LMFDB - Embedded newform 252.9.z.d.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, degree $2$, 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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 $ x^12 - 3x^11 + 148097x^10 + 46071824x^9 + 21578502553x^8 + 3561445462121x^7 + 576413321817541x^6 + 47217566733462528x^5 + 5214056955297543333x^4 + 358752845334081085965x^3 + 30962072851910211245661x^2 + 1221542968331193193318500*x + 45396580558961892385326096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{10}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.5
Root			$-72.3408 + 125.298i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.d.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(225.043 - 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +O(q^{10})$	$q+(225.043 - 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(-9723.49 + 16841.6i) q^{11} +46381.7i q^{13} +(105886. + 61133.6i) q^{17} +(18446.7 - 10650.2i) q^{19} +(-152199. - 263616. i) q^{23} +(-161550. + 279812. i) q^{25} -88119.4 q^{29} +(-1.54998e6 - 894884. i) q^{31} +(436564. + 445739. i) q^{35} +(755092. + 1.30786e6i) q^{37} -188022. i q^{41} -123402. q^{43} +(5.58909e6 - 3.22686e6i) q^{47} +(-5.05133e6 + 2.77796e6i) q^{49} +(6.88508e6 - 1.19253e7i) q^{53} +5.05343e6i q^{55} +(-1.00305e7 - 5.79109e6i) q^{59} +(-1.92663e7 + 1.11234e7i) q^{61} +(6.02630e6 + 1.04379e7i) q^{65} +(5.75873e6 - 9.97442e6i) q^{67} +3.11345e7 q^{71} +(-1.08437e7 - 6.26059e6i) q^{73} +(-4.49731e7 - 1.25532e7i) q^{77} +(2.13222e7 + 3.69312e7i) q^{79} +7.19982e7i q^{83} +3.17720e7 q^{85} +(-4.37683e7 + 2.52696e7i) q^{89} +(-1.07862e8 + 2.77026e7i) q^{91} +(2.76753e6 - 4.79351e6i) q^{95} -1.16642e8i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	225.043	−	129.928i	0.360068	−	0.207885i	−0.309042	−	0.951048i	$-0.600009\pi$
$5$	225.043	−	129.928i	0.360068	−	0.207885i	0.669111	+	0.743163i	$0.266675\pi$
$6$		0			0
$7$	597.275	+	2325.52i	0.248761	+	0.968565i
$7$	597.275	+	2325.52i	0.248761	+	0.968565i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−9723.49	+	16841.6i	−0.664127	+	1.15030i	0.315394	+	0.948961i	$0.397863\pi$
$11$	−9723.49	+	16841.6i	−0.664127	+	1.15030i	−0.979521	+	0.201341i	$0.935470\pi$
$12$		0			0
$13$			46381.7i			1.62395i	0.583690	+	0.811976i	$0.301608\pi$
$13$			46381.7i			1.62395i	−0.583690	+	0.811976i	$0.698392\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	105886.	+	61133.6i	1.26778	+	0.731955i	0.974568	−	0.224092i	$-0.0719416\pi$
$17$	105886.	+	61133.6i	1.26778	+	0.731955i	0.293215	+	0.956047i	$0.405275\pi$
$18$		0			0
$19$	18446.7	−	10650.2i	0.141548	−	0.0817230i	−0.427553	−	0.903990i	$-0.640624\pi$
$19$	18446.7	−	10650.2i	0.141548	−	0.0817230i	0.569102	+	0.822267i	$0.307291\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−152199.	−	263616.i	−0.543876	−	0.942020i	−0.998677	−	0.0514271i	$-0.983623\pi$
$23$	−152199.	−	263616.i	−0.543876	−	0.942020i	0.454801	−	0.890593i	$-0.349710\pi$
$24$		0			0
$25$	−161550.	+	279812.i	−0.413567	+	0.716320i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−88119.4			−0.124589			−0.0622945	−	0.998058i	$-0.519842\pi$
$29$	−88119.4			−0.124589			−0.0622945	+	0.998058i	$0.519842\pi$
$30$		0			0
$31$	−1.54998e6	−	894884.i	−1.67834	−	0.968991i	−0.962718	−	0.270505i	$-0.912809\pi$
$31$	−1.54998e6	−	894884.i	−1.67834	−	0.968991i	−0.715624	−	0.698486i	$-0.753857\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	436564.	+	445739.i	0.290921	+	0.297036i
$36$		0			0
$37$	755092.	+	1.30786e6i	0.402896	+	0.697836i	0.994074	−	0.108705i	$-0.0346703\pi$
$37$	755092.	+	1.30786e6i	0.402896	+	0.697836i	−0.591178	+	0.806541i	$0.701337\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	188022.i		−	0.0665385i	−0.999446	−	0.0332692i	$-0.989408\pi$
$41$		−	188022.i		−	0.0665385i	0.999446	−	0.0332692i	$-0.0105919\pi$
$42$		0			0
$43$	−123402.			−0.0360953			−0.0180476	−	0.999837i	$-0.505745\pi$
$43$	−123402.			−0.0360953			−0.0180476	+	0.999837i	$0.505745\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.58909e6	−	3.22686e6i	1.14538	−	0.661285i	0.197623	−	0.980278i	$-0.436678\pi$
$47$	5.58909e6	−	3.22686e6i	1.14538	−	0.661285i	0.947757	+	0.318993i	$0.103345\pi$
$48$		0			0
$49$	−5.05133e6	+	2.77796e6i	−0.876236	+	0.481882i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.88508e6	−	1.19253e7i	0.872580	−	1.51135i	0.0132616	−	0.999912i	$-0.495779\pi$
$53$	6.88508e6	−	1.19253e7i	0.872580	−	1.51135i	0.859318	−	0.511441i	$-0.170888\pi$
$54$		0			0
$55$			5.05343e6i			0.552250i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.00305e7	−	5.79109e6i	−0.827776	−	0.477917i	0.0253148	−	0.999680i	$-0.491941\pi$
$59$	−1.00305e7	−	5.79109e6i	−0.827776	−	0.477917i	−0.853090	+	0.521763i	$0.825275\pi$
$60$		0			0
$61$	−1.92663e7	+	1.11234e7i	−1.39149	+	0.803375i	−0.993480	−	0.114007i	$-0.963631\pi$
$61$	−1.92663e7	+	1.11234e7i	−1.39149	+	0.803375i	−0.398007	+	0.917383i	$0.630298\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.02630e6	+	1.04379e7i	0.337596	+	0.584734i
$66$		0			0
$67$	5.75873e6	−	9.97442e6i	0.285777	−	0.494981i	−0.687020	−	0.726638i	$-0.741082\pi$
$67$	5.75873e6	−	9.97442e6i	0.285777	−	0.494981i	0.972797	+	0.231658i	$0.0744149\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.11345e7			1.22520			0.612602	−	0.790392i	$-0.290123\pi$
$71$	3.11345e7			1.22520			0.612602	+	0.790392i	$0.290123\pi$
$72$		0			0
$73$	−1.08437e7	−	6.26059e6i	−0.381843	−	0.220457i	0.296777	−	0.954947i	$-0.404088\pi$
$73$	−1.08437e7	−	6.26059e6i	−0.381843	−	0.220457i	−0.678620	+	0.734490i	$0.737422\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.49731e7	−	1.25532e7i	−1.27935	−	0.357100i
$78$		0			0
$79$	2.13222e7	+	3.69312e7i	0.547424	+	0.948167i	0.998450	+	0.0556558i	$0.0177249\pi$
$79$	2.13222e7	+	3.69312e7i	0.547424	+	0.948167i	−0.451026	+	0.892511i	$0.648942\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			7.19982e7i			1.51708i	0.651625	+	0.758541i	$0.274088\pi$
$83$			7.19982e7i			1.51708i	−0.651625	+	0.758541i	$0.725912\pi$
$84$		0			0
$85$	3.17720e7			0.608651
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.37683e7	+	2.52696e7i	−0.697589	+	0.402753i	−0.806449	−	0.591304i	$-0.798613\pi$
$89$	−4.37683e7	+	2.52696e7i	−0.697589	+	0.402753i	0.108860	+	0.994057i	$0.465280\pi$
$90$		0			0
$91$	−1.07862e8	+	2.77026e7i	−1.57290	+	0.403976i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.76753e6	−	4.79351e6i	0.0339781	−	0.0588517i
$96$		0			0
$97$		−	1.16642e8i		−	1.31755i	−0.752339	−	0.658776i	$-0.771075\pi$
$97$		−	1.16642e8i		−	1.31755i	0.752339	−	0.658776i	$-0.228925\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.23786e7	−	5.33348e7i	−0.887740	−	0.512537i	−0.0145374	−	0.999894i	$-0.504628\pi$
$101$	−9.23786e7	−	5.33348e7i	−0.887740	−	0.512537i	−0.873203	+	0.487357i	$0.837961\pi$
$102$		0			0
$103$	1.77725e8	−	1.02609e8i	1.57906	−	0.911671i	0.584070	−	0.811703i	$-0.301459\pi$
$103$	1.77725e8	−	1.02609e8i	1.57906	−	0.911671i	0.994991	−	0.0999675i	$-0.0318739\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.90703e7	−	1.54274e8i	−0.679513	−	1.17695i	−0.975128	−	0.221644i	$-0.928858\pi$
$107$	−8.90703e7	−	1.54274e8i	−0.679513	−	1.17695i	0.295615	−	0.955307i	$-0.404476\pi$
$108$		0			0
$109$	−5.48168e7	+	9.49454e7i	−0.388336	+	0.672617i	−0.992226	−	0.124450i	$-0.960283\pi$
$109$	−5.48168e7	+	9.49454e7i	−0.388336	+	0.672617i	0.603890	+	0.797068i	$0.293617\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.74592e8			−1.68413			−0.842063	−	0.539379i	$-0.818659\pi$
$113$	−2.74592e8			−1.68413			−0.842063	+	0.539379i	$0.818659\pi$
$114$		0			0
$115$	−6.85024e7	−	3.95499e7i	−0.391665	−	0.226128i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.89243e7	+	2.82755e8i	−0.393571	+	1.41001i
$120$		0			0
$121$	−8.19129e7	−	1.41877e8i	−0.382130	−	0.661868i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.85466e8i			0.759669i
$126$		0			0
$127$	−3.97605e7			−0.152840			−0.0764199	−	0.997076i	$-0.524349\pi$
$127$	−3.97605e7			−0.152840			−0.0764199	+	0.997076i	$0.524349\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.31807e7	+	1.91569e7i	−0.112668	+	0.0650490i	−0.555275	−	0.831667i	$-0.687387\pi$
$131$	−3.31807e7	+	1.91569e7i	−0.112668	+	0.0650490i	0.442607	+	0.896716i	$0.354054\pi$
$132$		0			0
$133$	3.57851e7	+	3.65372e7i	0.114366	+	0.116769i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.07018e8	+	3.58565e8i	−0.587659	+	1.01786i	0.406879	+	0.913482i	$0.366617\pi$
$137$	−2.07018e8	+	3.58565e8i	−0.587659	+	1.01786i	−0.994538	+	0.104374i	$0.966716\pi$
$138$		0			0
$139$			2.15646e8i			0.577674i	0.957378	+	0.288837i	$0.0932686\pi$
$139$			2.15646e8i			0.577674i	−0.957378	+	0.288837i	$0.906731\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.81141e8	−	4.50992e8i	−1.86804	−	1.07851i
$144$		0			0
$145$	−1.98306e7	+	1.14492e7i	−0.0448605	+	0.0259002i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.59668e8	+	4.49759e8i	0.526834	+	0.912503i	0.999511	+	0.0312676i	$0.00995442\pi$
$149$	2.59668e8	+	4.49759e8i	0.526834	+	0.912503i	−0.472677	+	0.881236i	$0.656712\pi$
$150$		0			0
$151$	−1.65131e8	+	2.86015e8i	−0.317630	+	0.550151i	−0.979993	−	0.199032i	$-0.936220\pi$
$151$	−1.65131e8	+	2.86015e8i	−0.317630	+	0.550151i	0.662363	+	0.749183i	$0.269554\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.65083e8			−0.805757
$156$		0			0
$157$	−2.58909e8	−	1.49481e8i	−0.426137	−	0.246030i	0.271563	−	0.962421i	$-0.412460\pi$
$157$	−2.58909e8	−	1.49481e8i	−0.426137	−	0.246030i	−0.697700	+	0.716390i	$0.745793\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.22141e8	−	5.11393e8i	0.777113	−	0.761117i
$162$		0			0
$163$	2.92142e8	+	5.06004e8i	0.413850	+	0.716810i	0.995307	−	0.0967676i	$-0.0308504\pi$
$163$	2.92142e8	+	5.06004e8i	0.413850	+	0.716810i	−0.581457	+	0.813577i	$0.697517\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	7.46657e8i		−	0.959965i	−0.877278	−	0.479983i	$-0.840643\pi$
$167$		−	7.46657e8i		−	0.959965i	0.877278	−	0.479983i	$-0.159357\pi$
$168$		0			0
$169$	−1.33553e9			−1.63722
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.08205e8	+	5.24352e8i	−1.01391	+	0.585381i	−0.912334	−	0.409447i	$-0.865722\pi$
$173$	−9.08205e8	+	5.24352e8i	−1.01391	+	0.585381i	−0.101576	+	0.994828i	$0.532388\pi$
$174$		0			0
$175$	−7.47200e8	−	2.08563e8i	−0.796681	−	0.222374i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.24237e8	−	2.15185e8i	0.121015	−	0.209604i	−0.799153	−	0.601127i	$-0.794718\pi$
$179$	1.24237e8	−	2.15185e8i	0.121015	−	0.209604i	0.920168	+	0.391523i	$0.128052\pi$
$180$		0			0
$181$		−	4.91957e8i		−	0.458366i	−0.973383	−	0.229183i	$-0.926394\pi$
$181$		−	4.91957e8i		−	0.458366i	0.973383	−	0.229183i	$-0.0736055\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.39856e8	+	1.96216e8i	0.290140	+	0.167512i
$186$		0			0
$187$	−2.05917e9	+	1.18886e9i	−1.68394	+	0.972222i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.53669e8	−	1.65180e9i	−0.716579	−	1.24115i	−0.962347	−	0.271823i	$-0.912374\pi$
$191$	−9.53669e8	−	1.65180e9i	−0.716579	−	1.24115i	0.245768	−	0.969329i	$-0.420960\pi$
$192$		0			0
$193$	−4.70293e8	+	8.14571e8i	−0.338953	+	0.587083i	−0.984236	−	0.176860i	$-0.943406\pi$
$193$	−4.70293e8	+	8.14571e8i	−0.338953	+	0.587083i	0.645283	+	0.763943i	$0.276739\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.22807e9			−0.815379			−0.407689	−	0.913121i	$-0.633665\pi$
$197$	−1.22807e9			−0.815379			−0.407689	+	0.913121i	$0.633665\pi$
$198$		0			0
$199$	9.98896e7	+	5.76713e7i	0.0636954	+	0.0367745i	0.531509	−	0.847052i	$-0.321625\pi$
$199$	9.98896e7	+	5.76713e7i	0.0636954	+	0.0367745i	−0.467814	+	0.883827i	$0.654958\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.26315e7	−	2.04924e8i	−0.0309929	−	0.120672i
$204$		0			0
$205$	−2.44294e7	−	4.23129e7i	−0.0138324	−	0.0239584i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			4.14229e8i			0.217098i
$210$		0			0
$211$	2.33973e9			1.18042			0.590209	−	0.807250i	$-0.299045\pi$
$211$	2.33973e9			1.18042			0.590209	+	0.807250i	$0.299045\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.77708e7	+	1.60335e7i	−0.0129968	+	0.00750368i
$216$		0			0
$217$	1.15531e9	−	4.13902e9i	0.521025	−	1.86663i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.83548e9	+	4.91120e9i	−1.18866	+	2.05882i
$222$		0			0
$223$			1.14133e9i			0.461523i	0.973010	+	0.230762i	$0.0741218\pi$
$223$			1.14133e9i			0.461523i	−0.973010	+	0.230762i	$0.925878\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.82252e8	+	1.05223e8i	0.0686387	+	0.0396285i	0.533927	−	0.845531i	$-0.320716\pi$
$227$	1.82252e8	+	1.05223e8i	0.0686387	+	0.0396285i	−0.465288	+	0.885159i	$0.654049\pi$
$228$		0			0
$229$	−3.18730e9	+	1.84019e9i	−1.15899	+	0.669146i	−0.951063	−	0.308997i	$-0.900007\pi$
$229$	−3.18730e9	+	1.84019e9i	−1.15899	+	0.669146i	−0.207932	+	0.978143i	$0.566673\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.42196e8	−	2.46291e8i	−0.0482464	−	0.0835652i	0.840894	−	0.541200i	$-0.182030\pi$
$233$	−1.42196e8	−	2.46291e8i	−0.0482464	−	0.0835652i	−0.889140	+	0.457635i	$0.848697\pi$
$234$		0			0
$235$	8.38522e8	−	1.45236e9i	0.274943	−	0.476216i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.62607e9			−0.804850			−0.402425	−	0.915453i	$-0.631833\pi$
$239$	−2.62607e9			−0.804850			−0.402425	+	0.915453i	$0.631833\pi$
$240$		0			0
$241$	2.05781e8	+	1.18808e8i	0.0610011	+	0.0352190i	0.530190	−	0.847879i	$-0.322120\pi$
$241$	2.05781e8	+	1.18808e8i	0.0610011	+	0.0352190i	−0.469189	+	0.883098i	$0.655454\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.75828e8	+	1.28147e9i	−0.215328	+	0.355667i
$246$		0			0
$247$	4.93976e8	+	8.55591e8i	0.132714	+	0.229868i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			3.49203e9i			0.879797i	0.898047	+	0.439899i	$0.144986\pi$
$251$			3.49203e9i			0.879797i	−0.898047	+	0.439899i	$0.855014\pi$
$252$		0			0
$253$	5.91961e9			1.44481
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.36384e9	−	1.94211e9i	0.771086	−	0.445187i	−0.0621759	−	0.998065i	$-0.519804\pi$
$257$	3.36384e9	−	1.94211e9i	0.771086	−	0.445187i	0.833262	+	0.552879i	$0.186471\pi$
$258$		0			0
$259$	−2.59046e9	+	2.53714e9i	−0.575675	+	0.563825i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.40863e8	−	1.62962e9i	0.196654	−	0.340615i	−0.750787	−	0.660544i	$-0.770326\pi$
$263$	9.40863e8	−	1.62962e9i	0.196654	−	0.340615i	0.947442	+	0.319929i	$0.103659\pi$
$264$		0			0
$265$		−	3.57827e9i		−	0.725587i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.78854e9	−	1.60997e9i	−0.532559	−	0.307473i	0.209499	−	0.977809i	$-0.432817\pi$
$269$	−2.78854e9	−	1.60997e9i	−0.532559	−	0.307473i	−0.742058	+	0.670336i	$0.766150\pi$
$270$		0			0
$271$	4.42388e9	−	2.55413e9i	0.820212	−	0.473550i	−0.0302773	−	0.999542i	$-0.509639\pi$
$271$	4.42388e9	−	2.55413e9i	0.820212	−	0.473550i	0.850490	+	0.525992i	$0.176306\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.14165e9	−	5.44150e9i	−0.549323	−	0.951455i
$276$		0			0
$277$	5.20091e9	−	9.00825e9i	0.883406	−	1.53010i	0.0358772	−	0.999356i	$-0.488577\pi$
$277$	5.20091e9	−	9.00825e9i	0.883406	−	1.53010i	0.847529	−	0.530749i	$-0.178089\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.79146e9			1.57044			0.785222	−	0.619215i	$-0.212549\pi$
$281$	9.79146e9			1.57044			0.785222	+	0.619215i	$0.212549\pi$
$282$		0			0
$283$	−9.03261e8	−	5.21498e8i	−0.140821	−	0.0813031i	0.427934	−	0.903810i	$-0.359242\pi$
$283$	−9.03261e8	−	5.21498e8i	−0.140821	−	0.0813031i	−0.568755	+	0.822507i	$0.692575\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.37249e8	−	1.12301e8i	0.0644468	−	0.0165522i
$288$		0			0
$289$	3.98675e9	+	6.90526e9i	0.571515	+	0.989893i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			2.83834e9i			0.385118i	0.981285	+	0.192559i	$0.0616787\pi$
$293$			2.83834e9i			0.385118i	−0.981285	+	0.192559i	$0.938321\pi$
$294$		0			0
$295$	−3.00971e9			−0.397408
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.22270e10	−	7.05924e9i	1.52980	−	0.883228i
$300$		0			0
$301$	−7.37052e7	−	2.86975e8i	−0.00897909	−	0.0349606i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.89049e9	+	5.00648e9i	−0.334020	+	0.578540i
$306$		0			0
$307$			1.01655e10i			1.14439i	0.820116	+	0.572197i	$0.193909\pi$
$307$			1.01655e10i			1.14439i	−0.820116	+	0.572197i	$0.806091\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.35774e9	+	5.40269e9i	1.00030	+	0.577522i	0.908336	−	0.418240i	$-0.137353\pi$
$311$	9.35774e9	+	5.40269e9i	1.00030	+	0.577522i	0.0919614	+	0.995763i	$0.470686\pi$
$312$		0			0
$313$	−7.81261e9	+	4.51061e9i	−0.813989	+	0.469957i	−0.848339	−	0.529453i	$-0.822397\pi$
$313$	−7.81261e9	+	4.51061e9i	−0.813989	+	0.469957i	0.0343502	+	0.999410i	$0.489064\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.10486e9	−	3.64573e9i	−0.208443	−	0.361034i	0.742781	−	0.669534i	$-0.233506\pi$
$317$	−2.10486e9	−	3.64573e9i	−0.208443	−	0.361034i	−0.951224	+	0.308500i	$0.900173\pi$
$318$		0			0
$319$	8.56828e8	−	1.48407e9i	0.0827429	−	0.143315i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.60435e9			0.239270
$324$		0			0
$325$	−1.29782e10	−	7.49295e9i	−1.16327	−	0.671614i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.08424e10	+	1.10702e10i	0.925424	+	0.944873i
$330$		0			0
$331$	5.98155e9	+	1.03603e10i	0.498312	+	0.863102i	0.999998	−	0.00194777i	$-0.000619995\pi$
$331$	5.98155e9	+	1.03603e10i	0.498312	+	0.863102i	−0.501686	+	0.865050i	$0.667287\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	2.99289e9i		−	0.237636i
$336$		0			0
$337$	8.47484e9			0.657070			0.328535	−	0.944492i	$-0.393445\pi$
$337$	8.47484e9			0.657070			0.328535	+	0.944492i	$0.393445\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.01425e10	−	1.74028e10i	2.22927	−	1.28707i
$342$		0			0
$343$	−9.47723e9	−	1.00878e10i	−0.684708	−	0.728818i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.92809e9	−	1.37319e10i	0.546828	−	0.947134i	−0.451661	−	0.892190i	$-0.649168\pi$
$347$	7.92809e9	−	1.37319e10i	0.546828	−	0.947134i	0.998489	−	0.0549447i	$-0.0174983\pi$
$348$		0			0
$349$		−	7.90260e9i		−	0.532682i	−0.963879	−	0.266341i	$-0.914185\pi$
$349$		−	7.90260e9i		−	0.532682i	0.963879	−	0.266341i	$-0.0858148\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.28745e9	−	4.78476e9i	−0.533731	−	0.308150i	0.208804	−	0.977958i	$-0.433043\pi$
$353$	−8.28745e9	−	4.78476e9i	−0.533731	−	0.308150i	−0.742534	+	0.669808i	$0.766376\pi$
$354$		0			0
$355$	7.00658e9	−	4.04525e9i	0.441157	−	0.254702i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.12021e9	−	8.86847e9i	−0.308255	−	0.533914i	0.669726	−	0.742609i	$-0.266412\pi$
$359$	−5.12021e9	−	8.86847e9i	−0.308255	−	0.533914i	−0.977981	+	0.208695i	$0.933078\pi$
$360$		0			0
$361$	−8.26493e9	+	1.43153e10i	−0.486643	+	0.842890i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.25371e9			−0.183319
$366$		0			0
$367$	2.80339e10	+	1.61854e10i	1.54532	+	0.892193i	0.998489	+	0.0549514i	$0.0175004\pi$
$367$	2.80339e10	+	1.61854e10i	1.54532	+	0.892193i	0.546834	+	0.837241i	$0.315833\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.18449e10	+	8.88873e9i	1.68091	+	0.469185i
$372$		0			0
$373$	1.25975e10	+	2.18195e10i	0.650803	+	1.12722i	0.982928	+	0.183988i	$0.0589008\pi$
$373$	1.25975e10	+	2.18195e10i	0.650803	+	1.12722i	−0.332126	+	0.943235i	$0.607766\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	4.08713e9i		−	0.202327i
$378$		0			0
$379$	−6.03658e9			−0.292573			−0.146287	−	0.989242i	$-0.546732\pi$
$379$	−6.03658e9			−0.292573			−0.146287	+	0.989242i	$0.546732\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.57427e9	−	5.52771e9i	0.444949	−	0.256892i	−0.260745	−	0.965408i	$-0.583968\pi$
$383$	9.57427e9	−	5.52771e9i	0.444949	−	0.256892i	0.705695	+	0.708516i	$0.250635\pi$
$384$		0			0
$385$	−1.17519e10	+	3.01829e9i	−0.534890	+	0.137378i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.58412e10	+	2.74378e10i	−0.691814	+	1.19826i	0.279428	+	0.960167i	$0.409855\pi$
$389$	−1.58412e10	+	2.74378e10i	−0.691814	+	1.19826i	−0.971243	+	0.238091i	$0.923478\pi$
$390$		0			0
$391$		−	3.72178e10i		−	1.59237i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.59682e9	+	5.54072e9i	0.394220	+	0.227603i
$396$		0			0
$397$	−1.81623e10	+	1.04860e10i	−0.731155	+	0.422132i	−0.818844	−	0.574015i	$-0.805385\pi$
$397$	−1.81623e10	+	1.04860e10i	−0.731155	+	0.422132i	0.0876897	+	0.996148i	$0.472052\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.84375e9	+	1.01217e10i	0.226003	+	0.391449i	0.956620	−	0.291339i	$-0.0941007\pi$
$401$	5.84375e9	+	1.01217e10i	0.226003	+	0.391449i	−0.730617	+	0.682788i	$0.760767\pi$
$402$		0			0
$403$	4.15062e10	−	7.18909e10i	1.57360	−	2.72555i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.93685e10			−1.07030
$408$		0			0
$409$	2.98804e10	+	1.72515e10i	1.06781	+	0.616499i	0.927582	−	0.373620i	$-0.121884\pi$
$409$	2.98804e10	+	1.72515e10i	1.06781	+	0.616499i	0.140226	+	0.990119i	$0.455217\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.47637e9	−	2.67849e10i	0.256975	−	0.920642i
$414$		0			0
$415$	9.35461e9	+	1.62027e10i	0.315379	+	0.546253i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			1.71261e10i			0.555652i	0.960631	+	0.277826i	$0.0896139\pi$
$419$			1.71261e10i			0.555652i	−0.960631	+	0.277826i	$0.910386\pi$
$420$		0			0
$421$	3.64524e10			1.16037			0.580187	−	0.814484i	$-0.302980\pi$
$421$	3.64524e10			1.16037			0.580187	+	0.814484i	$0.302980\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.42119e10	+	1.97522e10i	−1.04863	+	0.605425i
$426$		0			0
$427$	−3.73750e10	−	3.81605e10i	−1.12427	−	1.14790i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.09904e10	+	1.90360e10i	−0.318497	+	0.551654i	−0.980175	−	0.198135i	$-0.936512\pi$
$431$	−1.09904e10	+	1.90360e10i	−0.318497	+	0.551654i	0.661677	+	0.749789i	$0.269845\pi$
$432$		0			0
$433$		−	1.35544e10i		−	0.385593i	−0.981239	−	0.192796i	$-0.938244\pi$
$433$		−	1.35544e10i		−	0.385593i	0.981239	−	0.192796i	$-0.0617557\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.61514e9	−	3.24190e9i	−0.153969	−	0.0888943i
$438$		0			0
$439$	−4.13004e10	+	2.38448e10i	−1.11198	+	0.642001i	−0.939341	−	0.342985i	$-0.888562\pi$
$439$	−4.13004e10	+	2.38448e10i	−1.11198	+	0.642001i	−0.172637	+	0.984986i	$0.555229\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.20913e9	−	1.59507e10i	−0.239113	−	0.414156i	0.721347	−	0.692574i	$-0.243523\pi$
$443$	−9.20913e9	−	1.59507e10i	−0.239113	−	0.414156i	−0.960460	+	0.278418i	$0.910190\pi$
$444$		0			0
$445$	−6.56648e9	+	1.13735e10i	−0.167453	+	0.290037i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.72530e10			−1.16264			−0.581319	−	0.813676i	$-0.697463\pi$
$449$	−4.72530e10			−1.16264			−0.581319	+	0.813676i	$0.697463\pi$
$450$		0			0
$451$	3.16658e9	+	1.82823e9i	0.0765393	+	0.0441900i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.06741e10	+	2.02486e10i	−0.482372	+	0.472443i
$456$		0			0
$457$	9.30524e9	+	1.61172e10i	0.213335	+	0.369508i	0.952756	−	0.303736i	$-0.0982340\pi$
$457$	9.30524e9	+	1.61172e10i	0.213335	+	0.369508i	−0.739421	+	0.673243i	$0.764901\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			9.20893e9i			0.203895i	0.994790	+	0.101947i	$0.0325073\pi$
$461$			9.20893e9i			0.203895i	−0.994790	+	0.101947i	$0.967493\pi$
$462$		0			0
$463$	−1.42010e10			−0.309025			−0.154513	−	0.987991i	$-0.549381\pi$
$463$	−1.42010e10			−0.309025			−0.154513	+	0.987991i	$0.549381\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.95507e10	−	1.70611e10i	0.621299	−	0.358707i	−0.156076	−	0.987745i	$-0.549884\pi$
$467$	2.95507e10	−	1.70611e10i	0.621299	−	0.358707i	0.777374	+	0.629038i	$0.216551\pi$
$468$		0			0
$469$	2.66353e10	+	7.43460e9i	0.550511	+	0.153662i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.19990e9	−	2.07829e9i	0.0239718	−	0.0415204i
$474$		0			0
$475$			6.88216e9i			0.135192i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.59507e9	−	4.38502e9i	−0.144275	−	0.0832970i	0.426125	−	0.904664i	$-0.359878\pi$
$479$	−7.59507e9	−	4.38502e9i	−0.144275	−	0.0832970i	−0.570400	+	0.821367i	$0.693212\pi$
$480$		0			0
$481$	−6.06607e10	+	3.50225e10i	−1.13325	+	0.654284i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.51551e10	−	2.62494e10i	−0.273900	−	0.474408i
$486$		0			0
$487$	−6.41038e9	+	1.11031e10i	−0.113964	+	0.197392i	−0.917365	−	0.398047i	$-0.869688\pi$
$487$	−6.41038e9	+	1.11031e10i	−0.113964	+	0.197392i	0.803401	+	0.595438i	$0.203022\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.34320e10			−1.09140			−0.545698	−	0.837982i	$-0.683735\pi$
$491$	−6.34320e10			−1.09140			−0.545698	+	0.837982i	$0.683735\pi$
$492$		0			0
$493$	−9.33065e9	−	5.38705e9i	−0.157952	−	0.0911934i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.85958e10	+	7.24040e10i	0.304783	+	1.18669i
$498$		0			0
$499$	−3.36380e10	−	5.82628e10i	−0.542536	−	0.939700i	−0.998758	−	0.0498336i	$-0.984131\pi$
$499$	−3.36380e10	−	5.82628e10i	−0.542536	−	0.939700i	0.456222	−	0.889866i	$-0.349202\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			1.04697e11i			1.63554i	0.575542	+	0.817772i	$0.304791\pi$
$503$			1.04697e11i			1.63554i	−0.575542	+	0.817772i	$0.695209\pi$
$504$		0			0
$505$	−2.77188e10			−0.426196
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.94469e10	−	2.85482e10i	0.736662	−	0.425312i	−0.0841923	−	0.996450i	$-0.526831\pi$
$509$	4.94469e10	−	2.85482e10i	0.736662	−	0.425312i	0.820854	+	0.571137i	$0.193498\pi$
$510$		0			0
$511$	8.08251e9	−	2.89565e10i	0.118539	−	0.424680i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.66637e10	−	4.61830e10i	0.379046	−	0.656527i
$516$		0			0
$517$			1.25505e11i			1.75671i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.48609e10	−	4.32210e10i	−1.01602	−	0.586602i	−0.103074	−	0.994674i	$-0.532868\pi$
$521$	−7.48609e10	−	4.32210e10i	−1.01602	−	0.586602i	−0.912950	+	0.408072i	$0.866201\pi$
$522$		0			0
$523$	1.27623e10	−	7.36833e9i	0.170578	−	0.0984832i	−0.412280	−	0.911057i	$-0.635268\pi$
$523$	1.27623e10	−	7.36833e9i	0.170578	−	0.0984832i	0.582858	+	0.812574i	$0.301934\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.09415e11	−	1.89512e11i	−1.41852	−	2.45694i
$528$		0			0
$529$	−7.17338e9	+	1.24247e10i	−0.0916012	+	0.158658i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8.72077e9			0.108055
$534$		0			0
$535$	−4.00892e10	−	2.31455e10i	−0.489342	−	0.282522i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.33136e9	−	1.12084e11i	0.0276220	−	1.32797i
$540$		0			0
$541$	−5.99660e10	−	1.03864e11i	−0.700029	−	1.21249i	−0.968456	−	0.249185i	$-0.919837\pi$
$541$	−5.99660e10	−	1.03864e11i	−0.700029	−	1.21249i	0.268427	−	0.963300i	$-0.413496\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			2.84890e10i			0.322917i
$546$		0			0
$547$	−7.72241e10			−0.862588			−0.431294	−	0.902211i	$-0.641943\pi$
$547$	−7.72241e10			−0.862588			−0.431294	+	0.902211i	$0.641943\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.62551e9	+	9.38491e8i	−0.0176354	+	0.0101818i
$552$		0			0
$553$	−7.31491e10	+	7.16434e10i	−0.782183	+	0.766083i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.89933e10	+	1.54141e11i	−0.924564	+	1.60139i	−0.132302	+	0.991209i	$0.542237\pi$
$557$	−8.89933e10	+	1.54141e11i	−0.924564	+	1.60139i	−0.792262	+	0.610182i	$0.791096\pi$
$558$		0			0
$559$		−	5.72362e9i		−	0.0586170i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.36022e11	+	7.85323e10i	1.35386	+	0.781654i	0.988788	−	0.149323i	$-0.0477096\pi$
$563$	1.36022e11	+	7.85323e10i	1.35386	+	0.781654i	0.365076	+	0.930978i	$0.381043\pi$
$564$		0			0
$565$	−6.17950e10	+	3.56774e10i	−0.606400	+	0.350105i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.78668e8	+	4.82667e8i	0.00265851	+	0.00460467i	0.867352	−	0.497696i	$-0.165820\pi$
$569$	2.78668e8	+	4.82667e8i	0.00265851	+	0.00460467i	−0.864693	+	0.502301i	$0.832487\pi$
$570$		0			0
$571$	1.85718e10	−	3.21672e10i	0.174706	−	0.302600i	−0.765353	−	0.643610i	$-0.777436\pi$
$571$	1.85718e10	−	3.21672e10i	0.174706	−	0.302600i	0.940060	+	0.341010i	$0.110769\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.83506e10			0.899716
$576$		0			0
$577$	3.46036e10	+	1.99784e10i	0.312189	+	0.180243i	0.647906	−	0.761721i	$-0.275645\pi$
$577$	3.46036e10	+	1.99784e10i	0.312189	+	0.180243i	−0.335716	+	0.941963i	$0.608978\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.67434e11	+	4.30027e10i	−1.46939	+	0.377391i
$582$		0			0
$583$	1.33894e11	+	2.31911e11i	1.15901	+	2.00746i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1.12252e11i		−	0.945460i	−0.881207	−	0.472730i	$-0.843269\pi$
$587$		−	1.12252e11i		−	0.945460i	0.881207	−	0.472730i	$-0.156731\pi$
$588$		0			0
$589$	−3.81229e10			−0.316756
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.84487e10	+	2.79719e10i	−0.391799	+	0.226205i	−0.682939	−	0.730475i	$-0.739299\pi$
$593$	−4.84487e10	+	2.79719e10i	−0.391799	+	0.226205i	0.291140	+	0.956680i	$0.405965\pi$
$594$		0			0
$595$	1.89766e10	+	7.38865e10i	0.151409	+	0.589518i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.46361e10	+	2.53505e10i	−0.113689	+	0.196916i	−0.917255	−	0.398300i	$-0.869600\pi$
$599$	−1.46361e10	+	2.53505e10i	−0.113689	+	0.196916i	0.803566	+	0.595216i	$0.202933\pi$
$600$		0			0
$601$			3.04406e10i			0.233322i	0.993172	+	0.116661i	$0.0372191\pi$
$601$			3.04406e10i			0.233322i	−0.993172	+	0.116661i	$0.962781\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.68678e10	−	2.12856e10i	−0.275186	−	0.158879i
$606$		0			0
$607$	1.87228e11	−	1.08096e11i	1.37917	−	0.796262i	0.387107	−	0.922035i	$-0.373474\pi$
$607$	1.87228e11	−	1.08096e11i	1.37917	−	0.796262i	0.992059	+	0.125772i	$0.0401409\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.49667e11	+	2.59232e11i	1.07390	+	1.86004i
$612$		0			0
$613$	3.15010e10	−	5.45613e10i	0.223091	−	0.386405i	−0.732654	−	0.680601i	$-0.761719\pi$
$613$	3.15010e10	−	5.45613e10i	0.223091	−	0.386405i	0.955745	+	0.294196i	$0.0950519\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.31396e11			−1.59667			−0.798336	−	0.602213i	$-0.794286\pi$
$617$	−2.31396e11			−1.59667			−0.798336	+	0.602213i	$0.794286\pi$
$618$		0			0
$619$	−8.62110e10	−	4.97739e10i	−0.587219	−	0.339031i	0.176778	−	0.984251i	$-0.443432\pi$
$619$	−8.62110e10	−	4.97739e10i	−0.587219	−	0.339031i	−0.763997	+	0.645220i	$0.776766\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.49068e10	−	8.66913e10i	−0.563625	−	0.575471i
$624$		0			0
$625$	−3.90080e10	−	6.75639e10i	−0.255643	−	0.442787i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.84646e11i			1.17961i
$630$		0			0
$631$	−3.88355e10			−0.244969			−0.122485	−	0.992470i	$-0.539086\pi$
$631$	−3.88355e10			−0.244969			−0.122485	+	0.992470i	$0.539086\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.94780e9	+	5.16602e9i	−0.0550328	+	0.0317732i
$636$		0			0
$637$	−1.28846e11	−	2.34289e11i	−0.782554	−	1.42297i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.01203e11	−	1.75289e11i	0.599462	−	1.03830i	−0.393439	−	0.919351i	$-0.628715\pi$
$641$	1.01203e11	−	1.75289e11i	0.599462	−	1.03830i	0.992901	−	0.118948i	$-0.0379521\pi$
$642$		0			0
$643$		−	1.46591e11i		−	0.857558i	−0.903409	−	0.428779i	$-0.858944\pi$
$643$		−	1.46591e11i		−	0.857558i	0.903409	−	0.428779i	$-0.141056\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.40431e11	−	1.38813e11i	−1.37206	−	0.792158i	−0.380871	−	0.924628i	$-0.624376\pi$
$647$	−2.40431e11	−	1.38813e11i	−1.37206	−	0.792158i	−0.991187	+	0.132470i	$0.957709\pi$
$648$		0			0
$649$	1.95062e11	−	1.12619e11i	1.09950	−	0.634795i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.35533e11	+	2.34750e11i	0.745406	+	1.29108i	0.950005	+	0.312236i	$0.101078\pi$
$653$	1.35533e11	+	2.34750e11i	0.745406	+	1.29108i	−0.204598	+	0.978846i	$0.565589\pi$
$654$		0			0
$655$	−4.97805e9	+	8.62224e9i	−0.0270455	+	0.0468441i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.76828e10			−0.464914			−0.232457	−	0.972607i	$-0.574676\pi$
$659$	−8.76828e10			−0.464914			−0.232457	+	0.972607i	$0.574676\pi$
$660$		0			0
$661$	−3.77894e10	−	2.18177e10i	−0.197954	−	0.114289i	0.397747	−	0.917495i	$-0.369792\pi$
$661$	−3.77894e10	−	2.18177e10i	−0.197954	−	0.114289i	−0.595701	+	0.803206i	$0.703126\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.28004e10	+	3.57292e9i	0.0654541	+	0.0182699i
$666$		0			0
$667$	1.34117e10	+	2.32297e10i	0.0677609	+	0.117365i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	4.32633e11i		−	2.13417i
$672$		0			0
$673$	1.88626e11			0.919480			0.459740	−	0.888054i	$-0.347943\pi$
$673$	1.88626e11			0.919480			0.459740	+	0.888054i	$0.347943\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.41068e10	+	1.96916e10i	−0.162363	+	0.0937401i	−0.578980	−	0.815342i	$-0.696549\pi$
$677$	−3.41068e10	+	1.96916e10i	−0.162363	+	0.0937401i	0.416617	+	0.909082i	$0.363216\pi$
$678$		0			0
$679$	2.71253e11	−	6.96673e10i	1.27613	−	0.327755i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.05360e11	−	1.82490e11i	0.484167	−	0.838601i	−0.515668	−	0.856788i	$-0.672456\pi$
$683$	1.05360e11	−	1.82490e11i	0.484167	−	0.838601i	0.999835	+	0.0181874i	$0.00578954\pi$
$684$		0			0
$685$			1.07590e11i			0.488663i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.53116e11	+	3.19342e11i	2.45437	+	1.41703i
$690$		0			0
$691$	−3.03078e10	+	1.74982e10i	−0.132936	+	0.0767505i	−0.564993	−	0.825096i	$-0.691121\pi$
$691$	−3.03078e10	+	1.74982e10i	−0.132936	+	0.0767505i	0.432057	+	0.901846i	$0.357788\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.80186e10	+	4.85296e10i	0.120090	+	0.208002i
$696$		0			0
$697$	1.14944e10	−	1.99090e10i	0.0487031	−	0.0843563i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.58032e10			−0.355330			−0.177665	−	0.984091i	$-0.556854\pi$
$701$	−8.58032e10			−0.355330			−0.177665	+	0.984091i	$0.556854\pi$
$702$		0			0
$703$	2.78580e10	+	1.60838e10i	0.114059	+	0.0658517i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.88559e10	−	2.46684e11i	0.275590	−	0.987333i
$708$		0			0
$709$	9.74057e10	+	1.68712e11i	0.385478	+	0.667668i	0.991835	−	0.127525i	$-0.0407032\pi$
$709$	9.74057e10	+	1.68712e11i	0.385478	+	0.667668i	−0.606357	+	0.795192i	$0.707370\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			5.44801e11i			2.10804i
$714$		0			0
$715$	−2.34387e11			−0.896827
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.89871e11	−	1.67357e11i	1.08465	−	0.626222i	0.152502	−	0.988303i	$-0.451267\pi$
$719$	2.89871e11	−	1.67357e11i	1.08465	−	0.626222i	0.932147	+	0.362081i	$0.117934\pi$
$720$		0			0
$721$	3.44771e11	+	3.52017e11i	1.27582	+	1.30263i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.42357e10	−	2.46569e10i	0.0515259	−	0.0892455i
$726$		0			0
$727$			9.86180e10i			0.353035i	0.984297	+	0.176518i	$0.0564833\pi$
$727$			9.86180e10i			0.353035i	−0.984297	+	0.176518i	$0.943517\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.30667e10	−	7.54404e9i	−0.0457609	−	0.0264201i
$732$		0			0
$733$	2.61192e11	−	1.50799e11i	0.904782	−	0.522376i	0.0260337	−	0.999661i	$-0.491712\pi$
$733$	2.61192e11	−	1.50799e11i	0.904782	−	0.522376i	0.878749	+	0.477285i	$0.158379\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.11990e11	+	1.93972e11i	0.379585	+	0.657460i
$738$		0			0
$739$	−1.82846e11	+	3.16698e11i	−0.613065	+	1.06186i	0.377655	+	0.925946i	$0.376730\pi$
$739$	−1.82846e11	+	3.16698e11i	−0.613065	+	1.06186i	−0.990721	+	0.135914i	$0.956603\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.52082e11			1.15528			0.577642	−	0.816290i	$-0.303973\pi$
$743$	3.52082e11			1.15528			0.577642	+	0.816290i	$0.303973\pi$
$744$		0			0
$745$	1.16873e11	+	6.74766e10i	0.379392	+	0.219042i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.05569e11	−	2.99279e11i	0.970917	−	0.950932i
$750$		0			0
$751$	−1.44039e11	−	2.49484e11i	−0.452816	−	0.784300i	0.545744	−	0.837952i	$-0.316247\pi$
$751$	−1.44039e11	−	2.49484e11i	−0.452816	−	0.784300i	−0.998560	+	0.0536517i	$0.982914\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			8.58209e10i			0.264122i
$756$		0			0
$757$	−5.34615e11			−1.62801			−0.814006	−	0.580857i	$-0.802718\pi$
$757$	−5.34615e11			−1.62801			−0.814006	+	0.580857i	$0.802718\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.20516e10	+	1.27315e10i	−0.0657507	+	0.0379612i	−0.532515	−	0.846421i	$-0.678753\pi$
$761$	−2.20516e10	+	1.27315e10i	−0.0657507	+	0.0379612i	0.466764	+	0.884382i	$0.345420\pi$
$762$		0			0
$763$	−2.53539e11	−	7.07692e10i	−0.748076	−	0.208807i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.68601e11	−	4.65230e11i	0.776114	−	1.34427i
$768$		0			0
$769$			1.61134e11i			0.460768i	0.973100	+	0.230384i	$0.0739982\pi$
$769$			1.61134e11i			0.460768i	−0.973100	+	0.230384i	$0.926002\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.00134e11	+	1.15547e11i	0.560535	+	0.323625i	0.753360	−	0.657608i	$-0.228432\pi$
$773$	2.00134e11	+	1.15547e11i	0.560535	+	0.323625i	−0.192825	+	0.981233i	$0.561765\pi$
$774$		0			0
$775$	5.00799e11	−	2.89136e11i	1.38821	−	0.801486i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.00247e9	−	3.46839e9i	−0.00543772	−	0.00941841i
$780$		0			0
$781$	−3.02736e11	+	5.24353e11i	−0.813691	+	1.40935i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.76875e10			−0.204585
$786$		0			0
$787$	8.19226e9	+	4.72980e9i	0.0213553	+	0.0123295i	0.510640	−	0.859795i	$-0.329409\pi$
$787$	8.19226e9	+	4.72980e9i	0.0213553	+	0.0123295i	−0.489284	+	0.872124i	$0.662742\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.64007e11	−	6.38571e11i	−0.418945	−	1.63119i
$792$		0			0
$793$	−5.15923e11	−	8.93604e11i	−1.30464	−	2.25971i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	1.06562e11i		−	0.264100i	−0.991243	−	0.132050i	$-0.957844\pi$
$797$		−	1.06562e11i		−	0.264100i	0.991243	−	0.132050i	$-0.0421559\pi$
$798$		0			0
$799$	7.89079e11			1.93612
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.10876e11	−	1.21750e11i	0.507184	−	0.292823i
$804$		0			0
$805$	5.10594e10	−	1.82926e11i	0.121588	−	0.435604i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.71049e11	−	2.96266e11i	0.399326	−	0.691652i	−0.594317	−	0.804231i	$-0.702578\pi$
$809$	1.71049e11	−	2.96266e11i	0.399326	−	0.691652i	0.993643	+	0.112578i	$0.0359110\pi$
$810$		0			0
$811$			2.89997e11i			0.670362i	0.942154	+	0.335181i	$0.108797\pi$
$811$			2.89997e11i			0.670362i	−0.942154	+	0.335181i	$0.891203\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.31489e11	+	7.59150e10i	0.298029	+	0.172067i
$816$		0			0
$817$	−2.27637e9	+	1.31426e9i	−0.00510923	+	0.00294981i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.60897e11	+	6.25091e11i	0.794347	+	1.37585i	0.923253	+	0.384193i	$0.125520\pi$
$821$	3.60897e11	+	6.25091e11i	0.794347	+	1.37585i	−0.128906	+	0.991657i	$0.541147\pi$
$822$		0			0
$823$	−7.88089e10	+	1.36501e11i	−0.171781	+	0.297534i	−0.939043	−	0.343801i	$-0.888286\pi$
$823$	−7.88089e10	+	1.36501e11i	−0.171781	+	0.297534i	0.767261	+	0.641335i	$0.221619\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.81570e11			1.45710			0.728549	−	0.684994i	$-0.240195\pi$
$827$	6.81570e11			1.45710			0.728549	+	0.684994i	$0.240195\pi$
$828$		0			0
$829$	4.06194e11	+	2.34516e11i	0.860034	+	0.496541i	0.864024	−	0.503451i	$-0.167937\pi$
$829$	4.06194e11	+	2.34516e11i	0.860034	+	0.496541i	−0.00398941	+	0.999992i	$0.501270\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.04693e11	−	1.46578e10i	−1.46359	−	0.0304430i
$834$		0			0
$835$	−9.70120e10	−	1.68030e11i	−0.199563	−	0.345653i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			9.20167e11i			1.85703i	0.371294	+	0.928515i	$0.378914\pi$
$839$			9.20167e11i			1.85703i	−0.371294	+	0.928515i	$0.621086\pi$
$840$		0			0
$841$	−4.92481e11			−0.984478
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.00552e11	+	1.73524e11i	−0.589512	+	0.340355i
$846$		0			0
$847$	2.81015e11	−	2.75230e11i	0.546004	−	0.534765i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.29848e11	−	3.98108e11i	0.438251	−	0.759072i
$852$		0			0
$853$			5.25940e11i			0.993437i	0.867912	+	0.496718i	$0.165462\pi$
$853$			5.25940e11i			0.993437i	−0.867912	+	0.496718i	$0.834538\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.85568e10	−	3.38078e10i	−0.108556	−	0.0626748i	0.444739	−	0.895660i	$-0.353296\pi$
$857$	−5.85568e10	−	3.38078e10i	−0.108556	−	0.0626748i	−0.553295	+	0.832985i	$0.686630\pi$
$858$		0			0
$859$	−2.39418e11	+	1.38228e11i	−0.439728	+	0.253877i	−0.703482	−	0.710713i	$-0.748373\pi$
$859$	−2.39418e11	+	1.38228e11i	−0.439728	+	0.253877i	0.263754	+	0.964590i	$0.415039\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.25121e11	−	3.89921e11i	−0.405857	−	0.702964i	0.588564	−	0.808450i	$-0.299693\pi$
$863$	−2.25121e11	−	3.89921e11i	−0.405857	−	0.702964i	−0.994421	+	0.105486i	$0.966360\pi$
$864$		0			0
$865$	−1.36256e11	+	2.36003e11i	−0.243384	+	0.421554i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.29305e11			−1.45424
$870$		0			0
$871$	4.62631e11	+	2.67100e11i	0.803825	+	0.464089i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.31306e11	+	1.10774e11i	−0.735789	+	0.188976i
$876$		0			0
$877$	−9.03817e10	−	1.56546e11i	−0.152786	−	0.264632i	0.779465	−	0.626446i	$-0.215491\pi$
$877$	−9.03817e10	−	1.56546e11i	−0.152786	−	0.264632i	−0.932250	+	0.361814i	$0.882158\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.07020e11i		−	0.343644i	−0.985128	−	0.171822i	$-0.945035\pi$
$881$		−	2.07020e11i		−	0.343644i	0.985128	−	0.171822i	$-0.0549655\pi$
$882$		0			0
$883$	−1.01138e11			−0.166369			−0.0831845	−	0.996534i	$-0.526509\pi$
$883$	−1.01138e11			−0.166369			−0.0831845	+	0.996534i	$0.526509\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.35333e11	−	7.81346e10i	0.218630	−	0.126226i	−0.386686	−	0.922212i	$-0.626380\pi$
$887$	1.35333e11	−	7.81346e10i	0.218630	−	0.126226i	0.605316	+	0.795985i	$0.293047\pi$
$888$		0			0
$889$	−2.37479e10	−	9.24640e10i	−0.0380206	−	0.148035i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.87336e10	−	1.19050e11i	0.108084	−	0.187208i
$894$		0			0
$895$		−	6.45676e10i		−	0.100629i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.36584e11	+	7.88566e10i	0.209103	+	0.120726i
$900$		0			0
$901$	1.45807e12	−	8.41819e11i	2.21248	−	1.27738i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.39192e10	−	1.10711e11i	−0.0952877	−	0.165043i
$906$		0			0
$907$	6.32401e11	−	1.09535e12i	0.934466	−	1.61854i	0.158882	−	0.987298i	$-0.449211\pi$
$907$	6.32401e11	−	1.09535e12i	0.934466	−	1.61854i	0.775584	−	0.631245i	$-0.217456\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.10755e12			−1.60801			−0.804005	−	0.594623i	$-0.797301\pi$
$911$	−1.10755e12			−1.60801			−0.804005	+	0.594623i	$0.797301\pi$
$912$		0			0
$913$	−1.21256e12	−	7.00074e11i	−1.74510	−	1.00754i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.43679e10	−	6.57207e10i	−0.0910316	−	0.0929447i
$918$		0			0
$919$	3.08017e10	+	5.33501e10i	0.0431830	+	0.0747951i	0.886809	−	0.462136i	$-0.152917\pi$
$919$	3.08017e10	+	5.33501e10i	0.0431830	+	0.0747951i	−0.843626	+	0.536931i	$0.819583\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			1.44407e12i			1.98967i
$924$		0			0
$925$	−4.87940e11			−0.666498
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.05667e11	+	1.76477e11i	−0.410379	+	0.236933i	−0.690953	−	0.722900i	$-0.742809\pi$
$929$	−3.05667e11	+	1.76477e11i	−0.410379	+	0.236933i	0.280573	+	0.959833i	$0.409475\pi$
$930$		0			0
$931$	−6.35946e10	+	1.05042e11i	−0.0846489	+	0.139818i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.08934e11	+	5.35090e11i	−0.404222	+	0.700132i
$936$		0			0
$937$			1.00546e12i			1.30439i	0.758051	+	0.652195i	$0.226152\pi$
$937$			1.00546e12i			1.30439i	−0.758051	+	0.652195i	$0.773848\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.52508e11	+	8.80503e10i	0.194506	+	0.112298i	0.594090	−	0.804398i	$-0.297512\pi$
$941$	1.52508e11	+	8.80503e10i	0.194506	+	0.112298i	−0.399584	+	0.916696i	$0.630846\pi$
$942$		0			0
$943$	−4.95655e10	+	2.86167e10i	−0.0626806	+	0.0361886i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.75622e11	+	4.77392e11i	0.342700	+	0.593574i	0.984933	−	0.172935i	$-0.0553251\pi$
$947$	2.75622e11	+	4.77392e11i	0.342700	+	0.593574i	−0.642233	+	0.766510i	$0.721992\pi$
$948$		0			0
$949$	2.90377e11	−	5.02947e11i	0.358012	−	0.620094i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.34459e11			−1.01166			−0.505829	−	0.862634i	$-0.668813\pi$
$953$	−8.34459e11			−1.01166			−0.505829	+	0.862634i	$0.668813\pi$
$954$		0			0
$955$	−4.29232e11	−	2.47817e11i	−0.516035	−	0.297933i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.57499e11	−	2.67263e11i	−1.13205	−	0.315983i
$960$		0			0
$961$	1.17519e12	+	2.03549e12i	1.37789	+	2.38657i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			2.44418e11i			0.281853i
$966$		0			0
$967$	−7.68610e11			−0.879022			−0.439511	−	0.898237i	$-0.644848\pi$
$967$	−7.68610e11			−0.879022			−0.439511	+	0.898237i	$0.644848\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.08759e11	+	2.35997e11i	−0.459823	+	0.265479i	−0.711970	−	0.702210i	$-0.752197\pi$
$971$	−4.08759e11	+	2.35997e11i	−0.459823	+	0.265479i	0.252147	+	0.967689i	$0.418863\pi$
$972$		0			0
$973$	−5.01491e11	+	1.28800e11i	−0.559515	+	0.143703i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.48912e11	+	1.29715e12i	−0.821964	+	1.42368i	0.0822542	+	0.996611i	$0.473788\pi$
$977$	−7.48912e11	+	1.29715e12i	−0.821964	+	1.42368i	−0.904218	+	0.427071i	$0.859545\pi$
$978$		0			0
$979$		−	9.82835e11i		−	1.06992i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.25935e11	−	3.03649e11i	−0.563272	−	0.325205i	0.191186	−	0.981554i	$-0.438767\pi$
$983$	−5.25935e11	−	3.03649e11i	−0.563272	−	0.325205i	−0.754458	+	0.656349i	$0.772100\pi$
$984$		0			0
$985$	−2.76369e11	+	1.59562e11i	−0.293592	+	0.169505i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.87817e10	+	3.25309e10i	0.0196313	+	0.0340025i
$990$		0			0
$991$	−4.64617e11	+	8.04740e11i	−0.481726	+	0.834374i	−0.999780	−	0.0209739i	$-0.993323\pi$
$991$	−4.64617e11	+	8.04740e11i	−0.481726	+	0.834374i	0.518054	+	0.855348i	$0.326657\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.99725e10			0.0305796
$996$		0			0
$997$	1.58181e12	+	9.13259e11i	1.60094	+	0.924300i	0.991301	+	0.131618i	$0.0420172\pi$
$997$	1.58181e12	+	9.13259e11i	1.60094	+	0.924300i	0.609635	+	0.792682i	$0.291316\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.73.5		12
3.2	odd	2		84.9.m.b.73.2	yes	12
7.5	odd	6	inner	252.9.z.d.145.5		12
21.5	even	6		84.9.m.b.61.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.2	✓	12	21.5	even	6
84.9.m.b.73.2	yes	12	3.2	odd	2
252.9.z.d.73.5		12	1.1	even	1	trivial
252.9.z.d.145.5		12	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(225.043 - 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +O(q^{10})\)	\(q+(225.043 - 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(-9723.49 + 16841.6i) q^{11} +46381.7i q^{13} +(105886. + 61133.6i) q^{17} +(18446.7 - 10650.2i) q^{19} +(-152199. - 263616. i) q^{23} +(-161550. + 279812. i) q^{25} -88119.4 q^{29} +(-1.54998e6 - 894884. i) q^{31} +(436564. + 445739. i) q^{35} +(755092. + 1.30786e6i) q^{37} -188022. i q^{41} -123402. q^{43} +(5.58909e6 - 3.22686e6i) q^{47} +(-5.05133e6 + 2.77796e6i) q^{49} +(6.88508e6 - 1.19253e7i) q^{53} +5.05343e6i q^{55} +(-1.00305e7 - 5.79109e6i) q^{59} +(-1.92663e7 + 1.11234e7i) q^{61} +(6.02630e6 + 1.04379e7i) q^{65} +(5.75873e6 - 9.97442e6i) q^{67} +3.11345e7 q^{71} +(-1.08437e7 - 6.26059e6i) q^{73} +(-4.49731e7 - 1.25532e7i) q^{77} +(2.13222e7 + 3.69312e7i) q^{79} +7.19982e7i q^{83} +3.17720e7 q^{85} +(-4.37683e7 + 2.52696e7i) q^{89} +(-1.07862e8 + 2.77026e7i) q^{91} +(2.76753e6 - 4.79351e6i) q^{95} -1.16642e8i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more