LMFDB - Embedded newform 23.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,6,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	23.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:	$3.68882785570$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.7925.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 13x + 12 $ x^3 - x^2 - 13*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.57511$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.15022 q^{2} +9.09413 q^{3} +51.7266 q^{4} +3.86330 q^{5} -83.2134 q^{6} -226.379 q^{7} -180.503 q^{8} -160.297 q^{9} +O(q^{10})$	\(q-9.15022 q^{2} +9.09413 q^{3} +51.7266 q^{4} +3.86330 q^{5} -83.2134 q^{6} -226.379 q^{7} -180.503 q^{8} -160.297 q^{9} -35.3501 q^{10} +18.3261 q^{11} +470.409 q^{12} -711.185 q^{13} +2071.42 q^{14} +35.1334 q^{15} -3.60999 q^{16} +165.441 q^{17} +1466.75 q^{18} +213.254 q^{19} +199.835 q^{20} -2058.72 q^{21} -167.688 q^{22} -529.000 q^{23} -1641.52 q^{24} -3110.07 q^{25} +6507.50 q^{26} -3667.63 q^{27} -11709.8 q^{28} +5475.82 q^{29} -321.478 q^{30} +6077.13 q^{31} +5809.12 q^{32} +166.660 q^{33} -1513.82 q^{34} -874.570 q^{35} -8291.60 q^{36} +11499.7 q^{37} -1951.32 q^{38} -6467.61 q^{39} -697.337 q^{40} -13183.0 q^{41} +18837.8 q^{42} -21455.2 q^{43} +947.948 q^{44} -619.274 q^{45} +4840.47 q^{46} +12960.8 q^{47} -32.8298 q^{48} +34440.5 q^{49} +28457.9 q^{50} +1504.54 q^{51} -36787.2 q^{52} -29103.4 q^{53} +33559.7 q^{54} +70.7993 q^{55} +40862.1 q^{56} +1939.36 q^{57} -50105.0 q^{58} +10506.2 q^{59} +1817.33 q^{60} -34103.3 q^{61} -55607.1 q^{62} +36287.8 q^{63} -53039.3 q^{64} -2747.52 q^{65} -1524.98 q^{66} +12988.2 q^{67} +8557.70 q^{68} -4810.80 q^{69} +8002.51 q^{70} +45243.0 q^{71} +28934.0 q^{72} -52589.2 q^{73} -105225. q^{74} -28283.4 q^{75} +11030.9 q^{76} -4148.65 q^{77} +59180.1 q^{78} +57603.3 q^{79} -13.9465 q^{80} +5598.14 q^{81} +120627. q^{82} -40816.8 q^{83} -106491. q^{84} +639.148 q^{85} +196320. q^{86} +49797.8 q^{87} -3307.92 q^{88} +54699.9 q^{89} +5666.50 q^{90} +160997. q^{91} -27363.4 q^{92} +55266.2 q^{93} -118594. q^{94} +823.864 q^{95} +52828.9 q^{96} -117497. q^{97} -315138. q^{98} -2937.62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9}+O(q^{10}) $ 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9} - 156 q^{10} + 136 q^{11} + 620 q^{12} - 1116 q^{13} + 2016 q^{14} + 750 q^{15} + 128 q^{16} - 896 q^{17} + 4282 q^{18} + 1654 q^{19} + 1504 q^{20} - 1670 q^{21} + 1352 q^{22} - 1587 q^{23} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} - 10264 q^{28} - 844 q^{29} + 3180 q^{30} - 3020 q^{31} + 6656 q^{32} - 7370 q^{33} - 11212 q^{34} + 1072 q^{35} - 2548 q^{36} + 8938 q^{37} + 10728 q^{38} + 16020 q^{39} + 3440 q^{40} - 12792 q^{41} + 20560 q^{42} - 16730 q^{43} + 5112 q^{44} - 3936 q^{45} + 2116 q^{46} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} + 50290 q^{51} - 47412 q^{52} + 17108 q^{53} - 7610 q^{54} - 436 q^{55} + 42640 q^{56} - 61960 q^{57} - 55678 q^{58} + 54176 q^{59} - 2400 q^{60} - 71324 q^{61} - 72710 q^{62} + 40696 q^{63} - 49984 q^{64} + 846 q^{65} - 42860 q^{66} - 62960 q^{67} - 8352 q^{68} + 10580 q^{69} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} - 59044 q^{74} + 44800 q^{75} + 31488 q^{76} - 304 q^{77} + 182070 q^{78} + 58224 q^{79} - 17568 q^{80} + 149947 q^{81} + 61926 q^{82} + 9892 q^{83} - 109720 q^{84} + 15536 q^{85} + 191140 q^{86} + 90500 q^{87} - 58400 q^{88} + 27542 q^{89} - 62112 q^{90} + 151974 q^{91} - 8464 q^{92} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} - 273672 q^{97} - 401276 q^{98} + 183082 q^{99}+O(q^{100}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9 - 156 * q^10 + 136 * q^11 + 620 * q^12 - 1116 * q^13 + 2016 * q^14 + 750 * q^15 + 128 * q^16 - 896 * q^17 + 4282 * q^18 + 1654 * q^19 + 1504 * q^20 - 1670 * q^21 + 1352 * q^22 - 1587 * q^23 + 3600 * q^24 - 7347 * q^25 + 1998 * q^26 - 10700 * q^27 - 10264 * q^28 - 844 * q^29 + 3180 * q^30 - 3020 * q^31 + 6656 * q^32 - 7370 * q^33 - 11212 * q^34 + 1072 * q^35 - 2548 * q^36 + 8938 * q^37 + 10728 * q^38 + 16020 * q^39 + 3440 * q^40 - 12792 * q^41 + 20560 * q^42 - 16730 * q^43 + 5112 * q^44 - 3936 * q^45 + 2116 * q^46 + 22500 * q^47 + 23120 * q^48 + 2887 * q^49 + 15156 * q^50 + 50290 * q^51 - 47412 * q^52 + 17108 * q^53 - 7610 * q^54 - 436 * q^55 + 42640 * q^56 - 61960 * q^57 - 55678 * q^58 + 54176 * q^59 - 2400 * q^60 - 71324 * q^61 - 72710 * q^62 + 40696 * q^63 - 49984 * q^64 + 846 * q^65 - 42860 * q^66 - 62960 * q^67 - 8352 * q^68 + 10580 * q^69 + 9224 * q^70 + 98400 * q^71 - 72840 * q^72 - 81772 * q^73 - 59044 * q^74 + 44800 * q^75 + 31488 * q^76 - 304 * q^77 + 182070 * q^78 + 58224 * q^79 - 17568 * q^80 + 149947 * q^81 + 61926 * q^82 + 9892 * q^83 - 109720 * q^84 + 15536 * q^85 + 191140 * q^86 + 90500 * q^87 - 58400 * q^88 + 27542 * q^89 - 62112 * q^90 + 151974 * q^91 - 8464 * q^92 + 157330 * q^93 - 146990 * q^94 - 20644 * q^95 + 16160 * q^96 - 273672 * q^97 - 401276 * q^98 + 183082 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.15022	−1.61755	−0.808773	−	0.588121i	$-0.799868\pi$
$2$	−9.15022	−1.61755	−0.808773	+	0.588121i	$0.799868\pi$
$3$	9.09413	0.583389	0.291694	−	0.956512i	$-0.405781\pi$
$3$	9.09413	0.583389	0.291694	+	0.956512i	$0.405781\pi$
$4$	51.7266	1.61646
$5$	3.86330	0.0691088	0.0345544	−	0.999403i	$-0.488999\pi$
$5$	3.86330	0.0691088	0.0345544	+	0.999403i	$0.488999\pi$
$6$	−83.2134	−0.943659
$7$	−226.379	−1.74619	−0.873094	−	0.487551i	$-0.837890\pi$
$7$	−226.379	−1.74619	−0.873094	+	0.487551i	$0.837890\pi$
$8$	−180.503	−0.997147
$9$	−160.297	−0.659657
$10$	−35.3501	−0.111787
$11$	18.3261	0.0456656	0.0228328	−	0.999739i	$-0.492731\pi$
$11$	18.3261	0.0456656	0.0228328	+	0.999739i	$0.492731\pi$
$12$	470.409	0.943023
$13$	−711.185	−1.16714	−0.583572	−	0.812062i	$-0.698345\pi$
$13$	−711.185	−1.16714	−0.583572	+	0.812062i	$0.698345\pi$
$14$	2071.42	2.82454
$15$	35.1334	0.0403173
$16$	−3.60999	−0.00352539
$17$	165.441	0.138842	0.0694210	−	0.997587i	$-0.477885\pi$
$17$	165.441	0.138842	0.0694210	+	0.997587i	$0.477885\pi$
$18$	1466.75	1.06703
$19$	213.254	0.135523	0.0677615	−	0.997702i	$-0.478414\pi$
$19$	213.254	0.135523	0.0677615	+	0.997702i	$0.478414\pi$
$20$	199.835	0.111711
$21$	−2058.72	−1.01871
$22$	−167.688	−0.0738662
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−1641.52	−0.581724
$25$	−3110.07	−0.995224
$26$	6507.50	1.88791
$27$	−3667.63	−0.968226
$28$	−11709.8	−2.82264
$29$	5475.82	1.20908	0.604539	−	0.796576i	$-0.293357\pi$
$29$	5475.82	1.20908	0.604539	+	0.796576i	$0.293357\pi$
$30$	−321.478	−0.0652151
$31$	6077.13	1.13578	0.567890	−	0.823104i	$-0.307760\pi$
$31$	6077.13	1.13578	0.567890	+	0.823104i	$0.307760\pi$
$32$	5809.12	1.00285
$33$	166.660	0.0266408
$34$	−1513.82	−0.224583
$35$	−874.570	−0.120677
$36$	−8291.60	−1.06631
$37$	11499.7	1.38096	0.690481	−	0.723350i	$-0.257399\pi$
$37$	11499.7	1.38096	0.690481	+	0.723350i	$0.257399\pi$
$38$	−1951.32	−0.219215
$39$	−6467.61	−0.680899
$40$	−697.337	−0.0689116
$41$	−13183.0	−1.22477	−0.612384	−	0.790561i	$-0.709789\pi$
$41$	−13183.0	−1.22477	−0.612384	+	0.790561i	$0.709789\pi$
$42$	18837.8	1.64781
$43$	−21455.2	−1.76955	−0.884773	−	0.466022i	$-0.845687\pi$
$43$	−21455.2	−1.76955	−0.884773	+	0.466022i	$0.845687\pi$
$44$	947.948	0.0738164
$45$	−619.274	−0.0455881
$46$	4840.47	0.337282
$47$	12960.8	0.855830	0.427915	−	0.903819i	$-0.359248\pi$
$47$	12960.8	0.855830	0.427915	+	0.903819i	$0.359248\pi$
$48$	−32.8298	−0.00205667
$49$	34440.5	2.04917
$50$	28457.9	1.60982
$51$	1504.54	0.0809988
$52$	−36787.2	−1.88664
$53$	−29103.4	−1.42316	−0.711581	−	0.702604i	$-0.752021\pi$
$53$	−29103.4	−1.42316	−0.711581	+	0.702604i	$0.752021\pi$
$54$	33559.7	1.56615
$55$	70.7993	0.00315589
$56$	40862.1	1.74121
$57$	1939.36	0.0790626
$58$	−50105.0	−1.95574
$59$	10506.2	0.392930	0.196465	−	0.980511i	$-0.437054\pi$
$59$	10506.2	0.392930	0.196465	+	0.980511i	$0.437054\pi$
$60$	1817.33	0.0651712
$61$	−34103.3	−1.17347	−0.586734	−	0.809780i	$-0.699587\pi$
$61$	−34103.3	−1.17347	−0.586734	+	0.809780i	$0.699587\pi$
$62$	−55607.1	−1.83718
$63$	36287.8	1.15189
$64$	−53039.3	−1.61863
$65$	−2747.52	−0.0806599
$66$	−1524.98	−0.0430927
$67$	12988.2	0.353476	0.176738	−	0.984258i	$-0.443445\pi$
$67$	12988.2	0.353476	0.176738	+	0.984258i	$0.443445\pi$
$68$	8557.70	0.224432
$69$	−4810.80	−0.121645
$70$	8002.51	0.195201
$71$	45243.0	1.06514	0.532569	−	0.846387i	$-0.321227\pi$
$71$	45243.0	1.06514	0.532569	+	0.846387i	$0.321227\pi$
$72$	28934.0	0.657775
$73$	−52589.2	−1.15502	−0.577510	−	0.816384i	$-0.695976\pi$
$73$	−52589.2	−1.15502	−0.577510	+	0.816384i	$0.695976\pi$
$74$	−105225.	−2.23377
$75$	−28283.4	−0.580603
$76$	11030.9	0.219067
$77$	−4148.65	−0.0797407
$78$	59180.1	1.10139
$79$	57603.3	1.03844	0.519218	−	0.854642i	$-0.326223\pi$
$79$	57603.3	1.03844	0.519218	+	0.854642i	$0.326223\pi$
$80$	−13.9465	−0.000243635 0
$81$	5598.14	0.0948051
$82$	120627.	1.98112
$83$	−40816.8	−0.650345	−0.325173	−	0.945655i	$-0.605422\pi$
$83$	−40816.8	−0.650345	−0.325173	+	0.945655i	$0.605422\pi$
$84$	−106491.	−1.64670
$85$	639.148	0.00959520
$86$	196320.	2.86232
$87$	49797.8	0.705362
$88$	−3307.92	−0.0455353
$89$	54699.9	0.732000	0.366000	−	0.930615i	$-0.380727\pi$
$89$	54699.9	0.732000	0.366000	+	0.930615i	$0.380727\pi$
$90$	5666.50	0.0737409
$91$	160997.	2.03805
$92$	−27363.4	−0.337054
$93$	55266.2	0.662602
$94$	−118594.	−1.38434
$95$	823.864	0.00936583
$96$	52828.9	0.585051
$97$	−117497.	−1.26794	−0.633968	−	0.773360i	$-0.718575\pi$
$97$	−117497.	−1.26794	−0.633968	+	0.773360i	$0.718575\pi$
$98$	−315138.	−3.31464
$99$	−2937.62	−0.0301236
$100$	−160874.	−1.60874
$101$	−141707.	−1.38226	−0.691128	−	0.722733i	$-0.742886\pi$
$101$	−141707.	−1.38226	−0.691128	+	0.722733i	$0.742886\pi$
$102$	−13766.9	−0.131019
$103$	60185.0	0.558979	0.279489	−	0.960149i	$-0.409835\pi$
$103$	60185.0	0.558979	0.279489	+	0.960149i	$0.409835\pi$
$104$	128371.	1.16381
$105$	−7953.46	−0.0704017
$106$	266303.	2.30203
$107$	−186999.	−1.57899	−0.789495	−	0.613757i	$-0.789658\pi$
$107$	−186999.	−1.57899	−0.789495	+	0.613757i	$0.789658\pi$
$108$	−189714.	−1.56509
$109$	−63597.2	−0.512710	−0.256355	−	0.966583i	$-0.582522\pi$
$109$	−63597.2	−0.512710	−0.256355	+	0.966583i	$0.582522\pi$
$110$	−647.830	−0.00510480
$111$	104580.	0.805638
$112$	817.227	0.00615599
$113$	42281.3	0.311496	0.155748	−	0.987797i	$-0.450221\pi$
$113$	42281.3	0.311496	0.155748	+	0.987797i	$0.450221\pi$
$114$	−17745.6	−0.127887
$115$	−2043.69	−0.0144102
$116$	283246.	1.95442
$117$	114001.	0.769915
$118$	−96134.0	−0.635583
$119$	−37452.4	−0.242444
$120$	−6341.67	−0.0402023
$121$	−160715.	−0.997915
$122$	312052.	1.89814
$123$	−119888.	−0.714516
$124$	314349.	1.83594
$125$	−24088.0	−0.137888
$126$	−332042.	−1.86323
$127$	−119942.	−0.659877	−0.329938	−	0.944002i	$-0.607028\pi$
$127$	−119942.	−0.659877	−0.329938	+	0.944002i	$0.607028\pi$
$128$	299429.	1.61536
$129$	−195117.	−1.03233
$130$	25140.4	0.130471
$131$	188708.	0.960753	0.480376	−	0.877062i	$-0.340500\pi$
$131$	188708.	0.960753	0.480376	+	0.877062i	$0.340500\pi$
$132$	8620.77	0.0430637
$133$	−48276.2	−0.236649
$134$	−118844.	−0.571764
$135$	−14169.2	−0.0669129
$136$	−29862.6	−0.138446
$137$	−320875.	−1.46061	−0.730305	−	0.683121i	$-0.760622\pi$
$137$	−320875.	−1.46061	−0.730305	+	0.683121i	$0.760622\pi$
$138$	44019.9	0.196766
$139$	174260.	0.765000	0.382500	−	0.923955i	$-0.375063\pi$
$139$	174260.	0.765000	0.382500	+	0.923955i	$0.375063\pi$
$140$	−45238.6	−0.195069
$141$	117867.	0.499282
$142$	−413984.	−1.72291
$143$	−13033.3	−0.0532983
$144$	578.670	0.00232555
$145$	21154.7	0.0835579
$146$	481203.	1.86830
$147$	313206.	1.19547
$148$	594840.	2.23227
$149$	−144356.	−0.532682	−0.266341	−	0.963879i	$-0.585815\pi$
$149$	−144356.	−0.532682	−0.266341	+	0.963879i	$0.585815\pi$
$150$	258800.	0.939152
$151$	−122240.	−0.436286	−0.218143	−	0.975917i	$-0.570000\pi$
$151$	−122240.	−0.436286	−0.218143	+	0.975917i	$0.570000\pi$
$152$	−38492.9	−0.135136
$153$	−26519.6	−0.0915881
$154$	37961.1	0.128984
$155$	23477.8	0.0784924
$156$	−334548.	−1.10064
$157$	−115272.	−0.373227	−0.186614	−	0.982433i	$-0.559751\pi$
$157$	−115272.	−0.373227	−0.186614	+	0.982433i	$0.559751\pi$
$158$	−527083.	−1.67972
$159$	−264670.	−0.830257
$160$	22442.4	0.0693057
$161$	119755.	0.364106
$162$	−51224.3	−0.153352
$163$	120609.	0.355557	0.177778	−	0.984071i	$-0.443109\pi$
$163$	120609.	0.355557	0.177778	+	0.984071i	$0.443109\pi$
$164$	−681910.	−1.97978
$165$	643.858	0.00184111
$166$	373483.	1.05196
$167$	476969.	1.32342	0.661711	−	0.749759i	$-0.269830\pi$
$167$	476969.	1.32342	0.661711	+	0.749759i	$0.269830\pi$
$168$	371605.	1.01580
$169$	134491.	0.362224
$170$	−5848.35	−0.0155207
$171$	−34183.9	−0.0893987
$172$	−1.10981e6	−2.86039
$173$	341220.	0.866801	0.433400	−	0.901202i	$-0.357314\pi$
$173$	341220.	0.866801	0.433400	+	0.901202i	$0.357314\pi$
$174$	−455661.	−1.14096
$175$	704056.	1.73785
$176$	−66.1572	−0.000160989 0
$177$	95544.7	0.229231
$178$	−500516.	−1.18404
$179$	157948.	0.368452	0.184226	−	0.982884i	$-0.441022\pi$
$179$	157948.	0.368452	0.184226	+	0.982884i	$0.441022\pi$
$180$	−32033.0	−0.0736912
$181$	−133395.	−0.302652	−0.151326	−	0.988484i	$-0.548354\pi$
$181$	−133395.	−0.302652	−0.151326	+	0.988484i	$0.548354\pi$
$182$	−1.47316e6	−3.29665
$183$	−310140.	−0.684588
$184$	95486.0	0.207919
$185$	44426.8	0.0954367
$186$	−505698.	−1.07179
$187$	3031.89	0.00634030
$188$	670418.	1.38341
$189$	830276.	1.69070
$190$	−7538.54	−0.0151497
$191$	−819880.	−1.62617	−0.813087	−	0.582142i	$-0.802215\pi$
$191$	−819880.	−1.62617	−0.813087	+	0.582142i	$0.802215\pi$
$192$	−482346.	−0.944291
$193$	389602.	0.752884	0.376442	−	0.926440i	$-0.377147\pi$
$193$	389602.	0.752884	0.376442	+	0.926440i	$0.377147\pi$
$194$	1.07512e6	2.05094
$195$	−24986.3	−0.0470561
$196$	1.78149e6	3.31240
$197$	251073.	0.460930	0.230465	−	0.973081i	$-0.425975\pi$
$197$	251073.	0.460930	0.230465	+	0.973081i	$0.425975\pi$
$198$	26879.9	0.0487264
$199$	487551.	0.872745	0.436373	−	0.899766i	$-0.356263\pi$
$199$	487551.	0.872745	0.436373	+	0.899766i	$0.356263\pi$
$200$	561377.	0.992384
$201$	118116.	0.206214
$202$	1.29665e6	2.23586
$203$	−1.23961e6	−2.11128
$204$	77824.8	0.130931
$205$	−50929.8	−0.0846423
$206$	−550707.	−0.904174
$207$	84797.0	0.137548
$208$	2567.37	0.00411463
$209$	3908.12	0.00618873
$210$	72775.9	0.113878
$211$	−274245.	−0.424064	−0.212032	−	0.977263i	$-0.568008\pi$
$211$	−274245.	−0.424064	−0.212032	+	0.977263i	$0.568008\pi$
$212$	−1.50542e6	−2.30048
$213$	411446.	0.621390
$214$	1.71108e6	2.55409
$215$	−82888.0	−0.122291
$216$	662018.	0.965463
$217$	−1.37573e6	−1.98329
$218$	581928.	0.829332
$219$	−478253.	−0.673826
$220$	3662.21	0.00510136
$221$	−117659.	−0.162048
$222$	−956928.	−1.30316
$223$	−215015.	−0.289539	−0.144769	−	0.989465i	$-0.546244\pi$
$223$	−215015.	−0.289539	−0.144769	+	0.989465i	$0.546244\pi$
$224$	−1.31506e6	−1.75116
$225$	498535.	0.656507
$226$	−386884.	−0.503859
$227$	837285.	1.07847	0.539236	−	0.842155i	$-0.318713\pi$
$227$	837285.	1.07847	0.539236	+	0.842155i	$0.318713\pi$
$228$	100316.	0.127801
$229$	−1.33914e6	−1.68748	−0.843740	−	0.536753i	$-0.819651\pi$
$229$	−1.33914e6	−1.68748	−0.843740	+	0.536753i	$0.819651\pi$
$230$	18700.2	0.0233091
$231$	−37728.4	−0.0465198
$232$	−988401.	−1.20563
$233$	−320747.	−0.387055	−0.193528	−	0.981095i	$-0.561993\pi$
$233$	−320747.	−0.387055	−0.193528	+	0.981095i	$0.561993\pi$
$234$	−1.04313e6	−1.24537
$235$	50071.5	0.0591454
$236$	543450.	0.635154
$237$	523852.	0.605812
$238$	342697.	0.392165
$239$	−278679.	−0.315580	−0.157790	−	0.987473i	$-0.550437\pi$
$239$	−278679.	−0.315580	−0.157790	+	0.987473i	$0.550437\pi$
$240$	−126.831	−0.000142134 0
$241$	−680862.	−0.755120	−0.377560	−	0.925985i	$-0.623237\pi$
$241$	−680862.	−0.755120	−0.377560	+	0.925985i	$0.623237\pi$
$242$	1.47058e6	1.61417
$243$	942145.	1.02353
$244$	−1.76405e6	−1.89686
$245$	133054.	0.141616
$246$	1.09700e6	1.15576
$247$	−151663.	−0.158175
$248$	−1.09694e6	−1.13254
$249$	−371194.	−0.379404
$250$	220410.	0.223040
$251$	410308.	0.411079	0.205540	−	0.978649i	$-0.434105\pi$
$251$	410308.	0.411079	0.205540	+	0.978649i	$0.434105\pi$
$252$	1.87705e6	1.86197
$253$	−9694.52	−0.00952193
$254$	1.09750e6	1.06738
$255$	5812.50	0.00559773
$256$	−1.04259e6	−0.994289
$257$	1.69725e6	1.60292	0.801460	−	0.598048i	$-0.204057\pi$
$257$	1.69725e6	1.60292	0.801460	+	0.598048i	$0.204057\pi$
$258$	1.78536e6	1.66985
$259$	−2.60329e6	−2.41142
$260$	−142120.	−0.130383
$261$	−877756.	−0.797577
$262$	−1.72672e6	−1.55406
$263$	1.11082e6	0.990269	0.495135	−	0.868816i	$-0.335119\pi$
$263$	1.11082e6	0.990269	0.495135	+	0.868816i	$0.335119\pi$
$264$	−30082.6	−0.0265648
$265$	−112435.	−0.0983531
$266$	441738.	0.382790
$267$	497448.	0.427041
$268$	671833.	0.571379
$269$	133948.	0.112864	0.0564322	−	0.998406i	$-0.482028\pi$
$269$	133948.	0.112864	0.0564322	+	0.998406i	$0.482028\pi$
$270$	129651.	0.108235
$271$	93482.4	0.0773226	0.0386613	−	0.999252i	$-0.487691\pi$
$271$	93482.4	0.0773226	0.0386613	+	0.999252i	$0.487691\pi$
$272$	−597.241	−0.000489471 0
$273$	1.46413e6	1.18898
$274$	2.93608e6	2.36261
$275$	−56995.6	−0.0454475
$276$	−248846.	−0.196634
$277$	576551.	0.451479	0.225740	−	0.974188i	$-0.427520\pi$
$277$	576551.	0.451479	0.225740	+	0.974188i	$0.427520\pi$
$278$	−1.59452e6	−1.23742
$279$	−974144.	−0.749226
$280$	157862.	0.120333
$281$	−434678.	−0.328399	−0.164200	−	0.986427i	$-0.552504\pi$
$281$	−434678.	−0.328399	−0.164200	+	0.986427i	$0.552504\pi$
$282$	−1.07851e6	−0.807611
$283$	−1.52198e6	−1.12965	−0.564823	−	0.825212i	$-0.691056\pi$
$283$	−1.52198e6	−1.12965	−0.564823	+	0.825212i	$0.691056\pi$
$284$	2.34027e6	1.72175
$285$	7492.33	0.00546392
$286$	119257.	0.0862124
$287$	2.98435e6	2.13868
$288$	−931183.	−0.661537
$289$	−1.39249e6	−0.980723
$290$	−193571.	−0.135159
$291$	−1.06853e6	−0.739699
$292$	−2.72026e6	−1.86704
$293$	1.36342e6	0.927813	0.463907	−	0.885884i	$-0.346447\pi$
$293$	1.36342e6	0.927813	0.463907	+	0.885884i	$0.346447\pi$
$294$	−2.86591e6	−1.93372
$295$	40588.6	0.0271549
$296$	−2.07573e6	−1.37702
$297$	−67213.5	−0.0442146
$298$	1.32089e6	0.861638
$299$	376217.	0.243366
$300$	−1.46301e6	−0.938519
$301$	4.85701e6	3.08996
$302$	1.11852e6	0.705713
$303$	−1.28870e6	−0.806392
$304$	−769.845	−0.000477771 0
$305$	−131751.	−0.0810970
$306$	242661.	0.148148
$307$	−3.03847e6	−1.83996	−0.919980	−	0.391966i	$-0.871795\pi$
$307$	−3.03847e6	−1.83996	−0.919980	+	0.391966i	$0.871795\pi$
$308$	−214596.	−0.128897
$309$	547331.	0.326102
$310$	−214827.	−0.126965
$311$	−3.32689e6	−1.95046	−0.975232	−	0.221186i	$-0.929007\pi$
$311$	−3.32689e6	−1.95046	−0.975232	+	0.221186i	$0.929007\pi$
$312$	1.16742e6	0.678956
$313$	−134964.	−0.0778677	−0.0389339	−	0.999242i	$-0.512396\pi$
$313$	−134964.	−0.0778677	−0.0389339	+	0.999242i	$0.512396\pi$
$314$	1.05476e6	0.603712
$315$	140191.	0.0796055
$316$	2.97962e6	1.67859
$317$	2.83907e6	1.58682	0.793411	−	0.608687i	$-0.208303\pi$
$317$	2.83907e6	1.58682	0.793411	+	0.608687i	$0.208303\pi$
$318$	2.42179e6	1.34298
$319$	100351.	0.0552132
$320$	−204907.	−0.111862
$321$	−1.70059e6	−0.921166
$322$	−1.09578e6	−0.588958
$323$	35280.9	0.0188163
$324$	289573.	0.153248
$325$	2.21184e6	1.16157
$326$	−1.10360e6	−0.575130
$327$	−578361.	−0.299109
$328$	2.37956e6	1.22127
$329$	−2.93406e6	−1.49444
$330$	−5891.45	−0.00297809
$331$	2.26789e6	1.13777	0.568883	−	0.822419i	$-0.307376\pi$
$331$	2.26789e6	1.13777	0.568883	+	0.822419i	$0.307376\pi$
$332$	−2.11132e6	−1.05125
$333$	−1.84336e6	−0.910962
$334$	−4.36437e6	−2.14070
$335$	50177.1	0.0244283
$336$	7431.97	0.00359134
$337$	−1.16585e6	−0.559199	−0.279599	−	0.960117i	$-0.590202\pi$
$337$	−1.16585e6	−0.559199	−0.279599	+	0.960117i	$0.590202\pi$
$338$	−1.23063e6	−0.585915
$339$	384512.	0.181723
$340$	33061.0	0.0155102
$341$	111370.	0.0518660
$342$	312790.	0.144607
$343$	−3.99185e6	−1.83206
$344$	3.87273e6	1.76450
$345$	−18585.6	−0.00840674
$346$	−3.12224e6	−1.40209
$347$	247150.	0.110189	0.0550944	−	0.998481i	$-0.482454\pi$
$347$	247150.	0.110189	0.0550944	+	0.998481i	$0.482454\pi$
$348$	2.57587e6	1.14019
$349$	869941.	0.382319	0.191160	−	0.981559i	$-0.438775\pi$
$349$	869941.	0.382319	0.191160	+	0.981559i	$0.438775\pi$
$350$	−6.44227e6	−2.81105
$351$	2.60837e6	1.13006
$352$	106459.	0.0457957
$353$	3.16976e6	1.35391	0.676954	−	0.736025i	$-0.263299\pi$
$353$	3.16976e6	1.35391	0.676954	+	0.736025i	$0.263299\pi$
$354$	−874256.	−0.370792
$355$	174787.	0.0736104
$356$	2.82944e6	1.18325
$357$	−340597.	−0.141439
$358$	−1.44526e6	−0.595988
$359$	1.48523e6	0.608215	0.304108	−	0.952638i	$-0.401642\pi$
$359$	1.48523e6	0.608215	0.304108	+	0.952638i	$0.401642\pi$
$360$	111781.	0.0454581
$361$	−2.43062e6	−0.981634
$362$	1.22060e6	0.489554
$363$	−1.46157e6	−0.582172
$364$	8.32785e6	3.29442
$365$	−203168.	−0.0798221
$366$	2.83785e6	1.10735
$367$	2.27000e6	0.879752	0.439876	−	0.898059i	$-0.355022\pi$
$367$	2.27000e6	0.879752	0.439876	+	0.898059i	$0.355022\pi$
$368$	1909.69	0.000735094 0
$369$	2.11319e6	0.807927
$370$	−406515.	−0.154373
$371$	6.58841e6	2.48511
$372$	2.85873e6	1.07107
$373$	2.90005e6	1.07928	0.539640	−	0.841896i	$-0.318560\pi$
$373$	2.90005e6	1.07928	0.539640	+	0.841896i	$0.318560\pi$
$374$	−27742.5	−0.0102557
$375$	−219059.	−0.0804421
$376$	−2.33946e6	−0.853388
$377$	−3.89432e6	−1.41117
$378$	−7.59721e6	−2.73479
$379$	1.01778e6	0.363960	0.181980	−	0.983302i	$-0.441749\pi$
$379$	1.01778e6	0.363960	0.181980	+	0.983302i	$0.441749\pi$
$380$	42615.7	0.0151395
$381$	−1.09077e6	−0.384965
$382$	7.50209e6	2.63041
$383$	−4.19874e6	−1.46259	−0.731293	−	0.682063i	$-0.761083\pi$
$383$	−4.19874e6	−1.46259	−0.731293	+	0.682063i	$0.761083\pi$
$384$	2.72305e6	0.942383
$385$	−16027.5	−0.00551079
$386$	−3.56495e6	−1.21783
$387$	3.43920e6	1.16729
$388$	−6.07772e6	−2.04956
$389$	1.67191e6	0.560193	0.280097	−	0.959972i	$-0.409634\pi$
$389$	1.67191e6	0.560193	0.280097	+	0.959972i	$0.409634\pi$
$390$	228631.	0.0761154
$391$	−87518.2	−0.0289505
$392$	−6.21660e6	−2.04333
$393$	1.71613e6	0.560493
$394$	−2.29738e6	−0.745576
$395$	222539.	0.0717651
$396$	−151953.	−0.0486935
$397$	−1.36652e6	−0.435152	−0.217576	−	0.976043i	$-0.569815\pi$
$397$	−1.36652e6	−0.435152	−0.217576	+	0.976043i	$0.569815\pi$
$398$	−4.46120e6	−1.41171
$399$	−439030.	−0.138058
$400$	11227.4	0.00350855
$401$	−1.30417e6	−0.405017	−0.202509	−	0.979280i	$-0.564909\pi$
$401$	−1.30417e6	−0.405017	−0.202509	+	0.979280i	$0.564909\pi$
$402$	−1.08079e6	−0.333561
$403$	−4.32196e6	−1.32562
$404$	−7.33003e6	−2.23436
$405$	21627.3	0.00655187
$406$	1.13427e7	3.41509
$407$	210745.	0.0630625
$408$	−271574.	−0.0807677
$409$	441139.	0.130397	0.0651984	−	0.997872i	$-0.479232\pi$
$409$	441139.	0.130397	0.0651984	+	0.997872i	$0.479232\pi$
$410$	466019.	0.136913
$411$	−2.91808e6	−0.852104
$412$	3.11317e6	0.903565
$413$	−2.37838e6	−0.686130
$414$	−775911.	−0.222490
$415$	−157688.	−0.0449446
$416$	−4.13136e6	−1.17047
$417$	1.58475e6	0.446293
$418$	−35760.1	−0.0100106
$419$	1.89676e6	0.527809	0.263904	−	0.964549i	$-0.414990\pi$
$419$	1.89676e6	0.527809	0.263904	+	0.964549i	$0.414990\pi$
$420$	−411405.	−0.113801
$421$	−1.39879e6	−0.384634	−0.192317	−	0.981333i	$-0.561600\pi$
$421$	−1.39879e6	−0.384634	−0.192317	+	0.981333i	$0.561600\pi$
$422$	2.50940e6	0.685944
$423$	−2.07757e6	−0.564554
$424$	5.25325e6	1.41910
$425$	−514534.	−0.138179
$426$	−3.76482e6	−1.00513
$427$	7.72026e6	2.04910
$428$	−9.67282e6	−2.55237
$429$	−118526.	−0.0310936
$430$	758443.	0.197812
$431$	−2.45338e6	−0.636168	−0.318084	−	0.948063i	$-0.603039\pi$
$431$	−2.45338e6	−0.636168	−0.318084	+	0.948063i	$0.603039\pi$
$432$	13240.1	0.00341337
$433$	−7.33998e6	−1.88137	−0.940686	−	0.339277i	$-0.889818\pi$
$433$	−7.33998e6	−1.88137	−0.940686	+	0.339277i	$0.889818\pi$
$434$	1.25883e7	3.20806
$435$	192384.	0.0487468
$436$	−3.28966e6	−0.828773
$437$	−112811.	−0.0282585
$438$	4.37613e6	1.08994
$439$	4.56023e6	1.12934	0.564671	−	0.825316i	$-0.309003\pi$
$439$	4.56023e6	1.12934	0.564671	+	0.825316i	$0.309003\pi$
$440$	−12779.5	−0.00314689
$441$	−5.52070e6	−1.35175
$442$	1.07661e6	0.262121
$443$	4.31520e6	1.04470	0.522350	−	0.852731i	$-0.325055\pi$
$443$	4.31520e6	1.04470	0.522350	+	0.852731i	$0.325055\pi$
$444$	5.40956e6	1.30228
$445$	211322.	0.0505877
$446$	1.96743e6	0.468342
$447$	−1.31279e6	−0.310761
$448$	1.20070e7	2.82643
$449$	2.53058e6	0.592386	0.296193	−	0.955128i	$-0.404283\pi$
$449$	2.53058e6	0.592386	0.296193	+	0.955128i	$0.404283\pi$
$450$	−4.56171e6	−1.06193
$451$	−241593.	−0.0559297
$452$	2.18707e6	0.503520
$453$	−1.11167e6	−0.254524
$454$	−7.66135e6	−1.74448
$455$	621981.	0.140847
$456$	−350060.	−0.0788370
$457$	1.61209e6	0.361077	0.180538	−	0.983568i	$-0.442216\pi$
$457$	1.61209e6	0.361077	0.180538	+	0.983568i	$0.442216\pi$
$458$	1.22535e7	2.72958
$459$	−606777.	−0.134430
$460$	−105713.	−0.0232934
$461$	360859.	0.0790833	0.0395417	−	0.999218i	$-0.487410\pi$
$461$	360859.	0.0790833	0.0395417	+	0.999218i	$0.487410\pi$
$462$	345223.	0.0752480
$463$	−4.98842e6	−1.08146	−0.540730	−	0.841196i	$-0.681852\pi$
$463$	−4.98842e6	−1.08146	−0.540730	+	0.841196i	$0.681852\pi$
$464$	−19767.7	−0.00426246
$465$	213510.	0.0457916
$466$	2.93491e6	0.626080
$467$	−3.38295e6	−0.717800	−0.358900	−	0.933376i	$-0.616848\pi$
$467$	−3.38295e6	−0.717800	−0.358900	+	0.933376i	$0.616848\pi$
$468$	5.89687e6	1.24453
$469$	−2.94025e6	−0.617236
$470$	−458165.	−0.0956704
$471$	−1.04830e6	−0.217737
$472$	−1.89640e6	−0.391809
$473$	−393191.	−0.0808073
$474$	−4.79336e6	−0.979929
$475$	−663235.	−0.134876
$476$	−1.93728e6	−0.391900
$477$	4.66518e6	0.938799
$478$	2.54997e6	0.510465
$479$	−8.41871e6	−1.67651	−0.838256	−	0.545276i	$-0.816425\pi$
$479$	−8.41871e6	−1.67651	−0.838256	+	0.545276i	$0.816425\pi$
$480$	204094.	0.0404322
$481$	−8.17841e6	−1.61178
$482$	6.23004e6	1.22144
$483$	1.08906e6	0.212415
$484$	−8.31325e6	−1.61309
$485$	−453926.	−0.0876255
$486$	−8.62084e6	−1.65561
$487$	5.35500e6	1.02314	0.511572	−	0.859240i	$-0.329063\pi$
$487$	5.35500e6	1.02314	0.511572	+	0.859240i	$0.329063\pi$
$488$	6.15573e6	1.17012
$489$	1.09683e6	0.207428
$490$	−1.21747e6	−0.229071
$491$	−2.09557e6	−0.392282	−0.196141	−	0.980576i	$-0.562841\pi$
$491$	−2.09557e6	−0.392282	−0.196141	+	0.980576i	$0.562841\pi$
$492$	−6.20139e6	−1.15498
$493$	905925.	0.167871
$494$	1.38775e6	0.255855
$495$	−11348.9	−0.00208181
$496$	−21938.4	−0.00400406
$497$	−1.02421e7	−1.85993
$498$	3.39651e6	0.613704
$499$	7.41055e6	1.33229	0.666146	−	0.745821i	$-0.267943\pi$
$499$	7.41055e6	1.33229	0.666146	+	0.745821i	$0.267943\pi$
$500$	−1.24599e6	−0.222889
$501$	4.33762e6	0.772070
$502$	−3.75441e6	−0.664940
$503$	8.19468e6	1.44415	0.722075	−	0.691815i	$-0.243189\pi$
$503$	8.19468e6	1.44415	0.722075	+	0.691815i	$0.243189\pi$
$504$	−6.55005e6	−1.14860
$505$	−547457.	−0.0955260
$506$	88707.0	0.0154022
$507$	1.22308e6	0.211318
$508$	−6.20420e6	−1.06666
$509$	−6.72046e6	−1.14975	−0.574876	−	0.818240i	$-0.694950\pi$
$509$	−6.72046e6	−1.14975	−0.574876	+	0.818240i	$0.694950\pi$
$510$	−53185.7	−0.00905460
$511$	1.19051e7	2.01688
$512$	−41822.6	−0.00705075
$513$	−782137.	−0.131217
$514$	−1.55302e7	−2.59280
$515$	232513.	0.0386304
$516$	−1.00927e7	−1.66872
$517$	237521.	0.0390820
$518$	2.38207e7	3.90059
$519$	3.10310e6	0.505682
$520$	495935.	0.0804298
$521$	−4.57081e6	−0.737732	−0.368866	−	0.929483i	$-0.620254\pi$
$521$	−4.57081e6	−0.737732	−0.368866	+	0.929483i	$0.620254\pi$
$522$	8.03166e6	1.29012
$523$	−35425.6	−0.00566321	−0.00283161	−	0.999996i	$-0.500901\pi$
$523$	−35425.6	−0.00566321	−0.00283161	+	0.999996i	$0.500901\pi$
$524$	9.76121e6	1.55301
$525$	6.40278e6	1.01384
$526$	−1.01642e7	−1.60181
$527$	1.00541e6	0.157694
$528$	−601.642	−9.39190e−5 0
$529$	279841.	0.0434783
$530$	1.02881e6	0.159091
$531$	−1.68411e6	−0.259199
$532$	−2.49716e6	−0.382532
$533$	9.37554e6	1.42948
$534$	−4.55176e6	−0.690758
$535$	−722433.	−0.109122
$536$	−2.34440e6	−0.352468
$537$	1.43640e6	0.214951
$538$	−1.22566e6	−0.182563
$539$	631160.	0.0935767
$540$	−732923.	−0.108162
$541$	2.95315e6	0.433803	0.216902	−	0.976193i	$-0.430405\pi$
$541$	2.95315e6	0.433803	0.216902	+	0.976193i	$0.430405\pi$
$542$	−855385.	−0.125073
$543$	−1.21312e6	−0.176564
$544$	961067.	0.139237
$545$	−245695.	−0.0354328
$546$	−1.33971e7	−1.92323
$547$	−3.04020e6	−0.434444	−0.217222	−	0.976122i	$-0.569700\pi$
$547$	−3.04020e6	−0.434444	−0.217222	+	0.976122i	$0.569700\pi$
$548$	−1.65978e7	−2.36101
$549$	5.46664e6	0.774087
$550$	521523.	0.0735134
$551$	1.16774e6	0.163858
$552$	868362.	0.121298
$553$	−1.30402e7	−1.81330
$554$	−5.27557e6	−0.730289
$555$	404023.	0.0556767
$556$	9.01390e6	1.23659
$557$	−3.03791e6	−0.414894	−0.207447	−	0.978246i	$-0.566516\pi$
$557$	−3.03791e6	−0.414894	−0.207447	+	0.978246i	$0.566516\pi$
$558$	8.91364e6	1.21191
$559$	1.52586e7	2.06531
$560$	3157.19	0.000425433 0
$561$	27572.4	0.00369886
$562$	3.97740e6	0.531201
$563$	−1.05140e6	−0.139796	−0.0698982	−	0.997554i	$-0.522267\pi$
$563$	−1.05140e6	−0.139796	−0.0698982	+	0.997554i	$0.522267\pi$
$564$	6.09688e6	0.807067
$565$	163345.	0.0215271
$566$	1.39264e7	1.82726
$567$	−1.26730e6	−0.165548
$568$	−8.16649e6	−1.06210
$569$	1.67008e6	0.216250	0.108125	−	0.994137i	$-0.465515\pi$
$569$	1.67008e6	0.216250	0.108125	+	0.994137i	$0.465515\pi$
$570$	−68556.5	−0.00883815
$571$	2.71320e6	0.348250	0.174125	−	0.984724i	$-0.444290\pi$
$571$	2.71320e6	0.348250	0.174125	+	0.984724i	$0.444290\pi$
$572$	−674167.	−0.0861543
$573$	−7.45610e6	−0.948692
$574$	−2.73075e7	−3.45941
$575$	1.64523e6	0.207519
$576$	8.50202e6	1.06774
$577$	8.83363e6	1.10459	0.552293	−	0.833650i	$-0.313753\pi$
$577$	8.83363e6	1.10459	0.552293	+	0.833650i	$0.313753\pi$
$578$	1.27416e7	1.58636
$579$	3.54310e6	0.439224
$580$	1.09426e6	0.135068
$581$	9.24008e6	1.13563
$582$	9.77731e6	1.19650
$583$	−533353.	−0.0649895
$584$	9.49250e6	1.15172
$585$	440419.	0.0532079
$586$	−1.24756e7	−1.50078
$587$	−1.35169e7	−1.61913	−0.809566	−	0.587029i	$-0.800298\pi$
$587$	−1.35169e7	−1.61913	−0.809566	+	0.587029i	$0.800298\pi$
$588$	1.62011e7	1.93242
$589$	1.29597e6	0.153924
$590$	−371395.	−0.0439244
$591$	2.28329e6	0.268901
$592$	−41513.8	−0.00486843
$593$	848223.	0.0990543	0.0495272	−	0.998773i	$-0.484229\pi$
$593$	848223.	0.0990543	0.0495272	+	0.998773i	$0.484229\pi$
$594$	615019.	0.0715191
$595$	−144690.	−0.0167550
$596$	−7.46703e6	−0.861057
$597$	4.43386e6	0.509150
$598$	−3.44247e6	−0.393656
$599$	−1.05945e7	−1.20646	−0.603229	−	0.797568i	$-0.706120\pi$
$599$	−1.05945e7	−1.20646	−0.603229	+	0.797568i	$0.706120\pi$
$600$	5.10524e6	0.578946
$601$	−209181.	−0.0236231	−0.0118115	−	0.999930i	$-0.503760\pi$
$601$	−209181.	−0.0236231	−0.0118115	+	0.999930i	$0.503760\pi$
$602$	−4.44428e7	−4.99816
$603$	−2.08196e6	−0.233173
$604$	−6.32306e6	−0.705237
$605$	−620891.	−0.0689647
$606$	1.17919e7	1.30438
$607$	1.02964e7	1.13427	0.567133	−	0.823627i	$-0.308053\pi$
$607$	1.02964e7	1.13427	0.567133	+	0.823627i	$0.308053\pi$
$608$	1.23882e6	0.135909
$609$	−1.12732e7	−1.23170
$610$	1.20555e6	0.131178
$611$	−9.21753e6	−0.998876
$612$	−1.37177e6	−0.148048
$613$	1.62158e7	1.74296	0.871479	−	0.490432i	$-0.163161\pi$
$613$	1.62158e7	1.74296	0.871479	+	0.490432i	$0.163161\pi$
$614$	2.78026e7	2.97622
$615$	−463162.	−0.0493794
$616$	748843.	0.0795132
$617$	6.25365e6	0.661334	0.330667	−	0.943747i	$-0.392726\pi$
$617$	6.25365e6	0.661334	0.330667	+	0.943747i	$0.392726\pi$
$618$	−5.00820e6	−0.527485
$619$	−1.06232e7	−1.11437	−0.557183	−	0.830390i	$-0.688118\pi$
$619$	−1.06232e7	−1.11437	−0.557183	+	0.830390i	$0.688118\pi$
$620$	1.21443e6	0.126880
$621$	1.94018e6	0.201889
$622$	3.04418e7	3.15496
$623$	−1.23829e7	−1.27821
$624$	23348.0	0.00240043
$625$	9.62593e6	0.985695
$626$	1.23495e6	0.125955
$627$	35540.9	0.00361044
$628$	−5.96261e6	−0.603305
$629$	1.90252e6	0.191736
$630$	−1.28278e6	−0.128766
$631$	8.45928e6	0.845785	0.422893	−	0.906180i	$-0.361015\pi$
$631$	8.45928e6	0.845785	0.422893	+	0.906180i	$0.361015\pi$
$632$	−1.03976e7	−1.03547
$633$	−2.49402e6	−0.247395
$634$	−2.59781e7	−2.56676
$635$	−463373.	−0.0456033
$636$	−1.36905e7	−1.34207
$637$	−2.44936e7	−2.39168
$638$	−918230.	−0.0893099
$639$	−7.25231e6	−0.702626
$640$	1.15678e6	0.111636
$641$	−2.03496e7	−1.95619	−0.978095	−	0.208157i	$-0.933253\pi$
$641$	−2.03496e7	−1.95619	−0.978095	+	0.208157i	$0.933253\pi$
$642$	1.55608e7	1.49003
$643$	−6.43818e6	−0.614095	−0.307047	−	0.951694i	$-0.599341\pi$
$643$	−6.43818e6	−0.614095	−0.307047	+	0.951694i	$0.599341\pi$
$644$	6.19449e6	0.588561
$645$	−753794.	−0.0713434
$646$	−322828.	−0.0304362
$647$	−9.20281e6	−0.864290	−0.432145	−	0.901804i	$-0.642243\pi$
$647$	−9.20281e6	−0.864290	−0.432145	+	0.901804i	$0.642243\pi$
$648$	−1.01048e6	−0.0945345
$649$	192538.	0.0179434
$650$	−2.02388e7	−1.87889
$651$	−1.25111e7	−1.15703
$652$	6.23867e6	0.574742
$653$	8.14140e6	0.747164	0.373582	−	0.927597i	$-0.378129\pi$
$653$	8.14140e6	0.747164	0.373582	+	0.927597i	$0.378129\pi$
$654$	5.29213e6	0.483823
$655$	729035.	0.0663965
$656$	47590.5	0.00431778
$657$	8.42988e6	0.761917
$658$	2.68473e7	2.41733
$659$	−8.11833e6	−0.728204	−0.364102	−	0.931359i	$-0.618624\pi$
$659$	−8.11833e6	−0.728204	−0.364102	+	0.931359i	$0.618624\pi$
$660$	33304.6	0.00297608
$661$	7.02602e6	0.625469	0.312735	−	0.949841i	$-0.398755\pi$
$661$	7.02602e6	0.625469	0.312735	+	0.949841i	$0.398755\pi$
$662$	−2.07517e7	−1.84039
$663$	−1.07001e6	−0.0945373
$664$	7.36755e6	0.648490
$665$	−186505.	−0.0163545
$666$	1.68672e7	1.47352
$667$	−2.89671e6	−0.252110
$668$	2.46720e7	2.13926
$669$	−1.95537e6	−0.168914
$670$	−459132.	−0.0395140
$671$	−624981.	−0.0535871
$672$	−1.19594e7	−1.02161
$673$	−1.13585e7	−0.966683	−0.483341	−	0.875432i	$-0.660577\pi$
$673$	−1.13585e7	−0.966683	−0.483341	+	0.875432i	$0.660577\pi$
$674$	1.06677e7	0.904530
$675$	1.14066e7	0.963601
$676$	6.95678e6	0.585520
$677$	7.60093e6	0.637375	0.318687	−	0.947860i	$-0.396758\pi$
$677$	7.60093e6	0.637375	0.318687	+	0.947860i	$0.396758\pi$
$678$	−3.51837e6	−0.293946
$679$	2.65988e7	2.21405
$680$	−115368.	−0.00956782
$681$	7.61439e6	0.629169
$682$	−1.01906e6	−0.0838957
$683$	−7.85446e6	−0.644265	−0.322133	−	0.946695i	$-0.604400\pi$
$683$	−7.85446e6	−0.644265	−0.322133	+	0.946695i	$0.604400\pi$
$684$	−1.76822e6	−0.144509
$685$	−1.23964e6	−0.100941
$686$	3.65263e7	2.96344
$687$	−1.21784e7	−0.984457
$688$	77453.2	0.00623833
$689$	2.06979e7	1.66103
$690$	170062.	0.0135983
$691$	−2.73211e6	−0.217672	−0.108836	−	0.994060i	$-0.534712\pi$
$691$	−2.73211e6	−0.217672	−0.108836	+	0.994060i	$0.534712\pi$
$692$	1.76502e7	1.40115
$693$	665015.	0.0526015
$694$	−2.26148e6	−0.178236
$695$	673220.	0.0528683
$696$	−8.98865e6	−0.703350
$697$	−2.18100e6	−0.170049
$698$	−7.96016e6	−0.618419
$699$	−2.91692e6	−0.225804
$700$	3.64184e7	2.80916
$701$	−3.62295e6	−0.278463	−0.139231	−	0.990260i	$-0.544463\pi$
$701$	−3.62295e6	−0.278463	−0.139231	+	0.990260i	$0.544463\pi$
$702$	−2.38671e7	−1.82792
$703$	2.45235e6	0.187152
$704$	−972004.	−0.0739156
$705$	455357.	0.0345048
$706$	−2.90040e7	−2.19001
$707$	3.20795e7	2.41368
$708$	4.94220e6	0.370542
$709$	−4.19896e6	−0.313708	−0.156854	−	0.987622i	$-0.550135\pi$
$709$	−4.19896e6	−0.313708	−0.156854	+	0.987622i	$0.550135\pi$
$710$	−1.59934e6	−0.119068
$711$	−9.23362e6	−0.685012
$712$	−9.87348e6	−0.729911
$713$	−3.21480e6	−0.236827
$714$	3.11654e6	0.228785
$715$	−50351.4	−0.00368338
$716$	8.17009e6	0.595586
$717$	−2.53434e6	−0.184106
$718$	−1.35902e7	−0.983816
$719$	1.31323e7	0.947369	0.473684	−	0.880695i	$-0.342924\pi$
$719$	1.31323e7	0.947369	0.473684	+	0.880695i	$0.342924\pi$
$720$	2235.58	0.000160716 0
$721$	−1.36246e7	−0.976083
$722$	2.22407e7	1.58784
$723$	−6.19185e6	−0.440529
$724$	−6.90009e6	−0.489224
$725$	−1.70302e7	−1.20330
$726$	1.33736e7	0.941691
$727$	−1.90858e7	−1.33929	−0.669644	−	0.742683i	$-0.733553\pi$
$727$	−1.90858e7	−1.33929	−0.669644	+	0.742683i	$0.733553\pi$
$728$	−2.90605e7	−2.03224
$729$	7.20765e6	0.502313
$730$	1.85903e6	0.129116
$731$	−3.54957e6	−0.245687
$732$	−1.60425e7	−1.10661
$733$	−1.58603e7	−1.09031	−0.545157	−	0.838334i	$-0.683530\pi$
$733$	−1.58603e7	−1.09031	−0.545157	+	0.838334i	$0.683530\pi$
$734$	−2.07710e7	−1.42304
$735$	1.21001e6	0.0826172
$736$	−3.07303e6	−0.209108
$737$	238022.	0.0161417
$738$	−1.93361e7	−1.30686
$739$	5.61015e6	0.377888	0.188944	−	0.981988i	$-0.439494\pi$
$739$	5.61015e6	0.377888	0.188944	+	0.981988i	$0.439494\pi$
$740$	2.29805e6	0.154269
$741$	−1.37924e6	−0.0922774
$742$	−6.02854e7	−4.01978
$743$	4.05128e6	0.269228	0.134614	−	0.990898i	$-0.457021\pi$
$743$	4.05128e6	0.269228	0.134614	+	0.990898i	$0.457021\pi$
$744$	−9.97571e6	−0.660711
$745$	−557689.	−0.0368130
$746$	−2.65362e7	−1.74579
$747$	6.54280e6	0.429005
$748$	156829.	0.0102488
$749$	4.23326e7	2.75722
$750$	2.00444e6	0.130119
$751$	−500386.	−0.0323747	−0.0161873	−	0.999869i	$-0.505153\pi$
$751$	−500386.	−0.0323747	−0.0161873	+	0.999869i	$0.505153\pi$
$752$	−46788.4	−0.00301713
$753$	3.73140e6	0.239819
$754$	3.56339e7	2.28263
$755$	−472250.	−0.0301512
$756$	4.29473e7	2.73295
$757$	2.77142e7	1.75777	0.878886	−	0.477032i	$-0.158288\pi$
$757$	2.77142e7	1.75777	0.878886	+	0.477032i	$0.158288\pi$
$758$	−9.31287e6	−0.588722
$759$	−88163.3	−0.00555499
$760$	−148710.	−0.00933911
$761$	2.10372e7	1.31682	0.658411	−	0.752659i	$-0.271229\pi$
$761$	2.10372e7	1.31682	0.658411	+	0.752659i	$0.271229\pi$
$762$	9.98080e6	0.622698
$763$	1.43971e7	0.895288
$764$	−4.24096e7	−2.62864
$765$	−102453.	−0.00632954
$766$	3.84194e7	2.36580
$767$	−7.47185e6	−0.458606
$768$	−9.48143e6	−0.580057
$769$	1.52722e7	0.931295	0.465647	−	0.884970i	$-0.345822\pi$
$769$	1.52722e7	0.931295	0.465647	+	0.884970i	$0.345822\pi$
$770$	146655.	0.00891395
$771$	1.54350e7	0.935126
$772$	2.01528e7	1.21700
$773$	−5.03712e6	−0.303203	−0.151602	−	0.988442i	$-0.548443\pi$
$773$	−5.03712e6	−0.303203	−0.151602	+	0.988442i	$0.548443\pi$
$774$	−3.14695e7	−1.88815
$775$	−1.89003e7	−1.13036
$776$	2.12085e7	1.26432
$777$	−2.36747e7	−1.40680
$778$	−1.52983e7	−0.906138
$779$	−2.81132e6	−0.165984
$780$	−1.29246e6	−0.0760641
$781$	829129.	0.0486401
$782$	800812.	0.0468288
$783$	−2.00833e7	−1.17066
$784$	−124330.	−0.00722413
$785$	−445329.	−0.0257933
$786$	−1.57030e7	−0.906623
$787$	−4.02266e6	−0.231514	−0.115757	−	0.993278i	$-0.536929\pi$
$787$	−4.02266e6	−0.231514	−0.115757	+	0.993278i	$0.536929\pi$
$788$	1.29872e7	0.745073
$789$	1.01019e7	0.577712
$790$	−2.03628e6	−0.116083
$791$	−9.57161e6	−0.543931
$792$	530248.	0.0300377
$793$	2.42537e7	1.36961
$794$	1.25040e7	0.703879
$795$	−1.02250e6	−0.0573781
$796$	2.52194e7	1.41075
$797$	−3.18310e7	−1.77503	−0.887514	−	0.460781i	$-0.847569\pi$
$797$	−3.18310e7	−1.77503	−0.887514	+	0.460781i	$0.847569\pi$
$798$	4.01723e6	0.223316
$799$	2.14425e6	0.118825
$800$	−1.80668e7	−0.998059
$801$	−8.76821e6	−0.482869
$802$	1.19335e7	0.655134
$803$	−963756.	−0.0527446
$804$	6.10974e6	0.333336
$805$	462648.	0.0251629
$806$	3.95469e7	2.14425
$807$	1.21814e6	0.0658438
$808$	2.55785e7	1.37831
$809$	1.26438e7	0.679213	0.339606	−	0.940568i	$-0.389706\pi$
$809$	1.26438e7	0.679213	0.339606	+	0.940568i	$0.389706\pi$
$810$	−197895.	−0.0105979
$811$	−1.06282e7	−0.567426	−0.283713	−	0.958909i	$-0.591566\pi$
$811$	−1.06282e7	−0.567426	−0.283713	+	0.958909i	$0.591566\pi$
$812$	−6.41209e7	−3.41279
$813$	850142.	0.0451092
$814$	−1.92836e6	−0.102006
$815$	465947.	0.0245721
$816$	−5431.39	−0.000285552 0
$817$	−4.57541e6	−0.239814
$818$	−4.03652e6	−0.210923
$819$	−2.58074e7	−1.34442
$820$	−2.63442e6	−0.136821
$821$	3.63064e7	1.87986	0.939930	−	0.341366i	$-0.110890\pi$
$821$	3.63064e7	1.87986	0.939930	+	0.341366i	$0.110890\pi$
$822$	2.67011e7	1.37832
$823$	−6.98474e6	−0.359460	−0.179730	−	0.983716i	$-0.557522\pi$
$823$	−6.98474e6	−0.359460	−0.179730	+	0.983716i	$0.557522\pi$
$824$	−1.08636e7	−0.557384
$825$	−518326.	−0.0265136
$826$	2.17627e7	1.10985
$827$	2.85277e7	1.45045	0.725227	−	0.688510i	$-0.241735\pi$
$827$	2.85277e7	1.45045	0.725227	+	0.688510i	$0.241735\pi$
$828$	4.38626e6	0.222340
$829$	−2.16227e7	−1.09276	−0.546378	−	0.837538i	$-0.683994\pi$
$829$	−2.16227e7	−1.09276	−0.546378	+	0.837538i	$0.683994\pi$
$830$	1.44288e6	0.0727000
$831$	5.24323e6	0.263388
$832$	3.77207e7	1.88917
$833$	5.69786e6	0.284511
$834$	−1.45008e7	−0.721899
$835$	1.84267e6	0.0914602
$836$	202154.	0.0100038
$837$	−2.22887e7	−1.09969
$838$	−1.73557e7	−0.853755
$839$	−3.42589e7	−1.68023	−0.840115	−	0.542408i	$-0.817513\pi$
$839$	−3.42589e7	−1.68023	−0.840115	+	0.542408i	$0.817513\pi$
$840$	1.43562e6	0.0702008
$841$	9.47345e6	0.461868
$842$	1.27992e7	0.622163
$843$	−3.95302e6	−0.191584
$844$	−1.41857e7	−0.685482
$845$	519581.	0.0250329
$846$	1.90103e7	0.913193
$847$	3.63825e7	1.74255
$848$	105063.	0.00501719
$849$	−1.38411e7	−0.659023
$850$	4.70810e6	0.223511
$851$	−6.08334e6	−0.287951
$852$	2.12827e7	1.00445
$853$	−3.62802e7	−1.70725	−0.853624	−	0.520890i	$-0.825600\pi$
$853$	−3.62802e7	−1.70725	−0.853624	+	0.520890i	$0.825600\pi$
$854$	−7.06421e7	−3.31451
$855$	−132063.	−0.00617824
$856$	3.37538e7	1.57449
$857$	−1.47179e7	−0.684531	−0.342265	−	0.939603i	$-0.611194\pi$
$857$	−1.47179e7	−0.684531	−0.342265	+	0.939603i	$0.611194\pi$
$858$	1.08454e6	0.0502954
$859$	−1.22343e7	−0.565713	−0.282856	−	0.959162i	$-0.591282\pi$
$859$	−1.22343e7	−0.565713	−0.282856	+	0.959162i	$0.591282\pi$
$860$	−4.28751e6	−0.197678
$861$	2.71401e7	1.24768
$862$	2.24490e7	1.02903
$863$	2.54861e7	1.16487	0.582434	−	0.812878i	$-0.302100\pi$
$863$	2.54861e7	1.16487	0.582434	+	0.812878i	$0.302100\pi$
$864$	−2.13057e7	−0.970984
$865$	1.31824e6	0.0599036
$866$	6.71624e7	3.04321
$867$	−1.26635e7	−0.572143
$868$	−7.11621e7	−3.20590
$869$	1.05565e6	0.0474208
$870$	−1.76036e6	−0.0788502
$871$	−9.23698e6	−0.412558
$872$	1.14795e7	0.511247
$873$	1.88344e7	0.836403
$874$	1.03225e6	0.0457094
$875$	5.45301e6	0.240778
$876$	−2.47384e7	−1.08921
$877$	1.28458e7	0.563978	0.281989	−	0.959418i	$-0.409006\pi$
$877$	1.28458e7	0.563978	0.281989	+	0.959418i	$0.409006\pi$
$878$	−4.17271e7	−1.82676
$879$	1.23991e7	0.541276
$880$	−255.585	−1.11257e−5 0
$881$	2.97345e7	1.29069	0.645344	−	0.763892i	$-0.276714\pi$
$881$	2.97345e7	1.29069	0.645344	+	0.763892i	$0.276714\pi$
$882$	5.05156e7	2.18652
$883$	7.58412e6	0.327343	0.163672	−	0.986515i	$-0.447666\pi$
$883$	7.58412e6	0.327343	0.163672	+	0.986515i	$0.447666\pi$
$884$	−6.08611e6	−0.261944
$885$	369118.	0.0158419
$886$	−3.94850e7	−1.68985
$887$	−4.35352e7	−1.85794	−0.928970	−	0.370155i	$-0.879305\pi$
$887$	−4.35352e7	−1.85794	−0.928970	+	0.370155i	$0.879305\pi$
$888$	−1.88769e7	−0.803340
$889$	2.71524e7	1.15227
$890$	−1.93364e6	−0.0818279
$891$	102592.	0.00432933
$892$	−1.11220e7	−0.468026
$893$	2.76394e6	0.115985
$894$	1.20123e7	0.502670
$895$	610199.	0.0254633
$896$	−6.77845e7	−2.82072
$897$	3.42137e6	0.141977
$898$	−2.31554e7	−0.958212
$899$	3.32773e7	1.37325
$900$	2.57875e7	1.06121
$901$	−4.81490e6	−0.197595
$902$	2.21063e6	0.0904689
$903$	4.41703e7	1.80265
$904$	−7.63190e6	−0.310607
$905$	−515346.	−0.0209160
$906$	1.01720e7	0.411705
$907$	3.27804e7	1.32311	0.661555	−	0.749897i	$-0.269897\pi$
$907$	3.27804e7	1.32311	0.661555	+	0.749897i	$0.269897\pi$
$908$	4.33099e7	1.74330
$909$	2.27152e7	0.911815
$910$	−5.69127e6	−0.227827
$911$	−3.93141e7	−1.56947	−0.784733	−	0.619834i	$-0.787200\pi$
$911$	−3.93141e7	−1.56947	−0.784733	+	0.619834i	$0.787200\pi$
$912$	−7001.08	−0.000278726 0
$913$	−748014.	−0.0296984
$914$	−1.47510e7	−0.584058
$915$	−1.19816e6	−0.0473111
$916$	−6.92693e7	−2.72774
$917$	−4.27195e7	−1.67766
$918$	5.55214e6	0.217447
$919$	−2.97680e7	−1.16268	−0.581342	−	0.813660i	$-0.697472\pi$
$919$	−2.97680e7	−1.16268	−0.581342	+	0.813660i	$0.697472\pi$
$920$	368891.	0.0143691
$921$	−2.76322e7	−1.07341
$922$	−3.30194e6	−0.127921
$923$	−3.21762e7	−1.24317
$924$	−1.95156e6	−0.0751973
$925$	−3.57649e7	−1.37437
$926$	4.56452e7	1.74931
$927$	−9.64746e6	−0.368735
$928$	3.18097e7	1.21252
$929$	3.60951e7	1.37217	0.686086	−	0.727521i	$-0.259327\pi$
$929$	3.60951e7	1.37217	0.686086	+	0.727521i	$0.259327\pi$
$930$	−1.95366e6	−0.0740701
$931$	7.34457e6	0.277710
$932$	−1.65912e7	−0.625658
$933$	−3.02552e7	−1.13788
$934$	3.09548e7	1.16108
$935$	11713.1	0.000438170 0
$936$	−2.05774e7	−0.767718
$937$	−4.14725e7	−1.54316	−0.771581	−	0.636131i	$-0.780534\pi$
$937$	−4.14725e7	−1.54316	−0.771581	+	0.636131i	$0.780534\pi$
$938$	2.69039e7	0.998408
$939$	−1.22738e6	−0.0454272
$940$	2.59003e6	0.0956059
$941$	3.05025e6	0.112295	0.0561476	−	0.998422i	$-0.482118\pi$
$941$	3.05025e6	0.112295	0.0561476	+	0.998422i	$0.482118\pi$
$942$	9.59214e6	0.352199
$943$	6.97379e6	0.255382
$944$	−37927.3	−0.00138523
$945$	3.20760e6	0.116843
$946$	3.59779e6	0.130710
$947$	−2.14155e7	−0.775983	−0.387992	−	0.921663i	$-0.626831\pi$
$947$	−2.14155e7	−0.775983	−0.387992	+	0.921663i	$0.626831\pi$
$948$	2.70971e7	0.979269
$949$	3.74007e7	1.34807
$950$	6.06875e6	0.218168
$951$	2.58189e7	0.925734
$952$	6.76026e6	0.241752
$953$	−4.74956e7	−1.69403	−0.847015	−	0.531569i	$-0.821602\pi$
$953$	−4.74956e7	−1.69403	−0.847015	+	0.531569i	$0.821602\pi$
$954$	−4.26875e7	−1.51855
$955$	−3.16744e6	−0.112383
$956$	−1.44151e7	−0.510121
$957$	912601.	0.0322108
$958$	7.70331e7	2.71184
$959$	7.26394e7	2.55050
$960$	−1.86345e6	−0.0652588
$961$	8.30235e6	0.289996
$962$	7.48343e7	2.60713
$963$	2.99753e7	1.04159
$964$	−3.52187e7	−1.22062
$965$	1.50515e6	0.0520309
$966$	−9.96518e6	−0.343591
$967$	761545.	0.0261896	0.0130948	−	0.999914i	$-0.495832\pi$
$967$	761545.	0.0261896	0.0130948	+	0.999914i	$0.495832\pi$
$968$	2.90095e7	0.995067
$969$	320849.	0.0109772
$970$	4.15352e6	0.141738
$971$	1.28371e7	0.436936	0.218468	−	0.975844i	$-0.429894\pi$
$971$	1.28371e7	0.436936	0.218468	+	0.975844i	$0.429894\pi$
$972$	4.87340e7	1.65450
$973$	−3.94489e7	−1.33583
$974$	−4.89994e7	−1.65498
$975$	2.01148e7	0.677647
$976$	123113.	0.00413693
$977$	−1.89960e7	−0.636688	−0.318344	−	0.947975i	$-0.603127\pi$
$977$	−1.89960e7	−0.636688	−0.318344	+	0.947975i	$0.603127\pi$
$978$	−1.00362e7	−0.335524
$979$	1.00244e6	0.0334272
$980$	6.88243e6	0.228916
$981$	1.01944e7	0.338213
$982$	1.91749e7	0.634534
$983$	3.27541e7	1.08114	0.540569	−	0.841300i	$-0.318209\pi$
$983$	3.27541e7	1.08114	0.540569	+	0.841300i	$0.318209\pi$
$984$	2.16401e7	0.712477
$985$	969972.	0.0318543
$986$	−8.28941e6	−0.271539
$987$	−2.66827e7	−0.871840
$988$	−7.84501e6	−0.255683
$989$	1.13498e7	0.368976
$990$	103845.	0.00336742
$991$	−7.38784e6	−0.238965	−0.119482	−	0.992836i	$-0.538123\pi$
$991$	−7.38784e6	−0.238965	−0.119482	+	0.992836i	$0.538123\pi$
$992$	3.53028e7	1.13902
$993$	2.06245e7	0.663760
$994$	9.37173e7	3.00853
$995$	1.88356e6	0.0603144
$996$	−1.92006e7	−0.613291
$997$	−3.41271e7	−1.08733	−0.543666	−	0.839302i	$-0.682964\pi$
$997$	−3.41271e7	−1.08733	−0.543666	+	0.839302i	$0.682964\pi$
$998$	−6.78082e7	−2.15504
$999$	−4.21767e7	−1.33708

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.6.a.a.1.1	✓	3
3.2	odd	2		207.6.a.b.1.3		3
4.3	odd	2		368.6.a.e.1.1		3
5.4	even	2		575.6.a.b.1.3		3
23.22	odd	2		529.6.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.6.a.a.1.1	✓	3	1.1	even	1	trivial
207.6.a.b.1.3		3	3.2	odd	2
368.6.a.e.1.1		3	4.3	odd	2
529.6.a.a.1.1		3	23.22	odd	2
575.6.a.b.1.3		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-9.15022 q^{2} +9.09413 q^{3} +51.7266 q^{4} +3.86330 q^{5} -83.2134 q^{6} -226.379 q^{7} -180.503 q^{8} -160.297 q^{9} +O(q^{10})\)	\(q-9.15022 q^{2} +9.09413 q^{3} +51.7266 q^{4} +3.86330 q^{5} -83.2134 q^{6} -226.379 q^{7} -180.503 q^{8} -160.297 q^{9} -35.3501 q^{10} +18.3261 q^{11} +470.409 q^{12} -711.185 q^{13} +2071.42 q^{14} +35.1334 q^{15} -3.60999 q^{16} +165.441 q^{17} +1466.75 q^{18} +213.254 q^{19} +199.835 q^{20} -2058.72 q^{21} -167.688 q^{22} -529.000 q^{23} -1641.52 q^{24} -3110.07 q^{25} +6507.50 q^{26} -3667.63 q^{27} -11709.8 q^{28} +5475.82 q^{29} -321.478 q^{30} +6077.13 q^{31} +5809.12 q^{32} +166.660 q^{33} -1513.82 q^{34} -874.570 q^{35} -8291.60 q^{36} +11499.7 q^{37} -1951.32 q^{38} -6467.61 q^{39} -697.337 q^{40} -13183.0 q^{41} +18837.8 q^{42} -21455.2 q^{43} +947.948 q^{44} -619.274 q^{45} +4840.47 q^{46} +12960.8 q^{47} -32.8298 q^{48} +34440.5 q^{49} +28457.9 q^{50} +1504.54 q^{51} -36787.2 q^{52} -29103.4 q^{53} +33559.7 q^{54} +70.7993 q^{55} +40862.1 q^{56} +1939.36 q^{57} -50105.0 q^{58} +10506.2 q^{59} +1817.33 q^{60} -34103.3 q^{61} -55607.1 q^{62} +36287.8 q^{63} -53039.3 q^{64} -2747.52 q^{65} -1524.98 q^{66} +12988.2 q^{67} +8557.70 q^{68} -4810.80 q^{69} +8002.51 q^{70} +45243.0 q^{71} +28934.0 q^{72} -52589.2 q^{73} -105225. q^{74} -28283.4 q^{75} +11030.9 q^{76} -4148.65 q^{77} +59180.1 q^{78} +57603.3 q^{79} -13.9465 q^{80} +5598.14 q^{81} +120627. q^{82} -40816.8 q^{83} -106491. q^{84} +639.148 q^{85} +196320. q^{86} +49797.8 q^{87} -3307.92 q^{88} +54699.9 q^{89} +5666.50 q^{90} +160997. q^{91} -27363.4 q^{92} +55266.2 q^{93} -118594. q^{94} +823.864 q^{95} +52828.9 q^{96} -117497. q^{97} -315138. q^{98} -2937.62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9}+O(q^{10}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9} - 156 q^{10} + 136 q^{11} + 620 q^{12} - 1116 q^{13} + 2016 q^{14} + 750 q^{15} + 128 q^{16} - 896 q^{17} + 4282 q^{18} + 1654 q^{19} + 1504 q^{20} - 1670 q^{21} + 1352 q^{22} - 1587 q^{23} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} - 10264 q^{28} - 844 q^{29} + 3180 q^{30} - 3020 q^{31} + 6656 q^{32} - 7370 q^{33} - 11212 q^{34} + 1072 q^{35} - 2548 q^{36} + 8938 q^{37} + 10728 q^{38} + 16020 q^{39} + 3440 q^{40} - 12792 q^{41} + 20560 q^{42} - 16730 q^{43} + 5112 q^{44} - 3936 q^{45} + 2116 q^{46} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} + 50290 q^{51} - 47412 q^{52} + 17108 q^{53} - 7610 q^{54} - 436 q^{55} + 42640 q^{56} - 61960 q^{57} - 55678 q^{58} + 54176 q^{59} - 2400 q^{60} - 71324 q^{61} - 72710 q^{62} + 40696 q^{63} - 49984 q^{64} + 846 q^{65} - 42860 q^{66} - 62960 q^{67} - 8352 q^{68} + 10580 q^{69} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} - 59044 q^{74} + 44800 q^{75} + 31488 q^{76} - 304 q^{77} + 182070 q^{78} + 58224 q^{79} - 17568 q^{80} + 149947 q^{81} + 61926 q^{82} + 9892 q^{83} - 109720 q^{84} + 15536 q^{85} + 191140 q^{86} + 90500 q^{87} - 58400 q^{88} + 27542 q^{89} - 62112 q^{90} + 151974 q^{91} - 8464 q^{92} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} - 273672 q^{97} - 401276 q^{98} + 183082 q^{99}+O(q^{100}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9 - 156 * q^10 + 136 * q^11 + 620 * q^12 - 1116 * q^13 + 2016 * q^14 + 750 * q^15 + 128 * q^16 - 896 * q^17 + 4282 * q^18 + 1654 * q^19 + 1504 * q^20 - 1670 * q^21 + 1352 * q^22 - 1587 * q^23 + 3600 * q^24 - 7347 * q^25 + 1998 * q^26 - 10700 * q^27 - 10264 * q^28 - 844 * q^29 + 3180 * q^30 - 3020 * q^31 + 6656 * q^32 - 7370 * q^33 - 11212 * q^34 + 1072 * q^35 - 2548 * q^36 + 8938 * q^37 + 10728 * q^38 + 16020 * q^39 + 3440 * q^40 - 12792 * q^41 + 20560 * q^42 - 16730 * q^43 + 5112 * q^44 - 3936 * q^45 + 2116 * q^46 + 22500 * q^47 + 23120 * q^48 + 2887 * q^49 + 15156 * q^50 + 50290 * q^51 - 47412 * q^52 + 17108 * q^53 - 7610 * q^54 - 436 * q^55 + 42640 * q^56 - 61960 * q^57 - 55678 * q^58 + 54176 * q^59 - 2400 * q^60 - 71324 * q^61 - 72710 * q^62 + 40696 * q^63 - 49984 * q^64 + 846 * q^65 - 42860 * q^66 - 62960 * q^67 - 8352 * q^68 + 10580 * q^69 + 9224 * q^70 + 98400 * q^71 - 72840 * q^72 - 81772 * q^73 - 59044 * q^74 + 44800 * q^75 + 31488 * q^76 - 304 * q^77 + 182070 * q^78 + 58224 * q^79 - 17568 * q^80 + 149947 * q^81 + 61926 * q^82 + 9892 * q^83 - 109720 * q^84 + 15536 * q^85 + 191140 * q^86 + 90500 * q^87 - 58400 * q^88 + 27542 * q^89 - 62112 * q^90 + 151974 * q^91 - 8464 * q^92 + 157330 * q^93 - 146990 * q^94 - 20644 * q^95 + 16160 * q^96 - 273672 * q^97 - 401276 * q^98 + 183082 * q^99

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