LMFDB - Embedded newform 722.6.a.r.1.15

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			1.15
Root			$-27.8974$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +26.3653 q^{3} +16.0000 q^{4} +84.5221 q^{5} +105.461 q^{6} +15.2607 q^{7} +64.0000 q^{8} +452.132 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +26.3653 q^{3} +16.0000 q^{4} +84.5221 q^{5} +105.461 q^{6} +15.2607 q^{7} +64.0000 q^{8} +452.132 q^{9} +338.089 q^{10} -450.397 q^{11} +421.846 q^{12} +802.449 q^{13} +61.0429 q^{14} +2228.46 q^{15} +256.000 q^{16} -1330.28 q^{17} +1808.53 q^{18} +1352.35 q^{20} +402.354 q^{21} -1801.59 q^{22} +379.765 q^{23} +1687.38 q^{24} +4018.99 q^{25} +3209.79 q^{26} +5513.83 q^{27} +244.172 q^{28} +8332.67 q^{29} +8913.82 q^{30} -6687.09 q^{31} +1024.00 q^{32} -11874.9 q^{33} -5321.11 q^{34} +1289.87 q^{35} +7234.11 q^{36} -4855.55 q^{37} +21156.8 q^{39} +5409.42 q^{40} +12578.2 q^{41} +1609.42 q^{42} +14725.8 q^{43} -7206.36 q^{44} +38215.1 q^{45} +1519.06 q^{46} -12336.3 q^{47} +6749.53 q^{48} -16574.1 q^{49} +16076.0 q^{50} -35073.2 q^{51} +12839.2 q^{52} +1648.83 q^{53} +22055.3 q^{54} -38068.5 q^{55} +976.687 q^{56} +33330.7 q^{58} +5537.16 q^{59} +35655.3 q^{60} +33618.4 q^{61} -26748.3 q^{62} +6899.86 q^{63} +4096.00 q^{64} +67824.7 q^{65} -47499.5 q^{66} +1075.80 q^{67} -21284.4 q^{68} +10012.6 q^{69} +5159.48 q^{70} +24655.4 q^{71} +28936.4 q^{72} -49796.7 q^{73} -19422.2 q^{74} +105962. q^{75} -6873.39 q^{77} +84627.3 q^{78} +30767.8 q^{79} +21637.7 q^{80} +35506.0 q^{81} +50312.9 q^{82} +37614.0 q^{83} +6437.67 q^{84} -112438. q^{85} +58903.1 q^{86} +219694. q^{87} -28825.4 q^{88} -92745.1 q^{89} +152861. q^{90} +12246.0 q^{91} +6076.24 q^{92} -176307. q^{93} -49345.1 q^{94} +26998.1 q^{96} -114665. q^{97} -66296.4 q^{98} -203639. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	26.3653	1.69134	0.845669	−	0.533708i	$-0.179202\pi$
$3$	26.3653	1.69134	0.845669	+	0.533708i	$0.179202\pi$
$4$	16.0000	0.500000
$5$	84.5221	1.51198	0.755989	−	0.654584i	$-0.227156\pi$
$5$	84.5221	1.51198	0.755989	+	0.654584i	$0.227156\pi$
$6$	105.461	1.19596
$7$	15.2607	0.117715	0.0588573	−	0.998266i	$-0.481254\pi$
$7$	15.2607	0.117715	0.0588573	+	0.998266i	$0.481254\pi$
$8$	64.0000	0.353553
$9$	452.132	1.86062
$10$	338.089	1.06913
$11$	−450.397	−1.12231	−0.561156	−	0.827710i	$-0.689643\pi$
$11$	−450.397	−1.12231	−0.561156	+	0.827710i	$0.689643\pi$
$12$	421.846	0.845669
$13$	802.449	1.31692	0.658459	−	0.752616i	$-0.271209\pi$
$13$	802.449	1.31692	0.658459	+	0.752616i	$0.271209\pi$
$14$	61.0429	0.0832368
$15$	2228.46	2.55727
$16$	256.000	0.250000
$17$	−1330.28	−1.11640	−0.558200	−	0.829706i	$-0.688508\pi$
$17$	−1330.28	−1.11640	−0.558200	+	0.829706i	$0.688508\pi$
$18$	1808.53	1.31566
$19$	0	0
$19$	0	0
$20$	1352.35	0.755989
$21$	402.354	0.199095
$22$	−1801.59	−0.793595
$23$	379.765	0.149691	0.0748455	−	0.997195i	$-0.476154\pi$
$23$	379.765	0.149691	0.0748455	+	0.997195i	$0.476154\pi$
$24$	1687.38	0.597978
$25$	4018.99	1.28608
$26$	3209.79	0.931202
$27$	5513.83	1.45561
$28$	244.172	0.0588573
$29$	8332.67	1.83988	0.919939	−	0.392061i	$-0.128238\pi$
$29$	8332.67	1.83988	0.919939	+	0.392061i	$0.128238\pi$
$30$	8913.82	1.80826
$31$	−6687.09	−1.24978	−0.624889	−	0.780714i	$-0.714856\pi$
$31$	−6687.09	−1.24978	−0.624889	+	0.780714i	$0.714856\pi$
$32$	1024.00	0.176777
$33$	−11874.9	−1.89821
$34$	−5321.11	−0.789414
$35$	1289.87	0.177982
$36$	7234.11	0.930312
$37$	−4855.55	−0.583088	−0.291544	−	0.956557i	$-0.594169\pi$
$37$	−4855.55	−0.583088	−0.291544	+	0.956557i	$0.594169\pi$
$38$	0	0
$39$	21156.8	2.22735
$40$	5409.42	0.534565
$41$	12578.2	1.16858	0.584292	−	0.811544i	$-0.301372\pi$
$41$	12578.2	1.16858	0.584292	+	0.811544i	$0.301372\pi$
$42$	1609.42	0.140781
$43$	14725.8	1.21453	0.607264	−	0.794500i	$-0.292267\pi$
$43$	14725.8	1.21453	0.607264	+	0.794500i	$0.292267\pi$
$44$	−7206.36	−0.561156
$45$	38215.1	2.81322
$46$	1519.06	0.105847
$47$	−12336.3	−0.814591	−0.407296	−	0.913296i	$-0.633528\pi$
$47$	−12336.3	−0.814591	−0.407296	+	0.913296i	$0.633528\pi$
$48$	6749.53	0.422834
$49$	−16574.1	−0.986143
$50$	16076.0	0.909394
$51$	−35073.2	−1.88821
$52$	12839.2	0.658459
$53$	1648.83	0.0806283	0.0403141	−	0.999187i	$-0.487164\pi$
$53$	1648.83	0.0806283	0.0403141	+	0.999187i	$0.487164\pi$
$54$	22055.3	1.02927
$55$	−38068.5	−1.69691
$56$	976.687	0.0416184
$57$	0	0
$58$	33330.7	1.30099
$59$	5537.16	0.207089	0.103544	−	0.994625i	$-0.466982\pi$
$59$	5537.16	0.207089	0.103544	+	0.994625i	$0.466982\pi$
$60$	35655.3	1.27863
$61$	33618.4	1.15678	0.578392	−	0.815759i	$-0.303681\pi$
$61$	33618.4	1.15678	0.578392	+	0.815759i	$0.303681\pi$
$62$	−26748.3	−0.883726
$63$	6899.86	0.219023
$64$	4096.00	0.125000
$65$	67824.7	1.99115
$66$	−47499.5	−1.34224
$67$	1075.80	0.0292783	0.0146391	−	0.999893i	$-0.495340\pi$
$67$	1075.80	0.0292783	0.0146391	+	0.999893i	$0.495340\pi$
$68$	−21284.4	−0.558200
$69$	10012.6	0.253178
$70$	5159.48	0.125852
$71$	24655.4	0.580452	0.290226	−	0.956958i	$-0.406270\pi$
$71$	24655.4	0.580452	0.290226	+	0.956958i	$0.406270\pi$
$72$	28936.4	0.657830
$73$	−49796.7	−1.09369	−0.546844	−	0.837235i	$-0.684171\pi$
$73$	−49796.7	−1.09369	−0.546844	+	0.837235i	$0.684171\pi$
$74$	−19422.2	−0.412306
$75$	105962.	2.17519
$76$	0	0
$77$	−6873.39	−0.132113
$78$	84627.3	1.57498
$79$	30767.8	0.554663	0.277331	−	0.960774i	$-0.410550\pi$
$79$	30767.8	0.554663	0.277331	+	0.960774i	$0.410550\pi$
$80$	21637.7	0.377994
$81$	35506.0	0.601297
$82$	50312.9	0.826313
$83$	37614.0	0.599314	0.299657	−	0.954047i	$-0.403128\pi$
$83$	37614.0	0.599314	0.299657	+	0.954047i	$0.403128\pi$
$84$	6437.67	0.0995476
$85$	−112438.	−1.68797
$86$	58903.1	0.858800
$87$	219694.	3.11186
$88$	−28825.4	−0.396798
$89$	−92745.1	−1.24113	−0.620563	−	0.784156i	$-0.713096\pi$
$89$	−92745.1	−1.24113	−0.620563	+	0.784156i	$0.713096\pi$
$90$	152861.	1.98925
$91$	12246.0	0.155020
$92$	6076.24	0.0748455
$93$	−176307.	−2.11380
$94$	−49345.1	−0.576003
$95$	0	0
$96$	26998.1	0.298989
$97$	−114665.	−1.23738	−0.618689	−	0.785636i	$-0.712336\pi$
$97$	−114665.	−1.23738	−0.618689	+	0.785636i	$0.712336\pi$
$98$	−66296.4	−0.697309
$99$	−203639.	−2.08820
$100$	64303.9	0.643039
$101$	−45228.4	−0.441171	−0.220586	−	0.975368i	$-0.570797\pi$
$101$	−45228.4	−0.441171	−0.220586	+	0.975368i	$0.570797\pi$
$102$	−140293.	−1.33517
$103$	−47420.8	−0.440428	−0.220214	−	0.975452i	$-0.570676\pi$
$103$	−47420.8	−0.440428	−0.220214	+	0.975452i	$0.570676\pi$
$104$	51356.7	0.465601
$105$	34007.9	0.301027
$106$	6595.34	0.0570128
$107$	−214213.	−1.80878	−0.904390	−	0.426707i	$-0.859673\pi$
$107$	−214213.	−1.80878	−0.904390	+	0.426707i	$0.859673\pi$
$108$	88221.2	0.727803
$109$	226865.	1.82895	0.914473	−	0.404648i	$-0.132606\pi$
$109$	226865.	1.82895	0.914473	+	0.404648i	$0.132606\pi$
$110$	−152274.	−1.19990
$111$	−128018.	−0.986200
$112$	3906.75	0.0294286
$113$	16431.9	0.121058	0.0605288	−	0.998166i	$-0.480721\pi$
$113$	16431.9	0.121058	0.0605288	+	0.998166i	$0.480721\pi$
$114$	0	0
$115$	32098.6	0.226329
$116$	133323.	0.919939
$117$	362812.	2.45029
$118$	22148.6	0.146434
$119$	−20301.0	−0.131417
$120$	142621.	0.904130
$121$	41806.6	0.259586
$122$	134473.	0.817969
$123$	331629.	1.97647
$124$	−106993.	−0.624889
$125$	75562.1	0.432543
$126$	27599.4	0.154872
$127$	46148.7	0.253893	0.126946	−	0.991910i	$-0.459482\pi$
$127$	46148.7	0.253893	0.126946	+	0.991910i	$0.459482\pi$
$128$	16384.0	0.0883883
$129$	388250.	2.05418
$130$	271299.	1.40796
$131$	−299435.	−1.52449	−0.762245	−	0.647289i	$-0.775903\pi$
$131$	−299435.	−1.52449	−0.762245	+	0.647289i	$0.775903\pi$
$132$	−189998.	−0.949105
$133$	0	0
$134$	4303.21	0.0207029
$135$	466040.	2.20084
$136$	−85137.8	−0.394707
$137$	136949.	0.623387	0.311693	−	0.950183i	$-0.399104\pi$
$137$	136949.	0.623387	0.311693	+	0.950183i	$0.399104\pi$
$138$	40050.6	0.179024
$139$	−294957.	−1.29486	−0.647429	−	0.762126i	$-0.724156\pi$
$139$	−294957.	−1.29486	−0.647429	+	0.762126i	$0.724156\pi$
$140$	20637.9	0.0889909
$141$	−325250.	−1.37775
$142$	98621.6	0.410441
$143$	−361421.	−1.47799
$144$	115746.	0.465156
$145$	704295.	2.78186
$146$	−199187.	−0.773354
$147$	−436982.	−1.66790
$148$	−77688.9	−0.291544
$149$	−183853.	−0.678428	−0.339214	−	0.940709i	$-0.610161\pi$
$149$	−183853.	−0.678428	−0.339214	+	0.940709i	$0.610161\pi$
$150$	423848.	1.53809
$151$	−444021.	−1.58475	−0.792376	−	0.610033i	$-0.791156\pi$
$151$	−444021.	−1.58475	−0.792376	+	0.610033i	$0.791156\pi$
$152$	0	0
$153$	−601460.	−2.07720
$154$	−27493.6	−0.0934177
$155$	−565207.	−1.88964
$156$	338509.	1.11368
$157$	463273.	1.49999	0.749994	−	0.661444i	$-0.230056\pi$
$157$	463273.	1.49999	0.749994	+	0.661444i	$0.230056\pi$
$158$	123071.	0.392206
$159$	43472.1	0.136370
$160$	86550.7	0.267282
$161$	5795.49	0.0176208
$162$	142024.	0.425181
$163$	−109972.	−0.324199	−0.162099	−	0.986774i	$-0.551827\pi$
$163$	−109972.	−0.324199	−0.162099	+	0.986774i	$0.551827\pi$
$164$	201252.	0.584292
$165$	−1.00369e6	−2.87005
$166$	150456.	0.423779
$167$	56327.2	0.156288	0.0781442	−	0.996942i	$-0.475101\pi$
$167$	56327.2	0.156288	0.0781442	+	0.996942i	$0.475101\pi$
$168$	25750.7	0.0703907
$169$	272631.	0.734274
$170$	−449752.	−1.19358
$171$	0	0
$172$	235613.	0.607264
$173$	−51544.8	−0.130939	−0.0654696	−	0.997855i	$-0.520855\pi$
$173$	−51544.8	−0.130939	−0.0654696	+	0.997855i	$0.520855\pi$
$174$	878775.	2.20041
$175$	61332.7	0.151390
$176$	−115302.	−0.280578
$177$	145989.	0.350257
$178$	−370981.	−0.877609
$179$	−648104.	−1.51186	−0.755930	−	0.654652i	$-0.772815\pi$
$179$	−648104.	−1.51186	−0.755930	+	0.654652i	$0.772815\pi$
$180$	611442.	1.40661
$181$	492363.	1.11709	0.558546	−	0.829474i	$-0.311360\pi$
$181$	492363.	1.11709	0.558546	+	0.829474i	$0.311360\pi$
$182$	48983.8	0.109616
$183$	886360.	1.95651
$184$	24305.0	0.0529237
$185$	−410402.	−0.881617
$186$	−705229.	−1.49468
$187$	599153.	1.25295
$188$	−197381.	−0.407296
$189$	84145.0	0.171346
$190$	0	0
$191$	67382.2	0.133648	0.0668239	−	0.997765i	$-0.478713\pi$
$191$	67382.2	0.133648	0.0668239	+	0.997765i	$0.478713\pi$
$192$	107992.	0.211417
$193$	−201463.	−0.389315	−0.194658	−	0.980871i	$-0.562360\pi$
$193$	−201463.	−0.389315	−0.194658	+	0.980871i	$0.562360\pi$
$194$	−458661.	−0.874959
$195$	1.78822e6	3.36771
$196$	−265186.	−0.493072
$197$	−95170.4	−0.174717	−0.0873587	−	0.996177i	$-0.527843\pi$
$197$	−95170.4	−0.174717	−0.0873587	+	0.996177i	$0.527843\pi$
$198$	−814555.	−1.47658
$199$	−120711.	−0.216080	−0.108040	−	0.994147i	$-0.534457\pi$
$199$	−120711.	−0.216080	−0.108040	+	0.994147i	$0.534457\pi$
$200$	257215.	0.454697
$201$	28363.9	0.0495194
$202$	−180913.	−0.311955
$203$	127163.	0.216581
$204$	−561172.	−0.944105
$205$	1.06314e6	1.76687
$206$	−189683.	−0.311430
$207$	171704.	0.278518
$208$	205427.	0.329230
$209$	0	0
$210$	136031.	0.212859
$211$	−386464.	−0.597589	−0.298794	−	0.954318i	$-0.596584\pi$
$211$	−386464.	−0.597589	−0.298794	+	0.954318i	$0.596584\pi$
$212$	26381.4	0.0403141
$213$	650048.	0.981740
$214$	−856851.	−1.27900
$215$	1.24465e6	1.83634
$216$	352885.	0.514634
$217$	−102050.	−0.147117
$218$	907459.	1.29326
$219$	−1.31291e6	−1.84979
$220$	−609097.	−0.848456
$221$	−1.06748e6	−1.47021
$222$	−512073.	−0.697348
$223$	−452658.	−0.609548	−0.304774	−	0.952425i	$-0.598581\pi$
$223$	−452658.	−0.609548	−0.304774	+	0.952425i	$0.598581\pi$
$224$	15627.0	0.0208092
$225$	1.81711e6	2.39291
$226$	65727.6	0.0856006
$227$	23094.4	0.0297469	0.0148734	−	0.999889i	$-0.495265\pi$
$227$	23094.4	0.0297469	0.0148734	+	0.999889i	$0.495265\pi$
$228$	0	0
$229$	311552.	0.392593	0.196296	−	0.980545i	$-0.437109\pi$
$229$	311552.	0.392593	0.196296	+	0.980545i	$0.437109\pi$
$230$	128394.	0.160039
$231$	−181219.	−0.223447
$232$	533291.	0.650495
$233$	−838769.	−1.01217	−0.506084	−	0.862484i	$-0.668907\pi$
$233$	−838769.	−1.01217	−0.506084	+	0.862484i	$0.668907\pi$
$234$	1.45125e6	1.73262
$235$	−1.04269e6	−1.23164
$236$	88594.5	0.103544
$237$	811204.	0.938122
$238$	−81204.0	−0.0929256
$239$	278361.	0.315220	0.157610	−	0.987501i	$-0.449621\pi$
$239$	278361.	0.315220	0.157610	+	0.987501i	$0.449621\pi$
$240$	570485.	0.639316
$241$	−962658.	−1.06765	−0.533826	−	0.845595i	$-0.679246\pi$
$241$	−962658.	−1.06765	−0.533826	+	0.845595i	$0.679246\pi$
$242$	167227.	0.183555
$243$	−403732.	−0.438609
$244$	537894.	0.578392
$245$	−1.40088e6	−1.49103
$246$	1.32652e6	1.39758
$247$	0	0
$248$	−427974.	−0.441863
$249$	991706.	1.01364
$250$	302248.	0.305854
$251$	−352423.	−0.353085	−0.176543	−	0.984293i	$-0.556491\pi$
$251$	−352423.	−0.353085	−0.176543	+	0.984293i	$0.556491\pi$
$252$	110398.	0.109511
$253$	−171045.	−0.168000
$254$	184595.	0.179529
$255$	−2.96446e6	−2.85493
$256$	65536.0	0.0625000
$257$	1.59171e6	1.50325	0.751625	−	0.659591i	$-0.229270\pi$
$257$	1.59171e6	1.50325	0.751625	+	0.659591i	$0.229270\pi$
$258$	1.55300e6	1.45252
$259$	−74099.3	−0.0686380
$260$	1.08519e6	0.995576
$261$	3.76746e6	3.42332
$262$	−1.19774e6	−1.07798
$263$	1.57606e6	1.40503	0.702514	−	0.711670i	$-0.252061\pi$
$263$	1.57606e6	1.40503	0.702514	+	0.711670i	$0.252061\pi$
$264$	−759992.	−0.671119
$265$	139363.	0.121908
$266$	0	0
$267$	−2.44526e6	−2.09916
$268$	17212.8	0.0146391
$269$	1.07411e6	0.905038	0.452519	−	0.891755i	$-0.350525\pi$
$269$	1.07411e6	0.905038	0.452519	+	0.891755i	$0.350525\pi$
$270$	1.86416e6	1.55623
$271$	829674.	0.686253	0.343126	−	0.939289i	$-0.388514\pi$
$271$	829674.	0.686253	0.343126	+	0.939289i	$0.388514\pi$
$272$	−340551.	−0.279100
$273$	322869.	0.262192
$274$	547796.	0.440801
$275$	−1.81014e6	−1.44338
$276$	160202.	0.126589
$277$	546621.	0.428043	0.214021	−	0.976829i	$-0.431344\pi$
$277$	546621.	0.428043	0.214021	+	0.976829i	$0.431344\pi$
$278$	−1.17983e6	−0.915603
$279$	−3.02344e6	−2.32537
$280$	82551.6	0.0629261
$281$	774356.	0.585026	0.292513	−	0.956262i	$-0.405509\pi$
$281$	774356.	0.585026	0.292513	+	0.956262i	$0.405509\pi$
$282$	−1.30100e6	−0.974216
$283$	636942.	0.472753	0.236376	−	0.971662i	$-0.424040\pi$
$283$	636942.	0.472753	0.236376	+	0.971662i	$0.424040\pi$
$284$	394486.	0.290226
$285$	0	0
$286$	−1.44568e6	−1.04510
$287$	191953.	0.137559
$288$	462983.	0.328915
$289$	349781.	0.246350
$290$	2.81718e6	1.96707
$291$	−3.02319e6	−2.09283
$292$	−796747.	−0.546844
$293$	−1.15173e6	−0.783759	−0.391880	−	0.920017i	$-0.628175\pi$
$293$	−1.15173e6	−0.783759	−0.391880	+	0.920017i	$0.628175\pi$
$294$	−1.74793e6	−1.17938
$295$	468012.	0.313114
$296$	−310755.	−0.206153
$297$	−2.48341e6	−1.63364
$298$	−735410.	−0.479721
$299$	304742.	0.197131
$300$	1.69539e6	1.08760
$301$	224726.	0.142968
$302$	−1.77608e6	−1.12059
$303$	−1.19246e6	−0.746170
$304$	0	0
$305$	2.84150e6	1.74903
$306$	−2.40584e6	−1.46880
$307$	2.16078e6	1.30847	0.654235	−	0.756291i	$-0.272991\pi$
$307$	2.16078e6	1.30847	0.654235	+	0.756291i	$0.272991\pi$
$308$	−109974.	−0.0660563
$309$	−1.25026e6	−0.744913
$310$	−2.26083e6	−1.33617
$311$	1.97202e6	1.15614	0.578069	−	0.815988i	$-0.303806\pi$
$311$	1.97202e6	1.15614	0.578069	+	0.815988i	$0.303806\pi$
$312$	1.35404e6	0.787488
$313$	−527176.	−0.304155	−0.152077	−	0.988369i	$-0.548596\pi$
$313$	−527176.	−0.304155	−0.152077	+	0.988369i	$0.548596\pi$
$314$	1.85309e6	1.06065
$315$	583191.	0.331157
$316$	492285.	0.277331
$317$	1.73044e6	0.967185	0.483592	−	0.875293i	$-0.339332\pi$
$317$	1.73044e6	0.967185	0.483592	+	0.875293i	$0.339332\pi$
$318$	173888.	0.0964279
$319$	−3.75301e6	−2.06492
$320$	346203.	0.188997
$321$	−5.64779e6	−3.05926
$322$	23182.0	0.0124598
$323$	0	0
$324$	568096.	0.300648
$325$	3.22503e6	1.69366
$326$	−439886.	−0.229243
$327$	5.98137e6	3.09336
$328$	805007.	0.413157
$329$	−188261.	−0.0958893
$330$	−4.01476e6	−2.02943
$331$	1.08497e6	0.544310	0.272155	−	0.962253i	$-0.412264\pi$
$331$	1.08497e6	0.544310	0.272155	+	0.962253i	$0.412264\pi$
$332$	601824.	0.299657
$333$	−2.19535e6	−1.08491
$334$	225309.	0.110513
$335$	90929.1	0.0442681
$336$	103003.	0.0497738
$337$	−1.92081e6	−0.921320	−0.460660	−	0.887577i	$-0.652387\pi$
$337$	−1.92081e6	−0.921320	−0.460660	+	0.887577i	$0.652387\pi$
$338$	1.09052e6	0.519210
$339$	433233.	0.204749
$340$	−1.79901e6	−0.843986
$341$	3.01185e6	1.40264
$342$	0	0
$343$	−509420.	−0.233798
$344$	942450.	0.429400
$345$	846290.	0.382799
$346$	−206179.	−0.0925881
$347$	−1.71545e6	−0.764812	−0.382406	−	0.923994i	$-0.624904\pi$
$347$	−1.71545e6	−0.764812	−0.382406	+	0.923994i	$0.624904\pi$
$348$	3.51510e6	1.55593
$349$	3.35326e6	1.47368	0.736842	−	0.676066i	$-0.236316\pi$
$349$	3.35326e6	1.47368	0.736842	+	0.676066i	$0.236316\pi$
$350$	245331.	0.107049
$351$	4.42456e6	1.91691
$352$	−461207.	−0.198399
$353$	2.01176e6	0.859289	0.429644	−	0.902998i	$-0.358639\pi$
$353$	2.01176e6	0.859289	0.429644	+	0.902998i	$0.358639\pi$
$354$	583956.	0.247669
$355$	2.08393e6	0.877630
$356$	−1.48392e6	−0.620563
$357$	−535243.	−0.222270
$358$	−2.59241e6	−1.06905
$359$	2.03110e6	0.831756	0.415878	−	0.909420i	$-0.363474\pi$
$359$	2.03110e6	0.831756	0.415878	+	0.909420i	$0.363474\pi$
$360$	2.44577e6	0.994624
$361$	0	0
$362$	1.96945e6	0.789903
$363$	1.10225e6	0.439048
$364$	195935.	0.0775102
$365$	−4.20892e6	−1.65363
$366$	3.54544e6	1.38346
$367$	353495.	0.136999	0.0684997	−	0.997651i	$-0.478179\pi$
$367$	353495.	0.136999	0.0684997	+	0.997651i	$0.478179\pi$
$368$	97219.9	0.0374227
$369$	5.68701e6	2.17429
$370$	−1.64161e6	−0.623397
$371$	25162.4	0.00949112
$372$	−2.82092e6	−1.05690
$373$	−2.76160e6	−1.02775	−0.513876	−	0.857864i	$-0.671791\pi$
$373$	−2.76160e6	−1.02775	−0.513876	+	0.857864i	$0.671791\pi$
$374$	2.39661e6	0.885970
$375$	1.99222e6	0.731576
$376$	−789522.	−0.288002
$377$	6.68654e6	2.42297
$378$	336580.	0.121160
$379$	−2.01627e6	−0.721025	−0.360513	−	0.932754i	$-0.617398\pi$
$379$	−2.01627e6	−0.721025	−0.360513	+	0.932754i	$0.617398\pi$
$380$	0	0
$381$	1.21673e6	0.429418
$382$	269529.	0.0945033
$383$	−5.64860e6	−1.96763	−0.983815	−	0.179185i	$-0.942654\pi$
$383$	−5.64860e6	−1.96763	−0.983815	+	0.179185i	$0.942654\pi$
$384$	431970.	0.149495
$385$	−580954.	−0.199751
$386$	−805850.	−0.275287
$387$	6.65799e6	2.25978
$388$	−1.83464e6	−0.618689
$389$	3.09188e6	1.03597	0.517986	−	0.855389i	$-0.326682\pi$
$389$	3.09188e6	1.03597	0.517986	+	0.855389i	$0.326682\pi$
$390$	7.15288e6	2.38133
$391$	−505193.	−0.167115
$392$	−1.06074e6	−0.348654
$393$	−7.89471e6	−2.57843
$394$	−380681.	−0.123544
$395$	2.60056e6	0.838638
$396$	−3.25822e6	−1.04410
$397$	1.60838e6	0.512168	0.256084	−	0.966655i	$-0.417568\pi$
$397$	1.60838e6	0.512168	0.256084	+	0.966655i	$0.417568\pi$
$398$	−482844.	−0.152791
$399$	0	0
$400$	1.02886e6	0.321519
$401$	−2.60056e6	−0.807616	−0.403808	−	0.914844i	$-0.632314\pi$
$401$	−2.60056e6	−0.807616	−0.403808	+	0.914844i	$0.632314\pi$
$402$	113456.	0.0350155
$403$	−5.36604e6	−1.64585
$404$	−723654.	−0.220586
$405$	3.00104e6	0.909148
$406$	508651.	0.153146
$407$	2.18693e6	0.654408
$408$	−2.24469e6	−0.667583
$409$	−1.24018e6	−0.366587	−0.183293	−	0.983058i	$-0.558676\pi$
$409$	−1.24018e6	−0.366587	−0.183293	+	0.983058i	$0.558676\pi$
$410$	4.25256e6	1.24937
$411$	3.61071e6	1.05436
$412$	−758732.	−0.220214
$413$	84501.1	0.0243774
$414$	686815.	0.196942
$415$	3.17922e6	0.906149
$416$	821707.	0.232800
$417$	−7.77665e6	−2.19004
$418$	0	0
$419$	1.66141e6	0.462318	0.231159	−	0.972916i	$-0.425748\pi$
$419$	1.66141e6	0.462318	0.231159	+	0.972916i	$0.425748\pi$
$420$	544126.	0.150514
$421$	5.13402e6	1.41173	0.705866	−	0.708346i	$-0.250558\pi$
$421$	5.13402e6	1.41173	0.705866	+	0.708346i	$0.250558\pi$
$422$	−1.54585e6	−0.422559
$423$	−5.57762e6	−1.51565
$424$	105525.	0.0285064
$425$	−5.34637e6	−1.43578
$426$	2.60019e6	0.694195
$427$	513041.	0.136170
$428$	−3.42740e6	−0.904390
$429$	−9.52898e6	−2.49979
$430$	4.97862e6	1.29849
$431$	−1.17229e6	−0.303978	−0.151989	−	0.988382i	$-0.548568\pi$
$431$	−1.17229e6	−0.303978	−0.151989	+	0.988382i	$0.548568\pi$
$432$	1.41154e6	0.363901
$433$	−3.50979e6	−0.899626	−0.449813	−	0.893123i	$-0.648509\pi$
$433$	−3.50979e6	−0.899626	−0.449813	+	0.893123i	$0.648509\pi$
$434$	−408199.	−0.104027
$435$	1.85690e7	4.70506
$436$	3.62984e6	0.914473
$437$	0	0
$438$	−5.25163e6	−1.30800
$439$	−3.37606e6	−0.836082	−0.418041	−	0.908428i	$-0.637283\pi$
$439$	−3.37606e6	−0.836082	−0.418041	+	0.908428i	$0.637283\pi$
$440$	−2.43639e6	−0.599949
$441$	−7.49368e6	−1.83484
$442$	−4.26992e6	−1.03959
$443$	1.50788e6	0.365053	0.182527	−	0.983201i	$-0.441572\pi$
$443$	1.50788e6	0.365053	0.182527	+	0.983201i	$0.441572\pi$
$444$	−2.04829e6	−0.493100
$445$	−7.83902e6	−1.87656
$446$	−1.81063e6	−0.431015
$447$	−4.84734e6	−1.14745
$448$	62507.9	0.0147143
$449$	−183807.	−0.0430275	−0.0215137	−	0.999769i	$-0.506849\pi$
$449$	−183807.	−0.0430275	−0.0215137	+	0.999769i	$0.506849\pi$
$450$	7.26845e6	1.69204
$451$	−5.66520e6	−1.31152
$452$	262910.	0.0605288
$453$	−1.17068e7	−2.68035
$454$	92377.5	0.0210342
$455$	1.03505e6	0.234388
$456$	0	0
$457$	5.18883e6	1.16219	0.581097	−	0.813834i	$-0.302624\pi$
$457$	5.18883e6	1.16219	0.581097	+	0.813834i	$0.302624\pi$
$458$	1.24621e6	0.277605
$459$	−7.33492e6	−1.62504
$460$	513577.	0.113165
$461$	3.46218e6	0.758748	0.379374	−	0.925243i	$-0.376139\pi$
$461$	3.46218e6	0.758748	0.379374	+	0.925243i	$0.376139\pi$
$462$	−724877.	−0.158001
$463$	−2.78786e6	−0.604392	−0.302196	−	0.953246i	$-0.597720\pi$
$463$	−2.78786e6	−0.604392	−0.302196	+	0.953246i	$0.597720\pi$
$464$	2.13316e6	0.459970
$465$	−1.49019e7	−3.19601
$466$	−3.35508e6	−0.715711
$467$	179812.	0.0381528	0.0190764	−	0.999818i	$-0.493927\pi$
$467$	179812.	0.0381528	0.0190764	+	0.999818i	$0.493927\pi$
$468$	5.80500e6	1.22514
$469$	16417.5	0.00344648
$470$	−4.17076e6	−0.870904
$471$	1.22144e7	2.53699
$472$	354378.	0.0732170
$473$	−6.63245e6	−1.36308
$474$	3.24482e6	0.663353
$475$	0	0
$476$	−324816.	−0.0657083
$477$	745490.	0.150019
$478$	1.11344e6	0.222894
$479$	−3.24343e6	−0.645900	−0.322950	−	0.946416i	$-0.604675\pi$
$479$	−3.24343e6	−0.645900	−0.322950	+	0.946416i	$0.604675\pi$
$480$	2.28194e6	0.452065
$481$	−3.89633e6	−0.767880
$482$	−3.85063e6	−0.754943
$483$	152800.	0.0298027
$484$	668906.	0.129793
$485$	−9.69176e6	−1.87089
$486$	−1.61493e6	−0.310144
$487$	5.47967e6	1.04696	0.523482	−	0.852037i	$-0.324633\pi$
$487$	5.47967e6	1.04696	0.523482	+	0.852037i	$0.324633\pi$
$488$	2.15158e6	0.408985
$489$	−2.89944e6	−0.548330
$490$	−5.60352e6	−1.05432
$491$	−6.46147e6	−1.20956	−0.604780	−	0.796393i	$-0.706739\pi$
$491$	−6.46147e6	−1.20956	−0.604780	+	0.796393i	$0.706739\pi$
$492$	5.30607e6	0.988235
$493$	−1.10848e7	−2.05404
$494$	0	0
$495$	−1.72120e7	−3.15732
$496$	−1.71189e6	−0.312444
$497$	376259.	0.0683276
$498$	3.96683e6	0.716753
$499$	215507.	0.0387445	0.0193722	−	0.999812i	$-0.493833\pi$
$499$	215507.	0.0387445	0.0193722	+	0.999812i	$0.493833\pi$
$500$	1.20899e6	0.216271
$501$	1.48509e6	0.264337
$502$	−1.40969e6	−0.249669
$503$	9.57985e6	1.68826	0.844128	−	0.536141i	$-0.180118\pi$
$503$	9.57985e6	1.68826	0.844128	+	0.536141i	$0.180118\pi$
$504$	441591.	0.0774362
$505$	−3.82280e6	−0.667041
$506$	−684181.	−0.118794
$507$	7.18800e6	1.24190
$508$	738379.	0.126946
$509$	1.53458e6	0.262540	0.131270	−	0.991347i	$-0.458094\pi$
$509$	1.53458e6	0.262540	0.131270	+	0.991347i	$0.458094\pi$
$510$	−1.18579e7	−2.01874
$511$	−759934.	−0.128743
$512$	262144.	0.0441942
$513$	0	0
$514$	6.36684e6	1.06296
$515$	−4.00810e6	−0.665918
$516$	6.21201e6	1.02709
$517$	5.55623e6	0.914226
$518$	−296397.	−0.0485344
$519$	−1.35900e6	−0.221463
$520$	4.34078e6	0.703978
$521$	−6.24839e6	−1.00850	−0.504248	−	0.863559i	$-0.668230\pi$
$521$	−6.24839e6	−1.00850	−0.504248	+	0.863559i	$0.668230\pi$
$522$	1.50699e7	2.42065
$523$	−1.46135e6	−0.233615	−0.116807	−	0.993155i	$-0.537266\pi$
$523$	−1.46135e6	−0.233615	−0.116807	+	0.993155i	$0.537266\pi$
$524$	−4.79096e6	−0.762245
$525$	1.61706e6	0.256052
$526$	6.30426e6	0.993504
$527$	8.89568e6	1.39525
$528$	−3.03997e6	−0.474553
$529$	−6.29212e6	−0.977593
$530$	557452.	0.0862021
$531$	2.50352e6	0.385315
$532$	0	0
$533$	1.00934e7	1.53893
$534$	−9.78103e6	−1.48433
$535$	−1.81057e7	−2.73483
$536$	68851.3	0.0103514
$537$	−1.70875e7	−2.55707
$538$	4.29643e6	0.639959
$539$	7.46493e6	1.10676
$540$	7.45665e6	1.10042
$541$	−9.78327e6	−1.43711	−0.718556	−	0.695469i	$-0.755197\pi$
$541$	−9.78327e6	−1.43711	−0.718556	+	0.695469i	$0.755197\pi$
$542$	3.31869e6	0.485254
$543$	1.29813e7	1.88938
$544$	−1.36220e6	−0.197354
$545$	1.91751e7	2.76532
$546$	1.29148e6	0.185398
$547$	−1.17209e7	−1.67492	−0.837460	−	0.546498i	$-0.815960\pi$
$547$	−1.17209e7	−1.67492	−0.837460	+	0.546498i	$0.815960\pi$
$548$	2.19118e6	0.311693
$549$	1.51999e7	2.15234
$550$	−7.24057e6	−1.02062
$551$	0	0
$552$	640809.	0.0895119
$553$	469539.	0.0652919
$554$	2.18648e6	0.302672
$555$	−1.08204e7	−1.49111
$556$	−4.71932e6	−0.647429
$557$	−1.08382e7	−1.48019	−0.740095	−	0.672502i	$-0.765220\pi$
$557$	−1.08382e7	−1.48019	−0.740095	+	0.672502i	$0.765220\pi$
$558$	−1.20938e7	−1.64428
$559$	1.18167e7	1.59943
$560$	330207.	0.0444955
$561$	1.57969e7	2.11916
$562$	3.09742e6	0.413676
$563$	−7.80000e6	−1.03711	−0.518554	−	0.855045i	$-0.673529\pi$
$563$	−7.80000e6	−1.03711	−0.518554	+	0.855045i	$0.673529\pi$
$564$	−5.20401e6	−0.688875
$565$	1.38886e6	0.183036
$566$	2.54777e6	0.334287
$567$	541847.	0.0707814
$568$	1.57795e6	0.205221
$569$	−5.60370e6	−0.725594	−0.362797	−	0.931868i	$-0.618178\pi$
$569$	−5.60370e6	−0.725594	−0.362797	+	0.931868i	$0.618178\pi$
$570$	0	0
$571$	−8.49811e6	−1.09077	−0.545383	−	0.838187i	$-0.683616\pi$
$571$	−8.49811e6	−1.09077	−0.545383	+	0.838187i	$0.683616\pi$
$572$	−5.78273e6	−0.738997
$573$	1.77656e6	0.226044
$574$	767812.	0.0972691
$575$	1.52627e6	0.192514
$576$	1.85193e6	0.232578
$577$	−9.65726e6	−1.20758	−0.603788	−	0.797145i	$-0.706343\pi$
$577$	−9.65726e6	−1.20758	−0.603788	+	0.797145i	$0.706343\pi$
$578$	1.39913e6	0.174196
$579$	−5.31163e6	−0.658463
$580$	1.12687e7	1.39093
$581$	574017.	0.0705480
$582$	−1.20928e7	−1.47985
$583$	−742631.	−0.0904902
$584$	−3.18699e6	−0.386677
$585$	3.06657e7	3.70478
$586$	−4.60693e6	−0.554201
$587$	−1.64588e6	−0.197153	−0.0985767	−	0.995129i	$-0.531429\pi$
$587$	−1.64588e6	−0.197153	−0.0985767	+	0.995129i	$0.531429\pi$
$588$	−6.99171e6	−0.833951
$589$	0	0
$590$	1.87205e6	0.221405
$591$	−2.50920e6	−0.295506
$592$	−1.24302e6	−0.145772
$593$	−6.15870e6	−0.719205	−0.359602	−	0.933106i	$-0.617088\pi$
$593$	−6.15870e6	−0.719205	−0.359602	+	0.933106i	$0.617088\pi$
$594$	−9.93365e6	−1.15516
$595$	−1.71588e6	−0.198699
$596$	−2.94164e6	−0.339214
$597$	−3.18259e6	−0.365464
$598$	1.21897e6	0.139392
$599$	−1.19969e7	−1.36616	−0.683078	−	0.730346i	$-0.739359\pi$
$599$	−1.19969e7	−1.36616	−0.683078	+	0.730346i	$0.739359\pi$
$600$	6.78158e6	0.769046
$601$	−8.53734e6	−0.964132	−0.482066	−	0.876135i	$-0.660113\pi$
$601$	−8.53734e6	−0.964132	−0.482066	+	0.876135i	$0.660113\pi$
$602$	898905.	0.101093
$603$	486404.	0.0544758
$604$	−7.10434e6	−0.792376
$605$	3.53359e6	0.392489
$606$	−4.76984e6	−0.527622
$607$	6.86609e6	0.756376	0.378188	−	0.925729i	$-0.376547\pi$
$607$	6.86609e6	0.756376	0.378188	+	0.925729i	$0.376547\pi$
$608$	0	0
$609$	3.35269e6	0.366311
$610$	1.13660e7	1.23675
$611$	−9.89923e6	−1.07275
$612$	−9.62337e6	−1.03860
$613$	1.19450e7	1.28391	0.641956	−	0.766742i	$-0.278123\pi$
$613$	1.19450e7	1.28391	0.641956	+	0.766742i	$0.278123\pi$
$614$	8.64310e6	0.925228
$615$	2.80300e7	2.98838
$616$	−439897.	−0.0467089
$617$	1.28809e6	0.136218	0.0681089	−	0.997678i	$-0.478303\pi$
$617$	1.28809e6	0.136218	0.0681089	+	0.997678i	$0.478303\pi$
$618$	−5.00106e6	−0.526733
$619$	5.27313e6	0.553149	0.276574	−	0.960993i	$-0.410801\pi$
$619$	5.27313e6	0.553149	0.276574	+	0.960993i	$0.410801\pi$
$620$	−9.04331e6	−0.944818
$621$	2.09396e6	0.217891
$622$	7.88807e6	0.817513
$623$	−1.41536e6	−0.146099
$624$	5.41615e6	0.556838
$625$	−6.17268e6	−0.632082
$626$	−2.10870e6	−0.215070
$627$	0	0
$628$	7.41237e6	0.749994
$629$	6.45923e6	0.650960
$630$	2.33276e6	0.234164
$631$	1.16692e7	1.16672	0.583360	−	0.812214i	$-0.301738\pi$
$631$	1.16692e7	1.16672	0.583360	+	0.812214i	$0.301738\pi$
$632$	1.96914e6	0.196103
$633$	−1.01892e7	−1.01072
$634$	6.92178e6	0.683903
$635$	3.90058e6	0.383880
$636$	695554.	0.0681848
$637$	−1.32999e7	−1.29867
$638$	−1.50120e7	−1.46012
$639$	1.11475e7	1.08000
$640$	1.38481e6	0.133641
$641$	−1.22438e7	−1.17699	−0.588494	−	0.808502i	$-0.700279\pi$
$641$	−1.22438e7	−1.17699	−0.588494	+	0.808502i	$0.700279\pi$
$642$	−2.25912e7	−2.16322
$643$	1.03196e7	0.984320	0.492160	−	0.870505i	$-0.336207\pi$
$643$	1.03196e7	0.984320	0.492160	+	0.870505i	$0.336207\pi$
$644$	92727.9	0.00881040
$645$	3.28158e7	3.10587
$646$	0	0
$647$	1.41105e7	1.32520	0.662601	−	0.748972i	$-0.269452\pi$
$647$	1.41105e7	1.32520	0.662601	+	0.748972i	$0.269452\pi$
$648$	2.27238e6	0.212591
$649$	−2.49392e6	−0.232419
$650$	1.29001e7	1.19760
$651$	−2.69058e6	−0.248825
$652$	−1.75955e6	−0.162099
$653$	8.05111e6	0.738878	0.369439	−	0.929255i	$-0.379550\pi$
$653$	8.05111e6	0.738878	0.369439	+	0.929255i	$0.379550\pi$
$654$	2.39255e7	2.18734
$655$	−2.53089e7	−2.30499
$656$	3.22003e6	0.292146
$657$	−2.25146e7	−2.03494
$658$	−753043.	−0.0678039
$659$	3.50112e6	0.314046	0.157023	−	0.987595i	$-0.449810\pi$
$659$	3.50112e6	0.314046	0.157023	+	0.987595i	$0.449810\pi$
$660$	−1.60590e7	−1.43503
$661$	8.08972e6	0.720161	0.360081	−	0.932921i	$-0.382749\pi$
$661$	8.08972e6	0.720161	0.360081	+	0.932921i	$0.382749\pi$
$662$	4.33987e6	0.384885
$663$	−2.81445e7	−2.48662
$664$	2.40730e6	0.211889
$665$	0	0
$666$	−8.78140e6	−0.767146
$667$	3.16446e6	0.275413
$668$	901235.	0.0781442
$669$	−1.19345e7	−1.03095
$670$	363716.	0.0313023
$671$	−1.51416e7	−1.29827
$672$	412011.	0.0351954
$673$	5.66480e6	0.482111	0.241055	−	0.970511i	$-0.422506\pi$
$673$	5.66480e6	0.482111	0.241055	+	0.970511i	$0.422506\pi$
$674$	−7.68326e6	−0.651472
$675$	2.21600e7	1.87202
$676$	4.36209e6	0.367137
$677$	4.24946e6	0.356338	0.178169	−	0.984000i	$-0.442983\pi$
$677$	4.24946e6	0.356338	0.178169	+	0.984000i	$0.442983\pi$
$678$	1.73293e6	0.144780
$679$	−1.74988e6	−0.145658
$680$	−7.19603e6	−0.596788
$681$	608891.	0.0503121
$682$	1.20474e7	0.991817
$683$	2.09008e7	1.71440	0.857200	−	0.514984i	$-0.172202\pi$
$683$	2.09008e7	1.71440	0.857200	+	0.514984i	$0.172202\pi$
$684$	0	0
$685$	1.15752e7	0.942547
$686$	−2.03768e6	−0.165320
$687$	8.21418e6	0.664007
$688$	3.76980e6	0.303632
$689$	1.32311e6	0.106181
$690$	3.38516e6	0.270680
$691$	−8.97377e6	−0.714957	−0.357479	−	0.933921i	$-0.616363\pi$
$691$	−8.97377e6	−0.714957	−0.357479	+	0.933921i	$0.616363\pi$
$692$	−824718.	−0.0654696
$693$	−3.10768e6	−0.245812
$694$	−6.86181e6	−0.540804
$695$	−2.49304e7	−1.95780
$696$	1.40604e7	1.10021
$697$	−1.67325e7	−1.30461
$698$	1.34131e7	1.04205
$699$	−2.21144e7	−1.71192
$700$	981324.	0.0756950
$701$	−1.55796e7	−1.19746	−0.598730	−	0.800951i	$-0.704328\pi$
$701$	−1.55796e7	−1.19746	−0.598730	+	0.800951i	$0.704328\pi$
$702$	1.76982e7	1.35546
$703$	0	0
$704$	−1.84483e6	−0.140289
$705$	−2.74909e7	−2.08313
$706$	8.04704e6	0.607609
$707$	−690218.	−0.0519323
$708$	2.33583e6	0.175129
$709$	4.54607e6	0.339641	0.169821	−	0.985475i	$-0.445681\pi$
$709$	4.54607e6	0.339641	0.169821	+	0.985475i	$0.445681\pi$
$710$	8.33571e6	0.620578
$711$	1.39111e7	1.03202
$712$	−5.93569e6	−0.438805
$713$	−2.53952e6	−0.187080
$714$	−2.14097e6	−0.157169
$715$	−3.05480e7	−2.23469
$716$	−1.03697e7	−0.755930
$717$	7.33908e6	0.533143
$718$	8.12442e6	0.588140
$719$	−1.78079e7	−1.28467	−0.642335	−	0.766424i	$-0.722034\pi$
$719$	−1.78079e7	−1.28467	−0.642335	+	0.766424i	$0.722034\pi$
$720$	9.78307e6	0.703306
$721$	−723675.	−0.0518448
$722$	0	0
$723$	−2.53808e7	−1.80576
$724$	7.87780e6	0.558546
$725$	3.34889e7	2.36623
$726$	4.40899e6	0.310454
$727$	2.21888e7	1.55703	0.778516	−	0.627625i	$-0.215973\pi$
$727$	2.21888e7	1.55703	0.778516	+	0.627625i	$0.215973\pi$
$728$	783741.	0.0548080
$729$	−1.92725e7	−1.34313
$730$	−1.68357e7	−1.16929
$731$	−1.95894e7	−1.35590
$732$	1.41818e7	0.978256
$733$	−1.39640e6	−0.0959951	−0.0479976	−	0.998847i	$-0.515284\pi$
$733$	−1.39640e6	−0.0959951	−0.0479976	+	0.998847i	$0.515284\pi$
$734$	1.41398e6	0.0968731
$735$	−3.69347e7	−2.52183
$736$	388879.	0.0264619
$737$	−484538.	−0.0328594
$738$	2.27481e7	1.53746
$739$	2.46795e7	1.66236	0.831179	−	0.556005i	$-0.187667\pi$
$739$	2.46795e7	1.66236	0.831179	+	0.556005i	$0.187667\pi$
$740$	−6.56643e6	−0.440808
$741$	0	0
$742$	100650.	0.00671124
$743$	3.60757e6	0.239741	0.119871	−	0.992790i	$-0.461752\pi$
$743$	3.60757e6	0.239741	0.119871	+	0.992790i	$0.461752\pi$
$744$	−1.12837e7	−0.747340
$745$	−1.55396e7	−1.02577
$746$	−1.10464e7	−0.726731
$747$	1.70065e7	1.11510
$748$	9.58645e6	0.626475
$749$	−3.26904e6	−0.212920
$750$	7.96888e6	0.517302
$751$	−1.49951e7	−0.970176	−0.485088	−	0.874465i	$-0.661212\pi$
$751$	−1.49951e7	−0.970176	−0.485088	+	0.874465i	$0.661212\pi$
$752$	−3.15809e6	−0.203648
$753$	−9.29175e6	−0.597186
$754$	2.67462e7	1.71330
$755$	−3.75296e7	−2.39611
$756$	1.34632e6	0.0856730
$757$	1.17051e7	0.742395	0.371198	−	0.928554i	$-0.378947\pi$
$757$	1.17051e7	0.742395	0.371198	+	0.928554i	$0.378947\pi$
$758$	−8.06507e6	−0.509842
$759$	−4.50966e6	−0.284145
$760$	0	0
$761$	−1.09596e7	−0.686016	−0.343008	−	0.939333i	$-0.611446\pi$
$761$	−1.09596e7	−0.686016	−0.343008	+	0.939333i	$0.611446\pi$
$762$	4.86690e6	0.303644
$763$	3.46212e6	0.215293
$764$	1.07812e6	0.0668239
$765$	−5.08367e7	−3.14068
$766$	−2.25944e7	−1.39133
$767$	4.44328e6	0.272719
$768$	1.72788e6	0.105709
$769$	2.92163e7	1.78160	0.890798	−	0.454399i	$-0.150146\pi$
$769$	2.92163e7	1.78160	0.890798	+	0.454399i	$0.150146\pi$
$770$	−2.32381e6	−0.141246
$771$	4.19660e7	2.54250
$772$	−3.22340e6	−0.194658
$773$	−9.03923e6	−0.544105	−0.272052	−	0.962282i	$-0.587702\pi$
$773$	−9.03923e6	−0.544105	−0.272052	+	0.962282i	$0.587702\pi$
$774$	2.66320e7	1.59790
$775$	−2.68753e7	−1.60731
$776$	−7.33858e6	−0.437479
$777$	−1.95365e6	−0.116090
$778$	1.23675e7	0.732543
$779$	0	0
$780$	2.86115e7	1.68385
$781$	−1.11047e7	−0.651448
$782$	−2.02077e6	−0.118168
$783$	4.59449e7	2.67814
$784$	−4.24297e6	−0.246536
$785$	3.91568e7	2.26795
$786$	−3.15788e7	−1.82322
$787$	1.05569e7	0.607572	0.303786	−	0.952740i	$-0.401749\pi$
$787$	1.05569e7	0.607572	0.303786	+	0.952740i	$0.401749\pi$
$788$	−1.52273e6	−0.0873587
$789$	4.15535e7	2.37638
$790$	1.04022e7	0.593007
$791$	250763.	0.0142502
$792$	−1.30329e7	−0.738291
$793$	2.69770e7	1.52339
$794$	6.43352e6	0.362157
$795$	3.67435e6	0.206188
$796$	−1.93138e6	−0.108040
$797$	−3.23295e7	−1.80282	−0.901411	−	0.432964i	$-0.857468\pi$
$797$	−3.23295e7	−1.80282	−0.901411	+	0.432964i	$0.857468\pi$
$798$	0	0
$799$	1.64107e7	0.909410
$800$	4.11545e6	0.227349
$801$	−4.19330e7	−2.30927
$802$	−1.04022e7	−0.571071
$803$	2.24283e7	1.22746
$804$	453822.	0.0247597
$805$	489847.	0.0266423
$806$	−2.14642e7	−1.16380
$807$	2.83192e7	1.53073
$808$	−2.89461e6	−0.155978
$809$	420464.	0.0225869	0.0112935	−	0.999936i	$-0.496405\pi$
$809$	420464.	0.0225869	0.0112935	+	0.999936i	$0.496405\pi$
$810$	1.20042e7	0.642865
$811$	2.57746e7	1.37607	0.688034	−	0.725679i	$-0.258474\pi$
$811$	2.57746e7	1.37607	0.688034	+	0.725679i	$0.258474\pi$
$812$	2.03460e6	0.108290
$813$	2.18746e7	1.16068
$814$	8.74771e6	0.462736
$815$	−9.29504e6	−0.490182
$816$	−8.97875e6	−0.472053
$817$	0	0
$818$	−4.96072e6	−0.259216
$819$	5.53678e6	0.288435
$820$	1.70102e7	0.883436
$821$	1.69701e7	0.878672	0.439336	−	0.898323i	$-0.355214\pi$
$821$	1.69701e7	0.878672	0.439336	+	0.898323i	$0.355214\pi$
$822$	1.44428e7	0.745543
$823$	−1.66003e7	−0.854313	−0.427157	−	0.904178i	$-0.640485\pi$
$823$	−1.66003e7	−0.854313	−0.427157	+	0.904178i	$0.640485\pi$
$824$	−3.03493e6	−0.155715
$825$	−4.77250e7	−2.44125
$826$	338004.	0.0172374
$827$	−2.11542e7	−1.07556	−0.537779	−	0.843086i	$-0.680736\pi$
$827$	−2.11542e7	−1.07556	−0.537779	+	0.843086i	$0.680736\pi$
$828$	2.74726e6	0.139259
$829$	−6.12637e6	−0.309611	−0.154806	−	0.987945i	$-0.549475\pi$
$829$	−6.12637e6	−0.309611	−0.154806	+	0.987945i	$0.549475\pi$
$830$	1.27169e7	0.640744
$831$	1.44119e7	0.723965
$832$	3.28683e6	0.164615
$833$	2.20482e7	1.10093
$834$	−3.11066e7	−1.54859
$835$	4.76089e6	0.236305
$836$	0	0
$837$	−3.68714e7	−1.81918
$838$	6.64562e6	0.326908
$839$	−6.14792e6	−0.301525	−0.150762	−	0.988570i	$-0.548173\pi$
$839$	−6.14792e6	−0.301525	−0.150762	+	0.988570i	$0.548173\pi$
$840$	2.17650e6	0.106429
$841$	4.89222e7	2.38515
$842$	2.05361e7	0.998245
$843$	2.04162e7	0.989476
$844$	−6.18342e6	−0.298794
$845$	2.30433e7	1.11021
$846$	−2.23105e7	−1.07172
$847$	638000.	0.0305571
$848$	422102.	0.0201571
$849$	1.67932e7	0.799584
$850$	−2.13855e7	−1.01525
$851$	−1.84397e6	−0.0872830
$852$	1.04008e7	0.490870
$853$	1.43957e7	0.677423	0.338711	−	0.940890i	$-0.390009\pi$
$853$	1.43957e7	0.677423	0.338711	+	0.940890i	$0.390009\pi$
$854$	2.05216e6	0.0962869
$855$	0	0
$856$	−1.37096e7	−0.639500
$857$	3.25050e7	1.51181	0.755907	−	0.654679i	$-0.227196\pi$
$857$	3.25050e7	1.51181	0.755907	+	0.654679i	$0.227196\pi$
$858$	−3.81159e7	−1.76762
$859$	−1.57754e7	−0.729453	−0.364726	−	0.931115i	$-0.618838\pi$
$859$	−1.57754e7	−0.729453	−0.364726	+	0.931115i	$0.618838\pi$
$860$	1.99145e7	0.918169
$861$	5.06091e6	0.232659
$862$	−4.68916e6	−0.214945
$863$	−3.79160e7	−1.73299	−0.866493	−	0.499189i	$-0.833631\pi$
$863$	−3.79160e7	−1.73299	−0.866493	+	0.499189i	$0.833631\pi$
$864$	5.64616e6	0.257317
$865$	−4.35668e6	−0.197977
$866$	−1.40392e7	−0.636132
$867$	9.22211e6	0.416661
$868$	−1.63280e6	−0.0735585
$869$	−1.38577e7	−0.622505
$870$	7.42759e7	3.32698
$871$	863276.	0.0385571
$872$	1.45193e7	0.646630
$873$	−5.18438e7	−2.30230
$874$	0	0
$875$	1.15313e6	0.0509166
$876$	−2.10065e7	−0.924897
$877$	−5.67995e6	−0.249371	−0.124685	−	0.992196i	$-0.539792\pi$
$877$	−5.67995e6	−0.249371	−0.124685	+	0.992196i	$0.539792\pi$
$878$	−1.35042e7	−0.591199
$879$	−3.03658e7	−1.32560
$880$	−9.74554e6	−0.424228
$881$	−3.32419e7	−1.44293	−0.721467	−	0.692449i	$-0.756532\pi$
$881$	−3.32419e7	−1.44293	−0.721467	+	0.692449i	$0.756532\pi$
$882$	−2.99747e7	−1.29743
$883$	2.00103e7	0.863678	0.431839	−	0.901951i	$-0.357865\pi$
$883$	2.00103e7	0.863678	0.431839	+	0.901951i	$0.357865\pi$
$884$	−1.70797e7	−0.735104
$885$	1.23393e7	0.529581
$886$	6.03150e6	0.258132
$887$	4.04408e7	1.72588	0.862941	−	0.505304i	$-0.168620\pi$
$887$	4.04408e7	1.72588	0.862941	+	0.505304i	$0.168620\pi$
$888$	−8.19317e6	−0.348674
$889$	704262.	0.0298868
$890$	−3.13561e7	−1.32693
$891$	−1.59918e7	−0.674843
$892$	−7.24252e6	−0.304774
$893$	0	0
$894$	−1.93893e7	−0.811371
$895$	−5.47791e7	−2.28590
$896$	250032.	0.0104046
$897$	8.03463e6	0.333415
$898$	−735227.	−0.0304250
$899$	−5.57213e7	−2.29944
$900$	2.90738e7	1.19645
$901$	−2.19341e6	−0.0900134
$902$	−2.26608e7	−0.927382
$903$	5.92498e6	0.241806
$904$	1.05164e6	0.0428003
$905$	4.16155e7	1.68902
$906$	−4.68271e7	−1.89529
$907$	2.90090e6	0.117088	0.0585442	−	0.998285i	$-0.481354\pi$
$907$	2.90090e6	0.117088	0.0585442	+	0.998285i	$0.481354\pi$
$908$	369510.	0.0148734
$909$	−2.04492e7	−0.820854
$910$	4.14022e6	0.165737
$911$	2.43185e7	0.970824	0.485412	−	0.874286i	$-0.338670\pi$
$911$	2.43185e7	0.970824	0.485412	+	0.874286i	$0.338670\pi$
$912$	0	0
$913$	−1.69412e7	−0.672618
$914$	2.07553e7	0.821795
$915$	7.49170e7	2.95820
$916$	4.98483e6	0.196296
$917$	−4.56960e6	−0.179455
$918$	−2.93397e7	−1.14908
$919$	8.22526e6	0.321263	0.160631	−	0.987014i	$-0.448647\pi$
$919$	8.22526e6	0.321263	0.160631	+	0.987014i	$0.448647\pi$
$920$	2.05431e6	0.0800195
$921$	5.69696e7	2.21307
$922$	1.38487e7	0.536516
$923$	1.97847e7	0.764407
$924$	−2.89951e6	−0.111724
$925$	−1.95144e7	−0.749897
$926$	−1.11514e7	−0.427369
$927$	−2.14404e7	−0.819472
$928$	8.53265e6	0.325248
$929$	4.19040e7	1.59300	0.796501	−	0.604638i	$-0.206682\pi$
$929$	4.19040e7	1.59300	0.796501	+	0.604638i	$0.206682\pi$
$930$	−5.96075e7	−2.25992
$931$	0	0
$932$	−1.34203e7	−0.506084
$933$	5.19929e7	1.95542
$934$	719248.	0.0269781
$935$	5.06417e7	1.89443
$936$	2.32200e7	0.866308
$937$	2.78186e7	1.03511	0.517554	−	0.855650i	$-0.326843\pi$
$937$	2.78186e7	1.03511	0.517554	+	0.855650i	$0.326843\pi$
$938$	65670.1	0.00243703
$939$	−1.38992e7	−0.514429
$940$	−1.66830e7	−0.615822
$941$	−1.92168e7	−0.707468	−0.353734	−	0.935346i	$-0.615088\pi$
$941$	−1.92168e7	−0.707468	−0.353734	+	0.935346i	$0.615088\pi$
$942$	4.88574e7	1.79392
$943$	4.77677e6	0.174926
$944$	1.41751e6	0.0517722
$945$	7.11212e6	0.259071
$946$	−2.65298e7	−0.963843
$947$	−1.85612e7	−0.672559	−0.336280	−	0.941762i	$-0.609169\pi$
$947$	−1.85612e7	−0.672559	−0.336280	+	0.941762i	$0.609169\pi$
$948$	1.29793e7	0.469061
$949$	−3.99593e7	−1.44030
$950$	0	0
$951$	4.56238e7	1.63584
$952$	−1.29926e6	−0.0464628
$953$	4.84999e7	1.72985	0.864926	−	0.501900i	$-0.167365\pi$
$953$	4.84999e7	1.72985	0.864926	+	0.501900i	$0.167365\pi$
$954$	2.98196e6	0.106079
$955$	5.69529e6	0.202073
$956$	4.45377e6	0.157610
$957$	−9.89495e7	−3.49248
$958$	−1.29737e7	−0.456720
$959$	2.08994e6	0.0733817
$960$	9.12775e6	0.319658
$961$	1.60880e7	0.561944
$962$	−1.55853e7	−0.542973
$963$	−9.68523e7	−3.36546
$964$	−1.54025e7	−0.533826
$965$	−1.70280e7	−0.588636
$966$	611201.	0.0210737
$967$	−1.02262e7	−0.351680	−0.175840	−	0.984419i	$-0.556264\pi$
$967$	−1.02262e7	−0.351680	−0.175840	+	0.984419i	$0.556264\pi$
$968$	2.67562e6	0.0917776
$969$	0	0
$970$	−3.87670e7	−1.32292
$971$	4.50010e7	1.53170	0.765851	−	0.643018i	$-0.222318\pi$
$971$	4.50010e7	1.53170	0.765851	+	0.643018i	$0.222318\pi$
$972$	−6.45972e6	−0.219305
$973$	−4.50126e6	−0.152424
$974$	2.19187e7	0.740315
$975$	8.50292e7	2.86455
$976$	8.60630e6	0.289196
$977$	1.34958e7	0.452336	0.226168	−	0.974088i	$-0.427380\pi$
$977$	1.34958e7	0.452336	0.226168	+	0.974088i	$0.427380\pi$
$978$	−1.15978e7	−0.387728
$979$	4.17721e7	1.39293
$980$	−2.24141e7	−0.745513
$981$	1.02573e8	3.40298
$982$	−2.58459e7	−0.855288
$983$	1.59856e7	0.527650	0.263825	−	0.964571i	$-0.415016\pi$
$983$	1.59856e7	0.527650	0.263825	+	0.964571i	$0.415016\pi$
$984$	2.12243e7	0.698788
$985$	−8.04400e6	−0.264169
$986$	−4.43391e7	−1.45243
$987$	−4.96356e6	−0.162181
$988$	0	0
$989$	5.59234e6	0.181804
$990$	−6.88479e7	−2.23256
$991$	5.93854e6	0.192086	0.0960430	−	0.995377i	$-0.469381\pi$
$991$	5.93854e6	0.192086	0.0960430	+	0.995377i	$0.469381\pi$
$992$	−6.84758e6	−0.220932
$993$	2.86055e7	0.920612
$994$	1.50504e6	0.0483149
$995$	−1.02028e7	−0.326708
$996$	1.58673e7	0.506821
$997$	−1.69917e7	−0.541377	−0.270689	−	0.962667i	$-0.587251\pi$
$997$	−1.69917e7	−0.541377	−0.270689	+	0.962667i	$0.587251\pi$
$998$	862028.	0.0273965
$999$	−2.67727e7	−0.848747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.r.1.15		15
19.4	even	9		38.6.e.b.35.1	yes	30
19.5	even	9		38.6.e.b.25.1	✓	30
19.18	odd	2		722.6.a.q.1.1		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.1	✓	30	19.5	even	9
38.6.e.b.35.1	yes	30	19.4	even	9
722.6.a.q.1.1		15	19.18	odd	2
722.6.a.r.1.15		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +26.3653 q^{3} +16.0000 q^{4} +84.5221 q^{5} +105.461 q^{6} +15.2607 q^{7} +64.0000 q^{8} +452.132 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +26.3653 q^{3} +16.0000 q^{4} +84.5221 q^{5} +105.461 q^{6} +15.2607 q^{7} +64.0000 q^{8} +452.132 q^{9} +338.089 q^{10} -450.397 q^{11} +421.846 q^{12} +802.449 q^{13} +61.0429 q^{14} +2228.46 q^{15} +256.000 q^{16} -1330.28 q^{17} +1808.53 q^{18} +1352.35 q^{20} +402.354 q^{21} -1801.59 q^{22} +379.765 q^{23} +1687.38 q^{24} +4018.99 q^{25} +3209.79 q^{26} +5513.83 q^{27} +244.172 q^{28} +8332.67 q^{29} +8913.82 q^{30} -6687.09 q^{31} +1024.00 q^{32} -11874.9 q^{33} -5321.11 q^{34} +1289.87 q^{35} +7234.11 q^{36} -4855.55 q^{37} +21156.8 q^{39} +5409.42 q^{40} +12578.2 q^{41} +1609.42 q^{42} +14725.8 q^{43} -7206.36 q^{44} +38215.1 q^{45} +1519.06 q^{46} -12336.3 q^{47} +6749.53 q^{48} -16574.1 q^{49} +16076.0 q^{50} -35073.2 q^{51} +12839.2 q^{52} +1648.83 q^{53} +22055.3 q^{54} -38068.5 q^{55} +976.687 q^{56} +33330.7 q^{58} +5537.16 q^{59} +35655.3 q^{60} +33618.4 q^{61} -26748.3 q^{62} +6899.86 q^{63} +4096.00 q^{64} +67824.7 q^{65} -47499.5 q^{66} +1075.80 q^{67} -21284.4 q^{68} +10012.6 q^{69} +5159.48 q^{70} +24655.4 q^{71} +28936.4 q^{72} -49796.7 q^{73} -19422.2 q^{74} +105962. q^{75} -6873.39 q^{77} +84627.3 q^{78} +30767.8 q^{79} +21637.7 q^{80} +35506.0 q^{81} +50312.9 q^{82} +37614.0 q^{83} +6437.67 q^{84} -112438. q^{85} +58903.1 q^{86} +219694. q^{87} -28825.4 q^{88} -92745.1 q^{89} +152861. q^{90} +12246.0 q^{91} +6076.24 q^{92} -176307. q^{93} -49345.1 q^{94} +26998.1 q^{96} -114665. q^{97} -66296.4 q^{98} -203639. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} + 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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