LMFDB - Embedded newform 37.6.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.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:	$5.93420133308$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 160x^{5} + 156x^{4} + 6495x^{3} - 2943x^{2} - 64880x + 53844 $ x^7 - x^6 - 160x^5 + 156x^4 + 6495x^3 - 2943x^2 - 64880*x + 53844
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-10.3821$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.38206 q^{2} -29.8081 q^{3} +56.0230 q^{4} -103.510 q^{5} -279.661 q^{6} -23.3438 q^{7} +225.385 q^{8} +645.520 q^{9} +O(q^{10})$	\(q+9.38206 q^{2} -29.8081 q^{3} +56.0230 q^{4} -103.510 q^{5} -279.661 q^{6} -23.3438 q^{7} +225.385 q^{8} +645.520 q^{9} -971.136 q^{10} -143.787 q^{11} -1669.94 q^{12} +18.7951 q^{13} -219.013 q^{14} +3085.43 q^{15} +321.839 q^{16} -680.511 q^{17} +6056.30 q^{18} -217.662 q^{19} -5798.94 q^{20} +695.833 q^{21} -1349.02 q^{22} -2511.94 q^{23} -6718.29 q^{24} +7589.31 q^{25} +176.337 q^{26} -11998.3 q^{27} -1307.79 q^{28} -3784.05 q^{29} +28947.7 q^{30} +3028.91 q^{31} -4192.81 q^{32} +4286.01 q^{33} -6384.59 q^{34} +2416.31 q^{35} +36163.9 q^{36} -1369.00 q^{37} -2042.11 q^{38} -560.246 q^{39} -23329.6 q^{40} +8659.04 q^{41} +6528.34 q^{42} -1762.24 q^{43} -8055.37 q^{44} -66817.7 q^{45} -23567.2 q^{46} -4804.99 q^{47} -9593.39 q^{48} -16262.1 q^{49} +71203.3 q^{50} +20284.7 q^{51} +1052.96 q^{52} +19058.5 q^{53} -112569. q^{54} +14883.4 q^{55} -5261.34 q^{56} +6488.07 q^{57} -35502.2 q^{58} -19980.3 q^{59} +172855. q^{60} +20194.1 q^{61} +28417.4 q^{62} -15068.9 q^{63} -49636.0 q^{64} -1945.48 q^{65} +40211.6 q^{66} -57952.1 q^{67} -38124.3 q^{68} +74876.1 q^{69} +22670.0 q^{70} -62469.7 q^{71} +145490. q^{72} +27394.1 q^{73} -12844.0 q^{74} -226222. q^{75} -12194.0 q^{76} +3356.53 q^{77} -5256.26 q^{78} +89019.3 q^{79} -33313.5 q^{80} +200786. q^{81} +81239.6 q^{82} -20966.0 q^{83} +38982.6 q^{84} +70439.7 q^{85} -16533.5 q^{86} +112795. q^{87} -32407.4 q^{88} +105127. q^{89} -626888. q^{90} -438.750 q^{91} -140726. q^{92} -90285.8 q^{93} -45080.7 q^{94} +22530.1 q^{95} +124979. q^{96} -68289.6 q^{97} -152572. q^{98} -92817.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * 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 $

$2$	9.38206	1.65853	0.829264	−	0.558856i	$-0.188760\pi$
$2$	9.38206	1.65853	0.829264	+	0.558856i	$0.188760\pi$
$3$	−29.8081	−1.91219	−0.956094	−	0.293061i	$-0.905326\pi$
$3$	−29.8081	−1.91219	−0.956094	+	0.293061i	$0.905326\pi$
$4$	56.0230	1.75072
$5$	−103.510	−1.85164	−0.925821	−	0.377962i	$-0.876625\pi$
$5$	−103.510	−1.85164	−0.925821	+	0.377962i	$0.876625\pi$
$6$	−279.661	−3.17142
$7$	−23.3438	−0.180064	−0.0900319	−	0.995939i	$-0.528697\pi$
$7$	−23.3438	−0.180064	−0.0900319	+	0.995939i	$0.528697\pi$
$8$	225.385	1.24509
$9$	645.520	2.65646
$10$	−971.136	−3.07100
$11$	−143.787	−0.358292	−0.179146	−	0.983822i	$-0.557334\pi$
$11$	−143.787	−0.358292	−0.179146	+	0.983822i	$0.557334\pi$
$12$	−1669.94	−3.34770
$13$	18.7951	0.0308452	0.0154226	−	0.999881i	$-0.495091\pi$
$13$	18.7951	0.0308452	0.0154226	+	0.999881i	$0.495091\pi$
$14$	−219.013	−0.298641
$15$	3085.43	3.54069
$16$	321.839	0.314296
$17$	−680.511	−0.571101	−0.285551	−	0.958364i	$-0.592176\pi$
$17$	−680.511	−0.571101	−0.285551	+	0.958364i	$0.592176\pi$
$18$	6056.30	4.40582
$19$	−217.662	−0.138324	−0.0691620	−	0.997605i	$-0.522033\pi$
$19$	−217.662	−0.138324	−0.0691620	+	0.997605i	$0.522033\pi$
$20$	−5798.94	−3.24170
$21$	695.833	0.344316
$22$	−1349.02	−0.594238
$23$	−2511.94	−0.990125	−0.495062	−	0.868857i	$-0.664855\pi$
$23$	−2511.94	−0.990125	−0.495062	+	0.868857i	$0.664855\pi$
$24$	−6718.29	−2.38084
$25$	7589.31	2.42858
$26$	176.337	0.0511576
$27$	−11998.3	−3.16746
$28$	−1307.79	−0.315241
$29$	−3784.05	−0.835531	−0.417765	−	0.908555i	$-0.637187\pi$
$29$	−3784.05	−0.835531	−0.417765	+	0.908555i	$0.637187\pi$
$30$	28947.7	5.87233
$31$	3028.91	0.566085	0.283042	−	0.959107i	$-0.408656\pi$
$31$	3028.91	0.566085	0.283042	+	0.959107i	$0.408656\pi$
$32$	−4192.81	−0.723819
$33$	4286.01	0.685122
$34$	−6384.59	−0.947188
$35$	2416.31	0.333414
$36$	36163.9	4.65071
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	−2042.11	−0.229414
$39$	−560.246	−0.0589817
$40$	−23329.6	−2.30546
$41$	8659.04	0.804471	0.402235	−	0.915536i	$-0.368233\pi$
$41$	8659.04	0.804471	0.402235	+	0.915536i	$0.368233\pi$
$42$	6528.34	0.571057
$43$	−1762.24	−0.145343	−0.0726716	−	0.997356i	$-0.523153\pi$
$43$	−1762.24	−0.145343	−0.0726716	+	0.997356i	$0.523153\pi$
$44$	−8055.37	−0.627269
$45$	−66817.7	−4.91881
$46$	−23567.2	−1.64215
$47$	−4804.99	−0.317284	−0.158642	−	0.987336i	$-0.550712\pi$
$47$	−4804.99	−0.317284	−0.158642	+	0.987336i	$0.550712\pi$
$48$	−9593.39	−0.600992
$49$	−16262.1	−0.967577
$50$	71203.3	4.02787
$51$	20284.7	1.09205
$52$	1052.96	0.0540012
$53$	19058.5	0.931965	0.465983	−	0.884794i	$-0.345701\pi$
$53$	19058.5	0.931965	0.465983	+	0.884794i	$0.345701\pi$
$54$	−112569.	−5.25333
$55$	14883.4	0.663429
$56$	−5261.34	−0.224195
$57$	6488.07	0.264502
$58$	−35502.2	−1.38575
$59$	−19980.3	−0.747261	−0.373630	−	0.927578i	$-0.621887\pi$
$59$	−19980.3	−0.747261	−0.373630	+	0.927578i	$0.621887\pi$
$60$	172855.	6.19874
$61$	20194.1	0.694866	0.347433	−	0.937705i	$-0.387053\pi$
$61$	20194.1	0.694866	0.347433	+	0.937705i	$0.387053\pi$
$62$	28417.4	0.938868
$63$	−15068.9	−0.478332
$64$	−49636.0	−1.51477
$65$	−1945.48	−0.0571142
$66$	40211.6	1.13629
$67$	−57952.1	−1.57718	−0.788591	−	0.614917i	$-0.789189\pi$
$67$	−57952.1	−1.57718	−0.788591	+	0.614917i	$0.789189\pi$
$68$	−38124.3	−0.999837
$69$	74876.1	1.89330
$70$	22670.0	0.552976
$71$	−62469.7	−1.47070	−0.735349	−	0.677688i	$-0.762982\pi$
$71$	−62469.7	−1.47070	−0.735349	+	0.677688i	$0.762982\pi$
$72$	145490.	3.30753
$73$	27394.1	0.601658	0.300829	−	0.953678i	$-0.402737\pi$
$73$	27394.1	0.601658	0.300829	+	0.953678i	$0.402737\pi$
$74$	−12844.0	−0.272660
$75$	−226222.	−4.64390
$76$	−12194.0	−0.242166
$77$	3356.53	0.0645155
$78$	−5256.26	−0.0978229
$79$	89019.3	1.60478	0.802392	−	0.596798i	$-0.203561\pi$
$79$	89019.3	1.60478	0.802392	+	0.596798i	$0.203561\pi$
$80$	−33313.5	−0.581963
$81$	200786.	3.40032
$82$	81239.6	1.33424
$83$	−20966.0	−0.334057	−0.167029	−	0.985952i	$-0.553417\pi$
$83$	−20966.0	−0.334057	−0.167029	+	0.985952i	$0.553417\pi$
$84$	38982.6	0.602799
$85$	70439.7	1.05747
$86$	−16533.5	−0.241056
$87$	112795.	1.59769
$88$	−32407.4	−0.446105
$89$	105127.	1.40682	0.703412	−	0.710782i	$-0.251659\pi$
$89$	105127.	1.40682	0.703412	+	0.710782i	$0.251659\pi$
$90$	−626888.	−8.15800
$91$	−438.750	−0.00555410
$92$	−140726.	−1.73343
$93$	−90285.8	−1.08246
$94$	−45080.7	−0.526224
$95$	22530.1	0.256127
$96$	124979.	1.38408
$97$	−68289.6	−0.736928	−0.368464	−	0.929642i	$-0.620116\pi$
$97$	−68289.6	−0.736928	−0.368464	+	0.929642i	$0.620116\pi$
$98$	−152572.	−1.60475
$99$	−92817.3	−0.951790
$100$	425176.	4.25176
$101$	105827.	1.03227	0.516133	−	0.856509i	$-0.327371\pi$
$101$	105827.	1.03227	0.516133	+	0.856509i	$0.327371\pi$
$102$	190312.	1.81120
$103$	−48464.2	−0.450120	−0.225060	−	0.974345i	$-0.572258\pi$
$103$	−48464.2	−0.450120	−0.225060	+	0.974345i	$0.572258\pi$
$104$	4236.14	0.0384049
$105$	−72025.6	−0.637549
$106$	178808.	1.54569
$107$	−140302.	−1.18469	−0.592345	−	0.805684i	$-0.701798\pi$
$107$	−140302.	−1.18469	−0.592345	+	0.805684i	$0.701798\pi$
$108$	−672182.	−5.54534
$109$	176467.	1.42265	0.711325	−	0.702863i	$-0.248095\pi$
$109$	176467.	1.42265	0.711325	+	0.702863i	$0.248095\pi$
$110$	139637.	1.10032
$111$	40807.2	0.314362
$112$	−7512.94	−0.0565932
$113$	28705.8	0.211482	0.105741	−	0.994394i	$-0.466279\pi$
$113$	28705.8	0.211482	0.105741	+	0.994394i	$0.466279\pi$
$114$	60871.4	0.438683
$115$	260011.	1.83336
$116$	−211994.	−1.46278
$117$	12132.6	0.0819390
$118$	−187456.	−1.23935
$119$	15885.7	0.102835
$120$	695409.	4.40847
$121$	−140376.	−0.871627
$122$	189463.	1.15245
$123$	−258109.	−1.53830
$124$	169688.	0.991055
$125$	−462100.	−2.64522
$126$	−141377.	−0.793328
$127$	102781.	0.565460	0.282730	−	0.959199i	$-0.408760\pi$
$127$	102781.	0.565460	0.282730	+	0.959199i	$0.408760\pi$
$128$	−331518.	−1.78847
$129$	52529.1	0.277924
$130$	−18252.6	−0.0947256
$131$	−91110.3	−0.463863	−0.231931	−	0.972732i	$-0.574504\pi$
$131$	−91110.3	−0.463863	−0.231931	+	0.972732i	$0.574504\pi$
$132$	240115.	1.19946
$133$	5081.05	0.0249071
$134$	−543710.	−2.61580
$135$	1.24195e6	5.86501
$136$	−153377.	−0.711071
$137$	−173727.	−0.790798	−0.395399	−	0.918509i	$-0.629394\pi$
$137$	−173727.	−0.790798	−0.395399	+	0.918509i	$0.629394\pi$
$138$	702492.	3.14010
$139$	−374342.	−1.64335	−0.821677	−	0.569953i	$-0.806961\pi$
$139$	−374342.	−1.64335	−0.821677	+	0.569953i	$0.806961\pi$
$140$	135369.	0.583713
$141$	143227.	0.606706
$142$	−586094.	−2.43920
$143$	−2702.49	−0.0110516
$144$	207753.	0.834914
$145$	391687.	1.54710
$146$	257013.	0.997868
$147$	484741.	1.85019
$148$	−76695.5	−0.287816
$149$	149009.	0.549853	0.274926	−	0.961465i	$-0.411347\pi$
$149$	149009.	0.549853	0.274926	+	0.961465i	$0.411347\pi$
$150$	−2.12243e6	−7.70204
$151$	−224155.	−0.800030	−0.400015	−	0.916509i	$-0.630995\pi$
$151$	−224155.	−0.800030	−0.400015	+	0.916509i	$0.630995\pi$
$152$	−49057.6	−0.172226
$153$	−439284.	−1.51711
$154$	31491.2	0.107001
$155$	−313522.	−1.04819
$156$	−31386.7	−0.103260
$157$	351703.	1.13875	0.569373	−	0.822079i	$-0.307186\pi$
$157$	351703.	1.13875	0.569373	+	0.822079i	$0.307186\pi$
$158$	835184.	2.66158
$159$	−568098.	−1.78209
$160$	433997.	1.34025
$161$	58638.2	0.178286
$162$	1.88378e6	5.63953
$163$	233902.	0.689549	0.344774	−	0.938686i	$-0.387955\pi$
$163$	233902.	0.689549	0.344774	+	0.938686i	$0.387955\pi$
$164$	485105.	1.40840
$165$	−443644.	−1.26860
$166$	−196705.	−0.554044
$167$	−301901.	−0.837671	−0.418835	−	0.908062i	$-0.637562\pi$
$167$	−301901.	−0.837671	−0.418835	+	0.908062i	$0.637562\pi$
$168$	156830.	0.428703
$169$	−370940.	−0.999049
$170$	660869.	1.75385
$171$	−140505.	−0.367452
$172$	−98726.1	−0.254455
$173$	−691001.	−1.75535	−0.877674	−	0.479258i	$-0.840906\pi$
$173$	−691001.	−1.75535	−0.877674	+	0.479258i	$0.840906\pi$
$174$	1.05825e6	2.64982
$175$	−177163.	−0.437299
$176$	−46276.2	−0.112610
$177$	595574.	1.42890
$178$	986309.	2.33326
$179$	34659.1	0.0808509	0.0404254	−	0.999183i	$-0.487129\pi$
$179$	34659.1	0.0808509	0.0404254	+	0.999183i	$0.487129\pi$
$180$	−3.74333e6	−8.61146
$181$	−640956.	−1.45422	−0.727112	−	0.686518i	$-0.759138\pi$
$181$	−640956.	−1.45422	−0.727112	+	0.686518i	$0.759138\pi$
$182$	−4116.37	−0.00921163
$183$	−601948.	−1.32871
$184$	−566154.	−1.23279
$185$	141705.	0.304408
$186$	−847066.	−1.79529
$187$	97848.6	0.204621
$188$	−269190.	−0.555474
$189$	280087.	0.570345
$190$	211379.	0.424793
$191$	−20841.2	−0.0413370	−0.0206685	−	0.999786i	$-0.506579\pi$
$191$	−20841.2	−0.0413370	−0.0206685	+	0.999786i	$0.506579\pi$
$192$	1.47955e6	2.89653
$193$	−126053.	−0.243590	−0.121795	−	0.992555i	$-0.538865\pi$
$193$	−126053.	−0.243590	−0.121795	+	0.992555i	$0.538865\pi$
$194$	−640696.	−1.22222
$195$	57991.1	0.109213
$196$	−911049.	−1.69395
$197$	−695875.	−1.27751	−0.638757	−	0.769409i	$-0.720551\pi$
$197$	−695875.	−1.27751	−0.638757	+	0.769409i	$0.720551\pi$
$198$	−870817.	−1.57857
$199$	443462.	0.793824	0.396912	−	0.917857i	$-0.370082\pi$
$199$	443462.	0.793824	0.396912	+	0.917857i	$0.370082\pi$
$200$	1.71052e6	3.02379
$201$	1.72744e6	3.01587
$202$	992871.	1.71204
$203$	88334.2	0.150449
$204$	1.13641e6	1.91188
$205$	−896297.	−1.48959
$206$	−454694.	−0.746536
$207$	−1.62151e6	−2.63023
$208$	6049.00	0.00969450
$209$	31296.9	0.0495605
$210$	−675748.	−1.05739
$211$	920125.	1.42279	0.711395	−	0.702793i	$-0.248064\pi$
$211$	920125.	1.42279	0.711395	+	0.702793i	$0.248064\pi$
$212$	1.06772e6	1.63161
$213$	1.86210e6	2.81225
$214$	−1.31632e6	−1.96484
$215$	182410.	0.269124
$216$	−2.70424e6	−3.94377
$217$	−70706.1	−0.101931
$218$	1.65563e6	2.35951
$219$	−816565.	−1.15048
$220$	833811.	1.16148
$221$	−12790.3	−0.0176157
$222$	382856.	0.521378
$223$	219448.	0.295509	0.147754	−	0.989024i	$-0.452796\pi$
$223$	219448.	0.295509	0.147754	+	0.989024i	$0.452796\pi$
$224$	97876.0	0.130334
$225$	4.89905e6	6.45142
$226$	269319.	0.350749
$227$	−312450.	−0.402453	−0.201227	−	0.979545i	$-0.564493\pi$
$227$	−312450.	−0.402453	−0.201227	+	0.979545i	$0.564493\pi$
$228$	363481.	0.463068
$229$	−822909.	−1.03696	−0.518482	−	0.855089i	$-0.673503\pi$
$229$	−822909.	−1.03696	−0.518482	+	0.855089i	$0.673503\pi$
$230$	2.43944e6	3.04067
$231$	−100052.	−0.123366
$232$	−852869.	−1.04031
$233$	317955.	0.383686	0.191843	−	0.981426i	$-0.438554\pi$
$233$	317955.	0.383686	0.191843	+	0.981426i	$0.438554\pi$
$234$	113829.	0.135898
$235$	497364.	0.587496
$236$	−1.11936e6	−1.30824
$237$	−2.65349e6	−3.06865
$238$	149041.	0.170554
$239$	−356198.	−0.403364	−0.201682	−	0.979451i	$-0.564641\pi$
$239$	−356198.	−0.403364	−0.201682	+	0.979451i	$0.564641\pi$
$240$	993011.	1.11282
$241$	1.38131e6	1.53196	0.765981	−	0.642863i	$-0.222254\pi$
$241$	1.38131e6	1.53196	0.765981	+	0.642863i	$0.222254\pi$
$242$	−1.31702e6	−1.44562
$243$	−3.06943e6	−3.33459
$244$	1.13134e6	1.21651
$245$	1.68329e6	1.79161
$246$	−2.42159e6	−2.55131
$247$	−4090.98	−0.00426663
$248$	682670.	0.704825
$249$	624957.	0.638780
$250$	−4.33545e6	−4.38717
$251$	−17459.5	−0.0174923	−0.00874616	−	0.999962i	$-0.502784\pi$
$251$	−17459.5	−0.0174923	−0.00874616	+	0.999962i	$0.502784\pi$
$252$	−844204.	−0.837425
$253$	361184.	0.354754
$254$	964294.	0.937832
$255$	−2.09967e6	−2.02209
$256$	−1.52197e6	−1.45146
$257$	−605855.	−0.572185	−0.286092	−	0.958202i	$-0.592356\pi$
$257$	−605855.	−0.572185	−0.286092	+	0.958202i	$0.592356\pi$
$258$	492831.	0.460944
$259$	31957.6	0.0296023
$260$	−108992.	−0.0999909
$261$	−2.44268e6	−2.21955
$262$	−854802.	−0.769330
$263$	1.12385e6	1.00189	0.500944	−	0.865480i	$-0.332986\pi$
$263$	1.12385e6	1.00189	0.500944	+	0.865480i	$0.332986\pi$
$264$	966001.	0.853037
$265$	−1.97275e6	−1.72567
$266$	47670.7	0.0413092
$267$	−3.13364e6	−2.69011
$268$	−3.24665e6	−2.76120
$269$	837599.	0.705758	0.352879	−	0.935669i	$-0.385203\pi$
$269$	837599.	0.705758	0.352879	+	0.935669i	$0.385203\pi$
$270$	1.16520e7	9.72729
$271$	1.16768e6	0.965831	0.482916	−	0.875667i	$-0.339578\pi$
$271$	1.16768e6	0.965831	0.482916	+	0.875667i	$0.339578\pi$
$272$	−219015.	−0.179495
$273$	13078.3	0.0106205
$274$	−1.62992e6	−1.31156
$275$	−1.09124e6	−0.870141
$276$	4.19478e6	3.31464
$277$	1.65182e6	1.29349	0.646744	−	0.762707i	$-0.276130\pi$
$277$	1.65182e6	1.29349	0.646744	+	0.762707i	$0.276130\pi$
$278$	−3.51210e6	−2.72555
$279$	1.95522e6	1.50378
$280$	544601.	0.415129
$281$	575280.	0.434624	0.217312	−	0.976102i	$-0.430271\pi$
$281$	575280.	0.434624	0.217312	+	0.976102i	$0.430271\pi$
$282$	1.34377e6	1.00624
$283$	2.47157e6	1.83445	0.917226	−	0.398367i	$-0.130423\pi$
$283$	2.47157e6	1.83445	0.917226	+	0.398367i	$0.130423\pi$
$284$	−3.49974e6	−2.57478
$285$	−671579.	−0.489762
$286$	−25355.0	−0.0183294
$287$	−202135.	−0.144856
$288$	−2.70654e6	−1.92280
$289$	−956762.	−0.673844
$290$	3.67483e6	2.56592
$291$	2.03558e6	1.40914
$292$	1.53470e6	1.05333
$293$	−15152.9	−0.0103116	−0.00515580	−	0.999987i	$-0.501641\pi$
$293$	−15152.9	−0.0103116	−0.00515580	+	0.999987i	$0.501641\pi$
$294$	4.54786e6	3.06859
$295$	2.06816e6	1.38366
$296$	−308552.	−0.204691
$297$	1.72520e6	1.13488
$298$	1.39801e6	0.911947
$299$	−47212.3	−0.0305406
$300$	−1.26737e7	−8.13015
$301$	41137.4	0.0261710
$302$	−2.10304e6	−1.32687
$303$	−3.15448e6	−1.97388
$304$	−70051.9	−0.0434747
$305$	−2.09029e6	−1.28664
$306$	−4.12138e6	−2.51617
$307$	−2.30856e6	−1.39796	−0.698981	−	0.715140i	$-0.746363\pi$
$307$	−2.30856e6	−1.39796	−0.698981	+	0.715140i	$0.746363\pi$
$308$	188043.	0.112948
$309$	1.44462e6	0.860713
$310$	−2.94148e6	−1.73845
$311$	−1.50302e6	−0.881178	−0.440589	−	0.897709i	$-0.645230\pi$
$311$	−1.50302e6	−0.881178	−0.440589	+	0.897709i	$0.645230\pi$
$312$	−126271.	−0.0734374
$313$	743006.	0.428678	0.214339	−	0.976759i	$-0.431240\pi$
$313$	743006.	0.428678	0.214339	+	0.976759i	$0.431240\pi$
$314$	3.29970e6	1.88864
$315$	1.55978e6	0.885700
$316$	4.98713e6	2.80952
$317$	1.28060e6	0.715759	0.357879	−	0.933768i	$-0.383500\pi$
$317$	1.28060e6	0.715759	0.357879	+	0.933768i	$0.383500\pi$
$318$	−5.32992e6	−2.95565
$319$	544097.	0.299364
$320$	5.13782e6	2.80481
$321$	4.18213e6	2.26535
$322$	550147.	0.295692
$323$	148121.	0.0789970
$324$	1.12486e7	5.95301
$325$	142642.	0.0749099
$326$	2.19448e6	1.14364
$327$	−5.26015e6	−2.72037
$328$	1.95162e6	1.00164
$329$	112167.	0.0571313
$330$	−4.16230e6	−2.10401
$331$	2.02925e6	1.01804	0.509021	−	0.860754i	$-0.330007\pi$
$331$	2.02925e6	1.01804	0.509021	+	0.860754i	$0.330007\pi$
$332$	−1.17458e6	−0.584840
$333$	−883717.	−0.436719
$334$	−2.83245e6	−1.38930
$335$	5.99862e6	2.92038
$336$	223946.	0.108217
$337$	−2.16422e6	−1.03807	−0.519036	−	0.854753i	$-0.673709\pi$
$337$	−2.16422e6	−1.03807	−0.519036	+	0.854753i	$0.673709\pi$
$338$	−3.48018e6	−1.65695
$339$	−855663.	−0.404393
$340$	3.94624e6	1.85134
$341$	−435517.	−0.202824
$342$	−1.31822e6	−0.609431
$343$	771957.	0.354289
$344$	−397183.	−0.180965
$345$	−7.75042e6	−3.50572
$346$	−6.48301e6	−2.91130
$347$	−1.51617e6	−0.675966	−0.337983	−	0.941152i	$-0.609745\pi$
$347$	−1.51617e6	−0.675966	−0.337983	+	0.941152i	$0.609745\pi$
$348$	6.31913e6	2.79711
$349$	3.14995e6	1.38433	0.692165	−	0.721739i	$-0.256657\pi$
$349$	3.14995e6	1.38433	0.692165	+	0.721739i	$0.256657\pi$
$350$	−1.66215e6	−0.725273
$351$	−225510.	−0.0977009
$352$	602871.	0.259339
$353$	−2.38503e6	−1.01873	−0.509364	−	0.860551i	$-0.670119\pi$
$353$	−2.38503e6	−1.01873	−0.509364	+	0.860551i	$0.670119\pi$
$354$	5.58771e6	2.36988
$355$	6.46624e6	2.72321
$356$	5.88954e6	2.46295
$357$	−473522.	−0.196639
$358$	325174.	0.134094
$359$	−3.17469e6	−1.30007	−0.650033	−	0.759906i	$-0.725245\pi$
$359$	−3.17469e6	−1.30007	−0.650033	+	0.759906i	$0.725245\pi$
$360$	−1.50597e7	−6.12435
$361$	−2.42872e6	−0.980866
$362$	−6.01348e6	−2.41187
$363$	4.18435e6	1.66671
$364$	−24580.1	−0.00972366
$365$	−2.83556e6	−1.11406
$366$	−5.64751e6	−2.20371
$367$	3.93806e6	1.52622	0.763111	−	0.646268i	$-0.223671\pi$
$367$	3.93806e6	1.52622	0.763111	+	0.646268i	$0.223671\pi$
$368$	−808440.	−0.311192
$369$	5.58958e6	2.13704
$370$	1.32949e6	0.504870
$371$	−444898.	−0.167813
$372$	−5.05808e6	−1.89508
$373$	167345.	0.0622789	0.0311394	−	0.999515i	$-0.490086\pi$
$373$	167345.	0.0622789	0.0311394	+	0.999515i	$0.490086\pi$
$374$	918021.	0.339370
$375$	1.37743e7	5.05815
$376$	−1.08297e6	−0.395046
$377$	−71121.8	−0.0257721
$378$	2.62779e6	0.945934
$379$	447738.	0.160113	0.0800563	−	0.996790i	$-0.474490\pi$
$379$	447738.	0.160113	0.0800563	+	0.996790i	$0.474490\pi$
$380$	1.26221e6	0.448406
$381$	−3.06369e6	−1.08127
$382$	−195533.	−0.0685587
$383$	−2.61554e6	−0.911098	−0.455549	−	0.890211i	$-0.650557\pi$
$383$	−2.61554e6	−0.911098	−0.455549	+	0.890211i	$0.650557\pi$
$384$	9.88190e6	3.41989
$385$	−347434.	−0.119460
$386$	−1.18263e6	−0.404000
$387$	−1.13756e6	−0.386099
$388$	−3.82578e6	−1.29015
$389$	−2.35608e6	−0.789436	−0.394718	−	0.918802i	$-0.629158\pi$
$389$	−2.35608e6	−0.789436	−0.394718	+	0.918802i	$0.629158\pi$
$390$	544076.	0.181133
$391$	1.70940e6	0.565461
$392$	−3.66522e6	−1.20472
$393$	2.71582e6	0.886992
$394$	−6.52873e6	−2.11879
$395$	−9.21438e6	−2.97148
$396$	−5.19990e6	−1.66632
$397$	1.43756e6	0.457771	0.228886	−	0.973453i	$-0.426492\pi$
$397$	1.43756e6	0.457771	0.228886	+	0.973453i	$0.426492\pi$
$398$	4.16059e6	1.31658
$399$	−151456.	−0.0476271
$400$	2.44253e6	0.763292
$401$	1.22476e6	0.380355	0.190177	−	0.981750i	$-0.439094\pi$
$401$	1.22476e6	0.380355	0.190177	+	0.981750i	$0.439094\pi$
$402$	1.62069e7	5.00191
$403$	56928.7	0.0174610
$404$	5.92872e6	1.80721
$405$	−2.07833e7	−6.29618
$406$	828756.	0.249524
$407$	196844.	0.0589029
$408$	4.57187e6	1.35970
$409$	−3.24578e6	−0.959426	−0.479713	−	0.877426i	$-0.659259\pi$
$409$	−3.24578e6	−0.959426	−0.479713	+	0.877426i	$0.659259\pi$
$410$	−8.40911e6	−2.47053
$411$	5.17846e6	1.51215
$412$	−2.71511e6	−0.788033
$413$	466416.	0.134555
$414$	−1.52131e7	−4.36231
$415$	2.17019e6	0.618555
$416$	−78804.4	−0.0223263
$417$	1.11584e7	3.14240
$418$	293629.	0.0821974
$419$	4.79763e6	1.33503	0.667516	−	0.744595i	$-0.267357\pi$
$419$	4.79763e6	1.33503	0.667516	+	0.744595i	$0.267357\pi$
$420$	−4.03509e6	−1.11617
$421$	381773.	0.104978	0.0524892	−	0.998621i	$-0.483285\pi$
$421$	381773.	0.104978	0.0524892	+	0.998621i	$0.483285\pi$
$422$	8.63266e6	2.35974
$423$	−3.10172e6	−0.842851
$424$	4.29550e6	1.16038
$425$	−5.16461e6	−1.38696
$426$	1.74703e7	4.66420
$427$	−471408.	−0.125120
$428$	−7.86015e6	−2.07406
$429$	80556.1	0.0211327
$430$	1.71138e6	0.446349
$431$	6.25708e6	1.62248	0.811238	−	0.584716i	$-0.198794\pi$
$431$	6.25708e6	1.62248	0.811238	+	0.584716i	$0.198794\pi$
$432$	−3.86153e6	−0.995520
$433$	−7.43349e6	−1.90534	−0.952671	−	0.304002i	$-0.901677\pi$
$433$	−7.43349e6	−1.90534	−0.952671	+	0.304002i	$0.901677\pi$
$434$	−663369.	−0.169056
$435$	−1.16754e7	−2.95835
$436$	9.88623e6	2.49066
$437$	546753.	0.136958
$438$	−7.66106e6	−1.90811
$439$	−5.56926e6	−1.37923	−0.689615	−	0.724176i	$-0.742220\pi$
$439$	−5.56926e6	−1.37923	−0.689615	+	0.724176i	$0.742220\pi$
$440$	3.35449e6	0.826027
$441$	−1.04975e7	−2.57033
$442$	−119999.	−0.0292162
$443$	−899323.	−0.217724	−0.108862	−	0.994057i	$-0.534721\pi$
$443$	−899323.	−0.217724	−0.108862	+	0.994057i	$0.534721\pi$
$444$	2.28614e6	0.550359
$445$	−1.08817e7	−2.60494
$446$	2.05888e6	0.490109
$447$	−4.44166e6	−1.05142
$448$	1.15869e6	0.272755
$449$	2.92825e6	0.685477	0.342739	−	0.939431i	$-0.388645\pi$
$449$	2.92825e6	0.685477	0.342739	+	0.939431i	$0.388645\pi$
$450$	4.59632e7	10.6999
$451$	−1.24506e6	−0.288236
$452$	1.60818e6	0.370245
$453$	6.68163e6	1.52981
$454$	−2.93142e6	−0.667480
$455$	45415.0	0.0102842
$456$	1.46231e6	0.329328
$457$	4.72735e6	1.05883	0.529417	−	0.848362i	$-0.322411\pi$
$457$	4.72735e6	1.05883	0.529417	+	0.848362i	$0.322411\pi$
$458$	−7.72058e6	−1.71983
$459$	8.16500e6	1.80894
$460$	1.45666e7	3.20969
$461$	493196.	0.108085	0.0540427	−	0.998539i	$-0.482789\pi$
$461$	493196.	0.108085	0.0540427	+	0.998539i	$0.482789\pi$
$462$	−938690.	−0.204605
$463$	−3.71373e6	−0.805116	−0.402558	−	0.915395i	$-0.631879\pi$
$463$	−3.71373e6	−0.805116	−0.402558	+	0.915395i	$0.631879\pi$
$464$	−1.21786e6	−0.262604
$465$	9.34548e6	2.00433
$466$	2.98308e6	0.636355
$467$	−3.47167e6	−0.736626	−0.368313	−	0.929702i	$-0.620064\pi$
$467$	−3.47167e6	−0.736626	−0.368313	+	0.929702i	$0.620064\pi$
$468$	679706.	0.143452
$469$	1.35282e6	0.283993
$470$	4.66630e6	0.974379
$471$	−1.04836e7	−2.17750
$472$	−4.50326e6	−0.930405
$473$	253388.	0.0520754
$474$	−2.48952e7	−5.08944
$475$	−1.65190e6	−0.335931
$476$	889965.	0.180034
$477$	1.23027e7	2.47573
$478$	−3.34187e6	−0.668990
$479$	3.20308e6	0.637865	0.318933	−	0.947777i	$-0.396676\pi$
$479$	3.20308e6	0.637865	0.318933	+	0.947777i	$0.396676\pi$
$480$	−1.29366e7	−2.56282
$481$	−25730.5	−0.00507091
$482$	1.29595e7	2.54080
$483$	−1.74789e6	−0.340915
$484$	−7.86430e6	−1.52597
$485$	7.06865e6	1.36453
$486$	−2.87976e7	−5.53052
$487$	−6.65811e6	−1.27212	−0.636060	−	0.771639i	$-0.719437\pi$
$487$	−6.65811e6	−1.27212	−0.636060	+	0.771639i	$0.719437\pi$
$488$	4.55146e6	0.865169
$489$	−6.97217e6	−1.31855
$490$	1.57927e7	2.97143
$491$	5.31309e6	0.994588	0.497294	−	0.867582i	$-0.334327\pi$
$491$	5.31309e6	0.994588	0.497294	+	0.867582i	$0.334327\pi$
$492$	−1.44600e7	−2.69313
$493$	2.57509e6	0.477172
$494$	−38381.8	−0.00707633
$495$	9.60751e6	1.76237
$496$	974819.	0.177918
$497$	1.45828e6	0.264819
$498$	5.86338e6	1.05944
$499$	−2.21587e6	−0.398375	−0.199188	−	0.979961i	$-0.563830\pi$
$499$	−2.21587e6	−0.398375	−0.199188	+	0.979961i	$0.563830\pi$
$500$	−2.58882e7	−4.63103
$501$	8.99908e6	1.60178
$502$	−163806.	−0.0290115
$503$	−5.95092e6	−1.04873	−0.524365	−	0.851493i	$-0.675697\pi$
$503$	−5.95092e6	−1.04873	−0.524365	+	0.851493i	$0.675697\pi$
$504$	−3.39630e6	−0.595565
$505$	−1.09541e7	−1.91139
$506$	3.38865e6	0.588370
$507$	1.10570e7	1.91037
$508$	5.75808e6	0.989962
$509$	6.97295e6	1.19295	0.596475	−	0.802632i	$-0.296568\pi$
$509$	6.97295e6	1.19295	0.596475	+	0.802632i	$0.296568\pi$
$510$	−1.96992e7	−3.35369
$511$	−639482.	−0.108337
$512$	−3.67061e6	−0.618819
$513$	2.61158e6	0.438136
$514$	−5.68417e6	−0.948985
$515$	5.01653e6	0.833460
$516$	2.94283e6	0.486566
$517$	690894.	0.113680
$518$	299828.	0.0490963
$519$	2.05974e7	3.35655
$520$	−438483.	−0.0711122
$521$	−3.97513e6	−0.641589	−0.320795	−	0.947149i	$-0.603950\pi$
$521$	−3.97513e6	−0.641589	−0.320795	+	0.947149i	$0.603950\pi$
$522$	−2.29174e7	−3.68120
$523$	−2.93948e6	−0.469911	−0.234956	−	0.972006i	$-0.575495\pi$
$523$	−2.93948e6	−0.469911	−0.234956	+	0.972006i	$0.575495\pi$
$524$	−5.10427e6	−0.812093
$525$	5.28089e6	0.836197
$526$	1.05440e7	1.66166
$527$	−2.06120e6	−0.323292
$528$	1.37940e6	0.215331
$529$	−126494.	−0.0196531
$530$	−1.85084e7	−2.86207
$531$	−1.28977e7	−1.98507
$532$	284655.	0.0436054
$533$	162748.	0.0248140
$534$	−2.94000e7	−4.46163
$535$	1.45227e7	2.19362
$536$	−1.30615e7	−1.96373
$537$	−1.03312e6	−0.154602
$538$	7.85840e6	1.17052
$539$	2.33827e6	0.346675
$540$	6.95776e7	10.2680
$541$	−1.09597e7	−1.60993	−0.804965	−	0.593323i	$-0.797816\pi$
$541$	−1.09597e7	−1.60993	−0.804965	+	0.593323i	$0.797816\pi$
$542$	1.09553e7	1.60186
$543$	1.91056e7	2.78075
$544$	2.85325e6	0.413374
$545$	−1.82661e7	−2.63424
$546$	122701.	0.0176144
$547$	−8.84531e6	−1.26399	−0.631997	−	0.774971i	$-0.717764\pi$
$547$	−8.84531e6	−1.26399	−0.631997	+	0.774971i	$0.717764\pi$
$548$	−9.73270e6	−1.38446
$549$	1.30357e7	1.84588
$550$	−1.02381e7	−1.44315
$551$	823643.	0.115574
$552$	1.68759e7	2.35733
$553$	−2.07805e6	−0.288963
$554$	1.54974e7	2.14529
$555$	−4.22395e6	−0.582085
$556$	−2.09717e7	−2.87705
$557$	−984.102	−0.000134401 0	−6.72004e−5	−	1.00000i	$-0.500021\pi$
$557$	−984.102	−0.000134401 0	−6.72004e−5		1.00000i	$0.500021\pi$
$558$	1.83440e7	2.49407
$559$	−33121.6	−0.00448314
$560$	777664.	0.104790
$561$	−2.91668e6	−0.391274
$562$	5.39731e6	0.720836
$563$	6.51133e6	0.865763	0.432882	−	0.901451i	$-0.357497\pi$
$563$	6.51133e6	0.865763	0.432882	+	0.901451i	$0.357497\pi$
$564$	8.02402e6	1.06217
$565$	−2.97133e6	−0.391589
$566$	2.31884e7	3.04249
$567$	−4.68710e6	−0.612275
$568$	−1.40797e7	−1.83115
$569$	1.29516e7	1.67704	0.838519	−	0.544872i	$-0.183422\pi$
$569$	1.29516e7	1.67704	0.838519	+	0.544872i	$0.183422\pi$
$570$	−6.30080e6	−0.812285
$571$	1.02361e7	1.31385	0.656924	−	0.753957i	$-0.271857\pi$
$571$	1.02361e7	1.31385	0.656924	+	0.753957i	$0.271857\pi$
$572$	−151402.	−0.0193482
$573$	621236.	0.0790442
$574$	−1.89644e6	−0.240248
$575$	−1.90639e7	−2.40460
$576$	−3.20410e7	−4.02393
$577$	−6.47900e6	−0.810156	−0.405078	−	0.914282i	$-0.632756\pi$
$577$	−6.47900e6	−0.810156	−0.405078	+	0.914282i	$0.632756\pi$
$578$	−8.97639e6	−1.11759
$579$	3.75738e6	0.465789
$580$	2.19435e7	2.70854
$581$	489427.	0.0601516
$582$	1.90979e7	2.33711
$583$	−2.74037e6	−0.333916
$584$	6.17422e6	0.749117
$585$	−1.25585e6	−0.151722
$586$	−142165.	−0.0171021
$587$	8.23312e6	0.986210	0.493105	−	0.869970i	$-0.335862\pi$
$587$	8.23312e6	0.986210	0.493105	+	0.869970i	$0.335862\pi$
$588$	2.71566e7	3.23916
$589$	−659276.	−0.0783032
$590$	1.94036e7	2.29484
$591$	2.07427e7	2.44284
$592$	−440597.	−0.0516699
$593$	−1.66873e7	−1.94872	−0.974361	−	0.224992i	$-0.927764\pi$
$593$	−1.66873e7	−1.94872	−0.974361	+	0.224992i	$0.927764\pi$
$594$	1.61860e7	1.88223
$595$	−1.64433e6	−0.190413
$596$	8.34792e6	0.962637
$597$	−1.32187e7	−1.51794
$598$	−442948.	−0.0506524
$599$	−1.25673e7	−1.43111	−0.715556	−	0.698556i	$-0.753826\pi$
$599$	−1.25673e7	−1.43111	−0.715556	+	0.698556i	$0.753826\pi$
$600$	−5.09871e7	−5.78206
$601$	7.97580e6	0.900716	0.450358	−	0.892848i	$-0.351296\pi$
$601$	7.97580e6	0.900716	0.450358	+	0.892848i	$0.351296\pi$
$602$	385954.	0.0434054
$603$	−3.74092e7	−4.18972
$604$	−1.25578e7	−1.40063
$605$	1.45303e7	1.61394
$606$	−2.95956e7	−3.27375
$607$	−7.19419e6	−0.792520	−0.396260	−	0.918138i	$-0.629692\pi$
$607$	−7.19419e6	−0.792520	−0.396260	+	0.918138i	$0.629692\pi$
$608$	912613.	0.100122
$609$	−2.63307e6	−0.287686
$610$	−1.96113e7	−2.13393
$611$	−90310.4	−0.00978667
$612$	−2.46100e7	−2.65603
$613$	7.20276e6	0.774190	0.387095	−	0.922040i	$-0.373478\pi$
$613$	7.20276e6	0.774190	0.387095	+	0.922040i	$0.373478\pi$
$614$	−2.16590e7	−2.31856
$615$	2.67169e7	2.84838
$616$	756511.	0.0803274
$617$	−7.61026e6	−0.804798	−0.402399	−	0.915464i	$-0.631824\pi$
$617$	−7.61026e6	−0.804798	−0.402399	+	0.915464i	$0.631824\pi$
$618$	1.35535e7	1.42752
$619$	−5.49138e6	−0.576043	−0.288021	−	0.957624i	$-0.592997\pi$
$619$	−5.49138e6	−0.576043	−0.288021	+	0.957624i	$0.592997\pi$
$620$	−1.75644e7	−1.83508
$621$	3.01391e7	3.13618
$622$	−1.41014e7	−1.46146
$623$	−2.45407e6	−0.253318
$624$	−180309.	−0.0185377
$625$	2.41154e7	2.46941
$626$	6.97093e6	0.710976
$627$	−932899.	−0.0947689
$628$	1.97034e7	1.99362
$629$	931620.	0.0938884
$630$	1.46339e7	1.46896
$631$	1.26501e7	1.26480	0.632398	−	0.774644i	$-0.282071\pi$
$631$	1.26501e7	1.26480	0.632398	+	0.774644i	$0.282071\pi$
$632$	2.00636e7	1.99810
$633$	−2.74271e7	−2.72064
$634$	1.20147e7	1.18711
$635$	−1.06388e7	−1.04703
$636$	−3.18265e7	−3.11994
$637$	−305648.	−0.0298451
$638$	5.10475e6	0.496504
$639$	−4.03254e7	−3.90685
$640$	3.43154e7	3.31161
$641$	−3.03674e6	−0.291920	−0.145960	−	0.989291i	$-0.546627\pi$
$641$	−3.03674e6	−0.291920	−0.145960	+	0.989291i	$0.546627\pi$
$642$	3.92370e7	3.75715
$643$	4.04000e6	0.385349	0.192675	−	0.981263i	$-0.438284\pi$
$643$	4.04000e6	0.385349	0.192675	+	0.981263i	$0.438284\pi$
$644$	3.28509e6	0.312128
$645$	−5.43728e6	−0.514615
$646$	1.38968e6	0.131019
$647$	4.81734e6	0.452425	0.226212	−	0.974078i	$-0.427366\pi$
$647$	4.81734e6	0.452425	0.226212	+	0.974078i	$0.427366\pi$
$648$	4.52541e7	4.23370
$649$	2.87291e6	0.267738
$650$	1.33828e6	0.124240
$651$	2.10761e6	0.194912
$652$	1.31039e7	1.20721
$653$	−5.61632e6	−0.515429	−0.257714	−	0.966221i	$-0.582969\pi$
$653$	−5.61632e6	−0.515429	−0.257714	+	0.966221i	$0.582969\pi$
$654$	−4.93510e7	−4.51182
$655$	9.43082e6	0.858908
$656$	2.78682e6	0.252842
$657$	1.76834e7	1.59828
$658$	1.05235e6	0.0947539
$659$	2.19550e6	0.196934	0.0984668	−	0.995140i	$-0.468606\pi$
$659$	2.19550e6	0.196934	0.0984668	+	0.995140i	$0.468606\pi$
$660$	−2.48543e7	−2.22096
$661$	−6.82480e6	−0.607556	−0.303778	−	0.952743i	$-0.598248\pi$
$661$	−6.82480e6	−0.607556	−0.303778	+	0.952743i	$0.598248\pi$
$662$	1.90386e7	1.68845
$663$	381254.	0.0336845
$664$	−4.72543e6	−0.415931
$665$	−525939.	−0.0461191
$666$	−8.29108e6	−0.724312
$667$	9.50532e6	0.827280
$668$	−1.69134e7	−1.46653
$669$	−6.54133e6	−0.565068
$670$	5.62794e7	4.84353
$671$	−2.90365e6	−0.248965
$672$	−2.91749e6	−0.249222
$673$	−2.73269e6	−0.232569	−0.116285	−	0.993216i	$-0.537098\pi$
$673$	−2.73269e6	−0.232569	−0.116285	+	0.993216i	$0.537098\pi$
$674$	−2.03049e7	−1.72167
$675$	−9.10591e7	−7.69243
$676$	−2.07811e7	−1.74905
$677$	2.30210e6	0.193043	0.0965213	−	0.995331i	$-0.469228\pi$
$677$	2.30210e6	0.193043	0.0965213	+	0.995331i	$0.469228\pi$
$678$	−8.02788e6	−0.670697
$679$	1.59414e6	0.132694
$680$	1.58760e7	1.31665
$681$	9.31351e6	0.769566
$682$	−4.08604e6	−0.336389
$683$	1.93085e7	1.58379	0.791894	−	0.610658i	$-0.209095\pi$
$683$	1.93085e7	1.58379	0.791894	+	0.610658i	$0.209095\pi$
$684$	−7.87150e6	−0.643306
$685$	1.79825e7	1.46428
$686$	7.24255e6	0.587599
$687$	2.45293e7	1.98287
$688$	−567158.	−0.0456808
$689$	358208.	0.0287466
$690$	−7.27149e7	−5.81434
$691$	−9.81295e6	−0.781815	−0.390908	−	0.920430i	$-0.627839\pi$
$691$	−9.81295e6	−0.781815	−0.390908	+	0.920430i	$0.627839\pi$
$692$	−3.87119e7	−3.07312
$693$	2.16671e6	0.171383
$694$	−1.42248e7	−1.12111
$695$	3.87481e7	3.04290
$696$	2.54224e7	1.98927
$697$	−5.89257e6	−0.459434
$698$	2.95530e7	2.29595
$699$	−9.47763e6	−0.733680
$700$	−9.92521e6	−0.765587
$701$	−3.09383e6	−0.237795	−0.118897	−	0.992907i	$-0.537936\pi$
$701$	−3.09383e6	−0.237795	−0.118897	+	0.992907i	$0.537936\pi$
$702$	−2.11575e6	−0.162040
$703$	297979.	0.0227403
$704$	7.13701e6	0.542731
$705$	−1.48255e7	−1.12340
$706$	−2.23765e7	−1.68959
$707$	−2.47039e6	−0.185874
$708$	3.33658e7	2.50161
$709$	−1.20196e7	−0.897998	−0.448999	−	0.893532i	$-0.648219\pi$
$709$	−1.20196e7	−0.897998	−0.448999	+	0.893532i	$0.648219\pi$
$710$	6.06666e7	4.51652
$711$	5.74637e7	4.26304
$712$	2.36941e7	1.75162
$713$	−7.60843e6	−0.560495
$714$	−4.44261e6	−0.326131
$715$	279735.	0.0204636
$716$	1.94171e6	0.141547
$717$	1.06176e7	0.771307
$718$	−2.97851e7	−2.15620
$719$	−6.45188e6	−0.465440	−0.232720	−	0.972544i	$-0.574763\pi$
$719$	−6.45188e6	−0.465440	−0.232720	+	0.972544i	$0.574763\pi$
$720$	−2.15045e7	−1.54596
$721$	1.13134e6	0.0810502
$722$	−2.27864e7	−1.62680
$723$	−4.11741e7	−2.92940
$724$	−3.59082e7	−2.54594
$725$	−2.87184e7	−2.02915
$726$	3.92578e7	2.76429
$727$	1.01862e7	0.714784	0.357392	−	0.933954i	$-0.383666\pi$
$727$	1.01862e7	0.714784	0.357392	+	0.933954i	$0.383666\pi$
$728$	−98887.6	−0.00691534
$729$	4.27029e7	2.97604
$730$	−2.66034e7	−1.84769
$731$	1.19923e6	0.0830057
$732$	−3.37229e7	−2.32620
$733$	2.73462e7	1.87991	0.939956	−	0.341296i	$-0.110866\pi$
$733$	2.73462e7	1.87991	0.939956	+	0.341296i	$0.110866\pi$
$734$	3.69471e7	2.53128
$735$	−5.01755e7	−3.42589
$736$	1.05321e7	0.716671
$737$	8.33275e6	0.565093
$738$	5.24418e7	3.54435
$739$	−2.55931e7	−1.72390	−0.861951	−	0.506991i	$-0.830758\pi$
$739$	−2.55931e7	−1.72390	−0.861951	+	0.506991i	$0.830758\pi$
$740$	7.93874e6	0.532933
$741$	121944.	0.00815860
$742$	−4.17406e6	−0.278323
$743$	1.73154e7	1.15070	0.575349	−	0.817908i	$-0.304866\pi$
$743$	1.73154e7	1.15070	0.575349	+	0.817908i	$0.304866\pi$
$744$	−2.03491e7	−1.34776
$745$	−1.54239e7	−1.01813
$746$	1.57004e6	0.103291
$747$	−1.35340e7	−0.887411
$748$	5.48177e6	0.358234
$749$	3.27518e6	0.213320
$750$	1.29231e8	8.38909
$751$	2.68439e6	0.173678	0.0868391	−	0.996222i	$-0.472323\pi$
$751$	2.68439e6	0.173678	0.0868391	+	0.996222i	$0.472323\pi$
$752$	−1.54643e6	−0.0997209
$753$	520434.	0.0334486
$754$	−667269.	−0.0427437
$755$	2.32023e7	1.48137
$756$	1.56913e7	0.998514
$757$	−2.03294e7	−1.28939	−0.644697	−	0.764438i	$-0.723016\pi$
$757$	−2.03294e7	−1.28939	−0.644697	+	0.764438i	$0.723016\pi$
$758$	4.20070e6	0.265551
$759$	−1.07662e7	−0.678356
$760$	5.07795e6	0.318900
$761$	−5.23788e6	−0.327864	−0.163932	−	0.986472i	$-0.552418\pi$
$761$	−5.23788e6	−0.327864	−0.163932	+	0.986472i	$0.552418\pi$
$762$	−2.87437e7	−1.79331
$763$	−4.11942e6	−0.256168
$764$	−1.16759e6	−0.0723695
$765$	4.54702e7	2.80914
$766$	−2.45392e7	−1.51108
$767$	−375533.	−0.0230494
$768$	4.53669e7	2.77547
$769$	−3.24296e7	−1.97754	−0.988772	−	0.149435i	$-0.952255\pi$
$769$	−3.24296e7	−1.97754	−0.988772	+	0.149435i	$0.952255\pi$
$770$	−3.25965e6	−0.198127
$771$	1.80594e7	1.09412
$772$	−7.06184e6	−0.426457
$773$	−1.94010e7	−1.16782	−0.583908	−	0.811820i	$-0.698477\pi$
$773$	−1.94010e7	−1.16782	−0.583908	+	0.811820i	$0.698477\pi$
$774$	−1.06727e7	−0.640356
$775$	2.29873e7	1.37478
$776$	−1.53914e7	−0.917540
$777$	−952595.	−0.0566051
$778$	−2.21049e7	−1.30930
$779$	−1.88474e6	−0.111278
$780$	3.24883e6	0.191201
$781$	8.98232e6	0.526940
$782$	1.60377e7	0.937834
$783$	4.54024e7	2.64651
$784$	−5.23376e6	−0.304105
$785$	−3.64048e7	−2.10855
$786$	2.54800e7	1.47110
$787$	−2.35480e7	−1.35524	−0.677621	−	0.735411i	$-0.736989\pi$
$787$	−2.35480e7	−1.35524	−0.677621	+	0.735411i	$0.736989\pi$
$788$	−3.89850e7	−2.23657
$789$	−3.34998e7	−1.91580
$790$	−8.64498e7	−4.92829
$791$	−670101.	−0.0380802
$792$	−2.09196e7	−1.18506
$793$	379552.	0.0214332
$794$	1.34872e7	0.759227
$795$	5.88037e7	3.29980
$796$	2.48441e7	1.38976
$797$	2.01087e6	0.112134	0.0560672	−	0.998427i	$-0.482144\pi$
$797$	2.01087e6	0.112134	0.0560672	+	0.998427i	$0.482144\pi$
$798$	−1.42097e6	−0.0789910
$799$	3.26985e6	0.181201
$800$	−3.18205e7	−1.75785
$801$	6.78617e7	3.73717
$802$	1.14907e7	0.630830
$803$	−3.93891e6	−0.215570
$804$	9.67763e7	5.27994
$805$	−6.06964e6	−0.330121
$806$	534108.	0.0289595
$807$	−2.49672e7	−1.34954
$808$	2.38517e7	1.28526
$809$	−2.95891e6	−0.158950	−0.0794749	−	0.996837i	$-0.525324\pi$
$809$	−2.95891e6	−0.158950	−0.0794749	+	0.996837i	$0.525324\pi$
$810$	−1.94990e8	−10.4424
$811$	−2.66351e7	−1.42201	−0.711003	−	0.703189i	$-0.751759\pi$
$811$	−2.66351e7	−1.42201	−0.711003	+	0.703189i	$0.751759\pi$
$812$	4.94874e6	0.263393
$813$	−3.48063e7	−1.84685
$814$	1.84680e6	0.0976922
$815$	−2.42112e7	−1.27680
$816$	6.52841e6	0.343227
$817$	383573.	0.0201045
$818$	−3.04521e7	−1.59124
$819$	−283222.	−0.0147542
$820$	−5.02132e7	−2.60785
$821$	1.80920e7	0.936758	0.468379	−	0.883528i	$-0.344838\pi$
$821$	1.80920e7	0.936758	0.468379	+	0.883528i	$0.344838\pi$
$822$	4.85846e7	2.50795
$823$	2.46425e7	1.26819	0.634097	−	0.773254i	$-0.281372\pi$
$823$	2.46425e7	1.26819	0.634097	+	0.773254i	$0.281372\pi$
$824$	−1.09231e7	−0.560438
$825$	3.25278e7	1.66387
$826$	4.37594e6	0.223163
$827$	1.25320e6	0.0637172	0.0318586	−	0.999492i	$-0.489857\pi$
$827$	1.25320e6	0.0637172	0.0318586	+	0.999492i	$0.489857\pi$
$828$	−9.08417e7	−4.60479
$829$	2.38722e7	1.20644	0.603222	−	0.797573i	$-0.293883\pi$
$829$	2.38722e7	1.20644	0.603222	+	0.797573i	$0.293883\pi$
$830$	2.03609e7	1.02589
$831$	−4.92375e7	−2.47339
$832$	−932916.	−0.0467234
$833$	1.10665e7	0.552584
$834$	1.04689e8	5.21176
$835$	3.12498e7	1.55107
$836$	1.75334e6	0.0867664
$837$	−3.63418e7	−1.79305
$838$	4.50117e7	2.21419
$839$	−2.04904e7	−1.00495	−0.502477	−	0.864591i	$-0.667578\pi$
$839$	−2.04904e7	−1.00495	−0.502477	+	0.864591i	$0.667578\pi$
$840$	−1.62335e7	−0.793805
$841$	−6.19208e6	−0.301889
$842$	3.58181e6	0.174110
$843$	−1.71480e7	−0.831082
$844$	5.15481e7	2.49090
$845$	3.83960e7	1.84988
$846$	−2.91005e7	−1.39789
$847$	3.27692e6	0.156948
$848$	6.13377e6	0.292913
$849$	−7.36726e7	−3.50782
$850$	−4.84546e7	−2.30032
$851$	3.43885e6	0.162775
$852$	1.04320e8	4.92346
$853$	1.80941e7	0.851463	0.425731	−	0.904850i	$-0.360017\pi$
$853$	1.80941e7	0.851463	0.425731	+	0.904850i	$0.360017\pi$
$854$	−4.42277e6	−0.207515
$855$	1.45437e7	0.680390
$856$	−3.16220e7	−1.47504
$857$	3.46313e7	1.61071	0.805353	−	0.592795i	$-0.201976\pi$
$857$	3.46313e7	1.61071	0.805353	+	0.592795i	$0.201976\pi$
$858$	755782.	0.0350492
$859$	−5.63360e6	−0.260497	−0.130249	−	0.991481i	$-0.541578\pi$
$859$	−5.63360e6	−0.260497	−0.130249	+	0.991481i	$0.541578\pi$
$860$	1.02191e7	0.471160
$861$	6.02524e6	0.276992
$862$	5.87043e7	2.69092
$863$	1.37529e6	0.0628589	0.0314294	−	0.999506i	$-0.489994\pi$
$863$	1.37529e6	0.0628589	0.0314294	+	0.999506i	$0.489994\pi$
$864$	5.03067e7	2.29267
$865$	7.15254e7	3.25028
$866$	−6.97414e7	−3.16007
$867$	2.85192e7	1.28852
$868$	−3.96117e6	−0.178453
$869$	−1.27998e7	−0.574982
$870$	−1.09540e8	−4.90651
$871$	−1.08922e6	−0.0486485
$872$	3.97731e7	1.77132
$873$	−4.40823e7	−1.95762
$874$	5.12967e6	0.227149
$875$	1.07872e7	0.476307
$876$	−4.57464e7	−2.01417
$877$	−1.11744e7	−0.490599	−0.245299	−	0.969447i	$-0.578886\pi$
$877$	−1.11744e7	−0.490599	−0.245299	+	0.969447i	$0.578886\pi$
$878$	−5.22512e7	−2.28749
$879$	451677.	0.0197177
$880$	4.79005e6	0.208513
$881$	−1.92594e7	−0.835995	−0.417998	−	0.908448i	$-0.637268\pi$
$881$	−1.92594e7	−0.835995	−0.417998	+	0.908448i	$0.637268\pi$
$882$	−9.84880e7	−4.26297
$883$	2.37744e7	1.02614	0.513072	−	0.858345i	$-0.328507\pi$
$883$	2.37744e7	1.02614	0.513072	+	0.858345i	$0.328507\pi$
$884$	−716551.	−0.0308401
$885$	−6.16479e7	−2.64582
$886$	−8.43750e6	−0.361102
$887$	1.09954e7	0.469249	0.234624	−	0.972086i	$-0.424614\pi$
$887$	1.09954e7	0.469249	0.234624	+	0.972086i	$0.424614\pi$
$888$	9.19733e6	0.391408
$889$	−2.39929e6	−0.101819
$890$	−1.02093e8	−4.32036
$891$	−2.88703e7	−1.21831
$892$	1.22941e7	0.517352
$893$	1.04586e6	0.0438880
$894$	−4.16719e7	−1.74381
$895$	−3.58756e6	−0.149707
$896$	7.73888e6	0.322039
$897$	1.40731e6	0.0583993
$898$	2.74730e7	1.13688
$899$	−1.14615e7	−0.472981
$900$	2.74459e8	11.2946
$901$	−1.29695e7	−0.532246
$902$	−1.16812e7	−0.478047
$903$	−1.22623e6	−0.0500439
$904$	6.46984e6	0.263313
$905$	6.63453e7	2.69270
$906$	6.26874e7	2.53723
$907$	−3.49064e7	−1.40892	−0.704460	−	0.709744i	$-0.748811\pi$
$907$	−3.49064e7	−1.40892	−0.704460	+	0.709744i	$0.748811\pi$
$908$	−1.75044e7	−0.704582
$909$	6.83132e7	2.74217
$910$	426086.	0.0170566
$911$	−2.01707e7	−0.805238	−0.402619	−	0.915368i	$-0.631900\pi$
$911$	−2.01707e7	−0.805238	−0.402619	+	0.915368i	$0.631900\pi$
$912$	2.08811e6	0.0831317
$913$	3.01464e6	0.119690
$914$	4.43523e7	1.75611
$915$	6.23076e7	2.46030
$916$	−4.61018e7	−1.81543
$917$	2.12686e6	0.0835248
$918$	7.66045e7	3.00018
$919$	6.51985e6	0.254653	0.127326	−	0.991861i	$-0.459360\pi$
$919$	6.51985e6	0.254653	0.127326	+	0.991861i	$0.459360\pi$
$920$	5.86025e7	2.28269
$921$	6.88137e7	2.67317
$922$	4.62719e6	0.179263
$923$	−1.17413e6	−0.0453639
$924$	−5.60519e6	−0.215978
$925$	−1.03898e7	−0.399256
$926$	−3.48425e7	−1.33531
$927$	−3.12846e7	−1.19573
$928$	1.58658e7	0.604773
$929$	1.41643e7	0.538462	0.269231	−	0.963076i	$-0.413230\pi$
$929$	1.41643e7	0.538462	0.269231	+	0.963076i	$0.413230\pi$
$930$	8.76798e7	3.32424
$931$	3.53963e6	0.133839
$932$	1.78128e7	0.671727
$933$	4.48021e7	1.68498
$934$	−3.25714e7	−1.22171
$935$	−1.01283e7	−0.378885
$936$	2.73451e6	0.102021
$937$	−2.97422e6	−0.110669	−0.0553343	−	0.998468i	$-0.517622\pi$
$937$	−2.97422e6	−0.110669	−0.0553343	+	0.998468i	$0.517622\pi$
$938$	1.26922e7	0.471011
$939$	−2.21476e7	−0.819714
$940$	2.78638e7	1.02854
$941$	−1.11860e6	−0.0411812	−0.0205906	−	0.999788i	$-0.506555\pi$
$941$	−1.11860e6	−0.0411812	−0.0205906	+	0.999788i	$0.506555\pi$
$942$	−9.83575e7	−3.61144
$943$	−2.17510e7	−0.796526
$944$	−6.43044e6	−0.234861
$945$	−2.89917e7	−1.05608
$946$	2.37730e6	0.0863685
$947$	−8.53925e6	−0.309417	−0.154709	−	0.987960i	$-0.549444\pi$
$947$	−8.53925e6	−0.309417	−0.154709	+	0.987960i	$0.549444\pi$
$948$	−1.48657e8	−5.37234
$949$	514876.	0.0185583
$950$	−1.54982e7	−0.557151
$951$	−3.81723e7	−1.36866
$952$	3.58040e6	0.128038
$953$	−2.73399e7	−0.975135	−0.487568	−	0.873085i	$-0.662116\pi$
$953$	−2.73399e7	−0.975135	−0.487568	+	0.873085i	$0.662116\pi$
$954$	1.15424e8	4.10607
$955$	2.15727e6	0.0765414
$956$	−1.99553e7	−0.706176
$957$	−1.62185e7	−0.572441
$958$	3.00515e7	1.05792
$959$	4.05544e6	0.142394
$960$	−1.53148e8	−5.36333
$961$	−1.94549e7	−0.679548
$962$	−241405.	−0.00841026
$963$	−9.05679e7	−3.14708
$964$	7.73850e7	2.68203
$965$	1.30477e7	0.451041
$966$	−1.63988e7	−0.565418
$967$	1.83503e7	0.631068	0.315534	−	0.948914i	$-0.397816\pi$
$967$	1.83503e7	0.631068	0.315534	+	0.948914i	$0.397816\pi$
$968$	−3.16387e7	−1.08525
$969$	−4.41520e6	−0.151057
$970$	6.63184e7	2.26311
$971$	−1.81599e7	−0.618109	−0.309055	−	0.951044i	$-0.600013\pi$
$971$	−1.81599e7	−0.618109	−0.309055	+	0.951044i	$0.600013\pi$
$972$	−1.71959e8	−5.83793
$973$	8.73856e6	0.295909
$974$	−6.24667e7	−2.10985
$975$	−4.25188e6	−0.143242
$976$	6.49926e6	0.218393
$977$	−3.94197e6	−0.132123	−0.0660613	−	0.997816i	$-0.521043\pi$
$977$	−3.94197e6	−0.132123	−0.0660613	+	0.997816i	$0.521043\pi$
$978$	−6.54132e7	−2.18685
$979$	−1.51159e7	−0.504055
$980$	9.43027e7	3.13660
$981$	1.13913e8	3.77921
$982$	4.98477e7	1.64955
$983$	−2.64682e7	−0.873658	−0.436829	−	0.899545i	$-0.643899\pi$
$983$	−2.64682e7	−0.873658	−0.436829	+	0.899545i	$0.643899\pi$
$984$	−5.81739e7	−1.91532
$985$	7.20299e7	2.36550
$986$	2.41597e7	0.791404
$987$	−3.34347e6	−0.109246
$988$	−229189.	−0.00746967
$989$	4.42665e6	0.143908
$990$	9.01382e7	2.92295
$991$	−1.71123e6	−0.0553510	−0.0276755	−	0.999617i	$-0.508811\pi$
$991$	−1.71123e6	−0.0553510	−0.0276755	+	0.999617i	$0.508811\pi$
$992$	−1.26996e7	−0.409743
$993$	−6.04881e7	−1.94669
$994$	1.36817e7	0.439211
$995$	−4.59028e7	−1.46988
$996$	3.50119e7	1.11832
$997$	1.72856e6	0.0550741	0.0275370	−	0.999621i	$-0.491234\pi$
$997$	1.72856e6	0.0550741	0.0275370	+	0.999621i	$0.491234\pi$
$998$	−2.07894e7	−0.660717
$999$	1.64257e7	0.520728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.a.a.1.7	✓	7
3.2	odd	2		333.6.a.c.1.1		7
4.3	odd	2		592.6.a.g.1.7		7
5.4	even	2		925.6.a.a.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.a.a.1.7	✓	7	1.1	even	1	trivial
333.6.a.c.1.1		7	3.2	odd	2
592.6.a.g.1.7		7	4.3	odd	2
925.6.a.a.1.1		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+9.38206 q^{2} -29.8081 q^{3} +56.0230 q^{4} -103.510 q^{5} -279.661 q^{6} -23.3438 q^{7} +225.385 q^{8} +645.520 q^{9} +O(q^{10})\)	\(q+9.38206 q^{2} -29.8081 q^{3} +56.0230 q^{4} -103.510 q^{5} -279.661 q^{6} -23.3438 q^{7} +225.385 q^{8} +645.520 q^{9} -971.136 q^{10} -143.787 q^{11} -1669.94 q^{12} +18.7951 q^{13} -219.013 q^{14} +3085.43 q^{15} +321.839 q^{16} -680.511 q^{17} +6056.30 q^{18} -217.662 q^{19} -5798.94 q^{20} +695.833 q^{21} -1349.02 q^{22} -2511.94 q^{23} -6718.29 q^{24} +7589.31 q^{25} +176.337 q^{26} -11998.3 q^{27} -1307.79 q^{28} -3784.05 q^{29} +28947.7 q^{30} +3028.91 q^{31} -4192.81 q^{32} +4286.01 q^{33} -6384.59 q^{34} +2416.31 q^{35} +36163.9 q^{36} -1369.00 q^{37} -2042.11 q^{38} -560.246 q^{39} -23329.6 q^{40} +8659.04 q^{41} +6528.34 q^{42} -1762.24 q^{43} -8055.37 q^{44} -66817.7 q^{45} -23567.2 q^{46} -4804.99 q^{47} -9593.39 q^{48} -16262.1 q^{49} +71203.3 q^{50} +20284.7 q^{51} +1052.96 q^{52} +19058.5 q^{53} -112569. q^{54} +14883.4 q^{55} -5261.34 q^{56} +6488.07 q^{57} -35502.2 q^{58} -19980.3 q^{59} +172855. q^{60} +20194.1 q^{61} +28417.4 q^{62} -15068.9 q^{63} -49636.0 q^{64} -1945.48 q^{65} +40211.6 q^{66} -57952.1 q^{67} -38124.3 q^{68} +74876.1 q^{69} +22670.0 q^{70} -62469.7 q^{71} +145490. q^{72} +27394.1 q^{73} -12844.0 q^{74} -226222. q^{75} -12194.0 q^{76} +3356.53 q^{77} -5256.26 q^{78} +89019.3 q^{79} -33313.5 q^{80} +200786. q^{81} +81239.6 q^{82} -20966.0 q^{83} +38982.6 q^{84} +70439.7 q^{85} -16533.5 q^{86} +112795. q^{87} -32407.4 q^{88} +105127. q^{89} -626888. q^{90} -438.750 q^{91} -140726. q^{92} -90285.8 q^{93} -45080.7 q^{94} +22530.1 q^{95} +124979. q^{96} -68289.6 q^{97} -152572. q^{98} -92817.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * q^99

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