LMFDB - Embedded newform 144.7.q.c.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,7,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.1277880413$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{13} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.4
Root			$8.88570i$ of defining polynomial
Character	$\chi$	$=$	144.113
Dual form			144.7.q.c.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.9408 - 22.4894i) q^{3} +(202.253 + 116.771i) q^{5} +(-95.5752 - 165.541i) q^{7} +(-282.543 - 672.020i) q^{9} +O(q^{10})$	\(q+(14.9408 - 22.4894i) q^{3} +(202.253 + 116.771i) q^{5} +(-95.5752 - 165.541i) q^{7} +(-282.543 - 672.020i) q^{9} +(673.077 - 388.601i) q^{11} +(45.5802 - 78.9472i) q^{13} +(5647.92 - 2803.88i) q^{15} -7047.39i q^{17} -2731.10 q^{19} +(-5150.89 - 323.897i) q^{21} +(17228.9 + 9947.14i) q^{23} +(19458.3 + 33702.7i) q^{25} +(-19334.7 - 3686.33i) q^{27} +(27104.3 - 15648.7i) q^{29} +(-6174.50 + 10694.6i) q^{31} +(1316.94 - 20943.1i) q^{33} -44641.5i q^{35} -27972.0 q^{37} +(-1094.47 - 2204.61i) q^{39} +(-37428.2 - 21609.2i) q^{41} +(-19256.1 - 33352.5i) q^{43} +(21327.2 - 168911. i) q^{45} +(143771. - 83006.2i) q^{47} +(40555.3 - 70243.8i) q^{49} +(-158491. - 105294. i) q^{51} +54741.5i q^{53} +181509. q^{55} +(-40804.8 + 61420.6i) q^{57} +(14102.1 + 8141.84i) q^{59} +(29443.7 + 50998.0i) q^{61} +(-84242.8 + 111001. i) q^{63} +(18437.4 - 10644.9i) q^{65} +(147998. - 256341. i) q^{67} +(481120. - 238849. i) q^{69} +157251. i q^{71} +80297.0 q^{73} +(1.04868e6 + 65942.7i) q^{75} +(-128659. - 74281.3i) q^{77} +(-188424. - 326360. i) q^{79} +(-371780. + 379749. i) q^{81} +(-733992. + 423771. i) q^{83} +(822929. - 1.42535e6i) q^{85} +(53032.3 - 843363. i) q^{87} -1128.91i q^{89} -17425.3 q^{91} +(148261. + 298646. i) q^{93} +(-552371. - 318912. i) q^{95} +(675152. + 1.16940e6i) q^{97} +(-451321. - 342525. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9	$ 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9} - 378 q^{11} + 1680 q^{13} + 10872 q^{15} + 2820 q^{19} + 24876 q^{21} + 76248 q^{23} + 8094 q^{25} - 127008 q^{27} + 97092 q^{29} - 21480 q^{31} - 246258 q^{33} - 25536 q^{37} - 42204 q^{39} - 410562 q^{41} - 71430 q^{43} + 13716 q^{45} - 347652 q^{47} - 135954 q^{49} - 336402 q^{51} - 580392 q^{55} - 522282 q^{57} - 369738 q^{59} + 135744 q^{61} + 103800 q^{63} - 753840 q^{65} + 289938 q^{67} + 2059272 q^{69} - 977700 q^{73} + 2115342 q^{75} - 159192 q^{77} + 764796 q^{79} - 1428282 q^{81} - 396900 q^{83} + 1619568 q^{85} - 3072636 q^{87} - 355584 q^{91} - 2526576 q^{93} + 2089260 q^{95} - 38874 q^{97} - 4398804 q^{99}+O(q^{100}) $ 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9 - 378 * q^11 + 1680 * q^13 + 10872 * q^15 + 2820 * q^19 + 24876 * q^21 + 76248 * q^23 + 8094 * q^25 - 127008 * q^27 + 97092 * q^29 - 21480 * q^31 - 246258 * q^33 - 25536 * q^37 - 42204 * q^39 - 410562 * q^41 - 71430 * q^43 + 13716 * q^45 - 347652 * q^47 - 135954 * q^49 - 336402 * q^51 - 580392 * q^55 - 522282 * q^57 - 369738 * q^59 + 135744 * q^61 + 103800 * q^63 - 753840 * q^65 + 289938 * q^67 + 2059272 * q^69 - 977700 * q^73 + 2115342 * q^75 - 159192 * q^77 + 764796 * q^79 - 1428282 * q^81 - 396900 * q^83 + 1619568 * q^85 - 3072636 * q^87 - 355584 * q^91 - 2526576 * q^93 + 2089260 * q^95 - 38874 * q^97 - 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	14.9408	−	22.4894i	0.553364	−	0.832939i
$3$	14.9408	−	22.4894i	0.553364	−	0.832939i
$4$		0			0
$5$	202.253	+	116.771i	1.61802	+	0.934165i	0.987431	+	0.158050i	$0.0505206\pi$
$5$	202.253	+	116.771i	1.61802	+	0.934165i	0.630591	+	0.776116i	$0.282813\pi$
$6$		0			0
$7$	−95.5752	−	165.541i	−0.278645	−	0.482627i	0.692403	−	0.721511i	$-0.256552\pi$
$7$	−95.5752	−	165.541i	−0.278645	−	0.482627i	−0.971048	+	0.238884i	$0.923219\pi$
$8$		0			0
$9$	−282.543	−	672.020i	−0.387576	−	0.921838i
$10$		0			0
$11$	673.077	−	388.601i	0.505693	−	0.291962i	−0.225369	−	0.974274i	$-0.572359\pi$
$11$	673.077	−	388.601i	0.505693	−	0.291962i	0.731061	+	0.682312i	$0.239025\pi$
$12$		0			0
$13$	45.5802	−	78.9472i	0.0207466	−	0.0359341i	−0.855466	−	0.517859i	$-0.826729\pi$
$13$	45.5802	−	78.9472i	0.0207466	−	0.0359341i	0.876212	+	0.481925i	$0.160062\pi$
$14$		0			0
$15$	5647.92	−	2803.88i	1.67346	−	0.830780i
$16$		0			0
$17$		−	7047.39i		−	1.43444i	−0.696848	−	0.717219i	$-0.745415\pi$
$17$		−	7047.39i		−	1.43444i	0.696848	−	0.717219i	$-0.254585\pi$
$18$		0			0
$19$	−2731.10			−0.398177			−0.199088	−	0.979982i	$-0.563798\pi$
$19$	−2731.10			−0.398177			−0.199088	+	0.979982i	$0.563798\pi$
$20$		0			0
$21$	−5150.89	−	323.897i	−0.556191	−	0.0349743i
$22$		0			0
$23$	17228.9	+	9947.14i	1.41604	+	0.817550i	0.995948	−	0.0899317i	$-0.0286649\pi$
$23$	17228.9	+	9947.14i	1.41604	+	0.817550i	0.420091	+	0.907482i	$0.361998\pi$
$24$		0			0
$25$	19458.3	+	33702.7i	1.24533	+	2.15697i
$26$		0			0
$27$	−19334.7	−	3686.33i	−0.982306	−	0.187285i
$28$		0			0
$29$	27104.3	−	15648.7i	1.11133	−	0.641629i	0.172159	−	0.985069i	$-0.444926\pi$
$29$	27104.3	−	15648.7i	1.11133	−	0.641629i	0.939175	+	0.343440i	$0.111592\pi$
$30$		0			0
$31$	−6174.50	+	10694.6i	−0.207261	+	0.358986i	−0.950851	−	0.309650i	$-0.899788\pi$
$31$	−6174.50	+	10694.6i	−0.207261	+	0.358986i	0.743590	+	0.668636i	$0.233121\pi$
$32$		0			0
$33$	1316.94	−	20943.1i	0.0366458	−	0.582773i
$34$		0			0
$35$		−	44641.5i		−	1.04120i
$36$		0			0
$37$	−27972.0			−0.552228			−0.276114	−	0.961125i	$-0.589047\pi$
$37$	−27972.0			−0.552228			−0.276114	+	0.961125i	$0.589047\pi$
$38$		0			0
$39$	−1094.47	−	2204.61i	−0.0184505	−	0.0371653i
$40$		0			0
$41$	−37428.2	−	21609.2i	−0.543059	−	0.313535i	0.203259	−	0.979125i	$-0.434847\pi$
$41$	−37428.2	−	21609.2i	−0.543059	−	0.313535i	−0.746318	+	0.665590i	$0.768180\pi$
$42$		0			0
$43$	−19256.1	−	33352.5i	−0.242193	−	0.419491i	0.719146	−	0.694860i	$-0.244533\pi$
$43$	−19256.1	−	33352.5i	−0.242193	−	0.419491i	−0.961339	+	0.275369i	$0.911200\pi$
$44$		0			0
$45$	21327.2	−	168911.i	0.234043	−	1.85361i
$46$		0			0
$47$	143771.	−	83006.2i	1.38477	−	0.799497i	0.392050	−	0.919944i	$-0.371766\pi$
$47$	143771.	−	83006.2i	1.38477	−	0.799497i	0.992720	+	0.120447i	$0.0384327\pi$
$48$		0			0
$49$	40555.3	−	70243.8i	0.344714	−	0.597062i
$50$		0			0
$51$	−158491.	−	105294.i	−1.19480	−	0.793767i
$52$		0			0
$53$			54741.5i			0.367696i	0.982955	+	0.183848i	$0.0588554\pi$
$53$			54741.5i			0.367696i	−0.982955	+	0.183848i	$0.941145\pi$
$54$		0			0
$55$	181509.			1.09096
$56$		0			0
$57$	−40804.8	+	61420.6i	−0.220337	+	0.331657i
$58$		0			0
$59$	14102.1	+	8141.84i	0.0686637	+	0.0396430i	0.533939	−	0.845523i	$-0.320711\pi$
$59$	14102.1	+	8141.84i	0.0686637	+	0.0396430i	−0.465275	+	0.885166i	$0.654045\pi$
$60$		0			0
$61$	29443.7	+	50998.0i	0.129719	+	0.224680i	0.923568	−	0.383436i	$-0.125259\pi$
$61$	29443.7	+	50998.0i	0.129719	+	0.224680i	−0.793849	+	0.608115i	$0.791926\pi$
$62$		0			0
$63$	−84242.8	+	111001.i	−0.336908	+	0.443920i
$64$		0			0
$65$	18437.4	−	10644.9i	0.0671368	−	0.0387614i
$66$		0			0
$67$	147998.	−	256341.i	0.492076	−	0.852301i	−0.507882	−	0.861427i	$-0.669571\pi$
$67$	147998.	−	256341.i	0.492076	−	0.852301i	0.999958	+	0.00912565i	$0.00290482\pi$
$68$		0			0
$69$	481120.	−	238849.i	1.46456	−	0.727071i
$70$		0			0
$71$			157251.i			0.439358i	0.975572	+	0.219679i	$0.0705010\pi$
$71$			157251.i			0.439358i	−0.975572	+	0.219679i	$0.929499\pi$
$72$		0			0
$73$	80297.0			0.206410			0.103205	−	0.994660i	$-0.467090\pi$
$73$	80297.0			0.206410			0.103205	+	0.994660i	$0.467090\pi$
$74$		0			0
$75$	1.04868e6	+	65942.7i	2.48575	+	0.156309i
$76$		0			0
$77$	−128659.	−	74281.3i	−0.281817	−	0.162707i
$78$		0			0
$79$	−188424.	−	326360.i	−0.382169	−	0.661936i	0.609203	−	0.793014i	$-0.291489\pi$
$79$	−188424.	−	326360.i	−0.382169	−	0.661936i	−0.991372	+	0.131078i	$0.958156\pi$
$80$		0			0
$81$	−371780.	+	379749.i	−0.699570	+	0.714564i
$82$		0			0
$83$	−733992.	+	423771.i	−1.28368	+	0.741134i	−0.977519	−	0.210846i	$-0.932378\pi$
$83$	−733992.	+	423771.i	−1.28368	+	0.741134i	−0.306162	+	0.951980i	$0.599045\pi$
$84$		0			0
$85$	822929.	−	1.42535e6i	1.34000	−	2.32095i
$86$		0			0
$87$	53032.3	−	843363.i	0.0805346	−	1.28073i
$88$		0			0
$89$		−	1128.91i		−	0.00160136i	−1.00000		0.000800679i	$-0.999745\pi$
$89$		−	1128.91i		−	0.00160136i	1.00000		0.000800679i	$-0.000254864\pi$
$90$		0			0
$91$	−17425.3			−0.0231237
$92$		0			0
$93$	148261.	+	298646.i	0.184323	+	0.371286i
$94$		0			0
$95$	−552371.	−	318912.i	−0.644259	−	0.371963i
$96$		0			0
$97$	675152.	+	1.16940e6i	0.739753	+	1.28129i	0.952607	+	0.304205i	$0.0983908\pi$
$97$	675152.	+	1.16940e6i	0.739753	+	1.28129i	−0.212854	+	0.977084i	$0.568276\pi$
$98$		0			0
$99$	−451321.	−	342525.i	−0.465136	−	0.353009i
$100$		0			0
$101$	−137557.	+	79418.5i	−0.133511	+	0.0770828i	−0.565268	−	0.824907i	$-0.691227\pi$
$101$	−137557.	+	79418.5i	−0.133511	+	0.0770828i	0.431757	+	0.901990i	$0.357894\pi$
$102$		0			0
$103$	248614.	−	430612.i	0.227517	−	0.394071i	−0.729555	−	0.683923i	$-0.760273\pi$
$103$	248614.	−	430612.i	0.227517	−	0.394071i	0.957072	+	0.289851i	$0.0936059\pi$
$104$		0			0
$105$	−1.00396e6	−	666981.i	−0.867257	−	0.576164i
$106$		0			0
$107$			207159.i			0.169103i	0.996419	+	0.0845516i	$0.0269458\pi$
$107$			207159.i			0.169103i	−0.996419	+	0.0845516i	$0.973054\pi$
$108$		0			0
$109$	−2.30287e6			−1.77824			−0.889120	−	0.457673i	$-0.848683\pi$
$109$	−2.30287e6			−1.77824			−0.889120	+	0.457673i	$0.848683\pi$
$110$		0			0
$111$	−417925.	+	629073.i	−0.305583	+	0.459973i
$112$		0			0
$113$	−677545.	−	391181.i	−0.469573	−	0.271108i	0.246488	−	0.969146i	$-0.420723\pi$
$113$	−677545.	−	391181.i	−0.469573	−	0.271108i	−0.716061	+	0.698038i	$0.754057\pi$
$114$		0			0
$115$	2.32307e6	+	4.02367e6i	1.52745	+	2.64563i
$116$		0			0
$117$	−65932.5	−	8324.83i	−0.0411663	−	0.00519778i
$118$		0			0
$119$	−1.16663e6	+	673556.i	−0.692298	+	0.399699i
$120$		0			0
$121$	−583759.	+	1.01110e6i	−0.329517	+	0.570739i
$122$		0			0
$123$	−1.04518e6	+	518876.i	−0.561665	+	0.278836i
$124$		0			0
$125$			5.43954e6i			2.78504i
$126$		0			0
$127$	−1.19415e6			−0.582970			−0.291485	−	0.956575i	$-0.594149\pi$
$127$	−1.19415e6			−0.582970			−0.291485	+	0.956575i	$0.594149\pi$
$128$		0			0
$129$	−1.03778e6	−	65257.4i	−0.483432	−	0.0303991i
$130$		0			0
$131$	2.17543e6	+	1.25598e6i	0.967678	+	0.558689i	0.898528	−	0.438917i	$-0.144638\pi$
$131$	2.17543e6	+	1.25598e6i	0.967678	+	0.558689i	0.0691503	+	0.997606i	$0.477971\pi$
$132$		0			0
$133$	261025.	+	452108.i	0.110950	+	0.192171i
$134$		0			0
$135$	−3.48004e6	−	3.00330e6i	−1.41444	−	1.22067i
$136$		0			0
$137$	703636.	−	406244.i	0.273644	−	0.157989i	−0.356898	−	0.934143i	$-0.616166\pi$
$137$	703636.	−	406244.i	0.273644	−	0.157989i	0.630543	+	0.776155i	$0.282832\pi$
$138$		0			0
$139$	350555.	−	607179.i	0.130530	−	0.226085i	−0.793351	−	0.608765i	$-0.791665\pi$
$139$	350555.	−	607179.i	0.130530	−	0.226085i	0.923881	+	0.382679i	$0.124999\pi$
$140$		0			0
$141$	281302.	−	4.47350e6i	0.100350	−	1.59584i
$142$		0			0
$143$		−	70850.1i		−	0.0242288i
$144$		0			0
$145$	7.30923e6			2.39755
$146$		0			0
$147$	−973808.	−	1.96156e6i	−0.306564	−	0.617519i
$148$		0			0
$149$	265134.	+	153075.i	0.0801505	+	0.0462749i	0.539540	−	0.841960i	$-0.318598\pi$
$149$	265134.	+	153075.i	0.0801505	+	0.0462749i	−0.459389	+	0.888235i	$0.651932\pi$
$150$		0			0
$151$	923784.	+	1.60004e6i	0.268312	+	0.464730i	0.968426	−	0.249301i	$-0.0802010\pi$
$151$	923784.	+	1.60004e6i	0.268312	+	0.464730i	−0.700114	+	0.714031i	$0.746868\pi$
$152$		0			0
$153$	−4.73599e6	+	1.99119e6i	−1.32232	+	0.555953i
$154$		0			0
$155$	−2.49762e6	+	1.44200e6i	−0.670704	+	0.387231i
$156$		0			0
$157$	−1.57533e6	+	2.72854e6i	−0.407072	+	0.705070i	−0.994560	−	0.104163i	$-0.966784\pi$
$157$	−1.57533e6	+	2.72854e6i	−0.407072	+	0.705070i	0.587488	+	0.809233i	$0.300117\pi$
$158$		0			0
$159$	1.23110e6	+	817883.i	0.306268	+	0.203470i
$160$		0			0
$161$		−	3.80280e6i		−	0.911225i
$162$		0			0
$163$	1.29782e6			0.299676			0.149838	−	0.988711i	$-0.452125\pi$
$163$	1.29782e6			0.299676			0.149838	+	0.988711i	$0.452125\pi$
$164$		0			0
$165$	2.71189e6	−	4.08202e6i	0.603700	−	0.908706i
$166$		0			0
$167$	1.41556e6	+	817272.i	0.303933	+	0.175476i	0.644208	−	0.764850i	$-0.277187\pi$
$167$	1.41556e6	+	817272.i	0.303933	+	0.175476i	−0.340275	+	0.940326i	$0.610520\pi$
$168$		0			0
$169$	2.40925e6	+	4.17294e6i	0.499139	+	0.864534i
$170$		0			0
$171$	771651.	+	1.83535e6i	0.154324	+	0.367055i
$172$		0			0
$173$	−8.21215e6	+	4.74129e6i	−1.58606	+	0.915710i	−0.592108	+	0.805859i	$0.701704\pi$
$173$	−8.21215e6	+	4.74129e6i	−1.58606	+	0.915710i	−0.993948	+	0.109851i	$0.964963\pi$
$174$		0			0
$175$	3.71946e6	−	6.44229e6i	0.694009	−	1.20206i
$176$		0			0
$177$	393802.	−	195501.i	0.0710162	−	0.0352557i
$178$		0			0
$179$			9.23510e6i			1.61021i	0.593133	+	0.805105i	$0.297891\pi$
$179$			9.23510e6i			1.61021i	−0.593133	+	0.805105i	$0.702109\pi$
$180$		0			0
$181$	4.59474e6			0.774864			0.387432	−	0.921898i	$-0.373362\pi$
$181$	4.59474e6			0.774864			0.387432	+	0.921898i	$0.373362\pi$
$182$		0			0
$183$	1.58683e6	+	99782.6i	0.258926	+	0.0162818i
$184$		0			0
$185$	−5.65742e6	−	3.26631e6i	−0.893517	−	0.515873i
$186$		0			0
$187$	−2.73863e6	−	4.74344e6i	−0.418801	−	0.725385i
$188$		0			0
$189$	1.23768e6	+	3.55301e6i	0.183326	+	0.526273i
$190$		0			0
$191$	−6.79391e6	+	3.92247e6i	−0.975034	+	0.562936i	−0.900767	−	0.434302i	$-0.856995\pi$
$191$	−6.79391e6	+	3.92247e6i	−0.975034	+	0.562936i	−0.0742671	+	0.997238i	$0.523662\pi$
$192$		0			0
$193$	2.71892e6	−	4.70931e6i	0.378203	−	0.655066i	−0.612598	−	0.790395i	$-0.709876\pi$
$193$	2.71892e6	−	4.70931e6i	0.378203	−	0.655066i	0.990801	+	0.135328i	$0.0432089\pi$
$194$		0			0
$195$	36074.7	−	573689.i	0.00486517	−	0.0773701i
$196$		0			0
$197$			1.01096e7i			1.32232i	0.750246	+	0.661159i	$0.229935\pi$
$197$			1.01096e7i			1.32232i	−0.750246	+	0.661159i	$0.770065\pi$
$198$		0			0
$199$	6.91799e6			0.877851			0.438925	−	0.898523i	$-0.355359\pi$
$199$	6.91799e6			0.877851			0.438925	+	0.898523i	$0.355359\pi$
$200$		0			0
$201$	−3.55372e6	−	7.15833e6i	−0.437618	−	0.881502i
$202$		0			0
$203$	−5.18100e6	−	2.99125e6i	−0.619335	−	0.357573i
$204$		0			0
$205$	−5.04663e6	−	8.74102e6i	−0.585787	−	1.01461i
$206$		0			0
$207$	1.81676e6	−	1.43887e7i	0.204826	−	1.62222i
$208$		0			0
$209$	−1.83824e6	+	1.06131e6i	−0.201355	+	0.116252i
$210$		0			0
$211$	−4.27596e6	+	7.40617e6i	−0.455183	+	0.788400i	−0.998699	−	0.0509990i	$-0.983759\pi$
$211$	−4.27596e6	+	7.40617e6i	−0.455183	+	0.788400i	0.543516	+	0.839399i	$0.317093\pi$
$212$		0			0
$213$	3.53648e6	+	2.34946e6i	0.365959	+	0.243125i
$214$		0			0
$215$		−	8.99417e6i		−	0.904994i
$216$		0			0
$217$	2.36052e6			0.231008
$218$		0			0
$219$	1.19970e6	−	1.80583e6i	0.114220	−	0.171927i
$220$		0			0
$221$	−556372.	−	321222.i	−0.0515452	−	0.0297597i
$222$		0			0
$223$	−2.62933e6	−	4.55413e6i	−0.237099	−	0.410668i	0.722782	−	0.691077i	$-0.242863\pi$
$223$	−2.62933e6	−	4.55413e6i	−0.237099	−	0.410668i	−0.959881	+	0.280409i	$0.909530\pi$
$224$		0			0
$225$	1.71511e7	−	2.25988e7i	1.50572	−	1.98398i
$226$		0			0
$227$	7.00311e6	−	4.04325e6i	0.598706	−	0.345663i	−0.169827	−	0.985474i	$-0.554321\pi$
$227$	7.00311e6	−	4.04325e6i	0.598706	−	0.345663i	0.768532	+	0.639811i	$0.220987\pi$
$228$		0			0
$229$	6.10057e6	−	1.05665e7i	0.508001	−	0.879883i	−0.491957	−	0.870620i	$-0.663718\pi$
$229$	6.10057e6	−	1.05665e7i	0.508001	−	0.879883i	0.999957	−	0.00926306i	$-0.00294857\pi$
$230$		0			0
$231$	−3.59281e6	+	1.78363e6i	−0.291473	+	0.144700i
$232$		0			0
$233$			5.57473e6i			0.440713i	0.975419	+	0.220357i	$0.0707221\pi$
$233$			5.57473e6i			0.440713i	−0.975419	+	0.220357i	$0.929278\pi$
$234$		0			0
$235$	3.87708e7			2.98745
$236$		0			0
$237$	−1.01549e7	−	638556.i	−0.762832	−	0.0479683i
$238$		0			0
$239$	−1.42628e7	−	8.23463e6i	−1.04475	−	0.603185i	−0.123573	−	0.992336i	$-0.539435\pi$
$239$	−1.42628e7	−	8.23463e6i	−1.04475	−	0.603185i	−0.921174	+	0.389151i	$0.872769\pi$
$240$		0			0
$241$	−2.30270e6	−	3.98840e6i	−0.164508	−	0.284936i	0.771972	−	0.635656i	$-0.219270\pi$
$241$	−2.30270e6	−	3.98840e6i	−0.164508	−	0.284936i	−0.936480	+	0.350720i	$0.885937\pi$
$242$		0			0
$243$	2.98560e6	+	1.40349e7i	0.208071	+	0.978114i
$244$		0			0
$245$	1.64048e7	−	9.47133e6i	1.11551	−	0.644040i
$246$		0			0
$247$	−124484.	+	215612.i	−0.00826080	+	0.0143081i
$248$		0			0
$249$	−1.43613e6	+	2.28385e7i	−0.0930240	+	1.47935i
$250$		0			0
$251$			1.58119e7i			0.999913i	0.866051	+	0.499956i	$0.166651\pi$
$251$			1.58119e7i			0.999913i	−0.866051	+	0.499956i	$0.833349\pi$
$252$		0			0
$253$	1.54619e7			0.954774
$254$		0			0
$255$	−1.97601e7	−	3.98031e7i	−1.19170	−	2.40047i
$256$		0			0
$257$	1.62608e7	+	9.38815e6i	0.957946	+	0.553071i	0.895540	−	0.444980i	$-0.146789\pi$
$257$	1.62608e7	+	9.38815e6i	0.957946	+	0.553071i	0.0624061	+	0.998051i	$0.480123\pi$
$258$		0			0
$259$	2.67343e6	+	4.63052e6i	0.153876	+	0.266520i
$260$		0			0
$261$	−1.81744e7	−	1.37932e7i	−1.02220	−	0.775790i
$262$		0			0
$263$	7.38572e6	−	4.26415e6i	0.406000	−	0.234404i	−0.283070	−	0.959099i	$-0.591353\pi$
$263$	7.38572e6	−	4.26415e6i	0.406000	−	0.234404i	0.689069	+	0.724695i	$0.258019\pi$
$264$		0			0
$265$	−6.39220e6	+	1.10716e7i	−0.343489	+	0.594940i
$266$		0			0
$267$	−25388.4	−	16866.8i	−0.00133383	−	0.000886134i
$268$		0			0
$269$		−	1.62898e7i		−	0.836871i	−0.908247	−	0.418436i	$-0.862579\pi$
$269$		−	1.62898e7i		−	0.836871i	0.908247	−	0.418436i	$-0.137421\pi$
$270$		0			0
$271$	−2.43919e7			−1.22557			−0.612785	−	0.790250i	$-0.709951\pi$
$271$	−2.43919e7			−1.22557			−0.612785	+	0.790250i	$0.709951\pi$
$272$		0			0
$273$	−260349.	+	391885.i	−0.0127958	+	0.0192606i
$274$		0			0
$275$	2.61938e7	+	1.51230e7i	1.25951	+	0.727177i
$276$		0			0
$277$	1.65615e7	+	2.86854e7i	0.779223	+	1.34965i	0.932390	+	0.361453i	$0.117719\pi$
$277$	1.65615e7	+	2.86854e7i	0.779223	+	1.34965i	−0.153168	+	0.988200i	$0.548947\pi$
$278$		0			0
$279$	8.93151e6	+	1.12772e6i	0.411256	+	0.0519264i
$280$		0			0
$281$	−3.13249e6	+	1.80854e6i	−0.141179	+	0.0815098i	−0.568926	−	0.822389i	$-0.692641\pi$
$281$	−3.13249e6	+	1.80854e6i	−0.141179	+	0.0815098i	0.427747	+	0.903899i	$0.359308\pi$
$282$		0			0
$283$	−1.61928e7	+	2.80467e7i	−0.714435	+	1.23744i	0.248742	+	0.968570i	$0.419983\pi$
$283$	−1.61928e7	+	2.80467e7i	−0.714435	+	1.23744i	−0.963177	+	0.268868i	$0.913351\pi$
$284$		0			0
$285$	−1.54250e7	+	7.65767e6i	−0.666333	+	0.330797i
$286$		0			0
$287$			8.26120e6i			0.349460i
$288$		0			0
$289$	−2.55282e7			−1.05761
$290$		0			0
$291$	3.63864e7	+	2.28804e6i	1.47659	+	0.0928507i
$292$		0			0
$293$	−1.44996e7	−	8.37133e6i	−0.576437	−	0.332806i	0.183279	−	0.983061i	$-0.441329\pi$
$293$	−1.44996e7	−	8.37133e6i	−0.576437	−	0.332806i	−0.759716	+	0.650255i	$0.774662\pi$
$294$		0			0
$295$	1.90146e6	+	3.29342e6i	0.0740662	+	0.128286i
$296$		0			0
$297$	−1.44463e7	+	5.03231e6i	−0.551425	+	0.192087i
$298$		0			0
$299$	1.57060e6	−	906785.i	0.0587559	−	0.0339227i
$300$		0			0
$301$	−3.68080e6	+	6.37534e6i	−0.134972	+	0.233778i
$302$		0			0
$303$	−269144.	+	4.28015e6i	−0.00967511	+	0.153862i
$304$		0			0
$305$			1.37527e7i			0.484716i
$306$		0			0
$307$	−1.09311e7			−0.377790			−0.188895	−	0.981997i	$-0.560491\pi$
$307$	−1.09311e7			−0.377790			−0.188895	+	0.981997i	$0.560491\pi$
$308$		0			0
$309$	−5.96969e6	−	1.20249e7i	−0.202338	−	0.407573i
$310$		0			0
$311$	−4.40580e7	−	2.54369e7i	−1.46468	−	0.845635i	−0.465461	−	0.885068i	$-0.654112\pi$
$311$	−4.40580e7	−	2.54369e7i	−1.46468	−	0.845635i	−0.999222	+	0.0394328i	$0.987445\pi$
$312$		0			0
$313$	−1.19934e7	−	2.07732e7i	−0.391120	−	0.677440i	0.601478	−	0.798890i	$-0.294579\pi$
$313$	−1.19934e7	−	2.07732e7i	−0.391120	−	0.677440i	−0.992598	+	0.121450i	$0.961246\pi$
$314$		0			0
$315$	−3.00000e7	+	1.26131e7i	−0.959819	+	0.403544i
$316$		0			0
$317$	1.93571e7	−	1.11758e7i	0.607662	−	0.350834i	−0.164388	−	0.986396i	$-0.552565\pi$
$317$	1.93571e7	−	1.11758e7i	0.607662	−	0.350834i	0.772050	+	0.635562i	$0.219232\pi$
$318$		0			0
$319$	1.21622e7	−	2.10655e7i	0.374662	−	0.648934i
$320$		0			0
$321$	4.65886e6	+	3.09512e6i	0.140853	+	0.0935756i
$322$		0			0
$323$			1.92471e7i			0.571160i
$324$		0			0
$325$	3.54765e6			0.103345
$326$		0			0
$327$	−3.44069e7	+	5.17902e7i	−0.984015	+	1.48117i
$328$		0			0
$329$	−2.74819e7	−	1.58667e7i	−0.771718	−	0.445551i
$330$		0			0
$331$	−2.20105e7	−	3.81233e7i	−0.606941	−	1.05125i	−0.991742	−	0.128252i	$-0.959063\pi$
$331$	−2.20105e7	−	3.81233e7i	−0.606941	−	1.05125i	0.384801	−	0.923000i	$-0.374270\pi$
$332$		0			0
$333$	7.90329e6	+	1.87978e7i	0.214030	+	0.509065i
$334$		0			0
$335$	5.98661e7	−	3.45637e7i	1.59238	−	0.919361i
$336$		0			0
$337$	−2.44378e7	+	4.23275e7i	−0.638516	+	1.10594i	0.347242	+	0.937776i	$0.387118\pi$
$337$	−2.44378e7	+	4.23275e7i	−0.638516	+	1.10594i	−0.985758	+	0.168167i	$0.946215\pi$
$338$		0			0
$339$	−1.89205e7	+	9.39298e6i	−0.485661	+	0.241104i
$340$		0			0
$341$			9.59768e6i			0.242049i
$342$		0			0
$343$	−3.79930e7			−0.941501
$344$		0			0
$345$	1.25198e8	+	7.87271e6i	3.04889	+	0.191720i
$346$		0			0
$347$	−4.77428e7	−	2.75643e7i	−1.14267	−	0.659719i	−0.195577	−	0.980688i	$-0.562658\pi$
$347$	−4.77428e7	−	2.75643e7i	−1.14267	−	0.659719i	−0.947089	+	0.320970i	$0.895991\pi$
$348$		0			0
$349$	−9.97084e6	−	1.72700e7i	−0.234561	−	0.406271i	0.724584	−	0.689186i	$-0.242032\pi$
$349$	−9.97084e6	−	1.72700e7i	−0.234561	−	0.406271i	−0.959145	+	0.282915i	$0.908699\pi$
$350$		0			0
$351$	−1.17231e6	+	1.35840e6i	−0.0271094	+	0.0314128i
$352$		0			0
$353$	−6.52970e7	+	3.76992e7i	−1.48446	+	0.857054i	−0.999844	−	0.0176724i	$-0.994374\pi$
$353$	−6.52970e7	+	3.76992e7i	−1.48446	+	0.857054i	−0.484617	+	0.874726i	$0.661041\pi$
$354$		0			0
$355$	−1.83623e7	+	3.18045e7i	−0.410433	+	0.710891i
$356$		0			0
$357$	−2.28263e6	+	3.63003e7i	−0.0501685	+	0.797821i
$358$		0			0
$359$			5.29978e7i			1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$359$			5.29978e7i			1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$360$		0			0
$361$	−3.95870e7			−0.841455
$362$		0			0
$363$	1.40171e7	+	2.82350e7i	0.293049	+	0.590294i
$364$		0			0
$365$	1.62403e7	+	9.37633e6i	0.333976	+	0.192821i
$366$		0			0
$367$	2.03953e7	+	3.53257e7i	0.412602	+	0.714648i	0.995173	−	0.0981316i	$-0.0312866\pi$
$367$	2.03953e7	+	3.53257e7i	0.412602	+	0.714648i	−0.582571	+	0.812780i	$0.697953\pi$
$368$		0			0
$369$	−3.94673e6	+	3.12580e7i	−0.0785521	+	0.622131i
$370$		0			0
$371$	9.06196e6	−	5.23192e6i	0.177460	−	0.102457i
$372$		0			0
$373$	2.14508e7	−	3.71539e7i	0.413349	−	0.715941i	−0.581905	−	0.813257i	$-0.697692\pi$
$373$	2.14508e7	−	3.71539e7i	0.413349	−	0.715941i	0.995254	+	0.0973156i	$0.0310256\pi$
$374$		0			0
$375$	1.22332e8	+	8.12713e7i	2.31977	+	1.54114i
$376$		0			0
$377$		−	2.85308e6i		−	0.0532464i
$378$		0			0
$379$	3.56353e6			0.0654579			0.0327290	−	0.999464i	$-0.489580\pi$
$379$	3.56353e6			0.0654579			0.0327290	+	0.999464i	$0.489580\pi$
$380$		0			0
$381$	−1.78416e7	+	2.68556e7i	−0.322595	+	0.485579i
$382$		0			0
$383$	5.10154e7	+	2.94538e7i	0.908040	+	0.524257i	0.879800	−	0.475344i	$-0.157676\pi$
$383$	5.10154e7	+	2.94538e7i	0.908040	+	0.524257i	0.0282400	+	0.999601i	$0.491010\pi$
$384$		0			0
$385$	−1.73477e7	−	3.00472e7i	−0.303991	−	0.526528i
$386$		0			0
$387$	−1.69729e7	+	2.23640e7i	−0.292834	+	0.385847i
$388$		0			0
$389$	3.81501e7	−	2.20260e7i	0.648108	−	0.374185i	−0.139623	−	0.990205i	$-0.544589\pi$
$389$	3.81501e7	−	2.20260e7i	0.648108	−	0.374185i	0.787731	+	0.616020i	$0.211256\pi$
$390$		0			0
$391$	7.01014e7	−	1.21419e8i	1.17273	−	2.03122i
$392$		0			0
$393$	6.07490e7	−	3.01585e7i	1.00083	−	0.496858i
$394$		0			0
$395$		−	8.80097e7i		−	1.42804i
$396$		0			0
$397$	2.93968e6			0.0469818			0.0234909	−	0.999724i	$-0.492522\pi$
$397$	2.93968e6			0.0469818			0.0234909	+	0.999724i	$0.492522\pi$
$398$		0			0
$399$	1.40676e7	+	884594.i	0.221462	+	0.0139260i
$400$		0			0
$401$	−1.38960e7	−	8.02289e6i	−0.215505	−	0.124422i	0.388362	−	0.921507i	$-0.373041\pi$
$401$	−1.38960e7	−	8.02289e6i	−0.215505	−	0.124422i	−0.603867	+	0.797085i	$0.706374\pi$
$402$		0			0
$403$	562870.	+	974920.i	0.00859989	+	0.0148955i
$404$		0			0
$405$	−1.19537e8	+	3.33922e7i	−1.79944	+	0.502666i
$406$		0			0
$407$	−1.88273e7	+	1.08700e7i	−0.279258	+	0.161230i
$408$		0			0
$409$	9.04280e6	−	1.56626e7i	0.132170	−	0.228925i	−0.792343	−	0.610076i	$-0.791139\pi$
$409$	9.04280e6	−	1.56626e7i	0.132170	−	0.228925i	0.924513	+	0.381151i	$0.124472\pi$
$410$		0			0
$411$	1.37673e6	−	2.18939e7i	0.0198301	−	0.315354i
$412$		0			0
$413$		−	3.11263e6i		−	0.0441853i
$414$		0			0
$415$	−1.97936e8			−2.76937
$416$		0			0
$417$	−8.41748e6	−	1.69555e7i	−0.116084	−	0.233831i
$418$		0			0
$419$	6.46244e6	+	3.73109e6i	0.0878525	+	0.0507217i	0.543283	−	0.839550i	$-0.317181\pi$
$419$	6.46244e6	+	3.73109e6i	0.0878525	+	0.0507217i	−0.455430	+	0.890272i	$0.650515\pi$
$420$		0			0
$421$	1.16773e7	+	2.02257e7i	0.156494	+	0.271055i	0.933602	−	0.358312i	$-0.116648\pi$
$421$	1.16773e7	+	2.02257e7i	0.156494	+	0.271055i	−0.777108	+	0.629367i	$0.783314\pi$
$422$		0			0
$423$	−9.64032e7	−	7.31641e7i	−1.27371	−	0.966667i
$424$		0			0
$425$	2.37516e8	−	1.37130e8i	3.09405	−	1.78635i
$426$		0			0
$427$	5.62818e6	−	9.74829e6i	0.0722910	−	0.125212i
$428$		0			0
$429$	−1.59337e6	−	1.05856e6i	−0.0201811	−	0.0134074i
$430$		0			0
$431$		−	7.00387e7i		−	0.874795i	−0.899268	−	0.437397i	$-0.855900\pi$
$431$		−	7.00387e7i		−	0.874795i	0.899268	−	0.437397i	$-0.144100\pi$
$432$		0			0
$433$	−8.83901e7			−1.08878			−0.544390	−	0.838832i	$-0.683239\pi$
$433$	−8.83901e7			−1.08878			−0.544390	+	0.838832i	$0.683239\pi$
$434$		0			0
$435$	1.09206e8	−	1.64380e8i	1.32672	−	1.99701i
$436$		0			0
$437$	−4.70539e7	−	2.71666e7i	−0.563834	−	0.325530i
$438$		0			0
$439$	5.11723e7	+	8.86331e7i	0.604842	+	1.04762i	0.992076	+	0.125635i	$0.0400969\pi$
$439$	5.11723e7	+	8.86331e7i	0.604842	+	1.04762i	−0.387235	+	0.921981i	$0.626570\pi$
$440$		0			0
$441$	−5.86638e7	−	7.40707e6i	−0.683998	−	0.0863636i
$442$		0			0
$443$	1.10522e8	−	6.38100e7i	1.27127	−	0.733969i	0.296045	−	0.955174i	$-0.404332\pi$
$443$	1.10522e8	−	6.38100e7i	1.27127	−	0.733969i	0.975227	+	0.221205i	$0.0709990\pi$
$444$		0			0
$445$	131823.	−	228325.i	0.00149593	−	0.00259103i
$446$		0			0
$447$	7.40388e6	−	3.67562e6i	0.0828966	−	0.0411536i
$448$		0			0
$449$		−	1.44858e8i		−	1.60031i	−0.599795	−	0.800154i	$-0.704751\pi$
$449$		−	1.44858e8i		−	1.60031i	0.599795	−	0.800154i	$-0.295249\pi$
$450$		0			0
$451$	−3.35894e7			−0.366161
$452$		0			0
$453$	4.97860e7	+	3.13064e6i	0.535566	+	0.0336774i
$454$		0			0
$455$	−3.52432e6	−	2.03477e6i	−0.0374146	−	0.0216014i
$456$		0			0
$457$	5.09129e7	+	8.81838e7i	0.533433	+	0.923933i	0.999237	+	0.0390451i	$0.0124316\pi$
$457$	5.09129e7	+	8.81838e7i	0.533433	+	0.923933i	−0.465805	+	0.884888i	$0.654235\pi$
$458$		0			0
$459$	−2.59790e7	+	1.36259e8i	−0.268649	+	1.40906i
$460$		0			0
$461$	5.98283e7	−	3.45419e7i	0.610666	−	0.352568i	−0.162560	−	0.986699i	$-0.551975\pi$
$461$	5.98283e7	−	3.45419e7i	0.610666	−	0.352568i	0.773226	+	0.634130i	$0.218642\pi$
$462$		0			0
$463$	−6.74662e7	+	1.16855e8i	−0.679741	+	1.17735i	0.295318	+	0.955399i	$0.404574\pi$
$463$	−6.74662e7	+	1.16855e8i	−0.679741	+	1.17735i	−0.975059	+	0.221947i	$0.928759\pi$
$464$		0			0
$465$	−4.88684e6	+	7.77146e7i	−0.0486037	+	0.772936i
$466$		0			0
$467$			1.23430e8i			1.21191i	0.795500	+	0.605954i	$0.207208\pi$
$467$			1.23430e8i			1.21191i	−0.795500	+	0.605954i	$0.792792\pi$
$468$		0			0
$469$	−5.65798e7			−0.548458
$470$		0			0
$471$	3.78265e7	+	7.61948e7i	0.362021	+	0.729227i
$472$		0			0
$473$	−2.59216e7	−	1.49659e7i	−0.244951	−	0.141422i
$474$		0			0
$475$	−5.31424e7	−	9.20453e7i	−0.495861	−	0.858857i
$476$		0			0
$477$	3.67873e7	−	1.54668e7i	0.338956	−	0.142510i
$478$		0			0
$479$	6.01036e7	−	3.47008e7i	0.546882	−	0.315743i	−0.200981	−	0.979595i	$-0.564413\pi$
$479$	6.01036e7	−	3.47008e7i	0.546882	−	0.315743i	0.747864	+	0.663852i	$0.231080\pi$
$480$		0			0
$481$	−1.27497e6	+	2.20831e6i	−0.0114568	+	0.0198438i
$482$		0			0
$483$	−8.55225e7	−	5.68170e7i	−0.758995	−	0.504239i
$484$		0			0
$485$			3.15352e8i			2.76420i
$486$		0			0
$487$	2.01197e8			1.74195			0.870973	−	0.491331i	$-0.163489\pi$
$487$	2.01197e8			1.74195			0.870973	+	0.491331i	$0.163489\pi$
$488$		0			0
$489$	1.93905e7	−	2.91872e7i	0.165830	−	0.249612i
$490$		0			0
$491$	−1.72658e8	−	9.96841e7i	−1.45862	−	0.842135i	−0.459676	−	0.888087i	$-0.652035\pi$
$491$	−1.72658e8	−	9.96841e7i	−1.45862	−	0.842135i	−0.998944	+	0.0459519i	$0.985368\pi$
$492$		0			0
$493$	−1.10282e8	−	1.91015e8i	−0.920377	−	1.59414i
$494$		0			0
$495$	−5.12840e7	−	1.21978e8i	−0.422831	−	1.00569i
$496$		0			0
$497$	2.60315e7	−	1.50293e7i	0.212046	−	0.122425i
$498$		0			0
$499$	−4.38674e7	+	7.59805e7i	−0.353053	+	0.611506i	−0.986783	−	0.162049i	$-0.948190\pi$
$499$	−4.38674e7	+	7.59805e7i	−0.353053	+	0.611506i	0.633730	+	0.773555i	$0.281523\pi$
$500$		0			0
$501$	3.95295e7	−	1.96242e7i	0.314346	−	0.156056i
$502$		0			0
$503$		−	1.53094e8i		−	1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$503$		−	1.53094e8i		−	1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$504$		0			0
$505$	−3.70950e7			−0.288032
$506$		0			0
$507$	1.29843e8	+	8.16477e6i	0.996310	+	0.0626499i
$508$		0			0
$509$	1.05471e8	+	6.08939e7i	0.799799	+	0.461764i	0.843401	−	0.537285i	$-0.180550\pi$
$509$	1.05471e8	+	6.08939e7i	0.799799	+	0.461764i	−0.0436020	+	0.999049i	$0.513883\pi$
$510$		0			0
$511$	−7.67440e6	−	1.32924e7i	−0.0575151	−	0.0996190i
$512$		0			0
$513$	5.28050e7	+	1.00677e7i	0.391131	+	0.0745726i
$514$		0			0
$515$	1.00566e8	−	5.80617e7i	0.736255	−	0.425077i
$516$		0			0
$517$	6.45126e7	−	1.11739e8i	0.466845	−	0.808600i
$518$		0			0
$519$	−1.60679e7	+	2.55525e8i	−0.114936	+	1.82781i
$520$		0			0
$521$		−	1.44805e8i		−	1.02393i	−0.859006	−	0.511965i	$-0.828918\pi$
$521$		−	1.44805e8i		−	1.02393i	0.859006	−	0.511965i	$-0.171082\pi$
$522$		0			0
$523$	2.14387e8			1.49863			0.749313	−	0.662216i	$-0.230384\pi$
$523$	2.14387e8			1.49863			0.749313	+	0.662216i	$0.230384\pi$
$524$		0			0
$525$	−8.93111e7	−	1.79901e8i	−0.617202	−	1.24324i
$526$		0			0
$527$	7.53687e7	+	4.35141e7i	0.514943	+	0.297302i
$528$		0			0
$529$	1.23873e8	+	2.14554e8i	0.836777	+	1.44934i
$530$		0			0
$531$	1.48704e6	−	1.17773e7i	0.00993203	−	0.0786614i
$532$		0			0
$533$	−3.41197e6	+	1.96990e6i	−0.0225332	+	0.0130096i
$534$		0			0
$535$	−2.41900e7	+	4.18984e7i	−0.157970	+	0.273612i
$536$		0			0
$537$	2.07691e8	+	1.37980e8i	1.34121	+	0.891032i
$538$		0			0
$539$		−	6.30393e7i		−	0.402573i
$540$		0			0
$541$	3.66711e7			0.231596			0.115798	−	0.993273i	$-0.463057\pi$
$541$	3.66711e7			0.231596			0.115798	+	0.993273i	$0.463057\pi$
$542$		0			0
$543$	6.86493e7	−	1.03333e8i	0.428782	−	0.645415i
$544$		0			0
$545$	−4.65762e8	−	2.68908e8i	−2.87723	−	1.66117i
$546$		0			0
$547$	−1.50211e8	−	2.60172e8i	−0.917780	−	1.58964i	−0.802779	−	0.596277i	$-0.796646\pi$
$547$	−1.50211e8	−	2.60172e8i	−0.917780	−	1.58964i	−0.115001	−	0.993365i	$-0.536687\pi$
$548$		0			0
$549$	2.59526e7	−	3.41959e7i	0.156842	−	0.206660i
$550$		0			0
$551$	−7.40245e7	+	4.27381e7i	−0.442507	+	0.255482i
$552$		0			0
$553$	−3.60174e7	+	6.23839e7i	−0.212979	+	0.368890i
$554$		0			0
$555$	−1.57984e8	+	7.84303e7i	−0.924131	+	0.458780i
$556$		0			0
$557$			2.64642e8i			1.53141i	0.643190	+	0.765707i	$0.277611\pi$
$557$			2.64642e8i			1.53141i	−0.643190	+	0.765707i	$0.722389\pi$
$558$		0			0
$559$	−3.51078e6			−0.0200987
$560$		0			0
$561$	−1.47594e8	−	9.28100e6i	−0.835951	−	0.0525662i
$562$		0			0
$563$	5.98361e7	+	3.45464e7i	0.335304	+	0.193588i	0.658193	−	0.752849i	$-0.271321\pi$
$563$	5.98361e7	+	3.45464e7i	0.335304	+	0.193588i	−0.322890	+	0.946437i	$0.604654\pi$
$564$		0			0
$565$	−9.13569e7	−	1.58235e8i	−0.506519	−	0.877317i
$566$		0			0
$567$	9.83969e7	+	2.52503e7i	0.539799	+	0.138522i
$568$		0			0
$569$	−1.21080e8	+	6.99054e7i	−0.657256	+	0.379467i	−0.791231	−	0.611518i	$-0.790559\pi$
$569$	−1.21080e8	+	6.99054e7i	−0.657256	+	0.379467i	0.133975	+	0.990985i	$0.457226\pi$
$570$		0			0
$571$	1.02493e8	−	1.77523e8i	0.550537	−	0.953557i	−0.447699	−	0.894184i	$-0.647756\pi$
$571$	1.02493e8	−	1.77523e8i	0.550537	−	0.953557i	0.998236	−	0.0593731i	$-0.0189102\pi$
$572$		0			0
$573$	−1.32930e7	+	2.11396e8i	−0.0706574	+	1.12365i
$574$		0			0
$575$			7.74216e8i			4.07248i
$576$		0			0
$577$	1.77665e8			0.924854			0.462427	−	0.886657i	$-0.346979\pi$
$577$	1.77665e8			0.924854			0.462427	+	0.886657i	$0.346979\pi$
$578$		0			0
$579$	−6.52864e7	−	1.31508e8i	−0.336347	−	0.677510i
$580$		0			0
$581$	1.40303e8	+	8.10039e7i	0.715382	+	0.413026i
$582$		0			0
$583$	2.12726e7	+	3.68452e7i	0.107353	+	0.185941i
$584$		0			0
$585$	−1.23629e7	−	9.38270e6i	−0.0617524	−	0.0468662i
$586$		0			0
$587$	−2.92418e8	+	1.68828e8i	−1.44574	+	0.834698i	−0.998224	−	0.0595787i	$-0.981024\pi$
$587$	−2.92418e8	+	1.68828e8i	−1.44574	+	0.834698i	−0.447515	+	0.894276i	$0.647691\pi$
$588$		0			0
$589$	1.68632e7	−	2.92078e7i	0.0825264	−	0.142940i
$590$		0			0
$591$	2.27359e8	+	1.51046e8i	1.10141	+	0.731723i
$592$		0			0
$593$			1.84023e8i			0.882488i	0.897387	+	0.441244i	$0.145463\pi$
$593$			1.84023e8i			0.882488i	−0.897387	+	0.441244i	$0.854537\pi$
$594$		0			0
$595$	−3.14606e8			−1.49354
$596$		0			0
$597$	1.03361e8	−	1.55581e8i	0.485771	−	0.731197i
$598$		0			0
$599$	−1.41355e8	−	8.16115e7i	−0.657705	−	0.379726i	0.133697	−	0.991022i	$-0.457315\pi$
$599$	−1.41355e8	−	8.16115e7i	−0.657705	−	0.379726i	−0.791402	+	0.611296i	$0.790649\pi$
$600$		0			0
$601$	8.57858e7	+	1.48585e8i	0.395177	+	0.684467i	0.993124	−	0.117069i	$-0.0373498\pi$
$601$	8.57858e7	+	1.48585e8i	0.395177	+	0.684467i	−0.597947	+	0.801536i	$0.704017\pi$
$602$		0			0
$603$	−2.14082e8	−	2.70306e7i	−0.976400	−	0.123283i
$604$		0			0
$605$	−2.36134e8	+	1.36332e8i	−1.06633	+	0.615646i
$606$		0			0
$607$	9.26524e6	−	1.60479e7i	0.0414277	−	0.0717549i	−0.844568	−	0.535448i	$-0.820143\pi$
$607$	9.26524e6	−	1.60479e7i	0.0414277	−	0.0717549i	0.885996	+	0.463693i	$0.153476\pi$
$608$		0			0
$609$	−1.44680e8	+	7.18256e7i	−0.640555	+	0.318000i
$610$		0			0
$611$		−	1.51338e7i		−	0.0663473i
$612$		0			0
$613$	3.64689e8			1.58322			0.791609	−	0.611028i	$-0.209244\pi$
$613$	3.64689e8			1.58322			0.791609	+	0.611028i	$0.209244\pi$
$614$		0			0
$615$	−2.71981e8	−	1.71027e7i	−1.16927	−	0.0735256i
$616$		0			0
$617$	−6.50805e7	−	3.75743e7i	−0.277074	−	0.159969i	0.355024	−	0.934857i	$-0.384473\pi$
$617$	−6.50805e7	−	3.75743e7i	−0.277074	−	0.159969i	−0.632098	+	0.774888i	$0.717806\pi$
$618$		0			0
$619$	−1.42862e6	−	2.47445e6i	−0.00602345	−	0.0104329i	0.862998	−	0.505207i	$-0.168584\pi$
$619$	−1.42862e6	−	2.47445e6i	−0.00602345	−	0.0104329i	−0.869021	+	0.494774i	$0.835251\pi$
$620$		0			0
$621$	−2.96448e8	−	2.55837e8i	−1.23787	−	1.06829i
$622$		0			0
$623$	−186881.	+	107896.i	−0.000772859	+	0.000446210i
$624$		0			0
$625$	−3.31143e8	+	5.73557e8i	−1.35636	+	2.34929i
$626$		0			0
$627$	−3.59669e6	+	5.71976e7i	−0.0145915	+	0.232047i
$628$		0			0
$629$			1.97130e8i			0.792137i
$630$		0			0
$631$	9.87283e7			0.392965			0.196482	−	0.980507i	$-0.437048\pi$
$631$	9.87283e7			0.392965			0.196482	+	0.980507i	$0.437048\pi$
$632$		0			0
$633$	1.02674e8	+	2.06818e8i	0.404807	+	0.815412i
$634$		0			0
$635$	−2.41519e8	−	1.39441e8i	−0.943259	−	0.544591i
$636$		0			0
$637$	−3.69704e6	−	6.40345e6i	−0.0143033	−	0.0247740i
$638$		0			0
$639$	1.05676e8	−	4.44301e7i	0.405017	−	0.170285i
$640$		0			0
$641$	4.02095e8	−	2.32150e8i	1.52670	−	0.881442i	0.527206	−	0.849738i	$-0.323240\pi$
$641$	4.02095e8	−	2.32150e8i	1.52670	−	0.881442i	0.999497	−	0.0317046i	$-0.0100936\pi$
$642$		0			0
$643$	−1.98827e8	+	3.44378e8i	−0.747897	+	1.29540i	0.200932	+	0.979605i	$0.435603\pi$
$643$	−1.98827e8	+	3.44378e8i	−0.747897	+	1.29540i	−0.948829	+	0.315790i	$0.897730\pi$
$644$		0			0
$645$	−2.02273e8	−	1.34380e8i	−0.753805	−	0.500791i
$646$		0			0
$647$		−	1.29737e8i		−	0.479017i	−0.970894	−	0.239509i	$-0.923014\pi$
$647$		−	1.29737e8i		−	0.479017i	0.970894	−	0.239509i	$-0.0769863\pi$
$648$		0			0
$649$	1.26557e7			0.0462970
$650$		0			0
$651$	3.52681e7	−	5.30865e7i	0.127832	−	0.192416i
$652$		0			0
$653$	−3.10514e8	−	1.79275e8i	−1.11517	−	0.643844i	−0.175007	−	0.984567i	$-0.555995\pi$
$653$	−3.10514e8	−	1.79275e8i	−1.11517	−	0.643844i	−0.940164	+	0.340723i	$0.889328\pi$
$654$		0			0
$655$	2.93324e8	+	5.08052e8i	1.04382	+	1.80794i
$656$		0			0
$657$	−2.26873e7	−	5.39612e7i	−0.0799995	−	0.190277i
$658$		0			0
$659$	3.63796e8	−	2.10038e8i	1.27117	−	0.733908i	0.295958	−	0.955201i	$-0.404361\pi$
$659$	3.63796e8	−	2.10038e8i	1.27117	−	0.733908i	0.975207	+	0.221293i	$0.0710278\pi$
$660$		0			0
$661$	2.06107e8	−	3.56988e8i	0.713655	−	1.23609i	−0.249821	−	0.968292i	$-0.580372\pi$
$661$	2.06107e8	−	3.56988e8i	0.713655	−	1.23609i	0.963476	−	0.267794i	$-0.0862948\pi$
$662$		0			0
$663$	−1.55367e7	+	7.71313e6i	−0.0533113	+	0.0264661i
$664$		0			0
$665$			1.21920e8i			0.414582i
$666$		0			0
$667$	6.22638e8			2.09826
$668$		0			0
$669$	−1.41704e8	−	8.91060e6i	−0.473264	−	0.0297597i
$670$		0			0
$671$	3.96358e7	+	2.28837e7i	0.131196	+	0.0757459i
$672$		0			0
$673$	−2.35837e8	−	4.08482e8i	−0.773690	−	1.34007i	−0.935528	−	0.353252i	$-0.885076\pi$
$673$	−2.35837e8	−	4.08482e8i	−0.773690	−	1.34007i	0.161838	−	0.986817i	$-0.448258\pi$
$674$		0			0
$675$	−2.51981e8	−	7.23362e8i	−0.819325	−	2.35204i
$676$		0			0
$677$	6.57025e7	−	3.79334e7i	0.211746	−	0.122252i	−0.390376	−	0.920655i	$-0.627655\pi$
$677$	6.57025e7	−	3.79334e7i	0.211746	−	0.122252i	0.602123	+	0.798404i	$0.294322\pi$
$678$		0			0
$679$	1.29056e8	−	2.23531e8i	0.412256	−	0.714049i
$680$		0			0
$681$	1.37023e7	−	2.17905e8i	0.0433862	−	0.689963i
$682$		0			0
$683$			2.50625e8i			0.786616i	0.919407	+	0.393308i	$0.128669\pi$
$683$			2.50625e8i			0.786616i	−0.919407	+	0.393308i	$0.871331\pi$
$684$		0			0
$685$	1.89750e8			0.590350
$686$		0			0
$687$	−1.46486e8	−	2.95070e8i	−0.451780	−	0.910029i
$688$		0			0
$689$	4.32169e6	+	2.49513e6i	0.0132128	+	0.00762843i
$690$		0			0
$691$	9.23965e7	+	1.60035e8i	0.280041	+	0.485045i	0.971394	−	0.237472i	$-0.0763187\pi$
$691$	9.23965e7	+	1.60035e8i	0.280041	+	0.485045i	−0.691354	+	0.722516i	$0.742985\pi$
$692$		0			0
$693$	−1.35668e7	+	1.07449e8i	−0.0407642	+	0.322851i
$694$		0			0
$695$	1.41801e8	−	8.18691e7i	0.422402	−	0.243874i
$696$		0			0
$697$	−1.52288e8	+	2.63771e8i	−0.449747	+	0.778984i
$698$		0			0
$699$	1.25372e8	+	8.32911e7i	0.367087	+	0.243875i
$700$		0			0
$701$			1.48993e8i			0.432525i	0.976335	+	0.216262i	$0.0693866\pi$
$701$			1.48993e8i			0.432525i	−0.976335	+	0.216262i	$0.930613\pi$
$702$		0			0
$703$	7.63942e7			0.219885
$704$		0			0
$705$	5.79267e8	−	8.71929e8i	1.65315	−	2.48836i
$706$		0			0
$707$	2.62940e7	+	1.51809e7i	0.0744045	+	0.0429575i
$708$		0			0
$709$	1.76797e8	+	3.06222e8i	0.496063	+	0.859206i	0.999990	−	0.00454038i	$-0.00144525\pi$
$709$	1.76797e8	+	3.06222e8i	0.496063	+	0.859206i	−0.503927	+	0.863746i	$0.668112\pi$
$710$		0			0
$711$	−1.66083e8	+	2.18836e8i	−0.462078	+	0.608848i
$712$		0			0
$713$	−2.12760e8	+	1.22837e8i	−0.586978	+	0.338892i
$714$		0			0
$715$	8.27321e6	−	1.43296e7i	0.0226337	−	0.0392028i
$716$		0			0
$717$	−3.98290e8	+	1.97729e8i	−1.08054	+	0.536430i
$718$		0			0
$719$		−	1.15532e8i		−	0.310824i	−0.987850	−	0.155412i	$-0.950330\pi$
$719$		−	1.15532e8i		−	0.310824i	0.987850	−	0.155412i	$-0.0496705\pi$
$720$		0			0
$721$	−9.50453e7			−0.253586
$722$		0			0
$723$	−1.24101e8	−	7.80369e6i	−0.328367	−	0.0206484i
$724$		0			0
$725$	1.05481e9	+	6.08993e8i	2.76795	+	1.59808i
$726$		0			0
$727$	−4.29149e7	−	7.43308e7i	−0.111688	−	0.193449i	0.804763	−	0.593596i	$-0.202292\pi$
$727$	−4.29149e7	−	7.43308e7i	−0.111688	−	0.193449i	−0.916451	+	0.400147i	$0.868959\pi$
$728$		0			0
$729$	3.60242e8	+	1.42548e8i	0.929849	+	0.367942i
$730$		0			0
$731$	−2.35048e8	+	1.35705e8i	−0.601734	+	0.347411i
$732$		0			0
$733$	1.65809e8	−	2.87190e8i	0.421014	−	0.729218i	−0.575025	−	0.818136i	$-0.695008\pi$
$733$	1.65809e8	−	2.87190e8i	0.421014	−	0.729218i	0.996039	+	0.0889179i	$0.0283409\pi$
$734$		0			0
$735$	3.20977e7	−	5.10444e8i	0.0808372	−	1.28554i
$736$		0			0
$737$		−	2.30049e8i		−	0.574670i
$738$		0			0
$739$	4.32705e7			0.107216			0.0536079	−	0.998562i	$-0.482928\pi$
$739$	4.32705e7			0.107216			0.0536079	+	0.998562i	$0.482928\pi$
$740$		0			0
$741$	2.98909e6	+	6.02099e6i	0.00734657	+	0.0147984i
$742$		0			0
$743$	−4.91261e8	−	2.83630e8i	−1.19770	−	0.691490i	−0.237654	−	0.971350i	$-0.576379\pi$
$743$	−4.91261e8	−	2.83630e8i	−1.19770	−	0.691490i	−0.960041	+	0.279860i	$0.909712\pi$
$744$		0			0
$745$	3.57493e7	+	6.19197e7i	0.0864568	+	0.149748i
$746$		0			0
$747$	4.92166e8	+	3.73524e8i	1.18073	+	0.896100i
$748$		0			0
$749$	3.42932e7	−	1.97992e7i	0.0816137	−	0.0471197i
$750$		0			0
$751$	−3.02087e7	+	5.23230e7i	−0.0713202	+	0.123530i	−0.899480	−	0.436962i	$-0.856055\pi$
$751$	−3.02087e7	+	5.23230e7i	−0.0713202	+	0.123530i	0.828160	+	0.560492i	$0.189388\pi$
$752$		0			0
$753$	3.55599e8	+	2.36243e8i	0.832867	+	0.553316i
$754$		0			0
$755$			4.31484e8i			1.00259i
$756$		0			0
$757$	2.57979e8			0.594697			0.297349	−	0.954769i	$-0.403898\pi$
$757$	2.57979e8			0.594697			0.297349	+	0.954769i	$0.403898\pi$
$758$		0			0
$759$	2.31013e8	−	3.47728e8i	0.528338	−	0.795269i
$760$		0			0
$761$	−2.59671e8	−	1.49921e8i	−0.589209	−	0.340180i	0.175576	−	0.984466i	$-0.443821\pi$
$761$	−2.59671e8	−	1.49921e8i	−0.589209	−	0.340180i	−0.764785	+	0.644286i	$0.777155\pi$
$762$		0			0
$763$	2.20098e8	+	3.81220e8i	0.495498	+	0.858227i
$764$		0			0
$765$	−1.19038e9	−	1.50301e8i	−2.65889	−	0.335720i
$766$		0			0
$767$	1.28555e6	−	742213.i	0.00284907	−	0.00164491i
$768$		0			0
$769$	2.17509e8	−	3.76737e8i	0.478299	−	0.828438i	−0.521392	−	0.853317i	$-0.674587\pi$
$769$	2.17509e8	−	3.76737e8i	0.478299	−	0.828438i	0.999690	+	0.0248798i	$0.00792030\pi$
$770$		0			0
$771$	4.54083e8	−	2.25427e8i	0.990768	−	0.491862i
$772$		0			0
$773$		−	5.68247e8i		−	1.23027i	−0.788423	−	0.615133i	$-0.789102\pi$
$773$		−	5.68247e8i		−	1.23027i	0.788423	−	0.615133i	$-0.210898\pi$
$774$		0			0
$775$	−4.80581e8			−1.03243
$776$		0			0
$777$	1.44081e8	+	9.06006e6i	0.307144	+	0.0193138i
$778$		0			0
$779$	1.02220e8	+	5.90167e7i	0.216233	+	0.124842i
$780$		0			0
$781$	6.11079e7	+	1.05842e8i	0.128276	+	0.222180i
$782$		0			0
$783$	−5.81741e8	+	2.02647e8i	−1.21184	+	0.422139i
$784$		0			0
$785$	−6.37228e8	+	3.67904e8i	−1.31730	+	0.760545i
$786$		0			0
$787$	4.11256e8	−	7.12316e8i	0.843700	−	1.46133i	−0.0430452	−	0.999073i	$-0.513706\pi$
$787$	4.11256e8	−	7.12316e8i	0.843700	−	1.46133i	0.886745	−	0.462258i	$-0.152961\pi$
$788$		0			0
$789$	1.44509e7	−	2.29810e8i	0.0294214	−	0.467884i
$790$		0			0
$791$			1.49549e8i			0.302171i
$792$		0			0
$793$	5.36820e6			0.0107649
$794$		0			0
$795$	1.53489e8	+	3.09175e8i	0.305474	+	0.615324i
$796$		0			0
$797$	−4.33986e8	−	2.50562e8i	−0.857236	−	0.494925i	0.00584980	−	0.999983i	$-0.498138\pi$
$797$	−4.33986e8	−	2.50562e8i	−0.857236	−	0.494925i	−0.863086	+	0.505058i	$0.831471\pi$
$798$		0			0
$799$	−5.84977e8	−	1.01321e9i	−1.14683	−	1.98637i
$800$		0			0
$801$	−758648.	+	318965.i	−0.00147619	+	0.000620648i
$802$		0			0
$803$	5.40461e7	−	3.12035e7i	0.104380	−	0.0602638i
$804$		0			0
$805$	4.44055e8	−	7.69126e8i	0.851234	−	1.47438i
$806$		0			0
$807$	−3.66347e8	−	2.43383e8i	−0.697063	−	0.463095i
$808$		0			0
$809$		−	4.25261e8i		−	0.803174i	−0.915821	−	0.401587i	$-0.868459\pi$
$809$		−	4.25261e8i		−	0.803174i	0.915821	−	0.401587i	$-0.131541\pi$
$810$		0			0
$811$	−3.17254e8			−0.594763			−0.297381	−	0.954759i	$-0.596113\pi$
$811$	−3.17254e8			−0.594763			−0.297381	+	0.954759i	$0.596113\pi$
$812$		0			0
$813$	−3.64436e8	+	5.48559e8i	−0.678187	+	1.02083i
$814$		0			0
$815$	2.62488e8	+	1.51548e8i	0.484883	+	0.279947i
$816$		0			0
$817$	5.25901e7	+	9.10888e7i	0.0964357	+	0.167032i
$818$		0			0
$819$	4.92340e6	+	1.17102e7i	0.00896218	+	0.0213163i
$820$		0			0
$821$	2.06773e7	−	1.19380e7i	0.0373649	−	0.0215726i	−0.481201	−	0.876610i	$-0.659799\pi$
$821$	2.06773e7	−	1.19380e7i	0.0373649	−	0.0215726i	0.518566	+	0.855038i	$0.326466\pi$
$822$		0			0
$823$	5.26330e8	−	9.11631e8i	0.944189	−	1.63538i	0.186821	−	0.982394i	$-0.440182\pi$
$823$	5.26330e8	−	9.11631e8i	0.944189	−	1.63538i	0.757368	−	0.652988i	$-0.226485\pi$
$824$		0			0
$825$	7.31465e8	−	3.63132e8i	1.30266	−	0.646700i
$826$		0			0
$827$			1.79106e8i			0.316660i	0.987386	+	0.158330i	$0.0506109\pi$
$827$			1.79106e8i			0.316660i	−0.987386	+	0.158330i	$0.949389\pi$
$828$		0			0
$829$	−1.21964e8			−0.214076			−0.107038	−	0.994255i	$-0.534137\pi$
$829$	−1.21964e8			−0.214076			−0.107038	+	0.994255i	$0.534137\pi$
$830$		0			0
$831$	8.92561e8	+	5.61259e7i	1.55537	+	0.0978048i
$832$		0			0
$833$	−4.95036e8	−	2.85809e8i	−0.856449	−	0.494471i
$834$		0			0
$835$	1.90867e8	+	3.30591e8i	0.327847	+	0.567848i
$836$		0			0
$837$	1.58806e8	−	1.84015e8i	0.270826	−	0.313817i
$838$		0			0
$839$	−4.91209e8	+	2.83600e8i	−0.831727	+	0.480198i	−0.854444	−	0.519544i	$-0.826102\pi$
$839$	−4.91209e8	+	2.83600e8i	−0.831727	+	0.480198i	0.0227168	+	0.999742i	$0.492768\pi$
$840$		0			0
$841$	1.92351e8	−	3.33162e8i	0.323375	−	0.560102i
$842$		0			0
$843$	−6.12902e6	+	9.74688e7i	−0.0102308	+	0.162698i
$844$		0			0
$845$			1.12532e9i			1.86511i
$846$		0			0
$847$	2.23171e8			0.367272
$848$		0			0
$849$	3.88819e8	+	7.83208e8i	0.635367	+	1.27983i
$850$		0			0
$851$	−4.81928e8	−	2.78241e8i	−0.781977	−	0.451474i
$852$		0			0
$853$	4.59944e8	+	7.96646e8i	0.741068	+	1.28357i	0.952010	+	0.306068i	$0.0990135\pi$
$853$	4.59944e8	+	7.96646e8i	0.741068	+	1.28357i	−0.210942	+	0.977499i	$0.567653\pi$
$854$		0			0
$855$	−5.82465e7	+	4.61311e8i	−0.0931904	+	0.738066i
$856$		0			0
$857$	5.10368e8	−	2.94661e8i	0.810851	−	0.468145i	−0.0364004	−	0.999337i	$-0.511589\pi$
$857$	5.10368e8	−	2.94661e8i	0.810851	−	0.468145i	0.847251	+	0.531192i	$0.178256\pi$
$858$		0			0
$859$	−5.10737e7	+	8.84623e7i	−0.0805783	+	0.139566i	−0.903498	−	0.428591i	$-0.859010\pi$
$859$	−5.10737e7	+	8.84623e7i	−0.0805783	+	0.139566i	0.822920	+	0.568157i	$0.192343\pi$
$860$		0			0
$861$	1.85789e8	+	1.23429e8i	0.291079	+	0.193379i
$862$		0			0
$863$		−	8.24326e8i		−	1.28253i	−0.767321	−	0.641264i	$-0.778410\pi$
$863$		−	8.24326e8i		−	1.28253i	0.767321	−	0.641264i	$-0.221590\pi$
$864$		0			0
$865$	−2.21457e9			−3.42170
$866$		0			0
$867$	−3.81412e8	+	5.74112e8i	−0.585244	+	0.880926i
$868$		0			0
$869$	−2.53648e8	−	1.46444e8i	−0.386520	−	0.223158i
$870$		0			0
$871$	−1.34916e7	−	2.33681e7i	−0.0204178	−	0.0353646i
$872$		0			0
$873$	5.95099e8	−	7.84121e8i	0.894431	−	1.17853i
$874$		0			0
$875$	9.00467e8	−	5.19885e8i	1.34414	−	0.776038i
$876$		0			0
$877$	−3.55715e8	+	6.16116e8i	−0.527355	+	0.913406i	0.472137	+	0.881525i	$0.343483\pi$
$877$	−3.55715e8	+	6.16116e8i	−0.527355	+	0.913406i	−0.999492	+	0.0318803i	$0.989850\pi$
$878$		0			0
$879$	−4.04901e8	+	2.01011e8i	−0.596187	+	0.295974i
$880$		0			0
$881$			1.35023e8i			0.197460i	0.995114	+	0.0987302i	$0.0314781\pi$
$881$			1.35023e8i			0.197460i	−0.995114	+	0.0987302i	$0.968522\pi$
$882$		0			0
$883$	−4.91077e8			−0.713293			−0.356646	−	0.934239i	$-0.616080\pi$
$883$	−4.91077e8			−0.713293			−0.356646	+	0.934239i	$0.616080\pi$
$884$		0			0
$885$	1.02476e8	+	6.44389e6i	0.147840	+	0.00929648i
$886$		0			0
$887$	8.12126e8	+	4.68881e8i	1.16373	+	0.671881i	0.952195	−	0.305490i	$-0.0988201\pi$
$887$	8.12126e8	+	4.68881e8i	1.16373	+	0.671881i	0.211536	+	0.977370i	$0.432153\pi$
$888$		0			0
$889$	1.14131e8	+	1.97680e8i	0.162442	+	0.281357i
$890$		0			0
$891$	−1.02666e8	+	4.00074e8i	−0.145142	+	0.565598i
$892$		0			0
$893$	−3.92652e8	+	2.26698e8i	−0.551383	+	0.318341i
$894$		0			0
$895$	−1.07839e9	+	1.86782e9i	−1.50420	+	2.60535i
$896$		0			0
$897$	3.07303e6	−	4.88699e7i	0.00425784	−	0.0677117i
$898$		0			0
$899$			3.86491e8i			0.531938i
$900$		0			0
$901$	3.85784e8			0.527437
$902$		0			0
$903$	8.83830e7	+	1.78032e8i	0.120034	+	0.241788i
$904$		0			0
$905$	9.29300e8	+	5.36531e8i	1.25375	+	0.723851i
$906$		0			0
$907$	3.58999e8	+	6.21805e8i	0.481140	+	0.833360i	0.999766	−	0.0216419i	$-0.00688937\pi$
$907$	3.58999e8	+	6.21805e8i	0.481140	+	0.833360i	−0.518625	+	0.855002i	$0.673556\pi$
$908$		0			0
$909$	9.22365e7	+	7.00018e7i	0.122804	+	0.0932004i
$910$		0			0
$911$	6.57988e8	−	3.79889e8i	0.870287	−	0.502461i	0.00284370	−	0.999996i	$-0.499095\pi$
$911$	6.57988e8	−	3.79889e8i	0.870287	−	0.502461i	0.867444	+	0.497535i	$0.165761\pi$
$912$		0			0
$913$	−3.29355e8	+	5.70460e8i	−0.432765	+	0.749572i
$914$		0			0
$915$	3.09288e8	+	2.05476e8i	0.403739	+	0.268224i
$916$		0			0
$917$		−	4.80163e8i		−	0.622703i
$918$		0			0
$919$	9.15355e8			1.17935			0.589676	−	0.807640i	$-0.299256\pi$
$919$	9.15355e8			1.17935			0.589676	+	0.807640i	$0.299256\pi$
$920$		0			0
$921$	−1.63320e8	+	2.45834e8i	−0.209055	+	0.314676i
$922$		0			0
$923$	1.24145e7	+	7.16754e6i	0.0157879	+	0.00911517i
$924$		0			0
$925$	−5.44287e8	−	9.42733e8i	−0.687706	−	1.19114i
$926$		0			0
$927$	−3.59624e8	−	4.54072e7i	−0.451450	−	0.0570014i
$928$		0			0
$929$	4.28783e8	−	2.47558e8i	0.534799	−	0.308766i	−0.208170	−	0.978093i	$-0.566751\pi$
$929$	4.28783e8	−	2.47558e8i	0.534799	−	0.308766i	0.742968	+	0.669327i	$0.233417\pi$
$930$		0			0
$931$	−1.10760e8	+	1.91842e8i	−0.137257	+	0.237736i
$932$		0			0
$933$	−1.23032e9	+	6.10788e8i	−1.51487	+	0.752048i
$934$		0			0
$935$		−	1.27916e9i		−	1.56492i
$936$		0			0
$937$	5.39309e8			0.655570			0.327785	−	0.944752i	$-0.393698\pi$
$937$	5.39309e8			0.655570			0.327785	+	0.944752i	$0.393698\pi$
$938$		0			0
$939$	−6.46368e8	−	4.06448e7i	−0.780698	−	0.0490918i
$940$		0			0
$941$	7.63585e8	+	4.40856e8i	0.916408	+	0.529088i	0.882487	−	0.470336i	$-0.155867\pi$
$941$	7.63585e8	+	4.40856e8i	0.916408	+	0.529088i	0.0339205	+	0.999425i	$0.489201\pi$
$942$		0			0
$943$	−4.29898e8	−	7.44606e8i	−0.512662	−	0.887956i
$944$		0			0
$945$	−1.64563e8	+	8.63131e8i	−0.195001	+	1.02278i
$946$		0			0
$947$	−7.71869e8	+	4.45639e8i	−0.908853	+	0.524727i	−0.880062	−	0.474859i	$-0.842499\pi$
$947$	−7.71869e8	+	4.45639e8i	−0.908853	+	0.524727i	−0.0287913	+	0.999585i	$0.509166\pi$
$948$		0			0
$949$	3.65995e6	−	6.33922e6i	0.00428230	−	0.00741716i
$950$		0			0
$951$	3.78740e7	−	6.02305e8i	0.0440352	−	0.700285i
$952$		0			0
$953$		−	2.13491e8i		−	0.246661i	−0.992366	−	0.123331i	$-0.960642\pi$
$953$		−	2.13491e8i		−	0.246661i	0.992366	−	0.123331i	$-0.0393576\pi$
$954$		0			0
$955$	−1.83212e9			−2.10350
$956$		0			0
$957$	−2.92037e8	−	5.88257e8i	−0.333198	−	0.671168i
$958$		0			0
$959$	−1.34500e8	−	7.76537e7i	−0.152499	−	0.0880454i
$960$		0			0
$961$	3.67503e8	+	6.36534e8i	0.414086	+	0.717218i
$962$		0			0
$963$	1.39215e8	−	5.85312e7i	0.155886	−	0.0655403i
$964$		0			0
$965$	1.09982e9	−	6.34981e8i	1.22388	−	0.706608i
$966$		0			0
$967$	−6.06482e8	+	1.05046e9i	−0.670716	+	1.16171i	0.306986	+	0.951714i	$0.400680\pi$
$967$	−6.06482e8	+	1.05046e9i	−0.670716	+	1.16171i	−0.977701	+	0.210000i	$0.932654\pi$
$968$		0			0
$969$	4.32855e8	+	2.87568e8i	0.475742	+	0.316060i
$970$		0			0
$971$		−	4.38734e8i		−	0.479230i	−0.970868	−	0.239615i	$-0.922979\pi$
$971$		−	4.38734e8i		−	0.479230i	0.970868	−	0.239615i	$-0.0770212\pi$
$972$		0			0
$973$	−1.34017e8			−0.145486
$974$		0			0
$975$	5.30048e7	−	7.97844e7i	0.0571876	−	0.0860803i
$976$		0			0
$977$	−1.03164e9	−	5.95616e8i	−1.10623	−	0.638679i	−0.168376	−	0.985723i	$-0.553852\pi$
$977$	−1.03164e9	−	5.95616e8i	−1.10623	−	0.638679i	−0.937849	+	0.347044i	$0.887186\pi$
$978$		0			0
$979$	−438695.	−	759842.i	−0.000467535	−	0.000809795i
$980$		0			0
$981$	6.50660e8	+	1.54758e9i	0.689203	+	1.63925i
$982$		0			0
$983$	−4.17380e8	+	2.40974e8i	−0.439411	+	0.253694i	−0.703348	−	0.710846i	$-0.748312\pi$
$983$	−4.17380e8	+	2.40974e8i	−0.439411	+	0.253694i	0.263937	+	0.964540i	$0.414979\pi$
$984$		0			0
$985$	−1.18051e9	+	2.04470e9i	−1.23526	+	2.13954i
$986$		0			0
$987$	−7.67433e8	+	3.80988e8i	−0.798158	+	0.396242i
$988$		0			0
$989$		−	7.66170e8i		−	0.792021i
$990$		0			0
$991$	8.26440e8			0.849162			0.424581	−	0.905390i	$-0.360421\pi$
$991$	8.26440e8			0.849162			0.424581	+	0.905390i	$0.360421\pi$
$992$		0			0
$993$	−1.18622e9	−	7.45920e7i	−1.21149	−	0.0761807i
$994$		0			0
$995$	1.39918e9	+	8.07818e8i	1.42038	+	0.820058i
$996$		0			0
$997$	−6.50181e8	−	1.12615e9i	−0.656068	−	1.13634i	−0.981625	−	0.190820i	$-0.938885\pi$
$997$	−6.50181e8	−	1.12615e9i	−0.656068	−	1.13634i	0.325557	−	0.945522i	$-0.394448\pi$
$998$		0			0
$999$	5.40831e8	+	1.03114e8i	0.542457	+	0.103424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.7.q.c.113.4		12
3.2	odd	2		432.7.q.b.17.1		12
4.3	odd	2		18.7.d.a.5.5	✓	12
9.2	odd	6	inner	144.7.q.c.65.4		12
9.7	even	3		432.7.q.b.305.1		12
12.11	even	2		54.7.d.a.17.1		12
36.7	odd	6		54.7.d.a.35.1		12
36.11	even	6		18.7.d.a.11.5	yes	12
36.23	even	6		162.7.b.c.161.6		12
36.31	odd	6		162.7.b.c.161.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.5	✓	12	4.3	odd	2
18.7.d.a.11.5	yes	12	36.11	even	6
54.7.d.a.17.1		12	12.11	even	2
54.7.d.a.35.1		12	36.7	odd	6
144.7.q.c.65.4		12	9.2	odd	6	inner
144.7.q.c.113.4		12	1.1	even	1	trivial
162.7.b.c.161.6		12	36.23	even	6
162.7.b.c.161.7		12	36.31	odd	6
432.7.q.b.17.1		12	3.2	odd	2
432.7.q.b.305.1		12	9.7	even	3

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(14.9408 - 22.4894i) q^{3} +(202.253 + 116.771i) q^{5} +(-95.5752 - 165.541i) q^{7} +(-282.543 - 672.020i) q^{9} +O(q^{10})\)	\(q+(14.9408 - 22.4894i) q^{3} +(202.253 + 116.771i) q^{5} +(-95.5752 - 165.541i) q^{7} +(-282.543 - 672.020i) q^{9} +(673.077 - 388.601i) q^{11} +(45.5802 - 78.9472i) q^{13} +(5647.92 - 2803.88i) q^{15} -7047.39i q^{17} -2731.10 q^{19} +(-5150.89 - 323.897i) q^{21} +(17228.9 + 9947.14i) q^{23} +(19458.3 + 33702.7i) q^{25} +(-19334.7 - 3686.33i) q^{27} +(27104.3 - 15648.7i) q^{29} +(-6174.50 + 10694.6i) q^{31} +(1316.94 - 20943.1i) q^{33} -44641.5i q^{35} -27972.0 q^{37} +(-1094.47 - 2204.61i) q^{39} +(-37428.2 - 21609.2i) q^{41} +(-19256.1 - 33352.5i) q^{43} +(21327.2 - 168911. i) q^{45} +(143771. - 83006.2i) q^{47} +(40555.3 - 70243.8i) q^{49} +(-158491. - 105294. i) q^{51} +54741.5i q^{53} +181509. q^{55} +(-40804.8 + 61420.6i) q^{57} +(14102.1 + 8141.84i) q^{59} +(29443.7 + 50998.0i) q^{61} +(-84242.8 + 111001. i) q^{63} +(18437.4 - 10644.9i) q^{65} +(147998. - 256341. i) q^{67} +(481120. - 238849. i) q^{69} +157251. i q^{71} +80297.0 q^{73} +(1.04868e6 + 65942.7i) q^{75} +(-128659. - 74281.3i) q^{77} +(-188424. - 326360. i) q^{79} +(-371780. + 379749. i) q^{81} +(-733992. + 423771. i) q^{83} +(822929. - 1.42535e6i) q^{85} +(53032.3 - 843363. i) q^{87} -1128.91i q^{89} -17425.3 q^{91} +(148261. + 298646. i) q^{93} +(-552371. - 318912. i) q^{95} +(675152. + 1.16940e6i) q^{97} +(-451321. - 342525. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9	\( 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9} - 378 q^{11} + 1680 q^{13} + 10872 q^{15} + 2820 q^{19} + 24876 q^{21} + 76248 q^{23} + 8094 q^{25} - 127008 q^{27} + 97092 q^{29} - 21480 q^{31} - 246258 q^{33} - 25536 q^{37} - 42204 q^{39} - 410562 q^{41} - 71430 q^{43} + 13716 q^{45} - 347652 q^{47} - 135954 q^{49} - 336402 q^{51} - 580392 q^{55} - 522282 q^{57} - 369738 q^{59} + 135744 q^{61} + 103800 q^{63} - 753840 q^{65} + 289938 q^{67} + 2059272 q^{69} - 977700 q^{73} + 2115342 q^{75} - 159192 q^{77} + 764796 q^{79} - 1428282 q^{81} - 396900 q^{83} + 1619568 q^{85} - 3072636 q^{87} - 355584 q^{91} - 2526576 q^{93} + 2089260 q^{95} - 38874 q^{97} - 4398804 q^{99}+O(q^{100}) \) 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9 - 378 * q^11 + 1680 * q^13 + 10872 * q^15 + 2820 * q^19 + 24876 * q^21 + 76248 * q^23 + 8094 * q^25 - 127008 * q^27 + 97092 * q^29 - 21480 * q^31 - 246258 * q^33 - 25536 * q^37 - 42204 * q^39 - 410562 * q^41 - 71430 * q^43 + 13716 * q^45 - 347652 * q^47 - 135954 * q^49 - 336402 * q^51 - 580392 * q^55 - 522282 * q^57 - 369738 * q^59 + 135744 * q^61 + 103800 * q^63 - 753840 * q^65 + 289938 * q^67 + 2059272 * q^69 - 977700 * q^73 + 2115342 * q^75 - 159192 * q^77 + 764796 * q^79 - 1428282 * q^81 - 396900 * q^83 + 1619568 * q^85 - 3072636 * q^87 - 355584 * q^91 - 2526576 * q^93 + 2089260 * q^95 - 38874 * q^97 - 4398804 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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