LMFDB - Embedded newform 115.6.a.e.1.11

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			1.11
Root			$-9.31650$ 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)

$f(q)$	$=$	$q+10.3165 q^{2} -11.9831 q^{3} +74.4302 q^{4} +25.0000 q^{5} -123.623 q^{6} +148.504 q^{7} +437.732 q^{8} -99.4063 q^{9} +O(q^{10})$	\(q+10.3165 q^{2} -11.9831 q^{3} +74.4302 q^{4} +25.0000 q^{5} -123.623 q^{6} +148.504 q^{7} +437.732 q^{8} -99.4063 q^{9} +257.913 q^{10} +396.243 q^{11} -891.902 q^{12} -847.211 q^{13} +1532.04 q^{14} -299.576 q^{15} +2134.09 q^{16} +1702.64 q^{17} -1025.53 q^{18} +2072.19 q^{19} +1860.76 q^{20} -1779.53 q^{21} +4087.84 q^{22} -529.000 q^{23} -5245.37 q^{24} +625.000 q^{25} -8740.26 q^{26} +4103.07 q^{27} +11053.2 q^{28} -2479.33 q^{29} -3090.58 q^{30} -471.923 q^{31} +8008.97 q^{32} -4748.20 q^{33} +17565.3 q^{34} +3712.59 q^{35} -7398.84 q^{36} +873.810 q^{37} +21377.8 q^{38} +10152.2 q^{39} +10943.3 q^{40} -14174.9 q^{41} -18358.5 q^{42} -11457.3 q^{43} +29492.4 q^{44} -2485.16 q^{45} -5457.43 q^{46} -26106.8 q^{47} -25573.0 q^{48} +5246.36 q^{49} +6447.81 q^{50} -20402.8 q^{51} -63058.1 q^{52} -8981.46 q^{53} +42329.4 q^{54} +9906.06 q^{55} +65004.8 q^{56} -24831.2 q^{57} -25578.0 q^{58} -27733.3 q^{59} -22297.6 q^{60} -40924.7 q^{61} -4868.60 q^{62} -14762.2 q^{63} +14333.6 q^{64} -21180.3 q^{65} -48984.8 q^{66} +48266.5 q^{67} +126728. q^{68} +6339.04 q^{69} +38301.0 q^{70} +74357.5 q^{71} -43513.3 q^{72} -17015.7 q^{73} +9014.66 q^{74} -7489.41 q^{75} +154234. q^{76} +58843.5 q^{77} +104735. q^{78} +69489.7 q^{79} +53352.4 q^{80} -25011.6 q^{81} -146236. q^{82} -9978.65 q^{83} -132451. q^{84} +42566.0 q^{85} -118200. q^{86} +29709.9 q^{87} +173448. q^{88} -81019.3 q^{89} -25638.1 q^{90} -125814. q^{91} -39373.6 q^{92} +5655.08 q^{93} -269331. q^{94} +51804.7 q^{95} -95972.0 q^{96} +25916.1 q^{97} +54124.1 q^{98} -39389.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.3165	1.82372	0.911859	−	0.410504i	$-0.134647\pi$
$2$	10.3165	1.82372	0.911859	+	0.410504i	$0.134647\pi$
$3$	−11.9831	−0.768714	−0.384357	−	0.923185i	$-0.625577\pi$
$3$	−11.9831	−0.768714	−0.384357	+	0.923185i	$0.625577\pi$
$4$	74.4302	2.32595
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−123.623	−1.40192
$7$	148.504	1.14549	0.572746	−	0.819733i	$-0.305878\pi$
$7$	148.504	1.14549	0.572746	+	0.819733i	$0.305878\pi$
$8$	437.732	2.41815
$9$	−99.4063	−0.409079
$10$	257.913	0.815591
$11$	396.243	0.987369	0.493684	−	0.869641i	$-0.335650\pi$
$11$	396.243	0.987369	0.493684	+	0.869641i	$0.335650\pi$
$12$	−891.902	−1.78799
$13$	−847.211	−1.39038	−0.695190	−	0.718826i	$-0.744680\pi$
$13$	−847.211	−1.39038	−0.695190	+	0.718826i	$0.744680\pi$
$14$	1532.04	2.08905
$15$	−299.576	−0.343779
$16$	2134.09	2.08408
$17$	1702.64	1.42890	0.714448	−	0.699688i	$-0.246678\pi$
$17$	1702.64	1.42890	0.714448	+	0.699688i	$0.246678\pi$
$18$	−1025.53	−0.746045
$19$	2072.19	1.31688	0.658439	−	0.752634i	$-0.271217\pi$
$19$	2072.19	1.31688	0.658439	+	0.752634i	$0.271217\pi$
$20$	1860.76	1.04019
$21$	−1779.53	−0.880556
$22$	4087.84	1.80068
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−5245.37	−1.85886
$25$	625.000	0.200000
$26$	−8740.26	−2.53566
$27$	4103.07	1.08318
$28$	11053.2	2.66435
$29$	−2479.33	−0.547443	−0.273722	−	0.961809i	$-0.588255\pi$
$29$	−2479.33	−0.547443	−0.273722	+	0.961809i	$0.588255\pi$
$30$	−3090.58	−0.626956
$31$	−471.923	−0.0881997	−0.0440998	−	0.999027i	$-0.514042\pi$
$31$	−471.923	−0.0881997	−0.0440998	+	0.999027i	$0.514042\pi$
$32$	8008.97	1.38262
$33$	−4748.20	−0.759004
$34$	17565.3	2.60590
$35$	3712.59	0.512280
$36$	−7398.84	−0.951497
$37$	873.810	0.104933	0.0524666	−	0.998623i	$-0.483292\pi$
$37$	873.810	0.104933	0.0524666	+	0.998623i	$0.483292\pi$
$38$	21377.8	2.40161
$39$	10152.2	1.06880
$40$	10943.3	1.08143
$41$	−14174.9	−1.31692	−0.658462	−	0.752614i	$-0.728793\pi$
$41$	−14174.9	−1.31692	−0.658462	+	0.752614i	$0.728793\pi$
$42$	−18358.5	−1.60588
$43$	−11457.3	−0.944959	−0.472479	−	0.881342i	$-0.656641\pi$
$43$	−11457.3	−0.944959	−0.472479	+	0.881342i	$0.656641\pi$
$44$	29492.4	2.29657
$45$	−2485.16	−0.182946
$46$	−5457.43	−0.380271
$47$	−26106.8	−1.72389	−0.861943	−	0.507006i	$-0.830752\pi$
$47$	−26106.8	−1.72389	−0.861943	+	0.507006i	$0.830752\pi$
$48$	−25573.0	−1.60206
$49$	5246.36	0.312153
$50$	6447.81	0.364743
$51$	−20402.8	−1.09841
$52$	−63058.1	−3.23395
$53$	−8981.46	−0.439195	−0.219597	−	0.975591i	$-0.570474\pi$
$53$	−8981.46	−0.439195	−0.219597	+	0.975591i	$0.570474\pi$
$54$	42329.4	1.97541
$55$	9906.06	0.441565
$56$	65004.8	2.76997
$57$	−24831.2	−1.01230
$58$	−25578.0	−0.998382
$59$	−27733.3	−1.03722	−0.518610	−	0.855011i	$-0.673550\pi$
$59$	−27733.3	−1.03722	−0.518610	+	0.855011i	$0.673550\pi$
$60$	−22297.6	−0.799611
$61$	−40924.7	−1.40819	−0.704095	−	0.710106i	$-0.748647\pi$
$61$	−40924.7	−1.40819	−0.704095	+	0.710106i	$0.748647\pi$
$62$	−4868.60	−0.160851
$63$	−14762.2	−0.468598
$64$	14333.6	0.437426
$65$	−21180.3	−0.621797
$66$	−48984.8	−1.38421
$67$	48266.5	1.31359	0.656793	−	0.754070i	$-0.271912\pi$
$67$	48266.5	1.31359	0.656793	+	0.754070i	$0.271912\pi$
$68$	126728.	3.32354
$69$	6339.04	0.160288
$70$	38301.0	0.934254
$71$	74357.5	1.75057	0.875284	−	0.483609i	$-0.160674\pi$
$71$	74357.5	1.75057	0.875284	+	0.483609i	$0.160674\pi$
$72$	−43513.3	−0.989215
$73$	−17015.7	−0.373718	−0.186859	−	0.982387i	$-0.559831\pi$
$73$	−17015.7	−0.373718	−0.186859	+	0.982387i	$0.559831\pi$
$74$	9014.66	0.191368
$75$	−7489.41	−0.153743
$76$	154234.	3.06299
$77$	58843.5	1.13102
$78$	104735.	1.94920
$79$	69489.7	1.25272	0.626358	−	0.779535i	$-0.284545\pi$
$79$	69489.7	1.25272	0.626358	+	0.779535i	$0.284545\pi$
$80$	53352.4	0.932027
$81$	−25011.6	−0.423574
$82$	−146236.	−2.40170
$83$	−9978.65	−0.158992	−0.0794962	−	0.996835i	$-0.525331\pi$
$83$	−9978.65	−0.158992	−0.0794962	+	0.996835i	$0.525331\pi$
$84$	−132451.	−2.04812
$85$	42566.0	0.639022
$86$	−118200.	−1.72334
$87$	29709.9	0.420827
$88$	173448.	2.38761
$89$	−81019.3	−1.08421	−0.542105	−	0.840311i	$-0.682373\pi$
$89$	−81019.3	−1.08421	−0.542105	+	0.840311i	$0.682373\pi$
$90$	−25638.1	−0.333642
$91$	−125814.	−1.59267
$92$	−39373.6	−0.484993
$93$	5655.08	0.0678003
$94$	−269331.	−3.14388
$95$	51804.7	0.588926
$96$	−95972.0	−1.06284
$97$	25916.1	0.279666	0.139833	−	0.990175i	$-0.455343\pi$
$97$	25916.1	0.279666	0.139833	+	0.990175i	$0.455343\pi$
$98$	54124.1	0.569280
$99$	−39389.0	−0.403912
$100$	46518.9	0.465189
$101$	62767.7	0.612256	0.306128	−	0.951990i	$-0.400966\pi$
$101$	62767.7	0.612256	0.306128	+	0.951990i	$0.400966\pi$
$102$	−210486.	−2.00319
$103$	−154970.	−1.43931	−0.719654	−	0.694332i	$-0.755700\pi$
$103$	−154970.	−1.43931	−0.719654	+	0.694332i	$0.755700\pi$
$104$	−370851.	−3.36214
$105$	−44488.2	−0.393796
$106$	−92657.2	−0.800967
$107$	−33391.7	−0.281955	−0.140977	−	0.990013i	$-0.545024\pi$
$107$	−33391.7	−0.281955	−0.140977	+	0.990013i	$0.545024\pi$
$108$	305393.	2.51941
$109$	103826.	0.837025	0.418513	−	0.908211i	$-0.362552\pi$
$109$	103826.	0.837025	0.418513	+	0.908211i	$0.362552\pi$
$110$	102196.	0.805289
$111$	−10470.9	−0.0806635
$112$	316921.	2.38729
$113$	244912.	1.80432	0.902160	−	0.431401i	$-0.141981\pi$
$113$	244912.	1.80432	0.902160	+	0.431401i	$0.141981\pi$
$114$	−256171.	−1.84615
$115$	−13225.0	−0.0932505
$116$	−184537.	−1.27332
$117$	84218.1	0.568776
$118$	−286111.	−1.89160
$119$	252849.	1.63679
$120$	−131134.	−0.831309
$121$	−4042.82	−0.0251027
$122$	−422200.	−2.56814
$123$	169859.	1.01234
$124$	−35125.4	−0.205148
$125$	15625.0	0.0894427
$126$	−152294.	−0.854590
$127$	−78768.7	−0.433356	−0.216678	−	0.976243i	$-0.569522\pi$
$127$	−78768.7	−0.433356	−0.216678	+	0.976243i	$0.569522\pi$
$128$	−108415.	−0.584876
$129$	137294.	0.726403
$130$	−218506.	−1.13398
$131$	−49208.2	−0.250530	−0.125265	−	0.992123i	$-0.539978\pi$
$131$	−49208.2	−0.250530	−0.125265	+	0.992123i	$0.539978\pi$
$132$	−353410.	−1.76540
$133$	307728.	1.50847
$134$	497942.	2.39561
$135$	102577.	0.484412
$136$	745300.	3.45529
$137$	−251804.	−1.14620	−0.573101	−	0.819485i	$-0.694260\pi$
$137$	−251804.	−1.14620	−0.573101	+	0.819485i	$0.694260\pi$
$138$	65396.7	0.292320
$139$	−210926.	−0.925964	−0.462982	−	0.886368i	$-0.653220\pi$
$139$	−210926.	−0.925964	−0.462982	+	0.886368i	$0.653220\pi$
$140$	276329.	1.19154
$141$	312839.	1.32517
$142$	767110.	3.19254
$143$	−335701.	−1.37282
$144$	−212142.	−0.852553
$145$	−61983.2	−0.244824
$146$	−175543.	−0.681555
$147$	−62867.5	−0.239957
$148$	65037.9	0.244069
$149$	18847.9	0.0695499	0.0347749	−	0.999395i	$-0.488929\pi$
$149$	18847.9	0.0695499	0.0347749	+	0.999395i	$0.488929\pi$
$150$	−77264.5	−0.280383
$151$	400457.	1.42927	0.714634	−	0.699499i	$-0.246593\pi$
$151$	400457.	1.42927	0.714634	+	0.699499i	$0.246593\pi$
$152$	907063.	3.18441
$153$	−169253.	−0.584532
$154$	607059.	2.06267
$155$	−11798.1	−0.0394441
$156$	755629.	2.48598
$157$	121321.	0.392816	0.196408	−	0.980522i	$-0.437072\pi$
$157$	121321.	0.392816	0.196408	+	0.980522i	$0.437072\pi$
$158$	716891.	2.28460
$159$	107625.	0.337615
$160$	200224.	0.618325
$161$	−78558.5	−0.238852
$162$	−258033.	−0.772480
$163$	−309186.	−0.911487	−0.455744	−	0.890111i	$-0.650627\pi$
$163$	−309186.	−0.911487	−0.455744	+	0.890111i	$0.650627\pi$
$164$	−1.05504e6	−3.06309
$165$	−118705.	−0.339437
$166$	−102945.	−0.289957
$167$	−573196.	−1.59042	−0.795211	−	0.606333i	$-0.792640\pi$
$167$	−573196.	−1.59042	−0.795211	+	0.606333i	$0.792640\pi$
$168$	−778957.	−2.12932
$169$	346474.	0.933154
$170$	439133.	1.16540
$171$	−205989.	−0.538708
$172$	−852773.	−2.19792
$173$	563746.	1.43208	0.716041	−	0.698058i	$-0.245952\pi$
$173$	563746.	1.43208	0.716041	+	0.698058i	$0.245952\pi$
$174$	306503.	0.767470
$175$	92814.8	0.229099
$176$	845619.	2.05775
$177$	332330.	0.797326
$178$	−835836.	−1.97729
$179$	−259092.	−0.604396	−0.302198	−	0.953245i	$-0.597720\pi$
$179$	−259092.	−0.604396	−0.302198	+	0.953245i	$0.597720\pi$
$180$	−184971.	−0.425522
$181$	721886.	1.63784	0.818922	−	0.573905i	$-0.194572\pi$
$181$	721886.	1.63784	0.818922	+	0.573905i	$0.194572\pi$
$182$	−1.29796e6	−2.90458
$183$	490403.	1.08249
$184$	−231560.	−0.504219
$185$	21845.2	0.0469275
$186$	58340.7	0.123649
$187$	674659.	1.41085
$188$	−1.94313e6	−4.00966
$189$	609322.	1.24077
$190$	534444.	1.07403
$191$	−42109.8	−0.0835218	−0.0417609	−	0.999128i	$-0.513297\pi$
$191$	−42109.8	−0.0835218	−0.0417609	+	0.999128i	$0.513297\pi$
$192$	−171760.	−0.336255
$193$	3102.58	0.00599556	0.00299778	−	0.999996i	$-0.499046\pi$
$193$	3102.58	0.00599556	0.00299778	+	0.999996i	$0.499046\pi$
$194$	267363.	0.510032
$195$	253805.	0.477983
$196$	390488.	0.726052
$197$	830866.	1.52534	0.762668	−	0.646790i	$-0.223889\pi$
$197$	830866.	1.52534	0.762668	+	0.646790i	$0.223889\pi$
$198$	−406357.	−0.736622
$199$	84136.6	0.150609	0.0753047	−	0.997161i	$-0.476007\pi$
$199$	84136.6	0.150609	0.0753047	+	0.997161i	$0.476007\pi$
$200$	273582.	0.483630
$201$	−578380.	−1.00977
$202$	647543.	1.11658
$203$	−368190.	−0.627092
$204$	−1.51859e6	−2.55485
$205$	−354373.	−0.588946
$206$	−1.59875e6	−2.62489
$207$	52585.9	0.0852990
$208$	−1.80803e6	−2.89766
$209$	821090.	1.30024
$210$	−458963.	−0.718174
$211$	942603.	1.45755	0.728774	−	0.684754i	$-0.240090\pi$
$211$	942603.	1.45755	0.728774	+	0.684754i	$0.240090\pi$
$212$	−668492.	−1.02154
$213$	−891031.	−1.34569
$214$	−344486.	−0.514206
$215$	−286434.	−0.422598
$216$	1.79605e6	2.61929
$217$	−70082.3	−0.101032
$218$	1.07112e6	1.52650
$219$	203901.	0.287282
$220$	737311.	1.02706
$221$	−1.44250e6	−1.98671
$222$	−108023.	−0.147107
$223$	−692866.	−0.933011	−0.466506	−	0.884518i	$-0.654487\pi$
$223$	−692866.	−0.933011	−0.466506	+	0.884518i	$0.654487\pi$
$224$	1.18936e6	1.58378
$225$	−62128.9	−0.0818159
$226$	2.52663e6	3.29057
$227$	560421.	0.721855	0.360927	−	0.932594i	$-0.382460\pi$
$227$	560421.	0.721855	0.360927	+	0.932594i	$0.382460\pi$
$228$	−1.84819e6	−2.35456
$229$	333626.	0.420408	0.210204	−	0.977658i	$-0.432587\pi$
$229$	333626.	0.420408	0.210204	+	0.977658i	$0.432587\pi$
$230$	−136436.	−0.170063
$231$	−705125.	−0.869433
$232$	−1.08528e6	−1.32380
$233$	−189832.	−0.229077	−0.114538	−	0.993419i	$-0.536539\pi$
$233$	−189832.	−0.229077	−0.114538	+	0.993419i	$0.536539\pi$
$234$	868837.	1.03729
$235$	−652669.	−0.770945
$236$	−2.06420e6	−2.41252
$237$	−832699.	−0.962980
$238$	2.60851e6	2.98504
$239$	695493.	0.787586	0.393793	−	0.919199i	$-0.371163\pi$
$239$	695493.	0.787586	0.393793	+	0.919199i	$0.371163\pi$
$240$	−639324.	−0.716462
$241$	1.54894e6	1.71788	0.858938	−	0.512079i	$-0.171125\pi$
$241$	1.54894e6	1.71788	0.858938	+	0.512079i	$0.171125\pi$
$242$	−41707.8	−0.0457803
$243$	−697331.	−0.757571
$244$	−3.04604e6	−3.27537
$245$	131159.	0.139599
$246$	1.75235e6	1.84622
$247$	−1.75558e6	−1.83096
$248$	−206576.	−0.213280
$249$	119575.	0.122220
$250$	161195.	0.163118
$251$	991579.	0.993443	0.496722	−	0.867910i	$-0.334537\pi$
$251$	991579.	0.993443	0.496722	+	0.867910i	$0.334537\pi$
$252$	−1.09876e6	−1.08993
$253$	−209612.	−0.205881
$254$	−812618.	−0.790318
$255$	−510071.	−0.491225
$256$	−1.57714e6	−1.50407
$257$	−1.36086e6	−1.28523	−0.642614	−	0.766190i	$-0.722150\pi$
$257$	−1.36086e6	−1.28523	−0.642614	+	0.766190i	$0.722150\pi$
$258$	1.41639e6	1.32475
$259$	129764.	0.120200
$260$	−1.57645e6	−1.44626
$261$	246461.	0.223948
$262$	−507657.	−0.456895
$263$	1.02828e6	0.916693	0.458346	−	0.888774i	$-0.348442\pi$
$263$	1.02828e6	0.916693	0.458346	+	0.888774i	$0.348442\pi$
$264$	−2.07844e6	−1.83538
$265$	−224536.	−0.196414
$266$	3.17468e6	2.75103
$267$	970859.	0.833447
$268$	3.59249e6	3.05533
$269$	−983084.	−0.828343	−0.414171	−	0.910199i	$-0.635929\pi$
$269$	−983084.	−0.828343	−0.414171	+	0.910199i	$0.635929\pi$
$270$	1.05823e6	0.883431
$271$	−946049.	−0.782511	−0.391255	−	0.920282i	$-0.627959\pi$
$271$	−946049.	−0.782511	−0.391255	+	0.920282i	$0.627959\pi$
$272$	3.63360e6	2.97793
$273$	1.50764e6	1.22431
$274$	−2.59773e6	−2.09035
$275$	247652.	0.197474
$276$	471816.	0.372821
$277$	−1.70495e6	−1.33509	−0.667546	−	0.744568i	$-0.732655\pi$
$277$	−1.70495e6	−1.33509	−0.667546	+	0.744568i	$0.732655\pi$
$278$	−2.17602e6	−1.68870
$279$	46912.1	0.0360807
$280$	1.62512e6	1.23877
$281$	1.64873e6	1.24561	0.622807	−	0.782376i	$-0.285992\pi$
$281$	1.64873e6	1.24561	0.622807	+	0.782376i	$0.285992\pi$
$282$	3.22740e6	2.41674
$283$	−1.66120e6	−1.23298	−0.616491	−	0.787362i	$-0.711446\pi$
$283$	−1.66120e6	−1.23298	−0.616491	+	0.787362i	$0.711446\pi$
$284$	5.53445e6	4.07173
$285$	−620779.	−0.452715
$286$	−3.46326e6	−2.50363
$287$	−2.10503e6	−1.50853
$288$	−796142.	−0.565600
$289$	1.47913e6	1.04175
$290$	−639450.	−0.446490
$291$	−310554.	−0.214983
$292$	−1.26649e6	−0.869247
$293$	1.42322e6	0.968505	0.484252	−	0.874928i	$-0.339092\pi$
$293$	1.42322e6	0.968505	0.484252	+	0.874928i	$0.339092\pi$
$294$	−648573.	−0.437613
$295$	−693332.	−0.463859
$296$	382494.	0.253744
$297$	1.62581e6	1.06950
$298$	194444.	0.126839
$299$	448175.	0.289914
$300$	−557439.	−0.357597
$301$	−1.70146e6	−1.08244
$302$	4.13132e6	2.60658
$303$	−752149.	−0.470649
$304$	4.42225e6	2.74447
$305$	−1.02312e6	−0.629762
$306$	−1.74610e6	−1.06602
$307$	−1.67261e6	−1.01286	−0.506430	−	0.862281i	$-0.669035\pi$
$307$	−1.67261e6	−1.01286	−0.506430	+	0.862281i	$0.669035\pi$
$308$	4.37974e6	2.63070
$309$	1.85701e6	1.10642
$310$	−121715.	−0.0719349
$311$	1.68026e6	0.985089	0.492545	−	0.870287i	$-0.336067\pi$
$311$	1.68026e6	0.985089	0.492545	+	0.870287i	$0.336067\pi$
$312$	4.44393e6	2.58453
$313$	208071.	0.120047	0.0600234	−	0.998197i	$-0.480882\pi$
$313$	208071.	0.120047	0.0600234	+	0.998197i	$0.480882\pi$
$314$	1.25161e6	0.716384
$315$	−369055.	−0.209563
$316$	5.17214e6	2.91375
$317$	−281204.	−0.157171	−0.0785857	−	0.996907i	$-0.525040\pi$
$317$	−281204.	−0.157171	−0.0785857	+	0.996907i	$0.525040\pi$
$318$	1.11032e6	0.615714
$319$	−982416.	−0.540528
$320$	358339.	0.195623
$321$	400135.	0.216742
$322$	−810449.	−0.435598
$323$	3.52820e6	1.88168
$324$	−1.86162e6	−0.985211
$325$	−529507.	−0.278076
$326$	−3.18972e6	−1.66230
$327$	−1.24415e6	−0.643433
$328$	−6.20481e6	−3.18452
$329$	−3.87695e6	−1.97470
$330$	−1.22462e6	−0.619037
$331$	−1.10569e6	−0.554705	−0.277352	−	0.960768i	$-0.589457\pi$
$331$	−1.10569e6	−0.554705	−0.277352	+	0.960768i	$0.589457\pi$
$332$	−742713.	−0.369808
$333$	−86862.2	−0.0429260
$334$	−5.91338e6	−2.90048
$335$	1.20666e6	0.587454
$336$	−3.79768e6	−1.83515
$337$	−1.63535e6	−0.784399	−0.392199	−	0.919880i	$-0.628286\pi$
$337$	−1.63535e6	−0.784399	−0.392199	+	0.919880i	$0.628286\pi$
$338$	3.57440e6	1.70181
$339$	−2.93479e6	−1.38701
$340$	3.16820e6	1.48633
$341$	−186996.	−0.0870856
$342$	−2.12508e6	−0.982451
$343$	−1.71680e6	−0.787923
$344$	−5.01525e6	−2.28505
$345$	158476.	0.0716829
$346$	5.81588e6	2.61171
$347$	−1.92106e6	−0.856481	−0.428240	−	0.903665i	$-0.640866\pi$
$347$	−1.92106e6	−0.856481	−0.428240	+	0.903665i	$0.640866\pi$
$348$	2.21132e6	0.978821
$349$	1.12250e6	0.493313	0.246656	−	0.969103i	$-0.420668\pi$
$349$	1.12250e6	0.493313	0.246656	+	0.969103i	$0.420668\pi$
$350$	957525.	0.417811
$351$	−3.47617e6	−1.50603
$352$	3.17350e6	1.36515
$353$	−2.08568e6	−0.890863	−0.445432	−	0.895316i	$-0.646950\pi$
$353$	−2.08568e6	−0.890863	−0.445432	+	0.895316i	$0.646950\pi$
$354$	3.42848e6	1.45410
$355$	1.85894e6	0.782878
$356$	−6.03029e6	−2.52181
$357$	−3.02990e6	−1.25822
$358$	−2.67292e6	−1.10225
$359$	794376.	0.325304	0.162652	−	0.986683i	$-0.447995\pi$
$359$	794376.	0.325304	0.162652	+	0.986683i	$0.447995\pi$
$360$	−1.08783e6	−0.442391
$361$	1.81787e6	0.734168
$362$	7.44734e6	2.98696
$363$	48445.4	0.0192968
$364$	−9.36437e6	−3.70446
$365$	−425393.	−0.167132
$366$	5.05925e6	1.97416
$367$	−2.75987e6	−1.06961	−0.534803	−	0.844976i	$-0.679614\pi$
$367$	−2.75987e6	−1.06961	−0.534803	+	0.844976i	$0.679614\pi$
$368$	−1.12894e6	−0.434560
$369$	1.40908e6	0.538727
$370$	225367.	0.0855825
$371$	−1.33378e6	−0.503094
$372$	420909.	0.157700
$373$	−2.25015e6	−0.837411	−0.418705	−	0.908122i	$-0.637516\pi$
$373$	−2.25015e6	−0.837411	−0.418705	+	0.908122i	$0.637516\pi$
$374$	6.96012e6	2.57299
$375$	−187235.	−0.0687558
$376$	−1.14278e7	−4.16861
$377$	2.10052e6	0.761154
$378$	6.28607e6	2.26282
$379$	1.75562e6	0.627816	0.313908	−	0.949453i	$-0.398362\pi$
$379$	1.75562e6	0.627816	0.313908	+	0.949453i	$0.398362\pi$
$380$	3.85584e6	1.36981
$381$	943890.	0.333126
$382$	−434426.	−0.152320
$383$	4.52690e6	1.57690	0.788450	−	0.615099i	$-0.210884\pi$
$383$	4.52690e6	1.57690	0.788450	+	0.615099i	$0.210884\pi$
$384$	1.29914e6	0.449602
$385$	1.47109e6	0.505809
$386$	32007.8	0.0109342
$387$	1.13893e6	0.386563
$388$	1.92894e6	0.650488
$389$	−1.21525e6	−0.407186	−0.203593	−	0.979056i	$-0.565262\pi$
$389$	−1.21525e6	−0.407186	−0.203593	+	0.979056i	$0.565262\pi$
$390$	2.61838e6	0.871707
$391$	−900697.	−0.297946
$392$	2.29650e6	0.754834
$393$	589665.	0.192586
$394$	8.57163e6	2.78178
$395$	1.73724e6	0.560232
$396$	−2.93173e6	−0.939478
$397$	3.95864e6	1.26058	0.630290	−	0.776360i	$-0.282936\pi$
$397$	3.95864e6	1.26058	0.630290	+	0.776360i	$0.282936\pi$
$398$	867995.	0.274669
$399$	−3.68752e6	−1.15958
$400$	1.33381e6	0.416815
$401$	−831953.	−0.258367	−0.129184	−	0.991621i	$-0.541236\pi$
$401$	−831953.	−0.258367	−0.129184	+	0.991621i	$0.541236\pi$
$402$	−5.96686e6	−1.84154
$403$	399818.	0.122631
$404$	4.67182e6	1.42407
$405$	−625291.	−0.189428
$406$	−3.79843e6	−1.14364
$407$	346241.	0.103608
$408$	−8.93097e6	−2.65612
$409$	6.49404e6	1.91958	0.959791	−	0.280716i	$-0.0905719\pi$
$409$	6.49404e6	1.91958	0.959791	+	0.280716i	$0.0905719\pi$
$410$	−3.65589e6	−1.07407
$411$	3.01738e6	0.881100
$412$	−1.15344e7	−3.34775
$413$	−4.11850e6	−1.18813
$414$	542503.	0.155561
$415$	−249466.	−0.0711036
$416$	−6.78529e6	−1.92236
$417$	2.52754e6	0.711801
$418$	8.47078e6	2.37128
$419$	7.04429e6	1.96021	0.980104	−	0.198486i	$-0.0636026\pi$
$419$	7.04429e6	1.96021	0.980104	+	0.198486i	$0.0636026\pi$
$420$	−3.31127e6	−0.915949
$421$	−1.79008e6	−0.492230	−0.246115	−	0.969241i	$-0.579154\pi$
$421$	−1.79008e6	−0.492230	−0.246115	+	0.969241i	$0.579154\pi$
$422$	9.72437e6	2.65816
$423$	2.59518e6	0.705206
$424$	−3.93147e6	−1.06204
$425$	1.06415e6	0.285779
$426$	−9.19232e6	−2.45415
$427$	−6.07747e6	−1.61307
$428$	−2.48535e6	−0.655811
$429$	4.02273e6	1.05530
$430$	−2.95499e6	−0.770700
$431$	−5.23495e6	−1.35744	−0.678718	−	0.734399i	$-0.737464\pi$
$431$	−5.23495e6	−1.35744	−0.678718	+	0.734399i	$0.737464\pi$
$432$	8.75635e6	2.25743
$433$	−5.47327e6	−1.40290	−0.701451	−	0.712718i	$-0.747464\pi$
$433$	−5.47327e6	−1.40290	−0.701451	+	0.712718i	$0.747464\pi$
$434$	−723005.	−0.184254
$435$	742749.	0.188200
$436$	7.72777e6	1.94688
$437$	−1.09619e6	−0.274588
$438$	2.10354e6	0.523921
$439$	156766.	0.0388232	0.0194116	−	0.999812i	$-0.493821\pi$
$439$	156766.	0.0388232	0.0194116	+	0.999812i	$0.493821\pi$
$440$	4.33620e6	1.06777
$441$	−521522.	−0.127696
$442$	−1.48815e7	−3.62319
$443$	4.08114e6	0.988036	0.494018	−	0.869452i	$-0.335528\pi$
$443$	4.08114e6	0.988036	0.494018	+	0.869452i	$0.335528\pi$
$444$	−779353.	−0.187619
$445$	−2.02548e6	−0.484874
$446$	−7.14795e6	−1.70155
$447$	−225855.	−0.0534639
$448$	2.12859e6	0.501068
$449$	−4.16389e6	−0.974729	−0.487364	−	0.873199i	$-0.662042\pi$
$449$	−4.16389e6	−0.974729	−0.487364	+	0.873199i	$0.662042\pi$
$450$	−640954.	−0.149209
$451$	−5.61670e6	−1.30029
$452$	1.82288e7	4.19675
$453$	−4.79870e6	−1.09870
$454$	5.78159e6	1.31646
$455$	−3.14535e6	−0.712263
$456$	−1.08694e7	−2.44790
$457$	−4.08537e6	−0.915041	−0.457521	−	0.889199i	$-0.651262\pi$
$457$	−4.08537e6	−0.915041	−0.457521	+	0.889199i	$0.651262\pi$
$458$	3.44185e6	0.766705
$459$	6.98606e6	1.54775
$460$	−984340.	−0.216896
$461$	8.02219e6	1.75809	0.879044	−	0.476740i	$-0.158182\pi$
$461$	8.02219e6	1.75809	0.879044	+	0.476740i	$0.158182\pi$
$462$	−7.27443e6	−1.58560
$463$	4.68378e6	1.01542	0.507708	−	0.861529i	$-0.330493\pi$
$463$	4.68378e6	1.01542	0.507708	+	0.861529i	$0.330493\pi$
$464$	−5.29112e6	−1.14091
$465$	141377.	0.0303212
$466$	−1.95841e6	−0.417771
$467$	1.26377e6	0.268148	0.134074	−	0.990971i	$-0.457194\pi$
$467$	1.26377e6	0.268148	0.134074	+	0.990971i	$0.457194\pi$
$468$	6.26838e6	1.32294
$469$	7.16776e6	1.50470
$470$	−6.73326e6	−1.40599
$471$	−1.45380e6	−0.301963
$472$	−1.21397e7	−2.50816
$473$	−4.53989e6	−0.933023
$474$	−8.59055e6	−1.75620
$475$	1.29512e6	0.263376
$476$	1.88196e7	3.80709
$477$	892814.	0.179666
$478$	7.17506e6	1.43633
$479$	2.10842e6	0.419873	0.209937	−	0.977715i	$-0.432674\pi$
$479$	2.10842e6	0.419873	0.209937	+	0.977715i	$0.432674\pi$
$480$	−2.39930e6	−0.475315
$481$	−740301.	−0.145897
$482$	1.59796e7	3.13292
$483$	941371.	0.183609
$484$	−300908.	−0.0583876
$485$	647902.	0.125070
$486$	−7.19402e6	−1.38160
$487$	2.34639e6	0.448310	0.224155	−	0.974553i	$-0.428038\pi$
$487$	2.34639e6	0.448310	0.224155	+	0.974553i	$0.428038\pi$
$488$	−1.79141e7	−3.40521
$489$	3.70499e6	0.700673
$490$	1.35310e6	0.254590
$491$	−5.19162e6	−0.971851	−0.485925	−	0.874000i	$-0.661517\pi$
$491$	−5.19162e6	−0.971851	−0.485925	+	0.874000i	$0.661517\pi$
$492$	1.26426e7	2.35464
$493$	−4.22141e6	−0.782240
$494$	−1.81115e7	−3.33915
$495$	−984725.	−0.180635
$496$	−1.00713e6	−0.183815
$497$	1.10424e7	2.00526
$498$	1.23359e6	0.222894
$499$	2.52226e6	0.453459	0.226730	−	0.973958i	$-0.427197\pi$
$499$	2.52226e6	0.453459	0.226730	+	0.973958i	$0.427197\pi$
$500$	1.16297e6	0.208039
$501$	6.86864e6	1.22258
$502$	1.02296e7	1.81176
$503$	−5.00872e6	−0.882687	−0.441344	−	0.897338i	$-0.645498\pi$
$503$	−5.00872e6	−0.882687	−0.441344	+	0.897338i	$0.645498\pi$
$504$	−6.46189e6	−1.13314
$505$	1.56919e6	0.273809
$506$	−2.16247e6	−0.375468
$507$	−4.15181e6	−0.717328
$508$	−5.86278e6	−1.00796
$509$	−4.69091e6	−0.802533	−0.401266	−	0.915961i	$-0.631430\pi$
$509$	−4.69091e6	−0.802533	−0.401266	+	0.915961i	$0.631430\pi$
$510$	−5.26215e6	−0.895855
$511$	−2.52690e6	−0.428091
$512$	−1.28013e7	−2.15813
$513$	8.50235e6	1.42641
$514$	−1.40393e7	−2.34389
$515$	−3.87424e6	−0.643678
$516$	1.02188e7	1.68957
$517$	−1.03446e7	−1.70211
$518$	1.33871e6	0.219211
$519$	−6.75540e6	−1.10086
$520$	−9.27128e6	−1.50360
$521$	9.71357e6	1.56778	0.783889	−	0.620901i	$-0.213233\pi$
$521$	9.71357e6	1.56778	0.783889	+	0.620901i	$0.213233\pi$
$522$	2.54262e6	0.408418
$523$	1.12037e6	0.179105	0.0895525	−	0.995982i	$-0.471456\pi$
$523$	1.12037e6	0.179105	0.0895525	+	0.995982i	$0.471456\pi$
$524$	−3.66258e6	−0.582718
$525$	−1.11221e6	−0.176111
$526$	1.06083e7	1.67179
$527$	−803516.	−0.126028
$528$	−1.01331e7	−1.58182
$529$	279841.	0.0434783
$530$	−2.31643e6	−0.358203
$531$	2.75686e6	0.424306
$532$	2.29043e7	3.50863
$533$	1.20091e7	1.83102
$534$	1.00159e7	1.51997
$535$	−834793.	−0.126094
$536$	2.11278e7	3.17645
$537$	3.10471e6	0.464607
$538$	−1.01420e7	−1.51066
$539$	2.07883e6	0.308211
$540$	7.63482e6	1.12672
$541$	8.46525e6	1.24350	0.621751	−	0.783215i	$-0.286421\pi$
$541$	8.46525e6	1.24350	0.621751	+	0.783215i	$0.286421\pi$
$542$	−9.75991e6	−1.42708
$543$	−8.65041e6	−1.25903
$544$	1.36364e7	1.97562
$545$	2.59564e6	0.374329
$546$	1.55535e7	2.23279
$547$	−1.07656e7	−1.53840	−0.769198	−	0.639011i	$-0.779344\pi$
$547$	−1.07656e7	−1.53840	−0.769198	+	0.639011i	$0.779344\pi$
$548$	−1.87418e7	−2.66600
$549$	4.06818e6	0.576062
$550$	2.55490e6	0.360136
$551$	−5.13764e6	−0.720916
$552$	2.77480e6	0.387600
$553$	1.03195e7	1.43498
$554$	−1.75891e7	−2.43483
$555$	−261773.	−0.0360738
$556$	−1.56993e7	−2.15374
$557$	1.02326e7	1.39749	0.698744	−	0.715372i	$-0.253743\pi$
$557$	1.02326e7	1.39749	0.698744	+	0.715372i	$0.253743\pi$
$558$	483969.	0.0658010
$559$	9.70679e6	1.31385
$560$	7.92302e6	1.06763
$561$	−8.08448e6	−1.08454
$562$	1.70091e7	2.27165
$563$	−4.57825e6	−0.608735	−0.304368	−	0.952555i	$-0.598445\pi$
$563$	−4.57825e6	−0.608735	−0.304368	+	0.952555i	$0.598445\pi$
$564$	2.32847e7	3.08228
$565$	6.12280e6	0.806917
$566$	−1.71378e7	−2.24861
$567$	−3.71432e6	−0.485201
$568$	3.25487e7	4.23314
$569$	−7.04198e6	−0.911831	−0.455915	−	0.890023i	$-0.650688\pi$
$569$	−7.04198e6	−0.911831	−0.455915	+	0.890023i	$0.650688\pi$
$570$	−6.40427e6	−0.825625
$571$	7.43950e6	0.954891	0.477445	−	0.878661i	$-0.341563\pi$
$571$	7.43950e6	0.954891	0.477445	+	0.878661i	$0.341563\pi$
$572$	−2.49863e7	−3.19310
$573$	504605.	0.0642044
$574$	−2.17165e7	−2.75113
$575$	−330625.	−0.0417029
$576$	−1.42485e6	−0.178942
$577$	1.09993e7	1.37539	0.687695	−	0.726000i	$-0.258623\pi$
$577$	1.09993e7	1.37539	0.687695	+	0.726000i	$0.258623\pi$
$578$	1.52594e7	1.89985
$579$	−37178.4	−0.00460887
$580$	−4.61343e6	−0.569447
$581$	−1.48187e6	−0.182125
$582$	−3.20383e6	−0.392068
$583$	−3.55884e6	−0.433647
$584$	−7.44833e6	−0.903705
$585$	2.10545e6	0.254364
$586$	1.46826e7	1.76628
$587$	−5.76512e6	−0.690578	−0.345289	−	0.938496i	$-0.612219\pi$
$587$	−5.76512e6	−0.690578	−0.345289	+	0.938496i	$0.612219\pi$
$588$	−4.67924e6	−0.558126
$589$	−977914.	−0.116148
$590$	−7.15276e6	−0.845948
$591$	−9.95632e6	−1.17255
$592$	1.86479e6	0.218689
$593$	−1.13131e7	−1.32112	−0.660561	−	0.750772i	$-0.729682\pi$
$593$	−1.13131e7	−1.32112	−0.660561	+	0.750772i	$0.729682\pi$
$594$	1.67727e7	1.95046
$595$	6.32121e6	0.731995
$596$	1.40285e6	0.161769
$597$	−1.00821e6	−0.115775
$598$	4.62360e6	0.528721
$599$	1.09080e7	1.24216	0.621081	−	0.783747i	$-0.286694\pi$
$599$	1.09080e7	1.24216	0.621081	+	0.783747i	$0.286694\pi$
$600$	−3.27835e6	−0.371773
$601$	−1.39041e7	−1.57021	−0.785103	−	0.619365i	$-0.787390\pi$
$601$	−1.39041e7	−1.57021	−0.785103	+	0.619365i	$0.787390\pi$
$602$	−1.75531e7	−1.97407
$603$	−4.79800e6	−0.537361
$604$	2.98061e7	3.32440
$605$	−101071.	−0.0112263
$606$	−7.75955e6	−0.858331
$607$	−9.58416e6	−1.05580	−0.527901	−	0.849306i	$-0.677021\pi$
$607$	−9.58416e6	−1.05580	−0.527901	+	0.849306i	$0.677021\pi$
$608$	1.65961e7	1.82074
$609$	4.41204e6	0.482054
$610$	−1.05550e7	−1.14851
$611$	2.21179e7	2.39685
$612$	−1.25976e7	−1.35959
$613$	8.67311e6	0.932231	0.466116	−	0.884724i	$-0.345653\pi$
$613$	8.67311e6	0.932231	0.466116	+	0.884724i	$0.345653\pi$
$614$	−1.72555e7	−1.84717
$615$	4.24647e6	0.452731
$616$	2.57577e7	2.73498
$617$	1.00676e6	0.106467	0.0532334	−	0.998582i	$-0.483047\pi$
$617$	1.00676e6	0.106467	0.0532334	+	0.998582i	$0.483047\pi$
$618$	1.91579e7	2.01779
$619$	−3.59962e6	−0.377598	−0.188799	−	0.982016i	$-0.560460\pi$
$619$	−3.59962e6	−0.377598	−0.188799	+	0.982016i	$0.560460\pi$
$620$	−878134.	−0.0917448
$621$	−2.17053e6	−0.225858
$622$	1.73344e7	1.79652
$623$	−1.20317e7	−1.24196
$624$	2.16657e7	2.22747
$625$	390625.	0.0400000
$626$	2.14657e6	0.218932
$627$	−9.83917e6	−0.999515
$628$	9.02999e6	0.913667
$629$	1.48778e6	0.149939
$630$	−3.80736e6	−0.382184
$631$	9.98175e6	0.998007	0.499003	−	0.866600i	$-0.333700\pi$
$631$	9.98175e6	0.998007	0.499003	+	0.866600i	$0.333700\pi$
$632$	3.04179e7	3.02926
$633$	−1.12953e7	−1.12044
$634$	−2.90104e6	−0.286636
$635$	−1.96922e6	−0.193803
$636$	8.01058e6	0.785274
$637$	−4.44478e6	−0.434012
$638$	−1.01351e7	−0.985771
$639$	−7.39161e6	−0.716122
$640$	−2.71037e6	−0.261564
$641$	8.22566e6	0.790726	0.395363	−	0.918525i	$-0.370619\pi$
$641$	8.22566e6	0.790726	0.395363	+	0.918525i	$0.370619\pi$
$642$	4.12799e6	0.395277
$643$	−1.02132e7	−0.974174	−0.487087	−	0.873354i	$-0.661940\pi$
$643$	−1.02132e7	−0.974174	−0.487087	+	0.873354i	$0.661940\pi$
$644$	−5.84713e6	−0.555556
$645$	3.43235e6	0.324857
$646$	3.63986e7	3.43166
$647$	2.12379e6	0.199458	0.0997288	−	0.995015i	$-0.468202\pi$
$647$	2.12379e6	0.199458	0.0997288	+	0.995015i	$0.468202\pi$
$648$	−1.09484e7	−1.02427
$649$	−1.09891e7	−1.02412
$650$	−5.46266e6	−0.507132
$651$	839801.	0.0776647
$652$	−2.30128e7	−2.12007
$653$	−1.51047e6	−0.138621	−0.0693106	−	0.997595i	$-0.522080\pi$
$653$	−1.51047e6	−0.138621	−0.0693106	+	0.997595i	$0.522080\pi$
$654$	−1.28353e7	−1.17344
$655$	−1.23020e6	−0.112040
$656$	−3.02506e7	−2.74457
$657$	1.69147e6	0.152880
$658$	−3.99966e7	−3.60129
$659$	2.00145e7	1.79527	0.897637	−	0.440736i	$-0.145283\pi$
$659$	2.00145e7	1.79527	0.897637	+	0.440736i	$0.145283\pi$
$660$	−8.83524e6	−0.789511
$661$	−5.18066e6	−0.461192	−0.230596	−	0.973050i	$-0.574068\pi$
$661$	−5.18066e6	−0.461192	−0.230596	+	0.973050i	$0.574068\pi$
$662$	−1.14068e7	−1.01162
$663$	1.72855e7	1.52721
$664$	−4.36797e6	−0.384468
$665$	7.69320e6	0.674610
$666$	−896114.	−0.0782849
$667$	1.31156e6	0.114150
$668$	−4.26631e7	−3.69923
$669$	8.30265e6	0.717218
$670$	1.24485e7	1.07135
$671$	−1.62161e7	−1.39040
$672$	−1.42522e7	−1.21747
$673$	−5.16715e6	−0.439758	−0.219879	−	0.975527i	$-0.570566\pi$
$673$	−5.16715e6	−0.439758	−0.219879	+	0.975527i	$0.570566\pi$
$674$	−1.68711e7	−1.43052
$675$	2.56442e6	0.216636
$676$	2.57881e7	2.17047
$677$	1.96222e7	1.64541	0.822707	−	0.568465i	$-0.192463\pi$
$677$	1.96222e7	1.64541	0.822707	+	0.568465i	$0.192463\pi$
$678$	−3.02768e7	−2.52951
$679$	3.84863e6	0.320355
$680$	1.86325e7	1.54525
$681$	−6.71556e6	−0.554900
$682$	−1.92915e6	−0.158820
$683$	1.46670e7	1.20306	0.601532	−	0.798848i	$-0.294557\pi$
$683$	1.46670e7	1.20306	0.601532	+	0.798848i	$0.294557\pi$
$684$	−1.53318e7	−1.25300
$685$	−6.29509e6	−0.512597
$686$	−1.77114e7	−1.43695
$687$	−3.99786e6	−0.323173
$688$	−2.44511e7	−1.96937
$689$	7.60919e6	0.610647
$690$	1.63492e6	0.130729
$691$	−2.40495e7	−1.91607	−0.958033	−	0.286659i	$-0.907455\pi$
$691$	−2.40495e7	−1.91607	−0.958033	+	0.286659i	$0.907455\pi$
$692$	4.19597e7	3.33095
$693$	−5.84942e6	−0.462679
$694$	−1.98186e7	−1.56198
$695$	−5.27316e6	−0.414104
$696$	1.30050e7	1.01762
$697$	−2.41348e7	−1.88175
$698$	1.15803e7	0.899663
$699$	2.27477e6	0.176094
$700$	6.90823e6	0.532871
$701$	−1.42632e7	−1.09628	−0.548142	−	0.836385i	$-0.684665\pi$
$701$	−1.42632e7	−1.09628	−0.548142	+	0.836385i	$0.684665\pi$
$702$	−3.58619e7	−2.74657
$703$	1.81070e6	0.138184
$704$	5.67957e6	0.431901
$705$	7.82097e6	0.592636
$706$	−2.15169e7	−1.62468
$707$	9.32124e6	0.701335
$708$	2.47354e7	1.85454
$709$	−1.26537e7	−0.945367	−0.472683	−	0.881232i	$-0.656715\pi$
$709$	−1.26537e7	−0.945367	−0.472683	+	0.881232i	$0.656715\pi$
$710$	1.91777e7	1.42775
$711$	−6.90772e6	−0.512461
$712$	−3.54647e7	−2.62178
$713$	249647.	0.0183909
$714$	−3.12580e7	−2.29464
$715$	−8.39253e6	−0.613943
$716$	−1.92843e7	−1.40579
$717$	−8.33413e6	−0.605428
$718$	8.19518e6	0.593263
$719$	1.26592e7	0.913237	0.456619	−	0.889663i	$-0.349060\pi$
$719$	1.26592e7	0.913237	0.456619	+	0.889663i	$0.349060\pi$
$720$	−5.30356e6	−0.381273
$721$	−2.30136e7	−1.64872
$722$	1.87541e7	1.33891
$723$	−1.85610e7	−1.32055
$724$	5.37302e7	3.80953
$725$	−1.54958e6	−0.109489
$726$	499787.	0.0351919
$727$	2.24414e7	1.57476	0.787378	−	0.616470i	$-0.211438\pi$
$727$	2.24414e7	1.57476	0.787378	+	0.616470i	$0.211438\pi$
$728$	−5.50728e7	−3.85131
$729$	1.44340e7	1.00593
$730$	−4.38857e6	−0.304801
$731$	−1.95077e7	−1.35025
$732$	3.65008e7	2.51782
$733$	1.71882e6	0.118160	0.0590800	−	0.998253i	$-0.481183\pi$
$733$	1.71882e6	0.118160	0.0590800	+	0.998253i	$0.481183\pi$
$734$	−2.84723e7	−1.95066
$735$	−1.57169e6	−0.107312
$736$	−4.23675e6	−0.288295
$737$	1.91252e7	1.29699
$738$	1.45367e7	0.982485
$739$	−7.12514e6	−0.479935	−0.239967	−	0.970781i	$-0.577137\pi$
$739$	−7.12514e6	−0.479935	−0.239967	+	0.970781i	$0.577137\pi$
$740$	1.62595e6	0.109151
$741$	2.10372e7	1.40748
$742$	−1.37599e7	−0.917502
$743$	−2.56987e6	−0.170781	−0.0853905	−	0.996348i	$-0.527214\pi$
$743$	−2.56987e6	−0.170781	−0.0853905	+	0.996348i	$0.527214\pi$
$744$	2.47541e6	0.163951
$745$	471196.	0.0311036
$746$	−2.32136e7	−1.52720
$747$	991941.	0.0650406
$748$	5.02150e7	3.28155
$749$	−4.95880e6	−0.322977
$750$	−1.93161e6	−0.125391
$751$	−1.39067e7	−0.899755	−0.449877	−	0.893090i	$-0.648532\pi$
$751$	−1.39067e7	−0.899755	−0.449877	+	0.893090i	$0.648532\pi$
$752$	−5.57143e7	−3.59271
$753$	−1.18821e7	−0.763673
$754$	2.16700e7	1.38813
$755$	1.00114e7	0.639188
$756$	4.53520e7	2.88597
$757$	2.49289e7	1.58111	0.790556	−	0.612390i	$-0.209792\pi$
$757$	2.49289e7	1.58111	0.790556	+	0.612390i	$0.209792\pi$
$758$	1.81119e7	1.14496
$759$	2.51180e6	0.158263
$760$	2.26766e7	1.42411
$761$	−5.89997e6	−0.369308	−0.184654	−	0.982804i	$-0.559116\pi$
$761$	−5.89997e6	−0.369308	−0.184654	+	0.982804i	$0.559116\pi$
$762$	9.73765e6	0.607528
$763$	1.54185e7	0.958807
$764$	−3.13424e6	−0.194267
$765$	−4.23133e6	−0.261411
$766$	4.67018e7	2.87582
$767$	2.34959e7	1.44213
$768$	1.88989e7	1.15620
$769$	−1.21738e7	−0.742353	−0.371176	−	0.928562i	$-0.621045\pi$
$769$	−1.21738e7	−0.742353	−0.371176	+	0.928562i	$0.621045\pi$
$770$	1.51765e7	0.922453
$771$	1.63073e7	0.987973
$772$	230926.	0.0139454
$773$	3.06169e7	1.84294	0.921472	−	0.388444i	$-0.126987\pi$
$773$	3.06169e7	1.84294	0.921472	+	0.388444i	$0.126987\pi$
$774$	1.17498e7	0.704982
$775$	−294952.	−0.0176399
$776$	1.13443e7	0.676274
$777$	−1.55497e6	−0.0923995
$778$	−1.25372e7	−0.742592
$779$	−2.93731e7	−1.73423
$780$	1.88907e7	1.11176
$781$	2.94636e7	1.72846
$782$	−9.29204e6	−0.543368
$783$	−1.01729e7	−0.592979
$784$	1.11962e7	0.650552
$785$	3.03304e6	0.175672
$786$	6.08328e6	0.351222
$787$	−1.13249e7	−0.651776	−0.325888	−	0.945408i	$-0.605663\pi$
$787$	−1.13249e7	−0.651776	−0.325888	+	0.945408i	$0.605663\pi$
$788$	6.18416e7	3.54785
$789$	−1.23220e7	−0.704674
$790$	1.79223e7	1.02170
$791$	3.63703e7	2.06684
$792$	−1.72418e7	−0.976720
$793$	3.46719e7	1.95792
$794$	4.08394e7	2.29894
$795$	2.69063e6	0.150986
$796$	6.26231e6	0.350309
$797$	−1.93793e7	−1.08067	−0.540334	−	0.841451i	$-0.681702\pi$
$797$	−1.93793e7	−1.08067	−0.540334	+	0.841451i	$0.681702\pi$
$798$	−3.80423e7	−2.11475
$799$	−4.44504e7	−2.46325
$800$	5.00561e6	0.276523
$801$	8.05383e6	0.443528
$802$	−8.58284e6	−0.471189
$803$	−6.74236e6	−0.368997
$804$	−4.30490e7	−2.34867
$805$	−1.96396e6	−0.106818
$806$	4.12473e6	0.223644
$807$	1.17804e7	0.636758
$808$	2.74754e7	1.48053
$809$	3.00699e6	0.161533	0.0807663	−	0.996733i	$-0.474263\pi$
$809$	3.00699e6	0.161533	0.0807663	+	0.996733i	$0.474263\pi$
$810$	−6.45082e6	−0.345464
$811$	−2.26605e7	−1.20981	−0.604906	−	0.796297i	$-0.706789\pi$
$811$	−2.26605e7	−1.20981	−0.604906	+	0.796297i	$0.706789\pi$
$812$	−2.74044e7	−1.45858
$813$	1.13366e7	0.601526
$814$	3.57199e6	0.188951
$815$	−7.72965e6	−0.407629
$816$	−4.35416e7	−2.28917
$817$	−2.37418e7	−1.24440
$818$	6.69958e7	3.50077
$819$	1.25067e7	0.651528
$820$	−2.63761e7	−1.36986
$821$	1.63553e7	0.846838	0.423419	−	0.905934i	$-0.360830\pi$
$821$	1.63553e7	0.846838	0.423419	+	0.905934i	$0.360830\pi$
$822$	3.11288e7	1.60688
$823$	−3.72059e7	−1.91475	−0.957376	−	0.288844i	$-0.906729\pi$
$823$	−3.72059e7	−1.91475	−0.957376	+	0.288844i	$0.906729\pi$
$824$	−6.78352e7	−3.48046
$825$	−2.96762e6	−0.151801
$826$	−4.24885e7	−2.16681
$827$	5.97546e6	0.303814	0.151907	−	0.988395i	$-0.451459\pi$
$827$	5.97546e6	0.303814	0.151907	+	0.988395i	$0.451459\pi$
$828$	3.91398e6	0.198401
$829$	−9.63806e6	−0.487083	−0.243542	−	0.969890i	$-0.578309\pi$
$829$	−9.63806e6	−0.487083	−0.243542	+	0.969890i	$0.578309\pi$
$830$	−2.57362e6	−0.129673
$831$	2.04305e7	1.02630
$832$	−1.21436e7	−0.608188
$833$	8.93267e6	0.446035
$834$	2.60754e7	1.29812
$835$	−1.43299e7	−0.711258
$836$	6.11139e7	3.02430
$837$	−1.93634e6	−0.0955360
$838$	7.26724e7	3.57486
$839$	−7.52407e6	−0.369019	−0.184509	−	0.982831i	$-0.559070\pi$
$839$	−7.52407e6	−0.369019	−0.184509	+	0.982831i	$0.559070\pi$
$840$	−1.94739e7	−0.952259
$841$	−1.43641e7	−0.700306
$842$	−1.84674e7	−0.897688
$843$	−1.97568e7	−0.957520
$844$	7.01582e7	3.39018
$845$	8.66184e6	0.417319
$846$	2.67732e7	1.28610
$847$	−600374.	−0.0287550
$848$	−1.91673e7	−0.915315
$849$	1.99063e7	0.947809
$850$	1.09783e7	0.521181
$851$	−462245.	−0.0218801
$852$	−6.63196e7	−3.12999
$853$	−1.41316e7	−0.664997	−0.332499	−	0.943104i	$-0.607892\pi$
$853$	−1.41316e7	−0.664997	−0.332499	+	0.943104i	$0.607892\pi$
$854$	−6.26983e7	−2.94179
$855$	−5.14972e6	−0.240917
$856$	−1.46166e7	−0.681809
$857$	2.09123e7	0.972635	0.486318	−	0.873782i	$-0.338340\pi$
$857$	2.09123e7	0.972635	0.486318	+	0.873782i	$0.338340\pi$
$858$	4.15005e7	1.92457
$859$	2.81680e7	1.30249	0.651244	−	0.758868i	$-0.274247\pi$
$859$	2.81680e7	1.30249	0.651244	+	0.758868i	$0.274247\pi$
$860$	−2.13193e7	−0.982941
$861$	2.52247e7	1.15962
$862$	−5.40064e7	−2.47558
$863$	4.34253e6	0.198480	0.0992398	−	0.995064i	$-0.468359\pi$
$863$	4.34253e6	0.198480	0.0992398	+	0.995064i	$0.468359\pi$
$864$	3.28614e7	1.49762
$865$	1.40936e7	0.640447
$866$	−5.64650e7	−2.55850
$867$	−1.77245e7	−0.800804
$868$	−5.21625e6	−0.234995
$869$	2.75348e7	1.23689
$870$	7.66257e6	0.343223
$871$	−4.08919e7	−1.82638
$872$	4.54478e7	2.02405
$873$	−2.57622e6	−0.114406
$874$	−1.13088e7	−0.500771
$875$	2.32037e6	0.102456
$876$	1.51764e7	0.668202
$877$	2.03738e7	0.894486	0.447243	−	0.894413i	$-0.352406\pi$
$877$	2.03738e7	0.894486	0.447243	+	0.894413i	$0.352406\pi$
$878$	1.61728e6	0.0708026
$879$	−1.70545e7	−0.744503
$880$	2.11405e7	0.920255
$881$	−2.30766e7	−1.00168	−0.500842	−	0.865538i	$-0.666976\pi$
$881$	−2.30766e7	−1.00168	−0.500842	+	0.865538i	$0.666976\pi$
$882$	−5.38028e6	−0.232881
$883$	3.13768e7	1.35427	0.677136	−	0.735857i	$-0.263221\pi$
$883$	3.13768e7	1.35427	0.677136	+	0.735857i	$0.263221\pi$
$884$	−1.07365e8	−4.62097
$885$	8.30824e6	0.356575
$886$	4.21031e7	1.80190
$887$	2.73608e7	1.16767	0.583834	−	0.811873i	$-0.301552\pi$
$887$	2.73608e7	1.16767	0.583834	+	0.811873i	$0.301552\pi$
$888$	−4.58345e6	−0.195056
$889$	−1.16975e7	−0.496406
$890$	−2.08959e7	−0.884272
$891$	−9.91068e6	−0.418224
$892$	−5.15702e7	−2.17013
$893$	−5.40982e7	−2.27015
$894$	−2.33003e6	−0.0975031
$895$	−6.47730e6	−0.270294
$896$	−1.61000e7	−0.669971
$897$	−5.37050e6	−0.222861
$898$	−4.29568e7	−1.77763
$899$	1.17005e6	0.0482843
$900$	−4.62427e6	−0.190299
$901$	−1.52922e7	−0.627564
$902$	−5.79447e7	−2.37136
$903$	2.03887e7	0.832089
$904$	1.07206e8	4.36312
$905$	1.80472e7	0.732466
$906$	−4.95058e7	−2.00371
$907$	4.33380e7	1.74925	0.874623	−	0.484804i	$-0.161109\pi$
$907$	4.33380e7	1.74925	0.874623	+	0.484804i	$0.161109\pi$
$908$	4.17123e7	1.67899
$909$	−6.23951e6	−0.250461
$910$	−3.24490e7	−1.29897
$911$	−1.53112e7	−0.611241	−0.305621	−	0.952153i	$-0.598864\pi$
$911$	−1.53112e7	−0.611241	−0.305621	+	0.952153i	$0.598864\pi$
$912$	−5.29921e7	−2.10971
$913$	−3.95397e6	−0.156984
$914$	−4.21467e7	−1.66878
$915$	1.22601e7	0.484106
$916$	2.48318e7	0.977845
$917$	−7.30760e6	−0.286980
$918$	7.20717e7	2.82266
$919$	6.11892e6	0.238993	0.119497	−	0.992835i	$-0.461872\pi$
$919$	6.11892e6	0.238993	0.119497	+	0.992835i	$0.461872\pi$
$920$	−5.78900e6	−0.225494
$921$	2.00430e7	0.778599
$922$	8.27610e7	3.20626
$923$	−6.29965e7	−2.43395
$924$	−5.24826e7	−2.02225
$925$	546131.	0.0209866
$926$	4.83202e7	1.85183
$927$	1.54050e7	0.588792
$928$	−1.98569e7	−0.756904
$929$	250386.	0.00951855	0.00475927	−	0.999989i	$-0.498485\pi$
$929$	250386.	0.00951855	0.00475927	+	0.999989i	$0.498485\pi$
$930$	1.45852e6	0.0552973
$931$	1.08715e7	0.411068
$932$	−1.41293e7	−0.532820
$933$	−2.01347e7	−0.757251
$934$	1.30377e7	0.489027
$935$	1.68665e7	0.630950
$936$	3.68650e7	1.37538
$937$	1.02965e7	0.383127	0.191563	−	0.981480i	$-0.438644\pi$
$937$	1.02965e7	0.383127	0.191563	+	0.981480i	$0.438644\pi$
$938$	7.39462e7	2.74416
$939$	−2.49333e6	−0.0922817
$940$	−4.85783e7	−1.79318
$941$	2.33419e7	0.859336	0.429668	−	0.902987i	$-0.358631\pi$
$941$	2.33419e7	0.859336	0.429668	+	0.902987i	$0.358631\pi$
$942$	−1.49982e7	−0.550694
$943$	7.49853e6	0.274598
$944$	−5.91854e7	−2.16165
$945$	1.52330e7	0.554891
$946$	−4.68358e7	−1.70157
$947$	−2.25665e7	−0.817689	−0.408845	−	0.912604i	$-0.634068\pi$
$947$	−2.25665e7	−0.817689	−0.408845	+	0.912604i	$0.634068\pi$
$948$	−6.19780e7	−2.23984
$949$	1.44159e7	0.519609
$950$	1.33611e7	0.480323
$951$	3.36969e6	0.120820
$952$	1.10680e8	3.95800
$953$	5.23298e6	0.186645	0.0933226	−	0.995636i	$-0.470251\pi$
$953$	5.23298e6	0.186645	0.0933226	+	0.995636i	$0.470251\pi$
$954$	9.21072e6	0.327659
$955$	−1.05275e6	−0.0373521
$956$	5.17657e7	1.83188
$957$	1.17723e7	0.415512
$958$	2.17515e7	0.765730
$959$	−3.73938e7	−1.31297
$960$	−4.29400e6	−0.150378
$961$	−2.84064e7	−0.992221
$962$	−7.63732e6	−0.266075
$963$	3.31935e6	0.115342
$964$	1.15288e8	3.99569
$965$	77564.6	0.00268130
$966$	9.71166e6	0.334850
$967$	−402186.	−0.0138312	−0.00691561	−	0.999976i	$-0.502201\pi$
$967$	−402186.	−0.0138312	−0.00691561	+	0.999976i	$0.502201\pi$
$968$	−1.76967e6	−0.0607022
$969$	−4.22786e7	−1.44647
$970$	6.68408e6	0.228093
$971$	5.50463e7	1.87361	0.936807	−	0.349846i	$-0.113766\pi$
$971$	5.50463e7	1.87361	0.936807	+	0.349846i	$0.113766\pi$
$972$	−5.19025e7	−1.76207
$973$	−3.13234e7	−1.06068
$974$	2.42066e7	0.817591
$975$	6.34511e6	0.213761
$976$	−8.73372e7	−2.93477
$977$	3.27010e7	1.09604	0.548018	−	0.836467i	$-0.315383\pi$
$977$	3.27010e7	1.09604	0.548018	+	0.836467i	$0.315383\pi$
$978$	3.82226e7	1.27783
$979$	−3.21033e7	−1.07052
$980$	9.76220e6	0.324700
$981$	−1.03209e7	−0.342410
$982$	−5.35594e7	−1.77238
$983$	−1.46126e7	−0.482328	−0.241164	−	0.970484i	$-0.577529\pi$
$983$	−1.46126e7	−0.482328	−0.241164	+	0.970484i	$0.577529\pi$
$984$	7.43526e7	2.44798
$985$	2.07717e7	0.682151
$986$	−4.35502e7	−1.42658
$987$	4.64577e7	1.51798
$988$	−1.30668e8	−4.25871
$989$	6.06094e6	0.197038
$990$	−1.01589e7	−0.329427
$991$	−3.23456e6	−0.104624	−0.0523120	−	0.998631i	$-0.516659\pi$
$991$	−3.23456e6	−0.104624	−0.0523120	+	0.998631i	$0.516659\pi$
$992$	−3.77962e6	−0.121946
$993$	1.32495e7	0.426409
$994$	1.13919e8	3.65703
$995$	2.10341e6	0.0673546
$996$	8.89998e6	0.284276
$997$	5.07141e7	1.61581	0.807906	−	0.589312i	$-0.200601\pi$
$997$	5.07141e7	1.61581	0.807906	+	0.589312i	$0.200601\pi$
$998$	2.60209e7	0.826982
$999$	3.58531e6	0.113661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.a.e.1.11	✓	12
3.2	odd	2		1035.6.a.m.1.2		12
5.4	even	2		575.6.a.g.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.a.e.1.11	✓	12	1.1	even	1	trivial
575.6.a.g.1.2		12	5.4	even	2
1035.6.a.m.1.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+10.3165 q^{2} -11.9831 q^{3} +74.4302 q^{4} +25.0000 q^{5} -123.623 q^{6} +148.504 q^{7} +437.732 q^{8} -99.4063 q^{9} +O(q^{10})\)	\(q+10.3165 q^{2} -11.9831 q^{3} +74.4302 q^{4} +25.0000 q^{5} -123.623 q^{6} +148.504 q^{7} +437.732 q^{8} -99.4063 q^{9} +257.913 q^{10} +396.243 q^{11} -891.902 q^{12} -847.211 q^{13} +1532.04 q^{14} -299.576 q^{15} +2134.09 q^{16} +1702.64 q^{17} -1025.53 q^{18} +2072.19 q^{19} +1860.76 q^{20} -1779.53 q^{21} +4087.84 q^{22} -529.000 q^{23} -5245.37 q^{24} +625.000 q^{25} -8740.26 q^{26} +4103.07 q^{27} +11053.2 q^{28} -2479.33 q^{29} -3090.58 q^{30} -471.923 q^{31} +8008.97 q^{32} -4748.20 q^{33} +17565.3 q^{34} +3712.59 q^{35} -7398.84 q^{36} +873.810 q^{37} +21377.8 q^{38} +10152.2 q^{39} +10943.3 q^{40} -14174.9 q^{41} -18358.5 q^{42} -11457.3 q^{43} +29492.4 q^{44} -2485.16 q^{45} -5457.43 q^{46} -26106.8 q^{47} -25573.0 q^{48} +5246.36 q^{49} +6447.81 q^{50} -20402.8 q^{51} -63058.1 q^{52} -8981.46 q^{53} +42329.4 q^{54} +9906.06 q^{55} +65004.8 q^{56} -24831.2 q^{57} -25578.0 q^{58} -27733.3 q^{59} -22297.6 q^{60} -40924.7 q^{61} -4868.60 q^{62} -14762.2 q^{63} +14333.6 q^{64} -21180.3 q^{65} -48984.8 q^{66} +48266.5 q^{67} +126728. q^{68} +6339.04 q^{69} +38301.0 q^{70} +74357.5 q^{71} -43513.3 q^{72} -17015.7 q^{73} +9014.66 q^{74} -7489.41 q^{75} +154234. q^{76} +58843.5 q^{77} +104735. q^{78} +69489.7 q^{79} +53352.4 q^{80} -25011.6 q^{81} -146236. q^{82} -9978.65 q^{83} -132451. q^{84} +42566.0 q^{85} -118200. q^{86} +29709.9 q^{87} +173448. q^{88} -81019.3 q^{89} -25638.1 q^{90} -125814. q^{91} -39373.6 q^{92} +5655.08 q^{93} -269331. q^{94} +51804.7 q^{95} -95972.0 q^{96} +25916.1 q^{97} +54124.1 q^{98} -39389.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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