LMFDB - Embedded newform 72.7.b.d.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 78x^{10} + 3408x^{8} + 73216x^{6} + 13959168x^{4} + 1308622848x^{2} + 68719476736 $ x^12 + 78x^10 + 3408x^8 + 73216x^6 + 13959168x^4 + 1308622848*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.5
Root			$1.98725 - 7.74925i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.d.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98725 - 7.74925i) q^{2} +(-56.1017 + 30.7994i) q^{4} -106.706i q^{5} -614.112i q^{7} +(350.160 + 373.539i) q^{8} +O(q^{10})$	\(q+(-1.98725 - 7.74925i) q^{2} +(-56.1017 + 30.7994i) q^{4} -106.706i q^{5} -614.112i q^{7} +(350.160 + 373.539i) q^{8} +(-826.887 + 212.051i) q^{10} +1319.04 q^{11} -626.417i q^{13} +(-4758.91 + 1220.40i) q^{14} +(2198.79 - 3455.80i) q^{16} -8177.05 q^{17} -9299.98 q^{19} +(3286.47 + 5986.36i) q^{20} +(-2621.26 - 10221.5i) q^{22} +14294.8i q^{23} +4238.93 q^{25} +(-4854.26 + 1244.85i) q^{26} +(18914.3 + 34452.7i) q^{28} +20120.8i q^{29} -10143.9i q^{31} +(-31149.4 - 10171.4i) q^{32} +(16249.9 + 63366.0i) q^{34} -65529.2 q^{35} -10007.8i q^{37} +(18481.4 + 72067.8i) q^{38} +(39858.7 - 37364.1i) q^{40} +42171.9 q^{41} -68524.3 q^{43} +(-74000.1 + 40625.6i) q^{44} +(110774. - 28407.3i) q^{46} +35528.8i q^{47} -259485. q^{49} +(-8423.83 - 32848.5i) q^{50} +(19293.3 + 35143.0i) q^{52} -187539. i q^{53} -140748. i q^{55} +(229395. - 215038. i) q^{56} +(155921. - 39985.0i) q^{58} +258570. q^{59} -363211. i q^{61} +(-78607.3 + 20158.4i) q^{62} +(-16919.3 + 261597. i) q^{64} -66842.1 q^{65} -287225. q^{67} +(458746. - 251848. i) q^{68} +(130223. + 507802. i) q^{70} +338581. i q^{71} -191677. q^{73} +(-77552.6 + 19888.0i) q^{74} +(521744. - 286434. i) q^{76} -810036. i q^{77} -63038.9i q^{79} +(-368753. - 234623. i) q^{80} +(-83806.2 - 326800. i) q^{82} -412151. q^{83} +872536. i q^{85} +(136175. + 531012. i) q^{86} +(461874. + 492712. i) q^{88} +1.13336e6 q^{89} -384690. q^{91} +(-440270. - 801960. i) q^{92} +(275321. - 70604.6i) q^{94} +992359. i q^{95} +867708. q^{97} +(515662. + 2.01081e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 156 q^{4}+O(q^{10}) $ 12 * q - 156 * q^4	$ 12 q - 156 q^{4} + 1416 q^{10} - 1464 q^{16} + 3936 q^{19} + 15888 q^{22} - 47796 q^{25} + 11256 q^{28} + 50016 q^{34} + 70896 q^{40} - 340704 q^{43} + 213696 q^{46} - 304644 q^{49} + 548016 q^{52} - 38616 q^{58} + 206544 q^{64} - 962112 q^{67} + 1074480 q^{70} - 1069560 q^{73} + 1064352 q^{76} - 694944 q^{82} - 3072672 q^{88} + 775008 q^{91} + 3752256 q^{94} - 86952 q^{97}+O(q^{100}) $ 12 * q - 156 * q^4 + 1416 * q^10 - 1464 * q^16 + 3936 * q^19 + 15888 * q^22 - 47796 * q^25 + 11256 * q^28 + 50016 * q^34 + 70896 * q^40 - 340704 * q^43 + 213696 * q^46 - 304644 * q^49 + 548016 * q^52 - 38616 * q^58 + 206544 * q^64 - 962112 * q^67 + 1074480 * q^70 - 1069560 * q^73 + 1064352 * q^76 - 694944 * q^82 - 3072672 * q^88 + 775008 * q^91 + 3752256 * q^94 - 86952 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.98725	−	7.74925i	−0.248407	−	0.968656i
$2$	−1.98725	−	7.74925i	−0.248407	−	0.968656i
$3$		0			0
$3$		0			0
$4$	−56.1017	+	30.7994i	−0.876588	+	0.481241i
$5$		−	106.706i		−	0.853644i	−0.904336	−	0.426822i	$-0.859633\pi$
$5$		−	106.706i		−	0.853644i	0.904336	−	0.426822i	$-0.140367\pi$
$6$		0			0
$7$		−	614.112i		−	1.79041i	−0.445650	−	0.895207i	$-0.647027\pi$
$7$		−	614.112i		−	1.79041i	0.445650	−	0.895207i	$-0.352973\pi$
$8$	350.160	+	373.539i	0.683907	+	0.729569i
$9$		0			0
$10$	−826.887	+	212.051i	−0.826887	+	0.212051i
$11$	1319.04			0.991011			0.495506	−	0.868605i	$-0.334983\pi$
$11$	1319.04			0.991011			0.495506	+	0.868605i	$0.334983\pi$
$12$		0			0
$13$		−	626.417i		−	0.285124i	−0.989786	−	0.142562i	$-0.954466\pi$
$13$		−	626.417i		−	0.285124i	0.989786	−	0.142562i	$-0.0455340\pi$
$14$	−4758.91	+	1220.40i	−1.73430	+	0.444751i
$15$		0			0
$16$	2198.79	−	3455.80i	0.536814	−	0.843700i
$17$	−8177.05			−1.66437			−0.832185	−	0.554498i	$-0.812910\pi$
$17$	−8177.05			−1.66437			−0.832185	+	0.554498i	$0.812910\pi$
$18$		0			0
$19$	−9299.98			−1.35588			−0.677940	−	0.735117i	$-0.737127\pi$
$19$	−9299.98			−1.35588			−0.677940	+	0.735117i	$0.737127\pi$
$20$	3286.47	+	5986.36i	0.410809	+	0.748294i
$21$		0			0
$22$	−2621.26	−	10221.5i	−0.246174	−	0.959949i
$23$			14294.8i			1.17488i	0.809268	+	0.587440i	$0.199864\pi$
$23$			14294.8i			1.17488i	−0.809268	+	0.587440i	$0.800136\pi$
$24$		0			0
$25$	4238.93			0.271292
$26$	−4854.26	+	1244.85i	−0.276187	+	0.0708266i
$27$		0			0
$28$	18914.3	+	34452.7i	0.861621	+	1.56946i
$29$			20120.8i			0.824993i	0.910959	+	0.412497i	$0.135343\pi$
$29$			20120.8i			0.824993i	−0.910959	+	0.412497i	$0.864657\pi$
$30$		0			0
$31$		−	10143.9i		−	0.340501i	−0.985401	−	0.170250i	$-0.945542\pi$
$31$		−	10143.9i		−	0.340501i	0.985401	−	0.170250i	$-0.0544576\pi$
$32$	−31149.4	−	10171.4i	−0.950604	−	0.310408i
$33$		0			0
$34$	16249.9	+	63366.0i	0.413440	+	1.61220i
$35$	−65529.2			−1.52838
$36$		0			0
$37$		−	10007.8i		−	0.197575i	−0.995109	−	0.0987875i	$-0.968504\pi$
$37$		−	10007.8i		−	0.197575i	0.995109	−	0.0987875i	$-0.0314964\pi$
$38$	18481.4	+	72067.8i	0.336809	+	1.31338i
$39$		0			0
$40$	39858.7	−	37364.1i	0.622792	−	0.583813i
$41$	42171.9			0.611887			0.305944	−	0.952050i	$-0.401028\pi$
$41$	42171.9			0.611887			0.305944	+	0.952050i	$0.401028\pi$
$42$		0			0
$43$	−68524.3			−0.861865			−0.430932	−	0.902384i	$-0.641815\pi$
$43$	−68524.3			−0.861865			−0.430932	+	0.902384i	$0.641815\pi$
$44$	−74000.1	+	40625.6i	−0.868709	+	0.476915i
$45$		0			0
$46$	110774.	−	28407.3i	1.13805	−	0.291848i
$47$			35528.8i			0.342205i	0.985253	+	0.171103i	$0.0547330\pi$
$47$			35528.8i			0.342205i	−0.985253	+	0.171103i	$0.945267\pi$
$48$		0			0
$49$	−259485.			−2.20559
$50$	−8423.83	−	32848.5i	−0.0673906	−	0.262788i
$51$		0			0
$52$	19293.3	+	35143.0i	0.137213	+	0.249936i
$53$		−	187539.i		−	1.25969i	−0.776720	−	0.629847i	$-0.783118\pi$
$53$		−	187539.i		−	1.25969i	0.776720	−	0.629847i	$-0.216882\pi$
$54$		0			0
$55$		−	140748.i		−	0.845971i
$56$	229395.	−	215038.i	1.30623	−	1.22448i
$57$		0			0
$58$	155921.	−	39985.0i	0.799135	−	0.204934i
$59$	258570.			1.25899			0.629496	−	0.777004i	$-0.283261\pi$
$59$	258570.			1.25899			0.629496	+	0.777004i	$0.283261\pi$
$60$		0			0
$61$		−	363211.i		−	1.60018i	−0.599877	−	0.800092i	$-0.704784\pi$
$61$		−	363211.i		−	1.60018i	0.599877	−	0.800092i	$-0.295216\pi$
$62$	−78607.3	+	20158.4i	−0.329828	+	0.0845826i
$63$		0			0
$64$	−16919.3	+	261597.i	−0.0645419	+	0.997915i
$65$	−66842.1			−0.243394
$66$		0			0
$67$	−287225.			−0.954987			−0.477493	−	0.878635i	$-0.658455\pi$
$67$	−287225.			−0.954987			−0.477493	+	0.878635i	$0.658455\pi$
$68$	458746.	−	251848.i	1.45897	−	0.800963i
$69$		0			0
$70$	130223.	+	507802.i	0.379659	+	1.48047i
$71$			338581.i			0.945993i	0.881064	+	0.472997i	$0.156828\pi$
$71$			338581.i			0.945993i	−0.881064	+	0.472997i	$0.843172\pi$
$72$		0			0
$73$	−191677.			−0.492721			−0.246361	−	0.969178i	$-0.579235\pi$
$73$	−191677.			−0.492721			−0.246361	+	0.969178i	$0.579235\pi$
$74$	−77552.6	+	19888.0i	−0.191382	+	0.0490789i
$75$		0			0
$76$	521744.	−	286434.i	1.18855	−	0.652505i
$77$		−	810036.i		−	1.77432i
$78$		0			0
$79$		−	63038.9i		−	0.127858i	−0.997954	−	0.0639289i	$-0.979637\pi$
$79$		−	63038.9i		−	0.127858i	0.997954	−	0.0639289i	$-0.0203631\pi$
$80$	−368753.	−	234623.i	−0.720220	−	0.458248i
$81$		0			0
$82$	−83806.2	−	326800.i	−0.151997	−	0.592708i
$83$	−412151.			−0.720811			−0.360406	−	0.932796i	$-0.617362\pi$
$83$	−412151.			−0.720811			−0.360406	+	0.932796i	$0.617362\pi$
$84$		0			0
$85$			872536.i			1.42078i
$86$	136175.	+	531012.i	0.214093	+	0.834851i
$87$		0			0
$88$	461874.	+	492712.i	0.677760	+	0.723011i
$89$	1.13336e6			1.60767			0.803834	−	0.594854i	$-0.202790\pi$
$89$	1.13336e6			1.60767			0.803834	+	0.594854i	$0.202790\pi$
$90$		0			0
$91$	−384690.			−0.510490
$92$	−440270.	−	801960.i	−0.565400	−	1.02989i
$93$		0			0
$94$	275321.	−	70604.6i	0.331479	−	0.0850060i
$95$			992359.i			1.15744i
$96$		0			0
$97$	867708.			0.950733			0.475366	−	0.879788i	$-0.342315\pi$
$97$	867708.			0.950733			0.475366	+	0.879788i	$0.342315\pi$
$98$	515662.	+	2.01081e6i	0.547882	+	2.13645i
$99$		0			0
$100$	−237811.	+	130557.i	−0.237811	+	0.130557i
$101$		−	739825.i		−	0.718066i	−0.933325	−	0.359033i	$-0.883106\pi$
$101$		−	739825.i		−	0.718066i	0.933325	−	0.359033i	$-0.116894\pi$
$102$		0			0
$103$			64405.8i			0.0589405i	0.999566	+	0.0294702i	$0.00938202\pi$
$103$			64405.8i			0.0589405i	−0.999566	+	0.0294702i	$0.990618\pi$
$104$	233991.	−	219346.i	0.208017	−	0.194998i
$105$		0			0
$106$	−1.45329e6	+	372688.i	−1.22021	+	0.312916i
$107$	−1.94056e6			−1.58408			−0.792039	−	0.610471i	$-0.790980\pi$
$107$	−1.94056e6			−1.58408			−0.792039	+	0.610471i	$0.790980\pi$
$108$		0			0
$109$		−	2.04154e6i		−	1.57644i	−0.615391	−	0.788222i	$-0.711002\pi$
$109$		−	2.04154e6i		−	1.57644i	0.615391	−	0.788222i	$-0.288998\pi$
$110$	−1.09069e6	+	279703.i	−0.819455	+	0.210145i
$111$		0			0
$112$	−2.12225e6	−	1.35030e6i	−1.51057	−	0.961120i
$113$	−1.34568e6			−0.932621			−0.466310	−	0.884621i	$-0.654417\pi$
$113$	−1.34568e6			−0.932621			−0.466310	+	0.884621i	$0.654417\pi$
$114$		0			0
$115$	1.52533e6			1.00293
$116$	−619708.	−	1.12881e6i	−0.397021	−	0.723179i
$117$		0			0
$118$	−513845.	−	2.00373e6i	−0.312742	−	1.21953i
$119$			5.02163e6i			2.97991i
$120$		0			0
$121$	−31704.5			−0.0178964
$122$	−2.81462e6	+	721793.i	−1.55003	+	0.397496i
$123$		0			0
$124$	312425.	+	569087.i	0.163863	+	0.298479i
$125$		−	2.11959e6i		−	1.08523i
$126$		0			0
$127$			1.11987e6i			0.546707i	0.961914	+	0.273354i	$0.0881329\pi$
$127$			1.11987e6i			0.546707i	−0.961914	+	0.273354i	$0.911867\pi$
$128$	2.06081e6	−	388748.i	0.982669	−	0.185370i
$129$		0			0
$130$	132832.	+	517976.i	0.0604607	+	0.235765i
$131$	2.33559e6			1.03892			0.519461	−	0.854494i	$-0.326133\pi$
$131$	2.33559e6			1.03892			0.519461	+	0.854494i	$0.326133\pi$
$132$		0			0
$133$			5.71123e6i			2.42759i
$134$	570788.	+	2.22578e6i	0.237225	+	0.925054i
$135$		0			0
$136$	−2.86328e6	−	3.05445e6i	−1.13827	−	1.21427i
$137$	−757982.			−0.294779			−0.147390	−	0.989079i	$-0.547087\pi$
$137$	−757982.			−0.294779			−0.147390	+	0.989079i	$0.547087\pi$
$138$		0			0
$139$	4.25539e6			1.58451			0.792256	−	0.610189i	$-0.208907\pi$
$139$	4.25539e6			1.58451			0.792256	+	0.610189i	$0.208907\pi$
$140$	3.67629e6	−	2.01826e6i	1.33976	−	0.735518i
$141$		0			0
$142$	2.62375e6	−	672847.i	0.916342	−	0.234991i
$143$		−	826266.i		−	0.282561i
$144$		0			0
$145$	2.14700e6			0.704251
$146$	380911.	+	1.48535e6i	0.122395	+	0.477277i
$147$		0			0
$148$	308233.	+	561452.i	0.0950812	+	0.173192i
$149$		−	5.93993e6i		−	1.79565i	−0.440348	−	0.897827i	$-0.645145\pi$
$149$		−	5.93993e6i		−	1.79565i	0.440348	−	0.897827i	$-0.354855\pi$
$150$		0			0
$151$			2.63498e6i			0.765327i	0.923888	+	0.382663i	$0.124993\pi$
$151$			2.63498e6i			0.765327i	−0.923888	+	0.382663i	$0.875007\pi$
$152$	−3.25648e6	−	3.47391e6i	−0.927296	−	0.989208i
$153$		0			0
$154$	−6.27717e6	+	1.60975e6i	−1.71871	+	0.440753i
$155$	−1.08241e6			−0.290666
$156$		0			0
$157$		−	4.85496e6i		−	1.25455i	−0.778800	−	0.627273i	$-0.784171\pi$
$157$		−	4.85496e6i		−	1.25455i	0.778800	−	0.627273i	$-0.215829\pi$
$158$	−488504.	+	125274.i	−0.123850	+	0.0317607i
$159$		0			0
$160$	−1.08535e6	+	3.32381e6i	−0.264978	+	0.811477i
$161$	8.77859e6			2.10352
$162$		0			0
$163$	−340073.			−0.0785254			−0.0392627	−	0.999229i	$-0.512501\pi$
$163$	−340073.			−0.0785254			−0.0392627	+	0.999229i	$0.512501\pi$
$164$	−2.36591e6	+	1.29887e6i	−0.536373	+	0.294465i
$165$		0			0
$166$	819047.	+	3.19386e6i	0.179054	+	0.698218i
$167$			1.52390e6i			0.327196i	0.986527	+	0.163598i	$0.0523100\pi$
$167$			1.52390e6i			0.327196i	−0.986527	+	0.163598i	$0.947690\pi$
$168$		0			0
$169$	4.43441e6			0.918704
$170$	6.76150e6	−	1.73395e6i	1.37625	−	0.352931i
$171$		0			0
$172$	3.84433e6	−	2.11051e6i	0.755501	−	0.414765i
$173$		−	256058.i		−	0.0494538i	−0.999694	−	0.0247269i	$-0.992128\pi$
$173$		−	256058.i		−	0.0494538i	0.999694	−	0.0247269i	$-0.00787162\pi$
$174$		0			0
$175$		−	2.60318e6i		−	0.485725i
$176$	2.90029e6	−	4.55832e6i	0.531989	−	0.836117i
$177$		0			0
$178$	−2.25226e6	−	8.78265e6i	−0.399355	−	1.55728i
$179$	−5.74628e6			−1.00191			−0.500954	−	0.865474i	$-0.667017\pi$
$179$	−5.74628e6			−1.00191			−0.500954	+	0.865474i	$0.667017\pi$
$180$		0			0
$181$			3.66899e6i			0.618744i	0.950941	+	0.309372i	$0.100119\pi$
$181$			3.66899e6i			0.618744i	−0.950941	+	0.309372i	$0.899881\pi$
$182$	764477.	+	2.98106e6i	0.126809	+	0.494489i
$183$		0			0
$184$	−5.33965e6	+	5.00546e6i	−0.857156	+	0.803509i
$185$	−1.06788e6			−0.168659
$186$		0			0
$187$	−1.07858e7			−1.64941
$188$	−1.09427e6	−	1.99322e6i	−0.164683	−	0.299973i
$189$		0			0
$190$	7.69003e6	−	1.97207e6i	1.12116	−	0.287515i
$191$		−	5.18600e6i		−	0.744273i	−0.928178	−	0.372137i	$-0.878625\pi$
$191$		−	5.18600e6i		−	0.744273i	0.928178	−	0.372137i	$-0.121375\pi$
$192$		0			0
$193$	−9.03431e6			−1.25668			−0.628338	−	0.777941i	$-0.716264\pi$
$193$	−9.03431e6			−1.25668			−0.628338	+	0.777941i	$0.716264\pi$
$194$	−1.72436e6	−	6.72409e6i	−0.236168	−	0.920933i
$195$		0			0
$196$	1.45575e7	−	7.99199e6i	1.93339	−	1.06142i
$197$			5.99880e6i			0.784631i	0.919831	+	0.392316i	$0.128326\pi$
$197$			5.99880e6i			0.784631i	−0.919831	+	0.392316i	$0.871674\pi$
$198$		0			0
$199$		−	6.14747e6i		−	0.780077i	−0.920799	−	0.390038i	$-0.872462\pi$
$199$		−	6.14747e6i		−	0.780077i	0.920799	−	0.390038i	$-0.127538\pi$
$200$	1.48431e6	+	1.58341e6i	0.185538	+	0.197926i
$201$		0			0
$202$	−5.73308e6	+	1.47022e6i	−0.695559	+	0.178372i
$203$	1.23564e7			1.47708
$204$		0			0
$205$		−	4.49997e6i		−	0.522334i
$206$	499097.	−	127991.i	0.0570930	−	0.0146412i
$207$		0			0
$208$	−2.16477e6	−	1.37736e6i	−0.240559	−	0.153058i
$209$	−1.22670e7			−1.34369
$210$		0			0
$211$	−1.99915e6			−0.212813			−0.106407	−	0.994323i	$-0.533935\pi$
$211$	−1.99915e6			−0.212813			−0.106407	+	0.994323i	$0.533935\pi$
$212$	5.77610e6	+	1.05213e7i	0.606216	+	1.10423i
$213$		0			0
$214$	3.85639e6	+	1.50379e7i	0.393495	+	1.53443i
$215$			7.31192e6i			0.735726i
$216$		0			0
$217$	−6.22947e6			−0.609638
$218$	−1.58204e7	+	4.05706e6i	−1.52703	+	0.391599i
$219$		0			0
$220$	4.33497e6	+	7.89622e6i	0.407116	+	0.741568i
$221$			5.12224e6i			0.474551i
$222$		0			0
$223$		−	1.20101e6i		−	0.108301i	−0.998533	−	0.0541504i	$-0.982755\pi$
$223$		−	1.20101e6i		−	0.108301i	0.998533	−	0.0541504i	$-0.0172450\pi$
$224$	−6.24640e6	+	1.91292e7i	−0.555758	+	1.70197i
$225$		0			0
$226$	2.67420e6	+	1.04280e7i	0.231669	+	0.903389i
$227$	−1.81763e6			−0.155392			−0.0776958	−	0.996977i	$-0.524756\pi$
$227$	−1.81763e6			−0.155392			−0.0776958	+	0.996977i	$0.524756\pi$
$228$		0			0
$229$		−	1.25720e7i		−	1.04688i	−0.852062	−	0.523440i	$-0.824648\pi$
$229$		−	1.25720e7i		−	1.04688i	0.852062	−	0.523440i	$-0.175352\pi$
$230$	−3.03122e6	−	1.18202e7i	−0.249134	−	0.971493i
$231$		0			0
$232$	−7.51590e6	+	7.04550e6i	−0.601890	+	0.564219i
$233$	−1.44902e7			−1.14553			−0.572764	−	0.819720i	$-0.694129\pi$
$233$	−1.44902e7			−1.14553			−0.572764	+	0.819720i	$0.694129\pi$
$234$		0			0
$235$	3.79112e6			0.292121
$236$	−1.45062e7	+	7.96382e6i	−1.10362	+	0.605878i
$237$		0			0
$238$	3.89138e7	−	9.97924e6i	2.88651	−	0.740230i
$239$		−	2.40777e7i		−	1.76369i	−0.471542	−	0.881843i	$-0.656303\pi$
$239$		−	2.40777e7i		−	1.76369i	0.471542	−	0.881843i	$-0.343697\pi$
$240$		0			0
$241$	−7.20745e6			−0.514909			−0.257454	−	0.966290i	$-0.582884\pi$
$241$	−7.20745e6			−0.514909			−0.257454	+	0.966290i	$0.582884\pi$
$242$	63004.9	+	245686.i	0.00444557	+	0.0173354i
$243$		0			0
$244$	1.11867e7	+	2.03768e7i	0.770074	+	1.40270i
$245$			2.76885e7i			1.88278i
$246$		0			0
$247$			5.82566e6i			0.386593i
$248$	3.78913e6	−	3.55198e6i	0.248419	−	0.232871i
$249$		0			0
$250$	−1.64252e7	+	4.21216e6i	−1.05122	+	0.269578i
$251$	−9.59331e6			−0.606662			−0.303331	−	0.952885i	$-0.598099\pi$
$251$	−9.59331e6			−0.606662			−0.303331	+	0.952885i	$0.598099\pi$
$252$		0			0
$253$			1.88553e7i			1.16432i
$254$	8.67812e6	−	2.22546e6i	0.529571	−	0.135806i
$255$		0			0
$256$	−7.10785e6	−	1.51972e7i	−0.423661	−	0.905821i
$257$	1.87001e7			1.10165			0.550827	−	0.834620i	$-0.314312\pi$
$257$	1.87001e7			1.10165			0.550827	+	0.834620i	$0.314312\pi$
$258$		0			0
$259$	−6.14589e6			−0.353741
$260$	3.74995e6	−	2.05870e6i	0.213356	−	0.117131i
$261$		0			0
$262$	−4.64141e6	−	1.80991e7i	−0.258075	−	1.00636i
$263$		−	1.37555e7i		−	0.756155i	−0.925774	−	0.378077i	$-0.876585\pi$
$263$		−	1.37555e7i		−	0.756155i	0.925774	−	0.378077i	$-0.123415\pi$
$264$		0			0
$265$	−2.00115e7			−1.07533
$266$	4.42577e7	−	1.13497e7i	2.35150	−	0.603029i
$267$		0			0
$268$	1.61138e7	−	8.84635e6i	0.837130	−	0.459579i
$269$			2.28855e7i			1.17572i	0.808963	+	0.587860i	$0.200029\pi$
$269$			2.28855e7i			1.17572i	−0.808963	+	0.587860i	$0.799971\pi$
$270$		0			0
$271$			148033.i			0.00743788i	0.999993	+	0.00371894i	$0.00118378\pi$
$271$			148033.i			0.00743788i	−0.999993	+	0.00371894i	$0.998816\pi$
$272$	−1.79796e7	+	2.82582e7i	−0.893457	+	1.40423i
$273$		0			0
$274$	1.50630e6	+	5.87379e6i	0.0732251	+	0.285540i
$275$	5.59131e6			0.268853
$276$		0			0
$277$		−	3.17460e7i		−	1.49365i	−0.665019	−	0.746827i	$-0.731576\pi$
$277$		−	3.17460e7i		−	1.49365i	0.665019	−	0.746827i	$-0.268424\pi$
$278$	−8.45654e6	−	3.29761e7i	−0.393603	−	1.53485i
$279$		0			0
$280$	−2.29457e7	−	2.44777e7i	−1.04527	−	1.11506i
$281$	1.43992e7			0.648961			0.324480	−	0.945892i	$-0.394811\pi$
$281$	1.43992e7			0.648961			0.324480	+	0.945892i	$0.394811\pi$
$282$		0			0
$283$	−1.18066e7			−0.520913			−0.260456	−	0.965486i	$-0.583873\pi$
$283$	−1.18066e7			−0.520913			−0.260456	+	0.965486i	$0.583873\pi$
$284$	−1.04281e7	−	1.89950e7i	−0.455251	−	0.829247i
$285$		0			0
$286$	−6.40294e6	+	1.64200e6i	−0.273704	+	0.0701900i
$287$		−	2.58983e7i		−	1.09553i
$288$		0			0
$289$	4.27265e7			1.77013
$290$	−4.26662e6	−	1.66376e7i	−0.174940	−	0.682177i
$291$		0			0
$292$	1.07534e7	−	5.90354e6i	0.431914	−	0.237118i
$293$		−	9.37604e6i		−	0.372749i	−0.982479	−	0.186374i	$-0.940326\pi$
$293$		−	9.37604e6i		−	0.372749i	0.982479	−	0.186374i	$-0.0596738\pi$
$294$		0			0
$295$		−	2.75909e7i		−	1.07473i
$296$	3.73829e6	−	3.50432e6i	0.144145	−	0.135123i
$297$		0			0
$298$	−4.60300e7	+	1.18041e7i	−1.73937	+	0.446052i
$299$	8.95448e6			0.334986
$300$		0			0
$301$			4.20816e7i			1.54310i
$302$	2.04191e7	−	5.23638e6i	0.741338	−	0.190112i
$303$		0			0
$304$	−2.04487e7	+	3.21388e7i	−0.727856	+	1.14396i
$305$	−3.87567e7			−1.36599
$306$		0			0
$307$	3.38190e7			1.16881			0.584407	−	0.811461i	$-0.301327\pi$
$307$	3.38190e7			1.16881			0.584407	+	0.811461i	$0.301327\pi$
$308$	2.49487e7	+	4.54444e7i	0.853876	+	1.55535i
$309$		0			0
$310$	2.15101e6	+	8.38783e6i	0.0722035	+	0.281556i
$311$		−	4.76754e7i		−	1.58494i	−0.609910	−	0.792470i	$-0.708795\pi$
$311$		−	4.76754e7i		−	1.58494i	0.609910	−	0.792470i	$-0.291205\pi$
$312$		0			0
$313$	3.27300e7			1.06736			0.533682	−	0.845685i	$-0.320808\pi$
$313$	3.27300e7			1.06736			0.533682	+	0.845685i	$0.320808\pi$
$314$	−3.76223e7	+	9.64803e6i	−1.21522	+	0.311637i
$315$		0			0
$316$	1.94156e6	+	3.53659e6i	0.0615304	+	0.112079i
$317$			8.57331e6i			0.269135i	0.990904	+	0.134568i	$0.0429646\pi$
$317$			8.57331e6i			0.269135i	−0.990904	+	0.134568i	$0.957035\pi$
$318$		0			0
$319$			2.65400e7i			0.817578i
$320$	2.79139e7	+	1.80538e6i	0.851864	+	0.0550958i
$321$		0			0
$322$	−1.74453e7	−	6.80274e7i	−0.522529	−	2.03759i
$323$	7.60464e7			2.25668
$324$		0			0
$325$		−	2.65534e6i		−	0.0773517i
$326$	675812.	+	2.63531e6i	0.0195062	+	0.0760641i
$327$		0			0
$328$	1.47669e7	+	1.57529e7i	0.418474	+	0.446414i
$329$	2.18187e7			0.612689
$330$		0			0
$331$	6.67715e6			0.184123			0.0920614	−	0.995753i	$-0.470654\pi$
$331$	6.67715e6			0.184123			0.0920614	+	0.995753i	$0.470654\pi$
$332$	2.31223e7	−	1.26940e7i	0.631855	−	0.346884i
$333$		0			0
$334$	1.18091e7	−	3.02838e6i	0.316940	−	0.0812777i
$335$			3.06485e7i			0.815219i
$336$		0			0
$337$	−118836.			−0.00310498			−0.00155249	−	0.999999i	$-0.500494\pi$
$337$	−118836.			−0.00310498			−0.00155249	+	0.999999i	$0.500494\pi$
$338$	−8.81229e6	−	3.43633e7i	−0.228212	−	0.889908i
$339$		0			0
$340$	−2.68736e7	−	4.89507e7i	−0.683737	−	1.24544i
$341$		−	1.33801e7i		−	0.337440i
$342$		0			0
$343$			8.71032e7i			2.15850i
$344$	−2.39945e7	−	2.55965e7i	−0.589436	−	0.628790i
$345$		0			0
$346$	−1.98426e6	+	508852.i	−0.0479037	+	0.0122847i
$347$	−3.54776e7			−0.849114			−0.424557	−	0.905401i	$-0.639570\pi$
$347$	−3.54776e7			−0.849114			−0.424557	+	0.905401i	$0.639570\pi$
$348$		0			0
$349$			4.47575e7i			1.05290i	0.850205	+	0.526452i	$0.176478\pi$
$349$			4.47575e7i			1.05290i	−0.850205	+	0.526452i	$0.823522\pi$
$350$	−2.01727e7	+	5.17318e6i	−0.470500	+	0.120657i
$351$		0			0
$352$	−4.10872e7	−	1.34165e7i	−0.942059	−	0.307617i
$353$	−4.00069e7			−0.909518			−0.454759	−	0.890615i	$-0.650275\pi$
$353$	−4.00069e7			−0.909518			−0.454759	+	0.890615i	$0.650275\pi$
$354$		0			0
$355$	3.61285e7			0.807542
$356$	−6.35831e7	+	3.49067e7i	−1.40926	+	0.773675i
$357$		0			0
$358$	1.14193e7	+	4.45294e7i	0.248881	+	0.970504i
$359$			3.62987e7i			0.784527i	0.919853	+	0.392263i	$0.128308\pi$
$359$			3.62987e7i			0.784527i	−0.919853	+	0.392263i	$0.871692\pi$
$360$		0			0
$361$	3.94437e7			0.838410
$362$	2.84319e7	−	7.29122e6i	0.599350	−	0.153700i
$363$		0			0
$364$	2.15818e7	−	1.18482e7i	0.447489	−	0.245669i
$365$			2.04530e7i			0.420609i
$366$		0			0
$367$		−	3.65053e7i		−	0.738512i	−0.929328	−	0.369256i	$-0.879613\pi$
$367$		−	3.65053e7i		−	0.738512i	0.929328	−	0.369256i	$-0.120387\pi$
$368$	4.93998e7	+	3.14312e7i	0.991246	+	0.630692i
$369$		0			0
$370$	2.12215e6	+	8.27529e6i	0.0418959	+	0.163372i
$371$	−1.15170e8			−2.25537
$372$		0			0
$373$		−	4.55269e7i		−	0.877287i	−0.898661	−	0.438644i	$-0.855459\pi$
$373$		−	4.55269e7i		−	0.877287i	0.898661	−	0.438644i	$-0.144541\pi$
$374$	2.14342e7	+	8.35820e7i	0.409724	+	1.59771i
$375$		0			0
$376$	−1.32714e7	+	1.24408e7i	−0.249662	+	0.234037i
$377$	1.26040e7			0.235225
$378$		0			0
$379$	3.98656e7			0.732286			0.366143	−	0.930559i	$-0.380678\pi$
$379$	3.98656e7			0.732286			0.366143	+	0.930559i	$0.380678\pi$
$380$	−3.05641e7	−	5.56730e7i	−0.557007	−	1.01460i
$381$		0			0
$382$	−4.01876e7	+	1.03059e7i	−0.720945	+	0.184882i
$383$			7.17905e7i			1.27782i	0.769280	+	0.638912i	$0.220615\pi$
$383$			7.17905e7i			1.27782i	−0.769280	+	0.638912i	$0.779385\pi$
$384$		0			0
$385$	−8.64353e7			−1.51464
$386$	1.79535e7	+	7.00091e7i	0.312167	+	1.21729i
$387$		0			0
$388$	−4.86799e7	+	2.67249e7i	−0.833401	+	0.457532i
$389$			4.20051e7i			0.713598i	0.934181	+	0.356799i	$0.116132\pi$
$389$			4.20051e7i			0.713598i	−0.934181	+	0.356799i	$0.883868\pi$
$390$		0			0
$391$		−	1.16889e8i		−	1.95543i
$392$	−9.08614e7	−	9.69278e7i	−1.50842	−	1.60913i
$393$		0			0
$394$	4.64862e7	−	1.19211e7i	0.760038	−	0.194908i
$395$	−6.72660e6			−0.109145
$396$		0			0
$397$		−	2.21160e7i		−	0.353456i	−0.984260	−	0.176728i	$-0.943449\pi$
$397$		−	2.21160e7i		−	0.353456i	0.984260	−	0.176728i	$-0.0565513\pi$
$398$	−4.76383e7	+	1.22166e7i	−0.755626	+	0.193776i
$399$		0			0
$400$	9.32053e6	−	1.46489e7i	0.145633	−	0.228889i
$401$	8.95337e7			1.38852			0.694262	−	0.719722i	$-0.255731\pi$
$401$	8.95337e7			1.38852			0.694262	+	0.719722i	$0.255731\pi$
$402$		0			0
$403$	−6.35428e6			−0.0970848
$404$	2.27862e7	+	4.15054e7i	0.345563	+	0.629449i
$405$		0			0
$406$	−2.45553e7	−	9.57528e7i	−0.366916	−	1.43078i
$407$		−	1.32006e7i		−	0.195799i
$408$		0			0
$409$	−4.01175e7			−0.586359			−0.293179	−	0.956057i	$-0.594713\pi$
$409$	−4.01175e7			−0.586359			−0.293179	+	0.956057i	$0.594713\pi$
$410$	−3.48714e7	+	8.94258e6i	−0.505962	+	0.129751i
$411$		0			0
$412$	−1.98366e6	−	3.61327e6i	−0.0283646	−	0.0516665i
$413$		−	1.58791e8i		−	2.25412i
$414$		0			0
$415$			4.39787e7i			0.615316i
$416$	−6.37156e6	+	1.95125e7i	−0.0885045	+	0.271040i
$417$		0			0
$418$	2.43776e7	+	9.50601e7i	0.333782	+	1.30158i
$419$	−1.49462e7			−0.203184			−0.101592	−	0.994826i	$-0.532394\pi$
$419$	−1.49462e7			−0.203184			−0.101592	+	0.994826i	$0.532394\pi$
$420$		0			0
$421$			2.40883e7i			0.322819i	0.986887	+	0.161410i	$0.0516040\pi$
$421$			2.40883e7i			0.322819i	−0.986887	+	0.161410i	$0.948396\pi$
$422$	3.97283e6	+	1.54919e7i	0.0528643	+	0.206143i
$423$		0			0
$424$	7.00533e7	−	6.56689e7i	0.919033	−	0.861513i
$425$	−3.46620e7			−0.451530
$426$		0			0
$427$	−2.23053e8			−2.86499
$428$	1.08869e8	−	5.97682e7i	1.38858	−	0.762323i
$429$		0			0
$430$	5.66619e7	−	1.45306e7i	0.712665	−	0.182759i
$431$			1.20299e8i			1.50255i	0.659990	+	0.751275i	$0.270561\pi$
$431$			1.20299e8i			1.50255i	−0.659990	+	0.751275i	$0.729439\pi$
$432$		0			0
$433$	4.84699e7			0.597047			0.298524	−	0.954402i	$-0.403506\pi$
$433$	4.84699e7			0.597047			0.298524	+	0.954402i	$0.403506\pi$
$434$	1.23795e7	+	4.82737e7i	0.151438	+	0.590529i
$435$		0			0
$436$	6.28783e7	+	1.14534e8i	0.758649	+	1.38189i
$437$		−	1.32941e8i		−	1.59300i
$438$		0			0
$439$			1.27798e8i			1.51054i	0.655414	+	0.755270i	$0.272494\pi$
$439$			1.27798e8i			1.51054i	−0.655414	+	0.755270i	$0.727506\pi$
$440$	5.25751e7	−	4.92845e7i	0.617194	−	0.578566i
$441$		0			0
$442$	3.96935e7	−	1.01792e7i	0.459677	−	0.117882i
$443$	1.52264e8			1.75140			0.875699	−	0.482857i	$-0.160401\pi$
$443$	1.52264e8			1.75140			0.875699	+	0.482857i	$0.160401\pi$
$444$		0			0
$445$		−	1.20935e8i		−	1.37238i
$446$	−9.30692e6	+	2.38671e6i	−0.104906	+	0.0269026i
$447$		0			0
$448$	1.60650e8	+	1.03903e7i	1.78668	+	0.115557i
$449$	−864756.			−0.00955332			−0.00477666	−	0.999989i	$-0.501520\pi$
$449$	−864756.			−0.00955332			−0.00477666	+	0.999989i	$0.501520\pi$
$450$		0			0
$451$	5.56263e7			0.606387
$452$	7.54946e7	−	4.14460e7i	0.817525	−	0.448815i
$453$		0			0
$454$	3.61209e6	+	1.40852e7i	0.0386003	+	0.150521i
$455$			4.10486e7i			0.435777i
$456$		0			0
$457$	−4.59684e7			−0.481627			−0.240813	−	0.970571i	$-0.577414\pi$
$457$	−4.59684e7			−0.481627			−0.240813	+	0.970571i	$0.577414\pi$
$458$	−9.74234e7	+	2.49837e7i	−1.01407	+	0.260052i
$459$		0			0
$460$	−8.55735e7	+	4.69793e7i	−0.879156	+	0.482650i
$461$		−	4.04162e7i		−	0.412527i	−0.978497	−	0.206263i	$-0.933870\pi$
$461$		−	4.04162e7i		−	0.412527i	0.978497	−	0.206263i	$-0.0661304\pi$
$462$		0			0
$463$		−	1.46066e8i		−	1.47165i	−0.677170	−	0.735826i	$-0.736794\pi$
$463$		−	1.46066e8i		−	1.47165i	0.677170	−	0.735826i	$-0.263206\pi$
$464$	6.95333e7	+	4.42414e7i	0.696047	+	0.442868i
$465$		0			0
$466$	2.87956e7	+	1.12288e8i	0.284557	+	1.10962i
$467$	−1.57779e7			−0.154917			−0.0774586	−	0.996996i	$-0.524681\pi$
$467$	−1.57779e7			−0.154917			−0.0774586	+	0.996996i	$0.524681\pi$
$468$		0			0
$469$			1.76388e8i			1.70982i
$470$	−7.53390e6	−	2.93783e7i	−0.0725649	−	0.282965i
$471$		0			0
$472$	9.05411e7	+	9.65862e7i	0.861033	+	0.918521i
$473$	−9.03860e7			−0.854118
$474$		0			0
$475$	−3.94220e7			−0.367839
$476$	−1.54663e8	−	2.81722e8i	−1.43406	−	2.61216i
$477$		0			0
$478$	−1.86584e8	+	4.78485e7i	−1.70841	+	0.438111i
$479$			4.67045e7i			0.424964i	0.977165	+	0.212482i	$0.0681547\pi$
$479$			4.67045e7i			0.424964i	−0.977165	+	0.212482i	$0.931845\pi$
$480$		0			0
$481$	−6.26903e6			−0.0563333
$482$	1.43230e7	+	5.58523e7i	0.127907	+	0.498769i
$483$		0			0
$484$	1.77868e6	−	976480.i	0.0156877	−	0.00861246i
$485$		−	9.25893e7i		−	0.811588i
$486$		0			0
$487$		−	1.94294e8i		−	1.68218i	−0.540893	−	0.841091i	$-0.681914\pi$
$487$		−	1.94294e8i		−	1.68218i	0.540893	−	0.841091i	$-0.318086\pi$
$488$	1.35674e8	−	1.27182e8i	1.16745	−	1.09438i
$489$		0			0
$490$	2.14565e8	−	5.50240e7i	1.82377	−	0.467696i
$491$	−6.39679e7			−0.540403			−0.270202	−	0.962804i	$-0.587090\pi$
$491$	−6.39679e7			−0.540403			−0.270202	+	0.962804i	$0.587090\pi$
$492$		0			0
$493$		−	1.64528e8i		−	1.37309i
$494$	4.51445e7	−	1.15771e7i	0.374476	−	0.0960323i
$495$		0			0
$496$	−3.50551e7	−	2.23042e7i	−0.287281	−	0.182786i
$497$	2.07927e8			1.69372
$498$		0			0
$499$	−7.20980e7			−0.580259			−0.290129	−	0.956987i	$-0.593698\pi$
$499$	−7.20980e7			−0.580259			−0.290129	+	0.956987i	$0.593698\pi$
$500$	6.52822e7	+	1.18913e8i	0.522257	+	0.951301i
$501$		0			0
$502$	1.90643e7	+	7.43409e7i	0.150699	+	0.587647i
$503$		−	3.67002e6i		−	0.0288380i	−0.999896	−	0.0144190i	$-0.995410\pi$
$503$		−	3.67002e6i		−	0.0288380i	0.999896	−	0.0144190i	$-0.00458987\pi$
$504$		0			0
$505$	−7.89434e7			−0.612973
$506$	1.46114e8	−	3.74703e7i	1.12782	−	0.289224i
$507$		0			0
$508$	−3.44912e7	−	6.28263e7i	−0.263098	−	0.479237i
$509$		−	1.14384e7i		−	0.0867384i	−0.999059	−	0.0433692i	$-0.986191\pi$
$509$		−	1.14384e7i		−	0.0867384i	0.999059	−	0.0433692i	$-0.0138092\pi$
$510$		0			0
$511$			1.17711e8i			0.882176i
$512$	−1.03641e8	+	8.52811e7i	−0.772189	+	0.635393i
$513$		0			0
$514$	−3.71619e7	−	1.44912e8i	−0.273658	−	1.06712i
$515$	6.87246e6			0.0503142
$516$		0			0
$517$			4.68637e7i			0.339129i
$518$	1.22134e7	+	4.76260e7i	0.0878716	+	0.342653i
$519$		0			0
$520$	−2.34055e7	−	2.49682e7i	−0.166459	−	0.177573i
$521$	2.14910e8			1.51965			0.759826	−	0.650127i	$-0.225284\pi$
$521$	2.14910e8			1.51965			0.759826	+	0.650127i	$0.225284\pi$
$522$		0			0
$523$	1.77335e7			0.123962			0.0619811	−	0.998077i	$-0.480258\pi$
$523$	1.77335e7			0.123962			0.0619811	+	0.998077i	$0.480258\pi$
$524$	−1.31031e8	+	7.19348e7i	−0.910707	+	0.499972i
$525$		0			0
$526$	−1.06595e8	+	2.73357e7i	−0.732454	+	0.187834i
$527$			8.29468e7i			0.566719i
$528$		0			0
$529$	−5.63042e7			−0.380342
$530$	3.97679e7	+	1.55074e8i	0.267119	+	1.04162i
$531$		0			0
$532$	−1.75903e8	−	3.20410e8i	−1.16825	−	2.12799i
$533$		−	2.64172e7i		−	0.174464i
$534$		0			0
$535$			2.07069e8i			1.35224i
$536$	−1.00575e8	−	1.07290e8i	−0.653122	−	0.696729i
$537$		0			0
$538$	1.77345e8	−	4.54793e7i	1.13887	−	0.292056i
$539$	−3.42270e8			−2.18576
$540$		0			0
$541$		−	1.19069e8i		−	0.751984i	−0.926623	−	0.375992i	$-0.877302\pi$
$541$		−	1.19069e8i		−	0.751984i	0.926623	−	0.375992i	$-0.122698\pi$
$542$	1.14714e6	−	294178.i	0.00720475	−	0.00184762i
$543$		0			0
$544$	2.54710e8	+	8.31723e7i	1.58216	+	0.516633i
$545$	−2.17844e8			−1.34572
$546$		0			0
$547$	3.01999e8			1.84520			0.922599	−	0.385760i	$-0.126061\pi$
$547$	3.01999e8			1.84520			0.922599	+	0.385760i	$0.126061\pi$
$548$	4.25240e7	−	2.33454e7i	0.258400	−	0.141860i
$549$		0			0
$550$	−1.11113e7	−	4.33284e7i	−0.0667849	−	0.260426i
$551$		−	1.87123e8i		−	1.11859i
$552$		0			0
$553$	−3.87130e7			−0.228918
$554$	−2.46008e8	+	6.30874e7i	−1.44684	+	0.371033i
$555$		0			0
$556$	−2.38735e8	+	1.31064e8i	−1.38896	+	0.762532i
$557$			2.12664e8i			1.23063i	0.788281	+	0.615315i	$0.210971\pi$
$557$			2.12664e8i			1.23063i	−0.788281	+	0.615315i	$0.789029\pi$
$558$		0			0
$559$			4.29248e7i			0.245738i
$560$	−1.44085e8	+	2.26456e8i	−0.820455	+	1.28949i
$561$		0			0
$562$	−2.86148e7	−	1.11583e8i	−0.161206	−	0.628620i
$563$	1.91234e8			1.07162			0.535809	−	0.844339i	$-0.320007\pi$
$563$	1.91234e8			1.07162			0.535809	+	0.844339i	$0.320007\pi$
$564$		0			0
$565$			1.43591e8i			0.796126i
$566$	2.34627e7	+	9.14921e7i	0.129398	+	0.504585i
$567$		0			0
$568$	−1.26473e8	+	1.18558e8i	−0.690167	+	0.646972i
$569$	−2.20873e8			−1.19896			−0.599481	−	0.800389i	$-0.704626\pi$
$569$	−2.20873e8			−1.19896			−0.599481	+	0.800389i	$0.704626\pi$
$570$		0			0
$571$	−1.58447e8			−0.851092			−0.425546	−	0.904937i	$-0.639918\pi$
$571$	−1.58447e8			−0.851092			−0.425546	+	0.904937i	$0.639918\pi$
$572$	2.54485e7	+	4.63549e7i	0.135980	+	0.247690i
$573$		0			0
$574$	−2.00692e8	+	5.14664e7i	−1.06119	+	0.272137i
$575$			6.05945e7i			0.318735i
$576$		0			0
$577$	3.14760e8			1.63852			0.819260	−	0.573422i	$-0.194385\pi$
$577$	3.14760e8			1.63852			0.819260	+	0.573422i	$0.194385\pi$
$578$	−8.49084e7	−	3.31099e8i	−0.439711	−	1.71464i
$579$		0			0
$580$	−1.20450e8	+	6.61262e7i	−0.617338	+	0.338914i
$581$			2.53107e8i			1.29055i
$582$		0			0
$583$		−	2.47371e8i		−	1.24837i
$584$	−6.71177e7	−	7.15989e7i	−0.336976	−	0.359474i
$585$		0			0
$586$	−7.26572e7	+	1.86326e7i	−0.361065	+	0.0925933i
$587$	1.93813e8			0.958227			0.479114	−	0.877753i	$-0.340958\pi$
$587$	1.93813e8			0.958227			0.479114	+	0.877753i	$0.340958\pi$
$588$		0			0
$589$			9.43377e7i			0.461678i
$590$	−2.13809e8	+	5.48301e7i	−1.04104	+	0.266970i
$591$		0			0
$592$	−3.45848e7	−	2.20050e7i	−0.166694	−	0.106061i
$593$	−1.04977e8			−0.503417			−0.251709	−	0.967803i	$-0.580992\pi$
$593$	−1.04977e8			−0.503417			−0.251709	+	0.967803i	$0.580992\pi$
$594$		0			0
$595$	5.35835e8			2.54378
$596$	1.82946e8	+	3.33240e8i	0.864142	+	1.57405i
$597$		0			0
$598$	−1.77948e7	−	6.93904e7i	−0.0832127	−	0.324486i
$599$			2.95910e8i			1.37683i	0.725318	+	0.688414i	$0.241693\pi$
$599$			2.95910e8i			1.37683i	−0.725318	+	0.688414i	$0.758307\pi$
$600$		0			0
$601$	3.27138e8			1.50698			0.753490	−	0.657459i	$-0.228369\pi$
$601$	3.27138e8			1.50698			0.753490	+	0.657459i	$0.228369\pi$
$602$	3.26101e8	−	8.36268e7i	1.49473	−	0.383315i
$603$		0			0
$604$	−8.11559e7	−	1.47827e8i	−0.368307	−	0.670877i
$605$			3.38305e6i			0.0152771i
$606$		0			0
$607$			1.47713e8i			0.660468i	0.943899	+	0.330234i	$0.107128\pi$
$607$			1.47713e8i			0.660468i	−0.943899	+	0.330234i	$0.892872\pi$
$608$	2.89689e8	+	9.45941e7i	1.28890	+	0.420875i
$609$		0			0
$610$	7.70193e7	+	3.00335e8i	0.339320	+	1.32317i
$611$	2.22558e7			0.0975708
$612$		0			0
$613$			2.17597e8i			0.944651i	0.881424	+	0.472325i	$0.156585\pi$
$613$			2.17597e8i			0.944651i	−0.881424	+	0.472325i	$0.843415\pi$
$614$	−6.72068e7	−	2.62072e8i	−0.290341	−	1.13218i
$615$		0			0
$616$	3.02580e8	−	2.83643e8i	1.29449	−	1.21347i
$617$	−2.03466e8			−0.866235			−0.433118	−	0.901337i	$-0.642587\pi$
$617$	−2.03466e8			−0.866235			−0.433118	+	0.901337i	$0.642587\pi$
$618$		0			0
$619$	−2.52848e8			−1.06607			−0.533037	−	0.846092i	$-0.678949\pi$
$619$	−2.52848e8			−1.06607			−0.533037	+	0.846092i	$0.678949\pi$
$620$	6.07247e7	−	3.33375e7i	0.254795	−	0.139881i
$621$		0			0
$622$	−3.69448e8	+	9.47430e7i	−1.53526	+	0.393710i
$623$		−	6.96008e8i		−	2.87839i
$624$		0			0
$625$	−1.59939e8			−0.655109
$626$	−6.50427e7	−	2.53633e8i	−0.265140	−	1.03391i
$627$		0			0
$628$	1.49530e8	+	2.72371e8i	0.603739	+	1.09972i
$629$			8.18340e7i			0.328838i
$630$		0			0
$631$			4.84715e8i			1.92929i	0.263549	+	0.964646i	$0.415107\pi$
$631$			4.84715e8i			1.92929i	−0.263549	+	0.964646i	$0.584893\pi$
$632$	2.35475e7	−	2.20737e7i	0.0932811	−	0.0874429i
$633$		0			0
$634$	6.64367e7	−	1.70373e7i	0.260700	−	0.0668550i
$635$	1.19496e8			0.466693
$636$		0			0
$637$			1.62546e8i			0.628865i
$638$	2.05665e8	−	5.27417e7i	0.791951	−	0.203092i
$639$		0			0
$640$	−4.14816e7	−	2.19899e8i	−0.158240	−	0.838849i
$641$	7.03019e7			0.266927			0.133464	−	0.991054i	$-0.457390\pi$
$641$	7.03019e7			0.266927			0.133464	+	0.991054i	$0.457390\pi$
$642$		0			0
$643$	−6.35206e7			−0.238936			−0.119468	−	0.992838i	$-0.538119\pi$
$643$	−6.35206e7			−0.238936			−0.119468	+	0.992838i	$0.538119\pi$
$644$	−4.92493e8	+	2.70375e8i	−1.84392	+	1.01230i
$645$		0			0
$646$	−1.51123e8	−	5.89302e8i	−0.560575	−	2.18595i
$647$		−	1.67479e8i		−	0.618370i	−0.951002	−	0.309185i	$-0.899944\pi$
$647$		−	1.67479e8i		−	0.618370i	0.951002	−	0.309185i	$-0.100056\pi$
$648$		0			0
$649$	3.41064e8			1.24768
$650$	−2.05769e7	+	5.27683e6i	−0.0749272	+	0.0192147i
$651$		0			0
$652$	1.90787e7	−	1.04741e7i	0.0688344	−	0.0377896i
$653$			2.44731e8i			0.878920i	0.898262	+	0.439460i	$0.144830\pi$
$653$			2.44731e8i			0.878920i	−0.898262	+	0.439460i	$0.855170\pi$
$654$		0			0
$655$		−	2.49220e8i		−	0.886870i
$656$	9.27272e7	−	1.45738e8i	0.328470	−	0.516250i
$657$		0			0
$658$	−4.33592e7	−	1.69078e8i	−0.152196	−	0.593485i
$659$	3.20476e7			0.111980			0.0559898	−	0.998431i	$-0.482169\pi$
$659$	3.20476e7			0.111980			0.0559898	+	0.998431i	$0.482169\pi$
$660$		0			0
$661$		−	4.02157e8i		−	1.39249i	−0.717806	−	0.696243i	$-0.754853\pi$
$661$		−	4.02157e8i		−	1.39249i	0.717806	−	0.696243i	$-0.245147\pi$
$662$	−1.32692e7	−	5.17429e7i	−0.0457373	−	0.178352i
$663$		0			0
$664$	−1.44319e8	−	1.53954e8i	−0.492968	−	0.525882i
$665$	6.09420e8			2.07230
$666$		0			0
$667$	−2.87621e8			−0.969268
$668$	−4.69353e7	−	8.54935e7i	−0.157460	−	0.286816i
$669$		0			0
$670$	2.37502e8	−	6.09062e7i	0.789667	−	0.202506i
$671$		−	4.79089e8i		−	1.58580i
$672$		0			0
$673$	−2.57142e8			−0.843584			−0.421792	−	0.906693i	$-0.638599\pi$
$673$	−2.57142e8			−0.843584			−0.421792	+	0.906693i	$0.638599\pi$
$674$	236157.	+	920891.i	0.000771298	+	0.00300766i
$675$		0			0
$676$	−2.48778e8	+	1.36577e8i	−0.805326	+	0.442118i
$677$			4.03555e8i			1.30058i	0.759687	+	0.650289i	$0.225352\pi$
$677$			4.03555e8i			1.30058i	−0.759687	+	0.650289i	$0.774648\pi$
$678$		0			0
$679$		−	5.32870e8i		−	1.70221i
$680$	−3.25927e8	+	3.05528e8i	−1.03656	+	0.971681i
$681$		0			0
$682$	−1.03686e8	+	2.65897e7i	−0.326863	+	0.0838223i
$683$	7.05011e7			0.221276			0.110638	−	0.993861i	$-0.464711\pi$
$683$	7.05011e7			0.221276			0.110638	+	0.993861i	$0.464711\pi$
$684$		0			0
$685$			8.08808e7i			0.251637i
$686$	6.74984e8	−	1.73096e8i	2.09084	−	0.536185i
$687$		0			0
$688$	−1.50671e8	+	2.36806e8i	−0.462661	+	0.727156i
$689$	−1.17478e8			−0.359168
$690$		0			0
$691$	2.12142e8			0.642974			0.321487	−	0.946914i	$-0.395817\pi$
$691$	2.12142e8			0.642974			0.321487	+	0.946914i	$0.395817\pi$
$692$	7.88644e6	+	1.43653e7i	0.0237992	+	0.0433507i
$693$		0			0
$694$	7.05030e7	+	2.74925e8i	0.210926	+	0.822499i
$695$		−	4.54074e8i		−	1.35261i
$696$		0			0
$697$	−3.44842e8			−1.01841
$698$	3.46837e8	−	8.89444e7i	1.01990	−	0.261548i
$699$		0			0
$700$	8.01765e7	+	1.46043e8i	0.233751	+	0.425781i
$701$		−	4.84794e8i		−	1.40735i	−0.710520	−	0.703677i	$-0.751540\pi$
$701$		−	4.84794e8i		−	1.40735i	0.710520	−	0.703677i	$-0.248460\pi$
$702$		0			0
$703$			9.30720e7i			0.267888i
$704$	−2.23171e7	+	3.45056e8i	−0.0639618	+	0.988945i
$705$		0			0
$706$	7.95039e7	+	3.10024e8i	0.225930	+	0.881010i
$707$	−4.54335e8			−1.28564
$708$		0			0
$709$		−	6.30105e8i		−	1.76797i	−0.467518	−	0.883984i	$-0.654852\pi$
$709$		−	6.30105e8i		−	1.76797i	0.467518	−	0.883984i	$-0.345148\pi$
$710$	−7.17965e7	−	2.79969e8i	−0.200599	−	0.782230i
$711$		0			0
$712$	3.96856e8	+	4.23353e8i	1.09950	+	1.17290i
$713$	1.45004e8			0.400047
$714$		0			0
$715$	−8.81672e7			−0.241206
$716$	3.22376e8	−	1.76982e8i	0.878261	−	0.482159i
$717$		0			0
$718$	2.81288e8	−	7.21347e7i	0.759937	−	0.194882i
$719$			1.71966e8i			0.462654i	0.972876	+	0.231327i	$0.0743067\pi$
$719$			1.71966e8i			0.462654i	−0.972876	+	0.231327i	$0.925693\pi$
$720$		0			0
$721$	3.95524e7			0.105528
$722$	−7.83846e7	−	3.05659e8i	−0.208266	−	0.812130i
$723$		0			0
$724$	−1.13003e8	−	2.05837e8i	−0.297765	−	0.542384i
$725$			8.52906e7i			0.223814i
$726$		0			0
$727$			2.97870e8i			0.775218i	0.921824	+	0.387609i	$0.126699\pi$
$727$			2.97870e8i			0.775218i	−0.921824	+	0.387609i	$0.873301\pi$
$728$	−1.34703e8	−	1.43697e8i	−0.349128	−	0.372437i
$729$		0			0
$730$	1.58495e8	−	4.06453e7i	0.407425	−	0.104482i
$731$	5.60326e8			1.43446
$732$		0			0
$733$			4.29075e8i			1.08949i	0.838603	+	0.544743i	$0.183373\pi$
$733$			4.29075e8i			1.08949i	−0.838603	+	0.544743i	$0.816627\pi$
$734$	−2.82889e8	+	7.25452e7i	−0.715364	+	0.183451i
$735$		0			0
$736$	1.45398e8	−	4.45273e8i	0.364691	−	1.11684i
$737$	−3.78860e8			−0.946403
$738$		0			0
$739$	4.49723e8			1.11432			0.557162	−	0.830404i	$-0.311890\pi$
$739$	4.49723e8			1.11432			0.557162	+	0.830404i	$0.311890\pi$
$740$	5.99100e7	−	3.28902e7i	0.147844	−	0.0811655i
$741$		0			0
$742$	2.28872e8	+	8.92482e8i	0.560250	+	2.18468i
$743$			3.43102e8i			0.836482i	0.908336	+	0.418241i	$0.137353\pi$
$743$			3.43102e8i			0.836482i	−0.908336	+	0.418241i	$0.862647\pi$
$744$		0			0
$745$	−6.33824e8			−1.53285
$746$	−3.52799e8	+	9.04735e7i	−0.849789	+	0.217924i
$747$		0			0
$748$	6.05102e8	−	3.32197e8i	1.44585	−	0.793763i
$749$			1.19172e9i			2.83616i
$750$		0			0
$751$		−	1.20827e8i		−	0.285262i	−0.989776	−	0.142631i	$-0.954444\pi$
$751$		−	1.20827e8i		−	0.285262i	0.989776	−	0.142631i	$-0.0455561\pi$
$752$	1.22780e8	+	7.81203e7i	0.288719	+	0.183701i
$753$		0			0
$754$	−2.50473e7	−	9.76714e7i	−0.0584315	−	0.227852i
$755$	2.81167e8			0.653317
$756$		0			0
$757$			4.35039e7i			0.100286i	0.998742	+	0.0501431i	$0.0159677\pi$
$757$			4.35039e7i			0.100286i	−0.998742	+	0.0501431i	$0.984032\pi$
$758$	−7.92230e7	−	3.08928e8i	−0.181905	−	0.709333i
$759$		0			0
$760$	−3.70685e8	+	3.47485e8i	−0.844431	+	0.791581i
$761$	−3.84973e8			−0.873526			−0.436763	−	0.899577i	$-0.643875\pi$
$761$	−3.84973e8			−0.873526			−0.436763	+	0.899577i	$0.643875\pi$
$762$		0			0
$763$	−1.25373e9			−2.82249
$764$	1.59726e8	+	2.90943e8i	0.358175	+	0.652421i
$765$		0			0
$766$	5.56323e8	−	1.42666e8i	1.23777	−	0.317420i
$767$		−	1.61973e8i		−	0.358968i
$768$		0			0
$769$	−1.79831e8			−0.395444			−0.197722	−	0.980258i	$-0.563354\pi$
$769$	−1.79831e8			−0.395444			−0.197722	+	0.980258i	$0.563354\pi$
$770$	1.71769e8	+	6.69809e8i	0.376246	+	1.46716i
$771$		0			0
$772$	5.06840e8	−	2.78252e8i	1.10159	−	0.604764i
$773$		−	5.27367e8i		−	1.14176i	−0.821034	−	0.570880i	$-0.806602\pi$
$773$		−	5.27367e8i		−	1.14176i	0.821034	−	0.570880i	$-0.193398\pi$
$774$		0			0
$775$		−	4.29991e7i		−	0.0923750i
$776$	3.03837e8	+	3.24123e8i	0.650213	+	0.693625i
$777$		0			0
$778$	3.25508e8	−	8.34748e7i	0.691231	−	0.177262i
$779$	−3.92198e8			−0.829646
$780$		0			0
$781$			4.46601e8i			0.937490i
$782$	−9.05801e8	+	2.32288e8i	−1.89414	+	0.485743i
$783$		0			0
$784$	−5.70553e8	+	8.96727e8i	−1.18399	+	1.86085i
$785$	−5.18051e8			−1.07094
$786$		0			0
$787$	6.50110e8			1.33371			0.666857	−	0.745186i	$-0.267639\pi$
$787$	6.50110e8			1.33371			0.666857	+	0.745186i	$0.267639\pi$
$788$	−1.84760e8	−	3.36543e8i	−0.377597	−	0.687799i
$789$		0			0
$790$	1.33674e7	+	5.21261e7i	0.0271123	+	0.105724i
$791$			8.26396e8i			1.66978i
$792$		0			0
$793$	−2.27522e8			−0.456251
$794$	−1.71382e8	+	4.39501e7i	−0.342377	+	0.0878008i
$795$		0			0
$796$	1.89339e8	+	3.44883e8i	0.375405	+	0.683806i
$797$		−	5.36676e8i		−	1.06008i	−0.847974	−	0.530038i	$-0.822178\pi$
$797$		−	5.36676e8i		−	1.06008i	0.847974	−	0.530038i	$-0.177822\pi$
$798$		0			0
$799$		−	2.90520e8i		−	0.569556i
$800$	−1.32040e8	−	4.31160e7i	−0.257891	−	0.0842110i
$801$		0			0
$802$	−1.77926e8	−	6.93819e8i	−0.344919	−	1.34500i
$803$	−2.52829e8			−0.488292
$804$		0			0
$805$		−	9.36724e8i		−	1.79566i
$806$	1.26276e7	+	4.92409e7i	0.0241165	+	0.0940418i
$807$		0			0
$808$	2.76354e8	−	2.59057e8i	0.523879	−	0.491091i
$809$	−6.69030e8			−1.26357			−0.631786	−	0.775143i	$-0.717678\pi$
$809$	−6.69030e8			−1.26357			−0.631786	+	0.775143i	$0.717678\pi$
$810$		0			0
$811$	−6.85808e8			−1.28570			−0.642851	−	0.765992i	$-0.722248\pi$
$811$	−6.85808e8			−1.28570			−0.642851	+	0.765992i	$0.722248\pi$
$812$	−6.93215e8	+	3.80570e8i	−1.29479	+	0.710831i
$813$		0			0
$814$	−1.02295e8	+	2.62329e7i	−0.189662	+	0.0486378i
$815$			3.62877e7i			0.0670327i
$816$		0			0
$817$	6.37274e8			1.16859
$818$	7.97235e7	+	3.10880e8i	0.145655	+	0.567980i
$819$		0			0
$820$	1.38597e8	+	2.52456e8i	0.251369	+	0.457872i
$821$		−	9.47304e7i		−	0.171183i	−0.996330	−	0.0855913i	$-0.972722\pi$
$821$		−	9.47304e7i		−	0.171183i	0.996330	−	0.0855913i	$-0.0272779\pi$
$822$		0			0
$823$		−	2.64366e8i		−	0.474249i	−0.971479	−	0.237125i	$-0.923795\pi$
$823$		−	2.64366e8i		−	0.474249i	0.971479	−	0.237125i	$-0.0762050\pi$
$824$	−2.40581e7	+	2.25524e7i	−0.0430011	+	0.0403098i
$825$		0			0
$826$	−1.23051e9	+	3.15558e8i	−2.18346	+	0.559938i
$827$	−6.97162e7			−0.123259			−0.0616293	−	0.998099i	$-0.519630\pi$
$827$	−6.97162e7			−0.123259			−0.0616293	+	0.998099i	$0.519630\pi$
$828$		0			0
$829$		−	3.50839e8i		−	0.615807i	−0.951418	−	0.307903i	$-0.900373\pi$
$829$		−	3.50839e8i		−	0.615807i	0.951418	−	0.307903i	$-0.0996274\pi$
$830$	3.40802e8	−	8.73969e7i	0.596030	−	0.152849i
$831$		0			0
$832$	1.63869e8	+	1.05985e7i	0.284529	+	0.0184024i
$833$	2.12182e9			3.67091
$834$		0			0
$835$	1.62609e8			0.279309
$836$	6.88199e8	−	3.77817e8i	1.17786	−	0.646640i
$837$		0			0
$838$	2.97019e7	+	1.15822e8i	0.0504722	+	0.196815i
$839$			1.19739e8i			0.202744i	0.994849	+	0.101372i	$0.0323233\pi$
$839$			1.19739e8i			0.202744i	−0.994849	+	0.101372i	$0.967677\pi$
$840$		0			0
$841$	1.89978e8			0.319386
$842$	1.86666e8	−	4.78695e7i	0.312701	−	0.0801905i
$843$		0			0
$844$	1.12156e8	−	6.15728e7i	0.186550	−	0.102415i
$845$		−	4.73176e8i		−	0.784247i
$846$		0			0
$847$			1.94701e7i			0.0320419i
$848$	−6.48098e8	−	4.12360e8i	−1.06280	−	0.676221i
$849$		0			0
$850$	6.88821e7	+	2.68604e8i	0.112163	+	0.437377i
$851$	1.43059e8			0.232127
$852$		0			0
$853$		−	2.12998e8i		−	0.343186i	−0.985168	−	0.171593i	$-0.945109\pi$
$853$		−	2.12998e8i		−	0.343186i	0.985168	−	0.171593i	$-0.0548913\pi$
$854$	4.43262e8	+	1.72849e9i	0.711683	+	2.77519i
$855$		0			0
$856$	−6.79509e8	−	7.24877e8i	−1.08336	−	1.15569i
$857$	1.64871e8			0.261940			0.130970	−	0.991386i	$-0.458191\pi$
$857$	1.64871e8			0.261940			0.130970	+	0.991386i	$0.458191\pi$
$858$		0			0
$859$	−5.90486e8			−0.931601			−0.465801	−	0.884890i	$-0.654234\pi$
$859$	−5.90486e8			−0.931601			−0.465801	+	0.884890i	$0.654234\pi$
$860$	−2.25203e8	−	4.10211e8i	−0.354061	−	0.644929i
$861$		0			0
$862$	9.32223e8	−	2.39064e8i	1.45545	−	0.373243i
$863$			5.20030e8i			0.809088i	0.914519	+	0.404544i	$0.132570\pi$
$863$			5.20030e8i			0.809088i	−0.914519	+	0.404544i	$0.867430\pi$
$864$		0			0
$865$	−2.73228e7			−0.0422160
$866$	−9.63220e7	−	3.75606e8i	−0.148310	−	0.578333i
$867$		0			0
$868$	3.49483e8	−	1.91864e8i	0.534401	−	0.293383i
$869$		−	8.31506e7i		−	0.126709i
$870$		0			0
$871$			1.79922e8i			0.272289i
$872$	7.62596e8	−	7.14867e8i	1.15012	−	1.07814i
$873$		0			0
$874$	−1.03019e9	+	2.64187e8i	−1.54306	+	0.395710i
$875$	−1.30167e9			−1.94301
$876$		0			0
$877$			7.97818e8i			1.18278i	0.806385	+	0.591392i	$0.201421\pi$
$877$			7.97818e8i			1.18278i	−0.806385	+	0.591392i	$0.798579\pi$
$878$	9.90342e8	−	2.53968e8i	1.46319	−	0.375228i
$879$		0			0
$880$	−4.86398e8	−	3.09476e8i	−0.713746	−	0.454129i
$881$	−5.02607e7			−0.0735023			−0.0367511	−	0.999324i	$-0.511701\pi$
$881$	−5.02607e7			−0.0735023			−0.0367511	+	0.999324i	$0.511701\pi$
$882$		0			0
$883$	5.96279e8			0.866099			0.433050	−	0.901370i	$-0.357437\pi$
$883$	5.96279e8			0.866099			0.433050	+	0.901370i	$0.357437\pi$
$884$	−1.57762e8	−	2.87366e8i	−0.228373	−	0.415986i
$885$		0			0
$886$	−3.02586e8	−	1.17993e9i	−0.435059	−	1.69650i
$887$		−	8.73580e7i		−	0.125179i	−0.998039	−	0.0625895i	$-0.980064\pi$
$887$		−	8.73580e7i		−	0.125179i	0.998039	−	0.0625895i	$-0.0199359\pi$
$888$		0			0
$889$	6.87723e8			0.978833
$890$	−9.37157e8	+	2.40329e8i	−1.32936	+	0.340907i
$891$		0			0
$892$	3.69904e7	+	6.73786e7i	0.0521188	+	0.0949353i
$893$		−	3.30417e8i		−	0.463989i
$894$		0			0
$895$			6.13160e8i			0.855273i
$896$	−2.38735e8	−	1.26557e9i	−0.331889	−	1.75938i
$897$		0			0
$898$	1.71849e6	+	6.70121e6i	0.00237311	+	0.00925388i
$899$	2.04102e8			0.280911
$900$		0			0
$901$			1.53352e9i			2.09660i
$902$	−1.10543e8	−	4.31062e8i	−0.150631	−	0.587381i
$903$		0			0
$904$	−4.71203e8	−	5.02663e8i	−0.637826	−	0.680411i
$905$	3.91502e8			0.528187
$906$		0			0
$907$	2.27491e8			0.304890			0.152445	−	0.988312i	$-0.451285\pi$
$907$	2.27491e8			0.304890			0.152445	+	0.988312i	$0.451285\pi$
$908$	1.01972e8	−	5.59819e7i	0.136214	−	0.0747808i
$909$		0			0
$910$	3.18095e8	−	8.15739e7i	0.422117	−	0.108250i
$911$			5.17066e8i			0.683897i	0.939719	+	0.341949i	$0.111087\pi$
$911$			5.17066e8i			0.683897i	−0.939719	+	0.341949i	$0.888913\pi$
$912$		0			0
$913$	−5.43642e8			−0.714332
$914$	9.13508e7	+	3.56221e8i	0.119639	+	0.466531i
$915$		0			0
$916$	3.87210e8	+	7.05309e8i	0.503802	+	0.917683i
$917$		−	1.43432e9i		−	1.86010i
$918$		0			0
$919$		−	3.65000e8i		−	0.470268i	−0.971963	−	0.235134i	$-0.924447\pi$
$919$		−	3.65000e8i		−	0.470268i	0.971963	−	0.235134i	$-0.0755530\pi$
$920$	5.34110e8	+	5.69771e8i	0.685910	+	0.731706i
$921$		0			0
$922$	−3.13195e8	+	8.03171e7i	−0.399597	+	0.102474i
$923$	2.12093e8			0.269725
$924$		0			0
$925$		−	4.24222e7i		−	0.0536004i
$926$	−1.13190e9	+	2.90269e8i	−1.42553	+	0.365568i
$927$		0			0
$928$	2.04657e8	−	6.26749e8i	0.256084	−	0.784242i
$929$	−5.29560e8			−0.660492			−0.330246	−	0.943895i	$-0.607132\pi$
$929$	−5.29560e8			−0.660492			−0.330246	+	0.943895i	$0.607132\pi$
$930$		0			0
$931$	2.41320e9			2.99051
$932$	8.12923e8	−	4.46289e8i	1.00416	−	0.551275i
$933$		0			0
$934$	3.13547e7	+	1.22267e8i	0.0384824	+	0.150061i
$935$			1.15091e9i			1.40801i
$936$		0			0
$937$	6.26903e8			0.762046			0.381023	−	0.924566i	$-0.375572\pi$
$937$	6.26903e8			0.762046			0.381023	+	0.924566i	$0.375572\pi$
$938$	1.36688e9	−	3.50528e8i	1.65623	−	0.424731i
$939$		0			0
$940$	−2.12688e8	+	1.16764e8i	−0.256070	+	0.140581i
$941$		−	1.56831e9i		−	1.88219i	−0.338145	−	0.941094i	$-0.609799\pi$
$941$		−	1.56831e9i		−	1.88219i	0.338145	−	0.941094i	$-0.390201\pi$
$942$		0			0
$943$			6.02837e8i			0.718894i
$944$	5.68542e8	−	8.93567e8i	0.675845	−	1.06221i
$945$		0			0
$946$	1.79620e8	+	7.00424e8i	0.212169	+	0.827346i
$947$	1.35949e9			1.60076			0.800379	−	0.599495i	$-0.204632\pi$
$947$	1.35949e9			1.60076			0.800379	+	0.599495i	$0.204632\pi$
$948$		0			0
$949$			1.20070e8i			0.140487i
$950$	7.83414e7	+	3.05491e8i	0.0913736	+	0.356309i
$951$		0			0
$952$	−1.87577e9	+	1.75837e9i	−2.17405	+	2.03798i
$953$	3.65392e8			0.422163			0.211081	−	0.977468i	$-0.432301\pi$
$953$	3.65392e8			0.422163			0.211081	+	0.977468i	$0.432301\pi$
$954$		0			0
$955$	−5.53375e8			−0.635344
$956$	7.41580e8	+	1.35080e9i	0.848758	+	1.54603i
$957$		0			0
$958$	3.61925e8	−	9.28137e7i	0.411644	−	0.105564i
$959$			4.65486e8i			0.527777i
$960$		0			0
$961$	7.84606e8			0.884059
$962$	1.24581e7	+	4.85803e7i	0.0139936	+	0.0545676i
$963$		0			0
$964$	4.04350e8	−	2.21985e8i	0.451363	−	0.247795i
$965$			9.64011e8i			1.07275i
$966$		0			0
$967$			1.64797e9i			1.82251i	0.411848	+	0.911253i	$0.364884\pi$
$967$			1.64797e9i			1.82251i	−0.411848	+	0.911253i	$0.635116\pi$
$968$	−1.11017e7	−	1.18429e7i	−0.0122395	−	0.0130566i
$969$		0			0
$970$	−7.17497e8	+	1.83998e8i	−0.786149	+	0.201604i
$971$	1.04873e9			1.14553			0.572765	−	0.819720i	$-0.305871\pi$
$971$	1.04873e9			1.14553			0.572765	+	0.819720i	$0.305871\pi$
$972$		0			0
$973$		−	2.61329e9i		−	2.83693i
$974$	−1.50563e9	+	3.86112e8i	−1.62946	+	0.417865i
$975$		0			0
$976$	−1.25519e9	−	7.98626e8i	−1.35008	−	0.859002i
$977$	−3.14506e8			−0.337245			−0.168622	−	0.985681i	$-0.553932\pi$
$977$	−3.14506e8			−0.337245			−0.168622	+	0.985681i	$0.553932\pi$
$978$		0			0
$979$	1.49494e9			1.59322
$980$	−8.52789e8	−	1.55337e9i	−0.906073	−	1.65043i
$981$		0			0
$982$	1.27120e8	+	4.95703e8i	0.134240	+	0.523465i
$983$		−	1.77174e9i		−	1.86527i	−0.360828	−	0.932633i	$-0.617506\pi$
$983$		−	1.77174e9i		−	1.86527i	0.360828	−	0.932633i	$-0.382494\pi$
$984$		0			0
$985$	6.40105e8			0.669796
$986$	−1.27497e9	+	3.26960e8i	−1.33006	+	0.341085i
$987$		0			0
$988$	−1.79427e8	−	3.26829e8i	−0.186045	−	0.338883i
$989$		−	9.79538e8i		−	1.01259i
$990$		0			0
$991$		−	7.95280e8i		−	0.817145i	−0.912726	−	0.408572i	$-0.866027\pi$
$991$		−	7.95280e8i		−	0.817145i	0.912726	−	0.408572i	$-0.133973\pi$
$992$	−1.03178e8	+	3.15975e8i	−0.105694	+	0.323681i
$993$		0			0
$994$	−4.13203e8	−	1.61128e9i	−0.420731	−	1.64063i
$995$	−6.55969e8			−0.665908
$996$		0			0
$997$			1.18207e9i			1.19277i	0.802698	+	0.596386i	$0.203397\pi$
$997$			1.18207e9i			1.19277i	−0.802698	+	0.596386i	$0.796603\pi$
$998$	1.43277e8	+	5.58705e8i	0.144140	+	0.562071i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.d.19.5	✓	12
3.2	odd	2	inner	72.7.b.d.19.8	yes	12
4.3	odd	2		288.7.b.c.271.4		12
8.3	odd	2	inner	72.7.b.d.19.6	yes	12
8.5	even	2		288.7.b.c.271.9		12
12.11	even	2		288.7.b.c.271.10		12
24.5	odd	2		288.7.b.c.271.3		12
24.11	even	2	inner	72.7.b.d.19.7	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.b.d.19.5	✓	12	1.1	even	1	trivial
72.7.b.d.19.6	yes	12	8.3	odd	2	inner
72.7.b.d.19.7	yes	12	24.11	even	2	inner
72.7.b.d.19.8	yes	12	3.2	odd	2	inner
288.7.b.c.271.3		12	24.5	odd	2
288.7.b.c.271.4		12	4.3	odd	2
288.7.b.c.271.9		12	8.5	even	2
288.7.b.c.271.10		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98725 - 7.74925i) q^{2} +(-56.1017 + 30.7994i) q^{4} -106.706i q^{5} -614.112i q^{7} +(350.160 + 373.539i) q^{8} +O(q^{10})\)	\(q+(-1.98725 - 7.74925i) q^{2} +(-56.1017 + 30.7994i) q^{4} -106.706i q^{5} -614.112i q^{7} +(350.160 + 373.539i) q^{8} +(-826.887 + 212.051i) q^{10} +1319.04 q^{11} -626.417i q^{13} +(-4758.91 + 1220.40i) q^{14} +(2198.79 - 3455.80i) q^{16} -8177.05 q^{17} -9299.98 q^{19} +(3286.47 + 5986.36i) q^{20} +(-2621.26 - 10221.5i) q^{22} +14294.8i q^{23} +4238.93 q^{25} +(-4854.26 + 1244.85i) q^{26} +(18914.3 + 34452.7i) q^{28} +20120.8i q^{29} -10143.9i q^{31} +(-31149.4 - 10171.4i) q^{32} +(16249.9 + 63366.0i) q^{34} -65529.2 q^{35} -10007.8i q^{37} +(18481.4 + 72067.8i) q^{38} +(39858.7 - 37364.1i) q^{40} +42171.9 q^{41} -68524.3 q^{43} +(-74000.1 + 40625.6i) q^{44} +(110774. - 28407.3i) q^{46} +35528.8i q^{47} -259485. q^{49} +(-8423.83 - 32848.5i) q^{50} +(19293.3 + 35143.0i) q^{52} -187539. i q^{53} -140748. i q^{55} +(229395. - 215038. i) q^{56} +(155921. - 39985.0i) q^{58} +258570. q^{59} -363211. i q^{61} +(-78607.3 + 20158.4i) q^{62} +(-16919.3 + 261597. i) q^{64} -66842.1 q^{65} -287225. q^{67} +(458746. - 251848. i) q^{68} +(130223. + 507802. i) q^{70} +338581. i q^{71} -191677. q^{73} +(-77552.6 + 19888.0i) q^{74} +(521744. - 286434. i) q^{76} -810036. i q^{77} -63038.9i q^{79} +(-368753. - 234623. i) q^{80} +(-83806.2 - 326800. i) q^{82} -412151. q^{83} +872536. i q^{85} +(136175. + 531012. i) q^{86} +(461874. + 492712. i) q^{88} +1.13336e6 q^{89} -384690. q^{91} +(-440270. - 801960. i) q^{92} +(275321. - 70604.6i) q^{94} +992359. i q^{95} +867708. q^{97} +(515662. + 2.01081e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 156 q^{4}+O(q^{10}) \) 12 * q - 156 * q^4	\( 12 q - 156 q^{4} + 1416 q^{10} - 1464 q^{16} + 3936 q^{19} + 15888 q^{22} - 47796 q^{25} + 11256 q^{28} + 50016 q^{34} + 70896 q^{40} - 340704 q^{43} + 213696 q^{46} - 304644 q^{49} + 548016 q^{52} - 38616 q^{58} + 206544 q^{64} - 962112 q^{67} + 1074480 q^{70} - 1069560 q^{73} + 1064352 q^{76} - 694944 q^{82} - 3072672 q^{88} + 775008 q^{91} + 3752256 q^{94} - 86952 q^{97}+O(q^{100}) \) 12 * q - 156 * q^4 + 1416 * q^10 - 1464 * q^16 + 3936 * q^19 + 15888 * q^22 - 47796 * q^25 + 11256 * q^28 + 50016 * q^34 + 70896 * q^40 - 340704 * q^43 + 213696 * q^46 - 304644 * q^49 + 548016 * q^52 - 38616 * q^58 + 206544 * q^64 - 962112 * q^67 + 1074480 * q^70 - 1069560 * q^73 + 1064352 * q^76 - 694944 * q^82 - 3072672 * q^88 + 775008 * q^91 + 3752256 * q^94 - 86952 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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