LMFDB - Embedded newform 70.6.c.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,6,Mod(29,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("70.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	70.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.2268673869$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	70.29
Dual form			70.6.c.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 + 10.0000i) q^{5} +49.0000i q^{7} +64.0000i q^{8} +243.000 q^{9} +(40.0000 + 220.000i) q^{10} +384.000 q^{11} +236.000i q^{13} +196.000 q^{14} +256.000 q^{16} +1172.00i q^{17} -972.000i q^{18} +1100.00 q^{19} +(880.000 - 160.000i) q^{20} -1536.00i q^{22} +1400.00i q^{23} +(2925.00 - 1100.00i) q^{25} +944.000 q^{26} -784.000i q^{28} +3854.00 q^{29} +88.0000 q^{31} -1024.00i q^{32} +4688.00 q^{34} +(-490.000 - 2695.00i) q^{35} -3888.00 q^{36} +13240.0i q^{37} -4400.00i q^{38} +(-640.000 - 3520.00i) q^{40} -13338.0 q^{41} -2504.00i q^{43} -6144.00 q^{44} +(-13365.0 + 2430.00i) q^{45} +5600.00 q^{46} +14728.0i q^{47} -2401.00 q^{49} +(-4400.00 - 11700.0i) q^{50} -3776.00i q^{52} +11232.0i q^{53} +(-21120.0 + 3840.00i) q^{55} -3136.00 q^{56} -15416.0i q^{58} -652.000 q^{59} -1494.00 q^{61} -352.000i q^{62} +11907.0i q^{63} -4096.00 q^{64} +(-2360.00 - 12980.0i) q^{65} -18232.0i q^{67} -18752.0i q^{68} +(-10780.0 + 1960.00i) q^{70} -28356.0 q^{71} +15552.0i q^{72} -70892.0i q^{73} +52960.0 q^{74} -17600.0 q^{76} +18816.0i q^{77} +79828.0 q^{79} +(-14080.0 + 2560.00i) q^{80} +59049.0 q^{81} +53352.0i q^{82} +83712.0i q^{83} +(-11720.0 - 64460.0i) q^{85} -10016.0 q^{86} +24576.0i q^{88} +93290.0 q^{89} +(9720.00 + 53460.0i) q^{90} -11564.0 q^{91} -22400.0i q^{92} +58912.0 q^{94} +(-60500.0 + 11000.0i) q^{95} -91068.0i q^{97} +9604.00i q^{98} +93312.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 110 q^{5} + 486 q^{9} + 80 q^{10} + 768 q^{11} + 392 q^{14} + 512 q^{16} + 2200 q^{19} + 1760 q^{20} + 5850 q^{25} + 1888 q^{26} + 7708 q^{29} + 176 q^{31} + 9376 q^{34} - 980 q^{35} - 7776 q^{36}+ \cdots + 186624 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 - 110 * q^5 + 486 * q^9 + 80 * q^10 + 768 * q^11 + 392 * q^14 + 512 * q^16 + 2200 * q^19 + 1760 * q^20 + 5850 * q^25 + 1888 * q^26 + 7708 * q^29 + 176 * q^31 + 9376 * q^34 - 980 * q^35 - 7776 * q^36 - 1280 * q^40 - 26676 * q^41 - 12288 * q^44 - 26730 * q^45 + 11200 * q^46 - 4802 * q^49 - 8800 * q^50 - 42240 * q^55 - 6272 * q^56 - 1304 * q^59 - 2988 * q^61 - 8192 * q^64 - 4720 * q^65 - 21560 * q^70 - 56712 * q^71 + 105920 * q^74 - 35200 * q^76 + 159656 * q^79 - 28160 * q^80 + 118098 * q^81 - 23440 * q^85 - 20032 * q^86 + 186580 * q^89 + 19440 * q^90 - 23128 * q^91 + 117824 * q^94 - 121000 * q^95 + 186624 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	−16.0000			−0.500000
$5$	−55.0000	+	10.0000i	−0.983870	+	0.178885i
$5$	−55.0000	+	10.0000i	−0.983870	+	0.178885i
$6$		0			0
$7$			49.0000i			0.377964i
$7$			49.0000i			0.377964i
$8$			64.0000i			0.353553i
$9$	243.000			1.00000
$10$	40.0000	+	220.000i	0.126491	+	0.695701i
$11$	384.000			0.956862			0.478431	−	0.878125i	$-0.341206\pi$
$11$	384.000			0.956862			0.478431	+	0.878125i	$0.341206\pi$
$12$		0			0
$13$			236.000i			0.387305i	0.981070	+	0.193653i	$0.0620335\pi$
$13$			236.000i			0.387305i	−0.981070	+	0.193653i	$0.937966\pi$
$14$	196.000			0.267261
$15$		0			0
$16$	256.000			0.250000
$17$			1172.00i			0.983570i	0.870717	+	0.491785i	$0.163655\pi$
$17$			1172.00i			0.983570i	−0.870717	+	0.491785i	$0.836345\pi$
$18$		−	972.000i		−	0.707107i
$19$	1100.00			0.699051			0.349525	−	0.936927i	$-0.386343\pi$
$19$	1100.00			0.699051			0.349525	+	0.936927i	$0.386343\pi$
$20$	880.000	−	160.000i	0.491935	−	0.0894427i
$21$		0			0
$22$		−	1536.00i		−	0.676604i
$23$			1400.00i			0.551834i	0.961181	+	0.275917i	$0.0889815\pi$
$23$			1400.00i			0.551834i	−0.961181	+	0.275917i	$0.911019\pi$
$24$		0			0
$25$	2925.00	−	1100.00i	0.936000	−	0.352000i
$26$	944.000			0.273866
$27$		0			0
$28$		−	784.000i		−	0.188982i
$29$	3854.00			0.850975			0.425487	−	0.904964i	$-0.360103\pi$
$29$	3854.00			0.850975			0.425487	+	0.904964i	$0.360103\pi$
$30$		0			0
$31$	88.0000			0.0164467			0.00822334	−	0.999966i	$-0.497382\pi$
$31$	88.0000			0.0164467			0.00822334	+	0.999966i	$0.497382\pi$
$32$		−	1024.00i		−	0.176777i
$33$		0			0
$34$	4688.00			0.695489
$35$	−490.000	−	2695.00i	−0.0676123	−	0.371868i
$36$	−3888.00			−0.500000
$37$			13240.0i			1.58995i	0.606642	+	0.794975i	$0.292516\pi$
$37$			13240.0i			1.58995i	−0.606642	+	0.794975i	$0.707484\pi$
$38$		−	4400.00i		−	0.494303i
$39$		0			0
$40$	−640.000	−	3520.00i	−0.0632456	−	0.347851i
$41$	−13338.0			−1.23917			−0.619585	−	0.784929i	$-0.712699\pi$
$41$	−13338.0			−1.23917			−0.619585	+	0.784929i	$0.712699\pi$
$42$		0			0
$43$		−	2504.00i		−	0.206521i	−0.994654	−	0.103260i	$-0.967073\pi$
$43$		−	2504.00i		−	0.206521i	0.994654	−	0.103260i	$-0.0329275\pi$
$44$	−6144.00			−0.478431
$45$	−13365.0	+	2430.00i	−0.983870	+	0.178885i
$46$	5600.00			0.390206
$47$			14728.0i			0.972521i	0.873814	+	0.486261i	$0.161639\pi$
$47$			14728.0i			0.972521i	−0.873814	+	0.486261i	$0.838361\pi$
$48$		0			0
$49$	−2401.00			−0.142857
$50$	−4400.00	−	11700.0i	−0.248902	−	0.661852i
$51$		0			0
$52$		−	3776.00i		−	0.193653i
$53$			11232.0i			0.549247i	0.961552	+	0.274623i	$0.0885532\pi$
$53$			11232.0i			0.549247i	−0.961552	+	0.274623i	$0.911447\pi$
$54$		0			0
$55$	−21120.0	+	3840.00i	−0.941428	+	0.171169i
$56$	−3136.00			−0.133631
$57$		0			0
$58$		−	15416.0i		−	0.601730i
$59$	−652.000			−0.0243847			−0.0121924	−	0.999926i	$-0.503881\pi$
$59$	−652.000			−0.0243847			−0.0121924	+	0.999926i	$0.503881\pi$
$60$		0			0
$61$	−1494.00			−0.0514074			−0.0257037	−	0.999670i	$-0.508183\pi$
$61$	−1494.00			−0.0514074			−0.0257037	+	0.999670i	$0.508183\pi$
$62$		−	352.000i		−	0.0116296i
$63$			11907.0i			0.377964i
$64$	−4096.00			−0.125000
$65$	−2360.00	−	12980.0i	−0.0692833	−	0.381058i
$66$		0			0
$67$		−	18232.0i		−	0.496189i	−0.968736	−	0.248095i	$-0.920196\pi$
$67$		−	18232.0i		−	0.496189i	0.968736	−	0.248095i	$-0.0798044\pi$
$68$		−	18752.0i		−	0.491785i
$69$		0			0
$70$	−10780.0	+	1960.00i	−0.262950	+	0.0478091i
$71$	−28356.0			−0.667574			−0.333787	−	0.942649i	$-0.608327\pi$
$71$	−28356.0			−0.667574			−0.333787	+	0.942649i	$0.608327\pi$
$72$			15552.0i			0.353553i
$73$		−	70892.0i		−	1.55701i	−0.627641	−	0.778503i	$-0.715980\pi$
$73$		−	70892.0i		−	1.55701i	0.627641	−	0.778503i	$-0.284020\pi$
$74$	52960.0			1.12426
$75$		0			0
$76$	−17600.0			−0.349525
$77$			18816.0i			0.361660i
$78$		0			0
$79$	79828.0			1.43909			0.719544	−	0.694447i	$-0.244351\pi$
$79$	79828.0			1.43909			0.719544	+	0.694447i	$0.244351\pi$
$80$	−14080.0	+	2560.00i	−0.245967	+	0.0447214i
$81$	59049.0			1.00000
$82$			53352.0i			0.876226i
$83$			83712.0i			1.33381i	0.745145	+	0.666903i	$0.232380\pi$
$83$			83712.0i			1.33381i	−0.745145	+	0.666903i	$0.767620\pi$
$84$		0			0
$85$	−11720.0	−	64460.0i	−0.175946	−	0.967705i
$86$	−10016.0			−0.146032
$87$		0			0
$88$			24576.0i			0.338302i
$89$	93290.0			1.24842			0.624209	−	0.781257i	$-0.285421\pi$
$89$	93290.0			1.24842			0.624209	+	0.781257i	$0.285421\pi$
$90$	9720.00	+	53460.0i	0.126491	+	0.695701i
$91$	−11564.0			−0.146388
$92$		−	22400.0i		−	0.275917i
$93$		0			0
$94$	58912.0			0.687676
$95$	−60500.0	+	11000.0i	−0.687775	+	0.125050i
$96$		0			0
$97$		−	91068.0i		−	0.982735i	−0.870952	−	0.491368i	$-0.836497\pi$
$97$		−	91068.0i		−	0.982735i	0.870952	−	0.491368i	$-0.163503\pi$
$98$			9604.00i			0.101015i
$99$	93312.0			0.956862
$100$	−46800.0	+	17600.0i	−0.468000	+	0.176000i
$101$	−54306.0			−0.529718			−0.264859	−	0.964287i	$-0.585325\pi$
$101$	−54306.0			−0.529718			−0.264859	+	0.964287i	$0.585325\pi$
$102$		0			0
$103$			135944.i			1.26260i	0.775537	+	0.631302i	$0.217479\pi$
$103$			135944.i			1.26260i	−0.775537	+	0.631302i	$0.782521\pi$
$104$	−15104.0			−0.136933
$105$		0			0
$106$	44928.0			0.388376
$107$			77512.0i			0.654500i	0.944938	+	0.327250i	$0.106122\pi$
$107$			77512.0i			0.654500i	−0.944938	+	0.327250i	$0.893878\pi$
$108$		0			0
$109$	151714.			1.22309			0.611546	−	0.791209i	$-0.290548\pi$
$109$	151714.			1.22309			0.611546	+	0.791209i	$0.290548\pi$
$110$	15360.0	+	84480.0i	0.121035	+	0.665690i
$111$		0			0
$112$			12544.0i			0.0944911i
$113$		−	235312.i		−	1.73360i	−0.498659	−	0.866798i	$-0.666174\pi$
$113$		−	235312.i		−	1.73360i	0.498659	−	0.866798i	$-0.333826\pi$
$114$		0			0
$115$	−14000.0	−	77000.0i	−0.0987151	−	0.542933i
$116$	−61664.0			−0.425487
$117$			57348.0i			0.387305i
$118$			2608.00i			0.0172426i
$119$	−57428.0			−0.371755
$120$		0			0
$121$	−13595.0			−0.0844143
$122$			5976.00i			0.0363506i
$123$		0			0
$124$	−1408.00			−0.00822334
$125$	−149875.	+	89750.0i	−0.857935	+	0.513759i
$126$	47628.0			0.267261
$127$		−	341768.i		−	1.88028i	−0.340791	−	0.940139i	$-0.610695\pi$
$127$		−	341768.i		−	1.88028i	0.340791	−	0.940139i	$-0.389305\pi$
$128$			16384.0i			0.0883883i
$129$		0			0
$130$	−51920.0	+	9440.00i	−0.269449	+	0.0489907i
$131$	−308276.			−1.56950			−0.784750	−	0.619812i	$-0.787209\pi$
$131$	−308276.			−1.56950			−0.784750	+	0.619812i	$0.787209\pi$
$132$		0			0
$133$			53900.0i			0.264216i
$134$	−72928.0			−0.350859
$135$		0			0
$136$	−75008.0			−0.347745
$137$		−	348136.i		−	1.58470i	−0.610066	−	0.792351i	$-0.708857\pi$
$137$		−	348136.i		−	1.58470i	0.610066	−	0.792351i	$-0.291143\pi$
$138$		0			0
$139$	292364.			1.28347			0.641737	−	0.766925i	$-0.278214\pi$
$139$	292364.			1.28347			0.641737	+	0.766925i	$0.278214\pi$
$140$	7840.00	+	43120.0i	0.0338062	+	0.185934i
$141$		0			0
$142$			113424.i			0.472046i
$143$			90624.0i			0.370598i
$144$	62208.0			0.250000
$145$	−211970.	+	38540.0i	−0.837249	+	0.152227i
$146$	−283568.			−1.10097
$147$		0			0
$148$		−	211840.i		−	0.794975i
$149$	−178806.			−0.659806			−0.329903	−	0.944015i	$-0.607016\pi$
$149$	−178806.			−0.659806			−0.329903	+	0.944015i	$0.607016\pi$
$150$		0			0
$151$	−173892.			−0.620636			−0.310318	−	0.950633i	$-0.600436\pi$
$151$	−173892.			−0.620636			−0.310318	+	0.950633i	$0.600436\pi$
$152$			70400.0i			0.247152i
$153$			284796.i			0.983570i
$154$	75264.0			0.255732
$155$	−4840.00	+	880.000i	−0.0161814	+	0.00294207i
$156$		0			0
$157$		−	228540.i		−	0.739968i	−0.929038	−	0.369984i	$-0.879363\pi$
$157$		−	228540.i		−	0.739968i	0.929038	−	0.369984i	$-0.120637\pi$
$158$		−	319312.i		−	1.01759i
$159$		0			0
$160$	10240.0	+	56320.0i	0.0316228	+	0.173925i
$161$	−68600.0			−0.208574
$162$		−	236196.i		−	0.707107i
$163$			609624.i			1.79719i	0.438783	+	0.898593i	$0.355410\pi$
$163$			609624.i			1.79719i	−0.438783	+	0.898593i	$0.644590\pi$
$164$	213408.			0.619585
$165$		0			0
$166$	334848.			0.943143
$167$			648600.i			1.79964i	0.436261	+	0.899820i	$0.356303\pi$
$167$			648600.i			1.79964i	−0.436261	+	0.899820i	$0.643697\pi$
$168$		0			0
$169$	315597.			0.849994
$170$	−257840.	+	46880.0i	−0.684271	+	0.124413i
$171$	267300.			0.699051
$172$			40064.0i			0.103260i
$173$			127812.i			0.324681i	0.986735	+	0.162340i	$0.0519042\pi$
$173$			127812.i			0.324681i	−0.986735	+	0.162340i	$0.948096\pi$
$174$		0			0
$175$	53900.0	+	143325.i	0.133043	+	0.353775i
$176$	98304.0			0.239216
$177$		0			0
$178$		−	373160.i		−	0.882765i
$179$	−637208.			−1.48644			−0.743222	−	0.669045i	$-0.766703\pi$
$179$	−637208.			−1.48644			−0.743222	+	0.669045i	$0.766703\pi$
$180$	213840.	−	38880.0i	0.491935	−	0.0894427i
$181$	461246.			1.04649			0.523246	−	0.852181i	$-0.324721\pi$
$181$	461246.			1.04649			0.523246	+	0.852181i	$0.324721\pi$
$182$			46256.0i			0.103512i
$183$		0			0
$184$	−89600.0			−0.195103
$185$	−132400.	−	728200.i	−0.284419	−	1.56430i
$186$		0			0
$187$			450048.i			0.941141i
$188$		−	235648.i		−	0.486261i
$189$		0			0
$190$	44000.0	+	242000.i	0.0884237	+	0.486330i
$191$	356444.			0.706981			0.353491	−	0.935438i	$-0.384995\pi$
$191$	356444.			0.706981			0.353491	+	0.935438i	$0.384995\pi$
$192$		0			0
$193$			191248.i			0.369576i	0.982778	+	0.184788i	$0.0591598\pi$
$193$			191248.i			0.369576i	−0.982778	+	0.184788i	$0.940840\pi$
$194$	−364272.			−0.694899
$195$		0			0
$196$	38416.0			0.0714286
$197$		−	624976.i		−	1.14735i	−0.819081	−	0.573677i	$-0.805516\pi$
$197$		−	624976.i		−	1.14735i	0.819081	−	0.573677i	$-0.194484\pi$
$198$		−	373248.i		−	0.676604i
$199$	247416.			0.442889			0.221445	−	0.975173i	$-0.428923\pi$
$199$	247416.			0.442889			0.221445	+	0.975173i	$0.428923\pi$
$200$	70400.0	+	187200.i	0.124451	+	0.330926i
$201$		0			0
$202$			217224.i			0.374567i
$203$			188846.i			0.321638i
$204$		0			0
$205$	733590.	−	133380.i	1.21918	−	0.221670i
$206$	543776.			0.892795
$207$			340200.i			0.551834i
$208$			60416.0i			0.0968264i
$209$	422400.			0.668895
$210$		0			0
$211$	300984.			0.465412			0.232706	−	0.972547i	$-0.425242\pi$
$211$	300984.			0.465412			0.232706	+	0.972547i	$0.425242\pi$
$212$		−	179712.i		−	0.274623i
$213$		0			0
$214$	310048.			0.462801
$215$	25040.0	+	137720.i	0.0369435	+	0.203189i
$216$		0			0
$217$			4312.00i			0.00621626i
$218$		−	606856.i		−	0.864857i
$219$		0			0
$220$	337920.	−	61440.0i	0.470714	−	0.0855844i
$221$	−276592.			−0.380942
$222$		0			0
$223$		−	102136.i		−	0.137536i	−0.997633	−	0.0687680i	$-0.978093\pi$
$223$		−	102136.i		−	0.137536i	0.997633	−	0.0687680i	$-0.0219068\pi$
$224$	50176.0			0.0668153
$225$	710775.	−	267300.i	0.936000	−	0.352000i
$226$	−941248.			−1.22584
$227$			595968.i			0.767641i	0.923408	+	0.383821i	$0.125392\pi$
$227$			595968.i			0.767641i	−0.923408	+	0.383821i	$0.874608\pi$
$228$		0			0
$229$	−1.01543e6			−1.27956			−0.639778	−	0.768559i	$-0.720974\pi$
$229$	−1.01543e6			−1.27956			−0.639778	+	0.768559i	$0.720974\pi$
$230$	−308000.	+	56000.0i	−0.383912	+	0.0698021i
$231$		0			0
$232$			246656.i			0.300865i
$233$		−	23384.0i		−	0.0282182i	−0.999900	−	0.0141091i	$-0.995509\pi$
$233$		−	23384.0i		−	0.0282182i	0.999900	−	0.0141091i	$-0.00449121\pi$
$234$	229392.			0.273866
$235$	−147280.	−	810040.i	−0.173970	−	0.956834i
$236$	10432.0			0.0121924
$237$		0			0
$238$			229712.i			0.262870i
$239$	−1.15844e6			−1.31183			−0.655915	−	0.754835i	$-0.727717\pi$
$239$	−1.15844e6			−1.31183			−0.655915	+	0.754835i	$0.727717\pi$
$240$		0			0
$241$	−977490.			−1.08410			−0.542050	−	0.840346i	$-0.682352\pi$
$241$	−977490.			−1.08410			−0.542050	+	0.840346i	$0.682352\pi$
$242$			54380.0i			0.0596899i
$243$		0			0
$244$	23904.0			0.0257037
$245$	132055.	−	24010.0i	0.140553	−	0.0255551i
$246$		0			0
$247$			259600.i			0.270746i
$248$			5632.00i			0.00581478i
$249$		0			0
$250$	359000.	+	599500.i	0.363282	+	0.606651i
$251$	−835700.			−0.837271			−0.418636	−	0.908154i	$-0.637492\pi$
$251$	−835700.			−0.837271			−0.418636	+	0.908154i	$0.637492\pi$
$252$		−	190512.i		−	0.188982i
$253$			537600.i			0.528029i
$254$	−1.36707e6			−1.32956
$255$		0			0
$256$	65536.0			0.0625000
$257$		−	587772.i		−	0.555106i	−0.960710	−	0.277553i	$-0.910477\pi$
$257$		−	587772.i		−	0.555106i	0.960710	−	0.277553i	$-0.0895234\pi$
$258$		0			0
$259$	−648760.			−0.600945
$260$	37760.0	+	207680.i	0.0346417	+	0.190529i
$261$	936522.			0.850975
$262$			1.23310e6i			1.10980i
$263$			149352.i			0.133144i	0.997782	+	0.0665720i	$0.0212062\pi$
$263$			149352.i			0.133144i	−0.997782	+	0.0665720i	$0.978794\pi$
$264$		0			0
$265$	−112320.	−	617760.i	−0.0982522	−	0.540387i
$266$	215600.			0.186829
$267$		0			0
$268$			291712.i			0.248095i
$269$	−2.00973e6			−1.69339			−0.846697	−	0.532076i	$-0.821412\pi$
$269$	−2.00973e6			−1.69339			−0.846697	+	0.532076i	$0.821412\pi$
$270$		0			0
$271$	499200.			0.412906			0.206453	−	0.978457i	$-0.433808\pi$
$271$	499200.			0.412906			0.206453	+	0.978457i	$0.433808\pi$
$272$			300032.i			0.245893i
$273$		0			0
$274$	−1.39254e6			−1.12055
$275$	1.12320e6	−	422400.i	0.895623	−	0.336816i
$276$		0			0
$277$		−	1.03093e6i		−	0.807289i	−0.914916	−	0.403644i	$-0.867743\pi$
$277$		−	1.03093e6i		−	0.807289i	0.914916	−	0.403644i	$-0.132257\pi$
$278$		−	1.16946e6i		−	0.907553i
$279$	21384.0			0.0164467
$280$	172480.	−	31360.0i	0.131475	−	0.0239046i
$281$	1.12849e6			0.852571			0.426285	−	0.904589i	$-0.359822\pi$
$281$	1.12849e6			0.852571			0.426285	+	0.904589i	$0.359822\pi$
$282$		0			0
$283$		−	49952.0i		−	0.0370755i	−0.999828	−	0.0185377i	$-0.994099\pi$
$283$		−	49952.0i		−	0.0370755i	0.999828	−	0.0185377i	$-0.00590108\pi$
$284$	453696.			0.333787
$285$		0			0
$286$	362496.			0.262052
$287$		−	653562.i		−	0.468362i
$288$		−	248832.i		−	0.176777i
$289$	46273.0			0.0325899
$290$	154160.	+	847880.i	0.107641	+	0.592024i
$291$		0			0
$292$			1.13427e6i			0.778503i
$293$			86340.0i			0.0587548i	0.999568	+	0.0293774i	$0.00935245\pi$
$293$			86340.0i			0.0587548i	−0.999568	+	0.0293774i	$0.990648\pi$
$294$		0			0
$295$	35860.0	−	6520.00i	0.0239914	−	0.00436207i
$296$	−847360.			−0.562132
$297$		0			0
$298$			715224.i			0.466553i
$299$	−330400.			−0.213728
$300$		0			0
$301$	122696.			0.0780574
$302$			695568.i			0.438856i
$303$		0			0
$304$	281600.			0.174763
$305$	82170.0	−	14940.0i	0.0505782	−	0.00919604i
$306$	1.13918e6			0.695489
$307$		−	2.86581e6i		−	1.73541i	−0.497083	−	0.867703i	$-0.665595\pi$
$307$		−	2.86581e6i		−	1.73541i	0.497083	−	0.867703i	$-0.334405\pi$
$308$		−	301056.i		−	0.180830i
$309$		0			0
$310$	3520.00	+	19360.0i	0.00208036	+	0.0114420i
$311$	−374904.			−0.219796			−0.109898	−	0.993943i	$-0.535052\pi$
$311$	−374904.			−0.219796			−0.109898	+	0.993943i	$0.535052\pi$
$312$		0			0
$313$		−	1.99147e6i		−	1.14898i	−0.818512	−	0.574490i	$-0.805200\pi$
$313$		−	1.99147e6i		−	1.14898i	0.818512	−	0.574490i	$-0.194800\pi$
$314$	−914160.			−0.523237
$315$	−119070.	−	654885.i	−0.0676123	−	0.371868i
$316$	−1.27725e6			−0.719544
$317$		−	417808.i		−	0.233522i	−0.993160	−	0.116761i	$-0.962749\pi$
$317$		−	417808.i		−	0.233522i	0.993160	−	0.116761i	$-0.0372512\pi$
$318$		0			0
$319$	1.47994e6			0.814266
$320$	225280.	−	40960.0i	0.122984	−	0.0223607i
$321$		0			0
$322$			274400.i			0.147484i
$323$			1.28920e6i			0.687565i
$324$	−944784.			−0.500000
$325$	259600.	+	690300.i	0.136332	+	0.362518i
$326$	2.43850e6			1.27080
$327$		0			0
$328$		−	853632.i		−	0.438113i
$329$	−721672.			−0.367579
$330$		0			0
$331$	3.22654e6			1.61870			0.809352	−	0.587323i	$-0.199818\pi$
$331$	3.22654e6			1.61870			0.809352	+	0.587323i	$0.199818\pi$
$332$		−	1.33939e6i		−	0.666903i
$333$			3.21732e6i			1.58995i
$334$	2.59440e6			1.27254
$335$	182320.	+	1.00276e6i	0.0887610	+	0.488186i
$336$		0			0
$337$			2.97302e6i			1.42601i	0.701159	+	0.713005i	$0.252666\pi$
$337$			2.97302e6i			1.42601i	−0.701159	+	0.713005i	$0.747334\pi$
$338$		−	1.26239e6i		−	0.601037i
$339$		0			0
$340$	187520.	+	1.03136e6i	0.0879732	+	0.483853i
$341$	33792.0			0.0157372
$342$		−	1.06920e6i		−	0.494303i
$343$		−	117649.i		−	0.0539949i
$344$	160256.			0.0730160
$345$		0			0
$346$	511248.			0.229584
$347$			584664.i			0.260665i	0.991470	+	0.130332i	$0.0416045\pi$
$347$			584664.i			0.260665i	−0.991470	+	0.130332i	$0.958396\pi$
$348$		0			0
$349$	3.62799e6			1.59442			0.797210	−	0.603703i	$-0.206309\pi$
$349$	3.62799e6			1.59442			0.797210	+	0.603703i	$0.206309\pi$
$350$	573300.	−	215600.i	0.250157	−	0.0940760i
$351$		0			0
$352$		−	393216.i		−	0.169151i
$353$			1.62880e6i			0.695713i	0.937548	+	0.347856i	$0.113090\pi$
$353$			1.62880e6i			0.695713i	−0.937548	+	0.347856i	$0.886910\pi$
$354$		0			0
$355$	1.55958e6	−	283560.i	0.656805	−	0.119419i
$356$	−1.49264e6			−0.624209
$357$		0			0
$358$			2.54883e6i			1.05107i
$359$	606052.			0.248184			0.124092	−	0.992271i	$-0.460398\pi$
$359$	606052.			0.248184			0.124092	+	0.992271i	$0.460398\pi$
$360$	−155520.	−	855360.i	−0.0632456	−	0.347851i
$361$	−1.26610e6			−0.511328
$362$		−	1.84498e6i		−	0.739982i
$363$		0			0
$364$	185024.			0.0731939
$365$	708920.	+	3.89906e6i	0.278526	+	1.53189i
$366$		0			0
$367$		−	2.15002e6i		−	0.833255i	−0.909077	−	0.416628i	$-0.863212\pi$
$367$		−	2.15002e6i		−	0.833255i	0.909077	−	0.416628i	$-0.136788\pi$
$368$			358400.i			0.137958i
$369$	−3.24113e6			−1.23917
$370$	−2.91280e6	+	529600.i	−1.10613	+	0.201115i
$371$	−550368.			−0.207596
$372$		0			0
$373$			1.64186e6i			0.611031i	0.952187	+	0.305515i	$0.0988287\pi$
$373$			1.64186e6i			0.611031i	−0.952187	+	0.305515i	$0.901171\pi$
$374$	1.80019e6			0.665487
$375$		0			0
$376$	−942592.			−0.343838
$377$			909544.i			0.329587i
$378$		0			0
$379$	−4.00041e6			−1.43056			−0.715280	−	0.698838i	$-0.753701\pi$
$379$	−4.00041e6			−1.43056			−0.715280	+	0.698838i	$0.753701\pi$
$380$	968000.	−	176000.i	0.343887	−	0.0625250i
$381$		0			0
$382$		−	1.42578e6i		−	0.499911i
$383$		−	5.71586e6i		−	1.99106i	−0.0944312	−	0.995531i	$-0.530103\pi$
$383$		−	5.71586e6i		−	1.99106i	0.0944312	−	0.995531i	$-0.469897\pi$
$384$		0			0
$385$	−188160.	−	1.03488e6i	−0.0646957	−	0.355826i
$386$	764992.			0.261330
$387$		−	608472.i		−	0.206521i
$388$			1.45709e6i			0.491368i
$389$	1.67611e6			0.561600			0.280800	−	0.959766i	$-0.409400\pi$
$389$	1.67611e6			0.561600			0.280800	+	0.959766i	$0.409400\pi$
$390$		0			0
$391$	−1.64080e6			−0.542767
$392$		−	153664.i		−	0.0505076i
$393$		0			0
$394$	−2.49990e6			−0.811302
$395$	−4.39054e6	+	798280.i	−1.41588	+	0.257432i
$396$	−1.49299e6			−0.478431
$397$		−	945140.i		−	0.300968i	−0.988612	−	0.150484i	$-0.951917\pi$
$397$		−	945140.i		−	0.300968i	0.988612	−	0.150484i	$-0.0480832\pi$
$398$		−	989664.i		−	0.313170i
$399$		0			0
$400$	748800.	−	281600.i	0.234000	−	0.0880000i
$401$	552786.			0.171671			0.0858353	−	0.996309i	$-0.472644\pi$
$401$	552786.			0.171671			0.0858353	+	0.996309i	$0.472644\pi$
$402$		0			0
$403$			20768.0i			0.00636989i
$404$	868896.			0.264859
$405$	−3.24770e6	+	590490.i	−0.983870	+	0.178885i
$406$	755384.			0.227433
$407$			5.08416e6i			1.52136i
$408$		0			0
$409$	1.04783e6			0.309729			0.154865	−	0.987936i	$-0.450506\pi$
$409$	1.04783e6			0.309729			0.154865	+	0.987936i	$0.450506\pi$
$410$	−533520.	−	2.93436e6i	−0.156744	−	0.862092i
$411$		0			0
$412$		−	2.17510e6i		−	0.631302i
$413$		−	31948.0i		−	0.00921655i
$414$	1.36080e6			0.390206
$415$	−837120.	−	4.60416e6i	−0.238598	−	1.31229i
$416$	241664.			0.0684666
$417$		0			0
$418$		−	1.68960e6i		−	0.472980i
$419$	6.88344e6			1.91545			0.957724	−	0.287690i	$-0.0928872\pi$
$419$	6.88344e6			1.91545			0.957724	+	0.287690i	$0.0928872\pi$
$420$		0			0
$421$	−4.56311e6			−1.25475			−0.627373	−	0.778719i	$-0.715870\pi$
$421$	−4.56311e6			−1.25475			−0.627373	+	0.778719i	$0.715870\pi$
$422$		−	1.20394e6i		−	0.329096i
$423$			3.57890e6i			0.972521i
$424$	−718848.			−0.194188
$425$	1.28920e6	+	3.42810e6i	0.346217	+	0.920622i
$426$		0			0
$427$		−	73206.0i		−	0.0194302i
$428$		−	1.24019e6i		−	0.327250i
$429$		0			0
$430$	550880.	−	100160.i	0.143677	−	0.0261230i
$431$	−2.49110e6			−0.645949			−0.322974	−	0.946408i	$-0.604683\pi$
$431$	−2.49110e6			−0.645949			−0.322974	+	0.946408i	$0.604683\pi$
$432$		0			0
$433$		−	4.42817e6i		−	1.13502i	−0.823365	−	0.567512i	$-0.807906\pi$
$433$		−	4.42817e6i		−	1.13502i	0.823365	−	0.567512i	$-0.192094\pi$
$434$	17248.0			0.00439556
$435$		0			0
$436$	−2.42742e6			−0.611546
$437$			1.54000e6i			0.385760i
$438$		0			0
$439$	−635432.			−0.157365			−0.0786824	−	0.996900i	$-0.525071\pi$
$439$	−635432.			−0.157365			−0.0786824	+	0.996900i	$0.525071\pi$
$440$	−245760.	−	1.35168e6i	−0.0605173	−	0.332845i
$441$	−583443.			−0.142857
$442$			1.10637e6i			0.269367i
$443$			1.80612e6i			0.437258i	0.975808	+	0.218629i	$0.0701584\pi$
$443$			1.80612e6i			0.437258i	−0.975808	+	0.218629i	$0.929842\pi$
$444$		0			0
$445$	−5.13095e6	+	932900.i	−1.22828	+	0.223324i
$446$	−408544.			−0.0972527
$447$		0			0
$448$		−	200704.i		−	0.0472456i
$449$	3.90323e6			0.913710			0.456855	−	0.889541i	$-0.348976\pi$
$449$	3.90323e6			0.913710			0.456855	+	0.889541i	$0.348976\pi$
$450$	−1.06920e6	−	2.84310e6i	−0.248902	−	0.661852i
$451$	−5.12179e6			−1.18572
$452$			3.76499e6i			0.866798i
$453$		0			0
$454$	2.38387e6			0.542804
$455$	636020.	−	115640.i	0.144026	−	0.0261866i
$456$		0			0
$457$		−	4.36264e6i		−	0.977145i	−0.872523	−	0.488572i	$-0.837518\pi$
$457$		−	4.36264e6i		−	0.977145i	0.872523	−	0.488572i	$-0.162482\pi$
$458$			4.06170e6i			0.904783i
$459$		0			0
$460$	224000.	+	1.23200e6i	0.0493575	+	0.271466i
$461$	846710.			0.185559			0.0927796	−	0.995687i	$-0.470425\pi$
$461$	846710.			0.185559			0.0927796	+	0.995687i	$0.470425\pi$
$462$		0			0
$463$		−	7.37970e6i		−	1.59988i	−0.600082	−	0.799938i	$-0.704866\pi$
$463$		−	7.37970e6i		−	1.59988i	0.600082	−	0.799938i	$-0.295134\pi$
$464$	986624.			0.212744
$465$		0			0
$466$	−93536.0			−0.0199533
$467$			2.88296e6i			0.611711i	0.952078	+	0.305856i	$0.0989425\pi$
$467$			2.88296e6i			0.611711i	−0.952078	+	0.305856i	$0.901058\pi$
$468$		−	917568.i		−	0.193653i
$469$	893368.			0.187542
$470$	−3.24016e6	+	589120.i	−0.676584	+	0.123015i
$471$		0			0
$472$		−	41728.0i		−	0.00862130i
$473$		−	961536.i		−	0.197612i
$474$		0			0
$475$	3.21750e6	−	1.21000e6i	0.654311	−	0.246066i
$476$	918848.			0.185877
$477$			2.72938e6i			0.549247i
$478$			4.63374e6i			0.927603i
$479$	6.63322e6			1.32095			0.660473	−	0.750849i	$-0.270356\pi$
$479$	6.63322e6			1.32095			0.660473	+	0.750849i	$0.270356\pi$
$480$		0			0
$481$	−3.12464e6			−0.615797
$482$			3.90996e6i			0.766575i
$483$		0			0
$484$	217520.			0.0422071
$485$	910680.	+	5.00874e6i	0.175797	+	0.966883i
$486$		0			0
$487$			2.17919e6i			0.416364i	0.978090	+	0.208182i	$0.0667546\pi$
$487$			2.17919e6i			0.416364i	−0.978090	+	0.208182i	$0.933245\pi$
$488$		−	95616.0i		−	0.0181753i
$489$		0			0
$490$	−96040.0	−	528220.i	−0.0180702	−	0.0993859i
$491$	7.92307e6			1.48317			0.741583	−	0.670861i	$-0.234075\pi$
$491$	7.92307e6			1.48317			0.741583	+	0.670861i	$0.234075\pi$
$492$		0			0
$493$			4.51689e6i			0.836993i
$494$	1.03840e6			0.191446
$495$	−5.13216e6	+	933120.i	−0.941428	+	0.171169i
$496$	22528.0			0.00411167
$497$		−	1.38944e6i		−	0.252319i
$498$		0			0
$499$	2.68311e6			0.482378			0.241189	−	0.970478i	$-0.422463\pi$
$499$	2.68311e6			0.482378			0.241189	+	0.970478i	$0.422463\pi$
$500$	2.39800e6	−	1.43600e6i	0.428967	−	0.256879i
$501$		0			0
$502$			3.34280e6i			0.592040i
$503$		−	5.90502e6i		−	1.04064i	−0.853971	−	0.520321i	$-0.825812\pi$
$503$		−	5.90502e6i		−	1.04064i	0.853971	−	0.520321i	$-0.174188\pi$
$504$	−762048.			−0.133631
$505$	2.98683e6	−	543060.i	0.521173	−	0.0947588i
$506$	2.15040e6			0.373373
$507$		0			0
$508$			5.46829e6i			0.940139i
$509$	2.57879e6			0.441186			0.220593	−	0.975366i	$-0.429201\pi$
$509$	2.57879e6			0.441186			0.220593	+	0.975366i	$0.429201\pi$
$510$		0			0
$511$	3.47371e6			0.588493
$512$		−	262144.i		−	0.0441942i
$513$		0			0
$514$	−2.35109e6			−0.392519
$515$	−1.35944e6	−	7.47692e6i	−0.225861	−	1.24224i
$516$		0			0
$517$			5.65555e6i			0.930569i
$518$			2.59504e6i			0.424932i
$519$		0			0
$520$	830720.	−	151040.i	0.134724	−	0.0244953i
$521$	1.03587e7			1.67190			0.835950	−	0.548806i	$-0.184917\pi$
$521$	1.03587e7			1.67190			0.835950	+	0.548806i	$0.184917\pi$
$522$		−	3.74609e6i		−	0.601730i
$523$		−	1.02151e7i		−	1.63301i	−0.577335	−	0.816507i	$-0.695908\pi$
$523$		−	1.02151e7i		−	1.63301i	0.577335	−	0.816507i	$-0.304092\pi$
$524$	4.93242e6			0.784750
$525$		0			0
$526$	597408.			0.0941470
$527$			103136.i			0.0161765i
$528$		0			0
$529$	4.47634e6			0.695479
$530$	−2.47104e6	+	449280.i	−0.382111	+	0.0694748i
$531$	−158436.			−0.0243847
$532$		−	862400.i		−	0.132108i
$533$		−	3.14777e6i		−	0.479938i
$534$		0			0
$535$	−775120.	−	4.26316e6i	−0.117080	−	0.643943i
$536$	1.16685e6			0.175429
$537$		0			0
$538$			8.03894e6i			1.19741i
$539$	−921984.			−0.136695
$540$		0			0
$541$	−3.21546e6			−0.472335			−0.236167	−	0.971712i	$-0.575891\pi$
$541$	−3.21546e6			−0.472335			−0.236167	+	0.971712i	$0.575891\pi$
$542$		−	1.99680e6i		−	0.291969i
$543$		0			0
$544$	1.20013e6			0.173872
$545$	−8.34427e6	+	1.51714e6i	−1.20336	+	0.218793i
$546$		0			0
$547$		−	3.71041e6i		−	0.530217i	−0.964219	−	0.265108i	$-0.914592\pi$
$547$		−	3.71041e6i		−	0.530217i	0.964219	−	0.265108i	$-0.0854077\pi$
$548$			5.57018e6i			0.792351i
$549$	−363042.			−0.0514074
$550$	−1.68960e6	−	4.49280e6i	−0.238165	−	0.633301i
$551$	4.23940e6			0.594875
$552$		0			0
$553$			3.91157e6i			0.543924i
$554$	−4.12371e6			−0.570839
$555$		0			0
$556$	−4.67782e6			−0.641737
$557$		−	4.69093e6i		−	0.640650i	−0.947308	−	0.320325i	$-0.896208\pi$
$557$		−	4.69093e6i		−	0.640650i	0.947308	−	0.320325i	$-0.103792\pi$
$558$		−	85536.0i		−	0.0116296i
$559$	590944.			0.0799865
$560$	−125440.	−	689920.i	−0.0169031	−	0.0929670i
$561$		0			0
$562$		−	4.51394e6i		−	0.602858i
$563$		−	1.14387e7i		−	1.52092i	−0.649386	−	0.760459i	$-0.724974\pi$
$563$		−	1.14387e7i		−	1.52092i	0.649386	−	0.760459i	$-0.275026\pi$
$564$		0			0
$565$	2.35312e6	+	1.29422e7i	0.310115	+	1.70563i
$566$	−199808.			−0.0262163
$567$			2.89340e6i			0.377964i
$568$		−	1.81478e6i		−	0.236023i
$569$	−8.01383e6			−1.03767			−0.518835	−	0.854874i	$-0.673634\pi$
$569$	−8.01383e6			−1.03767			−0.518835	+	0.854874i	$0.673634\pi$
$570$		0			0
$571$	−8.91239e6			−1.14394			−0.571971	−	0.820274i	$-0.693821\pi$
$571$	−8.91239e6			−1.14394			−0.571971	+	0.820274i	$0.693821\pi$
$572$		−	1.44998e6i		−	0.185299i
$573$		0			0
$574$	−2.61425e6			−0.331182
$575$	1.54000e6	+	4.09500e6i	0.194246	+	0.516517i
$576$	−995328.			−0.125000
$577$		−	9.12994e6i		−	1.14164i	−0.821076	−	0.570819i	$-0.806626\pi$
$577$		−	9.12994e6i		−	1.14164i	0.821076	−	0.570819i	$-0.193374\pi$
$578$		−	185092.i		−	0.0230445i
$579$		0			0
$580$	3.39152e6	−	616640.i	0.418624	−	0.0761135i
$581$	−4.10189e6			−0.504131
$582$		0			0
$583$			4.31309e6i			0.525553i
$584$	4.53709e6			0.550484
$585$	−573480.	−	3.15414e6i	−0.0692833	−	0.381058i
$586$	345360.			0.0415459
$587$			1.62764e7i			1.94968i	0.222895	+	0.974842i	$0.428449\pi$
$587$			1.62764e7i			1.94968i	−0.222895	+	0.974842i	$0.571551\pi$
$588$		0			0
$589$	96800.0			0.0114971
$590$	−26080.0	−	143440.i	−0.00308445	−	0.0169645i
$591$		0			0
$592$			3.38944e6i			0.397488i
$593$		−	1.40344e7i		−	1.63892i	−0.573134	−	0.819461i	$-0.694273\pi$
$593$		−	1.40344e7i		−	1.63892i	0.573134	−	0.819461i	$-0.305727\pi$
$594$		0			0
$595$	3.15854e6	−	574280.i	0.365758	−	0.0665015i
$596$	2.86090e6			0.329903
$597$		0			0
$598$			1.32160e6i			0.151129i
$599$	−1.93710e6			−0.220590			−0.110295	−	0.993899i	$-0.535179\pi$
$599$	−1.93710e6			−0.220590			−0.110295	+	0.993899i	$0.535179\pi$
$600$		0			0
$601$	−3.81246e6			−0.430545			−0.215273	−	0.976554i	$-0.569064\pi$
$601$	−3.81246e6			−0.430545			−0.215273	+	0.976554i	$0.569064\pi$
$602$		−	490784.i		−	0.0551949i
$603$		−	4.43038e6i		−	0.496189i
$604$	2.78227e6			0.310318
$605$	747725.	−	135950.i	0.0830526	−	0.0151005i
$606$		0			0
$607$			1.29742e7i			1.42925i	0.699508	+	0.714624i	$0.253402\pi$
$607$			1.29742e7i			1.42925i	−0.699508	+	0.714624i	$0.746598\pi$
$608$		−	1.12640e6i		−	0.123576i
$609$		0			0
$610$	−59760.0	−	328680.i	−0.00650258	−	0.0357642i
$611$	−3.47581e6			−0.376663
$612$		−	4.55674e6i		−	0.491785i
$613$			1.28775e7i			1.38414i	0.721832	+	0.692069i	$0.243300\pi$
$613$			1.28775e7i			1.38414i	−0.721832	+	0.692069i	$0.756700\pi$
$614$	−1.14632e7			−1.22712
$615$		0			0
$616$	−1.20422e6			−0.127866
$617$		−	1.55320e7i		−	1.64253i	−0.570544	−	0.821267i	$-0.693268\pi$
$617$		−	1.55320e7i		−	1.64253i	0.570544	−	0.821267i	$-0.306732\pi$
$618$		0			0
$619$	−9.95199e6			−1.04396			−0.521979	−	0.852958i	$-0.674806\pi$
$619$	−9.95199e6			−1.04396			−0.521979	+	0.852958i	$0.674806\pi$
$620$	77440.0	−	14080.0i	0.00809070	−	0.00147104i
$621$		0			0
$622$			1.49962e6i			0.155419i
$623$			4.57121e6i			0.471858i
$624$		0			0
$625$	7.34562e6	−	6.43500e6i	0.752192	−	0.658944i
$626$	−7.96587e6			−0.812452
$627$		0			0
$628$			3.65664e6i			0.369984i
$629$	−1.55173e7			−1.56383
$630$	−2.61954e6	+	476280.i	−0.262950	+	0.0478091i
$631$	−1.75371e7			−1.75341			−0.876706	−	0.481027i	$-0.840264\pi$
$631$	−1.75371e7			−1.75341			−0.876706	+	0.481027i	$0.840264\pi$
$632$			5.10899e6i			0.508795i
$633$		0			0
$634$	−1.67123e6			−0.165125
$635$	3.41768e6	+	1.87972e7i	0.336354	+	1.84995i
$636$		0			0
$637$		−	566636.i		−	0.0553294i
$638$		−	5.91974e6i		−	0.575773i
$639$	−6.89051e6			−0.667574
$640$	−163840.	−	901120.i	−0.0158114	−	0.0869626i
$641$	1.29073e7			1.24076			0.620382	−	0.784300i	$-0.286978\pi$
$641$	1.29073e7			1.24076			0.620382	+	0.784300i	$0.286978\pi$
$642$		0			0
$643$			4.99083e6i			0.476042i	0.971260	+	0.238021i	$0.0764988\pi$
$643$			4.99083e6i			0.476042i	−0.971260	+	0.238021i	$0.923501\pi$
$644$	1.09760e6			0.104287
$645$		0			0
$646$	5.15680e6			0.486182
$647$		−	951144.i		−	0.0893276i	−0.999002	−	0.0446638i	$-0.985778\pi$
$647$		−	951144.i		−	0.0893276i	0.999002	−	0.0446638i	$-0.0142217\pi$
$648$			3.77914e6i			0.353553i
$649$	−250368.			−0.0233328
$650$	2.76120e6	−	1.03840e6i	0.256339	−	0.0964009i
$651$		0			0
$652$		−	9.75398e6i		−	0.898593i
$653$			1.62012e7i			1.48684i	0.668826	+	0.743419i	$0.266797\pi$
$653$			1.62012e7i			1.48684i	−0.668826	+	0.743419i	$0.733203\pi$
$654$		0			0
$655$	1.69552e7	−	3.08276e6i	1.54418	−	0.280761i
$656$	−3.41453e6			−0.309793
$657$		−	1.72268e7i		−	1.55701i
$658$			2.88669e6i			0.259917i
$659$	−6.37817e6			−0.572114			−0.286057	−	0.958213i	$-0.592345\pi$
$659$	−6.37817e6			−0.572114			−0.286057	+	0.958213i	$0.592345\pi$
$660$		0			0
$661$	1.01756e7			0.905850			0.452925	−	0.891549i	$-0.350380\pi$
$661$	1.01756e7			0.905850			0.452925	+	0.891549i	$0.350380\pi$
$662$		−	1.29062e7i		−	1.14460i
$663$		0			0
$664$	−5.35757e6			−0.471571
$665$	−539000.	−	2.96450e6i	−0.0472645	−	0.259955i
$666$	1.28693e7			1.12426
$667$			5.39560e6i			0.469597i
$668$		−	1.03776e7i		−	0.899820i
$669$		0			0
$670$	4.01104e6	−	729280.i	0.345199	−	0.0627635i
$671$	−573696.			−0.0491899
$672$		0			0
$673$		−	1.87501e7i		−	1.59575i	−0.602823	−	0.797875i	$-0.705957\pi$
$673$		−	1.87501e7i		−	1.59575i	0.602823	−	0.797875i	$-0.294043\pi$
$674$	1.18921e7			1.00834
$675$		0			0
$676$	−5.04955e6			−0.424997
$677$			9.56143e6i			0.801772i	0.916128	+	0.400886i	$0.131298\pi$
$677$			9.56143e6i			0.801772i	−0.916128	+	0.400886i	$0.868702\pi$
$678$		0			0
$679$	4.46233e6			0.371439
$680$	4.12544e6	−	750080.i	0.342135	−	0.0622064i
$681$		0			0
$682$		−	135168.i		−	0.0111279i
$683$			1.20383e7i			0.987450i	0.869618	+	0.493725i	$0.164365\pi$
$683$			1.20383e7i			0.987450i	−0.869618	+	0.493725i	$0.835635\pi$
$684$	−4.27680e6			−0.349525
$685$	3.48136e6	+	1.91475e7i	0.283480	+	1.55914i
$686$	−470596.			−0.0381802
$687$		0			0
$688$		−	641024.i		−	0.0516301i
$689$	−2.65075e6			−0.212726
$690$		0			0
$691$	1.50689e7			1.20057			0.600284	−	0.799787i	$-0.295054\pi$
$691$	1.50689e7			1.20057			0.600284	+	0.799787i	$0.295054\pi$
$692$		−	2.04499e6i		−	0.162340i
$693$			4.57229e6i			0.361660i
$694$	2.33866e6			0.184318
$695$	−1.60800e7	+	2.92364e6i	−1.26277	+	0.229595i
$696$		0			0
$697$		−	1.56321e7i		−	1.21881i
$698$		−	1.45120e7i		−	1.12742i
$699$		0			0
$700$	−862400.	−	2.29320e6i	−0.0665217	−	0.176887i
$701$	5.00312e6			0.384544			0.192272	−	0.981342i	$-0.438414\pi$
$701$	5.00312e6			0.384544			0.192272	+	0.981342i	$0.438414\pi$
$702$		0			0
$703$			1.45640e7i			1.11146i
$704$	−1.57286e6			−0.119608
$705$		0			0
$706$	6.51518e6			0.491943
$707$		−	2.66099e6i		−	0.200214i
$708$		0			0
$709$	−6.39854e6			−0.478041			−0.239021	−	0.971015i	$-0.576826\pi$
$709$	−6.39854e6			−0.478041			−0.239021	+	0.971015i	$0.576826\pi$
$710$	−1.13424e6	−	6.23832e6i	−0.0844421	−	0.464432i
$711$	1.93982e7			1.43909
$712$			5.97056e6i			0.441382i
$713$			123200.i			0.00907584i
$714$		0			0
$715$	−906240.	−	4.98432e6i	−0.0662946	−	0.364620i
$716$	1.01953e7			0.743222
$717$		0			0
$718$		−	2.42421e6i		−	0.175493i
$719$	4.18314e6			0.301773			0.150886	−	0.988551i	$-0.451787\pi$
$719$	4.18314e6			0.301773			0.150886	+	0.988551i	$0.451787\pi$
$720$	−3.42144e6	+	622080.i	−0.245967	+	0.0447214i
$721$	−6.66126e6			−0.477219
$722$			5.06440e6i			0.361564i
$723$		0			0
$724$	−7.37994e6			−0.523246
$725$	1.12730e7	−	4.23940e6i	0.796512	−	0.299543i
$726$		0			0
$727$			6.29260e6i			0.441564i	0.975323	+	0.220782i	$0.0708610\pi$
$727$			6.29260e6i			0.441564i	−0.975323	+	0.220782i	$0.929139\pi$
$728$		−	740096.i		−	0.0517559i
$729$	1.43489e7			1.00000
$730$	1.55962e7	−	2.83568e6i	1.08321	−	0.196947i
$731$	2.93469e6			0.203127
$732$		0			0
$733$		−	6.62340e6i		−	0.455324i	−0.973740	−	0.227662i	$-0.926892\pi$
$733$		−	6.62340e6i		−	0.455324i	0.973740	−	0.227662i	$-0.0731082\pi$
$734$	−8.60010e6			−0.589201
$735$		0			0
$736$	1.43360e6			0.0975514
$737$		−	7.00109e6i		−	0.474785i
$738$			1.29645e7i			0.876226i
$739$	−3.44169e6			−0.231825			−0.115913	−	0.993259i	$-0.536979\pi$
$739$	−3.44169e6			−0.231825			−0.115913	+	0.993259i	$0.536979\pi$
$740$	2.11840e6	+	1.16512e7i	0.142210	+	0.782152i
$741$		0			0
$742$			2.20147e6i			0.146792i
$743$		−	1.85406e7i		−	1.23212i	−0.787699	−	0.616060i	$-0.788728\pi$
$743$		−	1.85406e7i		−	1.23212i	0.787699	−	0.616060i	$-0.211272\pi$
$744$		0			0
$745$	9.83433e6	−	1.78806e6i	0.649164	−	0.118030i
$746$	6.56742e6			0.432064
$747$			2.03420e7i			1.33381i
$748$		−	7.20077e6i		−	0.470571i
$749$	−3.79809e6			−0.247378
$750$		0			0
$751$	3.22428e6			0.208609			0.104305	−	0.994545i	$-0.466738\pi$
$751$	3.22428e6			0.208609			0.104305	+	0.994545i	$0.466738\pi$
$752$			3.77037e6i			0.243130i
$753$		0			0
$754$	3.63818e6			0.233053
$755$	9.56406e6	−	1.73892e6i	0.610625	−	0.111023i
$756$		0			0
$757$			2.34007e6i			0.148419i	0.997243	+	0.0742095i	$0.0236434\pi$
$757$			2.34007e6i			0.148419i	−0.997243	+	0.0742095i	$0.976357\pi$
$758$			1.60016e7i			1.01156i
$759$		0			0
$760$	−704000.	−	3.87200e6i	−0.0442118	−	0.243165i
$761$	−8.34242e6			−0.522192			−0.261096	−	0.965313i	$-0.584084\pi$
$761$	−8.34242e6			−0.522192			−0.261096	+	0.965313i	$0.584084\pi$
$762$		0			0
$763$			7.43399e6i			0.462286i
$764$	−5.70310e6			−0.353491
$765$	−2.84796e6	−	1.56638e7i	−0.175946	−	0.967705i
$766$	−2.28635e7			−1.40789
$767$		−	153872.i		−	0.00944433i
$768$		0			0
$769$	−3.29971e6			−0.201215			−0.100607	−	0.994926i	$-0.532079\pi$
$769$	−3.29971e6			−0.201215			−0.100607	+	0.994926i	$0.532079\pi$
$770$	−4.13952e6	+	752640.i	−0.251607	+	0.0457468i
$771$		0			0
$772$		−	3.05997e6i		−	0.184788i
$773$			7.19867e6i			0.433315i	0.976248	+	0.216657i	$0.0695154\pi$
$773$			7.19867e6i			0.433315i	−0.976248	+	0.216657i	$0.930485\pi$
$774$	−2.43389e6			−0.146032
$775$	257400.	−	96800.0i	0.0153941	−	0.00578923i
$776$	5.82835e6			0.347449
$777$		0			0
$778$		−	6.70442e6i		−	0.397112i
$779$	−1.46718e7			−0.866243
$780$		0			0
$781$	−1.08887e7			−0.638776
$782$			6.56320e6i			0.383795i
$783$		0			0
$784$	−614656.			−0.0357143
$785$	2.28540e6	+	1.25697e7i	0.132370	+	0.728033i
$786$		0			0
$787$			1.79424e7i			1.03262i	0.856400	+	0.516312i	$0.172696\pi$
$787$			1.79424e7i			1.03262i	−0.856400	+	0.516312i	$0.827304\pi$
$788$			9.99962e6i			0.573677i
$789$		0			0
$790$	3.19312e6	+	1.75622e7i	0.182032	+	1.00118i
$791$	1.15303e7			0.655238
$792$			5.97197e6i			0.338302i
$793$		−	352584.i		−	0.0199104i
$794$	−3.78056e6			−0.212816
$795$		0			0
$796$	−3.95866e6			−0.221445
$797$		−	1.53422e7i		−	0.855543i	−0.903887	−	0.427771i	$-0.859299\pi$
$797$		−	1.53422e7i		−	0.855543i	0.903887	−	0.427771i	$-0.140701\pi$
$798$		0			0
$799$	−1.72612e7			−0.956543
$800$	−1.12640e6	−	2.99520e6i	−0.0622254	−	0.165463i
$801$	2.26695e7			1.24842
$802$		−	2.21114e6i		−	0.121389i
$803$		−	2.72225e7i		−	1.48984i
$804$		0			0
$805$	3.77300e6	−	686000.i	0.205209	−	0.0373108i
$806$	83072.0			0.00450419
$807$		0			0
$808$		−	3.47558e6i		−	0.187283i
$809$	−9.88141e6			−0.530821			−0.265410	−	0.964136i	$-0.585507\pi$
$809$	−9.88141e6			−0.530821			−0.265410	+	0.964136i	$0.585507\pi$
$810$	2.36196e6	+	1.29908e7i	0.126491	+	0.695701i
$811$	−1.22149e7			−0.652137			−0.326069	−	0.945346i	$-0.605724\pi$
$811$	−1.22149e7			−0.652137			−0.326069	+	0.945346i	$0.605724\pi$
$812$		−	3.02154e6i		−	0.160819i
$813$		0			0
$814$	2.03366e7			1.07577
$815$	−6.09624e6	−	3.35293e7i	−0.321490	−	1.76820i
$816$		0			0
$817$		−	2.75440e6i		−	0.144368i
$818$		−	4.19132e6i		−	0.219012i
$819$	−2.81005e6			−0.146388
$820$	−1.17374e7	+	2.13408e6i	−0.609591	+	0.110835i
$821$	−2.12593e7			−1.10075			−0.550377	−	0.834916i	$-0.685516\pi$
$821$	−2.12593e7			−1.10075			−0.550377	+	0.834916i	$0.685516\pi$
$822$		0			0
$823$			1.76882e7i			0.910297i	0.890415	+	0.455149i	$0.150414\pi$
$823$			1.76882e7i			0.910297i	−0.890415	+	0.455149i	$0.849586\pi$
$824$	−8.70042e6			−0.446398
$825$		0			0
$826$	−127792.			−0.00651709
$827$			2.48044e7i			1.26115i	0.776130	+	0.630573i	$0.217180\pi$
$827$			2.48044e7i			1.26115i	−0.776130	+	0.630573i	$0.782820\pi$
$828$		−	5.44320e6i		−	0.275917i
$829$	879386.			0.0444420			0.0222210	−	0.999753i	$-0.492926\pi$
$829$	879386.			0.0444420			0.0222210	+	0.999753i	$0.492926\pi$
$830$	−1.84166e7	+	3.34848e6i	−0.927930	+	0.168715i
$831$		0			0
$832$		−	966656.i		−	0.0484132i
$833$		−	2.81397e6i		−	0.140510i
$834$		0			0
$835$	−6.48600e6	−	3.56730e7i	−0.321929	−	1.77061i
$836$	−6.75840e6			−0.334448
$837$		0			0
$838$		−	2.75337e7i		−	1.35443i
$839$	−2.27773e7			−1.11711			−0.558556	−	0.829467i	$-0.688644\pi$
$839$	−2.27773e7			−1.11711			−0.558556	+	0.829467i	$0.688644\pi$
$840$		0			0
$841$	−5.65783e6			−0.275842
$842$			1.82524e7i			0.887239i
$843$		0			0
$844$	−4.81574e6			−0.232706
$845$	−1.73578e7	+	3.15597e6i	−0.836284	+	0.152052i
$846$	1.43156e7			0.687676
$847$		−	666155.i		−	0.0319056i
$848$			2.87539e6i			0.137312i
$849$		0			0
$850$	1.37124e7	−	5.15680e6i	0.650978	−	0.244812i
$851$	−1.85360e7			−0.877389
$852$		0			0
$853$		−	1.13876e7i		−	0.535869i	−0.963437	−	0.267934i	$-0.913659\pi$
$853$		−	1.13876e7i		−	0.535869i	0.963437	−	0.267934i	$-0.0863410\pi$
$854$	−292824.			−0.0137392
$855$	−1.47015e7	+	2.67300e6i	−0.687775	+	0.125050i
$856$	−4.96077e6			−0.231401
$857$		−	3.74896e7i		−	1.74365i	−0.489819	−	0.871824i	$-0.662937\pi$
$857$		−	3.74896e7i		−	1.74365i	0.489819	−	0.871824i	$-0.337063\pi$
$858$		0			0
$859$	3.49422e7			1.61572			0.807862	−	0.589372i	$-0.200625\pi$
$859$	3.49422e7			1.61572			0.807862	+	0.589372i	$0.200625\pi$
$860$	−400640.	−	2.20352e6i	−0.0184718	−	0.101595i
$861$		0			0
$862$			9.96440e6i			0.456755i
$863$			3.40644e7i			1.55695i	0.627678	+	0.778473i	$0.284006\pi$
$863$			3.40644e7i			1.55695i	−0.627678	+	0.778473i	$0.715994\pi$
$864$		0			0
$865$	−1.27812e6	−	7.02966e6i	−0.0580806	−	0.319443i
$866$	−1.77127e7			−0.802583
$867$		0			0
$868$		−	68992.0i		−	0.00310813i
$869$	3.06540e7			1.37701
$870$		0			0
$871$	4.30275e6			0.192177
$872$			9.70970e6i			0.432429i
$873$		−	2.21295e7i		−	0.982735i
$874$	6.16000e6			0.272773
$875$	−4.39775e6	−	7.34388e6i	−0.194183	−	0.324269i
$876$		0			0
$877$		−	9.56406e6i		−	0.419897i	−0.977712	−	0.209949i	$-0.932670\pi$
$877$		−	9.56406e6i		−	0.419897i	0.977712	−	0.209949i	$-0.0673297\pi$
$878$			2.54173e6i			0.111274i
$879$		0			0
$880$	−5.40672e6	+	983040.i	−0.235357	+	0.0427922i
$881$	2.43742e6			0.105801			0.0529006	−	0.998600i	$-0.483153\pi$
$881$	2.43742e6			0.105801			0.0529006	+	0.998600i	$0.483153\pi$
$882$			2.33377e6i			0.101015i
$883$			1.08423e6i			0.0467973i	0.999726	+	0.0233986i	$0.00744870\pi$
$883$			1.08423e6i			0.0467973i	−0.999726	+	0.0233986i	$0.992551\pi$
$884$	4.42547e6			0.190471
$885$		0			0
$886$	7.22448e6			0.309188
$887$		−	1.35583e7i		−	0.578623i	−0.957235	−	0.289312i	$-0.906574\pi$
$887$		−	1.35583e7i		−	0.578623i	0.957235	−	0.289312i	$-0.0934264\pi$
$888$		0			0
$889$	1.67466e7			0.710678
$890$	3.73160e6	+	2.05238e7i	0.157914	+	0.868526i
$891$	2.26748e7			0.956862
$892$			1.63418e6i			0.0687680i
$893$			1.62008e7i			0.679842i
$894$		0			0
$895$	3.50464e7	−	6.37208e6i	1.46247	−	0.265903i
$896$	−802816.			−0.0334077
$897$		0			0
$898$		−	1.56129e7i		−	0.646090i
$899$	339152.			0.0139957
$900$	−1.13724e7	+	4.27680e6i	−0.468000	+	0.176000i
$901$	−1.31639e7			−0.540223
$902$			2.04872e7i			0.838428i
$903$		0			0
$904$	1.50600e7			0.612919
$905$	−2.53685e7	+	4.61246e6i	−1.02961	+	0.187202i
$906$		0			0
$907$		−	1.12138e7i		−	0.452619i	−0.974055	−	0.226309i	$-0.927334\pi$
$907$		−	1.12138e7i		−	0.452619i	0.974055	−	0.226309i	$-0.0726661\pi$
$908$		−	9.53549e6i		−	0.383821i
$909$	−1.31964e7			−0.529718
$910$	−462560.	−	2.54408e6i	−0.0185167	−	0.101842i
$911$	−4.15211e7			−1.65757			−0.828787	−	0.559564i	$-0.810969\pi$
$911$	−4.15211e7			−1.65757			−0.828787	+	0.559564i	$0.810969\pi$
$912$		0			0
$913$			3.21454e7i			1.27627i
$914$	−1.74506e7			−0.690946
$915$		0			0
$916$	1.62468e7			0.639778
$917$		−	1.51055e7i		−	0.593215i
$918$		0			0
$919$	4.13539e7			1.61520			0.807602	−	0.589728i	$-0.200765\pi$
$919$	4.13539e7			1.61520			0.807602	+	0.589728i	$0.200765\pi$
$920$	4.92800e6	−	896000.i	0.191956	−	0.0349010i
$921$		0			0
$922$		−	3.38684e6i		−	0.131210i
$923$		−	6.69202e6i		−	0.258555i
$924$		0			0
$925$	1.45640e7	+	3.87270e7i	0.559663	+	1.48819i
$926$	−2.95188e7			−1.13128
$927$			3.30344e7i			1.26260i
$928$		−	3.94650e6i		−	0.150433i
$929$	−945378.			−0.0359390			−0.0179695	−	0.999839i	$-0.505720\pi$
$929$	−945378.			−0.0359390			−0.0179695	+	0.999839i	$0.505720\pi$
$930$		0			0
$931$	−2.64110e6			−0.0998644
$932$			374144.i			0.0141091i
$933$		0			0
$934$	1.15318e7			0.432545
$935$	−4.50048e6	−	2.47526e7i	−0.168356	−	0.925961i
$936$	−3.67027e6			−0.136933
$937$		−	4.77950e6i		−	0.177842i	−0.996039	−	0.0889208i	$-0.971658\pi$
$937$		−	4.77950e6i		−	0.177842i	0.996039	−	0.0889208i	$-0.0283418\pi$
$938$		−	3.57347e6i		−	0.132612i
$939$		0			0
$940$	2.35648e6	+	1.29606e7i	0.0869850	+	0.478417i
$941$	2.87439e7			1.05821			0.529104	−	0.848557i	$-0.322528\pi$
$941$	2.87439e7			1.05821			0.529104	+	0.848557i	$0.322528\pi$
$942$		0			0
$943$		−	1.86732e7i		−	0.683816i
$944$	−166912.			−0.00609618
$945$		0			0
$946$	−3.84614e6			−0.139733
$947$			1.01090e6i			0.0366298i	0.999832	+	0.0183149i	$0.00583015\pi$
$947$			1.01090e6i			0.0366298i	−0.999832	+	0.0183149i	$0.994170\pi$
$948$		0			0
$949$	1.67305e7			0.603037
$950$	−4.84000e6	−	1.28700e7i	−0.173995	−	0.462668i
$951$		0			0
$952$		−	3.67539e6i		−	0.131435i
$953$			4.46529e7i			1.59264i	0.604877	+	0.796319i	$0.293222\pi$
$953$			4.46529e7i			1.59264i	−0.604877	+	0.796319i	$0.706778\pi$
$954$	1.09175e7			0.388376
$955$	−1.96044e7	+	3.56444e6i	−0.695578	+	0.126469i
$956$	1.85350e7			0.655915
$957$		0			0
$958$		−	2.65329e7i		−	0.934051i
$959$	1.70587e7			0.598961
$960$		0			0
$961$	−2.86214e7			−0.999730
$962$			1.24986e7i			0.435434i
$963$			1.88354e7i			0.654500i
$964$	1.56398e7			0.542050
$965$	−1.91248e6	−	1.05186e7i	−0.0661117	−	0.363615i
$966$		0			0
$967$			1.83956e7i			0.632626i	0.948655	+	0.316313i	$0.102445\pi$
$967$			1.83956e7i			0.632626i	−0.948655	+	0.316313i	$0.897555\pi$
$968$		−	870080.i		−	0.0298449i
$969$		0			0
$970$	2.00350e7	−	3.64272e6i	0.683690	−	0.124307i
$971$	3.72647e7			1.26838			0.634191	−	0.773177i	$-0.281333\pi$
$971$	3.72647e7			1.26838			0.634191	+	0.773177i	$0.281333\pi$
$972$		0			0
$973$			1.43258e7i			0.485107i
$974$	8.71677e6			0.294414
$975$		0			0
$976$	−382464.			−0.0128519
$977$		−	8.11308e6i		−	0.271925i	−0.990714	−	0.135963i	$-0.956587\pi$
$977$		−	8.11308e6i		−	0.271925i	0.990714	−	0.135963i	$-0.0434127\pi$
$978$		0			0
$979$	3.58234e7			1.19456
$980$	−2.11288e6	+	384160.i	−0.0702764	+	0.0127775i
$981$	3.68665e7			1.22309
$982$		−	3.16923e7i		−	1.04876i
$983$			2.83324e7i			0.935189i	0.883943	+	0.467594i	$0.154879\pi$
$983$			2.83324e7i			0.935189i	−0.883943	+	0.467594i	$0.845121\pi$
$984$		0			0
$985$	6.24976e6	+	3.43737e7i	0.205245	+	1.12885i
$986$	1.80676e7			0.591844
$987$		0			0
$988$		−	4.15360e6i		−	0.135373i
$989$	3.50560e6			0.113965
$990$	3.73248e6	+	2.05286e7i	0.121035	+	0.665690i
$991$	−4.96125e7			−1.60475			−0.802374	−	0.596822i	$-0.796430\pi$
$991$	−4.96125e7			−1.60475			−0.802374	+	0.596822i	$0.796430\pi$
$992$		−	90112.0i		−	0.00290739i
$993$		0			0
$994$	−5.55778e6			−0.178417
$995$	−1.36079e7	+	2.47416e6i	−0.435745	+	0.0792264i
$996$		0			0
$997$			3.47215e7i			1.10627i	0.833092	+	0.553135i	$0.186569\pi$
$997$			3.47215e7i			1.10627i	−0.833092	+	0.553135i	$0.813431\pi$
$998$		−	1.07324e7i		−	0.341093i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.6.c.a.29.1	✓	2
3.2	odd	2		630.6.g.c.379.2		2
4.3	odd	2		560.6.g.a.449.2		2
5.2	odd	4		350.6.a.j.1.1		1
5.3	odd	4		350.6.a.c.1.1		1
5.4	even	2	inner	70.6.c.a.29.2	yes	2
15.14	odd	2		630.6.g.c.379.1		2
20.19	odd	2		560.6.g.a.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.c.a.29.1	✓	2	1.1	even	1	trivial
70.6.c.a.29.2	yes	2	5.4	even	2	inner
350.6.a.c.1.1		1	5.3	odd	4
350.6.a.j.1.1		1	5.2	odd	4
560.6.g.a.449.1		2	20.19	odd	2
560.6.g.a.449.2		2	4.3	odd	2
630.6.g.c.379.1		2	15.14	odd	2
630.6.g.c.379.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	70.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 + 10.0000i) q^{5} +49.0000i q^{7} +64.0000i q^{8} +243.000 q^{9} +(40.0000 + 220.000i) q^{10} +384.000 q^{11} +236.000i q^{13} +196.000 q^{14} +256.000 q^{16} +1172.00i q^{17} -972.000i q^{18} +1100.00 q^{19} +(880.000 - 160.000i) q^{20} -1536.00i q^{22} +1400.00i q^{23} +(2925.00 - 1100.00i) q^{25} +944.000 q^{26} -784.000i q^{28} +3854.00 q^{29} +88.0000 q^{31} -1024.00i q^{32} +4688.00 q^{34} +(-490.000 - 2695.00i) q^{35} -3888.00 q^{36} +13240.0i q^{37} -4400.00i q^{38} +(-640.000 - 3520.00i) q^{40} -13338.0 q^{41} -2504.00i q^{43} -6144.00 q^{44} +(-13365.0 + 2430.00i) q^{45} +5600.00 q^{46} +14728.0i q^{47} -2401.00 q^{49} +(-4400.00 - 11700.0i) q^{50} -3776.00i q^{52} +11232.0i q^{53} +(-21120.0 + 3840.00i) q^{55} -3136.00 q^{56} -15416.0i q^{58} -652.000 q^{59} -1494.00 q^{61} -352.000i q^{62} +11907.0i q^{63} -4096.00 q^{64} +(-2360.00 - 12980.0i) q^{65} -18232.0i q^{67} -18752.0i q^{68} +(-10780.0 + 1960.00i) q^{70} -28356.0 q^{71} +15552.0i q^{72} -70892.0i q^{73} +52960.0 q^{74} -17600.0 q^{76} +18816.0i q^{77} +79828.0 q^{79} +(-14080.0 + 2560.00i) q^{80} +59049.0 q^{81} +53352.0i q^{82} +83712.0i q^{83} +(-11720.0 - 64460.0i) q^{85} -10016.0 q^{86} +24576.0i q^{88} +93290.0 q^{89} +(9720.00 + 53460.0i) q^{90} -11564.0 q^{91} -22400.0i q^{92} +58912.0 q^{94} +(-60500.0 + 11000.0i) q^{95} -91068.0i q^{97} +9604.00i q^{98} +93312.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 110 q^{5} + 486 q^{9} + 80 q^{10} + 768 q^{11} + 392 q^{14} + 512 q^{16} + 2200 q^{19} + 1760 q^{20} + 5850 q^{25} + 1888 q^{26} + 7708 q^{29} + 176 q^{31} + 9376 q^{34} - 980 q^{35} - 7776 q^{36}+ \cdots + 186624 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 - 110 * q^5 + 486 * q^9 + 80 * q^10 + 768 * q^11 + 392 * q^14 + 512 * q^16 + 2200 * q^19 + 1760 * q^20 + 5850 * q^25 + 1888 * q^26 + 7708 * q^29 + 176 * q^31 + 9376 * q^34 - 980 * q^35 - 7776 * q^36 - 1280 * q^40 - 26676 * q^41 - 12288 * q^44 - 26730 * q^45 + 11200 * q^46 - 4802 * q^49 - 8800 * q^50 - 42240 * q^55 - 6272 * q^56 - 1304 * q^59 - 2988 * q^61 - 8192 * q^64 - 4720 * q^65 - 21560 * q^70 - 56712 * q^71 + 105920 * q^74 - 35200 * q^76 + 159656 * q^79 - 28160 * q^80 + 118098 * q^81 - 23440 * q^85 - 20032 * q^86 + 186580 * q^89 + 19440 * q^90 - 23128 * q^91 + 117824 * q^94 - 121000 * q^95 + 186624 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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