LMFDB - Embedded newform 100.4.e.e.43.4

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$1.76129 - 0.947553i$ of defining polynomial
Character	$\chi$	$=$	100.43
Dual form			100.4.e.e.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.813737 + 2.70884i) q^{2} +(-2.61822 + 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 - 17.7783i) q^{7} +(-17.3744 - 14.4959i) q^{8} +13.2899i q^{9} +O(q^{10})$	\(q+(0.813737 + 2.70884i) q^{2} +(-2.61822 + 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 - 17.7783i) q^{7} +(-17.3744 - 14.4959i) q^{8} +13.2899i q^{9} -7.37590i q^{11} +(5.93575 - 29.0210i) q^{12} +(2.68249 + 2.68249i) q^{13} +(33.6917 - 62.6254i) q^{14} +(25.1290 - 58.8603i) q^{16} +(20.2367 - 20.2367i) q^{17} +(-36.0001 + 10.8144i) q^{18} -135.808 q^{19} +93.0948 q^{21} +(19.9802 - 6.00204i) q^{22} +(-71.0426 + 71.0426i) q^{23} +(83.4434 - 7.53642i) q^{24} +(-5.08361 + 9.44930i) q^{26} +(-105.488 - 105.488i) q^{27} +(197.059 + 40.3050i) q^{28} +34.2890i q^{29} +187.974i q^{31} +(179.892 + 20.1737i) q^{32} +(19.3117 + 19.3117i) q^{33} +(71.2855 + 38.3507i) q^{34} +(-58.5893 - 88.7186i) q^{36} +(-250.679 + 250.679i) q^{37} +(-110.512 - 367.882i) q^{38} -14.0467 q^{39} -211.105 q^{41} +(75.7547 + 252.179i) q^{42} +(46.7326 - 46.7326i) q^{43} +(32.5172 + 49.2390i) q^{44} +(-250.253 - 134.633i) q^{46} +(189.707 + 189.707i) q^{47} +(88.3159 + 219.902i) q^{48} +289.134i q^{49} +105.968i q^{51} +(-29.7334 - 6.08147i) q^{52} +(74.5742 + 74.5742i) q^{53} +(199.910 - 371.589i) q^{54} +(51.1739 + 566.598i) q^{56} +(355.575 - 355.575i) q^{57} +(-92.8835 + 27.9022i) q^{58} -101.072 q^{59} +232.112 q^{61} +(-509.191 + 152.961i) q^{62} +(236.271 - 236.271i) q^{63} +(91.7370 + 503.715i) q^{64} +(-36.5978 + 68.0271i) q^{66} +(-34.7419 - 34.7419i) q^{67} +(-45.8785 + 224.309i) q^{68} -372.010i q^{69} -614.600i q^{71} +(192.649 - 230.903i) q^{72} +(37.4378 + 37.4378i) q^{73} +(-883.036 - 475.063i) q^{74} +(906.607 - 598.718i) q^{76} +(-131.131 + 131.131i) q^{77} +(-11.4303 - 38.0504i) q^{78} +1002.91 q^{79} +193.554 q^{81} +(-171.784 - 571.850i) q^{82} +(-423.190 + 423.190i) q^{83} +(-621.470 + 410.415i) q^{84} +(164.619 + 88.5632i) q^{86} +(-89.7761 - 89.7761i) q^{87} +(-106.920 + 128.152i) q^{88} -1049.38i q^{89} -95.3802i q^{91} +(161.060 - 787.453i) q^{92} +(-492.156 - 492.156i) q^{93} +(-359.514 + 668.257i) q^{94} +(-523.815 + 418.177i) q^{96} +(536.526 - 536.526i) q^{97} +(-783.218 + 235.279i) q^{98} +98.0246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

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 $

$2$	0.813737	+	2.70884i	0.287699	+	0.957721i
$2$	0.813737	+	2.70884i	0.287699	+	0.957721i
$3$	−2.61822	+	2.61822i	−0.503877	+	0.503877i	−0.912640	−	0.408764i	$-0.865960\pi$
$3$	−2.61822	+	2.61822i	−0.503877	+	0.503877i	0.408764	+	0.912640i	$0.365960\pi$
$4$	−6.67566	+	4.40857i	−0.834458	+	0.551071i
$5$		0			0
$5$		0			0
$6$	−9.22289	−	4.96181i	−0.627538	−	0.337608i
$7$	−17.7783	−	17.7783i	−0.959936	−	0.959936i	0.0392914	−	0.999228i	$-0.487490\pi$
$7$	−17.7783	−	17.7783i	−0.959936	−	0.959936i	−0.999228	+	0.0392914i	$0.987490\pi$
$8$	−17.3744	−	14.4959i	−0.767846	−	0.640635i
$9$			13.2899i			0.492217i
$10$		0			0
$11$		−	7.37590i		−	0.202174i	−0.994878	−	0.101087i	$-0.967768\pi$
$11$		−	7.37590i		−	0.202174i	0.994878	−	0.101087i	$-0.0322321\pi$
$12$	5.93575	−	29.0210i	0.142792	−	0.698136i
$13$	2.68249	+	2.68249i	0.0572300	+	0.0572300i	0.735143	−	0.677913i	$-0.237115\pi$
$13$	2.68249	+	2.68249i	0.0572300	+	0.0572300i	−0.677913	+	0.735143i	$0.737115\pi$
$14$	33.6917	−	62.6254i	0.643178	−	1.19552i
$15$		0			0
$16$	25.1290	−	58.8603i	0.392641	−	0.919692i
$17$	20.2367	−	20.2367i	0.288713	−	0.288713i	−0.547858	−	0.836571i	$-0.684557\pi$
$17$	20.2367	−	20.2367i	0.288713	−	0.288713i	0.836571	+	0.547858i	$0.184557\pi$
$18$	−36.0001	+	10.8144i	−0.471406	+	0.141610i
$19$	−135.808			−1.63981			−0.819906	−	0.572498i	$-0.805975\pi$
$19$	−135.808			−1.63981			−0.819906	+	0.572498i	$0.805975\pi$
$20$		0			0
$21$	93.0948			0.967379
$22$	19.9802	−	6.00204i	0.193627	−	0.0581654i
$23$	−71.0426	+	71.0426i	−0.644061	+	0.644061i	−0.951551	−	0.307490i	$-0.900511\pi$
$23$	−71.0426	+	71.0426i	−0.644061	+	0.644061i	0.307490	+	0.951551i	$0.400511\pi$
$24$	83.4434	−	7.53642i	0.709700	−	0.0640985i
$25$		0			0
$26$	−5.08361	+	9.44930i	−0.0383453	+	0.0712754i
$27$	−105.488	−	105.488i	−0.751893	−	0.751893i
$28$	197.059	+	40.3050i	1.33002	+	0.272033i
$29$			34.2890i			0.219562i	0.993956	+	0.109781i	$0.0350150\pi$
$29$			34.2890i			0.219562i	−0.993956	+	0.109781i	$0.964985\pi$
$30$		0			0
$31$			187.974i			1.08907i	0.838739	+	0.544533i	$0.183293\pi$
$31$			187.974i			1.08907i	−0.838739	+	0.544533i	$0.816707\pi$
$32$	179.892	+	20.1737i	0.993771	+	0.111445i
$33$	19.3117	+	19.3117i	0.101871	+	0.101871i
$34$	71.2855	+	38.3507i	0.359569	+	0.193444i
$35$		0			0
$36$	−58.5893	−	88.7186i	−0.271247	−	0.410734i
$37$	−250.679	+	250.679i	−1.11382	+	1.11382i	−0.121190	+	0.992629i	$0.538671\pi$
$37$	−250.679	+	250.679i	−1.11382	+	1.11382i	−0.992629	+	0.121190i	$0.961329\pi$
$38$	−110.512	−	367.882i	−0.471773	−	1.57048i
$39$	−14.0467			−0.0576737
$40$		0			0
$41$	−211.105			−0.804122			−0.402061	−	0.915613i	$-0.631706\pi$
$41$	−211.105			−0.804122			−0.402061	+	0.915613i	$0.631706\pi$
$42$	75.7547	+	252.179i	0.278314	+	0.926479i
$43$	46.7326	−	46.7326i	0.165736	−	0.165736i	−0.619366	−	0.785102i	$-0.712610\pi$
$43$	46.7326	−	46.7326i	0.165736	−	0.165736i	0.785102	+	0.619366i	$0.212610\pi$
$44$	32.5172	+	49.2390i	0.111412	+	0.168706i
$45$		0			0
$46$	−250.253	−	134.633i	−0.802126	−	0.431535i
$47$	189.707	+	189.707i	0.588757	+	0.588757i	0.937295	−	0.348538i	$-0.113322\pi$
$47$	189.707	+	189.707i	0.588757	+	0.588757i	−0.348538	+	0.937295i	$0.613322\pi$
$48$	88.3159	+	219.902i	0.265569	+	0.661254i
$49$			289.134i			0.842956i
$50$		0			0
$51$			105.968i			0.290952i
$52$	−29.7334	−	6.08147i	−0.0792939	−	0.0162182i
$53$	74.5742	+	74.5742i	0.193275	+	0.193275i	0.797109	−	0.603835i	$-0.206361\pi$
$53$	74.5742	+	74.5742i	0.193275	+	0.193275i	−0.603835	+	0.797109i	$0.706361\pi$
$54$	199.910	−	371.589i	0.503784	−	0.936423i
$55$		0			0
$56$	51.1739	+	566.598i	0.122114	+	1.35205i
$57$	355.575	−	355.575i	0.826263	−	0.826263i
$58$	−92.8835	+	27.9022i	−0.210279	+	0.0631679i
$59$	−101.072			−0.223024			−0.111512	−	0.993763i	$-0.535569\pi$
$59$	−101.072			−0.223024			−0.111512	+	0.993763i	$0.535569\pi$
$60$		0			0
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	−509.191	+	152.961i	−1.04302	+	0.313324i
$63$	236.271	−	236.271i	0.472497	−	0.472497i
$64$	91.7370	+	503.715i	0.179174	+	0.983817i
$65$		0			0
$66$	−36.5978	+	68.0271i	−0.0682557	+	0.126872i
$67$	−34.7419	−	34.7419i	−0.0633493	−	0.0633493i	0.674722	−	0.738072i	$-0.264263\pi$
$67$	−34.7419	−	34.7419i	−0.0633493	−	0.0633493i	−0.738072	+	0.674722i	$0.764263\pi$
$68$	−45.8785	+	224.309i	−0.0818175	+	0.400021i
$69$		−	372.010i		−	0.649054i
$70$		0			0
$71$		−	614.600i		−	1.02732i	−0.857994	−	0.513660i	$-0.828289\pi$
$71$		−	614.600i		−	1.02732i	0.857994	−	0.513660i	$-0.171711\pi$
$72$	192.649	−	230.903i	0.315331	−	0.377946i
$73$	37.4378	+	37.4378i	0.0600242	+	0.0600242i	0.736482	−	0.676457i	$-0.236486\pi$
$73$	37.4378	+	37.4378i	0.0600242	+	0.0600242i	−0.676457	+	0.736482i	$0.736486\pi$
$74$	−883.036	−	475.063i	−1.38717	−	0.746283i
$75$		0			0
$76$	906.607	−	598.718i	1.36836	−	0.903654i
$77$	−131.131	+	131.131i	−0.194074	+	0.194074i
$78$	−11.4303	−	38.0504i	−0.0165927	−	0.0552353i
$79$	1002.91			1.42831			0.714153	−	0.699990i	$-0.246812\pi$
$79$	1002.91			1.42831			0.714153	+	0.699990i	$0.246812\pi$
$80$		0			0
$81$	193.554			0.265506
$82$	−171.784	−	571.850i	−0.231346	−	0.770125i
$83$	−423.190	+	423.190i	−0.559652	+	0.559652i	−0.929208	−	0.369556i	$-0.879510\pi$
$83$	−423.190	+	423.190i	−0.559652	+	0.559652i	0.369556	+	0.929208i	$0.379510\pi$
$84$	−621.470	+	410.415i	−0.807237	+	0.533095i
$85$		0			0
$86$	164.619	+	88.5632i	0.206411	+	0.111047i
$87$	−89.7761	−	89.7761i	−0.110632	−	0.110632i
$88$	−106.920	+	128.152i	−0.129520	+	0.155239i
$89$		−	1049.38i		−	1.24982i	−0.780695	−	0.624912i	$-0.785135\pi$
$89$		−	1049.38i		−	1.24982i	0.780695	−	0.624912i	$-0.214865\pi$
$90$		0			0
$91$		−	95.3802i		−	0.109874i
$92$	161.060	−	787.453i	0.182518	−	0.892365i
$93$	−492.156	−	492.156i	−0.548755	−	0.548755i
$94$	−359.514	+	668.257i	−0.394479	+	0.733249i
$95$		0			0
$96$	−523.815	+	418.177i	−0.556892	+	0.444583i
$97$	536.526	−	536.526i	0.561608	−	0.561608i	−0.368156	−	0.929764i	$-0.620011\pi$
$97$	536.526	−	536.526i	0.561608	−	0.561608i	0.929764	+	0.368156i	$0.120011\pi$
$98$	−783.218	+	235.279i	−0.807316	+	0.242518i
$99$	98.0246			0.0995136
$100$		0			0
$101$	−1415.80			−1.39483			−0.697414	−	0.716668i	$-0.745666\pi$
$101$	−1415.80			−1.39483			−0.697414	+	0.716668i	$0.745666\pi$
$102$	−287.052	+	86.2303i	−0.278650	+	0.0837066i
$103$	284.920	−	284.920i	0.272563	−	0.272563i	−0.557568	−	0.830131i	$-0.688265\pi$
$103$	284.920	−	284.920i	0.272563	−	0.272563i	0.830131	+	0.557568i	$0.188265\pi$
$104$	−7.72143	−	85.4919i	−0.00728027	−	0.0806074i
$105$		0			0
$106$	−141.326	+	262.694i	−0.129498	+	0.240708i
$107$	464.315	+	464.315i	0.419505	+	0.419505i	0.885033	−	0.465528i	$-0.154136\pi$
$107$	464.315	+	464.315i	0.419505	+	0.419505i	−0.465528	+	0.885033i	$0.654136\pi$
$108$	1169.25	+	239.150i	1.04177	+	0.213076i
$109$			638.365i			0.560957i	0.959860	+	0.280478i	$0.0904931\pi$
$109$			638.365i			0.560957i	−0.959860	+	0.280478i	$0.909507\pi$
$110$		0			0
$111$		−	1312.66i		−	1.12246i
$112$	−1493.18	+	599.684i	−1.25976	+	0.505936i
$113$	−1001.84	−	1001.84i	−0.834027	−	0.834027i	0.154038	−	0.988065i	$-0.450772\pi$
$113$	−1001.84	−	1001.84i	−0.834027	−	0.834027i	−0.988065	+	0.154038i	$0.950772\pi$
$114$	1252.54	+	673.852i	1.02905	+	0.553614i
$115$		0			0
$116$	−151.165	−	228.902i	−0.120994	−	0.183216i
$117$	−35.6500	+	35.6500i	−0.0281696	+	0.0281696i
$118$	−82.2456	−	273.787i	−0.0641638	−	0.213594i
$119$	−719.548			−0.554293
$120$		0			0
$121$	1276.60			0.959126
$122$	188.878	+	628.756i	0.140166	+	0.466598i
$123$	552.718	−	552.718i	0.405178	−	0.405178i
$124$	−828.695	−	1254.85i	−0.600153	−	0.908780i
$125$		0			0
$126$	832.282	+	447.758i	0.588457	+	0.316583i
$127$	619.456	+	619.456i	0.432818	+	0.432818i	0.889586	−	0.456768i	$-0.150993\pi$
$127$	619.456	+	619.456i	0.432818	+	0.432818i	−0.456768	+	0.889586i	$0.650993\pi$
$128$	−1289.83	+	658.392i	−0.890674	+	0.454642i
$129$			244.712i			0.167021i
$130$		0			0
$131$			1620.12i			1.08054i	0.841491	+	0.540270i	$0.181678\pi$
$131$			1620.12i			1.08054i	−0.841491	+	0.540270i	$0.818322\pi$
$132$	−214.056	−	43.7815i	−0.141145	−	0.0288689i
$133$	2414.43	+	2414.43i	1.57412	+	1.57412i
$134$	65.8397	−	122.381i	0.0424454	−	0.0788965i
$135$		0			0
$136$	−644.950	+	58.2504i	−0.406647	+	0.0367274i
$137$	−825.076	+	825.076i	−0.514533	+	0.514533i	−0.915912	−	0.401379i	$-0.868531\pi$
$137$	−825.076	+	825.076i	−0.514533	+	0.514533i	0.401379	+	0.915912i	$0.368531\pi$
$138$	1007.72	−	302.718i	0.621613	−	0.186733i
$139$	1264.21			0.771430			0.385715	−	0.922618i	$-0.373955\pi$
$139$	1264.21			0.771430			0.385715	+	0.922618i	$0.373955\pi$
$140$		0			0
$141$	−993.387			−0.593321
$142$	1664.86	−	500.123i	0.983885	−	0.295559i
$143$	19.7858	−	19.7858i	0.0115704	−	0.0115704i
$144$	782.244	+	333.961i	0.452688	+	0.193264i
$145$		0			0
$146$	−70.9487	+	131.878i	−0.0402175	+	0.0747553i
$147$	−757.016	−	757.016i	−0.424746	−	0.424746i
$148$	568.312	−	2778.58i	0.315642	−	1.54323i
$149$			1351.49i			0.743079i	0.928417	+	0.371539i	$0.121170\pi$
$149$			1351.49i			0.743079i	−0.928417	+	0.371539i	$0.878830\pi$
$150$		0			0
$151$			2325.64i			1.25336i	0.779275	+	0.626682i	$0.215588\pi$
$151$			2325.64i			1.25336i	−0.779275	+	0.626682i	$0.784412\pi$
$152$	2359.57	+	1968.66i	1.25912	+	1.05052i
$153$	268.943	+	268.943i	0.142109	+	0.142109i
$154$	−461.918	−	248.507i	−0.241704	−	0.130034i
$155$		0			0
$156$	93.7712	−	61.9260i	0.0481263	−	0.0317823i
$157$	−162.486	+	162.486i	−0.0825976	+	0.0825976i	−0.747199	−	0.664601i	$-0.768602\pi$
$157$	−162.486	+	162.486i	−0.0825976	+	0.0825976i	0.664601	+	0.747199i	$0.268602\pi$
$158$	816.105	+	2716.73i	0.410923	+	1.36792i
$159$	−390.503			−0.194773
$160$		0			0
$161$	2526.03			1.23651
$162$	157.502	+	524.307i	0.0763859	+	0.254281i
$163$	−932.441	+	932.441i	−0.448064	+	0.448064i	−0.894710	−	0.446647i	$-0.852618\pi$
$163$	−932.441	+	932.441i	−0.448064	+	0.448064i	0.446647	+	0.894710i	$0.352618\pi$
$164$	1409.26	−	930.670i	0.671006	−	0.443129i
$165$		0			0
$166$	−1490.72	−	801.990i	−0.697002	−	0.374979i
$167$	−976.461	−	976.461i	−0.452460	−	0.452460i	0.443710	−	0.896170i	$-0.353662\pi$
$167$	−976.461	−	976.461i	−0.452460	−	0.452460i	−0.896170	+	0.443710i	$0.853662\pi$
$168$	−1617.46	−	1349.49i	−0.742798	−	0.619737i
$169$		−	2182.61i		−	0.993449i
$170$		0			0
$171$		−	1804.87i		−	0.807143i
$172$	−105.947	+	517.995i	−0.0469674	+	0.229632i
$173$	−761.698	−	761.698i	−0.334745	−	0.334745i	0.519640	−	0.854385i	$-0.326066\pi$
$173$	−761.698	−	761.698i	−0.334745	−	0.334745i	−0.854385	+	0.519640i	$0.826066\pi$
$174$	170.135	−	316.244i	0.0741260	−	0.137784i
$175$		0			0
$176$	−434.148	−	185.349i	−0.185938	−	0.0793818i
$177$	264.628	−	264.628i	0.112376	−	0.112376i
$178$	2842.61	−	853.921i	1.19698	−	0.359574i
$179$	−4003.32			−1.67163			−0.835816	−	0.549009i	$-0.815005\pi$
$179$	−4003.32			−1.67163			−0.835816	+	0.549009i	$0.815005\pi$
$180$		0			0
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	258.370	−	77.6144i	0.105229	−	0.0316108i
$183$	−607.721	+	607.721i	−0.245487	+	0.245487i
$184$	2264.15	−	204.493i	0.907147	−	0.0819315i
$185$		0			0
$186$	932.688	−	1733.66i	0.367677	−	0.683430i
$187$	−149.264	−	149.264i	−0.0583704	−	0.0583704i
$188$	−2102.75	−	430.083i	−0.815740	−	0.166846i
$189$			3750.78i			1.44354i
$190$		0			0
$191$			1458.80i			0.552644i	0.961065	+	0.276322i	$0.0891156\pi$
$191$			1458.80i			0.552644i	−0.961065	+	0.276322i	$0.910884\pi$
$192$	−1559.02	−	1078.65i	−0.586004	−	0.405441i
$193$	−2264.70	−	2264.70i	−0.844647	−	0.844647i	0.144812	−	0.989459i	$-0.453742\pi$
$193$	−2264.70	−	2264.70i	−0.844647	−	0.844647i	−0.989459	+	0.144812i	$0.953742\pi$
$194$	1889.96	+	1016.77i	0.699438	+	0.376289i
$195$		0			0
$196$	−1274.67	−	1930.16i	−0.464529	−	0.703411i
$197$	−2092.70	+	2092.70i	−0.756845	+	0.756845i	−0.975747	−	0.218902i	$-0.929753\pi$
$197$	−2092.70	+	2092.70i	−0.756845	+	0.756845i	0.218902	+	0.975747i	$0.429753\pi$
$198$	79.7662	+	265.533i	0.0286300	+	0.0953062i
$199$	−2087.70			−0.743683			−0.371842	−	0.928296i	$-0.621274\pi$
$199$	−2087.70			−0.743683			−0.371842	+	0.928296i	$0.621274\pi$
$200$		0			0
$201$	181.924			0.0638405
$202$	−1152.09	−	3835.19i	−0.401291	−	1.33586i
$203$	609.599	−	609.599i	0.210766	−	0.210766i
$204$	−467.169	−	707.409i	−0.160335	−	0.242787i
$205$		0			0
$206$	1003.65	+	539.954i	0.339456	+	0.182623i
$207$	−944.145	−	944.145i	−0.317018	−	0.317018i
$208$	225.301	−	90.4840i	0.0751048	−	0.0301632i
$209$			1001.70i			0.331528i
$210$		0			0
$211$		−	199.597i		−	0.0651223i	−0.999470	−	0.0325611i	$-0.989634\pi$
$211$		−	199.597i		−	0.0651223i	0.999470	−	0.0325611i	$-0.0103664\pi$
$212$	−826.598	−	169.067i	−0.267788	−	0.0547714i
$213$	1609.16	+	1609.16i	0.517642	+	0.517642i
$214$	−879.926	+	1635.59i	−0.281077	+	0.522460i
$215$		0			0
$216$	303.641	+	3361.92i	0.0956489	+	1.05903i
$217$	3341.84	−	3341.84i	1.04543	−	1.04543i
$218$	−1729.23	+	519.461i	−0.537240	+	0.161387i
$219$	−196.041			−0.0604896
$220$		0			0
$221$	108.570			0.0330461
$222$	3555.80	−	1068.16i	1.07500	−	0.322930i
$223$	−3340.24	+	3340.24i	−1.00304	+	1.00304i	−0.00304854	+	0.999995i	$0.500970\pi$
$223$	−3340.24	+	3340.24i	−1.00304	+	1.00304i	−0.999995	+	0.00304854i	$0.999030\pi$
$224$	−2839.51	−	3556.82i	−0.846976	−	1.06094i
$225$		0			0
$226$	1898.59	−	3529.06i	0.558816	−	1.03871i
$227$	−824.316	−	824.316i	−0.241021	−	0.241021i	0.576251	−	0.817272i	$-0.304515\pi$
$227$	−824.316	−	824.316i	−0.241021	−	0.241021i	−0.817272	+	0.576251i	$0.804515\pi$
$228$	−806.121	+	3941.27i	−0.234152	+	1.14481i
$229$		−	4512.23i		−	1.30208i	−0.759043	−	0.651041i	$-0.774333\pi$
$229$		−	4512.23i		−	1.30208i	0.759043	−	0.651041i	$-0.225667\pi$
$230$		0			0
$231$		−	686.658i		−	0.195579i
$232$	497.050	−	595.749i	0.140659	−	0.168590i
$233$	292.574	+	292.574i	0.0822625	+	0.0822625i	0.747041	−	0.664778i	$-0.231474\pi$
$233$	292.574	+	292.574i	0.0822625	+	0.0822625i	−0.664778	+	0.747041i	$0.731474\pi$
$234$	−125.580	−	67.5605i	−0.0350829	−	0.0188742i
$235$		0			0
$236$	674.720	−	445.581i	0.186104	−	0.122902i
$237$	−2625.84	+	2625.84i	−0.719690	+	0.719690i
$238$	−585.522	−	1949.14i	−0.159470	−	0.530858i
$239$	2925.20			0.791696			0.395848	−	0.918316i	$-0.370451\pi$
$239$	2925.20			0.791696			0.395848	+	0.918316i	$0.370451\pi$
$240$		0			0
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	1038.81	+	3458.10i	0.275940	+	0.918574i
$243$	2341.40	−	2341.40i	0.618111	−	0.618111i
$244$	−1549.50	+	1023.28i	−0.406544	+	0.268480i
$245$		0			0
$246$	1947.00	+	1047.46i	0.504617	+	0.271478i
$247$	−364.304	−	364.304i	−0.0938465	−	0.0938465i
$248$	2724.85	−	3265.92i	0.697694	−	0.836235i
$249$		−	2216.01i		−	0.563991i
$250$		0			0
$251$		−	5268.72i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$251$		−	5268.72i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$252$	−535.647	+	2618.88i	−0.133899	+	0.654658i
$253$	524.003	+	524.003i	0.130213	+	0.130213i
$254$	−1173.94	+	2182.08i	−0.289997	+	0.539040i
$255$		0			0
$256$	−2833.07	−	2958.20i	−0.691667	−	0.722217i
$257$	5635.08	−	5635.08i	1.36773	−	1.36773i	0.504061	−	0.863668i	$-0.331839\pi$
$257$	5635.08	−	5635.08i	1.36773	−	1.36773i	0.863668	−	0.504061i	$-0.168161\pi$
$258$	−662.888	+	199.132i	−0.159960	+	0.0480519i
$259$	8913.27			2.13839
$260$		0			0
$261$	−455.696			−0.108072
$262$	−4388.66	+	1318.35i	−1.03486	+	0.310871i
$263$	2721.99	−	2721.99i	0.638195	−	0.638195i	−0.311915	−	0.950110i	$-0.600970\pi$
$263$	2721.99	−	2721.99i	0.638195	−	0.638195i	0.950110	+	0.311915i	$0.100970\pi$
$264$	−55.5878	−	615.470i	−0.0129591	−	0.143483i
$265$		0			0
$266$	−4575.60	+	8505.01i	−1.05469	+	1.96044i
$267$	2747.51	+	2747.51i	0.629757	+	0.629757i
$268$	385.088	+	78.7632i	0.0877723	+	0.0179523i
$269$			603.964i			0.136893i	0.997655	+	0.0684467i	$0.0218043\pi$
$269$			603.964i			0.136893i	−0.997655	+	0.0684467i	$0.978196\pi$
$270$		0			0
$271$			4232.24i			0.948672i	0.880344	+	0.474336i	$0.157312\pi$
$271$			4232.24i			0.948672i	−0.880344	+	0.474336i	$0.842688\pi$
$272$	−682.611	−	1699.67i	−0.152167	−	0.378888i
$273$	249.726	+	249.726i	0.0553631	+	0.0553631i
$274$	−2906.40	−	1563.61i	−0.640810	−	0.344748i
$275$		0			0
$276$	1640.03	+	2483.41i	0.357675	+	0.541609i
$277$	−3214.07	+	3214.07i	−0.697165	+	0.697165i	−0.963798	−	0.266633i	$-0.914089\pi$
$277$	−3214.07	+	3214.07i	−0.697165	+	0.697165i	0.266633	+	0.963798i	$0.414089\pi$
$278$	1028.73	+	3424.54i	0.221940	+	0.738815i
$279$	−2498.14			−0.536056
$280$		0			0
$281$	−7574.78			−1.60809			−0.804046	−	0.594567i	$-0.797323\pi$
$281$	−7574.78			−1.60809			−0.804046	+	0.594567i	$0.797323\pi$
$282$	−808.356	−	2690.93i	−0.170698	−	0.568236i
$283$	504.094	−	504.094i	0.105884	−	0.105884i	−0.652180	−	0.758064i	$-0.726145\pi$
$283$	504.094	−	504.094i	0.105884	−	0.105884i	0.758064	+	0.652180i	$0.226145\pi$
$284$	2709.51	+	4102.87i	0.566126	+	0.857255i
$285$		0			0
$286$	69.6971	+	37.4962i	0.0144101	+	0.00775244i
$287$	3753.08	+	3753.08i	0.771906	+	0.771906i
$288$	−268.106	+	2390.73i	−0.0548552	+	0.489150i
$289$			4093.95i			0.833289i
$290$		0			0
$291$			2809.49i			0.565962i
$292$	−414.970	−	84.8750i	−0.0831653	−	0.0170101i
$293$	244.144	+	244.144i	0.0486793	+	0.0486793i	0.731027	−	0.682348i	$-0.239041\pi$
$293$	244.144	+	244.144i	0.0486793	+	0.0486793i	−0.682348	+	0.731027i	$0.739041\pi$
$294$	1434.63	−	2666.65i	0.284589	−	0.528987i
$295$		0			0
$296$	7989.20	−	721.566i	1.56879	−	0.141690i
$297$	−778.066	+	778.066i	−0.152013	+	0.152013i
$298$	−3660.99	+	1099.76i	−0.711662	+	0.213783i
$299$	−381.143			−0.0737192
$300$		0			0
$301$	−1661.65			−0.318192
$302$	−6299.80	+	1892.46i	−1.20037	+	0.360592i
$303$	3706.88	−	3706.88i	0.702822	−	0.702822i
$304$	−3412.71	+	7993.69i	−0.643857	+	1.50812i
$305$		0			0
$306$	−509.676	+	947.373i	−0.0952164	+	0.176986i
$307$	6853.22	+	6853.22i	1.27405	+	1.27405i	0.943942	+	0.330110i	$0.107086\pi$
$307$	6853.22	+	6853.22i	1.27405	+	1.27405i	0.330110	+	0.943942i	$0.392914\pi$
$308$	297.286	−	1453.48i	0.0549981	−	0.268896i
$309$			1491.97i			0.274676i
$310$		0			0
$311$		−	10802.7i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$311$		−	10802.7i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$312$	244.053	+	203.620i	0.0442845	+	0.0369478i
$313$	−2618.43	−	2618.43i	−0.472851	−	0.472851i	0.429985	−	0.902836i	$-0.358519\pi$
$313$	−2618.43	−	2618.43i	−0.472851	−	0.472851i	−0.902836	+	0.429985i	$0.858519\pi$
$314$	−572.372	−	307.929i	−0.102869	−	0.0553422i
$315$		0			0
$316$	−6695.09	+	4421.40i	−1.19186	+	0.787098i
$317$	−3652.64	+	3652.64i	−0.647170	+	0.647170i	−0.952308	−	0.305138i	$-0.901297\pi$
$317$	−3652.64	+	3652.64i	−0.647170	+	0.647170i	0.305138	+	0.952308i	$0.401297\pi$
$318$	−317.767	−	1057.81i	−0.0560361	−	0.186538i
$319$	252.912			0.0443898
$320$		0			0
$321$	−2431.36			−0.422757
$322$	2055.52	+	6842.61i	0.355745	+	1.18424i
$323$	−2748.30	+	2748.30i	−0.473436	+	0.473436i
$324$	−1292.10	+	853.296i	−0.221554	+	0.146313i
$325$		0			0
$326$	−3284.60	−	1767.07i	−0.558028	−	0.300212i
$327$	−1671.38	−	1671.38i	−0.282653	−	0.282653i
$328$	3667.81	+	3060.16i	0.617442	+	0.515149i
$329$		−	6745.31i		−	1.13034i
$330$		0			0
$331$			7839.91i			1.30187i	0.759131	+	0.650937i	$0.225624\pi$
$331$			7839.91i			1.30187i	−0.759131	+	0.650937i	$0.774376\pi$
$332$	959.411	−	4690.74i	0.158598	−	0.775415i
$333$	−3331.48	−	3331.48i	−0.548241	−	0.548241i
$334$	1850.50	−	3439.66i	0.303158	−	0.563503i
$335$		0			0
$336$	2339.38	−	5479.59i	0.379832	−	0.889691i
$337$	4503.23	−	4503.23i	0.727912	−	0.727912i	−0.242291	−	0.970204i	$-0.577899\pi$
$337$	4503.23	−	4503.23i	0.727912	−	0.727912i	0.970204	+	0.242291i	$0.0778990\pi$
$338$	5912.34	−	1776.07i	0.951447	−	0.285815i
$339$	5246.07			0.840494
$340$		0			0
$341$	1386.47			0.220181
$342$	4889.10	−	1468.69i	0.773018	−	0.232215i
$343$	−957.648	+	957.648i	−0.150753	+	0.150753i
$344$	−1489.38	+	134.517i	−0.233436	+	0.0210834i
$345$		0			0
$346$	1443.50	−	2683.14i	0.224286	−	0.416898i
$347$	−8458.77	−	8458.77i	−1.30862	−	1.30862i	−0.922413	−	0.386205i	$-0.873786\pi$
$347$	−8458.77	−	8458.77i	−1.30862	−	1.30862i	−0.386205	−	0.922413i	$-0.626214\pi$
$348$	995.100	+	203.531i	0.153284	+	0.0313517i
$349$		−	5515.41i		−	0.845941i	−0.906144	−	0.422970i	$-0.860987\pi$
$349$		−	5515.41i		−	0.845941i	0.906144	−	0.422970i	$-0.139013\pi$
$350$		0			0
$351$		−	565.940i		−	0.0860617i
$352$	148.799	−	1326.86i	0.0225314	−	0.200915i
$353$	761.447	+	761.447i	0.114810	+	0.114810i	0.762178	−	0.647368i	$-0.224130\pi$
$353$	761.447	+	761.447i	0.114810	+	0.114810i	−0.647368	+	0.762178i	$0.724130\pi$
$354$	932.172	+	501.497i	0.139956	+	0.0752946i
$355$		0			0
$356$	4626.28	+	7005.33i	0.688742	+	1.04293i
$357$	1883.93	−	1883.93i	0.279295	−	0.279295i
$358$	−3257.65	−	10844.4i	−0.480928	−	1.60096i
$359$	3564.71			0.524062			0.262031	−	0.965059i	$-0.415608\pi$
$359$	3564.71			0.524062			0.262031	+	0.965059i	$0.415608\pi$
$360$		0			0
$361$	11584.8			1.68899
$362$	−1586.78	−	5282.23i	−0.230385	−	0.766928i
$363$	−3342.41	+	3342.41i	−0.483281	+	0.483281i
$364$	420.491	+	636.726i	0.0605486	+	0.0916855i
$365$		0			0
$366$	−2140.75	−	1151.70i	−0.305734	−	0.164481i
$367$	−4407.82	−	4407.82i	−0.626939	−	0.626939i	0.320358	−	0.947297i	$-0.396197\pi$
$367$	−4407.82	−	4407.82i	−0.626939	−	0.626939i	−0.947297	+	0.320358i	$0.896197\pi$
$368$	2396.36	+	5966.81i	0.339453	+	0.845222i
$369$		−	2805.55i		−	0.395802i
$370$		0			0
$371$		−	2651.60i		−	0.371063i
$372$	5455.17	+	1115.76i	0.760316	+	0.155510i
$373$	8371.19	+	8371.19i	1.16205	+	1.16205i	0.984027	+	0.178021i	$0.0569696\pi$
$373$	8371.19	+	8371.19i	1.16205	+	1.16205i	0.178021	+	0.984027i	$0.443030\pi$
$374$	282.871	−	525.794i	0.0391094	−	0.0726957i
$375$		0			0
$376$	−546.061	−	6046.00i	−0.0748962	−	0.829252i
$377$	−91.9800	+	91.9800i	−0.0125656	+	0.0125656i
$378$	−10160.3	+	3052.15i	−1.38251	+	0.415305i
$379$	−11130.1			−1.50848			−0.754240	−	0.656599i	$-0.771994\pi$
$379$	−11130.1			−1.50848			−0.754240	+	0.656599i	$0.771994\pi$
$380$		0			0
$381$	−3243.75			−0.436174
$382$	−3951.66	+	1187.08i	−0.529279	+	0.158995i
$383$	−1006.62	+	1006.62i	−0.134297	+	0.134297i	−0.771060	−	0.636763i	$-0.780273\pi$
$383$	−1006.62	+	1006.62i	−0.134297	+	0.134297i	0.636763	+	0.771060i	$0.280273\pi$
$384$	1653.25	−	5100.88i	0.219706	−	0.677873i
$385$		0			0
$386$	4291.85	−	7977.60i	0.565932	−	1.05194i
$387$	621.069	+	621.069i	0.0815781	+	0.0815781i
$388$	−1216.35	+	5946.98i	−0.159152	+	0.778124i
$389$			13548.4i			1.76589i	0.469478	+	0.882944i	$0.344442\pi$
$389$			13548.4i			1.76589i	−0.469478	+	0.882944i	$0.655558\pi$
$390$		0			0
$391$			2875.34i			0.371898i
$392$	4191.26	−	5023.52i	0.540027	−	0.647260i
$393$	−4241.84	−	4241.84i	−0.544459	−	0.544459i
$394$	−7371.69	−	3965.88i	−0.942590	−	0.507102i
$395$		0			0
$396$	−654.379	+	432.148i	−0.0830399	+	0.0548391i
$397$	−1822.81	+	1822.81i	−0.230439	+	0.230439i	−0.812876	−	0.582437i	$-0.802099\pi$
$397$	−1822.81	+	1822.81i	−0.230439	+	0.230439i	0.582437	+	0.812876i	$0.302099\pi$
$398$	−1698.84	−	5655.25i	−0.213957	−	0.712241i
$399$	−12643.0			−1.58632
$400$		0			0
$401$	5922.04			0.737488			0.368744	−	0.929531i	$-0.379788\pi$
$401$	5922.04			0.737488			0.368744	+	0.929531i	$0.379788\pi$
$402$	148.038	+	492.804i	0.0183669	+	0.0611413i
$403$	−504.238	+	504.238i	−0.0623273	+	0.0623273i
$404$	9451.43	−	6241.67i	1.16393	−	0.768650i
$405$		0			0
$406$	2147.36	+	1155.25i	0.262492	+	0.141218i
$407$	1848.98	+	1848.98i	0.225186	+	0.225186i
$408$	1536.11	−	1841.13i	0.186394	−	0.223406i
$409$			8533.05i			1.03162i	0.856703	+	0.515809i	$0.172509\pi$
$409$			8533.05i			1.03162i	−0.856703	+	0.515809i	$0.827491\pi$
$410$		0			0
$411$		−	4320.46i		−	0.518522i
$412$	−645.940	+	3158.12i	−0.0772408	+	0.377644i
$413$	1796.88	+	1796.88i	0.214088	+	0.214088i
$414$	1789.26	−	3325.83i	0.212408	−	0.394820i
$415$		0			0
$416$	428.443	+	536.674i	0.0504955	+	0.0632515i
$417$	−3309.98	+	3309.98i	−0.388706	+	0.388706i
$418$	−2713.46	+	815.124i	−0.317511	+	0.0953804i
$419$	−7128.02			−0.831089			−0.415545	−	0.909573i	$-0.636409\pi$
$419$	−7128.02			−0.831089			−0.415545	+	0.909573i	$0.636409\pi$
$420$		0			0
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	540.676	−	162.419i	0.0623690	−	0.0187356i
$423$	−2521.17	+	2521.17i	−0.289796	+	0.289796i
$424$	−214.658	−	2376.70i	−0.0245866	−	0.272223i
$425$		0			0
$426$	−3049.53	+	5668.39i	−0.346831	+	0.644682i
$427$	−4126.56	−	4126.56i	−0.467677	−	0.467677i
$428$	−5146.58	−	1052.65i	−0.581236	−	0.118882i
$429$			103.607i			0.0116601i
$430$		0			0
$431$			9361.72i			1.04626i	0.852253	+	0.523130i	$0.175236\pi$
$431$			9361.72i			1.04626i	−0.852253	+	0.523130i	$0.824764\pi$
$432$	−8859.84	+	3558.24i	−0.986734	+	0.396286i
$433$	1769.48	+	1769.48i	0.196388	+	0.196388i	0.798450	−	0.602062i	$-0.205654\pi$
$433$	1769.48	+	1769.48i	0.196388	+	0.196388i	−0.602062	+	0.798450i	$0.705654\pi$
$434$	11771.9	+	6333.15i	1.30200	+	0.700463i
$435$		0			0
$436$	−2814.28	−	4261.51i	−0.309127	−	0.468095i
$437$	9648.13	−	9648.13i	1.05614	−	1.05614i
$438$	−159.526	−	531.044i	−0.0174028	−	0.0579321i
$439$	7823.34			0.850541			0.425271	−	0.905066i	$-0.360179\pi$
$439$	7823.34			0.850541			0.425271	+	0.905066i	$0.360179\pi$
$440$		0			0
$441$	−3842.54			−0.414917
$442$	88.3472	+	294.099i	0.00950735	+	0.0316490i
$443$	9066.48	−	9066.48i	0.972374	−	0.972374i	−0.0272545	−	0.999629i	$-0.508676\pi$
$443$	9066.48	−	9066.48i	0.972374	−	0.972374i	0.999629	+	0.0272545i	$0.00867646\pi$
$444$	5786.97	+	8762.91i	0.618553	+	0.936642i
$445$		0			0
$446$	−11766.3	−	6330.10i	−1.24921	−	0.672061i
$447$	−3538.51	−	3538.51i	−0.374420	−	0.374420i
$448$	7324.25	−	10586.1i	0.772407	−	1.11640i
$449$		−	3381.93i		−	0.355464i	−0.984079	−	0.177732i	$-0.943124\pi$
$449$		−	3381.93i		−	0.355464i	0.984079	−	0.177732i	$-0.0568759\pi$
$450$		0			0
$451$			1557.09i			0.162573i
$452$	11104.6	+	2271.26i	1.15557	+	0.236352i
$453$	−6089.04	−	6089.04i	−0.631541	−	0.631541i
$454$	1562.17	−	2903.72i	0.161489	−	0.300173i
$455$		0			0
$456$	−11332.3	+	1023.50i	−1.16378	+	0.105110i
$457$	−10289.7	+	10289.7i	−1.05324	+	1.05324i	−0.0547399	+	0.998501i	$0.517433\pi$
$457$	−10289.7	+	10289.7i	−1.05324	+	1.05324i	−0.998501	+	0.0547399i	$0.982567\pi$
$458$	12222.9	−	3671.77i	1.24703	−	0.374608i
$459$	−4269.45			−0.434163
$460$		0			0
$461$	−5310.20			−0.536488			−0.268244	−	0.963351i	$-0.586443\pi$
$461$	−5310.20			−0.536488			−0.268244	+	0.963351i	$0.586443\pi$
$462$	1860.05	−	558.759i	0.187310	−	0.0562680i
$463$	−7686.78	+	7686.78i	−0.771566	+	0.771566i	−0.978380	−	0.206814i	$-0.933690\pi$
$463$	−7686.78	+	7686.78i	−0.771566	+	0.771566i	0.206814	+	0.978380i	$0.433690\pi$
$464$	2018.26	+	861.648i	0.201930	+	0.0862091i
$465$		0			0
$466$	−554.459	+	1030.62i	−0.0551176	+	0.102451i
$467$	−4535.99	−	4535.99i	−0.449466	−	0.449466i	0.445711	−	0.895177i	$-0.352951\pi$
$467$	−4535.99	−	4535.99i	−0.449466	−	0.449466i	−0.895177	+	0.445711i	$0.852951\pi$
$468$	80.8218	−	395.153i	0.00798288	−	0.0390298i
$469$			1235.30i			0.121623i
$470$		0			0
$471$		−	850.850i		−	0.0832380i
$472$	1756.05	+	1465.12i	0.171248	+	0.142877i
$473$	−344.695	−	344.695i	−0.0335076	−	0.0335076i
$474$	−9249.72	−	4976.24i	−0.896316	−	0.482208i
$475$		0			0
$476$	4803.46	−	3172.18i	0.462534	−	0.305455i
$477$	−991.080	+	991.080i	−0.0951330	+	0.0951330i
$478$	2380.34	+	7923.91i	0.227771	+	0.758224i
$479$	10969.6			1.04638			0.523189	−	0.852217i	$-0.324742\pi$
$479$	10969.6			1.04638			0.523189	+	0.852217i	$0.324742\pi$
$480$		0			0
$481$	−1344.89			−0.127488
$482$	3466.03	+	11538.0i	0.327538	+	1.09034i
$483$	−6613.70	+	6613.70i	−0.623051	+	0.623051i
$484$	−8522.13	+	5627.97i	−0.800350	+	0.528547i
$485$		0			0
$486$	8247.77	+	4437.20i	0.769808	+	0.414147i
$487$	12736.0	+	12736.0i	1.18506	+	1.18506i	0.978416	+	0.206646i	$0.0662547\pi$
$487$	12736.0	+	12736.0i	1.18506	+	1.18506i	0.206646	+	0.978416i	$0.433745\pi$
$488$	−4032.80	−	3364.68i	−0.374091	−	0.312115i
$489$		−	4882.67i		−	0.451538i
$490$		0			0
$491$			10518.6i			0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$491$			10518.6i			0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$492$	−1253.06	+	6126.46i	−0.114822	+	0.561387i
$493$	693.897	+	693.897i	0.0633905	+	0.0633905i
$494$	690.394	−	1283.29i	0.0628792	−	0.116878i
$495$		0			0
$496$	11064.2	+	4723.59i	1.00161	+	0.427612i
$497$	−10926.5	+	10926.5i	−0.986161	+	0.986161i
$498$	6002.82	−	1803.25i	0.540146	−	0.162260i
$499$	−2445.26			−0.219368			−0.109684	−	0.993966i	$-0.534984\pi$
$499$	−2445.26			−0.219368			−0.109684	+	0.993966i	$0.534984\pi$
$500$		0			0
$501$	5113.18			0.455968
$502$	14272.1	−	4287.35i	1.26892	−	0.381183i
$503$	12216.7	−	12216.7i	1.08293	−	1.08293i	0.0866986	−	0.996235i	$-0.472368\pi$
$503$	12216.7	−	12216.7i	1.08293	−	1.08293i	0.996235	−	0.0866986i	$-0.0276317\pi$
$504$	−7530.01	+	680.093i	−0.665502	+	0.0601066i
$505$		0			0
$506$	−993.041	+	1845.84i	−0.0872452	+	0.162169i
$507$	5714.55	+	5714.55i	0.500576	+	0.500576i
$508$	−6866.20	−	1404.37i	−0.599682	−	0.122655i
$509$		−	5615.75i		−	0.489025i	−0.969646	−	0.244512i	$-0.921372\pi$
$509$		−	5615.75i		−	0.489025i	0.969646	−	0.244512i	$-0.0786279\pi$
$510$		0			0
$511$		−	1331.16i		−	0.115239i
$512$	5707.93	−	10081.5i	0.492690	−	0.870205i
$513$	14326.0	+	14326.0i	1.23296	+	1.23296i
$514$	19850.0	+	10679.1i	1.70340	+	0.916408i
$515$		0			0
$516$	−1078.83	−	1633.62i	−0.0920406	−	0.139372i
$517$	1399.26	−	1399.26i	0.119031	−	0.119031i
$518$	7253.05	+	24144.6i	0.615214	+	2.04798i
$519$	3988.58			0.337340
$520$		0			0
$521$	5287.10			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$521$	5287.10			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$522$	−370.816	−	1234.41i	−0.0310923	−	0.103503i
$523$	−4328.34	+	4328.34i	−0.361883	+	0.361883i	−0.864506	−	0.502623i	$-0.832369\pi$
$523$	−4328.34	+	4328.34i	−0.361883	+	0.361883i	0.502623	+	0.864506i	$0.332369\pi$
$524$	−7142.43	−	10815.4i	−0.595455	−	0.901666i
$525$		0			0
$526$	9588.45	+	5158.47i	0.794821	+	0.427605i
$527$	3803.97	+	3803.97i	0.314428	+	0.314428i
$528$	1621.98	−	651.409i	0.133688	−	0.0536912i
$529$			2072.91i			0.170371i
$530$		0			0
$531$		−	1343.23i		−	0.109776i
$532$	−26762.1	−	5473.73i	−2.18098	−	0.446083i
$533$	−566.287	−	566.287i	−0.0460199	−	0.0460199i
$534$	−5206.83	+	9678.34i	−0.421951	+	0.784312i
$535$		0			0
$536$	100.003	+	1107.23i	0.00805871	+	0.0892262i
$537$	10481.6	−	10481.6i	0.842297	−	0.842297i
$538$	−1636.04	+	491.468i	−0.131106	+	0.0393841i
$539$	2132.62			0.170424
$540$		0			0
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	−11464.5	+	3443.93i	−0.908563	+	0.272932i
$543$	5105.52	−	5105.52i	0.403497	−	0.403497i
$544$	4048.67	−	3232.17i	0.319090	−	0.254739i
$545$		0			0
$546$	−473.258	+	879.681i	−0.0370945	+	0.0689503i
$547$	−2884.33	−	2884.33i	−0.225457	−	0.225457i	0.585335	−	0.810792i	$-0.300963\pi$
$547$	−2884.33	−	2884.33i	−0.225457	−	0.225457i	−0.810792	+	0.585335i	$0.800963\pi$
$548$	1870.52	−	9145.34i	0.145812	−	0.712901i
$549$			3084.74i			0.239806i
$550$		0			0
$551$		−	4656.71i		−	0.360041i
$552$	−5392.63	+	6463.44i	−0.415807	+	0.498374i
$553$	−17830.0	−	17830.0i	−1.37108	−	1.37108i
$554$	−11321.8	−	6091.00i	−0.868263	−	0.467115i
$555$		0			0
$556$	−8439.43	+	5573.35i	−0.643726	+	0.425113i
$557$	6538.87	−	6538.87i	0.497416	−	0.497416i	−0.413216	−	0.910633i	$-0.635595\pi$
$557$	6538.87	−	6538.87i	0.497416	−	0.497416i	0.910633	+	0.413216i	$0.135595\pi$
$558$	−2032.83	−	6767.07i	−0.154223	−	0.513392i
$559$	250.720			0.0189702
$560$		0			0
$561$	781.612			0.0588229
$562$	−6163.88	−	20518.9i	−0.462647	−	1.54010i
$563$	6499.93	−	6499.93i	0.486571	−	0.486571i	−0.420651	−	0.907222i	$-0.638198\pi$
$563$	6499.93	−	6499.93i	0.486571	−	0.486571i	0.907222	+	0.420651i	$0.138198\pi$
$564$	6631.52	−	4379.42i	0.495102	−	0.326962i
$565$		0			0
$566$	1775.71	+	955.311i	0.131870	+	0.0709447i
$567$	−3441.05	−	3441.05i	−0.254869	−	0.254869i
$568$	−8909.19	+	10678.3i	−0.658136	+	0.788822i
$569$			5264.67i			0.387885i	0.981013	+	0.193942i	$0.0621275\pi$
$569$			5264.67i			0.387885i	−0.981013	+	0.193942i	$0.937872\pi$
$570$		0			0
$571$		−	22034.0i		−	1.61488i	−0.589952	−	0.807438i	$-0.700853\pi$
$571$		−	22034.0i		−	1.61488i	0.589952	−	0.807438i	$-0.299147\pi$
$572$	−44.8563	+	219.311i	−0.00327891	+	0.0160312i
$573$	−3819.46	−	3819.46i	−0.278464	−	0.278464i
$574$	−7112.48	+	13220.5i	−0.517194	+	0.961348i
$575$		0			0
$576$	−6694.29	+	1219.17i	−0.484251	+	0.0881924i
$577$	9208.58	−	9208.58i	0.664399	−	0.664399i	−0.292015	−	0.956414i	$-0.594326\pi$
$577$	9208.58	−	9208.58i	0.664399	−	0.664399i	0.956414	+	0.292015i	$0.0943257\pi$
$578$	−11089.9	+	3331.40i	−0.798059	+	0.239737i
$579$	11859.0			0.851196
$580$		0			0
$581$	15047.2			1.07446
$582$	−7610.46	+	2286.18i	−0.542034	+	0.162827i
$583$	550.052	−	550.052i	0.0390751	−	0.0390751i
$584$	−107.763	−	1193.15i	−0.00763572	−	0.0845429i
$585$		0			0
$586$	−462.679	+	860.016i	−0.0326162	+	0.0606262i
$587$	6536.20	+	6536.20i	0.459587	+	0.459587i	0.898520	−	0.438933i	$-0.144643\pi$
$587$	6536.20	+	6536.20i	0.459587	+	0.459587i	−0.438933	+	0.898520i	$0.644643\pi$
$588$	8390.94	+	1716.23i	0.588498	+	0.120367i
$589$		−	25528.3i		−	1.78586i
$590$		0			0
$591$		−	10958.3i		−	0.762713i
$592$	8455.72	+	21054.3i	0.587040	+	1.46170i
$593$	11033.7	+	11033.7i	0.764079	+	0.764079i	0.977057	−	0.212978i	$-0.0683163\pi$
$593$	11033.7	+	11033.7i	0.764079	+	0.764079i	−0.212978	+	0.977057i	$0.568316\pi$
$594$	−2740.80	−	1474.52i	−0.189321	−	0.101852i
$595$		0			0
$596$	−5958.16	−	9022.12i	−0.409489	−	0.620068i
$597$	5466.05	−	5466.05i	0.374725	−	0.374725i
$598$	−310.150	−	1032.46i	−0.0212090	−	0.0706024i
$599$	−1861.62			−0.126985			−0.0634923	−	0.997982i	$-0.520224\pi$
$599$	−1861.62			−0.126985			−0.0634923	+	0.997982i	$0.520224\pi$
$600$		0			0
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	−1352.15	−	4501.15i	−0.0915437	−	0.304739i
$603$	461.715	−	461.715i	0.0311816	−	0.0311816i
$604$	−10252.8	−	15525.2i	−0.690693	−	1.04588i
$605$		0			0
$606$	13057.8	+	7024.94i	0.875308	+	0.470905i
$607$	617.817	+	617.817i	0.0413121	+	0.0413121i	0.727461	−	0.686149i	$-0.240700\pi$
$607$	617.817	+	617.817i	0.0413121	+	0.0413121i	−0.686149	+	0.727461i	$0.740700\pi$
$608$	−24430.7	−	2739.75i	−1.62960	−	0.182749i
$609$			3192.13i			0.212400i
$610$		0			0
$611$			1017.77i			0.0673891i
$612$	−2981.03	−	609.719i	−0.196897	−	0.0402719i
$613$	−5656.87	−	5656.87i	−0.372722	−	0.372722i	0.495745	−	0.868468i	$-0.334895\pi$
$613$	−5656.87	−	5656.87i	−0.372722	−	0.372722i	−0.868468	+	0.495745i	$0.834895\pi$
$614$	−12987.6	+	24141.0i	−0.853642	+	1.58673i
$615$		0			0
$616$	4179.17	−	377.453i	0.273350	−	0.0246884i
$617$	−12811.8	+	12811.8i	−0.835953	+	0.835953i	−0.988323	−	0.152370i	$-0.951309\pi$
$617$	−12811.8	+	12811.8i	−0.835953	+	0.835953i	0.152370	+	0.988323i	$0.451309\pi$
$618$	−4041.50	+	1214.07i	−0.263063	+	0.0790243i
$619$	12163.2			0.789788			0.394894	−	0.918727i	$-0.370781\pi$
$619$	12163.2			0.789788			0.394894	+	0.918727i	$0.370781\pi$
$620$		0			0
$621$	14988.2			0.968530
$622$	29262.9	−	8790.56i	1.88639	−	0.566671i
$623$	−18656.2	+	18656.2i	−1.19975	+	1.19975i
$624$	−352.980	+	826.794i	−0.0226450	+	0.0530421i
$625$		0			0
$626$	4962.20	−	9223.62i	0.316820	−	0.588898i
$627$	−2622.68	−	2622.68i	−0.167049	−	0.167049i
$628$	368.372	−	1801.04i	0.0234071	−	0.114441i
$629$			10145.8i			0.643149i
$630$		0			0
$631$		−	3347.17i		−	0.211171i	−0.994410	−	0.105585i	$-0.966328\pi$
$631$		−	3347.17i		−	0.211171i	0.994410	−	0.105585i	$-0.0336716\pi$
$632$	−17424.9	−	14538.1i	−1.09672	−	0.915023i
$633$	522.588	+	522.588i	0.0328136	+	0.0328136i
$634$	−12866.7	−	6922.14i	−0.805998	−	0.433617i
$635$		0			0
$636$	2606.87	−	1721.56i	0.162530	−	0.107334i
$637$	−775.600	+	775.600i	−0.0482424	+	0.0482424i
$638$	205.804	+	685.099i	0.0127709	+	0.0425131i
$639$	8167.95			0.505664
$640$		0			0
$641$	−24791.3			−1.52761			−0.763803	−	0.645449i	$-0.776670\pi$
$641$	−24791.3			−1.52761			−0.763803	+	0.645449i	$0.776670\pi$
$642$	−1978.48	−	6586.17i	−0.121627	−	0.404884i
$643$	12922.9	−	12922.9i	0.792583	−	0.792583i	−0.189330	−	0.981913i	$-0.560632\pi$
$643$	12922.9	−	12922.9i	0.792583	−	0.792583i	0.981913	+	0.189330i	$0.0606316\pi$
$644$	−16862.9	+	11136.2i	−1.03182	+	0.681408i
$645$		0			0
$646$	−9681.12	−	5208.33i	−0.589626	−	0.317212i
$647$	−16924.5	−	16924.5i	−1.02840	−	1.02840i	−0.999585	−	0.0288113i	$-0.990828\pi$
$647$	−16924.5	−	16924.5i	−1.02840	−	1.02840i	−0.0288113	−	0.999585i	$-0.509172\pi$
$648$	−3362.88	−	2805.74i	−0.203868	−	0.170092i
$649$			745.493i			0.0450896i
$650$		0			0
$651$			17499.4i			1.05354i
$652$	2113.93	−	10335.4i	0.126975	−	0.620806i
$653$	−10391.0	−	10391.0i	−0.622715	−	0.622715i	0.323510	−	0.946225i	$-0.395137\pi$
$653$	−10391.0	−	10391.0i	−0.622715	−	0.622715i	−0.946225	+	0.323510i	$0.895137\pi$
$654$	3167.44	−	5887.57i	0.189384	−	0.352022i
$655$		0			0
$656$	−5304.85	+	12425.7i	−0.315731	+	0.739545i
$657$	−497.543	+	497.543i	−0.0295449	+	0.0295449i
$658$	18272.0	−	5488.91i	1.08255	−	0.325197i
$659$	−773.045			−0.0456958			−0.0228479	−	0.999739i	$-0.507273\pi$
$659$	−773.045			−0.0456958			−0.0228479	+	0.999739i	$0.507273\pi$
$660$		0			0
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	−21237.1	+	6379.62i	−1.24683	+	0.374549i
$663$	−284.260	+	284.260i	−0.0166512	+	0.0166512i
$664$	13487.2	−	1218.13i	0.788259	−	0.0711938i
$665$		0			0
$666$	6313.51	−	11735.4i	0.367333	−	0.682790i
$667$	−2435.98	−	2435.98i	−0.141411	−	0.141411i
$668$	10823.3	+	2213.73i	0.626896	+	0.128221i
$669$		−	17490.9i		−	1.01082i
$670$		0			0
$671$		−	1712.04i		−	0.0984985i
$672$	16747.0	+	1878.07i	0.961353	+	0.107810i
$673$	19931.6	+	19931.6i	1.14161	+	1.14161i	0.988155	+	0.153459i	$0.0490414\pi$
$673$	19931.6	+	19931.6i	1.14161	+	1.14161i	0.153459	+	0.988155i	$0.450959\pi$
$674$	15863.0	+	8534.10i	0.906557	+	0.487717i
$675$		0			0
$676$	9622.18	+	14570.4i	0.547462	+	0.828992i
$677$	5515.73	−	5515.73i	0.313126	−	0.313126i	−0.532993	−	0.846120i	$-0.678933\pi$
$677$	5515.73	−	5515.73i	0.313126	−	0.313126i	0.846120	+	0.532993i	$0.178933\pi$
$678$	4268.92	+	14210.8i	0.241810	+	0.804958i
$679$	−19077.0			−1.07822
$680$		0			0
$681$	4316.48			0.242890
$682$	1128.22	+	3755.74i	0.0633460	+	0.210872i
$683$	−19946.1	+	19946.1i	−1.11745	+	1.11745i	−0.125331	+	0.992115i	$0.539999\pi$
$683$	−19946.1	+	19946.1i	−1.11745	+	1.11745i	−0.992115	+	0.125331i	$0.960001\pi$
$684$	7956.88	+	12048.7i	0.444794	+	0.673527i
$685$		0			0
$686$	−3373.39	−	1814.85i	−0.187750	−	0.101007i
$687$	11814.0	+	11814.0i	0.656089	+	0.656089i
$688$	−1576.35	−	3925.04i	−0.0873515	−	0.217501i
$689$			400.090i			0.0221222i
$690$		0			0
$691$			356.654i			0.0196350i	0.999952	+	0.00981748i	$0.00312505\pi$
$691$			356.654i			0.0196350i	−0.999952	+	0.00981748i	$0.996875\pi$
$692$	8442.84	+	1726.84i	0.463798	+	0.0948621i
$693$	−1742.71	−	1742.71i	−0.0955267	−	0.0955267i
$694$	16030.3	−	29796.7i	0.876802	−	1.62978i
$695$		0			0
$696$	258.416	+	2861.19i	0.0140736	+	0.155823i
$697$	−4272.07	+	4272.07i	−0.232161	+	0.232161i
$698$	14940.4	−	4488.09i	0.810175	−	0.243377i
$699$	−1532.05			−0.0829003
$700$		0			0
$701$	17230.0			0.928343			0.464172	−	0.885745i	$-0.346352\pi$
$701$	17230.0			0.928343			0.464172	+	0.885745i	$0.346352\pi$
$702$	1533.04	−	460.526i	0.0824231	−	0.0247599i
$703$	34044.1	−	34044.1i	1.82646	−	1.82646i
$704$	3715.35	−	676.643i	0.198903	−	0.0362243i
$705$		0			0
$706$	−1443.02	+	2682.26i	−0.0769248	+	0.142986i
$707$	25170.5	+	25170.5i	1.33895	+	1.33895i
$708$	−599.935	+	2933.19i	−0.0318460	+	0.155701i
$709$			8153.11i			0.431871i	0.976408	+	0.215935i	$0.0692801\pi$
$709$			8153.11i			0.431871i	−0.976408	+	0.215935i	$0.930720\pi$
$710$		0			0
$711$			13328.5i			0.703036i
$712$	−15211.8	+	18232.4i	−0.800681	+	0.959672i
$713$	−13354.1	−	13354.1i	−0.701425	−	0.701425i
$714$	6636.31	+	3570.26i	0.347840	+	0.187134i
$715$		0			0
$716$	26724.8	−	17648.9i	1.39491	−	0.921189i
$717$	−7658.81	+	7658.81i	−0.398917	+	0.398917i
$718$	2900.74	+	9656.25i	0.150772	+	0.501905i
$719$	−17219.3			−0.893147			−0.446573	−	0.894747i	$-0.647356\pi$
$719$	−17219.3			−0.893147			−0.446573	+	0.894747i	$0.647356\pi$
$720$		0			0
$721$	−10130.8			−0.523287
$722$	9426.94	+	31381.3i	0.485920	+	1.61758i
$723$	−11152.0	+	11152.0i	−0.573649	+	0.573649i
$724$	13017.5	−	8596.70i	0.668221	−	0.441290i
$725$		0			0
$726$	−11773.9	−	6334.22i	−0.601888	−	0.323809i
$727$	−8881.73	−	8881.73i	−0.453102	−	0.453102i	0.443281	−	0.896383i	$-0.353814\pi$
$727$	−8881.73	−	8881.73i	−0.453102	−	0.453102i	−0.896383	+	0.443281i	$0.853814\pi$
$728$	−1382.62	+	1657.17i	−0.0703893	+	0.0843665i
$729$			17486.6i			0.888409i
$730$		0			0
$731$		−	1891.43i		−	0.0957004i
$732$	1377.76	−	6736.12i	0.0695676	−	0.340129i
$733$	−4401.20	−	4401.20i	−0.221776	−	0.221776i	0.587470	−	0.809246i	$-0.300124\pi$
$733$	−4401.20	−	4401.20i	−0.221776	−	0.221776i	−0.809246	+	0.587470i	$0.800124\pi$
$734$	8353.30	−	15526.9i	0.420062	−	0.780802i
$735$		0			0
$736$	−14213.2	+	11346.8i	−0.711826	+	0.568271i
$737$	−256.253	+	256.253i	−0.0128076	+	0.0128076i
$738$	7599.79	−	2282.98i	0.379068	−	0.113872i
$739$	−23097.8			−1.14975			−0.574875	−	0.818241i	$-0.694949\pi$
$739$	−23097.8			−1.14975			−0.574875	+	0.818241i	$0.694949\pi$
$740$		0			0
$741$	1907.65			0.0945741
$742$	7182.77	−	2157.70i	0.355374	−	0.106754i
$743$	−17404.1	+	17404.1i	−0.859348	+	0.859348i	−0.991261	−	0.131913i	$-0.957888\pi$
$743$	−17404.1	+	17404.1i	−0.859348	+	0.859348i	0.131913	+	0.991261i	$0.457888\pi$
$744$	1416.65	+	15685.1i	0.0698075	+	0.772911i
$745$		0			0
$746$	−15864.3	+	29488.2i	−0.778597	+	1.44724i
$747$	−5624.13	−	5624.13i	−0.275470	−	0.275470i
$748$	1654.48	+	338.395i	0.0808739	+	0.0165414i
$749$		−	16509.4i		−	0.805396i
$750$		0			0
$751$		−	2347.75i		−	0.114075i	−0.998372	−	0.0570377i	$-0.981834\pi$
$751$		−	2347.75i		−	0.114075i	0.998372	−	0.0570377i	$-0.0181655\pi$
$752$	15933.3	−	6399.05i	0.772644	−	0.310305i
$753$	13794.7	+	13794.7i	0.667604	+	0.667604i
$754$	−324.007	−	174.312i	−0.0156494	−	0.00841919i
$755$		0			0
$756$	−16535.6	−	25038.9i	−0.795493	−	1.20457i
$757$	7078.12	−	7078.12i	0.339840	−	0.339840i	−0.516467	−	0.856307i	$-0.672753\pi$
$757$	7078.12	−	7078.12i	0.339840	−	0.339840i	0.856307	+	0.516467i	$0.172753\pi$
$758$	−9056.95	−	30149.6i	−0.433989	−	1.44470i
$759$	−2743.91			−0.131222
$760$		0			0
$761$	−27017.6			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$761$	−27017.6			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$762$	−2639.56	−	8786.80i	−0.125487	−	0.417732i
$763$	11349.0	−	11349.0i	0.538483	−	0.538483i
$764$	−6431.22	−	9738.45i	−0.304546	−	0.461158i
$765$		0			0
$766$	−3545.90	−	1907.65i	−0.167257	−	0.0899821i
$767$	−271.124	−	271.124i	−0.0127636	−	0.0127636i
$768$	15162.8	+	327.626i	0.712423	+	0.0153935i
$769$			41584.0i			1.95001i	0.222183	+	0.975005i	$0.428682\pi$
$769$			41584.0i			1.95001i	−0.222183	+	0.975005i	$0.571318\pi$
$770$		0			0
$771$			29507.7i			1.37833i
$772$	25102.5	+	5134.29i	1.17028	+	0.239362i
$773$	19799.8	+	19799.8i	0.921280	+	0.921280i	0.997120	−	0.0758404i	$-0.0241639\pi$
$773$	19799.8	+	19799.8i	0.921280	+	0.921280i	−0.0758404	+	0.997120i	$0.524164\pi$
$774$	−1176.99	+	2187.77i	−0.0546591	+	0.101599i
$775$		0			0
$776$	−17099.2	+	1544.36i	−0.791014	+	0.0714426i
$777$	−23336.9	+	23336.9i	−1.07749	+	1.07749i
$778$	−36700.5	+	11024.8i	−1.69123	+	0.508045i
$779$	28669.7			1.31861
$780$		0			0
$781$	−4533.23			−0.207697
$782$	−7788.84	+	2339.77i	−0.356174	+	0.106995i
$783$	3617.07	−	3617.07i	0.165087	−	0.165087i
$784$	17018.5	+	7265.64i	0.775260	+	0.330979i
$785$		0			0
$786$	8038.74	−	14942.2i	0.364799	−	0.678081i
$787$	−23772.7	−	23772.7i	−1.07675	−	1.07675i	−0.996799	−	0.0799542i	$-0.974523\pi$
$787$	−23772.7	−	23772.7i	−1.07675	−	1.07675i	−0.0799542	−	0.996799i	$-0.525477\pi$
$788$	4744.34	−	23195.9i	0.214480	−	1.04863i
$789$			14253.6i			0.643144i
$790$		0			0
$791$			35621.9i			1.60123i
$792$	−1703.11	−	1420.96i	−0.0764110	−	0.0637519i
$793$	622.640	+	622.640i	0.0278822	+	0.0278822i
$794$	−6420.99	−	3454.42i	−0.286993	−	0.154399i
$795$		0			0
$796$	13936.8	−	9203.77i	0.620573	−	0.409823i
$797$	−8760.69	+	8760.69i	−0.389359	+	0.389359i	−0.874459	−	0.485100i	$-0.838783\pi$
$797$	−8760.69	+	8760.69i	−0.389359	+	0.389359i	0.485100	+	0.874459i	$0.338783\pi$
$798$	−10288.1	−	34247.9i	−0.456383	−	1.51925i
$799$	7678.08			0.339964
$800$		0			0
$801$	13946.1			0.615184
$802$	4818.98	+	16041.9i	0.212175	+	0.706308i
$803$	276.138	−	276.138i	0.0121353	−	0.0121353i
$804$	−1214.46	+	802.025i	−0.0532722	+	0.0351806i
$805$		0			0
$806$	−1776.22	−	955.585i	−0.0776236	−	0.0417606i
$807$	−1581.31	−	1581.31i	−0.0689774	−	0.0689774i
$808$	24598.7	+	20523.4i	1.07101	+	0.893576i
$809$		−	27571.0i		−	1.19820i	−0.800673	−	0.599102i	$-0.795525\pi$
$809$		−	27571.0i		−	1.19820i	0.800673	−	0.599102i	$-0.204475\pi$
$810$		0			0
$811$		−	20085.4i		−	0.869661i	−0.900512	−	0.434831i	$-0.856808\pi$
$811$		−	20085.4i		−	0.869661i	0.900512	−	0.434831i	$-0.143192\pi$
$812$	−1382.02	+	6756.94i	−0.0597282	+	0.292022i
$813$	−11080.9	−	11080.9i	−0.478014	−	0.478014i
$814$	−3504.02	+	6513.18i	−0.150879	+	0.280451i
$815$		0			0
$816$	6237.33	+	2662.88i	0.267586	+	0.114239i
$817$	−6346.65	+	6346.65i	−0.271776	+	0.271776i
$818$	−23114.7	+	6943.65i	−0.988002	+	0.296796i
$819$	1267.59			0.0540820
$820$		0			0
$821$	14867.5			0.632008			0.316004	−	0.948758i	$-0.397659\pi$
$821$	14867.5			0.632008			0.316004	+	0.948758i	$0.397659\pi$
$822$	11703.5	−	3515.72i	0.496600	−	0.149179i
$823$	−23345.7	+	23345.7i	−0.988797	+	0.988797i	−0.999938	−	0.0111410i	$-0.996454\pi$
$823$	−23345.7	+	23345.7i	−0.988797	+	0.988797i	0.0111410	+	0.999938i	$0.496454\pi$
$824$	−9080.48	+	820.128i	−0.383900	+	0.0346730i
$825$		0			0
$826$	−3405.27	+	6329.64i	−0.143444	+	0.266630i
$827$	3330.46	+	3330.46i	0.140038	+	0.140038i	0.773651	−	0.633613i	$-0.218429\pi$
$827$	3330.46	+	3330.46i	0.140038	+	0.140038i	−0.633613	+	0.773651i	$0.718429\pi$
$828$	10465.1	+	2140.47i	0.439237	+	0.0898385i
$829$			11521.6i			0.482703i	0.970438	+	0.241351i	$0.0775906\pi$
$829$			11521.6i			0.482703i	−0.970438	+	0.241351i	$0.922409\pi$
$830$		0			0
$831$		−	16830.3i		−	0.702570i
$832$	−1105.13	+	1597.30i	−0.0460498	+	0.0665580i
$833$	5851.12	+	5851.12i	0.243372	+	0.243372i
$834$	−11659.7	−	6272.76i	−0.484102	−	0.260441i
$835$		0			0
$836$	−4416.09	−	6687.04i	−0.182696	−	0.276646i
$837$	19828.9	−	19828.9i	0.818861	−	0.818861i
$838$	−5800.33	−	19308.7i	−0.239104	−	0.795951i
$839$	−33130.1			−1.36326			−0.681631	−	0.731696i	$-0.738729\pi$
$839$	−33130.1			−1.36326			−0.681631	+	0.731696i	$0.738729\pi$
$840$		0			0
$841$	23213.3			0.951792
$842$	−497.388	−	1655.75i	−0.0203576	−	0.0677684i
$843$	19832.5	−	19832.5i	0.810280	−	0.810280i
$844$	879.936	+	1332.44i	0.0358870	+	0.0543418i
$845$		0			0
$846$	−8881.03	−	4777.89i	−0.360918	−	0.194169i
$847$	−22695.7	−	22695.7i	−0.920699	−	0.920699i
$848$	6263.43	−	2515.48i	0.253641	−	0.101866i
$849$			2639.66i			0.106705i
$850$		0			0
$851$		−	35617.7i		−	1.43474i
$852$	−17836.3	−	3648.11i	−0.717208	−	0.146693i
$853$	−12007.8	−	12007.8i	−0.481994	−	0.481994i	0.423774	−	0.905768i	$-0.360705\pi$
$853$	−12007.8	−	12007.8i	−0.481994	−	0.481994i	−0.905768	+	0.423774i	$0.860705\pi$
$854$	7820.26	−	14536.1i	0.313354	−	0.582454i
$855$		0			0
$856$	−1336.51	−	14797.8i	−0.0533655	−	0.590864i
$857$	9369.48	−	9369.48i	0.373460	−	0.373460i	−0.495276	−	0.868736i	$-0.664933\pi$
$857$	9369.48	−	9369.48i	0.373460	−	0.373460i	0.868736	+	0.495276i	$0.164933\pi$
$858$	−280.656	+	84.3090i	−0.0111672	+	0.00335462i
$859$	−17337.1			−0.688630			−0.344315	−	0.938854i	$-0.611889\pi$
$859$	−17337.1			−0.688630			−0.344315	+	0.938854i	$0.611889\pi$
$860$		0			0
$861$	−19652.8			−0.777891
$862$	−25359.4	+	7617.98i	−1.00203	+	0.301009i
$863$	−17345.8	+	17345.8i	−0.684191	+	0.684191i	−0.960942	−	0.276751i	$-0.910742\pi$
$863$	−17345.8	+	17345.8i	−0.684191	+	0.684191i	0.276751	+	0.960942i	$0.410742\pi$
$864$	−16848.3	−	21104.4i	−0.663414	−	0.831004i
$865$		0			0
$866$	−3353.36	+	6233.15i	−0.131584	+	0.244586i
$867$	−10718.9	−	10718.9i	−0.419875	−	0.419875i
$868$	−7576.27	+	37041.8i	−0.296262	+	1.44848i
$869$		−	7397.36i		−	0.288767i
$870$		0			0
$871$		−	186.390i		−	0.00725096i
$872$	9253.69	−	11091.2i	0.359368	−	0.430728i
$873$	7130.35	+	7130.35i	0.276433	+	0.276433i
$874$	33986.3	+	18284.2i	1.31534	+	0.707636i
$875$		0			0
$876$	1308.70	−	864.260i	0.0504760	−	0.0333341i
$877$	18857.4	−	18857.4i	0.726075	−	0.726075i	−0.243760	−	0.969836i	$-0.578381\pi$
$877$	18857.4	−	18857.4i	0.726075	−	0.726075i	0.969836	+	0.243760i	$0.0783810\pi$
$878$	6366.14	+	21192.2i	0.244700	+	0.814581i
$879$	−1278.44			−0.0490567
$880$		0			0
$881$	27095.7			1.03618			0.518092	−	0.855325i	$-0.326643\pi$
$881$	27095.7			1.03618			0.518092	+	0.855325i	$0.326643\pi$
$882$	−3126.82	−	10408.9i	−0.119371	−	0.397374i
$883$	−2484.93	+	2484.93i	−0.0947049	+	0.0947049i	−0.752872	−	0.658167i	$-0.771332\pi$
$883$	−2484.93	+	2484.93i	−0.0947049	+	0.0947049i	0.658167	+	0.752872i	$0.271332\pi$
$884$	−724.775	+	478.638i	−0.0275756	+	0.0182108i
$885$		0			0
$886$	31937.4	+	17182.0i	1.21101	+	0.651511i
$887$	26609.3	+	26609.3i	1.00727	+	1.00727i	0.999973	+	0.00730049i	$0.00232384\pi$
$887$	26609.3	+	26609.3i	1.00727	+	1.00727i	0.00730049	+	0.999973i	$0.497676\pi$
$888$	−19028.3	+	22806.7i	−0.719084	+	0.861873i
$889$		−	22025.7i		−	0.830955i
$890$		0			0
$891$		−	1427.63i		−	0.0536785i
$892$	7572.63	−	37024.0i	0.284249	−	1.38975i
$893$	−25763.6	−	25763.6i	−0.965451	−	0.965451i
$894$	6705.85	−	12464.7i	0.250869	−	0.466310i
$895$		0			0
$896$	34636.1	+	11225.9i	1.29142	+	0.418563i
$897$	997.915	−	997.915i	0.0371454	−	0.0371454i
$898$	9161.12	−	2752.00i	0.340435	−	0.102267i
$899$	−6445.42			−0.239118
$900$		0			0
$901$	3018.27			0.111602
$902$	−4217.90	+	1267.06i	−0.155699	+	0.0467721i
$903$	4350.56	−	4350.56i	0.160330	−	0.160330i
$904$	2883.74	+	31928.9i	0.106097	+	1.17471i
$905$		0			0
$906$	11539.4	−	21449.1i	0.423146	−	0.786534i
$907$	23802.0	+	23802.0i	0.871369	+	0.871369i	0.992622	−	0.121252i	$-0.0386910\pi$
$907$	23802.0	+	23802.0i	0.871369	+	0.871369i	−0.121252	+	0.992622i	$0.538691\pi$
$908$	9136.92	+	1868.80i	0.333942	+	0.0683022i
$909$		−	18815.8i		−	0.686558i
$910$		0			0
$911$			36580.4i			1.33036i	0.746681	+	0.665182i	$0.231646\pi$
$911$			36580.4i			1.33036i	−0.746681	+	0.665182i	$0.768354\pi$
$912$	−11994.0	−	29864.5i	−0.435483	−	1.08433i
$913$	3121.41	+	3121.41i	0.113147	+	0.113147i
$914$	−36246.2	−	19500.0i	−1.31173	−	0.705694i
$915$		0			0
$916$	19892.5	+	30122.2i	0.717540	+	1.08653i
$917$	28803.0	−	28803.0i	1.03725	−	1.03725i
$918$	−3474.21	−	11565.3i	−0.124908	−	0.415807i
$919$	32910.8			1.18131			0.590657	−	0.806923i	$-0.298869\pi$
$919$	32910.8			1.18131			0.590657	+	0.806923i	$0.298869\pi$
$920$		0			0
$921$	−35886.5			−1.28393
$922$	−4321.11	−	14384.5i	−0.154347	−	0.513806i
$923$	1648.66	−	1648.66i	0.0587935	−	0.0587935i
$924$	3027.18	+	4583.90i	0.107778	+	0.163203i
$925$		0			0
$926$	−27077.3	−	14567.3i	−0.960924	−	0.516966i
$927$	3786.55	+	3786.55i	0.134160	+	0.134160i
$928$	−691.737	+	6168.30i	−0.0244692	+	0.218195i
$929$		−	2662.19i		−	0.0940190i	−0.998894	−	0.0470095i	$-0.985031\pi$
$929$		−	2662.19i		−	0.0940190i	0.998894	−	0.0470095i	$-0.0149691\pi$
$930$		0			0
$931$		−	39266.6i		−	1.38229i
$932$	−3242.96	−	663.293i	−0.113977	−	0.0233121i
$933$	28283.9	+	28283.9i	0.992468	+	0.992468i
$934$	8596.18	−	15978.4i	0.301152	−	0.559774i
$935$		0			0
$936$	1136.17	−	102.617i	0.0396763	−	0.00358347i
$937$	−37885.5	+	37885.5i	−1.32088	+	1.32088i	−0.407818	+	0.913063i	$0.633710\pi$
$937$	−37885.5	+	37885.5i	−1.32088	+	1.32088i	−0.913063	+	0.407818i	$0.866290\pi$
$938$	−3346.24	+	1005.21i	−0.116480	+	0.0349907i
$939$	13711.2			0.476517
$940$		0			0
$941$	−6516.65			−0.225756			−0.112878	−	0.993609i	$-0.536007\pi$
$941$	−6516.65			−0.225756			−0.112878	+	0.993609i	$0.536007\pi$
$942$	2304.82	−	692.368i	0.0797188	−	0.0239475i
$943$	14997.4	−	14997.4i	0.517904	−	0.517904i
$944$	−2539.83	+	5949.10i	−0.0875681	+	0.205113i
$945$		0			0
$946$	653.234	−	1214.22i	0.0224508	−	0.0417310i
$947$	−10250.1	−	10250.1i	−0.351724	−	0.351724i	0.509026	−	0.860751i	$-0.330006\pi$
$947$	−10250.1	−	10250.1i	−0.351724	−	0.351724i	−0.860751	+	0.509026i	$0.830006\pi$
$948$	5953.02	−	29105.4i	0.203951	−	0.997152i
$949$			200.854i			0.00687037i
$950$		0			0
$951$		−	19126.8i		−	0.652187i
$952$	12501.7	+	10430.5i	0.425611	+	0.355099i
$953$	−19249.8	−	19249.8i	−0.654314	−	0.654314i	0.299715	−	0.954029i	$-0.403109\pi$
$953$	−19249.8	−	19249.8i	−0.654314	−	0.654314i	−0.954029	+	0.299715i	$0.903109\pi$
$954$	−3491.16	−	1878.20i	−0.118481	−	0.0637411i
$955$		0			0
$956$	−19527.7	+	12896.0i	−0.660637	+	0.436281i
$957$	−662.180	+	662.180i	−0.0223670	+	0.0223670i
$958$	8926.38	+	29715.0i	0.301042	+	1.00214i
$959$	29336.9			0.987838
$960$		0			0
$961$	−5543.06			−0.186065
$962$	−1094.39	−	3643.09i	−0.0366782	−	0.122098i
$963$	−6170.68	+	6170.68i	−0.206487	+	0.206487i
$964$	−28434.3	+	18777.8i	−0.950007	+	0.627379i
$965$		0			0
$966$	−23297.3	−	12533.7i	−0.775960	−	0.417457i
$967$	3744.56	+	3744.56i	0.124526	+	0.124526i	0.766623	−	0.642097i	$-0.221935\pi$
$967$	3744.56	+	3744.56i	0.124526	+	0.124526i	−0.642097	+	0.766623i	$0.721935\pi$
$968$	−22180.0	−	18505.4i	−0.736460	−	0.614449i
$969$		−	14391.3i		−	0.477106i
$970$		0			0
$971$			29491.0i			0.974677i	0.873213	+	0.487338i	$0.162032\pi$
$971$			29491.0i			0.974677i	−0.873213	+	0.487338i	$0.837968\pi$
$972$	−5308.17	+	25952.6i	−0.175164	+	0.856411i
$973$	−22475.4	−	22475.4i	−0.740524	−	0.740524i
$974$	−24136.1	+	44863.7i	−0.794016	+	1.47590i
$975$		0			0
$976$	5832.75	−	13662.2i	0.191293	−	0.448070i
$977$	−13592.2	+	13592.2i	−0.445092	+	0.445092i	−0.893719	−	0.448627i	$-0.851913\pi$
$977$	−13592.2	+	13592.2i	−0.445092	+	0.445092i	0.448627	+	0.893719i	$0.351913\pi$
$978$	13226.4	−	3973.21i	0.432447	−	0.129907i
$979$	−7740.14			−0.252682
$980$		0			0
$981$	−8483.78			−0.276112
$982$	−28493.2	+	8559.36i	−0.925921	+	0.278147i
$983$	12087.1	−	12087.1i	0.392185	−	0.392185i	−0.483280	−	0.875466i	$-0.660555\pi$
$983$	12087.1	−	12087.1i	0.392185	−	0.392185i	0.875466	+	0.483280i	$0.160555\pi$
$984$	−17615.3	+	1590.97i	−0.570686	+	0.0515430i
$985$		0			0
$986$	−1315.01	+	2444.31i	−0.0424730	+	0.0789478i
$987$	17660.7	+	17660.7i	0.569551	+	0.569551i
$988$	4038.03	+	825.910i	0.130027	+	0.0265949i
$989$			6640.01i			0.213488i
$990$		0			0
$991$		−	52539.6i		−	1.68413i	−0.539374	−	0.842066i	$-0.681339\pi$
$991$		−	52539.6i		−	1.68413i	0.539374	−	0.842066i	$-0.318661\pi$
$992$	−3792.13	+	33814.9i	−0.121371	+	1.08228i
$993$	−20526.6	−	20526.6i	−0.655984	−	0.655984i
$994$	−38489.6	−	20706.9i	−1.22818	−	0.660749i
$995$		0			0
$996$	9769.43	+	14793.3i	0.310799	+	0.470627i
$997$	−12067.7	+	12067.7i	−0.383337	+	0.383337i	−0.872303	−	0.488966i	$-0.837374\pi$
$997$	−12067.7	+	12067.7i	−0.383337	+	0.383337i	0.488966	+	0.872303i	$0.337374\pi$
$998$	−1989.80	−	6623.82i	−0.0631121	−	0.210094i
$999$	52887.0			1.67495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.e.43.4		12
4.3	odd	2	inner	100.4.e.e.43.1		12
5.2	odd	4	inner	100.4.e.e.7.1		12
5.3	odd	4		20.4.e.b.7.6	yes	12
5.4	even	2		20.4.e.b.3.3	✓	12
15.8	even	4		180.4.k.e.127.1		12
15.14	odd	2		180.4.k.e.163.4		12
20.3	even	4		20.4.e.b.7.3	yes	12
20.7	even	4	inner	100.4.e.e.7.4		12
20.19	odd	2		20.4.e.b.3.6	yes	12
40.3	even	4		320.4.n.k.127.3		12
40.13	odd	4		320.4.n.k.127.4		12
40.19	odd	2		320.4.n.k.63.4		12
40.29	even	2		320.4.n.k.63.3		12
60.23	odd	4		180.4.k.e.127.4		12
60.59	even	2		180.4.k.e.163.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.3	✓	12	5.4	even	2
20.4.e.b.3.6	yes	12	20.19	odd	2
20.4.e.b.7.3	yes	12	20.3	even	4
20.4.e.b.7.6	yes	12	5.3	odd	4
100.4.e.e.7.1		12	5.2	odd	4	inner
100.4.e.e.7.4		12	20.7	even	4	inner
100.4.e.e.43.1		12	4.3	odd	2	inner
100.4.e.e.43.4		12	1.1	even	1	trivial
180.4.k.e.127.1		12	15.8	even	4
180.4.k.e.127.4		12	60.23	odd	4
180.4.k.e.163.1		12	60.59	even	2
180.4.k.e.163.4		12	15.14	odd	2
320.4.n.k.63.3		12	40.29	even	2
320.4.n.k.63.4		12	40.19	odd	2
320.4.n.k.127.3		12	40.3	even	4
320.4.n.k.127.4		12	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.813737 + 2.70884i) q^{2} +(-2.61822 + 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 - 17.7783i) q^{7} +(-17.3744 - 14.4959i) q^{8} +13.2899i q^{9} +O(q^{10})\)	\(q+(0.813737 + 2.70884i) q^{2} +(-2.61822 + 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 - 17.7783i) q^{7} +(-17.3744 - 14.4959i) q^{8} +13.2899i q^{9} -7.37590i q^{11} +(5.93575 - 29.0210i) q^{12} +(2.68249 + 2.68249i) q^{13} +(33.6917 - 62.6254i) q^{14} +(25.1290 - 58.8603i) q^{16} +(20.2367 - 20.2367i) q^{17} +(-36.0001 + 10.8144i) q^{18} -135.808 q^{19} +93.0948 q^{21} +(19.9802 - 6.00204i) q^{22} +(-71.0426 + 71.0426i) q^{23} +(83.4434 - 7.53642i) q^{24} +(-5.08361 + 9.44930i) q^{26} +(-105.488 - 105.488i) q^{27} +(197.059 + 40.3050i) q^{28} +34.2890i q^{29} +187.974i q^{31} +(179.892 + 20.1737i) q^{32} +(19.3117 + 19.3117i) q^{33} +(71.2855 + 38.3507i) q^{34} +(-58.5893 - 88.7186i) q^{36} +(-250.679 + 250.679i) q^{37} +(-110.512 - 367.882i) q^{38} -14.0467 q^{39} -211.105 q^{41} +(75.7547 + 252.179i) q^{42} +(46.7326 - 46.7326i) q^{43} +(32.5172 + 49.2390i) q^{44} +(-250.253 - 134.633i) q^{46} +(189.707 + 189.707i) q^{47} +(88.3159 + 219.902i) q^{48} +289.134i q^{49} +105.968i q^{51} +(-29.7334 - 6.08147i) q^{52} +(74.5742 + 74.5742i) q^{53} +(199.910 - 371.589i) q^{54} +(51.1739 + 566.598i) q^{56} +(355.575 - 355.575i) q^{57} +(-92.8835 + 27.9022i) q^{58} -101.072 q^{59} +232.112 q^{61} +(-509.191 + 152.961i) q^{62} +(236.271 - 236.271i) q^{63} +(91.7370 + 503.715i) q^{64} +(-36.5978 + 68.0271i) q^{66} +(-34.7419 - 34.7419i) q^{67} +(-45.8785 + 224.309i) q^{68} -372.010i q^{69} -614.600i q^{71} +(192.649 - 230.903i) q^{72} +(37.4378 + 37.4378i) q^{73} +(-883.036 - 475.063i) q^{74} +(906.607 - 598.718i) q^{76} +(-131.131 + 131.131i) q^{77} +(-11.4303 - 38.0504i) q^{78} +1002.91 q^{79} +193.554 q^{81} +(-171.784 - 571.850i) q^{82} +(-423.190 + 423.190i) q^{83} +(-621.470 + 410.415i) q^{84} +(164.619 + 88.5632i) q^{86} +(-89.7761 - 89.7761i) q^{87} +(-106.920 + 128.152i) q^{88} -1049.38i q^{89} -95.3802i q^{91} +(161.060 - 787.453i) q^{92} +(-492.156 - 492.156i) q^{93} +(-359.514 + 668.257i) q^{94} +(-523.815 + 418.177i) q^{96} +(536.526 - 536.526i) q^{97} +(-783.218 + 235.279i) q^{98} +98.0246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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