LMFDB - Embedded newform 115.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,6,Mod(1,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	115.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:	$18.4441392785$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 329 x^{10} + 1059 x^{9} + 41059 x^{8} - 99023 x^{7} - 2392947 x^{6} + 3889937 x^{5} + \cdots + 4039776 $ x^12 - 4x^11 - 329x^10 + 1059x^9 + 41059x^8 - 99023x^7 - 2392947x^6 + 3889937x^5 + 63665212x^4 - 59034365x^3 - 601032676x^2 + 161487612*x + 4039776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$10.8081$ of defining polynomial
Character	$\chi$	$=$	115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.80811 q^{2} -29.7028 q^{3} +64.1990 q^{4} +25.0000 q^{5} +291.328 q^{6} -68.7900 q^{7} -315.812 q^{8} +639.254 q^{9} +O(q^{10})$	\(q-9.80811 q^{2} -29.7028 q^{3} +64.1990 q^{4} +25.0000 q^{5} +291.328 q^{6} -68.7900 q^{7} -315.812 q^{8} +639.254 q^{9} -245.203 q^{10} -393.750 q^{11} -1906.89 q^{12} -251.969 q^{13} +674.700 q^{14} -742.569 q^{15} +1043.15 q^{16} -1000.53 q^{17} -6269.87 q^{18} -2743.81 q^{19} +1604.98 q^{20} +2043.25 q^{21} +3861.94 q^{22} -529.000 q^{23} +9380.48 q^{24} +625.000 q^{25} +2471.34 q^{26} -11769.8 q^{27} -4416.25 q^{28} +7579.70 q^{29} +7283.20 q^{30} -3159.32 q^{31} -125.331 q^{32} +11695.5 q^{33} +9813.28 q^{34} -1719.75 q^{35} +41039.5 q^{36} -7626.55 q^{37} +26911.5 q^{38} +7484.17 q^{39} -7895.29 q^{40} -16821.4 q^{41} -20040.5 q^{42} -3785.83 q^{43} -25278.4 q^{44} +15981.4 q^{45} +5188.49 q^{46} -12375.0 q^{47} -30984.4 q^{48} -12074.9 q^{49} -6130.07 q^{50} +29718.4 q^{51} -16176.2 q^{52} +9780.34 q^{53} +115440. q^{54} -9843.75 q^{55} +21724.7 q^{56} +81498.6 q^{57} -74342.5 q^{58} -5344.99 q^{59} -47672.2 q^{60} -8400.49 q^{61} +30987.0 q^{62} -43974.3 q^{63} -32151.5 q^{64} -6299.22 q^{65} -114710. q^{66} +67681.7 q^{67} -64232.9 q^{68} +15712.8 q^{69} +16867.5 q^{70} +56401.2 q^{71} -201884. q^{72} +16501.4 q^{73} +74802.1 q^{74} -18564.2 q^{75} -176150. q^{76} +27086.1 q^{77} -73405.6 q^{78} -79498.5 q^{79} +26078.7 q^{80} +194258. q^{81} +164986. q^{82} +52755.3 q^{83} +131175. q^{84} -25013.2 q^{85} +37131.9 q^{86} -225138. q^{87} +124351. q^{88} -4196.50 q^{89} -156747. q^{90} +17332.9 q^{91} -33961.3 q^{92} +93840.6 q^{93} +121375. q^{94} -68595.1 q^{95} +3722.69 q^{96} +16173.7 q^{97} +118432. q^{98} -251706. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9}+O(q^{10}) $ 12 * q + 8 * q^2 + 22 * q^3 + 294 * q^4 + 300 * q^5 + 454 * q^6 + 16 * q^7 + 675 * q^8 + 1598 * q^9	\( 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9} + 200 q^{10} + 132 q^{11} + 728 q^{12} - 236 q^{13} + 359 q^{14} + 550 q^{15} + 4514 q^{16} + 1666 q^{17} - 3096 q^{18} + 616 q^{19} + 7350 q^{20} + 2732 q^{21} + 305 q^{22} - 6348 q^{23} + 18873 q^{24} + 7500 q^{25} - 4502 q^{26} + 11584 q^{27} + 5407 q^{28} + 23722 q^{29} + 11350 q^{30} + 18446 q^{31} + 35808 q^{32} + 4416 q^{33} + 53123 q^{34} + 400 q^{35} + 68916 q^{36} + 10394 q^{37} + 18681 q^{38} + 27032 q^{39} + 16875 q^{40} + 48232 q^{41} - 18980 q^{42} + 10732 q^{43} - 4765 q^{44} + 39950 q^{45} - 4232 q^{46} - 30448 q^{47} - 2052 q^{48} + 26948 q^{49} + 5000 q^{50} + 1524 q^{51} - 55346 q^{52} + 36494 q^{53} + 55567 q^{54} + 3300 q^{55} - 50981 q^{56} + 37572 q^{57} - 83373 q^{58} - 23870 q^{59} + 18200 q^{60} + 30862 q^{61} + 63582 q^{62} - 49698 q^{63} + 29965 q^{64} - 5900 q^{65} - 235225 q^{66} - 71910 q^{67} - 39371 q^{68} - 11638 q^{69} + 8975 q^{70} + 167158 q^{71} - 296052 q^{72} + 52152 q^{73} - 59356 q^{74} + 13750 q^{75} - 230417 q^{76} + 4808 q^{77} - 469771 q^{78} - 123092 q^{79} + 112850 q^{80} + 159868 q^{81} - 140098 q^{82} + 89322 q^{83} - 488082 q^{84} + 41650 q^{85} - 55318 q^{86} - 334376 q^{87} - 104551 q^{88} - 46184 q^{89} - 77400 q^{90} - 153444 q^{91} - 155526 q^{92} - 16576 q^{93} - 456595 q^{94} + 15400 q^{95} + 330540 q^{96} - 94220 q^{97} + 413841 q^{98} - 740784 q^{99}+O(q^{100}) \) 12 * q + 8 * q^2 + 22 * q^3 + 294 * q^4 + 300 * q^5 + 454 * q^6 + 16 * q^7 + 675 * q^8 + 1598 * q^9 + 200 * q^10 + 132 * q^11 + 728 * q^12 - 236 * q^13 + 359 * q^14 + 550 * q^15 + 4514 * q^16 + 1666 * q^17 - 3096 * q^18 + 616 * q^19 + 7350 * q^20 + 2732 * q^21 + 305 * q^22 - 6348 * q^23 + 18873 * q^24 + 7500 * q^25 - 4502 * q^26 + 11584 * q^27 + 5407 * q^28 + 23722 * q^29 + 11350 * q^30 + 18446 * q^31 + 35808 * q^32 + 4416 * q^33 + 53123 * q^34 + 400 * q^35 + 68916 * q^36 + 10394 * q^37 + 18681 * q^38 + 27032 * q^39 + 16875 * q^40 + 48232 * q^41 - 18980 * q^42 + 10732 * q^43 - 4765 * q^44 + 39950 * q^45 - 4232 * q^46 - 30448 * q^47 - 2052 * q^48 + 26948 * q^49 + 5000 * q^50 + 1524 * q^51 - 55346 * q^52 + 36494 * q^53 + 55567 * q^54 + 3300 * q^55 - 50981 * q^56 + 37572 * q^57 - 83373 * q^58 - 23870 * q^59 + 18200 * q^60 + 30862 * q^61 + 63582 * q^62 - 49698 * q^63 + 29965 * q^64 - 5900 * q^65 - 235225 * q^66 - 71910 * q^67 - 39371 * q^68 - 11638 * q^69 + 8975 * q^70 + 167158 * q^71 - 296052 * q^72 + 52152 * q^73 - 59356 * q^74 + 13750 * q^75 - 230417 * q^76 + 4808 * q^77 - 469771 * q^78 - 123092 * q^79 + 112850 * q^80 + 159868 * q^81 - 140098 * q^82 + 89322 * q^83 - 488082 * q^84 + 41650 * q^85 - 55318 * q^86 - 334376 * q^87 - 104551 * q^88 - 46184 * q^89 - 77400 * q^90 - 153444 * q^91 - 155526 * q^92 - 16576 * q^93 - 456595 * q^94 + 15400 * q^95 + 330540 * q^96 - 94220 * q^97 + 413841 * q^98 - 740784 * 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 $

$2$	−9.80811	−1.73385	−0.866923	−	0.498443i	$-0.833905\pi$
$2$	−9.80811	−1.73385	−0.866923	+	0.498443i	$0.833905\pi$
$3$	−29.7028	−1.90543	−0.952717	−	0.303861i	$-0.901724\pi$
$3$	−29.7028	−1.90543	−0.952717	+	0.303861i	$0.901724\pi$
$4$	64.1990	2.00622
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	291.328	3.30373
$7$	−68.7900	−0.530616	−0.265308	−	0.964164i	$-0.585474\pi$
$7$	−68.7900	−0.530616	−0.265308	+	0.964164i	$0.585474\pi$
$8$	−315.812	−1.74463
$9$	639.254	2.63068
$10$	−245.203	−0.775399
$11$	−393.750	−0.981158	−0.490579	−	0.871397i	$-0.663215\pi$
$11$	−393.750	−0.981158	−0.490579	+	0.871397i	$0.663215\pi$
$12$	−1906.89	−3.82272
$13$	−251.969	−0.413512	−0.206756	−	0.978393i	$-0.566291\pi$
$13$	−251.969	−0.413512	−0.206756	+	0.978393i	$0.566291\pi$
$14$	674.700	0.920006
$15$	−742.569	−0.852136
$16$	1043.15	1.01870
$17$	−1000.53	−0.839666	−0.419833	−	0.907601i	$-0.637911\pi$
$17$	−1000.53	−0.839666	−0.419833	+	0.907601i	$0.637911\pi$
$18$	−6269.87	−4.56118
$19$	−2743.81	−1.74369	−0.871845	−	0.489782i	$-0.837076\pi$
$19$	−2743.81	−1.74369	−0.871845	+	0.489782i	$0.837076\pi$
$20$	1604.98	0.897209
$21$	2043.25	1.01105
$22$	3861.94	1.70118
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	9380.48	3.32428
$25$	625.000	0.200000
$26$	2471.34	0.716966
$27$	−11769.8	−3.10714
$28$	−4416.25	−1.06453
$29$	7579.70	1.67362	0.836810	−	0.547494i	$-0.184418\pi$
$29$	7579.70	1.67362	0.836810	+	0.547494i	$0.184418\pi$
$30$	7283.20	1.47747
$31$	−3159.32	−0.590459	−0.295229	−	0.955426i	$-0.595396\pi$
$31$	−3159.32	−0.590459	−0.295229	+	0.955426i	$0.595396\pi$
$32$	−125.331	−0.0216364
$33$	11695.5	1.86953
$34$	9813.28	1.45585
$35$	−1719.75	−0.237299
$36$	41039.5	5.27771
$37$	−7626.55	−0.915849	−0.457925	−	0.888991i	$-0.651407\pi$
$37$	−7626.55	−0.915849	−0.457925	+	0.888991i	$0.651407\pi$
$38$	26911.5	3.02329
$39$	7484.17	0.787920
$40$	−7895.29	−0.780222
$41$	−16821.4	−1.56280	−0.781399	−	0.624032i	$-0.785493\pi$
$41$	−16821.4	−1.56280	−0.781399	+	0.624032i	$0.785493\pi$
$42$	−20040.5	−1.75301
$43$	−3785.83	−0.312241	−0.156121	−	0.987738i	$-0.549899\pi$
$43$	−3785.83	−0.312241	−0.156121	+	0.987738i	$0.549899\pi$
$44$	−25278.4	−1.96842
$45$	15981.4	1.17647
$46$	5188.49	0.361532
$47$	−12375.0	−0.817145	−0.408573	−	0.912726i	$-0.633973\pi$
$47$	−12375.0	−0.817145	−0.408573	+	0.912726i	$0.633973\pi$
$48$	−30984.4	−1.94106
$49$	−12074.9	−0.718447
$50$	−6130.07	−0.346769
$51$	29718.4	1.59993
$52$	−16176.2	−0.829597
$53$	9780.34	0.478260	0.239130	−	0.970988i	$-0.423138\pi$
$53$	9780.34	0.478260	0.239130	+	0.970988i	$0.423138\pi$
$54$	115440.	5.38730
$55$	−9843.75	−0.438787
$56$	21724.7	0.925729
$57$	81498.6	3.32248
$58$	−74342.5	−2.90180
$59$	−5344.99	−0.199902	−0.0999510	−	0.994992i	$-0.531869\pi$
$59$	−5344.99	−0.199902	−0.0999510	+	0.994992i	$0.531869\pi$
$60$	−47672.2	−1.70957
$61$	−8400.49	−0.289055	−0.144527	−	0.989501i	$-0.546166\pi$
$61$	−8400.49	−0.289055	−0.144527	+	0.989501i	$0.546166\pi$
$62$	30987.0	1.02376
$63$	−43974.3	−1.39588
$64$	−32151.5	−0.981185
$65$	−6299.22	−0.184928
$66$	−114710.	−3.24148
$67$	67681.7	1.84198	0.920988	−	0.389590i	$-0.127383\pi$
$67$	67681.7	1.84198	0.920988	+	0.389590i	$0.127383\pi$
$68$	−64232.9	−1.68456
$69$	15712.8	0.397310
$70$	16867.5	0.411439
$71$	56401.2	1.32783	0.663915	−	0.747808i	$-0.268893\pi$
$71$	56401.2	1.32783	0.663915	+	0.747808i	$0.268893\pi$
$72$	−201884.	−4.58956
$73$	16501.4	0.362421	0.181210	−	0.983444i	$-0.441999\pi$
$73$	16501.4	0.362421	0.181210	+	0.983444i	$0.441999\pi$
$74$	74802.1	1.58794
$75$	−18564.2	−0.381087
$76$	−176150.	−3.49823
$77$	27086.1	0.520618
$78$	−73405.6	−1.36613
$79$	−79498.5	−1.43315	−0.716574	−	0.697511i	$-0.754291\pi$
$79$	−79498.5	−1.43315	−0.716574	+	0.697511i	$0.754291\pi$
$80$	26078.7	0.455576
$81$	194258.	3.28978
$82$	164986.	2.70965
$83$	52755.3	0.840564	0.420282	−	0.907394i	$-0.361931\pi$
$83$	52755.3	0.840564	0.420282	+	0.907394i	$0.361931\pi$
$84$	131175.	2.02840
$85$	−25013.2	−0.375510
$86$	37131.9	0.541378
$87$	−225138.	−3.18897
$88$	124351.	1.71176
$89$	−4196.50	−0.0561581	−0.0280790	−	0.999606i	$-0.508939\pi$
$89$	−4196.50	−0.0561581	−0.0280790	+	0.999606i	$0.508939\pi$
$90$	−156747.	−2.03982
$91$	17332.9	0.219416
$92$	−33961.3	−0.418326
$93$	93840.6	1.12508
$94$	121375.	1.41680
$95$	−68595.1	−0.779802
$96$	3722.69	0.0412267
$97$	16173.7	0.174534	0.0872669	−	0.996185i	$-0.472187\pi$
$97$	16173.7	0.174534	0.0872669	+	0.996185i	$0.472187\pi$
$98$	118432.	1.24568
$99$	−251706.	−2.58111
$100$	40124.4	0.401244
$101$	178712.	1.74321	0.871605	−	0.490210i	$-0.163080\pi$
$101$	178712.	1.74321	0.871605	+	0.490210i	$0.163080\pi$
$102$	−291482.	−2.77403
$103$	−140142.	−1.30159	−0.650796	−	0.759253i	$-0.725565\pi$
$103$	−140142.	−1.30159	−0.650796	+	0.759253i	$0.725565\pi$
$104$	79574.7	0.721426
$105$	51081.3	0.452157
$106$	−95926.7	−0.829229
$107$	153885.	1.29938	0.649690	−	0.760199i	$-0.274899\pi$
$107$	153885.	1.29938	0.649690	+	0.760199i	$0.274899\pi$
$108$	−755612.	−6.23361
$109$	4297.43	0.0346451	0.0173226	−	0.999850i	$-0.494486\pi$
$109$	4297.43	0.0346451	0.0173226	+	0.999850i	$0.494486\pi$
$110$	96548.6	0.760789
$111$	226530.	1.74509
$112$	−71758.2	−0.540538
$113$	−149074.	−1.09826	−0.549132	−	0.835735i	$-0.685042\pi$
$113$	−149074.	−1.09826	−0.549132	+	0.835735i	$0.685042\pi$
$114$	−799347.	−5.76068
$115$	−13225.0	−0.0932505
$116$	486609.	3.35765
$117$	−161072.	−1.08782
$118$	52424.3	0.346599
$119$	68826.3	0.445540
$120$	234512.	1.48666
$121$	−6011.87	−0.0373290
$122$	82392.9	0.501176
$123$	499642.	2.97781
$124$	−202825.	−1.18459
$125$	15625.0	0.0894427
$126$	431305.	2.42024
$127$	245206.	1.34903	0.674517	−	0.738260i	$-0.264352\pi$
$127$	245206.	1.34903	0.674517	+	0.738260i	$0.264352\pi$
$128$	319356.	1.72286
$129$	112450.	0.594955
$130$	61783.5	0.320637
$131$	147628.	0.751606	0.375803	−	0.926700i	$-0.377367\pi$
$131$	147628.	0.751606	0.375803	+	0.926700i	$0.377367\pi$
$132$	750838.	3.75069
$133$	188746.	0.925230
$134$	−663829.	−3.19370
$135$	−294246.	−1.38956
$136$	315978.	1.46491
$137$	156795.	0.713726	0.356863	−	0.934157i	$-0.383846\pi$
$137$	156795.	0.713726	0.356863	+	0.934157i	$0.383846\pi$
$138$	−154113.	−0.688875
$139$	−172947.	−0.759233	−0.379616	−	0.925144i	$-0.623944\pi$
$139$	−172947.	−0.759233	−0.379616	+	0.925144i	$0.623944\pi$
$140$	−110406.	−0.476073
$141$	367570.	1.55702
$142$	−553190.	−2.30225
$143$	99212.7	0.405721
$144$	666836.	2.67987
$145$	189492.	0.748465
$146$	−161847.	−0.628381
$147$	358659.	1.36895
$148$	−489617.	−1.83740
$149$	253247.	0.934500	0.467250	−	0.884125i	$-0.345245\pi$
$149$	253247.	0.934500	0.467250	+	0.884125i	$0.345245\pi$
$150$	182080.	0.660745
$151$	190402.	0.679564	0.339782	−	0.940504i	$-0.389647\pi$
$151$	190402.	0.679564	0.339782	+	0.940504i	$0.389647\pi$
$152$	866526.	3.04209
$153$	−639591.	−2.20889
$154$	−265663.	−0.902671
$155$	−78983.0	−0.264061
$156$	480477.	1.58074
$157$	−285857.	−0.925550	−0.462775	−	0.886476i	$-0.653146\pi$
$157$	−285857.	−0.925550	−0.462775	+	0.886476i	$0.653146\pi$
$158$	779730.	2.48486
$159$	−290503.	−0.911293
$160$	−3133.29	−0.00967609
$161$	36389.9	0.110641
$162$	−1.90530e6	−5.70396
$163$	−271269.	−0.799708	−0.399854	−	0.916579i	$-0.630939\pi$
$163$	−271269.	−0.799708	−0.399854	+	0.916579i	$0.630939\pi$
$164$	−1.07992e6	−3.13532
$165$	292387.	0.836080
$166$	−517429.	−1.45741
$167$	218894.	0.607354	0.303677	−	0.952775i	$-0.401786\pi$
$167$	218894.	0.607354	0.303677	+	0.952775i	$0.401786\pi$
$168$	−645284.	−1.76391
$169$	−307805.	−0.829008
$170$	245332.	0.651077
$171$	−1.75399e6	−4.58708
$172$	−243047.	−0.626425
$173$	−97936.2	−0.248787	−0.124394	−	0.992233i	$-0.539699\pi$
$173$	−97936.2	−0.248787	−0.124394	+	0.992233i	$0.539699\pi$
$174$	2.20818e6	5.52918
$175$	−42993.8	−0.106123
$176$	−410739.	−0.999505
$177$	158761.	0.380900
$178$	41159.7	0.0973694
$179$	−52867.5	−0.123326	−0.0616632	−	0.998097i	$-0.519640\pi$
$179$	−52867.5	−0.123326	−0.0616632	+	0.998097i	$0.519640\pi$
$180$	1.02599e6	2.36027
$181$	−152719.	−0.346494	−0.173247	−	0.984878i	$-0.555426\pi$
$181$	−152719.	−0.346494	−0.173247	+	0.984878i	$0.555426\pi$
$182$	−170003.	−0.380434
$183$	249518.	0.550774
$184$	167064.	0.363781
$185$	−190664.	−0.409580
$186$	−920399.	−1.95071
$187$	393958.	0.823845
$188$	−794461.	−1.63937
$189$	809648.	1.64870
$190$	672789.	1.35206
$191$	−511434.	−1.01439	−0.507196	−	0.861831i	$-0.669318\pi$
$191$	−511434.	−1.01439	−0.507196	+	0.861831i	$0.669318\pi$
$192$	954987.	1.86958
$193$	855499.	1.65320	0.826601	−	0.562788i	$-0.190271\pi$
$193$	855499.	1.65320	0.826601	+	0.562788i	$0.190271\pi$
$194$	−158633.	−0.302615
$195$	187104.	0.352369
$196$	−775199.	−1.44136
$197$	210049.	0.385615	0.192808	−	0.981237i	$-0.438241\pi$
$197$	210049.	0.385615	0.192808	+	0.981237i	$0.438241\pi$
$198$	2.46876e6	4.47524
$199$	−930180.	−1.66508	−0.832539	−	0.553967i	$-0.813114\pi$
$199$	−930180.	−1.66508	−0.832539	+	0.553967i	$0.813114\pi$
$200$	−197382.	−0.348926
$201$	−2.01033e6	−3.50976
$202$	−1.75282e6	−3.02246
$203$	−521407.	−0.888049
$204$	1.90789e6	3.20981
$205$	−420535.	−0.698904
$206$	1.37453e6	2.25676
$207$	−338165.	−0.548534
$208$	−262841.	−0.421245
$209$	1.08037e6	1.71084
$210$	−501012.	−0.783970
$211$	1.17354e6	1.81464	0.907319	−	0.420442i	$-0.138125\pi$
$211$	1.17354e6	1.81464	0.907319	+	0.420442i	$0.138125\pi$
$212$	627888.	0.959495
$213$	−1.67527e6	−2.53009
$214$	−1.50932e6	−2.25293
$215$	−94645.8	−0.139639
$216$	3.71705e6	5.42081
$217$	217330.	0.313307
$218$	−42149.6	−0.0600693
$219$	−490136.	−0.690568
$220$	−631959.	−0.880304
$221$	252102.	0.347212
$222$	−2.22183e6	−3.02572
$223$	419263.	0.564579	0.282289	−	0.959329i	$-0.408906\pi$
$223$	419263.	0.564579	0.282289	+	0.959329i	$0.408906\pi$
$224$	8621.55	0.0114806
$225$	399534.	0.526135
$226$	1.46214e6	1.90422
$227$	−841472.	−1.08386	−0.541932	−	0.840422i	$-0.682307\pi$
$227$	−841472.	−1.08386	−0.541932	+	0.840422i	$0.682307\pi$
$228$	5.23213e6	6.66564
$229$	910350.	1.14715	0.573574	−	0.819154i	$-0.305556\pi$
$229$	910350.	1.14715	0.573574	+	0.819154i	$0.305556\pi$
$230$	129712.	0.161682
$231$	−804531.	−0.992003
$232$	−2.39376e6	−2.91985
$233$	−1.01067e6	−1.21961	−0.609805	−	0.792552i	$-0.708752\pi$
$233$	−1.01067e6	−1.21961	−0.609805	+	0.792552i	$0.708752\pi$
$234$	1.57981e6	1.88611
$235$	−309374.	−0.365438
$236$	−343143.	−0.401047
$237$	2.36132e6	2.73077
$238$	−675056.	−0.772498
$239$	−228004.	−0.258195	−0.129097	−	0.991632i	$-0.541208\pi$
$239$	−228004.	−0.258195	−0.129097	+	0.991632i	$0.541208\pi$
$240$	−774609.	−0.868070
$241$	1.73481e6	1.92402	0.962011	−	0.273012i	$-0.0880198\pi$
$241$	1.73481e6	1.92402	0.962011	+	0.273012i	$0.0880198\pi$
$242$	58965.1	0.0647227
$243$	−2.90993e6	−3.16131
$244$	−539303.	−0.579907
$245$	−301873.	−0.321299
$246$	−4.90055e6	−5.16306
$247$	691353.	0.721037
$248$	997751.	1.03013
$249$	−1.56698e6	−1.60164
$250$	−153252.	−0.155080
$251$	634765.	0.635959	0.317979	−	0.948098i	$-0.396996\pi$
$251$	634765.	0.635959	0.317979	+	0.948098i	$0.396996\pi$
$252$	−2.82311e6	−2.80044
$253$	208294.	0.204586
$254$	−2.40501e6	−2.33901
$255$	742961.	0.715509
$256$	−2.10343e6	−2.00599
$257$	−242441.	−0.228967	−0.114484	−	0.993425i	$-0.536521\pi$
$257$	−242441.	−0.228967	−0.114484	+	0.993425i	$0.536521\pi$
$258$	−1.10292e6	−1.03156
$259$	524631.	0.485964
$260$	−404404.	−0.371007
$261$	4.84535e6	4.40275
$262$	−1.44795e6	−1.30317
$263$	276583.	0.246568	0.123284	−	0.992371i	$-0.460657\pi$
$263$	276583.	0.246568	0.123284	+	0.992371i	$0.460657\pi$
$264$	−3.69357e6	−3.26164
$265$	244508.	0.213884
$266$	−1.85125e6	−1.60421
$267$	124648.	0.107005
$268$	4.34510e6	3.69541
$269$	693060.	0.583970	0.291985	−	0.956423i	$-0.405684\pi$
$269$	693060.	0.583970	0.291985	+	0.956423i	$0.405684\pi$
$270$	2.88600e6	2.40928
$271$	1.57317e6	1.30123	0.650615	−	0.759408i	$-0.274511\pi$
$271$	1.57317e6	1.30123	0.650615	+	0.759408i	$0.274511\pi$
$272$	−1.04370e6	−0.855367
$273$	−514836.	−0.418083
$274$	−1.53787e6	−1.23749
$275$	−246094.	−0.196232
$276$	1.00874e6	0.797092
$277$	−1.64977e6	−1.29188	−0.645942	−	0.763387i	$-0.723535\pi$
$277$	−1.64977e6	−1.29188	−0.645942	+	0.763387i	$0.723535\pi$
$278$	1.69628e6	1.31639
$279$	−2.01961e6	−1.55330
$280$	543118.	0.413998
$281$	−1.00188e6	−0.756920	−0.378460	−	0.925618i	$-0.623546\pi$
$281$	−1.00188e6	−0.756920	−0.378460	+	0.925618i	$0.623546\pi$
$282$	−3.60517e6	−2.69962
$283$	1.31053e6	0.972707	0.486354	−	0.873762i	$-0.338327\pi$
$283$	1.31053e6	0.972707	0.486354	+	0.873762i	$0.338327\pi$
$284$	3.62091e6	2.66392
$285$	2.03746e6	1.48586
$286$	−973090.	−0.703457
$287$	1.15715e6	0.829246
$288$	−80118.6	−0.0569183
$289$	−418802.	−0.294961
$290$	−1.85856e6	−1.29772
$291$	−480403.	−0.332563
$292$	1.05937e6	0.727096
$293$	500777.	0.340781	0.170390	−	0.985377i	$-0.445497\pi$
$293$	500777.	0.340781	0.170390	+	0.985377i	$0.445497\pi$
$294$	−3.51777e6	−2.37355
$295$	−133625.	−0.0893989
$296$	2.40856e6	1.59782
$297$	4.63438e6	3.04860
$298$	−2.48388e6	−1.62028
$299$	133292.	0.0862233
$300$	−1.19181e6	−0.764544
$301$	260428.	0.165680
$302$	−1.86749e6	−1.17826
$303$	−5.30823e6	−3.32157
$304$	−2.86219e6	−1.77630
$305$	−210012.	−0.129269
$306$	6.27318e6	3.82987
$307$	418263.	0.253282	0.126641	−	0.991949i	$-0.459580\pi$
$307$	418263.	0.253282	0.126641	+	0.991949i	$0.459580\pi$
$308$	1.73890e6	1.04447
$309$	4.16260e6	2.48010
$310$	774674.	0.457841
$311$	−2.53402e6	−1.48563	−0.742814	−	0.669498i	$-0.766509\pi$
$311$	−2.53402e6	−1.48563	−0.742814	+	0.669498i	$0.766509\pi$
$312$	−2.36359e6	−1.37463
$313$	−356577.	−0.205728	−0.102864	−	0.994695i	$-0.532801\pi$
$313$	−356577.	−0.205728	−0.102864	+	0.994695i	$0.532801\pi$
$314$	2.80372e6	1.60476
$315$	−1.09936e6	−0.624256
$316$	−5.10373e6	−2.87521
$317$	1.87801e6	1.04966	0.524831	−	0.851206i	$-0.324128\pi$
$317$	1.87801e6	1.04966	0.524831	+	0.851206i	$0.324128\pi$
$318$	2.84929e6	1.58004
$319$	−2.98451e6	−1.64209
$320$	−803787.	−0.438799
$321$	−4.57080e6	−2.47588
$322$	−356916.	−0.191835
$323$	2.74525e6	1.46412
$324$	1.24712e7	6.60002
$325$	−157481.	−0.0827025
$326$	2.66064e6	1.38657
$327$	−127645.	−0.0660140
$328$	5.31240e6	2.72650
$329$	851274.	0.433590
$330$	−2.86776e6	−1.44963
$331$	39858.5	0.0199964	0.00999818	−	0.999950i	$-0.496817\pi$
$331$	39858.5	0.0199964	0.00999818	+	0.999950i	$0.496817\pi$
$332$	3.38684e6	1.68636
$333$	−4.87531e6	−2.40930
$334$	−2.14693e6	−1.05306
$335$	1.69204e6	0.823757
$336$	2.13142e6	1.02996
$337$	−2.08374e6	−0.999467	−0.499734	−	0.866179i	$-0.666569\pi$
$337$	−2.08374e6	−0.999467	−0.499734	+	0.866179i	$0.666569\pi$
$338$	3.01898e6	1.43737
$339$	4.42792e6	2.09267
$340$	−1.60582e6	−0.753356
$341$	1.24398e6	0.579333
$342$	1.72033e7	7.95329
$343$	1.98679e6	0.911835
$344$	1.19561e6	0.544746
$345$	392819.	0.177683
$346$	960569.	0.431359
$347$	−1.78397e6	−0.795358	−0.397679	−	0.917525i	$-0.630184\pi$
$347$	−1.78397e6	−0.795358	−0.397679	+	0.917525i	$0.630184\pi$
$348$	−1.44536e7	−6.39778
$349$	3.65364e6	1.60569	0.802847	−	0.596186i	$-0.203318\pi$
$349$	3.65364e6	1.60569	0.802847	+	0.596186i	$0.203318\pi$
$350$	421688.	0.184001
$351$	2.96563e6	1.28484
$352$	49349.3	0.0212287
$353$	457806.	0.195544	0.0977720	−	0.995209i	$-0.468828\pi$
$353$	457806.	0.195544	0.0977720	+	0.995209i	$0.468828\pi$
$354$	−1.55715e6	−0.660421
$355$	1.41003e6	0.593824
$356$	−269411.	−0.112665
$357$	−2.04433e6	−0.848947
$358$	518530.	0.213829
$359$	1.08123e6	0.442775	0.221387	−	0.975186i	$-0.428941\pi$
$359$	1.08123e6	0.442775	0.221387	+	0.975186i	$0.428941\pi$
$360$	−5.04710e6	−2.05251
$361$	5.05237e6	2.04046
$362$	1.49788e6	0.600767
$363$	178569.	0.0711279
$364$	1.11276e6	0.440197
$365$	412534.	0.162079
$366$	−2.44730e6	−0.954958
$367$	1.26620e6	0.490725	0.245363	−	0.969431i	$-0.421093\pi$
$367$	1.26620e6	0.490725	0.245363	+	0.969431i	$0.421093\pi$
$368$	−551825.	−0.212413
$369$	−1.07532e7	−4.11121
$370$	1.87005e6	0.710149
$371$	−672790.	−0.253773
$372$	6.02447e6	2.25716
$373$	−4.33662e6	−1.61391	−0.806955	−	0.590613i	$-0.798886\pi$
$373$	−4.33662e6	−1.61391	−0.806955	+	0.590613i	$0.798886\pi$
$374$	−3.86398e6	−1.42842
$375$	−464106.	−0.170427
$376$	3.90816e6	1.42562
$377$	−1.90985e6	−0.692062
$378$	−7.94111e6	−2.85859
$379$	2.63431e6	0.942040	0.471020	−	0.882123i	$-0.343886\pi$
$379$	2.63431e6	0.942040	0.471020	+	0.882123i	$0.343886\pi$
$380$	−4.40374e6	−1.56445
$381$	−7.28331e6	−2.57049
$382$	5.01620e6	1.75880
$383$	868993.	0.302705	0.151352	−	0.988480i	$-0.451637\pi$
$383$	868993.	0.302705	0.151352	+	0.988480i	$0.451637\pi$
$384$	−9.48575e6	−3.28279
$385$	677152.	0.232828
$386$	−8.39083e6	−2.86640
$387$	−2.42011e6	−0.821405
$388$	1.03834e6	0.350153
$389$	−2.76641e6	−0.926919	−0.463460	−	0.886118i	$-0.653392\pi$
$389$	−2.76641e6	−0.926919	−0.463460	+	0.886118i	$0.653392\pi$
$390$	−1.83514e6	−0.610953
$391$	529279.	0.175082
$392$	3.81341e6	1.25342
$393$	−4.38496e6	−1.43214
$394$	−2.06018e6	−0.668598
$395$	−1.98746e6	−0.640923
$396$	−1.61593e7	−5.17827
$397$	373606.	0.118970	0.0594851	−	0.998229i	$-0.481054\pi$
$397$	373606.	0.118970	0.0594851	+	0.998229i	$0.481054\pi$
$398$	9.12331e6	2.88699
$399$	−5.60629e6	−1.76296
$400$	651967.	0.203740
$401$	1.04255e6	0.323771	0.161885	−	0.986810i	$-0.448242\pi$
$401$	1.04255e6	0.323771	0.161885	+	0.986810i	$0.448242\pi$
$402$	1.97176e7	6.08539
$403$	796050.	0.244162
$404$	1.14731e7	3.49726
$405$	4.85645e6	1.47123
$406$	5.11402e6	1.53974
$407$	3.00296e6	0.898593
$408$	−9.38543e6	−2.79128
$409$	5.73085e6	1.69399	0.846994	−	0.531602i	$-0.178410\pi$
$409$	5.73085e6	1.69399	0.846994	+	0.531602i	$0.178410\pi$
$410$	4.12466e6	1.21179
$411$	−4.65725e6	−1.35996
$412$	−8.99697e6	−2.61128
$413$	367682.	0.106071
$414$	3.31676e6	0.951073
$415$	1.31888e6	0.375911
$416$	31579.6	0.00894692
$417$	5.13699e6	1.44667
$418$	−1.05964e7	−2.96632
$419$	−874453.	−0.243333	−0.121667	−	0.992571i	$-0.538824\pi$
$419$	−874453.	−0.243333	−0.121667	+	0.992571i	$0.538824\pi$
$420$	3.27937e6	0.907126
$421$	−3.75437e6	−1.03236	−0.516181	−	0.856480i	$-0.672647\pi$
$421$	−3.75437e6	−1.03236	−0.516181	+	0.856480i	$0.672647\pi$
$422$	−1.15102e7	−3.14630
$423$	−7.91074e6	−2.14964
$424$	−3.08875e6	−0.834387
$425$	−625330.	−0.167933
$426$	1.64313e7	4.38679
$427$	577870.	0.153377
$428$	9.87926e6	2.60684
$429$	−2.94689e6	−0.773074
$430$	928297.	0.242112
$431$	3.79021e6	0.982811	0.491406	−	0.870931i	$-0.336483\pi$
$431$	3.79021e6	0.982811	0.491406	+	0.870931i	$0.336483\pi$
$432$	−1.22777e7	−3.16524
$433$	5.15134e6	1.32039	0.660193	−	0.751096i	$-0.270475\pi$
$433$	5.15134e6	1.32039	0.660193	+	0.751096i	$0.270475\pi$
$434$	−2.13159e6	−0.543226
$435$	−5.62845e6	−1.42615
$436$	275891.	0.0695057
$437$	1.45147e6	0.363585
$438$	4.80731e6	1.19734
$439$	−7.48501e6	−1.85366	−0.926832	−	0.375476i	$-0.877479\pi$
$439$	−7.48501e6	−1.85366	−0.926832	+	0.375476i	$0.877479\pi$
$440$	3.10877e6	0.765521
$441$	−7.71895e6	−1.89000
$442$	−2.47264e6	−0.602012
$443$	−1.67926e6	−0.406545	−0.203273	−	0.979122i	$-0.565158\pi$
$443$	−1.67926e6	−0.406545	−0.203273	+	0.979122i	$0.565158\pi$
$444$	1.45430e7	3.50103
$445$	−104913.	−0.0251147
$446$	−4.11218e6	−0.978893
$447$	−7.52215e6	−1.78063
$448$	2.21170e6	0.520632
$449$	637406.	0.149211	0.0746054	−	0.997213i	$-0.476230\pi$
$449$	637406.	0.149211	0.0746054	+	0.997213i	$0.476230\pi$
$450$	−3.91867e6	−0.912237
$451$	6.62343e6	1.53335
$452$	−9.57044e6	−2.20336
$453$	−5.65548e6	−1.29486
$454$	8.25325e6	1.87925
$455$	433324.	0.0981259
$456$	−2.57382e7	−5.79651
$457$	−4.91766e6	−1.10146	−0.550729	−	0.834684i	$-0.685650\pi$
$457$	−4.91766e6	−1.10146	−0.550729	+	0.834684i	$0.685650\pi$
$458$	−8.92881e6	−1.98898
$459$	1.17760e7	2.60896
$460$	−849032.	−0.187081
$461$	−2.26744e6	−0.496917	−0.248459	−	0.968643i	$-0.579924\pi$
$461$	−2.26744e6	−0.496917	−0.248459	+	0.968643i	$0.579924\pi$
$462$	7.89093e6	1.71998
$463$	−2.88174e6	−0.624745	−0.312373	−	0.949960i	$-0.601124\pi$
$463$	−2.88174e6	−0.624745	−0.312373	+	0.949960i	$0.601124\pi$
$464$	7.90674e6	1.70491
$465$	2.34601e6	0.503151
$466$	9.91279e6	2.11461
$467$	2.48584e6	0.527449	0.263725	−	0.964598i	$-0.415049\pi$
$467$	2.48584e6	0.527449	0.263725	+	0.964598i	$0.415049\pi$
$468$	−1.03407e7	−2.18240
$469$	−4.65582e6	−0.977382
$470$	3.03437e6	0.633614
$471$	8.49075e6	1.76357
$472$	1.68801e6	0.348755
$473$	1.49067e6	0.306358
$474$	−2.31601e7	−4.73473
$475$	−1.71488e6	−0.348738
$476$	4.41858e6	0.893852
$477$	6.25212e6	1.25815
$478$	2.23629e6	0.447670
$479$	−3.87017e6	−0.770710	−0.385355	−	0.922768i	$-0.625921\pi$
$479$	−3.87017e6	−0.770710	−0.385355	+	0.922768i	$0.625921\pi$
$480$	93067.2	0.0184371
$481$	1.92165e6	0.378715
$482$	−1.70152e7	−3.33596
$483$	−1.08088e6	−0.210819
$484$	−385956.	−0.0748901
$485$	404342.	0.0780539
$486$	2.85409e7	5.48122
$487$	4.16084e6	0.794985	0.397492	−	0.917605i	$-0.369881\pi$
$487$	4.16084e6	0.794985	0.397492	+	0.917605i	$0.369881\pi$
$488$	2.65297e6	0.504293
$489$	8.05745e6	1.52379
$490$	2.96081e6	0.557083
$491$	2.41637e6	0.452335	0.226168	−	0.974088i	$-0.427380\pi$
$491$	2.41637e6	0.452335	0.226168	+	0.974088i	$0.427380\pi$
$492$	3.20766e7	5.97413
$493$	−7.58369e6	−1.40528
$494$	−6.78087e6	−1.25017
$495$	−6.29266e6	−1.15431
$496$	−3.29564e6	−0.601500
$497$	−3.87984e6	−0.704568
$498$	1.53691e7	2.77699
$499$	−2.44587e6	−0.439725	−0.219863	−	0.975531i	$-0.570561\pi$
$499$	−2.44587e6	−0.439725	−0.219863	+	0.975531i	$0.570561\pi$
$500$	1.00311e6	0.179442
$501$	−6.50175e6	−1.15727
$502$	−6.22585e6	−1.10265
$503$	−1.80191e6	−0.317551	−0.158776	−	0.987315i	$-0.550755\pi$
$503$	−1.80191e6	−0.317551	−0.158776	+	0.987315i	$0.550755\pi$
$504$	1.38876e7	2.43529
$505$	4.46779e6	0.779587
$506$	−2.04297e6	−0.354720
$507$	9.14265e6	1.57962
$508$	1.57420e7	2.70646
$509$	−1.14423e7	−1.95757	−0.978787	−	0.204882i	$-0.934319\pi$
$509$	−1.14423e7	−1.95757	−0.978787	+	0.204882i	$0.934319\pi$
$510$	−7.28704e6	−1.24058
$511$	−1.13513e6	−0.192306
$512$	1.04113e7	1.75521
$513$	3.22942e7	5.41789
$514$	2.37789e6	0.396994
$515$	−3.50355e6	−0.582090
$516$	7.21916e6	1.19361
$517$	4.87264e6	0.801748
$518$	−5.14564e6	−0.842587
$519$	2.90898e6	0.474047
$520$	1.98937e6	0.322632
$521$	372546.	0.0601292	0.0300646	−	0.999548i	$-0.490429\pi$
$521$	372546.	0.0601292	0.0300646	+	0.999548i	$0.490429\pi$
$522$	−4.75237e7	−7.63369
$523$	2.61174e6	0.417518	0.208759	−	0.977967i	$-0.433057\pi$
$523$	2.61174e6	0.417518	0.208759	+	0.977967i	$0.433057\pi$
$524$	9.47757e6	1.50789
$525$	1.27703e6	0.202211
$526$	−2.71276e6	−0.427510
$527$	3.16099e6	0.495788
$528$	1.22001e7	1.90449
$529$	279841.	0.0434783
$530$	−2.39817e6	−0.370843
$531$	−3.41681e6	−0.525877
$532$	1.21173e7	1.85621
$533$	4.23847e6	0.646236
$534$	−1.22256e6	−0.185531
$535$	3.84712e6	0.581101
$536$	−2.13747e7	−3.21357
$537$	1.57031e6	0.234990
$538$	−6.79761e6	−1.01251
$539$	4.75451e6	0.704910
$540$	−1.88903e7	−2.78776
$541$	1.25955e6	0.185021	0.0925106	−	0.995712i	$-0.470511\pi$
$541$	1.25955e6	0.185021	0.0925106	+	0.995712i	$0.470511\pi$
$542$	−1.54299e7	−2.25613
$543$	4.53616e6	0.660221
$544$	125397.	0.0181674
$545$	107436.	0.0154938
$546$	5.04957e6	0.724891
$547$	−712618.	−0.101833	−0.0509165	−	0.998703i	$-0.516214\pi$
$547$	−712618.	−0.101833	−0.0509165	+	0.998703i	$0.516214\pi$
$548$	1.00661e7	1.43189
$549$	−5.37005e6	−0.760409
$550$	2.41372e6	0.340235
$551$	−2.07972e7	−2.91827
$552$	−4.96228e6	−0.693159
$553$	5.46870e6	0.760452
$554$	1.61811e7	2.23993
$555$	5.66324e6	0.780428
$556$	−1.11030e7	−1.52319
$557$	−4.83954e6	−0.660946	−0.330473	−	0.943815i	$-0.607208\pi$
$557$	−4.83954e6	−0.660946	−0.330473	+	0.943815i	$0.607208\pi$
$558$	1.98085e7	2.69319
$559$	953912.	0.129116
$560$	−1.79395e6	−0.241736
$561$	−1.17016e7	−1.56978
$562$	9.82656e6	1.31238
$563$	759499.	0.100985	0.0504924	−	0.998724i	$-0.483921\pi$
$563$	759499.	0.100985	0.0504924	+	0.998724i	$0.483921\pi$
$564$	2.35977e7	3.12371
$565$	−3.72686e6	−0.491159
$566$	−1.28539e7	−1.68652
$567$	−1.33630e7	−1.74561
$568$	−1.78122e7	−2.31657
$569$	−6.50304e6	−0.842047	−0.421023	−	0.907050i	$-0.638329\pi$
$569$	−6.50304e6	−0.842047	−0.421023	+	0.907050i	$0.638329\pi$
$570$	−1.99837e7	−2.57625
$571$	−8.91332e6	−1.14406	−0.572031	−	0.820232i	$-0.693844\pi$
$571$	−8.91332e6	−1.14406	−0.572031	+	0.820232i	$0.693844\pi$
$572$	6.36936e6	0.813965
$573$	1.51910e7	1.93286
$574$	−1.13494e7	−1.43778
$575$	−330625.	−0.0417029
$576$	−2.05530e7	−2.58118
$577$	−3.00465e6	−0.375711	−0.187856	−	0.982197i	$-0.560154\pi$
$577$	−3.00465e6	−0.375711	−0.187856	+	0.982197i	$0.560154\pi$
$578$	4.10766e6	0.511416
$579$	−2.54107e7	−3.15007
$580$	1.21652e7	1.50159
$581$	−3.62904e6	−0.446017
$582$	4.71185e6	0.576612
$583$	−3.85101e6	−0.469249
$584$	−5.21133e6	−0.632290
$585$	−4.02680e6	−0.486486
$586$	−4.91168e6	−0.590861
$587$	4.66683e6	0.559019	0.279510	−	0.960143i	$-0.409828\pi$
$587$	4.66683e6	0.559019	0.279510	+	0.960143i	$0.409828\pi$
$588$	2.30256e7	2.74642
$589$	8.66856e6	1.02958
$590$	1.31061e6	0.155004
$591$	−6.23903e6	−0.734764
$592$	−7.95562e6	−0.932975
$593$	−1.56499e6	−0.182757	−0.0913786	−	0.995816i	$-0.529127\pi$
$593$	−1.56499e6	−0.182757	−0.0913786	+	0.995816i	$0.529127\pi$
$594$	−4.54545e7	−5.28580
$595$	1.72066e6	0.199252
$596$	1.62582e7	1.87481
$597$	2.76289e7	3.17269
$598$	−1.30734e6	−0.149498
$599$	6.06726e6	0.690916	0.345458	−	0.938434i	$-0.387724\pi$
$599$	6.06726e6	0.690916	0.345458	+	0.938434i	$0.387724\pi$
$600$	5.86280e6	0.664855
$601$	1.42673e7	1.61122	0.805611	−	0.592445i	$-0.201837\pi$
$601$	1.42673e7	1.61122	0.805611	+	0.592445i	$0.201837\pi$
$602$	−2.55430e6	−0.287264
$603$	4.32658e7	4.84564
$604$	1.22237e7	1.36335
$605$	−150297.	−0.0166940
$606$	5.20637e7	5.75909
$607$	1.25733e6	0.138509	0.0692544	−	0.997599i	$-0.477938\pi$
$607$	1.25733e6	0.138509	0.0692544	+	0.997599i	$0.477938\pi$
$608$	343885.	0.0377272
$609$	1.54872e7	1.69212
$610$	2.05982e6	0.224133
$611$	3.11810e6	0.337899
$612$	−4.10611e7	−4.43152
$613$	−7.34492e6	−0.789470	−0.394735	−	0.918795i	$-0.629164\pi$
$613$	−7.34492e6	−0.789470	−0.394735	+	0.918795i	$0.629164\pi$
$614$	−4.10237e6	−0.439151
$615$	1.24911e7	1.33172
$616$	−8.55410e6	−0.908286
$617$	6.83417e6	0.722725	0.361362	−	0.932425i	$-0.382312\pi$
$617$	6.83417e6	0.722725	0.361362	+	0.932425i	$0.382312\pi$
$618$	−4.08272e7	−4.30010
$619$	−4.01227e6	−0.420885	−0.210443	−	0.977606i	$-0.567491\pi$
$619$	−4.01227e6	−0.420885	−0.210443	+	0.977606i	$0.567491\pi$
$620$	−5.07063e6	−0.529765
$621$	6.22625e6	0.647884
$622$	2.48540e7	2.57585
$623$	288677.	0.0297984
$624$	7.80709e6	0.802653
$625$	390625.	0.0400000
$626$	3.49735e6	0.356700
$627$	−3.20901e7	−3.25988
$628$	−1.83518e7	−1.85686
$629$	7.63058e6	0.769008
$630$	1.07826e7	1.08236
$631$	6.41695e6	0.641587	0.320793	−	0.947149i	$-0.396051\pi$
$631$	6.41695e6	0.641587	0.320793	+	0.947149i	$0.396051\pi$
$632$	2.51066e7	2.50031
$633$	−3.48573e7	−3.45767
$634$	−1.84197e7	−1.81995
$635$	6.13016e6	0.603306
$636$	−1.86500e7	−1.82825
$637$	3.04251e6	0.297086
$638$	2.92724e7	2.84712
$639$	3.60547e7	3.49309
$640$	7.98389e6	0.770486
$641$	4.26687e6	0.410171	0.205085	−	0.978744i	$-0.434253\pi$
$641$	4.26687e6	0.410171	0.205085	+	0.978744i	$0.434253\pi$
$642$	4.48310e7	4.29280
$643$	−7.25101e6	−0.691625	−0.345813	−	0.938304i	$-0.612397\pi$
$643$	−7.25101e6	−0.691625	−0.345813	+	0.938304i	$0.612397\pi$
$644$	2.33620e6	0.221970
$645$	2.81124e6	0.266072
$646$	−2.69257e7	−2.53855
$647$	−1.91218e7	−1.79584	−0.897921	−	0.440157i	$-0.854923\pi$
$647$	−1.91218e7	−1.79584	−0.897921	+	0.440157i	$0.854923\pi$
$648$	−6.13490e7	−5.73944
$649$	2.10459e6	0.196135
$650$	1.54459e6	0.143393
$651$	−6.45529e6	−0.596985
$652$	−1.74152e7	−1.60439
$653$	4.97013e6	0.456126	0.228063	−	0.973646i	$-0.426761\pi$
$653$	4.97013e6	0.456126	0.228063	+	0.973646i	$0.426761\pi$
$654$	1.25196e6	0.114458
$655$	3.69070e6	0.336128
$656$	−1.75472e7	−1.59202
$657$	1.05486e7	0.953411
$658$	−8.34939e6	−0.751779
$659$	1.88070e7	1.68697	0.843483	−	0.537156i	$-0.180501\pi$
$659$	1.88070e7	1.68697	0.843483	+	0.537156i	$0.180501\pi$
$660$	1.87709e7	1.67736
$661$	2.74389e6	0.244266	0.122133	−	0.992514i	$-0.461027\pi$
$661$	2.74389e6	0.244266	0.122133	+	0.992514i	$0.461027\pi$
$662$	−390937.	−0.0346706
$663$	−7.48812e6	−0.661590
$664$	−1.66607e7	−1.46647
$665$	4.71866e6	0.413775
$666$	4.78175e7	4.17736
$667$	−4.00966e6	−0.348974
$668$	1.40528e7	1.21849
$669$	−1.24533e7	−1.07577
$670$	−1.65957e7	−1.42827
$671$	3.30769e6	0.283608
$672$	−256084.	−0.0218756
$673$	−1.24176e6	−0.105682	−0.0528409	−	0.998603i	$-0.516828\pi$
$673$	−1.24176e6	−0.105682	−0.0528409	+	0.998603i	$0.516828\pi$
$674$	2.04375e7	1.73292
$675$	−7.35615e6	−0.621428
$676$	−1.97608e7	−1.66317
$677$	1.14893e7	0.963434	0.481717	−	0.876327i	$-0.340013\pi$
$677$	1.14893e7	0.963434	0.481717	+	0.876327i	$0.340013\pi$
$678$	−4.34296e7	−3.62837
$679$	−1.11259e6	−0.0926105
$680$	7.89946e6	0.655126
$681$	2.49940e7	2.06523
$682$	−1.22011e7	−1.00447
$683$	2.23513e7	1.83337	0.916685	−	0.399610i	$-0.130855\pi$
$683$	2.23513e7	1.83337	0.916685	+	0.399610i	$0.130855\pi$
$684$	−1.12604e8	−9.20270
$685$	3.91988e6	0.319188
$686$	−1.94866e7	−1.58098
$687$	−2.70399e7	−2.18581
$688$	−3.94918e6	−0.318080
$689$	−2.46434e6	−0.197766
$690$	−3.85281e6	−0.308074
$691$	1.26776e7	1.01005	0.505023	−	0.863106i	$-0.331484\pi$
$691$	1.26776e7	1.01005	0.505023	+	0.863106i	$0.331484\pi$
$692$	−6.28741e6	−0.499122
$693$	1.73149e7	1.36958
$694$	1.74973e7	1.37903
$695$	−4.32366e6	−0.339539
$696$	7.11012e7	5.56357
$697$	1.68303e7	1.31223
$698$	−3.58353e7	−2.78402
$699$	3.00198e7	2.32388
$700$	−2.76016e6	−0.212907
$701$	8.57840e6	0.659343	0.329671	−	0.944096i	$-0.393062\pi$
$701$	8.57840e6	0.659343	0.329671	+	0.944096i	$0.393062\pi$
$702$	−2.90873e7	−2.22772
$703$	2.09258e7	1.59696
$704$	1.26596e7	0.962697
$705$	9.18926e6	0.696318
$706$	−4.49021e6	−0.339043
$707$	−1.22936e7	−0.924975
$708$	1.01923e7	0.764169
$709$	−1.32517e7	−0.990048	−0.495024	−	0.868879i	$-0.664841\pi$
$709$	−1.32517e7	−0.990048	−0.495024	+	0.868879i	$0.664841\pi$
$710$	−1.38297e7	−1.02960
$711$	−5.08197e7	−3.77015
$712$	1.32530e6	0.0979751
$713$	1.67128e6	0.123119
$714$	2.00510e7	1.47194
$715$	2.48032e6	0.181444
$716$	−3.39404e6	−0.247420
$717$	6.77234e6	0.491973
$718$	−1.06048e7	−0.767703
$719$	4.45342e6	0.321271	0.160635	−	0.987014i	$-0.448646\pi$
$719$	4.45342e6	0.321271	0.160635	+	0.987014i	$0.448646\pi$
$720$	1.66709e7	1.19847
$721$	9.64036e6	0.690646
$722$	−4.95542e7	−3.53783
$723$	−5.15287e7	−3.66609
$724$	−9.80439e6	−0.695143
$725$	4.73731e6	0.334724
$726$	−1.75143e6	−0.123325
$727$	−2.84829e7	−1.99870	−0.999351	−	0.0360217i	$-0.988531\pi$
$727$	−2.84829e7	−1.99870	−0.999351	+	0.0360217i	$0.988531\pi$
$728$	−5.47395e6	−0.382800
$729$	3.92282e7	2.73388
$730$	−4.04618e6	−0.281021
$731$	3.78783e6	0.262178
$732$	1.60188e7	1.10497
$733$	−1.18781e7	−0.816558	−0.408279	−	0.912857i	$-0.633871\pi$
$733$	−1.18781e7	−0.816558	−0.408279	+	0.912857i	$0.633871\pi$
$734$	−1.24191e7	−0.850841
$735$	8.96647e6	0.612214
$736$	66300.3	0.00451150
$737$	−2.66497e7	−1.80727
$738$	1.05468e8	7.12821
$739$	−2.02463e6	−0.136375	−0.0681875	−	0.997673i	$-0.521722\pi$
$739$	−2.02463e6	−0.136375	−0.0681875	+	0.997673i	$0.521722\pi$
$740$	−1.22404e7	−0.821708
$741$	−2.05351e7	−1.37389
$742$	6.59880e6	0.440002
$743$	−1.11168e7	−0.738771	−0.369385	−	0.929276i	$-0.620432\pi$
$743$	−1.11168e7	−0.738771	−0.369385	+	0.929276i	$0.620432\pi$
$744$	−2.96360e7	−1.96285
$745$	6.33118e6	0.417921
$746$	4.25340e7	2.79827
$747$	3.37240e7	2.21125
$748$	2.52917e7	1.65281
$749$	−1.05857e7	−0.689472
$750$	4.55200e6	0.295494
$751$	−1.13519e7	−0.734464	−0.367232	−	0.930129i	$-0.619694\pi$
$751$	−1.13519e7	−0.734464	−0.367232	+	0.930129i	$0.619694\pi$
$752$	−1.29089e7	−0.832425
$753$	−1.88543e7	−1.21178
$754$	1.87320e7	1.19993
$755$	4.76006e6	0.303910
$756$	5.19786e7	3.30765
$757$	−1.01186e7	−0.641771	−0.320885	−	0.947118i	$-0.603980\pi$
$757$	−1.01186e7	−0.641771	−0.320885	+	0.947118i	$0.603980\pi$
$758$	−2.58376e7	−1.63335
$759$	−6.18690e6	−0.389824
$760$	2.16632e7	1.36047
$761$	8.70533e6	0.544909	0.272454	−	0.962169i	$-0.412165\pi$
$761$	8.70533e6	0.544909	0.272454	+	0.962169i	$0.412165\pi$
$762$	7.14355e7	4.45684
$763$	−295620.	−0.0183833
$764$	−3.28336e7	−2.03509
$765$	−1.59898e7	−0.987845
$766$	−8.52318e6	−0.524843
$767$	1.34677e6	0.0826619
$768$	6.24777e7	3.82227
$769$	−3.17299e6	−0.193487	−0.0967436	−	0.995309i	$-0.530843\pi$
$769$	−3.17299e6	−0.193487	−0.0967436	+	0.995309i	$0.530843\pi$
$770$	−6.64158e6	−0.403687
$771$	7.20117e6	0.436282
$772$	5.49222e7	3.31669
$773$	−2.39933e7	−1.44425	−0.722123	−	0.691765i	$-0.756833\pi$
$773$	−2.39933e7	−1.44425	−0.722123	+	0.691765i	$0.756833\pi$
$774$	2.37367e7	1.42419
$775$	−1.97458e6	−0.118092
$776$	−5.10784e6	−0.304497
$777$	−1.55830e7	−0.925973
$778$	2.71332e7	1.60713
$779$	4.61547e7	2.72503
$780$	1.20119e7	0.706929
$781$	−2.22080e7	−1.30281
$782$	−5.19123e6	−0.303566
$783$	−8.92118e7	−5.20017
$784$	−1.25959e7	−0.731881
$785$	−7.14643e6	−0.413919
$786$	4.30081e7	2.48310
$787$	−2.80846e7	−1.61633	−0.808167	−	0.588953i	$-0.799540\pi$
$787$	−2.80846e7	−1.61633	−0.808167	+	0.588953i	$0.799540\pi$
$788$	1.34849e7	0.773630
$789$	−8.21528e6	−0.469818
$790$	1.94933e7	1.11126
$791$	1.02548e7	0.582757
$792$	7.94918e7	4.50308
$793$	2.11666e6	0.119528
$794$	−3.66437e6	−0.206276
$795$	−7.26258e6	−0.407543
$796$	−5.97167e7	−3.34051
$797$	−1.78094e6	−0.0993123	−0.0496562	−	0.998766i	$-0.515813\pi$
$797$	−1.78094e6	−0.0993123	−0.0496562	+	0.998766i	$0.515813\pi$
$798$	5.49871e7	3.05671
$799$	1.23815e7	0.686129
$800$	−78332.1	−0.00432728
$801$	−2.68263e6	−0.147734
$802$	−1.02255e7	−0.561369
$803$	−6.49742e6	−0.355592
$804$	−1.29061e8	−7.04136
$805$	909748.	0.0494802
$806$	−7.80775e6	−0.423339
$807$	−2.05858e7	−1.11272
$808$	−5.64392e7	−3.04125
$809$	−2.56763e7	−1.37931	−0.689653	−	0.724140i	$-0.742237\pi$
$809$	−2.56763e7	−1.37931	−0.689653	+	0.724140i	$0.742237\pi$
$810$	−4.76326e7	−2.55089
$811$	−1.29788e7	−0.692921	−0.346461	−	0.938065i	$-0.612617\pi$
$811$	−1.29788e7	−0.692921	−0.346461	+	0.938065i	$0.612617\pi$
$812$	−3.34739e7	−1.78162
$813$	−4.67276e7	−2.47941
$814$	−2.94533e7	−1.55802
$815$	−6.78173e6	−0.357640
$816$	3.10007e7	1.62984
$817$	1.03876e7	0.544452
$818$	−5.62088e7	−2.93711
$819$	1.10802e7	0.577213
$820$	−2.69980e7	−1.40216
$821$	7.03514e6	0.364263	0.182131	−	0.983274i	$-0.441700\pi$
$821$	7.03514e6	0.364263	0.182131	+	0.983274i	$0.441700\pi$
$822$	4.56788e7	2.35796
$823$	−6.96680e6	−0.358537	−0.179268	−	0.983800i	$-0.557373\pi$
$823$	−6.96680e6	−0.358537	−0.179268	+	0.983800i	$0.557373\pi$
$824$	4.42585e7	2.27080
$825$	7.30967e6	0.373906
$826$	−3.60627e6	−0.183911
$827$	−1.32404e7	−0.673188	−0.336594	−	0.941650i	$-0.609275\pi$
$827$	−1.32404e7	−0.673188	−0.336594	+	0.941650i	$0.609275\pi$
$828$	−2.17099e7	−1.10048
$829$	2.43166e7	1.22890	0.614450	−	0.788956i	$-0.289378\pi$
$829$	2.43166e7	1.22890	0.614450	+	0.788956i	$0.289378\pi$
$830$	−1.29357e7	−0.651772
$831$	4.90026e7	2.46160
$832$	8.10117e6	0.405732
$833$	1.20813e7	0.603255
$834$	−5.03842e7	−2.50830
$835$	5.47234e6	0.271617
$836$	6.93590e7	3.43231
$837$	3.71847e7	1.83464
$838$	8.57673e6	0.421902
$839$	1.64880e7	0.808655	0.404328	−	0.914614i	$-0.367506\pi$
$839$	1.64880e7	0.808655	0.404328	+	0.914614i	$0.367506\pi$
$840$	−1.61321e7	−0.788846
$841$	3.69406e7	1.80100
$842$	3.68233e7	1.78996
$843$	2.97586e7	1.44226
$844$	7.53399e7	3.64056
$845$	−7.69512e6	−0.370743
$846$	7.75894e7	3.72715
$847$	413557.	0.0198074
$848$	1.02023e7	0.487203
$849$	−3.89265e7	−1.85343
$850$	6.13330e6	0.291170
$851$	4.03445e6	0.190968
$852$	−1.07551e8	−5.07592
$853$	2.86273e7	1.34712	0.673562	−	0.739130i	$-0.264763\pi$
$853$	2.86273e7	1.34712	0.673562	+	0.739130i	$0.264763\pi$
$854$	−5.66781e6	−0.265932
$855$	−4.38497e7	−2.05141
$856$	−4.85986e7	−2.26694
$857$	−1.63899e7	−0.762299	−0.381150	−	0.924513i	$-0.624472\pi$
$857$	−1.63899e7	−0.762299	−0.381150	+	0.924513i	$0.624472\pi$
$858$	2.89034e7	1.34039
$859$	2.81877e7	1.30340	0.651698	−	0.758479i	$-0.274057\pi$
$859$	2.81877e7	1.30340	0.651698	+	0.758479i	$0.274057\pi$
$860$	−6.07617e6	−0.280146
$861$	−3.43704e7	−1.58007
$862$	−3.71748e7	−1.70404
$863$	2.97821e6	0.136122	0.0680609	−	0.997681i	$-0.478319\pi$
$863$	2.97821e6	0.136122	0.0680609	+	0.997681i	$0.478319\pi$
$864$	1.47513e6	0.0672274
$865$	−2.44841e6	−0.111261
$866$	−5.05249e7	−2.28934
$867$	1.24396e7	0.562028
$868$	1.39524e7	0.628562
$869$	3.13025e7	1.40615
$870$	5.52044e7	2.47273
$871$	−1.70537e7	−0.761680
$872$	−1.35718e6	−0.0604429
$873$	1.03391e7	0.459142
$874$	−1.42362e7	−0.630399
$875$	−1.07484e6	−0.0474597
$876$	−3.14663e7	−1.38543
$877$	2.07182e7	0.909606	0.454803	−	0.890592i	$-0.349710\pi$
$877$	2.07182e7	0.909606	0.454803	+	0.890592i	$0.349710\pi$
$878$	7.34138e7	3.21397
$879$	−1.48745e7	−0.649335
$880$	−1.02685e7	−0.446992
$881$	3.05659e7	1.32677	0.663387	−	0.748276i	$-0.269118\pi$
$881$	3.05659e7	1.32677	0.663387	+	0.748276i	$0.269118\pi$
$882$	7.57083e7	3.27697
$883$	−2.98488e7	−1.28833	−0.644163	−	0.764888i	$-0.722794\pi$
$883$	−2.98488e7	−1.28833	−0.644163	+	0.764888i	$0.722794\pi$
$884$	1.61847e7	0.696584
$885$	3.96903e6	0.170344
$886$	1.64704e7	0.704887
$887$	−2.33649e7	−0.997135	−0.498568	−	0.866851i	$-0.666140\pi$
$887$	−2.33649e7	−0.997135	−0.498568	+	0.866851i	$0.666140\pi$
$888$	−7.15408e7	−3.04454
$889$	−1.68678e7	−0.715819
$890$	1.02899e6	0.0435449
$891$	−7.64891e7	−3.22779
$892$	2.69163e7	1.13267
$893$	3.39545e7	1.42485
$894$	7.37781e7	3.08733
$895$	−1.32169e6	−0.0551533
$896$	−2.19685e7	−0.914177
$897$	−3.95913e6	−0.164293
$898$	−6.25175e6	−0.258708
$899$	−2.39467e7	−0.988203
$900$	2.56497e7	1.05554
$901$	−9.78550e6	−0.401579
$902$	−6.49634e7	−2.65859
$903$	−7.73542e6	−0.315693
$904$	4.70795e7	1.91607
$905$	−3.81797e6	−0.154957
$906$	5.54696e7	2.24509
$907$	3.92570e7	1.58452	0.792261	−	0.610182i	$-0.208904\pi$
$907$	3.92570e7	1.58452	0.792261	+	0.610182i	$0.208904\pi$
$908$	−5.40217e7	−2.17447
$909$	1.14242e8	4.58582
$910$	−4.25009e6	−0.170135
$911$	−2.97031e7	−1.18579	−0.592893	−	0.805282i	$-0.702014\pi$
$911$	−2.97031e7	−1.18579	−0.592893	+	0.805282i	$0.702014\pi$
$912$	8.50151e7	3.38461
$913$	−2.07724e7	−0.824726
$914$	4.82329e7	1.90976
$915$	6.23794e6	0.246314
$916$	5.84436e7	2.30143
$917$	−1.01553e7	−0.398814
$918$	−1.15501e8	−4.52354
$919$	2.48587e7	0.970934	0.485467	−	0.874255i	$-0.338650\pi$
$919$	2.48587e7	0.970934	0.485467	+	0.874255i	$0.338650\pi$
$920$	4.17661e6	0.162688
$921$	−1.24236e7	−0.482611
$922$	2.22393e7	0.861577
$923$	−1.42114e7	−0.549074
$924$	−5.16501e7	−1.99018
$925$	−4.76660e6	−0.183170
$926$	2.82645e7	1.08321
$927$	−8.95863e7	−3.42407
$928$	−949974.	−0.0362111
$929$	−4.03580e7	−1.53423	−0.767114	−	0.641510i	$-0.778308\pi$
$929$	−4.03580e7	−1.53423	−0.767114	+	0.641510i	$0.778308\pi$
$930$	−2.30100e7	−0.872386
$931$	3.31313e7	1.25275
$932$	−6.48842e7	−2.44680
$933$	7.52675e7	2.83076
$934$	−2.43814e7	−0.914516
$935$	9.84894e6	0.368435
$936$	5.08685e7	1.89784
$937$	3.50048e7	1.30250	0.651251	−	0.758862i	$-0.274244\pi$
$937$	3.50048e7	1.30250	0.651251	+	0.758862i	$0.274244\pi$
$938$	4.56648e7	1.69463
$939$	1.05913e7	0.392001
$940$	−1.98615e7	−0.733150
$941$	2.48151e7	0.913569	0.456785	−	0.889577i	$-0.349001\pi$
$941$	2.48151e7	0.913569	0.456785	+	0.889577i	$0.349001\pi$
$942$	−8.32782e7	−3.05776
$943$	8.89853e6	0.325866
$944$	−5.57562e6	−0.203640
$945$	2.02412e7	0.737321
$946$	−1.46207e7	−0.531177
$947$	1.47167e7	0.533257	0.266628	−	0.963799i	$-0.414090\pi$
$947$	1.47167e7	0.533257	0.266628	+	0.963799i	$0.414090\pi$
$948$	1.51595e8	5.47852
$949$	−4.15783e6	−0.149865
$950$	1.68197e7	0.604658
$951$	−5.57821e7	−2.00006
$952$	−2.17362e7	−0.777303
$953$	−8.94677e6	−0.319105	−0.159553	−	0.987189i	$-0.551005\pi$
$953$	−8.94677e6	−0.319105	−0.159553	+	0.987189i	$0.551005\pi$
$954$	−6.13215e7	−2.18143
$955$	−1.27858e7	−0.453650
$956$	−1.46376e7	−0.517995
$957$	8.86481e7	3.12888
$958$	3.79590e7	1.33629
$959$	−1.07859e7	−0.378714
$960$	2.38747e7	0.836102
$961$	−1.86478e7	−0.651359
$962$	−1.88478e7	−0.656633
$963$	9.83715e7	3.41825
$964$	1.11373e8	3.86001
$965$	2.13875e7	0.739335
$966$	1.06014e7	0.365528
$967$	478664.	0.0164613	0.00823066	−	0.999966i	$-0.497380\pi$
$967$	478664.	0.0164613	0.00823066	+	0.999966i	$0.497380\pi$
$968$	1.89862e6	0.0651253
$969$	−8.15416e7	−2.78978
$970$	−3.96583e6	−0.135333
$971$	3.45956e6	0.117753	0.0588767	−	0.998265i	$-0.481248\pi$
$971$	3.45956e6	0.117753	0.0588767	+	0.998265i	$0.481248\pi$
$972$	−1.86815e8	−6.34228
$973$	1.18970e7	0.402861
$974$	−4.08100e7	−1.37838
$975$	4.67761e6	0.157584
$976$	−8.76295e6	−0.294460
$977$	−7.34718e6	−0.246255	−0.123127	−	0.992391i	$-0.539292\pi$
$977$	−7.34718e6	−0.246255	−0.123127	+	0.992391i	$0.539292\pi$
$978$	−7.90283e7	−2.64202
$979$	1.65237e6	0.0550999
$980$	−1.93800e7	−0.644597
$981$	2.74715e6	0.0911401
$982$	−2.37001e7	−0.784279
$983$	−2.74033e7	−0.904521	−0.452261	−	0.891886i	$-0.649382\pi$
$983$	−2.74033e7	−0.904521	−0.452261	+	0.891886i	$0.649382\pi$
$984$	−1.57793e8	−5.19517
$985$	5.25122e6	0.172452
$986$	7.43817e7	2.43654
$987$	−2.52852e7	−0.826177
$988$	4.43842e7	1.44656
$989$	2.00271e6	0.0651068
$990$	6.17191e7	2.00139
$991$	3.38090e6	0.109357	0.0546786	−	0.998504i	$-0.482587\pi$
$991$	3.38090e6	0.109357	0.0546786	+	0.998504i	$0.482587\pi$
$992$	395962.	0.0127754
$993$	−1.18391e6	−0.0381017
$994$	3.80539e7	1.22161
$995$	−2.32545e7	−0.744645
$996$	−1.00598e8	−3.21324
$997$	−2.07651e7	−0.661602	−0.330801	−	0.943701i	$-0.607319\pi$
$997$	−2.07651e7	−0.661602	−0.330801	+	0.943701i	$0.607319\pi$
$998$	2.39893e7	0.762416
$999$	8.97633e7	2.84567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.a.e.1.1	✓	12
3.2	odd	2		1035.6.a.m.1.12		12
5.4	even	2		575.6.a.g.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.a.e.1.1	✓	12	1.1	even	1	trivial
575.6.a.g.1.12		12	5.4	even	2
1035.6.a.m.1.12		12	3.2	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	115.a (trivial)

\(f(q)\)	\(=\)	\(q-9.80811 q^{2} -29.7028 q^{3} +64.1990 q^{4} +25.0000 q^{5} +291.328 q^{6} -68.7900 q^{7} -315.812 q^{8} +639.254 q^{9} +O(q^{10})\)	\(q-9.80811 q^{2} -29.7028 q^{3} +64.1990 q^{4} +25.0000 q^{5} +291.328 q^{6} -68.7900 q^{7} -315.812 q^{8} +639.254 q^{9} -245.203 q^{10} -393.750 q^{11} -1906.89 q^{12} -251.969 q^{13} +674.700 q^{14} -742.569 q^{15} +1043.15 q^{16} -1000.53 q^{17} -6269.87 q^{18} -2743.81 q^{19} +1604.98 q^{20} +2043.25 q^{21} +3861.94 q^{22} -529.000 q^{23} +9380.48 q^{24} +625.000 q^{25} +2471.34 q^{26} -11769.8 q^{27} -4416.25 q^{28} +7579.70 q^{29} +7283.20 q^{30} -3159.32 q^{31} -125.331 q^{32} +11695.5 q^{33} +9813.28 q^{34} -1719.75 q^{35} +41039.5 q^{36} -7626.55 q^{37} +26911.5 q^{38} +7484.17 q^{39} -7895.29 q^{40} -16821.4 q^{41} -20040.5 q^{42} -3785.83 q^{43} -25278.4 q^{44} +15981.4 q^{45} +5188.49 q^{46} -12375.0 q^{47} -30984.4 q^{48} -12074.9 q^{49} -6130.07 q^{50} +29718.4 q^{51} -16176.2 q^{52} +9780.34 q^{53} +115440. q^{54} -9843.75 q^{55} +21724.7 q^{56} +81498.6 q^{57} -74342.5 q^{58} -5344.99 q^{59} -47672.2 q^{60} -8400.49 q^{61} +30987.0 q^{62} -43974.3 q^{63} -32151.5 q^{64} -6299.22 q^{65} -114710. q^{66} +67681.7 q^{67} -64232.9 q^{68} +15712.8 q^{69} +16867.5 q^{70} +56401.2 q^{71} -201884. q^{72} +16501.4 q^{73} +74802.1 q^{74} -18564.2 q^{75} -176150. q^{76} +27086.1 q^{77} -73405.6 q^{78} -79498.5 q^{79} +26078.7 q^{80} +194258. q^{81} +164986. q^{82} +52755.3 q^{83} +131175. q^{84} -25013.2 q^{85} +37131.9 q^{86} -225138. q^{87} +124351. q^{88} -4196.50 q^{89} -156747. q^{90} +17332.9 q^{91} -33961.3 q^{92} +93840.6 q^{93} +121375. q^{94} -68595.1 q^{95} +3722.69 q^{96} +16173.7 q^{97} +118432. q^{98} -251706. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9}+O(q^{10}) \) 12 * q + 8 * q^2 + 22 * q^3 + 294 * q^4 + 300 * q^5 + 454 * q^6 + 16 * q^7 + 675 * q^8 + 1598 * q^9	\( 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9} + 200 q^{10} + 132 q^{11} + 728 q^{12} - 236 q^{13} + 359 q^{14} + 550 q^{15} + 4514 q^{16} + 1666 q^{17} - 3096 q^{18} + 616 q^{19} + 7350 q^{20} + 2732 q^{21} + 305 q^{22} - 6348 q^{23} + 18873 q^{24} + 7500 q^{25} - 4502 q^{26} + 11584 q^{27} + 5407 q^{28} + 23722 q^{29} + 11350 q^{30} + 18446 q^{31} + 35808 q^{32} + 4416 q^{33} + 53123 q^{34} + 400 q^{35} + 68916 q^{36} + 10394 q^{37} + 18681 q^{38} + 27032 q^{39} + 16875 q^{40} + 48232 q^{41} - 18980 q^{42} + 10732 q^{43} - 4765 q^{44} + 39950 q^{45} - 4232 q^{46} - 30448 q^{47} - 2052 q^{48} + 26948 q^{49} + 5000 q^{50} + 1524 q^{51} - 55346 q^{52} + 36494 q^{53} + 55567 q^{54} + 3300 q^{55} - 50981 q^{56} + 37572 q^{57} - 83373 q^{58} - 23870 q^{59} + 18200 q^{60} + 30862 q^{61} + 63582 q^{62} - 49698 q^{63} + 29965 q^{64} - 5900 q^{65} - 235225 q^{66} - 71910 q^{67} - 39371 q^{68} - 11638 q^{69} + 8975 q^{70} + 167158 q^{71} - 296052 q^{72} + 52152 q^{73} - 59356 q^{74} + 13750 q^{75} - 230417 q^{76} + 4808 q^{77} - 469771 q^{78} - 123092 q^{79} + 112850 q^{80} + 159868 q^{81} - 140098 q^{82} + 89322 q^{83} - 488082 q^{84} + 41650 q^{85} - 55318 q^{86} - 334376 q^{87} - 104551 q^{88} - 46184 q^{89} - 77400 q^{90} - 153444 q^{91} - 155526 q^{92} - 16576 q^{93} - 456595 q^{94} + 15400 q^{95} + 330540 q^{96} - 94220 q^{97} + 413841 q^{98} - 740784 q^{99}+O(q^{100}) \) 12 * q + 8 * q^2 + 22 * q^3 + 294 * q^4 + 300 * q^5 + 454 * q^6 + 16 * q^7 + 675 * q^8 + 1598 * q^9 + 200 * q^10 + 132 * q^11 + 728 * q^12 - 236 * q^13 + 359 * q^14 + 550 * q^15 + 4514 * q^16 + 1666 * q^17 - 3096 * q^18 + 616 * q^19 + 7350 * q^20 + 2732 * q^21 + 305 * q^22 - 6348 * q^23 + 18873 * q^24 + 7500 * q^25 - 4502 * q^26 + 11584 * q^27 + 5407 * q^28 + 23722 * q^29 + 11350 * q^30 + 18446 * q^31 + 35808 * q^32 + 4416 * q^33 + 53123 * q^34 + 400 * q^35 + 68916 * q^36 + 10394 * q^37 + 18681 * q^38 + 27032 * q^39 + 16875 * q^40 + 48232 * q^41 - 18980 * q^42 + 10732 * q^43 - 4765 * q^44 + 39950 * q^45 - 4232 * q^46 - 30448 * q^47 - 2052 * q^48 + 26948 * q^49 + 5000 * q^50 + 1524 * q^51 - 55346 * q^52 + 36494 * q^53 + 55567 * q^54 + 3300 * q^55 - 50981 * q^56 + 37572 * q^57 - 83373 * q^58 - 23870 * q^59 + 18200 * q^60 + 30862 * q^61 + 63582 * q^62 - 49698 * q^63 + 29965 * q^64 - 5900 * q^65 - 235225 * q^66 - 71910 * q^67 - 39371 * q^68 - 11638 * q^69 + 8975 * q^70 + 167158 * q^71 - 296052 * q^72 + 52152 * q^73 - 59356 * q^74 + 13750 * q^75 - 230417 * q^76 + 4808 * q^77 - 469771 * q^78 - 123092 * q^79 + 112850 * q^80 + 159868 * q^81 - 140098 * q^82 + 89322 * q^83 - 488082 * q^84 + 41650 * q^85 - 55318 * q^86 - 334376 * q^87 - 104551 * q^88 - 46184 * q^89 - 77400 * q^90 - 153444 * q^91 - 155526 * q^92 - 16576 * q^93 - 456595 * q^94 + 15400 * q^95 + 330540 * q^96 - 94220 * q^97 + 413841 * q^98 - 740784 * q^99

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