LMFDB - Embedded newform 75.12.e.d.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,12,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	75.e (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:	$57.6257385420$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.6
Character	$\chi$	$=$	75.32
Dual form			75.12.e.d.68.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-37.2586 + 37.2586i) q^{2} +(407.704 + 104.521i) q^{3} -728.404i q^{4} +(-19084.8 + 11296.2i) q^{6} +(5795.67 + 5795.67i) q^{7} +(-49166.3 - 49166.3i) q^{8} +(155298. + 85226.8i) q^{9} +O(q^{10})$	\(q+(-37.2586 + 37.2586i) q^{2} +(407.704 + 104.521i) q^{3} -728.404i q^{4} +(-19084.8 + 11296.2i) q^{6} +(5795.67 + 5795.67i) q^{7} +(-49166.3 - 49166.3i) q^{8} +(155298. + 85226.8i) q^{9} +364518. i q^{11} +(76133.2 - 296973. i) q^{12} +(-609210. + 609210. i) q^{13} -431877. q^{14} +5.15550e6 q^{16} +(3.57407e6 - 3.57407e6i) q^{17} +(-8.96161e6 + 2.61075e6i) q^{18} +1.30082e7i q^{19} +(1.75715e6 + 2.96868e6i) q^{21} +(-1.35814e7 - 1.35814e7i) q^{22} +(-3.07670e7 - 3.07670e7i) q^{23} +(-1.49064e7 - 2.51842e7i) q^{24} -4.53966e7i q^{26} +(5.44076e7 + 5.09791e7i) q^{27} +(4.22159e6 - 4.22159e6i) q^{28} -9.62766e7 q^{29} -1.54727e7 q^{31} +(-9.13942e7 + 9.13942e7i) q^{32} +(-3.80996e7 + 1.48615e8i) q^{33} +2.66330e8i q^{34} +(6.20796e7 - 1.13120e8i) q^{36} +(4.15338e8 + 4.15338e8i) q^{37} +(-4.84668e8 - 4.84668e8i) q^{38} +(-3.12052e8 + 1.84702e8i) q^{39} +1.11979e9i q^{41} +(-1.76078e8 - 4.51400e7i) q^{42} +(-1.03152e9 + 1.03152e9i) q^{43} +2.65516e8 q^{44} +2.29267e9 q^{46} +(-1.26480e9 + 1.26480e9i) q^{47} +(2.10192e9 + 5.38856e8i) q^{48} -1.91015e9i q^{49} +(1.83073e9 - 1.08360e9i) q^{51} +(4.43751e8 + 4.43751e8i) q^{52} +(-1.85642e9 - 1.85642e9i) q^{53} +(-3.92656e9 + 1.27740e8i) q^{54} -5.69903e8i q^{56} +(-1.35963e9 + 5.30351e9i) q^{57} +(3.58713e9 - 3.58713e9i) q^{58} +3.23793e9 q^{59} -5.92067e9 q^{61} +(5.76493e8 - 5.76493e8i) q^{62} +(4.06109e8 + 1.39400e9i) q^{63} +3.74803e9i q^{64} +(-4.11766e9 - 6.95674e9i) q^{66} +(-8.83271e9 - 8.83271e9i) q^{67} +(-2.60337e9 - 2.60337e9i) q^{68} +(-9.32805e9 - 1.57596e10i) q^{69} -1.82115e10i q^{71} +(-3.44513e9 - 1.18257e10i) q^{72} +(-3.15172e9 + 3.15172e9i) q^{73} -3.09498e10 q^{74} +9.47525e9 q^{76} +(-2.11263e9 + 2.11263e9i) q^{77} +(4.74488e9 - 1.85084e10i) q^{78} -2.48867e10i q^{79} +(1.68538e10 + 2.64711e10i) q^{81} +(-4.17220e10 - 4.17220e10i) q^{82} +(-2.65597e10 - 2.65597e10i) q^{83} +(2.16240e9 - 1.27992e9i) q^{84} -7.68659e10i q^{86} +(-3.92523e10 - 1.00629e10i) q^{87} +(1.79220e10 - 1.79220e10i) q^{88} -5.83244e10 q^{89} -7.06156e9 q^{91} +(-2.24108e10 + 2.24108e10i) q^{92} +(-6.30830e9 - 1.61722e9i) q^{93} -9.42496e10i q^{94} +(-4.68143e10 + 2.77092e10i) q^{96} +(9.17088e10 + 9.17088e10i) q^{97} +(7.11694e10 + 7.11694e10i) q^{98} +(-3.10667e10 + 5.66089e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−37.2586	+	37.2586i	−0.823306	+	0.823306i	−0.986581	−	0.163275i	$-0.947794\pi$
$2$	−37.2586	+	37.2586i	−0.823306	+	0.823306i	0.163275	+	0.986581i	$0.447794\pi$
$3$	407.704	+	104.521i	0.968675	+	0.248333i
$3$	407.704	+	104.521i	0.968675	+	0.248333i
$4$		−	728.404i		−	0.355666i
$5$		0			0
$5$		0			0
$6$	−19084.8	+	11296.2i	−1.00197	+	0.593062i
$7$	5795.67	+	5795.67i	0.130336	+	0.130336i	0.769265	−	0.638929i	$-0.220622\pi$
$7$	5795.67	+	5795.67i	0.130336	+	0.130336i	−0.638929	+	0.769265i	$0.720622\pi$
$8$	−49166.3	−	49166.3i	−0.530484	−	0.530484i
$9$	155298.	+	85226.8i	0.876661	+	0.481108i
$10$		0			0
$11$			364518.i			0.682432i	0.939985	+	0.341216i	$0.110839\pi$
$11$			364518.i			0.682432i	−0.939985	+	0.341216i	$0.889161\pi$
$12$	76133.2	−	296973.i	0.0883236	−	0.344525i
$13$	−609210.	+	609210.i	−0.455071	+	0.455071i	−0.897033	−	0.441963i	$-0.854282\pi$
$13$	−609210.	+	609210.i	−0.455071	+	0.455071i	0.441963	+	0.897033i	$0.354282\pi$
$14$	−431877.			−0.214613
$15$		0			0
$16$	5.15550e6			1.22917
$17$	3.57407e6	−	3.57407e6i	0.610513	−	0.610513i	−0.332567	−	0.943080i	$-0.607915\pi$
$17$	3.57407e6	−	3.57407e6i	0.610513	−	0.610513i	0.943080	+	0.332567i	$0.107915\pi$
$18$	−8.96161e6	+	2.61075e6i	−1.11786	+	0.325661i
$19$			1.30082e7i			1.20524i	0.798028	+	0.602620i	$0.205877\pi$
$19$			1.30082e7i			1.20524i	−0.798028	+	0.602620i	$0.794123\pi$
$20$		0			0
$21$	1.75715e6	+	2.96868e6i	0.0938864	+	0.158620i
$22$	−1.35814e7	−	1.35814e7i	−0.561850	−	0.561850i
$23$	−3.07670e7	−	3.07670e7i	−0.996741	−	0.996741i	0.00325393	−	0.999995i	$-0.498964\pi$
$23$	−3.07670e7	−	3.07670e7i	−0.996741	−	0.996741i	−0.999995	+	0.00325393i	$0.998964\pi$
$24$	−1.49064e7	−	2.51842e7i	−0.382130	−	0.645603i
$25$		0			0
$26$		−	4.53966e7i		−	0.749325i
$27$	5.44076e7	+	5.09791e7i	0.729725	+	0.683741i
$28$	4.22159e6	−	4.22159e6i	0.0463561	−	0.0463561i
$29$	−9.62766e7			−0.871629			−0.435814	−	0.900037i	$-0.643540\pi$
$29$	−9.62766e7			−0.871629			−0.435814	+	0.900037i	$0.643540\pi$
$30$		0			0
$31$	−1.54727e7			−0.0970684			−0.0485342	−	0.998822i	$-0.515455\pi$
$31$	−1.54727e7			−0.0970684			−0.0485342	+	0.998822i	$0.515455\pi$
$32$	−9.13942e7	+	9.13942e7i	−0.481497	+	0.481497i
$33$	−3.80996e7	+	1.48615e8i	−0.169470	+	0.661054i
$34$			2.66330e8i			1.00528i
$35$		0			0
$36$	6.20796e7	−	1.13120e8i	0.171114	−	0.311799i
$37$	4.15338e8	+	4.15338e8i	0.984673	+	0.984673i	0.999884	−	0.0152109i	$-0.00484196\pi$
$37$	4.15338e8	+	4.15338e8i	0.984673	+	0.984673i	−0.0152109	+	0.999884i	$0.504842\pi$
$38$	−4.84668e8	−	4.84668e8i	−0.992282	−	0.992282i
$39$	−3.12052e8	+	1.84702e8i	−0.553825	+	0.327806i
$40$		0			0
$41$			1.11979e9i			1.50948i	0.656024	+	0.754740i	$0.272237\pi$
$41$			1.11979e9i			1.50948i	−0.656024	+	0.754740i	$0.727763\pi$
$42$	−1.76078e8	−	4.51400e7i	−0.207890	−	0.0532955i
$43$	−1.03152e9	+	1.03152e9i	−1.07004	+	1.07004i	−0.0726869	+	0.997355i	$0.523157\pi$
$43$	−1.03152e9	+	1.03152e9i	−1.07004	+	1.07004i	−0.997355	+	0.0726869i	$0.976843\pi$
$44$	2.65516e8			0.242718
$45$		0			0
$46$	2.29267e9			1.64125
$47$	−1.26480e9	+	1.26480e9i	−0.804424	+	0.804424i	−0.983784	−	0.179360i	$-0.942597\pi$
$47$	−1.26480e9	+	1.26480e9i	−0.804424	+	0.804424i	0.179360	+	0.983784i	$0.442597\pi$
$48$	2.10192e9	+	5.38856e8i	1.19066	+	0.305243i
$49$		−	1.91015e9i		−	0.966025i
$50$		0			0
$51$	1.83073e9	−	1.08360e9i	0.742999	−	0.439778i
$52$	4.43751e8	+	4.43751e8i	0.161853	+	0.161853i
$53$	−1.85642e9	−	1.85642e9i	−0.609761	−	0.609761i	0.333123	−	0.942883i	$-0.391898\pi$
$53$	−1.85642e9	−	1.85642e9i	−0.609761	−	0.609761i	−0.942883	+	0.333123i	$0.891898\pi$
$54$	−3.92656e9	+	1.27740e8i	−1.16372	+	0.0378584i
$55$		0			0
$56$		−	5.69903e8i		−	0.138282i
$57$	−1.35963e9	+	5.30351e9i	−0.299301	+	1.16749i
$58$	3.58713e9	−	3.58713e9i	0.717617	−	0.717617i
$59$	3.23793e9			0.589632			0.294816	−	0.955554i	$-0.404742\pi$
$59$	3.23793e9			0.589632			0.294816	+	0.955554i	$0.404742\pi$
$60$		0			0
$61$	−5.92067e9			−0.897546			−0.448773	−	0.893646i	$-0.648139\pi$
$61$	−5.92067e9			−0.897546			−0.448773	+	0.893646i	$0.648139\pi$
$62$	5.76493e8	−	5.76493e8i	0.0799170	−	0.0799170i
$63$	4.06109e8	+	1.39400e9i	0.0515548	+	0.176966i
$64$			3.74803e9i			0.436329i
$65$		0			0
$66$	−4.11766e9	−	6.95674e9i	−0.404724	−	0.683776i
$67$	−8.83271e9	−	8.83271e9i	−0.799249	−	0.799249i	0.183728	−	0.982977i	$-0.441184\pi$
$67$	−8.83271e9	−	8.83271e9i	−0.799249	−	0.799249i	−0.982977	+	0.183728i	$0.941184\pi$
$68$	−2.60337e9	−	2.60337e9i	−0.217139	−	0.217139i
$69$	−9.32805e9	−	1.57596e10i	−0.717994	−	1.21304i
$70$		0			0
$71$		−	1.82115e10i		−	1.19791i	−0.800783	−	0.598955i	$-0.795583\pi$
$71$		−	1.82115e10i		−	1.19791i	0.800783	−	0.598955i	$-0.204417\pi$
$72$	−3.44513e9	−	1.18257e10i	−0.209835	−	0.720275i
$73$	−3.15172e9	+	3.15172e9i	−0.177940	+	0.177940i	−0.790457	−	0.612517i	$-0.790157\pi$
$73$	−3.15172e9	+	3.15172e9i	−0.177940	+	0.177940i	0.612517	+	0.790457i	$0.290157\pi$
$74$	−3.09498e10			−1.62138
$75$		0			0
$76$	9.47525e9			0.428663
$77$	−2.11263e9	+	2.11263e9i	−0.0889454	+	0.0889454i
$78$	4.74488e9	−	1.85084e10i	0.186082	−	0.725852i
$79$		−	2.48867e10i		−	0.909952i	−0.890504	−	0.454976i	$-0.849648\pi$
$79$		−	2.48867e10i		−	0.909952i	0.890504	−	0.454976i	$-0.150352\pi$
$80$		0			0
$81$	1.68538e10	+	2.64711e10i	0.537070	+	0.843538i
$82$	−4.17220e10	−	4.17220e10i	−1.24276	−	1.24276i
$83$	−2.65597e10	−	2.65597e10i	−0.740106	−	0.740106i	0.232493	−	0.972598i	$-0.425312\pi$
$83$	−2.65597e10	−	2.65597e10i	−0.740106	−	0.740106i	−0.972598	+	0.232493i	$0.925312\pi$
$84$	2.16240e9	−	1.27992e9i	0.0564157	−	0.0333922i
$85$		0			0
$86$		−	7.68659e10i		−	1.76194i
$87$	−3.92523e10	−	1.00629e10i	−0.844325	−	0.216454i
$88$	1.79220e10	−	1.79220e10i	0.362019	−	0.362019i
$89$	−5.83244e10			−1.10715			−0.553574	−	0.832800i	$-0.686736\pi$
$89$	−5.83244e10			−1.10715			−0.553574	+	0.832800i	$0.686736\pi$
$90$		0			0
$91$	−7.06156e9			−0.118624
$92$	−2.24108e10	+	2.24108e10i	−0.354507	+	0.354507i
$93$	−6.30830e9	−	1.61722e9i	−0.0940277	−	0.0241053i
$94$		−	9.42496e10i		−	1.32457i
$95$		0			0
$96$	−4.68143e10	+	2.77092e10i	−0.585986	+	0.346842i
$97$	9.17088e10	+	9.17088e10i	1.08434	+	1.08434i	0.996099	+	0.0882431i	$0.0281252\pi$
$97$	9.17088e10	+	9.17088e10i	1.08434	+	1.08434i	0.0882431	+	0.996099i	$0.471875\pi$
$98$	7.11694e10	+	7.11694e10i	0.795334	+	0.795334i
$99$	−3.10667e10	+	5.66089e10i	−0.328323	+	0.598262i
$100$		0			0
$101$		−	1.18748e11i		−	1.12424i	−0.827055	−	0.562122i	$-0.809985\pi$
$101$		−	1.18748e11i		−	1.12424i	0.827055	−	0.562122i	$-0.190015\pi$
$102$	−2.78369e10	+	1.08584e11i	−0.249644	+	0.973787i
$103$	2.64970e10	−	2.64970e10i	0.225212	−	0.225212i	−0.585477	−	0.810689i	$-0.699093\pi$
$103$	2.64970e10	−	2.64970e10i	0.225212	−	0.225212i	0.810689	+	0.585477i	$0.199093\pi$
$104$	5.99052e10			0.482816
$105$		0			0
$106$	1.38335e11			1.00404
$107$	−6.90276e10	+	6.90276e10i	−0.475786	+	0.475786i	−0.903781	−	0.427995i	$-0.859220\pi$
$107$	−6.90276e10	+	6.90276e10i	−0.475786	+	0.475786i	0.427995	+	0.903781i	$0.359220\pi$
$108$	3.71334e10	−	3.96307e10i	0.243183	−	0.259538i
$109$			1.72370e11i			1.07304i	0.843888	+	0.536520i	$0.180261\pi$
$109$			1.72370e11i			1.07304i	−0.843888	+	0.536520i	$0.819739\pi$
$110$		0			0
$111$	1.25924e11	+	2.12746e11i	0.709301	+	1.19836i
$112$	2.98796e10	+	2.98796e10i	0.160205	+	0.160205i
$113$	−1.89151e11	−	1.89151e11i	−0.965776	−	0.965776i	0.0336579	−	0.999433i	$-0.489284\pi$
$113$	−1.89151e11	−	1.89151e11i	−0.965776	−	0.965776i	−0.999433	+	0.0336579i	$0.989284\pi$
$114$	−1.46943e11	−	2.48259e11i	−0.714782	−	1.20761i
$115$		0			0
$116$			7.01282e10i			0.310009i
$117$	−1.46530e11	+	4.26880e10i	−0.617881	+	0.180005i
$118$	−1.20641e11	+	1.20641e11i	−0.485447	+	0.485447i
$119$	4.14283e10			0.159143
$120$		0			0
$121$	1.52438e11			0.534287
$122$	2.20596e11	−	2.20596e11i	0.738955	−	0.738955i
$123$	−1.17042e11	+	4.56545e11i	−0.374854	+	1.46219i
$124$			1.12704e10i			0.0345239i
$125$		0			0
$126$	−6.70696e10	−	3.68075e10i	−0.188143	−	0.103252i
$127$	−1.22572e11	−	1.22572e11i	−0.329208	−	0.329208i	0.523077	−	0.852285i	$-0.324784\pi$
$127$	−1.22572e11	−	1.22572e11i	−0.329208	−	0.329208i	−0.852285	+	0.523077i	$0.824784\pi$
$128$	−3.26822e11	−	3.26822e11i	−0.840729	−	0.840729i
$129$	−5.28369e11	+	3.12739e11i	−1.30225	+	0.770796i
$130$		0			0
$131$		−	1.08623e11i		−	0.245998i	−0.992407	−	0.122999i	$-0.960749\pi$
$131$		−	1.08623e11i		−	0.245998i	0.992407	−	0.122999i	$-0.0392511\pi$
$132$	1.08252e11	+	2.77519e10i	0.235115	+	0.0602749i
$133$	−7.53914e10	+	7.53914e10i	−0.157086	+	0.157086i
$134$	6.58188e11			1.31605
$135$		0			0
$136$	−3.51448e11			−0.647734
$137$	1.79707e11	−	1.79707e11i	0.318129	−	0.318129i	−0.529919	−	0.848048i	$-0.677778\pi$
$137$	1.79707e11	−	1.79707e11i	0.318129	−	0.318129i	0.848048	+	0.529919i	$0.177778\pi$
$138$	9.34731e11	+	2.39631e11i	1.58983	+	0.407576i
$139$			2.31389e11i			0.378235i	0.981955	+	0.189117i	$0.0605626\pi$
$139$			2.31389e11i			0.378235i	−0.981955	+	0.189117i	$0.939437\pi$
$140$		0			0
$141$	−6.47864e11	+	3.83468e11i	−0.978990	+	0.579460i
$142$	6.78534e11	+	6.78534e11i	0.986247	+	0.986247i
$143$	−2.22068e11	−	2.22068e11i	−0.310555	−	0.310555i
$144$	8.00639e11	+	4.39387e11i	1.07756	+	0.591362i
$145$		0			0
$146$		−	2.34858e11i		−	0.292998i
$147$	1.99650e11	−	7.78774e11i	0.239896	−	0.935764i
$148$	3.02534e11	−	3.02534e11i	0.350215	−	0.350215i
$149$	1.11597e12			1.24489			0.622443	−	0.782665i	$-0.286140\pi$
$149$	1.11597e12			1.24489			0.622443	+	0.782665i	$0.286140\pi$
$150$		0			0
$151$	−1.05047e12			−1.08895			−0.544477	−	0.838776i	$-0.683272\pi$
$151$	−1.05047e12			−1.08895			−0.544477	+	0.838776i	$0.683272\pi$
$152$	6.39566e11	−	6.39566e11i	0.639361	−	0.639361i
$153$	8.59654e11	−	2.50439e11i	0.828935	−	0.241490i
$154$		−	1.57427e11i		−	0.146459i
$155$		0			0
$156$	1.34538e11	+	2.27300e11i	0.116590	+	0.196977i
$157$	−4.99012e11	−	4.99012e11i	−0.417507	−	0.417507i	0.466837	−	0.884343i	$-0.345394\pi$
$157$	−4.99012e11	−	4.99012e11i	−0.417507	−	0.417507i	−0.884343	+	0.466837i	$0.845394\pi$
$158$	9.27244e11	+	9.27244e11i	0.749169	+	0.749169i
$159$	−5.62836e11	−	9.50905e11i	−0.439236	−	0.742083i
$160$		0			0
$161$		−	3.56631e11i		−	0.259822i
$162$	−1.61423e12	−	3.58326e11i	−1.13666	−	0.252317i
$163$	−1.59099e12	+	1.59099e12i	−1.08302	+	1.08302i	−0.0867936	+	0.996226i	$0.527662\pi$
$163$	−1.59099e12	+	1.59099e12i	−1.08302	+	1.08302i	−0.996226	+	0.0867936i	$0.972338\pi$
$164$	8.15663e11			0.536870
$165$		0			0
$166$	1.97915e12			1.21867
$167$	5.30791e11	−	5.30791e11i	0.316215	−	0.316215i	−0.531096	−	0.847312i	$-0.678220\pi$
$167$	5.30791e11	−	5.30791e11i	0.316215	−	0.316215i	0.847312	+	0.531096i	$0.178220\pi$
$168$	5.95665e10	−	2.32352e11i	0.0343401	−	0.133951i
$169$			1.04989e12i			0.585821i
$170$		0			0
$171$	−1.10865e12	+	2.02015e12i	−0.579851	+	1.05659i
$172$	7.51362e11	+	7.51362e11i	0.380577	+	0.380577i
$173$	6.26996e11	+	6.26996e11i	0.307618	+	0.307618i	0.843985	−	0.536367i	$-0.180204\pi$
$173$	6.26996e11	+	6.26996e11i	0.307618	+	0.307618i	−0.536367	+	0.843985i	$0.680204\pi$
$174$	1.83741e12	−	1.08756e12i	0.873346	−	0.516930i
$175$		0			0
$176$			1.87927e12i			0.838823i
$177$	1.32012e12	+	3.38430e11i	0.571161	+	0.146425i
$178$	2.17308e12	−	2.17308e12i	0.911521	−	0.911521i
$179$	7.46598e11			0.303665			0.151833	−	0.988406i	$-0.451483\pi$
$179$	7.46598e11			0.303665			0.151833	+	0.988406i	$0.451483\pi$
$180$		0			0
$181$	4.82562e11			0.184638			0.0923189	−	0.995729i	$-0.470572\pi$
$181$	4.82562e11			0.184638			0.0923189	+	0.995729i	$0.470572\pi$
$182$	2.63104e11	−	2.63104e11i	0.0976640	−	0.0976640i
$183$	−2.41388e12	−	6.18831e11i	−0.869430	−	0.222890i
$184$			3.02540e12i			1.05751i
$185$		0			0
$186$	2.95294e11	−	1.74783e11i	0.0972597	−	0.0575676i
$187$	1.30281e12	+	1.30281e12i	0.416633	+	0.416633i
$188$	9.21288e11	+	9.21288e11i	0.286106	+	0.286106i
$189$	1.98703e10	+	6.10787e11i	0.00599329	+	0.184225i
$190$		0			0
$191$		−	2.56686e12i		−	0.730667i	−0.930877	−	0.365333i	$-0.880955\pi$
$191$		−	2.56686e12i		−	0.730667i	0.930877	−	0.365333i	$-0.119045\pi$
$192$	−3.91746e11	+	1.52809e12i	−0.108355	+	0.422660i
$193$	−4.01466e12	+	4.01466e12i	−1.07915	+	1.07915i	−0.0825678	+	0.996585i	$0.526312\pi$
$193$	−4.01466e12	+	4.01466e12i	−1.07915	+	1.07915i	−0.996585	+	0.0825678i	$0.973688\pi$
$194$	−6.83388e12			−1.78549
$195$		0			0
$196$	−1.39136e12			−0.343582
$197$	−3.80667e12	+	3.80667e12i	−0.914073	+	0.914073i	−0.996590	−	0.0825165i	$-0.973704\pi$
$197$	−3.80667e12	+	3.80667e12i	−0.914073	+	0.914073i	0.0825165	+	0.996590i	$0.473704\pi$
$198$	−9.51665e11	−	3.26667e12i	−0.222242	−	0.762863i
$199$			3.78025e11i			0.0858675i	0.999078	+	0.0429338i	$0.0136704\pi$
$199$			3.78025e11i			0.0858675i	−0.999078	+	0.0429338i	$0.986330\pi$
$200$		0			0
$201$	−2.67793e12	−	4.52433e12i	−0.575733	−	0.972693i
$202$	4.42440e12	+	4.42440e12i	0.925596	+	0.925596i
$203$	−5.57987e11	−	5.57987e11i	−0.113605	−	0.113605i
$204$	−7.89299e11	−	1.33351e12i	−0.156414	−	0.264259i
$205$		0			0
$206$			1.97448e12i			0.370837i
$207$	−2.15588e12	−	7.40023e12i	−0.394264	−	1.35334i
$208$	−3.14079e12	+	3.14079e12i	−0.559358	+	0.559358i
$209$	−4.74174e12			−0.822494
$210$		0			0
$211$	1.01546e13			1.67151			0.835757	−	0.549100i	$-0.185029\pi$
$211$	1.01546e13			1.67151			0.835757	+	0.549100i	$0.185029\pi$
$212$	−1.35222e12	+	1.35222e12i	−0.216871	+	0.216871i
$213$	1.90347e12	−	7.42489e12i	0.297481	−	1.16039i
$214$		−	5.14374e12i		−	0.783435i
$215$		0			0
$216$	−1.68566e11	−	5.18147e12i	−0.0243934	−	0.749821i
$217$	−8.96749e10	−	8.96749e10i	−0.0126515	−	0.0126515i
$218$	−6.42226e12	−	6.42226e12i	−0.883440	−	0.883440i
$219$	−1.61439e12	+	9.55551e11i	−0.216554	+	0.128177i
$220$		0			0
$221$			4.35473e12i			0.555653i
$222$	−1.26184e13	−	3.23489e12i	−1.57059	−	0.402641i
$223$	2.79057e12	−	2.79057e12i	0.338857	−	0.338857i	−0.517080	−	0.855937i	$-0.672981\pi$
$223$	2.79057e12	−	2.79057e12i	0.338857	−	0.338857i	0.855937	+	0.517080i	$0.172981\pi$
$224$	−1.05938e12			−0.125513
$225$		0			0
$226$	1.40950e13			1.59026
$227$	−1.91237e12	+	1.91237e12i	−0.210586	+	0.210586i	−0.804516	−	0.593930i	$-0.797575\pi$
$227$	−1.91237e12	+	1.91237e12i	−0.210586	+	0.210586i	0.593930	+	0.804516i	$0.297575\pi$
$228$	3.86310e12	+	9.90358e11i	0.415235	+	0.106451i
$229$		−	3.95313e12i		−	0.414807i	−0.978255	−	0.207404i	$-0.933499\pi$
$229$		−	3.95313e12i		−	0.414807i	0.978255	−	0.207404i	$-0.0665013\pi$
$230$		0			0
$231$	−1.08214e12	+	6.40513e11i	−0.108247	+	0.0640711i
$232$	4.73356e12	+	4.73356e12i	0.462385	+	0.462385i
$233$	7.72989e12	+	7.72989e12i	0.737422	+	0.737422i	0.972078	−	0.234657i	$-0.0753966\pi$
$233$	7.72989e12	+	7.72989e12i	0.737422	+	0.737422i	−0.234657	+	0.972078i	$0.575397\pi$
$234$	3.86901e12	−	7.05000e12i	0.360506	−	0.656904i
$235$		0			0
$236$		−	2.35852e12i		−	0.209712i
$237$	2.60117e12	−	1.01464e13i	0.225971	−	0.881448i
$238$	−1.54356e12	+	1.54356e12i	−0.131024	+	0.131024i
$239$	−6.11968e12			−0.507622			−0.253811	−	0.967254i	$-0.581684\pi$
$239$	−6.11968e12			−0.507622			−0.253811	+	0.967254i	$0.581684\pi$
$240$		0			0
$241$	−2.37233e13			−1.87967			−0.939836	−	0.341625i	$-0.889023\pi$
$241$	−2.37233e13			−1.87967			−0.939836	+	0.341625i	$0.889023\pi$
$242$	−5.67963e12	+	5.67963e12i	−0.439882	+	0.439882i
$243$	4.10460e12	+	1.25539e13i	0.310768	+	0.950486i
$244$			4.31264e12i			0.319227i
$245$		0			0
$246$	−1.26494e13	−	2.13710e13i	−0.895214	−	1.51245i
$247$	−7.92475e12	−	7.92475e12i	−0.548469	−	0.548469i
$248$	7.60737e11	+	7.60737e11i	0.0514933	+	0.0514933i
$249$	−8.05246e12	−	1.36045e13i	−0.533129	−	0.900714i
$250$		0			0
$251$			1.46715e13i			0.929541i	0.885431	+	0.464771i	$0.153863\pi$
$251$			1.46715e13i			0.929541i	−0.885431	+	0.464771i	$0.846137\pi$
$252$	1.01540e12	−	2.95811e11i	0.0629408	−	0.0183363i
$253$	1.12151e13	−	1.12151e13i	0.680208	−	0.680208i
$254$	9.13372e12			0.542079
$255$		0			0
$256$	1.66779e13			0.948026
$257$	−3.28825e12	+	3.28825e12i	−0.182950	+	0.182950i	−0.792640	−	0.609690i	$-0.791294\pi$
$257$	−3.28825e12	+	3.28825e12i	−0.182950	+	0.182950i	0.609690	+	0.792640i	$0.291294\pi$
$258$	8.03406e12	−	3.13385e13i	0.437549	−	1.70675i
$259$			4.81432e12i			0.256677i
$260$		0			0
$261$	−1.49515e13	−	8.20535e12i	−0.764123	−	0.419348i
$262$	4.04715e12	+	4.04715e12i	0.202531	+	0.202531i
$263$	4.84899e12	+	4.84899e12i	0.237627	+	0.237627i	0.815867	−	0.578240i	$-0.196260\pi$
$263$	4.84899e12	+	4.84899e12i	0.237627	+	0.237627i	−0.578240	+	0.815867i	$0.696260\pi$
$264$	9.18008e12	−	5.43365e12i	0.440580	−	0.260778i
$265$		0			0
$266$		−	5.61795e12i		−	0.258660i
$267$	−2.37791e13	−	6.09610e12i	−1.07247	−	0.274941i
$268$	−6.43378e12	+	6.43378e12i	−0.284266	+	0.284266i
$269$	−5.30317e12			−0.229561			−0.114780	−	0.993391i	$-0.536616\pi$
$269$	−5.30317e12			−0.229561			−0.114780	+	0.993391i	$0.536616\pi$
$270$		0			0
$271$	1.77085e13			0.735955			0.367978	−	0.929835i	$-0.380050\pi$
$271$	1.77085e13			0.735955			0.367978	+	0.929835i	$0.380050\pi$
$272$	1.84262e13	−	1.84262e13i	0.750422	−	0.750422i
$273$	−2.87903e12	−	7.38078e11i	−0.114908	−	0.0294583i
$274$			1.33913e13i			0.523835i
$275$		0			0
$276$	−1.14794e13	+	6.79459e12i	−0.431438	+	0.255366i
$277$	3.24137e13	+	3.24137e13i	1.19424	+	1.19424i	0.975866	+	0.218371i	$0.0700744\pi$
$277$	3.24137e13	+	3.24137e13i	1.19424	+	1.19424i	0.218371	+	0.975866i	$0.429926\pi$
$278$	−8.62123e12	−	8.62123e12i	−0.311403	−	0.311403i
$279$	−2.40289e12	−	1.31869e12i	−0.0850961	−	0.0467004i
$280$		0			0
$281$			6.36044e12i			0.216572i	0.994120	+	0.108286i	$0.0345362\pi$
$281$			6.36044e12i			0.216572i	−0.994120	+	0.108286i	$0.965464\pi$
$282$	9.85102e12	−	3.84259e13i	0.328936	−	1.28308i
$283$	−3.56207e13	+	3.56207e13i	−1.16648	+	1.16648i	−0.183452	+	0.983029i	$0.558727\pi$
$283$	−3.56207e13	+	3.56207e13i	−1.16648	+	1.16648i	−0.983029	+	0.183452i	$0.941273\pi$
$284$	−1.32653e13			−0.426056
$285$		0			0
$286$	1.65479e13			0.511363
$287$	−6.48996e12	+	6.48996e12i	−0.196739	+	0.196739i
$288$	−2.19826e13	+	6.40409e12i	−0.653762	+	0.190458i
$289$			8.72387e12i			0.254549i
$290$		0			0
$291$	2.78046e13	+	4.69755e13i	0.781097	+	1.31965i
$292$	2.29573e12	+	2.29573e12i	0.0632871	+	0.0632871i
$293$	9.27902e12	+	9.27902e12i	0.251033	+	0.251033i	0.821394	−	0.570361i	$-0.193197\pi$
$293$	9.27902e12	+	9.27902e12i	0.251033	+	0.251033i	−0.570361	+	0.821394i	$0.693197\pi$
$294$	2.15774e13	+	3.64547e13i	0.572912	+	0.967928i
$295$		0			0
$296$		−	4.08413e13i		−	1.04471i
$297$	−1.85828e13	+	1.98326e13i	−0.466607	+	0.497987i
$298$	−4.15796e13	+	4.15796e13i	−1.02492	+	1.02492i
$299$	3.74872e13			0.907175
$300$		0			0
$301$	−1.19567e13			−0.278930
$302$	3.91390e13	−	3.91390e13i	0.896543	−	0.896543i
$303$	1.24116e13	−	4.84142e13i	0.279187	−	1.08903i
$304$			6.70640e13i			1.48144i
$305$		0			0
$306$	−2.26985e13	+	4.13605e13i	−0.483647	+	0.881288i
$307$	5.63217e13	+	5.63217e13i	1.17873	+	1.17873i	0.980068	+	0.198663i	$0.0636598\pi$
$307$	5.63217e13	+	5.63217e13i	1.17873	+	1.17873i	0.198663	+	0.980068i	$0.436340\pi$
$308$	1.53884e12	+	1.53884e12i	0.0316349	+	0.0316349i
$309$	1.35724e13	−	8.03345e12i	0.274085	−	0.162230i
$310$		0			0
$311$			9.11457e13i			1.77645i	0.459404	+	0.888227i	$0.348063\pi$
$311$			9.11457e13i			1.77645i	−0.459404	+	0.888227i	$0.651937\pi$
$312$	2.44236e13	+	6.26132e12i	0.467691	+	0.119899i
$313$	−2.10891e10	+	2.10891e10i	−0.000396793	+	0.000396793i	−0.707305	−	0.706908i	$-0.750089\pi$
$313$	−2.10891e10	+	2.10891e10i	−0.000396793	+	0.000396793i	0.706908	+	0.707305i	$0.250089\pi$
$314$	3.71850e13			0.687471
$315$		0			0
$316$	−1.81276e13			−0.323639
$317$	−3.12478e13	+	3.12478e13i	−0.548268	+	0.548268i	−0.925940	−	0.377672i	$-0.876725\pi$
$317$	−3.12478e13	+	3.12478e13i	−0.548268	+	0.548268i	0.377672	+	0.925940i	$0.376725\pi$
$318$	5.63998e13	+	1.44589e13i	0.972587	+	0.249336i
$319$		−	3.50945e13i		−	0.594827i
$320$		0			0
$321$	−3.53576e13	+	2.09280e13i	−0.579036	+	0.342729i
$322$	1.32876e13	+	1.32876e13i	0.213913	+	0.213913i
$323$	4.64924e13	+	4.64924e13i	0.735814	+	0.735814i
$324$	1.92817e13	−	1.22764e13i	0.300018	−	0.191018i
$325$		0			0
$326$		−	1.18556e14i		−	1.78331i
$327$	−1.80162e13	+	7.02759e13i	−0.266471	+	1.03943i
$328$	5.50561e13	−	5.50561e13i	0.800755	−	0.800755i
$329$	−1.46608e13			−0.209691
$330$		0			0
$331$	6.13855e13			0.849204			0.424602	−	0.905380i	$-0.360414\pi$
$331$	6.13855e13			0.849204			0.424602	+	0.905380i	$0.360414\pi$
$332$	−1.93462e13	+	1.93462e13i	−0.263230	+	0.263230i
$333$	2.91032e13	+	9.98991e13i	0.389491	+	1.33696i
$334$			3.95531e13i			0.520684i
$335$		0			0
$336$	9.05899e12	+	1.53051e13i	0.115402	+	0.194970i
$337$	−3.15556e13	−	3.15556e13i	−0.395469	−	0.395469i	0.481162	−	0.876631i	$-0.340215\pi$
$337$	−3.15556e13	−	3.15556e13i	−0.395469	−	0.395469i	−0.876631	+	0.481162i	$0.840215\pi$
$338$	−3.91173e13	−	3.91173e13i	−0.482310	−	0.482310i
$339$	−5.73473e13	−	9.68875e13i	−0.695688	−	1.17536i
$340$		0			0
$341$		−	5.64009e12i		−	0.0662426i
$342$	−3.39612e13	−	1.16575e14i	−0.392500	−	1.34729i
$343$	2.25305e13	−	2.25305e13i	0.256244	−	0.256244i
$344$	1.01432e14			1.13528
$345$		0			0
$346$	−4.67220e13			−0.506527
$347$	1.03387e14	−	1.03387e14i	1.10320	−	1.10320i	0.109174	−	0.994023i	$-0.465179\pi$
$347$	1.03387e14	−	1.03387e14i	1.10320	−	1.10320i	0.994023	−	0.109174i	$-0.0348205\pi$
$348$	−7.32984e12	+	2.85915e13i	−0.0769854	+	0.300298i
$349$		−	4.53075e13i		−	0.468414i	−0.972187	−	0.234207i	$-0.924751\pi$
$349$		−	4.53075e13i		−	0.468414i	0.972187	−	0.234207i	$-0.0752494\pi$
$350$		0			0
$351$	−6.42027e13	+	2.08866e12i	−0.643227	+	0.0209257i
$352$	−3.33148e13	−	3.33148e13i	−0.328589	−	0.328589i
$353$	−7.69219e13	−	7.69219e13i	−0.746946	−	0.746946i	0.226958	−	0.973904i	$-0.427122\pi$
$353$	−7.69219e13	−	7.69219e13i	−0.746946	−	0.746946i	−0.973904	+	0.226958i	$0.927122\pi$
$354$	−6.17950e13	+	3.65762e13i	−0.590793	+	0.349688i
$355$		0			0
$356$			4.24837e13i			0.393775i
$357$	1.68905e13	+	4.33011e12i	0.154158	+	0.0395206i
$358$	−2.78172e13	+	2.78172e13i	−0.250010	+	0.250010i
$359$	9.98869e13			0.884075			0.442037	−	0.896997i	$-0.354256\pi$
$359$	9.98869e13			0.884075			0.442037	+	0.896997i	$0.354256\pi$
$360$		0			0
$361$	−5.27239e13			−0.452604
$362$	−1.79796e13	+	1.79796e13i	−0.152013	+	0.152013i
$363$	6.21497e13	+	1.59329e13i	0.517550	+	0.132681i
$364$			5.14367e12i			0.0421906i
$365$		0			0
$366$	1.12994e14	−	6.68809e13i	0.899314	−	0.532300i
$367$	−1.32238e14	−	1.32238e14i	−1.03680	−	1.03680i	−0.999297	−	0.0374999i	$-0.988061\pi$
$367$	−1.32238e14	−	1.32238e14i	−1.03680	−	1.03680i	−0.0374999	−	0.999297i	$-0.511939\pi$
$368$	−1.58619e14	−	1.58619e14i	−1.22516	−	1.22516i
$369$	−9.54366e13	+	1.73902e14i	−0.726223	+	1.32330i
$370$		0			0
$371$		−	2.15184e13i		−	0.158947i
$372$	−1.17799e12	+	4.59499e12i	−0.00857344	+	0.0334425i
$373$	3.07861e12	−	3.07861e12i	0.0220778	−	0.0220778i	−0.695982	−	0.718060i	$-0.745031\pi$
$373$	3.07861e12	−	3.07861e12i	0.0220778	−	0.0220778i	0.718060	+	0.695982i	$0.245031\pi$
$374$	−9.70821e13			−0.686033
$375$		0			0
$376$	1.24371e14			0.853468
$377$	5.86527e13	−	5.86527e13i	0.396653	−	0.396653i
$378$	−2.34974e13	−	2.20167e13i	−0.156608	−	0.146740i
$379$		−	7.09881e13i		−	0.466305i	−0.972440	−	0.233153i	$-0.925096\pi$
$379$		−	7.09881e13i		−	0.466305i	0.972440	−	0.233153i	$-0.0749041\pi$
$380$		0			0
$381$	−3.71618e13	−	6.27844e13i	−0.237142	−	0.400649i
$382$	9.56377e13	+	9.56377e13i	0.601562	+	0.601562i
$383$	1.16691e14	+	1.16691e14i	0.723510	+	0.723510i	0.969318	−	0.245808i	$-0.0790534\pi$
$383$	1.16691e14	+	1.16691e14i	0.723510	+	0.723510i	−0.245808	+	0.969318i	$0.579053\pi$
$384$	−9.90869e13	−	1.67406e14i	−0.605612	−	1.02317i
$385$		0			0
$386$		−	2.99161e14i		−	1.77695i
$387$	−2.48106e14	+	7.22796e13i	−1.45287	+	0.423259i
$388$	6.68010e13	−	6.68010e13i	0.385664	−	0.385664i
$389$	−2.01585e14			−1.14746			−0.573728	−	0.819046i	$-0.694503\pi$
$389$	−2.01585e14			−1.14746			−0.573728	+	0.819046i	$0.694503\pi$
$390$		0			0
$391$	−2.19927e14			−1.21705
$392$	−9.39148e13	+	9.39148e13i	−0.512461	+	0.512461i
$393$	1.13534e13	−	4.42862e13i	0.0610894	−	0.238292i
$394$		−	2.83662e14i		−	1.50512i
$395$		0			0
$396$	4.12341e13	+	2.26291e13i	0.212781	+	0.116773i
$397$	−5.90284e13	−	5.90284e13i	−0.300409	−	0.300409i	0.540765	−	0.841174i	$-0.318135\pi$
$397$	−5.90284e13	−	5.90284e13i	−0.300409	−	0.300409i	−0.841174	+	0.540765i	$0.818135\pi$
$398$	−1.40847e13	−	1.40847e13i	−0.0706953	−	0.0706953i
$399$	−3.86173e13	+	2.28574e13i	−0.191175	+	0.113156i
$400$		0			0
$401$			1.83736e14i			0.884912i	0.896790	+	0.442456i	$0.145893\pi$
$401$			1.83736e14i			0.884912i	−0.896790	+	0.442456i	$0.854107\pi$
$402$	2.68346e14	+	6.87942e13i	1.27483	+	0.326820i
$403$	9.42616e12	−	9.42616e12i	0.0441730	−	0.0441730i
$404$	−8.64968e13			−0.399855
$405$		0			0
$406$	4.15796e13			0.187063
$407$	−1.51398e14	+	1.51398e14i	−0.671972	+	0.671972i
$408$	−1.43287e14	−	3.67335e13i	−0.627444	−	0.160854i
$409$		−	2.36871e13i		−	0.102337i	−0.998690	−	0.0511685i	$-0.983705\pi$
$409$		−	2.36871e13i		−	0.102337i	0.998690	−	0.0511685i	$-0.0162946\pi$
$410$		0			0
$411$	9.20505e13	−	5.44843e13i	0.387165	−	0.229161i
$412$	−1.93005e13	−	1.93005e13i	−0.0801003	−	0.0801003i
$413$	1.87659e13	+	1.87659e13i	0.0768502	+	0.0768502i
$414$	3.56047e14	+	1.95397e14i	1.43882	+	0.789616i
$415$		0			0
$416$		−	1.11357e14i		−	0.438230i
$417$	−2.41849e13	+	9.43382e13i	−0.0939282	+	0.366386i
$418$	1.76670e14	−	1.76670e14i	0.677164	−	0.677164i
$419$	−3.18981e14			−1.20667			−0.603333	−	0.797489i	$-0.706161\pi$
$419$	−3.18981e14			−1.20667			−0.603333	+	0.797489i	$0.706161\pi$
$420$		0			0
$421$	2.27039e14			0.836659			0.418329	−	0.908295i	$-0.362616\pi$
$421$	2.27039e14			0.836659			0.418329	+	0.908295i	$0.362616\pi$
$422$	−3.78347e14	+	3.78347e14i	−1.37617	+	1.37617i
$423$	−3.04217e14	+	8.86262e13i	−1.09222	+	0.318193i
$424$			1.82547e14i			0.646937i
$425$		0			0
$426$	2.05720e14	+	3.47562e14i	0.710435	+	1.20027i
$427$	−3.43142e13	−	3.43142e13i	−0.116982	−	0.116982i
$428$	5.02800e13	+	5.02800e13i	0.169221	+	0.169221i
$429$	−6.73274e13	−	1.13749e14i	−0.223705	−	0.377947i
$430$		0			0
$431$			1.90375e14i			0.616573i	0.951294	+	0.308286i	$0.0997555\pi$
$431$			1.90375e14i			0.616573i	−0.951294	+	0.308286i	$0.900245\pi$
$432$	2.80499e14	+	2.62823e14i	0.896954	+	0.840433i
$433$	−1.84614e14	+	1.84614e14i	−0.582883	+	0.582883i	−0.935695	−	0.352811i	$-0.885226\pi$
$433$	−1.84614e14	+	1.84614e14i	−0.582883	+	0.582883i	0.352811	+	0.935695i	$0.385226\pi$
$434$	6.68232e12			0.0208321
$435$		0			0
$436$	1.25555e14			0.381643
$437$	4.00225e14	−	4.00225e14i	1.20131	−	1.20131i
$438$	2.45474e13	−	9.57524e13i	0.0727610	−	0.283819i
$439$			1.78548e14i			0.522636i	0.965253	+	0.261318i	$0.0841572\pi$
$439$			1.78548e14i			0.522636i	−0.965253	+	0.261318i	$0.915843\pi$
$440$		0			0
$441$	1.62796e14	−	2.96642e14i	0.464762	−	0.846877i
$442$	−1.62251e14	−	1.62251e14i	−0.457472	−	0.457472i
$443$	3.32895e14	+	3.32895e14i	0.927015	+	0.927015i	0.997512	−	0.0704972i	$-0.0224586\pi$
$443$	3.32895e14	+	3.32895e14i	0.927015	+	0.927015i	−0.0704972	+	0.997512i	$0.522459\pi$
$444$	1.54965e14	−	9.17232e13i	0.426214	−	0.252274i
$445$		0			0
$446$			2.07946e14i			0.557966i
$447$	4.54987e14	+	1.16642e14i	1.20589	+	0.309146i
$448$	−2.17224e13	+	2.17224e13i	−0.0568693	+	0.0568693i
$449$	2.32621e14			0.601581			0.300790	−	0.953690i	$-0.402750\pi$
$449$	2.32621e14			0.601581			0.300790	+	0.953690i	$0.402750\pi$
$450$		0			0
$451$	−4.08185e14			−1.03012
$452$	−1.37778e14	+	1.37778e14i	−0.343494	+	0.343494i
$453$	−4.28280e14	−	1.09795e14i	−1.05484	−	0.270423i
$454$		−	1.42504e14i		−	0.346753i
$455$		0			0
$456$	3.27602e14	−	1.93906e14i	0.778107	−	0.460558i
$457$	−2.68182e14	−	2.68182e14i	−0.629349	−	0.629349i	0.318556	−	0.947904i	$-0.396802\pi$
$457$	−2.68182e14	−	2.68182e14i	−0.629349	−	0.629349i	−0.947904	+	0.318556i	$0.896802\pi$
$458$	1.47288e14	+	1.47288e14i	0.341513	+	0.341513i
$459$	3.76660e14	−	1.22536e13i	0.862939	−	0.0280734i
$460$		0			0
$461$			2.93579e14i			0.656705i	0.944555	+	0.328353i	$0.106493\pi$
$461$			2.93579e14i			0.656705i	−0.944555	+	0.328353i	$0.893507\pi$
$462$	1.64543e13	−	6.41835e13i	0.0363705	−	0.141871i
$463$	2.82602e14	−	2.82602e14i	0.617277	−	0.617277i	−0.327555	−	0.944832i	$-0.606225\pi$
$463$	2.82602e14	−	2.82602e14i	0.617277	−	0.617277i	0.944832	+	0.327555i	$0.106225\pi$
$464$	−4.96354e14			−1.07138
$465$		0			0
$466$	−5.76010e14			−1.21425
$467$	−2.13969e14	+	2.13969e14i	−0.445767	+	0.445767i	−0.893944	−	0.448178i	$-0.852073\pi$
$467$	−2.13969e14	+	2.13969e14i	−0.445767	+	0.445767i	0.448178	+	0.893944i	$0.352073\pi$
$468$	3.10941e13	+	1.06733e14i	0.0640215	+	0.219759i
$469$		−	1.02383e14i		−	0.208342i
$470$		0			0
$471$	−1.51292e14	−	2.55606e14i	−0.300747	−	0.508109i
$472$	−1.59197e14	−	1.59197e14i	−0.312790	−	0.312790i
$473$	−3.76007e14	−	3.76007e14i	−0.730231	−	0.730231i
$474$	2.81125e14	+	4.74957e14i	0.539658	+	0.911745i
$475$		0			0
$476$		−	3.01765e13i		−	0.0566019i
$477$	−1.30081e14	−	4.46515e14i	−0.241193	−	0.827914i
$478$	2.28011e14	−	2.28011e14i	0.417928	−	0.417928i
$479$	4.90904e14			0.889512			0.444756	−	0.895652i	$-0.353290\pi$
$479$	4.90904e14			0.889512			0.444756	+	0.895652i	$0.353290\pi$
$480$		0			0
$481$	−5.06056e14			−0.896192
$482$	8.83898e14	−	8.83898e14i	1.54755	−	1.54755i
$483$	3.72752e13	−	1.45400e14i	0.0645225	−	0.251683i
$484$		−	1.11037e14i		−	0.190028i
$485$		0			0
$486$	−6.20674e14	−	3.14811e14i	−1.03840	−	0.526684i
$487$	4.37542e14	+	4.37542e14i	0.723786	+	0.723786i	0.969374	−	0.245588i	$-0.0789812\pi$
$487$	4.37542e14	+	4.37542e14i	0.723786	+	0.723786i	−0.245588	+	0.969374i	$0.578981\pi$
$488$	2.91097e14	+	2.91097e14i	0.476134	+	0.476134i
$489$	−8.14945e14	+	4.82363e14i	−1.31804	+	0.780144i
$490$		0			0
$491$		−	9.43914e12i		−	0.0149274i	−0.999972	−	0.00746370i	$-0.997624\pi$
$491$		−	9.43914e12i		−	0.0149274i	0.999972	−	0.00746370i	$-0.00237579\pi$
$492$	3.32549e14	+	8.52535e13i	0.520053	+	0.133323i
$493$	−3.44100e14	+	3.44100e14i	−0.532140	+	0.532140i
$494$	5.90530e14			0.903116
$495$		0			0
$496$	−7.97698e13			−0.119313
$497$	1.05548e14	−	1.05548e14i	0.156131	−	0.156131i
$498$	8.06909e14	+	2.06862e14i	1.18049	+	0.302635i
$499$		−	1.90738e14i		−	0.275984i	−0.990433	−	0.137992i	$-0.955935\pi$
$499$		−	1.90738e14i		−	0.275984i	0.990433	−	0.137992i	$-0.0440649\pi$
$500$		0			0
$501$	2.71884e14	−	1.60927e14i	0.384837	−	0.227783i
$502$	−5.46639e14	−	5.46639e14i	−0.765297	−	0.765297i
$503$	3.32593e14	+	3.32593e14i	0.460563	+	0.460563i	0.898840	−	0.438277i	$-0.144411\pi$
$503$	3.32593e14	+	3.32593e14i	0.460563	+	0.460563i	−0.438277	+	0.898840i	$0.644411\pi$
$504$	4.85710e13	−	8.85047e13i	0.0665287	−	0.121227i
$505$		0			0
$506$			8.35720e14i			1.12004i
$507$	−1.09735e14	+	4.28043e14i	−0.145479	+	0.567470i
$508$	−8.92819e13	+	8.92819e13i	−0.117088	+	0.117088i
$509$	8.99976e14			1.16757			0.583785	−	0.811908i	$-0.301571\pi$
$509$	8.99976e14			1.16757			0.583785	+	0.811908i	$0.301571\pi$
$510$		0			0
$511$	−3.65327e13			−0.0463839
$512$	4.79377e13	−	4.79377e13i	0.0602132	−	0.0602132i
$513$	−6.63149e14	+	7.07747e14i	−0.824072	+	0.879493i
$514$		−	2.45031e14i		−	0.301248i
$515$		0			0
$516$	2.27801e14	+	3.84866e14i	0.274146	+	0.463166i
$517$	−4.61044e14	−	4.61044e14i	−0.548965	−	0.548965i
$518$	−1.79375e14	−	1.79375e14i	−0.211324	−	0.211324i
$519$	1.90095e14	+	3.21163e14i	0.221590	+	0.374373i
$520$		0			0
$521$			3.05891e14i			0.349108i	0.984648	+	0.174554i	$0.0558483\pi$
$521$			3.05891e14i			0.349108i	−0.984648	+	0.174554i	$0.944152\pi$
$522$	8.62793e14	−	2.51354e14i	0.974359	−	0.283856i
$523$	6.15855e14	−	6.15855e14i	0.688207	−	0.688207i	−0.273629	−	0.961835i	$-0.588224\pi$
$523$	6.15855e14	−	6.15855e14i	0.688207	−	0.688207i	0.961835	+	0.273629i	$0.0882240\pi$
$524$	−7.91217e13			−0.0874930
$525$		0			0
$526$	−3.61333e14			−0.391279
$527$	−5.53008e13	+	5.53008e13i	−0.0592615	+	0.0592615i
$528$	−1.96423e14	+	7.66187e14i	−0.208308	+	0.812547i
$529$			9.40408e14i			0.986984i
$530$		0			0
$531$	5.02843e14	+	2.75958e14i	0.516907	+	0.283677i
$532$	5.49154e13	+	5.49154e13i	0.0558702	+	0.0558702i
$533$	−6.82190e14	−	6.82190e14i	−0.686920	−	0.686920i
$534$	1.11311e15	−	6.58843e14i	1.10933	−	0.656606i
$535$		0			0
$536$			8.68543e14i			0.847978i
$537$	3.04391e14	+	7.80348e13i	0.294153	+	0.0754102i
$538$	1.97588e14	−	1.97588e14i	0.188999	−	0.188999i
$539$	6.96283e14			0.659246
$540$		0			0
$541$	8.49547e14			0.788139			0.394069	−	0.919081i	$-0.371067\pi$
$541$	8.49547e14			0.788139			0.394069	+	0.919081i	$0.371067\pi$
$542$	−6.59795e14	+	6.59795e14i	−0.605916	+	0.605916i
$543$	1.96742e14	+	5.04376e13i	0.178854	+	0.0458517i
$544$			6.53299e14i			0.587920i
$545$		0			0
$546$	1.34768e14	−	7.97687e13i	0.118858	−	0.0703514i
$547$	8.33911e14	+	8.33911e14i	0.728097	+	0.728097i	0.970240	−	0.242143i	$-0.0778505\pi$
$547$	8.33911e14	+	8.33911e14i	0.728097	+	0.728097i	−0.242143	+	0.970240i	$0.577850\pi$
$548$	−1.30900e14	−	1.30900e14i	−0.113148	−	0.113148i
$549$	−9.19467e14	−	5.04600e14i	−0.786844	−	0.431816i
$550$		0			0
$551$		−	1.25239e15i		−	1.05052i
$552$	−3.16216e14	+	1.23347e15i	−0.262615	+	1.02438i
$553$	1.44235e14	−	1.44235e14i	0.118599	−	0.118599i
$554$	−2.41538e15			−1.96645
$555$		0			0
$556$	1.68545e14			0.134525
$557$	−4.40609e14	+	4.40609e14i	−0.348217	+	0.348217i	−0.859445	−	0.511228i	$-0.829191\pi$
$557$	−4.40609e14	+	4.40609e14i	−0.348217	+	0.348217i	0.511228	+	0.859445i	$0.329191\pi$
$558$	1.38661e14	−	4.03955e13i	0.108509	−	0.0316114i
$559$		−	1.25682e15i		−	0.973889i
$560$		0			0
$561$	3.94992e14	+	6.67334e14i	0.300118	+	0.507046i
$562$	−2.36981e14	−	2.36981e14i	−0.178305	−	0.178305i
$563$	5.48238e14	+	5.48238e14i	0.408482	+	0.408482i	0.881209	−	0.472727i	$-0.156730\pi$
$563$	5.48238e14	+	5.48238e14i	0.408482	+	0.408482i	−0.472727	+	0.881209i	$0.656730\pi$
$564$	2.79319e14	+	4.71906e14i	0.206094	+	0.348194i
$565$		0			0
$566$		−	2.65436e15i		−	1.92074i
$567$	−5.57385e13	+	2.51097e14i	−0.0399437	+	0.179943i
$568$	−8.95391e14	+	8.95391e14i	−0.635473	+	0.635473i
$569$	1.49002e13			0.0104731			0.00523655	−	0.999986i	$-0.498333\pi$
$569$	1.49002e13			0.0104731			0.00523655	+	0.999986i	$0.498333\pi$
$570$		0			0
$571$	1.28451e15			0.885604			0.442802	−	0.896620i	$-0.353985\pi$
$571$	1.28451e15			0.885604			0.442802	+	0.896620i	$0.353985\pi$
$572$	−1.61755e14	+	1.61755e14i	−0.110454	+	0.110454i
$573$	2.68290e14	−	1.04652e15i	0.181449	−	0.707778i
$574$		−	4.83613e14i		−	0.323954i
$575$		0			0
$576$	−3.19433e14	+	5.82062e14i	−0.209921	+	0.382512i
$577$	5.67579e14	+	5.67579e14i	0.369453	+	0.369453i	0.867278	−	0.497825i	$-0.165868\pi$
$577$	5.67579e14	+	5.67579e14i	0.369453	+	0.369453i	−0.497825	+	0.867278i	$0.665868\pi$
$578$	−3.25039e14	−	3.25039e14i	−0.209572	−	0.209572i
$579$	−2.05640e15	+	1.21718e15i	−1.31334	+	0.777359i
$580$		0			0
$581$		−	3.07862e14i		−	0.192925i
$582$	−2.78620e15	−	7.14280e14i	−1.72956	−	0.443397i
$583$	6.76699e14	−	6.76699e14i	0.416120	−	0.416120i
$584$	3.09917e14			0.188788
$585$		0			0
$586$	−6.91446e14			−0.413353
$587$	2.27573e14	−	2.27573e14i	0.134776	−	0.134776i	−0.636501	−	0.771276i	$-0.719619\pi$
$587$	2.27573e14	−	2.27573e14i	0.134776	−	0.134776i	0.771276	+	0.636501i	$0.219619\pi$
$588$	−5.67262e14	−	1.45426e14i	−0.332819	−	0.0853229i
$589$		−	2.01273e14i		−	0.116991i
$590$		0			0
$591$	−1.94987e15	+	1.15412e15i	−1.11243	+	0.658445i
$592$	2.14128e15	+	2.14128e15i	1.21033	+	1.21033i
$593$	−4.06647e14	−	4.06647e14i	−0.227728	−	0.227728i	0.584015	−	0.811743i	$-0.301481\pi$
$593$	−4.06647e14	−	4.06647e14i	−0.227728	−	0.227728i	−0.811743	+	0.584015i	$0.801481\pi$
$594$	−4.65636e13	−	1.43130e15i	−0.0258358	−	0.794156i
$595$		0			0
$596$		−	8.12879e14i		−	0.442763i
$597$	−3.95114e13	+	1.54122e14i	−0.0213238	+	0.0831777i
$598$	−1.39672e15	+	1.39672e15i	−0.746883	+	0.746883i
$599$	4.47455e13			0.0237084			0.0118542	−	0.999930i	$-0.496227\pi$
$599$	4.47455e13			0.0237084			0.0118542	+	0.999930i	$0.496227\pi$
$600$		0			0
$601$	−1.35956e14			−0.0707275			−0.0353638	−	0.999375i	$-0.511259\pi$
$601$	−1.35956e14			−0.0707275			−0.0353638	+	0.999375i	$0.511259\pi$
$602$	4.45489e14	−	4.45489e14i	0.229645	−	0.229645i
$603$	−6.18917e14	−	2.12448e15i	−0.316146	−	1.08520i
$604$			7.65165e14i			0.387304i
$605$		0			0
$606$	1.34140e15	+	2.26628e15i	0.666746	+	1.12646i
$607$	−1.81384e15	−	1.81384e15i	−0.893430	−	0.893430i	0.101414	−	0.994844i	$-0.467663\pi$
$607$	−1.81384e15	−	1.81384e15i	−0.893430	−	0.893430i	−0.994844	+	0.101414i	$0.967663\pi$
$608$	−1.18888e15	−	1.18888e15i	−0.580320	−	0.580320i
$609$	−1.69172e14	−	2.85815e14i	−0.0818341	−	0.138258i
$610$		0			0
$611$		−	1.54106e15i		−	0.732140i
$612$	−1.82421e14	−	6.26175e14i	−0.0858899	−	0.294824i
$613$	−5.36783e14	+	5.36783e14i	−0.250476	+	0.250476i	−0.821166	−	0.570690i	$-0.806676\pi$
$613$	−5.36783e14	+	5.36783e14i	−0.250476	+	0.250476i	0.570690	+	0.821166i	$0.306676\pi$
$614$	−4.19693e15			−1.94091
$615$		0			0
$616$	2.07740e14			0.0943683
$617$	1.32391e15	−	1.32391e15i	0.596059	−	0.596059i	−0.343203	−	0.939261i	$-0.611512\pi$
$617$	1.32391e15	−	1.32391e15i	0.596059	−	0.596059i	0.939261	+	0.343203i	$0.111512\pi$
$618$	−2.06374e14	+	8.05003e14i	−0.0920911	+	0.359220i
$619$		−	2.58748e14i		−	0.114440i	−0.998362	−	0.0572201i	$-0.981776\pi$
$619$		−	2.58748e14i		−	0.114440i	0.998362	−	0.0572201i	$-0.0182237\pi$
$620$		0			0
$621$	−1.05484e14	−	3.24244e15i	−0.0458335	−	1.40886i
$622$	−3.39596e15	−	3.39596e15i	−1.46257	−	1.46257i
$623$	−3.38029e14	−	3.38029e14i	−0.144301	−	0.144301i
$624$	−1.60879e15	+	9.52234e14i	−0.680743	+	0.402929i
$625$		0			0
$626$		−	1.57150e12i		−	0.000653364i
$627$	−1.93322e15	−	4.95609e14i	−0.796729	−	0.204253i
$628$	−3.63483e14	+	3.63483e14i	−0.148493	+	0.148493i
$629$	2.96890e15			1.20231
$630$		0			0
$631$	4.87062e15			1.93831			0.969154	−	0.246456i	$-0.0792661\pi$
$631$	4.87062e15			1.93831			0.969154	+	0.246456i	$0.0792661\pi$
$632$	−1.22359e15	+	1.22359e15i	−0.482715	+	0.482715i
$633$	4.14008e15	+	1.06137e15i	1.61915	+	0.415092i
$634$		−	2.32849e15i		−	0.902785i
$635$		0			0
$636$	−6.92643e14	+	4.09972e14i	−0.263934	+	0.156221i
$637$	1.16368e15	+	1.16368e15i	0.439610	+	0.439610i
$638$	1.30757e15	+	1.30757e15i	0.489725	+	0.489725i
$639$	1.55211e15	−	2.82821e15i	0.576324	−	1.05016i
$640$		0			0
$641$		−	3.26181e15i		−	1.19053i	−0.803530	−	0.595264i	$-0.797047\pi$
$641$		−	3.26181e15i		−	1.19053i	0.803530	−	0.595264i	$-0.202953\pi$
$642$	5.37626e14	−	2.09712e15i	0.194553	−	0.758894i
$643$	1.71819e15	−	1.71819e15i	0.616470	−	0.616470i	−0.328154	−	0.944624i	$-0.606427\pi$
$643$	1.71819e15	−	1.71819e15i	0.616470	−	0.616470i	0.944624	+	0.328154i	$0.106427\pi$
$644$	−2.59771e14			−0.0924100
$645$		0			0
$646$	−3.46448e15			−1.21160
$647$	8.67225e14	−	8.67225e14i	0.300717	−	0.300717i	−0.540577	−	0.841294i	$-0.681794\pi$
$647$	8.67225e14	−	8.67225e14i	0.300717	−	0.300717i	0.841294	+	0.540577i	$0.181794\pi$
$648$	4.72846e14	−	2.13013e15i	0.162576	−	0.732391i
$649$			1.18028e15i			0.402383i
$650$		0			0
$651$	−2.71879e13	−	4.59337e13i	−0.00911341	−	0.0153970i
$652$	1.15889e15	+	1.15889e15i	0.385193	+	0.385193i
$653$	−3.29211e14	−	3.29211e14i	−0.108506	−	0.108506i	0.650770	−	0.759275i	$-0.274446\pi$
$653$	−3.29211e14	−	3.29211e14i	−0.108506	−	0.108506i	−0.759275	+	0.650770i	$0.774446\pi$
$654$	−1.94712e15	−	3.28964e15i	−0.636378	−	1.07515i
$655$		0			0
$656$			5.77310e15i			1.85540i
$657$	−7.58068e14	+	2.20845e14i	−0.241601	+	0.0703846i
$658$	5.46239e14	−	5.46239e14i	0.172640	−	0.172640i
$659$	2.85395e15			0.894493			0.447246	−	0.894411i	$-0.352405\pi$
$659$	2.85395e15			0.894493			0.447246	+	0.894411i	$0.352405\pi$
$660$		0			0
$661$	−1.38123e15			−0.425754			−0.212877	−	0.977079i	$-0.568283\pi$
$661$	−1.38123e15			−0.425754			−0.212877	+	0.977079i	$0.568283\pi$
$662$	−2.28714e15	+	2.28714e15i	−0.699155	+	0.699155i
$663$	−4.55158e14	+	1.77544e15i	−0.137987	+	0.538247i
$664$			2.61168e15i			0.785229i
$665$		0			0
$666$	−4.80644e15	−	2.63775e15i	−1.42140	−	0.780057i
$667$	2.96214e15	+	2.96214e15i	0.868788	+	0.868788i
$668$	−3.86630e14	−	3.86630e14i	−0.112467	−	0.112467i
$669$	1.42940e15	−	8.46056e14i	0.412392	−	0.244093i
$670$		0			0
$671$		−	2.15819e15i		−	0.612514i
$672$	−4.31914e14	−	1.10727e14i	−0.121581	−	0.0311690i
$673$	3.30225e15	−	3.30225e15i	0.921991	−	0.921991i	−0.0751787	−	0.997170i	$-0.523953\pi$
$673$	3.30225e15	−	3.30225e15i	0.921991	−	0.921991i	0.997170	+	0.0751787i	$0.0239527\pi$
$674$	2.35144e15			0.651184
$675$		0			0
$676$	7.64741e14			0.208357
$677$	4.99086e14	−	4.99086e14i	0.134877	−	0.134877i	−0.636445	−	0.771322i	$-0.719596\pi$
$677$	4.99086e14	−	4.99086e14i	0.134877	−	0.134877i	0.771322	+	0.636445i	$0.219596\pi$
$678$	5.74657e15	+	1.47321e15i	1.54044	+	0.394914i
$679$			1.06303e15i			0.282658i
$680$		0			0
$681$	−9.79562e14	+	5.79798e14i	−0.256285	+	0.151694i
$682$	2.10142e14	+	2.10142e14i	0.0545379	+	0.0545379i
$683$	−9.40627e14	−	9.40627e14i	−0.242161	−	0.242161i	0.575583	−	0.817743i	$-0.304775\pi$
$683$	−9.40627e14	−	9.40627e14i	−0.242161	−	0.242161i	−0.817743	+	0.575583i	$0.804775\pi$
$684$	1.47149e15	+	8.07546e14i	0.375792	+	0.206233i
$685$		0			0
$686$			1.67891e15i			0.421934i
$687$	4.13184e14	−	1.61171e15i	0.103010	−	0.401813i
$688$	−5.31800e15	+	5.31800e15i	−1.31526	+	1.31526i
$689$	2.26190e15			0.554968
$690$		0			0
$691$	1.60018e14			0.0386402			0.0193201	−	0.999813i	$-0.493850\pi$
$691$	1.60018e14			0.0386402			0.0193201	+	0.999813i	$0.493850\pi$
$692$	4.56707e14	−	4.56707e14i	0.109409	−	0.109409i
$693$	−5.08139e14	+	1.48034e14i	−0.120767	+	0.0351826i
$694$			7.70409e15i			1.81654i
$695$		0			0
$696$	1.43514e15	+	2.42464e15i	0.333075	+	0.562726i
$697$	4.00223e15	+	4.00223e15i	0.921556	+	0.921556i
$698$	1.68809e15	+	1.68809e15i	0.385648	+	0.385648i
$699$	2.34357e15	+	3.95944e15i	0.531195	+	0.897448i
$700$		0			0
$701$			8.36483e15i			1.86641i	0.359339	+	0.933207i	$0.383002\pi$
$701$			8.36483e15i			1.86641i	−0.359339	+	0.933207i	$0.616998\pi$
$702$	2.31428e15	−	2.46992e15i	0.512344	−	0.546801i
$703$	−5.40281e15	+	5.40281e15i	−1.18677	+	1.18677i
$704$	−1.36623e15			−0.297765
$705$		0			0
$706$	5.73200e15			1.22993
$707$	6.88226e14	−	6.88226e14i	0.146529	−	0.146529i
$708$	2.46514e14	−	9.61577e14i	0.0520784	−	0.203143i
$709$		−	5.61779e15i		−	1.17764i	−0.808266	−	0.588818i	$-0.799594\pi$
$709$		−	5.61779e15i		−	1.17764i	0.808266	−	0.588818i	$-0.200406\pi$
$710$		0			0
$711$	2.12102e15	−	3.86486e15i	0.437785	−	0.797720i
$712$	2.86759e15	+	2.86759e15i	0.587324	+	0.587324i
$713$	4.76050e14	+	4.76050e14i	0.0967521	+	0.0967521i
$714$	−7.90649e14	+	4.67982e14i	−0.159457	+	0.0943819i
$715$		0			0
$716$		−	5.43825e14i		−	0.108003i
$717$	−2.49502e15	−	6.39632e14i	−0.491721	−	0.126059i
$718$	−3.72164e15	+	3.72164e15i	−0.727864	+	0.727864i
$719$	−8.90969e15			−1.72923			−0.864617	−	0.502432i	$-0.832439\pi$
$719$	−8.90969e15			−1.72923			−0.864617	+	0.502432i	$0.832439\pi$
$720$		0			0
$721$	3.07136e14			0.0587065
$722$	1.96442e15	−	1.96442e15i	0.372631	−	0.372631i
$723$	−9.67210e15	−	2.47958e15i	−1.82079	−	0.466785i
$724$		−	3.51500e14i		−	0.0656694i
$725$		0			0
$726$	−2.90925e15	+	1.72197e15i	−0.535339	+	0.316865i
$727$	−1.58749e15	−	1.58749e15i	−0.289915	−	0.289915i	0.547132	−	0.837047i	$-0.315720\pi$
$727$	−1.58749e15	−	1.58749e15i	−0.289915	−	0.289915i	−0.837047	+	0.547132i	$0.815720\pi$
$728$	3.47191e14	+	3.47191e14i	0.0629282	+	0.0629282i
$729$	3.61316e14	+	5.54731e15i	0.0649959	+	0.997886i
$730$		0			0
$731$			7.37345e15i			1.30655i
$732$	−4.50759e14	+	1.75828e15i	−0.0792745	+	0.309227i
$733$	2.36905e15	−	2.36905e15i	0.413526	−	0.413526i	−0.469439	−	0.882965i	$-0.655544\pi$
$733$	2.36905e15	−	2.36905e15i	0.413526	−	0.413526i	0.882965	+	0.469439i	$0.155544\pi$
$734$	9.85402e15			1.70720
$735$		0			0
$736$	5.62385e15			0.959856
$737$	3.21968e15	−	3.21968e15i	0.545433	−	0.545433i
$738$	−2.92350e15	−	1.00352e16i	−0.491579	−	1.68739i
$739$		−	1.33084e15i		−	0.222117i	−0.993814	−	0.111059i	$-0.964576\pi$
$739$		−	1.33084e15i		−	0.222117i	0.993814	−	0.111059i	$-0.0354241\pi$
$740$		0			0
$741$	−2.40265e15	−	4.05925e15i	−0.395085	−	0.667491i
$742$	8.01745e14	+	8.01745e14i	0.130862	+	0.130862i
$743$	1.74860e15	+	1.74860e15i	0.283303	+	0.283303i	0.834425	−	0.551122i	$-0.185800\pi$
$743$	1.74860e15	+	1.74860e15i	0.283303	+	0.283303i	−0.551122	+	0.834425i	$0.685800\pi$
$744$	2.30643e14	+	3.89668e14i	0.0370927	+	0.0626677i
$745$		0			0
$746$			2.29409e14i			0.0363536i
$747$	−1.86107e15	−	6.38827e15i	−0.292751	−	1.00489i
$748$	9.48975e14	−	9.48975e14i	0.148182	−	0.148182i
$749$	−8.00122e14			−0.124024
$750$		0			0
$751$	−4.73650e15			−0.723500			−0.361750	−	0.932275i	$-0.617821\pi$
$751$	−4.73650e15			−0.723500			−0.361750	+	0.932275i	$0.617821\pi$
$752$	−6.52070e15	+	6.52070e15i	−0.988772	+	0.988772i
$753$	−1.53347e15	+	5.98162e15i	−0.230836	+	0.900423i
$754$			4.37063e15i			0.653133i
$755$		0			0
$756$	4.44899e14	−	1.44736e13i	0.0655227	−	0.00213161i
$757$	5.60589e15	+	5.60589e15i	0.819629	+	0.819629i	0.986054	−	0.166425i	$-0.0532224\pi$
$757$	5.60589e15	+	5.60589e15i	0.819629	+	0.819629i	−0.166425	+	0.986054i	$0.553222\pi$
$758$	2.64492e15	+	2.64492e15i	0.383912	+	0.383912i
$759$	5.74466e15	−	3.40024e15i	0.827818	−	0.489982i
$760$		0			0
$761$		−	8.47851e14i		−	0.120421i	−0.998186	−	0.0602107i	$-0.980823\pi$
$761$		−	8.47851e14i		−	0.120421i	0.998186	−	0.0602107i	$-0.0191773\pi$
$762$	3.72385e15	+	9.54661e14i	0.525098	+	0.134616i
$763$	−9.98998e14	+	9.98998e14i	−0.139856	+	0.139856i
$764$	−1.86971e15			−0.259873
$765$		0			0
$766$	−8.69549e15			−1.19134
$767$	−1.97258e15	+	1.97258e15i	−0.268324	+	0.268324i
$768$	6.79963e15	+	1.74318e15i	0.918329	+	0.235426i
$769$			1.07980e16i			1.44793i	0.689838	+	0.723964i	$0.257682\pi$
$769$			1.07980e16i			1.44793i	−0.689838	+	0.723964i	$0.742318\pi$
$770$		0			0
$771$	−1.68432e15	+	9.96942e14i	−0.222652	+	0.131786i
$772$	2.92429e15	+	2.92429e15i	0.383818	+	0.383818i
$773$	5.41677e15	+	5.41677e15i	0.705916	+	0.705916i	0.965674	−	0.259758i	$-0.0836428\pi$
$773$	5.41677e15	+	5.41677e15i	0.705916	+	0.705916i	−0.259758	+	0.965674i	$0.583643\pi$
$774$	6.55104e15	−	1.19371e16i	0.847685	−	1.54463i
$775$		0			0
$776$		−	9.01796e15i		−	1.15045i
$777$	−5.03195e14	+	1.96282e15i	−0.0637413	+	0.248636i
$778$	7.51078e15	−	7.51078e15i	0.944707	−	0.944707i
$779$	−1.45666e16			−1.81928
$780$		0			0
$781$	6.63841e15			0.817492
$782$	8.19418e15	−	8.19418e15i	1.00200	−	1.00200i
$783$	−5.23818e15	−	4.90810e15i	−0.636049	−	0.595968i
$784$		−	9.84777e15i		−	1.18741i
$785$		0			0
$786$	1.22703e15	+	2.07305e15i	0.145892	+	0.246482i
$787$	−5.60194e15	−	5.60194e15i	−0.661420	−	0.661420i	0.294294	−	0.955715i	$-0.404915\pi$
$787$	−5.60194e15	−	5.60194e15i	−0.661420	−	0.661420i	−0.955715	+	0.294294i	$0.904915\pi$
$788$	2.77279e15	+	2.77279e15i	0.325105	+	0.325105i
$789$	1.47013e15	+	2.48377e15i	0.171172	+	0.289193i
$790$		0			0
$791$		−	2.19251e15i		−	0.251751i
$792$	4.31068e15	−	1.25581e15i	0.491539	−	0.143198i
$793$	3.60693e15	−	3.60693e15i	0.408447	−	0.408447i
$794$	4.39863e15			0.494658
$795$		0			0
$796$	2.75355e14			0.0305402
$797$	−9.17975e15	+	9.17975e15i	−1.01114	+	1.01114i	−0.0112002	+	0.999937i	$0.503565\pi$
$797$	−9.17975e15	+	9.17975e15i	−1.01114	+	1.01114i	−0.999937	+	0.0112002i	$0.996435\pi$
$798$	5.87191e14	−	2.29046e15i	0.0642338	−	0.250557i
$799$			9.04101e15i			0.982222i
$800$		0			0
$801$	−9.05766e15	−	4.97081e15i	−0.970593	−	0.532657i
$802$	−6.84574e15	−	6.84574e15i	−0.728553	−	0.728553i
$803$	−1.14886e15	−	1.14886e15i	−0.121432	−	0.121432i
$804$	−3.29554e15	+	1.95061e15i	−0.345954	+	0.204768i
$805$		0			0
$806$			7.02410e14i			0.0727358i
$807$	−2.16212e15	−	5.54290e14i	−0.222370	−	0.0570075i
$808$	−5.83842e15	+	5.83842e15i	−0.596393	+	0.596393i
$809$	1.17976e16			1.19695			0.598474	−	0.801142i	$-0.295774\pi$
$809$	1.17976e16			1.19695			0.598474	+	0.801142i	$0.295774\pi$
$810$		0			0
$811$	−4.70032e15			−0.470450			−0.235225	−	0.971941i	$-0.575583\pi$
$811$	−4.70032e15			−0.470450			−0.235225	+	0.971941i	$0.575583\pi$
$812$	−4.06440e14	+	4.06440e14i	−0.0404053	+	0.0404053i
$813$	7.21984e15	+	1.85090e15i	0.712901	+	0.182762i
$814$		−	1.12818e16i		−	1.10648i
$815$		0			0
$816$	9.43833e15	−	5.58650e15i	0.913270	−	0.540560i
$817$	−1.34182e16	−	1.34182e16i	−1.28966	−	1.28966i
$818$	8.82546e14	+	8.82546e14i	0.0842547	+	0.0842547i
$819$	−1.09665e15	−	6.01835e14i	−0.103993	−	0.0570710i
$820$		0			0
$821$			6.54196e15i			0.612098i	0.952016	+	0.306049i	$0.0990071\pi$
$821$			6.54196e15i			0.612098i	−0.952016	+	0.306049i	$0.900993\pi$
$822$	−1.39966e15	+	5.45968e15i	−0.130086	+	0.507425i
$823$	1.70046e15	−	1.70046e15i	0.156988	−	0.156988i	−0.624243	−	0.781231i	$-0.714592\pi$
$823$	1.70046e15	−	1.70046e15i	0.156988	−	0.156988i	0.781231	+	0.624243i	$0.214592\pi$
$824$	−2.60552e15			−0.238943
$825$		0			0
$826$	−1.39838e15			−0.126543
$827$	6.46673e15	−	6.46673e15i	0.581306	−	0.581306i	−0.353956	−	0.935262i	$-0.615164\pi$
$827$	6.46673e15	−	6.46673e15i	0.581306	−	0.581306i	0.935262	+	0.353956i	$0.115164\pi$
$828$	−5.39036e15	+	1.57035e15i	−0.481338	+	0.140226i
$829$		−	1.98011e16i		−	1.75647i	−0.478231	−	0.878234i	$-0.658722\pi$
$829$		−	1.98011e16i		−	1.75647i	0.478231	−	0.878234i	$-0.341278\pi$
$830$		0			0
$831$	9.82731e15	+	1.66031e16i	0.860259	+	1.45340i
$832$	−2.28334e15	−	2.28334e15i	−0.198560	−	0.198560i
$833$	−6.82701e15	−	6.82701e15i	−0.589770	−	0.589770i
$834$	−2.61381e15	−	4.41600e15i	−0.224316	−	0.378980i
$835$		0			0
$836$			3.45390e15i			0.292533i
$837$	−8.41835e14	−	7.88787e14i	−0.0708332	−	0.0663697i
$838$	1.18848e16	−	1.18848e16i	0.993456	−	0.993456i
$839$	−2.36156e16			−1.96114			−0.980570	−	0.196170i	$-0.937150\pi$
$839$	−2.36156e16			−1.96114			−0.980570	+	0.196170i	$0.937150\pi$
$840$		0			0
$841$	−2.93134e15			−0.240263
$842$	−8.45914e15	+	8.45914e15i	−0.688826	+	0.688826i
$843$	−6.64796e14	+	2.59317e15i	−0.0537820	+	0.209788i
$844$		−	7.39666e15i		−	0.594501i
$845$		0			0
$846$	8.03260e15	−	1.46368e16i	0.637263	−	1.16120i
$847$	8.83482e14	+	8.83482e14i	0.0696368	+	0.0696368i
$848$	−9.57079e15	−	9.57079e15i	−0.749498	−	0.749498i
$849$	−1.82458e16	+	1.07996e16i	−1.41962	+	0.840264i
$850$		0			0
$851$		−	2.55574e16i		−	1.96293i
$852$	−5.40832e15	−	1.38650e15i	−0.412710	−	0.105804i
$853$	−8.39181e15	+	8.39181e15i	−0.636262	+	0.636262i	−0.949631	−	0.313370i	$-0.898542\pi$
$853$	−8.39181e15	+	8.39181e15i	−0.636262	+	0.636262i	0.313370	+	0.949631i	$0.398542\pi$
$854$	2.55700e15			0.192625
$855$		0			0
$856$	6.78766e15			0.504794
$857$	−2.09253e15	+	2.09253e15i	−0.154624	+	0.154624i	−0.780180	−	0.625556i	$-0.784872\pi$
$857$	−2.09253e15	+	2.09253e15i	−0.154624	+	0.154624i	0.625556	+	0.780180i	$0.284872\pi$
$858$	6.74664e15	+	1.72959e15i	0.495345	+	0.126988i
$859$		−	1.22031e16i		−	0.890243i	−0.895470	−	0.445122i	$-0.853160\pi$
$859$		−	1.22031e16i		−	0.890243i	0.895470	−	0.445122i	$-0.146840\pi$
$860$		0			0
$861$	−3.32431e15	+	1.96765e15i	−0.239433	+	0.141720i
$862$	−7.09309e15	−	7.09309e15i	−0.507628	−	0.507628i
$863$	−6.98725e15	−	6.98725e15i	−0.496875	−	0.496875i	0.413589	−	0.910464i	$-0.364275\pi$
$863$	−6.98725e15	−	6.98725e15i	−0.496875	−	0.496875i	−0.910464	+	0.413589i	$0.864275\pi$
$864$	−9.63174e15	+	3.13343e14i	−0.680580	+	0.0221409i
$865$		0			0
$866$		−	1.37569e16i		−	0.959783i
$867$	−9.11824e14	+	3.55676e15i	−0.0632129	+	0.246575i
$868$	−6.53195e13	+	6.53195e13i	−0.00449971	+	0.00449971i
$869$	9.07166e15			0.620980
$870$		0			0
$871$	1.07620e16			0.727430
$872$	8.47478e15	−	8.47478e15i	0.569230	−	0.569230i
$873$	6.42613e15	+	2.20582e16i	0.428915	+	1.47229i
$874$			2.98236e16i			1.97809i
$875$		0			0
$876$	6.96027e14	+	1.17593e15i	0.0455883	+	0.0770208i
$877$	1.68282e16	+	1.68282e16i	1.09532	+	1.09532i	0.994951	+	0.100367i	$0.0320015\pi$
$877$	1.68282e16	+	1.68282e16i	1.09532	+	1.09532i	0.100367	+	0.994951i	$0.467998\pi$
$878$	−6.65244e15	−	6.65244e15i	−0.430290	−	0.430290i
$879$	2.81324e15	+	4.75294e15i	0.180829	+	0.305509i
$880$		0			0
$881$			2.14085e16i			1.35900i	0.733677	+	0.679499i	$0.237803\pi$
$881$			2.14085e16i			1.35900i	−0.733677	+	0.679499i	$0.762197\pi$
$882$	4.98692e15	+	1.71180e16i	0.314597	+	1.07988i
$883$	−3.47737e15	+	3.47737e15i	−0.218005	+	0.218005i	−0.807657	−	0.589652i	$-0.799265\pi$
$883$	−3.47737e15	+	3.47737e15i	−0.218005	+	0.218005i	0.589652	+	0.807657i	$0.299265\pi$
$884$	3.17200e15			0.197627
$885$		0			0
$886$	−2.48064e16			−1.52643
$887$	−1.46192e16	+	1.46192e16i	−0.894012	+	0.894012i	−0.994898	−	0.100886i	$-0.967832\pi$
$887$	−1.46192e16	+	1.46192e16i	−0.894012	+	0.894012i	0.100886	+	0.994898i	$0.467832\pi$
$888$	4.26875e15	−	1.66511e16i	0.259435	−	1.01198i
$889$		−	1.42077e15i		−	0.0858154i
$890$		0			0
$891$	−9.64920e15	+	6.14353e15i	−0.575657	+	0.366514i
$892$	−2.03266e15	−	2.03266e15i	−0.120520	−	0.120520i
$893$	−1.64529e16	−	1.64529e16i	−0.969524	−	0.969524i
$894$	−2.12981e16	+	1.26062e16i	−1.24734	+	0.738294i
$895$		0			0
$896$		−	3.78830e15i		−	0.219154i
$897$	1.52837e16	+	3.91818e15i	0.878757	+	0.225282i
$898$	−8.66713e15	+	8.66713e15i	−0.495285	+	0.495285i
$899$	1.48966e15			0.0846076
$900$		0			0
$901$	−1.32700e16			−0.744533
$902$	1.52084e16	−	1.52084e16i	0.848101	−	0.848101i
$903$	−4.87479e15	−	1.24972e15i	−0.270192	−	0.0692675i
$904$			1.85997e16i			1.02466i
$905$		0			0
$906$	2.00479e16	−	1.18663e16i	1.09110	−	0.645817i
$907$	7.42996e14	+	7.42996e14i	0.0401926	+	0.0401926i	0.726917	−	0.686725i	$-0.240952\pi$
$907$	7.42996e14	+	7.42996e14i	0.0401926	+	0.0401926i	−0.686725	+	0.726917i	$0.740952\pi$
$908$	1.39298e15	+	1.39298e15i	0.0748983	+	0.0748983i
$909$	1.01206e16	−	1.84414e16i	0.540882	−	0.985581i
$910$		0			0
$911$		−	2.04045e16i		−	1.07740i	−0.842499	−	0.538698i	$-0.818917\pi$
$911$		−	2.04045e16i		−	1.07740i	0.842499	−	0.538698i	$-0.181083\pi$
$912$	−7.00956e15	+	2.73422e16i	−0.367891	+	1.43504i
$913$	9.68149e15	−	9.68149e15i	0.505072	−	0.505072i
$914$	1.99842e16			1.03629
$915$		0			0
$916$	−2.87948e15			−0.147533
$917$	6.29545e14	−	6.29545e14i	0.0320623	−	0.0320623i
$918$	−1.35773e16	+	1.44904e16i	−0.687350	+	0.733576i
$919$		−	1.48502e16i		−	0.747305i	−0.927569	−	0.373652i	$-0.878105\pi$
$919$		−	1.48502e16i		−	0.747305i	0.927569	−	0.373652i	$-0.121895\pi$
$920$		0			0
$921$	1.70758e16	+	2.88493e16i	0.849089	+	1.43452i
$922$	−1.09384e16	−	1.09384e16i	−0.540670	−	0.540670i
$923$	1.10946e16	+	1.10946e16i	0.545134	+	0.545134i
$924$	4.66552e14	+	7.88234e14i	0.0227879	+	0.0384999i
$925$		0			0
$926$			2.10587e16i			1.01642i
$927$	6.37318e15	−	1.85667e15i	0.305786	−	0.0890834i
$928$	8.79912e15	−	8.79912e15i	0.419687	−	0.419687i
$929$	−8.80213e15			−0.417351			−0.208675	−	0.977985i	$-0.566915\pi$
$929$	−8.80213e15			−0.417351			−0.208675	+	0.977985i	$0.566915\pi$
$930$		0			0
$931$	2.48476e16			1.16429
$932$	5.63048e15	−	5.63048e15i	0.262276	−	0.262276i
$933$	−9.52660e15	+	3.71605e16i	−0.441153	+	1.72081i
$934$		−	1.59443e16i		−	0.734005i
$935$		0			0
$936$	9.30315e15	+	5.10553e15i	0.423266	+	0.232286i
$937$	−1.70767e16	−	1.70767e16i	−0.772391	−	0.772391i	0.206133	−	0.978524i	$-0.433912\pi$
$937$	−1.70767e16	−	1.70767e16i	−0.772391	−	0.772391i	−0.978524	+	0.206133i	$0.933912\pi$
$938$	3.81464e15	+	3.81464e15i	0.171529	+	0.171529i
$939$	−1.08023e13	+	6.39386e12i	−0.000482900	+	0.000285826i
$940$		0			0
$941$		−	1.33392e13i		−	0.000589367i	−1.00000		0.000294683i	$-0.999906\pi$
$941$		−	1.33392e13i		−	0.000589367i	1.00000		0.000294683i	$-9.38007e-5\pi$
$942$	1.51605e16	+	3.88659e15i	0.665936	+	0.170722i
$943$	3.44527e16	−	3.44527e16i	1.50456	−	1.50456i
$944$	1.66931e16			0.724756
$945$		0			0
$946$	2.80190e16			1.20241
$947$	−2.26259e16	+	2.26259e16i	−0.965343	+	0.965343i	−0.999419	−	0.0340764i	$-0.989151\pi$
$947$	−2.26259e16	+	2.26259e16i	−0.965343	+	0.965343i	0.0340764	+	0.999419i	$0.489151\pi$
$948$	−7.39069e15	−	1.89470e15i	−0.313501	−	0.0803703i
$949$		−	3.84013e15i		−	0.161950i
$950$		0			0
$951$	−1.60059e16	+	9.47380e15i	−0.667247	+	0.394940i
$952$	−2.03688e15	−	2.03688e15i	−0.0844231	−	0.0844231i
$953$	2.66519e16	+	2.66519e16i	1.09829	+	1.09829i	0.994611	+	0.103679i	$0.0330615\pi$
$953$	2.66519e16	+	2.66519e16i	1.09829	+	1.09829i	0.103679	+	0.994611i	$0.466938\pi$
$954$	2.14832e16	+	1.17899e16i	0.880202	+	0.483051i
$955$		0			0
$956$			4.45760e15i			0.180544i
$957$	3.66810e15	−	1.43082e16i	0.147715	−	0.576194i
$958$	−1.82904e16	+	1.82904e16i	−0.732340	+	0.732340i
$959$	2.08305e15			0.0829272
$960$		0			0
$961$	−2.51691e16			−0.990578
$962$	1.88549e16	−	1.88549e16i	0.737840	−	0.737840i
$963$	−1.66028e16	+	4.83684e15i	−0.646008	+	0.188199i
$964$			1.72802e16i			0.668536i
$965$		0			0
$966$	4.02857e15	+	6.80621e15i	0.154091	+	0.260334i
$967$	3.34050e14	+	3.34050e14i	0.0127047	+	0.0127047i	0.713431	−	0.700726i	$-0.247140\pi$
$967$	3.34050e14	+	3.34050e14i	0.0127047	+	0.0127047i	−0.700726	+	0.713431i	$0.747140\pi$
$968$	−7.49482e15	−	7.49482e15i	−0.283431	−	0.283431i
$969$	1.40957e16	+	2.38145e16i	0.530038	+	0.895492i
$970$		0			0
$971$		−	4.37671e15i		−	0.162720i	−0.996685	−	0.0813602i	$-0.974074\pi$
$971$		−	4.37671e15i		−	0.162720i	0.996685	−	0.0813602i	$-0.0259264\pi$
$972$	9.14434e15	−	2.98981e15i	0.338055	−	0.110530i
$973$	−1.34105e15	+	1.34105e15i	−0.0492976	+	0.0492976i
$974$	−3.26044e16			−1.19179
$975$		0			0
$976$	−3.05240e16			−1.10323
$977$	1.77116e16	−	1.77116e16i	0.636559	−	0.636559i	−0.313146	−	0.949705i	$-0.601383\pi$
$977$	1.77116e16	−	1.77116e16i	0.636559	−	0.636559i	0.949705	+	0.313146i	$0.101383\pi$
$978$	1.23916e16	−	4.83359e16i	0.442856	−	1.72745i
$979$		−	2.12603e16i		−	0.755552i
$980$		0			0
$981$	−1.46905e16	+	2.67687e16i	−0.516248	+	0.940692i
$982$	3.51689e14	+	3.51689e14i	0.0122898	+	0.0122898i
$983$	2.35644e16	+	2.35644e16i	0.818866	+	0.818866i	0.985944	−	0.167078i	$-0.0534331\pi$
$983$	2.35644e16	+	2.35644e16i	0.818866	+	0.818866i	−0.167078	+	0.985944i	$0.553433\pi$
$984$	2.82011e16	−	1.66921e16i	0.974525	−	0.576817i
$985$		0			0
$986$		−	2.56413e16i		−	0.876229i
$987$	−5.97725e15	−	1.53235e15i	−0.203122	−	0.0520732i
$988$	−5.77242e15	+	5.77242e15i	−0.195072	+	0.195072i
$989$	6.34735e16			2.13311
$990$		0			0
$991$	−5.98291e16			−1.98842			−0.994208	−	0.107475i	$-0.965724\pi$
$991$	−5.98291e16			−1.98842			−0.994208	+	0.107475i	$0.965724\pi$
$992$	1.41412e15	−	1.41412e15i	0.0467382	−	0.0467382i
$993$	2.50271e16	+	6.41604e15i	0.822602	+	0.210885i
$994$			7.86512e15i			0.257087i
$995$		0			0
$996$	−9.90959e15	+	5.86544e15i	−0.320353	+	0.189616i
$997$	1.14360e16	+	1.14360e16i	0.367663	+	0.367663i	0.866624	−	0.498961i	$-0.166285\pi$
$997$	1.14360e16	+	1.14360e16i	0.367663	+	0.367663i	−0.498961	+	0.866624i	$0.666285\pi$
$998$	7.10663e15	+	7.10663e15i	0.227220	+	0.227220i
$999$	1.42398e15	+	4.37711e16i	0.0452786	+	1.39180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.12.e.d.32.6		40
3.2	odd	2	inner	75.12.e.d.32.15		40
5.2	odd	4		15.12.e.a.8.6	yes	40
5.3	odd	4	inner	75.12.e.d.68.15		40
5.4	even	2		15.12.e.a.2.15	yes	40
15.2	even	4		15.12.e.a.8.15	yes	40
15.8	even	4	inner	75.12.e.d.68.6		40
15.14	odd	2		15.12.e.a.2.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.e.a.2.6	✓	40	15.14	odd	2
15.12.e.a.2.15	yes	40	5.4	even	2
15.12.e.a.8.6	yes	40	5.2	odd	4
15.12.e.a.8.15	yes	40	15.2	even	4
75.12.e.d.32.6		40	1.1	even	1	trivial
75.12.e.d.32.15		40	3.2	odd	2	inner
75.12.e.d.68.6		40	15.8	even	4	inner
75.12.e.d.68.15		40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-37.2586 + 37.2586i) q^{2} +(407.704 + 104.521i) q^{3} -728.404i q^{4} +(-19084.8 + 11296.2i) q^{6} +(5795.67 + 5795.67i) q^{7} +(-49166.3 - 49166.3i) q^{8} +(155298. + 85226.8i) q^{9} +O(q^{10})\)	\(q+(-37.2586 + 37.2586i) q^{2} +(407.704 + 104.521i) q^{3} -728.404i q^{4} +(-19084.8 + 11296.2i) q^{6} +(5795.67 + 5795.67i) q^{7} +(-49166.3 - 49166.3i) q^{8} +(155298. + 85226.8i) q^{9} +364518. i q^{11} +(76133.2 - 296973. i) q^{12} +(-609210. + 609210. i) q^{13} -431877. q^{14} +5.15550e6 q^{16} +(3.57407e6 - 3.57407e6i) q^{17} +(-8.96161e6 + 2.61075e6i) q^{18} +1.30082e7i q^{19} +(1.75715e6 + 2.96868e6i) q^{21} +(-1.35814e7 - 1.35814e7i) q^{22} +(-3.07670e7 - 3.07670e7i) q^{23} +(-1.49064e7 - 2.51842e7i) q^{24} -4.53966e7i q^{26} +(5.44076e7 + 5.09791e7i) q^{27} +(4.22159e6 - 4.22159e6i) q^{28} -9.62766e7 q^{29} -1.54727e7 q^{31} +(-9.13942e7 + 9.13942e7i) q^{32} +(-3.80996e7 + 1.48615e8i) q^{33} +2.66330e8i q^{34} +(6.20796e7 - 1.13120e8i) q^{36} +(4.15338e8 + 4.15338e8i) q^{37} +(-4.84668e8 - 4.84668e8i) q^{38} +(-3.12052e8 + 1.84702e8i) q^{39} +1.11979e9i q^{41} +(-1.76078e8 - 4.51400e7i) q^{42} +(-1.03152e9 + 1.03152e9i) q^{43} +2.65516e8 q^{44} +2.29267e9 q^{46} +(-1.26480e9 + 1.26480e9i) q^{47} +(2.10192e9 + 5.38856e8i) q^{48} -1.91015e9i q^{49} +(1.83073e9 - 1.08360e9i) q^{51} +(4.43751e8 + 4.43751e8i) q^{52} +(-1.85642e9 - 1.85642e9i) q^{53} +(-3.92656e9 + 1.27740e8i) q^{54} -5.69903e8i q^{56} +(-1.35963e9 + 5.30351e9i) q^{57} +(3.58713e9 - 3.58713e9i) q^{58} +3.23793e9 q^{59} -5.92067e9 q^{61} +(5.76493e8 - 5.76493e8i) q^{62} +(4.06109e8 + 1.39400e9i) q^{63} +3.74803e9i q^{64} +(-4.11766e9 - 6.95674e9i) q^{66} +(-8.83271e9 - 8.83271e9i) q^{67} +(-2.60337e9 - 2.60337e9i) q^{68} +(-9.32805e9 - 1.57596e10i) q^{69} -1.82115e10i q^{71} +(-3.44513e9 - 1.18257e10i) q^{72} +(-3.15172e9 + 3.15172e9i) q^{73} -3.09498e10 q^{74} +9.47525e9 q^{76} +(-2.11263e9 + 2.11263e9i) q^{77} +(4.74488e9 - 1.85084e10i) q^{78} -2.48867e10i q^{79} +(1.68538e10 + 2.64711e10i) q^{81} +(-4.17220e10 - 4.17220e10i) q^{82} +(-2.65597e10 - 2.65597e10i) q^{83} +(2.16240e9 - 1.27992e9i) q^{84} -7.68659e10i q^{86} +(-3.92523e10 - 1.00629e10i) q^{87} +(1.79220e10 - 1.79220e10i) q^{88} -5.83244e10 q^{89} -7.06156e9 q^{91} +(-2.24108e10 + 2.24108e10i) q^{92} +(-6.30830e9 - 1.61722e9i) q^{93} -9.42496e10i q^{94} +(-4.68143e10 + 2.77092e10i) q^{96} +(9.17088e10 + 9.17088e10i) q^{97} +(7.11694e10 + 7.11694e10i) q^{98} +(-3.10667e10 + 5.66089e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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