LMFDB - Embedded newform 75.9.c.h.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$12$
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} + 64 x^{10} + 385774 x^{8} - 323639784 x^{6} - 48708595080 x^{4} + 21531002169600 x^{2} + 82\!\cdots\!00 $ x^12 + 64x^10 + 385774x^8 - 323639784x^6 - 48708595080x^4 + 21531002169600*x^2 + 8291960024040000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{18}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.3
Root			$-20.6227 - 2.01276i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.h.26.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.5844i q^{2} +(-31.2287 - 74.7380i) q^{3} -53.2123 q^{4} +(-1314.22 + 549.140i) q^{6} +3426.92 q^{7} -3565.91i q^{8} +(-4610.53 + 4667.95i) q^{9} +O(q^{10})$	\(q-17.5844i q^{2} +(-31.2287 - 74.7380i) q^{3} -53.2123 q^{4} +(-1314.22 + 549.140i) q^{6} +3426.92 q^{7} -3565.91i q^{8} +(-4610.53 + 4667.95i) q^{9} -15724.8i q^{11} +(1661.75 + 3976.98i) q^{12} -27065.2 q^{13} -60260.4i q^{14} -76326.8 q^{16} -14218.4i q^{17} +(82083.2 + 81073.6i) q^{18} -210073. q^{19} +(-107018. - 256121. i) q^{21} -276511. q^{22} +60230.4i q^{23} +(-266509. + 111359. i) q^{24} +475926. i q^{26} +(492854. + 198808. i) q^{27} -182354. q^{28} -758209. i q^{29} +333379. q^{31} +429291. i q^{32} +(-1.17524e6 + 491064. i) q^{33} -250023. q^{34} +(245337. - 248392. i) q^{36} +683328. q^{37} +3.69401e6i q^{38} +(845213. + 2.02280e6i) q^{39} +1.23950e6i q^{41} +(-4.50374e6 + 1.88186e6i) q^{42} -1.15567e6 q^{43} +836750. i q^{44} +1.05912e6 q^{46} -1.52165e6i q^{47} +(2.38359e6 + 5.70451e6i) q^{48} +5.97898e6 q^{49} +(-1.06266e6 + 444024. i) q^{51} +1.44020e6 q^{52} +4.73392e6i q^{53} +(3.49592e6 - 8.66656e6i) q^{54} -1.22201e7i q^{56} +(6.56030e6 + 1.57004e7i) q^{57} -1.33327e7 q^{58} +1.30629e7i q^{59} -6.62861e6 q^{61} -5.86228e6i q^{62} +(-1.57999e7 + 1.59967e7i) q^{63} -1.19908e7 q^{64} +(8.63509e6 + 2.06659e7i) q^{66} -2.47970e7 q^{67} +756595. i q^{68} +(4.50150e6 - 1.88092e6i) q^{69} +1.07106e7i q^{71} +(1.66455e7 + 1.64407e7i) q^{72} +3.48665e7 q^{73} -1.20159e7i q^{74} +1.11784e7 q^{76} -5.38875e7i q^{77} +(3.55698e7 - 1.48626e7i) q^{78} -5.01757e7 q^{79} +(-532723. - 4.30434e7i) q^{81} +2.17960e7 q^{82} -4.50568e7i q^{83} +(5.69469e6 + 1.36288e7i) q^{84} +2.03217e7i q^{86} +(-5.66670e7 + 2.36779e7i) q^{87} -5.60730e7 q^{88} -7.30781e7i q^{89} -9.27503e7 q^{91} -3.20500e6i q^{92} +(-1.04110e7 - 2.49161e7i) q^{93} -2.67573e7 q^{94} +(3.20843e7 - 1.34062e7i) q^{96} +1.45948e8 q^{97} -1.05137e8i q^{98} +(7.34023e7 + 7.24995e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9}+O(q^{10}) $ 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9	$ 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9} + 413328 q^{16} - 276192 q^{19} - 604044 q^{21} - 1173336 q^{24} - 279216 q^{31} + 1225344 q^{34} - 10311840 q^{36} - 3780864 q^{39} + 37414536 q^{46} + 6222300 q^{49} + 3931248 q^{51} + 53281692 q^{54} - 91958256 q^{61} - 57497760 q^{64} + 111065040 q^{66} - 8138748 q^{69} - 232646880 q^{76} - 420402672 q^{79} + 98480772 q^{81} + 528357816 q^{84} - 100211328 q^{91} - 543022776 q^{94} + 333306864 q^{96} + 640360080 q^{99}+O(q^{100}) $ 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9 + 413328 * q^16 - 276192 * q^19 - 604044 * q^21 - 1173336 * q^24 - 279216 * q^31 + 1225344 * q^34 - 10311840 * q^36 - 3780864 * q^39 + 37414536 * q^46 + 6222300 * q^49 + 3931248 * q^51 + 53281692 * q^54 - 91958256 * q^61 - 57497760 * q^64 + 111065040 * q^66 - 8138748 * q^69 - 232646880 * q^76 - 420402672 * q^79 + 98480772 * q^81 + 528357816 * q^84 - 100211328 * q^91 - 543022776 * q^94 + 333306864 * q^96 + 640360080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	17.5844i		−	1.09903i	−0.835485	−	0.549514i	$-0.814813\pi$
$2$		−	17.5844i		−	1.09903i	0.835485	−	0.549514i	$-0.185187\pi$
$3$	−31.2287	−	74.7380i	−0.385540	−	0.922691i
$3$	−31.2287	−	74.7380i	−0.385540	−	0.922691i
$4$	−53.2123			−0.207860
$5$		0			0
$5$		0			0
$6$	−1314.22	+	549.140i	−1.01406	+	0.423719i
$7$	3426.92			1.42729			0.713644	−	0.700508i	$-0.247043\pi$
$7$	3426.92			1.42729			0.713644	+	0.700508i	$0.247043\pi$
$8$		−	3565.91i		−	0.870583i
$9$	−4610.53	+	4667.95i	−0.702718	+	0.711469i
$10$		0			0
$11$		−	15724.8i		−	1.07402i	−0.843575	−	0.537011i	$-0.819553\pi$
$11$		−	15724.8i		−	1.07402i	0.843575	−	0.537011i	$-0.180447\pi$
$12$	1661.75	+	3976.98i	0.0801385	+	0.191791i
$13$	−27065.2			−0.947628			−0.473814	−	0.880625i	$-0.657123\pi$
$13$	−27065.2			−0.947628			−0.473814	+	0.880625i	$0.657123\pi$
$14$		−	60260.4i		−	1.56863i
$15$		0			0
$16$	−76326.8			−1.16465
$17$		−	14218.4i		−	0.170238i	−0.996371	−	0.0851189i	$-0.972873\pi$
$17$		−	14218.4i		−	0.170238i	0.996371	−	0.0851189i	$-0.0271270\pi$
$18$	82083.2	+	81073.6i	0.781923	+	0.772306i
$19$	−210073.			−1.61196			−0.805981	−	0.591941i	$-0.798362\pi$
$19$	−210073.			−1.61196			−0.805981	+	0.591941i	$0.798362\pi$
$20$		0			0
$21$	−107018.	−	256121.i	−0.550277	−	1.31695i
$22$	−276511.			−1.18038
$23$			60230.4i			0.215231i	0.994193	+	0.107615i	$0.0343215\pi$
$23$			60230.4i			0.215231i	−0.994193	+	0.107615i	$0.965678\pi$
$24$	−266509.	+	111359.i	−0.803279	+	0.335645i
$25$		0			0
$26$			475926.i			1.04147i
$27$	492854.	+	198808.i	0.927392	+	0.374092i
$28$	−182354.			−0.296677
$29$		−	758209.i		−	1.07201i	−0.844216	−	0.536003i	$-0.819934\pi$
$29$		−	758209.i		−	1.07201i	0.844216	−	0.536003i	$-0.180066\pi$
$30$		0			0
$31$	333379.			0.360987			0.180493	−	0.983576i	$-0.442231\pi$
$31$	333379.			0.360987			0.180493	+	0.983576i	$0.442231\pi$
$32$			429291.i			0.409404i
$33$	−1.17524e6	+	491064.i	−0.990990	+	0.414078i
$34$	−250023.			−0.187096
$35$		0			0
$36$	245337.	−	248392.i	0.146067	−	0.147886i
$37$	683328.			0.364605			0.182302	−	0.983243i	$-0.441645\pi$
$37$	683328.			0.364605			0.182302	+	0.983243i	$0.441645\pi$
$38$			3.69401e6i			1.77159i
$39$	845213.	+	2.02280e6i	0.365349	+	0.874368i
$40$		0			0
$41$			1.23950e6i			0.438644i	0.975653	+	0.219322i	$0.0703846\pi$
$41$			1.23950e6i			0.438644i	−0.975653	+	0.219322i	$0.929615\pi$
$42$	−4.50374e6	+	1.88186e6i	−1.44736	+	0.604769i
$43$	−1.15567e6			−0.338033			−0.169016	−	0.985613i	$-0.554059\pi$
$43$	−1.15567e6			−0.338033			−0.169016	+	0.985613i	$0.554059\pi$
$44$			836750.i			0.223247i
$45$		0			0
$46$	1.05912e6			0.236545
$47$		−	1.52165e6i		−	0.311833i	−0.987770	−	0.155917i	$-0.950167\pi$
$47$		−	1.52165e6i		−	0.311833i	0.987770	−	0.155917i	$-0.0498331\pi$
$48$	2.38359e6	+	5.70451e6i	0.449021	+	1.07462i
$49$	5.97898e6			1.03715
$50$		0			0
$51$	−1.06266e6	+	444024.i	−0.157077	+	0.0656335i
$52$	1.44020e6			0.196974
$53$			4.73392e6i			0.599954i	0.953947	+	0.299977i	$0.0969789\pi$
$53$			4.73392e6i			0.599954i	−0.953947	+	0.299977i	$0.903021\pi$
$54$	3.49592e6	−	8.66656e6i	0.411137	−	1.01923i
$55$		0			0
$56$		−	1.22201e7i		−	1.24257i
$57$	6.56030e6	+	1.57004e7i	0.621476	+	1.48734i
$58$	−1.33327e7			−1.17816
$59$			1.30629e7i			1.07803i	0.842296	+	0.539016i	$0.181204\pi$
$59$			1.30629e7i			1.07803i	−0.842296	+	0.539016i	$0.818796\pi$
$60$		0			0
$61$	−6.62861e6			−0.478744			−0.239372	−	0.970928i	$-0.576941\pi$
$61$	−6.62861e6			−0.478744			−0.239372	+	0.970928i	$0.576941\pi$
$62$		−	5.86228e6i		−	0.396734i
$63$	−1.57999e7	+	1.59967e7i	−1.00298	+	1.01547i
$64$	−1.19908e7			−0.714709
$65$		0			0
$66$	8.63509e6	+	2.06659e7i	0.455083	+	1.08913i
$67$	−2.47970e7			−1.23055			−0.615276	−	0.788312i	$-0.710955\pi$
$67$	−2.47970e7			−1.23055			−0.615276	+	0.788312i	$0.710955\pi$
$68$			756595.i			0.0353857i
$69$	4.50150e6	−	1.88092e6i	0.198592	−	0.0829801i
$70$		0			0
$71$			1.07106e7i			0.421485i	0.977542	+	0.210742i	$0.0675881\pi$
$71$			1.07106e7i			0.421485i	−0.977542	+	0.210742i	$0.932412\pi$
$72$	1.66455e7	+	1.64407e7i	0.619392	+	0.611774i
$73$	3.48665e7			1.22777			0.613885	−	0.789395i	$-0.289606\pi$
$73$	3.48665e7			1.22777			0.613885	+	0.789395i	$0.289606\pi$
$74$		−	1.20159e7i		−	0.400711i
$75$		0			0
$76$	1.11784e7			0.335063
$77$		−	5.38875e7i		−	1.53294i
$78$	3.55698e7	−	1.48626e7i	0.960954	−	0.401528i
$79$	−5.01757e7			−1.28820			−0.644102	−	0.764939i	$-0.722769\pi$
$79$	−5.01757e7			−1.28820			−0.644102	+	0.764939i	$0.722769\pi$
$80$		0			0
$81$	−532723.	−	4.30434e7i	−0.0123754	−	0.999923i
$82$	2.17960e7			0.482082
$83$		−	4.50568e7i		−	0.949398i	−0.880148	−	0.474699i	$-0.842557\pi$
$83$		−	4.50568e7i		−	0.949398i	0.880148	−	0.474699i	$-0.157443\pi$
$84$	5.69469e6	+	1.36288e7i	0.114381	+	0.273741i
$85$		0			0
$86$			2.03217e7i			0.371507i
$87$	−5.66670e7	+	2.36779e7i	−0.989130	+	0.413301i
$88$	−5.60730e7			−0.935025
$89$		−	7.30781e7i		−	1.16473i	−0.812926	−	0.582367i	$-0.802127\pi$
$89$		−	7.30781e7i		−	1.16473i	0.812926	−	0.582367i	$-0.197873\pi$
$90$		0			0
$91$	−9.27503e7			−1.35254
$92$		−	3.20500e6i		−	0.0447380i
$93$	−1.04110e7	−	2.49161e7i	−0.139175	−	0.333079i
$94$	−2.67573e7			−0.342713
$95$		0			0
$96$	3.20843e7	−	1.34062e7i	0.377753	−	0.157842i
$97$	1.45948e8			1.64858			0.824292	−	0.566165i	$-0.191574\pi$
$97$	1.45948e8			1.64858			0.824292	+	0.566165i	$0.191574\pi$
$98$		−	1.05137e8i		−	1.13986i
$99$	7.34023e7	+	7.24995e7i	0.764133	+	0.754734i
$100$		0			0
$101$		−	1.21312e7i		−	0.116579i	−0.998300	−	0.0582893i	$-0.981435\pi$
$101$		−	1.21312e7i		−	0.116579i	0.998300	−	0.0582893i	$-0.0185646\pi$
$102$	7.80790e6	+	1.86862e7i	0.0721330	+	0.172632i
$103$	1.23716e8			1.09920			0.549602	−	0.835427i	$-0.314780\pi$
$103$	1.23716e8			1.09920			0.549602	+	0.835427i	$0.314780\pi$
$104$			9.65120e7i			0.824989i
$105$		0			0
$106$	8.32433e7			0.659365
$107$		−	1.35805e8i		−	1.03605i	−0.855366	−	0.518024i	$-0.826668\pi$
$107$		−	1.35805e8i		−	1.03605i	0.855366	−	0.518024i	$-0.173332\pi$
$108$	−2.62259e7	−	1.05790e7i	−0.192768	−	0.0777589i
$109$	−2.65155e7			−0.187843			−0.0939214	−	0.995580i	$-0.529940\pi$
$109$	−2.65155e7			−0.187843			−0.0939214	+	0.995580i	$0.529940\pi$
$110$		0			0
$111$	−2.13395e7	−	5.10706e7i	−0.140570	−	0.336418i
$112$	−2.61566e8			−1.66230
$113$		−	1.84493e8i		−	1.13153i	−0.824567	−	0.565764i	$-0.808581\pi$
$113$		−	1.84493e8i		−	1.13153i	0.824567	−	0.565764i	$-0.191419\pi$
$114$	2.76083e8	−	1.15359e8i	1.63463	−	0.683019i
$115$		0			0
$116$			4.03460e7i			0.222827i
$117$	1.24785e8	−	1.26339e8i	0.665915	−	0.674208i
$118$	2.29704e8			1.18479
$119$		−	4.87254e7i		−	0.242978i
$120$		0			0
$121$	−3.29090e7			−0.153523
$122$			1.16560e8i			0.526152i
$123$	9.26380e7	−	3.87081e7i	0.404733	−	0.169115i
$124$	−1.77398e7			−0.0750348
$125$		0			0
$126$	2.81293e8	+	2.77833e8i	1.11603	+	1.10230i
$127$	3.35553e7			0.128987			0.0644936	−	0.997918i	$-0.479457\pi$
$127$	3.35553e7			0.128987			0.0644936	+	0.997918i	$0.479457\pi$
$128$			3.20750e8i			1.19489i
$129$	3.60900e7	+	8.63722e7i	0.130325	+	0.311900i
$130$		0			0
$131$			2.26563e7i			0.0769315i	0.999260	+	0.0384658i	$0.0122471\pi$
$131$			2.26563e7i			0.0769315i	−0.999260	+	0.0384658i	$0.987753\pi$
$132$	6.25370e7	−	2.61306e7i	0.205988	−	0.0860705i
$133$	−7.19902e8			−2.30074
$134$			4.36041e8i			1.35241i
$135$		0			0
$136$	−5.07016e7			−0.148206
$137$			4.06245e8i			1.15320i	0.817025	+	0.576602i	$0.195622\pi$
$137$			4.06245e8i			1.15320i	−0.817025	+	0.576602i	$0.804378\pi$
$138$	−3.30749e7	−	7.91563e7i	−0.0911974	−	0.218258i
$139$	−7.13135e8			−1.91035			−0.955174	−	0.296046i	$-0.904332\pi$
$139$	−7.13135e8			−1.91035			−0.955174	+	0.296046i	$0.904332\pi$
$140$		0			0
$141$	−1.13725e8	+	4.75191e7i	−0.287726	+	0.120224i
$142$	1.88340e8			0.463223
$143$			4.25594e8i			1.01777i
$144$	3.51907e8	−	3.56289e8i	0.818423	−	0.828615i
$145$		0			0
$146$		−	6.13108e8i		−	1.34935i
$147$	−1.86716e8	−	4.46857e8i	−0.399864	−	0.956972i
$148$	−3.63614e7			−0.0757869
$149$		−	6.69006e8i		−	1.35733i	−0.734448	−	0.678665i	$-0.762559\pi$
$149$		−	6.69006e8i		−	1.35733i	0.734448	−	0.678665i	$-0.237441\pi$
$150$		0			0
$151$	−5.63219e8			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$151$	−5.63219e8			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$152$			7.49100e8i			1.40335i
$153$	6.63709e7	+	6.55545e7i	0.121119	+	0.119629i
$154$	−9.47581e8			−1.68474
$155$		0			0
$156$	−4.49757e7	−	1.07638e8i	−0.0759415	−	0.181747i
$157$	−1.50502e8			−0.247710			−0.123855	−	0.992300i	$-0.539526\pi$
$157$	−1.50502e8			−0.247710			−0.123855	+	0.992300i	$0.539526\pi$
$158$			8.82311e8i			1.41577i
$159$	3.53804e8	−	1.47834e8i	0.553572	−	0.231306i
$160$		0			0
$161$			2.06405e8i			0.307197i
$162$	−7.56894e8	+	9.36762e6i	−1.09894	+	0.0136010i
$163$	1.13070e9			1.60175			0.800876	−	0.598830i	$-0.204367\pi$
$163$	1.13070e9			1.60175			0.800876	+	0.598830i	$0.204367\pi$
$164$		−	6.59568e7i		−	0.0911768i
$165$		0			0
$166$	−7.92299e8			−1.04341
$167$		−	5.40340e8i		−	0.694707i	−0.937734	−	0.347353i	$-0.887080\pi$
$167$		−	5.40340e8i		−	0.694707i	0.937734	−	0.347353i	$-0.112920\pi$
$168$	−9.13304e8	+	3.81618e8i	−1.14651	+	0.479062i
$169$	−8.32048e7			−0.102000
$170$		0			0
$171$	9.68546e8	−	9.80608e8i	1.13276	−	1.14686i
$172$	6.14956e7			0.0702636
$173$		−	2.02228e8i		−	0.225765i	−0.993608	−	0.112883i	$-0.963992\pi$
$173$		−	2.02228e8i		−	0.225765i	0.993608	−	0.112883i	$-0.0360084\pi$
$174$	4.16363e8	+	9.96457e8i	0.454229	+	1.08708i
$175$		0			0
$176$			1.20022e9i			1.25086i
$177$	9.76295e8	−	4.07938e8i	0.994690	−	0.415624i
$178$	−1.28504e9			−1.28008
$179$			8.47838e8i			0.825850i	0.910765	+	0.412925i	$0.135493\pi$
$179$			8.47838e8i			0.825850i	−0.910765	+	0.412925i	$0.864507\pi$
$180$		0			0
$181$	1.41633e9			1.31962			0.659810	−	0.751432i	$-0.270637\pi$
$181$	1.41633e9			1.31962			0.659810	+	0.751432i	$0.270637\pi$
$182$			1.63096e9i			1.48648i
$183$	2.07003e8	+	4.95409e8i	0.184575	+	0.441733i
$184$	2.14776e8			0.187376
$185$		0			0
$186$	−4.38135e8	+	1.83072e8i	−0.366063	+	0.152957i
$187$	−2.23581e8			−0.182839
$188$			8.09702e7i			0.0648177i
$189$	1.68897e9	+	6.81298e8i	1.32366	+	0.533937i
$190$		0			0
$191$			6.78044e8i			0.509476i	0.967010	+	0.254738i	$0.0819893\pi$
$191$			6.78044e8i			0.509476i	−0.967010	+	0.254738i	$0.918011\pi$
$192$	3.74458e8	+	8.96170e8i	0.275549	+	0.659455i
$193$	−7.99869e8			−0.576487			−0.288244	−	0.957557i	$-0.593071\pi$
$193$	−7.99869e8			−0.576487			−0.288244	+	0.957557i	$0.593071\pi$
$194$		−	2.56641e9i		−	1.81184i
$195$		0			0
$196$	−3.18155e8			−0.215583
$197$		−	2.31570e9i		−	1.53751i	−0.639546	−	0.768753i	$-0.720878\pi$
$197$		−	2.31570e9i		−	1.53751i	0.639546	−	0.768753i	$-0.279122\pi$
$198$	1.27486e9	−	1.29074e9i	0.829473	−	0.839803i
$199$	1.43493e9			0.914997			0.457498	−	0.889210i	$-0.348746\pi$
$199$	1.43493e9			0.914997			0.457498	+	0.889210i	$0.348746\pi$
$200$		0			0
$201$	7.74379e8	+	1.85328e9i	0.474427	+	1.13542i
$202$	−2.13320e8			−0.128123
$203$		−	2.59832e9i		−	1.53006i
$204$	5.65464e7	−	2.36275e7i	0.0326501	−	0.0136426i
$205$		0			0
$206$		−	2.17548e9i		−	1.20805i
$207$	−2.81152e8	−	2.77694e8i	−0.153130	−	0.151247i
$208$	2.06580e9			1.10366
$209$			3.30334e9i			1.73128i
$210$		0			0
$211$	7.19293e8			0.362891			0.181445	−	0.983401i	$-0.441922\pi$
$211$	7.19293e8			0.362891			0.181445	+	0.983401i	$0.441922\pi$
$212$		−	2.51903e8i		−	0.124707i
$213$	8.00491e8	−	3.34480e8i	0.388900	−	0.162499i
$214$	−2.38805e9			−1.13865
$215$		0			0
$216$	7.08930e8	−	1.75747e9i	0.325678	−	0.807371i
$217$	1.14246e9			0.515232
$218$			4.66261e8i			0.206444i
$219$	−1.08884e9	−	2.60585e9i	−0.473355	−	1.13285i
$220$		0			0
$221$			3.84825e8i			0.161322i
$222$	−8.98047e8	+	3.75243e8i	−0.369732	+	0.154490i
$223$	1.26189e9			0.510274			0.255137	−	0.966905i	$-0.417879\pi$
$223$	1.26189e9			0.510274			0.255137	+	0.966905i	$0.417879\pi$
$224$			1.47115e9i			0.584338i
$225$		0			0
$226$	−3.24420e9			−1.24358
$227$		−	4.20903e9i		−	1.58518i	−0.609755	−	0.792590i	$-0.708732\pi$
$227$		−	4.20903e9i		−	1.58518i	0.609755	−	0.792590i	$-0.291268\pi$
$228$	−3.49089e8	−	8.35454e8i	−0.129180	−	0.309160i
$229$	−7.15398e8			−0.260139			−0.130070	−	0.991505i	$-0.541520\pi$
$229$	−7.15398e8			−0.260139			−0.130070	+	0.991505i	$0.541520\pi$
$230$		0			0
$231$	−4.02744e9	+	1.68284e9i	−1.41443	+	0.591009i
$232$	−2.70370e9			−0.933269
$233$		−	3.80229e9i		−	1.29009i	−0.764143	−	0.645047i	$-0.776838\pi$
$233$		−	3.80229e9i		−	1.29009i	0.764143	−	0.645047i	$-0.223162\pi$
$234$	−2.22160e9	−	2.19427e9i	−0.740973	−	0.731859i
$235$		0			0
$236$		−	6.95106e8i		−	0.224080i
$237$	1.56692e9	+	3.75003e9i	0.496654	+	1.18861i
$238$	−8.56809e8			−0.267040
$239$		−	3.64896e9i		−	1.11835i	−0.829050	−	0.559175i	$-0.811118\pi$
$239$		−	3.64896e9i		−	1.11835i	0.829050	−	0.559175i	$-0.188882\pi$
$240$		0			0
$241$	1.36444e9			0.404471			0.202235	−	0.979337i	$-0.435179\pi$
$241$	1.36444e9			0.404471			0.202235	+	0.979337i	$0.435179\pi$
$242$			5.78686e8i			0.168726i
$243$	−3.20034e9	+	1.38401e9i	−0.917849	+	0.396929i
$244$	3.52723e8			0.0995119
$245$		0			0
$246$	−6.80661e8	−	1.62899e9i	−0.185862	−	0.444813i
$247$	5.68566e9			1.52754
$248$		−	1.18880e9i		−	0.314269i
$249$	−3.36746e9	+	1.40707e9i	−0.876001	+	0.366031i
$250$		0			0
$251$		−	7.18506e9i		−	1.81024i	−0.425160	−	0.905118i	$-0.639782\pi$
$251$		−	7.18506e9i		−	1.81024i	0.425160	−	0.905118i	$-0.360218\pi$
$252$	8.40750e8	−	8.51219e8i	0.208480	−	0.211076i
$253$	9.47109e8			0.231163
$254$		−	5.90051e8i		−	0.141760i
$255$		0			0
$256$	2.57056e9			0.598506
$257$		−	3.06178e9i		−	0.701846i	−0.936404	−	0.350923i	$-0.885868\pi$
$257$		−	3.06178e9i		−	0.701846i	0.936404	−	0.350923i	$-0.114132\pi$
$258$	1.51881e9	−	6.34622e8i	0.342786	−	0.143231i
$259$	2.34171e9			0.520396
$260$		0			0
$261$	3.53928e9	+	3.49575e9i	0.762698	+	0.753317i
$262$	3.98399e8			0.0845498
$263$		−	3.51144e9i		−	0.733943i	−0.930232	−	0.366971i	$-0.880395\pi$
$263$		−	3.51144e9i		−	0.733943i	0.930232	−	0.366971i	$-0.119605\pi$
$264$	1.75109e9	+	4.19078e9i	0.360490	+	0.862739i
$265$		0			0
$266$			1.26591e10i			2.52857i
$267$	−5.46171e9	+	2.28214e9i	−1.07469	+	0.449052i
$268$	1.31950e9			0.255783
$269$			1.89915e9i			0.362703i	0.983418	+	0.181352i	$0.0580472\pi$
$269$			1.89915e9i			0.362703i	−0.983418	+	0.181352i	$0.941953\pi$
$270$		0			0
$271$	6.54442e7			0.0121337			0.00606686	−	0.999982i	$-0.498069\pi$
$271$	6.54442e7			0.0121337			0.00606686	+	0.999982i	$0.498069\pi$
$272$			1.08525e9i			0.198268i
$273$	2.89648e9	+	6.93197e9i	0.521458	+	1.24798i
$274$	7.14359e9			1.26740
$275$		0			0
$276$	−2.39535e8	+	1.00088e8i	−0.0412793	+	0.0172483i
$277$	−6.90961e9			−1.17364			−0.586820	−	0.809718i	$-0.699620\pi$
$277$	−6.90961e9			−1.17364			−0.586820	+	0.809718i	$0.699620\pi$
$278$			1.25401e10i			2.09952i
$279$	−1.53705e9	+	1.55619e9i	−0.253672	+	0.256831i
$280$		0			0
$281$			1.73863e9i			0.278857i	0.990232	+	0.139428i	$0.0445265\pi$
$281$			1.73863e9i			0.278857i	−0.990232	+	0.139428i	$0.955474\pi$
$282$	8.35596e8	+	1.99978e9i	0.132130	+	0.316218i
$283$	−4.14006e9			−0.645448			−0.322724	−	0.946493i	$-0.604599\pi$
$283$	−4.14006e9			−0.645448			−0.322724	+	0.946493i	$0.604599\pi$
$284$		−	5.69937e8i		−	0.0876100i
$285$		0			0
$286$	7.48383e9			1.11856
$287$			4.24768e9i			0.626072i
$288$	−2.00391e9	−	1.97926e9i	−0.291278	−	0.287695i
$289$	6.77359e9			0.971019
$290$		0			0
$291$	−4.55777e9	−	1.09079e10i	−0.635595	−	1.52113i
$292$	−1.85533e9			−0.255205
$293$			6.87312e9i			0.932575i	0.884633	+	0.466287i	$0.154409\pi$
$293$			6.87312e9i			0.932575i	−0.884633	+	0.466287i	$0.845591\pi$
$294$	−7.85772e9	+	3.28330e9i	−1.05174	+	0.439461i
$295$		0			0
$296$		−	2.43668e9i		−	0.317419i
$297$	3.12620e9	−	7.75001e9i	0.401783	−	0.996039i
$298$	−1.17641e10			−1.49174
$299$		−	1.63015e9i		−	0.203959i
$300$		0			0
$301$	−3.96038e9			−0.482470
$302$			9.90389e9i			1.19063i
$303$	−9.06662e8	+	3.78842e8i	−0.107566	+	0.0449457i
$304$	1.60342e10			1.87738
$305$		0			0
$306$	1.15274e9	−	1.16709e9i	0.131476	−	0.133113i
$307$	2.34414e9			0.263894			0.131947	−	0.991257i	$-0.457877\pi$
$307$	2.34414e9			0.263894			0.131947	+	0.991257i	$0.457877\pi$
$308$			2.86747e9i			0.318637i
$309$	−3.86350e9	−	9.24630e9i	−0.423787	−	1.01422i
$310$		0			0
$311$			6.18587e9i			0.661240i	0.943764	+	0.330620i	$0.107258\pi$
$311$			6.18587e9i			0.661240i	−0.943764	+	0.330620i	$0.892742\pi$
$312$	7.21312e9	−	3.01395e9i	0.761210	−	0.318066i
$313$	6.33696e9			0.660243			0.330121	−	0.943939i	$-0.392910\pi$
$313$	6.33696e9			0.660243			0.330121	+	0.943939i	$0.392910\pi$
$314$			2.64649e9i			0.272240i
$315$		0			0
$316$	2.66996e9			0.267767
$317$			2.63659e9i			0.261099i	0.991442	+	0.130550i	$0.0416742\pi$
$317$			2.63659e9i			0.261099i	−0.991442	+	0.130550i	$0.958326\pi$
$318$	−2.59958e9	−	6.22144e9i	−0.254212	−	0.608390i
$319$	−1.19226e10			−1.15136
$320$		0			0
$321$	−1.01498e10	+	4.24101e9i	−0.955953	+	0.399438i
$322$	3.62951e9			0.337617
$323$			2.98690e9i			0.274417i
$324$	2.83474e7	+	2.29044e9i	0.00257237	+	0.207844i
$325$		0			0
$326$		−	1.98826e10i		−	1.76037i
$327$	8.28047e8	+	1.98172e9i	0.0724209	+	0.173321i
$328$	4.41996e9			0.381876
$329$		−	5.21456e9i		−	0.445076i
$330$		0			0
$331$	−6.06785e9			−0.505502			−0.252751	−	0.967531i	$-0.581335\pi$
$331$	−6.06785e9			−0.505502			−0.252751	+	0.967531i	$0.581335\pi$
$332$			2.39758e9i			0.197342i
$333$	−3.15051e9	+	3.18974e9i	−0.256214	+	0.259405i
$334$	−9.50158e9			−0.763501
$335$		0			0
$336$	8.16837e9	+	1.95489e10i	0.640882	+	1.53379i
$337$	−1.29810e10			−1.00644			−0.503220	−	0.864158i	$-0.667851\pi$
$337$	−1.29810e10			−1.00644			−0.503220	+	0.864158i	$0.667851\pi$
$338$			1.46311e9i			0.112101i
$339$	−1.37886e10	+	5.76148e9i	−1.04405	+	0.436249i
$340$		0			0
$341$		−	5.24230e9i		−	0.387708i
$342$	−1.72434e10	−	1.70313e10i	−1.26043	−	1.24493i
$343$	7.33974e8			0.0530279
$344$			4.12100e9i			0.294285i
$345$		0			0
$346$	−3.55607e9			−0.248122
$347$			1.27979e10i			0.882718i	0.897331	+	0.441359i	$0.145504\pi$
$347$			1.27979e10i			0.882718i	−0.897331	+	0.441359i	$0.854496\pi$
$348$	3.01538e9	−	1.25996e9i	0.205601	−	0.0859089i
$349$	7.93032e9			0.534551			0.267275	−	0.963620i	$-0.413877\pi$
$349$	7.93032e9			0.534551			0.267275	+	0.963620i	$0.413877\pi$
$350$		0			0
$351$	−1.33392e10	−	5.38077e9i	−0.878823	−	0.354500i
$352$	6.75050e9			0.439709
$353$		−	1.11540e10i		−	0.718342i	−0.933272	−	0.359171i	$-0.883059\pi$
$353$		−	1.11540e10i		−	0.718342i	0.933272	−	0.359171i	$-0.116941\pi$
$354$	−7.17336e9	−	1.71676e10i	−0.456782	−	1.09319i
$355$		0			0
$356$			3.88865e9i			0.242102i
$357$	−3.64164e9	+	1.52163e9i	−0.224194	+	0.0936779i
$358$	1.49088e10			0.907631
$359$			3.89548e9i			0.234522i	0.993101	+	0.117261i	$0.0374114\pi$
$359$			3.89548e9i			0.234522i	−0.993101	+	0.117261i	$0.962589\pi$
$360$		0			0
$361$	2.71469e10			1.59842
$362$		−	2.49053e10i		−	1.45030i
$363$	1.02771e9	+	2.45955e9i	0.0591893	+	0.141654i
$364$	4.93545e9			0.281139
$365$		0			0
$366$	8.71148e9	−	3.64003e9i	0.485476	−	0.202853i
$367$	2.72657e10			1.50298			0.751488	−	0.659747i	$-0.229337\pi$
$367$	2.72657e10			1.50298			0.751488	+	0.659747i	$0.229337\pi$
$368$		−	4.59720e9i		−	0.250670i
$369$	−5.78594e9	−	5.71477e9i	−0.312082	−	0.308243i
$370$		0			0
$371$			1.62228e10i			0.856307i
$372$	5.53993e8	+	1.32584e9i	0.0289289	+	0.0692340i
$373$	−8.68516e9			−0.448686			−0.224343	−	0.974510i	$-0.572024\pi$
$373$	−8.68516e9			−0.448686			−0.224343	+	0.974510i	$0.572024\pi$
$374$			3.93155e9i			0.200945i
$375$		0			0
$376$	−5.42605e9			−0.271476
$377$			2.05211e10i			1.01586i
$378$	1.19802e10	−	2.96996e10i	0.586811	−	1.45473i
$379$	2.18982e10			1.06133			0.530666	−	0.847581i	$-0.321942\pi$
$379$	2.18982e10			1.06133			0.530666	+	0.847581i	$0.321942\pi$
$380$		0			0
$381$	−1.04789e9	−	2.50786e9i	−0.0497297	−	0.119015i
$382$	1.19230e10			0.559928
$383$		−	3.16884e10i		−	1.47267i	−0.676618	−	0.736334i	$-0.736555\pi$
$383$		−	3.16884e10i		−	1.47267i	0.676618	−	0.736334i	$-0.263445\pi$
$384$	2.39722e10	−	1.00166e10i	1.10251	−	0.460677i
$385$		0			0
$386$			1.40652e10i			0.633575i
$387$	5.32824e9	−	5.39459e9i	0.237542	−	0.240500i
$388$	−7.76622e9			−0.342675
$389$			9.57908e9i			0.418336i	0.977880	+	0.209168i	$0.0670756\pi$
$389$			9.57908e9i			0.418336i	−0.977880	+	0.209168i	$0.932924\pi$
$390$		0			0
$391$	8.56382e8			0.0366404
$392$		−	2.13205e10i		−	0.902928i
$393$	1.69329e9	−	7.07528e8i	0.0709840	−	0.0296602i
$394$	−4.07202e10			−1.68976
$395$		0			0
$396$	−3.90590e9	−	3.85786e9i	−0.158833	−	0.156879i
$397$	−4.45553e10			−1.79365			−0.896824	−	0.442388i	$-0.854132\pi$
$397$	−4.45553e10			−1.79365			−0.896824	+	0.442388i	$0.854132\pi$
$398$		−	2.52325e10i		−	1.00561i
$399$	2.24816e10	+	5.38040e10i	0.887026	+	2.12287i
$400$		0			0
$401$		−	2.51147e10i		−	0.971293i	−0.874155	−	0.485647i	$-0.838584\pi$
$401$		−	2.51147e10i		−	0.971293i	0.874155	−	0.485647i	$-0.161416\pi$
$402$	3.25888e10	−	1.36170e10i	1.24786	−	0.521408i
$403$	−9.02297e9			−0.342081
$404$			6.45529e8i			0.0242321i
$405$		0			0
$406$	−4.56900e10			−1.68158
$407$		−	1.07452e10i		−	0.391594i
$408$	1.58335e9	+	3.78933e9i	0.0571394	+	0.136748i
$409$	1.11563e10			0.398683			0.199341	−	0.979930i	$-0.436120\pi$
$409$	1.11563e10			0.398683			0.199341	+	0.979930i	$0.436120\pi$
$410$		0			0
$411$	3.03620e10	−	1.26865e10i	1.06405	−	0.444606i
$412$	−6.58322e9			−0.228481
$413$			4.47655e10i			1.53866i
$414$	−4.88310e9	+	4.94391e9i	−0.166224	+	0.168294i
$415$		0			0
$416$		−	1.16189e10i		−	0.387963i
$417$	2.22703e10	+	5.32982e10i	0.736515	+	1.76266i
$418$	5.80874e10			1.90273
$419$		−	5.51814e10i		−	1.79034i	−0.445720	−	0.895172i	$-0.647052\pi$
$419$		−	5.51814e10i		−	1.79034i	0.445720	−	0.895172i	$-0.352948\pi$
$420$		0			0
$421$	2.21829e10			0.706139			0.353070	−	0.935597i	$-0.385138\pi$
$421$	2.21829e10			0.706139			0.353070	+	0.935597i	$0.385138\pi$
$422$		−	1.26484e10i		−	0.398827i
$423$	7.10296e9	+	7.01559e9i	0.221859	+	0.219131i
$424$	1.68807e10			0.522309
$425$		0			0
$426$	−5.88163e9	−	1.40762e10i	−0.178591	−	0.427412i
$427$	−2.27157e10			−0.683305
$428$			7.22648e9i			0.215354i
$429$	3.18080e10	−	1.32908e10i	0.939091	−	0.392392i
$430$		0			0
$431$			4.91950e10i			1.42565i	0.701343	+	0.712824i	$0.252584\pi$
$431$			4.91950e10i			1.42565i	−0.701343	+	0.712824i	$0.747416\pi$
$432$	−3.76180e10	−	1.51744e10i	−1.08009	−	0.435688i
$433$	−1.97041e10			−0.560537			−0.280268	−	0.959922i	$-0.590423\pi$
$433$	−1.97041e10			−0.560537			−0.280268	+	0.959922i	$0.590423\pi$
$434$		−	2.00896e10i		−	0.566254i
$435$		0			0
$436$	1.41095e9			0.0390451
$437$		−	1.26528e10i		−	0.346944i
$438$	−4.58224e10	+	1.91466e10i	−1.24504	+	0.520230i
$439$	−1.74433e10			−0.469647			−0.234824	−	0.972038i	$-0.575451\pi$
$439$	−1.74433e10			−0.469647			−0.234824	+	0.972038i	$0.575451\pi$
$440$		0			0
$441$	−2.75663e10	+	2.79096e10i	−0.728826	+	0.737902i
$442$	6.76693e9			0.177297
$443$		−	2.46881e10i		−	0.641022i	−0.947245	−	0.320511i	$-0.896145\pi$
$443$		−	2.46881e10i		−	0.641022i	0.947245	−	0.320511i	$-0.103855\pi$
$444$	1.13552e9	+	2.71758e9i	0.0292189	+	0.0699279i
$445$		0			0
$446$		−	2.21897e10i		−	0.560805i
$447$	−5.00002e10	+	2.08922e10i	−1.25240	+	0.523305i
$448$	−4.10916e10			−1.02010
$449$			4.94885e10i			1.21764i	0.793308	+	0.608820i	$0.208357\pi$
$449$			4.94885e10i			1.21764i	−0.793308	+	0.608820i	$0.791643\pi$
$450$		0			0
$451$	1.94909e10			0.471114
$452$			9.81727e9i			0.235200i
$453$	1.75886e10	+	4.20939e10i	0.417676	+	0.999599i
$454$	−7.40134e10			−1.74216
$455$		0			0
$456$	5.59862e10	−	2.33934e10i	1.29486	−	0.541047i
$457$	7.51747e10			1.72348			0.861741	−	0.507349i	$-0.169374\pi$
$457$	7.51747e10			1.72348			0.861741	+	0.507349i	$0.169374\pi$
$458$			1.25799e10i			0.285900i
$459$	2.82673e9	−	7.00761e9i	0.0636845	−	0.157877i
$460$		0			0
$461$			1.73856e10i			0.384933i	0.981304	+	0.192466i	$0.0616487\pi$
$461$			1.73856e10i			0.384933i	−0.981304	+	0.192466i	$0.938351\pi$
$462$	2.95918e10	+	7.08203e10i	0.649535	+	1.55450i
$463$	2.11164e10			0.459511			0.229755	−	0.973248i	$-0.426207\pi$
$463$	2.11164e10			0.459511			0.229755	+	0.973248i	$0.426207\pi$
$464$			5.78717e10i			1.24852i
$465$		0			0
$466$	−6.68610e10			−1.41785
$467$		−	1.49113e10i		−	0.313508i	−0.987638	−	0.156754i	$-0.949897\pi$
$467$		−	1.49113e10i		−	0.313508i	0.987638	−	0.156754i	$-0.0501030\pi$
$468$	−6.64009e9	+	6.72278e9i	−0.138417	+	0.140141i
$469$	−8.49774e10			−1.75635
$470$		0			0
$471$	4.69999e9	+	1.12482e10i	0.0955022	+	0.228560i
$472$	4.65811e10			0.938516
$473$			1.81726e10i			0.363054i
$474$	6.59421e10	−	2.75535e10i	1.30632	−	0.545837i
$475$		0			0
$476$			2.59279e9i			0.0505056i
$477$	−2.20977e10	−	2.18259e10i	−0.426848	−	0.421598i
$478$	−6.41649e10			−1.22910
$479$		−	5.15755e9i		−	0.0979718i	−0.998799	−	0.0489859i	$-0.984401\pi$
$479$		−	5.15755e9i		−	0.0979718i	0.998799	−	0.0489859i	$-0.0155989\pi$
$480$		0			0
$481$	−1.84944e10			−0.345510
$482$		−	2.39929e10i		−	0.444524i
$483$	1.54263e10	−	6.44576e9i	0.283448	−	0.118437i
$484$	1.75116e9			0.0319114
$485$		0			0
$486$	2.43370e10	+	5.62762e10i	0.436236	+	1.00874i
$487$	−3.79969e10			−0.675510			−0.337755	−	0.941234i	$-0.609668\pi$
$487$	−3.79969e10			−0.675510			−0.337755	+	0.941234i	$0.609668\pi$
$488$			2.36370e10i			0.416786i
$489$	−3.53102e10	−	8.45059e10i	−0.617540	−	1.47792i
$490$		0			0
$491$		−	7.21946e10i		−	1.24216i	−0.783746	−	0.621081i	$-0.786694\pi$
$491$		−	7.21946e10i		−	1.24216i	0.783746	−	0.621081i	$-0.213306\pi$
$492$	−4.92948e9	+	2.05975e9i	−0.0841280	+	0.0351523i
$493$	−1.07805e10			−0.182496
$494$		−	9.99791e10i		−	1.67881i
$495$		0			0
$496$	−2.54457e10			−0.420425
$497$			3.67045e10i			0.601580i
$498$	2.47425e10	+	5.92148e10i	0.402278	+	0.962749i
$499$	2.25403e10			0.363544			0.181772	−	0.983341i	$-0.441817\pi$
$499$	2.25403e10			0.363544			0.181772	+	0.983341i	$0.441817\pi$
$500$		0			0
$501$	−4.03839e10	+	1.68741e10i	−0.641000	+	0.267837i
$502$	−1.26345e11			−1.98950
$503$			1.10303e11i			1.72312i	0.507657	+	0.861559i	$0.330512\pi$
$503$			1.10303e11i			1.72312i	−0.507657	+	0.861559i	$0.669488\pi$
$504$	5.70427e10	+	5.63411e10i	0.884052	+	0.873178i
$505$		0			0
$506$		−	1.66544e10i		−	0.254054i
$507$	2.59838e9	+	6.21856e9i	0.0393252	+	0.0941148i
$508$	−1.78555e9			−0.0268113
$509$			9.85205e10i			1.46776i	0.679278	+	0.733881i	$0.262293\pi$
$509$			9.85205e10i			1.46776i	−0.679278	+	0.733881i	$0.737707\pi$
$510$		0			0
$511$	1.19485e11			1.75238
$512$			3.69102e10i			0.537114i
$513$	−1.03535e11	−	4.17641e10i	−1.49492	−	0.603022i
$514$	−5.38397e10			−0.771348
$515$		0			0
$516$	−1.92043e9	−	4.59606e9i	−0.0270894	−	0.0648316i
$517$	−2.39275e10			−0.334915
$518$		−	4.11777e10i		−	0.571930i
$519$	−1.51141e10	+	6.31533e9i	−0.208312	+	0.0870416i
$520$		0			0
$521$		−	7.84071e10i		−	1.06415i	−0.846696	−	0.532077i	$-0.821412\pi$
$521$		−	7.84071e10i		−	1.06415i	0.846696	−	0.532077i	$-0.178588\pi$
$522$	6.14707e10	−	6.22362e10i	0.827916	−	0.838226i
$523$	1.26646e11			1.69272			0.846359	−	0.532613i	$-0.178790\pi$
$523$	1.26646e11			1.69272			0.846359	+	0.532613i	$0.178790\pi$
$524$		−	1.20559e9i		−	0.0159910i
$525$		0			0
$526$	−6.17467e10			−0.806623
$527$		−	4.74012e9i		−	0.0614536i
$528$	8.97020e10	−	3.74814e10i	1.15416	−	0.482258i
$529$	7.46833e10			0.953676
$530$		0			0
$531$	−6.09769e10	−	6.02269e10i	−0.766986	−	0.757552i
$532$	3.83076e10			0.478232
$533$		−	3.35474e10i		−	0.415672i
$534$	4.01301e10	+	9.60410e10i	0.493520	+	1.18111i
$535$		0			0
$536$			8.84238e10i			1.07130i
$537$	6.33657e10	−	2.64769e10i	0.762004	−	0.318398i
$538$	3.33956e10			0.398620
$539$		−	9.40180e10i		−	1.11392i
$540$		0			0
$541$	−8.35314e10			−0.975126			−0.487563	−	0.873088i	$-0.662114\pi$
$541$	−8.35314e10			−0.975126			−0.487563	+	0.873088i	$0.662114\pi$
$542$		−	1.15080e9i		−	0.0133353i
$543$	−4.42301e10	−	1.05853e11i	−0.508767	−	1.21760i
$544$	6.10384e9			0.0696960
$545$		0			0
$546$	1.21895e11	−	5.09329e10i	1.37156	−	0.573096i
$547$	2.75997e10			0.308287			0.154144	−	0.988048i	$-0.450738\pi$
$547$	2.75997e10			0.308287			0.154144	+	0.988048i	$0.450738\pi$
$548$		−	2.16172e10i		−	0.239705i
$549$	3.05614e10	−	3.09420e10i	0.336422	−	0.340611i
$550$		0			0
$551$			1.59279e11i			1.72803i
$552$	−6.70719e9	−	1.60519e10i	−0.0722411	−	0.172890i
$553$	−1.71948e11			−1.83864
$554$			1.21502e11i			1.28986i
$555$		0			0
$556$	3.79475e10			0.397086
$557$			1.06328e11i			1.10465i	0.833628	+	0.552326i	$0.186260\pi$
$557$			1.06328e11i			1.10465i	−0.833628	+	0.552326i	$0.813740\pi$
$558$	2.73648e10	+	2.70282e10i	0.282264	+	0.278792i
$559$	3.12784e10			0.320329
$560$		0			0
$561$	6.98216e9	+	1.67100e10i	0.0704918	+	0.168704i
$562$	3.05728e10			0.306471
$563$		−	1.35823e11i		−	1.35188i	−0.736956	−	0.675941i	$-0.763737\pi$
$563$		−	1.35823e11i		−	1.35188i	0.736956	−	0.675941i	$-0.236263\pi$
$564$	6.05155e9	−	2.52860e9i	0.0598067	−	0.0249898i
$565$		0			0
$566$			7.28006e10i			0.709364i
$567$	−1.82560e9	−	1.47506e11i	−0.0176633	−	1.42718i
$568$	3.81931e10			0.366937
$569$		−	6.61732e10i		−	0.631296i	−0.948876	−	0.315648i	$-0.897778\pi$
$569$		−	6.61732e10i		−	0.631296i	0.948876	−	0.315648i	$-0.102222\pi$
$570$		0			0
$571$	9.17754e10			0.863340			0.431670	−	0.902032i	$-0.357925\pi$
$571$	9.17754e10			0.863340			0.431670	+	0.902032i	$0.357925\pi$
$572$		−	2.26468e10i		−	0.211555i
$573$	5.06756e10	−	2.11744e10i	0.470089	−	0.196424i
$574$	7.46931e10			0.688070
$575$		0			0
$576$	5.52840e10	−	5.59725e10i	0.502238	−	0.508493i
$577$	1.35583e11			1.22321			0.611607	−	0.791162i	$-0.290524\pi$
$577$	1.35583e11			1.22321			0.611607	+	0.791162i	$0.290524\pi$
$578$		−	1.19110e11i		−	1.06718i
$579$	2.49789e10	+	5.97806e10i	0.222259	+	0.531920i
$580$		0			0
$581$		−	1.54406e11i		−	1.35506i
$582$	−1.91808e11	+	8.01458e10i	−1.67177	+	0.698536i
$583$	7.44398e10			0.644363
$584$		−	1.24331e11i		−	1.06888i
$585$		0			0
$586$	1.20860e11			1.02492
$587$		−	6.90011e10i		−	0.581171i	−0.956849	−	0.290585i	$-0.906150\pi$
$587$		−	6.90011e10i		−	0.581171i	0.956849	−	0.290585i	$-0.0938500\pi$
$588$	9.93558e9	+	2.37783e10i	0.0831159	+	0.198917i
$589$	−7.00338e10			−0.581897
$590$		0			0
$591$	−1.73071e11	+	7.23163e10i	−1.41864	+	0.592770i
$592$	−5.21562e10			−0.424639
$593$			2.17447e11i			1.75847i	0.476391	+	0.879234i	$0.341945\pi$
$593$			2.17447e11i			1.75847i	−0.476391	+	0.879234i	$0.658055\pi$
$594$	−1.36279e11	−	5.49725e10i	−1.09467	−	0.441570i
$595$		0			0
$596$			3.55993e10i			0.282135i
$597$	−4.48112e10	−	1.07244e11i	−0.352768	−	0.844260i
$598$	−2.86653e10			−0.224156
$599$			1.17194e11i			0.910327i	0.890408	+	0.455163i	$0.150419\pi$
$599$			1.17194e11i			0.910327i	−0.890408	+	0.455163i	$0.849581\pi$
$600$		0			0
$601$	−4.03470e10			−0.309253			−0.154626	−	0.987973i	$-0.549417\pi$
$601$	−4.03470e10			−0.309253			−0.154626	+	0.987973i	$0.549417\pi$
$602$			6.96410e10i			0.530248i
$603$	1.14327e11	−	1.15751e11i	0.864731	−	0.875499i
$604$	2.99702e10			0.225186
$605$		0			0
$606$	6.66173e9	+	1.59431e10i	0.0493965	+	0.118218i
$607$	−4.42279e10			−0.325793			−0.162896	−	0.986643i	$-0.552084\pi$
$607$	−4.42279e10			−0.325793			−0.162896	+	0.986643i	$0.552084\pi$
$608$		−	9.01823e10i		−	0.659944i
$609$	−1.94193e11	+	8.11423e10i	−1.41177	+	0.589900i
$610$		0			0
$611$			4.11837e10i			0.295502i
$612$	−3.53174e9	−	3.48830e9i	−0.0251758	−	0.0248662i
$613$	2.22935e11			1.57883			0.789416	−	0.613858i	$-0.210383\pi$
$613$	2.22935e11			1.57883			0.789416	+	0.613858i	$0.210383\pi$
$614$		−	4.12204e10i		−	0.290027i
$615$		0			0
$616$	−1.92158e11			−1.33455
$617$		−	1.00709e11i		−	0.694906i	−0.937697	−	0.347453i	$-0.887047\pi$
$617$		−	1.00709e11i		−	0.694906i	0.937697	−	0.347453i	$-0.112953\pi$
$618$	−1.62591e11	+	6.79375e10i	−1.11466	+	0.465753i
$619$	−9.16635e10			−0.624358			−0.312179	−	0.950023i	$-0.601059\pi$
$619$	−9.16635e10			−0.624358			−0.312179	+	0.950023i	$0.601059\pi$
$620$		0			0
$621$	−1.19743e10	+	2.96848e10i	−0.0805161	+	0.199603i
$622$	1.08775e11			0.726721
$623$		−	2.50433e11i		−	1.66241i
$624$	−6.45124e10	−	1.54394e11i	−0.425505	−	1.01834i
$625$		0			0
$626$		−	1.11432e11i		−	0.725624i
$627$	2.46885e11	−	1.03159e11i	1.59744	−	0.667479i
$628$	8.00855e9			0.0514891
$629$		−	9.71585e9i		−	0.0620695i
$630$		0			0
$631$	−8.69834e10			−0.548680			−0.274340	−	0.961633i	$-0.588459\pi$
$631$	−8.69834e10			−0.548680			−0.274340	+	0.961633i	$0.588459\pi$
$632$			1.78922e11i			1.12149i
$633$	−2.24626e10	−	5.37585e10i	−0.139909	−	0.334836i
$634$	4.63629e10			0.286955
$635$		0			0
$636$	−1.88267e10	+	7.86660e9i	−0.115066	+	0.0480794i
$637$	−1.61822e11			−0.982836
$638$			2.09653e11i			1.26537i
$639$	−4.99967e10	−	4.93817e10i	−0.299873	−	0.296185i
$640$		0			0
$641$		−	1.68189e11i		−	0.996243i	−0.867107	−	0.498122i	$-0.834023\pi$
$641$		−	1.68189e11i		−	0.996243i	0.867107	−	0.498122i	$-0.165977\pi$
$642$	7.45758e10	+	1.78478e11i	0.438993	+	1.05062i
$643$	−1.47717e11			−0.864144			−0.432072	−	0.901839i	$-0.642217\pi$
$643$	−1.47717e11			−0.864144			−0.432072	+	0.901839i	$0.642217\pi$
$644$		−	1.09833e10i		−	0.0638540i
$645$		0			0
$646$	5.25230e10			0.301592
$647$		−	5.56399e10i		−	0.317518i	−0.987317	−	0.158759i	$-0.949251\pi$
$647$		−	5.56399e10i		−	0.317518i	0.987317	−	0.158759i	$-0.0507493\pi$
$648$	−1.53489e11	+	1.89964e9i	−0.870516	+	0.0107739i
$649$	2.05411e11			1.15783
$650$		0			0
$651$	−3.56777e10	−	8.53853e10i	−0.198643	−	0.475400i
$652$	−6.01669e10			−0.332941
$653$			3.03168e11i			1.66737i	0.552243	+	0.833683i	$0.313772\pi$
$653$			3.03168e11i			1.66737i	−0.552243	+	0.833683i	$0.686228\pi$
$654$	3.48474e10	−	1.45607e10i	0.190484	−	0.0795925i
$655$		0			0
$656$		−	9.46074e10i		−	0.510869i
$657$	−1.60753e11	+	1.62755e11i	−0.862776	+	0.873520i
$658$	−9.16950e10			−0.489150
$659$			4.09785e10i			0.217278i	0.994081	+	0.108639i	$0.0346492\pi$
$659$			4.09785e10i			0.217278i	−0.994081	+	0.108639i	$0.965351\pi$
$660$		0			0
$661$	2.42879e11			1.27229			0.636143	−	0.771571i	$-0.280529\pi$
$661$	2.42879e11			1.27229			0.636143	+	0.771571i	$0.280529\pi$
$662$			1.06700e11i			0.555560i
$663$	2.87610e10	−	1.20176e10i	0.148851	−	0.0621961i
$664$	−1.60668e11			−0.826530
$665$		0			0
$666$	5.60898e10	+	5.53999e10i	0.285093	+	0.281586i
$667$	4.56673e10			0.230729
$668$			2.87527e10i			0.144402i
$669$	−3.94074e10	−	9.43114e10i	−0.196731	−	0.470825i
$670$		0			0
$671$			1.04233e11i			0.514181i
$672$	1.09950e11	−	4.59420e10i	0.539163	−	0.225286i
$673$	−2.34992e11			−1.14549			−0.572747	−	0.819732i	$-0.694122\pi$
$673$	−2.34992e11			−1.14549			−0.572747	+	0.819732i	$0.694122\pi$
$674$			2.28263e11i			1.10610i
$675$		0			0
$676$	4.42752e9			0.0212018
$677$		−	2.35523e11i		−	1.12119i	−0.828090	−	0.560595i	$-0.810573\pi$
$677$		−	2.35523e11i		−	1.12119i	0.828090	−	0.560595i	$-0.189427\pi$
$678$	1.01312e11	+	2.42465e11i	0.479450	+	1.14744i
$679$	5.00152e11			2.35300
$680$		0			0
$681$	−3.14574e11	+	1.31443e11i	−1.46263	+	0.611150i
$682$	−9.21829e10			−0.426101
$683$			1.13979e11i			0.523772i	0.965099	+	0.261886i	$0.0843444\pi$
$683$			1.13979e11i			0.523772i	−0.965099	+	0.261886i	$0.915656\pi$
$684$	−5.15385e10	+	5.21804e10i	−0.235455	+	0.238387i
$685$		0			0
$686$		−	1.29065e10i		−	0.0582791i
$687$	2.23410e10	+	5.34674e10i	0.100294	+	0.240028i
$688$	8.82083e10			0.393691
$689$		−	1.28125e11i		−	0.568533i
$690$		0			0
$691$	2.47931e11			1.08747			0.543737	−	0.839256i	$-0.317009\pi$
$691$	2.47931e11			1.08747			0.543737	+	0.839256i	$0.317009\pi$
$692$			1.07610e10i			0.0469277i
$693$	2.51544e11	+	2.48450e11i	1.09064	+	1.07722i
$694$	2.25044e11			0.970131
$695$		0			0
$696$	8.44332e10	+	2.02069e11i	0.359813	+	0.861119i
$697$	1.76238e10			0.0746738
$698$		−	1.39450e11i		−	0.587485i
$699$	−2.84175e11	+	1.18741e11i	−1.19036	+	0.497383i
$700$		0			0
$701$			3.48469e11i			1.44308i	0.692370	+	0.721542i	$0.256566\pi$
$701$			3.48469e11i			1.44308i	−0.692370	+	0.721542i	$0.743434\pi$
$702$	−9.46178e10	+	2.34562e11i	−0.389605	+	0.965850i
$703$	−1.43549e11			−0.587730
$704$			1.88553e11i			0.767613i
$705$		0			0
$706$	−1.96137e11			−0.789477
$707$		−	4.15727e10i		−	0.166391i
$708$	−5.19508e10	+	2.17073e10i	−0.206757	+	0.0863918i
$709$	3.19932e11			1.26611			0.633057	−	0.774105i	$-0.281800\pi$
$709$	3.19932e11			1.26611			0.633057	+	0.774105i	$0.281800\pi$
$710$		0			0
$711$	2.31337e11	−	2.34217e11i	0.905244	−	0.916517i
$712$	−2.60590e11			−1.01400
$713$			2.00795e10i			0.0776955i
$714$	2.67571e10	+	6.40362e10i	0.102955	+	0.246395i
$715$		0			0
$716$		−	4.51154e10i		−	0.171661i
$717$	−2.72716e11	+	1.13952e11i	−1.03189	+	0.431169i
$718$	6.84998e10			0.257746
$719$			2.06854e11i			0.774014i	0.922077	+	0.387007i	$0.126491\pi$
$719$			2.06854e11i			0.774014i	−0.922077	+	0.387007i	$0.873509\pi$
$720$		0			0
$721$	4.23966e11			1.56888
$722$		−	4.77364e11i		−	1.75671i
$723$	−4.26098e10	−	1.01976e11i	−0.155940	−	0.373201i
$724$	−7.53659e10			−0.274297
$725$		0			0
$726$	4.32499e10	−	1.80716e10i	0.155682	−	0.0650506i
$727$	3.61835e11			1.29531			0.647654	−	0.761934i	$-0.275750\pi$
$727$	3.61835e11			1.29531			0.647654	+	0.761934i	$0.275750\pi$
$728$			3.30739e11i			1.17750i
$729$	2.03381e11	+	1.95966e11i	0.720111	+	0.693859i
$730$		0			0
$731$			1.64318e10i			0.0575459i
$732$	−1.10151e10	−	2.63618e10i	−0.0383658	−	0.0918187i
$733$	2.04728e11			0.709188			0.354594	−	0.935020i	$-0.384619\pi$
$733$	2.04728e11			0.709188			0.354594	+	0.935020i	$0.384619\pi$
$734$		−	4.79451e11i		−	1.65181i
$735$		0			0
$736$	−2.58564e10			−0.0881164
$737$			3.89927e11i			1.32164i
$738$	−1.00491e11	+	1.01742e11i	−0.338768	+	0.342986i
$739$	−4.92586e11			−1.65160			−0.825798	−	0.563966i	$-0.809275\pi$
$739$	−4.92586e11			−1.65160			−0.825798	+	0.563966i	$0.809275\pi$
$740$		0			0
$741$	−1.77556e11	−	4.24935e11i	−0.588929	−	1.40945i
$742$	2.85268e11			0.941104
$743$		−	5.52619e11i		−	1.81330i	−0.421880	−	0.906652i	$-0.638630\pi$
$743$		−	5.52619e11i		−	1.81330i	0.421880	−	0.906652i	$-0.361370\pi$
$744$	−8.88484e10	+	3.71247e10i	−0.289973	+	0.121163i
$745$		0			0
$746$			1.52724e11i			0.493118i
$747$	2.10323e11	+	2.07736e11i	0.675467	+	0.667159i
$748$	1.18973e10			0.0380050
$749$		−	4.65392e11i		−	1.47874i
$750$		0			0
$751$	−2.05834e11			−0.647079			−0.323540	−	0.946215i	$-0.604873\pi$
$751$	−2.05834e11			−0.647079			−0.323540	+	0.946215i	$0.604873\pi$
$752$			1.16142e11i			0.363178i
$753$	−5.36997e11	+	2.24380e11i	−1.67029	+	0.697919i
$754$	3.60852e11			1.11646
$755$		0			0
$756$	−8.98740e10	−	3.62534e10i	−0.275136	−	0.110984i
$757$	1.27946e10			0.0389622			0.0194811	−	0.999810i	$-0.493799\pi$
$757$	1.27946e10			0.0389622			0.0194811	+	0.999810i	$0.493799\pi$
$758$		−	3.85067e11i		−	1.16643i
$759$	−2.95770e10	−	7.07850e10i	−0.0891225	−	0.213292i
$760$		0			0
$761$			2.92493e11i			0.872120i	0.899918	+	0.436060i	$0.143627\pi$
$761$			2.92493e11i			0.872120i	−0.899918	+	0.436060i	$0.856373\pi$
$762$	−4.40992e10	+	1.84266e10i	−0.130801	+	0.0546543i
$763$	−9.08667e10			−0.268106
$764$		−	3.60802e10i		−	0.105900i
$765$		0			0
$766$	−5.57222e11			−1.61850
$767$		−	3.53550e11i		−	1.02157i
$768$	−8.02754e10	−	1.92119e11i	−0.230748	−	0.552236i
$769$	−4.81512e11			−1.37690			−0.688449	−	0.725285i	$-0.741708\pi$
$769$	−4.81512e11			−1.37690			−0.688449	+	0.725285i	$0.741708\pi$
$770$		0			0
$771$	−2.28831e11	+	9.56156e10i	−0.647587	+	0.270590i
$772$	4.25628e10			0.119829
$773$			4.38699e11i			1.22871i	0.789030	+	0.614354i	$0.210583\pi$
$773$			4.38699e11i			1.22871i	−0.789030	+	0.614354i	$0.789417\pi$
$774$	−9.48608e10	−	9.36940e10i	−0.264316	−	0.261065i
$775$		0			0
$776$		−	5.20437e11i		−	1.43523i
$777$	−7.31287e10	−	1.75015e11i	−0.200634	−	0.480165i
$778$	1.68443e11			0.459763
$779$		−	2.60386e11i		−	0.707078i
$780$		0			0
$781$	1.68422e11			0.452684
$782$		−	1.50590e10i		−	0.0402688i
$783$	1.50738e11	−	3.73686e11i	0.401028	−	0.994169i
$784$	−4.56356e11			−1.20792
$785$		0			0
$786$	−1.24415e10	−	2.97755e10i	−0.0325973	−	0.0780134i
$787$	−3.97244e11			−1.03552			−0.517760	−	0.855526i	$-0.673234\pi$
$787$	−3.97244e11			−1.03552			−0.517760	+	0.855526i	$0.673234\pi$
$788$			1.23223e11i			0.319587i
$789$	−2.62438e11	+	1.09658e11i	−0.677202	+	0.282964i
$790$		0			0
$791$		−	6.32242e11i		−	1.61502i
$792$	2.58526e11	−	2.61746e11i	0.657059	−	0.665241i
$793$	1.79405e11			0.453671
$794$			7.83479e11i			1.97127i
$795$		0			0
$796$	−7.63561e10			−0.190192
$797$		−	5.24995e10i		−	0.130113i	−0.997882	−	0.0650567i	$-0.979277\pi$
$797$		−	5.24995e10i		−	0.130113i	0.997882	−	0.0650567i	$-0.0207228\pi$
$798$	9.46113e11	−	3.95327e11i	2.33309	−	0.974866i
$799$	−2.16354e10			−0.0530858
$800$		0			0
$801$	3.41125e11	+	3.36929e11i	0.828672	+	0.818480i
$802$	−4.41628e11			−1.06748
$803$		−	5.48267e11i		−	1.31865i
$804$	−4.12065e10	−	9.86171e10i	−0.0986146	−	0.236009i
$805$		0			0
$806$			1.58664e11i			0.375957i
$807$	1.41939e11	−	5.93082e10i	0.334663	−	0.139837i
$808$	−4.32588e10			−0.101491
$809$			3.82829e11i			0.893739i	0.894599	+	0.446870i	$0.147461\pi$
$809$			3.82829e11i			0.893739i	−0.894599	+	0.446870i	$0.852539\pi$
$810$		0			0
$811$	−4.50313e11			−1.04095			−0.520477	−	0.853876i	$-0.674246\pi$
$811$	−4.50313e11			−1.04095			−0.520477	+	0.853876i	$0.674246\pi$
$812$			1.38263e11i			0.318039i
$813$	−2.04374e9	−	4.89117e9i	−0.00467803	−	0.0111957i
$814$	−1.88948e11			−0.430372
$815$		0			0
$816$	8.11092e10	−	3.38909e10i	0.182940	−	0.0764403i
$817$	2.42774e11			0.544896
$818$		−	1.96178e11i		−	0.438163i
$819$	4.27628e11	−	4.32954e11i	0.950453	−	0.962289i
$820$		0			0
$821$			4.00560e11i			0.881648i	0.897593	+	0.440824i	$0.145314\pi$
$821$			4.00560e11i			0.881648i	−0.897593	+	0.440824i	$0.854686\pi$
$822$	−2.23085e11	−	5.33898e11i	−0.488634	−	1.16942i
$823$	5.98531e11			1.30463			0.652315	−	0.757948i	$-0.273798\pi$
$823$	5.98531e11			1.30463			0.652315	+	0.757948i	$0.273798\pi$
$824$		−	4.41161e11i		−	0.956947i
$825$		0			0
$826$	7.87176e11			1.69103
$827$			1.33008e11i			0.284352i	0.989841	+	0.142176i	$0.0454098\pi$
$827$			1.33008e11i			0.284352i	−0.989841	+	0.142176i	$0.954590\pi$
$828$	1.49608e10	+	1.47767e10i	0.0318297	+	0.0314382i
$829$	3.30572e11			0.699920			0.349960	−	0.936765i	$-0.386195\pi$
$829$	3.30572e11			0.699920			0.349960	+	0.936765i	$0.386195\pi$
$830$		0			0
$831$	2.15779e11	+	5.16411e11i	0.452485	+	1.08291i
$832$	3.24534e11			0.677278
$833$		−	8.50117e10i		−	0.176563i
$834$	9.37219e11	−	3.91611e11i	1.93721	−	0.809450i
$835$		0			0
$836$		−	1.75778e11i		−	0.359865i
$837$	1.64307e11	+	6.62783e10i	0.334776	+	0.135042i
$838$	−9.70334e11			−1.96764
$839$		−	6.49466e10i		−	0.131072i	−0.997850	−	0.0655358i	$-0.979124\pi$
$839$		−	6.49466e10i		−	0.131072i	0.997850	−	0.0655358i	$-0.0208757\pi$
$840$		0			0
$841$	−7.46344e10			−0.149195
$842$		−	3.90074e11i		−	0.776066i
$843$	1.29941e11	−	5.42951e10i	0.257299	−	0.107510i
$844$	−3.82752e10			−0.0754306
$845$		0			0
$846$	1.23365e11	−	1.24902e11i	0.240830	−	0.243830i
$847$	−1.12777e11			−0.219122
$848$		−	3.61325e11i		−	0.698739i
$849$	1.29289e11	+	3.09420e11i	0.248846	+	0.595549i
$850$		0			0
$851$			4.11571e10i			0.0784742i
$852$	−4.25959e10	+	1.77984e10i	−0.0808369	+	0.0337772i
$853$	−4.77389e10			−0.0901730			−0.0450865	−	0.998983i	$-0.514356\pi$
$853$	−4.77389e10			−0.0901730			−0.0450865	+	0.998983i	$0.514356\pi$
$854$			3.99443e11i			0.750971i
$855$		0			0
$856$	−4.84268e11			−0.901966
$857$			8.80902e11i			1.63307i	0.577297	+	0.816534i	$0.304108\pi$
$857$			8.80902e11i			1.63307i	−0.577297	+	0.816534i	$0.695892\pi$
$858$	−2.33710e11	−	5.59326e11i	−0.431250	−	1.03209i
$859$	7.72690e9			0.0141916			0.00709582	−	0.999975i	$-0.497741\pi$
$859$	7.72690e9			0.0141916			0.00709582	+	0.999975i	$0.497741\pi$
$860$		0			0
$861$	3.17463e11	−	1.32650e11i	0.577671	−	0.241376i
$862$	8.65067e11			1.56683
$863$			4.51506e11i			0.813993i	0.913430	+	0.406996i	$0.133424\pi$
$863$			4.51506e11i			0.813993i	−0.913430	+	0.406996i	$0.866576\pi$
$864$	−8.53464e10	+	2.11578e11i	−0.153155	+	0.379678i
$865$		0			0
$866$			3.46485e11i			0.616045i
$867$	−2.11531e11	−	5.06245e11i	−0.374367	−	0.895951i
$868$	−6.07930e10			−0.107096
$869$			7.89000e11i			1.38356i
$870$		0			0
$871$	6.71136e11			1.16611
$872$			9.45520e10i			0.163533i
$873$	−6.72897e11	+	6.81277e11i	−1.15849	+	1.17292i
$874$	−2.22492e11			−0.381301
$875$		0			0
$876$	5.79395e10	+	1.38663e11i	0.0983917	+	0.235475i
$877$	−6.13569e11			−1.03721			−0.518603	−	0.855015i	$-0.673548\pi$
$877$	−6.13569e11			−1.03721			−0.518603	+	0.855015i	$0.673548\pi$
$878$			3.06731e11i			0.516155i
$879$	5.13683e11	−	2.14639e11i	0.860478	−	0.359545i
$880$		0			0
$881$		−	5.49493e11i		−	0.912134i	−0.889945	−	0.456067i	$-0.849258\pi$
$881$		−	5.49493e11i		−	0.912134i	0.889945	−	0.456067i	$-0.150742\pi$
$882$	4.90774e11	+	4.84737e11i	0.810974	+	0.800999i
$883$	2.86999e11			0.472104			0.236052	−	0.971740i	$-0.424146\pi$
$883$	2.86999e11			0.472104			0.236052	+	0.971740i	$0.424146\pi$
$884$		−	2.04774e10i		−	0.0335325i
$885$		0			0
$886$	−4.34127e11			−0.704501
$887$			6.67473e11i			1.07830i	0.842210	+	0.539150i	$0.181254\pi$
$887$			6.67473e11i			1.07830i	−0.842210	+	0.539150i	$0.818746\pi$
$888$	−1.82113e11	+	7.60946e10i	−0.292879	+	0.122378i
$889$	1.14991e11			0.184102
$890$		0			0
$891$	−6.76847e11	+	8.37693e9i	−1.07394	+	0.0132915i
$892$	−6.71482e10			−0.106066
$893$			3.19656e11i			0.502663i
$894$	3.67378e11	+	8.79225e11i	0.575126	+	1.37642i
$895$		0			0
$896$			1.09919e12i			1.70545i
$897$	−1.21834e11	+	5.09075e10i	−0.188191	+	0.0786343i
$898$	8.70228e11			1.33822
$899$		−	2.52771e11i		−	0.386980i
$900$		0			0
$901$	6.73089e10			0.102135
$902$		−	3.42736e11i		−	0.517767i
$903$	1.23678e11	+	2.95991e11i	0.186012	+	0.445171i
$904$	−6.57884e11			−0.985089
$905$		0			0
$906$	7.40197e11	−	3.09286e11i	1.09859	−	0.459037i
$907$	−8.49166e11			−1.25477			−0.627384	−	0.778710i	$-0.715874\pi$
$907$	−8.49166e11			−1.25477			−0.627384	+	0.778710i	$0.715874\pi$
$908$			2.23972e11i			0.329496i
$909$	5.66278e10	+	5.59313e10i	0.0829420	+	0.0819218i
$910$		0			0
$911$		−	1.01144e12i		−	1.46847i	−0.678895	−	0.734235i	$-0.737541\pi$
$911$		−	1.01144e12i		−	1.46847i	0.678895	−	0.734235i	$-0.262459\pi$
$912$	−5.00727e11	−	1.19836e12i	−0.723805	−	1.73224i
$913$	−7.08508e11			−1.01967
$914$		−	1.32190e12i		−	1.89415i
$915$		0			0
$916$	3.80679e10			0.0540726
$917$			7.76414e10i			0.109803i
$918$	−1.23225e11	−	4.97065e10i	−0.173511	−	0.0699910i
$919$	−2.59912e11			−0.364389			−0.182194	−	0.983263i	$-0.558320\pi$
$919$	−2.59912e11			−0.364389			−0.182194	+	0.983263i	$0.558320\pi$
$920$		0			0
$921$	−7.32046e10	−	1.75196e11i	−0.101742	−	0.243493i
$922$	3.05715e11			0.423052
$923$		−	2.89886e11i		−	0.399411i
$924$	2.14309e11	−	8.95476e10i	0.294004	−	0.122847i
$925$		0			0
$926$		−	3.71320e11i		−	0.505015i
$927$	−5.70398e11	+	5.77501e11i	−0.772430	+	0.782049i
$928$	3.25492e11			0.438883
$929$		−	4.58599e11i		−	0.615701i	−0.951435	−	0.307851i	$-0.900390\pi$
$929$		−	4.58599e11i		−	0.615701i	0.951435	−	0.307851i	$-0.0996097\pi$
$930$		0			0
$931$	−1.25602e12			−1.67185
$932$			2.02328e11i			0.268159i
$933$	4.62319e11	−	1.93177e11i	0.610120	−	0.254935i
$934$	−2.62207e11			−0.344554
$935$		0			0
$936$	−4.50513e11	−	4.44972e11i	−0.586954	−	0.579734i
$937$	7.74108e11			1.00425			0.502126	−	0.864794i	$-0.332551\pi$
$937$	7.74108e11			1.00425			0.502126	+	0.864794i	$0.332551\pi$
$938$			1.49428e12i			1.93028i
$939$	−1.97895e11	−	4.73612e11i	−0.254550	−	0.609200i
$940$		0			0
$941$			6.66336e11i			0.849836i	0.905232	+	0.424918i	$0.139697\pi$
$941$			6.66336e11i			0.849836i	−0.905232	+	0.424918i	$0.860303\pi$
$942$	1.97794e11	−	8.26466e10i	0.251194	−	0.104959i
$943$	−7.46558e10			−0.0944098
$944$		−	9.97049e11i		−	1.25553i
$945$		0			0
$946$	3.19554e11			0.399007
$947$		−	2.31471e11i		−	0.287804i	−0.989592	−	0.143902i	$-0.954035\pi$
$947$		−	2.31471e11i		−	0.287804i	0.989592	−	0.143902i	$-0.0459649\pi$
$948$	−8.33795e10	−	1.99547e11i	−0.103235	−	0.247066i
$949$	−9.43670e11			−1.16347
$950$		0			0
$951$	1.97053e11	−	8.23374e10i	0.240914	−	0.100664i
$952$	−1.73750e11			−0.211533
$953$			7.87320e11i			0.954509i	0.878765	+	0.477254i	$0.158368\pi$
$953$			7.87320e11i			0.954509i	−0.878765	+	0.477254i	$0.841632\pi$
$954$	−3.83796e11	+	3.88575e11i	−0.463348	+	0.469118i
$955$		0			0
$956$			1.94169e11i			0.232461i
$957$	3.72329e11	+	8.91075e11i	0.443894	+	1.06235i
$958$	−9.06926e10			−0.107674
$959$			1.39217e12i			1.64595i
$960$		0			0
$961$	−7.41750e11			−0.869689
$962$			3.25214e11i			0.379725i
$963$	6.33930e11	+	6.26133e11i	0.737116	+	0.728050i
$964$	−7.26050e10			−0.0840734
$965$		0			0
$966$	−1.13345e11	−	2.71262e11i	−0.130165	−	0.311517i
$967$	6.73055e11			0.769741			0.384871	−	0.922971i	$-0.374246\pi$
$967$	6.73055e11			0.769741			0.384871	+	0.922971i	$0.374246\pi$
$968$			1.17351e11i			0.133654i
$969$	2.23235e11	−	9.32772e10i	0.253202	−	0.105799i
$970$		0			0
$971$		−	9.86603e10i		−	0.110985i	−0.998459	−	0.0554927i	$-0.982327\pi$
$971$		−	9.86603e10i		−	0.110985i	0.998459	−	0.0554927i	$-0.0176729\pi$
$972$	1.70297e11	−	7.36461e10i	0.190785	−	0.0825059i
$973$	−2.44386e12			−2.72662
$974$			6.68153e11i			0.742404i
$975$		0			0
$976$	5.05940e11			0.557571
$977$			2.61518e11i			0.287028i	0.989648	+	0.143514i	$0.0458402\pi$
$977$			2.61518e11i			0.287028i	−0.989648	+	0.143514i	$0.954160\pi$
$978$	−1.48599e12	+	6.20910e11i	−1.62428	+	0.678693i
$979$	−1.14913e12			−1.25095
$980$		0			0
$981$	1.22251e11	−	1.23773e11i	0.132000	−	0.133644i
$982$	−1.26950e12			−1.36517
$983$		−	9.90776e11i		−	1.06111i	−0.847650	−	0.530556i	$-0.821983\pi$
$983$		−	9.90776e11i		−	1.06111i	0.847650	−	0.530556i	$-0.178017\pi$
$984$	−1.38030e11	−	3.30339e11i	−0.147229	−	0.352354i
$985$		0			0
$986$			1.89570e11i			0.200568i
$987$	−3.89726e11	+	1.62844e11i	−0.410667	+	0.171595i
$988$	−3.02547e11			−0.317515
$989$		−	6.96063e10i		−	0.0727551i
$990$		0			0
$991$	3.03368e11			0.314540			0.157270	−	0.987556i	$-0.449731\pi$
$991$	3.03368e11			0.314540			0.157270	+	0.987556i	$0.449731\pi$
$992$			1.43117e11i			0.147789i
$993$	1.89491e11	+	4.53499e11i	0.194891	+	0.466422i
$994$	6.45428e11			0.661153
$995$		0			0
$996$	1.79190e11	−	7.48733e10i	0.182086	−	0.0760833i
$997$	−2.24125e11			−0.226835			−0.113417	−	0.993547i	$-0.536180\pi$
$997$	−2.24125e11			−0.226835			−0.113417	+	0.993547i	$0.536180\pi$
$998$		−	3.96358e11i		−	0.399545i
$999$	3.36781e11	+	1.35851e11i	0.338132	+	0.136396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.c.h.26.3		12
3.2	odd	2	inner	75.9.c.h.26.9		12
5.2	odd	4		15.9.d.c.14.10	yes	12
5.3	odd	4		15.9.d.c.14.3	✓	12
5.4	even	2	inner	75.9.c.h.26.10		12
15.2	even	4		15.9.d.c.14.4	yes	12
15.8	even	4		15.9.d.c.14.9	yes	12
15.14	odd	2	inner	75.9.c.h.26.4		12
20.3	even	4		240.9.c.c.209.2		12
20.7	even	4		240.9.c.c.209.11		12
60.23	odd	4		240.9.c.c.209.12		12
60.47	odd	4		240.9.c.c.209.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.3	✓	12	5.3	odd	4
15.9.d.c.14.4	yes	12	15.2	even	4
15.9.d.c.14.9	yes	12	15.8	even	4
15.9.d.c.14.10	yes	12	5.2	odd	4
75.9.c.h.26.3		12	1.1	even	1	trivial
75.9.c.h.26.4		12	15.14	odd	2	inner
75.9.c.h.26.9		12	3.2	odd	2	inner
75.9.c.h.26.10		12	5.4	even	2	inner
240.9.c.c.209.1		12	60.47	odd	4
240.9.c.c.209.2		12	20.3	even	4
240.9.c.c.209.11		12	20.7	even	4
240.9.c.c.209.12		12	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-17.5844i q^{2} +(-31.2287 - 74.7380i) q^{3} -53.2123 q^{4} +(-1314.22 + 549.140i) q^{6} +3426.92 q^{7} -3565.91i q^{8} +(-4610.53 + 4667.95i) q^{9} +O(q^{10})\)	\(q-17.5844i q^{2} +(-31.2287 - 74.7380i) q^{3} -53.2123 q^{4} +(-1314.22 + 549.140i) q^{6} +3426.92 q^{7} -3565.91i q^{8} +(-4610.53 + 4667.95i) q^{9} -15724.8i q^{11} +(1661.75 + 3976.98i) q^{12} -27065.2 q^{13} -60260.4i q^{14} -76326.8 q^{16} -14218.4i q^{17} +(82083.2 + 81073.6i) q^{18} -210073. q^{19} +(-107018. - 256121. i) q^{21} -276511. q^{22} +60230.4i q^{23} +(-266509. + 111359. i) q^{24} +475926. i q^{26} +(492854. + 198808. i) q^{27} -182354. q^{28} -758209. i q^{29} +333379. q^{31} +429291. i q^{32} +(-1.17524e6 + 491064. i) q^{33} -250023. q^{34} +(245337. - 248392. i) q^{36} +683328. q^{37} +3.69401e6i q^{38} +(845213. + 2.02280e6i) q^{39} +1.23950e6i q^{41} +(-4.50374e6 + 1.88186e6i) q^{42} -1.15567e6 q^{43} +836750. i q^{44} +1.05912e6 q^{46} -1.52165e6i q^{47} +(2.38359e6 + 5.70451e6i) q^{48} +5.97898e6 q^{49} +(-1.06266e6 + 444024. i) q^{51} +1.44020e6 q^{52} +4.73392e6i q^{53} +(3.49592e6 - 8.66656e6i) q^{54} -1.22201e7i q^{56} +(6.56030e6 + 1.57004e7i) q^{57} -1.33327e7 q^{58} +1.30629e7i q^{59} -6.62861e6 q^{61} -5.86228e6i q^{62} +(-1.57999e7 + 1.59967e7i) q^{63} -1.19908e7 q^{64} +(8.63509e6 + 2.06659e7i) q^{66} -2.47970e7 q^{67} +756595. i q^{68} +(4.50150e6 - 1.88092e6i) q^{69} +1.07106e7i q^{71} +(1.66455e7 + 1.64407e7i) q^{72} +3.48665e7 q^{73} -1.20159e7i q^{74} +1.11784e7 q^{76} -5.38875e7i q^{77} +(3.55698e7 - 1.48626e7i) q^{78} -5.01757e7 q^{79} +(-532723. - 4.30434e7i) q^{81} +2.17960e7 q^{82} -4.50568e7i q^{83} +(5.69469e6 + 1.36288e7i) q^{84} +2.03217e7i q^{86} +(-5.66670e7 + 2.36779e7i) q^{87} -5.60730e7 q^{88} -7.30781e7i q^{89} -9.27503e7 q^{91} -3.20500e6i q^{92} +(-1.04110e7 - 2.49161e7i) q^{93} -2.67573e7 q^{94} +(3.20843e7 - 1.34062e7i) q^{96} +1.45948e8 q^{97} -1.05137e8i q^{98} +(7.34023e7 + 7.24995e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9}+O(q^{10}) \) 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9	\( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9} + 413328 q^{16} - 276192 q^{19} - 604044 q^{21} - 1173336 q^{24} - 279216 q^{31} + 1225344 q^{34} - 10311840 q^{36} - 3780864 q^{39} + 37414536 q^{46} + 6222300 q^{49} + 3931248 q^{51} + 53281692 q^{54} - 91958256 q^{61} - 57497760 q^{64} + 111065040 q^{66} - 8138748 q^{69} - 232646880 q^{76} - 420402672 q^{79} + 98480772 q^{81} + 528357816 q^{84} - 100211328 q^{91} - 543022776 q^{94} + 333306864 q^{96} + 640360080 q^{99}+O(q^{100}) \) 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9 + 413328 * q^16 - 276192 * q^19 - 604044 * q^21 - 1173336 * q^24 - 279216 * q^31 + 1225344 * q^34 - 10311840 * q^36 - 3780864 * q^39 + 37414536 * q^46 + 6222300 * q^49 + 3931248 * q^51 + 53281692 * q^54 - 91958256 * q^61 - 57497760 * q^64 + 111065040 * q^66 - 8138748 * q^69 - 232646880 * q^76 - 420402672 * q^79 + 98480772 * q^81 + 528357816 * q^84 - 100211328 * q^91 - 543022776 * q^94 + 333306864 * q^96 + 640360080 * q^99

Introduction

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