LMFDB - Embedded newform 13.7.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.d (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:	$2.99070308706$
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} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + \cdots + 56070144 $ x^12 - 6x^11 + 18x^10 + 488x^9 + 36205x^8 - 155430x^7 + 399962x^6 + 9502784x^5 + 275595012x^4 - 541321656x^3 + 523196552x^2 - 242221824*x + 56070144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$9.50218 - 9.50218i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.7.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.50218 - 8.50218i) q^{2} -17.1101 q^{3} +80.5742i q^{4} +(73.6481 + 73.6481i) q^{5} +(145.473 + 145.473i) q^{6} +(-214.232 + 214.232i) q^{7} +(140.917 - 140.917i) q^{8} -436.244 q^{9} +O(q^{10})$	\(q+(-8.50218 - 8.50218i) q^{2} -17.1101 q^{3} +80.5742i q^{4} +(73.6481 + 73.6481i) q^{5} +(145.473 + 145.473i) q^{6} +(-214.232 + 214.232i) q^{7} +(140.917 - 140.917i) q^{8} -436.244 q^{9} -1252.34i q^{10} +(231.998 - 231.998i) q^{11} -1378.63i q^{12} +(-2079.64 + 708.440i) q^{13} +3642.88 q^{14} +(-1260.13 - 1260.13i) q^{15} +2760.55 q^{16} +7527.26i q^{17} +(3709.02 + 3709.02i) q^{18} +(-8308.11 - 8308.11i) q^{19} +(-5934.13 + 5934.13i) q^{20} +(3665.53 - 3665.53i) q^{21} -3944.99 q^{22} +2393.16i q^{23} +(-2411.10 + 2411.10i) q^{24} -4776.92i q^{25} +(23704.8 + 11658.2i) q^{26} +19937.5 q^{27} +(-17261.6 - 17261.6i) q^{28} -923.972 q^{29} +21427.7i q^{30} +(-16413.9 - 16413.9i) q^{31} +(-32489.4 - 32489.4i) q^{32} +(-3969.52 + 3969.52i) q^{33} +(63998.2 - 63998.2i) q^{34} -31555.5 q^{35} -35150.0i q^{36} +(-36119.9 + 36119.9i) q^{37} +141274. i q^{38} +(35583.0 - 12121.5i) q^{39} +20756.5 q^{40} +(44410.3 + 44410.3i) q^{41} -62330.1 q^{42} +97972.1i q^{43} +(18693.1 + 18693.1i) q^{44} +(-32128.5 - 32128.5i) q^{45} +(20347.1 - 20347.1i) q^{46} +(112049. - 112049. i) q^{47} -47233.3 q^{48} +25858.3i q^{49} +(-40614.2 + 40614.2i) q^{50} -128792. i q^{51} +(-57081.9 - 167566. i) q^{52} -57734.9 q^{53} +(-169512. - 169512. i) q^{54} +34172.5 q^{55} +60377.7i q^{56} +(142153. + 142153. i) q^{57} +(7855.78 + 7855.78i) q^{58} +(-57409.6 + 57409.6i) q^{59} +(101534. - 101534. i) q^{60} +413374. q^{61} +279108. i q^{62} +(93457.4 - 93457.4i) q^{63} +375786. i q^{64} +(-205337. - 100987. i) q^{65} +67499.2 q^{66} +(-265261. - 265261. i) q^{67} -606503. q^{68} -40947.3i q^{69} +(268291. + 268291. i) q^{70} +(-28896.4 - 28896.4i) q^{71} +(-61474.0 + 61474.0i) q^{72} +(-395624. + 395624. i) q^{73} +614195. q^{74} +81733.7i q^{75} +(669419. - 669419. i) q^{76} +99403.0i q^{77} +(-405592. - 199474. i) q^{78} -419351. q^{79} +(203309. + 203309. i) q^{80} -23110.5 q^{81} -755169. i q^{82} +(59175.0 + 59175.0i) q^{83} +(295347. + 295347. i) q^{84} +(-554369. + 554369. i) q^{85} +(832977. - 832977. i) q^{86} +15809.3 q^{87} -65384.9i q^{88} +(-61088.3 + 61088.3i) q^{89} +546325. i q^{90} +(293756. - 597297. i) q^{91} -192827. q^{92} +(280844. + 280844. i) q^{93} -1.90533e6 q^{94} -1.22375e6i q^{95} +(555897. + 555897. i) q^{96} +(-235474. - 235474. i) q^{97} +(219852. - 219852. i) q^{98} +(-101208. + 101208. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−8.50218	−	8.50218i	−1.06277	−	1.06277i	−0.997893	−	0.0648795i	$-0.979334\pi$
$2$	−8.50218	−	8.50218i	−1.06277	−	1.06277i	−0.0648795	−	0.997893i	$-0.520666\pi$
$3$	−17.1101			−0.633708			−0.316854	−	0.948474i	$-0.602627\pi$
$3$	−17.1101			−0.633708			−0.316854	+	0.948474i	$0.602627\pi$
$4$			80.5742i			1.25897i
$5$	73.6481	+	73.6481i	0.589185	+	0.589185i	0.937411	−	0.348226i	$-0.113216\pi$
$5$	73.6481	+	73.6481i	0.589185	+	0.589185i	−0.348226	+	0.937411i	$0.613216\pi$
$6$	145.473	+	145.473i	0.673488	+	0.673488i
$7$	−214.232	+	214.232i	−0.624583	+	0.624583i	−0.946700	−	0.322117i	$-0.895606\pi$
$7$	−214.232	+	214.232i	−0.624583	+	0.624583i	0.322117	+	0.946700i	$0.395606\pi$
$8$	140.917	−	140.917i	0.275228	−	0.275228i
$9$	−436.244			−0.598414
$10$		−	1252.34i		−	1.25234i
$11$	231.998	−	231.998i	0.174304	−	0.174304i	−0.614563	−	0.788867i	$-0.710668\pi$
$11$	231.998	−	231.998i	0.174304	−	0.174304i	0.788867	+	0.614563i	$0.210668\pi$
$12$		−	1378.63i		−	0.797820i
$13$	−2079.64	+	708.440i	−0.946584	+	0.322458i
$13$	−2079.64	+	708.440i	−0.946584	+	0.322458i
$14$	3642.88			1.32758
$15$	−1260.13	−	1260.13i	−0.373371	−	0.373371i
$16$	2760.55			0.673962
$17$			7527.26i			1.53211i	0.642774	+	0.766056i	$0.277783\pi$
$17$			7527.26i			1.53211i	−0.642774	+	0.766056i	$0.722217\pi$
$18$	3709.02	+	3709.02i	0.635978	+	0.635978i
$19$	−8308.11	−	8308.11i	−1.21127	−	1.21127i	−0.970609	−	0.240662i	$-0.922636\pi$
$19$	−8308.11	−	8308.11i	−1.21127	−	1.21127i	−0.240662	−	0.970609i	$-0.577364\pi$
$20$	−5934.13	+	5934.13i	−0.741767	+	0.741767i
$21$	3665.53	−	3665.53i	0.395803	−	0.395803i
$22$	−3944.99			−0.370491
$23$			2393.16i			0.196693i	0.995152	+	0.0983465i	$0.0313554\pi$
$23$			2393.16i			0.196693i	−0.995152	+	0.0983465i	$0.968645\pi$
$24$	−2411.10	+	2411.10i	−0.174414	+	0.174414i
$25$		−	4776.92i		−	0.305723i
$26$	23704.8	+	11658.2i	1.34870	+	0.663304i
$27$	19937.5			1.01293
$28$	−17261.6	−	17261.6i	−0.786332	−	0.786332i
$29$	−923.972			−0.0378848			−0.0189424	−	0.999821i	$-0.506030\pi$
$29$	−923.972			−0.0378848			−0.0189424	+	0.999821i	$0.506030\pi$
$30$			21427.7i			0.793617i
$31$	−16413.9	−	16413.9i	−0.550968	−	0.550968i	0.375752	−	0.926720i	$-0.377384\pi$
$31$	−16413.9	−	16413.9i	−0.550968	−	0.550968i	−0.926720	+	0.375752i	$0.877384\pi$
$32$	−32489.4	−	32489.4i	−0.991497	−	0.991497i
$33$	−3969.52	+	3969.52i	−0.110458	+	0.110458i
$34$	63998.2	−	63998.2i	1.62829	−	1.62829i
$35$	−31555.5			−0.735989
$36$		−	35150.0i		−	0.753386i
$37$	−36119.9	+	36119.9i	−0.713085	+	0.713085i	−0.967179	−	0.254095i	$-0.918222\pi$
$37$	−36119.9	+	36119.9i	−0.713085	+	0.713085i	0.254095	+	0.967179i	$0.418222\pi$
$38$			141274.i			2.57461i
$39$	35583.0	−	12121.5i	0.599858	−	0.204344i
$40$	20756.5			0.324320
$41$	44410.3	+	44410.3i	0.644366	+	0.644366i	0.951626	−	0.307260i	$-0.0994121\pi$
$41$	44410.3	+	44410.3i	0.644366	+	0.644366i	−0.307260	+	0.951626i	$0.599412\pi$
$42$	−62330.1			−0.841298
$43$			97972.1i			1.23225i	0.787650	+	0.616123i	$0.211297\pi$
$43$			97972.1i			1.23225i	−0.787650	+	0.616123i	$0.788703\pi$
$44$	18693.1	+	18693.1i	0.219444	+	0.219444i
$45$	−32128.5	−	32128.5i	−0.352576	−	0.352576i
$46$	20347.1	−	20347.1i	0.209040	−	0.209040i
$47$	112049.	−	112049.i	1.07923	−	1.07923i	0.0826547	−	0.996578i	$-0.473660\pi$
$47$	112049.	−	112049.i	1.07923	−	1.07923i	0.996578	−	0.0826547i	$-0.0263398\pi$
$48$	−47233.3			−0.427095
$49$			25858.3i			0.219792i
$50$	−40614.2	+	40614.2i	−0.324914	+	0.324914i
$51$		−	128792.i		−	0.970912i
$52$	−57081.9	−	167566.i	−0.405965	−	1.19172i
$53$	−57734.9			−0.387803			−0.193901	−	0.981021i	$-0.562114\pi$
$53$	−57734.9			−0.387803			−0.193901	+	0.981021i	$0.562114\pi$
$54$	−169512.	−	169512.i	−1.07651	−	1.07651i
$55$	34172.5			0.205394
$56$			60377.7i			0.343805i
$57$	142153.	+	142153.i	0.767592	+	0.767592i
$58$	7855.78	+	7855.78i	0.0402629	+	0.0402629i
$59$	−57409.6	+	57409.6i	−0.279530	+	0.279530i	−0.832921	−	0.553391i	$-0.813333\pi$
$59$	−57409.6	+	57409.6i	−0.279530	+	0.279530i	0.553391	+	0.832921i	$0.313333\pi$
$60$	101534.	−	101534.i	0.470064	−	0.470064i
$61$	413374.			1.82118			0.910591	−	0.413309i	$-0.135627\pi$
$61$	413374.			1.82118			0.910591	+	0.413309i	$0.135627\pi$
$62$			279108.i			1.17111i
$63$	93457.4	−	93457.4i	0.373759	−	0.373759i
$64$			375786.i			1.43351i
$65$	−205337.	−	100987.i	−0.747700	−	0.367725i
$66$	67499.2			0.234783
$67$	−265261.	−	265261.i	−0.881960	−	0.881960i	0.111774	−	0.993734i	$-0.464347\pi$
$67$	−265261.	−	265261.i	−0.881960	−	0.881960i	−0.993734	+	0.111774i	$0.964347\pi$
$68$	−606503.			−1.92888
$69$		−	40947.3i		−	0.124646i
$70$	268291.	+	268291.i	0.782189	+	0.782189i
$71$	−28896.4	−	28896.4i	−0.0807364	−	0.0807364i	0.665585	−	0.746322i	$-0.268182\pi$
$71$	−28896.4	−	28896.4i	−0.0807364	−	0.0807364i	−0.746322	+	0.665585i	$0.768182\pi$
$72$	−61474.0	+	61474.0i	−0.164700	+	0.164700i
$73$	−395624.	+	395624.i	−1.01698	+	1.01698i	−0.0171315	+	0.999853i	$0.505453\pi$
$73$	−395624.	+	395624.i	−1.01698	+	1.01698i	−0.999853	+	0.0171315i	$0.994547\pi$
$74$	614195.			1.51569
$75$			81733.7i			0.193739i
$76$	669419.	−	669419.i	1.52496	−	1.52496i
$77$			99403.0i			0.217734i
$78$	−405592.	−	199474.i	−0.854684	−	0.420341i
$79$	−419351.			−0.850543			−0.425271	−	0.905066i	$-0.639821\pi$
$79$	−419351.			−0.850543			−0.425271	+	0.905066i	$0.639821\pi$
$80$	203309.	+	203309.i	0.397088	+	0.397088i
$81$	−23110.5			−0.0434865
$82$		−	755169.i		−	1.36963i
$83$	59175.0	+	59175.0i	0.103491	+	0.103491i	0.756957	−	0.653465i	$-0.226685\pi$
$83$	59175.0	+	59175.0i	0.103491	+	0.103491i	−0.653465	+	0.756957i	$0.726685\pi$
$84$	295347.	+	295347.i	0.498305	+	0.498305i
$85$	−554369.	+	554369.i	−0.902697	+	0.902697i
$86$	832977.	−	832977.i	1.30960	−	1.30960i
$87$	15809.3			0.0240079
$88$		−	65384.9i		−	0.0959465i
$89$	−61088.3	+	61088.3i	−0.0866538	+	0.0866538i	−0.749105	−	0.662451i	$-0.769516\pi$
$89$	−61088.3	+	61088.3i	−0.0866538	+	0.0866538i	0.662451	+	0.749105i	$0.269516\pi$
$90$			546325.i			0.749417i
$91$	293756.	−	597297.i	0.389818	−	0.792622i
$92$	−192827.			−0.247631
$93$	280844.	+	280844.i	0.349153	+	0.349153i
$94$	−1.90533e6			−2.29396
$95$		−	1.22375e6i		−	1.42732i
$96$	555897.	+	555897.i	0.628319	+	0.628319i
$97$	−235474.	−	235474.i	−0.258004	−	0.258004i	0.566238	−	0.824242i	$-0.308398\pi$
$97$	−235474.	−	235474.i	−0.258004	−	0.258004i	−0.824242	+	0.566238i	$0.808398\pi$
$98$	219852.	−	219852.i	0.233589	−	0.233589i
$99$	−101208.	+	101208.i	−0.104306	+	0.104306i
$100$	384896.			0.384896
$101$			1.08351e6i			1.05165i	0.850594	+	0.525823i	$0.176243\pi$
$101$			1.08351e6i			1.05165i	−0.850594	+	0.525823i	$0.823757\pi$
$102$	−1.09502e6	+	1.09502e6i	−1.03186	+	1.03186i
$103$		−	228949.i		−	0.209521i	−0.994497	−	0.104760i	$-0.966592\pi$
$103$		−	228949.i		−	0.209521i	0.994497	−	0.104760i	$-0.0334076\pi$
$104$	−193226.	+	392887.i	−0.171777	+	0.349275i
$105$	539919.			0.466402
$106$	490873.	+	490873.i	0.412146	+	0.412146i
$107$	1.77111e6			1.44575			0.722876	−	0.690978i	$-0.242820\pi$
$107$	1.77111e6			1.44575			0.722876	+	0.690978i	$0.242820\pi$
$108$			1.60644e6i			1.27525i
$109$	539118.	+	539118.i	0.416298	+	0.416298i	0.883926	−	0.467627i	$-0.154891\pi$
$109$	539118.	+	539118.i	0.416298	+	0.416298i	−0.467627	+	0.883926i	$0.654891\pi$
$110$	−290541.	−	290541.i	−0.218288	−	0.218288i
$111$	618015.	−	618015.i	0.451887	−	0.451887i
$112$	−591398.	+	591398.i	−0.420945	+	0.420945i
$113$	−1.11945e6			−0.775832			−0.387916	−	0.921695i	$-0.626805\pi$
$113$	−1.11945e6			−0.775832			−0.387916	+	0.921695i	$0.626805\pi$
$114$		−	2.41722e6i		−	1.63155i
$115$	−176252.	+	176252.i	−0.115889	+	0.115889i
$116$		−	74448.3i		−	0.0476959i
$117$	907232.	−	309052.i	0.566449	−	0.192963i
$118$	976214.			0.594154
$119$	−1.61258e6	−	1.61258e6i	−0.956931	−	0.956931i
$120$	−355146.			−0.205524
$121$			1.66391e6i			0.939236i
$122$	−3.51458e6	−	3.51458e6i	−1.93550	−	1.93550i
$123$	−759866.	−	759866.i	−0.408340	−	0.408340i
$124$	1.32254e6	−	1.32254e6i	0.693653	−	0.693653i
$125$	1.50256e6	−	1.50256e6i	0.769312	−	0.769312i
$126$	−1.58918e6			−0.794442
$127$			2.01939e6i			0.985846i	0.870073	+	0.492923i	$0.164072\pi$
$127$			2.01939e6i			0.985846i	−0.870073	+	0.492923i	$0.835928\pi$
$128$	1.11568e6	−	1.11568e6i	0.531997	−	0.531997i
$129$		−	1.67631e6i		−	0.780884i
$130$	887207.	+	2.60442e6i	0.403826	+	1.18544i
$131$	589259.			0.262115			0.131058	−	0.991375i	$-0.458163\pi$
$131$	589259.			0.262115			0.131058	+	0.991375i	$0.458163\pi$
$132$	−319841.	−	319841.i	−0.139063	−	0.139063i
$133$	3.55972e6			1.51308
$134$			4.51059e6i			1.87465i
$135$	1.46836e6	+	1.46836e6i	0.596802	+	0.596802i
$136$	1.06072e6	+	1.06072e6i	0.421680	+	0.421680i
$137$	−2.66749e6	+	2.66749e6i	−1.03739	+	1.03739i	−0.0381144	+	0.999273i	$0.512135\pi$
$137$	−2.66749e6	+	2.66749e6i	−1.03739	+	1.03739i	−0.999273	+	0.0381144i	$0.987865\pi$
$138$	−348142.	+	348142.i	−0.132470	+	0.132470i
$139$	−1.55840e6			−0.580277			−0.290139	−	0.956985i	$-0.593701\pi$
$139$	−1.55840e6			−0.580277			−0.290139	+	0.956985i	$0.593701\pi$
$140$		−	2.54256e6i		−	0.926590i
$141$	−1.91718e6	+	1.91718e6i	−0.683919	+	0.683919i
$142$			491366.i			0.171609i
$143$	−318117.	+	646831.i	−0.108788	+	0.221199i
$144$	−1.20427e6			−0.403309
$145$	−68048.8	−	68048.8i	−0.0223211	−	0.0223211i
$146$	6.72734e6			2.16165
$147$		−	442439.i		−	0.139284i
$148$	−2.91033e6	−	2.91033e6i	−0.897753	−	0.897753i
$149$	−962956.	−	962956.i	−0.291104	−	0.291104i	0.546413	−	0.837516i	$-0.315993\pi$
$149$	−962956.	−	962956.i	−0.291104	−	0.291104i	−0.837516	+	0.546413i	$0.815993\pi$
$150$	694914.	−	694914.i	0.205901	−	0.205901i
$151$	−2.31936e6	+	2.31936e6i	−0.673655	+	0.673655i	−0.958557	−	0.284902i	$-0.908039\pi$
$151$	−2.31936e6	+	2.31936e6i	−0.673655	+	0.673655i	0.284902	+	0.958557i	$0.408039\pi$
$152$	−2.34150e6			−0.666751
$153$		−	3.28372e6i		−	0.916837i
$154$	845142.	−	845142.i	0.231402	−	0.231402i
$155$		−	2.41770e6i		−	0.649244i
$156$	976679.	+	2.86707e6i	0.257263	+	0.755204i
$157$	−3.16541e6			−0.817958			−0.408979	−	0.912544i	$-0.634115\pi$
$157$	−3.16541e6			−0.817958			−0.408979	+	0.912544i	$0.634115\pi$
$158$	3.56540e6	+	3.56540e6i	0.903934	+	0.903934i
$159$	987851.			0.245754
$160$		−	4.78556e6i		−	1.16835i
$161$	−512692.	−	512692.i	−0.122851	−	0.122851i
$162$	196490.	+	196490.i	0.0462163	+	0.0462163i
$163$	3.38001e6	−	3.38001e6i	0.780467	−	0.780467i	−0.199442	−	0.979910i	$-0.563913\pi$
$163$	3.38001e6	−	3.38001e6i	0.780467	−	0.780467i	0.979910	+	0.199442i	$0.0639130\pi$
$164$	−3.57833e6	+	3.57833e6i	−0.811238	+	0.811238i
$165$	−584695.			−0.130160
$166$		−	1.00623e6i		−	0.219976i
$167$	−3.82024e6	+	3.82024e6i	−0.820241	+	0.820241i	−0.986142	−	0.165902i	$-0.946947\pi$
$167$	−3.82024e6	+	3.82024e6i	−0.820241	+	0.820241i	0.165902	+	0.986142i	$0.446947\pi$
$168$		−	1.03307e6i		−	0.217872i
$169$	3.82304e6	−	2.94661e6i	0.792042	−	0.610467i
$170$	9.42668e6			1.91872
$171$	3.62436e6	+	3.62436e6i	0.724842	+	0.724842i
$172$	−7.89402e6			−1.55136
$173$		−	7.45195e6i		−	1.43923i	−0.694371	−	0.719617i	$-0.744317\pi$
$173$		−	7.45195e6i		−	1.43923i	0.694371	−	0.719617i	$-0.255683\pi$
$174$	−134413.	−	134413.i	−0.0255149	−	0.0255149i
$175$	1.02337e6	+	1.02337e6i	0.190949	+	0.190949i
$176$	640443.	−	640443.i	0.117474	−	0.117474i
$177$	982285.	−	982285.i	0.177141	−	0.177141i
$178$	1.03877e6			0.184187
$179$			9.93321e6i			1.73193i	0.500104	+	0.865966i	$0.333295\pi$
$179$			9.93321e6i			1.73193i	−0.500104	+	0.865966i	$0.666705\pi$
$180$	2.58873e6	−	2.58873e6i	0.443884	−	0.443884i
$181$		−	8.22334e6i		−	1.38680i	−0.720555	−	0.693398i	$-0.756113\pi$
$181$		−	8.22334e6i		−	1.38680i	0.720555	−	0.693398i	$-0.243887\pi$
$182$	−7.57589e6	+	2.58076e6i	−1.25667	+	0.428088i
$183$	−7.07287e6			−1.15410
$184$	337237.	+	337237.i	0.0541354	+	0.0541354i
$185$	−5.32032e6			−0.840277
$186$		−	4.77557e6i		−	0.742141i
$187$	1.74631e6	+	1.74631e6i	0.267053	+	0.267053i
$188$	9.02827e6	+	9.02827e6i	1.35872	+	1.35872i
$189$	−4.27124e6	+	4.27124e6i	−0.632657	+	0.632657i
$190$	−1.04046e7	+	1.04046e7i	−1.51692	+	1.51692i
$191$	−1.03422e6			−0.148427			−0.0742136	−	0.997242i	$-0.523645\pi$
$191$	−1.03422e6			−0.148427			−0.0742136	+	0.997242i	$0.523645\pi$
$192$		−	6.42974e6i		−	0.908426i
$193$	5.78870e6	−	5.78870e6i	0.805210	−	0.805210i	−0.178695	−	0.983905i	$-0.557187\pi$
$193$	5.78870e6	−	5.78870e6i	0.805210	−	0.805210i	0.983905	+	0.178695i	$0.0571875\pi$
$194$			4.00408e6i			0.548400i
$195$	3.51334e6	+	1.72789e6i	0.473823	+	0.233031i
$196$	−2.08351e6			−0.276712
$197$	3.82189e6	+	3.82189e6i	0.499896	+	0.499896i	0.911405	−	0.411510i	$-0.134998\pi$
$197$	3.82189e6	+	3.82189e6i	0.499896	+	0.499896i	−0.411510	+	0.911405i	$0.634998\pi$
$198$	1.72098e6			0.221707
$199$		−	893097.i		−	0.113329i	−0.998393	−	0.0566643i	$-0.981954\pi$
$199$		−	893097.i		−	0.113329i	0.998393	−	0.0566643i	$-0.0180465\pi$
$200$	−673147.	−	673147.i	−0.0841434	−	0.0841434i
$201$	4.53865e6	+	4.53865e6i	0.558905	+	0.558905i
$202$	9.21222e6	−	9.21222e6i	1.11766	−	1.11766i
$203$	197944.	−	197944.i	0.0236622	−	0.0236622i
$204$	1.03773e7			1.22235
$205$			6.54147e6i			0.759301i
$206$	−1.94657e6	+	1.94657e6i	−0.222673	+	0.222673i
$207$		−	1.04400e6i		−	0.117704i
$208$	−5.74096e6	+	1.95568e6i	−0.637962	+	0.217324i
$209$	−3.85494e6			−0.422258
$210$	−4.59049e6	−	4.59049e6i	−0.495680	−	0.495680i
$211$	−92262.9			−0.00982154			−0.00491077	−	0.999988i	$-0.501563\pi$
$211$	−92262.9			−0.00982154			−0.00491077	+	0.999988i	$0.501563\pi$
$212$		−	4.65194e6i		−	0.488233i
$213$	494422.	+	494422.i	0.0511633	+	0.0511633i
$214$	−1.50583e7	−	1.50583e7i	−1.53651	−	1.53651i
$215$	−7.21546e6	+	7.21546e6i	−0.726020	+	0.726020i
$216$	2.80952e6	−	2.80952e6i	0.278786	−	0.278786i
$217$	7.03276e6			0.688251
$218$		−	9.16736e6i		−	0.884861i
$219$	6.76918e6	−	6.76918e6i	0.644471	−	0.644471i
$220$			2.75342e6i			0.258586i
$221$	−5.33261e6	−	1.56540e7i	−0.494041	−	1.45027i
$222$	−1.05090e7			−0.960507
$223$	−8.85625e6	−	8.85625e6i	−0.798611	−	0.798611i	0.184266	−	0.982876i	$-0.441009\pi$
$223$	−8.85625e6	−	8.85625e6i	−0.798611	−	0.798611i	−0.982876	+	0.184266i	$0.941009\pi$
$224$	1.39205e7			1.23854
$225$			2.08390e6i			0.182949i
$226$	9.51773e6	+	9.51773e6i	0.824533	+	0.824533i
$227$	7.90170e6	+	7.90170e6i	0.675527	+	0.675527i	0.958985	−	0.283457i	$-0.0914815\pi$
$227$	7.90170e6	+	7.90170e6i	0.675527	+	0.675527i	−0.283457	+	0.958985i	$0.591481\pi$
$228$	−1.14538e7	+	1.14538e7i	−0.966377	+	0.966377i
$229$	2.28875e6	−	2.28875e6i	0.190587	−	0.190587i	−0.605363	−	0.795950i	$-0.706972\pi$
$229$	2.28875e6	−	2.28875e6i	0.190587	−	0.190587i	0.795950	+	0.605363i	$0.206972\pi$
$230$	2.99705e6			0.246326
$231$		−	1.70080e6i		−	0.137980i
$232$	−130203.	+	130203.i	−0.0104269	+	0.0104269i
$233$			1.13768e7i			0.899401i	0.893179	+	0.449701i	$0.148469\pi$
$233$			1.13768e7i			0.899401i	−0.893179	+	0.449701i	$0.851531\pi$
$234$	−1.03411e7	−	5.08583e6i	−0.807083	−	0.396931i
$235$	1.65044e7			1.27173
$236$	−4.62573e6	−	4.62573e6i	−0.351920	−	0.351920i
$237$	7.17514e6			0.538996
$238$			2.74209e7i			2.03400i
$239$	−7.79723e6	−	7.79723e6i	−0.571145	−	0.571145i	0.361303	−	0.932448i	$-0.382332\pi$
$239$	−7.79723e6	−	7.79723e6i	−0.571145	−	0.571145i	−0.932448	+	0.361303i	$0.882332\pi$
$240$	−3.47864e6	−	3.47864e6i	−0.251638	−	0.251638i
$241$	81950.5	−	81950.5i	0.00585464	−	0.00585464i	−0.704173	−	0.710028i	$-0.748682\pi$
$241$	81950.5	−	81950.5i	0.00585464	−	0.00585464i	0.710028	+	0.704173i	$0.248682\pi$
$242$	1.41469e7	−	1.41469e7i	0.998195	−	0.998195i
$243$	−1.41390e7			−0.985370
$244$			3.33072e7i			2.29282i
$245$	−1.90442e6	+	1.90442e6i	−0.129498	+	0.129498i
$246$			1.29210e7i			0.867945i
$247$	2.31637e7	+	1.13921e7i	1.53715	+	0.755986i
$248$	−4.62598e6			−0.303284
$249$	−1.01249e6	−	1.01249e6i	−0.0655833	−	0.0655833i
$250$	−2.55501e7			−1.63521
$251$			9.96309e6i			0.630047i	0.949084	+	0.315023i	$0.102012\pi$
$251$			9.96309e6i			0.630047i	−0.949084	+	0.315023i	$0.897988\pi$
$252$	7.53025e6	+	7.53025e6i	0.470552	+	0.470552i
$253$	555210.	+	555210.i	0.0342844	+	0.0342844i
$254$	1.71692e7	−	1.71692e7i	1.04773	−	1.04773i
$255$	9.48531e6	−	9.48531e6i	0.572046	−	0.572046i
$256$	5.07888e6			0.302725
$257$		−	1.76493e7i		−	1.03975i	−0.854242	−	0.519875i	$-0.825978\pi$
$257$		−	1.76493e7i		−	1.03975i	0.854242	−	0.519875i	$-0.174022\pi$
$258$	−1.42523e7	+	1.42523e7i	−0.829902	+	0.829902i
$259$		−	1.54761e7i		−	0.890761i
$260$	8.13691e6	−	1.65449e7i	0.462956	−	0.941333i
$261$	403077.			0.0226708
$262$	−5.00999e6	−	5.00999e6i	−0.278569	−	0.278569i
$263$	−2.69228e7			−1.47997			−0.739985	−	0.672624i	$-0.765167\pi$
$263$	−2.69228e7			−1.47997			−0.739985	+	0.672624i	$0.765167\pi$
$264$			1.11874e6i			0.0608021i
$265$	−4.25207e6	−	4.25207e6i	−0.228487	−	0.228487i
$266$	−3.02654e7	−	3.02654e7i	−1.60806	−	1.60806i
$267$	1.04523e6	−	1.04523e6i	0.0549132	−	0.0549132i
$268$	2.13732e7	−	2.13732e7i	1.11036	−	1.11036i
$269$	−2.28689e7			−1.17487			−0.587433	−	0.809273i	$-0.699861\pi$
$269$	−2.28689e7			−1.17487			−0.587433	+	0.809273i	$0.699861\pi$
$270$		−	2.49685e7i		−	1.26853i
$271$	−1.13591e7	+	1.13591e7i	−0.570736	+	0.570736i	−0.932334	−	0.361598i	$-0.882231\pi$
$271$	−1.13591e7	+	1.13591e7i	−0.570736	+	0.570736i	0.361598	+	0.932334i	$0.382231\pi$
$272$			2.07794e7i			1.03259i
$273$	−5.02620e6	+	1.02198e7i	−0.247031	+	0.502291i
$274$	4.53590e7			2.20501
$275$	−1.10824e6	−	1.10824e6i	−0.0532887	−	0.0532887i
$276$	3.29930e6			0.156926
$277$			1.30080e7i			0.612028i	0.952027	+	0.306014i	$0.0989955\pi$
$277$			1.30080e7i			0.612028i	−0.952027	+	0.306014i	$0.901005\pi$
$278$	1.32498e7	+	1.32498e7i	0.616703	+	0.616703i
$279$	7.16046e6	+	7.16046e6i	0.329707	+	0.329707i
$280$	−4.44670e6	+	4.44670e6i	−0.202565	+	0.202565i
$281$	2.37985e7	−	2.37985e7i	1.07258	−	1.07258i	0.0754330	−	0.997151i	$-0.475966\pi$
$281$	2.37985e7	−	2.37985e7i	1.07258	−	1.07258i	0.997151	−	0.0754330i	$-0.0240339\pi$
$282$	3.26003e7			1.45370
$283$			1.24423e7i			0.548959i	0.961593	+	0.274480i	$0.0885056\pi$
$283$			1.24423e7i			0.548959i	−0.961593	+	0.274480i	$0.911494\pi$
$284$	2.32831e6	−	2.32831e6i	0.101645	−	0.101645i
$285$			2.09385e7i			0.904507i
$286$	8.20417e6	−	2.79479e6i	0.350701	−	0.119468i
$287$	−1.90282e7			−0.804920
$288$	1.41733e7	+	1.41733e7i	0.593325	+	0.593325i
$289$	−3.25221e7			−1.34737
$290$			1.15713e6i			0.0474446i
$291$	4.02898e6	+	4.02898e6i	0.163499	+	0.163499i
$292$	−3.18771e7	−	3.18771e7i	−1.28035	−	1.28035i
$293$	−9.08257e6	+	9.08257e6i	−0.361082	+	0.361082i	−0.864211	−	0.503129i	$-0.832182\pi$
$293$	−9.08257e6	+	9.08257e6i	−0.361082	+	0.361082i	0.503129	+	0.864211i	$0.332182\pi$
$294$	−3.76170e6	+	3.76170e6i	−0.148027	+	0.148027i
$295$	−8.45622e6			−0.329390
$296$			1.01798e7i			0.392521i
$297$	4.62546e6	−	4.62546e6i	0.176557	−	0.176557i
$298$			1.63745e7i			0.618754i
$299$	−1.69541e6	−	4.97693e6i	−0.0634252	−	0.186186i
$300$	−6.58562e6			−0.243912
$301$	−2.09888e7	−	2.09888e7i	−0.769639	−	0.769639i
$302$	3.94392e7			1.43188
$303$		−	1.85390e7i		−	0.666437i
$304$	−2.29349e7	−	2.29349e7i	−0.816351	−	0.816351i
$305$	3.04442e7	+	3.04442e7i	1.07301	+	1.07301i
$306$	−2.79188e7	+	2.79188e7i	−0.974389	+	0.974389i
$307$	−9.60324e6	+	9.60324e6i	−0.331897	+	0.331897i	−0.853306	−	0.521410i	$-0.825406\pi$
$307$	−9.60324e6	+	9.60324e6i	−0.331897	+	0.331897i	0.521410	+	0.853306i	$0.325406\pi$
$308$	−8.00931e6			−0.274121
$309$			3.91735e6i			0.132775i
$310$	−2.05558e7	+	2.05558e7i	−0.689999	+	0.689999i
$311$		−	3.04628e7i		−	1.01272i	−0.862323	−	0.506359i	$-0.830991\pi$
$311$		−	3.04628e7i		−	1.01272i	0.862323	−	0.506359i	$-0.169009\pi$
$312$	3.30611e6	−	6.72235e6i	0.108856	−	0.221339i
$313$	2.06729e7			0.674170			0.337085	−	0.941474i	$-0.390559\pi$
$313$	2.06729e7			0.674170			0.337085	+	0.941474i	$0.390559\pi$
$314$	2.69129e7	+	2.69129e7i	0.869303	+	0.869303i
$315$	1.37659e7			0.440426
$316$		−	3.37888e7i		−	1.07081i
$317$	3.69040e7	+	3.69040e7i	1.15850	+	1.15850i	0.984798	+	0.173701i	$0.0555727\pi$
$317$	3.69040e7	+	3.69040e7i	1.15850	+	1.15850i	0.173701	+	0.984798i	$0.444427\pi$
$318$	−8.39889e6	−	8.39889e6i	−0.261180	−	0.261180i
$319$	−214360.	+	214360.i	−0.00660347	+	0.00660347i
$320$	−2.76759e7	+	2.76759e7i	−0.844601	+	0.844601i
$321$	−3.03039e7			−0.916184
$322$			8.71800e6i			0.261126i
$323$	6.25373e7	−	6.25373e7i	1.85580	−	1.85580i
$324$		−	1.86211e6i		−	0.0547483i
$325$	3.38416e6	+	9.93430e6i	0.0985827	+	0.289392i
$326$	−5.74749e7			−1.65892
$327$	−9.22438e6	−	9.22438e6i	−0.263812	−	0.263812i
$328$	1.25163e7			0.354695
$329$			4.80090e7i			1.34814i
$330$	4.97119e6	+	4.97119e6i	0.138331	+	0.138331i
$331$	1.82030e7	+	1.82030e7i	0.501949	+	0.501949i	0.912043	−	0.410094i	$-0.134504\pi$
$331$	1.82030e7	+	1.82030e7i	0.501949	+	0.501949i	−0.410094	+	0.912043i	$0.634504\pi$
$332$	−4.76798e6	+	4.76798e6i	−0.130293	+	0.130293i
$333$	1.57571e7	−	1.57571e7i	0.426720	−	0.426720i
$334$	6.49608e7			1.74346
$335$		−	3.90719e7i		−	1.03927i
$336$	1.01189e7	−	1.01189e7i	0.266757	−	0.266757i
$337$		−	2.14657e7i		−	0.560860i	−0.959874	−	0.280430i	$-0.909523\pi$
$337$		−	2.14657e7i		−	0.560860i	0.959874	−	0.280430i	$-0.0904771\pi$
$338$	−5.75567e7	−	7.45156e6i	−1.49055	−	0.192973i
$339$	1.91538e7			0.491651
$340$	−4.46678e7	−	4.46678e7i	−1.13647	−	1.13647i
$341$	−7.61600e6			−0.192072
$342$		−	6.16299e7i		−	1.54068i
$343$	−3.07439e7	−	3.07439e7i	−0.761861	−	0.761861i
$344$	1.38059e7	+	1.38059e7i	0.339148	+	0.339148i
$345$	3.01569e6	−	3.01569e6i	0.0734395	−	0.0734395i
$346$	−6.33578e7	+	6.33578e7i	−1.52958	+	1.52958i
$347$	5.37467e7			1.28636			0.643181	−	0.765714i	$-0.277614\pi$
$347$	5.37467e7			1.28636			0.643181	+	0.765714i	$0.277614\pi$
$348$			1.27382e6i			0.0302253i
$349$	3.37710e7	−	3.37710e7i	0.794452	−	0.794452i	−0.187762	−	0.982214i	$-0.560123\pi$
$349$	3.37710e7	−	3.37710e7i	0.794452	−	0.794452i	0.982214	+	0.187762i	$0.0601235\pi$
$350$		−	1.74017e7i		−	0.405871i
$351$	−4.14628e7	+	1.41245e7i	−0.958821	+	0.326626i
$352$	−1.50750e7			−0.345643
$353$	9.93725e6	+	9.93725e6i	0.225914	+	0.225914i	0.810983	−	0.585070i	$-0.198933\pi$
$353$	9.93725e6	+	9.93725e6i	0.225914	+	0.225914i	−0.585070	+	0.810983i	$0.698933\pi$
$354$	−1.67031e7			−0.376520
$355$		−	4.25634e6i		−	0.0951373i
$356$	−4.92214e6	−	4.92214e6i	−0.109095	−	0.109095i
$357$	2.75914e7	+	2.75914e7i	0.606415	+	0.606415i
$358$	8.44540e7	−	8.44540e7i	1.84065	−	1.84065i
$359$	−3.97856e7	+	3.97856e7i	−0.859890	+	0.859890i	−0.991325	−	0.131435i	$-0.958042\pi$
$359$	−3.97856e7	+	3.97856e7i	−0.859890	+	0.859890i	0.131435	+	0.991325i	$0.458042\pi$
$360$	−9.05488e6			−0.194078
$361$			9.10034e7i			1.93435i
$362$	−6.99163e7	+	6.99163e7i	−1.47385	+	1.47385i
$363$		−	2.84698e7i		−	0.595202i
$364$	4.81267e7	+	2.36691e7i	0.997888	+	0.490770i
$365$	−5.82739e7			−1.19838
$366$	6.01348e7	+	6.01348e7i	1.22654	+	1.22654i
$367$	−2.88272e7			−0.583183			−0.291591	−	0.956543i	$-0.594185\pi$
$367$	−2.88272e7			−0.583183			−0.291591	+	0.956543i	$0.594185\pi$
$368$			6.60645e6i			0.132564i
$369$	−1.93737e7	−	1.93737e7i	−0.385597	−	0.385597i
$370$	4.52343e7	+	4.52343e7i	0.893023	+	0.893023i
$371$	1.23687e7	−	1.23687e7i	0.242215	−	0.242215i
$372$	−2.26287e7	+	2.26287e7i	−0.439574	+	0.439574i
$373$	−1.80799e7			−0.348393			−0.174196	−	0.984711i	$-0.555733\pi$
$373$	−1.80799e7			−0.348393			−0.174196	+	0.984711i	$0.555733\pi$
$374$		−	2.96950e7i		−	0.567633i
$375$	−2.57090e7	+	2.57090e7i	−0.487519	+	0.487519i
$376$		−	3.15792e7i		−	0.594070i
$377$	1.92153e6	−	654579.i	0.0358611	−	0.0122162i
$378$	7.26297e7			1.34474
$379$	3.50989e7	+	3.50989e7i	0.644727	+	0.644727i	0.951714	−	0.306987i	$-0.0993208\pi$
$379$	3.50989e7	+	3.50989e7i	0.644727	+	0.644727i	−0.306987	+	0.951714i	$0.599321\pi$
$380$	9.86028e7			1.79696
$381$		−	3.45520e7i		−	0.624738i
$382$	8.79314e6	+	8.79314e6i	0.157744	+	0.157744i
$383$	2.88898e7	+	2.88898e7i	0.514219	+	0.514219i	0.915816	−	0.401597i	$-0.131545\pi$
$383$	2.88898e7	+	2.88898e7i	0.514219	+	0.514219i	−0.401597	+	0.915816i	$0.631545\pi$
$384$	−1.90894e7	+	1.90894e7i	−0.337131	+	0.337131i
$385$	−7.32084e6	+	7.32084e6i	−0.128286	+	0.128286i
$386$	−9.84331e7			−1.71151
$387$		−	4.27397e7i		−	0.737393i
$388$	1.89731e7	−	1.89731e7i	0.324820	−	0.324820i
$389$			2.20087e7i			0.373891i	0.982370	+	0.186945i	$0.0598587\pi$
$389$			2.20087e7i			0.373891i	−0.982370	+	0.186945i	$0.940141\pi$
$390$	−1.51802e7	−	4.45619e7i	−0.255908	−	0.751225i
$391$	−1.80140e7			−0.301356
$392$	3.64387e6	+	3.64387e6i	0.0604929	+	0.0604929i
$393$	−1.00823e7			−0.166105
$394$		−	6.49888e7i		−	1.06255i
$395$	−3.08844e7	−	3.08844e7i	−0.501127	−	0.501127i
$396$	−8.15474e6	−	8.15474e6i	−0.131318	−	0.131318i
$397$	−1.81293e7	+	1.81293e7i	−0.289740	+	0.289740i	−0.836977	−	0.547237i	$-0.815679\pi$
$397$	−1.81293e7	+	1.81293e7i	−0.289740	+	0.289740i	0.547237	+	0.836977i	$0.315679\pi$
$398$	−7.59327e6	+	7.59327e6i	−0.120442	+	0.120442i
$399$	−6.09073e7			−0.958850
$400$		−	1.31869e7i		−	0.206046i
$401$	1.55442e7	−	1.55442e7i	0.241066	−	0.241066i	−0.576225	−	0.817291i	$-0.695475\pi$
$401$	1.55442e7	−	1.55442e7i	0.241066	−	0.241066i	0.817291	+	0.576225i	$0.195475\pi$
$402$		−	7.71768e7i		−	1.18798i
$403$	4.57633e7	+	2.25068e7i	0.699202	+	0.343874i
$404$	−8.73032e7			−1.32399
$405$	−1.70205e6	−	1.70205e6i	−0.0256216	−	0.0256216i
$406$	−3.36592e6			−0.0502951
$407$			1.67595e7i			0.248587i
$408$	−1.81490e7	−	1.81490e7i	−0.267222	−	0.267222i
$409$	−7.10021e7	−	7.10021e7i	−1.03777	−	1.03777i	−0.999258	−	0.0385117i	$-0.987738\pi$
$409$	−7.10021e7	−	7.10021e7i	−1.03777	−	1.03777i	−0.0385117	−	0.999258i	$-0.512262\pi$
$410$	5.56168e7	−	5.56168e7i	0.806964	−	0.806964i
$411$	4.56411e7	−	4.56411e7i	0.657401	−	0.657401i
$412$	1.84474e7			0.263781
$413$		−	2.45979e7i		−	0.349180i
$414$	−8.87630e6	+	8.87630e6i	−0.125092	+	0.125092i
$415$			8.71626e6i			0.121951i
$416$	9.05831e7	+	4.45496e7i	1.25825	+	0.618819i
$417$	2.66645e7			0.367726
$418$	3.27754e7	+	3.27754e7i	0.448765	+	0.448765i
$419$	8.55705e7			1.16327			0.581637	−	0.813448i	$-0.302412\pi$
$419$	8.55705e7			1.16327			0.581637	+	0.813448i	$0.302412\pi$
$420$			4.35035e7i			0.587187i
$421$	−2.05616e6	−	2.05616e6i	−0.0275557	−	0.0275557i	0.693195	−	0.720750i	$-0.256203\pi$
$421$	−2.05616e6	−	2.05616e6i	−0.0275557	−	0.0275557i	−0.720750	+	0.693195i	$0.756203\pi$
$422$	784436.	+	784436.i	0.0104381	+	0.0104381i
$423$	−4.88808e7	+	4.88808e7i	−0.645828	+	0.645828i
$424$	−8.13581e6	+	8.13581e6i	−0.106734	+	0.106734i
$425$	3.59571e7			0.468402
$426$		−	8.40732e6i		−	0.108750i
$427$	−8.85578e7	+	8.85578e7i	−1.13748	+	1.13748i
$428$			1.42706e8i			1.82016i
$429$	5.44303e6	−	1.10674e7i	0.0689396	−	0.140176i
$430$	1.22694e8			1.54319
$431$	−1.77261e7	−	1.77261e7i	−0.221402	−	0.221402i	0.587687	−	0.809089i	$-0.300039\pi$
$431$	−1.77261e7	−	1.77261e7i	−0.221402	−	0.221402i	−0.809089	+	0.587687i	$0.800039\pi$
$432$	5.50384e7			0.682675
$433$		−	2.97891e7i		−	0.366939i	−0.983025	−	0.183470i	$-0.941267\pi$
$433$		−	2.97891e7i		−	0.366939i	0.983025	−	0.183470i	$-0.0587329\pi$
$434$	−5.97938e7	−	5.97938e7i	−0.731454	−	0.731454i
$435$	1.16432e6	+	1.16432e6i	0.0141451	+	0.0141451i
$436$	−4.34390e7	+	4.34390e7i	−0.524108	+	0.524108i
$437$	1.98827e7	−	1.98827e7i	0.238249	−	0.238249i
$438$	−1.15106e8			−1.36985
$439$		−	3.81149e7i		−	0.450507i	−0.974300	−	0.225254i	$-0.927679\pi$
$439$		−	3.81149e7i		−	0.450507i	0.974300	−	0.225254i	$-0.0723210\pi$
$440$	4.81547e6	−	4.81547e6i	0.0565302	−	0.0565302i
$441$		−	1.12805e7i		−	0.131527i
$442$	−8.77546e7	+	1.78432e8i	−1.01626	+	2.06636i
$443$	−3.81620e6			−0.0438955			−0.0219478	−	0.999759i	$-0.506987\pi$
$443$	−3.81620e6			−0.0438955			−0.0219478	+	0.999759i	$0.506987\pi$
$444$	4.97961e7	+	4.97961e7i	0.568913	+	0.568913i
$445$	−8.99807e6			−0.102110
$446$			1.50595e8i			1.69748i
$447$	1.64763e7	+	1.64763e7i	0.184475	+	0.184475i
$448$	−8.05053e7	−	8.05053e7i	−0.895345	−	0.895345i
$449$	6.41269e6	−	6.41269e6i	0.0708437	−	0.0708437i	−0.670797	−	0.741641i	$-0.734048\pi$
$449$	6.41269e6	−	6.41269e6i	0.0708437	−	0.0708437i	0.741641	+	0.670797i	$0.234048\pi$
$450$	1.77177e7	−	1.77177e7i	0.194433	−	0.194433i
$451$	2.06063e7			0.224631
$452$		−	9.01984e7i		−	0.976750i
$453$	3.96845e7	−	3.96845e7i	0.426900	−	0.426900i
$454$		−	1.34363e8i		−	1.43586i
$455$	6.56243e7	−	2.23552e7i	0.696676	−	0.237326i
$456$	4.00634e7			0.422525
$457$	−9.92694e7	−	9.92694e7i	−1.04008	−	1.04008i	−0.999163	−	0.0409178i	$-0.986972\pi$
$457$	−9.92694e7	−	9.92694e7i	−1.04008	−	1.04008i	−0.0409178	−	0.999163i	$-0.513028\pi$
$458$	−3.89188e7			−0.405101
$459$			1.50075e8i			1.55192i
$460$	−1.42014e7	−	1.42014e7i	−0.145900	−	0.145900i
$461$	−9.89943e6	−	9.89943e6i	−0.101043	−	0.101043i	0.654778	−	0.755821i	$-0.272762\pi$
$461$	−9.89943e6	−	9.89943e6i	−0.101043	−	0.101043i	−0.755821	+	0.654778i	$0.772762\pi$
$462$	−1.44605e7	+	1.44605e7i	−0.146641	+	0.146641i
$463$	−3.23972e7	+	3.23972e7i	−0.326411	+	0.326411i	−0.851220	−	0.524809i	$-0.824137\pi$
$463$	−3.23972e7	+	3.23972e7i	−0.326411	+	0.326411i	0.524809	+	0.851220i	$0.324137\pi$
$464$	−2.55067e6			−0.0255329
$465$			4.13672e7i			0.411431i
$466$	9.67279e7	−	9.67279e7i	0.955859	−	0.955859i
$467$		−	4.30021e7i		−	0.422220i	−0.977462	−	0.211110i	$-0.932292\pi$
$467$		−	4.30021e7i		−	0.422220i	0.977462	−	0.211110i	$-0.0677079\pi$
$468$	2.49016e7	+	7.30995e7i	0.242935	+	0.713143i
$469$	1.13655e8			1.10171
$470$	−1.40324e8	−	1.40324e8i	−1.35157	−	1.35157i
$471$	5.41605e7			0.518346
$472$			1.61799e7i			0.153869i
$473$	2.27294e7	+	2.27294e7i	0.214785	+	0.214785i
$474$	−6.10043e7	−	6.10043e7i	−0.572830	−	0.572830i
$475$	−3.96872e7	+	3.96872e7i	−0.370313	+	0.370313i
$476$	1.29932e8	−	1.29932e8i	1.20475	−	1.20475i
$477$	2.51865e7			0.232067
$478$			1.32587e8i			1.21400i
$479$	−7.79320e7	+	7.79320e7i	−0.709103	+	0.709103i	−0.966347	−	0.257243i	$-0.917186\pi$
$479$	−7.79320e7	+	7.79320e7i	−0.709103	+	0.709103i	0.257243	+	0.966347i	$0.417186\pi$
$480$			8.18815e7i			0.740392i
$481$	4.95277e7	−	1.00705e8i	0.445055	−	0.904934i
$482$	−1.39352e6			−0.0124443
$483$	8.77222e6	+	8.77222e6i	0.0778517	+	0.0778517i
$484$	−1.34069e8			−1.18247
$485$		−	3.46843e7i		−	0.304024i
$486$	1.20212e8	+	1.20212e8i	1.04722	+	1.04722i
$487$	1.40906e6	+	1.40906e6i	0.0121995	+	0.0121995i	0.713180	−	0.700981i	$-0.247254\pi$
$487$	1.40906e6	+	1.40906e6i	0.0121995	+	0.0121995i	−0.700981	+	0.713180i	$0.747254\pi$
$488$	5.82512e7	−	5.82512e7i	0.501240	−	0.501240i
$489$	−5.78323e7	+	5.78323e7i	−0.494589	+	0.494589i
$490$	3.23834e7			0.275254
$491$			3.42671e7i			0.289490i	0.989469	+	0.144745i	$0.0462362\pi$
$491$			3.42671e7i			0.289490i	−0.989469	+	0.144745i	$0.953764\pi$
$492$	6.12256e7	−	6.12256e7i	0.514088	−	0.514088i
$493$		−	6.95498e6i		−	0.0580437i
$494$	−1.00084e8	−	2.93800e8i	−0.830203	−	2.43709i
$495$	−1.49075e7			−0.122911
$496$	−4.53114e7	−	4.53114e7i	−0.371332	−	0.371332i
$497$	1.23811e7			0.100853
$498$			1.72168e7i			0.139400i
$499$	9.89459e7	+	9.89459e7i	0.796336	+	0.796336i	0.982516	−	0.186180i	$-0.0596108\pi$
$499$	9.89459e7	+	9.89459e7i	0.796336	+	0.796336i	−0.186180	+	0.982516i	$0.559611\pi$
$500$	1.21068e8	+	1.21068e8i	0.968542	+	0.968542i
$501$	6.53648e7	−	6.53648e7i	0.519793	−	0.519793i
$502$	8.47080e7	−	8.47080e7i	0.669597	−	0.669597i
$503$	−7.51556e7			−0.590551			−0.295276	−	0.955412i	$-0.595411\pi$
$503$	−7.51556e7			−0.590551			−0.295276	+	0.955412i	$0.595411\pi$
$504$		−	2.63394e7i		−	0.205738i
$505$	−7.97986e7	+	7.97986e7i	−0.619614	+	0.619614i
$506$		−	9.44100e6i		−	0.0728730i
$507$	−6.54126e7	+	5.04168e7i	−0.501923	+	0.386858i
$508$	−1.62711e8			−1.24115
$509$	1.63158e8	+	1.63158e8i	1.23724	+	1.23724i	0.961124	+	0.276117i	$0.0890477\pi$
$509$	1.63158e8	+	1.63158e8i	1.23724	+	1.23724i	0.276117	+	0.961124i	$0.410952\pi$
$510$	−1.61292e8			−1.21591
$511$		−	1.69511e8i		−	1.27038i
$512$	−1.14585e8	−	1.14585e8i	−0.853725	−	0.853725i
$513$	−1.65643e8	−	1.65643e8i	−1.22693	−	1.22693i
$514$	−1.50058e8	+	1.50058e8i	−1.10502	+	1.10502i
$515$	1.68617e7	−	1.68617e7i	0.123447	−	0.123447i
$516$	1.35068e8			0.983110
$517$		−	5.19905e7i		−	0.376229i
$518$	−1.31580e8	+	1.31580e8i	−0.946676	+	0.946676i
$519$			1.27504e8i			0.912055i
$520$	−4.31661e7	+	1.47047e7i	−0.306996	+	0.104579i
$521$	6.71801e6			0.0475037			0.0237518	−	0.999718i	$-0.492439\pi$
$521$	6.71801e6			0.0475037			0.0237518	+	0.999718i	$0.492439\pi$
$522$	−3.42704e6	−	3.42704e6i	−0.0240939	−	0.0240939i
$523$	1.17314e8			0.820060			0.410030	−	0.912072i	$-0.365518\pi$
$523$	1.17314e8			0.820060			0.410030	+	0.912072i	$0.365518\pi$
$524$			4.74791e7i			0.329996i
$525$	−1.75100e7	−	1.75100e7i	−0.121006	−	0.121006i
$526$	2.28902e8	+	2.28902e8i	1.57287	+	1.57287i
$527$	1.23552e8	−	1.23552e8i	0.844145	−	0.844145i
$528$	−1.09581e7	+	1.09581e7i	−0.0744444	+	0.0744444i
$529$	1.42309e8			0.961312
$530$			7.23037e7i			0.485660i
$531$	2.50446e7	−	2.50446e7i	0.167275	−	0.167275i
$532$			2.86822e8i			1.90492i
$533$	−1.23820e8	−	6.08957e7i	−0.817727	−	0.402165i
$534$	−1.77734e7			−0.116721
$535$	1.30439e8	+	1.30439e8i	0.851815	+	0.851815i
$536$	−7.47593e7			−0.485480
$537$		−	1.69958e8i		−	1.09754i
$538$	1.94436e8	+	1.94436e8i	1.24862	+	1.24862i
$539$	5.99910e6	+	5.99910e6i	0.0383107	+	0.0383107i
$540$	−1.18312e8	+	1.18312e8i	−0.751356	+	0.751356i
$541$	−2.04171e7	+	2.04171e7i	−0.128944	+	0.128944i	−0.768634	−	0.639689i	$-0.779063\pi$
$541$	−2.04171e7	+	2.04171e7i	−0.128944	+	0.128944i	0.639689	+	0.768634i	$0.279063\pi$
$542$	1.93154e8			1.21312
$543$			1.40702e8i			0.878824i
$544$	2.44556e8	−	2.44556e8i	1.51908	−	1.51908i
$545$			7.94101e7i			0.490553i
$546$	1.29624e8	−	4.41571e7i	0.796359	−	0.271283i
$547$	−2.99984e8			−1.83289			−0.916444	−	0.400162i	$-0.868954\pi$
$547$	−2.99984e8			−1.83289			−0.916444	+	0.400162i	$0.868954\pi$
$548$	−2.14931e8	−	2.14931e8i	−1.30604	−	1.30604i
$549$	−1.80332e8			−1.08982
$550$			1.88449e7i			0.113268i
$551$	7.67646e6	+	7.67646e6i	0.0458887	+	0.0458887i
$552$	−5.77016e6	−	5.77016e6i	−0.0343060	−	0.0343060i
$553$	8.98383e7	−	8.98383e7i	0.531234	−	0.531234i
$554$	1.10596e8	−	1.10596e8i	0.650447	−	0.650447i
$555$	9.10313e7			0.532490
$556$		−	1.25567e8i		−	0.730552i
$557$	−4.42993e7	+	4.42993e7i	−0.256349	+	0.256349i	−0.823567	−	0.567218i	$-0.808020\pi$
$557$	−4.42993e7	+	4.42993e7i	−0.256349	+	0.256349i	0.567218	+	0.823567i	$0.308020\pi$
$558$		−	1.21759e8i		−	0.700808i
$559$	−6.94073e7	−	2.03747e8i	−0.397347	−	1.16642i
$560$	−8.71107e7			−0.496029
$561$	−2.98796e7	−	2.98796e7i	−0.169234	−	0.169234i
$562$	−4.04679e8			−2.27983
$563$		−	2.83040e8i		−	1.58607i	−0.609176	−	0.793035i	$-0.708500\pi$
$563$		−	2.83040e8i		−	1.58607i	0.609176	−	0.793035i	$-0.291500\pi$
$564$	−1.54475e8	−	1.54475e8i	−0.861034	−	0.861034i
$565$	−8.24450e7	−	8.24450e7i	−0.457108	−	0.457108i
$566$	1.05786e8	−	1.05786e8i	0.583419	−	0.583419i
$567$	4.95101e6	−	4.95101e6i	0.0271609	−	0.0271609i
$568$	−8.14398e6			−0.0444418
$569$			2.74227e8i			1.48858i	0.667854	+	0.744292i	$0.267213\pi$
$569$			2.74227e8i			1.48858i	−0.667854	+	0.744292i	$0.732787\pi$
$570$	1.78023e8	−	1.78023e8i	0.961285	−	0.961285i
$571$			5.50772e7i			0.295845i	0.988999	+	0.147922i	$0.0472585\pi$
$571$			5.50772e7i			0.295845i	−0.988999	+	0.147922i	$0.952741\pi$
$572$	−5.21179e7	−	2.56321e7i	−0.278483	−	0.136960i
$573$	1.76956e7			0.0940595
$574$	1.61781e8	+	1.61781e8i	0.855447	+	0.855447i
$575$	1.14320e7			0.0601336
$576$		−	1.63934e8i		−	0.857832i
$577$	8.09540e7	+	8.09540e7i	0.421416	+	0.421416i	0.885691	−	0.464275i	$-0.153685\pi$
$577$	8.09540e7	+	8.09540e7i	0.421416	+	0.421416i	−0.464275	+	0.885691i	$0.653685\pi$
$578$	2.76509e8	+	2.76509e8i	1.43194	+	1.43194i
$579$	−9.90453e7	+	9.90453e7i	−0.510268	+	0.510268i
$580$	5.48297e6	−	5.48297e6i	0.0281017	−	0.0281017i
$581$	−2.53544e7			−0.129278
$582$		−	6.85102e7i		−	0.347525i
$583$	−1.33944e7	+	1.33944e7i	−0.0675955	+	0.0675955i
$584$			1.11500e8i			0.559805i
$585$	8.95770e7	+	4.40548e7i	0.447434	+	0.220052i
$586$	1.54443e8			0.767497
$587$	−2.01036e8	−	2.01036e8i	−0.993938	−	0.993938i	0.00604390	−	0.999982i	$-0.498076\pi$
$587$	−2.01036e8	−	2.01036e8i	−0.993938	−	0.993938i	−0.999982	+	0.00604390i	$0.998076\pi$
$588$	3.56492e7			0.175355
$589$			2.72737e8i			1.33474i
$590$	7.18963e7	+	7.18963e7i	0.350066	+	0.350066i
$591$	−6.53930e7	−	6.53930e7i	−0.316788	−	0.316788i
$592$	−9.97107e7	+	9.97107e7i	−0.480592	+	0.480592i
$593$	−1.05754e8	+	1.05754e8i	−0.507147	+	0.507147i	−0.913650	−	0.406503i	$-0.866748\pi$
$593$	−1.05754e8	+	1.05754e8i	−0.507147	+	0.507147i	0.406503	+	0.913650i	$0.366748\pi$
$594$	−7.86530e7			−0.375281
$595$		−	2.37527e8i		−	1.12762i
$596$	7.75894e7	−	7.75894e7i	0.366491	−	0.366491i
$597$			1.52810e7i			0.0718172i
$598$	−2.79001e7	+	5.67295e7i	−0.130467	+	0.265280i
$599$	9.05205e7			0.421179			0.210589	−	0.977575i	$-0.432462\pi$
$599$	9.05205e7			0.421179			0.210589	+	0.977575i	$0.432462\pi$
$600$	1.15176e7	+	1.15176e7i	0.0533224	+	0.0533224i
$601$	2.05850e8			0.948262			0.474131	−	0.880454i	$-0.342762\pi$
$601$	2.05850e8			0.948262			0.474131	+	0.880454i	$0.342762\pi$
$602$			3.56900e8i			1.63590i
$603$	1.15718e8	+	1.15718e8i	0.527777	+	0.527777i
$604$	−1.86881e8	−	1.86881e8i	−0.848112	−	0.848112i
$605$	−1.22544e8	+	1.22544e8i	−0.553384	+	0.553384i
$606$	−1.57622e8	+	1.57622e8i	−0.708271	+	0.708271i
$607$	1.14080e8			0.510085			0.255043	−	0.966930i	$-0.417910\pi$
$607$	1.14080e8			0.510085			0.255043	+	0.966930i	$0.417910\pi$
$608$			5.39850e8i			2.40194i
$609$	−3.38685e6	+	3.38685e6i	−0.0149949	+	0.0149949i
$610$		−	5.17684e8i		−	2.28074i
$611$	−1.53642e8	+	3.12403e8i	−0.673577	+	1.36959i
$612$	2.64583e8			1.15427
$613$	−1.12421e6	−	1.12421e6i	−0.00488052	−	0.00488052i	0.704662	−	0.709543i	$-0.251099\pi$
$613$	−1.12421e6	−	1.12421e6i	−0.00488052	−	0.00488052i	−0.709543	+	0.704662i	$0.751099\pi$
$614$	1.63297e8			0.705461
$615$		−	1.11925e8i		−	0.481175i
$616$	1.40075e7	+	1.40075e7i	0.0599266	+	0.0599266i
$617$	−1.05308e8	−	1.05308e8i	−0.448336	−	0.448336i	0.446465	−	0.894801i	$-0.352683\pi$
$617$	−1.05308e8	−	1.05308e8i	−0.448336	−	0.448336i	−0.894801	+	0.446465i	$0.852683\pi$
$618$	3.33060e7	−	3.33060e7i	0.141110	−	0.141110i
$619$	3.88419e6	−	3.88419e6i	0.0163768	−	0.0163768i	−0.698871	−	0.715248i	$-0.746314\pi$
$619$	3.88419e6	−	3.88419e6i	0.0163768	−	0.0163768i	0.715248	+	0.698871i	$0.246314\pi$
$620$	1.94804e8			0.817380
$621$			4.77136e7i			0.199236i
$622$	−2.59000e8	+	2.59000e8i	−1.07629	+	1.07629i
$623$		−	2.61741e7i		−	0.108245i
$624$	9.82286e7	−	3.34620e7i	0.404282	−	0.137720i
$625$	1.46682e8			0.600811
$626$	−1.75765e8	−	1.75765e8i	−0.716489	−	0.716489i
$627$	6.59584e7			0.267589
$628$		−	2.55050e8i		−	1.02979i
$629$	−2.71884e8	−	2.71884e8i	−1.09253	−	1.09253i
$630$	−1.17040e8	−	1.17040e8i	−0.468073	−	0.468073i
$631$	−2.27959e7	+	2.27959e7i	−0.0907336	+	0.0907336i	−0.751017	−	0.660283i	$-0.770436\pi$
$631$	−2.27959e7	+	2.27959e7i	−0.0907336	+	0.0907336i	0.660283	+	0.751017i	$0.270436\pi$
$632$	−5.90935e7	+	5.90935e7i	−0.234093	+	0.234093i
$633$	1.57863e6			0.00622399
$634$		−	6.27529e8i		−	2.46244i
$635$	−1.48724e8	+	1.48724e8i	−0.580845	+	0.580845i
$636$			7.95953e7i			0.309397i
$637$	−1.83191e7	−	5.37762e7i	−0.0708737	−	0.208052i
$638$	3.64506e6			0.0140360
$639$	1.26059e7	+	1.26059e7i	0.0483138	+	0.0483138i
$640$	1.64335e8			0.626889
$641$			4.33034e8i			1.64417i	0.569363	+	0.822086i	$0.307190\pi$
$641$			4.33034e8i			1.64417i	−0.569363	+	0.822086i	$0.692810\pi$
$642$	2.57649e8	+	2.57649e8i	0.973696	+	0.973696i
$643$	−1.52097e8	−	1.52097e8i	−0.572122	−	0.572122i	0.360599	−	0.932721i	$-0.382572\pi$
$643$	−1.52097e8	−	1.52097e8i	−0.572122	−	0.572122i	−0.932721	+	0.360599i	$0.882572\pi$
$644$	4.13097e7	−	4.13097e7i	0.154666	−	0.154666i
$645$	1.23457e8	−	1.23457e8i	0.460085	−	0.460085i
$646$	−1.06341e9			−3.94459
$647$		−	3.36634e8i		−	1.24293i	−0.783444	−	0.621463i	$-0.786539\pi$
$647$		−	3.36634e8i		−	1.24293i	0.783444	−	0.621463i	$-0.213461\pi$
$648$	−3.25666e6	+	3.25666e6i	−0.0119687	+	0.0119687i
$649$			2.66379e7i			0.0974464i
$650$	5.56904e7	−	1.13236e8i	0.202787	−	0.412329i
$651$	−1.20331e8			−0.436150
$652$	2.72341e8	+	2.72341e8i	0.982586	+	0.982586i
$653$	2.78026e8			0.998496			0.499248	−	0.866459i	$-0.333610\pi$
$653$	2.78026e8			0.998496			0.499248	+	0.866459i	$0.333610\pi$
$654$			1.56855e8i			0.560744i
$655$	4.33978e7	+	4.33978e7i	0.154434	+	0.154434i
$656$	1.22597e8	+	1.22597e8i	0.434278	+	0.434278i
$657$	1.72589e8	−	1.72589e8i	0.608578	−	0.608578i
$658$	4.08182e8	−	4.08182e8i	1.43277	−	1.43277i
$659$	3.97164e8			1.38776			0.693878	−	0.720093i	$-0.255901\pi$
$659$	3.97164e8			1.38776			0.693878	+	0.720093i	$0.255901\pi$
$660$		−	4.71113e7i		−	0.163868i
$661$	1.57276e8	−	1.57276e8i	0.544577	−	0.544577i	−0.380290	−	0.924867i	$-0.624176\pi$
$661$	1.57276e8	−	1.57276e8i	0.544577	−	0.544577i	0.924867	+	0.380290i	$0.124176\pi$
$662$		−	3.09531e8i		−	1.06692i
$663$	9.12416e7	+	2.67842e8i	0.313078	+	0.919049i
$664$	1.66775e7			0.0569674
$665$	2.62167e8	+	2.62167e8i	0.891483	+	0.891483i
$666$	−2.67939e8			−0.907012
$667$		−	2.21122e6i		−	0.00745167i
$668$	−3.07813e8	−	3.07813e8i	−1.03266	−	1.03266i
$669$	1.51531e8	+	1.51531e8i	0.506086	+	0.506086i
$670$	−3.32196e8	+	3.32196e8i	−1.10451	+	1.10451i
$671$	9.59021e7	−	9.59021e7i	0.317439	−	0.317439i
$672$	−2.38182e8			−0.784875
$673$		−	1.93344e8i		−	0.634285i	−0.948378	−	0.317143i	$-0.897277\pi$
$673$		−	1.93344e8i		−	0.634285i	0.948378	−	0.317143i	$-0.102723\pi$
$674$	−1.82505e8	+	1.82505e8i	−0.596067	+	0.596067i
$675$		−	9.52396e7i		−	0.309675i
$676$	2.37420e8	+	3.08038e8i	0.768560	+	0.997158i
$677$	−4.36390e7			−0.140640			−0.0703201	−	0.997524i	$-0.522402\pi$
$677$	−4.36390e7			−0.140640			−0.0703201	+	0.997524i	$0.522402\pi$
$678$	−1.62849e8	−	1.62849e8i	−0.522513	−	0.522513i
$679$	1.00892e8			0.322290
$680$			1.56239e8i			0.496894i
$681$	−1.35199e8	−	1.35199e8i	−0.428087	−	0.428087i
$682$	6.47526e7	+	6.47526e7i	0.204129	+	0.204129i
$683$	4.34212e8	−	4.34212e8i	1.36282	−	1.36282i	0.492523	−	0.870299i	$-0.336075\pi$
$683$	4.34212e8	−	4.34212e8i	1.36282	−	1.36282i	0.870299	−	0.492523i	$-0.163925\pi$
$684$	−2.92030e8	+	2.92030e8i	−0.912555	+	0.912555i
$685$	−3.92911e8			−1.22243
$686$			5.22780e8i			1.61937i
$687$	−3.91609e7	+	3.91609e7i	−0.120776	+	0.120776i
$688$			2.70457e8i			0.830487i
$689$	1.20068e8	−	4.09017e7i	0.367088	−	0.125050i
$690$	−5.12799e7			−0.156099
$691$	−4.86878e7	−	4.86878e7i	−0.147566	−	0.147566i	0.629464	−	0.777030i	$-0.283275\pi$
$691$	−4.86878e7	−	4.86878e7i	−0.147566	−	0.147566i	−0.777030	+	0.629464i	$0.783275\pi$
$692$	6.00435e8			1.81196
$693$		−	4.33639e7i		−	0.130295i
$694$	−4.56964e8	−	4.56964e8i	−1.36711	−	1.36711i
$695$	−1.14773e8	−	1.14773e8i	−0.341890	−	0.341890i
$696$	2.22779e6	−	2.22779e6i	0.00660764	−	0.00660764i
$697$	−3.34288e8	+	3.34288e8i	−0.987240	+	0.987240i
$698$	−5.74255e8			−1.68864
$699$		−	1.94659e8i		−	0.569958i
$700$	−8.24571e7	+	8.24571e7i	−0.240400	+	0.240400i
$701$			2.55548e8i			0.741853i	0.928662	+	0.370926i	$0.120960\pi$
$701$			2.55548e8i			0.741853i	−0.928662	+	0.370926i	$0.879040\pi$
$702$	4.72613e8	+	2.32436e8i	1.36614	+	0.671879i
$703$	6.00176e8			1.72748
$704$	8.71817e7	+	8.71817e7i	0.249866	+	0.249866i
$705$	−2.82393e8			−0.805909
$706$		−	1.68977e8i		−	0.480190i
$707$	−2.32123e8	−	2.32123e8i	−0.656841	−	0.656841i
$708$	7.91468e7	+	7.91468e7i	0.223015	+	0.223015i
$709$	−2.99236e8	+	2.99236e8i	−0.839604	+	0.839604i	−0.988807	−	0.149202i	$-0.952329\pi$
$709$	−2.99236e8	+	2.99236e8i	−0.839604	+	0.839604i	0.149202	+	0.988807i	$0.452329\pi$
$710$	−3.61881e7	+	3.61881e7i	−0.101109	+	0.101109i
$711$	1.82939e8			0.508977
$712$			1.72167e7i			0.0476991i
$713$	3.92811e7	−	3.92811e7i	0.108372	−	0.108372i
$714$		−	4.69175e8i		−	1.28896i
$715$	−7.10666e7	+	2.42091e7i	−0.194423	+	0.0662310i
$716$	−8.00360e8			−2.18045
$717$	1.33412e8	+	1.33412e8i	0.361939	+	0.361939i
$718$	6.76530e8			1.82774
$719$			3.54786e8i			0.954508i	0.878766	+	0.477254i	$0.158368\pi$
$719$			3.54786e8i			0.954508i	−0.878766	+	0.477254i	$0.841632\pi$
$720$	−8.86924e7	−	8.86924e7i	−0.237623	−	0.237623i
$721$	4.90482e7	+	4.90482e7i	0.130863	+	0.130863i
$722$	7.73727e8	−	7.73727e8i	2.05578	−	2.05578i
$723$	−1.40218e6	+	1.40218e6i	−0.00371013	+	0.00371013i
$724$	6.62589e8			1.74594
$725$			4.41374e6i			0.0115822i
$726$	−2.42055e8	+	2.42055e8i	−0.632564	+	0.632564i
$727$			6.94762e8i			1.80814i	0.427380	+	0.904072i	$0.359437\pi$
$727$			6.94762e8i			1.80814i	−0.427380	+	0.904072i	$0.640563\pi$
$728$	−4.27739e7	−	1.25564e8i	−0.110863	−	0.325440i
$729$	2.58767e8			0.667924
$730$	4.95456e8	+	4.95456e8i	1.27361	+	1.27361i
$731$	−7.37462e8			−1.88794
$732$		−	5.69891e8i		−	1.45298i
$733$	1.25593e8	+	1.25593e8i	0.318898	+	0.318898i	0.848344	−	0.529446i	$-0.177600\pi$
$733$	1.25593e8	+	1.25593e8i	0.318898	+	0.318898i	−0.529446	+	0.848344i	$0.677600\pi$
$734$	2.45094e8	+	2.45094e8i	0.619791	+	0.619791i
$735$	3.25848e7	−	3.25848e7i	0.0820641	−	0.0820641i
$736$	7.77524e7	−	7.77524e7i	0.195020	−	0.195020i
$737$	−1.23080e8			−0.307458
$738$			3.29438e8i			0.819605i
$739$	−1.66032e8	+	1.66032e8i	−0.411395	+	0.411395i	−0.882224	−	0.470829i	$-0.843955\pi$
$739$	−1.66032e8	+	1.66032e8i	−0.411395	+	0.411395i	0.470829	+	0.882224i	$0.343955\pi$
$740$		−	4.28680e8i		−	1.05788i
$741$	−3.96334e8	−	1.94920e8i	−0.974106	−	0.479074i
$742$	−2.10321e8			−0.514839
$743$	−4.33230e8	−	4.33230e8i	−1.05621	−	1.05621i	−0.998323	−	0.0578917i	$-0.981562\pi$
$743$	−4.33230e8	−	4.33230e8i	−1.05621	−	1.05621i	−0.0578917	−	0.998323i	$-0.518438\pi$
$744$	7.91511e7			0.192193
$745$		−	1.41840e8i		−	0.343028i
$746$	1.53718e8	+	1.53718e8i	0.370262	+	0.370262i
$747$	−2.58148e7	−	2.58148e7i	−0.0619307	−	0.0619307i
$748$	−1.40708e8	+	1.40708e8i	−0.336212	+	0.336212i
$749$	−3.79428e8	+	3.79428e8i	−0.902992	+	0.902992i
$750$	4.37165e8			1.03624
$751$		−	4.61949e8i		−	1.09062i	−0.838234	−	0.545311i	$-0.816412\pi$
$751$		−	4.61949e8i		−	1.09062i	0.838234	−	0.545311i	$-0.183588\pi$
$752$	3.09317e8	−	3.09317e8i	0.727362	−	0.727362i
$753$		−	1.70470e8i		−	0.399266i
$754$	−2.19026e7	−	1.07719e7i	−0.0510953	−	0.0251291i
$755$	−3.41633e8			−0.793814
$756$	−3.44152e8	−	3.44152e8i	−0.796498	−	0.796498i
$757$	3.67377e8			0.846885			0.423443	−	0.905923i	$-0.360821\pi$
$757$	3.67377e8			0.846885			0.423443	+	0.905923i	$0.360821\pi$
$758$		−	5.96834e8i		−	1.37040i
$759$	−9.49972e6	−	9.49972e6i	−0.0217263	−	0.0217263i
$760$	−1.72447e8	−	1.72447e8i	−0.392839	−	0.392839i
$761$	2.78595e8	−	2.78595e8i	0.632150	−	0.632150i	−0.316457	−	0.948607i	$-0.602493\pi$
$761$	2.78595e8	−	2.78595e8i	0.632150	−	0.632150i	0.948607	+	0.316457i	$0.102493\pi$
$762$	−2.93767e8	+	2.93767e8i	−0.663955	+	0.663955i
$763$	−2.30993e8			−0.520026
$764$		−	8.33315e7i		−	0.186866i
$765$	2.41840e8	−	2.41840e8i	0.540186	−	0.540186i
$766$		−	4.91253e8i		−	1.09300i
$767$	7.87204e7	−	1.60063e8i	0.174462	−	0.354735i
$768$	−8.69002e7			−0.191839
$769$	4.33883e7	+	4.33883e7i	0.0954098	+	0.0954098i	0.753201	−	0.657791i	$-0.228509\pi$
$769$	4.33883e7	+	4.33883e7i	0.0954098	+	0.0954098i	−0.657791	+	0.753201i	$0.728509\pi$
$770$	1.24486e8			0.272677
$771$			3.01982e8i			0.658899i
$772$	4.66420e8	+	4.66420e8i	1.01374	+	1.01374i
$773$	1.03754e8	+	1.03754e8i	0.224629	+	0.224629i	0.810444	−	0.585815i	$-0.199226\pi$
$773$	1.03754e8	+	1.03754e8i	0.224629	+	0.224629i	−0.585815	+	0.810444i	$0.699226\pi$
$774$	−3.63381e8	+	3.63381e8i	−0.783681	+	0.783681i
$775$	−7.84079e7	+	7.84079e7i	−0.168444	+	0.168444i
$776$	−6.63643e7			−0.142020
$777$			2.64797e8i			0.564482i
$778$	1.87122e8	−	1.87122e8i	0.397361	−	0.397361i
$779$		−	7.37932e8i		−	1.56100i
$780$	−1.39224e8	+	2.83085e8i	−0.293379	+	0.596530i
$781$	−1.34079e7			−0.0281453
$782$	1.53158e8	+	1.53158e8i	0.320273	+	0.320273i
$783$	−1.84217e7			−0.0383746
$784$			7.13832e7i			0.148132i
$785$	−2.33126e8	−	2.33126e8i	−0.481928	−	0.481928i
$786$	8.57215e7	+	8.57215e7i	0.176531	+	0.176531i
$787$	−5.52470e8	+	5.52470e8i	−1.13340	+	1.13340i	−0.143795	+	0.989608i	$0.545931\pi$
$787$	−5.52470e8	+	5.52470e8i	−1.13340	+	1.13340i	−0.989608	+	0.143795i	$0.954069\pi$
$788$	−3.07946e8	+	3.07946e8i	−0.629355	+	0.629355i
$789$	4.60652e8			0.937868
$790$			5.25169e8i			1.06517i
$791$	2.39821e8	−	2.39821e8i	0.484571	−	0.484571i
$792$			2.85238e7i			0.0574158i
$793$	−8.59670e8	+	2.92850e8i	−1.72390	+	0.587254i
$794$	3.08277e8			0.615856
$795$	7.27533e7	+	7.27533e7i	0.144794	+	0.144794i
$796$	7.19605e7			0.142677
$797$			1.61019e7i			0.0318054i	0.999874	+	0.0159027i	$0.00506220\pi$
$797$			1.61019e7i			0.0318054i	−0.999874	+	0.0159027i	$0.994938\pi$
$798$	5.17845e8	+	5.17845e8i	1.01904	+	1.01904i
$799$	8.43424e8	+	8.43424e8i	1.65351	+	1.65351i
$800$	−1.55199e8	+	1.55199e8i	−0.303123	+	0.303123i
$801$	2.66494e7	−	2.66494e7i	0.0518549	−	0.0518549i
$802$	−2.64320e8			−0.512397
$803$			1.83568e8i			0.354529i
$804$	−3.65698e8	+	3.65698e8i	−0.703646	+	0.703646i
$805$		−	7.55176e7i		−	0.144764i
$806$	−1.97731e8	−	5.80445e8i	−0.377633	−	1.10855i
$807$	3.91290e8			0.744522
$808$	1.52685e8	+	1.52685e8i	0.289442	+	0.289442i
$809$	−4.23919e8			−0.800640			−0.400320	−	0.916375i	$-0.631101\pi$
$809$	−4.23919e8			−0.800640			−0.400320	+	0.916375i	$0.631101\pi$
$810$			2.89422e7i			0.0544599i
$811$	3.13841e8	+	3.13841e8i	0.588365	+	0.588365i	0.937189	−	0.348823i	$-0.113419\pi$
$811$	3.13841e8	+	3.13841e8i	0.588365	+	0.588365i	−0.348823	+	0.937189i	$0.613419\pi$
$812$	1.59492e7	+	1.59492e7i	0.0297900	+	0.0297900i
$813$	1.94355e8	−	1.94355e8i	0.361680	−	0.361680i
$814$	1.42492e8	−	1.42492e8i	0.264191	−	0.264191i
$815$	4.97862e8			0.919679
$816$		−	3.55538e8i		−	0.654358i
$817$	8.13963e8	−	8.13963e8i	1.49258	−	1.49258i
$818$			1.20734e9i			2.20583i
$819$	−1.28149e8	+	2.60567e8i	−0.233273	+	0.474316i
$820$	−5.27074e8			−0.955938
$821$	3.18406e8	+	3.18406e8i	0.575376	+	0.575376i	0.933626	−	0.358250i	$-0.116626\pi$
$821$	3.18406e8	+	3.18406e8i	0.575376	+	0.575376i	−0.358250	+	0.933626i	$0.616626\pi$
$822$	−7.76097e8			−1.39734
$823$		−	5.96016e8i		−	1.06920i	−0.845106	−	0.534599i	$-0.820463\pi$
$823$		−	5.96016e8i		−	1.06920i	0.845106	−	0.534599i	$-0.179537\pi$
$824$	−3.22627e7	−	3.22627e7i	−0.0576660	−	0.0576660i
$825$	1.89621e7	+	1.89621e7i	0.0337695	+	0.0337695i
$826$	−2.09136e8	+	2.09136e8i	−0.371098	+	0.371098i
$827$	3.09467e8	−	3.09467e8i	0.547140	−	0.547140i	−0.378473	−	0.925612i	$-0.623551\pi$
$827$	3.09467e8	−	3.09467e8i	0.547140	−	0.547140i	0.925612	+	0.378473i	$0.123551\pi$
$828$	8.41197e7			0.148186
$829$		−	6.94933e8i		−	1.21977i	−0.792489	−	0.609887i	$-0.791215\pi$
$829$		−	6.94933e8i		−	1.21977i	0.792489	−	0.609887i	$-0.208785\pi$
$830$	7.41072e7	−	7.41072e7i	0.129606	−	0.129606i
$831$		−	2.22569e8i		−	0.387847i
$832$	−2.66221e8	−	7.81501e8i	−0.462246	−	1.35694i
$833$	−1.94643e8			−0.336746
$834$	−2.26706e8	−	2.26706e8i	−0.390809	−	0.390809i
$835$	−5.62707e8			−0.966547
$836$		−	3.10608e8i		−	0.531611i
$837$	−3.27251e8	−	3.27251e8i	−0.558091	−	0.558091i
$838$	−7.27536e8	−	7.27536e8i	−1.23630	−	1.23630i
$839$	1.75155e6	−	1.75155e6i	0.00296577	−	0.00296577i	−0.705622	−	0.708588i	$-0.749332\pi$
$839$	1.75155e6	−	1.75155e6i	0.00296577	−	0.00296577i	0.708588	+	0.705622i	$0.249332\pi$
$840$	7.60836e7	−	7.60836e7i	0.128367	−	0.128367i
$841$	−5.93970e8			−0.998565
$842$			3.49638e7i			0.0585709i
$843$	−4.07196e8	+	4.07196e8i	−0.679705	+	0.679705i
$844$		−	7.43400e6i		−	0.0123650i
$845$	4.98571e8	+	6.45473e7i	0.826337	+	0.106981i
$846$	8.31186e8			1.37274
$847$	−3.56464e8	−	3.56464e8i	−0.586631	−	0.586631i
$848$	−1.59380e8			−0.261364
$849$		−	2.12889e8i		−	0.347880i
$850$	−3.05714e8	−	3.05714e8i	−0.497804	−	0.497804i
$851$	−8.64408e7	−	8.64408e7i	−0.140259	−	0.140259i
$852$	−3.98376e7	+	3.98376e7i	−0.0644131	+	0.0644131i
$853$	3.99606e8	−	3.99606e8i	0.643850	−	0.643850i	−0.307650	−	0.951500i	$-0.599543\pi$
$853$	3.99606e8	−	3.99606e8i	0.643850	−	0.643850i	0.951500	+	0.307650i	$0.0995425\pi$
$854$	1.50587e9			2.41776
$855$			5.33854e8i			0.854131i
$856$	2.49578e8	−	2.49578e8i	0.397911	−	0.397911i
$857$			9.84583e8i			1.56426i	0.623113	+	0.782132i	$0.285868\pi$
$857$			9.84583e8i			1.56426i	−0.623113	+	0.782132i	$0.714132\pi$
$858$	−1.40374e8	+	4.78191e7i	−0.222242	+	0.0757076i
$859$	−4.66714e8			−0.736328			−0.368164	−	0.929761i	$-0.620013\pi$
$859$	−4.66714e8			−0.736328			−0.368164	+	0.929761i	$0.620013\pi$
$860$	−5.81380e8	−	5.81380e8i	−0.914038	−	0.914038i
$861$	3.25575e8			0.510084
$862$			3.01421e8i			0.470600i
$863$	6.18379e8	+	6.18379e8i	0.962104	+	0.962104i	0.999308	−	0.0372036i	$-0.0118450\pi$
$863$	6.18379e8	+	6.18379e8i	0.962104	+	0.962104i	−0.0372036	+	0.999308i	$0.511845\pi$
$864$	−6.47755e8	−	6.47755e8i	−1.00431	−	1.00431i
$865$	5.48822e8	−	5.48822e8i	0.847975	−	0.847975i
$866$	−2.53273e8	+	2.53273e8i	−0.389973	+	0.389973i
$867$	5.56458e8			0.853837
$868$			5.66659e8i			0.866488i
$869$	−9.72887e7	+	9.72887e7i	−0.148253	+	0.148253i
$870$		−	1.97986e7i		−	0.0300660i
$871$	7.39570e8	+	3.63727e8i	1.11924	+	0.550454i
$872$	1.51941e8			0.229154
$873$	1.02724e8	+	1.02724e8i	0.154393	+	0.154393i
$874$	−3.38092e8			−0.506408
$875$			6.43794e8i			0.960998i
$876$	5.45421e8	+	5.45421e8i	0.811371	+	0.811371i
$877$	−3.05312e8	−	3.05312e8i	−0.452632	−	0.452632i	0.443595	−	0.896227i	$-0.353703\pi$
$877$	−3.05312e8	−	3.05312e8i	−0.452632	−	0.452632i	−0.896227	+	0.443595i	$0.853703\pi$
$878$	−3.24060e8	+	3.24060e8i	−0.478787	+	0.478787i
$879$	1.55404e8	−	1.55404e8i	0.228821	−	0.228821i
$880$	9.43349e7			0.138428
$881$			5.29881e6i			0.00774908i	0.999992	+	0.00387454i	$0.00123331\pi$
$881$			5.29881e6i			0.00774908i	−0.999992	+	0.00387454i	$0.998767\pi$
$882$	−9.59092e7	+	9.59092e7i	−0.139783	+	0.139783i
$883$			7.31615e8i			1.06268i	0.847160	+	0.531338i	$0.178310\pi$
$883$			7.31615e8i			1.06268i	−0.847160	+	0.531338i	$0.821690\pi$
$884$	1.26131e9	−	4.29671e8i	1.82585	−	0.621984i
$885$	1.44687e8			0.208737
$886$	3.24460e7	+	3.24460e7i	0.0466509	+	0.0466509i
$887$	−2.32665e8			−0.333396			−0.166698	−	0.986008i	$-0.553311\pi$
$887$	−2.32665e8			−0.333396			−0.166698	+	0.986008i	$0.553311\pi$
$888$		−	1.74177e8i		−	0.248744i
$889$	−4.32618e8	−	4.32618e8i	−0.615742	−	0.615742i
$890$	7.65032e7	+	7.65032e7i	0.108520	+	0.108520i
$891$	−5.36161e6	+	5.36161e6i	−0.00757987	+	0.00757987i
$892$	7.13585e8	−	7.13585e8i	1.00543	−	1.00543i
$893$	−1.86183e9			−2.61449
$894$		−	2.80169e8i		−	0.392109i
$895$	−7.31562e8	+	7.31562e8i	−1.02043	+	1.02043i
$896$			4.78028e8i			0.664553i
$897$	2.90087e7	+	8.51559e7i	0.0401931	+	0.117988i
$898$	−1.09044e8			−0.150582
$899$	1.51660e7	+	1.51660e7i	0.0208733	+	0.0208733i
$900$	−1.67909e8			−0.230327
$901$		−	4.34586e8i		−	0.594157i
$902$	−1.75198e8	−	1.75198e8i	−0.238732	−	0.238732i
$903$	3.59120e8	+	3.59120e8i	0.487727	+	0.487727i
$904$	−1.57748e8	+	1.57748e8i	−0.213530	+	0.213530i
$905$	6.05633e8	−	6.05633e8i	0.817079	−	0.817079i
$906$	−6.74810e8			−0.907396
$907$			5.05806e8i			0.677894i	0.940805	+	0.338947i	$0.110071\pi$
$907$			5.05806e8i			0.677894i	−0.940805	+	0.338947i	$0.889929\pi$
$908$	−6.36673e8	+	6.36673e8i	−0.850470	+	0.850470i
$909$		−	4.72676e8i		−	0.629320i
$910$	−7.48018e8	−	3.67882e8i	−0.992631	−	0.488185i
$911$	−1.00881e9			−1.33431			−0.667154	−	0.744920i	$-0.732488\pi$
$911$	−1.00881e9			−1.33431			−0.667154	+	0.744920i	$0.732488\pi$
$912$	3.92420e8	+	3.92420e8i	0.517328	+	0.517328i
$913$	2.74570e7			0.0360779
$914$			1.68801e9i			2.21074i
$915$	−5.20903e8	−	5.20903e8i	−0.679977	−	0.679977i
$916$	1.84414e8	+	1.84414e8i	0.239943	+	0.239943i
$917$	−1.26238e8	+	1.26238e8i	−0.163713	+	0.163713i
$918$	1.27596e9	−	1.27596e9i	1.64934	−	1.64934i
$919$	1.36736e9			1.76172			0.880860	−	0.473378i	$-0.156965\pi$
$919$	1.36736e9			1.76172			0.880860	+	0.473378i	$0.156965\pi$
$920$			4.96737e7i			0.0637915i
$921$	1.64313e8	−	1.64313e8i	0.210326	−	0.210326i
$922$			1.68334e8i			0.214772i
$923$	8.05657e7	+	3.96229e7i	0.102458	+	0.0503897i
$924$	1.37040e8			0.173713
$925$	1.72542e8	+	1.72542e8i	0.218006	+	0.218006i
$926$	5.50894e8			0.693801
$927$			9.98777e7i			0.125380i
$928$	3.00193e7	+	3.00193e7i	0.0375626	+	0.0375626i
$929$	−7.69217e8	−	7.69217e8i	−0.959404	−	0.959404i	0.0398032	−	0.999208i	$-0.487327\pi$
$929$	−7.69217e8	−	7.69217e8i	−0.959404	−	0.959404i	−0.999208	+	0.0398032i	$0.987327\pi$
$930$	3.51711e8	−	3.51711e8i	0.437258	−	0.437258i
$931$	2.14834e8	−	2.14834e8i	0.266228	−	0.266228i
$932$	−9.16679e8			−1.13232
$933$			5.21222e8i			0.641768i
$934$	−3.65612e8	+	3.65612e8i	−0.448724	+	0.448724i
$935$			2.57225e8i			0.314687i
$936$	8.42935e7	−	1.71395e8i	0.102794	−	0.209011i
$937$	1.42415e9			1.73116			0.865581	−	0.500769i	$-0.166949\pi$
$937$	1.42415e9			1.73116			0.865581	+	0.500769i	$0.166949\pi$
$938$	−9.66313e8	−	9.66313e8i	−1.17087	−	1.17087i
$939$	−3.53717e8			−0.427227
$940$			1.32983e9i			1.60108i
$941$	1.07583e9	+	1.07583e9i	1.29115	+	1.29115i	0.934077	+	0.357072i	$0.116225\pi$
$941$	1.07583e9	+	1.07583e9i	1.29115	+	1.29115i	0.357072	+	0.934077i	$0.383775\pi$
$942$	−4.60483e8	−	4.60483e8i	−0.550884	−	0.550884i
$943$	−1.06281e8	+	1.06281e8i	−0.126742	+	0.126742i
$944$	−1.58482e8	+	1.58482e8i	−0.188393	+	0.188393i
$945$	−6.29137e8			−0.745504
$946$		−	3.86499e8i		−	0.456536i
$947$	3.72519e8	−	3.72519e8i	0.438630	−	0.438630i	−0.452921	−	0.891551i	$-0.649618\pi$
$947$	3.72519e8	−	3.72519e8i	0.438630	−	0.438630i	0.891551	+	0.452921i	$0.149618\pi$
$948$			5.78131e8i			0.678580i
$949$	5.42482e8	−	1.10303e9i	0.634727	−	1.29060i
$950$	6.74855e8			0.787118
$951$	−6.31432e8	−	6.31432e8i	−0.734151	−	0.734151i
$952$	−4.54479e8			−0.526748
$953$			6.36621e8i			0.735534i	0.929918	+	0.367767i	$0.119878\pi$
$953$			6.36621e8i			0.735534i	−0.929918	+	0.367767i	$0.880122\pi$
$954$	−2.14140e8	−	2.14140e8i	−0.246634	−	0.246634i
$955$	−7.61684e7	−	7.61684e7i	−0.0874510	−	0.0874510i
$956$	6.28255e8	−	6.28255e8i	0.719056	−	0.719056i
$957$	3.66773e6	−	3.66773e6i	0.00418467	−	0.00418467i
$958$	1.32518e9			1.50723
$959$		−	1.14292e9i		−	1.29587i
$960$	4.73538e8	−	4.73538e8i	0.535231	−	0.535231i
$961$		−	3.48672e8i		−	0.392868i
$962$	−1.27731e9	+	4.35120e8i	−1.43473	+	0.488747i
$963$	−7.72635e8			−0.865158
$964$	6.60309e6	+	6.60309e6i	0.00737083	+	0.00737083i
$965$	8.52653e8			0.948834
$966$		−	1.49166e8i		−	0.165477i
$967$	−1.65872e8	−	1.65872e8i	−0.183440	−	0.183440i	0.609413	−	0.792853i	$-0.291405\pi$
$967$	−1.65872e8	−	1.65872e8i	−0.183440	−	0.183440i	−0.792853	+	0.609413i	$0.791405\pi$
$968$	2.34473e8	+	2.34473e8i	0.258504	+	0.258504i
$969$	−1.07002e9	+	1.07002e9i	−1.17604	+	1.17604i
$970$	−2.94893e8	+	2.94893e8i	−0.323109	+	0.323109i
$971$	−2.03038e8			−0.221779			−0.110889	−	0.993833i	$-0.535370\pi$
$971$	−2.03038e8			−0.221779			−0.110889	+	0.993833i	$0.535370\pi$
$972$		−	1.13924e9i		−	1.24055i
$973$	3.33860e8	−	3.33860e8i	0.362431	−	0.362431i
$974$		−	2.39602e7i		−	0.0259306i
$975$	−5.79034e7	−	1.69977e8i	−0.0624727	−	0.183390i
$976$	1.14114e9			1.22741
$977$	2.63431e8	+	2.63431e8i	0.282477	+	0.282477i	0.834096	−	0.551619i	$-0.185990\pi$
$977$	2.63431e8	+	2.63431e8i	0.282477	+	0.282477i	−0.551619	+	0.834096i	$0.685990\pi$
$978$	9.83402e8			1.05127
$979$			2.83448e7i			0.0302082i
$980$	−1.53447e8	−	1.53447e8i	−0.163035	−	0.163035i
$981$	−2.35187e8	−	2.35187e8i	−0.249119	−	0.249119i
$982$	2.91346e8	−	2.91346e8i	0.307662	−	0.307662i
$983$	3.97286e8	−	3.97286e8i	0.418256	−	0.418256i	−0.466346	−	0.884602i	$-0.654430\pi$
$983$	3.97286e8	−	3.97286e8i	0.418256	−	0.418256i	0.884602	+	0.466346i	$0.154430\pi$
$984$	−2.14155e8			−0.224773
$985$			5.62950e8i			0.589062i
$986$	−5.91325e7	+	5.91325e7i	−0.0616873	+	0.0616873i
$987$		−	8.21440e8i		−	0.854328i
$988$	−9.17910e8	+	1.86640e9i	−0.951764	+	1.93523i
$989$	−2.34463e8			−0.242374
$990$	1.26747e8	+	1.26747e8i	0.130626	+	0.130626i
$991$	1.89931e8			0.195153			0.0975763	−	0.995228i	$-0.468891\pi$
$991$	1.89931e8			0.195153			0.0975763	+	0.995228i	$0.468891\pi$
$992$			1.06655e9i			1.09257i
$993$	−3.11456e8	−	3.11456e8i	−0.318089	−	0.318089i
$994$	−1.05266e8	−	1.05266e8i	−0.107184	−	0.107184i
$995$	6.57749e7	−	6.57749e7i	0.0667714	−	0.0667714i
$996$	8.15807e7	−	8.15807e7i	0.0825676	−	0.0825676i
$997$	−1.93733e9			−1.95487			−0.977433	−	0.211244i	$-0.932249\pi$
$997$	−1.93733e9			−1.95487			−0.977433	+	0.211244i	$0.932249\pi$
$998$		−	1.68251e9i		−	1.69265i
$999$	−7.20139e8	+	7.20139e8i	−0.722303	+	0.722303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.d.a.8.1	yes	12
3.2	odd	2		117.7.j.b.73.6		12
4.3	odd	2		208.7.t.c.177.4		12
13.5	odd	4	inner	13.7.d.a.5.1	✓	12
39.5	even	4		117.7.j.b.109.6		12
52.31	even	4		208.7.t.c.161.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.d.a.5.1	✓	12	13.5	odd	4	inner
13.7.d.a.8.1	yes	12	1.1	even	1	trivial
117.7.j.b.73.6		12	3.2	odd	2
117.7.j.b.109.6		12	39.5	even	4
208.7.t.c.161.4		12	52.31	even	4
208.7.t.c.177.4		12	4.3	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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.50218 - 8.50218i) q^{2} -17.1101 q^{3} +80.5742i q^{4} +(73.6481 + 73.6481i) q^{5} +(145.473 + 145.473i) q^{6} +(-214.232 + 214.232i) q^{7} +(140.917 - 140.917i) q^{8} -436.244 q^{9} +O(q^{10})\)	\(q+(-8.50218 - 8.50218i) q^{2} -17.1101 q^{3} +80.5742i q^{4} +(73.6481 + 73.6481i) q^{5} +(145.473 + 145.473i) q^{6} +(-214.232 + 214.232i) q^{7} +(140.917 - 140.917i) q^{8} -436.244 q^{9} -1252.34i q^{10} +(231.998 - 231.998i) q^{11} -1378.63i q^{12} +(-2079.64 + 708.440i) q^{13} +3642.88 q^{14} +(-1260.13 - 1260.13i) q^{15} +2760.55 q^{16} +7527.26i q^{17} +(3709.02 + 3709.02i) q^{18} +(-8308.11 - 8308.11i) q^{19} +(-5934.13 + 5934.13i) q^{20} +(3665.53 - 3665.53i) q^{21} -3944.99 q^{22} +2393.16i q^{23} +(-2411.10 + 2411.10i) q^{24} -4776.92i q^{25} +(23704.8 + 11658.2i) q^{26} +19937.5 q^{27} +(-17261.6 - 17261.6i) q^{28} -923.972 q^{29} +21427.7i q^{30} +(-16413.9 - 16413.9i) q^{31} +(-32489.4 - 32489.4i) q^{32} +(-3969.52 + 3969.52i) q^{33} +(63998.2 - 63998.2i) q^{34} -31555.5 q^{35} -35150.0i q^{36} +(-36119.9 + 36119.9i) q^{37} +141274. i q^{38} +(35583.0 - 12121.5i) q^{39} +20756.5 q^{40} +(44410.3 + 44410.3i) q^{41} -62330.1 q^{42} +97972.1i q^{43} +(18693.1 + 18693.1i) q^{44} +(-32128.5 - 32128.5i) q^{45} +(20347.1 - 20347.1i) q^{46} +(112049. - 112049. i) q^{47} -47233.3 q^{48} +25858.3i q^{49} +(-40614.2 + 40614.2i) q^{50} -128792. i q^{51} +(-57081.9 - 167566. i) q^{52} -57734.9 q^{53} +(-169512. - 169512. i) q^{54} +34172.5 q^{55} +60377.7i q^{56} +(142153. + 142153. i) q^{57} +(7855.78 + 7855.78i) q^{58} +(-57409.6 + 57409.6i) q^{59} +(101534. - 101534. i) q^{60} +413374. q^{61} +279108. i q^{62} +(93457.4 - 93457.4i) q^{63} +375786. i q^{64} +(-205337. - 100987. i) q^{65} +67499.2 q^{66} +(-265261. - 265261. i) q^{67} -606503. q^{68} -40947.3i q^{69} +(268291. + 268291. i) q^{70} +(-28896.4 - 28896.4i) q^{71} +(-61474.0 + 61474.0i) q^{72} +(-395624. + 395624. i) q^{73} +614195. q^{74} +81733.7i q^{75} +(669419. - 669419. i) q^{76} +99403.0i q^{77} +(-405592. - 199474. i) q^{78} -419351. q^{79} +(203309. + 203309. i) q^{80} -23110.5 q^{81} -755169. i q^{82} +(59175.0 + 59175.0i) q^{83} +(295347. + 295347. i) q^{84} +(-554369. + 554369. i) q^{85} +(832977. - 832977. i) q^{86} +15809.3 q^{87} -65384.9i q^{88} +(-61088.3 + 61088.3i) q^{89} +546325. i q^{90} +(293756. - 597297. i) q^{91} -192827. q^{92} +(280844. + 280844. i) q^{93} -1.90533e6 q^{94} -1.22375e6i q^{95} +(555897. + 555897. i) q^{96} +(-235474. - 235474. i) q^{97} +(219852. - 219852. i) q^{98} +(-101208. + 101208. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

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