LMFDB - Embedded newform 529.6.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,6,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, 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("529.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	529.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:	$84.8430406811$
Analytic rank:	$0$
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:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.65736$ of defining polynomial
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.31473 q^{2} -27.6631 q^{3} -3.75366 q^{4} +23.8768 q^{5} -147.022 q^{6} +11.7843 q^{7} -190.021 q^{8} +522.249 q^{9} +O(q^{10})$	\(q+5.31473 q^{2} -27.6631 q^{3} -3.75366 q^{4} +23.8768 q^{5} -147.022 q^{6} +11.7843 q^{7} -190.021 q^{8} +522.249 q^{9} +126.899 q^{10} -280.887 q^{11} +103.838 q^{12} -835.171 q^{13} +62.6305 q^{14} -660.508 q^{15} -889.793 q^{16} +1801.86 q^{17} +2775.61 q^{18} -2357.32 q^{19} -89.6256 q^{20} -325.991 q^{21} -1492.84 q^{22} +5256.58 q^{24} -2554.90 q^{25} -4438.71 q^{26} -7724.90 q^{27} -44.2344 q^{28} -1206.86 q^{29} -3510.42 q^{30} -3394.53 q^{31} +1351.66 q^{32} +7770.22 q^{33} +9576.38 q^{34} +281.372 q^{35} -1960.35 q^{36} -8351.42 q^{37} -12528.5 q^{38} +23103.5 q^{39} -4537.10 q^{40} -10701.7 q^{41} -1732.56 q^{42} +803.535 q^{43} +1054.36 q^{44} +12469.7 q^{45} -4896.03 q^{47} +24614.5 q^{48} -16668.1 q^{49} -13578.6 q^{50} -49845.0 q^{51} +3134.95 q^{52} -39358.6 q^{53} -41055.8 q^{54} -6706.69 q^{55} -2239.27 q^{56} +65211.0 q^{57} -6414.13 q^{58} +39514.6 q^{59} +2479.32 q^{60} +15309.3 q^{61} -18041.0 q^{62} +6154.35 q^{63} +35657.1 q^{64} -19941.2 q^{65} +41296.6 q^{66} +60783.9 q^{67} -6763.56 q^{68} +1495.42 q^{70} +39125.6 q^{71} -99238.3 q^{72} -5872.67 q^{73} -44385.5 q^{74} +70676.5 q^{75} +8848.60 q^{76} -3310.07 q^{77} +122789. q^{78} +63656.1 q^{79} -21245.4 q^{80} +86788.5 q^{81} -56876.4 q^{82} +63639.8 q^{83} +1223.66 q^{84} +43022.6 q^{85} +4270.57 q^{86} +33385.5 q^{87} +53374.5 q^{88} -36262.8 q^{89} +66272.8 q^{90} -9841.93 q^{91} +93903.4 q^{93} -26021.1 q^{94} -56285.4 q^{95} -37391.3 q^{96} +64187.5 q^{97} -88586.6 q^{98} -146693. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} + 58 q^{5} - 230 q^{6} + 282 q^{7} - 360 q^{8} + 121 q^{9} + 156 q^{10} - 136 q^{11} + 620 q^{12} - 1116 q^{13} - 2016 q^{14} - 750 q^{15} + 128 q^{16} + 896 q^{17} + 4282 q^{18} - 1654 q^{19} - 1504 q^{20} + 1670 q^{21} - 1352 q^{22} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} + 10264 q^{28} - 844 q^{29} - 3180 q^{30} - 3020 q^{31} + 6656 q^{32} + 7370 q^{33} + 11212 q^{34} + 1072 q^{35} - 2548 q^{36} - 8938 q^{37} - 10728 q^{38} + 16020 q^{39} - 3440 q^{40} - 12792 q^{41} - 20560 q^{42} + 16730 q^{43} - 5112 q^{44} + 3936 q^{45} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} - 50290 q^{51} - 47412 q^{52} - 17108 q^{53} - 7610 q^{54} - 436 q^{55} - 42640 q^{56} + 61960 q^{57} - 55678 q^{58} + 54176 q^{59} + 2400 q^{60} + 71324 q^{61} - 72710 q^{62} - 40696 q^{63} - 49984 q^{64} - 846 q^{65} + 42860 q^{66} + 62960 q^{67} + 8352 q^{68} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} + 59044 q^{74} + 44800 q^{75} - 31488 q^{76} - 304 q^{77} + 182070 q^{78} - 58224 q^{79} + 17568 q^{80} + 149947 q^{81} + 61926 q^{82} - 9892 q^{83} + 109720 q^{84} + 15536 q^{85} - 191140 q^{86} + 90500 q^{87} + 58400 q^{88} - 27542 q^{89} + 62112 q^{90} - 151974 q^{91} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} + 273672 q^{97} - 401276 q^{98} - 183082 q^{99}+O(q^{100}) \) 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 + 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 + 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 + 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 + 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 $

$2$	5.31473	0.939520	0.469760	−	0.882794i	$-0.344340\pi$
$2$	5.31473	0.939520	0.469760	+	0.882794i	$0.344340\pi$
$3$	−27.6631	−1.77459	−0.887295	−	0.461202i	$-0.847419\pi$
$3$	−27.6631	−1.77459	−0.887295	+	0.461202i	$0.847419\pi$
$4$	−3.75366	−0.117302
$5$	23.8768	0.427122	0.213561	−	0.976930i	$-0.431494\pi$
$5$	23.8768	0.427122	0.213561	+	0.976930i	$0.431494\pi$
$6$	−147.022	−1.66726
$7$	11.7843	0.0908991	0.0454496	−	0.998967i	$-0.485528\pi$
$7$	11.7843	0.0908991	0.0454496	+	0.998967i	$0.485528\pi$
$8$	−190.021	−1.04973
$9$	522.249	2.14917
$10$	126.899	0.401289
$11$	−280.887	−0.699923	−0.349961	−	0.936764i	$-0.613805\pi$
$11$	−280.887	−0.699923	−0.349961	+	0.936764i	$0.613805\pi$
$12$	103.838	0.208163
$13$	−835.171	−1.37062	−0.685310	−	0.728251i	$-0.740333\pi$
$13$	−835.171	−1.37062	−0.685310	+	0.728251i	$0.740333\pi$
$14$	62.6305	0.0854015
$15$	−660.508	−0.757966
$16$	−889.793	−0.868938
$17$	1801.86	1.51216	0.756080	−	0.654479i	$-0.227112\pi$
$17$	1801.86	1.51216	0.756080	+	0.654479i	$0.227112\pi$
$18$	2775.61	2.01919
$19$	−2357.32	−1.49808	−0.749041	−	0.662524i	$-0.769485\pi$
$19$	−2357.32	−1.49808	−0.749041	+	0.662524i	$0.769485\pi$
$20$	−89.6256	−0.0501022
$21$	−325.991	−0.161309
$22$	−1492.84	−0.657592
$23$	0	0
$23$	0	0
$24$	5256.58	1.86284
$25$	−2554.90	−0.817567
$26$	−4438.71	−1.28773
$27$	−7724.90	−2.03931
$28$	−44.2344	−0.0106626
$29$	−1206.86	−0.266478	−0.133239	−	0.991084i	$-0.542538\pi$
$29$	−1206.86	−0.266478	−0.133239	+	0.991084i	$0.542538\pi$
$30$	−3510.42	−0.712125
$31$	−3394.53	−0.634418	−0.317209	−	0.948356i	$-0.602746\pi$
$31$	−3394.53	−0.634418	−0.317209	+	0.948356i	$0.602746\pi$
$32$	1351.66	0.233343
$33$	7770.22	1.24208
$34$	9576.38	1.42071
$35$	281.372	0.0388250
$36$	−1960.35	−0.252102
$37$	−8351.42	−1.00290	−0.501448	−	0.865188i	$-0.667199\pi$
$37$	−8351.42	−1.00290	−0.501448	+	0.865188i	$0.667199\pi$
$38$	−12528.5	−1.40748
$39$	23103.5	2.43229
$40$	−4537.10	−0.448362
$41$	−10701.7	−0.994240	−0.497120	−	0.867682i	$-0.665609\pi$
$41$	−10701.7	−0.994240	−0.497120	+	0.867682i	$0.665609\pi$
$42$	−1732.56	−0.151553
$43$	803.535	0.0662726	0.0331363	−	0.999451i	$-0.489450\pi$
$43$	803.535	0.0662726	0.0331363	+	0.999451i	$0.489450\pi$
$44$	1054.36	0.0821023
$45$	12469.7	0.917958
$46$	0	0
$47$	−4896.03	−0.323295	−0.161648	−	0.986849i	$-0.551681\pi$
$47$	−4896.03	−0.323295	−0.161648	+	0.986849i	$0.551681\pi$
$48$	24614.5	1.54201
$49$	−16668.1	−0.991737
$50$	−13578.6	−0.768121
$51$	−49845.0	−2.68347
$52$	3134.95	0.160776
$53$	−39358.6	−1.92464	−0.962322	−	0.271913i	$-0.912344\pi$
$53$	−39358.6	−1.92464	−0.962322	+	0.271913i	$0.912344\pi$
$54$	−41055.8	−1.91597
$55$	−6706.69	−0.298952
$56$	−2239.27	−0.0954193
$57$	65211.0	2.65848
$58$	−6414.13	−0.250362
$59$	39514.6	1.47784	0.738921	−	0.673792i	$-0.235336\pi$
$59$	39514.6	1.47784	0.738921	+	0.673792i	$0.235336\pi$
$60$	2479.32	0.0889109
$61$	15309.3	0.526783	0.263392	−	0.964689i	$-0.415159\pi$
$61$	15309.3	0.526783	0.263392	+	0.964689i	$0.415159\pi$
$62$	−18041.0	−0.596048
$63$	6154.35	0.195358
$64$	35657.1	1.08817
$65$	−19941.2	−0.585422
$66$	41296.6	1.16696
$67$	60783.9	1.65425	0.827126	−	0.562016i	$-0.189974\pi$
$67$	60783.9	1.65425	0.827126	+	0.562016i	$0.189974\pi$
$68$	−6763.56	−0.177379
$69$	0	0
$70$	1495.42	0.0364769
$71$	39125.6	0.921118	0.460559	−	0.887629i	$-0.347649\pi$
$71$	39125.6	0.921118	0.460559	+	0.887629i	$0.347649\pi$
$72$	−99238.3	−2.25605
$73$	−5872.67	−0.128982	−0.0644909	−	0.997918i	$-0.520542\pi$
$73$	−5872.67	−0.128982	−0.0644909	+	0.997918i	$0.520542\pi$
$74$	−44385.5	−0.942241
$75$	70676.5	1.45085
$76$	8848.60	0.175728
$77$	−3310.07	−0.0636224
$78$	122789.	2.28519
$79$	63656.1	1.14755	0.573776	−	0.819012i	$-0.305478\pi$
$79$	63656.1	1.14755	0.573776	+	0.819012i	$0.305478\pi$
$80$	−21245.4	−0.371142
$81$	86788.5	1.46977
$82$	−56876.4	−0.934109
$83$	63639.8	1.01399	0.506995	−	0.861949i	$-0.330756\pi$
$83$	63639.8	1.01399	0.506995	+	0.861949i	$0.330756\pi$
$84$	1223.66	0.0189218
$85$	43022.6	0.645877
$86$	4270.57	0.0622644
$87$	33385.5	0.472890
$88$	53374.5	0.734728
$89$	−36262.8	−0.485273	−0.242637	−	0.970117i	$-0.578012\pi$
$89$	−36262.8	−0.485273	−0.242637	+	0.970117i	$0.578012\pi$
$90$	66272.8	0.862440
$91$	−9841.93	−0.124588
$92$	0	0
$93$	93903.4	1.12583
$94$	−26021.1	−0.303742
$95$	−56285.4	−0.639863
$96$	−37391.3	−0.414088
$97$	64187.5	0.692662	0.346331	−	0.938112i	$-0.387427\pi$
$97$	64187.5	0.692662	0.346331	+	0.938112i	$0.387427\pi$
$98$	−88586.6	−0.931757
$99$	−146693.	−1.50425
$100$	9590.22	0.0959022
$101$	−108356.	−1.05693	−0.528467	−	0.848954i	$-0.677233\pi$
$101$	−108356.	−1.05693	−0.528467	+	0.848954i	$0.677233\pi$
$102$	−264913.	−2.52117
$103$	88102.3	0.818265	0.409133	−	0.912475i	$-0.365831\pi$
$103$	88102.3	0.818265	0.409133	+	0.912475i	$0.365831\pi$
$104$	158700.	1.43878
$105$	−7783.64	−0.0688985
$106$	−209180.	−1.80824
$107$	16813.2	0.141968	0.0709842	−	0.997477i	$-0.477386\pi$
$107$	16813.2	0.141968	0.0709842	+	0.997477i	$0.477386\pi$
$108$	28996.7	0.239215
$109$	192169.	1.54923	0.774616	−	0.632432i	$-0.217943\pi$
$109$	192169.	1.54923	0.774616	+	0.632432i	$0.217943\pi$
$110$	−35644.3	−0.280872
$111$	231026.	1.77973
$112$	−10485.6	−0.0789857
$113$	−24975.1	−0.183997	−0.0919985	−	0.995759i	$-0.529326\pi$
$113$	−24975.1	−0.183997	−0.0919985	+	0.995759i	$0.529326\pi$
$114$	346579.	2.49770
$115$	0	0
$116$	4530.14	0.0312584
$117$	−436167.	−2.94570
$118$	210010.	1.38846
$119$	21233.7	0.137454
$120$	125510.	0.795658
$121$	−82153.4	−0.510108
$122$	81365.0	0.494923
$123$	296041.	1.76437
$124$	12741.9	0.0744185
$125$	−135618.	−0.776322
$126$	32708.7	0.183543
$127$	215290.	1.18445	0.592223	−	0.805774i	$-0.298251\pi$
$127$	215290.	1.18445	0.592223	+	0.805774i	$0.298251\pi$
$128$	146255.	0.789013
$129$	−22228.3	−0.117607
$130$	−105982.	−0.550015
$131$	34626.7	0.176292	0.0881461	−	0.996108i	$-0.471906\pi$
$131$	34626.7	0.176292	0.0881461	+	0.996108i	$0.471906\pi$
$132$	−29166.8	−0.145698
$133$	−27779.5	−0.136174
$134$	323050.	1.55420
$135$	−184446.	−0.871034
$136$	−342391.	−1.58736
$137$	−172235.	−0.784007	−0.392003	−	0.919964i	$-0.628218\pi$
$137$	−172235.	−0.784007	−0.392003	+	0.919964i	$0.628218\pi$
$138$	0	0
$139$	153367.	0.673278	0.336639	−	0.941634i	$-0.390710\pi$
$139$	153367.	0.673278	0.336639	+	0.941634i	$0.390710\pi$
$140$	−1056.18	−0.00455425
$141$	135440.	0.573717
$142$	207942.	0.865409
$143$	234589.	0.959328
$144$	−464693.	−1.86750
$145$	−28816.0	−0.113819
$146$	−31211.7	−0.121181
$147$	461093.	1.75993
$148$	31348.4	0.117642
$149$	28131.3	0.103807	0.0519033	−	0.998652i	$-0.483471\pi$
$149$	28131.3	0.103807	0.0519033	+	0.998652i	$0.483471\pi$
$150$	375626.	1.36310
$151$	160593.	0.573172	0.286586	−	0.958055i	$-0.407480\pi$
$151$	160593.	0.573172	0.286586	+	0.958055i	$0.407480\pi$
$152$	447941.	1.57258
$153$	941018.	3.24989
$154$	−17592.1	−0.0597745
$155$	−81050.6	−0.270974
$156$	−86722.6	−0.285312
$157$	−242015.	−0.783599	−0.391800	−	0.920051i	$-0.628147\pi$
$157$	−242015.	−0.783599	−0.391800	+	0.920051i	$0.628147\pi$
$158$	338315.	1.07815
$159$	1.08878e6	3.41546
$160$	32273.5	0.0996657
$161$	0	0
$162$	461257.	1.38088
$163$	−136177.	−0.401453	−0.200727	−	0.979647i	$-0.564330\pi$
$163$	−136177.	−0.401453	−0.200727	+	0.979647i	$0.564330\pi$
$164$	40170.4	0.116626
$165$	185528.	0.530518
$166$	338228.	0.952664
$167$	−9384.75	−0.0260394	−0.0130197	−	0.999915i	$-0.504144\pi$
$167$	−9384.75	−0.0260394	−0.0130197	+	0.999915i	$0.504144\pi$
$168$	61945.2	0.169330
$169$	326218.	0.878600
$170$	228654.	0.606814
$171$	−1.23111e6	−3.21964
$172$	−3016.20	−0.00777390
$173$	−398962.	−1.01348	−0.506741	−	0.862098i	$-0.669150\pi$
$173$	−398962.	−1.01348	−0.506741	+	0.862098i	$0.669150\pi$
$174$	177435.	0.444290
$175$	−30107.7	−0.0743161
$176$	249931.	0.608190
$177$	−1.09310e6	−2.62256
$178$	−192727.	−0.455924
$179$	456085.	1.06393	0.531965	−	0.846766i	$-0.321454\pi$
$179$	456085.	1.06393	0.531965	+	0.846766i	$0.321454\pi$
$180$	−46806.9	−0.107678
$181$	120816.	0.274111	0.137056	−	0.990563i	$-0.456236\pi$
$181$	120816.	0.274111	0.137056	+	0.990563i	$0.456236\pi$
$182$	−52307.2	−0.117053
$183$	−423504.	−0.934825
$184$	0	0
$185$	−199405.	−0.428359
$186$	499071.	1.05774
$187$	−506118.	−1.05840
$188$	18378.0	0.0379232
$189$	−91032.8	−0.185372
$190$	−299142.	−0.601164
$191$	−416377.	−0.825854	−0.412927	−	0.910764i	$-0.635494\pi$
$191$	−416377.	−0.825854	−0.412927	+	0.910764i	$0.635494\pi$
$192$	−986387.	−1.93105
$193$	−381178.	−0.736605	−0.368302	−	0.929706i	$-0.620061\pi$
$193$	−381178.	−0.736605	−0.368302	+	0.929706i	$0.620061\pi$
$194$	341139.	0.650770
$195$	551637.	1.03888
$196$	62566.5	0.116333
$197$	617955.	1.13447	0.567233	−	0.823558i	$-0.308014\pi$
$197$	617955.	1.13447	0.567233	+	0.823558i	$0.308014\pi$
$198$	−779634.	−1.41328
$199$	−455121.	−0.814693	−0.407346	−	0.913274i	$-0.633546\pi$
$199$	−455121.	−0.814693	−0.407346	+	0.913274i	$0.633546\pi$
$200$	485484.	0.858223
$201$	−1.68147e6	−2.93562
$202$	−575881.	−0.993011
$203$	−14222.0	−0.0242226
$204$	187101.	0.314776
$205$	−255522.	−0.424662
$206$	468240.	0.768776
$207$	0	0
$208$	743129.	1.19098
$209$	662142.	1.04854
$210$	−41367.9	−0.0647315
$211$	−870625.	−1.34625	−0.673124	−	0.739530i	$-0.735048\pi$
$211$	−870625.	−1.34625	−0.673124	+	0.739530i	$0.735048\pi$
$212$	147739.	0.225764
$213$	−1.08234e6	−1.63461
$214$	89357.8	0.133382
$215$	19185.9	0.0283065
$216$	1.46789e6	2.14072
$217$	−40002.3	−0.0576680
$218$	1.02132e6	1.45553
$219$	162457.	0.228890
$220$	25174.7	0.0350677
$221$	−1.50486e6	−2.07260
$222$	1.22784e6	1.67209
$223$	−135558.	−0.182541	−0.0912707	−	0.995826i	$-0.529093\pi$
$223$	−135558.	−0.182541	−0.0912707	+	0.995826i	$0.529093\pi$
$224$	15928.5	0.0212106
$225$	−1.33429e6	−1.75709
$226$	−132736.	−0.172869
$227$	443206.	0.570875	0.285438	−	0.958397i	$-0.407861\pi$
$227$	443206.	0.570875	0.285438	+	0.958397i	$0.407861\pi$
$228$	−244780.	−0.311845
$229$	−689970.	−0.869444	−0.434722	−	0.900565i	$-0.643153\pi$
$229$	−689970.	−0.869444	−0.434722	+	0.900565i	$0.643153\pi$
$230$	0	0
$231$	91566.8	0.112904
$232$	229329.	0.279730
$233$	487389.	0.588147	0.294074	−	0.955783i	$-0.404989\pi$
$233$	487389.	0.588147	0.294074	+	0.955783i	$0.404989\pi$
$234$	−2.31811e6	−2.76754
$235$	−116902.	−0.138086
$236$	−148325.	−0.173354
$237$	−1.76093e6	−2.03644
$238$	112851.	0.129141
$239$	−1.12530e6	−1.27430	−0.637150	−	0.770740i	$-0.719887\pi$
$239$	−1.12530e6	−1.27430	−0.637150	+	0.770740i	$0.719887\pi$
$240$	587715.	0.658626
$241$	1.48985e6	1.65235	0.826173	−	0.563416i	$-0.190513\pi$
$241$	1.48985e6	1.65235	0.826173	+	0.563416i	$0.190513\pi$
$242$	−436623.	−0.479257
$243$	−523690.	−0.568930
$244$	−57466.1	−0.0617927
$245$	−397982.	−0.423593
$246$	1.57338e6	1.65766
$247$	1.96877e6	2.05330
$248$	645032.	0.665966
$249$	−1.76048e6	−1.79942
$250$	−720773.	−0.729371
$251$	−63456.5	−0.0635758	−0.0317879	−	0.999495i	$-0.510120\pi$
$251$	−63456.5	−0.0635758	−0.0317879	+	0.999495i	$0.510120\pi$
$252$	−23101.4	−0.0229159
$253$	0	0
$254$	1.14421e6	1.11281
$255$	−1.19014e6	−1.14617
$256$	−363724.	−0.346874
$257$	1.08874e6	1.02823	0.514116	−	0.857720i	$-0.328120\pi$
$257$	1.08874e6	1.02823	0.514116	+	0.857720i	$0.328120\pi$
$258$	−118137.	−0.110494
$259$	−98415.8	−0.0911624
$260$	74852.7	0.0686711
$261$	−630281.	−0.572708
$262$	184032.	0.165630
$263$	542790.	0.483885	0.241943	−	0.970291i	$-0.422215\pi$
$263$	542790.	0.483885	0.241943	+	0.970291i	$0.422215\pi$
$264$	−1.47650e6	−1.30384
$265$	−939760.	−0.822057
$266$	−147640.	−0.127938
$267$	1.00314e6	0.861162
$268$	−228162.	−0.194047
$269$	−1.66169e6	−1.40013	−0.700065	−	0.714079i	$-0.746846\pi$
$269$	−1.66169e6	−1.40013	−0.700065	+	0.714079i	$0.746846\pi$
$270$	−980281.	−0.818354
$271$	621380.	0.513966	0.256983	−	0.966416i	$-0.417272\pi$
$271$	621380.	0.513966	0.256983	+	0.966416i	$0.417272\pi$
$272$	−1.60328e6	−1.31397
$273$	272259.	0.221093
$274$	−915382.	−0.736590
$275$	717638.	0.572234
$276$	0	0
$277$	266442.	0.208643	0.104321	−	0.994544i	$-0.466733\pi$
$277$	266442.	0.208643	0.104321	+	0.994544i	$0.466733\pi$
$278$	815103.	0.632558
$279$	−1.77279e6	−1.36347
$280$	−53466.7	−0.0407557
$281$	−472574.	−0.357029	−0.178515	−	0.983937i	$-0.557129\pi$
$281$	−472574.	−0.357029	−0.178515	+	0.983937i	$0.557129\pi$
$282$	719824.	0.539018
$283$	−914756.	−0.678952	−0.339476	−	0.940615i	$-0.610250\pi$
$283$	−914756.	−0.678952	−0.339476	+	0.940615i	$0.610250\pi$
$284$	−146864.	−0.108049
$285$	1.55703e6	1.13550
$286$	1.24678e6	0.901308
$287$	−126112.	−0.0903755
$288$	705906.	0.501494
$289$	1.82683e6	1.28663
$290$	−153149.	−0.106935
$291$	−1.77563e6	−1.22919
$292$	22044.0	0.0151298
$293$	906414.	0.616819	0.308409	−	0.951254i	$-0.400203\pi$
$293$	906414.	0.616819	0.308409	+	0.951254i	$0.400203\pi$
$294$	2.45058e6	1.65349
$295$	943484.	0.631218
$296$	1.58695e6	1.05277
$297$	2.16983e6	1.42736
$298$	149510.	0.0975283
$299$	0	0
$300$	−265296.	−0.170187
$301$	9469.12	0.00602412
$302$	853509.	0.538506
$303$	2.99746e6	1.87563
$304$	2.09753e6	1.30174
$305$	365539.	0.225001
$306$	5.00125e6	3.05334
$307$	102614.	0.0621387	0.0310694	−	0.999517i	$-0.490109\pi$
$307$	102614.	0.0621387	0.0310694	+	0.999517i	$0.490109\pi$
$308$	12424.9	0.00746303
$309$	−2.43718e6	−1.45209
$310$	−430762.	−0.254585
$311$	1.21303e6	0.711168	0.355584	−	0.934644i	$-0.384282\pi$
$311$	1.21303e6	0.711168	0.355584	+	0.934644i	$0.384282\pi$
$312$	−4.39014e6	−2.55324
$313$	3.04190e6	1.75503	0.877514	−	0.479551i	$-0.159200\pi$
$313$	3.04190e6	1.75503	0.877514	+	0.479551i	$0.159200\pi$
$314$	−1.28625e6	−0.736207
$315$	146946.	0.0834416
$316$	−238944.	−0.134610
$317$	−2.10095e6	−1.17427	−0.587133	−	0.809490i	$-0.699744\pi$
$317$	−2.10095e6	−1.17427	−0.587133	+	0.809490i	$0.699744\pi$
$318$	5.78659e6	3.20889
$319$	338991.	0.186514
$320$	851379.	0.464780
$321$	−465107.	−0.251936
$322$	0	0
$323$	−4.24756e6	−2.26534
$324$	−325775.	−0.172407
$325$	2.13378e6	1.12057
$326$	−723744.	−0.377173
$327$	−5.31599e6	−2.74925
$328$	2.03354e6	1.04368
$329$	−57696.4	−0.0293873
$330$	986032.	0.498432
$331$	−2.91623e6	−1.46303	−0.731513	−	0.681827i	$-0.761186\pi$
$331$	−2.91623e6	−1.46303	−0.731513	+	0.681827i	$0.761186\pi$
$332$	−238882.	−0.118943
$333$	−4.36152e6	−2.15540
$334$	−49877.4	−0.0244646
$335$	1.45133e6	0.706567
$336$	290065.	0.140167
$337$	2.93330e6	1.40696	0.703480	−	0.710715i	$-0.251628\pi$
$337$	2.93330e6	1.40696	0.703480	+	0.710715i	$0.251628\pi$
$338$	1.73376e6	0.825462
$339$	690889.	0.326520
$340$	−161492.	−0.0757626
$341$	953480.	0.444044
$342$	−6.54302e6	−3.02491
$343$	−394482.	−0.181047
$344$	−152689.	−0.0695682
$345$	0	0
$346$	−2.12038e6	−0.952188
$347$	−1.48233e6	−0.660877	−0.330438	−	0.943828i	$-0.607197\pi$
$347$	−1.48233e6	−0.660877	−0.330438	+	0.943828i	$0.607197\pi$
$348$	−125318.	−0.0554709
$349$	3.14342e6	1.38146	0.690731	−	0.723112i	$-0.257289\pi$
$349$	3.14342e6	1.38146	0.690731	+	0.723112i	$0.257289\pi$
$350$	−160014.	−0.0698215
$351$	6.45162e6	2.79512
$352$	−379665.	−0.163322
$353$	2.99556e6	1.27950	0.639751	−	0.768582i	$-0.279037\pi$
$353$	2.99556e6	1.27950	0.639751	+	0.768582i	$0.279037\pi$
$354$	−5.80952e6	−2.46395
$355$	934196.	0.393430
$356$	136118.	0.0569235
$357$	−587390.	−0.243925
$358$	2.42397e6	0.999584
$359$	2.23362e6	0.914687	0.457344	−	0.889290i	$-0.348801\pi$
$359$	2.23362e6	0.914687	0.457344	+	0.889290i	$0.348801\pi$
$360$	−2.36950e6	−0.963606
$361$	3.08088e6	1.24425
$362$	642102.	0.257533
$363$	2.27262e6	0.905233
$364$	36943.3	0.0146144
$365$	−140221.	−0.0550910
$366$	−2.25081e6	−0.878287
$367$	923000.	0.357715	0.178857	−	0.983875i	$-0.442760\pi$
$367$	923000.	0.357715	0.178857	+	0.983875i	$0.442760\pi$
$368$	0	0
$369$	−5.58893e6	−2.13679
$370$	−1.05979e6	−0.402452
$371$	−463815.	−0.174948
$372$	−352481.	−0.132062
$373$	2.31000e6	0.859688	0.429844	−	0.902903i	$-0.358569\pi$
$373$	2.31000e6	0.859688	0.429844	+	0.902903i	$0.358569\pi$
$374$	−2.68988e6	−0.994384
$375$	3.75162e6	1.37765
$376$	930348.	0.339372
$377$	1.00793e6	0.365240
$378$	−483814.	−0.174160
$379$	1.89297e6	0.676934	0.338467	−	0.940978i	$-0.390092\pi$
$379$	1.89297e6	0.676934	0.338467	+	0.940978i	$0.390092\pi$
$380$	211277.	0.0750572
$381$	−5.95560e6	−2.10191
$382$	−2.21293e6	−0.775907
$383$	−2.56252e6	−0.892629	−0.446315	−	0.894876i	$-0.647264\pi$
$383$	−2.56252e6	−0.892629	−0.446315	+	0.894876i	$0.647264\pi$
$384$	−4.04586e6	−1.40018
$385$	−79033.9	−0.0271745
$386$	−2.02586e6	−0.692055
$387$	419645.	0.142431
$388$	−240938.	−0.0812506
$389$	−5.33851e6	−1.78873	−0.894367	−	0.447334i	$-0.852373\pi$
$389$	−5.33851e6	−1.78873	−0.894367	+	0.447334i	$0.852373\pi$
$390$	2.93180e6	0.976052
$391$	0	0
$392$	3.16729e6	1.04105
$393$	−957883.	−0.312846
$394$	3.28426e6	1.06585
$395$	1.51991e6	0.490145
$396$	550636.	0.176452
$397$	2.26002e6	0.719676	0.359838	−	0.933015i	$-0.382832\pi$
$397$	2.26002e6	0.719676	0.359838	+	0.933015i	$0.382832\pi$
$398$	−2.41884e6	−0.765420
$399$	768467.	0.241654
$400$	2.27333e6	0.710415
$401$	5.78253e6	1.79580	0.897899	−	0.440202i	$-0.145093\pi$
$401$	5.78253e6	1.79580	0.897899	+	0.440202i	$0.145093\pi$
$402$	−8.93658e6	−2.75808
$403$	2.83501e6	0.869546
$404$	406730.	0.123980
$405$	2.07223e6	0.627771
$406$	−75586.2	−0.0227577
$407$	2.34581e6	0.701950
$408$	9.47160e6	2.81691
$409$	−1.80868e6	−0.534629	−0.267315	−	0.963609i	$-0.586136\pi$
$409$	−1.80868e6	−0.534629	−0.267315	+	0.963609i	$0.586136\pi$
$410$	−1.35803e6	−0.398978
$411$	4.76456e6	1.39129
$412$	−330706.	−0.0959841
$413$	465653.	0.134335
$414$	0	0
$415$	1.51952e6	0.433097
$416$	−1.12887e6	−0.319824
$417$	−4.24261e6	−1.19479
$418$	3.51911e6	0.985126
$419$	2.44304e6	0.679822	0.339911	−	0.940458i	$-0.389603\pi$
$419$	2.44304e6	0.679822	0.339911	+	0.940458i	$0.389603\pi$
$420$	29217.2	0.00808192
$421$	66516.0	0.0182903	0.00914515	−	0.999958i	$-0.497089\pi$
$421$	66516.0	0.0182903	0.00914515	+	0.999958i	$0.497089\pi$
$422$	−4.62713e6	−1.26483
$423$	−2.55695e6	−0.694817
$424$	7.47897e6	2.02035
$425$	−4.60356e6	−1.23629
$426$	−5.75233e6	−1.53575
$427$	180410.	0.0478841
$428$	−63111.2	−0.0166532
$429$	−6.48946e6	−1.70242
$430$	101968.	0.0265945
$431$	583815.	0.151385	0.0756924	−	0.997131i	$-0.475883\pi$
$431$	583815.	0.151385	0.0756924	+	0.997131i	$0.475883\pi$
$432$	6.87356e6	1.77204
$433$	−2.28085e6	−0.584624	−0.292312	−	0.956323i	$-0.594425\pi$
$433$	−2.28085e6	−0.584624	−0.292312	+	0.956323i	$0.594425\pi$
$434$	−212601.	−0.0541803
$435$	797140.	0.201982
$436$	−721337.	−0.181728
$437$	0	0
$438$	863412.	0.215047
$439$	6.19515e6	1.53423	0.767116	−	0.641509i	$-0.221691\pi$
$439$	6.19515e6	1.53423	0.767116	+	0.641509i	$0.221691\pi$
$440$	1.27441e6	0.313818
$441$	−8.70491e6	−2.13141
$442$	−7.99791e6	−1.94725
$443$	−1.01675e6	−0.246153	−0.123076	−	0.992397i	$-0.539276\pi$
$443$	−1.01675e6	−0.246153	−0.123076	+	0.992397i	$0.539276\pi$
$444$	−867195.	−0.208766
$445$	−865841.	−0.207271
$446$	−720451.	−0.171501
$447$	−778201.	−0.184214
$448$	420195.	0.0989135
$449$	−3.04664e6	−0.713191	−0.356595	−	0.934259i	$-0.616062\pi$
$449$	−3.04664e6	−0.713191	−0.356595	+	0.934259i	$0.616062\pi$
$450$	−7.09140e6	−1.65082
$451$	3.00596e6	0.695891
$452$	93748.0	0.0215832
$453$	−4.44251e6	−1.01715
$454$	2.35552e6	0.536349
$455$	−234994.	−0.0532143
$456$	−1.23915e7	−2.79068
$457$	−4.24293e6	−0.950333	−0.475166	−	0.879896i	$-0.657612\pi$
$457$	−4.24293e6	−0.950333	−0.475166	+	0.879896i	$0.657612\pi$
$458$	−3.66700e6	−0.816860
$459$	−1.39192e7	−3.08377
$460$	0	0
$461$	1.08445e6	0.237662	0.118831	−	0.992915i	$-0.462085\pi$
$461$	1.08445e6	0.237662	0.118831	+	0.992915i	$0.462085\pi$
$462$	486653.	0.106075
$463$	932916.	0.202251	0.101125	−	0.994874i	$-0.467756\pi$
$463$	932916.	0.202251	0.101125	+	0.994874i	$0.467756\pi$
$464$	1.07386e6	0.231553
$465$	2.24211e6	0.480867
$466$	2.59034e6	0.552576
$467$	252067.	0.0534839	0.0267420	−	0.999642i	$-0.491487\pi$
$467$	252067.	0.0534839	0.0267420	+	0.999642i	$0.491487\pi$
$468$	1.63722e6	0.345536
$469$	716298.	0.150370
$470$	−621301.	−0.129735
$471$	6.69491e6	1.39057
$472$	−7.50861e6	−1.55133
$473$	−225703.	−0.0463857
$474$	−9.35885e6	−1.91327
$475$	6.02272e6	1.22478
$476$	−79704.0	−0.0161236
$477$	−2.05550e7	−4.13639
$478$	−5.98064e6	−1.19723
$479$	638652.	0.127182	0.0635909	−	0.997976i	$-0.479745\pi$
$479$	638652.	0.127182	0.0635909	+	0.997976i	$0.479745\pi$
$480$	−892786.	−0.176866
$481$	6.97487e6	1.37459
$482$	7.91817e6	1.55241
$483$	0	0
$484$	308376.	0.0598367
$485$	1.53259e6	0.295851
$486$	−2.78327e6	−0.534521
$487$	−6.40830e6	−1.22439	−0.612196	−	0.790706i	$-0.709714\pi$
$487$	−6.40830e6	−1.22439	−0.612196	+	0.790706i	$0.709714\pi$
$488$	−2.90910e6	−0.552979
$489$	3.76708e6	0.712415
$490$	−2.11517e6	−0.397974
$491$	−8.07458e6	−1.51153	−0.755764	−	0.654844i	$-0.772734\pi$
$491$	−8.07458e6	−1.51153	−0.755764	+	0.654844i	$0.772734\pi$
$492$	−1.11124e6	−0.206964
$493$	−2.17459e6	−0.402958
$494$	1.04635e7	1.92912
$495$	−3.50256e6	−0.642500
$496$	3.02043e6	0.551270
$497$	461069.	0.0837288
$498$	−9.35646e6	−1.69059
$499$	7.25360e6	1.30407	0.652037	−	0.758187i	$-0.273915\pi$
$499$	7.25360e6	1.30407	0.652037	+	0.758187i	$0.273915\pi$
$500$	509064.	0.0910641
$501$	259612.	0.0462093
$502$	−337254.	−0.0597308
$503$	4.02697e6	0.709673	0.354836	−	0.934928i	$-0.384537\pi$
$503$	4.02697e6	0.709673	0.354836	+	0.934928i	$0.384537\pi$
$504$	−1.16946e6	−0.205073
$505$	−2.58719e6	−0.451440
$506$	0	0
$507$	−9.02421e6	−1.55916
$508$	−808127.	−0.138938
$509$	−98493.6	−0.0168505	−0.00842526	−	0.999965i	$-0.502682\pi$
$509$	−98493.6	−0.0168505	−0.00842526	+	0.999965i	$0.502682\pi$
$510$	−6.32527e6	−1.07685
$511$	−69205.5	−0.0117243
$512$	−6.61324e6	−1.11491
$513$	1.82101e7	3.05505
$514$	5.78636e6	0.966045
$515$	2.10360e6	0.349499
$516$	83437.6	0.0137955
$517$	1.37523e6	0.226282
$518$	−523053.	−0.0856489
$519$	1.10365e7	1.79852
$520$	3.78925e6	0.614533
$521$	7.76729e6	1.25365	0.626824	−	0.779161i	$-0.284355\pi$
$521$	7.76729e6	1.25365	0.626824	+	0.779161i	$0.284355\pi$
$522$	−3.34977e6	−0.538070
$523$	−1.05753e7	−1.69058	−0.845292	−	0.534305i	$-0.820573\pi$
$523$	−1.05753e7	−1.69058	−0.845292	+	0.534305i	$0.820573\pi$
$524$	−129977.	−0.0206794
$525$	832874.	0.131881
$526$	2.88478e6	0.454620
$527$	−6.11646e6	−0.959342
$528$	−6.91388e6	−1.07929
$529$	0	0
$530$	−4.99457e6	−0.772339
$531$	2.06365e7	3.17614
$532$	104275.	0.0159735
$533$	8.93771e6	1.36273
$534$	5.33143e6	0.809079
$535$	401447.	0.0606378
$536$	−1.15502e7	−1.73651
$537$	−1.26167e7	−1.88804
$538$	−8.83141e6	−1.31545
$539$	4.68186e6	0.694140
$540$	692349.	0.102174
$541$	−2.72554e6	−0.400369	−0.200184	−	0.979758i	$-0.564154\pi$
$541$	−2.72554e6	−0.400369	−0.200184	+	0.979758i	$0.564154\pi$
$542$	3.30247e6	0.482881
$543$	−3.34214e6	−0.486435
$544$	2.43551e6	0.352852
$545$	4.58838e6	0.661711
$546$	1.44698e6	0.207721
$547$	−1.12681e7	−1.61020	−0.805101	−	0.593137i	$-0.797889\pi$
$547$	−1.12681e7	−1.61020	−0.805101	+	0.593137i	$0.797889\pi$
$548$	646512.	0.0919655
$549$	7.99529e6	1.13215
$550$	3.81405e6	0.537625
$551$	2.84496e6	0.399206
$552$	0	0
$553$	750145.	0.104311
$554$	1.41607e6	0.196024
$555$	5.51618e6	0.760162
$556$	−575687.	−0.0789768
$557$	−1.42068e7	−1.94025	−0.970125	−	0.242607i	$-0.921998\pi$
$557$	−1.42068e7	−1.94025	−0.970125	+	0.242607i	$0.921998\pi$
$558$	−9.42190e6	−1.28101
$559$	−671090.	−0.0908345
$560$	−250363.	−0.0337365
$561$	1.40008e7	1.87822
$562$	−2.51160e6	−0.335436
$563$	−9.93624e6	−1.32115	−0.660574	−	0.750761i	$-0.729687\pi$
$563$	−9.93624e6	−1.32115	−0.660574	+	0.750761i	$0.729687\pi$
$564$	−508394.	−0.0672981
$565$	−596326.	−0.0785892
$566$	−4.86168e6	−0.637889
$567$	1.02274e6	0.133601
$568$	−7.43469e6	−0.966923
$569$	2.43903e6	0.315818	0.157909	−	0.987454i	$-0.449525\pi$
$569$	2.43903e6	0.315818	0.157909	+	0.987454i	$0.449525\pi$
$570$	8.27520e6	1.06682
$571$	−1.54691e7	−1.98552	−0.992759	−	0.120124i	$-0.961671\pi$
$571$	−1.54691e7	−1.98552	−0.992759	+	0.120124i	$0.961671\pi$
$572$	−880567.	−0.112531
$573$	1.15183e7	1.46555
$574$	−670250.	−0.0849096
$575$	0	0
$576$	1.86219e7	2.33866
$577$	−1.30892e7	−1.63672	−0.818360	−	0.574706i	$-0.805116\pi$
$577$	−1.30892e7	−1.63672	−0.818360	+	0.574706i	$0.805116\pi$
$578$	9.70910e6	1.20881
$579$	1.05446e7	1.30717
$580$	108165.	0.0133511
$581$	749952.	0.0921708
$582$	−9.43698e6	−1.15485
$583$	1.10553e7	1.34710
$584$	1.11593e6	0.135396
$585$	−1.04143e7	−1.25817
$586$	4.81734e6	0.579514
$587$	2.37887e6	0.284954	0.142477	−	0.989798i	$-0.454493\pi$
$587$	2.37887e6	0.284954	0.142477	+	0.989798i	$0.454493\pi$
$588$	−1.73079e6	−0.206443
$589$	8.00201e6	0.950410
$590$	5.01436e6	0.593042
$591$	−1.70946e7	−2.01321
$592$	7.43103e6	0.871455
$593$	−3.47325e6	−0.405601	−0.202800	−	0.979220i	$-0.565004\pi$
$593$	−3.47325e6	−0.405601	−0.202800	+	0.979220i	$0.565004\pi$
$594$	1.15320e7	1.34103
$595$	506993.	0.0587096
$596$	−105596.	−0.0121767
$597$	1.25901e7	1.44575
$598$	0	0
$599$	5.31390e6	0.605127	0.302564	−	0.953129i	$-0.402158\pi$
$599$	5.31390e6	0.605127	0.302564	+	0.953129i	$0.402158\pi$
$600$	−1.34300e7	−1.52299
$601$	−1.35246e6	−0.152734	−0.0763672	−	0.997080i	$-0.524332\pi$
$601$	−1.35246e6	−0.152734	−0.0763672	+	0.997080i	$0.524332\pi$
$602$	50325.8	0.00565978
$603$	3.17443e7	3.55527
$604$	−602813.	−0.0672341
$605$	−1.96156e6	−0.217878
$606$	1.59307e7	1.76219
$607$	−384207.	−0.0423247	−0.0211623	−	0.999776i	$-0.506737\pi$
$607$	−384207.	−0.0423247	−0.0211623	+	0.999776i	$0.506737\pi$
$608$	−3.18631e6	−0.349566
$609$	393426.	0.0429853
$610$	1.94274e6	0.211393
$611$	4.08902e6	0.443115
$612$	−3.53226e6	−0.381219
$613$	1.67749e7	1.80306	0.901530	−	0.432718i	$-0.142445\pi$
$613$	1.67749e7	1.80306	0.901530	+	0.432718i	$0.142445\pi$
$614$	545368.	0.0583806
$615$	7.06853e6	0.753601
$616$	628982.	0.0667862
$617$	−1.27567e6	−0.134905	−0.0674523	−	0.997723i	$-0.521487\pi$
$617$	−1.27567e6	−0.134905	−0.0674523	+	0.997723i	$0.521487\pi$
$618$	−1.29530e7	−1.36426
$619$	−1.46795e7	−1.53988	−0.769938	−	0.638118i	$-0.779713\pi$
$619$	−1.46795e7	−1.53988	−0.769938	+	0.638118i	$0.779713\pi$
$620$	304237.	0.0317857
$621$	0	0
$622$	6.44695e6	0.668157
$623$	−427333.	−0.0441109
$624$	−2.05573e7	−2.11351
$625$	4.74593e6	0.485983
$626$	1.61669e7	1.64888
$627$	−1.83169e7	−1.86073
$628$	908444.	0.0919177
$629$	−1.50481e7	−1.51654
$630$	780980.	0.0783951
$631$	1.65066e7	1.65038	0.825190	−	0.564856i	$-0.191068\pi$
$631$	1.65066e7	1.65038	0.825190	+	0.564856i	$0.191068\pi$
$632$	−1.20960e7	−1.20462
$633$	2.40842e7	2.38904
$634$	−1.11660e7	−1.10325
$635$	5.14045e6	0.505902
$636$	−4.08692e6	−0.400640
$637$	1.39207e7	1.35930
$638$	1.80165e6	0.175234
$639$	2.04333e7	1.97964
$640$	3.49209e6	0.337005
$641$	−1.87653e6	−0.180389	−0.0901947	−	0.995924i	$-0.528749\pi$
$641$	−1.87653e6	−0.180389	−0.0901947	+	0.995924i	$0.528749\pi$
$642$	−2.47192e6	−0.236699
$643$	−1.72531e6	−0.164566	−0.0822830	−	0.996609i	$-0.526221\pi$
$643$	−1.72531e6	−0.164566	−0.0822830	+	0.996609i	$0.526221\pi$
$644$	0	0
$645$	−530741.	−0.0502324
$646$	−2.25746e7	−2.12833
$647$	1.18002e7	1.10822	0.554112	−	0.832442i	$-0.313058\pi$
$647$	1.18002e7	1.10822	0.554112	+	0.832442i	$0.313058\pi$
$648$	−1.64916e7	−1.54286
$649$	−1.10992e7	−1.03438
$650$	1.13404e7	1.05280
$651$	1.10659e6	0.102337
$652$	511163.	0.0470912
$653$	1.00372e7	0.921147	0.460573	−	0.887622i	$-0.347644\pi$
$653$	1.00372e7	0.921147	0.460573	+	0.887622i	$0.347644\pi$
$654$	−2.82530e7	−2.58298
$655$	826776.	0.0752982
$656$	9.52226e6	0.863933
$657$	−3.06700e6	−0.277204
$658$	−306641.	−0.0276099
$659$	−1.02223e7	−0.916929	−0.458464	−	0.888713i	$-0.651600\pi$
$659$	−1.02223e7	−0.916929	−0.458464	+	0.888713i	$0.651600\pi$
$660$	−696410.	−0.0622308
$661$	1.87007e6	0.166477	0.0832386	−	0.996530i	$-0.473474\pi$
$661$	1.87007e6	0.166477	0.0832386	+	0.996530i	$0.473474\pi$
$662$	−1.54990e7	−1.37454
$663$	4.16291e7	3.67801
$664$	−1.20929e7	−1.06441
$665$	−663286.	−0.0581630
$666$	−2.31803e7	−2.02504
$667$	0	0
$668$	35227.2	0.00305448
$669$	3.74995e6	0.323936
$670$	7.71341e6	0.663834
$671$	−4.30020e6	−0.368708
$672$	−440631.	−0.0376402
$673$	−2.14057e6	−0.182176	−0.0910881	−	0.995843i	$-0.529034\pi$
$673$	−2.14057e6	−0.182176	−0.0910881	+	0.995843i	$0.529034\pi$
$674$	1.55897e7	1.32187
$675$	1.97363e7	1.66727
$676$	−1.22451e6	−0.103061
$677$	−1.42893e7	−1.19822	−0.599112	−	0.800665i	$-0.704480\pi$
$677$	−1.42893e7	−1.19822	−0.599112	+	0.800665i	$0.704480\pi$
$678$	3.67189e6	0.306772
$679$	756407.	0.0629624
$680$	−8.17520e6	−0.677995
$681$	−1.22605e7	−1.01307
$682$	5.06749e6	0.417188
$683$	−7.29980e6	−0.598769	−0.299384	−	0.954133i	$-0.596781\pi$
$683$	−7.29980e6	−0.598769	−0.299384	+	0.954133i	$0.596781\pi$
$684$	4.62117e6	0.377670
$685$	−4.11242e6	−0.334866
$686$	−2.09656e6	−0.170097
$687$	1.90867e7	1.54291
$688$	−714980.	−0.0575868
$689$	3.28712e7	2.63796
$690$	0	0
$691$	3.77617e6	0.300855	0.150427	−	0.988621i	$-0.451935\pi$
$691$	3.77617e6	0.300855	0.150427	+	0.988621i	$0.451935\pi$
$692$	1.49757e6	0.118884
$693$	−1.72868e6	−0.136735
$694$	−7.87817e6	−0.620907
$695$	3.66191e6	0.287572
$696$	−6.34395e6	−0.496406
$697$	−1.92828e7	−1.50345
$698$	1.67064e7	1.29791
$699$	−1.34827e7	−1.04372
$700$	113014.	0.00871743
$701$	1.27732e7	0.981761	0.490880	−	0.871227i	$-0.336675\pi$
$701$	1.27732e7	0.981761	0.490880	+	0.871227i	$0.336675\pi$
$702$	3.42886e7	2.62607
$703$	1.96870e7	1.50242
$704$	−1.00156e7	−0.761634
$705$	3.23387e6	0.245047
$706$	1.59206e7	1.20212
$707$	−1.27690e6	−0.0960744
$708$	4.10312e6	0.307632
$709$	2.21287e7	1.65326	0.826628	−	0.562748i	$-0.190256\pi$
$709$	2.21287e7	1.65326	0.826628	+	0.562748i	$0.190256\pi$
$710$	4.96500e6	0.369635
$711$	3.32443e7	2.46629
$712$	6.89069e6	0.509405
$713$	0	0
$714$	−3.12182e6	−0.229172
$715$	5.60124e6	0.409750
$716$	−1.71199e6	−0.124801
$717$	3.11292e7	2.26136
$718$	1.18711e7	0.859367
$719$	−6.86509e6	−0.495249	−0.247625	−	0.968856i	$-0.579650\pi$
$719$	−6.86509e6	−0.495249	−0.247625	+	0.968856i	$0.579650\pi$
$720$	−1.10954e7	−0.797649
$721$	1.03823e6	0.0743796
$722$	1.63740e7	1.16900
$723$	−4.12140e7	−2.93224
$724$	−453501.	−0.0321538
$725$	3.08340e6	0.217864
$726$	1.20784e7	0.850485
$727$	−4.75733e6	−0.333831	−0.166916	−	0.985971i	$-0.553381\pi$
$727$	−4.75733e6	−0.333831	−0.166916	+	0.985971i	$0.553381\pi$
$728$	1.87017e6	0.130784
$729$	−6.60269e6	−0.460153
$730$	−745236.	−0.0517591
$731$	1.44786e6	0.100215
$732$	1.58969e6	0.109657
$733$	−2.41232e7	−1.65835	−0.829173	−	0.558993i	$-0.811188\pi$
$733$	−2.41232e7	−1.65835	−0.829173	+	0.558993i	$0.811188\pi$
$734$	4.90550e6	0.336080
$735$	1.10094e7	0.751704
$736$	0	0
$737$	−1.70734e7	−1.15785
$738$	−2.97036e7	−2.00756
$739$	−1.01851e7	−0.686050	−0.343025	−	0.939326i	$-0.611452\pi$
$739$	−1.01851e7	−0.686050	−0.343025	+	0.939326i	$0.611452\pi$
$740$	748501.	0.0502473
$741$	−5.44623e7	−3.64377
$742$	−2.46505e6	−0.164368
$743$	1.55515e7	1.03348	0.516738	−	0.856144i	$-0.327146\pi$
$743$	1.55515e7	1.03348	0.516738	+	0.856144i	$0.327146\pi$
$744$	−1.78436e7	−1.18182
$745$	671687.	0.0443380
$746$	1.22770e7	0.807694
$747$	3.32358e7	2.17924
$748$	1.89980e6	0.124152
$749$	198133.	0.0129048
$750$	1.99388e7	1.29433
$751$	1.03320e7	0.668473	0.334237	−	0.942489i	$-0.391522\pi$
$751$	1.03320e7	0.668473	0.334237	+	0.942489i	$0.391522\pi$
$752$	4.35645e6	0.280924
$753$	1.75541e6	0.112821
$754$	5.35690e6	0.343151
$755$	3.83446e6	0.244814
$756$	341706.	0.0217444
$757$	1.61676e7	1.02543	0.512714	−	0.858559i	$-0.328640\pi$
$757$	1.61676e7	1.02543	0.512714	+	0.858559i	$0.328640\pi$
$758$	1.00606e7	0.635993
$759$	0	0
$760$	1.06954e7	0.671682
$761$	8.40313e6	0.525993	0.262996	−	0.964797i	$-0.415289\pi$
$761$	8.40313e6	0.525993	0.262996	+	0.964797i	$0.415289\pi$
$762$	−3.16524e7	−1.97478
$763$	2.26458e6	0.140824
$764$	1.56294e6	0.0968743
$765$	2.24685e7	1.38810
$766$	−1.36191e7	−0.838643
$767$	−3.30015e7	−2.02556
$768$	1.00618e7	0.615560
$769$	1.74997e7	1.06713	0.533563	−	0.845760i	$-0.320853\pi$
$769$	1.74997e7	1.06713	0.533563	+	0.845760i	$0.320853\pi$
$770$	−420044.	−0.0255310
$771$	−3.01180e7	−1.82469
$772$	1.43081e6	0.0864052
$773$	2.11605e7	1.27373	0.636863	−	0.770977i	$-0.280232\pi$
$773$	2.11605e7	1.27373	0.636863	+	0.770977i	$0.280232\pi$
$774$	2.23030e6	0.133817
$775$	8.67268e6	0.518679
$776$	−1.21970e7	−0.727106
$777$	2.72249e6	0.161776
$778$	−2.83727e7	−1.68055
$779$	2.52273e7	1.48945
$780$	−2.07066e6	−0.121863
$781$	−1.09899e7	−0.644712
$782$	0	0
$783$	9.32287e6	0.543432
$784$	1.48312e7	0.861759
$785$	−5.77856e6	−0.334692
$786$	−5.09089e6	−0.293926
$787$	1.19600e7	0.688325	0.344163	−	0.938910i	$-0.388163\pi$
$787$	1.19600e7	0.688325	0.344163	+	0.938910i	$0.388163\pi$
$788$	−2.31959e6	−0.133075
$789$	−1.50153e7	−0.858698
$790$	8.07789e6	0.460501
$791$	−294315.	−0.0167252
$792$	2.78748e7	1.57906
$793$	−1.27859e7	−0.722020
$794$	1.20114e7	0.676150
$795$	2.59967e7	1.45882
$796$	1.70837e6	0.0955650
$797$	−1.32264e7	−0.737559	−0.368779	−	0.929517i	$-0.620224\pi$
$797$	−1.32264e7	−0.737559	−0.368779	+	0.929517i	$0.620224\pi$
$798$	4.08420e6	0.227038
$799$	−8.82194e6	−0.488874
$800$	−3.45336e6	−0.190773
$801$	−1.89382e7	−1.04294
$802$	3.07326e7	1.68719
$803$	1.64956e6	0.0902773
$804$	6.31169e6	0.344354
$805$	0	0
$806$	1.50673e7	0.816956
$807$	4.59674e7	2.48466
$808$	2.05898e7	1.10949
$809$	2.81536e6	0.151239	0.0756194	−	0.997137i	$-0.475907\pi$
$809$	2.81536e6	0.151239	0.0756194	+	0.997137i	$0.475907\pi$
$810$	1.10134e7	0.589803
$811$	2.03162e7	1.08465	0.542325	−	0.840169i	$-0.317544\pi$
$811$	2.03162e7	1.08465	0.542325	+	0.840169i	$0.317544\pi$
$812$	53384.7	0.00284136
$813$	−1.71893e7	−0.912079
$814$	1.24673e7	0.659496
$815$	−3.25148e6	−0.171469
$816$	4.43517e7	2.33177
$817$	−1.89419e6	−0.0992817
$818$	−9.61263e6	−0.502295
$819$	−5.13994e6	−0.267761
$820$	959142.	0.0498136
$821$	2.06237e7	1.06785	0.533924	−	0.845532i	$-0.320717\pi$
$821$	2.06237e7	1.06785	0.533924	+	0.845532i	$0.320717\pi$
$822$	2.53223e7	1.30715
$823$	3.05683e7	1.57316	0.786578	−	0.617491i	$-0.211851\pi$
$823$	3.05683e7	1.57316	0.786578	+	0.617491i	$0.211851\pi$
$824$	−1.67413e7	−0.858955
$825$	−1.98521e7	−1.01548
$826$	2.47482e6	0.126210
$827$	−3.23053e7	−1.64252	−0.821258	−	0.570556i	$-0.806728\pi$
$827$	−3.23053e7	−1.64252	−0.821258	+	0.570556i	$0.806728\pi$
$828$	0	0
$829$	1.30561e7	0.659823	0.329912	−	0.944012i	$-0.392981\pi$
$829$	1.30561e7	0.659823	0.329912	+	0.944012i	$0.392981\pi$
$830$	8.07582e6	0.406904
$831$	−7.37063e6	−0.370256
$832$	−2.97798e7	−1.49147
$833$	−3.00336e7	−1.49967
$834$	−2.25483e7	−1.12253
$835$	−224078.	−0.0111220
$836$	−2.48546e6	−0.122996
$837$	2.62224e7	1.29378
$838$	1.29841e7	0.638707
$839$	6.50241e6	0.318911	0.159455	−	0.987205i	$-0.449026\pi$
$839$	6.50241e6	0.318911	0.159455	+	0.987205i	$0.449026\pi$
$840$	1.47906e6	0.0723246
$841$	−1.90546e7	−0.928989
$842$	353514.	0.0171841
$843$	1.30729e7	0.633581
$844$	3.26803e6	0.157917
$845$	7.78905e6	0.375269
$846$	−1.35895e7	−0.652795
$847$	−968123.	−0.0463684
$848$	3.50210e7	1.67240
$849$	2.53050e7	1.20486
$850$	−2.44667e7	−1.16152
$851$	0	0
$852$	4.06273e6	0.191743
$853$	−3.18228e7	−1.49750	−0.748749	−	0.662854i	$-0.769345\pi$
$853$	−3.18228e7	−1.49750	−0.748749	+	0.662854i	$0.769345\pi$
$854$	958832.	0.0449881
$855$	−2.93950e7	−1.37518
$856$	−3.19487e6	−0.149028
$857$	−1.82430e7	−0.848487	−0.424243	−	0.905548i	$-0.639460\pi$
$857$	−1.82430e7	−0.848487	−0.424243	+	0.905548i	$0.639460\pi$
$858$	−3.44897e7	−1.59945
$859$	2.66125e7	1.23056	0.615281	−	0.788308i	$-0.289043\pi$
$859$	2.66125e7	1.23056	0.615281	+	0.788308i	$0.289043\pi$
$860$	−72017.3	−0.00332040
$861$	3.48865e6	0.160380
$862$	3.10282e6	0.142229
$863$	4.88600e6	0.223320	0.111660	−	0.993746i	$-0.464383\pi$
$863$	4.88600e6	0.223320	0.111660	+	0.993746i	$0.464383\pi$
$864$	−1.04415e7	−0.475858
$865$	−9.52595e6	−0.432881
$866$	−1.21221e7	−0.549266
$867$	−5.05358e7	−2.28324
$868$	150155.	0.00676457
$869$	−1.78802e7	−0.803198
$870$	4.23658e6	0.189766
$871$	−5.07650e7	−2.26735
$872$	−3.65161e7	−1.62627
$873$	3.35219e7	1.48865
$874$	0	0
$875$	−1.59817e6	−0.0705670
$876$	−609807.	−0.0268492
$877$	−2.36006e7	−1.03615	−0.518077	−	0.855334i	$-0.673352\pi$
$877$	−2.36006e7	−1.03615	−0.518077	+	0.855334i	$0.673352\pi$
$878$	3.29256e7	1.44144
$879$	−2.50743e7	−1.09460
$880$	5.96757e6	0.259771
$881$	−7.11920e6	−0.309023	−0.154512	−	0.987991i	$-0.549380\pi$
$881$	−7.11920e6	−0.309023	−0.154512	+	0.987991i	$0.549380\pi$
$882$	−4.62643e7	−2.00251
$883$	−3.69545e7	−1.59502	−0.797509	−	0.603307i	$-0.793849\pi$
$883$	−3.69545e7	−1.59502	−0.797509	+	0.603307i	$0.793849\pi$
$884$	5.64873e6	0.243120
$885$	−2.60997e7	−1.12015
$886$	−5.40374e6	−0.231265
$887$	2.40116e6	0.102474	0.0512368	−	0.998687i	$-0.483684\pi$
$887$	2.40116e6	0.102474	0.0512368	+	0.998687i	$0.483684\pi$
$888$	−4.38999e7	−1.86823
$889$	2.53705e6	0.107665
$890$	−4.60171e6	−0.194735
$891$	−2.43778e7	−1.02873
$892$	508837.	0.0214125
$893$	1.15415e7	0.484323
$894$	−4.13593e6	−0.173073
$895$	1.08899e7	0.454428
$896$	1.72351e6	0.0717206
$897$	0	0
$898$	−1.61921e7	−0.670057
$899$	4.09672e6	0.169059
$900$	5.00848e6	0.206110
$901$	−7.09186e7	−2.91037
$902$	1.59758e7	0.653804
$903$	−261946.	−0.0106903
$904$	4.74579e6	0.193147
$905$	2.88469e6	0.117079
$906$	−2.36107e7	−0.955628
$907$	−1.34643e7	−0.543458	−0.271729	−	0.962374i	$-0.587595\pi$
$907$	−1.34643e7	−0.543458	−0.271729	+	0.962374i	$0.587595\pi$
$908$	−1.66365e6	−0.0669648
$909$	−5.65886e7	−2.27153
$910$	−1.24893e6	−0.0499959
$911$	−3.07348e7	−1.22697	−0.613485	−	0.789707i	$-0.710233\pi$
$911$	−3.07348e7	−1.22697	−0.613485	+	0.789707i	$0.710233\pi$
$912$	−5.80243e7	−2.31006
$913$	−1.78756e7	−0.709715
$914$	−2.25500e7	−0.892857
$915$	−1.01119e7	−0.399284
$916$	2.58991e6	0.101987
$917$	408052.	0.0160248
$918$	−7.39766e7	−2.89726
$919$	−2.52416e7	−0.985888	−0.492944	−	0.870061i	$-0.664079\pi$
$919$	−2.52416e7	−0.985888	−0.492944	+	0.870061i	$0.664079\pi$
$920$	0	0
$921$	−2.83864e6	−0.110271
$922$	5.76358e6	0.223288
$923$	−3.26766e7	−1.26250
$924$	−343711.	−0.0132438
$925$	2.13370e7	0.819935
$926$	4.95820e6	0.190019
$927$	4.60113e7	1.75859
$928$	−1.63127e6	−0.0621807
$929$	1.43072e7	0.543897	0.271948	−	0.962312i	$-0.412332\pi$
$929$	1.43072e7	0.543897	0.271948	+	0.962312i	$0.412332\pi$
$930$	1.19162e7	0.451785
$931$	3.92922e7	1.48570
$932$	−1.82949e6	−0.0689908
$933$	−3.35563e7	−1.26203
$934$	1.33967e6	0.0502492
$935$	−1.20845e7	−0.452064
$936$	8.28810e7	3.09218
$937$	1.37068e7	0.510020	0.255010	−	0.966938i	$-0.417921\pi$
$937$	1.37068e7	0.510020	0.255010	+	0.966938i	$0.417921\pi$
$938$	3.80693e6	0.141276
$939$	−8.41485e7	−3.11446
$940$	438809.	0.0161978
$941$	−7.51582e6	−0.276696	−0.138348	−	0.990384i	$-0.544179\pi$
$941$	−7.51582e6	−0.276696	−0.138348	+	0.990384i	$0.544179\pi$
$942$	3.55816e7	1.30647
$943$	0	0
$944$	−3.51598e7	−1.28415
$945$	−2.17357e6	−0.0791762
$946$	−1.19955e6	−0.0435803
$947$	1.59343e7	0.577375	0.288688	−	0.957423i	$-0.406781\pi$
$947$	1.59343e7	0.577375	0.288688	+	0.957423i	$0.406781\pi$
$948$	6.60993e6	0.238878
$949$	4.90469e6	0.176785
$950$	3.20091e7	1.15071
$951$	5.81187e7	2.08384
$952$	−4.03484e6	−0.144289
$953$	−2.00561e7	−0.715343	−0.357672	−	0.933847i	$-0.616429\pi$
$953$	−2.00561e7	−0.715343	−0.357672	+	0.933847i	$0.616429\pi$
$954$	−1.09244e8	−3.88622
$955$	−9.94177e6	−0.352740
$956$	4.22398e6	0.149478
$957$	−9.37756e6	−0.330986
$958$	3.39426e6	0.119490
$959$	−2.02967e6	−0.0712655
$960$	−2.35518e7	−0.824795
$961$	−1.71063e7	−0.597514
$962$	3.70695e7	1.29145
$963$	8.78070e6	0.305115
$964$	−5.59241e6	−0.193823
$965$	−9.10132e6	−0.314620
$966$	0	0
$967$	1.66228e7	0.571661	0.285831	−	0.958280i	$-0.407731\pi$
$967$	1.66228e7	0.571661	0.285831	+	0.958280i	$0.407731\pi$
$968$	1.56109e7	0.535475
$969$	1.17501e8	4.02005
$970$	8.14533e6	0.277958
$971$	5.74792e7	1.95642	0.978212	−	0.207609i	$-0.0665680\pi$
$971$	5.74792e7	1.95642	0.978212	+	0.207609i	$0.0665680\pi$
$972$	1.96576e6	0.0667366
$973$	1.80732e6	0.0612004
$974$	−3.40584e7	−1.15034
$975$	−5.90269e7	−1.98856
$976$	−1.36221e7	−0.457742
$977$	−2.65537e7	−0.889996	−0.444998	−	0.895532i	$-0.646796\pi$
$977$	−2.65537e7	−0.889996	−0.444998	+	0.895532i	$0.646796\pi$
$978$	2.00210e7	0.669328
$979$	1.01858e7	0.339654
$980$	1.49389e6	0.0496882
$981$	1.00360e8	3.32957
$982$	−4.29142e7	−1.42011
$983$	−2.70907e6	−0.0894205	−0.0447102	−	0.999000i	$-0.514236\pi$
$983$	−2.70907e6	−0.0894205	−0.0447102	+	0.999000i	$0.514236\pi$
$984$	−5.62541e7	−1.85211
$985$	1.47548e7	0.484555
$986$	−1.15573e7	−0.378587
$987$	1.59606e6	0.0521503
$988$	−7.39010e6	−0.240856
$989$	0	0
$990$	−1.86152e7	−0.603642
$991$	2.13175e7	0.689530	0.344765	−	0.938689i	$-0.387959\pi$
$991$	2.13175e7	0.689530	0.344765	+	0.938689i	$0.387959\pi$
$992$	−4.58827e6	−0.148037
$993$	8.06721e7	2.59627
$994$	2.45046e6	0.0786649
$995$	−1.08668e7	−0.347973
$996$	6.60824e6	0.211075
$997$	4.42548e7	1.41001	0.705005	−	0.709202i	$-0.250945\pi$
$997$	4.42548e7	1.41001	0.705005	+	0.709202i	$0.250945\pi$
$998$	3.85509e7	1.22520
$999$	6.45139e7	2.04522

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.6.a.a.1.3	✓	3	23.22	odd	2
207.6.a.b.1.1		3	69.68	even	2
368.6.a.e.1.3		3	92.91	even	2
529.6.a.a.1.3		3	1.1	even	1	trivial
575.6.a.b.1.1		3	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+5.31473 q^{2} -27.6631 q^{3} -3.75366 q^{4} +23.8768 q^{5} -147.022 q^{6} +11.7843 q^{7} -190.021 q^{8} +522.249 q^{9} +O(q^{10})\)	\(q+5.31473 q^{2} -27.6631 q^{3} -3.75366 q^{4} +23.8768 q^{5} -147.022 q^{6} +11.7843 q^{7} -190.021 q^{8} +522.249 q^{9} +126.899 q^{10} -280.887 q^{11} +103.838 q^{12} -835.171 q^{13} +62.6305 q^{14} -660.508 q^{15} -889.793 q^{16} +1801.86 q^{17} +2775.61 q^{18} -2357.32 q^{19} -89.6256 q^{20} -325.991 q^{21} -1492.84 q^{22} +5256.58 q^{24} -2554.90 q^{25} -4438.71 q^{26} -7724.90 q^{27} -44.2344 q^{28} -1206.86 q^{29} -3510.42 q^{30} -3394.53 q^{31} +1351.66 q^{32} +7770.22 q^{33} +9576.38 q^{34} +281.372 q^{35} -1960.35 q^{36} -8351.42 q^{37} -12528.5 q^{38} +23103.5 q^{39} -4537.10 q^{40} -10701.7 q^{41} -1732.56 q^{42} +803.535 q^{43} +1054.36 q^{44} +12469.7 q^{45} -4896.03 q^{47} +24614.5 q^{48} -16668.1 q^{49} -13578.6 q^{50} -49845.0 q^{51} +3134.95 q^{52} -39358.6 q^{53} -41055.8 q^{54} -6706.69 q^{55} -2239.27 q^{56} +65211.0 q^{57} -6414.13 q^{58} +39514.6 q^{59} +2479.32 q^{60} +15309.3 q^{61} -18041.0 q^{62} +6154.35 q^{63} +35657.1 q^{64} -19941.2 q^{65} +41296.6 q^{66} +60783.9 q^{67} -6763.56 q^{68} +1495.42 q^{70} +39125.6 q^{71} -99238.3 q^{72} -5872.67 q^{73} -44385.5 q^{74} +70676.5 q^{75} +8848.60 q^{76} -3310.07 q^{77} +122789. q^{78} +63656.1 q^{79} -21245.4 q^{80} +86788.5 q^{81} -56876.4 q^{82} +63639.8 q^{83} +1223.66 q^{84} +43022.6 q^{85} +4270.57 q^{86} +33385.5 q^{87} +53374.5 q^{88} -36262.8 q^{89} +66272.8 q^{90} -9841.93 q^{91} +93903.4 q^{93} -26021.1 q^{94} -56285.4 q^{95} -37391.3 q^{96} +64187.5 q^{97} -88586.6 q^{98} -146693. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} + 58 q^{5} - 230 q^{6} + 282 q^{7} - 360 q^{8} + 121 q^{9}+O(q^{10}) \) 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	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} + 58 q^{5} - 230 q^{6} + 282 q^{7} - 360 q^{8} + 121 q^{9} + 156 q^{10} - 136 q^{11} + 620 q^{12} - 1116 q^{13} - 2016 q^{14} - 750 q^{15} + 128 q^{16} + 896 q^{17} + 4282 q^{18} - 1654 q^{19} - 1504 q^{20} + 1670 q^{21} - 1352 q^{22} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} + 10264 q^{28} - 844 q^{29} - 3180 q^{30} - 3020 q^{31} + 6656 q^{32} + 7370 q^{33} + 11212 q^{34} + 1072 q^{35} - 2548 q^{36} - 8938 q^{37} - 10728 q^{38} + 16020 q^{39} - 3440 q^{40} - 12792 q^{41} - 20560 q^{42} + 16730 q^{43} - 5112 q^{44} + 3936 q^{45} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} - 50290 q^{51} - 47412 q^{52} - 17108 q^{53} - 7610 q^{54} - 436 q^{55} - 42640 q^{56} + 61960 q^{57} - 55678 q^{58} + 54176 q^{59} + 2400 q^{60} + 71324 q^{61} - 72710 q^{62} - 40696 q^{63} - 49984 q^{64} - 846 q^{65} + 42860 q^{66} + 62960 q^{67} + 8352 q^{68} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} + 59044 q^{74} + 44800 q^{75} - 31488 q^{76} - 304 q^{77} + 182070 q^{78} - 58224 q^{79} + 17568 q^{80} + 149947 q^{81} + 61926 q^{82} - 9892 q^{83} + 109720 q^{84} + 15536 q^{85} - 191140 q^{86} + 90500 q^{87} + 58400 q^{88} - 27542 q^{89} + 62112 q^{90} - 151974 q^{91} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} + 273672 q^{97} - 401276 q^{98} - 183082 q^{99}+O(q^{100}) \) 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 + 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 + 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 + 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 + 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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