LMFDB - Embedded newform 75.9.d.d.74.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(74,75)]

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, 1]))

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

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

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 $ x^20 + 3278x^18 + 4245491x^16 + 2854629536x^14 + 1117319469691x^12 + 266849787342054x^10 + 38935163332201981x^8 + 3308855301815965532x^6 + 143709036159536320436x^4 + 2262672788809149782000*x^2 + 8995759125454185640000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{22}\cdot 5^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.18
Root			$-14.5890i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.9.d.d.74.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+24.1370 q^{2} +(-70.6742 + 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} +1042.22i q^{7} +1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +O(q^{10})$	\(q+24.1370 q^{2} +(-70.6742 + 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} +1042.22i q^{7} +1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +19553.4i q^{11} +(-23081.8 + 12924.8i) q^{12} -29037.8i q^{13} +25156.0i q^{14} -42480.5 q^{16} -122230. q^{17} +(82758.4 - 135018. i) q^{18} -189552. q^{19} +(-41245.5 - 73658.1i) q^{21} +471959. i q^{22} +112212. q^{23} +(-120424. + 67432.2i) q^{24} -700886. i q^{26} +(-20947.3 + 531028. i) q^{27} +340383. i q^{28} -108842. i q^{29} -1.19254e6 q^{31} -1.46155e6 q^{32} +(-773817. - 1.38192e6i) q^{33} -2.95026e6 q^{34} +(1.11979e6 - 1.82691e6i) q^{36} -2.84100e6i q^{37} -4.57521e6 q^{38} +(1.14916e6 + 2.05223e6i) q^{39} +3.90516e6i q^{41} +(-995541. - 1.77788e6i) q^{42} +864712. i q^{43} +6.38601e6i q^{44} +2.70846e6 q^{46} -1.48368e6 q^{47} +(3.00227e6 - 1.68115e6i) q^{48} +4.67858e6 q^{49} +(8.63850e6 - 4.83720e6i) q^{51} -9.48358e6i q^{52} -3.65103e6 q^{53} +(-505604. + 1.28174e7i) q^{54} +1.77586e6i q^{56} +(1.33964e7 - 7.50144e6i) q^{57} -2.62712e6i q^{58} +1.46586e7i q^{59} +1.60123e7 q^{61} -2.87844e7 q^{62} +(5.82998e6 + 3.57345e6i) q^{63} -2.44025e7 q^{64} +(-1.86776e7 - 3.33554e7i) q^{66} +2.14382e7i q^{67} -3.99195e7 q^{68} +(-7.93050e6 + 4.44075e6i) q^{69} +4.10459e7i q^{71} +(5.84224e6 - 9.53144e6i) q^{72} -4.70244e7i q^{73} -6.85731e7i q^{74} -6.19065e7 q^{76} -2.03789e7 q^{77} +(2.77373e7 + 4.95346e7i) q^{78} +2.43754e7 q^{79} +(-1.95348e7 - 3.83590e7i) q^{81} +9.42589e7i q^{82} +6.88381e6 q^{83} +(-1.34705e7 - 2.40563e7i) q^{84} +2.08715e7i q^{86} +(4.30738e6 + 7.69233e6i) q^{87} +3.33174e7i q^{88} -3.39808e7i q^{89} +3.02638e7 q^{91} +3.66478e7 q^{92} +(8.42822e7 - 4.71945e7i) q^{93} -3.58116e7 q^{94} +(1.03294e8 - 5.78405e7i) q^{96} +1.50338e7i q^{97} +1.12927e8 q^{98} +(1.09378e8 + 6.70425e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) $ 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9	$ 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) $ 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9 + 89268 * q^16 + 287868 * q^19 + 1346856 * q^21 + 2033718 * q^24 - 6028120 * q^31 - 9954292 * q^34 + 9001054 * q^36 + 15026564 * q^39 - 27877272 * q^46 - 17907092 * q^49 + 12418574 * q^51 + 17772544 * q^54 + 3040440 * q^61 + 9073996 * q^64 + 20930590 * q^66 - 22789956 * q^69 - 59058092 * q^76 - 17099792 * q^79 + 45225890 * q^81 + 273766584 * q^84 - 214448528 * q^91 - 712237192 * q^94 + 1050848002 * q^96 + 764842670 * 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 $

$2$	24.1370			1.50856			0.754281	−	0.656552i	$-0.227986\pi$
$2$	24.1370			1.50856			0.754281	+	0.656552i	$0.227986\pi$
$3$	−70.6742	+	39.5746i	−0.872521	+	0.488576i
$3$	−70.6742	+	39.5746i	−0.872521	+	0.488576i
$4$	326.594			1.27576
$5$		0			0
$5$		0			0
$6$	−1705.86	+	955.212i	−1.31625	+	0.737047i
$7$			1042.22i			0.434077i	0.976163	+	0.217039i	$0.0696398\pi$
$7$			1042.22i			0.434077i	−0.976163	+	0.217039i	$0.930360\pi$
$8$	1703.92			0.415997
$9$	3428.70	−	5593.81i	0.522587	−	0.852586i
$10$		0			0
$11$			19553.4i			1.33552i	0.744376	+	0.667761i	$0.232747\pi$
$11$			19553.4i			1.33552i	−0.744376	+	0.667761i	$0.767253\pi$
$12$	−23081.8	+	12924.8i	−1.11313	+	0.623304i
$13$		−	29037.8i		−	1.01670i	−0.861152	−	0.508348i	$-0.830257\pi$
$13$		−	29037.8i		−	1.01670i	0.861152	−	0.508348i	$-0.169743\pi$
$14$			25156.0i			0.654832i
$15$		0			0
$16$	−42480.5			−0.648200
$17$	−122230.			−1.46346			−0.731731	−	0.681594i	$-0.761287\pi$
$17$	−122230.			−1.46346			−0.731731	+	0.681594i	$0.761287\pi$
$18$	82758.4	−	135018.i	0.788355	−	1.28618i
$19$	−189552.			−1.45450			−0.727250	−	0.686373i	$-0.759202\pi$
$19$	−189552.			−1.45450			−0.727250	+	0.686373i	$0.759202\pi$
$20$		0			0
$21$	−41245.5	−	73658.1i	−0.212080	−	0.378742i
$22$			471959.i			2.01472i
$23$	112212.			0.400985			0.200493	−	0.979695i	$-0.435746\pi$
$23$	112212.			0.400985			0.200493	+	0.979695i	$0.435746\pi$
$24$	−120424.	+	67432.2i	−0.362966	+	0.203246i
$25$		0			0
$26$		−	700886.i		−	1.53375i
$27$	−20947.3	+	531028.i	−0.0394160	+	0.999223i
$28$			340383.i			0.553777i
$29$		−	108842.i		−	0.153888i	−0.997035	−	0.0769440i	$-0.975484\pi$
$29$		−	108842.i		−	0.153888i	0.997035	−	0.0769440i	$-0.0245163\pi$
$30$		0			0
$31$	−1.19254e6			−1.29130			−0.645651	−	0.763633i	$-0.723414\pi$
$31$	−1.19254e6			−1.29130			−0.645651	+	0.763633i	$0.723414\pi$
$32$	−1.46155e6			−1.39385
$33$	−773817.	−	1.38192e6i	−0.652503	−	1.16527i
$34$	−2.95026e6			−2.20772
$35$		0			0
$36$	1.11979e6	−	1.82691e6i	0.666695	−	1.08769i
$37$		−	2.84100e6i		−	1.51588i	−0.652326	−	0.757939i	$-0.726207\pi$
$37$		−	2.84100e6i		−	1.51588i	0.652326	−	0.757939i	$-0.273793\pi$
$38$	−4.57521e6			−2.19420
$39$	1.14916e6	+	2.05223e6i	0.496733	+	0.887088i
$40$		0			0
$41$			3.90516e6i			1.38199i	0.722861	+	0.690993i	$0.242827\pi$
$41$			3.90516e6i			1.38199i	−0.722861	+	0.690993i	$0.757173\pi$
$42$	−995541.	−	1.77788e6i	−0.319935	−	0.571355i
$43$			864712.i			0.252928i	0.991971	+	0.126464i	$0.0403629\pi$
$43$			864712.i			0.252928i	−0.991971	+	0.126464i	$0.959637\pi$
$44$			6.38601e6i			1.70380i
$45$		0			0
$46$	2.70846e6			0.604911
$47$	−1.48368e6			−0.304053			−0.152026	−	0.988376i	$-0.548580\pi$
$47$	−1.48368e6			−0.304053			−0.152026	+	0.988376i	$0.548580\pi$
$48$	3.00227e6	−	1.68115e6i	0.565569	−	0.316695i
$49$	4.67858e6			0.811577
$50$		0			0
$51$	8.63850e6	−	4.83720e6i	1.27690	−	0.715012i
$52$		−	9.48358e6i		−	1.29706i
$53$	−3.65103e6			−0.462713			−0.231357	−	0.972869i	$-0.574316\pi$
$53$	−3.65103e6			−0.462713			−0.231357	+	0.972869i	$0.574316\pi$
$54$	−505604.	+	1.28174e7i	−0.0594615	+	1.50739i
$55$		0			0
$56$			1.77586e6i			0.180575i
$57$	1.33964e7	−	7.50144e6i	1.26908	−	0.710633i
$58$		−	2.62712e6i		−	0.232149i
$59$			1.46586e7i			1.20972i	0.796332	+	0.604859i	$0.206771\pi$
$59$			1.46586e7i			1.20972i	−0.796332	+	0.604859i	$0.793229\pi$
$60$		0			0
$61$	1.60123e7			1.15647			0.578234	−	0.815871i	$-0.303742\pi$
$61$	1.60123e7			1.15647			0.578234	+	0.815871i	$0.303742\pi$
$62$	−2.87844e7			−1.94801
$63$	5.82998e6	+	3.57345e6i	0.370088	+	0.226843i
$64$	−2.44025e7			−1.45450
$65$		0			0
$66$	−1.86776e7	−	3.33554e7i	−0.984341	−	1.75788i
$67$			2.14382e7i			1.06387i	0.846784	+	0.531937i	$0.178536\pi$
$67$			2.14382e7i			1.06387i	−0.846784	+	0.531937i	$0.821464\pi$
$68$	−3.99195e7			−1.86702
$69$	−7.93050e6	+	4.44075e6i	−0.349868	+	0.195912i
$70$		0			0
$71$			4.10459e7i			1.61524i	0.589706	+	0.807618i	$0.299244\pi$
$71$			4.10459e7i			1.61524i	−0.589706	+	0.807618i	$0.700756\pi$
$72$	5.84224e6	−	9.53144e6i	0.217395	−	0.354673i
$73$		−	4.70244e7i		−	1.65589i	−0.560808	−	0.827946i	$-0.689509\pi$
$73$		−	4.70244e7i		−	1.65589i	0.560808	−	0.827946i	$-0.310491\pi$
$74$		−	6.85731e7i		−	2.28679i
$75$		0			0
$76$	−6.19065e7			−1.85559
$77$	−2.03789e7			−0.579719
$78$	2.77373e7	+	4.95346e7i	0.749352	+	1.33823i
$79$	2.43754e7			0.625811			0.312905	−	0.949784i	$-0.398698\pi$
$79$	2.43754e7			0.625811			0.312905	+	0.949784i	$0.398698\pi$
$80$		0			0
$81$	−1.95348e7	−	3.83590e7i	−0.453805	−	0.891101i
$82$			9.42589e7i			2.08481i
$83$	6.88381e6			0.145050			0.0725248	−	0.997367i	$-0.476894\pi$
$83$	6.88381e6			0.145050			0.0725248	+	0.997367i	$0.476894\pi$
$84$	−1.34705e7	−	2.40563e7i	−0.270562	−	0.483183i
$85$		0			0
$86$			2.08715e7i			0.381558i
$87$	4.30738e6	+	7.69233e6i	0.0751859	+	0.134271i
$88$			3.33174e7i			0.555573i
$89$		−	3.39808e7i		−	0.541593i	−0.962637	−	0.270796i	$-0.912713\pi$
$89$		−	3.39808e7i		−	0.541593i	0.962637	−	0.270796i	$-0.0872870\pi$
$90$		0			0
$91$	3.02638e7			0.441324
$92$	3.66478e7			0.511560
$93$	8.42822e7	−	4.71945e7i	1.12669	−	0.630899i
$94$	−3.58116e7			−0.458682
$95$		0			0
$96$	1.03294e8	−	5.78405e7i	1.21616	−	0.681000i
$97$			1.50338e7i			0.169817i	0.996389	+	0.0849086i	$0.0270598\pi$
$97$			1.50338e7i			0.169817i	−0.996389	+	0.0849086i	$0.972940\pi$
$98$	1.12927e8			1.22431
$99$	1.09378e8	+	6.70425e7i	1.13865	+	0.697927i
$100$		0			0
$101$			1.51577e8i			1.45663i	0.685244	+	0.728314i	$0.259696\pi$
$101$			1.51577e8i			1.45663i	−0.685244	+	0.728314i	$0.740304\pi$
$102$	2.08507e8	−	1.16755e8i	1.92628	−	1.07864i
$103$		−	4.88143e7i		−	0.433709i	−0.976204	−	0.216854i	$-0.930420\pi$
$103$		−	4.88143e7i		−	0.433709i	0.976204	−	0.216854i	$-0.0695797\pi$
$104$		−	4.94783e7i		−	0.422942i
$105$		0			0
$106$	−8.81248e7			−0.698031
$107$	−1.32340e6			−0.0100962			−0.00504808	−	0.999987i	$-0.501607\pi$
$107$	−1.32340e6			−0.0100962			−0.00504808	+	0.999987i	$0.501607\pi$
$108$	−6.84125e6	+	1.73431e8i	−0.0502853	+	1.27477i
$109$	1.70973e8			1.21122			0.605608	−	0.795763i	$-0.292930\pi$
$109$	1.70973e8			1.21122			0.605608	+	0.795763i	$0.292930\pi$
$110$		0			0
$111$	1.12432e8	+	2.00785e8i	0.740621	+	1.32264i
$112$		−	4.42740e7i		−	0.281369i
$113$	−3.37372e7			−0.206916			−0.103458	−	0.994634i	$-0.532991\pi$
$113$	−3.37372e7			−0.206916			−0.103458	+	0.994634i	$0.532991\pi$
$114$	3.23349e8	−	1.81062e8i	1.91449	−	1.07203i
$115$		0			0
$116$		−	3.55471e7i		−	0.196324i
$117$	−1.62432e8	−	9.95619e7i	−0.866820	−	0.531312i
$118$			3.53814e8i			1.82493i
$119$		−	1.27390e8i		−	0.635256i
$120$		0			0
$121$	−1.67975e8			−0.783617
$122$	3.86488e8			1.74460
$123$	−1.54545e8	−	2.75995e8i	−0.675205	−	1.20581i
$124$	−3.89478e8			−1.64739
$125$		0			0
$126$	1.40718e8	+	8.62524e7i	0.558301	+	0.342207i
$127$			9.39184e7i			0.361024i	0.983573	+	0.180512i	$0.0577754\pi$
$127$			9.39184e7i			0.361024i	−0.983573	+	0.180512i	$0.942225\pi$
$128$	−2.14845e8			−0.800361
$129$	−3.42206e7	−	6.11128e7i	−0.123575	−	0.220685i
$130$		0			0
$131$		−	2.71847e8i		−	0.923079i	−0.887120	−	0.461540i	$-0.847297\pi$
$131$		−	2.71847e8i		−	0.923079i	0.887120	−	0.461540i	$-0.152703\pi$
$132$	−2.52724e8	−	4.51326e8i	−0.832436	−	1.48660i
$133$		−	1.97555e8i		−	0.631365i
$134$			5.17455e8i			1.60492i
$135$		0			0
$136$	−2.08270e8			−0.608796
$137$	−2.18688e8			−0.620788			−0.310394	−	0.950608i	$-0.600461\pi$
$137$	−2.18688e8			−0.620788			−0.310394	+	0.950608i	$0.600461\pi$
$138$	−1.91418e8	+	1.07186e8i	−0.527798	+	0.295545i
$139$	−4.92467e8			−1.31922			−0.659611	−	0.751608i	$-0.729279\pi$
$139$	−4.92467e8			−1.31922			−0.659611	+	0.751608i	$0.729279\pi$
$140$		0			0
$141$	1.04858e8	−	5.87161e7i	0.265293	−	0.148553i
$142$			9.90724e8i			2.43668i
$143$	5.67787e8			1.35782
$144$	−1.45653e8	+	2.37628e8i	−0.338741	+	0.552646i
$145$		0			0
$146$		−	1.13503e9i		−	2.49801i
$147$	−3.30655e8	+	1.85153e8i	−0.708118	+	0.396517i
$148$		−	9.27853e8i		−	1.93389i
$149$			2.38202e6i			0.00483283i	0.999997	+	0.00241641i	$0.000769169\pi$
$149$			2.38202e6i			0.00483283i	−0.999997	+	0.00241641i	$0.999231\pi$
$150$		0			0
$151$	−2.94102e8			−0.565705			−0.282852	−	0.959163i	$-0.591281\pi$
$151$	−2.94102e8			−0.565705			−0.282852	+	0.959163i	$0.591281\pi$
$152$	−3.22982e8			−0.605067
$153$	−4.19089e8	+	6.83731e8i	−0.764787	+	1.24773i
$154$	−4.91885e8			−0.874542
$155$		0			0
$156$	3.75309e8	+	6.70245e8i	0.633710	+	1.13171i
$157$			5.15599e8i			0.848621i	0.905517	+	0.424310i	$0.139483\pi$
$157$			5.15599e8i			0.848621i	−0.905517	+	0.424310i	$0.860517\pi$
$158$	5.88348e8			0.944074
$159$	2.58034e8	−	1.44488e8i	0.403727	−	0.226070i
$160$		0			0
$161$			1.16950e8i			0.174059i
$162$	−4.71511e8	−	9.25870e8i	−0.684592	−	1.34428i
$163$		−	7.26841e8i		−	1.02965i	−0.857296	−	0.514824i	$-0.827857\pi$
$163$		−	7.26841e8i		−	1.02965i	0.857296	−	0.514824i	$-0.172143\pi$
$164$			1.27540e9i			1.76308i
$165$		0			0
$166$	1.66154e8			0.218816
$167$	−3.33903e8			−0.429294			−0.214647	−	0.976692i	$-0.568860\pi$
$167$	−3.33903e8			−0.429294			−0.214647	+	0.976692i	$0.568860\pi$
$168$	−7.02791e7	−	1.25508e8i	−0.0882245	−	0.157555i
$169$	−2.74650e7			−0.0336692
$170$		0			0
$171$	−6.49915e8	+	1.06032e9i	−0.760103	+	1.24009i
$172$			2.82410e8i			0.322675i
$173$	−1.32165e9			−1.47547			−0.737737	−	0.675088i	$-0.764106\pi$
$173$	−1.32165e9			−1.47547			−0.737737	+	0.675088i	$0.764106\pi$
$174$	1.03967e8	+	1.85670e8i	0.113423	+	0.202555i
$175$		0			0
$176$		−	8.30636e8i		−	0.865685i
$177$	−5.80109e8	−	1.03599e9i	−0.591039	−	1.05551i
$178$		−	8.20193e8i		−	0.817026i
$179$		−	1.09788e8i		−	0.106940i	−0.998569	−	0.0534701i	$-0.982972\pi$
$179$		−	1.09788e8i		−	0.106940i	0.998569	−	0.0534701i	$-0.0170282\pi$
$180$		0			0
$181$	−3.65073e8			−0.340146			−0.170073	−	0.985431i	$-0.554400\pi$
$181$	−3.65073e8			−0.340146			−0.170073	+	0.985431i	$0.554400\pi$
$182$	7.30477e8			0.665765
$183$	−1.13166e9	+	6.33680e8i	−1.00904	+	0.565023i
$184$	1.91201e8			0.166809
$185$		0			0
$186$	2.03432e9	−	1.13913e9i	1.69968	−	0.951750i
$187$		−	2.39000e9i		−	1.95448i
$188$	−4.84561e8			−0.387898
$189$	−5.53448e8	−	2.18317e7i	−0.433740	−	0.0171096i
$190$		0			0
$191$			2.14467e9i			1.61148i	0.592267	+	0.805742i	$0.298233\pi$
$191$			2.14467e9i			1.61148i	−0.592267	+	0.805742i	$0.701767\pi$
$192$	1.72463e9	−	9.65721e8i	1.26909	−	0.710635i
$193$			2.36470e9i			1.70431i	0.523293	+	0.852153i	$0.324703\pi$
$193$			2.36470e9i			1.70431i	−0.523293	+	0.852153i	$0.675297\pi$
$194$			3.62870e8i			0.256180i
$195$		0			0
$196$	1.52800e9			1.03538
$197$	2.37290e9			1.57548			0.787742	−	0.616006i	$-0.211250\pi$
$197$	2.37290e9			1.57548			0.787742	+	0.616006i	$0.211250\pi$
$198$	2.64005e9	+	1.61820e9i	1.71772	+	1.05287i
$199$	8.35564e8			0.532804			0.266402	−	0.963862i	$-0.414165\pi$
$199$	8.35564e8			0.532804			0.266402	+	0.963862i	$0.414165\pi$
$200$		0			0
$201$	−8.48411e8	−	1.51513e9i	−0.519783	−	0.928252i
$202$			3.65862e9i			2.19741i
$203$	1.13437e8			0.0667993
$204$	2.82128e9	−	1.57980e9i	1.62902	−	0.912182i
$205$		0			0
$206$		−	1.17823e9i		−	0.654276i
$207$	3.84741e8	−	6.27694e8i	0.209550	−	0.341874i
$208$			1.23354e9i			0.659022i
$209$		−	3.70638e9i		−	1.94251i
$210$		0			0
$211$	−2.31595e9			−1.16842			−0.584211	−	0.811602i	$-0.698596\pi$
$211$	−2.31595e9			−1.16842			−0.584211	+	0.811602i	$0.698596\pi$
$212$	−1.19240e9			−0.590310
$213$	−1.62438e9	−	2.90089e9i	−0.789165	−	1.40933i
$214$	−3.19429e7			−0.0152307
$215$		0			0
$216$	−3.56926e7	+	9.04831e8i	−0.0163969	+	0.415674i
$217$		−	1.24289e9i		−	0.560525i
$218$	4.12678e9			1.82720
$219$	1.86097e9	+	3.32341e9i	0.809029	+	1.44480i
$220$		0			0
$221$			3.54929e9i			1.48789i
$222$	2.71376e9	+	4.84635e9i	1.11727	+	1.99528i
$223$			4.75871e8i			0.192429i	0.995361	+	0.0962144i	$0.0306734\pi$
$223$			4.75871e8i			0.192429i	−0.995361	+	0.0962144i	$0.969327\pi$
$224$		−	1.52326e9i		−	0.605037i
$225$		0			0
$226$	−8.14313e8			−0.312146
$227$	−3.01408e9			−1.13515			−0.567573	−	0.823323i	$-0.692118\pi$
$227$	−3.01408e9			−1.13515			−0.567573	+	0.823323i	$0.692118\pi$
$228$	4.37519e9	−	2.44993e9i	1.61904	−	0.906595i
$229$	−3.75337e9			−1.36483			−0.682416	−	0.730964i	$-0.739071\pi$
$229$	−3.75337e9			−1.36483			−0.682416	+	0.730964i	$0.739071\pi$
$230$		0			0
$231$	1.44026e9	−	8.06488e8i	0.505818	−	0.283237i
$232$		−	1.85459e8i		−	0.0640169i
$233$	−3.63111e9			−1.23201			−0.616007	−	0.787741i	$-0.711251\pi$
$233$	−3.63111e9			−1.23201			−0.616007	+	0.787741i	$0.711251\pi$
$234$	−3.92062e9	−	2.40312e9i	−1.30765	−	0.801517i
$235$		0			0
$236$			4.78741e9i			1.54331i
$237$	−1.72271e9	+	9.64647e8i	−0.546033	+	0.305756i
$238$		−	3.07482e9i		−	0.958322i
$239$		−	4.69757e9i		−	1.43973i	−0.694112	−	0.719867i	$-0.744203\pi$
$239$		−	4.69757e9i		−	1.43973i	0.694112	−	0.719867i	$-0.255797\pi$
$240$		0			0
$241$	−3.46782e9			−1.02799			−0.513994	−	0.857794i	$-0.671835\pi$
$241$	−3.46782e9			−1.02799			−0.513994	+	0.857794i	$0.671835\pi$
$242$	−4.05441e9			−1.18213
$243$	2.89865e9	+	1.93791e9i	0.831325	+	0.555787i
$244$	5.22951e9			1.47537
$245$		0			0
$246$	−3.73026e9	−	6.66167e9i	−1.01859	−	1.81904i
$247$			5.50417e9i			1.47878i
$248$	−2.03200e9			−0.537178
$249$	−4.86508e8	+	2.72424e8i	−0.126559	+	0.0708677i
$250$		0			0
$251$			1.53777e9i			0.387432i	0.981058	+	0.193716i	$0.0620541\pi$
$251$			1.53777e9i			0.387432i	−0.981058	+	0.193716i	$0.937946\pi$
$252$	1.90404e9	+	1.16707e9i	0.472143	+	0.289397i
$253$			2.19412e9i			0.535524i
$254$			2.26691e9i			0.544626i
$255$		0			0
$256$	1.06133e9			0.247110
$257$	2.70241e9			0.619467			0.309734	−	0.950823i	$-0.399760\pi$
$257$	2.70241e9			0.619467			0.309734	+	0.950823i	$0.399760\pi$
$258$	−8.25983e8	−	1.47508e9i	−0.186420	−	0.332917i
$259$	2.96095e9			0.658008
$260$		0			0
$261$	−6.08842e8	−	3.73186e8i	−0.131203	−	0.0804199i
$262$		−	6.56156e9i		−	1.39252i
$263$	3.23085e9			0.675296			0.337648	−	0.941273i	$-0.390369\pi$
$263$	3.23085e9			0.675296			0.337648	+	0.941273i	$0.390369\pi$
$264$	−1.31853e9	−	2.35469e9i	−0.271439	−	0.484749i
$265$		0			0
$266$		−	4.76837e9i		−	0.952453i
$267$	1.34478e9	+	2.40156e9i	0.264609	+	0.472552i
$268$			7.00160e9i			1.35724i
$269$			8.82614e8i			0.168563i	0.996442	+	0.0842814i	$0.0268595\pi$
$269$			8.82614e8i			0.168563i	−0.996442	+	0.0842814i	$0.973141\pi$
$270$		0			0
$271$	8.69735e9			1.61254			0.806269	−	0.591549i	$-0.201483\pi$
$271$	8.69735e9			1.61254			0.806269	+	0.591549i	$0.201483\pi$
$272$	5.19238e9			0.948616
$273$	−2.13887e9	+	1.19768e9i	−0.385065	+	0.215620i
$274$	−5.27847e9			−0.936496
$275$		0			0
$276$	−2.59005e9	+	1.45032e9i	−0.446347	+	0.249936i
$277$		−	8.57729e9i		−	1.45690i	−0.685097	−	0.728452i	$-0.740240\pi$
$277$		−	8.57729e9i		−	1.45690i	0.685097	−	0.728452i	$-0.259760\pi$
$278$	−1.18867e10			−1.99013
$279$	−4.08887e9	+	6.67087e9i	−0.674818	+	1.10095i
$280$		0			0
$281$		−	2.84302e9i		−	0.455990i	−0.973662	−	0.227995i	$-0.926783\pi$
$281$		−	2.84302e9i		−	0.455990i	0.973662	−	0.227995i	$-0.0732169\pi$
$282$	2.53096e9	−	1.41723e9i	0.400210	−	0.224101i
$283$		−	9.94012e9i		−	1.54969i	−0.632149	−	0.774847i	$-0.717827\pi$
$283$		−	9.94012e9i		−	1.54969i	0.632149	−	0.774847i	$-0.282173\pi$
$284$			1.34053e10i			2.06065i
$285$		0			0
$286$	1.37047e10			2.04835
$287$	−4.07004e9			−0.599889
$288$	−5.01123e9	+	8.17567e9i	−0.728407	+	1.18837i
$289$	7.96436e9			1.14172
$290$		0			0
$291$	−5.94957e8	−	1.06250e9i	−0.0829686	−	0.148169i
$292$		−	1.53579e10i		−	2.11252i
$293$	4.76323e9			0.646295			0.323147	−	0.946349i	$-0.395259\pi$
$293$	4.76323e9			0.646295			0.323147	+	0.946349i	$0.395259\pi$
$294$	−7.98101e9	+	4.46904e9i	−1.06824	+	0.598170i
$295$		0			0
$296$		−	4.84085e9i		−	0.630601i
$297$	−1.03834e10	−	4.09590e8i	−1.33448	−	0.0526409i
$298$			5.74949e7i			0.00729062i
$299$		−	3.25840e9i		−	0.407680i
$300$		0			0
$301$	−9.01219e8			−0.109790
$302$	−7.09873e9			−0.853400
$303$	−5.99861e9	−	1.07126e10i	−0.711673	−	1.27094i
$304$	8.05225e9			0.942807
$305$		0			0
$306$	−1.01155e10	+	1.65032e10i	−1.15373	+	1.88227i
$307$		−	3.26248e9i		−	0.367277i	−0.982994	−	0.183639i	$-0.941212\pi$
$307$		−	3.26248e9i		−	0.367277i	0.982994	−	0.183639i	$-0.0587876\pi$
$308$	−6.65563e9			−0.739581
$309$	1.93181e9	+	3.44991e9i	0.211900	+	0.378420i
$310$		0			0
$311$			1.13691e10i			1.21530i	0.794204	+	0.607651i	$0.207888\pi$
$311$			1.13691e10i			1.21530i	−0.794204	+	0.607651i	$0.792112\pi$
$312$	1.95808e9	+	3.49684e9i	0.206639	+	0.369026i
$313$		−	2.83465e9i		−	0.295340i	−0.989037	−	0.147670i	$-0.952823\pi$
$313$		−	2.83465e9i		−	0.295340i	0.989037	−	0.147670i	$-0.0471774\pi$
$314$			1.24450e10i			1.28020i
$315$		0			0
$316$	7.96085e9			0.798383
$317$	4.84402e9			0.479699			0.239850	−	0.970810i	$-0.422902\pi$
$317$	4.84402e9			0.479699			0.239850	+	0.970810i	$0.422902\pi$
$318$	6.22816e9	−	3.48751e9i	0.609047	−	0.341041i
$319$	2.12823e9			0.205521
$320$		0			0
$321$	9.35303e7	−	5.23731e7i	0.00880911	−	0.00493274i
$322$			2.82281e9i			0.262578i
$323$	2.31689e10			2.12860
$324$	−6.37995e9	−	1.25278e10i	−0.578945	−	1.13683i
$325$		0			0
$326$		−	1.75437e10i		−	1.55329i
$327$	−1.20834e10	+	6.76620e9i	−1.05681	+	0.591771i
$328$			6.65410e9i			0.574902i
$329$		−	1.54632e9i		−	0.131982i
$330$		0			0
$331$	−5.47410e9			−0.456037			−0.228019	−	0.973657i	$-0.573225\pi$
$331$	−5.47410e9			−0.456037			−0.228019	+	0.973657i	$0.573225\pi$
$332$	2.24821e9			0.185048
$333$	−1.58920e10	−	9.74092e9i	−1.29242	−	0.792179i
$334$	−8.05942e9			−0.647616
$335$		0			0
$336$	1.75213e9	+	3.12903e9i	0.137470	+	0.245501i
$337$			2.30004e10i			1.78327i	0.452759	+	0.891633i	$0.350440\pi$
$337$			2.30004e10i			1.78327i	−0.452759	+	0.891633i	$0.649560\pi$
$338$	−6.62922e8			−0.0507920
$339$	2.38435e9	−	1.33514e9i	0.180539	−	0.101094i
$340$		0			0
$341$		−	2.33183e10i		−	1.72456i
$342$	−1.56870e10	+	2.55929e10i	−1.14666	+	1.87074i
$343$			1.08843e10i			0.786364i
$344$			1.47340e9i			0.105217i
$345$		0			0
$346$	−3.19006e10			−2.22584
$347$	2.27792e10			1.57116			0.785582	−	0.618758i	$-0.212364\pi$
$347$	2.27792e10			1.57116			0.785582	+	0.618758i	$0.212364\pi$
$348$	1.40677e9	+	2.51227e9i	0.0959190	+	0.171297i
$349$	−2.25621e10			−1.52082			−0.760410	−	0.649444i	$-0.775002\pi$
$349$	−2.25621e10			−1.52082			−0.760410	+	0.649444i	$0.775002\pi$
$350$		0			0
$351$	1.54199e10	+	6.08264e8i	1.01591	+	0.0400741i
$352$		−	2.85783e10i		−	1.86151i
$353$	8.56846e9			0.551828			0.275914	−	0.961182i	$-0.411019\pi$
$353$	8.56846e9			0.551828			0.275914	+	0.961182i	$0.411019\pi$
$354$	−1.40021e10	−	2.50056e10i	−0.891619	−	1.59229i
$355$		0			0
$356$		−	1.10979e10i		−	0.690941i
$357$	5.04142e9	+	9.00321e9i	0.310370	+	0.554274i
$358$		−	2.64994e9i		−	0.161326i
$359$			3.45337e9i			0.207905i	0.994582	+	0.103953i	$0.0331490\pi$
$359$			3.45337e9i			0.207905i	−0.994582	+	0.103953i	$0.966851\pi$
$360$		0			0
$361$	1.89463e10			1.11557
$362$	−8.81177e9			−0.513132
$363$	1.18715e10	−	6.64756e9i	0.683722	−	0.382856i
$364$	9.88397e9			0.563023
$365$		0			0
$366$	−2.73148e10	+	1.52951e10i	−1.52220	+	0.852371i
$367$		−	7.52594e9i		−	0.414855i	−0.978250	−	0.207428i	$-0.933491\pi$
$367$		−	7.52594e9i		−	0.414855i	0.978250	−	0.207428i	$-0.0665092\pi$
$368$	−4.76682e9			−0.259919
$369$	2.18448e10	+	1.33896e10i	1.17826	+	0.722209i
$370$		0			0
$371$		−	3.80518e9i		−	0.200853i
$372$	2.75260e10	−	1.54134e10i	1.43738	−	0.804874i
$373$			1.60977e10i			0.831625i	0.909450	+	0.415812i	$0.136503\pi$
$373$			1.60977e10i			0.831625i	−0.909450	+	0.415812i	$0.863497\pi$
$374$		−	5.76875e10i		−	2.94846i
$375$		0			0
$376$	−2.52808e9			−0.126485
$377$	−3.16054e9			−0.156457
$378$	−1.33586e10	−	5.26951e8i	−0.654323	−	0.0258109i
$379$	7.26804e9			0.352257			0.176129	−	0.984367i	$-0.443642\pi$
$379$	7.26804e9			0.352257			0.176129	+	0.984367i	$0.443642\pi$
$380$		0			0
$381$	−3.71679e9	−	6.63761e9i	−0.176387	−	0.315001i
$382$			5.17657e10i			2.43102i
$383$	3.84730e9			0.178797			0.0893987	−	0.995996i	$-0.471505\pi$
$383$	3.84730e9			0.178797			0.0893987	+	0.995996i	$0.471505\pi$
$384$	1.51840e10	−	8.50242e9i	0.698332	−	0.391037i
$385$		0			0
$386$			5.70768e10i			2.57105i
$387$	4.83704e9	+	2.96483e9i	0.215643	+	0.132177i
$388$			4.90995e9i			0.216646i
$389$		−	1.64582e10i		−	0.718761i	−0.933191	−	0.359380i	$-0.882988\pi$
$389$		−	1.64582e10i		−	0.718761i	0.933191	−	0.359380i	$-0.117012\pi$
$390$		0			0
$391$	−1.37157e10			−0.586826
$392$	7.97194e9			0.337614
$393$	1.07582e10	+	1.92126e10i	0.450994	+	0.805407i
$394$	5.72746e10			2.37671
$395$		0			0
$396$	3.57222e10	+	2.18957e10i	1.45264	+	0.890385i
$397$		−	3.57344e10i		−	1.43855i	−0.694727	−	0.719273i	$-0.744475\pi$
$397$		−	3.57344e10i		−	1.43855i	0.694727	−	0.719273i	$-0.255525\pi$
$398$	2.01680e10			0.803767
$399$	7.81815e9	+	1.39620e10i	0.308470	+	0.550880i
$400$		0			0
$401$			7.65267e9i			0.295962i	0.988990	+	0.147981i	$0.0472774\pi$
$401$			7.65267e9i			0.295962i	−0.988990	+	0.147981i	$0.952723\pi$
$402$	−2.04781e10	−	3.65707e10i	−0.784124	−	1.40033i
$403$			3.46289e10i			1.31286i
$404$			4.95042e10i			1.85830i
$405$		0			0
$406$	2.73803e9			0.100771
$407$	5.55511e10			2.02449
$408$	1.47193e10	−	8.24222e9i	0.531187	−	0.297443i
$409$	−1.89488e10			−0.677154			−0.338577	−	0.940939i	$-0.609946\pi$
$409$	−1.89488e10			−0.677154			−0.338577	+	0.940939i	$0.609946\pi$
$410$		0			0
$411$	1.54556e10	−	8.65450e9i	0.541650	−	0.303302i
$412$		−	1.59425e10i		−	0.553307i
$413$	−1.52775e10			−0.525111
$414$	9.28649e9	−	1.51506e10i	0.316119	−	0.515738i
$415$		0			0
$416$			4.24404e10i			1.41712i
$417$	3.48047e10	−	1.94892e10i	1.15105	−	0.644540i
$418$		−	8.94607e10i		−	2.93040i
$419$			8.62832e9i			0.279943i	0.990156	+	0.139972i	$0.0447012\pi$
$419$			8.62832e9i			0.279943i	−0.990156	+	0.139972i	$0.955299\pi$
$420$		0			0
$421$	3.38470e10			1.07744			0.538718	−	0.842486i	$-0.318909\pi$
$421$	3.38470e10			1.07744			0.538718	+	0.842486i	$0.318909\pi$
$422$	−5.59001e10			−1.76264
$423$	−5.08709e9	+	8.29944e9i	−0.158894	+	0.259231i
$424$	−6.22108e9			−0.192487
$425$		0			0
$426$	−3.92075e10	−	7.00186e10i	−1.19050	−	2.12606i
$427$			1.66883e10i			0.501997i
$428$	−4.32214e8			−0.0128802
$429$	−4.01279e10	+	2.24700e10i	−1.18473	+	0.663397i
$430$		0			0
$431$		−	2.98116e10i		−	0.863924i	−0.901892	−	0.431962i	$-0.857821\pi$
$431$		−	2.98116e10i		−	0.863924i	0.901892	−	0.431962i	$-0.142179\pi$
$432$	8.89850e8	−	2.25583e10i	0.0255495	−	0.647697i
$433$		−	2.54166e9i		−	0.0723047i	−0.999346	−	0.0361524i	$-0.988490\pi$
$433$		−	2.54166e9i		−	0.0723047i	0.999346	−	0.0361524i	$-0.0115102\pi$
$434$		−	2.99997e10i		−	0.845586i
$435$		0			0
$436$	5.58388e10			1.54522
$437$	−2.12700e10			−0.583233
$438$	4.49183e10	+	8.02172e10i	1.22047	+	2.17957i
$439$	−1.11261e10			−0.299559			−0.149780	−	0.988719i	$-0.547856\pi$
$439$	−1.11261e10			−0.299559			−0.149780	+	0.988719i	$0.547856\pi$
$440$		0			0
$441$	1.60414e10	−	2.61711e10i	0.424120	−	0.691939i
$442$			8.56691e10i			2.24458i
$443$	−3.00907e10			−0.781299			−0.390650	−	0.920539i	$-0.627750\pi$
$443$	−3.00907e10			−0.781299			−0.390650	+	0.920539i	$0.627750\pi$
$444$	3.67194e10	+	6.55753e10i	0.944853	+	1.68736i
$445$		0			0
$446$			1.14861e10i			0.290291i
$447$	−9.42678e7	−	1.68348e8i	−0.00236120	−	0.00421674i
$448$		−	2.54328e10i		−	0.631367i
$449$			2.46457e10i			0.606396i	0.952928	+	0.303198i	$0.0980543\pi$
$449$			2.46457e10i			0.606396i	−0.952928	+	0.303198i	$0.901946\pi$
$450$		0			0
$451$	−7.63591e10			−1.84567
$452$	−1.10184e10			−0.263975
$453$	2.07854e10	−	1.16390e10i	0.493589	−	0.276390i
$454$	−7.27509e10			−1.71244
$455$		0			0
$456$	2.28265e10	−	1.27819e10i	0.527934	−	0.295621i
$457$			1.18416e10i			0.271486i	0.990744	+	0.135743i	$0.0433421\pi$
$457$			1.18416e10i			0.271486i	−0.990744	+	0.135743i	$0.956658\pi$
$458$	−9.05950e10			−2.05893
$459$	2.56038e9	−	6.49074e10i	0.0576838	−	1.46232i
$460$		0			0
$461$			2.03656e10i			0.450913i	0.974253	+	0.225456i	$0.0723873\pi$
$461$			2.03656e10i			0.450913i	−0.974253	+	0.225456i	$0.927613\pi$
$462$	3.47636e10	−	1.94662e10i	0.763057	−	0.427280i
$463$			3.88105e10i			0.844550i	0.906468	+	0.422275i	$0.138768\pi$
$463$			3.88105e10i			0.844550i	−0.906468	+	0.422275i	$0.861232\pi$
$464$			4.62366e9i			0.0997502i
$465$		0			0
$466$	−8.76440e10			−1.85857
$467$	−6.67567e10			−1.40355			−0.701774	−	0.712400i	$-0.747608\pi$
$467$	−6.67567e10			−1.40355			−0.701774	+	0.712400i	$0.747608\pi$
$468$	−5.30494e10	−	3.25163e10i	−1.10585	−	0.677825i
$469$	−2.23434e10			−0.461803
$470$		0			0
$471$	−2.04047e10	−	3.64396e10i	−0.414616	−	0.740440i
$472$			2.49771e10i			0.503239i
$473$	−1.69080e10			−0.337791
$474$	−4.15810e10	+	2.32837e10i	−0.823725	+	0.461252i
$475$		0			0
$476$		−	4.16049e10i		−	0.810432i
$477$	−1.25183e10	+	2.04232e10i	−0.241808	+	0.394503i
$478$		−	1.13385e11i		−	2.17193i
$479$		−	1.01360e11i		−	1.92542i	−0.270529	−	0.962712i	$-0.587199\pi$
$479$		−	1.01360e11i		−	1.92542i	0.270529	−	0.962712i	$-0.412801\pi$
$480$		0			0
$481$	−8.24964e10			−1.54119
$482$	−8.37027e10			−1.55078
$483$	−4.62824e9	−	8.26533e9i	−0.0850408	−	0.151870i
$484$	−5.48597e10			−0.999705
$485$		0			0
$486$	6.99647e10	+	4.67753e10i	1.25410	+	0.838439i
$487$			1.08507e10i			0.192905i	0.995338	+	0.0964526i	$0.0307496\pi$
$487$			1.08507e10i			0.192905i	−0.995338	+	0.0964526i	$0.969250\pi$
$488$	2.72837e10			0.481088
$489$	2.87645e10	+	5.13689e10i	0.503061	+	0.898390i
$490$		0			0
$491$		−	1.02973e10i		−	0.177173i	−0.996068	−	0.0885864i	$-0.971765\pi$
$491$		−	1.02973e10i		−	0.177173i	0.996068	−	0.0885864i	$-0.0282349\pi$
$492$	−5.04736e10	−	9.01381e10i	−0.861398	−	1.53833i
$493$			1.33037e10i			0.225209i
$494$			1.32854e11i			2.23083i
$495$		0			0
$496$	5.06598e10			0.837022
$497$	−4.27788e10			−0.701138
$498$	−1.17428e10	+	6.57550e9i	−0.190922	+	0.106908i
$499$	−6.76597e10			−1.09126			−0.545630	−	0.838026i	$-0.683710\pi$
$499$	−6.76597e10			−1.09126			−0.545630	+	0.838026i	$0.683710\pi$
$500$		0			0
$501$	2.35984e10	−	1.32141e10i	0.374568	−	0.209743i
$502$			3.71171e10i			0.584465i
$503$	−2.55230e10			−0.398712			−0.199356	−	0.979927i	$-0.563885\pi$
$503$	−2.55230e10			−0.398712			−0.199356	+	0.979927i	$0.563885\pi$
$504$	9.93385e9	+	6.08890e9i	0.153956	+	0.0943662i
$505$		0			0
$506$			5.29595e10i			0.807871i
$507$	1.94107e9	−	1.08692e9i	0.0293771	−	0.0164500i
$508$			3.06732e10i			0.460579i
$509$			1.02891e11i			1.53287i	0.642320	+	0.766437i	$0.277972\pi$
$509$			1.02891e11i			1.53287i	−0.642320	+	0.766437i	$0.722028\pi$
$510$		0			0
$511$	4.90098e10			0.718785
$512$	8.06177e10			1.17314
$513$	3.97059e9	−	1.00657e11i	0.0573305	−	1.45337i
$514$	6.52280e10			0.934504
$515$		0			0
$516$	−1.11763e10	−	1.99591e10i	−0.157651	−	0.281541i
$517$		−	2.90110e10i		−	0.406069i
$518$	7.14683e10			0.992646
$519$	9.34065e10	−	5.23038e10i	1.28738	−	0.720881i
$520$		0			0
$521$		−	5.25006e10i		−	0.712547i	−0.934382	−	0.356273i	$-0.884047\pi$
$521$		−	5.25006e10i		−	0.712547i	0.934382	−	0.356273i	$-0.115953\pi$
$522$	−1.46956e10	−	9.00759e9i	−0.197927	−	0.121318i
$523$			8.56285e10i			1.14449i	0.820083	+	0.572245i	$0.193927\pi$
$523$			8.56285e10i			1.14449i	−0.820083	+	0.572245i	$0.806073\pi$
$524$		−	8.87835e10i		−	1.17763i
$525$		0			0
$526$	7.79830e10			1.01872
$527$	1.45764e11			1.88977
$528$	3.28721e10	+	5.87046e10i	0.422953	+	0.755329i
$529$	−6.57194e10			−0.839211
$530$		0			0
$531$	8.19975e10	+	5.02599e10i	1.03139	+	0.632184i
$532$		−	6.45201e10i		−	0.805469i
$533$	1.13398e11			1.40506
$534$	3.24588e10	+	5.79665e10i	0.399179	+	0.712873i
$535$		0			0
$536$			3.65291e10i			0.442568i
$537$	4.34480e9	+	7.75915e9i	0.0522484	+	0.0933076i
$538$			2.13036e10i			0.254287i
$539$			9.14820e10i			1.08388i
$540$		0			0
$541$	−2.14250e10			−0.250111			−0.125055	−	0.992150i	$-0.539911\pi$
$541$	−2.14250e10			−0.250111			−0.125055	+	0.992150i	$0.539911\pi$
$542$	2.09928e11			2.43261
$543$	2.58013e10	−	1.44476e10i	0.296785	−	0.166187i
$544$	1.78645e11			2.03984
$545$		0			0
$546$	−5.16259e10	+	2.89084e10i	−0.580894	+	0.325277i
$547$		−	9.14990e8i		−	0.0102204i	−0.999987	−	0.00511019i	$-0.998373\pi$
$547$		−	9.14990e8i		−	0.0102204i	0.999987	−	0.00511019i	$-0.00162663\pi$
$548$	−7.14222e10			−0.791974
$549$	5.49012e10	−	8.95697e10i	0.604356	−	0.985989i
$550$		0			0
$551$			2.06312e10i			0.223830i
$552$	−1.35130e10	+	7.56671e9i	−0.145544	+	0.0814987i
$553$			2.54045e10i			0.271650i
$554$		−	2.07030e11i		−	2.19783i
$555$		0			0
$556$	−1.60837e11			−1.68301
$557$	−1.81764e11			−1.88837			−0.944185	−	0.329416i	$-0.893148\pi$
$557$	−1.81764e11			−1.88837			−0.944185	+	0.329416i	$0.893148\pi$
$558$	−9.86930e10	+	1.61015e11i	−1.01800	+	1.66084i
$559$	2.51093e10			0.257151
$560$		0			0
$561$	9.45835e10	+	1.68912e11i	0.954913	+	1.70533i
$562$		−	6.86220e10i		−	0.687889i
$563$	4.19023e10			0.417066			0.208533	−	0.978015i	$-0.433131\pi$
$563$	4.19023e10			0.417066			0.208533	+	0.978015i	$0.433131\pi$
$564$	3.42460e10	−	1.91763e10i	0.338449	−	0.189517i
$565$		0			0
$566$		−	2.39924e11i		−	2.33781i
$567$	3.99785e10	−	2.03596e10i	0.386807	−	0.196986i
$568$			6.99391e10i			0.671934i
$569$			9.98358e10i			0.952439i	0.879326	+	0.476220i	$0.157993\pi$
$569$			9.98358e10i			0.952439i	−0.879326	+	0.476220i	$0.842007\pi$
$570$		0			0
$571$	7.00315e10			0.658793			0.329397	−	0.944192i	$-0.393155\pi$
$571$	7.00315e10			0.658793			0.329397	+	0.944192i	$0.393155\pi$
$572$	1.85436e11			1.73225
$573$	−8.48743e10	−	1.51573e11i	−0.787332	−	1.40605i
$574$	−9.82385e10			−0.904970
$575$		0			0
$576$	−8.36688e10	+	1.36503e11i	−0.760105	+	1.24009i
$577$			5.16977e10i			0.466410i	0.972428	+	0.233205i	$0.0749213\pi$
$577$			5.16977e10i			0.466410i	−0.972428	+	0.233205i	$0.925079\pi$
$578$	1.92236e11			1.72235
$579$	−9.35823e10	−	1.67124e11i	−0.832683	−	1.48704i
$580$		0			0
$581$			7.17444e9i			0.0629627i
$582$	−1.43605e10	−	2.56456e10i	−0.125163	−	0.223522i
$583$		−	7.13899e10i		−	0.617963i
$584$		−	8.01260e10i		−	0.688846i
$585$		0			0
$586$	1.14970e11			0.974976
$587$	−7.90362e10			−0.665693			−0.332846	−	0.942981i	$-0.608009\pi$
$587$	−7.90362e10			−0.665693			−0.332846	+	0.942981i	$0.608009\pi$
$588$	−1.07990e11	+	6.04699e10i	−0.903387	+	0.505859i
$589$	2.26049e11			1.87820
$590$		0			0
$591$	−1.67703e11	+	9.39065e10i	−1.37464	+	0.769743i
$592$			1.20687e11i			0.982592i
$593$	−2.38940e11			−1.93228			−0.966141	−	0.258015i	$-0.916932\pi$
$593$	−2.38940e11			−1.93228			−0.966141	+	0.258015i	$0.916932\pi$
$594$	−2.50624e11	−	9.88626e9i	−2.01315	−	0.0794120i
$595$		0			0
$596$			7.77955e8i			0.00616551i
$597$	−5.90528e10	+	3.30671e10i	−0.464883	+	0.260315i
$598$		−	7.86478e10i		−	0.615010i
$599$		−	1.75042e11i		−	1.35968i	−0.733363	−	0.679838i	$-0.762050\pi$
$599$		−	1.75042e11i		−	1.35968i	0.733363	−	0.679838i	$-0.237950\pi$
$600$		0			0
$601$	−7.78052e10			−0.596363			−0.298181	−	0.954509i	$-0.596380\pi$
$601$	−7.78052e10			−0.596363			−0.298181	+	0.954509i	$0.596380\pi$
$602$	−2.17527e10			−0.165626
$603$	1.19922e11	+	7.35052e10i	0.907043	+	0.555967i
$604$	−9.60518e10			−0.721702
$605$		0			0
$606$	−1.44788e11	−	2.58570e11i	−1.07360	−	1.91729i
$607$		−	1.00711e11i		−	0.741864i	−0.928660	−	0.370932i	$-0.879038\pi$
$607$		−	1.00711e11i		−	0.741864i	0.928660	−	0.370932i	$-0.120962\pi$
$608$	2.77040e11			2.02735
$609$	−8.01710e9	+	4.48924e9i	−0.0582838	+	0.0326365i
$610$		0			0
$611$			4.30829e10i			0.309129i
$612$	−1.36872e11	+	2.23302e11i	−0.975682	+	1.59180i
$613$		−	1.66738e11i		−	1.18084i	−0.807094	−	0.590422i	$-0.798961\pi$
$613$		−	1.66738e11i		−	1.18084i	0.807094	−	0.590422i	$-0.201039\pi$
$614$		−	7.87464e10i		−	0.554060i
$615$		0			0
$616$	−3.47241e10			−0.241162
$617$	5.98004e10			0.412632			0.206316	−	0.978485i	$-0.433852\pi$
$617$	5.98004e10			0.412632			0.206316	+	0.978485i	$0.433852\pi$
$618$	4.66280e10	+	8.32705e10i	0.319664	+	0.570870i
$619$	1.30260e11			0.887254			0.443627	−	0.896211i	$-0.353691\pi$
$619$	1.30260e11			0.887254			0.443627	+	0.896211i	$0.353691\pi$
$620$		0			0
$621$	−2.35054e9	+	5.95878e10i	−0.0158052	+	0.400674i
$622$			2.74416e11i			1.83336i
$623$	3.54154e10			0.235093
$624$	−4.88169e10	−	8.71795e10i	−0.321982	−	0.575011i
$625$		0			0
$626$		−	6.84200e10i		−	0.445539i
$627$	1.46678e11	+	2.61945e11i	0.949065	+	1.69489i
$628$			1.68392e11i			1.08263i
$629$			3.47255e11i			2.21843i
$630$		0			0
$631$	−2.11689e11			−1.33530			−0.667652	−	0.744473i	$-0.732701\pi$
$631$	−2.11689e11			−1.33530			−0.667652	+	0.744473i	$0.732701\pi$
$632$	4.15338e10			0.260335
$633$	1.63678e11	−	9.16529e10i	1.01947	−	0.570863i
$634$	1.16920e11			0.723656
$635$		0			0
$636$	8.42723e10	−	4.71890e10i	0.515058	−	0.288411i
$637$		−	1.35856e11i		−	0.825126i
$638$	5.13690e10			0.310040
$639$	2.29603e11	+	1.40734e11i	1.37713	+	0.844102i
$640$		0			0
$641$			9.94582e9i			0.0589126i	0.999566	+	0.0294563i	$0.00937759\pi$
$641$			9.94582e9i			0.0589126i	−0.999566	+	0.0294563i	$0.990622\pi$
$642$	2.25754e9	−	1.26413e9i	0.0132891	−	0.00744134i
$643$		−	4.35787e10i		−	0.254935i	−0.991843	−	0.127468i	$-0.959315\pi$
$643$		−	4.35787e10i		−	0.254935i	0.991843	−	0.127468i	$-0.0406849\pi$
$644$			3.81950e10i			0.222057i
$645$		0			0
$646$	5.59227e11			3.21113
$647$	−1.00404e11			−0.572973			−0.286487	−	0.958084i	$-0.592487\pi$
$647$	−1.00404e11			−0.572973			−0.286487	+	0.958084i	$0.592487\pi$
$648$	−3.32858e10	−	6.53608e10i	−0.188781	−	0.370695i
$649$	−2.86625e11			−1.61560
$650$		0			0
$651$	4.91871e10	+	8.78405e10i	0.273859	+	0.489070i
$652$		−	2.37382e11i		−	1.31358i
$653$	−9.51805e10			−0.523474			−0.261737	−	0.965139i	$-0.584295\pi$
$653$	−9.51805e10			−0.523474			−0.261737	+	0.965139i	$0.584295\pi$
$654$	−2.91657e11	+	1.63316e11i	−1.59427	+	0.892723i
$655$		0			0
$656$		−	1.65893e11i		−	0.895804i
$657$	−2.63046e11	−	1.61232e11i	−1.41179	−	0.865348i
$658$		−	3.73235e10i		−	0.199104i
$659$		−	2.93955e11i		−	1.55862i	−0.626641	−	0.779308i	$-0.715571\pi$
$659$		−	2.93955e11i		−	1.55862i	0.626641	−	0.779308i	$-0.284429\pi$
$660$		0			0
$661$	2.39956e11			1.25697			0.628485	−	0.777822i	$-0.283675\pi$
$661$	2.39956e11			1.25697			0.628485	+	0.777822i	$0.283675\pi$
$662$	−1.32128e11			−0.687960
$663$	−1.40462e11	−	2.50843e11i	−0.726949	−	1.29822i
$664$	1.17295e10			0.0603402
$665$		0			0
$666$	−3.83585e11	−	2.35116e11i	−1.94969	−	1.19505i
$667$		−	1.22134e10i		−	0.0617068i
$668$	−1.09051e11			−0.547675
$669$	−1.88324e10	−	3.36318e10i	−0.0940160	−	0.167898i
$670$		0			0
$671$			3.13094e11i			1.54449i
$672$	6.02825e10	+	1.07655e11i	0.295607	+	0.527908i
$673$			1.21923e11i			0.594326i	0.954827	+	0.297163i	$0.0960404\pi$
$673$			1.21923e11i			0.594326i	−0.954827	+	0.297163i	$0.903960\pi$
$674$			5.55161e11i			2.69017i
$675$		0			0
$676$	−8.96990e9			−0.0429537
$677$	3.04202e10			0.144813			0.0724066	−	0.997375i	$-0.476932\pi$
$677$	3.04202e10			0.144813			0.0724066	+	0.997375i	$0.476932\pi$
$678$	5.75510e10	−	3.22262e10i	0.272354	−	0.152507i
$679$	−1.56685e10			−0.0737138
$680$		0			0
$681$	2.13018e11	−	1.19281e11i	0.990440	−	0.554605i
$682$		−	5.62832e11i		−	2.60161i
$683$	−2.91193e11			−1.33813			−0.669065	−	0.743204i	$-0.733305\pi$
$683$	−2.91193e11			−1.33813			−0.669065	+	0.743204i	$0.733305\pi$
$684$	−2.12258e11	+	3.46293e11i	−0.969707	+	1.58205i
$685$		0			0
$686$			2.62714e11i			1.18628i
$687$	2.65267e11	−	1.48538e11i	1.19085	−	0.666824i
$688$		−	3.67333e10i		−	0.163948i
$689$			1.06018e11i			0.470438i
$690$		0			0
$691$	−3.48484e11			−1.52852			−0.764260	−	0.644908i	$-0.776896\pi$
$691$	−3.48484e11			−1.52852			−0.764260	+	0.644908i	$0.776896\pi$
$692$	−4.31642e11			−1.88235
$693$	−6.98731e10	+	1.13996e11i	−0.302954	+	0.494261i
$694$	5.49822e11			2.37020
$695$		0			0
$696$	7.33945e9	+	1.31071e10i	0.0312771	+	0.0558562i
$697$		−	4.77327e11i		−	2.02248i
$698$	−5.44581e11			−2.29425
$699$	2.56626e11	−	1.43700e11i	1.07496	−	0.601932i
$700$		0			0
$701$			1.23548e11i			0.511640i	0.966724	+	0.255820i	$0.0823455\pi$
$701$			1.23548e11i			0.511640i	−0.966724	+	0.255820i	$0.917655\pi$
$702$	3.72190e11	+	1.46816e10i	1.53256	+	0.0604542i
$703$			5.38516e11i			2.20484i
$704$		−	4.77151e11i		−	1.94252i
$705$		0			0
$706$	2.06817e11			0.832467
$707$	−1.57977e11			−0.632289
$708$	−1.89460e11	−	3.38346e11i	−0.754023	−	1.34657i
$709$	−3.17753e11			−1.25749			−0.628744	−	0.777612i	$-0.716431\pi$
$709$	−3.17753e11			−1.25749			−0.628744	+	0.777612i	$0.716431\pi$
$710$		0			0
$711$	8.35758e10	−	1.36351e11i	0.327041	−	0.533557i
$712$		−	5.79006e10i		−	0.225301i
$713$	−1.33818e11			−0.517793
$714$	1.21685e11	+	2.17310e11i	0.468213	+	0.836156i
$715$		0			0
$716$		−	3.58560e10i		−	0.136430i
$717$	1.85905e11	+	3.31997e11i	0.703419	+	1.25620i
$718$			8.33539e10i			0.313638i
$719$			2.47720e11i			0.926926i	0.886116	+	0.463463i	$0.153393\pi$
$719$			2.47720e11i			0.926926i	−0.886116	+	0.463463i	$0.846607\pi$
$720$		0			0
$721$	5.08752e10			0.188263
$722$	4.57307e11			1.68290
$723$	2.45085e11	−	1.37238e11i	0.896942	−	0.502250i
$724$	−1.19231e11			−0.433944
$725$		0			0
$726$	2.86543e11	−	1.60452e11i	1.03144	−	0.577562i
$727$			2.06831e11i			0.740420i	0.928948	+	0.370210i	$0.120714\pi$
$727$			2.06831e11i			0.740420i	−0.928948	+	0.370210i	$0.879286\pi$
$728$	5.15672e10			0.183590
$729$	−2.81552e11	−	2.22472e10i	−0.996893	−	0.0787707i
$730$		0			0
$731$		−	1.05693e11i		−	0.370151i
$732$	−3.69592e11	+	2.06956e11i	−1.28730	+	0.720832i
$733$			2.72921e11i			0.945412i	0.881220	+	0.472706i	$0.156723\pi$
$733$			2.72921e11i			0.945412i	−0.881220	+	0.472706i	$0.843277\pi$
$734$		−	1.81654e11i		−	0.625835i
$735$		0			0
$736$	−1.64004e11			−0.558912
$737$	−4.19190e11			−1.42083
$738$	5.27267e11	+	3.23185e11i	1.77748	+	1.08950i
$739$	−1.03105e10			−0.0345702			−0.0172851	−	0.999851i	$-0.505502\pi$
$739$	−1.03105e10			−0.0345702			−0.0172851	+	0.999851i	$0.505502\pi$
$740$		0			0
$741$	−2.17826e11	−	3.89003e11i	−0.722497	−	1.29027i
$742$		−	9.18454e10i		−	0.303000i
$743$	3.12920e11			1.02678			0.513392	−	0.858154i	$-0.328389\pi$
$743$	3.12920e11			1.02678			0.513392	+	0.858154i	$0.328389\pi$
$744$	1.43610e11	−	8.04159e10i	0.468699	−	0.262452i
$745$		0			0
$746$			3.88549e11i			1.25456i
$747$	2.36025e10	−	3.85067e10i	0.0758010	−	0.123667i
$748$		−	7.80561e11i		−	2.49345i
$749$		−	1.37927e9i		−	0.00438251i
$750$		0			0
$751$	2.76676e11			0.869783			0.434892	−	0.900483i	$-0.356787\pi$
$751$	2.76676e11			0.869783			0.434892	+	0.900483i	$0.356787\pi$
$752$	6.30275e10			0.197087
$753$	−6.08566e10	−	1.08681e11i	−0.189290	−	0.338043i
$754$	−7.62858e10			−0.236025
$755$		0			0
$756$	−1.80753e11	−	7.13009e9i	−0.553347	−	0.0218277i
$757$			1.25846e11i			0.383226i	0.981471	+	0.191613i	$0.0613718\pi$
$757$			1.25846e11i			0.383226i	−0.981471	+	0.191613i	$0.938628\pi$
$758$	1.75428e11			0.531402
$759$	−8.68317e10	−	1.55068e11i	−0.261644	−	0.467256i
$760$		0			0
$761$		−	4.11284e11i		−	1.22632i	−0.789960	−	0.613159i	$-0.789899\pi$
$761$		−	4.11284e11i		−	1.22632i	0.789960	−	0.613159i	$-0.210101\pi$
$762$	−8.97120e10	−	1.60212e11i	−0.266091	−	0.475198i
$763$			1.78192e11i			0.525762i
$764$			7.00435e11i			2.05586i
$765$		0			0
$766$	9.28622e10			0.269727
$767$	4.25654e11			1.22991
$768$	−7.50087e10	+	4.20018e10i	−0.215609	+	0.120732i
$769$	−4.51287e10			−0.129047			−0.0645235	−	0.997916i	$-0.520553\pi$
$769$	−4.51287e10			−0.129047			−0.0645235	+	0.997916i	$0.520553\pi$
$770$		0			0
$771$	−1.90991e11	+	1.06947e11i	−0.540498	+	0.302657i
$772$			7.72298e11i			2.17428i
$773$	−3.86868e11			−1.08354			−0.541770	−	0.840527i	$-0.682245\pi$
$773$	−3.86868e11			−1.08354			−0.541770	+	0.840527i	$0.682245\pi$
$774$	1.16751e11	+	7.15621e10i	0.325311	+	0.199397i
$775$		0			0
$776$			2.56164e10i			0.0706435i
$777$	−2.09263e11	+	1.17178e11i	−0.574126	+	0.321487i
$778$		−	3.97252e11i		−	1.08430i
$779$		−	7.40231e11i		−	2.01010i
$780$		0			0
$781$	−8.02585e11			−2.15718
$782$	−3.31055e11			−0.885264
$783$	5.77982e10	+	2.27994e9i	0.153768	+	0.00606565i
$784$	−1.98748e11			−0.526064
$785$		0			0
$786$	2.59671e11	+	4.63733e11i	0.680353	+	1.21501i
$787$			4.31897e11i			1.12585i	0.826508	+	0.562926i	$0.190324\pi$
$787$			4.31897e11i			1.12585i	−0.826508	+	0.562926i	$0.809676\pi$
$788$	7.74973e11			2.00993
$789$	−2.28338e11	+	1.27860e11i	−0.589210	+	0.329933i
$790$		0			0
$791$		−	3.51615e10i		−	0.0898177i
$792$	1.86372e11	+	1.14235e11i	0.473673	+	0.290335i
$793$		−	4.64962e11i		−	1.17578i
$794$		−	8.62519e11i		−	2.17014i
$795$		0			0
$796$	2.72890e11			0.679728
$797$	−1.89233e11			−0.468991			−0.234495	−	0.972117i	$-0.575344\pi$
$797$	−1.89233e11			−0.468991			−0.234495	+	0.972117i	$0.575344\pi$
$798$	1.88707e11	+	3.37001e11i	0.465346	+	0.831036i
$799$	1.81350e11			0.444970
$800$		0			0
$801$	−1.90082e11	−	1.16510e11i	−0.461754	−	0.283030i
$802$			1.84712e11i			0.446477i
$803$	9.19486e11			2.21148
$804$	−2.77086e11	−	4.94833e11i	−0.663117	−	1.18423i
$805$		0			0
$806$			8.35837e11i			1.98053i
$807$	−3.49291e10	−	6.23781e10i	−0.0823557	−	0.147075i
$808$			2.58276e11i			0.605953i
$809$		−	8.16650e10i		−	0.190652i	−0.995446	−	0.0953261i	$-0.969611\pi$
$809$		−	8.16650e10i		−	0.190652i	0.995446	−	0.0953261i	$-0.0303894\pi$
$810$		0			0
$811$	−2.05160e11			−0.474252			−0.237126	−	0.971479i	$-0.576205\pi$
$811$	−2.05160e11			−0.474252			−0.237126	+	0.971479i	$0.576205\pi$
$812$	3.70479e10			0.0852197
$813$	−6.14679e11	+	3.44195e11i	−1.40697	+	0.787847i
$814$	1.34084e12			3.05406
$815$		0			0
$816$	−3.66967e11	+	2.05486e11i	−0.827688	+	0.463471i
$817$		−	1.63908e11i		−	0.367884i
$818$	−4.57366e11			−1.02153
$819$	1.03765e11	−	1.69290e11i	0.230631	−	0.376267i
$820$		0			0
$821$		−	1.41950e10i		−	0.0312437i	−0.999878	−	0.0156218i	$-0.995027\pi$
$821$		−	1.41950e10i		−	0.0312437i	0.999878	−	0.0156218i	$-0.00497278\pi$
$822$	3.73052e11	−	2.08894e11i	0.817113	−	0.457549i
$823$			2.98009e11i			0.649576i	0.945787	+	0.324788i	$0.105293\pi$
$823$			2.98009e11i			0.649576i	−0.945787	+	0.324788i	$0.894707\pi$
$824$		−	8.31759e10i		−	0.180422i
$825$		0			0
$826$	−3.68752e11			−0.792163
$827$	3.12011e11			0.667034			0.333517	−	0.942744i	$-0.391765\pi$
$827$	3.12011e11			0.667034			0.333517	+	0.942744i	$0.391765\pi$
$828$	1.25654e11	−	2.05001e11i	0.267335	−	0.436149i
$829$	−2.42950e11			−0.514397			−0.257198	−	0.966359i	$-0.582799\pi$
$829$	−2.42950e11			−0.514397			−0.257198	+	0.966359i	$0.582799\pi$
$830$		0			0
$831$	3.39443e11	+	6.06193e11i	0.711808	+	1.27118i
$832$			7.08596e11i			1.47879i
$833$	−5.71862e11			−1.18771
$834$	8.40081e11	−	4.70410e11i	1.73643	−	0.972327i
$835$		0			0
$836$		−	1.21048e12i		−	2.47818i
$837$	2.49806e10	−	6.33274e11i	0.0508980	−	1.29030i
$838$			2.08262e11i			0.422312i
$839$		−	1.16205e11i		−	0.234519i	−0.993101	−	0.117259i	$-0.962589\pi$
$839$		−	1.16205e11i		−	0.234519i	0.993101	−	0.117259i	$-0.0374109\pi$
$840$		0			0
$841$	4.88400e11			0.976318
$842$	8.16963e11			1.62538
$843$	1.12512e11	+	2.00928e11i	0.222786	+	0.397861i
$844$	−7.56376e11			−1.49062
$845$		0			0
$846$	−1.22787e11	+	2.00323e11i	−0.239702	+	0.391066i
$847$		−	1.75067e11i		−	0.340150i
$848$	1.55097e11			0.299931
$849$	3.93377e11	+	7.02510e11i	0.757143	+	1.35214i
$850$		0			0
$851$		−	3.18794e11i		−	0.607844i
$852$	−5.30511e11	−	9.47412e11i	−1.00678	−	1.79796i
$853$			2.30678e11i			0.435723i	0.975980	+	0.217861i	$0.0699080\pi$
$853$			2.30678e11i			0.435723i	−0.975980	+	0.217861i	$0.930092\pi$
$854$			4.02806e11i			0.757293i
$855$		0			0
$856$	−2.25497e9			−0.00419997
$857$	6.99039e11			1.29592			0.647960	−	0.761674i	$-0.275622\pi$
$857$	6.99039e11			1.29592			0.647960	+	0.761674i	$0.275622\pi$
$858$	−9.68567e11	+	5.42357e11i	−1.78723	+	1.00078i
$859$	−9.39004e10			−0.172463			−0.0862313	−	0.996275i	$-0.527482\pi$
$859$	−9.39004e10			−0.172463			−0.0862313	+	0.996275i	$0.527482\pi$
$860$		0			0
$861$	2.87647e11	−	1.61070e11i	0.523416	−	0.293091i
$862$		−	7.19561e11i		−	1.30328i
$863$	7.27490e11			1.31155			0.655773	−	0.754958i	$-0.272343\pi$
$863$	7.27490e11			1.31155			0.655773	+	0.754958i	$0.272343\pi$
$864$	3.06156e10	−	7.76126e11i	0.0549399	−	1.39276i
$865$		0			0
$866$		−	6.13481e10i		−	0.109076i
$867$	−5.62875e11	+	3.15187e11i	−0.996175	+	0.557817i
$868$		−	4.05921e11i		−	0.715094i
$869$			4.76621e11i			0.835783i
$870$		0			0
$871$	6.22520e11			1.08164
$872$	2.91325e11			0.503863
$873$	8.40963e10	+	5.15463e10i	0.144784	+	0.0887443i
$874$	−5.13394e11			−0.879842
$875$		0			0
$876$	6.07783e11	+	1.08541e12i	1.03212	+	1.84322i
$877$		−	1.49532e11i		−	0.252775i	−0.991981	−	0.126388i	$-0.959662\pi$
$877$		−	1.49532e11i		−	0.252775i	0.991981	−	0.126388i	$-0.0403383\pi$
$878$	−2.68549e11			−0.451904
$879$	−3.36637e11	+	1.88503e11i	−0.563906	+	0.315764i
$880$		0			0
$881$		−	9.01607e11i		−	1.49663i	−0.663345	−	0.748314i	$-0.730864\pi$
$881$		−	9.01607e11i		−	1.49663i	0.663345	−	0.748314i	$-0.269136\pi$
$882$	3.87192e11	−	6.31691e11i	0.639811	−	1.04383i
$883$		−	7.05614e11i		−	1.16071i	−0.814363	−	0.580356i	$-0.802914\pi$
$883$		−	7.05614e11i		−	1.16071i	0.814363	−	0.580356i	$-0.197086\pi$
$884$			1.15918e12i			1.89819i
$885$		0			0
$886$	−7.26299e11			−1.17864
$887$	1.05583e12			1.70568			0.852842	−	0.522170i	$-0.174877\pi$
$887$	1.05583e12			1.70568			0.852842	+	0.522170i	$0.174877\pi$
$888$	1.91575e11	+	3.42123e11i	0.308096	+	0.550213i
$889$	−9.78836e10			−0.156712
$890$		0			0
$891$	7.50047e11	−	3.81971e11i	1.19008	−	0.606066i
$892$			1.55417e11i			0.245492i
$893$	2.81234e11			0.442245
$894$	−2.27534e9	−	4.06341e9i	−0.00356202	−	0.00636122i
$895$		0			0
$896$		−	2.23916e11i		−	0.347419i
$897$	1.28950e11	+	2.30285e11i	0.199182	+	0.355709i
$898$			5.94873e11i			0.914785i
$899$			1.29799e11i			0.198716i
$900$		0			0
$901$	4.46265e11			0.677163
$902$	−1.84308e12			−2.78431
$903$	6.36930e10	−	3.56654e10i	0.0957945	−	0.0536410i
$904$	−5.74856e10			−0.0860766
$905$		0			0
$906$	5.01697e11	−	2.80930e11i	0.744610	−	0.416951i
$907$			3.67842e11i			0.543541i	0.962362	+	0.271771i	$0.0876092\pi$
$907$			3.67842e11i			0.543541i	−0.962362	+	0.271771i	$0.912391\pi$
$908$	−9.84382e11			−1.44817
$909$	8.47895e11	+	5.19712e11i	1.24190	+	0.761215i
$910$		0			0
$911$			9.64432e11i			1.40023i	0.714032	+	0.700113i	$0.246867\pi$
$911$			9.64432e11i			1.40023i	−0.714032	+	0.700113i	$0.753133\pi$
$912$	−5.69086e11	+	3.18665e11i	−0.822619	+	0.460633i
$913$			1.34602e11i			0.193717i
$914$			2.85821e11i			0.409553i
$915$		0			0
$916$	−1.22583e12			−1.74120
$917$	2.83324e11			0.400688
$918$	6.17999e10	−	1.56667e12i	0.0870196	−	2.20601i
$919$	1.03446e12			1.45028			0.725138	−	0.688603i	$-0.241776\pi$
$919$	1.03446e12			1.45028			0.725138	+	0.688603i	$0.241776\pi$
$920$		0			0
$921$	1.29111e11	+	2.30573e11i	0.179443	+	0.320457i
$922$			4.91563e11i			0.680229i
$923$	1.19188e12			1.64220
$924$	4.70381e11	−	2.63394e11i	0.645301	−	0.361342i
$925$		0			0
$926$			9.36768e11i			1.27405i
$927$	−2.73058e11	−	1.67369e11i	−0.369774	−	0.226651i
$928$			1.59079e11i			0.214496i
$929$			1.47659e11i			0.198242i	0.995075	+	0.0991212i	$0.0316031\pi$
$929$			1.47659e11i			0.198242i	−0.995075	+	0.0991212i	$0.968397\pi$
$930$		0			0
$931$	−8.86833e11			−1.18044
$932$	−1.18590e12			−1.57175
$933$	−4.49928e11	−	8.03502e11i	−0.593767	−	1.06038i
$934$	−1.61131e12			−2.11734
$935$		0			0
$936$	−2.76772e11	−	1.69646e11i	−0.360595	−	0.221024i
$937$			3.27745e11i			0.425185i	0.977141	+	0.212593i	$0.0681908\pi$
$937$			3.27745e11i			0.425185i	−0.977141	+	0.212593i	$0.931809\pi$
$938$	−5.39301e11			−0.696659
$939$	1.12180e11	+	2.00337e11i	0.144296	+	0.257691i
$940$		0			0
$941$		−	3.29986e11i		−	0.420860i	−0.977609	−	0.210430i	$-0.932514\pi$
$941$		−	3.29986e11i		−	0.420860i	0.977609	−	0.210430i	$-0.0674864\pi$
$942$	−4.92507e11	−	8.79542e11i	−0.625473	−	1.11700i
$943$			4.38207e11i			0.554156i
$944$		−	6.22704e11i		−	0.784140i
$945$		0			0
$946$	−4.08109e11			−0.509579
$947$	2.28185e8			0.000283718			0.000141859	−	1.00000i	$-0.499955\pi$
$947$	2.28185e8			0.000283718			0.000141859		1.00000i	$0.499955\pi$
$948$	−5.62627e11	+	3.15048e11i	−0.696606	+	0.390070i
$949$	−1.36549e12			−1.68354
$950$		0			0
$951$	−3.42347e11	+	1.91700e11i	−0.418548	+	0.234369i
$952$		−	2.17063e11i		−	0.264264i
$953$	1.61330e11			0.195588			0.0977942	−	0.995207i	$-0.468821\pi$
$953$	1.61330e11			0.195588			0.0977942	+	0.995207i	$0.468821\pi$
$954$	−3.02153e11	+	4.92954e11i	−0.364782	+	0.595131i
$955$		0			0
$956$		−	1.53420e12i		−	1.83675i
$957$	−1.50411e11	+	8.42238e10i	−0.179321	+	0.100412i
$958$		−	2.44653e12i		−	2.90462i
$959$		−	2.27921e11i		−	0.269470i
$960$		0			0
$961$	5.69271e11			0.667460
$962$	−1.99122e12			−2.32497
$963$	−4.53754e9	+	7.40286e9i	−0.00527612	+	0.00860784i
$964$	−1.13257e12			−1.31146
$965$		0			0
$966$	−1.11712e11	−	1.99500e11i	−0.128289	−	0.229105i
$967$			1.49948e12i			1.71489i	0.514577	+	0.857444i	$0.327949\pi$
$967$			1.49948e12i			1.71489i	−0.514577	+	0.857444i	$0.672051\pi$
$968$	−2.86217e11			−0.325982
$969$	−1.63744e12	+	9.16900e11i	−1.85725	+	1.03998i
$970$		0			0
$971$		−	3.35149e11i		−	0.377017i	−0.982072	−	0.188509i	$-0.939635\pi$
$971$		−	3.35149e11i		−	0.377017i	0.982072	−	0.188509i	$-0.0603654\pi$
$972$	9.46682e11	+	6.32909e11i	1.06057	+	0.709049i
$973$		−	5.13258e11i		−	0.572644i
$974$			2.61904e11i			0.291009i
$975$		0			0
$976$	−6.80209e11			−0.749623
$977$	−8.22116e11			−0.902308			−0.451154	−	0.892446i	$-0.648988\pi$
$977$	−8.22116e11			−0.902308			−0.451154	+	0.892446i	$0.648988\pi$
$978$	6.94287e11	+	1.23989e12i	0.758898	+	1.35528i
$979$	6.64438e11			0.723309
$980$		0			0
$981$	5.86215e11	−	9.56392e11i	0.632967	−	1.03267i
$982$		−	2.48545e11i		−	0.267276i
$983$	−1.23984e12			−1.32786			−0.663930	−	0.747795i	$-0.731113\pi$
$983$	−1.23984e12			−1.32786			−0.663930	+	0.747795i	$0.731113\pi$
$984$	−2.63334e11	−	4.70274e11i	−0.280883	−	0.501615i
$985$		0			0
$986$			3.21112e11i			0.339742i
$987$	6.11951e10	+	1.09285e11i	0.0644834	+	0.115158i
$988$			1.79763e12i			1.88657i
$989$			9.70311e10i			0.101420i
$990$		0			0
$991$	1.44437e12			1.49756			0.748782	−	0.662817i	$-0.230639\pi$
$991$	1.44437e12			1.49756			0.748782	+	0.662817i	$0.230639\pi$
$992$	1.74297e12			1.79988
$993$	3.86878e11	−	2.16635e11i	0.397902	−	0.222809i
$994$	−1.03255e12			−1.05771
$995$		0			0
$996$	−1.58890e11	+	8.89721e10i	−0.161458	+	0.0904100i
$997$		−	4.69939e11i		−	0.475621i	−0.971312	−	0.237810i	$-0.923570\pi$
$997$		−	4.69939e11i		−	0.475621i	0.971312	−	0.237810i	$-0.0764297\pi$
$998$	−1.63310e12			−1.64623
$999$	1.50865e12	+	5.95112e10i	1.51470	+	0.0597498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.d.d.74.18		20
3.2	odd	2	inner	75.9.d.d.74.4		20
5.2	odd	4		75.9.c.e.26.9	yes	10
5.3	odd	4		75.9.c.f.26.2	yes	10
5.4	even	2	inner	75.9.d.d.74.3		20
15.2	even	4		75.9.c.e.26.2	✓	10
15.8	even	4		75.9.c.f.26.9	yes	10
15.14	odd	2	inner	75.9.d.d.74.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.c.e.26.2	✓	10	15.2	even	4
75.9.c.e.26.9	yes	10	5.2	odd	4
75.9.c.f.26.2	yes	10	5.3	odd	4
75.9.c.f.26.9	yes	10	15.8	even	4
75.9.d.d.74.3		20	5.4	even	2	inner
75.9.d.d.74.4		20	3.2	odd	2	inner
75.9.d.d.74.17		20	15.14	odd	2	inner
75.9.d.d.74.18		20	1.1	even	1	trivial

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+24.1370 q^{2} +(-70.6742 + 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} +1042.22i q^{7} +1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +O(q^{10})\)	\(q+24.1370 q^{2} +(-70.6742 + 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} +1042.22i q^{7} +1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +19553.4i q^{11} +(-23081.8 + 12924.8i) q^{12} -29037.8i q^{13} +25156.0i q^{14} -42480.5 q^{16} -122230. q^{17} +(82758.4 - 135018. i) q^{18} -189552. q^{19} +(-41245.5 - 73658.1i) q^{21} +471959. i q^{22} +112212. q^{23} +(-120424. + 67432.2i) q^{24} -700886. i q^{26} +(-20947.3 + 531028. i) q^{27} +340383. i q^{28} -108842. i q^{29} -1.19254e6 q^{31} -1.46155e6 q^{32} +(-773817. - 1.38192e6i) q^{33} -2.95026e6 q^{34} +(1.11979e6 - 1.82691e6i) q^{36} -2.84100e6i q^{37} -4.57521e6 q^{38} +(1.14916e6 + 2.05223e6i) q^{39} +3.90516e6i q^{41} +(-995541. - 1.77788e6i) q^{42} +864712. i q^{43} +6.38601e6i q^{44} +2.70846e6 q^{46} -1.48368e6 q^{47} +(3.00227e6 - 1.68115e6i) q^{48} +4.67858e6 q^{49} +(8.63850e6 - 4.83720e6i) q^{51} -9.48358e6i q^{52} -3.65103e6 q^{53} +(-505604. + 1.28174e7i) q^{54} +1.77586e6i q^{56} +(1.33964e7 - 7.50144e6i) q^{57} -2.62712e6i q^{58} +1.46586e7i q^{59} +1.60123e7 q^{61} -2.87844e7 q^{62} +(5.82998e6 + 3.57345e6i) q^{63} -2.44025e7 q^{64} +(-1.86776e7 - 3.33554e7i) q^{66} +2.14382e7i q^{67} -3.99195e7 q^{68} +(-7.93050e6 + 4.44075e6i) q^{69} +4.10459e7i q^{71} +(5.84224e6 - 9.53144e6i) q^{72} -4.70244e7i q^{73} -6.85731e7i q^{74} -6.19065e7 q^{76} -2.03789e7 q^{77} +(2.77373e7 + 4.95346e7i) q^{78} +2.43754e7 q^{79} +(-1.95348e7 - 3.83590e7i) q^{81} +9.42589e7i q^{82} +6.88381e6 q^{83} +(-1.34705e7 - 2.40563e7i) q^{84} +2.08715e7i q^{86} +(4.30738e6 + 7.69233e6i) q^{87} +3.33174e7i q^{88} -3.39808e7i q^{89} +3.02638e7 q^{91} +3.66478e7 q^{92} +(8.42822e7 - 4.71945e7i) q^{93} -3.58116e7 q^{94} +(1.03294e8 - 5.78405e7i) q^{96} +1.50338e7i q^{97} +1.12927e8 q^{98} +(1.09378e8 + 6.70425e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) \) 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9	\( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) \) 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9 + 89268 * q^16 + 287868 * q^19 + 1346856 * q^21 + 2033718 * q^24 - 6028120 * q^31 - 9954292 * q^34 + 9001054 * q^36 + 15026564 * q^39 - 27877272 * q^46 - 17907092 * q^49 + 12418574 * q^51 + 17772544 * q^54 + 3040440 * q^61 + 9073996 * q^64 + 20930590 * q^66 - 22789956 * q^69 - 59058092 * q^76 - 17099792 * q^79 + 45225890 * q^81 + 273766584 * q^84 - 214448528 * q^91 - 712237192 * q^94 + 1050848002 * q^96 + 764842670 * q^99

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