LMFDB - Embedded newform 100.4.e.f.43.2

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			43.2
Character	$\chi$	$=$	100.43
Dual form			100.4.e.f.7.2

$q$-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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.730167	−	0.683269i	$-0.760558\pi$
$3$	−0.243692	+	0.243692i	−0.0468986	+	0.0468986i	0.683269	+	0.730167i	$0.260558\pi$
$4$	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	0.401106	−	0.916032i	$-0.368626\pi$
$7$	−9.53656	−	9.53656i	−0.514926	−	0.514926i	−0.916032	+	0.401106i	$0.868626\pi$
$8$	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	$-0.803347\pi$
$11$		−	42.2652i		−	1.15849i	0.815152	−	0.579247i	$-0.196653\pi$
$12$	−2.58581	−	0.956545i	−0.0622049	−	0.0230109i
$13$	−41.7119	−	41.7119i	−0.889908	−	0.889908i	0.104606	−	0.994514i	$-0.466642\pi$
$13$	−41.7119	−	41.7119i	−0.889908	−	0.889908i	−0.994514	+	0.104606i	$0.966642\pi$
$14$	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	−0.907413	−	0.420239i	$-0.861946\pi$
$17$	−34.1474	+	34.1474i	−0.487174	+	0.487174i	0.420239	+	0.907413i	$0.361946\pi$
$18$	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	−0.999668	−	0.0257506i	$-0.991802\pi$
$23$	−107.427	+	107.427i	−0.973918	+	0.973918i	0.0257506	+	0.999668i	$0.491802\pi$
$24$	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	$-0.917119\pi$
$29$		−	80.4104i		−	0.514891i	0.966293	−	0.257446i	$-0.0828808\pi$
$30$		0			0
$31$		−	273.244i		−	1.58310i	−0.611105	−	0.791550i	$-0.709275\pi$
$31$		−	273.244i		−	1.58310i	0.611105	−	0.791550i	$-0.290725\pi$
$32$	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	−0.342059	−	0.939679i	$-0.611124\pi$
$37$	134.502	−	134.502i	0.597620	−	0.597620i	0.939679	+	0.342059i	$0.111124\pi$
$38$	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	−0.981947	−	0.189157i	$-0.939424\pi$
$43$	−223.543	+	223.543i	−0.792789	+	0.792789i	0.189157	+	0.981947i	$0.439424\pi$
$44$	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	0.586287	−	0.810103i	$-0.300589\pi$
$47$	−72.1171	−	72.1171i	−0.223816	−	0.223816i	−0.810103	+	0.586287i	$0.800589\pi$
$48$	−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	0.981884	−	0.189481i	$-0.0606806\pi$
$53$	305.746	+	305.746i	0.792403	+	0.792403i	−0.189481	+	0.981884i	$0.560681\pi$
$54$	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	0.904258	−	0.426987i	$-0.140425\pi$
$67$	261.744	+	261.744i	0.477271	+	0.477271i	−0.426987	+	0.904258i	$0.640425\pi$
$68$	−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	$0.212738\pi$
$71$			741.456i			1.23936i	−0.784854	+	0.619680i	$0.787262\pi$
$72$	602.406	+	84.1346i	0.986031	+	0.137713i
$73$	−516.828	−	516.828i	−0.828631	−	0.828631i	0.158696	−	0.987327i	$-0.449271\pi$
$73$	−516.828	−	516.828i	−0.828631	−	0.828631i	−0.987327	+	0.158696i	$0.949271\pi$
$74$	−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	0.0952072	−	0.995457i	$-0.469649\pi$
$83$	824.724	−	824.724i	1.09066	−	1.09066i	0.995457	−	0.0952072i	$-0.0303514\pi$
$84$	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	$0.330607\pi$
$89$			1447.03i			1.72342i	−0.507400	+	0.861711i	$0.669393\pi$
$90$		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	−0.802320	−	0.596894i	$-0.796401\pi$
$97$	−196.252	+	196.252i	−0.205426	+	0.205426i	0.596894	+	0.802320i	$0.296401\pi$
$98$	−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	−0.426388	−	0.904540i	$-0.640214\pi$
$103$	499.830	−	499.830i	0.478153	−	0.478153i	0.904540	+	0.426388i	$0.140214\pi$
$104$	−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	0.304989	−	0.952356i	$-0.401347\pi$
$107$	−716.517	−	716.517i	−0.647367	−	0.647367i	−0.952356	+	0.304989i	$0.901347\pi$
$108$	51.5398	−	139.327i	0.0459206	−	0.124136i
$109$		−	680.181i		−	0.597702i	−0.954300	−	0.298851i	$-0.903397\pi$
$109$		−	680.181i		−	0.597702i	0.954300	−	0.298851i	$-0.0966034\pi$
$110$		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	0.694359	−	0.719629i	$-0.255688\pi$
$113$	−30.3535	−	30.3535i	−0.0252692	−	0.0252692i	−0.719629	+	0.694359i	$0.755688\pi$
$114$	−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	0.993028	−	0.117880i	$-0.0376100\pi$
$127$	1252.53	+	1252.53i	0.875147	+	0.875147i	−0.117880	+	0.993028i	$0.537610\pi$
$128$	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	$-0.972074\pi$
$131$		−	262.746i		−	0.175238i	0.996154	−	0.0876192i	$-0.0279259\pi$
$132$	−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	−0.980024	−	0.198878i	$-0.936270\pi$
$137$	−1252.60	+	1252.60i	−0.781146	+	0.781146i	0.198878	+	0.980024i	$0.436270\pi$
$138$	−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	$-0.692434\pi$
$149$		−	2992.83i		−	1.64552i	0.568392	−	0.822758i	$-0.307566\pi$
$150$		0			0
$151$		−	184.103i		−	0.0992192i	−0.998769	−	0.0496096i	$-0.984202\pi$
$151$		−	184.103i		−	0.0992192i	0.998769	−	0.0496096i	$-0.0157977\pi$
$152$	−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	−0.294211	−	0.955741i	$-0.595057\pi$
$157$	1301.36	−	1301.36i	0.661530	−	0.661530i	0.955741	+	0.294211i	$0.0950568\pi$
$158$	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	−0.964806	−	0.262963i	$-0.915300\pi$
$163$	−1460.57	+	1460.57i	−0.701843	+	0.701843i	0.262963	+	0.964806i	$0.415300\pi$
$164$	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	0.210062	−	0.977688i	$-0.432633\pi$
$167$	−1656.63	−	1656.63i	−0.767626	−	0.767626i	−0.977688	+	0.210062i	$0.932633\pi$
$168$	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	0.965256	−	0.261304i	$-0.0841526\pi$
$173$	1601.81	+	1601.81i	0.703952	+	0.703952i	−0.261304	+	0.965256i	$0.584153\pi$
$174$	−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	$-0.762211\pi$
$191$		−	3587.14i		−	1.35893i	0.733706	−	0.679467i	$-0.237789\pi$
$192$	154.181	−	85.8108i	0.0579534	−	0.0322545i
$193$	−3631.68	−	3631.68i	−1.35448	−	1.35448i	−0.880582	−	0.473894i	$-0.842848\pi$
$193$	−3631.68	−	3631.68i	−1.35448	−	1.35448i	−0.473894	−	0.880582i	$-0.657152\pi$
$194$	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	−0.663183	−	0.748457i	$-0.730795\pi$
$197$	235.786	−	235.786i	0.0852746	−	0.0852746i	0.748457	+	0.663183i	$0.230795\pi$
$198$	−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	$0.160198\pi$
$211$			2956.45i			0.964599i	−0.876006	+	0.482300i	$0.839802\pi$
$212$	−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	−0.428565	−	0.903511i	$-0.640981\pi$
$223$	1581.62	−	1581.62i	0.474946	−	0.474946i	0.903511	+	0.428565i	$0.140981\pi$
$224$	−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	0.602595	−	0.798047i	$-0.294133\pi$
$227$	−668.464	−	668.464i	−0.195452	−	0.195452i	−0.798047	+	0.602595i	$0.794133\pi$
$228$	337.843	+	124.975i	0.0981325	+	0.0363013i
$229$		−	3515.88i		−	1.01457i	−0.861779	−	0.507284i	$-0.830650\pi$
$229$		−	3515.88i		−	1.01457i	0.861779	−	0.507284i	$-0.169350\pi$
$230$		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	0.434333	−	0.900752i	$-0.356984\pi$
$233$	−1658.86	−	1658.86i	−0.466420	−	0.466420i	−0.900752	+	0.434333i	$0.856984\pi$
$234$	−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	$0.0825897\pi$
$251$			2040.48i			0.513123i	−0.966528	+	0.256562i	$0.917410\pi$
$252$	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	−0.609227	−	0.792996i	$-0.708520\pi$
$257$	757.135	−	757.135i	0.183770	−	0.183770i	0.792996	+	0.609227i	$0.208520\pi$
$258$	−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	−0.457279	−	0.889323i	$-0.651176\pi$
$263$	1842.73	−	1842.73i	0.432045	−	0.432045i	0.889323	+	0.457279i	$0.151176\pi$
$264$	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	$-0.823254\pi$
$269$		−	4651.65i		−	1.05433i	0.849762	−	0.527167i	$-0.176746\pi$
$270$		0			0
$271$			8533.48i			1.91281i	0.292040	+	0.956406i	$0.405666\pi$
$271$			8533.48i			1.91281i	−0.292040	+	0.956406i	$0.594334\pi$
$272$	−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	−0.472652	−	0.881249i	$-0.656703\pi$
$277$	1883.72	−	1883.72i	0.408598	−	0.408598i	0.881249	+	0.472652i	$0.156703\pi$
$278$	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	−0.426456	−	0.904508i	$-0.640238\pi$
$283$	2275.91	−	2275.91i	0.478052	−	0.478052i	0.904508	+	0.426456i	$0.140238\pi$
$284$	−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	0.932175	−	0.362009i	$-0.117909\pi$
$293$	2859.58	+	2859.58i	0.570165	+	0.570165i	−0.362009	+	0.932175i	$0.617909\pi$
$294$	−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	0.656293	−	0.754507i	$-0.272124\pi$
$307$	−528.300	−	528.300i	−0.0982139	−	0.0982139i	−0.754507	+	0.656293i	$0.772124\pi$
$308$	−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	$0.0114766\pi$
$311$			395.402i			0.0720938i	−0.999350	+	0.0360469i	$0.988523\pi$
$312$	63.6293	−	455.587i	0.0115458	−	0.0826684i
$313$	804.658	+	804.658i	0.145310	+	0.145310i	0.776019	−	0.630709i	$-0.217236\pi$
$313$	804.658	+	804.658i	0.145310	+	0.145310i	−0.630709	+	0.776019i	$0.717236\pi$
$314$	−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	−0.299305	−	0.954157i	$-0.596755\pi$
$317$	3696.00	−	3696.00i	0.654852	−	0.654852i	0.954157	+	0.299305i	$0.0967549\pi$
$318$	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	$0.0367856\pi$
$331$			1388.78i			0.230617i	−0.993330	+	0.115308i	$0.963214\pi$
$332$	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	−0.894428	−	0.447212i	$-0.852417\pi$
$337$	−2766.70	+	2766.70i	−0.447216	+	0.447216i	0.447212	+	0.894428i	$0.352417\pi$
$338$	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	0.848854	−	0.528627i	$-0.177293\pi$
$347$	2069.91	+	2069.91i	0.320227	+	0.320227i	−0.528627	+	0.848854i	$0.677293\pi$
$348$	−76.9162	+	207.926i	−0.0118481	+	0.0320288i
$349$		−	5774.64i		−	0.885700i	−0.896596	−	0.442850i	$-0.853967\pi$
$349$		−	5774.64i		−	0.885700i	0.896596	−	0.442850i	$-0.146033\pi$
$350$		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	−0.973874	−	0.227089i	$-0.927079\pi$
$353$	−7965.11	−	7965.11i	−1.20096	−	1.20096i	−0.227089	−	0.973874i	$-0.572921\pi$
$354$	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	0.907474	−	0.420109i	$-0.138008\pi$
$367$	3426.52	+	3426.52i	0.487365	+	0.487365i	−0.420109	+	0.907474i	$0.638008\pi$
$368$	−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	0.308347	−	0.951274i	$-0.400224\pi$
$373$	−4631.53	−	4631.53i	−0.642926	−	0.642926i	−0.951274	+	0.308347i	$0.900224\pi$
$374$	−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	−0.536752	−	0.843740i	$-0.680349\pi$
$383$	2301.02	−	2301.02i	0.306988	−	0.306988i	0.843740	+	0.536752i	$0.180349\pi$
$384$	−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	$0.119736\pi$
$389$			5636.87i			0.734706i	−0.930082	+	0.367353i	$0.880264\pi$
$390$		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	−0.987054	−	0.160391i	$-0.948725\pi$
$397$	−6539.04	+	6539.04i	−0.826663	+	0.826663i	0.160391	+	0.987054i	$0.448725\pi$
$398$	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	$0.100781\pi$
$409$			5150.66i			0.622698i	−0.950296	+	0.311349i	$0.899219\pi$
$410$		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	$-0.741934\pi$
$431$		−	12970.7i		−	1.44959i	0.688963	−	0.724797i	$-0.258066\pi$
$432$	1184.93	−	91.1547i	0.131968	−	0.0101520i
$433$	181.752	+	181.752i	0.0201719	+	0.0201719i	0.717121	−	0.696949i	$-0.245460\pi$
$433$	181.752	+	181.752i	0.0201719	+	0.0201719i	−0.696949	+	0.717121i	$0.745460\pi$
$434$	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	−0.921882	−	0.387472i	$-0.873349\pi$
$443$	−4982.88	+	4982.88i	−0.534410	+	0.534410i	0.387472	+	0.921882i	$0.373349\pi$
$444$	−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	$-0.785270\pi$
$449$		−	11884.7i		−	1.24916i	0.780960	−	0.624581i	$-0.214730\pi$
$450$		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	−0.634036	−	0.773303i	$-0.718603\pi$
$457$	1360.58	−	1360.58i	0.139267	−	0.139267i	0.773303	+	0.634036i	$0.218603\pi$
$458$	−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	−0.797663	−	0.603103i	$-0.793931\pi$
$463$	−1938.32	+	1938.32i	−0.194560	+	0.194560i	0.603103	+	0.797663i	$0.293931\pi$
$464$	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	0.988668	−	0.150116i	$-0.0479648\pi$
$467$	8462.63	+	8462.63i	0.838552	+	0.838552i	−0.150116	+	0.988668i	$0.547965\pi$
$468$	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	0.109776	−	0.993956i	$-0.464987\pi$
$487$	−9502.42	−	9502.42i	−0.884181	−	0.884181i	−0.993956	+	0.109776i	$0.964987\pi$
$488$	−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	$0.122804\pi$
$491$			8188.17i			0.752601i	−0.926498	+	0.376300i	$0.877196\pi$
$492$	−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	−0.975313	−	0.220829i	$-0.929124\pi$
$503$	−8511.42	+	8511.42i	−0.754484	+	0.754484i	0.220829	+	0.975313i	$0.429124\pi$
$504$	−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	$0.0523802\pi$
$509$			3762.37i			0.327631i	−0.986491	+	0.163816i	$0.947620\pi$
$510$		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	0.297227	−	0.954807i	$-0.403938\pi$
$523$	14975.1	−	14975.1i	1.25203	−	1.25203i	0.954807	−	0.297227i	$-0.0960618\pi$
$524$	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	0.948447	−	0.316935i	$-0.102654\pi$
$547$	8079.10	+	8079.10i	0.631513	+	0.631513i	−0.316935	+	0.948447i	$0.602654\pi$
$548$	−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	−0.995884	−	0.0906404i	$-0.971109\pi$
$557$	−11900.0	+	11900.0i	−0.905243	+	0.905243i	0.0906404	+	0.995884i	$0.471109\pi$
$558$	−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	−0.113959	−	0.993485i	$-0.536353\pi$
$563$	11749.3	−	11749.3i	0.879526	−	0.879526i	0.993485	+	0.113959i	$0.0363533\pi$
$564$	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	$0.0254998\pi$
$569$			2172.30i			0.160049i	−0.996793	+	0.0800243i	$0.974500\pi$
$570$		0			0
$571$			5608.37i			0.411039i	0.978653	+	0.205519i	$0.0658884\pi$
$571$			5608.37i			0.411039i	−0.978653	+	0.205519i	$0.934112\pi$
$572$	−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	0.231010	−	0.972951i	$-0.425797\pi$
$577$	16686.9	−	16686.9i	1.20396	−	1.20396i	0.972951	−	0.231010i	$-0.0742029\pi$
$578$	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	−0.832749	−	0.553650i	$-0.813234\pi$
$587$	−19717.2	−	19717.2i	−1.38640	−	1.38640i	−0.553650	−	0.832749i	$-0.686766\pi$
$588$	−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	0.712907	−	0.701259i	$-0.247378\pi$
$593$	168.200	+	168.200i	0.0116478	+	0.0116478i	−0.701259	+	0.712907i	$0.747378\pi$
$594$	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	0.178294	−	0.983977i	$-0.442942\pi$
$607$	−12048.9	−	12048.9i	−0.805683	−	0.805683i	−0.983977	+	0.178294i	$0.942942\pi$
$608$	−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	0.401969	−	0.915653i	$-0.368326\pi$
$613$	−7796.28	−	7796.28i	−0.513685	−	0.513685i	−0.915653	+	0.401969i	$0.868326\pi$
$614$	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	−0.406791	+	0.913521i	$0.633352\pi$
$617$	−20235.1	+	20235.1i	−1.32031	+	1.32031i	−0.913521	+	0.406791i	$0.866648\pi$
$618$	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	$0.0584391\pi$
$631$			5787.42i			0.365125i	−0.983194	+	0.182562i	$0.941561\pi$
$632$	−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	−0.611261	−	0.791429i	$-0.709337\pi$
$643$	2937.61	−	2937.61i	0.180168	−	0.180168i	0.791429	+	0.611261i	$0.209337\pi$
$644$	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	0.994209	+	0.107465i	$0.0342733\pi$
$647$	18130.5	+	18130.5i	1.10167	+	1.10167i	0.107465	+	0.994209i	$0.465727\pi$
$648$	−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	0.130847	−	0.991403i	$-0.458230\pi$
$653$	−14359.8	−	14359.8i	−0.860555	−	0.860555i	−0.991403	+	0.130847i	$0.958230\pi$
$654$	−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	0.996822	−	0.0796554i	$-0.0253820\pi$
$673$	16012.9	+	16012.9i	0.917167	+	0.917167i	−0.0796554	+	0.996822i	$0.525382\pi$
$674$	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	−0.533670	−	0.845693i	$-0.679188\pi$
$677$	5496.28	−	5496.28i	0.312023	−	0.312023i	0.845693	+	0.533670i	$0.179188\pi$
$678$	−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	−0.968880	−	0.247530i	$-0.920381\pi$
$683$	−12875.9	+	12875.9i	−0.721351	+	0.721351i	0.247530	+	0.968880i	$0.420381\pi$
$684$	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	$-0.919484\pi$
$691$		−	9091.60i		−	0.500522i	0.968178	−	0.250261i	$-0.0805164\pi$
$692$	−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	$-0.909081\pi$
$709$		−	10638.6i		−	0.563525i	0.959484	−	0.281763i	$-0.0909190\pi$
$710$		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	0.192898	−	0.981219i	$-0.438211\pi$
$727$	−15452.7	−	15452.7i	−0.788321	−	0.788321i	−0.981219	+	0.192898i	$0.938211\pi$
$728$	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	0.691093	−	0.722766i	$-0.257130\pi$
$733$	−628.566	−	628.566i	−0.0316734	−	0.0316734i	−0.722766	+	0.691093i	$0.757130\pi$
$734$	−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	−0.999450	−	0.0331505i	$-0.989446\pi$
$743$	−19570.2	+	19570.2i	−0.966300	+	0.966300i	0.0331505	+	0.999450i	$0.489446\pi$
$744$	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	$-0.802015\pi$
$751$		−	23982.8i		−	1.16530i	0.812722	−	0.582652i	$-0.197985\pi$
$752$	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	−0.471272	−	0.881988i	$-0.656205\pi$
$757$	8554.31	−	8554.31i	0.410716	−	0.410716i	0.881988	+	0.471272i	$0.156205\pi$
$758$	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	$-0.990186\pi$
$769$		−	1314.72i		−	0.0616516i	0.999525	−	0.0308258i	$-0.00981371\pi$
$770$		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	0.357576	−	0.933884i	$-0.383603\pi$
$773$	−12385.8	−	12385.8i	−0.576307	−	0.576307i	−0.933884	+	0.357576i	$0.883603\pi$
$774$	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	−0.986546	−	0.163485i	$-0.947727\pi$
$787$	−25390.5	−	25390.5i	−1.15003	−	1.15003i	−0.163485	−	0.986546i	$-0.552273\pi$
$788$	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	−0.999992	−	0.00407064i	$-0.998704\pi$
$797$	−22408.5	+	22408.5i	−0.995921	+	0.995921i	0.00407064	+	0.999992i	$0.498704\pi$
$798$	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	$0.0107655\pi$
$809$			1556.16i			0.0676286i	−0.999428	+	0.0338143i	$0.989235\pi$
$810$		0			0
$811$		−	42796.7i		−	1.85302i	−0.376274	−	0.926508i	$-0.622795\pi$
$811$		−	42796.7i		−	1.85302i	0.376274	−	0.926508i	$-0.377205\pi$
$812$	−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	−0.0189236	−	0.999821i	$-0.506024\pi$
$823$	23159.2	−	23159.2i	0.980897	−	0.980897i	0.999821	+	0.0189236i	$0.00602393\pi$
$824$	−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	0.895714	−	0.444631i	$-0.146665\pi$
$827$	10727.9	+	10727.9i	0.451083	+	0.451083i	−0.444631	+	0.895714i	$0.646665\pi$
$828$	11335.1	−	30642.1i	0.475753	−	1.28609i
$829$			19535.2i			0.818437i	0.912436	+	0.409219i	$0.134199\pi$
$829$			19535.2i			0.818437i	−0.912436	+	0.409219i	$0.865801\pi$
$830$		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	0.233045	−	0.972466i	$-0.425131\pi$
$853$	−18421.1	−	18421.1i	−0.739421	−	0.739421i	−0.972466	+	0.233045i	$0.925131\pi$
$854$	−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	−0.886256	−	0.463196i	$-0.846703\pi$
$857$	−10613.8	+	10613.8i	−0.423060	+	0.423060i	0.463196	+	0.886256i	$0.346703\pi$
$858$	−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	−0.764833	−	0.644228i	$-0.777179\pi$
$863$	−3057.61	+	3057.61i	−0.120605	+	0.120605i	0.644228	+	0.764833i	$0.277179\pi$
$864$	−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	−0.0709256	+	0.997482i	$0.522595\pi$
$877$	−27748.3	+	27748.3i	−1.06841	+	1.06841i	−0.997482	+	0.0709256i	$0.977405\pi$
$878$	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	−0.347016	−	0.937859i	$-0.612805\pi$
$883$	15502.9	−	15502.9i	0.590844	−	0.590844i	0.937859	+	0.347016i	$0.112805\pi$
$884$	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	0.791836	−	0.610733i	$-0.209125\pi$
$887$	4784.23	+	4784.23i	0.181103	+	0.181103i	−0.610733	+	0.791836i	$0.709125\pi$
$888$	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	0.00140132	−	0.999999i	$-0.499554\pi$
$907$	−27277.3	−	27277.3i	−0.998598	−	0.998598i	−0.999999	+	0.00140132i	$0.999554\pi$
$908$	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	$0.238469\pi$
$911$			37452.0i			1.36206i	−0.732254	+	0.681032i	$0.761531\pi$
$912$	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	$0.0340442\pi$
$929$			6045.30i			0.213498i	−0.994286	+	0.106749i	$0.965956\pi$
$930$		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	−0.592844	−	0.805317i	$-0.701995\pi$
$937$	6094.14	−	6094.14i	0.212473	−	0.212473i	0.805317	+	0.592844i	$0.201995\pi$
$938$	−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	0.971537	+	0.236886i	$0.0761268\pi$
$947$	35216.3	+	35216.3i	1.20842	+	1.20842i	0.236886	+	0.971537i	$0.423873\pi$
$948$	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	0.999797	−	0.0201277i	$-0.00640729\pi$
$953$	28821.7	+	28821.7i	0.979670	+	0.979670i	−0.0201277	+	0.999797i	$0.506407\pi$
$954$	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	0.703361	−	0.710833i	$-0.251682\pi$
$967$	−224.697	−	224.697i	−0.00747237	−	0.00747237i	−0.710833	+	0.703361i	$0.751682\pi$
$968$	−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	$-0.993079\pi$
$971$		−	1315.64i		−	0.0434818i	0.999764	−	0.0217409i	$-0.00692089\pi$
$972$	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	−0.748528	−	0.663103i	$-0.769239\pi$
$977$	−2608.70	+	2608.70i	−0.0854246	+	0.0854246i	0.663103	+	0.748528i	$0.269239\pi$
$978$	−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	0.285109	−	0.958495i	$-0.407970\pi$
$983$	38327.7	−	38327.7i	1.24360	−	1.24360i	0.958495	−	0.285109i	$-0.0920297\pi$
$984$	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	$-0.980027\pi$
$991$		−	3912.43i		−	0.125411i	0.998032	−	0.0627055i	$-0.0199729\pi$
$992$	−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	0.415531	−	0.909579i	$-0.363596\pi$
$997$	41715.2	−	41715.2i	1.32511	−	1.32511i	0.909579	−	0.415531i	$-0.136404\pi$
$998$	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.43.2	yes	24
4.3	odd	2	inner	100.4.e.f.43.8	yes	24
5.2	odd	4	inner	100.4.e.f.7.8	yes	24
5.3	odd	4	inner	100.4.e.f.7.5	yes	24
5.4	even	2	inner	100.4.e.f.43.11	yes	24
20.3	even	4	inner	100.4.e.f.7.11	yes	24
20.7	even	4	inner	100.4.e.f.7.2	✓	24
20.19	odd	2	inner	100.4.e.f.43.5	yes	24

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