LMFDB - Embedded newform 912.2.bo.f.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			769.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.769
Dual form			912.2.bo.f.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-0.173648 - 0.300767i) q^{11} +(-1.26604 - 1.06234i) q^{13} +(3.20574 - 1.16679i) q^{15} +(1.20574 + 6.83807i) q^{17} +(2.82635 + 3.31839i) q^{19} +(0.500000 + 2.83564i) q^{21} +(6.39053 - 2.32596i) q^{23} +(5.08512 + 4.26692i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.10354 - 6.25849i) q^{29} +(0.798133 - 1.38241i) q^{31} +(-0.326352 - 0.118782i) q^{33} +(-7.52481 + 6.31407i) q^{35} -11.2121 q^{37} -1.65270 q^{39} +(-2.67365 + 2.24346i) q^{41} +(2.14543 + 0.780873i) q^{43} +(1.70574 - 2.95442i) q^{45} +(-0.971782 + 5.51125i) q^{47} +(-0.645430 - 1.11792i) q^{49} +(5.31908 + 4.46324i) q^{51} +(-1.86097 + 0.677337i) q^{53} +(-0.205737 - 1.16679i) q^{55} +(4.29813 + 0.725293i) q^{57} +(-0.0773815 - 0.438852i) q^{59} +(11.7763 - 4.28623i) q^{61} +(2.20574 + 1.85083i) q^{63} +(-2.81908 - 4.88279i) q^{65} +(0.187319 - 1.06234i) q^{67} +(3.40033 - 5.88954i) q^{69} +(-15.6211 - 5.68561i) q^{71} +(9.51367 - 7.98292i) q^{73} +6.63816 q^{75} +1.00000 q^{77} +(8.36824 - 7.02179i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(5.85844 - 10.1471i) q^{83} +(-4.11334 + 23.3279i) q^{85} +(-3.17752 - 5.50362i) q^{87} +(1.37346 + 1.15247i) q^{89} +(4.47178 - 1.62760i) q^{91} +(-0.277189 - 1.57202i) q^{93} +(5.18866 + 13.9357i) q^{95} +(0.634285 + 3.59721i) q^{97} +(-0.326352 + 0.118782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q + 9 * q^5 - 3 * q^7	$ 6 q + 9 q^{5} - 3 q^{7} - 3 q^{13} + 9 q^{15} - 3 q^{17} + 18 q^{19} + 3 q^{21} + 21 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{29} - 9 q^{31} - 3 q^{33} - 18 q^{35} - 18 q^{37} - 12 q^{39} - 15 q^{41} - 3 q^{43} + 9 q^{47} + 12 q^{49} + 15 q^{51} + 12 q^{53} + 9 q^{55} + 12 q^{57} - 27 q^{59} + 3 q^{61} + 3 q^{63} - 21 q^{67} + 6 q^{69} - 39 q^{71} + 36 q^{73} + 6 q^{75} + 6 q^{77} + 45 q^{79} + 27 q^{83} - 18 q^{85} + 6 q^{87} - 30 q^{89} + 12 q^{91} + 9 q^{93} - 6 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 9 * q^5 - 3 * q^7 - 3 * q^13 + 9 * q^15 - 3 * q^17 + 18 * q^19 + 3 * q^21 + 21 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^29 - 9 * q^31 - 3 * q^33 - 18 * q^35 - 18 * q^37 - 12 * q^39 - 15 * q^41 - 3 * q^43 + 9 * q^47 + 12 * q^49 + 15 * q^51 + 12 * q^53 + 9 * q^55 + 12 * q^57 - 27 * q^59 + 3 * q^61 + 3 * q^63 - 21 * q^67 + 6 * q^69 - 39 * q^71 + 36 * q^73 + 6 * q^75 + 6 * q^77 + 45 * q^79 + 27 * q^83 - 18 * q^85 + 6 * q^87 - 30 * q^89 + 12 * q^91 + 9 * q^93 - 6 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$		0			0
$5$	3.20574	+	1.16679i	1.43365	+	0.521806i	0.937975	−	0.346703i	$-0.112699\pi$
$5$	3.20574	+	1.16679i	1.43365	+	0.521806i	0.495674	+	0.868509i	$0.334921\pi$
$6$		0			0
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	0.454507	+	0.890743i	$0.349815\pi$
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	−0.998660	+	0.0517569i	$0.983518\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−0.173648	−	0.300767i	−0.0523569	−	0.0906848i	0.838659	−	0.544657i	$-0.183340\pi$
$11$	−0.173648	−	0.300767i	−0.0523569	−	0.0906848i	−0.891016	+	0.453972i	$0.850007\pi$
$12$		0			0
$13$	−1.26604	−	1.06234i	−0.351138	−	0.294639i	0.450109	−	0.892974i	$-0.351385\pi$
$13$	−1.26604	−	1.06234i	−0.351138	−	0.294639i	−0.801247	+	0.598334i	$0.795830\pi$
$14$		0			0
$15$	3.20574	−	1.16679i	0.827718	−	0.301265i
$16$		0			0
$17$	1.20574	+	6.83807i	0.292434	+	1.65848i	0.677452	+	0.735567i	$0.263084\pi$
$17$	1.20574	+	6.83807i	0.292434	+	1.65848i	−0.385017	+	0.922909i	$0.625805\pi$
$18$		0			0
$19$	2.82635	+	3.31839i	0.648410	+	0.761292i
$19$	2.82635	+	3.31839i	0.648410	+	0.761292i
$20$		0			0
$21$	0.500000	+	2.83564i	0.109109	+	0.618788i
$22$		0			0
$23$	6.39053	−	2.32596i	1.33252	−	0.484997i	0.425069	−	0.905161i	$-0.360250\pi$
$23$	6.39053	−	2.32596i	1.33252	−	0.484997i	0.907448	+	0.420164i	$0.138027\pi$
$24$		0			0
$25$	5.08512	+	4.26692i	1.01702	+	0.853385i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	1.10354	−	6.25849i	0.204922	−	1.16217i	−0.692640	−	0.721284i	$-0.743552\pi$
$29$	1.10354	−	6.25849i	0.204922	−	1.16217i	0.897562	−	0.440888i	$-0.145337\pi$
$30$		0			0
$31$	0.798133	−	1.38241i	0.143349	−	0.248288i	−0.785407	−	0.618980i	$-0.787546\pi$
$31$	0.798133	−	1.38241i	0.143349	−	0.248288i	0.928756	+	0.370692i	$0.120880\pi$
$32$		0			0
$33$	−0.326352	−	0.118782i	−0.0568106	−	0.0206774i
$34$		0			0
$35$	−7.52481	+	6.31407i	−1.27193	+	1.06727i
$36$		0			0
$37$	−11.2121			−1.84326			−0.921632	−	0.388066i	$-0.873143\pi$
$37$	−11.2121			−1.84326			−0.921632	+	0.388066i	$0.873143\pi$
$38$		0			0
$39$	−1.65270			−0.264644
$40$		0			0
$41$	−2.67365	+	2.24346i	−0.417554	+	0.350369i	−0.827232	−	0.561861i	$-0.810086\pi$
$41$	−2.67365	+	2.24346i	−0.417554	+	0.350369i	0.409678	+	0.912230i	$0.365641\pi$
$42$		0			0
$43$	2.14543	+	0.780873i	0.327175	+	0.119082i	0.500385	−	0.865803i	$-0.333192\pi$
$43$	2.14543	+	0.780873i	0.327175	+	0.119082i	−0.173210	+	0.984885i	$0.555414\pi$
$44$		0			0
$45$	1.70574	−	2.95442i	0.254276	−	0.440419i
$46$		0			0
$47$	−0.971782	+	5.51125i	−0.141749	+	0.803898i	0.828171	+	0.560475i	$0.189381\pi$
$47$	−0.971782	+	5.51125i	−0.141749	+	0.803898i	−0.969920	+	0.243423i	$0.921730\pi$
$48$		0			0
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$		0			0
$51$	5.31908	+	4.46324i	0.744820	+	0.624978i
$52$		0			0
$53$	−1.86097	+	0.677337i	−0.255623	+	0.0930393i	−0.466653	−	0.884440i	$-0.654540\pi$
$53$	−1.86097	+	0.677337i	−0.255623	+	0.0930393i	0.211030	+	0.977480i	$0.432318\pi$
$54$		0			0
$55$	−0.205737	−	1.16679i	−0.0277416	−	0.157330i
$56$		0			0
$57$	4.29813	+	0.725293i	0.569302	+	0.0960674i
$58$		0			0
$59$	−0.0773815	−	0.438852i	−0.0100742	−	0.0571337i	0.979356	−	0.202142i	$-0.0647902\pi$
$59$	−0.0773815	−	0.438852i	−0.0100742	−	0.0571337i	−0.989430	+	0.145008i	$0.953679\pi$
$60$		0			0
$61$	11.7763	−	4.28623i	1.50780	−	0.548795i	0.549735	−	0.835339i	$-0.314729\pi$
$61$	11.7763	−	4.28623i	1.50780	−	0.548795i	0.958067	+	0.286544i	$0.0925064\pi$
$62$		0			0
$63$	2.20574	+	1.85083i	0.277897	+	0.233183i
$64$		0			0
$65$	−2.81908	−	4.88279i	−0.349664	−	0.605635i
$66$		0			0
$67$	0.187319	−	1.06234i	0.0228846	−	0.129785i	−0.971225	−	0.238163i	$-0.923455\pi$
$67$	0.187319	−	1.06234i	0.0228846	−	0.129785i	0.994110	+	0.108378i	$0.0345657\pi$
$68$		0			0
$69$	3.40033	−	5.88954i	0.409352	−	0.709018i
$70$		0			0
$71$	−15.6211	−	5.68561i	−1.85388	−	0.674758i	−0.983095	−	0.183096i	$-0.941388\pi$
$71$	−15.6211	−	5.68561i	−1.85388	−	0.674758i	−0.870786	−	0.491662i	$-0.836390\pi$
$72$		0			0
$73$	9.51367	−	7.98292i	1.11349	−	0.934330i	0.115233	−	0.993338i	$-0.463238\pi$
$73$	9.51367	−	7.98292i	1.11349	−	0.934330i	0.998257	+	0.0590086i	$0.0187939\pi$
$74$		0			0
$75$	6.63816			0.766508
$76$		0			0
$77$	1.00000			0.113961
$78$		0			0
$79$	8.36824	−	7.02179i	0.941501	−	0.790013i	−0.0363452	−	0.999339i	$-0.511572\pi$
$79$	8.36824	−	7.02179i	0.941501	−	0.790013i	0.977846	+	0.209326i	$0.0671271\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	5.85844	−	10.1471i	0.643047	−	1.11379i	−0.341701	−	0.939809i	$-0.611003\pi$
$83$	5.85844	−	10.1471i	0.643047	−	1.11379i	0.984749	−	0.173982i	$-0.0556635\pi$
$84$		0			0
$85$	−4.11334	+	23.3279i	−0.446154	+	2.53027i
$86$		0			0
$87$	−3.17752	−	5.50362i	−0.340666	−	0.590050i
$88$		0			0
$89$	1.37346	+	1.15247i	0.145586	+	0.122161i	0.712672	−	0.701497i	$-0.247485\pi$
$89$	1.37346	+	1.15247i	0.145586	+	0.122161i	−0.567086	+	0.823659i	$0.691929\pi$
$90$		0			0
$91$	4.47178	−	1.62760i	0.468770	−	0.170618i
$92$		0			0
$93$	−0.277189	−	1.57202i	−0.0287431	−	0.163010i
$94$		0			0
$95$	5.18866	+	13.9357i	0.532346	+	1.42977i
$96$		0			0
$97$	0.634285	+	3.59721i	0.0644019	+	0.365241i	0.999928	+	0.0119843i	$0.00381481\pi$
$97$	0.634285	+	3.59721i	0.0644019	+	0.365241i	−0.935526	+	0.353257i	$0.885074\pi$
$98$		0			0
$99$	−0.326352	+	0.118782i	−0.0327996	+	0.0119381i
$100$		0			0
$101$	−7.58899	−	6.36792i	−0.755133	−	0.633632i	0.181722	−	0.983350i	$-0.441833\pi$
$101$	−7.58899	−	6.36792i	−0.755133	−	0.633632i	−0.936855	+	0.349718i	$0.886277\pi$
$102$		0			0
$103$	3.92262	+	6.79417i	0.386507	+	0.669450i	0.991977	−	0.126418i	$-0.0403481\pi$
$103$	3.92262	+	6.79417i	0.386507	+	0.669450i	−0.605470	+	0.795868i	$0.707015\pi$
$104$		0			0
$105$	−1.70574	+	9.67372i	−0.166463	+	0.944058i
$106$		0			0
$107$	−0.0136706	+	0.0236781i	−0.00132158	+	0.00228905i	−0.866685	−	0.498855i	$-0.833754\pi$
$107$	−0.0136706	+	0.0236781i	−0.00132158	+	0.00228905i	0.865364	+	0.501144i	$0.167087\pi$
$108$		0			0
$109$	10.1236	+	3.68469i	0.969666	+	0.352929i	0.777814	−	0.628494i	$-0.216329\pi$
$109$	10.1236	+	3.68469i	0.969666	+	0.352929i	0.191852	+	0.981424i	$0.438551\pi$
$110$		0			0
$111$	−8.58899	+	7.20702i	−0.815231	+	0.684060i
$112$		0			0
$113$	−11.6604			−1.09692			−0.548461	−	0.836176i	$-0.684786\pi$
$113$	−11.6604			−1.09692			−0.548461	+	0.836176i	$0.684786\pi$
$114$		0			0
$115$	23.2003			2.16344
$116$		0			0
$117$	−1.26604	+	1.06234i	−0.117046	+	0.0982131i
$118$		0			0
$119$	−18.7875	−	6.83807i	−1.72224	−	0.626845i
$120$		0			0
$121$	5.43969	−	9.42182i	0.494518	−	0.856529i
$122$		0			0
$123$	−0.606067	+	3.43718i	−0.0546472	+	0.309920i
$124$		0			0
$125$	2.79426	+	4.83981i	0.249926	+	0.432885i
$126$		0			0
$127$	−12.4192	−	10.4210i	−1.10203	−	0.924711i	−0.104467	−	0.994528i	$-0.533314\pi$
$127$	−12.4192	−	10.4210i	−1.10203	−	0.924711i	−0.997560	+	0.0698178i	$0.977758\pi$
$128$		0			0
$129$	2.14543	−	0.780873i	0.188895	−	0.0687520i
$130$		0			0
$131$	0.486329	+	2.75811i	0.0424908	+	0.240977i	0.998655	−	0.0518550i	$-0.0165134\pi$
$131$	0.486329	+	2.75811i	0.0424908	+	0.240977i	−0.956164	+	0.292832i	$0.905402\pi$
$132$		0			0
$133$	−12.3439	+	2.27038i	−1.07035	+	0.196867i
$134$		0			0
$135$	−0.592396	−	3.35965i	−0.0509854	−	0.289152i
$136$		0			0
$137$	−15.0680	+	5.48432i	−1.28735	+	0.468557i	−0.892856	−	0.450341i	$-0.851302\pi$
$137$	−15.0680	+	5.48432i	−1.28735	+	0.468557i	−0.394494	+	0.918899i	$0.629080\pi$
$138$		0			0
$139$	1.59240	+	1.33618i	0.135065	+	0.113333i	0.707818	−	0.706395i	$-0.249680\pi$
$139$	1.59240	+	1.33618i	0.135065	+	0.113333i	−0.572752	+	0.819728i	$0.694124\pi$
$140$		0			0
$141$	2.79813	+	4.84651i	0.235645	+	0.408150i
$142$		0			0
$143$	−0.0996702	+	0.565258i	−0.00833484	+	0.0472692i
$144$		0			0
$145$	10.8400	−	18.7755i	0.900215	−	1.55922i
$146$		0			0
$147$	−1.21301	−	0.441500i	−0.100047	−	0.0364143i
$148$		0			0
$149$	−1.27719	+	1.07169i	−0.104631	+	0.0877962i	−0.693603	−	0.720358i	$-0.743978\pi$
$149$	−1.27719	+	1.07169i	−0.104631	+	0.0877962i	0.588971	+	0.808154i	$0.299533\pi$
$150$		0			0
$151$	−20.0523			−1.63183			−0.815917	−	0.578169i	$-0.803768\pi$
$151$	−20.0523			−1.63183			−0.815917	+	0.578169i	$0.803768\pi$
$152$		0			0
$153$	6.94356			0.561354
$154$		0			0
$155$	4.17159	−	3.50038i	0.335070	−	0.281157i
$156$		0			0
$157$	3.85117	+	1.40171i	0.307357	+	0.111869i	0.491094	−	0.871107i	$-0.336597\pi$
$157$	3.85117	+	1.40171i	0.307357	+	0.111869i	−0.183737	+	0.982975i	$0.558820\pi$
$158$		0			0
$159$	−0.990200	+	1.71508i	−0.0785280	+	0.136014i
$160$		0			0
$161$	−3.40033	+	19.2842i	−0.267984	+	1.51981i
$162$		0			0
$163$	−4.06758	−	7.04526i	−0.318598	−	0.551827i	0.661598	−	0.749859i	$-0.269879\pi$
$163$	−4.06758	−	7.04526i	−0.318598	−	0.551827i	−0.980196	+	0.198031i	$0.936545\pi$
$164$		0			0
$165$	−0.907604	−	0.761570i	−0.0706569	−	0.0592881i
$166$		0			0
$167$	−12.5890	+	4.58202i	−0.974166	+	0.354567i	−0.779569	−	0.626316i	$-0.784562\pi$
$167$	−12.5890	+	4.58202i	−0.974166	+	0.354567i	−0.194596	+	0.980883i	$0.562340\pi$
$168$		0			0
$169$	−1.78312	−	10.1126i	−0.137163	−	0.777890i
$170$		0			0
$171$	3.75877	−	2.20718i	0.287440	−	0.168787i
$172$		0			0
$173$	−0.177519	−	1.00676i	−0.0134965	−	0.0765424i	0.977316	−	0.211788i	$-0.0679287\pi$
$173$	−0.177519	−	1.00676i	−0.0134965	−	0.0765424i	−0.990812	+	0.135246i	$0.956818\pi$
$174$		0			0
$175$	−17.9611	+	6.53731i	−1.35773	+	0.494174i
$176$		0			0
$177$	−0.341367	−	0.286441i	−0.0256587	−	0.0215302i
$178$		0			0
$179$	1.01754	+	1.76243i	0.0760546	+	0.131730i	0.901544	−	0.432687i	$-0.142434\pi$
$179$	1.01754	+	1.76243i	0.0760546	+	0.131730i	−0.825490	+	0.564417i	$0.809101\pi$
$180$		0			0
$181$	3.87299	−	21.9648i	0.287877	−	1.63263i	−0.406947	−	0.913452i	$-0.633407\pi$
$181$	3.87299	−	21.9648i	0.287877	−	1.63263i	0.694824	−	0.719180i	$-0.255482\pi$
$182$		0			0
$183$	6.26604	−	10.8531i	0.463199	−	0.802285i
$184$		0			0
$185$	−35.9432	−	13.0822i	−2.64259	−	0.961825i
$186$		0			0
$187$	1.84730	−	1.55007i	0.135088	−	0.113352i
$188$		0			0
$189$	2.87939			0.209444
$190$		0			0
$191$	−10.7861			−0.780456			−0.390228	−	0.920718i	$-0.627604\pi$
$191$	−10.7861			−0.780456			−0.390228	+	0.920718i	$0.627604\pi$
$192$		0			0
$193$	−2.19459	+	1.84148i	−0.157970	+	0.132553i	−0.718347	−	0.695685i	$-0.755101\pi$
$193$	−2.19459	+	1.84148i	−0.157970	+	0.132553i	0.560377	+	0.828238i	$0.310656\pi$
$194$		0			0
$195$	−5.29813	−	1.92836i	−0.379407	−	0.138093i
$196$		0			0
$197$	4.16772	−	7.21870i	0.296938	−	0.514311i	−0.678496	−	0.734604i	$-0.737368\pi$
$197$	4.16772	−	7.21870i	0.296938	−	0.514311i	0.975434	+	0.220293i	$0.0707013\pi$
$198$		0			0
$199$	0.526874	−	2.98805i	0.0373491	−	0.211817i	−0.960422	−	0.278550i	$-0.910146\pi$
$199$	0.526874	−	2.98805i	0.0373491	−	0.211817i	0.997771	+	0.0667324i	$0.0212574\pi$
$200$		0			0
$201$	−0.539363	−	0.934204i	−0.0380437	−	0.0658937i
$202$		0			0
$203$	14.0175	+	11.7621i	0.983839	+	0.825539i
$204$		0			0
$205$	−11.1887	+	4.07234i	−0.781450	+	0.284425i
$206$		0			0
$207$	−1.18092	−	6.69734i	−0.0820798	−	0.465497i
$208$		0			0
$209$	0.507274	−	1.42631i	0.0350889	−	0.0986598i
$210$		0			0
$211$	2.88919	+	16.3854i	0.198900	+	1.12802i	0.906755	+	0.421659i	$0.138552\pi$
$211$	2.88919	+	16.3854i	0.198900	+	1.12802i	−0.707855	+	0.706358i	$0.750337\pi$
$212$		0			0
$213$	−15.6211	+	5.68561i	−1.07034	+	0.389571i
$214$		0			0
$215$	5.96657	+	5.00654i	0.406916	+	0.341443i
$216$		0			0
$217$	2.29813	+	3.98048i	0.156007	+	0.270213i
$218$		0			0
$219$	2.15657	−	12.2305i	0.145728	−	0.826463i
$220$		0			0
$221$	5.73783	−	9.93821i	0.385968	−	0.668516i
$222$		0			0
$223$	−7.67752	−	2.79439i	−0.514125	−	0.187126i	0.0719114	−	0.997411i	$-0.477090\pi$
$223$	−7.67752	−	2.79439i	−0.514125	−	0.187126i	−0.586036	+	0.810285i	$0.699312\pi$
$224$		0			0
$225$	5.08512	−	4.26692i	0.339008	−	0.284462i
$226$		0			0
$227$	−1.80066			−0.119514			−0.0597570	−	0.998213i	$-0.519033\pi$
$227$	−1.80066			−0.119514			−0.0597570	+	0.998213i	$0.519033\pi$
$228$		0			0
$229$	−18.7392			−1.23832			−0.619160	−	0.785265i	$-0.712527\pi$
$229$	−18.7392			−1.23832			−0.619160	+	0.785265i	$0.712527\pi$
$230$		0			0
$231$	0.766044	−	0.642788i	0.0504020	−	0.0422923i
$232$		0			0
$233$	3.85117	+	1.40171i	0.252298	+	0.0918291i	0.465073	−	0.885272i	$-0.346028\pi$
$233$	3.85117	+	1.40171i	0.252298	+	0.0918291i	−0.212775	+	0.977101i	$0.568250\pi$
$234$		0			0
$235$	−9.54576	+	16.5337i	−0.622697	+	1.07854i
$236$		0			0
$237$	1.89693	−	10.7580i	0.123219	−	0.698807i
$238$		0			0
$239$	−14.1138	−	24.4458i	−0.912946	−	1.58127i	−0.809881	−	0.586595i	$-0.800468\pi$
$239$	−14.1138	−	24.4458i	−0.912946	−	1.58127i	−0.103066	−	0.994675i	$-0.532865\pi$
$240$		0			0
$241$	5.02687	+	4.21805i	0.323809	+	0.271708i	0.790172	−	0.612885i	$-0.209991\pi$
$241$	5.02687	+	4.21805i	0.323809	+	0.271708i	−0.466362	+	0.884594i	$0.654436\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$		0			0
$245$	−0.764700	−	4.33683i	−0.0488549	−	0.277070i
$246$		0			0
$247$	−0.0530334	−	7.20377i	−0.00337444	−	0.458365i
$248$		0			0
$249$	−2.03462	−	11.5389i	−0.128938	−	0.731247i
$250$		0			0
$251$	8.35756	−	3.04190i	0.527525	−	0.192003i	−0.0645080	−	0.997917i	$-0.520548\pi$
$251$	8.35756	−	3.04190i	0.527525	−	0.192003i	0.592033	+	0.805914i	$0.298326\pi$
$252$		0			0
$253$	−1.80928	−	1.51816i	−0.113748	−	0.0954462i
$254$		0			0
$255$	11.8439	+	20.5142i	0.741693	+	1.28465i
$256$		0			0
$257$	−2.33837	+	13.2616i	−0.145864	+	0.827234i	0.820806	+	0.571207i	$0.193525\pi$
$257$	−2.33837	+	13.2616i	−0.145864	+	0.827234i	−0.966670	+	0.256027i	$0.917586\pi$
$258$		0			0
$259$	16.1420	−	27.9588i	1.00302	−	1.73728i
$260$		0			0
$261$	−5.97178	−	2.17355i	−0.369644	−	0.134539i
$262$		0			0
$263$	12.8327	−	10.7680i	0.791301	−	0.663981i	−0.154766	−	0.987951i	$-0.549462\pi$
$263$	12.8327	−	10.7680i	0.791301	−	0.663981i	0.946067	+	0.323971i	$0.105018\pi$
$264$		0			0
$265$	−6.75608			−0.415023
$266$		0			0
$267$	1.79292			0.109725
$268$		0			0
$269$	2.74969	−	2.30726i	0.167651	−	0.140676i	−0.555102	−	0.831782i	$-0.687321\pi$
$269$	2.74969	−	2.30726i	0.167651	−	0.140676i	0.722753	+	0.691106i	$0.242876\pi$
$270$		0			0
$271$	22.5141	+	8.19448i	1.36764	+	0.497779i	0.918407	−	0.395637i	$-0.129476\pi$
$271$	22.5141	+	8.19448i	1.36764	+	0.497779i	0.449230	+	0.893416i	$0.351699\pi$
$272$		0			0
$273$	2.37939	−	4.12122i	0.144007	−	0.249427i
$274$		0			0
$275$	0.400330	−	2.27038i	0.0241408	−	0.136909i
$276$		0			0
$277$	9.36097	+	16.2137i	0.562446	+	0.974185i	0.997282	+	0.0736755i	$0.0234729\pi$
$277$	9.36097	+	16.2137i	0.562446	+	0.974185i	−0.434836	+	0.900510i	$0.643194\pi$
$278$		0			0
$279$	−1.22281	−	1.02606i	−0.0732078	−	0.0614286i
$280$		0			0
$281$	9.99660	−	3.63846i	0.596347	−	0.217053i	−0.0261718	−	0.999657i	$-0.508332\pi$
$281$	9.99660	−	3.63846i	0.596347	−	0.217053i	0.622519	+	0.782605i	$0.286109\pi$
$282$		0			0
$283$	2.43330	+	13.7999i	0.144644	+	0.820319i	0.967652	+	0.252289i	$0.0811833\pi$
$283$	2.43330	+	13.7999i	0.144644	+	0.820319i	−0.823008	+	0.568030i	$0.807706\pi$
$284$		0			0
$285$	12.9324	+	7.34013i	0.766050	+	0.434792i
$286$		0			0
$287$	−1.74510	−	9.89695i	−0.103010	−	0.584199i
$288$		0			0
$289$	−29.3307	+	10.6755i	−1.72533	+	0.627970i
$290$		0			0
$291$	2.79813	+	2.34791i	0.164029	+	0.137637i
$292$		0			0
$293$	5.76011	+	9.97681i	0.336509	+	0.582852i	0.983774	−	0.179414i	$-0.0574202\pi$
$293$	5.76011	+	9.97681i	0.336509	+	0.582852i	−0.647264	+	0.762266i	$0.724087\pi$
$294$		0			0
$295$	0.263985	−	1.49713i	0.0153698	−	0.0871665i
$296$		0			0
$297$	−0.173648	+	0.300767i	−0.0100761	+	0.0174523i
$298$		0			0
$299$	−10.5617	−	3.84413i	−0.610796	−	0.222312i
$300$		0			0
$301$	−5.03596	+	4.22567i	−0.290268	+	0.243564i
$302$		0			0
$303$	−9.90673			−0.569127
$304$		0			0
$305$	42.7529			2.44802
$306$		0			0
$307$	−3.29220	+	2.76249i	−0.187896	+	0.157663i	−0.731883	−	0.681430i	$-0.761358\pi$
$307$	−3.29220	+	2.76249i	−0.187896	+	0.157663i	0.543987	+	0.839093i	$0.316914\pi$
$308$		0			0
$309$	7.37211	+	2.68323i	0.419385	+	0.152644i
$310$		0			0
$311$	−11.4966	+	19.9127i	−0.651912	+	1.12915i	0.330746	+	0.943720i	$0.392700\pi$
$311$	−11.4966	+	19.9127i	−0.651912	+	1.12915i	−0.982658	+	0.185425i	$0.940634\pi$
$312$		0			0
$313$	−1.59926	+	9.06985i	−0.0903955	+	0.512658i	0.905666	+	0.423992i	$0.139372\pi$
$313$	−1.59926	+	9.06985i	−0.0903955	+	0.512658i	−0.996061	+	0.0886663i	$0.971740\pi$
$314$		0			0
$315$	4.91147	+	8.50692i	0.276730	+	0.479311i
$316$		0			0
$317$	2.57011	+	2.15658i	0.144352	+	0.121125i	0.712104	−	0.702074i	$-0.247742\pi$
$317$	2.57011	+	2.15658i	0.144352	+	0.121125i	−0.567752	+	0.823199i	$0.692187\pi$
$318$		0			0
$319$	−2.07398	+	0.754866i	−0.116120	+	0.0422644i
$320$		0			0
$321$	0.00474774	+	0.0269258i	0.000264993	+	0.00150285i
$322$		0			0
$323$	−19.2836	+	23.3279i	−1.07297	+	1.29800i
$324$		0			0
$325$	−1.90508	−	10.8042i	−0.105675	−	0.599311i
$326$		0			0
$327$	10.1236	−	3.68469i	0.559837	−	0.203764i
$328$		0			0
$329$	−12.3439	−	10.3578i	−0.680541	−	0.571042i
$330$		0			0
$331$	−11.0371	−	19.1169i	−0.606656	−	1.05076i	−0.991787	−	0.127897i	$-0.959177\pi$
$331$	−11.0371	−	19.1169i	−0.606656	−	1.05076i	0.385131	−	0.922862i	$-0.374156\pi$
$332$		0			0
$333$	−1.94697	+	11.0418i	−0.106693	+	0.605087i
$334$		0			0
$335$	1.84002	−	3.18701i	0.100531	−	0.174125i
$336$		0			0
$337$	12.3255	+	4.48611i	0.671411	+	0.244374i	0.655155	−	0.755494i	$-0.272603\pi$
$337$	12.3255	+	4.48611i	0.671411	+	0.244374i	0.0162559	+	0.999868i	$0.494825\pi$
$338$		0			0
$339$	−8.93242	+	7.49519i	−0.485142	+	0.407083i
$340$		0			0
$341$	−0.554378			−0.0300212
$342$		0			0
$343$	−16.4388			−0.887613
$344$		0			0
$345$	17.7724	−	14.9128i	0.956836	−	0.802881i
$346$		0			0
$347$	8.23055	+	2.99568i	0.441839	+	0.160816i	0.553354	−	0.832947i	$-0.313348\pi$
$347$	8.23055	+	2.99568i	0.441839	+	0.160816i	−0.111514	+	0.993763i	$0.535570\pi$
$348$		0			0
$349$	−1.63176	+	2.82629i	−0.0873461	+	0.151288i	−0.906389	−	0.422445i	$-0.861172\pi$
$349$	−1.63176	+	2.82629i	−0.0873461	+	0.151288i	0.819042	+	0.573733i	$0.194505\pi$
$350$		0			0
$351$	−0.286989	+	1.62760i	−0.0153183	+	0.0868746i
$352$		0			0
$353$	−14.5419	−	25.1873i	−0.773987	−	1.34058i	−0.935362	−	0.353691i	$-0.884926\pi$
$353$	−14.5419	−	25.1873i	−0.773987	−	1.34058i	0.161376	−	0.986893i	$-0.448407\pi$
$354$		0			0
$355$	−43.4432	−	36.4531i	−2.30572	−	1.93473i
$356$		0			0
$357$	−18.7875	+	6.83807i	−0.994338	+	0.361909i
$358$		0			0
$359$	−1.14796	−	6.51038i	−0.0605868	−	0.343605i	−1.00000		0.000817017i	$-0.999740\pi$
$359$	−1.14796	−	6.51038i	−0.0605868	−	0.343605i	0.939413	−	0.342788i	$-0.111371\pi$
$360$		0			0
$361$	−3.02347	+	18.7579i	−0.159130	+	0.987258i
$362$		0			0
$363$	−1.88919	−	10.7141i	−0.0991565	−	0.562345i
$364$		0			0
$365$	39.8127	−	14.4907i	2.08389	−	0.758475i
$366$		0			0
$367$	4.43969	+	3.72534i	0.231750	+	0.194461i	0.751266	−	0.659999i	$-0.229443\pi$
$367$	4.43969	+	3.72534i	0.231750	+	0.194461i	−0.519516	+	0.854461i	$0.673888\pi$
$368$		0			0
$369$	1.74510	+	3.02260i	0.0908463	+	0.157350i
$370$		0			0
$371$	0.990200	−	5.61570i	0.0514086	−	0.291553i
$372$		0			0
$373$	12.9449	−	22.4212i	0.670262	−	1.16093i	−0.307568	−	0.951526i	$-0.599515\pi$
$373$	12.9449	−	22.4212i	0.670262	−	1.16093i	0.977830	−	0.209401i	$-0.0671516\pi$
$374$		0			0
$375$	5.25150	+	1.91139i	0.271186	+	0.0987037i
$376$		0			0
$377$	−8.04576	+	6.75119i	−0.414378	+	0.347704i
$378$		0			0
$379$	19.1557			0.983962			0.491981	−	0.870606i	$-0.336273\pi$
$379$	19.1557			0.983962			0.491981	+	0.870606i	$0.336273\pi$
$380$		0			0
$381$	−16.2121			−0.830573
$382$		0			0
$383$	7.42649	−	6.23156i	0.379476	−	0.318418i	−0.433021	−	0.901384i	$-0.642552\pi$
$383$	7.42649	−	6.23156i	0.379476	−	0.318418i	0.812497	+	0.582966i	$0.198108\pi$
$384$		0			0
$385$	3.20574	+	1.16679i	0.163379	+	0.0594653i
$386$		0			0
$387$	1.14156	−	1.97724i	0.0580287	−	0.100509i
$388$		0			0
$389$	−0.142026	+	0.805470i	−0.00720101	+	0.0408390i	−0.988197	−	0.153191i	$-0.951045\pi$
$389$	−0.142026	+	0.805470i	−0.00720101	+	0.0408390i	0.980996	+	0.194030i	$0.0621560\pi$
$390$		0			0
$391$	23.6104	+	40.8944i	1.19403	+	2.06812i
$392$		0			0
$393$	2.14543	+	1.80023i	0.108223	+	0.0908096i
$394$		0			0
$395$	35.0194	−	12.7460i	1.76201	−	0.641321i
$396$		0			0
$397$	−0.642026	−	3.64111i	−0.0322224	−	0.182742i	0.964449	−	0.264270i	$-0.0851311\pi$
$397$	−0.642026	−	3.64111i	−0.0322224	−	0.182742i	−0.996671	+	0.0815281i	$0.974020\pi$
$398$		0			0
$399$	−7.99660	+	9.67372i	−0.400331	+	0.484292i
$400$		0			0
$401$	−3.77513	−	21.4098i	−0.188521	−	1.06916i	−0.921347	−	0.388740i	$-0.872910\pi$
$401$	−3.77513	−	21.4098i	−0.188521	−	1.06916i	0.732827	−	0.680416i	$-0.238201\pi$
$402$		0			0
$403$	−2.47906	+	0.902302i	−0.123491	+	0.0449469i
$404$		0			0
$405$	−2.61334	−	2.19285i	−0.129858	−	0.108964i
$406$		0			0
$407$	1.94697	+	3.37225i	0.0965076	+	0.167156i
$408$		0			0
$409$	−0.704088	+	3.99308i	−0.0348149	+	0.197445i	−0.997254	−	0.0740509i	$-0.976407\pi$
$409$	−0.704088	+	3.99308i	−0.0348149	+	0.197445i	0.962440	+	0.271496i	$0.0875184\pi$
$410$		0			0
$411$	−8.01754	+	13.8868i	−0.395476	+	0.684985i
$412$		0			0
$413$	1.20574	+	0.438852i	0.0593304	+	0.0215945i
$414$		0			0
$415$	30.6202	−	25.6934i	1.50309	−	1.26124i
$416$		0			0
$417$	2.07873			0.101796
$418$		0			0
$419$	−23.4989			−1.14800			−0.573998	−	0.818857i	$-0.694608\pi$
$419$	−23.4989			−1.14800			−0.573998	+	0.818857i	$0.694608\pi$
$420$		0			0
$421$	−17.6748	+	14.8309i	−0.861419	+	0.722816i	−0.962273	−	0.272085i	$-0.912287\pi$
$421$	−17.6748	+	14.8309i	−0.861419	+	0.722816i	0.100855	+	0.994901i	$0.467842\pi$
$422$		0			0
$423$	5.25877	+	1.91404i	0.255690	+	0.0930636i
$424$		0			0
$425$	−23.0462	+	39.9172i	−1.11791	+	1.93627i
$426$		0			0
$427$	−6.26604	+	35.5365i	−0.303235	+	1.71973i
$428$		0			0
$429$	0.286989	+	0.497079i	0.0138560	+	0.0239992i
$430$		0			0
$431$	2.69253	+	2.25930i	0.129695	+	0.108827i	0.705328	−	0.708881i	$-0.250800\pi$
$431$	2.69253	+	2.25930i	0.129695	+	0.108827i	−0.575633	+	0.817708i	$0.695244\pi$
$432$		0			0
$433$	32.0574	−	11.6679i	1.54058	−	0.560725i	0.574395	−	0.818578i	$-0.305237\pi$
$433$	32.0574	−	11.6679i	1.54058	−	0.560725i	0.966184	+	0.257853i	$0.0830152\pi$
$434$		0			0
$435$	−3.76470	−	21.3507i	−0.180504	−	1.02369i
$436$		0			0
$437$	25.7803	+	14.6323i	1.23324	+	0.699958i
$438$		0			0
$439$	−1.68463	−	9.55401i	−0.0804030	−	0.455988i	−0.998254	−	0.0590636i	$-0.981189\pi$
$439$	−1.68463	−	9.55401i	−0.0804030	−	0.455988i	0.917851	−	0.396925i	$-0.129923\pi$
$440$		0			0
$441$	−1.21301	+	0.441500i	−0.0577624	+	0.0210238i
$442$		0			0
$443$	−11.6302	−	9.75887i	−0.552566	−	0.463658i	0.323243	−	0.946316i	$-0.395227\pi$
$443$	−11.6302	−	9.75887i	−0.552566	−	0.463658i	−0.875809	+	0.482658i	$0.839671\pi$
$444$		0			0
$445$	3.05825	+	5.29704i	0.144975	+	0.251104i
$446$		0			0
$447$	−0.289515	+	1.64192i	−0.0136936	+	0.0776603i
$448$		0			0
$449$	−17.4192	+	30.1710i	−0.822064	+	1.42386i	0.0820794	+	0.996626i	$0.473844\pi$
$449$	−17.4192	+	30.1710i	−0.822064	+	1.42386i	−0.904143	+	0.427230i	$0.859489\pi$
$450$		0			0
$451$	1.13903	+	0.414574i	0.0536350	+	0.0195215i
$452$		0			0
$453$	−15.3610	+	12.8894i	−0.721721	+	0.605596i
$454$		0			0
$455$	16.2344			0.761081
$456$		0			0
$457$	−31.8749			−1.49105			−0.745523	−	0.666479i	$-0.767800\pi$
$457$	−31.8749			−1.49105			−0.745523	+	0.666479i	$0.767800\pi$
$458$		0			0
$459$	5.31908	−	4.46324i	0.248273	−	0.208326i
$460$		0			0
$461$	10.0449	+	3.65604i	0.467837	+	0.170279i	0.565172	−	0.824973i	$-0.308810\pi$
$461$	10.0449	+	3.65604i	0.467837	+	0.170279i	−0.0973354	+	0.995252i	$0.531032\pi$
$462$		0			0
$463$	7.65910	−	13.2660i	0.355949	−	0.616521i	−0.631331	−	0.775513i	$-0.717491\pi$
$463$	7.65910	−	13.2660i	0.355949	−	0.616521i	0.987280	+	0.158992i	$0.0508245\pi$
$464$		0			0
$465$	0.945622	−	5.36289i	0.0438522	−	0.248698i
$466$		0			0
$467$	14.2562	+	24.6925i	0.659700	+	1.14263i	0.980693	+	0.195553i	$0.0626501\pi$
$467$	14.2562	+	24.6925i	0.659700	+	1.14263i	−0.320993	+	0.947082i	$0.604017\pi$
$468$		0			0
$469$	2.37939	+	1.99654i	0.109870	+	0.0921917i
$470$		0			0
$471$	3.85117	−	1.40171i	0.177452	−	0.0645874i
$472$		0			0
$473$	−0.137689	−	0.780873i	−0.00633094	−	0.0359046i
$474$		0			0
$475$	0.213011	+	28.9343i	0.00977362	+	1.32760i
$476$		0			0
$477$	0.343893	+	1.95031i	0.0157458	+	0.0892987i
$478$		0			0
$479$	7.56583	−	2.75374i	0.345691	−	0.125821i	−0.163339	−	0.986570i	$-0.552226\pi$
$479$	7.56583	−	2.75374i	0.345691	−	0.125821i	0.509030	+	0.860749i	$0.330004\pi$
$480$		0			0
$481$	14.1951	+	11.9111i	0.647239	+	0.543098i
$482$		0			0
$483$	9.79086	+	16.9583i	0.445500	+	0.771628i
$484$		0			0
$485$	−2.16385	+	12.2718i	−0.0982553	+	0.557233i
$486$		0			0
$487$	3.05778	−	5.29623i	0.138561	−	0.239995i	−0.788391	−	0.615175i	$-0.789086\pi$
$487$	3.05778	−	5.29623i	0.138561	−	0.239995i	0.926952	+	0.375179i	$0.122419\pi$
$488$		0			0
$489$	−7.64455	−	2.78239i	−0.345699	−	0.125824i
$490$		0			0
$491$	17.3778	−	14.5817i	0.784249	−	0.658063i	−0.160066	−	0.987106i	$-0.551171\pi$
$491$	17.3778	−	14.5817i	0.784249	−	0.658063i	0.944315	+	0.329043i	$0.106726\pi$
$492$		0			0
$493$	44.1266			1.98736
$494$		0			0
$495$	−1.18479			−0.0532525
$496$		0			0
$497$	36.6673	−	30.7675i	1.64475	−	1.38011i
$498$		0			0
$499$	23.3567	+	8.50114i	1.04559	+	0.380563i	0.806996	−	0.590557i	$-0.201092\pi$
$499$	23.3567	+	8.50114i	1.04559	+	0.380563i	0.238593	+	0.971120i	$0.423314\pi$
$500$		0			0
$501$	−6.69846	+	11.6021i	−0.299265	+	0.518343i
$502$		0			0
$503$	−4.34524	+	24.6431i	−0.193745	+	1.09878i	0.720451	+	0.693506i	$0.243935\pi$
$503$	−4.34524	+	24.6431i	−0.193745	+	1.09878i	−0.914195	+	0.405274i	$0.867176\pi$
$504$		0			0
$505$	−16.8983	−	29.2687i	−0.751963	−	1.30244i
$506$		0			0
$507$	−7.86618	−	6.60051i	−0.349349	−	0.293139i
$508$		0			0
$509$	−0.845075	+	0.307582i	−0.0374573	+	0.0136333i	−0.360681	−	0.932689i	$-0.617456\pi$
$509$	−0.845075	+	0.307582i	−0.0374573	+	0.0136333i	0.323224	+	0.946323i	$0.395233\pi$
$510$		0			0
$511$	6.20961	+	35.2164i	0.274697	+	1.55788i
$512$		0			0
$513$	1.46064	−	4.10689i	0.0644887	−	0.181324i
$514$		0			0
$515$	4.64749	+	26.3572i	0.204793	+	1.16144i
$516$		0			0
$517$	1.82635	−	0.664738i	0.0803229	−	0.0292351i
$518$		0			0
$519$	−0.783119	−	0.657115i	−0.0343751	−	0.0288441i
$520$		0			0
$521$	3.31773	+	5.74648i	0.145353	+	0.251758i	0.929504	−	0.368811i	$-0.120235\pi$
$521$	3.31773	+	5.74648i	0.145353	+	0.251758i	−0.784152	+	0.620569i	$0.786902\pi$
$522$		0			0
$523$	−6.59034	+	37.3757i	−0.288175	+	1.63432i	0.405542	+	0.914076i	$0.367083\pi$
$523$	−6.59034	+	37.3757i	−0.288175	+	1.63432i	−0.693718	+	0.720247i	$0.744028\pi$
$524$		0			0
$525$	−9.55690	+	16.5530i	−0.417097	+	0.722434i
$526$		0			0
$527$	10.4153	+	3.79088i	0.453700	+	0.165133i
$528$		0			0
$529$	17.8097	−	14.9442i	0.774337	−	0.649746i
$530$		0			0
$531$	−0.445622			−0.0193384
$532$		0			0
$533$	5.76827			0.249851
$534$		0			0
$535$	−0.0714517	+	0.0599551i	−0.00308913	+	0.00259209i
$536$		0			0
$537$	1.91235	+	0.696039i	0.0825241	+	0.0300363i
$538$		0			0
$539$	−0.224155	+	0.388249i	−0.00965506	+	0.0167230i
$540$		0			0
$541$	2.62742	−	14.9009i	0.112962	−	0.640638i	−0.874778	−	0.484525i	$-0.838993\pi$
$541$	2.62742	−	14.9009i	0.112962	−	0.640638i	0.987739	−	0.156113i	$-0.0498963\pi$
$542$		0			0
$543$	−11.1518	−	19.3155i	−0.478571	−	0.828909i
$544$		0			0
$545$	28.1544	+	23.6243i	1.20600	+	1.01195i
$546$		0			0
$547$	30.6215	−	11.1453i	1.30928	−	0.476540i	0.409274	−	0.912412i	$-0.365782\pi$
$547$	30.6215	−	11.1453i	1.30928	−	0.476540i	0.900009	+	0.435872i	$0.143560\pi$
$548$		0			0
$549$	−2.17617	−	12.3417i	−0.0928769	−	0.526731i
$550$		0			0
$551$	23.8871	−	14.0267i	1.01763	−	0.597558i
$552$		0			0
$553$	5.46198	+	30.9764i	0.232267	+	1.31725i
$554$		0			0
$555$	−35.9432	+	13.0822i	−1.52570	+	0.555310i
$556$		0			0
$557$	−15.2777	−	12.8195i	−0.647335	−	0.543179i	0.258926	−	0.965897i	$-0.416631\pi$
$557$	−15.2777	−	12.8195i	−0.647335	−	0.543179i	−0.906261	+	0.422719i	$0.861076\pi$
$558$		0			0
$559$	−1.88666	−	3.26779i	−0.0797972	−	0.138213i
$560$		0			0
$561$	0.418748	−	2.37484i	0.0176796	−	0.100266i
$562$		0			0
$563$	1.98411	−	3.43658i	0.0836202	−	0.144834i	−0.821182	−	0.570666i	$-0.806685\pi$
$563$	1.98411	−	3.43658i	0.0836202	−	0.144834i	0.904802	+	0.425832i	$0.140018\pi$
$564$		0			0
$565$	−37.3803	−	13.6053i	−1.57260	−	0.572380i
$566$		0			0
$567$	2.20574	−	1.85083i	0.0926322	−	0.0777277i
$568$		0			0
$569$	14.8135			0.621012			0.310506	−	0.950571i	$-0.399501\pi$
$569$	14.8135			0.621012			0.310506	+	0.950571i	$0.399501\pi$
$570$		0			0
$571$	−21.0615			−0.881396			−0.440698	−	0.897655i	$-0.645269\pi$
$571$	−21.0615			−0.881396			−0.440698	+	0.897655i	$0.645269\pi$
$572$		0			0
$573$	−8.26264	+	6.93318i	−0.345177	+	0.289638i
$574$		0			0
$575$	42.4213	+	15.4401i	1.76909	+	0.643897i
$576$		0			0
$577$	22.1211	−	38.3148i	0.920913	−	1.59507i	0.122907	−	0.992418i	$-0.460778\pi$
$577$	22.1211	−	38.3148i	0.920913	−	1.59507i	0.798006	−	0.602649i	$-0.205888\pi$
$578$		0			0
$579$	−0.497474	+	2.82131i	−0.0206743	+	0.117250i
$580$		0			0
$581$	16.8687	+	29.2175i	0.699832	+	1.21214i
$582$		0			0
$583$	0.526874	+	0.442100i	0.0218209	+	0.0183099i
$584$		0			0
$585$	−5.29813	+	1.92836i	−0.219051	+	0.0797280i
$586$		0			0
$587$	−1.73689	−	9.85041i	−0.0716892	−	0.406570i	−0.999443	−	0.0333765i	$-0.989374\pi$
$587$	−1.73689	−	9.85041i	−0.0716892	−	0.406570i	0.927754	−	0.373193i	$-0.121737\pi$
$588$		0			0
$589$	6.84318	−	1.25865i	0.281968	−	0.0518617i
$590$		0			0
$591$	−1.44743	−	8.20880i	−0.0595395	−	0.337665i
$592$		0			0
$593$	10.7981	−	3.93020i	0.443426	−	0.161394i	−0.110651	−	0.993859i	$-0.535294\pi$
$593$	10.7981	−	3.93020i	0.443426	−	0.161394i	0.554077	+	0.832465i	$0.313071\pi$
$594$		0			0
$595$	−52.2490	−	43.8421i	−2.14200	−	1.79735i
$596$		0			0
$597$	−1.51707	−	2.62765i	−0.0620897	−	0.107543i
$598$		0			0
$599$	−1.11422	+	6.31905i	−0.0455257	+	0.258189i	−0.999073	−	0.0430552i	$-0.986291\pi$
$599$	−1.11422	+	6.31905i	−0.0455257	+	0.258189i	0.953547	+	0.301244i	$0.0974020\pi$
$600$		0			0
$601$	−15.7579	+	27.2935i	−0.642778	+	1.11332i	0.342032	+	0.939688i	$0.388885\pi$
$601$	−15.7579	+	27.2935i	−0.642778	+	1.11332i	−0.984810	+	0.173636i	$0.944448\pi$
$602$		0			0
$603$	−1.01367	−	0.368946i	−0.0412799	−	0.0150246i
$604$		0			0
$605$	28.4315	−	23.8569i	1.15591	−	0.969921i
$606$		0			0
$607$	−0.748341			−0.0303742			−0.0151871	−	0.999885i	$-0.504834\pi$
$607$	−0.748341			−0.0303742			−0.0151871	+	0.999885i	$0.504834\pi$
$608$		0			0
$609$	18.2986			0.741497
$610$		0			0
$611$	7.08512	−	5.94512i	0.286633	−	0.240514i
$612$		0			0
$613$	28.8371	+	10.4958i	1.16472	+	0.423923i	0.850781	−	0.525520i	$-0.176129\pi$
$613$	28.8371	+	10.4958i	1.16472	+	0.423923i	0.313938	+	0.949443i	$0.398352\pi$
$614$		0			0
$615$	−5.95336	+	10.3115i	−0.240063	+	0.415801i
$616$		0			0
$617$	−4.73917	+	26.8772i	−0.190792	+	1.08203i	0.727493	+	0.686115i	$0.240685\pi$
$617$	−4.73917	+	26.8772i	−0.190792	+	1.08203i	−0.918285	+	0.395919i	$0.870426\pi$
$618$		0			0
$619$	−6.61856	−	11.4637i	−0.266022	−	0.460764i	0.701809	−	0.712365i	$-0.252376\pi$
$619$	−6.61856	−	11.4637i	−0.266022	−	0.460764i	−0.967831	+	0.251601i	$0.919043\pi$
$620$		0			0
$621$	−5.20961	−	4.37138i	−0.209054	−	0.175417i
$622$		0			0
$623$	−4.85117	+	1.76568i	−0.194358	+	0.0707405i
$624$		0			0
$625$	−2.45290	−	13.9111i	−0.0981159	−	0.556443i
$626$		0			0
$627$	−0.528218	−	1.41868i	−0.0210950	−	0.0566568i
$628$		0			0
$629$	−13.5189	−	76.6694i	−0.539033	−	3.05701i
$630$		0			0
$631$	−11.5013	+	4.18615i	−0.457861	+	0.166648i	−0.560646	−	0.828056i	$-0.689447\pi$
$631$	−11.5013	+	4.18615i	−0.457861	+	0.166648i	0.102784	+	0.994704i	$0.467225\pi$
$632$		0			0
$633$	12.7456	+	10.6948i	0.506591	+	0.425080i
$634$		0			0
$635$	−27.6536	−	47.8975i	−1.09740	−	1.90075i
$636$		0			0
$637$	−0.370462	+	2.10100i	−0.0146783	+	0.0832445i
$638$		0			0
$639$	−8.31180	+	14.3965i	−0.328810	+	0.569515i
$640$		0			0
$641$	−8.41370	−	3.06233i	−0.332321	−	0.120955i	0.170470	−	0.985363i	$-0.445471\pi$
$641$	−8.41370	−	3.06233i	−0.332321	−	0.120955i	−0.502791	+	0.864408i	$0.667694\pi$
$642$		0			0
$643$	24.0305	−	20.1640i	0.947670	−	0.795190i	−0.0312334	−	0.999512i	$-0.509944\pi$
$643$	24.0305	−	20.1640i	0.947670	−	0.795190i	0.978904	+	0.204322i	$0.0654991\pi$
$644$		0			0
$645$	7.78880			0.306684
$646$		0			0
$647$	5.54933			0.218166			0.109083	−	0.994033i	$-0.465208\pi$
$647$	5.54933			0.218166			0.109083	+	0.994033i	$0.465208\pi$
$648$		0			0
$649$	−0.118555	+	0.0994798i	−0.00465371	+	0.00390492i
$650$		0			0
$651$	4.31908	+	1.57202i	0.169278	+	0.0616122i
$652$		0			0
$653$	−19.4552	+	33.6974i	−0.761340	+	1.31868i	0.180820	+	0.983516i	$0.442125\pi$
$653$	−19.4552	+	33.6974i	−0.761340	+	1.31868i	−0.942160	+	0.335163i	$0.891209\pi$
$654$		0			0
$655$	−1.65910	+	9.40923i	−0.0648264	+	0.367649i
$656$		0			0
$657$	−6.20961	−	10.7554i	−0.242260	−	0.419606i
$658$		0			0
$659$	30.2708	+	25.4003i	1.17918	+	0.989454i	0.999984	+	0.00564104i	$0.00179561\pi$
$659$	30.2708	+	25.4003i	1.17918	+	0.989454i	0.179201	+	0.983813i	$0.442649\pi$
$660$		0			0
$661$	0.0859997	−	0.0313013i	0.00334500	−	0.00121748i	−0.340347	−	0.940300i	$-0.610545\pi$
$661$	0.0859997	−	0.0313013i	0.00334500	−	0.00121748i	0.343692	+	0.939082i	$0.388322\pi$
$662$		0			0
$663$	−1.99273	−	11.3013i	−0.0773911	−	0.438907i
$664$		0			0
$665$	−42.2203	−	7.12452i	−1.63723	−	0.276277i
$666$		0			0
$667$	−7.50480	−	42.5619i	−0.290587	−	1.64800i
$668$		0			0
$669$	−7.67752	+	2.79439i	−0.296830	+	0.108037i
$670$		0			0
$671$	−3.33409	−	2.79764i	−0.128711	−	0.108002i
$672$		0			0
$673$	19.9281	+	34.5165i	0.768173	+	1.33052i	0.938552	+	0.345137i	$0.112167\pi$
$673$	19.9281	+	34.5165i	0.768173	+	1.33052i	−0.170379	+	0.985379i	$0.554499\pi$
$674$		0			0
$675$	1.15270	−	6.53731i	0.0443676	−	0.251621i
$676$		0			0
$677$	−14.6912	+	25.4459i	−0.564628	+	0.977965i	0.432456	+	0.901655i	$0.357647\pi$
$677$	−14.6912	+	25.4459i	−0.564628	+	0.977965i	−0.997084	+	0.0763098i	$0.975686\pi$
$678$		0			0
$679$	−9.88326	−	3.59721i	−0.379285	−	0.138048i
$680$		0			0
$681$	−1.37939	+	1.15744i	−0.0528582	+	0.0443533i
$682$		0			0
$683$	21.0933			0.807112			0.403556	−	0.914955i	$-0.367774\pi$
$683$	21.0933			0.807112			0.403556	+	0.914955i	$0.367774\pi$
$684$		0			0
$685$	−54.7033			−2.09010
$686$		0			0
$687$	−14.3550	+	12.0453i	−0.547679	+	0.459557i
$688$		0			0
$689$	3.07563	+	1.11944i	0.117172	+	0.0426471i
$690$		0			0
$691$	−8.08172	+	13.9979i	−0.307443	+	0.532507i	−0.977802	−	0.209530i	$-0.932807\pi$
$691$	−8.08172	+	13.9979i	−0.307443	+	0.532507i	0.670359	+	0.742037i	$0.266140\pi$
$692$		0			0
$693$	0.173648	−	0.984808i	0.00659635	−	0.0374098i
$694$		0			0
$695$	3.54576	+	6.14144i	0.134498	+	0.232958i
$696$		0			0
$697$	−18.5646	−	15.5776i	−0.703186	−	0.590043i
$698$		0			0
$699$	3.85117	−	1.40171i	0.145665	−	0.0530175i
$700$		0			0
$701$	−3.48561	−	19.7679i	−0.131650	−	0.746623i	−0.977134	−	0.212623i	$-0.931799\pi$
$701$	−3.48561	−	19.7679i	−0.131650	−	0.746623i	0.845484	−	0.534000i	$-0.179312\pi$
$702$		0			0
$703$	−31.6894	−	37.2063i	−1.19519	−	1.40326i
$704$		0			0
$705$	3.31521	+	18.8015i	0.124858	+	0.708105i
$706$		0			0
$707$	26.8050	−	9.75622i	1.00811	−	0.366920i
$708$		0			0
$709$	−29.7998	−	25.0050i	−1.11915	−	0.939082i	−0.120593	−	0.992702i	$-0.538480\pi$
$709$	−29.7998	−	25.0050i	−1.11915	−	0.939082i	−0.998561	+	0.0536201i	$0.982924\pi$
$710$		0			0
$711$	−5.46198	−	9.46043i	−0.204840	−	0.354794i
$712$		0			0
$713$	1.88507	−	10.6907i	0.0705963	−	0.400372i
$714$		0			0
$715$	−0.979055	+	1.69577i	−0.0366146	+	0.0634183i
$716$		0			0
$717$	−26.5253	−	9.65441i	−0.990605	−	0.360551i
$718$		0			0
$719$	−2.34549	+	1.96810i	−0.0874718	+	0.0733976i	−0.685475	−	0.728096i	$-0.740405\pi$
$719$	−2.34549	+	1.96810i	−0.0874718	+	0.0733976i	0.598003	+	0.801494i	$0.295961\pi$
$720$		0			0
$721$	−22.5895			−0.841275
$722$		0			0
$723$	6.56212			0.244048
$724$		0			0
$725$	32.3161	−	27.1165i	1.20019	−	1.00708i
$726$		0			0
$727$	−16.4226	−	5.97734i	−0.609081	−	0.221687i	0.0190200	−	0.999819i	$-0.493945\pi$
$727$	−16.4226	−	5.97734i	−0.609081	−	0.221687i	−0.628101	+	0.778132i	$0.716168\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−2.75284	+	15.6121i	−0.101817	+	0.577436i
$732$		0			0
$733$	20.7087	+	35.8686i	0.764894	+	1.32484i	0.940302	+	0.340340i	$0.110542\pi$
$733$	20.7087	+	35.8686i	0.764894	+	1.32484i	−0.175408	+	0.984496i	$0.556124\pi$
$734$		0			0
$735$	−3.37346	−	2.83067i	−0.124432	−	0.104411i
$736$		0			0
$737$	−0.352044	+	0.128134i	−0.0129677	+	0.00471986i
$738$		0			0
$739$	−4.59358	−	26.0515i	−0.168978	−	0.958319i	−0.944868	−	0.327451i	$-0.893810\pi$
$739$	−4.59358	−	26.0515i	−0.168978	−	0.958319i	0.775890	−	0.630868i	$-0.217301\pi$
$740$		0			0
$741$	−4.67112	−	5.48432i	−0.171598	−	0.201472i
$742$		0			0
$743$	2.61793	+	14.8470i	0.0960424	+	0.544684i	0.994423	+	0.105466i	$0.0336333\pi$
$743$	2.61793	+	14.8470i	0.0960424	+	0.544684i	−0.898381	+	0.439218i	$0.855256\pi$
$744$		0			0
$745$	−5.34477	+	1.94534i	−0.195817	+	0.0712716i
$746$		0			0
$747$	−8.97565	−	7.53147i	−0.328402	−	0.275562i
$748$		0			0
$749$	−0.0393628	−	0.0681784i	−0.00143829	−	0.00249119i
$750$		0			0
$751$	0.921274	−	5.22481i	0.0336178	−	0.190656i	−0.963374	−	0.268161i	$-0.913584\pi$
$751$	0.921274	−	5.22481i	0.0336178	−	0.190656i	0.996992	+	0.0775048i	$0.0246953\pi$
$752$		0			0
$753$	4.44697	−	7.70237i	0.162056	−	0.280690i
$754$		0			0
$755$	−64.2825	−	23.3969i	−2.33948	−	0.851500i
$756$		0			0
$757$	6.23442	−	5.23130i	0.226594	−	0.190135i	−0.522422	−	0.852687i	$-0.674971\pi$
$757$	6.23442	−	5.23130i	0.226594	−	0.190135i	0.749016	+	0.662552i	$0.230527\pi$
$758$		0			0
$759$	−2.36184			−0.0857295
$760$		0			0
$761$	−46.2113			−1.67516			−0.837579	−	0.546316i	$-0.816030\pi$
$761$	−46.2113			−1.67516			−0.837579	+	0.546316i	$0.816030\pi$
$762$		0			0
$763$	−23.7631	+	19.9396i	−0.860282	+	0.721863i
$764$		0			0
$765$	22.2592	+	8.10170i	0.804784	+	0.292918i
$766$		0			0
$767$	−0.368241	+	0.637812i	−0.0132964	+	0.0230301i
$768$		0			0
$769$	−4.66132	+	26.4357i	−0.168092	+	0.953295i	0.777728	+	0.628601i	$0.216372\pi$
$769$	−4.66132	+	26.4357i	−0.168092	+	0.953295i	−0.945819	+	0.324693i	$0.894739\pi$
$770$		0			0
$771$	6.73308	+	11.6620i	0.242486	+	0.419998i
$772$		0			0
$773$	−16.1065	−	13.5150i	−0.579312	−	0.486100i	0.305409	−	0.952221i	$-0.401207\pi$
$773$	−16.1065	−	13.5150i	−0.579312	−	0.486100i	−0.884721	+	0.466121i	$0.845651\pi$
$774$		0			0
$775$	9.95723	−	3.62414i	0.357674	−	0.130183i
$776$		0			0
$777$	−5.60607	−	31.7936i	−0.201117	−	1.14059i
$778$		0			0
$779$	−15.0013	−	2.53142i	−0.537479	−	0.0906974i
$780$		0			0
$781$	1.00253	+	5.68561i	0.0358732	+	0.203447i
$782$		0			0
$783$	−5.97178	+	2.17355i	−0.213414	+	0.0776764i
$784$		0			0
$785$	10.7103	+	8.98703i	0.382268	+	0.320761i
$786$		0			0
$787$	22.7656	+	39.4312i	0.811507	+	1.40557i	0.911809	+	0.410615i	$0.134686\pi$
$787$	22.7656	+	39.4312i	0.811507	+	1.40557i	−0.100302	+	0.994957i	$0.531981\pi$
$788$		0			0
$789$	2.90895	−	16.4975i	0.103561	−	0.587325i
$790$		0			0
$791$	16.7875	−	29.0767i	0.596893	−	1.03385i
$792$		0			0
$793$	−19.4628	−	7.08386i	−0.691143	−	0.251555i
$794$		0			0
$795$	−5.17546	+	4.34273i	−0.183555	+	0.154021i
$796$		0			0
$797$	36.1780			1.28149			0.640745	−	0.767754i	$-0.278626\pi$
$797$	36.1780			1.28149			0.640745	+	0.767754i	$0.278626\pi$
$798$		0			0
$799$	−38.8580			−1.37470
$800$		0			0
$801$	1.37346	−	1.15247i	0.0485287	−	0.0407204i
$802$		0			0
$803$	−4.05303	−	1.47518i	−0.143028	−	0.0520581i
$804$		0			0
$805$	−33.4013	+	57.8527i	−1.17724	+	2.03904i
$806$		0			0
$807$	0.623303	−	3.53493i	0.0219413	−	0.124435i
$808$		0			0
$809$	−1.18938	−	2.06006i	−0.0418163	−	0.0724280i	0.844360	−	0.535777i	$-0.179981\pi$
$809$	−1.18938	−	2.06006i	−0.0418163	−	0.0724280i	−0.886176	+	0.463349i	$0.846648\pi$
$810$		0			0
$811$	28.3904	+	23.8223i	0.996921	+	0.836516i	0.986555	−	0.163431i	$-0.0522560\pi$
$811$	28.3904	+	23.8223i	0.996921	+	0.836516i	0.0103658	+	0.999946i	$0.496700\pi$
$812$		0			0
$813$	22.5141	−	8.19448i	0.789605	−	0.287393i
$814$		0			0
$815$	−4.81924	−	27.3313i	−0.168811	−	0.957373i
$816$		0			0
$817$	3.47250	+	9.32640i	0.121487	+	0.326289i
$818$		0			0
$819$	−0.826352	−	4.68647i	−0.0288751	−	0.163759i
$820$		0			0
$821$	24.3949	−	8.87901i	0.851387	−	0.309879i	0.120781	−	0.992679i	$-0.461460\pi$
$821$	24.3949	−	8.87901i	0.851387	−	0.309879i	0.730606	+	0.682800i	$0.239238\pi$
$822$		0			0
$823$	34.4805	+	28.9325i	1.20191	+	1.00852i	0.999573	+	0.0292095i	$0.00929900\pi$
$823$	34.4805	+	28.9325i	1.20191	+	1.00852i	0.202340	+	0.979315i	$0.435145\pi$
$824$		0			0
$825$	−1.15270	−	1.99654i	−0.0401320	−	0.0695106i
$826$		0			0
$827$	2.92473	−	16.5870i	0.101703	−	0.576786i	−0.890783	−	0.454429i	$-0.849843\pi$
$827$	2.92473	−	16.5870i	0.101703	−	0.576786i	0.992486	−	0.122358i	$-0.0390455\pi$
$828$		0			0
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$		0			0
$831$	17.5929	+	6.40328i	0.610290	+	0.222127i
$832$		0			0
$833$	6.86618	−	5.76141i	0.237899	−	0.199621i
$834$		0			0
$835$	−45.7033			−1.58163
$836$		0			0
$837$	−1.59627			−0.0551750
$838$		0			0
$839$	−1.02687	+	0.861650i	−0.0354516	+	0.0297475i	−0.660341	−	0.750966i	$-0.729588\pi$
$839$	−1.02687	+	0.861650i	−0.0354516	+	0.0297475i	0.624890	+	0.780713i	$0.285144\pi$
$840$		0			0
$841$	−10.6998	−	3.89441i	−0.368959	−	0.134290i
$842$		0			0
$843$	5.31908	−	9.21291i	0.183199	−	0.317310i
$844$		0			0
$845$	6.08306	−	34.4988i	0.209264	−	1.18679i
$846$		0			0
$847$	15.6630	+	27.1291i	0.538186	+	0.932166i
$848$		0			0
$849$	10.7344	+	9.00725i	0.368404	+	0.309128i
$850$		0			0
$851$	−71.6515	+	26.0790i	−2.45618	+	0.893977i
$852$		0			0
$853$	−1.37969	−	7.82461i	−0.0472397	−	0.267910i	0.952035	−	0.305989i	$-0.0989871\pi$
$853$	−1.37969	−	7.82461i	−0.0472397	−	0.267910i	−0.999275	+	0.0380795i	$0.987876\pi$
$854$		0			0
$855$	14.6250	−	2.68993i	0.500163	−	0.0919938i
$856$		0			0
$857$	8.31356	+	47.1485i	0.283986	+	1.61056i	0.708886	+	0.705323i	$0.249198\pi$
$857$	8.31356	+	47.1485i	0.283986	+	1.61056i	−0.424900	+	0.905240i	$0.639691\pi$
$858$		0			0
$859$	1.53849	−	0.559963i	0.0524924	−	0.0191057i	−0.315640	−	0.948879i	$-0.602219\pi$
$859$	1.53849	−	0.559963i	0.0524924	−	0.0191057i	0.368133	+	0.929773i	$0.379997\pi$
$860$		0			0
$861$	−7.69846	−	6.45978i	−0.262363	−	0.220149i
$862$		0			0
$863$	17.4616	+	30.2443i	0.594399	+	1.02953i	0.993631	+	0.112679i	$0.0359432\pi$
$863$	17.4616	+	30.2443i	0.594399	+	1.02953i	−0.399233	+	0.916850i	$0.630723\pi$
$864$		0			0
$865$	0.605600	−	3.43453i	0.0205910	−	0.116777i
$866$		0			0
$867$	−15.6065	+	27.0313i	−0.530026	+	0.918031i
$868$		0			0
$869$	−3.56506	−	1.29757i	−0.120936	−	0.0440172i
$870$		0			0
$871$	−1.36571	+	1.14597i	−0.0462755	+	0.0388297i
$872$		0			0
$873$	3.65270			0.123625
$874$		0			0
$875$	−16.0915			−0.543993
$876$		0			0
$877$	−4.88120	+	4.09581i	−0.164826	+	0.138306i	−0.721470	−	0.692446i	$-0.756533\pi$
$877$	−4.88120	+	4.09581i	−0.164826	+	0.138306i	0.556644	+	0.830751i	$0.312089\pi$
$878$		0			0
$879$	10.8255	+	3.94015i	0.365134	+	0.132898i
$880$		0			0
$881$	−2.63697	+	4.56737i	−0.0888419	+	0.153879i	−0.907022	−	0.421084i	$-0.861650\pi$
$881$	−2.63697	+	4.56737i	−0.0888419	+	0.153879i	0.818180	+	0.574962i	$0.194983\pi$
$882$		0			0
$883$	0.564588	−	3.20194i	0.0189999	−	0.107754i	−0.973833	−	0.227265i	$-0.927022\pi$
$883$	0.564588	−	3.20194i	0.0189999	−	0.107754i	0.992833	+	0.119511i	$0.0381327\pi$
$884$		0			0
$885$	−0.760115	−	1.31656i	−0.0255510	−	0.0442556i
$886$		0			0
$887$	17.1368	+	14.3795i	0.575398	+	0.482816i	0.883432	−	0.468559i	$-0.155227\pi$
$887$	17.1368	+	14.3795i	0.575398	+	0.482816i	−0.308034	+	0.951375i	$0.599671\pi$
$888$		0			0
$889$	43.8658	−	15.9658i	1.47121	−	0.535477i
$890$		0			0
$891$	0.0603074	+	0.342020i	0.00202037	+	0.0114581i
$892$		0			0
$893$	−21.0351	+	12.3520i	−0.703912	+	0.413343i
$894$		0			0
$895$	1.20557	+	6.83716i	0.0402979	+	0.228541i
$896$		0			0
$897$	−10.5617	+	3.84413i	−0.352643	+	0.128352i
$898$		0			0
$899$	−7.77101	−	6.52065i	−0.259178	−	0.217476i
$900$		0			0
$901$	−6.87551	−	11.9087i	−0.229057	−	0.396738i
$902$		0			0
$903$	−1.14156	+	6.47410i	−0.0379887	+	0.215445i
$904$		0			0
$905$	38.0442	−	65.8944i	1.26463	−	2.19040i
$906$		0			0
$907$	2.96703	+	1.07991i	0.0985187	+	0.0358579i	0.390809	−	0.920472i	$-0.372195\pi$
$907$	2.96703	+	1.07991i	0.0985187	+	0.0358579i	−0.292291	+	0.956330i	$0.594417\pi$
$908$		0			0
$909$	−7.58899	+	6.36792i	−0.251711	+	0.211211i
$910$		0			0
$911$	44.3387			1.46901			0.734504	−	0.678604i	$-0.237415\pi$
$911$	44.3387			1.46901			0.734504	+	0.678604i	$0.237415\pi$
$912$		0			0
$913$	−4.06923			−0.134672
$914$		0			0
$915$	32.7506	−	27.4810i	1.08270	−	0.908495i
$916$		0			0
$917$	−7.57785	−	2.75811i	−0.250243	−	0.0910809i
$918$		0			0
$919$	7.10220	−	12.3014i	0.234280	−	0.405785i	−0.724783	−	0.688977i	$-0.758060\pi$
$919$	7.10220	−	12.3014i	0.234280	−	0.405785i	0.959063	+	0.283192i	$0.0913935\pi$
$920$		0			0
$921$	−0.746282	+	4.23238i	−0.0245908	+	0.139462i
$922$		0			0
$923$	13.7369	+	23.7931i	0.452157	+	0.783159i
$924$		0			0
$925$	−57.0151	−	47.8413i	−1.87464	−	1.57301i
$926$		0			0
$927$	7.37211	−	2.68323i	0.242132	−	0.0881288i
$928$		0			0
$929$	−2.67881	−	15.1923i	−0.0878888	−	0.498442i	−0.996696	−	0.0812253i	$-0.974117\pi$
$929$	−2.67881	−	15.1923i	−0.0878888	−	0.498442i	0.908807	−	0.417217i	$-0.136994\pi$
$930$		0			0
$931$	1.88548	−	5.30142i	0.0617940	−	0.173747i
$932$		0			0
$933$	3.99273	+	22.6439i	0.130716	+	0.741327i
$934$		0			0
$935$	7.73055	−	2.81369i	0.252816	−	0.0920175i
$936$		0			0
$937$	−7.42830	−	6.23308i	−0.242672	−	0.203626i	0.513337	−	0.858187i	$-0.328409\pi$
$937$	−7.42830	−	6.23308i	−0.242672	−	0.203626i	−0.756009	+	0.654561i	$0.772853\pi$
$938$		0			0
$939$	4.60488	+	7.97589i	0.150275	+	0.260283i
$940$		0			0
$941$	−3.12314	+	17.7122i	−0.101811	+	0.577402i	0.890635	+	0.454720i	$0.150261\pi$
$941$	−3.12314	+	17.7122i	−0.101811	+	0.577402i	−0.992446	+	0.122682i	$0.960851\pi$
$942$		0			0
$943$	−11.8678	+	20.5557i	−0.386470	+	0.669385i
$944$		0			0
$945$	9.23055	+	3.35965i	0.300270	+	0.109289i
$946$		0			0
$947$	−1.68067	+	1.41025i	−0.0546146	+	0.0458271i	−0.669686	−	0.742644i	$-0.733571\pi$
$947$	−1.68067	+	1.41025i	−0.0546146	+	0.0458271i	0.615072	+	0.788471i	$0.289127\pi$
$948$		0			0
$949$	−20.5253			−0.666279
$950$		0			0
$951$	3.35504			0.108795
$952$		0			0
$953$	−8.66456	+	7.27043i	−0.280673	+	0.235512i	−0.772246	−	0.635324i	$-0.780867\pi$
$953$	−8.66456	+	7.27043i	−0.280673	+	0.235512i	0.491573	+	0.870836i	$0.336422\pi$
$954$		0			0
$955$	−34.5774	−	12.5852i	−1.11890	−	0.407246i
$956$		0			0
$957$	−1.10354	+	1.91139i	−0.0356724	+	0.0617864i
$958$		0			0
$959$	8.01754	−	45.4697i	0.258900	−	1.46829i
$960$		0			0
$961$	14.2260	+	24.6401i	0.458902	+	0.794842i
$962$		0			0
$963$	0.0209445	+	0.0175745i	0.000674928	+	0.000566332i
$964$		0			0
$965$	−9.18392	+	3.34267i	−0.295641	+	0.107604i
$966$		0			0
$967$	−8.12402	−	46.0736i	−0.261251	−	1.48163i	−0.779503	−	0.626399i	$-0.784528\pi$
$967$	−8.12402	−	46.0736i	−0.261251	−	1.48163i	0.518252	−	0.855228i	$-0.326583\pi$
$968$		0			0
$969$	0.222811	+	30.2655i	0.00715773	+	0.972267i
$970$		0			0
$971$	−10.4834	−	59.4543i	−0.336428	−	1.90798i	−0.412654	−	0.910888i	$-0.635398\pi$
$971$	−10.4834	−	59.4543i	−0.336428	−	1.90798i	0.0762258	−	0.997091i	$-0.475713\pi$
$972$		0			0
$973$	−5.62449	+	2.04715i	−0.180313	+	0.0656285i
$974$		0			0
$975$	−8.40420	−	7.05196i	−0.269150	−	0.225844i
$976$		0			0
$977$	−11.3978	−	19.7416i	−0.364648	−	0.631589i	0.624072	−	0.781367i	$-0.285477\pi$
$977$	−11.3978	−	19.7416i	−0.364648	−	0.631589i	−0.988720	+	0.149778i	$0.952144\pi$
$978$		0			0
$979$	0.108126	−	0.613214i	0.00345573	−	0.0195984i
$980$		0			0
$981$	5.38666	−	9.32997i	0.171983	−	0.297883i
$982$		0			0
$983$	−28.9359	−	10.5318i	−0.922911	−	0.335912i	−0.163515	−	0.986541i	$-0.552283\pi$
$983$	−28.9359	−	10.5318i	−0.922911	−	0.335912i	−0.759396	+	0.650629i	$0.774505\pi$
$984$		0			0
$985$	21.7833	−	18.2784i	0.694075	−	0.582398i
$986$		0			0
$987$	−16.1138			−0.512908
$988$		0			0
$989$	15.5267			0.493721
$990$		0			0
$991$	29.2467	−	24.5409i	0.929054	−	0.779569i	−0.0465937	−	0.998914i	$-0.514837\pi$
$991$	29.2467	−	24.5409i	0.929054	−	0.779569i	0.975647	+	0.219345i	$0.0703922\pi$
$992$		0			0
$993$	−20.7430	−	7.54985i	−0.658260	−	0.239587i
$994$		0			0
$995$	5.17546	−	8.96416i	0.164073	−	0.284183i
$996$		0			0
$997$	5.37423	−	30.4788i	0.170203	−	0.965272i	−0.773332	−	0.634001i	$-0.781411\pi$
$997$	5.37423	−	30.4788i	0.170203	−	0.965272i	0.943536	−	0.331271i	$-0.107477\pi$
$998$		0			0
$999$	5.60607	+	9.70999i	0.177368	+	0.307211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.f.769.1		6
4.3	odd	2		114.2.i.d.85.1	yes	6
12.11	even	2		342.2.u.a.199.1		6
19.17	even	9	inner	912.2.bo.f.625.1		6
76.51	even	18		2166.2.a.u.1.1		3
76.55	odd	18		114.2.i.d.55.1	✓	6
76.63	odd	18		2166.2.a.o.1.1		3
228.131	even	18		342.2.u.a.55.1		6
228.203	odd	18		6498.2.a.bn.1.3		3
228.215	even	18		6498.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.55.1	✓	6	76.55	odd	18
114.2.i.d.85.1	yes	6	4.3	odd	2
342.2.u.a.55.1		6	228.131	even	18
342.2.u.a.199.1		6	12.11	even	2
912.2.bo.f.625.1		6	19.17	even	9	inner
912.2.bo.f.769.1		6	1.1	even	1	trivial
2166.2.a.o.1.1		3	76.63	odd	18
2166.2.a.u.1.1		3	76.51	even	18
6498.2.a.bn.1.3		3	228.203	odd	18
6498.2.a.bs.1.3		3	228.215	even	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-0.173648 - 0.300767i) q^{11} +(-1.26604 - 1.06234i) q^{13} +(3.20574 - 1.16679i) q^{15} +(1.20574 + 6.83807i) q^{17} +(2.82635 + 3.31839i) q^{19} +(0.500000 + 2.83564i) q^{21} +(6.39053 - 2.32596i) q^{23} +(5.08512 + 4.26692i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.10354 - 6.25849i) q^{29} +(0.798133 - 1.38241i) q^{31} +(-0.326352 - 0.118782i) q^{33} +(-7.52481 + 6.31407i) q^{35} -11.2121 q^{37} -1.65270 q^{39} +(-2.67365 + 2.24346i) q^{41} +(2.14543 + 0.780873i) q^{43} +(1.70574 - 2.95442i) q^{45} +(-0.971782 + 5.51125i) q^{47} +(-0.645430 - 1.11792i) q^{49} +(5.31908 + 4.46324i) q^{51} +(-1.86097 + 0.677337i) q^{53} +(-0.205737 - 1.16679i) q^{55} +(4.29813 + 0.725293i) q^{57} +(-0.0773815 - 0.438852i) q^{59} +(11.7763 - 4.28623i) q^{61} +(2.20574 + 1.85083i) q^{63} +(-2.81908 - 4.88279i) q^{65} +(0.187319 - 1.06234i) q^{67} +(3.40033 - 5.88954i) q^{69} +(-15.6211 - 5.68561i) q^{71} +(9.51367 - 7.98292i) q^{73} +6.63816 q^{75} +1.00000 q^{77} +(8.36824 - 7.02179i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(5.85844 - 10.1471i) q^{83} +(-4.11334 + 23.3279i) q^{85} +(-3.17752 - 5.50362i) q^{87} +(1.37346 + 1.15247i) q^{89} +(4.47178 - 1.62760i) q^{91} +(-0.277189 - 1.57202i) q^{93} +(5.18866 + 13.9357i) q^{95} +(0.634285 + 3.59721i) q^{97} +(-0.326352 + 0.118782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q + 9 * q^5 - 3 * q^7	\( 6 q + 9 q^{5} - 3 q^{7} - 3 q^{13} + 9 q^{15} - 3 q^{17} + 18 q^{19} + 3 q^{21} + 21 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{29} - 9 q^{31} - 3 q^{33} - 18 q^{35} - 18 q^{37} - 12 q^{39} - 15 q^{41} - 3 q^{43} + 9 q^{47} + 12 q^{49} + 15 q^{51} + 12 q^{53} + 9 q^{55} + 12 q^{57} - 27 q^{59} + 3 q^{61} + 3 q^{63} - 21 q^{67} + 6 q^{69} - 39 q^{71} + 36 q^{73} + 6 q^{75} + 6 q^{77} + 45 q^{79} + 27 q^{83} - 18 q^{85} + 6 q^{87} - 30 q^{89} + 12 q^{91} + 9 q^{93} - 6 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 9 * q^5 - 3 * q^7 - 3 * q^13 + 9 * q^15 - 3 * q^17 + 18 * q^19 + 3 * q^21 + 21 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^29 - 9 * q^31 - 3 * q^33 - 18 * q^35 - 18 * q^37 - 12 * q^39 - 15 * q^41 - 3 * q^43 + 9 * q^47 + 12 * q^49 + 15 * q^51 + 12 * q^53 + 9 * q^55 + 12 * q^57 - 27 * q^59 + 3 * q^61 + 3 * q^63 - 21 * q^67 + 6 * q^69 - 39 * q^71 + 36 * q^73 + 6 * q^75 + 6 * q^77 + 45 * q^79 + 27 * q^83 - 18 * q^85 + 6 * q^87 - 30 * q^89 + 12 * q^91 + 9 * q^93 - 6 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

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Database

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