LMFDB - Embedded newform 115.6.a.e.1.5

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			1.5
Root			$4.85960$ 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)

$f(q)$	$=$	$q-3.85960 q^{2} -12.6293 q^{3} -17.1035 q^{4} +25.0000 q^{5} +48.7440 q^{6} -113.441 q^{7} +189.520 q^{8} -83.5011 q^{9} +O(q^{10})$	\(q-3.85960 q^{2} -12.6293 q^{3} -17.1035 q^{4} +25.0000 q^{5} +48.7440 q^{6} -113.441 q^{7} +189.520 q^{8} -83.5011 q^{9} -96.4901 q^{10} -655.592 q^{11} +216.005 q^{12} -872.504 q^{13} +437.837 q^{14} -315.732 q^{15} -184.161 q^{16} -297.987 q^{17} +322.281 q^{18} +895.014 q^{19} -427.587 q^{20} +1432.68 q^{21} +2530.33 q^{22} -529.000 q^{23} -2393.50 q^{24} +625.000 q^{25} +3367.52 q^{26} +4123.48 q^{27} +1940.23 q^{28} -4676.96 q^{29} +1218.60 q^{30} +8773.61 q^{31} -5353.85 q^{32} +8279.67 q^{33} +1150.11 q^{34} -2836.03 q^{35} +1428.16 q^{36} +4878.31 q^{37} -3454.40 q^{38} +11019.1 q^{39} +4738.00 q^{40} +15864.4 q^{41} -5529.57 q^{42} -13187.7 q^{43} +11212.9 q^{44} -2087.53 q^{45} +2041.73 q^{46} -20035.2 q^{47} +2325.82 q^{48} -3938.13 q^{49} -2412.25 q^{50} +3763.36 q^{51} +14922.8 q^{52} +19070.7 q^{53} -15915.0 q^{54} -16389.8 q^{55} -21499.3 q^{56} -11303.4 q^{57} +18051.2 q^{58} +44533.7 q^{59} +5400.12 q^{60} +47699.8 q^{61} -33862.6 q^{62} +9472.45 q^{63} +26556.9 q^{64} -21812.6 q^{65} -31956.2 q^{66} -34303.2 q^{67} +5096.60 q^{68} +6680.89 q^{69} +10945.9 q^{70} -40272.3 q^{71} -15825.1 q^{72} +12161.9 q^{73} -18828.3 q^{74} -7893.31 q^{75} -15307.8 q^{76} +74371.1 q^{77} -42529.3 q^{78} -70124.0 q^{79} -4604.01 q^{80} -31785.8 q^{81} -61230.4 q^{82} -52557.6 q^{83} -24503.8 q^{84} -7449.67 q^{85} +50899.4 q^{86} +59066.6 q^{87} -124248. q^{88} -111806. q^{89} +8057.02 q^{90} +98977.7 q^{91} +9047.73 q^{92} -110804. q^{93} +77328.0 q^{94} +22375.4 q^{95} +67615.3 q^{96} -21136.1 q^{97} +15199.6 q^{98} +54742.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.85960	−0.682288	−0.341144	−	0.940011i	$-0.610814\pi$
$2$	−3.85960	−0.682288	−0.341144	+	0.940011i	$0.610814\pi$
$3$	−12.6293	−0.810169	−0.405085	−	0.914279i	$-0.632758\pi$
$3$	−12.6293	−0.810169	−0.405085	+	0.914279i	$0.632758\pi$
$4$	−17.1035	−0.534483
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	48.7440	0.552769
$7$	−113.441	−0.875034	−0.437517	−	0.899210i	$-0.644142\pi$
$7$	−113.441	−0.875034	−0.437517	+	0.899210i	$0.644142\pi$
$8$	189.520	1.04696
$9$	−83.5011	−0.343626
$10$	−96.4901	−0.305128
$11$	−655.592	−1.63362	−0.816812	−	0.576904i	$-0.804261\pi$
$11$	−655.592	−1.63362	−0.816812	+	0.576904i	$0.804261\pi$
$12$	216.005	0.433022
$13$	−872.504	−1.43189	−0.715944	−	0.698158i	$-0.754003\pi$
$13$	−872.504	−1.43189	−0.715944	+	0.698158i	$0.754003\pi$
$14$	437.837	0.597025
$15$	−315.732	−0.362319
$16$	−184.161	−0.179844
$17$	−297.987	−0.250077	−0.125039	−	0.992152i	$-0.539906\pi$
$17$	−297.987	−0.250077	−0.125039	+	0.992152i	$0.539906\pi$
$18$	322.281	0.234452
$19$	895.014	0.568782	0.284391	−	0.958708i	$-0.408209\pi$
$19$	895.014	0.568782	0.284391	+	0.958708i	$0.408209\pi$
$20$	−427.587	−0.239028
$21$	1432.68	0.708926
$22$	2530.33	1.11460
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−2393.50	−0.848214
$25$	625.000	0.200000
$26$	3367.52	0.976959
$27$	4123.48	1.08856
$28$	1940.23	0.467691
$29$	−4676.96	−1.03269	−0.516343	−	0.856382i	$-0.672707\pi$
$29$	−4676.96	−1.03269	−0.516343	+	0.856382i	$0.672707\pi$
$30$	1218.60	0.247206
$31$	8773.61	1.63974	0.819868	−	0.572552i	$-0.194047\pi$
$31$	8773.61	1.63974	0.819868	+	0.572552i	$0.194047\pi$
$32$	−5353.85	−0.924254
$33$	8279.67	1.32351
$34$	1150.11	0.170625
$35$	−2836.03	−0.391327
$36$	1428.16	0.183662
$37$	4878.31	0.585821	0.292910	−	0.956140i	$-0.405376\pi$
$37$	4878.31	0.585821	0.292910	+	0.956140i	$0.405376\pi$
$38$	−3454.40	−0.388073
$39$	11019.1	1.16007
$40$	4738.00	0.468214
$41$	15864.4	1.47389	0.736945	−	0.675953i	$-0.236268\pi$
$41$	15864.4	1.47389	0.736945	+	0.675953i	$0.236268\pi$
$42$	−5529.57	−0.483691
$43$	−13187.7	−1.08767	−0.543837	−	0.839191i	$-0.683029\pi$
$43$	−13187.7	−1.08767	−0.543837	+	0.839191i	$0.683029\pi$
$44$	11212.9	0.873145
$45$	−2087.53	−0.153674
$46$	2041.73	0.142267
$47$	−20035.2	−1.32297	−0.661485	−	0.749959i	$-0.730073\pi$
$47$	−20035.2	−1.32297	−0.661485	+	0.749959i	$0.730073\pi$
$48$	2325.82	0.145704
$49$	−3938.13	−0.234315
$50$	−2412.25	−0.136458
$51$	3763.36	0.202605
$52$	14922.8	0.765320
$53$	19070.7	0.932560	0.466280	−	0.884637i	$-0.345594\pi$
$53$	19070.7	0.932560	0.466280	+	0.884637i	$0.345594\pi$
$54$	−15915.0	−0.742714
$55$	−16389.8	−0.730579
$56$	−21499.3	−0.916125
$57$	−11303.4	−0.460810
$58$	18051.2	0.704589
$59$	44533.7	1.66556	0.832778	−	0.553608i	$-0.186749\pi$
$59$	44533.7	1.66556	0.832778	+	0.553608i	$0.186749\pi$
$60$	5400.12	0.193653
$61$	47699.8	1.64132	0.820658	−	0.571420i	$-0.193607\pi$
$61$	47699.8	1.64132	0.820658	+	0.571420i	$0.193607\pi$
$62$	−33862.6	−1.11877
$63$	9472.45	0.300684
$64$	26556.9	0.810451
$65$	−21812.6	−0.640359
$66$	−31956.2	−0.903016
$67$	−34303.2	−0.933572	−0.466786	−	0.884370i	$-0.654588\pi$
$67$	−34303.2	−0.933572	−0.466786	+	0.884370i	$0.654588\pi$
$68$	5096.60	0.133662
$69$	6680.89	0.168932
$70$	10945.9	0.266998
$71$	−40272.3	−0.948114	−0.474057	−	0.880494i	$-0.657211\pi$
$71$	−40272.3	−0.948114	−0.474057	+	0.880494i	$0.657211\pi$
$72$	−15825.1	−0.359762
$73$	12161.9	0.267113	0.133557	−	0.991041i	$-0.457360\pi$
$73$	12161.9	0.267113	0.133557	+	0.991041i	$0.457360\pi$
$74$	−18828.3	−0.399699
$75$	−7893.31	−0.162034
$76$	−15307.8	−0.304005
$77$	74371.1	1.42948
$78$	−42529.3	−0.791502
$79$	−70124.0	−1.26415	−0.632075	−	0.774907i	$-0.717797\pi$
$79$	−70124.0	−1.26415	−0.632075	+	0.774907i	$0.717797\pi$
$80$	−4604.01	−0.0804288
$81$	−31785.8	−0.538296
$82$	−61230.4	−1.00562
$83$	−52557.6	−0.837414	−0.418707	−	0.908121i	$-0.637516\pi$
$83$	−52557.6	−0.837414	−0.418707	+	0.908121i	$0.637516\pi$
$84$	−24503.8	−0.378909
$85$	−7449.67	−0.111838
$86$	50899.4	0.742107
$87$	59066.6	0.836651
$88$	−124248.	−1.71034
$89$	−111806.	−1.49620	−0.748101	−	0.663585i	$-0.769034\pi$
$89$	−111806.	−1.49620	−0.748101	+	0.663585i	$0.769034\pi$
$90$	8057.02	0.104850
$91$	98977.7	1.25295
$92$	9047.73	0.111447
$93$	−110804.	−1.32846
$94$	77328.0	0.902646
$95$	22375.4	0.254367
$96$	67615.3	0.748802
$97$	−21136.1	−0.228084	−0.114042	−	0.993476i	$-0.536380\pi$
$97$	−21136.1	−0.228084	−0.114042	+	0.993476i	$0.536380\pi$
$98$	15199.6	0.159870
$99$	54742.7	0.561355
$100$	−10689.7	−0.106897
$101$	200357.	1.95434	0.977172	−	0.212451i	$-0.0681446\pi$
$101$	200357.	1.95434	0.977172	+	0.212451i	$0.0681446\pi$
$102$	−14525.1	−0.138235
$103$	−59403.4	−0.551720	−0.275860	−	0.961198i	$-0.588963\pi$
$103$	−59403.4	−0.551720	−0.275860	+	0.961198i	$0.588963\pi$
$104$	−165357.	−1.49913
$105$	35817.0	0.317041
$106$	−73605.3	−0.636274
$107$	−130123.	−1.09874	−0.549370	−	0.835579i	$-0.685132\pi$
$107$	−130123.	−1.09874	−0.549370	+	0.835579i	$0.685132\pi$
$108$	−70525.7	−0.581819
$109$	67474.4	0.543967	0.271984	−	0.962302i	$-0.412320\pi$
$109$	67474.4	0.543967	0.271984	+	0.962302i	$0.412320\pi$
$110$	63258.2	0.498465
$111$	−61609.6	−0.474614
$112$	20891.4	0.157370
$113$	229012.	1.68718	0.843591	−	0.536987i	$-0.180438\pi$
$113$	229012.	1.68718	0.843591	+	0.536987i	$0.180438\pi$
$114$	43626.6	0.314405
$115$	−13225.0	−0.0932505
$116$	79992.2	0.551954
$117$	72855.0	0.492033
$118$	−171883.	−1.13639
$119$	33803.9	0.218826
$120$	−59837.5	−0.379333
$121$	268750.	1.66873
$122$	−184102.	−1.11985
$123$	−200357.	−1.19410
$124$	−150059.	−0.876412
$125$	15625.0	0.0894427
$126$	−36559.9	−0.205153
$127$	−56931.6	−0.313216	−0.156608	−	0.987661i	$-0.550056\pi$
$127$	−56931.6	−0.313216	−0.156608	+	0.987661i	$0.550056\pi$
$128$	68824.2	0.371293
$129$	166552.	0.881200
$130$	84187.9	0.436909
$131$	238422.	1.21386	0.606929	−	0.794756i	$-0.292401\pi$
$131$	238422.	1.21386	0.606929	+	0.794756i	$0.292401\pi$
$132$	−141611.	−0.707395
$133$	−101531.	−0.497704
$134$	132397.	0.636965
$135$	103087.	0.486821
$136$	−56474.4	−0.261821
$137$	66399.0	0.302246	0.151123	−	0.988515i	$-0.451711\pi$
$137$	66399.0	0.302246	0.151123	+	0.988515i	$0.451711\pi$
$138$	−25785.6	−0.115260
$139$	19283.5	0.0846541	0.0423271	−	0.999104i	$-0.486523\pi$
$139$	19283.5	0.0846541	0.0423271	+	0.999104i	$0.486523\pi$
$140$	48505.9	0.209158
$141$	253031.	1.07183
$142$	155435.	0.646887
$143$	572007.	2.33917
$144$	15377.6	0.0617991
$145$	−116924.	−0.461831
$146$	−46940.3	−0.182248
$147$	49735.8	0.189835
$148$	−83436.0	−0.313112
$149$	28075.3	0.103600	0.0517999	−	0.998657i	$-0.483504\pi$
$149$	28075.3	0.103600	0.0517999	+	0.998657i	$0.483504\pi$
$150$	30465.0	0.110554
$151$	−22986.2	−0.0820397	−0.0410198	−	0.999158i	$-0.513061\pi$
$151$	−22986.2	−0.0820397	−0.0410198	+	0.999158i	$0.513061\pi$
$152$	169623.	0.595492
$153$	24882.2	0.0859330
$154$	−287043.	−0.975315
$155$	219340.	0.733312
$156$	−188465.	−0.620039
$157$	−440364.	−1.42581	−0.712907	−	0.701259i	$-0.752622\pi$
$157$	−440364.	−1.42581	−0.712907	+	0.701259i	$0.752622\pi$
$158$	270651.	0.862514
$159$	−240849.	−0.755531
$160$	−133846.	−0.413339
$161$	60010.3	0.182457
$162$	122681.	0.367272
$163$	−320252.	−0.944110	−0.472055	−	0.881569i	$-0.656488\pi$
$163$	−320252.	−0.944110	−0.472055	+	0.881569i	$0.656488\pi$
$164$	−271337.	−0.787770
$165$	206992.	0.591893
$166$	202851.	0.571357
$167$	446963.	1.24017	0.620084	−	0.784536i	$-0.287099\pi$
$167$	446963.	1.24017	0.620084	+	0.784536i	$0.287099\pi$
$168$	271521.	0.742216
$169$	389969.	1.05030
$170$	28752.7	0.0763057
$171$	−74734.7	−0.195448
$172$	225556.	0.581344
$173$	−245792.	−0.624384	−0.312192	−	0.950019i	$-0.601063\pi$
$173$	−245792.	−0.624384	−0.312192	+	0.950019i	$0.601063\pi$
$174$	−227974.	−0.570837
$175$	−70900.6	−0.175007
$176$	120734.	0.293798
$177$	−562429.	−1.34938
$178$	431527.	1.02084
$179$	−754250.	−1.75947	−0.879737	−	0.475461i	$-0.842281\pi$
$179$	−754250.	−1.75947	−0.879737	+	0.475461i	$0.842281\pi$
$180$	35703.9	0.0821363
$181$	203854.	0.462512	0.231256	−	0.972893i	$-0.425716\pi$
$181$	203854.	0.462512	0.231256	+	0.972893i	$0.425716\pi$
$182$	−382015.	−0.854873
$183$	−602415.	−1.32974
$184$	−100256.	−0.218306
$185$	121958.	0.261987
$186$	427661.	0.906395
$187$	195358.	0.408533
$188$	342672.	0.707105
$189$	−467771.	−0.952531
$190$	−86360.0	−0.173552
$191$	−50520.8	−0.100204	−0.0501022	−	0.998744i	$-0.515955\pi$
$191$	−50520.8	−0.100204	−0.0501022	+	0.998744i	$0.515955\pi$
$192$	−335394.	−0.656603
$193$	223679.	0.432248	0.216124	−	0.976366i	$-0.430658\pi$
$193$	223679.	0.432248	0.216124	+	0.976366i	$0.430658\pi$
$194$	81576.8	0.155619
$195$	275477.	0.518800
$196$	67355.7	0.125238
$197$	−252025.	−0.462678	−0.231339	−	0.972873i	$-0.574311\pi$
$197$	−252025.	−0.462678	−0.231339	+	0.972873i	$0.574311\pi$
$198$	−211285.	−0.383006
$199$	442741.	0.792532	0.396266	−	0.918136i	$-0.370306\pi$
$199$	442741.	0.792532	0.396266	+	0.918136i	$0.370306\pi$
$200$	118450.	0.209392
$201$	433225.	0.756351
$202$	−773298.	−1.33342
$203$	530559.	0.903636
$204$	−64366.5	−0.108289
$205$	396611.	0.659144
$206$	229274.	0.376432
$207$	44172.1	0.0716509
$208$	160681.	0.257517
$209$	−586765.	−0.929177
$210$	−138239.	−0.216313
$211$	−688754.	−1.06502	−0.532510	−	0.846424i	$-0.678751\pi$
$211$	−688754.	−1.06502	−0.532510	+	0.846424i	$0.678751\pi$
$212$	−326175.	−0.498438
$213$	508611.	0.768133
$214$	502223.	0.749657
$215$	−329693.	−0.486423
$216$	781481.	1.13968
$217$	−995287.	−1.43483
$218$	−260424.	−0.371142
$219$	−153597.	−0.216407
$220$	280323.	0.390482
$221$	259994.	0.358083
$222$	237788.	0.323823
$223$	−1.35364e6	−1.82281	−0.911407	−	0.411506i	$-0.865003\pi$
$223$	−1.35364e6	−1.82281	−0.911407	+	0.411506i	$0.865003\pi$
$224$	607346.	0.808754
$225$	−52188.2	−0.0687252
$226$	−883895.	−1.15114
$227$	885208.	1.14020	0.570099	−	0.821576i	$-0.306905\pi$
$227$	885208.	1.14020	0.570099	+	0.821576i	$0.306905\pi$
$228$	193327.	0.246295
$229$	−6490.84	−0.00817923	−0.00408961	−	0.999992i	$-0.501302\pi$
$229$	−6490.84	−0.00817923	−0.00408961	+	0.999992i	$0.501302\pi$
$230$	51043.2	0.0636237
$231$	−939254.	−1.15812
$232$	−886376.	−1.08118
$233$	151856.	0.183249	0.0916246	−	0.995794i	$-0.470794\pi$
$233$	151856.	0.183249	0.0916246	+	0.995794i	$0.470794\pi$
$234$	−281191.	−0.335708
$235$	−500881.	−0.591650
$236$	−761681.	−0.890212
$237$	885616.	1.02418
$238$	−130470.	−0.149303
$239$	43630.2	0.0494074	0.0247037	−	0.999695i	$-0.492136\pi$
$239$	43630.2	0.0494074	0.0247037	+	0.999695i	$0.492136\pi$
$240$	58145.4	0.0651610
$241$	1.59327e6	1.76704	0.883520	−	0.468393i	$-0.155167\pi$
$241$	1.59327e6	1.76704	0.883520	+	0.468393i	$0.155167\pi$
$242$	−1.03727e6	−1.13855
$243$	−600573.	−0.652454
$244$	−815832.	−0.877256
$245$	−98453.4	−0.104789
$246$	773297.	0.814720
$247$	−780903.	−0.814432
$248$	1.66277e6	1.71674
$249$	663765.	0.678447
$250$	−60306.3	−0.0610257
$251$	1.15141e6	1.15357	0.576787	−	0.816895i	$-0.304306\pi$
$251$	1.15141e6	1.15357	0.576787	+	0.816895i	$0.304306\pi$
$252$	−162012.	−0.160711
$253$	346808.	0.340634
$254$	219733.	0.213703
$255$	94084.0	0.0906077
$256$	−1.11545e6	−1.06378
$257$	38324.7	0.0361948	0.0180974	−	0.999836i	$-0.494239\pi$
$257$	38324.7	0.0361948	0.0180974	+	0.999836i	$0.494239\pi$
$258$	−642823.	−0.601232
$259$	−553400.	−0.512613
$260$	373071.	0.342261
$261$	390531.	0.354858
$262$	−920214.	−0.828201
$263$	−139682.	−0.124523	−0.0622617	−	0.998060i	$-0.519831\pi$
$263$	−139682.	−0.124523	−0.0622617	+	0.998060i	$0.519831\pi$
$264$	1.56916e6	1.38566
$265$	476767.	0.417053
$266$	391871.	0.339577
$267$	1.41203e6	1.21218
$268$	586704.	0.498979
$269$	215689.	0.181739	0.0908695	−	0.995863i	$-0.471035\pi$
$269$	215689.	0.181739	0.0908695	+	0.995863i	$0.471035\pi$
$270$	−397875.	−0.332152
$271$	−1.07723e6	−0.891016	−0.445508	−	0.895278i	$-0.646977\pi$
$271$	−1.07723e6	−0.891016	−0.445508	+	0.895278i	$0.646977\pi$
$272$	54877.4	0.0449750
$273$	−1.25002e6	−1.01510
$274$	−256274.	−0.206218
$275$	−409745.	−0.326725
$276$	−114266.	−0.0902913
$277$	−1.19666e6	−0.937069	−0.468535	−	0.883445i	$-0.655218\pi$
$277$	−1.19666e6	−0.937069	−0.468535	+	0.883445i	$0.655218\pi$
$278$	−74426.5	−0.0577585
$279$	−732606.	−0.563456
$280$	−537483.	−0.409704
$281$	−1.70422e6	−1.28753	−0.643767	−	0.765221i	$-0.722630\pi$
$281$	−1.70422e6	−1.28753	−0.643767	+	0.765221i	$0.722630\pi$
$282$	−976598.	−0.731296
$283$	313521.	0.232702	0.116351	−	0.993208i	$-0.462880\pi$
$283$	313521.	0.232702	0.116351	+	0.993208i	$0.462880\pi$
$284$	688796.	0.506751
$285$	−282585.	−0.206080
$286$	−2.20772e6	−1.59598
$287$	−1.79968e6	−1.28970
$288$	447052.	0.317597
$289$	−1.33106e6	−0.937461
$290$	451280.	0.315102
$291$	266933.	0.184787
$292$	−208011.	−0.142768
$293$	1.44640e6	0.984285	0.492142	−	0.870515i	$-0.336214\pi$
$293$	1.44640e6	0.984285	0.492142	+	0.870515i	$0.336214\pi$
$294$	−191961.	−0.129522
$295$	1.11334e6	0.744859
$296$	924536.	0.613331
$297$	−2.70332e6	−1.77831
$298$	−108360.	−0.0706850
$299$	461554.	0.298569
$300$	135003.	0.0866044
$301$	1.49603e6	0.951752
$302$	88717.4	0.0559747
$303$	−2.53037e6	−1.58335
$304$	−164826.	−0.102292
$305$	1.19250e6	0.734019
$306$	−96035.4	−0.0586311
$307$	2.29224e6	1.38808	0.694040	−	0.719936i	$-0.255829\pi$
$307$	2.29224e6	1.38808	0.694040	+	0.719936i	$0.255829\pi$
$308$	−1.27200e6	−0.764032
$309$	750223.	0.446986
$310$	−846566.	−0.500330
$311$	2.97876e6	1.74636	0.873182	−	0.487394i	$-0.162052\pi$
$311$	2.97876e6	1.74636	0.873182	+	0.487394i	$0.162052\pi$
$312$	2.08834e6	1.21455
$313$	1.19453e6	0.689185	0.344592	−	0.938752i	$-0.388017\pi$
$313$	1.19453e6	0.689185	0.344592	+	0.938752i	$0.388017\pi$
$314$	1.69963e6	0.972815
$315$	236811.	0.134470
$316$	1.19936e6	0.675667
$317$	2.32385e6	1.29885	0.649425	−	0.760426i	$-0.275010\pi$
$317$	2.32385e6	1.29885	0.649425	+	0.760426i	$0.275010\pi$
$318$	929582.	0.515490
$319$	3.06618e6	1.68702
$320$	663922.	0.362445
$321$	1.64336e6	0.890165
$322$	−231616.	−0.124488
$323$	−266702.	−0.142240
$324$	543648.	0.287710
$325$	−545315.	−0.286377
$326$	1.23605e6	0.644155
$327$	−852154.	−0.440706
$328$	3.00663e6	1.54310
$329$	2.27282e6	1.15764
$330$	−798906.	−0.403841
$331$	682160.	0.342228	0.171114	−	0.985251i	$-0.445263\pi$
$331$	682160.	0.342228	0.171114	+	0.985251i	$0.445263\pi$
$332$	898916.	0.447584
$333$	−407344.	−0.201303
$334$	−1.72510e6	−0.846151
$335$	−857580.	−0.417506
$336$	−263843.	−0.127496
$337$	2.96289e6	1.42115	0.710577	−	0.703619i	$-0.248434\pi$
$337$	2.96289e6	1.42115	0.710577	+	0.703619i	$0.248434\pi$
$338$	−1.50513e6	−0.716608
$339$	−2.89226e6	−1.36690
$340$	127415.	0.0597755
$341$	−5.75191e6	−2.67871
$342$	288446.	0.133352
$343$	2.35335e6	1.08007
$344$	−2.49934e6	−1.13875
$345$	167022.	0.0755487
$346$	948658.	0.426010
$347$	2.27268e6	1.01324	0.506622	−	0.862168i	$-0.330894\pi$
$347$	2.27268e6	1.01324	0.506622	+	0.862168i	$0.330894\pi$
$348$	−1.01024e6	−0.447176
$349$	−641132.	−0.281763	−0.140882	−	0.990026i	$-0.544994\pi$
$349$	−641132.	−0.281763	−0.140882	+	0.990026i	$0.544994\pi$
$350$	273648.	0.119405
$351$	−3.59775e6	−1.55870
$352$	3.50994e6	1.50988
$353$	1.45039e6	0.619509	0.309754	−	0.950817i	$-0.399753\pi$
$353$	1.45039e6	0.619509	0.309754	+	0.950817i	$0.399753\pi$
$354$	2.17075e6	0.920667
$355$	−1.00681e6	−0.424010
$356$	1.91227e6	0.799695
$357$	−426919.	−0.177286
$358$	2.91111e6	1.20047
$359$	3.44492e6	1.41073	0.705363	−	0.708847i	$-0.250784\pi$
$359$	3.44492e6	1.41073	0.705363	+	0.708847i	$0.250784\pi$
$360$	−395628.	−0.160891
$361$	−1.67505e6	−0.676487
$362$	−786796.	−0.315567
$363$	−3.39413e6	−1.35195
$364$	−1.69286e6	−0.669681
$365$	304049.	0.119457
$366$	2.32508e6	0.907268
$367$	2.26537e6	0.877959	0.438979	−	0.898497i	$-0.355340\pi$
$367$	2.26537e6	0.877959	0.438979	+	0.898497i	$0.355340\pi$
$368$	97420.9	0.0375001
$369$	−1.32470e6	−0.506467
$370$	−470708.	−0.178751
$371$	−2.16340e6	−0.816022
$372$	1.89514e6	0.710042
$373$	−3.18023e6	−1.18355	−0.591776	−	0.806103i	$-0.701573\pi$
$373$	−3.18023e6	−1.18355	−0.591776	+	0.806103i	$0.701573\pi$
$374$	−754003.	−0.278737
$375$	−197333.	−0.0724637
$376$	−3.79707e6	−1.38509
$377$	4.08066e6	1.47869
$378$	1.80541e6	0.649900
$379$	−3.24324e6	−1.15980	−0.579898	−	0.814689i	$-0.696907\pi$
$379$	−3.24324e6	−1.15980	−0.579898	+	0.814689i	$0.696907\pi$
$380$	−382696.	−0.135955
$381$	719005.	0.253758
$382$	194990.	0.0683683
$383$	−3.79788e6	−1.32295	−0.661476	−	0.749966i	$-0.730070\pi$
$383$	−3.79788e6	−1.32295	−0.661476	+	0.749966i	$0.730070\pi$
$384$	−869201.	−0.300810
$385$	1.85928e6	0.639282
$386$	−863314.	−0.294917
$387$	1.10119e6	0.373753
$388$	361500.	0.121907
$389$	416153.	0.139437	0.0697186	−	0.997567i	$-0.477790\pi$
$389$	416153.	0.139437	0.0697186	+	0.997567i	$0.477790\pi$
$390$	−1.06323e6	−0.353971
$391$	157635.	0.0521447
$392$	−746355.	−0.245318
$393$	−3.01110e6	−0.983430
$394$	972718.	0.315680
$395$	−1.75310e6	−0.565345
$396$	−936289.	−0.300035
$397$	4.86421e6	1.54894	0.774472	−	0.632608i	$-0.218016\pi$
$397$	4.86421e6	1.54894	0.774472	+	0.632608i	$0.218016\pi$
$398$	−1.70880e6	−0.540735
$399$	1.28227e6	0.403224
$400$	−115100.	−0.0359689
$401$	−1.66439e6	−0.516886	−0.258443	−	0.966027i	$-0.583209\pi$
$401$	−1.66439e6	−0.516886	−0.258443	+	0.966027i	$0.583209\pi$
$402$	−1.67208e6	−0.516049
$403$	−7.65501e6	−2.34792
$404$	−3.42680e6	−1.04456
$405$	−794645.	−0.240733
$406$	−2.04775e6	−0.616540
$407$	−3.19818e6	−0.957011
$408$	713231.	0.212119
$409$	1.87631e6	0.554622	0.277311	−	0.960780i	$-0.410557\pi$
$409$	1.87631e6	0.554622	0.277311	+	0.960780i	$0.410557\pi$
$410$	−1.53076e6	−0.449726
$411$	−838572.	−0.244870
$412$	1.01600e6	0.294885
$413$	−5.05195e6	−1.45742
$414$	−170487.	−0.0488866
$415$	−1.31394e6	−0.374503
$416$	4.67125e6	1.32343
$417$	−243536.	−0.0685841
$418$	2.26468e6	0.633966
$419$	−46023.0	−0.0128068	−0.00640338	−	0.999979i	$-0.502038\pi$
$419$	−46023.0	−0.0128068	−0.00640338	+	0.999979i	$0.502038\pi$
$420$	−612595.	−0.169453
$421$	2.39634e6	0.658936	0.329468	−	0.944167i	$-0.393131\pi$
$421$	2.39634e6	0.658936	0.329468	+	0.944167i	$0.393131\pi$
$422$	2.65832e6	0.726651
$423$	1.67296e6	0.454606
$424$	3.61427e6	0.976352
$425$	−186242.	−0.0500155
$426$	−1.96304e6	−0.524088
$427$	−5.41112e6	−1.43621
$428$	2.22556e6	0.587258
$429$	−7.22404e6	−1.89512
$430$	1.27248e6	0.331880
$431$	−1.98910e6	−0.515780	−0.257890	−	0.966174i	$-0.583027\pi$
$431$	−1.98910e6	−0.515780	−0.257890	+	0.966174i	$0.583027\pi$
$432$	−759382.	−0.195772
$433$	2.52831e6	0.648054	0.324027	−	0.946048i	$-0.394963\pi$
$433$	2.52831e6	0.648054	0.324027	+	0.946048i	$0.394963\pi$
$434$	3.84141e6	0.978964
$435$	1.47667e6	0.374162
$436$	−1.15405e6	−0.290741
$437$	−473463.	−0.118599
$438$	592822.	0.147652
$439$	2.81904e6	0.698137	0.349068	−	0.937097i	$-0.386498\pi$
$439$	2.81904e6	0.698137	0.349068	+	0.937097i	$0.386498\pi$
$440$	−3.10619e6	−0.764886
$441$	328838.	0.0805167
$442$	−1.00347e6	−0.244315
$443$	7.44429e6	1.80225	0.901123	−	0.433564i	$-0.142744\pi$
$443$	7.44429e6	1.80225	0.901123	+	0.433564i	$0.142744\pi$
$444$	1.05374e6	0.253673
$445$	−2.79515e6	−0.669122
$446$	5.22453e6	1.24368
$447$	−354572.	−0.0839335
$448$	−3.01264e6	−0.709173
$449$	−46246.1	−0.0108258	−0.00541289	−	0.999985i	$-0.501723\pi$
$449$	−46246.1	−0.0108258	−0.00541289	+	0.999985i	$0.501723\pi$
$450$	201426.	0.0468903
$451$	−1.04006e7	−2.40778
$452$	−3.91690e6	−0.901770
$453$	290299.	0.0664660
$454$	−3.41655e6	−0.777944
$455$	2.47444e6	0.560336
$456$	−2.14222e6	−0.482449
$457$	−4.28266e6	−0.959231	−0.479615	−	0.877479i	$-0.659224\pi$
$457$	−4.28266e6	−0.959231	−0.479615	+	0.877479i	$0.659224\pi$
$458$	25052.1	0.00558059
$459$	−1.22874e6	−0.272225
$460$	226193.	0.0498408
$461$	−128545.	−0.0281710	−0.0140855	−	0.999901i	$-0.504484\pi$
$461$	−128545.	−0.0281710	−0.0140855	+	0.999901i	$0.504484\pi$
$462$	3.62515e6	0.790170
$463$	−4.95935e6	−1.07516	−0.537579	−	0.843213i	$-0.680661\pi$
$463$	−4.95935e6	−1.07516	−0.537579	+	0.843213i	$0.680661\pi$
$464$	861311.	0.185723
$465$	−2.77011e6	−0.594107
$466$	−586104.	−0.125029
$467$	2.19135e6	0.464965	0.232483	−	0.972601i	$-0.425315\pi$
$467$	2.19135e6	0.464965	0.232483	+	0.972601i	$0.425315\pi$
$468$	−1.24607e6	−0.262984
$469$	3.89139e6	0.816907
$470$	1.93320e6	0.403675
$471$	5.56148e6	1.15515
$472$	8.44003e6	1.74377
$473$	8.64577e6	1.77685
$474$	−3.41812e6	−0.698783
$475$	559384.	0.113756
$476$	−578164.	−0.116959
$477$	−1.59242e6	−0.320452
$478$	−168395.	−0.0337101
$479$	961351.	0.191445	0.0957223	−	0.995408i	$-0.469484\pi$
$479$	961351.	0.191445	0.0957223	+	0.995408i	$0.469484\pi$
$480$	1.69038e6	0.334874
$481$	−4.25634e6	−0.838830
$482$	−6.14938e6	−1.20563
$483$	−757887.	−0.147821
$484$	−4.59656e6	−0.891907
$485$	−528401.	−0.102002
$486$	2.31797e6	0.445161
$487$	−3.10439e6	−0.593135	−0.296567	−	0.955012i	$-0.595842\pi$
$487$	−3.10439e6	−0.593135	−0.296567	+	0.955012i	$0.595842\pi$
$488$	9.04007e6	1.71839
$489$	4.04455e6	0.764889
$490$	379991.	0.0714962
$491$	5.95558e6	1.11486	0.557430	−	0.830224i	$-0.311787\pi$
$491$	5.95558e6	1.11486	0.557430	+	0.830224i	$0.311787\pi$
$492$	3.42679e6	0.638227
$493$	1.39367e6	0.258251
$494$	3.01398e6	0.555677
$495$	1.36857e6	0.251046
$496$	−1.61575e6	−0.294897
$497$	4.56853e6	0.829632
$498$	−2.56187e6	−0.462896
$499$	1.71806e6	0.308878	0.154439	−	0.988002i	$-0.450643\pi$
$499$	1.71806e6	0.308878	0.154439	+	0.988002i	$0.450643\pi$
$500$	−267242.	−0.0478056
$501$	−5.64482e6	−1.00475
$502$	−4.44398e6	−0.787069
$503$	−2.61296e6	−0.460481	−0.230241	−	0.973134i	$-0.573951\pi$
$503$	−2.61296e6	−0.460481	−0.230241	+	0.973134i	$0.573951\pi$
$504$	1.79522e6	0.314804
$505$	5.00892e6	0.874009
$506$	−1.33854e6	−0.232411
$507$	−4.92504e6	−0.850922
$508$	973727.	0.167409
$509$	7.04431e6	1.20516	0.602579	−	0.798059i	$-0.294140\pi$
$509$	7.04431e6	1.20516	0.602579	+	0.798059i	$0.294140\pi$
$510$	−363127.	−0.0618205
$511$	−1.37966e6	−0.233733
$512$	2.10283e6	0.354511
$513$	3.69057e6	0.619156
$514$	−147918.	−0.0246953
$515$	−1.48509e6	−0.246737
$516$	−2.84861e6	−0.470987
$517$	1.31349e7	2.16123
$518$	2.13591e6	0.349750
$519$	3.10417e6	0.505857
$520$	−4.13392e6	−0.670430
$521$	−7.81709e6	−1.26168	−0.630842	−	0.775911i	$-0.717290\pi$
$521$	−7.81709e6	−1.26168	−0.630842	+	0.775911i	$0.717290\pi$
$522$	−1.50729e6	−0.242115
$523$	8.85485e6	1.41556	0.707778	−	0.706435i	$-0.249698\pi$
$523$	8.85485e6	1.41556	0.707778	+	0.706435i	$0.249698\pi$
$524$	−4.07784e6	−0.648787
$525$	895425.	0.141785
$526$	539117.	0.0849608
$527$	−2.61442e6	−0.410061
$528$	−1.52479e6	−0.238026
$529$	279841.	0.0434783
$530$	−1.84013e6	−0.284550
$531$	−3.71861e6	−0.572328
$532$	1.73654e6	0.266014
$533$	−1.38418e7	−2.11044
$534$	−5.44988e6	−0.827054
$535$	−3.25308e6	−0.491371
$536$	−6.50114e6	−0.977412
$537$	9.52564e6	1.42547
$538$	−832475.	−0.123998
$539$	2.58181e6	0.382783
$540$	−1.76314e6	−0.260198
$541$	2.39776e6	0.352219	0.176109	−	0.984371i	$-0.443649\pi$
$541$	2.39776e6	0.352219	0.176109	+	0.984371i	$0.443649\pi$
$542$	4.15768e6	0.607929
$543$	−2.57453e6	−0.374713
$544$	1.59538e6	0.231135
$545$	1.68686e6	0.243270
$546$	4.82457e6	0.692592
$547$	−225442.	−0.0322156	−0.0161078	−	0.999870i	$-0.505128\pi$
$547$	−225442.	−0.0322156	−0.0161078	+	0.999870i	$0.505128\pi$
$548$	−1.13565e6	−0.161545
$549$	−3.98299e6	−0.563999
$550$	1.58145e6	0.222920
$551$	−4.18594e6	−0.587374
$552$	1.26616e6	0.176865
$553$	7.95493e6	1.10617
$554$	4.61864e6	0.639351
$555$	−1.54024e6	−0.212254
$556$	−329814.	−0.0452462
$557$	2.86227e6	0.390906	0.195453	−	0.980713i	$-0.437382\pi$
$557$	2.86227e6	0.390906	0.195453	+	0.980713i	$0.437382\pi$
$558$	2.82757e6	0.384439
$559$	1.15063e7	1.55743
$560$	522284.	0.0703780
$561$	−2.46723e6	−0.330980
$562$	6.57760e6	0.878469
$563$	1.21293e7	1.61274	0.806368	−	0.591415i	$-0.201430\pi$
$563$	1.21293e7	1.61274	0.806368	+	0.591415i	$0.201430\pi$
$564$	−4.32770e6	−0.572875
$565$	5.72529e6	0.754530
$566$	−1.21007e6	−0.158770
$567$	3.60581e6	0.471027
$568$	−7.63240e6	−0.992637
$569$	6.63319e6	0.858899	0.429449	−	0.903091i	$-0.358708\pi$
$569$	6.63319e6	0.858899	0.429449	+	0.903091i	$0.358708\pi$
$570$	1.09067e6	0.140606
$571$	−3.60055e6	−0.462145	−0.231072	−	0.972937i	$-0.574223\pi$
$571$	−3.60055e6	−0.462145	−0.231072	+	0.972937i	$0.574223\pi$
$572$	−9.78330e6	−1.25025
$573$	638042.	0.0811826
$574$	6.94604e6	0.879950
$575$	−330625.	−0.0417029
$576$	−2.21753e6	−0.278492
$577$	376403.	0.0470667	0.0235334	−	0.999723i	$-0.492508\pi$
$577$	376403.	0.0470667	0.0235334	+	0.999723i	$0.492508\pi$
$578$	5.13737e6	0.639618
$579$	−2.82491e6	−0.350194
$580$	1.99980e6	0.246841
$581$	5.96218e6	0.732766
$582$	−1.03026e6	−0.126078
$583$	−1.25026e7	−1.52345
$584$	2.30493e6	0.279657
$585$	1.82137e6	0.220044
$586$	−5.58255e6	−0.671566
$587$	−1.42468e7	−1.70656	−0.853279	−	0.521454i	$-0.825390\pi$
$587$	−1.42468e7	−1.70656	−0.853279	+	0.521454i	$0.825390\pi$
$588$	−850655.	−0.101464
$589$	7.85251e6	0.932653
$590$	−4.29706e6	−0.508208
$591$	3.18290e6	0.374847
$592$	−898392.	−0.105357
$593$	5.03873e6	0.588416	0.294208	−	0.955741i	$-0.404944\pi$
$593$	5.03873e6	0.588416	0.294208	+	0.955741i	$0.404944\pi$
$594$	1.04337e7	1.21332
$595$	845098.	0.0978621
$596$	−480186.	−0.0553724
$597$	−5.59150e6	−0.642085
$598$	−1.78142e6	−0.203710
$599$	−5.40380e6	−0.615365	−0.307682	−	0.951489i	$-0.599553\pi$
$599$	−5.40380e6	−0.615365	−0.307682	+	0.951489i	$0.599553\pi$
$600$	−1.49594e6	−0.169643
$601$	67850.5	0.00766244	0.00383122	−	0.999993i	$-0.498780\pi$
$601$	67850.5	0.00766244	0.00383122	+	0.999993i	$0.498780\pi$
$602$	−5.77408e6	−0.649369
$603$	2.86436e6	0.320799
$604$	393143.	0.0438488
$605$	6.71876e6	0.746278
$606$	9.76620e6	1.08030
$607$	−6.82329e6	−0.751661	−0.375831	−	0.926688i	$-0.622643\pi$
$607$	−6.82329e6	−0.751661	−0.375831	+	0.926688i	$0.622643\pi$
$608$	−4.79177e6	−0.525699
$609$	−6.70058e6	−0.732098
$610$	−4.60256e6	−0.500812
$611$	1.74808e7	1.89434
$612$	−425572.	−0.0459298
$613$	3.77645e6	0.405913	0.202956	−	0.979188i	$-0.434945\pi$
$613$	3.77645e6	0.405913	0.202956	+	0.979188i	$0.434945\pi$
$614$	−8.84714e6	−0.947070
$615$	−5.00892e6	−0.534018
$616$	1.40948e7	1.49660
$617$	−1.31749e7	−1.39327	−0.696634	−	0.717427i	$-0.745320\pi$
$617$	−1.31749e7	−1.39327	−0.696634	+	0.717427i	$0.745320\pi$
$618$	−2.89556e6	−0.304973
$619$	1.37758e6	0.144508	0.0722539	−	0.997386i	$-0.476981\pi$
$619$	1.37758e6	0.144508	0.0722539	+	0.997386i	$0.476981\pi$
$620$	−3.75148e6	−0.391943
$621$	−2.18132e6	−0.226981
$622$	−1.14968e7	−1.19152
$623$	1.26834e7	1.30923
$624$	−2.02928e6	−0.208632
$625$	390625.	0.0400000
$626$	−4.61041e6	−0.470222
$627$	7.41042e6	0.752790
$628$	7.53175e6	0.762073
$629$	−1.45367e6	−0.146501
$630$	−913997.	−0.0917473
$631$	−3.64454e6	−0.364392	−0.182196	−	0.983262i	$-0.558321\pi$
$631$	−3.64454e6	−0.364392	−0.182196	+	0.983262i	$0.558321\pi$
$632$	−1.32899e7	−1.32351
$633$	8.69847e6	0.862847
$634$	−8.96912e6	−0.886190
$635$	−1.42329e6	−0.140074
$636$	4.11936e6	0.403819
$637$	3.43604e6	0.335513
$638$	−1.18342e7	−1.15103
$639$	3.36278e6	0.325797
$640$	1.72061e6	0.166047
$641$	1.81373e7	1.74352	0.871759	−	0.489935i	$-0.162979\pi$
$641$	1.81373e7	1.74352	0.871759	+	0.489935i	$0.162979\pi$
$642$	−6.34272e6	−0.607349
$643$	−2.45592e6	−0.234254	−0.117127	−	0.993117i	$-0.537368\pi$
$643$	−2.45592e6	−0.234254	−0.117127	+	0.993117i	$0.537368\pi$
$644$	−1.02638e6	−0.0975204
$645$	4.16379e6	0.394085
$646$	1.02937e6	0.0970483
$647$	1.78224e7	1.67381	0.836904	−	0.547350i	$-0.184363\pi$
$647$	1.78224e7	1.67381	0.836904	+	0.547350i	$0.184363\pi$
$648$	−6.02404e6	−0.563573
$649$	−2.91960e7	−2.72089
$650$	2.10470e6	0.195392
$651$	1.25698e7	1.16245
$652$	5.47742e6	0.504611
$653$	7.29879e6	0.669835	0.334918	−	0.942247i	$-0.391292\pi$
$653$	7.29879e6	0.669835	0.334918	+	0.942247i	$0.391292\pi$
$654$	3.28897e6	0.300688
$655$	5.96055e6	0.542854
$656$	−2.92160e6	−0.265071
$657$	−1.01554e6	−0.0917871
$658$	−8.77217e6	−0.789846
$659$	827205.	0.0741993	0.0370996	−	0.999312i	$-0.488188\pi$
$659$	827205.	0.0741993	0.0370996	+	0.999312i	$0.488188\pi$
$660$	−3.54027e6	−0.316357
$661$	−1.31111e7	−1.16717	−0.583586	−	0.812051i	$-0.698351\pi$
$661$	−1.31111e7	−1.16717	−0.583586	+	0.812051i	$0.698351\pi$
$662$	−2.63287e6	−0.233498
$663$	−3.28354e6	−0.290108
$664$	−9.96070e6	−0.876738
$665$	−2.53828e6	−0.222580
$666$	1.57219e6	0.137347
$667$	2.47411e6	0.215330
$668$	−7.64461e6	−0.662849
$669$	1.70956e7	1.47679
$670$	3.30992e6	0.284859
$671$	−3.12716e7	−2.68129
$672$	−7.67035e6	−0.655227
$673$	2.61206e6	0.222303	0.111152	−	0.993803i	$-0.464546\pi$
$673$	2.61206e6	0.222303	0.111152	+	0.993803i	$0.464546\pi$
$674$	−1.14356e7	−0.969637
$675$	2.57717e6	0.217713
$676$	−6.66983e6	−0.561368
$677$	−5.55714e6	−0.465993	−0.232997	−	0.972478i	$-0.574853\pi$
$677$	−5.55714e6	−0.465993	−0.232997	+	0.972478i	$0.574853\pi$
$678$	1.11630e7	0.932621
$679$	2.39770e6	0.199581
$680$	−1.41186e6	−0.117090
$681$	−1.11795e7	−0.923754
$682$	2.22001e7	1.82765
$683$	−6.44611e6	−0.528744	−0.264372	−	0.964421i	$-0.585165\pi$
$683$	−6.44611e6	−0.528744	−0.264372	+	0.964421i	$0.585165\pi$
$684$	1.27822e6	0.104464
$685$	1.65997e6	0.135168
$686$	−9.08299e6	−0.736917
$687$	81974.7	0.00662656
$688$	2.42866e6	0.195612
$689$	−1.66392e7	−1.33532
$690$	−644640.	−0.0515459
$691$	2.16156e6	0.172215	0.0861077	−	0.996286i	$-0.472557\pi$
$691$	2.16156e6	0.172215	0.0861077	+	0.996286i	$0.472557\pi$
$692$	4.20389e6	0.333723
$693$	−6.21006e6	−0.491205
$694$	−8.77163e6	−0.691324
$695$	482087.	0.0378585
$696$	1.11943e7	0.875939
$697$	−4.72739e6	−0.368587
$698$	2.47452e6	0.192243
$699$	−1.91783e6	−0.148463
$700$	1.21265e6	0.0935382
$701$	1.67771e7	1.28950	0.644749	−	0.764394i	$-0.276962\pi$
$701$	1.67771e7	1.28950	0.644749	+	0.764394i	$0.276962\pi$
$702$	1.38859e7	1.06348
$703$	4.36616e6	0.333205
$704$	−1.74105e7	−1.32397
$705$	6.32577e6	0.479337
$706$	−5.59792e6	−0.422683
$707$	−2.27287e7	−1.71012
$708$	9.61949e6	0.721222
$709$	2.41753e6	0.180616	0.0903082	−	0.995914i	$-0.471215\pi$
$709$	2.41753e6	0.180616	0.0903082	+	0.995914i	$0.471215\pi$
$710$	3.88588e6	0.289297
$711$	5.85543e6	0.434395
$712$	−2.11895e7	−1.56646
$713$	−4.64124e6	−0.341909
$714$	1.64774e6	0.120960
$715$	1.43002e7	1.04611
$716$	1.29003e7	0.940409
$717$	−551018.	−0.0400284
$718$	−1.32960e7	−0.962521
$719$	−9.40752e6	−0.678661	−0.339331	−	0.940667i	$-0.610201\pi$
$719$	−9.40752e6	−0.678661	−0.339331	+	0.940667i	$0.610201\pi$
$720$	384440.	0.0276374
$721$	6.73879e6	0.482774
$722$	6.46502e6	0.461559
$723$	−2.01218e7	−1.43160
$724$	−3.48661e6	−0.247205
$725$	−2.92310e6	−0.206537
$726$	1.31000e7	0.922421
$727$	−1.99628e7	−1.40083	−0.700413	−	0.713738i	$-0.747001\pi$
$727$	−1.99628e7	−1.40083	−0.700413	+	0.713738i	$0.747001\pi$
$728$	1.87582e7	1.31179
$729$	1.53088e7	1.06689
$730$	−1.17351e6	−0.0815039
$731$	3.92977e6	0.272003
$732$	1.03034e7	0.710726
$733$	−1.33511e7	−0.917821	−0.458910	−	0.888483i	$-0.651760\pi$
$733$	−1.33511e7	−0.917821	−0.458910	+	0.888483i	$0.651760\pi$
$734$	−8.74343e6	−0.599020
$735$	1.24340e6	0.0848968
$736$	2.83219e6	0.192720
$737$	2.24889e7	1.52511
$738$	5.11281e6	0.345556
$739$	4.30683e6	0.290099	0.145050	−	0.989424i	$-0.453666\pi$
$739$	4.30683e6	0.290099	0.145050	+	0.989424i	$0.453666\pi$
$740$	−2.08590e6	−0.140028
$741$	9.86225e6	0.659828
$742$	8.34986e6	0.556762
$743$	−6.35316e6	−0.422199	−0.211100	−	0.977465i	$-0.567704\pi$
$743$	−6.35316e6	−0.422199	−0.211100	+	0.977465i	$0.567704\pi$
$744$	−2.09996e7	−1.39085
$745$	701883.	0.0463313
$746$	1.22744e7	0.807523
$747$	4.38861e6	0.287757
$748$	−3.34129e6	−0.218354
$749$	1.47613e7	0.961435
$750$	761626.	0.0494411
$751$	−9.97877e6	−0.645621	−0.322810	−	0.946464i	$-0.604628\pi$
$751$	−9.97877e6	−0.645621	−0.322810	+	0.946464i	$0.604628\pi$
$752$	3.68970e6	0.237928
$753$	−1.45415e7	−0.934590
$754$	−1.57497e7	−1.00889
$755$	−574654.	−0.0366893
$756$	8.00051e6	0.509112
$757$	2.76767e7	1.75539	0.877696	−	0.479218i	$-0.159080\pi$
$757$	2.76767e7	1.75539	0.877696	+	0.479218i	$0.159080\pi$
$758$	1.25176e7	0.791314
$759$	−4.37994e6	−0.275971
$760$	4.24058e6	0.266312
$761$	−2.34916e7	−1.47045	−0.735227	−	0.677821i	$-0.762924\pi$
$761$	−2.34916e7	−1.47045	−0.735227	+	0.677821i	$0.762924\pi$
$762$	−2.77507e6	−0.173136
$763$	−7.65437e6	−0.475990
$764$	864081.	0.0535576
$765$	622055.	0.0384304
$766$	1.46583e7	0.902635
$767$	−3.88558e7	−2.38489
$768$	1.40874e7	0.861842
$769$	3.15857e7	1.92608	0.963042	−	0.269350i	$-0.0868090\pi$
$769$	3.15857e7	1.92608	0.963042	+	0.269350i	$0.0868090\pi$
$770$	−7.17607e6	−0.436174
$771$	−484014.	−0.0293239
$772$	−3.82569e6	−0.231029
$773$	6.36426e6	0.383089	0.191544	−	0.981484i	$-0.438650\pi$
$773$	6.36426e6	0.383089	0.191544	+	0.981484i	$0.438650\pi$
$774$	−4.25015e6	−0.255007
$775$	5.48351e6	0.327947
$776$	−4.00570e6	−0.238795
$777$	6.98905e6	0.415304
$778$	−1.60618e6	−0.0951364
$779$	1.41989e7	0.838323
$780$	−4.71162e6	−0.277290
$781$	2.64022e7	1.54886
$782$	−608408.	−0.0355777
$783$	−1.92853e7	−1.12415
$784$	725249.	0.0421402
$785$	−1.10091e7	−0.637643
$786$	1.16216e7	0.670983
$787$	−1.59517e7	−0.918056	−0.459028	−	0.888422i	$-0.651802\pi$
$787$	−1.59517e7	−0.918056	−0.459028	+	0.888422i	$0.651802\pi$
$788$	4.31051e6	0.247294
$789$	1.76408e6	0.100885
$790$	6.76627e6	0.385728
$791$	−2.59793e7	−1.47634
$792$	1.03748e7	0.587716
$793$	−4.16183e7	−2.35018
$794$	−1.87739e7	−1.05683
$795$	−6.02123e6	−0.337884
$796$	−7.57240e6	−0.423595
$797$	−1.83877e6	−0.102537	−0.0512687	−	0.998685i	$-0.516326\pi$
$797$	−1.83877e6	−0.102537	−0.0512687	+	0.998685i	$0.516326\pi$
$798$	−4.94905e6	−0.275115
$799$	5.97023e6	0.330845
$800$	−3.34616e6	−0.184851
$801$	9.33592e6	0.514134
$802$	6.42389e6	0.352665
$803$	−7.97328e6	−0.436363
$804$	−7.40965e6	−0.404257
$805$	1.50026e6	0.0815974
$806$	2.95453e7	1.60196
$807$	−2.72400e6	−0.147239
$808$	3.79716e7	2.04612
$809$	66316.3	0.00356245	0.00178123	−	0.999998i	$-0.499433\pi$
$809$	66316.3	0.00356245	0.00178123	+	0.999998i	$0.499433\pi$
$810$	3.06702e6	0.164249
$811$	3.47825e7	1.85699	0.928493	−	0.371350i	$-0.121105\pi$
$811$	3.47825e7	1.85699	0.928493	+	0.371350i	$0.121105\pi$
$812$	−9.07439e6	−0.482978
$813$	1.36047e7	0.721873
$814$	1.23437e7	0.652957
$815$	−8.00630e6	−0.422219
$816$	−693062.	−0.0364374
$817$	−1.18032e7	−0.618650
$818$	−7.24183e6	−0.378412
$819$	−8.26474e6	−0.430546
$820$	−6.78342e6	−0.352301
$821$	−1.48900e7	−0.770966	−0.385483	−	0.922715i	$-0.625965\pi$
$821$	−1.48900e7	−0.770966	−0.385483	+	0.922715i	$0.625965\pi$
$822$	3.23655e6	0.167072
$823$	−2.63602e7	−1.35659	−0.678295	−	0.734789i	$-0.737281\pi$
$823$	−2.63602e7	−1.35659	−0.678295	+	0.734789i	$0.737281\pi$
$824$	−1.12581e7	−0.577628
$825$	5.17479e6	0.264702
$826$	1.94985e7	0.994379
$827$	−2.43310e7	−1.23708	−0.618538	−	0.785755i	$-0.712275\pi$
$827$	−2.43310e7	−1.23708	−0.618538	+	0.785755i	$0.712275\pi$
$828$	−755495.	−0.0382962
$829$	2.24381e6	0.113396	0.0566982	−	0.998391i	$-0.481943\pi$
$829$	2.24381e6	0.113396	0.0566982	+	0.998391i	$0.481943\pi$
$830$	5.07128e6	0.255519
$831$	1.51130e7	0.759185
$832$	−2.31710e7	−1.16047
$833$	1.17351e6	0.0585969
$834$	939954.	0.0467941
$835$	1.11741e7	0.554620
$836$	1.00357e7	0.496629
$837$	3.61778e7	1.78496
$838$	177630.	0.00873790
$839$	3.03357e7	1.48782	0.743908	−	0.668282i	$-0.232970\pi$
$839$	3.03357e7	1.48782	0.743908	+	0.668282i	$0.232970\pi$
$840$	6.78803e6	0.331929
$841$	1.36278e6	0.0664407
$842$	−9.24892e6	−0.449584
$843$	2.15230e7	1.04312
$844$	1.17801e7	0.569236
$845$	9.74924e6	0.469709
$846$	−6.45697e6	−0.310172
$847$	−3.04873e7	−1.46019
$848$	−3.51207e6	−0.167716
$849$	−3.95955e6	−0.188528
$850$	718819.	0.0341250
$851$	−2.58062e6	−0.122152
$852$	−8.69901e6	−0.410554
$853$	−1.89457e7	−0.891535	−0.445767	−	0.895149i	$-0.647069\pi$
$853$	−1.89457e7	−0.891535	−0.445767	+	0.895149i	$0.647069\pi$
$854$	2.08848e7	0.979907
$855$	−1.86837e6	−0.0874071
$856$	−2.46609e7	−1.15034
$857$	−4.33006e6	−0.201392	−0.100696	−	0.994917i	$-0.532107\pi$
$857$	−4.33006e6	−0.201392	−0.100696	+	0.994917i	$0.532107\pi$
$858$	2.78819e7	1.29302
$859$	9.87188e6	0.456475	0.228237	−	0.973606i	$-0.426704\pi$
$859$	9.87188e6	0.456475	0.228237	+	0.973606i	$0.426704\pi$
$860$	5.63890e6	0.259985
$861$	2.27287e7	1.04488
$862$	7.67715e6	0.351910
$863$	−2.18605e7	−0.999156	−0.499578	−	0.866269i	$-0.666512\pi$
$863$	−2.18605e7	−0.999156	−0.499578	+	0.866269i	$0.666512\pi$
$864$	−2.20765e7	−1.00611
$865$	−6.14479e6	−0.279233
$866$	−9.75828e6	−0.442159
$867$	1.68104e7	0.759502
$868$	1.70229e7	0.766890
$869$	4.59727e7	2.06515
$870$	−5.69934e6	−0.255286
$871$	2.99297e7	1.33677
$872$	1.27877e7	0.569512
$873$	1.76488e6	0.0783755
$874$	1.82738e6	0.0809189
$875$	−1.77252e6	−0.0782654
$876$	2.62704e6	0.115666
$877$	−9.77214e6	−0.429033	−0.214517	−	0.976720i	$-0.568818\pi$
$877$	−9.77214e6	−0.429033	−0.214517	+	0.976720i	$0.568818\pi$
$878$	−1.08804e7	−0.476330
$879$	−1.82671e7	−0.797437
$880$	3.01836e6	0.131390
$881$	1.96746e7	0.854016	0.427008	−	0.904248i	$-0.359568\pi$
$881$	1.96746e7	0.854016	0.427008	+	0.904248i	$0.359568\pi$
$882$	−1.26919e6	−0.0549356
$883$	2.87227e7	1.23972	0.619860	−	0.784712i	$-0.287189\pi$
$883$	2.87227e7	1.23972	0.619860	+	0.784712i	$0.287189\pi$
$884$	−4.44680e6	−0.191389
$885$	−1.40607e7	−0.603462
$886$	−2.87320e7	−1.22965
$887$	−4.74464e6	−0.202486	−0.101243	−	0.994862i	$-0.532282\pi$
$887$	−4.74464e6	−0.202486	−0.101243	+	0.994862i	$0.532282\pi$
$888$	−1.16762e7	−0.496902
$889$	6.45838e6	0.274075
$890$	1.07882e7	0.456534
$891$	2.08385e7	0.879373
$892$	2.31520e7	0.974264
$893$	−1.79318e7	−0.752481
$894$	1.36851e6	0.0572668
$895$	−1.88562e7	−0.786860
$896$	−7.80749e6	−0.324894
$897$	−5.82910e6	−0.241892
$898$	178492.	0.00738630
$899$	−4.10338e7	−1.69333
$900$	892599.	0.0367325
$901$	−5.68281e6	−0.233212
$902$	4.01422e7	1.64280
$903$	−1.88938e7	−0.771080
$904$	4.34023e7	1.76641
$905$	5.09636e6	0.206842
$906$	−1.12044e6	−0.0453490
$907$	1.99896e7	0.806838	0.403419	−	0.915015i	$-0.367822\pi$
$907$	1.99896e7	0.806838	0.403419	+	0.915015i	$0.367822\pi$
$908$	−1.51401e7	−0.609417
$909$	−1.67300e7	−0.671563
$910$	−9.55036e6	−0.382311
$911$	−1.46003e7	−0.582863	−0.291432	−	0.956592i	$-0.594132\pi$
$911$	−1.46003e7	−0.582863	−0.291432	+	0.956592i	$0.594132\pi$
$912$	2.08164e6	0.0828740
$913$	3.44563e7	1.36802
$914$	1.65294e7	0.654472
$915$	−1.50604e7	−0.594680
$916$	111016.	0.00437166
$917$	−2.70468e7	−1.06217
$918$	4.74245e6	0.185736
$919$	−7.69434e6	−0.300526	−0.150263	−	0.988646i	$-0.548012\pi$
$919$	−7.69434e6	−0.300526	−0.150263	+	0.988646i	$0.548012\pi$
$920$	−2.50640e6	−0.0976295
$921$	−2.89494e7	−1.12458
$922$	496131.	0.0192207
$923$	3.51377e7	1.35759
$924$	1.60645e7	0.618995
$925$	3.04894e6	0.117164
$926$	1.91411e7	0.733567
$927$	4.96025e6	0.189585
$928$	2.50397e7	0.954464
$929$	3.00028e7	1.14057	0.570285	−	0.821447i	$-0.306833\pi$
$929$	3.00028e7	1.14057	0.570285	+	0.821447i	$0.306833\pi$
$930$	1.06915e7	0.405352
$931$	−3.52469e6	−0.133274
$932$	−2.59726e6	−0.0979436
$933$	−3.76197e7	−1.41485
$934$	−8.45776e6	−0.317240
$935$	4.88394e6	0.182701
$936$	1.38075e7	0.515139
$937$	9.50390e6	0.353633	0.176816	−	0.984244i	$-0.443420\pi$
$937$	9.50390e6	0.353633	0.176816	+	0.984244i	$0.443420\pi$
$938$	−1.50192e7	−0.557366
$939$	−1.50860e7	−0.558356
$940$	8.56680e6	0.316227
$941$	1.06420e6	0.0391786	0.0195893	−	0.999808i	$-0.493764\pi$
$941$	1.06420e6	0.0391786	0.0195893	+	0.999808i	$0.493764\pi$
$942$	−2.14651e7	−0.788145
$943$	−8.39229e6	−0.307327
$944$	−8.20136e6	−0.299541
$945$	−1.16943e7	−0.425985
$946$	−3.33692e7	−1.21232
$947$	1.20552e7	0.436816	0.218408	−	0.975858i	$-0.429914\pi$
$947$	1.20552e7	0.436816	0.218408	+	0.975858i	$0.429914\pi$
$948$	−1.51471e7	−0.547405
$949$	−1.06113e7	−0.382476
$950$	−2.15900e6	−0.0776146
$951$	−2.93485e7	−1.05229
$952$	6.40651e6	0.229102
$953$	−2.93389e6	−0.104643	−0.0523216	−	0.998630i	$-0.516662\pi$
$953$	−2.93389e6	−0.104643	−0.0523216	+	0.998630i	$0.516662\pi$
$954$	6.14612e6	0.218640
$955$	−1.26302e6	−0.0448128
$956$	−746227.	−0.0264074
$957$	−3.87236e7	−1.36677
$958$	−3.71043e6	−0.130620
$959$	−7.53237e6	−0.264475
$960$	−8.38486e6	−0.293642
$961$	4.83471e7	1.68874
$962$	1.64278e7	0.572323
$963$	1.08654e7	0.377555
$964$	−2.72504e7	−0.944453
$965$	5.59199e6	0.193307
$966$	2.92514e6	0.100857
$967$	−2.34324e7	−0.805844	−0.402922	−	0.915234i	$-0.632005\pi$
$967$	−2.34324e7	−0.805844	−0.402922	+	0.915234i	$0.632005\pi$
$968$	5.09335e7	1.74709
$969$	3.36826e6	0.115238
$970$	2.03942e6	0.0695949
$971$	−2.31868e7	−0.789212	−0.394606	−	0.918850i	$-0.629119\pi$
$971$	−2.31868e7	−0.789212	−0.394606	+	0.918850i	$0.629119\pi$
$972$	1.02719e7	0.348726
$973$	−2.18754e6	−0.0740752
$974$	1.19817e7	0.404688
$975$	6.88694e6	0.232014
$976$	−8.78443e6	−0.295181
$977$	−1.38454e7	−0.464055	−0.232028	−	0.972709i	$-0.574536\pi$
$977$	−1.38454e7	−0.464055	−0.232028	+	0.972709i	$0.574536\pi$
$978$	−1.56104e7	−0.521875
$979$	7.32992e7	2.44423
$980$	1.68389e6	0.0560079
$981$	−5.63418e6	−0.186921
$982$	−2.29862e7	−0.760656
$983$	2.04012e7	0.673400	0.336700	−	0.941612i	$-0.390689\pi$
$983$	2.04012e7	0.673400	0.336700	+	0.941612i	$0.390689\pi$
$984$	−3.79716e7	−1.25017
$985$	−6.30064e6	−0.206916
$986$	−5.37901e6	−0.176202
$987$	−2.87041e7	−0.937887
$988$	1.33562e7	0.435300
$989$	6.97631e6	0.226796
$990$	−5.28212e6	−0.171285
$991$	−3.60862e7	−1.16723	−0.583616	−	0.812030i	$-0.698363\pi$
$991$	−3.60862e7	−1.16723	−0.583616	+	0.812030i	$0.698363\pi$
$992$	−4.69726e7	−1.51553
$993$	−8.61519e6	−0.277263
$994$	−1.76327e7	−0.566048
$995$	1.10685e7	0.354431
$996$	−1.13527e7	−0.362618
$997$	−4.44362e7	−1.41579	−0.707895	−	0.706318i	$-0.750355\pi$
$997$	−4.44362e7	−1.41579	−0.707895	+	0.706318i	$0.750355\pi$
$998$	−6.63103e6	−0.210744
$999$	2.01156e7	0.637704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.a.e.1.5	✓	12
3.2	odd	2		1035.6.a.m.1.8		12
5.4	even	2		575.6.a.g.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.a.e.1.5	✓	12	1.1	even	1	trivial
575.6.a.g.1.8		12	5.4	even	2
1035.6.a.m.1.8		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)

\(f(q)\)	\(=\)	\(q-3.85960 q^{2} -12.6293 q^{3} -17.1035 q^{4} +25.0000 q^{5} +48.7440 q^{6} -113.441 q^{7} +189.520 q^{8} -83.5011 q^{9} +O(q^{10})\)	\(q-3.85960 q^{2} -12.6293 q^{3} -17.1035 q^{4} +25.0000 q^{5} +48.7440 q^{6} -113.441 q^{7} +189.520 q^{8} -83.5011 q^{9} -96.4901 q^{10} -655.592 q^{11} +216.005 q^{12} -872.504 q^{13} +437.837 q^{14} -315.732 q^{15} -184.161 q^{16} -297.987 q^{17} +322.281 q^{18} +895.014 q^{19} -427.587 q^{20} +1432.68 q^{21} +2530.33 q^{22} -529.000 q^{23} -2393.50 q^{24} +625.000 q^{25} +3367.52 q^{26} +4123.48 q^{27} +1940.23 q^{28} -4676.96 q^{29} +1218.60 q^{30} +8773.61 q^{31} -5353.85 q^{32} +8279.67 q^{33} +1150.11 q^{34} -2836.03 q^{35} +1428.16 q^{36} +4878.31 q^{37} -3454.40 q^{38} +11019.1 q^{39} +4738.00 q^{40} +15864.4 q^{41} -5529.57 q^{42} -13187.7 q^{43} +11212.9 q^{44} -2087.53 q^{45} +2041.73 q^{46} -20035.2 q^{47} +2325.82 q^{48} -3938.13 q^{49} -2412.25 q^{50} +3763.36 q^{51} +14922.8 q^{52} +19070.7 q^{53} -15915.0 q^{54} -16389.8 q^{55} -21499.3 q^{56} -11303.4 q^{57} +18051.2 q^{58} +44533.7 q^{59} +5400.12 q^{60} +47699.8 q^{61} -33862.6 q^{62} +9472.45 q^{63} +26556.9 q^{64} -21812.6 q^{65} -31956.2 q^{66} -34303.2 q^{67} +5096.60 q^{68} +6680.89 q^{69} +10945.9 q^{70} -40272.3 q^{71} -15825.1 q^{72} +12161.9 q^{73} -18828.3 q^{74} -7893.31 q^{75} -15307.8 q^{76} +74371.1 q^{77} -42529.3 q^{78} -70124.0 q^{79} -4604.01 q^{80} -31785.8 q^{81} -61230.4 q^{82} -52557.6 q^{83} -24503.8 q^{84} -7449.67 q^{85} +50899.4 q^{86} +59066.6 q^{87} -124248. q^{88} -111806. q^{89} +8057.02 q^{90} +98977.7 q^{91} +9047.73 q^{92} -110804. q^{93} +77328.0 q^{94} +22375.4 q^{95} +67615.3 q^{96} -21136.1 q^{97} +15199.6 q^{98} +54742.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 22 q^{3} + 294 q^{4} + 300 q^{5} + 454 q^{6} + 16 q^{7} + 675 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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