LMFDB - Embedded newform 74.6.f.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	74.9
Dual form			74.6.f.a.33.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694593 + 3.93923i) q^{2} +(1.57867 - 8.95310i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(22.3419 + 18.7471i) q^{5} +36.3648 q^{6} +(-145.430 - 122.031i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(150.680 + 54.8429i) q^{9} +O(q^{10})$	\(q+(0.694593 + 3.93923i) q^{2} +(1.57867 - 8.95310i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(22.3419 + 18.7471i) q^{5} +36.3648 q^{6} +(-145.430 - 122.031i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(150.680 + 54.8429i) q^{9} +(-58.3305 + 101.031i) q^{10} +(-198.929 - 344.555i) q^{11} +(25.2588 + 143.250i) q^{12} +(-33.1858 + 12.0786i) q^{13} +(379.692 - 657.646i) q^{14} +(203.115 - 170.433i) q^{15} +(196.107 - 164.554i) q^{16} +(-1658.35 - 603.590i) q^{17} +(-111.378 + 631.655i) q^{18} +(490.432 - 2781.38i) q^{19} +(-438.502 - 159.602i) q^{20} +(-1322.14 + 1109.41i) q^{21} +(1219.11 - 1022.95i) q^{22} +(641.421 - 1110.97i) q^{23} +(-546.748 + 199.000i) q^{24} +(-394.943 - 2239.84i) q^{25} +(-70.6311 - 122.337i) q^{26} +(1833.47 - 3175.66i) q^{27} +(2854.35 + 1038.90i) q^{28} +(4444.64 + 7698.33i) q^{29} +(812.459 + 681.734i) q^{30} +2907.26 q^{31} +(784.430 + 658.215i) q^{32} +(-3398.87 + 1237.09i) q^{33} +(1225.80 - 6951.87i) q^{34} +(-961.473 - 5452.79i) q^{35} -2565.60 q^{36} +(-4633.46 - 6919.18i) q^{37} +11297.1 q^{38} +(55.7517 + 316.183i) q^{39} +(324.127 - 1838.22i) q^{40} +(-3831.77 + 1394.65i) q^{41} +(-5288.56 - 4437.63i) q^{42} -21242.0 q^{43} +(4876.42 + 4091.80i) q^{44} +(2338.32 + 4050.09i) q^{45} +(4821.91 + 1755.03i) q^{46} +(-14132.5 + 24478.3i) q^{47} +(-1163.68 - 2015.54i) q^{48} +(3340.04 + 18942.3i) q^{49} +(8548.90 - 3111.55i) q^{50} +(-8021.98 + 13894.5i) q^{51} +(432.852 - 363.206i) q^{52} +(-3381.87 + 2837.72i) q^{53} +(13783.2 + 5016.67i) q^{54} +(2014.95 - 11427.3i) q^{55} +(-2109.85 + 11965.6i) q^{56} +(-24127.7 - 8781.77i) q^{57} +(-27238.3 + 22855.7i) q^{58} +(12987.3 - 10897.7i) q^{59} +(-2121.18 + 3673.99i) q^{60} +(14439.8 - 5255.66i) q^{61} +(2019.36 + 11452.4i) q^{62} +(-15220.9 - 26363.4i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-967.871 - 352.276i) q^{65} +(-7234.01 - 12529.7i) q^{66} +(55768.7 + 46795.5i) q^{67} +28236.4 q^{68} +(-8934.06 - 7496.57i) q^{69} +(20812.0 - 7574.93i) q^{70} +(-267.293 + 1515.89i) q^{71} +(-1782.05 - 10106.5i) q^{72} +36373.3 q^{73} +(24037.9 - 23058.3i) q^{74} -20676.9 q^{75} +(7846.91 + 44502.1i) q^{76} +(-13115.9 + 74384.1i) q^{77} +(-1206.79 + 439.237i) q^{78} +(-21865.2 - 18347.1i) q^{79} +7466.30 q^{80} +(4311.38 + 3617.68i) q^{81} +(-8155.36 - 14125.5i) q^{82} +(-49724.4 - 18098.2i) q^{83} +(13807.4 - 23915.2i) q^{84} +(-25735.1 - 44574.5i) q^{85} +(-14754.6 - 83677.2i) q^{86} +(75940.5 - 27640.1i) q^{87} +(-12731.4 + 22051.5i) q^{88} +(30014.2 - 25184.9i) q^{89} +(-14330.1 + 12024.4i) q^{90} +(6300.18 + 2293.08i) q^{91} +(-3564.21 + 20213.7i) q^{92} +(4589.62 - 26029.0i) q^{93} +(-106242. - 38668.9i) q^{94} +(63099.8 - 52947.1i) q^{95} +(7131.41 - 5983.97i) q^{96} +(-78662.2 + 136247. i) q^{97} +(-72298.1 + 26314.4i) q^{98} +(-11078.1 - 62827.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) $ 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.694593	+	3.93923i	0.122788	+	0.696364i
$2$	0.694593	+	3.93923i	0.122788	+	0.696364i
$3$	1.57867	−	8.95310i	0.101272	−	0.574341i	−0.891372	−	0.453272i	$-0.850257\pi$
$3$	1.57867	−	8.95310i	0.101272	−	0.574341i	0.992644	−	0.121069i	$-0.0386323\pi$
$4$	−15.0351	+	5.47232i	−0.469846	+	0.171010i
$5$	22.3419	+	18.7471i	0.399664	+	0.335358i	0.820364	−	0.571842i	$-0.193771\pi$
$5$	22.3419	+	18.7471i	0.399664	+	0.335358i	−0.420700	+	0.907200i	$0.638216\pi$
$6$	36.3648			0.412386
$7$	−145.430	−	122.031i	−1.12179	−	0.941291i	−0.123094	−	0.992395i	$-0.539282\pi$
$7$	−145.430	−	122.031i	−1.12179	−	0.941291i	−0.998693	+	0.0511041i	$0.983726\pi$
$8$	−32.0000	−	55.4256i	−0.176777	−	0.306186i
$9$	150.680	+	54.8429i	0.620081	+	0.225691i
$10$	−58.3305	+	101.031i	−0.184457	+	0.319489i
$11$	−198.929	−	344.555i	−0.495696	−	0.858571i	0.504291	−	0.863534i	$-0.331754\pi$
$11$	−198.929	−	344.555i	−0.495696	−	0.858571i	−0.999988	+	0.00496234i	$0.998420\pi$
$12$	25.2588	+	143.250i	0.0506359	+	0.287171i
$13$	−33.1858	+	12.0786i	−0.0544620	+	0.0198225i	−0.369107	−	0.929387i	$-0.620337\pi$
$13$	−33.1858	+	12.0786i	−0.0544620	+	0.0198225i	0.314646	+	0.949209i	$0.398114\pi$
$14$	379.692	−	657.646i	0.517740	−	0.896751i
$15$	203.115	−	170.433i	0.233084	−	0.195581i
$16$	196.107	−	164.554i	0.191511	−	0.160697i
$17$	−1658.35	−	603.590i	−1.39173	−	0.506547i	−0.466014	−	0.884777i	$-0.654310\pi$
$17$	−1658.35	−	603.590i	−1.39173	−	0.506547i	−0.925711	+	0.378231i	$0.876533\pi$
$18$	−111.378	+	631.655i	−0.0810247	+	0.459514i
$19$	490.432	−	2781.38i	0.311670	−	1.76757i	−0.278644	−	0.960394i	$-0.589885\pi$
$19$	490.432	−	2781.38i	0.311670	−	1.76757i	0.590314	−	0.807174i	$-0.299004\pi$
$20$	−438.502	−	159.602i	−0.245130	−	0.0892200i
$21$	−1322.14	+	1109.41i	−0.654228	+	0.548962i
$22$	1219.11	−	1022.95i	0.537013	−	0.450607i
$23$	641.421	−	1110.97i	0.252827	−	0.437909i	−0.711476	−	0.702710i	$-0.751973\pi$
$23$	641.421	−	1110.97i	0.252827	−	0.437909i	0.964303	+	0.264801i	$0.0853063\pi$
$24$	−546.748	+	199.000i	−0.193758	+	0.0705221i
$25$	−394.943	−	2239.84i	−0.126382	−	0.716747i
$26$	−70.6311	−	122.337i	−0.0204910	−	0.0354914i
$27$	1833.47	−	3175.66i	0.484021	−	0.838349i
$28$	2854.35	+	1038.90i	0.688038	+	0.250425i
$29$	4444.64	+	7698.33i	0.981389	+	1.69982i	0.656998	+	0.753892i	$0.271826\pi$
$29$	4444.64	+	7698.33i	0.981389	+	1.69982i	0.324391	+	0.945923i	$0.394841\pi$
$30$	812.459	+	681.734i	0.164816	+	0.138297i
$31$	2907.26			0.543351			0.271675	−	0.962389i	$-0.412422\pi$
$31$	2907.26			0.543351			0.271675	+	0.962389i	$0.412422\pi$
$32$	784.430	+	658.215i	0.135419	+	0.113630i
$33$	−3398.87	+	1237.09i	−0.543313	+	0.197750i
$34$	1225.80	−	6951.87i	0.181854	−	1.03135i
$35$	−961.473	−	5452.79i	−0.132668	−	0.752399i
$36$	−2565.60			−0.329938
$37$	−4633.46	−	6919.18i	−0.556418	−	0.830903i
$37$	−4633.46	−	6919.18i	−0.556418	−	0.830903i
$38$	11297.1			1.26914
$39$	55.7517	+	316.183i	0.00586944	+	0.0332872i
$40$	324.127	−	1838.22i	0.0320307	−	0.181655i
$41$	−3831.77	+	1394.65i	−0.355991	+	0.129570i	−0.513824	−	0.857896i	$-0.671772\pi$
$41$	−3831.77	+	1394.65i	−0.355991	+	0.129570i	0.157833	+	0.987466i	$0.449549\pi$
$42$	−5288.56	−	4437.63i	−0.462609	−	0.388175i
$43$	−21242.0			−1.75196			−0.875981	−	0.482345i	$-0.839785\pi$
$43$	−21242.0			−1.75196			−0.875981	+	0.482345i	$0.839785\pi$
$44$	4876.42	+	4091.80i	0.379725	+	0.318627i
$45$	2338.32	+	4050.09i	0.172136	+	0.298149i
$46$	4821.91	+	1755.03i	0.335989	+	0.122290i
$47$	−14132.5	+	24478.3i	−0.933202	+	1.61635i	−0.155394	+	0.987853i	$0.549665\pi$
$47$	−14132.5	+	24478.3i	−0.933202	+	1.61635i	−0.777809	+	0.628501i	$0.783669\pi$
$48$	−1163.68	−	2015.54i	−0.0729002	−	0.126267i
$49$	3340.04	+	18942.3i	0.198729	+	1.12705i
$50$	8548.90	−	3111.55i	0.483599	−	0.176016i
$51$	−8021.98	+	13894.5i	−0.431873	+	0.748027i
$52$	432.852	−	363.206i	0.0221989	−	0.0186271i
$53$	−3381.87	+	2837.72i	−0.165374	+	0.138765i	−0.721719	−	0.692186i	$-0.756648\pi$
$53$	−3381.87	+	2837.72i	−0.165374	+	0.138765i	0.556345	+	0.830951i	$0.312203\pi$
$54$	13783.2	+	5016.67i	0.643228	+	0.234116i
$55$	2014.95	−	11427.3i	0.0898166	−	0.509375i
$56$	−2109.85	+	11965.6i	−0.0899045	+	0.509874i
$57$	−24127.7	−	8781.77i	−0.983624	−	0.358010i
$58$	−27238.3	+	22855.7i	−1.06319	+	0.892121i
$59$	12987.3	−	10897.7i	0.485724	−	0.407571i	−0.366767	−	0.930313i	$-0.619535\pi$
$59$	12987.3	−	10897.7i	0.485724	−	0.407571i	0.852491	+	0.522742i	$0.175091\pi$
$60$	−2121.18	+	3673.99i	−0.0760675	+	0.131753i
$61$	14439.8	−	5255.66i	0.496863	−	0.180843i	−0.0814195	−	0.996680i	$-0.525945\pi$
$61$	14439.8	−	5255.66i	0.496863	−	0.180843i	0.578283	+	0.815837i	$0.303723\pi$
$62$	2019.36	+	11452.4i	0.0667168	+	0.378370i
$63$	−15220.9	−	26363.4i	−0.483158	−	0.836853i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	−967.871	−	352.276i	−0.0284141	−	0.0103419i
$66$	−7234.01	−	12529.7i	−0.204418	−	0.354063i
$67$	55768.7	+	46795.5i	1.51776	+	1.27355i	0.846582	+	0.532259i	$0.178657\pi$
$67$	55768.7	+	46795.5i	1.51776	+	1.27355i	0.671180	+	0.741294i	$0.265788\pi$
$68$	28236.4			0.740522
$69$	−8934.06	−	7496.57i	−0.225905	−	0.189557i
$70$	20812.0	−	7574.93i	0.507654	−	0.184771i
$71$	−267.293	+	1515.89i	−0.00629277	+	0.0356881i	−0.987792	−	0.155776i	$-0.950212\pi$
$71$	−267.293	+	1515.89i	−0.00629277	+	0.0356881i	0.981500	+	0.191464i	$0.0613234\pi$
$72$	−1782.05	−	10106.5i	−0.0405124	−	0.229757i
$73$	36373.3			0.798868			0.399434	−	0.916762i	$-0.369207\pi$
$73$	36373.3			0.798868			0.399434	+	0.916762i	$0.369207\pi$
$74$	24037.9	−	23058.3i	0.510290	−	0.489494i
$75$	−20676.9			−0.424457
$76$	7846.91	+	44502.1i	0.155835	+	0.883784i
$77$	−13115.9	+	74384.1i	−0.252100	+	1.42973i
$78$	−1206.79	+	439.237i	−0.0224593	+	0.00817453i
$79$	−21865.2	−	18347.1i	−0.394172	−	0.330749i	0.424064	−	0.905632i	$-0.360603\pi$
$79$	−21865.2	−	18347.1i	−0.394172	−	0.330749i	−0.818236	+	0.574883i	$0.805048\pi$
$80$	7466.30			0.130431
$81$	4311.38	+	3617.68i	0.0730136	+	0.0612656i
$82$	−8155.36	−	14125.5i	−0.133939	−	0.231990i
$83$	−49724.4	−	18098.2i	−0.792272	−	0.288364i	−0.0859921	−	0.996296i	$-0.527406\pi$
$83$	−49724.4	−	18098.2i	−0.792272	−	0.288364i	−0.706280	+	0.707932i	$0.749628\pi$
$84$	13807.4	−	23915.2i	0.213508	−	0.369807i
$85$	−25735.1	−	44574.5i	−0.386348	−	0.669174i
$86$	−14754.6	−	83677.2i	−0.215120	−	1.22000i
$87$	75940.5	−	27640.1i	1.07566	−	0.391509i
$88$	−12731.4	+	22051.5i	−0.175255	+	0.303551i
$89$	30014.2	−	25184.9i	0.401654	−	0.337028i	−0.419479	−	0.907765i	$-0.637787\pi$
$89$	30014.2	−	25184.9i	0.401654	−	0.337028i	0.821133	+	0.570738i	$0.193343\pi$
$90$	−14330.1	+	12024.4i	−0.186484	+	0.156479i
$91$	6300.18	+	2293.08i	0.0797535	+	0.0290279i
$92$	−3564.21	+	20213.7i	−0.0439030	+	0.248986i
$93$	4589.62	−	26029.0i	0.0550261	−	0.312069i
$94$	−106242.	−	38668.9i	−1.24016	−	0.451380i
$95$	63099.8	−	52947.1i	0.717330	−	0.601912i
$96$	7131.41	−	5983.97i	0.0789764	−	0.0662691i
$97$	−78662.2	+	136247.i	−0.848861	+	1.47027i	0.0333647	+	0.999443i	$0.489378\pi$
$97$	−78662.2	+	136247.i	−0.848861	+	1.47027i	−0.882226	+	0.470827i	$0.843956\pi$
$98$	−72298.1	+	26314.4i	−0.760434	+	0.276775i
$99$	−11078.1	−	62827.2i	−0.113600	−	0.644258i
$100$	18195.1	+	31514.9i	0.181951	+	0.315149i
$101$	70403.0	−	121942.i	0.686733	−	1.18946i	−0.286156	−	0.958183i	$-0.592378\pi$
$101$	70403.0	−	121942.i	0.686733	−	1.18946i	0.972889	−	0.231273i	$-0.0742892\pi$
$102$	−60305.6	−	21949.4i	−0.573928	−	0.208893i
$103$	−25624.6	−	44383.0i	−0.237993	−	0.412215i	0.722146	−	0.691741i	$-0.243156\pi$
$103$	−25624.6	−	44383.0i	−0.237993	−	0.412215i	−0.960138	+	0.279526i	$0.909823\pi$
$104$	1731.41	+	1452.83i	0.0156970	+	0.0131713i
$105$	−50337.2			−0.445570
$106$	−13527.5	−	11350.9i	−0.116937	−	0.0981217i
$107$	184623.	−	67197.2i	1.55893	−	0.567403i	0.588437	−	0.808543i	$-0.299744\pi$
$107$	184623.	−	67197.2i	1.55893	−	0.567403i	0.970490	+	0.241140i	$0.0775214\pi$
$108$	−10188.1	+	57779.7i	−0.0840494	+	0.476668i
$109$	−22324.9	−	126611.i	−0.179980	−	1.02071i	−0.932238	−	0.361846i	$-0.882146\pi$
$109$	−22324.9	−	126611.i	−0.179980	−	1.02071i	0.752258	−	0.658869i	$-0.228965\pi$
$110$	46414.4			0.365739
$111$	−69262.8	+	30560.7i	−0.533571	+	0.235427i
$112$	−48600.6			−0.366097
$113$	3916.79	+	22213.2i	0.0288559	+	0.163650i	0.995831	−	0.0912228i	$-0.0290775\pi$
$113$	3916.79	+	22213.2i	0.0288559	+	0.163650i	−0.966975	+	0.254873i	$0.917966\pi$
$114$	17834.5	−	101144.i	0.128528	−	0.728920i
$115$	35158.0	−	12796.5i	0.247902	−	0.0902290i
$116$	−108953.	−	91422.6i	−0.751788	−	0.630825i
$117$	−5662.84			−0.0382446
$118$	51949.3	+	43590.6i	0.343459	+	0.288196i
$119$	167518.	+	290150.i	1.08441	+	1.87826i
$120$	−15946.1	−	5803.89i	−0.101088	−	0.0367931i
$121$	1380.26	−	2390.67i	0.00857030	−	0.0148442i
$122$	30733.0	+	53231.2i	0.186942	+	0.323792i
$123$	6437.32	+	36507.9i	0.0383656	+	0.217582i
$124$	−43711.0	+	15909.5i	−0.255291	+	0.0929185i
$125$	78737.2	−	136377.i	0.450718	−	0.780667i
$126$	93279.0	−	78270.4i	0.523429	−	0.439209i
$127$	221420.	−	185793.i	1.21817	−	1.02216i	0.219250	−	0.975669i	$-0.429639\pi$
$127$	221420.	−	185793.i	1.21817	−	1.02216i	0.998918	−	0.0464958i	$-0.0148054\pi$
$128$	−15395.9	−	5603.66i	−0.0830579	−	0.0302306i
$129$	−33534.2	+	190182.i	−0.177425	+	1.00622i
$130$	715.421	−	4057.35i	0.00371281	−	0.0210564i
$131$	−133936.	−	48748.8i	−0.681899	−	0.248191i	−0.0222360	−	0.999753i	$-0.507079\pi$
$131$	−133936.	−	48748.8i	−0.681899	−	0.248191i	−0.659662	+	0.751562i	$0.729301\pi$
$132$	44332.6	−	37199.5i	0.221456	−	0.185824i
$133$	−410737.	+	344650.i	−2.01342	+	1.68946i
$134$	−145602.	+	252190.i	−0.700494	+	1.21329i
$135$	100497.	−	36578.1i	0.474592	−	0.172737i
$136$	19612.8	+	111230.i	0.0909270	+	0.515673i
$137$	−35628.0	−	61709.5i	−0.162177	−	0.280899i	0.773472	−	0.633831i	$-0.218518\pi$
$137$	−35628.0	−	61709.5i	−0.162177	−	0.280899i	−0.935649	+	0.352931i	$0.885185\pi$
$138$	23325.2	−	40400.4i	0.104262	−	0.180588i
$139$	−18317.3	−	6666.96i	−0.0804128	−	0.0292679i	0.301501	−	0.953466i	$-0.402512\pi$
$139$	−18317.3	−	6666.96i	−0.0804128	−	0.0292679i	−0.381913	+	0.924198i	$0.624735\pi$
$140$	44295.2	+	76721.6i	0.191002	+	0.330824i
$141$	196846.	+	165173.i	0.833832	+	0.699668i
$142$	−6157.12			−0.0256246
$143$	10763.3	+	9031.52i	0.0440157	+	0.0369335i
$144$	38574.0	−	14039.8i	0.155020	−	0.0564227i
$145$	−45019.6	+	255319.i	−0.177821	+	1.00847i
$146$	25264.6	+	143283.i	0.0980913	+	0.556303i
$147$	174865.			0.667436
$148$	107528.	+	78674.6i	0.403524	+	0.295244i
$149$	312405.			1.15280			0.576398	−	0.817169i	$-0.304458\pi$
$149$	312405.			1.15280			0.576398	+	0.817169i	$0.304458\pi$
$150$	−14362.1	−	81451.3i	−0.0521181	−	0.295576i
$151$	−259.580	+	1472.15i	−0.000926464	+	0.00525424i	−0.985267	−	0.171020i	$-0.945294\pi$
$151$	−259.580	+	1472.15i	−0.000926464	+	0.00525424i	0.984341	+	0.176275i	$0.0564047\pi$
$152$	−169854.	+	61821.6i	−0.596301	+	0.217036i
$153$	−216777.	−	181897.i	−0.748659	−	0.628200i
$154$	−302127.			−1.02657
$155$	64953.7	+	54502.6i	0.217157	+	0.182217i
$156$	−2568.49	−	4448.75i	−0.00845018	−	0.0146361i
$157$	−151985.	−	55317.9i	−0.492097	−	0.179109i	0.0840389	−	0.996462i	$-0.473218\pi$
$157$	−151985.	−	55317.9i	−0.492097	−	0.179109i	−0.576136	+	0.817354i	$0.695440\pi$
$158$	57086.0	−	98875.8i	0.181923	−	0.315099i
$159$	20067.5	+	34758.0i	0.0629508	+	0.109034i
$160$	5186.04	+	29411.5i	0.0160153	+	0.0908274i
$161$	−228855.	+	83296.4i	−0.695818	+	0.253257i
$162$	−11256.2	+	19496.3i	−0.0336980	+	0.0583667i
$163$	−220009.	+	184610.i	−0.648593	+	0.544234i	−0.906644	−	0.421897i	$-0.861364\pi$
$163$	−220009.	+	184610.i	−0.648593	+	0.544234i	0.258050	+	0.966131i	$0.416920\pi$
$164$	49978.9	−	41937.3i	0.145103	−	0.121756i
$165$	−99129.0	−	36080.0i	−0.283459	−	0.103171i
$166$	36754.8	−	208447.i	0.103525	−	0.587118i
$167$	−11207.8	+	63562.5i	−0.0310977	+	0.176364i	−0.996401	−	0.0847686i	$-0.972985\pi$
$167$	−11207.8	+	63562.5i	−0.0310977	+	0.176364i	0.965303	+	0.261133i	$0.0840960\pi$
$168$	103798.	+	37779.4i	0.283737	+	0.103272i
$169$	−283472.	+	237861.i	−0.763471	+	0.640628i
$170$	157714.	−	132338.i	0.418550	−	0.351205i
$171$	226437.	−	392200.i	0.592185	−	1.02569i
$172$	319376.	−	116243.i	0.823153	−	0.299603i
$173$	−90994.2	−	516054.i	−0.231152	−	1.31093i	−0.850567	−	0.525866i	$-0.823741\pi$
$173$	−90994.2	−	516054.i	−0.231152	−	1.31093i	0.619415	−	0.785064i	$-0.287370\pi$
$174$	161628.	+	279949.i	0.404711	+	0.700980i
$175$	−215892.	+	373936.i	−0.532894	+	0.923000i
$176$	−95709.1	−	34835.3i	−0.232901	−	0.0847691i
$177$	−77065.1	−	133481.i	−0.184895	−	0.320247i
$178$	120057.	+	100740.i	0.284012	+	0.238315i
$179$	421318.			0.982829			0.491414	−	0.870926i	$-0.336480\pi$
$179$	421318.			0.982829			0.491414	+	0.870926i	$0.336480\pi$
$180$	−57320.3	−	48097.4i	−0.131864	−	0.110647i
$181$	−29723.8	+	10818.6i	−0.0674384	+	0.0245456i	−0.375519	−	0.926815i	$-0.622536\pi$
$181$	−29723.8	+	10818.6i	−0.0674384	+	0.0245456i	0.308081	+	0.951360i	$0.400313\pi$
$182$	−4656.91	+	26410.6i	−0.0104212	+	0.0591017i
$183$	−24258.7	−	137578.i	−0.0535476	−	0.303683i
$184$	−82101.9			−0.178776
$185$	26194.1	−	241451.i	0.0562696	−	0.518680i
$186$	105722.			0.224070
$187$	121924.	+	691463.i	0.254967	+	1.44599i
$188$	78530.9	−	445371.i	0.162049	−	0.919025i
$189$	−654171.	+	238099.i	−1.33210	+	0.484844i
$190$	252399.	+	211788.i	0.507229	+	0.425616i
$191$	−38578.1			−0.0765168			−0.0382584	−	0.999268i	$-0.512181\pi$
$191$	−38578.1			−0.0765168			−0.0382584	+	0.999268i	$0.512181\pi$
$192$	28525.7	+	23935.9i	0.0558448	+	0.0468593i
$193$	−134893.	−	233641.i	−0.260672	−	0.451498i	0.705748	−	0.708463i	$-0.250611\pi$
$193$	−134893.	−	233641.i	−0.260672	−	0.451498i	−0.966421	+	0.256965i	$0.917278\pi$
$194$	−591346.	−	215232.i	−1.12807	−	0.410585i
$195$	−4681.91	+	8109.31i	−0.00881732	+	0.0152720i
$196$	−153876.	−	266521.i	−0.286109	−	0.495555i
$197$	115027.	+	652352.i	0.211172	+	1.19761i	0.887428	+	0.460947i	$0.152490\pi$
$197$	115027.	+	652352.i	0.211172	+	1.19761i	−0.676256	+	0.736666i	$0.736399\pi$
$198$	239796.	−	87278.6i	0.434689	−	0.158214i
$199$	−100510.	+	174088.i	−0.179919	+	0.311628i	−0.941853	−	0.336027i	$-0.890917\pi$
$199$	−100510.	+	174088.i	−0.179919	+	0.311628i	0.761934	+	0.647655i	$0.224250\pi$
$200$	−111506.	+	93564.7i	−0.197117	+	0.165401i
$201$	507005.	−	425428.i	0.885161	−	0.742738i
$202$	529258.	+	192634.i	0.912617	+	0.332166i
$203$	293047.	−	1.66195e6i	0.499112	−	2.83060i
$204$	44576.1	−	252804.i	0.0749940	−	0.425312i
$205$	−111754.	−	40675.3i	−0.185729	−	0.0675998i
$206$	157036.	−	131769.i	0.257829	−	0.216344i
$207$	157578.	−	132224.i	0.255605	−	0.214478i
$208$	−4520.39	+	7829.54i	−0.00724465	+	0.0125481i
$209$	−1.05590e6	+	384315.i	−1.67208	+	0.608586i
$210$	−34963.8	−	198290.i	−0.0547105	−	0.310279i
$211$	−294919.	−	510814.i	−0.456033	−	0.789872i	0.542714	−	0.839918i	$-0.317397\pi$
$211$	−294919.	−	510814.i	−0.456033	−	0.789872i	−0.998747	+	0.0500452i	$0.984063\pi$
$212$	35317.7	−	61172.0i	0.0539700	−	0.0934788i
$213$	13150.0	+	4786.20i	0.0198599	+	0.00722840i
$214$	392943.	+	680597.i	0.586536	+	1.01591i
$215$	−474587.	−	398225.i	−0.700196	−	0.587534i
$216$	−234684.			−0.342255
$217$	−422805.	−	354775.i	−0.609524	−	0.511451i
$218$	483242.	−	175886.i	0.688690	−	0.250663i
$219$	57421.5	−	325653.i	0.0809029	−	0.458823i
$220$	32239.1	+	182837.i	0.0449083	+	0.254688i
$221$	62324.1			0.0858371
$222$	−168495.	−	251615.i	−0.229459	−	0.342652i
$223$	997393.			1.34309			0.671543	−	0.740965i	$-0.265632\pi$
$223$	997393.			1.34309			0.671543	+	0.740965i	$0.265632\pi$
$224$	−33757.6	−	191449.i	−0.0449523	−	0.254937i
$225$	63329.1	−	359157.i	0.0833964	−	0.472964i
$226$	−84782.5	+	30858.3i	−0.110417	+	0.0401884i
$227$	346585.	+	290819.i	0.446421	+	0.374592i	0.838106	−	0.545508i	$-0.183663\pi$
$227$	346585.	+	290819.i	0.446421	+	0.374592i	−0.391685	+	0.920099i	$0.628108\pi$
$228$	410819.			0.523375
$229$	646905.	+	542817.i	0.815176	+	0.684014i	0.951837	−	0.306604i	$-0.0991926\pi$
$229$	646905.	+	542817.i	0.815176	+	0.684014i	−0.136661	+	0.990618i	$0.543637\pi$
$230$	74828.8	+	129607.i	0.0932716	+	0.161551i
$231$	645263.	+	234856.i	0.795621	+	0.289583i
$232$	284457.	−	492693.i	0.346973	−	0.600976i
$233$	500910.	+	867601.i	0.604463	+	1.04696i	0.992136	+	0.125164i	$0.0399457\pi$
$233$	500910.	+	867601.i	0.604463	+	1.04696i	−0.387673	+	0.921797i	$0.626721\pi$
$234$	−3933.37	−	22307.2i	−0.00469597	−	0.0266322i
$235$	−774643.	+	281947.i	−0.915023	+	0.333041i
$236$	−135630.	+	234918.i	−0.158517	+	0.274559i
$237$	−198781.	+	166797.i	−0.229882	+	0.192894i
$238$	−1.02661e6	+	861428.i	−1.17480	+	0.985772i
$239$	−654195.	−	238107.i	−0.740819	−	0.269636i	−0.0560820	−	0.998426i	$-0.517861\pi$
$239$	−654195.	−	238107.i	−0.740819	−	0.269636i	−0.684737	+	0.728790i	$0.740083\pi$
$240$	11786.8	−	66846.5i	0.0132090	−	0.0749119i
$241$	135012.	−	765693.i	0.149738	−	0.849204i	−0.813703	−	0.581281i	$-0.802552\pi$
$241$	135012.	−	765693.i	0.149738	−	0.849204i	0.963440	−	0.267923i	$-0.0863373\pi$
$242$	10376.1	+	3776.60i	0.0113893	+	0.00414536i
$243$	721792.	−	605655.i	0.784145	−	0.657976i
$244$	−188343.	+	158039.i	−0.202523	+	0.169937i
$245$	−280490.	+	485822.i	−0.298539	+	0.517085i
$246$	−139342.	+	50716.2i	−0.146806	+	0.0534329i
$247$	17319.9	+	98225.9i	0.0180635	+	0.102443i
$248$	−93032.5	−	161137.i	−0.0960517	−	0.166367i
$249$	−240534.	+	416616.i	−0.245854	+	0.425832i
$250$	591910.	+	215438.i	0.598971	+	0.218008i
$251$	−36105.8	−	62537.1i	−0.0361737	−	0.0626547i	0.847372	−	0.531000i	$-0.178184\pi$
$251$	−36105.8	−	62537.1i	−0.0361737	−	0.0626547i	−0.883545	+	0.468345i	$0.844850\pi$
$252$	373116.	+	313082.i	0.370120	+	0.310568i
$253$	−510388.			−0.501302
$254$	885680.	+	743173.i	0.861375	+	0.722780i
$255$	−439707.	+	160040.i	−0.423460	+	0.154127i
$256$	11380.2	−	64540.4i	0.0108530	−	0.0615505i
$257$	−166250.	−	942850.i	−0.157010	−	0.890451i	−0.956925	−	0.290336i	$-0.906233\pi$
$257$	−166250.	−	942850.i	−0.157010	−	0.890451i	0.799914	−	0.600114i	$-0.204878\pi$
$258$	−772463.			−0.722484
$259$	−170506.	+	1.57168e6i	−0.157939	+	1.45585i
$260$	16479.8			0.0151188
$261$	247517.	+	1.40374e6i	0.224907	+	1.27551i
$262$	99001.6	−	561466.i	0.0891024	−	0.505325i
$263$	1.19856e6	−	436239.i	1.06849	−	0.388898i	0.252877	−	0.967498i	$-0.418623\pi$
$263$	1.19856e6	−	436239.i	1.06849	−	0.388898i	0.815611	+	0.578601i	$0.196401\pi$
$264$	177330.	+	148798.i	0.156593	+	0.131397i
$265$	−128756.			−0.112630
$266$	−1.64295e6	−	1.37860e6i	−1.42371	−	1.19463i
$267$	−178100.	−	308479.i	−0.152893	−	0.264818i
$268$	−1.09457e6	−	398390.i	−0.930905	−	0.338822i
$269$	135233.	−	234230.i	0.113947	−	0.197361i	−0.803412	−	0.595424i	$-0.796984\pi$
$269$	135233.	−	234230.i	0.113947	−	0.197361i	0.917358	+	0.398063i	$0.130317\pi$
$270$	213894.	+	370476.i	0.178562	+	0.309279i
$271$	−175926.	−	997725.i	−0.145514	−	0.825254i	−0.966953	−	0.254956i	$-0.917939\pi$
$271$	−175926.	−	997725.i	−0.145514	−	0.825254i	0.821438	−	0.570298i	$-0.193172\pi$
$272$	−424537.	+	154519.i	−0.347931	+	0.126637i
$273$	30476.1	−	52786.1i	0.0247487	−	0.0428660i
$274$	218341.	−	183210.i	0.175695	−	0.147426i
$275$	−693180.	+	581647.i	−0.552732	+	0.463797i
$276$	175348.	+	63821.5i	0.138557	+	0.0504306i
$277$	−260141.	+	1.47533e6i	−0.203708	+	1.15529i	0.695751	+	0.718283i	$0.255072\pi$
$277$	−260141.	+	1.47533e6i	−0.203708	+	1.15529i	−0.899459	+	0.437004i	$0.856039\pi$
$278$	13539.6	−	76787.0i	0.0105074	−	0.0595903i
$279$	438065.	+	159443.i	0.336921	+	0.122629i
$280$	−271457.	+	227779.i	−0.206922	+	0.173628i
$281$	605275.	−	507886.i	0.457285	−	0.383708i	−0.384846	−	0.922981i	$-0.625745\pi$
$281$	605275.	−	507886.i	0.457285	−	0.383708i	0.842131	+	0.539273i	$0.181301\pi$
$282$	−513928.	+	890149.i	−0.384839	+	0.666561i
$283$	−1.00820e6	+	366955.i	−0.748308	+	0.272362i	−0.687894	−	0.725811i	$-0.741464\pi$
$283$	−1.00820e6	+	366955.i	−0.748308	+	0.272362i	−0.0604146	+	0.998173i	$0.519242\pi$
$284$	−4276.69	−	24254.3i	−0.00314639	−	0.0178440i
$285$	−374426.	−	648525.i	−0.273057	−	0.472949i
$286$	−28101.1	+	48672.5i	−0.0203146	+	0.0351859i
$287$	727445.	+	264768.i	0.521310	+	0.189741i
$288$	82099.1	+	142200.i	0.0583254	+	0.101022i
$289$	1.29813e6	+	1.08926e6i	0.914266	+	0.767160i
$290$	−1.03703e6			−0.724097
$291$	1.09565e6	+	919359.i	0.758471	+	0.636433i
$292$	−546875.	+	199046.i	−0.375345	+	0.136614i
$293$	35085.2	−	198978.i	0.0238756	−	0.135405i	−0.970540	−	0.240940i	$-0.922544\pi$
$293$	35085.2	−	198978.i	0.0238756	−	0.135405i	0.994416	+	0.105535i	$0.0336554\pi$
$294$	121460.	+	688834.i	0.0819530	+	0.464778i
$295$	494460.			0.330808
$296$	−235229.	+	478226.i	−0.156049	+	0.317252i
$297$	−1.45892e6			−0.959710
$298$	216994.	+	1.23064e6i	0.141549	+	0.802766i
$299$	−7867.00	+	44616.0i	−0.00508899	+	0.0288611i
$300$	310880.	−	113151.i	0.199429	−	0.0725863i
$301$	3.08924e6	+	2.59218e6i	1.96533	+	1.64911i
$302$	−5979.44			−0.00377262
$303$	−980612.	−	822831.i	−0.613607	−	0.514878i
$304$	−361509.	−	626151.i	−0.224354	−	0.388593i
$305$	421140.	+	153283.i	0.259225	+	0.0943503i
$306$	565964.	−	980278.i	0.345530	−	0.598475i
$307$	282602.	+	489481.i	0.171131	+	0.296408i	0.938816	−	0.344420i	$-0.111924\pi$
$307$	282602.	+	489481.i	0.171131	+	0.296408i	−0.767684	+	0.640828i	$0.778591\pi$
$308$	−209855.	−	1.19015e6i	−0.126050	−	0.714864i
$309$	−437818.	+	159353.i	−0.260854	+	0.0949431i
$310$	−169582.	+	293725.i	−0.100225	+	0.173595i
$311$	1.11560e6	−	936102.i	0.654047	−	0.548810i	−0.254249	−	0.967139i	$-0.581828\pi$
$311$	1.11560e6	−	936102.i	0.654047	−	0.548810i	0.908296	+	0.418328i	$0.137384\pi$
$312$	15740.6	−	13207.9i	0.00915451	−	0.00768155i
$313$	−2.63128e6	−	957707.i	−1.51812	−	0.552550i	−0.557441	−	0.830216i	$-0.688217\pi$
$313$	−2.63128e6	−	957707.i	−1.51812	−	0.552550i	−0.960678	+	0.277666i	$0.910439\pi$
$314$	112343.	−	637127.i	0.0643014	−	0.364671i
$315$	154172.	−	874354.i	0.0875446	−	0.496490i
$316$	429146.	+	156196.i	0.241762	+	0.0879941i
$317$	354222.	−	297227.i	0.197983	−	0.166127i	−0.538407	−	0.842685i	$-0.680974\pi$
$317$	354222.	−	297227.i	0.197983	−	0.166127i	0.736389	+	0.676558i	$0.236529\pi$
$318$	−122981.	+	103193.i	−0.0681978	+	0.0572247i
$319$	1.76833e6	−	3.06284e6i	0.972942	−	1.68518i
$320$	−112256.	+	40858.0i	−0.0612825	+	0.0223050i
$321$	−310164.	−	1.75903e6i	−0.168008	−	0.952818i
$322$	−487085.	−	843656.i	−0.261797	−	0.453446i
$323$	−2.49212e6	+	4.31648e6i	−1.32911	+	2.30209i
$324$	−84619.0	−	30798.8i	−0.0447822	−	0.0162994i
$325$	40160.6	+	69560.3i	0.0210908	+	0.0365303i
$326$	−880038.	−	738440.i	−0.458625	−	0.384832i
$327$	−1.16880e6			−0.604466
$328$	199916.	+	167749.i	0.102604	+	0.0860946i
$329$	5.04241e6	−	1.83529e6i	2.56831	−	0.934790i
$330$	73273.2	−	415553.i	0.0370391	−	0.210059i
$331$	270748.	+	1.53549e6i	0.135830	+	0.770331i	0.974278	+	0.225349i	$0.0723523\pi$
$331$	270748.	+	1.53549e6i	0.135830	+	0.770331i	−0.838448	+	0.544982i	$0.816537\pi$
$332$	846650.			0.421559
$333$	−318700.	−	1.29669e6i	−0.157497	−	0.640805i
$334$	−258172.			−0.126632
$335$	368699.	+	2.09100e6i	0.179498	+	1.01799i
$336$	−76724.4	+	435126.i	−0.0370753	+	0.210265i
$337$	−826226.	+	300722.i	−0.396300	+	0.144241i	−0.532480	−	0.846443i	$-0.678740\pi$
$337$	−826226.	+	300722.i	−0.396300	+	0.144241i	0.136180	+	0.990684i	$0.456518\pi$
$338$	−1.13389e6	−	951443.i	−0.539856	−	0.452993i
$339$	205061.			0.0969132
$340$	630855.	+	529350.i	0.295960	+	0.248340i
$341$	−578338.	−	1.00171e6i	−0.269337	−	0.466505i
$342$	1.70225e6	+	619568.i	0.786970	+	0.286433i
$343$	230426.	−	399110.i	0.105754	−	0.183171i
$344$	679745.	+	1.17735e6i	0.309706	+	0.536427i
$345$	−59065.1	−	334975.i	−0.0267167	−	0.151518i
$346$	1.96965e6	−	716894.i	0.884502	−	0.321933i
$347$	1.08130e6	−	1.87287e6i	0.482084	−	0.834994i	−0.517705	−	0.855559i	$-0.673213\pi$
$347$	1.08130e6	−	1.87287e6i	0.482084	−	0.834994i	0.999789	+	0.0205658i	$0.00654676\pi$
$348$	−990517.	+	831142.i	−0.438444	+	0.367898i
$349$	1.16833e6	−	980348.i	0.513456	−	0.430841i	−0.348887	−	0.937165i	$-0.613440\pi$
$349$	1.16833e6	−	980348.i	0.513456	−	0.430841i	0.862343	+	0.506324i	$0.168996\pi$
$350$	−1.62298e6	−	590715.i	−0.708177	−	0.257755i
$351$	−22487.4	+	127533.i	−0.00974253	+	0.0552527i
$352$	70745.3	−	401217.i	0.0304327	−	0.172593i
$353$	711013.	+	258788.i	0.303697	+	0.110537i	0.489374	−	0.872074i	$-0.337225\pi$
$353$	711013.	+	258788.i	0.303697	+	0.110537i	−0.185676	+	0.982611i	$0.559448\pi$
$354$	472282.	−	396292.i	0.200306	−	0.168076i
$355$	−34390.4	+	28857.0i	−0.0144833	+	0.0121529i
$356$	−313446.	+	542905.i	−0.131081	+	0.227038i
$357$	2.86219e6	−	1.04175e6i	1.18858	−	0.432608i
$358$	292645.	+	1.65967e6i	0.120679	+	0.684407i
$359$	−869963.	−	1.50682e6i	−0.356258	−	0.617057i	0.631074	−	0.775722i	$-0.282614\pi$
$359$	−869963.	−	1.50682e6i	−0.356258	−	0.617057i	−0.987332	+	0.158665i	$0.949281\pi$
$360$	149653.	−	259206.i	0.0608594	−	0.105412i
$361$	−5.16877e6	−	1.88128e6i	−2.08747	−	0.759776i
$362$	−63262.7	−	109574.i	−0.0253733	−	0.0439478i
$363$	−19224.9	−	16131.6i	−0.00765770	−	0.00642558i
$364$	−107272.			−0.0424359
$365$	812647.	+	681892.i	0.319278	+	0.267906i
$366$	525101.	−	191121.i	0.204899	−	0.0745772i
$367$	511462.	−	2.90065e6i	0.198221	−	1.12416i	−0.709537	−	0.704669i	$-0.751096\pi$
$367$	511462.	−	2.90065e6i	0.198221	−	1.12416i	0.907757	−	0.419496i	$-0.137793\pi$
$368$	−57027.4	−	323418.i	−0.0219515	−	0.124493i
$369$	−653855.			−0.249986
$370$	969326.	−	64525.6i	0.368100	−	0.0245035i
$371$	838115.			0.316132
$372$	73433.9	+	416464.i	0.0275131	+	0.156034i
$373$	−67283.5	+	381584.i	−0.0250401	+	0.142010i	−0.994765	−	0.102191i	$-0.967415\pi$
$373$	−67283.5	+	381584.i	−0.0250401	+	0.142010i	0.969725	+	0.244201i	$0.0785257\pi$
$374$	−2.63915e6	+	960570.i	−0.975628	+	0.355100i
$375$	−1.09670e6	−	920236.i	−0.402724	−	0.337926i
$376$	1.80897e6			0.659874
$377$	−240484.	−	201790.i	−0.0871430	−	0.0731217i
$378$	−1.39231e6	−	2.41155e6i	−0.501194	−	0.868093i
$379$	−3.93265e6	−	1.43137e6i	−1.40633	−	0.511863i	−0.476280	−	0.879294i	$-0.658015\pi$
$379$	−3.93265e6	−	1.43137e6i	−1.40633	−	0.511863i	−0.930051	+	0.367431i	$0.880237\pi$
$380$	−658968.	+	1.14137e6i	−0.234102	+	0.405477i
$381$	−1.31388e6	−	2.27570e6i	−0.463705	−	0.803161i
$382$	−26796.0	−	151968.i	−0.00939533	−	0.0532836i
$383$	−551454.	+	200713.i	−0.192093	+	0.0699162i	−0.436276	−	0.899813i	$-0.643703\pi$
$383$	−551454.	+	200713.i	−0.192093	+	0.0699162i	0.244182	+	0.969729i	$0.421480\pi$
$384$	−74475.2	+	128995.i	−0.0257741	+	0.0446421i
$385$	−1.68752e6	+	1.41600e6i	−0.580225	+	0.486867i
$386$	826670.	−	693659.i	0.282400	−	0.236961i
$387$	−3.20074e6	−	1.16497e6i	−1.08636	−	0.395402i
$388$	437105.	−	2.47895e6i	0.147403	−	0.835965i
$389$	2028.94	−	11506.7i	0.000679822	−	0.00385546i	−0.984466	−	0.175576i	$-0.943821\pi$
$389$	2028.94	−	11506.7i	0.000679822	−	0.00385546i	0.985146	+	0.171720i	$0.0549325\pi$
$390$	−35196.5	−	12810.5i	−0.0117176	−	0.00426485i
$391$	−1.73427e6	+	1.45523e6i	−0.573688	+	0.481381i
$392$	943007.	−	791277.i	0.309956	−	0.260084i
$393$	−647894.	+	1.12219e6i	−0.211603	+	0.366508i
$394$	−2.48987e6	+	906238.i	−0.808046	+	0.294105i
$395$	−144556.	−	819816.i	−0.0466168	−	0.264377i
$396$	510371.	+	883989.i	0.163549	+	0.283275i
$397$	276216.	−	478420.i	0.0879573	−	0.152347i	−0.818690	−	0.574235i	$-0.805299\pi$
$397$	276216.	−	478420.i	0.0879573	−	0.152347i	0.906648	+	0.421889i	$0.138633\pi$
$398$	−755588.	−	275011.i	−0.239099	−	0.0870248i
$399$	2.43726e6	+	4.22146e6i	0.766425	+	1.32749i
$400$	−446024.	−	374259.i	−0.139383	−	0.116956i
$401$	5.69512e6			1.76865			0.884326	−	0.466870i	$-0.154619\pi$
$401$	5.69512e6			1.76865			0.884326	+	0.466870i	$0.154619\pi$
$402$	2.02802e6	+	1.70171e6i	0.625903	+	0.525195i
$403$	−96479.7	+	35115.8i	−0.0295919	+	0.0107706i
$404$	−391211.	+	2.21867e6i	−0.119250	+	0.676300i
$405$	28503.5	+	161651.i	0.00863496	+	0.0489713i
$406$	6.75037e6			2.03242
$407$	−1.46231e6	+	2.97290e6i	−0.437575	+	0.889600i
$408$	1.02681e6			0.305381
$409$	504593.	+	2.86169e6i	0.149153	+	0.845891i	0.963938	+	0.266127i	$0.0857440\pi$
$409$	504593.	+	2.86169e6i	0.149153	+	0.845891i	−0.814785	+	0.579764i	$0.803145\pi$
$410$	82605.5	−	468479.i	0.0242689	−	0.137636i
$411$	−608736.	+	221562.i	−0.177756	+	0.0646980i
$412$	628146.	+	527077.i	0.182313	+	0.152979i
$413$	−3.21860e6			−0.928522
$414$	630312.	+	528895.i	0.180740	+	0.151659i
$415$	−771649.	−	1.33653e6i	−0.219938	−	0.380943i
$416$	−33982.2	−	12368.5i	−0.00962761	−	0.00350416i
$417$	−88607.0	+	153472.i	−0.0249533	+	0.0432204i
$418$	−2.24733e6	−	3.89248e6i	−0.629108	−	1.08965i
$419$	856091.	+	4.85514e6i	0.238224	+	1.35103i	0.835717	+	0.549160i	$0.185052\pi$
$419$	856091.	+	4.85514e6i	0.238224	+	1.35103i	−0.597493	+	0.801874i	$0.703837\pi$
$420$	756824.	−	275461.i	0.209349	−	0.0761969i
$421$	390439.	−	676260.i	0.107361	−	0.185955i	−0.807339	−	0.590088i	$-0.799093\pi$
$421$	390439.	−	676260.i	0.107361	−	0.185955i	0.914701	+	0.404132i	$0.132426\pi$
$422$	1.80737e6	−	1.51656e6i	0.494044	−	0.414552i
$423$	−3.47195e6	+	2.91331e6i	−0.943457	+	0.791654i
$424$	265502.	+	96634.9i	0.0717222	+	0.0261047i
$425$	−696988.	+	3.95281e6i	−0.187177	+	1.06153i
$426$	−9720.08	+	55125.3i	−0.00259505	+	0.0147173i
$427$	−2.74134e6	−	997766.i	−0.727601	−	0.264825i
$428$	−2.40809e6	+	2.02063e6i	−0.635425	+	0.533184i
$429$	97851.8	−	82107.4i	0.0256700	−	0.0215397i
$430$	1.23906e6	−	2.14611e6i	0.323162	−	0.559733i
$431$	1.91411e6	−	696678.i	0.496333	−	0.180650i	−0.0817111	−	0.996656i	$-0.526038\pi$
$431$	1.91411e6	−	696678.i	0.496333	−	0.180650i	0.578044	+	0.816006i	$0.303816\pi$
$432$	−163010.	−	924475.i	−0.0420247	−	0.238334i
$433$	966329.	+	1.67373e6i	0.247688	+	0.429008i	0.962884	−	0.269916i	$-0.0869958\pi$
$433$	966329.	+	1.67373e6i	0.247688	+	0.429008i	−0.715196	+	0.698924i	$0.753663\pi$
$434$	1.10387e6	−	1.91195e6i	0.281314	−	0.487250i
$435$	2.21482e6	+	806130.i	0.561198	+	0.204259i
$436$	1.02851e6	+	1.78143e6i	0.259115	+	0.448801i
$437$	−2.77547e6	−	2.32889e6i	−0.695236	−	0.583372i
$438$	1.32271e6			0.329442
$439$	2.03208e6	+	1.70511e6i	0.503244	+	0.422272i	0.858744	−	0.512404i	$-0.171245\pi$
$439$	2.03208e6	+	1.70511e6i	0.503244	+	0.422272i	−0.355500	+	0.934676i	$0.615689\pi$
$440$	−697845.	+	253995.i	−0.171841	+	0.0625451i
$441$	−535575.	+	3.03739e6i	−0.131136	+	0.743712i
$442$	43289.9	+	245509.i	0.0105398	+	0.0597739i
$443$	1.59204e6			0.385428			0.192714	−	0.981255i	$-0.438271\pi$
$443$	1.59204e6			0.385428			0.192714	+	0.981255i	$0.438271\pi$
$444$	874134.	−	838511.i	0.210436	−	0.201860i
$445$	1.14272e6			0.273551
$446$	692782.	+	3.92896e6i	0.164915	+	0.935278i
$447$	493185.	−	2.79699e6i	0.116746	−	0.662098i
$448$	730714.	−	265958.i	0.172009	−	0.0626063i
$449$	−553459.	−	464407.i	−0.129560	−	0.108713i	0.575705	−	0.817657i	$-0.304728\pi$
$449$	−553459.	−	464407.i	−0.129560	−	0.108713i	−0.705265	+	0.708944i	$0.749172\pi$
$450$	1.45879e6			0.339596
$451$	1.24278e6	+	1.04282e6i	0.287709	+	0.241416i
$452$	−180447.	−	312544.i	−0.0415436	−	0.0719556i
$453$	12770.5	+	4648.08i	0.00292390	+	0.00106421i
$454$	−904868.	+	1.56728e6i	−0.206037	+	0.356867i
$455$	97769.4	+	169342.i	0.0221398	+	0.0383473i
$456$	285352.	+	1.61831e6i	0.0642641	+	0.364460i
$457$	6.93600e6	−	2.52450e6i	1.55353	−	0.565438i	0.584285	−	0.811548i	$-0.301375\pi$
$457$	6.93600e6	−	2.52450e6i	1.55353	−	0.565438i	0.969242	+	0.246111i	$0.0791527\pi$
$458$	−1.68895e6	+	2.92534e6i	−0.376229	+	0.651648i
$459$	−4.95733e6	+	4.15969e6i	−1.09829	+	0.921573i
$460$	−458578.	+	384792.i	−0.101046	+	0.0847875i
$461$	7.08310e6	+	2.57804e6i	1.55228	+	0.564985i	0.968952	−	0.247248i	$-0.0795264\pi$
$461$	7.08310e6	+	2.57804e6i	1.55228	+	0.564985i	0.583332	+	0.812234i	$0.301749\pi$
$462$	−476959.	+	2.70497e6i	−0.103962	+	0.589600i
$463$	623284.	−	3.53482e6i	0.135124	−	0.766328i	−0.839649	−	0.543130i	$-0.817239\pi$
$463$	623284.	−	3.53482e6i	0.135124	−	0.766328i	0.974773	−	0.223198i	$-0.0716497\pi$
$464$	2.13841e6	+	778319.i	0.461102	+	0.167827i
$465$	590508.	−	495495.i	0.126647	−	0.106269i
$466$	−3.06975e6	+	2.57583e6i	−0.654845	+	0.549481i
$467$	−3.27836e6	+	5.67829e6i	−0.695608	+	1.20483i	0.274367	+	0.961625i	$0.411532\pi$
$467$	−3.27836e6	+	5.67829e6i	−0.695608	+	1.20483i	−0.969975	+	0.243204i	$0.921802\pi$
$468$	85141.3	−	30988.9i	0.0179691	−	0.00654021i
$469$	−2.39998e6	−	1.36110e7i	−0.503821	−	2.85731i
$470$	−1.64872e6	−	2.85566e6i	−0.344272	−	0.596296i
$471$	−735201.	+	1.27341e6i	−0.152705	+	0.264493i
$472$	−1.01960e6	−	371106.i	−0.210657	−	0.0766730i
$473$	4.22565e6	+	7.31904e6i	0.868441	+	1.50418i
$474$	−795124.	−	667189.i	−0.162551	−	0.136396i
$475$	−6.42352e6			−1.30629
$476$	−4.10644e6	−	3.44571e6i	−0.830708	−	0.697046i
$477$	−665207.	+	242116.i	−0.133863	+	0.0487222i
$478$	483561.	−	2.74241e6i	0.0968014	−	0.548988i
$479$	−862704.	−	4.89264e6i	−0.171800	−	0.974326i	−0.941773	−	0.336249i	$-0.890842\pi$
$479$	−862704.	−	4.89264e6i	−0.171800	−	0.974326i	0.769973	−	0.638076i	$-0.220270\pi$
$480$	271511.			0.0537879
$481$	237339.	+	173652.i	0.0467742	+	0.0342230i
$482$	3.11002e6			0.609741
$483$	384474.	+	2.18046e6i	0.0749892	+	0.425285i
$484$	−7669.72	+	43497.2i	−0.00148822	+	0.00844010i
$485$	−4.31169e6	+	1.56933e6i	−0.832325	+	0.302942i
$486$	2.88717e6	+	2.42262e6i	0.554474	+	0.465259i
$487$	4.07965e6			0.779472			0.389736	−	0.920927i	$-0.372566\pi$
$487$	4.07965e6			0.779472			0.389736	+	0.920927i	$0.372566\pi$
$488$	−753372.	−	632154.i	−0.143206	−	0.120164i
$489$	1.30551e6	+	2.26120e6i	0.246892	+	0.427630i
$490$	−2.10859e6	−	767465.i	−0.396737	−	0.144400i
$491$	−4.01541e6	+	6.95490e6i	−0.751668	+	1.30193i	0.195345	+	0.980735i	$0.437417\pi$
$491$	−4.01541e6	+	6.95490e6i	−0.751668	+	1.30193i	−0.947014	+	0.321193i	$0.895916\pi$
$492$	−296568.	−	513671.i	−0.0552347	−	0.0956693i
$493$	−2.72412e6	−	1.54493e7i	−0.504788	−	2.86280i
$494$	−374904.	+	136454.i	−0.0691199	+	0.0251576i
$495$	930318.	−	1.61136e6i	0.170655	−	0.295583i
$496$	570136.	−	478401.i	0.104058	−	0.0873148i
$497$	223858.	−	187839.i	0.0406520	−	0.0341111i
$498$	−1.80822e6	−	658139.i	−0.326722	−	0.118917i
$499$	−320118.	+	1.81548e6i	−0.0575518	+	0.326393i	−0.999968	−	0.00805103i	$-0.997437\pi$
$499$	−320118.	+	1.81548e6i	−0.0575518	+	0.326393i	0.942416	+	0.334444i	$0.108548\pi$
$500$	−437523.	+	2.48131e6i	−0.0782664	+	0.443871i
$501$	551388.	+	200689.i	0.0981438	+	0.0357214i
$502$	221269.	−	185667.i	0.0391888	−	0.0328833i
$503$	−1.29709e6	+	1.08839e6i	−0.228586	+	0.191806i	−0.749886	−	0.661567i	$-0.769892\pi$
$503$	−1.29709e6	+	1.08839e6i	−0.228586	+	0.191806i	0.521300	+	0.853373i	$0.325447\pi$
$504$	−974137.	+	1.68725e6i	−0.170822	+	0.295872i
$505$	3.85898e6	−	1.40455e6i	0.673355	−	0.245081i
$506$	−354512.	−	2.01054e6i	−0.0615538	−	0.349089i
$507$	1.68208e6	+	2.91345e6i	0.290621	+	0.503371i
$508$	−2.31234e6	+	4.00510e6i	−0.397551	+	0.688579i
$509$	−1.46687e6	−	533895.i	−0.250955	−	0.0913401i	0.213480	−	0.976947i	$-0.431520\pi$
$509$	−1.46687e6	−	533895.i	−0.250955	−	0.0913401i	−0.464435	+	0.885607i	$0.653742\pi$
$510$	−935853.	−	1.62094e6i	−0.159324	−	0.275958i
$511$	−5.28978e6	−	4.43865e6i	−0.896160	−	0.751967i
$512$	262144.			0.0441942
$513$	−7.93353e6	−	6.65702e6i	−1.33098	−	1.11683i
$514$	3.59863e6	−	1.30979e6i	0.600799	−	0.218673i
$515$	259551.	−	1.47199e6i	0.0431225	−	0.244560i
$516$	−536547.	−	3.04291e6i	−0.0887123	−	0.503112i
$517$	1.12455e7			1.85034
$518$	−6.30966e6	+	420018.i	−1.03319	+	0.0687771i
$519$	−4.76393e6			−0.776331
$520$	11446.7	+	64917.7i	0.00185641	+	0.0105282i
$521$	703375.	−	3.98904e6i	0.113525	−	0.643833i	−0.873945	−	0.486026i	$-0.838446\pi$
$521$	703375.	−	3.98904e6i	0.113525	−	0.643833i	0.987470	−	0.157808i	$-0.0504427\pi$
$522$	−5.35773e6	+	1.95005e6i	−0.860606	+	0.313235i
$523$	−3.28113e6	−	2.75320e6i	−0.524529	−	0.440132i	0.341678	−	0.939817i	$-0.389005\pi$
$523$	−3.28113e6	−	2.75320e6i	−0.524529	−	0.440132i	−0.866207	+	0.499685i	$0.833449\pi$
$524$	2.28051e6			0.362831
$525$	3.00706e6	+	2.52322e6i	0.476150	+	0.399537i
$526$	2.55096e6	+	4.41839e6i	0.402012	+	0.696305i
$527$	−4.82126e6	−	1.75479e6i	−0.756195	−	0.275233i
$528$	−462977.	+	801899.i	−0.0722727	+	0.125180i
$529$	2.39533e6	+	4.14883e6i	0.372157	+	0.644595i
$530$	−89433.1	−	507200.i	−0.0138296	−	0.0784314i
$531$	2.55458e6	−	929793.i	0.393173	−	0.143103i
$532$	4.28944e6	−	7.42952e6i	0.657084	−	1.13810i
$533$	110315.	−	92564.9i	0.0168196	−	0.0141133i
$534$	1.09146e6	−	915846.i	0.165636	−	0.138985i
$535$	5.38457e6	+	1.95982e6i	0.813329	+	0.296028i
$536$	809071.	−	4.58847e6i	0.121640	−	0.689852i
$537$	665124.	−	3.77210e6i	0.0995329	−	0.564479i
$538$	1.01662e6	+	370018.i	0.151426	+	0.0551147i
$539$	5.86222e6	−	4.91899e6i	0.869142	−	0.729296i
$540$	−1.31082e6	+	1.09991e6i	−0.193446	+	0.162320i
$541$	−6.29127e6	+	1.08968e7i	−0.924155	+	1.60068i	−0.131242	+	0.991350i	$0.541896\pi$
$541$	−6.29127e6	+	1.08968e7i	−0.924155	+	1.60068i	−0.792914	+	0.609334i	$0.791437\pi$
$542$	3.80807e6	−	1.38602e6i	0.556810	−	0.202662i
$543$	49935.6	+	283199.i	0.00726792	+	0.0412184i
$544$	−903566.	−	1.56502e6i	−0.130907	−	0.226738i
$545$	1.87480e6	−	3.24725e6i	0.270373	−	0.468300i
$546$	229105.	+	83387.5i	0.0328892	+	0.0119707i
$547$	−3.61104e6	−	6.25450e6i	−0.516017	−	0.893767i	−0.999827	−	0.0185942i	$-0.994081\pi$
$547$	−3.61104e6	−	6.25450e6i	−0.516017	−	0.893767i	0.483811	−	0.875173i	$-0.339252\pi$
$548$	873365.	+	732840.i	0.124235	+	0.104246i
$549$	2.46402e6			0.348910
$550$	−2.77272e6	−	2.32659e6i	−0.390840	−	0.327954i
$551$	2.35918e7	−	8.58671e6i	3.31041	−	1.20489i
$552$	−129612.	+	735066.i	−0.0181050	+	0.102678i
$553$	940960.	+	5.33645e6i	0.130845	+	0.742061i
$554$	−5.99236e6			−0.829513
$555$	−2.12038e6	−	615690.i	−0.292201	−	0.0848457i
$556$	311886.			0.0427868
$557$	1.59831e6	+	9.06445e6i	0.218284	+	1.23795i	0.875116	+	0.483914i	$0.160785\pi$
$557$	1.59831e6	+	9.06445e6i	0.218284	+	1.23795i	−0.656832	+	0.754037i	$0.728104\pi$
$558$	−323805.	+	1.83639e6i	−0.0440248	+	0.249677i
$559$	704933.	−	256574.i	0.0954153	−	0.0347283i
$560$	−1.08583e6	−	911118.i	−0.146316	−	0.122773i
$561$	6.38321e6			0.856312
$562$	2.42110e6	+	2.03154e6i	0.323349	+	0.271322i
$563$	−6.01738e6	−	1.04224e7i	−0.800086	−	1.38579i	−0.919559	−	0.392952i	$-0.871454\pi$
$563$	−6.01738e6	−	1.04224e7i	−0.800086	−	1.38579i	0.119473	−	0.992837i	$-0.461880\pi$
$564$	−3.86347e6	−	1.40619e6i	−0.511423	−	0.186143i
$565$	−328924.	+	569714.i	−0.0433486	+	0.0750819i
$566$	−2.14581e6	−	3.71665e6i	−0.281546	−	0.487652i
$567$	−185538.	−	1.05224e6i	−0.0242368	−	0.137454i
$568$	92572.8	−	33693.7i	0.0120396	−	0.00438206i
$569$	−481348.	+	833719.i	−0.0623273	+	0.107954i	−0.895505	−	0.445051i	$-0.853186\pi$
$569$	−481348.	+	833719.i	−0.0623273	+	0.107954i	0.833178	+	0.553005i	$0.186519\pi$
$570$	2.29462e6	−	1.92541e6i	0.295817	−	0.248220i
$571$	2.46906e6	−	2.07179e6i	0.316914	−	0.265922i	−0.470429	−	0.882438i	$-0.655901\pi$
$571$	2.46906e6	−	2.07179e6i	0.316914	−	0.265922i	0.787343	+	0.616516i	$0.211456\pi$
$572$	−211251.	−	76889.1i	−0.0269966	−	0.00982596i
$573$	−60902.1	+	345393.i	−0.00774900	+	0.0439468i
$574$	−537706.	+	3.04948e6i	−0.0681185	+	0.386319i
$575$	−2.74172e6	−	997906.i	−0.345823	−	0.125869i
$576$	−503133.	+	422178.i	−0.0631868	+	0.0530200i
$577$	7.64756e6	−	6.41707e6i	0.956277	−	0.802411i	−0.0240666	−	0.999710i	$-0.507661\pi$
$577$	7.64756e6	−	6.41707e6i	0.956277	−	0.802411i	0.980343	+	0.197299i	$0.0632169\pi$
$578$	−3.38917e6	+	5.87021e6i	−0.421962	+	0.730860i
$579$	−2.30476e6	+	838864.i	−0.285713	+	0.103991i
$580$	−720314.	−	4.08510e6i	−0.0889103	−	0.504235i
$581$	5.02291e6	+	8.69994e6i	0.617327	+	1.06924i
$582$	−2.86054e6	+	4.95460e6i	−0.350058	+	0.606318i
$583$	1.65050e6	+	600733.i	0.201115	+	0.0731998i
$584$	−1.16394e6	−	2.01601e6i	−0.141221	−	0.244602i
$585$	−126519.	−	106162.i	−0.0152850	−	0.0128256i
$586$	808190.			0.0972231
$587$	−8.34460e6	−	7.00195e6i	−0.999563	−	0.838733i	−0.0126390	−	0.999920i	$-0.504023\pi$
$587$	−8.34460e6	−	7.00195e6i	−0.999563	−	0.838733i	−0.986924	+	0.161187i	$0.948468\pi$
$588$	−2.62911e6	+	956918.i	−0.313592	+	0.114138i
$589$	1.42582e6	−	8.08620e6i	0.169346	−	0.960410i
$590$	343448.	+	1.94779e6i	0.0406192	+	0.230363i
$591$	6.02216e6			0.709224
$592$	−2.04723e6	−	594449.i	−0.240084	−	0.0697125i
$593$	−1.99974e6			−0.233527			−0.116764	−	0.993160i	$-0.537252\pi$
$593$	−1.99974e6			−0.233527			−0.116764	+	0.993160i	$0.537252\pi$
$594$	−1.01335e6	−	5.74702e6i	−0.117841	−	0.668308i
$595$	−1.69679e6	+	9.62296e6i	−0.196488	+	1.11434i
$596$	−4.69704e6	+	1.70958e6i	−0.541637	+	0.197140i
$597$	1.39996e6	+	1.17470e6i	0.160760	+	0.134894i
$598$	−181217.			−0.0207227
$599$	6.19333e6	+	5.19682e6i	0.705273	+	0.591794i	0.923268	−	0.384155i	$-0.125507\pi$
$599$	6.19333e6	+	5.19682e6i	0.705273	+	0.591794i	−0.217995	+	0.975950i	$0.569952\pi$
$600$	661662.	+	1.14603e6i	0.0750340	+	0.129963i
$601$	4.41719e6	+	1.60773e6i	0.498839	+	0.181562i	0.579172	−	0.815206i	$-0.303376\pi$
$601$	4.41719e6	+	1.60773e6i	0.498839	+	0.181562i	−0.0803330	+	0.996768i	$0.525598\pi$
$602$	−8.06543e6	+	1.39697e7i	−0.907060	+	1.57107i
$603$	5.83681e6	+	1.01096e7i	0.653705	+	1.13225i
$604$	−4153.28	−	23554.4i	−0.000463232	−	0.00262712i
$605$	75655.5	−	27536.4i	0.00840335	−	0.00305857i
$606$	2.56020e6	−	4.43439e6i	0.283199	−	0.490515i
$607$	−4.35972e6	+	3.65824e6i	−0.480272	+	0.402996i	−0.850525	−	0.525935i	$-0.823716\pi$
$607$	−4.35972e6	+	3.65824e6i	−0.480272	+	0.402996i	0.370253	+	0.928931i	$0.379271\pi$
$608$	2.21545e6	−	1.85899e6i	0.243055	−	0.203947i
$609$	−1.44170e7	−	5.24736e6i	−1.57519	−	0.573321i
$610$	−311294.	+	1.76544e6i	−0.0338725	+	0.192100i
$611$	173335.	−	983032.i	0.0187838	−	0.106528i
$612$	4.25466e6	+	1.54857e6i	0.459183	+	0.167129i
$613$	−6.79656e6	+	5.70299e6i	−0.730529	+	0.612987i	−0.930276	−	0.366861i	$-0.880433\pi$
$613$	−6.79656e6	+	5.70299e6i	−0.730529	+	0.612987i	0.199746	+	0.979848i	$0.435988\pi$
$614$	−1.73188e6	+	1.45322e6i	−0.185395	+	0.155565i
$615$	−540593.	+	936335.i	−0.0576345	+	0.0998259i
$616$	4.54250e6	−	1.65333e6i	0.482328	−	0.175553i
$617$	326624.	+	1.85238e6i	0.0345410	+	0.195892i	0.997195	−	0.0748413i	$-0.0238450\pi$
$617$	326624.	+	1.85238e6i	0.0345410	+	0.195892i	−0.962654	+	0.270733i	$0.912734\pi$
$618$	−931833.	−	1.61398e6i	−0.0981447	−	0.169992i
$619$	−806627.	+	1.39712e6i	−0.0846147	+	0.146557i	−0.905227	−	0.424928i	$-0.860299\pi$
$619$	−806627.	+	1.39712e6i	−0.0846147	+	0.146557i	0.820612	+	0.571485i	$0.193633\pi$
$620$	−1.27484e6	−	464004.i	−0.133192	−	0.0484778i
$621$	−2.35205e6	−	4.07387e6i	−0.244747	−	0.423915i
$622$	4.46241e6	+	3.74441e6i	0.462481	+	0.388068i
$623$	−7.43832e6			−0.767811
$624$	62962.4	+	52831.8i	0.00647322	+	0.00543167i
$625$	−2.36303e6	+	860072.i	−0.241974	+	0.0880714i
$626$	1.94496e6	−	1.10304e7i	0.198370	−	1.12501i
$627$	1.77390e6	+	1.00603e7i	0.180202	+	1.02198i
$628$	2.58782e6			0.261839
$629$	3.50755e6	+	1.42711e7i	0.353490	+	1.43824i
$630$	3.55137e6			0.356488
$631$	841356.	+	4.77157e6i	0.0841214	+	0.477076i	0.997543	+	0.0700607i	$0.0223193\pi$
$631$	841356.	+	4.77157e6i	0.0841214	+	0.477076i	−0.913421	+	0.407015i	$0.866570\pi$
$632$	−317212.	+	1.79900e6i	−0.0315905	+	0.179159i
$633$	−5.03895e6	+	1.83403e6i	−0.499840	+	0.181927i
$634$	1.41689e6	+	1.18891e6i	0.139995	+	0.117470i
$635$	8.43001e6			0.829648
$636$	−491924.	−	412773.i	−0.0482231	−	0.0404640i
$637$	−339639.	−	588271.i	−0.0331641	−	0.0574419i
$638$	1.32935e7	+	4.83844e6i	1.29297	+	0.470602i
$639$	−123412.	+	213755.i	−0.0119565	+	0.0207093i
$640$	−238922.	−	413824.i	−0.0230571	−	0.0399362i
$641$	626777.	+	3.55463e6i	0.0602515	+	0.341703i	1.00000		0.000163340i	$-5.19926e-5\pi$
$641$	626777.	+	3.55463e6i	0.0602515	+	0.341703i	−0.939748	+	0.341867i	$0.888941\pi$
$642$	6.71378e6	−	2.44362e6i	0.642879	−	0.233989i
$643$	−2.49175e6	+	4.31585e6i	−0.237672	+	0.411660i	−0.960046	−	0.279843i	$-0.909718\pi$
$643$	−2.49175e6	+	4.31585e6i	−0.237672	+	0.411660i	0.722374	+	0.691503i	$0.243051\pi$
$644$	2.98503e6	−	2.50474e6i	0.283618	−	0.237984i
$645$	−4.31457e6	+	3.62035e6i	−0.408355	+	0.342651i
$646$	−1.87346e7	−	6.81884e6i	−1.76630	−	0.642879i
$647$	562828.	−	3.19195e6i	0.0528585	−	0.299775i	−0.946905	−	0.321513i	$-0.895809\pi$
$647$	562828.	−	3.19195e6i	0.0528585	−	0.299775i	0.999764	+	0.0217374i	$0.00691978\pi$
$648$	62547.8	−	354726.i	0.00585160	−	0.0331861i
$649$	−6.33839e6	−	2.30699e6i	−0.590700	−	0.214997i
$650$	−246119.	+	206518.i	−0.0228487	+	0.0191723i
$651$	−3.84381e6	+	3.22534e6i	−0.355475	+	0.298279i
$652$	2.29762e6	−	3.97959e6i	0.211670	−	0.366622i
$653$	−8.75221e6	+	3.18554e6i	−0.803221	+	0.292348i	−0.710820	−	0.703374i	$-0.751676\pi$
$653$	−8.75221e6	+	3.18554e6i	−0.803221	+	0.292348i	−0.0924002	+	0.995722i	$0.529454\pi$
$654$	−811841.	−	4.60418e6i	−0.0742210	−	0.420928i
$655$	−2.07849e6	−	3.60005e6i	−0.189297	−	0.327873i
$656$	−521943.	+	904032.i	−0.0473547	+	0.0820208i
$657$	5.48071e6	+	1.99481e6i	0.495363	+	0.180297i
$658$	1.07320e7	+	1.85884e7i	0.966312	+	1.67370i
$659$	−1.10884e7	−	9.30425e6i	−0.994613	−	0.834579i	−0.00838401	−	0.999965i	$-0.502669\pi$
$659$	−1.10884e7	−	9.30425e6i	−0.994613	−	0.834579i	−0.986229	+	0.165385i	$0.947113\pi$
$660$	1.68785e6			0.150826
$661$	3.36005e6	+	2.81942e6i	0.299118	+	0.250990i	0.779977	−	0.625808i	$-0.215231\pi$
$661$	3.36005e6	+	2.81942e6i	0.299118	+	0.250990i	−0.480859	+	0.876798i	$0.659675\pi$
$662$	−5.86059e6	+	2.13308e6i	−0.519753	+	0.189174i
$663$	98389.3	−	557994.i	0.00869289	−	0.0492998i
$664$	588077.	+	3.33515e6i	0.0517624	+	0.293559i
$665$	−1.56378e7			−1.37127
$666$	4.88660e6	−	2.15610e6i	0.426895	−	0.188358i
$667$	1.14035e7			0.992487
$668$	−179325.	−	1.01700e6i	−0.0155489	−	0.0881820i
$669$	1.57456e6	−	8.92975e6i	0.136017	−	0.771390i
$670$	−7.98083e6	+	2.90478e6i	−0.686849	+	0.249992i
$671$	−4.68335e6	−	3.92980e6i	−0.401560	−	0.336949i
$672$	−1.76735e6			−0.150973
$673$	−1.14407e7	−	9.59985e6i	−0.973673	−	0.817009i	0.00944969	−	0.999955i	$-0.496992\pi$
$673$	−1.14407e7	−	9.59985e6i	−0.973673	−	0.817009i	−0.983123	+	0.182947i	$0.941436\pi$
$674$	−1.75850e6	−	3.04582e6i	−0.149105	−	0.258258i
$675$	−7.83708e6	−	2.85246e6i	−0.662056	−	0.240969i
$676$	2.96037e6	−	5.12751e6i	0.249160	−	0.431558i
$677$	−3.59453e6	−	6.22590e6i	−0.301419	−	0.522072i	0.675039	−	0.737782i	$-0.264127\pi$
$677$	−3.59453e6	−	6.22590e6i	−0.301419	−	0.522072i	−0.976458	+	0.215710i	$0.930793\pi$
$678$	142434.	+	807781.i	0.0118998	+	0.0674869i
$679$	2.80662e7	−	1.02153e7i	2.33619	−	0.850305i
$680$	−1.64705e6	+	2.85277e6i	−0.136595	+	0.236589i
$681$	3.15087e6	−	2.64390e6i	0.260353	−	0.218462i
$682$	3.54426e6	−	2.97399e6i	0.291786	−	0.244838i
$683$	3.29258e6	+	1.19840e6i	0.270075	+	0.0982994i	0.473508	−	0.880790i	$-0.342988\pi$
$683$	3.29258e6	+	1.19840e6i	0.270075	+	0.0982994i	−0.203433	+	0.979089i	$0.565210\pi$
$684$	−1.25825e6	+	7.13590e6i	−0.102832	+	0.583188i
$685$	360876.	−	2.04663e6i	0.0293854	−	0.166653i
$686$	1.73224e6	+	630484.i	0.140539	+	0.0511521i
$687$	5.88115e6	−	4.93487e6i	0.475412	−	0.398918i
$688$	−4.16572e6	+	3.49545e6i	−0.335520	+	0.281535i
$689$	77954.0	−	135020.i	0.00625590	−	0.0108355i
$690$	1.27852e6	−	465342.i	0.102231	−	0.0372091i
$691$	775626.	+	4.39879e6i	0.0617955	+	0.350460i	0.999991	+	0.00435271i	$0.00138552\pi$
$691$	775626.	+	4.39879e6i	0.0617955	+	0.350460i	−0.938195	+	0.346107i	$0.887503\pi$
$692$	4.19212e6	+	7.26096e6i	0.332788	+	0.576406i
$693$	−6.05574e6	+	1.04889e7i	−0.478999	+	0.829650i
$694$	8.12872e6	+	2.95861e6i	0.640654	+	0.233179i
$695$	−284258.	−	492348.i	−0.0223229	−	0.0386643i
$696$	−3.96207e6	−	3.32457e6i	−0.310026	−	0.260143i
$697$	7.19620e6			0.561075
$698$	4.67333e6	+	3.92139e6i	0.363068	+	0.304650i
$699$	8.55849e6	−	3.11504e6i	0.662528	−	0.241140i
$700$	1.19965e6	−	6.80358e6i	0.0925361	−	0.524798i
$701$	3.50097e6	+	1.98550e7i	0.269088	+	1.52607i	0.757137	+	0.653256i	$0.226598\pi$
$701$	3.50097e6	+	1.98550e7i	0.269088	+	1.52607i	−0.488049	+	0.872816i	$0.662291\pi$
$702$	−518000.			−0.0396722
$703$	−2.15173e7	+	9.49402e6i	−1.64210	+	0.724539i
$704$	1.62962e6			0.123924
$705$	1.30139e6	+	7.38056e6i	0.0986132	+	0.559264i
$706$	−525560.	+	2.98060e6i	−0.0396835	+	0.225057i
$707$	−2.51194e7	+	9.14270e6i	−1.88999	+	0.687901i
$708$	1.88913e6	+	1.58517e6i	0.141638	+	0.118848i
$709$	−2.43966e6			−0.182270			−0.0911348	−	0.995839i	$-0.529049\pi$
$709$	−2.43966e6			−0.182270			−0.0911348	+	0.995839i	$0.529049\pi$
$710$	−137562.	−	115428.i	−0.0102412	−	0.00859340i
$711$	−2.28843e6	−	3.96368e6i	−0.169771	−	0.294052i
$712$	−2.35635e6	−	857640.i	−0.174196	−	0.0634023i
$713$	1.86478e6	−	3.22990e6i	0.137374	−	0.237938i
$714$	6.09177e6	+	1.05513e7i	0.447196	+	0.774566i
$715$	71158.9	+	403562.i	0.00520552	+	0.0295220i
$716$	−6.33456e6	+	2.30559e6i	−0.461779	+	0.168074i
$717$	−3.16456e6	+	5.48117e6i	−0.229887	+	0.398177i
$718$	5.33144e6	−	4.47361e6i	0.385952	−	0.323852i
$719$	1.42721e7	−	1.19757e7i	1.02959	−	0.863932i	0.0387914	−	0.999247i	$-0.487649\pi$
$719$	1.42721e7	−	1.19757e7i	1.02959	−	0.863932i	0.990803	+	0.135315i	$0.0432048\pi$
$720$	1.12502e6	+	409474.i	0.0808777	+	0.0294371i
$721$	−1.68950e6	+	9.58163e6i	−0.121037	+	0.686438i
$722$	3.82060e6	−	2.16677e7i	0.272765	−	1.54693i
$723$	−6.64218e6	−	2.41756e6i	−0.472569	−	0.172001i
$724$	387696.	−	325316.i	0.0274881	−	0.0230653i
$725$	1.54876e7	−	1.29957e7i	1.09431	−	0.918234i
$726$	50192.8	−	86936.4i	0.00353427	−	0.00612153i
$727$	1.59291e7	−	5.79774e6i	1.11778	−	0.406839i	0.283939	−	0.958842i	$-0.408359\pi$
$727$	1.59291e7	−	5.79774e6i	1.11778	−	0.406839i	0.833842	+	0.552004i	$0.186137\pi$
$728$	−74510.5	−	422570.i	−0.00521062	−	0.0295509i
$729$	−3.59920e6	−	6.23400e6i	−0.250835	−	0.434458i
$730$	−2.12167e6	+	3.67484e6i	−0.147357	+	0.255230i
$731$	3.52267e7	+	1.28215e7i	2.43825	+	0.887451i
$732$	1.11760e6	+	1.93574e6i	0.0770920	+	0.133527i
$733$	−2.09785e7	−	1.76031e7i	−1.44216	−	1.21012i	−0.938058	−	0.346477i	$-0.887378\pi$
$733$	−2.09785e7	−	1.76031e7i	−1.44216	−	1.21012i	−0.504106	−	0.863642i	$-0.668178\pi$
$734$	1.17816e7			0.807167
$735$	3.90681e6	+	3.27820e6i	0.266750	+	0.223830i
$736$	1.23441e6	−	449288.i	0.0839971	−	0.0305725i
$737$	5.02961e6	−	2.85243e7i	0.341087	−	1.93440i
$738$	−454163.	−	2.57569e6i	−0.0306952	−	0.174081i
$739$	−9.59383e6			−0.646221			−0.323110	−	0.946361i	$-0.604729\pi$
$739$	−9.59383e6			−0.646221			−0.323110	+	0.946361i	$0.604729\pi$
$740$	927468.	+	3.77358e6i	0.0622615	+	0.253323i
$741$	906768.			0.0606668
$742$	582149.	+	3.30153e6i	0.0388172	+	0.220143i
$743$	−3.68884e6	+	2.09204e7i	−0.245142	+	1.39027i	0.575021	+	0.818139i	$0.304994\pi$
$743$	−3.68884e6	+	2.09204e7i	−0.245142	+	1.39027i	−0.820163	+	0.572130i	$0.806117\pi$
$744$	−1.58954e6	+	578546.i	−0.105279	+	0.0383182i
$745$	6.97972e6	+	5.85668e6i	0.460731	+	0.386599i
$746$	−1.54988e6			−0.101965
$747$	−6.49990e6	−	5.45406e6i	−0.426192	−	0.357617i
$748$	−5.61704e6	−	9.72900e6i	−0.367074	−	0.635791i
$749$	−3.50499e7	−	1.27571e7i	−2.28288	−	0.830899i
$750$	2.86327e6	−	4.95932e6i	0.185870	−	0.321936i
$751$	−1.12741e7	−	1.95273e7i	−0.729426	−	1.26340i	−0.957126	−	0.289671i	$-0.906454\pi$
$751$	−1.12741e7	−	1.95273e7i	−0.729426	−	1.26340i	0.227700	−	0.973731i	$-0.426879\pi$
$752$	1.25649e6	+	7.12594e6i	0.0810244	+	0.459512i
$753$	−616900.	+	224533.i	−0.0396486	+	0.0144309i
$754$	627859.	−	1.08748e6i	0.0402192	−	0.0696617i
$755$	−33398.0	+	28024.2i	−0.00213232	+	0.00178923i
$756$	8.53256e6	−	7.15966e6i	0.542968	−	0.455605i
$757$	−9.74712e6	−	3.54766e6i	−0.618211	−	0.225010i	0.0138812	−	0.999904i	$-0.495581\pi$
$757$	−9.74712e6	−	3.54766e6i	−0.618211	−	0.225010i	−0.632092	+	0.774893i	$0.717804\pi$
$758$	2.90690e6	−	1.64858e7i	0.183762	−	1.04217i
$759$	−805736.	+	4.56956e6i	−0.0507678	+	0.287918i
$760$	−4.95382e6	−	1.80304e6i	−0.311104	−	0.113233i
$761$	1.50223e7	−	1.26052e7i	0.940320	−	0.789022i	−0.0373212	−	0.999303i	$-0.511882\pi$
$761$	1.50223e7	−	1.26052e7i	0.940320	−	0.789022i	0.977641	+	0.210281i	$0.0674380\pi$
$762$	8.05190e6	−	6.75635e6i	0.502355	−	0.421526i
$763$	−1.22037e7	+	2.11374e7i	−0.758891	+	1.31444i
$764$	580024.	−	211112.i	0.0359511	−	0.0130851i
$765$	−1.43316e6	−	8.12785e6i	−0.0885403	−	0.502137i
$766$	−1.17369e6	−	2.03289e6i	−0.0722739	−	0.125182i
$767$	−299365.	+	518516.i	−0.0183744	+	0.0318254i
$768$	−559870.	−	203776.i	−0.0342519	−	0.0124667i
$769$	7.80192e6	+	1.35133e7i	0.475757	+	0.824036i	0.999614	−	0.0277705i	$-0.00884075\pi$
$769$	7.80192e6	+	1.35133e7i	0.475757	+	0.824036i	−0.523857	+	0.851806i	$0.675507\pi$
$770$	−6.75007e6	−	5.66398e6i	−0.410281	−	0.344267i
$771$	−8.70388e6			−0.527323
$772$	3.30668e6	+	2.77463e6i	0.199687	+	0.167557i
$773$	−1.85483e7	+	6.75104e6i	−1.11649	+	0.406370i	−0.833371	−	0.552714i	$-0.813592\pi$
$773$	−1.85483e7	+	6.75104e6i	−1.11649	+	0.406370i	−0.283122	+	0.959084i	$0.591370\pi$
$774$	2.36589e6	−	1.34176e7i	0.141952	−	0.805051i
$775$	−1.14820e6	−	6.51179e6i	−0.0686697	−	0.389445i
$776$	1.00688e7			0.600235
$777$	1.38023e7	+	4.00773e6i	0.820158	+	0.238147i
$778$	46736.8			0.00276828
$779$	1.99983e6	+	1.13416e7i	0.118072	+	0.669622i
$780$	26016.2	−	147545.i	0.00153111	−	0.00868337i
$781$	575481.	−	209458.i	0.0337601	−	0.0122877i
$782$	−6.93709e6	−	5.82091e6i	−0.405658	−	0.340388i
$783$	3.25964e7			1.90005
$784$	3.77203e6	+	3.16511e6i	0.219172	+	0.183907i
$785$	−2.35858e6	−	4.08517e6i	−0.136608	−	0.236612i
$786$	−4.87057e6	−	1.77274e6i	−0.281205	−	0.102350i
$787$	7.79997e6	−	1.35100e7i	0.448907	−	0.777530i	−0.549408	−	0.835554i	$-0.685147\pi$
$787$	7.79997e6	−	1.35100e7i	0.448907	−	0.777530i	0.998315	+	0.0580244i	$0.0184801\pi$
$788$	−5.29933e6	−	9.17870e6i	−0.304022	−	0.526582i
$789$	−2.01356e6	−	1.14195e7i	−0.115152	−	0.653061i
$790$	3.12904e6	−	1.13888e6i	0.178379	−	0.0649245i
$791$	2.14107e6	−	3.70845e6i	0.121672	−	0.210742i
$792$	−3.12774e6	+	2.62448e6i	−0.177181	+	0.148672i
$793$	−415715.	+	348826.i	−0.0234754	+	0.0196982i
$794$	2.07646e6	+	755770.i	0.116889	+	0.0425440i
$795$	−203264.	+	1.15277e6i	−0.0114062	+	0.0646879i
$796$	558508.	−	3.16746e6i	0.0312426	−	0.177185i
$797$	1.56644e7	+	5.70139e6i	0.873513	+	0.317933i	0.739589	−	0.673059i	$-0.235020\pi$
$797$	1.56644e7	+	5.70139e6i	0.873513	+	0.317933i	0.133924	+	0.990992i	$0.457242\pi$
$798$	−1.49364e7	+	1.25331e7i	−0.830307	+	0.696710i
$799$	3.82115e7	−	3.20633e7i	2.11752	−	1.77681i
$800$	1.16449e6	−	2.01695e6i	0.0643294	−	0.111422i
$801$	5.90374e6	−	2.14879e6i	0.325122	−	0.118335i
$802$	3.95579e6	+	2.24344e7i	0.217169	+	1.23163i
$803$	−7.23569e6	−	1.25326e7i	−0.395996	−	0.685885i
$804$	−5.29479e6	+	9.17084e6i	−0.288874	+	0.500344i
$805$	−6.67461e6	−	2.42936e6i	−0.363025	−	0.132130i
$806$	−205343.	−	355665.i	−0.0111338	−	0.0192843i
$807$	−1.88359e6	−	1.58052e6i	−0.101813	−	0.0854313i
$808$	−9.01159e6			−0.485594
$809$	−1.11181e7	−	9.32915e6i	−0.597252	−	0.501154i	0.293309	−	0.956018i	$-0.405243\pi$
$809$	−1.11181e7	−	9.32915e6i	−0.597252	−	0.501154i	−0.890561	+	0.454864i	$0.849688\pi$
$810$	−616983.	+	224564.i	−0.0330416	+	0.0120262i
$811$	−4.08908e6	+	2.31903e7i	−0.218310	+	1.23810i	0.656760	+	0.754099i	$0.271926\pi$
$811$	−4.08908e6	+	2.31903e7i	−0.218310	+	1.23810i	−0.875070	+	0.483996i	$0.839185\pi$
$812$	4.68876e6	+	2.65913e7i	0.249556	+	1.41530i
$813$	−9.21045e6			−0.488714
$814$	−1.27267e7	−	3.69541e6i	−0.673214	−	0.195480i
$815$	−8.37632e6			−0.441732
$816$	713218.	+	4.04486e6i	0.0374970	+	0.212656i
$817$	−1.04178e7	+	5.90821e7i	−0.546034	+	3.09671i
$818$	−1.09224e7	+	3.97542e6i	−0.570734	+	0.207730i
$819$	823550.	+	691040.i	0.0429023	+	0.0359993i
$820$	1.90282e6			0.0988244
$821$	−1.32637e6	−	1.11296e6i	−0.0686762	−	0.0576262i	0.607803	−	0.794088i	$-0.292051\pi$
$821$	−1.32637e6	−	1.11296e6i	−0.0686762	−	0.0576262i	−0.676480	+	0.736461i	$0.736495\pi$
$822$	−1.29561e6	−	2.24406e6i	−0.0668796	−	0.115839i
$823$	1.08384e7	+	3.94485e6i	0.557782	+	0.203016i	0.605501	−	0.795845i	$-0.292973\pi$
$823$	1.08384e7	+	3.94485e6i	0.557782	+	0.203016i	−0.0477187	+	0.998861i	$0.515195\pi$
$824$	−1.63997e6	+	2.84051e6i	−0.0841431	+	0.145740i
$825$	4.11324e6	+	7.12434e6i	0.210402	+	0.364426i
$826$	−2.23562e6	−	1.26788e7i	−0.114011	−	0.646589i
$827$	−4.01612e6	+	1.46175e6i	−0.204194	+	0.0743206i	−0.442093	−	0.896969i	$-0.645764\pi$
$827$	−4.01612e6	+	1.46175e6i	−0.204194	+	0.0743206i	0.237898	+	0.971290i	$0.423541\pi$
$828$	−1.64563e6	+	2.85031e6i	−0.0834173	+	0.144483i
$829$	1.15416e7	−	9.68456e6i	0.583284	−	0.489433i	−0.302740	−	0.953073i	$-0.597901\pi$
$829$	1.15416e7	−	9.68456e6i	0.583284	−	0.489433i	0.886024	+	0.463640i	$0.153457\pi$
$830$	4.72894e6	−	3.96805e6i	0.238269	−	0.199932i
$831$	1.27981e7	+	4.65813e6i	0.642899	+	0.233996i
$832$	25118.6	−	142455.i	0.00125802	−	0.00713459i
$833$	5.89442e6	−	3.34289e7i	0.294326	−	1.66921i
$834$	−666107.	−	242443.i	−0.0331611	−	0.0120696i
$835$	−1.44201e6	+	1.20999e6i	−0.0715736	+	0.0600574i
$836$	1.37724e7	−	1.15564e7i	0.681545	−	0.571884i
$837$	5.33038e6	−	9.23249e6i	0.262993	−	0.455518i
$838$	−1.85309e7	+	6.74468e6i	−0.911561	+	0.331781i
$839$	−6.21882e6	−	3.52687e7i	−0.305002	−	1.72975i	−0.623493	−	0.781829i	$-0.714287\pi$
$839$	−6.21882e6	−	3.52687e7i	−0.305002	−	1.72975i	0.318491	−	0.947926i	$-0.396824\pi$
$840$	1.61079e6	+	2.78997e6i	0.0787663	+	0.136427i
$841$	−2.92540e7	+	5.06694e7i	−1.42625	+	2.47033i
$842$	2.93514e6	+	1.06830e6i	0.142675	+	0.0519296i
$843$	−3.59162e6	−	6.22087e6i	−0.174069	−	0.301497i
$844$	7.22947e6	+	6.06625e6i	0.349342	+	0.293132i
$845$	−1.07925e7			−0.519971
$846$	−1.38878e7	−	1.16532e7i	−0.667125	−	0.559784i
$847$	−492466.	+	179243.i	−0.0235868	+	0.00858488i
$848$	−196251.	+	1.11300e6i	−0.00937180	+	0.0531501i
$849$	1.69376e6	+	9.60581e6i	0.0806461	+	0.457367i
$850$	−1.60552e7			−0.762197
$851$	−1.06590e7	+	709545.i	−0.504538	+	0.0335858i
$852$	−223903.			−0.0105672
$853$	2.33332e6	+	1.32329e7i	0.109800	+	0.622706i	0.989194	+	0.146612i	$0.0468368\pi$
$853$	2.33332e6	+	1.32329e7i	0.109800	+	0.622706i	−0.879394	+	0.476094i	$0.842052\pi$
$854$	2.02632e6	−	1.14918e7i	0.0950741	−	0.539192i
$855$	1.24116e7	−	4.51746e6i	0.580649	−	0.211339i
$856$	−9.63237e6	−	8.08252e6i	−0.449313	−	0.377018i
$857$	−6.77983e6			−0.315331			−0.157665	−	0.987493i	$-0.550397\pi$
$857$	−6.77983e6			−0.315331			−0.157665	+	0.987493i	$0.550397\pi$
$858$	391407.	+	328430.i	0.0181514	+	0.0152309i
$859$	2.01359e7	+	3.48764e7i	0.931083	+	1.61268i	0.781474	+	0.623938i	$0.214468\pi$
$859$	2.01359e7	+	3.48764e7i	0.931083	+	1.61268i	0.149610	+	0.988745i	$0.452198\pi$
$860$	9.31467e6	+	3.39026e6i	0.429458	+	0.156310i
$861$	3.51890e6	−	6.09491e6i	0.161770	−	0.280194i
$862$	4.07390e6	+	7.05620e6i	0.186742	+	0.323447i
$863$	−3.09387e6	−	1.75462e7i	−0.141408	−	0.801967i	−0.970181	−	0.242381i	$-0.922072\pi$
$863$	−3.09387e6	−	1.75462e7i	−0.141408	−	0.801967i	0.828773	−	0.559585i	$-0.189040\pi$
$864$	3.52849e6	−	1.28427e6i	0.160807	−	0.0585290i
$865$	7.64151e6	−	1.32355e7i	0.347247	−	0.601450i
$866$	−5.92201e6	+	4.96915e6i	−0.268333	+	0.225158i
$867$	1.18015e7	−	9.90267e6i	0.533201	−	0.447409i
$868$	8.29835e6	+	3.02035e6i	0.373846	+	0.136069i
$869$	−1.97196e6	+	1.11835e7i	−0.0885824	+	0.502376i
$870$	−1.63713e6	+	9.28464e6i	−0.0733307	+	0.415879i
$871$	−2.41595e6	−	879335.i	−0.107905	−	0.0392743i
$872$	−6.30309e6	+	5.28892e6i	−0.280713	+	0.235546i
$873$	−1.93250e7	+	1.62156e7i	−0.858189	+	0.720106i
$874$	7.24623e6	−	1.25508e7i	0.320873	−	0.555769i
$875$	−2.80930e7	+	1.02250e7i	−1.24044	+	0.451485i
$876$	918743.	+	5.21045e6i	0.0404514	+	0.229411i
$877$	1.66247e7	+	2.87948e7i	0.729884	+	1.26420i	0.956932	+	0.290313i	$0.0937593\pi$
$877$	1.66247e7	+	2.87948e7i	0.729884	+	1.26420i	−0.227048	+	0.973884i	$0.572907\pi$
$878$	−5.30538e6	+	9.18918e6i	−0.232263	+	0.402291i
$879$	−1.72608e6	−	628242.i	−0.0753510	−	0.0274255i
$880$	−1.48526e6	−	2.57255e6i	−0.0646541	−	0.111984i
$881$	−1.26907e7	−	1.06487e7i	−0.550864	−	0.462230i	0.324370	−	0.945930i	$-0.394848\pi$
$881$	−1.26907e7	−	1.06487e7i	−0.550864	−	0.462230i	−0.875233	+	0.483701i	$0.839292\pi$
$882$	−1.23370e7			−0.533996
$883$	−9.63313e6	−	8.08315e6i	−0.415782	−	0.348882i	0.410774	−	0.911737i	$-0.365259\pi$
$883$	−9.63313e6	−	8.08315e6i	−0.415782	−	0.348882i	−0.826556	+	0.562855i	$0.809703\pi$
$884$	−937048.	+	341057.i	−0.0403303	+	0.0146790i
$885$	780591.	−	4.42695e6i	0.0335016	−	0.189997i
$886$	1.10582e6	+	6.27140e6i	0.0473259	+	0.268399i
$887$	2.37395e7			1.01312			0.506561	−	0.862204i	$-0.330916\pi$
$887$	2.37395e7			1.01312			0.506561	+	0.862204i	$0.330916\pi$
$888$	3.91025e6	+	2.86099e6i	0.166407	+	0.121754i
$889$	−5.48737e7			−2.32868
$890$	793723.	+	4.50143e6i	0.0335888	+	0.190491i
$891$	388830.	−	2.20516e6i	0.0164084	−	0.0930565i
$892$	−1.49959e7	+	5.45806e6i	−0.631044	+	0.229681i
$893$	6.11524e7	+	5.13129e7i	2.56616	+	2.15327i
$894$	1.13606e7			0.475397
$895$	9.41304e6	+	7.89848e6i	0.392801	+	0.329599i
$896$	1.55522e6	+	2.69372e6i	0.0647175	+	0.112094i
$897$	387032.	+	140868.i	0.0160607	+	0.00584563i
$898$	1.44498e6	−	2.50278e6i	0.0597958	−	0.103569i
$899$	1.29217e7	+	2.23811e7i	0.533238	+	0.923596i
$900$	1.01327e6	+	5.74652e6i	0.0416982	+	0.236482i
$901$	7.32113e6	−	2.66467e6i	0.300446	−	0.109353i
$902$	−3.24467e6	+	5.61993e6i	−0.132787	+	0.229993i
$903$	2.80849e7	−	2.35660e7i	1.14618	−	0.961761i
$904$	1.10585e6	−	927914.i	0.0450063	−	0.0377648i
$905$	−866901.	−	315526.i	−0.0351842	−	0.0128060i
$906$	−9439.58	+	53534.5i	−0.000382060	+	0.00216677i
$907$	6.22651e6	−	3.53123e7i	0.251319	−	1.42530i	−0.554027	−	0.832499i	$-0.686909\pi$
$907$	6.22651e6	−	3.53123e7i	0.251319	−	1.42530i	0.805346	−	0.592805i	$-0.201979\pi$
$908$	−6.80238e6	−	2.47586e6i	−0.273808	−	0.0996580i
$909$	1.72959e7	−	1.45130e7i	0.694279	−	0.582570i
$910$	−599166.	+	502760.i	−0.0239852	+	0.0201260i
$911$	3.42821e6	−	5.93783e6i	0.136858	−	0.237046i	−0.789447	−	0.613818i	$-0.789633\pi$
$911$	3.42821e6	−	5.93783e6i	0.136858	−	0.237046i	0.926306	+	0.376772i	$0.122966\pi$
$912$	−6.17670e6	+	2.24813e6i	−0.245906	+	0.0895025i
$913$	3.65579e6	+	2.07330e7i	0.145146	+	0.823163i
$914$	1.47623e7	+	2.55690e7i	0.584505	+	1.01239i
$915$	2.03720e6	−	3.52853e6i	0.0804415	−	0.139329i
$916$	−1.26967e7	−	4.62123e6i	−0.499981	−	0.181978i
$917$	1.35296e7	+	2.34339e7i	0.531325	+	0.920282i
$918$	−1.98293e7	−	1.66388e7i	−0.776607	−	0.651650i
$919$	2.04324e6			0.0798053			0.0399026	−	0.999204i	$-0.487295\pi$
$919$	2.04324e6			0.0798053			0.0399026	+	0.999204i	$0.487295\pi$
$920$	−1.83431e6	−	1.53917e6i	−0.0714502	−	0.0599538i
$921$	4.82850e6	−	1.75743e6i	0.187570	−	0.0682699i
$922$	−5.23562e6	+	2.96927e7i	−0.202834	+	1.15033i
$923$	−9439.60	−	53534.6i	−0.000364712	−	0.00206838i
$924$	−1.09868e7			−0.423341
$925$	−1.36679e7	+	1.31109e7i	−0.525226	+	0.503822i
$926$	1.43574e7			0.550235
$927$	−1.42700e6	−	8.09294e6i	−0.0545413	−	0.309319i
$928$	−1.58065e6	+	8.96432e6i	−0.0602513	+	0.341702i
$929$	−6.55968e6	+	2.38753e6i	−0.249370	+	0.0907631i	−0.463681	−	0.886002i	$-0.653472\pi$
$929$	−6.55968e6	+	2.38753e6i	−0.249370	+	0.0907631i	0.214311	+	0.976765i	$0.431249\pi$
$930$	2.36203e6	+	1.98198e6i	0.0895526	+	0.0751436i
$931$	5.43238e7			2.05407
$932$	−1.22790e7	−	1.03033e7i	−0.463046	−	0.388541i
$933$	−6.61984e6	−	1.14659e7i	−0.248968	−	0.431225i
$934$	−2.46452e7	−	8.97013e6i	−0.924412	−	0.336458i
$935$	−1.02389e7	+	1.77343e7i	−0.383022	+	0.663414i
$936$	181211.	+	313867.i	0.00676075	+	0.0117100i
$937$	−7.80587e6	−	4.42693e7i	−0.290450	−	1.64723i	−0.685140	−	0.728412i	$-0.740259\pi$
$937$	−7.80587e6	−	4.42693e7i	−0.290450	−	1.64723i	0.394689	−	0.918815i	$-0.370852\pi$
$938$	5.19498e7	−	1.89082e7i	1.92787	−	0.701686i
$939$	−1.27284e7	+	2.20462e7i	−0.471095	+	0.815961i
$940$	1.01039e7	−	8.47820e6i	0.372967	−	0.312956i
$941$	3.15767e7	−	2.64960e7i	1.16250	−	0.975454i	0.162564	−	0.986698i	$-0.448024\pi$
$941$	3.15767e7	−	2.64960e7i	1.16250	−	0.975454i	0.999937	+	0.0112441i	$0.00357918\pi$
$942$	−5.52690e6	−	2.01163e6i	−0.202934	−	0.0738619i
$943$	−908357.	+	5.15155e6i	−0.0332642	+	0.188651i
$944$	753661.	−	4.27422e6i	0.0275262	−	0.156109i
$945$	−1.90790e7	−	6.94420e6i	−0.694988	−	0.252955i
$946$	−2.58963e7	+	2.17296e7i	−0.940826	+	0.789447i
$947$	−3.67126e7	+	3.08055e7i	−1.33027	+	1.11623i	−0.346257	+	0.938140i	$0.612548\pi$
$947$	−3.67126e7	+	3.08055e7i	−1.33027	+	1.11623i	−0.984014	+	0.178091i	$0.943008\pi$
$948$	2.07592e6	−	3.59560e6i	0.0750223	−	0.129942i
$949$	−1.20707e6	+	439339.i	−0.0435079	+	0.0158356i
$950$	−4.46173e6	−	2.53037e7i	−0.160396	−	0.909653i
$951$	−2.10190e6	−	3.64060e6i	−0.0753636	−	0.130534i
$952$	1.07212e7	−	1.85696e7i	0.383397	−	0.664064i
$953$	3.37810e7	+	1.22953e7i	1.20487	+	0.438537i	0.864922	−	0.501906i	$-0.167368\pi$
$953$	3.37810e7	+	1.22953e7i	1.20487	+	0.438537i	0.339950	+	0.940444i	$0.389590\pi$
$954$	−1.41580e6	−	2.45223e6i	−0.0503651	−	0.0872350i
$955$	−861906.	−	723225.i	−0.0305810	−	0.0256605i
$956$	1.11389e7			0.394182
$957$	−2.46303e7	−	2.06673e7i	−0.869340	−	0.729462i
$958$	1.86740e7	−	6.79678e6i	0.657391	−	0.239271i
$959$	−2.34906e6	+	1.33222e7i	−0.0824797	+	0.467765i
$960$	188590.	+	1.06954e6i	0.00660449	+	0.0374559i
$961$	−2.01770e7			−0.704770
$962$	−519203.	+	1.05555e6i	−0.0180884	+	0.0367740i
$963$	3.15042e7			1.09472
$964$	2.16020e6	+	1.22511e7i	0.0748688	+	0.424602i
$965$	1.36633e6	−	7.74882e6i	0.0472319	−	0.267866i
$966$	−8.32228e6	+	3.02906e6i	−0.286946	+	0.104440i
$967$	−4.17420e7	−	3.50257e7i	−1.43551	−	1.20454i	−0.942363	−	0.334592i	$-0.891401\pi$
$967$	−4.17420e7	−	3.50257e7i	−1.43551	−	1.20454i	−0.493149	−	0.869945i	$-0.664154\pi$
$968$	−176673.			−0.00606012
$969$	3.47116e7	+	2.91265e7i	1.18759	+	0.996503i
$970$	−9.17680e6	−	1.58947e7i	−0.313157	−	0.542404i
$971$	−6.60727e6	−	2.40485e6i	−0.224892	−	0.0818540i	0.227117	−	0.973868i	$-0.427070\pi$
$971$	−6.60727e6	−	2.40485e6i	−0.224892	−	0.0818540i	−0.452009	+	0.892014i	$0.649292\pi$
$972$	−7.53786e6	+	1.30560e7i	−0.255907	+	0.443244i
$973$	1.85032e6	+	3.20486e6i	0.0626564	+	0.108524i
$974$	2.83370e6	+	1.60707e7i	0.0957097	+	0.542796i
$975$	686180.	−	249749.i	0.0231167	−	0.00841380i
$976$	1.96691e6	−	3.40680e6i	0.0660938	−	0.114478i
$977$	3.07407e7	−	2.57945e7i	1.03033	−	0.864552i	0.0394426	−	0.999222i	$-0.487442\pi$
$977$	3.07407e7	−	2.57945e7i	1.03033	−	0.864552i	0.990891	+	0.134670i	$0.0429973\pi$
$978$	−8.00061e6	+	6.71331e6i	−0.267471	+	0.224434i
$979$	−1.46483e7	−	5.33153e6i	−0.488461	−	0.177785i
$980$	1.55861e6	−	8.83931e6i	0.0518408	−	0.294004i
$981$	3.57979e6	−	2.03020e7i	0.118764	−	0.673545i
$982$	−3.01860e7	−	1.09868e7i	−0.998912	−	0.363574i
$983$	−3.12448e7	+	2.62175e7i	−1.03132	+	0.865383i	−0.991008	−	0.133804i	$-0.957281\pi$
$983$	−3.12448e7	+	2.62175e7i	−1.03132	+	0.865383i	−0.0403150	+	0.999187i	$0.512836\pi$
$984$	1.81748e6	−	1.52504e6i	0.0598385	−	0.0502105i
$985$	−9.65976e6	+	1.67312e7i	−0.317231	+	0.549460i
$986$	5.89661e7	−	2.14619e7i	1.93157	−	0.703033i
$987$	−8.47118e6	−	4.80425e7i	−0.276790	−	1.56976i
$988$	−797930.	−	1.38205e6i	−0.0260059	−	0.0450436i
$989$	−1.36251e7	+	2.35993e7i	−0.442944	+	0.767201i
$990$	6.99371e6	+	2.54550e6i	0.226788	+	0.0825440i
$991$	2.04875e7	+	3.54854e7i	0.662682	+	1.14780i	0.979908	+	0.199449i	$0.0639154\pi$
$991$	2.04875e7	+	3.54854e7i	0.662682	+	1.14780i	−0.317226	+	0.948350i	$0.602751\pi$
$992$	2.28054e6	+	1.91360e6i	0.0735799	+	0.0617409i
$993$	1.41748e7			0.456189
$994$	895433.	+	751358.i	0.0287453	+	0.0241202i
$995$	−5.50922e6	+	2.00519e6i	−0.176414	+	0.0642094i
$996$	1.33658e6	−	7.58014e6i	0.0426921	−	0.242119i
$997$	−6.70133e6	−	3.80051e7i	−0.213512	−	1.21089i	−0.883469	−	0.468489i	$-0.844799\pi$
$997$	−6.70133e6	−	3.80051e7i	−0.213512	−	1.21089i	0.669957	−	0.742400i	$-0.266313\pi$
$998$	−7.37395e6			−0.234355
$999$	−3.04683e7	+	2.02820e6i	−0.965904	+	0.0642979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.9.6	✓	48
37.33	even	9	inner	74.6.f.a.33.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.9.6	✓	48	1.1	even	1	trivial
74.6.f.a.33.6	yes	48	37.33	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694593 + 3.93923i) q^{2} +(1.57867 - 8.95310i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(22.3419 + 18.7471i) q^{5} +36.3648 q^{6} +(-145.430 - 122.031i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(150.680 + 54.8429i) q^{9} +O(q^{10})\)	\(q+(0.694593 + 3.93923i) q^{2} +(1.57867 - 8.95310i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(22.3419 + 18.7471i) q^{5} +36.3648 q^{6} +(-145.430 - 122.031i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(150.680 + 54.8429i) q^{9} +(-58.3305 + 101.031i) q^{10} +(-198.929 - 344.555i) q^{11} +(25.2588 + 143.250i) q^{12} +(-33.1858 + 12.0786i) q^{13} +(379.692 - 657.646i) q^{14} +(203.115 - 170.433i) q^{15} +(196.107 - 164.554i) q^{16} +(-1658.35 - 603.590i) q^{17} +(-111.378 + 631.655i) q^{18} +(490.432 - 2781.38i) q^{19} +(-438.502 - 159.602i) q^{20} +(-1322.14 + 1109.41i) q^{21} +(1219.11 - 1022.95i) q^{22} +(641.421 - 1110.97i) q^{23} +(-546.748 + 199.000i) q^{24} +(-394.943 - 2239.84i) q^{25} +(-70.6311 - 122.337i) q^{26} +(1833.47 - 3175.66i) q^{27} +(2854.35 + 1038.90i) q^{28} +(4444.64 + 7698.33i) q^{29} +(812.459 + 681.734i) q^{30} +2907.26 q^{31} +(784.430 + 658.215i) q^{32} +(-3398.87 + 1237.09i) q^{33} +(1225.80 - 6951.87i) q^{34} +(-961.473 - 5452.79i) q^{35} -2565.60 q^{36} +(-4633.46 - 6919.18i) q^{37} +11297.1 q^{38} +(55.7517 + 316.183i) q^{39} +(324.127 - 1838.22i) q^{40} +(-3831.77 + 1394.65i) q^{41} +(-5288.56 - 4437.63i) q^{42} -21242.0 q^{43} +(4876.42 + 4091.80i) q^{44} +(2338.32 + 4050.09i) q^{45} +(4821.91 + 1755.03i) q^{46} +(-14132.5 + 24478.3i) q^{47} +(-1163.68 - 2015.54i) q^{48} +(3340.04 + 18942.3i) q^{49} +(8548.90 - 3111.55i) q^{50} +(-8021.98 + 13894.5i) q^{51} +(432.852 - 363.206i) q^{52} +(-3381.87 + 2837.72i) q^{53} +(13783.2 + 5016.67i) q^{54} +(2014.95 - 11427.3i) q^{55} +(-2109.85 + 11965.6i) q^{56} +(-24127.7 - 8781.77i) q^{57} +(-27238.3 + 22855.7i) q^{58} +(12987.3 - 10897.7i) q^{59} +(-2121.18 + 3673.99i) q^{60} +(14439.8 - 5255.66i) q^{61} +(2019.36 + 11452.4i) q^{62} +(-15220.9 - 26363.4i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-967.871 - 352.276i) q^{65} +(-7234.01 - 12529.7i) q^{66} +(55768.7 + 46795.5i) q^{67} +28236.4 q^{68} +(-8934.06 - 7496.57i) q^{69} +(20812.0 - 7574.93i) q^{70} +(-267.293 + 1515.89i) q^{71} +(-1782.05 - 10106.5i) q^{72} +36373.3 q^{73} +(24037.9 - 23058.3i) q^{74} -20676.9 q^{75} +(7846.91 + 44502.1i) q^{76} +(-13115.9 + 74384.1i) q^{77} +(-1206.79 + 439.237i) q^{78} +(-21865.2 - 18347.1i) q^{79} +7466.30 q^{80} +(4311.38 + 3617.68i) q^{81} +(-8155.36 - 14125.5i) q^{82} +(-49724.4 - 18098.2i) q^{83} +(13807.4 - 23915.2i) q^{84} +(-25735.1 - 44574.5i) q^{85} +(-14754.6 - 83677.2i) q^{86} +(75940.5 - 27640.1i) q^{87} +(-12731.4 + 22051.5i) q^{88} +(30014.2 - 25184.9i) q^{89} +(-14330.1 + 12024.4i) q^{90} +(6300.18 + 2293.08i) q^{91} +(-3564.21 + 20213.7i) q^{92} +(4589.62 - 26029.0i) q^{93} +(-106242. - 38668.9i) q^{94} +(63099.8 - 52947.1i) q^{95} +(7131.41 - 5983.97i) q^{96} +(-78662.2 + 136247. i) q^{97} +(-72298.1 + 26314.4i) q^{98} +(-11078.1 - 62827.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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