LMFDB - Embedded newform 74.6.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("74.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.a (trivial)

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:	yes
Analytic conductor:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 870x^{3} - 2235x^{2} + 121361x + 481504 $ x^5 - x^4 - 870x^3 - 2235x^2 + 121361*x + 481504
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-12.6478$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +16.6478 q^{3} +16.0000 q^{4} +46.0360 q^{5} +66.5913 q^{6} +16.5452 q^{7} +64.0000 q^{8} +34.1497 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +16.6478 q^{3} +16.0000 q^{4} +46.0360 q^{5} +66.5913 q^{6} +16.5452 q^{7} +64.0000 q^{8} +34.1497 q^{9} +184.144 q^{10} +514.335 q^{11} +266.365 q^{12} -1101.21 q^{13} +66.1809 q^{14} +766.400 q^{15} +256.000 q^{16} +1151.63 q^{17} +136.599 q^{18} -1499.14 q^{19} +736.577 q^{20} +275.442 q^{21} +2057.34 q^{22} +3068.31 q^{23} +1065.46 q^{24} -1005.68 q^{25} -4404.84 q^{26} -3476.90 q^{27} +264.723 q^{28} -2099.42 q^{29} +3065.60 q^{30} +6320.90 q^{31} +1024.00 q^{32} +8562.56 q^{33} +4606.51 q^{34} +761.676 q^{35} +546.396 q^{36} -1369.00 q^{37} -5996.56 q^{38} -18332.8 q^{39} +2946.31 q^{40} +9098.87 q^{41} +1101.77 q^{42} -21649.5 q^{43} +8229.36 q^{44} +1572.12 q^{45} +12273.3 q^{46} -172.689 q^{47} +4261.84 q^{48} -16533.3 q^{49} -4022.73 q^{50} +19172.1 q^{51} -17619.4 q^{52} -29702.0 q^{53} -13907.6 q^{54} +23678.0 q^{55} +1058.89 q^{56} -24957.4 q^{57} -8397.66 q^{58} -15961.3 q^{59} +12262.4 q^{60} -16766.6 q^{61} +25283.6 q^{62} +565.015 q^{63} +4096.00 q^{64} -50695.4 q^{65} +34250.2 q^{66} -21913.6 q^{67} +18426.0 q^{68} +51080.7 q^{69} +3046.70 q^{70} +24313.0 q^{71} +2185.58 q^{72} -47476.8 q^{73} -5476.00 q^{74} -16742.4 q^{75} -23986.2 q^{76} +8509.78 q^{77} -73331.0 q^{78} +38417.2 q^{79} +11785.2 q^{80} -66181.2 q^{81} +36395.5 q^{82} +57672.7 q^{83} +4407.07 q^{84} +53016.4 q^{85} -86597.9 q^{86} -34950.7 q^{87} +32917.5 q^{88} +109000. q^{89} +6288.47 q^{90} -18219.8 q^{91} +49093.0 q^{92} +105229. q^{93} -690.755 q^{94} -69014.4 q^{95} +17047.4 q^{96} +66914.0 q^{97} -66133.0 q^{98} +17564.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9} + 380 q^{10} + 903 q^{11} + 304 q^{12} + 1371 q^{13} + 680 q^{14} - 8 q^{15} + 1280 q^{16} + 2070 q^{17} + 2392 q^{18} + 2358 q^{19} + 1520 q^{20} + 2832 q^{21} + 3612 q^{22} + 2097 q^{23} + 1216 q^{24} - 390 q^{25} + 5484 q^{26} + 2614 q^{27} + 2720 q^{28} + 2927 q^{29} - 32 q^{30} - 5849 q^{31} + 5120 q^{32} - 11002 q^{33} + 8280 q^{34} - 10928 q^{35} + 9568 q^{36} - 6845 q^{37} + 9432 q^{38} - 9945 q^{39} + 6080 q^{40} - 14427 q^{41} + 11328 q^{42} - 6972 q^{43} + 14448 q^{44} - 6816 q^{45} + 8388 q^{46} - 18962 q^{47} + 4864 q^{48} - 11957 q^{49} - 1560 q^{50} - 67946 q^{51} + 21936 q^{52} - 23576 q^{53} + 10456 q^{54} - 31415 q^{55} + 10880 q^{56} - 70522 q^{57} + 11708 q^{58} - 18316 q^{59} - 128 q^{60} - 18695 q^{61} - 23396 q^{62} - 88094 q^{63} + 20480 q^{64} - 40706 q^{65} - 44008 q^{66} - 85273 q^{67} + 33120 q^{68} - 87171 q^{69} - 43712 q^{70} + 8760 q^{71} + 38272 q^{72} - 10425 q^{73} - 27380 q^{74} - 10542 q^{75} + 37728 q^{76} + 17238 q^{77} - 39780 q^{78} + 48425 q^{79} + 24320 q^{80} + 33449 q^{81} - 57708 q^{82} + 27704 q^{83} + 45312 q^{84} + 139062 q^{85} - 27888 q^{86} + 6227 q^{87} + 57792 q^{88} + 233646 q^{89} - 27264 q^{90} + 146434 q^{91} + 33552 q^{92} + 301866 q^{93} - 75848 q^{94} + 189498 q^{95} + 19456 q^{96} + 251694 q^{97} - 47828 q^{98} + 182486 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9 + 380 * q^10 + 903 * q^11 + 304 * q^12 + 1371 * q^13 + 680 * q^14 - 8 * q^15 + 1280 * q^16 + 2070 * q^17 + 2392 * q^18 + 2358 * q^19 + 1520 * q^20 + 2832 * q^21 + 3612 * q^22 + 2097 * q^23 + 1216 * q^24 - 390 * q^25 + 5484 * q^26 + 2614 * q^27 + 2720 * q^28 + 2927 * q^29 - 32 * q^30 - 5849 * q^31 + 5120 * q^32 - 11002 * q^33 + 8280 * q^34 - 10928 * q^35 + 9568 * q^36 - 6845 * q^37 + 9432 * q^38 - 9945 * q^39 + 6080 * q^40 - 14427 * q^41 + 11328 * q^42 - 6972 * q^43 + 14448 * q^44 - 6816 * q^45 + 8388 * q^46 - 18962 * q^47 + 4864 * q^48 - 11957 * q^49 - 1560 * q^50 - 67946 * q^51 + 21936 * q^52 - 23576 * q^53 + 10456 * q^54 - 31415 * q^55 + 10880 * q^56 - 70522 * q^57 + 11708 * q^58 - 18316 * q^59 - 128 * q^60 - 18695 * q^61 - 23396 * q^62 - 88094 * q^63 + 20480 * q^64 - 40706 * q^65 - 44008 * q^66 - 85273 * q^67 + 33120 * q^68 - 87171 * q^69 - 43712 * q^70 + 8760 * q^71 + 38272 * q^72 - 10425 * q^73 - 27380 * q^74 - 10542 * q^75 + 37728 * q^76 + 17238 * q^77 - 39780 * q^78 + 48425 * q^79 + 24320 * q^80 + 33449 * q^81 - 57708 * q^82 + 27704 * q^83 + 45312 * q^84 + 139062 * q^85 - 27888 * q^86 + 6227 * q^87 + 57792 * q^88 + 233646 * q^89 - 27264 * q^90 + 146434 * q^91 + 33552 * q^92 + 301866 * q^93 - 75848 * q^94 + 189498 * q^95 + 19456 * q^96 + 251694 * q^97 - 47828 * q^98 + 182486 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	16.6478	1.06796	0.533979	−	0.845498i	$-0.320696\pi$
$3$	16.6478	1.06796	0.533979	+	0.845498i	$0.320696\pi$
$4$	16.0000	0.500000
$5$	46.0360	0.823518	0.411759	−	0.911293i	$-0.364915\pi$
$5$	46.0360	0.823518	0.411759	+	0.911293i	$0.364915\pi$
$6$	66.5913	0.755160
$7$	16.5452	0.127623	0.0638113	−	0.997962i	$-0.479674\pi$
$7$	16.5452	0.127623	0.0638113	+	0.997962i	$0.479674\pi$
$8$	64.0000	0.353553
$9$	34.1497	0.140534
$10$	184.144	0.582315
$11$	514.335	1.28164	0.640818	−	0.767693i	$-0.278595\pi$
$11$	514.335	1.28164	0.640818	+	0.767693i	$0.278595\pi$
$12$	266.365	0.533979
$13$	−1101.21	−1.80723	−0.903613	−	0.428351i	$-0.859095\pi$
$13$	−1101.21	−1.80723	−0.903613	+	0.428351i	$0.859095\pi$
$14$	66.1809	0.0902427
$15$	766.400	0.879482
$16$	256.000	0.250000
$17$	1151.63	0.966473	0.483236	−	0.875490i	$-0.339461\pi$
$17$	1151.63	0.966473	0.483236	+	0.875490i	$0.339461\pi$
$18$	136.599	0.0993725
$19$	−1499.14	−0.952704	−0.476352	−	0.879255i	$-0.658041\pi$
$19$	−1499.14	−0.952704	−0.476352	+	0.879255i	$0.658041\pi$
$20$	736.577	0.411759
$21$	275.442	0.136295
$22$	2057.34	0.906253
$23$	3068.31	1.20943	0.604714	−	0.796443i	$-0.293287\pi$
$23$	3068.31	1.20943	0.604714	+	0.796443i	$0.293287\pi$
$24$	1065.46	0.377580
$25$	−1005.68	−0.321818
$26$	−4404.84	−1.27790
$27$	−3476.90	−0.917874
$28$	264.723	0.0638113
$29$	−2099.42	−0.463557	−0.231779	−	0.972769i	$-0.574454\pi$
$29$	−2099.42	−0.463557	−0.231779	+	0.972769i	$0.574454\pi$
$30$	3065.60	0.621888
$31$	6320.90	1.18134	0.590670	−	0.806913i	$-0.298864\pi$
$31$	6320.90	1.18134	0.590670	+	0.806913i	$0.298864\pi$
$32$	1024.00	0.176777
$33$	8562.56	1.36873
$34$	4606.51	0.683400
$35$	761.676	0.105099
$36$	546.396	0.0702669
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	−5996.56	−0.673663
$39$	−18332.8	−1.93004
$40$	2946.31	0.291158
$41$	9098.87	0.845333	0.422667	−	0.906285i	$-0.361094\pi$
$41$	9098.87	0.845333	0.422667	+	0.906285i	$0.361094\pi$
$42$	1101.77	0.0963754
$43$	−21649.5	−1.78557	−0.892783	−	0.450486i	$-0.851251\pi$
$43$	−21649.5	−1.78557	−0.892783	+	0.450486i	$0.851251\pi$
$44$	8229.36	0.640818
$45$	1572.12	0.115732
$46$	12273.3	0.855195
$47$	−172.689	−0.0114030	−0.00570150	−	0.999984i	$-0.501815\pi$
$47$	−172.689	−0.0114030	−0.00570150	+	0.999984i	$0.501815\pi$
$48$	4261.84	0.266989
$49$	−16533.3	−0.983712
$50$	−4022.73	−0.227560
$51$	19172.1	1.03215
$52$	−17619.4	−0.903613
$53$	−29702.0	−1.45243	−0.726215	−	0.687468i	$-0.758722\pi$
$53$	−29702.0	−1.45243	−0.726215	+	0.687468i	$0.758722\pi$
$54$	−13907.6	−0.649035
$55$	23678.0	1.05545
$56$	1058.89	0.0451214
$57$	−24957.4	−1.01745
$58$	−8397.66	−0.327784
$59$	−15961.3	−0.596949	−0.298474	−	0.954418i	$-0.596478\pi$
$59$	−15961.3	−0.596949	−0.298474	+	0.954418i	$0.596478\pi$
$60$	12262.4	0.439741
$61$	−16766.6	−0.576927	−0.288463	−	0.957491i	$-0.593144\pi$
$61$	−16766.6	−0.576927	−0.288463	+	0.957491i	$0.593144\pi$
$62$	25283.6	0.835333
$63$	565.015	0.0179353
$64$	4096.00	0.125000
$65$	−50695.4	−1.48828
$66$	34250.2	0.967840
$67$	−21913.6	−0.596384	−0.298192	−	0.954506i	$-0.596384\pi$
$67$	−21913.6	−0.596384	−0.298192	+	0.954506i	$0.596384\pi$
$68$	18426.0	0.483236
$69$	51080.7	1.29162
$70$	3046.70	0.0743165
$71$	24313.0	0.572390	0.286195	−	0.958171i	$-0.407609\pi$
$71$	24313.0	0.572390	0.286195	+	0.958171i	$0.407609\pi$
$72$	2185.58	0.0496862
$73$	−47476.8	−1.04273	−0.521367	−	0.853332i	$-0.674578\pi$
$73$	−47476.8	−1.04273	−0.521367	+	0.853332i	$0.674578\pi$
$74$	−5476.00	−0.116248
$75$	−16742.4	−0.343688
$76$	−23986.2	−0.476352
$77$	8509.78	0.163566
$78$	−73331.0	−1.36474
$79$	38417.2	0.692561	0.346280	−	0.938131i	$-0.387445\pi$
$79$	38417.2	0.692561	0.346280	+	0.938131i	$0.387445\pi$
$80$	11785.2	0.205879
$81$	−66181.2	−1.12078
$82$	36395.5	0.597741
$83$	57672.7	0.918915	0.459457	−	0.888200i	$-0.348044\pi$
$83$	57672.7	0.918915	0.459457	+	0.888200i	$0.348044\pi$
$84$	4407.07	0.0681477
$85$	53016.4	0.795908
$86$	−86597.9	−1.26259
$87$	−34950.7	−0.495060
$88$	32917.5	0.453127
$89$	109000.	1.45865	0.729326	−	0.684167i	$-0.239834\pi$
$89$	109000.	1.45865	0.729326	+	0.684167i	$0.239834\pi$
$90$	6288.47	0.0818350
$91$	−18219.8	−0.230643
$92$	49093.0	0.604714
$93$	105229.	1.26162
$94$	−690.755	−0.00806314
$95$	−69014.4	−0.784569
$96$	17047.4	0.188790
$97$	66914.0	0.722084	0.361042	−	0.932550i	$-0.382421\pi$
$97$	66914.0	0.722084	0.361042	+	0.932550i	$0.382421\pi$
$98$	−66133.0	−0.695590
$99$	17564.4	0.180113
$100$	−16090.9	−0.160909
$101$	9220.67	0.0899412	0.0449706	−	0.998988i	$-0.485681\pi$
$101$	9220.67	0.0899412	0.0449706	+	0.998988i	$0.485681\pi$
$102$	76688.3	0.729842
$103$	45745.5	0.424869	0.212435	−	0.977175i	$-0.431861\pi$
$103$	45745.5	0.424869	0.212435	+	0.977175i	$0.431861\pi$
$104$	−70477.5	−0.638951
$105$	12680.2	0.112242
$106$	−118808.	−1.02702
$107$	92495.5	0.781018	0.390509	−	0.920599i	$-0.372299\pi$
$107$	92495.5	0.781018	0.390509	+	0.920599i	$0.372299\pi$
$108$	−55630.4	−0.458937
$109$	232903.	1.87762	0.938811	−	0.344433i	$-0.111929\pi$
$109$	232903.	1.87762	0.938811	+	0.344433i	$0.111929\pi$
$110$	94711.8	0.746316
$111$	−22790.9	−0.175571
$112$	4235.57	0.0319056
$113$	128607.	0.947474	0.473737	−	0.880666i	$-0.342905\pi$
$113$	128607.	0.947474	0.473737	+	0.880666i	$0.342905\pi$
$114$	−99829.6	−0.719444
$115$	141253.	0.995986
$116$	−33590.6	−0.231779
$117$	−37606.1	−0.253976
$118$	−63845.0	−0.422107
$119$	19053.9	0.123344
$120$	49049.6	0.310944
$121$	103490.	0.642589
$122$	−67066.4	−0.407949
$123$	151476.	0.902780
$124$	101134.	0.590670
$125$	−190160.	−1.08854
$126$	2260.06	0.0126822
$127$	−170460.	−0.937806	−0.468903	−	0.883250i	$-0.655351\pi$
$127$	−170460.	−0.937806	−0.468903	+	0.883250i	$0.655351\pi$
$128$	16384.0	0.0883883
$129$	−360416.	−1.90691
$130$	−202782.	−1.05237
$131$	−77199.2	−0.393038	−0.196519	−	0.980500i	$-0.562964\pi$
$131$	−77199.2	−0.393038	−0.196519	+	0.980500i	$0.562964\pi$
$132$	137001.	0.684366
$133$	−24803.6	−0.121586
$134$	−87654.3	−0.421707
$135$	−160063.	−0.755885
$136$	73704.2	0.341700
$137$	318946.	1.45183	0.725916	−	0.687784i	$-0.241416\pi$
$137$	318946.	1.45183	0.725916	+	0.687784i	$0.241416\pi$
$138$	204323.	0.913312
$139$	−240477.	−1.05569	−0.527845	−	0.849340i	$-0.677000\pi$
$139$	−240477.	−1.05569	−0.527845	+	0.849340i	$0.677000\pi$
$140$	12186.8	0.0525497
$141$	−2874.89	−0.0121779
$142$	97251.9	0.404741
$143$	−566392.	−2.31620
$144$	8742.33	0.0351335
$145$	−96648.8	−0.381748
$146$	−189907.	−0.737325
$147$	−275243.	−1.05056
$148$	−21904.0	−0.0821995
$149$	165295.	0.609951	0.304976	−	0.952360i	$-0.401352\pi$
$149$	165295.	0.609951	0.304976	+	0.952360i	$0.401352\pi$
$150$	−66969.7	−0.243024
$151$	−400224.	−1.42843	−0.714217	−	0.699924i	$-0.753217\pi$
$151$	−400224.	−1.42843	−0.714217	+	0.699924i	$0.753217\pi$
$152$	−95944.9	−0.336832
$153$	39327.8	0.135822
$154$	34039.1	0.115658
$155$	290989.	0.972854
$156$	−293324.	−0.965020
$157$	53265.9	0.172465	0.0862324	−	0.996275i	$-0.472517\pi$
$157$	53265.9	0.172465	0.0862324	+	0.996275i	$0.472517\pi$
$158$	153669.	0.489714
$159$	−494473.	−1.55113
$160$	47140.9	0.145579
$161$	50765.9	0.154350
$162$	−264725.	−0.792514
$163$	−104548.	−0.308211	−0.154105	−	0.988054i	$-0.549250\pi$
$163$	−104548.	−0.308211	−0.154105	+	0.988054i	$0.549250\pi$
$164$	145582.	0.422667
$165$	394186.	1.12718
$166$	230691.	0.649771
$167$	236440.	0.656038	0.328019	−	0.944671i	$-0.393619\pi$
$167$	236440.	0.656038	0.328019	+	0.944671i	$0.393619\pi$
$168$	17628.3	0.0481877
$169$	841373.	2.26606
$170$	212066.	0.562792
$171$	−51195.2	−0.133887
$172$	−346392.	−0.892783
$173$	−44361.9	−0.112692	−0.0563462	−	0.998411i	$-0.517945\pi$
$173$	−44361.9	−0.112692	−0.0563462	+	0.998411i	$0.517945\pi$
$174$	−139803.	−0.350060
$175$	−16639.2	−0.0410713
$176$	131670.	0.320409
$177$	−265720.	−0.637516
$178$	436000.	1.03142
$179$	−655647.	−1.52946	−0.764728	−	0.644353i	$-0.777127\pi$
$179$	−655647.	−1.52946	−0.764728	+	0.644353i	$0.777127\pi$
$180$	25153.9	0.0578661
$181$	668150.	1.51592	0.757962	−	0.652299i	$-0.226195\pi$
$181$	668150.	1.51592	0.757962	+	0.652299i	$0.226195\pi$
$182$	−72879.1	−0.163089
$183$	−279127.	−0.616133
$184$	196372.	0.427597
$185$	−63023.3	−0.135386
$186$	420917.	0.892100
$187$	592322.	1.23867
$188$	−2763.02	−0.00570150
$189$	−57526.1	−0.117141
$190$	−276058.	−0.554774
$191$	566806.	1.12422	0.562110	−	0.827063i	$-0.309990\pi$
$191$	566806.	1.12422	0.562110	+	0.827063i	$0.309990\pi$
$192$	68189.4	0.133495
$193$	355598.	0.687172	0.343586	−	0.939121i	$-0.388358\pi$
$193$	355598.	0.687172	0.343586	+	0.939121i	$0.388358\pi$
$194$	267656.	0.510590
$195$	−843968.	−1.58942
$196$	−264532.	−0.491856
$197$	134928.	0.247706	0.123853	−	0.992301i	$-0.460475\pi$
$197$	134928.	0.247706	0.123853	+	0.992301i	$0.460475\pi$
$198$	70257.6	0.127359
$199$	1.05974e6	1.89699	0.948496	−	0.316790i	$-0.102605\pi$
$199$	1.05974e6	1.89699	0.948496	+	0.316790i	$0.102605\pi$
$200$	−64363.7	−0.113780
$201$	−364813.	−0.636913
$202$	36882.7	0.0635981
$203$	−34735.3	−0.0591603
$204$	306753.	0.516076
$205$	418876.	0.696147
$206$	182982.	0.300428
$207$	104782.	0.169966
$208$	−281910.	−0.451806
$209$	−771060.	−1.22102
$210$	50721.0	0.0793669
$211$	109166.	0.168803	0.0844016	−	0.996432i	$-0.473102\pi$
$211$	109166.	0.168803	0.0844016	+	0.996432i	$0.473102\pi$
$212$	−475231.	−0.726215
$213$	404758.	0.611289
$214$	369982.	0.552263
$215$	−996656.	−1.47045
$216$	−222522.	−0.324517
$217$	104581.	0.150765
$218$	931610.	1.32768
$219$	−790384.	−1.11360
$220$	378847.	0.527725
$221$	−1.26819e6	−1.74663
$222$	−91163.4	−0.124148
$223$	196905.	0.265151	0.132576	−	0.991173i	$-0.457675\pi$
$223$	196905.	0.265151	0.132576	+	0.991173i	$0.457675\pi$
$224$	16942.3	0.0225607
$225$	−34343.8	−0.0452264
$226$	514427.	0.669966
$227$	−165907.	−0.213698	−0.106849	−	0.994275i	$-0.534076\pi$
$227$	−165907.	−0.213698	−0.106849	+	0.994275i	$0.534076\pi$
$228$	−399318.	−0.508724
$229$	36542.9	0.0460484	0.0230242	−	0.999735i	$-0.492671\pi$
$229$	36542.9	0.0460484	0.0230242	+	0.999735i	$0.492671\pi$
$230$	565012.	0.704268
$231$	141669.	0.174681
$232$	−134363.	−0.163892
$233$	−198602.	−0.239659	−0.119830	−	0.992794i	$-0.538235\pi$
$233$	−198602.	−0.239659	−0.119830	+	0.992794i	$0.538235\pi$
$234$	−150424.	−0.179588
$235$	−7949.90	−0.00939058
$236$	−255380.	−0.298474
$237$	639562.	0.739625
$238$	76215.7	0.0872172
$239$	−1.31155e6	−1.48522	−0.742609	−	0.669725i	$-0.766412\pi$
$239$	−1.31155e6	−1.48522	−0.742609	+	0.669725i	$0.766412\pi$
$240$	196198.	0.219871
$241$	−986089.	−1.09364	−0.546819	−	0.837251i	$-0.684161\pi$
$241$	−986089.	−1.09364	−0.546819	+	0.837251i	$0.684161\pi$
$242$	413959.	0.454379
$243$	−256885.	−0.279077
$244$	−268266.	−0.288463
$245$	−761126.	−0.810105
$246$	605905.	0.638362
$247$	1.65087e6	1.72175
$248$	404538.	0.417667
$249$	960125.	0.981362
$250$	−760641.	−0.769715
$251$	888400.	0.890070	0.445035	−	0.895513i	$-0.353191\pi$
$251$	888400.	0.890070	0.445035	+	0.895513i	$0.353191\pi$
$252$	9040.23	0.00896764
$253$	1.57814e6	1.55005
$254$	−681840.	−0.663129
$255$	882607.	0.849996
$256$	65536.0	0.0625000
$257$	228586.	0.215882	0.107941	−	0.994157i	$-0.465574\pi$
$257$	228586.	0.215882	0.107941	+	0.994157i	$0.465574\pi$
$258$	−1.44167e6	−1.34839
$259$	−22650.4	−0.0209810
$260$	−811127.	−0.744141
$261$	−71694.5	−0.0651455
$262$	−308797.	−0.277920
$263$	161995.	0.144415	0.0722073	−	0.997390i	$-0.476996\pi$
$263$	161995.	0.144415	0.0722073	+	0.997390i	$0.476996\pi$
$264$	548004.	0.483920
$265$	−1.36736e6	−1.19610
$266$	−99214.3	−0.0859746
$267$	1.81461e6	1.55778
$268$	−350617.	−0.298192
$269$	−99977.9	−0.0842410	−0.0421205	−	0.999113i	$-0.513411\pi$
$269$	−99977.9	−0.0842410	−0.0421205	+	0.999113i	$0.513411\pi$
$270$	−640251.	−0.534492
$271$	92750.6	0.0767174	0.0383587	−	0.999264i	$-0.487787\pi$
$271$	92750.6	0.0767174	0.0383587	+	0.999264i	$0.487787\pi$
$272$	294817.	0.241618
$273$	−303319.	−0.246317
$274$	1.27578e6	1.02660
$275$	−517258.	−0.412454
$276$	817291.	0.645809
$277$	1.85355e6	1.45146	0.725731	−	0.687978i	$-0.241502\pi$
$277$	1.85355e6	1.45146	0.725731	+	0.687978i	$0.241502\pi$
$278$	−961908.	−0.746486
$279$	215857.	0.166018
$280$	48747.3	0.0371583
$281$	−2.31328e6	−1.74768	−0.873840	−	0.486213i	$-0.838378\pi$
$281$	−2.31328e6	−1.74768	−0.873840	+	0.486213i	$0.838378\pi$
$282$	−11499.6	−0.00861109
$283$	−2.07876e6	−1.54290	−0.771452	−	0.636288i	$-0.780469\pi$
$283$	−2.07876e6	−1.54290	−0.771452	+	0.636288i	$0.780469\pi$
$284$	389008.	0.286195
$285$	−1.14894e6	−0.837886
$286$	−2.26557e6	−1.63780
$287$	150543.	0.107884
$288$	34969.3	0.0248431
$289$	−93611.2	−0.0659300
$290$	−386595.	−0.269936
$291$	1.11397e6	0.771155
$292$	−759628.	−0.521367
$293$	1.94642e6	1.32455	0.662274	−	0.749261i	$-0.269591\pi$
$293$	1.94642e6	1.32455	0.662274	+	0.749261i	$0.269591\pi$
$294$	−1.10097e6	−0.742861
$295$	−734793.	−0.491598
$296$	−87616.0	−0.0581238
$297$	−1.78829e6	−1.17638
$298$	661182.	0.431301
$299$	−3.37886e6	−2.18571
$300$	−267879.	−0.171844
$301$	−358195.	−0.227879
$302$	−1.60089e6	−1.01006
$303$	153504.	0.0960534
$304$	−383780.	−0.238176
$305$	−771868.	−0.475109
$306$	157311.	0.0960408
$307$	2.00811e6	1.21602	0.608011	−	0.793929i	$-0.291968\pi$
$307$	2.00811e6	1.21602	0.608011	+	0.793929i	$0.291968\pi$
$308$	136157.	0.0817828
$309$	761563.	0.453742
$310$	1.16396e6	0.687912
$311$	−159414.	−0.0934599	−0.0467299	−	0.998908i	$-0.514880\pi$
$311$	−159414.	−0.0934599	−0.0467299	+	0.998908i	$0.514880\pi$
$312$	−1.17330e6	−0.682372
$313$	2.49671e6	1.44048	0.720239	−	0.693726i	$-0.244032\pi$
$313$	2.49671e6	1.44048	0.720239	+	0.693726i	$0.244032\pi$
$314$	213064.	0.121951
$315$	26011.0	0.0147700
$316$	614675.	0.346280
$317$	1.58207e6	0.884252	0.442126	−	0.896953i	$-0.354224\pi$
$317$	1.58207e6	0.884252	0.442126	+	0.896953i	$0.354224\pi$
$318$	−1.97789e6	−1.09682
$319$	−1.07980e6	−0.594111
$320$	188564.	0.102940
$321$	1.53985e6	0.834094
$322$	203064.	0.109142
$323$	−1.72645e6	−0.920762
$324$	−1.05890e6	−0.560392
$325$	1.10747e6	0.581598
$326$	−418193.	−0.217938
$327$	3.87732e6	2.00522
$328$	582328.	0.298870
$329$	−2857.17	−0.00145528
$330$	1.57675e6	0.797034
$331$	375017.	0.188140	0.0940701	−	0.995566i	$-0.470012\pi$
$331$	375017.	0.188140	0.0940701	+	0.995566i	$0.470012\pi$
$332$	922764.	0.459457
$333$	−46751.0	−0.0231036
$334$	945759.	0.463889
$335$	−1.00881e6	−0.491133
$336$	70513.1	0.0340739
$337$	−3.34060e6	−1.60232	−0.801161	−	0.598449i	$-0.795784\pi$
$337$	−3.34060e6	−1.60232	−0.801161	+	0.598449i	$0.795784\pi$
$338$	3.36549e6	1.60235
$339$	2.14102e6	1.01186
$340$	848262.	0.397954
$341$	3.25106e6	1.51405
$342$	−204781.	−0.0946725
$343$	−551622.	−0.253166
$344$	−1.38557e6	−0.631293
$345$	2.35155e6	1.06367
$346$	−177447.	−0.0796855
$347$	−2.52038e6	−1.12368	−0.561841	−	0.827245i	$-0.689907\pi$
$347$	−2.52038e6	−1.12368	−0.561841	+	0.827245i	$0.689907\pi$
$348$	−559211.	−0.247530
$349$	−1.25857e6	−0.553114	−0.276557	−	0.960998i	$-0.589193\pi$
$349$	−1.25857e6	−0.553114	−0.276557	+	0.960998i	$0.589193\pi$
$350$	−66556.9	−0.0290418
$351$	3.82880e6	1.65880
$352$	526679.	0.226563
$353$	−1.19752e6	−0.511502	−0.255751	−	0.966743i	$-0.582323\pi$
$353$	−1.19752e6	−0.511502	−0.255751	+	0.966743i	$0.582323\pi$
$354$	−1.06288e6	−0.450792
$355$	1.11927e6	0.471374
$356$	1.74400e6	0.729326
$357$	317206.	0.131726
$358$	−2.62259e6	−1.08149
$359$	4.31316e6	1.76628	0.883139	−	0.469112i	$-0.155426\pi$
$359$	4.31316e6	1.76628	0.883139	+	0.469112i	$0.155426\pi$
$360$	100616.	0.0409175
$361$	−228681.	−0.0923555
$362$	2.67260e6	1.07192
$363$	1.72288e6	0.686258
$364$	−291516.	−0.115321
$365$	−2.18564e6	−0.858711
$366$	−1.11651e6	−0.435672
$367$	−4.64877e6	−1.80166	−0.900829	−	0.434174i	$-0.857040\pi$
$367$	−4.64877e6	−1.80166	−0.900829	+	0.434174i	$0.857040\pi$
$368$	785488.	0.302357
$369$	310724.	0.118798
$370$	−252093.	−0.0957320
$371$	−491425.	−0.185363
$372$	1.68367e6	0.630810
$373$	−1.22979e6	−0.457677	−0.228839	−	0.973464i	$-0.573493\pi$
$373$	−1.22979e6	−0.457677	−0.228839	+	0.973464i	$0.573493\pi$
$374$	2.36929e6	0.875869
$375$	−3.16575e6	−1.16252
$376$	−11052.1	−0.00403157
$377$	2.31190e6	0.837752
$378$	−230104.	−0.0828314
$379$	−4.17693e6	−1.49369	−0.746843	−	0.665001i	$-0.768431\pi$
$379$	−4.17693e6	−1.49369	−0.746843	+	0.665001i	$0.768431\pi$
$380$	−1.10423e6	−0.392284
$381$	−2.83779e6	−1.00154
$382$	2.26722e6	0.794943
$383$	1.04097e6	0.362612	0.181306	−	0.983427i	$-0.441968\pi$
$383$	1.04097e6	0.362612	0.181306	+	0.983427i	$0.441968\pi$
$384$	272758.	0.0943950
$385$	391757.	0.134699
$386$	1.42239e6	0.485904
$387$	−739324.	−0.250933
$388$	1.07062e6	0.361042
$389$	−2.14342e6	−0.718179	−0.359090	−	0.933303i	$-0.616913\pi$
$389$	−2.14342e6	−0.718179	−0.359090	+	0.933303i	$0.616913\pi$
$390$	−3.37587e6	−1.12389
$391$	3.53355e6	1.16888
$392$	−1.05813e6	−0.347795
$393$	−1.28520e6	−0.419748
$394$	539711.	0.175154
$395$	1.76858e6	0.570336
$396$	281031.	0.0900566
$397$	2.83762e6	0.903604	0.451802	−	0.892118i	$-0.350781\pi$
$397$	2.83762e6	0.903604	0.451802	+	0.892118i	$0.350781\pi$
$398$	4.23895e6	1.34138
$399$	−412925.	−0.129849
$400$	−257455.	−0.0804546
$401$	5.27974e6	1.63965	0.819826	−	0.572613i	$-0.194070\pi$
$401$	5.27974e6	1.63965	0.819826	+	0.572613i	$0.194070\pi$
$402$	−1.45925e6	−0.450366
$403$	−6.96065e6	−2.13495
$404$	147531.	0.0449706
$405$	−3.04672e6	−0.922986
$406$	−138941.	−0.0418327
$407$	−704125.	−0.210700
$408$	1.22701e6	0.364921
$409$	2.19524e6	0.648895	0.324447	−	0.945904i	$-0.394822\pi$
$409$	2.19524e6	0.648895	0.324447	+	0.945904i	$0.394822\pi$
$410$	1.67550e6	0.492250
$411$	5.30976e6	1.55049
$412$	731928.	0.212435
$413$	−264082.	−0.0761841
$414$	419128.	0.120184
$415$	2.65502e6	0.756743
$416$	−1.12764e6	−0.319475
$417$	−4.00342e6	−1.12743
$418$	−3.08424e6	−0.863391
$419$	167926.	0.0467285	0.0233643	−	0.999727i	$-0.492562\pi$
$419$	167926.	0.0467285	0.0233643	+	0.999727i	$0.492562\pi$
$420$	202884.	0.0561209
$421$	490371.	0.134840	0.0674202	−	0.997725i	$-0.478523\pi$
$421$	490371.	0.134840	0.0674202	+	0.997725i	$0.478523\pi$
$422$	436663.	0.119362
$423$	−5897.27	−0.00160251
$424$	−1.90092e6	−0.513512
$425$	−1.15817e6	−0.311029
$426$	1.61903e6	0.432246
$427$	−277407.	−0.0736288
$428$	1.47993e6	0.390509
$429$	−9.42918e6	−2.47361
$430$	−3.98662e6	−1.03976
$431$	6.82461e6	1.76964	0.884819	−	0.465934i	$-0.154282\pi$
$431$	6.82461e6	1.76964	0.884819	+	0.465934i	$0.154282\pi$
$432$	−890087.	−0.229468
$433$	−7.26440e6	−1.86200	−0.931001	−	0.365016i	$-0.881063\pi$
$433$	−7.26440e6	−1.86200	−0.931001	+	0.365016i	$0.881063\pi$
$434$	418323.	0.106607
$435$	−1.60899e6	−0.407690
$436$	3.72644e6	0.938811
$437$	−4.59983e6	−1.15223
$438$	−3.16154e6	−0.787432
$439$	−3.70421e6	−0.917348	−0.458674	−	0.888605i	$-0.651675\pi$
$439$	−3.70421e6	−0.917348	−0.458674	+	0.888605i	$0.651675\pi$
$440$	1.51539e6	0.373158
$441$	−564606.	−0.138245
$442$	−5.07274e6	−1.23506
$443$	−7.37865e6	−1.78635	−0.893177	−	0.449706i	$-0.851529\pi$
$443$	−7.37865e6	−1.78635	−0.893177	+	0.449706i	$0.851529\pi$
$444$	−364654.	−0.0877856
$445$	5.01793e6	1.20123
$446$	787618.	0.187490
$447$	2.75181e6	0.651402
$448$	67769.2	0.0159528
$449$	−2.74274e6	−0.642050	−0.321025	−	0.947071i	$-0.604027\pi$
$449$	−2.74274e6	−0.642050	−0.321025	+	0.947071i	$0.604027\pi$
$450$	−137375.	−0.0319799
$451$	4.67987e6	1.08341
$452$	2.05771e6	0.473737
$453$	−6.66285e6	−1.52551
$454$	−663630.	−0.151108
$455$	−838766.	−0.189938
$456$	−1.59727e6	−0.359722
$457$	7.28966e6	1.63274	0.816370	−	0.577529i	$-0.195983\pi$
$457$	7.28966e6	1.63274	0.816370	+	0.577529i	$0.195983\pi$
$458$	146172.	0.0325611
$459$	−4.00409e6	−0.887100
$460$	2.26005e6	0.497993
$461$	2.44183e6	0.535134	0.267567	−	0.963539i	$-0.413780\pi$
$461$	2.44183e6	0.535134	0.267567	+	0.963539i	$0.413780\pi$
$462$	566677.	0.123518
$463$	2.21574e6	0.480360	0.240180	−	0.970728i	$-0.422794\pi$
$463$	2.21574e6	0.480360	0.240180	+	0.970728i	$0.422794\pi$
$464$	−537450.	−0.115889
$465$	4.84433e6	1.03897
$466$	−794408.	−0.169465
$467$	−1.78081e6	−0.377856	−0.188928	−	0.981991i	$-0.560501\pi$
$467$	−1.78081e6	−0.377856	−0.188928	+	0.981991i	$0.560501\pi$
$468$	−601697.	−0.126988
$469$	−362565.	−0.0761120
$470$	−31799.6	−0.00664014
$471$	886761.	0.184185
$472$	−1.02152e6	−0.211053
$473$	−1.11351e7	−2.28845
$474$	2.55825e6	0.522994
$475$	1.50766e6	0.306598
$476$	304863.	0.0616718
$477$	−1.01431e6	−0.204116
$478$	−5.24620e6	−1.05021
$479$	8.16479e6	1.62595	0.812974	−	0.582301i	$-0.197847\pi$
$479$	8.16479e6	1.62595	0.812974	+	0.582301i	$0.197847\pi$
$480$	784793.	0.155472
$481$	1.50756e6	0.297106
$482$	−3.94435e6	−0.773318
$483$	845141.	0.164840
$484$	1.65583e6	0.321295
$485$	3.08046e6	0.594649
$486$	−1.02754e6	−0.197337
$487$	−6.34024e6	−1.21139	−0.605694	−	0.795698i	$-0.707104\pi$
$487$	−6.34024e6	−1.21139	−0.605694	+	0.795698i	$0.707104\pi$
$488$	−1.07306e6	−0.203974
$489$	−1.74050e6	−0.329156
$490$	−3.04450e6	−0.572831
$491$	2.40838e6	0.450838	0.225419	−	0.974262i	$-0.427625\pi$
$491$	2.40838e6	0.450838	0.225419	+	0.974262i	$0.427625\pi$
$492$	2.42362e6	0.451390
$493$	−2.41774e6	−0.448015
$494$	6.60347e6	1.21746
$495$	808596.	0.148326
$496$	1.61815e6	0.295335
$497$	402263.	0.0730499
$498$	3.84050e6	0.693928
$499$	−9.02478e6	−1.62250	−0.811251	−	0.584698i	$-0.801213\pi$
$499$	−9.02478e6	−1.62250	−0.811251	+	0.584698i	$0.801213\pi$
$500$	−3.04256e6	−0.544271
$501$	3.93620e6	0.700621
$502$	3.55360e6	0.629374
$503$	2.00288e6	0.352968	0.176484	−	0.984303i	$-0.443528\pi$
$503$	2.00288e6	0.352968	0.176484	+	0.984303i	$0.443528\pi$
$504$	36160.9	0.00634108
$505$	424483.	0.0740682
$506$	6.31257e6	1.09605
$507$	1.40070e7	2.42006
$508$	−2.72736e6	−0.468903
$509$	867190.	0.148361	0.0741805	−	0.997245i	$-0.476366\pi$
$509$	867190.	0.148361	0.0741805	+	0.997245i	$0.476366\pi$
$510$	3.53043e6	0.601038
$511$	−785513.	−0.133076
$512$	262144.	0.0441942
$513$	5.21236e6	0.874462
$514$	914342.	0.152651
$515$	2.10594e6	0.349887
$516$	−5.76666e6	−0.953455
$517$	−88819.9	−0.0146145
$518$	−90601.6	−0.0148358
$519$	−738528.	−0.120351
$520$	−3.24451e6	−0.526187
$521$	3.35943e6	0.542215	0.271107	−	0.962549i	$-0.412610\pi$
$521$	3.35943e6	0.542215	0.271107	+	0.962549i	$0.412610\pi$
$522$	−286778.	−0.0460648
$523$	−837805.	−0.133933	−0.0669667	−	0.997755i	$-0.521332\pi$
$523$	−837805.	−0.133933	−0.0669667	+	0.997755i	$0.521332\pi$
$524$	−1.23519e6	−0.196519
$525$	−277007.	−0.0438624
$526$	647978.	0.102117
$527$	7.27932e6	1.14173
$528$	2.19201e6	0.342183
$529$	2.97820e6	0.462717
$530$	−5.46944e6	−0.845772
$531$	−545073.	−0.0838915
$532$	−396857.	−0.0607932
$533$	−1.00198e7	−1.52771
$534$	7.25845e6	1.10152
$535$	4.25813e6	0.643182
$536$	−1.40247e6	−0.210854
$537$	−1.09151e7	−1.63340
$538$	−399912.	−0.0595674
$539$	−8.50363e6	−1.26076
$540$	−2.56100e6	−0.377943
$541$	−7.82398e6	−1.14930	−0.574651	−	0.818398i	$-0.694862\pi$
$541$	−7.82398e6	−1.14930	−0.574651	+	0.818398i	$0.694862\pi$
$542$	371003.	0.0542474
$543$	1.11232e7	1.61894
$544$	1.17927e6	0.170850
$545$	1.07219e7	1.54625
$546$	−1.21328e6	−0.174172
$547$	6.99496e6	0.999579	0.499789	−	0.866147i	$-0.333411\pi$
$547$	6.99496e6	0.999579	0.499789	+	0.866147i	$0.333411\pi$
$548$	5.10314e6	0.725916
$549$	−572575.	−0.0810777
$550$	−2.06903e6	−0.291649
$551$	3.14731e6	0.441633
$552$	3.26917e6	0.456656
$553$	635620.	0.0883863
$554$	7.41421e6	1.02634
$555$	−1.04920e6	−0.144586
$556$	−3.84763e6	−0.527845
$557$	−7.01213e6	−0.957662	−0.478831	−	0.877907i	$-0.658939\pi$
$557$	−7.01213e6	−0.957662	−0.478831	+	0.877907i	$0.658939\pi$
$558$	863428.	0.117393
$559$	2.38406e7	3.22692
$560$	194989.	0.0262749
$561$	9.86087e6	1.32284
$562$	−9.25311e6	−1.23580
$563$	4.73934e6	0.630154	0.315077	−	0.949066i	$-0.397970\pi$
$563$	4.73934e6	0.630154	0.315077	+	0.949066i	$0.397970\pi$
$564$	−45998.2	−0.00608896
$565$	5.92054e6	0.780262
$566$	−8.31505e6	−1.09100
$567$	−1.09498e6	−0.143037
$568$	1.55603e6	0.202371
$569$	1.48430e7	1.92194	0.960971	−	0.276647i	$-0.0892234\pi$
$569$	1.48430e7	1.92194	0.960971	+	0.276647i	$0.0892234\pi$
$570$	−4.59576e6	−0.592475
$571$	−7.18161e6	−0.921789	−0.460895	−	0.887455i	$-0.652471\pi$
$571$	−7.18161e6	−0.921789	−0.460895	+	0.887455i	$0.652471\pi$
$572$	−9.06227e6	−1.15810
$573$	9.43608e6	1.20062
$574$	602171.	0.0762852
$575$	−3.08575e6	−0.389216
$576$	139877.	0.0175667
$577$	−6.80944e6	−0.851475	−0.425738	−	0.904847i	$-0.639985\pi$
$577$	−6.80944e6	−0.851475	−0.425738	+	0.904847i	$0.639985\pi$
$578$	−374445.	−0.0466196
$579$	5.91992e6	0.733871
$580$	−1.54638e6	−0.190874
$581$	954208.	0.117274
$582$	4.45589e6	0.545289
$583$	−1.52768e7	−1.86149
$584$	−3.03851e6	−0.368662
$585$	−1.73123e6	−0.209154
$586$	7.78569e6	0.936597
$587$	−8.09312e6	−0.969439	−0.484719	−	0.874670i	$-0.661078\pi$
$587$	−8.09312e6	−0.969439	−0.484719	+	0.874670i	$0.661078\pi$
$588$	−4.40388e6	−0.525282
$589$	−9.47591e6	−1.12547
$590$	−2.93917e6	−0.347612
$591$	2.24625e6	0.264539
$592$	−350464.	−0.0410997
$593$	−1.15869e7	−1.35310	−0.676549	−	0.736398i	$-0.736525\pi$
$593$	−1.15869e7	−1.35310	−0.676549	+	0.736398i	$0.736525\pi$
$594$	−7.15317e6	−0.831826
$595$	877167.	0.101576
$596$	2.64473e6	0.304976
$597$	1.76423e7	2.02591
$598$	−1.35154e7	−1.54553
$599$	−8.15638e6	−0.928817	−0.464409	−	0.885621i	$-0.653733\pi$
$599$	−8.15638e6	−0.928817	−0.464409	+	0.885621i	$0.653733\pi$
$600$	−1.07151e6	−0.121512
$601$	−7.98615e6	−0.901885	−0.450942	−	0.892553i	$-0.648912\pi$
$601$	−7.98615e6	−0.901885	−0.450942	+	0.892553i	$0.648912\pi$
$602$	−1.43278e6	−0.161134
$603$	−748343.	−0.0838122
$604$	−6.40358e6	−0.714217
$605$	4.76425e6	0.529184
$606$	614016.	0.0679200
$607$	−1.42495e7	−1.56974	−0.784869	−	0.619661i	$-0.787270\pi$
$607$	−1.42495e7	−1.56974	−0.784869	+	0.619661i	$0.787270\pi$
$608$	−1.53512e6	−0.168416
$609$	−578266.	−0.0631807
$610$	−3.08747e6	−0.335953
$611$	190167.	0.0206078
$612$	629244.	0.0679111
$613$	−1.30581e7	−1.40355	−0.701777	−	0.712397i	$-0.747610\pi$
$613$	−1.30581e7	−1.40355	−0.701777	+	0.712397i	$0.747610\pi$
$614$	8.03243e6	0.859857
$615$	6.97337e6	0.743456
$616$	544626.	0.0578291
$617$	4.35501e6	0.460549	0.230275	−	0.973126i	$-0.426038\pi$
$617$	4.35501e6	0.460549	0.230275	+	0.973126i	$0.426038\pi$
$618$	3.04625e6	0.320844
$619$	6.17508e6	0.647763	0.323881	−	0.946098i	$-0.395012\pi$
$619$	6.17508e6	0.647763	0.323881	+	0.946098i	$0.395012\pi$
$620$	4.65583e6	0.486427
$621$	−1.06682e7	−1.11010
$622$	−637655.	−0.0660861
$623$	1.80343e6	0.186157
$624$	−4.69319e6	−0.482510
$625$	−5.61147e6	−0.574615
$626$	9.98683e6	1.01857
$627$	−1.28365e7	−1.30400
$628$	852255.	0.0862324
$629$	−1.57658e6	−0.158887
$630$	104044.	0.0104440
$631$	1.53597e7	1.53571	0.767856	−	0.640622i	$-0.221323\pi$
$631$	1.53597e7	1.53571	0.767856	+	0.640622i	$0.221323\pi$
$632$	2.45870e6	0.244857
$633$	1.81737e6	0.180275
$634$	6.32826e6	0.625261
$635$	−7.84730e6	−0.772300
$636$	−7.91156e6	−0.775567
$637$	1.82066e7	1.77779
$638$	−4.31921e6	−0.420100
$639$	830282.	0.0804402
$640$	754255.	0.0727894
$641$	−907880.	−0.0872737	−0.0436369	−	0.999047i	$-0.513894\pi$
$641$	−907880.	−0.0872737	−0.0436369	+	0.999047i	$0.513894\pi$
$642$	6.15939e6	0.589794
$643$	3.81117e6	0.363522	0.181761	−	0.983343i	$-0.441820\pi$
$643$	3.81117e6	0.363522	0.181761	+	0.983343i	$0.441820\pi$
$644$	812254.	0.0771751
$645$	−1.65921e7	−1.57037
$646$	−6.90580e6	−0.651077
$647$	1.19372e6	0.112110	0.0560548	−	0.998428i	$-0.482148\pi$
$647$	1.19372e6	0.112110	0.0560548	+	0.998428i	$0.482148\pi$
$648$	−4.23560e6	−0.396257
$649$	−8.20944e6	−0.765071
$650$	4.42987e6	0.411252
$651$	1.74104e6	0.161011
$652$	−1.67277e6	−0.154105
$653$	1.55288e7	1.42513	0.712566	−	0.701605i	$-0.247533\pi$
$653$	1.55288e7	1.42513	0.712566	+	0.701605i	$0.247533\pi$
$654$	1.55093e7	1.41791
$655$	−3.55394e6	−0.323674
$656$	2.32931e6	0.211333
$657$	−1.62132e6	−0.146540
$658$	−11428.7	−0.00102904
$659$	−1.65892e7	−1.48803	−0.744015	−	0.668163i	$-0.767081\pi$
$659$	−1.65892e7	−1.48803	−0.744015	+	0.668163i	$0.767081\pi$
$660$	6.30698e6	0.563588
$661$	1.66794e7	1.48483	0.742417	−	0.669938i	$-0.233679\pi$
$661$	1.66794e7	1.48483	0.742417	+	0.669938i	$0.233679\pi$
$662$	1.50007e6	0.133035
$663$	−2.11125e7	−1.86533
$664$	3.69106e6	0.324886
$665$	−1.14186e6	−0.100129
$666$	−187004.	−0.0163367
$667$	−6.44166e6	−0.560639
$668$	3.78303e6	0.328019
$669$	3.27803e6	0.283170
$670$	−4.03526e6	−0.347284
$671$	−8.62365e6	−0.739409
$672$	282052.	0.0240939
$673$	−2.19553e7	−1.86854	−0.934269	−	0.356570i	$-0.883946\pi$
$673$	−2.19553e7	−1.86854	−0.934269	+	0.356570i	$0.883946\pi$
$674$	−1.33624e7	−1.13301
$675$	3.49666e6	0.295389
$676$	1.34620e7	1.13303
$677$	−1.52447e7	−1.27834	−0.639169	−	0.769066i	$-0.720722\pi$
$677$	−1.52447e7	−1.27834	−0.639169	+	0.769066i	$0.720722\pi$
$678$	8.56408e6	0.715495
$679$	1.10711e6	0.0921541
$680$	3.39305e6	0.281396
$681$	−2.76200e6	−0.228221
$682$	1.30042e7	1.07059
$683$	7.29915e6	0.598716	0.299358	−	0.954141i	$-0.403228\pi$
$683$	7.29915e6	0.598716	0.299358	+	0.954141i	$0.403228\pi$
$684$	−819123.	−0.0669436
$685$	1.46830e7	1.19561
$686$	−2.20649e6	−0.179016
$687$	608359.	0.0491777
$688$	−5.54226e6	−0.446392
$689$	3.27081e7	2.62487
$690$	9.40622e6	0.752129
$691$	1.06587e7	0.849200	0.424600	−	0.905381i	$-0.360415\pi$
$691$	1.06587e7	0.849200	0.424600	+	0.905381i	$0.360415\pi$
$692$	−709790.	−0.0563462
$693$	290607.	0.0229865
$694$	−1.00815e7	−0.794563
$695$	−1.10706e7	−0.869380
$696$	−2.23684e6	−0.175030
$697$	1.04785e7	0.816992
$698$	−5.03429e6	−0.391111
$699$	−3.30629e6	−0.255946
$700$	−266228.	−0.0205356
$701$	−1.94228e7	−1.49286	−0.746428	−	0.665466i	$-0.768233\pi$
$701$	−1.94228e7	−1.49286	−0.746428	+	0.665466i	$0.768233\pi$
$702$	1.53152e7	1.17295
$703$	2.05232e6	0.156624
$704$	2.10672e6	0.160204
$705$	−132349.	−0.0100287
$706$	−4.79010e6	−0.361687
$707$	152558.	0.0114785
$708$	−4.25152e6	−0.318758
$709$	−1.80589e6	−0.134920	−0.0674598	−	0.997722i	$-0.521489\pi$
$709$	−1.80589e6	−0.134920	−0.0674598	+	0.997722i	$0.521489\pi$
$710$	4.47709e6	0.333311
$711$	1.31194e6	0.0973282
$712$	6.97600e6	0.515711
$713$	1.93945e7	1.42875
$714$	1.26882e6	0.0931443
$715$	−2.60744e7	−1.90744
$716$	−1.04903e7	−0.764728
$717$	−2.18344e7	−1.58615
$718$	1.72526e7	1.24895
$719$	−2.06118e6	−0.148694	−0.0743469	−	0.997232i	$-0.523687\pi$
$719$	−2.06118e6	−0.148694	−0.0743469	+	0.997232i	$0.523687\pi$
$720$	402462.	0.0289330
$721$	756869.	0.0542229
$722$	−914725.	−0.0653052
$723$	−1.64162e7	−1.16796
$724$	1.06904e7	0.757962
$725$	2.11134e6	0.149181
$726$	6.89151e6	0.485258
$727$	1.01518e7	0.712372	0.356186	−	0.934415i	$-0.384077\pi$
$727$	1.01518e7	0.712372	0.356186	+	0.934415i	$0.384077\pi$
$728$	−1.16607e6	−0.0815445
$729$	1.18054e7	0.822742
$730$	−8.74257e6	−0.607200
$731$	−2.49321e7	−1.72570
$732$	−4.46604e6	−0.308067
$733$	−2.58836e7	−1.77936	−0.889682	−	0.456582i	$-0.849074\pi$
$733$	−2.58836e7	−1.77936	−0.889682	+	0.456582i	$0.849074\pi$
$734$	−1.85951e7	−1.27396
$735$	−1.26711e7	−0.865158
$736$	3.14195e6	0.213799
$737$	−1.12709e7	−0.764347
$738$	1.24290e6	0.0840029
$739$	2.91470e7	1.96328	0.981642	−	0.190734i	$-0.0610869\pi$
$739$	2.91470e7	1.96328	0.981642	+	0.190734i	$0.0610869\pi$
$740$	−1.00837e6	−0.0676928
$741$	2.74834e7	1.83876
$742$	−1.96570e6	−0.131071
$743$	2.57501e6	0.171122	0.0855611	−	0.996333i	$-0.472732\pi$
$743$	2.57501e6	0.171122	0.0855611	+	0.996333i	$0.472732\pi$
$744$	6.73467e6	0.446050
$745$	7.60955e6	0.502306
$746$	−4.91917e6	−0.323627
$747$	1.96951e6	0.129139
$748$	9.47716e6	0.619333
$749$	1.53036e6	0.0996755
$750$	−1.26630e7	−0.822023
$751$	−840915.	−0.0544067	−0.0272033	−	0.999630i	$-0.508660\pi$
$751$	−840915.	−0.0544067	−0.0272033	+	0.999630i	$0.508660\pi$
$752$	−44208.3	−0.00285075
$753$	1.47899e7	0.950557
$754$	9.24760e6	0.592380
$755$	−1.84247e7	−1.17634
$756$	−920417.	−0.0585707
$757$	−1.17737e6	−0.0746748	−0.0373374	−	0.999303i	$-0.511888\pi$
$757$	−1.17737e6	−0.0746748	−0.0373374	+	0.999303i	$0.511888\pi$
$758$	−1.67077e7	−1.05620
$759$	2.62726e7	1.65538
$760$	−4.41692e6	−0.277387
$761$	3.09498e7	1.93729	0.968647	−	0.248440i	$-0.0799179\pi$
$761$	3.09498e7	1.93729	0.968647	+	0.248440i	$0.0799179\pi$
$762$	−1.13511e7	−0.708194
$763$	3.85342e6	0.239627
$764$	9.06889e6	0.562110
$765$	1.81050e6	0.111852
$766$	4.16388e6	0.256405
$767$	1.75767e7	1.07882
$768$	1.09103e6	0.0667474
$769$	−7.62822e6	−0.465165	−0.232583	−	0.972577i	$-0.574718\pi$
$769$	−7.62822e6	−0.465165	−0.232583	+	0.972577i	$0.574718\pi$
$770$	1.56703e6	0.0952467
$771$	3.80545e6	0.230553
$772$	5.68956e6	0.343586
$773$	−1.75757e7	−1.05795	−0.528974	−	0.848638i	$-0.677423\pi$
$773$	−1.75757e7	−1.05795	−0.528974	+	0.848638i	$0.677423\pi$
$774$	−2.95729e6	−0.177436
$775$	−6.35682e6	−0.380177
$776$	4.28249e6	0.255295
$777$	−377080.	−0.0224068
$778$	−8.57367e6	−0.507829
$779$	−1.36405e7	−0.805352
$780$	−1.35035e7	−0.794711
$781$	1.25050e7	0.733596
$782$	1.41342e7	0.826523
$783$	7.29946e6	0.425487
$784$	−4.23251e6	−0.245928
$785$	2.45215e6	0.142028
$786$	−5.14079e6	−0.296806
$787$	1.80952e7	1.04142	0.520711	−	0.853733i	$-0.325667\pi$
$787$	1.80952e7	1.04142	0.520711	+	0.853733i	$0.325667\pi$
$788$	2.15884e6	0.123853
$789$	2.69685e6	0.154229
$790$	7.07430e6	0.403288
$791$	2.12783e6	0.120919
$792$	1.12412e6	0.0636796
$793$	1.84636e7	1.04264
$794$	1.13505e7	0.638945
$795$	−2.27636e7	−1.27739
$796$	1.69558e7	0.948496
$797$	2.69586e7	1.50332	0.751661	−	0.659550i	$-0.229253\pi$
$797$	2.69586e7	1.50332	0.751661	+	0.659550i	$0.229253\pi$
$798$	−1.65170e6	−0.0918172
$799$	−198873.	−0.0110207
$800$	−1.02982e6	−0.0568900
$801$	3.72232e6	0.204990
$802$	2.11190e7	1.15941
$803$	−2.44190e7	−1.33641
$804$	−5.83701e6	−0.318457
$805$	2.33706e6	0.127110
$806$	−2.78426e7	−1.50963
$807$	−1.66441e6	−0.0899658
$808$	590123.	0.0317990
$809$	3.97665e6	0.213622	0.106811	−	0.994279i	$-0.465936\pi$
$809$	3.97665e6	0.213622	0.106811	+	0.994279i	$0.465936\pi$
$810$	−1.21869e7	−0.652649
$811$	−2.46310e7	−1.31501	−0.657506	−	0.753449i	$-0.728389\pi$
$811$	−2.46310e7	−1.31501	−0.657506	+	0.753449i	$0.728389\pi$
$812$	−555764.	−0.0295802
$813$	1.54410e6	0.0819309
$814$	−2.81650e6	−0.148987
$815$	−4.81299e6	−0.253817
$816$	4.90805e6	0.258038
$817$	3.24556e7	1.70112
$818$	8.78097e6	0.458838
$819$	−622200.	−0.0324131
$820$	6.70202e6	0.348074
$821$	7.02343e6	0.363656	0.181828	−	0.983330i	$-0.441799\pi$
$821$	7.02343e6	0.363656	0.181828	+	0.983330i	$0.441799\pi$
$822$	2.12390e7	1.09637
$823$	−1.43490e6	−0.0738452	−0.0369226	−	0.999318i	$-0.511755\pi$
$823$	−1.43490e6	−0.0738452	−0.0369226	+	0.999318i	$0.511755\pi$
$824$	2.92771e6	0.150214
$825$	−8.61121e6	−0.440483
$826$	−1.05633e6	−0.0538703
$827$	1.77222e7	0.901058	0.450529	−	0.892762i	$-0.351235\pi$
$827$	1.77222e7	0.901058	0.450529	+	0.892762i	$0.351235\pi$
$828$	1.67651e6	0.0849828
$829$	−242232.	−0.0122418	−0.00612089	−	0.999981i	$-0.501948\pi$
$829$	−242232.	−0.0122418	−0.00612089	+	0.999981i	$0.501948\pi$
$830$	1.06201e7	0.535098
$831$	3.08576e7	1.55010
$832$	−4.51056e6	−0.225903
$833$	−1.90402e7	−0.950732
$834$	−1.60137e7	−0.797216
$835$	1.08847e7	0.540259
$836$	−1.23370e7	−0.610509
$837$	−2.19771e7	−1.08432
$838$	671703.	0.0330421
$839$	1.62866e6	0.0798777	0.0399388	−	0.999202i	$-0.487284\pi$
$839$	1.62866e6	0.0798777	0.0399388	+	0.999202i	$0.487284\pi$
$840$	811536.	0.0396834
$841$	−1.61036e7	−0.785115
$842$	1.96149e6	0.0953465
$843$	−3.85110e7	−1.86645
$844$	1.74665e6	0.0844016
$845$	3.87335e7	1.86614
$846$	−23589.1	−0.00113314
$847$	1.71226e6	0.0820089
$848$	−7.60370e6	−0.363108
$849$	−3.46068e7	−1.64776
$850$	−4.63269e6	−0.219931
$851$	−4.20052e6	−0.198829
$852$	6.47613e6	0.305644
$853$	1.11089e7	0.522756	0.261378	−	0.965236i	$-0.415823\pi$
$853$	1.11089e7	0.522756	0.261378	+	0.965236i	$0.415823\pi$
$854$	−1.10963e6	−0.0520634
$855$	−2.35682e6	−0.110258
$856$	5.91971e6	0.276132
$857$	1.19658e7	0.556529	0.278265	−	0.960504i	$-0.410241\pi$
$857$	1.19658e7	0.556529	0.278265	+	0.960504i	$0.410241\pi$
$858$	−3.77167e7	−1.74910
$859$	4.16117e6	0.192412	0.0962062	−	0.995361i	$-0.469329\pi$
$859$	4.16117e6	0.192412	0.0962062	+	0.995361i	$0.469329\pi$
$860$	−1.59465e7	−0.735223
$861$	2.50621e6	0.115215
$862$	2.72984e7	1.25132
$863$	−2.66329e7	−1.21728	−0.608642	−	0.793445i	$-0.708285\pi$
$863$	−2.66329e7	−1.21728	−0.608642	+	0.793445i	$0.708285\pi$
$864$	−3.56035e6	−0.162259
$865$	−2.04224e6	−0.0928042
$866$	−2.90576e7	−1.31663
$867$	−1.55842e6	−0.0704105
$868$	1.67329e6	0.0753827
$869$	1.97593e7	0.887610
$870$	−6.43596e6	−0.288281
$871$	2.41315e7	1.07780
$872$	1.49058e7	0.663839
$873$	2.28509e6	0.101477
$874$	−1.83993e7	−0.814747
$875$	−3.14624e6	−0.138922
$876$	−1.26461e7	−0.556798
$877$	−4.03256e6	−0.177044	−0.0885222	−	0.996074i	$-0.528214\pi$
$877$	−4.03256e6	−0.177044	−0.0885222	+	0.996074i	$0.528214\pi$
$878$	−1.48168e7	−0.648663
$879$	3.24037e7	1.41456
$880$	6.06156e6	0.263862
$881$	−1.76790e7	−0.767391	−0.383696	−	0.923460i	$-0.625349\pi$
$881$	−1.76790e7	−0.767391	−0.383696	+	0.923460i	$0.625349\pi$
$882$	−2.25843e6	−0.0977539
$883$	4.43311e6	0.191340	0.0956702	−	0.995413i	$-0.469501\pi$
$883$	4.43311e6	0.191340	0.0956702	+	0.995413i	$0.469501\pi$
$884$	−2.02910e7	−0.873317
$885$	−1.22327e7	−0.525006
$886$	−2.95146e7	−1.26314
$887$	−1.53518e7	−0.655166	−0.327583	−	0.944822i	$-0.606234\pi$
$887$	−1.53518e7	−0.655166	−0.327583	+	0.944822i	$0.606234\pi$
$888$	−1.45861e6	−0.0620738
$889$	−2.82030e6	−0.119685
$890$	2.00717e7	0.849395
$891$	−3.40393e7	−1.43644
$892$	3.15047e6	0.132576
$893$	258884.	0.0108637
$894$	1.10072e7	0.460611
$895$	−3.01834e7	−1.25953
$896$	271077.	0.0112803
$897$	−5.62506e7	−2.33424
$898$	−1.09710e7	−0.453998
$899$	−1.32702e7	−0.547618
$900$	−549501.	−0.0226132
$901$	−3.42056e7	−1.40373
$902$	1.87195e7	0.766086
$903$	−5.96317e6	−0.243365
$904$	8.23083e6	0.334983
$905$	3.07590e7	1.24839
$906$	−2.66514e7	−1.07870
$907$	−4.27902e7	−1.72713	−0.863566	−	0.504235i	$-0.831774\pi$
$907$	−4.27902e7	−1.72713	−0.863566	+	0.504235i	$0.831774\pi$
$908$	−2.65452e6	−0.106849
$909$	314883.	0.0126398
$910$	−3.35507e6	−0.134307
$911$	4.25842e7	1.70001	0.850006	−	0.526772i	$-0.176598\pi$
$911$	4.25842e7	1.70001	0.850006	+	0.526772i	$0.176598\pi$
$912$	−6.38909e6	−0.254362
$913$	2.96631e7	1.17771
$914$	2.91587e7	1.15452
$915$	−1.28499e7	−0.507397
$916$	584686.	0.0230242
$917$	−1.27728e6	−0.0501605
$918$	−1.60164e7	−0.627274
$919$	−2.61622e7	−1.02184	−0.510922	−	0.859627i	$-0.670696\pi$
$919$	−2.61622e7	−1.02184	−0.510922	+	0.859627i	$0.670696\pi$
$920$	9.04019e6	0.352134
$921$	3.34306e7	1.29866
$922$	9.76730e6	0.378397
$923$	−2.67737e7	−1.03444
$924$	2.26671e6	0.0873405
$925$	1.37678e6	0.0529066
$926$	8.86296e6	0.339666
$927$	1.56220e6	0.0597085
$928$	−2.14980e6	−0.0819461
$929$	−1.89795e7	−0.721515	−0.360758	−	0.932660i	$-0.617482\pi$
$929$	−1.89795e7	−0.721515	−0.360758	+	0.932660i	$0.617482\pi$
$930$	1.93773e7	0.734661
$931$	2.47856e7	0.937187
$932$	−3.17763e6	−0.119830
$933$	−2.65389e6	−0.0998112
$934$	−7.12325e6	−0.267184
$935$	2.72682e7	1.02006
$936$	−2.40679e6	−0.0897942
$937$	−2.97229e7	−1.10597	−0.552983	−	0.833193i	$-0.686511\pi$
$937$	−2.97229e7	−1.10597	−0.552983	+	0.833193i	$0.686511\pi$
$938$	−1.45026e6	−0.0538193
$939$	4.15647e7	1.53837
$940$	−127198.	−0.00469529
$941$	1.13914e7	0.419375	0.209687	−	0.977768i	$-0.432755\pi$
$941$	1.13914e7	0.419375	0.209687	+	0.977768i	$0.432755\pi$
$942$	3.54705e6	0.130239
$943$	2.79182e7	1.02237
$944$	−4.08608e6	−0.149237
$945$	−2.64827e6	−0.0964680
$946$	−4.45403e7	−1.61818
$947$	−1.59001e7	−0.576134	−0.288067	−	0.957610i	$-0.593013\pi$
$947$	−1.59001e7	−0.576134	−0.288067	+	0.957610i	$0.593013\pi$
$948$	1.02330e7	0.369813
$949$	5.22819e7	1.88446
$950$	6.03063e6	0.216797
$951$	2.63379e7	0.944344
$952$	1.21945e6	0.0436086
$953$	−3.77972e6	−0.134812	−0.0674058	−	0.997726i	$-0.521472\pi$
$953$	−3.77972e6	−0.134812	−0.0674058	+	0.997726i	$0.521472\pi$
$954$	−4.05725e6	−0.144332
$955$	2.60935e7	0.925814
$956$	−2.09848e7	−0.742609
$957$	−1.79764e7	−0.634486
$958$	3.26592e7	1.14972
$959$	5.27703e6	0.185286
$960$	3.13917e6	0.109935
$961$	1.13246e7	0.395563
$962$	6.03023e6	0.210086
$963$	3.15870e6	0.109760
$964$	−1.57774e7	−0.546819
$965$	1.63703e7	0.565898
$966$	3.38056e6	0.116559
$967$	−2.40547e7	−0.827245	−0.413622	−	0.910448i	$-0.635737\pi$
$967$	−2.40547e7	−0.827245	−0.413622	+	0.910448i	$0.635737\pi$
$968$	6.62334e6	0.227190
$969$	−2.87416e7	−0.983335
$970$	1.23218e7	0.420480
$971$	−1.42836e7	−0.486172	−0.243086	−	0.970005i	$-0.578160\pi$
$971$	−1.42836e7	−0.486172	−0.243086	+	0.970005i	$0.578160\pi$
$972$	−4.11016e6	−0.139538
$973$	−3.97875e6	−0.134730
$974$	−2.53609e7	−0.856580
$975$	1.84369e7	0.621122
$976$	−4.29225e6	−0.144232
$977$	5.51121e6	0.184719	0.0923593	−	0.995726i	$-0.470559\pi$
$977$	5.51121e6	0.184719	0.0923593	+	0.995726i	$0.470559\pi$
$978$	−6.96200e6	−0.232749
$979$	5.60625e7	1.86946
$980$	−1.21780e7	−0.405052
$981$	7.95356e6	0.263869
$982$	9.63351e6	0.318791
$983$	3.37762e7	1.11488	0.557438	−	0.830218i	$-0.311784\pi$
$983$	3.37762e7	1.11488	0.557438	+	0.830218i	$0.311784\pi$
$984$	9.69449e6	0.319181
$985$	6.21154e6	0.203990
$986$	−9.67098e6	−0.316795
$987$	−47565.6	−0.00155418
$988$	2.64139e7	0.860875
$989$	−6.64274e7	−2.15951
$990$	3.23438e6	0.104883
$991$	3.17657e7	1.02748	0.513741	−	0.857945i	$-0.328259\pi$
$991$	3.17657e7	1.02748	0.513741	+	0.857945i	$0.328259\pi$
$992$	6.47260e6	0.208833
$993$	6.24322e6	0.200926
$994$	1.60905e6	0.0516541
$995$	4.87861e7	1.56221
$996$	1.53620e7	0.490681
$997$	2.95431e7	0.941280	0.470640	−	0.882325i	$-0.344023\pi$
$997$	2.95431e7	0.941280	0.470640	+	0.882325i	$0.344023\pi$
$998$	−3.60991e7	−1.14728
$999$	4.75988e6	0.150897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.a.e.1.4	✓	5
3.2	odd	2		666.6.a.l.1.2		5
4.3	odd	2		592.6.a.e.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.e.1.4	✓	5	1.1	even	1	trivial
592.6.a.e.1.2		5	4.3	odd	2
666.6.a.l.1.2		5	3.2	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +16.6478 q^{3} +16.0000 q^{4} +46.0360 q^{5} +66.5913 q^{6} +16.5452 q^{7} +64.0000 q^{8} +34.1497 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +16.6478 q^{3} +16.0000 q^{4} +46.0360 q^{5} +66.5913 q^{6} +16.5452 q^{7} +64.0000 q^{8} +34.1497 q^{9} +184.144 q^{10} +514.335 q^{11} +266.365 q^{12} -1101.21 q^{13} +66.1809 q^{14} +766.400 q^{15} +256.000 q^{16} +1151.63 q^{17} +136.599 q^{18} -1499.14 q^{19} +736.577 q^{20} +275.442 q^{21} +2057.34 q^{22} +3068.31 q^{23} +1065.46 q^{24} -1005.68 q^{25} -4404.84 q^{26} -3476.90 q^{27} +264.723 q^{28} -2099.42 q^{29} +3065.60 q^{30} +6320.90 q^{31} +1024.00 q^{32} +8562.56 q^{33} +4606.51 q^{34} +761.676 q^{35} +546.396 q^{36} -1369.00 q^{37} -5996.56 q^{38} -18332.8 q^{39} +2946.31 q^{40} +9098.87 q^{41} +1101.77 q^{42} -21649.5 q^{43} +8229.36 q^{44} +1572.12 q^{45} +12273.3 q^{46} -172.689 q^{47} +4261.84 q^{48} -16533.3 q^{49} -4022.73 q^{50} +19172.1 q^{51} -17619.4 q^{52} -29702.0 q^{53} -13907.6 q^{54} +23678.0 q^{55} +1058.89 q^{56} -24957.4 q^{57} -8397.66 q^{58} -15961.3 q^{59} +12262.4 q^{60} -16766.6 q^{61} +25283.6 q^{62} +565.015 q^{63} +4096.00 q^{64} -50695.4 q^{65} +34250.2 q^{66} -21913.6 q^{67} +18426.0 q^{68} +51080.7 q^{69} +3046.70 q^{70} +24313.0 q^{71} +2185.58 q^{72} -47476.8 q^{73} -5476.00 q^{74} -16742.4 q^{75} -23986.2 q^{76} +8509.78 q^{77} -73331.0 q^{78} +38417.2 q^{79} +11785.2 q^{80} -66181.2 q^{81} +36395.5 q^{82} +57672.7 q^{83} +4407.07 q^{84} +53016.4 q^{85} -86597.9 q^{86} -34950.7 q^{87} +32917.5 q^{88} +109000. q^{89} +6288.47 q^{90} -18219.8 q^{91} +49093.0 q^{92} +105229. q^{93} -690.755 q^{94} -69014.4 q^{95} +17047.4 q^{96} +66914.0 q^{97} -66133.0 q^{98} +17564.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9} + 380 q^{10} + 903 q^{11} + 304 q^{12} + 1371 q^{13} + 680 q^{14} - 8 q^{15} + 1280 q^{16} + 2070 q^{17} + 2392 q^{18} + 2358 q^{19} + 1520 q^{20} + 2832 q^{21} + 3612 q^{22} + 2097 q^{23} + 1216 q^{24} - 390 q^{25} + 5484 q^{26} + 2614 q^{27} + 2720 q^{28} + 2927 q^{29} - 32 q^{30} - 5849 q^{31} + 5120 q^{32} - 11002 q^{33} + 8280 q^{34} - 10928 q^{35} + 9568 q^{36} - 6845 q^{37} + 9432 q^{38} - 9945 q^{39} + 6080 q^{40} - 14427 q^{41} + 11328 q^{42} - 6972 q^{43} + 14448 q^{44} - 6816 q^{45} + 8388 q^{46} - 18962 q^{47} + 4864 q^{48} - 11957 q^{49} - 1560 q^{50} - 67946 q^{51} + 21936 q^{52} - 23576 q^{53} + 10456 q^{54} - 31415 q^{55} + 10880 q^{56} - 70522 q^{57} + 11708 q^{58} - 18316 q^{59} - 128 q^{60} - 18695 q^{61} - 23396 q^{62} - 88094 q^{63} + 20480 q^{64} - 40706 q^{65} - 44008 q^{66} - 85273 q^{67} + 33120 q^{68} - 87171 q^{69} - 43712 q^{70} + 8760 q^{71} + 38272 q^{72} - 10425 q^{73} - 27380 q^{74} - 10542 q^{75} + 37728 q^{76} + 17238 q^{77} - 39780 q^{78} + 48425 q^{79} + 24320 q^{80} + 33449 q^{81} - 57708 q^{82} + 27704 q^{83} + 45312 q^{84} + 139062 q^{85} - 27888 q^{86} + 6227 q^{87} + 57792 q^{88} + 233646 q^{89} - 27264 q^{90} + 146434 q^{91} + 33552 q^{92} + 301866 q^{93} - 75848 q^{94} + 189498 q^{95} + 19456 q^{96} + 251694 q^{97} - 47828 q^{98} + 182486 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9 + 380 * q^10 + 903 * q^11 + 304 * q^12 + 1371 * q^13 + 680 * q^14 - 8 * q^15 + 1280 * q^16 + 2070 * q^17 + 2392 * q^18 + 2358 * q^19 + 1520 * q^20 + 2832 * q^21 + 3612 * q^22 + 2097 * q^23 + 1216 * q^24 - 390 * q^25 + 5484 * q^26 + 2614 * q^27 + 2720 * q^28 + 2927 * q^29 - 32 * q^30 - 5849 * q^31 + 5120 * q^32 - 11002 * q^33 + 8280 * q^34 - 10928 * q^35 + 9568 * q^36 - 6845 * q^37 + 9432 * q^38 - 9945 * q^39 + 6080 * q^40 - 14427 * q^41 + 11328 * q^42 - 6972 * q^43 + 14448 * q^44 - 6816 * q^45 + 8388 * q^46 - 18962 * q^47 + 4864 * q^48 - 11957 * q^49 - 1560 * q^50 - 67946 * q^51 + 21936 * q^52 - 23576 * q^53 + 10456 * q^54 - 31415 * q^55 + 10880 * q^56 - 70522 * q^57 + 11708 * q^58 - 18316 * q^59 - 128 * q^60 - 18695 * q^61 - 23396 * q^62 - 88094 * q^63 + 20480 * q^64 - 40706 * q^65 - 44008 * q^66 - 85273 * q^67 + 33120 * q^68 - 87171 * q^69 - 43712 * q^70 + 8760 * q^71 + 38272 * q^72 - 10425 * q^73 - 27380 * q^74 - 10542 * q^75 + 37728 * q^76 + 17238 * q^77 - 39780 * q^78 + 48425 * q^79 + 24320 * q^80 + 33449 * q^81 - 57708 * q^82 + 27704 * q^83 + 45312 * q^84 + 139062 * q^85 - 27888 * q^86 + 6227 * q^87 + 57792 * q^88 + 233646 * q^89 - 27264 * q^90 + 146434 * q^91 + 33552 * q^92 + 301866 * q^93 - 75848 * q^94 + 189498 * q^95 + 19456 * q^96 + 251694 * q^97 - 47828 * q^98 + 182486 * q^99

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