LMFDB - Embedded newform 38.7.b.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(37,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("38.37");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.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:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 5050x^{8} + 7354489x^{6} + 2475755792x^{4} + 232626987584x^{2} + 2900002611200 $ x^10 + 5050x^8 + 7354489x^6 + 2475755792x^4 + 232626987584x^2 + 2900002611200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.2
Root			$-16.6843i$ of defining polynomial
Character	$\chi$	$=$	38.37
Dual form			38.7.b.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -13.8558i q^{3} -32.0000 q^{4} -9.64927 q^{5} -78.3804 q^{6} -472.908 q^{7} +181.019i q^{8} +537.016 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} -13.8558i q^{3} -32.0000 q^{4} -9.64927 q^{5} -78.3804 q^{6} -472.908 q^{7} +181.019i q^{8} +537.016 q^{9} +54.5845i q^{10} -1634.10 q^{11} +443.386i q^{12} +2508.42i q^{13} +2675.17i q^{14} +133.699i q^{15} +1024.00 q^{16} +1388.52 q^{17} -3037.82i q^{18} +(-5907.82 + 3484.76i) q^{19} +308.777 q^{20} +6552.52i q^{21} +9243.87i q^{22} -4752.09 q^{23} +2508.17 q^{24} -15531.9 q^{25} +14189.8 q^{26} -17541.7i q^{27} +15133.0 q^{28} -42974.6i q^{29} +756.313 q^{30} +7233.23i q^{31} -5792.62i q^{32} +22641.8i q^{33} -7854.64i q^{34} +4563.21 q^{35} -17184.5 q^{36} -96014.3i q^{37} +(19712.8 + 33419.7i) q^{38} +34756.3 q^{39} -1746.70i q^{40} -2720.23i q^{41} +37066.7 q^{42} -39722.9 q^{43} +52291.2 q^{44} -5181.81 q^{45} +26881.9i q^{46} -78447.0 q^{47} -14188.4i q^{48} +105993. q^{49} +87861.6i q^{50} -19239.1i q^{51} -80269.6i q^{52} +230526. i q^{53} -99230.8 q^{54} +15767.9 q^{55} -85605.4i q^{56} +(48284.2 + 81857.8i) q^{57} -243101. q^{58} +112061. i q^{59} -4278.35i q^{60} -143589. q^{61} +40917.3 q^{62} -253959. q^{63} -32768.0 q^{64} -24204.5i q^{65} +128082. q^{66} +223311. i q^{67} -44432.6 q^{68} +65844.1i q^{69} -25813.4i q^{70} -281325. i q^{71} +97210.3i q^{72} +339869. q^{73} -543139. q^{74} +215207. i q^{75} +(189050. - 111512. i) q^{76} +772779. q^{77} -196611. i q^{78} -467067. i q^{79} -9880.85 q^{80} +148430. q^{81} -15388.0 q^{82} +838605. q^{83} -209681. i q^{84} -13398.2 q^{85} +224707. i q^{86} -595449. q^{87} -295804. i q^{88} +865320. i q^{89} +29312.8i q^{90} -1.18625e6i q^{91} +152067. q^{92} +100222. q^{93} +443763. i q^{94} +(57006.1 - 33625.3i) q^{95} -80261.5 q^{96} -1.02215e6i q^{97} -599584. i q^{98} -877539. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 320 q^{4} - 112 q^{5} + 160 q^{6} - 224 q^{7} - 2890 q^{9}+O(q^{10}) $ 10 * q - 320 * q^4 - 112 * q^5 + 160 * q^6 - 224 * q^7 - 2890 * q^9	$ 10 q - 320 q^{4} - 112 q^{5} + 160 q^{6} - 224 q^{7} - 2890 q^{9} + 3644 q^{11} + 10240 q^{16} - 10420 q^{17} - 17230 q^{19} + 3584 q^{20} + 37712 q^{23} - 5120 q^{24} - 52078 q^{25} - 7104 q^{26} + 7168 q^{28} + 94688 q^{30} - 161720 q^{35} + 92480 q^{36} + 25152 q^{38} - 78876 q^{39} + 53792 q^{42} + 6308 q^{43} - 116608 q^{44} + 309808 q^{45} + 322220 q^{47} - 235770 q^{49} - 321728 q^{54} - 377880 q^{55} + 24228 q^{57} + 445920 q^{58} + 426304 q^{61} + 59424 q^{62} - 517916 q^{63} - 327680 q^{64} - 1417312 q^{66} + 333440 q^{68} - 786076 q^{73} - 293280 q^{74} + 551360 q^{76} + 2303716 q^{77} - 114688 q^{80} + 5261090 q^{81} - 455136 q^{82} - 101500 q^{83} - 1261380 q^{85} - 2460732 q^{87} - 1206784 q^{92} - 2827032 q^{93} + 3106292 q^{95} + 163840 q^{96} + 1061428 q^{99}+O(q^{100}) $ 10 * q - 320 * q^4 - 112 * q^5 + 160 * q^6 - 224 * q^7 - 2890 * q^9 + 3644 * q^11 + 10240 * q^16 - 10420 * q^17 - 17230 * q^19 + 3584 * q^20 + 37712 * q^23 - 5120 * q^24 - 52078 * q^25 - 7104 * q^26 + 7168 * q^28 + 94688 * q^30 - 161720 * q^35 + 92480 * q^36 + 25152 * q^38 - 78876 * q^39 + 53792 * q^42 + 6308 * q^43 - 116608 * q^44 + 309808 * q^45 + 322220 * q^47 - 235770 * q^49 - 321728 * q^54 - 377880 * q^55 + 24228 * q^57 + 445920 * q^58 + 426304 * q^61 + 59424 * q^62 - 517916 * q^63 - 327680 * q^64 - 1417312 * q^66 + 333440 * q^68 - 786076 * q^73 - 293280 * q^74 + 551360 * q^76 + 2303716 * q^77 - 114688 * q^80 + 5261090 * q^81 - 455136 * q^82 - 101500 * q^83 - 1261380 * q^85 - 2460732 * q^87 - 1206784 * q^92 - 2827032 * q^93 + 3106292 * q^95 + 163840 * q^96 + 1061428 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$-1$

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
$3$		−	13.8558i		−	0.513179i	−0.966521	−	0.256589i	$-0.917401\pi$
$3$		−	13.8558i		−	0.513179i	0.966521	−	0.256589i	$-0.0825988\pi$
$4$	−32.0000			−0.500000
$5$	−9.64927			−0.0771941			−0.0385971	−	0.999255i	$-0.512289\pi$
$5$	−9.64927			−0.0771941			−0.0385971	+	0.999255i	$0.512289\pi$
$6$	−78.3804			−0.362872
$7$	−472.908			−1.37874			−0.689370	−	0.724410i	$-0.742112\pi$
$7$	−472.908			−1.37874			−0.689370	+	0.724410i	$0.742112\pi$
$8$			181.019i			0.353553i
$9$	537.016			0.736648
$10$			54.5845i			0.0545845i
$11$	−1634.10			−1.22772			−0.613862	−	0.789413i	$-0.710385\pi$
$11$	−1634.10			−1.22772			−0.613862	+	0.789413i	$0.710385\pi$
$12$			443.386i			0.256589i
$13$			2508.42i			1.14175i	0.821037	+	0.570875i	$0.193396\pi$
$13$			2508.42i			1.14175i	−0.821037	+	0.570875i	$0.806604\pi$
$14$			2675.17i			0.974916i
$15$			133.699i			0.0396144i
$16$	1024.00			0.250000
$17$	1388.52			0.282621			0.141311	−	0.989965i	$-0.454868\pi$
$17$	1388.52			0.282621			0.141311	+	0.989965i	$0.454868\pi$
$18$		−	3037.82i		−	0.520888i
$19$	−5907.82	+	3484.76i	−0.861324	+	0.508056i
$19$	−5907.82	+	3484.76i	−0.861324	+	0.508056i
$20$	308.777			0.0385971
$21$			6552.52i			0.707540i
$22$			9243.87i			0.868132i
$23$	−4752.09			−0.390572			−0.195286	−	0.980746i	$-0.562564\pi$
$23$	−4752.09			−0.390572			−0.195286	+	0.980746i	$0.562564\pi$
$24$	2508.17			0.181436
$25$	−15531.9			−0.994041
$26$	14189.8			0.807339
$27$		−	17541.7i		−	0.891211i
$28$	15133.0			0.689370
$29$		−	42974.6i		−	1.76205i	−0.473071	−	0.881024i	$-0.656855\pi$
$29$		−	42974.6i		−	1.76205i	0.473071	−	0.881024i	$-0.343145\pi$
$30$	756.313			0.0280116
$31$			7233.23i			0.242799i	0.992604	+	0.121400i	$0.0387382\pi$
$31$			7233.23i			0.242799i	−0.992604	+	0.121400i	$0.961262\pi$
$32$		−	5792.62i		−	0.176777i
$33$			22641.8i			0.630042i
$34$		−	7854.64i		−	0.199843i
$35$	4563.21			0.106431
$36$	−17184.5			−0.368324
$37$		−	96014.3i		−	1.89553i	−0.318969	−	0.947765i	$-0.603337\pi$
$37$		−	96014.3i		−	1.89553i	0.318969	−	0.947765i	$-0.396663\pi$
$38$	19712.8	+	33419.7i	0.359250	+	0.609048i
$39$	34756.3			0.585922
$40$		−	1746.70i		−	0.0272922i
$41$		−	2720.23i		−	0.0394689i	−0.999805	−	0.0197344i	$-0.993718\pi$
$41$		−	2720.23i		−	0.0394689i	0.999805	−	0.0197344i	$-0.00628207\pi$
$42$	37066.7			0.500306
$43$	−39722.9			−0.499615			−0.249808	−	0.968296i	$-0.580367\pi$
$43$	−39722.9			−0.499615			−0.249808	+	0.968296i	$0.580367\pi$
$44$	52291.2			0.613862
$45$	−5181.81			−0.0568649
$46$			26881.9i			0.276176i
$47$	−78447.0			−0.755584			−0.377792	−	0.925891i	$-0.623317\pi$
$47$	−78447.0			−0.755584			−0.377792	+	0.925891i	$0.623317\pi$
$48$		−	14188.4i		−	0.128295i
$49$	105993.			0.900922
$50$			87861.6i			0.702893i
$51$		−	19239.1i		−	0.145035i
$52$		−	80269.6i		−	0.570875i
$53$			230526.i			1.54843i	0.632921	+	0.774217i	$0.281856\pi$
$53$			230526.i			1.54843i	−0.632921	+	0.774217i	$0.718144\pi$
$54$	−99230.8			−0.630181
$55$	15767.9			0.0947731
$56$		−	85605.4i		−	0.487458i
$57$	48284.2	+	81857.8i	0.260724	+	0.442013i
$58$	−243101.			−1.24596
$59$			112061.i			0.545630i	0.962066	+	0.272815i	$0.0879547\pi$
$59$			112061.i			0.545630i	−0.962066	+	0.272815i	$0.912045\pi$
$60$		−	4278.35i		−	0.0198072i
$61$	−143589.			−0.632602			−0.316301	−	0.948659i	$-0.602441\pi$
$61$	−143589.			−0.632602			−0.316301	+	0.948659i	$0.602441\pi$
$62$	40917.3			0.171685
$63$	−253959.			−1.01564
$64$	−32768.0			−0.125000
$65$		−	24204.5i		−	0.0881364i
$66$	128082.			0.445507
$67$			223311.i			0.742483i	0.928536	+	0.371242i	$0.121068\pi$
$67$			223311.i			0.742483i	−0.928536	+	0.371242i	$0.878932\pi$
$68$	−44432.6			−0.141311
$69$			65844.1i			0.200433i
$70$		−	25813.4i		−	0.0752578i
$71$		−	281325.i		−	0.786018i	−0.919535	−	0.393009i	$-0.871434\pi$
$71$		−	281325.i		−	0.786018i	0.919535	−	0.393009i	$-0.128566\pi$
$72$			97210.3i			0.260444i
$73$	339869.			0.873660			0.436830	−	0.899544i	$-0.356101\pi$
$73$	339869.			0.873660			0.436830	+	0.899544i	$0.356101\pi$
$74$	−543139.			−1.34034
$75$			215207.i			0.510121i
$76$	189050.	−	111512.i	0.430662	−	0.254028i
$77$	772779.			1.69271
$78$		−	196611.i		−	0.414309i
$79$		−	467067.i		−	0.947323i	−0.880707	−	0.473661i	$-0.842932\pi$
$79$		−	467067.i		−	0.947323i	0.880707	−	0.473661i	$-0.157068\pi$
$80$	−9880.85			−0.0192985
$81$	148430.			0.279297
$82$	−15388.0			−0.0279087
$83$	838605.			1.46664			0.733320	−	0.679884i	$-0.237970\pi$
$83$	838605.			1.46664			0.733320	+	0.679884i	$0.237970\pi$
$84$		−	209681.i		−	0.353770i
$85$	−13398.2			−0.0218167
$86$			224707.i			0.353281i
$87$	−595449.			−0.904246
$88$		−	295804.i		−	0.434066i
$89$			865320.i			1.22746i	0.789517	+	0.613729i	$0.210331\pi$
$89$			865320.i			1.22746i	−0.789517	+	0.613729i	$0.789669\pi$
$90$			29312.8i			0.0402095i
$91$		−	1.18625e6i		−	1.57417i
$92$	152067.			0.195286
$93$	100222.			0.124599
$94$			443763.i			0.534278i
$95$	57006.1	−	33625.3i	0.0664892	−	0.0392189i
$96$	−80261.5			−0.0907180
$97$		−	1.02215e6i		−	1.11995i	−0.828509	−	0.559976i	$-0.810810\pi$
$97$		−	1.02215e6i		−	1.11995i	0.828509	−	0.559976i	$-0.189190\pi$
$98$		−	599584.i		−	0.637048i
$99$	−877539.			−0.904400
$100$	497021.			0.497021
$101$	−905440.			−0.878811			−0.439406	−	0.898289i	$-0.644811\pi$
$101$	−905440.			−0.878811			−0.439406	+	0.898289i	$0.644811\pi$
$102$	−108833.			−0.102555
$103$		−	863375.i		−	0.790110i	−0.918657	−	0.395055i	$-0.870725\pi$
$103$		−	863375.i		−	0.790110i	0.918657	−	0.395055i	$-0.129275\pi$
$104$	−454073.			−0.403669
$105$		−	63227.1i		−	0.0546179i
$106$	1.30405e6			1.09491
$107$			1.03377e6i			0.843866i	0.906627	+	0.421933i	$0.138648\pi$
$107$			1.03377e6i			0.843866i	−0.906627	+	0.421933i	$0.861352\pi$
$108$			561334.i			0.445605i
$109$			537697.i			0.415201i	0.978214	+	0.207601i	$0.0665654\pi$
$109$			537697.i			0.415201i	−0.978214	+	0.207601i	$0.933435\pi$
$110$		−	89196.6i		−	0.0670147i
$111$	−1.33036e6			−0.972746
$112$	−484257.			−0.344685
$113$			1.05648e6i			0.732191i	0.930577	+	0.366096i	$0.119306\pi$
$113$			1.05648e6i			0.732191i	−0.930577	+	0.366096i	$0.880694\pi$
$114$	463057.	−	273137.i	0.312551	−	0.184359i
$115$	45854.2			0.0301499
$116$			1.37519e6i			0.881024i
$117$			1.34706e6i			0.841067i
$118$	633913.			0.385819
$119$	−656640.			−0.389661
$120$	−24202.0			−0.0140058
$121$	898727.			0.507308
$122$			812260.i			0.447317i
$123$	−37691.1			−0.0202546
$124$		−	231463.i		−	0.121400i
$125$	300641.			0.153928
$126$			1.43661e6i			0.718169i
$127$			315081.i			0.153819i	0.997038	+	0.0769097i	$0.0245053\pi$
$127$			315081.i			0.153819i	−0.997038	+	0.0769097i	$0.975495\pi$
$128$			185364.i			0.0883883i
$129$			550394.i			0.256392i
$130$	−136921.			−0.0623218
$131$	−3.44846e6			−1.53395			−0.766976	−	0.641675i	$-0.778240\pi$
$131$	−3.44846e6			−1.53395			−0.766976	+	0.641675i	$0.778240\pi$
$132$		−	724538.i		−	0.315021i
$133$	2.79385e6	−	1.64797e6i	1.18754	−	0.700477i
$134$	1.26324e6			0.525015
$135$			169265.i			0.0687962i
$136$			251348.i			0.0999216i
$137$	509674.			0.198213			0.0991063	−	0.995077i	$-0.468402\pi$
$137$	509674.			0.198213			0.0991063	+	0.995077i	$0.468402\pi$
$138$	372471.			0.141728
$139$	−2.94266e6			−1.09571			−0.547856	−	0.836573i	$-0.684556\pi$
$139$	−2.94266e6			−1.09571			−0.547856	+	0.836573i	$0.684556\pi$
$140$	−146023.			−0.0532153
$141$			1.08695e6i			0.387750i
$142$	−1.59141e6			−0.555799
$143$		−	4.09902e6i		−	1.40175i
$144$	549904.			0.184162
$145$			414673.i			0.136020i
$146$		−	1.92259e6i		−	0.617771i
$147$		−	1.46861e6i		−	0.462334i
$148$			3.07246e6i			0.947765i
$149$	−1.20237e6			−0.363480			−0.181740	−	0.983347i	$-0.558173\pi$
$149$	−1.20237e6			−0.363480			−0.181740	+	0.983347i	$0.558173\pi$
$150$	1.21740e6			0.360710
$151$		−	2.78708e6i		−	0.809504i	−0.914426	−	0.404752i	$-0.867358\pi$
$151$		−	2.78708e6i		−	0.809504i	0.914426	−	0.404752i	$-0.132642\pi$
$152$	−630808.	−	1.06943e6i	−0.179625	−	0.304524i
$153$	745656.			0.208192
$154$		−	4.37150e6i		−	1.19693i
$155$		−	69795.4i		−	0.0187427i
$156$	−1.11220e6			−0.292961
$157$	6.72543e6			1.73789			0.868943	−	0.494913i	$-0.164800\pi$
$157$	6.72543e6			1.73789			0.868943	+	0.494913i	$0.164800\pi$
$158$	−2.64213e6			−0.669858
$159$	3.19413e6			0.794623
$160$			55894.5i			0.0136461i
$161$	2.24730e6			0.538497
$162$		−	839647.i		−	0.197493i
$163$	−960216.			−0.221721			−0.110860	−	0.993836i	$-0.535361\pi$
$163$	−960216.			−0.221721			−0.110860	+	0.993836i	$0.535361\pi$
$164$			87047.5i			0.0197344i
$165$		−	218477.i		−	0.0486356i
$166$		−	4.74387e6i		−	1.03707i
$167$			8.48234e6i			1.82124i	0.413249	+	0.910618i	$0.364394\pi$
$167$			8.48234e6i			1.82124i	−0.413249	+	0.910618i	$0.635606\pi$
$168$	−1.18613e6			−0.250153
$169$	−1.46538e6			−0.303592
$170$			75791.5i			0.0154267i
$171$	−3.17260e6	+	1.87137e6i	−0.634492	+	0.374258i
$172$	1.27113e6			0.249808
$173$		−	727113.i		−	0.140431i	−0.997532	−	0.0702156i	$-0.977631\pi$
$173$		−	727113.i		−	0.140431i	0.997532	−	0.0702156i	$-0.0223687\pi$
$174$			3.36837e6i			0.639398i
$175$	7.34515e6			1.37052
$176$	−1.67332e6			−0.306931
$177$	1.55270e6			0.280006
$178$	4.89499e6			0.867944
$179$		−	4.93941e6i		−	0.861225i	−0.902537	−	0.430612i	$-0.858298\pi$
$179$		−	4.93941e6i		−	0.861225i	0.902537	−	0.430612i	$-0.141702\pi$
$180$	165818.			0.0284324
$181$		−	8.72459e6i		−	1.47133i	−0.677347	−	0.735664i	$-0.736870\pi$
$181$		−	8.72459e6i		−	1.47133i	0.677347	−	0.735664i	$-0.263130\pi$
$182$	−6.71046e6			−1.11311
$183$			1.98954e6i			0.324638i
$184$		−	860220.i		−	0.138088i
$185$			926467.i			0.146324i
$186$		−	566943.i		−	0.0881051i
$187$	−2.26898e6			−0.346981
$188$	2.51030e6			0.377792
$189$			8.29560e6i			1.22875i
$190$	−190214.	−	322475.i	−0.0277320	−	0.0470149i
$191$	7.16640e6			1.02849			0.514246	−	0.857643i	$-0.328072\pi$
$191$	7.16640e6			1.02849			0.514246	+	0.857643i	$0.328072\pi$
$192$			454028.i			0.0641473i
$193$			8.94301e6i			1.24398i	0.783027	+	0.621988i	$0.213675\pi$
$193$			8.94301e6i			1.24398i	−0.783027	+	0.621988i	$0.786325\pi$
$194$	−5.78216e6			−0.791926
$195$	−335373.			−0.0452297
$196$	−3.39176e6			−0.450461
$197$	−1.36456e7			−1.78482			−0.892411	−	0.451224i	$-0.850987\pi$
$197$	−1.36456e7			−1.78482			−0.892411	+	0.451224i	$0.850987\pi$
$198$			4.96411e6i			0.639508i
$199$	−8.34059e6			−1.05837			−0.529185	−	0.848506i	$-0.677502\pi$
$199$	−8.34059e6			−1.05837			−0.529185	+	0.848506i	$0.677502\pi$
$200$		−	2.81157e6i		−	0.351447i
$201$	3.09417e6			0.381027
$202$			5.12194e6i			0.621414i
$203$			2.03230e7i			2.42941i
$204$			615650.i			0.0725176i
$205$			26248.3i			0.00304677i
$206$	−4.88399e6			−0.558692
$207$	−2.55195e6			−0.287714
$208$			2.56863e6i			0.285437i
$209$	9.65398e6	−	5.69444e6i	1.05747	−	0.623753i
$210$	−357666.			−0.0386207
$211$		−	1.79407e7i		−	1.90982i	−0.296893	−	0.954911i	$-0.595951\pi$
$211$		−	1.79407e7i		−	1.90982i	0.296893	−	0.954911i	$-0.404049\pi$
$212$		−	7.37683e6i		−	0.774217i
$213$	−3.89798e6			−0.403368
$214$	5.84790e6			0.596703
$215$	383297.			0.0385674
$216$	3.17539e6			0.315091
$217$		−	3.42065e6i		−	0.334757i
$218$	3.04168e6			0.293591
$219$		−	4.70916e6i		−	0.448344i
$220$	−504572.			−0.0473866
$221$			3.48299e6i			0.322682i
$222$			7.52564e6i			0.687835i
$223$		−	2.46176e6i		−	0.221988i	−0.993821	−	0.110994i	$-0.964597\pi$
$223$		−	2.46176e6i		−	0.221988i	0.993821	−	0.110994i	$-0.0354035\pi$
$224$			2.73937e6i			0.243729i
$225$	−8.34088e6			−0.732258
$226$	5.97634e6			0.517738
$227$			9.88619e6i			0.845184i	0.906320	+	0.422592i	$0.138880\pi$
$227$			9.88619e6i			0.845184i	−0.906320	+	0.422592i	$0.861120\pi$
$228$	−1.54509e6	−	2.61945e6i	−0.130362	−	0.221007i
$229$	−1.00715e7			−0.838664			−0.419332	−	0.907833i	$-0.637736\pi$
$229$	−1.00715e7			−0.838664			−0.419332	+	0.907833i	$0.637736\pi$
$230$		−	259390.i		−	0.0213192i
$231$		−	1.07075e7i		−	0.868664i
$232$	7.77923e6			0.622978
$233$	5.53511e6			0.437581			0.218791	−	0.975772i	$-0.429789\pi$
$233$	5.53511e6			0.437581			0.218791	+	0.975772i	$0.429789\pi$
$234$	7.62014e6			0.594724
$235$	756956.			0.0583266
$236$		−	3.58595e6i		−	0.272815i
$237$	−6.47160e6			−0.486146
$238$			3.71452e6i			0.275532i
$239$	7.53830e6			0.552178			0.276089	−	0.961132i	$-0.410961\pi$
$239$	7.53830e6			0.552178			0.276089	+	0.961132i	$0.410961\pi$
$240$			136907.i			0.00990360i
$241$			1.33471e7i			0.953531i	0.879030	+	0.476766i	$0.158191\pi$
$241$			1.33471e7i			0.953531i	−0.879030	+	0.476766i	$0.841809\pi$
$242$		−	5.08397e6i		−	0.358721i
$243$		−	1.48445e7i		−	1.03454i
$244$	4.59483e6			0.316301
$245$	−1.02275e6			−0.0695459
$246$			213213.i			0.0143222i
$247$	−8.74125e6	−	1.48193e7i	−0.580073	−	0.983416i
$248$	−1.30935e6			−0.0858425
$249$		−	1.16196e7i		−	0.752648i
$250$		−	1.70068e6i		−	0.108844i
$251$	2.04811e7			1.29519			0.647594	−	0.761985i	$-0.275775\pi$
$251$	2.04811e7			1.29519			0.647594	+	0.761985i	$0.275775\pi$
$252$	8.12669e6			0.507822
$253$	7.76540e6			0.479515
$254$	1.78237e6			0.108767
$255$			185643.i			0.0111959i
$256$	1.04858e6			0.0625000
$257$		−	2.09743e7i		−	1.23563i	−0.786325	−	0.617813i	$-0.788019\pi$
$257$		−	2.09743e7i		−	1.23563i	0.786325	−	0.617813i	$-0.211981\pi$
$258$	3.11350e6			0.181296
$259$			4.54059e7i			2.61344i
$260$			774542.i			0.0440682i
$261$		−	2.30781e7i		−	1.29801i
$262$			1.95075e7i			1.08467i
$263$	5.31930e6			0.292407			0.146203	−	0.989255i	$-0.453295\pi$
$263$	5.31930e6			0.292407			0.146203	+	0.989255i	$0.453295\pi$
$264$	−4.09861e6			−0.222754
$265$		−	2.22441e6i		−	0.119530i
$266$	−9.32231e6	−	1.58044e7i	−0.495312	−	0.839718i
$267$	1.19897e7			0.629906
$268$		−	7.14597e6i		−	0.371242i
$269$		−	1.26540e7i		−	0.650088i	−0.945699	−	0.325044i	$-0.894621\pi$
$269$		−	1.26540e7i		−	0.650088i	0.945699	−	0.325044i	$-0.105379\pi$
$270$	957505.			0.0486463
$271$	−3.10780e7			−1.56151			−0.780755	−	0.624838i	$-0.785165\pi$
$271$	−3.10780e7			−1.56151			−0.780755	+	0.624838i	$0.785165\pi$
$272$	1.42184e6			0.0706553
$273$	−1.64365e7			−0.807833
$274$		−	2.88315e6i		−	0.140157i
$275$	2.53807e7			1.22041
$276$		−	2.10701e6i		−	0.100217i
$277$	−3.69996e7			−1.74084			−0.870418	−	0.492313i	$-0.836151\pi$
$277$	−3.69996e7			−1.74084			−0.870418	+	0.492313i	$0.836151\pi$
$278$			1.66462e7i			0.774785i
$279$			3.88436e6i			0.178857i
$280$			826029.i			0.0376289i
$281$			2.49023e7i			1.12233i	0.827704	+	0.561165i	$0.189647\pi$
$281$			2.49023e7i			1.12233i	−0.827704	+	0.561165i	$0.810353\pi$
$282$	6.14871e6			0.274180
$283$	3.04574e7			1.34380			0.671899	−	0.740643i	$-0.265479\pi$
$283$	3.04574e7			1.34380			0.671899	+	0.740643i	$0.265479\pi$
$284$			9.00239e6i			0.393009i
$285$	−465907.	−	789867.i	−0.0201263	−	0.0341208i
$286$	−2.31876e7			−0.991190
$287$			1.28642e6i			0.0544173i
$288$		−	3.11073e6i		−	0.130222i
$289$	−2.22096e7			−0.920125
$290$	2.34575e6			0.0961805
$291$	−1.41627e7			−0.574736
$292$	−1.08758e7			−0.436830
$293$		−	1.05939e7i		−	0.421166i	−0.977576	−	0.210583i	$-0.932464\pi$
$293$		−	1.05939e7i		−	0.421166i	0.977576	−	0.210583i	$-0.0675362\pi$
$294$	−8.30774e6			−0.326919
$295$		−	1.08131e6i		−	0.0421194i
$296$	1.73804e7			0.670171
$297$			2.86649e7i			1.09416i
$298$			6.80165e6i			0.257019i
$299$		−	1.19203e7i		−	0.445936i
$300$		−	6.88663e6i		−	0.255060i
$301$	1.87853e7			0.688839
$302$	−1.57661e7			−0.572406
$303$			1.25456e7i			0.450987i
$304$	−6.04961e6	+	3.56839e6i	−0.215331	+	0.127014i
$305$	1.38552e6			0.0488331
$306$		−	4.21807e6i		−	0.147214i
$307$			4.13446e7i			1.42891i	0.699684	+	0.714453i	$0.253324\pi$
$307$			4.13446e7i			1.42891i	−0.699684	+	0.714453i	$0.746676\pi$
$308$	−2.47289e7			−0.846356
$309$	−1.19628e7			−0.405468
$310$	−394822.			−0.0132531
$311$	3.84490e7			1.27821			0.639107	−	0.769118i	$-0.279304\pi$
$311$	3.84490e7			1.27821			0.639107	+	0.769118i	$0.279304\pi$
$312$			6.29156e6i			0.207155i
$313$	9.67627e6			0.315555			0.157777	−	0.987475i	$-0.449567\pi$
$313$	9.67627e6			0.315555			0.157777	+	0.987475i	$0.449567\pi$
$314$		−	3.80448e7i		−	1.22887i
$315$	2.45052e6			0.0784018
$316$			1.49461e7i			0.473661i
$317$			4.81542e7i			1.51167i	0.654763	+	0.755834i	$0.272768\pi$
$317$			4.81542e7i			1.51167i	−0.654763	+	0.755834i	$0.727232\pi$
$318$		−	1.80687e7i		−	0.561883i
$319$			7.02249e7i			2.16331i
$320$	316187.			0.00964927
$321$	1.43238e7			0.433054
$322$		−	1.27126e7i		−	0.380775i
$323$	−8.20311e6	+	4.83864e6i	−0.243428	+	0.143587i
$324$	−4.74976e6			−0.139649
$325$		−	3.89606e7i		−	1.13495i
$326$			5.43180e6i			0.156780i
$327$	7.45024e6			0.213072
$328$	492415.			0.0139544
$329$	3.70982e7			1.04175
$330$	−1.23589e6			−0.0343905
$331$		−	5.41915e7i		−	1.49433i	−0.664638	−	0.747166i	$-0.731414\pi$
$331$		−	5.41915e7i		−	1.49433i	0.664638	−	0.747166i	$-0.268586\pi$
$332$	−2.68354e7			−0.733320
$333$		−	5.15612e7i		−	1.39634i
$334$	4.79834e7			1.28781
$335$		−	2.15479e6i		−	0.0573153i
$336$			6.70979e6i			0.176885i
$337$		−	9.69896e6i		−	0.253417i	−0.991940	−	0.126708i	$-0.959559\pi$
$337$		−	9.69896e6i		−	0.253417i	0.991940	−	0.126708i	$-0.0404412\pi$
$338$			8.28945e6i			0.214672i
$339$	1.46384e7			0.375745
$340$	428742.			0.0109083
$341$		−	1.18198e7i		−	0.298091i
$342$	1.05861e7	+	1.79469e7i	0.264641	+	0.448654i
$343$	5.51243e6			0.136603
$344$		−	7.19061e6i		−	0.176641i
$345$		−	635348.i		−	0.0154723i
$346$	−4.11317e6			−0.0992999
$347$	−6.40984e7			−1.53412			−0.767060	−	0.641576i	$-0.778281\pi$
$347$	−6.40984e7			−1.53412			−0.767060	+	0.641576i	$0.778281\pi$
$348$	1.90544e7			0.452123
$349$	−5.19318e7			−1.22168			−0.610839	−	0.791755i	$-0.709168\pi$
$349$	−5.19318e7			−1.22168			−0.610839	+	0.791755i	$0.709168\pi$
$350$		−	4.15504e7i		−	0.969106i
$351$	4.40020e7			1.01754
$352$			9.46573e6i			0.217033i
$353$	−9.56961e6			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$353$	−9.56961e6			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$354$		−	8.78338e6i		−	0.197994i
$355$			2.71458e6i			0.0606760i
$356$		−	2.76902e7i		−	0.613729i
$357$			9.09829e6i			0.199966i
$358$	−2.79415e7			−0.608978
$359$	−1.21238e7			−0.262033			−0.131016	−	0.991380i	$-0.541824\pi$
$359$	−1.21238e7			−0.262033			−0.131016	+	0.991380i	$0.541824\pi$
$360$		−	938008.i		−	0.0201048i
$361$	2.27588e7	−	4.11746e7i	0.483758	−	0.875202i
$362$	−4.93537e7			−1.04039
$363$		−	1.24526e7i		−	0.260340i
$364$			3.79601e7i			0.787087i
$365$	−3.27948e6			−0.0674414
$366$	1.12545e7			0.229554
$367$	5.28300e6			0.106877			0.0534383	−	0.998571i	$-0.482982\pi$
$367$	5.28300e6			0.106877			0.0534383	+	0.998571i	$0.482982\pi$
$368$	−4.86614e6			−0.0976430
$369$		−	1.46081e6i		−	0.0290746i
$370$	5.24089e6			0.103467
$371$		−	1.09018e8i		−	2.13489i
$372$	−3.20712e6			−0.0622997
$373$			4.00964e7i			0.772643i	0.922364	+	0.386322i	$0.126255\pi$
$373$			4.00964e7i			0.772643i	−0.922364	+	0.386322i	$0.873745\pi$
$374$			1.28353e7i			0.245352i
$375$		−	4.16563e6i		−	0.0789927i
$376$		−	1.42004e7i		−	0.267139i
$377$	1.07799e8			2.01182
$378$	4.69270e7			0.868855
$379$			3.15013e7i			0.578643i	0.957232	+	0.289322i	$0.0934297\pi$
$379$			3.15013e7i			0.578643i	−0.957232	+	0.289322i	$0.906570\pi$
$380$	−1.82420e6	+	1.07601e6i	−0.0332446	+	0.0196095i
$381$	4.36571e6			0.0789368
$382$		−	4.05393e7i		−	0.727254i
$383$		−	3.23666e7i		−	0.576104i	−0.957615	−	0.288052i	$-0.906992\pi$
$383$		−	3.23666e7i		−	0.576104i	0.957615	−	0.288052i	$-0.0930076\pi$
$384$	2.56837e6			0.0453590
$385$	−7.45675e6			−0.130667
$386$	5.05893e7			0.879624
$387$	−2.13318e7			−0.368040
$388$			3.27088e7i			0.559976i
$389$	−3.75613e7			−0.638105			−0.319052	−	0.947737i	$-0.603365\pi$
$389$	−3.75613e7			−0.638105			−0.319052	+	0.947737i	$0.603365\pi$
$390$			1.89715e6i			0.0319822i
$391$	−6.59836e6			−0.110384
$392$			1.91867e7i			0.318524i
$393$			4.77813e7i			0.787192i
$394$			7.71913e7i			1.26206i
$395$			4.50685e6i			0.0731278i
$396$	2.80812e7			0.452200
$397$	−1.02896e8			−1.64448			−0.822240	−	0.569140i	$-0.807276\pi$
$397$	−1.02896e8			−1.64448			−0.822240	+	0.569140i	$0.807276\pi$
$398$			4.71815e7i			0.748381i
$399$	−2.28339e7	−	3.87111e7i	−0.359470	−	0.609421i
$400$	−1.59047e7			−0.248510
$401$		−	2.52950e7i		−	0.392285i	−0.980575	−	0.196142i	$-0.937159\pi$
$401$		−	2.52950e7i		−	0.392285i	0.980575	−	0.196142i	$-0.0628415\pi$
$402$		−	1.75032e7i		−	0.269427i
$403$	−1.81440e7			−0.277216
$404$	2.89741e7			0.439406
$405$	−1.43224e6			−0.0215601
$406$	1.14964e8			1.71785
$407$			1.56897e8i			2.32719i
$408$	3.48264e6			0.0512777
$409$			1.10450e8i			1.61435i	0.590314	+	0.807173i	$0.299004\pi$
$409$			1.10450e8i			1.61435i	−0.590314	+	0.807173i	$0.700996\pi$
$410$	148483.			0.00215439
$411$		−	7.06196e6i		−	0.101718i
$412$			2.76280e7i			0.395055i
$413$		−	5.29945e7i		−	0.752282i
$414$			1.44360e7i			0.203444i
$415$	−8.09193e6			−0.113216
$416$	1.45303e7			0.201835
$417$			4.07730e7i			0.562296i
$418$	−3.22126e7	−	5.46112e7i	−0.441060	−	0.747743i
$419$	−2.99012e7			−0.406487			−0.203244	−	0.979128i	$-0.565148\pi$
$419$	−2.99012e7			−0.406487			−0.203244	+	0.979128i	$0.565148\pi$
$420$			2.02327e6i			0.0273090i
$421$		−	1.56945e7i		−	0.210330i	−0.994455	−	0.105165i	$-0.966463\pi$
$421$		−	1.56945e7i		−	0.210330i	0.994455	−	0.105165i	$-0.0335370\pi$
$422$	−1.01488e8			−1.35045
$423$	−4.21273e7			−0.556599
$424$	−4.17297e7			−0.547454
$425$	−2.15663e7			−0.280937
$426$			2.20503e7i			0.285224i
$427$	6.79041e7			0.872193
$428$		−	3.30807e7i		−	0.421933i
$429$	−5.67953e7			−0.719350
$430$		−	2.16825e6i		−	0.0272712i
$431$		−	1.57257e7i		−	0.196417i	−0.995166	−	0.0982084i	$-0.968689\pi$
$431$		−	1.57257e7i		−	0.196417i	0.995166	−	0.0982084i	$-0.0313112\pi$
$432$		−	1.79627e7i		−	0.222803i
$433$			1.77952e7i			0.219199i	0.993976	+	0.109600i	$0.0349569\pi$
$433$			1.77952e7i			0.219199i	−0.993976	+	0.109600i	$0.965043\pi$
$434$	−1.93501e7			−0.236709
$435$	5.74564e6			0.0698025
$436$		−	1.72063e7i		−	0.207601i
$437$	2.80745e7	−	1.65599e7i	0.336409	−	0.198432i
$438$	−2.66390e7			−0.317027
$439$		−	1.05023e8i		−	1.24134i	−0.784072	−	0.620670i	$-0.786861\pi$
$439$		−	1.05023e8i		−	1.24134i	0.784072	−	0.620670i	$-0.213139\pi$
$440$			2.85429e6i			0.0335074i
$441$	5.69197e7			0.663662
$442$	1.97028e7			0.228171
$443$	−1.45746e8			−1.67643			−0.838217	−	0.545337i	$-0.816402\pi$
$443$	−1.45746e8			−1.67643			−0.838217	+	0.545337i	$0.816402\pi$
$444$	4.25714e7			0.486373
$445$		−	8.34970e6i		−	0.0947526i
$446$	−1.39258e7			−0.156969
$447$			1.66599e7i			0.186530i
$448$	1.54962e7			0.172342
$449$			6.53747e7i			0.722222i	0.932523	+	0.361111i	$0.117603\pi$
$449$			6.53747e7i			0.722222i	−0.932523	+	0.361111i	$0.882397\pi$
$450$			4.71831e7i			0.517785i
$451$			4.44514e6i			0.0484569i
$452$		−	3.38073e7i		−	0.366096i
$453$	−3.86173e7			−0.415420
$454$	5.59247e7			0.597635
$455$			1.14465e7i			0.121517i
$456$	−1.48178e7	+	8.74037e6i	−0.156275	+	0.0921797i
$457$	1.83159e8			1.91902			0.959512	−	0.281668i	$-0.0908876\pi$
$457$	1.83159e8			1.91902			0.959512	+	0.281668i	$0.0908876\pi$
$458$			5.69730e7i			0.593025i
$459$		−	2.43570e7i		−	0.251875i
$460$	−1.46733e6			−0.0150749
$461$	−2.60728e7			−0.266125			−0.133062	−	0.991108i	$-0.542481\pi$
$461$	−2.60728e7			−0.266125			−0.133062	+	0.991108i	$0.542481\pi$
$462$	−6.05707e7			−0.614238
$463$	−1.71590e8			−1.72882			−0.864409	−	0.502790i	$-0.832307\pi$
$463$	−1.71590e8			−1.72882			−0.864409	+	0.502790i	$0.832307\pi$
$464$		−	4.40060e7i		−	0.440512i
$465$	−967073.			−0.00961834
$466$		−	3.13113e7i		−	0.309417i
$467$	1.06676e8			1.04741			0.523704	−	0.851900i	$-0.324550\pi$
$467$	1.06676e8			1.04741			0.523704	+	0.851900i	$0.324550\pi$
$468$		−	4.31060e7i		−	0.420534i
$469$		−	1.05606e8i		−	1.02369i
$470$		−	4.28199e6i		−	0.0412432i
$471$		−	9.31864e7i		−	0.891846i
$472$	−2.02852e7			−0.192909
$473$	6.49112e7			0.613390
$474$			3.66089e7i			0.343757i
$475$	9.17596e7	−	5.41249e7i	0.856191	−	0.505029i
$476$	2.10125e7			0.194830
$477$			1.23796e8i			1.14065i
$478$		−	4.26430e7i		−	0.390449i
$479$	1.35426e8			1.23224			0.616118	−	0.787654i	$-0.288704\pi$
$479$	1.35426e8			1.23224			0.616118	+	0.787654i	$0.288704\pi$
$480$	774465.			0.00700290
$481$	2.40845e8			2.16422
$482$	7.55025e7			0.674249
$483$		−	3.11382e7i		−	0.276345i
$484$	−2.87592e7			−0.253654
$485$			9.86300e6i			0.0864538i
$486$	−8.39733e7			−0.731530
$487$		−	4.81682e7i		−	0.417036i	−0.978019	−	0.208518i	$-0.933136\pi$
$487$		−	4.81682e7i		−	0.417036i	0.978019	−	0.208518i	$-0.0668640\pi$
$488$		−	2.59923e7i		−	0.223658i
$489$			1.33046e7i			0.113782i
$490$			5.78555e6i			0.0491764i
$491$	−9.28354e7			−0.784276			−0.392138	−	0.919906i	$-0.628265\pi$
$491$	−9.28354e7			−0.784276			−0.392138	+	0.919906i	$0.628265\pi$
$492$	1.20611e6			0.0101273
$493$		−	5.96710e7i		−	0.497992i
$494$	−8.38307e7	+	4.94480e7i	−0.695380	+	0.410173i
$495$	8.46761e6			0.0698144
$496$			7.40683e6i			0.0606998i
$497$			1.33040e8i			1.08371i
$498$	−6.57302e7			−0.532203
$499$	2.26039e6			0.0181921			0.00909603	−	0.999959i	$-0.497105\pi$
$499$	2.26039e6			0.0181921			0.00909603	+	0.999959i	$0.497105\pi$
$500$	−9.62052e6			−0.0769641
$501$	1.17530e8			0.934620
$502$		−	1.15859e8i		−	0.915836i
$503$	−2.74066e7			−0.215353			−0.107677	−	0.994186i	$-0.534341\pi$
$503$	−2.74066e7			−0.215353			−0.107677	+	0.994186i	$0.534341\pi$
$504$		−	4.59715e7i		−	0.359085i
$505$	8.73683e6			0.0678391
$506$		−	4.39277e7i		−	0.339068i
$507$			2.03041e7i			0.155797i
$508$		−	1.00826e7i		−	0.0769097i
$509$		−	1.70353e7i		−	0.129180i	−0.997912	−	0.0645902i	$-0.979426\pi$
$509$		−	1.70353e7i		−	0.129180i	0.997912	−	0.0645902i	$-0.0205740\pi$
$510$	1.05015e6			0.00791667
$511$	−1.60726e8			−1.20455
$512$		−	5.93164e6i		−	0.0441942i
$513$	6.11285e7	+	1.03633e8i	0.452785	+	0.767621i
$514$	−1.18648e8			−0.873720
$515$			8.33093e6i			0.0609919i
$516$		−	1.76126e7i		−	0.128196i
$517$	1.28190e8			0.927649
$518$	2.56854e8			1.84798
$519$	−1.00748e7			−0.0720663
$520$	4.38147e6			0.0311609
$521$		−	6.32639e7i		−	0.447345i	−0.974664	−	0.223673i	$-0.928195\pi$
$521$		−	6.32639e7i		−	0.447345i	0.974664	−	0.223673i	$-0.0718046\pi$
$522$	−1.30549e8			−0.917831
$523$		−	1.95444e7i		−	0.136621i	−0.997664	−	0.0683105i	$-0.978239\pi$
$523$		−	1.95444e7i		−	0.136621i	0.997664	−	0.0683105i	$-0.0217608\pi$
$524$	1.10351e8			0.766976
$525$		−	1.01773e8i		−	0.703323i
$526$		−	3.00905e7i		−	0.206763i
$527$			1.00435e7i			0.0686202i
$528$			2.31852e7i			0.157511i
$529$	−1.25454e8			−0.847453
$530$	−1.25831e7			−0.0845204
$531$			6.01785e7i			0.401937i
$532$	−8.94033e7	+	5.27350e7i	−0.593771	+	0.350238i
$533$	6.82350e6			0.0450636
$534$		−	6.78241e7i		−	0.445410i
$535$		−	9.97514e6i		−	0.0651415i
$536$	−4.04237e7			−0.262507
$537$	−6.84397e7			−0.441962
$538$	−7.15821e7			−0.459682
$539$	−1.73203e8			−1.10608
$540$		−	5.41646e6i		−	0.0343981i
$541$	2.62822e7			0.165985			0.0829926	−	0.996550i	$-0.473552\pi$
$541$	2.62822e7			0.165985			0.0829926	+	0.996550i	$0.473552\pi$
$542$			1.75803e8i			1.10415i
$543$	−1.20886e8			−0.755054
$544$		−	8.04315e6i		−	0.0499608i
$545$		−	5.18839e6i		−	0.0320511i
$546$			9.29789e7i			0.571224i
$547$			2.05283e8i			1.25427i	0.778911	+	0.627134i	$0.215772\pi$
$547$			2.05283e8i			1.25427i	−0.778911	+	0.627134i	$0.784228\pi$
$548$	−1.63096e7			−0.0991063
$549$	−7.71094e7			−0.466004
$550$		−	1.43575e8i		−	0.862959i
$551$	1.49756e8	+	2.53886e8i	0.895219	+	1.51769i
$552$	−1.19191e7			−0.0708639
$553$			2.20880e8i			1.30611i
$554$			2.09301e8i			1.23096i
$555$	1.28370e7			0.0750903
$556$	9.41652e7			0.547856
$557$	−2.78316e8			−1.61054			−0.805271	−	0.592907i	$-0.797980\pi$
$557$	−2.78316e8			−1.61054			−0.805271	+	0.592907i	$0.797980\pi$
$558$	2.19733e7			0.126471
$559$		−	9.96419e7i		−	0.570435i
$560$	4.67273e6			0.0266076
$561$			3.14386e7i			0.178063i
$562$	1.40869e8			0.793607
$563$			6.32238e7i			0.354287i	0.984185	+	0.177144i	$0.0566857\pi$
$563$			6.32238e7i			0.354287i	−0.984185	+	0.177144i	$0.943314\pi$
$564$		−	3.47823e7i		−	0.193875i
$565$		−	1.01942e7i		−	0.0565209i
$566$		−	1.72293e8i		−	0.950208i
$567$	−7.01937e7			−0.385078
$568$	5.09252e7			0.277899
$569$		−	2.18717e8i		−	1.18726i	−0.804738	−	0.593630i	$-0.797694\pi$
$569$		−	2.18717e8i		−	1.18726i	0.804738	−	0.593630i	$-0.202306\pi$
$570$	−4.46816e6	+	2.63557e6i	−0.0241271	+	0.0142315i
$571$	1.97167e8			1.05907			0.529537	−	0.848287i	$-0.322366\pi$
$571$	1.97167e8			1.05907			0.529537	+	0.848287i	$0.322366\pi$
$572$			1.31169e8i			0.700877i
$573$		−	9.92964e7i		−	0.527800i
$574$	7.27709e6			0.0384788
$575$	7.38090e7			0.388245
$576$	−1.75969e7			−0.0920809
$577$	4.22316e7			0.219842			0.109921	−	0.993940i	$-0.464940\pi$
$577$	4.22316e7			0.219842			0.109921	+	0.993940i	$0.464940\pi$
$578$			1.25636e8i			0.650627i
$579$	1.23913e8			0.638382
$580$		−	1.32695e7i		−	0.0680099i
$581$	−3.96583e8			−2.02211
$582$			8.01166e7i			0.406400i
$583$		−	3.76703e8i		−	1.90105i
$584$			6.15228e7i			0.308886i
$585$		−	1.29982e7i		−	0.0649254i
$586$	−5.99282e7			−0.297809
$587$	−5.30184e7			−0.262128			−0.131064	−	0.991374i	$-0.541839\pi$
$587$	−5.30184e7			−0.262128			−0.131064	+	0.991374i	$0.541839\pi$
$588$			4.69957e7i			0.231167i
$589$	−2.52060e7	−	4.27326e7i	−0.123356	−	0.209129i
$590$	−6.11679e6			−0.0297829
$591$			1.89071e8i			0.915932i
$592$		−	9.83186e7i		−	0.473883i
$593$	2.05727e8			0.986569			0.493285	−	0.869868i	$-0.335796\pi$
$593$	2.05727e8			0.986569			0.493285	+	0.869868i	$0.335796\pi$
$594$	1.62153e8			0.773689
$595$	6.33610e6			0.0300795
$596$	3.84760e7			0.181740
$597$			1.15566e8i			0.543133i
$598$	−6.74312e7			−0.315324
$599$			3.40243e8i			1.58310i	0.611104	+	0.791551i	$0.290726\pi$
$599$			3.40243e8i			1.58310i	−0.611104	+	0.791551i	$0.709274\pi$
$600$	−3.89567e7			−0.180355
$601$		−	2.46936e8i		−	1.13753i	−0.822501	−	0.568763i	$-0.807422\pi$
$601$		−	2.46936e8i		−	1.13753i	0.822501	−	0.568763i	$-0.192578\pi$
$602$		−	1.06265e8i		−	0.487083i
$603$			1.19922e8i			0.546948i
$604$			8.91867e7i			0.404752i
$605$	−8.67205e6			−0.0391612
$606$	7.09688e7			0.318896
$607$		−	2.96009e8i		−	1.32355i	−0.749704	−	0.661773i	$-0.769804\pi$
$607$		−	2.96009e8i		−	1.32355i	0.749704	−	0.661773i	$-0.230196\pi$
$608$	2.01859e7	+	3.42218e7i	0.0898125	+	0.152262i
$609$	2.81592e8			1.24672
$610$		−	7.83771e6i		−	0.0345302i
$611$		−	1.96778e8i		−	0.862688i
$612$	−2.38610e7			−0.104096
$613$	1.90648e6			0.00827656			0.00413828	−	0.999991i	$-0.498683\pi$
$613$	1.90648e6			0.00827656			0.00413828	+	0.999991i	$0.498683\pi$
$614$	2.33880e8			1.01039
$615$	363691.			0.00156354
$616$			1.39888e8i			0.598464i
$617$	−1.42858e8			−0.608203			−0.304101	−	0.952640i	$-0.598356\pi$
$617$	−1.42858e8			−0.608203			−0.304101	+	0.952640i	$0.598356\pi$
$618$			6.76717e7i			0.286709i
$619$	−2.26461e8			−0.954819			−0.477409	−	0.878681i	$-0.658424\pi$
$619$	−2.26461e8			−0.954819			−0.477409	+	0.878681i	$0.658424\pi$
$620$			2.23345e6i			0.00937134i
$621$			8.33597e7i			0.348082i
$622$		−	2.17500e8i		−	0.903834i
$623$		−	4.09216e8i		−	1.69234i
$624$	3.55904e7			0.146480
$625$	2.39785e8			0.982159
$626$		−	5.47372e7i		−	0.223131i
$627$	−7.89012e7	−	1.33764e8i	−0.320097	−	0.542670i
$628$	−2.15214e8			−0.868943
$629$		−	1.33317e8i		−	0.535717i
$630$		−	1.38622e7i		−	0.0554385i
$631$	−7.98719e7			−0.317911			−0.158956	−	0.987286i	$-0.550813\pi$
$631$	−7.98719e7			−0.317911			−0.158956	+	0.987286i	$0.550813\pi$
$632$	8.45482e7			0.334929
$633$	−2.48584e8			−0.980080
$634$	2.72401e8			1.06891
$635$		−	3.04030e6i		−	0.0118740i
$636$	−1.02212e8			−0.397311
$637$			2.65874e8i			1.02863i
$638$	3.97252e8			1.52969
$639$		−	1.51076e8i		−	0.579018i
$640$		−	1.78862e6i		−	0.00682306i
$641$			1.89252e8i			0.718566i	0.933229	+	0.359283i	$0.116979\pi$
$641$			1.89252e8i			0.718566i	−0.933229	+	0.359283i	$0.883021\pi$
$642$		−	8.10274e7i		−	0.306215i
$643$	8.55663e7			0.321862			0.160931	−	0.986966i	$-0.448550\pi$
$643$	8.55663e7			0.321862			0.160931	+	0.986966i	$0.448550\pi$
$644$	−7.19136e7			−0.269248
$645$		−	5.31089e6i		−	0.0197919i
$646$	2.73715e7	+	4.64038e7i	0.101532	+	0.172130i
$647$	2.73076e8			1.00826			0.504128	−	0.863629i	$-0.331814\pi$
$647$	2.73076e8			1.00826			0.504128	+	0.863629i	$0.331814\pi$
$648$			2.68687e7i			0.0987465i
$649$		−	1.83119e8i		−	0.669884i
$650$	−2.20394e8			−0.802528
$651$	−4.73959e7			−0.171790
$652$	3.07269e7			0.110860
$653$	−2.67437e8			−0.960466			−0.480233	−	0.877141i	$-0.659448\pi$
$653$	−2.67437e8			−0.960466			−0.480233	+	0.877141i	$0.659448\pi$
$654$		−	4.21449e7i		−	0.150665i
$655$	3.32752e7			0.118412
$656$		−	2.78552e6i		−	0.00986722i
$657$	1.82515e8			0.643580
$658$		−	2.09859e8i		−	0.736631i
$659$		−	1.53966e8i		−	0.537982i	−0.963143	−	0.268991i	$-0.913310\pi$
$659$		−	1.53966e8i		−	0.537982i	0.963143	−	0.268991i	$-0.0866901\pi$
$660$			6.99126e6i			0.0243178i
$661$		−	4.02363e8i		−	1.39320i	−0.717459	−	0.696600i	$-0.754695\pi$
$661$		−	4.02363e8i		−	1.39320i	0.717459	−	0.696600i	$-0.245305\pi$
$662$	−3.06553e8			−1.05665
$663$	4.82597e7			0.165594
$664$			1.51804e8i			0.518535i
$665$	−2.69586e7	+	1.59017e7i	−0.0916712	+	0.0540727i
$666$	−2.91674e8			−0.987360
$667$			2.04219e8i			0.688207i
$668$		−	2.71435e8i		−	0.910618i
$669$	−3.41097e7			−0.113920
$670$	−1.21893e7			−0.0405281
$671$	2.34638e8			0.776661
$672$	3.79563e7			0.125077
$673$			5.68390e8i			1.86467i	0.361601	+	0.932333i	$0.382230\pi$
$673$			5.68390e8i			1.86467i	−0.361601	+	0.932333i	$0.617770\pi$
$674$	−5.48656e7			−0.179193
$675$			2.72456e8i			0.885900i
$676$	4.68922e7			0.151796
$677$		−	5.64167e8i		−	1.81820i	−0.416579	−	0.909099i	$-0.636771\pi$
$677$		−	5.64167e8i		−	1.81820i	0.416579	−	0.909099i	$-0.363229\pi$
$678$		−	8.28071e7i		−	0.265692i
$679$			4.83383e8i			1.54412i
$680$		−	2.42533e6i		−	0.00771336i
$681$	1.36981e8			0.433731
$682$	−6.68631e7			−0.210782
$683$			2.44741e8i			0.768146i	0.923303	+	0.384073i	$0.125479\pi$
$683$			2.44741e8i			0.768146i	−0.923303	+	0.384073i	$0.874521\pi$
$684$	1.01523e8	−	5.98838e7i	0.317246	−	0.187129i
$685$	−4.91798e6			−0.0153008
$686$		−	3.11830e7i		−	0.0965930i
$687$			1.39549e8i			0.430384i
$688$	−4.06762e7			−0.124904
$689$	−5.78257e8			−1.76792
$690$	−3.59407e6			−0.0109405
$691$	6.39295e7			0.193761			0.0968807	−	0.995296i	$-0.469113\pi$
$691$	6.39295e7			0.193761			0.0968807	+	0.995296i	$0.469113\pi$
$692$			2.32676e7i			0.0702156i
$693$	4.14995e8			1.24693
$694$			3.62596e8i			1.08479i
$695$	2.83945e7			0.0845825
$696$		−	1.07788e8i		−	0.319699i
$697$		−	3.77709e6i		−	0.0111547i
$698$			2.93770e8i			0.863857i
$699$		−	7.66935e7i		−	0.224557i
$700$	−2.35045e8			−0.685262
$701$	−5.13530e8			−1.49077			−0.745387	−	0.666632i	$-0.767735\pi$
$701$	−5.13530e8			−1.49077			−0.745387	+	0.666632i	$0.767735\pi$
$702$		−	2.48913e8i		−	0.719509i
$703$	3.34586e8	+	5.67235e8i	0.963035	+	1.63267i
$704$	5.35462e7			0.153466
$705$		−	1.04882e7i		−	0.0299320i
$706$			5.41339e7i			0.153835i
$707$	4.28190e8			1.21165
$708$	−4.96863e7			−0.140003
$709$	−5.18914e8			−1.45598			−0.727992	−	0.685586i	$-0.759546\pi$
$709$	−5.18914e8			−1.45598			−0.727992	+	0.685586i	$0.759546\pi$
$710$	1.53560e7			0.0429044
$711$		−	2.50823e8i		−	0.697843i
$712$	−1.56640e8			−0.433972
$713$		−	3.43730e7i		−	0.0948306i
$714$	5.14677e7			0.141397
$715$			3.95525e7i			0.108207i
$716$			1.58061e8i			0.430612i
$717$		−	1.04449e8i		−	0.283366i
$718$			6.85826e7i			0.185285i
$719$	5.73118e8			1.54190			0.770952	−	0.636894i	$-0.219781\pi$
$719$	5.73118e8			1.54190			0.770952	+	0.636894i	$0.219781\pi$
$720$	−5.30617e6			−0.0142162
$721$			4.08296e8i			1.08936i
$722$	−2.32919e8	−	1.28743e8i	−0.618861	−	0.342069i
$723$	1.84935e8			0.489332
$724$			2.79187e8i			0.735664i
$725$			6.67477e8i			1.75155i
$726$	−7.04425e7			−0.184088
$727$	6.05704e7			0.157637			0.0788183	−	0.996889i	$-0.474885\pi$
$727$	6.05704e7			0.157637			0.0788183	+	0.996889i	$0.474885\pi$
$728$	2.14735e8			0.556555
$729$	−9.74776e7			−0.251607
$730$			1.85516e7i			0.0476883i
$731$	−5.51559e7			−0.141202
$732$		−	6.36652e7i		−	0.162319i
$733$	6.98711e7			0.177413			0.0887065	−	0.996058i	$-0.471727\pi$
$733$	6.98711e7			0.177413			0.0887065	+	0.996058i	$0.471727\pi$
$734$		−	2.98852e7i		−	0.0755732i
$735$			1.41710e7i			0.0356895i
$736$			2.75270e7i			0.0690440i
$737$		−	3.64914e8i		−	0.911565i
$738$	−8.26359e6			−0.0205589
$739$	−2.80863e8			−0.695924			−0.347962	−	0.937509i	$-0.613126\pi$
$739$	−2.80863e8			−0.695924			−0.347962	+	0.937509i	$0.613126\pi$
$740$		−	2.96470e7i		−	0.0731619i
$741$	−2.05334e8	+	1.21117e8i	−0.504668	+	0.297681i
$742$	−6.16696e8			−1.50959
$743$			2.83181e8i			0.690395i	0.938530	+	0.345197i	$0.112188\pi$
$743$			2.83181e8i			0.690395i	−0.938530	+	0.345197i	$0.887812\pi$
$744$			1.81422e7i			0.0440525i
$745$	1.16020e7			0.0280585
$746$	2.26820e8			0.546341
$747$	4.50345e8			1.08040
$748$	7.26073e7			0.173490
$749$		−	4.88878e8i		−	1.16347i
$750$	−2.35644e7			−0.0558563
$751$			1.57212e7i			0.0371165i	0.999828	+	0.0185582i	$0.00590761\pi$
$751$			1.57212e7i			0.0371165i	−0.999828	+	0.0185582i	$0.994092\pi$
$752$	−8.03297e7			−0.188896
$753$		−	2.83783e8i		−	0.664663i
$754$		−	6.09801e8i		−	1.42257i
$755$			2.68933e7i			0.0624890i
$756$		−	2.65459e8i		−	0.614374i
$757$	1.88211e8			0.433869			0.216934	−	0.976186i	$-0.430394\pi$
$757$	1.88211e8			0.433869			0.216934	+	0.976186i	$0.430394\pi$
$758$	1.78198e8			0.409163
$759$		−	1.07596e8i		−	0.246077i
$760$	6.08684e6	+	1.03192e7i	0.0138660	+	0.0235075i
$761$	−3.69808e8			−0.839117			−0.419558	−	0.907728i	$-0.637815\pi$
$761$	−3.69808e8			−0.839117			−0.419558	+	0.907728i	$0.637815\pi$
$762$		−	2.46962e7i		−	0.0558168i
$763$		−	2.54281e8i		−	0.572454i
$764$	−2.29325e8			−0.514246
$765$	−7.19503e6			−0.0160712
$766$	−1.83093e8			−0.407367
$767$	−2.81096e8			−0.622973
$768$		−	1.45289e7i		−	0.0320737i
$769$	3.65650e8			0.804057			0.402028	−	0.915627i	$-0.368305\pi$
$769$	3.65650e8			0.804057			0.402028	+	0.915627i	$0.368305\pi$
$770$			4.21817e7i			0.0923958i
$771$	−2.90616e8			−0.634097
$772$		−	2.86176e8i		−	0.621988i
$773$		−	5.71935e8i		−	1.23825i	−0.785293	−	0.619125i	$-0.787488\pi$
$773$		−	5.71935e8i		−	1.23825i	0.785293	−	0.619125i	$-0.212512\pi$
$774$			1.20671e8i			0.260244i
$775$		−	1.12346e8i		−	0.241352i
$776$	1.85029e8			0.395963
$777$	6.29136e8			1.34116
$778$			2.12479e8i			0.451208i
$779$	9.47935e6	+	1.60707e7i	0.0200524	+	0.0339955i
$780$	1.07319e7			0.0226149
$781$			4.59713e8i			0.965014i
$782$			3.73260e7i			0.0780532i
$783$	−7.53848e8			−1.57036
$784$	1.08536e8			0.225230
$785$	−6.48955e7			−0.134155
$786$	2.70292e8			0.556629
$787$			4.97162e8i			1.01994i	0.860193	+	0.509969i	$0.170343\pi$
$787$			4.97162e8i			1.01994i	−0.860193	+	0.509969i	$0.829657\pi$
$788$	4.36660e8			0.892411
$789$		−	7.37033e7i		−	0.150057i
$790$	2.54946e7			0.0517091
$791$		−	4.99616e8i		−	1.00950i
$792$		−	1.58851e8i		−	0.319754i
$793$		−	3.60181e8i		−	0.722273i
$794$			5.82070e8i			1.16282i
$795$	−3.08210e7			−0.0613402
$796$	2.66899e8			0.529185
$797$		−	7.50819e8i		−	1.48307i	−0.670917	−	0.741533i	$-0.734099\pi$
$797$		−	7.50819e8i		−	1.48307i	0.670917	−	0.741533i	$-0.265901\pi$
$798$	−2.18983e8	+	1.29168e8i	−0.430926	+	0.254183i
$799$	−1.08925e8			−0.213544
$800$			8.99703e7i			0.175723i
$801$			4.64691e8i			0.904204i
$802$	−1.43090e8			−0.277387
$803$	−5.55380e8			−1.07261
$804$	−9.90133e7			−0.190513
$805$	−2.16848e7			−0.0415688
$806$			1.02638e8i			0.196021i
$807$	−1.75332e8			−0.333612
$808$		−	1.63902e8i		−	0.310707i
$809$	4.01105e8			0.757553			0.378776	−	0.925488i	$-0.376345\pi$
$809$	4.01105e8			0.757553			0.378776	+	0.925488i	$0.376345\pi$
$810$			8.10197e6i			0.0152453i
$811$		−	2.80614e8i		−	0.526074i	−0.964786	−	0.263037i	$-0.915276\pi$
$811$		−	2.80614e8i		−	0.526074i	0.964786	−	0.263037i	$-0.0847242\pi$
$812$		−	6.50336e8i		−	1.21470i
$813$			4.30611e8i			0.801333i
$814$	8.87544e8			1.64557
$815$	9.26538e6			0.0171155
$816$		−	1.97008e7i		−	0.0362588i
$817$	2.34676e8	−	1.38425e8i	0.430331	−	0.253832i
$818$	6.24801e8			1.14152
$819$		−	6.37037e8i		−	1.15961i
$820$		−	839944.i		−	0.00152338i
$821$	5.80542e8			1.04907			0.524535	−	0.851389i	$-0.324239\pi$
$821$	5.80542e8			1.04907			0.524535	+	0.851389i	$0.324239\pi$
$822$	−3.99485e7			−0.0719258
$823$	9.20747e8			1.65174			0.825868	−	0.563864i	$-0.190686\pi$
$823$	9.20747e8			1.65174			0.825868	+	0.563864i	$0.190686\pi$
$824$	1.56288e8			0.279346
$825$		−	3.51670e8i		−	0.626288i
$826$	−2.99782e8			−0.531943
$827$		−	1.11948e8i		−	0.197924i	−0.995091	−	0.0989620i	$-0.968448\pi$
$827$		−	1.11948e8i		−	0.197924i	0.995091	−	0.0989620i	$-0.0315522\pi$
$828$	8.16624e7			0.143857
$829$			3.15311e8i			0.553447i	0.960950	+	0.276724i	$0.0892486\pi$
$829$			3.15311e8i			0.553447i	−0.960950	+	0.276724i	$0.910751\pi$
$830$			4.57749e7i			0.0800558i
$831$			5.12660e8i			0.893360i
$832$		−	8.21960e7i		−	0.142719i
$833$	1.47172e8			0.254619
$834$	2.30647e8			0.397603
$835$		−	8.18483e7i		−	0.140589i
$836$	−3.08927e8	+	1.82222e8i	−0.528734	+	0.311876i
$837$	1.26883e8			0.216385
$838$			1.69147e8i			0.287430i
$839$		−	3.64801e8i		−	0.617689i	−0.951113	−	0.308844i	$-0.900058\pi$
$839$		−	3.64801e8i		−	0.617689i	0.951113	−	0.308844i	$-0.0999423\pi$
$840$	1.14453e7			0.0193103
$841$	−1.25199e9			−2.10482
$842$	−8.87814e7			−0.148726
$843$	3.45042e8			0.575956
$844$			5.74103e8i			0.954911i
$845$	1.41399e7			0.0234355
$846$			2.38308e8i			0.393575i
$847$	−4.25015e8			−0.699445
$848$			2.36059e8i			0.387108i
$849$		−	4.22013e8i		−	0.689608i
$850$			1.21997e8i			0.198652i
$851$			4.56269e8i			0.740341i
$852$	1.24735e8			0.201684
$853$	−3.14653e8			−0.506973			−0.253487	−	0.967339i	$-0.581577\pi$
$853$	−3.14653e8			−0.506973			−0.253487	+	0.967339i	$0.581577\pi$
$854$		−	3.84124e8i		−	0.616733i
$855$	3.06132e7	−	1.80573e7i	0.0489791	−	0.0288905i
$856$	−1.87133e8			−0.298352
$857$			9.74513e8i			1.54826i	0.633024	+	0.774132i	$0.281814\pi$
$857$			9.74513e8i			1.54826i	−0.633024	+	0.774132i	$0.718186\pi$
$858$			3.21283e8i			0.508658i
$859$	−1.39208e8			−0.219627			−0.109813	−	0.993952i	$-0.535025\pi$
$859$	−1.39208e8			−0.219627			−0.109813	+	0.993952i	$0.535025\pi$
$860$	−1.22655e7			−0.0192837
$861$	1.78244e7			0.0279258
$862$	−8.89581e7			−0.138888
$863$		−	6.93999e7i		−	0.107976i	−0.998542	−	0.0539879i	$-0.982807\pi$
$863$		−	6.93999e7i		−	0.107976i	0.998542	−	0.0539879i	$-0.0171933\pi$
$864$	−1.01612e8			−0.157545
$865$			7.01611e6i			0.0108405i
$866$	1.00665e8			0.154997
$867$			3.07732e8i			0.472189i
$868$			1.09461e8i			0.167378i
$869$			7.63235e8i			1.16305i
$870$		−	3.25023e7i		−	0.0493578i
$871$	−5.60160e8			−0.847730
$872$	−9.73336e7			−0.146796
$873$		−	5.48911e8i		−	0.825010i
$874$	−9.36768e7	−	1.58813e8i	−0.140313	−	0.237877i
$875$	−1.42175e8			−0.212227
$876$			1.50693e8i			0.224172i
$877$		−	2.44029e8i		−	0.361779i	−0.983503	−	0.180889i	$-0.942102\pi$
$877$		−	2.44029e8i		−	0.361779i	0.983503	−	0.180889i	$-0.0578976\pi$
$878$	−5.94100e8			−0.877760
$879$	−1.46787e8			−0.216133
$880$	1.61463e7			0.0236933
$881$	−1.14619e9			−1.67621			−0.838103	−	0.545512i	$-0.816335\pi$
$881$	−1.14619e9			−1.67621			−0.838103	+	0.545512i	$0.816335\pi$
$882$		−	3.21986e8i		−	0.469280i
$883$	−2.03516e8			−0.295608			−0.147804	−	0.989017i	$-0.547220\pi$
$883$	−2.03516e8			−0.295608			−0.147804	+	0.989017i	$0.547220\pi$
$884$		−	1.11456e8i		−	0.161341i
$885$	−1.49824e7			−0.0216148
$886$			8.24466e8i			1.18542i
$887$			2.87945e8i			0.412609i	0.978488	+	0.206304i	$0.0661437\pi$
$887$			2.87945e8i			0.412609i	−0.978488	+	0.206304i	$0.933856\pi$
$888$		−	2.40820e8i		−	0.343918i
$889$		−	1.49004e8i		−	0.212077i
$890$	−4.72331e7			−0.0670002
$891$	−2.42550e8			−0.342900
$892$			7.87762e7i			0.110994i
$893$	4.63451e8	−	2.73369e8i	0.650803	−	0.383879i
$894$	9.42425e7			0.131897
$895$			4.76617e7i			0.0664815i
$896$		−	8.76599e7i		−	0.121864i
$897$	−1.65165e8			−0.228845
$898$	3.69815e8			0.510688
$899$	3.10845e8			0.427824
$900$	2.66908e8			0.366129
$901$			3.20089e8i			0.437620i
$902$	2.51455e7			0.0342642
$903$		−	2.60285e8i		−	0.353497i
$904$	−1.91243e8			−0.258869
$905$			8.41859e7i			0.113578i
$906$			2.18453e8i			0.293747i
$907$		−	8.95772e8i		−	1.20054i	−0.799798	−	0.600269i	$-0.795060\pi$
$907$		−	8.95772e8i		−	1.20054i	0.799798	−	0.600269i	$-0.204940\pi$
$908$		−	3.16358e8i		−	0.422592i
$909$	−4.86236e8			−0.647374
$910$	6.47510e7			0.0859255
$911$			9.25190e8i			1.22370i	0.790973	+	0.611851i	$0.209575\pi$
$911$			9.25190e8i			1.22370i	−0.790973	+	0.611851i	$0.790425\pi$
$912$	4.94430e7	+	8.38223e7i	0.0651809	+	0.110503i
$913$	−1.37037e9			−1.80063
$914$		−	1.03611e9i		−	1.35695i
$915$		−	1.91976e7i		−	0.0250601i
$916$	3.22288e8			0.419332
$917$	1.63081e9			2.11492
$918$	−1.37784e8			−0.178102
$919$	−6.74771e8			−0.869380			−0.434690	−	0.900580i	$-0.643142\pi$
$919$	−6.74771e8			−0.869380			−0.434690	+	0.900580i	$0.643142\pi$
$920$			8.30049e6i			0.0106596i
$921$	5.72864e8			0.733284
$922$			1.47490e8i			0.188179i
$923$	7.05681e8			0.897436
$924$			3.42640e8i			0.434332i
$925$			1.49128e9i			1.88423i
$926$			9.70660e8i			1.22246i
$927$		−	4.63646e8i		−	0.582033i
$928$	−2.48935e8			−0.311489
$929$	7.51138e8			0.936856			0.468428	−	0.883502i	$-0.344821\pi$
$929$	7.51138e8			0.936856			0.468428	+	0.883502i	$0.344821\pi$
$930$			5.47059e6i			0.00680119i
$931$	−6.26185e8	+	3.69358e8i	−0.775985	+	0.457719i
$932$	−1.77124e8			−0.218791
$933$		−	5.32742e8i		−	0.655952i
$934$		−	6.03451e8i		−	0.740630i
$935$	2.18940e7			0.0267849
$936$	−2.43845e8			−0.297362
$937$	8.80785e8			1.07066			0.535330	−	0.844643i	$-0.320187\pi$
$937$	8.80785e8			1.07066			0.535330	+	0.844643i	$0.320187\pi$
$938$	−5.97396e8			−0.723859
$939$		−	1.34073e8i		−	0.161936i
$940$	−2.42226e7			−0.0291633
$941$			9.01544e8i			1.08198i	0.841030	+	0.540989i	$0.181950\pi$
$941$			9.01544e8i			1.08198i	−0.841030	+	0.540989i	$0.818050\pi$
$942$	−5.27142e8			−0.630630
$943$			1.29268e7i			0.0154154i
$944$			1.14750e8i			0.136408i
$945$		−	8.00465e7i		−	0.0948521i
$946$		−	3.67193e8i		−	0.433732i
$947$	8.54143e8			1.00573			0.502864	−	0.864366i	$-0.332280\pi$
$947$	8.54143e8			1.00573			0.502864	+	0.864366i	$0.332280\pi$
$948$	2.07091e8			0.243073
$949$			8.52535e8i			0.997501i
$950$	−3.06176e8	−	5.19071e8i	−0.357109	−	0.605419i
$951$	6.67217e8			0.775756
$952$		−	1.18865e8i		−	0.137766i
$953$		−	6.17774e8i		−	0.713758i	−0.934151	−	0.356879i	$-0.883841\pi$
$953$		−	6.17774e8i		−	0.713758i	0.934151	−	0.356879i	$-0.116159\pi$
$954$	7.00297e8			0.806561
$955$	−6.91505e7			−0.0793936
$956$	−2.41225e8			−0.276089
$957$	9.73024e8			1.11016
$958$		−	7.66083e8i		−	0.871323i
$959$	−2.41029e8			−0.273283
$960$		−	4.38103e6i		−	0.00495180i
$961$	8.35184e8			0.941049
$962$		−	1.36242e9i		−	1.53034i
$963$			5.55152e8i			0.621632i
$964$		−	4.27106e8i		−	0.476766i
$965$		−	8.62935e7i		−	0.0960276i
$966$	−1.76144e8			−0.195406
$967$	−1.21378e8			−0.134234			−0.0671168	−	0.997745i	$-0.521380\pi$
$967$	−1.21378e8			−0.134234			−0.0671168	+	0.997745i	$0.521380\pi$
$968$			1.62687e8i			0.179360i
$969$	6.70434e7	+	1.13661e8i	0.0736860	+	0.124922i
$970$	5.57936e7			0.0611321
$971$		−	1.24345e9i		−	1.35822i	−0.734037	−	0.679110i	$-0.762366\pi$
$971$		−	1.24345e9i		−	1.35822i	0.734037	−	0.679110i	$-0.237634\pi$
$972$			4.75025e8i			0.517270i
$973$	1.39161e9			1.51070
$974$	−2.72481e8			−0.294889
$975$	−5.39831e8			−0.582430
$976$	−1.47035e8			−0.158150
$977$		−	4.52867e8i		−	0.485610i	−0.970075	−	0.242805i	$-0.921933\pi$
$977$		−	4.52867e8i		−	0.485610i	0.970075	−	0.242805i	$-0.0780675\pi$
$978$	7.52621e7			0.0804563
$979$		−	1.41402e9i		−	1.50698i
$980$	3.27280e7			0.0347729
$981$			2.88752e8i			0.305857i
$982$			5.25156e8i			0.554567i
$983$		−	2.72752e7i		−	0.0287149i	−0.999897	−	0.0143574i	$-0.995430\pi$
$983$		−	2.72752e7i		−	0.0287149i	0.999897	−	0.0143574i	$-0.00457027\pi$
$984$		−	6.82282e6i		−	0.00716108i
$985$	1.31670e8			0.137778
$986$	−3.37550e8			−0.352134
$987$		−	5.14026e8i		−	0.534606i
$988$	2.79720e8	+	4.74218e8i	0.290036	+	0.491708i
$989$	1.88767e8			0.195136
$990$		−	4.79000e7i		−	0.0493662i
$991$		−	3.87538e8i		−	0.398193i	−0.979980	−	0.199096i	$-0.936199\pi$
$991$		−	3.87538e8i		−	0.398193i	0.979980	−	0.199096i	$-0.0638007\pi$
$992$	4.18993e7			0.0429212
$993$	−7.50868e8			−0.766859
$994$	7.52591e8			0.766301
$995$	8.04806e7			0.0817000
$996$			3.71826e8i			0.376324i
$997$	8.39760e8			0.847364			0.423682	−	0.905811i	$-0.360737\pi$
$997$	8.39760e8			0.847364			0.423682	+	0.905811i	$0.360737\pi$
$998$		−	1.27867e7i		−	0.0128637i
$999$	−1.68425e9			−1.68932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.b.a.37.2	✓	10
3.2	odd	2		342.7.d.a.37.8		10
4.3	odd	2		304.7.e.e.113.7		10
19.18	odd	2	inner	38.7.b.a.37.9	yes	10
57.56	even	2		342.7.d.a.37.3		10
76.75	even	2		304.7.e.e.113.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.b.a.37.2	✓	10	1.1	even	1	trivial
38.7.b.a.37.9	yes	10	19.18	odd	2	inner
304.7.e.e.113.4		10	76.75	even	2
304.7.e.e.113.7		10	4.3	odd	2
342.7.d.a.37.3		10	57.56	even	2
342.7.d.a.37.8		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -13.8558i q^{3} -32.0000 q^{4} -9.64927 q^{5} -78.3804 q^{6} -472.908 q^{7} +181.019i q^{8} +537.016 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} -13.8558i q^{3} -32.0000 q^{4} -9.64927 q^{5} -78.3804 q^{6} -472.908 q^{7} +181.019i q^{8} +537.016 q^{9} +54.5845i q^{10} -1634.10 q^{11} +443.386i q^{12} +2508.42i q^{13} +2675.17i q^{14} +133.699i q^{15} +1024.00 q^{16} +1388.52 q^{17} -3037.82i q^{18} +(-5907.82 + 3484.76i) q^{19} +308.777 q^{20} +6552.52i q^{21} +9243.87i q^{22} -4752.09 q^{23} +2508.17 q^{24} -15531.9 q^{25} +14189.8 q^{26} -17541.7i q^{27} +15133.0 q^{28} -42974.6i q^{29} +756.313 q^{30} +7233.23i q^{31} -5792.62i q^{32} +22641.8i q^{33} -7854.64i q^{34} +4563.21 q^{35} -17184.5 q^{36} -96014.3i q^{37} +(19712.8 + 33419.7i) q^{38} +34756.3 q^{39} -1746.70i q^{40} -2720.23i q^{41} +37066.7 q^{42} -39722.9 q^{43} +52291.2 q^{44} -5181.81 q^{45} +26881.9i q^{46} -78447.0 q^{47} -14188.4i q^{48} +105993. q^{49} +87861.6i q^{50} -19239.1i q^{51} -80269.6i q^{52} +230526. i q^{53} -99230.8 q^{54} +15767.9 q^{55} -85605.4i q^{56} +(48284.2 + 81857.8i) q^{57} -243101. q^{58} +112061. i q^{59} -4278.35i q^{60} -143589. q^{61} +40917.3 q^{62} -253959. q^{63} -32768.0 q^{64} -24204.5i q^{65} +128082. q^{66} +223311. i q^{67} -44432.6 q^{68} +65844.1i q^{69} -25813.4i q^{70} -281325. i q^{71} +97210.3i q^{72} +339869. q^{73} -543139. q^{74} +215207. i q^{75} +(189050. - 111512. i) q^{76} +772779. q^{77} -196611. i q^{78} -467067. i q^{79} -9880.85 q^{80} +148430. q^{81} -15388.0 q^{82} +838605. q^{83} -209681. i q^{84} -13398.2 q^{85} +224707. i q^{86} -595449. q^{87} -295804. i q^{88} +865320. i q^{89} +29312.8i q^{90} -1.18625e6i q^{91} +152067. q^{92} +100222. q^{93} +443763. i q^{94} +(57006.1 - 33625.3i) q^{95} -80261.5 q^{96} -1.02215e6i q^{97} -599584. i q^{98} -877539. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 320 q^{4} - 112 q^{5} + 160 q^{6} - 224 q^{7} - 2890 q^{9}+O(q^{10}) \) 10 * q - 320 * q^4 - 112 * q^5 + 160 * q^6 - 224 * q^7 - 2890 * q^9	\( 10 q - 320 q^{4} - 112 q^{5} + 160 q^{6} - 224 q^{7} - 2890 q^{9} + 3644 q^{11} + 10240 q^{16} - 10420 q^{17} - 17230 q^{19} + 3584 q^{20} + 37712 q^{23} - 5120 q^{24} - 52078 q^{25} - 7104 q^{26} + 7168 q^{28} + 94688 q^{30} - 161720 q^{35} + 92480 q^{36} + 25152 q^{38} - 78876 q^{39} + 53792 q^{42} + 6308 q^{43} - 116608 q^{44} + 309808 q^{45} + 322220 q^{47} - 235770 q^{49} - 321728 q^{54} - 377880 q^{55} + 24228 q^{57} + 445920 q^{58} + 426304 q^{61} + 59424 q^{62} - 517916 q^{63} - 327680 q^{64} - 1417312 q^{66} + 333440 q^{68} - 786076 q^{73} - 293280 q^{74} + 551360 q^{76} + 2303716 q^{77} - 114688 q^{80} + 5261090 q^{81} - 455136 q^{82} - 101500 q^{83} - 1261380 q^{85} - 2460732 q^{87} - 1206784 q^{92} - 2827032 q^{93} + 3106292 q^{95} + 163840 q^{96} + 1061428 q^{99}+O(q^{100}) \) 10 * q - 320 * q^4 - 112 * q^5 + 160 * q^6 - 224 * q^7 - 2890 * q^9 + 3644 * q^11 + 10240 * q^16 - 10420 * q^17 - 17230 * q^19 + 3584 * q^20 + 37712 * q^23 - 5120 * q^24 - 52078 * q^25 - 7104 * q^26 + 7168 * q^28 + 94688 * q^30 - 161720 * q^35 + 92480 * q^36 + 25152 * q^38 - 78876 * q^39 + 53792 * q^42 + 6308 * q^43 - 116608 * q^44 + 309808 * q^45 + 322220 * q^47 - 235770 * q^49 - 321728 * q^54 - 377880 * q^55 + 24228 * q^57 + 445920 * q^58 + 426304 * q^61 + 59424 * q^62 - 517916 * q^63 - 327680 * q^64 - 1417312 * q^66 + 333440 * q^68 - 786076 * q^73 - 293280 * q^74 + 551360 * q^76 + 2303716 * q^77 - 114688 * q^80 + 5261090 * q^81 - 455136 * q^82 - 101500 * q^83 - 1261380 * q^85 - 2460732 * q^87 - 1206784 * q^92 - 2827032 * q^93 + 3106292 * q^95 + 163840 * q^96 + 1061428 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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