LMFDB - Embedded newform 384.7.l.b.31.11

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			31.11
Character	$\chi$	$=$	384.31
Dual form			384.7.l.b.223.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(-145.472 - 145.472i) q^{5} +535.877 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(-145.472 - 145.472i) q^{5} +535.877 q^{7} +243.000i q^{9} +(1236.38 - 1236.38i) q^{11} +(-1765.46 + 1765.46i) q^{13} +3206.99i q^{15} -5538.46 q^{17} +(3224.38 + 3224.38i) q^{19} +(-5906.81 - 5906.81i) q^{21} -2832.41 q^{23} +26699.2i q^{25} +(2678.52 - 2678.52i) q^{27} +(-11711.9 + 11711.9i) q^{29} -31141.3i q^{31} -27256.4 q^{33} +(-77955.0 - 77955.0i) q^{35} +(-30054.0 - 30054.0i) q^{37} +38920.3 q^{39} -24286.6i q^{41} +(-30960.8 + 30960.8i) q^{43} +(35349.7 - 35349.7i) q^{45} +6262.62i q^{47} +169515. q^{49} +(61048.8 + 61048.8i) q^{51} +(-198895. - 198895. i) q^{53} -359716. q^{55} -71082.7i q^{57} +(-134053. + 134053. i) q^{59} +(-103162. + 103162. i) q^{61} +130218. i q^{63} +513650. q^{65} +(396383. + 396383. i) q^{67} +(31220.8 + 31220.8i) q^{69} -334941. q^{71} +436170. i q^{73} +(294297. - 294297. i) q^{75} +(662546. - 662546. i) q^{77} +350208. i q^{79} -59049.0 q^{81} +(460817. + 460817. i) q^{83} +(805691. + 805691. i) q^{85} +258193. q^{87} -137632. i q^{89} +(-946068. + 946068. i) q^{91} +(-343261. + 343261. i) q^{93} -938113. i q^{95} -347536. q^{97} +(300440. + 300440. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−145.472	−	145.472i	−1.16378	−	1.16378i	−0.983642	−	0.180133i	$-0.942347\pi$
$5$	−145.472	−	145.472i	−1.16378	−	1.16378i	−0.180133	−	0.983642i	$-0.557653\pi$
$6$		0			0
$7$	535.877			1.56232			0.781161	−	0.624329i	$-0.214628\pi$
$7$	535.877			1.56232			0.781161	+	0.624329i	$0.214628\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	1236.38	−	1236.38i	0.928909	−	0.928909i	−0.0687268	−	0.997636i	$-0.521894\pi$
$11$	1236.38	−	1236.38i	0.928909	−	0.928909i	0.997636	+	0.0687268i	$0.0218937\pi$
$12$		0			0
$13$	−1765.46	+	1765.46i	−0.803577	+	0.803577i	−0.983653	−	0.180076i	$-0.942366\pi$
$13$	−1765.46	+	1765.46i	−0.803577	+	0.803577i	0.180076	+	0.983653i	$0.442366\pi$
$14$		0			0
$15$			3206.99i			0.950219i
$16$		0			0
$17$	−5538.46			−1.12731			−0.563654	−	0.826011i	$-0.690605\pi$
$17$	−5538.46			−1.12731			−0.563654	+	0.826011i	$0.690605\pi$
$18$		0			0
$19$	3224.38	+	3224.38i	0.470094	+	0.470094i	0.901945	−	0.431851i	$-0.142139\pi$
$19$	3224.38	+	3224.38i	0.470094	+	0.470094i	−0.431851	+	0.901945i	$0.642139\pi$
$20$		0			0
$21$	−5906.81	−	5906.81i	−0.637816	−	0.637816i
$22$		0			0
$23$	−2832.41			−0.232795			−0.116397	−	0.993203i	$-0.537135\pi$
$23$	−2832.41			−0.232795			−0.116397	+	0.993203i	$0.537135\pi$
$24$		0			0
$25$			26699.2i			1.70875i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	−11711.9	+	11711.9i	−0.480210	+	0.480210i	−0.905199	−	0.424988i	$-0.860278\pi$
$29$	−11711.9	+	11711.9i	−0.480210	+	0.480210i	0.424988	+	0.905199i	$0.360278\pi$
$30$		0			0
$31$		−	31141.3i		−	1.04532i	−0.852540	−	0.522662i	$-0.824939\pi$
$31$		−	31141.3i		−	1.04532i	0.852540	−	0.522662i	$-0.175061\pi$
$32$		0			0
$33$	−27256.4			−0.758451
$34$		0			0
$35$	−77955.0	−	77955.0i	−1.81819	−	1.81819i
$36$		0			0
$37$	−30054.0	−	30054.0i	−0.593331	−	0.593331i	0.345198	−	0.938530i	$-0.387812\pi$
$37$	−30054.0	−	30054.0i	−0.593331	−	0.593331i	−0.938530	+	0.345198i	$0.887812\pi$
$38$		0			0
$39$	38920.3			0.656118
$40$		0			0
$41$		−	24286.6i		−	0.352384i	−0.984356	−	0.176192i	$-0.943622\pi$
$41$		−	24286.6i		−	0.352384i	0.984356	−	0.176192i	$-0.0563779\pi$
$42$		0			0
$43$	−30960.8	+	30960.8i	−0.389410	+	0.389410i	−0.874477	−	0.485067i	$-0.838795\pi$
$43$	−30960.8	+	30960.8i	−0.389410	+	0.389410i	0.485067	+	0.874477i	$0.338795\pi$
$44$		0			0
$45$	35349.7	−	35349.7i	0.387925	−	0.387925i
$46$		0			0
$47$			6262.62i			0.0603202i	0.999545	+	0.0301601i	$0.00960171\pi$
$47$			6262.62i			0.0603202i	−0.999545	+	0.0301601i	$0.990398\pi$
$48$		0			0
$49$	169515.			1.44085
$50$		0			0
$51$	61048.8	+	61048.8i	0.460221	+	0.460221i
$52$		0			0
$53$	−198895.	−	198895.i	−1.33597	−	1.33597i	−0.899923	−	0.436048i	$-0.856378\pi$
$53$	−198895.	−	198895.i	−1.33597	−	1.33597i	−0.436048	−	0.899923i	$-0.643622\pi$
$54$		0			0
$55$	−359716.			−2.16208
$56$		0			0
$57$		−	71082.7i		−	0.383830i
$58$		0			0
$59$	−134053.	+	134053.i	−0.652711	+	0.652711i	−0.953645	−	0.300934i	$-0.902702\pi$
$59$	−134053.	+	134053.i	−0.652711	+	0.652711i	0.300934	+	0.953645i	$0.402702\pi$
$60$		0			0
$61$	−103162.	+	103162.i	−0.454494	+	0.454494i	−0.896843	−	0.442349i	$-0.854145\pi$
$61$	−103162.	+	103162.i	−0.454494	+	0.454494i	0.442349	+	0.896843i	$0.354145\pi$
$62$		0			0
$63$			130218.i			0.520774i
$64$		0			0
$65$	513650.			1.87037
$66$		0			0
$67$	396383.	+	396383.i	1.31792	+	1.31792i	0.915417	+	0.402507i	$0.131861\pi$
$67$	396383.	+	396383.i	1.31792	+	1.31792i	0.402507	+	0.915417i	$0.368139\pi$
$68$		0			0
$69$	31220.8	+	31220.8i	0.0950380	+	0.0950380i
$70$		0			0
$71$	−334941.			−0.935822			−0.467911	−	0.883776i	$-0.654993\pi$
$71$	−334941.			−0.935822			−0.467911	+	0.883776i	$0.654993\pi$
$72$		0			0
$73$			436170.i			1.12121i	0.828083	+	0.560605i	$0.189431\pi$
$73$			436170.i			1.12121i	−0.828083	+	0.560605i	$0.810569\pi$
$74$		0			0
$75$	294297.	−	294297.i	0.697593	−	0.697593i
$76$		0			0
$77$	662546.	−	662546.i	1.45126	−	1.45126i
$78$		0			0
$79$			350208.i			0.710305i	0.934808	+	0.355153i	$0.115571\pi$
$79$			350208.i			0.710305i	−0.934808	+	0.355153i	$0.884429\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	460817.	+	460817.i	0.805924	+	0.805924i	0.984014	−	0.178090i	$-0.0569918\pi$
$83$	460817.	+	460817.i	0.805924	+	0.805924i	−0.178090	+	0.984014i	$0.556992\pi$
$84$		0			0
$85$	805691.	+	805691.i	1.31193	+	1.31193i
$86$		0			0
$87$	258193.			0.392090
$88$		0			0
$89$		−	137632.i		−	0.195231i	−0.995224	−	0.0976156i	$-0.968878\pi$
$89$		−	137632.i		−	0.195231i	0.995224	−	0.0976156i	$-0.0311216\pi$
$90$		0			0
$91$	−946068.	+	946068.i	−1.25545	+	1.25545i
$92$		0			0
$93$	−343261.	+	343261.i	−0.426752	+	0.426752i
$94$		0			0
$95$		−	938113.i		−	1.09417i
$96$		0			0
$97$	−347536.			−0.380789			−0.190394	−	0.981708i	$-0.560977\pi$
$97$	−347536.			−0.380789			−0.190394	+	0.981708i	$0.560977\pi$
$98$		0			0
$99$	300440.	+	300440.i	0.309636	+	0.309636i
$100$		0			0
$101$	−221778.	−	221778.i	−0.215255	−	0.215255i	0.591240	−	0.806496i	$-0.298639\pi$
$101$	−221778.	−	221778.i	−0.215255	−	0.215255i	−0.806496	+	0.591240i	$0.798639\pi$
$102$		0			0
$103$	115317.			0.105531			0.0527655	−	0.998607i	$-0.483196\pi$
$103$	115317.			0.105531			0.0527655	+	0.998607i	$0.483196\pi$
$104$		0			0
$105$			1.71855e6i			1.48455i
$106$		0			0
$107$	54216.7	−	54216.7i	0.0442570	−	0.0442570i	−0.684632	−	0.728889i	$-0.740037\pi$
$107$	54216.7	−	54216.7i	0.0442570	−	0.0442570i	0.728889	+	0.684632i	$0.240037\pi$
$108$		0			0
$109$	−1.73348e6	+	1.73348e6i	−1.33857	+	1.33857i	−0.441117	+	0.897449i	$0.645418\pi$
$109$	−1.73348e6	+	1.73348e6i	−1.33857	+	1.33857i	−0.897449	+	0.441117i	$0.854582\pi$
$110$		0			0
$111$			662553.i			0.484453i
$112$		0			0
$113$	1.90390e6			1.31950			0.659748	−	0.751487i	$-0.270663\pi$
$113$	1.90390e6			1.31950			0.659748	+	0.751487i	$0.270663\pi$
$114$		0			0
$115$	412036.	+	412036.i	0.270921	+	0.270921i
$116$		0			0
$117$	−429007.	−	429007.i	−0.267859	−	0.267859i
$118$		0			0
$119$	−2.96793e6			−1.76122
$120$		0			0
$121$		−	1.28570e6i		−	0.725743i
$122$		0			0
$123$	−267705.	+	267705.i	−0.143860	+	0.143860i
$124$		0			0
$125$	1.61098e6	−	1.61098e6i	0.824823	−	0.824823i
$126$		0			0
$127$		−	1.14285e6i		−	0.557929i	−0.960301	−	0.278964i	$-0.910009\pi$
$127$		−	1.14285e6i		−	0.557929i	0.960301	−	0.278964i	$-0.0899912\pi$
$128$		0			0
$129$	682544.			0.317952
$130$		0			0
$131$	−2.02195e6	−	2.02195e6i	−0.899409	−	0.899409i	0.0959746	−	0.995384i	$-0.469403\pi$
$131$	−2.02195e6	−	2.02195e6i	−0.899409	−	0.899409i	−0.995384	+	0.0959746i	$0.969403\pi$
$132$		0			0
$133$	1.72787e6	+	1.72787e6i	0.734439	+	0.734439i
$134$		0			0
$135$	−779298.			−0.316740
$136$		0			0
$137$			4.00355e6i			1.55698i	0.627657	+	0.778490i	$0.284014\pi$
$137$			4.00355e6i			1.55698i	−0.627657	+	0.778490i	$0.715986\pi$
$138$		0			0
$139$	846736.	−	846736.i	0.315285	−	0.315285i	−0.531668	−	0.846953i	$-0.678434\pi$
$139$	846736.	−	846736.i	0.315285	−	0.315285i	0.846953	+	0.531668i	$0.178434\pi$
$140$		0			0
$141$	69031.0	−	69031.0i	0.0246256	−	0.0246256i
$142$		0			0
$143$			4.36555e6i			1.49290i
$144$		0			0
$145$	3.40749e6			1.11771
$146$		0			0
$147$	−1.86851e6	−	1.86851e6i	−0.588226	−	0.588226i
$148$		0			0
$149$	2.26451e6	+	2.26451e6i	0.684566	+	0.684566i	0.961025	−	0.276460i	$-0.0891613\pi$
$149$	2.26451e6	+	2.26451e6i	0.684566	+	0.684566i	−0.276460	+	0.961025i	$0.589161\pi$
$150$		0			0
$151$	5.05014e6			1.46681			0.733403	−	0.679794i	$-0.237931\pi$
$151$	5.05014e6			1.46681			0.733403	+	0.679794i	$0.237931\pi$
$152$		0			0
$153$		−	1.34585e6i		−	0.375769i
$154$		0			0
$155$	−4.53018e6	+	4.53018e6i	−1.21652	+	1.21652i
$156$		0			0
$157$	3.39343e6	−	3.39343e6i	0.876879	−	0.876879i	−0.116332	−	0.993210i	$-0.537114\pi$
$157$	3.39343e6	−	3.39343e6i	0.876879	−	0.876879i	0.993210	+	0.116332i	$0.0371135\pi$
$158$		0			0
$159$			4.38473e6i			1.09082i
$160$		0			0
$161$	−1.51782e6			−0.363700
$162$		0			0
$163$	1.40633e6	+	1.40633e6i	0.324731	+	0.324731i	0.850579	−	0.525848i	$-0.176252\pi$
$163$	1.40633e6	+	1.40633e6i	0.324731	+	0.324731i	−0.525848	+	0.850579i	$0.676252\pi$
$164$		0			0
$165$	3.96505e6	+	3.96505e6i	0.882666	+	0.882666i
$166$		0			0
$167$	908840.			0.195136			0.0975681	−	0.995229i	$-0.468894\pi$
$167$	908840.			0.195136			0.0975681	+	0.995229i	$0.468894\pi$
$168$		0			0
$169$		−	1.40688e6i		−	0.291473i
$170$		0			0
$171$	−783524.	+	783524.i	−0.156698	+	0.156698i
$172$		0			0
$173$	−1.55642e6	+	1.55642e6i	−0.300600	+	0.300600i	−0.841249	−	0.540648i	$-0.818179\pi$
$173$	−1.55642e6	+	1.55642e6i	−0.300600	+	0.300600i	0.540648	+	0.841249i	$0.318179\pi$
$174$		0			0
$175$			1.43075e7i			2.66962i
$176$		0			0
$177$	2.95526e6			0.532937
$178$		0			0
$179$	6.29438e6	+	6.29438e6i	1.09747	+	1.09747i	0.994705	+	0.102768i	$0.0327701\pi$
$179$	6.29438e6	+	6.29438e6i	1.09747	+	1.09747i	0.102768	+	0.994705i	$0.467230\pi$
$180$		0			0
$181$	15726.6	+	15726.6i	0.00265216	+	0.00265216i	0.708432	−	0.705779i	$-0.249403\pi$
$181$	15726.6	+	15726.6i	0.00265216	+	0.00265216i	−0.705779	+	0.708432i	$0.749403\pi$
$182$		0			0
$183$	2.27424e6			0.371093
$184$		0			0
$185$			8.74403e6i			1.38101i
$186$		0			0
$187$	−6.84763e6	+	6.84763e6i	−1.04717	+	1.04717i
$188$		0			0
$189$	1.43535e6	−	1.43535e6i	0.212605	−	0.212605i
$190$		0			0
$191$		−	2.16399e6i		−	0.310568i	−0.987870	−	0.155284i	$-0.950371\pi$
$191$		−	2.16399e6i		−	0.310568i	0.987870	−	0.155284i	$-0.0496292\pi$
$192$		0			0
$193$	−766464.			−0.106615			−0.0533077	−	0.998578i	$-0.516976\pi$
$193$	−766464.			−0.106615			−0.0533077	+	0.998578i	$0.516976\pi$
$194$		0			0
$195$	−5.66181e6	−	5.66181e6i	−0.763574	−	0.763574i
$196$		0			0
$197$	6.95317e6	+	6.95317e6i	0.909461	+	0.909461i	0.996229	−	0.0867679i	$-0.0276539\pi$
$197$	6.95317e6	+	6.95317e6i	0.909461	+	0.909461i	−0.0867679	+	0.996229i	$0.527654\pi$
$198$		0			0
$199$	−1.25456e7			−1.59196			−0.795981	−	0.605321i	$-0.793045\pi$
$199$	−1.25456e7			−1.59196			−0.795981	+	0.605321i	$0.793045\pi$
$200$		0			0
$201$		−	8.73842e6i		−	1.07608i
$202$		0			0
$203$	−6.27611e6	+	6.27611e6i	−0.750244	+	0.750244i
$204$		0			0
$205$	−3.53303e6	+	3.53303e6i	−0.410096	+	0.410096i
$206$		0			0
$207$		−	688276.i		−	0.0775982i
$208$		0			0
$209$	7.97309e6			0.873349
$210$		0			0
$211$	−3.58271e6	−	3.58271e6i	−0.381385	−	0.381385i	0.490216	−	0.871601i	$-0.336918\pi$
$211$	−3.58271e6	−	3.58271e6i	−0.381385	−	0.381385i	−0.871601	+	0.490216i	$0.836918\pi$
$212$		0			0
$213$	3.69195e6	+	3.69195e6i	0.382048	+	0.382048i
$214$		0			0
$215$	9.00786e6			0.906371
$216$		0			0
$217$		−	1.66879e7i		−	1.63313i
$218$		0			0
$219$	4.80777e6	−	4.80777e6i	0.457732	−	0.457732i
$220$		0			0
$221$	9.77793e6	−	9.77793e6i	0.905879	−	0.905879i
$222$		0			0
$223$		−	1.31347e6i		−	0.118442i	−0.998245	−	0.0592210i	$-0.981138\pi$
$223$		−	1.31347e6i		−	0.118442i	0.998245	−	0.0592210i	$-0.0188617\pi$
$224$		0			0
$225$	−6.48790e6			−0.569582
$226$		0			0
$227$	260632.	+	260632.i	0.0222818	+	0.0222818i	0.718160	−	0.695878i	$-0.244985\pi$
$227$	260632.	+	260632.i	0.0222818	+	0.0222818i	−0.695878	+	0.718160i	$0.744985\pi$
$228$		0			0
$229$	1.05934e7	+	1.05934e7i	0.882119	+	0.882119i	0.993750	−	0.111631i	$-0.0356075\pi$
$229$	1.05934e7	+	1.05934e7i	0.882119	+	0.882119i	−0.111631	+	0.993750i	$0.535607\pi$
$230$		0			0
$231$	−1.46061e7			−1.18494
$232$		0			0
$233$			2.69360e6i			0.212944i	0.994316	+	0.106472i	$0.0339554\pi$
$233$			2.69360e6i			0.212944i	−0.994316	+	0.106472i	$0.966045\pi$
$234$		0			0
$235$	911036.	−	911036.i	0.0701992	−	0.0701992i
$236$		0			0
$237$	3.86024e6	−	3.86024e6i	0.289981	−	0.289981i
$238$		0			0
$239$		−	1.77382e7i		−	1.29932i	−0.760226	−	0.649658i	$-0.774912\pi$
$239$		−	1.77382e7i		−	1.29932i	0.760226	−	0.649658i	$-0.225088\pi$
$240$		0			0
$241$	−1.89892e7			−1.35661			−0.678306	−	0.734779i	$-0.737286\pi$
$241$	−1.89892e7			−1.35661			−0.678306	+	0.734779i	$0.737286\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−2.46597e7	−	2.46597e7i	−1.67683	−	1.67683i
$246$		0			0
$247$	−1.13850e7			−0.755514
$248$		0			0
$249$		−	1.01589e7i		−	0.658034i
$250$		0			0
$251$	7.83702e6	−	7.83702e6i	0.495598	−	0.495598i	−0.414467	−	0.910065i	$-0.636032\pi$
$251$	7.83702e6	−	7.83702e6i	0.495598	−	0.495598i	0.910065	+	0.414467i	$0.136032\pi$
$252$		0			0
$253$	−3.50193e6	+	3.50193e6i	−0.216245	+	0.216245i
$254$		0			0
$255$		−	1.77618e7i		−	1.07119i
$256$		0			0
$257$	−4.89707e6			−0.288494			−0.144247	−	0.989542i	$-0.546076\pi$
$257$	−4.89707e6			−0.288494			−0.144247	+	0.989542i	$0.546076\pi$
$258$		0			0
$259$	−1.61052e7	−	1.61052e7i	−0.926975	−	0.926975i
$260$		0			0
$261$	−2.84598e6	−	2.84598e6i	−0.160070	−	0.160070i
$262$		0			0
$263$	4.33510e6			0.238305			0.119152	−	0.992876i	$-0.461982\pi$
$263$	4.33510e6			0.238305			0.119152	+	0.992876i	$0.461982\pi$
$264$		0			0
$265$			5.78674e7i			3.10954i
$266$		0			0
$267$	−1.51708e6	+	1.51708e6i	−0.0797028	+	0.0797028i
$268$		0			0
$269$	−2.08895e7	+	2.08895e7i	−1.07317	+	1.07317i	−0.0760718	+	0.997102i	$0.524238\pi$
$269$	−2.08895e7	+	2.08895e7i	−1.07317	+	1.07317i	−0.997102	+	0.0760718i	$0.975762\pi$
$270$		0			0
$271$			2.69056e7i			1.35187i	0.736961	+	0.675935i	$0.236260\pi$
$271$			2.69056e7i			1.35187i	−0.736961	+	0.675935i	$0.763740\pi$
$272$		0			0
$273$	2.08565e7			1.02507
$274$		0			0
$275$	3.30103e7	+	3.30103e7i	1.58727	+	1.58727i
$276$		0			0
$277$	−1.09909e7	−	1.09909e7i	−0.517125	−	0.517125i	0.399576	−	0.916700i	$-0.369157\pi$
$277$	−1.09909e7	−	1.09909e7i	−0.517125	−	0.517125i	−0.916700	+	0.399576i	$0.869157\pi$
$278$		0			0
$279$	7.56733e6			0.348442
$280$		0			0
$281$			6.61562e6i			0.298162i	0.988825	+	0.149081i	$0.0476315\pi$
$281$			6.61562e6i			0.298162i	−0.988825	+	0.149081i	$0.952369\pi$
$282$		0			0
$283$	1.31465e7	−	1.31465e7i	0.580031	−	0.580031i	−0.354881	−	0.934912i	$-0.615478\pi$
$283$	1.31465e7	−	1.31465e7i	0.580031	−	0.580031i	0.934912	+	0.354881i	$0.115478\pi$
$284$		0			0
$285$	−1.03405e7	+	1.03405e7i	−0.446693	+	0.446693i
$286$		0			0
$287$		−	1.30147e7i		−	0.550537i
$288$		0			0
$289$	6.53700e6			0.270823
$290$		0			0
$291$	3.83078e6	+	3.83078e6i	0.155456	+	0.155456i
$292$		0			0
$293$	6.90837e6	+	6.90837e6i	0.274645	+	0.274645i	0.830967	−	0.556322i	$-0.187788\pi$
$293$	6.90837e6	+	6.90837e6i	0.274645	+	0.274645i	−0.556322	+	0.830967i	$0.687788\pi$
$294$		0			0
$295$	3.90020e7			1.51922
$296$		0			0
$297$		−	6.62332e6i		−	0.252817i
$298$		0			0
$299$	5.00051e6	−	5.00051e6i	0.187068	−	0.187068i
$300$		0			0
$301$	−1.65912e7	+	1.65912e7i	−0.608384	+	0.608384i
$302$		0			0
$303$			4.88919e6i			0.175755i
$304$		0			0
$305$	3.00142e7			1.05786
$306$		0			0
$307$	2.45753e7	+	2.45753e7i	0.849346	+	0.849346i	0.990051	−	0.140706i	$-0.0449372\pi$
$307$	2.45753e7	+	2.45753e7i	0.849346	+	0.849346i	−0.140706	+	0.990051i	$0.544937\pi$
$308$		0			0
$309$	−1.27110e6	−	1.27110e6i	−0.0430829	−	0.0430829i
$310$		0			0
$311$	−3.42156e7			−1.13748			−0.568739	−	0.822518i	$-0.692569\pi$
$311$	−3.42156e7			−1.13748			−0.568739	+	0.822518i	$0.692569\pi$
$312$		0			0
$313$		−	2.52240e7i		−	0.822586i	−0.911503	−	0.411293i	$-0.865077\pi$
$313$		−	2.52240e7i		−	0.822586i	0.911503	−	0.411293i	$-0.134923\pi$
$314$		0			0
$315$	1.89431e7	−	1.89431e7i	0.606064	−	0.606064i
$316$		0			0
$317$	3.84721e7	−	3.84721e7i	1.20773	−	1.20773i	0.235964	−	0.971762i	$-0.424175\pi$
$317$	3.84721e7	−	3.84721e7i	1.20773	−	1.20773i	0.971762	−	0.235964i	$-0.0758247\pi$
$318$		0			0
$319$			2.89605e7i			0.892143i
$320$		0			0
$321$	−1.19523e6			−0.0361357
$322$		0			0
$323$	−1.78581e7	−	1.78581e7i	−0.529941	−	0.529941i
$324$		0			0
$325$	−4.71363e7	−	4.71363e7i	−1.37311	−	1.37311i
$326$		0			0
$327$	3.82153e7			1.09294
$328$		0			0
$329$			3.35599e6i			0.0942396i
$330$		0			0
$331$	4.43814e6	−	4.43814e6i	0.122382	−	0.122382i	−0.643263	−	0.765645i	$-0.722420\pi$
$331$	4.43814e6	−	4.43814e6i	0.122382	−	0.122382i	0.765645	+	0.643263i	$0.222420\pi$
$332$		0			0
$333$	7.30313e6	−	7.30313e6i	0.197777	−	0.197777i
$334$		0			0
$335$		−	1.15325e8i		−	3.06754i
$336$		0			0
$337$	−3.37306e6			−0.0881321			−0.0440661	−	0.999029i	$-0.514031\pi$
$337$	−3.37306e6			−0.0881321			−0.0440661	+	0.999029i	$0.514031\pi$
$338$		0			0
$339$	−2.09861e7	−	2.09861e7i	−0.538682	−	0.538682i
$340$		0			0
$341$	−3.85024e7	−	3.85024e7i	−0.971011	−	0.971011i
$342$		0			0
$343$	2.77937e7			0.688754
$344$		0			0
$345$		−	9.08351e6i		−	0.221206i
$346$		0			0
$347$	−9.54280e6	+	9.54280e6i	−0.228395	+	0.228395i	−0.812022	−	0.583627i	$-0.801633\pi$
$347$	−9.54280e6	+	9.54280e6i	−0.228395	+	0.228395i	0.583627	+	0.812022i	$0.301633\pi$
$348$		0			0
$349$	−1.68909e7	+	1.68909e7i	−0.397353	+	0.397353i	−0.877298	−	0.479946i	$-0.840656\pi$
$349$	−1.68909e7	+	1.68909e7i	−0.397353	+	0.397353i	0.479946	+	0.877298i	$0.340656\pi$
$350$		0			0
$351$			9.45762e6i			0.218706i
$352$		0			0
$353$	−1.31221e7			−0.298317			−0.149159	−	0.988813i	$-0.547657\pi$
$353$	−1.31221e7			−0.298317			−0.149159	+	0.988813i	$0.547657\pi$
$354$		0			0
$355$	4.87245e7	+	4.87245e7i	1.08909	+	1.08909i
$356$		0			0
$357$	3.27146e7	+	3.27146e7i	0.719014	+	0.719014i
$358$		0			0
$359$	−1.90357e7			−0.411419			−0.205710	−	0.978613i	$-0.565950\pi$
$359$	−1.90357e7			−0.411419			−0.205710	+	0.978613i	$0.565950\pi$
$360$		0			0
$361$		−	2.62527e7i		−	0.558023i
$362$		0			0
$363$	−1.41719e7	+	1.41719e7i	−0.296283	+	0.296283i
$364$		0			0
$365$	6.34504e7	−	6.34504e7i	1.30484	−	1.30484i
$366$		0			0
$367$			7.78214e6i			0.157435i	0.996897	+	0.0787175i	$0.0250825\pi$
$367$			7.78214e6i			0.157435i	−0.996897	+	0.0787175i	$0.974918\pi$
$368$		0			0
$369$	5.90166e6			0.117461
$370$		0			0
$371$	−1.06583e8	−	1.06583e8i	−2.08722	−	2.08722i
$372$		0			0
$373$	−2.58166e7	−	2.58166e7i	−0.497477	−	0.497477i	0.413175	−	0.910652i	$-0.364420\pi$
$373$	−2.58166e7	−	2.58166e7i	−0.497477	−	0.497477i	−0.910652	+	0.413175i	$0.864420\pi$
$374$		0			0
$375$	−3.55148e7			−0.673465
$376$		0			0
$377$		−	4.13536e7i		−	0.771772i
$378$		0			0
$379$	2.69041e7	−	2.69041e7i	0.494197	−	0.494197i	−0.415429	−	0.909626i	$-0.636368\pi$
$379$	2.69041e7	−	2.69041e7i	0.494197	−	0.494197i	0.909626	+	0.415429i	$0.136368\pi$
$380$		0			0
$381$	−1.25973e7	+	1.25973e7i	−0.227774	+	0.227774i
$382$		0			0
$383$			4.81558e6i			0.0857141i	0.999081	+	0.0428570i	$0.0136460\pi$
$383$			4.81558e6i			0.0857141i	−0.999081	+	0.0428570i	$0.986354\pi$
$384$		0			0
$385$	−1.92764e8			−3.37787
$386$		0			0
$387$	−7.52348e6	−	7.52348e6i	−0.129803	−	0.129803i
$388$		0			0
$389$	4.60201e7	+	4.60201e7i	0.781805	+	0.781805i	0.980135	−	0.198330i	$-0.0635518\pi$
$389$	4.60201e7	+	4.60201e7i	0.781805	+	0.781805i	−0.198330	+	0.980135i	$0.563552\pi$
$390$		0			0
$391$	1.56872e7			0.262431
$392$		0			0
$393$			4.45748e7i			0.734365i
$394$		0			0
$395$	5.09455e7	−	5.09455e7i	0.826636	−	0.826636i
$396$		0			0
$397$	−8.03943e7	+	8.03943e7i	−1.28485	+	1.28485i	−0.346982	+	0.937872i	$0.612793\pi$
$397$	−8.03943e7	+	8.03943e7i	−1.28485	+	1.28485i	−0.937872	+	0.346982i	$0.887207\pi$
$398$		0			0
$399$		−	3.80916e7i		−	0.599667i
$400$		0			0
$401$	−5.84354e7			−0.906240			−0.453120	−	0.891450i	$-0.649689\pi$
$401$	−5.84354e7			−0.906240			−0.453120	+	0.891450i	$0.649689\pi$
$402$		0			0
$403$	5.49786e7	+	5.49786e7i	0.839999	+	0.839999i
$404$		0			0
$405$	8.58997e6	+	8.58997e6i	0.129308	+	0.129308i
$406$		0			0
$407$	−7.43162e7			−1.10230
$408$		0			0
$409$		−	5.13262e7i		−	0.750186i	−0.926987	−	0.375093i	$-0.877611\pi$
$409$		−	5.13262e7i		−	0.750186i	0.926987	−	0.375093i	$-0.122389\pi$
$410$		0			0
$411$	4.41299e7	−	4.41299e7i	0.635634	−	0.635634i
$412$		0			0
$413$	−7.18360e7	+	7.18360e7i	−1.01975	+	1.01975i
$414$		0			0
$415$		−	1.34072e8i		−	1.87583i
$416$		0			0
$417$	−1.86666e7			−0.257429
$418$		0			0
$419$	5.16116e6	+	5.16116e6i	0.0701626	+	0.0701626i	0.741317	−	0.671155i	$-0.234201\pi$
$419$	5.16116e6	+	5.16116e6i	0.0701626	+	0.0701626i	−0.671155	+	0.741317i	$0.734201\pi$
$420$		0			0
$421$	−8.03596e7	−	8.03596e7i	−1.07694	−	1.07694i	−0.996782	−	0.0801578i	$-0.974458\pi$
$421$	−8.03596e7	−	8.03596e7i	−1.07694	−	1.07694i	−0.0801578	−	0.996782i	$-0.525542\pi$
$422$		0			0
$423$	−1.52182e6			−0.0201067
$424$		0			0
$425$		−	1.47872e8i		−	1.92628i
$426$		0			0
$427$	−5.52819e7	+	5.52819e7i	−0.710067	+	0.710067i
$428$		0			0
$429$	4.81201e7	−	4.81201e7i	0.609474	−	0.609474i
$430$		0			0
$431$			9.50753e7i			1.18751i	0.804647	+	0.593753i	$0.202354\pi$
$431$			9.50753e7i			1.18751i	−0.804647	+	0.593753i	$0.797646\pi$
$432$		0			0
$433$	−9.11600e7			−1.12290			−0.561449	−	0.827511i	$-0.689756\pi$
$433$	−9.11600e7			−1.12290			−0.561449	+	0.827511i	$0.689756\pi$
$434$		0			0
$435$	−3.75598e7	−	3.75598e7i	−0.456305	−	0.456305i
$436$		0			0
$437$	−9.13276e6	−	9.13276e6i	−0.109435	−	0.109435i
$438$		0			0
$439$	4.26310e7			0.503885			0.251943	−	0.967742i	$-0.418931\pi$
$439$	4.26310e7			0.503885			0.251943	+	0.967742i	$0.418931\pi$
$440$		0			0
$441$			4.11921e7i			0.480284i
$442$		0			0
$443$	7.14662e7	−	7.14662e7i	0.822034	−	0.822034i	−0.164366	−	0.986399i	$-0.552558\pi$
$443$	7.14662e7	−	7.14662e7i	0.822034	−	0.822034i	0.986399	+	0.164366i	$0.0525578\pi$
$444$		0			0
$445$	−2.00216e7	+	2.00216e7i	−0.227205	+	0.227205i
$446$		0			0
$447$		−	4.99220e7i		−	0.558946i
$448$		0			0
$449$	1.45742e8			1.61008			0.805038	−	0.593224i	$-0.202145\pi$
$449$	1.45742e8			1.61008			0.805038	+	0.593224i	$0.202145\pi$
$450$		0			0
$451$	−3.00275e7	−	3.00275e7i	−0.327332	−	0.327332i
$452$		0			0
$453$	−5.56662e7	−	5.56662e7i	−0.598821	−	0.598821i
$454$		0			0
$455$	2.75253e8			2.92212
$456$		0			0
$457$			2.81700e7i			0.295147i	0.989051	+	0.147574i	$0.0471463\pi$
$457$			2.81700e7i			0.295147i	−0.989051	+	0.147574i	$0.952854\pi$
$458$		0			0
$459$	−1.48349e7	+	1.48349e7i	−0.153407	+	0.153407i
$460$		0			0
$461$	−7.86316e6	+	7.86316e6i	−0.0802591	+	0.0802591i	−0.746097	−	0.665838i	$-0.768074\pi$
$461$	−7.86316e6	+	7.86316e6i	−0.0802591	+	0.0802591i	0.665838	+	0.746097i	$0.268074\pi$
$462$		0			0
$463$			1.84089e8i			1.85475i	0.374138	+	0.927373i	$0.377939\pi$
$463$			1.84089e8i			1.85475i	−0.374138	+	0.927373i	$0.622061\pi$
$464$		0			0
$465$	9.98697e7			0.993287
$466$		0			0
$467$	−5.25346e7	−	5.25346e7i	−0.515816	−	0.515816i	0.400487	−	0.916303i	$-0.368841\pi$
$467$	−5.25346e7	−	5.25346e7i	−0.515816	−	0.515816i	−0.916303	+	0.400487i	$0.868841\pi$
$468$		0			0
$469$	2.12412e8	+	2.12412e8i	2.05902	+	2.05902i
$470$		0			0
$471$	−7.48095e7			−0.715969
$472$		0			0
$473$			7.65585e7i			0.723452i
$474$		0			0
$475$	−8.60882e7	+	8.60882e7i	−0.803273	+	0.803273i
$476$		0			0
$477$	4.83316e7	−	4.83316e7i	0.445324	−	0.445324i
$478$		0			0
$479$			2.29063e7i			0.208424i	0.994555	+	0.104212i	$0.0332321\pi$
$479$			2.29063e7i			0.208424i	−0.994555	+	0.104212i	$0.966768\pi$
$480$		0			0
$481$	1.06118e8			0.953575
$482$		0			0
$483$	1.67305e7	+	1.67305e7i	0.148480	+	0.148480i
$484$		0			0
$485$	5.05567e7	+	5.05567e7i	0.443153	+	0.443153i
$486$		0			0
$487$	1.35812e7			0.117585			0.0587925	−	0.998270i	$-0.481275\pi$
$487$	1.35812e7			0.117585			0.0587925	+	0.998270i	$0.481275\pi$
$488$		0			0
$489$		−	3.10031e7i		−	0.265142i
$490$		0			0
$491$	−1.24541e8	+	1.24541e8i	−1.05213	+	1.05213i	−0.0535658	+	0.998564i	$0.517059\pi$
$491$	−1.24541e8	+	1.24541e8i	−1.05213	+	1.05213i	−0.998564	+	0.0535658i	$0.982941\pi$
$492$		0			0
$493$	6.48657e7	−	6.48657e7i	0.541345	−	0.541345i
$494$		0			0
$495$		−	8.74111e7i		−	0.720694i
$496$		0			0
$497$	−1.79487e8			−1.46206
$498$		0			0
$499$	2.80187e7	+	2.80187e7i	0.225500	+	0.225500i	0.810810	−	0.585310i	$-0.199027\pi$
$499$	2.80187e7	+	2.80187e7i	0.225500	+	0.225500i	−0.585310	+	0.810810i	$0.699027\pi$
$500$		0			0
$501$	−1.00179e7	−	1.00179e7i	−0.0796640	−	0.0796640i
$502$		0			0
$503$	−3.44756e7			−0.270899			−0.135450	−	0.990784i	$-0.543248\pi$
$503$	−3.44756e7			−0.270899			−0.135450	+	0.990784i	$0.543248\pi$
$504$		0			0
$505$			6.45249e7i			0.501018i
$506$		0			0
$507$	−1.55076e7	+	1.55076e7i	−0.118993	+	0.118993i
$508$		0			0
$509$	1.25286e8	−	1.25286e8i	0.950055	−	0.950055i	−0.0487556	−	0.998811i	$-0.515526\pi$
$509$	1.25286e8	−	1.25286e8i	0.950055	−	0.950055i	0.998811	+	0.0487556i	$0.0155255\pi$
$510$		0			0
$511$			2.33733e8i			1.75169i
$512$		0			0
$513$	1.72731e7			0.127943
$514$		0			0
$515$	−1.67753e7	−	1.67753e7i	−0.122814	−	0.122814i
$516$		0			0
$517$	7.74296e6	+	7.74296e6i	0.0560319	+	0.0560319i
$518$		0			0
$519$	3.43120e7			0.245439
$520$		0			0
$521$		−	5.76803e6i		−	0.0407863i	−0.999792	−	0.0203931i	$-0.993508\pi$
$521$		−	5.76803e6i		−	0.0407863i	0.999792	−	0.0203931i	$-0.00649179\pi$
$522$		0			0
$523$	−7.94955e7	+	7.94955e7i	−0.555696	+	0.555696i	−0.928079	−	0.372383i	$-0.878541\pi$
$523$	−7.94955e7	+	7.94955e7i	−0.555696	+	0.555696i	0.372383	+	0.928079i	$0.378541\pi$
$524$		0			0
$525$	1.57707e8	−	1.57707e8i	1.08987	−	1.08987i
$526$		0			0
$527$			1.72475e8i			1.17840i
$528$		0			0
$529$	−1.40013e8			−0.945807
$530$		0			0
$531$	−3.25749e7	−	3.25749e7i	−0.217570	−	0.217570i
$532$		0			0
$533$	4.28771e7	+	4.28771e7i	0.283168	+	0.283168i
$534$		0			0
$535$	−1.57740e7			−0.103010
$536$		0			0
$537$		−	1.38762e8i		−	0.896084i
$538$		0			0
$539$	2.09584e8	−	2.09584e8i	1.33842	−	1.33842i
$540$		0			0
$541$	−1.59344e8	+	1.59344e8i	−1.00634	+	1.00634i	−0.00636149	+	0.999980i	$0.502025\pi$
$541$	−1.59344e8	+	1.59344e8i	−1.00634	+	1.00634i	−0.999980	+	0.00636149i	$0.997975\pi$
$542$		0			0
$543$		−	346699.i		−	0.00216548i
$544$		0			0
$545$	5.04346e8			3.11558
$546$		0			0
$547$	4.17772e7	+	4.17772e7i	0.255257	+	0.255257i	0.823122	−	0.567865i	$-0.192230\pi$
$547$	4.17772e7	+	4.17772e7i	0.255257	+	0.255257i	−0.567865	+	0.823122i	$0.692230\pi$
$548$		0			0
$549$	−2.50683e7	−	2.50683e7i	−0.151498	−	0.151498i
$550$		0			0
$551$	−7.55269e7			−0.451488
$552$		0			0
$553$			1.87668e8i			1.10973i
$554$		0			0
$555$	9.63829e7	−	9.63829e7i	0.563795	−	0.563795i
$556$		0			0
$557$	−1.77039e8	+	1.77039e8i	−1.02448	+	1.02448i	−0.0247890	+	0.999693i	$0.507891\pi$
$557$	−1.77039e8	+	1.77039e8i	−1.02448	+	1.02448i	−0.999693	+	0.0247890i	$0.992109\pi$
$558$		0			0
$559$		−	1.09320e8i		−	0.625842i
$560$		0			0
$561$	1.50959e8			0.855007
$562$		0			0
$563$	6.27789e7	+	6.27789e7i	0.351794	+	0.351794i	0.860777	−	0.508983i	$-0.169978\pi$
$563$	6.27789e7	+	6.27789e7i	0.351794	+	0.351794i	−0.508983	+	0.860777i	$0.669978\pi$
$564$		0			0
$565$	−2.76964e8	−	2.76964e8i	−1.53560	−	1.53560i
$566$		0			0
$567$	−3.16430e7			−0.173591
$568$		0			0
$569$			3.39955e8i			1.84537i	0.385549	+	0.922687i	$0.374012\pi$
$569$			3.39955e8i			1.84537i	−0.385549	+	0.922687i	$0.625988\pi$
$570$		0			0
$571$	−2.30280e8	+	2.30280e8i	−1.23694	+	1.23694i	−0.275694	+	0.961246i	$0.588908\pi$
$571$	−2.30280e8	+	2.30280e8i	−1.23694	+	1.23694i	−0.961246	+	0.275694i	$0.911092\pi$
$572$		0			0
$573$	−2.38531e7	+	2.38531e7i	−0.126789	+	0.126789i
$574$		0			0
$575$		−	7.56231e7i		−	0.397787i
$576$		0			0
$577$	2.48141e8			1.29173			0.645864	−	0.763453i	$-0.276497\pi$
$577$	2.48141e8			1.29173			0.645864	+	0.763453i	$0.276497\pi$
$578$		0			0
$579$	8.44851e6	+	8.44851e6i	0.0435255	+	0.0435255i
$580$		0			0
$581$	2.46941e8	+	2.46941e8i	1.25911	+	1.25911i
$582$		0			0
$583$	−4.91820e8			−2.48199
$584$		0			0
$585$			1.24817e8i			0.623456i
$586$		0			0
$587$	6.85751e7	−	6.85751e7i	0.339041	−	0.339041i	−0.516965	−	0.856006i	$-0.672938\pi$
$587$	6.85751e7	−	6.85751e7i	0.339041	−	0.339041i	0.856006	+	0.516965i	$0.172938\pi$
$588$		0			0
$589$	1.00411e8	−	1.00411e8i	0.491401	−	0.491401i
$590$		0			0
$591$		−	1.53285e8i		−	0.742572i
$592$		0			0
$593$	−2.69568e8			−1.29272			−0.646359	−	0.763033i	$-0.723709\pi$
$593$	−2.69568e8			−1.29272			−0.646359	+	0.763033i	$0.723709\pi$
$594$		0			0
$595$	4.31751e8	+	4.31751e8i	2.04966	+	2.04966i
$596$		0			0
$597$	1.38287e8	+	1.38287e8i	0.649916	+	0.649916i
$598$		0			0
$599$	−6.72390e7			−0.312853			−0.156427	−	0.987690i	$-0.549997\pi$
$599$	−6.72390e7			−0.312853			−0.156427	+	0.987690i	$0.549997\pi$
$600$		0			0
$601$			1.03346e8i			0.476069i	0.971257	+	0.238034i	$0.0765031\pi$
$601$			1.03346e8i			0.476069i	−0.971257	+	0.238034i	$0.923497\pi$
$602$		0			0
$603$	−9.63210e7	+	9.63210e7i	−0.439308	+	0.439308i
$604$		0			0
$605$	−1.87033e8	+	1.87033e8i	−0.844602	+	0.844602i
$606$		0			0
$607$		−	8.75931e7i		−	0.391655i	−0.980638	−	0.195827i	$-0.937261\pi$
$607$		−	8.75931e7i		−	0.391655i	0.980638	−	0.195827i	$-0.0627393\pi$
$608$		0			0
$609$	1.38359e8			0.612571
$610$		0			0
$611$	−1.10564e7	−	1.10564e7i	−0.0484719	−	0.0484719i
$612$		0			0
$613$	−3.72611e7	−	3.72611e7i	−0.161761	−	0.161761i	0.621585	−	0.783346i	$-0.286489\pi$
$613$	−3.72611e7	−	3.72611e7i	−0.161761	−	0.161761i	−0.783346	+	0.621585i	$0.786489\pi$
$614$		0			0
$615$	7.78870e7			0.334842
$616$		0			0
$617$		−	3.65354e8i		−	1.55546i	−0.628601	−	0.777728i	$-0.716372\pi$
$617$		−	3.65354e8i		−	1.55546i	0.628601	−	0.777728i	$-0.283628\pi$
$618$		0			0
$619$	5.22259e7	−	5.22259e7i	0.220198	−	0.220198i	−0.588384	−	0.808582i	$-0.700236\pi$
$619$	5.22259e7	−	5.22259e7i	0.220198	−	0.220198i	0.808582	+	0.588384i	$0.200236\pi$
$620$		0			0
$621$	−7.58666e6	+	7.58666e6i	−0.0316793	+	0.0316793i
$622$		0			0
$623$		−	7.37537e7i		−	0.305014i
$624$		0			0
$625$	−5.15308e7			−0.211070
$626$		0			0
$627$	−8.78851e7	−	8.78851e7i	−0.356543	−	0.356543i
$628$		0			0
$629$	1.66453e8	+	1.66453e8i	0.668867	+	0.668867i
$630$		0			0
$631$	3.83796e8			1.52761			0.763805	−	0.645447i	$-0.223329\pi$
$631$	3.83796e8			1.52761			0.763805	+	0.645447i	$0.223329\pi$
$632$		0			0
$633$			7.89823e7i			0.311400i
$634$		0			0
$635$	−1.66253e8	+	1.66253e8i	−0.649304	+	0.649304i
$636$		0			0
$637$	−2.99272e8	+	2.99272e8i	−1.15784	+	1.15784i
$638$		0			0
$639$		−	8.13906e7i		−	0.311941i
$640$		0			0
$641$	−2.90560e8			−1.10322			−0.551609	−	0.834103i	$-0.685986\pi$
$641$	−2.90560e8			−1.10322			−0.551609	+	0.834103i	$0.685986\pi$
$642$		0			0
$643$	−2.10759e8	−	2.10759e8i	−0.792781	−	0.792781i	0.189165	−	0.981945i	$-0.439422\pi$
$643$	−2.10759e8	−	2.10759e8i	−0.792781	−	0.792781i	−0.981945	+	0.189165i	$0.939422\pi$
$644$		0			0
$645$	−9.92910e7	−	9.92910e7i	−0.370025	−	0.370025i
$646$		0			0
$647$	−3.25608e8			−1.20221			−0.601107	−	0.799169i	$-0.705273\pi$
$647$	−3.25608e8			−1.20221			−0.601107	+	0.799169i	$0.705273\pi$
$648$		0			0
$649$			3.31481e8i			1.21262i
$650$		0			0
$651$	−1.83946e8	+	1.83946e8i	−0.666724	+	0.666724i
$652$		0			0
$653$	2.50356e8	−	2.50356e8i	0.899122	−	0.899122i	−0.0962366	−	0.995358i	$-0.530681\pi$
$653$	2.50356e8	−	2.50356e8i	0.899122	−	0.899122i	0.995358	+	0.0962366i	$0.0306806\pi$
$654$		0			0
$655$			5.88275e8i			2.09342i
$656$		0			0
$657$	−1.05989e8			−0.373737
$658$		0			0
$659$	8.18780e7	+	8.18780e7i	0.286096	+	0.286096i	0.835534	−	0.549439i	$-0.185158\pi$
$659$	8.18780e7	+	8.18780e7i	0.286096	+	0.286096i	−0.549439	+	0.835534i	$0.685158\pi$
$660$		0			0
$661$	−1.76024e8	−	1.76024e8i	−0.609490	−	0.609490i	0.333323	−	0.942813i	$-0.391830\pi$
$661$	−1.76024e8	−	1.76024e8i	−0.609490	−	0.609490i	−0.942813	+	0.333323i	$0.891830\pi$
$662$		0			0
$663$	−2.15558e8			−0.739647
$664$		0			0
$665$		−	5.02713e8i		−	1.70944i
$666$		0			0
$667$	3.31728e7	−	3.31728e7i	0.111790	−	0.111790i
$668$		0			0
$669$	−1.44780e7	+	1.44780e7i	−0.0483538	+	0.0483538i
$670$		0			0
$671$			2.55093e8i			0.844367i
$672$		0			0
$673$	−3.82475e7			−0.125475			−0.0627377	−	0.998030i	$-0.519983\pi$
$673$	−3.82475e7			−0.125475			−0.0627377	+	0.998030i	$0.519983\pi$
$674$		0			0
$675$	7.15142e7	+	7.15142e7i	0.232531	+	0.232531i
$676$		0			0
$677$	4.83767e7	+	4.83767e7i	0.155909	+	0.155909i	0.780751	−	0.624842i	$-0.214837\pi$
$677$	4.83767e7	+	4.83767e7i	0.155909	+	0.155909i	−0.624842	+	0.780751i	$0.714837\pi$
$678$		0			0
$679$	−1.86236e8			−0.594915
$680$		0			0
$681$		−	5.74574e6i		−	0.0181930i
$682$		0			0
$683$	−4.18333e8	+	4.18333e8i	−1.31299	+	1.31299i	−0.393783	+	0.919203i	$0.628834\pi$
$683$	−4.18333e8	+	4.18333e8i	−1.31299	+	1.31299i	−0.919203	+	0.393783i	$0.871166\pi$
$684$		0			0
$685$	5.82404e8	−	5.82404e8i	1.81198	−	1.81198i
$686$		0			0
$687$		−	2.33535e8i		−	0.720247i
$688$		0			0
$689$	7.02283e8			2.14711
$690$		0			0
$691$	2.55773e8	+	2.55773e8i	0.775211	+	0.775211i	0.979012	−	0.203801i	$-0.0653295\pi$
$691$	2.55773e8	+	2.55773e8i	0.775211	+	0.775211i	−0.203801	+	0.979012i	$0.565330\pi$
$692$		0			0
$693$	1.60999e8	+	1.60999e8i	0.483752	+	0.483752i
$694$		0			0
$695$	−2.46353e8			−0.733843
$696$		0			0
$697$			1.34511e8i			0.397245i
$698$		0			0
$699$	2.96907e7	−	2.96907e7i	0.0869340	−	0.0869340i
$700$		0			0
$701$	3.93965e8	−	3.93965e8i	1.14368	−	1.14368i	0.155904	−	0.987772i	$-0.450171\pi$
$701$	3.93965e8	−	3.93965e8i	1.14368	−	1.14368i	0.987772	−	0.155904i	$-0.0498291\pi$
$702$		0			0
$703$		−	1.93811e8i		−	0.557844i
$704$		0			0
$705$	−2.00842e7			−0.0573174
$706$		0			0
$707$	−1.18846e8	−	1.18846e8i	−0.336299	−	0.336299i
$708$		0			0
$709$	1.00070e7	+	1.00070e7i	0.0280778	+	0.0280778i	0.721006	−	0.692928i	$-0.243680\pi$
$709$	1.00070e7	+	1.00070e7i	0.0280778	+	0.0280778i	−0.692928	+	0.721006i	$0.743680\pi$
$710$		0			0
$711$	−8.51006e7			−0.236768
$712$		0			0
$713$			8.82049e7i			0.243346i
$714$		0			0
$715$	6.35065e8	−	6.35065e8i	1.73740	−	1.73740i
$716$		0			0
$717$	−1.95523e8	+	1.95523e8i	−0.530444	+	0.530444i
$718$		0			0
$719$		−	8.71884e7i		−	0.234570i	−0.993098	−	0.117285i	$-0.962581\pi$
$719$		−	8.71884e7i		−	0.234570i	0.993098	−	0.117285i	$-0.0374191\pi$
$720$		0			0
$721$	6.17955e7			0.164874
$722$		0			0
$723$	2.09312e8	+	2.09312e8i	0.553835	+	0.553835i
$724$		0			0
$725$	−3.12697e8	−	3.12697e8i	−0.820558	−	0.820558i
$726$		0			0
$727$	3.28334e8			0.854501			0.427251	−	0.904133i	$-0.359482\pi$
$727$	3.28334e8			0.854501			0.427251	+	0.904133i	$0.359482\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	1.71475e8	−	1.71475e8i	0.438985	−	0.438985i
$732$		0			0
$733$	−3.94217e7	+	3.94217e7i	−0.100097	+	0.100097i	−0.755382	−	0.655285i	$-0.772549\pi$
$733$	−3.94217e7	+	3.94217e7i	−0.100097	+	0.100097i	0.655285	+	0.755382i	$0.272549\pi$
$734$		0			0
$735$			5.43632e8i			1.36913i
$736$		0			0
$737$	9.80157e8			2.44846
$738$		0			0
$739$	−4.66490e8	−	4.66490e8i	−1.15587	−	1.15587i	−0.985355	−	0.170515i	$-0.945457\pi$
$739$	−4.66490e8	−	4.66490e8i	−1.15587	−	1.15587i	−0.170515	−	0.985355i	$-0.554543\pi$
$740$		0			0
$741$	1.25494e8	+	1.25494e8i	0.308437	+	0.308437i
$742$		0			0
$743$	1.46699e7			0.0357653			0.0178826	−	0.999840i	$-0.494307\pi$
$743$	1.46699e7			0.0357653			0.0178826	+	0.999840i	$0.494307\pi$
$744$		0			0
$745$		−	6.58845e8i		−	1.59336i
$746$		0			0
$747$	−1.11979e8	+	1.11979e8i	−0.268641	+	0.268641i
$748$		0			0
$749$	2.90535e7	−	2.90535e7i	0.0691437	−	0.0691437i
$750$		0			0
$751$			6.15313e8i			1.45270i	0.687324	+	0.726351i	$0.258785\pi$
$751$			6.15313e8i			1.45270i	−0.687324	+	0.726351i	$0.741215\pi$
$752$		0			0
$753$	−1.72770e8			−0.404654
$754$		0			0
$755$	−7.34654e8	−	7.34654e8i	−1.70703	−	1.70703i
$756$		0			0
$757$	5.14992e8	+	5.14992e8i	1.18717	+	1.18717i	0.977847	+	0.209323i	$0.0671260\pi$
$757$	5.14992e8	+	5.14992e8i	1.18717	+	1.18717i	0.209323	+	0.977847i	$0.432874\pi$
$758$		0			0
$759$	7.72015e7			0.176563
$760$		0			0
$761$			1.10112e8i			0.249850i	0.992166	+	0.124925i	$0.0398690\pi$
$761$			1.10112e8i			0.249850i	−0.992166	+	0.124925i	$0.960131\pi$
$762$		0			0
$763$	−9.28933e8	+	9.28933e8i	−2.09127	+	2.09127i
$764$		0			0
$765$	−1.95783e8	+	1.95783e8i	−0.437311	+	0.437311i
$766$		0			0
$767$		−	4.73331e8i		−	1.04901i
$768$		0			0
$769$	−8.57293e8			−1.88517			−0.942584	−	0.333969i	$-0.891612\pi$
$769$	−8.57293e8			−1.88517			−0.942584	+	0.333969i	$0.891612\pi$
$770$		0			0
$771$	5.39790e7	+	5.39790e7i	0.117777	+	0.117777i
$772$		0			0
$773$	−3.72620e8	−	3.72620e8i	−0.806730	−	0.806730i	0.177408	−	0.984137i	$-0.443229\pi$
$773$	−3.72620e8	−	3.72620e8i	−0.806730	−	0.806730i	−0.984137	+	0.177408i	$0.943229\pi$
$774$		0			0
$775$	8.31446e8			1.78620
$776$		0			0
$777$			3.55047e8i			0.756872i
$778$		0			0
$779$	7.83093e7	−	7.83093e7i	0.165654	−	0.165654i
$780$		0			0
$781$	−4.14113e8	+	4.14113e8i	−0.869293	+	0.869293i
$782$		0			0
$783$			6.27408e7i			0.130697i
$784$		0			0
$785$	−9.87297e8			−2.04098
$786$		0			0
$787$	1.50053e7	+	1.50053e7i	0.0307837	+	0.0307837i	0.722331	−	0.691547i	$-0.243071\pi$
$787$	1.50053e7	+	1.50053e7i	0.0307837	+	0.0307837i	−0.691547	+	0.722331i	$0.743071\pi$
$788$		0			0
$789$	−4.77846e7	−	4.77846e7i	−0.0972874	−	0.0972874i
$790$		0			0
$791$	1.02025e9			2.06148
$792$		0			0
$793$		−	3.64255e8i		−	0.730442i
$794$		0			0
$795$	6.37855e8	−	6.37855e8i	1.26947	−	1.26947i
$796$		0			0
$797$	−2.33117e8	+	2.33117e8i	−0.460468	+	0.460468i	−0.898809	−	0.438341i	$-0.855566\pi$
$797$	−2.33117e8	+	2.33117e8i	−0.460468	+	0.460468i	0.438341	+	0.898809i	$0.355566\pi$
$798$		0			0
$799$		−	3.46853e7i		−	0.0679994i
$800$		0			0
$801$	3.34445e7			0.0650770
$802$		0			0
$803$	5.39270e8	+	5.39270e8i	1.04150	+	1.04150i
$804$		0			0
$805$	2.20801e8	+	2.20801e8i	0.423266	+	0.423266i
$806$		0			0
$807$	4.60516e8			0.876243
$808$		0			0
$809$			9.22625e8i			1.74253i	0.490815	+	0.871264i	$0.336699\pi$
$809$			9.22625e8i			1.74253i	−0.490815	+	0.871264i	$0.663301\pi$
$810$		0			0
$811$	6.02256e8	−	6.02256e8i	1.12906	−	1.12906i	0.138734	−	0.990330i	$-0.455697\pi$
$811$	6.02256e8	−	6.02256e8i	1.12906	−	1.12906i	0.990330	−	0.138734i	$-0.0443033\pi$
$812$		0			0
$813$	2.96573e8	−	2.96573e8i	0.551899	−	0.551899i
$814$		0			0
$815$		−	4.09163e8i		−	0.755828i
$816$		0			0
$817$	−1.99659e8			−0.366119
$818$		0			0
$819$	−2.29895e8	−	2.29895e8i	−0.418482	−	0.418482i
$820$		0			0
$821$	−1.97953e8	−	1.97953e8i	−0.357711	−	0.357711i	0.505258	−	0.862968i	$-0.331397\pi$
$821$	−1.97953e8	−	1.97953e8i	−0.357711	−	0.357711i	−0.862968	+	0.505258i	$0.831397\pi$
$822$		0			0
$823$	2.63867e8			0.473353			0.236677	−	0.971588i	$-0.423942\pi$
$823$	2.63867e8			0.473353			0.236677	+	0.971588i	$0.423942\pi$
$824$		0			0
$825$		−	7.27725e8i		−	1.29600i
$826$		0			0
$827$	−3.18932e8	+	3.18932e8i	−0.563874	+	0.563874i	−0.930406	−	0.366531i	$-0.880545\pi$
$827$	−3.18932e8	+	3.18932e8i	−0.563874	+	0.563874i	0.366531	+	0.930406i	$0.380545\pi$
$828$		0			0
$829$	−4.50448e8	+	4.50448e8i	−0.790644	+	0.790644i	−0.981599	−	0.190955i	$-0.938841\pi$
$829$	−4.50448e8	+	4.50448e8i	−0.790644	+	0.790644i	0.190955	+	0.981599i	$0.438841\pi$
$830$		0			0
$831$			2.42300e8i			0.422230i
$832$		0			0
$833$	−9.38852e8			−1.62428
$834$		0			0
$835$	−1.32211e8	−	1.32211e8i	−0.227095	−	0.227095i
$836$		0			0
$837$	−8.34124e7	−	8.34124e7i	−0.142251	−	0.142251i
$838$		0			0
$839$	−3.60095e8			−0.609720			−0.304860	−	0.952397i	$-0.598610\pi$
$839$	−3.60095e8			−0.609720			−0.304860	+	0.952397i	$0.598610\pi$
$840$		0			0
$841$			3.20488e8i			0.538796i
$842$		0			0
$843$	7.29220e7	−	7.29220e7i	0.121724	−	0.121724i
$844$		0			0
$845$	−2.04662e8	+	2.04662e8i	−0.339209	+	0.339209i
$846$		0			0
$847$		−	6.88975e8i		−	1.13384i
$848$		0			0
$849$	−2.89820e8			−0.473593
$850$		0			0
$851$	8.51253e7	+	8.51253e7i	0.138124	+	0.138124i
$852$		0			0
$853$	−6.53328e8	−	6.53328e8i	−1.05265	−	1.05265i	−0.998535	−	0.0541155i	$-0.982766\pi$
$853$	−6.53328e8	−	6.53328e8i	−1.05265	−	1.05265i	−0.0541155	−	0.998535i	$-0.517234\pi$
$854$		0			0
$855$	2.27961e8			0.364723
$856$		0			0
$857$		−	5.10642e8i		−	0.811287i	−0.914031	−	0.405643i	$-0.867048\pi$
$857$		−	5.10642e8i		−	0.811287i	0.914031	−	0.405643i	$-0.132952\pi$
$858$		0			0
$859$	8.71919e8	−	8.71919e8i	1.37561	−	1.37561i	0.523728	−	0.851885i	$-0.324541\pi$
$859$	8.71919e8	−	8.71919e8i	1.37561	−	1.37561i	0.851885	−	0.523728i	$-0.175459\pi$
$860$		0			0
$861$	−1.43457e8	+	1.43457e8i	−0.224756	+	0.224756i
$862$		0			0
$863$		−	3.96363e8i		−	0.616682i	−0.951276	−	0.308341i	$-0.900226\pi$
$863$		−	3.96363e8i		−	0.616682i	0.951276	−	0.308341i	$-0.0997737\pi$
$864$		0			0
$865$	4.52832e8			0.699663
$866$		0			0
$867$	−7.20554e7	−	7.20554e7i	−0.110563	−	0.110563i
$868$		0			0
$869$	4.32989e8	+	4.32989e8i	0.659809	+	0.659809i
$870$		0			0
$871$	−1.39960e9			−2.11811
$872$		0			0
$873$		−	8.44512e7i		−	0.126930i
$874$		0			0
$875$	8.63288e8	−	8.63288e8i	1.28864	−	1.28864i
$876$		0			0
$877$	5.92413e7	−	5.92413e7i	0.0878265	−	0.0878265i	−0.661829	−	0.749655i	$-0.730219\pi$
$877$	5.92413e7	−	5.92413e7i	0.0878265	−	0.0878265i	0.749655	+	0.661829i	$0.230219\pi$
$878$		0			0
$879$		−	1.52298e8i		−	0.224247i
$880$		0			0
$881$	−9.60597e8			−1.40480			−0.702399	−	0.711784i	$-0.747888\pi$
$881$	−9.60597e8			−1.40480			−0.702399	+	0.711784i	$0.747888\pi$
$882$		0			0
$883$	−8.58829e8	−	8.58829e8i	−1.24745	−	1.24745i	−0.956841	−	0.290613i	$-0.906141\pi$
$883$	−8.58829e8	−	8.58829e8i	−1.24745	−	1.24745i	−0.290613	−	0.956841i	$-0.593859\pi$
$884$		0			0
$885$	−4.29907e8	−	4.29907e8i	−0.620219	−	0.620219i
$886$		0			0
$887$	−4.31865e8			−0.618838			−0.309419	−	0.950926i	$-0.600135\pi$
$887$	−4.31865e8			−0.618838			−0.309419	+	0.950926i	$0.600135\pi$
$888$		0			0
$889$		−	6.12428e8i		−	0.871665i
$890$		0			0
$891$	−7.30069e7	+	7.30069e7i	−0.103212	+	0.103212i
$892$		0			0
$893$	−2.01931e7	+	2.01931e7i	−0.0283562	+	0.0283562i
$894$		0			0
$895$		−	1.83131e9i		−	2.55443i
$896$		0			0
$897$	−1.10238e8			−0.152741
$898$		0			0
$899$	3.64722e8	+	3.64722e8i	0.501976	+	0.501976i
$900$		0			0
$901$	1.10157e9	+	1.10157e9i	1.50605	+	1.50605i
$902$		0			0
$903$	3.65759e8			0.496743
$904$		0			0
$905$		−	4.57556e6i		−	0.00617303i
$906$		0			0
$907$	−6.74468e8	+	6.74468e8i	−0.903940	+	0.903940i	−0.995774	−	0.0918347i	$-0.970727\pi$
$907$	−6.74468e8	+	6.74468e8i	−0.903940	+	0.903940i	0.0918347	+	0.995774i	$0.470727\pi$
$908$		0			0
$909$	5.38920e7	−	5.38920e7i	0.0717518	−	0.0717518i
$910$		0			0
$911$		−	4.20518e8i		−	0.556198i	−0.960552	−	0.278099i	$-0.910296\pi$
$911$		−	4.20518e8i		−	0.556198i	0.960552	−	0.278099i	$-0.0897044\pi$
$912$		0			0
$913$	1.13949e9			1.49726
$914$		0			0
$915$	−3.30838e8	−	3.30838e8i	−0.431869	−	0.431869i
$916$		0			0
$917$	−1.08352e9	−	1.08352e9i	−1.40517	−	1.40517i
$918$		0			0
$919$	−1.10301e9			−1.42112			−0.710560	−	0.703636i	$-0.751559\pi$
$919$	−1.10301e9			−1.42112			−0.710560	+	0.703636i	$0.751559\pi$
$920$		0			0
$921$		−	5.41773e8i		−	0.693488i
$922$		0			0
$923$	5.91324e8	−	5.91324e8i	0.752005	−	0.752005i
$924$		0			0
$925$	8.02417e8	−	8.02417e8i	1.01385	−	1.01385i
$926$		0			0
$927$			2.80219e7i			0.0351770i
$928$		0			0
$929$	−1.88375e8			−0.234951			−0.117475	−	0.993076i	$-0.537480\pi$
$929$	−1.88375e8			−0.234951			−0.117475	+	0.993076i	$0.537480\pi$
$930$		0			0
$931$	5.46580e8	+	5.46580e8i	0.677337	+	0.677337i
$932$		0			0
$933$	3.77148e8	+	3.77148e8i	0.464373	+	0.464373i
$934$		0			0
$935$	1.99228e9			2.43733
$936$		0			0
$937$			1.01609e7i			0.0123513i	0.999981	+	0.00617565i	$0.00196578\pi$
$937$			1.01609e7i			0.0123513i	−0.999981	+	0.00617565i	$0.998034\pi$
$938$		0			0
$939$	−2.78037e8	+	2.78037e8i	−0.335819	+	0.335819i
$940$		0			0
$941$	5.55575e7	−	5.55575e7i	0.0666767	−	0.0666767i	−0.672982	−	0.739659i	$-0.734987\pi$
$941$	5.55575e7	−	5.55575e7i	0.0666767	−	0.0666767i	0.739659	+	0.672982i	$0.234987\pi$
$942$		0			0
$943$			6.87898e7i			0.0820331i
$944$		0			0
$945$	−4.17608e8			−0.494850
$946$		0			0
$947$	2.27194e8	+	2.27194e8i	0.267514	+	0.267514i	0.828098	−	0.560584i	$-0.189423\pi$
$947$	2.27194e8	+	2.27194e8i	0.267514	+	0.267514i	−0.560584	+	0.828098i	$0.689423\pi$
$948$		0			0
$949$	−7.70040e8	−	7.70040e8i	−0.900978	−	0.900978i
$950$		0			0
$951$	−8.48134e8			−0.986104
$952$		0			0
$953$			5.77206e7i			0.0666887i	0.999444	+	0.0333444i	$0.0106158\pi$
$953$			5.77206e7i			0.0666887i	−0.999444	+	0.0333444i	$0.989384\pi$
$954$		0			0
$955$	−3.14801e8	+	3.14801e8i	−0.361431	+	0.361431i
$956$		0			0
$957$	3.19223e8	−	3.19223e8i	0.364216	−	0.364216i
$958$		0			0
$959$			2.14541e9i			2.43251i
$960$		0			0
$961$	−8.22750e7			−0.0927039
$962$		0			0
$963$	1.31747e7	+	1.31747e7i	0.0147523	+	0.0147523i
$964$		0			0
$965$	1.11499e8	+	1.11499e8i	0.124076	+	0.124076i
$966$		0			0
$967$	2.84793e8			0.314956			0.157478	−	0.987522i	$-0.449664\pi$
$967$	2.84793e8			0.314956			0.157478	+	0.987522i	$0.449664\pi$
$968$		0			0
$969$			3.93689e8i			0.432695i
$970$		0			0
$971$	−8.17596e8	+	8.17596e8i	−0.893061	+	0.893061i	−0.994810	−	0.101749i	$-0.967556\pi$
$971$	−8.17596e8	+	8.17596e8i	−0.893061	+	0.893061i	0.101749	+	0.994810i	$0.467556\pi$
$972$		0			0
$973$	4.53746e8	−	4.53746e8i	0.492578	−	0.492578i
$974$		0			0
$975$			1.03914e9i			1.12114i
$976$		0			0
$977$	4.30295e7			0.0461406			0.0230703	−	0.999734i	$-0.492656\pi$
$977$	4.30295e7			0.0461406			0.0230703	+	0.999734i	$0.492656\pi$
$978$		0			0
$979$	−1.70165e8	−	1.70165e8i	−0.181352	−	0.181352i
$980$		0			0
$981$	−4.21236e8	−	4.21236e8i	−0.446189	−	0.446189i
$982$		0			0
$983$	−4.86582e8			−0.512266			−0.256133	−	0.966642i	$-0.582449\pi$
$983$	−4.86582e8			−0.512266			−0.256133	+	0.966642i	$0.582449\pi$
$984$		0			0
$985$		−	2.02298e9i		−	2.11682i
$986$		0			0
$987$	3.69921e7	−	3.69921e7i	0.0384732	−	0.0384732i
$988$		0			0
$989$	8.76938e7	−	8.76938e7i	0.0906525	−	0.0906525i
$990$		0			0
$991$		−	1.01206e9i		−	1.03988i	−0.854202	−	0.519942i	$-0.825954\pi$
$991$		−	1.01206e9i		−	1.03988i	0.854202	−	0.519942i	$-0.174046\pi$
$992$		0			0
$993$	−9.78406e7			−0.0999243
$994$		0			0
$995$	1.82504e9	+	1.82504e9i	1.85269	+	1.85269i
$996$		0			0
$997$	5.39770e8	+	5.39770e8i	0.544658	+	0.544658i	0.924891	−	0.380233i	$-0.124156\pi$
$997$	5.39770e8	+	5.39770e8i	0.544658	+	0.544658i	−0.380233	+	0.924891i	$0.624156\pi$
$998$		0			0
$999$	−1.61000e8			−0.161484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.b.31.11		48
4.3	odd	2		384.7.l.a.31.14		48
8.3	odd	2		192.7.l.a.79.11		48
8.5	even	2		48.7.l.a.43.13	yes	48
16.3	odd	4	inner	384.7.l.b.223.11		48
16.5	even	4		192.7.l.a.175.11		48
16.11	odd	4		48.7.l.a.19.13	✓	48
16.13	even	4		384.7.l.a.223.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.13	✓	48	16.11	odd	4
48.7.l.a.43.13	yes	48	8.5	even	2
192.7.l.a.79.11		48	8.3	odd	2
192.7.l.a.175.11		48	16.5	even	4
384.7.l.a.31.14		48	4.3	odd	2
384.7.l.a.223.14		48	16.13	even	4
384.7.l.b.31.11		48	1.1	even	1	trivial
384.7.l.b.223.11		48	16.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-145.472 - 145.472i) q^{5} +535.877 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-145.472 - 145.472i) q^{5} +535.877 q^{7} +243.000i q^{9} +(1236.38 - 1236.38i) q^{11} +(-1765.46 + 1765.46i) q^{13} +3206.99i q^{15} -5538.46 q^{17} +(3224.38 + 3224.38i) q^{19} +(-5906.81 - 5906.81i) q^{21} -2832.41 q^{23} +26699.2i q^{25} +(2678.52 - 2678.52i) q^{27} +(-11711.9 + 11711.9i) q^{29} -31141.3i q^{31} -27256.4 q^{33} +(-77955.0 - 77955.0i) q^{35} +(-30054.0 - 30054.0i) q^{37} +38920.3 q^{39} -24286.6i q^{41} +(-30960.8 + 30960.8i) q^{43} +(35349.7 - 35349.7i) q^{45} +6262.62i q^{47} +169515. q^{49} +(61048.8 + 61048.8i) q^{51} +(-198895. - 198895. i) q^{53} -359716. q^{55} -71082.7i q^{57} +(-134053. + 134053. i) q^{59} +(-103162. + 103162. i) q^{61} +130218. i q^{63} +513650. q^{65} +(396383. + 396383. i) q^{67} +(31220.8 + 31220.8i) q^{69} -334941. q^{71} +436170. i q^{73} +(294297. - 294297. i) q^{75} +(662546. - 662546. i) q^{77} +350208. i q^{79} -59049.0 q^{81} +(460817. + 460817. i) q^{83} +(805691. + 805691. i) q^{85} +258193. q^{87} -137632. i q^{89} +(-946068. + 946068. i) q^{91} +(-343261. + 343261. i) q^{93} -938113. i q^{95} -347536. q^{97} +(300440. + 300440. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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