LMFDB - Embedded newform 230.6.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 1168x^{4} - 2857x^{3} + 297325x^{2} + 680040x - 8930700 $ x^6 - x^5 - 1168x^4 - 2857x^3 + 297325x^2 + 680040x - 8930700
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			1.6
Root			$-24.6560$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +26.6560 q^{3} +16.0000 q^{4} +25.0000 q^{5} +106.624 q^{6} +15.2806 q^{7} +64.0000 q^{8} +467.540 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +26.6560 q^{3} +16.0000 q^{4} +25.0000 q^{5} +106.624 q^{6} +15.2806 q^{7} +64.0000 q^{8} +467.540 q^{9} +100.000 q^{10} +590.940 q^{11} +426.495 q^{12} -513.344 q^{13} +61.1225 q^{14} +666.399 q^{15} +256.000 q^{16} -795.921 q^{17} +1870.16 q^{18} -1142.11 q^{19} +400.000 q^{20} +407.320 q^{21} +2363.76 q^{22} +529.000 q^{23} +1705.98 q^{24} +625.000 q^{25} -2053.37 q^{26} +5985.33 q^{27} +244.490 q^{28} +1452.68 q^{29} +2665.60 q^{30} -2163.89 q^{31} +1024.00 q^{32} +15752.1 q^{33} -3183.68 q^{34} +382.016 q^{35} +7480.64 q^{36} +6746.54 q^{37} -4568.42 q^{38} -13683.7 q^{39} +1600.00 q^{40} -4185.43 q^{41} +1629.28 q^{42} -13595.8 q^{43} +9455.05 q^{44} +11688.5 q^{45} +2116.00 q^{46} +6960.01 q^{47} +6823.93 q^{48} -16573.5 q^{49} +2500.00 q^{50} -21216.0 q^{51} -8213.50 q^{52} +15146.8 q^{53} +23941.3 q^{54} +14773.5 q^{55} +977.960 q^{56} -30443.9 q^{57} +5810.71 q^{58} +24369.8 q^{59} +10662.4 q^{60} -47086.1 q^{61} -8655.56 q^{62} +7144.31 q^{63} +4096.00 q^{64} -12833.6 q^{65} +63008.3 q^{66} +29592.3 q^{67} -12734.7 q^{68} +14101.0 q^{69} +1528.06 q^{70} +6016.77 q^{71} +29922.6 q^{72} -25209.0 q^{73} +26986.2 q^{74} +16660.0 q^{75} -18273.7 q^{76} +9029.94 q^{77} -54734.7 q^{78} -40220.1 q^{79} +6400.00 q^{80} +45932.6 q^{81} -16741.7 q^{82} -75788.5 q^{83} +6517.12 q^{84} -19898.0 q^{85} -54383.1 q^{86} +38722.5 q^{87} +37820.2 q^{88} +128246. q^{89} +46754.0 q^{90} -7844.21 q^{91} +8464.00 q^{92} -57680.5 q^{93} +27840.1 q^{94} -28552.6 q^{95} +27295.7 q^{96} +93910.6 q^{97} -66294.0 q^{98} +276288. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) $ 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9} + 600 q^{10} + 151 q^{11} + 176 q^{12} + 463 q^{13} + 1464 q^{14} + 275 q^{15} + 1536 q^{16} + 644 q^{17} + 3596 q^{18} + 3431 q^{19} + 2400 q^{20} - 3846 q^{21} + 604 q^{22} + 3174 q^{23} + 704 q^{24} + 3750 q^{25} + 1852 q^{26} - 3364 q^{27} + 5856 q^{28} + 5973 q^{29} + 1100 q^{30} + 10262 q^{31} + 6144 q^{32} + 23025 q^{33} + 2576 q^{34} + 9150 q^{35} + 14384 q^{36} + 17207 q^{37} + 13724 q^{38} + 14136 q^{39} + 9600 q^{40} + 784 q^{41} - 15384 q^{42} + 13452 q^{43} + 2416 q^{44} + 22475 q^{45} + 12696 q^{46} + 24572 q^{47} + 2816 q^{48} + 28050 q^{49} + 15000 q^{50} + 26125 q^{51} + 7408 q^{52} + 17563 q^{53} - 13456 q^{54} + 3775 q^{55} + 23424 q^{56} - 41798 q^{57} + 23892 q^{58} + 62911 q^{59} + 4400 q^{60} + 32851 q^{61} + 41048 q^{62} + 138693 q^{63} + 24576 q^{64} + 11575 q^{65} + 92100 q^{66} + 54177 q^{67} + 10304 q^{68} + 5819 q^{69} + 36600 q^{70} - 14368 q^{71} + 57536 q^{72} + 33276 q^{73} + 68828 q^{74} + 6875 q^{75} + 54896 q^{76} - 143678 q^{77} + 56544 q^{78} + 74296 q^{79} + 38400 q^{80} + 150834 q^{81} + 3136 q^{82} + 65145 q^{83} - 61536 q^{84} + 16100 q^{85} + 53808 q^{86} - 790 q^{87} + 9664 q^{88} - 67562 q^{89} + 89900 q^{90} - 89487 q^{91} + 50784 q^{92} - 209450 q^{93} + 98288 q^{94} + 85775 q^{95} + 11264 q^{96} - 13201 q^{97} + 112200 q^{98} - 355951 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9 + 600 * q^10 + 151 * q^11 + 176 * q^12 + 463 * q^13 + 1464 * q^14 + 275 * q^15 + 1536 * q^16 + 644 * q^17 + 3596 * q^18 + 3431 * q^19 + 2400 * q^20 - 3846 * q^21 + 604 * q^22 + 3174 * q^23 + 704 * q^24 + 3750 * q^25 + 1852 * q^26 - 3364 * q^27 + 5856 * q^28 + 5973 * q^29 + 1100 * q^30 + 10262 * q^31 + 6144 * q^32 + 23025 * q^33 + 2576 * q^34 + 9150 * q^35 + 14384 * q^36 + 17207 * q^37 + 13724 * q^38 + 14136 * q^39 + 9600 * q^40 + 784 * q^41 - 15384 * q^42 + 13452 * q^43 + 2416 * q^44 + 22475 * q^45 + 12696 * q^46 + 24572 * q^47 + 2816 * q^48 + 28050 * q^49 + 15000 * q^50 + 26125 * q^51 + 7408 * q^52 + 17563 * q^53 - 13456 * q^54 + 3775 * q^55 + 23424 * q^56 - 41798 * q^57 + 23892 * q^58 + 62911 * q^59 + 4400 * q^60 + 32851 * q^61 + 41048 * q^62 + 138693 * q^63 + 24576 * q^64 + 11575 * q^65 + 92100 * q^66 + 54177 * q^67 + 10304 * q^68 + 5819 * q^69 + 36600 * q^70 - 14368 * q^71 + 57536 * q^72 + 33276 * q^73 + 68828 * q^74 + 6875 * q^75 + 54896 * q^76 - 143678 * q^77 + 56544 * q^78 + 74296 * q^79 + 38400 * q^80 + 150834 * q^81 + 3136 * q^82 + 65145 * q^83 - 61536 * q^84 + 16100 * q^85 + 53808 * q^86 - 790 * q^87 + 9664 * q^88 - 67562 * q^89 + 89900 * q^90 - 89487 * q^91 + 50784 * q^92 - 209450 * q^93 + 98288 * q^94 + 85775 * q^95 + 11264 * q^96 - 13201 * q^97 + 112200 * q^98 - 355951 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	26.6560	1.70998	0.854990	−	0.518644i	$-0.173563\pi$
$3$	26.6560	1.70998	0.854990	+	0.518644i	$0.173563\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	106.624	1.20914
$7$	15.2806	0.117868	0.0589340	−	0.998262i	$-0.481230\pi$
$7$	15.2806	0.117868	0.0589340	+	0.998262i	$0.481230\pi$
$8$	64.0000	0.353553
$9$	467.540	1.92403
$10$	100.000	0.316228
$11$	590.940	1.47252	0.736261	−	0.676697i	$-0.236589\pi$
$11$	590.940	1.47252	0.736261	+	0.676697i	$0.236589\pi$
$12$	426.495	0.854990
$13$	−513.344	−0.842461	−0.421231	−	0.906954i	$-0.638402\pi$
$13$	−513.344	−0.842461	−0.421231	+	0.906954i	$0.638402\pi$
$14$	61.1225	0.0833453
$15$	666.399	0.764727
$16$	256.000	0.250000
$17$	−795.921	−0.667956	−0.333978	−	0.942581i	$-0.608391\pi$
$17$	−795.921	−0.667956	−0.333978	+	0.942581i	$0.608391\pi$
$18$	1870.16	1.36050
$19$	−1142.11	−0.725809	−0.362904	−	0.931826i	$-0.618215\pi$
$19$	−1142.11	−0.725809	−0.362904	+	0.931826i	$0.618215\pi$
$20$	400.000	0.223607
$21$	407.320	0.201552
$22$	2363.76	1.04123
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	1705.98	0.604569
$25$	625.000	0.200000
$26$	−2053.37	−0.595710
$27$	5985.33	1.58008
$28$	244.490	0.0589340
$29$	1452.68	0.320755	0.160378	−	0.987056i	$-0.448729\pi$
$29$	1452.68	0.320755	0.160378	+	0.987056i	$0.448729\pi$
$30$	2665.60	0.540743
$31$	−2163.89	−0.404418	−0.202209	−	0.979342i	$-0.564812\pi$
$31$	−2163.89	−0.404418	−0.202209	+	0.979342i	$0.564812\pi$
$32$	1024.00	0.176777
$33$	15752.1	2.51799
$34$	−3183.68	−0.472316
$35$	382.016	0.0527122
$36$	7480.64	0.962017
$37$	6746.54	0.810171	0.405086	−	0.914279i	$-0.367242\pi$
$37$	6746.54	0.810171	0.405086	+	0.914279i	$0.367242\pi$
$38$	−4568.42	−0.513224
$39$	−13683.7	−1.44059
$40$	1600.00	0.158114
$41$	−4185.43	−0.388849	−0.194424	−	0.980917i	$-0.562284\pi$
$41$	−4185.43	−0.388849	−0.194424	+	0.980917i	$0.562284\pi$
$42$	1629.28	0.142519
$43$	−13595.8	−1.12133	−0.560664	−	0.828043i	$-0.689454\pi$
$43$	−13595.8	−1.12133	−0.560664	+	0.828043i	$0.689454\pi$
$44$	9455.05	0.736261
$45$	11688.5	0.860454
$46$	2116.00	0.147442
$47$	6960.01	0.459585	0.229792	−	0.973240i	$-0.426195\pi$
$47$	6960.01	0.459585	0.229792	+	0.973240i	$0.426195\pi$
$48$	6823.93	0.427495
$49$	−16573.5	−0.986107
$50$	2500.00	0.141421
$51$	−21216.0	−1.14219
$52$	−8213.50	−0.421231
$53$	15146.8	0.740680	0.370340	−	0.928896i	$-0.379241\pi$
$53$	15146.8	0.740680	0.370340	+	0.928896i	$0.379241\pi$
$54$	23941.3	1.11729
$55$	14773.5	0.658532
$56$	977.960	0.0416726
$57$	−30443.9	−1.24112
$58$	5810.71	0.226808
$59$	24369.8	0.911427	0.455713	−	0.890127i	$-0.349384\pi$
$59$	24369.8	0.911427	0.455713	+	0.890127i	$0.349384\pi$
$60$	10662.4	0.382363
$61$	−47086.1	−1.62020	−0.810100	−	0.586292i	$-0.800587\pi$
$61$	−47086.1	−1.62020	−0.810100	+	0.586292i	$0.800587\pi$
$62$	−8655.56	−0.285967
$63$	7144.31	0.226782
$64$	4096.00	0.125000
$65$	−12833.6	−0.376760
$66$	63008.3	1.78048
$67$	29592.3	0.805363	0.402681	−	0.915340i	$-0.368078\pi$
$67$	29592.3	0.805363	0.402681	+	0.915340i	$0.368078\pi$
$68$	−12734.7	−0.333978
$69$	14101.0	0.356556
$70$	1528.06	0.0372731
$71$	6016.77	0.141650	0.0708251	−	0.997489i	$-0.477437\pi$
$71$	6016.77	0.141650	0.0708251	+	0.997489i	$0.477437\pi$
$72$	29922.6	0.680249
$73$	−25209.0	−0.553666	−0.276833	−	0.960918i	$-0.589285\pi$
$73$	−25209.0	−0.553666	−0.276833	+	0.960918i	$0.589285\pi$
$74$	26986.2	0.572877
$75$	16660.0	0.341996
$76$	−18273.7	−0.362904
$77$	9029.94	0.173563
$78$	−54734.7	−1.01865
$79$	−40220.1	−0.725062	−0.362531	−	0.931972i	$-0.618087\pi$
$79$	−40220.1	−0.725062	−0.362531	+	0.931972i	$0.618087\pi$
$80$	6400.00	0.111803
$81$	45932.6	0.777872
$82$	−16741.7	−0.274958
$83$	−75788.5	−1.20756	−0.603779	−	0.797152i	$-0.706339\pi$
$83$	−75788.5	−1.20756	−0.603779	+	0.797152i	$0.706339\pi$
$84$	6517.12	0.100776
$85$	−19898.0	−0.298719
$86$	−54383.1	−0.792899
$87$	38722.5	0.548486
$88$	37820.2	0.520615
$89$	128246.	1.71621	0.858104	−	0.513476i	$-0.171642\pi$
$89$	128246.	1.71621	0.858104	+	0.513476i	$0.171642\pi$
$90$	46754.0	0.608433
$91$	−7844.21	−0.0992992
$92$	8464.00	0.104257
$93$	−57680.5	−0.691548
$94$	27840.1	0.324975
$95$	−28552.6	−0.324592
$96$	27295.7	0.302285
$97$	93910.6	1.01341	0.506705	−	0.862120i	$-0.330863\pi$
$97$	93910.6	1.01341	0.506705	+	0.862120i	$0.330863\pi$
$98$	−66294.0	−0.697283
$99$	276288.	2.83318
$100$	10000.0	0.100000
$101$	−93510.1	−0.912127	−0.456063	−	0.889947i	$-0.650741\pi$
$101$	−93510.1	−0.912127	−0.456063	+	0.889947i	$0.650741\pi$
$102$	−84864.2	−0.807651
$103$	−168581.	−1.56573	−0.782864	−	0.622193i	$-0.786242\pi$
$103$	−168581.	−1.56573	−0.782864	+	0.622193i	$0.786242\pi$
$104$	−32854.0	−0.297855
$105$	10183.0	0.0901368
$106$	60587.1	0.523740
$107$	153735.	1.29811	0.649057	−	0.760740i	$-0.275164\pi$
$107$	153735.	1.29811	0.649057	+	0.760740i	$0.275164\pi$
$108$	95765.4	0.790040
$109$	72425.7	0.583884	0.291942	−	0.956436i	$-0.405699\pi$
$109$	72425.7	0.583884	0.291942	+	0.956436i	$0.405699\pi$
$110$	59094.0	0.465653
$111$	179835.	1.38538
$112$	3911.84	0.0294670
$113$	172864.	1.27353	0.636765	−	0.771058i	$-0.280272\pi$
$113$	172864.	1.27353	0.636765	+	0.771058i	$0.280272\pi$
$114$	−121776.	−0.877603
$115$	13225.0	0.0932505
$116$	23242.8	0.160378
$117$	−240009.	−1.62092
$118$	97479.2	0.644476
$119$	−12162.2	−0.0787306
$120$	42649.5	0.270372
$121$	188160.	1.16832
$122$	−188345.	−1.14565
$123$	−111567.	−0.664924
$124$	−34622.2	−0.202209
$125$	15625.0	0.0894427
$126$	28577.2	0.160359
$127$	−167010.	−0.918827	−0.459413	−	0.888223i	$-0.651940\pi$
$127$	−167010.	−0.918827	−0.459413	+	0.888223i	$0.651940\pi$
$128$	16384.0	0.0883883
$129$	−362408.	−1.91745
$130$	−51334.4	−0.266410
$131$	−233391.	−1.18824	−0.594121	−	0.804376i	$-0.702500\pi$
$131$	−233391.	−1.18824	−0.594121	+	0.804376i	$0.702500\pi$
$132$	252033.	1.25899
$133$	−17452.1	−0.0855496
$134$	118369.	0.569477
$135$	149633.	0.706633
$136$	−50939.0	−0.236158
$137$	−85228.6	−0.387957	−0.193979	−	0.981006i	$-0.562139\pi$
$137$	−85228.6	−0.387957	−0.193979	+	0.981006i	$0.562139\pi$
$138$	56404.0	0.252123
$139$	−113421.	−0.497918	−0.248959	−	0.968514i	$-0.580088\pi$
$139$	−113421.	−0.497918	−0.248959	+	0.968514i	$0.580088\pi$
$140$	6112.25	0.0263561
$141$	185526.	0.785881
$142$	24067.1	0.100162
$143$	−303356.	−1.24054
$144$	119690.	0.481008
$145$	36316.9	0.143446
$146$	−100836.	−0.391501
$147$	−441783.	−1.68622
$148$	107945.	0.405086
$149$	−111669.	−0.412067	−0.206034	−	0.978545i	$-0.566056\pi$
$149$	−111669.	−0.412067	−0.206034	+	0.978545i	$0.566056\pi$
$150$	66639.9	0.241828
$151$	−74238.8	−0.264965	−0.132483	−	0.991185i	$-0.542295\pi$
$151$	−74238.8	−0.264965	−0.132483	+	0.991185i	$0.542295\pi$
$152$	−73094.7	−0.256612
$153$	−372125.	−1.28517
$154$	36119.8	0.122728
$155$	−54097.2	−0.180861
$156$	−218939.	−0.720296
$157$	115034.	0.372457	0.186228	−	0.982507i	$-0.440374\pi$
$157$	115034.	0.372457	0.186228	+	0.982507i	$0.440374\pi$
$158$	−160880.	−0.512696
$159$	403752.	1.26655
$160$	25600.0	0.0790569
$161$	8083.45	0.0245772
$162$	183730.	0.550039
$163$	−359441.	−1.05964	−0.529820	−	0.848110i	$-0.677741\pi$
$163$	−359441.	−1.05964	−0.529820	+	0.848110i	$0.677741\pi$
$164$	−66966.9	−0.194424
$165$	393802.	1.12608
$166$	−303154.	−0.853872
$167$	−533437.	−1.48010	−0.740052	−	0.672550i	$-0.765199\pi$
$167$	−533437.	−1.48010	−0.740052	+	0.672550i	$0.765199\pi$
$168$	26068.5	0.0712594
$169$	−107771.	−0.290259
$170$	−79592.1	−0.211226
$171$	−533980.	−1.39648
$172$	−217532.	−0.560664
$173$	−443013.	−1.12538	−0.562692	−	0.826667i	$-0.690234\pi$
$173$	−443013.	−1.12538	−0.562692	+	0.826667i	$0.690234\pi$
$174$	154890.	0.387838
$175$	9550.39	0.0235736
$176$	151281.	0.368131
$177$	649600.	1.55852
$178$	512985.	1.21354
$179$	572856.	1.33633	0.668164	−	0.744014i	$-0.267081\pi$
$179$	572856.	1.33633	0.668164	+	0.744014i	$0.267081\pi$
$180$	187016.	0.430227
$181$	−9825.78	−0.0222931	−0.0111466	−	0.999938i	$-0.503548\pi$
$181$	−9825.78	−0.0222931	−0.0111466	+	0.999938i	$0.503548\pi$
$182$	−31376.8	−0.0702151
$183$	−1.25513e6	−2.77051
$184$	33856.0	0.0737210
$185$	168663.	0.362320
$186$	−230722.	−0.488998
$187$	−470342.	−0.983580
$188$	111360.	0.229792
$189$	91459.7	0.186241
$190$	−114211.	−0.229521
$191$	547656.	1.08624	0.543118	−	0.839656i	$-0.317243\pi$
$191$	547656.	1.08624	0.543118	+	0.839656i	$0.317243\pi$
$192$	109183.	0.213748
$193$	648128.	1.25247	0.626235	−	0.779634i	$-0.284595\pi$
$193$	648128.	1.25247	0.626235	+	0.779634i	$0.284595\pi$
$194$	375642.	0.716589
$195$	−342092.	−0.644252
$196$	−265176.	−0.493054
$197$	155985.	0.286363	0.143181	−	0.989696i	$-0.454267\pi$
$197$	155985.	0.286363	0.143181	+	0.989696i	$0.454267\pi$
$198$	1.10515e6	2.00336
$199$	−933973.	−1.67187	−0.835933	−	0.548831i	$-0.815073\pi$
$199$	−933973.	−1.67187	−0.835933	+	0.548831i	$0.815073\pi$
$200$	40000.0	0.0707107
$201$	788811.	1.37715
$202$	−374041.	−0.644971
$203$	22197.8	0.0378068
$204$	−339457.	−0.571096
$205$	−104636.	−0.173899
$206$	−674325.	−1.10714
$207$	247329.	0.401189
$208$	−131416.	−0.210615
$209$	−674916.	−1.06877
$210$	40732.0	0.0637363
$211$	−140526.	−0.217295	−0.108648	−	0.994080i	$-0.534652\pi$
$211$	−140526.	−0.217295	−0.108648	+	0.994080i	$0.534652\pi$
$212$	242349.	0.370340
$213$	160383.	0.242219
$214$	614939.	0.917905
$215$	−339894.	−0.501473
$216$	383061.	0.558643
$217$	−33065.6	−0.0476680
$218$	289703.	0.412868
$219$	−671969.	−0.946758
$220$	236376.	0.329266
$221$	408581.	0.562727
$222$	719342.	0.979609
$223$	−605154.	−0.814899	−0.407449	−	0.913228i	$-0.633582\pi$
$223$	−605154.	−0.814899	−0.407449	+	0.913228i	$0.633582\pi$
$224$	15647.4	0.0208363
$225$	292213.	0.384807
$226$	691458.	0.900522
$227$	64590.0	0.0831956	0.0415978	−	0.999134i	$-0.486755\pi$
$227$	64590.0	0.0831956	0.0415978	+	0.999134i	$0.486755\pi$
$228$	−487103.	−0.620559
$229$	−1.18196e6	−1.48941	−0.744706	−	0.667393i	$-0.767410\pi$
$229$	−1.18196e6	−1.48941	−0.744706	+	0.667393i	$0.767410\pi$
$230$	52900.0	0.0659380
$231$	240702.	0.296790
$232$	92971.3	0.113404
$233$	−1.30264e6	−1.57193	−0.785966	−	0.618270i	$-0.787834\pi$
$233$	−1.30264e6	−1.57193	−0.785966	+	0.618270i	$0.787834\pi$
$234$	−960035.	−1.14617
$235$	174000.	0.205532
$236$	389917.	0.455713
$237$	−1.07210e6	−1.23984
$238$	−48648.7	−0.0556710
$239$	−133507.	−0.151186	−0.0755928	−	0.997139i	$-0.524085\pi$
$239$	−133507.	−0.151186	−0.0755928	+	0.997139i	$0.524085\pi$
$240$	170598.	0.191182
$241$	1.46113e6	1.62049	0.810246	−	0.586090i	$-0.199334\pi$
$241$	1.46113e6	1.62049	0.810246	+	0.586090i	$0.199334\pi$
$242$	752638.	0.826129
$243$	−230059.	−0.249933
$244$	−753378.	−0.810100
$245$	−414338.	−0.441001
$246$	−446267.	−0.470172
$247$	586293.	0.611466
$248$	−138489.	−0.142983
$249$	−2.02021e6	−2.06490
$250$	62500.0	0.0632456
$251$	193195.	0.193558	0.0967790	−	0.995306i	$-0.469146\pi$
$251$	193195.	0.193558	0.0967790	+	0.995306i	$0.469146\pi$
$252$	114309.	0.113391
$253$	312607.	0.307042
$254$	−668041.	−0.649708
$255$	−530401.	−0.510804
$256$	65536.0	0.0625000
$257$	2.00392e6	1.89255	0.946276	−	0.323361i	$-0.104813\pi$
$257$	2.00392e6	1.89255	0.946276	+	0.323361i	$0.104813\pi$
$258$	−1.44963e6	−1.35584
$259$	103091.	0.0954933
$260$	−205337.	−0.188380
$261$	679185.	0.617144
$262$	−933562.	−0.840214
$263$	1.96744e6	1.75393	0.876965	−	0.480553i	$-0.159564\pi$
$263$	1.96744e6	1.75393	0.876965	+	0.480553i	$0.159564\pi$
$264$	1.00813e6	0.890242
$265$	378670.	0.331242
$266$	−69808.3	−0.0604927
$267$	3.41853e6	2.93468
$268$	473476.	0.402681
$269$	−1.29643e6	−1.09237	−0.546184	−	0.837665i	$-0.683920\pi$
$269$	−1.29643e6	−1.09237	−0.546184	+	0.837665i	$0.683920\pi$
$270$	598533.	0.499665
$271$	768923.	0.636003	0.318002	−	0.948090i	$-0.396988\pi$
$271$	768923.	0.636003	0.318002	+	0.948090i	$0.396988\pi$
$272$	−203756.	−0.166989
$273$	−209095.	−0.169800
$274$	−340914.	−0.274327
$275$	369338.	0.294505
$276$	225616.	0.178278
$277$	−49248.6	−0.0385651	−0.0192826	−	0.999814i	$-0.506138\pi$
$277$	−49248.6	−0.0385651	−0.0192826	+	0.999814i	$0.506138\pi$
$278$	−453686.	−0.352081
$279$	−1.01171e6	−0.778115
$280$	24449.0	0.0186366
$281$	1.52733e6	1.15390	0.576949	−	0.816780i	$-0.304243\pi$
$281$	1.52733e6	1.15390	0.576949	+	0.816780i	$0.304243\pi$
$282$	742103.	0.555702
$283$	1.72871e6	1.28309	0.641545	−	0.767086i	$-0.278294\pi$
$283$	1.72871e6	1.28309	0.641545	+	0.767086i	$0.278294\pi$
$284$	96268.3	0.0708251
$285$	−761098.	−0.555045
$286$	−1.21342e6	−0.877196
$287$	−63956.0	−0.0458328
$288$	478761.	0.340124
$289$	−786367.	−0.553835
$290$	145268.	0.101432
$291$	2.50328e6	1.73291
$292$	−403343.	−0.276833
$293$	−183369.	−0.124783	−0.0623916	−	0.998052i	$-0.519873\pi$
$293$	−183369.	−0.124783	−0.0623916	+	0.998052i	$0.519873\pi$
$294$	−1.76713e6	−1.19234
$295$	609245.	0.407602
$296$	431779.	0.286439
$297$	3.53698e6	2.32670
$298$	−446677.	−0.291376
$299$	−271559.	−0.175665
$300$	266560.	0.170998
$301$	−207752.	−0.132169
$302$	−296955.	−0.187359
$303$	−2.49260e6	−1.55972
$304$	−292379.	−0.181452
$305$	−1.17715e6	−0.724575
$306$	−1.48850e6	−0.908752
$307$	836706.	0.506672	0.253336	−	0.967378i	$-0.418472\pi$
$307$	836706.	0.506672	0.253336	+	0.967378i	$0.418472\pi$
$308$	144479.	0.0867817
$309$	−4.49369e6	−2.67736
$310$	−216389.	−0.127888
$311$	−3.00757e6	−1.76326	−0.881628	−	0.471945i	$-0.843552\pi$
$311$	−3.00757e6	−1.76326	−0.881628	+	0.471945i	$0.843552\pi$
$312$	−875755.	−0.509326
$313$	−409391.	−0.236199	−0.118099	−	0.993002i	$-0.537680\pi$
$313$	−409391.	−0.236199	−0.118099	+	0.993002i	$0.537680\pi$
$314$	460134.	0.263367
$315$	178608.	0.101420
$316$	−643521.	−0.362531
$317$	2.54549e6	1.42273	0.711365	−	0.702823i	$-0.248077\pi$
$317$	2.54549e6	1.42273	0.711365	+	0.702823i	$0.248077\pi$
$318$	1.61501e6	0.895585
$319$	858446.	0.472320
$320$	102400.	0.0559017
$321$	4.09795e6	2.21975
$322$	32333.8	0.0173787
$323$	909026.	0.484808
$324$	734921.	0.388936
$325$	−320840.	−0.168492
$326$	−1.43776e6	−0.749279
$327$	1.93058e6	0.998430
$328$	−267868.	−0.137479
$329$	106353.	0.0541703
$330$	1.57521e6	0.796257
$331$	165588.	0.0830726	0.0415363	−	0.999137i	$-0.486775\pi$
$331$	165588.	0.0830726	0.0415363	+	0.999137i	$0.486775\pi$
$332$	−1.21262e6	−0.603779
$333$	3.15428e6	1.55880
$334$	−2.13375e6	−1.04659
$335$	739807.	0.360169
$336$	104274.	0.0503880
$337$	894673.	0.429131	0.214565	−	0.976710i	$-0.431167\pi$
$337$	894673.	0.429131	0.214565	+	0.976710i	$0.431167\pi$
$338$	−431085.	−0.205244
$339$	4.60787e6	2.17771
$340$	−318368.	−0.149359
$341$	−1.27873e6	−0.595515
$342$	−2.13592e6	−0.987461
$343$	−510075.	−0.234099
$344$	−870129.	−0.396449
$345$	352525.	0.159457
$346$	−1.77205e6	−0.795767
$347$	3.19279e6	1.42347	0.711733	−	0.702450i	$-0.247911\pi$
$347$	3.19279e6	1.42347	0.711733	+	0.702450i	$0.247911\pi$
$348$	619560.	0.274243
$349$	2.43928e6	1.07201	0.536004	−	0.844216i	$-0.319933\pi$
$349$	2.43928e6	1.07201	0.536004	+	0.844216i	$0.319933\pi$
$350$	38201.6	0.0166691
$351$	−3.07253e6	−1.33116
$352$	605123.	0.260308
$353$	3.54188e6	1.51285	0.756426	−	0.654079i	$-0.226944\pi$
$353$	3.54188e6	1.51285	0.756426	+	0.654079i	$0.226944\pi$
$354$	2.59840e6	1.10204
$355$	150419.	0.0633479
$356$	2.05194e6	0.858104
$357$	−324194.	−0.134628
$358$	2.29142e6	0.944926
$359$	249105.	0.102011	0.0510054	−	0.998698i	$-0.483757\pi$
$359$	249105.	0.102011	0.0510054	+	0.998698i	$0.483757\pi$
$360$	748064.	0.304216
$361$	−1.17169e6	−0.473202
$362$	−39303.1	−0.0157636
$363$	5.01557e6	1.99781
$364$	−125507.	−0.0496496
$365$	−630224.	−0.247607
$366$	−5.02050e6	−1.95905
$367$	4.82143e6	1.86858	0.934288	−	0.356518i	$-0.116036\pi$
$367$	4.82143e6	1.86858	0.934288	+	0.356518i	$0.116036\pi$
$368$	135424.	0.0521286
$369$	−1.95686e6	−0.748158
$370$	674654.	0.256199
$371$	231452.	0.0873025
$372$	−922889.	−0.345774
$373$	4.57727e6	1.70347	0.851736	−	0.523972i	$-0.175550\pi$
$373$	4.57727e6	1.70347	0.851736	+	0.523972i	$0.175550\pi$
$374$	−1.88137e6	−0.695496
$375$	416499.	0.152945
$376$	445441.	0.162488
$377$	−745722.	−0.270224
$378$	365839.	0.131692
$379$	452370.	0.161769	0.0808845	−	0.996723i	$-0.474226\pi$
$379$	452370.	0.161769	0.0808845	+	0.996723i	$0.474226\pi$
$380$	−456842.	−0.162296
$381$	−4.45182e6	−1.57118
$382$	2.19062e6	0.768085
$383$	−1.47890e6	−0.515159	−0.257580	−	0.966257i	$-0.582925\pi$
$383$	−1.47890e6	−0.515159	−0.257580	+	0.966257i	$0.582925\pi$
$384$	436731.	0.151142
$385$	225748.	0.0776199
$386$	2.59251e6	0.885630
$387$	−6.35657e6	−2.15747
$388$	1.50257e6	0.506705
$389$	−1.60068e6	−0.536328	−0.268164	−	0.963373i	$-0.586417\pi$
$389$	−1.60068e6	−0.536328	−0.268164	+	0.963373i	$0.586417\pi$
$390$	−1.36837e6	−0.455555
$391$	−421042.	−0.139278
$392$	−1.06070e6	−0.348642
$393$	−6.22125e6	−2.03187
$394$	623939.	0.202489
$395$	−1.00550e6	−0.324257
$396$	4.42061e6	1.41659
$397$	−2.93872e6	−0.935796	−0.467898	−	0.883782i	$-0.654989\pi$
$397$	−2.93872e6	−0.935796	−0.467898	+	0.883782i	$0.654989\pi$
$398$	−3.73589e6	−1.18219
$399$	−465202.	−0.146288
$400$	160000.	0.0500000
$401$	−1.12195e6	−0.348428	−0.174214	−	0.984708i	$-0.555739\pi$
$401$	−1.12195e6	−0.348428	−0.174214	+	0.984708i	$0.555739\pi$
$402$	3.15524e6	0.973795
$403$	1.11082e6	0.340707
$404$	−1.49616e6	−0.456063
$405$	1.14831e6	0.347875
$406$	88791.2	0.0267335
$407$	3.98680e6	1.19300
$408$	−1.35783e6	−0.403826
$409$	872155.	0.257802	0.128901	−	0.991657i	$-0.458855\pi$
$409$	872155.	0.257802	0.128901	+	0.991657i	$0.458855\pi$
$410$	−418543.	−0.122965
$411$	−2.27185e6	−0.663400
$412$	−2.69730e6	−0.782864
$413$	372386.	0.107428
$414$	989315.	0.283683
$415$	−1.89471e6	−0.540036
$416$	−525664.	−0.148927
$417$	−3.02336e6	−0.851430
$418$	−2.69966e6	−0.755734
$419$	511313.	0.142282	0.0711412	−	0.997466i	$-0.477336\pi$
$419$	511313.	0.142282	0.0711412	+	0.997466i	$0.477336\pi$
$420$	162928.	0.0450684
$421$	3.29914e6	0.907183	0.453591	−	0.891210i	$-0.350143\pi$
$421$	3.29914e6	0.907183	0.453591	+	0.891210i	$0.350143\pi$
$422$	−562104.	−0.153651
$423$	3.25409e6	0.884256
$424$	969394.	0.261870
$425$	−497451.	−0.133591
$426$	641531.	0.171275
$427$	−719506.	−0.190970
$428$	2.45976e6	0.649057
$429$	−8.08623e6	−2.12130
$430$	−1.35958e6	−0.354595
$431$	2.07516e6	0.538095	0.269048	−	0.963127i	$-0.413291\pi$
$431$	2.07516e6	0.538095	0.269048	+	0.963127i	$0.413291\pi$
$432$	1.53225e6	0.395020
$433$	−5.60530e6	−1.43674	−0.718372	−	0.695659i	$-0.755112\pi$
$433$	−5.60530e6	−1.43674	−0.718372	+	0.695659i	$0.755112\pi$
$434$	−132262.	−0.0337064
$435$	968062.	0.245290
$436$	1.15881e6	0.291942
$437$	−604174.	−0.151342
$438$	−2.68788e6	−0.669459
$439$	582556.	0.144270	0.0721351	−	0.997395i	$-0.477019\pi$
$439$	582556.	0.144270	0.0721351	+	0.997395i	$0.477019\pi$
$440$	945505.	0.232826
$441$	−7.74878e6	−1.89730
$442$	1.63432e6	0.397908
$443$	−7.81819e6	−1.89277	−0.946383	−	0.323046i	$-0.895293\pi$
$443$	−7.81819e6	−1.89277	−0.946383	+	0.323046i	$0.895293\pi$
$444$	2.87737e6	0.692688
$445$	3.20616e6	0.767512
$446$	−2.42062e6	−0.576220
$447$	−2.97665e6	−0.704627
$448$	62589.4	0.0147335
$449$	−692204.	−0.162039	−0.0810193	−	0.996713i	$-0.525818\pi$
$449$	−692204.	−0.162039	−0.0810193	+	0.996713i	$0.525818\pi$
$450$	1.16885e6	0.272099
$451$	−2.47334e6	−0.572589
$452$	2.76583e6	0.636765
$453$	−1.97891e6	−0.453085
$454$	258360.	0.0588282
$455$	−196105.	−0.0444080
$456$	−1.94841e6	−0.438802
$457$	−3.49967e6	−0.783857	−0.391928	−	0.919996i	$-0.628192\pi$
$457$	−3.49967e6	−0.783857	−0.391928	+	0.919996i	$0.628192\pi$
$458$	−4.72785e6	−1.05317
$459$	−4.76385e6	−1.05542
$460$	211600.	0.0466252
$461$	−3.54531e6	−0.776965	−0.388483	−	0.921456i	$-0.627001\pi$
$461$	−3.54531e6	−0.776965	−0.388483	+	0.921456i	$0.627001\pi$
$462$	962807.	0.209862
$463$	−6.53280e6	−1.41627	−0.708137	−	0.706075i	$-0.750464\pi$
$463$	−6.53280e6	−1.41627	−0.708137	+	0.706075i	$0.750464\pi$
$464$	371885.	0.0801889
$465$	−1.44201e6	−0.309269
$466$	−5.21055e6	−1.11152
$467$	6.64502e6	1.40995	0.704975	−	0.709232i	$-0.250958\pi$
$467$	6.64502e6	1.40995	0.704975	+	0.709232i	$0.250958\pi$
$468$	−3.84014e6	−0.810462
$469$	452189.	0.0949265
$470$	696001.	0.145333
$471$	3.06633e6	0.636893
$472$	1.55967e6	0.322238
$473$	−8.03429e6	−1.65118
$474$	−4.28842e6	−0.876700
$475$	−713816.	−0.145162
$476$	−194595.	−0.0393653
$477$	7.08173e6	1.42509
$478$	−534030.	−0.106904
$479$	7.70995e6	1.53537	0.767684	−	0.640829i	$-0.221409\pi$
$479$	7.70995e6	1.53537	0.767684	+	0.640829i	$0.221409\pi$
$480$	682393.	0.135186
$481$	−3.46329e6	−0.682538
$482$	5.84453e6	1.14586
$483$	215472.	0.0420265
$484$	3.01055e6	0.584162
$485$	2.34776e6	0.453211
$486$	−920238.	−0.176730
$487$	−3.48115e6	−0.665120	−0.332560	−	0.943082i	$-0.607912\pi$
$487$	−3.48115e6	−0.665120	−0.332560	+	0.943082i	$0.607912\pi$
$488$	−3.01351e6	−0.572827
$489$	−9.58125e6	−1.81197
$490$	−1.65735e6	−0.311834
$491$	5.79243e6	1.08432	0.542160	−	0.840276i	$-0.317607\pi$
$491$	5.79243e6	1.08432	0.542160	+	0.840276i	$0.317607\pi$
$492$	−1.78507e6	−0.332462
$493$	−1.15622e6	−0.214250
$494$	2.34517e6	0.432371
$495$	6.90721e6	1.26704
$496$	−553956.	−0.101105
$497$	91940.0	0.0166960
$498$	−8.08086e6	−1.46011
$499$	7.31795e6	1.31564	0.657821	−	0.753174i	$-0.271478\pi$
$499$	7.31795e6	1.31564	0.657821	+	0.753174i	$0.271478\pi$
$500$	250000.	0.0447214
$501$	−1.42193e7	−2.53095
$502$	772779.	0.136866
$503$	2.45659e6	0.432925	0.216463	−	0.976291i	$-0.430548\pi$
$503$	2.45659e6	0.432925	0.216463	+	0.976291i	$0.430548\pi$
$504$	457236.	0.0801796
$505$	−2.33775e6	−0.407916
$506$	1.25043e6	0.217112
$507$	−2.87275e6	−0.496338
$508$	−2.67216e6	−0.459413
$509$	1.10997e7	1.89896	0.949482	−	0.313821i	$-0.101609\pi$
$509$	1.10997e7	1.89896	0.949482	+	0.313821i	$0.101609\pi$
$510$	−2.12160e6	−0.361193
$511$	−385209.	−0.0652595
$512$	262144.	0.0441942
$513$	−6.83588e6	−1.14684
$514$	8.01568e6	1.33824
$515$	−4.21453e6	−0.700214
$516$	−5.79853e6	−0.958725
$517$	4.11295e6	0.676749
$518$	412365.	0.0675239
$519$	−1.18089e7	−1.92439
$520$	−821350.	−0.133205
$521$	−1.46922e6	−0.237133	−0.118567	−	0.992946i	$-0.537830\pi$
$521$	−1.46922e6	−0.237133	−0.118567	+	0.992946i	$0.537830\pi$
$522$	2.71674e6	0.436387
$523$	4.99461e6	0.798449	0.399225	−	0.916853i	$-0.369279\pi$
$523$	4.99461e6	0.798449	0.399225	+	0.916853i	$0.369279\pi$
$524$	−3.73425e6	−0.594121
$525$	254575.	0.0403104
$526$	7.86977e6	1.24022
$527$	1.72229e6	0.270134
$528$	4.03253e6	0.629496
$529$	279841.	0.0434783
$530$	1.51468e6	0.234224
$531$	1.13939e7	1.75362
$532$	−279233.	−0.0427748
$533$	2.14857e6	0.327590
$534$	1.36741e7	2.07513
$535$	3.84337e6	0.580534
$536$	1.89391e6	0.284739
$537$	1.52700e7	2.28509
$538$	−5.18573e6	−0.772421
$539$	−9.79395e6	−1.45207
$540$	2.39413e6	0.353317
$541$	7.11573e6	1.04527	0.522633	−	0.852558i	$-0.324950\pi$
$541$	7.11573e6	1.04527	0.522633	+	0.852558i	$0.324950\pi$
$542$	3.07569e6	0.449722
$543$	−261916.	−0.0381208
$544$	−815023.	−0.118079
$545$	1.81064e6	0.261121
$546$	−836380.	−0.120067
$547$	1.20186e7	1.71746	0.858728	−	0.512432i	$-0.171255\pi$
$547$	1.20186e7	1.71746	0.858728	+	0.512432i	$0.171255\pi$
$548$	−1.36366e6	−0.193979
$549$	−2.20147e7	−3.11732
$550$	1.47735e6	0.208246
$551$	−1.65911e6	−0.232807
$552$	902464.	0.126061
$553$	−614588.	−0.0854616
$554$	−196995.	−0.0272697
$555$	4.49589e6	0.619559
$556$	−1.81474e6	−0.248959
$557$	−4.55097e6	−0.621536	−0.310768	−	0.950486i	$-0.600586\pi$
$557$	−4.55097e6	−0.621536	−0.310768	+	0.950486i	$0.600586\pi$
$558$	−4.04682e6	−0.550210
$559$	6.97930e6	0.944675
$560$	97796.0	0.0131780
$561$	−1.25374e7	−1.68190
$562$	6.10932e6	0.815929
$563$	1.39922e7	1.86044	0.930221	−	0.366999i	$-0.119615\pi$
$563$	1.39922e7	1.86044	0.930221	+	0.366999i	$0.119615\pi$
$564$	2.96841e6	0.392940
$565$	4.32161e6	0.569540
$566$	6.91485e6	0.907281
$567$	701878.	0.0916863
$568$	385073.	0.0500809
$569$	−1.00431e7	−1.30043	−0.650214	−	0.759751i	$-0.725321\pi$
$569$	−1.00431e7	−1.30043	−0.650214	+	0.759751i	$0.725321\pi$
$570$	−3.04439e6	−0.392476
$571$	1.35291e7	1.73652	0.868261	−	0.496109i	$-0.165238\pi$
$571$	1.35291e7	1.73652	0.868261	+	0.496109i	$0.165238\pi$
$572$	−4.85369e6	−0.620271
$573$	1.45983e7	1.85744
$574$	−255824.	−0.0324087
$575$	330625.	0.0417029
$576$	1.91504e6	0.240504
$577$	1.32937e7	1.66228	0.831142	−	0.556060i	$-0.187688\pi$
$577$	1.32937e7	1.66228	0.831142	+	0.556060i	$0.187688\pi$
$578$	−3.14547e6	−0.391620
$579$	1.72765e7	2.14170
$580$	581071.	0.0717231
$581$	−1.15810e6	−0.142332
$582$	1.00131e7	1.22535
$583$	8.95085e6	1.09067
$584$	−1.61337e6	−0.195750
$585$	−6.00022e6	−0.724899
$586$	−733474.	−0.0882350
$587$	−1.26268e7	−1.51251	−0.756254	−	0.654278i	$-0.772973\pi$
$587$	−1.26268e7	−1.51251	−0.756254	+	0.654278i	$0.772973\pi$
$588$	−7.06852e6	−0.843112
$589$	2.47139e6	0.293530
$590$	2.43698e6	0.288218
$591$	4.15792e6	0.489675
$592$	1.72711e6	0.202543
$593$	8.76950e6	1.02409	0.512045	−	0.858959i	$-0.328888\pi$
$593$	8.76950e6	1.02409	0.512045	+	0.858959i	$0.328888\pi$
$594$	1.41479e7	1.64523
$595$	−304054.	−0.0352094
$596$	−1.78671e6	−0.206034
$597$	−2.48959e7	−2.85886
$598$	−1.08624e6	−0.124214
$599$	1.32722e7	1.51139	0.755696	−	0.654922i	$-0.227299\pi$
$599$	1.32722e7	1.51139	0.755696	+	0.654922i	$0.227299\pi$
$600$	1.06624e6	0.120914
$601$	−6.54962e6	−0.739656	−0.369828	−	0.929100i	$-0.620583\pi$
$601$	−6.54962e6	−0.739656	−0.369828	+	0.929100i	$0.620583\pi$
$602$	−831007.	−0.0934574
$603$	1.38356e7	1.54954
$604$	−1.18782e6	−0.132483
$605$	4.70399e6	0.522490
$606$	−9.97041e6	−1.10289
$607$	428144.	0.0471649	0.0235824	−	0.999722i	$-0.492493\pi$
$607$	428144.	0.0471649	0.0235824	+	0.999722i	$0.492493\pi$
$608$	−1.16952e6	−0.128306
$609$	591704.	0.0646489
$610$	−4.70861e6	−0.512352
$611$	−3.57288e6	−0.387182
$612$	−5.95400e6	−0.642585
$613$	−4.95662e6	−0.532764	−0.266382	−	0.963868i	$-0.585828\pi$
$613$	−4.95662e6	−0.532764	−0.266382	+	0.963868i	$0.585828\pi$
$614$	3.34683e6	0.358271
$615$	−2.78917e6	−0.297363
$616$	577916.	0.0613639
$617$	−6.58903e6	−0.696801	−0.348400	−	0.937346i	$-0.613275\pi$
$617$	−6.58903e6	−0.696801	−0.348400	+	0.937346i	$0.613275\pi$
$618$	−1.79748e7	−1.89318
$619$	−3.94623e6	−0.413957	−0.206979	−	0.978345i	$-0.566363\pi$
$619$	−3.94623e6	−0.413957	−0.206979	+	0.978345i	$0.566363\pi$
$620$	−865556.	−0.0904307
$621$	3.16624e6	0.329469
$622$	−1.20303e7	−1.24681
$623$	1.95968e6	0.202286
$624$	−3.50302e6	−0.360148
$625$	390625.	0.0400000
$626$	−1.63756e6	−0.167018
$627$	−1.79905e7	−1.82758
$628$	1.84054e6	0.186228
$629$	−5.36971e6	−0.541159
$630$	714431.	0.0717148
$631$	5.71344e6	0.571247	0.285624	−	0.958342i	$-0.407799\pi$
$631$	5.71344e6	0.571247	0.285624	+	0.958342i	$0.407799\pi$
$632$	−2.57408e6	−0.256348
$633$	−3.74586e6	−0.371571
$634$	1.01819e7	1.00602
$635$	−4.17525e6	−0.410912
$636$	6.46003e6	0.633274
$637$	8.50790e6	0.830757
$638$	3.43378e6	0.333980
$639$	2.81308e6	0.272540
$640$	409600.	0.0395285
$641$	−9.11991e6	−0.876688	−0.438344	−	0.898807i	$-0.644435\pi$
$641$	−9.11991e6	−0.876688	−0.438344	+	0.898807i	$0.644435\pi$
$642$	1.63918e7	1.56960
$643$	8.44392e6	0.805409	0.402705	−	0.915330i	$-0.368070\pi$
$643$	8.44392e6	0.805409	0.402705	+	0.915330i	$0.368070\pi$
$644$	129335.	0.0122886
$645$	−9.06021e6	−0.857509
$646$	3.63610e6	0.342811
$647$	7.24130e6	0.680074	0.340037	−	0.940412i	$-0.389560\pi$
$647$	7.24130e6	0.680074	0.340037	+	0.940412i	$0.389560\pi$
$648$	2.93968e6	0.275019
$649$	1.44011e7	1.34210
$650$	−1.28336e6	−0.119142
$651$	−881395.	−0.0815113
$652$	−5.75106e6	−0.529820
$653$	−1.12506e7	−1.03251	−0.516253	−	0.856436i	$-0.672674\pi$
$653$	−1.12506e7	−1.03251	−0.516253	+	0.856436i	$0.672674\pi$
$654$	7.72230e6	0.705996
$655$	−5.83476e6	−0.531398
$656$	−1.07147e6	−0.0972122
$657$	−1.17862e7	−1.06527
$658$	425413.	0.0383042
$659$	−2.44847e6	−0.219625	−0.109812	−	0.993952i	$-0.535025\pi$
$659$	−2.44847e6	−0.219625	−0.109812	+	0.993952i	$0.535025\pi$
$660$	6.30083e6	0.563039
$661$	1.80096e7	1.60325	0.801626	−	0.597826i	$-0.203969\pi$
$661$	1.80096e7	1.60325	0.801626	+	0.597826i	$0.203969\pi$
$662$	662351.	0.0587412
$663$	1.08911e7	0.962252
$664$	−4.85046e6	−0.426936
$665$	−436302.	−0.0382590
$666$	1.26171e7	1.10224
$667$	768466.	0.0668821
$668$	−8.53499e6	−0.740052
$669$	−1.61310e7	−1.39346
$670$	2.95923e6	0.254678
$671$	−2.78251e7	−2.38578
$672$	417095.	0.0356297
$673$	8.35786e6	0.711308	0.355654	−	0.934618i	$-0.384258\pi$
$673$	8.35786e6	0.711308	0.355654	+	0.934618i	$0.384258\pi$
$674$	3.57869e6	0.303441
$675$	3.74083e6	0.316016
$676$	−1.72434e6	−0.145130
$677$	9.38655e6	0.787108	0.393554	−	0.919302i	$-0.371245\pi$
$677$	9.38655e6	0.787108	0.393554	+	0.919302i	$0.371245\pi$
$678$	1.84315e7	1.53988
$679$	1.43501e6	0.119449
$680$	−1.27347e6	−0.105613
$681$	1.72171e6	0.142263
$682$	−5.11492e6	−0.421093
$683$	−1.12665e6	−0.0924141	−0.0462070	−	0.998932i	$-0.514713\pi$
$683$	−1.12665e6	−0.0924141	−0.0462070	+	0.998932i	$0.514713\pi$
$684$	−8.54368e6	−0.698240
$685$	−2.13072e6	−0.173500
$686$	−2.04030e6	−0.165533
$687$	−3.15063e7	−2.54686
$688$	−3.48052e6	−0.280332
$689$	−7.77550e6	−0.623994
$690$	1.41010e6	0.112753
$691$	1.36151e7	1.08474	0.542372	−	0.840139i	$-0.317526\pi$
$691$	1.36151e7	1.08474	0.542372	+	0.840139i	$0.317526\pi$
$692$	−7.08820e6	−0.562692
$693$	4.22186e6	0.333942
$694$	1.27712e7	1.00654
$695$	−2.83554e6	−0.222676
$696$	2.47824e6	0.193919
$697$	3.33128e6	0.259734
$698$	9.75711e6	0.758023
$699$	−3.47230e7	−2.68797
$700$	152806.	0.0117868
$701$	−652129.	−0.0501231	−0.0250616	−	0.999686i	$-0.507978\pi$
$701$	−652129.	−0.0501231	−0.0250616	+	0.999686i	$0.507978\pi$
$702$	−1.22901e7	−0.941269
$703$	−7.70526e6	−0.588029
$704$	2.42049e6	0.184065
$705$	4.63815e6	0.351457
$706$	1.41675e7	1.06975
$707$	−1.42889e6	−0.107511
$708$	1.03936e7	0.779261
$709$	1.39228e7	1.04019	0.520095	−	0.854109i	$-0.325897\pi$
$709$	1.39228e7	1.04019	0.520095	+	0.854109i	$0.325897\pi$
$710$	601677.	0.0447938
$711$	−1.88045e7	−1.39504
$712$	8.20776e6	0.606771
$713$	−1.14470e6	−0.0843270
$714$	−1.29678e6	−0.0951963
$715$	−7.58389e6	−0.554788
$716$	9.16569e6	0.668164
$717$	−3.55877e6	−0.258525
$718$	996419.	0.0721325
$719$	−2.51878e7	−1.81705	−0.908526	−	0.417829i	$-0.862791\pi$
$719$	−2.51878e7	−1.81705	−0.908526	+	0.417829i	$0.862791\pi$
$720$	2.99226e6	0.215114
$721$	−2.57603e6	−0.184549
$722$	−4.68678e6	−0.334604
$723$	3.89479e7	2.77101
$724$	−157212.	−0.0111466
$725$	907923.	0.0641511
$726$	2.00623e7	1.41266
$727$	1.99882e6	0.140261	0.0701306	−	0.997538i	$-0.477658\pi$
$727$	1.99882e6	0.140261	0.0701306	+	0.997538i	$0.477658\pi$
$728$	−502030.	−0.0351076
$729$	−1.72941e7	−1.20525
$730$	−2.52090e6	−0.175085
$731$	1.08212e7	0.748998
$732$	−2.00820e7	−1.38525
$733$	−9.45485e6	−0.649972	−0.324986	−	0.945719i	$-0.605360\pi$
$733$	−9.45485e6	−0.649972	−0.324986	+	0.945719i	$0.605360\pi$
$734$	1.92857e7	1.32128
$735$	−1.10446e7	−0.754102
$736$	541696.	0.0368605
$737$	1.74873e7	1.18591
$738$	−7.82743e6	−0.529028
$739$	6.36305e6	0.428602	0.214301	−	0.976768i	$-0.431253\pi$
$739$	6.36305e6	0.428602	0.214301	+	0.976768i	$0.431253\pi$
$740$	2.69862e6	0.181160
$741$	1.56282e7	1.04559
$742$	925809.	0.0617322
$743$	−2.57418e7	−1.71067	−0.855336	−	0.518073i	$-0.826649\pi$
$743$	−2.57418e7	−1.71067	−0.855336	+	0.518073i	$0.826649\pi$
$744$	−3.69156e6	−0.244499
$745$	−2.79173e6	−0.184282
$746$	1.83091e7	1.20454
$747$	−3.54342e7	−2.32338
$748$	−7.52547e6	−0.491790
$749$	2.34916e6	0.153006
$750$	1.66600e6	0.108149
$751$	4.96421e6	0.321182	0.160591	−	0.987021i	$-0.448660\pi$
$751$	4.96421e6	0.321182	0.160591	+	0.987021i	$0.448660\pi$
$752$	1.78176e6	0.114896
$753$	5.14979e6	0.330980
$754$	−2.98289e6	−0.191077
$755$	−1.85597e6	−0.118496
$756$	1.46335e6	0.0931204
$757$	1.11040e7	0.704270	0.352135	−	0.935949i	$-0.385456\pi$
$757$	1.11040e7	0.704270	0.352135	+	0.935949i	$0.385456\pi$
$758$	1.80948e6	0.114388
$759$	8.33285e6	0.525036
$760$	−1.82737e6	−0.114760
$761$	−3.07123e7	−1.92243	−0.961214	−	0.275803i	$-0.911056\pi$
$761$	−3.07123e7	−1.92243	−0.961214	+	0.275803i	$0.911056\pi$
$762$	−1.78073e7	−1.11099
$763$	1.10671e6	0.0688212
$764$	8.76250e6	0.543118
$765$	−9.30313e6	−0.574745
$766$	−5.91559e6	−0.364273
$767$	−1.25101e7	−0.767842
$768$	1.74693e6	0.106874
$769$	−1.75837e7	−1.07225	−0.536123	−	0.844140i	$-0.680112\pi$
$769$	−1.75837e7	−1.07225	−0.536123	+	0.844140i	$0.680112\pi$
$770$	902994.	0.0548855
$771$	5.34164e7	3.23623
$772$	1.03700e7	0.626235
$773$	−1.24585e7	−0.749921	−0.374961	−	0.927041i	$-0.622344\pi$
$773$	−1.24585e7	−0.749921	−0.374961	+	0.927041i	$0.622344\pi$
$774$	−2.54263e7	−1.52556
$775$	−1.35243e6	−0.0808837
$776$	6.01028e6	0.358295
$777$	2.74800e6	0.163292
$778$	−6.40271e6	−0.379241
$779$	4.78021e6	0.282230
$780$	−5.47347e6	−0.322126
$781$	3.55555e6	0.208583
$782$	−1.68417e6	−0.0984847
$783$	8.69476e6	0.506819
$784$	−4.24282e6	−0.246527
$785$	2.87584e6	0.166568
$786$	−2.48850e7	−1.43675
$787$	3.15127e7	1.81363	0.906815	−	0.421529i	$-0.138506\pi$
$787$	3.15127e7	1.81363	0.906815	+	0.421529i	$0.138506\pi$
$788$	2.49576e6	0.143181
$789$	5.24440e7	2.99919
$790$	−4.02201e6	−0.229285
$791$	2.64148e6	0.150109
$792$	1.76825e7	1.00168
$793$	2.41714e7	1.36495
$794$	−1.17549e7	−0.661708
$795$	1.00938e7	0.566418
$796$	−1.49436e7	−0.835933
$797$	19267.8	0.00107445	0.000537224	−	1.00000i	$-0.499829\pi$
$797$	19267.8	0.00107445	0.000537224		1.00000i	$0.499829\pi$
$798$	−1.86081e6	−0.103441
$799$	−5.53962e6	−0.306982
$800$	640000.	0.0353553
$801$	5.99603e7	3.30204
$802$	−4.48781e6	−0.246376
$803$	−1.48970e7	−0.815286
$804$	1.26210e7	0.688577
$805$	202086.	0.0109912
$806$	4.44328e6	0.240916
$807$	−3.45577e7	−1.86793
$808$	−5.98465e6	−0.322486
$809$	−2.91678e6	−0.156687	−0.0783435	−	0.996926i	$-0.524963\pi$
$809$	−2.91678e6	−0.156687	−0.0783435	+	0.996926i	$0.524963\pi$
$810$	4.59326e6	0.245985
$811$	1.52734e6	0.0815425	0.0407713	−	0.999169i	$-0.487019\pi$
$811$	1.52734e6	0.0815425	0.0407713	+	0.999169i	$0.487019\pi$
$812$	355165.	0.0189034
$813$	2.04964e7	1.08755
$814$	1.59472e7	0.843575
$815$	−8.98603e6	−0.473886
$816$	−5.43131e6	−0.285548
$817$	1.55278e7	0.813870
$818$	3.48862e6	0.182293
$819$	−3.66748e6	−0.191055
$820$	−1.67417e6	−0.0869493
$821$	−8.90732e6	−0.461200	−0.230600	−	0.973049i	$-0.574069\pi$
$821$	−8.90732e6	−0.461200	−0.230600	+	0.973049i	$0.574069\pi$
$822$	−9.08740e6	−0.469094
$823$	1.12925e7	0.581153	0.290576	−	0.956852i	$-0.406153\pi$
$823$	1.12925e7	0.581153	0.290576	+	0.956852i	$0.406153\pi$
$824$	−1.07892e7	−0.553568
$825$	9.84505e6	0.503597
$826$	1.48954e6	0.0759631
$827$	−1.45840e7	−0.741504	−0.370752	−	0.928732i	$-0.620900\pi$
$827$	−1.45840e7	−0.741504	−0.370752	+	0.928732i	$0.620900\pi$
$828$	3.95726e6	0.200594
$829$	−1.04707e7	−0.529165	−0.264583	−	0.964363i	$-0.585234\pi$
$829$	−1.04707e7	−0.529165	−0.264583	+	0.964363i	$0.585234\pi$
$830$	−7.57885e6	−0.381863
$831$	−1.31277e6	−0.0659456
$832$	−2.10266e6	−0.105308
$833$	1.31912e7	0.658676
$834$	−1.20934e7	−0.602052
$835$	−1.33359e7	−0.661922
$836$	−1.07987e7	−0.534385
$837$	−1.29516e7	−0.639013
$838$	2.04525e6	0.100609
$839$	−2.39914e7	−1.17666	−0.588330	−	0.808621i	$-0.700214\pi$
$839$	−2.39914e7	−1.17666	−0.588330	+	0.808621i	$0.700214\pi$
$840$	651712.	0.0318682
$841$	−1.84009e7	−0.897116
$842$	1.31965e7	0.641475
$843$	4.07125e7	1.97314
$844$	−2.24842e6	−0.108648
$845$	−2.69428e6	−0.129808
$846$	1.30163e7	0.625264
$847$	2.87520e6	0.137708
$848$	3.87758e6	0.185170
$849$	4.60805e7	2.19406
$850$	−1.98980e6	−0.0944632
$851$	3.56892e6	0.168932
$852$	2.56612e6	0.121110
$853$	2.10833e7	0.992124	0.496062	−	0.868287i	$-0.334779\pi$
$853$	2.10833e7	0.992124	0.496062	+	0.868287i	$0.334779\pi$
$854$	−2.87802e6	−0.135036
$855$	−1.33495e7	−0.624525
$856$	9.83903e6	0.458953
$857$	1.60173e7	0.744967	0.372484	−	0.928039i	$-0.378506\pi$
$857$	1.60173e7	0.744967	0.372484	+	0.928039i	$0.378506\pi$
$858$	−3.23449e7	−1.49999
$859$	8.91055e6	0.412023	0.206012	−	0.978550i	$-0.433952\pi$
$859$	8.91055e6	0.412023	0.206012	+	0.978550i	$0.433952\pi$
$860$	−5.43831e6	−0.250737
$861$	−1.70481e6	−0.0783733
$862$	8.30065e6	0.380491
$863$	1.91815e7	0.876710	0.438355	−	0.898802i	$-0.355561\pi$
$863$	1.91815e7	0.876710	0.438355	+	0.898802i	$0.355561\pi$
$864$	6.12898e6	0.279321
$865$	−1.10753e7	−0.503287
$866$	−2.24212e7	−1.01593
$867$	−2.09614e7	−0.947047
$868$	−529049.	−0.0238340
$869$	−2.37677e7	−1.06767
$870$	3.87225e6	0.173446
$871$	−1.51910e7	−0.678487
$872$	4.63524e6	0.206434
$873$	4.39070e7	1.94983
$874$	−2.41669e6	−0.107015
$875$	238760.	0.0105424
$876$	−1.07515e7	−0.473379
$877$	−3.28679e7	−1.44302	−0.721510	−	0.692404i	$-0.756552\pi$
$877$	−3.28679e7	−1.44302	−0.721510	+	0.692404i	$0.756552\pi$
$878$	2.33022e6	0.102014
$879$	−4.88787e6	−0.213377
$880$	3.78202e6	0.164633
$881$	−2.29173e7	−0.994772	−0.497386	−	0.867529i	$-0.665707\pi$
$881$	−2.29173e7	−0.994772	−0.497386	+	0.867529i	$0.665707\pi$
$882$	−3.09951e7	−1.34160
$883$	−1.32584e7	−0.572254	−0.286127	−	0.958192i	$-0.592368\pi$
$883$	−1.32584e7	−0.572254	−0.286127	+	0.958192i	$0.592368\pi$
$884$	6.53730e6	0.281363
$885$	1.62400e7	0.696992
$886$	−3.12728e7	−1.33839
$887$	−2.17179e7	−0.926848	−0.463424	−	0.886137i	$-0.653379\pi$
$887$	−2.17179e7	−0.926848	−0.463424	+	0.886137i	$0.653379\pi$
$888$	1.15095e7	0.489805
$889$	−2.55202e6	−0.108300
$890$	1.28246e7	0.542713
$891$	2.71434e7	1.14543
$892$	−9.68246e6	−0.407449
$893$	−7.94907e6	−0.333570
$894$	−1.19066e7	−0.498247
$895$	1.43214e7	0.597624
$896$	250358.	0.0104182
$897$	−7.23866e6	−0.300384
$898$	−2.76882e6	−0.114579
$899$	−3.14343e6	−0.129719
$900$	4.67540e6	0.192403
$901$	−1.20556e7	−0.494742
$902$	−9.89337e6	−0.404881
$903$	−5.53783e6	−0.226006
$904$	1.10633e7	0.450261
$905$	−245644.	−0.00996978
$906$	−7.91563e6	−0.320380
$907$	1.39952e7	0.564887	0.282443	−	0.959284i	$-0.408855\pi$
$907$	1.39952e7	0.564887	0.282443	+	0.959284i	$0.408855\pi$
$908$	1.03344e6	0.0415978
$909$	−4.37197e7	−1.75496
$910$	−784421.	−0.0314012
$911$	−2.72679e7	−1.08857	−0.544284	−	0.838901i	$-0.683199\pi$
$911$	−2.72679e7	−1.08857	−0.544284	+	0.838901i	$0.683199\pi$
$912$	−7.79364e6	−0.310280
$913$	−4.47865e7	−1.77816
$914$	−1.39987e7	−0.554270
$915$	−3.13782e7	−1.23901
$916$	−1.89114e7	−0.744706
$917$	−3.56635e6	−0.140056
$918$	−1.90554e7	−0.746297
$919$	−1.29540e7	−0.505958	−0.252979	−	0.967472i	$-0.581410\pi$
$919$	−1.29540e7	−0.505958	−0.252979	+	0.967472i	$0.581410\pi$
$920$	846400.	0.0329690
$921$	2.23032e7	0.866400
$922$	−1.41812e7	−0.549397
$923$	−3.08867e6	−0.119335
$924$	3.85123e6	0.148395
$925$	4.21659e6	0.162034
$926$	−2.61312e7	−1.00146
$927$	−7.88185e7	−3.01251
$928$	1.48754e6	0.0567021
$929$	−9.48160e6	−0.360448	−0.180224	−	0.983626i	$-0.557682\pi$
$929$	−9.48160e6	−0.360448	−0.180224	+	0.983626i	$0.557682\pi$
$930$	−5.76805e6	−0.218687
$931$	1.89287e7	0.715725
$932$	−2.08422e7	−0.785966
$933$	−8.01698e7	−3.01513
$934$	2.65801e7	0.996986
$935$	−1.17585e7	−0.439870
$936$	−1.53606e7	−0.573083
$937$	8.87629e6	0.330280	0.165140	−	0.986270i	$-0.447192\pi$
$937$	8.87629e6	0.330280	0.165140	+	0.986270i	$0.447192\pi$
$938$	1.80875e6	0.0671232
$939$	−1.09127e7	−0.403895
$940$	2.78401e6	0.102766
$941$	−1.01066e7	−0.372074	−0.186037	−	0.982543i	$-0.559564\pi$
$941$	−1.01066e7	−0.372074	−0.186037	+	0.982543i	$0.559564\pi$
$942$	1.22653e7	0.450352
$943$	−2.21409e6	−0.0810806
$944$	6.23867e6	0.227857
$945$	2.28649e6	0.0832895
$946$	−3.21372e7	−1.16756
$947$	2.05931e7	0.746185	0.373093	−	0.927794i	$-0.378297\pi$
$947$	2.05931e7	0.746185	0.373093	+	0.927794i	$0.378297\pi$
$948$	−1.71537e7	−0.619921
$949$	1.29409e7	0.466442
$950$	−2.85526e6	−0.102645
$951$	6.78524e7	2.43284
$952$	−778379.	−0.0278355
$953$	−2.49739e7	−0.890746	−0.445373	−	0.895345i	$-0.646929\pi$
$953$	−2.49739e7	−0.890746	−0.445373	+	0.895345i	$0.646929\pi$
$954$	2.83269e7	1.00769
$955$	1.36914e7	0.485780
$956$	−2.13612e6	−0.0755928
$957$	2.28827e7	0.807657
$958$	3.08398e7	1.08567
$959$	−1.30235e6	−0.0457278
$960$	2.72957e6	0.0955908
$961$	−2.39467e7	−0.836446
$962$	−1.38532e7	−0.482627
$963$	7.18772e7	2.49762
$964$	2.33781e7	0.810246
$965$	1.62032e7	0.560122
$966$	861888.	0.0297172
$967$	−2.42874e7	−0.835247	−0.417624	−	0.908620i	$-0.637137\pi$
$967$	−2.42874e7	−0.835247	−0.417624	+	0.908620i	$0.637137\pi$
$968$	1.20422e7	0.413065
$969$	2.42310e7	0.829013
$970$	9.39106e6	0.320468
$971$	8.99233e6	0.306072	0.153036	−	0.988221i	$-0.451095\pi$
$971$	8.99233e6	0.306072	0.153036	+	0.988221i	$0.451095\pi$
$972$	−3.68095e6	−0.124967
$973$	−1.73315e6	−0.0586886
$974$	−1.39246e7	−0.470311
$975$	−8.55229e6	−0.288118
$976$	−1.20541e7	−0.405050
$977$	4.27577e6	0.143310	0.0716552	−	0.997429i	$-0.477172\pi$
$977$	4.27577e6	0.143310	0.0716552	+	0.997429i	$0.477172\pi$
$978$	−3.83250e7	−1.28125
$979$	7.57859e7	2.52716
$980$	−6.62940e6	−0.220500
$981$	3.38619e7	1.12341
$982$	2.31697e7	0.766730
$983$	5.01130e7	1.65412	0.827059	−	0.562115i	$-0.190012\pi$
$983$	5.01130e7	1.65412	0.827059	+	0.562115i	$0.190012\pi$
$984$	−7.14027e6	−0.235086
$985$	3.89962e6	0.128065
$986$	−4.62487e6	−0.151498
$987$	2.83495e6	0.0926302
$988$	9.38068e6	0.305733
$989$	−7.19216e6	−0.233813
$990$	2.76288e7	0.895931
$991$	2.28927e7	0.740480	0.370240	−	0.928936i	$-0.379275\pi$
$991$	2.28927e7	0.740480	0.370240	+	0.928936i	$0.379275\pi$
$992$	−2.21582e6	−0.0714917
$993$	4.41390e6	0.142053
$994$	367760.	0.0118059
$995$	−2.33493e7	−0.747681
$996$	−3.23234e7	−1.03245
$997$	−1.48072e7	−0.471776	−0.235888	−	0.971780i	$-0.575800\pi$
$997$	−1.48072e7	−0.471776	−0.235888	+	0.971780i	$0.575800\pi$
$998$	2.92718e7	0.930300
$999$	4.03803e7	1.28014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.h.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.h.1.6	✓	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +26.6560 q^{3} +16.0000 q^{4} +25.0000 q^{5} +106.624 q^{6} +15.2806 q^{7} +64.0000 q^{8} +467.540 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +26.6560 q^{3} +16.0000 q^{4} +25.0000 q^{5} +106.624 q^{6} +15.2806 q^{7} +64.0000 q^{8} +467.540 q^{9} +100.000 q^{10} +590.940 q^{11} +426.495 q^{12} -513.344 q^{13} +61.1225 q^{14} +666.399 q^{15} +256.000 q^{16} -795.921 q^{17} +1870.16 q^{18} -1142.11 q^{19} +400.000 q^{20} +407.320 q^{21} +2363.76 q^{22} +529.000 q^{23} +1705.98 q^{24} +625.000 q^{25} -2053.37 q^{26} +5985.33 q^{27} +244.490 q^{28} +1452.68 q^{29} +2665.60 q^{30} -2163.89 q^{31} +1024.00 q^{32} +15752.1 q^{33} -3183.68 q^{34} +382.016 q^{35} +7480.64 q^{36} +6746.54 q^{37} -4568.42 q^{38} -13683.7 q^{39} +1600.00 q^{40} -4185.43 q^{41} +1629.28 q^{42} -13595.8 q^{43} +9455.05 q^{44} +11688.5 q^{45} +2116.00 q^{46} +6960.01 q^{47} +6823.93 q^{48} -16573.5 q^{49} +2500.00 q^{50} -21216.0 q^{51} -8213.50 q^{52} +15146.8 q^{53} +23941.3 q^{54} +14773.5 q^{55} +977.960 q^{56} -30443.9 q^{57} +5810.71 q^{58} +24369.8 q^{59} +10662.4 q^{60} -47086.1 q^{61} -8655.56 q^{62} +7144.31 q^{63} +4096.00 q^{64} -12833.6 q^{65} +63008.3 q^{66} +29592.3 q^{67} -12734.7 q^{68} +14101.0 q^{69} +1528.06 q^{70} +6016.77 q^{71} +29922.6 q^{72} -25209.0 q^{73} +26986.2 q^{74} +16660.0 q^{75} -18273.7 q^{76} +9029.94 q^{77} -54734.7 q^{78} -40220.1 q^{79} +6400.00 q^{80} +45932.6 q^{81} -16741.7 q^{82} -75788.5 q^{83} +6517.12 q^{84} -19898.0 q^{85} -54383.1 q^{86} +38722.5 q^{87} +37820.2 q^{88} +128246. q^{89} +46754.0 q^{90} -7844.21 q^{91} +8464.00 q^{92} -57680.5 q^{93} +27840.1 q^{94} -28552.6 q^{95} +27295.7 q^{96} +93910.6 q^{97} -66294.0 q^{98} +276288. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9} + 600 q^{10} + 151 q^{11} + 176 q^{12} + 463 q^{13} + 1464 q^{14} + 275 q^{15} + 1536 q^{16} + 644 q^{17} + 3596 q^{18} + 3431 q^{19} + 2400 q^{20} - 3846 q^{21} + 604 q^{22} + 3174 q^{23} + 704 q^{24} + 3750 q^{25} + 1852 q^{26} - 3364 q^{27} + 5856 q^{28} + 5973 q^{29} + 1100 q^{30} + 10262 q^{31} + 6144 q^{32} + 23025 q^{33} + 2576 q^{34} + 9150 q^{35} + 14384 q^{36} + 17207 q^{37} + 13724 q^{38} + 14136 q^{39} + 9600 q^{40} + 784 q^{41} - 15384 q^{42} + 13452 q^{43} + 2416 q^{44} + 22475 q^{45} + 12696 q^{46} + 24572 q^{47} + 2816 q^{48} + 28050 q^{49} + 15000 q^{50} + 26125 q^{51} + 7408 q^{52} + 17563 q^{53} - 13456 q^{54} + 3775 q^{55} + 23424 q^{56} - 41798 q^{57} + 23892 q^{58} + 62911 q^{59} + 4400 q^{60} + 32851 q^{61} + 41048 q^{62} + 138693 q^{63} + 24576 q^{64} + 11575 q^{65} + 92100 q^{66} + 54177 q^{67} + 10304 q^{68} + 5819 q^{69} + 36600 q^{70} - 14368 q^{71} + 57536 q^{72} + 33276 q^{73} + 68828 q^{74} + 6875 q^{75} + 54896 q^{76} - 143678 q^{77} + 56544 q^{78} + 74296 q^{79} + 38400 q^{80} + 150834 q^{81} + 3136 q^{82} + 65145 q^{83} - 61536 q^{84} + 16100 q^{85} + 53808 q^{86} - 790 q^{87} + 9664 q^{88} - 67562 q^{89} + 89900 q^{90} - 89487 q^{91} + 50784 q^{92} - 209450 q^{93} + 98288 q^{94} + 85775 q^{95} + 11264 q^{96} - 13201 q^{97} + 112200 q^{98} - 355951 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9 + 600 * q^10 + 151 * q^11 + 176 * q^12 + 463 * q^13 + 1464 * q^14 + 275 * q^15 + 1536 * q^16 + 644 * q^17 + 3596 * q^18 + 3431 * q^19 + 2400 * q^20 - 3846 * q^21 + 604 * q^22 + 3174 * q^23 + 704 * q^24 + 3750 * q^25 + 1852 * q^26 - 3364 * q^27 + 5856 * q^28 + 5973 * q^29 + 1100 * q^30 + 10262 * q^31 + 6144 * q^32 + 23025 * q^33 + 2576 * q^34 + 9150 * q^35 + 14384 * q^36 + 17207 * q^37 + 13724 * q^38 + 14136 * q^39 + 9600 * q^40 + 784 * q^41 - 15384 * q^42 + 13452 * q^43 + 2416 * q^44 + 22475 * q^45 + 12696 * q^46 + 24572 * q^47 + 2816 * q^48 + 28050 * q^49 + 15000 * q^50 + 26125 * q^51 + 7408 * q^52 + 17563 * q^53 - 13456 * q^54 + 3775 * q^55 + 23424 * q^56 - 41798 * q^57 + 23892 * q^58 + 62911 * q^59 + 4400 * q^60 + 32851 * q^61 + 41048 * q^62 + 138693 * q^63 + 24576 * q^64 + 11575 * q^65 + 92100 * q^66 + 54177 * q^67 + 10304 * q^68 + 5819 * q^69 + 36600 * q^70 - 14368 * q^71 + 57536 * q^72 + 33276 * q^73 + 68828 * q^74 + 6875 * q^75 + 54896 * q^76 - 143678 * q^77 + 56544 * q^78 + 74296 * q^79 + 38400 * q^80 + 150834 * q^81 + 3136 * q^82 + 65145 * q^83 - 61536 * q^84 + 16100 * q^85 + 53808 * q^86 - 790 * q^87 + 9664 * q^88 - 67562 * q^89 + 89900 * q^90 - 89487 * q^91 + 50784 * q^92 - 209450 * q^93 + 98288 * q^94 + 85775 * q^95 + 11264 * q^96 - 13201 * q^97 + 112200 * q^98 - 355951 * q^99

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