LMFDB - Embedded newform 40.6.k.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.946365 - 5.57713i) q^{2} +(4.45554 + 4.45554i) q^{3} +(-30.2088 + 10.5560i) q^{4} +(49.9881 - 25.0237i) q^{5} +(20.6326 - 29.0657i) q^{6} +(-169.279 - 169.279i) q^{7} +(87.4607 + 158.489i) q^{8} -203.296i q^{9} +O(q^{10})$	\(q+(-0.946365 - 5.57713i) q^{2} +(4.45554 + 4.45554i) q^{3} +(-30.2088 + 10.5560i) q^{4} +(49.9881 - 25.0237i) q^{5} +(20.6326 - 29.0657i) q^{6} +(-169.279 - 169.279i) q^{7} +(87.4607 + 158.489i) q^{8} -203.296i q^{9} +(-186.868 - 255.109i) q^{10} -207.026 q^{11} +(-181.629 - 87.5639i) q^{12} +(-249.136 + 249.136i) q^{13} +(-783.891 + 1104.29i) q^{14} +(334.219 + 111.230i) q^{15} +(801.142 - 637.768i) q^{16} +(-424.145 + 424.145i) q^{17} +(-1133.81 + 192.392i) q^{18} -2282.02i q^{19} +(-1245.93 + 1283.61i) q^{20} -1508.46i q^{21} +(195.922 + 1154.61i) q^{22} +(351.205 - 351.205i) q^{23} +(-316.468 + 1095.84i) q^{24} +(1872.62 - 2501.78i) q^{25} +(1625.24 + 1153.69i) q^{26} +(1988.49 - 1988.49i) q^{27} +(6900.62 + 3326.80i) q^{28} +7256.22 q^{29} +(304.051 - 1969.25i) q^{30} +7244.36i q^{31} +(-4315.09 - 3864.51i) q^{32} +(-922.415 - 922.415i) q^{33} +(2766.91 + 1964.11i) q^{34} +(-12697.9 - 4225.95i) q^{35} +(2146.00 + 6141.33i) q^{36} +(266.347 + 266.347i) q^{37} +(-12727.1 + 2159.62i) q^{38} -2220.08 q^{39} +(8337.97 + 5733.95i) q^{40} +16812.6 q^{41} +(-8412.88 + 1427.55i) q^{42} +(-4601.16 - 4601.16i) q^{43} +(6254.01 - 2185.37i) q^{44} +(-5087.23 - 10162.4i) q^{45} +(-2291.08 - 1626.35i) q^{46} +(-5614.39 - 5614.39i) q^{47} +(6411.13 + 727.919i) q^{48} +40503.7i q^{49} +(-15724.9 - 8076.28i) q^{50} -3779.59 q^{51} +(4896.23 - 10156.0i) q^{52} +(937.132 - 937.132i) q^{53} +(-12971.9 - 9208.25i) q^{54} +(-10348.9 + 5180.57i) q^{55} +(12023.5 - 41634.0i) q^{56} +(10167.6 - 10167.6i) q^{57} +(-6867.03 - 40468.9i) q^{58} +16983.7i q^{59} +(-11270.5 + 167.892i) q^{60} -27237.2i q^{61} +(40402.7 - 6855.81i) q^{62} +(-34413.8 + 34413.8i) q^{63} +(-17469.2 + 27723.1i) q^{64} +(-6219.54 + 18688.2i) q^{65} +(-4271.49 + 6017.37i) q^{66} +(-7571.99 + 7571.99i) q^{67} +(8335.62 - 17290.2i) q^{68} +3129.62 q^{69} +(-11551.8 + 74817.3i) q^{70} -17125.0i q^{71} +(32220.1 - 17780.4i) q^{72} +(15977.8 + 15977.8i) q^{73} +(1233.39 - 1737.52i) q^{74} +(19490.4 - 2803.23i) q^{75} +(24089.0 + 68937.0i) q^{76} +(35045.2 + 35045.2i) q^{77} +(2101.00 + 12381.7i) q^{78} +72486.1 q^{79} +(24088.2 - 51928.4i) q^{80} -31681.3 q^{81} +(-15910.9 - 93766.2i) q^{82} +(-58657.5 - 58657.5i) q^{83} +(15923.3 + 45568.8i) q^{84} +(-10588.5 + 31815.9i) q^{85} +(-21306.9 + 30015.6i) q^{86} +(32330.4 + 32330.4i) q^{87} +(-18106.7 - 32811.3i) q^{88} -34335.8i q^{89} +(-51862.6 + 37989.5i) q^{90} +84347.1 q^{91} +(-6902.16 + 14316.8i) q^{92} +(-32277.6 + 32277.6i) q^{93} +(-25998.9 + 36625.4i) q^{94} +(-57104.6 - 114074. i) q^{95} +(-2007.57 - 36444.6i) q^{96} +(62650.0 - 62650.0i) q^{97} +(225895. - 38331.3i) q^{98} +42087.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.946365	−	5.57713i	−0.167295	−	0.985907i
$2$	−0.946365	−	5.57713i	−0.167295	−	0.985907i
$3$	4.45554	+	4.45554i	0.285823	+	0.285823i	0.835426	−	0.549603i	$-0.185221\pi$
$3$	4.45554	+	4.45554i	0.285823	+	0.285823i	−0.549603	+	0.835426i	$0.685221\pi$
$4$	−30.2088	+	10.5560i	−0.944025	+	0.329875i
$5$	49.9881	−	25.0237i	0.894215	−	0.447638i
$5$	49.9881	−	25.0237i	0.894215	−	0.447638i
$6$	20.6326	−	29.0657i	0.233978	−	0.329612i
$7$	−169.279	−	169.279i	−1.30574	−	1.30574i	−0.924457	−	0.381287i	$-0.875481\pi$
$7$	−169.279	−	169.279i	−1.30574	−	1.30574i	−0.381287	−	0.924457i	$-0.624519\pi$
$8$	87.4607	+	158.489i	0.483157	+	0.875534i
$9$		−	203.296i		−	0.836610i
$10$	−186.868	−	255.109i	−0.590927	−	0.806725i
$11$	−207.026			−0.515874			−0.257937	−	0.966162i	$-0.583043\pi$
$11$	−207.026			−0.515874			−0.257937	+	0.966162i	$0.583043\pi$
$12$	−181.629	−	87.5639i	−0.364110	−	0.175538i
$13$	−249.136	+	249.136i	−0.408864	+	0.408864i	−0.881342	−	0.472478i	$-0.843360\pi$
$13$	−249.136	+	249.136i	−0.408864	+	0.408864i	0.472478	+	0.881342i	$0.343360\pi$
$14$	−783.891	+	1104.29i	−1.06890	+	1.50579i
$15$	334.219	+	111.230i	0.383533	+	0.127642i
$16$	801.142	−	637.768i	0.782365	−	0.622820i
$17$	−424.145	+	424.145i	−0.355952	+	0.355952i	−0.862318	−	0.506366i	$-0.830988\pi$
$17$	−424.145	+	424.145i	−0.355952	+	0.355952i	0.506366	+	0.862318i	$0.330988\pi$
$18$	−1133.81	+	192.392i	−0.824820	+	0.139961i
$19$		−	2282.02i		−	1.45022i	−0.688631	−	0.725112i	$-0.741788\pi$
$19$		−	2282.02i		−	1.45022i	0.688631	−	0.725112i	$-0.258212\pi$
$20$	−1245.93	+	1283.61i	−0.696496	+	0.717561i
$21$		−	1508.46i		−	0.746424i
$22$	195.922	+	1154.61i	0.0863033	+	0.508604i
$23$	351.205	−	351.205i	0.138433	−	0.138433i	−0.634494	−	0.772928i	$-0.718792\pi$
$23$	351.205	−	351.205i	0.138433	−	0.138433i	0.772928	+	0.634494i	$0.218792\pi$
$24$	−316.468	+	1095.84i	−0.112150	+	0.388346i
$25$	1872.62	−	2501.78i	0.599240	−	0.800569i
$26$	1625.24	+	1153.69i	0.471503	+	0.334701i
$27$	1988.49	−	1988.49i	0.524946	−	0.524946i
$28$	6900.62	+	3326.80i	1.66339	+	0.801922i
$29$	7256.22			1.60219			0.801097	−	0.598534i	$-0.204250\pi$
$29$	7256.22			1.60219			0.801097	+	0.598534i	$0.204250\pi$
$30$	304.051	−	1969.25i	0.0616799	−	0.399482i
$31$			7244.36i			1.35393i	0.736016	+	0.676964i	$0.236705\pi$
$31$			7244.36i			1.35393i	−0.736016	+	0.676964i	$0.763295\pi$
$32$	−4315.09	−	3864.51i	−0.744929	−	0.667144i
$33$	−922.415	−	922.415i	−0.147449	−	0.147449i
$34$	2766.91	+	1964.11i	0.410485	+	0.291387i
$35$	−12697.9	−	4225.95i	−1.75212	−	0.583114i
$36$	2146.00	+	6141.33i	0.275977	+	0.789780i
$37$	266.347	+	266.347i	0.0319848	+	0.0319848i	0.722918	−	0.690933i	$-0.242800\pi$
$37$	266.347	+	266.347i	0.0319848	+	0.0319848i	−0.690933	+	0.722918i	$0.742800\pi$
$38$	−12727.1	+	2159.62i	−1.42979	+	0.242616i
$39$	−2220.08			−0.233726
$40$	8337.97	+	5733.95i	0.823968	+	0.566636i
$41$	16812.6			1.56198			0.780990	−	0.624543i	$-0.214715\pi$
$41$	16812.6			1.56198			0.780990	+	0.624543i	$0.214715\pi$
$42$	−8412.88	+	1427.55i	−0.735905	+	0.124873i
$43$	−4601.16	−	4601.16i	−0.379486	−	0.379486i	0.491431	−	0.870917i	$-0.336474\pi$
$43$	−4601.16	−	4601.16i	−0.379486	−	0.379486i	−0.870917	+	0.491431i	$0.836474\pi$
$44$	6254.01	−	2185.37i	0.486998	−	0.170174i
$45$	−5087.23	−	10162.4i	−0.374499	−	0.748109i
$46$	−2291.08	−	1626.35i	−0.159642	−	0.113323i
$47$	−5614.39	−	5614.39i	−0.370730	−	0.370730i	0.497013	−	0.867743i	$-0.334430\pi$
$47$	−5614.39	−	5614.39i	−0.370730	−	0.370730i	−0.867743	+	0.497013i	$0.834430\pi$
$48$	6411.13	+	727.919i	0.401635	+	0.0456016i
$49$			40503.7i			2.40993i
$50$	−15724.9	−	8076.28i	−0.889537	−	0.456863i
$51$	−3779.59			−0.203479
$52$	4896.23	−	10156.0i	0.251104	−	0.520852i
$53$	937.132	−	937.132i	0.0458259	−	0.0458259i	−0.683822	−	0.729648i	$-0.739684\pi$
$53$	937.132	−	937.132i	0.0458259	−	0.0458259i	0.729648	+	0.683822i	$0.239684\pi$
$54$	−12971.9	−	9208.25i	−0.605369	−	0.429727i
$55$	−10348.9	+	5180.57i	−0.461302	+	0.230925i
$56$	12023.5	−	41634.0i	0.512344	−	1.77410i
$57$	10167.6	−	10167.6i	0.414508	−	0.414508i
$58$	−6867.03	−	40468.9i	−0.268039	−	1.57961i
$59$			16983.7i			0.635189i	0.948227	+	0.317595i	$0.102875\pi$
$59$			16983.7i			0.635189i	−0.948227	+	0.317595i	$0.897125\pi$
$60$	−11270.5	+	167.892i	−0.404170	+	0.00602076i
$61$		−	27237.2i		−	0.937212i	−0.883407	−	0.468606i	$-0.844756\pi$
$61$		−	27237.2i		−	0.937212i	0.883407	−	0.468606i	$-0.155244\pi$
$62$	40402.7	−	6855.81i	1.33485	−	0.226506i
$63$	−34413.8	+	34413.8i	−1.09240	+	1.09240i
$64$	−17469.2	+	27723.1i	−0.533119	+	0.846040i
$65$	−6219.54	+	18688.2i	−0.182589	+	0.548635i
$66$	−4271.49	+	6017.37i	−0.120703	+	0.170038i
$67$	−7571.99	+	7571.99i	−0.206074	+	0.206074i	−0.802596	−	0.596523i	$-0.796549\pi$
$67$	−7571.99	+	7571.99i	−0.206074	+	0.206074i	0.596523	+	0.802596i	$0.296549\pi$
$68$	8335.62	−	17290.2i	0.218608	−	0.453447i
$69$	3129.62			0.0791350
$70$	−11551.8	+	74817.3i	−0.281776	+	1.82498i
$71$		−	17125.0i		−	0.403167i	−0.979471	−	0.201583i	$-0.935391\pi$
$71$		−	17125.0i		−	0.403167i	0.979471	−	0.201583i	$-0.0646087\pi$
$72$	32220.1	−	17780.4i	0.732480	−	0.404214i
$73$	15977.8	+	15977.8i	0.350922	+	0.350922i	0.860453	−	0.509530i	$-0.170181\pi$
$73$	15977.8	+	15977.8i	0.350922	+	0.350922i	−0.509530	+	0.860453i	$0.670181\pi$
$74$	1233.39	−	1737.52i	0.0261832	−	0.0368850i
$75$	19490.4	−	2803.23i	0.400098	−	0.0575447i
$76$	24089.0	+	68937.0i	0.478393	+	1.36905i
$77$	35045.2	+	35045.2i	0.673599	+	0.673599i
$78$	2101.00	+	12381.7i	0.0391012	+	0.230432i
$79$	72486.1			1.30673			0.653367	−	0.757041i	$-0.273356\pi$
$79$	72486.1			1.30673			0.653367	+	0.757041i	$0.273356\pi$
$80$	24088.2	−	51928.4i	0.420804	−	0.907152i
$81$	−31681.3			−0.536526
$82$	−15910.9	−	93766.2i	−0.261312	−	1.53997i
$83$	−58657.5	−	58657.5i	−0.934606	−	0.934606i	0.0633833	−	0.997989i	$-0.479811\pi$
$83$	−58657.5	−	58657.5i	−0.934606	−	0.934606i	−0.997989	+	0.0633833i	$0.979811\pi$
$84$	15923.3	+	45568.8i	0.246227	+	0.704643i
$85$	−10588.5	+	31815.9i	−0.158960	+	0.477636i
$86$	−21306.9	+	30015.6i	−0.310652	+	0.437624i
$87$	32330.4	+	32330.4i	0.457944	+	0.457944i
$88$	−18106.7	−	32811.3i	−0.249248	−	0.451665i
$89$		−	34335.8i		−	0.459486i	−0.973251	−	0.229743i	$-0.926211\pi$
$89$		−	34335.8i		−	0.459486i	0.973251	−	0.229743i	$-0.0737886\pi$
$90$	−51862.6	+	37989.5i	−0.674914	+	0.494376i
$91$	84347.1			1.06774
$92$	−6902.16	+	14316.8i	−0.0850188	+	0.176350i
$93$	−32277.6	+	32277.6i	−0.386984	+	0.386984i
$94$	−25998.9	+	36625.4i	−0.303484	+	0.427527i
$95$	−57104.6	−	114074.i	−0.649176	−	1.29681i
$96$	−2007.57	−	36444.6i	−0.0222327	−	0.403603i
$97$	62650.0	−	62650.0i	0.676070	−	0.676070i	−0.283039	−	0.959109i	$-0.591342\pi$
$97$	62650.0	−	62650.0i	0.676070	−	0.676070i	0.959109	+	0.283039i	$0.0913425\pi$
$98$	225895.	−	38331.3i	2.37597	−	0.403170i
$99$			42087.6i			0.431585i
$100$	−30160.9	+	95343.2i	−0.301609	+	0.953432i
$101$		−	79446.8i		−	0.774948i	−0.921881	−	0.387474i	$-0.873348\pi$
$101$		−	79446.8i		−	0.774948i	0.921881	−	0.387474i	$-0.126652\pi$
$102$	3576.87	+	21079.3i	0.0340410	+	0.200611i
$103$	−15635.6	+	15635.6i	−0.145219	+	0.145219i	−0.775978	−	0.630760i	$-0.782743\pi$
$103$	−15635.6	+	15635.6i	−0.145219	+	0.145219i	0.630760	+	0.775978i	$0.282743\pi$
$104$	−61274.9	−	17695.6i	−0.555520	−	0.160429i
$105$	−37747.3	−	75405.1i	−0.334128	−	0.667463i
$106$	−6113.38	−	4339.64i	−0.0528465	−	0.0375136i
$107$	−18399.8	+	18399.8i	−0.155365	+	0.155365i	−0.780509	−	0.625144i	$-0.785040\pi$
$107$	−18399.8	+	18399.8i	−0.155365	+	0.155365i	0.625144	+	0.780509i	$0.285040\pi$
$108$	−39079.4	+	81060.5i	−0.322395	+	0.668729i
$109$	−30952.5			−0.249534			−0.124767	−	0.992186i	$-0.539818\pi$
$109$	−30952.5			−0.249534			−0.124767	+	0.992186i	$0.539818\pi$
$110$	38686.5	+	52814.2i	0.304844	+	0.416168i
$111$			2373.45i			0.0182840i
$112$	−243577.	−	27655.7i	−1.83481	−	0.208324i
$113$	−125022.	−	125022.i	−0.921068	−	0.921068i	0.0760370	−	0.997105i	$-0.475773\pi$
$113$	−125022.	−	125022.i	−0.921068	−	0.921068i	−0.997105	+	0.0760370i	$0.975773\pi$
$114$	−66328.5	−	47083.9i	−0.478011	−	0.339321i
$115$	8767.62	−	26344.5i	0.0618211	−	0.185757i
$116$	−219201.	+	76596.6i	−1.51251	+	0.528524i
$117$	50648.5	+	50648.5i	0.342060	+	0.342060i
$118$	94720.5	−	16072.8i	0.626238	−	0.106264i
$119$	143598.			0.929565
$120$	11602.3	+	62698.1i	0.0735517	+	0.397467i
$121$	−118191.			−0.733874
$122$	−151906.	+	25776.3i	−0.924004	+	0.156791i
$123$	74909.4	+	74909.4i	0.446451	+	0.446451i
$124$	−76471.5	−	218843.i	−0.446627	−	1.27814i
$125$	31005.1	−	171919.i	0.177484	−	0.984124i
$126$	224498.	+	159362.i	1.25976	+	0.894250i
$127$	−5560.02	−	5560.02i	−0.0305892	−	0.0305892i	0.691647	−	0.722236i	$-0.256886\pi$
$127$	−5560.02	−	5560.02i	−0.0305892	−	0.0305892i	−0.722236	+	0.691647i	$0.756886\pi$
$128$	171147.	+	71192.1i	0.923305	+	0.384067i
$129$		−	41001.3i		−	0.216932i
$130$	110112.	+	17001.3i	0.571450	+	0.0882317i
$131$	207693.			1.05741			0.528705	−	0.848805i	$-0.322678\pi$
$131$	207693.			1.05741			0.528705	+	0.848805i	$0.322678\pi$
$132$	37602.0	+	18128.0i	0.187835	+	0.0905556i
$133$	−386298.	+	386298.i	−1.89362	+	1.89362i
$134$	49395.8	+	35064.1i	0.237645	+	0.168694i
$135$	49641.5	−	149161.i	0.234429	−	0.704400i
$136$	−104318.	−	30126.1i	−0.483629	−	0.139667i
$137$	−254454.	+	254454.i	−1.15827	+	1.15827i	−0.173418	+	0.984848i	$0.555481\pi$
$137$	−254454.	+	254454.i	−1.15827	+	1.15827i	−0.984848	+	0.173418i	$0.944519\pi$
$138$	−2961.76	−	17454.3i	−0.0132389	−	0.0780198i
$139$		−	145526.i		−	0.638856i	−0.947610	−	0.319428i	$-0.896509\pi$
$139$		−	145526.i		−	0.638856i	0.947610	−	0.319428i	$-0.103491\pi$
$140$	428198.	−	6378.70i	1.84640	−	0.0275050i
$141$		−	50030.3i		−	0.211927i
$142$	−95508.4	+	16206.5i	−0.397485	+	0.0674479i
$143$	51577.8	−	51577.8i	0.210922	−	0.210922i
$144$	−129656.	−	162869.i	−0.521058	−	0.654534i
$145$	362725.	−	181578.i	1.43271	−	0.717203i
$146$	73989.7	−	104231.i	0.287269	−	0.404685i
$147$	−180466.	+	180466.i	−0.688815	+	0.688815i
$148$	−10857.6	−	5234.47i	−0.0407455	−	0.0196435i
$149$	209820.			0.774252			0.387126	−	0.922027i	$-0.373468\pi$
$149$	209820.			0.774252			0.387126	+	0.922027i	$0.373468\pi$
$150$	−34078.9	−	106047.i	−0.123668	−	0.384833i
$151$			91400.1i			0.326215i	0.986608	+	0.163108i	$0.0521518\pi$
$151$			91400.1i			0.326215i	−0.986608	+	0.163108i	$0.947848\pi$
$152$	361674.	−	199587.i	1.26972	−	0.700686i
$153$	86227.0	+	86227.0i	0.297793	+	0.297793i
$154$	162286.	−	228617.i	0.551416	−	0.776796i
$155$	181281.	+	362132.i	0.606070	+	1.21070i
$156$	67065.8	−	23435.1i	0.220643	−	0.0771003i
$157$	239586.	+	239586.i	0.775734	+	0.775734i	0.979102	−	0.203368i	$-0.0651888\pi$
$157$	239586.	+	239586.i	0.775734	+	0.775734i	−0.203368	+	0.979102i	$0.565189\pi$
$158$	−68598.3	−	404265.i	−0.218610	−	1.28832i
$159$	8350.87			0.0261962
$160$	−312408.	−	85200.0i	−0.964765	−	0.263111i
$161$	−118903.			−0.361517
$162$	29982.1	+	176691.i	0.0897583	+	0.528965i
$163$	235878.	+	235878.i	0.695375	+	0.695375i	0.963409	−	0.268034i	$-0.0863741\pi$
$163$	235878.	+	235878.i	0.695375	+	0.695375i	−0.268034	+	0.963409i	$0.586374\pi$
$164$	−507889.	+	177474.i	−1.47455	+	0.515258i
$165$	−69192.0	−	23027.5i	−0.197855	−	0.0658472i
$166$	−271629.	+	382652.i	−0.765079	+	1.07779i
$167$	−28120.6	−	28120.6i	−0.0780249	−	0.0780249i	0.667017	−	0.745042i	$-0.267571\pi$
$167$	−28120.6	−	28120.6i	−0.0780249	−	0.0780249i	−0.745042	+	0.667017i	$0.767571\pi$
$168$	239074.	−	131931.i	0.653519	−	0.360640i
$169$			247155.i			0.665660i
$170$	187462.	+	28944.1i	0.497497	+	0.0768135i
$171$	−463926.			−1.21327
$172$	187565.	+	90425.6i	0.483427	+	0.233061i
$173$	65641.2	−	65641.2i	0.166748	−	0.166748i	−0.618800	−	0.785548i	$-0.712381\pi$
$173$	65641.2	−	65641.2i	0.166748	−	0.166748i	0.785548	+	0.618800i	$0.212381\pi$
$174$	149714.	−	210907.i	0.374879	−	0.528103i
$175$	−740495.	+	106503.i	−1.82779	+	0.262885i
$176$	−165857.	+	132035.i	−0.403602	+	0.321297i
$177$	−75671.8	+	75671.8i	−0.181552	+	0.181552i
$178$	−191495.	+	32494.2i	−0.453010	+	0.0768698i
$179$		−	377529.i		−	0.880679i	−0.897831	−	0.440340i	$-0.854858\pi$
$179$		−	377529.i		−	0.880679i	0.897831	−	0.440340i	$-0.145142\pi$
$180$	260953.	+	253293.i	0.600318	+	0.582696i
$181$		−	523723.i		−	1.18824i	−0.804376	−	0.594121i	$-0.797500\pi$
$181$		−	523723.i		−	1.18824i	0.804376	−	0.594121i	$-0.202500\pi$
$182$	−79823.1	−	470415.i	−0.178628	−	1.05270i
$183$	121357.	−	121357.i	0.267877	−	0.267877i
$184$	86378.6	+	24945.3i	0.188088	+	0.0543181i
$185$	19979.2	+	6649.20i	0.0429190	+	0.0142837i
$186$	210563.	+	149470.i	0.446271	+	0.316790i
$187$	87809.1	−	87809.1i	0.183626	−	0.183626i
$188$	228869.	+	110338.i	0.472273	+	0.227684i
$189$	−673220.			−1.37089
$190$	−582163.	+	426435.i	−1.16993	+	0.856977i
$191$			601520.i			1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$191$			601520.i			1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$192$	−201356.	+	45686.3i	−0.394196	+	0.0894403i
$193$	423362.	+	423362.i	0.818123	+	0.818123i	0.985836	−	0.167713i	$-0.0536381\pi$
$193$	423362.	+	423362.i	0.818123	+	0.818123i	−0.167713	+	0.985836i	$0.553638\pi$
$194$	−408697.	−	290117.i	−0.779645	−	0.553439i
$195$	−110977.	+	55554.6i	−0.209001	+	0.104625i
$196$	−427558.	−	1.22357e6i	−0.794977	−	2.27504i
$197$	−164947.	−	164947.i	−0.302815	−	0.302815i	0.539299	−	0.842114i	$-0.318689\pi$
$197$	−164947.	−	164947.i	−0.302815	−	0.302815i	−0.842114	+	0.539299i	$0.818689\pi$
$198$	234728.	−	39830.3i	0.425503	−	0.0722022i
$199$	609467.			1.09098			0.545491	−	0.838117i	$-0.316343\pi$
$199$	609467.			1.09098			0.545491	+	0.838117i	$0.316343\pi$
$200$	560285.	+	77982.1i	0.990453	+	0.137854i
$201$	−67474.7			−0.117801
$202$	−443085.	+	75185.6i	−0.764027	+	0.129645i
$203$	−1.22832e6	−	1.22832e6i	−2.09205	−	2.09205i
$204$	114177.	−	39897.4i	0.192089	−	0.0671226i
$205$	840431.	−	420715.i	1.39675	−	0.699202i
$206$	101999.	+	72405.0i	0.167467	+	0.118878i
$207$	−71398.7	−	71398.7i	−0.115815	−	0.115815i
$208$	−40702.3	+	358485.i	−0.0652320	+	0.574530i
$209$			472437.i			0.748133i
$210$	−384821.	+	281882.i	−0.602159	+	0.441082i
$211$	582093.			0.900090			0.450045	−	0.893006i	$-0.351408\pi$
$211$	582093.			0.900090			0.450045	+	0.893006i	$0.351408\pi$
$212$	−18417.3	+	38202.0i	−0.0281440	+	0.0583776i
$213$	76301.2	−	76301.2i	0.115234	−	0.115234i
$214$	120031.	+	85205.3i	0.179168	+	0.127184i
$215$	−345141.	−	114865.i	−0.509215	−	0.169470i
$216$	489068.	+	141238.i	0.713239	+	0.205977i
$217$	1.22632e6	−	1.22632e6i	1.76788	−	1.76788i
$218$	29292.3	+	172626.i	0.0417458	+	0.246017i
$219$			142380.i			0.200604i
$220$	257940.	−	265741.i	0.359304	−	0.370171i
$221$		−	211340.i		−	0.291072i
$222$	13237.0	−	2246.15i	0.0180264	−	0.00305883i
$223$	−27105.9	+	27105.9i	−0.0365007	+	0.0365007i	−0.725122	−	0.688621i	$-0.758216\pi$
$223$	−27105.9	+	27105.9i	−0.0365007	+	0.0365007i	0.688621	+	0.725122i	$0.258216\pi$
$224$	76273.2	+	1.38463e6i	0.101567	+	1.84381i
$225$	−508602.	−	380698.i	−0.669764	−	0.501330i
$226$	−578950.	+	815583.i	−0.753997	+	1.06218i
$227$	−23392.5	+	23392.5i	−0.0301309	+	0.0301309i	−0.722012	−	0.691881i	$-0.756782\pi$
$227$	−23392.5	+	23392.5i	−0.0301309	+	0.0301309i	0.691881	+	0.722012i	$0.256782\pi$
$228$	−199822.	+	414481.i	−0.254570	+	0.528041i
$229$	637450.			0.803262			0.401631	−	0.915801i	$-0.368443\pi$
$229$	637450.			0.803262			0.401631	+	0.915801i	$0.368443\pi$
$230$	−155224.	−	23966.6i	−0.193482	−	0.0298736i
$231$			312291.i			0.385061i
$232$	634634.	+	1.15003e6i	0.774111	+	1.40278i
$233$	401694.	+	401694.i	0.484737	+	0.484737i	0.906641	−	0.421904i	$-0.138638\pi$
$233$	401694.	+	401694.i	0.484737	+	0.484737i	−0.421904	+	0.906641i	$0.638638\pi$
$234$	234541.	−	330405.i	0.280014	−	0.394464i
$235$	−421146.	−	140160.i	−0.497465	−	0.165559i
$236$	−179280.	−	513058.i	−0.209533	−	0.599634i
$237$	322965.	+	322965.i	0.373495	+	0.373495i
$238$	−135896.	−	800862.i	−0.155512	−	0.916464i
$239$	−797896.			−0.903548			−0.451774	−	0.892132i	$-0.649209\pi$
$239$	−797896.			−0.903548			−0.451774	+	0.892132i	$0.649209\pi$
$240$	338695.	−	124043.i	0.379561	−	0.139009i
$241$	−313970.			−0.348214			−0.174107	−	0.984727i	$-0.555704\pi$
$241$	−313970.			−0.348214			−0.174107	+	0.984727i	$0.555704\pi$
$242$	111852.	+	659168.i	0.122774	+	0.723531i
$243$	−624361.	−	624361.i	−0.678298	−	0.678298i
$244$	287516.	+	822803.i	0.309163	+	0.884752i
$245$	1.01356e6	+	2.02471e6i	1.07878	+	2.15500i
$246$	346888.	−	488671.i	0.365470	−	0.514848i
$247$	568534.	+	568534.i	0.592944	+	0.592944i
$248$	−1.14815e6	+	633597.i	−1.18541	+	0.654160i
$249$		−	522703.i		−	0.534264i
$250$	−988159.	−	10221.2i	−0.999947	−	0.0103432i
$251$	972796.			0.974624			0.487312	−	0.873228i	$-0.337977\pi$
$251$	972796.			0.974624			0.487312	+	0.873228i	$0.337977\pi$
$252$	676327.	−	1.40287e6i	0.670896	−	1.39161i
$253$	−72708.6	+	72708.6i	−0.0714142	+	0.0714142i
$254$	−25747.2	+	36270.8i	−0.0250406	+	0.0352755i
$255$	−188935.	+	94579.5i	−0.181954	+	0.0910849i
$256$	235080.	−	1.02189e6i	0.224190	−	0.974546i
$257$	−736633.	+	736633.i	−0.695694	+	0.695694i	−0.963479	−	0.267785i	$-0.913708\pi$
$257$	−736633.	+	736633.i	−0.695694	+	0.695694i	0.267785	+	0.963479i	$0.413708\pi$
$258$	−228670.	+	38802.2i	−0.213875	+	0.0362917i
$259$		−	90174.1i		−	0.0835280i
$260$	−9387.85	−	630201.i	−0.00861257	−	0.578157i
$261$		−	1.47516e6i		−	1.34041i
$262$	−196553.	−	1.15833e6i	−0.176900	−	1.04251i
$263$	1.10841e6	−	1.10841e6i	0.988125	−	0.988125i	−0.0118057	−	0.999930i	$-0.503758\pi$
$263$	1.10841e6	−	1.10841e6i	0.988125	−	0.988125i	0.999930	+	0.0118057i	$0.00375796\pi$
$264$	65517.1	−	226867.i	0.0578555	−	0.200337i
$265$	23394.9	−	70296.0i	0.0204648	−	0.0614916i
$266$	2.52001e6	+	1.78885e6i	2.18373	+	1.55014i
$267$	152985.	−	152985.i	0.131332	−	0.131332i
$268$	148811.	−	308670.i	0.126560	−	0.262517i
$269$	−2.08719e6			−1.75866			−0.879328	−	0.476216i	$-0.842008\pi$
$269$	−2.08719e6			−1.75866			−0.879328	+	0.476216i	$0.842008\pi$
$270$	−878867.	−	135697.i	−0.733692	−	0.113282i
$271$			869347.i			0.719068i	0.933132	+	0.359534i	$0.117064\pi$
$271$			869347.i			0.719068i	−0.933132	+	0.359534i	$0.882936\pi$
$272$	−69294.1	+	610306.i	−0.0567903	+	0.500179i
$273$	375812.	+	375812.i	0.305186	+	0.305186i
$274$	1.65993e6	+	1.17832e6i	1.33571	+	0.948170i
$275$	−387682.	+	517934.i	−0.309132	+	0.412993i
$276$	−94542.0	+	33036.3i	−0.0747054	+	0.0261047i
$277$	−1.39022e6	−	1.39022e6i	−1.08864	−	1.08864i	−0.995669	−	0.0929676i	$-0.970365\pi$
$277$	−1.39022e6	−	1.39022e6i	−1.08864	−	1.08864i	−0.0929676	−	0.995669i	$-0.529635\pi$
$278$	−811617.	+	137721.i	−0.629853	+	0.106878i
$279$	1.47275e6			1.13271
$280$	−440807.	−	2.38208e6i	−0.336011	−	1.81577i
$281$	−620023.			−0.468427			−0.234214	−	0.972185i	$-0.575252\pi$
$281$	−620023.			−0.468427			−0.234214	+	0.972185i	$0.575252\pi$
$282$	−279026.	+	47346.9i	−0.208940	+	0.0354543i
$283$	1.76320e6	+	1.76320e6i	1.30869	+	1.30869i	0.922362	+	0.386327i	$0.126256\pi$
$283$	1.76320e6	+	1.76320e6i	1.30869	+	1.30869i	0.386327	+	0.922362i	$0.373744\pi$
$284$	180772.	+	517326.i	0.132995	+	0.380599i
$285$	253829.	−	762693.i	0.185109	−	0.556209i
$286$	−336467.	−	238845.i	−0.243236	−	0.172663i
$287$	−2.84602e6	−	2.84602e6i	−2.03955	−	2.03955i
$288$	−785641.	+	877241.i	−0.558139	+	0.623215i
$289$			1.06006e6i			0.746596i
$290$	−1.35595e6	−	1.85112e6i	−0.946781	−	1.29253i
$291$	558280.			0.386473
$292$	−651334.	−	314009.i	−0.447040	−	0.215519i
$293$	−729494.	+	729494.i	−0.496424	+	0.496424i	−0.910323	−	0.413899i	$-0.864167\pi$
$293$	−729494.	+	729494.i	−0.496424	+	0.496424i	0.413899	+	0.910323i	$0.364167\pi$
$294$	1.17727e6	+	835697.i	0.794343	+	0.563872i
$295$	424997.	+	848985.i	0.284335	+	0.567996i
$296$	−18918.1	+	65508.0i	−0.0125501	+	0.0434575i
$297$	−411670.	+	411670.i	−0.270806	+	0.270806i
$298$	−198567.	−	1.17020e6i	−0.129529	−	0.763340i
$299$			174996.i			0.113201i
$300$	−559189.	+	290422.i	−0.358720	+	0.186306i
$301$			1.55776e6i			0.991023i
$302$	509750.	−	86497.8i	0.321618	−	0.0545742i
$303$	353979.	−	353979.i	0.221498	−	0.221498i
$304$	−1.45540e6	−	1.82822e6i	−0.903229	−	1.13460i
$305$	−681577.	−	1.36154e6i	−0.419532	−	0.838069i
$306$	399297.	−	562502.i	0.243777	−	0.343416i
$307$	−907649.	+	907649.i	−0.549632	+	0.549632i	−0.926334	−	0.376702i	$-0.877058\pi$
$307$	−907649.	+	907649.i	−0.549632	+	0.549632i	0.376702	+	0.926334i	$0.377058\pi$
$308$	−1.42861e6	−	688735.i	−0.858098	−	0.413691i
$309$	−139331.			−0.0830138
$310$	1.84810e6	−	1.35374e6i	1.09225	−	0.800074i
$311$			1.31610e6i			0.771594i	0.922584	+	0.385797i	$0.126073\pi$
$311$			1.31610e6i			0.771594i	−0.922584	+	0.385797i	$0.873927\pi$
$312$	−194170.	−	351857.i	−0.112926	−	0.204635i
$313$	−896253.	−	896253.i	−0.517094	−	0.517094i	0.399597	−	0.916691i	$-0.369150\pi$
$313$	−896253.	−	896253.i	−0.517094	−	0.517094i	−0.916691	+	0.399597i	$0.869150\pi$
$314$	1.10947e6	−	1.56294e6i	0.635025	−	0.894579i
$315$	−859119.	+	2.58144e6i	−0.487839	+	1.46584i
$316$	−2.18972e6	+	765164.i	−1.23359	+	0.431059i
$317$	1.81983e6	+	1.81983e6i	1.01715	+	1.01715i	0.999850	+	0.0172954i	$0.00550557\pi$
$317$	1.81983e6	+	1.81983e6i	1.01715	+	1.01715i	0.0172954	+	0.999850i	$0.494494\pi$
$318$	−7902.97	−	46573.9i	−0.00438250	−	0.0258270i
$319$	−1.50223e6			−0.826530
$320$	−179520.	+	1.82297e6i	−0.0980027	+	0.995186i
$321$	−163963.			−0.0888141
$322$	112526.	+	663139.i	0.0604801	+	0.356422i
$323$	967906.	+	967906.i	0.516210	+	0.516210i
$324$	957055.	−	334428.i	0.506494	−	0.176987i
$325$	156745.	+	1.08982e6i	0.0823164	+	0.572332i
$326$	1.09230e6	−	1.53875e6i	0.569242	−	0.801908i
$327$	−137910.	−	137910.i	−0.0713225	−	0.0713225i
$328$	1.47044e6	+	2.66461e6i	0.754682	+	1.36757i
$329$			1.90080e6i			0.968157i
$330$	−62946.5	+	407685.i	−0.0318190	+	0.206082i
$331$	979058.			0.491178			0.245589	−	0.969374i	$-0.421019\pi$
$331$	979058.			0.491178			0.245589	+	0.969374i	$0.421019\pi$
$332$	2.39116e6	+	1.15278e6i	1.19059	+	0.573988i
$333$	54147.4	−	54147.4i	0.0267588	−	0.0267588i
$334$	−130220.	+	183445.i	−0.0638721	+	0.0899785i
$335$	−189030.	+	567989.i	−0.0920277	+	0.276521i
$336$	−962048.	−	1.20849e6i	−0.464888	−	0.583976i
$337$	2.59947e6	−	2.59947e6i	1.24684	−	1.24684i	0.289731	−	0.957108i	$-0.406434\pi$
$337$	2.59947e6	−	2.59947e6i	1.24684	−	1.24684i	0.957108	−	0.289731i	$-0.0935659\pi$
$338$	1.37842e6	−	233899.i	0.656279	−	0.111362i
$339$		−	1.11409e6i		−	0.526525i
$340$	−15982.4	−	1.07289e6i	−0.00749800	−	0.503337i
$341$		−	1.49977e6i		−	0.698457i
$342$	439043.	+	2.58737e6i	0.202975	+	1.19617i
$343$	4.01136e6	−	4.01136e6i	1.84101	−	1.84101i
$344$	326810.	−	1.13165e6i	0.148902	−	0.515604i
$345$	156444.	−	78314.8i	0.0707637	−	0.0354239i
$346$	−428210.	−	303969.i	−0.192294	−	0.136502i
$347$	1.85742e6	−	1.85742e6i	0.828107	−	0.828107i	−0.159148	−	0.987255i	$-0.550875\pi$
$347$	1.85742e6	−	1.85742e6i	0.828107	−	0.828107i	0.987255	+	0.159148i	$0.0508746\pi$
$348$	−1.31794e6	−	635382.i	−0.583375	−	0.281246i
$349$	−3.47861e6			−1.52877			−0.764385	−	0.644760i	$-0.776957\pi$
$349$	−3.47861e6			−1.52877			−0.764385	+	0.644760i	$0.776957\pi$
$350$	1.29476e6	+	4.02905e6i	0.564961	+	1.75805i
$351$			990812.i			0.429263i
$352$	893336.	+	800055.i	0.384289	+	0.344162i
$353$	−846494.	−	846494.i	−0.361566	−	0.361566i	0.502823	−	0.864389i	$-0.332295\pi$
$353$	−846494.	−	846494.i	−0.361566	−	0.361566i	−0.864389	+	0.502823i	$0.832295\pi$
$354$	493645.	+	350419.i	0.209366	+	0.148621i
$355$	−428532.	−	856047.i	−0.180473	−	0.360518i
$356$	362449.	+	1.03724e6i	0.151573	+	0.433766i
$357$	639805.	+	639805.i	0.265691	+	0.265691i
$358$	−2.10553e6	+	357280.i	−0.868268	+	0.147333i
$359$	2.26831e6			0.928892			0.464446	−	0.885601i	$-0.346253\pi$
$359$	2.26831e6			0.928892			0.464446	+	0.885601i	$0.346253\pi$
$360$	1.16569e6	−	1.69508e6i	0.474053	−	0.689340i
$361$	−2.73151e6			−1.10315
$362$	−2.92087e6	+	495633.i	−1.17150	+	0.198787i
$363$	−526606.	−	526606.i	−0.209758	−	0.209758i
$364$	−2.54802e6	+	890368.i	−1.00798	+	0.352222i
$365$	1.19853e6	+	398877.i	0.470886	+	0.156714i
$366$	−791669.	−	561974.i	−0.308917	−	0.219287i
$367$	936339.	+	936339.i	0.362884	+	0.362884i	0.864874	−	0.501990i	$-0.167398\pi$
$367$	936339.	+	936339.i	0.362884	+	0.362884i	−0.501990	+	0.864874i	$0.667398\pi$
$368$	57377.6	−	505352.i	0.0220863	−	0.194525i
$369$		−	3.41794e6i		−	1.30677i
$370$	18175.8	−	117719.i	0.00690224	−	0.0447037i
$371$	−317273.			−0.119674
$372$	634344.	−	1.31579e6i	0.237666	−	0.492979i
$373$	529380.	−	529380.i	0.197013	−	0.197013i	−0.601705	−	0.798718i	$-0.705512\pi$
$373$	529380.	−	529380.i	0.197013	−	0.197013i	0.798718	+	0.601705i	$0.205512\pi$
$374$	−572822.	−	406623.i	−0.211758	−	0.150319i
$375$	904139.	−	627850.i	0.332015	−	0.230557i
$376$	398778.	−	1.38085e6i	0.145466	−	0.503707i
$377$	−1.80779e6	+	1.80779e6i	−0.655080	+	0.655080i
$378$	637112.	+	3.75464e6i	0.229343	+	1.35157i
$379$		−	1.76855e6i		−	0.632439i	−0.948686	−	0.316220i	$-0.897586\pi$
$379$		−	1.76855e6i		−	0.632439i	0.948686	−	0.316220i	$-0.102414\pi$
$380$	2.92922e6	+	2.84323e6i	1.04062	+	1.01008i
$381$		−	49545.9i		−	0.0174862i
$382$	3.35476e6	−	569257.i	1.17626	−	0.199595i
$383$	−2.62315e6	+	2.62315e6i	−0.913746	+	0.913746i	−0.996565	−	0.0828182i	$-0.973608\pi$
$383$	−2.62315e6	+	2.62315e6i	−0.913746	+	0.913746i	0.0828182	+	0.996565i	$0.473608\pi$
$384$	445355.	+	1.07975e6i	0.154127	+	0.373677i
$385$	2.62880e6	+	874881.i	0.903871	+	0.300814i
$386$	1.96049e6	−	2.76180e6i	0.669725	−	0.943461i
$387$	−935398.	+	935398.i	−0.317482	+	0.317482i
$388$	−1.23125e6	+	2.55391e6i	−0.415208	+	0.861245i
$389$	2.62506e6			0.879561			0.439780	−	0.898105i	$-0.355056\pi$
$389$	2.62506e6			0.879561			0.439780	+	0.898105i	$0.355056\pi$
$390$	414861.	+	566361.i	0.138115	+	0.188552i
$391$			297923.i			0.0985514i
$392$	−6.41938e6	+	3.54249e6i	−2.10998	+	1.16438i
$393$	925386.	+	925386.i	0.302233	+	0.302233i
$394$	−763830.	+	1.07603e6i	−0.247888	+	0.349207i
$395$	3.62344e6	−	1.81387e6i	1.16850	−	0.584944i
$396$	−444277.	−	1.27142e6i	−0.142369	−	0.407427i
$397$	−1.09332e6	−	1.09332e6i	−0.348153	−	0.348153i	0.511268	−	0.859421i	$-0.329176\pi$
$397$	−1.09332e6	−	1.09332e6i	−0.348153	−	0.348153i	−0.859421	+	0.511268i	$0.829176\pi$
$398$	−576778.	−	3.39908e6i	−0.182516	−	1.07561i
$399$	−3.44233e6			−1.08248
$400$	−95317.1	−	3.19858e6i	−0.0297866	−	0.999556i
$401$	−3.31952e6			−1.03089			−0.515447	−	0.856922i	$-0.672374\pi$
$401$	−3.31952e6			−1.03089			−0.515447	+	0.856922i	$0.672374\pi$
$402$	63855.6	+	376315.i	0.0197076	+	0.116141i
$403$	−1.80483e6	−	1.80483e6i	−0.553573	−	0.553573i
$404$	838640.	+	2.39999e6i	0.255636	+	0.731570i
$405$	−1.58369e6	+	792786.i	−0.479770	+	0.240170i
$406$	−5.68808e6	+	8.01297e6i	−1.71258	+	2.41256i
$407$	−55140.9	−	55140.9i	−0.0165001	−	0.0165001i
$408$	−330566.	−	599022.i	−0.0983122	−	0.178153i
$409$		−	3.60316e6i		−	1.06506i	−0.846410	−	0.532531i	$-0.821241\pi$
$409$		−	3.60316e6i		−	1.06506i	0.846410	−	0.532531i	$-0.178759\pi$
$410$	−3.14173e6	−	4.28905e6i	−0.923017	−	1.26009i
$411$	−2.26747e6			−0.662119
$412$	307284.	−	637384.i	0.0891860	−	0.184994i
$413$	2.87499e6	−	2.87499e6i	0.829395	−	0.829395i
$414$	−330630.	+	465769.i	−0.0948074	+	0.133558i
$415$	−4.40001e6	−	1.46435e6i	−1.25410	−	0.417373i
$416$	2.03784e6	−	112255.i	0.577346	−	0.0318034i
$417$	648397.	−	648397.i	0.182600	−	0.182600i
$418$	2.63485e6	−	447098.i	0.737589	−	0.125159i
$419$		−	1.60065e6i		−	0.445410i	−0.974886	−	0.222705i	$-0.928511\pi$
$419$		−	1.60065e6i		−	0.445410i	0.974886	−	0.222705i	$-0.0714887\pi$
$420$	1.93628e6	+	1.87944e6i	0.535605	+	0.519881i
$421$		−	387801.i		−	0.106636i	−0.998578	−	0.0533180i	$-0.983020\pi$
$421$		−	387801.i		−	0.106636i	0.998578	−	0.0533180i	$-0.0169797\pi$
$422$	−550872.	−	3.24641e6i	−0.150581	−	0.887405i
$423$	−1.14138e6	+	1.14138e6i	−0.310156	+	0.310156i
$424$	230487.	+	66562.4i	0.0622632	+	0.0179810i
$425$	266853.	+	1.85538e6i	0.0716637	+	0.498265i
$426$	−497751.	−	353333.i	−0.132889	−	0.0943323i
$427$	−4.61069e6	+	4.61069e6i	−1.22376	+	1.22376i
$428$	361608.	−	750065.i	0.0954176	−	0.197920i
$429$	459614.			0.120573
$430$	−313988.	+	2.03360e6i	−0.0818921	+	0.530390i
$431$		−	2.12752e6i		−	0.551673i	−0.961205	−	0.275836i	$-0.911045\pi$
$431$		−	2.12752e6i		−	0.551673i	0.961205	−	0.275836i	$-0.0889548\pi$
$432$	324867.	−	2.86126e6i	0.0837523	−	0.737646i
$433$	4.65162e6	+	4.65162e6i	1.19230	+	1.19230i	0.976420	+	0.215877i	$0.0692612\pi$
$433$	4.65162e6	+	4.65162e6i	1.19230	+	1.19230i	0.215877	+	0.976420i	$0.430739\pi$
$434$	−7.99988e6	−	5.67879e6i	−2.03873	−	1.44721i
$435$	2.42516e6	+	807108.i	0.614494	+	0.204507i
$436$	935036.	−	326734.i	0.235566	−	0.0823149i
$437$	−801456.	−	801456.i	−0.200760	−	0.200760i
$438$	794072.	−	134743.i	0.197777	−	0.0335600i
$439$	4.59779e6			1.13864			0.569321	−	0.822115i	$-0.307206\pi$
$439$	4.59779e6			1.13864			0.569321	+	0.822115i	$0.307206\pi$
$440$	−1.72618e6	−	1.18708e6i	−0.425064	−	0.292313i
$441$	8.23426e6			2.01617
$442$	−1.17867e6	+	200005.i	−0.286970	+	0.0486950i
$443$	−1.69307e6	−	1.69307e6i	−0.409889	−	0.409889i	0.471811	−	0.881700i	$-0.343600\pi$
$443$	−1.69307e6	−	1.69307e6i	−0.409889	−	0.409889i	−0.881700	+	0.471811i	$0.843600\pi$
$444$	−25054.1	−	71698.9i	−0.00603145	−	0.0172606i
$445$	−859211.	−	1.71638e6i	−0.205684	−	0.410879i
$446$	176825.	+	125521.i	0.0420927	+	0.0298799i
$447$	934865.	+	934865.i	0.221299	+	0.221299i
$448$	7.65010e6	−	1.73575e6i	1.80083	−	0.408595i
$449$			3.17626e6i			0.743533i	0.928326	+	0.371766i	$0.121248\pi$
$449$			3.17626e6i			0.743533i	−0.928326	+	0.371766i	$0.878752\pi$
$450$	−1.64188e6	+	3.19682e6i	−0.382216	+	0.744195i
$451$	−3.48065e6			−0.805785
$452$	5.09651e6	+	2.45704e6i	1.17335	+	0.565674i
$453$	−407237.	+	407237.i	−0.0932399	+	0.0932399i
$454$	152601.	+	108325.i	0.0347470	+	0.0246655i
$455$	4.21635e6	−	2.11068e6i	0.954792	−	0.477963i
$456$	2.50072e6	+	722185.i	0.563188	+	0.162643i
$457$	−1.52765e6	+	1.52765e6i	−0.342163	+	0.342163i	−0.857180	−	0.515017i	$-0.827786\pi$
$457$	−1.52765e6	+	1.52765e6i	−0.342163	+	0.342163i	0.515017	+	0.857180i	$0.327786\pi$
$458$	−603260.	−	3.55514e6i	−0.134382	−	0.791942i
$459$			1.68682e6i			0.373711i
$460$	13234.0	+	888388.i	0.00291605	+	0.195753i
$461$			2.42900e6i			0.532323i	0.963928	+	0.266161i	$0.0857554\pi$
$461$			2.42900e6i			0.532323i	−0.963928	+	0.266161i	$0.914245\pi$
$462$	1.74169e6	−	295541.i	0.379634	−	0.0644188i
$463$	−5.98030e6	+	5.98030e6i	−1.29649	+	1.29649i	−0.365801	+	0.930693i	$0.619205\pi$
$463$	−5.98030e6	+	5.98030e6i	−1.29649	+	1.29649i	−0.930693	+	0.365801i	$0.880795\pi$
$464$	5.81326e6	−	4.62778e6i	1.25350	−	0.997879i
$465$	−805790.	+	2.42120e6i	−0.172818	+	0.519276i
$466$	1.86015e6	−	2.62045e6i	0.396811	−	0.558999i
$467$	3.69887e6	−	3.69887e6i	0.784833	−	0.784833i	−0.195809	−	0.980642i	$-0.562733\pi$
$467$	3.69887e6	−	3.69887e6i	0.784833	−	0.784833i	0.980642	+	0.195809i	$0.0627333\pi$
$468$	−2.06468e6	−	995384.i	−0.435750	−	0.210076i
$469$	2.56356e6			0.538159
$470$	−383132.	+	2.48143e6i	−0.0800025	+	0.518152i
$471$			2.13498e6i			0.443446i
$472$	−2.69173e6	+	1.48541e6i	−0.556130	+	0.306896i
$473$	952560.	+	952560.i	0.195767	+	0.195767i
$474$	1.49558e6	−	2.10686e6i	0.305747	−	0.430715i
$475$	−5.70911e6	−	4.27336e6i	−1.16100	−	0.869032i
$476$	−4.33791e6	+	1.51582e6i	−0.877532	+	0.306640i
$477$	−190515.	−	190515.i	−0.0383384	−	0.0383384i
$478$	755100.	+	4.44997e6i	0.151159	+	0.890814i
$479$	−5.88773e6			−1.17249			−0.586245	−	0.810134i	$-0.699394\pi$
$479$	−5.88773e6			−1.17249			−0.586245	+	0.810134i	$0.699394\pi$
$480$	−1.01233e6	−	1.77156e6i	−0.200549	−	0.350956i
$481$	−132714.			−0.0261549
$482$	297130.	+	1.75105e6i	0.0582545	+	0.343306i
$483$	−529779.	−	529779.i	−0.103330	−	0.103330i
$484$	3.57041e6	−	1.24763e6i	0.692795	−	0.242087i
$485$	1.56402e6	−	4.69949e6i	0.301917	−	0.907186i
$486$	−2.89127e6	+	4.07302e6i	−0.555262	+	0.782214i
$487$	4.54087e6	+	4.54087e6i	0.867594	+	0.867594i	0.992206	−	0.124612i	$-0.0397685\pi$
$487$	4.54087e6	+	4.54087e6i	0.867594	+	0.867594i	−0.124612	+	0.992206i	$0.539768\pi$
$488$	4.31679e6	−	2.38219e6i	0.820561	−	0.452821i
$489$			2.10193e6i			0.397509i
$490$	1.03329e7	−	7.56884e6i	1.94415	−	1.42410i
$491$	2.71881e6			0.508951			0.254475	−	0.967079i	$-0.418097\pi$
$491$	2.71881e6			0.508951			0.254475	+	0.967079i	$0.418097\pi$
$492$	−3.05366e6	−	1.47218e6i	−0.568733	−	0.274187i
$493$	−3.07768e6	+	3.07768e6i	−0.570305	+	0.570305i
$494$	2.63275e6	−	3.70883e6i	0.485391	−	0.683785i
$495$	1.05319e6	+	2.10388e6i	0.193194	+	0.385930i
$496$	4.62022e6	+	5.80376e6i	0.843254	+	1.05927i
$497$	−2.89890e6	+	2.89890e6i	−0.526433	+	0.526433i
$498$	−2.91518e6	+	494667.i	−0.526735	+	0.0893799i
$499$			1.02884e7i			1.84967i	0.380366	+	0.924836i	$0.375798\pi$
$499$			1.02884e7i			1.84967i	−0.380366	+	0.924836i	$0.624202\pi$
$500$	878154.	+	5.52077e6i	0.157089	+	0.987584i
$501$		−	250585.i		−	0.0446027i
$502$	−920620.	−	5.42541e6i	−0.163050	−	0.960889i
$503$	−2.13863e6	+	2.13863e6i	−0.376891	+	0.376891i	−0.869979	−	0.493088i	$-0.835868\pi$
$503$	−2.13863e6	+	2.13863e6i	−0.376891	+	0.376891i	0.493088	+	0.869979i	$0.335868\pi$
$504$	−8.46404e6	−	2.44434e6i	−1.48423	−	0.428632i
$505$	−1.98805e6	−	3.97139e6i	−0.346897	−	0.692970i
$506$	474314.	+	336697.i	0.0823550	+	0.0584605i
$507$	−1.10121e6	+	1.10121e6i	−0.190261	+	0.190261i
$508$	226653.	+	109270.i	0.0389675	+	0.0187863i
$509$	7.79654e6			1.33385			0.666926	−	0.745124i	$-0.267610\pi$
$509$	7.79654e6			1.33385			0.666926	+	0.745124i	$0.267610\pi$
$510$	706283.	+	964207.i	0.120241	+	0.164151i
$511$		−	5.40943e6i		−	0.916430i
$512$	−5.92166e6	−	343996.i	−0.998317	−	0.0579934i
$513$	−4.53778e6	−	4.53778e6i	−0.761289	−	0.761289i
$514$	4.80542e6	+	3.41117e6i	0.802276	+	0.569503i
$515$	−390334.	+	1.17286e6i	−0.0648513	+	0.194862i
$516$	432810.	+	1.23860e6i	0.0715605	+	0.204789i
$517$	1.16233e6	+	1.16233e6i	0.191250	+	0.191250i
$518$	−502913.	+	85337.5i	−0.0823508	+	0.0139738i
$519$	584934.			0.0953210
$520$	−3.50583e6	+	648757.i	−0.568568	+	0.105214i
$521$	9.36971e6			1.51228			0.756139	−	0.654411i	$-0.227083\pi$
$521$	9.36971e6			1.51228			0.756139	+	0.654411i	$0.227083\pi$
$522$	−8.22717e6	+	1.39604e6i	−1.32152	+	0.224244i
$523$	5.04052e6	+	5.04052e6i	0.805789	+	0.805789i	0.983994	−	0.178204i	$-0.0570287\pi$
$523$	5.04052e6	+	5.04052e6i	0.805789	+	0.805789i	−0.178204	+	0.983994i	$0.557029\pi$
$524$	−6.27416e6	+	2.19241e6i	−0.998222	+	0.348813i
$525$	−3.77383e6	−	2.82478e6i	−0.597564	−	0.447287i
$526$	−7.23072e6	−	5.13280e6i	−1.13951	−	0.808890i
$527$	−3.07266e6	−	3.07266e6i	−0.481934	−	0.481934i
$528$	−1.32727e6	−	150698.i	−0.207193	−	0.0235247i
$529$			6.18965e6i			0.961672i
$530$	−414190.	−	63950.9i	−0.0640487	−	0.00988910i
$531$	3.45273e6			0.531406
$532$	7.59182e6	−	1.57473e7i	1.16297	−	2.41228i
$533$	−4.18864e6	+	4.18864e6i	−0.638638	+	0.638638i
$534$	−997996.	−	708437.i	−0.151452	−	0.107510i
$535$	−459340.	+	1.38021e6i	−0.0693825	+	0.208478i
$536$	−1.86232e6	−	537822.i	−0.279991	−	0.0808586i
$537$	1.68210e6	−	1.68210e6i	0.251719	−	0.251719i
$538$	1.97524e6	+	1.16405e7i	0.294215	+	1.73387i
$539$		−	8.38534e6i		−	1.24322i
$540$	74929.5	+	5.02998e6i	0.0110578	+	0.742303i
$541$		−	5.33336e6i		−	0.783443i	−0.920084	−	0.391721i	$-0.871880\pi$
$541$		−	5.33336e6i		−	0.783443i	0.920084	−	0.391721i	$-0.128120\pi$
$542$	4.84846e6	−	822719.i	0.708934	−	0.120297i
$543$	2.33347e6	−	2.33347e6i	0.339627	−	0.339627i
$544$	3.46933e6	−	191110.i	0.502630	−	0.0276876i
$545$	−1.54726e6	+	774546.i	−0.223137	+	0.111701i
$546$	1.74030e6	−	2.45161e6i	0.249829	−	0.351941i
$547$	4.38265e6	−	4.38265e6i	0.626280	−	0.626280i	−0.320850	−	0.947130i	$-0.603969\pi$
$547$	4.38265e6	−	4.38265e6i	0.626280	−	0.626280i	0.947130	+	0.320850i	$0.103969\pi$
$548$	5.00074e6	−	1.03728e7i	0.711349	−	1.47551i
$549$	−5.53722e6			−0.784081
$550$	3.25547e6	+	1.67200e6i	0.458889	+	0.235684i
$551$		−	1.65588e7i		−	2.32354i
$552$	273719.	+	496009.i	0.0382346	+	0.0692854i
$553$	−1.22704e7	−	1.22704e7i	−1.70626	−	1.70626i
$554$	−6.43777e6	+	9.06907e6i	−0.891171	+	1.25542i
$555$	59392.5	+	118644.i	0.00818463	+	0.0163498i
$556$	1.53617e6	+	4.39616e6i	0.210743	+	0.603096i
$557$	803306.	+	803306.i	0.109709	+	0.109709i	0.759830	−	0.650121i	$-0.225282\pi$
$557$	803306.	+	803306.i	0.109709	+	0.109709i	−0.650121	+	0.759830i	$0.725282\pi$
$558$	−1.39376e6	−	8.21373e6i	−0.189497	−	1.11675i
$559$	2.29263e6			0.310316
$560$	−1.28680e7	+	4.71275e6i	−1.73397	+	0.635045i
$561$	782474.			0.104969
$562$	586768.	+	3.45795e6i	0.0783656	+	0.461826i
$563$	804076.	+	804076.i	0.106912	+	0.106912i	0.758539	−	0.651627i	$-0.225913\pi$
$563$	804076.	+	804076.i	0.106912	+	0.106912i	−0.651627	+	0.758539i	$0.725913\pi$
$564$	528120.	+	1.51135e6i	0.0699093	+	0.200064i
$565$	−9.37816e6	−	3.12111e6i	−1.23594	−	0.411327i
$566$	8.16499e6	−	1.15023e7i	1.07131	−	1.50918i
$567$	5.36299e6	+	5.36299e6i	0.700566	+	0.700566i
$568$	2.71412e6	−	1.49777e6i	0.352986	−	0.194793i
$569$		−	3.92427e6i		−	0.508134i	−0.967187	−	0.254067i	$-0.918232\pi$
$569$		−	3.92427e6i		−	0.508134i	0.967187	−	0.254067i	$-0.0817683\pi$
$570$	−4.49385e6	−	693850.i	−0.579338	−	0.0894496i
$571$	−1.25466e7			−1.61040			−0.805201	−	0.593002i	$-0.797943\pi$
$571$	−1.25466e7			−1.61040			−0.805201	+	0.593002i	$0.797943\pi$
$572$	−1.01365e6	+	2.10256e6i	−0.129538	+	0.268694i
$573$	−2.68010e6	+	2.68010e6i	−0.341008	+	0.341008i
$574$	−1.31793e7	+	1.85660e7i	−1.66960	+	2.35201i
$575$	−220962.	−	1.53631e6i	−0.0278707	−	0.193780i
$576$	5.63599e6	+	3.55143e6i	0.707806	+	0.446013i
$577$	−1.21454e6	+	1.21454e6i	−0.151870	+	0.151870i	−0.778953	−	0.627083i	$-0.784249\pi$
$577$	−1.21454e6	+	1.21454e6i	−0.151870	+	0.151870i	0.627083	+	0.778953i	$0.284249\pi$
$578$	5.91209e6	−	1.00320e6i	0.736074	−	0.124902i
$579$			3.77262e6i			0.467677i
$580$	−9.04074e6	+	9.31416e6i	−1.11592	+	1.14967i
$581$			1.98590e7i			2.44071i
$582$	−528336.	−	3.11360e6i	−0.0646551	−	0.381026i
$583$	−194011.	+	194011.i	−0.0236404	+	0.0236404i
$584$	−1.13487e6	+	3.92974e6i	−0.137694	+	0.476795i
$585$	3.79924e6	+	1.26441e6i	0.458994	+	0.152756i
$586$	4.75885e6	+	3.37812e6i	0.572477	+	0.406378i
$587$	6.81043e6	−	6.81043e6i	0.815791	−	0.815791i	−0.169704	−	0.985495i	$-0.554281\pi$
$587$	6.81043e6	−	6.81043e6i	0.815791	−	0.815791i	0.985495	+	0.169704i	$0.0542811\pi$
$588$	3.54666e6	−	7.35667e6i	0.423035	−	0.877481i
$589$	1.65318e7			1.96350
$590$	4.33270e6	−	3.17371e6i	0.512423	−	0.375351i
$591$		−	1.46985e6i		−	0.173103i
$592$	383250.	+	43514.2i	0.0449446	+	0.00510301i
$593$	−6.21457e6	−	6.21457e6i	−0.725729	−	0.725729i	0.244037	−	0.969766i	$-0.421528\pi$
$593$	−6.21457e6	−	6.21457e6i	−0.725729	−	0.725729i	−0.969766	+	0.244037i	$0.921528\pi$
$594$	2.68553e6	+	1.90635e6i	0.312294	+	0.221685i
$595$	7.17817e6	−	3.59335e6i	0.831230	−	0.416109i
$596$	−6.33842e6	+	2.21487e6i	−0.730913	+	0.255406i
$597$	2.71551e6	+	2.71551e6i	0.311828	+	0.311828i
$598$	975975.	−	165610.i	0.111606	−	0.0189380i
$599$	6.64825e6			0.757078			0.378539	−	0.925585i	$-0.376427\pi$
$599$	6.64825e6			0.757078			0.378539	+	0.925585i	$0.376427\pi$
$600$	2.14892e6	+	2.84383e6i	0.243693	+	0.322496i
$601$	−7.82874e6			−0.884109			−0.442055	−	0.896988i	$-0.645750\pi$
$601$	−7.82874e6			−0.884109			−0.442055	+	0.896988i	$0.645750\pi$
$602$	8.68782e6	−	1.47421e6i	0.977057	−	0.165793i
$603$	1.53936e6	+	1.53936e6i	0.172403	+	0.172403i
$604$	−964819.	−	2.76108e6i	−0.107610	−	0.307955i
$605$	−5.90815e6	+	2.95758e6i	−0.656241	+	0.328510i
$606$	−2.30918e6	−	1.63919e6i	−0.255432	−	0.181321i
$607$	−76234.2	−	76234.2i	−0.00839804	−	0.00839804i	0.702895	−	0.711293i	$-0.251890\pi$
$607$	−76234.2	−	76234.2i	−0.00839804	−	0.00839804i	−0.711293	+	0.702895i	$0.751890\pi$
$608$	−8.81888e6	+	9.84711e6i	−0.967508	+	1.08031i
$609$		−	1.09457e7i		−	1.19592i
$610$	−6.94845e6	+	5.08975e6i	−0.756072	+	0.553825i
$611$	2.79750e6			0.303156
$612$	−3.51503e6	−	1.69460e6i	−0.379359	−	0.182890i
$613$	9.22892e6	−	9.22892e6i	0.991973	−	0.991973i	−0.00799526	−	0.999968i	$-0.502545\pi$
$613$	9.22892e6	−	9.22892e6i	0.991973	−	0.991973i	0.999968	+	0.00799526i	$0.00254500\pi$
$614$	5.92105e6	+	4.20311e6i	0.633837	+	0.449935i
$615$	5.61909e6	+	1.87007e6i	0.599071	+	0.199374i
$616$	−2.48918e6	+	8.61934e6i	−0.264305	+	0.915213i
$617$	−60556.8	+	60556.8i	−0.00640398	+	0.00640398i	−0.710302	−	0.703898i	$-0.751441\pi$
$617$	−60556.8	+	60556.8i	−0.00640398	+	0.00640398i	0.703898	+	0.710302i	$0.251441\pi$
$618$	131858.	+	777065.i	0.0138878	+	0.0818439i
$619$			1.44485e7i			1.51564i	0.652466	+	0.757818i	$0.273734\pi$
$619$			1.44485e7i			1.51564i	−0.652466	+	0.757818i	$0.726266\pi$
$620$	−9.29894e6	−	9.02597e6i	−0.971526	−	0.943006i
$621$		−	1.39674e6i		−	0.145340i
$622$	7.34008e6	−	1.24551e6i	0.760719	−	0.129084i
$623$	−5.81233e6	+	5.81233e6i	−0.599971	+	0.599971i
$624$	−1.77860e6	+	1.41589e6i	−0.182859	+	0.145569i
$625$	−2.75218e6	−	9.36979e6i	−0.281823	−	0.959466i
$626$	−4.15034e6	+	5.84670e6i	−0.423299	+	0.596314i
$627$	−2.10497e6	+	2.10497e6i	−0.213834	+	0.213834i
$628$	−9.76669e6	−	4.70854e6i	−0.988208	−	0.476417i
$629$	−225940.			−0.0227702
$630$	1.52101e7	+	2.34843e6i	1.52679	+	0.235736i
$631$		−	998279.i		−	0.0998110i	−0.998754	−	0.0499055i	$-0.984108\pi$
$631$		−	998279.i		−	0.0998110i	0.998754	−	0.0499055i	$-0.0158920\pi$
$632$	6.33969e6	+	1.14882e7i	0.631357	+	1.14409i
$633$	2.59354e6	+	2.59354e6i	0.257267	+	0.257267i
$634$	8.42722e6	−	1.18717e7i	0.832647	−	1.17297i
$635$	−417068.	−	138803.i	−0.0410461	−	0.0136604i
$636$	−252270.	+	88151.8i	−0.0247299	+	0.00864148i
$637$	−1.00910e7	−	1.00910e7i	−0.985335	−	0.985335i
$638$	1.42165e6	+	8.37812e6i	0.138275	+	0.814882i
$639$	−3.48145e6			−0.337293
$640$	1.03368e7	−	723987.i	0.997556	−	0.0698684i
$641$	6.95063e6			0.668158			0.334079	−	0.942545i	$-0.391575\pi$
$641$	6.95063e6			0.668158			0.334079	+	0.942545i	$0.391575\pi$
$642$	155168.	+	914441.i	0.0148582	+	0.0875624i
$643$	−2.82012e6	−	2.82012e6i	−0.268993	−	0.268993i	0.559702	−	0.828694i	$-0.310916\pi$
$643$	−2.82012e6	−	2.82012e6i	−0.268993	−	0.268993i	−0.828694	+	0.559702i	$0.810916\pi$
$644$	3.59192e6	−	1.25514e6i	0.341281	−	0.119256i
$645$	−1.02601e6	−	2.04958e6i	−0.0971071	−	0.193984i
$646$	4.48215e6	−	6.31413e6i	0.422576	−	0.595295i
$647$	5.26200e6	+	5.26200e6i	0.494186	+	0.494186i	0.909622	−	0.415437i	$-0.136371\pi$
$647$	5.26200e6	+	5.26200e6i	0.494186	+	0.494186i	−0.415437	+	0.909622i	$0.636371\pi$
$648$	−2.77087e6	−	5.02113e6i	−0.259226	−	0.469747i
$649$		−	3.51608e6i		−	0.327678i
$650$	5.92975e6	−	1.90556e6i	0.550495	−	0.176905i
$651$	1.09278e7			1.01060
$652$	−9.61553e6	−	4.63567e6i	−0.885838	−	0.427064i
$653$	−1.68361e6	+	1.68361e6i	−0.154511	+	0.154511i	−0.780129	−	0.625618i	$-0.784847\pi$
$653$	−1.68361e6	+	1.68361e6i	−0.154511	+	0.154511i	0.625618	+	0.780129i	$0.284847\pi$
$654$	−638629.	+	899656.i	−0.0583854	+	0.0822493i
$655$	1.03822e7	−	5.19726e6i	0.945552	−	0.473338i
$656$	1.34693e7	−	1.07225e7i	1.22204	−	0.972833i
$657$	3.24824e6	−	3.24824e6i	0.293585	−	0.293585i
$658$	1.06010e7	−	1.79885e6i	0.954512	−	0.161968i
$659$			6.34724e6i			0.569339i	0.958626	+	0.284670i	$0.0918839\pi$
$659$			6.34724e6i			0.569339i	−0.958626	+	0.284670i	$0.908116\pi$
$660$	2.33329e6	−	34758.0i	0.208501	−	0.00310596i
$661$			3.70354e6i			0.329696i	0.986319	+	0.164848i	$0.0527133\pi$
$661$			3.70354e6i			0.329696i	−0.986319	+	0.164848i	$0.947287\pi$
$662$	−926546.	−	5.46034e6i	−0.0821717	−	0.484255i
$663$	941634.	−	941634.i	0.0831952	−	0.0831952i
$664$	4.16632e6	−	1.44268e7i	0.366718	−	1.26984i
$665$	−9.64368e6	+	2.89769e7i	−0.845646	+	2.54096i
$666$	−353231.	−	250744.i	−0.0308584	−	0.0219051i
$667$	2.54842e6	−	2.54842e6i	0.221797	−	0.221797i
$668$	1.14633e6	+	552648.i	0.0993959	+	0.0479190i
$669$	−241543.			−0.0208655
$670$	3.34664e6	+	516720.i	0.288020	+	0.0444702i
$671$			5.63882e6i			0.483483i
$672$	−5.82946e6	+	6.50914e6i	−0.497972	+	0.556033i
$673$	1.25751e7	+	1.25751e7i	1.07022	+	1.07022i	0.997341	+	0.0728820i	$0.0232197\pi$
$673$	1.25751e7	+	1.25751e7i	1.07022	+	1.07022i	0.0728820	+	0.997341i	$0.476780\pi$
$674$	−1.69576e7	−	1.20376e7i	−1.43786	−	1.02068i
$675$	−1.25107e6	−	8.69847e6i	−0.105687	−	0.734824i
$676$	−2.60897e6	−	7.46625e6i	−0.219585	−	0.628400i
$677$	−1.12742e6	−	1.12742e6i	−0.0945397	−	0.0945397i	0.658255	−	0.752795i	$-0.271295\pi$
$677$	−1.12742e6	−	1.12742e6i	−0.0945397	−	0.0945397i	−0.752795	+	0.658255i	$0.771295\pi$
$678$	−6.21340e6	+	1.05433e6i	−0.519105	+	0.0880852i
$679$	−2.12106e7			−1.76555
$680$	−5.96853e6	+	1.10448e6i	−0.494989	+	0.0915981i
$681$	−208453.			−0.0172242
$682$	−8.36443e6	+	1.41933e6i	−0.688613	+	0.116848i
$683$	6.77294e6	+	6.77294e6i	0.555553	+	0.555553i	0.928038	−	0.372485i	$-0.121494\pi$
$683$	6.77294e6	+	6.77294e6i	0.555553	+	0.555553i	−0.372485	+	0.928038i	$0.621494\pi$
$684$	1.40146e7	−	4.89720e6i	1.14536	−	0.400228i
$685$	−6.35229e6	+	1.90871e7i	−0.517254	+	1.55422i
$686$	−2.61681e7	−	1.85757e7i	−2.12306	−	1.50707i
$687$	2.84019e6	+	2.84019e6i	0.229591	+	0.229591i
$688$	−6.62065e6	−	751708.i	−0.533248	−	0.0605450i
$689$			466947.i			0.0374731i
$690$	−584825.	−	798393.i	−0.0467631	−	0.0638402i
$691$	−1.88767e7			−1.50394			−0.751969	−	0.659198i	$-0.770896\pi$
$691$	−1.88767e7			−1.50394			−0.751969	+	0.659198i	$0.770896\pi$
$692$	−1.29003e6	+	2.67585e6i	−0.102408	+	0.212420i
$693$	7.12455e6	−	7.12455e6i	0.563540	−	0.563540i
$694$	−1.21169e7	−	8.60128e6i	−0.954975	−	0.677898i
$695$	−3.64160e6	−	7.27457e6i	−0.285977	−	0.571275i
$696$	−2.29636e6	+	7.95164e6i	−0.179687	+	0.622205i
$697$	−7.13098e6	+	7.13098e6i	−0.555991	+	0.555991i
$698$	3.29203e6	+	1.94007e7i	0.255756	+	1.50722i
$699$			3.57953e6i			0.277098i
$700$	2.12452e7	−	1.10340e7i	1.63876	−	0.851113i
$701$			4.36760e6i			0.335697i	0.985813	+	0.167849i	$0.0536820\pi$
$701$			4.36760e6i			0.335697i	−0.985813	+	0.167849i	$0.946318\pi$
$702$	5.52589e6	−	937670.i	0.423213	−	0.0718137i
$703$	607810.	−	607810.i	0.0463852	−	0.0463852i
$704$	3.61659e6	−	5.73940e6i	0.275022	−	0.436450i
$705$	−1.25195e6	−	2.50092e6i	−0.0948664	−	0.189508i
$706$	−3.91992e6	+	5.52210e6i	−0.295982	+	0.416958i
$707$	−1.34487e7	+	1.34487e7i	−1.01188	+	1.01188i
$708$	1.48716e6	−	3.08475e6i	0.111500	−	0.231279i
$709$	−2.34469e7			−1.75174			−0.875871	−	0.482545i	$-0.839713\pi$
$709$	−2.34469e7			−1.75174			−0.875871	+	0.482545i	$0.839713\pi$
$710$	−4.36874e6	+	3.20011e6i	−0.325245	+	0.238242i
$711$		−	1.47362e7i		−	1.09323i
$712$	5.44183e6	−	3.00304e6i	0.402296	−	0.222004i
$713$	2.54426e6	+	2.54426e6i	0.187429	+	0.187429i
$714$	2.96279e6	−	4.17377e6i	0.217498	−	0.306396i
$715$	1.28761e6	−	3.86894e6i	0.0941929	−	0.283027i
$716$	3.98520e6	+	1.14047e7i	0.290514	+	0.831383i
$717$	−3.55506e6	−	3.55506e6i	−0.258255	−	0.258255i
$718$	−2.14664e6	−	1.26506e7i	−0.155399	−	0.915801i
$719$	3.10054e6			0.223674			0.111837	−	0.993727i	$-0.464327\pi$
$719$	3.10054e6			0.223674			0.111837	+	0.993727i	$0.464327\pi$
$720$	−1.05568e7	−	4.89705e6i	−0.758932	−	0.352049i
$721$	5.29357e6			0.379237
$722$	2.58500e6	+	1.52340e7i	0.184552	+	1.08760i
$723$	−1.39891e6	−	1.39891e6i	−0.0995276	−	0.0995276i
$724$	5.52842e6	+	1.58210e7i	0.391972	+	1.12173i
$725$	1.35882e7	−	1.81535e7i	0.960099	−	1.28267i
$726$	−2.43859e6	+	3.43531e6i	−0.171711	+	0.241894i
$727$	−1.31022e7	−	1.31022e7i	−0.919406	−	0.919406i	0.0775805	−	0.996986i	$-0.475281\pi$
$727$	−1.31022e7	−	1.31022e7i	−0.919406	−	0.919406i	−0.996986	+	0.0775805i	$0.975281\pi$
$728$	7.37706e6	+	1.33681e7i	0.515887	+	0.934845i
$729$			2.13483e6i			0.148780i
$730$	1.09035e6	−	7.06183e6i	0.0757281	−	0.490468i
$731$	3.90311e6			0.270158
$732$	−2.38500e6	+	4.94708e6i	−0.164517	+	0.341249i
$733$	1.58810e7	−	1.58810e7i	1.09174	−	1.09174i	0.0963958	−	0.995343i	$-0.469269\pi$
$733$	1.58810e7	−	1.58810e7i	1.09174	−	1.09174i	0.995343	−	0.0963958i	$-0.0307315\pi$
$734$	4.33597e6	−	6.10820e6i	0.297061	−	0.418479i
$735$	−4.50523e6	+	1.35371e7i	−0.307609	+	0.924289i
$736$	−2.87272e6	+	158245.i	−0.195478	+	0.0107680i
$737$	1.56760e6	−	1.56760e6i	0.106308	−	0.106308i
$738$	−1.90623e7	+	3.23462e6i	−1.28835	+	0.218616i
$739$		−	1.89695e7i		−	1.27774i	−0.769313	−	0.638872i	$-0.779401\pi$
$739$		−	1.89695e7i		−	1.27774i	0.769313	−	0.638872i	$-0.220599\pi$
$740$	−673737.	+	10036.4i	−0.0452284	+	0.000673749i
$741$			5.06626e6i			0.338955i
$742$	300256.	+	1.76948e6i	0.0200209	+	0.117987i
$743$	−1.76147e7	+	1.76147e7i	−1.17058	+	1.17058i	−0.188512	+	0.982071i	$0.560366\pi$
$743$	−1.76147e7	+	1.76147e7i	−1.17058	+	1.17058i	−0.982071	+	0.188512i	$0.939634\pi$
$744$	−7.93865e6	−	2.29261e6i	−0.525792	−	0.151844i
$745$	1.04885e7	−	5.25049e6i	0.692347	−	0.346585i
$746$	−3.45341e6	−	2.45144e6i	−0.227196	−	0.161277i
$747$	−1.19249e7	+	1.19249e7i	−0.781901	+	0.781901i
$748$	−1.72569e6	+	3.57952e6i	−0.112774	+	0.233922i
$749$	6.22941e6			0.405735
$750$	−4.35725e6	−	4.44833e6i	−0.282852	−	0.288764i
$751$			4.68412e6i			0.303060i	0.988453	+	0.151530i	$0.0484200\pi$
$751$			4.68412e6i			0.303060i	−0.988453	+	0.151530i	$0.951580\pi$
$752$	−8.07860e6	−	917243.i	−0.520944	−	0.0591480i
$753$	4.33433e6	+	4.33433e6i	0.278570	+	0.278570i
$754$	1.17931e7	+	8.37144e6i	0.755439	+	0.536256i
$755$	2.28717e6	+	4.56892e6i	0.146026	+	0.291706i
$756$	2.03372e7	−	7.10651e6i	1.29415	−	0.452222i
$757$	9.09156e6	+	9.09156e6i	0.576632	+	0.576632i	0.933974	−	0.357342i	$-0.116317\pi$
$757$	9.09156e6	+	9.09156e6i	0.576632	+	0.576632i	−0.357342	+	0.933974i	$0.616317\pi$
$758$	−9.86343e6	+	1.67369e6i	−0.623526	+	0.105804i
$759$	−647913.			−0.0408237
$760$	1.30850e7	−	1.90274e7i	0.821749	−	1.19494i
$761$	−4.93887e6			−0.309148			−0.154574	−	0.987981i	$-0.549400\pi$
$761$	−4.93887e6			−0.309148			−0.154574	+	0.987981i	$0.549400\pi$
$762$	−276324.	+	46888.5i	−0.0172398	+	0.00292536i
$763$	5.23960e6	+	5.23960e6i	0.325827	+	0.325827i
$764$	−6.34965e6	−	1.81712e7i	−0.393565	−	1.12629i
$765$	6.46805e6	+	2.15260e6i	0.399595	+	0.132987i
$766$	1.71121e7	+	1.21472e7i	1.05373	+	0.748003i
$767$	−4.23127e6	−	4.23127e6i	−0.259706	−	0.259706i
$768$	5.60046e6	−	3.50565e6i	0.342627	−	0.214469i
$769$		−	1.04569e6i		−	0.0637656i	−0.999492	−	0.0318828i	$-0.989850\pi$
$769$		−	1.04569e6i		−	0.0637656i	0.999492	−	0.0318828i	$-0.0101503\pi$
$770$	2.39152e6	−	1.54891e7i	0.145361	−	0.941457i
$771$	−6.56420e6			−0.397691
$772$	−1.72583e7	−	8.32025e6i	−1.04221	−	0.502450i
$773$	4.05820e6	−	4.05820e6i	0.244278	−	0.244278i	−0.574339	−	0.818617i	$-0.694741\pi$
$773$	4.05820e6	−	4.05820e6i	0.244278	−	0.244278i	0.818617	+	0.574339i	$0.194741\pi$
$774$	6.10207e6	+	4.33161e6i	0.366121	+	0.259894i
$775$	1.81238e7	+	1.35660e7i	1.08391	+	0.811328i
$776$	1.54087e7	+	4.44989e6i	0.918570	+	0.265274i
$777$	401775.	−	401775.i	0.0238743	−	0.0238743i
$778$	−2.48427e6	−	1.46403e7i	−0.147146	−	0.867165i
$779$		−	3.83667e7i		−	2.26522i
$780$	2.76606e6	−	2.84972e6i	0.162789	−	0.167712i
$781$			3.54532e6i			0.207983i
$782$	1.66156e6	−	281944.i	0.0971625	−	0.0164872i
$783$	1.44289e7	−	1.44289e7i	0.841065	−	0.841065i
$784$	2.58320e7	+	3.24492e7i	1.50096	+	1.88545i
$785$	1.79718e7	+	5.98113e6i	1.04092	+	0.346425i
$786$	4.28525e6	−	6.03675e6i	0.247411	−	0.348535i
$787$	1.09025e7	−	1.09025e7i	0.627464	−	0.627464i	−0.319966	−	0.947429i	$-0.603671\pi$
$787$	1.09025e7	−	1.09025e7i	0.627464	−	0.627464i	0.947429	+	0.319966i	$0.103671\pi$
$788$	6.72402e6	+	3.24166e6i	0.385757	+	0.185974i
$789$	9.87716e6			0.564858
$790$	−1.35453e7	−	1.84918e7i	−0.772185	−	1.05417i
$791$			4.23273e7i			2.40536i
$792$	−6.67041e6	+	3.68102e6i	−0.377868	+	0.208523i
$793$	6.78578e6	+	6.78578e6i	0.383192	+	0.383192i
$794$	−5.06290e6	+	7.13225e6i	−0.285002	+	0.401491i
$795$	417444.	−	208970.i	0.0234251	−	0.0117264i
$796$	−1.84113e7	+	6.43353e6i	−1.02991	+	0.359888i
$797$	−1.70728e7	−	1.70728e7i	−0.952049	−	0.952049i	0.0468526	−	0.998902i	$-0.485081\pi$
$797$	−1.70728e7	−	1.70728e7i	−0.952049	−	0.952049i	−0.998902	+	0.0468526i	$0.985081\pi$
$798$	3.25770e6	+	1.91983e7i	0.181094	+	1.06723i
$799$	4.76262e6			0.263924
$800$	−1.77487e7	+	3.55862e6i	−0.980486	+	0.196588i
$801$	−6.98034e6			−0.384411
$802$	3.14147e6	+	1.85134e7i	0.172464	+	1.01637i
$803$	−3.30783e6	−	3.30783e6i	−0.181032	−	0.181032i
$804$	2.03833e6	−	712263.i	0.111207	−	0.0388597i
$805$	−5.94375e6	+	2.97540e6i	−0.323274	+	0.161829i
$806$	−8.35777e6	+	1.17738e7i	−0.453161	+	0.638381i
$807$	−9.29957e6	−	9.29957e6i	−0.502665	−	0.502665i
$808$	1.25914e7	−	6.94847e6i	0.678493	−	0.374422i
$809$		−	1.78529e7i		−	0.959040i	−0.877531	−	0.479520i	$-0.840811\pi$
$809$		−	1.78529e7i		−	0.959040i	0.877531	−	0.479520i	$-0.159189\pi$
$810$	5.92022e6	+	8.08219e6i	0.317048	+	0.432829i
$811$	−2.39804e7			−1.28028			−0.640139	−	0.768259i	$-0.721123\pi$
$811$	−2.39804e7			−1.28028			−0.640139	+	0.768259i	$0.721123\pi$
$812$	5.00724e7	+	2.41400e7i	2.66507	+	1.28483i
$813$	−3.87341e6	+	3.87341e6i	−0.205526	+	0.205526i
$814$	−255345.	+	359711.i	−0.0135072	+	0.0190280i
$815$	1.76937e7	+	5.88856e6i	0.933091	+	0.310538i
$816$	−3.02799e6	+	2.41050e6i	−0.159195	+	0.126731i
$817$	−1.04999e7	+	1.04999e7i	−0.550340	+	0.550340i
$818$	−2.00953e7	+	3.40990e6i	−1.05005	+	0.178180i
$819$		−	1.71475e7i		−	0.893285i
$820$	−2.09473e7	+	2.15809e7i	−1.08791	+	1.12082i
$821$		−	1.28789e7i		−	0.666841i	−0.942778	−	0.333421i	$-0.891797\pi$
$821$		−	1.28789e7i		−	0.666841i	0.942778	−	0.333421i	$-0.108203\pi$
$822$	2.14585e6	+	1.26460e7i	0.110769	+	0.652788i
$823$	1.48554e7	−	1.48554e7i	0.764515	−	0.764515i	−0.212620	−	0.977135i	$-0.568200\pi$
$823$	1.48554e7	−	1.48554e7i	0.764515	−	0.764515i	0.977135	+	0.212620i	$0.0681997\pi$
$824$	−3.84557e6	−	1.11057e6i	−0.197307	−	0.0569805i
$825$	−4.03501e6	+	580341.i	−0.206400	+	0.0296858i
$826$	−1.87550e7	−	1.33134e7i	−0.956460	−	0.678952i
$827$	1.43004e7	−	1.43004e7i	0.727084	−	0.727084i	−0.242954	−	0.970038i	$-0.578116\pi$
$827$	1.43004e7	−	1.43004e7i	0.727084	−	0.727084i	0.970038	+	0.242954i	$0.0781164\pi$
$828$	2.91055e6	+	1.40318e6i	0.147536	+	0.0711276i
$829$	−1.83120e6			−0.0925443			−0.0462722	−	0.998929i	$-0.514734\pi$
$829$	−1.83120e6			−0.0925443			−0.0462722	+	0.998929i	$0.514734\pi$
$830$	−4.00285e6	+	2.59252e7i	−0.201685	+	1.30625i
$831$		−	1.23883e7i		−	0.622316i
$832$	−2.55460e6	−	1.12590e7i	−0.127942	−	0.563889i
$833$	−1.71794e7	−	1.71794e7i	−0.857821	−	0.857821i
$834$	−4.22982e6	−	3.00258e6i	−0.210575	−	0.149479i
$835$	−2.10938e6	−	702013.i	−0.104698	−	0.0348441i
$836$	−4.98705e6	−	1.42718e7i	−0.246790	−	0.706256i
$837$	1.44054e7	+	1.44054e7i	0.710739	+	0.710739i
$838$	−8.92701e6	+	1.51479e6i	−0.439133	+	0.0745150i
$839$	−2.93770e7			−1.44080			−0.720398	−	0.693561i	$-0.756041\pi$
$839$	−2.93770e7			−1.44080			−0.720398	+	0.693561i	$0.756041\pi$
$840$	8.64944e6	−	1.25775e7i	0.422951	−	0.615030i
$841$	3.21415e7			1.56703
$842$	−2.16282e6	+	367002.i	−0.105133	+	0.0178397i
$843$	−2.76254e6	−	2.76254e6i	−0.133887	−	0.133887i
$844$	−1.75843e7	+	6.14457e6i	−0.849707	+	0.296917i
$845$	6.18474e6	+	1.23548e7i	0.297975	+	0.595243i
$846$	7.44581e6	+	5.28548e6i	0.357673	+	0.253898i
$847$	2.00073e7	+	2.00073e7i	0.958251	+	0.958251i
$848$	153103.	−	1.34845e6i	0.00731128	−	0.0643939i
$849$			1.57121e7i			0.748108i
$850$	1.00952e7	−	3.24414e6i	0.479254	−	0.154011i
$851$	187085.			0.00885555
$852$	−1.49953e6	+	3.11040e6i	−0.0707712	+	0.146797i
$853$	6.76720e6	−	6.76720e6i	0.318446	−	0.318446i	−0.529724	−	0.848170i	$-0.677704\pi$
$853$	6.76720e6	−	6.76720e6i	0.318446	−	0.318446i	0.848170	+	0.529724i	$0.177704\pi$
$854$	3.00778e7	+	2.13510e7i	1.41124	+	1.00178i
$855$	−2.31908e7	+	1.16092e7i	−1.08493	+	0.543107i
$856$	−4.52542e6	−	1.30690e6i	−0.211094	−	0.0609618i
$857$	2.35330e7	−	2.35330e7i	1.09452	−	1.09452i	0.0994857	−	0.995039i	$-0.468280\pi$
$857$	2.35330e7	−	2.35330e7i	1.09452	−	1.09452i	0.995039	−	0.0994857i	$-0.0317198\pi$
$858$	−434963.	−	2.56333e6i	−0.0201713	−	0.118874i
$859$			2.12302e7i			0.981681i	0.871250	+	0.490840i	$0.163310\pi$
$859$			2.12302e7i			0.981681i	−0.871250	+	0.490840i	$0.836690\pi$
$860$	1.16388e7	−	173379.i	0.536615	−	0.00799374i
$861$		−	2.53612e7i		−	1.16590i
$862$	−1.18655e7	+	2.01341e6i	−0.543898	+	0.0922922i
$863$	1.84791e7	−	1.84791e7i	0.844605	−	0.844605i	−0.144849	−	0.989454i	$-0.546270\pi$
$863$	1.84791e7	−	1.84791e7i	0.844605	−	0.844605i	0.989454	+	0.144849i	$0.0462695\pi$
$864$	−1.62651e7	+	895969.i	−0.741262	+	0.0408328i
$865$	1.63869e6	−	4.92387e6i	0.0744658	−	0.223751i
$866$	2.15406e7	−	3.03448e7i	0.976029	−	1.37496i
$867$	−4.72314e6	+	4.72314e6i	−0.213395	+	0.213395i
$868$	−2.41006e7	+	4.99906e7i	−1.08575	+	2.25211i
$869$	−1.50065e7			−0.674110
$870$	2.20626e6	−	1.42893e7i	0.0988231	−	0.640047i
$871$		−	3.77292e6i		−	0.168512i
$872$	−2.70713e6	−	4.90561e6i	−0.120564	−	0.218475i
$873$	−1.27365e7	−	1.27365e7i	−0.565607	−	0.565607i
$874$	−3.71136e6	+	5.22830e6i	−0.164344	+	0.231516i
$875$	−3.43508e7	+	2.38538e7i	−1.51676	+	1.05327i
$876$	−1.50296e6	−	4.30113e6i	−0.0661741	−	0.189375i
$877$	2.31623e7	+	2.31623e7i	1.01691	+	1.01691i	0.999855	+	0.0170541i	$0.00542874\pi$
$877$	2.31623e7	+	2.31623e7i	1.01691	+	1.01691i	0.0170541	+	0.999855i	$0.494571\pi$
$878$	−4.35118e6	−	2.56425e7i	−0.190489	−	1.12260i
$879$	−6.50059e6			−0.283779
$880$	−4.98689e6	+	1.07505e7i	−0.217082	+	0.467976i
$881$	−3.17232e7			−1.37701			−0.688505	−	0.725232i	$-0.741733\pi$
$881$	−3.17232e7			−1.37701			−0.688505	+	0.725232i	$0.741733\pi$
$882$	−7.79261e6	−	4.59235e7i	−0.337296	−	1.98776i
$883$	991053.	+	991053.i	0.0427755	+	0.0427755i	0.728171	−	0.685395i	$-0.240371\pi$
$883$	991053.	+	991053.i	0.0427755	+	0.0427755i	−0.685395	+	0.728171i	$0.740371\pi$
$884$	2.23090e6	+	6.38432e6i	0.0960174	+	0.274779i
$885$	−1.88910e6	+	5.67628e6i	−0.0810768	+	0.243616i
$886$	−7.84022e6	+	1.10447e7i	−0.335540	+	0.472684i
$887$	−2.16096e7	−	2.16096e7i	−0.922228	−	0.922228i	0.0749584	−	0.997187i	$-0.476118\pi$
$887$	−2.16096e7	−	2.16096e7i	−0.922228	−	0.922228i	−0.997187	+	0.0749584i	$0.976118\pi$
$888$	−376164.	+	207583.i	−0.0160083	+	0.00883406i
$889$			1.88239e6i			0.0798832i
$890$	−8.75937e6	+	6.41625e6i	−0.370679	+	0.271523i
$891$	6.55887e6			0.276780
$892$	532706.	−	1.10496e6i	0.0224169	−	0.0464982i
$893$	−1.28121e7	+	1.28121e7i	−0.537641	+	0.537641i
$894$	4.32914e6	−	6.09859e6i	0.181158	−	0.255203i
$895$	−9.44719e6	−	1.88720e7i	−0.394226	−	0.787516i
$896$	−1.69203e7	−	4.10230e7i	−0.704107	−	1.70709i
$897$	−779702.	+	779702.i	−0.0323555	+	0.0323555i
$898$	1.77144e7	−	3.00590e6i	0.733054	−	0.124389i
$899$			5.25666e7i			2.16926i
$900$	1.93829e7	+	6.13161e6i	0.797650	+	0.252329i
$901$			794959.i			0.0326237i
$902$	3.29397e6	+	1.94121e7i	0.134804	+	0.794429i
$903$	−6.94066e6	+	6.94066e6i	−0.283258	+	0.283258i
$904$	8.88007e6	−	3.07492e7i	0.361406	−	1.25145i
$905$	−1.31055e7	−	2.61799e7i	−0.531903	−	1.06254i
$906$	2.65661e6	+	1.88582e6i	0.107524	+	0.0763273i
$907$	3.16848e7	−	3.16848e7i	1.27889	−	1.27889i	0.337601	−	0.941289i	$-0.390385\pi$
$907$	3.16848e7	−	3.16848e7i	1.27889	−	1.27889i	0.941289	−	0.337601i	$-0.109615\pi$
$908$	459728.	−	953591.i	0.0185049	−	0.0383838i
$909$	−1.61512e7			−0.648330
$910$	−1.57618e7	−	2.15177e7i	−0.630959	−	0.861375i
$911$		−	1.77379e7i		−	0.708121i	−0.935223	−	0.354060i	$-0.884801\pi$
$911$		−	1.77379e7i		−	0.708121i	0.935223	−	0.354060i	$-0.115199\pi$
$912$	1.66112e6	−	1.46303e7i	0.0661325	−	0.582460i
$913$	1.21436e7	+	1.21436e7i	0.482139	+	0.482139i
$914$	9.96562e6	+	7.07419e6i	0.394583	+	0.280099i
$915$	3.02959e6	−	9.10319e6i	0.119628	−	0.359452i
$916$	−1.92566e7	+	6.72892e6i	−0.758299	+	0.264976i
$917$	−3.51581e7	−	3.51581e7i	−1.38071	−	1.38071i
$918$	9.40760e6	−	1.59634e6i	0.368445	−	0.0625201i
$919$	−3.13742e6			−0.122542			−0.0612708	−	0.998121i	$-0.519515\pi$
$919$	−3.13742e6			−0.122542			−0.0612708	+	0.998121i	$0.519515\pi$
$920$	4.94213e6	−	914546.i	0.192506	−	0.0356235i
$921$	−8.08815e6			−0.314195
$922$	1.35469e7	−	2.29872e6i	0.524821	−	0.0890551i
$923$	4.26646e6	+	4.26646e6i	0.164840	+	0.164840i
$924$	−3.29654e6	−	9.43393e6i	−0.127022	−	0.363507i
$925$	1.16511e6	−	167574.i	0.0447727	−	0.00643949i
$926$	3.90125e7	+	2.76934e7i	1.49512	+	1.06133i
$927$	3.17867e6	+	3.17867e6i	0.121491	+	0.121491i
$928$	−3.13112e7	−	2.80417e7i	−1.19352	−	1.06889i
$929$			3.33387e7i			1.26739i	0.773584	+	0.633694i	$0.218462\pi$
$929$			3.33387e7i			1.26739i	−0.773584	+	0.633694i	$0.781538\pi$
$930$	1.42659e7	+	2.20266e6i	0.540870	+	0.0835101i
$931$	9.24303e7			3.49494
$932$	−1.63750e7	−	7.89441e6i	−0.617506	−	0.297701i
$933$	−5.86395e6	+	5.86395e6i	−0.220539	+	0.220539i
$934$	−2.41296e7	−	1.71286e7i	−0.905071	−	0.642473i
$935$	2.19210e6	−	6.58672e6i	0.0820033	−	0.246400i
$936$	−3.59745e6	+	1.24570e7i	−0.134216	+	0.464753i
$937$	−8.71957e6	+	8.71957e6i	−0.324449	+	0.324449i	−0.850471	−	0.526022i	$-0.823683\pi$
$937$	−8.71957e6	+	8.71957e6i	−0.324449	+	0.324449i	0.526022	+	0.850471i	$0.323683\pi$
$938$	−2.42606e6	−	1.42973e7i	−0.0900315	−	0.530575i
$939$		−	7.98659e6i		−	0.295595i
$940$	1.42018e7	−	211559.i	0.524233	−	0.00780929i
$941$			3.11580e7i			1.14708i	0.819176	+	0.573542i	$0.194431\pi$
$941$			3.11580e7i			1.14708i	−0.819176	+	0.573542i	$0.805569\pi$
$942$	1.19070e7	−	2.02047e6i	0.437196	−	0.0741864i
$943$	5.90468e6	−	5.90468e6i	0.216230	−	0.216230i
$944$	1.08317e7	+	1.36064e7i	0.395609	+	0.496950i
$945$	−3.36530e7	+	1.68465e7i	−1.22587	+	0.613663i
$946$	4.41108e6	−	6.21402e6i	0.160257	−	0.225759i
$947$	−2.99596e7	+	2.99596e7i	−1.08558	+	1.08558i	−0.0895993	+	0.995978i	$0.528559\pi$
$947$	−2.99596e7	+	2.99596e7i	−1.08558	+	1.08558i	−0.995978	+	0.0895993i	$0.971441\pi$
$948$	−1.31656e7	−	6.34717e6i	−0.475795	−	0.229382i
$949$	−7.96133e6			−0.286959
$950$	−1.84302e7	+	3.58846e7i	−0.662554	+	1.29003i
$951$			1.62167e7i			0.581448i
$952$	1.25591e7	+	2.27586e7i	0.449126	+	0.813865i
$953$	1.16784e7	+	1.16784e7i	0.416534	+	0.416534i	0.884007	−	0.467473i	$-0.154835\pi$
$953$	1.16784e7	+	1.16784e7i	0.416534	+	0.416534i	−0.467473	+	0.884007i	$0.654835\pi$
$954$	−882232.	+	1.24283e6i	−0.0313843	+	0.0442119i
$955$	1.50523e7	+	3.00689e7i	0.534065	+	1.06686i
$956$	2.41035e7	−	8.42259e6i	0.852972	−	0.298058i
$957$	−6.69324e6	−	6.69324e6i	−0.236242	−	0.236242i
$958$	5.57194e6	+	3.28366e7i	0.196152	+	1.15596i
$959$	8.61475e7			3.02480
$960$	−8.92218e6	+	7.32246e6i	−0.312459	+	0.256436i
$961$	−2.38516e7			−0.833123
$962$	125596.	+	740162.i	0.00437559	+	0.0257863i
$963$	3.74062e6	+	3.74062e6i	0.129980	+	0.129980i
$964$	9.48466e6	−	3.31427e6i	0.328722	−	0.114867i
$965$	3.17572e7	+	1.05690e7i	1.09780	+	0.365355i
$966$	−2.45328e6	+	3.45601e6i	−0.0845872	+	0.119160i
$967$	6.11322e6	+	6.11322e6i	0.210234	+	0.210234i	0.804367	−	0.594133i	$-0.202505\pi$
$967$	6.11322e6	+	6.11322e6i	0.210234	+	0.210234i	−0.594133	+	0.804367i	$0.702505\pi$
$968$	−1.03371e7	−	1.87319e7i	−0.354576	−	0.642532i
$969$			8.62509e6i			0.295090i
$970$	−2.76898e7	−	4.27530e6i	−0.944911	−	0.145894i
$971$	−3.60288e7			−1.22631			−0.613157	−	0.789961i	$-0.710101\pi$
$971$	−3.60288e7			−1.22631			−0.613157	+	0.789961i	$0.710101\pi$
$972$	2.54520e7	+	1.22704e7i	0.864083	+	0.416576i
$973$	−2.46345e7	+	2.46345e7i	−0.834183	+	0.834183i
$974$	2.10277e7	−	2.96223e7i	0.710223	−	1.00051i
$975$	−4.15737e6	+	5.55414e6i	−0.140058	+	0.187114i
$976$	−1.73710e7	−	2.18209e7i	−0.583715	−	0.733242i
$977$	2.67594e7	−	2.67594e7i	0.896892	−	0.896892i	−0.0982680	−	0.995160i	$-0.531330\pi$
$977$	2.67594e7	−	2.67594e7i	0.896892	−	0.896892i	0.995160	+	0.0982680i	$0.0313303\pi$
$978$	1.17228e7	−	1.98920e6i	0.391907	−	0.0665013i
$979$			7.10841e6i			0.237037i
$980$	−5.19911e7	−	5.04648e7i	−1.72927	−	1.67851i
$981$			6.29252e6i			0.208762i
$982$	−2.57299e6	−	1.51632e7i	−0.0851450	−	0.501778i
$983$	1.14544e7	−	1.14544e7i	0.378084	−	0.378084i	−0.492326	−	0.870411i	$-0.663853\pi$
$983$	1.14544e7	−	1.14544e7i	0.378084	−	0.378084i	0.870411	+	0.492326i	$0.163853\pi$
$984$	−5.32065e6	+	1.84239e7i	−0.175177	+	0.606588i
$985$	−1.23730e7	−	4.11779e6i	−0.406334	−	0.135230i
$986$	2.00773e7	+	1.42520e7i	0.657676	+	0.466858i
$987$	−8.46908e6	+	8.46908e6i	−0.276722	+	0.276722i
$988$	−2.31762e7	−	1.11733e7i	−0.755352	−	0.364156i
$989$	−3.23190e6			−0.105067
$990$	1.07369e7	−	7.86482e6i	0.348171	−	0.255036i
$991$			4.84941e7i			1.56857i	0.620399	+	0.784286i	$0.286971\pi$
$991$			4.84941e7i			1.56857i	−0.620399	+	0.784286i	$0.713029\pi$
$992$	2.79959e7	−	3.12601e7i	0.903265	−	1.00858i
$993$	4.36224e6	+	4.36224e6i	0.140390	+	0.140390i
$994$	1.89110e7	+	1.34241e7i	0.607083	+	0.430944i
$995$	3.04661e7	−	1.52511e7i	0.975572	−	0.488365i
$996$	5.51765e6	+	1.57902e7i	0.176240	+	0.504359i
$997$	8.47473e6	+	8.47473e6i	0.270015	+	0.270015i	0.829106	−	0.559091i	$-0.188850\pi$
$997$	8.47473e6	+	8.47473e6i	0.270015	+	0.270015i	−0.559091	+	0.829106i	$0.688850\pi$
$998$	5.73795e7	−	9.73654e6i	1.82360	−	0.309441i
$999$	1.05926e6			0.0335806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.13	✓	56
4.3	odd	2		160.6.o.a.143.11		56
5.2	odd	4	inner	40.6.k.a.27.27	yes	56
8.3	odd	2	inner	40.6.k.a.3.27	yes	56
8.5	even	2		160.6.o.a.143.12		56
20.7	even	4		160.6.o.a.47.12		56
40.27	even	4	inner	40.6.k.a.27.13	yes	56
40.37	odd	4		160.6.o.a.47.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.13	✓	56	1.1	even	1	trivial
40.6.k.a.3.27	yes	56	8.3	odd	2	inner
40.6.k.a.27.13	yes	56	40.27	even	4	inner
40.6.k.a.27.27	yes	56	5.2	odd	4	inner
160.6.o.a.47.11		56	40.37	odd	4
160.6.o.a.47.12		56	20.7	even	4
160.6.o.a.143.11		56	4.3	odd	2
160.6.o.a.143.12		56	8.5	even	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.946365 - 5.57713i) q^{2} +(4.45554 + 4.45554i) q^{3} +(-30.2088 + 10.5560i) q^{4} +(49.9881 - 25.0237i) q^{5} +(20.6326 - 29.0657i) q^{6} +(-169.279 - 169.279i) q^{7} +(87.4607 + 158.489i) q^{8} -203.296i q^{9} +O(q^{10})\)	\(q+(-0.946365 - 5.57713i) q^{2} +(4.45554 + 4.45554i) q^{3} +(-30.2088 + 10.5560i) q^{4} +(49.9881 - 25.0237i) q^{5} +(20.6326 - 29.0657i) q^{6} +(-169.279 - 169.279i) q^{7} +(87.4607 + 158.489i) q^{8} -203.296i q^{9} +(-186.868 - 255.109i) q^{10} -207.026 q^{11} +(-181.629 - 87.5639i) q^{12} +(-249.136 + 249.136i) q^{13} +(-783.891 + 1104.29i) q^{14} +(334.219 + 111.230i) q^{15} +(801.142 - 637.768i) q^{16} +(-424.145 + 424.145i) q^{17} +(-1133.81 + 192.392i) q^{18} -2282.02i q^{19} +(-1245.93 + 1283.61i) q^{20} -1508.46i q^{21} +(195.922 + 1154.61i) q^{22} +(351.205 - 351.205i) q^{23} +(-316.468 + 1095.84i) q^{24} +(1872.62 - 2501.78i) q^{25} +(1625.24 + 1153.69i) q^{26} +(1988.49 - 1988.49i) q^{27} +(6900.62 + 3326.80i) q^{28} +7256.22 q^{29} +(304.051 - 1969.25i) q^{30} +7244.36i q^{31} +(-4315.09 - 3864.51i) q^{32} +(-922.415 - 922.415i) q^{33} +(2766.91 + 1964.11i) q^{34} +(-12697.9 - 4225.95i) q^{35} +(2146.00 + 6141.33i) q^{36} +(266.347 + 266.347i) q^{37} +(-12727.1 + 2159.62i) q^{38} -2220.08 q^{39} +(8337.97 + 5733.95i) q^{40} +16812.6 q^{41} +(-8412.88 + 1427.55i) q^{42} +(-4601.16 - 4601.16i) q^{43} +(6254.01 - 2185.37i) q^{44} +(-5087.23 - 10162.4i) q^{45} +(-2291.08 - 1626.35i) q^{46} +(-5614.39 - 5614.39i) q^{47} +(6411.13 + 727.919i) q^{48} +40503.7i q^{49} +(-15724.9 - 8076.28i) q^{50} -3779.59 q^{51} +(4896.23 - 10156.0i) q^{52} +(937.132 - 937.132i) q^{53} +(-12971.9 - 9208.25i) q^{54} +(-10348.9 + 5180.57i) q^{55} +(12023.5 - 41634.0i) q^{56} +(10167.6 - 10167.6i) q^{57} +(-6867.03 - 40468.9i) q^{58} +16983.7i q^{59} +(-11270.5 + 167.892i) q^{60} -27237.2i q^{61} +(40402.7 - 6855.81i) q^{62} +(-34413.8 + 34413.8i) q^{63} +(-17469.2 + 27723.1i) q^{64} +(-6219.54 + 18688.2i) q^{65} +(-4271.49 + 6017.37i) q^{66} +(-7571.99 + 7571.99i) q^{67} +(8335.62 - 17290.2i) q^{68} +3129.62 q^{69} +(-11551.8 + 74817.3i) q^{70} -17125.0i q^{71} +(32220.1 - 17780.4i) q^{72} +(15977.8 + 15977.8i) q^{73} +(1233.39 - 1737.52i) q^{74} +(19490.4 - 2803.23i) q^{75} +(24089.0 + 68937.0i) q^{76} +(35045.2 + 35045.2i) q^{77} +(2101.00 + 12381.7i) q^{78} +72486.1 q^{79} +(24088.2 - 51928.4i) q^{80} -31681.3 q^{81} +(-15910.9 - 93766.2i) q^{82} +(-58657.5 - 58657.5i) q^{83} +(15923.3 + 45568.8i) q^{84} +(-10588.5 + 31815.9i) q^{85} +(-21306.9 + 30015.6i) q^{86} +(32330.4 + 32330.4i) q^{87} +(-18106.7 - 32811.3i) q^{88} -34335.8i q^{89} +(-51862.6 + 37989.5i) q^{90} +84347.1 q^{91} +(-6902.16 + 14316.8i) q^{92} +(-32277.6 + 32277.6i) q^{93} +(-25998.9 + 36625.4i) q^{94} +(-57104.6 - 114074. i) q^{95} +(-2007.57 - 36444.6i) q^{96} +(62650.0 - 62650.0i) q^{97} +(225895. - 38331.3i) q^{98} +42087.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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