LMFDB - Embedded newform 30.6.e.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,6,Mod(17,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("30.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	30.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:	$4.81151459439$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1126 x^{18} + 420245 x^{16} + 66878446 x^{14} + 5652274660 x^{12} + 280235806770 x^{10} + \cdots + 87\!\cdots\!24 $ x^20 + 1126x^18 + 420245x^16 + 66878446x^14 + 5652274660x^12 + 280235806770x^10 + 8434804524517x^8 + 152000977499746x^6 + 1527059794861601x^4 + 7117033734175912*x^2 + 8701432272235024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{25}\cdot 3^{14}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.5
Root			$-23.6117i$ of defining polynomial
Character	$\chi$	$=$	30.17
Dual form			30.6.e.a.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 + 2.82843i) q^{2} +(14.1646 + 6.50878i) q^{3} -16.0000i q^{4} +(55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 + 1.93288i) q^{7} +(45.2548 + 45.2548i) q^{8} +(158.272 + 184.389i) q^{9} +O(q^{10})$	\(q+(-2.82843 + 2.82843i) q^{2} +(14.1646 + 6.50878i) q^{3} -16.0000i q^{4} +(55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 + 1.93288i) q^{7} +(45.2548 + 45.2548i) q^{8} +(158.272 + 184.389i) q^{9} +(-138.214 + 175.775i) q^{10} +615.555i q^{11} +(104.141 - 226.634i) q^{12} +(211.952 - 211.952i) q^{13} -10.9340 q^{14} +(829.437 + 267.224i) q^{15} -256.000 q^{16} +(-272.840 + 272.840i) q^{17} +(-969.189 - 73.8700i) q^{18} -2042.57i q^{19} +(-106.239 - 888.095i) q^{20} +(14.7978 + 39.9593i) q^{21} +(-1741.05 - 1741.05i) q^{22} +(-2977.03 - 2977.03i) q^{23} +(346.463 + 935.570i) q^{24} +(3036.82 - 737.114i) q^{25} +1198.98i q^{26} +(1041.71 + 3641.94i) q^{27} +(30.9262 - 30.9262i) q^{28} +3178.83 q^{29} +(-3101.83 + 1590.18i) q^{30} +1657.55 q^{31} +(724.077 - 724.077i) q^{32} +(-4006.52 + 8719.09i) q^{33} -1543.42i q^{34} +(120.121 + 94.4523i) q^{35} +(2950.22 - 2532.34i) q^{36} +(-9486.85 - 9486.85i) q^{37} +(5777.25 + 5777.25i) q^{38} +(4381.76 - 1622.66i) q^{39} +(2812.40 + 2211.42i) q^{40} +1391.07i q^{41} +(-154.876 - 71.1673i) q^{42} +(-11513.8 + 11513.8i) q^{43} +9848.89 q^{44} +(10009.3 + 9183.74i) q^{45} +16840.6 q^{46} +(4029.48 - 4029.48i) q^{47} +(-3626.14 - 1666.25i) q^{48} -16799.5i q^{49} +(-6504.56 + 10674.3i) q^{50} +(-5640.53 + 2088.81i) q^{51} +(-3391.23 - 3391.23i) q^{52} +(-20105.3 - 20105.3i) q^{53} +(-13247.4 - 7354.58i) q^{54} +(4087.26 + 34167.0i) q^{55} +174.945i q^{56} +(13294.6 - 28932.1i) q^{57} +(-8991.10 + 8991.10i) q^{58} -36465.5 q^{59} +(4275.58 - 13271.0i) q^{60} +16657.4 q^{61} +(-4688.26 + 4688.26i) q^{62} +(-50.4811 + 662.322i) q^{63} +4096.00i q^{64} +(10357.2 - 13171.9i) q^{65} +(-13329.2 - 35993.5i) q^{66} +(8472.23 + 8472.23i) q^{67} +(4365.44 + 4365.44i) q^{68} +(-22791.6 - 61545.2i) q^{69} +(-606.905 + 72.6016i) q^{70} +42867.4i q^{71} +(-1181.92 + 15507.0i) q^{72} +(22731.5 - 22731.5i) q^{73} +53665.7 q^{74} +(47813.1 + 9325.09i) q^{75} -32681.1 q^{76} +(-1189.80 + 1189.80i) q^{77} +(-7803.89 + 16983.1i) q^{78} +77720.3i q^{79} +(-14209.5 + 1699.83i) q^{80} +(-8949.25 + 58366.9i) q^{81} +(-3934.53 - 3934.53i) q^{82} +(-247.467 - 247.467i) q^{83} +(639.348 - 236.765i) q^{84} +(-13332.6 + 16955.9i) q^{85} -65132.1i q^{86} +(45026.9 + 20690.3i) q^{87} +(-27856.9 + 27856.9i) q^{88} +109920. q^{89} +(-54286.3 + 2335.15i) q^{90} +819.356 q^{91} +(-47632.5 + 47632.5i) q^{92} +(23478.6 + 10788.6i) q^{93} +22794.2i q^{94} +(-13562.6 - 113375. i) q^{95} +(14969.1 - 5543.40i) q^{96} +(-39430.4 - 39430.4i) q^{97} +(47516.2 + 47516.2i) q^{98} +(-113501. + 97424.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} + 80 q^{6} + 76 q^{7}+O(q^{10}) $ 20 * q - 4 * q^3 + 80 * q^6 + 76 * q^7	$ 20 q - 4 q^{3} + 80 q^{6} + 76 q^{7} - 496 q^{10} + 64 q^{12} + 2640 q^{13} + 3128 q^{15} - 5120 q^{16} - 2272 q^{18} - 760 q^{21} - 464 q^{22} - 15776 q^{25} + 16556 q^{27} + 1216 q^{28} + 3408 q^{30} + 23960 q^{31} - 7684 q^{33} - 13120 q^{36} - 60696 q^{37} - 512 q^{40} + 46864 q^{42} + 48024 q^{43} + 31912 q^{45} + 58880 q^{46} + 1024 q^{48} - 155240 q^{51} - 42240 q^{52} - 132228 q^{55} + 167744 q^{57} + 38000 q^{58} + 19136 q^{60} + 160680 q^{61} - 219364 q^{63} - 158560 q^{66} - 118736 q^{67} - 55216 q^{70} + 36352 q^{72} + 379100 q^{73} + 365548 q^{75} + 78080 q^{76} - 25440 q^{78} - 282260 q^{81} - 262976 q^{82} - 227432 q^{85} + 249380 q^{87} - 7424 q^{88} - 128992 q^{90} + 499200 q^{91} - 304072 q^{93} - 20480 q^{96} - 288228 q^{97}+O(q^{100}) $ 20 * q - 4 * q^3 + 80 * q^6 + 76 * q^7 - 496 * q^10 + 64 * q^12 + 2640 * q^13 + 3128 * q^15 - 5120 * q^16 - 2272 * q^18 - 760 * q^21 - 464 * q^22 - 15776 * q^25 + 16556 * q^27 + 1216 * q^28 + 3408 * q^30 + 23960 * q^31 - 7684 * q^33 - 13120 * q^36 - 60696 * q^37 - 512 * q^40 + 46864 * q^42 + 48024 * q^43 + 31912 * q^45 + 58880 * q^46 + 1024 * q^48 - 155240 * q^51 - 42240 * q^52 - 132228 * q^55 + 167744 * q^57 + 38000 * q^58 + 19136 * q^60 + 160680 * q^61 - 219364 * q^63 - 158560 * q^66 - 118736 * q^67 - 55216 * q^70 + 36352 * q^72 + 379100 * q^73 + 365548 * q^75 + 78080 * q^76 - 25440 * q^78 - 282260 * q^81 - 262976 * q^82 - 227432 * q^85 + 249380 * q^87 - 7424 * q^88 - 128992 * q^90 + 499200 * q^91 - 304072 * q^93 - 20480 * q^96 - 288228 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$3$	14.1646	+	6.50878i	0.908659	+	0.417539i
$3$	14.1646	+	6.50878i	0.908659	+	0.417539i
$4$		−	16.0000i		−	0.500000i
$5$	55.5060	−	6.63996i	0.992921	−	0.118779i
$5$	55.5060	−	6.63996i	0.992921	−	0.118779i
$6$	−58.4731	+	21.6539i	−0.663099	+	0.245560i
$7$	1.93288	+	1.93288i	0.0149094	+	0.0149094i	0.714522	−	0.699613i	$-0.246644\pi$
$7$	1.93288	+	1.93288i	0.0149094	+	0.0149094i	−0.699613	+	0.714522i	$0.746644\pi$
$8$	45.2548	+	45.2548i	0.250000	+	0.250000i
$9$	158.272	+	184.389i	0.651323	+	0.758800i
$10$	−138.214	+	175.775i	−0.437071	+	0.555850i
$11$			615.555i			1.53386i	0.641731	+	0.766929i	$0.278216\pi$
$11$			615.555i			1.53386i	−0.641731	+	0.766929i	$0.721784\pi$
$12$	104.141	−	226.634i	0.208769	−	0.454330i
$13$	211.952	−	211.952i	0.347839	−	0.347839i	−0.511465	−	0.859304i	$-0.670897\pi$
$13$	211.952	−	211.952i	0.347839	−	0.347839i	0.859304	+	0.511465i	$0.170897\pi$
$14$	−10.9340			−0.0149094
$15$	829.437	+	267.224i	0.951821	+	0.306653i
$16$	−256.000			−0.250000
$17$	−272.840	+	272.840i	−0.228974	+	0.228974i	−0.812264	−	0.583290i	$-0.801765\pi$
$17$	−272.840	+	272.840i	−0.228974	+	0.228974i	0.583290	+	0.812264i	$0.301765\pi$
$18$	−969.189	−	73.8700i	−0.705062	−	0.0537387i
$19$		−	2042.57i		−	1.29805i	−0.760766	−	0.649026i	$-0.775177\pi$
$19$		−	2042.57i		−	1.29805i	0.760766	−	0.649026i	$-0.224823\pi$
$20$	−106.239	−	888.095i	−0.0593896	−	0.496460i
$21$	14.7978	+	39.9593i	0.00732233	+	0.0197728i
$22$	−1741.05	−	1741.05i	−0.766929	−	0.766929i
$23$	−2977.03	−	2977.03i	−1.17345	−	1.17345i	−0.981382	−	0.192065i	$-0.938482\pi$
$23$	−2977.03	−	2977.03i	−1.17345	−	1.17345i	−0.192065	−	0.981382i	$-0.561518\pi$
$24$	346.463	+	935.570i	0.122780	+	0.331549i
$25$	3036.82	−	737.114i	0.971783	−	0.235877i
$26$			1198.98i			0.347839i
$27$	1041.71	+	3641.94i	0.275002	+	0.961444i
$28$	30.9262	−	30.9262i	0.00745471	−	0.00745471i
$29$	3178.83			0.701896			0.350948	−	0.936395i	$-0.385859\pi$
$29$	3178.83			0.701896			0.350948	+	0.936395i	$0.385859\pi$
$30$	−3101.83	+	1590.18i	−0.629237	+	0.322584i
$31$	1657.55			0.309787			0.154893	−	0.987931i	$-0.450497\pi$
$31$	1657.55			0.309787			0.154893	+	0.987931i	$0.450497\pi$
$32$	724.077	−	724.077i	0.125000	−	0.125000i
$33$	−4006.52	+	8719.09i	−0.640445	+	1.39376i
$34$		−	1543.42i		−	0.228974i
$35$	120.121	+	94.4523i	0.0165748	+	0.0130329i
$36$	2950.22	−	2532.34i	0.379400	−	0.325662i
$37$	−9486.85	−	9486.85i	−1.13925	−	1.13925i	−0.988585	−	0.150661i	$-0.951860\pi$
$37$	−9486.85	−	9486.85i	−1.13925	−	1.13925i	−0.150661	−	0.988585i	$-0.548140\pi$
$38$	5777.25	+	5777.25i	0.649026	+	0.649026i
$39$	4381.76	−	1622.66i	0.461303	−	0.170831i
$40$	2812.40	+	2211.42i	0.277925	+	0.218535i
$41$			1391.07i			0.129237i	0.997910	+	0.0646187i	$0.0205831\pi$
$41$			1391.07i			0.129237i	−0.997910	+	0.0646187i	$0.979417\pi$
$42$	−154.876	−	71.1673i	−0.0135476	−	0.00622526i
$43$	−11513.8	+	11513.8i	−0.949617	+	0.949617i	−0.998790	−	0.0491729i	$-0.984341\pi$
$43$	−11513.8	+	11513.8i	−0.949617	+	0.949617i	0.0491729	+	0.998790i	$0.484341\pi$
$44$	9848.89			0.766929
$45$	10009.3	+	9183.74i	0.736842	+	0.676065i
$46$	16840.6			1.17345
$47$	4029.48	−	4029.48i	0.266075	−	0.266075i	−0.561441	−	0.827517i	$-0.689753\pi$
$47$	4029.48	−	4029.48i	0.266075	−	0.266075i	0.827517	+	0.561441i	$0.189753\pi$
$48$	−3626.14	−	1666.25i	−0.227165	−	0.104385i
$49$		−	16799.5i		−	0.999555i
$50$	−6504.56	+	10674.3i	−0.367953	+	0.603830i
$51$	−5640.53	+	2088.81i	−0.303665	+	0.112454i
$52$	−3391.23	−	3391.23i	−0.173920	−	0.173920i
$53$	−20105.3	−	20105.3i	−0.983151	−	0.983151i	0.0167091	−	0.999860i	$-0.494681\pi$
$53$	−20105.3	−	20105.3i	−0.983151	−	0.983151i	−0.999860	+	0.0167091i	$0.994681\pi$
$54$	−13247.4	−	7354.58i	−0.618223	−	0.343221i
$55$	4087.26	+	34167.0i	0.182190	+	1.52300i
$56$			174.945i			0.00745471i
$57$	13294.6	−	28932.1i	0.541987	−	1.17949i
$58$	−8991.10	+	8991.10i	−0.350948	+	0.350948i
$59$	−36465.5			−1.36381			−0.681903	−	0.731443i	$-0.738847\pi$
$59$	−36465.5			−1.36381			−0.681903	+	0.731443i	$0.738847\pi$
$60$	4275.58	−	13271.0i	0.153326	−	0.475911i
$61$	16657.4			0.573170			0.286585	−	0.958055i	$-0.407480\pi$
$61$	16657.4			0.573170			0.286585	+	0.958055i	$0.407480\pi$
$62$	−4688.26	+	4688.26i	−0.154893	+	0.154893i
$63$	−50.4811	+	662.322i	−0.00160243	+	0.0210241i
$64$			4096.00i			0.125000i
$65$	10357.2	−	13171.9i	0.304061	−	0.386693i
$66$	−13329.2	−	35993.5i	−0.376655	−	1.01710i
$67$	8472.23	+	8472.23i	0.230574	+	0.230574i	0.812932	−	0.582358i	$-0.197870\pi$
$67$	8472.23	+	8472.23i	0.230574	+	0.230574i	−0.582358	+	0.812932i	$0.697870\pi$
$68$	4365.44	+	4365.44i	0.114487	+	0.114487i
$69$	−22791.6	−	61545.2i	−0.576304	−	1.55622i
$70$	−606.905	+	72.6016i	−0.0148039	+	0.00177093i
$71$			42867.4i			1.00921i	0.863350	+	0.504605i	$0.168362\pi$
$71$			42867.4i			1.00921i	−0.863350	+	0.504605i	$0.831638\pi$
$72$	−1181.92	+	15507.0i	−0.0268693	+	0.352531i
$73$	22731.5	−	22731.5i	0.499254	−	0.499254i	−0.411952	−	0.911206i	$-0.635153\pi$
$73$	22731.5	−	22731.5i	0.499254	−	0.499254i	0.911206	+	0.411952i	$0.135153\pi$
$74$	53665.7			1.13925
$75$	47813.1	+	9325.09i	0.981507	+	0.191425i
$76$	−32681.1			−0.649026
$77$	−1189.80	+	1189.80i	−0.0228690	+	0.0228690i
$78$	−7803.89	+	16983.1i	−0.145236	+	0.316067i
$79$			77720.3i			1.40109i	0.713607	+	0.700547i	$0.247060\pi$
$79$			77720.3i			1.40109i	−0.713607	+	0.700547i	$0.752940\pi$
$80$	−14209.5	+	1699.83i	−0.248230	+	0.0296948i
$81$	−8949.25	+	58366.9i	−0.151556	+	0.988449i
$82$	−3934.53	−	3934.53i	−0.0646187	−	0.0646187i
$83$	−247.467	−	247.467i	−0.00394296	−	0.00394296i	0.705133	−	0.709076i	$-0.250887\pi$
$83$	−247.467	−	247.467i	−0.00394296	−	0.00394296i	−0.709076	+	0.705133i	$0.750887\pi$
$84$	639.348	−	236.765i	0.00988642	−	0.00366116i
$85$	−13332.6	+	16955.9i	−0.200156	+	0.254550i
$86$		−	65132.1i		−	0.949617i
$87$	45026.9	+	20690.3i	0.637785	+	0.293069i
$88$	−27856.9	+	27856.9i	−0.383465	+	0.383465i
$89$	109920.			1.47096			0.735482	−	0.677544i	$-0.236956\pi$
$89$	109920.			1.47096			0.735482	+	0.677544i	$0.236956\pi$
$90$	−54286.3	+	2335.15i	−0.706453	+	0.0303884i
$91$	819.356			0.0103722
$92$	−47632.5	+	47632.5i	−0.586724	+	0.586724i
$93$	23478.6	+	10788.6i	0.281491	+	0.129348i
$94$			22794.2i			0.266075i
$95$	−13562.6	−	113375.i	−0.154182	−	1.28886i
$96$	14969.1	−	5543.40i	0.165775	−	0.0613901i
$97$	−39430.4	−	39430.4i	−0.425502	−	0.425502i	0.461591	−	0.887093i	$-0.347279\pi$
$97$	−39430.4	−	39430.4i	−0.425502	−	0.425502i	−0.887093	+	0.461591i	$0.847279\pi$
$98$	47516.2	+	47516.2i	0.499778	+	0.499778i
$99$	−113501.	+	97424.9i	−1.16389	+	0.999038i
$100$	−11793.8	−	48589.2i	−0.117938	−	0.485892i
$101$			78317.6i			0.763934i	0.924176	+	0.381967i	$0.124753\pi$
$101$			78317.6i			0.763934i	−0.924176	+	0.381967i	$0.875247\pi$
$102$	10045.8	−	21861.9i	0.0956054	−	0.208059i
$103$	119058.	−	119058.i	1.10578	−	1.10578i	0.112075	−	0.993700i	$-0.464250\pi$
$103$	119058.	−	119058.i	1.10578	−	1.10578i	0.993700	−	0.112075i	$-0.0357498\pi$
$104$	19183.7			0.173920
$105$	1086.69	+	2119.72i	0.00961909	+	0.0187631i
$106$	113733.			0.983151
$107$	−79786.7	+	79786.7i	−0.673707	+	0.673707i	−0.958569	−	0.284862i	$-0.908052\pi$
$107$	−79786.7	+	79786.7i	−0.673707	+	0.673707i	0.284862	+	0.958569i	$0.408052\pi$
$108$	58271.1	−	16667.3i	0.480722	−	0.137501i
$109$		−	34102.3i		−	0.274927i	−0.990507	−	0.137464i	$-0.956105\pi$
$109$		−	34102.3i		−	0.274927i	0.990507	−	0.137464i	$-0.0438950\pi$
$110$	−108199.	−	85078.3i	−0.852595	−	0.670405i
$111$	−72629.6	−	196125.i	−0.559508	−	1.51087i
$112$	−494.819	−	494.819i	−0.00372736	−	0.00372736i
$113$	−103180.	−	103180.i	−0.760150	−	0.760150i	0.216199	−	0.976349i	$-0.430634\pi$
$113$	−103180.	−	103180.i	−0.760150	−	0.760150i	−0.976349	+	0.216199i	$0.930634\pi$
$114$	44229.6	+	119435.i	0.318750	+	0.860737i
$115$	−185010.	−	145475.i	−1.30452	−	1.02576i
$116$		−	50861.4i		−	0.350948i
$117$	72627.3	+	5535.54i	0.490496	+	0.0373848i
$118$	103140.	−	103140.i	0.681903	−	0.681903i
$119$	−1054.74			−0.00682774
$120$	25442.9	+	49629.2i	0.161292	+	0.314619i
$121$	−217857.			−1.35272
$122$	−47114.3	+	47114.3i	−0.286585	+	0.286585i
$123$	−9054.15	+	19703.9i	−0.0539616	+	0.117433i
$124$		−	26520.8i		−	0.154893i
$125$	163667.	−	61078.6i	0.936886	−	0.349634i
$126$	−1730.55	−	2016.11i	−0.00971085	−	0.0113133i
$127$	167198.	+	167198.i	0.919861	+	0.919861i	0.997019	−	0.0771578i	$-0.0245845\pi$
$127$	167198.	+	167198.i	0.919861	+	0.919861i	−0.0771578	+	0.997019i	$0.524585\pi$
$128$	−11585.2	−	11585.2i	−0.0625000	−	0.0625000i
$129$	−238030.	+	88147.7i	−1.25938	+	0.466377i
$130$	7961.17	+	66550.5i	0.0413160	+	0.345377i
$131$			238726.i			1.21541i	0.794164	+	0.607704i	$0.207909\pi$
$131$			238726.i			1.21541i	−0.794164	+	0.607704i	$0.792091\pi$
$132$	139505.	+	64104.2i	0.696878	+	0.320223i
$133$	3948.05	−	3948.05i	0.0193532	−	0.0193532i
$134$	−47926.2			−0.230574
$135$	82003.3	+	195233.i	0.387255	+	0.921973i
$136$	−24694.7			−0.114487
$137$	−15989.0	+	15989.0i	−0.0727812	+	0.0727812i	−0.742560	−	0.669779i	$-0.766389\pi$
$137$	−15989.0	+	15989.0i	−0.0727812	+	0.0727812i	0.669779	+	0.742560i	$0.266389\pi$
$138$	238541.	+	109612.i	1.06626	+	0.489959i
$139$		−	61223.8i		−	0.268772i	−0.990929	−	0.134386i	$-0.957094\pi$
$139$		−	61223.8i		−	0.268772i	0.990929	−	0.134386i	$-0.0429062\pi$
$140$	1511.24	−	1921.93i	0.00651647	−	0.00828740i
$141$	83303.0	−	30849.0i	0.352868	−	0.130675i
$142$	−121247.	−	121247.i	−0.504605	−	0.504605i
$143$	130468.	+	130468.i	0.533536	+	0.533536i
$144$	−40517.5	−	47203.5i	−0.162831	−	0.189700i
$145$	176444.	−	21107.3i	0.696927	−	0.0833707i
$146$			128589.i			0.499254i
$147$	109344.	−	237959.i	0.417353	−	0.908255i
$148$	−151790.	+	151790.i	−0.569623	+	0.569623i
$149$	259868.			0.958930			0.479465	−	0.877561i	$-0.340831\pi$
$149$	259868.			0.958930			0.479465	+	0.877561i	$0.340831\pi$
$150$	−161611.	+	108860.i	−0.586466	+	0.395041i
$151$	−186012.			−0.663894			−0.331947	−	0.943298i	$-0.607705\pi$
$151$	−186012.			−0.663894			−0.331947	+	0.943298i	$0.607705\pi$
$152$	92436.0	−	92436.0i	0.324513	−	0.324513i
$153$	−93491.4	−	7125.76i	−0.322881	−	0.0246095i
$154$		−	6730.51i		−	0.0228690i
$155$	92004.0	−	11006.1i	0.307594	−	0.0367962i
$156$	−25962.6	−	70108.1i	−0.0854155	−	0.230652i
$157$	157614.	+	157614.i	0.510324	+	0.510324i	0.914626	−	0.404302i	$-0.132485\pi$
$157$	157614.	+	157614.i	0.510324	+	0.510324i	−0.404302	+	0.914626i	$0.632485\pi$
$158$	−219826.	−	219826.i	−0.700547	−	0.700547i
$159$	−153922.	−	415644.i	−0.482846	−	1.30385i
$160$	35382.8	−	44998.4i	0.109268	−	0.138962i
$161$		−	11508.5i		−	0.0349908i
$162$	−139774.	−	190399.i	−0.418446	−	0.570002i
$163$	64473.4	−	64473.4i	0.190069	−	0.190069i	−0.605657	−	0.795726i	$-0.707090\pi$
$163$	64473.4	−	64473.4i	0.190069	−	0.190069i	0.795726	+	0.605657i	$0.207090\pi$
$164$	22257.1			0.0646187
$165$	−164491.	+	510565.i	−0.470362	+	1.45996i
$166$	1399.89			0.00394296
$167$	−100742.	+	100742.i	−0.279523	+	0.279523i	−0.832919	−	0.553396i	$-0.813332\pi$
$167$	−100742.	+	100742.i	−0.279523	+	0.279523i	0.553396	+	0.832919i	$0.313332\pi$
$168$	−1138.68	+	2478.02i	−0.00311263	+	0.00677379i
$169$			281446.i			0.758016i
$170$	−10248.2	−	85668.8i	−0.0271973	−	0.227353i
$171$	376626.	−	323280.i	0.984963	−	0.845451i
$172$	184221.	+	184221.i	0.474809	+	0.474809i
$173$	−114178.	−	114178.i	−0.290047	−	0.290047i	0.547052	−	0.837099i	$-0.315750\pi$
$173$	−114178.	−	114178.i	−0.290047	−	0.290047i	−0.837099	+	0.547052i	$0.815750\pi$
$174$	−185876.	+	68834.2i	−0.465427	+	0.172358i
$175$	7294.58	+	4445.07i	0.0180055	+	0.0109719i
$176$		−	157582.i		−	0.383465i
$177$	−516520.	−	237346.i	−1.23923	−	0.569442i
$178$	−310901.	+	310901.i	−0.735482	+	0.735482i
$179$	15895.1			0.0370792			0.0185396	−	0.999828i	$-0.494098\pi$
$179$	15895.1			0.0370792			0.0185396	+	0.999828i	$0.494098\pi$
$180$	146940.	−	160150.i	0.338033	−	0.368421i
$181$	751524.			1.70509			0.852543	−	0.522657i	$-0.175059\pi$
$181$	751524.			1.70509			0.852543	+	0.522657i	$0.175059\pi$
$182$	−2317.49	+	2317.49i	−0.00518608	+	0.00518608i
$183$	235946.	+	108420.i	0.520816	+	0.239320i
$184$		−	269450.i		−	0.586724i
$185$	−589569.	−	463585.i	−1.26650	−	0.995863i
$186$	−96922.3	+	35892.5i	−0.205419	+	0.0760714i
$187$	−167948.	−	167948.i	−0.351214	−	0.351214i
$188$	−64471.7	−	64471.7i	−0.133038	−	0.133038i
$189$	−5025.96	+	9052.96i	−0.0102344	+	0.0184347i
$190$	359032.	+	282311.i	0.721522	+	0.567341i
$191$		−	109522.i		−	0.217229i	−0.994084	−	0.108615i	$-0.965359\pi$
$191$		−	109522.i		−	0.217229i	0.994084	−	0.108615i	$-0.0346415\pi$
$192$	−26660.0	+	58018.2i	−0.0521923	+	0.113582i
$193$	−613686.	+	613686.i	−1.18591	+	1.18591i	−0.207727	+	0.978187i	$0.566607\pi$
$193$	−613686.	+	613686.i	−1.18591	+	1.18591i	−0.978187	+	0.207727i	$0.933393\pi$
$194$	223052.			0.425502
$195$	232439.	−	119162.i	0.437746	−	0.224415i
$196$	−268792.			−0.499778
$197$	−78711.3	+	78711.3i	−0.144501	+	0.144501i	−0.775657	−	0.631155i	$-0.782581\pi$
$197$	−78711.3	+	78711.3i	−0.144501	+	0.144501i	0.631155	+	0.775657i	$0.282581\pi$
$198$	45471.1	−	596589.i	0.0824275	−	1.08147i
$199$		−	175358.i		−	0.313901i	−0.987606	−	0.156951i	$-0.949834\pi$
$199$		−	175358.i		−	0.313901i	0.987606	−	0.156951i	$-0.0501663\pi$
$200$	170789.	+	104073.i	0.301915	+	0.183977i
$201$	64861.8	+	175150.i	0.113240	+	0.305787i
$202$	−221516.	−	221516.i	−0.381967	−	0.381967i
$203$	6144.32	+	6144.32i	0.0104649	+	0.0104649i
$204$	33421.0	+	90248.4i	0.0562269	+	0.151832i
$205$	9236.63	+	77212.5i	0.0153507	+	0.128323i
$206$			673496.i			1.10578i
$207$	77751.0	−	1.02011e6i	0.126119	−	1.65471i
$208$	−54259.6	+	54259.6i	−0.0869598	+	0.0869598i
$209$	1.25731e6			1.99103
$210$	−9069.11	−	2921.84i	−0.0141911	−	0.00457202i
$211$	−137396.			−0.212456			−0.106228	−	0.994342i	$-0.533877\pi$
$211$	−137396.			−0.212456			−0.106228	+	0.994342i	$0.533877\pi$
$212$	−321684.	+	321684.i	−0.491576	+	0.491576i
$213$	−279015.	+	607200.i	−0.421384	+	0.917028i
$214$		−	451342.i		−	0.673707i
$215$	−562635.	+	715537.i	−0.830100	+	1.05569i
$216$	−117673.	+	211958.i	−0.171610	+	0.309111i
$217$	3203.86	+	3203.86i	0.00461874	+	0.00461874i
$218$	96455.9	+	96455.9i	0.137464	+	0.137464i
$219$	469938.	−	174028.i	0.662110	−	0.245194i
$220$	546672.	−	65396.2i	0.761500	−	0.0910952i
$221$			115658.i			0.159292i
$222$	760154.	+	349299.i	1.03519	+	0.475679i
$223$	−74950.4	+	74950.4i	−0.100928	+	0.100928i	−0.755768	−	0.654840i	$-0.772736\pi$
$223$	−74950.4	+	74950.4i	−0.100928	+	0.100928i	0.654840	+	0.755768i	$0.272736\pi$
$224$	2799.12			0.00372736
$225$	616558.	+	443291.i	0.811928	+	0.583758i
$226$	583674.			0.760150
$227$	−240353.	+	240353.i	−0.309588	+	0.309588i	−0.844750	−	0.535162i	$-0.820251\pi$
$227$	−240353.	+	240353.i	−0.309588	+	0.309588i	0.535162	+	0.844750i	$0.320251\pi$
$228$	−462914.	−	212714.i	−0.589744	−	0.270993i
$229$			151951.i			0.191476i	0.995407	+	0.0957378i	$0.0305210\pi$
$229$			151951.i			0.191476i	−0.995407	+	0.0957378i	$0.969479\pi$
$230$	934755.	−	111821.i	1.16514	−	0.139381i
$231$	−24597.1	+	9108.87i	−0.0303288	+	0.0112314i
$232$	143858.	+	143858.i	0.175474	+	0.175474i
$233$	−269671.	−	269671.i	−0.325420	−	0.325420i	0.525422	−	0.850842i	$-0.323907\pi$
$233$	−269671.	−	269671.i	−0.325420	−	0.325420i	−0.850842	+	0.525422i	$0.823907\pi$
$234$	−221078.	+	189764.i	−0.263940	+	0.226556i
$235$	196905.	−	250416.i	0.232587	−	0.295796i
$236$			583449.i			0.681903i
$237$	−505865.	+	1.10088e6i	−0.585010	+	1.27312i
$238$	2983.25	−	2983.25i	0.00341387	−	0.00341387i
$239$	−995618.			−1.12745			−0.563726	−	0.825962i	$-0.690633\pi$
$239$	−995618.			−1.12745			−0.563726	+	0.825962i	$0.690633\pi$
$240$	−212336.	−	68409.3i	−0.237955	−	0.0766632i
$241$	−1.63448e6			−1.81275			−0.906373	−	0.422478i	$-0.861160\pi$
$241$	−1.63448e6			−1.81275			−0.906373	+	0.422478i	$0.861160\pi$
$242$	616194.	−	616194.i	0.676362	−	0.676362i
$243$	−506660.	+	768495.i	−0.550428	+	0.834882i
$244$		−	266519.i		−	0.286585i
$245$	−111548.	−	932474.i	−0.118726	−	0.992479i
$246$	−30122.0	−	81340.1i	−0.0317356	−	0.0856972i
$247$	−432925.	−	432925.i	−0.451513	−	0.451513i
$248$	75012.2	+	75012.2i	0.0774467	+	0.0774467i
$249$	−1894.56	−	5115.99i	−0.00193647	−	0.00522915i
$250$	−290165.	+	635677.i	−0.293626	+	0.643260i
$251$		−	1.42939e6i		−	1.43207i	−0.698062	−	0.716037i	$-0.745954\pi$
$251$		−	1.42939e6i		−	1.43207i	0.698062	−	0.716037i	$-0.254046\pi$
$252$	10597.2	+	807.698i	0.0105121	+	0.000801213i
$253$	1.83253e6	−	1.83253e6i	1.79990	−	1.79990i
$254$	−945816.			−0.919861
$255$	−299213.	+	153394.i	−0.288158	+	0.147727i
$256$	65536.0			0.0625000
$257$	399795.	−	399795.i	0.377576	−	0.377576i	−0.492651	−	0.870227i	$-0.663972\pi$
$257$	399795.	−	399795.i	0.377576	−	0.377576i	0.870227	+	0.492651i	$0.163972\pi$
$258$	423930.	−	922569.i	0.396502	−	0.862879i
$259$		−	36674.0i		−	0.0339710i
$260$	−210751.	−	165716.i	−0.193346	−	0.152030i
$261$	503119.	+	586141.i	0.457161	+	0.532599i
$262$	−675220.	−	675220.i	−0.607704	−	0.607704i
$263$	33111.1	+	33111.1i	0.0295178	+	0.0295178i	0.721712	−	0.692194i	$-0.243356\pi$
$263$	33111.1	+	33111.1i	0.0295178	+	0.0295178i	−0.692194	+	0.721712i	$0.743356\pi$
$264$	−575895.	+	213267.i	−0.508550	+	0.188327i
$265$	−1.24946e6	−	982464.i	−1.09297	−	0.859413i
$266$			22333.5i			0.0193532i
$267$	1.55697e6	+	715446.i	1.33661	+	0.614184i
$268$	135556.	−	135556.i	0.115287	−	0.115287i
$269$	−764920.			−0.644518			−0.322259	−	0.946652i	$-0.604442\pi$
$269$	−764920.			−0.644518			−0.322259	+	0.946652i	$0.604442\pi$
$270$	−784142.	−	320261.i	−0.654614	−	0.267359i
$271$	2.00900e6			1.66172			0.830859	−	0.556483i	$-0.187850\pi$
$271$	2.00900e6			1.66172			0.830859	+	0.556483i	$0.187850\pi$
$272$	69847.1	−	69847.1i	0.0572435	−	0.0572435i
$273$	11605.8	+	5333.01i	0.00942476	+	0.00433078i
$274$		−	90447.3i		−	0.0727812i
$275$	453735.	+	1.86933e6i	0.361801	+	1.49058i
$276$	−984724.	+	364665.i	−0.778111	+	0.288152i
$277$	484721.	+	484721.i	0.379571	+	0.379571i	0.870947	−	0.491377i	$-0.163506\pi$
$277$	484721.	+	484721.i	0.379571	+	0.379571i	−0.491377	+	0.870947i	$0.663506\pi$
$278$	173167.	+	173167.i	0.134386	+	0.134386i
$279$	262343.	+	305634.i	0.201771	+	0.235066i
$280$	1161.63	+	9710.48i	0.000885464	+	0.00740194i
$281$		−	1.45938e6i		−	1.10256i	−0.834320	−	0.551281i	$-0.814139\pi$
$281$		−	1.45938e6i		−	1.10256i	0.834320	−	0.551281i	$-0.185861\pi$
$282$	−148362.	+	322870.i	−0.111097	+	0.241772i
$283$	57871.0	−	57871.0i	0.0429531	−	0.0429531i	−0.685304	−	0.728257i	$-0.740331\pi$
$283$	57871.0	−	57871.0i	0.0429531	−	0.0429531i	0.728257	+	0.685304i	$0.240331\pi$
$284$	685879.			0.504605
$285$	545822.	−	1.69418e6i	0.398051	−	1.23551i
$286$	−738038.			−0.533536
$287$	−2688.77	+	2688.77i	−0.00192686	+	0.00192686i
$288$	248112.	+	18910.7i	0.176265	+	0.0134347i
$289$			1.27097e6i			0.895142i
$290$	−439359.	+	558760.i	−0.306778	+	0.390149i
$291$	−301872.	−	815159.i	−0.208973	−	0.564300i
$292$	−363705.	−	363705.i	−0.249627	−	0.249627i
$293$	1.67259e6	+	1.67259e6i	1.13821	+	1.13821i	0.988772	+	0.149433i	$0.0477450\pi$
$293$	1.67259e6	+	1.67259e6i	1.13821	+	1.13821i	0.149433	+	0.988772i	$0.452255\pi$
$294$	363775.	+	982321.i	0.245451	+	0.662804i
$295$	−2.02405e6	+	242130.i	−1.35415	+	0.161992i
$296$		−	858652.i		−	0.569623i
$297$	−2.24182e6	+	641229.i	−1.47472	+	0.421815i
$298$	−735017.	+	735017.i	−0.479465	+	0.479465i
$299$	−1.26197e6			−0.816341
$300$	149201.	−	765009.i	0.0957127	−	0.490754i
$301$	−44509.8			−0.0283165
$302$	526121.	−	526121.i	0.331947	−	0.331947i
$303$	−509752.	+	1.10934e6i	−0.318972	+	0.694156i
$304$			522897.i			0.324513i
$305$	924586.	−	110605.i	0.569112	−	0.0680806i
$306$	284588.	−	244279.i	0.173745	−	0.149136i
$307$	2.10290e6	+	2.10290e6i	1.27342	+	1.27342i	0.944280	+	0.329143i	$0.106760\pi$
$307$	2.10290e6	+	2.10290e6i	1.27342	+	1.27342i	0.329143	+	0.944280i	$0.393240\pi$
$308$	19036.8	+	19036.8i	0.0114345	+	0.0114345i
$309$	2.46134e6	−	911489.i	1.46648	−	0.543069i
$310$	−229097.	+	291356.i	−0.135399	+	0.172195i
$311$			1.10864e6i			0.649964i	0.945720	+	0.324982i	$0.105358\pi$
$311$			1.10864e6i			0.649964i	−0.945720	+	0.324982i	$0.894642\pi$
$312$	271729.	+	124862.i	0.158034	+	0.0726181i
$313$	1.15125e6	−	1.15125e6i	0.664214	−	0.664214i	−0.292157	−	0.956370i	$-0.594373\pi$
$313$	1.15125e6	−	1.15125e6i	0.664214	−	0.664214i	0.956370	+	0.292157i	$0.0943728\pi$
$314$	−891600.			−0.510324
$315$	1595.79	+	37098.0i	0.000906148	+	0.0210656i
$316$	1.24353e6			0.700547
$317$	−177254.	+	177254.i	−0.0990715	+	0.0990715i	−0.754905	−	0.655834i	$-0.772317\pi$
$317$	−177254.	+	177254.i	−0.0990715	+	0.0990715i	0.655834	+	0.754905i	$0.272317\pi$
$318$	1.61098e6	+	740261.i	0.893349	+	0.410504i
$319$			1.95675e6i			1.07661i
$320$	27197.3	+	227352.i	0.0148474	+	0.124115i
$321$	−1.64946e6	+	610832.i	−0.893468	+	0.330871i
$322$	32551.0	+	32551.0i	0.0174954	+	0.0174954i
$323$	557294.	+	557294.i	0.297220	+	0.297220i
$324$	933870.	+	143188.i	0.494224	+	0.0757782i
$325$	487427.	−	799892.i	0.255977	−	0.420071i
$326$			364717.i			0.190069i
$327$	221964.	−	483045.i	0.114793	−	0.249815i
$328$	−62952.5	+	62952.5i	−0.0323094	+	0.0323094i
$329$	15577.0			0.00793406
$330$	−978844.	−	1.90935e6i	−0.494799	−	0.965161i
$331$	−2.03500e6			−1.02093			−0.510464	−	0.859899i	$-0.670526\pi$
$331$	−2.03500e6			−1.02093			−0.510464	+	0.859899i	$0.670526\pi$
$332$	−3959.48	+	3959.48i	−0.00197148	+	0.00197148i
$333$	247768.	−	3.25077e6i	0.122443	−	1.60648i
$334$		−	569880.i		−	0.279523i
$335$	526514.	+	414004.i	0.256329	+	0.201555i
$336$	−3788.24	−	10229.6i	−0.00183058	−	0.00494321i
$337$	−1.02552e6	−	1.02552e6i	−0.491889	−	0.491889i	0.417012	−	0.908901i	$-0.363077\pi$
$337$	−1.02552e6	−	1.02552e6i	−0.491889	−	0.491889i	−0.908901	+	0.417012i	$0.863077\pi$
$338$	−796050.	−	796050.i	−0.379008	−	0.379008i
$339$	−789927.	−	2.13308e6i	−0.373325	−	1.00811i
$340$	271294.	+	213322.i	0.127275	+	0.100078i
$341$			1.02032e6i			0.475169i
$342$	−150884.	+	1.97963e6i	−0.0697556	+	0.915207i
$343$	64957.5	−	64957.5i	0.0298122	−	0.0298122i
$344$	−1.04211e6			−0.474809
$345$	−1.67373e6	−	3.26479e6i	−0.757071	−	1.47675i
$346$	645890.			0.290047
$347$	1.31759e6	−	1.31759e6i	0.587431	−	0.587431i	−0.349504	−	0.936935i	$-0.613650\pi$
$347$	1.31759e6	−	1.31759e6i	0.587431	−	0.587431i	0.936935	+	0.349504i	$0.113650\pi$
$348$	331045.	−	720431.i	0.146534	−	0.318892i
$349$			2.12112e6i			0.932182i	0.884737	+	0.466091i	$0.154338\pi$
$349$			2.12112e6i			0.932182i	−0.884737	+	0.466091i	$0.845662\pi$
$350$	−33204.8	+	8059.64i	−0.0144887	+	0.00351678i
$351$	992707.	+	551124.i	0.430084	+	0.238771i
$352$	445710.	+	445710.i	0.191732	+	0.191732i
$353$	−1.43096e6	−	1.43096e6i	−0.611211	−	0.611211i	0.332050	−	0.943262i	$-0.392260\pi$
$353$	−1.43096e6	−	1.43096e6i	−0.611211	−	0.611211i	−0.943262	+	0.332050i	$0.892260\pi$
$354$	2.13225e6	−	789621.i	0.904338	−	0.334897i
$355$	284638.	+	2.37940e6i	0.119873	+	1.00207i
$356$		−	1.75872e6i		−	0.735482i
$357$	−14939.9	−	6865.05i	−0.00620409	−	0.00285084i
$358$	−44958.1	+	44958.1i	−0.0185396	+	0.0185396i
$359$	−3.53537e6			−1.44777			−0.723884	−	0.689921i	$-0.757645\pi$
$359$	−3.53537e6			−1.44777			−0.723884	+	0.689921i	$0.757645\pi$
$360$	37362.4	+	868580.i	0.0151942	+	0.353227i
$361$	−1.69598e6			−0.684940
$362$	−2.12563e6	+	2.12563e6i	−0.852543	+	0.852543i
$363$	−3.08586e6	−	1.41799e6i	−1.22916	−	0.564814i
$364$		−	13109.7i		−	0.00518608i
$365$	1.11080e6	−	1.41267e6i	0.436419	−	0.555021i
$366$	−974012.	+	360698.i	−0.380068	+	0.140748i
$367$	−810434.	−	810434.i	−0.314089	−	0.314089i	0.532402	−	0.846491i	$-0.321289\pi$
$367$	−810434.	−	810434.i	−0.314089	−	0.314089i	−0.846491	+	0.532402i	$0.821289\pi$
$368$	762119.	+	762119.i	0.293362	+	0.293362i
$369$	−256497.	+	220166.i	−0.0980655	+	0.0841754i
$370$	2.97877e6	−	356338.i	1.13118	−	0.135319i
$371$		−	77722.4i		−	0.0293164i
$372$	172618.	−	375657.i	0.0646740	−	0.140745i
$373$	−202954.	+	202954.i	−0.0755310	+	0.0755310i	−0.743863	−	0.668332i	$-0.767009\pi$
$373$	−202954.	+	202954.i	−0.0755310	+	0.0755310i	0.668332	+	0.743863i	$0.267009\pi$
$374$	950058.			0.351214
$375$	2.71583e6	+	200121.i	0.997296	+	0.0734877i
$376$	364707.			0.133038
$377$	673759.	−	673759.i	0.244147	−	0.244147i
$378$	−11390.1	−	39821.2i	−0.00410013	−	0.0143346i
$379$		−	2.26580e6i		−	0.810257i	−0.914260	−	0.405128i	$-0.867227\pi$
$379$		−	2.26580e6i		−	0.810257i	0.914260	−	0.405128i	$-0.132773\pi$
$380$	−1.81399e6	+	217001.i	−0.644431	+	0.0770908i
$381$	1.28004e6	+	3.45655e6i	0.451763	+	1.21992i
$382$	309775.	+	309775.i	0.108615	+	0.108615i
$383$	−348083.	−	348083.i	−0.121251	−	0.121251i	0.643878	−	0.765129i	$-0.277325\pi$
$383$	−348083.	−	348083.i	−0.121251	−	0.121251i	−0.765129	+	0.643878i	$0.777325\pi$
$384$	−88694.4	−	239506.i	−0.0306950	−	0.0828874i
$385$	−58140.7	+	73941.1i	−0.0199907	+	0.0254234i
$386$		−	3.47153e6i		−	1.18591i
$387$	−3.94533e6	−	300707.i	−1.33908	−	0.102062i
$388$	−630886.	+	630886.i	−0.212751	+	0.212751i
$389$	3.80422e6			1.27465			0.637326	−	0.770594i	$-0.280040\pi$
$389$	3.80422e6			1.27465			0.637326	+	0.770594i	$0.280040\pi$
$390$	−320396.	+	994478.i	−0.106666	+	0.331081i
$391$	1.62451e6			0.537377
$392$	760260.	−	760260.i	0.249889	−	0.249889i
$393$	−1.55382e6	+	3.38146e6i	−0.507479	+	1.10439i
$394$		−	445258.i		−	0.144501i
$395$	516060.	+	4.31394e6i	0.166421	+	1.39117i
$396$	1.55880e6	+	1.81602e6i	0.499519	+	0.581946i
$397$	−357043.	−	357043.i	−0.113696	−	0.113696i	0.647970	−	0.761666i	$-0.275618\pi$
$397$	−357043.	−	357043.i	−0.113696	−	0.113696i	−0.761666	+	0.647970i	$0.775618\pi$
$398$	495987.	+	495987.i	0.156951	+	0.156951i
$399$	81619.4	−	30225.5i	0.0256662	−	0.00950476i
$400$	−777426.	+	188701.i	−0.242946	+	0.0589691i
$401$			4.80511e6i			1.49225i	0.665804	+	0.746126i	$0.268089\pi$
$401$			4.80511e6i			1.49225i	−0.665804	+	0.746126i	$0.731911\pi$
$402$	−678855.	−	311941.i	−0.209513	−	0.0962736i
$403$	351321.	−	351321.i	0.107756	−	0.107756i
$404$	1.25308e6			0.381967
$405$	−109183.	+	3.29913e6i	−0.0330763	+	0.999453i
$406$	−34757.5			−0.0104649
$407$	5.83968e6	−	5.83968e6i	1.74744	−	1.74744i
$408$	−349790.	−	160732.i	−0.104030	−	0.0478027i
$409$		−	4.72643e6i		−	1.39709i	−0.715565	−	0.698546i	$-0.753831\pi$
$409$		−	4.72643e6i		−	1.39709i	0.715565	−	0.698546i	$-0.246169\pi$
$410$	−244515.	−	192265.i	−0.0718366	−	0.0564859i
$411$	−330546.	+	122409.i	−0.0965222	+	0.0357443i
$412$	−1.90493e6	−	1.90493e6i	−0.552888	−	0.552888i
$413$	−70483.7	−	70483.7i	−0.0203336	−	0.0203336i
$414$	2.66539e6	+	3.10522e6i	0.764293	+	0.890412i
$415$	−15379.1	−	12092.7i	−0.00438339	−	0.00344671i
$416$		−	306939.i		−	0.0869598i
$417$	398493.	−	867211.i	0.112223	−	0.244222i
$418$	−3.55622e6	+	3.55622e6i	−0.995515	+	0.995515i
$419$	−2.40614e6			−0.669556			−0.334778	−	0.942297i	$-0.608661\pi$
$419$	−2.40614e6			−0.669556			−0.334778	+	0.942297i	$0.608661\pi$
$420$	33915.5	−	17387.1i	0.00938156	−	0.00480955i
$421$	2.26063e6			0.621618			0.310809	−	0.950472i	$-0.399400\pi$
$421$	2.26063e6			0.621618			0.310809	+	0.950472i	$0.399400\pi$
$422$	388616.	−	388616.i	0.106228	−	0.106228i
$423$	1.38074e6	+	105238.i	0.375199	+	0.0285971i
$424$		−	1.81972e6i		−	0.491576i
$425$	−627452.	+	1.02968e6i	−0.168503	+	0.276522i
$426$	−928247.	−	2.50659e6i	−0.247822	−	0.669206i
$427$	32196.9	+	32196.9i	0.00854563	+	0.00854563i
$428$	1.27659e6	+	1.27659e6i	0.336853	+	0.336853i
$429$	998838.	+	2.69721e6i	0.262031	+	0.707574i
$430$	−432474.	−	3.61522e6i	−0.112795	−	0.942895i
$431$		−	3.91972e6i		−	1.01639i	−0.861241	−	0.508196i	$-0.830312\pi$
$431$		−	3.91972e6i		−	1.01639i	0.861241	−	0.508196i	$-0.169688\pi$
$432$	−266677.	−	932338.i	−0.0687506	−	0.240361i
$433$	−3.06422e6	+	3.06422e6i	−0.785416	+	0.785416i	−0.980739	−	0.195323i	$-0.937424\pi$
$433$	−3.06422e6	+	3.06422e6i	−0.785416	+	0.785416i	0.195323	+	0.980739i	$0.437424\pi$
$434$	−18123.8			−0.00461874
$435$	2.63664e6	+	849460.i	0.668080	+	0.215239i
$436$	−545637.			−0.137464
$437$	−6.08078e6	+	6.08078e6i	−1.52320	+	1.52320i
$438$	−836958.	+	1.82141e6i	−0.208458	+	0.453652i
$439$		−	3.10595e6i		−	0.769188i	−0.923086	−	0.384594i	$-0.874341\pi$
$439$		−	3.10595e6i		−	0.769188i	0.923086	−	0.384594i	$-0.125659\pi$
$440$	−1.36125e6	+	1.73119e6i	−0.335202	+	0.426298i
$441$	3.09764e6	−	2.65889e6i	0.758463	−	0.651034i
$442$	−327130.	−	327130.i	−0.0796460	−	0.0796460i
$443$	2.85228e6	+	2.85228e6i	0.690532	+	0.690532i	0.962349	−	0.271817i	$-0.0876246\pi$
$443$	2.85228e6	+	2.85228e6i	0.690532	+	0.690532i	−0.271817	+	0.962349i	$0.587625\pi$
$444$	−3.13800e6	+	1.16207e6i	−0.755433	+	0.279754i
$445$	6.10122e6	−	729865.i	1.46055	−	0.174720i
$446$		−	423983.i		−	0.100928i
$447$	3.68092e6	+	1.69142e6i	0.871340	+	0.400390i
$448$	−7917.10	+	7917.10i	−0.00186368	+	0.00186368i
$449$	−522216.			−0.122246			−0.0611229	−	0.998130i	$-0.519468\pi$
$449$	−522216.			−0.122246			−0.0611229	+	0.998130i	$0.519468\pi$
$450$	−2.99770e6	+	490073.i	−0.697843	+	0.114085i
$451$	−856279.			−0.198232
$452$	−1.65088e6	+	1.65088e6i	−0.380075	+	0.380075i
$453$	−2.63479e6	−	1.21071e6i	−0.603253	−	0.277201i
$454$		−	1.35964e6i		−	0.309588i
$455$	45479.1	−	5440.49i	0.0102987	−	0.00123200i
$456$	1.91096e6	−	707673.i	0.430368	−	0.159375i
$457$	3.29898e6	+	3.29898e6i	0.738905	+	0.738905i	0.972366	−	0.233461i	$-0.0750052\pi$
$457$	3.29898e6	+	3.29898e6i	0.738905	+	0.738905i	−0.233461	+	0.972366i	$0.575005\pi$
$458$	−429781.	−	429781.i	−0.0957378	−	0.0957378i
$459$	−1.27789e6	−	709449.i	−0.283114	−	0.157177i
$460$	−2.32761e6	+	2.96016e6i	−0.512879	+	0.652260i
$461$		−	2.80680e6i		−	0.615118i	−0.951529	−	0.307559i	$-0.900488\pi$
$461$		−	2.80680e6i		−	0.615118i	0.951529	−	0.307559i	$-0.0995122\pi$
$462$	43807.4	−	95335.0i	0.00954867	−	0.0207801i
$463$	535649.	−	535649.i	0.116126	−	0.116126i	−0.646656	−	0.762782i	$-0.723833\pi$
$463$	535649.	−	535649.i	0.116126	−	0.116126i	0.762782	+	0.646656i	$0.223833\pi$
$464$	−813782.			−0.175474
$465$	1.37484e6	+	442937.i	0.294862	+	0.0949970i
$466$	1.52549e6			0.325420
$467$	−406464.	+	406464.i	−0.0862441	+	0.0862441i	−0.748913	−	0.662669i	$-0.769424\pi$
$467$	−406464.	+	406464.i	−0.0862441	+	0.0862441i	0.662669	+	0.748913i	$0.269424\pi$
$468$	88568.6	−	1.16204e6i	0.0186924	−	0.245248i
$469$			32751.7i			0.00687546i
$470$	151352.	+	1.26521e6i	0.0316042	+	0.264192i
$471$	1.20666e6	+	3.25842e6i	0.250631	+	0.676791i
$472$	−1.65024e6	−	1.65024e6i	−0.340951	−	0.340951i
$473$	−7.08740e6	−	7.08740e6i	−1.45658	−	1.45658i
$474$	−1.68295e6	−	4.54455e6i	−0.344053	−	0.929063i
$475$	−1.50560e6	−	6.20291e6i	−0.306180	−	1.26143i
$476$			16875.8i			0.00341387i
$477$	525089.	−	6.88927e6i	0.105666	−	1.38636i
$478$	2.81603e6	−	2.81603e6i	0.563726	−	0.563726i
$479$	−2.36702e6			−0.471371			−0.235686	−	0.971829i	$-0.575734\pi$
$479$	−2.36702e6			−0.471371			−0.235686	+	0.971829i	$0.575734\pi$
$480$	794068.	−	407086.i	0.157309	−	0.0806461i
$481$	−4.02151e6			−0.792549
$482$	4.62301e6	−	4.62301e6i	0.906373	−	0.906373i
$483$	74906.4	−	163013.i	0.0146100	−	0.0317947i
$484$			3.48572e6i			0.676362i
$485$	−2.45044e6	−	1.92680e6i	−0.473030	−	0.371949i
$486$	−740581.	−	3.60668e6i	−0.142227	−	0.692655i
$487$	−3.33072e6	−	3.33072e6i	−0.636378	−	0.636378i	0.313282	−	0.949660i	$-0.398571\pi$
$487$	−3.33072e6	−	3.33072e6i	−0.636378	−	0.636378i	−0.949660	+	0.313282i	$0.898571\pi$
$488$	753829.	+	753829.i	0.143292	+	0.143292i
$489$	1.33288e6	−	493596.i	0.252069	−	0.0933469i
$490$	2.95294e6	+	2.32193e6i	0.555603	+	0.436876i
$491$		−	785451.i		−	0.147033i	−0.997294	−	0.0735166i	$-0.976578\pi$
$491$		−	785451.i		−	0.147033i	0.997294	−	0.0735166i	$-0.0234222\pi$
$492$	315262.	+	144866.i	0.0587164	+	0.0269808i
$493$	−867314.	+	867314.i	−0.160716	+	0.160716i
$494$	2.44899e6			0.451513
$495$	−5.65310e6	+	6.16131e6i	−1.03699	+	1.13021i
$496$	−424333.			−0.0774467
$497$	−82857.8	+	82857.8i	−0.0150467	+	0.0150467i
$498$	19828.8	+	9111.56i	0.00358281	+	0.00164634i
$499$		−	968793.i		−	0.174173i	−0.996201	−	0.0870863i	$-0.972244\pi$
$499$		−	968793.i		−	0.174173i	0.996201	−	0.0870863i	$-0.0277556\pi$
$500$	−977258.	−	2.61868e6i	−0.174817	−	0.468443i
$501$	−2.08267e6	+	771258.i	−0.370703	+	0.137279i
$502$	4.04292e6	+	4.04292e6i	0.716037	+	0.716037i
$503$	1.69640e6	+	1.69640e6i	0.298958	+	0.298958i	0.840605	−	0.541648i	$-0.182199\pi$
$503$	1.69640e6	+	1.69640e6i	0.298958	+	0.298958i	−0.541648	+	0.840605i	$0.682199\pi$
$504$	−32257.8	+	27688.8i	−0.00565664	+	0.00485543i
$505$	520026.	+	4.34709e6i	0.0907395	+	0.758526i
$506$			1.03663e7i			1.79990i
$507$	−1.83187e6	+	3.98657e6i	−0.316501	+	0.688778i
$508$	2.67517e6	−	2.67517e6i	0.459931	−	0.459931i
$509$	−1.32955e6			−0.227463			−0.113731	−	0.993512i	$-0.536280\pi$
$509$	−1.32955e6			−0.227463			−0.113731	+	0.993512i	$0.536280\pi$
$510$	412438.	−	1.28017e6i	0.0702155	−	0.217942i
$511$	87874.9			0.0148872
$512$	−185364.	+	185364.i	−0.0312500	+	0.0312500i
$513$	7.43891e6	−	2.12776e6i	1.24800	−	0.356967i
$514$			2.26158e6i			0.377576i
$515$	5.81791e6	−	7.39899e6i	0.966604	−	1.22929i
$516$	1.41036e6	+	3.80848e6i	0.233188	+	0.629690i
$517$	2.48037e6	+	2.48037e6i	0.408122	+	0.408122i
$518$	103730.	+	103730.i	0.0169855	+	0.0169855i
$519$	−874128.	−	2.36045e6i	−0.142448	−	0.384660i
$520$	1.06481e6	−	127379.i	0.172688	−	0.0206580i
$521$			9.14428e6i			1.47589i	0.674858	+	0.737947i	$0.264205\pi$
$521$			9.14428e6i			1.47589i	−0.674858	+	0.737947i	$0.735795\pi$
$522$	−3.08089e6	−	234821.i	−0.494880	−	0.0377190i
$523$	−1.87262e6	+	1.87262e6i	−0.299361	+	0.299361i	−0.840763	−	0.541403i	$-0.817893\pi$
$523$	−1.87262e6	+	1.87262e6i	−0.299361	+	0.299361i	0.541403	+	0.840763i	$0.317893\pi$
$524$	3.81962e6			0.607704
$525$	74392.8	+	110441.i	0.0117797	+	0.0174878i
$526$	−187305.			−0.0295178
$527$	−452247.	+	452247.i	−0.0709331	+	0.0709331i
$528$	1.02567e6	−	2.23209e6i	0.160111	−	0.348439i
$529$			1.12891e7i			1.75396i
$530$	6.31284e6	−	755180.i	0.976191	−	0.116778i
$531$	−5.77146e6	−	6.72383e6i	−0.888278	−	1.03486i
$532$	−63168.7	−	63168.7i	−0.00967661	−	0.00967661i
$533$	294839.	+	294839.i	0.0449538	+	0.0449538i
$534$	−6.42737e6	+	2.38020e6i	−0.975395	+	0.361210i
$535$	−3.89886e6	+	4.95842e6i	−0.588915	+	0.748960i
$536$			766819.i			0.115287i
$537$	225148.	+	103458.i	0.0336924	+	0.0154820i
$538$	2.16352e6	−	2.16352e6i	0.322259	−	0.322259i
$539$	1.03410e7			1.53318
$540$	3.12372e6	−	1.31205e6i	0.460986	−	0.193627i
$541$	−7.21750e6			−1.06021			−0.530107	−	0.847931i	$-0.677848\pi$
$541$	−7.21750e6			−1.06021			−0.530107	+	0.847931i	$0.677848\pi$
$542$	−5.68232e6	+	5.68232e6i	−0.830859	+	0.830859i
$543$	1.06450e7	+	4.89151e6i	1.54934	+	0.711939i
$544$			395115.i			0.0572435i
$545$	−226438.	−	1.89288e6i	−0.0326556	−	0.272981i
$546$	−47910.3	+	17742.3i	−0.00687777	+	0.00254699i
$547$	5.27000e6	+	5.27000e6i	0.753082	+	0.753082i	0.975053	−	0.221971i	$-0.0712490\pi$
$547$	5.27000e6	+	5.27000e6i	0.753082	+	0.753082i	−0.221971	+	0.975053i	$0.571249\pi$
$548$	255824.	+	255824.i	0.0363906	+	0.0363906i
$549$	2.63640e6	+	3.07144e6i	0.373319	+	0.434921i
$550$	−6.57063e6	−	4.00391e6i	−0.926190	−	0.564388i
$551$		−	6.49298e6i		−	0.911098i
$552$	1.75379e6	−	3.81665e6i	0.244980	−	0.533132i
$553$	−150224.	+	150224.i	−0.0208895	+	0.0208895i
$554$	−2.74200e6			−0.379571
$555$	−5.33364e6	−	1.04039e7i	−0.735006	−	1.43371i
$556$	−979581.			−0.134386
$557$	−4.43782e6	+	4.43782e6i	−0.606083	+	0.606083i	−0.941920	−	0.335837i	$-0.890981\pi$
$557$	−4.43782e6	+	4.43782e6i	−0.606083	+	0.606083i	0.335837	+	0.941920i	$0.390981\pi$
$558$	−1.60648e6	−	122443.i	−0.218419	−	0.0166475i
$559$			4.88075e6i			0.660628i
$560$	−30750.9	−	24179.8i	−0.00414370	−	0.00325824i
$561$	−1.28578e6	−	3.47206e6i	−0.172488	−	0.465779i
$562$	4.12775e6	+	4.12775e6i	0.551281	+	0.551281i
$563$	−3.22886e6	−	3.22886e6i	−0.429318	−	0.429318i	0.459078	−	0.888396i	$-0.348180\pi$
$563$	−3.22886e6	−	3.22886e6i	−0.429318	−	0.429318i	−0.888396	+	0.459078i	$0.848180\pi$
$564$	−493583.	−	1.33285e6i	−0.0653375	−	0.176434i
$565$	−6.41221e6	−	5.04199e6i	−0.845059	−	0.664479i
$566$			327368.i			0.0429531i
$567$	−130114.	+	95518.6i	−0.0169968	+	0.0124776i
$568$	−1.93996e6	+	1.93996e6i	−0.252302	+	0.252302i
$569$	7.44498e6			0.964013			0.482007	−	0.876168i	$-0.339908\pi$
$569$	7.44498e6			0.964013			0.482007	+	0.876168i	$0.339908\pi$
$570$	3.24805e6	+	6.33569e6i	0.418731	+	0.816783i
$571$	9.56951e6			1.22829			0.614143	−	0.789195i	$-0.289502\pi$
$571$	9.56951e6			1.22829			0.614143	+	0.789195i	$0.289502\pi$
$572$	2.08749e6	−	2.08749e6i	0.266768	−	0.266768i
$573$	712856.	−	1.55134e6i	0.0907017	−	0.197388i
$574$		−	15210.0i		−	0.00192686i
$575$	−1.12351e7	−	6.84630e6i	−1.41712	−	0.863547i
$576$	−755255.	+	648280.i	−0.0948501	+	0.0814154i
$577$	−4.11905e6	−	4.11905e6i	−0.515060	−	0.515060i	0.401013	−	0.916073i	$-0.368658\pi$
$577$	−4.11905e6	−	4.11905e6i	−0.515060	−	0.515060i	−0.916073	+	0.401013i	$0.868658\pi$
$578$	−3.59486e6	−	3.59486e6i	−0.447571	−	0.447571i
$579$	−1.26870e7	+	4.69827e6i	−1.57276	+	0.582427i
$580$	−337717.	−	2.82311e6i	−0.0416853	−	0.348464i
$581$		−	956.652i		−	0.000117575i
$582$	3.15944e6	+	1.45180e6i	0.386636	+	0.177663i
$583$	1.23759e7	−	1.23759e7i	1.50802	−	1.50802i
$584$	2.05742e6			0.249627
$585$	4.06801e6	−	174987.i	0.491464	−	0.0211406i
$586$	−9.46160e6			−1.13821
$587$	−3.62213e6	+	3.62213e6i	−0.433879	+	0.433879i	−0.889946	−	0.456066i	$-0.849258\pi$
$587$	−3.62213e6	+	3.62213e6i	−0.433879	+	0.433879i	0.456066	+	0.889946i	$0.349258\pi$
$588$	−3.80734e6	−	1.74951e6i	−0.454128	−	0.208676i
$589$		−	3.38566e6i		−	0.402119i
$590$	5.04004e6	−	6.40974e6i	0.596080	−	0.758071i
$591$	−1.62723e6	+	602599.i	−0.191637	+	0.0709676i
$592$	2.42863e6	+	2.42863e6i	0.284812	+	0.284812i
$593$	6.47872e6	+	6.47872e6i	0.756575	+	0.756575i	0.975697	−	0.219122i	$-0.0703193\pi$
$593$	6.47872e6	+	6.47872e6i	0.756575	+	0.756575i	−0.219122	+	0.975697i	$0.570319\pi$
$594$	4.52715e6	−	8.15449e6i	0.526452	−	0.948267i
$595$	−58544.2	+	7003.41i	−0.00677940	+	0.000810993i
$596$		−	4.15788e6i		−	0.479465i
$597$	1.14137e6	−	2.48388e6i	0.131066	−	0.285229i
$598$	3.56940e6	−	3.56940e6i	0.408171	−	0.408171i
$599$	−2.21327e6			−0.252039			−0.126019	−	0.992028i	$-0.540220\pi$
$599$	−2.21327e6			−0.252039			−0.126019	+	0.992028i	$0.540220\pi$
$600$	1.74177e6	+	2.58578e6i	0.197520	+	0.293233i
$601$	1.51975e7			1.71627			0.858135	−	0.513424i	$-0.171623\pi$
$601$	1.51975e7			1.71627			0.858135	+	0.513424i	$0.171623\pi$
$602$	125893.	−	125893.i	0.0141582	−	0.0141582i
$603$	−221269.	+	2.90309e6i	−0.0247815	+	0.325138i
$604$			2.97619e6i			0.331947i
$605$	−1.20924e7	+	1.44656e6i	−1.34315	+	0.160675i
$606$	−1.69588e6	−	4.57948e6i	−0.187592	−	0.506564i
$607$	−6.37228e6	−	6.37228e6i	−0.701978	−	0.701978i	0.262857	−	0.964835i	$-0.415335\pi$
$607$	−6.37228e6	−	6.37228e6i	−0.701978	−	0.701978i	−0.964835	+	0.262857i	$0.915335\pi$
$608$	−1.47898e6	−	1.47898e6i	−0.162257	−	0.162257i
$609$	47039.8	+	127024.i	0.00513951	+	0.0138785i
$610$	−2.30229e6	+	2.92796e6i	−0.250516	+	0.318596i
$611$		−	1.70811e6i		−	0.185103i
$612$	−114012.	+	1.49586e6i	−0.0123047	+	0.161441i
$613$	−7.00623e6	+	7.00623e6i	−0.753066	+	0.753066i	−0.975050	−	0.221984i	$-0.928747\pi$
$613$	−7.00623e6	+	7.00623e6i	−0.753066	+	0.753066i	0.221984	+	0.975050i	$0.428747\pi$
$614$	−1.18958e7			−1.27342
$615$	−371726.	+	1.15380e6i	−0.0396310	+	0.123011i
$616$	−107688.			−0.0114345
$617$	−2.77828e6	+	2.77828e6i	−0.293808	+	0.293808i	−0.838582	−	0.544775i	$-0.816615\pi$
$617$	−2.77828e6	+	2.77828e6i	−0.293808	+	0.293808i	0.544775	+	0.838582i	$0.316615\pi$
$618$	−4.38364e6	+	9.53980e6i	−0.461704	+	1.00477i
$619$			6.32328e6i			0.663309i	0.943401	+	0.331654i	$0.107607\pi$
$619$			6.32328e6i			0.663309i	−0.943401	+	0.331654i	$0.892393\pi$
$620$	−176097.	−	1.47206e6i	−0.0183981	−	0.153797i
$621$	7.74098e6	−	1.39434e7i	0.805502	−	1.45090i
$622$	−3.13571e6	−	3.13571e6i	−0.324982	−	0.324982i
$623$	212463.	+	212463.i	0.0219312	+	0.0219312i
$624$	−1.12173e6	+	415401.i	−0.115326	+	0.0427077i
$625$	8.67895e6	−	4.47697e6i	0.888724	−	0.458442i
$626$			6.51244e6i			0.664214i
$627$	1.78093e7	+	8.18357e6i	1.80917	+	0.831331i
$628$	2.52183e6	−	2.52183e6i	0.255162	−	0.255162i
$629$	5.17679e6			0.521715
$630$	−109443.	−	100416.i	−0.0109859	−	0.0100797i
$631$	−2.83767e6			−0.283719			−0.141859	−	0.989887i	$-0.545308\pi$
$631$	−2.83767e6			−0.283719			−0.141859	+	0.989887i	$0.545308\pi$
$632$	−3.51722e6	+	3.51722e6i	−0.350273	+	0.350273i
$633$	−1.94616e6	−	894283.i	−0.193050	−	0.0887086i
$634$		−	1.00270e6i		−	0.0990715i
$635$	1.03907e7	+	8.17031e6i	1.02261	+	0.804089i
$636$	−6.65030e6	+	2.46276e6i	−0.651927	+	0.241423i
$637$	−3.56069e6	−	3.56069e6i	−0.347684	−	0.347684i
$638$	−5.53452e6	−	5.53452e6i	−0.538305	−	0.538305i
$639$	−7.90426e6	+	6.78469e6i	−0.765789	+	0.657322i
$640$	−719975.	−	566124.i	−0.0694812	−	0.0546338i
$641$			1.78673e6i			0.171757i	0.996306	+	0.0858783i	$0.0273696\pi$
$641$			1.78673e6i			0.171757i	−0.996306	+	0.0858783i	$0.972630\pi$
$642$	2.93768e6	−	6.39307e6i	0.281299	−	0.612170i
$643$	−5.31029e6	+	5.31029e6i	−0.506513	+	0.506513i	−0.913454	−	0.406941i	$-0.866595\pi$
$643$	−5.31029e6	+	5.31029e6i	−0.506513	+	0.506513i	0.406941	+	0.913454i	$0.366595\pi$
$644$	−184136.			−0.0174954
$645$	−1.26268e7	+	6.47323e6i	−1.19507	+	0.612663i
$646$	−3.15253e6			−0.297220
$647$	−1.93842e6	+	1.93842e6i	−0.182048	+	0.182048i	−0.792248	−	0.610199i	$-0.791089\pi$
$647$	−1.93842e6	+	1.93842e6i	−0.182048	+	0.182048i	0.610199	+	0.792248i	$0.291089\pi$
$648$	−3.04638e6	+	2.23639e6i	−0.285001	+	0.209223i
$649$		−	2.24466e7i		−	2.09189i
$650$	883785.	+	3.64109e6i	0.0820471	+	0.338024i
$651$	24528.1	+	66234.5i	0.00226836	+	0.00612537i
$652$	−1.03157e6	−	1.03157e6i	−0.0950346	−	0.0950346i
$653$	6.54118e6	+	6.54118e6i	0.600306	+	0.600306i	0.940394	−	0.340087i	$-0.110457\pi$
$653$	6.54118e6	+	6.54118e6i	0.600306	+	0.600306i	−0.340087	+	0.940394i	$0.610457\pi$
$654$	738448.	+	1.99407e6i	0.0675112	+	0.182304i
$655$	1.58513e6	+	1.32507e7i	0.144365	+	1.20680i
$656$		−	356113.i		−	0.0323094i
$657$	7.78919e6	+	593679.i	0.704010	+	0.0536585i
$658$	−44058.5	+	44058.5i	−0.00396703	+	0.00396703i
$659$	1.55193e7			1.39206			0.696030	−	0.718013i	$-0.254948\pi$
$659$	1.55193e7			1.39206			0.696030	+	0.718013i	$0.254948\pi$
$660$	8.16903e6	+	2.63186e6i	0.729980	+	0.235181i
$661$	260063.			0.0231513			0.0115757	−	0.999933i	$-0.496315\pi$
$661$	260063.			0.0231513			0.0115757	+	0.999933i	$0.496315\pi$
$662$	5.75586e6	−	5.75586e6i	0.510464	−	0.510464i
$663$	−752791.	+	1.63825e6i	−0.0665106	+	0.144742i
$664$		−	22398.2i		−	0.00197148i
$665$	192925.	−	245355.i	0.0169174	−	0.0215150i
$666$	8.49376e6	+	9.89535e6i	0.742018	+	0.864461i
$667$	−9.46348e6	−	9.46348e6i	−0.823638	−	0.823638i
$668$	1.61186e6	+	1.61186e6i	0.139761	+	0.139761i
$669$	−1.54948e6	+	573806.i	−0.133850	+	0.0495678i
$670$	−2.66019e6	+	318228.i	−0.228942	+	0.0273874i
$671$			1.02536e7i			0.879161i
$672$	39648.3	+	18218.8i	0.00338690	+	0.00155631i
$673$	9.33490e6	−	9.33490e6i	0.794460	−	0.794460i	−0.187756	−	0.982216i	$-0.560121\pi$
$673$	9.33490e6	−	9.33490e6i	0.794460	−	0.794460i	0.982216	+	0.187756i	$0.0601213\pi$
$674$	5.80119e6			0.491889
$675$	5.84801e6	+	1.02921e7i	0.494025	+	0.869448i
$676$	4.50314e6			0.379008
$677$	9.53310e6	−	9.53310e6i	0.799397	−	0.799397i	−0.183604	−	0.983000i	$-0.558776\pi$
$677$	9.53310e6	−	9.53310e6i	0.799397	−	0.799397i	0.983000	+	0.183604i	$0.0587763\pi$
$678$	8.26751e6	+	3.79901e6i	0.690717	+	0.317392i
$679$		−	152429.i		−	0.0126880i
$680$	−1.37070e6	+	163971.i	−0.113676	+	0.0135987i
$681$	−4.96890e6	+	1.84010e6i	−0.410575	+	0.152045i
$682$	−2.88589e6	−	2.88589e6i	−0.237585	−	0.237585i
$683$	1.57744e6	+	1.57744e6i	0.129390	+	0.129390i	0.768836	−	0.639446i	$-0.220836\pi$
$683$	1.57744e6	+	1.57744e6i	0.129390	+	0.129390i	−0.639446	+	0.768836i	$0.720836\pi$
$684$	−5.17248e6	−	6.02601e6i	−0.422726	−	0.492481i
$685$	−781317.	+	993649.i	−0.0636211	+	0.0809108i
$686$			367455.i			0.0298122i
$687$	−989013.	+	2.15232e6i	−0.0799485	+	0.173986i
$688$	2.94754e6	−	2.94754e6i	0.237404	−	0.237404i
$689$	−8.52269e6			−0.683957
$690$	1.39682e7	+	4.50021e6i	1.11691	+	0.359841i
$691$	−3.72618e6			−0.296872			−0.148436	−	0.988922i	$-0.547424\pi$
$691$	−3.72618e6			−0.296872			−0.148436	+	0.988922i	$0.547424\pi$
$692$	−1.82685e6	+	1.82685e6i	−0.145024	+	0.145024i
$693$	−407696.	−	31073.9i	−0.0322481	−	0.00245789i
$694$			7.45342e6i			0.587431i
$695$	−406524.	−	3.39829e6i	−0.0319245	−	0.266869i
$696$	1.10135e6	+	2.97402e6i	0.0861790	+	0.232713i
$697$	−379539.	−	379539.i	−0.0295920	−	0.0295920i
$698$	−5.99942e6	−	5.99942e6i	−0.466091	−	0.466091i
$699$	−2.06455e6	−	5.57500e6i	−0.159820	−	0.431571i
$700$	71121.1	−	116713.i	0.00548597	−	0.00900275i
$701$		−	9.29171e6i		−	0.714168i	−0.934072	−	0.357084i	$-0.883771\pi$
$701$		−	9.29171e6i		−	0.714168i	0.934072	−	0.357084i	$-0.116229\pi$
$702$	−4.36661e6	+	1.24899e6i	−0.334428	+	0.0956565i
$703$	−1.93775e7	+	1.93775e7i	−1.47880	+	1.47880i
$704$	−2.52131e6			−0.191732
$705$	4.41898e6	−	2.26543e6i	0.334849	−	0.171663i
$706$	8.09474e6			0.611211
$707$	−151379.	+	151379.i	−0.0113898	+	0.0113898i
$708$	−3.79754e6	+	8.26431e6i	−0.284721	+	0.619617i
$709$		−	1.87653e7i		−	1.40197i	−0.713174	−	0.700987i	$-0.752743\pi$
$709$		−	1.87653e7i		−	1.40197i	0.713174	−	0.700987i	$-0.247257\pi$
$710$	−7.53503e6	−	5.92487e6i	−0.560969	−	0.441096i
$711$	−1.43307e7	+	1.23009e7i	−1.06315	+	0.912564i
$712$	4.97442e6	+	4.97442e6i	0.367741	+	0.367741i
$713$	−4.93458e6	−	4.93458e6i	−0.363518	−	0.363518i
$714$	61673.8	−	22839.2i	0.00452746	−	0.00167662i
$715$	8.10805e6	+	6.37545e6i	0.593132	+	0.466386i
$716$		−	254321.i		−	0.0185396i
$717$	−1.41025e7	−	6.48026e6i	−1.02447	−	0.470755i
$718$	9.99955e6	−	9.99955e6i	0.723884	−	0.723884i
$719$	3.20828e6			0.231446			0.115723	−	0.993282i	$-0.463082\pi$
$719$	3.20828e6			0.231446			0.115723	+	0.993282i	$0.463082\pi$
$720$	−2.56239e6	−	2.35104e6i	−0.184210	−	0.169016i
$721$	460252.			0.0329729
$722$	4.79695e6	−	4.79695e6i	0.342470	−	0.342470i
$723$	−2.31518e7	−	1.06385e7i	−1.64717	−	0.756892i
$724$		−	1.20244e7i		−	0.852543i
$725$	9.65356e6	−	2.34316e6i	0.682091	−	0.165561i
$726$	1.27388e7	−	4.71747e6i	0.896989	−	0.332175i
$727$	971909.	+	971909.i	0.0682008	+	0.0682008i	0.740384	−	0.672184i	$-0.234643\pi$
$727$	971909.	+	971909.i	0.0682008	+	0.0682008i	−0.672184	+	0.740384i	$0.734643\pi$
$728$	37079.8	+	37079.8i	0.00259304	+	0.00259304i
$729$	−1.21786e7	+	7.58768e6i	−0.848747	+	0.528798i
$730$	853826.	+	7.13746e6i	0.0593010	+	0.495720i
$731$		−	6.28287e6i		−	0.434875i
$732$	1.73471e6	−	3.77513e6i	0.119660	−	0.260408i
$733$	−1.95035e7	+	1.95035e7i	−1.34077	+	1.34077i	−0.445471	+	0.895296i	$0.646964\pi$
$733$	−1.95035e7	+	1.95035e7i	−1.34077	+	1.34077i	−0.895296	+	0.445471i	$0.853036\pi$
$734$	4.58451e6			0.314089
$735$	4.48923e6	−	1.39342e7i	0.306517	−	0.951398i
$736$	−4.31120e6			−0.293362
$737$	−5.21513e6	+	5.21513e6i	−0.353668	+	0.353668i
$738$	102758.	−	1.34821e6i	0.00694505	−	0.0911204i
$739$			3.62268e6i			0.244016i	0.992529	+	0.122008i	$0.0389334\pi$
$739$			3.62268e6i			0.244016i	−0.992529	+	0.122008i	$0.961067\pi$
$740$	−7.41735e6	+	9.43311e6i	−0.497931	+	0.633250i
$741$	−3.31439e6	−	8.95003e6i	−0.221747	−	0.598796i
$742$	219832.	+	219832.i	0.0146582	+	0.0146582i
$743$	−1.70630e7	−	1.70630e7i	−1.13393	−	1.13393i	−0.989518	−	0.144407i	$-0.953872\pi$
$743$	−1.70630e7	−	1.70630e7i	−1.13393	−	1.13393i	−0.144407	−	0.989518i	$-0.546128\pi$
$744$	574280.	+	1.55076e6i	0.0380357	+	0.102710i
$745$	1.44242e7	−	1.72551e6i	0.952141	−	0.113901i
$746$		−	1.14808e6i		−	0.0755310i
$747$	6463.10	−	84797.2i	0.000423779	−	0.00556006i
$748$	−2.68717e6	+	2.68717e6i	−0.175607	+	0.175607i
$749$	−308437.			−0.0200892
$750$	−8.24755e6	+	7.11549e6i	−0.535392	+	0.461904i
$751$	2.46605e7			1.59552			0.797760	−	0.602975i	$-0.206018\pi$
$751$	2.46605e7			1.59552			0.797760	+	0.602975i	$0.206018\pi$
$752$	−1.03155e6	+	1.03155e6i	−0.0665188	+	0.0665188i
$753$	9.30357e6	−	2.02467e7i	0.597946	−	1.30127i
$754$			3.81136e6i			0.244147i
$755$	−1.03248e7	+	1.23511e6i	−0.659194	+	0.0788568i
$756$	144847.	+	80415.3i	0.00921735	+	0.00511722i
$757$	2.31958e6	+	2.31958e6i	0.147119	+	0.147119i	0.776830	−	0.629710i	$-0.216826\pi$
$757$	2.31958e6	+	2.31958e6i	0.147119	+	0.147119i	−0.629710	+	0.776830i	$0.716826\pi$
$758$	6.40864e6	+	6.40864e6i	0.405128	+	0.405128i
$759$	3.78845e7	−	1.40295e7i	2.38703	−	0.883969i
$760$	4.51698e6	−	5.74452e6i	0.283670	−	0.360761i
$761$			1.57529e7i			0.986048i	0.870016	+	0.493024i	$0.164109\pi$
$761$			1.57529e7i			0.986048i	−0.870016	+	0.493024i	$0.835891\pi$
$762$	−1.33971e7	−	6.15611e6i	−0.835840	−	0.384077i
$763$	65915.8	−	65915.8i	0.00409900	−	0.00409900i
$764$	−1.75235e6			−0.108615
$765$	−5.23664e6	+	225257.i	−0.323519	+	0.0139163i
$766$	1.96905e6			0.121251
$767$	−7.72893e6	+	7.72893e6i	−0.474385	+	0.474385i
$768$	928291.	+	426560.i	0.0567912	+	0.0260962i
$769$			8.72370e6i			0.531967i	0.963978	+	0.265984i	$0.0856967\pi$
$769$			8.72370e6i			0.531967i	−0.963978	+	0.265984i	$0.914303\pi$
$770$	−44690.3	−	373583.i	−0.00271636	−	0.0227071i
$771$	8.26512e6	−	3.06076e6i	0.500741	−	0.185436i
$772$	9.81898e6	+	9.81898e6i	0.592957	+	0.592957i
$773$	666455.	+	666455.i	0.0401164	+	0.0401164i	0.726880	−	0.686764i	$-0.240969\pi$
$773$	666455.	+	666455.i	0.0401164	+	0.0401164i	−0.686764	+	0.726880i	$0.740969\pi$
$774$	1.20096e7	−	1.03086e7i	0.720570	−	0.618508i
$775$	5.03369e6	−	1.22181e6i	0.301046	−	0.0730714i
$776$		−	3.56883e6i		−	0.212751i
$777$	238703.	−	519472.i	0.0141842	−	0.0308681i
$778$	−1.07600e7	+	1.07600e7i	−0.637326	+	0.637326i
$779$	2.84135e6			0.167757
$780$	−1.90659e6	−	3.71903e6i	−0.112207	−	0.218873i
$781$	−2.63873e7			−1.54799
$782$	−4.59480e6	+	4.59480e6i	−0.268689	+	0.268689i
$783$	3.31142e6	+	1.15771e7i	0.193023	+	0.674834i
$784$			4.30068e6i			0.249889i
$785$	9.79507e6	+	7.70197e6i	0.567327	+	0.446095i
$786$	−5.16936e6	−	1.39591e7i	−0.298456	−	0.805935i
$787$	−5.83122e6	−	5.83122e6i	−0.335601	−	0.335601i	0.519108	−	0.854709i	$-0.326264\pi$
$787$	−5.83122e6	−	5.83122e6i	−0.335601	−	0.335601i	−0.854709	+	0.519108i	$0.826264\pi$
$788$	1.25938e6	+	1.25938e6i	0.0722506	+	0.0722506i
$789$	253492.	+	684518.i	0.0144968	+	0.0391464i
$790$	−1.36613e7	−	1.07420e7i	−0.778798	−	0.612377i
$791$		−	398870.i		−	0.0226668i
$792$	−9.54543e6	−	727537.i	−0.540733	−	0.0412138i
$793$	3.53057e6	−	3.53057e6i	0.199371	−	0.199371i
$794$	2.01974e6			0.113696
$795$	−1.13035e7	−	2.20487e7i	−0.634298	−	1.23727i
$796$	−2.80573e6			−0.156951
$797$	1.23360e7	−	1.23360e7i	0.687903	−	0.687903i	−0.273865	−	0.961768i	$-0.588302\pi$
$797$	1.23360e7	−	1.23360e7i	0.687903	−	0.687903i	0.961768	+	0.273865i	$0.0883021\pi$
$798$	−145364.	+	316345.i	−0.00808071	+	0.0175855i
$799$			2.19881e6i			0.121849i
$800$	1.66517e6	−	2.73262e6i	0.0919883	−	0.150957i
$801$	1.73972e7	+	2.02680e7i	0.958073	+	1.11617i
$802$	−1.35909e7	−	1.35909e7i	−0.746126	−	0.746126i
$803$	1.39925e7	+	1.39925e7i	0.765786	+	0.765786i
$804$	2.80239e6	−	1.03779e6i	0.152894	−	0.0566199i
$805$	−76416.0	−	638791.i	−0.00415618	−	0.0347431i
$806$			1.98737e6i			0.107756i
$807$	−1.08348e7	−	4.97869e6i	−0.585647	−	0.269111i
$808$	−3.54425e6	+	3.54425e6i	−0.190984	+	0.190984i
$809$	−1.48239e7			−0.796328			−0.398164	−	0.917314i	$-0.630353\pi$
$809$	−1.48239e7			−0.796328			−0.398164	+	0.917314i	$0.630353\pi$
$810$	−9.02254e6	−	9.64017e6i	−0.483188	−	0.516265i
$811$	−366386.			−0.0195608			−0.00978039	−	0.999952i	$-0.503113\pi$
$811$	−366386.			−0.0195608			−0.00978039	+	0.999952i	$0.503113\pi$
$812$	98309.2	−	98309.2i	0.00523244	−	0.00523244i
$813$	2.84567e7	+	1.30762e7i	1.50994	+	0.693831i
$814$			3.30342e7i			1.74744i
$815$	3.15056e6	−	4.00676e6i	0.166147	−	0.211300i
$816$	1.44397e6	−	534736.i	0.0759161	−	0.0281134i
$817$	2.35178e7	+	2.35178e7i	1.23265	+	1.23265i
$818$	1.33684e7	+	1.33684e7i	0.698546	+	0.698546i
$819$	129681.	+	151080.i	0.00675563	+	0.00787040i
$820$	1.23540e6	−	147786.i	0.0641613	−	0.00767536i
$821$		−	1.39801e7i		−	0.723855i	−0.932206	−	0.361928i	$-0.882119\pi$
$821$		−	1.39801e7i		−	0.723855i	0.932206	−	0.361928i	$-0.117881\pi$
$822$	588702.	−	1.28115e6i	0.0303889	−	0.0661333i
$823$	1.09055e7	−	1.09055e7i	0.561237	−	0.561237i	−0.368422	−	0.929659i	$-0.620102\pi$
$823$	1.09055e7	−	1.09055e7i	0.561237	−	0.561237i	0.929659	+	0.368422i	$0.120102\pi$
$824$	1.07759e7			0.552888
$825$	−5.74011e6	+	2.94316e7i	−0.293620	+	1.50549i
$826$	398716.			0.0203336
$827$	802797.	−	802797.i	0.0408171	−	0.0408171i	−0.686404	−	0.727221i	$-0.740812\pi$
$827$	802797.	−	802797.i	0.0408171	−	0.0408171i	0.727221	+	0.686404i	$0.240812\pi$
$828$	−1.63217e7	−	1.24402e6i	−0.827353	−	0.0630595i
$829$			2.52860e7i			1.27789i	0.769252	+	0.638946i	$0.220629\pi$
$829$			2.52860e7i			1.27789i	−0.769252	+	0.638946i	$0.779371\pi$
$830$	77702.0	−	9295.19i	0.00391505	−	0.000468342i
$831$	3.71094e6	+	1.00208e7i	0.186415	+	0.503386i
$832$	868154.	+	868154.i	0.0434799	+	0.0434799i
$833$	4.58358e6	+	4.58358e6i	0.228872	+	0.228872i
$834$	1.32574e6	+	3.57995e6i	0.0659997	+	0.178222i
$835$	−4.92284e6	+	6.26067e6i	−0.244343	+	0.310746i
$836$		−	2.01170e7i		−	0.995515i
$837$	1.72668e6	+	6.03671e6i	0.0851921	+	0.297843i
$838$	6.80560e6	−	6.80560e6i	0.334778	−	0.334778i
$839$	−2.22871e7			−1.09307			−0.546536	−	0.837435i	$-0.684054\pi$
$839$	−2.22871e7			−1.09307			−0.546536	+	0.837435i	$0.684054\pi$
$840$	−46749.4	+	145106.i	−0.00228601	+	0.00709555i
$841$	−1.04062e7			−0.507342
$842$	−6.39402e6	+	6.39402e6i	−0.310809	+	0.310809i
$843$	9.49880e6	−	2.06716e7i	0.460362	−	1.00185i
$844$			2.19834e6i			0.106228i
$845$	1.86879e6	+	1.56219e7i	0.0900365	+	0.752650i
$846$	−4.20299e6	+	3.60767e6i	−0.201898	+	0.173301i
$847$	−421093.	−	421093.i	−0.0201683	−	0.0201683i
$848$	5.14695e6	+	5.14695e6i	0.245788	+	0.245788i
$849$	1.19639e6	−	443050.i	0.0569644	−	0.0210952i
$850$	−1.13767e6	−	4.68708e6i	−0.0540096	−	0.222513i
$851$			5.64853e7i			2.67369i
$852$	9.71520e6	+	4.46424e6i	0.458514	+	0.210692i
$853$	808864.	−	808864.i	0.0380630	−	0.0380630i	−0.687819	−	0.725882i	$-0.741432\pi$
$853$	808864.	−	808864.i	0.0380630	−	0.0380630i	0.725882	+	0.687819i	$0.241432\pi$
$854$	−182133.			−0.00854563
$855$	1.87584e7	−	2.04447e7i	0.877568	−	0.956459i
$856$	−7.22147e6			−0.336853
$857$	1.82494e7	−	1.82494e7i	0.848783	−	0.848783i	−0.141198	−	0.989981i	$-0.545096\pi$
$857$	1.82494e7	−	1.82494e7i	0.848783	−	0.848783i	0.989981	+	0.141198i	$0.0450956\pi$
$858$	−1.04540e7	−	4.80373e6i	−0.484802	−	0.222772i
$859$		−	3.76682e7i		−	1.74177i	−0.491483	−	0.870887i	$-0.663545\pi$
$859$		−	3.76682e7i		−	1.74177i	0.491483	−	0.870887i	$-0.336455\pi$
$860$	1.14486e7	+	9.00216e6i	0.527845	+	0.415050i
$861$	−55586.0	+	20584.7i	−0.00255539	+	0.000946319i
$862$	1.10866e7	+	1.10866e7i	0.508196	+	0.508196i
$863$	−2.54896e7	−	2.54896e7i	−1.16503	−	1.16503i	−0.983360	−	0.181668i	$-0.941850\pi$
$863$	−2.54896e7	−	2.54896e7i	−1.16503	−	1.16503i	−0.181668	−	0.983360i	$-0.558150\pi$
$864$	3.39133e6	+	1.88277e6i	0.154556	+	0.0858052i
$865$	−7.09572e6	−	5.57944e6i	−0.322445	−	0.253542i
$866$		−	1.73338e7i		−	0.785416i
$867$	−8.27249e6	+	1.80028e7i	−0.373756	+	0.813379i
$868$	51261.7	−	51261.7i	0.00230937	−	0.00230937i
$869$	−4.78412e7			−2.14908
$870$	−9.86019e6	+	5.05492e6i	−0.441659	+	0.226421i
$871$	3.59141e6			0.160405
$872$	1.54329e6	−	1.54329e6i	0.0687318	−	0.0687318i
$873$	1.02980e6	−	1.35112e7i	0.0457318	−	0.600010i
$874$		−	3.43981e7i		−	1.52320i
$875$	434408.	+	198292.i	0.0191813	+	0.00875559i
$876$	−2.78446e6	−	7.51900e6i	−0.122597	−	0.331055i
$877$	1.32079e7	+	1.32079e7i	0.579873	+	0.579873i	0.934868	−	0.354995i	$-0.115517\pi$
$877$	1.32079e7	+	1.32079e7i	0.579873	+	0.579873i	−0.354995	+	0.934868i	$0.615517\pi$
$878$	8.78494e6	+	8.78494e6i	0.384594	+	0.384594i
$879$	1.28050e7	+	3.45781e7i	0.558996	+	1.50949i
$880$	−1.04634e6	−	8.74675e6i	−0.0455476	−	0.380750i
$881$		−	4.17368e7i		−	1.81167i	−0.423628	−	0.905836i	$-0.639244\pi$
$881$		−	4.17368e7i		−	1.81167i	0.423628	−	0.905836i	$-0.360756\pi$
$882$	−1.24098e6	+	1.62819e7i	−0.0537148	+	0.704748i
$883$	2.31670e7	−	2.31670e7i	0.999927	−	0.999927i	−7.31900e−5	−	1.00000i	$-0.500023\pi$
$883$	2.31670e7	−	2.31670e7i	0.999927	−	0.999927i	1.00000		7.31900e-5i	$2.32971e-5\pi$
$884$	1.85052e6			0.0796460
$885$	−3.02459e7	−	9.74446e6i	−1.29810	−	0.418215i
$886$	−1.61350e7			−0.690532
$887$	2.36679e7	−	2.36679e7i	1.01007	−	1.01007i	0.0101211	−	0.999949i	$-0.496778\pi$
$887$	2.36679e7	−	2.36679e7i	1.01007	−	1.01007i	0.999949	−	0.0101211i	$-0.00322169\pi$
$888$	5.58878e6	−	1.21625e7i	0.237840	−	0.517594i
$889$			646350.i			0.0274292i
$890$	−1.51925e7	+	1.93212e7i	−0.642915	+	0.817635i
$891$	−3.59281e7	−	5.50876e6i	−1.51614	−	0.232466i
$892$	1.19921e6	+	1.19921e6i	0.0504640	+	0.0504640i
$893$	−8.23048e6	−	8.23048e6i	−0.345380	−	0.345380i
$894$	−1.51953e7	+	5.62715e6i	−0.635865	+	0.235475i
$895$	882272.	−	105543.i	0.0368167	−	0.00440424i
$896$		−	44785.9i		−	0.00186368i
$897$	−1.78753e7	−	8.21390e6i	−0.741776	−	0.340854i
$898$	1.47705e6	−	1.47705e6i	0.0611229	−	0.0611229i
$899$	5.26908e6			0.217438
$900$	7.09265e6	−	9.86493e6i	0.291879	−	0.405964i
$901$	1.09710e7			0.450232
$902$	2.42192e6	−	2.42192e6i	0.0991160	−	0.0991160i
$903$	−630464.	−	289705.i	−0.0257300	−	0.0118232i
$904$		−	9.33879e6i		−	0.380075i
$905$	4.17141e7	−	4.99009e6i	1.69302	−	0.202529i
$906$	1.08767e7	−	4.02789e6i	0.440227	−	0.163026i
$907$	−2.80206e7	−	2.80206e7i	−1.13099	−	1.13099i	−0.990013	−	0.140977i	$-0.954976\pi$
$907$	−2.80206e7	−	2.80206e7i	−1.13099	−	1.13099i	−0.140977	−	0.990013i	$-0.545024\pi$
$908$	3.84564e6	+	3.84564e6i	0.154794	+	0.154794i
$909$	−1.44409e7	+	1.23954e7i	−0.579674	+	0.497568i
$910$	−113246.	+	144022.i	−0.00453337	+	0.00576536i
$911$		−	1.80401e7i		−	0.720182i	−0.932917	−	0.360091i	$-0.882746\pi$
$911$		−	1.80401e7i		−	0.720182i	0.932917	−	0.360091i	$-0.117254\pi$
$912$	−3.40342e6	+	7.40662e6i	−0.135497	+	0.294872i
$913$	152330.	−	152330.i	0.00604795	−	0.00604795i
$914$	−1.86618e7			−0.738905
$915$	1.38163e7	+	4.45126e6i	0.545555	+	0.175764i
$916$	2.43121e6			0.0957378
$917$	−461430.	+	461430.i	−0.0181210	+	0.0181210i
$918$	5.62104e6	−	1.60779e6i	0.220145	−	0.0629683i
$919$		−	3.85473e6i		−	0.150559i	−0.997162	−	0.0752793i	$-0.976015\pi$
$919$		−	3.85473e6i		−	0.150559i	0.997162	−	0.0752793i	$-0.0239848\pi$
$920$	−1.78914e6	−	1.49561e7i	−0.0696905	−	0.582570i
$921$	1.60994e7	+	4.34740e7i	0.625404	+	1.68881i
$922$	7.93882e6	+	7.93882e6i	0.307559	+	0.307559i
$923$	9.08582e6	+	9.08582e6i	0.351043	+	0.351043i
$924$	145742.	+	393554.i	0.00561571	+	0.0151644i
$925$	−3.58028e7	−	2.18170e7i	−1.37582	−	0.838379i
$926$			3.03009e6i			0.116126i
$927$	4.07965e7	+	3.10945e6i	1.55928	+	0.118846i
$928$	2.30172e6	−	2.30172e6i	0.0877370	−	0.0877370i
$929$	−4.71857e7			−1.79379			−0.896895	−	0.442244i	$-0.854183\pi$
$929$	−4.71857e7			−1.79379			−0.896895	+	0.442244i	$0.854183\pi$
$930$	−5.14144e6	+	2.63581e6i	−0.194929	+	0.0999324i
$931$	−3.43142e7			−1.29748
$932$	−4.31473e6	+	4.31473e6i	−0.162710	+	0.162710i
$933$	−7.21589e6	+	1.57034e7i	−0.271385	+	0.590596i
$934$		−	2.29931e6i		−	0.0862441i
$935$	−1.04373e7	−	8.20695e6i	−0.390444	−	0.307010i
$936$	3.03623e6	+	3.53725e6i	0.113278	+	0.131970i
$937$	3.50679e7	+	3.50679e7i	1.30485	+	1.30485i	0.925080	+	0.379771i	$0.123997\pi$
$937$	3.50679e7	+	3.50679e7i	1.30485	+	1.30485i	0.379771	+	0.925080i	$0.376003\pi$
$938$	−92635.8	−	92635.8i	−0.00343773	−	0.00343773i
$939$	2.38002e7	−	8.81374e6i	0.880879	−	0.326209i
$940$	−4.00665e6	−	3.15047e6i	−0.147898	−	0.116294i
$941$		−	3.28687e7i		−	1.21007i	−0.796201	−	0.605033i	$-0.793160\pi$
$941$		−	3.28687e7i		−	1.21007i	0.796201	−	0.605033i	$-0.206840\pi$
$942$	−1.26292e7	−	5.80323e6i	−0.463711	−	0.213080i
$943$	4.14125e6	−	4.14125e6i	0.151653	−	0.151653i
$944$	9.33518e6			0.340951
$945$	−218859.	+	535865.i	−0.00797233	+	0.0195198i
$946$	4.00924e7			1.45658
$947$	−2.17688e7	+	2.17688e7i	−0.788787	+	0.788787i	−0.981295	−	0.192509i	$-0.938338\pi$
$947$	−2.17688e7	+	2.17688e7i	−0.788787	+	0.788787i	0.192509	+	0.981295i	$0.438338\pi$
$948$	1.76140e7	+	8.09384e6i	0.636558	+	0.292505i
$949$		−	9.63597e6i		−	0.347320i
$950$	2.18030e7	+	1.32860e7i	0.783803	+	0.477623i
$951$	−3.66445e6	+	1.35703e6i	−0.131388	+	0.0486561i
$952$	−47731.9	−	47731.9i	−0.00170693	−	0.00170693i
$953$	3.08708e7	+	3.08708e7i	1.10107	+	1.10107i	0.994282	+	0.106790i	$0.0340574\pi$
$953$	3.08708e7	+	3.08708e7i	1.10107	+	1.10107i	0.106790	+	0.994282i	$0.465943\pi$
$954$	1.80006e7	+	2.09710e7i	0.640349	+	0.746016i
$955$	−727223.	−	6.07913e6i	−0.0258023	−	0.215692i
$956$			1.59299e7i			0.563726i
$957$	−1.27361e7	+	2.77166e7i	−0.449526	+	0.978272i
$958$	6.69495e6	−	6.69495e6i	0.235686	−	0.235686i
$959$	−61809.7			−0.00217025
$960$	−1.09455e6	+	3.39738e6i	−0.0383316	+	0.118978i
$961$	−2.58817e7			−0.904032
$962$	1.13745e7	−	1.13745e7i	0.396274	−	0.396274i
$963$	−2.73397e7	−	2.08379e6i	−0.950010	−	0.0724082i
$964$			2.61517e7i			0.906373i
$965$	−2.99884e7	+	3.81381e7i	−1.03666	+	1.31838i
$966$	249204.	+	672939.i	0.00859236	+	0.0232024i
$967$	−2.40260e7	−	2.40260e7i	−0.826258	−	0.826258i	0.160739	−	0.986997i	$-0.448612\pi$
$967$	−2.40260e7	−	2.40260e7i	−0.826258	−	0.826258i	−0.986997	+	0.160739i	$0.948612\pi$
$968$	−9.85910e6	−	9.85910e6i	−0.338181	−	0.338181i
$969$	4.26654e6	+	1.15211e7i	0.145971	+	0.394172i
$970$	1.23807e7	−	1.48105e6i	0.422490	−	0.0505408i
$971$			7.01170e6i			0.238657i	0.992855	+	0.119329i	$0.0380742\pi$
$971$			7.01170e6i			0.238657i	−0.992855	+	0.119329i	$0.961926\pi$
$972$	1.22959e7	+	8.10656e6i	0.417441	+	0.275214i
$973$	118339.	−	118339.i	0.00400723	−	0.00400723i
$974$	1.88414e7			0.636378
$975$	1.21105e7	−	8.15759e6i	0.407992	−	0.274821i
$976$	−4.26430e6			−0.143292
$977$	1.55490e7	−	1.55490e7i	0.521154	−	0.521154i	−0.396766	−	0.917920i	$-0.629868\pi$
$977$	1.55490e7	−	1.55490e7i	0.521154	−	0.521154i	0.917920	+	0.396766i	$0.129868\pi$
$978$	−2.37386e6	+	5.16606e6i	−0.0793612	+	0.172708i
$979$			6.76619e7i			2.25625i
$980$	−1.49196e7	+	1.78477e6i	−0.496240	+	0.0593632i
$981$	6.28807e6	−	5.39742e6i	0.208615	−	0.179066i
$982$	2.22159e6	+	2.22159e6i	0.0735166	+	0.0735166i
$983$	2.90905e7	+	2.90905e7i	0.960213	+	0.960213i	0.999238	−	0.0390251i	$-0.0124252\pi$
$983$	2.90905e7	+	2.90905e7i	0.960213	+	0.960213i	−0.0390251	+	0.999238i	$0.512425\pi$
$984$	−1.30144e6	+	481953.i	−0.0428486	+	0.0158678i
$985$	−3.84631e6	+	4.89159e6i	−0.126315	+	0.160642i
$986$		−	4.90627e6i		−	0.160716i
$987$	220643.	+	101388.i	0.00720936	+	0.00331278i
$988$	−6.92680e6	+	6.92680e6i	−0.225757	+	0.225757i
$989$	6.85540e7			2.22865
$990$	−1.43741e6	−	3.34162e7i	−0.0466115	−	1.08360i
$991$	3.48056e6			0.112581			0.0562905	−	0.998414i	$-0.482073\pi$
$991$	3.48056e6			0.112581			0.0562905	+	0.998414i	$0.482073\pi$
$992$	1.20020e6	−	1.20020e6i	0.0387234	−	0.0387234i
$993$	−2.88250e7	−	1.32454e7i	−0.927675	−	0.426277i
$994$		−	468714.i		−	0.0150467i
$995$	−1.16437e6	−	9.73341e6i	−0.0372849	−	0.311679i
$996$	−81855.8	+	30313.0i	−0.00261457	+	0.000968235i
$997$	−2.04407e7	−	2.04407e7i	−0.651264	−	0.651264i	0.302033	−	0.953297i	$-0.402335\pi$
$997$	−2.04407e7	−	2.04407e7i	−0.651264	−	0.651264i	−0.953297	+	0.302033i	$0.902335\pi$
$998$	2.74016e6	+	2.74016e6i	0.0870863	+	0.0870863i
$999$	2.46681e7	−	4.44331e7i	0.782026	−	1.40862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.6.e.a.17.5	✓	20
3.2	odd	2	inner	30.6.e.a.17.7	yes	20
5.2	odd	4		150.6.e.b.143.4		20
5.3	odd	4	inner	30.6.e.a.23.7	yes	20
5.4	even	2		150.6.e.b.107.6		20
15.2	even	4		150.6.e.b.143.6		20
15.8	even	4	inner	30.6.e.a.23.5	yes	20
15.14	odd	2		150.6.e.b.107.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.6.e.a.17.5	✓	20	1.1	even	1	trivial
30.6.e.a.17.7	yes	20	3.2	odd	2	inner
30.6.e.a.23.5	yes	20	15.8	even	4	inner
30.6.e.a.23.7	yes	20	5.3	odd	4	inner
150.6.e.b.107.4		20	15.14	odd	2
150.6.e.b.107.6		20	5.4	even	2
150.6.e.b.143.4		20	5.2	odd	4
150.6.e.b.143.6		20	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 2.82843i) q^{2} +(14.1646 + 6.50878i) q^{3} -16.0000i q^{4} +(55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 + 1.93288i) q^{7} +(45.2548 + 45.2548i) q^{8} +(158.272 + 184.389i) q^{9} +O(q^{10})\)	\(q+(-2.82843 + 2.82843i) q^{2} +(14.1646 + 6.50878i) q^{3} -16.0000i q^{4} +(55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 + 1.93288i) q^{7} +(45.2548 + 45.2548i) q^{8} +(158.272 + 184.389i) q^{9} +(-138.214 + 175.775i) q^{10} +615.555i q^{11} +(104.141 - 226.634i) q^{12} +(211.952 - 211.952i) q^{13} -10.9340 q^{14} +(829.437 + 267.224i) q^{15} -256.000 q^{16} +(-272.840 + 272.840i) q^{17} +(-969.189 - 73.8700i) q^{18} -2042.57i q^{19} +(-106.239 - 888.095i) q^{20} +(14.7978 + 39.9593i) q^{21} +(-1741.05 - 1741.05i) q^{22} +(-2977.03 - 2977.03i) q^{23} +(346.463 + 935.570i) q^{24} +(3036.82 - 737.114i) q^{25} +1198.98i q^{26} +(1041.71 + 3641.94i) q^{27} +(30.9262 - 30.9262i) q^{28} +3178.83 q^{29} +(-3101.83 + 1590.18i) q^{30} +1657.55 q^{31} +(724.077 - 724.077i) q^{32} +(-4006.52 + 8719.09i) q^{33} -1543.42i q^{34} +(120.121 + 94.4523i) q^{35} +(2950.22 - 2532.34i) q^{36} +(-9486.85 - 9486.85i) q^{37} +(5777.25 + 5777.25i) q^{38} +(4381.76 - 1622.66i) q^{39} +(2812.40 + 2211.42i) q^{40} +1391.07i q^{41} +(-154.876 - 71.1673i) q^{42} +(-11513.8 + 11513.8i) q^{43} +9848.89 q^{44} +(10009.3 + 9183.74i) q^{45} +16840.6 q^{46} +(4029.48 - 4029.48i) q^{47} +(-3626.14 - 1666.25i) q^{48} -16799.5i q^{49} +(-6504.56 + 10674.3i) q^{50} +(-5640.53 + 2088.81i) q^{51} +(-3391.23 - 3391.23i) q^{52} +(-20105.3 - 20105.3i) q^{53} +(-13247.4 - 7354.58i) q^{54} +(4087.26 + 34167.0i) q^{55} +174.945i q^{56} +(13294.6 - 28932.1i) q^{57} +(-8991.10 + 8991.10i) q^{58} -36465.5 q^{59} +(4275.58 - 13271.0i) q^{60} +16657.4 q^{61} +(-4688.26 + 4688.26i) q^{62} +(-50.4811 + 662.322i) q^{63} +4096.00i q^{64} +(10357.2 - 13171.9i) q^{65} +(-13329.2 - 35993.5i) q^{66} +(8472.23 + 8472.23i) q^{67} +(4365.44 + 4365.44i) q^{68} +(-22791.6 - 61545.2i) q^{69} +(-606.905 + 72.6016i) q^{70} +42867.4i q^{71} +(-1181.92 + 15507.0i) q^{72} +(22731.5 - 22731.5i) q^{73} +53665.7 q^{74} +(47813.1 + 9325.09i) q^{75} -32681.1 q^{76} +(-1189.80 + 1189.80i) q^{77} +(-7803.89 + 16983.1i) q^{78} +77720.3i q^{79} +(-14209.5 + 1699.83i) q^{80} +(-8949.25 + 58366.9i) q^{81} +(-3934.53 - 3934.53i) q^{82} +(-247.467 - 247.467i) q^{83} +(639.348 - 236.765i) q^{84} +(-13332.6 + 16955.9i) q^{85} -65132.1i q^{86} +(45026.9 + 20690.3i) q^{87} +(-27856.9 + 27856.9i) q^{88} +109920. q^{89} +(-54286.3 + 2335.15i) q^{90} +819.356 q^{91} +(-47632.5 + 47632.5i) q^{92} +(23478.6 + 10788.6i) q^{93} +22794.2i q^{94} +(-13562.6 - 113375. i) q^{95} +(14969.1 - 5543.40i) q^{96} +(-39430.4 - 39430.4i) q^{97} +(47516.2 + 47516.2i) q^{98} +(-113501. + 97424.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + 80 q^{6} + 76 q^{7}+O(q^{10}) \) 20 * q - 4 * q^3 + 80 * q^6 + 76 * q^7	\( 20 q - 4 q^{3} + 80 q^{6} + 76 q^{7} - 496 q^{10} + 64 q^{12} + 2640 q^{13} + 3128 q^{15} - 5120 q^{16} - 2272 q^{18} - 760 q^{21} - 464 q^{22} - 15776 q^{25} + 16556 q^{27} + 1216 q^{28} + 3408 q^{30} + 23960 q^{31} - 7684 q^{33} - 13120 q^{36} - 60696 q^{37} - 512 q^{40} + 46864 q^{42} + 48024 q^{43} + 31912 q^{45} + 58880 q^{46} + 1024 q^{48} - 155240 q^{51} - 42240 q^{52} - 132228 q^{55} + 167744 q^{57} + 38000 q^{58} + 19136 q^{60} + 160680 q^{61} - 219364 q^{63} - 158560 q^{66} - 118736 q^{67} - 55216 q^{70} + 36352 q^{72} + 379100 q^{73} + 365548 q^{75} + 78080 q^{76} - 25440 q^{78} - 282260 q^{81} - 262976 q^{82} - 227432 q^{85} + 249380 q^{87} - 7424 q^{88} - 128992 q^{90} + 499200 q^{91} - 304072 q^{93} - 20480 q^{96} - 288228 q^{97}+O(q^{100}) \) 20 * q - 4 * q^3 + 80 * q^6 + 76 * q^7 - 496 * q^10 + 64 * q^12 + 2640 * q^13 + 3128 * q^15 - 5120 * q^16 - 2272 * q^18 - 760 * q^21 - 464 * q^22 - 15776 * q^25 + 16556 * q^27 + 1216 * q^28 + 3408 * q^30 + 23960 * q^31 - 7684 * q^33 - 13120 * q^36 - 60696 * q^37 - 512 * q^40 + 46864 * q^42 + 48024 * q^43 + 31912 * q^45 + 58880 * q^46 + 1024 * q^48 - 155240 * q^51 - 42240 * q^52 - 132228 * q^55 + 167744 * q^57 + 38000 * q^58 + 19136 * q^60 + 160680 * q^61 - 219364 * q^63 - 158560 * q^66 - 118736 * q^67 - 55216 * q^70 + 36352 * q^72 + 379100 * q^73 + 365548 * q^75 + 78080 * q^76 - 25440 * q^78 - 282260 * q^81 - 262976 * q^82 - 227432 * q^85 + 249380 * q^87 - 7424 * q^88 - 128992 * q^90 + 499200 * q^91 - 304072 * q^93 - 20480 * q^96 - 288228 * q^97

Introduction

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