	−0.720079	−	0.492377i	−0.0276545	−	0.0189096i
$679$		0			0
$680$		0			0
$681$	25.3565	−	39.4554i	0.971661	−	1.51193i
$682$		0			0
$683$	42.9187	−	27.5822i	1.64224	−	1.05540i	0.703544	−	0.710651i	$-0.251600\pi$
$683$	42.9187	−	27.5822i	1.64224	−	1.05540i	0.938694	−	0.344751i	$-0.112037\pi$
$684$	−0.252581	−	4.41713i	−0.00965767	−	0.168893i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	16.5415	−	46.3608i	0.630639	−	1.76749i
$689$		0			0
$690$		0			0
$691$	25.2029	−	8.99236i	0.958762	−	0.342085i	0.190117	−	0.981761i	$-0.439113\pi$
$691$	25.2029	−	8.99236i	0.958762	−	0.342085i	0.768645	+	0.639676i	$0.220931\pi$
$692$		0			0
$693$		0			0
$694$	−17.8300	−	39.0422i	−0.676816	−	1.48202i
$695$		0			0
$696$		0			0
$697$	12.9966	+	11.9282i	0.492282	+	0.451812i
$698$		0			0
$699$	27.6609	−	38.0720i	1.04623	−	1.44001i
$700$		0			0
$701$		0			0		−0.676175	−	0.736741i	$-0.736364\pi$
$701$		0			0		0.676175	+	0.736741i	$0.263636\pi$
$702$		0			0
$703$		0			0
$704$	−23.3150	−	12.6654i	−0.878716	−	0.477345i
$705$		0			0
$706$	26.5257	+	2.27829i	0.998306	+	0.0857446i
$707$		0			0
$708$	2.47134	−	1.04440i	0.0928788	−	0.0392509i
$709$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$709$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$710$		0			0
$711$		0			0
$712$	41.1754	+	10.8231i	1.54311	+	0.405613i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−5.48678	−	38.1614i	−0.205051	−	1.42616i
$717$		0			0
$718$		0			0
$719$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$719$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$720$		0			0
$721$		0			0
$722$	−1.41044	+	2.86868i	−0.0524910	+	0.106761i
$723$	31.5528	−	10.2521i	1.17346	−	0.381281i
$724$		0			0
$725$		0			0
$726$	6.30411	+	23.5672i	0.233968	+	0.874660i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	9.25631	+	28.4880i	0.342826	+	1.05511i
$730$		0			0
$731$	−36.5088	−	93.7720i	−1.35033	−	3.46828i
$732$		0			0
$733$		0			0		−0.999592	−	0.0285561i	$-0.990909\pi$
$733$		0			0		0.999592	+	0.0285561i	$0.00909091\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.4149	−	0.204222i	0.457309	−	0.00752262i
$738$	−0.234757	+	1.63277i	−0.00864151	+	0.0601030i
$739$	31.1300	−	16.4256i	1.14513	−	0.604225i	0.216890	−	0.976196i	$-0.430409\pi$
$739$	31.1300	−	16.4256i	1.14513	−	0.604225i	0.928245	+	0.371971i	$0.121318\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.980083	−	0.198590i	$-0.936364\pi$
$743$		0			0		0.980083	+	0.198590i	$0.0636364\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.26310	+	4.30172i	0.0462143	+	0.157392i
$748$	−52.9772	+	11.6449i	−1.93704	+	0.425778i
$749$		0			0
$750$		0			0
$751$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$751$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$752$		0			0
$753$	−3.81694	−	2.77317i	−0.139097	−	0.101060i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$757$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$758$	50.0857	−	22.8734i	1.81919	−	0.830798i
$759$		0			0
$760$		0			0
$761$	−11.4186	−	32.0028i	−0.413923	−	1.16010i	−0.948994	−	0.315293i	$-0.897897\pi$
$761$	−11.4186	−	32.0028i	−0.413923	−	1.16010i	0.535071	−	0.844807i	$-0.320285\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−25.0506	+	1.43244i	−0.903935	+	0.0516889i
$769$	23.0590	+	35.8805i	0.831530	+	1.29389i	0.953513	+	0.301353i	$0.0974384\pi$
$769$	23.0590	+	35.8805i	0.831530	+	1.29389i	−0.121983	+	0.992532i	$0.538925\pi$
$770$		0			0
$771$	35.1689	+	22.6017i	1.26658	+	0.813979i
$772$	5.42198	−	9.60108i	0.195141	−	0.345551i
$773$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$773$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$774$	5.31121	−	7.76740i	0.190908	−	0.279193i
$775$		0			0
$776$	−22.3264	−	39.5349i	−0.801471	−	1.41922i
$777$		0			0
$778$		0			0
$779$	−5.38977	+	6.98957i	−0.193108	+	0.250427i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	15.8044	+	23.1132i	0.564443	+	0.825472i
$785$		0			0
$786$	49.0729	−	11.4114i	1.75037	−	0.407032i
$787$	8.98887	+	38.6552i	0.320419	+	1.37791i	0.848716	+	0.528848i	$0.177376\pi$
$787$	8.98887	+	38.6552i	0.320419	+	1.37791i	−0.528298	+	0.849059i	$0.677169\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−3.69501	−	3.47463i	−0.131297	−	0.123466i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$797$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$798$		0			0
$799$		0			0
$800$	11.0102	−	26.0533i	0.389270	−	0.921124i
$801$	7.08661	+	4.00199i	0.250393	+	0.141403i
$802$	−26.7769	+	41.6656i	−0.945525	+	1.47126i
$803$	33.1891	−	9.31010i	1.17122	−	0.328546i
$804$	9.87802	−	6.34822i	0.348371	−	0.223884i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.0752	+	53.4621i	−0.670649	+	1.87963i	−0.273501	+	0.961872i	$0.588182\pi$
$809$	−19.0752	+	53.4621i	−0.670649	+	1.87963i	−0.397149	+	0.917754i	$0.630000\pi$
$810$		0			0
$811$	−9.54922	−	55.1797i	−0.335319	−	1.93762i	−0.347460	−	0.937695i	$-0.612956\pi$
$811$	−9.54922	−	55.1797i	−0.335319	−	1.93762i	0.0121411	−	0.999926i	$-0.496135\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−36.7853	+	35.7495i	−1.28774	+	1.25148i
$817$	45.1825	−	22.2147i	1.58073	−	0.777195i
$818$	35.5411	+	32.6194i	1.24267	+	1.14051i
$819$		0			0
$820$		0			0
$821$		0			0		0.967147	−	0.254218i	$-0.0818182\pi$
$821$		0			0		−0.967147	+	0.254218i	$0.918182\pi$
$822$	7.04587	+	7.67698i	0.245753	+	0.267766i
$823$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$823$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$824$		0			0
$825$	−24.3465	+	9.14097i	−0.847637	+	0.318248i
$826$		0			0
$827$	25.7307	+	2.21001i	0.894745	+	0.0768497i	0.523836	−	0.851819i	$-0.324501\pi$
$827$	25.7307	+	2.21001i	0.894745	+	0.0768497i	0.370910	+	0.928669i	$0.379046\pi$
$828$		0			0
$829$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$829$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	55.3604	+	14.5517i	1.91812	+	0.504187i
$834$	−23.7875	−	45.0823i	−0.823693	−	1.56107i
$835$		0			0
$836$	−8.07329	−	25.9107i	−0.279221	−	0.896141i
$837$		0			0
$838$	−32.9275	−	45.3208i	−1.13746	−	1.56558i
$839$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$839$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$840$		0			0
$841$	−2.48168	−	28.8936i	−0.0855750	−	0.996332i
$842$		0			0
$843$	22.6180	−	46.0028i	0.779007	−	1.58442i
$844$	−42.3823	+	13.7708i	−1.45886	+	0.474012i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.38173	+	14.5426i	−0.116061	+	0.499099i
$850$	−17.8680	−	54.9921i	−0.612868	−	1.88621i
$851$		0			0
$852$		0			0
$853$		0			0		0.996332	−	0.0855750i	$-0.0272727\pi$
$853$		0			0		−0.996332	+	0.0855750i	$0.972727\pi$
$854$		0			0
$855$		0			0
$856$	−46.0149	+	33.4318i	−1.57276	+	1.14267i
$857$	−6.78111	+	0.974977i	−0.231638	+	0.0333046i	−0.257156	−	0.966370i	$-0.582786\pi$
$857$	−6.78111	+	0.974977i	−0.231638	+	0.0333046i	0.0255181	+	0.999674i	$0.491876\pi$
$858$		0			0
$859$	6.89779	−	47.9752i	0.235350	−	1.63689i	−0.439005	−	0.898485i	$-0.644669\pi$
$859$	6.89779	−	47.9752i	0.235350	−	1.63689i	0.674355	−	0.738408i	$-0.264422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$863$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$864$	−30.7845	−	6.23775i	−1.04731	−	0.212213i
$865$		0			0
$866$	6.70768	−	58.4602i	0.227936	−	1.98656i
$867$	−6.69230	+	77.9170i	−0.227282	+	2.64620i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−2.20647	−	8.39428i	−0.0746776	−	0.284103i
$874$		0			0
$875$		0			0
$876$	22.0416	−	24.0159i	0.744717	−	0.811423i
$877$		0			0		−0.441221	−	0.897398i	$-0.645455\pi$
$877$		0			0		0.441221	+	0.897398i	$0.354545\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.8620	+	43.4917i	−0.669168	+	1.46527i	0.204557	+	0.978855i	$0.434425\pi$
$881$	−19.8620	+	43.4917i	−0.669168	+	1.46527i	−0.873725	+	0.486419i	$0.838303\pi$
$882$	1.79872	+	5.04126i	0.0605659	+	0.169748i
$883$	30.4957	−	5.27748i	1.02626	−	0.177601i	0.367555	−	0.930002i	$-0.380195\pi$
$883$	30.4957	−	5.27748i	1.02626	−	0.177601i	0.658706	+	0.752401i	$0.271104\pi$
$884$		0			0
$885$		0			0
$886$	−0.787102	−	0.764937i	−0.0264432	−	0.0256986i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	12.4648	+	19.9221i	0.417587	+	0.667415i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−4.37166	−	38.1008i	−0.145884	−	1.27144i
$899$		0			0
$900$	3.30170	−	4.28172i	0.110057	−	0.142724i
$901$		0			0
$902$	1.03159	+	10.0658i	0.0343482	+	0.335155i
$903$		0			0
$904$	1.09034	−	0.220932i	0.0362643	−	0.00734810i
$905$		0			0
$906$		0			0
$907$	58.4288	−	13.5870i	1.94010	−	0.451150i	0.949636	−	0.313355i	$-0.101453\pi$
$907$	58.4288	−	13.5870i	1.94010	−	0.451150i	0.990461	−	0.137795i	$-0.0440015\pi$
$908$	13.5477	+	58.2595i	0.449595	+	1.93341i
$909$		0			0
$910$		0			0
$911$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$911$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$912$	−19.3962	−	16.8069i	−0.642274	−	0.556533i
$913$	13.9152	+	23.7208i	0.460527	+	0.785044i
$914$	−39.5833	−	45.6816i	−1.30930	−	1.51101i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−55.9126	+	31.5753i	−1.84539	+	1.04214i
$919$		0			0		0.0570888	−	0.998369i	$-0.481818\pi$
$919$		0			0		−0.0570888	+	0.998369i	$0.518182\pi$
$920$		0			0
$921$	21.1228	−	49.9826i	0.696020	−	1.64698i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.6564	+	17.1390i	−0.546477	+	0.562312i	−0.932958	−	0.359986i	$-0.882782\pi$
$929$	−16.6564	+	17.1390i	−0.546477	+	0.562312i	0.386481	+	0.922298i	$0.373691\pi$
$930$		0			0
$931$	−4.88373	+	28.2204i	−0.160058	+	0.924886i
$932$	10.2342	+	59.1375i	0.335231	+	1.93711i
$933$		0			0
$934$	54.1045	+	24.7087i	1.77035	+	0.808493i
$935$		0			0
$936$		0			0
$937$	−33.4930	+	32.5499i	−1.09417	+	1.06336i	−0.0964853	+	0.995334i	$0.530760\pi$
$937$	−33.4930	+	32.5499i	−1.09417	+	1.06336i	−0.997684	+	0.0680231i	$0.978331\pi$
$938$		0			0
$939$	18.0038	+	16.5238i	0.587533	+	0.539233i
$940$		0			0
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$		0			0
$944$	−1.24141	+	3.18853i	−0.0404044	+	0.103778i
$945$		0			0
$946$	20.0536	−	54.1239i	0.651999	−	1.75972i
$947$	−10.3567	+	3.04100i	−0.336547	+	0.0988191i	−0.445640	−	0.895212i	$-0.647024\pi$
$947$	−10.3567	+	3.04100i	−0.336547	+	0.0988191i	0.109093	+	0.994032i	$0.465206\pi$
$948$		0			0
$949$		0			0
$950$	26.6487	−	11.2618i	0.864597	−	0.365382i
$951$		0			0
$952$		0			0
$953$	−20.3680	−	24.9090i	−0.659784	−	0.806882i	0.330813	−	0.943696i	$-0.392677\pi$
$953$	−20.3680	−	24.9090i	−0.659784	−	0.806882i	−0.990597	+	0.136815i	$0.956314\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.885238	+	30.9874i	−0.0285561	+	0.999592i
$962$		0			0
$963$	−10.1320	+	3.94474i	−0.326499	+	0.127118i
$964$	−18.6686	+	37.9700i	−0.601275	+	1.22293i
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−27.1574	−	15.1815i	−0.872870	−	0.487952i
$969$	−52.4673			−1.68549
$970$		0			0
$971$	7.14170	+	21.9799i	0.229188	+	0.705368i	0.997839	+	0.0657001i	$0.0209281\pi$
$971$	7.14170	+	21.9799i	0.229188	+	0.705368i	−0.768651	+	0.639668i	$0.779072\pi$
$972$	−9.95387	−	4.89399i	−0.319271	−	0.156975i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.1331	−	16.8072i	0.740093	−	0.537709i	−0.152647	−	0.988281i	$-0.548780\pi$
$977$	23.1331	−	16.8072i	0.740093	−	0.537709i	0.892740	+	0.450572i	$0.148780\pi$
$978$	−5.20285	+	0.748057i	−0.166369	+	0.0239202i
$979$	48.1252	+	13.2751i	1.53809	+	0.424273i
$980$		0			0
$981$		0			0
$982$	−7.28506	+	27.7152i	−0.232476	+	0.884429i
$983$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$983$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$984$	5.84318	+	7.57756i	0.186274	+	0.241564i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$991$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$992$		0			0
$993$	42.0273	−	38.5723i	1.33370	−	1.22406i
$994$		0			0
$995$		0			0
$996$	23.0014	+	12.1366i	0.728829	+	0.384563i
$997$		0			0		0.676175	−	0.736741i	$-0.263636\pi$
$997$		0			0		−0.676175	+	0.736741i	$0.736364\pi$
$998$	0.668625	+	1.35991i	0.0211650	+	0.0430473i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.ba.a.107.1	✓	80
8.3	odd	2	CM	968.2.ba.a.107.1	✓	80
121.95	odd	110	inner	968.2.ba.a.579.1	yes	80
968.579	even	110	inner	968.2.ba.a.579.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.ba.a.107.1	✓	80	1.1	even	1	trivial
968.2.ba.a.107.1	✓	80	8.3	odd	2	CM
968.2.ba.a.579.1	yes	80	121.95	odd	110	inner
968.2.ba.a.579.1	yes	80	968.579	even	110	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.ba (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.320315 + 1.37746i) q^{2} +(0.484606 + 1.49147i) q^{3} +(-1.79480 - 0.882442i) q^{4} +(-2.20966 + 0.189788i) q^{6} +(1.79043 - 2.18960i) q^{8} +(0.437426 - 0.317808i) q^{9} +(2.13041 - 2.54192i) q^{11} +(0.446362 - 3.10451i) q^{12} +(2.44259 + 3.16761i) q^{16} +(8.01441 + 1.62393i) q^{17} +(0.297655 + 0.704335i) q^{18} +(-0.466385 + 4.06474i) q^{19} +(2.81900 + 3.74877i) q^{22} +(4.13337 + 1.60927i) q^{24} +(-3.68371 + 3.38087i) q^{25} +(4.49213 + 3.26372i) q^{27} +(-5.14566 + 2.34994i) q^{32} +(4.82360 + 1.94560i) q^{33} +(-4.80403 + 10.5194i) q^{34} +(-1.06554 + 0.184399i) q^{36} +(-5.44963 - 1.94442i) q^{38} +(1.84738 + 1.11401i) q^{41} +(-6.65305 - 10.3523i) q^{43} +(-6.06675 + 2.68227i) q^{44} +(-3.54068 + 5.17808i) q^{48} +(6.98858 + 0.399622i) q^{49} +(-3.47708 - 6.15710i) q^{50} +(1.46180 + 12.7402i) q^{51} +(-5.93454 + 5.14231i) q^{54} +(-6.28843 + 1.27420i) q^{57} +(0.441736 + 0.732536i) q^{59} +(-1.58872 - 7.84066i) q^{64} +(-4.22505 + 6.02111i) q^{66} +(2.45163 + 2.82933i) q^{67} +(-12.9512 - 9.98688i) q^{68} +(0.0873057 - 1.52680i) q^{72} +(8.57926 + 5.86635i) q^{73} +(-6.82760 - 3.85573i) q^{75} +(4.42396 - 6.88382i) q^{76} +(-2.18957 + 6.73880i) q^{81} +(-2.12625 + 2.18786i) q^{82} +(-2.78648 + 7.80967i) q^{83} +(16.3910 - 5.84830i) q^{86} +(-1.75146 - 9.21588i) q^{88} +(6.25292 + 13.6920i) q^{89} +(-5.99848 - 6.53577i) q^{96} +(5.82399 - 14.9588i) q^{97} +(-2.78901 + 9.49850i) q^{98} +(0.124051 - 1.78896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} - 4 q^{4} + 20 q^{6} - 64 q^{9} - 6 q^{11} + 36 q^{12} + 8 q^{16} - 40 q^{18} + 10 q^{19} + 4 q^{22} + 40 q^{24} + 10 q^{25} - 38 q^{27} + 38 q^{33} - 16 q^{34} - 24 q^{36} + 24 q^{38} - 48 q^{44}+ \cdots - 6 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 - 4 * q^4 + 20 * q^6 - 64 * q^9 - 6 * q^11 + 36 * q^12 + 8 * q^16 - 40 * q^18 + 10 * q^19 + 4 * q^22 + 40 * q^24 + 10 * q^25 - 38 * q^27 + 38 * q^33 - 16 * q^34 - 24 * q^36 + 24 * q^38 - 48 * q^44 + 16 * q^48 - 14 * q^49 + 48 * q^51 - 180 * q^57 + 18 * q^59 - 16 * q^64 - 168 * q^66 + 28 * q^67 - 30 * q^75 - 44 * q^76 - 190 * q^81 + 48 * q^82 - 90 * q^83 + 36 * q^86 + 80 * q^88 + 36 * q^89 - 30 * q^97 - 6 * q^99

Introduction

L-functions

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