LMFDB - Embedded newform 384.7.l.a.31.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,7,Mod(31,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("384.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	384.l (of order $4$, degree $2$, 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:	$88.3407681100$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 + 11.0227i) q^{3} +(-132.791 - 132.791i) q^{5} +560.492 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(11.0227 + 11.0227i) q^{3} +(-132.791 - 132.791i) q^{5} +560.492 q^{7} +243.000i q^{9} +(-1673.14 + 1673.14i) q^{11} +(327.008 - 327.008i) q^{13} -2927.44i q^{15} +5118.78 q^{17} +(-3620.04 - 3620.04i) q^{19} +(6178.14 + 6178.14i) q^{21} -15988.9 q^{23} +19642.0i q^{25} +(-2678.52 + 2678.52i) q^{27} +(17101.9 - 17101.9i) q^{29} -21428.4i q^{31} -36885.2 q^{33} +(-74428.4 - 74428.4i) q^{35} +(15173.5 + 15173.5i) q^{37} +7209.02 q^{39} -48941.5i q^{41} +(-37389.4 + 37389.4i) q^{43} +(32268.3 - 32268.3i) q^{45} +99673.8i q^{47} +196502. q^{49} +(56422.8 + 56422.8i) q^{51} +(-25106.1 - 25106.1i) q^{53} +444358. q^{55} -79805.3i q^{57} +(-235769. + 235769. i) q^{59} +(-137685. + 137685. i) q^{61} +136200. i q^{63} -86847.5 q^{65} +(154676. + 154676. i) q^{67} +(-176241. - 176241. i) q^{69} -456860. q^{71} +479436. i q^{73} +(-216508. + 216508. i) q^{75} +(-937785. + 937785. i) q^{77} +49299.4i q^{79} -59049.0 q^{81} +(-313544. - 313544. i) q^{83} +(-679729. - 679729. i) q^{85} +377017. q^{87} +697194. i q^{89} +(183285. - 183285. i) q^{91} +(236199. - 236199. i) q^{93} +961419. i q^{95} +388112. q^{97} +(-406574. - 406574. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) $ 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		0			0
$5$	−132.791	−	132.791i	−1.06233	−	1.06233i	−0.997924	−	0.0644055i	$-0.979485\pi$
$5$	−132.791	−	132.791i	−1.06233	−	1.06233i	−0.0644055	−	0.997924i	$-0.520515\pi$
$6$		0			0
$7$	560.492			1.63409			0.817044	−	0.576575i	$-0.195611\pi$
$7$	560.492			1.63409			0.817044	+	0.576575i	$0.195611\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−1673.14	+	1673.14i	−1.25706	+	1.25706i	−0.304568	+	0.952491i	$0.598512\pi$
$11$	−1673.14	+	1673.14i	−1.25706	+	1.25706i	−0.952491	+	0.304568i	$0.901488\pi$
$12$		0			0
$13$	327.008	−	327.008i	0.148843	−	0.148843i	−0.628758	−	0.777601i	$-0.716436\pi$
$13$	327.008	−	327.008i	0.148843	−	0.148843i	0.777601	+	0.628758i	$0.216436\pi$
$14$		0			0
$15$		−	2927.44i		−	0.867388i
$16$		0			0
$17$	5118.78			1.04189			0.520943	−	0.853592i	$-0.325581\pi$
$17$	5118.78			1.04189			0.520943	+	0.853592i	$0.325581\pi$
$18$		0			0
$19$	−3620.04	−	3620.04i	−0.527780	−	0.527780i	0.392130	−	0.919910i	$-0.371738\pi$
$19$	−3620.04	−	3620.04i	−0.527780	−	0.527780i	−0.919910	+	0.392130i	$0.871738\pi$
$20$		0			0
$21$	6178.14	+	6178.14i	0.667114	+	0.667114i
$22$		0			0
$23$	−15988.9			−1.31412			−0.657060	−	0.753838i	$-0.728200\pi$
$23$	−15988.9			−1.31412			−0.657060	+	0.753838i	$0.728200\pi$
$24$		0			0
$25$			19642.0i			1.25709i
$26$		0			0
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$		0			0
$29$	17101.9	−	17101.9i	0.701212	−	0.701212i	−0.263459	−	0.964671i	$-0.584863\pi$
$29$	17101.9	−	17101.9i	0.701212	−	0.701212i	0.964671	+	0.263459i	$0.0848634\pi$
$30$		0			0
$31$		−	21428.4i		−	0.719290i	−0.933089	−	0.359645i	$-0.882898\pi$
$31$		−	21428.4i		−	0.719290i	0.933089	−	0.359645i	$-0.117102\pi$
$32$		0			0
$33$	−36885.2			−1.02638
$34$		0			0
$35$	−74428.4	−	74428.4i	−1.73594	−	1.73594i
$36$		0			0
$37$	15173.5	+	15173.5i	0.299558	+	0.299558i	0.840841	−	0.541283i	$-0.182061\pi$
$37$	15173.5	+	15173.5i	0.299558	+	0.299558i	−0.541283	+	0.840841i	$0.682061\pi$
$38$		0			0
$39$	7209.02			0.121530
$40$		0			0
$41$		−	48941.5i		−	0.710110i	−0.934845	−	0.355055i	$-0.884462\pi$
$41$		−	48941.5i		−	0.710110i	0.934845	−	0.355055i	$-0.115538\pi$
$42$		0			0
$43$	−37389.4	+	37389.4i	−0.470266	+	0.470266i	−0.902001	−	0.431735i	$-0.857902\pi$
$43$	−37389.4	+	37389.4i	−0.470266	+	0.470266i	0.431735	+	0.902001i	$0.357902\pi$
$44$		0			0
$45$	32268.3	−	32268.3i	0.354110	−	0.354110i
$46$		0			0
$47$			99673.8i			0.960036i	0.877259	+	0.480018i	$0.159370\pi$
$47$			99673.8i			0.960036i	−0.877259	+	0.480018i	$0.840630\pi$
$48$		0			0
$49$	196502.			1.67024
$50$		0			0
$51$	56422.8	+	56422.8i	0.425348	+	0.425348i
$52$		0			0
$53$	−25106.1	−	25106.1i	−0.168636	−	0.168636i	0.617743	−	0.786380i	$-0.288047\pi$
$53$	−25106.1	−	25106.1i	−0.168636	−	0.168636i	−0.786380	+	0.617743i	$0.788047\pi$
$54$		0			0
$55$	444358.			2.67082
$56$		0			0
$57$		−	79805.3i		−	0.430930i
$58$		0			0
$59$	−235769.	+	235769.i	−1.14797	+	1.14797i	−0.161018	+	0.986951i	$0.551478\pi$
$59$	−235769.	+	235769.i	−1.14797	+	1.14797i	−0.986951	+	0.161018i	$0.948522\pi$
$60$		0			0
$61$	−137685.	+	137685.i	−0.606594	+	0.606594i	−0.942054	−	0.335460i	$-0.891108\pi$
$61$	−137685.	+	137685.i	−0.606594	+	0.606594i	0.335460	+	0.942054i	$0.391108\pi$
$62$		0			0
$63$			136200.i			0.544696i
$64$		0			0
$65$	−86847.5			−0.316240
$66$		0			0
$67$	154676.	+	154676.i	0.514279	+	0.514279i	0.915835	−	0.401556i	$-0.131530\pi$
$67$	154676.	+	154676.i	0.514279	+	0.514279i	−0.401556	+	0.915835i	$0.631530\pi$
$68$		0			0
$69$	−176241.	−	176241.i	−0.536487	−	0.536487i
$70$		0			0
$71$	−456860.			−1.27646			−0.638232	−	0.769844i	$-0.720334\pi$
$71$	−456860.			−1.27646			−0.638232	+	0.769844i	$0.720334\pi$
$72$		0			0
$73$			479436.i			1.23243i	0.787579	+	0.616214i	$0.211334\pi$
$73$			479436.i			1.23243i	−0.787579	+	0.616214i	$0.788666\pi$
$74$		0			0
$75$	−216508.	+	216508.i	−0.513204	+	0.513204i
$76$		0			0
$77$	−937785.	+	937785.i	−2.05414	+	2.05414i
$78$		0			0
$79$			49299.4i			0.0999909i	0.998749	+	0.0499954i	$0.0159207\pi$
$79$			49299.4i			0.0999909i	−0.998749	+	0.0499954i	$0.984079\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−313544.	−	313544.i	−0.548358	−	0.548358i	0.377608	−	0.925966i	$-0.376747\pi$
$83$	−313544.	−	313544.i	−0.548358	−	0.548358i	−0.925966	+	0.377608i	$0.876747\pi$
$84$		0			0
$85$	−679729.	−	679729.i	−1.10683	−	1.10683i
$86$		0			0
$87$	377017.			0.572537
$88$		0			0
$89$			697194.i			0.988972i	0.869186	+	0.494486i	$0.164644\pi$
$89$			697194.i			0.988972i	−0.869186	+	0.494486i	$0.835356\pi$
$90$		0			0
$91$	183285.	−	183285.i	0.243222	−	0.243222i
$92$		0			0
$93$	236199.	−	236199.i	0.293649	−	0.293649i
$94$		0			0
$95$			961419.i			1.12135i
$96$		0			0
$97$	388112.			0.425248			0.212624	−	0.977134i	$-0.431799\pi$
$97$	388112.			0.425248			0.212624	+	0.977134i	$0.431799\pi$
$98$		0			0
$99$	−406574.	−	406574.i	−0.419019	−	0.419019i
$100$		0			0
$101$	−454228.	−	454228.i	−0.440869	−	0.440869i	0.451435	−	0.892304i	$-0.350912\pi$
$101$	−454228.	−	454228.i	−0.440869	−	0.440869i	−0.892304	+	0.451435i	$0.850912\pi$
$102$		0			0
$103$	−1.40870e6			−1.28916			−0.644581	−	0.764536i	$-0.722968\pi$
$103$	−1.40870e6			−1.28916			−0.644581	+	0.764536i	$0.722968\pi$
$104$		0			0
$105$		−	1.64080e6i		−	1.41739i
$106$		0			0
$107$	−656612.	+	656612.i	−0.535991	+	0.535991i	−0.922349	−	0.386358i	$-0.873733\pi$
$107$	−656612.	+	656612.i	−0.535991	+	0.535991i	0.386358	+	0.922349i	$0.373733\pi$
$108$		0			0
$109$	293810.	−	293810.i	0.226875	−	0.226875i	−0.584511	−	0.811386i	$-0.698714\pi$
$109$	293810.	−	293810.i	0.226875	−	0.226875i	0.811386	+	0.584511i	$0.198714\pi$
$110$		0			0
$111$			334506.i			0.244588i
$112$		0			0
$113$	−208639.			−0.144597			−0.0722986	−	0.997383i	$-0.523033\pi$
$113$	−208639.			−0.144597			−0.0722986	+	0.997383i	$0.523033\pi$
$114$		0			0
$115$	2.12318e6	+	2.12318e6i	1.39603	+	1.39603i
$116$		0			0
$117$	79462.9	+	79462.9i	0.0496143	+	0.0496143i
$118$		0			0
$119$	2.86904e6			1.70253
$120$		0			0
$121$		−	3.82727e6i		−	2.16039i
$122$		0			0
$123$	539467.	−	539467.i	0.289901	−	0.289901i
$124$		0			0
$125$	533420.	−	533420.i	0.273111	−	0.273111i
$126$		0			0
$127$		−	69320.9i		−	0.0338418i	−0.999857	−	0.0169209i	$-0.994614\pi$
$127$		−	69320.9i		−	0.0338418i	0.999857	−	0.0169209i	$-0.00538634\pi$
$128$		0			0
$129$	−824265.			−0.383971
$130$		0			0
$131$	−2.56219e6	−	2.56219e6i	−1.13972	−	1.13972i	−0.988500	−	0.151219i	$-0.951680\pi$
$131$	−2.56219e6	−	2.56219e6i	−1.13972	−	1.13972i	−0.151219	−	0.988500i	$-0.548320\pi$
$132$		0			0
$133$	−2.02900e6	−	2.02900e6i	−0.862438	−	0.862438i
$134$		0			0
$135$	711367.			0.289129
$136$		0			0
$137$			1.95217e6i			0.759198i	0.925151	+	0.379599i	$0.123938\pi$
$137$			1.95217e6i			0.759198i	−0.925151	+	0.379599i	$0.876062\pi$
$138$		0			0
$139$	−1.63384e6	+	1.63384e6i	−0.608366	+	0.608366i	−0.942519	−	0.334153i	$-0.891550\pi$
$139$	−1.63384e6	+	1.63384e6i	−0.608366	+	0.608366i	0.334153	+	0.942519i	$0.391550\pi$
$140$		0			0
$141$	−1.09867e6	+	1.09867e6i	−0.391933	+	0.391933i
$142$		0			0
$143$			1.09426e6i			0.374209i
$144$		0			0
$145$	−4.54195e6			−1.48984
$146$		0			0
$147$	2.16599e6	+	2.16599e6i	0.681874	+	0.681874i
$148$		0			0
$149$	−2.37938e6	−	2.37938e6i	−0.719292	−	0.719292i	0.249168	−	0.968460i	$-0.419843\pi$
$149$	−2.37938e6	−	2.37938e6i	−0.719292	−	0.719292i	−0.968460	+	0.249168i	$0.919843\pi$
$150$		0			0
$151$	−2.01189e6			−0.584350			−0.292175	−	0.956365i	$-0.594379\pi$
$151$	−2.01189e6			−0.584350			−0.292175	+	0.956365i	$0.594379\pi$
$152$		0			0
$153$			1.24386e6i			0.347295i
$154$		0			0
$155$	−2.84550e6	+	2.84550e6i	−0.764123	+	0.764123i
$156$		0			0
$157$	−294875.	+	294875.i	−0.0761972	+	0.0761972i	−0.744178	−	0.667981i	$-0.767159\pi$
$157$	−294875.	+	294875.i	−0.0761972	+	0.0761972i	0.667981	+	0.744178i	$0.267159\pi$
$158$		0			0
$159$		−	553474.i		−	0.137691i
$160$		0			0
$161$	−8.96165e6			−2.14739
$162$		0			0
$163$	2.68096e6	+	2.68096e6i	0.619053	+	0.619053i	0.945289	−	0.326235i	$-0.105780\pi$
$163$	2.68096e6	+	2.68096e6i	0.619053	+	0.619053i	−0.326235	+	0.945289i	$0.605780\pi$
$164$		0			0
$165$	4.89802e6	+	4.89802e6i	1.09036	+	1.09036i
$166$		0			0
$167$	−6.04102e6			−1.29706			−0.648531	−	0.761188i	$-0.724616\pi$
$167$	−6.04102e6			−1.29706			−0.648531	+	0.761188i	$0.724616\pi$
$168$		0			0
$169$			4.61294e6i			0.955692i
$170$		0			0
$171$	879670.	−	879670.i	0.175927	−	0.175927i
$172$		0			0
$173$	−49503.9	+	49503.9i	−0.00956096	+	0.00956096i	−0.711871	−	0.702310i	$-0.752152\pi$
$173$	−49503.9	+	49503.9i	−0.00956096	+	0.00956096i	0.702310	+	0.711871i	$0.252152\pi$
$174$		0			0
$175$			1.10092e7i			2.05419i
$176$		0			0
$177$	−5.19762e6			−0.937313
$178$		0			0
$179$	5.69400e6	+	5.69400e6i	0.992792	+	0.992792i	0.999974	−	0.00718209i	$-0.00228615\pi$
$179$	5.69400e6	+	5.69400e6i	0.992792	+	0.992792i	−0.00718209	+	0.999974i	$0.502286\pi$
$180$		0			0
$181$	−277060.	−	277060.i	−0.0467238	−	0.0467238i	0.683359	−	0.730083i	$-0.260518\pi$
$181$	−277060.	−	277060.i	−0.0467238	−	0.0467238i	−0.730083	+	0.683359i	$0.760518\pi$
$182$		0			0
$183$	−3.03533e6			−0.495282
$184$		0			0
$185$		−	4.02981e6i		−	0.636458i
$186$		0			0
$187$	−8.56446e6	+	8.56446e6i	−1.30971	+	1.30971i
$188$		0			0
$189$	−1.50129e6	+	1.50129e6i	−0.222371	+	0.222371i
$190$		0			0
$191$			1.07220e7i			1.53878i	0.638782	+	0.769388i	$0.279439\pi$
$191$			1.07220e7i			1.53878i	−0.638782	+	0.769388i	$0.720561\pi$
$192$		0			0
$193$	−7.22298e6			−1.00472			−0.502360	−	0.864659i	$-0.667535\pi$
$193$	−7.22298e6			−1.00472			−0.502360	+	0.864659i	$0.667535\pi$
$194$		0			0
$195$	−957295.	−	957295.i	−0.129105	−	0.129105i
$196$		0			0
$197$	−1.12752e6	−	1.12752e6i	−0.147478	−	0.147478i	0.629512	−	0.776990i	$-0.283255\pi$
$197$	−1.12752e6	−	1.12752e6i	−0.147478	−	0.147478i	−0.776990	+	0.629512i	$0.783255\pi$
$198$		0			0
$199$	−6.18664e6			−0.785047			−0.392523	−	0.919742i	$-0.628398\pi$
$199$	−6.18664e6			−0.785047			−0.392523	+	0.919742i	$0.628398\pi$
$200$		0			0
$201$			3.40990e6i			0.419907i
$202$		0			0
$203$	9.58545e6	−	9.58545e6i	1.14584	−	1.14584i
$204$		0			0
$205$	−6.49899e6	+	6.49899e6i	−0.754370	+	0.754370i
$206$		0			0
$207$		−	3.88530e6i		−	0.438040i
$208$		0			0
$209$	1.21137e7			1.32690
$210$		0			0
$211$	2.61586e6	+	2.61586e6i	0.278463	+	0.278463i	0.832495	−	0.554032i	$-0.186912\pi$
$211$	2.61586e6	+	2.61586e6i	0.278463	+	0.278463i	−0.554032	+	0.832495i	$0.686912\pi$
$212$		0			0
$213$	−5.03584e6	−	5.03584e6i	−0.521114	−	0.521114i
$214$		0			0
$215$	9.92997e6			0.999155
$216$		0			0
$217$		−	1.20104e7i		−	1.17538i
$218$		0			0
$219$	−5.28468e6	+	5.28468e6i	−0.503137	+	0.503137i
$220$		0			0
$221$	1.67388e6	−	1.67388e6i	0.155077	−	0.155077i
$222$		0			0
$223$		−	1.17253e7i		−	1.05733i	−0.848830	−	0.528665i	$-0.822693\pi$
$223$		−	1.17253e7i		−	1.05733i	0.848830	−	0.528665i	$-0.177307\pi$
$224$		0			0
$225$	−4.77300e6			−0.419029
$226$		0			0
$227$	−1.13559e6	−	1.13559e6i	−0.0970828	−	0.0970828i	0.656897	−	0.753980i	$-0.271869\pi$
$227$	−1.13559e6	−	1.13559e6i	−0.0970828	−	0.0970828i	−0.753980	+	0.656897i	$0.771869\pi$
$228$		0			0
$229$	1.04290e7	+	1.04290e7i	0.868430	+	0.868430i	0.992299	−	0.123869i	$-0.0395303\pi$
$229$	1.04290e7	+	1.04290e7i	0.868430	+	0.868430i	−0.123869	+	0.992299i	$0.539530\pi$
$230$		0			0
$231$	−2.06738e7			−1.67720
$232$		0			0
$233$			4.37367e6i			0.345762i	0.984943	+	0.172881i	$0.0553077\pi$
$233$			4.37367e6i			0.345762i	−0.984943	+	0.172881i	$0.944692\pi$
$234$		0			0
$235$	1.32358e7	−	1.32358e7i	1.01987	−	1.01987i
$236$		0			0
$237$	−543413.	+	543413.i	−0.0408211	+	0.0408211i
$238$		0			0
$239$			1.38859e7i			1.01714i	0.861022	+	0.508568i	$0.169825\pi$
$239$			1.38859e7i			1.01714i	−0.861022	+	0.508568i	$0.830175\pi$
$240$		0			0
$241$	1.25616e7			0.897414			0.448707	−	0.893679i	$-0.351885\pi$
$241$	1.25616e7			0.897414			0.448707	+	0.893679i	$0.351885\pi$
$242$		0			0
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−2.60938e7	−	2.60938e7i	−1.77435	−	1.77435i
$246$		0			0
$247$	−2.36756e6			−0.157113
$248$		0			0
$249$		−	6.91221e6i		−	0.447733i
$250$		0			0
$251$	−6.04598e6	+	6.04598e6i	−0.382336	+	0.382336i	−0.871943	−	0.489607i	$-0.837140\pi$
$251$	−6.04598e6	+	6.04598e6i	−0.382336	+	0.382336i	0.489607	+	0.871943i	$0.337140\pi$
$252$		0			0
$253$	2.67517e7	−	2.67517e7i	1.65193	−	1.65193i
$254$		0			0
$255$		−	1.49849e7i		−	0.903719i
$256$		0			0
$257$	6.01294e6			0.354232			0.177116	−	0.984190i	$-0.443323\pi$
$257$	6.01294e6			0.354232			0.177116	+	0.984190i	$0.443323\pi$
$258$		0			0
$259$	8.50462e6	+	8.50462e6i	0.489503	+	0.489503i
$260$		0			0
$261$	4.15575e6	+	4.15575e6i	0.233737	+	0.233737i
$262$		0			0
$263$	1.84676e7			1.01518			0.507591	−	0.861598i	$-0.330536\pi$
$263$	1.84676e7			1.01518			0.507591	+	0.861598i	$0.330536\pi$
$264$		0			0
$265$			6.66773e6i			0.358295i
$266$		0			0
$267$	−7.68497e6	+	7.68497e6i	−0.403746	+	0.403746i
$268$		0			0
$269$	−9.12122e6	+	9.12122e6i	−0.468593	+	0.468593i	−0.901459	−	0.432865i	$-0.857503\pi$
$269$	−9.12122e6	+	9.12122e6i	−0.468593	+	0.468593i	0.432865	+	0.901459i	$0.357503\pi$
$270$		0			0
$271$		−	3.27431e6i		−	0.164517i	−0.996611	−	0.0822586i	$-0.973787\pi$
$271$		−	3.27431e6i		−	0.164517i	0.996611	−	0.0822586i	$-0.0262134\pi$
$272$		0			0
$273$	4.04060e6			0.198590
$274$		0			0
$275$	−3.28639e7	−	3.28639e7i	−1.58023	−	1.58023i
$276$		0			0
$277$	2.86856e7	+	2.86856e7i	1.34966	+	1.34966i	0.886024	+	0.463639i	$0.153456\pi$
$277$	2.86856e7	+	2.86856e7i	1.34966	+	1.34966i	0.463639	+	0.886024i	$0.346544\pi$
$278$		0			0
$279$	5.20709e6			0.239763
$280$		0			0
$281$			1.54278e7i			0.695320i	0.937621	+	0.347660i	$0.113024\pi$
$281$			1.54278e7i			0.695320i	−0.937621	+	0.347660i	$0.886976\pi$
$282$		0			0
$283$	−6.04042e6	+	6.04042e6i	−0.266507	+	0.266507i	−0.827691	−	0.561184i	$-0.810346\pi$
$283$	−6.04042e6	+	6.04042e6i	−0.266507	+	0.266507i	0.561184	+	0.827691i	$0.310346\pi$
$284$		0			0
$285$	−1.05974e7	+	1.05974e7i	−0.457790	+	0.457790i
$286$		0			0
$287$		−	2.74313e7i		−	1.16038i
$288$		0			0
$289$	2.06436e6			0.0855249
$290$		0			0
$291$	4.27804e6	+	4.27804e6i	0.173607	+	0.173607i
$292$		0			0
$293$	−1.42188e7	−	1.42188e7i	−0.565275	−	0.565275i	0.365526	−	0.930801i	$-0.380889\pi$
$293$	−1.42188e7	−	1.42188e7i	−0.565275	−	0.565275i	−0.930801	+	0.365526i	$0.880889\pi$
$294$		0			0
$295$	6.26160e7			2.43904
$296$		0			0
$297$		−	8.96309e6i		−	0.342128i
$298$		0			0
$299$	−5.22850e6	+	5.22850e6i	−0.195598	+	0.195598i
$300$		0			0
$301$	−2.09565e7	+	2.09565e7i	−0.768456	+	0.768456i
$302$		0			0
$303$		−	1.00136e7i		−	0.359968i
$304$		0			0
$305$	3.65668e7			1.28880
$306$		0			0
$307$	−1.87885e7	−	1.87885e7i	−0.649348	−	0.649348i	0.303488	−	0.952835i	$-0.401849\pi$
$307$	−1.87885e7	−	1.87885e7i	−0.649348	−	0.649348i	−0.952835	+	0.303488i	$0.901849\pi$
$308$		0			0
$309$	−1.55277e7	−	1.55277e7i	−0.526299	−	0.526299i
$310$		0			0
$311$	−4.87418e6			−0.162039			−0.0810196	−	0.996713i	$-0.525818\pi$
$311$	−4.87418e6			−0.162039			−0.0810196	+	0.996713i	$0.525818\pi$
$312$		0			0
$313$		−	4.20692e7i		−	1.37193i	−0.727636	−	0.685963i	$-0.759381\pi$
$313$		−	4.20692e7i		−	1.37193i	0.727636	−	0.685963i	$-0.240619\pi$
$314$		0			0
$315$	1.80861e7	−	1.80861e7i	0.578646	−	0.578646i
$316$		0			0
$317$	−1.72312e7	+	1.72312e7i	−0.540924	+	0.540924i	−0.923800	−	0.382876i	$-0.874934\pi$
$317$	−1.72312e7	+	1.72312e7i	−0.540924	+	0.540924i	0.382876	+	0.923800i	$0.374934\pi$
$318$		0			0
$319$			5.72277e7i			1.76293i
$320$		0			0
$321$	−1.44753e7			−0.437635
$322$		0			0
$323$	−1.85302e7	−	1.85302e7i	−0.549886	−	0.549886i
$324$		0			0
$325$	6.42309e6	+	6.42309e6i	0.187109	+	0.187109i
$326$		0			0
$327$	6.47715e6			0.185243
$328$		0			0
$329$			5.58664e7i			1.56878i
$330$		0			0
$331$	−3.49517e6	+	3.49517e6i	−0.0963795	+	0.0963795i	−0.753653	−	0.657273i	$-0.771710\pi$
$331$	−3.49517e6	+	3.49517e6i	−0.0963795	+	0.0963795i	0.657273	+	0.753653i	$0.271710\pi$
$332$		0			0
$333$	−3.68716e6	+	3.68716e6i	−0.0998525	+	0.0998525i
$334$		0			0
$335$		−	4.10792e7i		−	1.09267i
$336$		0			0
$337$	8.16812e6			0.213419			0.106709	−	0.994290i	$-0.465969\pi$
$337$	8.16812e6			0.213419			0.106709	+	0.994290i	$0.465969\pi$
$338$		0			0
$339$	−2.29976e6	−	2.29976e6i	−0.0590315	−	0.0590315i
$340$		0			0
$341$	3.58528e7	+	3.58528e7i	0.904190	+	0.904190i
$342$		0			0
$343$	4.41967e7			1.09524
$344$		0			0
$345$			4.68065e7i			1.13985i
$346$		0			0
$347$	1.60429e7	−	1.60429e7i	0.383967	−	0.383967i	−0.488562	−	0.872529i	$-0.662478\pi$
$347$	1.60429e7	−	1.60429e7i	0.383967	−	0.383967i	0.872529	+	0.488562i	$0.162478\pi$
$348$		0			0
$349$	5.65693e7	−	5.65693e7i	1.33077	−	1.33077i	0.426096	−	0.904678i	$-0.359888\pi$
$349$	5.65693e7	−	5.65693e7i	1.33077	−	1.33077i	0.904678	−	0.426096i	$-0.140112\pi$
$350$		0			0
$351$			1.75179e6i			0.0405099i
$352$		0			0
$353$	−6.54203e7			−1.48726			−0.743632	−	0.668589i	$-0.766899\pi$
$353$	−6.54203e7			−1.48726			−0.743632	+	0.668589i	$0.766899\pi$
$354$		0			0
$355$	6.06670e7	+	6.06670e7i	1.35602	+	1.35602i
$356$		0			0
$357$	3.16245e7	+	3.16245e7i	0.695056	+	0.695056i
$358$		0			0
$359$	−3.48626e7			−0.753488			−0.376744	−	0.926317i	$-0.622956\pi$
$359$	−3.48626e7			−0.753488			−0.376744	+	0.926317i	$0.622956\pi$
$360$		0			0
$361$		−	2.08365e7i		−	0.442897i
$362$		0			0
$363$	4.21868e7	−	4.21868e7i	0.881976	−	0.881976i
$364$		0			0
$365$	6.36648e7	−	6.36648e7i	1.30925	−	1.30925i
$366$		0			0
$367$		−	5.60118e7i		−	1.13313i	−0.824016	−	0.566567i	$-0.808271\pi$
$367$		−	5.60118e7i		−	1.13313i	0.824016	−	0.566567i	$-0.191729\pi$
$368$		0			0
$369$	1.18928e7			0.236703
$370$		0			0
$371$	−1.40718e7	−	1.40718e7i	−0.275567	−	0.275567i
$372$		0			0
$373$	−7.15514e7	−	7.15514e7i	−1.37877	−	1.37877i	−0.846701	−	0.532068i	$-0.821415\pi$
$373$	−7.15514e7	−	7.15514e7i	−1.37877	−	1.37877i	−0.532068	−	0.846701i	$-0.678585\pi$
$374$		0			0
$375$	1.17595e7			0.222994
$376$		0			0
$377$		−	1.11849e7i		−	0.208741i
$378$		0			0
$379$	3.95045e7	−	3.95045e7i	0.725654	−	0.725654i	−0.244097	−	0.969751i	$-0.578492\pi$
$379$	3.95045e7	−	3.95045e7i	0.725654	−	0.725654i	0.969751	+	0.244097i	$0.0784916\pi$
$380$		0			0
$381$	764104.	−	764104.i	0.0138159	−	0.0138159i
$382$		0			0
$383$		−	3.82446e7i		−	0.680728i	−0.940294	−	0.340364i	$-0.889450\pi$
$383$		−	3.82446e7i		−	0.680728i	0.940294	−	0.340364i	$-0.110550\pi$
$384$		0			0
$385$	2.49059e8			4.36435
$386$		0			0
$387$	−9.08563e6	−	9.08563e6i	−0.156755	−	0.156755i
$388$		0			0
$389$	5.74810e7	+	5.74810e7i	0.976507	+	0.976507i	0.999730	−	0.0232232i	$-0.00739284\pi$
$389$	5.74810e7	+	5.74810e7i	0.976507	+	0.976507i	−0.0232232	+	0.999730i	$0.507393\pi$
$390$		0			0
$391$	−8.18437e7			−1.36916
$392$		0			0
$393$		−	5.64846e7i		−	0.930577i
$394$		0			0
$395$	6.54653e6	−	6.54653e6i	0.106223	−	0.106223i
$396$		0			0
$397$	3.61932e7	−	3.61932e7i	0.578437	−	0.578437i	−0.356036	−	0.934472i	$-0.615872\pi$
$397$	3.61932e7	−	3.61932e7i	0.578437	−	0.578437i	0.934472	+	0.356036i	$0.115872\pi$
$398$		0			0
$399$		−	4.47302e7i		−	0.704178i
$400$		0			0
$401$	8.87303e7			1.37606			0.688032	−	0.725680i	$-0.258475\pi$
$401$	8.87303e7			1.37606			0.688032	+	0.725680i	$0.258475\pi$
$402$		0			0
$403$	−7.00725e6	−	7.00725e6i	−0.107061	−	0.107061i
$404$		0			0
$405$	7.84119e6	+	7.84119e6i	0.118037	+	0.118037i
$406$		0			0
$407$	−5.07749e7			−0.753123
$408$		0			0
$409$		−	2.62206e7i		−	0.383242i	−0.981469	−	0.191621i	$-0.938626\pi$
$409$		−	2.62206e7i		−	0.383242i	0.981469	−	0.191621i	$-0.0613744\pi$
$410$		0			0
$411$	−2.15182e7	+	2.15182e7i	−0.309941	+	0.309941i
$412$		0			0
$413$	−1.32147e8	+	1.32147e8i	−1.87588	+	1.87588i
$414$		0			0
$415$			8.32718e7i			1.16507i
$416$		0			0
$417$	−3.60186e7			−0.496728
$418$		0			0
$419$	−6.38322e7	−	6.38322e7i	−0.867756	−	0.867756i	0.124468	−	0.992224i	$-0.460278\pi$
$419$	−6.38322e7	−	6.38322e7i	−0.867756	−	0.867756i	−0.992224	+	0.124468i	$0.960278\pi$
$420$		0			0
$421$	6.55005e7	+	6.55005e7i	0.877806	+	0.877806i	0.993307	−	0.115502i	$-0.0368475\pi$
$421$	6.55005e7	+	6.55005e7i	0.877806	+	0.877806i	−0.115502	+	0.993307i	$0.536848\pi$
$422$		0			0
$423$	−2.42207e7			−0.320012
$424$		0			0
$425$			1.00543e8i			1.30974i
$426$		0			0
$427$	−7.71715e7	+	7.71715e7i	−0.991228	+	0.991228i
$428$		0			0
$429$	−1.20617e7	+	1.20617e7i	−0.152770	+	0.152770i
$430$		0			0
$431$		−	9.90574e7i		−	1.23724i	−0.785689	−	0.618622i	$-0.787691\pi$
$431$		−	9.90574e7i		−	1.23724i	0.785689	−	0.618622i	$-0.212309\pi$
$432$		0			0
$433$	−1.27390e8			−1.56918			−0.784590	−	0.620016i	$-0.787126\pi$
$433$	−1.27390e8			−1.56918			−0.784590	+	0.620016i	$0.787126\pi$
$434$		0			0
$435$	−5.00646e7	−	5.00646e7i	−0.608223	−	0.608223i
$436$		0			0
$437$	5.78805e7	+	5.78805e7i	0.693566	+	0.693566i
$438$		0			0
$439$	−8.97377e7			−1.06067			−0.530336	−	0.847787i	$-0.677934\pi$
$439$	−8.97377e7			−1.06067			−0.530336	+	0.847787i	$0.677934\pi$
$440$		0			0
$441$			4.77501e7i			0.556748i
$442$		0			0
$443$	8.30466e7	−	8.30466e7i	0.955236	−	0.955236i	−0.0438039	−	0.999040i	$-0.513948\pi$
$443$	8.30466e7	−	8.30466e7i	0.955236	−	0.955236i	0.999040	+	0.0438039i	$0.0139477\pi$
$444$		0			0
$445$	9.25812e7	−	9.25812e7i	1.05061	−	1.05061i
$446$		0			0
$447$		−	5.24544e7i		−	0.587300i
$448$		0			0
$449$	−1.03831e8			−1.14706			−0.573532	−	0.819183i	$-0.694427\pi$
$449$	−1.03831e8			−1.14706			−0.573532	+	0.819183i	$0.694427\pi$
$450$		0			0
$451$	8.18862e7	+	8.18862e7i	0.892649	+	0.892649i
$452$		0			0
$453$	−2.21764e7	−	2.21764e7i	−0.238560	−	0.238560i
$454$		0			0
$455$	−4.86774e7			−0.516765
$456$		0			0
$457$			9.59794e6i			0.100561i	0.998735	+	0.0502805i	$0.0160115\pi$
$457$			9.59794e6i			0.100561i	−0.998735	+	0.0502805i	$0.983988\pi$
$458$		0			0
$459$	−1.37107e7	+	1.37107e7i	−0.141783	+	0.141783i
$460$		0			0
$461$	−2.51797e7	+	2.51797e7i	−0.257009	+	0.257009i	−0.823836	−	0.566828i	$-0.808171\pi$
$461$	−2.51797e7	+	2.51797e7i	−0.257009	+	0.257009i	0.566828	+	0.823836i	$0.308171\pi$
$462$		0			0
$463$		−	6.04452e7i		−	0.609003i	−0.952512	−	0.304501i	$-0.901510\pi$
$463$		−	6.04452e7i		−	0.609003i	0.952512	−	0.304501i	$-0.0984898\pi$
$464$		0			0
$465$	−6.27302e7			−0.623904
$466$		0			0
$467$	5.93152e7	+	5.93152e7i	0.582392	+	0.582392i	0.935560	−	0.353168i	$-0.114896\pi$
$467$	5.93152e7	+	5.93152e7i	0.582392	+	0.582392i	−0.353168	+	0.935560i	$0.614896\pi$
$468$		0			0
$469$	8.66947e7	+	8.66947e7i	0.840377	+	0.840377i
$470$		0			0
$471$	−6.50064e6			−0.0622148
$472$		0			0
$473$		−	1.25116e8i		−	1.18230i
$474$		0			0
$475$	7.11048e7	−	7.11048e7i	0.663465	−	0.663465i
$476$		0			0
$477$	6.10077e6	−	6.10077e6i	0.0562121	−	0.0562121i
$478$		0			0
$479$			1.73580e8i			1.57940i	0.613493	+	0.789700i	$0.289764\pi$
$479$			1.73580e8i			1.57940i	−0.613493	+	0.789700i	$0.710236\pi$
$480$		0			0
$481$	9.92371e6			0.0891741
$482$		0			0
$483$	−9.87816e7	−	9.87816e7i	−0.876667	−	0.876667i
$484$		0			0
$485$	−5.15378e7	−	5.15378e7i	−0.451753	−	0.451753i
$486$		0			0
$487$	1.73860e8			1.50527			0.752634	−	0.658440i	$-0.228783\pi$
$487$	1.73860e8			1.50527			0.752634	+	0.658440i	$0.228783\pi$
$488$		0			0
$489$			5.91029e7i			0.505455i
$490$		0			0
$491$	6.40466e7	−	6.40466e7i	0.541068	−	0.541068i	−0.382774	−	0.923842i	$-0.625031\pi$
$491$	6.40466e7	−	6.40466e7i	0.541068	−	0.541068i	0.923842	+	0.382774i	$0.125031\pi$
$492$		0			0
$493$	8.75406e7	−	8.75406e7i	0.730582	−	0.730582i
$494$		0			0
$495$			1.07979e8i			0.890273i
$496$		0			0
$497$	−2.56067e8			−2.08585
$498$		0			0
$499$	1.51462e8	+	1.51462e8i	1.21900	+	1.21900i	0.967984	+	0.251011i	$0.0807630\pi$
$499$	1.51462e8	+	1.51462e8i	1.21900	+	1.21900i	0.251011	+	0.967984i	$0.419237\pi$
$500$		0			0
$501$	−6.65884e7	−	6.65884e7i	−0.529523	−	0.529523i
$502$		0			0
$503$	1.33145e8			1.04621			0.523106	−	0.852268i	$-0.324773\pi$
$503$	1.33145e8			1.04621			0.523106	+	0.852268i	$0.324773\pi$
$504$		0			0
$505$			1.20635e8i			0.936697i
$506$		0			0
$507$	−5.08471e7	+	5.08471e7i	−0.390159	+	0.390159i
$508$		0			0
$509$	7.84910e7	−	7.84910e7i	0.595205	−	0.595205i	−0.343828	−	0.939033i	$-0.611724\pi$
$509$	7.84910e7	−	7.84910e7i	0.595205	−	0.595205i	0.939033	+	0.343828i	$0.111724\pi$
$510$		0			0
$511$			2.68720e8i			2.01390i
$512$		0			0
$513$	1.93927e7			0.143643
$514$		0			0
$515$	1.87063e8	+	1.87063e8i	1.36952	+	1.36952i
$516$		0			0
$517$	−1.66769e8	−	1.66769e8i	−1.20682	−	1.20682i
$518$		0			0
$519$	−1.09133e6			−0.00780649
$520$		0			0
$521$		−	2.75710e8i		−	1.94957i	−0.223143	−	0.974786i	$-0.571632\pi$
$521$		−	2.75710e8i		−	1.94957i	0.223143	−	0.974786i	$-0.428368\pi$
$522$		0			0
$523$	−2.08104e7	+	2.08104e7i	−0.145471	+	0.145471i	−0.776091	−	0.630621i	$-0.782800\pi$
$523$	−2.08104e7	+	2.08104e7i	−0.145471	+	0.145471i	0.630621	+	0.776091i	$0.282800\pi$
$524$		0			0
$525$	−1.21351e8	+	1.21351e8i	−0.838620	+	0.838620i
$526$		0			0
$527$		−	1.09687e8i		−	0.749418i
$528$		0			0
$529$	1.07609e8			0.726911
$530$		0			0
$531$	−5.72918e7	−	5.72918e7i	−0.382656	−	0.382656i
$532$		0			0
$533$	−1.60043e7	−	1.60043e7i	−0.105695	−	0.105695i
$534$		0			0
$535$	1.74385e8			1.13880
$536$		0			0
$537$			1.25527e8i			0.810611i
$538$		0			0
$539$	−3.28777e8	+	3.28777e8i	−2.09959	+	2.09959i
$540$		0			0
$541$	−1.38547e8	+	1.38547e8i	−0.874996	+	0.874996i	−0.993012	−	0.118016i	$-0.962347\pi$
$541$	−1.38547e8	+	1.38547e8i	−0.874996	+	0.874996i	0.118016	+	0.993012i	$0.462347\pi$
$542$		0			0
$543$		−	6.10790e6i		−	0.0381498i
$544$		0			0
$545$	−7.80306e7			−0.482032
$546$		0			0
$547$	5.69309e7	+	5.69309e7i	0.347845	+	0.347845i	0.859306	−	0.511461i	$-0.170896\pi$
$547$	5.69309e7	+	5.69309e7i	0.347845	+	0.347845i	−0.511461	+	0.859306i	$0.670896\pi$
$548$		0			0
$549$	−3.34575e7	−	3.34575e7i	−0.202198	−	0.202198i
$550$		0			0
$551$	−1.23819e8			−0.740170
$552$		0			0
$553$			2.76319e7i			0.163394i
$554$		0			0
$555$	4.44194e7	−	4.44194e7i	0.259833	−	0.259833i
$556$		0			0
$557$	2.05807e8	−	2.05807e8i	1.19095	−	1.19095i	0.214154	−	0.976800i	$-0.431301\pi$
$557$	2.05807e8	−	2.05807e8i	1.19095	−	1.19095i	0.976800	−	0.214154i	$-0.0686994\pi$
$558$		0			0
$559$			2.44533e7i			0.139992i
$560$		0			0
$561$	−1.88807e8			−1.06937
$562$		0			0
$563$	−1.07206e8	−	1.07206e8i	−0.600749	−	0.600749i	0.339762	−	0.940511i	$-0.389653\pi$
$563$	−1.07206e8	−	1.07206e8i	−0.600749	−	0.600749i	−0.940511	+	0.339762i	$0.889653\pi$
$564$		0			0
$565$	2.77054e7	+	2.77054e7i	0.153610	+	0.153610i
$566$		0			0
$567$	−3.30965e7			−0.181565
$568$		0			0
$569$		−	3.00408e8i		−	1.63070i	−0.578965	−	0.815352i	$-0.696543\pi$
$569$		−	3.00408e8i		−	1.63070i	0.578965	−	0.815352i	$-0.303457\pi$
$570$		0			0
$571$	1.32017e7	−	1.32017e7i	0.0709123	−	0.0709123i	−0.670761	−	0.741673i	$-0.734032\pi$
$571$	1.32017e7	−	1.32017e7i	0.0709123	−	0.0709123i	0.741673	+	0.670761i	$0.234032\pi$
$572$		0			0
$573$	−1.18185e8	+	1.18185e8i	−0.628203	+	0.628203i
$574$		0			0
$575$		−	3.14054e8i		−	1.65196i
$576$		0			0
$577$	2.19319e8			1.14169			0.570846	−	0.821057i	$-0.306615\pi$
$577$	2.19319e8			1.14169			0.570846	+	0.821057i	$0.306615\pi$
$578$		0			0
$579$	−7.96168e7	−	7.96168e7i	−0.410175	−	0.410175i
$580$		0			0
$581$	−1.75739e8	−	1.75739e8i	−0.896066	−	0.896066i
$582$		0			0
$583$	8.40122e7			0.423971
$584$		0			0
$585$		−	2.11040e7i		−	0.105413i
$586$		0			0
$587$	7.34402e7	−	7.34402e7i	0.363094	−	0.363094i	−0.501857	−	0.864951i	$-0.667349\pi$
$587$	7.34402e7	−	7.34402e7i	0.363094	−	0.363094i	0.864951	+	0.501857i	$0.167349\pi$
$588$		0			0
$589$	−7.75716e7	+	7.75716e7i	−0.379627	+	0.379627i
$590$		0			0
$591$		−	2.48567e7i		−	0.120415i
$592$		0			0
$593$	−1.53563e8			−0.736414			−0.368207	−	0.929744i	$-0.620028\pi$
$593$	−1.53563e8			−0.736414			−0.368207	+	0.929744i	$0.620028\pi$
$594$		0			0
$595$	−3.80983e8	−	3.80983e8i	−1.80865	−	1.80865i
$596$		0			0
$597$	−6.81935e7	−	6.81935e7i	−0.320494	−	0.320494i
$598$		0			0
$599$	−1.80702e8			−0.840781			−0.420390	−	0.907343i	$-0.638107\pi$
$599$	−1.80702e8			−0.840781			−0.420390	+	0.907343i	$0.638107\pi$
$600$		0			0
$601$			5.35723e7i			0.246784i	0.992358	+	0.123392i	$0.0393772\pi$
$601$			5.35723e7i			0.246784i	−0.992358	+	0.123392i	$0.960623\pi$
$602$		0			0
$603$	−3.75863e7	+	3.75863e7i	−0.171426	+	0.171426i
$604$		0			0
$605$	−5.08227e8	+	5.08227e8i	−2.29505	+	2.29505i
$606$		0			0
$607$			2.17298e8i			0.971605i	0.874069	+	0.485802i	$0.161473\pi$
$607$			2.17298e8i			0.971605i	−0.874069	+	0.485802i	$0.838527\pi$
$608$		0			0
$609$	2.11315e8			0.935576
$610$		0			0
$611$	3.25941e7	+	3.25941e7i	0.142895	+	0.142895i
$612$		0			0
$613$	−6.93329e7	−	6.93329e7i	−0.300994	−	0.300994i	0.540409	−	0.841403i	$-0.318270\pi$
$613$	−6.93329e7	−	6.93329e7i	−0.300994	−	0.300994i	−0.841403	+	0.540409i	$0.818270\pi$
$614$		0			0
$615$	−1.43273e8			−0.615941
$616$		0			0
$617$			3.88737e8i			1.65501i	0.561458	+	0.827505i	$0.310241\pi$
$617$			3.88737e8i			1.65501i	−0.561458	+	0.827505i	$0.689759\pi$
$618$		0			0
$619$	−2.99986e8	+	2.99986e8i	−1.26482	+	1.26482i	−0.316095	+	0.948728i	$0.602372\pi$
$619$	−2.99986e8	+	2.99986e8i	−1.26482	+	1.26482i	−0.948728	+	0.316095i	$0.897628\pi$
$620$		0			0
$621$	4.28265e7	−	4.28265e7i	0.178829	−	0.178829i
$622$		0			0
$623$			3.90772e8i			1.61607i
$624$		0			0
$625$	1.65239e8			0.676819
$626$		0			0
$627$	1.33526e8	+	1.33526e8i	0.541705	+	0.541705i
$628$		0			0
$629$	7.76698e7	+	7.76698e7i	0.312105	+	0.312105i
$630$		0			0
$631$	−1.52851e7			−0.0608388			−0.0304194	−	0.999537i	$-0.509684\pi$
$631$	−1.52851e7			−0.0608388			−0.0304194	+	0.999537i	$0.509684\pi$
$632$		0			0
$633$			5.76678e7i			0.227364i
$634$		0			0
$635$	−9.20521e6	+	9.20521e6i	−0.0359511	+	0.0359511i
$636$		0			0
$637$	6.42579e7	−	6.42579e7i	0.248604	−	0.248604i
$638$		0			0
$639$		−	1.11017e8i		−	0.425488i
$640$		0			0
$641$	2.96095e8			1.12423			0.562117	−	0.827058i	$-0.309987\pi$
$641$	2.96095e8			1.12423			0.562117	+	0.827058i	$0.309987\pi$
$642$		0			0
$643$	9.15106e7	+	9.15106e7i	0.344222	+	0.344222i	0.857952	−	0.513730i	$-0.171737\pi$
$643$	9.15106e7	+	9.15106e7i	0.344222	+	0.344222i	−0.513730	+	0.857952i	$0.671737\pi$
$644$		0			0
$645$	1.09455e8	+	1.09455e8i	0.407903	+	0.407903i
$646$		0			0
$647$	−1.40944e8			−0.520396			−0.260198	−	0.965555i	$-0.583788\pi$
$647$	−1.40944e8			−0.520396			−0.260198	+	0.965555i	$0.583788\pi$
$648$		0			0
$649$		−	7.88951e8i		−	2.88613i
$650$		0			0
$651$	1.32387e8	−	1.32387e8i	0.479848	−	0.479848i
$652$		0			0
$653$	7.82470e7	−	7.82470e7i	0.281014	−	0.281014i	−0.552499	−	0.833513i	$-0.686326\pi$
$653$	7.82470e7	−	7.82470e7i	0.281014	−	0.281014i	0.833513	+	0.552499i	$0.186326\pi$
$654$		0			0
$655$			6.80473e8i			2.42152i
$656$		0			0
$657$	−1.16503e8			−0.410810
$658$		0			0
$659$	1.80906e8	+	1.80906e8i	0.632117	+	0.632117i	0.948599	−	0.316482i	$-0.102502\pi$
$659$	1.80906e8	+	1.80906e8i	0.632117	+	0.632117i	−0.316482	+	0.948599i	$0.602502\pi$
$660$		0			0
$661$	−2.65068e8	−	2.65068e8i	−0.917809	−	0.917809i	0.0790605	−	0.996870i	$-0.474808\pi$
$661$	−2.65068e8	−	2.65068e8i	−0.917809	−	0.917809i	−0.996870	+	0.0790605i	$0.974808\pi$
$662$		0			0
$663$	3.69014e7			0.126620
$664$		0			0
$665$			5.38868e8i			1.83239i
$666$		0			0
$667$	−2.73440e8	+	2.73440e8i	−0.921476	+	0.921476i
$668$		0			0
$669$	1.29245e8	−	1.29245e8i	0.431653	−	0.431653i
$670$		0			0
$671$		−	4.60735e8i		−	1.52505i
$672$		0			0
$673$	−2.68730e8			−0.881598			−0.440799	−	0.897606i	$-0.645305\pi$
$673$	−2.68730e8			−0.881598			−0.440799	+	0.897606i	$0.645305\pi$
$674$		0			0
$675$	−5.26114e7	−	5.26114e7i	−0.171068	−	0.171068i
$676$		0			0
$677$	−1.59297e8	−	1.59297e8i	−0.513382	−	0.513382i	0.402179	−	0.915561i	$-0.368253\pi$
$677$	−1.59297e8	−	1.59297e8i	−0.513382	−	0.513382i	−0.915561	+	0.402179i	$0.868253\pi$
$678$		0			0
$679$	2.17534e8			0.694892
$680$		0			0
$681$		−	2.50344e7i		−	0.0792678i
$682$		0			0
$683$	1.06220e8	−	1.06220e8i	0.333384	−	0.333384i	−0.520486	−	0.853870i	$-0.674249\pi$
$683$	1.06220e8	−	1.06220e8i	0.333384	−	0.333384i	0.853870	+	0.520486i	$0.174249\pi$
$684$		0			0
$685$	2.59230e8	−	2.59230e8i	0.806518	−	0.806518i
$686$		0			0
$687$			2.29911e8i			0.709070i
$688$		0			0
$689$	−1.64198e7			−0.0502007
$690$		0			0
$691$	3.88395e8	+	3.88395e8i	1.17717	+	1.17717i	0.980462	+	0.196708i	$0.0630252\pi$
$691$	3.88395e8	+	3.88395e8i	1.17717	+	1.17717i	0.196708	+	0.980462i	$0.436975\pi$
$692$		0			0
$693$	−2.27882e8	−	2.27882e8i	−0.684715	−	0.684715i
$694$		0			0
$695$	4.33918e8			1.29257
$696$		0			0
$697$		−	2.50521e8i		−	0.739853i
$698$		0			0
$699$	−4.82096e7	+	4.82096e7i	−0.141157	+	0.141157i
$700$		0			0
$701$	−1.76804e8	+	1.76804e8i	−0.513261	+	0.513261i	−0.915524	−	0.402263i	$-0.868224\pi$
$701$	−1.76804e8	+	1.76804e8i	−0.513261	+	0.513261i	0.402263	+	0.915524i	$0.368224\pi$
$702$		0			0
$703$		−	1.09857e8i		−	0.316201i
$704$		0			0
$705$	2.91789e8			0.832724
$706$		0			0
$707$	−2.54591e8	−	2.54591e8i	−0.720419	−	0.720419i
$708$		0			0
$709$	3.48418e8	+	3.48418e8i	0.977601	+	0.977601i	0.999755	−	0.0221537i	$-0.00705233\pi$
$709$	3.48418e8	+	3.48418e8i	0.977601	+	0.977601i	−0.0221537	+	0.999755i	$0.507052\pi$
$710$		0			0
$711$	−1.19798e7			−0.0333303
$712$		0			0
$713$			3.42616e8i			0.945233i
$714$		0			0
$715$	1.45309e8	−	1.45309e8i	0.397533	−	0.397533i
$716$		0			0
$717$	−1.53060e8	+	1.53060e8i	−0.415244	+	0.415244i
$718$		0			0
$719$			4.83217e8i			1.30004i	0.759919	+	0.650018i	$0.225239\pi$
$719$			4.83217e8i			1.30004i	−0.759919	+	0.650018i	$0.774761\pi$
$720$		0			0
$721$	−7.89567e8			−2.10661
$722$		0			0
$723$	1.38462e8	+	1.38462e8i	0.366368	+	0.366368i
$724$		0			0
$725$	3.35914e8	+	3.35914e8i	0.881484	+	0.881484i
$726$		0			0
$727$	−4.97084e8			−1.29368			−0.646839	−	0.762626i	$-0.723910\pi$
$727$	−4.97084e8			−1.29368			−0.646839	+	0.762626i	$0.723910\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	−1.91388e8	+	1.91388e8i	−0.489963	+	0.489963i
$732$		0			0
$733$	−1.17482e8	+	1.17482e8i	−0.298305	+	0.298305i	−0.840350	−	0.542045i	$-0.817650\pi$
$733$	−1.17482e8	+	1.17482e8i	−0.298305	+	0.298305i	0.542045	+	0.840350i	$0.317650\pi$
$734$		0			0
$735$		−	5.75248e8i		−	1.44875i
$736$		0			0
$737$	−5.17591e8			−1.29296
$738$		0			0
$739$	−3.86420e7	−	3.86420e7i	−0.0957472	−	0.0957472i	0.657611	−	0.753358i	$-0.271567\pi$
$739$	−3.86420e7	−	3.86420e7i	−0.0957472	−	0.0957472i	−0.753358	+	0.657611i	$0.771567\pi$
$740$		0			0
$741$	−2.60970e7	−	2.60970e7i	−0.0641409	−	0.0641409i
$742$		0			0
$743$	−4.36772e8			−1.06485			−0.532424	−	0.846478i	$-0.678719\pi$
$743$	−4.36772e8			−1.06485			−0.532424	+	0.846478i	$0.678719\pi$
$744$		0			0
$745$			6.31922e8i			1.52825i
$746$		0			0
$747$	7.61912e7	−	7.61912e7i	0.182786	−	0.182786i
$748$		0			0
$749$	−3.68026e8	+	3.68026e8i	−0.875857	+	0.875857i
$750$		0			0
$751$		−	5.13454e8i		−	1.21222i	−0.795380	−	0.606111i	$-0.792729\pi$
$751$		−	5.13454e8i		−	1.21222i	0.795380	−	0.606111i	$-0.207271\pi$
$752$		0			0
$753$	−1.33286e8			−0.312176
$754$		0			0
$755$	2.67161e8	+	2.67161e8i	0.620772	+	0.620772i
$756$		0			0
$757$	−3.19198e8	−	3.19198e8i	−0.735822	−	0.735822i	0.235944	−	0.971767i	$-0.424182\pi$
$757$	−3.19198e8	−	3.19198e8i	−0.735822	−	0.735822i	−0.971767	+	0.235944i	$0.924182\pi$
$758$		0			0
$759$	5.89753e8			1.34879
$760$		0			0
$761$		−	7.70838e8i		−	1.74908i	−0.484955	−	0.874539i	$-0.661164\pi$
$761$		−	7.70838e8i		−	1.74908i	0.484955	−	0.874539i	$-0.338836\pi$
$762$		0			0
$763$	1.64678e8	−	1.64678e8i	0.370733	−	0.370733i
$764$		0			0
$765$	1.65174e8	−	1.65174e8i	0.368942	−	0.368942i
$766$		0			0
$767$			1.54197e8i			0.341734i
$768$		0			0
$769$	2.13304e8			0.469050			0.234525	−	0.972110i	$-0.424646\pi$
$769$	2.13304e8			0.469050			0.234525	+	0.972110i	$0.424646\pi$
$770$		0			0
$771$	6.62789e7	+	6.62789e7i	0.144615	+	0.144615i
$772$		0			0
$773$	2.47431e8	+	2.47431e8i	0.535693	+	0.535693i	0.922261	−	0.386568i	$-0.126340\pi$
$773$	2.47431e8	+	2.47431e8i	0.535693	+	0.535693i	−0.386568	+	0.922261i	$0.626340\pi$
$774$		0			0
$775$	4.20896e8			0.904210
$776$		0			0
$777$			1.87488e8i			0.399678i
$778$		0			0
$779$	−1.77170e8	+	1.77170e8i	−0.374781	+	0.374781i
$780$		0			0
$781$	7.64394e8	−	7.64394e8i	1.60459	−	1.60459i
$782$		0			0
$783$			9.16152e7i			0.190846i
$784$		0			0
$785$	7.83136e7			0.161893
$786$		0			0
$787$	−4.82283e8	−	4.82283e8i	−0.989414	−	0.989414i	0.0105302	−	0.999945i	$-0.496648\pi$
$787$	−4.82283e8	−	4.82283e8i	−0.989414	−	0.989414i	−0.999945	+	0.0105302i	$0.996648\pi$
$788$		0			0
$789$	2.03563e8	+	2.03563e8i	0.414446	+	0.414446i
$790$		0			0
$791$	−1.16940e8			−0.236284
$792$		0			0
$793$			9.00484e7i			0.180574i
$794$		0			0
$795$	−7.34964e7	+	7.34964e7i	−0.146273	+	0.146273i
$796$		0			0
$797$	5.37448e8	−	5.37448e8i	1.06160	−	1.06160i	0.0636270	−	0.997974i	$-0.479733\pi$
$797$	5.37448e8	−	5.37448e8i	1.06160	−	1.06160i	0.997974	−	0.0636270i	$-0.0202668\pi$
$798$		0			0
$799$			5.10208e8i			1.00025i
$800$		0			0
$801$	−1.69418e8			−0.329657
$802$		0			0
$803$	−8.02165e8	−	8.02165e8i	−1.54923	−	1.54923i
$804$		0			0
$805$	1.19003e9	+	1.19003e9i	2.28123	+	2.28123i
$806$		0			0
$807$	−2.01081e8			−0.382605
$808$		0			0
$809$			4.57488e8i			0.864041i	0.901864	+	0.432021i	$0.142199\pi$
$809$			4.57488e8i			0.864041i	−0.901864	+	0.432021i	$0.857801\pi$
$810$		0			0
$811$	5.60541e8	−	5.60541e8i	1.05086	−	1.05086i	0.0522240	−	0.998635i	$-0.483369\pi$
$811$	5.60541e8	−	5.60541e8i	1.05086	−	1.05086i	0.998635	−	0.0522240i	$-0.0166310\pi$
$812$		0			0
$813$	3.60917e7	−	3.60917e7i	0.0671639	−	0.0671639i
$814$		0			0
$815$		−	7.12017e8i		−	1.31528i
$816$		0			0
$817$	2.70703e8			0.496394
$818$		0			0
$819$	4.45384e7	+	4.45384e7i	0.0810742	+	0.0810742i
$820$		0			0
$821$	−1.46448e8	−	1.46448e8i	−0.264640	−	0.264640i	0.562296	−	0.826936i	$-0.309918\pi$
$821$	−1.46448e8	−	1.46448e8i	−0.264640	−	0.264640i	−0.826936	+	0.562296i	$0.809918\pi$
$822$		0			0
$823$	−5.09429e8			−0.913869			−0.456935	−	0.889500i	$-0.651053\pi$
$823$	−5.09429e8			−0.913869			−0.456935	+	0.889500i	$0.651053\pi$
$824$		0			0
$825$		−	7.24498e8i		−	1.29025i
$826$		0			0
$827$	7.41882e8	−	7.41882e8i	1.31165	−	1.31165i	0.391453	−	0.920198i	$-0.371972\pi$
$827$	7.41882e8	−	7.41882e8i	1.31165	−	1.31165i	0.920198	−	0.391453i	$-0.128028\pi$
$828$		0			0
$829$	−6.56805e8	+	6.56805e8i	−1.15285	+	1.15285i	−0.166871	+	0.985979i	$0.553366\pi$
$829$	−6.56805e8	+	6.56805e8i	−1.15285	+	1.15285i	−0.985979	+	0.166871i	$0.946634\pi$
$830$		0			0
$831$			6.32387e8i			1.10200i
$832$		0			0
$833$	1.00585e9			1.74020
$834$		0			0
$835$	8.02194e8	+	8.02194e8i	1.37791	+	1.37791i
$836$		0			0
$837$	5.73963e7	+	5.73963e7i	0.0978830	+	0.0978830i
$838$		0			0
$839$	−5.03084e8			−0.851833			−0.425916	−	0.904763i	$-0.640048\pi$
$839$	−5.03084e8			−0.851833			−0.425916	+	0.904763i	$0.640048\pi$
$840$		0			0
$841$			9.87677e6i			0.0166045i
$842$		0			0
$843$	−1.70056e8	+	1.70056e8i	−0.283863	+	0.283863i
$844$		0			0
$845$	6.12558e8	−	6.12558e8i	1.01526	−	1.01526i
$846$		0			0
$847$		−	2.14515e9i		−	3.53027i
$848$		0			0
$849$	−1.33164e8			−0.217602
$850$		0			0
$851$	−2.42607e8	−	2.42607e8i	−0.393655	−	0.393655i
$852$		0			0
$853$	−4.05722e8	−	4.05722e8i	−0.653705	−	0.653705i	0.300178	−	0.953883i	$-0.402954\pi$
$853$	−4.05722e8	−	4.05722e8i	−0.653705	−	0.653705i	−0.953883	+	0.300178i	$0.902954\pi$
$854$		0			0
$855$	−2.33625e8			−0.373784
$856$		0			0
$857$		−	5.52484e8i		−	0.877763i	−0.898545	−	0.438881i	$-0.855375\pi$
$857$		−	5.52484e8i		−	0.877763i	0.898545	−	0.438881i	$-0.144625\pi$
$858$		0			0
$859$	7.20731e8	−	7.20731e8i	1.13709	−	1.13709i	0.148117	−	0.988970i	$-0.452679\pi$
$859$	7.20731e8	−	7.20731e8i	1.13709	−	1.13709i	0.988970	−	0.148117i	$-0.0473213\pi$
$860$		0			0
$861$	3.02367e8	−	3.02367e8i	0.473724	−	0.473724i
$862$		0			0
$863$			1.61048e7i			0.0250566i	0.999922	+	0.0125283i	$0.00398799\pi$
$863$			1.61048e7i			0.0250566i	−0.999922	+	0.0125283i	$0.996012\pi$
$864$		0			0
$865$	1.31474e7			0.0203138
$866$		0			0
$867$	2.27549e7	+	2.27549e7i	0.0349154	+	0.0349154i
$868$		0			0
$869$	−8.24850e7	−	8.24850e7i	−0.125694	−	0.125694i
$870$		0			0
$871$	1.01161e8			0.153094
$872$		0			0
$873$			9.43112e7i			0.141749i
$874$		0			0
$875$	2.98978e8	−	2.98978e8i	0.446287	−	0.446287i
$876$		0			0
$877$	−2.91723e8	+	2.91723e8i	−0.432486	+	0.432486i	−0.889473	−	0.456987i	$-0.848929\pi$
$877$	−2.91723e8	+	2.91723e8i	−0.432486	+	0.432486i	0.456987	+	0.889473i	$0.348929\pi$
$878$		0			0
$879$		−	3.13459e8i		−	0.461545i
$880$		0			0
$881$	5.75240e8			0.841243			0.420621	−	0.907236i	$-0.361812\pi$
$881$	5.75240e8			0.841243			0.420621	+	0.907236i	$0.361812\pi$
$882$		0			0
$883$	3.60694e7	+	3.60694e7i	0.0523911	+	0.0523911i	0.732817	−	0.680426i	$-0.238205\pi$
$883$	3.60694e7	+	3.60694e7i	0.0523911	+	0.0523911i	−0.680426	+	0.732817i	$0.738205\pi$
$884$		0			0
$885$	6.90198e8	+	6.90198e8i	0.995735	+	0.995735i
$886$		0			0
$887$	6.18480e8			0.886247			0.443123	−	0.896461i	$-0.353870\pi$
$887$	6.18480e8			0.886247			0.443123	+	0.896461i	$0.353870\pi$
$888$		0			0
$889$		−	3.88538e7i		−	0.0553005i
$890$		0			0
$891$	9.87975e7	−	9.87975e7i	0.139673	−	0.139673i
$892$		0			0
$893$	3.60823e8	−	3.60823e8i	0.506687	−	0.506687i
$894$		0			0
$895$		−	1.51223e9i		−	2.10934i
$896$		0			0
$897$	−1.15264e8			−0.159705
$898$		0			0
$899$	−3.66465e8	−	3.66465e8i	−0.504375	−	0.504375i
$900$		0			0
$901$	−1.28513e8	−	1.28513e8i	−0.175700	−	0.175700i
$902$		0			0
$903$	−4.61994e8			−0.627442
$904$		0			0
$905$			7.35822e7i			0.0992721i
$906$		0			0
$907$	−8.80041e8	+	8.80041e8i	−1.17945	+	1.17945i	−0.199571	+	0.979883i	$0.563955\pi$
$907$	−8.80041e8	+	8.80041e8i	−1.17945	+	1.17945i	−0.979883	+	0.199571i	$0.936045\pi$
$908$		0			0
$909$	1.10377e8	−	1.10377e8i	0.146956	−	0.146956i
$910$		0			0
$911$			7.56900e8i			1.00111i	0.865704	+	0.500557i	$0.166871\pi$
$911$			7.56900e8i			1.00111i	−0.865704	+	0.500557i	$0.833129\pi$
$912$		0			0
$913$	1.04921e9			1.37864
$914$		0			0
$915$	4.03065e8	+	4.03065e8i	0.526152	+	0.526152i
$916$		0			0
$917$	−1.43609e9	−	1.43609e9i	−1.86240	−	1.86240i
$918$		0			0
$919$	−2.28186e8			−0.293997			−0.146999	−	0.989137i	$-0.546961\pi$
$919$	−2.28186e8			−0.293997			−0.146999	+	0.989137i	$0.546961\pi$
$920$		0			0
$921$		−	4.14200e8i		−	0.530190i
$922$		0			0
$923$	−1.49397e8	+	1.49397e8i	−0.189993	+	0.189993i
$924$		0			0
$925$	−2.98037e8	+	2.98037e8i	−0.376570	+	0.376570i
$926$		0			0
$927$		−	3.42315e8i		−	0.429721i
$928$		0			0
$929$	3.19845e8			0.398927			0.199463	−	0.979905i	$-0.436080\pi$
$929$	3.19845e8			0.398927			0.199463	+	0.979905i	$0.436080\pi$
$930$		0			0
$931$	−7.11347e8	−	7.11347e8i	−0.881520	−	0.881520i
$932$		0			0
$933$	−5.37266e7	−	5.37266e7i	−0.0661522	−	0.0661522i
$934$		0			0
$935$	2.27457e9			2.78269
$936$		0			0
$937$			1.27994e9i			1.55586i	0.628353	+	0.777929i	$0.283730\pi$
$937$			1.27994e9i			1.55586i	−0.628353	+	0.777929i	$0.716270\pi$
$938$		0			0
$939$	4.63716e8	−	4.63716e8i	0.560087	−	0.560087i
$940$		0			0
$941$	2.32998e8	−	2.32998e8i	0.279630	−	0.279630i	−0.553331	−	0.832961i	$-0.686644\pi$
$941$	2.32998e8	−	2.32998e8i	0.279630	−	0.279630i	0.832961	+	0.553331i	$0.186644\pi$
$942$		0			0
$943$			7.82520e8i			0.933169i
$944$		0			0
$945$	3.98715e8			0.472463
$946$		0			0
$947$	1.05889e9	+	1.05889e9i	1.24681	+	1.24681i	0.957122	+	0.289686i	$0.0935508\pi$
$947$	1.05889e9	+	1.05889e9i	1.24681	+	1.24681i	0.289686	+	0.957122i	$0.406449\pi$
$948$		0			0
$949$	1.56779e8	+	1.56779e8i	0.183438	+	0.183438i
$950$		0			0
$951$	−3.79868e8			−0.441663
$952$		0			0
$953$			5.31924e8i			0.614570i	0.951618	+	0.307285i	$0.0994204\pi$
$953$			5.31924e8i			0.614570i	−0.951618	+	0.307285i	$0.900580\pi$
$954$		0			0
$955$	1.42379e9	−	1.42379e9i	1.63469	−	1.63469i
$956$		0			0
$957$	−6.30804e8	+	6.30804e8i	−0.719712	+	0.719712i
$958$		0			0
$959$			1.09417e9i			1.24060i
$960$		0			0
$961$	4.28329e8			0.482622
$962$		0			0
$963$	−1.59557e8	−	1.59557e8i	−0.178664	−	0.178664i
$964$		0			0
$965$	9.59148e8	+	9.59148e8i	1.06734	+	1.06734i
$966$		0			0
$967$	−2.95224e7			−0.0326492			−0.0163246	−	0.999867i	$-0.505197\pi$
$967$	−2.95224e7			−0.0326492			−0.0163246	+	0.999867i	$0.505197\pi$
$968$		0			0
$969$		−	4.08506e8i		−	0.448980i
$970$		0			0
$971$	−5.62884e8	+	5.62884e8i	−0.614838	+	0.614838i	−0.944203	−	0.329365i	$-0.893165\pi$
$971$	−5.62884e8	+	5.62884e8i	−0.614838	+	0.614838i	0.329365	+	0.944203i	$0.393165\pi$
$972$		0			0
$973$	−9.15753e8	+	9.15753e8i	−0.994123	+	0.994123i
$974$		0			0
$975$			1.41600e8i			0.152774i
$976$		0			0
$977$	−5.34479e7			−0.0573122			−0.0286561	−	0.999589i	$-0.509123\pi$
$977$	−5.34479e7			−0.0573122			−0.0286561	+	0.999589i	$0.509123\pi$
$978$		0			0
$979$	−1.16651e9	−	1.16651e9i	−1.24320	−	1.24320i
$980$		0			0
$981$	7.13957e7	+	7.13957e7i	0.0756249	+	0.0756249i
$982$		0			0
$983$	5.90263e8			0.621419			0.310710	−	0.950505i	$-0.399433\pi$
$983$	5.90263e8			0.621419			0.310710	+	0.950505i	$0.399433\pi$
$984$		0			0
$985$			2.99451e8i			0.313340i
$986$		0			0
$987$	−6.15798e8	+	6.15798e8i	−0.640453	+	0.640453i
$988$		0			0
$989$	5.97816e8	−	5.97816e8i	0.617986	−	0.617986i
$990$		0			0
$991$			6.65979e8i			0.684289i	0.939647	+	0.342144i	$0.111153\pi$
$991$			6.65979e8i			0.684289i	−0.939647	+	0.342144i	$0.888847\pi$
$992$		0			0
$993$	−7.70525e7			−0.0786935
$994$		0			0
$995$	8.21531e8	+	8.21531e8i	0.833978	+	0.833978i
$996$		0			0
$997$	6.01193e8	+	6.01193e8i	0.606636	+	0.606636i	0.942065	−	0.335429i	$-0.108881\pi$
$997$	6.01193e8	+	6.01193e8i	0.606636	+	0.606636i	−0.335429	+	0.942065i	$0.608881\pi$
$998$		0			0
$999$	−8.12849e7			−0.0815292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.15		48
4.3	odd	2		384.7.l.b.31.10		48
8.3	odd	2		48.7.l.a.43.14	yes	48
8.5	even	2		192.7.l.a.79.10		48
16.3	odd	4	inner	384.7.l.a.223.15		48
16.5	even	4		48.7.l.a.19.14	✓	48
16.11	odd	4		192.7.l.a.175.10		48
16.13	even	4		384.7.l.b.223.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.14	✓	48	16.5	even	4
48.7.l.a.43.14	yes	48	8.3	odd	2
192.7.l.a.79.10		48	8.5	even	2
192.7.l.a.175.10		48	16.11	odd	4
384.7.l.a.31.15		48	1.1	even	1	trivial
384.7.l.a.223.15		48	16.3	odd	4	inner
384.7.l.b.31.10		48	4.3	odd	2
384.7.l.b.223.10		48	16.13	even	4

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 + 11.0227i) q^{3} +(-132.791 - 132.791i) q^{5} +560.492 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 + 11.0227i) q^{3} +(-132.791 - 132.791i) q^{5} +560.492 q^{7} +243.000i q^{9} +(-1673.14 + 1673.14i) q^{11} +(327.008 - 327.008i) q^{13} -2927.44i q^{15} +5118.78 q^{17} +(-3620.04 - 3620.04i) q^{19} +(6178.14 + 6178.14i) q^{21} -15988.9 q^{23} +19642.0i q^{25} +(-2678.52 + 2678.52i) q^{27} +(17101.9 - 17101.9i) q^{29} -21428.4i q^{31} -36885.2 q^{33} +(-74428.4 - 74428.4i) q^{35} +(15173.5 + 15173.5i) q^{37} +7209.02 q^{39} -48941.5i q^{41} +(-37389.4 + 37389.4i) q^{43} +(32268.3 - 32268.3i) q^{45} +99673.8i q^{47} +196502. q^{49} +(56422.8 + 56422.8i) q^{51} +(-25106.1 - 25106.1i) q^{53} +444358. q^{55} -79805.3i q^{57} +(-235769. + 235769. i) q^{59} +(-137685. + 137685. i) q^{61} +136200. i q^{63} -86847.5 q^{65} +(154676. + 154676. i) q^{67} +(-176241. - 176241. i) q^{69} -456860. q^{71} +479436. i q^{73} +(-216508. + 216508. i) q^{75} +(-937785. + 937785. i) q^{77} +49299.4i q^{79} -59049.0 q^{81} +(-313544. - 313544. i) q^{83} +(-679729. - 679729. i) q^{85} +377017. q^{87} +697194. i q^{89} +(183285. - 183285. i) q^{91} +(236199. - 236199. i) q^{93} +961419. i q^{95} +388112. q^{97} +(-406574. - 406574. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) \) 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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