LMFDB - Embedded newform 175.10.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,10,Mod(1,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$90.1312713287$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ 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)

$f(q)$	$=$	\(q+9.17157 q^{2} -65.7351 q^{3} -427.882 q^{4} -602.894 q^{6} -2401.00 q^{7} -8620.20 q^{8} -15361.9 q^{9} +35089.6 q^{11} +28126.9 q^{12} +77401.4 q^{13} -22020.9 q^{14} +140015. q^{16} +229907. q^{17} -140893. q^{18} +16433.6 q^{19} +157830. q^{21} +321827. q^{22} +2.57284e6 q^{23} +566649. q^{24} +709892. q^{26} +2.30368e6 q^{27} +1.02735e6 q^{28} -6.62817e6 q^{29} -8.17416e6 q^{31} +5.69770e6 q^{32} -2.30662e6 q^{33} +2.10861e6 q^{34} +6.57308e6 q^{36} -9.70272e6 q^{37} +150722. q^{38} -5.08798e6 q^{39} +2.98108e7 q^{41} +1.44755e6 q^{42} +1.95343e7 q^{43} -1.50142e7 q^{44} +2.35970e7 q^{46} -5.93794e6 q^{47} -9.20389e6 q^{48} +5.76480e6 q^{49} -1.51130e7 q^{51} -3.31187e7 q^{52} +2.74263e7 q^{53} +2.11284e7 q^{54} +2.06971e7 q^{56} -1.08026e6 q^{57} -6.07908e7 q^{58} +5.24915e7 q^{59} +2.23282e7 q^{61} -7.49699e7 q^{62} +3.68839e7 q^{63} -1.94308e7 q^{64} -2.11553e7 q^{66} -2.74351e8 q^{67} -9.83733e7 q^{68} -1.69126e8 q^{69} -3.63673e8 q^{71} +1.32423e8 q^{72} -2.09245e7 q^{73} -8.89892e7 q^{74} -7.03163e6 q^{76} -8.42501e7 q^{77} -4.66648e7 q^{78} -2.65896e8 q^{79} +1.50936e8 q^{81} +2.73412e8 q^{82} +9.43764e6 q^{83} -6.75326e7 q^{84} +1.79160e8 q^{86} +4.35704e8 q^{87} -3.02479e8 q^{88} -6.64876e8 q^{89} -1.85841e8 q^{91} -1.10087e9 q^{92} +5.37329e8 q^{93} -5.44603e7 q^{94} -3.74539e8 q^{96} +1.20731e9 q^{97} +5.28723e7 q^{98} -5.39042e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 57624 q^{14} + 112768 q^{16} + 373910 q^{17} + 419472 q^{18} - 143276 q^{19}+ \cdots - 1163466540 q^{99}+O(q^{100}) $ 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 57624 * q^14 + 112768 * q^16 + 373910 * q^17 + 419472 * q^18 - 143276 * q^19 - 417774 * q^21 + 76808 * q^22 + 498908 * q^23 - 2291904 * q^24 + 319736 * q^26 + 6644538 * q^27 + 1728720 * q^28 - 11577554 * q^29 - 3953760 * q^31 + 11398656 * q^32 - 6267894 * q^33 + 4243944 * q^34 - 4466016 * q^36 + 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 + 1058992 * q^41 - 7087752 * q^42 - 15948180 * q^43 - 10187376 * q^44 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 + 11529602 * q^49 + 19409466 * q^51 - 25432656 * q^52 + 25114688 * q^53 + 85496472 * q^54 + 49326144 * q^56 - 39368244 * q^57 - 134182296 * q^58 - 116159208 * q^59 - 44688544 * q^61 - 12388000 * q^62 - 53849628 * q^63 + 79055872 * q^64 - 79894824 * q^66 - 118092496 * q^67 - 140439024 * q^68 - 666320892 * q^69 - 294165824 * q^71 - 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 39622368 * q^76 - 44576966 * q^77 - 140199000 * q^78 - 692852854 * q^79 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 + 100611504 * q^84 - 346989008 * q^86 - 750836190 * q^87 - 105455296 * q^88 - 779043704 * q^89 - 122667090 * q^91 - 495040608 * q^92 + 1549107360 * q^93 - 937691032 * q^94 + 992180736 * q^96 + 2673039406 * q^97 + 138355224 * q^98 - 1163466540 * q^99

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 $

$2$	9.17157	0.405330	0.202665	−	0.979248i	$-0.435040\pi$
$2$	9.17157	0.405330	0.202665	+	0.979248i	$0.435040\pi$
$3$	−65.7351	−0.468545	−0.234273	−	0.972171i	$-0.575271\pi$
$3$	−65.7351	−0.468545	−0.234273	+	0.972171i	$0.575271\pi$
$4$	−427.882	−0.835708
$5$	0	0
$5$	0	0
$6$	−602.894	−0.189915
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−8620.20	−0.744067
$9$	−15361.9	−0.780465
$10$	0	0
$11$	35089.6	0.722622	0.361311	−	0.932445i	$-0.382329\pi$
$11$	35089.6	0.722622	0.361311	+	0.932445i	$0.382329\pi$
$12$	28126.9	0.391567
$13$	77401.4	0.751629	0.375815	−	0.926695i	$-0.377363\pi$
$13$	77401.4	0.751629	0.375815	+	0.926695i	$0.377363\pi$
$14$	−22020.9	−0.153200
$15$	0	0
$16$	140015.	0.534115
$17$	229907.	0.667626	0.333813	−	0.942639i	$-0.391665\pi$
$17$	229907.	0.667626	0.333813	+	0.942639i	$0.391665\pi$
$18$	−140893.	−0.316346
$19$	16433.6	0.0289295	0.0144647	−	0.999895i	$-0.495396\pi$
$19$	16433.6	0.0289295	0.0144647	+	0.999895i	$0.495396\pi$
$20$	0	0
$21$	157830.	0.177093
$22$	321827.	0.292900
$23$	2.57284e6	1.91707	0.958535	−	0.284975i	$-0.0919852\pi$
$23$	2.57284e6	1.91707	0.958535	+	0.284975i	$0.0919852\pi$
$24$	566649.	0.348629
$25$	0	0
$26$	709892.	0.304658
$27$	2.30368e6	0.834228
$28$	1.02735e6	0.315868
$29$	−6.62817e6	−1.74022	−0.870108	−	0.492862i	$-0.835951\pi$
$29$	−6.62817e6	−1.74022	−0.870108	+	0.492862i	$0.835951\pi$
$30$	0	0
$31$	−8.17416e6	−1.58970	−0.794851	−	0.606805i	$-0.792451\pi$
$31$	−8.17416e6	−1.58970	−0.794851	+	0.606805i	$0.792451\pi$
$32$	5.69770e6	0.960560
$33$	−2.30662e6	−0.338581
$34$	2.10861e6	0.270609
$35$	0	0
$36$	6.57308e6	0.652241
$37$	−9.70272e6	−0.851110	−0.425555	−	0.904933i	$-0.639921\pi$
$37$	−9.70272e6	−0.851110	−0.425555	+	0.904933i	$0.639921\pi$
$38$	150722.	0.0117260
$39$	−5.08798e6	−0.352172
$40$	0	0
$41$	2.98108e7	1.64758	0.823789	−	0.566896i	$-0.191856\pi$
$41$	2.98108e7	1.64758	0.823789	+	0.566896i	$0.191856\pi$
$42$	1.44755e6	0.0717813
$43$	1.95343e7	0.871343	0.435672	−	0.900106i	$-0.356511\pi$
$43$	1.95343e7	0.871343	0.435672	+	0.900106i	$0.356511\pi$
$44$	−1.50142e7	−0.603900
$45$	0	0
$46$	2.35970e7	0.777046
$47$	−5.93794e6	−0.177499	−0.0887494	−	0.996054i	$-0.528287\pi$
$47$	−5.93794e6	−0.177499	−0.0887494	+	0.996054i	$0.528287\pi$
$48$	−9.20389e6	−0.250257
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−1.51130e7	−0.312813
$52$	−3.31187e7	−0.628142
$53$	2.74263e7	0.477448	0.238724	−	0.971088i	$-0.423271\pi$
$53$	2.74263e7	0.477448	0.238724	+	0.971088i	$0.423271\pi$
$54$	2.11284e7	0.338138
$55$	0	0
$56$	2.06971e7	0.281231
$57$	−1.08026e6	−0.0135548
$58$	−6.07908e7	−0.705362
$59$	5.24915e7	0.563969	0.281984	−	0.959419i	$-0.409007\pi$
$59$	5.24915e7	0.563969	0.281984	+	0.959419i	$0.409007\pi$
$60$	0	0
$61$	2.23282e7	0.206476	0.103238	−	0.994657i	$-0.467080\pi$
$61$	2.23282e7	0.206476	0.103238	+	0.994657i	$0.467080\pi$
$62$	−7.49699e7	−0.644354
$63$	3.68839e7	0.294988
$64$	−1.94308e7	−0.144771
$65$	0	0
$66$	−2.11553e7	−0.137237
$67$	−2.74351e8	−1.66330	−0.831649	−	0.555302i	$-0.812603\pi$
$67$	−2.74351e8	−1.66330	−0.831649	+	0.555302i	$0.812603\pi$
$68$	−9.83733e7	−0.557940
$69$	−1.69126e8	−0.898234
$70$	0	0
$71$	−3.63673e8	−1.69843	−0.849216	−	0.528046i	$-0.822925\pi$
$71$	−3.63673e8	−1.69843	−0.849216	+	0.528046i	$0.822925\pi$
$72$	1.32423e8	0.580719
$73$	−2.09245e7	−0.0862387	−0.0431193	−	0.999070i	$-0.513730\pi$
$73$	−2.09245e7	−0.0862387	−0.0431193	+	0.999070i	$0.513730\pi$
$74$	−8.89892e7	−0.344980
$75$	0	0
$76$	−7.03163e6	−0.0241766
$77$	−8.42501e7	−0.273125
$78$	−4.66648e7	−0.142746
$79$	−2.65896e8	−0.768051	−0.384025	−	0.923323i	$-0.625462\pi$
$79$	−2.65896e8	−0.768051	−0.384025	+	0.923323i	$0.625462\pi$
$80$	0	0
$81$	1.50936e8	0.389592
$82$	2.73412e8	0.667813
$83$	9.43764e6	0.0218279	0.0109140	−	0.999940i	$-0.496526\pi$
$83$	9.43764e6	0.0218279	0.0109140	+	0.999940i	$0.496526\pi$
$84$	−6.75326e7	−0.147998
$85$	0	0
$86$	1.79160e8	0.353182
$87$	4.35704e8	0.815369
$88$	−3.02479e8	−0.537679
$89$	−6.64876e8	−1.12327	−0.561637	−	0.827384i	$-0.689828\pi$
$89$	−6.64876e8	−1.12327	−0.561637	+	0.827384i	$0.689828\pi$
$90$	0	0
$91$	−1.85841e8	−0.284089
$92$	−1.10087e9	−1.60211
$93$	5.37329e8	0.744847
$94$	−5.44603e7	−0.0719456
$95$	0	0
$96$	−3.74539e8	−0.450066
$97$	1.20731e9	1.38467	0.692336	−	0.721575i	$-0.256582\pi$
$97$	1.20731e9	1.38467	0.692336	+	0.721575i	$0.256582\pi$
$98$	5.28723e7	0.0579043
$99$	−5.39042e8	−0.563981
$100$	0	0
$101$	1.18204e9	1.13028	0.565139	−	0.824996i	$-0.308823\pi$
$101$	1.18204e9	1.13028	0.565139	+	0.824996i	$0.308823\pi$
$102$	−1.38610e8	−0.126792
$103$	−1.97811e9	−1.73174	−0.865870	−	0.500268i	$-0.833235\pi$
$103$	−1.97811e9	−1.73174	−0.865870	+	0.500268i	$0.833235\pi$
$104$	−6.67215e8	−0.559263
$105$	0	0
$106$	2.51542e8	0.193524
$107$	−1.67828e8	−0.123776	−0.0618881	−	0.998083i	$-0.519712\pi$
$107$	−1.67828e8	−0.123776	−0.0618881	+	0.998083i	$0.519712\pi$
$108$	−9.85703e8	−0.697171
$109$	−1.02540e9	−0.695784	−0.347892	−	0.937535i	$-0.613102\pi$
$109$	−1.02540e9	−0.695784	−0.347892	+	0.937535i	$0.613102\pi$
$110$	0	0
$111$	6.37809e8	0.398783
$112$	−3.36176e8	−0.201876
$113$	−1.27533e9	−0.735814	−0.367907	−	0.929863i	$-0.619926\pi$
$113$	−1.27533e9	−0.735814	−0.367907	+	0.929863i	$0.619926\pi$
$114$	−9.90770e6	−0.00549415
$115$	0	0
$116$	2.83608e9	1.45431
$117$	−1.18903e9	−0.586621
$118$	4.81430e8	0.228594
$119$	−5.52008e8	−0.252339
$120$	0	0
$121$	−1.12667e9	−0.477818
$122$	2.04785e8	0.0836909
$123$	−1.95961e9	−0.771965
$124$	3.49758e9	1.32853
$125$	0	0
$126$	3.38284e8	0.119568
$127$	2.90339e9	0.990349	0.495174	−	0.868794i	$-0.335104\pi$
$127$	2.90339e9	0.990349	0.495174	+	0.868794i	$0.335104\pi$
$128$	−3.09543e9	−1.01924
$129$	−1.28409e9	−0.408264
$130$	0	0
$131$	2.05173e9	0.608694	0.304347	−	0.952561i	$-0.401562\pi$
$131$	2.05173e9	0.608694	0.304347	+	0.952561i	$0.401562\pi$
$132$	9.86960e8	0.282955
$133$	−3.94570e7	−0.0109343
$134$	−2.51623e9	−0.674185
$135$	0	0
$136$	−1.98185e9	−0.496759
$137$	−3.25539e9	−0.789514	−0.394757	−	0.918786i	$-0.629171\pi$
$137$	−3.25539e9	−0.789514	−0.394757	+	0.918786i	$0.629171\pi$
$138$	−1.55115e9	−0.364081
$139$	−8.26776e9	−1.87854	−0.939272	−	0.343173i	$-0.888498\pi$
$139$	−8.26776e9	−1.87854	−0.939272	+	0.343173i	$0.888498\pi$
$140$	0	0
$141$	3.90331e8	0.0831662
$142$	−3.33545e9	−0.688425
$143$	2.71598e9	0.543143
$144$	−2.15090e9	−0.416858
$145$	0	0
$146$	−1.91910e8	−0.0349551
$147$	−3.78950e8	−0.0669350
$148$	4.15162e9	0.711279
$149$	1.07127e9	0.178058	0.0890289	−	0.996029i	$-0.471624\pi$
$149$	1.07127e9	0.178058	0.0890289	+	0.996029i	$0.471624\pi$
$150$	0	0
$151$	1.97304e9	0.308844	0.154422	−	0.988005i	$-0.450649\pi$
$151$	1.97304e9	0.308844	0.154422	+	0.988005i	$0.450649\pi$
$152$	−1.41661e8	−0.0215255
$153$	−3.53182e9	−0.521059
$154$	−7.72706e8	−0.110706
$155$	0	0
$156$	2.17706e9	0.294313
$157$	4.61623e9	0.606372	0.303186	−	0.952931i	$-0.401950\pi$
$157$	4.61623e9	0.606372	0.303186	+	0.952931i	$0.401950\pi$
$158$	−2.43868e9	−0.311314
$159$	−1.80287e9	−0.223706
$160$	0	0
$161$	−6.17740e9	−0.724584
$162$	1.38432e9	0.157913
$163$	−6.26525e9	−0.695175	−0.347588	−	0.937648i	$-0.612999\pi$
$163$	−6.26525e9	−0.695175	−0.347588	+	0.937648i	$0.612999\pi$
$164$	−1.27555e10	−1.37689
$165$	0	0
$166$	8.65580e7	0.00884751
$167$	6.21672e9	0.618496	0.309248	−	0.950981i	$-0.399923\pi$
$167$	6.21672e9	0.618496	0.309248	+	0.950981i	$0.399923\pi$
$168$	−1.36052e9	−0.131769
$169$	−4.61353e9	−0.435054
$170$	0	0
$171$	−2.52451e8	−0.0225785
$172$	−8.35837e9	−0.728188
$173$	−8.97209e9	−0.761528	−0.380764	−	0.924672i	$-0.624339\pi$
$173$	−8.97209e9	−0.761528	−0.380764	+	0.924672i	$0.624339\pi$
$174$	3.99609e9	0.330494
$175$	0	0
$176$	4.91306e9	0.385963
$177$	−3.45053e9	−0.264245
$178$	−6.09796e9	−0.455297
$179$	1.76242e10	1.28313	0.641565	−	0.767069i	$-0.278286\pi$
$179$	1.76242e10	1.28313	0.641565	+	0.767069i	$0.278286\pi$
$180$	0	0
$181$	1.62250e9	0.112365	0.0561824	−	0.998421i	$-0.482107\pi$
$181$	1.62250e9	0.112365	0.0561824	+	0.998421i	$0.482107\pi$
$182$	−1.70445e9	−0.115150
$183$	−1.46775e9	−0.0967433
$184$	−2.21784e10	−1.42643
$185$	0	0
$186$	4.92815e9	0.301909
$187$	8.06735e9	0.482441
$188$	2.54074e9	0.148337
$189$	−5.53113e9	−0.315309
$190$	0	0
$191$	1.66601e10	0.905788	0.452894	−	0.891564i	$-0.350392\pi$
$191$	1.66601e10	0.905788	0.452894	+	0.891564i	$0.350392\pi$
$192$	1.27728e9	0.0678316
$193$	−2.41341e10	−1.25206	−0.626028	−	0.779801i	$-0.715320\pi$
$193$	−2.41341e10	−1.25206	−0.626028	+	0.779801i	$0.715320\pi$
$194$	1.10730e10	0.561249
$195$	0	0
$196$	−2.46666e9	−0.119387
$197$	3.89843e9	0.184413	0.0922066	−	0.995740i	$-0.470608\pi$
$197$	3.89843e9	0.184413	0.0922066	+	0.995740i	$0.470608\pi$
$198$	−4.94387e9	−0.228599
$199$	−1.87489e10	−0.847493	−0.423747	−	0.905781i	$-0.639285\pi$
$199$	−1.87489e10	−0.847493	−0.423747	+	0.905781i	$0.639285\pi$
$200$	0	0
$201$	1.80345e10	0.779330
$202$	1.08411e10	0.458135
$203$	1.59142e10	0.657740
$204$	6.46658e9	0.261420
$205$	0	0
$206$	−1.81424e10	−0.701927
$207$	−3.95238e10	−1.49621
$208$	1.08373e10	0.401456
$209$	5.76647e8	0.0209051
$210$	0	0
$211$	−2.20489e9	−0.0765801	−0.0382900	−	0.999267i	$-0.512191\pi$
$211$	−2.20489e9	−0.0765801	−0.0382900	+	0.999267i	$0.512191\pi$
$212$	−1.17352e10	−0.399007
$213$	2.39060e10	0.795792
$214$	−1.53925e9	−0.0501702
$215$	0	0
$216$	−1.98582e10	−0.620722
$217$	1.96262e10	0.600851
$218$	−9.40454e9	−0.282022
$219$	1.37547e9	0.0404067
$220$	0	0
$221$	1.77952e10	0.501807
$222$	5.84971e9	0.161639
$223$	2.65324e10	0.718463	0.359231	−	0.933249i	$-0.383039\pi$
$223$	2.65324e10	0.718463	0.359231	+	0.933249i	$0.383039\pi$
$224$	−1.36802e10	−0.363058
$225$	0	0
$226$	−1.16967e10	−0.298248
$227$	−7.78091e10	−1.94498	−0.972488	−	0.232955i	$-0.925161\pi$
$227$	−7.78091e10	−1.94498	−0.972488	+	0.232955i	$0.925161\pi$
$228$	4.62225e8	0.0113278
$229$	4.84637e10	1.16455	0.582274	−	0.812993i	$-0.302163\pi$
$229$	4.84637e10	1.16455	0.582274	+	0.812993i	$0.302163\pi$
$230$	0	0
$231$	5.53818e9	0.127972
$232$	5.71362e10	1.29484
$233$	2.38429e10	0.529978	0.264989	−	0.964251i	$-0.414632\pi$
$233$	2.38429e10	0.529978	0.264989	+	0.964251i	$0.414632\pi$
$234$	−1.09053e10	−0.237775
$235$	0	0
$236$	−2.24602e10	−0.471313
$237$	1.74787e10	0.359866
$238$	−5.06278e9	−0.102280
$239$	6.25895e10	1.24083	0.620413	−	0.784275i	$-0.286965\pi$
$239$	6.25895e10	1.24083	0.620413	+	0.784275i	$0.286965\pi$
$240$	0	0
$241$	−7.96605e10	−1.52113	−0.760565	−	0.649262i	$-0.775078\pi$
$241$	−7.96605e10	−1.52113	−0.760565	+	0.649262i	$0.775078\pi$
$242$	−1.03333e10	−0.193674
$243$	−5.52651e10	−1.01677
$244$	−9.55384e9	−0.172554
$245$	0	0
$246$	−1.79727e10	−0.312901
$247$	1.27198e9	0.0217442
$248$	7.04629e10	1.18285
$249$	−6.20384e8	−0.0102274
$250$	0	0
$251$	−5.44549e10	−0.865975	−0.432988	−	0.901400i	$-0.642541\pi$
$251$	−5.44549e10	−0.865975	−0.432988	+	0.901400i	$0.642541\pi$
$252$	−1.57820e10	−0.246524
$253$	9.02799e10	1.38532
$254$	2.66286e10	0.401418
$255$	0	0
$256$	−1.84414e10	−0.268358
$257$	5.35278e10	0.765385	0.382693	−	0.923876i	$-0.374997\pi$
$257$	5.35278e10	0.765385	0.382693	+	0.923876i	$0.374997\pi$
$258$	−1.17771e10	−0.165482
$259$	2.32962e10	0.321689
$260$	0	0
$261$	1.01821e11	1.35818
$262$	1.88176e10	0.246722
$263$	5.81425e10	0.749364	0.374682	−	0.927153i	$-0.377752\pi$
$263$	5.81425e10	0.749364	0.374682	+	0.927153i	$0.377752\pi$
$264$	1.98835e10	0.251927
$265$	0	0
$266$	−3.61883e8	−0.00443201
$267$	4.37057e10	0.526304
$268$	1.17390e11	1.39003
$269$	4.67380e10	0.544233	0.272116	−	0.962264i	$-0.412276\pi$
$269$	4.67380e10	0.544233	0.272116	+	0.962264i	$0.412276\pi$
$270$	0	0
$271$	2.68147e10	0.302003	0.151001	−	0.988534i	$-0.451750\pi$
$271$	2.68147e10	0.302003	0.151001	+	0.988534i	$0.451750\pi$
$272$	3.21905e10	0.356589
$273$	1.22163e10	0.133109
$274$	−2.98570e10	−0.320014
$275$	0	0
$276$	7.23660e10	0.750661
$277$	−1.12549e11	−1.14863	−0.574316	−	0.818633i	$-0.694732\pi$
$277$	−1.12549e11	−1.14863	−0.574316	+	0.818633i	$0.694732\pi$
$278$	−7.58284e10	−0.761431
$279$	1.25571e11	1.24071
$280$	0	0
$281$	−4.60761e10	−0.440857	−0.220428	−	0.975403i	$-0.570746\pi$
$281$	−4.60761e10	−0.440857	−0.220428	+	0.975403i	$0.570746\pi$
$282$	3.57995e9	0.0337098
$283$	−7.94071e10	−0.735902	−0.367951	−	0.929845i	$-0.619941\pi$
$283$	−7.94071e10	−0.735902	−0.367951	+	0.929845i	$0.619941\pi$
$284$	1.55609e11	1.41939
$285$	0	0
$286$	2.49098e10	0.220152
$287$	−7.15757e10	−0.622726
$288$	−8.75275e10	−0.749684
$289$	−6.57304e10	−0.554276
$290$	0	0
$291$	−7.93628e10	−0.648782
$292$	8.95322e9	0.0720703
$293$	1.41265e11	1.11977	0.559887	−	0.828569i	$-0.310844\pi$
$293$	1.41265e11	1.11977	0.559887	+	0.828569i	$0.310844\pi$
$294$	−3.47556e9	−0.0271308
$295$	0	0
$296$	8.36393e10	0.633283
$297$	8.08351e10	0.602832
$298$	9.82523e9	0.0721721
$299$	1.99142e11	1.44093
$300$	0	0
$301$	−4.69018e10	−0.329337
$302$	1.80958e10	0.125184
$303$	−7.77013e10	−0.529586
$304$	2.30094e9	0.0154517
$305$	0	0
$306$	−3.23923e10	−0.211201
$307$	5.58349e10	0.358742	0.179371	−	0.983781i	$-0.442594\pi$
$307$	5.58349e10	0.358742	0.179371	+	0.983781i	$0.442594\pi$
$308$	3.60491e10	0.228253
$309$	1.30031e11	0.811399
$310$	0	0
$311$	5.26501e10	0.319137	0.159569	−	0.987187i	$-0.448990\pi$
$311$	5.26501e10	0.319137	0.159569	+	0.987187i	$0.448990\pi$
$312$	4.38594e10	0.262040
$313$	2.51256e11	1.47968	0.739838	−	0.672785i	$-0.234902\pi$
$313$	2.51256e11	1.47968	0.739838	+	0.672785i	$0.234902\pi$
$314$	4.23381e10	0.245781
$315$	0	0
$316$	1.13772e11	0.641866
$317$	1.16999e11	0.650749	0.325375	−	0.945585i	$-0.394510\pi$
$317$	1.16999e11	0.650749	0.325375	+	0.945585i	$0.394510\pi$
$318$	−1.65351e10	−0.0906747
$319$	−2.32580e11	−1.25752
$320$	0	0
$321$	1.10322e10	0.0579948
$322$	−5.66564e10	−0.293696
$323$	3.77820e9	0.0193141
$324$	−6.45828e10	−0.325585
$325$	0	0
$326$	−5.74622e10	−0.281775
$327$	6.74048e10	0.326006
$328$	−2.56975e11	−1.22591
$329$	1.42570e10	0.0670883
$330$	0	0
$331$	−2.51419e11	−1.15126	−0.575629	−	0.817711i	$-0.695243\pi$
$331$	−2.51419e11	−1.15126	−0.575629	+	0.817711i	$0.695243\pi$
$332$	−4.03820e9	−0.0182417
$333$	1.49052e11	0.664262
$334$	5.70171e10	0.250695
$335$	0	0
$336$	2.20985e10	0.0945882
$337$	−6.11427e10	−0.258232	−0.129116	−	0.991630i	$-0.541214\pi$
$337$	−6.11427e10	−0.258232	−0.129116	+	0.991630i	$0.541214\pi$
$338$	−4.23133e10	−0.176340
$339$	8.38336e10	0.344762
$340$	0	0
$341$	−2.86828e11	−1.14875
$342$	−2.31537e9	−0.00915173
$343$	−1.38413e10	−0.0539949
$344$	−1.68389e11	−0.648338
$345$	0	0
$346$	−8.22882e10	−0.308670
$347$	1.68668e11	0.624524	0.312262	−	0.949996i	$-0.398913\pi$
$347$	1.68668e11	0.624524	0.312262	+	0.949996i	$0.398913\pi$
$348$	−1.86430e11	−0.681410
$349$	−3.31182e11	−1.19496	−0.597479	−	0.801885i	$-0.703831\pi$
$349$	−3.31182e11	−1.19496	−0.597479	+	0.801885i	$0.703831\pi$
$350$	0	0
$351$	1.78308e11	0.627030
$352$	1.99930e11	0.694122
$353$	−3.78560e11	−1.29762	−0.648811	−	0.760949i	$-0.724734\pi$
$353$	−3.78560e11	−1.29762	−0.648811	+	0.760949i	$0.724734\pi$
$354$	−3.16468e10	−0.107106
$355$	0	0
$356$	2.84489e11	0.938728
$357$	3.62863e10	0.118232
$358$	1.61641e11	0.520091
$359$	−1.60137e11	−0.508822	−0.254411	−	0.967096i	$-0.581882\pi$
$359$	−1.60137e11	−0.508822	−0.254411	+	0.967096i	$0.581882\pi$
$360$	0	0
$361$	−3.22418e11	−0.999163
$362$	1.48809e10	0.0455449
$363$	7.40617e10	0.223879
$364$	7.95179e10	0.237415
$365$	0	0
$366$	−1.34615e10	−0.0392130
$367$	−5.13837e11	−1.47852	−0.739261	−	0.673419i	$-0.764825\pi$
$367$	−5.13837e11	−1.47852	−0.739261	+	0.673419i	$0.764825\pi$
$368$	3.60236e11	1.02394
$369$	−4.57950e11	−1.28588
$370$	0	0
$371$	−6.58505e10	−0.180458
$372$	−2.29914e11	−0.622474
$373$	6.70900e10	0.179460	0.0897301	−	0.995966i	$-0.471400\pi$
$373$	6.70900e10	0.179460	0.0897301	+	0.995966i	$0.471400\pi$
$374$	7.39903e10	0.195548
$375$	0	0
$376$	5.11862e10	0.132071
$377$	−5.13030e11	−1.30800
$378$	−5.07292e10	−0.127804
$379$	4.15471e11	1.03434	0.517171	−	0.855882i	$-0.326985\pi$
$379$	4.15471e11	1.03434	0.517171	+	0.855882i	$0.326985\pi$
$380$	0	0
$381$	−1.90854e11	−0.464023
$382$	1.52799e11	0.367143
$383$	3.51976e11	0.835831	0.417915	−	0.908486i	$-0.362761\pi$
$383$	3.51976e11	0.835831	0.417915	+	0.908486i	$0.362761\pi$
$384$	2.03478e11	0.477560
$385$	0	0
$386$	−2.21348e11	−0.507496
$387$	−3.00084e11	−0.680053
$388$	−5.16588e11	−1.15718
$389$	−2.60061e11	−0.575840	−0.287920	−	0.957654i	$-0.592964\pi$
$389$	−2.60061e11	−0.575840	−0.287920	+	0.957654i	$0.592964\pi$
$390$	0	0
$391$	5.91516e11	1.27989
$392$	−4.96937e10	−0.106295
$393$	−1.34871e11	−0.285201
$394$	3.57548e10	0.0747482
$395$	0	0
$396$	2.30647e11	0.471323
$397$	−7.34338e11	−1.48367	−0.741837	−	0.670580i	$-0.766045\pi$
$397$	−7.34338e11	−1.48367	−0.741837	+	0.670580i	$0.766045\pi$
$398$	−1.71957e11	−0.343514
$399$	2.59371e9	0.00512322
$400$	0	0
$401$	8.08296e11	1.56106	0.780532	−	0.625116i	$-0.214948\pi$
$401$	8.08296e11	1.56106	0.780532	+	0.625116i	$0.214948\pi$
$402$	1.65405e11	0.315886
$403$	−6.32691e11	−1.19487
$404$	−5.05773e11	−0.944581
$405$	0	0
$406$	1.45959e11	0.266602
$407$	−3.40464e11	−0.615030
$408$	1.30277e11	0.232754
$409$	−9.11153e11	−1.61004	−0.805020	−	0.593248i	$-0.797845\pi$
$409$	−9.11153e11	−1.61004	−0.805020	+	0.593248i	$0.797845\pi$
$410$	0	0
$411$	2.13993e11	0.369923
$412$	8.46398e11	1.44723
$413$	−1.26032e11	−0.213160
$414$	−3.62495e11	−0.606458
$415$	0	0
$416$	4.41010e11	0.721985
$417$	5.43482e11	0.880183
$418$	5.28876e9	0.00847345
$419$	4.94109e11	0.783177	0.391589	−	0.920140i	$-0.371926\pi$
$419$	4.94109e11	0.783177	0.391589	+	0.920140i	$0.371926\pi$
$420$	0	0
$421$	−1.15145e10	−0.0178639	−0.00893197	−	0.999960i	$-0.502843\pi$
$421$	−1.15145e10	−0.0178639	−0.00893197	+	0.999960i	$0.502843\pi$
$422$	−2.02223e10	−0.0310402
$423$	9.12181e10	0.138532
$424$	−2.36420e11	−0.355253
$425$	0	0
$426$	2.19256e11	0.322558
$427$	−5.36100e10	−0.0780406
$428$	7.18106e10	0.103441
$429$	−1.78535e11	−0.254487
$430$	0	0
$431$	−9.42534e11	−1.31568	−0.657839	−	0.753159i	$-0.728529\pi$
$431$	−9.42534e11	−1.31568	−0.657839	+	0.753159i	$0.728529\pi$
$432$	3.22549e11	0.445574
$433$	−1.01849e12	−1.39239	−0.696196	−	0.717852i	$-0.745125\pi$
$433$	−1.01849e12	−1.39239	−0.696196	+	0.717852i	$0.745125\pi$
$434$	1.80003e11	0.243543
$435$	0	0
$436$	4.38751e11	0.581472
$437$	4.22810e10	0.0554598
$438$	1.26152e10	0.0163781
$439$	−7.89357e11	−1.01434	−0.507169	−	0.861847i	$-0.669308\pi$
$439$	−7.89357e11	−1.01434	−0.507169	+	0.861847i	$0.669308\pi$
$440$	0	0
$441$	−8.85583e10	−0.111495
$442$	1.63210e11	0.203397
$443$	−1.06770e12	−1.31714	−0.658572	−	0.752518i	$-0.728839\pi$
$443$	−1.06770e12	−1.31714	−0.658572	+	0.752518i	$0.728839\pi$
$444$	−2.72907e11	−0.333266
$445$	0	0
$446$	2.43344e11	0.291215
$447$	−7.04200e10	−0.0834281
$448$	4.66533e10	0.0547182
$449$	−3.31695e9	−0.00385150	−0.00192575	−	0.999998i	$-0.500613\pi$
$449$	−3.31695e9	−0.00385150	−0.00192575	+	0.999998i	$0.500613\pi$
$450$	0	0
$451$	1.04605e12	1.19058
$452$	5.45689e11	0.614926
$453$	−1.29698e11	−0.144707
$454$	−7.13632e11	−0.788357
$455$	0	0
$456$	9.31207e9	0.0100857
$457$	7.03146e11	0.754089	0.377045	−	0.926195i	$-0.376940\pi$
$457$	7.03146e11	0.754089	0.377045	+	0.926195i	$0.376940\pi$
$458$	4.44489e11	0.472026
$459$	5.29633e11	0.556952
$460$	0	0
$461$	−1.86192e12	−1.92003	−0.960015	−	0.279950i	$-0.909682\pi$
$461$	−1.86192e12	−1.92003	−0.960015	+	0.279950i	$0.909682\pi$
$462$	5.07938e10	0.0518707
$463$	1.06950e11	0.108160	0.0540799	−	0.998537i	$-0.482777\pi$
$463$	1.06950e11	0.108160	0.0540799	+	0.998537i	$0.482777\pi$
$464$	−9.28043e11	−0.929474
$465$	0	0
$466$	2.18677e11	0.214816
$467$	−4.13997e11	−0.402783	−0.201392	−	0.979511i	$-0.564546\pi$
$467$	−4.13997e11	−0.402783	−0.201392	+	0.979511i	$0.564546\pi$
$468$	5.08766e11	0.490243
$469$	6.58717e11	0.628667
$470$	0	0
$471$	−3.03448e11	−0.284113
$472$	−4.52487e11	−0.419631
$473$	6.85450e11	0.629652
$474$	1.60307e11	0.145865
$475$	0	0
$476$	2.36194e11	0.210881
$477$	−4.21320e11	−0.372631
$478$	5.74044e11	0.502944
$479$	−8.54131e10	−0.0741336	−0.0370668	−	0.999313i	$-0.511801\pi$
$479$	−8.54131e10	−0.0741336	−0.0370668	+	0.999313i	$0.511801\pi$
$480$	0	0
$481$	−7.51004e11	−0.639719
$482$	−7.30612e11	−0.616560
$483$	4.06072e11	0.339501
$484$	4.82082e11	0.399316
$485$	0	0
$486$	−5.06868e11	−0.412127
$487$	−4.94789e11	−0.398602	−0.199301	−	0.979938i	$-0.563867\pi$
$487$	−4.94789e11	−0.398602	−0.199301	+	0.979938i	$0.563867\pi$
$488$	−1.92474e11	−0.153632
$489$	4.11847e11	0.325721
$490$	0	0
$491$	1.11163e12	0.863168	0.431584	−	0.902073i	$-0.357955\pi$
$491$	1.11163e12	0.863168	0.431584	+	0.902073i	$0.357955\pi$
$492$	8.38484e11	0.645137
$493$	−1.52387e12	−1.16181
$494$	1.16661e10	0.00881359
$495$	0	0
$496$	−1.14450e12	−0.849083
$497$	8.73178e11	0.641947
$498$	−5.68990e9	−0.00414546
$499$	8.18377e11	0.590882	0.295441	−	0.955361i	$-0.404533\pi$
$499$	8.18377e11	0.590882	0.295441	+	0.955361i	$0.404533\pi$
$500$	0	0
$501$	−4.08656e11	−0.289793
$502$	−4.99437e11	−0.351006
$503$	−3.13384e11	−0.218284	−0.109142	−	0.994026i	$-0.534810\pi$
$503$	−3.13384e11	−0.218284	−0.109142	+	0.994026i	$0.534810\pi$
$504$	−3.17947e11	−0.219491
$505$	0	0
$506$	8.28009e11	0.561510
$507$	3.03270e11	0.203842
$508$	−1.24231e12	−0.827642
$509$	−1.02554e12	−0.677211	−0.338606	−	0.940928i	$-0.609955\pi$
$509$	−1.02554e12	−0.677211	−0.338606	+	0.940928i	$0.609955\pi$
$510$	0	0
$511$	5.02397e10	0.0325951
$512$	1.41572e12	0.910467
$513$	3.78577e10	0.0241338
$514$	4.90934e11	0.310234
$515$	0	0
$516$	5.49438e11	0.341189
$517$	−2.08360e11	−0.128265
$518$	2.13663e11	0.130390
$519$	5.89781e11	0.356810
$520$	0	0
$521$	−3.18952e12	−1.89651	−0.948255	−	0.317510i	$-0.897153\pi$
$521$	−3.18952e12	−1.89651	−0.948255	+	0.317510i	$0.897153\pi$
$522$	9.33862e11	0.550510
$523$	−9.43708e11	−0.551544	−0.275772	−	0.961223i	$-0.588933\pi$
$523$	−9.43708e11	−0.551544	−0.275772	+	0.961223i	$0.588933\pi$
$524$	−8.77898e11	−0.508690
$525$	0	0
$526$	5.33258e11	0.303740
$527$	−1.87930e12	−1.06133
$528$	−3.22961e11	−0.180841
$529$	4.81837e12	2.67516
$530$	0	0
$531$	−8.06370e11	−0.440158
$532$	1.68829e10	0.00913789
$533$	2.30740e12	1.23837
$534$	4.00850e11	0.213327
$535$	0	0
$536$	2.36496e12	1.23761
$537$	−1.15853e12	−0.601204
$538$	4.28661e11	0.220594
$539$	2.02284e11	0.103232
$540$	0	0
$541$	−8.78618e11	−0.440973	−0.220487	−	0.975390i	$-0.570765\pi$
$541$	−8.78618e11	−0.440973	−0.220487	+	0.975390i	$0.570765\pi$
$542$	2.45933e11	0.122411
$543$	−1.06655e11	−0.0526480
$544$	1.30994e12	0.641295
$545$	0	0
$546$	1.12042e11	0.0539529
$547$	−4.56216e11	−0.217885	−0.108943	−	0.994048i	$-0.534746\pi$
$547$	−4.56216e11	−0.217885	−0.108943	+	0.994048i	$0.534746\pi$
$548$	1.39292e12	0.659803
$549$	−3.43004e11	−0.161147
$550$	0	0
$551$	−1.08925e11	−0.0503435
$552$	1.45790e12	0.668347
$553$	6.38416e11	0.290296
$554$	−1.03225e12	−0.465575
$555$	0	0
$556$	3.53763e12	1.56991
$557$	−1.63980e12	−0.721842	−0.360921	−	0.932596i	$-0.617538\pi$
$557$	−1.63980e12	−0.721842	−0.360921	+	0.932596i	$0.617538\pi$
$558$	1.15168e12	0.502896
$559$	1.51198e12	0.654927
$560$	0	0
$561$	−5.30308e11	−0.226045
$562$	−4.22590e11	−0.178692
$563$	−4.36151e11	−0.182957	−0.0914786	−	0.995807i	$-0.529159\pi$
$563$	−4.36151e11	−0.182957	−0.0914786	+	0.995807i	$0.529159\pi$
$564$	−1.67016e11	−0.0695026
$565$	0	0
$566$	−7.28288e11	−0.298283
$567$	−3.62397e11	−0.147252
$568$	3.13493e12	1.26375
$569$	1.76284e12	0.705029	0.352514	−	0.935806i	$-0.385327\pi$
$569$	1.76284e12	0.705029	0.352514	+	0.935806i	$0.385327\pi$
$570$	0	0
$571$	2.37232e11	0.0933922	0.0466961	−	0.998909i	$-0.485131\pi$
$571$	2.37232e11	0.0933922	0.0466961	+	0.998909i	$0.485131\pi$
$572$	−1.16212e12	−0.453909
$573$	−1.09515e12	−0.424403
$574$	−6.56462e11	−0.252410
$575$	0	0
$576$	2.98494e11	0.112988
$577$	3.72080e12	1.39748	0.698739	−	0.715377i	$-0.253745\pi$
$577$	3.72080e12	1.39748	0.698739	+	0.715377i	$0.253745\pi$
$578$	−6.02851e11	−0.224665
$579$	1.58646e12	0.586644
$580$	0	0
$581$	−2.26598e10	−0.00825017
$582$	−7.27882e11	−0.262971
$583$	9.62377e11	0.345014
$584$	1.80373e11	0.0641674
$585$	0	0
$586$	1.29562e12	0.453878
$587$	6.46176e11	0.224636	0.112318	−	0.993672i	$-0.464172\pi$
$587$	6.46176e11	0.224636	0.112318	+	0.993672i	$0.464172\pi$
$588$	1.62146e11	0.0559381
$589$	−1.34331e11	−0.0459892
$590$	0	0
$591$	−2.56264e11	−0.0864059
$592$	−1.35853e12	−0.454590
$593$	5.05774e12	1.67962	0.839808	−	0.542883i	$-0.182667\pi$
$593$	5.05774e12	1.67962	0.839808	+	0.542883i	$0.182667\pi$
$594$	7.41385e11	0.244346
$595$	0	0
$596$	−4.58377e11	−0.148804
$597$	1.23246e12	0.397089
$598$	1.82644e12	0.584051
$599$	−4.61588e11	−0.146499	−0.0732494	−	0.997314i	$-0.523337\pi$
$599$	−4.61588e11	−0.146499	−0.0732494	+	0.997314i	$0.523337\pi$
$600$	0	0
$601$	−6.31800e12	−1.97535	−0.987677	−	0.156509i	$-0.949976\pi$
$601$	−6.31800e12	−1.97535	−0.987677	+	0.156509i	$0.949976\pi$
$602$	−4.30163e11	−0.133490
$603$	4.21455e12	1.29815
$604$	−8.44227e11	−0.258103
$605$	0	0
$606$	−7.12643e11	−0.214657
$607$	1.45276e12	0.434356	0.217178	−	0.976132i	$-0.430315\pi$
$607$	1.45276e12	0.434356	0.217178	+	0.976132i	$0.430315\pi$
$608$	9.36335e10	0.0277885
$609$	−1.04612e12	−0.308181
$610$	0	0
$611$	−4.59605e11	−0.133413
$612$	1.51120e12	0.435453
$613$	−1.20124e12	−0.343603	−0.171802	−	0.985132i	$-0.554959\pi$
$613$	−1.20124e12	−0.343603	−0.171802	+	0.985132i	$0.554959\pi$
$614$	5.12094e11	0.145409
$615$	0	0
$616$	7.26252e11	0.203224
$617$	−3.13545e12	−0.870997	−0.435498	−	0.900189i	$-0.643428\pi$
$617$	−3.13545e12	−0.870997	−0.435498	+	0.900189i	$0.643428\pi$
$618$	1.19259e12	0.328884
$619$	−5.17127e12	−1.41576	−0.707880	−	0.706333i	$-0.750348\pi$
$619$	−5.17127e12	−1.41576	−0.707880	+	0.706333i	$0.750348\pi$
$620$	0	0
$621$	5.92700e12	1.59927
$622$	4.82884e11	0.129356
$623$	1.59637e12	0.424557
$624$	−7.12394e11	−0.188100
$625$	0	0
$626$	2.30441e12	0.599757
$627$	−3.79059e10	−0.00979497
$628$	−1.97520e12	−0.506749
$629$	−2.23073e12	−0.568223
$630$	0	0
$631$	−6.37331e12	−1.60042	−0.800208	−	0.599723i	$-0.795278\pi$
$631$	−6.37331e12	−1.60042	−0.800208	+	0.599723i	$0.795278\pi$
$632$	2.29208e12	0.571481
$633$	1.44939e11	0.0358812
$634$	1.07306e12	0.263768
$635$	0	0
$636$	7.71416e11	0.186953
$637$	4.46204e11	0.107376
$638$	−2.13312e12	−0.509710
$639$	5.58670e12	1.32557
$640$	0	0
$641$	−5.74174e12	−1.34333	−0.671665	−	0.740855i	$-0.734421\pi$
$641$	−5.74174e12	−1.34333	−0.671665	+	0.740855i	$0.734421\pi$
$642$	1.01182e11	0.0235070
$643$	5.85135e11	0.134992	0.0674958	−	0.997720i	$-0.478499\pi$
$643$	5.85135e11	0.134992	0.0674958	+	0.997720i	$0.478499\pi$
$644$	2.64320e12	0.605541
$645$	0	0
$646$	3.46520e10	0.00782857
$647$	1.80915e12	0.405887	0.202943	−	0.979190i	$-0.434949\pi$
$647$	1.80915e12	0.405887	0.202943	+	0.979190i	$0.434949\pi$
$648$	−1.30110e12	−0.289883
$649$	1.84191e12	0.407536
$650$	0	0
$651$	−1.29013e12	−0.281526
$652$	2.68079e12	0.580963
$653$	−2.43900e12	−0.524932	−0.262466	−	0.964941i	$-0.584536\pi$
$653$	−2.43900e12	−0.524932	−0.262466	+	0.964941i	$0.584536\pi$
$654$	6.18208e11	0.132140
$655$	0	0
$656$	4.17396e12	0.879996
$657$	3.21440e11	0.0673063
$658$	1.30759e11	0.0271929
$659$	7.42836e12	1.53429	0.767147	−	0.641471i	$-0.221676\pi$
$659$	7.42836e12	1.53429	0.767147	+	0.641471i	$0.221676\pi$
$660$	0	0
$661$	−6.34861e12	−1.29352	−0.646759	−	0.762695i	$-0.723876\pi$
$661$	−6.34861e12	−1.29352	−0.646759	+	0.762695i	$0.723876\pi$
$662$	−2.30591e12	−0.466640
$663$	−1.16977e12	−0.235119
$664$	−8.13544e10	−0.0162414
$665$	0	0
$666$	1.36704e12	0.269245
$667$	−1.70533e13	−3.33611
$668$	−2.66002e12	−0.516882
$669$	−1.74411e12	−0.336632
$670$	0	0
$671$	7.83487e11	0.149204
$672$	8.99267e11	0.170109
$673$	−3.17186e12	−0.596000	−0.298000	−	0.954566i	$-0.596320\pi$
$673$	−3.17186e12	−0.596000	−0.298000	+	0.954566i	$0.596320\pi$
$674$	−5.60774e11	−0.104669
$675$	0	0
$676$	1.97405e12	0.363578
$677$	2.32240e12	0.424901	0.212450	−	0.977172i	$-0.431856\pi$
$677$	2.32240e12	0.424901	0.212450	+	0.977172i	$0.431856\pi$
$678$	7.68886e11	0.139742
$679$	−2.89876e12	−0.523357
$680$	0	0
$681$	5.11479e12	0.911309
$682$	−2.63066e12	−0.465624
$683$	−3.78639e12	−0.665782	−0.332891	−	0.942965i	$-0.608024\pi$
$683$	−3.78639e12	−0.665782	−0.332891	+	0.942965i	$0.608024\pi$
$684$	1.08019e11	0.0188690
$685$	0	0
$686$	−1.26946e11	−0.0218858
$687$	−3.18577e12	−0.545643
$688$	2.73509e12	0.465397
$689$	2.12283e12	0.358864
$690$	0	0
$691$	−5.70532e12	−0.951982	−0.475991	−	0.879450i	$-0.657911\pi$
$691$	−5.70532e12	−0.951982	−0.475991	+	0.879450i	$0.657911\pi$
$692$	3.83900e12	0.636415
$693$	1.29424e12	0.213165
$694$	1.54695e12	0.253138
$695$	0	0
$696$	−3.75585e12	−0.606690
$697$	6.85372e12	1.09997
$698$	−3.03746e12	−0.484352
$699$	−1.56732e12	−0.248318
$700$	0	0
$701$	6.25160e12	0.977823	0.488912	−	0.872333i	$-0.337394\pi$
$701$	6.25160e12	0.977823	0.488912	+	0.872333i	$0.337394\pi$
$702$	1.63536e12	0.254154
$703$	−1.59450e11	−0.0246222
$704$	−6.81818e11	−0.104614
$705$	0	0
$706$	−3.47199e12	−0.525965
$707$	−2.83807e12	−0.427205
$708$	1.47642e12	0.220831
$709$	−8.01996e12	−1.19197	−0.595983	−	0.802997i	$-0.703238\pi$
$709$	−8.01996e12	−1.19197	−0.595983	+	0.802997i	$0.703238\pi$
$710$	0	0
$711$	4.08467e12	0.599437
$712$	5.73136e12	0.835791
$713$	−2.10308e13	−3.04757
$714$	3.32802e11	0.0479230
$715$	0	0
$716$	−7.54107e12	−1.07232
$717$	−4.11433e12	−0.581383
$718$	−1.46871e12	−0.206241
$719$	1.35002e12	0.188391	0.0941953	−	0.995554i	$-0.469972\pi$
$719$	1.35002e12	0.188391	0.0941953	+	0.995554i	$0.469972\pi$
$720$	0	0
$721$	4.74944e12	0.654537
$722$	−2.95708e12	−0.404991
$723$	5.23649e12	0.712718
$724$	−6.94238e11	−0.0939042
$725$	0	0
$726$	6.79262e11	0.0907450
$727$	1.47778e13	1.96203	0.981013	−	0.193941i	$-0.0621270\pi$
$727$	1.47778e13	1.96203	0.981013	+	0.193941i	$0.0621270\pi$
$728$	1.60198e12	0.211381
$729$	6.61984e11	0.0868108
$730$	0	0
$731$	4.49108e12	0.581731
$732$	6.28022e11	0.0808491
$733$	6.70116e12	0.857398	0.428699	−	0.903447i	$-0.358972\pi$
$733$	6.70116e12	0.857398	0.428699	+	0.903447i	$0.358972\pi$
$734$	−4.71269e12	−0.599290
$735$	0	0
$736$	1.46593e13	1.84146
$737$	−9.62686e12	−1.20193
$738$	−4.20013e12	−0.521205
$739$	−1.39054e13	−1.71508	−0.857540	−	0.514417i	$-0.828008\pi$
$739$	−1.39054e13	−1.71508	−0.857540	+	0.514417i	$0.828008\pi$
$740$	0	0
$741$	−8.36137e10	−0.0101882
$742$	−6.03953e11	−0.0731452
$743$	3.43953e12	0.414047	0.207024	−	0.978336i	$-0.433622\pi$
$743$	3.43953e12	0.414047	0.207024	+	0.978336i	$0.433622\pi$
$744$	−4.63188e12	−0.554216
$745$	0	0
$746$	6.15321e11	0.0727407
$747$	−1.44980e11	−0.0170359
$748$	−3.45188e12	−0.403179
$749$	4.02955e11	0.0467830
$750$	0	0
$751$	1.00823e13	1.15660	0.578298	−	0.815826i	$-0.303717\pi$
$751$	1.00823e13	1.15660	0.578298	+	0.815826i	$0.303717\pi$
$752$	−8.31401e11	−0.0948047
$753$	3.57960e12	0.405748
$754$	−4.70529e12	−0.530170
$755$	0	0
$756$	2.36667e12	0.263506
$757$	1.02703e13	1.13672	0.568360	−	0.822780i	$-0.307578\pi$
$757$	1.02703e13	1.13672	0.568360	+	0.822780i	$0.307578\pi$
$758$	3.81052e12	0.419250
$759$	−5.93456e12	−0.649083
$760$	0	0
$761$	−3.20840e12	−0.346783	−0.173391	−	0.984853i	$-0.555473\pi$
$761$	−3.20840e12	−0.346783	−0.173391	+	0.984853i	$0.555473\pi$
$762$	−1.75043e12	−0.188083
$763$	2.46199e12	0.262982
$764$	−7.12855e12	−0.756974
$765$	0	0
$766$	3.22817e12	0.338787
$767$	4.06292e12	0.423896
$768$	1.21225e12	0.125738
$769$	1.52349e13	1.57098	0.785491	−	0.618872i	$-0.212410\pi$
$769$	1.52349e13	1.57098	0.785491	+	0.618872i	$0.212410\pi$
$770$	0	0
$771$	−3.51865e12	−0.358618
$772$	1.03266e13	1.04635
$773$	8.54195e11	0.0860497	0.0430249	−	0.999074i	$-0.486301\pi$
$773$	8.54195e11	0.0860497	0.0430249	+	0.999074i	$0.486301\pi$
$774$	−2.75224e12	−0.275646
$775$	0	0
$776$	−1.04073e13	−1.03029
$777$	−1.53138e12	−0.150726
$778$	−2.38517e12	−0.233405
$779$	4.89898e11	0.0476636
$780$	0	0
$781$	−1.27611e13	−1.22732
$782$	5.42513e12	0.518776
$783$	−1.52692e13	−1.45174
$784$	8.07158e11	0.0763021
$785$	0	0
$786$	−1.23697e12	−0.115600
$787$	−4.25016e12	−0.394929	−0.197465	−	0.980310i	$-0.563271\pi$
$787$	−4.25016e12	−0.394929	−0.197465	+	0.980310i	$0.563271\pi$
$788$	−1.66807e12	−0.154116
$789$	−3.82200e12	−0.351111
$790$	0	0
$791$	3.06206e12	0.278112
$792$	4.64665e12	0.419640
$793$	1.72823e12	0.155193
$794$	−6.73503e12	−0.601378
$795$	0	0
$796$	8.02231e12	0.708256
$797$	−2.02157e13	−1.77470	−0.887352	−	0.461093i	$-0.847458\pi$
$797$	−2.02157e13	−1.77470	−0.887352	+	0.461093i	$0.847458\pi$
$798$	2.37884e10	0.00207660
$799$	−1.36518e12	−0.118503
$800$	0	0
$801$	1.02138e13	0.876676
$802$	7.41334e12	0.632746
$803$	−7.34231e11	−0.0623179
$804$	−7.71664e12	−0.651292
$805$	0	0
$806$	−5.80278e12	−0.484315
$807$	−3.07232e12	−0.254998
$808$	−1.01894e13	−0.841002
$809$	−6.65781e12	−0.546466	−0.273233	−	0.961948i	$-0.588093\pi$
$809$	−6.65781e12	−0.546466	−0.273233	+	0.961948i	$0.588093\pi$
$810$	0	0
$811$	−9.35525e12	−0.759384	−0.379692	−	0.925113i	$-0.623970\pi$
$811$	−9.35525e12	−0.759384	−0.379692	+	0.925113i	$0.623970\pi$
$812$	−6.80942e12	−0.549678
$813$	−1.76267e12	−0.141502
$814$	−3.12259e12	−0.249290
$815$	0	0
$816$	−2.11604e12	−0.167078
$817$	3.21018e11	0.0252075
$818$	−8.35671e12	−0.652597
$819$	2.85487e12	0.221722
$820$	0	0
$821$	1.61631e13	1.24160	0.620798	−	0.783971i	$-0.286809\pi$
$821$	1.61631e13	1.24160	0.620798	+	0.783971i	$0.286809\pi$
$822$	1.96265e12	0.149941
$823$	−5.97042e12	−0.453634	−0.226817	−	0.973937i	$-0.572832\pi$
$823$	−5.97042e12	−0.453634	−0.226817	+	0.973937i	$0.572832\pi$
$824$	1.70517e13	1.28853
$825$	0	0
$826$	−1.15591e12	−0.0864003
$827$	−7.76424e12	−0.577197	−0.288599	−	0.957450i	$-0.593189\pi$
$827$	−7.76424e12	−0.577197	−0.288599	+	0.957450i	$0.593189\pi$
$828$	1.69115e13	1.25039
$829$	−4.09585e12	−0.301195	−0.150598	−	0.988595i	$-0.548120\pi$
$829$	−4.09585e12	−0.301195	−0.150598	+	0.988595i	$0.548120\pi$
$830$	0	0
$831$	7.39839e12	0.538186
$832$	−1.50397e12	−0.108814
$833$	1.32537e12	0.0953751
$834$	4.98458e12	0.356765
$835$	0	0
$836$	−2.46737e11	−0.0174705
$837$	−1.88306e13	−1.32617
$838$	4.53176e12	0.317445
$839$	4.46741e11	0.0311263	0.0155631	−	0.999879i	$-0.495046\pi$
$839$	4.46741e11	0.0311263	0.0155631	+	0.999879i	$0.495046\pi$
$840$	0	0
$841$	2.94256e13	2.02835
$842$	−1.05606e11	−0.00724079
$843$	3.02882e12	0.206561
$844$	9.43433e11	0.0639985
$845$	0	0
$846$	8.36613e11	0.0561511
$847$	2.70513e12	0.180598
$848$	3.84009e12	0.255012
$849$	5.21983e12	0.344803
$850$	0	0
$851$	−2.49636e13	−1.63164
$852$	−1.02290e13	−0.665049
$853$	−2.72968e13	−1.76539	−0.882696	−	0.469945i	$-0.844274\pi$
$853$	−2.72968e13	−1.76539	−0.882696	+	0.469945i	$0.844274\pi$
$854$	−4.91688e11	−0.0316322
$855$	0	0
$856$	1.44671e12	0.0920979
$857$	−7.67571e12	−0.486077	−0.243038	−	0.970017i	$-0.578144\pi$
$857$	−7.67571e12	−0.486077	−0.243038	+	0.970017i	$0.578144\pi$
$858$	−1.63745e12	−0.103151
$859$	−1.67172e13	−1.04759	−0.523797	−	0.851843i	$-0.675485\pi$
$859$	−1.67172e13	−1.04759	−0.523797	+	0.851843i	$0.675485\pi$
$860$	0	0
$861$	4.70503e12	0.291775
$862$	−8.64452e12	−0.533284
$863$	2.85615e13	1.75280	0.876401	−	0.481582i	$-0.159938\pi$
$863$	2.85615e13	1.75280	0.876401	+	0.481582i	$0.159938\pi$
$864$	1.31257e13	0.801327
$865$	0	0
$866$	−9.34116e12	−0.564378
$867$	4.32079e12	0.259703
$868$	−8.39769e12	−0.502135
$869$	−9.33018e12	−0.555010
$870$	0	0
$871$	−2.12351e13	−1.25018
$872$	8.83916e12	0.517710
$873$	−1.85466e13	−1.08069
$874$	3.87783e11	0.0224795
$875$	0	0
$876$	−5.88540e11	−0.0337682
$877$	8.40714e12	0.479899	0.239950	−	0.970785i	$-0.422869\pi$
$877$	8.40714e12	0.479899	0.239950	+	0.970785i	$0.422869\pi$
$878$	−7.23964e12	−0.411142
$879$	−9.28607e12	−0.524665
$880$	0	0
$881$	−1.99694e13	−1.11680	−0.558398	−	0.829573i	$-0.688584\pi$
$881$	−1.99694e13	−1.11680	−0.558398	+	0.829573i	$0.688584\pi$
$882$	−8.12219e11	−0.0451923
$883$	2.36498e13	1.30919	0.654597	−	0.755978i	$-0.272838\pi$
$883$	2.36498e13	1.30919	0.654597	+	0.755978i	$0.272838\pi$
$884$	−7.61423e12	−0.419364
$885$	0	0
$886$	−9.79250e12	−0.533878
$887$	3.83859e12	0.208217	0.104108	−	0.994566i	$-0.466801\pi$
$887$	3.83859e12	0.208217	0.104108	+	0.994566i	$0.466801\pi$
$888$	−5.49804e12	−0.296722
$889$	−6.97103e12	−0.374317
$890$	0	0
$891$	5.29627e12	0.281527
$892$	−1.13527e13	−0.600425
$893$	−9.75816e10	−0.00513495
$894$	−6.45862e11	−0.0338159
$895$	0	0
$896$	7.43213e12	0.385237
$897$	−1.30906e13	−0.675139
$898$	−3.04216e10	−0.00156113
$899$	5.41798e13	2.76642
$900$	0	0
$901$	6.30551e12	0.318756
$902$	9.59390e12	0.482576
$903$	3.08309e12	0.154309
$904$	1.09936e13	0.547495
$905$	0	0
$906$	−1.18953e12	−0.0586542
$907$	2.31944e13	1.13802	0.569009	−	0.822331i	$-0.307327\pi$
$907$	2.31944e13	1.13802	0.569009	+	0.822331i	$0.307327\pi$
$908$	3.32931e13	1.62543
$909$	−1.81583e13	−0.882142
$910$	0	0
$911$	1.70743e13	0.821317	0.410659	−	0.911789i	$-0.365299\pi$
$911$	1.70743e13	0.821317	0.410659	+	0.911789i	$0.365299\pi$
$912$	−1.51253e11	−0.00723980
$913$	3.31163e11	0.0157733
$914$	6.44896e12	0.305655
$915$	0	0
$916$	−2.07368e13	−0.973221
$917$	−4.92620e12	−0.230065
$918$	4.85757e12	0.225750
$919$	1.49265e13	0.690301	0.345151	−	0.938547i	$-0.387828\pi$
$919$	1.49265e13	0.690301	0.345151	+	0.938547i	$0.387828\pi$
$920$	0	0
$921$	−3.67031e12	−0.168087
$922$	−1.70768e13	−0.778246
$923$	−2.81488e13	−1.27659
$924$	−2.36969e12	−0.106947
$925$	0	0
$926$	9.80898e11	0.0438404
$927$	3.03875e13	1.35156
$928$	−3.77653e13	−1.67158
$929$	2.92103e12	0.128666	0.0643332	−	0.997928i	$-0.479508\pi$
$929$	2.92103e12	0.128666	0.0643332	+	0.997928i	$0.479508\pi$
$930$	0	0
$931$	9.47362e10	0.00413278
$932$	−1.02020e13	−0.442906
$933$	−3.46096e12	−0.149530
$934$	−3.79701e12	−0.163260
$935$	0	0
$936$	1.02497e13	0.436485
$937$	3.53996e13	1.50027	0.750135	−	0.661284i	$-0.229988\pi$
$937$	3.53996e13	1.50027	0.750135	+	0.661284i	$0.229988\pi$
$938$	6.04147e12	0.254818
$939$	−1.65163e13	−0.693295
$940$	0	0
$941$	−4.67286e13	−1.94280	−0.971402	−	0.237439i	$-0.923692\pi$
$941$	−4.67286e13	−1.94280	−0.971402	+	0.237439i	$0.923692\pi$
$942$	−2.78310e12	−0.115159
$943$	7.66985e13	3.15852
$944$	7.34960e12	0.301224
$945$	0	0
$946$	6.28665e12	0.255217
$947$	5.22799e12	0.211232	0.105616	−	0.994407i	$-0.466319\pi$
$947$	5.22799e12	0.211232	0.105616	+	0.994407i	$0.466319\pi$
$948$	−7.47882e12	−0.300743
$949$	−1.61958e12	−0.0648195
$950$	0	0
$951$	−7.69091e12	−0.304905
$952$	4.75842e12	0.187757
$953$	2.46017e13	0.966156	0.483078	−	0.875577i	$-0.339519\pi$
$953$	2.46017e13	0.966156	0.483078	+	0.875577i	$0.339519\pi$
$954$	−3.86417e12	−0.151039
$955$	0	0
$956$	−2.67809e13	−1.03697
$957$	1.52886e13	0.589204
$958$	−7.83373e11	−0.0300486
$959$	7.81618e12	0.298408
$960$	0	0
$961$	4.03773e13	1.52715
$962$	−6.88788e12	−0.259297
$963$	2.57816e12	0.0966031
$964$	3.40853e13	1.27122
$965$	0	0
$966$	3.72431e12	0.137610
$967$	−1.24062e13	−0.456267	−0.228134	−	0.973630i	$-0.573262\pi$
$967$	−1.24062e13	−0.456267	−0.228134	+	0.973630i	$0.573262\pi$
$968$	9.71212e12	0.355529
$969$	−2.48360e11	−0.00904951
$970$	0	0
$971$	5.30324e12	0.191450	0.0957248	−	0.995408i	$-0.469483\pi$
$971$	5.30324e12	0.191450	0.0957248	+	0.995408i	$0.469483\pi$
$972$	2.36469e13	0.849722
$973$	1.98509e13	0.710023
$974$	−4.53799e12	−0.161565
$975$	0	0
$976$	3.12628e12	0.110282
$977$	1.45131e13	0.509606	0.254803	−	0.966993i	$-0.417989\pi$
$977$	1.45131e13	0.509606	0.254803	+	0.966993i	$0.417989\pi$
$978$	3.77728e12	0.132024
$979$	−2.33302e13	−0.811702
$980$	0	0
$981$	1.57521e13	0.543035
$982$	1.01954e13	0.349868
$983$	3.61534e13	1.23498	0.617488	−	0.786580i	$-0.288150\pi$
$983$	3.61534e13	1.23498	0.617488	+	0.786580i	$0.288150\pi$
$984$	1.68923e13	0.574394
$985$	0	0
$986$	−1.39763e13	−0.470917
$987$	−9.37185e11	−0.0314339
$988$	−5.44258e11	−0.0181718
$989$	5.02586e13	1.67043
$990$	0	0
$991$	4.94162e13	1.62756	0.813782	−	0.581170i	$-0.197405\pi$
$991$	4.94162e13	1.62756	0.813782	+	0.581170i	$0.197405\pi$
$992$	−4.65739e13	−1.52700
$993$	1.65271e13	0.539417
$994$	8.00841e12	0.260200
$995$	0	0
$996$	2.65451e11	0.00854708
$997$	3.03522e13	0.972886	0.486443	−	0.873712i	$-0.338294\pi$
$997$	3.03522e13	0.972886	0.486443	+	0.873712i	$0.338294\pi$
$998$	7.50580e12	0.239502
$999$	−2.23519e13	−0.710020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.a.c.1.1		2
5.2	odd	4		175.10.b.c.99.3		4
5.3	odd	4		175.10.b.c.99.2		4
5.4	even	2		35.10.a.b.1.2	✓	2
15.14	odd	2		315.10.a.b.1.1		2
35.34	odd	2		245.10.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.b.1.2	✓	2	5.4	even	2
175.10.a.c.1.1		2	1.1	even	1	trivial
175.10.b.c.99.2		4	5.3	odd	4
175.10.b.c.99.3		4	5.2	odd	4
245.10.a.c.1.2		2	35.34	odd	2
315.10.a.b.1.1		2	15.14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+9.17157 q^{2} -65.7351 q^{3} -427.882 q^{4} -602.894 q^{6} -2401.00 q^{7} -8620.20 q^{8} -15361.9 q^{9} +35089.6 q^{11} +28126.9 q^{12} +77401.4 q^{13} -22020.9 q^{14} +140015. q^{16} +229907. q^{17} -140893. q^{18} +16433.6 q^{19} +157830. q^{21} +321827. q^{22} +2.57284e6 q^{23} +566649. q^{24} +709892. q^{26} +2.30368e6 q^{27} +1.02735e6 q^{28} -6.62817e6 q^{29} -8.17416e6 q^{31} +5.69770e6 q^{32} -2.30662e6 q^{33} +2.10861e6 q^{34} +6.57308e6 q^{36} -9.70272e6 q^{37} +150722. q^{38} -5.08798e6 q^{39} +2.98108e7 q^{41} +1.44755e6 q^{42} +1.95343e7 q^{43} -1.50142e7 q^{44} +2.35970e7 q^{46} -5.93794e6 q^{47} -9.20389e6 q^{48} +5.76480e6 q^{49} -1.51130e7 q^{51} -3.31187e7 q^{52} +2.74263e7 q^{53} +2.11284e7 q^{54} +2.06971e7 q^{56} -1.08026e6 q^{57} -6.07908e7 q^{58} +5.24915e7 q^{59} +2.23282e7 q^{61} -7.49699e7 q^{62} +3.68839e7 q^{63} -1.94308e7 q^{64} -2.11553e7 q^{66} -2.74351e8 q^{67} -9.83733e7 q^{68} -1.69126e8 q^{69} -3.63673e8 q^{71} +1.32423e8 q^{72} -2.09245e7 q^{73} -8.89892e7 q^{74} -7.03163e6 q^{76} -8.42501e7 q^{77} -4.66648e7 q^{78} -2.65896e8 q^{79} +1.50936e8 q^{81} +2.73412e8 q^{82} +9.43764e6 q^{83} -6.75326e7 q^{84} +1.79160e8 q^{86} +4.35704e8 q^{87} -3.02479e8 q^{88} -6.64876e8 q^{89} -1.85841e8 q^{91} -1.10087e9 q^{92} +5.37329e8 q^{93} -5.44603e7 q^{94} -3.74539e8 q^{96} +1.20731e9 q^{97} +5.28723e7 q^{98} -5.39042e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 57624 q^{14} + 112768 q^{16} + 373910 q^{17} + 419472 q^{18} - 143276 q^{19}+ \cdots - 1163466540 q^{99}+O(q^{100}) \) 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 57624 * q^14 + 112768 * q^16 + 373910 * q^17 + 419472 * q^18 - 143276 * q^19 - 417774 * q^21 + 76808 * q^22 + 498908 * q^23 - 2291904 * q^24 + 319736 * q^26 + 6644538 * q^27 + 1728720 * q^28 - 11577554 * q^29 - 3953760 * q^31 + 11398656 * q^32 - 6267894 * q^33 + 4243944 * q^34 - 4466016 * q^36 + 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 + 1058992 * q^41 - 7087752 * q^42 - 15948180 * q^43 - 10187376 * q^44 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 + 11529602 * q^49 + 19409466 * q^51 - 25432656 * q^52 + 25114688 * q^53 + 85496472 * q^54 + 49326144 * q^56 - 39368244 * q^57 - 134182296 * q^58 - 116159208 * q^59 - 44688544 * q^61 - 12388000 * q^62 - 53849628 * q^63 + 79055872 * q^64 - 79894824 * q^66 - 118092496 * q^67 - 140439024 * q^68 - 666320892 * q^69 - 294165824 * q^71 - 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 39622368 * q^76 - 44576966 * q^77 - 140199000 * q^78 - 692852854 * q^79 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 + 100611504 * q^84 - 346989008 * q^86 - 750836190 * q^87 - 105455296 * q^88 - 779043704 * q^89 - 122667090 * q^91 - 495040608 * q^92 + 1549107360 * q^93 - 937691032 * q^94 + 992180736 * q^96 + 2673039406 * q^97 + 138355224 * q^98 - 1163466540 * q^99

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