LMFDB - Embedded newform 350.4.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("350.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.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:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.51960.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 70x + 82 $ x^3 - x^2 - 70*x + 82
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.17488$ of defining polynomial
Character	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.17488 q^{3} +4.00000 q^{4} +6.34975 q^{6} +7.00000 q^{7} -8.00000 q^{8} -16.9202 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.17488 q^{3} +4.00000 q^{4} +6.34975 q^{6} +7.00000 q^{7} -8.00000 q^{8} -16.9202 q^{9} +50.2699 q^{11} -12.6995 q^{12} -17.8744 q^{13} -14.0000 q^{14} +16.0000 q^{16} -93.9202 q^{17} +33.8403 q^{18} +84.9965 q^{19} -22.2241 q^{21} -100.540 q^{22} -119.688 q^{23} +25.3990 q^{24} +35.7488 q^{26} +139.441 q^{27} +28.0000 q^{28} +165.509 q^{29} -134.227 q^{31} -32.0000 q^{32} -159.601 q^{33} +187.840 q^{34} -67.6806 q^{36} -129.681 q^{37} -169.993 q^{38} +56.7490 q^{39} -118.486 q^{41} +44.4483 q^{42} +533.246 q^{43} +201.080 q^{44} +239.375 q^{46} +142.504 q^{47} -50.7980 q^{48} +49.0000 q^{49} +298.185 q^{51} -71.4975 q^{52} +549.664 q^{53} -278.882 q^{54} -56.0000 q^{56} -269.853 q^{57} -331.018 q^{58} +566.008 q^{59} +523.703 q^{61} +268.455 q^{62} -118.441 q^{63} +64.0000 q^{64} +319.202 q^{66} +503.840 q^{67} -375.681 q^{68} +379.993 q^{69} +179.059 q^{71} +135.361 q^{72} +1105.92 q^{73} +259.361 q^{74} +339.986 q^{76} +351.889 q^{77} -113.498 q^{78} -499.227 q^{79} +14.1359 q^{81} +236.971 q^{82} -626.803 q^{83} -88.8966 q^{84} -1066.49 q^{86} -525.471 q^{87} -402.159 q^{88} +721.623 q^{89} -125.121 q^{91} -478.750 q^{92} +426.156 q^{93} -285.009 q^{94} +101.596 q^{96} +543.221 q^{97} -98.0000 q^{98} -850.575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - 7 q^{3} + 12 q^{4} + 14 q^{6} + 21 q^{7} - 24 q^{8} + 76 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - 7 * q^3 + 12 * q^4 + 14 * q^6 + 21 * q^7 - 24 * q^8 + 76 * q^9	$ 3 q - 6 q^{2} - 7 q^{3} + 12 q^{4} + 14 q^{6} + 21 q^{7} - 24 q^{8} + 76 q^{9} + 19 q^{11} - 28 q^{12} - 41 q^{13} - 42 q^{14} + 48 q^{16} - 155 q^{17} - 152 q^{18} + 156 q^{19} - 49 q^{21} - 38 q^{22} - 50 q^{23} + 56 q^{24} + 82 q^{26} - 469 q^{27} + 84 q^{28} + 91 q^{29} + 170 q^{31} - 96 q^{32} + 155 q^{33} + 310 q^{34} + 304 q^{36} + 118 q^{37} - 312 q^{38} + 799 q^{39} - 6 q^{41} + 98 q^{42} + 216 q^{43} + 76 q^{44} + 100 q^{46} - 79 q^{47} - 112 q^{48} + 147 q^{49} - 119 q^{51} - 164 q^{52} + 742 q^{53} + 938 q^{54} - 168 q^{56} + 1664 q^{57} - 182 q^{58} + 590 q^{59} + 352 q^{61} - 340 q^{62} + 532 q^{63} + 192 q^{64} - 310 q^{66} + 1258 q^{67} - 620 q^{68} + 2250 q^{69} + 724 q^{71} - 608 q^{72} + 1326 q^{73} - 236 q^{74} + 624 q^{76} + 133 q^{77} - 1598 q^{78} + 1037 q^{79} + 2407 q^{81} + 12 q^{82} + 580 q^{83} - 196 q^{84} - 432 q^{86} - 177 q^{87} - 152 q^{88} - 1048 q^{89} - 287 q^{91} - 200 q^{92} + 1338 q^{93} + 158 q^{94} + 224 q^{96} + 2821 q^{97} - 294 q^{98} - 3278 q^{99}+O(q^{100}) $ 3 * q - 6 * q^2 - 7 * q^3 + 12 * q^4 + 14 * q^6 + 21 * q^7 - 24 * q^8 + 76 * q^9 + 19 * q^11 - 28 * q^12 - 41 * q^13 - 42 * q^14 + 48 * q^16 - 155 * q^17 - 152 * q^18 + 156 * q^19 - 49 * q^21 - 38 * q^22 - 50 * q^23 + 56 * q^24 + 82 * q^26 - 469 * q^27 + 84 * q^28 + 91 * q^29 + 170 * q^31 - 96 * q^32 + 155 * q^33 + 310 * q^34 + 304 * q^36 + 118 * q^37 - 312 * q^38 + 799 * q^39 - 6 * q^41 + 98 * q^42 + 216 * q^43 + 76 * q^44 + 100 * q^46 - 79 * q^47 - 112 * q^48 + 147 * q^49 - 119 * q^51 - 164 * q^52 + 742 * q^53 + 938 * q^54 - 168 * q^56 + 1664 * q^57 - 182 * q^58 + 590 * q^59 + 352 * q^61 - 340 * q^62 + 532 * q^63 + 192 * q^64 - 310 * q^66 + 1258 * q^67 - 620 * q^68 + 2250 * q^69 + 724 * q^71 - 608 * q^72 + 1326 * q^73 - 236 * q^74 + 624 * q^76 + 133 * q^77 - 1598 * q^78 + 1037 * q^79 + 2407 * q^81 + 12 * q^82 + 580 * q^83 - 196 * q^84 - 432 * q^86 - 177 * q^87 - 152 * q^88 - 1048 * q^89 - 287 * q^91 - 200 * q^92 + 1338 * q^93 + 158 * q^94 + 224 * q^96 + 2821 * q^97 - 294 * q^98 - 3278 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.17488	−0.611005	−0.305503	−	0.952191i	$-0.598824\pi$
$3$	−3.17488	−0.611005	−0.305503	+	0.952191i	$0.598824\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	6.34975	0.432046
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	−16.9202	−0.626672
$10$	0	0
$11$	50.2699	1.37790	0.688952	−	0.724807i	$-0.258071\pi$
$11$	50.2699	1.37790	0.688952	+	0.724807i	$0.258071\pi$
$12$	−12.6995	−0.305503
$13$	−17.8744	−0.381343	−0.190672	−	0.981654i	$-0.561067\pi$
$13$	−17.8744	−0.381343	−0.190672	+	0.981654i	$0.561067\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−93.9202	−1.33994	−0.669970	−	0.742388i	$-0.733693\pi$
$17$	−93.9202	−1.33994	−0.669970	+	0.742388i	$0.733693\pi$
$18$	33.8403	0.443124
$19$	84.9965	1.02629	0.513146	−	0.858302i	$-0.328480\pi$
$19$	84.9965	1.02629	0.513146	+	0.858302i	$0.328480\pi$
$20$	0	0
$21$	−22.2241	−0.230938
$22$	−100.540	−0.974326
$23$	−119.688	−1.08507	−0.542535	−	0.840033i	$-0.682535\pi$
$23$	−119.688	−1.08507	−0.542535	+	0.840033i	$0.682535\pi$
$24$	25.3990	0.216023
$25$	0	0
$26$	35.7488	0.269650
$27$	139.441	0.993906
$28$	28.0000	0.188982
$29$	165.509	1.05980	0.529902	−	0.848059i	$-0.322229\pi$
$29$	165.509	1.05980	0.529902	+	0.848059i	$0.322229\pi$
$30$	0	0
$31$	−134.227	−0.777676	−0.388838	−	0.921306i	$-0.627123\pi$
$31$	−134.227	−0.777676	−0.388838	+	0.921306i	$0.627123\pi$
$32$	−32.0000	−0.176777
$33$	−159.601	−0.841907
$34$	187.840	0.947481
$35$	0	0
$36$	−67.6806	−0.313336
$37$	−129.681	−0.576199	−0.288100	−	0.957600i	$-0.593023\pi$
$37$	−129.681	−0.576199	−0.288100	+	0.957600i	$0.593023\pi$
$38$	−169.993	−0.725698
$39$	56.7490	0.233003
$40$	0	0
$41$	−118.486	−0.451326	−0.225663	−	0.974205i	$-0.572455\pi$
$41$	−118.486	−0.451326	−0.225663	+	0.974205i	$0.572455\pi$
$42$	44.4483	0.163298
$43$	533.246	1.89115	0.945573	−	0.325411i	$-0.105503\pi$
$43$	533.246	1.89115	0.945573	+	0.325411i	$0.105503\pi$
$44$	201.080	0.688952
$45$	0	0
$46$	239.375	0.767260
$47$	142.504	0.442264	0.221132	−	0.975244i	$-0.429025\pi$
$47$	142.504	0.442264	0.221132	+	0.975244i	$0.429025\pi$
$48$	−50.7980	−0.152751
$49$	49.0000	0.142857
$50$	0	0
$51$	298.185	0.818711
$52$	−71.4975	−0.190672
$53$	549.664	1.42457	0.712284	−	0.701891i	$-0.247661\pi$
$53$	549.664	1.42457	0.712284	+	0.701891i	$0.247661\pi$
$54$	−278.882	−0.702797
$55$	0	0
$56$	−56.0000	−0.133631
$57$	−269.853	−0.627070
$58$	−331.018	−0.749394
$59$	566.008	1.24895	0.624474	−	0.781045i	$-0.285313\pi$
$59$	566.008	1.24895	0.624474	+	0.781045i	$0.285313\pi$
$60$	0	0
$61$	523.703	1.09923	0.549617	−	0.835417i	$-0.314774\pi$
$61$	523.703	1.09923	0.549617	+	0.835417i	$0.314774\pi$
$62$	268.455	0.549900
$63$	−118.441	−0.236860
$64$	64.0000	0.125000
$65$	0	0
$66$	319.202	0.595318
$67$	503.840	0.918715	0.459357	−	0.888252i	$-0.348080\pi$
$67$	503.840	0.918715	0.459357	+	0.888252i	$0.348080\pi$
$68$	−375.681	−0.669970
$69$	379.993	0.662983
$70$	0	0
$71$	179.059	0.299301	0.149651	−	0.988739i	$-0.452185\pi$
$71$	179.059	0.299301	0.149651	+	0.988739i	$0.452185\pi$
$72$	135.361	0.221562
$73$	1105.92	1.77313	0.886564	−	0.462606i	$-0.153086\pi$
$73$	1105.92	1.77313	0.886564	+	0.462606i	$0.153086\pi$
$74$	259.361	0.407434
$75$	0	0
$76$	339.986	0.513146
$77$	351.889	0.520799
$78$	−113.498	−0.164758
$79$	−499.227	−0.710980	−0.355490	−	0.934680i	$-0.615686\pi$
$79$	−499.227	−0.710980	−0.355490	+	0.934680i	$0.615686\pi$
$80$	0	0
$81$	14.1359	0.0193908
$82$	236.971	0.319135
$83$	−626.803	−0.828922	−0.414461	−	0.910067i	$-0.636030\pi$
$83$	−626.803	−0.828922	−0.414461	+	0.910067i	$0.636030\pi$
$84$	−88.8966	−0.115469
$85$	0	0
$86$	−1066.49	−1.33724
$87$	−525.471	−0.647545
$88$	−402.159	−0.487163
$89$	721.623	0.859459	0.429730	−	0.902958i	$-0.358609\pi$
$89$	721.623	0.859459	0.429730	+	0.902958i	$0.358609\pi$
$90$	0	0
$91$	−125.121	−0.144134
$92$	−478.750	−0.542535
$93$	426.156	0.475164
$94$	−285.009	−0.312728
$95$	0	0
$96$	101.596	0.108012
$97$	543.221	0.568616	0.284308	−	0.958733i	$-0.408236\pi$
$97$	543.221	0.568616	0.284308	+	0.958733i	$0.408236\pi$
$98$	−98.0000	−0.101015
$99$	−850.575	−0.863495
$100$	0	0
$101$	−923.244	−0.909567	−0.454783	−	0.890602i	$-0.650283\pi$
$101$	−923.244	−0.909567	−0.454783	+	0.890602i	$0.650283\pi$
$102$	−596.370	−0.578916
$103$	−561.917	−0.537547	−0.268773	−	0.963203i	$-0.586618\pi$
$103$	−561.917	−0.537547	−0.268773	+	0.963203i	$0.586618\pi$
$104$	142.995	0.134825
$105$	0	0
$106$	−1099.33	−1.00732
$107$	1053.44	0.951779	0.475890	−	0.879505i	$-0.342126\pi$
$107$	1053.44	0.951779	0.475890	+	0.879505i	$0.342126\pi$
$108$	557.764	0.496953
$109$	1766.04	1.55189	0.775946	−	0.630800i	$-0.217273\pi$
$109$	1766.04	1.55189	0.775946	+	0.630800i	$0.217273\pi$
$110$	0	0
$111$	411.720	0.352061
$112$	112.000	0.0944911
$113$	134.333	0.111831	0.0559157	−	0.998435i	$-0.482192\pi$
$113$	134.333	0.111831	0.0559157	+	0.998435i	$0.482192\pi$
$114$	539.707	0.443405
$115$	0	0
$116$	662.037	0.529902
$117$	302.437	0.238977
$118$	−1132.02	−0.883140
$119$	−657.441	−0.506450
$120$	0	0
$121$	1196.06	0.898620
$122$	−1047.41	−0.777275
$123$	376.177	0.275762
$124$	−536.910	−0.388838
$125$	0	0
$126$	236.882	0.167485
$127$	−194.736	−0.136063	−0.0680316	−	0.997683i	$-0.521672\pi$
$127$	−194.736	−0.136063	−0.0680316	+	0.997683i	$0.521672\pi$
$128$	−128.000	−0.0883883
$129$	−1692.99	−1.15550
$130$	0	0
$131$	−1874.59	−1.25026	−0.625129	−	0.780522i	$-0.714953\pi$
$131$	−1874.59	−1.25026	−0.625129	+	0.780522i	$0.714953\pi$
$132$	−638.403	−0.420953
$133$	594.976	0.387902
$134$	−1007.68	−0.649629
$135$	0	0
$136$	751.361	0.473740
$137$	−437.479	−0.272820	−0.136410	−	0.990652i	$-0.543556\pi$
$137$	−437.479	−0.272820	−0.136410	+	0.990652i	$0.543556\pi$
$138$	−759.987	−0.468800
$139$	−727.734	−0.444069	−0.222034	−	0.975039i	$-0.571270\pi$
$139$	−727.734	−0.444069	−0.222034	+	0.975039i	$0.571270\pi$
$140$	0	0
$141$	−452.434	−0.270225
$142$	−358.118	−0.211638
$143$	−898.544	−0.525455
$144$	−270.722	−0.156668
$145$	0	0
$146$	−2211.84	−1.25379
$147$	−155.569	−0.0872865
$148$	−518.722	−0.288100
$149$	−3079.34	−1.69308	−0.846541	−	0.532324i	$-0.821319\pi$
$149$	−3079.34	−1.69308	−0.846541	+	0.532324i	$0.821319\pi$
$150$	0	0
$151$	1735.58	0.935362	0.467681	−	0.883897i	$-0.345090\pi$
$151$	1735.58	0.935362	0.467681	+	0.883897i	$0.345090\pi$
$152$	−679.972	−0.362849
$153$	1589.14	0.839704
$154$	−703.779	−0.368260
$155$	0	0
$156$	226.996	0.116501
$157$	1864.22	0.947652	0.473826	−	0.880619i	$-0.342873\pi$
$157$	1864.22	0.947652	0.473826	+	0.880619i	$0.342873\pi$
$158$	998.454	0.502739
$159$	−1745.11	−0.870419
$160$	0	0
$161$	−837.813	−0.410118
$162$	−28.2718	−0.0137114
$163$	2659.74	1.27808	0.639039	−	0.769175i	$-0.279332\pi$
$163$	2659.74	1.27808	0.639039	+	0.769175i	$0.279332\pi$
$164$	−473.943	−0.225663
$165$	0	0
$166$	1253.61	0.586137
$167$	−3051.35	−1.41389	−0.706947	−	0.707266i	$-0.749928\pi$
$167$	−3051.35	−1.41389	−0.706947	+	0.707266i	$0.749928\pi$
$168$	177.793	0.0816490
$169$	−1877.51	−0.854577
$170$	0	0
$171$	−1438.15	−0.643149
$172$	2132.98	0.945573
$173$	−2717.13	−1.19410	−0.597050	−	0.802204i	$-0.703661\pi$
$173$	−2717.13	−1.19410	−0.597050	+	0.802204i	$0.703661\pi$
$174$	1050.94	0.457884
$175$	0	0
$176$	804.319	0.344476
$177$	−1797.01	−0.763114
$178$	−1443.25	−0.607729
$179$	−760.380	−0.317505	−0.158753	−	0.987318i	$-0.550747\pi$
$179$	−760.380	−0.317505	−0.158753	+	0.987318i	$0.550747\pi$
$180$	0	0
$181$	1629.22	0.669056	0.334528	−	0.942386i	$-0.391423\pi$
$181$	1629.22	0.669056	0.334528	+	0.942386i	$0.391423\pi$
$182$	250.241	0.101918
$183$	−1662.69	−0.671638
$184$	957.501	0.383630
$185$	0	0
$186$	−852.311	−0.335992
$187$	−4721.36	−1.84631
$188$	570.017	0.221132
$189$	976.088	0.375661
$190$	0	0
$191$	−1436.35	−0.544140	−0.272070	−	0.962277i	$-0.587708\pi$
$191$	−1436.35	−0.544140	−0.272070	+	0.962277i	$0.587708\pi$
$192$	−203.192	−0.0763757
$193$	2622.38	0.978045	0.489023	−	0.872271i	$-0.337354\pi$
$193$	2622.38	0.978045	0.489023	+	0.872271i	$0.337354\pi$
$194$	−1086.44	−0.402072
$195$	0	0
$196$	196.000	0.0714286
$197$	5329.93	1.92763	0.963813	−	0.266581i	$-0.0858940\pi$
$197$	5329.93	1.92763	0.963813	+	0.266581i	$0.0858940\pi$
$198$	1701.15	0.610583
$199$	4558.21	1.62373	0.811867	−	0.583843i	$-0.198452\pi$
$199$	4558.21	1.62373	0.811867	+	0.583843i	$0.198452\pi$
$200$	0	0
$201$	−1599.63	−0.561340
$202$	1846.49	0.643161
$203$	1158.56	0.400568
$204$	1192.74	0.409355
$205$	0	0
$206$	1123.83	0.380103
$207$	2025.13	0.679983
$208$	−285.990	−0.0953358
$209$	4272.77	1.41413
$210$	0	0
$211$	−2728.87	−0.890347	−0.445174	−	0.895444i	$-0.646858\pi$
$211$	−2728.87	−0.890347	−0.445174	+	0.895444i	$0.646858\pi$
$212$	2198.66	0.712284
$213$	−568.491	−0.182875
$214$	−2106.89	−0.673010
$215$	0	0
$216$	−1115.53	−0.351399
$217$	−939.592	−0.293934
$218$	−3532.09	−1.09735
$219$	−3511.17	−1.08339
$220$	0	0
$221$	1678.77	0.510977
$222$	−823.440	−0.248944
$223$	611.653	0.183674	0.0918370	−	0.995774i	$-0.470726\pi$
$223$	611.653	0.183674	0.0918370	+	0.995774i	$0.470726\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−268.665	−0.0790767
$227$	1803.39	0.527292	0.263646	−	0.964620i	$-0.415075\pi$
$227$	1803.39	0.527292	0.263646	+	0.964620i	$0.415075\pi$
$228$	−1079.41	−0.313535
$229$	−1192.02	−0.343978	−0.171989	−	0.985099i	$-0.555019\pi$
$229$	−1192.02	−0.343978	−0.171989	+	0.985099i	$0.555019\pi$
$230$	0	0
$231$	−1117.21	−0.318211
$232$	−1324.07	−0.374697
$233$	1436.20	0.403815	0.201907	−	0.979405i	$-0.435286\pi$
$233$	1436.20	0.403815	0.201907	+	0.979405i	$0.435286\pi$
$234$	−604.875	−0.168982
$235$	0	0
$236$	2264.03	0.624474
$237$	1584.98	0.434412
$238$	1314.88	0.358114
$239$	−1887.15	−0.510752	−0.255376	−	0.966842i	$-0.582199\pi$
$239$	−1887.15	−0.510752	−0.255376	+	0.966842i	$0.582199\pi$
$240$	0	0
$241$	−1718.30	−0.459275	−0.229638	−	0.973276i	$-0.573754\pi$
$241$	−1718.30	−0.459275	−0.229638	+	0.973276i	$0.573754\pi$
$242$	−2392.13	−0.635421
$243$	−3809.79	−1.00575
$244$	2094.81	0.549617
$245$	0	0
$246$	−752.355	−0.194993
$247$	−1519.26	−0.391369
$248$	1073.82	0.274950
$249$	1990.02	0.506476
$250$	0	0
$251$	3320.10	0.834912	0.417456	−	0.908697i	$-0.362922\pi$
$251$	3320.10	0.834912	0.417456	+	0.908697i	$0.362922\pi$
$252$	−473.764	−0.118430
$253$	−6016.69	−1.49512
$254$	389.472	0.0962112
$255$	0	0
$256$	256.000	0.0625000
$257$	−2609.13	−0.633281	−0.316641	−	0.948546i	$-0.602555\pi$
$257$	−2609.13	−0.633281	−0.316641	+	0.948546i	$0.602555\pi$
$258$	3385.98	0.817062
$259$	−907.764	−0.217783
$260$	0	0
$261$	−2800.44	−0.664149
$262$	3749.18	0.884065
$263$	1058.86	0.248258	0.124129	−	0.992266i	$-0.460386\pi$
$263$	1058.86	0.248258	0.124129	+	0.992266i	$0.460386\pi$
$264$	1276.81	0.297659
$265$	0	0
$266$	−1189.95	−0.274288
$267$	−2291.06	−0.525134
$268$	2015.36	0.459357
$269$	−1571.46	−0.356184	−0.178092	−	0.984014i	$-0.556992\pi$
$269$	−1571.46	−0.356184	−0.178092	+	0.984014i	$0.556992\pi$
$270$	0	0
$271$	3967.40	0.889307	0.444654	−	0.895703i	$-0.353327\pi$
$271$	3967.40	0.889307	0.444654	+	0.895703i	$0.353327\pi$
$272$	−1502.72	−0.334985
$273$	397.243	0.0880668
$274$	874.957	0.192913
$275$	0	0
$276$	1519.97	0.331492
$277$	4059.99	0.880653	0.440327	−	0.897838i	$-0.354863\pi$
$277$	4059.99	0.880653	0.440327	+	0.897838i	$0.354863\pi$
$278$	1455.47	0.314004
$279$	2271.15	0.487348
$280$	0	0
$281$	8768.49	1.86151	0.930755	−	0.365643i	$-0.119151\pi$
$281$	8768.49	1.86151	0.930755	+	0.365643i	$0.119151\pi$
$282$	904.867	0.191078
$283$	4138.47	0.869281	0.434641	−	0.900604i	$-0.356875\pi$
$283$	4138.47	0.869281	0.434641	+	0.900604i	$0.356875\pi$
$284$	716.236	0.149651
$285$	0	0
$286$	1797.09	0.371552
$287$	−829.399	−0.170585
$288$	541.445	0.110781
$289$	3908.00	0.795440
$290$	0	0
$291$	−1724.66	−0.347427
$292$	4423.69	0.886564
$293$	−9248.12	−1.84396	−0.921982	−	0.387234i	$-0.873431\pi$
$293$	−9248.12	−1.84396	−0.921982	+	0.387234i	$0.873431\pi$
$294$	311.138	0.0617209
$295$	0	0
$296$	1037.44	0.203717
$297$	7009.69	1.36951
$298$	6158.67	1.19719
$299$	2139.34	0.413784
$300$	0	0
$301$	3732.72	0.714786
$302$	−3471.16	−0.661400
$303$	2931.19	0.555750
$304$	1359.94	0.256573
$305$	0	0
$306$	−3178.29	−0.593760
$307$	−6805.83	−1.26524	−0.632621	−	0.774461i	$-0.718021\pi$
$307$	−6805.83	−1.26524	−0.632621	+	0.774461i	$0.718021\pi$
$308$	1407.56	0.260399
$309$	1784.02	0.328444
$310$	0	0
$311$	1901.30	0.346665	0.173333	−	0.984863i	$-0.444546\pi$
$311$	1901.30	0.346665	0.173333	+	0.984863i	$0.444546\pi$
$312$	−453.992	−0.0823789
$313$	−8870.98	−1.60197	−0.800986	−	0.598683i	$-0.795691\pi$
$313$	−8870.98	−1.60197	−0.800986	+	0.598683i	$0.795691\pi$
$314$	−3728.45	−0.670091
$315$	0	0
$316$	−1996.91	−0.355490
$317$	9550.80	1.69220	0.846098	−	0.533027i	$-0.178946\pi$
$317$	9550.80	1.69220	0.846098	+	0.533027i	$0.178946\pi$
$318$	3490.23	0.615479
$319$	8320.13	1.46031
$320$	0	0
$321$	−3344.56	−0.581542
$322$	1675.63	0.289997
$323$	−7982.89	−1.37517
$324$	56.5436	0.00969540
$325$	0	0
$326$	−5319.47	−0.903737
$327$	−5606.97	−0.948214
$328$	947.885	0.159568
$329$	997.530	0.167160
$330$	0	0
$331$	2564.72	0.425891	0.212946	−	0.977064i	$-0.431694\pi$
$331$	2564.72	0.425891	0.212946	+	0.977064i	$0.431694\pi$
$332$	−2507.21	−0.414461
$333$	2194.22	0.361088
$334$	6102.70	0.999774
$335$	0	0
$336$	−355.586	−0.0577346
$337$	−3535.22	−0.571442	−0.285721	−	0.958313i	$-0.592233\pi$
$337$	−3535.22	−0.571442	−0.285721	+	0.958313i	$0.592233\pi$
$338$	3755.01	0.604277
$339$	−426.489	−0.0683295
$340$	0	0
$341$	−6747.60	−1.07156
$342$	2876.31	0.454775
$343$	343.000	0.0539949
$344$	−4265.97	−0.668621
$345$	0	0
$346$	5434.25	0.844356
$347$	−4382.81	−0.678045	−0.339023	−	0.940778i	$-0.610096\pi$
$347$	−4382.81	−0.678045	−0.339023	+	0.940778i	$0.610096\pi$
$348$	−2101.89	−0.323773
$349$	2414.14	0.370276	0.185138	−	0.982713i	$-0.440727\pi$
$349$	2414.14	0.370276	0.185138	+	0.982713i	$0.440727\pi$
$350$	0	0
$351$	−2492.42	−0.379019
$352$	−1608.64	−0.243581
$353$	11564.0	1.74360	0.871801	−	0.489860i	$-0.162952\pi$
$353$	11564.0	1.74360	0.871801	+	0.489860i	$0.162952\pi$
$354$	3594.01	0.539603
$355$	0	0
$356$	2886.49	0.429730
$357$	2087.29	0.309444
$358$	1520.76	0.224510
$359$	6453.41	0.948742	0.474371	−	0.880325i	$-0.342676\pi$
$359$	6453.41	0.948742	0.474371	+	0.880325i	$0.342676\pi$
$360$	0	0
$361$	365.407	0.0532740
$362$	−3258.44	−0.473094
$363$	−3797.36	−0.549062
$364$	−500.483	−0.0720671
$365$	0	0
$366$	3325.38	0.474919
$367$	−5131.76	−0.729907	−0.364953	−	0.931026i	$-0.618915\pi$
$367$	−5131.76	−0.729907	−0.364953	+	0.931026i	$0.618915\pi$
$368$	−1915.00	−0.271267
$369$	2004.80	0.282833
$370$	0	0
$371$	3847.65	0.538436
$372$	1704.62	0.237582
$373$	6506.75	0.903235	0.451617	−	0.892212i	$-0.350847\pi$
$373$	6506.75	0.903235	0.451617	+	0.892212i	$0.350847\pi$
$374$	9442.72	1.30554
$375$	0	0
$376$	−1140.03	−0.156364
$377$	−2958.38	−0.404149
$378$	−1952.18	−0.265632
$379$	12932.0	1.75270	0.876350	−	0.481676i	$-0.159972\pi$
$379$	12932.0	1.75270	0.876350	+	0.481676i	$0.159972\pi$
$380$	0	0
$381$	618.263	0.0831353
$382$	2872.70	0.384765
$383$	−13062.0	−1.74266	−0.871328	−	0.490701i	$-0.836741\pi$
$383$	−13062.0	−1.74266	−0.871328	+	0.490701i	$0.836741\pi$
$384$	406.384	0.0540058
$385$	0	0
$386$	−5244.75	−0.691582
$387$	−9022.60	−1.18513
$388$	2172.88	0.284308
$389$	−12364.3	−1.61156	−0.805780	−	0.592215i	$-0.798254\pi$
$389$	−12364.3	−1.61156	−0.805780	+	0.592215i	$0.798254\pi$
$390$	0	0
$391$	11241.1	1.45393
$392$	−392.000	−0.0505076
$393$	5951.59	0.763914
$394$	−10659.9	−1.36304
$395$	0	0
$396$	−3402.30	−0.431747
$397$	5195.33	0.656792	0.328396	−	0.944540i	$-0.393492\pi$
$397$	5195.33	0.656792	0.328396	+	0.944540i	$0.393492\pi$
$398$	−9116.42	−1.14815
$399$	−1888.97	−0.237010
$400$	0	0
$401$	−9343.04	−1.16351	−0.581757	−	0.813363i	$-0.697634\pi$
$401$	−9343.04	−1.16351	−0.581757	+	0.813363i	$0.697634\pi$
$402$	3199.26	0.396927
$403$	2399.23	0.296562
$404$	−3692.98	−0.454783
$405$	0	0
$406$	−2317.13	−0.283244
$407$	−6519.03	−0.793947
$408$	−2385.48	−0.289458
$409$	−11930.1	−1.44231	−0.721155	−	0.692774i	$-0.756388\pi$
$409$	−11930.1	−1.44231	−0.721155	+	0.692774i	$0.756388\pi$
$410$	0	0
$411$	1388.94	0.166694
$412$	−2247.67	−0.268773
$413$	3962.06	0.472058
$414$	−4050.27	−0.480821
$415$	0	0
$416$	571.980	0.0674126
$417$	2310.47	0.271328
$418$	−8545.53	−0.999942
$419$	−5113.86	−0.596250	−0.298125	−	0.954527i	$-0.596361\pi$
$419$	−5113.86	−0.596250	−0.298125	+	0.954527i	$0.596361\pi$
$420$	0	0
$421$	14255.5	1.65028	0.825141	−	0.564927i	$-0.191096\pi$
$421$	14255.5	1.65028	0.825141	+	0.564927i	$0.191096\pi$
$422$	5457.74	0.629571
$423$	−2411.20	−0.277154
$424$	−4397.31	−0.503661
$425$	0	0
$426$	1136.98	0.129312
$427$	3665.92	0.415471
$428$	4213.78	0.475890
$429$	2852.77	0.321056
$430$	0	0
$431$	−8773.25	−0.980494	−0.490247	−	0.871584i	$-0.663093\pi$
$431$	−8773.25	−0.980494	−0.490247	+	0.871584i	$0.663093\pi$
$432$	2231.06	0.248476
$433$	−2530.92	−0.280897	−0.140448	−	0.990088i	$-0.544854\pi$
$433$	−2530.92	−0.280897	−0.140448	+	0.990088i	$0.544854\pi$
$434$	1879.18	0.207843
$435$	0	0
$436$	7064.17	0.775946
$437$	−10173.0	−1.11360
$438$	7022.33	0.766073
$439$	−13842.6	−1.50494	−0.752472	−	0.658624i	$-0.771139\pi$
$439$	−13842.6	−1.50494	−0.752472	+	0.658624i	$0.771139\pi$
$440$	0	0
$441$	−829.088	−0.0895246
$442$	−3357.53	−0.361315
$443$	−16388.0	−1.75760	−0.878800	−	0.477190i	$-0.841655\pi$
$443$	−16388.0	−1.75760	−0.878800	+	0.477190i	$0.841655\pi$
$444$	1646.88	0.176030
$445$	0	0
$446$	−1223.31	−0.129877
$447$	9776.52	1.03448
$448$	448.000	0.0472456
$449$	−3165.01	−0.332664	−0.166332	−	0.986070i	$-0.553192\pi$
$449$	−3165.01	−0.332664	−0.166332	+	0.986070i	$0.553192\pi$
$450$	0	0
$451$	−5956.26	−0.621883
$452$	537.330	0.0559157
$453$	−5510.26	−0.571511
$454$	−3606.78	−0.372852
$455$	0	0
$456$	2158.83	0.221703
$457$	10685.9	1.09380	0.546899	−	0.837198i	$-0.315808\pi$
$457$	10685.9	1.09380	0.546899	+	0.837198i	$0.315808\pi$
$458$	2384.04	0.243229
$459$	−13096.3	−1.33177
$460$	0	0
$461$	−14153.1	−1.42988	−0.714941	−	0.699185i	$-0.753547\pi$
$461$	−14153.1	−1.42988	−0.714941	+	0.699185i	$0.753547\pi$
$462$	2234.41	0.225009
$463$	5347.76	0.536785	0.268392	−	0.963310i	$-0.413508\pi$
$463$	5347.76	0.536785	0.268392	+	0.963310i	$0.413508\pi$
$464$	2648.15	0.264951
$465$	0	0
$466$	−2872.41	−0.285540
$467$	−863.874	−0.0856002	−0.0428001	−	0.999084i	$-0.513628\pi$
$467$	−863.874	−0.0856002	−0.0428001	+	0.999084i	$0.513628\pi$
$468$	1209.75	0.119489
$469$	3526.88	0.347242
$470$	0	0
$471$	−5918.68	−0.579020
$472$	−4528.06	−0.441570
$473$	26806.2	2.60582
$474$	−3169.97	−0.307176
$475$	0	0
$476$	−2629.76	−0.253225
$477$	−9300.40	−0.892738
$478$	3774.31	0.361156
$479$	−935.617	−0.0892473	−0.0446236	−	0.999004i	$-0.514209\pi$
$479$	−935.617	−0.0892473	−0.0446236	+	0.999004i	$0.514209\pi$
$480$	0	0
$481$	2317.96	0.219730
$482$	3436.60	0.324757
$483$	2659.95	0.250584
$484$	4784.26	0.449310
$485$	0	0
$486$	7619.58	0.711175
$487$	−4610.03	−0.428954	−0.214477	−	0.976729i	$-0.568805\pi$
$487$	−4610.03	−0.428954	−0.214477	+	0.976729i	$0.568805\pi$
$488$	−4189.62	−0.388638
$489$	−8444.33	−0.780912
$490$	0	0
$491$	−16184.3	−1.48755	−0.743775	−	0.668430i	$-0.766967\pi$
$491$	−16184.3	−1.48755	−0.743775	+	0.668430i	$0.766967\pi$
$492$	1504.71	0.137881
$493$	−15544.7	−1.42007
$494$	3038.52	0.276740
$495$	0	0
$496$	−2147.64	−0.194419
$497$	1253.41	0.113125
$498$	−3980.04	−0.358133
$499$	777.051	0.0697106	0.0348553	−	0.999392i	$-0.488903\pi$
$499$	777.051	0.0697106	0.0348553	+	0.999392i	$0.488903\pi$
$500$	0	0
$501$	9687.65	0.863897
$502$	−6640.20	−0.590372
$503$	2775.36	0.246018	0.123009	−	0.992406i	$-0.460746\pi$
$503$	2775.36	0.246018	0.123009	+	0.992406i	$0.460746\pi$
$504$	947.529	0.0837426
$505$	0	0
$506$	12033.4	1.05721
$507$	5960.85	0.522151
$508$	−778.944	−0.0680316
$509$	6544.58	0.569908	0.284954	−	0.958541i	$-0.408022\pi$
$509$	6544.58	0.569908	0.284954	+	0.958541i	$0.408022\pi$
$510$	0	0
$511$	7741.45	0.670179
$512$	−512.000	−0.0441942
$513$	11852.0	1.02004
$514$	5218.27	0.447797
$515$	0	0
$516$	−6771.96	−0.577750
$517$	7163.68	0.609397
$518$	1815.53	0.153996
$519$	8626.54	0.729601
$520$	0	0
$521$	−14477.2	−1.21739	−0.608694	−	0.793405i	$-0.708306\pi$
$521$	−14477.2	−1.21739	−0.608694	+	0.793405i	$0.708306\pi$
$522$	5600.88	0.469625
$523$	−18110.0	−1.51414	−0.757070	−	0.653334i	$-0.773370\pi$
$523$	−18110.0	−1.51414	−0.757070	+	0.653334i	$0.773370\pi$
$524$	−7498.36	−0.625129
$525$	0	0
$526$	−2117.72	−0.175545
$527$	12606.7	1.04204
$528$	−2553.61	−0.210477
$529$	2158.12	0.177375
$530$	0	0
$531$	−9576.94	−0.782682
$532$	2379.90	0.193951
$533$	2117.86	0.172110
$534$	4582.13	0.371326
$535$	0	0
$536$	−4030.72	−0.324815
$537$	2414.11	0.193998
$538$	3142.91	0.251860
$539$	2463.23	0.196843
$540$	0	0
$541$	−6723.03	−0.534280	−0.267140	−	0.963658i	$-0.586079\pi$
$541$	−6723.03	−0.534280	−0.267140	+	0.963658i	$0.586079\pi$
$542$	−7934.79	−0.628835
$543$	−5172.58	−0.408796
$544$	3005.44	0.236870
$545$	0	0
$546$	−794.486	−0.0622726
$547$	8128.96	0.635410	0.317705	−	0.948190i	$-0.397088\pi$
$547$	8128.96	0.635410	0.317705	+	0.948190i	$0.397088\pi$
$548$	−1749.91	−0.136410
$549$	−8861.13	−0.688859
$550$	0	0
$551$	14067.7	1.08767
$552$	−3039.95	−0.234400
$553$	−3494.59	−0.268725
$554$	−8119.97	−0.622716
$555$	0	0
$556$	−2910.94	−0.222034
$557$	22542.4	1.71481	0.857407	−	0.514638i	$-0.172074\pi$
$557$	22542.4	1.71481	0.857407	+	0.514638i	$0.172074\pi$
$558$	−4542.30	−0.344607
$559$	−9531.44	−0.721175
$560$	0	0
$561$	14989.7	1.12811
$562$	−17537.0	−1.31629
$563$	22232.9	1.66431	0.832154	−	0.554545i	$-0.187108\pi$
$563$	22232.9	1.66431	0.832154	+	0.554545i	$0.187108\pi$
$564$	−1809.73	−0.135113
$565$	0	0
$566$	−8276.94	−0.614675
$567$	98.9513	0.00732904
$568$	−1432.47	−0.105819
$569$	−6113.48	−0.450423	−0.225211	−	0.974310i	$-0.572307\pi$
$569$	−6113.48	−0.450423	−0.225211	+	0.974310i	$0.572307\pi$
$570$	0	0
$571$	22721.7	1.66528	0.832640	−	0.553815i	$-0.186828\pi$
$571$	22721.7	1.66528	0.832640	+	0.553815i	$0.186828\pi$
$572$	−3594.17	−0.262727
$573$	4560.24	0.332472
$574$	1658.80	0.120622
$575$	0	0
$576$	−1082.89	−0.0783341
$577$	1519.61	0.109640	0.0548199	−	0.998496i	$-0.482542\pi$
$577$	1519.61	0.109640	0.0548199	+	0.998496i	$0.482542\pi$
$578$	−7815.99	−0.562461
$579$	−8325.72	−0.597591
$580$	0	0
$581$	−4387.62	−0.313303
$582$	3449.32	0.245668
$583$	27631.5	1.96292
$584$	−8847.37	−0.626895
$585$	0	0
$586$	18496.2	1.30388
$587$	10440.9	0.734143	0.367071	−	0.930193i	$-0.380360\pi$
$587$	10440.9	0.734143	0.367071	+	0.930193i	$0.380360\pi$
$588$	−622.276	−0.0436432
$589$	−11408.9	−0.798122
$590$	0	0
$591$	−16921.9	−1.17779
$592$	−2074.89	−0.144050
$593$	19081.2	1.32136	0.660682	−	0.750666i	$-0.270267\pi$
$593$	19081.2	1.32136	0.660682	+	0.750666i	$0.270267\pi$
$594$	−14019.4	−0.968388
$595$	0	0
$596$	−12317.3	−0.846541
$597$	−14471.8	−0.992110
$598$	−4278.68	−0.292589
$599$	5175.38	0.353022	0.176511	−	0.984299i	$-0.443519\pi$
$599$	5175.38	0.353022	0.176511	+	0.984299i	$0.443519\pi$
$600$	0	0
$601$	4472.56	0.303560	0.151780	−	0.988414i	$-0.451500\pi$
$601$	4472.56	0.303560	0.151780	+	0.988414i	$0.451500\pi$
$602$	−7465.44	−0.505430
$603$	−8525.06	−0.575733
$604$	6942.32	0.467681
$605$	0	0
$606$	−5862.37	−0.392975
$607$	−15446.8	−1.03289	−0.516447	−	0.856319i	$-0.672746\pi$
$607$	−15446.8	−1.03289	−0.516447	+	0.856319i	$0.672746\pi$
$608$	−2719.89	−0.181424
$609$	−3678.30	−0.244749
$610$	0	0
$611$	−2547.18	−0.168654
$612$	6356.57	0.419852
$613$	−8024.00	−0.528689	−0.264344	−	0.964428i	$-0.585156\pi$
$613$	−8024.00	−0.528689	−0.264344	+	0.964428i	$0.585156\pi$
$614$	13611.7	0.894661
$615$	0	0
$616$	−2815.11	−0.184130
$617$	10712.9	0.699003	0.349501	−	0.936936i	$-0.386351\pi$
$617$	10712.9	0.699003	0.349501	+	0.936936i	$0.386351\pi$
$618$	−3568.03	−0.232245
$619$	−7260.60	−0.471451	−0.235726	−	0.971820i	$-0.575747\pi$
$619$	−7260.60	−0.471451	−0.235726	+	0.971820i	$0.575747\pi$
$620$	0	0
$621$	−16689.4	−1.07846
$622$	−3802.60	−0.245129
$623$	5051.36	0.324845
$624$	907.984	0.0582507
$625$	0	0
$626$	17742.0	1.13277
$627$	−13565.5	−0.864042
$628$	7456.90	0.473826
$629$	12179.6	0.772072
$630$	0	0
$631$	5154.44	0.325190	0.162595	−	0.986693i	$-0.448014\pi$
$631$	5154.44	0.325190	0.162595	+	0.986693i	$0.448014\pi$
$632$	3993.81	0.251369
$633$	8663.83	0.544007
$634$	−19101.6	−1.19656
$635$	0	0
$636$	−6980.46	−0.435209
$637$	−875.845	−0.0544776
$638$	−16640.3	−1.03259
$639$	−3029.71	−0.187564
$640$	0	0
$641$	−2623.50	−0.161657	−0.0808284	−	0.996728i	$-0.525757\pi$
$641$	−2623.50	−0.161657	−0.0808284	+	0.996728i	$0.525757\pi$
$642$	6689.12	0.411212
$643$	−1598.88	−0.0980614	−0.0490307	−	0.998797i	$-0.515613\pi$
$643$	−1598.88	−0.0980614	−0.0490307	+	0.998797i	$0.515613\pi$
$644$	−3351.25	−0.205059
$645$	0	0
$646$	15965.8	0.972391
$647$	−873.932	−0.0531033	−0.0265516	−	0.999647i	$-0.508453\pi$
$647$	−873.932	−0.0531033	−0.0265516	+	0.999647i	$0.508453\pi$
$648$	−113.087	−0.00685569
$649$	28453.2	1.72093
$650$	0	0
$651$	2983.09	0.179595
$652$	10638.9	0.639039
$653$	−5974.47	−0.358039	−0.179019	−	0.983846i	$-0.557292\pi$
$653$	−5974.47	−0.358039	−0.179019	+	0.983846i	$0.557292\pi$
$654$	11213.9	0.670489
$655$	0	0
$656$	−1895.77	−0.112831
$657$	−18712.4	−1.11117
$658$	−1995.06	−0.118200
$659$	20011.0	1.18288	0.591439	−	0.806350i	$-0.298560\pi$
$659$	20011.0	1.18288	0.591439	+	0.806350i	$0.298560\pi$
$660$	0	0
$661$	22177.7	1.30501	0.652506	−	0.757784i	$-0.273718\pi$
$661$	22177.7	1.30501	0.652506	+	0.757784i	$0.273718\pi$
$662$	−5129.45	−0.301151
$663$	−5329.87	−0.312210
$664$	5014.42	0.293068
$665$	0	0
$666$	−4388.43	−0.255328
$667$	−19809.4	−1.14996
$668$	−12205.4	−0.706947
$669$	−1941.92	−0.112226
$670$	0	0
$671$	26326.5	1.51464
$672$	711.172	0.0408245
$673$	−13666.5	−0.782770	−0.391385	−	0.920227i	$-0.628004\pi$
$673$	−13666.5	−0.782770	−0.391385	+	0.920227i	$0.628004\pi$
$674$	7070.45	0.404070
$675$	0	0
$676$	−7510.03	−0.427289
$677$	−14583.9	−0.827923	−0.413962	−	0.910294i	$-0.635855\pi$
$677$	−14583.9	−0.827923	−0.413962	+	0.910294i	$0.635855\pi$
$678$	852.978	0.0483163
$679$	3802.55	0.214917
$680$	0	0
$681$	−5725.54	−0.322178
$682$	13495.2	0.757710
$683$	920.211	0.0515533	0.0257766	−	0.999668i	$-0.491794\pi$
$683$	920.211	0.0515533	0.0257766	+	0.999668i	$0.491794\pi$
$684$	−5752.62	−0.321574
$685$	0	0
$686$	−686.000	−0.0381802
$687$	3784.52	0.210173
$688$	8531.93	0.472786
$689$	−9824.90	−0.543250
$690$	0	0
$691$	−16707.7	−0.919815	−0.459907	−	0.887967i	$-0.652117\pi$
$691$	−16707.7	−0.919815	−0.459907	+	0.887967i	$0.652117\pi$
$692$	−10868.5	−0.597050
$693$	−5954.02	−0.326370
$694$	8765.62	0.479450
$695$	0	0
$696$	4203.77	0.228942
$697$	11128.2	0.604749
$698$	−4828.29	−0.261824
$699$	−4559.77	−0.246733
$700$	0	0
$701$	11097.6	0.597931	0.298966	−	0.954264i	$-0.403358\pi$
$701$	11097.6	0.597931	0.298966	+	0.954264i	$0.403358\pi$
$702$	4984.85	0.268007
$703$	−11022.4	−0.591348
$704$	3217.27	0.172238
$705$	0	0
$706$	−23128.1	−1.23291
$707$	−6462.71	−0.343784
$708$	−7188.02	−0.381557
$709$	29650.1	1.57057	0.785284	−	0.619136i	$-0.212517\pi$
$709$	29650.1	1.57057	0.785284	+	0.619136i	$0.212517\pi$
$710$	0	0
$711$	8447.00	0.445551
$712$	−5772.98	−0.303865
$713$	16065.4	0.843832
$714$	−4174.59	−0.218810
$715$	0	0
$716$	−3041.52	−0.158753
$717$	5991.48	0.312072
$718$	−12906.8	−0.670862
$719$	2341.15	0.121433	0.0607164	−	0.998155i	$-0.480661\pi$
$719$	2341.15	0.121433	0.0607164	+	0.998155i	$0.480661\pi$
$720$	0	0
$721$	−3933.42	−0.203174
$722$	−730.813	−0.0376704
$723$	5455.39	0.280620
$724$	6516.88	0.334528
$725$	0	0
$726$	7594.71	0.388245
$727$	−24729.2	−1.26156	−0.630781	−	0.775961i	$-0.717266\pi$
$727$	−24729.2	−1.26156	−0.630781	+	0.775961i	$0.717266\pi$
$728$	1000.97	0.0509591
$729$	11713.9	0.595130
$730$	0	0
$731$	−50082.5	−2.53402
$732$	−6650.77	−0.335819
$733$	18246.1	0.919420	0.459710	−	0.888069i	$-0.347953\pi$
$733$	18246.1	0.919420	0.459710	+	0.888069i	$0.347953\pi$
$734$	10263.5	0.516122
$735$	0	0
$736$	3830.00	0.191815
$737$	25328.0	1.26590
$738$	−4009.59	−0.199993
$739$	34838.2	1.73416	0.867080	−	0.498168i	$-0.165994\pi$
$739$	34838.2	1.73416	0.867080	+	0.498168i	$0.165994\pi$
$740$	0	0
$741$	4823.46	0.239129
$742$	−7695.29	−0.380732
$743$	−12774.2	−0.630739	−0.315370	−	0.948969i	$-0.602128\pi$
$743$	−12774.2	−0.630739	−0.315370	+	0.948969i	$0.602128\pi$
$744$	−3409.24	−0.167996
$745$	0	0
$746$	−13013.5	−0.638684
$747$	10605.6	0.519463
$748$	−18885.4	−0.923155
$749$	7374.11	0.359739
$750$	0	0
$751$	17229.9	0.837189	0.418594	−	0.908173i	$-0.362523\pi$
$751$	17229.9	0.837189	0.418594	+	0.908173i	$0.362523\pi$
$752$	2280.07	0.110566
$753$	−10540.9	−0.510136
$754$	5916.75	0.285776
$755$	0	0
$756$	3904.35	0.187831
$757$	−3671.89	−0.176297	−0.0881486	−	0.996107i	$-0.528095\pi$
$757$	−3671.89	−0.176297	−0.0881486	+	0.996107i	$0.528095\pi$
$758$	−25864.0	−1.23935
$759$	19102.2	0.913527
$760$	0	0
$761$	29675.3	1.41357	0.706786	−	0.707427i	$-0.250144\pi$
$761$	29675.3	1.41357	0.706786	+	0.707427i	$0.250144\pi$
$762$	−1236.53	−0.0587856
$763$	12362.3	0.586560
$764$	−5745.40	−0.272070
$765$	0	0
$766$	26124.0	1.23224
$767$	−10117.0	−0.476278
$768$	−812.769	−0.0381878
$769$	1561.06	0.0732032	0.0366016	−	0.999330i	$-0.488347\pi$
$769$	1561.06	0.0732032	0.0366016	+	0.999330i	$0.488347\pi$
$770$	0	0
$771$	8283.68	0.386938
$772$	10489.5	0.489023
$773$	−5248.94	−0.244232	−0.122116	−	0.992516i	$-0.538968\pi$
$773$	−5248.94	−0.244232	−0.122116	+	0.992516i	$0.538968\pi$
$774$	18045.2	0.838012
$775$	0	0
$776$	−4345.77	−0.201036
$777$	2882.04	0.133066
$778$	24728.7	1.13954
$779$	−10070.9	−0.463192
$780$	0	0
$781$	9001.29	0.412409
$782$	−22482.2	−1.02808
$783$	23078.8	1.05334
$784$	784.000	0.0357143
$785$	0	0
$786$	−11903.2	−0.540169
$787$	−14479.1	−0.655813	−0.327907	−	0.944710i	$-0.606343\pi$
$787$	−14479.1	−0.655813	−0.327907	+	0.944710i	$0.606343\pi$
$788$	21319.7	0.963813
$789$	−3361.74	−0.151687
$790$	0	0
$791$	940.328	0.0422683
$792$	6804.60	0.305291
$793$	−9360.86	−0.419185
$794$	−10390.7	−0.464422
$795$	0	0
$796$	18232.8	0.811867
$797$	34842.2	1.54853	0.774263	−	0.632864i	$-0.218121\pi$
$797$	34842.2	1.54853	0.774263	+	0.632864i	$0.218121\pi$
$798$	3777.95	0.167591
$799$	−13384.0	−0.592607
$800$	0	0
$801$	−12210.0	−0.538599
$802$	18686.1	0.822728
$803$	55594.6	2.44320
$804$	−6398.52	−0.280670
$805$	0	0
$806$	−4798.47	−0.209701
$807$	4989.18	0.217630
$808$	7385.95	0.321580
$809$	608.467	0.0264432	0.0132216	−	0.999913i	$-0.495791\pi$
$809$	608.467	0.0264432	0.0132216	+	0.999913i	$0.495791\pi$
$810$	0	0
$811$	1060.59	0.0459217	0.0229609	−	0.999736i	$-0.492691\pi$
$811$	1060.59	0.0459217	0.0229609	+	0.999736i	$0.492691\pi$
$812$	4634.26	0.200284
$813$	−12596.0	−0.543371
$814$	13038.1	0.561405
$815$	0	0
$816$	4770.96	0.204678
$817$	45324.0	1.94087
$818$	23860.2	1.01987
$819$	2117.06	0.0903249
$820$	0	0
$821$	12614.1	0.536216	0.268108	−	0.963389i	$-0.413602\pi$
$821$	12614.1	0.536216	0.268108	+	0.963389i	$0.413602\pi$
$822$	−2777.88	−0.117871
$823$	−24322.8	−1.03018	−0.515091	−	0.857135i	$-0.672242\pi$
$823$	−24322.8	−1.03018	−0.515091	+	0.857135i	$0.672242\pi$
$824$	4495.34	0.190051
$825$	0	0
$826$	−7924.11	−0.333796
$827$	5878.95	0.247196	0.123598	−	0.992332i	$-0.460557\pi$
$827$	5878.95	0.247196	0.123598	+	0.992332i	$0.460557\pi$
$828$	8100.53	0.339991
$829$	13627.4	0.570927	0.285464	−	0.958390i	$-0.407852\pi$
$829$	13627.4	0.570927	0.285464	+	0.958390i	$0.407852\pi$
$830$	0	0
$831$	−12890.0	−0.538084
$832$	−1143.96	−0.0476679
$833$	−4602.09	−0.191420
$834$	−4620.93	−0.191858
$835$	0	0
$836$	17091.1	0.707066
$837$	−18716.8	−0.772937
$838$	10227.7	0.421612
$839$	−26823.3	−1.10374	−0.551872	−	0.833929i	$-0.686086\pi$
$839$	−26823.3	−1.10374	−0.551872	+	0.833929i	$0.686086\pi$
$840$	0	0
$841$	3004.31	0.123183
$842$	−28510.9	−1.16693
$843$	−27838.9	−1.13739
$844$	−10915.5	−0.445174
$845$	0	0
$846$	4822.39	0.195978
$847$	8372.45	0.339647
$848$	8794.62	0.356142
$849$	−13139.1	−0.531135
$850$	0	0
$851$	15521.2	0.625216
$852$	−2273.96	−0.0914374
$853$	−22815.2	−0.915799	−0.457899	−	0.889004i	$-0.651398\pi$
$853$	−22815.2	−0.915799	−0.457899	+	0.889004i	$0.651398\pi$
$854$	−7331.84	−0.293783
$855$	0	0
$856$	−8427.56	−0.336505
$857$	16137.1	0.643210	0.321605	−	0.946874i	$-0.395778\pi$
$857$	16137.1	0.643210	0.321605	+	0.946874i	$0.395778\pi$
$858$	−5705.53	−0.227021
$859$	−30538.8	−1.21301	−0.606503	−	0.795081i	$-0.707428\pi$
$859$	−30538.8	−1.21301	−0.606503	+	0.795081i	$0.707428\pi$
$860$	0	0
$861$	2633.24	0.104228
$862$	17546.5	0.693314
$863$	−25921.0	−1.02243	−0.511217	−	0.859451i	$-0.670805\pi$
$863$	−25921.0	−1.02243	−0.511217	+	0.859451i	$0.670805\pi$
$864$	−4462.11	−0.175699
$865$	0	0
$866$	5061.84	0.198624
$867$	−12407.4	−0.486018
$868$	−3758.37	−0.146967
$869$	−25096.1	−0.979662
$870$	0	0
$871$	−9005.84	−0.350346
$872$	−14128.3	−0.548677
$873$	−9191.39	−0.356336
$874$	20346.1	0.787432
$875$	0	0
$876$	−14044.7	−0.541695
$877$	−24691.0	−0.950689	−0.475345	−	0.879800i	$-0.657677\pi$
$877$	−24691.0	−0.950689	−0.475345	+	0.879800i	$0.657677\pi$
$878$	27685.2	1.06416
$879$	29361.7	1.12667
$880$	0	0
$881$	−5281.51	−0.201974	−0.100987	−	0.994888i	$-0.532200\pi$
$881$	−5281.51	−0.201974	−0.100987	+	0.994888i	$0.532200\pi$
$882$	1658.18	0.0633035
$883$	41189.3	1.56980	0.784898	−	0.619625i	$-0.212715\pi$
$883$	41189.3	1.56980	0.784898	+	0.619625i	$0.212715\pi$
$884$	6715.06	0.255489
$885$	0	0
$886$	32776.0	1.24281
$887$	29315.1	1.10970	0.554850	−	0.831951i	$-0.312776\pi$
$887$	29315.1	1.10970	0.554850	+	0.831951i	$0.312776\pi$
$888$	−3293.76	−0.124472
$889$	−1363.15	−0.0514271
$890$	0	0
$891$	710.610	0.0267187
$892$	2446.61	0.0918370
$893$	12112.4	0.453891
$894$	−19553.0	−0.731489
$895$	0	0
$896$	−896.000	−0.0334077
$897$	−6792.15	−0.252824
$898$	6330.03	0.235229
$899$	−22215.9	−0.824184
$900$	0	0
$901$	−51624.5	−1.90884
$902$	11912.5	0.439738
$903$	−11850.9	−0.436738
$904$	−1074.66	−0.0395383
$905$	0	0
$906$	11020.5	0.404119
$907$	19000.2	0.695581	0.347791	−	0.937572i	$-0.386932\pi$
$907$	19000.2	0.695581	0.347791	+	0.937572i	$0.386932\pi$
$908$	7213.56	0.263646
$909$	15621.4	0.570000
$910$	0	0
$911$	19449.0	0.707327	0.353664	−	0.935373i	$-0.384936\pi$
$911$	19449.0	0.707327	0.353664	+	0.935373i	$0.384936\pi$
$912$	−4317.66	−0.156767
$913$	−31509.3	−1.14218
$914$	−21371.8	−0.773433
$915$	0	0
$916$	−4768.09	−0.171989
$917$	−13122.1	−0.472553
$918$	26192.7	0.941706
$919$	−25521.1	−0.916064	−0.458032	−	0.888936i	$-0.651445\pi$
$919$	−25521.1	−0.916064	−0.458032	+	0.888936i	$0.651445\pi$
$920$	0	0
$921$	21607.7	0.773070
$922$	28306.2	1.01108
$923$	−3200.57	−0.114137
$924$	−4468.82	−0.159105
$925$	0	0
$926$	−10695.5	−0.379564
$927$	9507.72	0.336866
$928$	−5296.30	−0.187349
$929$	30156.2	1.06501	0.532504	−	0.846428i	$-0.321251\pi$
$929$	30156.2	1.06501	0.532504	+	0.846428i	$0.321251\pi$
$930$	0	0
$931$	4164.83	0.146613
$932$	5744.81	0.201907
$933$	−6036.39	−0.211814
$934$	1727.75	0.0605285
$935$	0	0
$936$	−2419.50	−0.0844912
$937$	−7569.52	−0.263912	−0.131956	−	0.991256i	$-0.542126\pi$
$937$	−7569.52	−0.263912	−0.131956	+	0.991256i	$0.542126\pi$
$938$	−7053.76	−0.245537
$939$	28164.3	0.978814
$940$	0	0
$941$	−38612.4	−1.33765	−0.668824	−	0.743420i	$-0.733202\pi$
$941$	−38612.4	−1.33765	−0.668824	+	0.743420i	$0.733202\pi$
$942$	11837.4	0.409429
$943$	14181.3	0.489719
$944$	9056.13	0.312237
$945$	0	0
$946$	−53612.4	−1.84259
$947$	15811.3	0.542555	0.271278	−	0.962501i	$-0.412554\pi$
$947$	15811.3	0.542555	0.271278	+	0.962501i	$0.412554\pi$
$948$	6339.93	0.217206
$949$	−19767.7	−0.676170
$950$	0	0
$951$	−30322.6	−1.03394
$952$	5259.53	0.179057
$953$	19159.9	0.651259	0.325630	−	0.945497i	$-0.394424\pi$
$953$	19159.9	0.651259	0.325630	+	0.945497i	$0.394424\pi$
$954$	18600.8	0.631261
$955$	0	0
$956$	−7548.61	−0.255376
$957$	−26415.4	−0.892256
$958$	1871.23	0.0631074
$959$	−3062.35	−0.103116
$960$	0	0
$961$	−11774.0	−0.395220
$962$	−4635.92	−0.155372
$963$	−17824.5	−0.596454
$964$	−6873.19	−0.229638
$965$	0	0
$966$	−5319.91	−0.177190
$967$	−32756.8	−1.08933	−0.544667	−	0.838652i	$-0.683344\pi$
$967$	−32756.8	−1.08933	−0.544667	+	0.838652i	$0.683344\pi$
$968$	−9568.51	−0.317710
$969$	25344.7	0.840236
$970$	0	0
$971$	27170.3	0.897977	0.448989	−	0.893537i	$-0.351784\pi$
$971$	27170.3	0.897977	0.448989	+	0.893537i	$0.351784\pi$
$972$	−15239.2	−0.502877
$973$	−5094.14	−0.167842
$974$	9220.06	0.303316
$975$	0	0
$976$	8379.24	0.274808
$977$	−39982.6	−1.30927	−0.654635	−	0.755945i	$-0.727178\pi$
$977$	−39982.6	−1.30927	−0.654635	+	0.755945i	$0.727178\pi$
$978$	16888.7	0.552188
$979$	36275.9	1.18425
$980$	0	0
$981$	−29881.7	−0.972528
$982$	32368.6	1.05186
$983$	24423.6	0.792462	0.396231	−	0.918151i	$-0.370318\pi$
$983$	24423.6	0.792462	0.396231	+	0.918151i	$0.370318\pi$
$984$	−3009.42	−0.0974967
$985$	0	0
$986$	31089.3	1.00414
$987$	−3167.04	−0.102136
$988$	−6077.04	−0.195685
$989$	−63822.9	−2.05202
$990$	0	0
$991$	−44963.2	−1.44127	−0.720637	−	0.693313i	$-0.756150\pi$
$991$	−44963.2	−1.44127	−0.720637	+	0.693313i	$0.756150\pi$
$992$	4295.28	0.137475
$993$	−8142.68	−0.260222
$994$	−2506.83	−0.0799917
$995$	0	0
$996$	7960.09	0.253238
$997$	−39374.4	−1.25075	−0.625376	−	0.780323i	$-0.715055\pi$
$997$	−39374.4	−1.25075	−0.625376	+	0.780323i	$0.715055\pi$
$998$	−1554.10	−0.0492928
$999$	−18082.8	−0.572687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.a.w.1.2		3
5.2	odd	4		70.4.c.b.29.2	✓	6
5.3	odd	4		70.4.c.b.29.5	yes	6
5.4	even	2		350.4.a.x.1.2		3
7.6	odd	2		2450.4.a.cf.1.2		3
15.2	even	4		630.4.g.j.379.4		6
15.8	even	4		630.4.g.j.379.1		6
20.3	even	4		560.4.g.e.449.4		6
20.7	even	4		560.4.g.e.449.3		6
35.13	even	4		490.4.c.c.99.5		6
35.27	even	4		490.4.c.c.99.2		6
35.34	odd	2		2450.4.a.cg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.b.29.2	✓	6	5.2	odd	4
70.4.c.b.29.5	yes	6	5.3	odd	4
350.4.a.w.1.2		3	1.1	even	1	trivial
350.4.a.x.1.2		3	5.4	even	2
490.4.c.c.99.2		6	35.27	even	4
490.4.c.c.99.5		6	35.13	even	4
560.4.g.e.449.3		6	20.7	even	4
560.4.g.e.449.4		6	20.3	even	4
630.4.g.j.379.1		6	15.8	even	4
630.4.g.j.379.4		6	15.2	even	4
2450.4.a.cf.1.2		3	7.6	odd	2
2450.4.a.cg.1.2		3	35.34	odd	2

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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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.17488 q^{3} +4.00000 q^{4} +6.34975 q^{6} +7.00000 q^{7} -8.00000 q^{8} -16.9202 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.17488 q^{3} +4.00000 q^{4} +6.34975 q^{6} +7.00000 q^{7} -8.00000 q^{8} -16.9202 q^{9} +50.2699 q^{11} -12.6995 q^{12} -17.8744 q^{13} -14.0000 q^{14} +16.0000 q^{16} -93.9202 q^{17} +33.8403 q^{18} +84.9965 q^{19} -22.2241 q^{21} -100.540 q^{22} -119.688 q^{23} +25.3990 q^{24} +35.7488 q^{26} +139.441 q^{27} +28.0000 q^{28} +165.509 q^{29} -134.227 q^{31} -32.0000 q^{32} -159.601 q^{33} +187.840 q^{34} -67.6806 q^{36} -129.681 q^{37} -169.993 q^{38} +56.7490 q^{39} -118.486 q^{41} +44.4483 q^{42} +533.246 q^{43} +201.080 q^{44} +239.375 q^{46} +142.504 q^{47} -50.7980 q^{48} +49.0000 q^{49} +298.185 q^{51} -71.4975 q^{52} +549.664 q^{53} -278.882 q^{54} -56.0000 q^{56} -269.853 q^{57} -331.018 q^{58} +566.008 q^{59} +523.703 q^{61} +268.455 q^{62} -118.441 q^{63} +64.0000 q^{64} +319.202 q^{66} +503.840 q^{67} -375.681 q^{68} +379.993 q^{69} +179.059 q^{71} +135.361 q^{72} +1105.92 q^{73} +259.361 q^{74} +339.986 q^{76} +351.889 q^{77} -113.498 q^{78} -499.227 q^{79} +14.1359 q^{81} +236.971 q^{82} -626.803 q^{83} -88.8966 q^{84} -1066.49 q^{86} -525.471 q^{87} -402.159 q^{88} +721.623 q^{89} -125.121 q^{91} -478.750 q^{92} +426.156 q^{93} -285.009 q^{94} +101.596 q^{96} +543.221 q^{97} -98.0000 q^{98} -850.575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 7 q^{3} + 12 q^{4} + 14 q^{6} + 21 q^{7} - 24 q^{8} + 76 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - 7 * q^3 + 12 * q^4 + 14 * q^6 + 21 * q^7 - 24 * q^8 + 76 * q^9	\( 3 q - 6 q^{2} - 7 q^{3} + 12 q^{4} + 14 q^{6} + 21 q^{7} - 24 q^{8} + 76 q^{9} + 19 q^{11} - 28 q^{12} - 41 q^{13} - 42 q^{14} + 48 q^{16} - 155 q^{17} - 152 q^{18} + 156 q^{19} - 49 q^{21} - 38 q^{22} - 50 q^{23} + 56 q^{24} + 82 q^{26} - 469 q^{27} + 84 q^{28} + 91 q^{29} + 170 q^{31} - 96 q^{32} + 155 q^{33} + 310 q^{34} + 304 q^{36} + 118 q^{37} - 312 q^{38} + 799 q^{39} - 6 q^{41} + 98 q^{42} + 216 q^{43} + 76 q^{44} + 100 q^{46} - 79 q^{47} - 112 q^{48} + 147 q^{49} - 119 q^{51} - 164 q^{52} + 742 q^{53} + 938 q^{54} - 168 q^{56} + 1664 q^{57} - 182 q^{58} + 590 q^{59} + 352 q^{61} - 340 q^{62} + 532 q^{63} + 192 q^{64} - 310 q^{66} + 1258 q^{67} - 620 q^{68} + 2250 q^{69} + 724 q^{71} - 608 q^{72} + 1326 q^{73} - 236 q^{74} + 624 q^{76} + 133 q^{77} - 1598 q^{78} + 1037 q^{79} + 2407 q^{81} + 12 q^{82} + 580 q^{83} - 196 q^{84} - 432 q^{86} - 177 q^{87} - 152 q^{88} - 1048 q^{89} - 287 q^{91} - 200 q^{92} + 1338 q^{93} + 158 q^{94} + 224 q^{96} + 2821 q^{97} - 294 q^{98} - 3278 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 7 * q^3 + 12 * q^4 + 14 * q^6 + 21 * q^7 - 24 * q^8 + 76 * q^9 + 19 * q^11 - 28 * q^12 - 41 * q^13 - 42 * q^14 + 48 * q^16 - 155 * q^17 - 152 * q^18 + 156 * q^19 - 49 * q^21 - 38 * q^22 - 50 * q^23 + 56 * q^24 + 82 * q^26 - 469 * q^27 + 84 * q^28 + 91 * q^29 + 170 * q^31 - 96 * q^32 + 155 * q^33 + 310 * q^34 + 304 * q^36 + 118 * q^37 - 312 * q^38 + 799 * q^39 - 6 * q^41 + 98 * q^42 + 216 * q^43 + 76 * q^44 + 100 * q^46 - 79 * q^47 - 112 * q^48 + 147 * q^49 - 119 * q^51 - 164 * q^52 + 742 * q^53 + 938 * q^54 - 168 * q^56 + 1664 * q^57 - 182 * q^58 + 590 * q^59 + 352 * q^61 - 340 * q^62 + 532 * q^63 + 192 * q^64 - 310 * q^66 + 1258 * q^67 - 620 * q^68 + 2250 * q^69 + 724 * q^71 - 608 * q^72 + 1326 * q^73 - 236 * q^74 + 624 * q^76 + 133 * q^77 - 1598 * q^78 + 1037 * q^79 + 2407 * q^81 + 12 * q^82 + 580 * q^83 - 196 * q^84 - 432 * q^86 - 177 * q^87 - 152 * q^88 - 1048 * q^89 - 287 * q^91 - 200 * q^92 + 1338 * q^93 + 158 * q^94 + 224 * q^96 + 2821 * q^97 - 294 * q^98 - 3278 * q^99

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