LMFDB - Embedded newform 968.2.i.q.729.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1305015625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 5x^{6} - 9x^{5} + 29x^{4} + 36x^{3} + 80x^{2} + 64x + 256 $ x^8 - x^7 + 5x^6 - 9x^5 + 29x^4 + 36x^3 + 80x^2 + 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.2
Root			$2.07234 - 1.50564i$ of defining polynomial
Character	$\chi$	$=$	968.729
Dual form			968.2.i.q.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.791563 + 2.43618i) q^{3} +(0.454306 + 0.330072i) q^{5} +(1.58313 - 4.87236i) q^{7} +(-2.88136 + 2.09343i) q^{9} +(2.52665 - 1.83572i) q^{13} +(-0.444505 + 1.36804i) q^{15} +(1.61803 + 1.17557i) q^{17} +(1.23607 + 3.80423i) q^{19} +13.1231 q^{21} +6.56155 q^{23} +(-1.44764 - 4.45537i) q^{25} +(-1.16373 - 0.845498i) q^{27} +(-0.965093 + 2.97025i) q^{29} +(1.16373 - 0.845498i) q^{31} +(2.32746 - 1.69100i) q^{35} +(-1.06254 + 3.27016i) q^{37} +(6.47214 + 4.70228i) q^{39} +(-2.20116 - 6.77448i) q^{41} -1.12311 q^{43} -2.00000 q^{45} +(2.47214 + 7.60845i) q^{47} +(-15.5705 - 11.3126i) q^{49} +(-1.58313 + 4.87236i) q^{51} +(3.43526 - 2.49586i) q^{53} +(-8.28936 + 6.02257i) q^{57} +(-3.95782 + 12.1809i) q^{59} +(-5.76271 - 4.18686i) q^{61} +(5.63839 + 17.3532i) q^{63} +1.75379 q^{65} +5.43845 q^{67} +(5.19388 + 15.9851i) q^{69} +(-2.98095 - 2.16579i) q^{71} +(0.965093 - 2.97025i) q^{73} +(9.70820 - 7.05342i) q^{75} +(-2.32746 + 1.69100i) q^{79} +(-2.16312 + 6.65740i) q^{81} +(7.38075 + 5.36243i) q^{83} +(0.347059 + 1.06814i) q^{85} -8.00000 q^{87} -9.68466 q^{89} +(-4.94427 - 15.2169i) q^{91} +(2.98095 + 2.16579i) q^{93} +(-0.694117 + 2.13627i) q^{95} +(-9.25390 + 6.72335i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} - 2 q^{13} + 7 q^{15} + 4 q^{17} - 8 q^{19} + 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} - 2 q^{29} + 7 q^{31} + 14 q^{35} + 11 q^{37} + 16 q^{39} + 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 - 2 * q^13 + 7 * q^15 + 4 * q^17 - 8 * q^19 + 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 - 2 * q^29 + 7 * q^31 + 14 * q^35 + 11 * q^37 + 16 * q^39 + 6 * q^41 + 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 + 2 * q^51 - 8 * q^53 - 4 * q^57 + 5 * q^59 - 6 * q^61 - 20 * q^63 + 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 + 2 * q^73 + 24 * q^75 - 14 * q^79 + 14 * q^81 + 10 * q^83 + 6 * q^85 - 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 - 12 * q^95 - 27 * q^97

Character values

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

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.791563	+	2.43618i	0.457009	+	1.40653i	0.868760	+	0.495233i	$0.164917\pi$
$3$	0.791563	+	2.43618i	0.457009	+	1.40653i	−0.411751	+	0.911297i	$0.635083\pi$
$4$		0			0
$5$	0.454306	+	0.330072i	0.203172	+	0.147613i	0.684719	−	0.728807i	$-0.259925\pi$
$5$	0.454306	+	0.330072i	0.203172	+	0.147613i	−0.481547	+	0.876420i	$0.659925\pi$
$6$		0			0
$7$	1.58313	−	4.87236i	0.598366	−	1.84158i	0.0611615	−	0.998128i	$-0.480520\pi$
$7$	1.58313	−	4.87236i	0.598366	−	1.84158i	0.537204	−	0.843452i	$-0.319480\pi$
$8$		0			0
$9$	−2.88136	+	2.09343i	−0.960452	+	0.697809i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	2.52665	−	1.83572i	0.700765	−	0.509136i	−0.179416	−	0.983773i	$-0.557421\pi$
$13$	2.52665	−	1.83572i	0.700765	−	0.509136i	0.880181	+	0.474637i	$0.157421\pi$
$14$		0			0
$15$	−0.444505	+	1.36804i	−0.114771	+	0.353228i
$16$		0			0
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	0.766451	−	0.642303i	$-0.222021\pi$
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	−0.374020	+	0.927421i	$0.622021\pi$
$18$		0			0
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	0.986823	+	0.161806i	$0.0517318\pi$
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	−0.703249	+	0.710943i	$0.748268\pi$
$20$		0			0
$21$	13.1231			2.86370
$22$		0			0
$23$	6.56155			1.36818			0.684089	−	0.729398i	$-0.260200\pi$
$23$	6.56155			1.36818			0.684089	+	0.729398i	$0.260200\pi$
$24$		0			0
$25$	−1.44764	−	4.45537i	−0.289528	−	0.891075i
$26$		0			0
$27$	−1.16373	−	0.845498i	−0.223960	−	0.162716i
$28$		0			0
$29$	−0.965093	+	2.97025i	−0.179213	+	0.551562i	−0.999801	−	0.0199592i	$-0.993646\pi$
$29$	−0.965093	+	2.97025i	−0.179213	+	0.551562i	0.820588	+	0.571521i	$0.193646\pi$
$30$		0			0
$31$	1.16373	−	0.845498i	0.209012	−	0.151856i	−0.478355	−	0.878167i	$-0.658767\pi$
$31$	1.16373	−	0.845498i	0.209012	−	0.151856i	0.687366	+	0.726311i	$0.258767\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.32746	−	1.69100i	0.393412	−	0.285831i
$36$		0			0
$37$	−1.06254	+	3.27016i	−0.174680	+	0.537611i	−0.999619	−	0.0276120i	$-0.991210\pi$
$37$	−1.06254	+	3.27016i	−0.174680	+	0.537611i	0.824938	+	0.565223i	$0.191210\pi$
$38$		0			0
$39$	6.47214	+	4.70228i	1.03637	+	0.752968i
$40$		0			0
$41$	−2.20116	−	6.77448i	−0.343764	−	1.05800i	−0.962242	−	0.272194i	$-0.912251\pi$
$41$	−2.20116	−	6.77448i	−0.343764	−	1.05800i	0.618479	−	0.785801i	$-0.287749\pi$
$42$		0			0
$43$	−1.12311			−0.171272			−0.0856360	−	0.996326i	$-0.527292\pi$
$43$	−1.12311			−0.171272			−0.0856360	+	0.996326i	$0.527292\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	0.952692	+	0.303938i	$0.0983015\pi$
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	−0.592094	+	0.805869i	$0.701699\pi$
$48$		0			0
$49$	−15.5705	−	11.3126i	−2.22436	−	1.61609i
$50$		0			0
$51$	−1.58313	+	4.87236i	−0.221682	+	0.682267i
$52$		0			0
$53$	3.43526	−	2.49586i	0.471869	−	0.342833i	−0.326300	−	0.945266i	$-0.605802\pi$
$53$	3.43526	−	2.49586i	0.471869	−	0.342833i	0.798169	+	0.602433i	$0.205802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.28936	+	6.02257i	−1.09795	+	0.797709i
$58$		0			0
$59$	−3.95782	+	12.1809i	−0.515264	+	1.58582i	0.267538	+	0.963547i	$0.413790\pi$
$59$	−3.95782	+	12.1809i	−0.515264	+	1.58582i	−0.782801	+	0.622272i	$0.786210\pi$
$60$		0			0
$61$	−5.76271	−	4.18686i	−0.737840	−	0.536072i	0.154194	−	0.988041i	$-0.450722\pi$
$61$	−5.76271	−	4.18686i	−0.737840	−	0.536072i	−0.892034	+	0.451969i	$0.850722\pi$
$62$		0			0
$63$	5.63839	+	17.3532i	0.710370	+	2.18629i
$64$		0			0
$65$	1.75379			0.217531
$66$		0			0
$67$	5.43845			0.664412			0.332206	−	0.943207i	$-0.392207\pi$
$67$	5.43845			0.664412			0.332206	+	0.943207i	$0.392207\pi$
$68$		0			0
$69$	5.19388	+	15.9851i	0.625270	+	1.92438i
$70$		0			0
$71$	−2.98095	−	2.16579i	−0.353774	−	0.257032i	0.396677	−	0.917958i	$-0.370163\pi$
$71$	−2.98095	−	2.16579i	−0.353774	−	0.257032i	−0.750450	+	0.660927i	$0.770163\pi$
$72$		0			0
$73$	0.965093	−	2.97025i	0.112956	−	0.347641i	−0.878560	−	0.477633i	$-0.841495\pi$
$73$	0.965093	−	2.97025i	0.112956	−	0.347641i	0.991515	+	0.129991i	$0.0414949\pi$
$74$		0			0
$75$	9.70820	−	7.05342i	1.12101	−	0.814459i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.32746	+	1.69100i	−0.261859	+	0.190252i	−0.710966	−	0.703226i	$-0.751742\pi$
$79$	−2.32746	+	1.69100i	−0.261859	+	0.190252i	0.449107	+	0.893478i	$0.351742\pi$
$80$		0			0
$81$	−2.16312	+	6.65740i	−0.240347	+	0.739711i
$82$		0			0
$83$	7.38075	+	5.36243i	0.810142	+	0.588603i	0.913872	−	0.406003i	$-0.133078\pi$
$83$	7.38075	+	5.36243i	0.810142	+	0.588603i	−0.103730	+	0.994606i	$0.533078\pi$
$84$		0			0
$85$	0.347059	+	1.06814i	0.0376438	+	0.115856i
$86$		0			0
$87$	−8.00000			−0.857690
$88$		0			0
$89$	−9.68466			−1.02657			−0.513286	−	0.858218i	$-0.671572\pi$
$89$	−9.68466			−1.02657			−0.513286	+	0.858218i	$0.671572\pi$
$90$		0			0
$91$	−4.94427	−	15.2169i	−0.518301	−	1.59516i
$92$		0			0
$93$	2.98095	+	2.16579i	0.309110	+	0.224582i
$94$		0			0
$95$	−0.694117	+	2.13627i	−0.0712149	+	0.219177i
$96$		0			0
$97$	−9.25390	+	6.72335i	−0.939591	+	0.682653i	−0.948322	−	0.317309i	$-0.897221\pi$
$97$	−9.25390	+	6.72335i	−0.939591	+	0.682653i	0.00873118	+	0.999962i	$0.497221\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	−0.665368	−	0.746515i	$-0.731726\pi$
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	0.504368	+	0.863489i	$0.331726\pi$
$102$		0			0
$103$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$103$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$104$		0			0
$105$	5.96190	+	4.33158i	0.581822	+	0.422719i
$106$		0			0
$107$	−3.51331	−	10.8129i	−0.339645	−	1.04532i	−0.964389	−	0.264489i	$-0.914797\pi$
$107$	−3.51331	−	10.8129i	−0.339645	−	1.04532i	0.624744	−	0.780830i	$-0.285203\pi$
$108$		0			0
$109$	4.24621			0.406713			0.203357	−	0.979105i	$-0.434815\pi$
$109$	4.24621			0.406713			0.203357	+	0.979105i	$0.434815\pi$
$110$		0			0
$111$	−8.80776			−0.835996
$112$		0			0
$113$	−1.40960	−	4.33829i	−0.132604	−	0.408112i	0.862606	−	0.505877i	$-0.168831\pi$
$113$	−1.40960	−	4.33829i	−0.132604	−	0.408112i	−0.995210	+	0.0977642i	$0.968831\pi$
$114$		0			0
$115$	2.98095	+	2.16579i	0.277975	+	0.201961i
$116$		0			0
$117$	−3.43723	+	10.5787i	−0.317772	+	0.978001i
$118$		0			0
$119$	8.28936	−	6.02257i	0.759884	−	0.552088i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	14.7615	−	10.7249i	1.33100	−	0.967028i
$124$		0			0
$125$	1.68057	−	5.17227i	0.150315	−	0.462622i
$126$		0			0
$127$	−8.28936	−	6.02257i	−0.735562	−	0.534417i	0.155756	−	0.987796i	$-0.450219\pi$
$127$	−8.28936	−	6.02257i	−0.735562	−	0.534417i	−0.891318	+	0.453379i	$0.850219\pi$
$128$		0			0
$129$	−0.889009	−	2.73609i	−0.0782729	−	0.240899i
$130$		0			0
$131$	11.3693			0.993342			0.496671	−	0.867939i	$-0.334556\pi$
$131$	11.3693			0.993342			0.496671	+	0.867939i	$0.334556\pi$
$132$		0			0
$133$	20.4924			1.77692
$134$		0			0
$135$	−0.249613	−	0.768229i	−0.0214833	−	0.0661186i
$136$		0			0
$137$	10.1625	+	7.38350i	0.868242	+	0.630815i	0.930115	−	0.367269i	$-0.119707\pi$
$137$	10.1625	+	7.38350i	0.868242	+	0.630815i	−0.0618728	+	0.998084i	$0.519707\pi$
$138$		0			0
$139$	−2.12508	+	6.54032i	−0.180247	+	0.554742i	−0.999834	−	0.0182118i	$-0.994203\pi$
$139$	−2.12508	+	6.54032i	−0.180247	+	0.554742i	0.819587	+	0.572954i	$0.194203\pi$
$140$		0			0
$141$	−16.5787	+	12.0451i	−1.39618	+	1.01438i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−1.41884	+	1.03085i	−0.117829	+	0.0856075i
$146$		0			0
$147$	15.2346	−	46.8873i	1.25653	−	3.86720i
$148$		0			0
$149$	−9.90739	−	7.19814i	−0.811645	−	0.589695i	0.102662	−	0.994716i	$-0.467264\pi$
$149$	−9.90739	−	7.19814i	−0.811645	−	0.589695i	−0.914307	+	0.405022i	$0.867264\pi$
$150$		0			0
$151$	−4.74938	−	14.6171i	−0.386499	−	1.18952i	−0.935387	−	0.353626i	$-0.884949\pi$
$151$	−4.74938	−	14.6171i	−0.386499	−	1.18952i	0.548888	−	0.835896i	$-0.315051\pi$
$152$		0			0
$153$	−7.12311			−0.575869
$154$		0			0
$155$	0.807764			0.0648812
$156$		0			0
$157$	−2.64567	−	8.14252i	−0.211147	−	0.649844i	−0.999405	−	0.0344986i	$-0.989017\pi$
$157$	−2.64567	−	8.14252i	−0.211147	−	0.649844i	0.788258	−	0.615345i	$-0.210983\pi$
$158$		0			0
$159$	8.79959	+	6.39328i	0.697853	+	0.507020i
$160$		0			0
$161$	10.3878	−	31.9703i	0.818671	−	2.51961i
$162$		0			0
$163$	3.23607	−	2.35114i	0.253468	−	0.184156i	−0.453794	−	0.891107i	$-0.649930\pi$
$163$	3.23607	−	2.35114i	0.253468	−	0.184156i	0.707263	+	0.706951i	$0.249930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.47214	−	4.70228i	0.500829	−	0.363874i	−0.308505	−	0.951223i	$-0.599829\pi$
$167$	6.47214	−	4.70228i	0.500829	−	0.363874i	0.809334	+	0.587349i	$0.199829\pi$
$168$		0			0
$169$	−1.00313	+	3.08733i	−0.0771642	+	0.237487i
$170$		0			0
$171$	−11.5254	−	8.37371i	−0.881371	−	0.640354i
$172$		0			0
$173$	1.31215	+	4.03839i	0.0997610	+	0.307033i	0.988465	−	0.151448i	$-0.0483937\pi$
$173$	1.31215	+	4.03839i	0.0997610	+	0.307033i	−0.888704	+	0.458481i	$0.848394\pi$
$174$		0			0
$175$	−24.0000			−1.81423
$176$		0			0
$177$	−32.8078			−2.46598
$178$		0			0
$179$	−3.26370	−	10.0446i	−0.243940	−	0.750771i	−0.995809	−	0.0914582i	$-0.970847\pi$
$179$	−3.26370	−	10.0446i	−0.243940	−	0.750771i	0.751869	−	0.659313i	$-0.229153\pi$
$180$		0			0
$181$	11.0711	+	8.04364i	0.822910	+	0.597879i	0.917545	−	0.397633i	$-0.130168\pi$
$181$	11.0711	+	8.04364i	0.822910	+	0.597879i	−0.0946346	+	0.995512i	$0.530168\pi$
$182$		0			0
$183$	5.63839	−	17.3532i	0.416802	−	1.28278i
$184$		0			0
$185$	−1.56211	+	1.13494i	−0.114848	+	0.0834422i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−5.96190	+	4.33158i	−0.433665	+	0.315076i
$190$		0			0
$191$	−4.49977	+	13.8489i	−0.325592	+	1.00207i	0.645581	+	0.763692i	$0.276615\pi$
$191$	−4.49977	+	13.8489i	−0.325592	+	1.00207i	−0.971173	+	0.238377i	$0.923385\pi$
$192$		0			0
$193$	−0.709422	−	0.515426i	−0.0510653	−	0.0371011i	0.561960	−	0.827165i	$-0.310048\pi$
$193$	−0.709422	−	0.515426i	−0.0510653	−	0.0371011i	−0.613025	+	0.790063i	$0.710048\pi$
$194$		0			0
$195$	1.38823	+	4.27255i	0.0994136	+	0.305963i
$196$		0			0
$197$	−18.4924			−1.31753			−0.658765	−	0.752349i	$-0.728921\pi$
$197$	−18.4924			−1.31753			−0.658765	+	0.752349i	$0.728921\pi$
$198$		0			0
$199$	20.4924			1.45267			0.726335	−	0.687341i	$-0.241222\pi$
$199$	20.4924			1.45267			0.726335	+	0.687341i	$0.241222\pi$
$200$		0			0
$201$	4.30488	+	13.2490i	0.303643	+	0.934516i
$202$		0			0
$203$	12.9443	+	9.40456i	0.908510	+	0.660071i
$204$		0			0
$205$	1.23607	−	3.80423i	0.0863307	−	0.265699i
$206$		0			0
$207$	−18.9062	+	13.7361i	−1.31407	+	0.954728i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−19.8148	+	14.3963i	−1.36411	+	0.991081i	−0.365934	+	0.930641i	$0.619251\pi$
$211$	−19.8148	+	14.3963i	−1.36411	+	0.991081i	−0.998172	+	0.0604404i	$0.980749\pi$
$212$		0			0
$213$	2.91664	−	8.97650i	0.199845	−	0.615059i
$214$		0			0
$215$	−0.510233	−	0.370706i	−0.0347976	−	0.0252820i
$216$		0			0
$217$	−2.27724	−	7.00864i	−0.154589	−	0.475777i
$218$		0			0
$219$	8.00000			0.540590
$220$		0			0
$221$	6.24621			0.420166
$222$		0			0
$223$	2.72175	+	8.37668i	0.182262	+	0.560944i	0.999890	−	0.0148018i	$-0.00471174\pi$
$223$	2.72175	+	8.37668i	0.182262	+	0.560944i	−0.817629	+	0.575746i	$0.804712\pi$
$224$		0			0
$225$	13.4982	+	9.80700i	0.899878	+	0.653800i
$226$		0			0
$227$	−4.59721	+	14.1488i	−0.305128	+	0.939087i	0.674502	+	0.738273i	$0.264358\pi$
$227$	−4.59721	+	14.1488i	−0.305128	+	0.939087i	−0.979630	+	0.200813i	$0.935642\pi$
$228$		0			0
$229$	−1.87315	+	1.36092i	−0.123781	+	0.0899324i	−0.647953	−	0.761680i	$-0.724375\pi$
$229$	−1.87315	+	1.36092i	−0.123781	+	0.0899324i	0.524172	+	0.851612i	$0.324375\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.0521	−	10.2094i	0.920582	−	0.668842i	−0.0230869	−	0.999733i	$-0.507349\pi$
$233$	14.0521	−	10.2094i	0.920582	−	0.668842i	0.943669	+	0.330892i	$0.107349\pi$
$234$		0			0
$235$	−1.38823	+	4.27255i	−0.0905585	+	0.278710i
$236$		0			0
$237$	−5.96190	−	4.33158i	−0.387267	−	0.281366i
$238$		0			0
$239$	4.05526	+	12.4808i	0.262313	+	0.807317i	0.992300	+	0.123856i	$0.0395260\pi$
$239$	4.05526	+	12.4808i	0.262313	+	0.807317i	−0.729987	+	0.683461i	$0.760474\pi$
$240$		0			0
$241$	−20.8769			−1.34480			−0.672399	−	0.740188i	$-0.734736\pi$
$241$	−20.8769			−1.34480			−0.672399	+	0.740188i	$0.734736\pi$
$242$		0			0
$243$	−22.2462			−1.42710
$244$		0			0
$245$	−3.33978	−	10.2788i	−0.213371	−	0.656688i
$246$		0			0
$247$	10.1066	+	7.34286i	0.643066	+	0.467215i
$248$		0			0
$249$	−7.22152	+	22.2255i	−0.457645	+	1.40849i
$250$		0			0
$251$	2.07234	−	1.50564i	0.130805	−	0.0950353i	−0.520459	−	0.853887i	$-0.674239\pi$
$251$	2.07234	−	1.50564i	0.130805	−	0.0950353i	0.651264	+	0.758851i	$0.274239\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−2.32746	+	1.69100i	−0.145751	+	0.105894i
$256$		0			0
$257$	8.72856	−	26.8637i	0.544473	−	1.67571i	−0.177768	−	0.984072i	$-0.556888\pi$
$257$	8.72856	−	26.8637i	0.544473	−	1.67571i	0.722241	−	0.691642i	$-0.243112\pi$
$258$		0			0
$259$	14.2513	+	10.3541i	0.885530	+	0.643375i
$260$		0			0
$261$	−3.43723	−	10.5787i	−0.212759	−	0.654805i
$262$		0			0
$263$	−10.8769			−0.670698			−0.335349	−	0.942094i	$-0.608854\pi$
$263$	−10.8769			−0.670698			−0.335349	+	0.942094i	$0.608854\pi$
$264$		0			0
$265$	2.38447			0.146477
$266$		0			0
$267$	−7.66602	−	23.5936i	−0.469153	−	1.44390i
$268$		0			0
$269$	−23.2500	−	16.8921i	−1.41758	−	1.02993i	−0.992165	−	0.124934i	$-0.960128\pi$
$269$	−23.2500	−	16.8921i	−1.41758	−	1.02993i	−0.425415	−	0.904998i	$-0.639872\pi$
$270$		0			0
$271$	−1.38823	+	4.27255i	−0.0843293	+	0.259539i	−0.984326	−	0.176357i	$-0.943569\pi$
$271$	−1.38823	+	4.27255i	−0.0843293	+	0.259539i	0.899997	+	0.435896i	$0.143569\pi$
$272$		0			0
$273$	33.1574	−	24.0903i	2.00678	−	1.45801i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−14.5623	+	10.5801i	−0.874964	+	0.635699i	−0.931914	−	0.362678i	$-0.881862\pi$
$277$	−14.5623	+	10.5801i	−0.874964	+	0.635699i	0.0569502	+	0.998377i	$0.481862\pi$
$278$		0			0
$279$	−1.58313	+	4.87236i	−0.0947793	+	0.291701i
$280$		0			0
$281$	−0.199189	−	0.144719i	−0.0118826	−	0.00863323i	0.581828	−	0.813312i	$-0.302338\pi$
$281$	−0.199189	−	0.144719i	−0.0118826	−	0.00863323i	−0.593711	+	0.804679i	$0.702338\pi$
$282$		0			0
$283$	−6.18034	−	19.0211i	−0.367383	−	1.13069i	−0.948475	−	0.316851i	$-0.897374\pi$
$283$	−6.18034	−	19.0211i	−0.367383	−	1.13069i	0.581092	−	0.813838i	$-0.302626\pi$
$284$		0			0
$285$	−5.75379			−0.340825
$286$		0			0
$287$	−36.4924			−2.15408
$288$		0			0
$289$	−4.01722	−	12.3637i	−0.236307	−	0.727279i
$290$		0			0
$291$	−23.7043	−	17.2222i	−1.38957	−	1.00958i
$292$		0			0
$293$	−6.60348	+	20.3234i	−0.385780	+	1.18731i	0.550134	+	0.835077i	$0.314577\pi$
$293$	−6.60348	+	20.3234i	−0.385780	+	1.18731i	−0.935913	+	0.352231i	$0.885423\pi$
$294$		0			0
$295$	−5.81864	+	4.22749i	−0.338774	+	0.246134i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.5787	−	12.0451i	0.958772	−	0.696589i
$300$		0			0
$301$	−1.77802	+	5.47218i	−0.102483	+	0.315411i
$302$		0			0
$303$	−4.14468	−	3.01129i	−0.238106	−	0.172994i
$304$		0			0
$305$	−1.23607	−	3.80423i	−0.0707770	−	0.217829i
$306$		0			0
$307$	−0.492423			−0.0281040			−0.0140520	−	0.999901i	$-0.504473\pi$
$307$	−0.492423			−0.0281040			−0.0140520	+	0.999901i	$0.504473\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.11053	+	24.9616i	0.459906	+	1.41544i	0.865278	+	0.501292i	$0.167142\pi$
$311$	8.11053	+	24.9616i	0.459906	+	1.41544i	−0.405372	+	0.914152i	$0.632858\pi$
$312$		0			0
$313$	−8.74366	−	6.35264i	−0.494221	−	0.359073i	0.312584	−	0.949890i	$-0.398805\pi$
$313$	−8.74366	−	6.35264i	−0.494221	−	0.359073i	−0.806805	+	0.590817i	$0.798805\pi$
$314$		0			0
$315$	−3.16625	+	9.74473i	−0.178398	+	0.549053i
$316$		0			0
$317$	28.1601	−	20.4595i	1.58163	−	1.14912i	0.666827	−	0.745212i	$-0.267652\pi$
$317$	28.1601	−	20.4595i	1.58163	−	1.14912i	0.914800	−	0.403907i	$-0.132348\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	23.5611	−	17.1181i	1.31505	−	0.955441i
$322$		0			0
$323$	−2.47214	+	7.60845i	−0.137553	+	0.423346i
$324$		0			0
$325$	−11.8365	−	8.59970i	−0.656569	−	0.477026i
$326$		0			0
$327$	3.36115	+	10.3445i	0.185872	+	0.572054i
$328$		0			0
$329$	40.9848			2.25957
$330$		0			0
$331$	6.06913			0.333590			0.166795	−	0.985992i	$-0.446658\pi$
$331$	6.06913			0.333590			0.166795	+	0.985992i	$0.446658\pi$
$332$		0			0
$333$	−3.78429	−	11.6468i	−0.207378	−	0.638243i
$334$		0			0
$335$	2.47072	+	1.79508i	0.134990	+	0.0980758i
$336$		0			0
$337$	−10.1168	+	31.1363i	−0.551097	+	1.69610i	0.154937	+	0.987924i	$0.450482\pi$
$337$	−10.1168	+	31.1363i	−0.551097	+	1.69610i	−0.706034	+	0.708178i	$0.749518\pi$
$338$		0			0
$339$	9.45309	−	6.86807i	0.513421	−	0.373022i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−50.7566	+	36.8768i	−2.74060	+	1.99116i
$344$		0			0
$345$	−2.91664	+	8.97650i	−0.157027	+	0.483278i
$346$		0			0
$347$	−21.6320	−	15.7166i	−1.16127	−	0.843710i	−0.171329	−	0.985214i	$-0.554806\pi$
$347$	−21.6320	−	15.7166i	−1.16127	−	0.843710i	−0.989938	+	0.141504i	$0.954806\pi$
$348$		0			0
$349$	4.86819	+	14.9827i	0.260588	+	0.802008i	0.992677	+	0.120799i	$0.0385456\pi$
$349$	4.86819	+	14.9827i	0.260588	+	0.802008i	−0.732089	+	0.681209i	$0.761454\pi$
$350$		0			0
$351$	−4.49242			−0.239788
$352$		0			0
$353$	13.0540			0.694793			0.347397	−	0.937718i	$-0.387066\pi$
$353$	13.0540			0.694793			0.347397	+	0.937718i	$0.387066\pi$
$354$		0			0
$355$	−0.639396	−	1.96786i	−0.0339356	−	0.104443i
$356$		0			0
$357$	21.2336	+	15.4271i	1.12380	+	0.816491i
$358$		0			0
$359$	8.80464	−	27.0979i	0.464691	−	1.43017i	−0.394679	−	0.918819i	$-0.629144\pi$
$359$	8.80464	−	27.0979i	0.464691	−	1.43017i	0.859370	−	0.511354i	$-0.170856\pi$
$360$		0			0
$361$	2.42705	−	1.76336i	0.127740	−	0.0928082i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.41884	−	1.03085i	0.0742657	−	0.0539572i
$366$		0			0
$367$	−1.83274	+	5.64059i	−0.0956682	+	0.294437i	−0.987427	−	0.158074i	$-0.949472\pi$
$367$	−1.83274	+	5.64059i	−0.0956682	+	0.294437i	0.891759	+	0.452511i	$0.149472\pi$
$368$		0			0
$369$	20.5242	+	14.9117i	1.06845	+	0.776273i
$370$		0			0
$371$	−6.72229	−	20.6891i	−0.349004	−	1.07412i
$372$		0			0
$373$	−8.24621			−0.426973			−0.213486	−	0.976946i	$-0.568482\pi$
$373$	−8.24621			−0.426973			−0.213486	+	0.976946i	$0.568482\pi$
$374$		0			0
$375$	13.9309			0.719387
$376$		0			0
$377$	3.01409	+	9.27640i	0.155233	+	0.477759i
$378$		0			0
$379$	−16.8338	−	12.2305i	−0.864696	−	0.628238i	0.0644624	−	0.997920i	$-0.479467\pi$
$379$	−16.8338	−	12.2305i	−0.864696	−	0.628238i	−0.929158	+	0.369682i	$0.879467\pi$
$380$		0			0
$381$	8.11053	−	24.9616i	0.415515	−	1.27882i
$382$		0			0
$383$	−28.3593	+	20.6042i	−1.44909	+	1.05283i	−0.463048	+	0.886333i	$0.653244\pi$
$383$	−28.3593	+	20.6042i	−1.44909	+	1.05283i	−0.986043	+	0.166493i	$0.946756\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.23607	−	2.35114i	0.164499	−	0.119515i
$388$		0			0
$389$	−0.173529	+	0.534068i	−0.00879829	+	0.0270783i	−0.955359	−	0.295447i	$-0.904532\pi$
$389$	−0.173529	+	0.534068i	−0.00879829	+	0.0270783i	0.946561	+	0.322525i	$0.104532\pi$
$390$		0			0
$391$	10.6168	+	7.71357i	0.536915	+	0.390092i
$392$		0			0
$393$	8.99953	+	27.6977i	0.453966	+	1.39717i
$394$		0			0
$395$	−1.61553			−0.0812860
$396$		0			0
$397$	−22.4924			−1.12886			−0.564431	−	0.825480i	$-0.690904\pi$
$397$	−22.4924			−1.12886			−0.564431	+	0.825480i	$0.690904\pi$
$398$		0			0
$399$	16.2211	+	49.9233i	0.812068	+	2.49929i
$400$		0			0
$401$	2.01641	+	1.46501i	0.100695	+	0.0731591i	0.636993	−	0.770869i	$-0.280178\pi$
$401$	2.01641	+	1.46501i	0.100695	+	0.0731591i	−0.536299	+	0.844028i	$0.680178\pi$
$402$		0			0
$403$	1.38823	−	4.27255i	0.0691529	−	0.212831i
$404$		0			0
$405$	−3.18014	+	2.31051i	−0.158022	+	0.114810i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−8.48855	+	6.16729i	−0.419732	+	0.304953i	−0.777530	−	0.628846i	$-0.783528\pi$
$409$	−8.48855	+	6.16729i	−0.419732	+	0.304953i	0.357798	+	0.933799i	$0.383528\pi$
$410$		0			0
$411$	−9.94326	+	30.6022i	−0.490465	+	1.50950i
$412$		0			0
$413$	53.0841	+	38.5678i	2.61210	+	1.89780i
$414$		0			0
$415$	1.58313	+	4.87236i	0.0777126	+	0.239175i
$416$		0			0
$417$	−17.6155			−0.862636
$418$		0			0
$419$	0.492423			0.0240564			0.0120282	−	0.999928i	$-0.496171\pi$
$419$	0.492423			0.0240564			0.0120282	+	0.999928i	$0.496171\pi$
$420$		0			0
$421$	−9.42268	−	29.0000i	−0.459233	−	1.41337i	−0.866093	−	0.499884i	$-0.833376\pi$
$421$	−9.42268	−	29.0000i	−0.459233	−	1.41337i	0.406859	−	0.913491i	$-0.366624\pi$
$422$		0			0
$423$	−23.0509	−	16.7474i	−1.12077	−	0.814288i
$424$		0			0
$425$	2.89528	−	8.91075i	0.140442	−	0.432235i
$426$		0			0
$427$	−29.5230	+	21.4497i	−1.42872	+	1.03802i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.2717	−	11.0956i	0.735613	−	0.534454i	−0.155721	−	0.987801i	$-0.549770\pi$
$431$	15.2717	−	11.0956i	0.735613	−	0.534454i	0.891334	+	0.453347i	$0.149770\pi$
$432$		0			0
$433$	−3.18762	+	9.81047i	−0.153187	+	0.471461i	−0.997973	−	0.0636436i	$-0.979728\pi$
$433$	−3.18762	+	9.81047i	−0.153187	+	0.471461i	0.844786	+	0.535105i	$0.179728\pi$
$434$		0			0
$435$	−3.63445	−	2.64058i	−0.174258	−	0.126606i
$436$		0			0
$437$	8.11053	+	24.9616i	0.387979	+	1.19408i
$438$		0			0
$439$	28.4924			1.35987			0.679935	−	0.733273i	$-0.262008\pi$
$439$	28.4924			1.35987			0.679935	+	0.733273i	$0.262008\pi$
$440$		0			0
$441$	68.5464			3.26411
$442$		0			0
$443$	7.31896	+	22.5254i	0.347734	+	1.07022i	0.960104	+	0.279644i	$0.0902166\pi$
$443$	7.31896	+	22.5254i	0.347734	+	1.07022i	−0.612369	+	0.790572i	$0.709783\pi$
$444$		0			0
$445$	−4.39980	−	3.19664i	−0.208570	−	0.151535i
$446$		0			0
$447$	9.69365	−	29.8340i	0.458494	−	1.41110i
$448$		0			0
$449$	−27.1396	+	19.7181i	−1.28080	+	0.930554i	−0.999577	−	0.0290896i	$-0.990739\pi$
$449$	−27.1396	+	19.7181i	−1.28080	+	0.930554i	−0.281220	+	0.959643i	$0.590739\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	31.8504	−	23.1407i	1.49646	−	1.08725i
$454$		0			0
$455$	2.77647	−	8.54510i	0.130163	−	0.400600i
$456$		0			0
$457$	−27.3947	−	19.9034i	−1.28147	−	0.931043i	−0.281875	−	0.959451i	$-0.590956\pi$
$457$	−27.3947	−	19.9034i	−1.28147	−	0.931043i	−0.999596	+	0.0284080i	$0.990956\pi$
$458$		0			0
$459$	−0.889009	−	2.73609i	−0.0414954	−	0.127710i
$460$		0			0
$461$	7.12311			0.331756			0.165878	−	0.986146i	$-0.446954\pi$
$461$	7.12311			0.331756			0.165878	+	0.986146i	$0.446954\pi$
$462$		0			0
$463$	27.6847			1.28662			0.643308	−	0.765608i	$-0.277562\pi$
$463$	27.6847			1.28662			0.643308	+	0.765608i	$0.277562\pi$
$464$		0			0
$465$	0.639396	+	1.96786i	0.0296513	+	0.0912573i
$466$		0			0
$467$	20.4683	+	14.8711i	0.947159	+	0.688151i	0.950133	−	0.311844i	$-0.100947\pi$
$467$	20.4683	+	14.8711i	0.947159	+	0.688151i	−0.00297416	+	0.999996i	$0.500947\pi$
$468$		0			0
$469$	8.60975	−	26.4981i	0.397561	−	1.22357i
$470$		0			0
$471$	17.7424	−	12.8906i	0.817529	−	0.593969i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	15.1599	−	11.0143i	0.695583	−	0.505370i
$476$		0			0
$477$	−4.67330	+	14.3829i	−0.213976	+	0.658549i
$478$		0			0
$479$	−12.9443	−	9.40456i	−0.591439	−	0.429705i	0.251391	−	0.967886i	$-0.419112\pi$
$479$	−12.9443	−	9.40456i	−0.591439	−	0.429705i	−0.842830	+	0.538180i	$0.819112\pi$
$480$		0			0
$481$	3.31842	+	10.2130i	0.151307	+	0.465675i
$482$		0			0
$483$	86.1080			3.91805
$484$		0			0
$485$	−6.42329			−0.291667
$486$		0			0
$487$	−4.30488	−	13.2490i	−0.195073	−	0.600372i	−0.999976	−	0.00696539i	$-0.997783\pi$
$487$	−4.30488	−	13.2490i	−0.195073	−	0.600372i	0.804903	−	0.593406i	$-0.202217\pi$
$488$		0			0
$489$	8.28936	+	6.02257i	0.374858	+	0.272350i
$490$		0			0
$491$	−9.34659	+	28.7659i	−0.421806	+	1.29818i	0.484214	+	0.874950i	$0.339106\pi$
$491$	−9.34659	+	28.7659i	−0.421806	+	1.29818i	−0.906020	+	0.423235i	$0.860894\pi$
$492$		0			0
$493$	−5.05329	+	3.67143i	−0.227589	+	0.165353i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.2717	+	11.0956i	−0.685031	+	0.497704i
$498$		0			0
$499$	11.4289	−	35.1747i	0.511630	−	1.57463i	−0.277701	−	0.960667i	$-0.589573\pi$
$499$	11.4289	−	35.1747i	0.511630	−	1.57463i	0.789331	−	0.613967i	$-0.210427\pi$
$500$		0			0
$501$	16.5787	+	12.0451i	0.740682	+	0.538137i
$502$		0			0
$503$	−2.97136	−	9.14491i	−0.132486	−	0.407751i	0.862704	−	0.505709i	$-0.168769\pi$
$503$	−2.97136	−	9.14491i	−0.132486	−	0.407751i	−0.995191	+	0.0979576i	$0.968769\pi$
$504$		0			0
$505$	−1.12311			−0.0499775
$506$		0			0
$507$	−8.31534			−0.369297
$508$		0			0
$509$	10.9084	+	33.5725i	0.483504	+	1.48807i	0.834135	+	0.551560i	$0.185967\pi$
$509$	10.9084	+	33.5725i	0.483504	+	1.48807i	−0.350631	+	0.936514i	$0.614033\pi$
$510$		0			0
$511$	−12.9443	−	9.40456i	−0.572621	−	0.416033i
$512$		0			0
$513$	1.77802	−	5.47218i	0.0785014	−	0.241603i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−8.79959	+	6.39328i	−0.386259	+	0.280634i
$520$		0			0
$521$	4.22879	−	13.0149i	0.185267	−	0.570192i	−0.814686	−	0.579902i	$-0.803091\pi$
$521$	4.22879	−	13.0149i	0.185267	−	0.570192i	0.999953	+	0.00970977i	$0.00309076\pi$
$522$		0			0
$523$	−9.70820	−	7.05342i	−0.424510	−	0.308425i	0.354940	−	0.934889i	$-0.384501\pi$
$523$	−9.70820	−	7.05342i	−0.424510	−	0.308425i	−0.779450	+	0.626464i	$0.784501\pi$
$524$		0			0
$525$	−18.9975	−	58.4684i	−0.829120	−	2.55177i
$526$		0			0
$527$	2.87689			0.125319
$528$		0			0
$529$	20.0540			0.871912
$530$		0			0
$531$	−14.0960	−	43.3829i	−0.611713	−	1.88266i
$532$		0			0
$533$	−17.9976	−	13.0760i	−0.779561	−	0.566384i
$534$		0			0
$535$	1.97291	−	6.07199i	0.0852964	−	0.262515i
$536$		0			0
$537$	21.8871	−	15.9019i	0.944499	−	0.686219i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	27.3947	−	19.9034i	1.17779	−	0.855715i	0.185870	−	0.982574i	$-0.440490\pi$
$541$	27.3947	−	19.9034i	1.17779	−	0.855715i	0.991921	+	0.126859i	$0.0404896\pi$
$542$		0			0
$543$	−10.8323	+	33.3383i	−0.464857	+	1.43068i
$544$		0			0
$545$	1.92908	+	1.40156i	0.0826326	+	0.0600361i
$546$		0			0
$547$	7.95836	+	24.4933i	0.340275	+	1.04726i	0.964065	+	0.265666i	$0.0855920\pi$
$547$	7.95836	+	24.4933i	0.340275	+	1.04726i	−0.623790	+	0.781592i	$0.714408\pi$
$548$		0			0
$549$	25.3693			1.08274
$550$		0			0
$551$	−12.4924			−0.532195
$552$		0			0
$553$	4.55449	+	14.0173i	0.193677	+	0.596075i
$554$		0			0
$555$	−4.00142	−	2.90720i	−0.169851	−	0.123404i
$556$		0			0
$557$	6.25642	−	19.2553i	0.265093	−	0.815873i	−0.726579	−	0.687083i	$-0.758891\pi$
$557$	6.25642	−	19.2553i	0.265093	−	0.815873i	0.991672	−	0.128790i	$-0.0411092\pi$
$558$		0			0
$559$	−2.83769	+	2.06170i	−0.120021	+	0.0872007i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.87051	+	4.99172i	−0.289558	+	0.210376i	−0.723075	−	0.690769i	$-0.757272\pi$
$563$	−6.87051	+	4.99172i	−0.289558	+	0.210376i	0.433518	+	0.901145i	$0.357272\pi$
$564$		0			0
$565$	0.791563	−	2.43618i	0.0333013	−	0.102491i
$566$		0			0
$567$	29.0128	+	21.0790i	1.21842	+	0.885235i
$568$		0			0
$569$	10.8536	+	33.4041i	0.455008	+	1.40037i	0.871126	+	0.491060i	$0.163390\pi$
$569$	10.8536	+	33.4041i	0.455008	+	1.40037i	−0.416118	+	0.909311i	$0.636610\pi$
$570$		0			0
$571$	16.4924			0.690186			0.345093	−	0.938568i	$-0.387847\pi$
$571$	16.4924			0.690186			0.345093	+	0.938568i	$0.387847\pi$
$572$		0			0
$573$	−37.3002			−1.55824
$574$		0			0
$575$	−9.49876	−	29.2342i	−0.396126	−	1.21915i
$576$		0			0
$577$	−9.25390	−	6.72335i	−0.385245	−	0.279897i	0.378259	−	0.925700i	$-0.376523\pi$
$577$	−9.25390	−	6.72335i	−0.385245	−	0.279897i	−0.763504	+	0.645803i	$0.776523\pi$
$578$		0			0
$579$	0.694117	−	2.13627i	0.0288465	−	0.0887805i
$580$		0			0
$581$	37.8123	−	27.4723i	1.56872	−	1.13974i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−5.05329	+	3.67143i	−0.208928	+	0.151795i
$586$		0			0
$587$	2.62430	−	8.07677i	0.108317	−	0.333364i	−0.882178	−	0.470916i	$-0.843923\pi$
$587$	2.62430	−	8.07677i	0.108317	−	0.333364i	0.990495	+	0.137552i	$0.0439234\pi$
$588$		0			0
$589$	4.65491	+	3.38199i	0.191802	+	0.139353i
$590$		0			0
$591$	−14.6379	−	45.0509i	−0.602124	−	1.85315i
$592$		0			0
$593$	21.3693			0.877533			0.438766	−	0.898601i	$-0.355416\pi$
$593$	21.3693			0.877533			0.438766	+	0.898601i	$0.355416\pi$
$594$		0			0
$595$	5.75379			0.235882
$596$		0			0
$597$	16.2211	+	49.9233i	0.663883	+	2.04322i
$598$		0			0
$599$	12.9443	+	9.40456i	0.528889	+	0.384260i	0.819942	−	0.572447i	$-0.194006\pi$
$599$	12.9443	+	9.40456i	0.528889	+	0.384260i	−0.291053	+	0.956707i	$0.594006\pi$
$600$		0			0
$601$	−6.25642	+	19.2553i	−0.255205	+	0.785440i	0.738584	+	0.674161i	$0.235495\pi$
$601$	−6.25642	+	19.2553i	−0.255205	+	0.785440i	−0.993789	+	0.111279i	$0.964505\pi$
$602$		0			0
$603$	−15.6701	+	11.3850i	−0.638136	+	0.463633i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.59635	−	6.97216i	0.389504	−	0.282991i	−0.375748	−	0.926722i	$-0.622614\pi$
$607$	9.59635	−	6.97216i	0.389504	−	0.282991i	0.765252	+	0.643731i	$0.222614\pi$
$608$		0			0
$609$	−12.6650	+	38.9789i	−0.513212	+	1.57950i
$610$		0			0
$611$	20.2132	+	14.6857i	0.817737	+	0.594121i
$612$		0			0
$613$	14.1721	+	43.6171i	0.572404	+	1.76168i	0.644853	+	0.764306i	$0.276918\pi$
$613$	14.1721	+	43.6171i	0.572404	+	1.76168i	−0.0724495	+	0.997372i	$0.523082\pi$
$614$		0			0
$615$	10.2462			0.413167
$616$		0			0
$617$	30.4924			1.22758			0.613789	−	0.789470i	$-0.289644\pi$
$617$	30.4924			1.22758			0.613789	+	0.789470i	$0.289644\pi$
$618$		0			0
$619$	−3.06881	−	9.44482i	−0.123346	−	0.379619i	0.870250	−	0.492610i	$-0.163957\pi$
$619$	−3.06881	−	9.44482i	−0.123346	−	0.379619i	−0.993596	+	0.112991i	$0.963957\pi$
$620$		0			0
$621$	−7.63586	−	5.54778i	−0.306417	−	0.222625i
$622$		0			0
$623$	−15.3320	+	47.1872i	−0.614265	+	1.89051i
$624$		0			0
$625$	−16.4791	+	11.9728i	−0.659165	+	0.478911i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.56352	+	4.04214i	−0.221832	+	0.161171i
$630$		0			0
$631$	−1.52841	+	4.70395i	−0.0608449	+	0.187261i	−0.976859	−	0.213885i	$-0.931388\pi$
$631$	−1.52841	+	4.70395i	−0.0608449	+	0.187261i	0.916014	+	0.401146i	$0.131388\pi$
$632$		0			0
$633$	−50.7566	−	36.8768i	−2.01739	−	1.46572i
$634$		0			0
$635$	−1.77802	−	5.47218i	−0.0705585	−	0.217157i
$636$		0			0
$637$	−60.1080			−2.38156
$638$		0			0
$639$	13.1231			0.519142
$640$		0			0
$641$	2.25588	+	6.94289i	0.0891020	+	0.274228i	0.985672	−	0.168675i	$-0.0539488\pi$
$641$	2.25588	+	6.94289i	0.0891020	+	0.274228i	−0.896570	+	0.442903i	$0.853949\pi$
$642$		0			0
$643$	−29.2679	−	21.2644i	−1.15421	−	0.838584i	−0.165177	−	0.986264i	$-0.552820\pi$
$643$	−29.2679	−	21.2644i	−1.15421	−	0.838584i	−0.989035	+	0.147680i	$0.952820\pi$
$644$		0			0
$645$	0.499226	−	1.53646i	0.0196570	−	0.0604980i
$646$		0			0
$647$	−7.63586	+	5.54778i	−0.300197	+	0.218106i	−0.727679	−	0.685918i	$-0.759401\pi$
$647$	−7.63586	+	5.54778i	−0.300197	+	0.218106i	0.427482	+	0.904024i	$0.359401\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	15.2717	−	11.0956i	0.598546	−	0.434869i
$652$		0			0
$653$	−3.14489	+	9.67898i	−0.123069	+	0.378768i	−0.993544	−	0.113444i	$-0.963812\pi$
$653$	−3.14489	+	9.67898i	−0.123069	+	0.378768i	0.870475	+	0.492212i	$0.163812\pi$
$654$		0			0
$655$	5.16515	+	3.75270i	0.201819	+	0.146630i
$656$		0			0
$657$	3.43723	+	10.5787i	0.134099	+	0.412714i
$658$		0			0
$659$	−29.6155			−1.15366			−0.576829	−	0.816865i	$-0.695710\pi$
$659$	−29.6155			−1.15366			−0.576829	+	0.816865i	$0.695710\pi$
$660$		0			0
$661$	21.1922			0.824282			0.412141	−	0.911120i	$-0.364781\pi$
$661$	21.1922			0.824282			0.412141	+	0.911120i	$0.364781\pi$
$662$		0			0
$663$	4.94427	+	15.2169i	0.192020	+	0.590976i
$664$		0			0
$665$	9.30983	+	6.76398i	0.361020	+	0.262296i
$666$		0			0
$667$	−6.33251	+	19.4895i	−0.245196	+	0.754635i
$668$		0			0
$669$	−18.2527	+	13.2613i	−0.705689	+	0.512713i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−39.8288	+	28.9373i	−1.53529	+	1.11545i	−0.582079	+	0.813132i	$0.697761\pi$
$673$	−39.8288	+	28.9373i	−1.53529	+	1.11545i	−0.953207	+	0.302318i	$0.902239\pi$
$674$		0			0
$675$	−2.08235	+	6.40882i	−0.0801498	+	0.246676i
$676$		0			0
$677$	23.2500	+	16.8921i	0.893572	+	0.649218i	0.936807	−	0.349847i	$-0.113766\pi$
$677$	23.2500	+	16.8921i	0.893572	+	0.649218i	−0.0432351	+	0.999065i	$0.513766\pi$
$678$		0			0
$679$	18.1085	+	55.7323i	0.694941	+	2.13881i
$680$		0			0
$681$	−38.1080			−1.46030
$682$		0			0
$683$	−42.7386			−1.63535			−0.817674	−	0.575681i	$-0.804737\pi$
$683$	−42.7386			−1.63535			−0.817674	+	0.575681i	$0.804737\pi$
$684$		0			0
$685$	2.17980	+	6.70873i	0.0832858	+	0.256327i
$686$		0			0
$687$	−4.79817	−	3.48608i	−0.183062	−	0.133002i
$688$		0			0
$689$	4.09799	−	12.6123i	0.156121	−	0.480491i
$690$		0			0
$691$	38.0675	−	27.6576i	1.44815	−	1.05215i	0.461897	−	0.886934i	$-0.347169\pi$
$691$	38.0675	−	27.6576i	1.44815	−	1.05215i	0.986258	−	0.165212i	$-0.0528309\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.12421	+	2.26987i	−0.118508	+	0.0861012i
$696$		0			0
$697$	4.40232	−	13.5490i	0.166750	−	0.513203i
$698$		0			0
$699$	35.9951	+	26.1520i	1.36146	+	0.989159i
$700$		0			0
$701$	−5.41014	−	16.6507i	−0.204338	−	0.628888i	−0.999740	−	0.0228056i	$-0.992740\pi$
$701$	−5.41014	−	16.6507i	−0.204338	−	0.628888i	0.795402	−	0.606082i	$-0.207260\pi$
$702$		0			0
$703$	−13.7538			−0.518734
$704$		0			0
$705$	−11.5076			−0.433400
$706$		0			0
$707$	3.16625	+	9.74473i	0.119079	+	0.366488i
$708$		0			0
$709$	−18.4519	−	13.4061i	−0.692974	−	0.503475i	0.184662	−	0.982802i	$-0.440881\pi$
$709$	−18.4519	−	13.4061i	−0.692974	−	0.503475i	−0.877637	+	0.479327i	$0.840881\pi$
$710$		0			0
$711$	3.16625	−	9.74473i	0.118744	−	0.365456i
$712$		0			0
$713$	7.63586	−	5.54778i	0.285965	−	0.207766i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−27.1955	+	19.7587i	−1.01564	+	0.737903i
$718$		0			0
$719$	−8.16525	+	25.1300i	−0.304512	+	0.937193i	0.675346	+	0.737501i	$0.263994\pi$
$719$	−8.16525	+	25.1300i	−0.304512	+	0.937193i	−0.979859	+	0.199692i	$0.936006\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−16.5254	−	50.8599i	−0.614586	−	1.89150i
$724$		0			0
$725$	14.6307			0.543370
$726$		0			0
$727$	−35.6847			−1.32347			−0.661735	−	0.749737i	$-0.730180\pi$
$727$	−35.6847			−1.32347			−0.661735	+	0.749737i	$0.730180\pi$
$728$		0			0
$729$	−11.1199	−	34.2236i	−0.411849	−	1.26754i
$730$		0			0
$731$	−1.81722	−	1.32029i	−0.0672124	−	0.0488327i
$732$		0			0
$733$	2.20116	−	6.77448i	0.0813017	−	0.250221i	−0.902141	−	0.431442i	$-0.858005\pi$
$733$	2.20116	−	6.77448i	0.0813017	−	0.250221i	0.983442	+	0.181221i	$0.0580049\pi$
$734$		0			0
$735$	22.3974	−	16.2726i	0.826139	−	0.600225i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−22.1422	+	16.0873i	−0.814516	+	0.591780i	−0.915136	−	0.403145i	$-0.867917\pi$
$739$	−22.1422	+	16.0873i	−0.814516	+	0.591780i	0.100621	+	0.994925i	$0.467917\pi$
$740$		0			0
$741$	−9.88854	+	30.4338i	−0.363265	+	1.11801i
$742$		0			0
$743$	−31.3402	−	22.7700i	−1.14976	−	0.835350i	−0.161312	−	0.986903i	$-0.551572\pi$
$743$	−31.3402	−	22.7700i	−1.14976	−	0.835350i	−0.988449	+	0.151553i	$0.951572\pi$
$744$		0			0
$745$	−2.12508	−	6.54032i	−0.0778568	−	0.239619i
$746$		0			0
$747$	−32.4924			−1.18884
$748$		0			0
$749$	−58.2462			−2.12827
$750$		0			0
$751$	0.444505	+	1.36804i	0.0162202	+	0.0499207i	0.958839	−	0.283950i	$-0.0916450\pi$
$751$	0.444505	+	1.36804i	0.0162202	+	0.0499207i	−0.942619	+	0.333871i	$0.891645\pi$
$752$		0			0
$753$	5.30841	+	3.85678i	0.193449	+	0.140549i
$754$		0			0
$755$	2.66703	−	8.20827i	0.0970631	−	0.298729i
$756$		0			0
$757$	−26.0877	+	18.9538i	−0.948175	+	0.688889i	−0.950374	−	0.311108i	$-0.899300\pi$
$757$	−26.0877	+	18.9538i	−0.948175	+	0.688889i	0.00219969	+	0.999998i	$0.499300\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.52665	+	1.83572i	−0.0915908	+	0.0665446i	−0.632638	−	0.774447i	$-0.718028\pi$
$761$	−2.52665	+	1.83572i	−0.0915908	+	0.0665446i	0.541047	+	0.840992i	$0.318028\pi$
$762$		0			0
$763$	6.72229	−	20.6891i	0.243363	−	0.748995i
$764$		0			0
$765$	−3.23607	−	2.35114i	−0.117000	−	0.0850057i
$766$		0			0
$767$	12.3607	+	38.0423i	0.446318	+	1.37363i
$768$		0			0
$769$	15.6155			0.563110			0.281555	−	0.959545i	$-0.409150\pi$
$769$	15.6155			0.563110			0.281555	+	0.959545i	$0.409150\pi$
$770$		0			0
$771$	72.3542			2.60577
$772$		0			0
$773$	−2.70039	−	8.31093i	−0.0971261	−	0.298924i	0.890676	−	0.454639i	$-0.150232\pi$
$773$	−2.70039	−	8.31093i	−0.0971261	−	0.298924i	−0.987802	+	0.155715i	$0.950232\pi$
$774$		0			0
$775$	−5.45167	−	3.96087i	−0.195830	−	0.142279i
$776$		0			0
$777$	−13.9438	+	42.9146i	−0.500231	+	1.53955i
$778$		0			0
$779$	23.0509	−	16.7474i	0.825883	−	0.600039i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	3.63445	−	2.64058i	0.129885	−	0.0943666i
$784$		0			0
$785$	1.48568	−	4.57246i	0.0530262	−	0.163198i
$786$		0			0
$787$	−37.4140	−	27.1828i	−1.33366	−	0.968964i	−0.999652	−	0.0263950i	$-0.991597\pi$
$787$	−37.4140	−	27.1828i	−1.33366	−	0.968964i	−0.334012	−	0.942569i	$-0.608403\pi$
$788$		0			0
$789$	−8.60975	−	26.4981i	−0.306515	−	0.943357i
$790$		0			0
$791$	−23.3693			−0.830917
$792$		0			0
$793$	−22.2462			−0.789986
$794$		0			0
$795$	1.88746	+	5.80901i	0.0669413	+	0.206024i
$796$		0			0
$797$	28.1601	+	20.4595i	0.997481	+	0.724712i	0.961547	−	0.274642i	$-0.0885593\pi$
$797$	28.1601	+	20.4595i	0.997481	+	0.724712i	0.0359343	+	0.999354i	$0.488559\pi$
$798$		0			0
$799$	−4.94427	+	15.2169i	−0.174916	+	0.538335i
$800$		0			0
$801$	27.9050	−	20.2741i	0.985973	−	0.716351i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	15.2717	−	11.0956i	0.538258	−	0.391067i
$806$		0			0
$807$	22.7484	−	70.0125i	0.800783	−	2.46456i
$808$		0			0
$809$	−3.54711	−	2.57713i	−0.124710	−	0.0906070i	0.523682	−	0.851914i	$-0.324558\pi$
$809$	−3.54711	−	2.57713i	−0.124710	−	0.0906070i	−0.648392	+	0.761307i	$0.724558\pi$
$810$		0			0
$811$	−0.347059	−	1.06814i	−0.0121869	−	0.0375074i	0.944778	−	0.327711i	$-0.106277\pi$
$811$	−0.347059	−	1.06814i	−0.0121869	−	0.0375074i	−0.956965	+	0.290203i	$0.906277\pi$
$812$		0			0
$813$	−11.5076			−0.403588
$814$		0			0
$815$	2.24621			0.0786813
$816$		0			0
$817$	−1.38823	−	4.27255i	−0.0485682	−	0.149478i
$818$		0			0
$819$	46.1017	+	33.4949i	1.61092	+	1.17040i
$820$		0			0
$821$	−7.10271	+	21.8599i	−0.247886	+	0.762915i	0.747262	+	0.664529i	$0.231368\pi$
$821$	−7.10271	+	21.8599i	−0.247886	+	0.762915i	−0.995148	+	0.0983859i	$0.968632\pi$
$822$		0			0
$823$	−12.5773	+	9.13794i	−0.438417	+	0.318529i	−0.785006	−	0.619489i	$-0.787340\pi$
$823$	−12.5773	+	9.13794i	−0.438417	+	0.318529i	0.346589	+	0.938017i	$0.387340\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.68774	+	6.31201i	−0.302102	+	0.219490i	−0.728500	−	0.685046i	$-0.759782\pi$
$827$	−8.68774	+	6.31201i	−0.302102	+	0.219490i	0.426398	+	0.904536i	$0.359782\pi$
$828$		0			0
$829$	13.5754	−	41.7807i	0.471493	−	1.45111i	−0.379137	−	0.925340i	$-0.623779\pi$
$829$	13.5754	−	41.7807i	0.471493	−	1.45111i	0.850630	−	0.525765i	$-0.176221\pi$
$830$		0			0
$831$	−37.3021	−	27.1016i	−1.29400	−	0.940143i
$832$		0			0
$833$	−11.8948	−	36.6085i	−0.412131	−	1.26841i
$834$		0			0
$835$	4.49242			0.155467
$836$		0			0
$837$	−2.06913			−0.0715196
$838$		0			0
$839$	0.249613	+	0.768229i	0.00861759	+	0.0265222i	0.955273	−	0.295726i	$-0.0955615\pi$
$839$	0.249613	+	0.768229i	0.00861759	+	0.0265222i	−0.946655	+	0.322248i	$0.895561\pi$
$840$		0			0
$841$	15.5705	+	11.3126i	0.536914	+	0.390091i
$842$		0			0
$843$	0.194892	−	0.599815i	0.00671243	−	0.0206587i
$844$		0			0
$845$	−1.47477	+	1.07148i	−0.0507337	+	0.0368602i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	41.4468	−	30.1129i	1.42245	−	1.03347i
$850$		0			0
$851$	−6.97190	+	21.4573i	−0.238994	+	0.735547i
$852$		0			0
$853$	−10.9279	−	7.93955i	−0.374163	−	0.271845i	0.384772	−	0.923012i	$-0.374280\pi$
$853$	−10.9279	−	7.93955i	−0.374163	−	0.271845i	−0.758935	+	0.651166i	$0.774280\pi$
$854$		0			0
$855$	−2.47214	−	7.60845i	−0.0845453	−	0.260204i
$856$		0			0
$857$	44.1080			1.50670			0.753349	−	0.657620i	$-0.228437\pi$
$857$	44.1080			1.50670			0.753349	+	0.657620i	$0.228437\pi$
$858$		0			0
$859$	−7.05398			−0.240679			−0.120339	−	0.992733i	$-0.538398\pi$
$859$	−7.05398			−0.240679			−0.120339	+	0.992733i	$0.538398\pi$
$860$		0			0
$861$	−28.8861	−	88.9022i	−0.984434	−	3.02978i
$862$		0			0
$863$	2.83769	+	2.06170i	0.0965961	+	0.0701812i	0.635035	−	0.772483i	$-0.280986\pi$
$863$	2.83769	+	2.06170i	0.0965961	+	0.0701812i	−0.538439	+	0.842665i	$0.680986\pi$
$864$		0			0
$865$	−0.736842	+	2.26777i	−0.0250534	+	0.0771064i
$866$		0			0
$867$	26.9404	−	19.5734i	0.914945	−	0.664746i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	13.7410	−	9.98344i	0.465597	−	0.338276i
$872$		0			0
$873$	12.5889	−	38.7447i	0.426071	−	1.31131i
$874$		0			0
$875$	−22.5406	−	16.3767i	−0.762012	−	0.553634i
$876$		0			0
$877$	−9.46540	−	29.1315i	−0.319624	−	0.983701i	−0.973809	−	0.227367i	$-0.926988\pi$
$877$	−9.46540	−	29.1315i	−0.319624	−	0.983701i	0.654185	−	0.756334i	$-0.273012\pi$
$878$		0			0
$879$	−54.7386			−1.84629
$880$		0			0
$881$	−19.3002			−0.650240			−0.325120	−	0.945673i	$-0.605405\pi$
$881$	−19.3002			−0.650240			−0.325120	+	0.945673i	$0.605405\pi$
$882$		0			0
$883$	−7.56857	−	23.2937i	−0.254703	−	0.783895i	−0.993888	−	0.110393i	$-0.964789\pi$
$883$	−7.56857	−	23.2937i	−0.254703	−	0.783895i	0.739185	−	0.673502i	$-0.235211\pi$
$884$		0			0
$885$	−14.9048	−	10.8289i	−0.501018	−	0.364011i
$886$		0			0
$887$	2.97136	−	9.14491i	0.0997686	−	0.307056i	−0.888699	−	0.458492i	$-0.848390\pi$
$887$	2.97136	−	9.14491i	0.0997686	−	0.307056i	0.988467	+	0.151436i	$0.0483897\pi$
$888$		0			0
$889$	−42.4673	+	30.8543i	−1.42431	+	1.03482i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−25.8885	+	18.8091i	−0.866327	+	0.629423i
$894$		0			0
$895$	1.83274	−	5.64059i	0.0612617	−	0.188544i
$896$		0			0
$897$	42.4673	+	30.8543i	1.41794	+	1.03019i
$898$		0			0
$899$	1.38823	+	4.27255i	0.0463002	+	0.142497i
$900$		0			0
$901$	8.49242			0.282924
$902$		0			0
$903$	−14.7386			−0.490471
$904$		0			0
$905$	2.37469	+	7.30854i	0.0789374	+	0.242944i
$906$		0			0
$907$	13.3427	+	9.69400i	0.443035	+	0.321884i	0.786840	−	0.617157i	$-0.211716\pi$
$907$	13.3427	+	9.69400i	0.443035	+	0.321884i	−0.343804	+	0.939041i	$0.611716\pi$
$908$		0			0
$909$	2.20116	−	6.77448i	0.0730079	−	0.224695i
$910$		0			0
$911$	−18.3959	+	13.3654i	−0.609485	+	0.442817i	−0.849233	−	0.528019i	$-0.822935\pi$
$911$	−18.3959	+	13.3654i	−0.609485	+	0.442817i	0.239748	+	0.970835i	$0.422935\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	8.28936	−	6.02257i	0.274038	−	0.199100i
$916$		0			0
$917$	17.9991	−	55.3954i	0.594382	−	1.82932i
$918$		0			0
$919$	25.3783	+	18.4384i	0.837153	+	0.608227i	0.921574	−	0.388203i	$-0.126904\pi$
$919$	25.3783	+	18.4384i	0.837153	+	0.608227i	−0.0844208	+	0.996430i	$0.526904\pi$
$920$		0			0
$921$	−0.389784	−	1.19963i	−0.0128438	−	0.0395292i
$922$		0			0
$923$	−11.5076			−0.378777
$924$		0			0
$925$	16.1080			0.529626
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.9279	−	7.93955i	−0.358531	−	0.260488i	0.393908	−	0.919150i	$-0.371123\pi$
$929$	−10.9279	−	7.93955i	−0.358531	−	0.260488i	−0.752439	+	0.658662i	$0.771123\pi$
$930$		0			0
$931$	23.7896	−	73.2169i	0.779673	−	2.39959i
$932$		0			0
$933$	−54.3911	+	39.5174i	−1.78068	+	1.29374i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	25.9759	−	18.8726i	0.848595	−	0.616540i	−0.0761633	−	0.997095i	$-0.524267\pi$
$937$	25.9759	−	18.8726i	0.848595	−	0.616540i	0.924758	+	0.380555i	$0.124267\pi$
$938$		0			0
$939$	8.55503	−	26.3297i	0.279183	−	0.859236i
$940$		0			0
$941$	−12.7451	−	9.25984i	−0.415478	−	0.301862i	0.360338	−	0.932822i	$-0.382661\pi$
$941$	−12.7451	−	9.25984i	−0.415478	−	0.301862i	−0.775816	+	0.630960i	$0.782661\pi$
$942$		0			0
$943$	−14.4430	−	44.4511i	−0.470330	−	1.44753i
$944$		0			0
$945$	−4.13826			−0.134618
$946$		0			0
$947$	−0.315342			−0.0102472			−0.00512361	−	0.999987i	$-0.501631\pi$
$947$	−0.315342			−0.0102472			−0.00512361	+	0.999987i	$0.501631\pi$
$948$		0			0
$949$	−3.01409	−	9.27640i	−0.0978414	−	0.301125i
$950$		0			0
$951$	72.1335	+	52.4081i	2.33909	+	1.69945i
$952$		0			0
$953$	5.02036	−	15.4511i	0.162625	−	0.500509i	−0.836228	−	0.548382i	$-0.815244\pi$
$953$	5.02036	−	15.4511i	0.162625	−	0.500509i	0.998853	+	0.0478725i	$0.0152441\pi$
$954$		0			0
$955$	−6.61540	+	4.80637i	−0.214069	+	0.155530i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	52.0636	−	37.8264i	1.68122	−	1.22148i
$960$		0			0
$961$	−8.94013	+	27.5149i	−0.288391	+	0.887577i
$962$		0			0
$963$	32.7591	+	23.8008i	1.05565	+	0.766972i
$964$		0			0
$965$	−0.152167	−	0.468322i	−0.00489843	−	0.0150758i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	−20.4924			−0.658311
$970$		0			0
$971$	10.9844	+	33.8066i	0.352507	+	1.08491i	0.957441	+	0.288630i	$0.0931998\pi$
$971$	10.9844	+	33.8066i	0.352507	+	1.08491i	−0.604933	+	0.796276i	$0.706800\pi$
$972$		0			0
$973$	28.5025	+	20.7083i	0.913749	+	0.663877i
$974$		0			0
$975$	11.5811	−	35.6430i	0.370892	−	1.14149i
$976$		0			0
$977$	−26.8531	+	19.5099i	−0.859106	+	0.624177i	−0.927642	−	0.373471i	$-0.878167\pi$
$977$	−26.8531	+	19.5099i	−0.859106	+	0.624177i	0.0685354	+	0.997649i	$0.478167\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−12.2348	+	8.88914i	−0.390629	+	0.283808i
$982$		0			0
$983$	0.639396	−	1.96786i	0.0203936	−	0.0627650i	−0.940342	−	0.340231i	$-0.889495\pi$
$983$	0.639396	−	1.96786i	0.0203936	−	0.0627650i	0.960735	+	0.277466i	$0.0894947\pi$
$984$		0			0
$985$	−8.40121	−	6.10384i	−0.267685	−	0.194484i
$986$		0			0
$987$	32.4421	+	99.8465i	1.03264	+	3.17815i
$988$		0			0
$989$	−7.36932			−0.234331
$990$		0			0
$991$	28.4924			0.905092			0.452546	−	0.891741i	$-0.350516\pi$
$991$	28.4924			0.905092			0.452546	+	0.891741i	$0.350516\pi$
$992$		0			0
$993$	4.80410	+	14.7855i	0.152454	+	0.469204i
$994$		0			0
$995$	9.30983	+	6.76398i	0.295141	+	0.214433i
$996$		0			0
$997$	−11.0485	+	34.0039i	−0.349910	+	1.07691i	0.608992	+	0.793177i	$0.291574\pi$
$997$	−11.0485	+	34.0039i	−0.349910	+	1.07691i	−0.958902	+	0.283737i	$0.908426\pi$
$998$		0			0
$999$	4.00142	−	2.90720i	0.126599	−	0.0919797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.q.729.2		8
11.2	odd	10		88.2.a.b.1.2	✓	2
11.3	even	5	inner	968.2.i.q.753.1		8
11.4	even	5	inner	968.2.i.q.81.2		8
11.5	even	5	inner	968.2.i.q.9.1		8
11.6	odd	10		968.2.i.r.9.1		8
11.7	odd	10		968.2.i.r.81.2		8
11.8	odd	10		968.2.i.r.753.1		8
11.9	even	5		968.2.a.j.1.2		2
11.10	odd	2		968.2.i.r.729.2		8
33.2	even	10		792.2.a.h.1.2		2
33.20	odd	10		8712.2.a.bb.1.2		2
44.31	odd	10		1936.2.a.r.1.1		2
44.35	even	10		176.2.a.d.1.1		2
55.2	even	20		2200.2.b.g.1849.1		4
55.13	even	20		2200.2.b.g.1849.4		4
55.24	odd	10		2200.2.a.o.1.1		2
77.13	even	10		4312.2.a.n.1.1		2
88.13	odd	10		704.2.a.m.1.1		2
88.35	even	10		704.2.a.p.1.2		2
88.53	even	10		7744.2.a.by.1.1		2
88.75	odd	10		7744.2.a.cl.1.2		2
132.35	odd	10		1584.2.a.t.1.2		2
176.13	odd	20		2816.2.c.w.1409.4		4
176.35	even	20		2816.2.c.p.1409.1		4
176.101	odd	20		2816.2.c.w.1409.1		4
176.123	even	20		2816.2.c.p.1409.4		4
220.79	even	10		4400.2.a.bp.1.2		2
220.123	odd	20		4400.2.b.v.4049.1		4
220.167	odd	20		4400.2.b.v.4049.4		4
264.35	odd	10		6336.2.a.cx.1.1		2
264.101	even	10		6336.2.a.cu.1.1		2
308.167	odd	10		8624.2.a.cb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.a.b.1.2	✓	2	11.2	odd	10
176.2.a.d.1.1		2	44.35	even	10
704.2.a.m.1.1		2	88.13	odd	10
704.2.a.p.1.2		2	88.35	even	10
792.2.a.h.1.2		2	33.2	even	10
968.2.a.j.1.2		2	11.9	even	5
968.2.i.q.9.1		8	11.5	even	5	inner
968.2.i.q.81.2		8	11.4	even	5	inner
968.2.i.q.729.2		8	1.1	even	1	trivial
968.2.i.q.753.1		8	11.3	even	5	inner
968.2.i.r.9.1		8	11.6	odd	10
968.2.i.r.81.2		8	11.7	odd	10
968.2.i.r.729.2		8	11.10	odd	2
968.2.i.r.753.1		8	11.8	odd	10
1584.2.a.t.1.2		2	132.35	odd	10
1936.2.a.r.1.1		2	44.31	odd	10
2200.2.a.o.1.1		2	55.24	odd	10
2200.2.b.g.1849.1		4	55.2	even	20
2200.2.b.g.1849.4		4	55.13	even	20
2816.2.c.p.1409.1		4	176.35	even	20
2816.2.c.p.1409.4		4	176.123	even	20
2816.2.c.w.1409.1		4	176.101	odd	20
2816.2.c.w.1409.4		4	176.13	odd	20
4312.2.a.n.1.1		2	77.13	even	10
4400.2.a.bp.1.2		2	220.79	even	10
4400.2.b.v.4049.1		4	220.123	odd	20
4400.2.b.v.4049.4		4	220.167	odd	20
6336.2.a.cu.1.1		2	264.101	even	10
6336.2.a.cx.1.1		2	264.35	odd	10
7744.2.a.by.1.1		2	88.53	even	10
7744.2.a.cl.1.2		2	88.75	odd	10
8624.2.a.cb.1.2		2	308.167	odd	10
8712.2.a.bb.1.2		2	33.20	odd	10

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.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.791563 + 2.43618i) q^{3} +(0.454306 + 0.330072i) q^{5} +(1.58313 - 4.87236i) q^{7} +(-2.88136 + 2.09343i) q^{9} +(2.52665 - 1.83572i) q^{13} +(-0.444505 + 1.36804i) q^{15} +(1.61803 + 1.17557i) q^{17} +(1.23607 + 3.80423i) q^{19} +13.1231 q^{21} +6.56155 q^{23} +(-1.44764 - 4.45537i) q^{25} +(-1.16373 - 0.845498i) q^{27} +(-0.965093 + 2.97025i) q^{29} +(1.16373 - 0.845498i) q^{31} +(2.32746 - 1.69100i) q^{35} +(-1.06254 + 3.27016i) q^{37} +(6.47214 + 4.70228i) q^{39} +(-2.20116 - 6.77448i) q^{41} -1.12311 q^{43} -2.00000 q^{45} +(2.47214 + 7.60845i) q^{47} +(-15.5705 - 11.3126i) q^{49} +(-1.58313 + 4.87236i) q^{51} +(3.43526 - 2.49586i) q^{53} +(-8.28936 + 6.02257i) q^{57} +(-3.95782 + 12.1809i) q^{59} +(-5.76271 - 4.18686i) q^{61} +(5.63839 + 17.3532i) q^{63} +1.75379 q^{65} +5.43845 q^{67} +(5.19388 + 15.9851i) q^{69} +(-2.98095 - 2.16579i) q^{71} +(0.965093 - 2.97025i) q^{73} +(9.70820 - 7.05342i) q^{75} +(-2.32746 + 1.69100i) q^{79} +(-2.16312 + 6.65740i) q^{81} +(7.38075 + 5.36243i) q^{83} +(0.347059 + 1.06814i) q^{85} -8.00000 q^{87} -9.68466 q^{89} +(-4.94427 - 15.2169i) q^{91} +(2.98095 + 2.16579i) q^{93} +(-0.694117 + 2.13627i) q^{95} +(-9.25390 + 6.72335i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} - 2 q^{13} + 7 q^{15} + 4 q^{17} - 8 q^{19} + 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} - 2 q^{29} + 7 q^{31} + 14 q^{35} + 11 q^{37} + 16 q^{39} + 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 - 2 * q^13 + 7 * q^15 + 4 * q^17 - 8 * q^19 + 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 - 2 * q^29 + 7 * q^31 + 14 * q^35 + 11 * q^37 + 16 * q^39 + 6 * q^41 + 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 + 2 * q^51 - 8 * q^53 - 4 * q^57 + 5 * q^59 - 6 * q^61 - 20 * q^63 + 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 + 2 * q^73 + 24 * q^75 - 14 * q^79 + 14 * q^81 + 10 * q^83 + 6 * q^85 - 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 - 12 * q^95 - 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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