LMFDB - Embedded newform 60.7.k.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(13,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("60.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.k (of order $4$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} + 66x^{10} + 1601x^{8} + 17520x^{6} + 84208x^{4} + 136704x^{2} + 14400 $ x^12 + 66x^10 + 1601x^8 + 17520x^6 + 84208x^4 + 136704*x^2 + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{10}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.2
Root			$3.51909i$ of defining polynomial
Character	$\chi$	$=$	60.37
Dual form			60.7.k.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 + 11.0227i) q^{3} +(-23.5531 - 122.761i) q^{5} +(312.733 + 312.733i) q^{7} -243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 + 11.0227i) q^{3} +(-23.5531 - 122.761i) q^{5} +(312.733 + 312.733i) q^{7} -243.000i q^{9} -524.296 q^{11} +(-2815.91 + 2815.91i) q^{13} +(1612.78 + 1093.54i) q^{15} +(-6552.59 - 6552.59i) q^{17} -7554.63i q^{19} -6894.32 q^{21} +(-8761.99 + 8761.99i) q^{23} +(-14515.5 + 5782.80i) q^{25} +(2678.52 + 2678.52i) q^{27} +23363.5i q^{29} -48026.9 q^{31} +(5779.16 - 5779.16i) q^{33} +(31025.5 - 45757.2i) q^{35} +(34199.0 + 34199.0i) q^{37} -62078.0i q^{39} -30870.8 q^{41} +(-21790.4 + 21790.4i) q^{43} +(-29830.9 + 5723.40i) q^{45} +(37819.6 + 37819.6i) q^{47} +77954.4i q^{49} +144454. q^{51} +(179394. - 179394. i) q^{53} +(12348.8 + 64363.1i) q^{55} +(83272.4 + 83272.4i) q^{57} -200563. i q^{59} -19690.2 q^{61} +(75994.0 - 75994.0i) q^{63} +(412008. + 279361. i) q^{65} +(94194.5 + 94194.5i) q^{67} -193162. i q^{69} -281712. q^{71} +(-454330. + 454330. i) q^{73} +(96258.1 - 223742. i) q^{75} +(-163965. - 163965. i) q^{77} -134576. i q^{79} -59049.0 q^{81} +(535168. - 535168. i) q^{83} +(-650068. + 958736. i) q^{85} +(-257529. - 257529. i) q^{87} +78207.3i q^{89} -1.76126e6 q^{91} +(529386. - 529386. i) q^{93} +(-927413. + 177935. i) q^{95} +(-94504.5 - 94504.5i) q^{97} +127404. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) $ 12 * q + 312 * q^5 + 120 * q^7	$ 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) $ 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$		0			0
$5$	−23.5531	−	122.761i	−0.188425	−	0.982088i
$5$	−23.5531	−	122.761i	−0.188425	−	0.982088i
$6$		0			0
$7$	312.733	+	312.733i	0.911757	+	0.911757i	0.996410	−	0.0846534i	$-0.0269783\pi$
$7$	312.733	+	312.733i	0.911757	+	0.911757i	−0.0846534	+	0.996410i	$0.526978\pi$
$8$		0			0
$9$		−	243.000i		−	0.333333i
$10$		0			0
$11$	−524.296			−0.393911			−0.196956	−	0.980412i	$-0.563106\pi$
$11$	−524.296			−0.393911			−0.196956	+	0.980412i	$0.563106\pi$
$12$		0			0
$13$	−2815.91	+	2815.91i	−1.28171	+	1.28171i	−0.342014	+	0.939695i	$0.611109\pi$
$13$	−2815.91	+	2815.91i	−1.28171	+	1.28171i	−0.939695	+	0.342014i	$0.888891\pi$
$14$		0			0
$15$	1612.78	+	1093.54i	0.477860	+	0.324012i
$16$		0			0
$17$	−6552.59	−	6552.59i	−1.33372	−	1.33372i	−0.902011	−	0.431714i	$-0.857909\pi$
$17$	−6552.59	−	6552.59i	−1.33372	−	1.33372i	−0.431714	−	0.902011i	$-0.642091\pi$
$18$		0			0
$19$		−	7554.63i		−	1.10142i	−0.834697	−	0.550709i	$-0.814357\pi$
$19$		−	7554.63i		−	1.10142i	0.834697	−	0.550709i	$-0.185643\pi$
$20$		0			0
$21$	−6894.32			−0.744447
$22$		0			0
$23$	−8761.99	+	8761.99i	−0.720143	+	0.720143i	−0.968634	−	0.248491i	$-0.920065\pi$
$23$	−8761.99	+	8761.99i	−0.720143	+	0.720143i	0.248491	+	0.968634i	$0.420065\pi$
$24$		0			0
$25$	−14515.5	+	5782.80i	−0.928992	+	0.370099i
$26$		0			0
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$		0			0
$29$			23363.5i			0.957952i	0.877828	+	0.478976i	$0.158992\pi$
$29$			23363.5i			0.957952i	−0.877828	+	0.478976i	$0.841008\pi$
$30$		0			0
$31$	−48026.9			−1.61213			−0.806064	−	0.591828i	$-0.798406\pi$
$31$	−48026.9			−1.61213			−0.806064	+	0.591828i	$0.798406\pi$
$32$		0			0
$33$	5779.16	−	5779.16i	0.160814	−	0.160814i
$34$		0			0
$35$	31025.5	−	45757.2i	0.723628	−	1.06722i
$36$		0			0
$37$	34199.0	+	34199.0i	0.675163	+	0.675163i	0.958902	−	0.283739i	$-0.0915749\pi$
$37$	34199.0	+	34199.0i	0.675163	+	0.675163i	−0.283739	+	0.958902i	$0.591575\pi$
$38$		0			0
$39$		−	62078.0i		−	1.04651i
$40$		0			0
$41$	−30870.8			−0.447916			−0.223958	−	0.974599i	$-0.571898\pi$
$41$	−30870.8			−0.447916			−0.223958	+	0.974599i	$0.571898\pi$
$42$		0			0
$43$	−21790.4	+	21790.4i	−0.274068	+	0.274068i	−0.830736	−	0.556667i	$-0.812080\pi$
$43$	−21790.4	+	21790.4i	−0.274068	+	0.274068i	0.556667	+	0.830736i	$0.312080\pi$
$44$		0			0
$45$	−29830.9	+	5723.40i	−0.327363	+	0.0628082i
$46$		0			0
$47$	37819.6	+	37819.6i	0.364270	+	0.364270i	0.865382	−	0.501113i	$-0.167076\pi$
$47$	37819.6	+	37819.6i	0.364270	+	0.364270i	−0.501113	+	0.865382i	$0.667076\pi$
$48$		0			0
$49$			77954.4i			0.662602i
$50$		0			0
$51$	144454.			1.08898
$52$		0			0
$53$	179394.	−	179394.i	1.20498	−	1.20498i	0.232349	−	0.972632i	$-0.425359\pi$
$53$	179394.	−	179394.i	1.20498	−	1.20498i	0.972632	−	0.232349i	$-0.0746412\pi$
$54$		0			0
$55$	12348.8	+	64363.1i	0.0742226	+	0.386856i
$56$		0			0
$57$	83272.4	+	83272.4i	0.449652	+	0.449652i
$58$		0			0
$59$		−	200563.i		−	0.976552i	−0.872689	−	0.488276i	$-0.837626\pi$
$59$		−	200563.i		−	0.976552i	0.872689	−	0.488276i	$-0.162374\pi$
$60$		0			0
$61$	−19690.2			−0.0867481			−0.0433741	−	0.999059i	$-0.513811\pi$
$61$	−19690.2			−0.0867481			−0.0433741	+	0.999059i	$0.513811\pi$
$62$		0			0
$63$	75994.0	−	75994.0i	0.303919	−	0.303919i
$64$		0			0
$65$	412008.	+	279361.i	1.50026	+	1.01724i
$66$		0			0
$67$	94194.5	+	94194.5i	0.313185	+	0.313185i	0.846142	−	0.532957i	$-0.178919\pi$
$67$	94194.5	+	94194.5i	0.313185	+	0.313185i	−0.532957	+	0.846142i	$0.678919\pi$
$68$		0			0
$69$		−	193162.i		−	0.587995i
$70$		0			0
$71$	−281712.			−0.787100			−0.393550	−	0.919303i	$-0.628753\pi$
$71$	−281712.			−0.787100			−0.393550	+	0.919303i	$0.628753\pi$
$72$		0			0
$73$	−454330.	+	454330.i	−1.16789	+	1.16789i	−0.185189	+	0.982703i	$0.559290\pi$
$73$	−454330.	+	454330.i	−1.16789	+	1.16789i	−0.982703	+	0.185189i	$0.940710\pi$
$74$		0			0
$75$	96258.1	−	223742.i	0.228167	−	0.530352i
$76$		0			0
$77$	−163965.	−	163965.i	−0.359152	−	0.359152i
$78$		0			0
$79$		−	134576.i		−	0.272951i	−0.990643	−	0.136476i	$-0.956422\pi$
$79$		−	134576.i		−	0.272951i	0.990643	−	0.136476i	$-0.0435776\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	535168.	−	535168.i	0.935957	−	0.935957i	−0.0621126	−	0.998069i	$-0.519784\pi$
$83$	535168.	−	535168.i	0.935957	−	0.935957i	0.998069	+	0.0621126i	$0.0197838\pi$
$84$		0			0
$85$	−650068.	+	958736.i	−1.05853	+	1.56114i
$86$		0			0
$87$	−257529.	−	257529.i	−0.391082	−	0.391082i
$88$		0			0
$89$			78207.3i			0.110937i	0.998460	+	0.0554686i	$0.0176653\pi$
$89$			78207.3i			0.110937i	−0.998460	+	0.0554686i	$0.982335\pi$
$90$		0			0
$91$	−1.76126e6			−2.33721
$92$		0			0
$93$	529386.	−	529386.i	0.658149	−	0.658149i
$94$		0			0
$95$	−927413.	+	177935.i	−1.08169	+	0.207534i
$96$		0			0
$97$	−94504.5	−	94504.5i	−0.103547	−	0.103547i	0.653435	−	0.756982i	$-0.273327\pi$
$97$	−94504.5	−	94504.5i	−0.103547	−	0.103547i	−0.756982	+	0.653435i	$0.773327\pi$
$98$		0			0
$99$			127404.i			0.131304i
$100$		0			0
$101$	−139520.			−0.135417			−0.0677085	−	0.997705i	$-0.521569\pi$
$101$	−139520.			−0.135417			−0.0677085	+	0.997705i	$0.521569\pi$
$102$		0			0
$103$	1.00305e6	−	1.00305e6i	0.917935	−	0.917935i	−0.0789444	−	0.996879i	$-0.525155\pi$
$103$	1.00305e6	−	1.00305e6i	0.917935	−	0.917935i	0.996879	+	0.0789444i	$0.0251550\pi$
$104$		0			0
$105$	162382.	+	846353.i	0.140272	+	0.731112i
$106$		0			0
$107$	444305.	+	444305.i	0.362686	+	0.362686i	0.864801	−	0.502115i	$-0.167445\pi$
$107$	444305.	+	444305.i	0.362686	+	0.362686i	−0.502115	+	0.864801i	$0.667445\pi$
$108$		0			0
$109$			670544.i			0.517783i	0.965906	+	0.258892i	$0.0833572\pi$
$109$			670544.i			0.517783i	−0.965906	+	0.258892i	$0.916643\pi$
$110$		0			0
$111$	−753931.			−0.551268
$112$		0			0
$113$	−912083.	+	912083.i	−0.632119	+	0.632119i	−0.948599	−	0.316480i	$-0.897499\pi$
$113$	−912083.	+	912083.i	−0.632119	+	0.632119i	0.316480	+	0.948599i	$0.397499\pi$
$114$		0			0
$115$	1.28200e6	+	869258.i	0.842937	+	0.571551i
$116$		0			0
$117$	684267.	+	684267.i	0.427236	+	0.427236i
$118$		0			0
$119$		−	4.09842e6i		−	2.43207i
$120$		0			0
$121$	−1.49667e6			−0.844834
$122$		0			0
$123$	340280.	−	340280.i	0.182861	−	0.182861i
$124$		0			0
$125$	1.05179e6	+	1.64573e6i	0.538515	+	0.842616i
$126$		0			0
$127$	600626.	+	600626.i	0.293220	+	0.293220i	0.838351	−	0.545131i	$-0.183520\pi$
$127$	600626.	+	600626.i	0.293220	+	0.293220i	−0.545131	+	0.838351i	$0.683520\pi$
$128$		0			0
$129$		−	480377.i		−	0.223776i
$130$		0			0
$131$	132740.			0.0590455			0.0295227	−	0.999564i	$-0.490601\pi$
$131$	132740.			0.0590455			0.0295227	+	0.999564i	$0.490601\pi$
$132$		0			0
$133$	2.36258e6	−	2.36258e6i	1.00423	−	1.00423i
$134$		0			0
$135$	265730.	−	391905.i	0.108004	−	0.159287i
$136$		0			0
$137$	1.77153e6	+	1.77153e6i	0.688948	+	0.688948i	0.961999	−	0.273051i	$-0.0880329\pi$
$137$	1.77153e6	+	1.77153e6i	0.688948	+	0.688948i	−0.273051	+	0.961999i	$0.588033\pi$
$138$		0			0
$139$		−	1.48696e6i		−	0.553675i	−0.960917	−	0.276837i	$-0.910714\pi$
$139$		−	1.48696e6i		−	0.553675i	0.960917	−	0.276837i	$-0.0892863\pi$
$140$		0			0
$141$	−833748.			−0.297425
$142$		0			0
$143$	1.47637e6	−	1.47637e6i	0.504880	−	0.504880i
$144$		0			0
$145$	2.86813e6	−	550282.i	0.940793	−	0.180502i
$146$		0			0
$147$	−859269.	−	859269.i	−0.270506	−	0.270506i
$148$		0			0
$149$			982054.i			0.296877i	0.988922	+	0.148439i	$0.0474247\pi$
$149$			982054.i			0.296877i	−0.988922	+	0.148439i	$0.952575\pi$
$150$		0			0
$151$	2.61844e6			0.760521			0.380261	−	0.924879i	$-0.375834\pi$
$151$	2.61844e6			0.760521			0.380261	+	0.924879i	$0.375834\pi$
$152$		0			0
$153$	−1.59228e6	+	1.59228e6i	−0.444575	+	0.444575i
$154$		0			0
$155$	1.13118e6	+	5.89583e6i	0.303765	+	1.58325i
$156$		0			0
$157$	2.03939e6	+	2.03939e6i	0.526989	+	0.526989i	0.919673	−	0.392685i	$-0.128454\pi$
$157$	2.03939e6	+	2.03939e6i	0.526989	+	0.526989i	−0.392685	+	0.919673i	$0.628454\pi$
$158$		0			0
$159$			3.95481e6i			0.983863i
$160$		0			0
$161$	−5.48032e6			−1.31319
$162$		0			0
$163$	2.34500e6	−	2.34500e6i	0.541477	−	0.541477i	−0.382485	−	0.923962i	$-0.624932\pi$
$163$	2.34500e6	−	2.34500e6i	0.541477	−	0.541477i	0.923962	+	0.382485i	$0.124932\pi$
$164$		0			0
$165$	−845572.	−	573338.i	−0.188234	−	0.127632i
$166$		0			0
$167$	107293.	+	107293.i	0.0230369	+	0.0230369i	0.718531	−	0.695495i	$-0.244815\pi$
$167$	107293.	+	107293.i	0.0230369	+	0.0230369i	−0.695495	+	0.718531i	$0.744815\pi$
$168$		0			0
$169$		−	1.10319e7i		−	2.28556i
$170$		0			0
$171$	−1.83577e6			−0.367139
$172$		0			0
$173$	−2.16801e6	+	2.16801e6i	−0.418718	+	0.418718i	−0.884762	−	0.466043i	$-0.845679\pi$
$173$	−2.16801e6	+	2.16801e6i	−0.418718	+	0.418718i	0.466043	+	0.884762i	$0.345679\pi$
$174$		0			0
$175$	−6.34794e6	−	2.73100e6i	−1.18446	−	0.509575i
$176$		0			0
$177$	2.21075e6	+	2.21075e6i	0.398676	+	0.398676i
$178$		0			0
$179$		−	22081.4i		−	0.00385006i	−0.999998	−	0.00192503i	$-0.999387\pi$
$179$		−	22081.4i		−	0.00385006i	0.999998	−	0.00192503i	$-0.000612757\pi$
$180$		0			0
$181$	−4.79204e6			−0.808137			−0.404069	−	0.914729i	$-0.632404\pi$
$181$	−4.79204e6			−0.808137			−0.404069	+	0.914729i	$0.632404\pi$
$182$		0			0
$183$	217039.	−	217039.i	0.0354148	−	0.0354148i
$184$		0			0
$185$	3.39281e6	−	5.00380e6i	0.535852	−	0.790286i
$186$		0			0
$187$	3.43550e6	+	3.43550e6i	0.525369	+	0.525369i
$188$		0			0
$189$			1.67532e6i			0.248149i
$190$		0			0
$191$	−1.35557e7			−1.94546			−0.972730	−	0.231942i	$-0.925492\pi$
$191$	−1.35557e7			−1.94546			−0.972730	+	0.231942i	$0.925492\pi$
$192$		0			0
$193$	2.38486e6	−	2.38486e6i	0.331735	−	0.331735i	−0.521510	−	0.853245i	$-0.674631\pi$
$193$	2.38486e6	−	2.38486e6i	0.331735	−	0.331735i	0.853245	+	0.521510i	$0.174631\pi$
$194$		0			0
$195$	−7.62075e6	+	1.46213e6i	−1.02777	+	0.197188i
$196$		0			0
$197$	−9.12238e6	−	9.12238e6i	−1.19319	−	1.19319i	−0.976166	−	0.217024i	$-0.930365\pi$
$197$	−9.12238e6	−	9.12238e6i	−1.19319	−	1.19319i	−0.217024	−	0.976166i	$-0.569635\pi$
$198$		0			0
$199$			1.23227e7i			1.56367i	0.623484	+	0.781836i	$0.285717\pi$
$199$			1.23227e7i			1.56367i	−0.623484	+	0.781836i	$0.714283\pi$
$200$		0			0
$201$	−2.07656e6			−0.255715
$202$		0			0
$203$	−7.30653e6	+	7.30653e6i	−0.873420	+	0.873420i
$204$		0			0
$205$	727102.	+	3.78973e6i	0.0843983	+	0.439892i
$206$		0			0
$207$	2.12916e6	+	2.12916e6i	0.240048	+	0.240048i
$208$		0			0
$209$			3.96086e6i			0.433861i
$210$		0			0
$211$	1.27619e7			1.35852			0.679262	−	0.733896i	$-0.262300\pi$
$211$	1.27619e7			1.35852			0.679262	+	0.733896i	$0.262300\pi$
$212$		0			0
$213$	3.10523e6	−	3.10523e6i	0.321332	−	0.321332i
$214$		0			0
$215$	3.18824e6	+	2.16178e6i	0.320801	+	0.217518i
$216$		0			0
$217$	−1.50196e7	−	1.50196e7i	−1.46987	−	1.46987i
$218$		0			0
$219$		−	1.00159e7i		−	0.953580i
$220$		0			0
$221$	3.69031e7			3.41889
$222$		0			0
$223$	−2.06607e6	+	2.06607e6i	−0.186307	+	0.186307i	−0.794098	−	0.607790i	$-0.792056\pi$
$223$	−2.06607e6	+	2.06607e6i	−0.186307	+	0.186307i	0.607790	+	0.794098i	$0.292056\pi$
$224$		0			0
$225$	1.40522e6	+	3.52727e6i	0.123366	+	0.309664i
$226$		0			0
$227$	−3.69282e6	−	3.69282e6i	−0.315705	−	0.315705i	0.531410	−	0.847115i	$-0.321662\pi$
$227$	−3.69282e6	−	3.69282e6i	−0.315705	−	0.315705i	−0.847115	+	0.531410i	$0.821662\pi$
$228$		0			0
$229$		−	2.50689e6i		−	0.208751i	−0.994538	−	0.104376i	$-0.966716\pi$
$229$		−	2.50689e6i		−	0.208751i	0.994538	−	0.104376i	$-0.0332844\pi$
$230$		0			0
$231$	3.61466e6			0.293246
$232$		0			0
$233$	−6.79869e6	+	6.79869e6i	−0.537474	+	0.537474i	−0.922786	−	0.385312i	$-0.874094\pi$
$233$	−6.79869e6	+	6.79869e6i	−0.537474	+	0.537474i	0.385312	+	0.922786i	$0.374094\pi$
$234$		0			0
$235$	3.75200e6	−	5.53353e6i	0.289107	−	0.426382i
$236$		0			0
$237$	1.48339e6	+	1.48339e6i	0.111432	+	0.111432i
$238$		0			0
$239$			1.99520e6i			0.146148i	0.997327	+	0.0730739i	$0.0232809\pi$
$239$			1.99520e6i			0.146148i	−0.997327	+	0.0730739i	$0.976719\pi$
$240$		0			0
$241$	−1.49921e7			−1.07106			−0.535528	−	0.844517i	$-0.679887\pi$
$241$	−1.49921e7			−1.07106			−0.535528	+	0.844517i	$0.679887\pi$
$242$		0			0
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$		0			0
$245$	9.56976e6	−	1.83607e6i	0.650733	−	0.124851i
$246$		0			0
$247$	2.12732e7	+	2.12732e7i	1.41170	+	1.41170i
$248$		0			0
$249$			1.17980e7i			0.764205i
$250$		0			0
$251$	1.81622e7			1.14854			0.574272	−	0.818665i	$-0.305285\pi$
$251$	1.81622e7			1.14854			0.574272	+	0.818665i	$0.305285\pi$
$252$		0			0
$253$	4.59388e6	−	4.59388e6i	0.283673	−	0.283673i
$254$		0			0
$255$	−3.40235e6	−	1.77334e7i	−0.205191	−	1.06948i
$256$		0			0
$257$	−6.05915e6	−	6.05915e6i	−0.356954	−	0.356954i	0.505735	−	0.862689i	$-0.331221\pi$
$257$	−6.05915e6	−	6.05915e6i	−0.356954	−	0.356954i	−0.862689	+	0.505735i	$0.831221\pi$
$258$		0			0
$259$			2.13903e7i			1.23117i
$260$		0			0
$261$	5.67733e6			0.319317
$262$		0			0
$263$	−230685.	+	230685.i	−0.0126810	+	0.0126810i	−0.713419	−	0.700738i	$-0.752854\pi$
$263$	−230685.	+	230685.i	−0.0126810	+	0.0126810i	0.700738	+	0.713419i	$0.252854\pi$
$264$		0			0
$265$	−2.62479e7	−	1.77973e7i	−1.41045	−	0.956349i
$266$		0			0
$267$	−862055.	−	862055.i	−0.0452899	−	0.0452899i
$268$		0			0
$269$		−	2.30197e7i		−	1.18261i	−0.806447	−	0.591307i	$-0.798612\pi$
$269$		−	2.30197e7i		−	1.18261i	0.806447	−	0.591307i	$-0.201388\pi$
$270$		0			0
$271$	2.58489e7			1.29878			0.649389	−	0.760456i	$-0.275025\pi$
$271$	2.58489e7			1.29878			0.649389	+	0.760456i	$0.275025\pi$
$272$		0			0
$273$	1.94138e7	−	1.94138e7i	0.954164	−	0.954164i
$274$		0			0
$275$	7.61042e6	−	3.03190e6i	0.365941	−	0.145786i
$276$		0			0
$277$	−3.76177e6	−	3.76177e6i	−0.176992	−	0.176992i	0.613051	−	0.790043i	$-0.289942\pi$
$277$	−3.76177e6	−	3.76177e6i	−0.176992	−	0.176992i	−0.790043	+	0.613051i	$0.789942\pi$
$278$		0			0
$279$			1.16705e7i			0.537376i
$280$		0			0
$281$	9.53259e6			0.429627			0.214814	−	0.976655i	$-0.431086\pi$
$281$	9.53259e6			0.429627			0.214814	+	0.976655i	$0.431086\pi$
$282$		0			0
$283$	−2.62576e7	+	2.62576e7i	−1.15850	+	1.15850i	−0.173699	+	0.984799i	$0.555572\pi$
$283$	−2.62576e7	+	2.62576e7i	−1.15850	+	1.15850i	−0.984799	+	0.173699i	$0.944428\pi$
$284$		0			0
$285$	8.26128e6	−	1.21839e7i	0.356872	−	0.526323i
$286$		0			0
$287$	−9.65430e6	−	9.65430e6i	−0.408390	−	0.408390i
$288$		0			0
$289$			6.17352e7i			2.55764i
$290$		0			0
$291$	2.08339e6			0.0845457
$292$		0			0
$293$	−1.82060e7	+	1.82060e7i	−0.723790	+	0.723790i	−0.969375	−	0.245585i	$-0.921020\pi$
$293$	−1.82060e7	+	1.82060e7i	−0.723790	+	0.723790i	0.245585	+	0.969375i	$0.421020\pi$
$294$		0			0
$295$	−2.46213e7	+	4.72388e6i	−0.959060	+	0.184006i
$296$		0			0
$297$	−1.40434e6	−	1.40434e6i	−0.0536046	−	0.0536046i
$298$		0			0
$299$		−	4.93460e7i		−	1.84603i
$300$		0			0
$301$	−1.36291e7			−0.499768
$302$		0			0
$303$	1.53789e6	−	1.53789e6i	0.0552837	−	0.0552837i
$304$		0			0
$305$	463764.	+	2.41719e6i	0.0163455	+	0.0851943i
$306$		0			0
$307$	−1.23071e7	−	1.23071e7i	−0.425346	−	0.425346i	0.461694	−	0.887039i	$-0.347242\pi$
$307$	−1.23071e7	−	1.23071e7i	−0.425346	−	0.425346i	−0.887039	+	0.461694i	$0.847242\pi$
$308$		0			0
$309$			2.21127e7i			0.749490i
$310$		0			0
$311$	1.48687e6			0.0494301			0.0247151	−	0.999695i	$-0.492132\pi$
$311$	1.48687e6			0.0494301			0.0247151	+	0.999695i	$0.492132\pi$
$312$		0			0
$313$	−1.23460e7	+	1.23460e7i	−0.402618	+	0.402618i	−0.879155	−	0.476537i	$-0.841892\pi$
$313$	−1.23460e7	+	1.23460e7i	−0.402618	+	0.402618i	0.476537	+	0.879155i	$0.341892\pi$
$314$		0			0
$315$	−1.11190e7	−	7.53921e6i	−0.355741	−	0.241209i
$316$		0			0
$317$	8.48737e6	+	8.48737e6i	0.266437	+	0.266437i	0.827663	−	0.561225i	$-0.189670\pi$
$317$	8.48737e6	+	8.48737e6i	0.266437	+	0.266437i	−0.561225	+	0.827663i	$0.689670\pi$
$318$		0			0
$319$		−	1.22494e7i		−	0.377348i
$320$		0			0
$321$	−9.79489e6			−0.296131
$322$		0			0
$323$	−4.95024e7	+	4.95024e7i	−1.46899	+	1.46899i
$324$		0			0
$325$	2.45906e7	−	5.71583e7i	0.716338	−	1.66506i
$326$		0			0
$327$	−7.39121e6	−	7.39121e6i	−0.211384	−	0.211384i
$328$		0			0
$329$			2.36548e7i			0.664251i
$330$		0			0
$331$	−4.20247e7			−1.15883			−0.579417	−	0.815031i	$-0.696720\pi$
$331$	−4.20247e7			−1.15883			−0.579417	+	0.815031i	$0.696720\pi$
$332$		0			0
$333$	8.31036e6	−	8.31036e6i	0.225054	−	0.225054i
$334$		0			0
$335$	9.34484e6	−	1.37820e7i	0.248563	−	0.366587i
$336$		0			0
$337$	−2.18920e7	−	2.18920e7i	−0.572000	−	0.572000i	0.360687	−	0.932687i	$-0.382542\pi$
$337$	−2.18920e7	−	2.18920e7i	−0.572000	−	0.572000i	−0.932687	+	0.360687i	$0.882542\pi$
$338$		0			0
$339$		−	2.01072e7i		−	0.516123i
$340$		0			0
$341$	2.51803e7			0.635036
$342$		0			0
$343$	1.24138e7	−	1.24138e7i	0.307625	−	0.307625i
$344$		0			0
$345$	−2.37127e7	+	4.54955e6i	−0.577462	+	0.110793i
$346$		0			0
$347$	−1.92252e7	−	1.92252e7i	−0.460132	−	0.460132i	0.438567	−	0.898699i	$-0.355486\pi$
$347$	−1.92252e7	−	1.92252e7i	−0.460132	−	0.460132i	−0.898699	+	0.438567i	$0.855486\pi$
$348$		0			0
$349$			3.16328e6i			0.0744152i	0.999308	+	0.0372076i	$0.0118463\pi$
$349$			3.16328e6i			0.0744152i	−0.999308	+	0.0372076i	$0.988154\pi$
$350$		0			0
$351$	−1.50849e7			−0.348837
$352$		0			0
$353$	−4.03601e7	+	4.03601e7i	−0.917546	+	0.917546i	−0.996850	−	0.0793047i	$-0.974730\pi$
$353$	−4.03601e7	+	4.03601e7i	−0.917546	+	0.917546i	0.0793047	+	0.996850i	$0.474730\pi$
$354$		0			0
$355$	6.63518e6	+	3.45832e7i	0.148309	+	0.773002i
$356$		0			0
$357$	4.51756e7	+	4.51756e7i	0.992886	+	0.992886i
$358$		0			0
$359$		−	6.51722e7i		−	1.40857i	−0.709916	−	0.704286i	$-0.751267\pi$
$359$		−	6.51722e7i		−	1.40857i	0.709916	−	0.704286i	$-0.248733\pi$
$360$		0			0
$361$	−1.00265e7			−0.213122
$362$		0			0
$363$	1.64974e7	−	1.64974e7i	0.344902	−	0.344902i
$364$		0			0
$365$	6.64748e7	+	4.50731e7i	1.36703	+	0.926913i
$366$		0			0
$367$	6.30942e7	+	6.30942e7i	1.27641	+	1.27641i	0.942661	+	0.333752i	$0.108315\pi$
$367$	6.30942e7	+	6.30942e7i	1.27641	+	1.27641i	0.333752	+	0.942661i	$0.391685\pi$
$368$		0			0
$369$			7.50160e6i			0.149305i
$370$		0			0
$371$	1.12205e8			2.19730
$372$		0			0
$373$	5.23236e7	−	5.23236e7i	1.00826	−	1.00826i	0.00829139	−	0.999966i	$-0.497361\pi$
$373$	5.23236e7	−	5.23236e7i	1.00826	−	1.00826i	0.999966	−	0.00829139i	$-0.00263926\pi$
$374$		0			0
$375$	−2.97340e7	−	6.54691e6i	−0.563844	−	0.124149i
$376$		0			0
$377$	−6.57896e7	−	6.57896e7i	−1.22782	−	1.22782i
$378$		0			0
$379$		−	2.16294e7i		−	0.397308i	−0.980070	−	0.198654i	$-0.936343\pi$
$379$		−	2.16294e7i		−	0.397308i	0.980070	−	0.198654i	$-0.0636571\pi$
$380$		0			0
$381$	−1.32410e7			−0.239413
$382$		0			0
$383$	−3.45802e6	+	3.45802e6i	−0.0615505	+	0.0615505i	−0.737212	−	0.675662i	$-0.763858\pi$
$383$	−3.45802e6	+	3.45802e6i	−0.0615505	+	0.0615505i	0.675662	+	0.737212i	$0.263858\pi$
$384$		0			0
$385$	−1.62666e7	+	2.39903e7i	−0.285045	+	0.420391i
$386$		0			0
$387$	5.29506e6	+	5.29506e6i	0.0913562	+	0.0913562i
$388$		0			0
$389$			9.91167e7i			1.68383i	0.539611	+	0.841915i	$0.318572\pi$
$389$			9.91167e7i			1.68383i	−0.539611	+	0.841915i	$0.681428\pi$
$390$		0			0
$391$	1.14827e8			1.92095
$392$		0			0
$393$	−1.46315e6	+	1.46315e6i	−0.0241052	+	0.0241052i
$394$		0			0
$395$	−1.65206e7	+	3.16967e6i	−0.268062	+	0.0514308i
$396$		0			0
$397$	3.80721e7	+	3.80721e7i	0.608464	+	0.608464i	0.942545	−	0.334080i	$-0.108426\pi$
$397$	3.80721e7	+	3.80721e7i	0.608464	+	0.608464i	−0.334080	+	0.942545i	$0.608426\pi$
$398$		0			0
$399$			5.20840e7i			0.819947i
$400$		0			0
$401$	−1.01890e8			−1.58014			−0.790072	−	0.613014i	$-0.789957\pi$
$401$	−1.01890e8			−1.58014			−0.790072	+	0.613014i	$0.789957\pi$
$402$		0			0
$403$	1.35240e8	−	1.35240e8i	2.06628	−	2.06628i
$404$		0			0
$405$	1.39079e6	+	7.24891e6i	0.0209361	+	0.109121i
$406$		0			0
$407$	−1.79304e7	−	1.79304e7i	−0.265954	−	0.265954i
$408$		0			0
$409$		−	2.97072e7i		−	0.434201i	−0.976149	−	0.217101i	$-0.930340\pi$
$409$		−	2.97072e7i		−	0.434201i	0.976149	−	0.217101i	$-0.0696600\pi$
$410$		0			0
$411$	−3.90541e7			−0.562524
$412$		0			0
$413$	6.27227e7	−	6.27227e7i	0.890378	−	0.890378i
$414$		0			0
$415$	−7.83026e7	−	5.30929e7i	−1.09555	−	0.742834i
$416$		0			0
$417$	1.63903e7	+	1.63903e7i	0.226037	+	0.226037i
$418$		0			0
$419$		−	5.47424e7i		−	0.744187i	−0.928195	−	0.372093i	$-0.878640\pi$
$419$		−	5.47424e7i		−	0.744187i	0.928195	−	0.372093i	$-0.121360\pi$
$420$		0			0
$421$	−4.56931e7			−0.612357			−0.306178	−	0.951974i	$-0.599050\pi$
$421$	−4.56931e7			−0.612357			−0.306178	+	0.951974i	$0.599050\pi$
$422$		0			0
$423$	9.19015e6	−	9.19015e6i	0.121423	−	0.121423i
$424$		0			0
$425$	1.33006e8	+	5.72218e7i	1.73263	+	0.745410i
$426$		0			0
$427$	−6.15776e6	−	6.15776e6i	−0.0790932	−	0.0790932i
$428$		0			0
$429$			3.25472e7i			0.412233i
$430$		0			0
$431$	−1.36803e8			−1.70870			−0.854348	−	0.519701i	$-0.826043\pi$
$431$	−1.36803e8			−1.70870			−0.854348	+	0.519701i	$0.826043\pi$
$432$		0			0
$433$	−1.42469e7	+	1.42469e7i	−0.175492	+	0.175492i	−0.789388	−	0.613895i	$-0.789602\pi$
$433$	−1.42469e7	+	1.42469e7i	−0.175492	+	0.175492i	0.613895	+	0.789388i	$0.289602\pi$
$434$		0			0
$435$	−2.55489e7	+	3.76801e7i	−0.310388	+	0.457767i
$436$		0			0
$437$	6.61935e7	+	6.61935e7i	0.793179	+	0.793179i
$438$		0			0
$439$		−	1.22508e8i		−	1.44801i	−0.689793	−	0.724007i	$-0.742298\pi$
$439$		−	1.22508e8i		−	1.44801i	0.689793	−	0.724007i	$-0.257702\pi$
$440$		0			0
$441$	1.89429e7			0.220867
$442$		0			0
$443$	−1.09099e8	+	1.09099e8i	−1.25490	+	1.25490i	−0.301401	+	0.953497i	$0.597454\pi$
$443$	−1.09099e8	+	1.09099e8i	−1.25490	+	1.25490i	−0.953497	+	0.301401i	$0.902546\pi$
$444$		0			0
$445$	9.60080e6	−	1.84202e6i	0.108950	−	0.0209033i
$446$		0			0
$447$	−1.08249e7	−	1.08249e7i	−0.121200	−	0.121200i
$448$		0			0
$449$		−	5.72987e7i		−	0.633003i	−0.948592	−	0.316502i	$-0.897492\pi$
$449$		−	5.72987e7i		−	0.633003i	0.948592	−	0.316502i	$-0.102508\pi$
$450$		0			0
$451$	1.61854e7			0.176439
$452$		0			0
$453$	−2.88623e7	+	2.88623e7i	−0.310481	+	0.310481i
$454$		0			0
$455$	4.14830e7	+	2.16214e8i	0.440389	+	2.29535i
$456$		0			0
$457$	−1.62737e7	−	1.62737e7i	−0.170505	−	0.170505i	0.616696	−	0.787201i	$-0.288471\pi$
$457$	−1.62737e7	−	1.62737e7i	−0.170505	−	0.170505i	−0.787201	+	0.616696i	$0.788471\pi$
$458$		0			0
$459$		−	3.51024e7i		−	0.362994i
$460$		0			0
$461$	−9.23525e7			−0.942640			−0.471320	−	0.881962i	$-0.656222\pi$
$461$	−9.23525e7			−0.942640			−0.471320	+	0.881962i	$0.656222\pi$
$462$		0			0
$463$	−3.18877e7	+	3.18877e7i	−0.321278	+	0.321278i	−0.849257	−	0.527979i	$-0.822950\pi$
$463$	−3.18877e7	+	3.18877e7i	−0.321278	+	0.321278i	0.527979	+	0.849257i	$0.322950\pi$
$464$		0			0
$465$	−7.74567e7	−	5.25193e7i	−0.770371	−	0.522348i
$466$		0			0
$467$	−6.91385e7	−	6.91385e7i	−0.678843	−	0.678843i	0.280895	−	0.959738i	$-0.409369\pi$
$467$	−6.91385e7	−	6.91385e7i	−0.678843	−	0.678843i	−0.959738	+	0.280895i	$0.909369\pi$
$468$		0			0
$469$			5.89154e7i			0.571097i
$470$		0			0
$471$	−4.49592e7			−0.430284
$472$		0			0
$473$	1.14246e7	−	1.14246e7i	0.107959	−	0.107959i
$474$		0			0
$475$	4.36869e7	+	1.09659e8i	0.407634	+	1.02321i
$476$		0			0
$477$	−4.35927e7	−	4.35927e7i	−0.401660	−	0.401660i
$478$		0			0
$479$		−	1.78196e8i		−	1.62140i	−0.585461	−	0.810701i	$-0.699086\pi$
$479$		−	1.78196e8i		−	1.62140i	0.585461	−	0.810701i	$-0.300914\pi$
$480$		0			0
$481$	−1.92603e8			−1.73072
$482$		0			0
$483$	6.04079e7	−	6.04079e7i	0.536108	−	0.536108i
$484$		0			0
$485$	−9.37559e6	+	1.38273e7i	−0.0821814	+	0.121203i
$486$		0			0
$487$	1.09058e7	+	1.09058e7i	0.0944212	+	0.0944212i	0.752740	−	0.658318i	$-0.228732\pi$
$487$	1.09058e7	+	1.09058e7i	0.0944212	+	0.0944212i	−0.658318	+	0.752740i	$0.728732\pi$
$488$		0			0
$489$			5.16965e7i			0.442114i
$490$		0			0
$491$	1.74098e8			1.47079			0.735395	−	0.677639i	$-0.236997\pi$
$491$	1.74098e8			1.47079			0.735395	+	0.677639i	$0.236997\pi$
$492$		0			0
$493$	1.53091e8	−	1.53091e8i	1.27764	−	1.27764i
$494$		0			0
$495$	1.56402e7	−	3.00076e6i	0.128952	−	0.0247409i
$496$		0			0
$497$	−8.81005e7	−	8.81005e7i	−0.717644	−	0.717644i
$498$		0			0
$499$			1.39200e8i			1.12031i	0.828387	+	0.560156i	$0.189259\pi$
$499$			1.39200e8i			1.12031i	−0.828387	+	0.560156i	$0.810741\pi$
$500$		0			0
$501$	−2.36533e6			−0.0188095
$502$		0			0
$503$	−1.04234e8	+	1.04234e8i	−0.819044	+	0.819044i	−0.985969	−	0.166926i	$-0.946616\pi$
$503$	−1.04234e8	+	1.04234e8i	−0.819044	+	0.819044i	0.166926	+	0.985969i	$0.446616\pi$
$504$		0			0
$505$	3.28613e6	+	1.71276e7i	0.0255159	+	0.132991i
$506$		0			0
$507$	1.21602e8	+	1.21602e8i	0.933074	+	0.933074i
$508$		0			0
$509$		−	1.18629e8i		−	0.899576i	−0.893135	−	0.449788i	$-0.851500\pi$
$509$		−	1.18629e8i		−	0.899576i	0.893135	−	0.449788i	$-0.148500\pi$
$510$		0			0
$511$	−2.84168e8			−2.12967
$512$		0			0
$513$	2.02352e7	−	2.02352e7i	0.149884	−	0.149884i
$514$		0			0
$515$	−1.46761e8	−	9.95107e7i	−1.07445	−	0.728531i
$516$		0			0
$517$	−1.98286e7	−	1.98286e7i	−0.143490	−	0.143490i
$518$		0			0
$519$		−	4.77946e7i		−	0.341882i
$520$		0			0
$521$	−9.44367e7			−0.667771			−0.333886	−	0.942614i	$-0.608360\pi$
$521$	−9.44367e7			−0.667771			−0.333886	+	0.942614i	$0.608360\pi$
$522$		0			0
$523$	−1.29920e8	+	1.29920e8i	−0.908177	+	0.908177i	−0.996125	−	0.0879478i	$-0.971969\pi$
$523$	−1.29920e8	+	1.29920e8i	−0.908177	+	0.908177i	0.0879478	+	0.996125i	$0.471969\pi$
$524$		0			0
$525$	1.00075e8	−	3.98684e7i	0.691585	−	0.275519i
$526$		0			0
$527$	3.14701e8	+	3.14701e8i	2.15013	+	2.15013i
$528$		0			0
$529$		−	5.50890e6i		−	0.0372133i
$530$		0			0
$531$	−4.87369e7			−0.325517
$532$		0			0
$533$	8.69295e7	−	8.69295e7i	0.574097	−	0.574097i
$534$		0			0
$535$	4.40786e7	−	6.50081e7i	0.287850	−	0.424528i
$536$		0			0
$537$	243397.	+	243397.i	0.00157178	+	0.00157178i
$538$		0			0
$539$		−	4.08712e7i		−	0.261006i
$540$		0			0
$541$	1.48167e8			0.935750			0.467875	−	0.883795i	$-0.345020\pi$
$541$	1.48167e8			0.935750			0.467875	+	0.883795i	$0.345020\pi$
$542$		0			0
$543$	5.28213e7	−	5.28213e7i	0.329921	−	0.329921i
$544$		0			0
$545$	8.23167e7	−	1.57934e7i	0.508509	−	0.0975631i
$546$		0			0
$547$	1.81777e8	+	1.81777e8i	1.11065	+	1.11065i	0.993063	+	0.117583i	$0.0375147\pi$
$547$	1.81777e8	+	1.81777e8i	1.11065	+	1.11065i	0.117583	+	0.993063i	$0.462485\pi$
$548$		0			0
$549$			4.78471e6i			0.0289160i
$550$		0			0
$551$	1.76503e8			1.05511
$552$		0			0
$553$	4.20862e7	−	4.20862e7i	0.248865	−	0.248865i
$554$		0			0
$555$	1.77574e7	+	9.25533e7i	0.103872	+	0.541394i
$556$		0			0
$557$	−2.04488e8	−	2.04488e8i	−1.18332	−	1.18332i	−0.978879	−	0.204442i	$-0.934462\pi$
$557$	−2.04488e8	−	2.04488e8i	−1.18332	−	1.18332i	−0.204442	−	0.978879i	$-0.565538\pi$
$558$		0			0
$559$		−	1.22720e8i		−	0.702552i
$560$		0			0
$561$	−7.57369e7			−0.428962
$562$		0			0
$563$	1.28944e8	−	1.28944e8i	0.722565	−	0.722565i	−0.246562	−	0.969127i	$-0.579301\pi$
$563$	1.28944e8	−	1.28944e8i	0.722565	−	0.722565i	0.969127	+	0.246562i	$0.0793009\pi$
$564$		0			0
$565$	1.33451e8	+	9.04858e7i	0.739903	+	0.501690i
$566$		0			0
$567$	−1.84666e7	−	1.84666e7i	−0.101306	−	0.101306i
$568$		0			0
$569$			7.27289e7i			0.394794i	0.980324	+	0.197397i	$0.0632487\pi$
$569$			7.27289e7i			0.394794i	−0.980324	+	0.197397i	$0.936751\pi$
$570$		0			0
$571$	−6.23414e7			−0.334864			−0.167432	−	0.985884i	$-0.553547\pi$
$571$	−6.23414e7			−0.334864			−0.167432	+	0.985884i	$0.553547\pi$
$572$		0			0
$573$	1.49421e8	−	1.49421e8i	0.794230	−	0.794230i
$574$		0			0
$575$	7.65159e7	−	1.77853e8i	0.402483	−	0.935532i
$576$		0			0
$577$	1.65224e7	+	1.65224e7i	0.0860096	+	0.0860096i	0.748803	−	0.662793i	$-0.230629\pi$
$577$	1.65224e7	+	1.65224e7i	0.0860096	+	0.0860096i	−0.662793	+	0.748803i	$0.730629\pi$
$578$		0			0
$579$			5.25753e7i			0.270861i
$580$		0			0
$581$	3.34729e8			1.70673
$582$		0			0
$583$	−9.40556e7	+	9.40556e7i	−0.474656	+	0.474656i
$584$		0			0
$585$	6.78847e7	−	1.00118e8i	0.339082	−	0.500085i
$586$		0			0
$587$	1.40171e8	+	1.40171e8i	0.693016	+	0.693016i	0.962894	−	0.269879i	$-0.0869836\pi$
$587$	1.40171e8	+	1.40171e8i	0.693016	+	0.693016i	−0.269879	+	0.962894i	$0.586984\pi$
$588$		0			0
$589$			3.62826e8i			1.77563i
$590$		0			0
$591$	2.01107e8			0.974235
$592$		0			0
$593$	−4.73100e7	+	4.73100e7i	−0.226876	+	0.226876i	−0.811386	−	0.584510i	$-0.801287\pi$
$593$	−4.73100e7	+	4.73100e7i	−0.226876	+	0.226876i	0.584510	+	0.811386i	$0.301287\pi$
$594$		0			0
$595$	−5.03126e8	+	9.65303e7i	−2.38850	+	0.458261i
$596$		0			0
$597$	−1.35829e8	−	1.35829e8i	−0.638367	−	0.638367i
$598$		0			0
$599$			2.08410e8i			0.969701i	0.874597	+	0.484851i	$0.161126\pi$
$599$			2.08410e8i			0.969701i	−0.874597	+	0.484851i	$0.838874\pi$
$600$		0			0
$601$	7.41018e7			0.341354			0.170677	−	0.985327i	$-0.445404\pi$
$601$	7.41018e7			0.341354			0.170677	+	0.985327i	$0.445404\pi$
$602$		0			0
$603$	2.28893e7	−	2.28893e7i	0.104395	−	0.104395i
$604$		0			0
$605$	3.52513e7	+	1.83733e8i	0.159187	+	0.829701i
$606$		0			0
$607$	−1.12886e8	−	1.12886e8i	−0.504749	−	0.504749i	0.408161	−	0.912910i	$-0.366170\pi$
$607$	−1.12886e8	−	1.12886e8i	−0.504749	−	0.504749i	−0.912910	+	0.408161i	$0.866170\pi$
$608$		0			0
$609$		−	1.61075e8i		−	0.713144i
$610$		0			0
$611$	−2.12993e8			−0.933775
$612$		0			0
$613$	−2.41064e8	+	2.41064e8i	−1.04653	+	1.04653i	−0.0476639	+	0.998863i	$0.515178\pi$
$613$	−2.41064e8	+	2.41064e8i	−1.04653	+	1.04653i	−0.998863	+	0.0476639i	$0.984822\pi$
$614$		0			0
$615$	−4.97877e7	−	3.37584e7i	−0.214041	−	0.145130i
$616$		0			0
$617$	−6.28924e7	−	6.28924e7i	−0.267758	−	0.267758i	0.560438	−	0.828196i	$-0.310633\pi$
$617$	−6.28924e7	−	6.28924e7i	−0.267758	−	0.267758i	−0.828196	+	0.560438i	$0.810633\pi$
$618$		0			0
$619$		−	1.20452e8i		−	0.507859i	−0.967223	−	0.253930i	$-0.918277\pi$
$619$		−	1.20452e8i		−	0.507859i	0.967223	−	0.253930i	$-0.0817232\pi$
$620$		0			0
$621$	−4.69383e7			−0.195998
$622$		0			0
$623$	−2.44580e7	+	2.44580e7i	−0.101148	+	0.101148i
$624$		0			0
$625$	1.77259e8	−	1.67880e8i	0.726053	−	0.687638i
$626$		0			0
$627$	−4.36594e7	−	4.36594e7i	−0.177123	−	0.177123i
$628$		0			0
$629$		−	4.48184e8i		−	1.80096i
$630$		0			0
$631$	3.28657e8			1.30814			0.654071	−	0.756433i	$-0.273060\pi$
$631$	3.28657e8			1.30814			0.654071	+	0.756433i	$0.273060\pi$
$632$		0			0
$633$	−1.40670e8	+	1.40670e8i	−0.554615	+	0.554615i
$634$		0			0
$635$	5.95868e7	−	8.78800e7i	0.232718	−	0.343217i
$636$		0			0
$637$	−2.19513e8	−	2.19513e8i	−0.849263	−	0.849263i
$638$		0			0
$639$			6.84560e7i			0.262367i
$640$		0			0
$641$	−1.45954e8			−0.554169			−0.277085	−	0.960845i	$-0.589368\pi$
$641$	−1.45954e8			−0.554169			−0.277085	+	0.960845i	$0.589368\pi$
$642$		0			0
$643$	9.18706e6	−	9.18706e6i	0.0345576	−	0.0345576i	−0.689617	−	0.724174i	$-0.742221\pi$
$643$	9.18706e6	−	9.18706e6i	0.0345576	−	0.0345576i	0.724174	+	0.689617i	$0.242221\pi$
$644$		0			0
$645$	−5.89716e7	+	1.13144e7i	−0.219768	+	0.0421649i
$646$		0			0
$647$	−2.48972e8	−	2.48972e8i	−0.919260	−	0.919260i	0.0777156	−	0.996976i	$-0.475237\pi$
$647$	−2.48972e8	−	2.48972e8i	−0.919260	−	0.919260i	−0.996976	+	0.0777156i	$0.975237\pi$
$648$		0			0
$649$			1.05155e8i			0.384675i
$650$		0			0
$651$	3.31113e8			1.20014
$652$		0			0
$653$	−1.70989e8	+	1.70989e8i	−0.614084	+	0.614084i	−0.944008	−	0.329924i	$-0.892977\pi$
$653$	−1.70989e8	+	1.70989e8i	−0.614084	+	0.614084i	0.329924	+	0.944008i	$0.392977\pi$
$654$		0			0
$655$	−3.12643e6	−	1.62952e7i	−0.0111256	−	0.0579878i
$656$		0			0
$657$	1.10402e8	+	1.10402e8i	0.389297	+	0.389297i
$658$		0			0
$659$			3.67582e8i			1.28439i	0.766540	+	0.642197i	$0.221977\pi$
$659$			3.67582e8i			1.28439i	−0.766540	+	0.642197i	$0.778023\pi$
$660$		0			0
$661$	−9.82639e7			−0.340243			−0.170122	−	0.985423i	$-0.554416\pi$
$661$	−9.82639e7			−0.340243			−0.170122	+	0.985423i	$0.554416\pi$
$662$		0			0
$663$	−4.06771e8	+	4.06771e8i	−1.39576	+	1.39576i
$664$		0			0
$665$	−3.45678e8	−	2.34386e8i	−1.17546	−	0.797017i
$666$		0			0
$667$	−2.04711e8	−	2.04711e8i	−0.689863	−	0.689863i
$668$		0			0
$669$		−	4.55473e7i		−	0.152119i
$670$		0			0
$671$	1.03235e7			0.0341711
$672$		0			0
$673$	−2.33286e8	+	2.33286e8i	−0.765320	+	0.765320i	−0.977279	−	0.211959i	$-0.932016\pi$
$673$	−2.33286e8	+	2.33286e8i	−0.765320	+	0.765320i	0.211959	+	0.977279i	$0.432016\pi$
$674$		0			0
$675$	−5.43693e7	−	2.33907e7i	−0.176784	−	0.0760557i
$676$		0			0
$677$	2.14487e7	+	2.14487e7i	0.0691251	+	0.0691251i	0.740824	−	0.671699i	$-0.234435\pi$
$677$	2.14487e7	+	2.14487e7i	0.0691251	+	0.0691251i	−0.671699	+	0.740824i	$0.734435\pi$
$678$		0			0
$679$		−	5.91093e7i		−	0.188819i
$680$		0			0
$681$	8.14098e7			0.257772
$682$		0			0
$683$	2.59602e8	−	2.59602e8i	0.814790	−	0.814790i	−0.170558	−	0.985348i	$-0.554557\pi$
$683$	2.59602e8	−	2.59602e8i	0.814790	−	0.814790i	0.985348	+	0.170558i	$0.0545570\pi$
$684$		0			0
$685$	1.75750e8	−	2.59199e8i	0.546793	−	0.806422i
$686$		0			0
$687$	2.76327e7	+	2.76327e7i	0.0852224	+	0.0852224i
$688$		0			0
$689$			1.01032e9i			3.08887i
$690$		0			0
$691$	1.02213e8			0.309792			0.154896	−	0.987931i	$-0.450496\pi$
$691$	1.02213e8			0.309792			0.154896	+	0.987931i	$0.450496\pi$
$692$		0			0
$693$	−3.98434e7	+	3.98434e7i	−0.119717	+	0.119717i
$694$		0			0
$695$	−1.82541e8	+	3.50225e7i	−0.543757	+	0.104326i
$696$		0			0
$697$	2.02284e8	+	2.02284e8i	0.597396	+	0.597396i
$698$		0			0
$699$		−	1.49880e8i		−	0.438846i
$700$		0			0
$701$	−3.00343e8			−0.871894			−0.435947	−	0.899972i	$-0.643587\pi$
$701$	−3.00343e8			−0.871894			−0.435947	+	0.899972i	$0.643587\pi$
$702$		0			0
$703$	2.58361e8	−	2.58361e8i	0.743637	−	0.743637i
$704$		0			0
$705$	1.96373e7	+	1.02352e8i	0.0560422	+	0.292097i
$706$		0			0
$707$	−4.36325e7	−	4.36325e7i	−0.123467	−	0.123467i
$708$		0			0
$709$			2.55379e8i			0.716550i	0.933616	+	0.358275i	$0.116635\pi$
$709$			2.55379e8i			0.716550i	−0.933616	+	0.358275i	$0.883365\pi$
$710$		0			0
$711$	−3.27019e7			−0.0909838
$712$		0			0
$713$	4.20811e8	−	4.20811e8i	1.16096	−	1.16096i
$714$		0			0
$715$	−2.16014e8	−	1.46468e8i	−0.590968	−	0.400704i
$716$		0			0
$717$	−2.19925e7	−	2.19925e7i	−0.0596646	−	0.0596646i
$718$		0			0
$719$		−	3.42719e6i		−	0.00922044i	−0.999989	−	0.00461022i	$-0.998533\pi$
$719$		−	3.42719e6i		−	0.00922044i	0.999989	−	0.00461022i	$-0.00146748\pi$
$720$		0			0
$721$	6.27374e8			1.67387
$722$		0			0
$723$	1.65254e8	−	1.65254e8i	0.437257	−	0.437257i
$724$		0			0
$725$	−1.35106e8	−	3.39133e8i	−0.354537	−	0.889930i
$726$		0			0
$727$	−1.94321e8	−	1.94321e8i	−0.505729	−	0.505729i	0.407484	−	0.913212i	$-0.366406\pi$
$727$	−1.94321e8	−	1.94321e8i	−0.505729	−	0.505729i	−0.913212	+	0.407484i	$0.866406\pi$
$728$		0			0
$729$			1.43489e7i			0.0370370i
$730$		0			0
$731$	2.85567e8			0.731064
$732$		0			0
$733$	1.01995e8	−	1.01995e8i	0.258980	−	0.258980i	−0.565659	−	0.824639i	$-0.691378\pi$
$733$	1.01995e8	−	1.01995e8i	0.258980	−	0.258980i	0.824639	+	0.565659i	$0.191378\pi$
$734$		0			0
$735$	−8.52462e7	+	1.25723e8i	−0.214691	+	0.316631i
$736$		0			0
$737$	−4.93858e7	−	4.93858e7i	−0.123367	−	0.123367i
$738$		0			0
$739$		−	5.45928e8i		−	1.35270i	−0.736579	−	0.676351i	$-0.763560\pi$
$739$		−	5.45928e8i		−	1.35270i	0.736579	−	0.676351i	$-0.236440\pi$
$740$		0			0
$741$	−4.68976e8			−1.15265
$742$		0			0
$743$	−3.99074e8	+	3.99074e8i	−0.972942	+	0.972942i	−0.999643	−	0.0267014i	$-0.991500\pi$
$743$	−3.99074e8	+	3.99074e8i	−0.972942	+	0.972942i	0.0267014	+	0.999643i	$0.491500\pi$
$744$		0			0
$745$	1.20558e8	−	2.31304e7i	0.291559	−	0.0559389i
$746$		0			0
$747$	−1.30046e8	−	1.30046e8i	−0.311986	−	0.311986i
$748$		0			0
$749$			2.77898e8i			0.661362i
$750$		0			0
$751$	5.75259e8			1.35814			0.679069	−	0.734074i	$-0.262384\pi$
$751$	5.75259e8			1.35814			0.679069	+	0.734074i	$0.262384\pi$
$752$		0			0
$753$	−2.00197e8	+	2.00197e8i	−0.468891	+	0.468891i
$754$		0			0
$755$	−6.16723e7	−	3.21442e8i	−0.143301	−	0.746898i
$756$		0			0
$757$	4.27701e8	+	4.27701e8i	0.985946	+	0.985946i	0.999903	−	0.0139566i	$-0.00444267\pi$
$757$	4.27701e8	+	4.27701e8i	0.985946	+	0.985946i	−0.0139566	+	0.999903i	$0.504443\pi$
$758$		0			0
$759$			1.01274e8i			0.231618i
$760$		0			0
$761$	8.12040e8			1.84257			0.921284	−	0.388891i	$-0.127142\pi$
$761$	8.12040e8			1.84257			0.921284	+	0.388891i	$0.127142\pi$
$762$		0			0
$763$	−2.09701e8	+	2.09701e8i	−0.472093	+	0.472093i
$764$		0			0
$765$	2.32973e8	+	1.57967e8i	0.520380	+	0.352843i
$766$		0			0
$767$	5.64769e8	+	5.64769e8i	1.25166	+	1.25166i
$768$		0			0
$769$		−	6.57679e8i		−	1.44622i	−0.690731	−	0.723111i	$-0.742711\pi$
$769$		−	6.57679e8i		−	1.44622i	0.690731	−	0.723111i	$-0.257289\pi$
$770$		0			0
$771$	1.33577e8			0.291452
$772$		0			0
$773$	−3.20098e8	+	3.20098e8i	−0.693018	+	0.693018i	−0.962895	−	0.269877i	$-0.913017\pi$
$773$	−3.20098e8	+	3.20098e8i	−0.693018	+	0.693018i	0.269877	+	0.962895i	$0.413017\pi$
$774$		0			0
$775$	6.97135e8	−	2.77730e8i	1.49765	−	0.596647i
$776$		0			0
$777$	−2.35779e8	−	2.35779e8i	−0.502623	−	0.502623i
$778$		0			0
$779$			2.33217e8i			0.493342i
$780$		0			0
$781$	1.47700e8			0.310048
$782$		0			0
$783$	−6.25795e7	+	6.25795e7i	−0.130361	+	0.130361i
$784$		0			0
$785$	2.02324e8	−	2.98391e8i	0.418251	−	0.616847i
$786$		0			0
$787$	−4.19160e8	−	4.19160e8i	−0.859916	−	0.859916i	0.131412	−	0.991328i	$-0.458049\pi$
$787$	−4.19160e8	−	4.19160e8i	−0.859916	−	0.859916i	−0.991328	+	0.131412i	$0.958049\pi$
$788$		0			0
$789$		−	5.08555e6i		−	0.0103540i
$790$		0			0
$791$	−5.70476e8			−1.15268
$792$		0			0
$793$	5.54459e7	−	5.54459e7i	0.111186	−	0.111186i
$794$		0			0
$795$	4.85497e8	−	9.31481e7i	0.966240	−	0.185384i
$796$		0			0
$797$	4.71446e8	+	4.71446e8i	0.931230	+	0.931230i	0.997783	−	0.0665526i	$-0.0212000\pi$
$797$	4.71446e8	+	4.71446e8i	0.931230	+	0.931230i	−0.0665526	+	0.997783i	$0.521200\pi$
$798$		0			0
$799$		−	4.95632e8i		−	0.971670i
$800$		0			0
$801$	1.90044e7			0.0369791
$802$		0			0
$803$	2.38203e8	−	2.38203e8i	0.460046	−	0.460046i
$804$		0			0
$805$	1.29078e8	+	6.72769e8i	0.247438	+	1.28967i
$806$		0			0
$807$	2.53739e8	+	2.53739e8i	0.482800	+	0.482800i
$808$		0			0
$809$			3.01131e8i			0.568735i	0.958715	+	0.284368i	$0.0917836\pi$
$809$			3.01131e8i			0.568735i	−0.958715	+	0.284368i	$0.908216\pi$
$810$		0			0
$811$	−3.82474e8			−0.717034			−0.358517	−	0.933523i	$-0.616718\pi$
$811$	−3.82474e8			−0.717034			−0.358517	+	0.933523i	$0.616718\pi$
$812$		0			0
$813$	−2.84925e8	+	2.84925e8i	−0.530224	+	0.530224i
$814$		0			0
$815$	−3.43106e8	−	2.32642e8i	−0.633805	−	0.429750i
$816$		0			0
$817$	1.64618e8	+	1.64618e8i	0.301864	+	0.301864i
$818$		0			0
$819$			4.27985e8i			0.779071i
$820$		0			0
$821$	−5.20534e8			−0.940633			−0.470316	−	0.882498i	$-0.655860\pi$
$821$	−5.20534e8			−0.940633			−0.470316	+	0.882498i	$0.655860\pi$
$822$		0			0
$823$	5.86832e7	−	5.86832e7i	0.105272	−	0.105272i	−0.652509	−	0.757781i	$-0.726283\pi$
$823$	5.86832e7	−	5.86832e7i	0.105272	−	0.105272i	0.757781	+	0.652509i	$0.226283\pi$
$824$		0			0
$825$	−5.04677e7	+	1.17307e8i	−0.0898777	+	0.208912i
$826$		0			0
$827$	1.82617e8	+	1.82617e8i	0.322867	+	0.322867i	0.849866	−	0.526999i	$-0.176683\pi$
$827$	1.82617e8	+	1.82617e8i	0.322867	+	0.322867i	−0.526999	+	0.849866i	$0.676683\pi$
$828$		0			0
$829$		−	6.42030e7i		−	0.112692i	−0.998411	−	0.0563458i	$-0.982055\pi$
$829$		−	6.42030e7i		−	0.112692i	0.998411	−	0.0563458i	$-0.0179449\pi$
$830$		0			0
$831$	8.29298e7			0.144513
$832$		0			0
$833$	5.10803e8	−	5.10803e8i	0.883728	−	0.883728i
$834$		0			0
$835$	1.06444e7	−	1.56985e7i	0.0182835	−	0.0269650i
$836$		0			0
$837$	−1.28641e8	−	1.28641e8i	−0.219383	−	0.219383i
$838$		0			0
$839$		−	8.94555e8i		−	1.51468i	−0.653020	−	0.757341i	$-0.726498\pi$
$839$		−	8.94555e8i		−	1.51468i	0.653020	−	0.757341i	$-0.273502\pi$
$840$		0			0
$841$	4.89702e7			0.0823272
$842$		0			0
$843$	−1.05075e8	+	1.05075e8i	−0.175395	+	0.175395i
$844$		0			0
$845$	−1.35429e9	+	2.59836e8i	−2.24462	+	0.430655i
$846$		0			0
$847$	−4.68059e8	−	4.68059e8i	−0.770283	−	0.770283i
$848$		0			0
$849$		−	5.78859e8i		−	0.945909i
$850$		0			0
$851$	−5.99303e8			−0.972428
$852$		0			0
$853$	−2.04315e8	+	2.04315e8i	−0.329195	+	0.329195i	−0.852280	−	0.523085i	$-0.824781\pi$
$853$	−2.04315e8	+	2.04315e8i	−0.329195	+	0.329195i	0.523085	+	0.852280i	$0.324781\pi$
$854$		0			0
$855$	4.32381e7	+	2.25361e8i	0.0691781	+	0.360563i
$856$		0			0
$857$	−6.92490e8	−	6.92490e8i	−1.10020	−	1.10020i	−0.994386	−	0.105812i	$-0.966256\pi$
$857$	−6.92490e8	−	6.92490e8i	−1.10020	−	1.10020i	−0.105812	−	0.994386i	$-0.533744\pi$
$858$		0			0
$859$			1.16995e9i			1.84581i	0.385025	+	0.922906i	$0.374193\pi$
$859$			1.16995e9i			1.84581i	−0.385025	+	0.922906i	$0.625807\pi$
$860$		0			0
$861$	2.12833e8			0.333449
$862$		0			0
$863$	4.85739e8	−	4.85739e8i	0.755737	−	0.755737i	−0.219807	−	0.975543i	$-0.570543\pi$
$863$	4.85739e8	−	4.85739e8i	0.755737	−	0.755737i	0.975543	+	0.219807i	$0.0705427\pi$
$864$		0			0
$865$	3.17210e8	+	2.15083e8i	0.490115	+	0.332321i
$866$		0			0
$867$	−6.80489e8	−	6.80489e8i	−1.04415	−	1.04415i
$868$		0			0
$869$			7.05575e7i			0.107519i
$870$		0			0
$871$	−5.30487e8			−0.802824
$872$		0			0
$873$	−2.29646e7	+	2.29646e7i	−0.0345156	+	0.0345156i
$874$		0			0
$875$	−1.85747e8	+	8.43603e8i	−0.277267	+	1.25926i
$876$		0			0
$877$	−1.41359e8	−	1.41359e8i	−0.209568	−	0.209568i	0.594516	−	0.804084i	$-0.297344\pi$
$877$	−1.41359e8	−	1.41359e8i	−0.209568	−	0.209568i	−0.804084	+	0.594516i	$0.797344\pi$
$878$		0			0
$879$		−	4.01360e8i		−	0.590972i
$880$		0			0
$881$	−1.09131e8			−0.159595			−0.0797975	−	0.996811i	$-0.525427\pi$
$881$	−1.09131e8			−0.159595			−0.0797975	+	0.996811i	$0.525427\pi$
$882$		0			0
$883$	−3.96518e8	+	3.96518e8i	−0.575944	+	0.575944i	−0.933783	−	0.357839i	$-0.883514\pi$
$883$	−3.96518e8	+	3.96518e8i	−0.575944	+	0.575944i	0.357839	+	0.933783i	$0.383514\pi$
$884$		0			0
$885$	2.19324e8	−	3.23464e8i	0.316414	−	0.466655i
$886$		0			0
$887$	8.71187e8	+	8.71187e8i	1.24836	+	1.24836i	0.956443	+	0.291920i	$0.0942940\pi$
$887$	8.71187e8	+	8.71187e8i	1.24836	+	1.24836i	0.291920	+	0.956443i	$0.405706\pi$
$888$		0			0
$889$			3.75671e8i			0.534690i
$890$		0			0
$891$	3.09592e7			0.0437679
$892$		0			0
$893$	2.85713e8	−	2.85713e8i	0.401213	−	0.401213i
$894$		0			0
$895$	−2.71074e6	+	520086.i	−0.00378110	+	0.000725447i
$896$		0			0
$897$	5.43926e8	+	5.43926e8i	0.753638	+	0.753638i
$898$		0			0
$899$		−	1.12208e9i		−	1.54434i
$900$		0			0
$901$	−2.35099e9			−3.21423
$902$		0			0
$903$	1.50230e8	−	1.50230e8i	0.204029	−	0.204029i
$904$		0			0
$905$	1.12867e8	+	5.88276e8i	0.152273	+	0.793661i
$906$		0			0
$907$	1.20008e8	+	1.20008e8i	0.160838	+	0.160838i	0.782938	−	0.622100i	$-0.213720\pi$
$907$	1.20008e8	+	1.20008e8i	0.160838	+	0.160838i	−0.622100	+	0.782938i	$0.713720\pi$
$908$		0			0
$909$			3.39034e7i			0.0451390i
$910$		0			0
$911$	−8.44658e8			−1.11719			−0.558593	−	0.829442i	$-0.688659\pi$
$911$	−8.44658e8			−1.11719			−0.558593	+	0.829442i	$0.688659\pi$
$912$		0			0
$913$	−2.80586e8	+	2.80586e8i	−0.368684	+	0.368684i
$914$		0			0
$915$	−3.17559e7	−	2.15320e7i	−0.0414534	−	0.0281074i
$916$		0			0
$917$	4.15120e7	+	4.15120e7i	0.0538351	+	0.0538351i
$918$		0			0
$919$			8.94371e8i			1.15232i	0.817339	+	0.576158i	$0.195449\pi$
$919$			8.94371e8i			1.15232i	−0.817339	+	0.576158i	$0.804551\pi$
$920$		0			0
$921$	2.71316e8			0.347293
$922$		0			0
$923$	7.93277e8	−	7.93277e8i	1.00883	−	1.00883i
$924$		0			0
$925$	−6.94182e8	−	2.98650e8i	−0.877098	−	0.377344i
$926$		0			0
$927$	−2.43742e8	−	2.43742e8i	−0.305978	−	0.305978i
$928$		0			0
$929$			9.36762e8i			1.16837i	0.811619	+	0.584187i	$0.198587\pi$
$929$			9.36762e8i			1.16837i	−0.811619	+	0.584187i	$0.801413\pi$
$930$		0			0
$931$	5.88917e8			0.729802
$932$		0			0
$933$	−1.63893e7	+	1.63893e7i	−0.0201798	+	0.0201798i
$934$		0			0
$935$	3.40828e8	−	5.02661e8i	0.416966	−	0.614951i
$936$		0			0
$937$	−4.41572e7	−	4.41572e7i	−0.0536763	−	0.0536763i	0.679759	−	0.733435i	$-0.262084\pi$
$937$	−4.41572e7	−	4.41572e7i	−0.0536763	−	0.0536763i	−0.733435	+	0.679759i	$0.762084\pi$
$938$		0			0
$939$		−	2.72173e8i		−	0.328736i
$940$		0			0
$941$	3.95331e8			0.474452			0.237226	−	0.971455i	$-0.423762\pi$
$941$	3.95331e8			0.474452			0.237226	+	0.971455i	$0.423762\pi$
$942$		0			0
$943$	2.70489e8	−	2.70489e8i	0.322563	−	0.322563i
$944$		0			0
$945$	2.05664e8	−	3.94589e7i	0.243704	−	0.0467574i
$946$		0			0
$947$	8.00979e8	+	8.00979e8i	0.943129	+	0.943129i	0.998468	−	0.0553386i	$-0.0176238\pi$
$947$	8.00979e8	+	8.00979e8i	0.943129	+	0.943129i	−0.0553386	+	0.998468i	$0.517624\pi$
$948$		0			0
$949$		−	2.55871e9i		−	2.99379i
$950$		0			0
$951$	−1.87108e8			−0.217545
$952$		0			0
$953$	9.59999e8	−	9.59999e8i	1.10916	−	1.10916i	0.115893	−	0.993262i	$-0.463027\pi$
$953$	9.59999e8	−	9.59999e8i	1.10916	−	1.10916i	0.993262	−	0.115893i	$-0.0369731\pi$
$954$		0			0
$955$	3.19279e8	+	1.66411e9i	0.366572	+	1.91061i
$956$		0			0
$957$	1.35021e8	+	1.35021e8i	0.154052	+	0.154052i
$958$		0			0
$959$			1.10803e9i			1.25631i
$960$		0			0
$961$	1.41908e9			1.59896
$962$		0			0
$963$	1.07966e8	−	1.07966e8i	0.120895	−	0.120895i
$964$		0			0
$965$	−3.48939e8	−	2.36597e8i	−0.388300	−	0.263286i
$966$		0			0
$967$	4.20606e8	+	4.20606e8i	0.465153	+	0.465153i	0.900340	−	0.435187i	$-0.143318\pi$
$967$	4.20606e8	+	4.20606e8i	0.465153	+	0.465153i	−0.435187	+	0.900340i	$0.643318\pi$
$968$		0			0
$969$		−	1.09130e9i		−	1.19942i
$970$		0			0
$971$	−6.58106e8			−0.718850			−0.359425	−	0.933174i	$-0.617027\pi$
$971$	−6.58106e8			−0.718850			−0.359425	+	0.933174i	$0.617027\pi$
$972$		0			0
$973$	4.65021e8	−	4.65021e8i	0.504817	−	0.504817i
$974$		0			0
$975$	3.58984e8	+	9.01093e8i	0.387313	+	0.972201i
$976$		0			0
$977$	−7.52427e7	−	7.52427e7i	−0.0806828	−	0.0806828i	0.665614	−	0.746296i	$-0.268170\pi$
$977$	−7.52427e7	−	7.52427e7i	−0.0806828	−	0.0806828i	−0.746296	+	0.665614i	$0.768170\pi$
$978$		0			0
$979$		−	4.10038e7i		−	0.0436994i
$980$		0			0
$981$	1.62942e8			0.172594
$982$		0			0
$983$	−3.89903e8	+	3.89903e8i	−0.410484	+	0.410484i	−0.881907	−	0.471423i	$-0.843740\pi$
$983$	−3.89903e8	+	3.89903e8i	−0.410484	+	0.410484i	0.471423	+	0.881907i	$0.343740\pi$
$984$		0			0
$985$	−9.05012e8	+	1.33473e9i	−0.946991	+	1.39664i
$986$		0			0
$987$	−2.60740e8	−	2.60740e8i	−0.271179	−	0.271179i
$988$		0			0
$989$		−	3.81854e8i		−	0.394737i
$990$		0			0
$991$	−2.98613e8			−0.306823			−0.153411	−	0.988162i	$-0.549026\pi$
$991$	−2.98613e8			−0.306823			−0.153411	+	0.988162i	$0.549026\pi$
$992$		0			0
$993$	4.63226e8	−	4.63226e8i	0.473092	−	0.473092i
$994$		0			0
$995$	1.51274e9	−	2.90237e8i	1.53566	−	0.294634i
$996$		0			0
$997$	−2.31492e7	−	2.31492e7i	−0.0233588	−	0.0233588i	0.695331	−	0.718690i	$-0.255258\pi$
$997$	−2.31492e7	−	2.31492e7i	−0.0233588	−	0.0233588i	−0.718690	+	0.695331i	$0.755258\pi$
$998$		0			0
$999$			1.83205e8i			0.183756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.k.a.37.2	yes	12
3.2	odd	2		180.7.l.b.37.4		12
4.3	odd	2		240.7.bg.d.97.5		12
5.2	odd	4		300.7.k.d.193.4		12
5.3	odd	4	inner	60.7.k.a.13.2	✓	12
5.4	even	2		300.7.k.d.157.4		12
15.8	even	4		180.7.l.b.73.4		12
20.3	even	4		240.7.bg.d.193.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.k.a.13.2	✓	12	5.3	odd	4	inner
60.7.k.a.37.2	yes	12	1.1	even	1	trivial
180.7.l.b.37.4		12	3.2	odd	2
180.7.l.b.73.4		12	15.8	even	4
240.7.bg.d.97.5		12	4.3	odd	2
240.7.bg.d.193.5		12	20.3	even	4
300.7.k.d.157.4		12	5.4	even	2
300.7.k.d.193.4		12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.0227 + 11.0227i) q^{3} +(-23.5531 - 122.761i) q^{5} +(312.733 + 312.733i) q^{7} -243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 + 11.0227i) q^{3} +(-23.5531 - 122.761i) q^{5} +(312.733 + 312.733i) q^{7} -243.000i q^{9} -524.296 q^{11} +(-2815.91 + 2815.91i) q^{13} +(1612.78 + 1093.54i) q^{15} +(-6552.59 - 6552.59i) q^{17} -7554.63i q^{19} -6894.32 q^{21} +(-8761.99 + 8761.99i) q^{23} +(-14515.5 + 5782.80i) q^{25} +(2678.52 + 2678.52i) q^{27} +23363.5i q^{29} -48026.9 q^{31} +(5779.16 - 5779.16i) q^{33} +(31025.5 - 45757.2i) q^{35} +(34199.0 + 34199.0i) q^{37} -62078.0i q^{39} -30870.8 q^{41} +(-21790.4 + 21790.4i) q^{43} +(-29830.9 + 5723.40i) q^{45} +(37819.6 + 37819.6i) q^{47} +77954.4i q^{49} +144454. q^{51} +(179394. - 179394. i) q^{53} +(12348.8 + 64363.1i) q^{55} +(83272.4 + 83272.4i) q^{57} -200563. i q^{59} -19690.2 q^{61} +(75994.0 - 75994.0i) q^{63} +(412008. + 279361. i) q^{65} +(94194.5 + 94194.5i) q^{67} -193162. i q^{69} -281712. q^{71} +(-454330. + 454330. i) q^{73} +(96258.1 - 223742. i) q^{75} +(-163965. - 163965. i) q^{77} -134576. i q^{79} -59049.0 q^{81} +(535168. - 535168. i) q^{83} +(-650068. + 958736. i) q^{85} +(-257529. - 257529. i) q^{87} +78207.3i q^{89} -1.76126e6 q^{91} +(529386. - 529386. i) q^{93} +(-927413. + 177935. i) q^{95} +(-94504.5 - 94504.5i) q^{97} +127404. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) \) 12 * q + 312 * q^5 + 120 * q^7	\( 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) \) 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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