LMFDB - Embedded newform 294.7.b.a.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,7,Mod(197,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("294.197");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	294.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$67.6359005842$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	294.197
Dual form			294.7.b.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} +(-21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(96.0000 + 118.794i) q^{6} +181.019i q^{8} +(153.000 - 712.764i) q^{9} +O(q^{10})$	\(q-5.65685i q^{2} +(-21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(96.0000 + 118.794i) q^{6} +181.019i q^{8} +(153.000 - 712.764i) q^{9} -960.000 q^{10} +33.9411i q^{11} +(672.000 - 543.058i) q^{12} +2950.00 q^{13} +(2880.00 + 3563.82i) q^{15} +1024.00 q^{16} +4480.23i q^{17} +(-4032.00 - 865.499i) q^{18} -5258.00 q^{19} +5430.58i q^{20} +192.000 q^{22} +10250.2i q^{23} +(-3072.00 - 3801.41i) q^{24} -13175.0 q^{25} -16687.7i q^{26} +(8883.00 + 17564.5i) q^{27} -2206.17i q^{29} +(20160.0 - 16291.7i) q^{30} -22898.0 q^{31} -5792.62i q^{32} +(-576.000 - 712.764i) q^{33} +25344.0 q^{34} +(-4896.00 + 22808.4i) q^{36} +34058.0 q^{37} +29743.7i q^{38} +(-61950.0 + 50063.2i) q^{39} +30720.0 q^{40} -16766.9i q^{41} -6406.00 q^{43} -1086.12i q^{44} +(-120960. - 25965.0i) q^{45} +57984.0 q^{46} +179888. i q^{47} +(-21504.0 + 17377.9i) q^{48} +74529.1i q^{50} +(-76032.0 - 94084.8i) q^{51} -94400.0 q^{52} +192548. i q^{53} +(99360.0 - 50249.8i) q^{54} +5760.00 q^{55} +(110418. - 89231.2i) q^{57} -12480.0 q^{58} -326819. i q^{59} +(-92160.0 - 114042. i) q^{60} +62566.0 q^{61} +129531. i q^{62} -32768.0 q^{64} -500632. i q^{65} +(-4032.00 + 3258.35i) q^{66} +438698. q^{67} -143367. i q^{68} +(-173952. - 215255. i) q^{69} +68221.7i q^{71} +(129024. + 27696.0i) q^{72} +730510. q^{73} -192661. i q^{74} +(276675. - 223587. i) q^{75} +168256. q^{76} +(283200. + 350442. i) q^{78} +340562. q^{79} -173779. i q^{80} +(-484623. - 218106. i) q^{81} -94848.0 q^{82} +496253. i q^{83} +760320. q^{85} +36237.8i q^{86} +(37440.0 + 46329.6i) q^{87} -6144.00 q^{88} -386725. i q^{89} +(-146880. + 684253. i) q^{90} -328007. i q^{92} +(480858. - 388592. i) q^{93} +1.01760e6 q^{94} +892312. i q^{95} +(98304.0 + 121645. i) q^{96} +281086. q^{97} +(24192.0 + 5192.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 42 q^{3} - 64 q^{4} + 192 q^{6} + 306 q^{9}+O(q^{10}) $ 2 * q - 42 * q^3 - 64 * q^4 + 192 * q^6 + 306 * q^9	$ 2 q - 42 q^{3} - 64 q^{4} + 192 q^{6} + 306 q^{9} - 1920 q^{10} + 1344 q^{12} + 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} - 10516 q^{19} + 384 q^{22} - 6144 q^{24} - 26350 q^{25} + 17766 q^{27} + 40320 q^{30} - 45796 q^{31} - 1152 q^{33} + 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} + 61440 q^{40} - 12812 q^{43} - 241920 q^{45} + 115968 q^{46} - 43008 q^{48} - 152064 q^{51} - 188800 q^{52} + 198720 q^{54} + 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} + 125132 q^{61} - 65536 q^{64} - 8064 q^{66} + 877396 q^{67} - 347904 q^{69} + 258048 q^{72} + 1461020 q^{73} + 553350 q^{75} + 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} - 189696 q^{82} + 1520640 q^{85} + 74880 q^{87} - 12288 q^{88} - 293760 q^{90} + 961716 q^{93} + 2035200 q^{94} + 196608 q^{96} + 562172 q^{97} + 48384 q^{99}+O(q^{100}) $ 2 * q - 42 * q^3 - 64 * q^4 + 192 * q^6 + 306 * q^9 - 1920 * q^10 + 1344 * q^12 + 5900 * q^13 + 5760 * q^15 + 2048 * q^16 - 8064 * q^18 - 10516 * q^19 + 384 * q^22 - 6144 * q^24 - 26350 * q^25 + 17766 * q^27 + 40320 * q^30 - 45796 * q^31 - 1152 * q^33 + 50688 * q^34 - 9792 * q^36 + 68116 * q^37 - 123900 * q^39 + 61440 * q^40 - 12812 * q^43 - 241920 * q^45 + 115968 * q^46 - 43008 * q^48 - 152064 * q^51 - 188800 * q^52 + 198720 * q^54 + 11520 * q^55 + 220836 * q^57 - 24960 * q^58 - 184320 * q^60 + 125132 * q^61 - 65536 * q^64 - 8064 * q^66 + 877396 * q^67 - 347904 * q^69 + 258048 * q^72 + 1461020 * q^73 + 553350 * q^75 + 336512 * q^76 + 566400 * q^78 + 681124 * q^79 - 969246 * q^81 - 189696 * q^82 + 1520640 * q^85 + 74880 * q^87 - 12288 * q^88 - 293760 * q^90 + 961716 * q^93 + 2035200 * q^94 + 196608 * q^96 + 562172 * q^97 + 48384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	−21.0000	+	16.9706i	−0.777778	+	0.628539i
$3$	−21.0000	+	16.9706i	−0.777778	+	0.628539i
$4$	−32.0000			−0.500000
$5$		−	169.706i		−	1.35765i	−0.734302	−	0.678823i	$-0.762491\pi$
$5$		−	169.706i		−	1.35765i	0.734302	−	0.678823i	$-0.237509\pi$
$6$	96.0000	+	118.794i	0.444444	+	0.549972i
$7$		0			0
$7$		0			0
$8$			181.019i			0.353553i
$9$	153.000	−	712.764i	0.209877	−	0.977728i
$10$	−960.000			−0.960000
$11$			33.9411i			0.0255005i	0.999919	+	0.0127502i	$0.00405864\pi$
$11$			33.9411i			0.0255005i	−0.999919	+	0.0127502i	$0.995941\pi$
$12$	672.000	−	543.058i	0.388889	−	0.314270i
$13$	2950.00			1.34274			0.671370	−	0.741122i	$-0.265706\pi$
$13$	2950.00			1.34274			0.671370	+	0.741122i	$0.265706\pi$
$14$		0			0
$15$	2880.00	+	3563.82i	0.853333	+	1.05595i
$16$	1024.00			0.250000
$17$			4480.23i			0.911913i	0.890002	+	0.455956i	$0.150703\pi$
$17$			4480.23i			0.911913i	−0.890002	+	0.455956i	$0.849297\pi$
$18$	−4032.00	−	865.499i	−0.691358	−	0.148405i
$19$	−5258.00			−0.766584			−0.383292	−	0.923627i	$-0.625210\pi$
$19$	−5258.00			−0.766584			−0.383292	+	0.923627i	$0.625210\pi$
$20$			5430.58i			0.678823i
$21$		0			0
$22$	192.000			0.0180316
$23$			10250.2i			0.842461i	0.906954	+	0.421230i	$0.138402\pi$
$23$			10250.2i			0.842461i	−0.906954	+	0.421230i	$0.861598\pi$
$24$	−3072.00	−	3801.41i	−0.222222	−	0.274986i
$25$	−13175.0			−0.843200
$26$		−	16687.7i		−	0.949461i
$27$	8883.00	+	17564.5i	0.451303	+	0.892371i
$28$		0			0
$29$		−	2206.17i		−	0.0904577i	−0.998977	−	0.0452289i	$-0.985598\pi$
$29$		−	2206.17i		−	0.0904577i	0.998977	−	0.0452289i	$-0.0144017\pi$
$30$	20160.0	−	16291.7i	0.746667	−	0.603398i
$31$	−22898.0			−0.768621			−0.384311	−	0.923204i	$-0.625561\pi$
$31$	−22898.0			−0.768621			−0.384311	+	0.923204i	$0.625561\pi$
$32$		−	5792.62i		−	0.176777i
$33$	−576.000	−	712.764i	−0.0160280	−	0.0198337i
$34$	25344.0			0.644820
$35$		0			0
$36$	−4896.00	+	22808.4i	−0.104938	+	0.488864i
$37$	34058.0			0.672379			0.336189	−	0.941794i	$-0.390862\pi$
$37$	34058.0			0.672379			0.336189	+	0.941794i	$0.390862\pi$
$38$			29743.7i			0.542057i
$39$	−61950.0	+	50063.2i	−1.04435	+	0.843965i
$40$	30720.0			0.480000
$41$		−	16766.9i		−	0.243277i	−0.992574	−	0.121639i	$-0.961185\pi$
$41$		−	16766.9i		−	0.243277i	0.992574	−	0.121639i	$-0.0388149\pi$
$42$		0			0
$43$	−6406.00			−0.0805715			−0.0402858	−	0.999188i	$-0.512827\pi$
$43$	−6406.00			−0.0805715			−0.0402858	+	0.999188i	$0.512827\pi$
$44$		−	1086.12i		−	0.0127502i
$45$	−120960.	−	25965.0i	−1.32741	−	0.284938i
$46$	57984.0			0.595710
$47$			179888.i			1.73264i	0.499489	+	0.866320i	$0.333521\pi$
$47$			179888.i			1.73264i	−0.499489	+	0.866320i	$0.666479\pi$
$48$	−21504.0	+	17377.9i	−0.194444	+	0.157135i
$49$		0			0
$50$			74529.1i			0.596232i
$51$	−76032.0	−	94084.8i	−0.573173	−	0.709266i
$52$	−94400.0			−0.671370
$53$			192548.i			1.29334i	0.762772	+	0.646668i	$0.223838\pi$
$53$			192548.i			1.29334i	−0.762772	+	0.646668i	$0.776162\pi$
$54$	99360.0	−	50249.8i	0.631001	−	0.319120i
$55$	5760.00			0.0346206
$56$		0			0
$57$	110418.	−	89231.2i	0.596232	−	0.481828i
$58$	−12480.0			−0.0639633
$59$		−	326819.i		−	1.59130i	−0.605758	−	0.795649i	$-0.707130\pi$
$59$		−	326819.i		−	1.59130i	0.605758	−	0.795649i	$-0.292870\pi$
$60$	−92160.0	−	114042.i	−0.426667	−	0.527973i
$61$	62566.0			0.275644			0.137822	−	0.990457i	$-0.455990\pi$
$61$	62566.0			0.275644			0.137822	+	0.990457i	$0.455990\pi$
$62$			129531.i			0.543497i
$63$		0			0
$64$	−32768.0			−0.125000
$65$		−	500632.i		−	1.82296i
$66$	−4032.00	+	3258.35i	−0.0140245	+	0.0113335i
$67$	438698.			1.45862			0.729308	−	0.684185i	$-0.239842\pi$
$67$	438698.			1.45862			0.729308	+	0.684185i	$0.239842\pi$
$68$		−	143367.i		−	0.455956i
$69$	−173952.	−	215255.i	−0.529520	−	0.655247i
$70$		0			0
$71$			68221.7i			0.190611i	0.995448	+	0.0953053i	$0.0303827\pi$
$71$			68221.7i			0.190611i	−0.995448	+	0.0953053i	$0.969617\pi$
$72$	129024.	+	27696.0i	0.345679	+	0.0742026i
$73$	730510.			1.87784			0.938918	−	0.344141i	$-0.111830\pi$
$73$	730510.			1.87784			0.938918	+	0.344141i	$0.111830\pi$
$74$		−	192661.i		−	0.475444i
$75$	276675.	−	223587.i	0.655822	−	0.529984i
$76$	168256.			0.383292
$77$		0			0
$78$	283200.	+	350442.i	0.596773	+	0.738469i
$79$	340562.			0.690740			0.345370	−	0.938467i	$-0.387753\pi$
$79$	340562.			0.690740			0.345370	+	0.938467i	$0.387753\pi$
$80$		−	173779.i		−	0.339411i
$81$	−484623.	−	218106.i	−0.911904	−	0.410404i
$82$	−94848.0			−0.172023
$83$			496253.i			0.867899i	0.900937	+	0.433949i	$0.142880\pi$
$83$			496253.i			0.867899i	−0.900937	+	0.433949i	$0.857120\pi$
$84$		0			0
$85$	760320.			1.23805
$86$			36237.8i			0.0569727i
$87$	37440.0	+	46329.6i	0.0568562	+	0.0703560i
$88$	−6144.00			−0.00901578
$89$		−	386725.i		−	0.548570i	−0.961648	−	0.274285i	$-0.911559\pi$
$89$		−	386725.i		−	0.548570i	0.961648	−	0.274285i	$-0.0884412\pi$
$90$	−146880.	+	684253.i	−0.201481	+	0.938619i
$91$		0			0
$92$		−	328007.i		−	0.421230i
$93$	480858.	−	388592.i	0.597817	−	0.483109i
$94$	1.01760e6			1.22516
$95$			892312.i			1.04075i
$96$	98304.0	+	121645.i	0.111111	+	0.137493i
$97$	281086.			0.307981			0.153991	−	0.988072i	$-0.450787\pi$
$97$	281086.			0.307981			0.153991	+	0.988072i	$0.450787\pi$
$98$		0			0
$99$	24192.0	+	5192.99i	0.0249325	+	0.00535195i
$100$	421600.			0.421600
$101$		−	945362.i		−	0.917559i	−0.888550	−	0.458780i	$-0.848287\pi$
$101$		−	945362.i		−	0.917559i	0.888550	−	0.458780i	$-0.151713\pi$
$102$	−532224.	+	430102.i	−0.501527	+	0.405295i
$103$	865726.			0.792262			0.396131	−	0.918194i	$-0.370353\pi$
$103$	865726.			0.792262			0.396131	+	0.918194i	$0.370353\pi$
$104$			534007.i			0.474730i
$105$		0			0
$106$	1.08922e6			0.914527
$107$		−	1.47410e6i		−	1.20330i	−0.798759	−	0.601651i	$-0.794510\pi$
$107$		−	1.47410e6i		−	1.20330i	0.798759	−	0.601651i	$-0.205490\pi$
$108$	−284256.	−	562065.i	−0.225652	−	0.446185i
$109$	650810.			0.502545			0.251272	−	0.967916i	$-0.419151\pi$
$109$	650810.			0.502545			0.251272	+	0.967916i	$0.419151\pi$
$110$		−	32583.5i		−	0.0244805i
$111$	−715218.	+	577983.i	−0.522961	+	0.422616i
$112$		0			0
$113$		−	1.74417e6i		−	1.20879i	−0.796683	−	0.604397i	$-0.793414\pi$
$113$		−	1.74417e6i		−	1.20879i	0.796683	−	0.604397i	$-0.206586\pi$
$114$	−504768.	−	624619.i	−0.340704	−	0.421600i
$115$	1.73952e6			1.14376
$116$			70597.5i			0.0452289i
$117$	451350.	−	2.10265e6i	0.281810	−	1.31283i
$118$	−1.84877e6			−1.12522
$119$		0			0
$120$	−645120.	+	521336.i	−0.373333	+	0.301699i
$121$	1.77041e6			0.999350
$122$		−	353927.i		−	0.194910i
$123$	284544.	+	352105.i	0.152909	+	0.189216i
$124$	732736.			0.384311
$125$		−	415779.i		−	0.212879i
$126$		0			0
$127$	−2.28053e6			−1.11333			−0.556665	−	0.830737i	$-0.687919\pi$
$127$	−2.28053e6			−1.11333			−0.556665	+	0.830737i	$0.687919\pi$
$128$			185364.i			0.0883883i
$129$	134526.	−	108713.i	0.0626667	−	0.0506424i
$130$	−2.83200e6			−1.28903
$131$		−	1.07196e6i		−	0.476832i	−0.971163	−	0.238416i	$-0.923372\pi$
$131$		−	1.07196e6i		−	0.476832i	0.971163	−	0.238416i	$-0.0766282\pi$
$132$	18432.0	+	22808.4i	0.00801402	+	0.00991685i
$133$		0			0
$134$		−	2.48165e6i		−	1.03140i
$135$	2.98080e6	−	1.50750e6i	1.21152	−	0.612709i
$136$	−811008.			−0.322410
$137$			2.78338e6i			1.08246i	0.840876	+	0.541228i	$0.182040\pi$
$137$			2.78338e6i			1.08246i	−0.840876	+	0.541228i	$0.817960\pi$
$138$	−1.21766e6	+	984021.i	−0.463330	+	0.374427i
$139$	−4.57395e6			−1.70313			−0.851563	−	0.524253i	$-0.824345\pi$
$139$	−4.57395e6			−1.70313			−0.851563	+	0.524253i	$0.824345\pi$
$140$		0			0
$141$	−3.05280e6	−	3.77765e6i	−1.08903	−	1.34761i
$142$	385920.			0.134782
$143$			100126.i			0.0342405i
$144$	156672.	−	729870.i	0.0524691	−	0.244432i
$145$	−374400.			−0.122809
$146$		−	4.13239e6i		−	1.32783i
$147$		0			0
$148$	−1.08986e6			−0.336189
$149$		−	4.46010e6i		−	1.34830i	−0.738595	−	0.674149i	$-0.764511\pi$
$149$		−	4.46010e6i		−	1.34830i	0.738595	−	0.674149i	$-0.235489\pi$
$150$	−1.26480e6	−	1.56511e6i	−0.374756	−	0.463736i
$151$	−2.20809e6			−0.641338			−0.320669	−	0.947191i	$-0.603908\pi$
$151$	−2.20809e6			−0.641338			−0.320669	+	0.947191i	$0.603908\pi$
$152$		−	951800.i		−	0.271028i
$153$	3.19334e6	+	685475.i	0.891603	+	0.191389i
$154$		0			0
$155$			3.88592e6i			1.04352i
$156$	1.98240e6	−	1.60202e6i	0.522177	−	0.421983i
$157$	1.28887e6			0.333051			0.166525	−	0.986037i	$-0.446745\pi$
$157$	1.28887e6			0.333051			0.166525	+	0.986037i	$0.446745\pi$
$158$		−	1.92651e6i		−	0.488427i
$159$	−3.26765e6	−	4.04351e6i	−0.812913	−	1.00593i
$160$	−983040.			−0.240000
$161$		0			0
$162$	−1.23379e6	+	2.74144e6i	−0.290200	+	0.644813i
$163$	879914.			0.203178			0.101589	−	0.994826i	$-0.467607\pi$
$163$	879914.			0.203178			0.101589	+	0.994826i	$0.467607\pi$
$164$			536541.i			0.121639i
$165$	−120960.	+	97750.4i	−0.0269271	+	0.0217604i
$166$	2.80723e6			0.613697
$167$			5.96760e6i			1.28130i	0.767834	+	0.640649i	$0.221335\pi$
$167$			5.96760e6i			1.28130i	−0.767834	+	0.640649i	$0.778665\pi$
$168$		0			0
$169$	3.87569e6			0.802951
$170$		−	4.30102e6i		−	0.875436i
$171$	−804474.	+	3.74771e6i	−0.160888	+	0.749511i
$172$	204992.			0.0402858
$173$			418867.i			0.0808981i	0.999182	+	0.0404490i	$0.0128788\pi$
$173$			418867.i			0.0808981i	−0.999182	+	0.0404490i	$0.987121\pi$
$174$	262080.	−	211793.i	0.0497492	−	0.0402034i
$175$		0			0
$176$			34755.7i			0.00637512i
$177$	5.54630e6	+	6.86320e6i	1.00019	+	1.23768i
$178$	−2.18765e6			−0.387898
$179$		−	302110.i		−	0.0526752i	−0.999653	−	0.0263376i	$-0.991616\pi$
$179$		−	302110.i		−	0.0526752i	0.999653	−	0.0263376i	$-0.00838448\pi$
$180$	3.87072e6	+	830879.i	0.663704	+	0.142469i
$181$	6.47618e6			1.09215			0.546076	−	0.837735i	$-0.316121\pi$
$181$	6.47618e6			1.09215			0.546076	+	0.837735i	$0.316121\pi$
$182$		0			0
$183$	−1.31389e6	+	1.06178e6i	−0.214390	+	0.173253i
$184$	−1.85549e6			−0.297855
$185$		−	5.77983e6i		−	0.912852i
$186$	−2.19821e6	−	2.72014e6i	−0.341610	−	0.422720i
$187$	−152064.			−0.0232542
$188$		−	5.75641e6i		−	0.866320i
$189$		0			0
$190$	5.04768e6			0.735921
$191$			5.02166e6i			0.720687i	0.932820	+	0.360344i	$0.117341\pi$
$191$			5.02166e6i			0.720687i	−0.932820	+	0.360344i	$0.882659\pi$
$192$	688128.	−	556091.i	0.0972222	−	0.0785674i
$193$	3.50093e6			0.486980			0.243490	−	0.969903i	$-0.421708\pi$
$193$	3.50093e6			0.486980			0.243490	+	0.969903i	$0.421708\pi$
$194$		−	1.59006e6i		−	0.217775i
$195$	8.49600e6	+	1.05133e7i	1.14580	+	1.41786i
$196$		0			0
$197$		−	4.85423e6i		−	0.634923i	−0.948271	−	0.317462i	$-0.897170\pi$
$197$		−	4.85423e6i		−	0.634923i	0.948271	−	0.317462i	$-0.102830\pi$
$198$	29376.0	−	136851.i	0.00378440	−	0.0176300i
$199$	9.50976e6			1.20673			0.603365	−	0.797465i	$-0.293826\pi$
$199$	9.50976e6			1.20673			0.603365	+	0.797465i	$0.293826\pi$
$200$		−	2.38493e6i		−	0.298116i
$201$	−9.21266e6	+	7.44495e6i	−1.13448	+	0.916798i
$202$	−5.34778e6			−0.648812
$203$		0			0
$204$	2.43302e6	+	3.01071e6i	0.286587	+	0.354633i
$205$	−2.84544e6			−0.330284
$206$		−	4.89729e6i		−	0.560214i
$207$	7.30598e6	+	1.56828e6i	0.823697	+	0.176813i
$208$	3.02080e6			0.335685
$209$		−	178462.i		−	0.0195483i
$210$		0			0
$211$	7.06414e6			0.751990			0.375995	−	0.926622i	$-0.377301\pi$
$211$	7.06414e6			0.751990			0.375995	+	0.926622i	$0.377301\pi$
$212$		−	6.16154e6i		−	0.646668i
$213$	−1.15776e6	−	1.43265e6i	−0.119806	−	0.148253i
$214$	−8.33875e6			−0.850863
$215$			1.08713e6i			0.109388i
$216$	−3.17952e6	+	1.60799e6i	−0.315501	+	0.159560i
$217$		0			0
$218$		−	3.68154e6i		−	0.355353i
$219$	−1.53407e7	+	1.23972e7i	−1.46054	+	1.18029i
$220$	−184320.			−0.0173103
$221$			1.32167e7i			1.22446i
$222$	3.26957e6	+	4.04588e6i	0.298835	+	0.369789i
$223$	−4.66891e6			−0.421019			−0.210509	−	0.977592i	$-0.567512\pi$
$223$	−4.66891e6			−0.421019			−0.210509	+	0.977592i	$0.567512\pi$
$224$		0			0
$225$	−2.01578e6	+	9.39066e6i	−0.176968	+	0.824420i
$226$	−9.86650e6			−0.854747
$227$			1.96525e7i			1.68012i	0.542494	+	0.840059i	$0.317480\pi$
$227$			1.96525e7i			1.68012i	−0.542494	+	0.840059i	$0.682520\pi$
$228$	−3.53338e6	+	2.85540e6i	−0.298116	+	0.240914i
$229$	4.48178e6			0.373202			0.186601	−	0.982436i	$-0.440253\pi$
$229$	4.48178e6			0.373202			0.186601	+	0.982436i	$0.440253\pi$
$230$		−	9.84021e6i		−	0.808762i
$231$		0			0
$232$	399360.			0.0319816
$233$		−	2.29286e6i		−	0.181263i	−0.995884	−	0.0906316i	$-0.971111\pi$
$233$		−	2.29286e6i		−	0.181263i	0.995884	−	0.0906316i	$-0.0288886\pi$
$234$	−1.18944e7	−	2.55322e6i	−0.928314	−	0.199270i
$235$	3.05280e7			2.35231
$236$			1.04582e7i			0.795649i
$237$	−7.15180e6	+	5.77953e6i	−0.537243	+	0.434158i
$238$		0			0
$239$			2.64564e6i			0.193793i	0.995294	+	0.0968964i	$0.0308915\pi$
$239$			2.64564e6i			0.193793i	−0.995294	+	0.0968964i	$0.969108\pi$
$240$	2.94912e6	+	3.64935e6i	0.213333	+	0.263987i
$241$	6.99581e6			0.499789			0.249894	−	0.968273i	$-0.419604\pi$
$241$	6.99581e6			0.499789			0.249894	+	0.968273i	$0.419604\pi$
$242$		−	1.00149e7i		−	0.706647i
$243$	1.38785e7	−	3.64411e6i	0.967214	−	0.253964i
$244$	−2.00211e6			−0.137822
$245$		0			0
$246$	1.99181e6	−	1.60962e6i	0.133796	−	0.108123i
$247$	−1.55111e7			−1.02932
$248$		−	4.14498e6i		−	0.271749i
$249$	−8.42170e6	−	1.04213e7i	−0.545508	−	0.675032i
$250$	−2.35200e6			−0.150528
$251$		−	2.84990e7i		−	1.80223i	−0.433585	−	0.901113i	$-0.642752\pi$
$251$		−	2.84990e7i		−	1.80223i	0.433585	−	0.901113i	$-0.357248\pi$
$252$		0			0
$253$	−347904.			−0.0214831
$254$			1.29006e7i			0.787243i
$255$	−1.59667e7	+	1.29031e7i	−0.962931	+	0.778166i
$256$	1.04858e6			0.0625000
$257$		−	186812.i		−	0.0110054i	−0.999985	−	0.00550269i	$-0.998248\pi$
$257$		−	186812.i		−	0.0110054i	0.999985	−	0.00550269i	$-0.00175157\pi$
$258$	−614976.	−	760994.i	−0.0358096	−	0.0443121i
$259$		0			0
$260$			1.60202e7i			0.911482i
$261$	−1.57248e6	−	337544.i	−0.0884430	−	0.0189850i
$262$	−6.06394e6			−0.337171
$263$			8.61541e6i			0.473597i	0.971559	+	0.236798i	$0.0760981\pi$
$263$			8.61541e6i			0.473597i	−0.971559	+	0.236798i	$0.923902\pi$
$264$	129024.	−	104267.i	0.00701227	−	0.00566677i
$265$	3.26765e7			1.75589
$266$		0			0
$267$	6.56294e6	+	8.12123e6i	0.344798	+	0.426666i
$268$	−1.40383e7			−0.729308
$269$		−	7.55132e6i		−	0.387941i	−0.981007	−	0.193971i	$-0.937863\pi$
$269$		−	7.55132e6i		−	0.387941i	0.981007	−	0.193971i	$-0.0621367\pi$
$270$	−8.52768e6	−	1.68620e7i	−0.433251	−	0.856676i
$271$	−1.39445e7			−0.700642			−0.350321	−	0.936630i	$-0.613927\pi$
$271$	−1.39445e7			−0.700642			−0.350321	+	0.936630i	$0.613927\pi$
$272$			4.58775e6i			0.227978i
$273$		0			0
$274$	1.57452e7			0.765412
$275$		−	447174.i		−	0.0215020i
$276$	5.56646e6	+	6.88815e6i	0.264760	+	0.327624i
$277$	2.81293e7			1.32349			0.661744	−	0.749730i	$-0.269817\pi$
$277$	2.81293e7			1.32349			0.661744	+	0.749730i	$0.269817\pi$
$278$			2.58741e7i			1.20429i
$279$	−3.50339e6	+	1.63209e7i	−0.161316	+	0.751503i
$280$		0			0
$281$		−	2.23430e7i		−	1.00698i	−0.864000	−	0.503491i	$-0.832049\pi$
$281$		−	2.23430e7i		−	1.00698i	0.864000	−	0.503491i	$-0.167951\pi$
$282$	−2.13696e7	+	1.72692e7i	−0.952904	+	0.770063i
$283$	−1.01418e7			−0.447464			−0.223732	−	0.974651i	$-0.571824\pi$
$283$	−1.01418e7			−0.447464			−0.223732	+	0.974651i	$0.571824\pi$
$284$		−	2.18309e6i		−	0.0953053i
$285$	−1.51430e7	−	1.87386e7i	−0.654152	−	0.809471i
$286$	566400.			0.0242117
$287$		0			0
$288$	−4.12877e6	−	886271.i	−0.172840	−	0.0371013i
$289$	4.06512e6			0.168415
$290$			2.11793e6i			0.0868394i
$291$	−5.90281e6	+	4.77019e6i	−0.239541	+	0.193578i
$292$	−2.33763e7			−0.938918
$293$		−	2.78468e7i		−	1.10706i	−0.832828	−	0.553532i	$-0.813280\pi$
$293$		−	2.78468e7i		−	1.10706i	0.832828	−	0.553532i	$-0.186720\pi$
$294$		0			0
$295$	−5.54630e7			−2.16042
$296$			6.16516e6i			0.237722i
$297$	−596160.	+	301499.i	−0.0227559	+	0.0115084i
$298$	−2.52301e7			−0.953391
$299$			3.02381e7i			1.13121i
$300$	−8.85360e6	+	7.15479e6i	−0.327911	+	0.264992i
$301$		0			0
$302$			1.24909e7i			0.453494i
$303$	1.60433e7	+	1.98526e7i	0.576722	+	0.713657i
$304$	−5.38419e6			−0.191646
$305$		−	1.06178e7i		−	0.374227i
$306$	3.87763e6	−	1.80643e7i	0.135333	−	0.630458i
$307$	3.63254e7			1.25544			0.627718	−	0.778440i	$-0.283989\pi$
$307$	3.63254e7			1.25544			0.627718	+	0.778440i	$0.283989\pi$
$308$		0			0
$309$	−1.81802e7	+	1.46919e7i	−0.616204	+	0.497968i
$310$	2.19821e7			0.737877
$311$			3.59921e7i			1.19654i	0.801296	+	0.598268i	$0.204144\pi$
$311$			3.59921e7i			1.19654i	−0.801296	+	0.598268i	$0.795856\pi$
$312$	−9.06240e6	−	1.12141e7i	−0.298387	−	0.369235i
$313$	−4.01099e7			−1.30803			−0.654016	−	0.756480i	$-0.726917\pi$
$313$	−4.01099e7			−1.30803			−0.654016	+	0.756480i	$0.726917\pi$
$314$		−	7.29095e6i		−	0.235502i
$315$		0			0
$316$	−1.08980e7			−0.345370
$317$			3.94377e7i			1.23804i	0.785377	+	0.619018i	$0.212469\pi$
$317$			3.94377e7i			1.23804i	−0.785377	+	0.619018i	$0.787531\pi$
$318$	−2.28735e7	+	1.84846e7i	−0.711299	+	0.574816i
$319$	74880.0			0.00230671
$320$			5.56091e6i			0.169706i
$321$	2.50163e7	+	3.09560e7i	0.756323	+	0.935902i
$322$		0			0
$323$		−	2.35570e7i		−	0.699058i
$324$	1.55079e7	+	6.97938e6i	0.455952	+	0.205202i
$325$	−3.88662e7			−1.13220
$326$		−	4.97755e6i		−	0.143669i
$327$	−1.36670e7	+	1.10446e7i	−0.390868	+	0.315869i
$328$	3.03514e6			0.0860115
$329$		0			0
$330$	552960.	+	684253.i	0.0153869	+	0.0190404i
$331$	2.78363e7			0.767586			0.383793	−	0.923419i	$-0.374618\pi$
$331$	2.78363e7			0.767586			0.383793	+	0.923419i	$0.374618\pi$
$332$		−	1.58801e7i		−	0.433949i
$333$	5.21087e6	−	2.42753e7i	0.141117	−	0.657403i
$334$	3.37578e7			0.906014
$335$		−	7.44495e7i		−	1.98028i
$336$		0			0
$337$	−2.37897e7			−0.621582			−0.310791	−	0.950478i	$-0.600594\pi$
$337$	−2.37897e7			−0.621582			−0.310791	+	0.950478i	$0.600594\pi$
$338$		−	2.19242e7i		−	0.567772i
$339$	2.95995e7	+	3.66275e7i	0.759775	+	0.940174i
$340$	−2.43302e7			−0.619027
$341$		−	777184.i		−	0.0196002i
$342$	2.12003e7	+	4.55079e6i	0.529984	+	0.113765i
$343$		0			0
$344$		−	1.15961e6i		−	0.0284863i
$345$	−3.65299e7	+	2.95206e7i	−0.889593	+	0.718900i
$346$	2.36947e6			0.0572036
$347$			5.34078e7i			1.27825i	0.769103	+	0.639125i	$0.220703\pi$
$347$			5.34078e7i			1.27825i	−0.769103	+	0.639125i	$0.779297\pi$
$348$	−1.19808e6	−	1.48255e6i	−0.0284281	−	0.0351780i
$349$	−4.71677e7			−1.10961			−0.554803	−	0.831982i	$-0.687206\pi$
$349$	−4.71677e7			−1.10961			−0.554803	+	0.831982i	$0.687206\pi$
$350$		0			0
$351$	2.62048e7	+	5.18154e7i	0.605983	+	1.19822i
$352$	196608.			0.00450789
$353$		−	1.75443e7i		−	0.398852i	−0.979913	−	0.199426i	$-0.936092\pi$
$353$		−	1.75443e7i		−	0.398852i	0.979913	−	0.199426i	$-0.0639078\pi$
$354$	3.88241e7	−	3.13746e7i	0.875169	−	0.707243i
$355$	1.15776e7			0.258782
$356$			1.23752e7i			0.274285i
$357$		0			0
$358$	−1.70899e6			−0.0372470
$359$		−	6.18249e7i		−	1.33623i	−0.744059	−	0.668113i	$-0.767102\pi$
$359$		−	6.18249e7i		−	1.33623i	0.744059	−	0.668113i	$-0.232898\pi$
$360$	4.70016e6	−	2.18961e7i	0.100741	−	0.469309i
$361$	−1.93993e7			−0.412349
$362$		−	3.66348e7i		−	0.772269i
$363$	−3.71786e7	+	3.00448e7i	−0.777272	+	0.628131i
$364$		0			0
$365$		−	1.23972e8i		−	2.54943i
$366$	6.00634e6	+	7.43246e6i	0.122509	+	0.151597i
$367$	3.40461e7			0.688761			0.344381	−	0.938830i	$-0.388089\pi$
$367$	3.40461e7			0.688761			0.344381	+	0.938830i	$0.388089\pi$
$368$			1.04962e7i			0.210615i
$369$	−1.19508e7	−	2.56534e6i	−0.237859	−	0.0510582i
$370$	−3.26957e7			−0.645484
$371$		0			0
$372$	−1.53875e7	+	1.24349e7i	−0.298908	+	0.241554i
$373$	−5.15781e7			−0.993892			−0.496946	−	0.867782i	$-0.665545\pi$
$373$	−5.15781e7			−0.993892			−0.496946	+	0.867782i	$0.665545\pi$
$374$			860204.i			0.0164432i
$375$	7.05600e6	+	8.73135e6i	0.133803	+	0.165572i
$376$	−3.25632e7			−0.612581
$377$		−	6.50821e6i		−	0.121461i
$378$		0			0
$379$	4.28828e7			0.787709			0.393855	−	0.919173i	$-0.371141\pi$
$379$	4.28828e7			0.787709			0.393855	+	0.919173i	$0.371141\pi$
$380$		−	2.85540e7i		−	0.520375i
$381$	4.78910e7	−	3.87018e7i	0.865923	−	0.699772i
$382$	2.84068e7			0.509603
$383$			1.51307e7i			0.269316i	0.990892	+	0.134658i	$0.0429936\pi$
$383$			1.51307e7i			0.269316i	−0.990892	+	0.134658i	$0.957006\pi$
$384$	−3.14573e6	−	3.89264e6i	−0.0555556	−	0.0687465i
$385$		0			0
$386$		−	1.98043e7i		−	0.344347i
$387$	−980118.	+	4.56596e6i	−0.0169101	+	0.0787770i
$388$	−8.99475e6			−0.153991
$389$			6.15319e7i			1.04533i	0.852540	+	0.522663i	$0.175061\pi$
$389$			6.15319e7i			1.04533i	−0.852540	+	0.522663i	$0.824939\pi$
$390$	5.94720e7	−	4.80606e7i	1.00258	−	0.810206i
$391$	−4.59233e7			−0.768251
$392$		0			0
$393$	1.81918e7	+	2.25112e7i	0.299708	+	0.370870i
$394$	−2.74596e7			−0.448959
$395$		−	5.77953e7i		−	0.937780i
$396$	−774144.	−	166176.i	−0.0124663	−	0.00267598i
$397$	8.55816e7			1.36776			0.683878	−	0.729596i	$-0.260292\pi$
$397$	8.55816e7			1.36776			0.683878	+	0.729596i	$0.260292\pi$
$398$		−	5.37953e7i		−	0.853287i
$399$		0			0
$400$	−1.34912e7			−0.210800
$401$		−	4.09739e7i		−	0.635439i	−0.948185	−	0.317719i	$-0.897083\pi$
$401$		−	4.09739e7i		−	0.635439i	0.948185	−	0.317719i	$-0.102917\pi$
$402$	4.21150e7	+	5.21147e7i	0.648274	+	0.802198i
$403$	−6.75491e7			−1.03206
$404$			3.02516e7i			0.458780i
$405$	−3.70138e7	+	8.22433e7i	−0.557183	+	1.23804i
$406$		0			0
$407$			1.15597e6i			0.0171460i
$408$	1.70312e7	−	1.37633e7i	0.250763	−	0.202647i
$409$	−6.10556e7			−0.892391			−0.446196	−	0.894935i	$-0.647221\pi$
$409$	−6.10556e7			−0.892391			−0.446196	+	0.894935i	$0.647221\pi$
$410$			1.60962e7i			0.233546i
$411$	−4.72355e7	−	5.84509e7i	−0.680366	−	0.841910i
$412$	−2.77032e7			−0.396131
$413$		0			0
$414$	8.87155e6	−	4.13289e7i	0.125025	−	0.582442i
$415$	8.42170e7			1.17830
$416$		−	1.70882e7i		−	0.237365i
$417$	9.60529e7	−	7.76224e7i	1.32465	−	1.07048i
$418$	−1.00954e6			−0.0138227
$419$		−	3.38860e7i		−	0.460657i	−0.973113	−	0.230329i	$-0.926020\pi$
$419$		−	3.38860e7i		−	0.460657i	0.973113	−	0.230329i	$-0.0739801\pi$
$420$		0			0
$421$	−1.96156e7			−0.262879			−0.131439	−	0.991324i	$-0.541960\pi$
$421$	−1.96156e7			−0.262879			−0.131439	+	0.991324i	$0.541960\pi$
$422$		−	3.99608e7i		−	0.531737i
$423$	1.28218e8	+	2.75229e7i	1.69405	+	0.363641i
$424$	−3.48549e7			−0.457263
$425$		−	5.90270e7i		−	0.768925i
$426$	−8.10432e6	+	6.54928e6i	−0.104831	+	0.0847159i
$427$		0			0
$428$			4.71711e7i			0.601651i
$429$	−1.69920e6	−	2.10265e6i	−0.0215215	−	0.0266315i
$430$	6.14976e6			0.0773487
$431$		−	4.01587e7i		−	0.501589i	−0.968040	−	0.250795i	$-0.919308\pi$
$431$		−	4.01587e7i		−	0.501589i	0.968040	−	0.250795i	$-0.0806919\pi$
$432$	9.09619e6	+	1.79861e7i	0.112826	+	0.223093i
$433$	845854.			0.0104191			0.00520957	−	0.999986i	$-0.498342\pi$
$433$	845854.			0.0104191			0.00520957	+	0.999986i	$0.498342\pi$
$434$		0			0
$435$	7.86240e6	−	6.35378e6i	0.0955185	−	0.0771906i
$436$	−2.08259e7			−0.251272
$437$		−	5.38957e7i		−	0.645817i
$438$	7.01290e7	+	8.67802e7i	0.834594	+	1.03276i
$439$	7.48204e7			0.884354			0.442177	−	0.896928i	$-0.354206\pi$
$439$	7.48204e7			0.884354			0.442177	+	0.896928i	$0.354206\pi$
$440$			1.04267e6i			0.0122402i
$441$		0			0
$442$	7.47648e7			0.865825
$443$		−	1.25246e8i		−	1.44063i	−0.693649	−	0.720313i	$-0.743998\pi$
$443$		−	1.25246e8i		−	1.44063i	0.693649	−	0.720313i	$-0.256002\pi$
$444$	2.28870e7	−	1.84955e7i	0.261481	−	0.211308i
$445$	−6.56294e7			−0.744764
$446$			2.64114e7i			0.297705i
$447$	7.56904e7	+	9.36621e7i	0.847458	+	1.04868i
$448$		0			0
$449$			1.12812e8i			1.24628i	0.782109	+	0.623142i	$0.214144\pi$
$449$			1.12812e8i			1.24628i	−0.782109	+	0.623142i	$0.785856\pi$
$450$	5.31216e7	+	1.14029e7i	0.582953	+	0.125135i
$451$	569088.			0.00620369
$452$			5.58133e7i			0.604397i
$453$	4.63700e7	−	3.74726e7i	0.498818	−	0.403106i
$454$	1.11171e8			1.18802
$455$		0			0
$456$	1.61526e7	+	1.99878e7i	0.170352	+	0.210800i
$457$	1.57358e8			1.64870			0.824350	−	0.566081i	$-0.191541\pi$
$457$	1.57358e8			1.64870			0.824350	+	0.566081i	$0.191541\pi$
$458$		−	2.53528e7i		−	0.263894i
$459$	−7.86931e7	+	3.97979e7i	−0.813764	+	0.411549i
$460$	−5.56646e7			−0.571881
$461$			1.83107e8i			1.86897i	0.356002	+	0.934485i	$0.384140\pi$
$461$			1.83107e8i			1.86897i	−0.356002	+	0.934485i	$0.615860\pi$
$462$		0			0
$463$	1.77978e8			1.79318			0.896588	−	0.442866i	$-0.146038\pi$
$463$	1.77978e8			1.79318			0.896588	+	0.442866i	$0.146038\pi$
$464$		−	2.25912e6i		−	0.0226144i
$465$	−6.59462e7	−	8.16043e7i	−0.655890	−	0.811623i
$466$	−1.29704e7			−0.128172
$467$			9.35797e7i			0.918821i	0.888224	+	0.459410i	$0.151939\pi$
$467$			9.35797e7i			0.918821i	−0.888224	+	0.459410i	$0.848061\pi$
$468$	−1.44432e7	+	6.72849e7i	−0.140905	+	0.656417i
$469$		0			0
$470$		−	1.72692e8i		−	1.66334i
$471$	−2.70663e7	+	2.18728e7i	−0.259039	+	0.209335i
$472$	5.91606e7			0.562609
$473$		−	217427.i		−	0.00205461i
$474$	3.26940e7	+	4.04567e7i	0.306996	+	0.379888i
$475$	6.92742e7			0.646384
$476$		0			0
$477$	1.37241e8	+	2.94598e7i	1.26453	+	0.271441i
$478$	1.49660e7			0.137032
$479$		−	1.07662e8i		−	0.979617i	−0.871830	−	0.489808i	$-0.837067\pi$
$479$		−	1.07662e8i		−	0.979617i	0.871830	−	0.489808i	$-0.162933\pi$
$480$	2.06438e7	−	1.66827e7i	0.186667	−	0.150849i
$481$	1.00471e8			0.902830
$482$		−	3.95743e7i		−	0.353404i
$483$		0			0
$484$	−5.66531e7			−0.499675
$485$		−	4.77019e7i		−	0.418129i
$486$	−2.06142e7	−	7.85084e7i	−0.179580	−	0.683923i
$487$	−4.14432e6			−0.0358811			−0.0179406	−	0.999839i	$-0.505711\pi$
$487$	−4.14432e6			−0.0358811			−0.0179406	+	0.999839i	$0.505711\pi$
$488$			1.13257e7i			0.0974549i
$489$	−1.84782e7	+	1.49326e7i	−0.158028	+	0.127706i
$490$		0			0
$491$			1.19347e8i			1.00824i	0.863633	+	0.504122i	$0.168184\pi$
$491$			1.19347e8i			1.00824i	−0.863633	+	0.504122i	$0.831816\pi$
$492$	−9.10541e6	−	1.12674e7i	−0.0764547	−	0.0946078i
$493$	9.88416e6			0.0824896
$494$			8.77440e7i			0.727841i
$495$	881280.	−	4.10552e6i	0.00726605	−	0.0338495i
$496$	−2.34476e7			−0.192155
$497$		0			0
$498$	−5.89519e7	+	4.76403e7i	−0.477320	+	0.385733i
$499$	1.17436e8			0.945144			0.472572	−	0.881292i	$-0.343326\pi$
$499$	1.17436e8			0.945144			0.472572	+	0.881292i	$0.343326\pi$
$500$			1.33049e7i			0.106439i
$501$	−1.01273e8	−	1.25320e8i	−0.805346	−	0.996565i
$502$	−1.61215e8			−1.27437
$503$		−	1.99753e8i		−	1.56960i	−0.619747	−	0.784802i	$-0.712765\pi$
$503$		−	1.99753e8i		−	1.56960i	0.619747	−	0.784802i	$-0.287235\pi$
$504$		0			0
$505$	−1.60433e8			−1.24572
$506$			1.96804e6i			0.0151909i
$507$	−8.13895e7	+	6.57727e7i	−0.624517	+	0.504686i
$508$	7.29768e7			0.556665
$509$		−	1.12725e8i		−	0.854804i	−0.904062	−	0.427402i	$-0.859429\pi$
$509$		−	1.12725e8i		−	0.854804i	0.904062	−	0.427402i	$-0.140571\pi$
$510$	7.29907e7	+	9.03214e7i	0.550246	+	0.680895i
$511$		0			0
$512$		−	5.93164e6i		−	0.0441942i
$513$	−4.67068e7	−	9.23543e7i	−0.345962	−	0.684077i
$514$	−1.05677e6			−0.00778198
$515$		−	1.46919e8i		−	1.07561i
$516$	−4.30483e6	+	3.47883e6i	−0.0313334	+	0.0253212i
$517$	−6.10560e6			−0.0441832
$518$		0			0
$519$	−7.10842e6	−	8.79622e6i	−0.0508476	−	0.0629207i
$520$	9.06240e7			0.644515
$521$			1.14581e8i			0.810215i	0.914269	+	0.405108i	$0.132766\pi$
$521$			1.14581e8i			0.810215i	−0.914269	+	0.405108i	$0.867234\pi$
$522$	−1.90944e6	+	8.89529e6i	−0.0134244	+	0.0625387i
$523$	1.49806e8			1.04719			0.523594	−	0.851968i	$-0.324591\pi$
$523$	1.49806e8			1.04719			0.523594	+	0.851968i	$0.324591\pi$
$524$			3.43028e7i			0.238416i
$525$		0			0
$526$	4.87361e7			0.334884
$527$		−	1.02588e8i		−	0.700916i
$528$	−589824.	−	729870.i	−0.00400701	−	0.00495842i
$529$	4.29689e7			0.290260
$530$		−	1.84846e8i		−	1.24160i
$531$	−2.32945e8	−	5.00033e7i	−1.55586	−	0.333976i
$532$		0			0
$533$		−	4.94624e7i		−	0.326658i
$534$	4.59406e7	−	3.71256e7i	0.301698	−	0.243809i
$535$	−2.50163e8			−1.63366
$536$			7.94128e7i			0.515699i
$537$	5.12698e6	+	6.34431e6i	0.0331084	+	0.0409696i
$538$	−4.27167e7			−0.274316
$539$		0			0
$540$	−9.53856e7	+	4.82398e7i	−0.605761	+	0.306355i
$541$	−1.57017e8			−0.991644			−0.495822	−	0.868424i	$-0.665133\pi$
$541$	−1.57017e8			−0.991644			−0.495822	+	0.868424i	$0.665133\pi$
$542$			7.88822e7i			0.495429i
$543$	−1.36000e8	+	1.09904e8i	−0.849452	+	0.686461i
$544$	2.59523e7			0.161205
$545$		−	1.10446e8i		−	0.682277i
$546$		0			0
$547$	−2.79469e8			−1.70754			−0.853770	−	0.520650i	$-0.825690\pi$
$547$	−2.79469e8			−1.70754			−0.853770	+	0.520650i	$0.825690\pi$
$548$		−	8.90680e7i		−	0.541228i
$549$	9.57260e6	−	4.45948e7i	0.0578513	−	0.269505i
$550$	−2.52960e6			−0.0152042
$551$			1.16001e7i			0.0693434i
$552$	3.89652e7	−	3.14887e7i	0.231665	−	0.187213i
$553$		0			0
$554$		−	1.59123e8i		−	0.935847i
$555$	9.80870e7	+	1.21377e8i	0.573763	+	0.709996i
$556$	1.46366e8			0.851563
$557$			1.50294e8i			0.869712i	0.900500	+	0.434856i	$0.143201\pi$
$557$			1.50294e8i			0.869712i	−0.900500	+	0.434856i	$0.856799\pi$
$558$	9.23247e7	+	1.98182e7i	0.531393	+	0.114067i
$559$	−1.88977e7			−0.108187
$560$		0			0
$561$	3.19334e6	−	2.58061e6i	0.0180866	−	0.0146162i
$562$	−1.26391e8			−0.712044
$563$		−	8.27836e7i		−	0.463894i	−0.972728	−	0.231947i	$-0.925490\pi$
$563$		−	8.27836e7i		−	0.463894i	0.972728	−	0.231947i	$-0.0745097\pi$
$564$	9.76896e7	+	1.20885e8i	0.544516	+	0.673805i
$565$	−2.95995e8			−1.64111
$566$			5.73710e7i			0.316405i
$567$		0			0
$568$	−1.23494e7			−0.0673911
$569$		−	2.57230e8i		−	1.39632i	−0.715942	−	0.698160i	$-0.754003\pi$
$569$		−	2.57230e8i		−	1.39632i	0.715942	−	0.698160i	$-0.245997\pi$
$570$	−1.06001e8	+	8.56620e7i	−0.572383	+	0.462555i
$571$	2.84039e7			0.152570			0.0762852	−	0.997086i	$-0.475694\pi$
$571$	2.84039e7			0.152570			0.0762852	+	0.997086i	$0.475694\pi$
$572$		−	3.20404e6i		−	0.0171203i
$573$	−8.52204e7	−	1.05455e8i	−0.452980	−	0.560535i
$574$		0			0
$575$		−	1.35047e8i		−	0.710363i
$576$	−5.01350e6	+	2.33558e7i	−0.0262346	+	0.122216i
$577$	−6.52476e7			−0.339654			−0.169827	−	0.985474i	$-0.554321\pi$
$577$	−6.52476e7			−0.339654			−0.169827	+	0.985474i	$0.554321\pi$
$578$		−	2.29958e7i		−	0.119087i
$579$	−7.35195e7	+	5.94128e7i	−0.378763	+	0.306086i
$580$	1.19808e7			0.0614047
$581$		0			0
$582$	2.69843e7	+	3.33913e7i	0.136880	+	0.169381i
$583$	−6.53530e6			−0.0329807
$584$			1.32236e8i			0.663915i
$585$	−3.56832e8	−	7.65966e7i	−1.78236	−	0.382597i
$586$	−1.57525e8			−0.782813
$587$		−	6.66740e7i		−	0.329642i	−0.986324	−	0.164821i	$-0.947295\pi$
$587$		−	6.66740e7i		−	0.329642i	0.986324	−	0.164821i	$-0.0527046\pi$
$588$		0			0
$589$	1.20398e8			0.589213
$590$			3.13746e8i			1.52765i
$591$	8.23789e7	+	1.01939e8i	0.399074	+	0.493829i
$592$	3.48754e7			0.168095
$593$			1.53324e8i			0.735271i	0.929970	+	0.367635i	$0.119833\pi$
$593$			1.53324e8i			0.735271i	−0.929970	+	0.367635i	$0.880167\pi$
$594$	1.70554e6	+	3.37239e6i	0.00813770	+	0.0160908i
$595$		0			0
$596$			1.42723e8i			0.674149i
$597$	−1.99705e8	+	1.61386e8i	−0.938568	+	0.758478i
$598$	1.71053e8			0.799883
$599$		−	2.18294e8i		−	1.01569i	−0.861448	−	0.507846i	$-0.830442\pi$
$599$		−	2.18294e8i		−	1.01569i	0.861448	−	0.507846i	$-0.169558\pi$
$600$	4.04736e7	+	5.00835e7i	0.187378	+	0.231868i
$601$	−1.08478e8			−0.499709			−0.249854	−	0.968283i	$-0.580383\pi$
$601$	−1.08478e8			−0.499709			−0.249854	+	0.968283i	$0.580383\pi$
$602$		0			0
$603$	6.71208e7	−	3.12688e8i	0.306129	−	1.42613i
$604$	7.06590e7			0.320669
$605$		−	3.00448e8i		−	1.35676i
$606$	1.12303e8	−	9.07548e7i	0.504632	−	0.407804i
$607$	3.43321e8			1.53509			0.767547	−	0.640993i	$-0.221477\pi$
$607$	3.43321e8			1.53509			0.767547	+	0.640993i	$0.221477\pi$
$608$			3.04576e7i			0.135514i
$609$		0			0
$610$	−6.00634e7			−0.264618
$611$			5.30669e8i			2.32649i
$612$	−1.02187e8	−	2.19352e7i	−0.445801	−	0.0956946i
$613$	2.96325e8			1.28643			0.643216	−	0.765685i	$-0.277600\pi$
$613$	2.96325e8			1.28643			0.643216	+	0.765685i	$0.277600\pi$
$614$		−	2.05487e8i		−	0.887728i
$615$	5.97542e7	−	4.82887e7i	0.256888	−	0.207597i
$616$		0			0
$617$			1.32676e8i			0.564853i	0.959289	+	0.282426i	$0.0911393\pi$
$617$			1.32676e8i			0.564853i	−0.959289	+	0.282426i	$0.908861\pi$
$618$	8.31097e7	+	1.02843e8i	0.352116	+	0.435722i
$619$	4.14773e8			1.74879			0.874397	−	0.485211i	$-0.161257\pi$
$619$	4.14773e8			1.74879			0.874397	+	0.485211i	$0.161257\pi$
$620$		−	1.24349e8i		−	0.521758i
$621$	−1.80040e8	+	9.10527e7i	−0.751787	+	0.380205i
$622$	2.03602e8			0.846078
$623$		0			0
$624$	−6.34368e7	+	5.12647e7i	−0.261088	+	0.210991i
$625$	−2.76419e8			−1.13221
$626$			2.26896e8i			0.924919i
$627$	3.02861e6	+	3.74771e6i	0.0122868	+	0.0152042i
$628$	−4.12438e7			−0.166525
$629$			1.52588e8i			0.613151i
$630$		0			0
$631$	3.03858e8			1.20944			0.604718	−	0.796440i	$-0.293286\pi$
$631$	3.03858e8			1.20944			0.604718	+	0.796440i	$0.293286\pi$
$632$			6.16483e7i			0.244214i
$633$	−1.48347e8	+	1.19882e8i	−0.584881	+	0.472655i
$634$	2.23093e8			0.875424
$635$			3.87018e8i			1.51151i
$636$	1.04565e8	+	1.29392e8i	0.406456	+	0.502964i
$637$		0			0
$638$		−	423585.i		−	0.00163109i
$639$	4.86259e7	+	1.04379e7i	0.186365	+	0.0400047i
$640$	3.14573e7			0.120000
$641$			1.81629e8i			0.689622i	0.938672	+	0.344811i	$0.112057\pi$
$641$			1.81629e8i			0.689622i	−0.938672	+	0.344811i	$0.887943\pi$
$642$	1.75114e8	−	1.41513e8i	0.661782	−	0.534801i
$643$	−1.73811e8			−0.653798			−0.326899	−	0.945059i	$-0.606004\pi$
$643$	−1.73811e8			−0.653798			−0.326899	+	0.945059i	$0.606004\pi$
$644$		0			0
$645$	−1.84493e7	−	2.28298e7i	−0.0687544	−	0.0850792i
$646$	−1.33259e8			−0.494309
$647$			2.43137e8i			0.897713i	0.893604	+	0.448856i	$0.148168\pi$
$647$			2.43137e8i			0.897713i	−0.893604	+	0.448856i	$0.851832\pi$
$648$	3.94813e7	−	8.77261e7i	0.145100	−	0.322407i
$649$	1.10926e7			0.0405788
$650$			2.19861e8i			0.800585i
$651$		0			0
$652$	−2.81572e7			−0.101589
$653$			4.47562e7i			0.160736i	0.996765	+	0.0803681i	$0.0256096\pi$
$653$			4.47562e7i			0.160736i	−0.996765	+	0.0803681i	$0.974390\pi$
$654$	6.24778e7	+	7.73123e7i	0.223353	+	0.276386i
$655$	−1.81918e8			−0.647369
$656$		−	1.71693e7i		−	0.0608193i
$657$	1.11768e8	−	5.20681e8i	0.394114	−	1.83601i
$658$		0			0
$659$			1.13574e8i			0.396845i	0.980117	+	0.198423i	$0.0635819\pi$
$659$			1.13574e8i			0.396845i	−0.980117	+	0.198423i	$0.936418\pi$
$660$	3.87072e6	−	3.12801e6i	0.0134636	−	0.0108802i
$661$	9.93464e7			0.343992			0.171996	−	0.985098i	$-0.444978\pi$
$661$	9.93464e7			0.343992			0.171996	+	0.985098i	$0.444978\pi$
$662$		−	1.57466e8i		−	0.542766i
$663$	−2.24294e8	−	2.77550e8i	−0.769623	−	0.952359i
$664$	−8.98314e7			−0.306849
$665$		0			0
$666$	−1.37322e8	−	2.94772e7i	−0.464854	−	0.0997845i
$667$	2.26138e7			0.0762071
$668$		−	1.90963e8i		−	0.640649i
$669$	9.80472e7	−	7.92341e7i	0.327459	−	0.264627i
$670$	−4.21150e8			−1.40027
$671$			2.12356e6i			0.00702906i
$672$		0			0
$673$	−2.79412e8			−0.916642			−0.458321	−	0.888787i	$-0.651549\pi$
$673$	−2.79412e8			−0.916642			−0.458321	+	0.888787i	$0.651549\pi$
$674$			1.34575e8i			0.439525i
$675$	−1.17034e8	−	2.31413e8i	−0.380539	−	0.752447i
$676$	−1.24022e8			−0.401475
$677$			4.09293e7i			0.131907i	0.997823	+	0.0659536i	$0.0210089\pi$
$677$			4.09293e7i			0.131907i	−0.997823	+	0.0659536i	$0.978991\pi$
$678$	2.07196e8	−	1.67440e8i	0.664803	−	0.537242i
$679$		0			0
$680$			1.37633e8i			0.437718i
$681$	−3.33514e8	−	4.12702e8i	−1.05602	−	1.30676i
$682$	−4.39642e6			−0.0138594
$683$		−	3.74260e8i		−	1.17466i	−0.809348	−	0.587329i	$-0.800180\pi$
$683$		−	3.74260e8i		−	1.17466i	0.809348	−	0.587329i	$-0.199820\pi$
$684$	2.57432e7	−	1.19927e8i	0.0804440	−	0.374755i
$685$	4.72355e8			1.46959
$686$		0			0
$687$	−9.41174e7	+	7.60584e7i	−0.290268	+	0.234572i
$688$	−6.55974e6			−0.0201429
$689$			5.68017e8i			1.73661i
$690$	1.66994e8	+	2.06644e8i	0.508339	+	0.629037i
$691$	−1.15164e8			−0.349047			−0.174524	−	0.984653i	$-0.555839\pi$
$691$	−1.15164e8			−0.349047			−0.174524	+	0.984653i	$0.555839\pi$
$692$		−	1.34038e7i		−	0.0404490i
$693$		0			0
$694$	3.02120e8			0.903859
$695$			7.76224e8i			2.31224i
$696$	−8.38656e6	+	6.77736e6i	−0.0248746	+	0.0201017i
$697$	7.51196e7			0.221848
$698$			2.66821e8i			0.784609i
$699$	3.89111e7	+	4.81500e7i	0.113931	+	0.140982i
$700$		0			0
$701$		−	5.65717e7i		−	0.164227i	−0.996623	−	0.0821137i	$-0.973833\pi$
$701$		−	5.65717e7i		−	0.164227i	0.996623	−	0.0821137i	$-0.0261671\pi$
$702$	2.93112e8	−	1.48237e8i	0.847271	−	0.428495i
$703$	−1.79077e8			−0.515435
$704$		−	1.11218e6i		−	0.00318756i
$705$	−6.41088e8	+	5.18077e8i	−1.82958	+	1.47852i
$706$	−9.92456e7			−0.282031
$707$		0			0
$708$	−1.77482e8	−	2.19622e8i	−0.500097	−	0.618838i
$709$	−1.28652e8			−0.360975			−0.180488	−	0.983577i	$-0.557768\pi$
$709$	−1.28652e8			−0.360975			−0.180488	+	0.983577i	$0.557768\pi$
$710$		−	6.54928e7i		−	0.182986i
$711$	5.21060e7	−	2.42740e8i	0.144970	−	0.675356i
$712$	7.00047e7			0.193949
$713$		−	2.34710e8i		−	0.647533i
$714$		0			0
$715$	1.69920e7			0.0464864
$716$			9.66752e6i			0.0263376i
$717$	−4.48980e7	−	5.55585e7i	−0.121806	−	0.150728i
$718$	−3.49735e8			−0.944855
$719$		−	2.01053e8i		−	0.540908i	−0.962733	−	0.270454i	$-0.912826\pi$
$719$		−	2.01053e8i		−	0.540908i	0.962733	−	0.270454i	$-0.0871738\pi$
$720$	−1.23863e8	−	2.65881e7i	−0.331852	−	0.0712345i
$721$		0			0
$722$			1.09739e8i			0.291575i
$723$	−1.46912e8	+	1.18723e8i	−0.388725	+	0.314137i
$724$	−2.07238e8			−0.546076
$725$			2.90663e7i			0.0762739i
$726$	1.69959e8	+	2.10314e8i	0.444155	+	0.549614i
$727$	−5.23208e8			−1.36167			−0.680833	−	0.732438i	$-0.738382\pi$
$727$	−5.23208e8			−1.36167			−0.680833	+	0.732438i	$0.738382\pi$
$728$		0			0
$729$	−2.29605e8	+	3.12051e8i	−0.592651	+	0.805459i
$730$	−7.01290e8			−1.80272
$731$		−	2.87003e7i		−	0.0734742i
$732$	4.20444e7	−	3.39770e7i	0.107195	−	0.0866266i
$733$	6.57372e8			1.66917			0.834583	−	0.550882i	$-0.185709\pi$
$733$	6.57372e8			1.66917			0.834583	+	0.550882i	$0.185709\pi$
$734$		−	1.92594e8i		−	0.487028i
$735$		0			0
$736$	5.93756e7			0.148927
$737$			1.48899e7i			0.0371954i
$738$	−1.45117e7	+	6.76042e7i	−0.0361036	+	0.168192i
$739$	3.50495e8			0.868458			0.434229	−	0.900803i	$-0.357021\pi$
$739$	3.50495e8			0.868458			0.434229	+	0.900803i	$0.357021\pi$
$740$			1.84955e8i			0.456426i
$741$	3.25733e8	−	2.63232e8i	0.800585	−	0.646970i
$742$		0			0
$743$			4.66667e8i			1.13773i	0.822429	+	0.568867i	$0.192618\pi$
$743$			4.66667e8i			1.13773i	−0.822429	+	0.568867i	$0.807382\pi$
$744$	7.03427e7	+	8.70446e7i	0.170805	+	0.211360i
$745$	−7.56904e8			−1.83051
$746$			2.91770e8i			0.702788i
$747$	3.53711e8	+	7.59267e7i	0.848569	+	0.182152i
$748$	4.86605e6			0.0116271
$749$		0			0
$750$	4.93920e7	−	3.99148e7i	0.117077	−	0.0946128i
$751$	−3.36993e7			−0.0795612			−0.0397806	−	0.999208i	$-0.512666\pi$
$751$	−3.36993e7			−0.0795612			−0.0397806	+	0.999208i	$0.512666\pi$
$752$			1.84205e8i			0.433160i
$753$	4.83645e8	+	5.98480e8i	1.13277	+	1.40173i
$754$	−3.68160e7			−0.0858860
$755$			3.74726e8i			0.870709i
$756$		0			0
$757$	2.98552e8			0.688227			0.344113	−	0.938928i	$-0.388180\pi$
$757$	2.98552e8			0.688227			0.344113	+	0.938928i	$0.388180\pi$
$758$		−	2.42582e8i		−	0.556995i
$759$	7.30598e6	−	5.90413e6i	0.0167091	−	0.0135030i
$760$	−1.61526e8			−0.367960
$761$		−	3.98702e8i		−	0.904679i	−0.891846	−	0.452340i	$-0.850590\pi$
$761$		−	3.98702e8i		−	0.904679i	0.891846	−	0.452340i	$-0.149410\pi$
$762$	−2.18930e8	−	2.70913e8i	−0.494813	−	0.612300i
$763$		0			0
$764$		−	1.60693e8i		−	0.360344i
$765$	1.16329e8	−	5.41928e8i	0.259839	−	1.21048i
$766$	8.55921e7			0.190435
$767$		−	9.64116e8i		−	2.13670i
$768$	−2.20201e7	+	1.77949e7i	−0.0486111	+	0.0392837i
$769$	5.17372e8			1.13769			0.568845	−	0.822444i	$-0.307390\pi$
$769$	5.17372e8			1.13769			0.568845	+	0.822444i	$0.307390\pi$
$770$		0			0
$771$	3.17030e6	+	3.92305e6i	0.00691732	+	0.00855974i
$772$	−1.12030e8			−0.243490
$773$			1.83241e8i			0.396719i	0.980129	+	0.198360i	$0.0635614\pi$
$773$			1.83241e8i			0.396719i	−0.980129	+	0.198360i	$0.936439\pi$
$774$	2.58290e7	+	5.54438e6i	0.0557038	+	0.0119572i
$775$	3.01681e8			0.648102
$776$			5.08820e7i			0.108888i
$777$		0			0
$778$	3.48077e8			0.739157
$779$			8.81604e7i			0.186493i
$780$	−2.71872e8	−	3.36424e8i	−0.572902	−	0.708931i
$781$	−2.31552e6			−0.00486066
$782$			2.59782e8i			0.543235i
$783$	3.87504e7	−	1.95974e7i	0.0807218	−	0.0408239i
$784$		0			0
$785$		−	2.18728e8i		−	0.452164i
$786$	1.27343e8	−	1.02908e8i	0.262244	−	0.211925i
$787$	−3.14718e8			−0.645650			−0.322825	−	0.946459i	$-0.604633\pi$
$787$	−3.14718e8			−0.645650			−0.322825	+	0.946459i	$0.604633\pi$
$788$			1.55335e8i			0.317462i
$789$	−1.46208e8	−	1.80924e8i	−0.297674	−	0.368353i
$790$	−3.26940e8			−0.663111
$791$		0			0
$792$	−940032.	+	4.37922e6i	−0.00189220	+	0.00881498i
$793$	1.84570e8			0.370119
$794$		−	4.84122e8i		−	0.967150i
$795$	−6.86206e8	+	5.54538e8i	−1.36569	+	1.10365i
$796$	−3.04312e8			−0.603365
$797$			7.88168e8i			1.55684i	0.627744	+	0.778420i	$0.283979\pi$
$797$			7.88168e8i			1.55684i	−0.627744	+	0.778420i	$0.716021\pi$
$798$		0			0
$799$	−8.05939e8			−1.58002
$800$			7.63178e7i			0.149058i
$801$	−2.75644e8	−	5.91690e7i	−0.536353	−	0.115132i
$802$	−2.31783e8			−0.449323
$803$			2.47943e7i			0.0478857i
$804$	2.94805e8	−	2.38238e8i	0.567240	−	0.458399i
$805$		0			0
$806$			3.82115e8i			0.729776i
$807$	1.28150e8	+	1.58578e8i	0.243836	+	0.301732i
$808$	1.71129e8			0.324406
$809$			1.04745e9i			1.97828i	0.146993	+	0.989138i	$0.453041\pi$
$809$			1.04745e9i			1.97828i	−0.146993	+	0.989138i	$0.546959\pi$
$810$	4.65238e8	+	2.09381e8i	0.875428	+	0.393988i
$811$	1.17930e8			0.221086			0.110543	−	0.993871i	$-0.464741\pi$
$811$	1.17930e8			0.221086			0.110543	+	0.993871i	$0.464741\pi$
$812$		0			0
$813$	2.92835e8	−	2.36647e8i	0.544944	−	0.440381i
$814$	6.53914e6			0.0121240
$815$		−	1.49326e8i		−	0.275844i
$816$	−7.78568e7	−	9.63428e7i	−0.143293	−	0.177316i
$817$	3.36827e7			0.0617648
$818$			3.45382e8i			0.631016i
$819$		0			0
$820$	9.10541e7			0.165142
$821$			6.01939e7i			0.108774i	0.998520	+	0.0543868i	$0.0173204\pi$
$821$			6.01939e7i			0.108774i	−0.998520	+	0.0543868i	$0.982680\pi$
$822$	−3.30648e8	+	2.67204e8i	−0.595320	+	0.481091i
$823$	1.60620e7			0.0288139			0.0144069	−	0.999896i	$-0.495414\pi$
$823$	1.60620e7			0.0288139			0.0144069	+	0.999896i	$0.495414\pi$
$824$			1.56713e8i			0.280107i
$825$	7.58880e6	+	9.39066e6i	0.0135149	+	0.0167238i
$826$		0			0
$827$			3.66665e8i			0.648266i	0.946012	+	0.324133i	$0.105072\pi$
$827$			3.66665e8i			0.648266i	−0.946012	+	0.324133i	$0.894928\pi$
$828$	−2.33791e8	−	5.01851e7i	−0.411849	−	0.0884064i
$829$	3.63153e8			0.637421			0.318711	−	0.947852i	$-0.396750\pi$
$829$	3.63153e8			0.637421			0.318711	+	0.947852i	$0.396750\pi$
$830$		−	4.76403e8i		−	0.833183i
$831$	−5.90716e8	+	4.77370e8i	−1.02938	+	0.831864i
$832$	−9.66656e7			−0.167843
$833$		0			0
$834$	−4.39099e8	−	5.43357e8i	−0.756945	−	0.936671i
$835$	1.01273e9			1.73955
$836$			5.71080e6i			0.00977413i
$837$	−2.03403e8	−	4.02193e8i	−0.346881	−	0.685895i
$838$	−1.91688e8			−0.325734
$839$			8.80700e8i			1.49122i	0.666382	+	0.745611i	$0.267842\pi$
$839$			8.80700e8i			1.49122i	−0.666382	+	0.745611i	$0.732158\pi$
$840$		0			0
$841$	5.89956e8			0.991817
$842$			1.10963e8i			0.185883i
$843$	3.79173e8	+	4.69202e8i	0.632928	+	0.783209i
$844$	−2.26052e8			−0.375995
$845$		−	6.57727e8i		−	1.09012i
$846$	1.55693e8	−	7.25308e8i	0.257133	−	1.19788i
$847$		0			0
$848$			1.97169e8i			0.323334i
$849$	2.12979e8	−	1.72113e8i	0.348027	−	0.281249i
$850$	−3.33907e8			−0.543712
$851$			3.49102e8i			0.566453i
$852$	3.70483e7	+	4.58450e7i	0.0599032	+	0.0741264i
$853$	3.84724e8			0.619873			0.309936	−	0.950757i	$-0.399692\pi$
$853$	3.84724e8			0.619873			0.309936	+	0.950757i	$0.399692\pi$
$854$		0			0
$855$	6.36008e8	+	1.36524e8i	1.01757	+	0.218429i
$856$	2.66840e8			0.425432
$857$			3.42647e8i			0.544382i	0.962243	+	0.272191i	$0.0877483\pi$
$857$			3.42647e8i			0.544382i	−0.962243	+	0.272191i	$0.912252\pi$
$858$	−1.18944e7	+	9.61213e6i	−0.0188313	+	0.0152180i
$859$	3.87443e8			0.611263			0.305631	−	0.952150i	$-0.401132\pi$
$859$	3.87443e8			0.611263			0.305631	+	0.952150i	$0.401132\pi$
$860$		−	3.47883e7i		−	0.0546938i
$861$		0			0
$862$	−2.27172e8			−0.354677
$863$			6.46530e7i			0.100590i	0.998734	+	0.0502951i	$0.0160162\pi$
$863$			6.46530e7i			0.100590i	−0.998734	+	0.0502951i	$0.983984\pi$
$864$	1.01745e8	−	5.14558e7i	0.157750	−	0.0797799i
$865$	7.10842e7			0.109831
$866$		−	4.78487e6i		−	0.00736744i
$867$	−8.53675e7	+	6.89874e7i	−0.130989	+	0.105855i
$868$		0			0
$869$			1.15591e7i			0.0176142i
$870$	−3.59424e7	−	4.44765e7i	−0.0545820	−	0.0675418i
$871$	1.29416e9			1.95854
$872$			1.17809e8i			0.177676i
$873$	4.30062e7	−	2.00348e8i	0.0646380	−	0.301122i
$874$	−3.04880e8			−0.456662
$875$		0			0
$876$	4.90903e8	−	3.96709e8i	0.730269	−	0.590147i
$877$	−4.99281e8			−0.740196			−0.370098	−	0.928993i	$-0.620676\pi$
$877$	−4.99281e8			−0.740196			−0.370098	+	0.928993i	$0.620676\pi$
$878$		−	4.23248e8i		−	0.625333i
$879$	4.72576e8	+	5.84783e8i	0.695833	+	0.861050i
$880$	5.89824e6			0.00865515
$881$			9.14796e8i			1.33782i	0.743345	+	0.668908i	$0.233238\pi$
$881$			9.14796e8i			1.33782i	−0.743345	+	0.668908i	$0.766762\pi$
$882$		0			0
$883$	7.85211e6			0.0114052			0.00570261	−	0.999984i	$-0.498185\pi$
$883$	7.85211e6			0.0114052			0.00570261	+	0.999984i	$0.498185\pi$
$884$		−	4.22934e8i		−	0.612231i
$885$	1.16472e9	−	9.41239e8i	1.68032	−	1.35791i
$886$	−7.08496e8			−1.01868
$887$		−	1.10737e9i		−	1.58679i	−0.608704	−	0.793397i	$-0.708310\pi$
$887$		−	1.10737e9i		−	1.58679i	0.608704	−	0.793397i	$-0.291690\pi$
$888$	−1.04626e8	−	1.29468e8i	−0.149417	−	0.184895i
$889$		0			0
$890$			3.71256e8i			0.526628i
$891$	7.40275e6	−	1.64487e7i	0.0104655	−	0.0232540i
$892$	1.49405e8			0.210509
$893$		−	9.45851e8i		−	1.32821i
$894$	5.29833e8	−	4.28170e8i	0.741526	−	0.599244i
$895$	−5.12698e7			−0.0715142
$896$		0			0
$897$	−5.13158e8	−	6.35001e8i	−0.711007	−	0.879827i
$898$	6.38162e8			0.881256
$899$			5.05170e7i			0.0695277i
$900$	6.45048e7	−	3.00501e8i	0.0884840	−	0.412210i
$901$	−8.62659e8			−1.17941
$902$		−	3.21925e6i		−	0.00438667i
$903$		0			0
$904$	3.15728e8			0.427374
$905$		−	1.09904e9i		−	1.48276i
$906$	−2.11977e8	−	2.62308e8i	−0.285039	−	0.352718i
$907$	1.16193e9			1.55725			0.778623	−	0.627492i	$-0.215918\pi$
$907$	1.16193e9			1.55725			0.778623	+	0.627492i	$0.215918\pi$
$908$		−	6.28880e8i		−	0.840059i
$909$	−6.73820e8	−	1.44640e8i	−0.897123	−	0.192574i
$910$		0			0
$911$		−	3.61439e8i		−	0.478057i	−0.971013	−	0.239028i	$-0.923171\pi$
$911$		−	3.61439e8i		−	0.478057i	0.971013	−	0.239028i	$-0.0768289\pi$
$912$	1.13068e8	−	9.13728e7i	0.149058	−	0.120457i
$913$	−1.68434e7			−0.0221318
$914$		−	8.90154e8i		−	1.16581i
$915$	1.80190e8	+	2.22974e8i	0.235216	+	0.291065i
$916$	−1.43417e8			−0.186601
$917$		0			0
$918$	2.25131e8	+	4.45156e8i	0.291009	+	0.575418i
$919$	1.20431e9			1.55164			0.775820	−	0.630954i	$-0.217336\pi$
$919$	1.20431e9			1.55164			0.775820	+	0.630954i	$0.217336\pi$
$920$			3.14887e8i			0.404381i
$921$	−7.62833e8	+	6.16462e8i	−0.976451	+	0.789091i
$922$	1.03581e9			1.32156
$923$			2.01254e8i			0.255941i
$924$		0			0
$925$	−4.48714e8			−0.566950
$926$		−	1.00679e9i		−	1.26797i
$927$	1.32456e8	−	6.17058e8i	0.166277	−	0.774617i
$928$	−1.27795e7			−0.0159908
$929$		−	6.33924e8i		−	0.790661i	−0.918539	−	0.395330i	$-0.870630\pi$
$929$		−	6.33924e8i		−	0.790661i	0.918539	−	0.395330i	$-0.129370\pi$
$930$	−4.61624e8	+	3.73048e8i	−0.573904	+	0.463784i
$931$		0			0
$932$			7.33715e7i			0.0906316i
$933$	−6.10805e8	−	7.55833e8i	−0.752069	−	0.930638i
$934$	5.29366e8			0.649704
$935$			2.58061e7i			0.0315710i
$936$	3.80621e8	+	8.17031e7i	0.464157	+	0.0996348i
$937$	2.47138e8			0.300414			0.150207	−	0.988655i	$-0.452006\pi$
$937$	2.47138e8			0.300414			0.150207	+	0.988655i	$0.452006\pi$
$938$		0			0
$939$	8.42308e8	−	6.80688e8i	1.01736	−	0.822150i
$940$	−9.76896e8			−1.17616
$941$		−	9.37355e8i		−	1.12496i	−0.826812	−	0.562478i	$-0.809848\pi$
$941$		−	9.37355e8i		−	1.12496i	0.826812	−	0.562478i	$-0.190152\pi$
$942$	1.23732e8	+	1.53110e8i	0.148022	+	0.183168i
$943$	1.71865e8			0.204952
$944$		−	3.34663e8i		−	0.397824i
$945$		0			0
$946$	−1.22995e6			−0.00145283
$947$			1.49756e9i			1.76333i	0.471877	+	0.881664i	$0.343576\pi$
$947$			1.49756e9i			1.76333i	−0.471877	+	0.881664i	$0.656424\pi$
$948$	2.28858e8	−	1.84945e8i	0.268621	−	0.217079i
$949$	2.15500e9			2.52145
$950$		−	3.91874e8i		−	0.457062i
$951$	−6.69279e8	−	8.28191e8i	−0.778154	−	0.962917i
$952$		0			0
$953$		−	4.28296e7i		−	0.0494840i	−0.999694	−	0.0247420i	$-0.992124\pi$
$953$		−	4.28296e7i		−	0.0494840i	0.999694	−	0.0247420i	$-0.00787643\pi$
$954$	1.66650e8	−	7.76354e8i	0.191938	−	0.894158i
$955$	8.52204e8			0.978438
$956$		−	8.46606e7i		−	0.0968964i
$957$	−1.57248e6	+	1.27076e6i	−0.00179411	+	0.00144986i
$958$	−6.09029e8			−0.692694
$959$		0			0
$960$	−9.43718e7	−	1.16779e8i	−0.106667	−	0.131993i
$961$	−3.63185e8			−0.409221
$962$		−	5.68350e8i		−	0.638397i
$963$	−1.05068e9	−	2.25537e8i	−1.17650	−	0.252545i
$964$	−2.23866e8			−0.249894
$965$		−	5.94128e8i		−	0.661147i
$966$		0			0
$967$	−1.16322e9			−1.28642			−0.643210	−	0.765690i	$-0.722398\pi$
$967$	−1.16322e9			−1.28642			−0.643210	+	0.765690i	$0.722398\pi$
$968$			3.20478e8i			0.353323i
$969$	3.99776e8	+	4.94698e8i	0.439385	+	0.543712i
$970$	−2.69843e8			−0.295662
$971$			1.39293e9i			1.52150i	0.649045	+	0.760750i	$0.275169\pi$
$971$			1.39293e9i			1.52150i	−0.649045	+	0.760750i	$0.724831\pi$
$972$	−4.44111e8	+	1.16611e8i	−0.483607	+	0.126982i
$973$		0			0
$974$			2.34438e7i			0.0253718i
$975$	8.16191e8	−	6.59582e8i	0.880599	−	0.711631i
$976$	6.40676e7			0.0689111
$977$			7.81956e8i			0.838492i	0.907873	+	0.419246i	$0.137705\pi$
$977$			7.81956e8i			0.838492i	−0.907873	+	0.419246i	$0.862295\pi$
$978$	8.44717e7	+	1.04528e8i	0.0903015	+	0.111742i
$979$	1.31259e7			0.0139888
$980$		0			0
$981$	9.95739e7	−	4.63874e8i	0.105472	−	0.491352i
$982$	6.75126e8			0.712936
$983$			8.80220e8i			0.926682i	0.886180	+	0.463341i	$0.153349\pi$
$983$			8.80220e8i			0.926682i	−0.886180	+	0.463341i	$0.846651\pi$
$984$	−6.37379e7	+	5.15080e7i	−0.0668978	+	0.0540616i
$985$	−8.23789e8			−0.862001
$986$		−	5.59133e7i		−	0.0583289i
$987$		0			0
$988$	4.96355e8			0.514662
$989$		−	6.56629e7i		−	0.0678783i
$990$	−2.32243e7	−	4.98527e6i	−0.0239352	−	0.00513787i
$991$	−1.83915e9			−1.88971			−0.944857	−	0.327483i	$-0.893800\pi$
$991$	−1.83915e9			−1.88971			−0.944857	+	0.327483i	$0.893800\pi$
$992$			1.32639e8i			0.135874i
$993$	−5.84562e8	+	4.72397e8i	−0.597012	+	0.482458i
$994$		0			0
$995$		−	1.61386e9i		−	1.63831i
$996$	2.69494e8	+	3.33482e8i	0.272754	+	0.337516i
$997$	−5.69927e8			−0.575088			−0.287544	−	0.957767i	$-0.592839\pi$
$997$	−5.69927e8			−0.575088			−0.287544	+	0.957767i	$0.592839\pi$
$998$		−	6.64316e8i		−	0.668318i
$999$	3.02537e8	+	5.98213e8i	0.303447	+	0.600011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.7.b.a.197.1		2
3.2	odd	2	inner	294.7.b.a.197.2		2
7.6	odd	2		6.7.b.a.5.1	✓	2
21.20	even	2		6.7.b.a.5.2	yes	2
28.27	even	2		48.7.e.b.17.2		2
35.13	even	4		150.7.b.a.149.2		4
35.27	even	4		150.7.b.a.149.3		4
35.34	odd	2		150.7.d.a.101.2		2
56.13	odd	2		192.7.e.c.65.2		2
56.27	even	2		192.7.e.f.65.1		2
63.13	odd	6		162.7.d.b.107.2		4
63.20	even	6		162.7.d.b.53.2		4
63.34	odd	6		162.7.d.b.53.1		4
63.41	even	6		162.7.d.b.107.1		4
84.83	odd	2		48.7.e.b.17.1		2
105.62	odd	4		150.7.b.a.149.1		4
105.83	odd	4		150.7.b.a.149.4		4
105.104	even	2		150.7.d.a.101.1		2
168.83	odd	2		192.7.e.f.65.2		2
168.125	even	2		192.7.e.c.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.7.b.a.5.1	✓	2	7.6	odd	2
6.7.b.a.5.2	yes	2	21.20	even	2
48.7.e.b.17.1		2	84.83	odd	2
48.7.e.b.17.2		2	28.27	even	2
150.7.b.a.149.1		4	105.62	odd	4
150.7.b.a.149.2		4	35.13	even	4
150.7.b.a.149.3		4	35.27	even	4
150.7.b.a.149.4		4	105.83	odd	4
150.7.d.a.101.1		2	105.104	even	2
150.7.d.a.101.2		2	35.34	odd	2
162.7.d.b.53.1		4	63.34	odd	6
162.7.d.b.53.2		4	63.20	even	6
162.7.d.b.107.1		4	63.41	even	6
162.7.d.b.107.2		4	63.13	odd	6
192.7.e.c.65.1		2	168.125	even	2
192.7.e.c.65.2		2	56.13	odd	2
192.7.e.f.65.1		2	56.27	even	2
192.7.e.f.65.2		2	168.83	odd	2
294.7.b.a.197.1		2	1.1	even	1	trivial
294.7.b.a.197.2		2	3.2	odd	2	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	294.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} +(-21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(96.0000 + 118.794i) q^{6} +181.019i q^{8} +(153.000 - 712.764i) q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} +(-21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(96.0000 + 118.794i) q^{6} +181.019i q^{8} +(153.000 - 712.764i) q^{9} -960.000 q^{10} +33.9411i q^{11} +(672.000 - 543.058i) q^{12} +2950.00 q^{13} +(2880.00 + 3563.82i) q^{15} +1024.00 q^{16} +4480.23i q^{17} +(-4032.00 - 865.499i) q^{18} -5258.00 q^{19} +5430.58i q^{20} +192.000 q^{22} +10250.2i q^{23} +(-3072.00 - 3801.41i) q^{24} -13175.0 q^{25} -16687.7i q^{26} +(8883.00 + 17564.5i) q^{27} -2206.17i q^{29} +(20160.0 - 16291.7i) q^{30} -22898.0 q^{31} -5792.62i q^{32} +(-576.000 - 712.764i) q^{33} +25344.0 q^{34} +(-4896.00 + 22808.4i) q^{36} +34058.0 q^{37} +29743.7i q^{38} +(-61950.0 + 50063.2i) q^{39} +30720.0 q^{40} -16766.9i q^{41} -6406.00 q^{43} -1086.12i q^{44} +(-120960. - 25965.0i) q^{45} +57984.0 q^{46} +179888. i q^{47} +(-21504.0 + 17377.9i) q^{48} +74529.1i q^{50} +(-76032.0 - 94084.8i) q^{51} -94400.0 q^{52} +192548. i q^{53} +(99360.0 - 50249.8i) q^{54} +5760.00 q^{55} +(110418. - 89231.2i) q^{57} -12480.0 q^{58} -326819. i q^{59} +(-92160.0 - 114042. i) q^{60} +62566.0 q^{61} +129531. i q^{62} -32768.0 q^{64} -500632. i q^{65} +(-4032.00 + 3258.35i) q^{66} +438698. q^{67} -143367. i q^{68} +(-173952. - 215255. i) q^{69} +68221.7i q^{71} +(129024. + 27696.0i) q^{72} +730510. q^{73} -192661. i q^{74} +(276675. - 223587. i) q^{75} +168256. q^{76} +(283200. + 350442. i) q^{78} +340562. q^{79} -173779. i q^{80} +(-484623. - 218106. i) q^{81} -94848.0 q^{82} +496253. i q^{83} +760320. q^{85} +36237.8i q^{86} +(37440.0 + 46329.6i) q^{87} -6144.00 q^{88} -386725. i q^{89} +(-146880. + 684253. i) q^{90} -328007. i q^{92} +(480858. - 388592. i) q^{93} +1.01760e6 q^{94} +892312. i q^{95} +(98304.0 + 121645. i) q^{96} +281086. q^{97} +(24192.0 + 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 42 q^{3} - 64 q^{4} + 192 q^{6} + 306 q^{9}+O(q^{10}) \) 2 * q - 42 * q^3 - 64 * q^4 + 192 * q^6 + 306 * q^9	\( 2 q - 42 q^{3} - 64 q^{4} + 192 q^{6} + 306 q^{9} - 1920 q^{10} + 1344 q^{12} + 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} - 10516 q^{19} + 384 q^{22} - 6144 q^{24} - 26350 q^{25} + 17766 q^{27} + 40320 q^{30} - 45796 q^{31} - 1152 q^{33} + 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} + 61440 q^{40} - 12812 q^{43} - 241920 q^{45} + 115968 q^{46} - 43008 q^{48} - 152064 q^{51} - 188800 q^{52} + 198720 q^{54} + 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} + 125132 q^{61} - 65536 q^{64} - 8064 q^{66} + 877396 q^{67} - 347904 q^{69} + 258048 q^{72} + 1461020 q^{73} + 553350 q^{75} + 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} - 189696 q^{82} + 1520640 q^{85} + 74880 q^{87} - 12288 q^{88} - 293760 q^{90} + 961716 q^{93} + 2035200 q^{94} + 196608 q^{96} + 562172 q^{97} + 48384 q^{99}+O(q^{100}) \) 2 * q - 42 * q^3 - 64 * q^4 + 192 * q^6 + 306 * q^9 - 1920 * q^10 + 1344 * q^12 + 5900 * q^13 + 5760 * q^15 + 2048 * q^16 - 8064 * q^18 - 10516 * q^19 + 384 * q^22 - 6144 * q^24 - 26350 * q^25 + 17766 * q^27 + 40320 * q^30 - 45796 * q^31 - 1152 * q^33 + 50688 * q^34 - 9792 * q^36 + 68116 * q^37 - 123900 * q^39 + 61440 * q^40 - 12812 * q^43 - 241920 * q^45 + 115968 * q^46 - 43008 * q^48 - 152064 * q^51 - 188800 * q^52 + 198720 * q^54 + 11520 * q^55 + 220836 * q^57 - 24960 * q^58 - 184320 * q^60 + 125132 * q^61 - 65536 * q^64 - 8064 * q^66 + 877396 * q^67 - 347904 * q^69 + 258048 * q^72 + 1461020 * q^73 + 553350 * q^75 + 336512 * q^76 + 566400 * q^78 + 681124 * q^79 - 969246 * q^81 - 189696 * q^82 + 1520640 * q^85 + 74880 * q^87 - 12288 * q^88 - 293760 * q^90 + 961716 * q^93 + 2035200 * q^94 + 196608 * q^96 + 562172 * q^97 + 48384 * q^99

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