LMFDB - Embedded newform 722.6.a.q.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,6,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, 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("722.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	722.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:	$115.797117905$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 $ x^15 - 2871x^13 - 4674x^12 + 3170019x^11 + 9081402x^10 - 1680307373x^9 - 6060225486x^8 + 437045334939x^7 + 1625551725606x^6 - 51993847360191x^5 - 166593470925336x^4 + 2435236025483701x^3 + 5743342864926480x^2 - 19853455953893436*x - 34308015556724472
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 19^{6} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-10.7498$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -10.4025 q^{3} +16.0000 q^{4} +95.5276 q^{5} +41.6100 q^{6} +232.219 q^{7} -64.0000 q^{8} -134.788 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -10.4025 q^{3} +16.0000 q^{4} +95.5276 q^{5} +41.6100 q^{6} +232.219 q^{7} -64.0000 q^{8} -134.788 q^{9} -382.111 q^{10} +345.880 q^{11} -166.440 q^{12} -506.327 q^{13} -928.874 q^{14} -993.725 q^{15} +256.000 q^{16} -797.089 q^{17} +539.153 q^{18} +1528.44 q^{20} -2415.65 q^{21} -1383.52 q^{22} -1190.67 q^{23} +665.760 q^{24} +6000.53 q^{25} +2025.31 q^{26} +3929.94 q^{27} +3715.50 q^{28} +425.364 q^{29} +3974.90 q^{30} -6647.85 q^{31} -1024.00 q^{32} -3598.01 q^{33} +3188.36 q^{34} +22183.3 q^{35} -2156.61 q^{36} +7850.99 q^{37} +5267.06 q^{39} -6113.77 q^{40} +16080.1 q^{41} +9662.61 q^{42} +12922.4 q^{43} +5534.07 q^{44} -12876.0 q^{45} +4762.67 q^{46} -21190.2 q^{47} -2663.04 q^{48} +37118.5 q^{49} -24002.1 q^{50} +8291.71 q^{51} -8101.23 q^{52} +29091.8 q^{53} -15719.8 q^{54} +33041.1 q^{55} -14862.0 q^{56} -1701.45 q^{58} -9346.25 q^{59} -15899.6 q^{60} -8320.98 q^{61} +26591.4 q^{62} -31300.3 q^{63} +4096.00 q^{64} -48368.2 q^{65} +14392.0 q^{66} +14347.1 q^{67} -12753.4 q^{68} +12385.9 q^{69} -88733.1 q^{70} +31200.2 q^{71} +8626.44 q^{72} +1992.28 q^{73} -31404.0 q^{74} -62420.4 q^{75} +80319.7 q^{77} -21068.2 q^{78} +9623.27 q^{79} +24455.1 q^{80} -8127.64 q^{81} -64320.3 q^{82} -34179.5 q^{83} -38650.4 q^{84} -76144.0 q^{85} -51689.4 q^{86} -4424.84 q^{87} -22136.3 q^{88} +111322. q^{89} +51504.0 q^{90} -117578. q^{91} -19050.7 q^{92} +69154.2 q^{93} +84760.6 q^{94} +10652.2 q^{96} -96994.8 q^{97} -148474. q^{98} -46620.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) $ 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9} - 432 q^{10} + 126 q^{11} + 114 q^{13} - 336 q^{14} + 3840 q^{16} + 4119 q^{17} - 8508 q^{18} + 1728 q^{20} - 3408 q^{21} - 504 q^{22} + 3936 q^{23} + 26895 q^{25} - 456 q^{26} + 13017 q^{27} + 1344 q^{28} - 14658 q^{29} - 6840 q^{31} - 15360 q^{32} + 3945 q^{33} - 16476 q^{34} + 12636 q^{35} + 34032 q^{36} + 4278 q^{37} + 4956 q^{39} - 6912 q^{40} - 5112 q^{41} + 13632 q^{42} + 94191 q^{43} + 2016 q^{44} + 31770 q^{45} - 15744 q^{46} + 702 q^{47} + 63777 q^{49} - 107580 q^{50} + 108 q^{51} + 1824 q^{52} - 47544 q^{53} - 52068 q^{54} + 16848 q^{55} - 5376 q^{56} + 58632 q^{58} + 8832 q^{59} + 119196 q^{61} + 27360 q^{62} - 88068 q^{63} + 61440 q^{64} - 80646 q^{65} - 15780 q^{66} - 64248 q^{67} + 65904 q^{68} - 124224 q^{69} - 50544 q^{70} + 53364 q^{71} - 136128 q^{72} - 4908 q^{73} - 17112 q^{74} + 87480 q^{75} + 121218 q^{77} - 19824 q^{78} + 115500 q^{79} + 27648 q^{80} + 481659 q^{81} + 20448 q^{82} + 201630 q^{83} - 54528 q^{84} - 150282 q^{85} - 376764 q^{86} + 376512 q^{87} - 8064 q^{88} + 101505 q^{89} - 127080 q^{90} - 414918 q^{91} + 62976 q^{92} + 165960 q^{93} - 2808 q^{94} - 297114 q^{97} - 255108 q^{98} - 149895 q^{99}+O(q^{100}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9 - 432 * q^10 + 126 * q^11 + 114 * q^13 - 336 * q^14 + 3840 * q^16 + 4119 * q^17 - 8508 * q^18 + 1728 * q^20 - 3408 * q^21 - 504 * q^22 + 3936 * q^23 + 26895 * q^25 - 456 * q^26 + 13017 * q^27 + 1344 * q^28 - 14658 * q^29 - 6840 * q^31 - 15360 * q^32 + 3945 * q^33 - 16476 * q^34 + 12636 * q^35 + 34032 * q^36 + 4278 * q^37 + 4956 * q^39 - 6912 * q^40 - 5112 * q^41 + 13632 * q^42 + 94191 * q^43 + 2016 * q^44 + 31770 * q^45 - 15744 * q^46 + 702 * q^47 + 63777 * q^49 - 107580 * q^50 + 108 * q^51 + 1824 * q^52 - 47544 * q^53 - 52068 * q^54 + 16848 * q^55 - 5376 * q^56 + 58632 * q^58 + 8832 * q^59 + 119196 * q^61 + 27360 * q^62 - 88068 * q^63 + 61440 * q^64 - 80646 * q^65 - 15780 * q^66 - 64248 * q^67 + 65904 * q^68 - 124224 * q^69 - 50544 * q^70 + 53364 * q^71 - 136128 * q^72 - 4908 * q^73 - 17112 * q^74 + 87480 * q^75 + 121218 * q^77 - 19824 * q^78 + 115500 * q^79 + 27648 * q^80 + 481659 * q^81 + 20448 * q^82 + 201630 * q^83 - 54528 * q^84 - 150282 * q^85 - 376764 * q^86 + 376512 * q^87 - 8064 * q^88 + 101505 * q^89 - 127080 * q^90 - 414918 * q^91 + 62976 * q^92 + 165960 * q^93 - 2808 * q^94 - 297114 * q^97 - 255108 * q^98 - 149895 * 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
$3$	−10.4025	−0.667320	−0.333660	−	0.942693i	$-0.608284\pi$
$3$	−10.4025	−0.667320	−0.333660	+	0.942693i	$0.608284\pi$
$4$	16.0000	0.500000
$5$	95.5276	1.70885	0.854425	−	0.519575i	$-0.173910\pi$
$5$	95.5276	1.70885	0.854425	+	0.519575i	$0.173910\pi$
$6$	41.6100	0.471867
$7$	232.219	1.79123	0.895616	−	0.444828i	$-0.146735\pi$
$7$	232.219	1.79123	0.895616	+	0.444828i	$0.146735\pi$
$8$	−64.0000	−0.353553
$9$	−134.788	−0.554684
$10$	−382.111	−1.20834
$11$	345.880	0.861873	0.430936	−	0.902382i	$-0.358183\pi$
$11$	345.880	0.861873	0.430936	+	0.902382i	$0.358183\pi$
$12$	−166.440	−0.333660
$13$	−506.327	−0.830946	−0.415473	−	0.909606i	$-0.636384\pi$
$13$	−506.327	−0.830946	−0.415473	+	0.909606i	$0.636384\pi$
$14$	−928.874	−1.26659
$15$	−993.725	−1.14035
$16$	256.000	0.250000
$17$	−797.089	−0.668936	−0.334468	−	0.942407i	$-0.608557\pi$
$17$	−797.089	−0.668936	−0.334468	+	0.942407i	$0.608557\pi$
$18$	539.153	0.392221
$19$	0	0
$19$	0	0
$20$	1528.44	0.854425
$21$	−2415.65	−1.19533
$22$	−1383.52	−0.609436
$23$	−1190.67	−0.469322	−0.234661	−	0.972077i	$-0.575398\pi$
$23$	−1190.67	−0.469322	−0.234661	+	0.972077i	$0.575398\pi$
$24$	665.760	0.235933
$25$	6000.53	1.92017
$26$	2025.31	0.587567
$27$	3929.94	1.03747
$28$	3715.50	0.895616
$29$	425.364	0.0939216	0.0469608	−	0.998897i	$-0.485046\pi$
$29$	425.364	0.0939216	0.0469608	+	0.998897i	$0.485046\pi$
$30$	3974.90	0.806349
$31$	−6647.85	−1.24244	−0.621222	−	0.783635i	$-0.713363\pi$
$31$	−6647.85	−1.24244	−0.621222	+	0.783635i	$0.713363\pi$
$32$	−1024.00	−0.176777
$33$	−3598.01	−0.575145
$34$	3188.36	0.473009
$35$	22183.3	3.06095
$36$	−2156.61	−0.277342
$37$	7850.99	0.942801	0.471401	−	0.881919i	$-0.343749\pi$
$37$	7850.99	0.942801	0.471401	+	0.881919i	$0.343749\pi$
$38$	0	0
$39$	5267.06	0.554507
$40$	−6113.77	−0.604170
$41$	16080.1	1.49392	0.746962	−	0.664867i	$-0.231512\pi$
$41$	16080.1	1.49392	0.746962	+	0.664867i	$0.231512\pi$
$42$	9662.61	0.845223
$43$	12922.4	1.06579	0.532894	−	0.846182i	$-0.321105\pi$
$43$	12922.4	1.06579	0.532894	+	0.846182i	$0.321105\pi$
$44$	5534.07	0.430936
$45$	−12876.0	−0.947871
$46$	4762.67	0.331861
$47$	−21190.2	−1.39923	−0.699616	−	0.714519i	$-0.746645\pi$
$47$	−21190.2	−1.39923	−0.699616	+	0.714519i	$0.746645\pi$
$48$	−2663.04	−0.166830
$49$	37118.5	2.20851
$50$	−24002.1	−1.35776
$51$	8291.71	0.446395
$52$	−8101.23	−0.415473
$53$	29091.8	1.42259	0.711296	−	0.702893i	$-0.248109\pi$
$53$	29091.8	1.42259	0.711296	+	0.702893i	$0.248109\pi$
$54$	−15719.8	−0.733603
$55$	33041.1	1.47281
$56$	−14862.0	−0.633296
$57$	0	0
$58$	−1701.45	−0.0664126
$59$	−9346.25	−0.349549	−0.174774	−	0.984609i	$-0.555920\pi$
$59$	−9346.25	−0.349549	−0.174774	+	0.984609i	$0.555920\pi$
$60$	−15899.6	−0.570175
$61$	−8320.98	−0.286319	−0.143159	−	0.989700i	$-0.545726\pi$
$61$	−8320.98	−0.286319	−0.143159	+	0.989700i	$0.545726\pi$
$62$	26591.4	0.878541
$63$	−31300.3	−0.993567
$64$	4096.00	0.125000
$65$	−48368.2	−1.41996
$66$	14392.0	0.406689
$67$	14347.1	0.390459	0.195230	−	0.980758i	$-0.437455\pi$
$67$	14347.1	0.390459	0.195230	+	0.980758i	$0.437455\pi$
$68$	−12753.4	−0.334468
$69$	12385.9	0.313188
$70$	−88733.1	−2.16442
$71$	31200.2	0.734532	0.367266	−	0.930116i	$-0.380294\pi$
$71$	31200.2	0.734532	0.367266	+	0.930116i	$0.380294\pi$
$72$	8626.44	0.196110
$73$	1992.28	0.0437566	0.0218783	−	0.999761i	$-0.493035\pi$
$73$	1992.28	0.0437566	0.0218783	+	0.999761i	$0.493035\pi$
$74$	−31404.0	−0.666661
$75$	−62420.4	−1.28137
$76$	0	0
$77$	80319.7	1.54381
$78$	−21068.2	−0.392096
$79$	9623.27	0.173482	0.0867411	−	0.996231i	$-0.472355\pi$
$79$	9623.27	0.173482	0.0867411	+	0.996231i	$0.472355\pi$
$80$	24455.1	0.427213
$81$	−8127.64	−0.137642
$82$	−64320.3	−1.05636
$83$	−34179.5	−0.544590	−0.272295	−	0.962214i	$-0.587783\pi$
$83$	−34179.5	−0.544590	−0.272295	+	0.962214i	$0.587783\pi$
$84$	−38650.4	−0.597663
$85$	−76144.0	−1.14311
$86$	−51689.4	−0.753625
$87$	−4424.84	−0.0626758
$88$	−22136.3	−0.304718
$89$	111322.	1.48973	0.744863	−	0.667218i	$-0.232515\pi$
$89$	111322.	1.48973	0.744863	+	0.667218i	$0.232515\pi$
$90$	51504.0	0.670246
$91$	−117578.	−1.48842
$92$	−19050.7	−0.234661
$93$	69154.2	0.829108
$94$	84760.6	0.989406
$95$	0	0
$96$	10652.2	0.117967
$97$	−96994.8	−1.04669	−0.523346	−	0.852120i	$-0.675316\pi$
$97$	−96994.8	−1.04669	−0.523346	+	0.852120i	$0.675316\pi$
$98$	−148474.	−1.56165
$99$	−46620.5	−0.478067
$100$	96008.4	0.960084
$101$	−170094.	−1.65915	−0.829575	−	0.558396i	$-0.811417\pi$
$101$	−170094.	−1.65915	−0.829575	+	0.558396i	$0.811417\pi$
$102$	−33166.9	−0.315649
$103$	72570.9	0.674015	0.337008	−	0.941502i	$-0.390585\pi$
$103$	72570.9	0.674015	0.337008	+	0.941502i	$0.390585\pi$
$104$	32404.9	0.293784
$105$	−230761.	−2.04263
$106$	−116367.	−1.00592
$107$	68021.4	0.574363	0.287181	−	0.957876i	$-0.407282\pi$
$107$	68021.4	0.574363	0.287181	+	0.957876i	$0.407282\pi$
$108$	62879.0	0.518736
$109$	19382.6	0.156259	0.0781296	−	0.996943i	$-0.475105\pi$
$109$	19382.6	0.156259	0.0781296	+	0.996943i	$0.475105\pi$
$110$	−132164.	−1.04144
$111$	−81669.9	−0.629150
$112$	59448.0	0.447808
$113$	128260.	0.944917	0.472458	−	0.881353i	$-0.343367\pi$
$113$	128260.	0.944917	0.472458	+	0.881353i	$0.343367\pi$
$114$	0	0
$115$	−113742.	−0.802001
$116$	6805.82	0.0469608
$117$	68246.9	0.460912
$118$	37385.0	0.247168
$119$	−185099.	−1.19822
$120$	63598.4	0.403175
$121$	−41418.3	−0.257175
$122$	33283.9	0.202458
$123$	−167273.	−0.996926
$124$	−106366.	−0.621222
$125$	274692.	1.57243
$126$	125201.	0.702558
$127$	−94926.0	−0.522247	−0.261123	−	0.965305i	$-0.584093\pi$
$127$	−94926.0	−0.522247	−0.261123	+	0.965305i	$0.584093\pi$
$128$	−16384.0	−0.0883883
$129$	−134425.	−0.711221
$130$	193473.	1.00406
$131$	265435.	1.35139	0.675695	−	0.737182i	$-0.263844\pi$
$131$	265435.	1.35139	0.675695	+	0.737182i	$0.263844\pi$
$132$	−57568.2	−0.287573
$133$	0	0
$134$	−57388.2	−0.276096
$135$	375418.	1.77288
$136$	51013.7	0.236505
$137$	−69622.2	−0.316918	−0.158459	−	0.987366i	$-0.550652\pi$
$137$	−69622.2	−0.316918	−0.158459	+	0.987366i	$0.550652\pi$
$138$	−49543.6	−0.221457
$139$	369479.	1.62201	0.811004	−	0.585041i	$-0.198922\pi$
$139$	369479.	1.62201	0.811004	+	0.585041i	$0.198922\pi$
$140$	354933.	1.53047
$141$	220430.	0.933735
$142$	−124801.	−0.519393
$143$	−175128.	−0.716170
$144$	−34505.8	−0.138671
$145$	40634.0	0.160498
$146$	−7969.13	−0.0309406
$147$	−386124.	−1.47378
$148$	125616.	0.471401
$149$	10845.5	0.0400206	0.0200103	−	0.999800i	$-0.493630\pi$
$149$	10845.5	0.0400206	0.0200103	+	0.999800i	$0.493630\pi$
$150$	249682.	0.906064
$151$	−33593.4	−0.119898	−0.0599489	−	0.998201i	$-0.519094\pi$
$151$	−33593.4	−0.119898	−0.0599489	+	0.998201i	$0.519094\pi$
$152$	0	0
$153$	107438.	0.371048
$154$	−321279.	−1.09164
$155$	−635053.	−2.12315
$156$	84273.0	0.277253
$157$	571612.	1.85077	0.925385	−	0.379029i	$-0.123742\pi$
$157$	571612.	1.85077	0.925385	+	0.379029i	$0.123742\pi$
$158$	−38493.1	−0.122670
$159$	−302627.	−0.949324
$160$	−97820.3	−0.302085
$161$	−276495.	−0.840665
$162$	32510.5	0.0973277
$163$	441057.	1.30025	0.650123	−	0.759829i	$-0.274717\pi$
$163$	441057.	1.30025	0.650123	+	0.759829i	$0.274717\pi$
$164$	257281.	0.746962
$165$	−343709.	−0.982837
$166$	136718.	0.385084
$167$	32306.8	0.0896401	0.0448200	−	0.998995i	$-0.485729\pi$
$167$	32306.8	0.0896401	0.0448200	+	0.998995i	$0.485729\pi$
$168$	154602.	0.422611
$169$	−114926.	−0.309529
$170$	304576.	0.808302
$171$	0	0
$172$	206758.	0.532894
$173$	140107.	0.355915	0.177957	−	0.984038i	$-0.443051\pi$
$173$	140107.	0.355915	0.177957	+	0.984038i	$0.443051\pi$
$174$	17699.4	0.0443185
$175$	1.39343e6	3.43947
$176$	88545.2	0.215468
$177$	97224.3	0.233261
$178$	−445288.	−1.05339
$179$	−205087.	−0.478416	−0.239208	−	0.970968i	$-0.576888\pi$
$179$	−205087.	−0.478416	−0.239208	+	0.970968i	$0.576888\pi$
$180$	−206016.	−0.473936
$181$	596816.	1.35408	0.677039	−	0.735947i	$-0.263263\pi$
$181$	596816.	1.35408	0.677039	+	0.735947i	$0.263263\pi$
$182$	470314.	1.05247
$183$	86558.9	0.191066
$184$	76202.7	0.165930
$185$	749986.	1.61111
$186$	−276617.	−0.586268
$187$	−275697.	−0.576538
$188$	−339042.	−0.699616
$189$	912605.	1.85835
$190$	0	0
$191$	374224.	0.742246	0.371123	−	0.928584i	$-0.378973\pi$
$191$	374224.	0.742246	0.371123	+	0.928584i	$0.378973\pi$
$192$	−42608.6	−0.0834150
$193$	−185090.	−0.357676	−0.178838	−	0.983879i	$-0.557234\pi$
$193$	−185090.	−0.357676	−0.178838	+	0.983879i	$0.557234\pi$
$194$	387979.	0.740123
$195$	503150.	0.947569
$196$	593895.	1.10426
$197$	149519.	0.274493	0.137247	−	0.990537i	$-0.456175\pi$
$197$	149519.	0.274493	0.137247	+	0.990537i	$0.456175\pi$
$198$	186482.	0.338044
$199$	−305923.	−0.547619	−0.273810	−	0.961784i	$-0.588284\pi$
$199$	−305923.	−0.547619	−0.273810	+	0.961784i	$0.588284\pi$
$200$	−384034.	−0.678882
$201$	−149245.	−0.260561
$202$	680376.	1.17320
$203$	98777.3	0.168235
$204$	132667.	0.223197
$205$	1.53609e6	2.55289
$206$	−290284.	−0.476601
$207$	160488.	0.260325
$208$	−129620.	−0.207736
$209$	0	0
$210$	923046.	1.44436
$211$	−809738.	−1.25210	−0.626049	−	0.779784i	$-0.715329\pi$
$211$	−809738.	−1.25210	−0.626049	+	0.779784i	$0.715329\pi$
$212$	465468.	0.711296
$213$	−324559.	−0.490168
$214$	−272086.	−0.406136
$215$	1.23444e6	1.82127
$216$	−251516.	−0.366802
$217$	−1.54375e6	−2.22551
$218$	−77530.4	−0.110492
$219$	−20724.7	−0.0291997
$220$	528657.	0.736406
$221$	403588.	0.555849
$222$	326679.	0.444876
$223$	−634589.	−0.854536	−0.427268	−	0.904125i	$-0.640524\pi$
$223$	−634589.	−0.854536	−0.427268	+	0.904125i	$0.640524\pi$
$224$	−237792.	−0.316648
$225$	−808800.	−1.06509
$226$	−513038.	−0.668157
$227$	93859.7	0.120897	0.0604484	−	0.998171i	$-0.480747\pi$
$227$	93859.7	0.120897	0.0604484	+	0.998171i	$0.480747\pi$
$228$	0	0
$229$	176185.	0.222014	0.111007	−	0.993820i	$-0.464592\pi$
$229$	176185.	0.222014	0.111007	+	0.993820i	$0.464592\pi$
$230$	454967.	0.567100
$231$	−835525.	−1.03022
$232$	−27223.3	−0.0332063
$233$	−226160.	−0.272915	−0.136457	−	0.990646i	$-0.543572\pi$
$233$	−226160.	−0.272915	−0.136457	+	0.990646i	$0.543572\pi$
$234$	−272987.	−0.325914
$235$	−2.02425e6	−2.39108
$236$	−149540.	−0.174774
$237$	−100106.	−0.115768
$238$	740395.	0.847269
$239$	−343996.	−0.389546	−0.194773	−	0.980848i	$-0.562397\pi$
$239$	−343996.	−0.389546	−0.194773	+	0.980848i	$0.562397\pi$
$240$	−254394.	−0.285088
$241$	−1.58686e6	−1.75993	−0.879966	−	0.475036i	$-0.842435\pi$
$241$	−1.58686e6	−1.75993	−0.879966	+	0.475036i	$0.842435\pi$
$242$	165673.	0.181850
$243$	−870427.	−0.945620
$244$	−133136.	−0.143159
$245$	3.54584e6	3.77402
$246$	669092.	0.704933
$247$	0	0
$248$	425462.	0.439270
$249$	355552.	0.363416
$250$	−1.09877e6	−1.11188
$251$	745968.	0.747370	0.373685	−	0.927556i	$-0.378094\pi$
$251$	745968.	0.747370	0.373685	+	0.927556i	$0.378094\pi$
$252$	−500805.	−0.496784
$253$	−411828.	−0.404496
$254$	379704.	0.369284
$255$	792088.	0.762821
$256$	65536.0	0.0625000
$257$	−1.92630e6	−1.81925	−0.909623	−	0.415436i	$-0.863629\pi$
$257$	−1.92630e6	−1.81925	−0.909623	+	0.415436i	$0.863629\pi$
$258$	537699.	0.502910
$259$	1.82315e6	1.68878
$260$	−773891.	−0.709981
$261$	−57334.0	−0.0520968
$262$	−1.06174e6	−0.955577
$263$	−964619.	−0.859937	−0.429968	−	0.902844i	$-0.641475\pi$
$263$	−964619.	−0.859937	−0.429968	+	0.902844i	$0.641475\pi$
$264$	230273.	0.203345
$265$	2.77907e6	2.43100
$266$	0	0
$267$	−1.15803e6	−0.994124
$268$	229553.	0.195230
$269$	1.61062e6	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$269$	1.61062e6	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$270$	−1.50167e6	−1.25362
$271$	1.13650e6	0.940038	0.470019	−	0.882656i	$-0.344247\pi$
$271$	1.13650e6	0.940038	0.470019	+	0.882656i	$0.344247\pi$
$272$	−204055.	−0.167234
$273$	1.22311e6	0.993250
$274$	278489.	0.224095
$275$	2.07546e6	1.65494
$276$	198175.	0.156594
$277$	648448.	0.507780	0.253890	−	0.967233i	$-0.418290\pi$
$277$	648448.	0.507780	0.253890	+	0.967233i	$0.418290\pi$
$278$	−1.47792e6	−1.14693
$279$	896051.	0.689163
$280$	−1.41973e6	−1.08221
$281$	501822.	0.379126	0.189563	−	0.981869i	$-0.439293\pi$
$281$	501822.	0.379126	0.189563	+	0.981869i	$0.439293\pi$
$282$	−881722.	−0.660251
$283$	1.36912e6	1.01619	0.508096	−	0.861301i	$-0.330350\pi$
$283$	1.36912e6	1.01619	0.508096	+	0.861301i	$0.330350\pi$
$284$	499203.	0.367266
$285$	0	0
$286$	700513.	0.506408
$287$	3.73409e6	2.67596
$288$	138023.	0.0980552
$289$	−784506.	−0.552525
$290$	−162536.	−0.113489
$291$	1.00899e6	0.698479
$292$	31876.5	0.0218783
$293$	684715.	0.465952	0.232976	−	0.972483i	$-0.425154\pi$
$293$	684715.	0.465952	0.232976	+	0.972483i	$0.425154\pi$
$294$	1.54450e6	1.04212
$295$	−892825.	−0.597326
$296$	−502463.	−0.333331
$297$	1.35929e6	0.894169
$298$	−43382.0	−0.0282988
$299$	602867.	0.389981
$300$	−998727.	−0.640684
$301$	3.00081e6	1.90907
$302$	134373.	0.0847805
$303$	1.76940e6	1.10718
$304$	0	0
$305$	−794883.	−0.489276
$306$	−429753.	−0.262370
$307$	1.43283e6	0.867656	0.433828	−	0.900996i	$-0.357163\pi$
$307$	1.43283e6	0.867656	0.433828	+	0.900996i	$0.357163\pi$
$308$	1.28511e6	0.771907
$309$	−754919.	−0.449784
$310$	2.54021e6	1.50129
$311$	−286576.	−0.168012	−0.0840058	−	0.996465i	$-0.526771\pi$
$311$	−286576.	−0.168012	−0.0840058	+	0.996465i	$0.526771\pi$
$312$	−337092.	−0.196048
$313$	326263.	0.188238	0.0941189	−	0.995561i	$-0.469997\pi$
$313$	326263.	0.188238	0.0941189	+	0.995561i	$0.469997\pi$
$314$	−2.28645e6	−1.30869
$315$	−2.99004e6	−1.69786
$316$	153972.	0.0867411
$317$	−3.04382e6	−1.70126	−0.850631	−	0.525764i	$-0.823780\pi$
$317$	−3.04382e6	−1.70126	−0.850631	+	0.525764i	$0.823780\pi$
$318$	1.21051e6	0.671274
$319$	147125.	0.0809485
$320$	391281.	0.213606
$321$	−707592.	−0.383284
$322$	1.10598e6	0.594440
$323$	0	0
$324$	−130042.	−0.0688211
$325$	−3.03823e6	−1.59556
$326$	−1.76423e6	−0.919412
$327$	−201627.	−0.104275
$328$	−1.02912e6	−0.528182
$329$	−4.92075e6	−2.50635
$330$	1.37484e6	0.694971
$331$	2.26302e6	1.13532	0.567660	−	0.823263i	$-0.307849\pi$
$331$	2.26302e6	1.13532	0.567660	+	0.823263i	$0.307849\pi$
$332$	−546871.	−0.272295
$333$	−1.05822e6	−0.522956
$334$	−129227.	−0.0633851
$335$	1.37054e6	0.667237
$336$	−618407.	−0.298831
$337$	−2.34013e6	−1.12245	−0.561223	−	0.827665i	$-0.689669\pi$
$337$	−2.34013e6	−1.12245	−0.561223	+	0.827665i	$0.689669\pi$
$338$	459704.	0.218870
$339$	−1.33422e6	−0.630562
$340$	−1.21830e6	−0.571556
$341$	−2.29936e6	−1.07083
$342$	0	0
$343$	4.71670e6	2.16472
$344$	−827031.	−0.376813
$345$	1.18320e6	0.535191
$346$	−560430.	−0.251670
$347$	−1.61523e6	−0.720128	−0.360064	−	0.932928i	$-0.617245\pi$
$347$	−1.61523e6	−0.720128	−0.360064	+	0.932928i	$0.617245\pi$
$348$	−70797.5	−0.0313379
$349$	49878.2	0.0219203	0.0109602	−	0.999940i	$-0.496511\pi$
$349$	49878.2	0.0219203	0.0109602	+	0.999940i	$0.496511\pi$
$350$	−5.57374e6	−2.43207
$351$	−1.98983e6	−0.862083
$352$	−354181.	−0.152359
$353$	3.46683e6	1.48080	0.740399	−	0.672167i	$-0.234636\pi$
$353$	3.46683e6	1.48080	0.740399	+	0.672167i	$0.234636\pi$
$354$	−388897.	−0.164940
$355$	2.98048e6	1.25521
$356$	1.78115e6	0.744863
$357$	1.92549e6	0.799596
$358$	820348.	0.338291
$359$	2.97986e6	1.22028	0.610140	−	0.792294i	$-0.291113\pi$
$359$	2.97986e6	1.22028	0.610140	+	0.792294i	$0.291113\pi$
$360$	824063.	0.335123
$361$	0	0
$362$	−2.38726e6	−0.957478
$363$	430853.	0.171618
$364$	−1.88126e6	−0.744208
$365$	190318.	0.0747735
$366$	−346236.	−0.135104
$367$	2.23837e6	0.867495	0.433748	−	0.901034i	$-0.357191\pi$
$367$	2.23837e6	0.867495	0.433748	+	0.901034i	$0.357191\pi$
$368$	−304811.	−0.117331
$369$	−2.16740e6	−0.828655
$370$	−2.99995e6	−1.13922
$371$	6.75565e6	2.54819
$372$	1.10647e6	0.414554
$373$	−1.11334e6	−0.414338	−0.207169	−	0.978305i	$-0.566425\pi$
$373$	−1.11334e6	−0.414338	−0.207169	+	0.978305i	$0.566425\pi$
$374$	1.10279e6	0.407674
$375$	−2.85748e6	−1.04931
$376$	1.35617e6	0.494703
$377$	−215373.	−0.0780437
$378$	−3.65042e6	−1.31405
$379$	−3.21599e6	−1.15005	−0.575026	−	0.818135i	$-0.695008\pi$
$379$	−3.21599e6	−1.15005	−0.575026	+	0.818135i	$0.695008\pi$
$380$	0	0
$381$	987467.	0.348506
$382$	−1.49690e6	−0.524847
$383$	−491800.	−0.171313	−0.0856567	−	0.996325i	$-0.527299\pi$
$383$	−491800.	−0.171313	−0.0856567	+	0.996325i	$0.527299\pi$
$384$	170434.	0.0589833
$385$	7.67275e6	2.63815
$386$	740360.	0.252915
$387$	−1.74178e6	−0.591175
$388$	−1.55192e6	−0.523346
$389$	−2.10114e6	−0.704015	−0.352007	−	0.935997i	$-0.614501\pi$
$389$	−2.10114e6	−0.704015	−0.352007	+	0.935997i	$0.614501\pi$
$390$	−2.01260e6	−0.670032
$391$	949068.	0.313946
$392$	−2.37558e6	−0.780827
$393$	−2.76119e6	−0.901809
$394$	−598077.	−0.194096
$395$	919288.	0.296455
$396$	−745928.	−0.239033
$397$	−5.27092e6	−1.67846	−0.839229	−	0.543778i	$-0.816993\pi$
$397$	−5.27092e6	−1.67846	−0.839229	+	0.543778i	$0.816993\pi$
$398$	1.22369e6	0.387225
$399$	0	0
$400$	1.53614e6	0.480042
$401$	4.12441e6	1.28086	0.640430	−	0.768017i	$-0.278756\pi$
$401$	4.12441e6	1.28086	0.640430	+	0.768017i	$0.278756\pi$
$402$	596981.	0.184245
$403$	3.36598e6	1.03240
$404$	−2.72150e6	−0.829575
$405$	−776414.	−0.235210
$406$	−395109.	−0.118960
$407$	2.71550e6	0.812575
$408$	−530670.	−0.157824
$409$	4.71220e6	1.39289	0.696443	−	0.717613i	$-0.254765\pi$
$409$	4.71220e6	1.39289	0.696443	+	0.717613i	$0.254765\pi$
$410$	−6.14437e6	−1.80517
$411$	724244.	0.211485
$412$	1.16113e6	0.337008
$413$	−2.17037e6	−0.626122
$414$	−641951.	−0.184078
$415$	−3.26508e6	−0.930623
$416$	518479.	0.146892
$417$	−3.84350e6	−1.08240
$418$	0	0
$419$	−3.47084e6	−0.965827	−0.482914	−	0.875668i	$-0.660422\pi$
$419$	−3.47084e6	−0.965827	−0.482914	+	0.875668i	$0.660422\pi$
$420$	−3.69218e6	−1.02132
$421$	1.19223e6	0.327835	0.163918	−	0.986474i	$-0.447587\pi$
$421$	1.19223e6	0.327835	0.163918	+	0.986474i	$0.447587\pi$
$422$	3.23895e6	0.885367
$423$	2.85618e6	0.776131
$424$	−1.86187e6	−0.502962
$425$	−4.78295e6	−1.28447
$426$	1.29824e6	0.346601
$427$	−1.93229e6	−0.512863
$428$	1.08834e6	0.287181
$429$	1.82177e6	0.477914
$430$	−4.93777e6	−1.28783
$431$	679294.	0.176143	0.0880714	−	0.996114i	$-0.471930\pi$
$431$	679294.	0.176143	0.0880714	+	0.996114i	$0.471930\pi$
$432$	1.00606e6	0.259368
$433$	7.14219e6	1.83068	0.915339	−	0.402685i	$-0.131923\pi$
$433$	7.14219e6	1.83068	0.915339	+	0.402685i	$0.131923\pi$
$434$	6.17501e6	1.57367
$435$	−422695.	−0.107103
$436$	310121.	0.0781296
$437$	0	0
$438$	82898.8	0.0206473
$439$	−1.61627e6	−0.400271	−0.200135	−	0.979768i	$-0.564138\pi$
$439$	−1.61627e6	−0.400271	−0.200135	+	0.979768i	$0.564138\pi$
$440$	−2.11463e6	−0.520718
$441$	−5.00313e6	−1.22503
$442$	−1.61435e6	−0.393045
$443$	−3.15786e6	−0.764511	−0.382255	−	0.924057i	$-0.624853\pi$
$443$	−3.15786e6	−0.764511	−0.382255	+	0.924057i	$0.624853\pi$
$444$	−1.30672e6	−0.314575
$445$	1.06343e7	2.54572
$446$	2.53836e6	0.604249
$447$	−112820.	−0.0267066
$448$	951167.	0.223904
$449$	−1.47951e6	−0.346338	−0.173169	−	0.984892i	$-0.555401\pi$
$449$	−1.47951e6	−0.346338	−0.173169	+	0.984892i	$0.555401\pi$
$450$	3.23520e6	0.753130
$451$	5.56177e6	1.28757
$452$	2.05215e6	0.472458
$453$	349455.	0.0800102
$454$	−375439.	−0.0854869
$455$	−1.12320e7	−2.54348
$456$	0	0
$457$	−5.30763e6	−1.18880	−0.594402	−	0.804168i	$-0.702611\pi$
$457$	−5.30763e6	−1.18880	−0.594402	+	0.804168i	$0.702611\pi$
$458$	−704739.	−0.156987
$459$	−3.13251e6	−0.694002
$460$	−1.81987e6	−0.401000
$461$	−1.54790e6	−0.339227	−0.169613	−	0.985511i	$-0.554252\pi$
$461$	−1.54790e6	−0.339227	−0.169613	+	0.985511i	$0.554252\pi$
$462$	3.34210e6	0.728474
$463$	7.32198e6	1.58736	0.793682	−	0.608333i	$-0.208162\pi$
$463$	7.32198e6	1.58736	0.793682	+	0.608333i	$0.208162\pi$
$464$	108893.	0.0234804
$465$	6.60614e6	1.41682
$466$	904642.	0.192980
$467$	6.91574e6	1.46739	0.733696	−	0.679478i	$-0.237794\pi$
$467$	6.91574e6	1.46739	0.733696	+	0.679478i	$0.237794\pi$
$468$	1.09195e6	0.230456
$469$	3.33165e6	0.699403
$470$	8.09698e6	1.69075
$471$	−5.94619e6	−1.23506
$472$	598160.	0.123584
$473$	4.46958e6	0.918573
$474$	400424.	0.0818605
$475$	0	0
$476$	−2.96158e6	−0.599110
$477$	−3.92122e6	−0.789089
$478$	1.37599e6	0.275451
$479$	3.22667e6	0.642563	0.321281	−	0.946984i	$-0.395886\pi$
$479$	3.22667e6	0.642563	0.321281	+	0.946984i	$0.395886\pi$
$480$	1.01757e6	0.201587
$481$	−3.97517e6	−0.783416
$482$	6.34744e6	1.24446
$483$	2.87624e6	0.560992
$484$	−662693.	−0.128588
$485$	−9.26568e6	−1.78864
$486$	3.48171e6	0.668655
$487$	4.64992e6	0.888430	0.444215	−	0.895920i	$-0.353483\pi$
$487$	4.64992e6	0.888430	0.444215	+	0.895920i	$0.353483\pi$
$488$	532543.	0.101229
$489$	−4.58809e6	−0.867680
$490$	−1.41834e7	−2.66863
$491$	8.23773e6	1.54207	0.771034	−	0.636794i	$-0.219740\pi$
$491$	8.23773e6	1.54207	0.771034	+	0.636794i	$0.219740\pi$
$492$	−2.67637e6	−0.498463
$493$	−339053.	−0.0628275
$494$	0	0
$495$	−4.45354e6	−0.816945
$496$	−1.70185e6	−0.310611
$497$	7.24526e6	1.31572
$498$	−1.42221e6	−0.256974
$499$	−3.72990e6	−0.670572	−0.335286	−	0.942116i	$-0.608833\pi$
$499$	−3.72990e6	−0.670572	−0.335286	+	0.942116i	$0.608833\pi$
$500$	4.39508e6	0.786215
$501$	−336071.	−0.0598186
$502$	−2.98387e6	−0.528470
$503$	−1.51655e6	−0.267261	−0.133630	−	0.991031i	$-0.542664\pi$
$503$	−1.51655e6	−0.267261	−0.133630	+	0.991031i	$0.542664\pi$
$504$	2.00322e6	0.351279
$505$	−1.62487e7	−2.83524
$506$	1.64731e6	0.286022
$507$	1.19552e6	0.206555
$508$	−1.51882e6	−0.261123
$509$	−1.12361e7	−1.92231	−0.961154	−	0.276014i	$-0.910987\pi$
$509$	−1.12361e7	−1.92231	−0.961154	+	0.276014i	$0.910987\pi$
$510$	−3.16835e6	−0.539396
$511$	462645.	0.0783782
$512$	−262144.	−0.0441942
$513$	0	0
$514$	7.70520e6	1.28640
$515$	6.93253e6	1.15179
$516$	−2.15080e6	−0.355611
$517$	−7.32924e6	−1.20596
$518$	−7.29258e6	−1.19414
$519$	−1.45747e6	−0.237509
$520$	3.09557e6	0.502032
$521$	−4.99957e6	−0.806934	−0.403467	−	0.914994i	$-0.632195\pi$
$521$	−4.99957e6	−0.806934	−0.403467	+	0.914994i	$0.632195\pi$
$522$	229336.	0.0368380
$523$	4.90563e6	0.784225	0.392113	−	0.919917i	$-0.371744\pi$
$523$	4.90563e6	0.784225	0.392113	+	0.919917i	$0.371744\pi$
$524$	4.24697e6	0.675695
$525$	−1.44952e7	−2.29523
$526$	3.85848e6	0.608067
$527$	5.29893e6	0.831116
$528$	−921091.	−0.143786
$529$	−5.01865e6	−0.779737
$530$	−1.11163e7	−1.71897
$531$	1.25976e6	0.193889
$532$	0	0
$533$	−8.14178e6	−1.24137
$534$	4.63211e6	0.702952
$535$	6.49792e6	0.981500
$536$	−918212.	−0.138048
$537$	2.13342e6	0.319256
$538$	−6.44248e6	−0.959616
$539$	1.28385e7	1.90346
$540$	6.00668e6	0.886442
$541$	3.83360e6	0.563137	0.281568	−	0.959541i	$-0.409145\pi$
$541$	3.83360e6	0.563137	0.281568	+	0.959541i	$0.409145\pi$
$542$	−4.54599e6	−0.664707
$543$	−6.20837e6	−0.903604
$544$	816219.	0.118252
$545$	1.85157e6	0.267024
$546$	−4.89244e6	−0.702334
$547$	5.83247e6	0.833458	0.416729	−	0.909031i	$-0.363176\pi$
$547$	5.83247e6	0.833458	0.416729	+	0.909031i	$0.363176\pi$
$548$	−1.11396e6	−0.158459
$549$	1.12157e6	0.158816
$550$	−8.30184e6	−1.17022
$551$	0	0
$552$	−792698.	−0.110729
$553$	2.23470e6	0.310747
$554$	−2.59379e6	−0.359055
$555$	−7.80173e6	−1.07512
$556$	5.91166e6	0.811004
$557$	1.47427e6	0.201344	0.100672	−	0.994920i	$-0.467901\pi$
$557$	1.47427e6	0.201344	0.100672	+	0.994920i	$0.467901\pi$
$558$	−3.58420e6	−0.487312
$559$	−6.54294e6	−0.885611
$560$	5.67892e6	0.765237
$561$	2.86793e6	0.384735
$562$	−2.00729e6	−0.268083
$563$	1.71502e6	0.228033	0.114016	−	0.993479i	$-0.463628\pi$
$563$	1.71502e6	0.228033	0.114016	+	0.993479i	$0.463628\pi$
$564$	3.52689e6	0.466868
$565$	1.22523e7	1.61472
$566$	−5.47648e6	−0.718556
$567$	−1.88739e6	−0.246549
$568$	−1.99681e6	−0.259696
$569$	−1.09443e7	−1.41712	−0.708558	−	0.705652i	$-0.750654\pi$
$569$	−1.09443e7	−1.41712	−0.708558	+	0.705652i	$0.750654\pi$
$570$	0	0
$571$	−7.80064e6	−1.00124	−0.500622	−	0.865666i	$-0.666895\pi$
$571$	−7.80064e6	−1.00124	−0.500622	+	0.865666i	$0.666895\pi$
$572$	−2.80205e6	−0.358085
$573$	−3.89286e6	−0.495316
$574$	−1.49364e7	−1.89219
$575$	−7.14463e6	−0.901177
$576$	−552092.	−0.0693355
$577$	−8.00141e6	−1.00052	−0.500262	−	0.865874i	$-0.666763\pi$
$577$	−8.00141e6	−1.00052	−0.500262	+	0.865874i	$0.666763\pi$
$578$	3.13802e6	0.390694
$579$	1.92540e6	0.238684
$580$	650144.	0.0802489
$581$	−7.93711e6	−0.975488
$582$	−4.03595e6	−0.493899
$583$	1.00622e7	1.22609
$584$	−127506.	−0.0154703
$585$	6.51946e6	0.787630
$586$	−2.73886e6	−0.329478
$587$	−7.68911e6	−0.921045	−0.460523	−	0.887648i	$-0.652338\pi$
$587$	−7.68911e6	−0.921045	−0.460523	+	0.887648i	$0.652338\pi$
$588$	−6.17799e6	−0.736892
$589$	0	0
$590$	3.57130e6	0.422373
$591$	−1.55537e6	−0.183175
$592$	2.00985e6	0.235700
$593$	3.87367e6	0.452362	0.226181	−	0.974085i	$-0.427376\pi$
$593$	3.87367e6	0.452362	0.226181	+	0.974085i	$0.427376\pi$
$594$	−5.43714e6	−0.632273
$595$	−1.76821e7	−2.04758
$596$	173528.	0.0200103
$597$	3.18236e6	0.365438
$598$	−2.41147e6	−0.275758
$599$	1.25262e7	1.42644	0.713220	−	0.700940i	$-0.247236\pi$
$599$	1.25262e7	1.42644	0.713220	+	0.700940i	$0.247236\pi$
$600$	3.99491e6	0.453032
$601$	−293637.	−0.0331608	−0.0165804	−	0.999863i	$-0.505278\pi$
$601$	−293637.	−0.0331608	−0.0165804	+	0.999863i	$0.505278\pi$
$602$	−1.20032e7	−1.34992
$603$	−1.93381e6	−0.216581
$604$	−537494.	−0.0599489
$605$	−3.95659e6	−0.439474
$606$	−7.07761e6	−0.782897
$607$	4.13932e6	0.455993	0.227996	−	0.973662i	$-0.426783\pi$
$607$	4.13932e6	0.455993	0.227996	+	0.973662i	$0.426783\pi$
$608$	0	0
$609$	−1.02753e6	−0.112267
$610$	3.17953e6	0.345970
$611$	1.07291e7	1.16269
$612$	1.71901e6	0.185524
$613$	5.73897e6	0.616854	0.308427	−	0.951248i	$-0.400197\pi$
$613$	5.73897e6	0.616854	0.308427	+	0.951248i	$0.400197\pi$
$614$	−5.73130e6	−0.613525
$615$	−1.59792e7	−1.70360
$616$	−5.14046e6	−0.545821
$617$	−1.15672e7	−1.22325	−0.611627	−	0.791146i	$-0.709485\pi$
$617$	−1.15672e7	−1.22325	−0.611627	+	0.791146i	$0.709485\pi$
$618$	3.01967e6	0.318045
$619$	−1.84780e7	−1.93833	−0.969167	−	0.246404i	$-0.920751\pi$
$619$	−1.84780e7	−1.93833	−0.969167	+	0.246404i	$0.920751\pi$
$620$	−1.01608e7	−1.06158
$621$	−4.67925e6	−0.486908
$622$	1.14630e6	0.118802
$623$	2.58510e7	2.66844
$624$	1.34837e6	0.138627
$625$	7.48906e6	0.766879
$626$	−1.30505e6	−0.133104
$627$	0	0
$628$	9.14580e6	0.925385
$629$	−6.25794e6	−0.630674
$630$	1.19602e7	1.20057
$631$	8.95725e6	0.895573	0.447787	−	0.894140i	$-0.352212\pi$
$631$	8.95725e6	0.895573	0.447787	+	0.894140i	$0.352212\pi$
$632$	−615889.	−0.0613352
$633$	8.42329e6	0.835550
$634$	1.21753e7	1.20297
$635$	−9.06805e6	−0.892441
$636$	−4.84203e6	−0.474662
$637$	−1.87941e7	−1.83515
$638$	−588498.	−0.0572392
$639$	−4.20541e6	−0.407433
$640$	−1.56512e6	−0.151042
$641$	−1.46979e7	−1.41290	−0.706450	−	0.707763i	$-0.749704\pi$
$641$	−1.46979e7	−1.41290	−0.706450	+	0.707763i	$0.749704\pi$
$642$	2.83037e6	0.271023
$643$	1.55533e7	1.48352	0.741762	−	0.670664i	$-0.233991\pi$
$643$	1.55533e7	1.48352	0.741762	+	0.670664i	$0.233991\pi$
$644$	−4.42392e6	−0.420332
$645$	−1.28413e7	−1.21537
$646$	0	0
$647$	−5.91558e6	−0.555567	−0.277784	−	0.960644i	$-0.589600\pi$
$647$	−5.91558e6	−0.555567	−0.277784	+	0.960644i	$0.589600\pi$
$648$	520169.	0.0486639
$649$	−3.23268e6	−0.301266
$650$	1.21529e7	1.12823
$651$	1.60589e7	1.48512
$652$	7.05691e6	0.650123
$653$	1.27377e6	0.116898	0.0584492	−	0.998290i	$-0.481384\pi$
$653$	1.27377e6	0.116898	0.0584492	+	0.998290i	$0.481384\pi$
$654$	806509.	0.0737335
$655$	2.53564e7	2.30932
$656$	4.11650e6	0.373481
$657$	−268536.	−0.0242711
$658$	1.96830e7	1.77226
$659$	6.98055e6	0.626147	0.313073	−	0.949729i	$-0.398641\pi$
$659$	6.98055e6	0.626147	0.313073	+	0.949729i	$0.398641\pi$
$660$	−5.49935e6	−0.491419
$661$	1.02987e7	0.916812	0.458406	−	0.888743i	$-0.348421\pi$
$661$	1.02987e7	0.916812	0.458406	+	0.888743i	$0.348421\pi$
$662$	−9.05208e6	−0.802792
$663$	−4.19832e6	−0.370930
$664$	2.18749e6	0.192542
$665$	0	0
$666$	4.23288e6	0.369786
$667$	−506467.	−0.0440795
$668$	516908.	0.0448200
$669$	6.60131e6	0.570249
$670$	−5.48216e6	−0.471808
$671$	−2.87806e6	−0.246770
$672$	2.47363e6	0.211306
$673$	5.48362e6	0.466692	0.233346	−	0.972394i	$-0.425033\pi$
$673$	5.48362e6	0.466692	0.233346	+	0.972394i	$0.425033\pi$
$674$	9.36052e6	0.793689
$675$	2.35817e7	1.99212
$676$	−1.83882e6	−0.154765
$677$	−4.99313e6	−0.418698	−0.209349	−	0.977841i	$-0.567134\pi$
$677$	−4.99313e6	−0.418698	−0.209349	+	0.977841i	$0.567134\pi$
$678$	5.33687e6	0.445875
$679$	−2.25240e7	−1.87487
$680$	4.87322e6	0.404151
$681$	−976375.	−0.0806768
$682$	9.19742e6	0.757190
$683$	6.96239e6	0.571093	0.285546	−	0.958365i	$-0.407825\pi$
$683$	6.96239e6	0.571093	0.285546	+	0.958365i	$0.407825\pi$
$684$	0	0
$685$	−6.65084e6	−0.541565
$686$	−1.88668e7	−1.53069
$687$	−1.83276e6	−0.148154
$688$	3.30812e6	0.266447
$689$	−1.47299e7	−1.18210
$690$	−4.73279e6	−0.378438
$691$	9.29521e6	0.740566	0.370283	−	0.928919i	$-0.379261\pi$
$691$	9.29521e6	0.740566	0.370283	+	0.928919i	$0.379261\pi$
$692$	2.24172e6	0.177957
$693$	−1.08261e7	−0.856329
$694$	6.46091e6	0.509208
$695$	3.52955e7	2.77177
$696$	283190.	0.0221592
$697$	−1.28173e7	−0.999340
$698$	−199513.	−0.0155000
$699$	2.35263e6	0.182121
$700$	2.22949e7	1.71973
$701$	−7.70223e6	−0.591999	−0.296000	−	0.955188i	$-0.595653\pi$
$701$	−7.70223e6	−0.591999	−0.296000	+	0.955188i	$0.595653\pi$
$702$	7.95933e6	0.609585
$703$	0	0
$704$	1.41672e6	0.107734
$705$	2.10572e7	1.59561
$706$	−1.38673e7	−1.04708
$707$	−3.94990e7	−2.97192
$708$	1.55559e6	0.116630
$709$	513218.	0.0383430	0.0191715	−	0.999816i	$-0.493897\pi$
$709$	513218.	0.0383430	0.0191715	+	0.999816i	$0.493897\pi$
$710$	−1.19219e7	−0.887565
$711$	−1.29710e6	−0.0962278
$712$	−7.12461e6	−0.526697
$713$	7.91538e6	0.583106
$714$	−7.70196e6	−0.565400
$715$	−1.67296e7	−1.22383
$716$	−3.28139e6	−0.239208
$717$	3.57842e6	0.259952
$718$	−1.19194e7	−0.862868
$719$	3.80611e6	0.274574	0.137287	−	0.990531i	$-0.456162\pi$
$719$	3.80611e6	0.274574	0.137287	+	0.990531i	$0.456162\pi$
$720$	−3.29625e6	−0.236968
$721$	1.68523e7	1.20732
$722$	0	0
$723$	1.65073e7	1.17444
$724$	9.54905e6	0.677039
$725$	2.55241e6	0.180345
$726$	−1.72341e6	−0.121352
$727$	−2.43735e7	−1.71033	−0.855167	−	0.518352i	$-0.826546\pi$
$727$	−2.43735e7	−1.71033	−0.855167	+	0.518352i	$0.826546\pi$
$728$	7.52502e6	0.526235
$729$	1.10296e7	0.768674
$730$	−761272.	−0.0528728
$731$	−1.03003e7	−0.712944
$732$	1.38494e6	0.0955331
$733$	4.46559e6	0.306986	0.153493	−	0.988150i	$-0.450948\pi$
$733$	4.46559e6	0.306986	0.153493	+	0.988150i	$0.450948\pi$
$734$	−8.95349e6	−0.613412
$735$	−3.68856e7	−2.51848
$736$	1.21924e6	0.0829652
$737$	4.96236e6	0.336526
$738$	8.66962e6	0.585948
$739$	−2.04421e6	−0.137694	−0.0688468	−	0.997627i	$-0.521932\pi$
$739$	−2.04421e6	−0.137694	−0.0688468	+	0.997627i	$0.521932\pi$
$740$	1.19998e7	0.805553
$741$	0	0
$742$	−2.70226e7	−1.80184
$743$	−1.90490e7	−1.26590	−0.632950	−	0.774193i	$-0.718156\pi$
$743$	−1.90490e7	−1.26590	−0.632950	+	0.774193i	$0.718156\pi$
$744$	−4.42587e6	−0.293134
$745$	1.03604e6	0.0683892
$746$	4.45335e6	0.292981
$747$	4.60699e6	0.302075
$748$	−4.41115e6	−0.288269
$749$	1.57958e7	1.02882
$750$	1.14299e7	0.741978
$751$	−1.08826e7	−0.704097	−0.352048	−	0.935982i	$-0.614515\pi$
$751$	−1.08826e7	−0.704097	−0.352048	+	0.935982i	$0.614515\pi$
$752$	−5.42468e6	−0.349808
$753$	−7.75992e6	−0.498735
$754$	861492.	0.0551852
$755$	−3.20909e6	−0.204887
$756$	1.46017e7	0.929176
$757$	2.24795e6	0.142576	0.0712881	−	0.997456i	$-0.477289\pi$
$757$	2.24795e6	0.142576	0.0712881	+	0.997456i	$0.477289\pi$
$758$	1.28640e7	0.813209
$759$	4.28403e6	0.269928
$760$	0	0
$761$	1.37969e7	0.863614	0.431807	−	0.901966i	$-0.357876\pi$
$761$	1.37969e7	0.863614	0.431807	+	0.901966i	$0.357876\pi$
$762$	−3.94987e6	−0.246431
$763$	4.50100e6	0.279896
$764$	5.98758e6	0.371123
$765$	1.02633e7	0.634065
$766$	1.96720e6	0.121137
$767$	4.73226e6	0.290456
$768$	−681738.	−0.0417075
$769$	3.16040e7	1.92720	0.963599	−	0.267352i	$-0.0861487\pi$
$769$	3.16040e7	1.92720	0.963599	+	0.267352i	$0.0861487\pi$
$770$	−3.06910e7	−1.86545
$771$	2.00383e7	1.21402
$772$	−2.96144e6	−0.178838
$773$	2.13708e7	1.28639	0.643195	−	0.765702i	$-0.277608\pi$
$773$	2.13708e7	1.28639	0.643195	+	0.765702i	$0.277608\pi$
$774$	6.96712e6	0.418024
$775$	−3.98906e7	−2.38570
$776$	6.20767e6	0.370062
$777$	−1.89653e7	−1.12695
$778$	8.40458e6	0.497814
$779$	0	0
$780$	8.05040e6	0.473785
$781$	1.07915e7	0.633074
$782$	−3.79627e6	−0.221994
$783$	1.67165e6	0.0974410
$784$	9.50233e6	0.552128
$785$	5.46048e7	3.16269
$786$	1.10448e7	0.637676
$787$	1.91269e7	1.10080	0.550399	−	0.834901i	$-0.314475\pi$
$787$	1.91269e7	1.10080	0.550399	+	0.834901i	$0.314475\pi$
$788$	2.39231e6	0.137247
$789$	1.00344e7	0.573853
$790$	−3.67715e6	−0.209625
$791$	2.97842e7	1.69256
$792$	2.98371e6	0.169022
$793$	4.21313e6	0.237915
$794$	2.10837e7	1.18685
$795$	−2.89092e7	−1.62225
$796$	−4.89476e6	−0.273810
$797$	8.28296e6	0.461891	0.230946	−	0.972967i	$-0.425818\pi$
$797$	8.28296e6	0.461891	0.230946	+	0.972967i	$0.425818\pi$
$798$	0	0
$799$	1.68904e7	0.935996
$800$	−6.14454e6	−0.339441
$801$	−1.50049e7	−0.826326
$802$	−1.64977e7	−0.905704
$803$	689090.	0.0377126
$804$	−2.38792e6	−0.130281
$805$	−2.64129e7	−1.43657
$806$	−1.34639e7	−0.730019
$807$	−1.67545e7	−0.905622
$808$	1.08860e7	0.586598
$809$	−8.91658e6	−0.478991	−0.239495	−	0.970898i	$-0.576982\pi$
$809$	−8.91658e6	−0.478991	−0.239495	+	0.970898i	$0.576982\pi$
$810$	3.10565e6	0.166319
$811$	1.52149e7	0.812302	0.406151	−	0.913806i	$-0.366871\pi$
$811$	1.52149e7	0.812302	0.406151	+	0.913806i	$0.366871\pi$
$812$	1.58044e6	0.0841177
$813$	−1.18224e7	−0.627306
$814$	−1.08620e7	−0.574577
$815$	4.21331e7	2.22192
$816$	2.12268e6	0.111599
$817$	0	0
$818$	−1.88488e7	−0.984918
$819$	1.58482e7	0.825600
$820$	2.45775e7	1.27645
$821$	2.23907e7	1.15934	0.579669	−	0.814852i	$-0.303182\pi$
$821$	2.23907e7	1.15934	0.579669	+	0.814852i	$0.303182\pi$
$822$	−2.89698e6	−0.149543
$823$	−2.10545e7	−1.08354	−0.541772	−	0.840526i	$-0.682246\pi$
$823$	−2.10545e7	−1.08354	−0.541772	+	0.840526i	$0.682246\pi$
$824$	−4.64454e6	−0.238300
$825$	−2.15900e7	−1.10438
$826$	8.68149e6	0.442735
$827$	−2.23530e7	−1.13651	−0.568253	−	0.822854i	$-0.692381\pi$
$827$	−2.23530e7	−1.13651	−0.568253	+	0.822854i	$0.692381\pi$
$828$	2.56781e6	0.130163
$829$	3.04175e7	1.53723	0.768613	−	0.639714i	$-0.220947\pi$
$829$	3.04175e7	1.53723	0.768613	+	0.639714i	$0.220947\pi$
$830$	1.30603e7	0.658050
$831$	−6.74548e6	−0.338852
$832$	−2.07391e6	−0.103868
$833$	−2.95867e7	−1.47735
$834$	1.53740e7	0.765371
$835$	3.08619e6	0.153181
$836$	0	0
$837$	−2.61256e7	−1.28900
$838$	1.38834e7	0.682943
$839$	2.41182e7	1.18288	0.591439	−	0.806350i	$-0.298560\pi$
$839$	2.41182e7	1.18288	0.591439	+	0.806350i	$0.298560\pi$
$840$	1.47687e7	0.722179
$841$	−2.03302e7	−0.991179
$842$	−4.76893e6	−0.231814
$843$	−5.22020e6	−0.252999
$844$	−1.29558e7	−0.626049
$845$	−1.09786e7	−0.528939
$846$	−1.14247e7	−0.548807
$847$	−9.61810e6	−0.460660
$848$	7.44749e6	0.355648
$849$	−1.42423e7	−0.678125
$850$	1.91318e7	0.908257
$851$	−9.34792e6	−0.442477
$852$	−5.19295e6	−0.245084
$853$	1.65084e7	0.776842	0.388421	−	0.921482i	$-0.373021\pi$
$853$	1.65084e7	0.776842	0.388421	+	0.921482i	$0.373021\pi$
$854$	7.72914e6	0.362649
$855$	0	0
$856$	−4.35337e6	−0.203068
$857$	1.13507e7	0.527923	0.263962	−	0.964533i	$-0.414971\pi$
$857$	1.13507e7	0.527923	0.263962	+	0.964533i	$0.414971\pi$
$858$	−7.28708e6	−0.337937
$859$	2.00932e7	0.929108	0.464554	−	0.885545i	$-0.346215\pi$
$859$	2.00932e7	0.929108	0.464554	+	0.885545i	$0.346215\pi$
$860$	1.97511e7	0.910635
$861$	−3.88439e7	−1.78573
$862$	−2.71718e6	−0.124552
$863$	−1.97337e7	−0.901950	−0.450975	−	0.892537i	$-0.648924\pi$
$863$	−1.97337e7	−0.901950	−0.450975	+	0.892537i	$0.648924\pi$
$864$	−4.02426e6	−0.183401
$865$	1.33841e7	0.608205
$866$	−2.85688e7	−1.29448
$867$	8.16082e6	0.368711
$868$	−2.47001e7	−1.11275
$869$	3.32849e6	0.149520
$870$	1.69078e6	0.0757336
$871$	−7.26430e6	−0.324451
$872$	−1.24049e6	−0.0552460
$873$	1.30737e7	0.580583
$874$	0	0
$875$	6.37887e7	2.81659
$876$	−331595.	−0.0145998
$877$	−1.84073e7	−0.808149	−0.404074	−	0.914726i	$-0.632406\pi$
$877$	−1.84073e7	−0.808149	−0.404074	+	0.914726i	$0.632406\pi$
$878$	6.46510e6	0.283034
$879$	−7.12275e6	−0.310939
$880$	8.45851e6	0.368203
$881$	1.42310e7	0.617727	0.308864	−	0.951106i	$-0.400051\pi$
$881$	1.42310e7	0.617727	0.308864	+	0.951106i	$0.400051\pi$
$882$	2.00125e7	0.866224
$883$	1.06212e7	0.458430	0.229215	−	0.973376i	$-0.426384\pi$
$883$	1.06212e7	0.458430	0.229215	+	0.973376i	$0.426384\pi$
$884$	6.45740e6	0.277925
$885$	9.28761e6	0.398608
$886$	1.26314e7	0.540591
$887$	−4.79046e6	−0.204441	−0.102220	−	0.994762i	$-0.532595\pi$
$887$	−4.79046e6	−0.204441	−0.102220	+	0.994762i	$0.532595\pi$
$888$	5.22687e6	0.222438
$889$	−2.20436e7	−0.935465
$890$	−4.25373e7	−1.80009
$891$	−2.81118e6	−0.118630
$892$	−1.01534e7	−0.427268
$893$	0	0
$894$	451281.	0.0188844
$895$	−1.95915e7	−0.817541
$896$	−3.80467e6	−0.158324
$897$	−6.27132e6	−0.260242
$898$	5.91802e6	0.244898
$899$	−2.82775e6	−0.116692
$900$	−1.29408e7	−0.532543
$901$	−2.31887e7	−0.951623
$902$	−2.22471e7	−0.910451
$903$	−3.12159e7	−1.27396
$904$	−8.20861e6	−0.334078
$905$	5.70124e7	2.31392
$906$	−1.39782e6	−0.0565758
$907$	3.87079e7	1.56236	0.781180	−	0.624306i	$-0.214618\pi$
$907$	3.87079e7	1.56236	0.781180	+	0.624306i	$0.214618\pi$
$908$	1.50176e6	0.0604484
$909$	2.29267e7	0.920303
$910$	4.49280e7	1.79851
$911$	−2.75114e7	−1.09829	−0.549146	−	0.835727i	$-0.685047\pi$
$911$	−2.75114e7	−1.09829	−0.549146	+	0.835727i	$0.685047\pi$
$912$	0	0
$913$	−1.18220e7	−0.469368
$914$	2.12305e7	0.840612
$915$	8.26877e6	0.326504
$916$	2.81896e6	0.111007
$917$	6.16390e7	2.42065
$918$	1.25300e7	0.490734
$919$	−1.32340e7	−0.516896	−0.258448	−	0.966025i	$-0.583211\pi$
$919$	−1.32340e7	−0.516896	−0.258448	+	0.966025i	$0.583211\pi$
$920$	7.27947e6	0.283550
$921$	−1.49050e7	−0.579004
$922$	6.19159e6	0.239870
$923$	−1.57975e7	−0.610357
$924$	−1.33684e7	−0.515109
$925$	4.71101e7	1.81034
$926$	−2.92879e7	−1.12244
$927$	−9.78170e6	−0.373865
$928$	−435572.	−0.0166031
$929$	−1.94057e7	−0.737717	−0.368858	−	0.929486i	$-0.620251\pi$
$929$	−1.94057e7	−0.737717	−0.368858	+	0.929486i	$0.620251\pi$
$930$	−2.64245e7	−1.00184
$931$	0	0
$932$	−3.61857e6	−0.136457
$933$	2.98111e6	0.112118
$934$	−2.76629e7	−1.03760
$935$	−2.63367e7	−0.985217
$936$	−4.36780e6	−0.162957
$937$	4.70727e7	1.75154	0.875770	−	0.482729i	$-0.160354\pi$
$937$	4.70727e7	1.75154	0.875770	+	0.482729i	$0.160354\pi$
$938$	−1.33266e7	−0.494553
$939$	−3.39395e6	−0.125615
$940$	−3.23879e7	−1.19554
$941$	−5.01568e7	−1.84653	−0.923264	−	0.384167i	$-0.874489\pi$
$941$	−5.01568e7	−1.84653	−0.923264	+	0.384167i	$0.874489\pi$
$942$	2.37848e7	0.873317
$943$	−1.91460e7	−0.701131
$944$	−2.39264e6	−0.0873871
$945$	8.71790e7	3.17565
$946$	−1.78783e7	−0.649529
$947$	1.85612e7	0.672561	0.336281	−	0.941762i	$-0.390831\pi$
$947$	1.85612e7	0.672561	0.336281	+	0.941762i	$0.390831\pi$
$948$	−1.60170e6	−0.0578841
$949$	−1.00875e6	−0.0363594
$950$	0	0
$951$	3.16633e7	1.13529
$952$	1.18463e7	0.423635
$953$	−3.60296e7	−1.28507	−0.642536	−	0.766255i	$-0.722118\pi$
$953$	−3.60296e7	−1.28507	−0.642536	+	0.766255i	$0.722118\pi$
$954$	1.56849e7	0.557970
$955$	3.57487e7	1.26839
$956$	−5.50394e6	−0.194773
$957$	−1.53046e6	−0.0540185
$958$	−1.29067e7	−0.454361
$959$	−1.61676e7	−0.567673
$960$	−4.07030e6	−0.142544
$961$	1.55647e7	0.543667
$962$	1.59007e7	0.553959
$963$	−9.16848e6	−0.318590
$964$	−2.53898e7	−0.879966
$965$	−1.76812e7	−0.611215
$966$	−1.15050e7	−0.396682
$967$	1.22925e7	0.422740	0.211370	−	0.977406i	$-0.432207\pi$
$967$	1.22925e7	0.422740	0.211370	+	0.977406i	$0.432207\pi$
$968$	2.65077e6	0.0909251
$969$	0	0
$970$	3.70627e7	1.26476
$971$	−1.73779e7	−0.591493	−0.295746	−	0.955267i	$-0.595568\pi$
$971$	−1.73779e7	−0.591493	−0.295746	+	0.955267i	$0.595568\pi$
$972$	−1.39268e7	−0.472810
$973$	8.57999e7	2.90539
$974$	−1.85997e7	−0.628215
$975$	3.16051e7	1.06475
$976$	−2.13017e6	−0.0715797
$977$	1.54100e7	0.516496	0.258248	−	0.966079i	$-0.416855\pi$
$977$	1.54100e7	0.516496	0.258248	+	0.966079i	$0.416855\pi$
$978$	1.83524e7	0.613542
$979$	3.85040e7	1.28395
$980$	5.67334e7	1.88701
$981$	−2.61254e6	−0.0866744
$982$	−3.29509e7	−1.09041
$983$	−5.45907e7	−1.80192	−0.900959	−	0.433903i	$-0.857136\pi$
$983$	−5.45907e7	−1.80192	−0.900959	+	0.433903i	$0.857136\pi$
$984$	1.07055e7	0.352466
$985$	1.42832e7	0.469068
$986$	1.35621e6	0.0444258
$987$	5.11880e7	1.67254
$988$	0	0
$989$	−1.53862e7	−0.500197
$990$	1.78142e7	0.577667
$991$	−4.29839e7	−1.39034	−0.695171	−	0.718845i	$-0.744671\pi$
$991$	−4.29839e7	−1.39034	−0.695171	+	0.718845i	$0.744671\pi$
$992$	6.80740e6	0.219635
$993$	−2.35410e7	−0.757622
$994$	−2.89810e7	−0.930353
$995$	−2.92241e7	−0.935800
$996$	5.68883e6	0.181708
$997$	−5.32456e7	−1.69647	−0.848234	−	0.529622i	$-0.822334\pi$
$997$	−5.32456e7	−1.69647	−0.848234	+	0.529622i	$0.822334\pi$
$998$	1.49196e7	0.474166
$999$	3.08539e7	0.978130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.6		15
19.3	odd	18		38.6.e.b.9.4	✓	30
19.13	odd	18		38.6.e.b.17.4	yes	30
19.18	odd	2		722.6.a.r.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.4	✓	30	19.3	odd	18
38.6.e.b.17.4	yes	30	19.13	odd	18
722.6.a.q.1.6		15	1.1	even	1	trivial
722.6.a.r.1.10		15	19.18	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -10.4025 q^{3} +16.0000 q^{4} +95.5276 q^{5} +41.6100 q^{6} +232.219 q^{7} -64.0000 q^{8} -134.788 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -10.4025 q^{3} +16.0000 q^{4} +95.5276 q^{5} +41.6100 q^{6} +232.219 q^{7} -64.0000 q^{8} -134.788 q^{9} -382.111 q^{10} +345.880 q^{11} -166.440 q^{12} -506.327 q^{13} -928.874 q^{14} -993.725 q^{15} +256.000 q^{16} -797.089 q^{17} +539.153 q^{18} +1528.44 q^{20} -2415.65 q^{21} -1383.52 q^{22} -1190.67 q^{23} +665.760 q^{24} +6000.53 q^{25} +2025.31 q^{26} +3929.94 q^{27} +3715.50 q^{28} +425.364 q^{29} +3974.90 q^{30} -6647.85 q^{31} -1024.00 q^{32} -3598.01 q^{33} +3188.36 q^{34} +22183.3 q^{35} -2156.61 q^{36} +7850.99 q^{37} +5267.06 q^{39} -6113.77 q^{40} +16080.1 q^{41} +9662.61 q^{42} +12922.4 q^{43} +5534.07 q^{44} -12876.0 q^{45} +4762.67 q^{46} -21190.2 q^{47} -2663.04 q^{48} +37118.5 q^{49} -24002.1 q^{50} +8291.71 q^{51} -8101.23 q^{52} +29091.8 q^{53} -15719.8 q^{54} +33041.1 q^{55} -14862.0 q^{56} -1701.45 q^{58} -9346.25 q^{59} -15899.6 q^{60} -8320.98 q^{61} +26591.4 q^{62} -31300.3 q^{63} +4096.00 q^{64} -48368.2 q^{65} +14392.0 q^{66} +14347.1 q^{67} -12753.4 q^{68} +12385.9 q^{69} -88733.1 q^{70} +31200.2 q^{71} +8626.44 q^{72} +1992.28 q^{73} -31404.0 q^{74} -62420.4 q^{75} +80319.7 q^{77} -21068.2 q^{78} +9623.27 q^{79} +24455.1 q^{80} -8127.64 q^{81} -64320.3 q^{82} -34179.5 q^{83} -38650.4 q^{84} -76144.0 q^{85} -51689.4 q^{86} -4424.84 q^{87} -22136.3 q^{88} +111322. q^{89} +51504.0 q^{90} -117578. q^{91} -19050.7 q^{92} +69154.2 q^{93} +84760.6 q^{94} +10652.2 q^{96} -96994.8 q^{97} -148474. q^{98} -46620.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9} - 432 q^{10} + 126 q^{11} + 114 q^{13} - 336 q^{14} + 3840 q^{16} + 4119 q^{17} - 8508 q^{18} + 1728 q^{20} - 3408 q^{21} - 504 q^{22} + 3936 q^{23} + 26895 q^{25} - 456 q^{26} + 13017 q^{27} + 1344 q^{28} - 14658 q^{29} - 6840 q^{31} - 15360 q^{32} + 3945 q^{33} - 16476 q^{34} + 12636 q^{35} + 34032 q^{36} + 4278 q^{37} + 4956 q^{39} - 6912 q^{40} - 5112 q^{41} + 13632 q^{42} + 94191 q^{43} + 2016 q^{44} + 31770 q^{45} - 15744 q^{46} + 702 q^{47} + 63777 q^{49} - 107580 q^{50} + 108 q^{51} + 1824 q^{52} - 47544 q^{53} - 52068 q^{54} + 16848 q^{55} - 5376 q^{56} + 58632 q^{58} + 8832 q^{59} + 119196 q^{61} + 27360 q^{62} - 88068 q^{63} + 61440 q^{64} - 80646 q^{65} - 15780 q^{66} - 64248 q^{67} + 65904 q^{68} - 124224 q^{69} - 50544 q^{70} + 53364 q^{71} - 136128 q^{72} - 4908 q^{73} - 17112 q^{74} + 87480 q^{75} + 121218 q^{77} - 19824 q^{78} + 115500 q^{79} + 27648 q^{80} + 481659 q^{81} + 20448 q^{82} + 201630 q^{83} - 54528 q^{84} - 150282 q^{85} - 376764 q^{86} + 376512 q^{87} - 8064 q^{88} + 101505 q^{89} - 127080 q^{90} - 414918 q^{91} + 62976 q^{92} + 165960 q^{93} - 2808 q^{94} - 297114 q^{97} - 255108 q^{98} - 149895 q^{99}+O(q^{100}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9 - 432 * q^10 + 126 * q^11 + 114 * q^13 - 336 * q^14 + 3840 * q^16 + 4119 * q^17 - 8508 * q^18 + 1728 * q^20 - 3408 * q^21 - 504 * q^22 + 3936 * q^23 + 26895 * q^25 - 456 * q^26 + 13017 * q^27 + 1344 * q^28 - 14658 * q^29 - 6840 * q^31 - 15360 * q^32 + 3945 * q^33 - 16476 * q^34 + 12636 * q^35 + 34032 * q^36 + 4278 * q^37 + 4956 * q^39 - 6912 * q^40 - 5112 * q^41 + 13632 * q^42 + 94191 * q^43 + 2016 * q^44 + 31770 * q^45 - 15744 * q^46 + 702 * q^47 + 63777 * q^49 - 107580 * q^50 + 108 * q^51 + 1824 * q^52 - 47544 * q^53 - 52068 * q^54 + 16848 * q^55 - 5376 * q^56 + 58632 * q^58 + 8832 * q^59 + 119196 * q^61 + 27360 * q^62 - 88068 * q^63 + 61440 * q^64 - 80646 * q^65 - 15780 * q^66 - 64248 * q^67 + 65904 * q^68 - 124224 * q^69 - 50544 * q^70 + 53364 * q^71 - 136128 * q^72 - 4908 * q^73 - 17112 * q^74 + 87480 * q^75 + 121218 * q^77 - 19824 * q^78 + 115500 * q^79 + 27648 * q^80 + 481659 * q^81 + 20448 * q^82 + 201630 * q^83 - 54528 * q^84 - 150282 * q^85 - 376764 * q^86 + 376512 * q^87 - 8064 * q^88 + 101505 * q^89 - 127080 * q^90 - 414918 * q^91 + 62976 * q^92 + 165960 * q^93 - 2808 * q^94 - 297114 * q^97 - 255108 * q^98 - 149895 * q^99

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