LMFDB - Embedded newform 756.2.bf.b.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.b.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40043 - 0.196974i) q^{2} +(1.92240 + 0.551696i) q^{4} +(-1.71130 - 0.988019i) q^{5} +(-2.27191 + 1.35588i) q^{7} +(-2.58352 - 1.15127i) q^{8} +O(q^{10})$	\(q+(-1.40043 - 0.196974i) q^{2} +(1.92240 + 0.551696i) q^{4} +(-1.71130 - 0.988019i) q^{5} +(-2.27191 + 1.35588i) q^{7} +(-2.58352 - 1.15127i) q^{8} +(2.20194 + 1.72073i) q^{10} +(4.16608 - 2.40529i) q^{11} +6.20168i q^{13} +(3.44873 - 1.45131i) q^{14} +(3.39126 + 2.12116i) q^{16} +(-0.655890 + 0.378678i) q^{17} +(3.65579 - 6.33201i) q^{19} +(-2.74472 - 2.84349i) q^{20} +(-6.30808 + 2.54783i) q^{22} +(-4.09984 - 2.36705i) q^{23} +(-0.547638 - 0.948537i) q^{25} +(1.22157 - 8.68501i) q^{26} +(-5.11557 + 1.35314i) q^{28} -3.09904 q^{29} +(-3.85546 - 6.67786i) q^{31} +(-4.33141 - 3.63853i) q^{32} +(0.993118 - 0.401119i) q^{34} +(5.22756 - 0.0756214i) q^{35} +(3.98879 - 6.90878i) q^{37} +(-6.36691 + 8.14744i) q^{38} +(3.28369 + 4.52274i) q^{40} +6.55939i q^{41} -1.68401i q^{43} +(9.33588 - 2.32552i) q^{44} +(5.27529 + 4.12244i) q^{46} +(-1.30195 + 2.25504i) q^{47} +(3.32318 - 6.16088i) q^{49} +(0.580091 + 1.43623i) q^{50} +(-3.42144 + 11.9221i) q^{52} +(-7.08914 - 12.2788i) q^{53} -9.50588 q^{55} +(7.43052 - 0.887345i) q^{56} +(4.33998 + 0.610429i) q^{58} +(0.705675 + 1.22226i) q^{59} +(-5.09038 - 2.93893i) q^{61} +(4.08394 + 10.1113i) q^{62} +(5.34914 + 5.94868i) q^{64} +(6.12738 - 10.6129i) q^{65} +(-4.74455 + 2.73927i) q^{67} +(-1.46980 + 0.366120i) q^{68} +(-7.33572 - 0.923790i) q^{70} -13.5839i q^{71} +(4.77149 - 2.75482i) q^{73} +(-6.94686 + 8.88957i) q^{74} +(10.5212 - 10.1558i) q^{76} +(-6.20370 + 11.1133i) q^{77} +(-3.07352 - 1.77450i) q^{79} +(-3.70772 - 6.98058i) q^{80} +(1.29203 - 9.18596i) q^{82} -1.69786 q^{83} +1.49657 q^{85} +(-0.331705 + 2.35833i) q^{86} +(-13.5323 + 1.41781i) q^{88} +(3.63341 + 2.09775i) q^{89} +(-8.40873 - 14.0897i) q^{91} +(-6.57566 - 6.81228i) q^{92} +(2.26747 - 2.90158i) q^{94} +(-12.5123 + 7.22398i) q^{95} -2.34249i q^{97} +(-5.86741 + 7.97330i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 6 q^{11} - 17 q^{14} - 4 q^{16} + 8 q^{20} + 2 q^{22} + 14 q^{25} + 15 q^{26} - 13 q^{28} + 15 q^{32} + 6 q^{35} + 4 q^{37} - q^{38} - 15 q^{40} - 42 q^{44} - 9 q^{46} - 4 q^{47} + 14 q^{49} - 9 q^{52} + 45 q^{56} + 10 q^{58} - 16 q^{59} - 42 q^{64} - 49 q^{68} - 33 q^{70} + 36 q^{73} - 54 q^{74} - 15 q^{80} - 51 q^{82} + 20 q^{83} + 16 q^{85} + 78 q^{86} - 2 q^{88} - 27 q^{94} + 24 q^{95} - 46 q^{98}+O(q^{100}) $ 32 * q - 6 * q^11 - 17 * q^14 - 4 * q^16 + 8 * q^20 + 2 * q^22 + 14 * q^25 + 15 * q^26 - 13 * q^28 + 15 * q^32 + 6 * q^35 + 4 * q^37 - q^38 - 15 * q^40 - 42 * q^44 - 9 * q^46 - 4 * q^47 + 14 * q^49 - 9 * q^52 + 45 * q^56 + 10 * q^58 - 16 * q^59 - 42 * q^64 - 49 * q^68 - 33 * q^70 + 36 * q^73 - 54 * q^74 - 15 * q^80 - 51 * q^82 + 20 * q^83 + 16 * q^85 + 78 * q^86 - 2 * q^88 - 27 * q^94 + 24 * q^95 - 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.40043	−	0.196974i	−0.990253	−	0.139282i
$2$	−1.40043	−	0.196974i	−0.990253	−	0.139282i
$3$		0			0
$3$		0			0
$4$	1.92240	+	0.551696i	0.961201	+	0.275848i
$5$	−1.71130	−	0.988019i	−0.765316	−	0.441855i	0.0658851	−	0.997827i	$-0.479013\pi$
$5$	−1.71130	−	0.988019i	−0.765316	−	0.441855i	−0.831201	+	0.555972i	$0.812346\pi$
$6$		0			0
$7$	−2.27191	+	1.35588i	−0.858703	+	0.512474i
$7$	−2.27191	+	1.35588i	−0.858703	+	0.512474i
$8$	−2.58352	−	1.15127i	−0.913412	−	0.407037i
$9$		0			0
$10$	2.20194	+	1.72073i	0.696314	+	0.544143i
$11$	4.16608	−	2.40529i	1.25612	−	0.725222i	0.283803	−	0.958883i	$-0.408404\pi$
$11$	4.16608	−	2.40529i	1.25612	−	0.725222i	0.972318	+	0.233660i	$0.0750704\pi$
$12$		0			0
$13$			6.20168i			1.72004i	0.510263	+	0.860018i	$0.329548\pi$
$13$			6.20168i			1.72004i	−0.510263	+	0.860018i	$0.670452\pi$
$14$	3.44873	−	1.45131i	0.921711	−	0.387878i
$15$		0			0
$16$	3.39126	+	2.12116i	0.847816	+	0.530291i
$17$	−0.655890	+	0.378678i	−0.159077	+	0.0918430i	−0.577425	−	0.816444i	$-0.695942\pi$
$17$	−0.655890	+	0.378678i	−0.159077	+	0.0918430i	0.418348	+	0.908287i	$0.362609\pi$
$18$		0			0
$19$	3.65579	−	6.33201i	0.838695	−	1.45266i	−0.0522903	−	0.998632i	$-0.516652\pi$
$19$	3.65579	−	6.33201i	0.838695	−	1.45266i	0.890986	−	0.454031i	$-0.150015\pi$
$20$	−2.74472	−	2.84349i	−0.613738	−	0.635823i
$21$		0			0
$22$	−6.30808	+	2.54783i	−1.34489	+	0.543199i
$23$	−4.09984	−	2.36705i	−0.854877	−	0.493563i	0.00741666	−	0.999972i	$-0.497639\pi$
$23$	−4.09984	−	2.36705i	−0.854877	−	0.493563i	−0.862293	+	0.506409i	$0.830973\pi$
$24$		0			0
$25$	−0.547638	−	0.948537i	−0.109528	−	0.189707i
$26$	1.22157	−	8.68501i	0.239569	−	1.70327i
$27$		0			0
$28$	−5.11557	+	1.35314i	−0.966751	+	0.255720i
$29$	−3.09904			−0.575476			−0.287738	−	0.957709i	$-0.592903\pi$
$29$	−3.09904			−0.575476			−0.287738	+	0.957709i	$0.592903\pi$
$30$		0			0
$31$	−3.85546	−	6.67786i	−0.692462	−	1.19938i	−0.971029	−	0.238962i	$-0.923193\pi$
$31$	−3.85546	−	6.67786i	−0.692462	−	1.19938i	0.278567	−	0.960417i	$-0.410140\pi$
$32$	−4.33141	−	3.63853i	−0.765692	−	0.643207i
$33$		0			0
$34$	0.993118	−	0.401119i	0.170318	−	0.0687913i
$35$	5.22756	−	0.0756214i	0.883618	−	0.0127824i
$36$		0			0
$37$	3.98879	−	6.90878i	0.655753	−	1.13580i	−0.325952	−	0.945386i	$-0.605685\pi$
$37$	3.98879	−	6.90878i	0.655753	−	1.13580i	0.981705	−	0.190411i	$-0.0609819\pi$
$38$	−6.36691	+	8.14744i	−1.03285	+	1.32169i
$39$		0			0
$40$	3.28369	+	4.52274i	0.519197	+	0.715108i
$41$			6.55939i			1.02441i	0.858865	+	0.512203i	$0.171170\pi$
$41$			6.55939i			1.02441i	−0.858865	+	0.512203i	$0.828830\pi$
$42$		0			0
$43$		−	1.68401i		−	0.256809i	−0.991722	−	0.128404i	$-0.959014\pi$
$43$		−	1.68401i		−	0.256809i	0.991722	−	0.128404i	$-0.0409855\pi$
$44$	9.33588	−	2.32552i	1.40744	−	0.350586i
$45$		0			0
$46$	5.27529	+	4.12244i	0.777800	+	0.607821i
$47$	−1.30195	+	2.25504i	−0.189909	+	0.328932i	−0.945220	−	0.326435i	$-0.894153\pi$
$47$	−1.30195	+	2.25504i	−0.189909	+	0.328932i	0.755311	+	0.655367i	$0.227486\pi$
$48$		0			0
$49$	3.32318	−	6.16088i	0.474740	−	0.880126i
$50$	0.580091	+	1.43623i	0.0820373	+	0.203113i
$51$		0			0
$52$	−3.42144	+	11.9221i	−0.474469	+	1.65330i
$53$	−7.08914	−	12.2788i	−0.973769	−	1.68662i	−0.683939	−	0.729539i	$-0.739735\pi$
$53$	−7.08914	−	12.2788i	−0.973769	−	1.68662i	−0.289830	−	0.957078i	$-0.593599\pi$
$54$		0			0
$55$	−9.50588			−1.28177
$56$	7.43052	−	0.887345i	0.992945	−	0.118576i
$57$		0			0
$58$	4.33998	+	0.610429i	0.569867	+	0.0801533i
$59$	0.705675	+	1.22226i	0.0918710	+	0.159125i	0.908298	−	0.418323i	$-0.137382\pi$
$59$	0.705675	+	1.22226i	0.0918710	+	0.159125i	−0.816427	+	0.577448i	$0.804049\pi$
$60$		0			0
$61$	−5.09038	−	2.93893i	−0.651757	−	0.376292i	0.137372	−	0.990519i	$-0.456134\pi$
$61$	−5.09038	−	2.93893i	−0.651757	−	0.376292i	−0.789129	+	0.614228i	$0.789468\pi$
$62$	4.08394	+	10.1113i	0.518661	+	1.28414i
$63$		0			0
$64$	5.34914	+	5.94868i	0.668642	+	0.743584i
$65$	6.12738	−	10.6129i	0.760008	−	1.31637i
$66$		0			0
$67$	−4.74455	+	2.73927i	−0.579640	+	0.334655i	−0.760990	−	0.648763i	$-0.775286\pi$
$67$	−4.74455	+	2.73927i	−0.579640	+	0.334655i	0.181351	+	0.983419i	$0.441953\pi$
$68$	−1.46980	+	0.366120i	−0.178239	+	0.0443986i
$69$		0			0
$70$	−7.33572	−	0.923790i	−0.876786	−	0.110414i
$71$		−	13.5839i		−	1.61211i	−0.591842	−	0.806054i	$-0.701599\pi$
$71$		−	13.5839i		−	1.61211i	0.591842	−	0.806054i	$-0.298401\pi$
$72$		0			0
$73$	4.77149	−	2.75482i	0.558460	−	0.322427i	−0.194067	−	0.980988i	$-0.562168\pi$
$73$	4.77149	−	2.75482i	0.558460	−	0.322427i	0.752527	+	0.658561i	$0.228835\pi$
$74$	−6.94686	+	8.88957i	−0.807557	+	1.03339i
$75$		0			0
$76$	10.5212	−	10.1558i	1.20687	−	1.16495i
$77$	−6.20370	+	11.1133i	−0.706977	+	1.26648i
$78$		0			0
$79$	−3.07352	−	1.77450i	−0.345798	−	0.199646i	0.317035	−	0.948414i	$-0.397313\pi$
$79$	−3.07352	−	1.77450i	−0.345798	−	0.199646i	−0.662833	+	0.748767i	$0.730646\pi$
$80$	−3.70772	−	6.98058i	−0.414535	−	0.780452i
$81$		0			0
$82$	1.29203	−	9.18596i	0.142681	−	1.01442i
$83$	−1.69786			−0.186365			−0.0931823	−	0.995649i	$-0.529704\pi$
$83$	−1.69786			−0.186365			−0.0931823	+	0.995649i	$0.529704\pi$
$84$		0			0
$85$	1.49657			0.162325
$86$	−0.331705	+	2.35833i	−0.0357687	+	0.254305i
$87$		0			0
$88$	−13.5323	+	1.41781i	−1.44255	+	0.151139i
$89$	3.63341	+	2.09775i	0.385140	+	0.222361i	0.680052	−	0.733164i	$-0.261957\pi$
$89$	3.63341	+	2.09775i	0.385140	+	0.222361i	−0.294912	+	0.955524i	$0.595290\pi$
$90$		0			0
$91$	−8.40873	−	14.0897i	−0.881474	−	1.47700i
$92$	−6.57566	−	6.81228i	−0.685560	−	0.710230i
$93$		0			0
$94$	2.26747	−	2.90158i	0.233872	−	0.299275i
$95$	−12.5123	+	7.22398i	−1.28373	+	0.741164i
$96$		0			0
$97$		−	2.34249i		−	0.237844i	−0.992904	−	0.118922i	$-0.962056\pi$
$97$		−	2.34249i		−	0.237844i	0.992904	−	0.118922i	$-0.0379439\pi$
$98$	−5.86741	+	7.97330i	−0.592698	+	0.805425i
$99$		0			0
$100$	−0.529477	−	2.12560i	−0.0529477	−	0.212560i
$101$	7.25423	−	4.18823i	0.721823	−	0.416745i	−0.0936004	−	0.995610i	$-0.529838\pi$
$101$	7.25423	−	4.18823i	0.721823	−	0.416745i	0.815423	+	0.578865i	$0.196504\pi$
$102$		0			0
$103$	4.97152	−	8.61093i	0.489859	−	0.848460i	−0.510073	−	0.860131i	$-0.670382\pi$
$103$	4.97152	−	8.61093i	0.489859	−	0.848460i	0.999932	+	0.0116708i	$0.00371503\pi$
$104$	7.13983	−	16.0222i	0.700118	−	1.57110i
$105$		0			0
$106$	7.50925	+	18.5919i	0.729363	+	1.80581i
$107$	−3.80698	−	2.19796i	−0.368035	−	0.212485i	0.304565	−	0.952492i	$-0.401489\pi$
$107$	−3.80698	−	2.19796i	−0.368035	−	0.212485i	−0.672600	+	0.740007i	$0.734822\pi$
$108$		0			0
$109$	0.717301	+	1.24240i	0.0687050	+	0.119000i	0.898331	−	0.439318i	$-0.144780\pi$
$109$	0.717301	+	1.24240i	0.0687050	+	0.119000i	−0.829627	+	0.558319i	$0.811447\pi$
$110$	13.3123	+	1.87241i	1.26928	+	0.178527i
$111$		0			0
$112$	−10.5807	−	0.220955i	−0.999782	−	0.0208783i
$113$	9.63176			0.906080			0.453040	−	0.891490i	$-0.350340\pi$
$113$	9.63176			0.906080			0.453040	+	0.891490i	$0.350340\pi$
$114$		0			0
$115$	4.67737	+	8.10145i	0.436167	+	0.755464i
$116$	−5.95759	−	1.70972i	−0.553149	−	0.158744i
$117$		0			0
$118$	−0.747493	−	1.85069i	−0.0688123	−	0.170370i
$119$	0.976684	−	1.74963i	0.0895325	−	0.160389i
$120$		0			0
$121$	6.07083	−	10.5150i	0.551894	−	0.955909i
$122$	6.54982	+	5.11844i	0.592993	+	0.463402i
$123$		0			0
$124$	−3.72761	−	14.9646i	−0.334749	−	1.34386i
$125$			12.0445i			1.07729i
$126$		0			0
$127$		−	6.40278i		−	0.568155i	−0.958801	−	0.284077i	$-0.908313\pi$
$127$		−	6.40278i		−	0.568155i	0.958801	−	0.284077i	$-0.0916873\pi$
$128$	−6.31935	−	9.38434i	−0.558557	−	0.829466i
$129$		0			0
$130$	−10.6714	+	13.6557i	−0.935946	+	1.19769i
$131$	2.50668	−	4.34170i	0.219010	−	0.379336i	−0.735496	−	0.677529i	$-0.763051\pi$
$131$	2.50668	−	4.34170i	0.219010	−	0.379336i	0.954505	+	0.298193i	$0.0963840\pi$
$132$		0			0
$133$	0.279808	+	19.3426i	0.0242625	+	1.67722i
$134$	7.18398	−	2.90160i	0.620601	−	0.250660i
$135$		0			0
$136$	2.13047	−	0.223213i	0.182686	−	0.0191404i
$137$	−3.66512	−	6.34817i	−0.313132	−	0.542361i	0.665906	−	0.746035i	$-0.268045\pi$
$137$	−3.66512	−	6.34817i	−0.313132	−	0.542361i	−0.979039	+	0.203674i	$0.934712\pi$
$138$		0			0
$139$	−9.10443			−0.772228			−0.386114	−	0.922451i	$-0.626183\pi$
$139$	−9.10443			−0.772228			−0.386114	+	0.922451i	$0.626183\pi$
$140$	10.0912	+	2.73865i	0.852861	+	0.231458i
$141$		0			0
$142$	−2.67567	+	19.0232i	−0.224537	+	1.59640i
$143$	14.9168	+	25.8367i	1.24741	+	2.16058i
$144$		0			0
$145$	5.30337	+	3.06190i	0.440421	+	0.254277i
$146$	−7.22476	+	2.91807i	−0.597925	+	0.241501i
$147$		0			0
$148$	11.4796	−	11.0809i	0.943618	−	0.910841i
$149$	−10.1483	+	17.5773i	−0.831378	+	1.43999i	0.0655670	+	0.997848i	$0.479114\pi$
$149$	−10.1483	+	17.5773i	−0.831378	+	1.43999i	−0.896945	+	0.442141i	$0.854219\pi$
$150$		0			0
$151$	−3.56070	+	2.05577i	−0.289765	+	0.167296i	−0.637836	−	0.770172i	$-0.720170\pi$
$151$	−3.56070	+	2.05577i	−0.289765	+	0.167296i	0.348071	+	0.937468i	$0.386837\pi$
$152$	−16.7347	+	12.1501i	−1.35736	+	0.985500i
$153$		0			0
$154$	10.8769	−	14.3414i	0.876483	−	1.15567i
$155$			15.2371i			1.22387i
$156$		0			0
$157$	−1.79813	+	1.03815i	−0.143506	+	0.0828535i	−0.570034	−	0.821621i	$-0.693070\pi$
$157$	−1.79813	+	1.03815i	−0.143506	+	0.0828535i	0.426528	+	0.904475i	$0.359737\pi$
$158$	3.95471	+	3.09046i	0.314620	+	0.245864i
$159$		0			0
$160$	3.81740	+	10.5061i	0.301792	+	0.830582i
$161$	12.5239	−	0.181170i	0.987023	−	0.0142782i
$162$		0			0
$163$	9.41077	+	5.43331i	0.737108	+	0.425570i	0.821017	−	0.570904i	$-0.193407\pi$
$163$	9.41077	+	5.43331i	0.737108	+	0.425570i	−0.0839087	+	0.996473i	$0.526740\pi$
$164$	−3.61879	+	12.6098i	−0.282580	+	0.984659i
$165$		0			0
$166$	2.37774	+	0.334435i	0.184548	+	0.0259572i
$167$	−0.304029			−0.0235264			−0.0117632	−	0.999931i	$-0.503744\pi$
$167$	−0.304029			−0.0235264			−0.0117632	+	0.999931i	$0.503744\pi$
$168$		0			0
$169$	−25.4608			−1.95853
$170$	−2.09583	−	0.294784i	−0.160743	−	0.0226089i
$171$		0			0
$172$	0.929060	−	3.23734i	0.0708401	−	0.246845i
$173$	14.2752	+	8.24177i	1.08532	+	0.626610i	0.932327	−	0.361617i	$-0.117775\pi$
$173$	14.2752	+	8.24177i	1.08532	+	0.626610i	0.152993	+	0.988227i	$0.451109\pi$
$174$		0			0
$175$	2.53029	+	1.41246i	0.191272	+	0.106772i
$176$	19.2303	+	0.679973i	1.44954	+	0.0512549i
$177$		0			0
$178$	−4.67513	−	3.65343i	−0.350416	−	0.273836i
$179$	−6.41981	+	3.70648i	−0.479839	+	0.277035i	−0.720349	−	0.693611i	$-0.756018\pi$
$179$	−6.41981	+	3.70648i	−0.479839	+	0.277035i	0.240511	+	0.970647i	$0.422685\pi$
$180$		0			0
$181$			9.53385i			0.708645i	0.935123	+	0.354323i	$0.115289\pi$
$181$			9.53385i			0.708645i	−0.935123	+	0.354323i	$0.884711\pi$
$182$	9.00053	+	21.3879i	0.667164	+	1.58538i
$183$		0			0
$184$	7.86690	+	10.8354i	0.579956	+	0.798793i
$185$	−13.6520	+	7.88199i	−1.00372	+	0.579496i
$186$		0			0
$187$	−1.82166	+	3.15521i	−0.133213	+	0.230732i
$188$	−3.74697	+	3.61682i	−0.273276	+	0.263784i
$189$		0			0
$190$	18.9455	−	7.65207i	1.37445	−	0.555139i
$191$	9.51327	+	5.49249i	0.688356	+	0.397423i	0.802996	−	0.595984i	$-0.203238\pi$
$191$	9.51327	+	5.49249i	0.688356	+	0.397423i	−0.114640	+	0.993407i	$0.536571\pi$
$192$		0			0
$193$	−2.04048	−	3.53422i	−0.146877	−	0.254399i	0.783195	−	0.621777i	$-0.213589\pi$
$193$	−2.04048	−	3.53422i	−0.146877	−	0.254399i	−0.930072	+	0.367378i	$0.880256\pi$
$194$	−0.461410	+	3.28050i	−0.0331273	+	0.235526i
$195$		0			0
$196$	9.78743	−	10.0103i	0.699102	−	0.715022i
$197$	16.9828			1.20997			0.604986	−	0.796236i	$-0.293179\pi$
$197$	16.9828			1.20997			0.604986	+	0.796236i	$0.293179\pi$
$198$		0			0
$199$	6.24122	+	10.8101i	0.442428	+	0.766308i	0.997869	−	0.0652480i	$-0.0207839\pi$
$199$	6.24122	+	10.8101i	0.442428	+	0.766308i	−0.555441	+	0.831556i	$0.687451\pi$
$200$	0.322807	+	3.08104i	0.0228259	+	0.217863i
$201$		0			0
$202$	−10.9840	+	4.43643i	−0.772832	+	0.312146i
$203$	7.04074	−	4.20192i	0.494163	−	0.294917i
$204$		0			0
$205$	6.48080	−	11.2251i	0.452639	−	0.783994i
$206$	−8.65839	+	11.0797i	−0.603259	+	0.771962i
$207$		0			0
$208$	−13.1548	+	21.0315i	−0.912120	+	1.45827i
$209$		−	35.1729i		−	2.43296i
$210$		0			0
$211$		−	5.89818i		−	0.406048i	−0.979174	−	0.203024i	$-0.934923\pi$
$211$		−	5.89818i		−	0.406048i	0.979174	−	0.203024i	$-0.0650769\pi$
$212$	−6.85405	−	27.5158i	−0.470738	−	1.88979i
$213$		0			0
$214$	4.89847	+	3.82796i	0.334852	+	0.261674i
$215$	−1.66383	+	2.88184i	−0.113472	+	0.196540i
$216$		0			0
$217$	17.8136	+	9.94397i	1.20927	+	0.675041i
$218$	−0.759808	−	1.88118i	−0.0514607	−	0.127410i
$219$		0			0
$220$	−18.2741	−	5.24436i	−1.23204	−	0.353574i
$221$	−2.34844	−	4.06762i	−0.157973	−	0.273618i
$222$		0			0
$223$	9.14283			0.612249			0.306125	−	0.951991i	$-0.400968\pi$
$223$	9.14283			0.612249			0.306125	+	0.951991i	$0.400968\pi$
$224$	14.7740	+	2.39355i	0.987129	+	0.159926i
$225$		0			0
$226$	−13.4886	−	1.89721i	−0.897248	−	0.126200i
$227$	−0.209496	−	0.362857i	−0.0139047	−	0.0240837i	0.858989	−	0.511994i	$-0.171093\pi$
$227$	−0.209496	−	0.362857i	−0.0139047	−	0.0240837i	−0.872894	+	0.487910i	$0.837759\pi$
$228$		0			0
$229$	−7.23831	−	4.17904i	−0.478321	−	0.276159i	0.241395	−	0.970427i	$-0.422395\pi$
$229$	−7.23831	−	4.17904i	−0.478321	−	0.276159i	−0.719717	+	0.694268i	$0.755728\pi$
$230$	−4.95455	−	12.2668i	−0.326694	−	0.808850i
$231$		0			0
$232$	8.00641	+	3.56784i	0.525647	+	0.234240i
$233$	7.94314	−	13.7579i	0.520373	−	0.901312i	−0.479347	−	0.877626i	$-0.659126\pi$
$233$	7.94314	−	13.7579i	0.520373	−	0.901312i	0.999719	−	0.0236862i	$-0.00754024\pi$
$234$		0			0
$235$	4.45605	−	2.57270i	0.290681	−	0.167825i
$236$	0.682273	+	2.73900i	0.0444122	+	0.178294i
$237$		0			0
$238$	−1.71241	+	2.25786i	−0.110999	+	0.146355i
$239$		−	14.2548i		−	0.922066i	−0.887383	−	0.461033i	$-0.847479\pi$
$239$		−	14.2548i		−	0.922066i	0.887383	−	0.461033i	$-0.152521\pi$
$240$		0			0
$241$	17.8755	−	10.3204i	1.15146	−	0.664798i	0.202220	−	0.979340i	$-0.435184\pi$
$241$	17.8755	−	10.3204i	1.15146	−	0.664798i	0.949244	+	0.314542i	$0.101851\pi$
$242$	−10.5730	+	13.5297i	−0.679655	+	0.869722i
$243$		0			0
$244$	−8.16437	−	8.45816i	−0.522670	−	0.541478i
$245$	−11.7740	+	7.25974i	−0.752215	+	0.463808i
$246$		0			0
$247$	39.2691	+	22.6720i	2.49863	+	1.44259i
$248$	2.27262	+	21.6911i	0.144311	+	1.37738i
$249$		0			0
$250$	2.37245	−	16.8675i	0.150047	−	1.06679i
$251$	−25.1877			−1.58983			−0.794916	−	0.606719i	$-0.792485\pi$
$251$	−25.1877			−1.58983			−0.794916	+	0.606719i	$0.792485\pi$
$252$		0			0
$253$	−22.7737			−1.43177
$254$	−1.26118	+	8.96664i	−0.0791335	+	0.562617i
$255$		0			0
$256$	7.00133	+	14.3868i	0.437583	+	0.899178i
$257$	9.88611	+	5.70775i	0.616679	+	0.356040i	0.775575	−	0.631256i	$-0.217460\pi$
$257$	9.88611	+	5.70775i	0.616679	+	0.356040i	−0.158896	+	0.987295i	$0.550793\pi$
$258$		0			0
$259$	0.305296	+	21.1045i	0.0189701	+	1.31137i
$260$	17.6344	−	17.0219i	1.09364	−	1.05565i
$261$		0			0
$262$	−4.36563	+	5.58649i	−0.269709	+	0.345134i
$263$	−10.8107	+	6.24157i	−0.666618	+	0.384872i	−0.794794	−	0.606879i	$-0.792421\pi$
$263$	−10.8107	+	6.24157i	−0.666618	+	0.384872i	0.128176	+	0.991751i	$0.459088\pi$
$264$		0			0
$265$			28.0168i			1.72106i
$266$	3.41813	−	27.1430i	0.209579	−	1.66425i
$267$		0			0
$268$	−10.6322	+	2.64843i	−0.649464	+	0.161778i
$269$	−24.1273	+	13.9299i	−1.47107	+	0.849320i	−0.999472	−	0.0324965i	$-0.989654\pi$
$269$	−24.1273	+	13.9299i	−1.47107	+	0.849320i	−0.471593	+	0.881816i	$0.656321\pi$
$270$		0			0
$271$	0.180937	−	0.313392i	0.0109911	−	0.0190372i	−0.860478	−	0.509488i	$-0.829835\pi$
$271$	0.180937	−	0.313392i	0.0109911	−	0.0190372i	0.871469	+	0.490451i	$0.163168\pi$
$272$	−3.02754	−	0.107052i	−0.183571	−	0.00649098i
$273$		0			0
$274$	3.88231	+	9.61210i	0.234539	+	0.580688i
$275$	−4.56301	−	2.63446i	−0.275160	−	0.158864i
$276$		0			0
$277$	0.0981669	+	0.170030i	0.00589828	+	0.0102161i	0.868959	−	0.494883i	$-0.164789\pi$
$277$	0.0981669	+	0.170030i	0.00589828	+	0.0102161i	−0.863061	+	0.505099i	$0.831456\pi$
$278$	12.7501	+	1.79334i	0.764701	+	0.107557i
$279$		0			0
$280$	−13.5926	−	5.82298i	−0.812310	−	0.347990i
$281$	11.3060			0.674460			0.337230	−	0.941422i	$-0.390510\pi$
$281$	11.3060			0.674460			0.337230	+	0.941422i	$0.390510\pi$
$282$		0			0
$283$	−3.29624	−	5.70926i	−0.195941	−	0.339380i	0.751267	−	0.659998i	$-0.229443\pi$
$283$	−3.29624	−	5.70926i	−0.195941	−	0.339380i	−0.947209	+	0.320618i	$0.896110\pi$
$284$	7.49416	−	26.1137i	0.444697	−	1.54956i
$285$		0			0
$286$	−15.8008	−	39.1207i	−0.934322	−	2.31326i
$287$	−8.89375	−	14.9024i	−0.524981	−	0.879659i
$288$		0			0
$289$	−8.21321	+	14.2257i	−0.483130	+	0.836805i
$290$	−6.82388	−	5.33261i	−0.400712	−	0.313141i
$291$		0			0
$292$	10.6925	−	2.66346i	0.625734	−	0.155867i
$293$			11.8939i			0.694850i	0.937708	+	0.347425i	$0.112944\pi$
$293$			11.8939i			0.694850i	−0.937708	+	0.347425i	$0.887056\pi$
$294$		0			0
$295$		−	2.78888i		−	0.162375i
$296$	−18.2590	+	13.2568i	−1.06128	+	0.770535i
$297$		0			0
$298$	17.6742	−	22.6168i	1.02384	−	1.31016i
$299$	14.6797	−	25.4259i	0.848947	−	1.47042i
$300$		0			0
$301$	2.28331	+	3.82592i	0.131608	+	0.220522i
$302$	5.39143	−	2.17759i	0.310242	−	0.125306i
$303$		0			0
$304$	25.8290	−	13.7190i	1.48139	−	0.786838i
$305$	5.80744	+	10.0588i	0.332533	+	0.575964i
$306$		0			0
$307$	−6.94580			−0.396418			−0.198209	−	0.980160i	$-0.563512\pi$
$307$	−6.94580			−0.396418			−0.198209	+	0.980160i	$0.563512\pi$
$308$	−18.0572	+	17.9417i	−1.02890	+	1.02232i
$309$		0			0
$310$	3.00131	−	21.3384i	0.170463	−	1.21194i
$311$	−6.75653	−	11.7026i	−0.383127	−	0.663596i	0.608380	−	0.793646i	$-0.291820\pi$
$311$	−6.75653	−	11.7026i	−0.383127	−	0.663596i	−0.991507	+	0.130050i	$0.958486\pi$
$312$		0			0
$313$	−13.8092	−	7.97276i	−0.780544	−	0.450647i	0.0560793	−	0.998426i	$-0.482140\pi$
$313$	−13.8092	−	7.97276i	−0.780544	−	0.450647i	−0.836623	+	0.547779i	$0.815473\pi$
$314$	2.72264	−	1.09967i	0.153648	−	0.0620581i
$315$		0			0
$316$	−4.92956	−	5.10694i	−0.277309	−	0.287288i
$317$	−2.04296	+	3.53851i	−0.114744	+	0.198742i	−0.917677	−	0.397326i	$-0.869938\pi$
$317$	−2.04296	+	3.53851i	−0.114744	+	0.198742i	0.802933	+	0.596069i	$0.203271\pi$
$318$		0			0
$319$	−12.9108	+	7.45408i	−0.722868	+	0.417348i
$320$	−3.27657	−	15.4650i	−0.183166	−	0.864520i
$321$		0			0
$322$	−17.5745	−	2.21317i	−0.979391	−	0.123335i
$323$			5.53747i			0.308113i
$324$		0			0
$325$	5.88252	−	3.39628i	0.326304	−	0.188392i
$326$	−12.1089	−	9.46264i	−0.670650	−	0.524087i
$327$		0			0
$328$	7.55166	−	16.9463i	0.416971	−	0.935704i
$329$	−0.0996493	−	6.88855i	−0.00549384	−	0.379778i
$330$		0			0
$331$	−2.18945	−	1.26408i	−0.120343	−	0.0694802i	0.438620	−	0.898673i	$-0.355467\pi$
$331$	−2.18945	−	1.26408i	−0.120343	−	0.0694802i	−0.558963	+	0.829192i	$0.688801\pi$
$332$	−3.26398	−	0.936704i	−0.179134	−	0.0514083i
$333$		0			0
$334$	0.425771	+	0.0598857i	0.0232971	+	0.00327680i
$335$	10.8258			0.591477
$336$		0			0
$337$	−22.5751			−1.22974			−0.614871	−	0.788628i	$-0.710792\pi$
$337$	−22.5751			−1.22974			−0.614871	+	0.788628i	$0.710792\pi$
$338$	35.6561	+	5.01512i	1.93944	+	0.272787i
$339$		0			0
$340$	2.87700	+	0.825649i	0.156027	+	0.0447771i
$341$	−32.1244	−	18.5470i	−1.73963	−	1.00438i
$342$		0			0
$343$	0.803429	+	18.5028i	0.0433811	+	0.999059i
$344$	−1.93875	+	4.35066i	−0.104531	+	0.234572i
$345$		0			0
$346$	−18.3679	−	14.3538i	−0.987466	−	0.771667i
$347$	−17.6758	+	10.2051i	−0.948887	+	0.547840i	−0.892735	−	0.450582i	$-0.851217\pi$
$347$	−17.6758	+	10.2051i	−0.948887	+	0.547840i	−0.0561522	+	0.998422i	$0.517883\pi$
$348$		0			0
$349$			25.8627i			1.38440i	0.721707	+	0.692198i	$0.243358\pi$
$349$			25.8627i			1.38440i	−0.721707	+	0.692198i	$0.756642\pi$
$350$	−3.26527	−	2.47645i	−0.174536	−	0.132372i
$351$		0			0
$352$	−26.7967	−	4.74012i	−1.42827	−	0.252649i
$353$	8.02023	−	4.63048i	0.426874	−	0.246456i	−0.271140	−	0.962540i	$-0.587401\pi$
$353$	8.02023	−	4.63048i	0.426874	−	0.246456i	0.698014	+	0.716084i	$0.254067\pi$
$354$		0			0
$355$	−13.4211	+	23.2461i	−0.712319	+	1.23377i
$356$	5.82755	+	6.03725i	0.308860	+	0.319974i
$357$		0			0
$358$	9.72056	−	3.92612i	0.513748	−	0.207502i
$359$	3.83076	+	2.21169i	0.202180	+	0.116729i	0.597672	−	0.801741i	$-0.296093\pi$
$359$	3.83076	+	2.21169i	0.202180	+	0.116729i	−0.395492	+	0.918469i	$0.629426\pi$
$360$		0			0
$361$	−17.2296	−	29.8425i	−0.906820	−	1.57066i
$362$	1.87792	−	13.3515i	0.0987012	−	0.701738i
$363$		0			0
$364$	−8.39175	−	31.7251i	−0.439847	−	1.66285i
$365$	−10.8873			−0.569865
$366$		0			0
$367$	−5.06778	−	8.77764i	−0.264536	−	0.458189i	0.702906	−	0.711283i	$-0.251885\pi$
$367$	−5.06778	−	8.77764i	−0.264536	−	0.458189i	−0.967442	+	0.253093i	$0.918552\pi$
$368$	−8.88276	−	16.7237i	−0.463046	−	0.871784i
$369$		0			0
$370$	20.6712	−	8.34908i	1.07465	−	0.434048i
$371$	32.7544	+	18.2843i	1.70053	+	0.949271i
$372$		0			0
$373$	15.8755	−	27.4972i	0.822004	−	1.42375i	−0.0821834	−	0.996617i	$-0.526189\pi$
$373$	15.8755	−	27.4972i	0.822004	−	1.42375i	0.904188	−	0.427136i	$-0.140477\pi$
$374$	3.17260	−	4.05983i	0.164051	−	0.209929i
$375$		0			0
$376$	5.95979	−	4.32705i	0.307353	−	0.223150i
$377$		−	19.2192i		−	0.989840i
$378$		0			0
$379$			28.7095i			1.47471i	0.675507	+	0.737353i	$0.263925\pi$
$379$			28.7095i			1.47471i	−0.675507	+	0.737353i	$0.736075\pi$
$380$	−28.0391	+	6.98441i	−1.43838	+	0.358293i
$381$		0			0
$382$	−12.2408	−	9.56571i	−0.626293	−	0.489424i
$383$	2.28944	−	3.96542i	0.116985	−	0.202624i	−0.801587	−	0.597879i	$-0.796010\pi$
$383$	2.28944	−	3.96542i	0.116985	−	0.202624i	0.918571	+	0.395255i	$0.129344\pi$
$384$		0			0
$385$	21.5965	−	12.8888i	1.10066	−	0.656876i
$386$	2.16140	+	5.35135i	0.110012	+	0.272376i
$387$		0			0
$388$	1.29234	−	4.50322i	0.0656089	−	0.228616i
$389$	−9.00917	−	15.6043i	−0.456783	−	0.791172i	0.542005	−	0.840375i	$-0.317665\pi$
$389$	−9.00917	−	15.6043i	−0.456783	−	0.791172i	−0.998789	+	0.0492031i	$0.984332\pi$
$390$		0			0
$391$	3.58540			0.181321
$392$	−15.6784	+	12.0909i	−0.791877	+	0.610681i
$393$		0			0
$394$	−23.7832	−	3.34516i	−1.19818	−	0.168527i
$395$	3.50647	+	6.07339i	0.176430	+	0.305585i
$396$		0			0
$397$	−20.9333	−	12.0859i	−1.05061	−	0.606571i	−0.127792	−	0.991801i	$-0.540789\pi$
$397$	−20.9333	−	12.0859i	−1.05061	−	0.606571i	−0.922821	+	0.385230i	$0.874122\pi$
$398$	−6.61107	−	16.3681i	−0.331383	−	0.820461i
$399$		0			0
$400$	0.154817	−	4.37837i	0.00774084	−	0.218918i
$401$	0.218547	−	0.378535i	0.0109137	−	0.0189031i	−0.860517	−	0.509422i	$-0.829859\pi$
$401$	0.218547	−	0.378535i	0.0109137	−	0.0189031i	0.871431	+	0.490519i	$0.163193\pi$
$402$		0			0
$403$	41.4139	−	23.9103i	2.06298	−	1.19106i
$404$	16.2562	−	4.04934i	0.808775	−	0.201462i
$405$		0			0
$406$	−10.6877	+	4.49765i	−0.530423	+	0.223214i
$407$		−	38.3768i		−	1.90227i
$408$		0			0
$409$	−25.2698	+	14.5895i	−1.24951	+	0.721406i	−0.971012	−	0.239030i	$-0.923171\pi$
$409$	−25.2698	+	14.5895i	−1.24951	+	0.721406i	−0.278500	+	0.960436i	$0.589837\pi$
$410$	−11.2870	+	14.4434i	−0.557423	+	0.713308i
$411$		0			0
$412$	14.3079	−	13.8109i	0.704899	−	0.680414i
$413$	−3.26048	−	1.82007i	−0.160438	−	0.0895598i
$414$		0			0
$415$	2.90555	+	1.67752i	0.142628	+	0.0823462i
$416$	22.5650	−	26.8620i	1.10634	−	1.31702i
$417$		0			0
$418$	−6.92815	+	49.2572i	−0.338867	+	2.40925i
$419$	28.9081			1.41225			0.706126	−	0.708086i	$-0.250441\pi$
$419$	28.9081			1.41225			0.706126	+	0.708086i	$0.250441\pi$
$420$		0			0
$421$	25.1451			1.22550			0.612748	−	0.790279i	$-0.290064\pi$
$421$	25.1451			1.22550			0.612748	+	0.790279i	$0.290064\pi$
$422$	−1.16179	+	8.25999i	−0.0565550	+	0.402090i
$423$		0			0
$424$	4.17872	+	39.8840i	0.202937	+	1.93694i
$425$	0.718381	+	0.414757i	0.0348466	+	0.0201187i
$426$		0			0
$427$	15.5497	−	0.224941i	0.752505	−	0.0108857i
$428$	−6.10594	−	6.32566i	−0.295142	−	0.305762i
$429$		0			0
$430$	2.89772	−	3.70808i	0.139741	−	0.178819i
$431$	31.3591	−	18.1052i	1.51051	−	0.872096i	0.510590	−	0.859824i	$-0.329427\pi$
$431$	31.3591	−	18.1052i	1.51051	−	0.872096i	0.999925	−	0.0122715i	$-0.00390624\pi$
$432$		0			0
$433$			16.6847i			0.801815i	0.916118	+	0.400908i	$0.131305\pi$
$433$			16.6847i			0.801815i	−0.916118	+	0.400908i	$0.868695\pi$
$434$	−22.9880	−	17.4347i	−1.10346	−	0.836890i
$435$		0			0
$436$	0.693513	+	2.78413i	0.0332133	+	0.133336i
$437$	−29.9763	+	17.3068i	−1.43396	+	0.827898i
$438$		0			0
$439$	1.97873	−	3.42726i	0.0944397	−	0.163574i	−0.814935	−	0.579552i	$-0.803227\pi$
$439$	1.97873	−	3.42726i	0.0944397	−	0.163574i	0.909375	+	0.415978i	$0.136561\pi$
$440$	24.5586	+	10.9439i	1.17079	+	0.521729i
$441$		0			0
$442$	2.48761	+	6.15900i	0.118324	+	0.292954i
$443$	−28.3695	−	16.3791i	−1.34788	−	0.778197i	−0.359928	−	0.932980i	$-0.617199\pi$
$443$	−28.3695	−	16.3791i	−1.34788	−	0.778197i	−0.987948	+	0.154783i	$0.950532\pi$
$444$		0			0
$445$	−4.14523	−	7.17975i	−0.196503	−	0.340353i
$446$	−12.8039	−	1.80090i	−0.606281	−	0.0852750i
$447$		0			0
$448$	−20.2185	−	6.26209i	−0.955233	−	0.295856i
$449$	19.0426			0.898674			0.449337	−	0.893362i	$-0.351660\pi$
$449$	19.0426			0.898674			0.449337	+	0.893362i	$0.351660\pi$
$450$		0			0
$451$	15.7772	+	27.3270i	0.742921	+	1.28678i
$452$	18.5161	+	5.31380i	0.870925	+	0.249940i
$453$		0			0
$454$	0.221910	+	0.549421i	0.0104148	+	0.0257856i
$455$	0.468980	+	32.4196i	0.0219861	+	1.51986i
$456$		0			0
$457$	−7.15834	+	12.3986i	−0.334853	+	0.579982i	−0.983457	−	0.181144i	$-0.942020\pi$
$457$	−7.15834	+	12.3986i	−0.334853	+	0.579982i	0.648604	+	0.761126i	$0.275353\pi$
$458$	9.31358	+	7.27821i	0.435195	+	0.340088i
$459$		0			0
$460$	4.52226	+	18.1547i	0.210851	+	0.846468i
$461$		−	9.65993i		−	0.449908i	−0.974369	−	0.224954i	$-0.927777\pi$
$461$		−	9.65993i		−	0.449908i	0.974369	−	0.224954i	$-0.0722232\pi$
$462$		0			0
$463$		−	1.82546i		−	0.0848364i	−0.999100	−	0.0424182i	$-0.986494\pi$
$463$		−	1.82546i		−	0.0848364i	0.999100	−	0.0424182i	$-0.0135062\pi$
$464$	−10.5096	−	6.57356i	−0.487898	−	0.305170i
$465$		0			0
$466$	−13.8338	+	17.7024i	−0.640836	+	0.820048i
$467$	−10.2609	+	17.7724i	−0.474819	+	0.822411i	−0.999584	−	0.0288364i	$-0.990820\pi$
$467$	−10.2609	+	17.7724i	−0.474819	+	0.822411i	0.524765	+	0.851247i	$0.324153\pi$
$468$		0			0
$469$	7.06510	−	12.6564i	0.326236	−	0.584419i
$470$	−6.74714	+	2.72516i	−0.311222	+	0.125702i
$471$		0			0
$472$	−0.415963	−	3.97017i	−0.0191462	−	0.182742i
$473$	−4.05052	−	7.01571i	−0.186243	−	0.322583i
$474$		0			0
$475$	−8.00820			−0.367441
$476$	2.84284	−	2.82467i	0.130302	−	0.129468i
$477$		0			0
$478$	−2.80782	+	19.9628i	−0.128427	+	0.913078i
$479$	7.97795	+	13.8182i	0.364522	+	0.631370i	0.988699	−	0.149912i	$-0.0478991\pi$
$479$	7.97795	+	13.8182i	0.364522	+	0.631370i	−0.624177	+	0.781283i	$0.714566\pi$
$480$		0			0
$481$	42.8461	+	24.7372i	1.95361	+	1.12792i
$482$	−27.0663	+	10.9320i	−1.23283	+	0.497940i
$483$		0			0
$484$	17.4717	−	16.8648i	0.794167	−	0.766582i
$485$	−2.31443	+	4.00871i	−0.105093	+	0.182026i
$486$		0			0
$487$	3.89609	−	2.24941i	0.176549	−	0.101930i	−0.409121	−	0.912480i	$-0.634165\pi$
$487$	3.89609	−	2.24941i	0.176549	−	0.101930i	0.585670	+	0.810549i	$0.300831\pi$
$488$	9.76758	+	13.4532i	0.442157	+	0.608998i
$489$		0			0
$490$	17.9187	−	7.84758i	0.809483	−	0.354517i
$491$		−	13.6569i		−	0.616326i	−0.951334	−	0.308163i	$-0.900286\pi$
$491$		−	13.6569i		−	0.616326i	0.951334	−	0.308163i	$-0.0997141\pi$
$492$		0			0
$493$	2.03263	−	1.17354i	0.0915449	−	0.0528535i
$494$	−50.5278	−	39.4856i	−2.27335	−	1.77654i
$495$		0			0
$496$	1.08994	−	30.8244i	0.0489396	−	1.38406i
$497$	18.4181	+	30.8614i	0.826164	+	1.38432i
$498$		0			0
$499$	−22.1621	−	12.7953i	−0.992111	−	0.572795i	−0.0862061	−	0.996277i	$-0.527474\pi$
$499$	−22.1621	−	12.7953i	−0.992111	−	0.572795i	−0.905905	+	0.423482i	$0.860808\pi$
$500$	−6.64490	+	23.1544i	−0.297169	+	1.03549i
$501$		0			0
$502$	35.2736	+	4.96132i	1.57434	+	0.221434i
$503$	21.1389			0.942538			0.471269	−	0.881989i	$-0.343796\pi$
$503$	21.1389			0.942538			0.471269	+	0.881989i	$0.343796\pi$
$504$		0			0
$505$	−16.5522			−0.736563
$506$	31.8930	+	4.48583i	1.41782	+	0.199419i
$507$		0			0
$508$	3.53239	−	12.3087i	0.156724	−	0.546111i
$509$	9.04476	+	5.22200i	0.400902	+	0.231461i	0.686873	−	0.726777i	$-0.258983\pi$
$509$	9.04476	+	5.22200i	0.400902	+	0.231461i	−0.285971	+	0.958238i	$0.592316\pi$
$510$		0			0
$511$	−7.10520	+	12.7283i	−0.314316	+	0.563066i
$512$	−6.97104	−	21.5268i	−0.308079	−	0.951361i
$513$		0			0
$514$	−12.7205	−	9.94060i	−0.561078	−	0.438461i
$515$	−17.0155	+	9.82392i	−0.749793	+	0.432893i
$516$		0			0
$517$			12.5263i			0.550905i
$518$	3.72949	−	29.6155i	0.163864	−	1.30123i
$519$		0			0
$520$	−28.0486	+	20.3644i	−1.23001	+	0.893038i
$521$	1.00866	−	0.582350i	0.0441902	−	0.0255132i	−0.477742	−	0.878500i	$-0.658545\pi$
$521$	1.00866	−	0.582350i	0.0441902	−	0.0255132i	0.521932	+	0.852987i	$0.325211\pi$
$522$		0			0
$523$	4.63052	−	8.02030i	0.202479	−	0.350703i	−0.746848	−	0.664995i	$-0.768434\pi$
$523$	4.63052	−	8.02030i	0.202479	−	0.350703i	0.949326	+	0.314292i	$0.101767\pi$
$524$	7.21414	−	6.96356i	0.315151	−	0.304205i
$525$		0			0
$526$	16.3691	−	6.61145i	0.713726	−	0.288273i
$527$	5.05752	+	2.91996i	0.220309	+	0.127196i
$528$		0			0
$529$	−0.294186	−	0.509544i	−0.0127907	−	0.0221541i
$530$	5.51858	−	39.2356i	0.239712	−	1.70428i
$531$		0			0
$532$	−10.1333	+	37.3386i	−0.439335	+	1.61883i
$533$	−40.6793			−1.76201
$534$		0			0
$535$	4.34325	+	7.52274i	0.187775	+	0.325236i
$536$	15.4113	−	1.61467i	0.665666	−	0.0697432i
$537$		0			0
$538$	36.5323	−	14.7554i	1.57502	−	0.636149i
$539$	−0.974048	−	33.6600i	−0.0419552	−	1.44984i
$540$		0			0
$541$	11.4477	−	19.8280i	0.492176	−	0.852474i	−0.507783	−	0.861485i	$-0.669535\pi$
$541$	11.4477	−	19.8280i	0.492176	−	0.852474i	0.999959	+	0.00901057i	$0.00286819\pi$
$542$	−0.315120	+	0.403244i	−0.0135356	+	0.0173208i
$543$		0			0
$544$	4.21876	+	0.746264i	0.180878	+	0.0319958i
$545$		−	2.83483i		−	0.121431i
$546$		0			0
$547$		−	25.4471i		−	1.08804i	−0.839072	−	0.544021i	$-0.816901\pi$
$547$		−	25.4471i		−	1.08804i	0.839072	−	0.544021i	$-0.183099\pi$
$548$	−3.54357	−	14.2258i	−0.151374	−	0.607695i
$549$		0			0
$550$	5.87125	+	4.58816i	0.250351	+	0.195640i
$551$	−11.3294	+	19.6231i	−0.482649	+	0.835973i
$552$		0			0
$553$	9.38877	−	0.135817i	0.399251	−	0.00577553i
$554$	−0.103984	−	0.257451i	−0.00441787	−	0.0109381i
$555$		0			0
$556$	−17.5024	−	5.02288i	−0.742266	−	0.213017i
$557$	20.9316	+	36.2546i	0.886900	+	1.53616i	0.843520	+	0.537098i	$0.180479\pi$
$557$	20.9316	+	36.2546i	0.886900	+	1.53616i	0.0433802	+	0.999059i	$0.486187\pi$
$558$		0			0
$559$	10.4437			0.441720
$560$	17.8884	+	10.8320i	0.755924	+	0.457738i
$561$		0			0
$562$	−15.8333	−	2.22699i	−0.667886	−	0.0939399i
$563$	−12.2973	−	21.2995i	−0.518268	−	0.897666i	−0.999775	−	0.0212241i	$-0.993244\pi$
$563$	−12.2973	−	21.2995i	−0.518268	−	0.897666i	0.481507	−	0.876442i	$-0.340090\pi$
$564$		0			0
$565$	−16.4828	−	9.51636i	−0.693437	−	0.400356i
$566$	3.49158	+	8.64469i	0.146762	+	0.363363i
$567$		0			0
$568$	−15.6388	+	35.0942i	−0.656188	+	1.47252i
$569$	15.6153	−	27.0464i	0.654625	−	1.13384i	−0.327362	−	0.944899i	$-0.606160\pi$
$569$	15.6153	−	27.0464i	0.654625	−	1.13384i	0.981988	−	0.188946i	$-0.0605070\pi$
$570$		0			0
$571$	27.9035	−	16.1101i	1.16772	−	0.674186i	0.214582	−	0.976706i	$-0.431161\pi$
$571$	27.9035	−	16.1101i	1.16772	−	0.674186i	0.953143	+	0.302520i	$0.0978279\pi$
$572$	14.4222	+	57.8981i	0.603021	+	2.42084i
$573$		0			0
$574$	9.51968	+	22.6216i	0.397344	+	0.944205i
$575$			5.18514i			0.216235i
$576$		0			0
$577$	−18.8951	+	10.9091i	−0.786613	+	0.454151i	−0.838769	−	0.544488i	$-0.816724\pi$
$577$	−18.8951	+	10.9091i	−0.786613	+	0.454151i	0.0521558	+	0.998639i	$0.483391\pi$
$578$	14.3041	−	18.3043i	0.594972	−	0.761358i
$579$		0			0
$580$	8.50598	+	8.81206i	0.353192	+	0.365901i
$581$	3.85740	−	2.30210i	0.160032	−	0.0955071i
$582$		0			0
$583$	−59.0679	−	34.1029i	−2.44634	−	1.41240i
$584$	−15.4988	+	1.62384i	−0.641344	+	0.0671949i
$585$		0			0
$586$	2.34279	−	16.6566i	0.0967798	−	0.688077i
$587$	−24.3095			−1.00336			−0.501680	−	0.865053i	$-0.667285\pi$
$587$	−24.3095			−1.00336			−0.501680	+	0.865053i	$0.667285\pi$
$588$		0			0
$589$	−56.3790			−2.32306
$590$	−0.549337	+	3.90563i	−0.0226158	+	0.160792i
$591$		0			0
$592$	28.1817	−	14.9686i	1.15826	−	0.615207i
$593$	−11.1015	−	6.40944i	−0.455883	−	0.263204i	0.254429	−	0.967092i	$-0.418113\pi$
$593$	−11.1015	−	6.40944i	−0.455883	−	0.263204i	−0.710312	+	0.703887i	$0.751446\pi$
$594$		0			0
$595$	−3.40007	+	2.02916i	−0.139389	+	0.0831875i
$596$	−29.2064	+	28.1919i	−1.19634	+	1.15479i
$597$		0			0
$598$	−25.5661	+	32.7157i	−1.04547	+	1.33784i
$599$	−3.83331	+	2.21316i	−0.156625	+	0.0904273i	−0.576264	−	0.817264i	$-0.695490\pi$
$599$	−3.83331	+	2.21316i	−0.156625	+	0.0904273i	0.419639	+	0.907691i	$0.362157\pi$
$600$		0			0
$601$			23.2898i			0.950013i	0.879982	+	0.475006i	$0.157554\pi$
$601$			23.2898i			0.950013i	−0.879982	+	0.475006i	$0.842446\pi$
$602$	−2.44401	−	5.80768i	−0.0996103	−	0.236703i
$603$		0			0
$604$	−7.97925	+	1.98759i	−0.324671	+	0.0808740i
$605$	−20.7780	+	11.9962i	−0.844747	+	0.487715i
$606$		0			0
$607$	−12.2761	+	21.2629i	−0.498273	+	0.863034i	−0.999998	−	0.00199302i	$-0.999366\pi$
$607$	−12.2761	+	21.2629i	−0.498273	+	0.863034i	0.501725	+	0.865027i	$0.332699\pi$
$608$	−38.8739	+	14.1248i	−1.57655	+	0.572838i
$609$		0			0
$610$	−6.15159	−	15.2305i	−0.249071	−	0.616666i
$611$	−13.9851	−	8.07428i	−0.565775	−	0.326650i
$612$		0			0
$613$	12.1773	+	21.0918i	0.491838	+	0.851889i	0.999956	−	0.00939906i	$-0.00299186\pi$
$613$	12.1773	+	21.0918i	0.491838	+	0.851889i	−0.508118	+	0.861288i	$0.669659\pi$
$614$	9.72710	+	1.36814i	0.392554	+	0.0552137i
$615$		0			0
$616$	28.8218	−	21.5693i	1.16127	−	0.869052i
$617$	12.8122			0.515802			0.257901	−	0.966171i	$-0.416969\pi$
$617$	12.8122			0.515802			0.257901	+	0.966171i	$0.416969\pi$
$618$		0			0
$619$	17.9749	+	31.1335i	0.722474	+	1.25136i	0.960005	+	0.279981i	$0.0903282\pi$
$619$	17.9749	+	31.1335i	0.722474	+	1.25136i	−0.237532	+	0.971380i	$0.576338\pi$
$620$	−8.40623	+	29.2918i	−0.337602	+	1.17639i
$621$		0			0
$622$	7.15692	+	17.7196i	0.286966	+	0.710491i
$623$	−11.0991	+	0.160558i	−0.444675	+	0.00643264i
$624$		0			0
$625$	9.16199	−	15.8690i	0.366480	−	0.634762i
$626$	17.7684	+	13.8853i	0.710169	+	0.554970i
$627$		0			0
$628$	−4.02947	+	1.00372i	−0.160793	+	0.0400529i
$629$			6.04187i			0.240905i
$630$		0			0
$631$		−	34.7338i		−	1.38273i	−0.722505	−	0.691365i	$-0.757009\pi$
$631$		−	34.7338i		−	1.38273i	0.722505	−	0.691365i	$-0.242991\pi$
$632$	5.89756	+	8.12290i	0.234592	+	0.323112i
$633$		0			0
$634$	3.55801	−	4.55302i	0.141307	−	0.180824i
$635$	−6.32607	+	10.9571i	−0.251042	+	0.434818i
$636$		0			0
$637$	38.2078	+	20.6093i	1.51385	+	0.816571i
$638$	19.5490	−	7.89581i	0.773951	−	0.312598i
$639$		0			0
$640$	1.54240	+	22.3030i	0.0609686	+	0.881605i
$641$	15.2754	+	26.4577i	0.603341	+	1.04502i	0.992311	+	0.123767i	$0.0394974\pi$
$641$	15.2754	+	26.4577i	0.603341	+	1.04502i	−0.388971	+	0.921250i	$0.627169\pi$
$642$		0			0
$643$	−34.7066			−1.36869			−0.684347	−	0.729156i	$-0.739913\pi$
$643$	−34.7066			−1.36869			−0.684347	+	0.729156i	$0.739913\pi$
$644$	24.1760	+	6.56111i	0.952667	+	0.258544i
$645$		0			0
$646$	1.09074	−	7.75484i	0.0429145	−	0.305110i
$647$	−1.93040	−	3.34356i	−0.0758920	−	0.131449i	0.825582	−	0.564282i	$-0.190847\pi$
$647$	−1.93040	−	3.34356i	−0.0758920	−	0.131449i	−0.901474	+	0.432834i	$0.857514\pi$
$648$		0			0
$649$	5.87980	+	3.39470i	0.230802	+	0.133254i
$650$	−8.90703	+	3.59754i	−0.349363	+	0.141107i
$651$		0			0
$652$	15.0938	+	15.6369i	0.591117	+	0.612388i
$653$	18.8640	−	32.6734i	0.738206	−	1.27861i	−0.215096	−	0.976593i	$-0.569006\pi$
$653$	18.8640	−	32.6734i	0.738206	−	1.27861i	0.953302	−	0.302018i	$-0.0976602\pi$
$654$		0			0
$655$	−8.57936	+	4.95329i	−0.335223	+	0.193541i
$656$	−13.9135	+	22.2446i	−0.543233	+	0.868507i
$657$		0			0
$658$	−1.21731	+	9.66656i	−0.0474558	+	0.376842i
$659$			33.1672i			1.29201i	0.763332	+	0.646006i	$0.223562\pi$
$659$			33.1672i			1.29201i	−0.763332	+	0.646006i	$0.776438\pi$
$660$		0			0
$661$	28.4996	−	16.4543i	1.10851	−	0.639996i	0.170064	−	0.985433i	$-0.445602\pi$
$661$	28.4996	−	16.4543i	1.10851	−	0.639996i	0.938442	+	0.345437i	$0.112269\pi$
$662$	2.81718	+	2.20152i	0.109493	+	0.0855645i
$663$		0			0
$664$	4.38646	+	1.95470i	0.170228	+	0.0758573i
$665$	18.6320	−	33.3774i	0.722518	−	1.29432i
$666$		0			0
$667$	12.7056	+	7.33556i	0.491961	+	0.284034i
$668$	−0.584466	−	0.167731i	−0.0226137	−	0.00648972i
$669$		0			0
$670$	−15.1608	−	2.13240i	−0.585711	−	0.0823818i
$671$	−28.2759			−1.09158
$672$		0			0
$673$	0.164681			0.00634798			0.00317399	−	0.999995i	$-0.498990\pi$
$673$	0.164681			0.00634798			0.00317399	+	0.999995i	$0.498990\pi$
$674$	31.6148	+	4.44670i	1.21776	+	0.171280i
$675$		0			0
$676$	−48.9460	−	14.0466i	−1.88254	−	0.540255i
$677$	−4.72248	−	2.72653i	−0.181500	−	0.104789i	0.406497	−	0.913652i	$-0.366750\pi$
$677$	−4.72248	−	2.72653i	−0.181500	−	0.104789i	−0.587997	+	0.808863i	$0.700083\pi$
$678$		0			0
$679$	3.17614	+	5.32195i	0.121889	+	0.204238i
$680$	−3.86640	−	1.72296i	−0.148270	−	0.0660724i
$681$		0			0
$682$	41.3346	+	32.3014i	1.58278	+	1.23689i
$683$	37.1520	−	21.4497i	1.42158	−	0.820751i	0.425149	−	0.905124i	$-0.360222\pi$
$683$	37.1520	−	21.4497i	1.42158	−	0.820751i	0.996434	+	0.0843723i	$0.0268885\pi$
$684$		0			0
$685$			14.4848i			0.553437i
$686$	2.51943	−	26.0701i	0.0961922	−	0.995363i
$687$		0			0
$688$	3.57205	−	5.71091i	0.136183	−	0.217726i
$689$	76.1489	−	43.9646i	2.90104	−	1.67492i
$690$		0			0
$691$	15.0893	−	26.1354i	0.574023	−	0.994237i	−0.422124	−	0.906538i	$-0.638715\pi$
$691$	15.0893	−	26.1354i	0.574023	−	0.994237i	0.996147	−	0.0876990i	$-0.0279514\pi$
$692$	22.8956	+	23.7195i	0.870362	+	0.901681i
$693$		0			0
$694$	26.7639	−	10.8099i	1.01594	−	0.410338i
$695$	15.5804	+	8.99535i	0.590998	+	0.341213i
$696$		0			0
$697$	−2.48390	−	4.30224i	−0.0940844	−	0.162959i
$698$	5.09427	−	36.2188i	0.192821	−	1.37090i
$699$		0			0
$700$	4.08498	+	4.11127i	0.154398	+	0.155391i
$701$	−16.4790			−0.622402			−0.311201	−	0.950344i	$-0.600731\pi$
$701$	−16.4790			−0.622402			−0.311201	+	0.950344i	$0.600731\pi$
$702$		0			0
$703$	−29.1643	−	50.5141i	−1.09995	−	1.90518i
$704$	36.5932	+	11.9165i	1.37916	+	0.449118i
$705$		0			0
$706$	−12.1438	+	4.90488i	−0.457040	+	0.184598i
$707$	−10.8022	+	19.3512i	−0.406260	+	0.727775i
$708$		0			0
$709$	5.26207	−	9.11417i	0.197621	−	0.342290i	−0.750135	−	0.661284i	$-0.770012\pi$
$709$	5.26207	−	9.11417i	0.197621	−	0.342290i	0.947757	+	0.318994i	$0.103345\pi$
$710$	23.3742	−	29.9108i	0.877218	−	1.12253i
$711$		0			0
$712$	−6.97189	−	9.60262i	−0.261283	−	0.359873i
$713$			36.5042i			1.36709i
$714$		0			0
$715$		−	58.9525i		−	2.20470i
$716$	−14.3863	+	3.58356i	−0.537641	+	0.133924i
$717$		0			0
$718$	−4.92907	−	3.85188i	−0.183951	−	0.143751i
$719$	−3.40805	+	5.90292i	−0.127099	+	0.220142i	−0.922551	−	0.385874i	$-0.873900\pi$
$719$	−3.40805	+	5.90292i	−0.127099	+	0.220142i	0.795453	+	0.606016i	$0.207233\pi$
$720$		0			0
$721$	0.380513	+	26.3041i	0.0141710	+	0.979615i
$722$	18.2506	+	45.1861i	0.679217	+	1.68165i
$723$		0			0
$724$	−5.25978	+	18.3279i	−0.195478	+	0.681151i
$725$	1.69715	+	2.93955i	0.0630306	+	0.109172i
$726$		0			0
$727$	−9.85151			−0.365372			−0.182686	−	0.983171i	$-0.558479\pi$
$727$	−9.85151			−0.365372			−0.182686	+	0.983171i	$0.558479\pi$
$728$	5.50303	+	46.0817i	0.203956	+	1.70790i
$729$		0			0
$730$	15.2468	+	2.14450i	0.564310	+	0.0793717i
$731$	0.637697	+	1.10452i	0.0235861	+	0.0408523i
$732$		0			0
$733$	34.0496	+	19.6586i	1.25765	+	0.726106i	0.972618	−	0.232411i	$-0.0746616\pi$
$733$	34.0496	+	19.6586i	1.25765	+	0.726106i	0.285035	+	0.958517i	$0.407995\pi$
$734$	5.36809	+	13.2907i	0.198140	+	0.490568i
$735$		0			0
$736$	9.14554	+	25.1700i	0.337109	+	0.927780i
$737$	−13.1775	+	22.8241i	−0.485398	+	0.840735i
$738$		0			0
$739$	−33.5511	+	19.3707i	−1.23420	+	0.712564i	−0.967902	−	0.251328i	$-0.919133\pi$
$739$	−33.5511	+	19.3707i	−1.23420	+	0.712564i	−0.266294	+	0.963892i	$0.585799\pi$
$740$	−30.5931	+	7.62061i	−1.12463	+	0.280139i
$741$		0			0
$742$	−42.2687	−	32.0576i	−1.55173	−	1.17687i
$743$			32.3439i			1.18658i	0.804988	+	0.593291i	$0.202172\pi$
$743$			32.3439i			1.18658i	−0.804988	+	0.593291i	$0.797828\pi$
$744$		0			0
$745$	34.7334	−	20.0534i	1.27253	−	0.734698i
$746$	−27.6488	+	35.3809i	−1.01229	+	1.29539i
$747$		0			0
$748$	−5.24269	+	5.06058i	−0.191692	+	0.185033i
$749$	11.6293	−	0.168229i	0.424925	−	0.00614694i
$750$		0			0
$751$	26.5577	+	15.3331i	0.969104	+	0.559513i	0.898963	−	0.438024i	$-0.144322\pi$
$751$	26.5577	+	15.3331i	0.969104	+	0.559513i	0.0701413	+	0.997537i	$0.477655\pi$
$752$	−9.19858	+	4.88580i	−0.335438	+	0.178167i
$753$		0			0
$754$	−3.78569	+	26.9152i	−0.137867	+	0.980192i
$755$	8.12455			0.295683
$756$		0			0
$757$	−20.2226			−0.735004			−0.367502	−	0.930023i	$-0.619787\pi$
$757$	−20.2226			−0.735004			−0.367502	+	0.930023i	$0.619787\pi$
$758$	5.65502	−	40.2056i	0.205399	−	1.46033i
$759$		0			0
$760$	40.6425	−	4.25820i	1.47426	−	0.154461i
$761$	−13.1845	−	7.61208i	−0.477938	−	0.275938i	0.241619	−	0.970371i	$-0.422322\pi$
$761$	−13.1845	−	7.61208i	−0.477938	−	0.275938i	−0.719557	+	0.694434i	$0.755655\pi$
$762$		0			0
$763$	−3.31419	−	1.85006i	−0.119982	−	0.0669765i
$764$	15.2582	+	15.8072i	0.552021	+	0.571885i
$765$		0			0
$766$	−3.98728	+	5.10233i	−0.144066	+	0.184355i
$767$	−7.58010	+	4.37637i	−0.273701	+	0.158022i
$768$		0			0
$769$		−	36.0780i		−	1.30101i	−0.759503	−	0.650504i	$-0.774558\pi$
$769$		−	36.0780i		−	1.30101i	0.759503	−	0.650504i	$-0.225442\pi$
$770$	−32.7832	+	13.7959i	−1.18142	+	0.497171i
$771$		0			0
$772$	−1.97282	−	7.91992i	−0.0710032	−	0.285044i
$773$	−11.1535	+	6.43945i	−0.401162	+	0.231611i	−0.686985	−	0.726671i	$-0.741066\pi$
$773$	−11.1535	+	6.43945i	−0.401162	+	0.231611i	0.285823	+	0.958282i	$0.407733\pi$
$774$		0			0
$775$	−4.22280	+	7.31410i	−0.151687	+	0.262730i
$776$	−2.69685	+	6.05188i	−0.0968114	+	0.217250i
$777$		0			0
$778$	9.54306	+	23.6274i	0.342135	+	0.847082i
$779$	41.5342	+	23.9798i	1.48812	+	0.859164i
$780$		0			0
$781$	−32.6731	−	56.5915i	−1.16914	−	2.02500i
$782$	−5.02109	−	0.706230i	−0.179554	−	0.0252547i
$783$		0			0
$784$	24.3380	−	13.8442i	0.869215	−	0.494434i
$785$	4.10285			0.146437
$786$		0			0
$787$	−20.4007	−	35.3351i	−0.727207	−	1.25956i	−0.958059	−	0.286571i	$-0.907485\pi$
$787$	−20.4007	−	35.3351i	−0.727207	−	1.25956i	0.230852	−	0.972989i	$-0.425849\pi$
$788$	32.6477	+	9.36932i	1.16303	+	0.333768i
$789$		0			0
$790$	−3.71427	−	9.19603i	−0.132148	−	0.327180i
$791$	−21.8825	+	13.0595i	−0.778053	+	0.464343i
$792$		0			0
$793$	18.2263	−	31.5689i	0.647236	−	1.12105i
$794$	26.9350	+	21.0487i	0.955888	+	0.746990i
$795$		0			0
$796$	6.03424	+	24.2246i	0.213878	+	0.858619i
$797$			29.4028i			1.04150i	0.853710	+	0.520749i	$0.174347\pi$
$797$			29.4028i			1.04150i	−0.853710	+	0.520749i	$0.825653\pi$
$798$		0			0
$799$		−	1.97208i		−	0.0697673i
$800$	−1.07923	+	6.10110i	−0.0381567	+	0.215706i
$801$		0			0
$802$	−0.380622	+	0.487063i	−0.0134402	+	0.0171988i
$803$	13.2523	−	22.9536i	0.467663	−	0.810015i
$804$		0			0
$805$	−21.6112	−	12.0638i	−0.761694	−	0.425194i
$806$	−62.7070	+	25.3273i	−2.20876	+	0.892115i
$807$		0			0
$808$	−23.5632	+	2.46877i	−0.828952	+	0.0868509i
$809$	−23.6683	−	40.9948i	−0.832135	−	1.44130i	−0.896342	−	0.443363i	$-0.853785\pi$
$809$	−23.6683	−	40.9948i	−0.832135	−	1.44130i	0.0642073	−	0.997937i	$-0.479548\pi$
$810$		0			0
$811$	−15.8075			−0.555078			−0.277539	−	0.960714i	$-0.589519\pi$
$811$	−15.8075			−0.555078			−0.277539	+	0.960714i	$0.589519\pi$
$812$	15.8533	−	4.19343i	0.556342	−	0.147161i
$813$		0			0
$814$	−7.55922	+	53.7439i	−0.264950	+	1.88372i
$815$	−10.7364	−	18.5960i	−0.376081	−	0.651391i
$816$		0			0
$817$	−10.6632	−	6.15637i	−0.373056	−	0.215384i
$818$	38.2624	−	15.4541i	1.33781	−	0.540341i
$819$		0			0
$820$	18.6515	−	18.0037i	0.651340	−	0.628716i
$821$	−27.6602	+	47.9089i	−0.965348	+	1.67203i	−0.256671	+	0.966499i	$0.582626\pi$
$821$	−27.6602	+	47.9089i	−0.965348	+	1.67203i	−0.708677	+	0.705533i	$0.750708\pi$
$822$		0			0
$823$	8.76958	−	5.06312i	0.305688	−	0.176489i	−0.339307	−	0.940676i	$-0.610193\pi$
$823$	8.76958	−	5.06312i	0.305688	−	0.176489i	0.644996	+	0.764186i	$0.276859\pi$
$824$	−22.7576	+	16.5229i	−0.792797	+	0.575603i
$825$		0			0
$826$	4.20756	+	3.19111i	0.146400	+	0.111033i
$827$			44.1097i			1.53384i	0.641740	+	0.766922i	$0.278213\pi$
$827$			44.1097i			1.53384i	−0.641740	+	0.766922i	$0.721787\pi$
$828$		0			0
$829$	28.7412	−	16.5937i	0.998224	−	0.576325i	0.0905014	−	0.995896i	$-0.471153\pi$
$829$	28.7412	−	16.5937i	0.998224	−	0.576325i	0.907722	+	0.419572i	$0.137820\pi$
$830$	−3.73859	−	2.92156i	−0.129768	−	0.101409i
$831$		0			0
$832$	−36.8918	+	33.1736i	−1.27899	+	1.15009i
$833$	0.153350	+	5.29928i	0.00531326	+	0.183609i
$834$		0			0
$835$	0.520284	+	0.300386i	0.0180052	+	0.0103953i
$836$	19.4048	−	67.6165i	0.671128	−	2.33857i
$837$		0			0
$838$	−40.4837	−	5.69414i	−1.39849	−	0.196701i
$839$	−15.9248			−0.549787			−0.274893	−	0.961475i	$-0.588643\pi$
$839$	−15.9248			−0.549787			−0.274893	+	0.961475i	$0.588643\pi$
$840$		0			0
$841$	−19.3960			−0.668827
$842$	−35.2139	−	4.95292i	−1.21355	−	0.170689i
$843$		0			0
$844$	3.25400	−	11.3387i	0.112007	−	0.390294i
$845$	43.5711	+	25.1558i	1.49889	+	0.865385i
$846$		0			0
$847$	0.464652	+	32.1205i	0.0159656	+	1.10367i
$848$	2.00409	−	56.6777i	0.0688209	−	1.94632i
$849$		0			0
$850$	−0.924345	−	0.722341i	−0.0317048	−	0.0247761i
$851$	−32.7068	+	18.8833i	−1.12118	+	0.647311i
$852$		0			0
$853$		−	32.9959i		−	1.12976i	−0.825174	−	0.564878i	$-0.808923\pi$
$853$		−	32.9959i		−	1.12976i	0.825174	−	0.564878i	$-0.191077\pi$
$854$	−21.8206	−	2.74788i	−0.746686	−	0.0940305i
$855$		0			0
$856$	7.30495	+	10.0614i	0.249678	+	0.343890i
$857$	9.77167	−	5.64168i	0.333794	−	0.192716i	−0.323730	−	0.946149i	$-0.604937\pi$
$857$	9.77167	−	5.64168i	0.333794	−	0.192716i	0.657524	+	0.753433i	$0.271604\pi$
$858$		0			0
$859$	−25.2465	+	43.7282i	−0.861399	+	1.49199i	0.00918033	+	0.999958i	$0.497078\pi$
$859$	−25.2465	+	43.7282i	−0.861399	+	1.49199i	−0.870579	+	0.492029i	$0.836256\pi$
$860$	−4.78845	+	4.62213i	−0.163285	+	0.157613i
$861$		0			0
$862$	−47.4824	+	19.1781i	−1.61726	+	0.653209i
$863$	−12.3988	−	7.15844i	−0.422060	−	0.243676i	0.273899	−	0.961759i	$-0.411687\pi$
$863$	−12.3988	−	7.15844i	−0.422060	−	0.243676i	−0.695958	+	0.718082i	$0.745020\pi$
$864$		0			0
$865$	−16.2860	−	28.2082i	−0.553742	−	0.959109i
$866$	3.28645	−	23.3657i	0.111678	−	0.794000i
$867$		0			0
$868$	28.7590	+	28.9440i	0.976142	+	0.982425i
$869$	−17.0727			−0.579152
$870$		0			0
$871$	−16.9881	−	29.4242i	−0.575619	−	0.997001i
$872$	−0.422815	−	4.03558i	−0.0143183	−	0.136662i
$873$		0			0
$874$	45.3887	−	18.3324i	1.53530	−	0.620104i
$875$	−16.3309	−	27.3640i	−0.552085	−	0.925074i
$876$		0			0
$877$	6.83804	−	11.8438i	0.230904	−	0.399938i	−0.727170	−	0.686457i	$-0.759165\pi$
$877$	6.83804	−	11.8438i	0.230904	−	0.399938i	0.958074	+	0.286519i	$0.0924982\pi$
$878$	−3.44615	+	4.40988i	−0.116302	+	0.148826i
$879$		0			0
$880$	−32.2370	−	20.1635i	−1.08671	−	0.679712i
$881$			9.65113i			0.325155i	0.986696	+	0.162577i	$0.0519808\pi$
$881$			9.65113i			0.325155i	−0.986696	+	0.162577i	$0.948019\pi$
$882$		0			0
$883$		−	17.0014i		−	0.572143i	−0.958208	−	0.286071i	$-0.907651\pi$
$883$		−	17.0014i		−	0.572143i	0.958208	−	0.286071i	$-0.0923494\pi$
$884$	−2.27056	−	9.11523i	−0.0763673	−	0.306578i
$885$		0			0
$886$	36.5032	+	28.5259i	1.22635	+	0.958346i
$887$	27.0861	−	46.9144i	0.909461	−	1.57523i	0.0946460	−	0.995511i	$-0.469828\pi$
$887$	27.0861	−	46.9144i	0.909461	−	1.57523i	0.814815	−	0.579721i	$-0.196839\pi$
$888$		0			0
$889$	8.68140	+	14.5466i	0.291165	+	0.487876i
$890$	4.39088	+	10.8712i	0.147182	+	0.364404i
$891$		0			0
$892$	17.5762	+	5.04406i	0.588495	+	0.168888i
$893$	9.51931	+	16.4879i	0.318552	+	0.551748i
$894$		0			0
$895$	14.6483			0.489638
$896$	27.0811	+	12.7521i	0.904714	+	0.426019i
$897$		0			0
$898$	−26.6678	−	3.75089i	−0.889915	−	0.125169i
$899$	11.9482	+	20.6949i	0.398495	+	0.690214i
$900$		0			0
$901$	9.29940	+	5.36901i	0.309808	+	0.178868i
$902$	−16.7122	−	41.3772i	−0.556455	−	1.37771i
$903$		0			0
$904$	−24.8838	−	11.0888i	−0.827624	−	0.368808i
$905$	9.41962	−	16.3153i	0.313119	−	0.542338i
$906$		0			0
$907$	−2.59813	+	1.50003i	−0.0862694	+	0.0498077i	−0.542514	−	0.840047i	$-0.682528\pi$
$907$	−2.59813	+	1.50003i	−0.0862694	+	0.0498077i	0.456245	+	0.889854i	$0.349194\pi$
$908$	−0.202548	−	0.813136i	−0.00672180	−	0.0269849i
$909$		0			0
$910$	5.72905	−	45.4938i	0.189916	−	1.50810i
$911$		−	17.0111i		−	0.563604i	−0.959473	−	0.281802i	$-0.909068\pi$
$911$		−	17.0111i		−	0.563604i	0.959473	−	0.281802i	$-0.0909321\pi$
$912$		0			0
$913$	−7.07344	+	4.08385i	−0.234097	+	0.135156i
$914$	12.4669	−	15.9534i	0.412370	−	0.527690i
$915$		0			0
$916$	−11.6094	−	12.0271i	−0.383585	−	0.397388i
$917$	0.191857	+	13.2627i	0.00633569	+	0.437973i
$918$		0			0
$919$	−38.9794	−	22.5048i	−1.28581	−	0.742363i	−0.307907	−	0.951417i	$-0.599628\pi$
$919$	−38.9794	−	22.5048i	−1.28581	−	0.742363i	−0.977904	+	0.209053i	$0.932962\pi$
$920$	−2.75709	−	26.3152i	−0.0908987	−	0.867585i
$921$		0			0
$922$	−1.90275	+	13.5280i	−0.0626639	+	0.445522i
$923$	84.2428			2.77289
$924$		0			0
$925$	−8.73765			−0.287292
$926$	−0.359568	+	2.55643i	−0.0118161	+	0.0840095i
$927$		0			0
$928$	13.4232	+	11.2759i	0.440638	+	0.370150i
$929$	19.5971	+	11.3144i	0.642960	+	0.371213i	0.785754	−	0.618539i	$-0.212275\pi$
$929$	19.5971	+	11.3144i	0.642960	+	0.371213i	−0.142794	+	0.989752i	$0.545609\pi$
$930$		0			0
$931$	−26.8619	−	43.5653i	−0.880364	−	1.42780i
$932$	22.8601	−	22.0661i	0.748808	−	0.722798i
$933$		0			0
$934$	17.8704	−	22.8679i	0.584737	−	0.748261i
$935$	6.23482	−	3.59967i	0.203900	−	0.117722i
$936$		0			0
$937$			5.14595i			0.168111i	0.996461	+	0.0840554i	$0.0267873\pi$
$937$			5.14595i			0.168111i	−0.996461	+	0.0840554i	$0.973213\pi$
$938$	−12.3872	+	16.3328i	−0.404455	+	0.533284i
$939$		0			0
$940$	9.98568	−	2.48739i	0.325697	−	0.0811296i
$941$	41.9955	−	24.2461i	1.36901	−	0.790400i	0.378212	−	0.925719i	$-0.376539\pi$
$941$	41.9955	−	24.2461i	1.36901	−	0.790400i	0.990802	+	0.135319i	$0.0432058\pi$
$942$		0			0
$943$	15.5264	−	26.8925i	0.505609	−	0.875740i
$944$	−0.199494	+	5.64187i	−0.00649297	+	0.183627i
$945$		0			0
$946$	4.29056	+	10.6229i	0.139498	+	0.345379i
$947$	9.63797	+	5.56448i	0.313192	+	0.180821i	0.648354	−	0.761339i	$-0.275458\pi$
$947$	9.63797	+	5.56448i	0.313192	+	0.180821i	−0.335162	+	0.942161i	$0.608791\pi$
$948$		0			0
$949$	17.0845	+	29.5912i	0.554587	+	0.960572i
$950$	11.2149	+	1.57741i	0.363860	+	0.0511778i
$951$		0			0
$952$	−4.53759	+	3.39578i	−0.147064	+	0.110058i
$953$	−21.0412			−0.681590			−0.340795	−	0.940138i	$-0.610696\pi$
$953$	−21.0412			−0.681590			−0.340795	+	0.940138i	$0.610696\pi$
$954$		0			0
$955$	−10.8534	−	18.7986i	−0.351207	−	0.608308i
$956$	7.86431	−	27.4034i	0.254350	−	0.886291i
$957$		0			0
$958$	−8.45073	−	20.9229i	−0.273031	−	0.675988i
$959$	16.9342	+	9.45304i	0.546833	+	0.305255i
$960$		0			0
$961$	−14.2292	+	24.6457i	−0.459006	+	0.795022i
$962$	−55.1303	−	43.0822i	−1.77747	−	1.38903i
$963$		0			0
$964$	40.0577	−	9.97819i	1.29017	−	0.321376i
$965$			8.06414i			0.259594i
$966$		0			0
$967$			8.38736i			0.269719i	0.990865	+	0.134860i	$0.0430584\pi$
$967$			8.38736i			0.269719i	−0.990865	+	0.134860i	$0.956942\pi$
$968$	−27.7898	+	20.1765i	−0.893197	+	0.648497i
$969$		0			0
$970$	4.03080	−	5.15803i	0.129421	−	0.165614i
$971$	−14.7470	+	25.5426i	−0.473255	+	0.819701i	−0.999531	−	0.0306124i	$-0.990254\pi$
$971$	−14.7470	+	25.5426i	−0.473255	+	0.819701i	0.526277	+	0.850313i	$0.323588\pi$
$972$		0			0
$973$	20.6845	−	12.3445i	0.663114	−	0.395747i
$974$	−5.89928	+	2.38271i	−0.189025	+	0.0763470i
$975$		0			0
$976$	−11.0289	−	20.7642i	−0.353025	−	0.664647i
$977$	−29.1599	−	50.5064i	−0.932908	−	1.61584i	−0.778322	−	0.627865i	$-0.783929\pi$
$977$	−29.1599	−	50.5064i	−0.932908	−	1.61584i	−0.154586	−	0.987979i	$-0.549404\pi$
$978$		0			0
$979$	20.1828			0.645044
$980$	−26.6396	+	7.46047i	−0.850970	+	0.238316i
$981$		0			0
$982$	−2.69005	+	19.1255i	−0.0858428	+	0.610318i
$983$	−22.9661	−	39.7784i	−0.732505	−	1.26874i	−0.955810	−	0.293987i	$-0.905018\pi$
$983$	−22.9661	−	39.7784i	−0.732505	−	1.26874i	0.223305	−	0.974749i	$-0.428315\pi$
$984$		0			0
$985$	−29.0626	−	16.7793i	−0.926011	−	0.534633i
$986$	−3.07771	+	1.24308i	−0.0980141	+	0.0395878i
$987$		0			0
$988$	62.9830	+	65.2494i	2.00376	+	2.07586i
$989$	−3.98612	+	6.90417i	−0.126751	+	0.219540i
$990$		0			0
$991$	15.9329	−	9.19889i	0.506127	−	0.292212i	−0.225113	−	0.974333i	$-0.572275\pi$
$991$	15.9329	−	9.19889i	0.506127	−	0.292212i	0.731240	+	0.682120i	$0.238942\pi$
$992$	−7.59799	+	42.9527i	−0.241236	+	1.36375i
$993$		0			0
$994$	−19.7143	−	46.8470i	−0.625301	−	1.48590i
$995$		−	24.6658i		−	0.781957i
$996$		0			0
$997$	−17.3664	+	10.0265i	−0.549998	+	0.317542i	−0.749121	−	0.662433i	$-0.769524\pi$
$997$	−17.3664	+	10.0265i	−0.549998	+	0.317542i	0.199123	+	0.979975i	$0.436191\pi$
$998$	28.5161	+	22.2842i	0.902660	+	0.705395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.b.271.1	✓	32
3.2	odd	2		756.2.bf.c.271.16	yes	32
4.3	odd	2		756.2.bf.c.271.11	yes	32
7.3	odd	6		756.2.bf.c.703.11	yes	32
12.11	even	2	inner	756.2.bf.b.271.6	yes	32
21.17	even	6	inner	756.2.bf.b.703.6	yes	32
28.3	even	6	inner	756.2.bf.b.703.1	yes	32
84.59	odd	6		756.2.bf.c.703.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.1	✓	32	1.1	even	1	trivial
756.2.bf.b.271.6	yes	32	12.11	even	2	inner
756.2.bf.b.703.1	yes	32	28.3	even	6	inner
756.2.bf.b.703.6	yes	32	21.17	even	6	inner
756.2.bf.c.271.11	yes	32	4.3	odd	2
756.2.bf.c.271.16	yes	32	3.2	odd	2
756.2.bf.c.703.11	yes	32	7.3	odd	6
756.2.bf.c.703.16	yes	32	84.59	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40043 - 0.196974i) q^{2} +(1.92240 + 0.551696i) q^{4} +(-1.71130 - 0.988019i) q^{5} +(-2.27191 + 1.35588i) q^{7} +(-2.58352 - 1.15127i) q^{8} +O(q^{10})\)	\(q+(-1.40043 - 0.196974i) q^{2} +(1.92240 + 0.551696i) q^{4} +(-1.71130 - 0.988019i) q^{5} +(-2.27191 + 1.35588i) q^{7} +(-2.58352 - 1.15127i) q^{8} +(2.20194 + 1.72073i) q^{10} +(4.16608 - 2.40529i) q^{11} +6.20168i q^{13} +(3.44873 - 1.45131i) q^{14} +(3.39126 + 2.12116i) q^{16} +(-0.655890 + 0.378678i) q^{17} +(3.65579 - 6.33201i) q^{19} +(-2.74472 - 2.84349i) q^{20} +(-6.30808 + 2.54783i) q^{22} +(-4.09984 - 2.36705i) q^{23} +(-0.547638 - 0.948537i) q^{25} +(1.22157 - 8.68501i) q^{26} +(-5.11557 + 1.35314i) q^{28} -3.09904 q^{29} +(-3.85546 - 6.67786i) q^{31} +(-4.33141 - 3.63853i) q^{32} +(0.993118 - 0.401119i) q^{34} +(5.22756 - 0.0756214i) q^{35} +(3.98879 - 6.90878i) q^{37} +(-6.36691 + 8.14744i) q^{38} +(3.28369 + 4.52274i) q^{40} +6.55939i q^{41} -1.68401i q^{43} +(9.33588 - 2.32552i) q^{44} +(5.27529 + 4.12244i) q^{46} +(-1.30195 + 2.25504i) q^{47} +(3.32318 - 6.16088i) q^{49} +(0.580091 + 1.43623i) q^{50} +(-3.42144 + 11.9221i) q^{52} +(-7.08914 - 12.2788i) q^{53} -9.50588 q^{55} +(7.43052 - 0.887345i) q^{56} +(4.33998 + 0.610429i) q^{58} +(0.705675 + 1.22226i) q^{59} +(-5.09038 - 2.93893i) q^{61} +(4.08394 + 10.1113i) q^{62} +(5.34914 + 5.94868i) q^{64} +(6.12738 - 10.6129i) q^{65} +(-4.74455 + 2.73927i) q^{67} +(-1.46980 + 0.366120i) q^{68} +(-7.33572 - 0.923790i) q^{70} -13.5839i q^{71} +(4.77149 - 2.75482i) q^{73} +(-6.94686 + 8.88957i) q^{74} +(10.5212 - 10.1558i) q^{76} +(-6.20370 + 11.1133i) q^{77} +(-3.07352 - 1.77450i) q^{79} +(-3.70772 - 6.98058i) q^{80} +(1.29203 - 9.18596i) q^{82} -1.69786 q^{83} +1.49657 q^{85} +(-0.331705 + 2.35833i) q^{86} +(-13.5323 + 1.41781i) q^{88} +(3.63341 + 2.09775i) q^{89} +(-8.40873 - 14.0897i) q^{91} +(-6.57566 - 6.81228i) q^{92} +(2.26747 - 2.90158i) q^{94} +(-12.5123 + 7.22398i) q^{95} -2.34249i q^{97} +(-5.86741 + 7.97330i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 6 q^{11} - 17 q^{14} - 4 q^{16} + 8 q^{20} + 2 q^{22} + 14 q^{25} + 15 q^{26} - 13 q^{28} + 15 q^{32} + 6 q^{35} + 4 q^{37} - q^{38} - 15 q^{40} - 42 q^{44} - 9 q^{46} - 4 q^{47} + 14 q^{49} - 9 q^{52} + 45 q^{56} + 10 q^{58} - 16 q^{59} - 42 q^{64} - 49 q^{68} - 33 q^{70} + 36 q^{73} - 54 q^{74} - 15 q^{80} - 51 q^{82} + 20 q^{83} + 16 q^{85} + 78 q^{86} - 2 q^{88} - 27 q^{94} + 24 q^{95} - 46 q^{98}+O(q^{100}) \) 32 * q - 6 * q^11 - 17 * q^14 - 4 * q^16 + 8 * q^20 + 2 * q^22 + 14 * q^25 + 15 * q^26 - 13 * q^28 + 15 * q^32 + 6 * q^35 + 4 * q^37 - q^38 - 15 * q^40 - 42 * q^44 - 9 * q^46 - 4 * q^47 + 14 * q^49 - 9 * q^52 + 45 * q^56 + 10 * q^58 - 16 * q^59 - 42 * q^64 - 49 * q^68 - 33 * q^70 + 36 * q^73 - 54 * q^74 - 15 * q^80 - 51 * q^82 + 20 * q^83 + 16 * q^85 + 78 * q^86 - 2 * q^88 - 27 * q^94 + 24 * q^95 - 46 * q^98

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