LMFDB - Embedded newform 825.4.c.m.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.245110336.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 19x^{4} + 101x^{2} + 100 $ x^6 + 19x^4 + 101x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$-2.91150i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.m.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.38835i q^{2} +3.00000i q^{3} -11.2577 q^{4} +13.1651 q^{6} -11.7304i q^{7} +14.2958i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-4.38835i q^{2} +3.00000i q^{3} -11.2577 q^{4} +13.1651 q^{6} -11.7304i q^{7} +14.2958i q^{8} -9.00000 q^{9} +11.0000 q^{11} -33.7730i q^{12} +72.8298i q^{13} -51.4772 q^{14} -27.3264 q^{16} -9.89921i q^{17} +39.4952i q^{18} -0.0238576 q^{19} +35.1912 q^{21} -48.2719i q^{22} -73.0456i q^{23} -42.8873 q^{24} +319.603 q^{26} -27.0000i q^{27} +132.057i q^{28} -202.097 q^{29} +181.642 q^{31} +234.284i q^{32} +33.0000i q^{33} -43.4413 q^{34} +101.319 q^{36} +299.887i q^{37} +0.104695i q^{38} -218.489 q^{39} +88.5438 q^{41} -154.432i q^{42} +146.114i q^{43} -123.834 q^{44} -320.550 q^{46} +185.746i q^{47} -81.9792i q^{48} +205.397 q^{49} +29.6976 q^{51} -819.893i q^{52} +347.001i q^{53} -118.486 q^{54} +167.695 q^{56} -0.0715727i q^{57} +886.874i q^{58} -691.824 q^{59} +491.854 q^{61} -797.108i q^{62} +105.574i q^{63} +809.510 q^{64} +144.816 q^{66} +715.379i q^{67} +111.442i q^{68} +219.137 q^{69} +541.957 q^{71} -128.662i q^{72} +159.702i q^{73} +1316.01 q^{74} +0.268580 q^{76} -129.035i q^{77} +958.809i q^{78} +212.257 q^{79} +81.0000 q^{81} -388.562i q^{82} -413.252i q^{83} -396.171 q^{84} +641.202 q^{86} -606.292i q^{87} +157.253i q^{88} +1099.40 q^{89} +854.323 q^{91} +822.322i q^{92} +544.925i q^{93} +815.121 q^{94} -702.852 q^{96} +567.999i q^{97} -901.357i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9	$ 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9} + 66 q^{11} - 288 q^{14} + 50 q^{16} - 232 q^{19} - 36 q^{21} - 18 q^{24} + 604 q^{26} - 476 q^{29} + 184 q^{31} - 708 q^{34} + 306 q^{36} - 120 q^{39} - 92 q^{41} - 374 q^{44} - 480 q^{46} + 914 q^{49} - 192 q^{51} + 54 q^{54} + 1376 q^{56} - 2472 q^{59} + 684 q^{61} + 3838 q^{64} - 66 q^{66} + 1440 q^{69} + 3632 q^{71} + 3748 q^{74} + 792 q^{76} + 192 q^{79} + 486 q^{81} + 960 q^{84} + 376 q^{86} - 1676 q^{89} + 664 q^{91} + 6224 q^{94} - 1182 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9 + 66 * q^11 - 288 * q^14 + 50 * q^16 - 232 * q^19 - 36 * q^21 - 18 * q^24 + 604 * q^26 - 476 * q^29 + 184 * q^31 - 708 * q^34 + 306 * q^36 - 120 * q^39 - 92 * q^41 - 374 * q^44 - 480 * q^46 + 914 * q^49 - 192 * q^51 + 54 * q^54 + 1376 * q^56 - 2472 * q^59 + 684 * q^61 + 3838 * q^64 - 66 * q^66 + 1440 * q^69 + 3632 * q^71 + 3748 * q^74 + 792 * q^76 + 192 * q^79 + 486 * q^81 + 960 * q^84 + 376 * q^86 - 1676 * q^89 + 664 * q^91 + 6224 * q^94 - 1182 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 4.38835i	− 1.55152i	−0.631029	−	0.775759i	$-0.717367\pi$
$2$	− 4.38835i	− 1.55152i	0.631029	−	0.775759i	$-0.282633\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−11.2577	−1.40721
$5$	0	0
$5$	0	0
$6$	13.1651	0.895769
$7$	− 11.7304i	− 0.633383i	−0.948529	−	0.316691i	$-0.897428\pi$
$7$	− 11.7304i	− 0.633383i	0.948529	−	0.316691i	$-0.102572\pi$
$8$	14.2958i	0.631789i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	− 33.7730i	− 0.812452i
$13$	72.8298i	1.55380i	0.629627	+	0.776898i	$0.283208\pi$
$13$	72.8298i	1.55380i	−0.629627	+	0.776898i	$0.716792\pi$
$14$	−51.4772	−0.982705
$15$	0	0
$16$	−27.3264	−0.426975
$17$	− 9.89921i	− 0.141230i	−0.997504	−	0.0706150i	$-0.977504\pi$
$17$	− 9.89921i	− 0.141230i	0.997504	−	0.0706150i	$-0.0224962\pi$
$18$	39.4952i	0.517173i
$19$	−0.0238576	−0.000288069 0	−0.000144034	−	1.00000i	$-0.500046\pi$
$19$	−0.0238576	−0.000288069 0	−0.000144034		1.00000i	$0.500046\pi$
$20$	0	0
$21$	35.1912	0.365684
$22$	− 48.2719i	− 0.467800i
$23$	− 73.0456i	− 0.662220i	−0.943592	−	0.331110i	$-0.892577\pi$
$23$	− 73.0456i	− 0.662220i	0.943592	−	0.331110i	$-0.107423\pi$
$24$	−42.8873	−0.364764
$25$	0	0
$26$	319.603	2.41074
$27$	− 27.0000i	− 0.192450i
$28$	132.057i	0.891301i
$29$	−202.097	−1.29409	−0.647043	−	0.762453i	$-0.723995\pi$
$29$	−202.097	−1.29409	−0.647043	+	0.762453i	$0.723995\pi$
$30$	0	0
$31$	181.642	1.05238	0.526191	−	0.850367i	$-0.323620\pi$
$31$	181.642	1.05238	0.526191	+	0.850367i	$0.323620\pi$
$32$	234.284i	1.29425i
$33$	33.0000i	0.174078i
$34$	−43.4413	−0.219121
$35$	0	0
$36$	101.319	0.469069
$37$	299.887i	1.33246i	0.745746	+	0.666231i	$0.232093\pi$
$37$	299.887i	1.33246i	−0.745746	+	0.666231i	$0.767907\pi$
$38$	0.104695i	0 0.000446943i
$39$	−218.489	−0.897085
$40$	0	0
$41$	88.5438	0.337274	0.168637	−	0.985678i	$-0.446063\pi$
$41$	88.5438	0.337274	0.168637	+	0.985678i	$0.446063\pi$
$42$	− 154.432i	− 0.567365i
$43$	146.114i	0.518191i	0.965852	+	0.259096i	$0.0834245\pi$
$43$	146.114i	0.518191i	−0.965852	+	0.259096i	$0.916576\pi$
$44$	−123.834	−0.424289
$45$	0	0
$46$	−320.550	−1.02745
$47$	185.746i	0.576466i	0.957560	+	0.288233i	$0.0930678\pi$
$47$	185.746i	0.576466i	−0.957560	+	0.288233i	$0.906932\pi$
$48$	− 81.9792i	− 0.246514i
$49$	205.397	0.598826
$50$	0	0
$51$	29.6976	0.0815392
$52$	− 819.893i	− 2.18651i
$53$	347.001i	0.899325i	0.893199	+	0.449662i	$0.148456\pi$
$53$	347.001i	0.899325i	−0.893199	+	0.449662i	$0.851544\pi$
$54$	−118.486	−0.298590
$55$	0	0
$56$	167.695	0.400164
$57$	− 0.0715727i	0 0.000166316i
$58$	886.874i	2.00780i
$59$	−691.824	−1.52657	−0.763287	−	0.646060i	$-0.776416\pi$
$59$	−691.824	−1.52657	−0.763287	+	0.646060i	$0.776416\pi$
$60$	0	0
$61$	491.854	1.03238	0.516192	−	0.856473i	$-0.327349\pi$
$61$	491.854	1.03238	0.516192	+	0.856473i	$0.327349\pi$
$62$	− 797.108i	− 1.63279i
$63$	105.574i	0.211128i
$64$	809.510	1.58107
$65$	0	0
$66$	144.816	0.270085
$67$	715.379i	1.30444i	0.758030	+	0.652220i	$0.226162\pi$
$67$	715.379i	1.30444i	−0.758030	+	0.652220i	$0.773838\pi$
$68$	111.442i	0.198740i
$69$	219.137	0.382333
$70$	0	0
$71$	541.957	0.905893	0.452947	−	0.891538i	$-0.350373\pi$
$71$	541.957	0.905893	0.452947	+	0.891538i	$0.350373\pi$
$72$	− 128.662i	− 0.210596i
$73$	159.702i	0.256051i	0.991771	+	0.128026i	$0.0408640\pi$
$73$	159.702i	0.256051i	−0.991771	+	0.128026i	$0.959136\pi$
$74$	1316.01	2.06734
$75$	0	0
$76$	0.268580	0.000405372 0
$77$	− 129.035i	− 0.190972i
$78$	958.809i	1.39184i
$79$	212.257	0.302288	0.151144	−	0.988512i	$-0.451704\pi$
$79$	212.257	0.302288	0.151144	+	0.988512i	$0.451704\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 388.562i	− 0.523286i
$83$	− 413.252i	− 0.546510i	−0.961942	−	0.273255i	$-0.911900\pi$
$83$	− 413.252i	− 0.546510i	0.961942	−	0.273255i	$-0.0881003\pi$
$84$	−396.171	−0.514593
$85$	0	0
$86$	641.202	0.803983
$87$	− 606.292i	− 0.747141i
$88$	157.253i	0.190492i
$89$	1099.40	1.30939	0.654697	−	0.755891i	$-0.272796\pi$
$89$	1099.40	1.30939	0.654697	+	0.755891i	$0.272796\pi$
$90$	0	0
$91$	854.323	0.984148
$92$	822.322i	0.931880i
$93$	544.925i	0.607593i
$94$	815.121	0.894397
$95$	0	0
$96$	−702.852	−0.747235
$97$	567.999i	0.594553i	0.954791	+	0.297276i	$0.0960783\pi$
$97$	567.999i	0.594553i	−0.954791	+	0.297276i	$0.903922\pi$
$98$	− 901.357i	− 0.929090i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	944.617	0.930623	0.465311	−	0.885147i	$-0.345942\pi$
$101$	944.617	0.930623	0.465311	+	0.885147i	$0.345942\pi$
$102$	− 130.324i	− 0.126510i
$103$	− 1832.42i	− 1.75295i	−0.481448	−	0.876475i	$-0.659889\pi$
$103$	− 1832.42i	− 1.75295i	0.481448	−	0.876475i	$-0.340111\pi$
$104$	−1041.16	−0.981672
$105$	0	0
$106$	1522.76	1.39532
$107$	− 706.148i	− 0.637999i	−0.947755	−	0.319000i	$-0.896653\pi$
$107$	− 706.148i	− 0.637999i	0.947755	−	0.319000i	$-0.103347\pi$
$108$	303.957i	0.270817i
$109$	1830.83	1.60882	0.804411	−	0.594074i	$-0.202481\pi$
$109$	1830.83	1.60882	0.804411	+	0.594074i	$0.202481\pi$
$110$	0	0
$111$	−899.660	−0.769297
$112$	320.550i	0.270439i
$113$	− 654.436i	− 0.544815i	−0.962182	−	0.272408i	$-0.912180\pi$
$113$	− 654.436i	− 0.544815i	0.962182	−	0.272408i	$-0.0878200\pi$
$114$	−0.314086	−0.000258043 0
$115$	0	0
$116$	2275.14	1.82105
$117$	− 655.468i	− 0.517932i
$118$	3035.97i	2.36851i
$119$	−116.122	−0.0894527
$120$	0	0
$121$	121.000	0.0909091
$122$	− 2158.43i	− 1.60176i
$123$	265.631i	0.194725i
$124$	−2044.86	−1.48092
$125$	0	0
$126$	463.295	0.327568
$127$	814.399i	0.569025i	0.958672	+	0.284513i	$0.0918318\pi$
$127$	814.399i	0.569025i	−0.958672	+	0.284513i	$0.908168\pi$
$128$	− 1678.15i	− 1.15882i
$129$	−438.343	−0.299178
$130$	0	0
$131$	2320.98	1.54798	0.773989	−	0.633199i	$-0.218259\pi$
$131$	2320.98	1.54798	0.773989	+	0.633199i	$0.218259\pi$
$132$	− 371.503i	− 0.244963i
$133$	0.279859i	0 0.000182458i
$134$	3139.34	2.02386
$135$	0	0
$136$	141.517	0.0892277
$137$	2014.15i	1.25606i	0.778189	+	0.628030i	$0.216139\pi$
$137$	2014.15i	1.25606i	−0.778189	+	0.628030i	$0.783861\pi$
$138$	− 961.650i	− 0.593196i
$139$	−1832.51	−1.11821	−0.559106	−	0.829096i	$-0.688856\pi$
$139$	−1832.51	−1.11821	−0.559106	+	0.829096i	$0.688856\pi$
$140$	0	0
$141$	−557.239	−0.332823
$142$	− 2378.30i	− 1.40551i
$143$	801.128i	0.468487i
$144$	245.938	0.142325
$145$	0	0
$146$	700.830	0.397268
$147$	616.192i	0.345733i
$148$	− 3376.02i	− 1.87505i
$149$	3583.75	1.97042	0.985208	−	0.171365i	$-0.0548177\pi$
$149$	3583.75	1.97042	0.985208	+	0.171365i	$0.0548177\pi$
$150$	0	0
$151$	−2822.48	−1.52112	−0.760562	−	0.649265i	$-0.775077\pi$
$151$	−2822.48	−1.52112	−0.760562	+	0.649265i	$0.775077\pi$
$152$	− 0.341062i	0 0.000181999i
$153$	89.0929i	0.0470767i
$154$	−566.249	−0.296297
$155$	0	0
$156$	2459.68	1.26238
$157$	2052.04i	1.04313i	0.853212	+	0.521564i	$0.174651\pi$
$157$	2052.04i	1.04313i	−0.853212	+	0.521564i	$0.825349\pi$
$158$	− 931.459i	− 0.469005i
$159$	−1041.00	−0.519225
$160$	0	0
$161$	−856.855	−0.419439
$162$	− 355.457i	− 0.172391i
$163$	742.552i	0.356817i	0.983956	+	0.178409i	$0.0570949\pi$
$163$	742.552i	0.356817i	−0.983956	+	0.178409i	$0.942905\pi$
$164$	−996.796	−0.474614
$165$	0	0
$166$	−1813.50	−0.847920
$167$	− 699.537i	− 0.324143i	−0.986779	−	0.162071i	$-0.948183\pi$
$167$	− 699.537i	− 0.324143i	0.986779	−	0.162071i	$-0.0518174\pi$
$168$	503.086i	0.231035i
$169$	−3107.18	−1.41428
$170$	0	0
$171$	0.214718	9.60228e−5 0
$172$	− 1644.91i	− 0.729203i
$173$	734.967i	0.322997i	0.986873	+	0.161499i	$0.0516328\pi$
$173$	734.967i	0.322997i	−0.986873	+	0.161499i	$0.948367\pi$
$174$	−2660.62	−1.15920
$175$	0	0
$176$	−300.590	−0.128738
$177$	− 2075.47i	− 0.881367i
$178$	− 4824.56i	− 2.03155i
$179$	2687.28	1.12211	0.561053	−	0.827780i	$-0.310396\pi$
$179$	2687.28	1.12211	0.561053	+	0.827780i	$0.310396\pi$
$180$	0	0
$181$	−3766.56	−1.54677	−0.773387	−	0.633934i	$-0.781439\pi$
$181$	−3766.56	−1.54677	−0.773387	+	0.633934i	$0.781439\pi$
$182$	− 3749.07i	− 1.52692i
$183$	1475.56i	0.596047i
$184$	1044.24	0.418383
$185$	0	0
$186$	2391.33	0.942691
$187$	− 108.891i	− 0.0425825i
$188$	− 2091.07i	− 0.811207i
$189$	−316.721	−0.121895
$190$	0	0
$191$	−1784.15	−0.675899	−0.337950	−	0.941164i	$-0.609733\pi$
$191$	−1784.15	−0.675899	−0.337950	+	0.941164i	$0.609733\pi$
$192$	2428.53i	0.912834i
$193$	4463.74i	1.66480i	0.554173	+	0.832402i	$0.313035\pi$
$193$	4463.74i	1.66480i	−0.554173	+	0.832402i	$0.686965\pi$
$194$	2492.58	0.922459
$195$	0	0
$196$	−2312.29	−0.842673
$197$	1166.19i	0.421765i	0.977511	+	0.210883i	$0.0676338\pi$
$197$	1166.19i	0.421765i	−0.977511	+	0.210883i	$0.932366\pi$
$198$	434.447i	0.155933i
$199$	1747.63	0.622542	0.311271	−	0.950321i	$-0.399245\pi$
$199$	1747.63	0.622542	0.311271	+	0.950321i	$0.399245\pi$
$200$	0	0
$201$	−2146.14	−0.753119
$202$	− 4145.31i	− 1.44388i
$203$	2370.68i	0.819652i
$204$	−334.326	−0.114743
$205$	0	0
$206$	−8041.31	−2.71973
$207$	657.410i	0.220740i
$208$	− 1990.18i	− 0.663432i
$209$	−0.262433	−8.68559e−5 0
$210$	0	0
$211$	−415.081	−0.135428	−0.0677141	−	0.997705i	$-0.521571\pi$
$211$	−415.081	−0.135428	−0.0677141	+	0.997705i	$0.521571\pi$
$212$	− 3906.42i	− 1.26554i
$213$	1625.87i	0.523018i
$214$	−3098.83	−0.989867
$215$	0	0
$216$	385.986	0.121588
$217$	− 2130.73i	− 0.666560i
$218$	− 8034.32i	− 2.49611i
$219$	−479.107	−0.147831
$220$	0	0
$221$	720.957	0.219443
$222$	3948.03i	1.19358i
$223$	72.9064i	0.0218932i	0.999940	+	0.0109466i	$0.00348447\pi$
$223$	72.9064i	0.0218932i	−0.999940	+	0.0109466i	$0.996516\pi$
$224$	2748.25	0.819755
$225$	0	0
$226$	−2871.90	−0.845291
$227$	2362.35i	0.690727i	0.938469	+	0.345363i	$0.112244\pi$
$227$	2362.35i	0.690727i	−0.938469	+	0.345363i	$0.887756\pi$
$228$	0.805741i	0 0.000234042i
$229$	−4534.32	−1.30846	−0.654228	−	0.756297i	$-0.727007\pi$
$229$	−4534.32	−1.30846	−0.654228	+	0.756297i	$0.727007\pi$
$230$	0	0
$231$	387.104	0.110258
$232$	− 2889.13i	− 0.817590i
$233$	− 231.076i	− 0.0649713i	−0.999472	−	0.0324856i	$-0.989658\pi$
$233$	− 231.076i	− 0.0649713i	0.999472	−	0.0324856i	$-0.0103423\pi$
$234$	−2876.43	−0.803581
$235$	0	0
$236$	7788.32	2.14821
$237$	636.771i	0.174526i
$238$	509.584i	0.138787i
$239$	−4463.18	−1.20795	−0.603973	−	0.797004i	$-0.706417\pi$
$239$	−4463.18	−1.20795	−0.603973	+	0.797004i	$0.706417\pi$
$240$	0	0
$241$	−2097.51	−0.560633	−0.280316	−	0.959908i	$-0.590439\pi$
$241$	−2097.51	−0.560633	−0.280316	+	0.959908i	$0.590439\pi$
$242$	− 530.991i	− 0.141047i
$243$	243.000i	0.0641500i
$244$	−5537.12	−1.45278
$245$	0	0
$246$	1165.68	0.302119
$247$	− 1.73754i	0 0.000447600i
$248$	2596.71i	0.664883i
$249$	1239.76	0.315528
$250$	0	0
$251$	3400.42	0.855110	0.427555	−	0.903989i	$-0.359375\pi$
$251$	3400.42	0.855110	0.427555	+	0.903989i	$0.359375\pi$
$252$	− 1188.51i	− 0.297100i
$253$	− 803.501i	− 0.199667i
$254$	3573.87	0.882853
$255$	0	0
$256$	−888.218	−0.216850
$257$	4994.11i	1.21215i	0.795406	+	0.606077i	$0.207258\pi$
$257$	4994.11i	1.21215i	−0.795406	+	0.606077i	$0.792742\pi$
$258$	1923.60i	0.464180i
$259$	3517.80	0.843958
$260$	0	0
$261$	1818.88	0.431362
$262$	− 10185.3i	− 2.40172i
$263$	− 6869.81i	− 1.61069i	−0.592808	−	0.805344i	$-0.701981\pi$
$263$	− 6869.81i	− 1.61069i	0.592808	−	0.805344i	$-0.298019\pi$
$264$	−471.760	−0.109980
$265$	0	0
$266$	1.22812	0.000283086 0
$267$	3298.20i	0.755979i
$268$	− 8053.49i	− 1.83562i
$269$	2019.60	0.457758	0.228879	−	0.973455i	$-0.426494\pi$
$269$	2019.60	0.457758	0.228879	+	0.973455i	$0.426494\pi$
$270$	0	0
$271$	5191.61	1.16372	0.581859	−	0.813289i	$-0.302325\pi$
$271$	5191.61	1.16372	0.581859	+	0.813289i	$0.302325\pi$
$272$	270.510i	0.0603017i
$273$	2562.97i	0.568198i
$274$	8838.80	1.94880
$275$	0	0
$276$	−2466.97	−0.538021
$277$	− 456.134i	− 0.0989402i	−0.998776	−	0.0494701i	$-0.984247\pi$
$277$	− 456.134i	− 0.0989402i	0.998776	−	0.0494701i	$-0.0157532\pi$
$278$	8041.70i	1.73493i
$279$	−1634.78	−0.350794
$280$	0	0
$281$	3004.92	0.637930	0.318965	−	0.947767i	$-0.396665\pi$
$281$	3004.92	0.637930	0.318965	+	0.947767i	$0.396665\pi$
$282$	2445.36i	0.516380i
$283$	409.156i	0.0859428i	0.999076	+	0.0429714i	$0.0136824\pi$
$283$	409.156i	0.0859428i	−0.999076	+	0.0429714i	$0.986318\pi$
$284$	−6101.16	−1.27478
$285$	0	0
$286$	3515.63	0.726866
$287$	− 1038.66i	− 0.213623i
$288$	− 2108.56i	− 0.431416i
$289$	4815.01	0.980054
$290$	0	0
$291$	−1704.00	−0.343265
$292$	− 1797.87i	− 0.360317i
$293$	7410.14i	1.47749i	0.673985	+	0.738745i	$0.264581\pi$
$293$	7410.14i	1.47749i	−0.673985	+	0.738745i	$0.735419\pi$
$294$	2704.07	0.536410
$295$	0	0
$296$	−4287.11	−0.841835
$297$	− 297.000i	− 0.0580259i
$298$	− 15726.7i	− 3.05713i
$299$	5319.89	1.02895
$300$	0	0
$301$	1713.98	0.328213
$302$	12386.0i	2.36005i
$303$	2833.85i	0.537295i
$304$	0.651941	0.000122998 0
$305$	0	0
$306$	390.971	0.0730403
$307$	4985.77i	0.926883i	0.886127	+	0.463442i	$0.153386\pi$
$307$	4985.77i	0.926883i	−0.886127	+	0.463442i	$0.846614\pi$
$308$	1452.63i	0.268737i
$309$	5497.26	1.01207
$310$	0	0
$311$	−6238.99	−1.13756	−0.568779	−	0.822491i	$-0.692584\pi$
$311$	−6238.99	−1.13756	−0.568779	+	0.822491i	$0.692584\pi$
$312$	− 3123.47i	− 0.566768i
$313$	9821.30i	1.77359i	0.462166	+	0.886794i	$0.347072\pi$
$313$	9821.30i	1.77359i	−0.462166	+	0.886794i	$0.652928\pi$
$314$	9005.10	1.61843
$315$	0	0
$316$	−2389.52	−0.425382
$317$	− 1747.26i	− 0.309577i	−0.987948	−	0.154789i	$-0.950530\pi$
$317$	− 1747.26i	− 0.309577i	0.987948	−	0.154789i	$-0.0494696\pi$
$318$	4568.29i	0.805588i
$319$	−2223.07	−0.390182
$320$	0	0
$321$	2118.44	0.368349
$322$	3760.18i	0.650766i
$323$	0.236171i	0 4.06839e-5i
$324$	−911.870	−0.156356
$325$	0	0
$326$	3258.58	0.553608
$327$	5492.48i	0.928853i
$328$	1265.80i	0.213086i
$329$	2178.88	0.365124
$330$	0	0
$331$	−7209.01	−1.19711	−0.598554	−	0.801082i	$-0.704258\pi$
$331$	−7209.01	−1.19711	−0.598554	+	0.801082i	$0.704258\pi$
$332$	4652.25i	0.769053i
$333$	− 2698.98i	− 0.444154i
$334$	−3069.82	−0.502913
$335$	0	0
$336$	−961.650	−0.156138
$337$	53.0763i	0.00857938i	0.999991	+	0.00428969i	$0.00136545\pi$
$337$	53.0763i	0.00857938i	−0.999991	+	0.00428969i	$0.998635\pi$
$338$	13635.4i	2.19428i
$339$	1963.31	0.314549
$340$	0	0
$341$	1998.06	0.317305
$342$	− 0.942259i	0 0.000148981i
$343$	− 6432.93i	− 1.01267i
$344$	−2088.82	−0.327388
$345$	0	0
$346$	3225.30	0.501136
$347$	3326.14i	0.514572i	0.966335	+	0.257286i	$0.0828282\pi$
$347$	3326.14i	0.514572i	−0.966335	+	0.257286i	$0.917172\pi$
$348$	6825.42i	1.05138i
$349$	−12042.6	−1.84706	−0.923530	−	0.383526i	$-0.874710\pi$
$349$	−12042.6	−1.84706	−0.923530	+	0.383526i	$0.874710\pi$
$350$	0	0
$351$	1966.40	0.299028
$352$	2577.12i	0.390231i
$353$	− 10994.7i	− 1.65775i	−0.559432	−	0.828876i	$-0.688981\pi$
$353$	− 10994.7i	− 1.65775i	0.559432	−	0.828876i	$-0.311019\pi$
$354$	−9107.91	−1.36746
$355$	0	0
$356$	−12376.7	−1.84259
$357$	− 348.366i	− 0.0516455i
$358$	− 11792.8i	− 1.74097i
$359$	−2385.44	−0.350694	−0.175347	−	0.984507i	$-0.556105\pi$
$359$	−2385.44	−0.350694	−0.175347	+	0.984507i	$0.556105\pi$
$360$	0	0
$361$	−6859.00	−1.00000
$362$	16529.0i	2.39985i
$363$	363.000i	0.0524864i
$364$	−9617.68	−1.38490
$365$	0	0
$366$	6475.29	0.924778
$367$	3227.78i	0.459098i	0.973297	+	0.229549i	$0.0737251\pi$
$367$	3227.78i	0.459098i	−0.973297	+	0.229549i	$0.926275\pi$
$368$	1996.07i	0.282751i
$369$	−796.894	−0.112425
$370$	0	0
$371$	4070.46	0.569617
$372$	− 6134.58i	− 0.855009i
$373$	5948.20i	0.825700i	0.910799	+	0.412850i	$0.135467\pi$
$373$	5948.20i	0.825700i	−0.910799	+	0.412850i	$0.864533\pi$
$374$	−477.854	−0.0660675
$375$	0	0
$376$	−2655.39	−0.364205
$377$	− 14718.7i	− 2.01075i
$378$	1389.88i	0.189122i
$379$	−10332.2	−1.40034	−0.700170	−	0.713976i	$-0.746893\pi$
$379$	−10332.2	−1.40034	−0.700170	+	0.713976i	$0.746893\pi$
$380$	0	0
$381$	−2443.20	−0.328527
$382$	7829.50i	1.04867i
$383$	6686.90i	0.892127i	0.895001	+	0.446063i	$0.147174\pi$
$383$	6686.90i	0.892127i	−0.895001	+	0.446063i	$0.852826\pi$
$384$	5034.44	0.669043
$385$	0	0
$386$	19588.5	2.58297
$387$	− 1315.03i	− 0.172730i
$388$	− 6394.34i	− 0.836659i
$389$	−6099.57	−0.795014	−0.397507	−	0.917599i	$-0.630125\pi$
$389$	−6099.57	−0.795014	−0.397507	+	0.917599i	$0.630125\pi$
$390$	0	0
$391$	−723.094	−0.0935254
$392$	2936.31i	0.378332i
$393$	6962.94i	0.893725i
$394$	5117.67	0.654376
$395$	0	0
$396$	1114.51	0.141430
$397$	2640.37i	0.333795i	0.985974	+	0.166897i	$0.0533748\pi$
$397$	2640.37i	0.333795i	−0.985974	+	0.166897i	$0.946625\pi$
$398$	− 7669.20i	− 0.965885i
$399$	−0.839578	−0.000105342 0
$400$	0	0
$401$	8787.59	1.09434	0.547171	−	0.837021i	$-0.315705\pi$
$401$	8787.59	1.09434	0.547171	+	0.837021i	$0.315705\pi$
$402$	9418.01i	1.16848i
$403$	13228.9i	1.63519i
$404$	−10634.2	−1.30958
$405$	0	0
$406$	10403.4	1.27170
$407$	3298.75i	0.401752i
$408$	424.550i	0.0515156i
$409$	5870.27	0.709698	0.354849	−	0.934924i	$-0.384532\pi$
$409$	5870.27	0.709698	0.354849	+	0.934924i	$0.384532\pi$
$410$	0	0
$411$	−6042.44	−0.725187
$412$	20628.8i	2.46676i
$413$	8115.38i	0.966905i
$414$	2884.95	0.342482
$415$	0	0
$416$	−17062.9	−2.01100
$417$	− 5497.53i	− 0.645600i
$418$	1.15165i	0 0.000134759i
$419$	−14208.8	−1.65667	−0.828337	−	0.560231i	$-0.810712\pi$
$419$	−14208.8	−1.65667	−0.828337	+	0.560231i	$0.810712\pi$
$420$	0	0
$421$	−12301.9	−1.42413	−0.712063	−	0.702115i	$-0.752239\pi$
$421$	−12301.9	−1.42413	−0.712063	+	0.702115i	$0.752239\pi$
$422$	1821.52i	0.210119i
$423$	− 1671.72i	− 0.192155i
$424$	−4960.64	−0.568184
$425$	0	0
$426$	7134.89	0.811471
$427$	− 5769.65i	− 0.653895i
$428$	7949.57i	0.897797i
$429$	−2403.38	−0.270481
$430$	0	0
$431$	−5640.08	−0.630331	−0.315166	−	0.949037i	$-0.602060\pi$
$431$	−5640.08	−0.630331	−0.315166	+	0.949037i	$0.602060\pi$
$432$	737.813i	0.0821714i
$433$	− 10122.9i	− 1.12350i	−0.827308	−	0.561749i	$-0.810129\pi$
$433$	− 10122.9i	− 1.12350i	0.827308	−	0.561749i	$-0.189871\pi$
$434$	−9350.41	−1.03418
$435$	0	0
$436$	−20610.8	−2.26394
$437$	1.74269i	0 0.000190765i
$438$	2102.49i	0.229363i
$439$	10753.2	1.16907	0.584534	−	0.811369i	$-0.301277\pi$
$439$	10753.2	1.16907	0.584534	+	0.811369i	$0.301277\pi$
$440$	0	0
$441$	−1848.58	−0.199609
$442$	− 3163.82i	− 0.340469i
$443$	10346.6i	1.10967i	0.831961	+	0.554834i	$0.187218\pi$
$443$	10346.6i	1.10967i	−0.831961	+	0.554834i	$0.812782\pi$
$444$	10128.1	1.08256
$445$	0	0
$446$	319.939	0.0339676
$447$	10751.2i	1.13762i
$448$	− 9495.89i	− 1.00143i
$449$	−9569.21	−1.00579	−0.502894	−	0.864348i	$-0.667731\pi$
$449$	−9569.21	−1.00579	−0.502894	+	0.864348i	$0.667731\pi$
$450$	0	0
$451$	973.982	0.101692
$452$	7367.42i	0.766668i
$453$	− 8467.43i	− 0.878222i
$454$	10366.8	1.07167
$455$	0	0
$456$	1.02319	0.000105077 0
$457$	7446.31i	0.762197i	0.924535	+	0.381098i	$0.124454\pi$
$457$	7446.31i	0.762197i	−0.924535	+	0.381098i	$0.875546\pi$
$458$	19898.2i	2.03009i
$459$	−267.279	−0.0271797
$460$	0	0
$461$	10934.9	1.10475	0.552373	−	0.833597i	$-0.313722\pi$
$461$	10934.9	1.10475	0.552373	+	0.833597i	$0.313722\pi$
$462$	− 1698.75i	− 0.171067i
$463$	9889.15i	0.992630i	0.868142	+	0.496315i	$0.165314\pi$
$463$	9889.15i	0.992630i	−0.868142	+	0.496315i	$0.834686\pi$
$464$	5522.59	0.552543
$465$	0	0
$466$	−1014.04	−0.100804
$467$	− 100.396i	− 0.00994808i	−0.999988	−	0.00497404i	$-0.998417\pi$
$467$	− 100.396i	− 0.00994808i	0.999988	−	0.00497404i	$-0.00158329\pi$
$468$	7379.04i	0.728838i
$469$	8391.69	0.826210
$470$	0	0
$471$	−6156.13	−0.602250
$472$	− 9890.15i	− 0.964473i
$473$	1607.26i	0.156241i
$474$	2794.38	0.270780
$475$	0	0
$476$	1307.26	0.125878
$477$	− 3123.01i	− 0.299775i
$478$	19586.0i	1.87415i
$479$	4413.85	0.421032	0.210516	−	0.977590i	$-0.432486\pi$
$479$	4413.85	0.421032	0.210516	+	0.977590i	$0.432486\pi$
$480$	0	0
$481$	−21840.7	−2.07037
$482$	9204.62i	0.869832i
$483$	− 2570.56i	− 0.242163i
$484$	−1362.18	−0.127928
$485$	0	0
$486$	1066.37	0.0995299
$487$	− 16795.6i	− 1.56279i	−0.624035	−	0.781396i	$-0.714508\pi$
$487$	− 16795.6i	− 1.56279i	0.624035	−	0.781396i	$-0.285492\pi$
$488$	7031.43i	0.652250i
$489$	−2227.66	−0.206008
$490$	0	0
$491$	19003.5	1.74667	0.873336	−	0.487118i	$-0.161952\pi$
$491$	19003.5	1.74667	0.873336	+	0.487118i	$0.161952\pi$
$492$	− 2990.39i	− 0.274018i
$493$	2000.60i	0.182764i
$494$	−7.62495	−0.000694459 0
$495$	0	0
$496$	−4963.61	−0.449340
$497$	− 6357.37i	− 0.573777i
$498$	− 5440.49i	− 0.489547i
$499$	19969.5	1.79150	0.895748	−	0.444562i	$-0.146641\pi$
$499$	19969.5	1.79150	0.895748	+	0.444562i	$0.146641\pi$
$500$	0	0
$501$	2098.61	0.187144
$502$	− 14922.2i	− 1.32672i
$503$	− 15076.5i	− 1.33643i	−0.743967	−	0.668217i	$-0.767058\pi$
$503$	− 15076.5i	− 1.33643i	0.743967	−	0.668217i	$-0.232942\pi$
$504$	−1509.26	−0.133388
$505$	0	0
$506$	−3526.05	−0.309787
$507$	− 9321.53i	− 0.816536i
$508$	− 9168.23i	− 0.800737i
$509$	−12404.7	−1.08022	−0.540108	−	0.841596i	$-0.681616\pi$
$509$	−12404.7	−1.08022	−0.540108	+	0.841596i	$0.681616\pi$
$510$	0	0
$511$	1873.37	0.162178
$512$	− 9527.35i	− 0.822370i
$513$	0.644154i	0 5.54388e-5i
$514$	21915.9	1.88068
$515$	0	0
$516$	4934.72	0.421005
$517$	2043.21i	0.173811i
$518$	− 15437.3i	− 1.30942i
$519$	−2204.90	−0.186483
$520$	0	0
$521$	−18075.1	−1.51993	−0.759964	−	0.649965i	$-0.774784\pi$
$521$	−18075.1	−1.51993	−0.759964	+	0.649965i	$0.774784\pi$
$522$	− 7981.87i	− 0.669266i
$523$	− 9878.08i	− 0.825886i	−0.910757	−	0.412943i	$-0.864501\pi$
$523$	− 9878.08i	− 0.825886i	0.910757	−	0.412943i	$-0.135499\pi$
$524$	−26128.8	−2.17833
$525$	0	0
$526$	−30147.2	−2.49901
$527$	− 1798.11i	− 0.148628i
$528$	− 901.771i	− 0.0743268i
$529$	6831.34	0.561465
$530$	0	0
$531$	6226.42	0.508858
$532$	− 3.15056i	0 0.000256756i
$533$	6448.63i	0.524054i
$534$	14473.7	1.17292
$535$	0	0
$536$	−10226.9	−0.824131
$537$	8061.85i	0.647848i
$538$	− 8862.71i	− 0.710220i
$539$	2259.37	0.180553
$540$	0	0
$541$	−4740.76	−0.376749	−0.188374	−	0.982097i	$-0.560322\pi$
$541$	−4740.76	−0.376749	−0.188374	+	0.982097i	$0.560322\pi$
$542$	− 22782.6i	− 1.80553i
$543$	− 11299.7i	− 0.893030i
$544$	2319.23	0.182787
$545$	0	0
$546$	11247.2	0.881569
$547$	20441.4i	1.59782i	0.601448	+	0.798912i	$0.294591\pi$
$547$	20441.4i	1.59782i	−0.601448	+	0.798912i	$0.705409\pi$
$548$	− 22674.6i	− 1.76754i
$549$	−4426.69	−0.344128
$550$	0	0
$551$	4.82155	0.000372786 0
$552$	3132.73i	0.241554i
$553$	− 2489.86i	− 0.191464i
$554$	−2001.68	−0.153507
$555$	0	0
$556$	20629.8	1.57356
$557$	3587.32i	0.272890i	0.990648	+	0.136445i	$0.0435677\pi$
$557$	3587.32i	0.272890i	−0.990648	+	0.136445i	$0.956432\pi$
$558$	7173.98i	0.544263i
$559$	−10641.5	−0.805164
$560$	0	0
$561$	326.674	0.0245850
$562$	− 13186.6i	− 0.989759i
$563$	− 8.82275i	0 0.000660452i	−1.00000		0.000330226i	$-0.999895\pi$
$563$	− 8.82275i	0 0.000660452i	1.00000		0.000330226i	$-0.000105114\pi$
$564$	6273.21	0.468351
$565$	0	0
$566$	1795.52	0.133342
$567$	− 950.163i	− 0.0703759i
$568$	7747.68i	0.572334i
$569$	−17601.2	−1.29681	−0.648403	−	0.761297i	$-0.724563\pi$
$569$	−17601.2	−1.29681	−0.648403	+	0.761297i	$0.724563\pi$
$570$	0	0
$571$	10826.5	0.793477	0.396738	−	0.917932i	$-0.370142\pi$
$571$	10826.5	0.793477	0.396738	+	0.917932i	$0.370142\pi$
$572$	− 9018.82i	− 0.659258i
$573$	− 5352.46i	− 0.390231i
$574$	−4557.99	−0.331440
$575$	0	0
$576$	−7285.59	−0.527025
$577$	− 20294.7i	− 1.46426i	−0.681163	−	0.732131i	$-0.738526\pi$
$577$	− 20294.7i	− 1.46426i	0.681163	−	0.732131i	$-0.261474\pi$
$578$	− 21130.0i	− 1.52057i
$579$	−13391.2	−0.961175
$580$	0	0
$581$	−4847.62	−0.346150
$582$	7477.75i	0.532582i
$583$	3817.01i	0.271157i
$584$	−2283.07	−0.161770
$585$	0	0
$586$	32518.3	2.29235
$587$	1338.81i	0.0941375i	0.998892	+	0.0470687i	$0.0149880\pi$
$587$	1338.81i	0.0941375i	−0.998892	+	0.0470687i	$0.985012\pi$
$588$	− 6936.88i	− 0.486517i
$589$	−4.33353	−0.000303158 0
$590$	0	0
$591$	−3498.58	−0.243506
$592$	− 8194.82i	− 0.568928i
$593$	11326.3i	0.784345i	0.919892	+	0.392173i	$0.128276\pi$
$593$	11326.3i	0.784345i	−0.919892	+	0.392173i	$0.871724\pi$
$594$	−1303.34	−0.0900282
$595$	0	0
$596$	−40344.6	−2.77278
$597$	5242.88i	0.359425i
$598$	− 23345.6i	− 1.59644i
$599$	13279.5	0.905822	0.452911	−	0.891556i	$-0.350386\pi$
$599$	13279.5	0.905822	0.452911	+	0.891556i	$0.350386\pi$
$600$	0	0
$601$	6423.07	0.435944	0.217972	−	0.975955i	$-0.430056\pi$
$601$	6423.07	0.435944	0.217972	+	0.975955i	$0.430056\pi$
$602$	− 7521.56i	− 0.509229i
$603$	− 6438.41i	− 0.434813i
$604$	31774.5	2.14054
$605$	0	0
$606$	12435.9	0.833623
$607$	4767.58i	0.318798i	0.987214	+	0.159399i	$0.0509556\pi$
$607$	4767.58i	0.318798i	−0.987214	+	0.159399i	$0.949044\pi$
$608$	− 5.58945i	0 0.000372832i
$609$	−7112.05	−0.473226
$610$	0	0
$611$	−13527.9	−0.895710
$612$	− 1002.98i	− 0.0662467i
$613$	− 26476.3i	− 1.74448i	−0.489078	−	0.872240i	$-0.662667\pi$
$613$	− 26476.3i	− 1.74448i	0.489078	−	0.872240i	$-0.337333\pi$
$614$	21879.3	1.43808
$615$	0	0
$616$	1844.65	0.120654
$617$	− 23097.5i	− 1.50708i	−0.657400	−	0.753542i	$-0.728344\pi$
$617$	− 23097.5i	− 1.50708i	0.657400	−	0.753542i	$-0.271656\pi$
$618$	− 24123.9i	− 1.57024i
$619$	−8579.27	−0.557076	−0.278538	−	0.960425i	$-0.589850\pi$
$619$	−8579.27	−0.557076	−0.278538	+	0.960425i	$0.589850\pi$
$620$	0	0
$621$	−1972.23	−0.127444
$622$	27378.9i	1.76494i
$623$	− 12896.4i	− 0.829348i
$624$	5970.53	0.383033
$625$	0	0
$626$	43099.4	2.75175
$627$	− 0.787300i	0 5.01463e-5i
$628$	− 23101.2i	− 1.46790i
$629$	2968.64	0.188184
$630$	0	0
$631$	17464.3	1.10181	0.550905	−	0.834568i	$-0.314282\pi$
$631$	17464.3	1.10181	0.550905	+	0.834568i	$0.314282\pi$
$632$	3034.37i	0.190982i
$633$	− 1245.24i	− 0.0781895i
$634$	−7667.60	−0.480314
$635$	0	0
$636$	11719.2	0.730658
$637$	14959.0i	0.930454i
$638$	9755.62i	0.605374i
$639$	−4877.61	−0.301964
$640$	0	0
$641$	13105.0	0.807513	0.403756	−	0.914867i	$-0.367704\pi$
$641$	13105.0	0.807513	0.403756	+	0.914867i	$0.367704\pi$
$642$	− 9296.49i	− 0.571500i
$643$	− 2748.22i	− 0.168553i	−0.996442	−	0.0842763i	$-0.973142\pi$
$643$	− 2748.22i	− 0.168553i	0.996442	−	0.0842763i	$-0.0268579\pi$
$644$	9646.18	0.590237
$645$	0	0
$646$	1.03640	6.31219e−5 0
$647$	− 2332.01i	− 0.141701i	−0.997487	−	0.0708506i	$-0.977429\pi$
$647$	− 2332.01i	− 0.141701i	0.997487	−	0.0708506i	$-0.0225714\pi$
$648$	1157.96i	0.0701988i
$649$	−7610.06	−0.460279
$650$	0	0
$651$	6392.20	0.384839
$652$	− 8359.40i	− 0.502116i
$653$	4241.59i	0.254190i	0.991891	+	0.127095i	$0.0405653\pi$
$653$	4241.59i	0.254190i	−0.991891	+	0.127095i	$0.959435\pi$
$654$	24103.0	1.44113
$655$	0	0
$656$	−2419.58	−0.144007
$657$	− 1437.32i	− 0.0853504i
$658$	− 9561.71i	− 0.566496i
$659$	−32050.8	−1.89457	−0.947285	−	0.320391i	$-0.896186\pi$
$659$	−32050.8	−1.89457	−0.947285	+	0.320391i	$0.896186\pi$
$660$	0	0
$661$	−27446.2	−1.61503	−0.807513	−	0.589850i	$-0.799187\pi$
$661$	−27446.2	−1.61503	−0.807513	+	0.589850i	$0.799187\pi$
$662$	31635.7i	1.85734i
$663$	2162.87i	0.126695i
$664$	5907.76	0.345279
$665$	0	0
$666$	−11844.1	−0.689113
$667$	14762.3i	0.856970i
$668$	7875.15i	0.456136i
$669$	−218.719	−0.0126400
$670$	0	0
$671$	5410.39	0.311276
$672$	8244.74i	0.473286i
$673$	− 24175.8i	− 1.38471i	−0.721558	−	0.692354i	$-0.756574\pi$
$673$	− 24175.8i	− 1.38471i	0.721558	−	0.692354i	$-0.243426\pi$
$674$	232.918	0.0133111
$675$	0	0
$676$	34979.5	1.99019
$677$	− 30852.6i	− 1.75150i	−0.482769	−	0.875748i	$-0.660369\pi$
$677$	− 30852.6i	− 1.75150i	0.482769	−	0.875748i	$-0.339631\pi$
$678$	− 8615.69i	− 0.488029i
$679$	6662.87	0.376579
$680$	0	0
$681$	−7087.06	−0.398791
$682$	− 8768.19i	− 0.492304i
$683$	15562.9i	0.871883i	0.899975	+	0.435941i	$0.143585\pi$
$683$	15562.9i	0.871883i	−0.899975	+	0.435941i	$0.856415\pi$
$684$	−2.41722	−0.000135124 0
$685$	0	0
$686$	−28230.0	−1.57117
$687$	− 13603.0i	− 0.755438i
$688$	− 3992.78i	− 0.221255i
$689$	−25272.0	−1.39737
$690$	0	0
$691$	19228.0	1.05856	0.529281	−	0.848446i	$-0.322462\pi$
$691$	19228.0	1.05856	0.529281	+	0.848446i	$0.322462\pi$
$692$	− 8274.01i	− 0.454524i
$693$	1161.31i	0.0636574i
$694$	14596.3	0.798367
$695$	0	0
$696$	8667.40	0.472036
$697$	− 876.514i	− 0.0476332i
$698$	52847.1i	2.86575i
$699$	693.228	0.0375112
$700$	0	0
$701$	15681.1	0.844891	0.422446	−	0.906388i	$-0.361172\pi$
$701$	15681.1	0.844891	0.422446	+	0.906388i	$0.361172\pi$
$702$	− 8629.28i	− 0.463948i
$703$	− 7.15457i	0 0.000383840i
$704$	8904.61	0.476712
$705$	0	0
$706$	−48248.5	−2.57203
$707$	− 11080.7i	− 0.589440i
$708$	23365.0i	1.24027i
$709$	−21226.9	−1.12439	−0.562196	−	0.827004i	$-0.690043\pi$
$709$	−21226.9	−1.12439	−0.562196	+	0.827004i	$0.690043\pi$
$710$	0	0
$711$	−1910.31	−0.100763
$712$	15716.8i	0.827262i
$713$	− 13268.1i	− 0.696908i
$714$	−1528.75	−0.0801290
$715$	0	0
$716$	−30252.5	−1.57904
$717$	− 13389.5i	− 0.697408i
$718$	10468.2i	0.544107i
$719$	17928.4	0.929928	0.464964	−	0.885330i	$-0.346067\pi$
$719$	17928.4	0.929928	0.464964	+	0.885330i	$0.346067\pi$
$720$	0	0
$721$	−21495.1	−1.11029
$722$	30099.7i	1.55152i
$723$	− 6292.53i	− 0.323682i
$724$	42402.6	2.17663
$725$	0	0
$726$	1592.97	0.0814336
$727$	− 11876.7i	− 0.605890i	−0.953008	−	0.302945i	$-0.902030\pi$
$727$	− 11876.7i	− 0.605890i	0.953008	−	0.302945i	$-0.0979699\pi$
$728$	12213.2i	0.621774i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	1446.42	0.0731842
$732$	− 16611.4i	− 0.838762i
$733$	25344.9i	1.27713i	0.769569	+	0.638563i	$0.220471\pi$
$733$	25344.9i	1.27713i	−0.769569	+	0.638563i	$0.779529\pi$
$734$	14164.7	0.712299
$735$	0	0
$736$	17113.4	0.857077
$737$	7869.17i	0.393303i
$738$	3497.05i	0.174429i
$739$	12511.6	0.622795	0.311398	−	0.950280i	$-0.399203\pi$
$739$	12511.6	0.622795	0.311398	+	0.950280i	$0.399203\pi$
$740$	0	0
$741$	5.21263	0.000258422 0
$742$	− 17862.6i	− 0.883771i
$743$	32707.2i	1.61495i	0.589899	+	0.807477i	$0.299168\pi$
$743$	32707.2i	1.61495i	−0.589899	+	0.807477i	$0.700832\pi$
$744$	−7790.12	−0.383871
$745$	0	0
$746$	26102.8	1.28109
$747$	3719.27i	0.182170i
$748$	1225.86i	0.0599224i
$749$	−8283.41	−0.404098
$750$	0	0
$751$	20409.8	0.991694	0.495847	−	0.868410i	$-0.334858\pi$
$751$	20409.8	0.991694	0.495847	+	0.868410i	$0.334858\pi$
$752$	− 5075.78i	− 0.246137i
$753$	10201.3i	0.493698i
$754$	−64590.9	−3.11971
$755$	0	0
$756$	3565.54	0.171531
$757$	5746.29i	0.275895i	0.990440	+	0.137948i	$0.0440505\pi$
$757$	5746.29i	0.275895i	−0.990440	+	0.137948i	$0.955949\pi$
$758$	45341.3i	2.17265i
$759$	2410.50	0.115278
$760$	0	0
$761$	−2595.93	−0.123656	−0.0618282	−	0.998087i	$-0.519693\pi$
$761$	−2595.93	−0.123656	−0.0618282	+	0.998087i	$0.519693\pi$
$762$	10721.6i	0.509715i
$763$	− 21476.4i	− 1.01900i
$764$	20085.4	0.951130
$765$	0	0
$766$	29344.5	1.38415
$767$	− 50385.4i	− 2.37198i
$768$	− 2664.66i	− 0.125199i
$769$	−12449.7	−0.583807	−0.291903	−	0.956448i	$-0.594289\pi$
$769$	−12449.7	−0.583807	−0.291903	+	0.956448i	$0.594289\pi$
$770$	0	0
$771$	−14982.3	−0.699838
$772$	− 50251.3i	− 2.34272i
$773$	− 21032.1i	− 0.978621i	−0.872110	−	0.489310i	$-0.837249\pi$
$773$	− 21032.1i	− 0.978621i	0.872110	−	0.489310i	$-0.162751\pi$
$774$	−5770.81	−0.267994
$775$	0	0
$776$	−8119.98	−0.375632
$777$	10553.4i	0.487260i
$778$	26767.1i	1.23348i
$779$	−2.11244	−9.71579e−5 0
$780$	0	0
$781$	5961.52	0.273137
$782$	3173.19i	0.145106i
$783$	5456.63i	0.249047i
$784$	−5612.77	−0.255684
$785$	0	0
$786$	30555.9	1.38663
$787$	31784.6i	1.43964i	0.694160	+	0.719821i	$0.255776\pi$
$787$	31784.6i	1.43964i	−0.694160	+	0.719821i	$0.744224\pi$
$788$	− 13128.6i	− 0.593511i
$789$	20609.4	0.929931
$790$	0	0
$791$	−7676.80	−0.345077
$792$	− 1415.28i	− 0.0634972i
$793$	35821.6i	1.60411i
$794$	11586.9	0.517888
$795$	0	0
$796$	−19674.2	−0.876046
$797$	30740.5i	1.36623i	0.730311	+	0.683115i	$0.239375\pi$
$797$	30740.5i	1.36623i	−0.730311	+	0.683115i	$0.760625\pi$
$798$	3.68436i	0 0.000163440i
$799$	1838.74	0.0814143
$800$	0	0
$801$	−9894.60	−0.436465
$802$	− 38563.0i	− 1.69789i
$803$	1756.72i	0.0772023i
$804$	24160.5	1.05979
$805$	0	0
$806$	58053.2	2.53702
$807$	6058.79i	0.264287i
$808$	13504.0i	0.587958i
$809$	−821.592	−0.0357054	−0.0178527	−	0.999841i	$-0.505683\pi$
$809$	−821.592	−0.0357054	−0.0178527	+	0.999841i	$0.505683\pi$
$810$	0	0
$811$	35151.8	1.52201	0.761003	−	0.648749i	$-0.224707\pi$
$811$	35151.8	1.52201	0.761003	+	0.648749i	$0.224707\pi$
$812$	− 26688.3i	− 1.15342i
$813$	15574.8i	0.671873i
$814$	14476.1	0.623326
$815$	0	0
$816$	−811.529	−0.0348152
$817$	− 3.48593i	0 0.000149275i
$818$	− 25760.8i	− 1.10111i
$819$	−7688.91	−0.328049
$820$	0	0
$821$	5435.02	0.231040	0.115520	−	0.993305i	$-0.463147\pi$
$821$	5435.02	0.231040	0.115520	+	0.993305i	$0.463147\pi$
$822$	26516.4i	1.12514i
$823$	− 36291.6i	− 1.53711i	−0.639781	−	0.768557i	$-0.720975\pi$
$823$	− 36291.6i	− 1.53711i	0.639781	−	0.768557i	$-0.279025\pi$
$824$	26195.9	1.10749
$825$	0	0
$826$	35613.2	1.50017
$827$	− 18370.7i	− 0.772443i	−0.922406	−	0.386222i	$-0.873780\pi$
$827$	− 18370.7i	− 0.772443i	0.922406	−	0.386222i	$-0.126220\pi$
$828$	− 7400.90i	− 0.310627i
$829$	−33861.4	−1.41864	−0.709322	−	0.704885i	$-0.750999\pi$
$829$	−33861.4	−1.41864	−0.709322	+	0.704885i	$0.750999\pi$
$830$	0	0
$831$	1368.40	0.0571231
$832$	58956.5i	2.45667i
$833$	− 2033.27i	− 0.0845723i
$834$	−24125.1	−1.00166
$835$	0	0
$836$	2.95438	0.000122224 0
$837$	− 4904.33i	− 0.202531i
$838$	62353.3i	2.57036i
$839$	22131.3	0.910676	0.455338	−	0.890319i	$-0.349518\pi$
$839$	22131.3	0.910676	0.455338	+	0.890319i	$0.349518\pi$
$840$	0	0
$841$	16454.3	0.674660
$842$	53985.0i	2.20956i
$843$	9014.75i	0.368309i
$844$	4672.84	0.190576
$845$	0	0
$846$	−7336.09	−0.298132
$847$	− 1419.38i	− 0.0575803i
$848$	− 9482.28i	− 0.383989i
$849$	−1227.47	−0.0496191
$850$	0	0
$851$	21905.4	0.882383
$852$	− 18303.5i	− 0.735994i
$853$	34402.7i	1.38092i	0.723370	+	0.690460i	$0.242592\pi$
$853$	34402.7i	1.38092i	−0.723370	+	0.690460i	$0.757408\pi$
$854$	−25319.3	−1.01453
$855$	0	0
$856$	10094.9	0.403081
$857$	− 26140.0i	− 1.04192i	−0.853581	−	0.520960i	$-0.825574\pi$
$857$	− 26140.0i	− 1.04192i	0.853581	−	0.520960i	$-0.174426\pi$
$858$	10546.9i	0.419656i
$859$	−38993.9	−1.54884	−0.774421	−	0.632671i	$-0.781958\pi$
$859$	−38993.9	−1.54884	−0.774421	+	0.632671i	$0.781958\pi$
$860$	0	0
$861$	3115.97	0.123335
$862$	24750.7i	0.977970i
$863$	43742.0i	1.72537i	0.505741	+	0.862685i	$0.331219\pi$
$863$	43742.0i	1.72537i	−0.505741	+	0.862685i	$0.668781\pi$
$864$	6325.67	0.249078
$865$	0	0
$866$	−44422.8	−1.74313
$867$	14445.0i	0.565834i
$868$	23987.1i	0.937988i
$869$	2334.83	0.0911433
$870$	0	0
$871$	−52100.9	−2.02683
$872$	26173.1i	1.01644i
$873$	− 5111.99i	− 0.198184i
$874$	7.64754	0.000295975 0
$875$	0	0
$876$	5393.62	0.208029
$877$	− 3327.46i	− 0.128119i	−0.997946	−	0.0640596i	$-0.979595\pi$
$877$	− 3327.46i	− 0.128119i	0.997946	−	0.0640596i	$-0.0204048\pi$
$878$	− 47188.7i	− 1.81383i
$879$	−22230.4	−0.853030
$880$	0	0
$881$	−2068.21	−0.0790915	−0.0395458	−	0.999218i	$-0.512591\pi$
$881$	−2068.21	−0.0790915	−0.0395458	+	0.999218i	$0.512591\pi$
$882$	8112.21i	0.309697i
$883$	24764.3i	0.943812i	0.881649	+	0.471906i	$0.156434\pi$
$883$	24764.3i	0.943812i	−0.881649	+	0.471906i	$0.843566\pi$
$884$	−8116.29	−0.308801
$885$	0	0
$886$	45404.7	1.72167
$887$	− 34771.6i	− 1.31625i	−0.752908	−	0.658125i	$-0.771350\pi$
$887$	− 34771.6i	− 1.31625i	0.752908	−	0.658125i	$-0.228650\pi$
$888$	− 12861.3i	− 0.486034i
$889$	9553.24	0.360411
$890$	0	0
$891$	891.000	0.0335013
$892$	− 820.755i	− 0.0308082i
$893$	− 4.43146i	0 0.000166062i
$894$	47180.2	1.76504
$895$	0	0
$896$	−19685.3	−0.733975
$897$	15959.7i	0.594067i
$898$	41993.1i	1.56050i
$899$	−36709.3	−1.36187
$900$	0	0
$901$	3435.03	0.127012
$902$	− 4274.18i	− 0.157777i
$903$	5141.94i	0.189494i
$904$	9355.66	0.344209
$905$	0	0
$906$	−37158.1	−1.36258
$907$	− 12892.0i	− 0.471965i	−0.971757	−	0.235983i	$-0.924169\pi$
$907$	− 12892.0i	− 0.471965i	0.971757	−	0.235983i	$-0.0758309\pi$
$908$	− 26594.6i	− 0.971995i
$909$	−8501.55	−0.310208
$910$	0	0
$911$	−20530.9	−0.746673	−0.373337	−	0.927696i	$-0.621786\pi$
$911$	−20530.9	−0.746673	−0.373337	+	0.927696i	$0.621786\pi$
$912$	1.95582i	0 7.10130e-5i
$913$	− 4545.78i	− 0.164779i
$914$	32677.1	1.18256
$915$	0	0
$916$	51045.9	1.84127
$917$	− 27226.1i	− 0.980462i
$918$	1172.91i	0.0421699i
$919$	19937.9	0.715658	0.357829	−	0.933787i	$-0.383517\pi$
$919$	19937.9	0.715658	0.357829	+	0.933787i	$0.383517\pi$
$920$	0	0
$921$	−14957.3	−0.535136
$922$	− 47986.1i	− 1.71403i
$923$	39470.6i	1.40757i
$924$	−4357.88	−0.155156
$925$	0	0
$926$	43397.1	1.54008
$927$	16491.8i	0.584317i
$928$	− 47348.1i	− 1.67487i
$929$	55075.7	1.94508	0.972538	−	0.232746i	$-0.0747711\pi$
$929$	55075.7	1.94508	0.972538	+	0.232746i	$0.0747711\pi$
$930$	0	0
$931$	−4.90028	−0.000172503 0
$932$	2601.38i	0.0914280i
$933$	− 18717.0i	− 0.656769i
$934$	−440.571	−0.0154346
$935$	0	0
$936$	9370.41	0.327224
$937$	− 29820.6i	− 1.03970i	−0.854259	−	0.519848i	$-0.825989\pi$
$937$	− 29820.6i	− 1.03970i	0.854259	−	0.519848i	$-0.174011\pi$
$938$	− 36825.7i	− 1.28188i
$939$	−29463.9	−1.02398
$940$	0	0
$941$	32262.4	1.11767	0.558833	−	0.829280i	$-0.311249\pi$
$941$	32262.4	1.11767	0.558833	+	0.829280i	$0.311249\pi$
$942$	27015.3i	0.934401i
$943$	− 6467.73i	− 0.223349i
$944$	18905.1	0.651808
$945$	0	0
$946$	7053.22	0.242410
$947$	− 20302.5i	− 0.696666i	−0.937371	−	0.348333i	$-0.886748\pi$
$947$	− 20302.5i	− 0.696666i	0.937371	−	0.348333i	$-0.113252\pi$
$948$	− 7168.55i	− 0.245594i
$949$	−11631.1	−0.397851
$950$	0	0
$951$	5241.78	0.178734
$952$	− 1660.05i	− 0.0565153i
$953$	− 7243.13i	− 0.246199i	−0.992394	−	0.123100i	$-0.960717\pi$
$953$	− 7243.13i	− 0.246199i	0.992394	−	0.123100i	$-0.0392835\pi$
$954$	−13704.9	−0.465106
$955$	0	0
$956$	50245.0	1.69983
$957$	− 6669.21i	− 0.225272i
$958$	− 19369.6i	− 0.653238i
$959$	23626.8	0.795567
$960$	0	0
$961$	3202.72	0.107506
$962$	95844.7i	3.21222i
$963$	6355.33i	0.212666i
$964$	23613.1	0.788927
$965$	0	0
$966$	−11280.5	−0.375720
$967$	− 35402.4i	− 1.17732i	−0.808382	−	0.588658i	$-0.799656\pi$
$967$	− 35402.4i	− 1.17732i	0.808382	−	0.588658i	$-0.200344\pi$
$968$	1729.79i	0.0574354i
$969$	−0.708513	−2.34889e−5 0
$970$	0	0
$971$	−4236.86	−0.140028	−0.0700140	−	0.997546i	$-0.522304\pi$
$971$	−4236.86	−0.140028	−0.0700140	+	0.997546i	$0.522304\pi$
$972$	− 2735.61i	− 0.0902724i
$973$	21496.1i	0.708256i
$974$	−73704.9	−2.42470
$975$	0	0
$976$	−13440.6	−0.440802
$977$	31833.5i	1.04242i	0.853429	+	0.521210i	$0.174519\pi$
$977$	31833.5i	1.04242i	−0.853429	+	0.521210i	$0.825481\pi$
$978$	9775.75i	0.319626i
$979$	12093.4	0.394797
$980$	0	0
$981$	−16477.5	−0.536274
$982$	− 83394.1i	− 2.70999i
$983$	36137.8i	1.17255i	0.810113	+	0.586274i	$0.199406\pi$
$983$	36137.8i	1.17255i	−0.810113	+	0.586274i	$0.800594\pi$
$984$	−3797.40	−0.123025
$985$	0	0
$986$	8779.36	0.283562
$987$	6536.65i	0.210804i
$988$	19.5607i	0 0.000629866i
$989$	10673.0	0.343157
$990$	0	0
$991$	13795.5	0.442207	0.221103	−	0.975250i	$-0.429034\pi$
$991$	13795.5	0.442207	0.221103	+	0.975250i	$0.429034\pi$
$992$	42555.8i	1.36204i
$993$	− 21627.0i	− 0.691151i
$994$	−27898.4	−0.890225
$995$	0	0
$996$	−13956.8	−0.444013
$997$	52392.7i	1.66429i	0.554560	+	0.832144i	$0.312887\pi$
$997$	52392.7i	1.66429i	−0.554560	+	0.832144i	$0.687113\pi$
$998$	− 87633.2i	− 2.77954i
$999$	8096.94	0.256432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.m.199.2		6
5.2	odd	4		825.4.a.p.1.3		3
5.3	odd	4		165.4.a.g.1.1	✓	3
5.4	even	2	inner	825.4.c.m.199.5		6
15.2	even	4		2475.4.a.z.1.1		3
15.8	even	4		495.4.a.i.1.3		3
55.43	even	4		1815.4.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.g.1.1	✓	3	5.3	odd	4
495.4.a.i.1.3		3	15.8	even	4
825.4.a.p.1.3		3	5.2	odd	4
825.4.c.m.199.2		6	1.1	even	1	trivial
825.4.c.m.199.5		6	5.4	even	2	inner
1815.4.a.q.1.3		3	55.43	even	4
2475.4.a.z.1.1		3	15.2	even	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.38835i q^{2} +3.00000i q^{3} -11.2577 q^{4} +13.1651 q^{6} -11.7304i q^{7} +14.2958i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-4.38835i q^{2} +3.00000i q^{3} -11.2577 q^{4} +13.1651 q^{6} -11.7304i q^{7} +14.2958i q^{8} -9.00000 q^{9} +11.0000 q^{11} -33.7730i q^{12} +72.8298i q^{13} -51.4772 q^{14} -27.3264 q^{16} -9.89921i q^{17} +39.4952i q^{18} -0.0238576 q^{19} +35.1912 q^{21} -48.2719i q^{22} -73.0456i q^{23} -42.8873 q^{24} +319.603 q^{26} -27.0000i q^{27} +132.057i q^{28} -202.097 q^{29} +181.642 q^{31} +234.284i q^{32} +33.0000i q^{33} -43.4413 q^{34} +101.319 q^{36} +299.887i q^{37} +0.104695i q^{38} -218.489 q^{39} +88.5438 q^{41} -154.432i q^{42} +146.114i q^{43} -123.834 q^{44} -320.550 q^{46} +185.746i q^{47} -81.9792i q^{48} +205.397 q^{49} +29.6976 q^{51} -819.893i q^{52} +347.001i q^{53} -118.486 q^{54} +167.695 q^{56} -0.0715727i q^{57} +886.874i q^{58} -691.824 q^{59} +491.854 q^{61} -797.108i q^{62} +105.574i q^{63} +809.510 q^{64} +144.816 q^{66} +715.379i q^{67} +111.442i q^{68} +219.137 q^{69} +541.957 q^{71} -128.662i q^{72} +159.702i q^{73} +1316.01 q^{74} +0.268580 q^{76} -129.035i q^{77} +958.809i q^{78} +212.257 q^{79} +81.0000 q^{81} -388.562i q^{82} -413.252i q^{83} -396.171 q^{84} +641.202 q^{86} -606.292i q^{87} +157.253i q^{88} +1099.40 q^{89} +854.323 q^{91} +822.322i q^{92} +544.925i q^{93} +815.121 q^{94} -702.852 q^{96} +567.999i q^{97} -901.357i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9	\( 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9} + 66 q^{11} - 288 q^{14} + 50 q^{16} - 232 q^{19} - 36 q^{21} - 18 q^{24} + 604 q^{26} - 476 q^{29} + 184 q^{31} - 708 q^{34} + 306 q^{36} - 120 q^{39} - 92 q^{41} - 374 q^{44} - 480 q^{46} + 914 q^{49} - 192 q^{51} + 54 q^{54} + 1376 q^{56} - 2472 q^{59} + 684 q^{61} + 3838 q^{64} - 66 q^{66} + 1440 q^{69} + 3632 q^{71} + 3748 q^{74} + 792 q^{76} + 192 q^{79} + 486 q^{81} + 960 q^{84} + 376 q^{86} - 1676 q^{89} + 664 q^{91} + 6224 q^{94} - 1182 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9 + 66 * q^11 - 288 * q^14 + 50 * q^16 - 232 * q^19 - 36 * q^21 - 18 * q^24 + 604 * q^26 - 476 * q^29 + 184 * q^31 - 708 * q^34 + 306 * q^36 - 120 * q^39 - 92 * q^41 - 374 * q^44 - 480 * q^46 + 914 * q^49 - 192 * q^51 + 54 * q^54 + 1376 * q^56 - 2472 * q^59 + 684 * q^61 + 3838 * q^64 - 66 * q^66 + 1440 * q^69 + 3632 * q^71 + 3748 * q^74 + 792 * q^76 + 192 * q^79 + 486 * q^81 + 960 * q^84 + 376 * q^86 - 1676 * q^89 + 664 * q^91 + 6224 * q^94 - 1182 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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