LMFDB - Embedded newform 30.6.e.a.23.7

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			23.7
Root			$1.34618i$ of defining polynomial
Character	$\chi$	$=$	30.23
Dual form			30.6.e.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82843 + 2.82843i) q^{2} +(-6.50878 + 14.1646i) q^{3} +16.0000i q^{4} +(-55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 - 1.93288i) q^{7} +(-45.2548 + 45.2548i) q^{8} +(-158.272 - 184.389i) q^{9} +O(q^{10})$	\(q+(2.82843 + 2.82843i) q^{2} +(-6.50878 + 14.1646i) 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} +(-226.634 - 104.141i) q^{12} +(211.952 + 211.952i) q^{13} +10.9340 q^{14} +(455.328 - 743.001i) q^{15} -256.000 q^{16} +(272.840 + 272.840i) q^{17} +(73.8700 - 969.189i) 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} +(3641.94 - 1041.71i) q^{27} +(30.9262 + 30.9262i) q^{28} -3178.83 q^{29} +(3389.39 - 813.662i) q^{30} +1657.55 q^{31} +(-724.077 - 724.077i) q^{32} +(-8719.09 - 4006.52i) 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} +(-71.1673 + 154.876i) q^{42} +(-11513.8 - 11513.8i) q^{43} -9848.89 q^{44} +(7560.68 + 11285.6i) q^{45} +16840.6 q^{46} +(-4029.48 - 4029.48i) q^{47} +(1666.25 - 3626.14i) 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} +(-28932.1 - 13294.6i) q^{57} +(-8991.10 - 8991.10i) q^{58} +36465.5 q^{59} +(11888.0 + 7285.25i) q^{60} +16657.4 q^{61} +(4688.26 + 4688.26i) q^{62} +(-662.322 - 50.4811i) 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} +(15507.0 + 1181.92i) q^{72} +(22731.5 + 22731.5i) q^{73} -53665.7 q^{74} +(-30206.9 + 38217.6i) q^{75} -32681.1 q^{76} +(1189.80 + 1189.80i) q^{77} +(-16983.1 - 7803.89i) 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} +(20690.3 - 45026.9i) q^{87} +(-27856.9 - 27856.9i) q^{88} -109920. q^{89} +(-10535.6 + 53305.3i) q^{90} +819.356 q^{91} +(47632.5 + 47632.5i) q^{92} +(-10788.6 + 23478.6i) 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 $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−6.50878	+	14.1646i	−0.417539	+	0.908659i
$3$	−6.50878	+	14.1646i	−0.417539	+	0.908659i
$4$			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	−0.699613	−	0.714522i	$-0.746644\pi$
$7$	1.93288	−	1.93288i	0.0149094	−	0.0149094i	0.714522	+	0.699613i	$0.246644\pi$
$8$	−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	$0.721784\pi$
$12$	−226.634	−	104.141i	−0.454330	−	0.208769i
$13$	211.952	+	211.952i	0.347839	+	0.347839i	0.859304	−	0.511465i	$-0.170897\pi$
$13$	211.952	+	211.952i	0.347839	+	0.347839i	−0.511465	+	0.859304i	$0.670897\pi$
$14$	10.9340			0.0149094
$15$	455.328	−	743.001i	0.522512	−	0.852632i
$16$	−256.000			−0.250000
$17$	272.840	+	272.840i	0.228974	+	0.228974i	0.812264	−	0.583290i	$-0.198235\pi$
$17$	272.840	+	272.840i	0.228974	+	0.228974i	−0.583290	+	0.812264i	$0.698235\pi$
$18$	73.8700	−	969.189i	0.0537387	−	0.705062i
$19$			2042.57i			1.29805i	0.760766	+	0.649026i	$0.224823\pi$
$19$			2042.57i			1.29805i	−0.760766	+	0.649026i	$0.775177\pi$
$20$	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	0.192065	−	0.981382i	$-0.438482\pi$
$23$	2977.03	−	2977.03i	1.17345	−	1.17345i	0.981382	−	0.192065i	$-0.0615184\pi$
$24$	−346.463	−	935.570i	−0.122780	−	0.331549i
$25$	3036.82	+	737.114i	0.971783	+	0.235877i
$26$			1198.98i			0.347839i
$27$	3641.94	−	1041.71i	0.961444	−	0.275002i
$28$	30.9262	+	30.9262i	0.00745471	+	0.00745471i
$29$	−3178.83			−0.701896			−0.350948	−	0.936395i	$-0.614141\pi$
$29$	−3178.83			−0.701896			−0.350948	+	0.936395i	$0.614141\pi$
$30$	3389.39	−	813.662i	0.687572	−	0.165060i
$31$	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
$33$	−8719.09	−	4006.52i	−1.39376	−	0.640445i
$34$			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	−0.150661	+	0.988585i	$0.548140\pi$
$37$	−9486.85	+	9486.85i	−1.13925	+	1.13925i	−0.988585	+	0.150661i	$0.951860\pi$
$38$	−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	$0.979417\pi$
$42$	−71.1673	+	154.876i	−0.00622526	+	0.0135476i
$43$	−11513.8	−	11513.8i	−0.949617	−	0.949617i	0.0491729	−	0.998790i	$-0.484341\pi$
$43$	−11513.8	−	11513.8i	−0.949617	−	0.949617i	−0.998790	+	0.0491729i	$0.984341\pi$
$44$	−9848.89			−0.766929
$45$	7560.68	+	11285.6i	0.556583	+	0.830792i
$46$	16840.6			1.17345
$47$	−4029.48	−	4029.48i	−0.266075	−	0.266075i	0.561441	−	0.827517i	$-0.310247\pi$
$47$	−4029.48	−	4029.48i	−0.266075	−	0.266075i	−0.827517	+	0.561441i	$0.810247\pi$
$48$	1666.25	−	3626.14i	0.104385	−	0.227165i
$49$			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	$-0.505319\pi$
$53$	20105.3	−	20105.3i	0.983151	−	0.983151i	0.999860	+	0.0167091i	$0.00531893\pi$
$54$	13247.4	+	7354.58i	0.618223	+	0.343221i
$55$	4087.26	−	34167.0i	0.182190	−	1.52300i
$56$			174.945i			0.00745471i
$57$	−28932.1	−	13294.6i	−1.17949	−	0.541987i
$58$	−8991.10	−	8991.10i	−0.350948	−	0.350948i
$59$	36465.5			1.36381			0.681903	−	0.731443i	$-0.261153\pi$
$59$	36465.5			1.36381			0.681903	+	0.731443i	$0.261153\pi$
$60$	11888.0	+	7285.25i	0.426316	+	0.261256i
$61$	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
$63$	−662.322	−	50.4811i	−0.0210241	−	0.00160243i
$64$		−	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	−0.582358	−	0.812932i	$-0.697870\pi$
$67$	8472.23	−	8472.23i	0.230574	−	0.230574i	0.812932	+	0.582358i	$0.197870\pi$
$68$	−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	$0.831638\pi$
$72$	15507.0	+	1181.92i	0.352531	+	0.0268693i
$73$	22731.5	+	22731.5i	0.499254	+	0.499254i	0.911206	−	0.411952i	$-0.135153\pi$
$73$	22731.5	+	22731.5i	0.499254	+	0.499254i	−0.411952	+	0.911206i	$0.635153\pi$
$74$	−53665.7			−1.13925
$75$	−30206.9	+	38217.6i	−0.620088	+	0.784532i
$76$	−32681.1			−0.649026
$77$	1189.80	+	1189.80i	0.0228690	+	0.0228690i
$78$	−16983.1	−	7803.89i	−0.316067	−	0.145236i
$79$		−	77720.3i		−	1.40109i	−0.713607	−	0.700547i	$-0.752940\pi$
$79$		−	77720.3i		−	1.40109i	0.713607	−	0.700547i	$-0.247060\pi$
$80$	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	$-0.749113\pi$
$83$	247.467	−	247.467i	0.00394296	−	0.00394296i	0.709076	+	0.705133i	$0.249113\pi$
$84$	−639.348	+	236.765i	−0.00988642	+	0.00366116i
$85$	−13332.6	−	16955.9i	−0.200156	−	0.254550i
$86$		−	65132.1i		−	0.949617i
$87$	20690.3	−	45026.9i	0.293069	−	0.637785i
$88$	−27856.9	−	27856.9i	−0.383465	−	0.383465i
$89$	−109920.			−1.47096			−0.735482	−	0.677544i	$-0.763044\pi$
$89$	−109920.			−1.47096			−0.735482	+	0.677544i	$0.763044\pi$
$90$	−10535.6	+	53305.3i	−0.137105	+	0.693687i
$91$	819.356			0.0103722
$92$	47632.5	+	47632.5i	0.586724	+	0.586724i
$93$	−10788.6	+	23478.6i	−0.129348	+	0.281491i
$94$		−	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	−0.887093	−	0.461591i	$-0.847279\pi$
$97$	−39430.4	+	39430.4i	−0.425502	+	0.425502i	0.461591	+	0.887093i	$0.347279\pi$
$98$	−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	$0.875247\pi$
$102$	−21861.9	−	10045.8i	−0.208059	−	0.0956054i
$103$	119058.	+	119058.i	1.10578	+	1.10578i	0.993700	+	0.112075i	$0.0357498\pi$
$103$	119058.	+	119058.i	1.10578	+	1.10578i	0.112075	+	0.993700i	$0.464250\pi$
$104$	−19183.7			−0.173920
$105$	−556.039	−	2316.23i	−0.00492189	−	0.0205026i
$106$	113733.			0.983151
$107$	79786.7	+	79786.7i	0.673707	+	0.673707i	0.958569	−	0.284862i	$-0.0919477\pi$
$107$	79786.7	+	79786.7i	0.673707	+	0.673707i	−0.284862	+	0.958569i	$0.591948\pi$
$108$	16667.3	+	58271.1i	0.137501	+	0.480722i
$109$			34102.3i			0.274927i	0.990507	+	0.137464i	$0.0438950\pi$
$109$			34102.3i			0.274927i	−0.990507	+	0.137464i	$0.956105\pi$
$110$	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	$-0.569366\pi$
$113$	103180.	−	103180.i	0.760150	−	0.760150i	0.976349	+	0.216199i	$0.0693660\pi$
$114$	−44229.6	−	119435.i	−0.318750	−	0.860737i
$115$	−185010.	+	145475.i	−1.30452	+	1.02576i
$116$		−	50861.4i		−	0.350948i
$117$	5535.54	−	72627.3i	0.0373848	−	0.490496i
$118$	103140.	+	103140.i	0.681903	+	0.681903i
$119$	1054.74			0.00682774
$120$	13018.6	+	54230.2i	0.0825298	+	0.343786i
$121$	−217857.			−1.35272
$122$	47114.3	+	47114.3i	0.286585	+	0.286585i
$123$	−19703.9	−	9054.15i	−0.117433	−	0.0539616i
$124$			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	−0.0771578	−	0.997019i	$-0.524585\pi$
$127$	167198.	−	167198.i	0.919861	−	0.919861i	0.997019	+	0.0771578i	$0.0245845\pi$
$128$	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	$0.792091\pi$
$132$	64104.2	−	139505.i	0.320223	−	0.696878i
$133$	3948.05	+	3948.05i	0.0193532	+	0.0193532i
$134$	47926.2			0.230574
$135$	−209066.	+	33638.6i	−0.987302	+	0.158856i
$136$	−24694.7			−0.114487
$137$	15989.0	+	15989.0i	0.0727812	+	0.0727812i	0.742560	−	0.669779i	$-0.233611\pi$
$137$	15989.0	+	15989.0i	0.0727812	+	0.0727812i	−0.669779	+	0.742560i	$0.733611\pi$
$138$	−109612.	+	238541.i	−0.489959	+	1.06626i
$139$			61223.8i			0.268772i	0.990929	+	0.134386i	$0.0429062\pi$
$139$			61223.8i			0.268772i	−0.990929	+	0.134386i	$0.957094\pi$
$140$	−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
$147$	−237959.	−	109344.i	−0.908255	−	0.417353i
$148$	−151790.	−	151790.i	−0.569623	−	0.569623i
$149$	−259868.			−0.958930			−0.479465	−	0.877561i	$-0.659169\pi$
$149$	−259868.			−0.958930			−0.479465	+	0.877561i	$0.659169\pi$
$150$	−193534.	+	22657.7i	−0.702310	+	0.0822219i
$151$	−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
$153$	7125.76	−	93491.4i	0.0246095	−	0.322881i
$154$			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	−0.404302	−	0.914626i	$-0.632485\pi$
$157$	157614.	−	157614.i	0.510324	−	0.510324i	0.914626	+	0.404302i	$0.132485\pi$
$158$	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
$162$	−190399.	+	139774.i	−0.570002	+	0.418446i
$163$	64473.4	+	64473.4i	0.190069	+	0.190069i	0.795726	−	0.605657i	$-0.207090\pi$
$163$	64473.4	+	64473.4i	0.190069	+	0.190069i	−0.605657	+	0.795726i	$0.707090\pi$
$164$	−22257.1			−0.0646187
$165$	457358.	+	280280.i	1.30782	+	0.801460i
$166$	1399.89			0.00394296
$167$	100742.	+	100742.i	0.279523	+	0.279523i	0.832919	−	0.553396i	$-0.186668\pi$
$167$	100742.	+	100742.i	0.279523	+	0.279523i	−0.553396	+	0.832919i	$0.686668\pi$
$168$	−2478.02	−	1138.68i	−0.00677379	−	0.00311263i
$169$		−	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	$-0.684250\pi$
$173$	114178.	−	114178.i	0.290047	−	0.290047i	0.837099	+	0.547052i	$0.184250\pi$
$174$	185876.	−	68834.2i	0.465427	−	0.172358i
$175$	7294.58	−	4445.07i	0.0180055	−	0.0109719i
$176$		−	157582.i		−	0.383465i
$177$	−237346.	+	516520.i	−0.569442	+	1.23923i
$178$	−310901.	−	310901.i	−0.735482	−	0.735482i
$179$	−15895.1			−0.0370792			−0.0185396	−	0.999828i	$-0.505902\pi$
$179$	−15895.1			−0.0370792			−0.0185396	+	0.999828i	$0.505902\pi$
$180$	−180569.	+	120971.i	−0.415396	+	0.278291i
$181$	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
$183$	−108420.	+	235946.i	−0.239320	+	0.520816i
$184$			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	$-0.0346415\pi$
$192$	58018.2	+	26660.0i	0.113582	+	0.0521923i
$193$	−613686.	−	613686.i	−1.18591	−	1.18591i	−0.978187	−	0.207727i	$-0.933393\pi$
$193$	−613686.	−	613686.i	−1.18591	−	1.18591i	−0.207727	−	0.978187i	$-0.566607\pi$
$194$	−223052.			−0.425502
$195$	253988.	−	60972.7i	0.478329	−	0.114828i
$196$	−268792.			−0.499778
$197$	78711.3	+	78711.3i	0.144501	+	0.144501i	0.775657	−	0.631155i	$-0.217419\pi$
$197$	78711.3	+	78711.3i	0.144501	+	0.144501i	−0.631155	+	0.775657i	$0.717419\pi$
$198$	596589.	+	45471.1i	1.08147	+	0.0824275i
$199$			175358.i			0.313901i	0.987606	+	0.156951i	$0.0501663\pi$
$199$			175358.i			0.313901i	−0.987606	+	0.156951i	$0.949834\pi$
$200$	−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
$207$	−1.02011e6	−	77751.0i	−1.65471	−	0.126119i
$208$	−54259.6	−	54259.6i	−0.0869598	−	0.0869598i
$209$	−1.25731e6			−1.99103
$210$	4978.58	−	8124.01i	0.00779036	−	0.0127122i
$211$	−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
$213$	−607200.	−	279015.i	−0.917028	−	0.421384i
$214$			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
$222$	349299.	−	760154.i	0.475679	−	1.03519i
$223$	−74950.4	−	74950.4i	−0.100928	−	0.100928i	0.654840	−	0.755768i	$-0.272736\pi$
$223$	−74950.4	−	74950.4i	−0.100928	−	0.100928i	−0.755768	+	0.654840i	$0.772736\pi$
$224$	−2799.12			−0.00372736
$225$	−344727.	−	676619.i	−0.453962	−	0.891021i
$226$	583674.			0.760150
$227$	240353.	+	240353.i	0.309588	+	0.309588i	0.844750	−	0.535162i	$-0.179749\pi$
$227$	240353.	+	240353.i	0.309588	+	0.309588i	−0.535162	+	0.844750i	$0.679749\pi$
$228$	212714.	−	462914.i	0.270993	−	0.589744i
$229$		−	151951.i		−	0.191476i	−0.995407	−	0.0957378i	$-0.969479\pi$
$229$		−	151951.i		−	0.191476i	0.995407	−	0.0957378i	$-0.0305210\pi$
$230$	−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	$-0.676093\pi$
$233$	269671.	−	269671.i	0.325420	−	0.325420i	0.850842	+	0.525422i	$0.176093\pi$
$234$	221078.	−	189764.i	0.263940	−	0.226556i
$235$	196905.	+	250416.i	0.232587	+	0.295796i
$236$			583449.i			0.681903i
$237$	1.10088e6	+	505865.i	1.27312	+	0.585010i
$238$	2983.25	+	2983.25i	0.00341387	+	0.00341387i
$239$	995618.			1.12745			0.563726	−	0.825962i	$-0.309367\pi$
$239$	995618.			1.12745			0.563726	+	0.825962i	$0.309367\pi$
$240$	−116564.	+	190208.i	−0.130628	+	0.213158i
$241$	−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
$243$	−768495.	−	506660.i	−0.834882	−	0.550428i
$244$			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	$-0.254046\pi$
$252$	807.698	−	10597.2i	0.000801213	−	0.0105121i
$253$	1.83253e6	+	1.83253e6i	1.79990	+	1.79990i
$254$	945816.			0.919861
$255$	326952.	−	78488.7i	0.314872	−	0.0755887i
$256$	65536.0			0.0625000
$257$	−399795.	−	399795.i	−0.377576	−	0.377576i	0.492651	−	0.870227i	$-0.336028\pi$
$257$	−399795.	−	399795.i	−0.377576	−	0.377576i	−0.870227	+	0.492651i	$0.836028\pi$
$258$	922569.	+	423930.i	0.862879	+	0.396502i
$259$			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	$-0.756644\pi$
$263$	−33111.1	+	33111.1i	−0.0295178	+	0.0295178i	0.692194	+	0.721712i	$0.256644\pi$
$264$	575895.	−	213267.i	0.508550	−	0.188327i
$265$	−1.24946e6	+	982464.i	−1.09297	+	0.859413i
$266$			22333.5i			0.0193532i
$267$	715446.	−	1.55697e6i	0.614184	−	1.33661i
$268$	135556.	+	135556.i	0.115287	+	0.115287i
$269$	764920.			0.644518			0.322259	−	0.946652i	$-0.395558\pi$
$269$	764920.			0.644518			0.322259	+	0.946652i	$0.395558\pi$
$270$	−686474.	−	496185.i	−0.573079	−	0.414223i
$271$	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
$273$	−5333.01	+	11605.8i	−0.00433078	+	0.00942476i
$274$			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	−0.491377	−	0.870947i	$-0.663506\pi$
$277$	484721.	−	484721.i	0.379571	−	0.379571i	0.870947	+	0.491377i	$0.163506\pi$
$278$	−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	$-0.185861\pi$
$282$	322870.	+	148362.i	0.241772	+	0.111097i
$283$	57871.0	+	57871.0i	0.0429531	+	0.0429531i	0.728257	−	0.685304i	$-0.240331\pi$
$283$	57871.0	+	57871.0i	0.0429531	+	0.0429531i	−0.685304	+	0.728257i	$0.740331\pi$
$284$	−685879.			−0.504605
$285$	1.51763e6	+	930039.i	1.10676	+	0.678248i
$286$	−738038.			−0.533536
$287$	2688.77	+	2688.77i	0.00192686	+	0.00192686i
$288$	−18910.7	+	248112.i	−0.0134347	+	0.176265i
$289$		−	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	−0.149433	+	0.988772i	$0.547745\pi$
$293$	−1.67259e6	+	1.67259e6i	−1.13821	+	1.13821i	−0.988772	+	0.149433i	$0.952255\pi$
$294$	−363775.	−	982321.i	−0.245451	−	0.662804i
$295$	−2.02405e6	−	242130.i	−1.35415	−	0.161992i
$296$		−	858652.i		−	0.569623i
$297$	641229.	+	2.24182e6i	0.421815	+	1.47472i
$298$	−735017.	−	735017.i	−0.479465	−	0.479465i
$299$	1.26197e6			0.816341
$300$	−611482.	−	483311.i	−0.392266	−	0.310044i
$301$	−44509.8			−0.0283165
$302$	−526121.	−	526121.i	−0.331947	−	0.331947i
$303$	−1.10934e6	−	509752.i	−0.694156	−	0.318972i
$304$		−	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	0.329143	−	0.944280i	$-0.393240\pi$
$307$	2.10290e6	−	2.10290e6i	1.27342	−	1.27342i	0.944280	−	0.329143i	$-0.106760\pi$
$308$	−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	$0.894642\pi$
$312$	124862.	−	271729.i	0.0726181	−	0.158034i
$313$	1.15125e6	+	1.15125e6i	0.664214	+	0.664214i	0.956370	−	0.292157i	$-0.0943728\pi$
$313$	1.15125e6	+	1.15125e6i	0.664214	+	0.664214i	−0.292157	+	0.956370i	$0.594373\pi$
$314$	891600.			0.510324
$315$	36427.6	+	7199.80i	0.0206850	+	0.00408831i
$316$	1.24353e6			0.700547
$317$	177254.	+	177254.i	0.0990715	+	0.0990715i	0.754905	−	0.655834i	$-0.227683\pi$
$317$	177254.	+	177254.i	0.0990715	+	0.0990715i	−0.655834	+	0.754905i	$0.727683\pi$
$318$	−740261.	+	1.61098e6i	−0.410504	+	0.893349i
$319$		−	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
$327$	−483045.	−	221964.i	−0.249815	−	0.114793i
$328$	−62952.5	−	62952.5i	−0.0323094	−	0.0323094i
$329$	−15577.0			−0.00793406
$330$	500854.	+	2.08636e6i	0.253178	+	1.05464i
$331$	−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
$333$	3.25077e6	+	247768.i	1.60648	+	0.122443i
$334$			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	−0.908901	−	0.417012i	$-0.863077\pi$
$337$	−1.02552e6	+	1.02552e6i	−0.491889	+	0.491889i	0.417012	+	0.908901i	$0.363077\pi$
$338$	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
$342$	1.97963e6	+	150884.i	0.915207	+	0.0697556i
$343$	64957.5	+	64957.5i	0.0298122	+	0.0298122i
$344$	1.04211e6			0.474809
$345$	−856411.	−	3.56746e6i	−0.387377	−	1.61366i
$346$	645890.			0.290047
$347$	−1.31759e6	−	1.31759e6i	−0.587431	−	0.587431i	0.349504	−	0.936935i	$-0.386350\pi$
$347$	−1.31759e6	−	1.31759e6i	−0.587431	−	0.587431i	−0.936935	+	0.349504i	$0.886350\pi$
$348$	720431.	+	331045.i	0.318892	+	0.146534i
$349$		−	2.12112e6i		−	0.932182i	−0.884737	−	0.466091i	$-0.845662\pi$
$349$		−	2.12112e6i		−	0.932182i	0.884737	−	0.466091i	$-0.154338\pi$
$350$	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	$-0.607740\pi$
$353$	1.43096e6	−	1.43096e6i	0.611211	−	0.611211i	0.943262	+	0.332050i	$0.107740\pi$
$354$	−2.13225e6	+	789621.i	−0.904338	+	0.334897i
$355$	284638.	−	2.37940e6i	0.119873	−	1.00207i
$356$		−	1.75872e6i		−	0.735482i
$357$	−6865.05	+	14939.9i	−0.00285084	+	0.00620409i
$358$	−44958.1	−	44958.1i	−0.0185396	−	0.0185396i
$359$	3.53537e6			1.44777			0.723884	−	0.689921i	$-0.242355\pi$
$359$	3.53537e6			1.44777			0.723884	+	0.689921i	$0.242355\pi$
$360$	−852884.	−	168570.i	−0.346844	−	0.0685524i
$361$	−1.69598e6			−0.684940
$362$	2.12563e6	+	2.12563e6i	0.852543	+	0.852543i
$363$	1.41799e6	−	3.08586e6i	0.564814	−	1.22916i
$364$			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	−0.846491	−	0.532402i	$-0.821289\pi$
$367$	−810434.	+	810434.i	−0.314089	+	0.314089i	0.532402	+	0.846491i	$0.321289\pi$
$368$	−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
$372$	−375657.	−	172618.i	−0.140745	−	0.0646740i
$373$	−202954.	−	202954.i	−0.0755310	−	0.0755310i	0.668332	−	0.743863i	$-0.267009\pi$
$373$	−202954.	−	202954.i	−0.0755310	−	0.0755310i	−0.743863	+	0.668332i	$0.767009\pi$
$374$	−950058.			−0.351214
$375$	1.93043e6	−	1.92073e6i	0.708885	−	0.705325i
$376$	364707.			0.133038
$377$	−673759.	−	673759.i	−0.244147	−	0.244147i
$378$	39821.2	−	11390.1i	0.0143346	−	0.00410013i
$379$			2.26580e6i			0.810257i	0.914260	+	0.405128i	$0.132773\pi$
$379$			2.26580e6i			0.810257i	−0.914260	+	0.405128i	$0.867227\pi$
$380$	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	$-0.722675\pi$
$383$	348083.	−	348083.i	0.121251	−	0.121251i	0.765129	+	0.643878i	$0.222675\pi$
$384$	88694.4	+	239506.i	0.0306950	+	0.0828874i
$385$	−58140.7	−	73941.1i	−0.0199907	−	0.0254234i
$386$		−	3.47153e6i		−	1.18591i
$387$	−300707.	+	3.94533e6i	−0.102062	+	1.33908i
$388$	−630886.	−	630886.i	−0.212751	−	0.212751i
$389$	−3.80422e6			−1.27465			−0.637326	−	0.770594i	$-0.719960\pi$
$389$	−3.80422e6			−1.27465			−0.637326	+	0.770594i	$0.719960\pi$
$390$	890843.	+	545929.i	0.296579	+	0.181750i
$391$	1.62451e6			0.537377
$392$	−760260.	−	760260.i	−0.249889	−	0.249889i
$393$	−3.38146e6	−	1.55382e6i	−1.10439	−	0.507479i
$394$			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	−0.761666	−	0.647970i	$-0.775618\pi$
$397$	−357043.	+	357043.i	−0.113696	+	0.113696i	0.647970	+	0.761666i	$0.275618\pi$
$398$	−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	$0.731911\pi$
$402$	−311941.	+	678855.i	−0.0962736	+	0.209513i
$403$	351321.	+	351321.i	0.107756	+	0.107756i
$404$	−1.25308e6			−0.381967
$405$	884290.	−	3.18029e6i	0.267890	−	0.963449i
$406$	−34757.5			−0.0104649
$407$	−5.83968e6	−	5.83968e6i	−1.74744	−	1.74744i
$408$	160732.	−	349790.i	0.0478027	−	0.104030i
$409$			4.72643e6i			1.39709i	0.715565	+	0.698546i	$0.246169\pi$
$409$			4.72643e6i			1.39709i	−0.715565	+	0.698546i	$0.753831\pi$
$410$	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
$417$	−867211.	−	398493.i	−0.244222	−	0.112223i
$418$	−3.55622e6	−	3.55622e6i	−0.995515	−	0.995515i
$419$	2.40614e6			0.669556			0.334778	−	0.942297i	$-0.391339\pi$
$419$	2.40614e6			0.669556			0.334778	+	0.942297i	$0.391339\pi$
$420$	37059.7	−	8896.62i	0.0102513	−	0.00246094i
$421$	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
$423$	−105238.	+	1.38074e6i	−0.0285971	+	0.375199i
$424$			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	$-0.169688\pi$
$432$	−932338.	+	266677.i	−0.240361	+	0.0687506i
$433$	−3.06422e6	−	3.06422e6i	−0.785416	−	0.785416i	0.195323	−	0.980739i	$-0.437424\pi$
$433$	−3.06422e6	−	3.06422e6i	−0.785416	−	0.785416i	−0.980739	+	0.195323i	$0.937424\pi$
$434$	18123.8			0.00461874
$435$	−1.44741e6	+	2.36188e6i	−0.366750	+	0.598459i
$436$	−545637.			−0.137464
$437$	6.08078e6	+	6.08078e6i	1.52320	+	1.52320i
$438$	−1.82141e6	−	836958.i	−0.453652	−	0.208458i
$439$			3.10595e6i			0.769188i	0.923086	+	0.384594i	$0.125659\pi$
$439$			3.10595e6i			0.769188i	−0.923086	+	0.384594i	$0.874341\pi$
$440$	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	$-0.912375\pi$
$443$	−2.85228e6	+	2.85228e6i	−0.690532	+	0.690532i	0.271817	+	0.962349i	$0.412375\pi$
$444$	3.13800e6	−	1.16207e6i	0.755433	−	0.279754i
$445$	6.10122e6	+	729865.i	1.46055	+	0.174720i
$446$		−	423983.i		−	0.100928i
$447$	1.69142e6	−	3.68092e6i	0.400390	−	0.871340i
$448$	−7917.10	−	7917.10i	−0.00186368	−	0.00186368i
$449$	522216.			0.122246			0.0611229	−	0.998130i	$-0.480532\pi$
$449$	522216.			0.122246			0.0611229	+	0.998130i	$0.480532\pi$
$450$	938733.	−	2.88880e6i	0.218530	−	0.672491i
$451$	−856279.			−0.198232
$452$	1.65088e6	+	1.65088e6i	0.380075	+	0.380075i
$453$	1.21071e6	−	2.63479e6i	0.277201	−	0.603253i
$454$			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	−0.233461	−	0.972366i	$-0.575005\pi$
$457$	3.29898e6	−	3.29898e6i	0.738905	−	0.738905i	0.972366	+	0.233461i	$0.0750052\pi$
$458$	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	$-0.0995122\pi$
$462$	−95335.0	−	43807.4i	−0.0207801	−	0.00954867i
$463$	535649.	+	535649.i	0.116126	+	0.116126i	0.762782	−	0.646656i	$-0.223833\pi$
$463$	535649.	+	535649.i	0.116126	+	0.116126i	−0.646656	+	0.762782i	$0.723833\pi$
$464$	813782.			0.175474
$465$	754731.	−	1.23156e6i	0.161867	−	0.264134i
$466$	1.52549e6			0.325420
$467$	406464.	+	406464.i	0.0862441	+	0.0862441i	0.748913	−	0.662669i	$-0.230576\pi$
$467$	406464.	+	406464.i	0.0862441	+	0.0862441i	−0.662669	+	0.748913i	$0.730576\pi$
$468$	1.16204e6	+	88568.6i	0.245248	+	0.0186924i
$469$		−	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
$477$	−6.88927e6	−	525089.i	−1.38636	−	0.105666i
$478$	2.81603e6	+	2.81603e6i	0.563726	+	0.563726i
$479$	2.36702e6			0.471371			0.235686	−	0.971829i	$-0.424266\pi$
$479$	2.36702e6			0.471371			0.235686	+	0.971829i	$0.424266\pi$
$480$	−867683.	+	208297.i	−0.171893	+	0.0412649i
$481$	−4.02151e6			−0.792549
$482$	−4.62301e6	−	4.62301e6i	−0.906373	−	0.906373i
$483$	163013.	+	74906.4i	0.0317947	+	0.0146100i
$484$		−	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	−0.949660	−	0.313282i	$-0.898571\pi$
$487$	−3.33072e6	+	3.33072e6i	−0.636378	+	0.636378i	0.313282	+	0.949660i	$0.398571\pi$
$488$	−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	$-0.0234222\pi$
$492$	144866.	−	315262.i	0.0269808	−	0.0587164i
$493$	−867314.	−	867314.i	−0.160716	−	0.160716i
$494$	−2.44899e6			−0.451513
$495$	−6.94690e6	+	4.65402e6i	−1.27432	+	0.853719i
$496$	−424333.			−0.0774467
$497$	82857.8	+	82857.8i	0.0150467	+	0.0150467i
$498$	−9111.56	+	19828.8i	−0.00164634	+	0.00358281i
$499$			968793.i			0.174173i	0.996201	+	0.0870863i	$0.0277556\pi$
$499$			968793.i			0.174173i	−0.996201	+	0.0870863i	$0.972244\pi$
$500$	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	$-0.817801\pi$
$503$	−1.69640e6	+	1.69640e6i	−0.298958	+	0.298958i	0.541648	+	0.840605i	$0.317801\pi$
$504$	32257.8	−	27688.8i	0.00565664	−	0.00485543i
$505$	520026.	−	4.34709e6i	0.0907395	−	0.758526i
$506$			1.03663e7i			1.79990i
$507$	3.98657e6	+	1.83187e6i	0.688778	+	0.316501i
$508$	2.67517e6	+	2.67517e6i	0.459931	+	0.459931i
$509$	1.32955e6			0.227463			0.113731	−	0.993512i	$-0.463720\pi$
$509$	1.32955e6			0.227463			0.113731	+	0.993512i	$0.463720\pi$
$510$	1.14676e6	+	702761.i	0.195230	+	0.119642i
$511$	87874.9			0.0148872
$512$	185364.	+	185364.i	0.0312500	+	0.0312500i
$513$	2.12776e6	+	7.43891e6i	0.356967	+	1.24800i
$514$		−	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	$0.735795\pi$
$522$	−234821.	+	3.08089e6i	−0.0377190	+	0.494880i
$523$	−1.87262e6	−	1.87262e6i	−0.299361	−	0.299361i	0.541403	−	0.840763i	$-0.317893\pi$
$523$	−1.87262e6	−	1.87262e6i	−0.299361	−	0.299361i	−0.840763	+	0.541403i	$0.817893\pi$
$524$	−3.81962e6			−0.607704
$525$	15483.8	+	132257.i	0.00245176	+	0.0209421i
$526$	−187305.			−0.0295178
$527$	452247.	+	452247.i	0.0709331	+	0.0709331i
$528$	2.23209e6	+	1.02567e6i	0.348439	+	0.160111i
$529$		−	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
$537$	103458.	−	225148.i	0.0154820	−	0.0336924i
$538$	2.16352e6	+	2.16352e6i	0.322259	+	0.322259i
$539$	−1.03410e7			−1.53318
$540$	−538218.	−	3.34506e6i	−0.0794280	−	0.493651i
$541$	−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
$543$	−4.89151e6	+	1.06450e7i	−0.711939	+	1.54934i
$544$		−	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	−0.221971	−	0.975053i	$-0.571249\pi$
$547$	5.27000e6	−	5.27000e6i	0.753082	−	0.753082i	0.975053	+	0.221971i	$0.0712490\pi$
$548$	−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
$552$	−3.81665e6	−	1.75379e6i	−0.533132	−	0.244980i
$553$	−150224.	−	150224.i	−0.0208895	−	0.0208895i
$554$	2.74200e6			0.379571
$555$	2.72911e6	+	1.13684e7i	0.376087	+	1.56663i
$556$	−979581.			−0.134386
$557$	4.43782e6	+	4.43782e6i	0.606083	+	0.606083i	0.941920	−	0.335837i	$-0.109019\pi$
$557$	4.43782e6	+	4.43782e6i	0.606083	+	0.606083i	−0.335837	+	0.941920i	$0.609019\pi$
$558$	122443.	−	1.60648e6i	0.0166475	−	0.218419i
$559$		−	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	$-0.651820\pi$
$563$	3.22886e6	−	3.22886e6i	0.429318	−	0.429318i	0.888396	+	0.459078i	$0.151820\pi$
$564$	493583.	+	1.33285e6i	0.0653375	+	0.176434i
$565$	−6.41221e6	+	5.04199e6i	−0.845059	+	0.664479i
$566$			327368.i			0.0429531i
$567$	95518.6	+	130114.i	0.0124776	+	0.0169968i
$568$	−1.93996e6	−	1.93996e6i	−0.252302	−	0.252302i
$569$	−7.44498e6			−0.964013			−0.482007	−	0.876168i	$-0.660092\pi$
$569$	−7.44498e6			−0.964013			−0.482007	+	0.876168i	$0.660092\pi$
$570$	1.66196e6	+	6.92305e6i	0.214256	+	0.892504i
$571$	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
$573$	1.55134e6	+	712856.i	0.197388	+	0.0907017i
$574$			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	−0.916073	−	0.401013i	$-0.868658\pi$
$577$	−4.11905e6	+	4.11905e6i	−0.515060	+	0.515060i	0.401013	+	0.916073i	$0.368658\pi$
$578$	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
$582$	1.45180e6	−	3.15944e6i	0.177663	−	0.386636i
$583$	1.23759e7	+	1.23759e7i	1.50802	+	1.50802i
$584$	−2.05742e6			−0.249627
$585$	−789498.	+	3.99449e6i	−0.0953809	+	0.482583i
$586$	−9.46160e6			−1.13821
$587$	3.62213e6	+	3.62213e6i	0.433879	+	0.433879i	0.889946	−	0.456066i	$-0.150742\pi$
$587$	3.62213e6	+	3.62213e6i	0.433879	+	0.433879i	−0.456066	+	0.889946i	$0.650742\pi$
$588$	1.74951e6	−	3.80734e6i	0.208676	−	0.454128i
$589$			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	$-0.929681\pi$
$593$	−6.47872e6	+	6.47872e6i	−0.756575	+	0.756575i	0.219122	+	0.975697i	$0.429681\pi$
$594$	−4.52715e6	+	8.15449e6i	−0.526452	+	0.948267i
$595$	−58544.2	−	7003.41i	−0.00677940	−	0.000810993i
$596$		−	4.15788e6i		−	0.479465i
$597$	−2.48388e6	−	1.14137e6i	−0.285229	−	0.131066i
$598$	3.56940e6	+	3.56940e6i	0.408171	+	0.408171i
$599$	2.21327e6			0.252039			0.126019	−	0.992028i	$-0.459780\pi$
$599$	2.21327e6			0.252039			0.126019	+	0.992028i	$0.459780\pi$
$600$	−362523.	−	3.09654e6i	−0.0411109	−	0.351155i
$601$	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
$603$	−2.90309e6	−	221269.i	−0.325138	−	0.0247815i
$604$		−	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	−0.964835	−	0.262857i	$-0.915335\pi$
$607$	−6.37228e6	+	6.37228e6i	−0.701978	+	0.701978i	0.262857	+	0.964835i	$0.415335\pi$
$608$	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
$612$	1.49586e6	+	114012.i	0.161441	+	0.0123047i
$613$	−7.00623e6	−	7.00623e6i	−0.753066	−	0.753066i	0.221984	−	0.975050i	$-0.428747\pi$
$613$	−7.00623e6	−	7.00623e6i	−0.753066	−	0.753066i	−0.975050	+	0.221984i	$0.928747\pi$
$614$	1.18958e7			1.27342
$615$	1.03356e6	+	633392.i	0.110192	+	0.0675282i
$616$	−107688.			−0.0114345
$617$	2.77828e6	+	2.77828e6i	0.293808	+	0.293808i	0.838582	−	0.544775i	$-0.183385\pi$
$617$	2.77828e6	+	2.77828e6i	0.293808	+	0.293808i	−0.544775	+	0.838582i	$0.683385\pi$
$618$	−9.53980e6	−	4.38364e6i	−1.00477	−	0.461704i
$619$		−	6.32328e6i		−	0.663309i	−0.943401	−	0.331654i	$-0.892393\pi$
$619$		−	6.32328e6i		−	0.663309i	0.943401	−	0.331654i	$-0.107607\pi$
$620$	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
$627$	8.18357e6	−	1.78093e7i	0.831331	−	1.80917i
$628$	2.52183e6	+	2.52183e6i	0.255162	+	0.255162i
$629$	−5.17679e6			−0.521715
$630$	82668.8	+	123397.i	0.00829833	+	0.0123866i
$631$	−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
$633$	894283.	−	1.94616e6i	0.0887086	−	0.193050i
$634$			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	$0.972630\pi$
$642$	−6.39307e6	−	2.93768e6i	−0.612170	−	0.281299i
$643$	−5.31029e6	−	5.31029e6i	−0.506513	−	0.506513i	0.406941	−	0.913454i	$-0.366595\pi$
$643$	−5.31029e6	−	5.31029e6i	−0.506513	−	0.506513i	−0.913454	+	0.406941i	$0.866595\pi$
$644$	184136.			0.0174954
$645$	−1.37974e7	+	3.31222e6i	−1.30586	+	0.313487i
$646$	−3.15253e6			−0.297220
$647$	1.93842e6	+	1.93842e6i	0.182048	+	0.182048i	0.792248	−	0.610199i	$-0.208911\pi$
$647$	1.93842e6	+	1.93842e6i	0.182048	+	0.182048i	−0.610199	+	0.792248i	$0.708911\pi$
$648$	−2.23639e6	−	3.04638e6i	−0.209223	−	0.285001i
$649$			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	$-0.889543\pi$
$653$	−6.54118e6	+	6.54118e6i	−0.600306	+	0.600306i	0.340087	+	0.940394i	$0.389543\pi$
$654$	−738448.	−	1.99407e6i	−0.0675112	−	0.182304i
$655$	1.58513e6	−	1.32507e7i	0.144365	−	1.20680i
$656$		−	356113.i		−	0.0323094i
$657$	593679.	−	7.78919e6i	0.0536585	−	0.704010i
$658$	−44058.5	−	44058.5i	−0.00396703	−	0.00396703i
$659$	−1.55193e7			−1.39206			−0.696030	−	0.718013i	$-0.745052\pi$
$659$	−1.55193e7			−1.39206			−0.696030	+	0.718013i	$0.745052\pi$
$660$	−4.48448e6	+	7.31774e6i	−0.400730	+	0.653908i
$661$	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
$663$	−1.63825e6	−	752791.i	−0.144742	−	0.0665106i
$664$			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
$672$	18218.8	−	39648.3i	0.00155631	−	0.00338690i
$673$	9.33490e6	+	9.33490e6i	0.794460	+	0.794460i	0.982216	−	0.187756i	$-0.0601213\pi$
$673$	9.33490e6	+	9.33490e6i	0.794460	+	0.794460i	−0.187756	+	0.982216i	$0.560121\pi$
$674$	−5.80119e6			−0.491889
$675$	1.18278e7	−	478952.i	0.999181	−	0.0404606i
$676$	4.50314e6			0.379008
$677$	−9.53310e6	−	9.53310e6i	−0.799397	−	0.799397i	0.183604	−	0.983000i	$-0.441224\pi$
$677$	−9.53310e6	−	9.53310e6i	−0.799397	−	0.799397i	−0.983000	+	0.183604i	$0.941224\pi$
$678$	−3.79901e6	+	8.26751e6i	−0.317392	+	0.690717i
$679$			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	$-0.779164\pi$
$683$	−1.57744e6	+	1.57744e6i	−0.129390	+	0.129390i	0.639446	+	0.768836i	$0.279164\pi$
$684$	5.17248e6	+	6.02601e6i	0.422726	+	0.492481i
$685$	−781317.	−	993649.i	−0.0636211	−	0.0809108i
$686$			367455.i			0.0298122i
$687$	2.15232e6	+	989013.i	0.173986	+	0.0799485i
$688$	2.94754e6	+	2.94754e6i	0.237404	+	0.237404i
$689$	8.52269e6			0.683957
$690$	7.66801e6	−	1.25126e7i	0.613141	−	1.00052i
$691$	−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
$693$	31073.9	−	407696.i	0.00245789	−	0.0322481i
$694$		−	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	$-0.116229\pi$
$702$	1.24899e6	+	4.36661e6i	0.0956565	+	0.334428i
$703$	−1.93775e7	−	1.93775e7i	−1.47880	−	1.47880i
$704$	2.52131e6			0.191732
$705$	−4.82865e6	+	1.15917e6i	−0.365892	+	0.0878366i
$706$	8.09474e6			0.611211
$707$	151379.	+	151379.i	0.0113898	+	0.0113898i
$708$	−8.26431e6	−	3.79754e6i	−0.619617	−	0.284721i
$709$			1.87653e7i			1.40197i	0.713174	+	0.700987i	$0.247257\pi$
$709$			1.87653e7i			1.40197i	−0.713174	+	0.700987i	$0.752743\pi$
$710$	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
$717$	−6.48026e6	+	1.41025e7i	−0.470755	+	1.02447i
$718$	9.99955e6	+	9.99955e6i	0.723884	+	0.723884i
$719$	−3.20828e6			−0.231446			−0.115723	−	0.993282i	$-0.536918\pi$
$719$	−3.20828e6			−0.231446			−0.115723	+	0.993282i	$0.536918\pi$
$720$	−1.93553e6	−	2.88911e6i	−0.139146	−	0.207698i
$721$	460252.			0.0329729
$722$	−4.79695e6	−	4.79695e6i	−0.342470	−	0.342470i
$723$	1.06385e7	−	2.31518e7i	0.756892	−	1.64717i
$724$			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	−0.672184	−	0.740384i	$-0.734643\pi$
$727$	971909.	−	971909.i	0.0682008	−	0.0682008i	0.740384	+	0.672184i	$0.234643\pi$
$728$	−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
$732$	−3.77513e6	−	1.73471e6i	−0.260408	−	0.119660i
$733$	−1.95035e7	−	1.95035e7i	−1.34077	−	1.34077i	−0.895296	−	0.445471i	$-0.853036\pi$
$733$	−1.95035e7	−	1.95035e7i	−1.34077	−	1.34077i	−0.445471	−	0.895296i	$-0.646964\pi$
$734$	−4.58451e6			−0.314089
$735$	1.24821e7	+	7.64930e6i	0.852253	+	0.522280i
$736$	−4.31120e6			−0.293362
$737$	5.21513e6	+	5.21513e6i	0.353668	+	0.353668i
$738$	1.34821e6	+	102758.i	0.0911204	+	0.00694505i
$739$		−	3.62268e6i		−	0.244016i	−0.992529	−	0.122008i	$-0.961067\pi$
$739$		−	3.62268e6i		−	0.244016i	0.992529	−	0.122008i	$-0.0389334\pi$
$740$	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	0.144407	−	0.989518i	$-0.453872\pi$
$743$	1.70630e7	−	1.70630e7i	1.13393	−	1.13393i	0.989518	−	0.144407i	$-0.0461276\pi$
$744$	−574280.	−	1.55076e6i	−0.0380357	−	0.102710i
$745$	1.44242e7	+	1.72551e6i	0.952141	+	0.113901i
$746$		−	1.14808e6i		−	0.0755310i
$747$	−84797.2	−	6463.10i	−0.00556006	−	0.000423779i
$748$	−2.68717e6	−	2.68717e6i	−0.175607	−	0.175607i
$749$	308437.			0.0200892
$750$	1.08927e7	+	27420.3i	0.707105	+	0.00178000i
$751$	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
$753$	2.02467e7	+	9.30357e6i	1.30127	+	0.597946i
$754$		−	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	−0.629710	−	0.776830i	$-0.716826\pi$
$757$	2.31958e6	−	2.31958e6i	0.147119	−	0.147119i	0.776830	+	0.629710i	$0.216826\pi$
$758$	−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	$0.835891\pi$
$762$	−6.15611e6	+	1.33971e7i	−0.384077	+	0.835840i
$763$	65915.8	+	65915.8i	0.00409900	+	0.00409900i
$764$	1.75235e6			0.108615
$765$	−1.01630e6	+	5.14201e6i	−0.0627869	+	0.317673i
$766$	1.96905e6			0.121251
$767$	7.72893e6	+	7.72893e6i	0.474385	+	0.474385i
$768$	−426560.	+	928291.i	−0.0260962	+	0.0567912i
$769$		−	8.72370e6i		−	0.531967i	−0.963978	−	0.265984i	$-0.914303\pi$
$769$		−	8.72370e6i		−	0.531967i	0.963978	−	0.265984i	$-0.0856967\pi$
$770$	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	$-0.759031\pi$
$773$	−666455.	+	666455.i	−0.0401164	+	0.0401164i	0.686764	+	0.726880i	$0.259031\pi$
$774$	−1.20096e7	+	1.03086e7i	−0.720570	+	0.618508i
$775$	5.03369e6	+	1.22181e6i	0.301046	+	0.0730714i
$776$		−	3.56883e6i		−	0.212751i
$777$	−519472.	−	238703.i	−0.0308681	−	0.0141842i
$778$	−1.07600e7	−	1.07600e7i	−0.637326	−	0.637326i
$779$	−2.84135e6			−0.167757
$780$	975564.	+	4.06381e6i	0.0574142	+	0.239164i
$781$	−2.63873e7			−1.54799
$782$	4.59480e6	+	4.59480e6i	0.268689	+	0.268689i
$783$	−1.15771e7	+	3.31142e6i	−0.674834	+	0.193023i
$784$		−	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	−0.854709	−	0.519108i	$-0.826264\pi$
$787$	−5.83122e6	+	5.83122e6i	−0.335601	+	0.335601i	0.519108	+	0.854709i	$0.326264\pi$
$788$	−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
$792$	−727537.	+	9.54543e6i	−0.0412138	+	0.540733i
$793$	3.53057e6	+	3.53057e6i	0.199371	+	0.199371i
$794$	−2.01974e6			−0.113696
$795$	−5.78374e6	−	2.40928e7i	−0.324557	−	1.35197i
$796$	−2.80573e6			−0.156951
$797$	−1.23360e7	−	1.23360e7i	−0.687903	−	0.687903i	0.273865	−	0.961768i	$-0.411698\pi$
$797$	−1.23360e7	−	1.23360e7i	−0.687903	−	0.687903i	−0.961768	+	0.273865i	$0.911698\pi$
$798$	−316345.	−	145364.i	−0.0175855	−	0.00808071i
$799$		−	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
$807$	−4.97869e6	+	1.08348e7i	−0.269111	+	0.585647i
$808$	−3.54425e6	−	3.54425e6i	−0.190984	−	0.190984i
$809$	1.48239e7			0.796328			0.398164	−	0.917314i	$-0.369647\pi$
$809$	1.48239e7			0.796328			0.398164	+	0.917314i	$0.369647\pi$
$810$	1.14964e7	−	6.49406e6i	0.615670	−	0.347779i
$811$	−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
$813$	−1.30762e7	+	2.84567e7i	−0.693831	+	1.50994i
$814$		−	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	$-0.117881\pi$
$822$	−1.28115e6	−	588702.i	−0.0661333	−	0.0303889i
$823$	1.09055e7	+	1.09055e7i	0.561237	+	0.561237i	0.929659	−	0.368422i	$-0.120102\pi$
$823$	1.09055e7	+	1.09055e7i	0.561237	+	0.561237i	−0.368422	+	0.929659i	$0.620102\pi$
$824$	−1.07759e7			−0.552888
$825$	−2.35251e7	−	1.85940e7i	−1.20336	−	0.951128i
$826$	398716.			0.0203336
$827$	−802797.	−	802797.i	−0.0408171	−	0.0408171i	0.686404	−	0.727221i	$-0.259188\pi$
$827$	−802797.	−	802797.i	−0.0408171	−	0.0408171i	−0.727221	+	0.686404i	$0.759188\pi$
$828$	1.24402e6	−	1.63217e7i	0.0630595	−	0.827353i
$829$		−	2.52860e7i		−	1.27789i	−0.769252	−	0.638946i	$-0.779371\pi$
$829$		−	2.52860e7i		−	1.27789i	0.769252	−	0.638946i	$-0.220629\pi$
$830$	−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
$837$	6.03671e6	−	1.72668e6i	0.297843	−	0.0851921i
$838$	6.80560e6	+	6.80560e6i	0.334778	+	0.334778i
$839$	2.22871e7			1.09307			0.546536	−	0.837435i	$-0.315946\pi$
$839$	2.22871e7			1.09307			0.546536	+	0.837435i	$0.315946\pi$
$840$	129984.	+	79657.3i	0.00635612	+	0.00389518i
$841$	−1.04062e7			−0.507342
$842$	6.39402e6	+	6.39402e6i	0.310809	+	0.310809i
$843$	2.06716e7	+	9.49880e6i	1.00185	+	0.460362i
$844$		−	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
$852$	4.46424e6	−	9.71520e6i	0.210692	−	0.458514i
$853$	808864.	+	808864.i	0.0380630	+	0.0380630i	0.725882	−	0.687819i	$-0.241432\pi$
$853$	808864.	+	808864.i	0.0380630	+	0.0380630i	−0.687819	+	0.725882i	$0.741432\pi$
$854$	182133.			0.00854563
$855$	−2.30515e7	+	1.54432e7i	−1.07841	+	0.722473i
$856$	−7.22147e6			−0.336853
$857$	−1.82494e7	−	1.82494e7i	−0.848783	−	0.848783i	0.141198	−	0.989981i	$-0.454904\pi$
$857$	−1.82494e7	−	1.82494e7i	−0.848783	−	0.848783i	−0.989981	+	0.141198i	$0.954904\pi$
$858$	4.80373e6	−	1.04540e7i	0.222772	−	0.484802i
$859$			3.76682e7i			1.74177i	0.491483	+	0.870887i	$0.336455\pi$
$859$			3.76682e7i			1.74177i	−0.491483	+	0.870887i	$0.663545\pi$
$860$	−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	0.181668	−	0.983360i	$-0.441850\pi$
$863$	2.54896e7	−	2.54896e7i	1.16503	−	1.16503i	0.983360	−	0.181668i	$-0.0581498\pi$
$864$	−3.39133e6	−	1.88277e6i	−0.154556	−	0.0858052i
$865$	−7.09572e6	+	5.57944e6i	−0.322445	+	0.253542i
$866$		−	1.73338e7i		−	0.785416i
$867$	1.80028e7	+	8.27249e6i	0.813379	+	0.373756i
$868$	51261.7	+	51261.7i	0.00230937	+	0.00230937i
$869$	4.78412e7			2.14908
$870$	−1.07743e7	+	2.58650e6i	−0.482604	+	0.115855i
$871$	3.59141e6			0.160405
$872$	−1.54329e6	−	1.54329e6i	−0.0687318	−	0.0687318i
$873$	1.35112e7	+	1.02980e6i	0.600010	+	0.0457318i
$874$			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	−0.354995	−	0.934868i	$-0.615517\pi$
$877$	1.32079e7	−	1.32079e7i	0.579873	−	0.579873i	0.934868	+	0.354995i	$0.115517\pi$
$878$	−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	$-0.360756\pi$
$882$	1.62819e7	+	1.24098e6i	0.704748	+	0.0537148i
$883$	2.31670e7	+	2.31670e7i	0.999927	+	0.999927i	1.00000		7.31900e-5i	$-2.32971e-5\pi$
$883$	2.31670e7	+	2.31670e7i	0.999927	+	0.999927i	−7.31900e−5		1.00000i	$0.500023\pi$
$884$	−1.85052e6			−0.0796460
$885$	1.66038e7	−	2.70939e7i	0.712606	−	1.16282i
$886$	−1.61350e7			−0.690532
$887$	−2.36679e7	−	2.36679e7i	−1.01007	−	1.01007i	−0.999949	−	0.0101211i	$-0.996778\pi$
$887$	−2.36679e7	−	2.36679e7i	−1.01007	−	1.01007i	−0.0101211	−	0.999949i	$-0.503222\pi$
$888$	1.21625e7	+	5.58878e6i	0.517594	+	0.237840i
$889$		−	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
$897$	−8.21390e6	+	1.78753e7i	−0.340854	+	0.741776i
$898$	1.47705e6	+	1.47705e6i	0.0611229	+	0.0611229i
$899$	−5.26908e6			−0.217438
$900$	1.08259e7	−	5.51563e6i	0.445511	−	0.226981i
$901$	1.09710e7			0.450232
$902$	−2.42192e6	−	2.42192e6i	−0.0991160	−	0.0991160i
$903$	289705.	−	630464.i	0.0118232	−	0.0257300i
$904$			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	−0.140977	+	0.990013i	$0.545024\pi$
$907$	−2.80206e7	+	2.80206e7i	−1.13099	+	1.13099i	−0.990013	+	0.140977i	$0.954976\pi$
$908$	−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	$-0.117254\pi$
$912$	7.40662e6	+	3.40342e6i	0.294872	+	0.135497i
$913$	152330.	+	152330.i	0.00604795	+	0.00604795i
$914$	1.86618e7			0.738905
$915$	7.58460e6	−	1.23765e7i	0.299488	−	0.488703i
$916$	2.43121e6			0.0957378
$917$	461430.	+	461430.i	0.0181210	+	0.0181210i
$918$	1.60779e6	+	5.62104e6i	0.0629683	+	0.220145i
$919$			3.85473e6i			0.150559i	0.997162	+	0.0752793i	$0.0239848\pi$
$919$			3.85473e6i			0.150559i	−0.997162	+	0.0752793i	$0.976015\pi$
$920$	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
$927$	3.10945e6	−	4.07965e7i	0.118846	−	1.55928i
$928$	2.30172e6	+	2.30172e6i	0.0877370	+	0.0877370i
$929$	4.71857e7			1.79379			0.896895	−	0.442244i	$-0.145817\pi$
$929$	4.71857e7			1.79379			0.896895	+	0.442244i	$0.145817\pi$
$930$	5.61809e6	−	1.34869e6i	0.213001	−	0.0511333i
$931$	−3.43142e7			−1.29748
$932$	4.31473e6	+	4.31473e6i	0.162710	+	0.162710i
$933$	−1.57034e7	−	7.21589e6i	−0.590596	−	0.271385i
$934$			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	0.379771	−	0.925080i	$-0.376003\pi$
$937$	3.50679e7	−	3.50679e7i	1.30485	−	1.30485i	0.925080	−	0.379771i	$-0.123997\pi$
$938$	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	$-0.206840\pi$
$942$	−5.80323e6	+	1.26292e7i	−0.213080	+	0.463711i
$943$	4.14125e6	+	4.14125e6i	0.151653	+	0.151653i
$944$	−9.33518e6			−0.340951
$945$	−339082.	+	469121.i	−0.0123516	+	0.0170886i
$946$	4.00924e7			1.45658
$947$	2.17688e7	+	2.17688e7i	0.788787	+	0.788787i	0.981295	−	0.192509i	$-0.0616623\pi$
$947$	2.17688e7	+	2.17688e7i	0.788787	+	0.788787i	−0.192509	+	0.981295i	$0.561662\pi$
$948$	−8.09384e6	+	1.76140e7i	−0.292505	+	0.636558i
$949$			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	−0.106790	+	0.994282i	$0.534057\pi$
$953$	−3.08708e7	+	3.08708e7i	−1.10107	+	1.10107i	−0.994282	+	0.106790i	$0.965943\pi$
$954$	−1.80006e7	−	2.09710e7i	−0.640349	−	0.746016i
$955$	−727223.	+	6.07913e6i	−0.0258023	+	0.215692i
$956$			1.59299e7i			0.563726i
$957$	2.77166e7	+	1.27361e7i	0.978272	+	0.449526i
$958$	6.69495e6	+	6.69495e6i	0.235686	+	0.235686i
$959$	61809.7			0.00217025
$960$	−3.04333e6	−	1.86503e6i	−0.106579	−	0.0653141i
$961$	−2.58817e7			−0.904032
$962$	−1.13745e7	−	1.13745e7i	−0.396274	−	0.396274i
$963$	2.08379e6	−	2.73397e7i	0.0724082	−	0.950010i
$964$		−	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	−0.986997	−	0.160739i	$-0.948612\pi$
$967$	−2.40260e7	+	2.40260e7i	−0.826258	+	0.826258i	0.160739	+	0.986997i	$0.448612\pi$
$968$	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	$0.961926\pi$
$972$	8.10656e6	−	1.22959e7i	0.275214	−	0.417441i
$973$	118339.	+	118339.i	0.00400723	+	0.00400723i
$974$	−1.88414e7			−0.636378
$975$	−1.45027e7	+	1.69788e6i	−0.488582	+	0.0572000i
$976$	−4.26430e6			−0.143292
$977$	−1.55490e7	−	1.55490e7i	−0.521154	−	0.521154i	0.396766	−	0.917920i	$-0.370132\pi$
$977$	−1.55490e7	−	1.55490e7i	−0.521154	−	0.521154i	−0.917920	+	0.396766i	$0.870132\pi$
$978$	−5.16606e6	−	2.37386e6i	−0.172708	−	0.0793612i
$979$		−	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	$-0.987575\pi$
$983$	−2.90905e7	+	2.90905e7i	−0.960213	+	0.960213i	0.0390251	+	0.999238i	$0.487575\pi$
$984$	1.30144e6	−	481953.i	0.0428486	−	0.0158678i
$985$	−3.84631e6	−	4.89159e6i	−0.126315	−	0.160642i
$986$		−	4.90627e6i		−	0.160716i
$987$	101388.	−	220643.i	0.00331278	−	0.00720936i
$988$	−6.92680e6	−	6.92680e6i	−0.225757	−	0.225757i
$989$	−6.85540e7			−2.22865
$990$	−3.28123e7	−	6.48524e6i	−1.06402	−	0.210300i
$991$	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
$993$	1.32454e7	−	2.88250e7i	0.426277	−	0.927675i
$994$			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	−0.953297	−	0.302033i	$-0.902335\pi$
$997$	−2.04407e7	+	2.04407e7i	−0.651264	+	0.651264i	0.302033	+	0.953297i	$0.402335\pi$
$998$	−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.23.7	yes	20
3.2	odd	2	inner	30.6.e.a.23.5	yes	20
5.2	odd	4	inner	30.6.e.a.17.5	✓	20
5.3	odd	4		150.6.e.b.107.6		20
5.4	even	2		150.6.e.b.143.4		20
15.2	even	4	inner	30.6.e.a.17.7	yes	20
15.8	even	4		150.6.e.b.107.4		20
15.14	odd	2		150.6.e.b.143.6		20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.82843 + 2.82843i) q^{2} +(-6.50878 + 14.1646i) q^{3} +16.0000i q^{4} +(-55.5060 - 6.63996i) q^{5} +(-58.4731 + 21.6539i) q^{6} +(1.93288 - 1.93288i) q^{7} +(-45.2548 + 45.2548i) q^{8} +(-158.272 - 184.389i) q^{9} +O(q^{10})\)	\(q+(2.82843 + 2.82843i) q^{2} +(-6.50878 + 14.1646i) 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} +(-226.634 - 104.141i) q^{12} +(211.952 + 211.952i) q^{13} +10.9340 q^{14} +(455.328 - 743.001i) q^{15} -256.000 q^{16} +(272.840 + 272.840i) q^{17} +(73.8700 - 969.189i) 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} +(3641.94 - 1041.71i) q^{27} +(30.9262 + 30.9262i) q^{28} -3178.83 q^{29} +(3389.39 - 813.662i) q^{30} +1657.55 q^{31} +(-724.077 - 724.077i) q^{32} +(-8719.09 - 4006.52i) 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} +(-71.1673 + 154.876i) q^{42} +(-11513.8 - 11513.8i) q^{43} -9848.89 q^{44} +(7560.68 + 11285.6i) q^{45} +16840.6 q^{46} +(-4029.48 - 4029.48i) q^{47} +(1666.25 - 3626.14i) 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} +(-28932.1 - 13294.6i) q^{57} +(-8991.10 - 8991.10i) q^{58} +36465.5 q^{59} +(11888.0 + 7285.25i) q^{60} +16657.4 q^{61} +(4688.26 + 4688.26i) q^{62} +(-662.322 - 50.4811i) 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} +(15507.0 + 1181.92i) q^{72} +(22731.5 + 22731.5i) q^{73} -53665.7 q^{74} +(-30206.9 + 38217.6i) q^{75} -32681.1 q^{76} +(1189.80 + 1189.80i) q^{77} +(-16983.1 - 7803.89i) 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} +(20690.3 - 45026.9i) q^{87} +(-27856.9 - 27856.9i) q^{88} -109920. q^{89} +(-10535.6 + 53305.3i) q^{90} +819.356 q^{91} +(47632.5 + 47632.5i) q^{92} +(-10788.6 + 23478.6i) 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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