LMFDB - Embedded newform 722.6.a.q.1.12

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			1.12
Root			$18.3407$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +19.8728 q^{3} +16.0000 q^{4} +105.633 q^{5} -79.4911 q^{6} +36.4788 q^{7} -64.0000 q^{8} +151.927 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +19.8728 q^{3} +16.0000 q^{4} +105.633 q^{5} -79.4911 q^{6} +36.4788 q^{7} -64.0000 q^{8} +151.927 q^{9} -422.533 q^{10} +514.540 q^{11} +317.964 q^{12} +314.397 q^{13} -145.915 q^{14} +2099.23 q^{15} +256.000 q^{16} +2286.25 q^{17} -607.709 q^{18} +1690.13 q^{20} +724.934 q^{21} -2058.16 q^{22} -2018.30 q^{23} -1271.86 q^{24} +8033.38 q^{25} -1257.59 q^{26} -1809.87 q^{27} +583.660 q^{28} +1115.15 q^{29} -8396.90 q^{30} -5177.83 q^{31} -1024.00 q^{32} +10225.3 q^{33} -9145.00 q^{34} +3853.37 q^{35} +2430.84 q^{36} -4294.05 q^{37} +6247.94 q^{39} -6760.53 q^{40} +2126.13 q^{41} -2899.74 q^{42} +6792.60 q^{43} +8232.64 q^{44} +16048.6 q^{45} +8073.21 q^{46} -2623.74 q^{47} +5087.43 q^{48} -15476.3 q^{49} -32133.5 q^{50} +45434.1 q^{51} +5030.35 q^{52} -2066.25 q^{53} +7239.47 q^{54} +54352.5 q^{55} -2334.64 q^{56} -4460.58 q^{58} +30720.0 q^{59} +33587.6 q^{60} -24465.7 q^{61} +20711.3 q^{62} +5542.12 q^{63} +4096.00 q^{64} +33210.8 q^{65} -40901.3 q^{66} +20113.7 q^{67} +36580.0 q^{68} -40109.3 q^{69} -15413.5 q^{70} +60143.6 q^{71} -9723.35 q^{72} -40926.2 q^{73} +17176.2 q^{74} +159646. q^{75} +18769.8 q^{77} -24991.8 q^{78} -82597.4 q^{79} +27042.1 q^{80} -72885.4 q^{81} -8504.54 q^{82} -43089.8 q^{83} +11599.0 q^{84} +241504. q^{85} -27170.4 q^{86} +22161.0 q^{87} -32930.5 q^{88} -95174.1 q^{89} -64194.3 q^{90} +11468.8 q^{91} -32292.9 q^{92} -102898. q^{93} +10495.0 q^{94} -20349.7 q^{96} -103891. q^{97} +61905.2 q^{98} +78172.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	19.8728	1.27484	0.637420	−	0.770517i	$-0.280002\pi$
$3$	19.8728	1.27484	0.637420	+	0.770517i	$0.280002\pi$
$4$	16.0000	0.500000
$5$	105.633	1.88962	0.944812	−	0.327612i	$-0.106244\pi$
$5$	105.633	1.88962	0.944812	+	0.327612i	$0.106244\pi$
$6$	−79.4911	−0.901448
$7$	36.4788	0.281381	0.140691	−	0.990054i	$-0.455068\pi$
$7$	36.4788	0.281381	0.140691	+	0.990054i	$0.455068\pi$
$8$	−64.0000	−0.353553
$9$	151.927	0.625215
$10$	−422.533	−1.33617
$11$	514.540	1.28215	0.641073	−	0.767480i	$-0.278490\pi$
$11$	514.540	1.28215	0.641073	+	0.767480i	$0.278490\pi$
$12$	317.964	0.637420
$13$	314.397	0.515965	0.257982	−	0.966150i	$-0.416942\pi$
$13$	314.397	0.515965	0.257982	+	0.966150i	$0.416942\pi$
$14$	−145.915	−0.198967
$15$	2099.23	2.40897
$16$	256.000	0.250000
$17$	2286.25	1.91867	0.959337	−	0.282263i	$-0.0910850\pi$
$17$	2286.25	1.91867	0.959337	+	0.282263i	$0.0910850\pi$
$18$	−607.709	−0.442094
$19$	0	0
$19$	0	0
$20$	1690.13	0.944812
$21$	724.934	0.358716
$22$	−2058.16	−0.906614
$23$	−2018.30	−0.795549	−0.397774	−	0.917483i	$-0.630217\pi$
$23$	−2018.30	−0.795549	−0.397774	+	0.917483i	$0.630217\pi$
$24$	−1271.86	−0.450724
$25$	8033.38	2.57068
$26$	−1257.59	−0.364842
$27$	−1809.87	−0.477790
$28$	583.660	0.140691
$29$	1115.15	0.246227	0.123114	−	0.992393i	$-0.460712\pi$
$29$	1115.15	0.246227	0.123114	+	0.992393i	$0.460712\pi$
$30$	−8396.90	−1.70340
$31$	−5177.83	−0.967706	−0.483853	−	0.875149i	$-0.660763\pi$
$31$	−5177.83	−0.967706	−0.483853	+	0.875149i	$0.660763\pi$
$32$	−1024.00	−0.176777
$33$	10225.3	1.63453
$34$	−9145.00	−1.35671
$35$	3853.37	0.531705
$36$	2430.84	0.312608
$37$	−4294.05	−0.515659	−0.257829	−	0.966190i	$-0.583007\pi$
$37$	−4294.05	−0.515659	−0.257829	+	0.966190i	$0.583007\pi$
$38$	0	0
$39$	6247.94	0.657772
$40$	−6760.53	−0.668083
$41$	2126.13	0.197529	0.0987645	−	0.995111i	$-0.468511\pi$
$41$	2126.13	0.197529	0.0987645	+	0.995111i	$0.468511\pi$
$42$	−2899.74	−0.253650
$43$	6792.60	0.560228	0.280114	−	0.959967i	$-0.409628\pi$
$43$	6792.60	0.560228	0.280114	+	0.959967i	$0.409628\pi$
$44$	8232.64	0.641073
$45$	16048.6	1.18142
$46$	8073.21	0.562538
$47$	−2623.74	−0.173251	−0.0866257	−	0.996241i	$-0.527608\pi$
$47$	−2623.74	−0.173251	−0.0866257	+	0.996241i	$0.527608\pi$
$48$	5087.43	0.318710
$49$	−15476.3	−0.920825
$50$	−32133.5	−1.81775
$51$	45434.1	2.44600
$52$	5030.35	0.257982
$53$	−2066.25	−0.101040	−0.0505201	−	0.998723i	$-0.516088\pi$
$53$	−2066.25	−0.101040	−0.0505201	+	0.998723i	$0.516088\pi$
$54$	7239.47	0.337849
$55$	54352.5	2.42277
$56$	−2334.64	−0.0994833
$57$	0	0
$58$	−4460.58	−0.174109
$59$	30720.0	1.14892	0.574461	−	0.818532i	$-0.305212\pi$
$59$	30720.0	1.14892	0.574461	+	0.818532i	$0.305212\pi$
$60$	33587.6	1.20448
$61$	−24465.7	−0.841846	−0.420923	−	0.907096i	$-0.638294\pi$
$61$	−24465.7	−0.841846	−0.420923	+	0.907096i	$0.638294\pi$
$62$	20711.3	0.684271
$63$	5542.12	0.175924
$64$	4096.00	0.125000
$65$	33210.8	0.974980
$66$	−40901.3	−1.15579
$67$	20113.7	0.547400	0.273700	−	0.961815i	$-0.411752\pi$
$67$	20113.7	0.547400	0.273700	+	0.961815i	$0.411752\pi$
$68$	36580.0	0.959337
$69$	−40109.3	−1.01420
$70$	−15413.5	−0.375972
$71$	60143.6	1.41594	0.707968	−	0.706244i	$-0.249612\pi$
$71$	60143.6	1.41594	0.707968	+	0.706244i	$0.249612\pi$
$72$	−9723.35	−0.221047
$73$	−40926.2	−0.898865	−0.449432	−	0.893314i	$-0.648374\pi$
$73$	−40926.2	−0.898865	−0.449432	+	0.893314i	$0.648374\pi$
$74$	17176.2	0.364626
$75$	159646.	3.27720
$76$	0	0
$77$	18769.8	0.360772
$78$	−24991.8	−0.465115
$79$	−82597.4	−1.48901	−0.744507	−	0.667615i	$-0.767315\pi$
$79$	−82597.4	−1.48901	−0.744507	+	0.667615i	$0.767315\pi$
$80$	27042.1	0.472406
$81$	−72885.4	−1.23432
$82$	−8504.54	−0.139674
$83$	−43089.8	−0.686562	−0.343281	−	0.939233i	$-0.611538\pi$
$83$	−43089.8	−0.686562	−0.343281	+	0.939233i	$0.611538\pi$
$84$	11599.0	0.179358
$85$	241504.	3.62557
$86$	−27170.4	−0.396141
$87$	22161.0	0.313900
$88$	−32930.5	−0.453307
$89$	−95174.1	−1.27363	−0.636816	−	0.771016i	$-0.719749\pi$
$89$	−95174.1	−1.27363	−0.636816	+	0.771016i	$0.719749\pi$
$90$	−64194.3	−0.835392
$91$	11468.8	0.145183
$92$	−32292.9	−0.397774
$93$	−102898.	−1.23367
$94$	10495.0	0.122507
$95$	0	0
$96$	−20349.7	−0.225362
$97$	−103891.	−1.12111	−0.560553	−	0.828118i	$-0.689411\pi$
$97$	−103891.	−1.12111	−0.560553	+	0.828118i	$0.689411\pi$
$98$	61905.2	0.651121
$99$	78172.7	0.801617
$100$	128534.	1.28534
$101$	81668.9	0.796623	0.398312	−	0.917250i	$-0.369596\pi$
$101$	81668.9	0.796623	0.398312	+	0.917250i	$0.369596\pi$
$102$	−181736.	−1.72958
$103$	32328.6	0.300258	0.150129	−	0.988666i	$-0.452031\pi$
$103$	32328.6	0.300258	0.150129	+	0.988666i	$0.452031\pi$
$104$	−20121.4	−0.182421
$105$	76577.2	0.677838
$106$	8265.01	0.0714461
$107$	−29421.8	−0.248434	−0.124217	−	0.992255i	$-0.539642\pi$
$107$	−29421.8	−0.248434	−0.124217	+	0.992255i	$0.539642\pi$
$108$	−28957.9	−0.238895
$109$	−209950.	−1.69258	−0.846289	−	0.532723i	$-0.821169\pi$
$109$	−209950.	−1.69258	−0.846289	+	0.532723i	$0.821169\pi$
$110$	−217410.	−1.71316
$111$	−85334.6	−0.657382
$112$	9338.56	0.0703453
$113$	−5018.45	−0.0369721	−0.0184860	−	0.999829i	$-0.505885\pi$
$113$	−5018.45	−0.0369721	−0.0184860	+	0.999829i	$0.505885\pi$
$114$	0	0
$115$	−213200.	−1.50329
$116$	17842.3	0.123114
$117$	47765.5	0.322589
$118$	−122880.	−0.812411
$119$	83399.5	0.539879
$120$	−134350.	−0.851699
$121$	103700.	0.643896
$122$	97862.7	0.595275
$123$	42252.2	0.251818
$124$	−82845.2	−0.483853
$125$	518488.	2.96800
$126$	−22168.5	−0.124397
$127$	195517.	1.07566	0.537829	−	0.843054i	$-0.319244\pi$
$127$	195517.	1.07566	0.537829	+	0.843054i	$0.319244\pi$
$128$	−16384.0	−0.0883883
$129$	134988.	0.714201
$130$	−132843.	−0.689415
$131$	35216.8	0.179296	0.0896482	−	0.995973i	$-0.471426\pi$
$131$	35216.8	0.179296	0.0896482	+	0.995973i	$0.471426\pi$
$132$	163605.	0.817265
$133$	0	0
$134$	−80454.8	−0.387071
$135$	−191182.	−0.902844
$136$	−146320.	−0.678354
$137$	−180514.	−0.821694	−0.410847	−	0.911704i	$-0.634767\pi$
$137$	−180514.	−0.821694	−0.410847	+	0.911704i	$0.634767\pi$
$138$	160437.	0.717146
$139$	−202675.	−0.889739	−0.444869	−	0.895595i	$-0.646750\pi$
$139$	−202675.	−0.889739	−0.444869	+	0.895595i	$0.646750\pi$
$140$	61653.9	0.265852
$141$	−52141.1	−0.220868
$142$	−240574.	−1.00122
$143$	161770.	0.661542
$144$	38893.4	0.156304
$145$	117796.	0.465277
$146$	163705.	0.635593
$147$	−307557.	−1.17390
$148$	−68704.7	−0.257829
$149$	429579.	1.58517	0.792587	−	0.609759i	$-0.208734\pi$
$149$	429579.	1.58517	0.792587	+	0.609759i	$0.208734\pi$
$150$	−638582.	−2.31733
$151$	154063.	0.549864	0.274932	−	0.961464i	$-0.411345\pi$
$151$	154063.	0.549864	0.274932	+	0.961464i	$0.411345\pi$
$152$	0	0
$153$	347344.	1.19958
$154$	−75079.1	−0.255104
$155$	−546950.	−1.82860
$156$	99967.1	0.328886
$157$	−4059.41	−0.0131436	−0.00657180	−	0.999978i	$-0.502092\pi$
$157$	−4059.41	−0.0131436	−0.00657180	+	0.999978i	$0.502092\pi$
$158$	330390.	1.05289
$159$	−41062.2	−0.128810
$160$	−108168.	−0.334042
$161$	−73625.2	−0.223852
$162$	291542.	0.872797
$163$	−633471.	−1.86749	−0.933744	−	0.357941i	$-0.883479\pi$
$163$	−633471.	−1.86749	−0.933744	+	0.357941i	$0.883479\pi$
$164$	34018.1	0.0987645
$165$	1.08013e6	3.08865
$166$	172359.	0.485472
$167$	7353.99	0.0204048	0.0102024	−	0.999948i	$-0.496752\pi$
$167$	7353.99	0.0204048	0.0102024	+	0.999948i	$0.496752\pi$
$168$	−46395.8	−0.126825
$169$	−272447.	−0.733780
$170$	−966015.	−2.56367
$171$	0	0
$172$	108682.	0.280114
$173$	−688985.	−1.75023	−0.875114	−	0.483917i	$-0.839214\pi$
$173$	−688985.	−1.75023	−0.875114	+	0.483917i	$0.839214\pi$
$174$	−88644.1	−0.221961
$175$	293048.	0.723341
$176$	131722.	0.320536
$177$	610491.	1.46469
$178$	380696.	0.900593
$179$	−53478.1	−0.124751	−0.0623755	−	0.998053i	$-0.519868\pi$
$179$	−53478.1	−0.124751	−0.0623755	+	0.998053i	$0.519868\pi$
$180$	256777.	0.590711
$181$	−692575.	−1.57134	−0.785671	−	0.618645i	$-0.787682\pi$
$181$	−692575.	−1.57134	−0.785671	+	0.618645i	$0.787682\pi$
$182$	−45875.3	−0.102660
$183$	−486201.	−1.07322
$184$	129171.	0.281269
$185$	−453594.	−0.974401
$186$	411591.	0.872336
$187$	1.17637e6	2.46002
$188$	−41979.9	−0.0866257
$189$	−66021.7	−0.134441
$190$	0	0
$191$	943184.	1.87074	0.935369	−	0.353674i	$-0.115068\pi$
$191$	943184.	1.87074	0.935369	+	0.353674i	$0.115068\pi$
$192$	81398.9	0.159355
$193$	−373952.	−0.722642	−0.361321	−	0.932442i	$-0.617674\pi$
$193$	−373952.	−0.722642	−0.361321	+	0.932442i	$0.617674\pi$
$194$	415562.	0.792742
$195$	659990.	1.24294
$196$	−247621.	−0.460412
$197$	354262.	0.650367	0.325183	−	0.945651i	$-0.394574\pi$
$197$	354262.	0.650367	0.325183	+	0.945651i	$0.394574\pi$
$198$	−312691.	−0.566829
$199$	−14371.4	−0.0257256	−0.0128628	−	0.999917i	$-0.504094\pi$
$199$	−14371.4	−0.0257256	−0.0128628	+	0.999917i	$0.504094\pi$
$200$	−514136.	−0.908873
$201$	399715.	0.697848
$202$	−326675.	−0.563298
$203$	40679.1	0.0692838
$204$	726946.	1.22300
$205$	224590.	0.373256
$206$	−129314.	−0.212314
$207$	−306635.	−0.497389
$208$	80485.7	0.128991
$209$	0	0
$210$	−306309.	−0.479304
$211$	−381900.	−0.590532	−0.295266	−	0.955415i	$-0.595408\pi$
$211$	−381900.	−0.590532	−0.295266	+	0.955415i	$0.595408\pi$
$212$	−33060.0	−0.0505201
$213$	1.19522e6	1.80509
$214$	117687.	0.175669
$215$	717525.	1.05862
$216$	115831.	0.168924
$217$	−188881.	−0.272294
$218$	839799.	1.19683
$219$	−813317.	−1.14591
$220$	869640.	1.21139
$221$	718790.	0.989969
$222$	341338.	0.464839
$223$	106134.	0.142920	0.0714598	−	0.997443i	$-0.477234\pi$
$223$	106134.	0.142920	0.0714598	+	0.997443i	$0.477234\pi$
$224$	−37354.3	−0.0497416
$225$	1.22049e6	1.60723
$226$	20073.8	0.0261432
$227$	343284.	0.442169	0.221085	−	0.975255i	$-0.429040\pi$
$227$	343284.	0.442169	0.221085	+	0.975255i	$0.429040\pi$
$228$	0	0
$229$	−518105.	−0.652874	−0.326437	−	0.945219i	$-0.605848\pi$
$229$	−518105.	−0.652874	−0.326437	+	0.945219i	$0.605848\pi$
$230$	852799.	1.06299
$231$	373008.	0.459926
$232$	−71369.3	−0.0870545
$233$	1.13537e6	1.37009	0.685044	−	0.728502i	$-0.259783\pi$
$233$	1.13537e6	1.37009	0.685044	+	0.728502i	$0.259783\pi$
$234$	−191062.	−0.228105
$235$	−277155.	−0.327380
$236$	491519.	0.574461
$237$	−1.64144e6	−1.89825
$238$	−333598.	−0.381752
$239$	1.00585e6	1.13904	0.569522	−	0.821976i	$-0.307128\pi$
$239$	1.00585e6	1.13904	0.569522	+	0.821976i	$0.307128\pi$
$240$	537402.	0.602242
$241$	882353.	0.978588	0.489294	−	0.872119i	$-0.337255\pi$
$241$	882353.	0.978588	0.489294	+	0.872119i	$0.337255\pi$
$242$	−414801.	−0.455303
$243$	−1.00864e6	−1.09577
$244$	−391451.	−0.420923
$245$	−1.63481e6	−1.74001
$246$	−169009.	−0.178062
$247$	0	0
$248$	331381.	0.342136
$249$	−856315.	−0.875256
$250$	−2.07395e6	−2.09869
$251$	−582902.	−0.583998	−0.291999	−	0.956419i	$-0.594320\pi$
$251$	−582902.	−0.583998	−0.291999	+	0.956419i	$0.594320\pi$
$252$	88674.0	0.0879619
$253$	−1.03850e6	−1.02001
$254$	−782067.	−0.760606
$255$	4.79935e6	4.62202
$256$	65536.0	0.0625000
$257$	1.08199e6	1.02186	0.510928	−	0.859623i	$-0.329302\pi$
$257$	1.08199e6	1.02186	0.510928	+	0.859623i	$0.329302\pi$
$258$	−539952.	−0.505017
$259$	−156641.	−0.145097
$260$	531372.	0.487490
$261$	169421.	0.153945
$262$	−140867.	−0.126782
$263$	902835.	0.804858	0.402429	−	0.915451i	$-0.368166\pi$
$263$	902835.	0.804858	0.402429	+	0.915451i	$0.368166\pi$
$264$	−654421.	−0.577893
$265$	−218265.	−0.190928
$266$	0	0
$267$	−1.89137e6	−1.62368
$268$	321819.	0.273700
$269$	1.53894e6	1.29671	0.648353	−	0.761340i	$-0.275458\pi$
$269$	1.53894e6	1.29671	0.648353	+	0.761340i	$0.275458\pi$
$270$	764728.	0.638407
$271$	168314.	0.139218	0.0696091	−	0.997574i	$-0.477825\pi$
$271$	168314.	0.139218	0.0696091	+	0.997574i	$0.477825\pi$
$272$	585280.	0.479669
$273$	227917.	0.185085
$274$	722057.	0.581025
$275$	4.13349e6	3.29599
$276$	−641749.	−0.507098
$277$	−704962.	−0.552035	−0.276017	−	0.961153i	$-0.589015\pi$
$277$	−704962.	−0.552035	−0.276017	+	0.961153i	$0.589015\pi$
$278$	810699.	0.629140
$279$	−786653.	−0.605024
$280$	−246616.	−0.187986
$281$	−1.40399e6	−1.06072	−0.530358	−	0.847774i	$-0.677942\pi$
$281$	−1.40399e6	−1.06072	−0.530358	+	0.847774i	$0.677942\pi$
$282$	208564.	0.156177
$283$	1.82029e6	1.35106	0.675531	−	0.737331i	$-0.263914\pi$
$283$	1.82029e6	1.35106	0.675531	+	0.737331i	$0.263914\pi$
$284$	962298.	0.707968
$285$	0	0
$286$	−647079.	−0.467781
$287$	77558.8	0.0555810
$288$	−155574.	−0.110524
$289$	3.80708e6	2.68131
$290$	−471186.	−0.329001
$291$	−2.06459e6	−1.42923
$292$	−654819.	−0.449432
$293$	64091.1	0.0436143	0.0218071	−	0.999762i	$-0.493058\pi$
$293$	64091.1	0.0436143	0.0218071	+	0.999762i	$0.493058\pi$
$294$	1.23023e6	0.830075
$295$	3.24505e6	2.17103
$296$	274819.	0.182313
$297$	−931248.	−0.612596
$298$	−1.71831e6	−1.12089
$299$	−634549.	−0.410475
$300$	2.55433e6	1.63860
$301$	247786.	0.157638
$302$	−616251.	−0.388813
$303$	1.62299e6	1.01557
$304$	0	0
$305$	−2.58439e6	−1.59077
$306$	−1.38938e6	−0.848235
$307$	202199.	0.122443	0.0612214	−	0.998124i	$-0.480500\pi$
$307$	202199.	0.122443	0.0612214	+	0.998124i	$0.480500\pi$
$308$	300316.	0.180386
$309$	642459.	0.382780
$310$	2.18780e6	1.29302
$311$	−1.45243e6	−0.851516	−0.425758	−	0.904837i	$-0.639993\pi$
$311$	−1.45243e6	−0.851516	−0.425758	+	0.904837i	$0.639993\pi$
$312$	−399868.	−0.232558
$313$	−900819.	−0.519729	−0.259864	−	0.965645i	$-0.583678\pi$
$313$	−900819.	−0.519729	−0.259864	+	0.965645i	$0.583678\pi$
$314$	16237.6	0.00929392
$315$	585432.	0.332430
$316$	−1.32156e6	−0.744507
$317$	833417.	0.465816	0.232908	−	0.972499i	$-0.425176\pi$
$317$	833417.	0.465816	0.232908	+	0.972499i	$0.425176\pi$
$318$	164249.	0.0910824
$319$	573787.	0.315699
$320$	432674.	0.236203
$321$	−584694.	−0.316713
$322$	294501.	0.158288
$323$	0	0
$324$	−1.16617e6	−0.617161
$325$	2.52567e6	1.32638
$326$	2.53389e6	1.32051
$327$	−4.17228e6	−2.15777
$328$	−136073.	−0.0698371
$329$	−95711.0	−0.0487497
$330$	−4.32054e6	−2.18400
$331$	2.43690e6	1.22255	0.611277	−	0.791417i	$-0.290656\pi$
$331$	2.43690e6	1.22255	0.611277	+	0.791417i	$0.290656\pi$
$332$	−689437.	−0.343281
$333$	−652383.	−0.322398
$334$	−29416.0	−0.0144284
$335$	2.12468e6	1.03438
$336$	185583.	0.0896789
$337$	−2.63966e6	−1.26612	−0.633058	−	0.774104i	$-0.718201\pi$
$337$	−2.63966e6	−1.26612	−0.633058	+	0.774104i	$0.718201\pi$
$338$	1.08979e6	0.518861
$339$	−99730.6	−0.0471334
$340$	3.86406e6	1.81279
$341$	−2.66420e6	−1.24074
$342$	0	0
$343$	−1.17765e6	−0.540484
$344$	−434727.	−0.198071
$345$	−4.23687e6	−1.91645
$346$	2.75594e6	1.23760
$347$	−2.78007e6	−1.23946	−0.619728	−	0.784816i	$-0.712757\pi$
$347$	−2.78007e6	−1.23946	−0.619728	+	0.784816i	$0.712757\pi$
$348$	354577.	0.156950
$349$	938778.	0.412571	0.206286	−	0.978492i	$-0.433862\pi$
$349$	938778.	0.412571	0.206286	+	0.978492i	$0.433862\pi$
$350$	−1.17219e6	−0.511479
$351$	−569017.	−0.246523
$352$	−526889.	−0.226653
$353$	691500.	0.295363	0.147681	−	0.989035i	$-0.452819\pi$
$353$	691500.	0.295363	0.147681	+	0.989035i	$0.452819\pi$
$354$	−2.44196e6	−1.03569
$355$	6.35316e6	2.67559
$356$	−1.52279e6	−0.636816
$357$	1.65738e6	0.688259
$358$	213913.	0.0882122
$359$	−1.43524e6	−0.587745	−0.293872	−	0.955845i	$-0.594944\pi$
$359$	−1.43524e6	−0.587745	−0.293872	+	0.955845i	$0.594944\pi$
$360$	−1.02711e6	−0.417696
$361$	0	0
$362$	2.77030e6	1.11111
$363$	2.06081e6	0.820864
$364$	183501.	0.0725914
$365$	−4.32317e6	−1.69852
$366$	1.94480e6	0.758880
$367$	2.61119e6	1.01198	0.505992	−	0.862538i	$-0.331127\pi$
$367$	2.61119e6	1.01198	0.505992	+	0.862538i	$0.331127\pi$
$368$	−516686.	−0.198887
$369$	323018.	0.123498
$370$	1.81438e6	0.689006
$371$	−75374.4	−0.0284308
$372$	−1.64636e6	−0.616835
$373$	−604301.	−0.224896	−0.112448	−	0.993658i	$-0.535869\pi$
$373$	−604301.	−0.224896	−0.112448	+	0.993658i	$0.535869\pi$
$374$	−4.70546e6	−1.73950
$375$	1.03038e7	3.78372
$376$	167920.	0.0612536
$377$	350598.	0.127045
$378$	264087.	0.0950642
$379$	3.98951e6	1.42666	0.713332	−	0.700827i	$-0.247185\pi$
$379$	3.98951e6	1.42666	0.713332	+	0.700827i	$0.247185\pi$
$380$	0	0
$381$	3.88546e6	1.37129
$382$	−3.77273e6	−1.32281
$383$	3.83890e6	1.33724	0.668621	−	0.743603i	$-0.266885\pi$
$383$	3.83890e6	1.33724	0.668621	+	0.743603i	$0.266885\pi$
$384$	−325596.	−0.112681
$385$	1.98271e6	0.681723
$386$	1.49581e6	0.510985
$387$	1.03198e6	0.350263
$388$	−1.66225e6	−0.560553
$389$	1.44259e6	0.483358	0.241679	−	0.970356i	$-0.422302\pi$
$389$	1.44259e6	0.483358	0.241679	+	0.970356i	$0.422302\pi$
$390$	−2.63996e6	−0.878893
$391$	−4.61434e6	−1.52640
$392$	990483.	0.325561
$393$	699856.	0.228574
$394$	−1.41705e6	−0.459879
$395$	−8.72503e6	−2.81368
$396$	1.25076e6	0.400808
$397$	−1.00819e6	−0.321046	−0.160523	−	0.987032i	$-0.551318\pi$
$397$	−1.00819e6	−0.321046	−0.160523	+	0.987032i	$0.551318\pi$
$398$	57485.4	0.0181907
$399$	0	0
$400$	2.05654e6	0.642670
$401$	−1.47386e6	−0.457715	−0.228858	−	0.973460i	$-0.573499\pi$
$401$	−1.47386e6	−0.457715	−0.228858	+	0.973460i	$0.573499\pi$
$402$	−1.59886e6	−0.493453
$403$	−1.62789e6	−0.499302
$404$	1.30670e6	0.398312
$405$	−7.69912e6	−2.33240
$406$	−162716.	−0.0489910
$407$	−2.20946e6	−0.661149
$408$	−2.90778e6	−0.864792
$409$	1.60387e6	0.474090	0.237045	−	0.971499i	$-0.423821\pi$
$409$	1.60387e6	0.474090	0.237045	+	0.971499i	$0.423821\pi$
$410$	−898362.	−0.263932
$411$	−3.58732e6	−1.04753
$412$	517258.	0.150129
$413$	1.12063e6	0.323285
$414$	1.22654e6	0.351707
$415$	−4.55172e6	−1.29734
$416$	−321943.	−0.0912106
$417$	−4.02771e6	−1.13427
$418$	0	0
$419$	−1.72554e6	−0.480165	−0.240082	−	0.970753i	$-0.577174\pi$
$419$	−1.72554e6	−0.480165	−0.240082	+	0.970753i	$0.577174\pi$
$420$	1.22523e6	0.338919
$421$	5.79099e6	1.59238	0.796192	−	0.605044i	$-0.206844\pi$
$421$	5.79099e6	1.59238	0.796192	+	0.605044i	$0.206844\pi$
$422$	1.52760e6	0.417569
$423$	−398619.	−0.108319
$424$	132240.	0.0357231
$425$	1.83663e7	4.93230
$426$	−4.78088e6	−1.27639
$427$	−892478.	−0.236880
$428$	−470749.	−0.124217
$429$	3.21482e6	0.843360
$430$	−2.87010e6	−0.748558
$431$	−126415.	−0.0327797	−0.0163899	−	0.999866i	$-0.505217\pi$
$431$	−126415.	−0.0327797	−0.0163899	+	0.999866i	$0.505217\pi$
$432$	−463326.	−0.119448
$433$	2.63210e6	0.674657	0.337329	−	0.941387i	$-0.390477\pi$
$433$	2.63210e6	0.674657	0.337329	+	0.941387i	$0.390477\pi$
$434$	755523.	0.192541
$435$	2.34094e6	0.593154
$436$	−3.35919e6	−0.846289
$437$	0	0
$438$	3.25327e6	0.810279
$439$	−1.76459e6	−0.437000	−0.218500	−	0.975837i	$-0.570116\pi$
$439$	−1.76459e6	−0.437000	−0.218500	+	0.975837i	$0.570116\pi$
$440$	−3.47856e6	−0.856580
$441$	−2.35127e6	−0.575714
$442$	−2.87516e6	−0.700014
$443$	4.75395e6	1.15092	0.575460	−	0.817830i	$-0.304823\pi$
$443$	4.75395e6	1.15092	0.575460	+	0.817830i	$0.304823\pi$
$444$	−1.36535e6	−0.328691
$445$	−1.00535e7	−2.40668
$446$	−424536.	−0.101059
$447$	8.53692e6	2.02084
$448$	149417.	0.0351726
$449$	7.41895e6	1.73671	0.868353	−	0.495946i	$-0.165179\pi$
$449$	7.41895e6	1.73671	0.868353	+	0.495946i	$0.165179\pi$
$450$	−4.88196e6	−1.13648
$451$	1.09398e6	0.253261
$452$	−80295.2	−0.0184860
$453$	3.06166e6	0.700988
$454$	−1.37313e6	−0.312661
$455$	1.21149e6	0.274341
$456$	0	0
$457$	1.37859e6	0.308777	0.154388	−	0.988010i	$-0.450659\pi$
$457$	1.37859e6	0.308777	0.154388	+	0.988010i	$0.450659\pi$
$458$	2.07242e6	0.461651
$459$	−4.13781e6	−0.916724
$460$	−3.41120e6	−0.751644
$461$	−2.32321e6	−0.509138	−0.254569	−	0.967055i	$-0.581934\pi$
$461$	−2.32321e6	−0.509138	−0.254569	+	0.967055i	$0.581934\pi$
$462$	−1.49203e6	−0.325217
$463$	−1.65321e6	−0.358405	−0.179203	−	0.983812i	$-0.557352\pi$
$463$	−1.65321e6	−0.358405	−0.179203	+	0.983812i	$0.557352\pi$
$464$	285477.	0.0615569
$465$	−1.08694e7	−2.33117
$466$	−4.54149e6	−0.968798
$467$	−1.23138e6	−0.261275	−0.130638	−	0.991430i	$-0.541702\pi$
$467$	−1.23138e6	−0.261275	−0.130638	+	0.991430i	$0.541702\pi$
$468$	764248.	0.161295
$469$	733723.	0.154028
$470$	1.10862e6	0.231493
$471$	−80671.8	−0.0167560
$472$	−1.96608e6	−0.406205
$473$	3.49506e6	0.718294
$474$	6.56576e6	1.34227
$475$	0	0
$476$	1.33439e6	0.269939
$477$	−313920.	−0.0631718
$478$	−4.02342e6	−0.805426
$479$	2.69667e6	0.537018	0.268509	−	0.963277i	$-0.413469\pi$
$479$	2.69667e6	0.537018	0.268509	+	0.963277i	$0.413469\pi$
$480$	−2.14961e6	−0.425849
$481$	−1.35004e6	−0.266062
$482$	−3.52941e6	−0.691966
$483$	−1.46314e6	−0.285376
$484$	1.65920e6	0.321948
$485$	−1.09743e7	−2.11847
$486$	4.03455e6	0.774827
$487$	−2.49833e6	−0.477339	−0.238670	−	0.971101i	$-0.576711\pi$
$487$	−2.49833e6	−0.477339	−0.238670	+	0.971101i	$0.576711\pi$
$488$	1.56580e6	0.297638
$489$	−1.25888e7	−2.38075
$490$	6.53925e6	1.23037
$491$	−5.96226e6	−1.11611	−0.558055	−	0.829804i	$-0.688452\pi$
$491$	−5.96226e6	−1.11611	−0.558055	+	0.829804i	$0.688452\pi$
$492$	676035.	0.125909
$493$	2.54950e6	0.472430
$494$	0	0
$495$	8.25763e6	1.51476
$496$	−1.32552e6	−0.241926
$497$	2.19396e6	0.398418
$498$	3.42526e6	0.618899
$499$	−3.49822e6	−0.628921	−0.314461	−	0.949271i	$-0.601824\pi$
$499$	−3.49822e6	−0.628921	−0.314461	+	0.949271i	$0.601824\pi$
$500$	8.29580e6	1.48400
$501$	146144.	0.0260128
$502$	2.33161e6	0.412949
$503$	427274.	0.0752985	0.0376493	−	0.999291i	$-0.488013\pi$
$503$	427274.	0.0752985	0.0376493	+	0.999291i	$0.488013\pi$
$504$	−354696.	−0.0621985
$505$	8.62694e6	1.50532
$506$	4.15399e6	0.721255
$507$	−5.41429e6	−0.935452
$508$	3.12827e6	0.537829
$509$	−8.19837e6	−1.40260	−0.701299	−	0.712867i	$-0.747396\pi$
$509$	−8.19837e6	−1.40260	−0.701299	+	0.712867i	$0.747396\pi$
$510$	−1.91974e7	−3.26826
$511$	−1.49294e6	−0.252924
$512$	−262144.	−0.0441942
$513$	0	0
$514$	−4.32795e6	−0.722562
$515$	3.41498e6	0.567374
$516$	2.15981e6	0.357101
$517$	−1.35002e6	−0.222134
$518$	626566.	0.102599
$519$	−1.36920e7	−2.23126
$520$	−2.12549e6	−0.344707
$521$	14510.9	0.00234207	0.00117103	−	0.999999i	$-0.499627\pi$
$521$	14510.9	0.00234207	0.00117103	+	0.999999i	$0.499627\pi$
$522$	−677684.	−0.108856
$523$	−3.47043e6	−0.554791	−0.277395	−	0.960756i	$-0.589471\pi$
$523$	−3.47043e6	−0.554791	−0.277395	+	0.960756i	$0.589471\pi$
$524$	563469.	0.0896482
$525$	5.82367e6	0.922144
$526$	−3.61134e6	−0.569120
$527$	−1.18378e7	−1.85671
$528$	2.61769e6	0.408632
$529$	−2.36279e6	−0.367102
$530$	873060.	0.135006
$531$	4.66720e6	0.718324
$532$	0	0
$533$	668450.	0.101918
$534$	7.56549e6	1.14811
$535$	−3.10792e6	−0.469446
$536$	−1.28728e6	−0.193535
$537$	−1.06276e6	−0.159037
$538$	−6.15577e6	−0.916910
$539$	−7.96317e6	−1.18063
$540$	−3.05891e6	−0.451422
$541$	−1.04570e7	−1.53608	−0.768039	−	0.640403i	$-0.778767\pi$
$541$	−1.04570e7	−1.53608	−0.768039	+	0.640403i	$0.778767\pi$
$542$	−673254.	−0.0984421
$543$	−1.37634e7	−2.00321
$544$	−2.34112e6	−0.339177
$545$	−2.21777e7	−3.19834
$546$	−911669.	−0.130875
$547$	−2.63668e6	−0.376781	−0.188391	−	0.982094i	$-0.560327\pi$
$547$	−2.63668e6	−0.376781	−0.188391	+	0.982094i	$0.560327\pi$
$548$	−2.88823e6	−0.410847
$549$	−3.71701e6	−0.526335
$550$	−1.65340e7	−2.33061
$551$	0	0
$552$	2.56699e6	0.358573
$553$	−3.01305e6	−0.418980
$554$	2.81985e6	0.390348
$555$	−9.01417e6	−1.24220
$556$	−3.24279e6	−0.444869
$557$	6.01825e6	0.821925	0.410963	−	0.911652i	$-0.365193\pi$
$557$	6.01825e6	0.821925	0.410963	+	0.911652i	$0.365193\pi$
$558$	3.14661e6	0.427817
$559$	2.13558e6	0.289058
$560$	986463.	0.132926
$561$	2.33777e7	3.13613
$562$	5.61597e6	0.750039
$563$	−690559.	−0.0918184	−0.0459092	−	0.998946i	$-0.514618\pi$
$563$	−690559.	−0.0918184	−0.0459092	+	0.998946i	$0.514618\pi$
$564$	−834258.	−0.110434
$565$	−530115.	−0.0698633
$566$	−7.28117e6	−0.955345
$567$	−2.65877e6	−0.347315
$568$	−3.84919e6	−0.500609
$569$	−1.03995e7	−1.34657	−0.673287	−	0.739382i	$-0.735118\pi$
$569$	−1.03995e7	−1.34657	−0.673287	+	0.739382i	$0.735118\pi$
$570$	0	0
$571$	−6.69684e6	−0.859567	−0.429784	−	0.902932i	$-0.641410\pi$
$571$	−6.69684e6	−0.859567	−0.429784	+	0.902932i	$0.641410\pi$
$572$	2.58832e6	0.330771
$573$	1.87437e7	2.38489
$574$	−310235.	−0.0393017
$575$	−1.62138e7	−2.04510
$576$	622294.	0.0781519
$577$	−2.48114e6	−0.310250	−0.155125	−	0.987895i	$-0.549578\pi$
$577$	−2.48114e6	−0.310250	−0.155125	+	0.987895i	$0.549578\pi$
$578$	−1.52283e7	−1.89597
$579$	−7.43147e6	−0.921252
$580$	1.88474e6	0.232639
$581$	−1.57186e6	−0.193186
$582$	8.25838e6	1.01062
$583$	−1.06317e6	−0.129548
$584$	2.61928e6	0.317797
$585$	5.04563e6	0.609573
$586$	−256364.	−0.0308400
$587$	5.07388e6	0.607778	0.303889	−	0.952707i	$-0.401715\pi$
$587$	5.07388e6	0.607778	0.303889	+	0.952707i	$0.401715\pi$
$588$	−4.92091e6	−0.586952
$589$	0	0
$590$	−1.29802e7	−1.53515
$591$	7.04016e6	0.829113
$592$	−1.09928e6	−0.128915
$593$	−7.41158e6	−0.865514	−0.432757	−	0.901511i	$-0.642459\pi$
$593$	−7.41158e6	−0.865514	−0.432757	+	0.901511i	$0.642459\pi$
$594$	3.72499e6	0.433171
$595$	8.80976e6	1.02017
$596$	6.87326e6	0.792587
$597$	−285599.	−0.0327960
$598$	2.53820e6	0.290250
$599$	2.79428e6	0.318202	0.159101	−	0.987262i	$-0.449140\pi$
$599$	2.79428e6	0.318202	0.159101	+	0.987262i	$0.449140\pi$
$600$	−1.02173e7	−1.15867
$601$	−2.48636e6	−0.280788	−0.140394	−	0.990096i	$-0.544837\pi$
$601$	−2.48636e6	−0.280788	−0.140394	+	0.990096i	$0.544837\pi$
$602$	−991143.	−0.111467
$603$	3.05582e6	0.342243
$604$	2.46500e6	0.274932
$605$	1.09542e7	1.21672
$606$	−6.49195e6	−0.718114
$607$	1.54213e7	1.69882	0.849412	−	0.527731i	$-0.176957\pi$
$607$	1.54213e7	1.69882	0.849412	+	0.527731i	$0.176957\pi$
$608$	0	0
$609$	808407.	0.0883257
$610$	1.03376e7	1.12485
$611$	−824898.	−0.0893917
$612$	5.55750e6	0.599792
$613$	−2.50112e6	−0.268834	−0.134417	−	0.990925i	$-0.542916\pi$
$613$	−2.50112e6	−0.268834	−0.134417	+	0.990925i	$0.542916\pi$
$614$	−808796.	−0.0865801
$615$	4.46324e6	0.475841
$616$	−1.20127e6	−0.127552
$617$	8.73438e6	0.923675	0.461838	−	0.886964i	$-0.347190\pi$
$617$	8.73438e6	0.923675	0.461838	+	0.886964i	$0.347190\pi$
$618$	−2.56984e6	−0.270667
$619$	4.48808e6	0.470797	0.235398	−	0.971899i	$-0.424360\pi$
$619$	4.48808e6	0.470797	0.235398	+	0.971899i	$0.424360\pi$
$620$	−8.75121e6	−0.914300
$621$	3.65286e6	0.380105
$622$	5.80970e6	0.602113
$623$	−3.47183e6	−0.358376
$624$	1.59947e6	0.164443
$625$	2.96652e7	3.03772
$626$	3.60328e6	0.367504
$627$	0	0
$628$	−64950.6	−0.00657180
$629$	−9.81726e6	−0.989381
$630$	−2.34173e6	−0.235064
$631$	−9.55926e6	−0.955765	−0.477882	−	0.878424i	$-0.658596\pi$
$631$	−9.55926e6	−0.955765	−0.477882	+	0.878424i	$0.658596\pi$
$632$	5.28623e6	0.526446
$633$	−7.58942e6	−0.752834
$634$	−3.33367e6	−0.329382
$635$	2.06531e7	2.03259
$636$	−656995.	−0.0644050
$637$	−4.86570e6	−0.475113
$638$	−2.29515e6	−0.223233
$639$	9.13746e6	0.885265
$640$	−1.73069e6	−0.167021
$641$	1.71724e7	1.65076	0.825382	−	0.564575i	$-0.190960\pi$
$641$	1.71724e7	1.65076	0.825382	+	0.564575i	$0.190960\pi$
$642$	2.33877e6	0.223950
$643$	4.89861e6	0.467245	0.233623	−	0.972327i	$-0.424942\pi$
$643$	4.89861e6	0.467245	0.233623	+	0.972327i	$0.424942\pi$
$644$	−1.17800e6	−0.111926
$645$	1.42592e7	1.34957
$646$	0	0
$647$	1.38340e7	1.29924	0.649618	−	0.760261i	$-0.274929\pi$
$647$	1.38340e7	1.29924	0.649618	+	0.760261i	$0.274929\pi$
$648$	4.66467e6	0.436398
$649$	1.58066e7	1.47308
$650$	−1.01027e7	−0.937893
$651$	−3.75358e6	−0.347131
$652$	−1.01355e7	−0.933744
$653$	−9.05786e6	−0.831271	−0.415636	−	0.909531i	$-0.636441\pi$
$653$	−9.05786e6	−0.831271	−0.415636	+	0.909531i	$0.636441\pi$
$654$	1.66891e7	1.52577
$655$	3.72007e6	0.338803
$656$	544290.	0.0493823
$657$	−6.21781e6	−0.561984
$658$	382844.	0.0344712
$659$	1.86324e7	1.67130	0.835650	−	0.549262i	$-0.185091\pi$
$659$	1.86324e7	1.67130	0.835650	+	0.549262i	$0.185091\pi$
$660$	1.72822e7	1.54432
$661$	1.22858e7	1.09371	0.546853	−	0.837228i	$-0.315825\pi$
$661$	1.22858e7	1.09371	0.546853	+	0.837228i	$0.315825\pi$
$662$	−9.74760e6	−0.864476
$663$	1.42844e7	1.26205
$664$	2.75775e6	0.242736
$665$	0	0
$666$	2.60953e6	0.227970
$667$	−2.25070e6	−0.195886
$668$	117664.	0.0102024
$669$	2.10918e6	0.182200
$670$	−8.49870e6	−0.731418
$671$	−1.25886e7	−1.07937
$672$	−742333.	−0.0634126
$673$	−1.71385e7	−1.45860	−0.729299	−	0.684196i	$-0.760153\pi$
$673$	−1.71385e7	−1.45860	−0.729299	+	0.684196i	$0.760153\pi$
$674$	1.05586e7	0.895279
$675$	−1.45393e7	−1.22825
$676$	−4.35916e6	−0.366890
$677$	−2.32082e7	−1.94612	−0.973060	−	0.230552i	$-0.925947\pi$
$677$	−2.32082e7	−1.94612	−0.973060	+	0.230552i	$0.925947\pi$
$678$	398922.	0.0333284
$679$	−3.78980e6	−0.315458
$680$	−1.54562e7	−1.28183
$681$	6.82200e6	0.563695
$682$	1.06568e7	0.877335
$683$	−7.59592e6	−0.623058	−0.311529	−	0.950237i	$-0.600841\pi$
$683$	−7.59592e6	−0.623058	−0.311529	+	0.950237i	$0.600841\pi$
$684$	0	0
$685$	−1.90683e7	−1.55269
$686$	4.71062e6	0.382180
$687$	−1.02962e7	−0.832309
$688$	1.73891e6	0.140057
$689$	−649624.	−0.0521332
$690$	1.69475e7	1.35514
$691$	1.57917e7	1.25815	0.629076	−	0.777344i	$-0.283434\pi$
$691$	1.57917e7	1.25815	0.629076	+	0.777344i	$0.283434\pi$
$692$	−1.10238e7	−0.875114
$693$	2.85164e6	0.225560
$694$	1.11203e7	0.876428
$695$	−2.14092e7	−1.68127
$696$	−1.41831e6	−0.110981
$697$	4.86087e6	0.378994
$698$	−3.75511e6	−0.291732
$699$	2.25630e7	1.74664
$700$	4.68876e6	0.361671
$701$	9.93160e6	0.763351	0.381676	−	0.924296i	$-0.375347\pi$
$701$	9.93160e6	0.763351	0.381676	+	0.924296i	$0.375347\pi$
$702$	2.27607e6	0.174318
$703$	0	0
$704$	2.10755e6	0.160268
$705$	−5.50783e6	−0.417357
$706$	−2.76600e6	−0.208853
$707$	2.97918e6	0.224155
$708$	9.76785e6	0.732346
$709$	1.80348e7	1.34740	0.673698	−	0.739007i	$-0.264705\pi$
$709$	1.80348e7	1.34740	0.673698	+	0.739007i	$0.264705\pi$
$710$	−2.54127e7	−1.89193
$711$	−1.25488e7	−0.930954
$712$	6.09114e6	0.450297
$713$	1.04504e7	0.769857
$714$	−6.62952e6	−0.486672
$715$	1.70883e7	1.25007
$716$	−855650.	−0.0623755
$717$	1.99891e7	1.45210
$718$	5.74096e6	0.415598
$719$	1.64194e7	1.18450	0.592251	−	0.805754i	$-0.298239\pi$
$719$	1.64194e7	1.18450	0.592251	+	0.805754i	$0.298239\pi$
$720$	4.10844e6	0.295356
$721$	1.17931e6	0.0844868
$722$	0	0
$723$	1.75348e7	1.24754
$724$	−1.10812e7	−0.785671
$725$	8.95838e6	0.632972
$726$	−8.24324e6	−0.580439
$727$	313043.	0.0219669	0.0109834	−	0.999940i	$-0.496504\pi$
$727$	313043.	0.0219669	0.0109834	+	0.999940i	$0.496504\pi$
$728$	−734004.	−0.0513299
$729$	−2.33329e6	−0.162611
$730$	1.72927e7	1.20103
$731$	1.55296e7	1.07490
$732$	−7.77922e6	−0.536609
$733$	−1.49740e7	−1.02938	−0.514692	−	0.857375i	$-0.672094\pi$
$733$	−1.49740e7	−1.02938	−0.514692	+	0.857375i	$0.672094\pi$
$734$	−1.04448e7	−0.715580
$735$	−3.24882e7	−2.21824
$736$	2.06674e6	0.140634
$737$	1.03493e7	0.701847
$738$	−1.29207e6	−0.0873264
$739$	−1.11922e7	−0.753887	−0.376943	−	0.926236i	$-0.623025\pi$
$739$	−1.11922e7	−0.753887	−0.376943	+	0.926236i	$0.623025\pi$
$740$	−7.25750e6	−0.487201
$741$	0	0
$742$	301497.	0.0201036
$743$	1.30213e7	0.865329	0.432664	−	0.901555i	$-0.357574\pi$
$743$	1.30213e7	0.865329	0.432664	+	0.901555i	$0.357574\pi$
$744$	6.58546e6	0.436168
$745$	4.53778e7	2.99538
$746$	2.41720e6	0.159025
$747$	−6.54652e6	−0.429249
$748$	1.88219e7	1.23001
$749$	−1.07327e6	−0.0699045
$750$	−4.12152e7	−2.67549
$751$	−5.61944e6	−0.363575	−0.181787	−	0.983338i	$-0.558188\pi$
$751$	−5.61944e6	−0.363575	−0.181787	+	0.983338i	$0.558188\pi$
$752$	−671679.	−0.0433129
$753$	−1.15839e7	−0.744504
$754$	−1.40239e6	−0.0898342
$755$	1.62741e7	1.03904
$756$	−1.05635e6	−0.0672206
$757$	−707300.	−0.0448605	−0.0224302	−	0.999748i	$-0.507140\pi$
$757$	−707300.	−0.0448605	−0.0224302	+	0.999748i	$0.507140\pi$
$758$	−1.59580e7	−1.00880
$759$	−2.06378e7	−1.30035
$760$	0	0
$761$	−3.14417e7	−1.96809	−0.984044	−	0.177924i	$-0.943062\pi$
$761$	−3.14417e7	−1.96809	−0.984044	+	0.177924i	$0.943062\pi$
$762$	−1.55418e7	−0.969650
$763$	−7.65870e6	−0.476260
$764$	1.50909e7	0.935369
$765$	3.66910e7	2.26676
$766$	−1.53556e7	−0.945573
$767$	9.65827e6	0.592803
$768$	1.30238e6	0.0796775
$769$	1.57898e7	0.962855	0.481427	−	0.876486i	$-0.340119\pi$
$769$	1.57898e7	0.962855	0.481427	+	0.876486i	$0.340119\pi$
$770$	−7.93085e6	−0.482051
$771$	2.15021e7	1.30270
$772$	−5.98324e6	−0.361321
$773$	−3.32352e6	−0.200055	−0.100027	−	0.994985i	$-0.531893\pi$
$773$	−3.32352e6	−0.200055	−0.100027	+	0.994985i	$0.531893\pi$
$774$	−4.12793e6	−0.247674
$775$	−4.15954e7	−2.48766
$776$	6.64900e6	0.396371
$777$	−3.11290e6	−0.184975
$778$	−5.77036e6	−0.341786
$779$	0	0
$780$	1.05598e7	0.621471
$781$	3.09463e7	1.81544
$782$	1.84574e7	1.07933
$783$	−2.01826e6	−0.117645
$784$	−3.96193e6	−0.230206
$785$	−428809.	−0.0248365
$786$	−2.79942e6	−0.161626
$787$	−4.52783e6	−0.260587	−0.130294	−	0.991475i	$-0.541592\pi$
$787$	−4.52783e6	−0.260587	−0.130294	+	0.991475i	$0.541592\pi$
$788$	5.66818e6	0.325183
$789$	1.79418e7	1.02606
$790$	3.49001e7	1.98957
$791$	−183067.	−0.0104032
$792$	−5.00305e6	−0.283414
$793$	−7.69194e6	−0.434363
$794$	4.03276e6	0.227013
$795$	−4.33753e6	−0.243402
$796$	−229942.	−0.0128628
$797$	9.25818e6	0.516273	0.258137	−	0.966108i	$-0.416892\pi$
$797$	9.25818e6	0.516273	0.258137	+	0.966108i	$0.416892\pi$
$798$	0	0
$799$	−5.99853e6	−0.332413
$800$	−8.22618e6	−0.454436
$801$	−1.44595e7	−0.796294
$802$	5.89544e6	0.323653
$803$	−2.10582e7	−1.15247
$804$	6.39544e6	0.348924
$805$	−7.77727e6	−0.422997
$806$	6.51157e6	0.353060
$807$	3.05831e7	1.65309
$808$	−5.22681e6	−0.281649
$809$	3.75899e6	0.201930	0.100965	−	0.994890i	$-0.467807\pi$
$809$	3.75899e6	0.201930	0.100965	+	0.994890i	$0.467807\pi$
$810$	3.07965e7	1.64926
$811$	2.75163e7	1.46905	0.734527	−	0.678579i	$-0.237404\pi$
$811$	2.75163e7	1.46905	0.734527	+	0.678579i	$0.237404\pi$
$812$	650866.	0.0346419
$813$	3.34486e6	0.177481
$814$	8.83783e6	0.467503
$815$	−6.69156e7	−3.52885
$816$	1.16311e7	0.611500
$817$	0	0
$818$	−6.41547e6	−0.335232
$819$	1.74243e6	0.0907705
$820$	3.59345e6	0.186628
$821$	−7.97247e6	−0.412796	−0.206398	−	0.978468i	$-0.566174\pi$
$821$	−7.97247e6	−0.412796	−0.206398	+	0.978468i	$0.566174\pi$
$822$	1.43493e7	0.740714
$823$	2.00497e7	1.03183	0.515916	−	0.856639i	$-0.327452\pi$
$823$	2.00497e7	1.03183	0.515916	+	0.856639i	$0.327452\pi$
$824$	−2.06903e6	−0.106157
$825$	8.21440e7	4.20185
$826$	−4.48250e6	−0.228597
$827$	1.82156e7	0.926148	0.463074	−	0.886320i	$-0.346746\pi$
$827$	1.82156e7	0.926148	0.463074	+	0.886320i	$0.346746\pi$
$828$	−4.90617e6	−0.248695
$829$	2.28878e7	1.15669	0.578346	−	0.815792i	$-0.303698\pi$
$829$	2.28878e7	1.15669	0.578346	+	0.815792i	$0.303698\pi$
$830$	1.82069e7	0.917361
$831$	−1.40096e7	−0.703756
$832$	1.28777e6	0.0644956
$833$	−3.53827e7	−1.76676
$834$	1.61108e7	0.802053
$835$	776826.	0.0385574
$836$	0	0
$837$	9.37117e6	0.462360
$838$	6.90216e6	0.339528
$839$	−3.87913e7	−1.90252	−0.951260	−	0.308391i	$-0.900210\pi$
$839$	−3.87913e7	−1.90252	−0.951260	+	0.308391i	$0.900210\pi$
$840$	−4.90094e6	−0.239652
$841$	−1.92676e7	−0.939372
$842$	−2.31640e7	−1.12599
$843$	−2.79012e7	−1.35224
$844$	−6.11040e6	−0.295266
$845$	−2.87795e7	−1.38657
$846$	1.59447e6	0.0765935
$847$	3.78285e6	0.181180
$848$	−528961.	−0.0252600
$849$	3.61743e7	1.72239
$850$	−7.34652e7	−3.48766
$851$	8.66669e6	0.410232
$852$	1.91235e7	0.902546
$853$	2.73058e6	0.128494	0.0642469	−	0.997934i	$-0.479535\pi$
$853$	2.73058e6	0.128494	0.0642469	+	0.997934i	$0.479535\pi$
$854$	3.56991e6	0.167499
$855$	0	0
$856$	1.88300e6	0.0878345
$857$	−1.36772e7	−0.636131	−0.318065	−	0.948069i	$-0.603033\pi$
$857$	−1.36772e7	−0.636131	−0.318065	+	0.948069i	$0.603033\pi$
$858$	−1.28593e7	−0.596345
$859$	−2.84138e7	−1.31385	−0.656927	−	0.753954i	$-0.728144\pi$
$859$	−2.84138e7	−1.31385	−0.656927	+	0.753954i	$0.728144\pi$
$860$	1.14804e7	0.529311
$861$	1.54131e6	0.0708568
$862$	505660.	0.0231788
$863$	−3.06964e7	−1.40301	−0.701503	−	0.712666i	$-0.747487\pi$
$863$	−3.06964e7	−1.40301	−0.701503	+	0.712666i	$0.747487\pi$
$864$	1.85330e6	0.0844622
$865$	−7.27797e7	−3.30727
$866$	−1.05284e7	−0.477055
$867$	7.56572e7	3.41824
$868$	−3.02209e6	−0.136147
$869$	−4.24997e7	−1.90913
$870$	−9.36377e6	−0.419423
$871$	6.32369e6	0.282439
$872$	1.34368e7	0.598417
$873$	−1.57838e7	−0.700933
$874$	0	0
$875$	1.89138e7	0.835138
$876$	−1.30131e7	−0.572954
$877$	1.60191e7	0.703299	0.351650	−	0.936132i	$-0.385621\pi$
$877$	1.60191e7	0.703299	0.351650	+	0.936132i	$0.385621\pi$
$878$	7.05835e6	0.309006
$879$	1.27367e6	0.0556012
$880$	1.39142e7	0.605693
$881$	−2.24123e6	−0.0972850	−0.0486425	−	0.998816i	$-0.515489\pi$
$881$	−2.24123e6	−0.0972850	−0.0486425	+	0.998816i	$0.515489\pi$
$882$	9.40509e6	0.407091
$883$	−3.11716e7	−1.34542	−0.672710	−	0.739906i	$-0.734870\pi$
$883$	−3.11716e7	−1.34542	−0.672710	+	0.739906i	$0.734870\pi$
$884$	1.15006e7	0.494984
$885$	6.44881e7	2.76772
$886$	−1.90158e7	−0.813824
$887$	2.47127e7	1.05466	0.527328	−	0.849662i	$-0.323194\pi$
$887$	2.47127e7	1.05466	0.527328	+	0.849662i	$0.323194\pi$
$888$	5.46141e6	0.232420
$889$	7.13221e6	0.302670
$890$	4.02142e7	1.70178
$891$	−3.75024e7	−1.58258
$892$	1.69814e6	0.0714598
$893$	0	0
$894$	−3.41477e7	−1.42895
$895$	−5.64907e6	−0.235732
$896$	−597668.	−0.0248708
$897$	−1.26102e7	−0.523290
$898$	−2.96758e7	−1.22804
$899$	−5.77403e6	−0.238276
$900$	1.95278e7	0.803615
$901$	−4.72397e6	−0.193863
$902$	−4.37592e6	−0.179083
$903$	4.92419e6	0.200963
$904$	321181.	0.0130716
$905$	−7.31590e7	−2.96925
$906$	−1.22466e7	−0.495674
$907$	−9.05136e6	−0.365339	−0.182669	−	0.983174i	$-0.558474\pi$
$907$	−9.05136e6	−0.365339	−0.182669	+	0.983174i	$0.558474\pi$
$908$	5.49254e6	0.221085
$909$	1.24077e7	0.498061
$910$	−4.84595e6	−0.193988
$911$	−3.20523e7	−1.27957	−0.639783	−	0.768555i	$-0.720976\pi$
$911$	−3.20523e7	−1.27957	−0.639783	+	0.768555i	$0.720976\pi$
$912$	0	0
$913$	−2.21714e7	−0.880272
$914$	−5.51436e6	−0.218338
$915$	−5.13590e7	−2.02798
$916$	−8.28968e6	−0.326437
$917$	1.28467e6	0.0504507
$918$	1.65512e7	0.648221
$919$	1.51491e7	0.591695	0.295848	−	0.955235i	$-0.404398\pi$
$919$	1.51491e7	0.591695	0.295848	+	0.955235i	$0.404398\pi$
$920$	1.36448e7	0.531493
$921$	4.01826e6	0.156095
$922$	9.29283e6	0.360015
$923$	1.89090e7	0.730573
$924$	5.96812e6	0.229963
$925$	−3.44957e7	−1.32559
$926$	6.61282e6	0.253431
$927$	4.91160e6	0.187726
$928$	−1.14191e6	−0.0435273
$929$	−1.53601e7	−0.583920	−0.291960	−	0.956431i	$-0.594307\pi$
$929$	−1.53601e7	−0.583920	−0.291960	+	0.956431i	$0.594307\pi$
$930$	4.34777e7	1.64839
$931$	0	0
$932$	1.81659e7	0.685044
$933$	−2.88637e7	−1.08555
$934$	4.92550e6	0.184750
$935$	1.24263e8	4.64851
$936$	−3.05699e6	−0.114053
$937$	−3.30323e7	−1.22911	−0.614554	−	0.788875i	$-0.710664\pi$
$937$	−3.30323e7	−1.22911	−0.614554	+	0.788875i	$0.710664\pi$
$938$	−2.93489e6	−0.108914
$939$	−1.79018e7	−0.662571
$940$	−4.43447e6	−0.163690
$941$	2.03032e7	0.747463	0.373732	−	0.927537i	$-0.378078\pi$
$941$	2.03032e7	0.747463	0.373732	+	0.927537i	$0.378078\pi$
$942$	322687.	0.0118483
$943$	−4.29118e6	−0.157144
$944$	7.86431e6	0.287231
$945$	−6.97408e6	−0.254043
$946$	−1.39803e7	−0.507911
$947$	−2.49259e7	−0.903184	−0.451592	−	0.892225i	$-0.649144\pi$
$947$	−2.49259e7	−0.903184	−0.451592	+	0.892225i	$0.649144\pi$
$948$	−2.62630e7	−0.949127
$949$	−1.28671e7	−0.463783
$950$	0	0
$951$	1.65623e7	0.593841
$952$	−5.33757e6	−0.190876
$953$	−1.21620e7	−0.433785	−0.216892	−	0.976196i	$-0.569592\pi$
$953$	−1.21620e7	−0.433785	−0.216892	+	0.976196i	$0.569592\pi$
$954$	1.25568e6	0.0446692
$955$	9.96315e7	3.53499
$956$	1.60937e7	0.569522
$957$	1.14027e7	0.402466
$958$	−1.07867e7	−0.379729
$959$	−6.58494e6	−0.231209
$960$	8.59843e6	0.301121
$961$	−1.81927e6	−0.0635459
$962$	5.40014e6	0.188134
$963$	−4.46998e6	−0.155325
$964$	1.41176e7	0.489294
$965$	−3.95018e7	−1.36552
$966$	5.85255e6	0.201791
$967$	−4.01385e7	−1.38037	−0.690184	−	0.723634i	$-0.742470\pi$
$967$	−4.01385e7	−1.38037	−0.690184	+	0.723634i	$0.742470\pi$
$968$	−6.63681e6	−0.227652
$969$	0	0
$970$	4.38972e7	1.49798
$971$	−3.57419e7	−1.21655	−0.608275	−	0.793726i	$-0.708138\pi$
$971$	−3.57419e7	−1.21655	−0.608275	+	0.793726i	$0.708138\pi$
$972$	−1.61382e7	−0.547886
$973$	−7.39332e6	−0.250356
$974$	9.99331e6	0.337530
$975$	5.01921e7	1.69092
$976$	−6.26321e6	−0.210462
$977$	−5.97471e6	−0.200254	−0.100127	−	0.994975i	$-0.531925\pi$
$977$	−5.97471e6	−0.200254	−0.100127	+	0.994975i	$0.531925\pi$
$978$	5.03553e7	1.68344
$979$	−4.89708e7	−1.63298
$980$	−2.61570e7	−0.870006
$981$	−3.18971e7	−1.05823
$982$	2.38490e7	0.789209
$983$	2.39900e7	0.791856	0.395928	−	0.918282i	$-0.370423\pi$
$983$	2.39900e7	0.791856	0.395928	+	0.918282i	$0.370423\pi$
$984$	−2.70414e6	−0.0890311
$985$	3.74218e7	1.22895
$986$	−1.01980e7	−0.334059
$987$	−1.90204e6	−0.0621480
$988$	0	0
$989$	−1.37095e7	−0.445689
$990$	−3.30305e7	−1.07109
$991$	3.90313e7	1.26249	0.631246	−	0.775583i	$-0.282544\pi$
$991$	3.90313e7	1.26249	0.631246	+	0.775583i	$0.282544\pi$
$992$	5.30209e6	0.171068
$993$	4.84280e7	1.55856
$994$	−8.77586e6	−0.281724
$995$	−1.51809e6	−0.0486117
$996$	−1.37010e7	−0.437628
$997$	3.09487e7	0.986062	0.493031	−	0.870012i	$-0.335889\pi$
$997$	3.09487e7	0.986062	0.493031	+	0.870012i	$0.335889\pi$
$998$	1.39929e7	0.444714
$999$	7.77165e6	0.246377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.12		15
19.14	odd	18		38.6.e.b.25.4	✓	30
19.15	odd	18		38.6.e.b.35.4	yes	30
19.18	odd	2		722.6.a.r.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.4	✓	30	19.14	odd	18
38.6.e.b.35.4	yes	30	19.15	odd	18
722.6.a.q.1.12		15	1.1	even	1	trivial
722.6.a.r.1.4		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +19.8728 q^{3} +16.0000 q^{4} +105.633 q^{5} -79.4911 q^{6} +36.4788 q^{7} -64.0000 q^{8} +151.927 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +19.8728 q^{3} +16.0000 q^{4} +105.633 q^{5} -79.4911 q^{6} +36.4788 q^{7} -64.0000 q^{8} +151.927 q^{9} -422.533 q^{10} +514.540 q^{11} +317.964 q^{12} +314.397 q^{13} -145.915 q^{14} +2099.23 q^{15} +256.000 q^{16} +2286.25 q^{17} -607.709 q^{18} +1690.13 q^{20} +724.934 q^{21} -2058.16 q^{22} -2018.30 q^{23} -1271.86 q^{24} +8033.38 q^{25} -1257.59 q^{26} -1809.87 q^{27} +583.660 q^{28} +1115.15 q^{29} -8396.90 q^{30} -5177.83 q^{31} -1024.00 q^{32} +10225.3 q^{33} -9145.00 q^{34} +3853.37 q^{35} +2430.84 q^{36} -4294.05 q^{37} +6247.94 q^{39} -6760.53 q^{40} +2126.13 q^{41} -2899.74 q^{42} +6792.60 q^{43} +8232.64 q^{44} +16048.6 q^{45} +8073.21 q^{46} -2623.74 q^{47} +5087.43 q^{48} -15476.3 q^{49} -32133.5 q^{50} +45434.1 q^{51} +5030.35 q^{52} -2066.25 q^{53} +7239.47 q^{54} +54352.5 q^{55} -2334.64 q^{56} -4460.58 q^{58} +30720.0 q^{59} +33587.6 q^{60} -24465.7 q^{61} +20711.3 q^{62} +5542.12 q^{63} +4096.00 q^{64} +33210.8 q^{65} -40901.3 q^{66} +20113.7 q^{67} +36580.0 q^{68} -40109.3 q^{69} -15413.5 q^{70} +60143.6 q^{71} -9723.35 q^{72} -40926.2 q^{73} +17176.2 q^{74} +159646. q^{75} +18769.8 q^{77} -24991.8 q^{78} -82597.4 q^{79} +27042.1 q^{80} -72885.4 q^{81} -8504.54 q^{82} -43089.8 q^{83} +11599.0 q^{84} +241504. q^{85} -27170.4 q^{86} +22161.0 q^{87} -32930.5 q^{88} -95174.1 q^{89} -64194.3 q^{90} +11468.8 q^{91} -32292.9 q^{92} -102898. q^{93} +10495.0 q^{94} -20349.7 q^{96} -103891. q^{97} +61905.2 q^{98} +78172.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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