LMFDB - Embedded newform 25.34.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.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:	$172.457072203$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 $ x^5 - 2x^4 - 1372039866x^3 - 648067657640x^2 + 285631173782445856x - 33409741805340964224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-16460.4$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-71937.8 q^{2} -1.37573e8 q^{3} -3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14 q^{7} +8.63600e14 q^{8} +1.33673e16 q^{9} +O(q^{10})$	\(q-71937.8 q^{2} -1.37573e8 q^{3} -3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14 q^{7} +8.63600e14 q^{8} +1.33673e16 q^{9} -2.33530e17 q^{11} +4.69797e17 q^{12} +2.28395e18 q^{13} -7.74658e18 q^{14} -3.27918e19 q^{16} +2.09885e20 q^{17} -9.61615e20 q^{18} +6.01644e20 q^{19} -1.48145e22 q^{21} +1.67997e22 q^{22} -4.84991e22 q^{23} -1.18808e23 q^{24} -1.64302e23 q^{26} -1.07421e24 q^{27} -3.67730e23 q^{28} -8.15476e22 q^{29} -1.49925e24 q^{31} -5.05930e24 q^{32} +3.21275e25 q^{33} -1.50986e25 q^{34} -4.56479e25 q^{36} -1.78708e25 q^{37} -4.32809e25 q^{38} -3.14210e26 q^{39} -1.94621e26 q^{41} +1.06572e27 q^{42} +9.48110e26 q^{43} +7.97481e26 q^{44} +3.48891e27 q^{46} +6.29157e26 q^{47} +4.51128e27 q^{48} +3.86494e27 q^{49} -2.88745e28 q^{51} -7.79943e27 q^{52} +8.56042e27 q^{53} +7.72760e28 q^{54} +9.29963e28 q^{56} -8.27701e28 q^{57} +5.86635e27 q^{58} +5.43089e27 q^{59} +1.79220e29 q^{61} +1.07853e29 q^{62} +1.43945e30 q^{63} +6.45635e29 q^{64} -2.31118e30 q^{66} +3.33703e29 q^{67} -7.16732e29 q^{68} +6.67217e30 q^{69} -3.44997e30 q^{71} +1.15440e31 q^{72} +7.11823e30 q^{73} +1.28559e30 q^{74} -2.05455e30 q^{76} -2.51476e31 q^{77} +2.26036e31 q^{78} -1.57830e31 q^{79} +7.34723e31 q^{81} +1.40006e31 q^{82} -3.45599e31 q^{83} +5.05898e31 q^{84} -6.82049e31 q^{86} +1.12188e31 q^{87} -2.01677e32 q^{88} -2.35733e32 q^{89} +2.45946e32 q^{91} +1.65619e32 q^{92} +2.06256e32 q^{93} -4.52602e31 q^{94} +6.96024e32 q^{96} +3.55763e32 q^{97} -2.78035e32 q^{98} -3.12168e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * 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 $

$2$	−71937.8	−0.776180	−0.388090	−	0.921622i	$-0.626865\pi$
$2$	−71937.8	−0.776180	−0.388090	+	0.921622i	$0.626865\pi$
$3$	−1.37573e8	−1.84516	−0.922578	−	0.385811i	$-0.873922\pi$
$3$	−1.37573e8	−1.84516	−0.922578	+	0.385811i	$0.873922\pi$
$4$	−3.41489e9	−0.397545
$5$	0	0
$5$	0	0
$6$	9.89671e12	1.43217
$7$	1.07684e14	1.22472	0.612358	−	0.790581i	$-0.290221\pi$
$7$	1.07684e14	1.22472	0.612358	+	0.790581i	$0.290221\pi$
$8$	8.63600e14	1.08475
$9$	1.33673e16	2.40460
$10$	0	0
$11$	−2.33530e17	−1.53237	−0.766186	−	0.642619i	$-0.777848\pi$
$11$	−2.33530e17	−1.53237	−0.766186	+	0.642619i	$0.777848\pi$
$12$	4.69797e17	0.733533
$13$	2.28395e18	0.951965	0.475983	−	0.879455i	$-0.342092\pi$
$13$	2.28395e18	0.951965	0.475983	+	0.879455i	$0.342092\pi$
$14$	−7.74658e18	−0.950599
$15$	0	0
$16$	−3.27918e19	−0.444412
$17$	2.09885e20	1.04610	0.523050	−	0.852302i	$-0.324794\pi$
$17$	2.09885e20	1.04610	0.523050	+	0.852302i	$0.324794\pi$
$18$	−9.61615e20	−1.86640
$19$	6.01644e20	0.478526	0.239263	−	0.970955i	$-0.423094\pi$
$19$	6.01644e20	0.478526	0.239263	+	0.970955i	$0.423094\pi$
$20$	0	0
$21$	−1.48145e22	−2.25979
$22$	1.67997e22	1.18940
$23$	−4.84991e22	−1.64901	−0.824506	−	0.565853i	$-0.808547\pi$
$23$	−4.84991e22	−1.64901	−0.824506	+	0.565853i	$0.808547\pi$
$24$	−1.18808e23	−2.00153
$25$	0	0
$26$	−1.64302e23	−0.738896
$27$	−1.07421e24	−2.59171
$28$	−3.67730e23	−0.486880
$29$	−8.15476e22	−0.0605124	−0.0302562	−	0.999542i	$-0.509632\pi$
$29$	−8.15476e22	−0.0605124	−0.0302562	+	0.999542i	$0.509632\pi$
$30$	0	0
$31$	−1.49925e24	−0.370174	−0.185087	−	0.982722i	$-0.559257\pi$
$31$	−1.49925e24	−0.370174	−0.185087	+	0.982722i	$0.559257\pi$
$32$	−5.05930e24	−0.739802
$33$	3.21275e25	2.82747
$34$	−1.50986e25	−0.811961
$35$	0	0
$36$	−4.56479e25	−0.955938
$37$	−1.78708e25	−0.238131	−0.119066	−	0.992886i	$-0.537990\pi$
$37$	−1.78708e25	−0.238131	−0.119066	+	0.992886i	$0.537990\pi$
$38$	−4.32809e25	−0.371422
$39$	−3.14210e26	−1.75652
$40$	0	0
$41$	−1.94621e26	−0.476712	−0.238356	−	0.971178i	$-0.576608\pi$
$41$	−1.94621e26	−0.476712	−0.238356	+	0.971178i	$0.576608\pi$
$42$	1.06572e27	1.75400
$43$	9.48110e26	1.05835	0.529175	−	0.848513i	$-0.322502\pi$
$43$	9.48110e26	1.05835	0.529175	+	0.848513i	$0.322502\pi$
$44$	7.97481e26	0.609187
$45$	0	0
$46$	3.48891e27	1.27993
$47$	6.29157e26	0.161862	0.0809309	−	0.996720i	$-0.474211\pi$
$47$	6.29157e26	0.161862	0.0809309	+	0.996720i	$0.474211\pi$
$48$	4.51128e27	0.820010
$49$	3.86494e27	0.499927
$50$	0	0
$51$	−2.88745e28	−1.93022
$52$	−7.79943e27	−0.378449
$53$	8.56042e27	0.303350	0.151675	−	0.988430i	$-0.451533\pi$
$53$	8.56042e27	0.303350	0.151675	+	0.988430i	$0.451533\pi$
$54$	7.72760e28	2.01163
$55$	0	0
$56$	9.29963e28	1.32851
$57$	−8.27701e28	−0.882954
$58$	5.86635e27	0.0469685
$59$	5.43089e27	0.0327954	0.0163977	−	0.999866i	$-0.494780\pi$
$59$	5.43089e27	0.0327954	0.0163977	+	0.999866i	$0.494780\pi$
$60$	0	0
$61$	1.79220e29	0.624373	0.312186	−	0.950021i	$-0.398939\pi$
$61$	1.79220e29	0.624373	0.312186	+	0.950021i	$0.398939\pi$
$62$	1.07853e29	0.287321
$63$	1.43945e30	2.94495
$64$	6.45635e29	1.01863
$65$	0	0
$66$	−2.31118e30	−2.19462
$67$	3.33703e29	0.247244	0.123622	−	0.992329i	$-0.460549\pi$
$67$	3.33703e29	0.247244	0.123622	+	0.992329i	$0.460549\pi$
$68$	−7.16732e29	−0.415872
$69$	6.67217e30	3.04269
$70$	0	0
$71$	−3.44997e30	−0.981866	−0.490933	−	0.871197i	$-0.663344\pi$
$71$	−3.44997e30	−0.981866	−0.490933	+	0.871197i	$0.663344\pi$
$72$	1.15440e31	2.60838
$73$	7.11823e30	1.28099	0.640494	−	0.767963i	$-0.278730\pi$
$73$	7.11823e30	1.28099	0.640494	+	0.767963i	$0.278730\pi$
$74$	1.28559e30	0.184833
$75$	0	0
$76$	−2.05455e30	−0.190236
$77$	−2.51476e31	−1.87672
$78$	2.26036e31	1.36338
$79$	−1.57830e31	−0.771510	−0.385755	−	0.922601i	$-0.626059\pi$
$79$	−1.57830e31	−0.771510	−0.385755	+	0.922601i	$0.626059\pi$
$80$	0	0
$81$	7.34723e31	2.37750
$82$	1.40006e31	0.370014
$83$	−3.45599e31	−0.747798	−0.373899	−	0.927470i	$-0.621979\pi$
$83$	−3.45599e31	−0.747798	−0.373899	+	0.927470i	$0.621979\pi$
$84$	5.05898e31	0.898369
$85$	0	0
$86$	−6.82049e31	−0.821469
$87$	1.12188e31	0.111655
$88$	−2.01677e32	−1.66223
$89$	−2.35733e32	−1.61244	−0.806222	−	0.591613i	$-0.798491\pi$
$89$	−2.35733e32	−1.61244	−0.806222	+	0.591613i	$0.798491\pi$
$90$	0	0
$91$	2.45946e32	1.16589
$92$	1.65619e32	0.655557
$93$	2.06256e32	0.683029
$94$	−4.52602e31	−0.125634
$95$	0	0
$96$	6.96024e32	1.36505
$97$	3.55763e32	0.588067	0.294033	−	0.955795i	$-0.405002\pi$
$97$	3.55763e32	0.588067	0.294033	+	0.955795i	$0.405002\pi$
$98$	−2.78035e32	−0.388033
$99$	−3.12168e33	−3.68474
$100$	0	0
$101$	9.03859e32	0.767004	0.383502	−	0.923540i	$-0.374718\pi$
$101$	9.03859e32	0.767004	0.383502	+	0.923540i	$0.374718\pi$
$102$	2.07717e33	1.49820
$103$	−2.36642e33	−1.45304	−0.726519	−	0.687146i	$-0.758863\pi$
$103$	−2.36642e33	−1.45304	−0.726519	+	0.687146i	$0.758863\pi$
$104$	1.97242e33	1.03264
$105$	0	0
$106$	−6.15818e32	−0.235454
$107$	−2.84756e33	−0.932482	−0.466241	−	0.884658i	$-0.654392\pi$
$107$	−2.84756e33	−0.932482	−0.466241	+	0.884658i	$0.654392\pi$
$108$	3.66830e33	1.03032
$109$	3.46217e33	0.835241	0.417620	−	0.908622i	$-0.362864\pi$
$109$	3.46217e33	0.835241	0.417620	+	0.908622i	$0.362864\pi$
$110$	0	0
$111$	2.45855e33	0.439389
$112$	−3.53117e33	−0.544279
$113$	9.04247e33	1.20363	0.601815	−	0.798636i	$-0.294444\pi$
$113$	9.04247e33	1.20363	0.601815	+	0.798636i	$0.294444\pi$
$114$	5.95430e33	0.685331
$115$	0	0
$116$	2.78476e32	0.0240564
$117$	3.05303e34	2.28910
$118$	−3.90687e32	−0.0254551
$119$	2.26013e34	1.28117
$120$	0	0
$121$	3.13113e34	1.34816
$122$	−1.28927e34	−0.484626
$123$	2.67746e34	0.879608
$124$	5.11977e33	0.147161
$125$	0	0
$126$	−1.03551e35	−2.28581
$127$	4.59458e33	0.0890194	0.0445097	−	0.999009i	$-0.485827\pi$
$127$	4.59458e33	0.0890194	0.0445097	+	0.999009i	$0.485827\pi$
$128$	−2.98648e33	−0.0508388
$129$	−1.30434e35	−1.95282
$130$	0	0
$131$	−2.50614e34	−0.291091	−0.145545	−	0.989352i	$-0.546494\pi$
$131$	−2.50614e34	−0.291091	−0.145545	+	0.989352i	$0.546494\pi$
$132$	−1.09712e35	−1.12405
$133$	6.47877e34	0.586058
$134$	−2.40059e34	−0.191906
$135$	0	0
$136$	1.81256e35	1.13475
$137$	−2.78859e35	−1.54702	−0.773510	−	0.633784i	$-0.781501\pi$
$137$	−2.78859e35	−1.54702	−0.773510	+	0.633784i	$0.781501\pi$
$138$	−4.79981e35	−2.36167
$139$	1.40995e35	0.615827	0.307914	−	0.951414i	$-0.400369\pi$
$139$	1.40995e35	0.615827	0.307914	+	0.951414i	$0.400369\pi$
$140$	0	0
$141$	−8.65551e34	−0.298660
$142$	2.48183e35	0.762104
$143$	−5.33372e35	−1.45877
$144$	−4.38339e35	−1.06863
$145$	0	0
$146$	−5.12070e35	−0.994277
$147$	−5.31711e35	−0.922444
$148$	6.10269e34	0.0946680
$149$	−4.84716e35	−0.672844	−0.336422	−	0.941711i	$-0.609217\pi$
$149$	−4.84716e35	−0.672844	−0.336422	+	0.941711i	$0.609217\pi$
$150$	0	0
$151$	−1.29129e35	−0.143848	−0.0719238	−	0.997410i	$-0.522914\pi$
$151$	−1.29129e35	−0.143848	−0.0719238	+	0.997410i	$0.522914\pi$
$152$	5.19580e35	0.519079
$153$	2.80559e36	2.51545
$154$	1.80906e36	1.45667
$155$	0	0
$156$	1.07299e36	0.698298
$157$	−1.48727e36	−0.871052	−0.435526	−	0.900176i	$-0.643438\pi$
$157$	−1.48727e36	−0.871052	−0.435526	+	0.900176i	$0.643438\pi$
$158$	1.13539e36	0.598830
$159$	−1.17768e36	−0.559727
$160$	0	0
$161$	−5.22259e36	−2.01957
$162$	−5.28543e36	−1.84537
$163$	5.65066e36	1.78240	0.891198	−	0.453615i	$-0.149866\pi$
$163$	5.65066e36	1.78240	0.891198	+	0.453615i	$0.149866\pi$
$164$	6.64609e35	0.189515
$165$	0	0
$166$	2.48616e36	0.580425
$167$	8.79383e36	1.85933	0.929665	−	0.368407i	$-0.120097\pi$
$167$	8.79383e36	1.85933	0.929665	+	0.368407i	$0.120097\pi$
$168$	−1.27938e37	−2.45130
$169$	−5.39705e35	−0.0937617
$170$	0	0
$171$	8.04237e36	1.15066
$172$	−3.23769e36	−0.420742
$173$	5.34130e36	0.630792	0.315396	−	0.948960i	$-0.397863\pi$
$173$	5.34130e36	0.630792	0.315396	+	0.948960i	$0.397863\pi$
$174$	−8.07053e35	−0.0866641
$175$	0	0
$176$	7.65790e36	0.681005
$177$	−7.47145e35	−0.0605127
$178$	1.69581e37	1.25155
$179$	−1.75097e37	−1.17816	−0.589080	−	0.808075i	$-0.700510\pi$
$179$	−1.75097e37	−1.17816	−0.589080	+	0.808075i	$0.700510\pi$
$180$	0	0
$181$	1.00404e37	0.562411	0.281205	−	0.959648i	$-0.409266\pi$
$181$	1.00404e37	0.562411	0.281205	+	0.959648i	$0.409266\pi$
$182$	−1.76928e37	−0.904937
$183$	−2.46559e37	−1.15207
$184$	−4.18838e37	−1.78876
$185$	0	0
$186$	−1.48376e37	−0.530153
$187$	−4.90144e37	−1.60301
$188$	−2.14850e36	−0.0643474
$189$	−1.15675e38	−3.17410
$190$	0	0
$191$	−1.96610e37	−0.453477	−0.226739	−	0.973956i	$-0.572806\pi$
$191$	−1.96610e37	−0.453477	−0.226739	+	0.973956i	$0.572806\pi$
$192$	−8.88220e37	−1.87953
$193$	−3.92456e37	−0.762246	−0.381123	−	0.924524i	$-0.624463\pi$
$193$	−3.92456e37	−0.762246	−0.381123	+	0.924524i	$0.624463\pi$
$194$	−2.55928e37	−0.456446
$195$	0	0
$196$	−1.31983e37	−0.198744
$197$	1.18069e38	1.63471	0.817357	−	0.576131i	$-0.195438\pi$
$197$	1.18069e38	1.63471	0.817357	+	0.576131i	$0.195438\pi$
$198$	2.24566e38	2.86002
$199$	1.43693e38	1.68407	0.842035	−	0.539423i	$-0.181358\pi$
$199$	1.43693e38	1.68407	0.842035	+	0.539423i	$0.181358\pi$
$200$	0	0
$201$	−4.59086e37	−0.456204
$202$	−6.50216e37	−0.595333
$203$	−8.78140e36	−0.0741104
$204$	9.86031e37	0.767349
$205$	0	0
$206$	1.70235e38	1.12782
$207$	−6.48302e38	−3.96522
$208$	−7.48949e37	−0.423065
$209$	−1.40502e38	−0.733279
$210$	0	0
$211$	−2.97825e38	−1.32831	−0.664157	−	0.747593i	$-0.731210\pi$
$211$	−2.97825e38	−1.32831	−0.664157	+	0.747593i	$0.731210\pi$
$212$	−2.92329e37	−0.120595
$213$	4.74623e38	1.81170
$214$	2.04847e38	0.723773
$215$	0	0
$216$	−9.27685e38	−2.81134
$217$	−1.61446e38	−0.453358
$218$	−2.49061e38	−0.648297
$219$	−9.79278e38	−2.36362
$220$	0	0
$221$	4.79366e38	0.995851
$222$	−1.76863e38	−0.341045
$223$	1.05983e38	0.189761	0.0948804	−	0.995489i	$-0.469753\pi$
$223$	1.05983e38	0.189761	0.0948804	+	0.995489i	$0.469753\pi$
$224$	−5.44808e38	−0.906047
$225$	0	0
$226$	−6.50496e38	−0.934233
$227$	−7.63192e38	−1.01908	−0.509538	−	0.860448i	$-0.670184\pi$
$227$	−7.63192e38	−1.01908	−0.509538	+	0.860448i	$0.670184\pi$
$228$	2.82651e38	0.351014
$229$	2.74424e38	0.317057	0.158528	−	0.987354i	$-0.449325\pi$
$229$	2.74424e38	0.317057	0.158528	+	0.987354i	$0.449325\pi$
$230$	0	0
$231$	3.45963e39	3.46284
$232$	−7.04245e37	−0.0656406
$233$	7.50623e38	0.651702	0.325851	−	0.945421i	$-0.394349\pi$
$233$	7.50623e38	0.651702	0.325851	+	0.945421i	$0.394349\pi$
$234$	−2.19628e39	−1.77675
$235$	0	0
$236$	−1.85459e37	−0.0130377
$237$	2.17131e39	1.42356
$238$	−1.62589e39	−0.994422
$239$	−9.41651e38	−0.537434	−0.268717	−	0.963219i	$-0.586600\pi$
$239$	−9.41651e38	−0.537434	−0.268717	+	0.963219i	$0.586600\pi$
$240$	0	0
$241$	−4.90507e38	−0.243985	−0.121993	−	0.992531i	$-0.538928\pi$
$241$	−4.90507e38	−0.243985	−0.121993	+	0.992531i	$0.538928\pi$
$242$	−2.25247e39	−1.04642
$243$	−4.13623e39	−1.79515
$244$	−6.12016e38	−0.248217
$245$	0	0
$246$	−1.92611e39	−0.682734
$247$	1.37412e39	0.455540
$248$	−1.29475e39	−0.401545
$249$	4.75452e39	1.37980
$250$	0	0
$251$	5.96650e39	1.51741	0.758705	−	0.651434i	$-0.225832\pi$
$251$	5.96650e39	1.51741	0.758705	+	0.651434i	$0.225832\pi$
$252$	−4.91557e39	−1.17075
$253$	1.13260e40	2.52690
$254$	−3.30524e38	−0.0690950
$255$	0	0
$256$	−5.33112e39	−0.979172
$257$	8.25525e39	1.42178	0.710892	−	0.703301i	$-0.248291\pi$
$257$	8.25525e39	1.42178	0.710892	+	0.703301i	$0.248291\pi$
$258$	9.38317e39	1.51574
$259$	−1.92441e39	−0.291643
$260$	0	0
$261$	−1.09007e39	−0.145508
$262$	1.80286e39	0.225939
$263$	−6.74712e39	−0.794051	−0.397026	−	0.917808i	$-0.629958\pi$
$263$	−6.74712e39	−0.794051	−0.397026	+	0.917808i	$0.629958\pi$
$264$	2.77454e40	3.06708
$265$	0	0
$266$	−4.66068e39	−0.454886
$267$	3.24305e40	2.97521
$268$	−1.13956e39	−0.0982907
$269$	−2.97390e39	−0.241220	−0.120610	−	0.992700i	$-0.538485\pi$
$269$	−2.97390e39	−0.241220	−0.120610	+	0.992700i	$0.538485\pi$
$270$	0	0
$271$	−7.89524e39	−0.566725	−0.283362	−	0.959013i	$-0.591450\pi$
$271$	−7.89524e39	−0.566725	−0.283362	+	0.959013i	$0.591450\pi$
$272$	−6.88250e39	−0.464900
$273$	−3.38355e40	−2.15124
$274$	2.00605e40	1.20076
$275$	0	0
$276$	−2.27847e40	−1.20961
$277$	−2.12171e40	−1.06113	−0.530566	−	0.847644i	$-0.678020\pi$
$277$	−2.12171e40	−1.06113	−0.530566	+	0.847644i	$0.678020\pi$
$278$	−1.01429e40	−0.477993
$279$	−2.00409e40	−0.890120
$280$	0	0
$281$	4.91397e40	1.93989	0.969947	−	0.243317i	$-0.0782355\pi$
$281$	4.91397e40	1.93989	0.969947	+	0.243317i	$0.0782355\pi$
$282$	6.22658e39	0.231814
$283$	4.22019e40	1.48203	0.741013	−	0.671491i	$-0.234346\pi$
$283$	4.22019e40	1.48203	0.741013	+	0.671491i	$0.234346\pi$
$284$	1.17813e40	0.390336
$285$	0	0
$286$	3.83696e40	1.13226
$287$	−2.09576e40	−0.583836
$288$	−6.76292e40	−1.77893
$289$	3.79702e39	0.0943253
$290$	0	0
$291$	−4.89434e40	−1.08508
$292$	−2.43080e40	−0.509251
$293$	−2.96004e40	−0.586115	−0.293057	−	0.956095i	$-0.594673\pi$
$293$	−2.96004e40	−0.586115	−0.293057	+	0.956095i	$0.594673\pi$
$294$	3.82502e40	0.715982
$295$	0	0
$296$	−1.54333e40	−0.258312
$297$	2.50860e41	3.97146
$298$	3.48694e40	0.522248
$299$	−1.10769e41	−1.56980
$300$	0	0
$301$	1.02097e41	1.29618
$302$	9.28922e39	0.111652
$303$	−1.24347e41	−1.41524
$304$	−1.97290e40	−0.212663
$305$	0	0
$306$	−2.01828e41	−1.95244
$307$	1.70501e41	1.56295	0.781474	−	0.623938i	$-0.214468\pi$
$307$	1.70501e41	1.56295	0.781474	+	0.623938i	$0.214468\pi$
$308$	8.58762e40	0.746081
$309$	3.25556e41	2.68108
$310$	0	0
$311$	1.09238e41	0.808774	0.404387	−	0.914588i	$-0.367485\pi$
$311$	1.09238e41	0.808774	0.404387	+	0.914588i	$0.367485\pi$
$312$	−2.71352e41	−1.90538
$313$	2.55151e41	1.69948	0.849738	−	0.527205i	$-0.176760\pi$
$313$	2.55151e41	1.69948	0.849738	+	0.527205i	$0.176760\pi$
$314$	1.06991e41	0.676093
$315$	0	0
$316$	5.38971e40	0.306710
$317$	−1.40033e41	−0.756400	−0.378200	−	0.925724i	$-0.623457\pi$
$317$	−1.40033e41	−0.756400	−0.378200	+	0.925724i	$0.623457\pi$
$318$	8.47200e40	0.434449
$319$	1.90438e40	0.0927275
$320$	0	0
$321$	3.91748e41	1.72057
$322$	3.75702e41	1.56755
$323$	1.26276e41	0.500586
$324$	−2.50900e41	−0.945164
$325$	0	0
$326$	−4.06496e41	−1.38346
$327$	−4.76302e41	−1.54115
$328$	−1.68075e41	−0.517111
$329$	6.77504e40	0.198235
$330$	0	0
$331$	−2.36103e41	−0.625086	−0.312543	−	0.949904i	$-0.601181\pi$
$331$	−2.36103e41	−0.625086	−0.312543	+	0.949904i	$0.601181\pi$
$332$	1.18018e41	0.297283
$333$	−2.38885e41	−0.572611
$334$	−6.32609e41	−1.44317
$335$	0	0
$336$	4.85794e41	1.00428
$337$	−5.72695e41	−1.12728	−0.563638	−	0.826022i	$-0.690599\pi$
$337$	−5.72695e41	−1.12728	−0.563638	+	0.826022i	$0.690599\pi$
$338$	3.88252e40	0.0727759
$339$	−1.24400e42	−2.22088
$340$	0	0
$341$	3.50120e41	0.567244
$342$	−5.78550e41	−0.893121
$343$	−4.16314e41	−0.612446
$344$	8.18788e41	1.14804
$345$	0	0
$346$	−3.84241e41	−0.489608
$347$	−7.23409e41	−0.878917	−0.439458	−	0.898263i	$-0.644830\pi$
$347$	−7.23409e41	−0.878917	−0.439458	+	0.898263i	$0.644830\pi$
$348$	−3.83108e40	−0.0443878
$349$	−1.72145e42	−1.90228	−0.951140	−	0.308761i	$-0.900086\pi$
$349$	−1.72145e42	−1.90228	−0.951140	+	0.308761i	$0.900086\pi$
$350$	0	0
$351$	−2.45343e42	−2.46721
$352$	1.18150e42	1.13365
$353$	1.10466e42	1.01145	0.505725	−	0.862695i	$-0.331225\pi$
$353$	1.10466e42	1.01145	0.505725	+	0.862695i	$0.331225\pi$
$354$	5.37480e40	0.0469687
$355$	0	0
$356$	8.05001e41	0.641020
$357$	−3.10933e42	−2.36397
$358$	1.25961e42	0.914464
$359$	1.24115e42	0.860528	0.430264	−	0.902703i	$-0.358420\pi$
$359$	1.24115e42	0.860528	0.430264	+	0.902703i	$0.358420\pi$
$360$	0	0
$361$	−1.21880e42	−0.771013
$362$	−7.22283e41	−0.436532
$363$	−4.30760e42	−2.48757
$364$	−8.39877e41	−0.463493
$365$	0	0
$366$	1.77369e42	0.894210
$367$	−7.83869e41	−0.377792	−0.188896	−	0.981997i	$-0.560491\pi$
$367$	−7.83869e41	−0.377792	−0.188896	+	0.981997i	$0.560491\pi$
$368$	1.59037e42	0.732842
$369$	−2.60156e42	−1.14630
$370$	0	0
$371$	9.21824e41	0.371517
$372$	−7.04343e41	−0.271535
$373$	4.48131e42	1.65276	0.826378	−	0.563116i	$-0.190397\pi$
$373$	4.48131e42	1.65276	0.826378	+	0.563116i	$0.190397\pi$
$374$	3.52599e42	1.24423
$375$	0	0
$376$	5.43340e41	0.175579
$377$	−1.86251e41	−0.0576057
$378$	8.32142e42	2.46367
$379$	5.32753e42	1.51001	0.755003	−	0.655721i	$-0.227635\pi$
$379$	5.32753e42	1.51001	0.755003	+	0.655721i	$0.227635\pi$
$380$	0	0
$381$	−6.32091e41	−0.164255
$382$	1.41437e42	0.351980
$383$	−7.66000e42	−1.82578	−0.912891	−	0.408203i	$-0.866156\pi$
$383$	−7.66000e42	−1.82578	−0.912891	+	0.408203i	$0.866156\pi$
$384$	4.10860e41	0.0938055
$385$	0	0
$386$	2.82324e42	0.591640
$387$	1.26737e43	2.54491
$388$	−1.21489e42	−0.233783
$389$	2.42415e42	0.447085	0.223543	−	0.974694i	$-0.428238\pi$
$389$	2.42415e42	0.447085	0.223543	+	0.974694i	$0.428238\pi$
$390$	0	0
$391$	−1.01792e43	−1.72503
$392$	3.33776e42	0.542294
$393$	3.44777e42	0.537108
$394$	−8.49360e42	−1.26883
$395$	0	0
$396$	1.06602e43	1.46485
$397$	−4.43937e42	−0.585164	−0.292582	−	0.956240i	$-0.594514\pi$
$397$	−4.43937e42	−0.585164	−0.292582	+	0.956240i	$0.594514\pi$
$398$	−1.03370e43	−1.30714
$399$	−8.91304e42	−1.08137
$400$	0	0
$401$	6.39786e41	0.0714747	0.0357374	−	0.999361i	$-0.488622\pi$
$401$	6.39786e41	0.0714747	0.0357374	+	0.999361i	$0.488622\pi$
$402$	3.30256e42	0.354096
$403$	−3.42421e42	−0.352393
$404$	−3.08658e42	−0.304919
$405$	0	0
$406$	6.31715e41	0.0575230
$407$	4.17339e42	0.364906
$408$	−2.49360e43	−2.09380
$409$	−1.16096e43	−0.936227	−0.468114	−	0.883668i	$-0.655066\pi$
$409$	−1.16096e43	−0.936227	−0.468114	+	0.883668i	$0.655066\pi$
$410$	0	0
$411$	3.83636e43	2.85449
$412$	8.08105e42	0.577649
$413$	5.84823e41	0.0401650
$414$	4.66374e43	3.07772
$415$	0	0
$416$	−1.15552e43	−0.704266
$417$	−1.93971e43	−1.13630
$418$	1.01074e43	0.569156
$419$	−7.07188e42	−0.382828	−0.191414	−	0.981509i	$-0.561307\pi$
$419$	−7.07188e42	−0.382828	−0.191414	+	0.981509i	$0.561307\pi$
$420$	0	0
$421$	−2.32219e43	−1.16210	−0.581050	−	0.813868i	$-0.697358\pi$
$421$	−2.32219e43	−1.16210	−0.581050	+	0.813868i	$0.697358\pi$
$422$	2.14249e43	1.03101
$423$	8.41014e42	0.389213
$424$	7.39279e42	0.329057
$425$	0	0
$426$	−3.41433e43	−1.40620
$427$	1.92992e43	0.764679
$428$	9.72410e42	0.370704
$429$	7.33777e43	2.69165
$430$	0	0
$431$	−3.01488e43	−1.02422	−0.512112	−	0.858919i	$-0.671137\pi$
$431$	−3.01488e43	−1.02422	−0.512112	+	0.858919i	$0.671137\pi$
$432$	3.52252e43	1.15179
$433$	−3.63888e43	−1.14530	−0.572648	−	0.819802i	$-0.694084\pi$
$433$	−3.63888e43	−1.14530	−0.572648	+	0.819802i	$0.694084\pi$
$434$	1.16141e43	0.351887
$435$	0	0
$436$	−1.18229e43	−0.332046
$437$	−2.91792e43	−0.789095
$438$	7.04471e43	1.83460
$439$	−3.62391e42	−0.0908893	−0.0454446	−	0.998967i	$-0.514470\pi$
$439$	−3.62391e42	−0.0908893	−0.0454446	+	0.998967i	$0.514470\pi$
$440$	0	0
$441$	5.16638e43	1.20213
$442$	−3.44845e43	−0.772959
$443$	−2.84653e43	−0.614686	−0.307343	−	0.951599i	$-0.599440\pi$
$443$	−2.84653e43	−0.614686	−0.307343	+	0.951599i	$0.599440\pi$
$444$	−8.39567e42	−0.174677
$445$	0	0
$446$	−7.62419e42	−0.147288
$447$	6.66840e43	1.24150
$448$	6.95248e43	1.24753
$449$	−3.05597e43	−0.528548	−0.264274	−	0.964448i	$-0.585132\pi$
$449$	−3.05597e43	−0.528548	−0.264274	+	0.964448i	$0.585132\pi$
$450$	0	0
$451$	4.54499e43	0.730500
$452$	−3.08790e43	−0.478497
$453$	1.77646e43	0.265421
$454$	5.49023e43	0.790987
$455$	0	0
$456$	−7.14803e43	−0.957781
$457$	8.70256e42	0.112468	0.0562341	−	0.998418i	$-0.482091\pi$
$457$	8.70256e42	0.112468	0.0562341	+	0.998418i	$0.482091\pi$
$458$	−1.97415e43	−0.246093
$459$	−2.25459e44	−2.71118
$460$	0	0
$461$	7.28964e43	0.815907	0.407954	−	0.913003i	$-0.366243\pi$
$461$	7.28964e43	0.815907	0.407954	+	0.913003i	$0.366243\pi$
$462$	−2.48878e44	−2.68779
$463$	−1.54940e44	−1.61465	−0.807324	−	0.590108i	$-0.799085\pi$
$463$	−1.54940e44	−1.61465	−0.807324	+	0.590108i	$0.799085\pi$
$464$	2.67410e42	0.0268924
$465$	0	0
$466$	−5.39982e43	−0.505838
$467$	9.15725e43	0.828011	0.414006	−	0.910274i	$-0.364129\pi$
$467$	9.15725e43	0.828011	0.414006	+	0.910274i	$0.364129\pi$
$468$	−1.04257e44	−0.910020
$469$	3.59346e43	0.302804
$470$	0	0
$471$	2.04608e44	1.60723
$472$	4.69012e42	0.0355747
$473$	−2.21413e44	−1.62179
$474$	−1.56199e44	−1.10494
$475$	0	0
$476$	−7.71809e43	−0.509325
$477$	1.14430e44	0.729434
$478$	6.77403e43	0.417145
$479$	3.67745e43	0.218782	0.109391	−	0.993999i	$-0.465110\pi$
$479$	3.67745e43	0.218782	0.109391	+	0.993999i	$0.465110\pi$
$480$	0	0
$481$	−4.08161e43	−0.226693
$482$	3.52860e43	0.189376
$483$	7.18488e44	3.72642
$484$	−1.06925e44	−0.535957
$485$	0	0
$486$	2.97552e44	1.39336
$487$	−2.46290e44	−1.11485	−0.557427	−	0.830226i	$-0.688211\pi$
$487$	−2.46290e44	−1.11485	−0.557427	+	0.830226i	$0.688211\pi$
$488$	1.54774e44	0.677286
$489$	−7.77380e44	−3.28880
$490$	0	0
$491$	1.21128e44	0.479071	0.239535	−	0.970888i	$-0.423005\pi$
$491$	1.21128e44	0.479071	0.239535	+	0.970888i	$0.423005\pi$
$492$	−9.14324e43	−0.349684
$493$	−1.71156e43	−0.0633020
$494$	−9.88515e43	−0.353581
$495$	0	0
$496$	4.91632e43	0.164510
$497$	−3.71508e44	−1.20251
$498$	−3.42029e44	−1.07097
$499$	4.07835e44	1.23545	0.617726	−	0.786393i	$-0.288054\pi$
$499$	4.07835e44	1.23545	0.617726	+	0.786393i	$0.288054\pi$
$500$	0	0
$501$	−1.20980e45	−3.43075
$502$	−4.29217e44	−1.17778
$503$	5.88791e44	1.56347	0.781734	−	0.623612i	$-0.214335\pi$
$503$	5.88791e44	1.56347	0.781734	+	0.623612i	$0.214335\pi$
$504$	1.24311e45	3.19452
$505$	0	0
$506$	−8.14768e44	−1.96133
$507$	7.42489e43	0.173005
$508$	−1.56900e43	−0.0353892
$509$	7.13633e44	1.55823	0.779115	−	0.626881i	$-0.215669\pi$
$509$	7.13633e44	1.55823	0.779115	+	0.626881i	$0.215669\pi$
$510$	0	0
$511$	7.66523e44	1.56885
$512$	4.09163e44	0.810852
$513$	−6.46290e44	−1.24020
$514$	−5.93864e44	−1.10356
$515$	0	0
$516$	4.45419e44	0.776335
$517$	−1.46927e44	−0.248033
$518$	1.38438e44	0.226367
$519$	−7.34820e44	−1.16391
$520$	0	0
$521$	−1.39893e44	−0.207957	−0.103978	−	0.994580i	$-0.533157\pi$
$521$	−1.39893e44	−0.207957	−0.103978	+	0.994580i	$0.533157\pi$
$522$	7.84174e43	0.112940
$523$	4.12677e44	0.575880	0.287940	−	0.957648i	$-0.407030\pi$
$523$	4.12677e44	0.575880	0.287940	+	0.957648i	$0.407030\pi$
$524$	8.55818e43	0.115722
$525$	0	0
$526$	4.85373e44	0.616326
$527$	−3.14669e44	−0.387239
$528$	−1.05352e45	−1.25656
$529$	1.48715e45	1.71924
$530$	0	0
$531$	7.25965e43	0.0788599
$532$	−2.21243e44	−0.232984
$533$	−4.44504e44	−0.453813
$534$	−2.33298e45	−2.30930
$535$	0	0
$536$	2.88186e44	0.268197
$537$	2.40887e45	2.17389
$538$	2.13936e44	0.187230
$539$	−9.02580e44	−0.766075
$540$	0	0
$541$	−2.35683e45	−1.88180	−0.940899	−	0.338687i	$-0.890017\pi$
$541$	−2.35683e45	−1.88180	−0.940899	+	0.338687i	$0.890017\pi$
$542$	5.67966e44	0.439880
$543$	−1.38129e45	−1.03774
$544$	−1.06187e45	−0.773907
$545$	0	0
$546$	2.43405e45	1.66975
$547$	−2.11321e45	−1.40654	−0.703270	−	0.710923i	$-0.748277\pi$
$547$	−2.11321e45	−1.40654	−0.703270	+	0.710923i	$0.748277\pi$
$548$	9.52274e44	0.615010
$549$	2.39569e45	1.50137
$550$	0	0
$551$	−4.90626e43	−0.0289567
$552$	5.76209e45	3.30054
$553$	−1.69958e45	−0.944880
$554$	1.52631e45	0.823628
$555$	0	0
$556$	−4.81482e44	−0.244819
$557$	−2.27438e45	−1.12267	−0.561335	−	0.827589i	$-0.689712\pi$
$557$	−2.27438e45	−1.12267	−0.561335	+	0.827589i	$0.689712\pi$
$558$	1.44170e45	0.690893
$559$	2.16544e45	1.00751
$560$	0	0
$561$	6.74307e45	2.95781
$562$	−3.53500e45	−1.50571
$563$	1.75752e45	0.726962	0.363481	−	0.931602i	$-0.381588\pi$
$563$	1.75752e45	0.726962	0.363481	+	0.931602i	$0.381588\pi$
$564$	2.95576e44	0.118731
$565$	0	0
$566$	−3.03591e45	−1.15032
$567$	7.91182e45	2.91176
$568$	−2.97939e45	−1.06508
$569$	9.61177e44	0.333773	0.166886	−	0.985976i	$-0.446629\pi$
$569$	9.61177e44	0.333773	0.166886	+	0.985976i	$0.446629\pi$
$570$	0	0
$571$	−5.28842e45	−1.73313	−0.866563	−	0.499067i	$-0.833676\pi$
$571$	−5.28842e45	−1.73313	−0.866563	+	0.499067i	$0.833676\pi$
$572$	1.82141e45	0.579925
$573$	2.70483e45	0.836737
$574$	1.50765e45	0.453162
$575$	0	0
$576$	8.63040e45	2.44940
$577$	1.11538e45	0.307626	0.153813	−	0.988100i	$-0.450845\pi$
$577$	1.11538e45	0.307626	0.153813	+	0.988100i	$0.450845\pi$
$578$	−2.73149e44	−0.0732134
$579$	5.39914e45	1.40646
$580$	0	0
$581$	−3.72156e45	−0.915839
$582$	3.52088e45	0.842213
$583$	−1.99912e45	−0.464845
$584$	6.14731e45	1.38955
$585$	0	0
$586$	2.12939e45	0.454930
$587$	−3.02679e45	−0.628714	−0.314357	−	0.949305i	$-0.601789\pi$
$587$	−3.02679e45	−0.628714	−0.314357	+	0.949305i	$0.601789\pi$
$588$	1.81574e45	0.366713
$589$	−9.02014e44	−0.177138
$590$	0	0
$591$	−1.62431e46	−3.01630
$592$	5.86018e44	0.105829
$593$	−2.02049e45	−0.354857	−0.177428	−	0.984134i	$-0.556778\pi$
$593$	−2.02049e45	−0.354857	−0.177428	+	0.984134i	$0.556778\pi$
$594$	−1.80463e46	−3.08256
$595$	0	0
$596$	1.65525e45	0.267486
$597$	−1.97683e46	−3.10737
$598$	7.96851e45	1.21845
$599$	−7.17593e45	−1.06742	−0.533710	−	0.845667i	$-0.679203\pi$
$599$	−7.17593e45	−1.06742	−0.533710	+	0.845667i	$0.679203\pi$
$600$	0	0
$601$	−8.79572e44	−0.123835	−0.0619174	−	0.998081i	$-0.519722\pi$
$601$	−8.79572e44	−0.123835	−0.0619174	+	0.998081i	$0.519722\pi$
$602$	−7.34461e45	−1.00607
$603$	4.46071e45	0.594523
$604$	4.40960e44	0.0571859
$605$	0	0
$606$	8.94523e45	1.09848
$607$	1.35040e46	1.61380	0.806902	−	0.590686i	$-0.201143\pi$
$607$	1.35040e46	1.61380	0.806902	+	0.590686i	$0.201143\pi$
$608$	−3.04390e45	−0.354014
$609$	1.20809e45	0.136745
$610$	0	0
$611$	1.43696e45	0.154087
$612$	−9.58079e45	−1.00001
$613$	1.09063e45	0.110810	0.0554052	−	0.998464i	$-0.482355\pi$
$613$	1.09063e45	0.110810	0.0554052	+	0.998464i	$0.482355\pi$
$614$	−1.22655e46	−1.21313
$615$	0	0
$616$	−2.17175e46	−2.03576
$617$	−1.20780e46	−1.10227	−0.551137	−	0.834415i	$-0.685806\pi$
$617$	−1.20780e46	−1.10227	−0.551137	+	0.834415i	$0.685806\pi$
$618$	−2.34197e46	−2.08100
$619$	−3.00533e45	−0.260014	−0.130007	−	0.991513i	$-0.541500\pi$
$619$	−3.00533e45	−0.260014	−0.130007	+	0.991513i	$0.541500\pi$
$620$	0	0
$621$	5.20980e46	4.27376
$622$	−7.85834e45	−0.627754
$623$	−2.53847e46	−1.97478
$624$	1.03035e46	0.780621
$625$	0	0
$626$	−1.83550e46	−1.31910
$627$	1.93293e46	1.35301
$628$	5.07885e45	0.346283
$629$	−3.75081e45	−0.249109
$630$	0	0
$631$	−2.08614e46	−1.31480	−0.657400	−	0.753542i	$-0.728344\pi$
$631$	−2.08614e46	−1.31480	−0.657400	+	0.753542i	$0.728344\pi$
$632$	−1.36302e46	−0.836892
$633$	4.09728e46	2.45095
$634$	1.00736e46	0.587102
$635$	0	0
$636$	4.02166e45	0.222517
$637$	8.82732e45	0.475914
$638$	−1.36997e45	−0.0719732
$639$	−4.61168e46	−2.36099
$640$	0	0
$641$	−1.91329e46	−0.930299	−0.465149	−	0.885232i	$-0.653999\pi$
$641$	−1.91329e46	−0.930299	−0.465149	+	0.885232i	$0.653999\pi$
$642$	−2.81815e46	−1.33547
$643$	3.18460e46	1.47087	0.735434	−	0.677597i	$-0.236978\pi$
$643$	3.18460e46	1.47087	0.735434	+	0.677597i	$0.236978\pi$
$644$	1.78346e46	0.802871
$645$	0	0
$646$	−9.08400e45	−0.388544
$647$	−3.25342e46	−1.35650	−0.678250	−	0.734831i	$-0.737261\pi$
$647$	−3.25342e46	−1.35650	−0.678250	+	0.734831i	$0.737261\pi$
$648$	6.34507e46	2.57898
$649$	−1.26828e45	−0.0502548
$650$	0	0
$651$	2.22106e46	0.836516
$652$	−1.92964e46	−0.708583
$653$	−1.98304e46	−0.710009	−0.355005	−	0.934865i	$-0.615521\pi$
$653$	−1.98304e46	−0.710009	−0.355005	+	0.934865i	$0.615521\pi$
$654$	3.42641e46	1.19621
$655$	0	0
$656$	6.38198e45	0.211857
$657$	9.51517e46	3.08026
$658$	−4.87381e45	−0.153866
$659$	2.96542e45	0.0913011	0.0456506	−	0.998957i	$-0.485464\pi$
$659$	2.96542e45	0.0913011	0.0456506	+	0.998957i	$0.485464\pi$
$660$	0	0
$661$	1.20833e46	0.353886	0.176943	−	0.984221i	$-0.443379\pi$
$661$	1.20833e46	0.353886	0.176943	+	0.984221i	$0.443379\pi$
$662$	1.69847e46	0.485179
$663$	−6.59479e46	−1.83750
$664$	−2.98460e46	−0.811170
$665$	0	0
$666$	1.71849e46	0.444449
$667$	3.95498e45	0.0997857
$668$	−3.00300e46	−0.739168
$669$	−1.45804e46	−0.350138
$670$	0	0
$671$	−4.18533e46	−0.956772
$672$	7.49509e46	1.67180
$673$	−2.52503e46	−0.549565	−0.274782	−	0.961506i	$-0.588606\pi$
$673$	−2.52503e46	−0.549565	−0.274782	+	0.961506i	$0.588606\pi$
$674$	4.11984e46	0.874968
$675$	0	0
$676$	1.84303e45	0.0372745
$677$	−3.98633e46	−0.786793	−0.393396	−	0.919369i	$-0.628700\pi$
$677$	−3.98633e46	−0.786793	−0.393396	+	0.919369i	$0.628700\pi$
$678$	8.94908e46	1.72381
$679$	3.83101e46	0.720215
$680$	0	0
$681$	1.04995e47	1.88036
$682$	−2.51869e46	−0.440284
$683$	3.89128e46	0.663973	0.331986	−	0.943284i	$-0.392281\pi$
$683$	3.89128e46	0.663973	0.331986	+	0.943284i	$0.392281\pi$
$684$	−2.74638e46	−0.457441
$685$	0	0
$686$	2.99487e46	0.475368
$687$	−3.77534e46	−0.585019
$688$	−3.10903e46	−0.470344
$689$	1.95516e46	0.288778
$690$	0	0
$691$	−3.16293e46	−0.445350	−0.222675	−	0.974893i	$-0.571479\pi$
$691$	−3.16293e46	−0.445350	−0.222675	+	0.974893i	$0.571479\pi$
$692$	−1.82399e46	−0.250769
$693$	−3.36156e47	−4.51276
$694$	5.20405e46	0.682197
$695$	0	0
$696$	9.68853e45	0.121117
$697$	−4.08479e46	−0.498688
$698$	1.23837e47	1.47651
$699$	−1.03266e47	−1.20249
$700$	0	0
$701$	−5.26072e46	−0.584384	−0.292192	−	0.956360i	$-0.594385\pi$
$701$	−5.26072e46	−0.584384	−0.292192	+	0.956360i	$0.594385\pi$
$702$	1.76495e47	1.91500
$703$	−1.07519e46	−0.113952
$704$	−1.50775e47	−1.56092
$705$	0	0
$706$	−7.94665e46	−0.785066
$707$	9.73315e46	0.939362
$708$	2.55142e45	0.0240565
$709$	1.31306e47	1.20954	0.604771	−	0.796399i	$-0.293265\pi$
$709$	1.31306e47	1.20954	0.604771	+	0.796399i	$0.293265\pi$
$710$	0	0
$711$	−2.10976e47	−1.85517
$712$	−2.03579e47	−1.74909
$713$	7.27122e46	0.610422
$714$	2.23678e47	1.83486
$715$	0	0
$716$	5.97938e46	0.468372
$717$	1.29546e47	0.991649
$718$	−8.92855e46	−0.667925
$719$	1.58298e47	1.15731	0.578653	−	0.815574i	$-0.303579\pi$
$719$	1.58298e47	1.15731	0.578653	+	0.815574i	$0.303579\pi$
$720$	0	0
$721$	−2.54826e47	−1.77956
$722$	8.76774e46	0.598445
$723$	6.74806e46	0.450191
$724$	−3.42868e46	−0.223584
$725$	0	0
$726$	3.09879e47	1.93080
$727$	2.56013e47	1.55935	0.779676	−	0.626184i	$-0.215384\pi$
$727$	2.56013e47	1.55935	0.779676	+	0.626184i	$0.215384\pi$
$728$	2.12399e47	1.26469
$729$	1.60598e47	0.934838
$730$	0	0
$731$	1.98994e47	1.10714
$732$	8.41970e46	0.457998
$733$	5.58232e46	0.296893	0.148446	−	0.988920i	$-0.452573\pi$
$733$	5.58232e46	0.296893	0.148446	+	0.988920i	$0.452573\pi$
$734$	5.63898e46	0.293235
$735$	0	0
$736$	2.45371e47	1.21994
$737$	−7.79298e46	−0.378870
$738$	1.87150e47	0.889736
$739$	1.40164e47	0.651634	0.325817	−	0.945433i	$-0.394361\pi$
$739$	1.40164e47	0.651634	0.325817	+	0.945433i	$0.394361\pi$
$740$	0	0
$741$	−1.89043e47	−0.840542
$742$	−6.63140e46	−0.288364
$743$	−3.74285e46	−0.159180	−0.0795898	−	0.996828i	$-0.525361\pi$
$743$	−3.74285e46	−0.159180	−0.0795898	+	0.996828i	$0.525361\pi$
$744$	1.78123e47	0.740913
$745$	0	0
$746$	−3.22375e47	−1.28284
$747$	−4.61973e47	−1.79815
$748$	1.67379e47	0.637271
$749$	−3.06638e47	−1.14202
$750$	0	0
$751$	2.45331e47	0.874365	0.437182	−	0.899373i	$-0.355976\pi$
$751$	2.45331e47	0.874365	0.437182	+	0.899373i	$0.355976\pi$
$752$	−2.06312e46	−0.0719334
$753$	−8.20830e47	−2.79986
$754$	1.33985e46	0.0447124
$755$	0	0
$756$	3.95018e47	1.26185
$757$	−3.89117e47	−1.21618	−0.608090	−	0.793868i	$-0.708064\pi$
$757$	−3.89117e47	−1.21618	−0.608090	+	0.793868i	$0.708064\pi$
$758$	−3.83251e47	−1.17204
$759$	−1.55815e48	−4.66253
$760$	0	0
$761$	−2.57108e47	−0.736662	−0.368331	−	0.929695i	$-0.620071\pi$
$761$	−2.57108e47	−0.736662	−0.368331	+	0.929695i	$0.620071\pi$
$762$	4.54712e46	0.127491
$763$	3.72822e47	1.02293
$764$	6.71402e46	0.180278
$765$	0	0
$766$	5.51044e47	1.41714
$767$	1.24039e46	0.0312201
$768$	7.33419e47	1.80672
$769$	1.74753e47	0.421348	0.210674	−	0.977556i	$-0.432434\pi$
$769$	1.74753e47	0.421348	0.210674	+	0.977556i	$0.432434\pi$
$770$	0	0
$771$	−1.13570e48	−2.62341
$772$	1.34019e47	0.303027
$773$	−1.07838e47	−0.238676	−0.119338	−	0.992854i	$-0.538077\pi$
$773$	−1.07838e47	−0.238676	−0.119338	+	0.992854i	$0.538077\pi$
$774$	−9.11717e47	−1.97531
$775$	0	0
$776$	3.07237e47	0.637903
$777$	2.64747e47	0.538127
$778$	−1.74388e47	−0.347019
$779$	−1.17093e47	−0.228119
$780$	0	0
$781$	8.05672e47	1.50458
$782$	7.32269e47	1.33893
$783$	8.75990e46	0.156830
$784$	−1.26738e47	−0.222174
$785$	0	0
$786$	−2.48025e47	−0.416892
$787$	2.21953e47	0.365324	0.182662	−	0.983176i	$-0.441529\pi$
$787$	2.21953e47	0.365324	0.182662	+	0.983176i	$0.441529\pi$
$788$	−4.03191e47	−0.649873
$789$	9.28223e47	1.46515
$790$	0	0
$791$	9.73733e47	1.47410
$792$	−2.69588e48	−3.99701
$793$	4.09329e47	0.594382
$794$	3.19358e47	0.454192
$795$	0	0
$796$	−4.90696e47	−0.669494
$797$	−9.77934e47	−1.30691	−0.653457	−	0.756963i	$-0.726682\pi$
$797$	−9.77934e47	−1.30691	−0.653457	+	0.756963i	$0.726682\pi$
$798$	6.41185e47	0.839335
$799$	1.32050e47	0.169324
$800$	0	0
$801$	−3.15111e48	−3.87728
$802$	−4.60248e46	−0.0554772
$803$	−1.66232e48	−1.96295
$804$	1.56773e47	0.181362
$805$	0	0
$806$	2.46330e47	0.273520
$807$	4.09129e47	0.445089
$808$	7.80573e47	0.832005
$809$	−6.43989e47	−0.672555	−0.336278	−	0.941763i	$-0.609168\pi$
$809$	−6.43989e47	−0.672555	−0.336278	+	0.941763i	$0.609168\pi$
$810$	0	0
$811$	−3.92035e47	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$811$	−3.92035e47	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$812$	2.99875e46	0.0294623
$813$	1.08617e48	1.04570
$814$	−3.00224e47	−0.283232
$815$	0	0
$816$	9.46847e47	0.857813
$817$	5.70425e47	0.506447
$818$	8.35166e47	0.726680
$819$	3.28763e48	2.80349
$820$	0	0
$821$	−3.66301e47	−0.300038	−0.150019	−	0.988683i	$-0.547934\pi$
$821$	−3.66301e47	−0.300038	−0.150019	+	0.988683i	$0.547934\pi$
$822$	−2.75979e48	−2.21560
$823$	−6.74278e47	−0.530569	−0.265284	−	0.964170i	$-0.585466\pi$
$823$	−6.74278e47	−0.530569	−0.265284	+	0.964170i	$0.585466\pi$
$824$	−2.04364e48	−1.57618
$825$	0	0
$826$	−4.20708e46	−0.0311753
$827$	1.83329e48	1.33165	0.665827	−	0.746106i	$-0.268079\pi$
$827$	1.83329e48	1.33165	0.665827	+	0.746106i	$0.268079\pi$
$828$	2.21388e48	1.57635
$829$	1.99989e48	1.39591	0.697954	−	0.716142i	$-0.254094\pi$
$829$	1.99989e48	1.39591	0.697954	+	0.716142i	$0.254094\pi$
$830$	0	0
$831$	2.91890e48	1.95795
$832$	1.47460e48	0.969702
$833$	8.11190e47	0.522974
$834$	1.39539e48	0.881971
$835$	0	0
$836$	4.79799e47	0.291512
$837$	1.61050e48	0.959382
$838$	5.08735e47	0.297143
$839$	−7.68878e47	−0.440337	−0.220168	−	0.975462i	$-0.570661\pi$
$839$	−7.68878e47	−0.440337	−0.220168	+	0.975462i	$0.570661\pi$
$840$	0	0
$841$	−1.80943e48	−0.996338
$842$	1.67053e48	0.901998
$843$	−6.76030e48	−3.57941
$844$	1.01704e48	0.528065
$845$	0	0
$846$	−6.05007e47	−0.302099
$847$	3.37174e48	1.65112
$848$	−2.80712e47	−0.134812
$849$	−5.80585e48	−2.73457
$850$	0	0
$851$	8.66719e47	0.392682
$852$	−1.62078e48	−0.720231
$853$	−1.63399e47	−0.0712180	−0.0356090	−	0.999366i	$-0.511337\pi$
$853$	−1.63399e47	−0.0712180	−0.0356090	+	0.999366i	$0.511337\pi$
$854$	−1.38834e48	−0.593528
$855$	0	0
$856$	−2.45915e48	−1.01151
$857$	5.35960e47	0.216247	0.108123	−	0.994137i	$-0.465516\pi$
$857$	5.35960e47	0.216247	0.108123	+	0.994137i	$0.465516\pi$
$858$	−5.27863e48	−2.08920
$859$	−3.45793e48	−1.34255	−0.671273	−	0.741210i	$-0.734252\pi$
$859$	−3.45793e48	−1.34255	−0.671273	+	0.741210i	$0.734252\pi$
$860$	0	0
$861$	2.88321e48	1.07727
$862$	2.16884e48	0.794982
$863$	−1.95932e48	−0.704574	−0.352287	−	0.935892i	$-0.614596\pi$
$863$	−1.95932e48	−0.704574	−0.352287	+	0.935892i	$0.614596\pi$
$864$	5.43473e48	1.91735
$865$	0	0
$866$	2.61773e48	0.888955
$867$	−5.22368e47	−0.174045
$868$	5.51319e47	0.180230
$869$	3.68580e48	1.18224
$870$	0	0
$871$	7.62161e47	0.235368
$872$	2.98994e48	0.906024
$873$	4.75559e48	1.41407
$874$	2.09908e48	0.612479
$875$	0	0
$876$	3.34413e48	0.939647
$877$	−1.31812e48	−0.363464	−0.181732	−	0.983348i	$-0.558170\pi$
$877$	−1.31812e48	−0.363464	−0.181732	+	0.983348i	$0.558170\pi$
$878$	2.60696e47	0.0705464
$879$	4.07223e48	1.08147
$880$	0	0
$881$	6.02351e48	1.54080	0.770401	−	0.637559i	$-0.220056\pi$
$881$	6.02351e48	1.54080	0.770401	+	0.637559i	$0.220056\pi$
$882$	−3.71658e48	−0.933065
$883$	5.51914e48	1.35994	0.679970	−	0.733240i	$-0.261993\pi$
$883$	5.51914e48	1.35994	0.679970	+	0.733240i	$0.261993\pi$
$884$	−1.63698e48	−0.395896
$885$	0	0
$886$	2.04773e48	0.477107
$887$	−2.46908e48	−0.564672	−0.282336	−	0.959316i	$-0.591109\pi$
$887$	−2.46908e48	−0.564672	−0.282336	+	0.959316i	$0.591109\pi$
$888$	2.12320e48	0.476626
$889$	4.94765e47	0.109023
$890$	0	0
$891$	−1.71580e49	−3.64322
$892$	−3.61921e47	−0.0754385
$893$	3.78528e47	0.0774550
$894$	−4.79710e48	−0.963628
$895$	0	0
$896$	−3.21597e47	−0.0622631
$897$	1.52389e49	2.89653
$898$	2.19840e48	0.410248
$899$	1.22260e47	0.0224001
$900$	0	0
$901$	1.79670e48	0.317334
$902$	−3.26957e48	−0.566999
$903$	−1.40458e49	−2.39165
$904$	7.80909e48	1.30563
$905$	0	0
$906$	−1.27795e48	−0.206015
$907$	−1.76568e48	−0.279507	−0.139753	−	0.990186i	$-0.544631\pi$
$907$	−1.76568e48	−0.279507	−0.139753	+	0.990186i	$0.544631\pi$
$908$	2.60621e48	0.405129
$909$	1.20822e49	1.84434
$910$	0	0
$911$	−4.90626e48	−0.722266	−0.361133	−	0.932514i	$-0.617610\pi$
$911$	−4.90626e48	−0.722266	−0.361133	+	0.932514i	$0.617610\pi$
$912$	2.71418e48	0.392396
$913$	8.07079e48	1.14590
$914$	−6.26043e47	−0.0872955
$915$	0	0
$916$	−9.37128e47	−0.126044
$917$	−2.69872e48	−0.356503
$918$	1.62190e49	2.10437
$919$	−7.03091e48	−0.895994	−0.447997	−	0.894035i	$-0.647863\pi$
$919$	−7.03091e48	−0.895994	−0.447997	+	0.894035i	$0.647863\pi$
$920$	0	0
$921$	−2.34564e49	−2.88388
$922$	−5.24400e48	−0.633290
$923$	−7.87955e48	−0.934702
$924$	−1.18143e49	−1.37664
$925$	0	0
$926$	1.11461e49	1.25326
$927$	−3.16327e49	−3.49398
$928$	4.12574e47	0.0447672
$929$	3.42900e48	0.365517	0.182759	−	0.983158i	$-0.441497\pi$
$929$	3.42900e48	0.365517	0.182759	+	0.983158i	$0.441497\pi$
$930$	0	0
$931$	2.32532e48	0.239228
$932$	−2.56329e48	−0.259081
$933$	−1.50282e49	−1.49231
$934$	−6.58752e48	−0.642686
$935$	0	0
$936$	2.63660e49	2.48309
$937$	2.88611e48	0.267060	0.133530	−	0.991045i	$-0.457369\pi$
$937$	2.88611e48	0.267060	0.133530	+	0.991045i	$0.457369\pi$
$938$	−2.58506e48	−0.235030
$939$	−3.51019e49	−3.13580
$940$	0	0
$941$	−1.90690e49	−1.64475	−0.822373	−	0.568949i	$-0.807350\pi$
$941$	−1.90690e49	−1.64475	−0.822373	+	0.568949i	$0.807350\pi$
$942$	−1.47190e49	−1.24750
$943$	9.43893e48	0.786104
$944$	−1.78089e47	−0.0145747
$945$	0	0
$946$	1.59279e49	1.25880
$947$	−7.16410e48	−0.556400	−0.278200	−	0.960523i	$-0.589738\pi$
$947$	−7.16410e48	−0.556400	−0.278200	+	0.960523i	$0.589738\pi$
$948$	−7.41479e48	−0.565928
$949$	1.62577e49	1.21946
$950$	0	0
$951$	1.92647e49	1.39568
$952$	1.95185e49	1.38975
$953$	−3.01662e48	−0.211100	−0.105550	−	0.994414i	$-0.533660\pi$
$953$	−3.01662e48	−0.211100	−0.105550	+	0.994414i	$0.533660\pi$
$954$	−8.23183e48	−0.566172
$955$	0	0
$956$	3.21563e48	0.213654
$957$	−2.61992e48	−0.171097
$958$	−2.64548e48	−0.169814
$959$	−3.00288e49	−1.89466
$960$	0	0
$961$	−1.41557e49	−0.862971
$962$	2.93622e48	0.175954
$963$	−3.80642e49	−2.24225
$964$	1.67503e48	0.0969952
$965$	0	0
$966$	−5.16865e49	−2.89237
$967$	9.56534e48	0.526216	0.263108	−	0.964766i	$-0.415252\pi$
$967$	9.56534e48	0.526216	0.263108	+	0.964766i	$0.415252\pi$
$968$	2.70405e49	1.46242
$969$	−1.73722e49	−0.923658
$970$	0	0
$971$	3.02376e49	1.55392	0.776961	−	0.629548i	$-0.216760\pi$
$971$	3.02376e49	1.55392	0.776961	+	0.629548i	$0.216760\pi$
$972$	1.41248e49	0.713655
$973$	1.51829e49	0.754213
$974$	1.77175e49	0.865327
$975$	0	0
$976$	−5.87695e48	−0.277479
$977$	−5.10941e48	−0.237198	−0.118599	−	0.992942i	$-0.537840\pi$
$977$	−5.10941e48	−0.237198	−0.118599	+	0.992942i	$0.537840\pi$
$978$	5.59230e49	2.55270
$979$	5.50508e49	2.47086
$980$	0	0
$981$	4.62800e49	2.00842
$982$	−8.71368e48	−0.371845
$983$	1.15145e49	0.483183	0.241591	−	0.970378i	$-0.422331\pi$
$983$	1.15145e49	0.483183	0.241591	+	0.970378i	$0.422331\pi$
$984$	2.31226e49	0.954151
$985$	0	0
$986$	1.23126e48	0.0491337
$987$	−9.32064e48	−0.365774
$988$	−4.69248e48	−0.181098
$989$	−4.59824e49	−1.74523
$990$	0	0
$991$	6.06784e48	0.222751	0.111375	−	0.993778i	$-0.464474\pi$
$991$	6.06784e48	0.222751	0.111375	+	0.993778i	$0.464474\pi$
$992$	7.58515e48	0.273856
$993$	3.24815e49	1.15338
$994$	2.67254e49	0.933361
$995$	0	0
$996$	−1.62361e49	−0.548534
$997$	−3.14175e49	−1.04400	−0.522000	−	0.852945i	$-0.674814\pi$
$997$	−3.14175e49	−1.04400	−0.522000	+	0.852945i	$0.674814\pi$
$998$	−2.93388e49	−0.958932
$999$	1.91970e49	0.617166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.b.1.2		5
5.2	odd	4		25.34.b.b.24.3		10
5.3	odd	4		25.34.b.b.24.8		10
5.4	even	2		5.34.a.a.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.4	✓	5	5.4	even	2
25.34.a.b.1.2		5	1.1	even	1	trivial
25.34.b.b.24.3		10	5.2	odd	4
25.34.b.b.24.8		10	5.3	odd	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-71937.8 q^{2} -1.37573e8 q^{3} -3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14 q^{7} +8.63600e14 q^{8} +1.33673e16 q^{9} +O(q^{10})\)	\(q-71937.8 q^{2} -1.37573e8 q^{3} -3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14 q^{7} +8.63600e14 q^{8} +1.33673e16 q^{9} -2.33530e17 q^{11} +4.69797e17 q^{12} +2.28395e18 q^{13} -7.74658e18 q^{14} -3.27918e19 q^{16} +2.09885e20 q^{17} -9.61615e20 q^{18} +6.01644e20 q^{19} -1.48145e22 q^{21} +1.67997e22 q^{22} -4.84991e22 q^{23} -1.18808e23 q^{24} -1.64302e23 q^{26} -1.07421e24 q^{27} -3.67730e23 q^{28} -8.15476e22 q^{29} -1.49925e24 q^{31} -5.05930e24 q^{32} +3.21275e25 q^{33} -1.50986e25 q^{34} -4.56479e25 q^{36} -1.78708e25 q^{37} -4.32809e25 q^{38} -3.14210e26 q^{39} -1.94621e26 q^{41} +1.06572e27 q^{42} +9.48110e26 q^{43} +7.97481e26 q^{44} +3.48891e27 q^{46} +6.29157e26 q^{47} +4.51128e27 q^{48} +3.86494e27 q^{49} -2.88745e28 q^{51} -7.79943e27 q^{52} +8.56042e27 q^{53} +7.72760e28 q^{54} +9.29963e28 q^{56} -8.27701e28 q^{57} +5.86635e27 q^{58} +5.43089e27 q^{59} +1.79220e29 q^{61} +1.07853e29 q^{62} +1.43945e30 q^{63} +6.45635e29 q^{64} -2.31118e30 q^{66} +3.33703e29 q^{67} -7.16732e29 q^{68} +6.67217e30 q^{69} -3.44997e30 q^{71} +1.15440e31 q^{72} +7.11823e30 q^{73} +1.28559e30 q^{74} -2.05455e30 q^{76} -2.51476e31 q^{77} +2.26036e31 q^{78} -1.57830e31 q^{79} +7.34723e31 q^{81} +1.40006e31 q^{82} -3.45599e31 q^{83} +5.05898e31 q^{84} -6.82049e31 q^{86} +1.12188e31 q^{87} -2.01677e32 q^{88} -2.35733e32 q^{89} +2.45946e32 q^{91} +1.65619e32 q^{92} +2.06256e32 q^{93} -4.52602e31 q^{94} +6.96024e32 q^{96} +3.55763e32 q^{97} -2.78035e32 q^{98} -3.12168e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * q^99

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