LMFDB - Embedded newform 175.4.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, 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("175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 32x^{2} - 35x + 120 $ x^4 - 32x^2 - 35x + 120
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.50478$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.504784 q^{2} -4.26379 q^{3} -7.74519 q^{4} -2.15229 q^{6} -7.00000 q^{7} -7.94792 q^{8} -8.82008 q^{9} +O(q^{10})$	\(q+0.504784 q^{2} -4.26379 q^{3} -7.74519 q^{4} -2.15229 q^{6} -7.00000 q^{7} -7.94792 q^{8} -8.82008 q^{9} +54.8800 q^{11} +33.0239 q^{12} -16.0073 q^{13} -3.53349 q^{14} +57.9496 q^{16} +0.422056 q^{17} -4.45223 q^{18} +127.501 q^{19} +29.8465 q^{21} +27.7025 q^{22} -51.1101 q^{23} +33.8883 q^{24} -8.08024 q^{26} +152.729 q^{27} +54.2164 q^{28} +41.4750 q^{29} +192.354 q^{31} +92.8353 q^{32} -233.997 q^{33} +0.213047 q^{34} +68.3132 q^{36} +189.232 q^{37} +64.3605 q^{38} +68.2519 q^{39} -76.3187 q^{41} +15.0660 q^{42} -294.499 q^{43} -425.056 q^{44} -25.7996 q^{46} -540.297 q^{47} -247.085 q^{48} +49.0000 q^{49} -1.79956 q^{51} +123.980 q^{52} +661.316 q^{53} +77.0953 q^{54} +55.6354 q^{56} -543.639 q^{57} +20.9359 q^{58} +410.312 q^{59} +46.0495 q^{61} +97.0974 q^{62} +61.7405 q^{63} -416.735 q^{64} -118.118 q^{66} -10.4074 q^{67} -3.26890 q^{68} +217.923 q^{69} -491.117 q^{71} +70.1012 q^{72} +814.540 q^{73} +95.5215 q^{74} -987.522 q^{76} -384.160 q^{77} +34.4525 q^{78} -858.725 q^{79} -413.064 q^{81} -38.5244 q^{82} +1055.80 q^{83} -231.167 q^{84} -148.658 q^{86} -176.841 q^{87} -436.182 q^{88} +341.567 q^{89} +112.051 q^{91} +395.858 q^{92} -820.159 q^{93} -272.733 q^{94} -395.831 q^{96} +1417.21 q^{97} +24.7344 q^{98} -484.046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 3 q^{3} + 36 q^{4} + q^{6} - 28 q^{7} - 27 q^{8} + 61 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 3 * q^3 + 36 * q^4 + q^6 - 28 * q^7 - 27 * q^8 + 61 * q^9	\( 4 q - 4 q^{2} + 3 q^{3} + 36 q^{4} + q^{6} - 28 q^{7} - 27 q^{8} + 61 q^{9} + 100 q^{11} + 165 q^{12} - 44 q^{13} + 28 q^{14} + 160 q^{16} + 53 q^{17} - 433 q^{18} - 29 q^{19} - 21 q^{21} + 152 q^{22} - 295 q^{23} - 21 q^{24} + 700 q^{26} + 441 q^{27} - 252 q^{28} + 129 q^{29} + 114 q^{31} + 310 q^{32} + 865 q^{33} + 203 q^{34} + 1101 q^{36} - 403 q^{37} - 555 q^{38} + 674 q^{39} + 671 q^{41} - 7 q^{42} + 411 q^{43} + 438 q^{44} - 997 q^{46} + 8 q^{47} + 523 q^{48} + 196 q^{49} - 885 q^{51} - 74 q^{52} - 90 q^{53} - 2777 q^{54} + 189 q^{56} - 233 q^{57} - 673 q^{58} + 1018 q^{59} + 50 q^{61} + 1626 q^{62} - 427 q^{63} - 2421 q^{64} - 3841 q^{66} - 424 q^{67} + 617 q^{68} + 1080 q^{69} + 215 q^{71} - 2940 q^{72} + 1207 q^{73} + 623 q^{74} - 3257 q^{76} - 700 q^{77} - 278 q^{78} - 951 q^{79} + 28 q^{81} - 1695 q^{82} + 3035 q^{83} - 1155 q^{84} - 99 q^{86} - 2210 q^{87} - 163 q^{88} + 2819 q^{89} + 308 q^{91} - 3073 q^{92} + 852 q^{93} - 3056 q^{94} - 1345 q^{96} + 1100 q^{97} - 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 + 36 * q^4 + q^6 - 28 * q^7 - 27 * q^8 + 61 * q^9 + 100 * q^11 + 165 * q^12 - 44 * q^13 + 28 * q^14 + 160 * q^16 + 53 * q^17 - 433 * q^18 - 29 * q^19 - 21 * q^21 + 152 * q^22 - 295 * q^23 - 21 * q^24 + 700 * q^26 + 441 * q^27 - 252 * q^28 + 129 * q^29 + 114 * q^31 + 310 * q^32 + 865 * q^33 + 203 * q^34 + 1101 * q^36 - 403 * q^37 - 555 * q^38 + 674 * q^39 + 671 * q^41 - 7 * q^42 + 411 * q^43 + 438 * q^44 - 997 * q^46 + 8 * q^47 + 523 * q^48 + 196 * q^49 - 885 * q^51 - 74 * q^52 - 90 * q^53 - 2777 * q^54 + 189 * q^56 - 233 * q^57 - 673 * q^58 + 1018 * q^59 + 50 * q^61 + 1626 * q^62 - 427 * q^63 - 2421 * q^64 - 3841 * q^66 - 424 * q^67 + 617 * q^68 + 1080 * q^69 + 215 * q^71 - 2940 * q^72 + 1207 * q^73 + 623 * q^74 - 3257 * q^76 - 700 * q^77 - 278 * q^78 - 951 * q^79 + 28 * q^81 - 1695 * q^82 + 3035 * q^83 - 1155 * q^84 - 99 * q^86 - 2210 * q^87 - 163 * q^88 + 2819 * q^89 + 308 * q^91 - 3073 * q^92 + 852 * q^93 - 3056 * q^94 - 1345 * q^96 + 1100 * q^97 - 196 * q^98 + 2383 * 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 $

$2$	0.504784	0.178468	0.0892340	−	0.996011i	$-0.471558\pi$
$2$	0.504784	0.178468	0.0892340	+	0.996011i	$0.471558\pi$
$3$	−4.26379	−0.820567	−0.410284	−	0.911958i	$-0.634570\pi$
$3$	−4.26379	−0.820567	−0.410284	+	0.911958i	$0.634570\pi$
$4$	−7.74519	−0.968149
$5$	0	0
$5$	0	0
$6$	−2.15229	−0.146445
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−7.94792	−0.351252
$9$	−8.82008	−0.326670
$10$	0	0
$11$	54.8800	1.50427	0.752134	−	0.659010i	$-0.229025\pi$
$11$	54.8800	1.50427	0.752134	+	0.659010i	$0.229025\pi$
$12$	33.0239	0.794431
$13$	−16.0073	−0.341510	−0.170755	−	0.985313i	$-0.554621\pi$
$13$	−16.0073	−0.341510	−0.170755	+	0.985313i	$0.554621\pi$
$14$	−3.53349	−0.0674546
$15$	0	0
$16$	57.9496	0.905462
$17$	0.422056	0.00602139	0.00301069	−	0.999995i	$-0.499042\pi$
$17$	0.422056	0.00602139	0.00301069	+	0.999995i	$0.499042\pi$
$18$	−4.45223	−0.0583000
$19$	127.501	1.53952	0.769758	−	0.638336i	$-0.220377\pi$
$19$	127.501	1.53952	0.769758	+	0.638336i	$0.220377\pi$
$20$	0	0
$21$	29.8465	0.310145
$22$	27.7025	0.268464
$23$	−51.1101	−0.463357	−0.231678	−	0.972792i	$-0.574422\pi$
$23$	−51.1101	−0.463357	−0.231678	+	0.972792i	$0.574422\pi$
$24$	33.8883	0.288226
$25$	0	0
$26$	−8.08024	−0.0609487
$27$	152.729	1.08862
$28$	54.2164	0.365926
$29$	41.4750	0.265576	0.132788	−	0.991144i	$-0.457607\pi$
$29$	41.4750	0.265576	0.132788	+	0.991144i	$0.457607\pi$
$30$	0	0
$31$	192.354	1.11445	0.557224	−	0.830362i	$-0.311866\pi$
$31$	192.354	1.11445	0.557224	+	0.830362i	$0.311866\pi$
$32$	92.8353	0.512848
$33$	−233.997	−1.23435
$34$	0.213047	0.00107462
$35$	0	0
$36$	68.3132	0.316265
$37$	189.232	0.840801	0.420400	−	0.907339i	$-0.361890\pi$
$37$	189.232	0.840801	0.420400	+	0.907339i	$0.361890\pi$
$38$	64.3605	0.274754
$39$	68.2519	0.280232
$40$	0	0
$41$	−76.3187	−0.290707	−0.145353	−	0.989380i	$-0.546432\pi$
$41$	−76.3187	−0.290707	−0.145353	+	0.989380i	$0.546432\pi$
$42$	15.0660	0.0553510
$43$	−294.499	−1.04443	−0.522216	−	0.852813i	$-0.674895\pi$
$43$	−294.499	−1.04443	−0.522216	+	0.852813i	$0.674895\pi$
$44$	−425.056	−1.45636
$45$	0	0
$46$	−25.7996	−0.0826943
$47$	−540.297	−1.67682	−0.838408	−	0.545043i	$-0.816513\pi$
$47$	−540.297	−1.67682	−0.838408	+	0.545043i	$0.816513\pi$
$48$	−247.085	−0.742992
$49$	49.0000	0.142857
$50$	0	0
$51$	−1.79956	−0.00494095
$52$	123.980	0.330633
$53$	661.316	1.71394	0.856969	−	0.515368i	$-0.172345\pi$
$53$	661.316	1.71394	0.856969	+	0.515368i	$0.172345\pi$
$54$	77.0953	0.194284
$55$	0	0
$56$	55.6354	0.132761
$57$	−543.639	−1.26328
$58$	20.9359	0.0473969
$59$	410.312	0.905390	0.452695	−	0.891665i	$-0.350463\pi$
$59$	410.312	0.905390	0.452695	+	0.891665i	$0.350463\pi$
$60$	0	0
$61$	46.0495	0.0966563	0.0483281	−	0.998832i	$-0.484611\pi$
$61$	46.0495	0.0966563	0.0483281	+	0.998832i	$0.484611\pi$
$62$	97.0974	0.198893
$63$	61.7405	0.123469
$64$	−416.735	−0.813935
$65$	0	0
$66$	−118.118	−0.220292
$67$	−10.4074	−0.0189771	−0.00948854	−	0.999955i	$-0.503020\pi$
$67$	−10.4074	−0.0189771	−0.00948854	+	0.999955i	$0.503020\pi$
$68$	−3.26890	−0.00582960
$69$	217.923	0.380215
$70$	0	0
$71$	−491.117	−0.820913	−0.410456	−	0.911880i	$-0.634631\pi$
$71$	−491.117	−0.820913	−0.410456	+	0.911880i	$0.634631\pi$
$72$	70.1012	0.114743
$73$	814.540	1.30595	0.652977	−	0.757378i	$-0.273520\pi$
$73$	814.540	1.30595	0.652977	+	0.757378i	$0.273520\pi$
$74$	95.5215	0.150056
$75$	0	0
$76$	−987.522	−1.49048
$77$	−384.160	−0.568560
$78$	34.4525	0.0500125
$79$	−858.725	−1.22296	−0.611482	−	0.791258i	$-0.709426\pi$
$79$	−858.725	−1.22296	−0.611482	+	0.791258i	$0.709426\pi$
$80$	0	0
$81$	−413.064	−0.566617
$82$	−38.5244	−0.0518818
$83$	1055.80	1.39626	0.698129	−	0.715972i	$-0.254016\pi$
$83$	1055.80	1.39626	0.698129	+	0.715972i	$0.254016\pi$
$84$	−231.167	−0.300267
$85$	0	0
$86$	−148.658	−0.186398
$87$	−176.841	−0.217923
$88$	−436.182	−0.528376
$89$	341.567	0.406809	0.203405	−	0.979095i	$-0.434799\pi$
$89$	341.567	0.406809	0.203405	+	0.979095i	$0.434799\pi$
$90$	0	0
$91$	112.051	0.129079
$92$	395.858	0.448598
$93$	−820.159	−0.914479
$94$	−272.733	−0.299258
$95$	0	0
$96$	−395.831	−0.420826
$97$	1417.21	1.48346	0.741731	−	0.670697i	$-0.234005\pi$
$97$	1417.21	1.48346	0.741731	+	0.670697i	$0.234005\pi$
$98$	24.7344	0.0254954
$99$	−484.046	−0.491398
$100$	0	0
$101$	−121.051	−0.119258	−0.0596289	−	0.998221i	$-0.518992\pi$
$101$	−121.051	−0.119258	−0.0596289	+	0.998221i	$0.518992\pi$
$102$	−0.908388	−0.000881802 0
$103$	655.594	0.627161	0.313581	−	0.949562i	$-0.398471\pi$
$103$	655.594	0.627161	0.313581	+	0.949562i	$0.398471\pi$
$104$	127.225	0.119956
$105$	0	0
$106$	333.821	0.305883
$107$	−2069.81	−1.87006	−0.935031	−	0.354567i	$-0.884628\pi$
$107$	−2069.81	−1.87006	−0.935031	+	0.354567i	$0.884628\pi$
$108$	−1182.92	−1.05395
$109$	904.218	0.794573	0.397286	−	0.917695i	$-0.369952\pi$
$109$	904.218	0.794573	0.397286	+	0.917695i	$0.369952\pi$
$110$	0	0
$111$	−806.848	−0.689934
$112$	−405.647	−0.342232
$113$	843.350	0.702086	0.351043	−	0.936359i	$-0.385827\pi$
$113$	843.350	0.702086	0.351043	+	0.936359i	$0.385827\pi$
$114$	−274.420	−0.225454
$115$	0	0
$116$	−321.232	−0.257117
$117$	141.186	0.111561
$118$	207.119	0.161583
$119$	−2.95439	−0.00227587
$120$	0	0
$121$	1680.81	1.26282
$122$	23.2450	0.0172501
$123$	325.407	0.238544
$124$	−1489.82	−1.07895
$125$	0	0
$126$	31.1656	0.0220353
$127$	−2030.50	−1.41872	−0.709362	−	0.704845i	$-0.751017\pi$
$127$	−2030.50	−1.41872	−0.709362	+	0.704845i	$0.751017\pi$
$128$	−953.043	−0.658109
$129$	1255.68	0.857027
$130$	0	0
$131$	2872.47	1.91579	0.957897	−	0.287113i	$-0.0926954\pi$
$131$	2872.47	1.91579	0.957897	+	0.287113i	$0.0926954\pi$
$132$	1812.35	1.19504
$133$	−892.509	−0.581882
$134$	−5.25348	−0.00338680
$135$	0	0
$136$	−3.35446	−0.00211502
$137$	1621.62	1.01127	0.505636	−	0.862747i	$-0.331258\pi$
$137$	1621.62	1.01127	0.505636	+	0.862747i	$0.331258\pi$
$138$	110.004	0.0678562
$139$	2617.72	1.59735	0.798677	−	0.601760i	$-0.205534\pi$
$139$	2617.72	1.59735	0.798677	+	0.601760i	$0.205534\pi$
$140$	0	0
$141$	2303.71	1.37594
$142$	−247.908	−0.146507
$143$	−878.482	−0.513723
$144$	−511.120	−0.295787
$145$	0	0
$146$	411.166	0.233071
$147$	−208.926	−0.117224
$148$	−1465.64	−0.814021
$149$	2252.63	1.23854	0.619270	−	0.785178i	$-0.287429\pi$
$149$	2252.63	1.23854	0.619270	+	0.785178i	$0.287429\pi$
$150$	0	0
$151$	−1849.61	−0.996813	−0.498407	−	0.866943i	$-0.666081\pi$
$151$	−1849.61	−0.996813	−0.498407	+	0.866943i	$0.666081\pi$
$152$	−1013.37	−0.540757
$153$	−3.72257	−0.00196700
$154$	−193.918	−0.101470
$155$	0	0
$156$	−528.624	−0.271307
$157$	3337.59	1.69661	0.848307	−	0.529505i	$-0.177622\pi$
$157$	3337.59	1.69661	0.848307	+	0.529505i	$0.177622\pi$
$158$	−433.471	−0.218260
$159$	−2819.71	−1.40640
$160$	0	0
$161$	357.771	0.175132
$162$	−208.508	−0.101123
$163$	471.099	0.226376	0.113188	−	0.993574i	$-0.463894\pi$
$163$	471.099	0.226376	0.113188	+	0.993574i	$0.463894\pi$
$164$	591.103	0.281447
$165$	0	0
$166$	532.952	0.249187
$167$	3676.72	1.70367	0.851836	−	0.523809i	$-0.175489\pi$
$167$	3676.72	1.70367	0.851836	+	0.523809i	$0.175489\pi$
$168$	−237.218	−0.108939
$169$	−1940.77	−0.883371
$170$	0	0
$171$	−1124.57	−0.502913
$172$	2280.95	1.01117
$173$	−1009.11	−0.443475	−0.221737	−	0.975106i	$-0.571173\pi$
$173$	−1009.11	−0.443475	−0.221737	+	0.975106i	$0.571173\pi$
$174$	−89.2663	−0.0388923
$175$	0	0
$176$	3180.27	1.36206
$177$	−1749.48	−0.742934
$178$	172.417	0.0726024
$179$	3201.27	1.33673	0.668364	−	0.743835i	$-0.266995\pi$
$179$	3201.27	1.33673	0.668364	+	0.743835i	$0.266995\pi$
$180$	0	0
$181$	−1970.14	−0.809056	−0.404528	−	0.914526i	$-0.632564\pi$
$181$	−1970.14	−0.809056	−0.404528	+	0.914526i	$0.632564\pi$
$182$	56.5617	0.0230364
$183$	−196.345	−0.0793130
$184$	406.219	0.162755
$185$	0	0
$186$	−414.003	−0.163205
$187$	23.1624	0.00905778
$188$	4184.70	1.62341
$189$	−1069.11	−0.411460
$190$	0	0
$191$	3953.39	1.49768	0.748842	−	0.662749i	$-0.230610\pi$
$191$	3953.39	1.49768	0.748842	+	0.662749i	$0.230610\pi$
$192$	1776.87	0.667888
$193$	−2425.45	−0.904598	−0.452299	−	0.891866i	$-0.649396\pi$
$193$	−2425.45	−0.904598	−0.452299	+	0.891866i	$0.649396\pi$
$194$	715.385	0.264751
$195$	0	0
$196$	−379.514	−0.138307
$197$	−3126.50	−1.13073	−0.565366	−	0.824840i	$-0.691265\pi$
$197$	−3126.50	−1.13073	−0.565366	+	0.824840i	$0.691265\pi$
$198$	−244.338	−0.0876989
$199$	−3566.13	−1.27033	−0.635166	−	0.772376i	$-0.719068\pi$
$199$	−3566.13	−1.27033	−0.635166	+	0.772376i	$0.719068\pi$
$200$	0	0
$201$	44.3749	0.0155720
$202$	−61.1046	−0.0212837
$203$	−290.325	−0.100378
$204$	13.9379	0.00478358
$205$	0	0
$206$	330.933	0.111928
$207$	450.795	0.151364
$208$	−927.618	−0.309225
$209$	6997.27	2.31584
$210$	0	0
$211$	−3699.18	−1.20693	−0.603465	−	0.797389i	$-0.706214\pi$
$211$	−3699.18	−1.20693	−0.603465	+	0.797389i	$0.706214\pi$
$212$	−5122.02	−1.65935
$213$	2094.02	0.673614
$214$	−1044.81	−0.333746
$215$	0	0
$216$	−1213.88	−0.382380
$217$	−1346.48	−0.421222
$218$	456.435	0.141806
$219$	−3473.03	−1.07162
$220$	0	0
$221$	−6.75599	−0.00205637
$222$	−407.284	−0.123131
$223$	102.041	0.0306419	0.0153210	−	0.999883i	$-0.495123\pi$
$223$	102.041	0.0306419	0.0153210	+	0.999883i	$0.495123\pi$
$224$	−649.847	−0.193838
$225$	0	0
$226$	425.709	0.125300
$227$	−5739.91	−1.67829	−0.839144	−	0.543909i	$-0.816943\pi$
$227$	−5739.91	−1.67829	−0.839144	+	0.543909i	$0.816943\pi$
$228$	4210.59	1.22304
$229$	−843.125	−0.243298	−0.121649	−	0.992573i	$-0.538818\pi$
$229$	−843.125	−0.243298	−0.121649	+	0.992573i	$0.538818\pi$
$230$	0	0
$231$	1637.98	0.466541
$232$	−329.640	−0.0932841
$233$	2017.65	0.567300	0.283650	−	0.958928i	$-0.408455\pi$
$233$	2017.65	0.567300	0.283650	+	0.958928i	$0.408455\pi$
$234$	71.2683	0.0199101
$235$	0	0
$236$	−3177.94	−0.876553
$237$	3661.43	1.00352
$238$	−1.49133	−0.000406170 0
$239$	243.685	0.0659526	0.0329763	−	0.999456i	$-0.489501\pi$
$239$	243.685	0.0659526	0.0329763	+	0.999456i	$0.489501\pi$
$240$	0	0
$241$	−3060.58	−0.818048	−0.409024	−	0.912524i	$-0.634131\pi$
$241$	−3060.58	−0.818048	−0.409024	+	0.912524i	$0.634131\pi$
$242$	848.448	0.225373
$243$	−2362.47	−0.623674
$244$	−356.662	−0.0935777
$245$	0	0
$246$	164.260	0.0425725
$247$	−2040.95	−0.525760
$248$	−1528.82	−0.391452
$249$	−4501.72	−1.14572
$250$	0	0
$251$	−6594.14	−1.65824	−0.829120	−	0.559070i	$-0.811158\pi$
$251$	−6594.14	−1.65824	−0.829120	+	0.559070i	$0.811158\pi$
$252$	−478.192	−0.119537
$253$	−2804.92	−0.697012
$254$	−1024.96	−0.253197
$255$	0	0
$256$	2852.80	0.696484
$257$	−512.646	−0.124428	−0.0622139	−	0.998063i	$-0.519816\pi$
$257$	−512.646	−0.124428	−0.0622139	+	0.998063i	$0.519816\pi$
$258$	633.847	0.152952
$259$	−1324.63	−0.317793
$260$	0	0
$261$	−365.813	−0.0867557
$262$	1449.98	0.341908
$263$	3560.04	0.834681	0.417341	−	0.908750i	$-0.362962\pi$
$263$	3560.04	0.834681	0.417341	+	0.908750i	$0.362962\pi$
$264$	1859.79	0.433568
$265$	0	0
$266$	−450.524	−0.103847
$267$	−1456.37	−0.333814
$268$	80.6072	0.0183726
$269$	−549.744	−0.124604	−0.0623020	−	0.998057i	$-0.519844\pi$
$269$	−549.744	−0.124604	−0.0623020	+	0.998057i	$0.519844\pi$
$270$	0	0
$271$	−3944.91	−0.884267	−0.442134	−	0.896949i	$-0.645778\pi$
$271$	−3944.91	−0.884267	−0.442134	+	0.896949i	$0.645778\pi$
$272$	24.4580	0.00545214
$273$	−477.764	−0.105918
$274$	818.567	0.180480
$275$	0	0
$276$	−1687.86	−0.368105
$277$	1254.67	0.272150	0.136075	−	0.990699i	$-0.456551\pi$
$277$	1254.67	0.272150	0.136075	+	0.990699i	$0.456551\pi$
$278$	1321.38	0.285077
$279$	−1696.58	−0.364056
$280$	0	0
$281$	−681.496	−0.144679	−0.0723393	−	0.997380i	$-0.523046\pi$
$281$	−681.496	−0.144679	−0.0723393	+	0.997380i	$0.523046\pi$
$282$	1162.88	0.245561
$283$	5946.88	1.24914	0.624568	−	0.780970i	$-0.285275\pi$
$283$	5946.88	1.24914	0.624568	+	0.780970i	$0.285275\pi$
$284$	3803.79	0.794766
$285$	0	0
$286$	−443.444	−0.0916831
$287$	534.231	0.109877
$288$	−818.815	−0.167532
$289$	−4912.82	−0.999964
$290$	0	0
$291$	−6042.69	−1.21728
$292$	−6308.77	−1.26436
$293$	−2171.03	−0.432877	−0.216438	−	0.976296i	$-0.569444\pi$
$293$	−2171.03	−0.432877	−0.216438	+	0.976296i	$0.569444\pi$
$294$	−105.462	−0.0209207
$295$	0	0
$296$	−1504.00	−0.295333
$297$	8381.79	1.63758
$298$	1137.09	0.221040
$299$	818.137	0.158241
$300$	0	0
$301$	2061.49	0.394759
$302$	−933.651	−0.177899
$303$	516.137	0.0978590
$304$	7388.64	1.39397
$305$	0	0
$306$	−1.87909	−0.000351047 0
$307$	3644.59	0.677549	0.338775	−	0.940868i	$-0.389988\pi$
$307$	3644.59	0.677549	0.338775	+	0.940868i	$0.389988\pi$
$308$	2975.39	0.550451
$309$	−2795.32	−0.514628
$310$	0	0
$311$	2584.19	0.471177	0.235589	−	0.971853i	$-0.424298\pi$
$311$	2584.19	0.471177	0.235589	+	0.971853i	$0.424298\pi$
$312$	−542.461	−0.0984320
$313$	−6693.63	−1.20878	−0.604388	−	0.796690i	$-0.706582\pi$
$313$	−6693.63	−1.20878	−0.604388	+	0.796690i	$0.706582\pi$
$314$	1684.76	0.302791
$315$	0	0
$316$	6650.99	1.18401
$317$	3843.36	0.680962	0.340481	−	0.940251i	$-0.389410\pi$
$317$	3843.36	0.680962	0.340481	+	0.940251i	$0.389410\pi$
$318$	−1423.35	−0.250998
$319$	2276.15	0.399498
$320$	0	0
$321$	8825.26	1.53451
$322$	180.597	0.0312555
$323$	53.8126	0.00927002
$324$	3199.26	0.548570
$325$	0	0
$326$	237.803	0.0404009
$327$	−3855.40	−0.652000
$328$	606.575	0.102111
$329$	3782.08	0.633777
$330$	0	0
$331$	−821.922	−0.136486	−0.0682431	−	0.997669i	$-0.521739\pi$
$331$	−821.922	−0.136486	−0.0682431	+	0.997669i	$0.521739\pi$
$332$	−8177.39	−1.35179
$333$	−1669.05	−0.274664
$334$	1855.95	0.304051
$335$	0	0
$336$	1729.59	0.280825
$337$	−1032.55	−0.166904	−0.0834520	−	0.996512i	$-0.526595\pi$
$337$	−1032.55	−0.166904	−0.0834520	+	0.996512i	$0.526595\pi$
$338$	−979.667	−0.157653
$339$	−3595.87	−0.576108
$340$	0	0
$341$	10556.4	1.67643
$342$	−567.665	−0.0897538
$343$	−343.000	−0.0539949
$344$	2340.65	0.366859
$345$	0	0
$346$	−509.382	−0.0791461
$347$	2587.70	0.400332	0.200166	−	0.979762i	$-0.435852\pi$
$347$	2587.70	0.400332	0.200166	+	0.979762i	$0.435852\pi$
$348$	1369.67	0.210982
$349$	−8454.24	−1.29669	−0.648345	−	0.761346i	$-0.724539\pi$
$349$	−8454.24	−1.29669	−0.648345	+	0.761346i	$0.724539\pi$
$350$	0	0
$351$	−2444.79	−0.371776
$352$	5094.80	0.771460
$353$	4129.63	0.622658	0.311329	−	0.950302i	$-0.399226\pi$
$353$	4129.63	0.622658	0.311329	+	0.950302i	$0.399226\pi$
$354$	−883.111	−0.132590
$355$	0	0
$356$	−2645.50	−0.393852
$357$	12.5969	0.00186750
$358$	1615.95	0.238563
$359$	−4536.69	−0.666957	−0.333478	−	0.942758i	$-0.608222\pi$
$359$	−4536.69	−0.666957	−0.333478	+	0.942758i	$0.608222\pi$
$360$	0	0
$361$	9397.56	1.37011
$362$	−994.492	−0.144390
$363$	−7166.65	−1.03623
$364$	−867.859	−0.124968
$365$	0	0
$366$	−99.1120	−0.0141548
$367$	−1643.00	−0.233689	−0.116844	−	0.993150i	$-0.537278\pi$
$367$	−1643.00	−0.233689	−0.116844	+	0.993150i	$0.537278\pi$
$368$	−2961.81	−0.419552
$369$	673.137	0.0949650
$370$	0	0
$371$	−4629.21	−0.647808
$372$	6352.29	0.885352
$373$	−9019.53	−1.25205	−0.626024	−	0.779804i	$-0.715319\pi$
$373$	−9019.53	−1.25205	−0.626024	+	0.779804i	$0.715319\pi$
$374$	11.6920	0.00161652
$375$	0	0
$376$	4294.23	0.588984
$377$	−663.904	−0.0906971
$378$	−539.667	−0.0734325
$379$	−2463.63	−0.333900	−0.166950	−	0.985965i	$-0.553392\pi$
$379$	−2463.63	−0.333900	−0.166950	+	0.985965i	$0.553392\pi$
$380$	0	0
$381$	8657.63	1.16416
$382$	1995.61	0.267289
$383$	11007.2	1.46852	0.734261	−	0.678867i	$-0.237529\pi$
$383$	11007.2	1.46852	0.734261	+	0.678867i	$0.237529\pi$
$384$	4063.58	0.540023
$385$	0	0
$386$	−1224.33	−0.161442
$387$	2597.50	0.341184
$388$	−10976.6	−1.43621
$389$	6162.79	0.803254	0.401627	−	0.915803i	$-0.368445\pi$
$389$	6162.79	0.803254	0.401627	+	0.915803i	$0.368445\pi$
$390$	0	0
$391$	−21.5713	−0.00279005
$392$	−389.448	−0.0501788
$393$	−12247.6	−1.57204
$394$	−1578.21	−0.201799
$395$	0	0
$396$	3749.03	0.475747
$397$	15137.9	1.91373	0.956864	−	0.290537i	$-0.0938338\pi$
$397$	15137.9	1.91373	0.956864	+	0.290537i	$0.0938338\pi$
$398$	−1800.12	−0.226714
$399$	3805.47	0.477473
$400$	0	0
$401$	3302.29	0.411243	0.205622	−	0.978632i	$-0.434078\pi$
$401$	3302.29	0.411243	0.205622	+	0.978632i	$0.434078\pi$
$402$	22.3997	0.00277910
$403$	−3079.08	−0.380596
$404$	937.564	0.115459
$405$	0	0
$406$	−146.551	−0.0179143
$407$	10385.1	1.26479
$408$	14.3027	0.00173552
$409$	4576.40	0.553273	0.276636	−	0.960975i	$-0.410780\pi$
$409$	4576.40	0.553273	0.276636	+	0.960975i	$0.410780\pi$
$410$	0	0
$411$	−6914.25	−0.829817
$412$	−5077.70	−0.607186
$413$	−2872.18	−0.342205
$414$	227.554	0.0270137
$415$	0	0
$416$	−1486.05	−0.175143
$417$	−11161.4	−1.31074
$418$	3532.11	0.413304
$419$	−6778.05	−0.790285	−0.395142	−	0.918620i	$-0.629305\pi$
$419$	−6778.05	−0.790285	−0.395142	+	0.918620i	$0.629305\pi$
$420$	0	0
$421$	−3952.68	−0.457582	−0.228791	−	0.973476i	$-0.573477\pi$
$421$	−3952.68	−0.457582	−0.228791	+	0.973476i	$0.573477\pi$
$422$	−1867.29	−0.215398
$423$	4765.46	0.547765
$424$	−5256.08	−0.602024
$425$	0	0
$426$	1057.03	0.120219
$427$	−322.346	−0.0365326
$428$	16031.1	1.81050
$429$	3745.67	0.421544
$430$	0	0
$431$	−3435.10	−0.383905	−0.191952	−	0.981404i	$-0.561482\pi$
$431$	−3435.10	−0.383905	−0.191952	+	0.981404i	$0.561482\pi$
$432$	8850.60	0.985705
$433$	5457.82	0.605742	0.302871	−	0.953032i	$-0.402055\pi$
$433$	5457.82	0.605742	0.302871	+	0.953032i	$0.402055\pi$
$434$	−679.682	−0.0751746
$435$	0	0
$436$	−7003.35	−0.769265
$437$	−6516.61	−0.713344
$438$	−1753.13	−0.191250
$439$	4188.10	0.455323	0.227662	−	0.973740i	$-0.426892\pi$
$439$	4188.10	0.455323	0.227662	+	0.973740i	$0.426892\pi$
$440$	0	0
$441$	−432.184	−0.0466671
$442$	−3.41031	−0.000366996 0
$443$	−2097.50	−0.224955	−0.112478	−	0.993654i	$-0.535879\pi$
$443$	−2097.50	−0.224955	−0.112478	+	0.993654i	$0.535879\pi$
$444$	6249.19	0.667959
$445$	0	0
$446$	51.5085	0.00546860
$447$	−9604.74	−1.01631
$448$	2917.14	0.307639
$449$	11318.2	1.18962	0.594809	−	0.803867i	$-0.297228\pi$
$449$	11318.2	1.18962	0.594809	+	0.803867i	$0.297228\pi$
$450$	0	0
$451$	−4188.37	−0.437301
$452$	−6531.91	−0.679724
$453$	7886.34	0.817952
$454$	−2897.41	−0.299521
$455$	0	0
$456$	4320.79	0.443728
$457$	11696.4	1.19723	0.598617	−	0.801036i	$-0.295717\pi$
$457$	11696.4	1.19723	0.598617	+	0.801036i	$0.295717\pi$
$458$	−425.596	−0.0434209
$459$	64.4603	0.00655501
$460$	0	0
$461$	10685.0	1.07951	0.539753	−	0.841823i	$-0.318518\pi$
$461$	10685.0	1.07951	0.539753	+	0.841823i	$0.318518\pi$
$462$	826.825	0.0832627
$463$	10407.2	1.04463	0.522315	−	0.852752i	$-0.325068\pi$
$463$	10407.2	1.04463	0.522315	+	0.852752i	$0.325068\pi$
$464$	2403.46	0.240469
$465$	0	0
$466$	1018.48	0.101245
$467$	2978.24	0.295111	0.147555	−	0.989054i	$-0.452860\pi$
$467$	2978.24	0.295111	0.147555	+	0.989054i	$0.452860\pi$
$468$	−1093.51	−0.108008
$469$	72.8517	0.00717266
$470$	0	0
$471$	−14230.8	−1.39219
$472$	−3261.12	−0.318020
$473$	−16162.1	−1.57111
$474$	1848.23	0.179097
$475$	0	0
$476$	22.8823	0.00220338
$477$	−5832.86	−0.559892
$478$	123.008	0.0117704
$479$	−14214.3	−1.35588	−0.677940	−	0.735117i	$-0.737127\pi$
$479$	−14214.3	−1.35588	−0.677940	+	0.735117i	$0.737127\pi$
$480$	0	0
$481$	−3029.11	−0.287142
$482$	−1544.93	−0.145995
$483$	−1525.46	−0.143708
$484$	−13018.2	−1.22260
$485$	0	0
$486$	−1192.54	−0.111306
$487$	−18097.0	−1.68389	−0.841946	−	0.539562i	$-0.818590\pi$
$487$	−18097.0	−1.68389	−0.841946	+	0.539562i	$0.818590\pi$
$488$	−365.998	−0.0339507
$489$	−2008.67	−0.185757
$490$	0	0
$491$	−13750.8	−1.26388	−0.631940	−	0.775017i	$-0.717741\pi$
$491$	−13750.8	−1.26388	−0.631940	+	0.775017i	$0.717741\pi$
$492$	−2520.34	−0.230947
$493$	17.5048	0.00159914
$494$	−1030.24	−0.0938314
$495$	0	0
$496$	11146.9	1.00909
$497$	3437.82	0.310276
$498$	−2272.40	−0.204475
$499$	15684.2	1.40706	0.703528	−	0.710667i	$-0.251607\pi$
$499$	15684.2	1.40706	0.703528	+	0.710667i	$0.251607\pi$
$500$	0	0
$501$	−15676.8	−1.39798
$502$	−3328.61	−0.295943
$503$	−977.937	−0.0866880	−0.0433440	−	0.999060i	$-0.513801\pi$
$503$	−977.937	−0.0866880	−0.0433440	+	0.999060i	$0.513801\pi$
$504$	−490.709	−0.0433689
$505$	0	0
$506$	−1415.88	−0.124394
$507$	8275.02	0.724865
$508$	15726.6	1.37354
$509$	−19664.6	−1.71242	−0.856208	−	0.516632i	$-0.827186\pi$
$509$	−19664.6	−1.71242	−0.856208	+	0.516632i	$0.827186\pi$
$510$	0	0
$511$	−5701.78	−0.493604
$512$	9064.39	0.782409
$513$	19473.2	1.67595
$514$	−258.775	−0.0222064
$515$	0	0
$516$	−9725.49	−0.829730
$517$	−29651.5	−2.52238
$518$	−668.650	−0.0567158
$519$	4302.63	0.363901
$520$	0	0
$521$	12522.8	1.05304	0.526519	−	0.850163i	$-0.323497\pi$
$521$	12522.8	1.05304	0.526519	+	0.850163i	$0.323497\pi$
$522$	−184.656	−0.0154831
$523$	−1104.42	−0.0923382	−0.0461691	−	0.998934i	$-0.514701\pi$
$523$	−1104.42	−0.0923382	−0.0461691	+	0.998934i	$0.514701\pi$
$524$	−22247.8	−1.85477
$525$	0	0
$526$	1797.05	0.148964
$527$	81.1843	0.00671052
$528$	−13560.0	−1.11766
$529$	−9554.75	−0.785301
$530$	0	0
$531$	−3618.98	−0.295763
$532$	6912.65	0.563349
$533$	1221.66	0.0992794
$534$	−735.152	−0.0595751
$535$	0	0
$536$	82.7170	0.00666573
$537$	−13649.5	−1.09687
$538$	−277.502	−0.0222378
$539$	2689.12	0.214895
$540$	0	0
$541$	−2126.45	−0.168989	−0.0844945	−	0.996424i	$-0.526928\pi$
$541$	−2126.45	−0.168989	−0.0844945	+	0.996424i	$0.526928\pi$
$542$	−1991.33	−0.157813
$543$	8400.25	0.663884
$544$	39.1817	0.00308805
$545$	0	0
$546$	−241.167	−0.0189029
$547$	2137.04	0.167044	0.0835220	−	0.996506i	$-0.473383\pi$
$547$	2137.04	0.167044	0.0835220	+	0.996506i	$0.473383\pi$
$548$	−12559.8	−0.979063
$549$	−406.160	−0.0315747
$550$	0	0
$551$	5288.11	0.408859
$552$	−1732.03	−0.133551
$553$	6011.08	0.462237
$554$	633.335	0.0485701
$555$	0	0
$556$	−20274.8	−1.54648
$557$	19435.1	1.47844	0.739219	−	0.673465i	$-0.235195\pi$
$557$	19435.1	1.47844	0.739219	+	0.673465i	$0.235195\pi$
$558$	−856.407	−0.0649724
$559$	4714.14	0.356685
$560$	0	0
$561$	−98.7598	−0.00743252
$562$	−344.008	−0.0258205
$563$	−1467.52	−0.109855	−0.0549276	−	0.998490i	$-0.517493\pi$
$563$	−1467.52	−0.109855	−0.0549276	+	0.998490i	$0.517493\pi$
$564$	−17842.7	−1.33212
$565$	0	0
$566$	3001.89	0.222931
$567$	2891.45	0.214161
$568$	3903.35	0.288347
$569$	15080.3	1.11107	0.555536	−	0.831493i	$-0.312513\pi$
$569$	15080.3	1.11107	0.555536	+	0.831493i	$0.312513\pi$
$570$	0	0
$571$	15800.8	1.15804	0.579022	−	0.815312i	$-0.303435\pi$
$571$	15800.8	1.15804	0.579022	+	0.815312i	$0.303435\pi$
$572$	6804.02	0.497361
$573$	−16856.5	−1.22895
$574$	269.671	0.0196095
$575$	0	0
$576$	3675.63	0.265888
$577$	−6165.64	−0.444851	−0.222425	−	0.974950i	$-0.571397\pi$
$577$	−6165.64	−0.444851	−0.222425	+	0.974950i	$0.571397\pi$
$578$	−2479.91	−0.178461
$579$	10341.6	0.742283
$580$	0	0
$581$	−7390.62	−0.527736
$582$	−3050.25	−0.217246
$583$	36293.0	2.57822
$584$	−6473.89	−0.458719
$585$	0	0
$586$	−1095.90	−0.0772547
$587$	−23104.0	−1.62454	−0.812268	−	0.583285i	$-0.801767\pi$
$587$	−23104.0	−1.62454	−0.812268	+	0.583285i	$0.801767\pi$
$588$	1618.17	0.113490
$589$	24525.4	1.71571
$590$	0	0
$591$	13330.8	0.927841
$592$	10965.9	0.761313
$593$	−6544.43	−0.453200	−0.226600	−	0.973988i	$-0.572761\pi$
$593$	−6544.43	−0.453200	−0.226600	+	0.973988i	$0.572761\pi$
$594$	4230.99	0.292255
$595$	0	0
$596$	−17447.0	−1.19909
$597$	15205.2	1.04239
$598$	412.982	0.0282410
$599$	3215.71	0.219349	0.109675	−	0.993968i	$-0.465019\pi$
$599$	3215.71	0.219349	0.109675	+	0.993968i	$0.465019\pi$
$600$	0	0
$601$	−234.653	−0.0159263	−0.00796313	−	0.999968i	$-0.502535\pi$
$601$	−234.653	−0.0159263	−0.00796313	+	0.999968i	$0.502535\pi$
$602$	1040.61	0.0704517
$603$	91.7939	0.00619923
$604$	14325.6	0.965064
$605$	0	0
$606$	260.537	0.0174647
$607$	14528.7	0.971501	0.485750	−	0.874098i	$-0.338546\pi$
$607$	14528.7	0.971501	0.485750	+	0.874098i	$0.338546\pi$
$608$	11836.6	0.789537
$609$	1237.89	0.0823672
$610$	0	0
$611$	8648.71	0.572650
$612$	28.8320	0.00190435
$613$	−11332.7	−0.746696	−0.373348	−	0.927691i	$-0.621790\pi$
$613$	−11332.7	−0.746696	−0.373348	+	0.927691i	$0.621790\pi$
$614$	1839.73	0.120921
$615$	0	0
$616$	3053.27	0.199708
$617$	17400.2	1.13534	0.567672	−	0.823255i	$-0.307844\pi$
$617$	17400.2	1.13534	0.567672	+	0.823255i	$0.307844\pi$
$618$	−1411.03	−0.0918446
$619$	−11987.8	−0.778402	−0.389201	−	0.921153i	$-0.627249\pi$
$619$	−11987.8	−0.778402	−0.389201	+	0.921153i	$0.627249\pi$
$620$	0	0
$621$	−7806.02	−0.504420
$622$	1304.46	0.0840900
$623$	−2390.97	−0.153759
$624$	3955.17	0.253740
$625$	0	0
$626$	−3378.84	−0.215728
$627$	−29834.9	−1.90030
$628$	−25850.3	−1.64258
$629$	79.8667	0.00506279
$630$	0	0
$631$	−3800.38	−0.239764	−0.119882	−	0.992788i	$-0.538252\pi$
$631$	−3800.38	−0.239764	−0.119882	+	0.992788i	$0.538252\pi$
$632$	6825.08	0.429568
$633$	15772.6	0.990368
$634$	1940.07	0.121530
$635$	0	0
$636$	21839.2	1.36161
$637$	−784.359	−0.0487872
$638$	1148.96	0.0712976
$639$	4331.69	0.268167
$640$	0	0
$641$	12294.2	0.757552	0.378776	−	0.925488i	$-0.376345\pi$
$641$	12294.2	0.757552	0.378776	+	0.925488i	$0.376345\pi$
$642$	4454.85	0.273861
$643$	−14615.4	−0.896382	−0.448191	−	0.893938i	$-0.647932\pi$
$643$	−14615.4	−0.896382	−0.448191	+	0.893938i	$0.647932\pi$
$644$	−2771.01	−0.169554
$645$	0	0
$646$	27.1637	0.00165440
$647$	16047.0	0.975071	0.487536	−	0.873103i	$-0.337896\pi$
$647$	16047.0	0.975071	0.487536	+	0.873103i	$0.337896\pi$
$648$	3283.00	0.199025
$649$	22517.9	1.36195
$650$	0	0
$651$	5741.12	0.345641
$652$	−3648.75	−0.219166
$653$	−623.425	−0.0373607	−0.0186803	−	0.999826i	$-0.505946\pi$
$653$	−623.425	−0.0373607	−0.0186803	+	0.999826i	$0.505946\pi$
$654$	−1946.14	−0.116361
$655$	0	0
$656$	−4422.63	−0.263224
$657$	−7184.30	−0.426616
$658$	1909.13	0.113109
$659$	963.459	0.0569515	0.0284758	−	0.999594i	$-0.490935\pi$
$659$	963.459	0.0569515	0.0284758	+	0.999594i	$0.490935\pi$
$660$	0	0
$661$	24183.6	1.42304	0.711522	−	0.702664i	$-0.248006\pi$
$661$	24183.6	1.42304	0.711522	+	0.702664i	$0.248006\pi$
$662$	−414.893	−0.0243584
$663$	28.8061	0.00168739
$664$	−8391.43	−0.490438
$665$	0	0
$666$	−842.507	−0.0490187
$667$	−2119.79	−0.123057
$668$	−28476.9	−1.64941
$669$	−435.080	−0.0251438
$670$	0	0
$671$	2527.20	0.145397
$672$	2770.81	0.159057
$673$	−14167.0	−0.811437	−0.405718	−	0.913998i	$-0.632979\pi$
$673$	−14167.0	−0.811437	−0.405718	+	0.913998i	$0.632979\pi$
$674$	−521.215	−0.0297870
$675$	0	0
$676$	15031.6	0.855235
$677$	19397.1	1.10117	0.550584	−	0.834780i	$-0.314405\pi$
$677$	19397.1	1.10117	0.550584	+	0.834780i	$0.314405\pi$
$678$	−1815.14	−0.102817
$679$	−9920.47	−0.560696
$680$	0	0
$681$	24473.8	1.37715
$682$	5328.71	0.299189
$683$	−20984.8	−1.17564	−0.587820	−	0.808992i	$-0.700014\pi$
$683$	−20984.8	−1.17564	−0.587820	+	0.808992i	$0.700014\pi$
$684$	8710.02	0.486895
$685$	0	0
$686$	−173.141	−0.00963636
$687$	3594.91	0.199643
$688$	−17066.1	−0.945694
$689$	−10585.9	−0.585328
$690$	0	0
$691$	−18079.2	−0.995320	−0.497660	−	0.867372i	$-0.665807\pi$
$691$	−18079.2	−0.995320	−0.497660	+	0.867372i	$0.665807\pi$
$692$	7815.75	0.429350
$693$	3388.32	0.185731
$694$	1306.23	0.0714465
$695$	0	0
$696$	1405.52	0.0765459
$697$	−32.2107	−0.00175046
$698$	−4267.56	−0.231418
$699$	−8602.86	−0.465508
$700$	0	0
$701$	18660.6	1.00542	0.502711	−	0.864455i	$-0.332336\pi$
$701$	18660.6	1.00542	0.502711	+	0.864455i	$0.332336\pi$
$702$	−1234.09	−0.0663500
$703$	24127.4	1.29443
$704$	−22870.4	−1.22438
$705$	0	0
$706$	2084.57	0.111125
$707$	847.358	0.0450752
$708$	13550.1	0.719271
$709$	−24545.4	−1.30017	−0.650085	−	0.759862i	$-0.725267\pi$
$709$	−24545.4	−1.30017	−0.650085	+	0.759862i	$0.725267\pi$
$710$	0	0
$711$	7574.02	0.399505
$712$	−2714.74	−0.142892
$713$	−9831.26	−0.516387
$714$	6.35871	0.000333290 0
$715$	0	0
$716$	−24794.5	−1.29415
$717$	−1039.02	−0.0541185
$718$	−2290.05	−0.119030
$719$	−7300.32	−0.378659	−0.189330	−	0.981914i	$-0.560631\pi$
$719$	−7300.32	−0.378659	−0.189330	+	0.981914i	$0.560631\pi$
$720$	0	0
$721$	−4589.16	−0.237045
$722$	4743.74	0.244520
$723$	13049.7	0.671263
$724$	15259.1	0.783286
$725$	0	0
$726$	−3617.61	−0.184934
$727$	−15466.0	−0.788998	−0.394499	−	0.918896i	$-0.629082\pi$
$727$	−15466.0	−0.788998	−0.394499	+	0.918896i	$0.629082\pi$
$728$	−890.574	−0.0453391
$729$	21225.8	1.07838
$730$	0	0
$731$	−124.295	−0.00628893
$732$	1520.73	0.0767868
$733$	13830.5	0.696917	0.348459	−	0.937324i	$-0.386705\pi$
$733$	13830.5	0.696917	0.348459	+	0.937324i	$0.386705\pi$
$734$	−829.358	−0.0417060
$735$	0	0
$736$	−4744.83	−0.237631
$737$	−571.157	−0.0285466
$738$	339.788	0.0169482
$739$	11714.5	0.583118	0.291559	−	0.956553i	$-0.405826\pi$
$739$	11714.5	0.583118	0.291559	+	0.956553i	$0.405826\pi$
$740$	0	0
$741$	8702.20	0.431422
$742$	−2336.75	−0.115613
$743$	−28963.4	−1.43010	−0.715050	−	0.699074i	$-0.753596\pi$
$743$	−28963.4	−1.43010	−0.715050	+	0.699074i	$0.753596\pi$
$744$	6518.56	0.321212
$745$	0	0
$746$	−4552.91	−0.223450
$747$	−9312.26	−0.456115
$748$	−179.397	−0.00876928
$749$	14488.7	0.706817
$750$	0	0
$751$	6331.99	0.307667	0.153833	−	0.988097i	$-0.450838\pi$
$751$	6331.99	0.307667	0.153833	+	0.988097i	$0.450838\pi$
$752$	−31310.0	−1.51829
$753$	28116.0	1.36070
$754$	−335.128	−0.0161865
$755$	0	0
$756$	8280.43	0.398355
$757$	6256.80	0.300406	0.150203	−	0.988655i	$-0.452007\pi$
$757$	6256.80	0.300406	0.150203	+	0.988655i	$0.452007\pi$
$758$	−1243.60	−0.0595905
$759$	11959.6	0.571945
$760$	0	0
$761$	13953.7	0.664679	0.332340	−	0.943160i	$-0.392162\pi$
$761$	13953.7	0.664679	0.332340	+	0.943160i	$0.392162\pi$
$762$	4370.23	0.207765
$763$	−6329.53	−0.300320
$764$	−30619.8	−1.44998
$765$	0	0
$766$	5556.28	0.262084
$767$	−6568.00	−0.309200
$768$	−12163.7	−0.571512
$769$	34278.1	1.60741	0.803707	−	0.595025i	$-0.202858\pi$
$769$	34278.1	1.60741	0.803707	+	0.595025i	$0.202858\pi$
$770$	0	0
$771$	2185.82	0.102101
$772$	18785.5	0.875786
$773$	−8769.31	−0.408034	−0.204017	−	0.978967i	$-0.565400\pi$
$773$	−8769.31	−0.408034	−0.204017	+	0.978967i	$0.565400\pi$
$774$	1311.18	0.0608905
$775$	0	0
$776$	−11263.9	−0.521069
$777$	5647.94	0.260770
$778$	3110.88	0.143355
$779$	−9730.73	−0.447547
$780$	0	0
$781$	−26952.5	−1.23487
$782$	−10.8889	−0.000497934 0
$783$	6334.45	0.289112
$784$	2839.53	0.129352
$785$	0	0
$786$	−6182.40	−0.280558
$787$	3546.15	0.160618	0.0803092	−	0.996770i	$-0.474409\pi$
$787$	3546.15	0.160618	0.0803092	+	0.996770i	$0.474409\pi$
$788$	24215.4	1.09472
$789$	−15179.3	−0.684912
$790$	0	0
$791$	−5903.45	−0.265363
$792$	3847.16	0.172604
$793$	−737.130	−0.0330091
$794$	7641.37	0.341539
$795$	0	0
$796$	27620.3	1.22987
$797$	18169.4	0.807520	0.403760	−	0.914865i	$-0.367703\pi$
$797$	18169.4	0.807520	0.403760	+	0.914865i	$0.367703\pi$
$798$	1920.94	0.0852137
$799$	−228.035	−0.0100968
$800$	0	0
$801$	−3012.65	−0.132892
$802$	1666.94	0.0733938
$803$	44702.0	1.96451
$804$	−343.692	−0.0150760
$805$	0	0
$806$	−1554.27	−0.0679241
$807$	2343.99	0.102246
$808$	962.104	0.0418895
$809$	11853.0	0.515115	0.257557	−	0.966263i	$-0.417082\pi$
$809$	11853.0	0.515115	0.257557	+	0.966263i	$0.417082\pi$
$810$	0	0
$811$	−11921.1	−0.516161	−0.258080	−	0.966123i	$-0.583090\pi$
$811$	−11921.1	−0.516161	−0.258080	+	0.966123i	$0.583090\pi$
$812$	2248.62	0.0971813
$813$	16820.3	0.725601
$814$	5242.22	0.225724
$815$	0	0
$816$	−104.284	−0.00447384
$817$	−37548.9	−1.60792
$818$	2310.09	0.0987415
$819$	−988.301	−0.0421661
$820$	0	0
$821$	−42094.1	−1.78940	−0.894698	−	0.446671i	$-0.852610\pi$
$821$	−42094.1	−1.78940	−0.894698	+	0.446671i	$0.852610\pi$
$822$	−3490.20	−0.148096
$823$	−1622.17	−0.0687064	−0.0343532	−	0.999410i	$-0.510937\pi$
$823$	−1622.17	−0.0687064	−0.0343532	+	0.999410i	$0.510937\pi$
$824$	−5210.61	−0.220291
$825$	0	0
$826$	−1449.83	−0.0610727
$827$	−28171.7	−1.18455	−0.592277	−	0.805735i	$-0.701771\pi$
$827$	−28171.7	−1.18455	−0.592277	+	0.805735i	$0.701771\pi$
$828$	−3491.50	−0.146543
$829$	−9244.23	−0.387293	−0.193646	−	0.981071i	$-0.562031\pi$
$829$	−9244.23	−0.387293	−0.193646	+	0.981071i	$0.562031\pi$
$830$	0	0
$831$	−5349.63	−0.223317
$832$	6670.81	0.277967
$833$	20.6807	0.000860198 0
$834$	−5634.10	−0.233924
$835$	0	0
$836$	−54195.2	−2.24208
$837$	29378.2	1.21321
$838$	−3421.45	−0.141041
$839$	−43012.5	−1.76991	−0.884956	−	0.465674i	$-0.845812\pi$
$839$	−43012.5	−1.76991	−0.884956	+	0.465674i	$0.845812\pi$
$840$	0	0
$841$	−22668.8	−0.929469
$842$	−1995.25	−0.0816637
$843$	2905.76	0.118718
$844$	28650.9	1.16849
$845$	0	0
$846$	2405.53	0.0977585
$847$	−11765.7	−0.477302
$848$	38323.0	1.55191
$849$	−25356.3	−1.02500
$850$	0	0
$851$	−9671.70	−0.389591
$852$	−16218.6	−0.652159
$853$	19756.9	0.793041	0.396521	−	0.918026i	$-0.370217\pi$
$853$	19756.9	0.793041	0.396521	+	0.918026i	$0.370217\pi$
$854$	−162.715	−0.00651991
$855$	0	0
$856$	16450.7	0.656862
$857$	−325.658	−0.0129805	−0.00649024	−	0.999979i	$-0.502066\pi$
$857$	−325.658	−0.0129805	−0.00649024	+	0.999979i	$0.502066\pi$
$858$	1890.75	0.0752321
$859$	3275.22	0.130092	0.0650461	−	0.997882i	$-0.479281\pi$
$859$	3275.22	0.130092	0.0650461	+	0.997882i	$0.479281\pi$
$860$	0	0
$861$	−2277.85	−0.0901613
$862$	−1733.98	−0.0685147
$863$	−44585.0	−1.75862	−0.879311	−	0.476247i	$-0.841997\pi$
$863$	−44585.0	−1.75862	−0.879311	+	0.476247i	$0.841997\pi$
$864$	14178.7	0.558297
$865$	0	0
$866$	2755.02	0.108106
$867$	20947.3	0.820537
$868$	10428.8	0.407805
$869$	−47126.9	−1.83967
$870$	0	0
$871$	166.594	0.00648087
$872$	−7186.65	−0.279095
$873$	−12499.9	−0.484602
$874$	−3289.48	−0.127309
$875$	0	0
$876$	26899.3	1.03749
$877$	−16433.8	−0.632761	−0.316380	−	0.948632i	$-0.602468\pi$
$877$	−16433.8	−0.632761	−0.316380	+	0.948632i	$0.602468\pi$
$878$	2114.08	0.0812607
$879$	9256.82	0.355205
$880$	0	0
$881$	−39080.2	−1.49449	−0.747245	−	0.664549i	$-0.768624\pi$
$881$	−39080.2	−1.49449	−0.747245	+	0.664549i	$0.768624\pi$
$882$	−218.159	−0.00832858
$883$	−48548.2	−1.85026	−0.925129	−	0.379652i	$-0.876044\pi$
$883$	−48548.2	−1.85026	−0.925129	+	0.379652i	$0.876044\pi$
$884$	52.3264	0.00199087
$885$	0	0
$886$	−1058.78	−0.0401473
$887$	13447.1	0.509029	0.254514	−	0.967069i	$-0.418084\pi$
$887$	13447.1	0.509029	0.254514	+	0.967069i	$0.418084\pi$
$888$	6412.76	0.242340
$889$	14213.5	0.536227
$890$	0	0
$891$	−22669.0	−0.852344
$892$	−790.325	−0.0296660
$893$	−68888.5	−2.58148
$894$	−4848.32	−0.181378
$895$	0	0
$896$	6671.30	0.248742
$897$	−3488.37	−0.129847
$898$	5713.24	0.212309
$899$	7977.90	0.295971
$900$	0	0
$901$	279.112	0.0103203
$902$	−2114.22	−0.0780442
$903$	−8789.76	−0.323926
$904$	−6702.87	−0.246609
$905$	0	0
$906$	3980.89	0.145978
$907$	−15750.3	−0.576604	−0.288302	−	0.957539i	$-0.593091\pi$
$907$	−15750.3	−0.576604	−0.288302	+	0.957539i	$0.593091\pi$
$908$	44456.7	1.62483
$909$	1067.68	0.0389579
$910$	0	0
$911$	31449.7	1.14377	0.571886	−	0.820333i	$-0.306212\pi$
$911$	31449.7	1.14377	0.571886	+	0.820333i	$0.306212\pi$
$912$	−31503.6	−1.14385
$913$	57942.4	2.10034
$914$	5904.16	0.213668
$915$	0	0
$916$	6530.17	0.235549
$917$	−20107.3	−0.724102
$918$	32.5385	0.00116986
$919$	−30355.6	−1.08960	−0.544798	−	0.838567i	$-0.683394\pi$
$919$	−30355.6	−1.08960	−0.544798	+	0.838567i	$0.683394\pi$
$920$	0	0
$921$	−15539.8	−0.555975
$922$	5393.64	0.192657
$923$	7861.46	0.280350
$924$	−12686.5	−0.451682
$925$	0	0
$926$	5253.39	0.186433
$927$	−5782.39	−0.204874
$928$	3850.34	0.136200
$929$	−28533.8	−1.00771	−0.503856	−	0.863788i	$-0.668086\pi$
$929$	−28533.8	−1.00771	−0.503856	+	0.863788i	$0.668086\pi$
$930$	0	0
$931$	6247.56	0.219931
$932$	−15627.1	−0.549231
$933$	−11018.5	−0.386632
$934$	1503.37	0.0526678
$935$	0	0
$936$	−1122.13	−0.0391860
$937$	19269.1	0.671817	0.335908	−	0.941895i	$-0.390957\pi$
$937$	19269.1	0.671817	0.335908	+	0.941895i	$0.390957\pi$
$938$	36.7743	0.00128009
$939$	28540.3	0.991881
$940$	0	0
$941$	−2097.84	−0.0726756	−0.0363378	−	0.999340i	$-0.511569\pi$
$941$	−2097.84	−0.0726756	−0.0363378	+	0.999340i	$0.511569\pi$
$942$	−7183.46	−0.248461
$943$	3900.66	0.134701
$944$	23777.4	0.819797
$945$	0	0
$946$	−8158.36	−0.280392
$947$	−5072.14	−0.174047	−0.0870235	−	0.996206i	$-0.527736\pi$
$947$	−5072.14	−0.174047	−0.0870235	+	0.996206i	$0.527736\pi$
$948$	−28358.5	−0.971561
$949$	−13038.6	−0.445997
$950$	0	0
$951$	−16387.3	−0.558775
$952$	23.4813	0.000799403 0
$953$	23464.1	0.797564	0.398782	−	0.917046i	$-0.369433\pi$
$953$	23464.1	0.797564	0.398782	+	0.917046i	$0.369433\pi$
$954$	−2944.33	−0.0999227
$955$	0	0
$956$	−1887.39	−0.0638519
$957$	−9705.02	−0.327815
$958$	−7175.13	−0.241981
$959$	−11351.3	−0.382225
$960$	0	0
$961$	7209.24	0.241994
$962$	−1529.04	−0.0512457
$963$	18255.9	0.610892
$964$	23704.8	0.791992
$965$	0	0
$966$	−770.028	−0.0256472
$967$	6994.27	0.232596	0.116298	−	0.993214i	$-0.462897\pi$
$967$	6994.27	0.232596	0.116298	+	0.993214i	$0.462897\pi$
$968$	−13359.0	−0.443568
$969$	−229.446	−0.00760667
$970$	0	0
$971$	37752.5	1.24772	0.623860	−	0.781536i	$-0.285564\pi$
$971$	37752.5	1.24772	0.623860	+	0.781536i	$0.285564\pi$
$972$	18297.8	0.603809
$973$	−18324.0	−0.603743
$974$	−9135.09	−0.300521
$975$	0	0
$976$	2668.55	0.0875186
$977$	6380.21	0.208926	0.104463	−	0.994529i	$-0.466688\pi$
$977$	6380.21	0.208926	0.104463	+	0.994529i	$0.466688\pi$
$978$	−1013.94	−0.0331517
$979$	18745.2	0.611950
$980$	0	0
$981$	−7975.28	−0.259563
$982$	−6941.18	−0.225562
$983$	−17330.0	−0.562299	−0.281150	−	0.959664i	$-0.590716\pi$
$983$	−17330.0	−0.562299	−0.281150	+	0.959664i	$0.590716\pi$
$984$	−2586.31	−0.0837891
$985$	0	0
$986$	8.83612	0.000285395 0
$987$	−16126.0	−0.520057
$988$	15807.6	0.509014
$989$	15051.9	0.483945
$990$	0	0
$991$	32191.8	1.03189	0.515947	−	0.856621i	$-0.327440\pi$
$991$	32191.8	1.03189	0.515947	+	0.856621i	$0.327440\pi$
$992$	17857.3	0.571542
$993$	3504.50	0.111996
$994$	1735.35	0.0553743
$995$	0	0
$996$	34866.7	1.10923
$997$	2678.20	0.0850748	0.0425374	−	0.999095i	$-0.486456\pi$
$997$	2678.20	0.0850748	0.0425374	+	0.999095i	$0.486456\pi$
$998$	7917.13	0.251114
$999$	28901.4	0.915314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.a.g.1.3	✓	4
3.2	odd	2		1575.4.a.bl.1.2		4
5.2	odd	4		175.4.b.f.99.5		8
5.3	odd	4		175.4.b.f.99.4		8
5.4	even	2		175.4.a.h.1.2	yes	4
7.6	odd	2		1225.4.a.z.1.3		4
15.14	odd	2		1575.4.a.bg.1.3		4
35.34	odd	2		1225.4.a.bd.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.a.g.1.3	✓	4	1.1	even	1	trivial
175.4.a.h.1.2	yes	4	5.4	even	2
175.4.b.f.99.4		8	5.3	odd	4
175.4.b.f.99.5		8	5.2	odd	4
1225.4.a.z.1.3		4	7.6	odd	2
1225.4.a.bd.1.2		4	35.34	odd	2
1575.4.a.bg.1.3		4	15.14	odd	2
1575.4.a.bl.1.2		4	3.2	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+0.504784 q^{2} -4.26379 q^{3} -7.74519 q^{4} -2.15229 q^{6} -7.00000 q^{7} -7.94792 q^{8} -8.82008 q^{9} +O(q^{10})\)	\(q+0.504784 q^{2} -4.26379 q^{3} -7.74519 q^{4} -2.15229 q^{6} -7.00000 q^{7} -7.94792 q^{8} -8.82008 q^{9} +54.8800 q^{11} +33.0239 q^{12} -16.0073 q^{13} -3.53349 q^{14} +57.9496 q^{16} +0.422056 q^{17} -4.45223 q^{18} +127.501 q^{19} +29.8465 q^{21} +27.7025 q^{22} -51.1101 q^{23} +33.8883 q^{24} -8.08024 q^{26} +152.729 q^{27} +54.2164 q^{28} +41.4750 q^{29} +192.354 q^{31} +92.8353 q^{32} -233.997 q^{33} +0.213047 q^{34} +68.3132 q^{36} +189.232 q^{37} +64.3605 q^{38} +68.2519 q^{39} -76.3187 q^{41} +15.0660 q^{42} -294.499 q^{43} -425.056 q^{44} -25.7996 q^{46} -540.297 q^{47} -247.085 q^{48} +49.0000 q^{49} -1.79956 q^{51} +123.980 q^{52} +661.316 q^{53} +77.0953 q^{54} +55.6354 q^{56} -543.639 q^{57} +20.9359 q^{58} +410.312 q^{59} +46.0495 q^{61} +97.0974 q^{62} +61.7405 q^{63} -416.735 q^{64} -118.118 q^{66} -10.4074 q^{67} -3.26890 q^{68} +217.923 q^{69} -491.117 q^{71} +70.1012 q^{72} +814.540 q^{73} +95.5215 q^{74} -987.522 q^{76} -384.160 q^{77} +34.4525 q^{78} -858.725 q^{79} -413.064 q^{81} -38.5244 q^{82} +1055.80 q^{83} -231.167 q^{84} -148.658 q^{86} -176.841 q^{87} -436.182 q^{88} +341.567 q^{89} +112.051 q^{91} +395.858 q^{92} -820.159 q^{93} -272.733 q^{94} -395.831 q^{96} +1417.21 q^{97} +24.7344 q^{98} -484.046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 3 q^{3} + 36 q^{4} + q^{6} - 28 q^{7} - 27 q^{8} + 61 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 3 * q^3 + 36 * q^4 + q^6 - 28 * q^7 - 27 * q^8 + 61 * q^9	\( 4 q - 4 q^{2} + 3 q^{3} + 36 q^{4} + q^{6} - 28 q^{7} - 27 q^{8} + 61 q^{9} + 100 q^{11} + 165 q^{12} - 44 q^{13} + 28 q^{14} + 160 q^{16} + 53 q^{17} - 433 q^{18} - 29 q^{19} - 21 q^{21} + 152 q^{22} - 295 q^{23} - 21 q^{24} + 700 q^{26} + 441 q^{27} - 252 q^{28} + 129 q^{29} + 114 q^{31} + 310 q^{32} + 865 q^{33} + 203 q^{34} + 1101 q^{36} - 403 q^{37} - 555 q^{38} + 674 q^{39} + 671 q^{41} - 7 q^{42} + 411 q^{43} + 438 q^{44} - 997 q^{46} + 8 q^{47} + 523 q^{48} + 196 q^{49} - 885 q^{51} - 74 q^{52} - 90 q^{53} - 2777 q^{54} + 189 q^{56} - 233 q^{57} - 673 q^{58} + 1018 q^{59} + 50 q^{61} + 1626 q^{62} - 427 q^{63} - 2421 q^{64} - 3841 q^{66} - 424 q^{67} + 617 q^{68} + 1080 q^{69} + 215 q^{71} - 2940 q^{72} + 1207 q^{73} + 623 q^{74} - 3257 q^{76} - 700 q^{77} - 278 q^{78} - 951 q^{79} + 28 q^{81} - 1695 q^{82} + 3035 q^{83} - 1155 q^{84} - 99 q^{86} - 2210 q^{87} - 163 q^{88} + 2819 q^{89} + 308 q^{91} - 3073 q^{92} + 852 q^{93} - 3056 q^{94} - 1345 q^{96} + 1100 q^{97} - 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 + 36 * q^4 + q^6 - 28 * q^7 - 27 * q^8 + 61 * q^9 + 100 * q^11 + 165 * q^12 - 44 * q^13 + 28 * q^14 + 160 * q^16 + 53 * q^17 - 433 * q^18 - 29 * q^19 - 21 * q^21 + 152 * q^22 - 295 * q^23 - 21 * q^24 + 700 * q^26 + 441 * q^27 - 252 * q^28 + 129 * q^29 + 114 * q^31 + 310 * q^32 + 865 * q^33 + 203 * q^34 + 1101 * q^36 - 403 * q^37 - 555 * q^38 + 674 * q^39 + 671 * q^41 - 7 * q^42 + 411 * q^43 + 438 * q^44 - 997 * q^46 + 8 * q^47 + 523 * q^48 + 196 * q^49 - 885 * q^51 - 74 * q^52 - 90 * q^53 - 2777 * q^54 + 189 * q^56 - 233 * q^57 - 673 * q^58 + 1018 * q^59 + 50 * q^61 + 1626 * q^62 - 427 * q^63 - 2421 * q^64 - 3841 * q^66 - 424 * q^67 + 617 * q^68 + 1080 * q^69 + 215 * q^71 - 2940 * q^72 + 1207 * q^73 + 623 * q^74 - 3257 * q^76 - 700 * q^77 - 278 * q^78 - 951 * q^79 + 28 * q^81 - 1695 * q^82 + 3035 * q^83 - 1155 * q^84 - 99 * q^86 - 2210 * q^87 - 163 * q^88 + 2819 * q^89 + 308 * q^91 - 3073 * q^92 + 852 * q^93 - 3056 * q^94 - 1345 * q^96 + 1100 * q^97 - 196 * q^98 + 2383 * q^99

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