LMFDB - Embedded newform 150.7.b.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,7,Mod(149,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, 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:	$34.5081125430$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.7.b.a.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685 q^{2} +(16.9706 + 21.0000i) q^{3} +32.0000 q^{4} +(-96.0000 - 118.794i) q^{6} -2.00000i q^{7} -181.019 q^{8} +(-153.000 + 712.764i) q^{9} +O(q^{10})$	\(q-5.65685 q^{2} +(16.9706 + 21.0000i) q^{3} +32.0000 q^{4} +(-96.0000 - 118.794i) q^{6} -2.00000i q^{7} -181.019 q^{8} +(-153.000 + 712.764i) q^{9} +33.9411i q^{11} +(543.058 + 672.000i) q^{12} -2950.00i q^{13} +11.3137i q^{14} +1024.00 q^{16} -4480.23 q^{17} +(865.499 - 4032.00i) q^{18} -5258.00 q^{19} +(42.0000 - 33.9411i) q^{21} -192.000i q^{22} -10250.2 q^{23} +(-3072.00 - 3801.41i) q^{24} +16687.7i q^{26} +(-17564.5 + 8883.00i) q^{27} -64.0000i q^{28} +2206.17i q^{29} +22898.0 q^{31} -5792.62 q^{32} +(-712.764 + 576.000i) q^{33} +25344.0 q^{34} +(-4896.00 + 22808.4i) q^{36} -34058.0i q^{37} +29743.7 q^{38} +(61950.0 - 50063.2i) q^{39} +16766.9i q^{41} +(-237.588 + 192.000i) q^{42} -6406.00i q^{43} +1086.12i q^{44} +57984.0 q^{46} -179888. q^{47} +(17377.9 + 21504.0i) q^{48} +117645. q^{49} +(-76032.0 - 94084.8i) q^{51} -94400.0i q^{52} -192548. q^{53} +(99360.0 - 50249.8i) q^{54} +362.039i q^{56} +(-89231.2 - 110418. i) q^{57} -12480.0i q^{58} -326819. i q^{59} -62566.0 q^{61} -129531. q^{62} +(1425.53 + 306.000i) q^{63} +32768.0 q^{64} +(4032.00 - 3258.35i) q^{66} -438698. i q^{67} -143367. q^{68} +(-173952. - 215255. i) q^{69} +68221.7i q^{71} +(27696.0 - 129024. i) q^{72} -730510. i q^{73} +192661. i q^{74} -168256. q^{76} +67.8823 q^{77} +(-350442. + 283200. i) q^{78} -340562. q^{79} +(-484623. - 218106. i) q^{81} -94848.0i q^{82} +496253. q^{83} +(1344.00 - 1086.12i) q^{84} +36237.8i q^{86} +(-46329.6 + 37440.0i) q^{87} -6144.00i q^{88} -386725. i q^{89} -5900.00 q^{91} -328007. q^{92} +(388592. + 480858. i) q^{93} +1.01760e6 q^{94} +(-98304.0 - 121645. i) q^{96} +281086. i q^{97} -665501. q^{98} +(-24192.0 - 5192.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 128 q^{4} - 384 q^{6} - 612 q^{9}+O(q^{10}) $ 4 * q + 128 * q^4 - 384 * q^6 - 612 * q^9	$ 4 q + 128 q^{4} - 384 q^{6} - 612 q^{9} + 4096 q^{16} - 21032 q^{19} + 168 q^{21} - 12288 q^{24} + 91592 q^{31} + 101376 q^{34} - 19584 q^{36} + 247800 q^{39} + 231936 q^{46} + 470580 q^{49} - 304128 q^{51} + 397440 q^{54} - 250264 q^{61} + 131072 q^{64} + 16128 q^{66} - 695808 q^{69} - 673024 q^{76} - 1362248 q^{79} - 1938492 q^{81} + 5376 q^{84} - 23600 q^{91} + 4070400 q^{94} - 393216 q^{96} - 96768 q^{99}+O(q^{100}) $ 4 * q + 128 * q^4 - 384 * q^6 - 612 * q^9 + 4096 * q^16 - 21032 * q^19 + 168 * q^21 - 12288 * q^24 + 91592 * q^31 + 101376 * q^34 - 19584 * q^36 + 247800 * q^39 + 231936 * q^46 + 470580 * q^49 - 304128 * q^51 + 397440 * q^54 - 250264 * q^61 + 131072 * q^64 + 16128 * q^66 - 695808 * q^69 - 673024 * q^76 - 1362248 * q^79 - 1938492 * q^81 + 5376 * q^84 - 23600 * q^91 + 4070400 * q^94 - 393216 * q^96 - 96768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−5.65685			−0.707107
$2$	−5.65685			−0.707107
$3$	16.9706	+	21.0000i	0.628539	+	0.777778i
$3$	16.9706	+	21.0000i	0.628539	+	0.777778i
$4$	32.0000			0.500000
$5$		0			0
$5$		0			0
$6$	−96.0000	−	118.794i	−0.444444	−	0.549972i
$7$		−	2.00000i		−	0.00583090i	−0.999996	−	0.00291545i	$-0.999072\pi$
$7$		−	2.00000i		−	0.00583090i	0.999996	−	0.00291545i	$-0.000928018\pi$
$8$	−181.019			−0.353553
$9$	−153.000	+	712.764i	−0.209877	+	0.977728i
$10$		0			0
$11$			33.9411i			0.0255005i	0.999919	+	0.0127502i	$0.00405864\pi$
$11$			33.9411i			0.0255005i	−0.999919	+	0.0127502i	$0.995941\pi$
$12$	543.058	+	672.000i	0.314270	+	0.388889i
$13$		−	2950.00i		−	1.34274i	−0.741122	−	0.671370i	$-0.765706\pi$
$13$		−	2950.00i		−	1.34274i	0.741122	−	0.671370i	$-0.234294\pi$
$14$			11.3137i			0.00412307i
$15$		0			0
$16$	1024.00			0.250000
$17$	−4480.23			−0.911913			−0.455956	−	0.890002i	$-0.650703\pi$
$17$	−4480.23			−0.911913			−0.455956	+	0.890002i	$0.650703\pi$
$18$	865.499	−	4032.00i	0.148405	−	0.691358i
$19$	−5258.00			−0.766584			−0.383292	−	0.923627i	$-0.625210\pi$
$19$	−5258.00			−0.766584			−0.383292	+	0.923627i	$0.625210\pi$
$20$		0			0
$21$	42.0000	−	33.9411i	0.00453515	−	0.00366495i
$22$		−	192.000i		−	0.0180316i
$23$	−10250.2			−0.842461			−0.421230	−	0.906954i	$-0.638402\pi$
$23$	−10250.2			−0.842461			−0.421230	+	0.906954i	$0.638402\pi$
$24$	−3072.00	−	3801.41i	−0.222222	−	0.274986i
$25$		0			0
$26$			16687.7i			0.949461i
$27$	−17564.5	+	8883.00i	−0.892371	+	0.451303i
$28$		−	64.0000i		−	0.00291545i
$29$			2206.17i			0.0904577i	0.998977	+	0.0452289i	$0.0144017\pi$
$29$			2206.17i			0.0904577i	−0.998977	+	0.0452289i	$0.985598\pi$
$30$		0			0
$31$	22898.0			0.768621			0.384311	−	0.923204i	$-0.374439\pi$
$31$	22898.0			0.768621			0.384311	+	0.923204i	$0.374439\pi$
$32$	−5792.62			−0.176777
$33$	−712.764	+	576.000i	−0.0198337	+	0.0160280i
$34$	25344.0			0.644820
$35$		0			0
$36$	−4896.00	+	22808.4i	−0.104938	+	0.488864i
$37$		−	34058.0i		−	0.672379i	−0.941794	−	0.336189i	$-0.890862\pi$
$37$		−	34058.0i		−	0.672379i	0.941794	−	0.336189i	$-0.109138\pi$
$38$	29743.7			0.542057
$39$	61950.0	−	50063.2i	1.04435	−	0.843965i
$40$		0			0
$41$			16766.9i			0.243277i	0.992574	+	0.121639i	$0.0388149\pi$
$41$			16766.9i			0.243277i	−0.992574	+	0.121639i	$0.961185\pi$
$42$	−237.588	+	192.000i	−0.00320683	+	0.00259151i
$43$		−	6406.00i		−	0.0805715i	−0.999188	−	0.0402858i	$-0.987173\pi$
$43$		−	6406.00i		−	0.0805715i	0.999188	−	0.0402858i	$-0.0128268\pi$
$44$			1086.12i			0.0127502i
$45$		0			0
$46$	57984.0			0.595710
$47$	−179888.			−1.73264			−0.866320	−	0.499489i	$-0.833521\pi$
$47$	−179888.			−1.73264			−0.866320	+	0.499489i	$0.833521\pi$
$48$	17377.9	+	21504.0i	0.157135	+	0.194444i
$49$	117645.			0.999966
$50$		0			0
$51$	−76032.0	−	94084.8i	−0.573173	−	0.709266i
$52$		−	94400.0i		−	0.671370i
$53$	−192548.			−1.29334			−0.646668	−	0.762772i	$-0.723838\pi$
$53$	−192548.			−1.29334			−0.646668	+	0.762772i	$0.723838\pi$
$54$	99360.0	−	50249.8i	0.631001	−	0.319120i
$55$		0			0
$56$			362.039i			0.00206154i
$57$	−89231.2	−	110418.i	−0.481828	−	0.596232i
$58$		−	12480.0i		−	0.0639633i
$59$		−	326819.i		−	1.59130i	−0.605758	−	0.795649i	$-0.707130\pi$
$59$		−	326819.i		−	1.59130i	0.605758	−	0.795649i	$-0.292870\pi$
$60$		0			0
$61$	−62566.0			−0.275644			−0.137822	−	0.990457i	$-0.544010\pi$
$61$	−62566.0			−0.275644			−0.137822	+	0.990457i	$0.544010\pi$
$62$	−129531.			−0.543497
$63$	1425.53	+	306.000i	0.00570104	+	0.00122377i
$64$	32768.0			0.125000
$65$		0			0
$66$	4032.00	−	3258.35i	0.0140245	−	0.0113335i
$67$		−	438698.i		−	1.45862i	−0.684185	−	0.729308i	$-0.739842\pi$
$67$		−	438698.i		−	1.45862i	0.684185	−	0.729308i	$-0.260158\pi$
$68$	−143367.			−0.455956
$69$	−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	$0.969617\pi$
$72$	27696.0	−	129024.i	0.0742026	−	0.345679i
$73$		−	730510.i		−	1.87784i	−0.344141	−	0.938918i	$-0.611830\pi$
$73$		−	730510.i		−	1.87784i	0.344141	−	0.938918i	$-0.388170\pi$
$74$			192661.i			0.475444i
$75$		0			0
$76$	−168256.			−0.383292
$77$	67.8823			0.000148691
$78$	−350442.	+	283200.i	−0.738469	+	0.596773i
$79$	−340562.			−0.690740			−0.345370	−	0.938467i	$-0.612247\pi$
$79$	−340562.			−0.690740			−0.345370	+	0.938467i	$0.612247\pi$
$80$		0			0
$81$	−484623.	−	218106.i	−0.911904	−	0.410404i
$82$		−	94848.0i		−	0.172023i
$83$	496253.			0.867899			0.433949	−	0.900937i	$-0.357120\pi$
$83$	496253.			0.867899			0.433949	+	0.900937i	$0.357120\pi$
$84$	1344.00	−	1086.12i	0.00226757	−	0.00183248i
$85$		0			0
$86$			36237.8i			0.0569727i
$87$	−46329.6	+	37440.0i	−0.0703560	+	0.0568562i
$88$		−	6144.00i		−	0.00901578i
$89$		−	386725.i		−	0.548570i	−0.961648	−	0.274285i	$-0.911559\pi$
$89$		−	386725.i		−	0.548570i	0.961648	−	0.274285i	$-0.0884412\pi$
$90$		0			0
$91$	−5900.00			−0.00782939
$92$	−328007.			−0.421230
$93$	388592.	+	480858.i	0.483109	+	0.597817i
$94$	1.01760e6			1.22516
$95$		0			0
$96$	−98304.0	−	121645.i	−0.111111	−	0.137493i
$97$			281086.i			0.307981i	0.988072	+	0.153991i	$0.0492125\pi$
$97$			281086.i			0.307981i	−0.988072	+	0.153991i	$0.950787\pi$
$98$	−665501.			−0.707083
$99$	−24192.0	−	5192.99i	−0.0249325	−	0.00535195i
$100$		0			0
$101$			945362.i			0.917559i	0.888550	+	0.458780i	$0.151713\pi$
$101$			945362.i			0.917559i	−0.888550	+	0.458780i	$0.848287\pi$
$102$	430102.	+	532224.i	0.405295	+	0.501527i
$103$		−	865726.i		−	0.792262i	−0.918194	−	0.396131i	$-0.870353\pi$
$103$		−	865726.i		−	0.792262i	0.918194	−	0.396131i	$-0.129647\pi$
$104$			534007.i			0.474730i
$105$		0			0
$106$	1.08922e6			0.914527
$107$	−1.47410e6			−1.20330			−0.601651	−	0.798759i	$-0.705490\pi$
$107$	−1.47410e6			−1.20330			−0.601651	+	0.798759i	$0.705490\pi$
$108$	−562065.	+	284256.i	−0.446185	+	0.225652i
$109$	−650810.			−0.502545			−0.251272	−	0.967916i	$-0.580849\pi$
$109$	−650810.			−0.502545			−0.251272	+	0.967916i	$0.580849\pi$
$110$		0			0
$111$	715218.	−	577983.i	0.522961	−	0.422616i
$112$		−	2048.00i		−	0.00145773i
$113$	1.74417e6			1.20879			0.604397	−	0.796683i	$-0.293414\pi$
$113$	1.74417e6			1.20879			0.604397	+	0.796683i	$0.293414\pi$
$114$	504768.	+	624619.i	0.340704	+	0.421600i
$115$		0			0
$116$			70597.5i			0.0452289i
$117$	2.10265e6	+	451350.i	1.31283	+	0.281810i
$118$			1.84877e6i			1.12522i
$119$			8960.46i			0.00531728i
$120$		0			0
$121$	1.77041e6			0.999350
$122$	353927.			0.194910
$123$	−352105.	+	284544.i	−0.189216	+	0.152909i
$124$	732736.			0.384311
$125$		0			0
$126$	−8064.00	−	1731.00i	−0.00403124	−	0.000865336i
$127$			2.28053e6i			1.11333i	0.830737	+	0.556665i	$0.187919\pi$
$127$			2.28053e6i			1.11333i	−0.830737	+	0.556665i	$0.812081\pi$
$128$	−185364.			−0.0883883
$129$	134526.	−	108713.i	0.0626667	−	0.0506424i
$130$		0			0
$131$			1.07196e6i			0.476832i	0.971163	+	0.238416i	$0.0766282\pi$
$131$			1.07196e6i			0.476832i	−0.971163	+	0.238416i	$0.923372\pi$
$132$	−22808.4	+	18432.0i	−0.00991685	+	0.00801402i
$133$			10516.0i			0.00446988i
$134$			2.48165e6i			1.03140i
$135$		0			0
$136$	811008.			0.322410
$137$	2.78338e6			1.08246			0.541228	−	0.840876i	$-0.317960\pi$
$137$	2.78338e6			1.08246			0.541228	+	0.840876i	$0.317960\pi$
$138$	984021.	+	1.21766e6i	0.374427	+	0.463330i
$139$	−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.i		−	0.134782i
$143$	100126.			0.0342405
$144$	−156672.	+	729870.i	−0.0524691	+	0.244432i
$145$		0			0
$146$			4.13239e6i			1.32783i
$147$	1.99650e6	+	2.47054e6i	0.628518	+	0.777751i
$148$		−	1.08986e6i		−	0.336189i
$149$			4.46010e6i			1.34830i	0.738595	+	0.674149i	$0.235489\pi$
$149$			4.46010e6i			1.34830i	−0.738595	+	0.674149i	$0.764511\pi$
$150$		0			0
$151$	−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.			0.271028
$153$	685475.	−	3.19334e6i	0.191389	−	0.891603i
$154$	−384.000			−0.000105140
$155$		0			0
$156$	1.98240e6	−	1.60202e6i	0.522177	−	0.421983i
$157$			1.28887e6i			0.333051i	0.986037	+	0.166525i	$0.0532547\pi$
$157$			1.28887e6i			0.333051i	−0.986037	+	0.166525i	$0.946745\pi$
$158$	1.92651e6			0.488427
$159$	−3.26765e6	−	4.04351e6i	−0.812913	−	1.00593i
$160$		0			0
$161$			20500.4i			0.00491231i
$162$	2.74144e6	+	1.23379e6i	0.644813	+	0.290200i
$163$			879914.i			0.203178i	0.994826	+	0.101589i	$0.0323927\pi$
$163$			879914.i			0.203178i	−0.994826	+	0.101589i	$0.967607\pi$
$164$			536541.i			0.121639i
$165$		0			0
$166$	−2.80723e6			−0.613697
$167$	−5.96760e6			−1.28130			−0.640649	−	0.767834i	$-0.721335\pi$
$167$	−5.96760e6			−1.28130			−0.640649	+	0.767834i	$0.721335\pi$
$168$	−7602.81	+	6144.00i	−0.00160342	+	0.00129576i
$169$	−3.87569e6			−0.802951
$170$		0			0
$171$	804474.	−	3.74771e6i	0.160888	−	0.749511i
$172$		−	204992.i		−	0.0402858i
$173$	418867.			0.0808981			0.0404490	−	0.999182i	$-0.487121\pi$
$173$	418867.			0.0808981			0.0404490	+	0.999182i	$0.487121\pi$
$174$	262080.	−	211793.i	0.0497492	−	0.0402034i
$175$		0			0
$176$			34755.7i			0.00637512i
$177$	6.86320e6	−	5.54630e6i	1.23768	−	1.00019i
$178$			2.18765e6i			0.387898i
$179$			302110.i			0.0526752i	0.999653	+	0.0263376i	$0.00838448\pi$
$179$			302110.i			0.0526752i	−0.999653	+	0.0263376i	$0.991616\pi$
$180$		0			0
$181$	−6.47618e6			−1.09215			−0.546076	−	0.837735i	$-0.683879\pi$
$181$	−6.47618e6			−1.09215			−0.546076	+	0.837735i	$0.683879\pi$
$182$	33375.4			0.00553621
$183$	−1.06178e6	−	1.31389e6i	−0.173253	−	0.214390i
$184$	1.85549e6			0.297855
$185$		0			0
$186$	−2.19821e6	−	2.72014e6i	−0.341610	−	0.422720i
$187$		−	152064.i		−	0.0232542i
$188$	−5.75641e6			−0.866320
$189$	17766.0	+	35129.1i	0.00263151	+	0.00520333i
$190$		0			0
$191$			5.02166e6i			0.720687i	0.932820	+	0.360344i	$0.117341\pi$
$191$			5.02166e6i			0.720687i	−0.932820	+	0.360344i	$0.882659\pi$
$192$	556091.	+	688128.i	0.0785674	+	0.0972222i
$193$			3.50093e6i			0.486980i	0.969903	+	0.243490i	$0.0782924\pi$
$193$			3.50093e6i			0.486980i	−0.969903	+	0.243490i	$0.921708\pi$
$194$		−	1.59006e6i		−	0.217775i
$195$		0			0
$196$	3.76464e6			0.499983
$197$	−4.85423e6			−0.634923			−0.317462	−	0.948271i	$-0.602830\pi$
$197$	−4.85423e6			−0.634923			−0.317462	+	0.948271i	$0.602830\pi$
$198$	136851.	+	29376.0i	0.0176300	+	0.00378440i
$199$	9.50976e6			1.20673			0.603365	−	0.797465i	$-0.293826\pi$
$199$	9.50976e6			1.20673			0.603365	+	0.797465i	$0.293826\pi$
$200$		0			0
$201$	9.21266e6	−	7.44495e6i	1.13448	−	0.916798i
$202$		−	5.34778e6i		−	0.648812i
$203$	4412.35			0.000527450
$204$	−2.43302e6	−	3.01071e6i	−0.286587	−	0.354633i
$205$		0			0
$206$			4.89729e6i			0.560214i
$207$	1.56828e6	−	7.30598e6i	0.176813	−	0.823697i
$208$		−	3.02080e6i		−	0.335685i
$209$		−	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	$0.377301\pi$
$212$	−6.16154e6			−0.646668
$213$	−1.43265e6	+	1.15776e6i	−0.148253	+	0.119806i
$214$	8.33875e6			0.850863
$215$		0			0
$216$	3.17952e6	−	1.60799e6i	0.315501	−	0.159560i
$217$		−	45796.0i		−	0.00448176i
$218$	3.68154e6			0.355353
$219$	1.53407e7	−	1.23972e7i	1.46054	−	1.18029i
$220$		0			0
$221$			1.32167e7i			1.22446i
$222$	−4.04588e6	+	3.26957e6i	−0.369789	+	0.298835i
$223$			4.66891e6i			0.421019i	0.977592	+	0.210509i	$0.0675122\pi$
$223$			4.66891e6i			0.421019i	−0.977592	+	0.210509i	$0.932488\pi$
$224$			11585.2i			0.00103077i
$225$		0			0
$226$	−9.86650e6			−0.854747
$227$	−1.96525e7			−1.68012			−0.840059	−	0.542494i	$-0.817480\pi$
$227$	−1.96525e7			−1.68012			−0.840059	+	0.542494i	$0.817480\pi$
$228$	−2.85540e6	−	3.53338e6i	−0.240914	−	0.298116i
$229$	4.48178e6			0.373202			0.186601	−	0.982436i	$-0.440253\pi$
$229$	4.48178e6			0.373202			0.186601	+	0.982436i	$0.440253\pi$
$230$		0			0
$231$	1152.00	+	1425.53i	9.34580e−5	+	0.000115648i
$232$		−	399360.i		−	0.0319816i
$233$	2.29286e6			0.181263			0.0906316	−	0.995884i	$-0.471111\pi$
$233$	2.29286e6			0.181263			0.0906316	+	0.995884i	$0.471111\pi$
$234$	−1.18944e7	−	2.55322e6i	−0.928314	−	0.199270i
$235$		0			0
$236$		−	1.04582e7i		−	0.795649i
$237$	−5.77953e6	−	7.15180e6i	−0.434158	−	0.537243i
$238$		−	50688.0i		−	0.00375988i
$239$		−	2.64564e6i		−	0.193793i	−0.995294	−	0.0968964i	$-0.969108\pi$
$239$		−	2.64564e6i		−	0.193793i	0.995294	−	0.0968964i	$-0.0308915\pi$
$240$		0			0
$241$	−6.99581e6			−0.499789			−0.249894	−	0.968273i	$-0.580396\pi$
$241$	−6.99581e6			−0.499789			−0.249894	+	0.968273i	$0.580396\pi$
$242$	−1.00149e7			−0.706647
$243$	−3.64411e6	−	1.38785e7i	−0.253964	−	0.967214i
$244$	−2.00211e6			−0.137822
$245$		0			0
$246$	1.99181e6	−	1.60962e6i	0.133796	−	0.108123i
$247$			1.55111e7i			1.02932i
$248$	−4.14498e6			−0.271749
$249$	8.42170e6	+	1.04213e7i	0.545508	+	0.675032i
$250$		0			0
$251$			2.84990e7i			1.80223i	0.433585	+	0.901113i	$0.357248\pi$
$251$			2.84990e7i			1.80223i	−0.433585	+	0.901113i	$0.642752\pi$
$252$	45616.9	+	9792.00i	0.00285052	+	0.000611885i
$253$		−	347904.i		−	0.0214831i
$254$		−	1.29006e7i		−	0.787243i
$255$		0			0
$256$	1.04858e6			0.0625000
$257$	186812.			0.0110054			0.00550269	−	0.999985i	$-0.498248\pi$
$257$	186812.			0.0110054			0.00550269	+	0.999985i	$0.498248\pi$
$258$	−760994.	+	614976.i	−0.0443121	+	0.0358096i
$259$	−68116.0			−0.00392058
$260$		0			0
$261$	−1.57248e6	−	337544.i	−0.0884430	−	0.0189850i
$262$		−	6.06394e6i		−	0.337171i
$263$	−8.61541e6			−0.473597			−0.236798	−	0.971559i	$-0.576098\pi$
$263$	−8.61541e6			−0.473597			−0.236798	+	0.971559i	$0.576098\pi$
$264$	129024.	−	104267.i	0.00701227	−	0.00566677i
$265$		0			0
$266$		−	59487.5i		−	0.00316068i
$267$	8.12123e6	−	6.56294e6i	0.426666	−	0.344798i
$268$		−	1.40383e7i		−	0.729308i
$269$		−	7.55132e6i		−	0.387941i	−0.981007	−	0.193971i	$-0.937863\pi$
$269$		−	7.55132e6i		−	0.387941i	0.981007	−	0.193971i	$-0.0621367\pi$
$270$		0			0
$271$	1.39445e7			0.700642			0.350321	−	0.936630i	$-0.386073\pi$
$271$	1.39445e7			0.700642			0.350321	+	0.936630i	$0.386073\pi$
$272$	−4.58775e6			−0.227978
$273$	−100126.	−	123900.i	−0.00492108	−	0.00608952i
$274$	−1.57452e7			−0.765412
$275$		0			0
$276$	−5.56646e6	−	6.88815e6i	−0.264760	−	0.327624i
$277$		−	2.81293e7i		−	1.32349i	−0.749730	−	0.661744i	$-0.769817\pi$
$277$		−	2.81293e7i		−	1.32349i	0.749730	−	0.661744i	$-0.230183\pi$
$278$	2.58741e7			1.20429
$279$	−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	$-0.167951\pi$
$282$	1.72692e7	+	2.13696e7i	0.770063	+	0.952904i
$283$			1.01418e7i			0.447464i	0.974651	+	0.223732i	$0.0718240\pi$
$283$			1.01418e7i			0.447464i	−0.974651	+	0.223732i	$0.928176\pi$
$284$			2.18309e6i			0.0953053i
$285$		0			0
$286$	−566400.			−0.0242117
$287$	33533.8			0.00141853
$288$	886271.	−	4.12877e6i	0.0371013	−	0.172840i
$289$	−4.06512e6			−0.168415
$290$		0			0
$291$	−5.90281e6	+	4.77019e6i	−0.239541	+	0.193578i
$292$		−	2.33763e7i		−	0.938918i
$293$	−2.78468e7			−1.10706			−0.553532	−	0.832828i	$-0.686720\pi$
$293$	−2.78468e7			−1.10706			−0.553532	+	0.832828i	$0.686720\pi$
$294$	−1.12939e7	−	1.39755e7i	−0.444429	−	0.549953i
$295$		0			0
$296$			6.16516e6i			0.237722i
$297$	−301499.	−	596160.i	−0.0115084	−	0.0227559i
$298$		−	2.52301e7i		−	0.953391i
$299$			3.02381e7i			1.13121i
$300$		0			0
$301$	−12812.0			−0.000469805
$302$	1.24909e7			0.453494
$303$	−1.98526e7	+	1.60433e7i	−0.713657	+	0.576722i
$304$	−5.38419e6			−0.191646
$305$		0			0
$306$	−3.87763e6	+	1.80643e7i	−0.135333	+	0.630458i
$307$			3.63254e7i			1.25544i	0.778440	+	0.627718i	$0.216011\pi$
$307$			3.63254e7i			1.25544i	−0.778440	+	0.627718i	$0.783989\pi$
$308$	2172.23			7.43454e−5
$309$	1.81802e7	−	1.46919e7i	0.616204	−	0.497968i
$310$		0			0
$311$		−	3.59921e7i		−	1.19654i	−0.801296	−	0.598268i	$-0.795856\pi$
$311$		−	3.59921e7i		−	1.19654i	0.801296	−	0.598268i	$-0.204144\pi$
$312$	−1.12141e7	+	9.06240e6i	−0.369235	+	0.298387i
$313$			4.01099e7i			1.30803i	0.756480	+	0.654016i	$0.226917\pi$
$313$			4.01099e7i			1.30803i	−0.756480	+	0.654016i	$0.773083\pi$
$314$		−	7.29095e6i		−	0.235502i
$315$		0			0
$316$	−1.08980e7			−0.345370
$317$	3.94377e7			1.23804			0.619018	−	0.785377i	$-0.287531\pi$
$317$	3.94377e7			1.23804			0.619018	+	0.785377i	$0.287531\pi$
$318$	1.84846e7	+	2.28735e7i	0.574816	+	0.711299i
$319$	−74880.0			−0.00230671
$320$		0			0
$321$	−2.50163e7	−	3.09560e7i	−0.756323	−	0.935902i
$322$		−	115968.i		−	0.00347353i
$323$	2.35570e7			0.699058
$324$	−1.55079e7	−	6.97938e6i	−0.455952	−	0.205202i
$325$		0			0
$326$		−	4.97755e6i		−	0.143669i
$327$	−1.10446e7	−	1.36670e7i	−0.315869	−	0.390868i
$328$		−	3.03514e6i		−	0.0860115i
$329$			359776.i			0.0101029i
$330$		0			0
$331$	2.78363e7			0.767586			0.383793	−	0.923419i	$-0.374618\pi$
$331$	2.78363e7			0.767586			0.383793	+	0.923419i	$0.374618\pi$
$332$	1.58801e7			0.433949
$333$	2.42753e7	+	5.21087e6i	0.657403	+	0.141117i
$334$	3.37578e7			0.906014
$335$		0			0
$336$	43008.0	−	34755.7i	0.00113379	−	0.000916238i
$337$			2.37897e7i			0.621582i	0.950478	+	0.310791i	$0.100594\pi$
$337$			2.37897e7i			0.621582i	−0.950478	+	0.310791i	$0.899406\pi$
$338$	2.19242e7			0.567772
$339$	2.95995e7	+	3.66275e7i	0.759775	+	0.940174i
$340$		0			0
$341$			777184.i			0.0196002i
$342$	−4.55079e6	+	2.12003e7i	−0.113765	+	0.529984i
$343$		−	470588.i		−	0.0116616i
$344$			1.15961e6i			0.0284863i
$345$		0			0
$346$	−2.36947e6			−0.0572036
$347$	5.34078e7			1.27825			0.639125	−	0.769103i	$-0.279297\pi$
$347$	5.34078e7			1.27825			0.639125	+	0.769103i	$0.279297\pi$
$348$	−1.48255e6	+	1.19808e6i	−0.0351780	+	0.0284281i
$349$	−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.i		−	0.00450789i
$353$	−1.75443e7			−0.398852			−0.199426	−	0.979913i	$-0.563908\pi$
$353$	−1.75443e7			−0.398852			−0.199426	+	0.979913i	$0.563908\pi$
$354$	−3.88241e7	+	3.13746e7i	−0.875169	+	0.707243i
$355$		0			0
$356$		−	1.23752e7i		−	0.274285i
$357$	−188170.	+	152064.i	−0.00413566	+	0.00334212i
$358$		−	1.70899e6i		−	0.0372470i
$359$			6.18249e7i			1.33623i	0.744059	+	0.668113i	$0.232898\pi$
$359$			6.18249e7i			1.33623i	−0.744059	+	0.668113i	$0.767102\pi$
$360$		0			0
$361$	−1.93993e7			−0.412349
$362$	3.66348e7			0.772269
$363$	3.00448e7	+	3.71786e7i	0.628131	+	0.777272i
$364$	−188800.			−0.00391469
$365$		0			0
$366$	6.00634e6	+	7.43246e6i	0.122509	+	0.151597i
$367$			3.40461e7i			0.688761i	0.938830	+	0.344381i	$0.111911\pi$
$367$			3.40461e7i			0.688761i	−0.938830	+	0.344381i	$0.888089\pi$
$368$	−1.04962e7			−0.210615
$369$	−1.19508e7	−	2.56534e6i	−0.237859	−	0.0510582i
$370$		0			0
$371$			385096.i			0.00754132i
$372$	1.24349e7	+	1.53875e7i	0.241554	+	0.298908i
$373$		−	5.15781e7i		−	0.993892i	−0.867782	−	0.496946i	$-0.834455\pi$
$373$		−	5.15781e7i		−	0.993892i	0.867782	−	0.496946i	$-0.165545\pi$
$374$			860204.i			0.0164432i
$375$		0			0
$376$	3.25632e7			0.612581
$377$	6.50821e6			0.121461
$378$	−100500.	−	198720.i	−0.00186076	−	0.00367931i
$379$	−4.28828e7			−0.787709			−0.393855	−	0.919173i	$-0.628859\pi$
$379$	−4.28828e7			−0.787709			−0.393855	+	0.919173i	$0.628859\pi$
$380$		0			0
$381$	−4.78910e7	+	3.87018e7i	−0.865923	+	0.699772i
$382$		−	2.84068e7i		−	0.509603i
$383$	1.51307e7			0.269316			0.134658	−	0.990892i	$-0.457006\pi$
$383$	1.51307e7			0.269316			0.134658	+	0.990892i	$0.457006\pi$
$384$	−3.14573e6	−	3.89264e6i	−0.0555556	−	0.0687465i
$385$		0			0
$386$		−	1.98043e7i		−	0.344347i
$387$	4.56596e6	+	980118.i	0.0787770	+	0.0169101i
$388$			8.99475e6i			0.153991i
$389$		−	6.15319e7i		−	1.04533i	−0.852540	−	0.522663i	$-0.824939\pi$
$389$		−	6.15319e7i		−	1.04533i	0.852540	−	0.522663i	$-0.175061\pi$
$390$		0			0
$391$	4.59233e7			0.768251
$392$	−2.12960e7			−0.353541
$393$	−2.25112e7	+	1.81918e7i	−0.370870	+	0.299708i
$394$	2.74596e7			0.448959
$395$		0			0
$396$	−774144.	−	166176.i	−0.0124663	−	0.00267598i
$397$			8.55816e7i			1.36776i	0.729596	+	0.683878i	$0.239708\pi$
$397$			8.55816e7i			1.36776i	−0.729596	+	0.683878i	$0.760292\pi$
$398$	−5.37953e7			−0.853287
$399$	−220836.	+	178462.i	−0.00347657	+	0.00280949i
$400$		0			0
$401$		−	4.09739e7i		−	0.635439i	−0.948185	−	0.317719i	$-0.897083\pi$
$401$		−	4.09739e7i		−	0.635439i	0.948185	−	0.317719i	$-0.102917\pi$
$402$	−5.21147e7	+	4.21150e7i	−0.802198	+	0.648274i
$403$		−	6.75491e7i		−	1.03206i
$404$			3.02516e7i			0.458780i
$405$		0			0
$406$	−24960.0			−0.000372964
$407$	1.15597e6			0.0171460
$408$	1.37633e7	+	1.70312e7i	0.202647	+	0.250763i
$409$	−6.10556e7			−0.892391			−0.446196	−	0.894935i	$-0.647221\pi$
$409$	−6.10556e7			−0.892391			−0.446196	+	0.894935i	$0.647221\pi$
$410$		0			0
$411$	4.72355e7	+	5.84509e7i	0.680366	+	0.841910i
$412$		−	2.77032e7i		−	0.396131i
$413$	−653638.			−0.00927870
$414$	−8.87155e6	+	4.13289e7i	−0.125025	+	0.582442i
$415$		0			0
$416$			1.70882e7i			0.237365i
$417$	−7.76224e7	−	9.60529e7i	−1.07048	−	1.32465i
$418$			1.00954e6i			0.0138227i
$419$		−	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	$0.541960\pi$
$422$	−3.99608e7			−0.531737
$423$	2.75229e7	−	1.28218e8i	0.363641	−	1.69405i
$424$	3.48549e7			0.457263
$425$		0			0
$426$	8.10432e6	−	6.54928e6i	0.104831	−	0.0847159i
$427$			125132.i			0.00160725i
$428$	−4.71711e7			−0.601651
$429$	1.69920e6	+	2.10265e6i	0.0215215	+	0.0266315i
$430$		0			0
$431$		−	4.01587e7i		−	0.501589i	−0.968040	−	0.250795i	$-0.919308\pi$
$431$		−	4.01587e7i		−	0.501589i	0.968040	−	0.250795i	$-0.0806919\pi$
$432$	−1.79861e7	+	9.09619e6i	−0.223093	+	0.112826i
$433$		−	845854.i		−	0.0104191i	−0.999986	−	0.00520957i	$-0.998342\pi$
$433$		−	845854.i		−	0.0104191i	0.999986	−	0.00520957i	$-0.00165826\pi$
$434$			259061.i			0.00316908i
$435$		0			0
$436$	−2.08259e7			−0.251272
$437$	5.38957e7			0.645817
$438$	−8.67802e7	+	7.01290e7i	−1.03276	+	0.834594i
$439$	7.48204e7			0.884354			0.442177	−	0.896928i	$-0.354206\pi$
$439$	7.48204e7			0.884354			0.442177	+	0.896928i	$0.354206\pi$
$440$		0			0
$441$	−1.79997e7	+	8.38531e7i	−0.209869	+	0.977695i
$442$		−	7.47648e7i		−	0.865825i
$443$	1.25246e8			1.44063			0.720313	−	0.693649i	$-0.243998\pi$
$443$	1.25246e8			1.44063			0.720313	+	0.693649i	$0.243998\pi$
$444$	2.28870e7	−	1.84955e7i	0.261481	−	0.211308i
$445$		0			0
$446$		−	2.64114e7i		−	0.297705i
$447$	−9.36621e7	+	7.56904e7i	−1.04868	+	0.847458i
$448$		−	65536.0i		−	0.000728863i
$449$		−	1.12812e8i		−	1.24628i	−0.782109	−	0.623142i	$-0.785856\pi$
$449$		−	1.12812e8i		−	1.24628i	0.782109	−	0.623142i	$-0.214144\pi$
$450$		0			0
$451$	−569088.			−0.00620369
$452$	5.58133e7			0.604397
$453$	−3.74726e7	−	4.63700e7i	−0.403106	−	0.498818i
$454$	1.11171e8			1.18802
$455$		0			0
$456$	1.61526e7	+	1.99878e7i	0.170352	+	0.210800i
$457$		−	1.57358e8i		−	1.64870i	−0.566081	−	0.824350i	$-0.691541\pi$
$457$		−	1.57358e8i		−	1.64870i	0.566081	−	0.824350i	$-0.308459\pi$
$458$	−2.53528e7			−0.263894
$459$	7.86931e7	−	3.97979e7i	0.813764	−	0.411549i
$460$		0			0
$461$		−	1.83107e8i		−	1.86897i	−0.356002	−	0.934485i	$-0.615860\pi$
$461$		−	1.83107e8i		−	1.86897i	0.356002	−	0.934485i	$-0.384140\pi$
$462$	−6516.70	−	8064.00i	−6.60848e−5	−	8.17758e-5i
$463$			1.77978e8i			1.79318i	0.442866	+	0.896588i	$0.353962\pi$
$463$			1.77978e8i			1.79318i	−0.442866	+	0.896588i	$0.646038\pi$
$464$			2.25912e6i			0.0226144i
$465$		0			0
$466$	−1.29704e7			−0.128172
$467$	−9.35797e7			−0.918821			−0.459410	−	0.888224i	$-0.651939\pi$
$467$	−9.35797e7			−0.918821			−0.459410	+	0.888224i	$0.651939\pi$
$468$	6.72849e7	+	1.44432e7i	0.656417	+	0.140905i
$469$	−877396.			−0.00850505
$470$		0			0
$471$	−2.70663e7	+	2.18728e7i	−0.259039	+	0.209335i
$472$			5.91606e7i			0.562609i
$473$	217427.			0.00205461
$474$	3.26940e7	+	4.04567e7i	0.306996	+	0.379888i
$475$		0			0
$476$			286735.i			0.00265864i
$477$	2.94598e7	−	1.37241e8i	0.271441	−	1.26453i
$478$			1.49660e7i			0.137032i
$479$		−	1.07662e8i		−	0.979617i	−0.871830	−	0.489808i	$-0.837067\pi$
$479$		−	1.07662e8i		−	0.979617i	0.871830	−	0.489808i	$-0.162933\pi$
$480$		0			0
$481$	−1.00471e8			−0.902830
$482$	3.95743e7			0.353404
$483$	−430509.	+	347904.i	−0.00382068	+	0.00308758i
$484$	5.66531e7			0.499675
$485$		0			0
$486$	2.06142e7	+	7.85084e7i	0.179580	+	0.683923i
$487$			4.14432e6i			0.0358811i	0.999839	+	0.0179406i	$0.00571097\pi$
$487$			4.14432e6i			0.0358811i	−0.999839	+	0.0179406i	$0.994289\pi$
$488$	1.13257e7			0.0974549
$489$	−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	$0.831816\pi$
$492$	−1.12674e7	+	9.10541e6i	−0.0946078	+	0.0764547i
$493$		−	9.88416e6i		−	0.0824896i
$494$		−	8.77440e7i		−	0.727841i
$495$		0			0
$496$	2.34476e7			0.192155
$497$	136443.			0.00111143
$498$	−4.76403e7	−	5.89519e7i	−0.385733	−	0.477320i
$499$	−1.17436e8			−0.945144			−0.472572	−	0.881292i	$-0.656674\pi$
$499$	−1.17436e8			−0.945144			−0.472572	+	0.881292i	$0.656674\pi$
$500$		0			0
$501$	−1.01273e8	−	1.25320e8i	−0.805346	−	0.996565i
$502$		−	1.61215e8i		−	1.27437i
$503$	−1.99753e8			−1.56960			−0.784802	−	0.619747i	$-0.787235\pi$
$503$	−1.99753e8			−1.56960			−0.784802	+	0.619747i	$0.787235\pi$
$504$	−258048.	−	55391.9i	−0.00201562	−	0.000432668i
$505$		0			0
$506$			1.96804e6i			0.0151909i
$507$	−6.57727e7	−	8.13895e7i	−0.504686	−	0.624517i
$508$			7.29768e7i			0.556665i
$509$		−	1.12725e8i		−	0.854804i	−0.904062	−	0.427402i	$-0.859429\pi$
$509$		−	1.12725e8i		−	0.854804i	0.904062	−	0.427402i	$-0.140571\pi$
$510$		0			0
$511$	−1.46102e6			−0.0109495
$512$	−5.93164e6			−0.0441942
$513$	9.23543e7	−	4.67068e7i	0.684077	−	0.345962i
$514$	−1.05677e6			−0.00778198
$515$		0			0
$516$	4.30483e6	−	3.47883e6i	0.0313334	−	0.0253212i
$517$		−	6.10560e6i		−	0.0441832i
$518$	385322.			0.00277227
$519$	7.10842e6	+	8.79622e6i	0.0508476	+	0.0629207i
$520$		0			0
$521$		−	1.14581e8i		−	0.810215i	−0.914269	−	0.405108i	$-0.867234\pi$
$521$		−	1.14581e8i		−	0.810215i	0.914269	−	0.405108i	$-0.132766\pi$
$522$	8.89529e6	+	1.90944e6i	0.0625387	+	0.0134244i
$523$		−	1.49806e8i		−	1.04719i	−0.851968	−	0.523594i	$-0.824591\pi$
$523$		−	1.49806e8i		−	1.04719i	0.851968	−	0.523594i	$-0.175409\pi$
$524$			3.43028e7i			0.238416i
$525$		0			0
$526$	4.87361e7			0.334884
$527$	−1.02588e8			−0.700916
$528$	−729870.	+	589824.i	−0.00495842	+	0.00400701i
$529$	−4.29689e7			−0.290260
$530$		0			0
$531$	2.32945e8	+	5.00033e7i	1.55586	+	0.333976i
$532$			336512.i			0.00223494i
$533$	4.94624e7			0.326658
$534$	−4.59406e7	+	3.71256e7i	−0.301698	+	0.243809i
$535$		0			0
$536$			7.94128e7i			0.515699i
$537$	−6.34431e6	+	5.12698e6i	−0.0409696	+	0.0331084i
$538$			4.27167e7i			0.274316i
$539$			3.99300e6i			0.0254996i
$540$		0			0
$541$	−1.57017e8			−0.991644			−0.495822	−	0.868424i	$-0.665133\pi$
$541$	−1.57017e8			−0.991644			−0.495822	+	0.868424i	$0.665133\pi$
$542$	−7.88822e7			−0.495429
$543$	−1.09904e8	−	1.36000e8i	−0.686461	−	0.849452i
$544$	2.59523e7			0.161205
$545$		0			0
$546$	566400.	+	700884.i	0.00347973	+	0.00430594i
$547$			2.79469e8i			1.70754i	0.520650	+	0.853770i	$0.325690\pi$
$547$			2.79469e8i			1.70754i	−0.520650	+	0.853770i	$0.674310\pi$
$548$	8.90680e7			0.541228
$549$	9.57260e6	−	4.45948e7i	0.0578513	−	0.269505i
$550$		0			0
$551$		−	1.16001e7i		−	0.0693434i
$552$	3.14887e7	+	3.89652e7i	0.187213	+	0.231665i
$553$			681124.i			0.00402764i
$554$			1.59123e8i			0.935847i
$555$		0			0
$556$	−1.46366e8			−0.851563
$557$	1.50294e8			0.869712			0.434856	−	0.900500i	$-0.356799\pi$
$557$	1.50294e8			0.869712			0.434856	+	0.900500i	$0.356799\pi$
$558$	1.98182e7	−	9.23247e7i	0.114067	−	0.531393i
$559$	−1.88977e7			−0.108187
$560$		0			0
$561$	3.19334e6	−	2.58061e6i	0.0180866	−	0.0146162i
$562$			1.26391e8i			0.712044i
$563$	−8.27836e7			−0.463894			−0.231947	−	0.972728i	$-0.574510\pi$
$563$	−8.27836e7			−0.463894			−0.231947	+	0.972728i	$0.574510\pi$
$564$	−9.76896e7	−	1.20885e8i	−0.544516	−	0.673805i
$565$		0			0
$566$		−	5.73710e7i		−	0.316405i
$567$	−436211.	+	969246.i	−0.00239303	+	0.00531722i
$568$		−	1.23494e7i		−	0.0673911i
$569$			2.57230e8i			1.39632i	0.715942	+	0.698160i	$0.245997\pi$
$569$			2.57230e8i			1.39632i	−0.715942	+	0.698160i	$0.754003\pi$
$570$		0			0
$571$	2.84039e7			0.152570			0.0762852	−	0.997086i	$-0.475694\pi$
$571$	2.84039e7			0.152570			0.0762852	+	0.997086i	$0.475694\pi$
$572$	3.20404e6			0.0171203
$573$	−1.05455e8	+	8.52204e7i	−0.560535	+	0.452980i
$574$	−189696.			−0.00100305
$575$		0			0
$576$	−5.01350e6	+	2.33558e7i	−0.0262346	+	0.122216i
$577$		−	6.52476e7i		−	0.339654i	−0.985474	−	0.169827i	$-0.945679\pi$
$577$		−	6.52476e7i		−	0.339654i	0.985474	−	0.169827i	$-0.0543209\pi$
$578$	2.29958e7			0.119087
$579$	−7.35195e7	+	5.94128e7i	−0.378763	+	0.306086i
$580$		0			0
$581$		−	992506.i		−	0.00506063i
$582$	3.33913e7	−	2.69843e7i	0.169381	−	0.136880i
$583$		−	6.53530e6i		−	0.0329807i
$584$			1.32236e8i			0.663915i
$585$		0			0
$586$	1.57525e8			0.782813
$587$	6.66740e7			0.329642			0.164821	−	0.986324i	$-0.447295\pi$
$587$	6.66740e7			0.329642			0.164821	+	0.986324i	$0.447295\pi$
$588$	6.38881e7	+	7.90574e7i	0.314259	+	0.388876i
$589$	−1.20398e8			−0.589213
$590$		0			0
$591$	−8.23789e7	−	1.01939e8i	−0.399074	−	0.493829i
$592$		−	3.48754e7i		−	0.168095i
$593$	1.53324e8			0.735271			0.367635	−	0.929970i	$-0.380167\pi$
$593$	1.53324e8			0.735271			0.367635	+	0.929970i	$0.380167\pi$
$594$	1.70554e6	+	3.37239e6i	0.00813770	+	0.0160908i
$595$		0			0
$596$			1.42723e8i			0.674149i
$597$	1.61386e8	+	1.99705e8i	0.758478	+	0.938568i
$598$		−	1.71053e8i		−	0.799883i
$599$			2.18294e8i			1.01569i	0.861448	+	0.507846i	$0.169558\pi$
$599$			2.18294e8i			1.01569i	−0.861448	+	0.507846i	$0.830442\pi$
$600$		0			0
$601$	1.08478e8			0.499709			0.249854	−	0.968283i	$-0.419617\pi$
$601$	1.08478e8			0.499709			0.249854	+	0.968283i	$0.419617\pi$
$602$	72475.6			0.000332202
$603$	3.12688e8	+	6.71208e7i	1.42613	+	0.306129i
$604$	−7.06590e7			−0.320669
$605$		0			0
$606$	1.12303e8	−	9.07548e7i	0.504632	−	0.407804i
$607$			3.43321e8i			1.53509i	0.640993	+	0.767547i	$0.278523\pi$
$607$			3.43321e8i			1.53509i	−0.640993	+	0.767547i	$0.721477\pi$
$608$	3.04576e7			0.135514
$609$	74880.0	+	92659.3i	0.000331523	+	0.000410239i
$610$		0			0
$611$			5.30669e8i			2.32649i
$612$	2.19352e7	−	1.02187e8i	0.0956946	−	0.445801i
$613$			2.96325e8i			1.28643i	0.765685	+	0.643216i	$0.222400\pi$
$613$			2.96325e8i			1.28643i	−0.765685	+	0.643216i	$0.777600\pi$
$614$		−	2.05487e8i		−	0.887728i
$615$		0			0
$616$	−12288.0			−5.25701e−5
$617$	1.32676e8			0.564853			0.282426	−	0.959289i	$-0.408861\pi$
$617$	1.32676e8			0.564853			0.282426	+	0.959289i	$0.408861\pi$
$618$	−1.02843e8	+	8.31097e7i	−0.435722	+	0.352116i
$619$	4.14773e8			1.74879			0.874397	−	0.485211i	$-0.161257\pi$
$619$	4.14773e8			1.74879			0.874397	+	0.485211i	$0.161257\pi$
$620$		0			0
$621$	1.80040e8	−	9.10527e7i	0.751787	−	0.380205i
$622$			2.03602e8i			0.846078i
$623$	−773450.			−0.00319866
$624$	6.34368e7	−	5.12647e7i	0.261088	−	0.210991i
$625$		0			0
$626$		−	2.26896e8i		−	0.924919i
$627$	3.74771e6	−	3.02861e6i	0.0152042	−	0.0122868i
$628$			4.12438e7i			0.166525i
$629$			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	$0.293286\pi$
$632$	6.16483e7			0.244214
$633$	1.19882e8	+	1.48347e8i	0.472655	+	0.584881i
$634$	−2.23093e8			−0.875424
$635$		0			0
$636$	−1.04565e8	−	1.29392e8i	−0.406456	−	0.502964i
$637$		−	3.47053e8i		−	1.34269i
$638$	423585.			0.00163109
$639$	−4.86259e7	−	1.04379e7i	−0.186365	−	0.0400047i
$640$		0			0
$641$			1.81629e8i			0.689622i	0.938672	+	0.344811i	$0.112057\pi$
$641$			1.81629e8i			0.689622i	−0.938672	+	0.344811i	$0.887943\pi$
$642$	1.41513e8	+	1.75114e8i	0.534801	+	0.661782i
$643$			1.73811e8i			0.653798i	0.945059	+	0.326899i	$0.106004\pi$
$643$			1.73811e8i			0.653798i	−0.945059	+	0.326899i	$0.893996\pi$
$644$			656014.i			0.00245615i
$645$		0			0
$646$	−1.33259e8			−0.494309
$647$	−2.43137e8			−0.897713			−0.448856	−	0.893604i	$-0.648168\pi$
$647$	−2.43137e8			−0.897713			−0.448856	+	0.893604i	$0.648168\pi$
$648$	8.77261e7	+	3.94813e7i	0.322407	+	0.145100i
$649$	1.10926e7			0.0405788
$650$		0			0
$651$	961716.	−	777184.i	0.00348581	−	0.00281696i
$652$			2.81572e7i			0.101589i
$653$	−4.47562e7			−0.160736			−0.0803681	−	0.996765i	$-0.525610\pi$
$653$	−4.47562e7			−0.160736			−0.0803681	+	0.996765i	$0.525610\pi$
$654$	6.24778e7	+	7.73123e7i	0.223353	+	0.276386i
$655$		0			0
$656$			1.71693e7i			0.0608193i
$657$	5.20681e8	+	1.11768e8i	1.83601	+	0.394114i
$658$		−	2.03520e6i		−	0.00714380i
$659$		−	1.13574e8i		−	0.396845i	−0.980117	−	0.198423i	$-0.936418\pi$
$659$		−	1.13574e8i		−	0.396845i	0.980117	−	0.198423i	$-0.0635819\pi$
$660$		0			0
$661$	−9.93464e7			−0.343992			−0.171996	−	0.985098i	$-0.555022\pi$
$661$	−9.93464e7			−0.343992			−0.171996	+	0.985098i	$0.555022\pi$
$662$	−1.57466e8			−0.542766
$663$	−2.77550e8	+	2.24294e8i	−0.952359	+	0.769623i
$664$	−8.98314e7			−0.306849
$665$		0			0
$666$	−1.37322e8	−	2.94772e7i	−0.464854	−	0.0997845i
$667$		−	2.26138e7i		−	0.0762071i
$668$	−1.90963e8			−0.640649
$669$	−9.80472e7	+	7.92341e7i	−0.327459	+	0.264627i
$670$		0			0
$671$		−	2.12356e6i		−	0.00702906i
$672$	−243290.	+	196608.i	−0.000801708	+	0.000647878i
$673$		−	2.79412e8i		−	0.916642i	−0.888787	−	0.458321i	$-0.848451\pi$
$673$		−	2.79412e8i		−	0.916642i	0.888787	−	0.458321i	$-0.151549\pi$
$674$		−	1.34575e8i		−	0.439525i
$675$		0			0
$676$	−1.24022e8			−0.401475
$677$	−4.09293e7			−0.131907			−0.0659536	−	0.997823i	$-0.521009\pi$
$677$	−4.09293e7			−0.131907			−0.0659536	+	0.997823i	$0.521009\pi$
$678$	−1.67440e8	−	2.07196e8i	−0.537242	−	0.664803i
$679$	562172.			0.00179581
$680$		0			0
$681$	−3.33514e8	−	4.12702e8i	−1.05602	−	1.30676i
$682$		−	4.39642e6i		−	0.0138594i
$683$	3.74260e8			1.17466			0.587329	−	0.809348i	$-0.300180\pi$
$683$	3.74260e8			1.17466			0.587329	+	0.809348i	$0.300180\pi$
$684$	2.57432e7	−	1.19927e8i	0.0804440	−	0.374755i
$685$		0			0
$686$			2.66205e6i			0.00824600i
$687$	7.60584e7	+	9.41174e7i	0.234572	+	0.290268i
$688$		−	6.55974e6i		−	0.0201429i
$689$			5.68017e8i			1.73661i
$690$		0			0
$691$	1.15164e8			0.349047			0.174524	−	0.984653i	$-0.444161\pi$
$691$	1.15164e8			0.349047			0.174524	+	0.984653i	$0.444161\pi$
$692$	1.34038e7			0.0404490
$693$	−10386.0	+	48384.0i	−3.12067e−5	+	0.000145379i
$694$	−3.02120e8			−0.903859
$695$		0			0
$696$	8.38656e6	−	6.77736e6i	0.0248746	−	0.0201017i
$697$		−	7.51196e7i		−	0.221848i
$698$	2.66821e8			0.784609
$699$	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	$-0.0261671\pi$
$702$	−1.48237e8	−	2.93112e8i	−0.428495	−	0.847271i
$703$			1.79077e8i			0.515435i
$704$			1.11218e6i			0.00318756i
$705$		0			0
$706$	9.92456e7			0.282031
$707$	1.89072e6			0.00535020
$708$	2.19622e8	−	1.77482e8i	0.618838	−	0.500097i
$709$	1.28652e8			0.360975			0.180488	−	0.983577i	$-0.442232\pi$
$709$	1.28652e8			0.360975			0.180488	+	0.983577i	$0.442232\pi$
$710$		0			0
$711$	5.21060e7	−	2.42740e8i	0.144970	−	0.675356i
$712$			7.00047e7i			0.193949i
$713$	−2.34710e8			−0.647533
$714$	1.06445e6	−	860204.i	0.00292435	−	0.00236323i
$715$		0			0
$716$			9.66752e6i			0.0263376i
$717$	5.55585e7	−	4.48980e7i	0.150728	−	0.121806i
$718$		−	3.49735e8i		−	0.944855i
$719$		−	2.01053e8i		−	0.540908i	−0.962733	−	0.270454i	$-0.912826\pi$
$719$		−	2.01053e8i		−	0.540908i	0.962733	−	0.270454i	$-0.0871738\pi$
$720$		0			0
$721$	−1.73145e6			−0.00461960
$722$	1.09739e8			0.291575
$723$	−1.18723e8	−	1.46912e8i	−0.314137	−	0.388725i
$724$	−2.07238e8			−0.546076
$725$		0			0
$726$	−1.69959e8	−	2.10314e8i	−0.444155	−	0.549614i
$727$		−	5.23208e8i		−	1.36167i	−0.732438	−	0.680833i	$-0.761618\pi$
$727$		−	5.23208e8i		−	1.36167i	0.732438	−	0.680833i	$-0.238382\pi$
$728$	1.06801e6			0.00276811
$729$	2.29605e8	−	3.12051e8i	0.592651	−	0.805459i
$730$		0			0
$731$			2.87003e7i			0.0734742i
$732$	−3.39770e7	−	4.20444e7i	−0.0866266	−	0.107195i
$733$		−	6.57372e8i		−	1.66917i	−0.550882	−	0.834583i	$-0.685709\pi$
$733$		−	6.57372e8i		−	1.66917i	0.550882	−	0.834583i	$-0.314291\pi$
$734$		−	1.92594e8i		−	0.487028i
$735$		0			0
$736$	5.93756e7			0.148927
$737$	1.48899e7			0.0371954
$738$	6.76042e7	+	1.45117e7i	0.168192	+	0.0361036i
$739$	−3.50495e8			−0.868458			−0.434229	−	0.900803i	$-0.642979\pi$
$739$	−3.50495e8			−0.868458			−0.434229	+	0.900803i	$0.642979\pi$
$740$		0			0
$741$	−3.25733e8	+	2.63232e8i	−0.800585	+	0.646970i
$742$		−	2.17843e6i		−	0.00533252i
$743$	−4.66667e8			−1.13773			−0.568867	−	0.822429i	$-0.692618\pi$
$743$	−4.66667e8			−1.13773			−0.568867	+	0.822429i	$0.692618\pi$
$744$	−7.03427e7	−	8.70446e7i	−0.170805	−	0.211360i
$745$		0			0
$746$			2.91770e8i			0.702788i
$747$	−7.59267e7	+	3.53711e8i	−0.182152	+	0.848569i
$748$		−	4.86605e6i		−	0.0116271i
$749$			2.94819e6i			0.00701634i
$750$		0			0
$751$	−3.36993e7			−0.0795612			−0.0397806	−	0.999208i	$-0.512666\pi$
$751$	−3.36993e7			−0.0795612			−0.0397806	+	0.999208i	$0.512666\pi$
$752$	−1.84205e8			−0.433160
$753$	−5.98480e8	+	4.83645e8i	−1.40173	+	1.13277i
$754$	−3.68160e7			−0.0858860
$755$		0			0
$756$	568512.	+	1.12413e6i	0.00131575	+	0.00260166i
$757$		−	2.98552e8i		−	0.688227i	−0.938928	−	0.344113i	$-0.888180\pi$
$757$		−	2.98552e8i		−	0.688227i	0.938928	−	0.344113i	$-0.111820\pi$
$758$	2.42582e8			0.556995
$759$	7.30598e6	−	5.90413e6i	0.0167091	−	0.0135030i
$760$		0			0
$761$			3.98702e8i			0.904679i	0.891846	+	0.452340i	$0.149410\pi$
$761$			3.98702e8i			0.904679i	−0.891846	+	0.452340i	$0.850590\pi$
$762$	2.70913e8	−	2.18930e8i	0.612300	−	0.494813i
$763$			1.30162e6i			0.00293029i
$764$			1.60693e8i			0.360344i
$765$		0			0
$766$	−8.55921e7			−0.190435
$767$	−9.64116e8			−2.13670
$768$	1.77949e7	+	2.20201e7i	0.0392837	+	0.0486111i
$769$	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
$772$			1.12030e8i			0.243490i
$773$	1.83241e8			0.396719			0.198360	−	0.980129i	$-0.436439\pi$
$773$	1.83241e8			0.396719			0.198360	+	0.980129i	$0.436439\pi$
$774$	−2.58290e7	−	5.54438e6i	−0.0557038	−	0.0119572i
$775$		0			0
$776$		−	5.08820e7i		−	0.108888i
$777$	−1.15597e6	−	1.43044e6i	−0.00246424	−	0.00304934i
$778$			3.48077e8i			0.739157i
$779$		−	8.81604e7i		−	0.186493i
$780$		0			0
$781$	−2.31552e6			−0.00486066
$782$	−2.59782e8			−0.543235
$783$	−1.95974e7	−	3.87504e7i	−0.0408239	−	0.0807218i
$784$	1.20468e8			0.249992
$785$		0			0
$786$	1.27343e8	−	1.02908e8i	0.262244	−	0.211925i
$787$		−	3.14718e8i		−	0.645650i	−0.946459	−	0.322825i	$-0.895367\pi$
$787$		−	3.14718e8i		−	0.645650i	0.946459	−	0.322825i	$-0.104633\pi$
$788$	−1.55335e8			−0.317462
$789$	−1.46208e8	−	1.80924e8i	−0.297674	−	0.368353i
$790$		0			0
$791$		−	3.48833e6i		−	0.00704837i
$792$	4.37922e6	+	940032.i	0.00881498	+	0.00189220i
$793$			1.84570e8i			0.370119i
$794$		−	4.84122e8i		−	0.967150i
$795$		0			0
$796$	3.04312e8			0.603365
$797$	−7.88168e8			−1.55684			−0.778420	−	0.627744i	$-0.783979\pi$
$797$	−7.88168e8			−1.55684			−0.778420	+	0.627744i	$0.783979\pi$
$798$	1.24924e6	−	1.00954e6i	0.00245831	−	0.00198661i
$799$	8.05939e8			1.58002
$800$		0			0
$801$	2.75644e8	+	5.91690e7i	0.536353	+	0.115132i
$802$			2.31783e8i			0.449323i
$803$	2.47943e7			0.0478857
$804$	2.94805e8	−	2.38238e8i	0.567240	−	0.458399i
$805$		0			0
$806$			3.82115e8i			0.729776i
$807$	1.58578e8	−	1.28150e8i	0.301732	−	0.243836i
$808$		−	1.71129e8i		−	0.324406i
$809$		−	1.04745e9i		−	1.97828i	−0.146993	−	0.989138i	$-0.546959\pi$
$809$		−	1.04745e9i		−	1.97828i	0.146993	−	0.989138i	$-0.453041\pi$
$810$		0			0
$811$	−1.17930e8			−0.221086			−0.110543	−	0.993871i	$-0.535259\pi$
$811$	−1.17930e8			−0.221086			−0.110543	+	0.993871i	$0.535259\pi$
$812$	141195.			0.000263725
$813$	2.36647e8	+	2.92835e8i	0.440381	+	0.544944i
$814$	−6.53914e6			−0.0121240
$815$		0			0
$816$	−7.78568e7	−	9.63428e7i	−0.143293	−	0.177316i
$817$			3.36827e7i			0.0617648i
$818$	3.45382e8			0.631016
$819$	902700.	−	4.20531e6i	0.00164320	−	0.00765501i
$820$		0			0
$821$			6.01939e7i			0.108774i	0.998520	+	0.0543868i	$0.0173204\pi$
$821$			6.01939e7i			0.108774i	−0.998520	+	0.0543868i	$0.982680\pi$
$822$	−2.67204e8	−	3.30648e8i	−0.481091	−	0.595320i
$823$			1.60620e7i			0.0288139i	0.999896	+	0.0144069i	$0.00458603\pi$
$823$			1.60620e7i			0.0288139i	−0.999896	+	0.0144069i	$0.995414\pi$
$824$			1.56713e8i			0.280107i
$825$		0			0
$826$	3.69754e6			0.00656103
$827$	3.66665e8			0.648266			0.324133	−	0.946012i	$-0.394928\pi$
$827$	3.66665e8			0.648266			0.324133	+	0.946012i	$0.394928\pi$
$828$	5.01851e7	−	2.33791e8i	0.0884064	−	0.411849i
$829$	3.63153e8			0.637421			0.318711	−	0.947852i	$-0.396750\pi$
$829$	3.63153e8			0.637421			0.318711	+	0.947852i	$0.396750\pi$
$830$		0			0
$831$	5.90716e8	−	4.77370e8i	1.02938	−	0.831864i
$832$		−	9.66656e7i		−	0.167843i
$833$	−5.27076e8			−0.911882
$834$	4.39099e8	+	5.43357e8i	0.756945	+	0.936671i
$835$		0			0
$836$		−	5.71080e6i		−	0.00977413i
$837$	−4.02193e8	+	2.03403e8i	−0.685895	+	0.346881i
$838$			1.91688e8i			0.325734i
$839$			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
$842$	1.10963e8			0.185883
$843$	4.69202e8	−	3.79173e8i	0.783209	−	0.632928i
$844$	2.26052e8			0.375995
$845$		0			0
$846$	−1.55693e8	+	7.25308e8i	−0.257133	+	1.19788i
$847$		−	3.54082e6i		−	0.00582711i
$848$	−1.97169e8			−0.323334
$849$	−2.12979e8	+	1.72113e8i	−0.348027	+	0.281249i
$850$		0			0
$851$			3.49102e8i			0.566453i
$852$	−4.58450e7	+	3.70483e7i	−0.0741264	+	0.0599032i
$853$		−	3.84724e8i		−	0.619873i	−0.950757	−	0.309936i	$-0.899692\pi$
$853$		−	3.84724e8i		−	0.619873i	0.950757	−	0.309936i	$-0.100308\pi$
$854$		−	707853.i		−	0.00113650i
$855$		0			0
$856$	2.66840e8			0.425432
$857$	−3.42647e8			−0.544382			−0.272191	−	0.962243i	$-0.587748\pi$
$857$	−3.42647e8			−0.544382			−0.272191	+	0.962243i	$0.587748\pi$
$858$	−9.61213e6	−	1.18944e7i	−0.0152180	−	0.0188313i
$859$	3.87443e8			0.611263			0.305631	−	0.952150i	$-0.401132\pi$
$859$	3.87443e8			0.611263			0.305631	+	0.952150i	$0.401132\pi$
$860$		0			0
$861$	569088.	+	704210.i	0.000891600	+	0.00110330i
$862$			2.27172e8i			0.354677i
$863$	−6.46530e7			−0.100590			−0.0502951	−	0.998734i	$-0.516016\pi$
$863$	−6.46530e7			−0.100590			−0.0502951	+	0.998734i	$0.516016\pi$
$864$	1.01745e8	−	5.14558e7i	0.157750	−	0.0797799i
$865$		0			0
$866$			4.78487e6i			0.00736744i
$867$	−6.89874e7	−	8.53675e7i	−0.105855	−	0.130989i
$868$		−	1.46547e6i		−	0.00224088i
$869$		−	1.15591e7i		−	0.0176142i
$870$		0			0
$871$	−1.29416e9			−1.95854
$872$	1.17809e8			0.177676
$873$	−2.00348e8	−	4.30062e7i	−0.301122	−	0.0646380i
$874$	−3.04880e8			−0.456662
$875$		0			0
$876$	4.90903e8	−	3.96709e8i	0.730269	−	0.590147i
$877$			4.99281e8i			0.740196i	0.928993	+	0.370098i	$0.120676\pi$
$877$			4.99281e8i			0.740196i	−0.928993	+	0.370098i	$0.879324\pi$
$878$	−4.23248e8			−0.625333
$879$	−4.72576e8	−	5.84783e8i	−0.695833	−	0.861050i
$880$		0			0
$881$		−	9.14796e8i		−	1.33782i	−0.743345	−	0.668908i	$-0.766762\pi$
$881$		−	9.14796e8i		−	1.33782i	0.743345	−	0.668908i	$-0.233238\pi$
$882$	1.01822e8	−	4.74345e8i	0.148400	−	0.691335i
$883$			7.85211e6i			0.0114052i	0.999984	+	0.00570261i	$0.00181521\pi$
$883$			7.85211e6i			0.0114052i	−0.999984	+	0.00570261i	$0.998185\pi$
$884$			4.22934e8i			0.612231i
$885$		0			0
$886$	−7.08496e8			−1.01868
$887$	1.10737e9			1.58679			0.793397	−	0.608704i	$-0.208310\pi$
$887$	1.10737e9			1.58679			0.793397	+	0.608704i	$0.208310\pi$
$888$	−1.29468e8	+	1.04626e8i	−0.184895	+	0.149417i
$889$	4.56105e6			0.00649172
$890$		0			0
$891$	7.40275e6	−	1.64487e7i	0.0104655	−	0.0232540i
$892$			1.49405e8i			0.210509i
$893$	9.45851e8			1.32821
$894$	5.29833e8	−	4.28170e8i	0.741526	−	0.599244i
$895$		0			0
$896$			370728.i			0.000515384i
$897$	−6.35001e8	+	5.13158e8i	−0.879827	+	0.711007i
$898$			6.38162e8i			0.881256i
$899$			5.05170e7i			0.0695277i
$900$		0			0
$901$	8.62659e8			1.17941
$902$	3.21925e6			0.00438667
$903$	−217427.	−	269052.i	−0.000295291	−	0.000365404i
$904$	−3.15728e8			−0.427374
$905$		0			0
$906$	2.11977e8	+	2.62308e8i	0.285039	+	0.352718i
$907$		−	1.16193e9i		−	1.55725i	−0.627492	−	0.778623i	$-0.715918\pi$
$907$		−	1.16193e9i		−	1.55725i	0.627492	−	0.778623i	$-0.284082\pi$
$908$	−6.28880e8			−0.840059
$909$	−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	$-0.0768289\pi$
$912$	−9.13728e7	−	1.13068e8i	−0.120457	−	0.149058i
$913$			1.68434e7i			0.0221318i
$914$			8.90154e8i			1.16581i
$915$		0			0
$916$	1.43417e8			0.186601
$917$	2.14393e6			0.00278036
$918$	−4.45156e8	+	2.25131e8i	−0.575418	+	0.291009i
$919$	−1.20431e9			−1.55164			−0.775820	−	0.630954i	$-0.782664\pi$
$919$	−1.20431e9			−1.55164			−0.775820	+	0.630954i	$0.782664\pi$
$920$		0			0
$921$	−7.62833e8	+	6.16462e8i	−0.976451	+	0.789091i
$922$			1.03581e9i			1.32156i
$923$	2.01254e8			0.255941
$924$	36864.0	+	45616.9i	4.67290e−5	+	5.78242e-5i
$925$		0			0
$926$		−	1.00679e9i		−	1.26797i
$927$	6.17058e8	+	1.32456e8i	0.774617	+	0.166277i
$928$		−	1.27795e7i		−	0.0159908i
$929$		−	6.33924e8i		−	0.790661i	−0.918539	−	0.395330i	$-0.870630\pi$
$929$		−	6.33924e8i		−	0.790661i	0.918539	−	0.395330i	$-0.129370\pi$
$930$		0			0
$931$	−6.18577e8			−0.766558
$932$	7.33715e7			0.0906316
$933$	7.55833e8	−	6.10805e8i	0.930638	−	0.752069i
$934$	5.29366e8			0.649704
$935$		0			0
$936$	−3.80621e8	−	8.17031e7i	−0.464157	−	0.0996348i
$937$			2.47138e8i			0.300414i	0.988655	+	0.150207i	$0.0479940\pi$
$937$			2.47138e8i			0.300414i	−0.988655	+	0.150207i	$0.952006\pi$
$938$	4.96330e6			0.00601398
$939$	−8.42308e8	+	6.80688e8i	−1.01736	+	0.822150i
$940$		0			0
$941$			9.37355e8i			1.12496i	0.826812	+	0.562478i	$0.190152\pi$
$941$			9.37355e8i			1.12496i	−0.826812	+	0.562478i	$0.809848\pi$
$942$	1.53110e8	−	1.23732e8i	0.183168	−	0.148022i
$943$		−	1.71865e8i		−	0.204952i
$944$		−	3.34663e8i		−	0.397824i
$945$		0			0
$946$	−1.22995e6			−0.00145283
$947$	1.49756e9			1.76333			0.881664	−	0.471877i	$-0.156424\pi$
$947$	1.49756e9			1.76333			0.881664	+	0.471877i	$0.156424\pi$
$948$	−1.84945e8	−	2.28858e8i	−0.217079	−	0.268621i
$949$	−2.15500e9			−2.52145
$950$		0			0
$951$	6.69279e8	+	8.28191e8i	0.778154	+	0.962917i
$952$		−	1.62202e6i		−	0.00187994i
$953$	4.28296e7			0.0494840			0.0247420	−	0.999694i	$-0.492124\pi$
$953$	4.28296e7			0.0494840			0.0247420	+	0.999694i	$0.492124\pi$
$954$	−1.66650e8	+	7.76354e8i	−0.191938	+	0.894158i
$955$		0			0
$956$		−	8.46606e7i		−	0.0968964i
$957$	−1.27076e6	−	1.57248e6i	−0.00144986	−	0.00179411i
$958$			6.09029e8i			0.692694i
$959$		−	5.56675e6i		−	0.00631170i
$960$		0			0
$961$	−3.63185e8			−0.409221
$962$	5.68350e8			0.638397
$963$	2.25537e8	−	1.05068e9i	0.252545	−	1.17650i
$964$	−2.23866e8			−0.249894
$965$		0			0
$966$	2.43533e6	−	1.96804e6i	0.00270163	−	0.00218325i
$967$			1.16322e9i			1.28642i	0.765690	+	0.643210i	$0.222398\pi$
$967$			1.16322e9i			1.28642i	−0.765690	+	0.643210i	$0.777602\pi$
$968$	−3.20478e8			−0.353323
$969$	3.99776e8	+	4.94698e8i	0.439385	+	0.543712i
$970$		0			0
$971$		−	1.39293e9i		−	1.52150i	−0.649045	−	0.760750i	$-0.724831\pi$
$971$		−	1.39293e9i		−	1.52150i	0.649045	−	0.760750i	$-0.275169\pi$
$972$	−1.16611e8	−	4.44111e8i	−0.126982	−	0.483607i
$973$			9.14789e6i			0.00993076i
$974$		−	2.34438e7i		−	0.0253718i
$975$		0			0
$976$	−6.40676e7			−0.0689111
$977$	7.81956e8			0.838492			0.419246	−	0.907873i	$-0.362295\pi$
$977$	7.81956e8			0.838492			0.419246	+	0.907873i	$0.362295\pi$
$978$	1.04528e8	−	8.44717e7i	0.111742	−	0.0903015i
$979$	1.31259e7			0.0139888
$980$		0			0
$981$	9.95739e7	−	4.63874e8i	0.105472	−	0.491352i
$982$		−	6.75126e8i		−	0.712936i
$983$	8.80220e8			0.926682			0.463341	−	0.886180i	$-0.346651\pi$
$983$	8.80220e8			0.926682			0.463341	+	0.886180i	$0.346651\pi$
$984$	6.37379e7	−	5.15080e7i	0.0668978	−	0.0540616i
$985$		0			0
$986$			5.59133e7i			0.0583289i
$987$	−7.55529e6	+	6.10560e6i	−0.00785778	+	0.00635005i
$988$			4.96355e8i			0.514662i
$989$			6.56629e7i			0.0678783i
$990$		0			0
$991$	−1.83915e9			−1.88971			−0.944857	−	0.327483i	$-0.893800\pi$
$991$	−1.83915e9			−1.88971			−0.944857	+	0.327483i	$0.893800\pi$
$992$	−1.32639e8			−0.135874
$993$	4.72397e8	+	5.84562e8i	0.482458	+	0.597012i
$994$	−771840.			−0.000785902
$995$		0			0
$996$	2.69494e8	+	3.33482e8i	0.272754	+	0.337516i
$997$		−	5.69927e8i		−	0.575088i	−0.957767	−	0.287544i	$-0.907161\pi$
$997$		−	5.69927e8i		−	0.575088i	0.957767	−	0.287544i	$-0.0928387\pi$
$998$	6.64316e8			0.668318
$999$	3.02537e8	+	5.98213e8i	0.303447	+	0.600011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.7.b.a.149.2		4
3.2	odd	2	inner	150.7.b.a.149.4		4
5.2	odd	4		6.7.b.a.5.1	✓	2
5.3	odd	4		150.7.d.a.101.2		2
5.4	even	2	inner	150.7.b.a.149.3		4
15.2	even	4		6.7.b.a.5.2	yes	2
15.8	even	4		150.7.d.a.101.1		2
15.14	odd	2	inner	150.7.b.a.149.1		4
20.7	even	4		48.7.e.b.17.2		2
35.27	even	4		294.7.b.a.197.1		2
40.27	even	4		192.7.e.f.65.1		2
40.37	odd	4		192.7.e.c.65.2		2
45.2	even	12		162.7.d.b.53.2		4
45.7	odd	12		162.7.d.b.53.1		4
45.22	odd	12		162.7.d.b.107.2		4
45.32	even	12		162.7.d.b.107.1		4
60.47	odd	4		48.7.e.b.17.1		2
105.62	odd	4		294.7.b.a.197.2		2
120.77	even	4		192.7.e.c.65.1		2
120.107	odd	4		192.7.e.f.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.7.b.a.5.1	✓	2	5.2	odd	4
6.7.b.a.5.2	yes	2	15.2	even	4
48.7.e.b.17.1		2	60.47	odd	4
48.7.e.b.17.2		2	20.7	even	4
150.7.b.a.149.1		4	15.14	odd	2	inner
150.7.b.a.149.2		4	1.1	even	1	trivial
150.7.b.a.149.3		4	5.4	even	2	inner
150.7.b.a.149.4		4	3.2	odd	2	inner
150.7.d.a.101.1		2	15.8	even	4
150.7.d.a.101.2		2	5.3	odd	4
162.7.d.b.53.1		4	45.7	odd	12
162.7.d.b.53.2		4	45.2	even	12
162.7.d.b.107.1		4	45.32	even	12
162.7.d.b.107.2		4	45.22	odd	12
192.7.e.c.65.1		2	120.77	even	4
192.7.e.c.65.2		2	40.37	odd	4
192.7.e.f.65.1		2	40.27	even	4
192.7.e.f.65.2		2	120.107	odd	4
294.7.b.a.197.1		2	35.27	even	4
294.7.b.a.197.2		2	105.62	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.65685 q^{2} +(16.9706 + 21.0000i) q^{3} +32.0000 q^{4} +(-96.0000 - 118.794i) q^{6} -2.00000i q^{7} -181.019 q^{8} +(-153.000 + 712.764i) q^{9} +O(q^{10})\)	\(q-5.65685 q^{2} +(16.9706 + 21.0000i) q^{3} +32.0000 q^{4} +(-96.0000 - 118.794i) q^{6} -2.00000i q^{7} -181.019 q^{8} +(-153.000 + 712.764i) q^{9} +33.9411i q^{11} +(543.058 + 672.000i) q^{12} -2950.00i q^{13} +11.3137i q^{14} +1024.00 q^{16} -4480.23 q^{17} +(865.499 - 4032.00i) q^{18} -5258.00 q^{19} +(42.0000 - 33.9411i) q^{21} -192.000i q^{22} -10250.2 q^{23} +(-3072.00 - 3801.41i) q^{24} +16687.7i q^{26} +(-17564.5 + 8883.00i) q^{27} -64.0000i q^{28} +2206.17i q^{29} +22898.0 q^{31} -5792.62 q^{32} +(-712.764 + 576.000i) q^{33} +25344.0 q^{34} +(-4896.00 + 22808.4i) q^{36} -34058.0i q^{37} +29743.7 q^{38} +(61950.0 - 50063.2i) q^{39} +16766.9i q^{41} +(-237.588 + 192.000i) q^{42} -6406.00i q^{43} +1086.12i q^{44} +57984.0 q^{46} -179888. q^{47} +(17377.9 + 21504.0i) q^{48} +117645. q^{49} +(-76032.0 - 94084.8i) q^{51} -94400.0i q^{52} -192548. q^{53} +(99360.0 - 50249.8i) q^{54} +362.039i q^{56} +(-89231.2 - 110418. i) q^{57} -12480.0i q^{58} -326819. i q^{59} -62566.0 q^{61} -129531. q^{62} +(1425.53 + 306.000i) q^{63} +32768.0 q^{64} +(4032.00 - 3258.35i) q^{66} -438698. i q^{67} -143367. q^{68} +(-173952. - 215255. i) q^{69} +68221.7i q^{71} +(27696.0 - 129024. i) q^{72} -730510. i q^{73} +192661. i q^{74} -168256. q^{76} +67.8823 q^{77} +(-350442. + 283200. i) q^{78} -340562. q^{79} +(-484623. - 218106. i) q^{81} -94848.0i q^{82} +496253. q^{83} +(1344.00 - 1086.12i) q^{84} +36237.8i q^{86} +(-46329.6 + 37440.0i) q^{87} -6144.00i q^{88} -386725. i q^{89} -5900.00 q^{91} -328007. q^{92} +(388592. + 480858. i) q^{93} +1.01760e6 q^{94} +(-98304.0 - 121645. i) q^{96} +281086. i q^{97} -665501. q^{98} +(-24192.0 - 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{4} - 384 q^{6} - 612 q^{9}+O(q^{10}) \) 4 * q + 128 * q^4 - 384 * q^6 - 612 * q^9	\( 4 q + 128 q^{4} - 384 q^{6} - 612 q^{9} + 4096 q^{16} - 21032 q^{19} + 168 q^{21} - 12288 q^{24} + 91592 q^{31} + 101376 q^{34} - 19584 q^{36} + 247800 q^{39} + 231936 q^{46} + 470580 q^{49} - 304128 q^{51} + 397440 q^{54} - 250264 q^{61} + 131072 q^{64} + 16128 q^{66} - 695808 q^{69} - 673024 q^{76} - 1362248 q^{79} - 1938492 q^{81} + 5376 q^{84} - 23600 q^{91} + 4070400 q^{94} - 393216 q^{96} - 96768 q^{99}+O(q^{100}) \) 4 * q + 128 * q^4 - 384 * q^6 - 612 * q^9 + 4096 * q^16 - 21032 * q^19 + 168 * q^21 - 12288 * q^24 + 91592 * q^31 + 101376 * q^34 - 19584 * q^36 + 247800 * q^39 + 231936 * q^46 + 470580 * q^49 - 304128 * q^51 + 397440 * q^54 - 250264 * q^61 + 131072 * q^64 + 16128 * q^66 - 695808 * q^69 - 673024 * q^76 - 1362248 * q^79 - 1938492 * q^81 + 5376 * q^84 - 23600 * q^91 + 4070400 * q^94 - 393216 * q^96 - 96768 * q^99

Introduction

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