LMFDB - Embedded newform 37.6.a.a.1.6

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			1.6
Root			$-5.27747$ 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)

$f(q)$	$=$	$q+4.27747 q^{2} -11.5828 q^{3} -13.7033 q^{4} +12.1163 q^{5} -49.5451 q^{6} -81.5934 q^{7} -195.494 q^{8} -108.839 q^{9} +O(q^{10})$	\(q+4.27747 q^{2} -11.5828 q^{3} -13.7033 q^{4} +12.1163 q^{5} -49.5451 q^{6} -81.5934 q^{7} -195.494 q^{8} -108.839 q^{9} +51.8273 q^{10} -669.522 q^{11} +158.722 q^{12} +731.302 q^{13} -349.013 q^{14} -140.341 q^{15} -397.717 q^{16} +2139.30 q^{17} -465.554 q^{18} -1873.50 q^{19} -166.033 q^{20} +945.080 q^{21} -2863.86 q^{22} +1805.94 q^{23} +2264.37 q^{24} -2978.19 q^{25} +3128.12 q^{26} +4075.28 q^{27} +1118.09 q^{28} -7021.16 q^{29} -600.305 q^{30} +1027.32 q^{31} +4554.60 q^{32} +7754.95 q^{33} +9150.81 q^{34} -988.613 q^{35} +1491.44 q^{36} -1369.00 q^{37} -8013.85 q^{38} -8470.53 q^{39} -2368.68 q^{40} +3981.24 q^{41} +4042.55 q^{42} -10090.7 q^{43} +9174.64 q^{44} -1318.73 q^{45} +7724.87 q^{46} -24945.1 q^{47} +4606.67 q^{48} -10149.5 q^{49} -12739.1 q^{50} -24779.1 q^{51} -10021.2 q^{52} -17506.0 q^{53} +17431.9 q^{54} -8112.16 q^{55} +15951.0 q^{56} +21700.4 q^{57} -30032.8 q^{58} +19971.5 q^{59} +1923.13 q^{60} +2448.28 q^{61} +4394.34 q^{62} +8880.51 q^{63} +32209.1 q^{64} +8860.70 q^{65} +33171.5 q^{66} +33346.1 q^{67} -29315.4 q^{68} -20917.9 q^{69} -4228.76 q^{70} -28905.6 q^{71} +21277.3 q^{72} +52166.7 q^{73} -5855.86 q^{74} +34495.8 q^{75} +25673.1 q^{76} +54628.6 q^{77} -36232.4 q^{78} -63554.1 q^{79} -4818.87 q^{80} -20755.4 q^{81} +17029.6 q^{82} -76458.7 q^{83} -12950.7 q^{84} +25920.6 q^{85} -43162.5 q^{86} +81324.8 q^{87} +130888. q^{88} +28317.8 q^{89} -5640.81 q^{90} -59669.4 q^{91} -24747.3 q^{92} -11899.3 q^{93} -106702. q^{94} -22700.0 q^{95} -52755.0 q^{96} -33835.5 q^{97} -43414.3 q^{98} +72869.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.27747	0.756157	0.378078	−	0.925774i	$-0.376585\pi$
$2$	4.27747	0.756157	0.378078	+	0.925774i	$0.376585\pi$
$3$	−11.5828	−0.743037	−0.371519	−	0.928425i	$-0.621163\pi$
$3$	−11.5828	−0.743037	−0.371519	+	0.928425i	$0.621163\pi$
$4$	−13.7033	−0.428227
$5$	12.1163	0.216744	0.108372	−	0.994110i	$-0.465436\pi$
$5$	12.1163	0.216744	0.108372	+	0.994110i	$0.465436\pi$
$6$	−49.5451	−0.561853
$7$	−81.5934	−0.629375	−0.314688	−	0.949195i	$-0.601900\pi$
$7$	−81.5934	−0.629375	−0.314688	+	0.949195i	$0.601900\pi$
$8$	−195.494	−1.07996
$9$	−108.839	−0.447896
$10$	51.8273	0.163892
$11$	−669.522	−1.66834	−0.834168	−	0.551511i	$-0.814052\pi$
$11$	−669.522	−1.66834	−0.834168	+	0.551511i	$0.814052\pi$
$12$	158.722	0.318188
$13$	731.302	1.20016	0.600079	−	0.799941i	$-0.295136\pi$
$13$	731.302	1.20016	0.600079	+	0.799941i	$0.295136\pi$
$14$	−349.013	−0.475907
$15$	−140.341	−0.161049
$16$	−397.717	−0.388395
$17$	2139.30	1.79536	0.897678	−	0.440653i	$-0.145253\pi$
$17$	2139.30	1.79536	0.897678	+	0.440653i	$0.145253\pi$
$18$	−465.554	−0.338679
$19$	−1873.50	−1.19061	−0.595306	−	0.803499i	$-0.702969\pi$
$19$	−1873.50	−1.19061	−0.595306	+	0.803499i	$0.702969\pi$
$20$	−166.033	−0.0928155
$21$	945.080	0.467649
$22$	−2863.86	−1.26152
$23$	1805.94	0.711844	0.355922	−	0.934516i	$-0.384167\pi$
$23$	1805.94	0.711844	0.355922	+	0.934516i	$0.384167\pi$
$24$	2264.37	0.802453
$25$	−2978.19	−0.953022
$26$	3128.12	0.907507
$27$	4075.28	1.07584
$28$	1118.09	0.269515
$29$	−7021.16	−1.55029	−0.775147	−	0.631781i	$-0.782324\pi$
$29$	−7021.16	−1.55029	−0.775147	+	0.631781i	$0.782324\pi$
$30$	−600.305	−0.121778
$31$	1027.32	0.192000	0.0960002	−	0.995381i	$-0.469395\pi$
$31$	1027.32	0.192000	0.0960002	+	0.995381i	$0.469395\pi$
$32$	4554.60	0.786276
$33$	7754.95	1.23964
$34$	9150.81	1.35757
$35$	−988.613	−0.136413
$36$	1491.44	0.191801
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	−8013.85	−0.900290
$39$	−8470.53	−0.891762
$40$	−2368.68	−0.234075
$41$	3981.24	0.369878	0.184939	−	0.982750i	$-0.440791\pi$
$41$	3981.24	0.369878	0.184939	+	0.982750i	$0.440791\pi$
$42$	4042.55	0.353616
$43$	−10090.7	−0.832240	−0.416120	−	0.909310i	$-0.636610\pi$
$43$	−10090.7	−0.832240	−0.416120	+	0.909310i	$0.636610\pi$
$44$	9174.64	0.714426
$45$	−1318.73	−0.0970786
$46$	7724.87	0.538266
$47$	−24945.1	−1.64718	−0.823589	−	0.567188i	$-0.808031\pi$
$47$	−24945.1	−1.64718	−0.823589	+	0.567188i	$0.808031\pi$
$48$	4606.67	0.288592
$49$	−10149.5	−0.603887
$50$	−12739.1	−0.720634
$51$	−24779.1	−1.33402
$52$	−10021.2	−0.513940
$53$	−17506.0	−0.856047	−0.428023	−	0.903768i	$-0.640790\pi$
$53$	−17506.0	−0.856047	−0.428023	+	0.903768i	$0.640790\pi$
$54$	17431.9	0.813504
$55$	−8112.16	−0.361601
$56$	15951.0	0.679702
$57$	21700.4	0.884670
$58$	−30032.8	−1.17227
$59$	19971.5	0.746933	0.373466	−	0.927644i	$-0.378169\pi$
$59$	19971.5	0.746933	0.373466	+	0.927644i	$0.378169\pi$
$60$	1923.13	0.0689654
$61$	2448.28	0.0842436	0.0421218	−	0.999112i	$-0.486588\pi$
$61$	2448.28	0.0842436	0.0421218	+	0.999112i	$0.486588\pi$
$62$	4394.34	0.145182
$63$	8880.51	0.281894
$64$	32209.1	0.982943
$65$	8860.70	0.260127
$66$	33171.5	0.937359
$67$	33346.1	0.907523	0.453761	−	0.891123i	$-0.350082\pi$
$67$	33346.1	0.907523	0.453761	+	0.891123i	$0.350082\pi$
$68$	−29315.4	−0.768819
$69$	−20917.9	−0.528926
$70$	−4228.76	−0.103150
$71$	−28905.6	−0.680512	−0.340256	−	0.940333i	$-0.610514\pi$
$71$	−28905.6	−0.680512	−0.340256	+	0.940333i	$0.610514\pi$
$72$	21277.3	0.483711
$73$	52166.7	1.14574	0.572870	−	0.819646i	$-0.305830\pi$
$73$	52166.7	1.14574	0.572870	+	0.819646i	$0.305830\pi$
$74$	−5855.86	−0.124311
$75$	34495.8	0.708131
$76$	25673.1	0.509852
$77$	54628.6	1.05001
$78$	−36232.4	−0.674312
$79$	−63554.1	−1.14571	−0.572856	−	0.819656i	$-0.694165\pi$
$79$	−63554.1	−1.14571	−0.572856	+	0.819656i	$0.694165\pi$
$80$	−4818.87	−0.0841822
$81$	−20755.4	−0.351494
$82$	17029.6	0.279686
$83$	−76458.7	−1.21824	−0.609118	−	0.793079i	$-0.708477\pi$
$83$	−76458.7	−1.21824	−0.609118	+	0.793079i	$0.708477\pi$
$84$	−12950.7	−0.200260
$85$	25920.6	0.389132
$86$	−43162.5	−0.629304
$87$	81324.8	1.15193
$88$	130888.	1.80174
$89$	28317.8	0.378952	0.189476	−	0.981885i	$-0.439321\pi$
$89$	28317.8	0.378952	0.189476	+	0.981885i	$0.439321\pi$
$90$	−5640.81	−0.0734066
$91$	−59669.4	−0.755350
$92$	−24747.3	−0.304831
$93$	−11899.3	−0.142664
$94$	−106702.	−1.24552
$95$	−22700.0	−0.258058
$96$	−52755.0	−0.584232
$97$	−33835.5	−0.365126	−0.182563	−	0.983194i	$-0.558439\pi$
$97$	−33835.5	−0.365126	−0.182563	+	0.983194i	$0.558439\pi$
$98$	−43414.3	−0.456633
$99$	72869.9	0.747240
$100$	40811.0	0.408110
$101$	49212.3	0.480032	0.240016	−	0.970769i	$-0.422847\pi$
$101$	49212.3	0.480032	0.240016	+	0.970769i	$0.422847\pi$
$102$	−105992.	−1.00873
$103$	−805.348	−0.00747981	−0.00373991	−	0.999993i	$-0.501190\pi$
$103$	−805.348	−0.00747981	−0.00373991	+	0.999993i	$0.501190\pi$
$104$	−142965.	−1.29613
$105$	11450.9	0.101360
$106$	−74881.4	−0.647306
$107$	82005.5	0.692443	0.346221	−	0.938153i	$-0.387465\pi$
$107$	82005.5	0.692443	0.346221	+	0.938153i	$0.387465\pi$
$108$	−55844.6	−0.460704
$109$	143816.	1.15942	0.579712	−	0.814821i	$-0.303165\pi$
$109$	143816.	1.15942	0.579712	+	0.814821i	$0.303165\pi$
$110$	−34699.5	−0.273427
$111$	15856.9	0.122155
$112$	32451.0	0.244446
$113$	−245838.	−1.81114	−0.905571	−	0.424195i	$-0.860557\pi$
$113$	−245838.	−1.81114	−0.905571	+	0.424195i	$0.860557\pi$
$114$	92822.9	0.668949
$115$	21881.4	0.154288
$116$	96212.8	0.663877
$117$	−79593.9	−0.537545
$118$	85427.6	0.564798
$119$	−174553.	−1.12995
$120$	27435.9	0.173927
$121$	287209.	1.78334
$122$	10472.5	0.0637014
$123$	−46113.9	−0.274833
$124$	−14077.7	−0.0822197
$125$	−73948.4	−0.423305
$126$	37986.1	0.213156
$127$	192636.	1.05981	0.529905	−	0.848057i	$-0.322228\pi$
$127$	192636.	1.05981	0.529905	+	0.848057i	$0.322228\pi$
$128$	−7973.75	−0.0430168
$129$	116878.	0.618385
$130$	37901.4	0.196697
$131$	−128679.	−0.655132	−0.327566	−	0.944828i	$-0.606228\pi$
$131$	−128679.	−0.655132	−0.327566	+	0.944828i	$0.606228\pi$
$132$	−106268.	−0.530845
$133$	152865.	0.749342
$134$	142637.	0.686230
$135$	49377.5	0.233182
$136$	−418222.	−1.93892
$137$	353184.	1.60768	0.803840	−	0.594845i	$-0.202787\pi$
$137$	353184.	1.60768	0.803840	+	0.594845i	$0.202787\pi$
$138$	−89475.7	−0.399951
$139$	68287.9	0.299783	0.149891	−	0.988702i	$-0.452108\pi$
$139$	68287.9	0.299783	0.149891	+	0.988702i	$0.452108\pi$
$140$	13547.2	0.0584158
$141$	288934.	1.22391
$142$	−123643.	−0.514574
$143$	−489623.	−2.00227
$144$	43286.9	0.173960
$145$	−85070.8	−0.336017
$146$	223141.	0.866359
$147$	117560.	0.448710
$148$	18759.8	0.0704000
$149$	−394019.	−1.45396	−0.726978	−	0.686661i	$-0.759076\pi$
$149$	−394019.	−1.45396	−0.726978	+	0.686661i	$0.759076\pi$
$150$	147555.	0.535458
$151$	−78647.7	−0.280701	−0.140350	−	0.990102i	$-0.544823\pi$
$151$	−78647.7	−0.280701	−0.140350	+	0.990102i	$0.544823\pi$
$152$	366259.	1.28582
$153$	−232839.	−0.804132
$154$	233672.	0.793972
$155$	12447.4	0.0416149
$156$	116074.	0.381876
$157$	517280.	1.67485	0.837427	−	0.546550i	$-0.184059\pi$
$157$	517280.	1.67485	0.837427	+	0.546550i	$0.184059\pi$
$158$	−271851.	−0.866338
$159$	202769.	0.636075
$160$	55185.1	0.170420
$161$	−147353.	−0.448017
$162$	−88780.4	−0.265785
$163$	−480721.	−1.41718	−0.708588	−	0.705622i	$-0.750668\pi$
$163$	−480721.	−1.41718	−0.708588	+	0.705622i	$0.750668\pi$
$164$	−54555.9	−0.158392
$165$	93961.6	0.268683
$166$	−327050.	−0.921178
$167$	−102004.	−0.283027	−0.141513	−	0.989936i	$-0.545197\pi$
$167$	−102004.	−0.283027	−0.141513	+	0.989936i	$0.545197\pi$
$168$	−184758.	−0.505044
$169$	163509.	0.440378
$170$	110874.	0.294245
$171$	203910.	0.533270
$172$	138275.	0.356388
$173$	−214693.	−0.545385	−0.272693	−	0.962101i	$-0.587914\pi$
$173$	−214693.	−0.545385	−0.272693	+	0.962101i	$0.587914\pi$
$174$	347864.	0.871037
$175$	243001.	0.599809
$176$	266280.	0.647973
$177$	−231326.	−0.554999
$178$	121128.	0.286547
$179$	−297917.	−0.694963	−0.347482	−	0.937687i	$-0.612963\pi$
$179$	−297917.	−0.694963	−0.347482	+	0.937687i	$0.612963\pi$
$180$	18070.8	0.0415716
$181$	−499706.	−1.13375	−0.566876	−	0.823803i	$-0.691848\pi$
$181$	−499706.	−1.13375	−0.566876	+	0.823803i	$0.691848\pi$
$182$	−255234.	−0.571163
$183$	−28358.0	−0.0625962
$184$	−353052.	−0.768765
$185$	−16587.3	−0.0356325
$186$	−50898.8	−0.107876
$187$	−1.43231e6	−2.99525
$188$	341829.	0.705365
$189$	−332516.	−0.677107
$190$	−97098.6	−0.195132
$191$	−12466.6	−0.0247265	−0.0123633	−	0.999924i	$-0.503935\pi$
$191$	−12466.6	−0.0247265	−0.0123633	+	0.999924i	$0.503935\pi$
$192$	−373071.	−0.730363
$193$	330639.	0.638940	0.319470	−	0.947596i	$-0.396495\pi$
$193$	330639.	0.638940	0.319470	+	0.947596i	$0.396495\pi$
$194$	−144730.	−0.276093
$195$	−102632.	−0.193284
$196$	139082.	0.258600
$197$	−537950.	−0.987589	−0.493794	−	0.869579i	$-0.664390\pi$
$197$	−537950.	−0.987589	−0.493794	+	0.869579i	$0.664390\pi$
$198$	311699.	0.565031
$199$	787829.	1.41026	0.705130	−	0.709078i	$-0.250889\pi$
$199$	787829.	1.41026	0.705130	+	0.709078i	$0.250889\pi$
$200$	582220.	1.02923
$201$	−386241.	−0.674323
$202$	210504.	0.362979
$203$	572880.	0.975717
$204$	339555.	0.571261
$205$	48238.0	0.0801687
$206$	−3444.85	−0.00565591
$207$	−196556.	−0.318832
$208$	−290851.	−0.466135
$209$	1.25435e6	1.98634
$210$	48980.9	0.0766441
$211$	67475.5	0.104337	0.0521687	−	0.998638i	$-0.483387\pi$
$211$	67475.5	0.104337	0.0521687	+	0.998638i	$0.483387\pi$
$212$	239889.	0.366582
$213$	334808.	0.505646
$214$	350776.	0.523595
$215$	−122262.	−0.180383
$216$	−796694.	−1.16187
$217$	−83822.6	−0.120840
$218$	615171.	0.876707
$219$	−604236.	−0.851327
$220$	111163.	0.154847
$221$	1.56448e6	2.15471
$222$	67827.2	0.0923680
$223$	545873.	0.735071	0.367535	−	0.930010i	$-0.380202\pi$
$223$	545873.	0.735071	0.367535	+	0.930010i	$0.380202\pi$
$224$	−371625.	−0.494863
$225$	324143.	0.426854
$226$	−1.05156e6	−1.36951
$227$	821170.	1.05771	0.528857	−	0.848711i	$-0.322621\pi$
$227$	821170.	1.05771	0.528857	+	0.848711i	$0.322621\pi$
$228$	−297366.	−0.378839
$229$	591.070	0.000744818 0	0.000372409	−	1.00000i	$-0.499881\pi$
$229$	591.070	0.000744818 0	0.000372409		1.00000i	$0.499881\pi$
$230$	93597.2	0.116666
$231$	−632752.	−0.780196
$232$	1.37260e6	1.67426
$233$	539034.	0.650469	0.325235	−	0.945633i	$-0.394557\pi$
$233$	539034.	0.650469	0.325235	+	0.945633i	$0.394557\pi$
$234$	−340460.	−0.406469
$235$	−302243.	−0.357015
$236$	−273675.	−0.319857
$237$	736134.	0.851307
$238$	−746645.	−0.854421
$239$	−651874.	−0.738191	−0.369095	−	0.929391i	$-0.620332\pi$
$239$	−651874.	−0.738191	−0.369095	+	0.929391i	$0.620332\pi$
$240$	55816.0	0.0625505
$241$	−52912.5	−0.0586835	−0.0293417	−	0.999569i	$-0.509341\pi$
$241$	−52912.5	−0.0586835	−0.0293417	+	0.999569i	$0.509341\pi$
$242$	1.22853e6	1.34849
$243$	−749887.	−0.814667
$244$	−33549.5	−0.0360754
$245$	−122975.	−0.130889
$246$	−197251.	−0.207817
$247$	−1.37010e6	−1.42892
$248$	−200836.	−0.207354
$249$	885606.	0.905195
$250$	−316312.	−0.320085
$251$	−1.10700e6	−1.10908	−0.554542	−	0.832156i	$-0.687107\pi$
$251$	−1.10700e6	−1.10908	−0.554542	+	0.832156i	$0.687107\pi$
$252$	−121692.	−0.120715
$253$	−1.20912e6	−1.18759
$254$	823994.	0.801382
$255$	−300233.	−0.289140
$256$	−1.06480e6	−1.01547
$257$	511017.	0.482617	0.241309	−	0.970448i	$-0.422423\pi$
$257$	511017.	0.482617	0.241309	+	0.970448i	$0.422423\pi$
$258$	499943.	0.467596
$259$	111701.	0.103469
$260$	−121421.	−0.111393
$261$	764174.	0.694370
$262$	−550420.	−0.495382
$263$	−1.16780e6	−1.04107	−0.520535	−	0.853840i	$-0.674268\pi$
$263$	−1.16780e6	−1.04107	−0.520535	+	0.853840i	$0.674268\pi$
$264$	−1.51605e6	−1.33876
$265$	−212109.	−0.185543
$266$	653877.	0.566620
$267$	−327999.	−0.281575
$268$	−456950.	−0.388626
$269$	−1.12421e6	−0.947251	−0.473626	−	0.880726i	$-0.657055\pi$
$269$	−1.12421e6	−0.947251	−0.473626	+	0.880726i	$0.657055\pi$
$270$	211211.	0.176322
$271$	383957.	0.317585	0.158792	−	0.987312i	$-0.449240\pi$
$271$	383957.	0.317585	0.158792	+	0.987312i	$0.449240\pi$
$272$	−850837.	−0.697307
$273$	691139.	0.561253
$274$	1.51073e6	1.21566
$275$	1.99397e6	1.58996
$276$	286643.	0.226500
$277$	−1.65434e6	−1.29546	−0.647732	−	0.761868i	$-0.724282\pi$
$277$	−1.65434e6	−1.29546	−0.647732	+	0.761868i	$0.724282\pi$
$278$	292099.	0.226683
$279$	−111812.	−0.0859962
$280$	193268.	0.147321
$281$	371797.	0.280893	0.140446	−	0.990088i	$-0.455146\pi$
$281$	371797.	0.280893	0.140446	+	0.990088i	$0.455146\pi$
$282$	1.23591e6	0.925471
$283$	274548.	0.203775	0.101888	−	0.994796i	$-0.467512\pi$
$283$	274548.	0.203775	0.101888	+	0.994796i	$0.467512\pi$
$284$	396101.	0.291413
$285$	262930.	0.191747
$286$	−2.09435e6	−1.51403
$287$	−324842.	−0.232792
$288$	−495716.	−0.352170
$289$	3.15677e6	2.22330
$290$	−363888.	−0.254081
$291$	391910.	0.271302
$292$	−714853.	−0.490636
$293$	−1.49181e6	−1.01518	−0.507591	−	0.861598i	$-0.669464\pi$
$293$	−1.49181e6	−1.01518	−0.507591	+	0.861598i	$0.669464\pi$
$294$	502859.	0.339295
$295$	241982.	0.161893
$296$	267632.	0.177545
$297$	−2.72849e6	−1.79486
$298$	−1.68540e6	−1.09942
$299$	1.32069e6	0.854325
$300$	−472705.	−0.303241
$301$	823331.	0.523791
$302$	−336413.	−0.212254
$303$	−570016.	−0.356682
$304$	745123.	0.462428
$305$	29664.2	0.0182593
$306$	−995962.	−0.608050
$307$	2.67117e6	1.61754	0.808770	−	0.588125i	$-0.200134\pi$
$307$	2.67117e6	1.61754	0.808770	+	0.588125i	$0.200134\pi$
$308$	−748590.	−0.449642
$309$	9328.19	0.00555778
$310$	53243.3	0.0314674
$311$	−140283.	−0.0822438	−0.0411219	−	0.999154i	$-0.513093\pi$
$311$	−140283.	−0.0822438	−0.0411219	+	0.999154i	$0.513093\pi$
$312$	1.65594e6	0.963070
$313$	3.02770e6	1.74684	0.873418	−	0.486971i	$-0.161898\pi$
$313$	3.02770e6	1.74684	0.873418	+	0.486971i	$0.161898\pi$
$314$	2.21265e6	1.26645
$315$	107599.	0.0610989
$316$	870898.	0.490625
$317$	−940821.	−0.525846	−0.262923	−	0.964817i	$-0.584687\pi$
$317$	−940821.	−0.525846	−0.262923	+	0.964817i	$0.584687\pi$
$318$	867337.	0.480972
$319$	4.70083e6	2.58641
$320$	390256.	0.213047
$321$	−949854.	−0.514511
$322$	−630298.	−0.338771
$323$	−4.00799e6	−2.13757
$324$	284416.	0.150519
$325$	−2.17796e6	−1.14378
$326$	−2.05627e6	−1.07161
$327$	−1.66580e6	−0.861495
$328$	−778309.	−0.399455
$329$	2.03535e6	1.03669
$330$	401918.	0.203167
$331$	−3.04532e6	−1.52779	−0.763894	−	0.645341i	$-0.776715\pi$
$331$	−3.04532e6	−1.52779	−0.763894	+	0.645341i	$0.776715\pi$
$332$	1.04773e6	0.521682
$333$	149000.	0.0736336
$334$	−436320.	−0.214013
$335$	404032.	0.196700
$336$	−375874.	−0.181633
$337$	503472.	0.241491	0.120746	−	0.992683i	$-0.461472\pi$
$337$	503472.	0.241491	0.120746	+	0.992683i	$0.461472\pi$
$338$	699406.	0.332995
$339$	2.84749e6	1.34575
$340$	−355196.	−0.166637
$341$	−687815.	−0.320321
$342$	872217.	0.403236
$343$	2.19947e6	1.00945
$344$	1.97267e6	0.898789
$345$	−253448.	−0.114642
$346$	−918344.	−0.412397
$347$	−167515.	−0.0746843	−0.0373422	−	0.999303i	$-0.511889\pi$
$347$	−167515.	−0.0746843	−0.0373422	+	0.999303i	$0.511889\pi$
$348$	−1.11441e6	−0.493286
$349$	−1.11562e6	−0.490289	−0.245145	−	0.969487i	$-0.578835\pi$
$349$	−1.11562e6	−0.490289	−0.245145	+	0.969487i	$0.578835\pi$
$350$	1.03943e6	0.453549
$351$	2.98026e6	1.29118
$352$	−3.04940e6	−1.31177
$353$	−1.02604e6	−0.438254	−0.219127	−	0.975696i	$-0.570321\pi$
$353$	−1.02604e6	−0.438254	−0.219127	+	0.975696i	$0.570321\pi$
$354$	−989492.	−0.419666
$355$	−350230.	−0.147497
$356$	−388046.	−0.162277
$357$	2.02181e6	0.839597
$358$	−1.27433e6	−0.525501
$359$	3.60399e6	1.47587	0.737934	−	0.674873i	$-0.235802\pi$
$359$	3.60399e6	1.47587	0.737934	+	0.674873i	$0.235802\pi$
$360$	257803.	0.104841
$361$	1.03392e6	0.417559
$362$	−2.13748e6	−0.857294
$363$	−3.32669e6	−1.32509
$364$	817665.	0.323461
$365$	632069.	0.248332
$366$	−121300.	−0.0473325
$367$	1.31278e6	0.508777	0.254389	−	0.967102i	$-0.418126\pi$
$367$	1.31278e6	0.508777	0.254389	+	0.967102i	$0.418126\pi$
$368$	−718254.	−0.276477
$369$	−433312.	−0.165667
$370$	−70951.6	−0.0269437
$371$	1.42837e6	0.538775
$372$	163059.	0.0610923
$373$	−781555.	−0.290862	−0.145431	−	0.989368i	$-0.546457\pi$
$373$	−781555.	−0.290862	−0.145431	+	0.989368i	$0.546457\pi$
$374$	−6.12667e6	−2.26488
$375$	856530.	0.314532
$376$	4.87662e6	1.77889
$377$	−5.13459e6	−1.86060
$378$	−1.42233e6	−0.511999
$379$	−4.79904e6	−1.71616	−0.858078	−	0.513520i	$-0.828341\pi$
$379$	−4.79904e6	−1.71616	−0.858078	+	0.513520i	$0.828341\pi$
$380$	311064.	0.110507
$381$	−2.23126e6	−0.787478
$382$	−53325.3	−0.0186971
$383$	−3.72685e6	−1.29821	−0.649105	−	0.760699i	$-0.724857\pi$
$383$	−3.72685e6	−1.29821	−0.649105	+	0.760699i	$0.724857\pi$
$384$	92358.4	0.0319631
$385$	661899.	0.227583
$386$	1.41430e6	0.483139
$387$	1.09825e6	0.372757
$388$	463656.	0.156357
$389$	3.75802e6	1.25917	0.629587	−	0.776930i	$-0.283224\pi$
$389$	3.75802e6	1.25917	0.629587	+	0.776930i	$0.283224\pi$
$390$	−439004.	−0.146153
$391$	3.86346e6	1.27801
$392$	1.98417e6	0.652176
$393$	1.49046e6	0.486787
$394$	−2.30106e6	−0.746772
$395$	−770043.	−0.248326
$396$	−998555.	−0.319988
$397$	−3.24861e6	−1.03448	−0.517239	−	0.855841i	$-0.673040\pi$
$397$	−3.24861e6	−1.03448	−0.517239	+	0.855841i	$0.673040\pi$
$398$	3.36991e6	1.06638
$399$	−1.77061e6	−0.556789
$400$	1.18448e6	0.370149
$401$	−4.39851e6	−1.36598	−0.682991	−	0.730427i	$-0.739321\pi$
$401$	−4.39851e6	−1.36598	−0.682991	+	0.730427i	$0.739321\pi$
$402$	−1.65213e6	−0.509894
$403$	751282.	0.230431
$404$	−674369.	−0.205563
$405$	−251479.	−0.0761841
$406$	2.45048e6	0.737795
$407$	916576.	0.274273
$408$	4.84418e6	1.44069
$409$	−2.89752e6	−0.856481	−0.428241	−	0.903665i	$-0.640866\pi$
$409$	−2.89752e6	−0.856481	−0.428241	+	0.903665i	$0.640866\pi$
$410$	206337.	0.0606201
$411$	−4.09086e6	−1.19457
$412$	11035.9	0.00320306
$413$	−1.62954e6	−0.470101
$414$	−840764.	−0.241087
$415$	−926400.	−0.264045
$416$	3.33078e6	0.943655
$417$	−790965.	−0.222750
$418$	5.36545e6	1.50199
$419$	−1.38938e6	−0.386622	−0.193311	−	0.981137i	$-0.561923\pi$
$419$	−1.38938e6	−0.386622	−0.193311	+	0.981137i	$0.561923\pi$
$420$	−156915.	−0.0434051
$421$	3.96894e6	1.09136	0.545681	−	0.837993i	$-0.316271\pi$
$421$	3.96894e6	1.09136	0.545681	+	0.837993i	$0.316271\pi$
$422$	288624.	0.0788954
$423$	2.71499e6	0.737763
$424$	3.42232e6	0.924499
$425$	−6.37126e6	−1.71101
$426$	1.43213e6	0.382348
$427$	−199764.	−0.0530209
$428$	−1.12374e6	−0.296522
$429$	5.67121e6	1.48776
$430$	−522972.	−0.136398
$431$	951391.	0.246698	0.123349	−	0.992363i	$-0.460637\pi$
$431$	951391.	0.246698	0.123349	+	0.992363i	$0.460637\pi$
$432$	−1.62081e6	−0.417851
$433$	−4.83408e6	−1.23906	−0.619532	−	0.784971i	$-0.712678\pi$
$433$	−4.83408e6	−1.23906	−0.619532	+	0.784971i	$0.712678\pi$
$434$	−358549.	−0.0913743
$435$	985359.	0.249673
$436$	−1.97075e6	−0.496497
$437$	−3.38344e6	−0.847530
$438$	−2.58460e6	−0.643737
$439$	6.69545e6	1.65813	0.829065	−	0.559152i	$-0.188873\pi$
$439$	6.69545e6	1.65813	0.829065	+	0.559152i	$0.188873\pi$
$440$	1.58588e6	0.390516
$441$	1.10466e6	0.270478
$442$	6.69200e6	1.62930
$443$	−363801.	−0.0880755	−0.0440377	−	0.999030i	$-0.514022\pi$
$443$	−363801.	−0.0880755	−0.0440377	+	0.999030i	$0.514022\pi$
$444$	−217291.	−0.0523099
$445$	343108.	0.0821354
$446$	2.33495e6	0.555829
$447$	4.56384e6	1.08034
$448$	−2.62805e6	−0.618640
$449$	−8.35332e6	−1.95543	−0.977717	−	0.209925i	$-0.932678\pi$
$449$	−8.35332e6	−1.95543	−0.977717	+	0.209925i	$0.932678\pi$
$450$	1.38651e6	0.322769
$451$	−2.66553e6	−0.617080
$452$	3.36878e6	0.775579
$453$	910961.	0.208571
$454$	3.51253e6	0.799798
$455$	−722975.	−0.163717
$456$	−4.24231e6	−0.955411
$457$	−4.53628e6	−1.01604	−0.508019	−	0.861346i	$-0.669622\pi$
$457$	−4.53628e6	−1.01604	−0.508019	+	0.861346i	$0.669622\pi$
$458$	2528.28	0.000563199 0
$459$	8.71826e6	1.93152
$460$	−299847.	−0.0660701
$461$	6.57076e6	1.44000	0.720002	−	0.693972i	$-0.244141\pi$
$461$	6.57076e6	1.44000	0.720002	+	0.693972i	$0.244141\pi$
$462$	−2.70658e6	−0.589951
$463$	2.49078e6	0.539987	0.269994	−	0.962862i	$-0.412978\pi$
$463$	2.49078e6	0.539987	0.269994	+	0.962862i	$0.412978\pi$
$464$	2.79243e6	0.602127
$465$	−144176.	−0.0309214
$466$	2.30570e6	0.491857
$467$	−46124.1	−0.00978669	−0.00489335	−	0.999988i	$-0.501558\pi$
$467$	−46124.1	−0.00978669	−0.00489335	+	0.999988i	$0.501558\pi$
$468$	1.09070e6	0.230191
$469$	−2.72082e6	−0.571172
$470$	−1.29284e6	−0.269960
$471$	−5.99156e6	−1.24448
$472$	−3.90432e6	−0.806660
$473$	6.75593e6	1.38846
$474$	3.14879e6	0.643722
$475$	5.57966e6	1.13468
$476$	2.39195e6	0.483876
$477$	1.90533e6	0.383420
$478$	−2.78837e6	−0.558188
$479$	−5.03288e6	−1.00225	−0.501127	−	0.865374i	$-0.667081\pi$
$479$	−5.03288e6	−1.00225	−0.501127	+	0.865374i	$0.667081\pi$
$480$	−639198.	−0.126629
$481$	−1.00115e6	−0.197305
$482$	−226332.	−0.0443739
$483$	1.70676e6	0.332893
$484$	−3.93570e6	−0.763675
$485$	−409962.	−0.0791388
$486$	−3.20762e6	−0.616016
$487$	569313.	0.108775	0.0543874	−	0.998520i	$-0.482679\pi$
$487$	569313.	0.108775	0.0543874	+	0.998520i	$0.482679\pi$
$488$	−478625.	−0.0909801
$489$	5.56809e6	1.05301
$490$	−526022.	−0.0989724
$491$	2.58240e6	0.483415	0.241708	−	0.970349i	$-0.422292\pi$
$491$	2.58240e6	0.483415	0.241708	+	0.970349i	$0.422292\pi$
$492$	631910.	0.117691
$493$	−1.50204e7	−2.78333
$494$	−5.86055e6	−1.08049
$495$	882917.	0.161960
$496$	−408583.	−0.0745720
$497$	2.35850e6	0.428298
$498$	3.78815e6	0.684470
$499$	−6.58011e6	−1.18299	−0.591496	−	0.806308i	$-0.701462\pi$
$499$	−6.58011e6	−1.18299	−0.591496	+	0.806308i	$0.701462\pi$
$500$	1.01333e6	0.181271
$501$	1.18150e6	0.210299
$502$	−4.73517e6	−0.838642
$503$	−452702.	−0.0797798	−0.0398899	−	0.999204i	$-0.512701\pi$
$503$	−452702.	−0.0797798	−0.0398899	+	0.999204i	$0.512701\pi$
$504$	−1.73609e6	−0.304436
$505$	596273.	0.104044
$506$	−5.17197e6	−0.898008
$507$	−1.89390e6	−0.327217
$508$	−2.63974e6	−0.453839
$509$	−7.52962e6	−1.28819	−0.644093	−	0.764947i	$-0.722765\pi$
$509$	−7.52962e6	−1.28819	−0.644093	+	0.764947i	$0.722765\pi$
$510$	−1.28424e6	−0.218635
$511$	−4.25645e6	−0.721100
$512$	−4.29948e6	−0.724838
$513$	−7.63505e6	−1.28091
$514$	2.18586e6	0.364934
$515$	−9757.88	−0.00162120
$516$	−1.60161e6	−0.264809
$517$	1.67013e7	2.74804
$518$	477799.	0.0782385
$519$	2.48675e6	0.405242
$520$	−1.73222e6	−0.280927
$521$	−7.31545e6	−1.18072	−0.590359	−	0.807140i	$-0.701014\pi$
$521$	−7.31545e6	−1.18072	−0.590359	+	0.807140i	$0.701014\pi$
$522$	3.26873e6	0.525053
$523$	8.43842e6	1.34898	0.674492	−	0.738282i	$-0.264363\pi$
$523$	8.43842e6	1.34898	0.674492	+	0.738282i	$0.264363\pi$
$524$	1.76332e6	0.280545
$525$	−2.81463e6	−0.445680
$526$	−4.99524e6	−0.787213
$527$	2.19775e6	0.344709
$528$	−3.08427e6	−0.481468
$529$	−3.17491e6	−0.493278
$530$	−907289.	−0.140299
$531$	−2.17367e6	−0.334548
$532$	−2.09475e6	−0.320888
$533$	2.91149e6	0.443912
$534$	−1.40301e6	−0.212915
$535$	993607.	0.150083
$536$	−6.51896e6	−0.980091
$537$	3.45071e6	0.516384
$538$	−4.80876e6	−0.716270
$539$	6.79533e6	1.00749
$540$	−676632.	−0.0998546
$541$	9.92699e6	1.45822	0.729112	−	0.684394i	$-0.239933\pi$
$541$	9.92699e6	1.45822	0.729112	+	0.684394i	$0.239933\pi$
$542$	1.64237e6	0.240144
$543$	5.78800e6	0.842420
$544$	9.74367e6	1.41164
$545$	1.74253e6	0.251298
$546$	2.95632e6	0.424395
$547$	−4.84665e6	−0.692585	−0.346293	−	0.938127i	$-0.612560\pi$
$547$	−4.84665e6	−0.692585	−0.346293	+	0.938127i	$0.612560\pi$
$548$	−4.83977e6	−0.688452
$549$	−266468.	−0.0377324
$550$	8.52914e6	1.20226
$551$	1.31542e7	1.84580
$552$	4.08933e6	0.571221
$553$	5.18559e6	0.721083
$554$	−7.07639e6	−0.979574
$555$	192127.	0.0264762
$556$	−935766.	−0.128375
$557$	−4.37984e6	−0.598164	−0.299082	−	0.954227i	$-0.596680\pi$
$557$	−4.37984e6	−0.598164	−0.299082	+	0.954227i	$0.596680\pi$
$558$	−478274.	−0.0650266
$559$	−7.37932e6	−0.998819
$560$	393188.	0.0529822
$561$	1.65902e7	2.22559
$562$	1.59035e6	0.212399
$563$	−7.14982e6	−0.950657	−0.475328	−	0.879808i	$-0.657671\pi$
$563$	−7.14982e6	−0.950657	−0.475328	+	0.879808i	$0.657671\pi$
$564$	−3.95934e6	−0.524113
$565$	−2.97866e6	−0.392554
$566$	1.17437e6	0.154086
$567$	1.69350e6	0.221222
$568$	5.65088e6	0.734928
$569$	1.60424e6	0.207724	0.103862	−	0.994592i	$-0.466880\pi$
$569$	1.60424e6	0.207724	0.103862	+	0.994592i	$0.466880\pi$
$570$	1.12467e6	0.144991
$571$	−3.70387e6	−0.475407	−0.237704	−	0.971338i	$-0.576395\pi$
$571$	−3.70387e6	−0.475407	−0.237704	+	0.971338i	$0.576395\pi$
$572$	6.70943e6	0.857424
$573$	144398.	0.0183727
$574$	−1.38950e6	−0.176027
$575$	−5.37845e6	−0.678403
$576$	−3.50559e6	−0.440256
$577$	2.70357e6	0.338064	0.169032	−	0.985611i	$-0.445936\pi$
$577$	2.70357e6	0.338064	0.169032	+	0.985611i	$0.445936\pi$
$578$	1.35030e7	1.68116
$579$	−3.82972e6	−0.474756
$580$	1.16575e6	0.143891
$581$	6.23852e6	0.766728
$582$	1.67638e6	0.205147
$583$	1.17207e7	1.42817
$584$	−1.01983e7	−1.23736
$585$	−964387.	−0.116510
$586$	−6.38117e6	−0.767637
$587$	−565564.	−0.0677464	−0.0338732	−	0.999426i	$-0.510784\pi$
$587$	−565564.	−0.0677464	−0.0338732	+	0.999426i	$0.510784\pi$
$588$	−1.61095e6	−0.192150
$589$	−1.92469e6	−0.228598
$590$	1.03507e6	0.122417
$591$	6.23097e6	0.733815
$592$	544474.	0.0638518
$593$	5.29646e6	0.618513	0.309256	−	0.950979i	$-0.399920\pi$
$593$	5.29646e6	0.618513	0.309256	+	0.950979i	$0.399920\pi$
$594$	−1.16710e7	−1.35720
$595$	−2.11495e6	−0.244910
$596$	5.39934e6	0.622623
$597$	−9.12527e6	−1.04788
$598$	5.64921e6	0.646004
$599$	−1.59632e6	−0.181783	−0.0908915	−	0.995861i	$-0.528972\pi$
$599$	−1.59632e6	−0.181783	−0.0908915	+	0.995861i	$0.528972\pi$
$600$	−6.74374e6	−0.764756
$601$	5.03043e6	0.568093	0.284046	−	0.958811i	$-0.408323\pi$
$601$	5.03043e6	0.568093	0.284046	+	0.958811i	$0.408323\pi$
$602$	3.52177e6	0.396069
$603$	−3.62934e6	−0.406475
$604$	1.07773e6	0.120204
$605$	3.47993e6	0.386529
$606$	−2.43823e6	−0.269707
$607$	−443509.	−0.0488574	−0.0244287	−	0.999702i	$-0.507777\pi$
$607$	−443509.	−0.0488574	−0.0244287	+	0.999702i	$0.507777\pi$
$608$	−8.53305e6	−0.936150
$609$	−6.63556e6	−0.724994
$610$	126888.	0.0138069
$611$	−1.82424e7	−1.97687
$612$	3.19065e6	0.344351
$613$	−2.78729e6	−0.299592	−0.149796	−	0.988717i	$-0.547862\pi$
$613$	−2.78729e6	−0.299592	−0.149796	+	0.988717i	$0.547862\pi$
$614$	1.14258e7	1.22311
$615$	−558732.	−0.0595683
$616$	−1.06796e7	−1.13397
$617$	6.09435e6	0.644487	0.322244	−	0.946657i	$-0.395563\pi$
$617$	6.09435e6	0.644487	0.322244	+	0.946657i	$0.395563\pi$
$618$	39901.1	0.00420255
$619$	−1.23277e7	−1.29317	−0.646587	−	0.762841i	$-0.723804\pi$
$619$	−1.23277e7	−1.29317	−0.646587	+	0.762841i	$0.723804\pi$
$620$	−170570.	−0.0178206
$621$	7.35972e6	0.765830
$622$	−600055.	−0.0621892
$623$	−2.31054e6	−0.238503
$624$	3.36887e6	0.346356
$625$	8.41087e6	0.861273
$626$	1.29509e7	1.32088
$627$	−1.45289e7	−1.47593
$628$	−7.08842e6	−0.717217
$629$	−2.92871e6	−0.295155
$630$	460253.	0.0462003
$631$	1.13411e7	1.13392	0.566960	−	0.823745i	$-0.308119\pi$
$631$	1.13411e7	1.13392	0.566960	+	0.823745i	$0.308119\pi$
$632$	1.24245e7	1.23733
$633$	−781556.	−0.0775266
$634$	−4.02433e6	−0.397622
$635$	2.33404e6	0.229707
$636$	−2.77859e6	−0.272384
$637$	−7.42236e6	−0.724759
$638$	2.01076e7	1.95573
$639$	3.14604e6	0.304798
$640$	−96612.7	−0.00932362
$641$	−1.10272e7	−1.06003	−0.530016	−	0.847987i	$-0.677814\pi$
$641$	−1.10272e7	−1.06003	−0.530016	+	0.847987i	$0.677814\pi$
$642$	−4.06297e6	−0.389051
$643$	9.84783e6	0.939319	0.469659	−	0.882848i	$-0.344377\pi$
$643$	9.84783e6	0.939319	0.469659	+	0.882848i	$0.344377\pi$
$644$	2.01922e6	0.191853
$645$	1.41614e6	0.134031
$646$	−1.71441e7	−1.61634
$647$	1.17238e7	1.10105	0.550527	−	0.834818i	$-0.314427\pi$
$647$	1.17238e7	1.10105	0.550527	+	0.834818i	$0.314427\pi$
$648$	4.05755e6	0.379601
$649$	−1.33714e7	−1.24613
$650$	−9.31615e6	−0.864875
$651$	970901.	0.0897889
$652$	6.58744e6	0.606873
$653$	3.44983e6	0.316603	0.158302	−	0.987391i	$-0.449398\pi$
$653$	3.44983e6	0.316603	0.158302	+	0.987391i	$0.449398\pi$
$654$	−7.12540e6	−0.651426
$655$	−1.55912e6	−0.141996
$656$	−1.58340e6	−0.143659
$657$	−5.67775e6	−0.513172
$658$	8.70616e6	0.783902
$659$	7.27544e6	0.652598	0.326299	−	0.945267i	$-0.394198\pi$
$659$	7.27544e6	0.652598	0.326299	+	0.945267i	$0.394198\pi$
$660$	−1.28758e6	−0.115057
$661$	−2.44329e6	−0.217506	−0.108753	−	0.994069i	$-0.534686\pi$
$661$	−2.44329e6	−0.217506	−0.108753	+	0.994069i	$0.534686\pi$
$662$	−1.30263e7	−1.15525
$663$	−1.81210e7	−1.60103
$664$	1.49472e7	1.31565
$665$	1.85217e6	0.162415
$666$	637343.	0.0556785
$667$	−1.26798e7	−1.10357
$668$	1.39779e6	0.121200
$669$	−6.32274e6	−0.546185
$670$	1.72824e6	0.148736
$671$	−1.63918e6	−0.140547
$672$	4.30446e6	0.367701
$673$	925504.	0.0787663	0.0393832	−	0.999224i	$-0.487461\pi$
$673$	925504.	0.0787663	0.0393832	+	0.999224i	$0.487461\pi$
$674$	2.15359e6	0.182605
$675$	−1.21370e7	−1.02530
$676$	−2.24061e6	−0.188582
$677$	4.07130e6	0.341398	0.170699	−	0.985323i	$-0.445397\pi$
$677$	4.07130e6	0.341398	0.170699	+	0.985323i	$0.445397\pi$
$678$	1.21801e7	1.01760
$679$	2.76075e6	0.229801
$680$	−5.06732e6	−0.420248
$681$	−9.51145e6	−0.785921
$682$	−2.94211e6	−0.242213
$683$	1.50409e7	1.23373	0.616867	−	0.787067i	$-0.288402\pi$
$683$	1.50409e7	1.23373	0.616867	+	0.787067i	$0.288402\pi$
$684$	−2.79422e6	−0.228361
$685$	4.27930e6	0.348455
$686$	9.40818e6	0.763300
$687$	−6846.24	−0.000553427 0
$688$	4.01322e6	0.323238
$689$	−1.28022e7	−1.02739
$690$	−1.08412e6	−0.0866870
$691$	3.00305e6	0.239259	0.119629	−	0.992819i	$-0.461829\pi$
$691$	3.00305e6	0.239259	0.119629	+	0.992819i	$0.461829\pi$
$692$	2.94200e6	0.233549
$693$	−5.94570e6	−0.470295
$694$	−716539.	−0.0564731
$695$	827399.	0.0649760
$696$	−1.58985e7	−1.24404
$697$	8.51708e6	0.664062
$698$	−4.77203e6	−0.370736
$699$	−6.24353e6	−0.483323
$700$	−3.32990e6	−0.256854
$701$	1.06649e7	0.819716	0.409858	−	0.912149i	$-0.365578\pi$
$701$	1.06649e7	0.819716	0.409858	+	0.912149i	$0.365578\pi$
$702$	1.27480e7	0.976333
$703$	2.56483e6	0.195736
$704$	−2.15647e7	−1.63988
$705$	3.50082e6	0.265276
$706$	−4.38884e6	−0.331389
$707$	−4.01540e6	−0.302120
$708$	3.16993e6	0.237665
$709$	−2.02490e7	−1.51282	−0.756411	−	0.654097i	$-0.773049\pi$
$709$	−2.02490e7	−1.51282	−0.756411	+	0.654097i	$0.773049\pi$
$710$	−1.49810e6	−0.111531
$711$	6.91714e6	0.513160
$712$	−5.53596e6	−0.409254
$713$	1.85529e6	0.136674
$714$	8.64825e6	0.634867
$715$	−5.93244e6	−0.433979
$716$	4.08243e6	0.297602
$717$	7.55053e6	0.548503
$718$	1.54160e7	1.11599
$719$	8.00856e6	0.577740	0.288870	−	0.957368i	$-0.406721\pi$
$719$	8.00856e6	0.577740	0.288870	+	0.957368i	$0.406721\pi$
$720$	524479.	0.0377048
$721$	65711.1	0.00470761
$722$	4.42254e6	0.315740
$723$	612875.	0.0436040
$724$	6.84760e6	0.485503
$725$	2.09104e7	1.47746
$726$	−1.42298e7	−1.00198
$727$	2.11197e7	1.48201	0.741005	−	0.671500i	$-0.234350\pi$
$727$	2.11197e7	1.48201	0.741005	+	0.671500i	$0.234350\pi$
$728$	1.16650e7	0.815750
$729$	1.37294e7	0.956822
$730$	2.70366e6	0.187778
$731$	−2.15870e7	−1.49417
$732$	388597.	0.0268054
$733$	434571.	0.0298745	0.0149373	−	0.999888i	$-0.495245\pi$
$733$	434571.	0.0298745	0.0149373	+	0.999888i	$0.495245\pi$
$734$	5.61539e6	0.384716
$735$	1.42440e6	0.0972552
$736$	8.22535e6	0.559706
$737$	−2.23259e7	−1.51405
$738$	−1.85348e6	−0.125270
$739$	−9.09483e6	−0.612609	−0.306305	−	0.951934i	$-0.599093\pi$
$739$	−9.09483e6	−0.612609	−0.306305	+	0.951934i	$0.599093\pi$
$740$	227300.	0.0152588
$741$	1.58696e7	1.06174
$742$	6.10983e6	0.407398
$743$	−1.56230e6	−0.103822	−0.0519112	−	0.998652i	$-0.516531\pi$
$743$	−1.56230e6	−0.103822	−0.0519112	+	0.998652i	$0.516531\pi$
$744$	2.32624e6	0.154071
$745$	−4.77407e6	−0.315136
$746$	−3.34308e6	−0.219938
$747$	8.32166e6	0.545643
$748$	1.96273e7	1.28265
$749$	−6.69111e6	−0.435806
$750$	3.66378e6	0.237835
$751$	−9.74091e6	−0.630231	−0.315115	−	0.949053i	$-0.602043\pi$
$751$	−9.74091e6	−0.630231	−0.315115	+	0.949053i	$0.602043\pi$
$752$	9.92107e6	0.639756
$753$	1.28222e7	0.824091
$754$	−2.19631e7	−1.40690
$755$	−952923.	−0.0608402
$756$	4.55655e6	0.289956
$757$	−1.61469e7	−1.02411	−0.512057	−	0.858952i	$-0.671116\pi$
$757$	−1.61469e7	−1.02411	−0.512057	+	0.858952i	$0.671116\pi$
$758$	−2.05278e7	−1.29768
$759$	1.40050e7	0.882427
$760$	4.43772e6	0.278693
$761$	2.66724e7	1.66955	0.834777	−	0.550588i	$-0.185597\pi$
$761$	2.66724e7	1.66955	0.834777	+	0.550588i	$0.185597\pi$
$762$	−9.54416e6	−0.595457
$763$	−1.17345e7	−0.729713
$764$	170832.	0.0105886
$765$	−2.82116e6	−0.174291
$766$	−1.59415e7	−0.981651
$767$	1.46052e7	0.896437
$768$	1.23333e7	0.754532
$769$	−7.35082e6	−0.448250	−0.224125	−	0.974560i	$-0.571952\pi$
$769$	−7.35082e6	−0.448250	−0.224125	+	0.974560i	$0.571952\pi$
$770$	2.83125e6	0.172088
$771$	−5.91901e6	−0.358603
$772$	−4.53082e6	−0.273611
$773$	4.31711e6	0.259863	0.129932	−	0.991523i	$-0.458524\pi$
$773$	4.31711e6	0.259863	0.129932	+	0.991523i	$0.458524\pi$
$774$	4.69775e6	0.281863
$775$	−3.05956e6	−0.182981
$776$	6.61464e6	0.394323
$777$	−1.29381e6	−0.0768811
$778$	1.60748e7	0.952132
$779$	−7.45886e6	−0.440381
$780$	1.40639e6	0.0827693
$781$	1.93529e7	1.13532
$782$	1.65259e7	0.966378
$783$	−2.86132e7	−1.66787
$784$	4.03663e6	0.234547
$785$	6.26754e6	0.363014
$786$	6.37540e6	0.368088
$787$	−3.59210e6	−0.206734	−0.103367	−	0.994643i	$-0.532962\pi$
$787$	−3.59210e6	−0.206734	−0.103367	+	0.994643i	$0.532962\pi$
$788$	7.37166e6	0.422912
$789$	1.35264e7	0.773554
$790$	−3.29384e6	−0.187773
$791$	2.00587e7	1.13989
$792$	−1.42456e7	−0.806992
$793$	1.79043e6	0.101106
$794$	−1.38958e7	−0.782227
$795$	2.45682e6	0.137865
$796$	−1.07958e7	−0.603911
$797$	6.78134e6	0.378155	0.189077	−	0.981962i	$-0.439450\pi$
$797$	6.78134e6	0.378155	0.189077	+	0.981962i	$0.439450\pi$
$798$	−7.57373e6	−0.421020
$799$	−5.33651e7	−2.95727
$800$	−1.35645e7	−0.749338
$801$	−3.08207e6	−0.169731
$802$	−1.88145e7	−1.03290
$803$	−3.49267e7	−1.91148
$804$	5.29276e6	0.288763
$805$	−1.78538e6	−0.0971049
$806$	3.21359e6	0.174242
$807$	1.30215e7	0.703843
$808$	−9.62072e6	−0.518417
$809$	−7.63218e6	−0.409994	−0.204997	−	0.978763i	$-0.565718\pi$
$809$	−7.63218e6	−0.409994	−0.204997	+	0.978763i	$0.565718\pi$
$810$	−1.07569e6	−0.0576071
$811$	3.35783e7	1.79270	0.896349	−	0.443350i	$-0.146210\pi$
$811$	3.35783e7	1.79270	0.896349	+	0.443350i	$0.146210\pi$
$812$	−7.85033e6	−0.417828
$813$	−4.44730e6	−0.235977
$814$	3.92063e6	0.207393
$815$	−5.82458e6	−0.307164
$816$	9.85508e6	0.518125
$817$	1.89049e7	0.990876
$818$	−1.23940e7	−0.647634
$819$	6.49433e6	0.338318
$820$	−661018.	−0.0343304
$821$	−6.69035e6	−0.346410	−0.173205	−	0.984886i	$-0.555412\pi$
$821$	−6.69035e6	−0.346410	−0.173205	+	0.984886i	$0.555412\pi$
$822$	−1.74985e7	−0.903280
$823$	3.75909e6	0.193456	0.0967282	−	0.995311i	$-0.469162\pi$
$823$	3.75909e6	0.193456	0.0967282	+	0.995311i	$0.469162\pi$
$824$	157441.	0.00807793
$825$	−2.30957e7	−1.18140
$826$	−6.97033e6	−0.355470
$827$	3.47936e6	0.176903	0.0884515	−	0.996080i	$-0.471808\pi$
$827$	3.47936e6	0.176903	0.0884515	+	0.996080i	$0.471808\pi$
$828$	2.69346e6	0.136532
$829$	2.92116e6	0.147628	0.0738140	−	0.997272i	$-0.476483\pi$
$829$	2.92116e6	0.147628	0.0738140	+	0.997272i	$0.476483\pi$
$830$	−3.96265e6	−0.199660
$831$	1.91619e7	0.962578
$832$	2.35546e7	1.17969
$833$	−2.17129e7	−1.08419
$834$	−3.38333e6	−0.168434
$835$	−1.23592e6	−0.0613442
$836$	−1.71887e7	−0.850605
$837$	4.18662e6	0.206562
$838$	−5.94304e6	−0.292347
$839$	−3.02591e7	−1.48406	−0.742030	−	0.670367i	$-0.766137\pi$
$839$	−3.02591e7	−1.48406	−0.742030	+	0.670367i	$0.766137\pi$
$840$	−2.23859e6	−0.109465
$841$	2.87856e7	1.40341
$842$	1.69770e7	0.825241
$843$	−4.30646e6	−0.208714
$844$	−924634.	−0.0446801
$845$	1.98114e6	0.0954492
$846$	1.16133e7	0.557865
$847$	−2.34344e7	−1.12239
$848$	6.96243e6	0.332484
$849$	−3.18003e6	−0.151413
$850$	−2.72529e7	−1.29379
$851$	−2.47234e6	−0.117026
$852$	−4.58796e6	−0.216531
$853$	−2.88062e7	−1.35555	−0.677773	−	0.735272i	$-0.737055\pi$
$853$	−2.88062e7	−1.35555	−0.677773	+	0.735272i	$0.737055\pi$
$854$	−854483.	−0.0400921
$855$	2.47064e6	0.115583
$856$	−1.60316e7	−0.747813
$857$	−1.93014e7	−0.897711	−0.448856	−	0.893604i	$-0.648168\pi$
$857$	−1.93014e7	−0.897711	−0.448856	+	0.893604i	$0.648168\pi$
$858$	2.42584e7	1.12498
$859$	1.67081e7	0.772580	0.386290	−	0.922377i	$-0.373756\pi$
$859$	1.67081e7	0.772580	0.386290	+	0.922377i	$0.373756\pi$
$860$	1.67539e6	0.0772448
$861$	3.76259e6	0.172973
$862$	4.06954e6	0.186542
$863$	3.66970e7	1.67727	0.838635	−	0.544694i	$-0.183354\pi$
$863$	3.66970e7	1.67727	0.838635	+	0.544694i	$0.183354\pi$
$864$	1.85612e7	0.845907
$865$	−2.60130e6	−0.118209
$866$	−2.06776e7	−0.936927
$867$	−3.65642e7	−1.65199
$868$	1.14864e6	0.0517471
$869$	4.25509e7	1.91143
$870$	4.21484e6	0.188792
$871$	2.43860e7	1.08917
$872$	−2.81153e7	−1.25214
$873$	3.68261e6	0.163538
$874$	−1.44726e7	−0.640866
$875$	6.03370e6	0.266418
$876$	8.28000e6	0.364561
$877$	3.34044e7	1.46657	0.733287	−	0.679919i	$-0.237985\pi$
$877$	3.34044e7	1.46657	0.733287	+	0.679919i	$0.237985\pi$
$878$	2.86396e7	1.25381
$879$	1.72793e7	0.754318
$880$	3.22634e6	0.140444
$881$	3.04149e7	1.32022	0.660111	−	0.751168i	$-0.270509\pi$
$881$	3.04149e7	1.32022	0.660111	+	0.751168i	$0.270509\pi$
$882$	4.72515e6	0.204524
$883$	−8.41286e6	−0.363113	−0.181557	−	0.983381i	$-0.558114\pi$
$883$	−8.41286e6	−0.363113	−0.181557	+	0.983381i	$0.558114\pi$
$884$	−2.14384e7	−0.922704
$885$	−2.80283e6	−0.120293
$886$	−1.55615e6	−0.0665989
$887$	−2.47151e7	−1.05476	−0.527380	−	0.849630i	$-0.676825\pi$
$887$	−2.47151e7	−1.05476	−0.527380	+	0.849630i	$0.676825\pi$
$888$	−3.09993e6	−0.131922
$889$	−1.57178e7	−0.667018
$890$	1.46763e6	0.0621073
$891$	1.38962e7	0.586410
$892$	−7.48023e6	−0.314777
$893$	4.67347e7	1.96115
$894$	1.95217e7	0.816909
$895$	−3.60966e6	−0.150629
$896$	650605.	0.0270737
$897$	−1.52973e7	−0.634795
$898$	−3.57311e7	−1.47862
$899$	−7.21300e6	−0.297657
$900$	−4.44181e6	−0.182790
$901$	−3.74507e7	−1.53691
$902$	−1.14017e7	−0.466610
$903$	−9.53649e6	−0.389197
$904$	4.80599e7	1.95597
$905$	−6.05461e6	−0.245734
$906$	3.89661e6	0.157713
$907$	3.76738e7	1.52062	0.760311	−	0.649560i	$-0.225047\pi$
$907$	3.76738e7	1.52062	0.760311	+	0.649560i	$0.225047\pi$
$908$	−1.12527e7	−0.452941
$909$	−5.35620e6	−0.215004
$910$	−3.09250e6	−0.123796
$911$	2.68818e7	1.07315	0.536577	−	0.843851i	$-0.319717\pi$
$911$	2.68818e7	1.07315	0.536577	+	0.843851i	$0.319717\pi$
$912$	−8.63062e6	−0.343601
$913$	5.11908e7	2.03243
$914$	−1.94038e7	−0.768284
$915$	−343595.	−0.0135673
$916$	−8099.58	−0.000318951 0
$917$	1.04993e7	0.412324
$918$	3.72921e7	1.46053
$919$	2.62087e7	1.02366	0.511831	−	0.859086i	$-0.328967\pi$
$919$	2.62087e7	1.02366	0.511831	+	0.859086i	$0.328967\pi$
$920$	−4.27770e6	−0.166625
$921$	−3.09396e7	−1.20189
$922$	2.81062e7	1.08887
$923$	−2.11387e7	−0.816722
$924$	8.67077e6	0.334101
$925$	4.07715e6	0.156676
$926$	1.06542e7	0.408315
$927$	87653.0	0.00335018
$928$	−3.19786e7	−1.21896
$929$	3.89877e7	1.48214	0.741068	−	0.671430i	$-0.234320\pi$
$929$	3.89877e7	1.48214	0.741068	+	0.671430i	$0.234320\pi$
$930$	−616707.	−0.0233814
$931$	1.90152e7	0.718995
$932$	−7.38653e6	−0.278548
$933$	1.62487e6	0.0611102
$934$	−197295.	−0.00740028
$935$	−1.73544e7	−0.649203
$936$	1.55602e7	0.580529
$937$	3.68666e7	1.37178	0.685889	−	0.727707i	$-0.259414\pi$
$937$	3.68666e7	1.37178	0.685889	+	0.727707i	$0.259414\pi$
$938$	−1.16382e7	−0.431896
$939$	−3.50693e7	−1.29796
$940$	4.14172e6	0.152884
$941$	−1.16091e7	−0.427391	−0.213696	−	0.976900i	$-0.568550\pi$
$941$	−1.16091e7	−0.427391	−0.213696	+	0.976900i	$0.568550\pi$
$942$	−2.56287e7	−0.941021
$943$	7.18989e6	0.263295
$944$	−7.94301e6	−0.290105
$945$	−4.02887e6	−0.146759
$946$	2.88983e7	1.04989
$947$	−2.88246e7	−1.04445	−0.522227	−	0.852807i	$-0.674899\pi$
$947$	−2.88246e7	−1.04445	−0.522227	+	0.852807i	$0.674899\pi$
$948$	−1.00874e7	−0.364552
$949$	3.81496e7	1.37507
$950$	2.38668e7	0.857996
$951$	1.08973e7	0.390724
$952$	3.41241e7	1.22031
$953$	−5.57355e6	−0.198792	−0.0993962	−	0.995048i	$-0.531691\pi$
$953$	−5.57355e6	−0.198792	−0.0993962	+	0.995048i	$0.531691\pi$
$954$	8.14999e6	0.289925
$955$	−151049.	−0.00535932
$956$	8.93279e6	0.316113
$957$	−5.44488e7	−1.92180
$958$	−2.15280e7	−0.757861
$959$	−2.88175e7	−1.01183
$960$	−4.52026e6	−0.158302
$961$	−2.75738e7	−0.963136
$962$	−4.28240e6	−0.149193
$963$	−8.92537e6	−0.310142
$964$	725074.	0.0251298
$965$	4.00613e6	0.138486
$966$	7.30062e6	0.251720
$967$	−1.91665e7	−0.659137	−0.329568	−	0.944132i	$-0.606903\pi$
$967$	−1.91665e7	−0.659137	−0.329568	+	0.944132i	$0.606903\pi$
$968$	−5.61478e7	−1.92595
$969$	4.64238e7	1.58830
$970$	−1.75360e6	−0.0598413
$971$	−5.59710e7	−1.90509	−0.952544	−	0.304399i	$-0.901544\pi$
$971$	−5.59710e7	−1.90509	−0.952544	+	0.304399i	$0.901544\pi$
$972$	1.02759e7	0.348862
$973$	−5.57184e6	−0.188676
$974$	2.43522e6	0.0822509
$975$	2.52269e7	0.849869
$976$	−973723.	−0.0327198
$977$	−3.61480e7	−1.21157	−0.605784	−	0.795629i	$-0.707140\pi$
$977$	−3.61480e7	−1.21157	−0.605784	+	0.795629i	$0.707140\pi$
$978$	2.38174e7	0.796244
$979$	−1.89594e7	−0.632219
$980$	1.68516e6	0.0560500
$981$	−1.56528e7	−0.519301
$982$	1.10462e7	0.365538
$983$	−6.34806e6	−0.209535	−0.104768	−	0.994497i	$-0.533410\pi$
$983$	−6.34806e6	−0.209535	−0.104768	+	0.994497i	$0.533410\pi$
$984$	9.01500e6	0.296810
$985$	−6.51798e6	−0.214054
$986$	−6.42493e7	−2.10463
$987$	−2.35751e7	−0.770301
$988$	1.87748e7	0.611903
$989$	−1.82232e7	−0.592425
$990$	3.77665e6	0.122467
$991$	4.88790e6	0.158102	0.0790512	−	0.996871i	$-0.474811\pi$
$991$	4.88790e6	0.158102	0.0790512	+	0.996871i	$0.474811\pi$
$992$	4.67904e6	0.150965
$993$	3.52734e7	1.13520
$994$	1.00884e7	0.323860
$995$	9.54560e6	0.305665
$996$	−1.21357e7	−0.387629
$997$	−3.85715e7	−1.22894	−0.614468	−	0.788942i	$-0.710629\pi$
$997$	−3.85715e7	−1.22894	−0.614468	+	0.788942i	$0.710629\pi$
$998$	−2.81462e7	−0.894527
$999$	−5.57906e6	−0.176867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.a.a.1.6	✓	7
3.2	odd	2		333.6.a.c.1.2		7
4.3	odd	2		592.6.a.g.1.5		7
5.4	even	2		925.6.a.a.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.a.a.1.6	✓	7	1.1	even	1	trivial
333.6.a.c.1.2		7	3.2	odd	2
592.6.a.g.1.5		7	4.3	odd	2
925.6.a.a.1.2		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)

\(f(q)\)	\(=\)	\(q+4.27747 q^{2} -11.5828 q^{3} -13.7033 q^{4} +12.1163 q^{5} -49.5451 q^{6} -81.5934 q^{7} -195.494 q^{8} -108.839 q^{9} +O(q^{10})\)	\(q+4.27747 q^{2} -11.5828 q^{3} -13.7033 q^{4} +12.1163 q^{5} -49.5451 q^{6} -81.5934 q^{7} -195.494 q^{8} -108.839 q^{9} +51.8273 q^{10} -669.522 q^{11} +158.722 q^{12} +731.302 q^{13} -349.013 q^{14} -140.341 q^{15} -397.717 q^{16} +2139.30 q^{17} -465.554 q^{18} -1873.50 q^{19} -166.033 q^{20} +945.080 q^{21} -2863.86 q^{22} +1805.94 q^{23} +2264.37 q^{24} -2978.19 q^{25} +3128.12 q^{26} +4075.28 q^{27} +1118.09 q^{28} -7021.16 q^{29} -600.305 q^{30} +1027.32 q^{31} +4554.60 q^{32} +7754.95 q^{33} +9150.81 q^{34} -988.613 q^{35} +1491.44 q^{36} -1369.00 q^{37} -8013.85 q^{38} -8470.53 q^{39} -2368.68 q^{40} +3981.24 q^{41} +4042.55 q^{42} -10090.7 q^{43} +9174.64 q^{44} -1318.73 q^{45} +7724.87 q^{46} -24945.1 q^{47} +4606.67 q^{48} -10149.5 q^{49} -12739.1 q^{50} -24779.1 q^{51} -10021.2 q^{52} -17506.0 q^{53} +17431.9 q^{54} -8112.16 q^{55} +15951.0 q^{56} +21700.4 q^{57} -30032.8 q^{58} +19971.5 q^{59} +1923.13 q^{60} +2448.28 q^{61} +4394.34 q^{62} +8880.51 q^{63} +32209.1 q^{64} +8860.70 q^{65} +33171.5 q^{66} +33346.1 q^{67} -29315.4 q^{68} -20917.9 q^{69} -4228.76 q^{70} -28905.6 q^{71} +21277.3 q^{72} +52166.7 q^{73} -5855.86 q^{74} +34495.8 q^{75} +25673.1 q^{76} +54628.6 q^{77} -36232.4 q^{78} -63554.1 q^{79} -4818.87 q^{80} -20755.4 q^{81} +17029.6 q^{82} -76458.7 q^{83} -12950.7 q^{84} +25920.6 q^{85} -43162.5 q^{86} +81324.8 q^{87} +130888. q^{88} +28317.8 q^{89} -5640.81 q^{90} -59669.4 q^{91} -24747.3 q^{92} -11899.3 q^{93} -106702. q^{94} -22700.0 q^{95} -52755.0 q^{96} -33835.5 q^{97} -43414.3 q^{98} +72869.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) \) 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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