LMFDB - Embedded newform 100.4.e.f.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, degree $2$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	100.7
Dual form			100.4.e.f.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38148 + 1.52596i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(3.34287 - 7.26809i) q^{4} +(0.952213 + 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(3.12986 + 22.4099i) q^{8} -26.8812i q^{9} +O(q^{10})$	\(q+(-2.38148 + 1.52596i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(3.34287 - 7.26809i) q^{4} +(0.952213 + 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(3.12986 + 22.4099i) q^{8} -26.8812i q^{9} +42.2652i q^{11} +(-2.58581 + 0.956545i) q^{12} +(-41.7119 + 41.7119i) q^{13} +(8.15866 - 37.2635i) q^{14} +(-41.6504 - 48.5926i) q^{16} +(-34.1474 - 34.1474i) q^{17} +(41.0198 + 64.0170i) q^{18} -130.653 q^{19} +4.64797 q^{21} +(-64.4951 - 100.654i) q^{22} +(-107.427 - 107.427i) q^{23} +(4.69839 - 6.22384i) q^{24} +(35.6852 - 162.987i) q^{26} +(-13.1304 + 13.1304i) q^{27} +(37.4331 + 101.192i) q^{28} +80.4104i q^{29} +273.244i q^{31} +(173.340 + 52.1653i) q^{32} +(10.2997 - 10.2997i) q^{33} +(133.429 + 29.2136i) q^{34} +(-195.375 - 89.8605i) q^{36} +(134.502 + 134.502i) q^{37} +(311.147 - 199.371i) q^{38} +20.3297 q^{39} +155.583 q^{41} +(-11.0690 + 7.09263i) q^{42} +(-223.543 - 223.543i) q^{43} +(307.187 + 141.287i) q^{44} +(419.765 + 91.9055i) q^{46} +(-72.1171 + 72.1171i) q^{47} +(-1.69177 + 21.9915i) q^{48} +161.108i q^{49} +16.6429i q^{51} +(163.728 + 442.604i) q^{52} +(305.746 - 305.746i) q^{53} +(11.2333 - 51.3064i) q^{54} +(-243.561 - 183.865i) q^{56} +(31.8391 + 31.8391i) q^{57} +(-122.703 - 191.496i) q^{58} +177.142 q^{59} -41.4688 q^{61} +(-416.960 - 650.725i) q^{62} +(256.354 + 256.354i) q^{63} +(-492.408 + 140.280i) q^{64} +(-8.81153 + 40.2454i) q^{66} +(261.744 - 261.744i) q^{67} +(-362.337 + 134.036i) q^{68} +52.3583i q^{69} -741.456i q^{71} +(602.406 - 84.1346i) q^{72} +(-516.828 + 516.828i) q^{73} +(-525.557 - 115.068i) q^{74} +(-436.756 + 949.597i) q^{76} +(-403.064 - 403.064i) q^{77} +(-48.4148 + 31.0224i) q^{78} -222.727 q^{79} -719.394 q^{81} +(-370.518 + 237.414i) q^{82} +(824.724 + 824.724i) q^{83} +(15.5376 - 33.7819i) q^{84} +(873.480 + 191.244i) q^{86} +(19.5954 - 19.5954i) q^{87} +(-947.158 + 132.284i) q^{88} -1447.03i q^{89} -795.576i q^{91} +(-1139.91 + 421.675i) q^{92} +(66.5874 - 66.5874i) q^{93} +(61.6973 - 281.793i) q^{94} +(-29.5293 - 54.9539i) q^{96} +(-196.252 - 196.252i) q^{97} +(-245.845 - 383.676i) q^{98} +1136.14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.38148	+	1.52596i	−0.841980	+	0.539509i
$2$	−2.38148	+	1.52596i	−0.841980	+	0.539509i
$3$	−0.243692	−	0.243692i	−0.0468986	−	0.0468986i	0.683269	−	0.730167i	$-0.260558\pi$
$3$	−0.243692	−	0.243692i	−0.0468986	−	0.0468986i	−0.730167	+	0.683269i	$0.760558\pi$
$4$	3.34287	−	7.26809i	0.417859	−	0.908512i
$5$		0			0
$5$		0			0
$6$	0.952213	+	0.208482i	0.0647899	+	0.0141854i
$7$	−9.53656	+	9.53656i	−0.514926	+	0.514926i	−0.916032	−	0.401106i	$-0.868626\pi$
$7$	−9.53656	+	9.53656i	−0.514926	+	0.514926i	0.401106	+	0.916032i	$0.368626\pi$
$8$	3.12986	+	22.4099i	0.138322	+	0.990387i
$9$		−	26.8812i		−	0.995601i
$10$		0			0
$11$			42.2652i			1.15849i	0.815152	+	0.579247i	$0.196653\pi$
$11$			42.2652i			1.15849i	−0.815152	+	0.579247i	$0.803347\pi$
$12$	−2.58581	+	0.956545i	−0.0622049	+	0.0230109i
$13$	−41.7119	+	41.7119i	−0.889908	+	0.889908i	−0.994514	−	0.104606i	$-0.966642\pi$
$13$	−41.7119	+	41.7119i	−0.889908	+	0.889908i	0.104606	+	0.994514i	$0.466642\pi$
$14$	8.15866	−	37.2635i	0.155750	−	0.711364i
$15$		0			0
$16$	−41.6504	−	48.5926i	−0.650787	−	0.759260i
$17$	−34.1474	−	34.1474i	−0.487174	−	0.487174i	0.420239	−	0.907413i	$-0.361946\pi$
$17$	−34.1474	−	34.1474i	−0.487174	−	0.487174i	−0.907413	+	0.420239i	$0.861946\pi$
$18$	41.0198	+	64.0170i	0.537136	+	0.838276i
$19$	−130.653			−1.57757			−0.788784	−	0.614670i	$-0.789289\pi$
$19$	−130.653			−1.57757			−0.788784	+	0.614670i	$0.789289\pi$
$20$		0			0
$21$	4.64797			0.0482986
$22$	−64.4951	−	100.654i	−0.625018	−	0.975428i
$23$	−107.427	−	107.427i	−0.973918	−	0.973918i	0.0257506	−	0.999668i	$-0.491802\pi$
$23$	−107.427	−	107.427i	−0.973918	−	0.973918i	−0.999668	+	0.0257506i	$0.991802\pi$
$24$	4.69839	−	6.22384i	0.0399607	−	0.0529348i
$25$		0			0
$26$	35.6852	−	162.987i	0.269171	−	1.22940i
$27$	−13.1304	+	13.1304i	−0.0935908	+	0.0935908i
$28$	37.4331	+	101.192i	0.252650	+	0.682982i
$29$			80.4104i			0.514891i	0.966293	+	0.257446i	$0.0828808\pi$
$29$			80.4104i			0.514891i	−0.966293	+	0.257446i	$0.917119\pi$
$30$		0			0
$31$			273.244i			1.58310i	0.611105	+	0.791550i	$0.290725\pi$
$31$			273.244i			1.58310i	−0.611105	+	0.791550i	$0.709275\pi$
$32$	173.340	+	52.1653i	0.957578	+	0.288175i
$33$	10.2997	−	10.2997i	0.0543317	−	0.0543317i
$34$	133.429	+	29.2136i	0.673026	+	0.147356i
$35$		0			0
$36$	−195.375	−	89.8605i	−0.904515	−	0.416021i
$37$	134.502	+	134.502i	0.597620	+	0.597620i	0.939679	−	0.342059i	$-0.111124\pi$
$37$	134.502	+	134.502i	0.597620	+	0.597620i	−0.342059	+	0.939679i	$0.611124\pi$
$38$	311.147	−	199.371i	1.32828	−	0.851113i
$39$	20.3297			0.0834708
$40$		0			0
$41$	155.583			0.592635			0.296317	−	0.955090i	$-0.404241\pi$
$41$	155.583			0.592635			0.296317	+	0.955090i	$0.404241\pi$
$42$	−11.0690	+	7.09263i	−0.0406664	+	0.0260575i
$43$	−223.543	−	223.543i	−0.792789	−	0.792789i	0.189157	−	0.981947i	$-0.439424\pi$
$43$	−223.543	−	223.543i	−0.792789	−	0.792789i	−0.981947	+	0.189157i	$0.939424\pi$
$44$	307.187	+	141.287i	1.05250	+	0.484087i
$45$		0			0
$46$	419.765	+	91.9055i	1.34546	+	0.294581i
$47$	−72.1171	+	72.1171i	−0.223816	+	0.223816i	−0.810103	−	0.586287i	$-0.800589\pi$
$47$	−72.1171	+	72.1171i	−0.223816	+	0.223816i	0.586287	+	0.810103i	$0.300589\pi$
$48$	−1.69177	+	21.9915i	−0.00508721	+	0.0661292i
$49$			161.108i			0.469703i
$50$		0			0
$51$			16.6429i			0.0456955i
$52$	163.728	+	442.604i	0.436636	+	1.18035i
$53$	305.746	−	305.746i	0.792403	−	0.792403i	−0.189481	−	0.981884i	$-0.560681\pi$
$53$	305.746	−	305.746i	0.792403	−	0.792403i	0.981884	+	0.189481i	$0.0606806\pi$
$54$	11.2333	−	51.3064i	0.0283084	−	0.129295i
$55$		0			0
$56$	−243.561	−	183.865i	−0.581201	−	0.438750i
$57$	31.8391	+	31.8391i	0.0739857	+	0.0739857i
$58$	−122.703	−	191.496i	−0.277789	−	0.433528i
$59$	177.142			0.390880			0.195440	−	0.980716i	$-0.437387\pi$
$59$	177.142			0.390880			0.195440	+	0.980716i	$0.437387\pi$
$60$		0			0
$61$	−41.4688			−0.0870416			−0.0435208	−	0.999053i	$-0.513857\pi$
$61$	−41.4688			−0.0870416			−0.0435208	+	0.999053i	$0.513857\pi$
$62$	−416.960	−	650.725i	−0.854097	−	1.33294i
$63$	256.354	+	256.354i	0.512660	+	0.512660i
$64$	−492.408	+	140.280i	−0.961734	+	0.273984i
$65$		0			0
$66$	−8.81153	+	40.2454i	−0.0164337	+	0.0750586i
$67$	261.744	−	261.744i	0.477271	−	0.477271i	−0.426987	−	0.904258i	$-0.640425\pi$
$67$	261.744	−	261.744i	0.477271	−	0.477271i	0.904258	+	0.426987i	$0.140425\pi$
$68$	−362.337	+	134.036i	−0.646174	+	0.239033i
$69$			52.3583i			0.0913507i
$70$		0			0
$71$		−	741.456i		−	1.23936i	−0.784854	−	0.619680i	$-0.787262\pi$
$71$		−	741.456i		−	1.23936i	0.784854	−	0.619680i	$-0.212738\pi$
$72$	602.406	−	84.1346i	0.986031	−	0.137713i
$73$	−516.828	+	516.828i	−0.828631	+	0.828631i	−0.987327	−	0.158696i	$-0.949271\pi$
$73$	−516.828	+	516.828i	−0.828631	+	0.828631i	0.158696	+	0.987327i	$0.449271\pi$
$74$	−525.557	−	115.068i	−0.825605	−	0.180762i
$75$		0			0
$76$	−436.756	+	949.597i	−0.659202	+	1.43324i
$77$	−403.064	−	403.064i	−0.596538	−	0.596538i
$78$	−48.4148	+	31.0224i	−0.0702807	+	0.0450333i
$79$	−222.727			−0.317200			−0.158600	−	0.987343i	$-0.550698\pi$
$79$	−222.727			−0.317200			−0.158600	+	0.987343i	$0.550698\pi$
$80$		0			0
$81$	−719.394			−0.986822
$82$	−370.518	+	237.414i	−0.498986	+	0.319732i
$83$	824.724	+	824.724i	1.09066	+	1.09066i	0.995457	+	0.0952072i	$0.0303514\pi$
$83$	824.724	+	824.724i	1.09066	+	1.09066i	0.0952072	+	0.995457i	$0.469649\pi$
$84$	15.5376	−	33.7819i	0.0201820	−	0.0438798i
$85$		0			0
$86$	873.480	+	191.244i	1.09523	+	0.239795i
$87$	19.5954	−	19.5954i	0.0241477	−	0.0241477i
$88$	−947.158	+	132.284i	−1.14736	+	0.160245i
$89$		−	1447.03i		−	1.72342i	−0.507400	−	0.861711i	$-0.669393\pi$
$89$		−	1447.03i		−	1.72342i	0.507400	−	0.861711i	$-0.330607\pi$
$90$		0			0
$91$		−	795.576i		−	0.916473i
$92$	−1139.91	+	421.675i	−1.29178	+	0.477855i
$93$	66.5874	−	66.5874i	0.0742451	−	0.0742451i
$94$	61.6973	−	281.793i	0.0676977	−	0.309200i
$95$		0			0
$96$	−29.5293	−	54.9539i	−0.0313940	−	0.0584240i
$97$	−196.252	−	196.252i	−0.205426	−	0.205426i	0.596894	−	0.802320i	$-0.296401\pi$
$97$	−196.252	−	196.252i	−0.205426	−	0.205426i	−0.802320	+	0.596894i	$0.796401\pi$
$98$	−245.845	−	383.676i	−0.253409	−	0.395481i
$99$	1136.14			1.15340
$100$		0			0
$101$	594.739			0.585928			0.292964	−	0.956123i	$-0.405358\pi$
$101$	594.739			0.585928			0.292964	+	0.956123i	$0.405358\pi$
$102$	−25.3965	−	39.6347i	−0.0246532	−	0.0384747i
$103$	499.830	+	499.830i	0.478153	+	0.478153i	0.904540	−	0.426388i	$-0.140214\pi$
$103$	499.830	+	499.830i	0.478153	+	0.478153i	−0.426388	+	0.904540i	$0.640214\pi$
$104$	−1065.31	−	804.207i	−1.00445	−	0.758260i
$105$		0			0
$106$	−261.570	+	1194.68i	−0.239678	+	1.09470i
$107$	−716.517	+	716.517i	−0.647367	+	0.647367i	−0.952356	−	0.304989i	$-0.901347\pi$
$107$	−716.517	+	716.517i	−0.647367	+	0.647367i	0.304989	+	0.952356i	$0.401347\pi$
$108$	51.5398	+	139.327i	0.0459206	+	0.124136i
$109$			680.181i			0.597702i	0.954300	+	0.298851i	$0.0966034\pi$
$109$			680.181i			0.597702i	−0.954300	+	0.298851i	$0.903397\pi$
$110$		0			0
$111$		−	65.5540i		−	0.0560550i
$112$	860.608	+	66.2051i	0.726070	+	0.0558553i
$113$	−30.3535	+	30.3535i	−0.0252692	+	0.0252692i	−0.719629	−	0.694359i	$-0.755688\pi$
$113$	−30.3535	+	30.3535i	−0.0252692	+	0.0252692i	0.694359	+	0.719629i	$0.255688\pi$
$114$	−124.409	−	27.2388i	−0.102210	−	0.0223785i
$115$		0			0
$116$	584.431	+	268.802i	0.467785	+	0.215152i
$117$	1121.27	+	1121.27i	0.885993	+	0.885993i
$118$	−421.859	+	270.312i	−0.329113	+	0.210883i
$119$	651.297			0.501717
$120$		0			0
$121$	−455.344			−0.342107
$122$	98.7571	−	63.2799i	0.0732872	−	0.0469598i
$123$	−37.9144	−	37.9144i	−0.0277937	−	0.0277937i
$124$	1985.96	+	913.420i	1.43826	+	0.661513i
$125$		0			0
$126$	−1001.69	−	219.315i	−0.708235	−	0.155064i
$127$	1252.53	−	1252.53i	0.875147	−	0.875147i	−0.117880	−	0.993028i	$-0.537610\pi$
$127$	1252.53	−	1252.53i	0.875147	−	0.875147i	0.993028	+	0.117880i	$0.0376100\pi$
$128$	958.596	−	1085.47i	0.661943	−	0.749554i
$129$			108.951i			0.0743614i
$130$		0			0
$131$			262.746i			0.175238i	0.996154	+	0.0876192i	$0.0279259\pi$
$131$			262.746i			0.175238i	−0.996154	+	0.0876192i	$0.972074\pi$
$132$	−40.4285	−	109.290i	−0.0266580	−	0.0720640i
$133$	1245.98	−	1245.98i	0.812331	−	0.812331i
$134$	−223.926	+	1022.75i	−0.144360	+	0.659345i
$135$		0			0
$136$	658.363	−	872.117i	0.415104	−	0.549878i
$137$	−1252.60	−	1252.60i	−0.781146	−	0.781146i	0.198878	−	0.980024i	$-0.436270\pi$
$137$	−1252.60	−	1252.60i	−0.781146	−	0.781146i	−0.980024	+	0.198878i	$0.936270\pi$
$138$	−79.8968	−	124.690i	−0.0492846	−	0.0769154i
$139$	−2028.30			−1.23768			−0.618842	−	0.785516i	$-0.712398\pi$
$139$	−2028.30			−1.23768			−0.618842	+	0.785516i	$0.712398\pi$
$140$		0			0
$141$	35.1487			0.0209933
$142$	1131.43	+	1765.76i	0.668647	+	1.04352i
$143$	−1762.96	−	1762.96i	−1.03095	−	1.03095i
$144$	−1306.23	+	1119.61i	−0.755920	+	0.647925i
$145$		0			0
$146$	442.154	−	2019.47i	0.250636	−	1.14475i
$147$	39.2608	−	39.2608i	0.0220284	−	0.0220284i
$148$	1427.19	−	527.948i	0.792665	−	0.293224i
$149$			2992.83i			1.64552i	0.568392	+	0.822758i	$0.307566\pi$
$149$			2992.83i			1.64552i	−0.568392	+	0.822758i	$0.692434\pi$
$150$		0			0
$151$			184.103i			0.0992192i	0.998769	+	0.0496096i	$0.0157977\pi$
$151$			184.103i			0.0992192i	−0.998769	+	0.0496096i	$0.984202\pi$
$152$	−408.926	−	2927.92i	−0.218212	−	1.56240i
$153$	−917.924	+	917.924i	−0.485031	+	0.485031i
$154$	1574.95	+	344.827i	0.824110	+	0.180435i
$155$		0			0
$156$	67.9597	−	147.758i	0.0348790	−	0.0758342i
$157$	1301.36	+	1301.36i	0.661530	+	0.661530i	0.955741	−	0.294211i	$-0.0950568\pi$
$157$	1301.36	+	1301.36i	0.661530	+	0.661530i	−0.294211	+	0.955741i	$0.595057\pi$
$158$	530.420	−	339.874i	0.267076	−	0.171132i
$159$	−149.016			−0.0743252
$160$		0			0
$161$	2048.97			1.00299
$162$	1713.22	−	1097.77i	0.830884	−	0.532400i
$163$	−1460.57	−	1460.57i	−0.701843	−	0.701843i	0.262963	−	0.964806i	$-0.415300\pi$
$163$	−1460.57	−	1460.57i	−0.701843	−	0.701843i	−0.964806	+	0.262963i	$0.915300\pi$
$164$	520.095	−	1130.79i	0.247638	−	0.538416i
$165$		0			0
$166$	−3222.56	−	705.563i	−1.50674	−	0.329894i
$167$	−1656.63	+	1656.63i	−0.767626	+	0.767626i	−0.977688	−	0.210062i	$-0.932633\pi$
$167$	−1656.63	+	1656.63i	−0.767626	+	0.767626i	0.210062	+	0.977688i	$0.432633\pi$
$168$	14.5475	+	104.161i	0.00668074	+	0.0478343i
$169$		−	1282.77i		−	0.583872i
$170$		0			0
$171$			3512.11i			1.57063i
$172$	−2372.00	+	877.455i	−1.05153	+	0.388984i
$173$	1601.81	−	1601.81i	0.703952	−	0.703952i	−0.261304	−	0.965256i	$-0.584153\pi$
$173$	1601.81	−	1601.81i	0.703952	−	0.703952i	0.965256	+	0.261304i	$0.0841526\pi$
$174$	−16.7641	+	76.5678i	−0.00730395	+	0.0333597i
$175$		0			0
$176$	2053.78	−	1760.36i	0.879598	−	0.753933i
$177$	−43.1681	−	43.1681i	−0.0183317	−	0.0183317i
$178$	2208.11	+	3446.06i	0.929802	+	1.45109i
$179$	−37.6748			−0.0157316			−0.00786578	−	0.999969i	$-0.502504\pi$
$179$	−37.6748			−0.0157316			−0.00786578	+	0.999969i	$0.502504\pi$
$180$		0			0
$181$	−1360.64			−0.558762			−0.279381	−	0.960180i	$-0.590129\pi$
$181$	−1360.64			−0.558762			−0.279381	+	0.960180i	$0.590129\pi$
$182$	1214.02	+	1894.65i	0.494446	+	0.771651i
$183$	10.1056	+	10.1056i	0.00408213	+	0.00408213i
$184$	2071.20	−	2743.66i	0.829842	−	1.09927i
$185$		0			0
$186$	−56.9665	+	260.186i	−0.0224569	+	0.102569i
$187$	1443.24	−	1443.24i	0.564388	−	0.564388i
$188$	283.076	+	765.232i	0.109816	+	0.296863i
$189$		−	250.438i		−	0.0963846i
$190$		0			0
$191$			3587.14i			1.35893i	0.733706	+	0.679467i	$0.237789\pi$
$191$			3587.14i			1.35893i	−0.733706	+	0.679467i	$0.762211\pi$
$192$	154.181	+	85.8108i	0.0579534	+	0.0322545i
$193$	−3631.68	+	3631.68i	−1.35448	+	1.35448i	−0.473894	+	0.880582i	$0.657152\pi$
$193$	−3631.68	+	3631.68i	−1.35448	+	1.35448i	−0.880582	+	0.473894i	$0.842848\pi$
$194$	766.843	+	167.896i	0.283794	+	0.0621354i
$195$		0			0
$196$	1170.95	+	538.564i	0.426731	+	0.196270i
$197$	235.786	+	235.786i	0.0852746	+	0.0852746i	0.748457	−	0.663183i	$-0.230795\pi$
$197$	235.786	+	235.786i	0.0852746	+	0.0852746i	−0.663183	+	0.748457i	$0.730795\pi$
$198$	−2705.69	+	1733.71i	−0.971137	+	0.622269i
$199$	−2893.75			−1.03081			−0.515407	−	0.856945i	$-0.672359\pi$
$199$	−2893.75			−1.03081			−0.515407	+	0.856945i	$0.672359\pi$
$200$		0			0
$201$	−127.570			−0.0447667
$202$	−1416.36	+	907.550i	−0.493340	+	0.316114i
$203$	−766.838	−	766.838i	−0.265131	−	0.265131i
$204$	120.962	+	55.6351i	0.0415149	+	0.0190943i
$205$		0			0
$206$	−1953.06	−	427.612i	−0.660563	−	0.144627i
$207$	−2887.77	+	2887.77i	−0.969634	+	0.969634i
$208$	3764.21	+	289.574i	1.25481	+	0.0965306i
$209$		−	5522.06i		−	1.82760i
$210$		0			0
$211$		−	2956.45i		−	0.964599i	−0.876006	−	0.482300i	$-0.839802\pi$
$211$		−	2956.45i		−	0.964599i	0.876006	−	0.482300i	$-0.160198\pi$
$212$	−1200.12	−	3244.26i	−0.388795	−	1.05102i
$213$	−180.687	+	180.687i	−0.0581242	+	0.0581242i
$214$	612.991	−	2799.75i	0.195809	−	0.894331i
$215$		0			0
$216$	−335.348	−	253.155i	−0.105637	−	0.0797455i
$217$	−2605.81	−	2605.81i	−0.815178	−	0.815178i
$218$	−1037.93	−	1619.84i	−0.322466	−	0.503253i
$219$	251.894			0.0777233
$220$		0			0
$221$	2848.71			0.867080
$222$	100.033	+	156.115i	0.0302422	+	0.0471972i
$223$	1581.62	+	1581.62i	0.474946	+	0.474946i	0.903511	−	0.428565i	$-0.140981\pi$
$223$	1581.62	+	1581.62i	0.474946	+	0.474946i	−0.428565	+	0.903511i	$0.640981\pi$
$224$	−2150.54	+	1155.59i	−0.641470	+	0.344692i
$225$		0			0
$226$	25.9679	−	118.605i	0.00764318	−	0.0349091i
$227$	−668.464	+	668.464i	−0.195452	+	0.195452i	−0.798047	−	0.602595i	$-0.794133\pi$
$227$	−668.464	+	668.464i	−0.195452	+	0.195452i	0.602595	+	0.798047i	$0.294133\pi$
$228$	337.843	−	124.975i	0.0981325	−	0.0363013i
$229$			3515.88i			1.01457i	0.861779	+	0.507284i	$0.169350\pi$
$229$			3515.88i			1.01457i	−0.861779	+	0.507284i	$0.830650\pi$
$230$		0			0
$231$			196.447i			0.0559535i
$232$	−1801.99	+	251.674i	−0.509942	+	0.0712206i
$233$	−1658.86	+	1658.86i	−0.466420	+	0.466420i	−0.900752	−	0.434333i	$-0.856984\pi$
$233$	−1658.86	+	1658.86i	−0.466420	+	0.466420i	0.434333	+	0.900752i	$0.356984\pi$
$234$	−4381.29	−	959.261i	−1.22399	−	0.267986i
$235$		0			0
$236$	592.163	−	1287.48i	0.163333	−	0.355119i
$237$	54.2769	+	54.2769i	0.0148762	+	0.0148762i
$238$	−1551.05	+	993.855i	−0.422435	+	0.270681i
$239$	1712.05			0.463360			0.231680	−	0.972792i	$-0.425578\pi$
$239$	1712.05			0.463360			0.231680	+	0.972792i	$0.425578\pi$
$240$		0			0
$241$	−5796.70			−1.54937			−0.774685	−	0.632348i	$-0.782091\pi$
$241$	−5796.70			−1.54937			−0.774685	+	0.632348i	$0.782091\pi$
$242$	1084.39	−	694.838i	0.288047	−	0.184570i
$243$	529.832	+	529.832i	0.139871	+	0.139871i
$244$	−138.625	+	301.399i	−0.0363711	+	0.0790783i
$245$		0			0
$246$	148.148	+	32.4364i	0.0383967	+	0.00840677i
$247$	5449.78	−	5449.78i	1.40389	−	1.40389i
$248$	−6123.37	+	855.217i	−1.56788	+	0.218977i
$249$		−	401.957i		−	0.102301i
$250$		0			0
$251$		−	2040.48i		−	0.513123i	−0.966528	−	0.256562i	$-0.917410\pi$
$251$		−	2040.48i		−	0.513123i	0.966528	−	0.256562i	$-0.0825897\pi$
$252$	2720.17	−	1006.25i	0.679978	−	0.251538i
$253$	4540.43	−	4540.43i	1.12828	−	1.12828i
$254$	−1071.55	+	4894.17i	−0.264706	+	1.20901i
$255$		0			0
$256$	−626.489	+	4047.81i	−0.152952	+	0.988234i
$257$	757.135	+	757.135i	0.183770	+	0.183770i	0.792996	−	0.609227i	$-0.208520\pi$
$257$	757.135	+	757.135i	0.183770	+	0.183770i	−0.609227	+	0.792996i	$0.708520\pi$
$258$	−166.256	−	259.465i	−0.0401187	−	0.0626108i
$259$	−2565.36			−0.615459
$260$		0			0
$261$	2161.53			0.512626
$262$	−400.941	−	625.724i	−0.0945428	−	0.147547i
$263$	1842.73	+	1842.73i	0.432045	+	0.432045i	0.889323	−	0.457279i	$-0.151176\pi$
$263$	1842.73	+	1842.73i	0.432045	+	0.432045i	−0.457279	+	0.889323i	$0.651176\pi$
$264$	263.052	+	198.578i	0.0613247	+	0.0462942i
$265$		0			0
$266$	−1065.95	+	4868.58i	−0.245706	+	1.12223i
$267$	−352.629	+	352.629i	−0.0808260	+	0.0808260i
$268$	−1027.40	−	2777.36i	−0.234174	−	0.633039i
$269$			4651.65i			1.05433i	0.849762	+	0.527167i	$0.176746\pi$
$269$			4651.65i			1.05433i	−0.849762	+	0.527167i	$0.823254\pi$
$270$		0			0
$271$		−	8533.48i		−	1.91281i	−0.292040	−	0.956406i	$-0.594334\pi$
$271$		−	8533.48i		−	1.91281i	0.292040	−	0.956406i	$-0.405666\pi$
$272$	−237.060	+	3081.56i	−0.0528450	+	0.686939i
$273$	−193.876	+	193.876i	−0.0429813	+	0.0429813i
$274$	4894.47	+	1071.62i	1.07914	+	0.236273i
$275$		0			0
$276$	380.545	+	175.027i	0.0829932	+	0.0381717i
$277$	1883.72	+	1883.72i	0.408598	+	0.408598i	0.881249	−	0.472652i	$-0.156703\pi$
$277$	1883.72	+	1883.72i	0.408598	+	0.408598i	−0.472652	+	0.881249i	$0.656703\pi$
$278$	4830.35	−	3095.11i	1.04210	−	0.667742i
$279$	7345.13			1.57614
$280$		0			0
$281$	−1365.56			−0.289902			−0.144951	−	0.989439i	$-0.546303\pi$
$281$	−1365.56			−0.289902			−0.144951	+	0.989439i	$0.546303\pi$
$282$	−83.7060	+	53.6357i	−0.0176759	+	0.0113261i
$283$	2275.91	+	2275.91i	0.478052	+	0.478052i	0.904508	−	0.426456i	$-0.140238\pi$
$283$	2275.91	+	2275.91i	0.478052	+	0.478052i	−0.426456	+	0.904508i	$0.640238\pi$
$284$	−5388.97	−	2478.59i	−1.12597	−	0.517878i
$285$		0			0
$286$	6888.66	+	1508.24i	1.42425	+	0.311832i
$287$	−1483.73	+	1483.73i	−0.305163	+	0.305163i
$288$	1402.27	−	4659.59i	0.286908	−	0.953365i
$289$		−	2580.91i		−	0.525323i
$290$		0			0
$291$			95.6501i			0.0192684i
$292$	2028.66	+	5484.04i	0.406570	+	1.09907i
$293$	2859.58	−	2859.58i	0.570165	−	0.570165i	−0.362009	−	0.932175i	$-0.617909\pi$
$293$	2859.58	−	2859.58i	0.570165	−	0.570165i	0.932175	+	0.362009i	$0.117909\pi$
$294$	−33.5882	+	153.409i	−0.00666294	+	0.0304320i
$295$		0			0
$296$	−2593.20	+	3435.14i	−0.509211	+	0.674539i
$297$	−554.960	−	554.960i	−0.108424	−	0.108424i
$298$	−4566.94	−	7127.35i	−0.887771	−	1.38549i
$299$	8961.98			1.73339
$300$		0			0
$301$	4263.66			0.816455
$302$	−280.935	−	438.437i	−0.0535297	−	0.0835405i
$303$	−144.933	−	144.933i	−0.0274792	−	0.0274792i
$304$	5441.74	+	6348.76i	1.02666	+	1.19778i
$305$		0			0
$306$	785.297	−	3586.73i	0.146707	−	0.670065i
$307$	−528.300	+	528.300i	−0.0982139	+	0.0982139i	−0.754507	−	0.656293i	$-0.772124\pi$
$307$	−528.300	+	528.300i	−0.0982139	+	0.0982139i	0.656293	+	0.754507i	$0.272124\pi$
$308$	−4276.90	+	1582.12i	−0.791230	+	0.292693i
$309$		−	243.609i		−	0.0448494i
$310$		0			0
$311$		−	395.402i		−	0.0720938i	−0.999350	−	0.0360469i	$-0.988523\pi$
$311$		−	395.402i		−	0.0720938i	0.999350	−	0.0360469i	$-0.0114766\pi$
$312$	63.6293	+	455.587i	0.0115458	+	0.0826684i
$313$	804.658	−	804.658i	0.145310	−	0.145310i	−0.630709	−	0.776019i	$-0.717236\pi$
$313$	804.658	−	804.658i	0.145310	−	0.145310i	0.776019	+	0.630709i	$0.217236\pi$
$314$	−5085.00	−	1113.34i	−0.913896	−	0.200093i
$315$		0			0
$316$	−744.549	+	1618.80i	−0.132545	+	0.288180i
$317$	3696.00	+	3696.00i	0.654852	+	0.654852i	0.954157	−	0.299305i	$-0.0967549\pi$
$317$	3696.00	+	3696.00i	0.654852	+	0.654852i	−0.299305	+	0.954157i	$0.596755\pi$
$318$	354.877	−	227.392i	0.0625803	−	0.0400991i
$319$	−3398.56			−0.596498
$320$		0			0
$321$	349.219			0.0607212
$322$	−4879.58	+	3126.65i	−0.844497	+	0.541123i
$323$	4461.45	+	4461.45i	0.768551	+	0.768551i
$324$	−2404.84	+	5228.62i	−0.412353	+	0.896540i
$325$		0			0
$326$	5707.08	+	1249.54i	0.969588	+	0.212287i
$327$	165.755	−	165.755i	0.0280314	−	0.0280314i
$328$	486.955	+	3486.61i	0.0819743	+	0.586938i
$329$		−	1375.50i		−	0.230497i
$330$		0			0
$331$		−	1388.78i		−	0.230617i	−0.993330	−	0.115308i	$-0.963214\pi$
$331$		−	1388.78i		−	0.230617i	0.993330	−	0.115308i	$-0.0367856\pi$
$332$	8751.11	−	3237.22i	1.44663	−	0.535137i
$333$	3615.57	−	3615.57i	0.594991	−	0.594991i
$334$	1417.27	−	6473.17i	0.232184	−	1.06047i
$335$		0			0
$336$	−193.590	−	225.857i	−0.0314321	−	0.0366712i
$337$	−2766.70	−	2766.70i	−0.447216	−	0.447216i	0.447212	−	0.894428i	$-0.352417\pi$
$337$	−2766.70	−	2766.70i	−0.447216	−	0.447216i	−0.894428	+	0.447212i	$0.852417\pi$
$338$	1957.45	+	3054.88i	0.315004	+	0.491608i
$339$	14.7938			0.00237018
$340$		0			0
$341$	−11548.7			−1.83401
$342$	−5359.35	−	8364.01i	−0.847369	−	1.32244i
$343$	−4807.46	−	4807.46i	−0.756788	−	0.756788i
$344$	4309.91	−	5709.23i	0.675509	−	0.894829i
$345$		0			0
$346$	−1370.38	+	6259.00i	−0.212925	+	0.972502i
$347$	2069.91	−	2069.91i	0.320227	−	0.320227i	−0.528627	−	0.848854i	$-0.677293\pi$
$347$	2069.91	−	2069.91i	0.320227	−	0.320227i	0.848854	+	0.528627i	$0.177293\pi$
$348$	−76.9162	−	207.926i	−0.0118481	−	0.0320288i
$349$			5774.64i			0.885700i	0.896596	+	0.442850i	$0.146033\pi$
$349$			5774.64i			0.885700i	−0.896596	+	0.442850i	$0.853967\pi$
$350$		0			0
$351$		−	1095.39i		−	0.166574i
$352$	−2204.78	+	7326.25i	−0.333849	+	1.10935i
$353$	−7965.11	+	7965.11i	−1.20096	+	1.20096i	−0.227089	+	0.973874i	$0.572921\pi$
$353$	−7965.11	+	7965.11i	−1.20096	+	1.20096i	−0.973874	+	0.227089i	$0.927079\pi$
$354$	168.677	+	36.9309i	0.0253250	+	0.00554479i
$355$		0			0
$356$	−10517.1	−	4837.23i	−1.56575	−	0.720148i
$357$	−158.716	−	158.716i	−0.0235298	−	0.0235298i
$358$	89.7218	−	57.4904i	0.0132457	−	0.00848733i
$359$	−6227.61			−0.915545			−0.457773	−	0.889069i	$-0.651353\pi$
$359$	−6227.61			−0.915545			−0.457773	+	0.889069i	$0.651353\pi$
$360$		0			0
$361$	10211.2			1.48872
$362$	3240.35	−	2076.29i	0.470466	−	0.301457i
$363$	110.964	+	110.964i	0.0160443	+	0.0160443i
$364$	−5782.32	−	2659.51i	−0.832626	−	0.382956i
$365$		0			0
$366$	−39.4871	−	8.64551i	−0.00563941	−	0.00123472i
$367$	3426.52	−	3426.52i	0.487365	−	0.487365i	−0.420109	−	0.907474i	$-0.638008\pi$
$367$	3426.52	−	3426.52i	0.487365	−	0.487365i	0.907474	+	0.420109i	$0.138008\pi$
$368$	−745.786	+	9694.55i	−0.105643	+	1.37327i
$369$		−	4182.27i		−	0.590028i
$370$		0			0
$371$			5831.52i			0.816058i
$372$	−261.370	−	706.557i	−0.0364285	−	0.0984765i
$373$	−4631.53	+	4631.53i	−0.642926	+	0.642926i	−0.951274	−	0.308347i	$-0.900224\pi$
$373$	−4631.53	+	4631.53i	−0.642926	+	0.642926i	0.308347	+	0.951274i	$0.400224\pi$
$374$	−1234.72	+	5639.39i	−0.170710	+	0.779696i
$375$		0			0
$376$	−1841.85	−	1390.42i	−0.252623	−	0.190706i
$377$	−3354.07	−	3354.07i	−0.458206	−	0.458206i
$378$	382.159	+	596.413i	0.0520004	+	0.0811539i
$379$	−10644.7			−1.44269			−0.721347	−	0.692574i	$-0.756477\pi$
$379$	−10644.7			−1.44269			−0.721347	+	0.692574i	$0.756477\pi$
$380$		0			0
$381$	−610.461			−0.0820863
$382$	−5473.85	−	8542.70i	−0.733158	−	1.14419i
$383$	2301.02	+	2301.02i	0.306988	+	0.306988i	0.843740	−	0.536752i	$-0.180349\pi$
$383$	2301.02	+	2301.02i	0.306988	+	0.306988i	−0.536752	+	0.843740i	$0.680349\pi$
$384$	−498.123	+	30.9180i	−0.0661972	+	0.00410880i
$385$		0			0
$386$	3106.95	−	14190.6i	0.409688	−	1.87119i
$387$	−6009.10	+	6009.10i	−0.789302	+	0.789302i
$388$	−2082.42	+	770.332i	−0.272472	+	0.100793i
$389$		−	5636.87i		−	0.734706i	−0.930082	−	0.367353i	$-0.880264\pi$
$389$		−	5636.87i		−	0.734706i	0.930082	−	0.367353i	$-0.119736\pi$
$390$		0			0
$391$			7336.71i			0.948935i
$392$	−3610.42	+	504.247i	−0.465188	+	0.0649702i
$393$	64.0291	−	64.0291i	0.00821843	−	0.00821843i
$394$	−921.322	−	201.719i	−0.117806	−	0.0257930i
$395$		0			0
$396$	3797.97	−	8257.57i	0.481958	−	1.04787i
$397$	−6539.04	−	6539.04i	−0.826663	−	0.826663i	0.160391	−	0.987054i	$-0.448725\pi$
$397$	−6539.04	−	6539.04i	−0.826663	−	0.826663i	−0.987054	+	0.160391i	$0.948725\pi$
$398$	6891.39	−	4415.75i	0.867925	−	0.556134i
$399$	−607.270			−0.0761943
$400$		0			0
$401$	−5980.28			−0.744740			−0.372370	−	0.928084i	$-0.621455\pi$
$401$	−5980.28			−0.744740			−0.372370	+	0.928084i	$0.621455\pi$
$402$	303.805	−	194.667i	0.0376926	−	0.0241521i
$403$	−11397.5	−	11397.5i	−1.40881	−	1.40881i
$404$	1988.14	−	4322.62i	0.244835	−	0.532323i
$405$		0			0
$406$	2996.38	+	656.042i	0.366275	+	0.0801941i
$407$	−5684.73	+	5684.73i	−0.692338	+	0.692338i
$408$	−372.966	+	52.0900i	−0.0452563	+	0.00632069i
$409$		−	5150.66i		−	0.622698i	−0.950296	−	0.311349i	$-0.899219\pi$
$409$		−	5150.66i		−	0.622698i	0.950296	−	0.311349i	$-0.100781\pi$
$410$		0			0
$411$			610.499i			0.0732693i
$412$	5303.68	−	1961.94i	0.634208	−	0.234607i
$413$	−1689.32	+	1689.32i	−0.201274	+	0.201274i
$414$	2470.53	−	11283.8i	0.293285	−	1.33954i
$415$		0			0
$416$	−9406.26	+	5054.43i	−1.10861	+	0.595706i
$417$	494.280	+	494.280i	0.0580456	+	0.0580456i
$418$	8426.46	+	13150.7i	0.986009	+	1.53880i
$419$	3080.65			0.359188			0.179594	−	0.983741i	$-0.442522\pi$
$419$	3080.65			0.359188			0.179594	+	0.983741i	$0.442522\pi$
$420$		0			0
$421$	5636.62			0.652523			0.326261	−	0.945280i	$-0.394211\pi$
$421$	5636.62			0.652523			0.326261	+	0.945280i	$0.394211\pi$
$422$	4511.43	+	7040.72i	0.520410	+	0.812173i
$423$	1938.60	+	1938.60i	0.222832	+	0.222832i
$424$	7808.67	+	5894.79i	0.894393	+	0.675180i
$425$		0			0
$426$	154.580	−	706.023i	0.0175808	−	0.0802980i
$427$	395.470	−	395.470i	0.0448199	−	0.0448199i
$428$	2812.49	+	7602.94i	0.317632	+	0.858649i
$429$			859.239i			0.0967004i
$430$		0			0
$431$			12970.7i			1.44959i	0.688963	+	0.724797i	$0.258066\pi$
$431$			12970.7i			1.44959i	−0.688963	+	0.724797i	$0.741934\pi$
$432$	1184.93	+	91.1547i	0.131968	+	0.0101520i
$433$	181.752	−	181.752i	0.0201719	−	0.0201719i	−0.696949	−	0.717121i	$-0.745460\pi$
$433$	181.752	−	181.752i	0.0201719	−	0.0201719i	0.717121	+	0.696949i	$0.245460\pi$
$434$	10182.0	+	2229.31i	1.12616	+	0.246567i
$435$		0			0
$436$	4943.62	+	2273.76i	0.543020	+	0.249755i
$437$	14035.7	+	14035.7i	1.53642	+	1.53642i
$438$	−599.879	+	384.380i	−0.0654414	+	0.0419324i
$439$	−5465.06			−0.594153			−0.297076	−	0.954854i	$-0.596012\pi$
$439$	−5465.06			−0.594153			−0.297076	+	0.954854i	$0.596012\pi$
$440$		0			0
$441$	4330.79			0.467637
$442$	−6784.13	+	4347.02i	−0.730064	+	0.467798i
$443$	−4982.88	−	4982.88i	−0.534410	−	0.534410i	0.387472	−	0.921882i	$-0.373349\pi$
$443$	−4982.88	−	4982.88i	−0.534410	−	0.534410i	−0.921882	+	0.387472i	$0.873349\pi$
$444$	−476.452	−	219.139i	−0.0509266	−	0.0234231i
$445$		0			0
$446$	−6180.07	−	1353.10i	−0.656132	−	0.143657i
$447$	729.328	−	729.328i	0.0771724	−	0.0771724i
$448$	3358.09	−	6033.66i	0.354140	−	0.636303i
$449$			11884.7i			1.24916i	0.780960	+	0.624581i	$0.214730\pi$
$449$			11884.7i			1.24916i	−0.780960	+	0.624581i	$0.785270\pi$
$450$		0			0
$451$			6575.75i			0.686563i
$452$	119.144	+	322.080i	0.0123984	+	0.0335164i
$453$	44.8645	−	44.8645i	0.00465324	−	0.00465324i
$454$	571.881	−	2611.98i	0.0591183	−	0.270014i
$455$		0			0
$456$	−613.858	+	813.162i	−0.0630407	+	0.0835084i
$457$	1360.58	+	1360.58i	0.139267	+	0.139267i	0.773303	−	0.634036i	$-0.218603\pi$
$457$	1360.58	+	1360.58i	0.139267	+	0.139267i	−0.634036	+	0.773303i	$0.718603\pi$
$458$	−5365.10	−	8372.99i	−0.547369	−	0.854245i
$459$	896.740			0.0911901
$460$		0			0
$461$	8133.56			0.821730			0.410865	−	0.911696i	$-0.365227\pi$
$461$	8133.56			0.821730			0.410865	+	0.911696i	$0.365227\pi$
$462$	−299.771	−	467.834i	−0.0301875	−	0.0471117i
$463$	−1938.32	−	1938.32i	−0.194560	−	0.194560i	0.603103	−	0.797663i	$-0.293931\pi$
$463$	−1938.32	−	1938.32i	−0.194560	−	0.194560i	−0.797663	+	0.603103i	$0.793931\pi$
$464$	3907.35	−	3349.13i	0.390936	−	0.335085i
$465$		0			0
$466$	1419.18	−	6481.91i	0.141078	−	0.644354i
$467$	8462.63	−	8462.63i	0.838552	−	0.838552i	−0.150116	−	0.988668i	$-0.547965\pi$
$467$	8462.63	−	8462.63i	0.838552	−	0.838552i	0.988668	+	0.150116i	$0.0479648\pi$
$468$	11897.7	−	4401.22i	1.17516	−	0.434715i
$469$			4992.28i			0.491518i
$470$		0			0
$471$		−	634.264i		−	0.0620496i
$472$	554.430	+	3969.73i	0.0540671	+	0.387122i
$473$	9448.07	−	9448.07i	0.918441	−	0.918441i
$474$	−212.084	−	46.4347i	−0.0205513	−	0.00449961i
$475$		0			0
$476$	2177.20	−	4733.69i	0.209647	−	0.455816i
$477$	−8218.81	−	8218.81i	−0.788918	−	0.788918i
$478$	−4077.20	+	2612.52i	−0.390140	+	0.249987i
$479$	7570.70			0.722158			0.361079	−	0.932535i	$-0.382408\pi$
$479$	7570.70			0.722158			0.361079	+	0.932535i	$0.382408\pi$
$480$		0			0
$481$	−11220.6			−1.06365
$482$	13804.7	−	8845.55i	1.30454	−	0.835899i
$483$	−499.318	−	499.318i	−0.0470388	−	0.0470388i
$484$	−1522.16	+	3309.48i	−0.142952	+	0.310808i
$485$		0			0
$486$	−2070.29	−	453.279i	−0.193231	−	0.0423069i
$487$	−9502.42	+	9502.42i	−0.884181	+	0.884181i	−0.993956	−	0.109776i	$-0.964987\pi$
$487$	−9502.42	+	9502.42i	−0.884181	+	0.884181i	0.109776	+	0.993956i	$0.464987\pi$
$488$	−129.792	−	929.312i	−0.0120397	−	0.0862049i
$489$			711.857i			0.0658309i
$490$		0			0
$491$		−	8188.17i		−	0.752601i	−0.926498	−	0.376300i	$-0.877196\pi$
$491$		−	8188.17i		−	0.752601i	0.926498	−	0.376300i	$-0.122804\pi$
$492$	−402.309	+	148.823i	−0.0368648	+	0.0136371i
$493$	2745.81	−	2745.81i	0.250842	−	0.250842i
$494$	−4662.36	+	21294.7i	−0.424635	+	1.93946i
$495$		0			0
$496$	13277.6	−	11380.7i	1.20198	−	1.03026i
$497$	7070.93	+	7070.93i	0.638178	+	0.638178i
$498$	613.372	+	957.252i	0.0551925	+	0.0861355i
$499$	−429.740			−0.0385527			−0.0192764	−	0.999814i	$-0.506136\pi$
$499$	−429.740			−0.0385527			−0.0192764	+	0.999814i	$0.506136\pi$
$500$		0			0
$501$	807.414			0.0720012
$502$	3113.70	+	4859.36i	0.276835	+	0.432039i
$503$	−8511.42	−	8511.42i	−0.754484	−	0.754484i	0.220829	−	0.975313i	$-0.429124\pi$
$503$	−8511.42	−	8511.42i	−0.754484	−	0.754484i	−0.975313	+	0.220829i	$0.929124\pi$
$504$	−4942.52	+	6547.23i	−0.436820	+	0.578645i
$505$		0			0
$506$	−3884.40	+	17741.4i	−0.341270	+	1.55870i
$507$	−312.600	+	312.600i	−0.0273827	+	0.0273827i
$508$	−4916.44	−	13290.5i	−0.429393	−	1.16077i
$509$		−	3762.37i		−	0.327631i	−0.986491	−	0.163816i	$-0.947620\pi$
$509$		−	3762.37i		−	0.327631i	0.986491	−	0.163816i	$-0.0523802\pi$
$510$		0			0
$511$		−	9857.51i		−	0.853367i
$512$	−4684.83	−	10595.8i	−0.404379	−	0.914591i
$513$	1715.53	−	1715.53i	0.147646	−	0.147646i
$514$	−2958.46	−	647.740i	−0.253876	−	0.0555848i
$515$		0			0
$516$	791.868	+	364.210i	0.0675582	+	0.0310726i
$517$	−3048.04	−	3048.04i	−0.259290	−	0.259290i
$518$	6109.36	−	3914.65i	0.518204	−	0.332046i
$519$	−780.699			−0.0660287
$520$		0			0
$521$	818.504			0.0688279			0.0344139	−	0.999408i	$-0.489044\pi$
$521$	818.504			0.0688279			0.0344139	+	0.999408i	$0.489044\pi$
$522$	−5147.64	+	3298.42i	−0.431621	+	0.276567i
$523$	14975.1	+	14975.1i	1.25203	+	1.25203i	0.954807	+	0.297227i	$0.0960618\pi$
$523$	14975.1	+	14975.1i	1.25203	+	1.25203i	0.297227	+	0.954807i	$0.403938\pi$
$524$	1909.66	+	878.327i	0.159206	+	0.0732250i
$525$		0			0
$526$	−7200.37	−	1576.48i	−0.596865	−	0.130681i
$527$	9330.57	−	9330.57i	0.771245	−	0.771245i
$528$	−929.475	−	71.5030i	−0.0766102	−	0.00589350i
$529$			10914.2i			0.897032i
$530$		0			0
$531$		−	4761.79i		−	0.389160i
$532$	−4890.74	−	13221.0i	−0.398572	−	1.07745i
$533$	−6489.68	+	6489.68i	−0.527390	+	0.527390i
$534$	301.679	−	1377.88i	0.0244475	−	0.111660i
$535$		0			0
$536$	6684.89	+	5046.45i	0.538701	+	0.406666i
$537$	9.18106	+	9.18106i	0.000737788	+	0.000737788i
$538$	−7098.24	−	11077.8i	−0.568823	−	0.887728i
$539$	−6809.26			−0.544148
$540$		0			0
$541$	−1894.75			−0.150576			−0.0752879	−	0.997162i	$-0.523988\pi$
$541$	−1894.75			−0.150576			−0.0752879	+	0.997162i	$0.523988\pi$
$542$	13021.8	+	20322.3i	1.03198	+	1.61055i
$543$	331.578	+	331.578i	0.0262051	+	0.0262051i
$544$	−4137.80	−	7700.42i	−0.326115	−	0.606899i
$545$		0			0
$546$	165.863	−	757.557i	0.0130005	−	0.0593781i
$547$	8079.10	−	8079.10i	0.631513	−	0.631513i	−0.316935	−	0.948447i	$-0.602654\pi$
$547$	8079.10	−	8079.10i	0.631513	−	0.631513i	0.948447	+	0.316935i	$0.102654\pi$
$548$	−13291.3	+	4916.74i	−1.03609	+	0.383271i
$549$			1114.73i			0.0866587i
$550$		0			0
$551$		−	10505.8i		−	0.812276i
$552$	−1173.34	+	163.874i	−0.0904726	+	0.0126358i
$553$	2124.05	−	2124.05i	0.163334	−	0.163334i
$554$	−7360.51	−	1611.55i	−0.564473	−	0.123589i
$555$		0			0
$556$	−6780.34	+	14741.9i	−0.517177	+	1.12445i
$557$	−11900.0	−	11900.0i	−0.905243	−	0.905243i	0.0906404	−	0.995884i	$-0.471109\pi$
$557$	−11900.0	−	11900.0i	−0.905243	−	0.905243i	−0.995884	+	0.0906404i	$0.971109\pi$
$558$	−17492.3	+	11208.4i	−1.32707	+	0.850340i
$559$	18648.8			1.41102
$560$		0			0
$561$	−703.415			−0.0529380
$562$	3252.06	−	2083.80i	0.244092	−	0.156405i
$563$	11749.3	+	11749.3i	0.879526	+	0.879526i	0.993485	−	0.113959i	$-0.0363533\pi$
$563$	11749.3	+	11749.3i	0.879526	+	0.879526i	−0.113959	+	0.993485i	$0.536353\pi$
$564$	117.498	−	255.464i	0.00877225	−	0.0190727i
$565$		0			0
$566$	−8892.97	−	1947.07i	−0.660423	−	0.144596i
$567$	6860.54	−	6860.54i	0.508140	−	0.508140i
$568$	16616.0	−	2320.66i	1.22745	−	0.171431i
$569$		−	2172.30i		−	0.160049i	−0.996793	−	0.0800243i	$-0.974500\pi$
$569$		−	2172.30i		−	0.160049i	0.996793	−	0.0800243i	$-0.0254998\pi$
$570$		0			0
$571$		−	5608.37i		−	0.411039i	−0.978653	−	0.205519i	$-0.934112\pi$
$571$		−	5608.37i		−	0.411039i	0.978653	−	0.205519i	$-0.0658884\pi$
$572$	−18706.7	+	6920.01i	−1.36742	+	0.505839i
$573$	874.158	−	874.158i	0.0637321	−	0.0637321i
$574$	1269.35	−	5797.58i	0.0923027	−	0.421579i
$575$		0			0
$576$	3770.90	+	13236.5i	0.272779	+	0.957504i
$577$	16686.9	+	16686.9i	1.20396	+	1.20396i	0.972951	+	0.231010i	$0.0742029\pi$
$577$	16686.9	+	16686.9i	1.20396	+	1.20396i	0.231010	+	0.972951i	$0.425797\pi$
$578$	3938.38	+	6146.38i	0.283417	+	0.442311i
$579$	1770.02			0.127046
$580$		0			0
$581$	−15730.0			−1.12322
$582$	−145.959	−	227.789i	−0.0103955	−	0.0162236i
$583$	12922.4	+	12922.4i	0.917994	+	0.917994i
$584$	−13199.7	−	9964.46i	−0.935284	−	0.706048i
$585$		0			0
$586$	−2446.41	+	11173.6i	−0.172458	+	0.787677i
$587$	−19717.2	+	19717.2i	−1.38640	+	1.38640i	−0.553650	+	0.832749i	$0.686766\pi$
$587$	−19717.2	+	19717.2i	−1.38640	+	1.38640i	−0.832749	+	0.553650i	$0.813234\pi$
$588$	−154.107	−	416.595i	−0.0108083	−	0.0292178i
$589$		−	35700.1i		−	2.49745i
$590$		0			0
$591$		−	114.919i		−	0.00799851i
$592$	933.743	−	12137.8i	0.0648254	−	0.842672i
$593$	168.200	−	168.200i	0.0116478	−	0.0116478i	−0.701259	−	0.712907i	$-0.747378\pi$
$593$	168.200	−	168.200i	0.0116478	−	0.0116478i	0.712907	+	0.701259i	$0.247378\pi$
$594$	2168.47	+	474.776i	0.149787	+	0.0327951i
$595$		0			0
$596$	21752.1	+	10004.6i	1.49497	+	0.687594i
$597$	705.183	+	705.183i	0.0483438	+	0.0483438i
$598$	−21342.8	+	13675.7i	−1.45948	+	0.935182i
$599$	3488.67			0.237969			0.118984	−	0.992896i	$-0.462036\pi$
$599$	3488.67			0.237969			0.118984	+	0.992896i	$0.462036\pi$
$600$		0			0
$601$	10909.5			0.740443			0.370222	−	0.928943i	$-0.379282\pi$
$601$	10909.5			0.740443			0.370222	+	0.928943i	$0.379282\pi$
$602$	−10153.8	+	6506.18i	−0.687439	+	0.440485i
$603$	−7036.01	−	7036.01i	−0.475172	−	0.475172i
$604$	1338.08	+	615.433i	0.0901418	+	0.0414596i
$605$		0			0
$606$	566.318	+	123.993i	0.0379622	+	0.00831164i
$607$	−12048.9	+	12048.9i	−0.805683	+	0.805683i	−0.983977	−	0.178294i	$-0.942942\pi$
$607$	−12048.9	+	12048.9i	−0.805683	+	0.805683i	0.178294	+	0.983977i	$0.442942\pi$
$608$	−22647.4	−	6815.55i	−1.51064	−	0.454617i
$609$			373.745i			0.0248685i
$610$		0			0
$611$		−	6016.28i		−	0.398352i
$612$	3603.05	+	9740.06i	0.237982	+	0.643331i
$613$	−7796.28	+	7796.28i	−0.513685	+	0.513685i	−0.915653	−	0.401969i	$-0.868326\pi$
$613$	−7796.28	+	7796.28i	−0.513685	+	0.513685i	0.401969	+	0.915653i	$0.368326\pi$
$614$	451.969	−	2064.30i	0.0297068	−	0.135681i
$615$		0			0
$616$	7771.09	−	10294.2i	0.508289	−	0.673318i
$617$	−20235.1	−	20235.1i	−1.32031	−	1.32031i	−0.913521	−	0.406791i	$-0.866648\pi$
$617$	−20235.1	−	20235.1i	−1.32031	−	1.32031i	−0.406791	−	0.913521i	$-0.633352\pi$
$618$	371.739	+	580.150i	0.0241967	+	0.0377622i
$619$	22702.2			1.47411			0.737057	−	0.675830i	$-0.236215\pi$
$619$	22702.2			1.47411			0.737057	+	0.675830i	$0.236215\pi$
$620$		0			0
$621$	2821.13			0.182300
$622$	603.369	+	941.641i	0.0388953	+	0.0607015i
$623$	13799.7	+	13799.7i	0.887434	+	0.887434i
$624$	−846.741	−	987.875i	−0.0543218	−	0.0633760i
$625$		0			0
$626$	−688.397	+	3144.15i	−0.0439519	+	0.200744i
$627$	−1345.68	+	1345.68i	−0.0857120	+	0.0857120i
$628$	13808.7	−	5108.14i	0.877434	−	0.324581i
$629$		−	9185.76i		−	0.582289i
$630$		0			0
$631$		−	5787.42i		−	0.365125i	−0.983194	−	0.182562i	$-0.941561\pi$
$631$		−	5787.42i		−	0.365125i	0.983194	−	0.182562i	$-0.0584391\pi$
$632$	−697.106	−	4991.30i	−0.0438756	−	0.314151i
$633$	−720.464	+	720.464i	−0.0452383	+	0.0452383i
$634$	−14441.9	−	3161.98i	−0.904671	−	0.198073i
$635$		0			0
$636$	−498.140	+	1083.06i	−0.0310575	+	0.0675253i
$637$	−6720.13	−	6720.13i	−0.417993	−	0.417993i
$638$	8093.59	−	5186.08i	0.502239	−	0.321816i
$639$	−19931.2			−1.23391
$640$		0			0
$641$	8721.43			0.537404			0.268702	−	0.963223i	$-0.413405\pi$
$641$	8721.43			0.537404			0.268702	+	0.963223i	$0.413405\pi$
$642$	−831.658	+	532.895i	−0.0511260	+	0.0327597i
$643$	2937.61	+	2937.61i	0.180168	+	0.180168i	0.791429	−	0.611261i	$-0.209337\pi$
$643$	2937.61	+	2937.61i	0.180168	+	0.180168i	−0.611261	+	0.791429i	$0.709337\pi$
$644$	6849.45	−	14892.1i	0.419109	−	0.911229i
$645$		0			0
$646$	−17432.9	−	3816.84i	−1.06174	−	0.232464i
$647$	18130.5	−	18130.5i	1.10167	−	1.10167i	0.107465	−	0.994209i	$-0.465727\pi$
$647$	18130.5	−	18130.5i	1.10167	−	1.10167i	0.994209	−	0.107465i	$-0.0342733\pi$
$648$	−2251.60	−	16121.5i	−0.136499	−	0.977337i
$649$			7486.92i			0.452831i
$650$		0			0
$651$			1270.03i			0.0764614i
$652$	−15498.0	+	5733.05i	−0.930904	+	0.344361i
$653$	−14359.8	+	14359.8i	−0.860555	+	0.860555i	−0.991403	−	0.130847i	$-0.958230\pi$
$653$	−14359.8	+	14359.8i	−0.860555	+	0.860555i	0.130847	+	0.991403i	$0.458230\pi$
$654$	−141.806	+	647.677i	−0.00847866	+	0.0387251i
$655$		0			0
$656$	−6480.11	−	7560.20i	−0.385679	−	0.449964i
$657$	13893.0	+	13893.0i	0.824986	+	0.824986i
$658$	2098.96	+	3275.72i	0.124356	+	0.194074i
$659$	−14608.8			−0.863550			−0.431775	−	0.901981i	$-0.642113\pi$
$659$	−14608.8			−0.863550			−0.431775	+	0.901981i	$0.642113\pi$
$660$		0			0
$661$	−26434.7			−1.55551			−0.777755	−	0.628567i	$-0.783642\pi$
$661$	−26434.7			−1.55551			−0.777755	+	0.628567i	$0.783642\pi$
$662$	2119.22	+	3307.34i	0.124420	+	0.194175i
$663$	−694.207	−	694.207i	−0.0406648	−	0.0406648i
$664$	−15900.7	+	21063.3i	−0.929318	+	1.23104i
$665$		0			0
$666$	−3093.17	+	14127.6i	−0.179967	+	0.821973i
$667$	8638.26	−	8638.26i	0.501462	−	0.501462i
$668$	6502.62	+	17578.4i	0.376638	+	1.01816i
$669$		−	770.855i		−	0.0445485i
$670$		0			0
$671$		−	1752.69i		−	0.100837i
$672$	805.679	+	242.463i	0.0462496	+	0.0139185i
$673$	16012.9	−	16012.9i	0.917167	−	0.917167i	−0.0796554	−	0.996822i	$-0.525382\pi$
$673$	16012.9	−	16012.9i	0.917167	−	0.917167i	0.996822	+	0.0796554i	$0.0253820\pi$
$674$	10810.7	+	2366.95i	0.617824	+	0.135269i
$675$		0			0
$676$	−9323.26	−	4288.12i	−0.530454	−	0.243976i
$677$	5496.28	+	5496.28i	0.312023	+	0.312023i	0.845693	−	0.533670i	$-0.179188\pi$
$677$	5496.28	+	5496.28i	0.312023	+	0.312023i	−0.533670	+	0.845693i	$0.679188\pi$
$678$	−35.2312	+	22.5749i	−0.00199564	+	0.00127873i
$679$	3743.14			0.211559
$680$		0			0
$681$	325.799			0.0183328
$682$	27503.0	−	17622.9i	1.54420	−	0.989465i
$683$	−12875.9	−	12875.9i	−0.721351	−	0.721351i	0.247530	−	0.968880i	$-0.420381\pi$
$683$	−12875.9	−	12875.9i	−0.721351	−	0.721351i	−0.968880	+	0.247530i	$0.920381\pi$
$684$	25526.3	+	11740.5i	1.42694	+	0.656302i
$685$		0			0
$686$	18784.9	+	4112.85i	1.04549	+	0.228906i
$687$	856.792	−	856.792i	0.0475818	−	0.0475818i
$688$	−1551.89	+	20173.2i	−0.0859959	+	1.11787i
$689$			25506.5i			1.41033i
$690$		0			0
$691$			9091.60i			0.500522i	0.968178	+	0.250261i	$0.0805164\pi$
$691$			9091.60i			0.500522i	−0.968178	+	0.250261i	$0.919484\pi$
$692$	−6287.48	−	16996.8i	−0.345396	−	0.933702i
$693$	−10834.9	+	10834.9i	−0.593914	+	0.593914i
$694$	−1770.84	+	8088.07i	−0.0968592	+	0.442390i
$695$		0			0
$696$	500.462	+	377.800i	0.0272557	+	0.0205754i
$697$	−5312.76	−	5312.76i	−0.288716	−	0.288716i
$698$	−8811.88	−	13752.2i	−0.477843	−	0.745741i
$699$	808.504			0.0437488
$700$		0			0
$701$	19437.4			1.04728			0.523639	−	0.851941i	$-0.324574\pi$
$701$	19437.4			1.04728			0.523639	+	0.851941i	$0.324574\pi$
$702$	1671.53	+	2608.65i	0.0898685	+	0.140252i
$703$	−17573.0	−	17573.0i	−0.942786	−	0.942786i
$704$	−5928.95	−	20811.7i	−0.317409	−	1.11416i
$705$		0			0
$706$	6814.27	−	31123.2i	0.363255	−	1.65912i
$707$	−5671.76	+	5671.76i	−0.301709	+	0.301709i
$708$	−458.055	+	169.444i	−0.0243146	+	0.00899449i
$709$			10638.6i			0.563525i	0.959484	+	0.281763i	$0.0909190\pi$
$709$			10638.6i			0.563525i	−0.959484	+	0.281763i	$0.909081\pi$
$710$		0			0
$711$			5987.18i			0.315804i
$712$	32427.7	−	4529.00i	1.70685	−	0.238387i
$713$	29353.8	−	29353.8i	1.54181	−	1.54181i
$714$	620.173	+	135.784i	0.0325062	+	0.00711706i
$715$		0			0
$716$	−125.942	+	273.824i	−0.00657358	+	0.0142923i
$717$	−417.213	−	417.213i	−0.0217309	−	0.0217309i
$718$	14830.9	−	9503.10i	0.770870	−	0.493945i
$719$	−26377.6			−1.36818			−0.684089	−	0.729399i	$-0.739800\pi$
$719$	−26377.6			−1.36818			−0.684089	+	0.729399i	$0.739800\pi$
$720$		0			0
$721$	−9533.32			−0.492426
$722$	−24317.6	+	15581.8i	−1.25347	+	0.803180i
$723$	1412.61	+	1412.61i	0.0726632	+	0.0726632i
$724$	−4548.46	+	9889.29i	−0.233484	+	0.507642i
$725$		0			0
$726$	−433.584	−	94.9311i	−0.0221650	−	0.00485292i
$727$	−15452.7	+	15452.7i	−0.788321	+	0.788321i	−0.981219	−	0.192898i	$-0.938211\pi$
$727$	−15452.7	+	15452.7i	−0.788321	+	0.788321i	0.192898	+	0.981219i	$0.438211\pi$
$728$	17828.8	−	2490.04i	0.907663	−	0.126768i
$729$			19165.4i			0.973703i
$730$		0			0
$731$			15266.8i			0.772453i
$732$	107.230	−	39.6668i	0.00541441	−	0.00200291i
$733$	−628.566	+	628.566i	−0.0316734	+	0.0316734i	−0.722766	−	0.691093i	$-0.757130\pi$
$733$	−628.566	+	628.566i	−0.0316734	+	0.0316734i	0.691093	+	0.722766i	$0.257130\pi$
$734$	−2931.44	+	13388.9i	−0.147413	+	0.673290i
$735$		0			0
$736$	−13017.5	−	24225.4i	−0.651943	−	1.21326i
$737$	11062.7	+	11062.7i	0.552916	+	0.552916i
$738$	6381.99	+	9959.98i	0.318326	+	0.496791i
$739$	27295.7			1.35871			0.679356	−	0.733809i	$-0.262259\pi$
$739$	27295.7			1.35871			0.679356	+	0.733809i	$0.262259\pi$
$740$		0			0
$741$	−2656.14			−0.131681
$742$	−8898.68	−	13887.6i	−0.440271	−	0.687104i
$743$	−19570.2	−	19570.2i	−0.966300	−	0.966300i	0.0331505	−	0.999450i	$-0.489446\pi$
$743$	−19570.2	−	19570.2i	−0.966300	−	0.966300i	−0.999450	+	0.0331505i	$0.989446\pi$
$744$	1700.63	+	1283.81i	0.0838011	+	0.0632617i
$745$		0			0
$746$	3962.34	−	18097.4i	0.194466	−	0.888196i
$747$	22169.6	−	22169.6i	1.08587	−	1.08587i
$748$	−5665.06	−	15314.2i	−0.276918	−	0.748588i
$749$		−	13666.2i		−	0.666692i
$750$		0			0
$751$			23982.8i			1.16530i	0.812722	+	0.582652i	$0.197985\pi$
$751$			23982.8i			1.16530i	−0.812722	+	0.582652i	$0.802015\pi$
$752$	6508.07	+	500.655i	0.315591	+	0.0242779i
$753$	−497.249	+	497.249i	−0.0240648	+	0.0240648i
$754$	13105.8	+	2869.46i	0.633006	+	0.138594i
$755$		0			0
$756$	−1820.21	−	837.183i	−0.0875666	−	0.0402752i
$757$	8554.31	+	8554.31i	0.410716	+	0.410716i	0.881988	−	0.471272i	$-0.156205\pi$
$757$	8554.31	+	8554.31i	0.410716	+	0.410716i	−0.471272	+	0.881988i	$0.656205\pi$
$758$	25350.1	−	16243.4i	1.21472	−	0.778347i
$759$	−2212.93			−0.105829
$760$		0			0
$761$	32552.3			1.55062			0.775308	−	0.631583i	$-0.217594\pi$
$761$	32552.3			1.55062			0.775308	+	0.631583i	$0.217594\pi$
$762$	1453.80	−	931.542i	0.0691150	−	0.0442863i
$763$	−6486.59	−	6486.59i	−0.307772	−	0.307772i
$764$	26071.7	+	11991.4i	1.23461	+	0.567843i
$765$		0			0
$766$	−8991.08	−	1968.55i	−0.424100	−	0.0928547i
$767$	−7388.92	+	7388.92i	−0.347847	+	0.347847i
$768$	1139.09	−	833.748i	0.0535200	−	0.0391735i
$769$			1314.72i			0.0616516i	0.999525	+	0.0308258i	$0.00981371\pi$
$769$			1314.72i			0.0616516i	−0.999525	+	0.0308258i	$0.990186\pi$
$770$		0			0
$771$		−	369.016i		−	0.0172371i
$772$	14255.1	+	38535.6i	0.664577	+	1.79654i
$773$	−12385.8	+	12385.8i	−0.576307	+	0.576307i	−0.933884	−	0.357576i	$-0.883603\pi$
$773$	−12385.8	+	12385.8i	−0.576307	+	0.576307i	0.357576	+	0.933884i	$0.383603\pi$
$774$	5140.88	−	23480.2i	0.238740	−	1.09041i
$775$		0			0
$776$	3783.75	−	5012.23i	0.175037	−	0.231867i
$777$	625.159	+	625.159i	0.0288642	+	0.0288642i
$778$	8601.65	+	13424.1i	0.396381	+	0.618607i
$779$	−20327.4			−0.934922
$780$		0			0
$781$	31337.7			1.43579
$782$	−11195.6	−	17472.2i	−0.511959	−	0.798984i
$783$	−1055.82	−	1055.82i	−0.0481891	−	0.0481891i
$784$	7828.67	−	6710.22i	0.356627	−	0.305677i
$785$		0			0
$786$	−54.7779	+	250.190i	−0.00248583	+	0.0113537i
$787$	−25390.5	+	25390.5i	−1.15003	+	1.15003i	−0.163485	+	0.986546i	$0.552273\pi$
$787$	−25390.5	+	25390.5i	−1.15003	+	1.15003i	−0.986546	+	0.163485i	$0.947727\pi$
$788$	2501.92	−	925.514i	0.113106	−	0.0418402i
$789$		−	898.119i		−	0.0405245i
$790$		0			0
$791$		−	578.937i		−	0.0260235i
$792$	3555.96	+	25460.8i	0.159540	+	1.14231i
$793$	1729.74	−	1729.74i	0.0774590	−	0.0774590i
$794$	25550.9	+	5594.25i	1.14203	+	0.250041i
$795$		0			0
$796$	−9673.43	+	21032.0i	−0.430736	+	0.936508i
$797$	−22408.5	−	22408.5i	−0.995921	−	0.995921i	0.00407064	−	0.999992i	$-0.498704\pi$
$797$	−22408.5	−	22408.5i	−0.995921	−	0.995921i	−0.999992	+	0.00407064i	$0.998704\pi$
$798$	1446.20	−	926.671i	0.0641540	−	0.0411075i
$799$	4925.22			0.218075
$800$		0			0
$801$	−38897.9			−1.71584
$802$	14241.9	−	9125.68i	0.627056	−	0.401794i
$803$	−21843.8	−	21843.8i	−0.959964	−	0.959964i
$804$	−426.451	+	927.192i	−0.0187062	+	0.0406711i
$805$		0			0
$806$	44535.2	+	9750.75i	1.94626	+	0.426124i
$807$	1133.57	−	1133.57i	0.0494468	−	0.0494468i
$808$	1861.45	+	13328.0i	0.0810466	+	0.580296i
$809$		−	1556.16i		−	0.0676286i	−0.999428	−	0.0338143i	$-0.989235\pi$
$809$		−	1556.16i		−	0.0676286i	0.999428	−	0.0338143i	$-0.0107655\pi$
$810$		0			0
$811$			42796.7i			1.85302i	0.376274	+	0.926508i	$0.377205\pi$
$811$			42796.7i			1.85302i	−0.376274	+	0.926508i	$0.622795\pi$
$812$	−8136.90	+	3010.01i	−0.351662	+	0.130087i
$813$	−2079.54	+	2079.54i	−0.0897082	+	0.0897082i
$814$	4863.37	−	22212.8i	0.209412	−	0.956458i
$815$		0			0
$816$	808.723	−	693.183i	0.0346948	−	0.0297381i
$817$	29206.5	+	29206.5i	1.25068	+	1.25068i
$818$	7859.71	+	12266.2i	0.335952	+	0.524299i
$819$	−21386.1			−0.912441
$820$		0			0
$821$	−23614.4			−1.00384			−0.501918	−	0.864915i	$-0.667372\pi$
$821$	−23614.4			−1.00384			−0.501918	+	0.864915i	$0.667372\pi$
$822$	−931.598	−	1453.89i	−0.0395295	−	0.0616912i
$823$	23159.2	+	23159.2i	0.980897	+	0.980897i	0.999821	−	0.0189236i	$-0.00602393\pi$
$823$	23159.2	+	23159.2i	0.980897	+	0.980897i	−0.0189236	+	0.999821i	$0.506024\pi$
$824$	−9636.75	+	12765.5i	−0.407417	+	0.539695i
$825$		0			0
$826$	1445.24	−	6600.93i	0.0608793	−	0.278058i
$827$	10727.9	−	10727.9i	0.451083	−	0.451083i	−0.444631	−	0.895714i	$-0.646665\pi$
$827$	10727.9	−	10727.9i	0.451083	−	0.451083i	0.895714	+	0.444631i	$0.146665\pi$
$828$	11335.1	+	30642.1i	0.475753	+	1.28609i
$829$		−	19535.2i		−	0.818437i	−0.912436	−	0.409219i	$-0.865801\pi$
$829$		−	19535.2i		−	0.818437i	0.912436	−	0.409219i	$-0.134199\pi$
$830$		0			0
$831$		−	918.094i		−	0.0383253i
$832$	14687.9	−	26390.6i	0.612034	−	1.09968i
$833$	5501.43	−	5501.43i	0.228827	−	0.228827i
$834$	−1931.37	−	422.864i	−0.0801893	−	0.0175571i
$835$		0			0
$836$	−40134.9	−	18459.6i	−1.66040	−	0.763681i
$837$	−3587.81	−	3587.81i	−0.148164	−	0.148164i
$838$	−7336.50	+	4700.96i	−0.302429	+	0.193785i
$839$	25953.9			1.06797			0.533986	−	0.845493i	$-0.320693\pi$
$839$	25953.9			1.06797			0.533986	+	0.845493i	$0.320693\pi$
$840$		0			0
$841$	17923.2			0.734887
$842$	−13423.5	+	8601.27i	−0.549411	+	0.352042i
$843$	332.777	+	332.777i	0.0135960	+	0.0135960i
$844$	−21487.8	−	9883.04i	−0.876350	−	0.403067i
$845$		0			0
$846$	−7574.95	−	1658.50i	−0.307839	−	0.0673999i
$847$	4342.41	−	4342.41i	0.176159	−	0.176159i
$848$	−27591.4	−	2122.56i	−1.11733	−	0.0859541i
$849$		−	1109.24i		−	0.0448399i
$850$		0			0
$851$		−	28898.2i		−	1.16406i
$852$	709.236	+	1917.26i	0.0285188	+	0.0770943i
$853$	−18421.1	+	18421.1i	−0.739421	+	0.739421i	−0.972466	−	0.233045i	$-0.925131\pi$
$853$	−18421.1	+	18421.1i	−0.739421	+	0.739421i	0.233045	+	0.972466i	$0.425131\pi$
$854$	−338.330	+	1545.27i	−0.0135567	+	0.0619183i
$855$		0			0
$856$	−18299.7	−	13814.5i	−0.730689	−	0.551599i
$857$	−10613.8	−	10613.8i	−0.423060	−	0.423060i	0.463196	−	0.886256i	$-0.346703\pi$
$857$	−10613.8	−	10613.8i	−0.423060	−	0.423060i	−0.886256	+	0.463196i	$0.846703\pi$
$858$	−1311.17	−	2046.26i	−0.0521708	−	0.0814197i
$859$	−16534.0			−0.656732			−0.328366	−	0.944551i	$-0.606498\pi$
$859$	−16534.0			−0.656732			−0.328366	+	0.944551i	$0.606498\pi$
$860$		0			0
$861$	723.146			0.0286234
$862$	−19792.7	−	30889.3i	−0.782069	−	1.22053i
$863$	−3057.61	−	3057.61i	−0.120605	−	0.120605i	0.644228	−	0.764833i	$-0.277179\pi$
$863$	−3057.61	−	3057.61i	−0.120605	−	0.120605i	−0.764833	+	0.644228i	$0.777179\pi$
$864$	−2960.98	+	1591.08i	−0.116591	+	0.0626499i
$865$		0			0
$866$	−155.491	+	710.184i	−0.00610140	+	0.0278673i
$867$	−628.948	+	628.948i	−0.0246369	+	0.0246369i
$868$	−27650.1	+	10228.4i	−1.08123	+	0.399969i
$869$		−	9413.60i		−	0.367474i
$870$		0			0
$871$			21835.7i			0.849455i
$872$	−15242.8	+	2128.88i	−0.591957	+	0.0826753i
$873$	−5275.49	+	5275.49i	−0.204523	+	0.204523i
$874$	−54843.5	−	12007.7i	−2.12255	−	0.464722i
$875$		0			0
$876$	842.049	−	1830.79i	0.0324774	−	0.0706125i
$877$	−27748.3	−	27748.3i	−1.06841	−	1.06841i	−0.997482	−	0.0709256i	$-0.977405\pi$
$877$	−27748.3	−	27748.3i	−1.06841	−	1.06841i	−0.0709256	−	0.997482i	$-0.522595\pi$
$878$	13014.9	−	8339.48i	0.500264	−	0.320551i
$879$	−1393.71			−0.0534799
$880$		0			0
$881$	11660.4			0.445911			0.222955	−	0.974829i	$-0.428430\pi$
$881$	11660.4			0.445911			0.222955	+	0.974829i	$0.428430\pi$
$882$	−10313.7	+	6608.62i	−0.393741	+	0.252295i
$883$	15502.9	+	15502.9i	0.590844	+	0.590844i	0.937859	−	0.347016i	$-0.112805\pi$
$883$	15502.9	+	15502.9i	0.590844	+	0.590844i	−0.347016	+	0.937859i	$0.612805\pi$
$884$	9522.86	−	20704.7i	0.362317	−	0.787752i
$885$		0			0
$886$	19470.3	+	4262.93i	0.738282	+	0.161643i
$887$	4784.23	−	4784.23i	0.181103	−	0.181103i	−0.610733	−	0.791836i	$-0.709125\pi$
$887$	4784.23	−	4784.23i	0.181103	−	0.181103i	0.791836	+	0.610733i	$0.209125\pi$
$888$	1469.06	−	205.175i	0.0555162	−	0.00775363i
$889$			23889.6i			0.901272i
$890$		0			0
$891$		−	30405.3i		−	1.14323i
$892$	16782.5	−	6208.19i	0.629954	−	0.233033i
$893$	9422.30	−	9422.30i	0.353085	−	0.353085i
$894$	−623.951	+	2849.81i	−0.0233423	+	0.106613i
$895$		0			0
$896$	1209.93	+	19493.4i	0.0451128	+	0.726816i
$897$	−2183.96	−	2183.96i	−0.0812937	−	0.0812937i
$898$	−18135.6	−	28303.1i	−0.673934	−	1.05177i
$899$	−21971.7			−0.815124
$900$		0			0
$901$	−20880.8			−0.772077
$902$	−10034.4	−	15660.0i	−0.370407	−	0.578072i
$903$	−1039.02	−	1039.02i	−0.0382906	−	0.0382906i
$904$	−775.223	−	585.218i	−0.0285216	−	0.0215310i
$905$		0			0
$906$	−38.3822	+	175.305i	−0.00140747	+	0.00642840i
$907$	−27277.3	+	27277.3i	−0.998598	+	0.998598i	−0.999999	−	0.00140132i	$-0.999554\pi$
$907$	−27277.3	+	27277.3i	−0.998598	+	0.998598i	0.00140132	+	0.999999i	$0.499554\pi$
$908$	2623.87	+	7093.05i	0.0958989	+	0.259241i
$909$		−	15987.3i		−	0.583351i
$910$		0			0
$911$		−	37452.0i		−	1.36206i	−0.732254	−	0.681032i	$-0.761531\pi$
$911$		−	37452.0i		−	1.36206i	0.732254	−	0.681032i	$-0.238469\pi$
$912$	221.035	−	2873.25i	0.00802542	−	0.104323i
$913$	−34857.1	+	34857.1i	−1.26353	+	1.26353i
$914$	−5316.37	−	1163.99i	−0.192396	−	0.0421242i
$915$		0			0
$916$	25553.7	+	11753.1i	0.921746	+	0.423946i
$917$	−2505.69	−	2505.69i	−0.0902347	−	0.0902347i
$918$	−2135.57	+	1368.39i	−0.0767802	+	0.0491979i
$919$	7803.81			0.280113			0.140057	−	0.990144i	$-0.455272\pi$
$919$	7803.81			0.280113			0.140057	+	0.990144i	$0.455272\pi$
$920$		0			0
$921$	257.485			0.00921219
$922$	−19369.9	+	12411.5i	−0.691880	+	0.443331i
$923$	30927.5	+	30927.5i	1.10292	+	1.10292i
$924$	1427.80	+	656.698i	0.0508345	+	0.0233807i
$925$		0			0
$926$	7573.88	+	1658.26i	0.268783	+	0.0588487i
$927$	13436.0	−	13436.0i	0.476049	−	0.476049i
$928$	−4194.64	+	13938.3i	−0.148379	+	0.493048i
$929$		−	6045.30i		−	0.213498i	−0.994286	−	0.106749i	$-0.965956\pi$
$929$		−	6045.30i		−	0.213498i	0.994286	−	0.106749i	$-0.0340442\pi$
$930$		0			0
$931$		−	21049.2i		−	0.740989i
$932$	6511.41	+	17602.1i	0.228850	+	0.618645i
$933$	−96.3563	+	96.3563i	−0.00338110	+	0.00338110i
$934$	−7239.91	+	33067.2i	−0.253637	+	1.15845i
$935$		0			0
$936$	−21618.1	+	28636.9i	−0.754924	+	1.00003i
$937$	6094.14	+	6094.14i	0.212473	+	0.212473i	0.805317	−	0.592844i	$-0.201995\pi$
$937$	6094.14	+	6094.14i	0.212473	+	0.212473i	−0.592844	+	0.805317i	$0.701995\pi$
$938$	−7618.04	−	11889.0i	−0.265179	−	0.413849i
$939$	−392.178			−0.0136296
$940$		0			0
$941$	−11090.5			−0.384207			−0.192103	−	0.981375i	$-0.561531\pi$
$941$	−11090.5			−0.384207			−0.192103	+	0.981375i	$0.561531\pi$
$942$	967.864	+	1510.49i	0.0334763	+	0.0522445i
$943$	−16713.9	−	16713.9i	−0.577178	−	0.577178i
$944$	−7378.02	−	8607.79i	−0.254379	−	0.296779i
$945$		0			0
$946$	−8082.96	+	36917.8i	−0.277801	+	1.26882i
$947$	35216.3	−	35216.3i	1.20842	−	1.20842i	0.236886	−	0.971537i	$-0.423873\pi$
$947$	35216.3	−	35216.3i	1.20842	−	1.20842i	0.971537	−	0.236886i	$-0.0761268\pi$
$948$	575.930	−	213.049i	0.0197314	−	0.00729905i
$949$		−	43115.7i		−	1.47481i
$950$		0			0
$951$		−	1801.37i		−	0.0614233i
$952$	2038.47	+	14595.5i	0.0693984	+	0.496894i
$953$	28821.7	−	28821.7i	0.979670	−	0.979670i	−0.0201277	−	0.999797i	$-0.506407\pi$
$953$	28821.7	−	28821.7i	0.979670	−	0.979670i	0.999797	+	0.0201277i	$0.00640729\pi$
$954$	32114.5	+	7031.32i	1.08988	+	0.238624i
$955$		0			0
$956$	5723.16	−	12443.3i	0.193619	−	0.420968i
$957$	828.202	+	828.202i	0.0279749	+	0.0279749i
$958$	−18029.4	+	11552.6i	−0.608043	+	0.389611i
$959$	23891.0			0.804464
$960$		0			0
$961$	−44871.3			−1.50620
$962$	26721.7	−	17122.3i	0.895574	−	0.573851i
$963$	19260.9	+	19260.9i	0.644520	+	0.644520i
$964$	−19377.6	+	42130.9i	−0.647418	+	1.40762i
$965$		0			0
$966$	1951.06	+	427.174i	0.0649836	+	0.0142278i
$967$	−224.697	+	224.697i	−0.00747237	+	0.00747237i	−0.710833	−	0.703361i	$-0.751682\pi$
$967$	−224.697	+	224.697i	−0.00747237	+	0.00747237i	0.703361	+	0.710833i	$0.251682\pi$
$968$	−1425.16	−	10204.2i	−0.0473208	−	0.338818i
$969$		−	2174.44i		−	0.0720878i
$970$		0			0
$971$			1315.64i			0.0434818i	0.999764	+	0.0217409i	$0.00692089\pi$
$971$			1315.64i			0.0434818i	−0.999764	+	0.0217409i	$0.993079\pi$
$972$	5622.03	−	2079.71i	0.185521	−	0.0686283i
$973$	19343.0	−	19343.0i	0.637315	−	0.637315i
$974$	8129.46	−	37130.2i	0.267438	−	1.22149i
$975$		0			0
$976$	1727.19	+	2015.08i	0.0566456	+	0.0660872i
$977$	−2608.70	−	2608.70i	−0.0854246	−	0.0854246i	0.663103	−	0.748528i	$-0.269239\pi$
$977$	−2608.70	−	2608.70i	−0.0854246	−	0.0854246i	−0.748528	+	0.663103i	$0.769239\pi$
$978$	−1086.27	−	1695.27i	−0.0355164	−	0.0554283i
$979$	61158.8			1.99657
$980$		0			0
$981$	18284.1			0.595073
$982$	12494.8	+	19500.0i	0.406035	+	0.633675i
$983$	38327.7	+	38327.7i	1.24360	+	1.24360i	0.958495	+	0.285109i	$0.0920297\pi$
$983$	38327.7	+	38327.7i	1.24360	+	1.24360i	0.285109	+	0.958495i	$0.407970\pi$
$984$	730.992	−	968.326i	0.0236821	−	0.0313710i
$985$		0			0
$986$	−2349.08	+	10729.1i	−0.0758721	+	0.346535i
$987$	−335.198	+	335.198i	−0.0108100	+	0.0108100i
$988$	−21391.6	−	57827.4i	−0.688823	−	1.86208i
$989$			48029.1i			1.54422i
$990$		0			0
$991$			3912.43i			0.125411i	0.998032	+	0.0627055i	$0.0199729\pi$
$991$			3912.43i			0.125411i	−0.998032	+	0.0627055i	$0.980027\pi$
$992$	−14253.9	+	47364.1i	−0.456210	+	1.51594i
$993$	−338.434	+	338.434i	−0.0108156	+	0.0108156i
$994$	−27629.2	−	6049.29i	−0.881636	−	0.193030i
$995$		0			0
$996$	−2921.46	−	1343.69i	−0.0929419	−	0.0427475i
$997$	41715.2	+	41715.2i	1.32511	+	1.32511i	0.909579	+	0.415531i	$0.136404\pi$
$997$	41715.2	+	41715.2i	1.32511	+	1.32511i	0.415531	+	0.909579i	$0.363596\pi$
$998$	1023.42	−	655.767i	0.0324606	−	0.0207995i
$999$	−3532.13			−0.111863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.f.7.2	✓	24
4.3	odd	2	inner	100.4.e.f.7.8	yes	24
5.2	odd	4	inner	100.4.e.f.43.5	yes	24
5.3	odd	4	inner	100.4.e.f.43.8	yes	24
5.4	even	2	inner	100.4.e.f.7.11	yes	24
20.3	even	4	inner	100.4.e.f.43.2	yes	24
20.7	even	4	inner	100.4.e.f.43.11	yes	24
20.19	odd	2	inner	100.4.e.f.7.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.e.f.7.2	✓	24	1.1	even	1	trivial
100.4.e.f.7.5	yes	24	20.19	odd	2	inner
100.4.e.f.7.8	yes	24	4.3	odd	2	inner
100.4.e.f.7.11	yes	24	5.4	even	2	inner
100.4.e.f.43.2	yes	24	20.3	even	4	inner
100.4.e.f.43.5	yes	24	5.2	odd	4	inner
100.4.e.f.43.8	yes	24	5.3	odd	4	inner
100.4.e.f.43.11	yes	24	20.7	even	4	inner

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38148 + 1.52596i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(3.34287 - 7.26809i) q^{4} +(0.952213 + 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(3.12986 + 22.4099i) q^{8} -26.8812i q^{9} +O(q^{10})\)	\(q+(-2.38148 + 1.52596i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(3.34287 - 7.26809i) q^{4} +(0.952213 + 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(3.12986 + 22.4099i) q^{8} -26.8812i q^{9} +42.2652i q^{11} +(-2.58581 + 0.956545i) q^{12} +(-41.7119 + 41.7119i) q^{13} +(8.15866 - 37.2635i) q^{14} +(-41.6504 - 48.5926i) q^{16} +(-34.1474 - 34.1474i) q^{17} +(41.0198 + 64.0170i) q^{18} -130.653 q^{19} +4.64797 q^{21} +(-64.4951 - 100.654i) q^{22} +(-107.427 - 107.427i) q^{23} +(4.69839 - 6.22384i) q^{24} +(35.6852 - 162.987i) q^{26} +(-13.1304 + 13.1304i) q^{27} +(37.4331 + 101.192i) q^{28} +80.4104i q^{29} +273.244i q^{31} +(173.340 + 52.1653i) q^{32} +(10.2997 - 10.2997i) q^{33} +(133.429 + 29.2136i) q^{34} +(-195.375 - 89.8605i) q^{36} +(134.502 + 134.502i) q^{37} +(311.147 - 199.371i) q^{38} +20.3297 q^{39} +155.583 q^{41} +(-11.0690 + 7.09263i) q^{42} +(-223.543 - 223.543i) q^{43} +(307.187 + 141.287i) q^{44} +(419.765 + 91.9055i) q^{46} +(-72.1171 + 72.1171i) q^{47} +(-1.69177 + 21.9915i) q^{48} +161.108i q^{49} +16.6429i q^{51} +(163.728 + 442.604i) q^{52} +(305.746 - 305.746i) q^{53} +(11.2333 - 51.3064i) q^{54} +(-243.561 - 183.865i) q^{56} +(31.8391 + 31.8391i) q^{57} +(-122.703 - 191.496i) q^{58} +177.142 q^{59} -41.4688 q^{61} +(-416.960 - 650.725i) q^{62} +(256.354 + 256.354i) q^{63} +(-492.408 + 140.280i) q^{64} +(-8.81153 + 40.2454i) q^{66} +(261.744 - 261.744i) q^{67} +(-362.337 + 134.036i) q^{68} +52.3583i q^{69} -741.456i q^{71} +(602.406 - 84.1346i) q^{72} +(-516.828 + 516.828i) q^{73} +(-525.557 - 115.068i) q^{74} +(-436.756 + 949.597i) q^{76} +(-403.064 - 403.064i) q^{77} +(-48.4148 + 31.0224i) q^{78} -222.727 q^{79} -719.394 q^{81} +(-370.518 + 237.414i) q^{82} +(824.724 + 824.724i) q^{83} +(15.5376 - 33.7819i) q^{84} +(873.480 + 191.244i) q^{86} +(19.5954 - 19.5954i) q^{87} +(-947.158 + 132.284i) q^{88} -1447.03i q^{89} -795.576i q^{91} +(-1139.91 + 421.675i) q^{92} +(66.5874 - 66.5874i) q^{93} +(61.6973 - 281.793i) q^{94} +(-29.5293 - 54.9539i) q^{96} +(-196.252 - 196.252i) q^{97} +(-245.845 - 383.676i) q^{98} +1136.14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Introduction

L-functions

Modular forms

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