LMFDB - Embedded newform 225.4.h.d.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	225.91
Dual form			225.4.h.d.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68030 - 1.94735i) q^{2} +(0.919680 + 2.83048i) q^{4} +(-2.31093 - 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 + 15.8295i) q^{8} +O(q^{10})$	\(q+(-2.68030 - 1.94735i) q^{2} +(0.919680 + 2.83048i) q^{4} +(-2.31093 - 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 + 15.8295i) q^{8} +(-15.1079 + 33.8197i) q^{10} +(-43.0382 - 31.2691i) q^{11} +(-29.8370 + 21.6778i) q^{13} +(-28.8808 - 20.9831i) q^{14} +(63.8733 - 46.4067i) q^{16} +(21.1745 - 65.1683i) q^{17} +(-1.49479 + 4.60048i) q^{19} +(28.8371 - 16.6014i) q^{20} +(54.4633 + 167.621i) q^{22} +(-67.0563 - 48.7193i) q^{23} +(-114.319 + 50.5582i) q^{25} +122.186 q^{26} +(9.90977 + 30.4991i) q^{28} +(51.1534 + 157.434i) q^{29} +(-97.3566 + 299.633i) q^{31} -128.416 q^{32} +(-183.659 + 133.436i) q^{34} +(-24.9009 - 117.869i) q^{35} +(202.266 - 146.955i) q^{37} +(12.9652 - 9.41977i) q^{38} +(185.044 + 19.6814i) q^{40} +(-292.377 + 212.424i) q^{41} +180.805 q^{43} +(48.9253 - 150.576i) q^{44} +(84.8573 + 261.164i) q^{46} +(68.6994 + 211.435i) q^{47} -226.894 q^{49} +(404.863 + 87.1085i) q^{50} +(-88.7992 - 64.5164i) q^{52} +(162.370 + 499.723i) q^{53} +(-242.591 + 543.051i) q^{55} +(-55.4206 + 170.567i) q^{56} +(169.473 - 521.583i) q^{58} +(-34.9106 + 25.3641i) q^{59} +(502.015 + 364.735i) q^{61} +(844.434 - 613.517i) q^{62} +(-166.794 - 121.183i) q^{64} +(306.083 + 276.288i) q^{65} +(71.8608 - 221.165i) q^{67} +203.932 q^{68} +(-162.791 + 364.415i) q^{70} +(195.891 + 602.890i) q^{71} +(-770.064 - 559.484i) q^{73} -828.305 q^{74} -14.3963 q^{76} +(-463.747 - 336.932i) q^{77} +(-281.459 - 866.243i) q^{79} +(-655.245 - 591.461i) q^{80} +1197.32 q^{82} +(61.3942 - 188.952i) q^{83} +(-761.802 - 81.0258i) q^{85} +(-484.612 - 352.091i) q^{86} +(716.334 - 520.447i) q^{88} +(-703.370 - 511.028i) q^{89} +(-321.500 + 233.584i) q^{91} +(76.2288 - 234.608i) q^{92} +(227.603 - 700.490i) q^{94} +(53.7785 + 5.71992i) q^{95} +(-68.4303 - 210.607i) q^{97} +(608.144 + 441.842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.68030	−	1.94735i	−0.947627	−	0.688492i	0.00261710	−	0.999997i	$-0.499167\pi$
$2$	−2.68030	−	1.94735i	−0.947627	−	0.688492i	−0.950245	+	0.311505i	$0.899167\pi$
$3$		0			0
$3$		0			0
$4$	0.919680	+	2.83048i	0.114960	+	0.353811i
$5$	−2.31093	−	10.9389i	−0.206696	−	0.978405i
$5$	−2.31093	−	10.9389i	−0.206696	−	0.978405i
$6$		0			0
$7$	10.7752			0.581808			0.290904	−	0.956752i	$-0.406044\pi$
$7$	10.7752			0.581808			0.290904	+	0.956752i	$0.406044\pi$
$8$	−5.14333	+	15.8295i	−0.227305	+	0.699573i
$9$		0			0
$10$	−15.1079	+	33.8197i	−0.477753	+	1.06947i
$11$	−43.0382	−	31.2691i	−1.17968	−	0.857089i	−0.187546	−	0.982256i	$-0.560053\pi$
$11$	−43.0382	−	31.2691i	−1.17968	−	0.857089i	−0.992136	+	0.125167i	$0.960053\pi$
$12$		0			0
$13$	−29.8370	+	21.6778i	−0.636560	+	0.462488i	−0.858667	−	0.512534i	$-0.828707\pi$
$13$	−29.8370	+	21.6778i	−0.636560	+	0.462488i	0.222107	+	0.975022i	$0.428707\pi$
$14$	−28.8808	−	20.9831i	−0.551337	−	0.400570i
$15$		0			0
$16$	63.8733	−	46.4067i	0.998020	−	0.725104i
$17$	21.1745	−	65.1683i	0.302092	−	0.929743i	−0.678655	−	0.734458i	$-0.737437\pi$
$17$	21.1745	−	65.1683i	0.302092	−	0.929743i	0.980746	−	0.195286i	$-0.0625634\pi$
$18$		0			0
$19$	−1.49479	+	4.60048i	−0.0180488	+	0.0555485i	−0.959675	−	0.281111i	$-0.909297\pi$
$19$	−1.49479	+	4.60048i	−0.0180488	+	0.0555485i	0.941626	+	0.336659i	$0.109297\pi$
$20$	28.8371	−	16.6014i	0.322408	−	0.185609i
$21$		0			0
$22$	54.4633	+	167.621i	0.527800	+	1.62440i
$23$	−67.0563	−	48.7193i	−0.607922	−	0.441681i	0.240760	−	0.970585i	$-0.422603\pi$
$23$	−67.0563	−	48.7193i	−0.607922	−	0.441681i	−0.848682	+	0.528903i	$0.822603\pi$
$24$		0			0
$25$	−114.319	+	50.5582i	−0.914553	+	0.404465i
$26$	122.186			0.921641
$27$		0			0
$28$	9.90977	+	30.4991i	0.0668847	+	0.205850i
$29$	51.1534	+	157.434i	0.327550	+	1.00809i	0.970276	+	0.241999i	$0.0778031\pi$
$29$	51.1534	+	157.434i	0.327550	+	1.00809i	−0.642727	+	0.766096i	$0.722197\pi$
$30$		0			0
$31$	−97.3566	+	299.633i	−0.564057	+	1.73599i	0.106680	+	0.994293i	$0.465978\pi$
$31$	−97.3566	+	299.633i	−0.564057	+	1.73599i	−0.670737	+	0.741695i	$0.734022\pi$
$32$	−128.416			−0.709405
$33$		0			0
$34$	−183.659	+	133.436i	−0.926391	+	0.673062i
$35$	−24.9009	−	117.869i	−0.120258	−	0.569244i
$36$		0			0
$37$	202.266	−	146.955i	0.898712	−	0.652952i	−0.0394231	−	0.999223i	$-0.512552\pi$
$37$	202.266	−	146.955i	0.898712	−	0.652952i	0.938135	+	0.346270i	$0.112552\pi$
$38$	12.9652	−	9.41977i	0.0553483	−	0.0402129i
$39$		0			0
$40$	185.044	+	19.6814i	0.731449	+	0.0777974i
$41$	−292.377	+	212.424i	−1.11370	+	0.809148i	−0.983242	−	0.182307i	$-0.941644\pi$
$41$	−292.377	+	212.424i	−1.11370	+	0.809148i	−0.130454	+	0.991454i	$0.541644\pi$
$42$		0			0
$43$	180.805			0.641223			0.320611	−	0.947211i	$-0.396112\pi$
$43$	180.805			0.641223			0.320611	+	0.947211i	$0.396112\pi$
$44$	48.9253	−	150.576i	0.167631	−	0.515915i
$45$		0			0
$46$	84.8573	+	261.164i	0.271990	+	0.837099i
$47$	68.6994	+	211.435i	0.213209	+	0.656191i	0.999276	+	0.0380490i	$0.0121143\pi$
$47$	68.6994	+	211.435i	0.213209	+	0.656191i	−0.786067	+	0.618142i	$0.787886\pi$
$48$		0			0
$49$	−226.894			−0.661499
$50$	404.863	+	87.1085i	1.14513	+	0.246380i
$51$		0			0
$52$	−88.7992	−	64.5164i	−0.236812	−	0.172054i
$53$	162.370	+	499.723i	0.420815	+	1.29514i	0.906945	+	0.421249i	$0.138408\pi$
$53$	162.370	+	499.723i	0.420815	+	1.29514i	−0.486130	+	0.873886i	$0.661592\pi$
$54$		0			0
$55$	−242.591	+	543.051i	−0.594745	+	1.33136i
$56$	−55.4206	+	170.567i	−0.132248	+	0.407017i
$57$		0			0
$58$	169.473	−	521.583i	0.383670	−	1.18081i
$59$	−34.9106	+	25.3641i	−0.0770335	+	0.0559681i	−0.625635	−	0.780116i	$-0.715160\pi$
$59$	−34.9106	+	25.3641i	−0.0770335	+	0.0559681i	0.548602	+	0.836084i	$0.315160\pi$
$60$		0			0
$61$	502.015	+	364.735i	1.05371	+	0.765566i	0.972915	−	0.231165i	$-0.0742536\pi$
$61$	502.015	+	364.735i	1.05371	+	0.765566i	0.0807964	+	0.996731i	$0.474254\pi$
$62$	844.434	−	613.517i	1.72973	−	1.25672i
$63$		0			0
$64$	−166.794	−	121.183i	−0.325769	−	0.236685i
$65$	306.083	+	276.288i	0.584075	+	0.527219i
$66$		0			0
$67$	71.8608	−	221.165i	0.131033	−	0.403277i	−0.863919	−	0.503631i	$-0.831997\pi$
$67$	71.8608	−	221.165i	0.131033	−	0.403277i	0.994952	+	0.100353i	$0.0319973\pi$
$68$	203.932			0.363681
$69$		0			0
$70$	−162.791	+	364.415i	−0.277960	+	0.622228i
$71$	195.891	+	602.890i	0.327436	+	1.00774i	0.970329	+	0.241788i	$0.0777339\pi$
$71$	195.891	+	602.890i	0.327436	+	1.00774i	−0.642893	+	0.765956i	$0.722266\pi$
$72$		0			0
$73$	−770.064	−	559.484i	−1.23465	−	0.897022i	−0.237416	−	0.971408i	$-0.576300\pi$
$73$	−770.064	−	559.484i	−1.23465	−	0.897022i	−0.997230	+	0.0743856i	$0.976300\pi$
$74$	−828.305			−1.30120
$75$		0			0
$76$	−14.3963			−0.0217286
$77$	−463.747	−	336.932i	−0.686349	−	0.498661i
$78$		0			0
$79$	−281.459	−	866.243i	−0.400844	−	1.23367i	−0.924316	−	0.381627i	$-0.875364\pi$
$79$	−281.459	−	866.243i	−0.400844	−	1.23367i	0.523473	−	0.852043i	$-0.324636\pi$
$80$	−655.245	−	591.461i	−0.915733	−	0.826592i
$81$		0			0
$82$	1197.32			1.61246
$83$	61.3942	−	188.952i	0.0811915	−	0.249882i	−0.902218	−	0.431280i	$-0.858062\pi$
$83$	61.3942	−	188.952i	0.0811915	−	0.249882i	0.983410	+	0.181398i	$0.0580622\pi$
$84$		0			0
$85$	−761.802	−	81.0258i	−0.972107	−	0.103394i
$86$	−484.612	−	352.091i	−0.607640	−	0.441476i
$87$		0			0
$88$	716.334	−	520.447i	0.867744	−	0.630453i
$89$	−703.370	−	511.028i	−0.837719	−	0.608639i	0.0840133	−	0.996465i	$-0.473226\pi$
$89$	−703.370	−	511.028i	−0.837719	−	0.608639i	−0.921733	+	0.387826i	$0.873226\pi$
$90$		0			0
$91$	−321.500	+	233.584i	−0.370356	+	0.269079i
$92$	76.2288	−	234.608i	0.0863848	−	0.265865i
$93$		0			0
$94$	227.603	−	700.490i	0.249739	−	0.768617i
$95$	53.7785	+	5.71992i	0.0580796	+	0.00617738i
$96$		0			0
$97$	−68.4303	−	210.607i	−0.0716293	−	0.220452i	0.908833	−	0.417161i	$-0.136975\pi$
$97$	−68.4303	−	210.607i	−0.0716293	−	0.220452i	−0.980462	+	0.196708i	$0.936975\pi$
$98$	608.144	+	441.842i	0.626855	+	0.455437i
$99$		0			0
$100$	−248.241	−	277.081i	−0.248241	−	0.277081i
$101$	−800.883			−0.789019			−0.394509	−	0.918892i	$-0.629085\pi$
$101$	−800.883			−0.789019			−0.394509	+	0.918892i	$0.629085\pi$
$102$		0			0
$103$	−418.585	−	1288.27i	−0.400431	−	1.23240i	−0.924650	−	0.380817i	$-0.875643\pi$
$103$	−418.585	−	1288.27i	−0.400431	−	1.23240i	0.524219	−	0.851584i	$-0.324357\pi$
$104$	−189.689	−	583.801i	−0.178851	−	0.550446i
$105$		0			0
$106$	537.935	−	1655.59i	0.492914	−	1.51703i
$107$	−1010.72			−0.913177			−0.456589	−	0.889678i	$-0.650929\pi$
$107$	−1010.72			−0.913177			−0.456589	+	0.889678i	$0.650929\pi$
$108$		0			0
$109$	−642.415	+	466.742i	−0.564515	+	0.410144i	−0.833109	−	0.553109i	$-0.813441\pi$
$109$	−642.415	+	466.742i	−0.564515	+	0.410144i	0.268593	+	0.963254i	$0.413441\pi$
$110$	1707.73	−	983.129i	1.48023	−	0.852160i
$111$		0			0
$112$	688.250	−	500.043i	0.580656	−	0.421871i
$113$	−437.943	+	318.184i	−0.364586	+	0.264887i	−0.754962	−	0.655768i	$-0.772345\pi$
$113$	−437.943	+	318.184i	−0.364586	+	0.264887i	0.390376	+	0.920655i	$0.372345\pi$
$114$		0			0
$115$	−377.973	+	846.110i	−0.306488	+	0.686088i
$116$	−398.570	+	289.578i	−0.319019	+	0.231781i
$117$		0			0
$118$	142.963			0.111533
$119$	228.160	−	702.204i	0.175759	−	0.540932i
$120$		0			0
$121$	463.229	+	1425.67i	0.348031	+	1.07113i
$122$	−635.281	−	1955.19i	−0.471440	−	1.45094i
$123$		0			0
$124$	−937.643			−0.679055
$125$	817.235	+	1133.69i	0.584766	+	0.811202i
$126$		0			0
$127$	1063.06	+	772.361i	0.742769	+	0.539654i	0.893577	−	0.448910i	$-0.148187\pi$
$127$	1063.06	+	772.361i	0.742769	+	0.539654i	−0.150808	+	0.988563i	$0.548187\pi$
$128$	528.533	+	1626.66i	0.364970	+	1.12326i
$129$		0			0
$130$	−282.364	−	1336.58i	−0.190500	−	0.901738i
$131$	−103.644	+	318.984i	−0.0691255	+	0.212746i	−0.979652	−	0.200705i	$-0.935677\pi$
$131$	−103.644	+	318.984i	−0.0691255	+	0.212746i	0.910526	+	0.413451i	$0.135677\pi$
$132$		0			0
$133$	−16.1067	+	49.5713i	−0.0105009	+	0.0323186i
$134$	−623.293	+	452.849i	−0.401823	+	0.291942i
$135$		0			0
$136$	922.677	+	670.364i	0.581756	+	0.422671i
$137$	973.264	−	707.118i	0.606946	−	0.440972i	−0.241392	−	0.970428i	$-0.577604\pi$
$137$	973.264	−	707.118i	0.606946	−	0.440972i	0.848337	+	0.529456i	$0.177604\pi$
$138$		0			0
$139$	−1583.61	−	1150.56i	−0.966334	−	0.702083i	−0.0117211	−	0.999931i	$-0.503731\pi$
$139$	−1583.61	−	1150.56i	−0.966334	−	0.702083i	−0.954613	+	0.297848i	$0.903731\pi$
$140$	310.726	−	178.884i	0.187580	−	0.107989i
$141$		0			0
$142$	648.991	−	1997.39i	0.383536	−	1.18040i
$143$	1961.97			1.14733
$144$		0			0
$145$	1603.94	−	923.381i	0.918622	−	0.528846i
$146$	974.487	+	2999.16i	0.552391	+	1.70009i
$147$		0			0
$148$	601.974	+	437.359i	0.334337	+	0.242910i
$149$	−2620.38			−1.44074			−0.720369	−	0.693591i	$-0.756028\pi$
$149$	−2620.38			−1.44074			−0.720369	+	0.693591i	$0.756028\pi$
$150$		0			0
$151$	−562.774			−0.303298			−0.151649	−	0.988434i	$-0.548458\pi$
$151$	−562.774			−0.303298			−0.151649	+	0.988434i	$0.548458\pi$
$152$	−65.1353	−	47.3235i	−0.0347577	−	0.0252529i
$153$		0			0
$154$	586.855	+	1806.15i	0.307078	+	0.945090i
$155$	3502.64	+	372.543i	1.81509	+	0.193054i
$156$		0			0
$157$	−2954.02			−1.50163			−0.750817	−	0.660510i	$-0.770340\pi$
$157$	−2954.02			−1.50163			−0.750817	+	0.660510i	$0.770340\pi$
$158$	−932.482	+	2869.89i	−0.469521	+	1.44504i
$159$		0			0
$160$	296.761	+	1404.73i	0.146631	+	0.694085i
$161$	−722.548	−	524.962i	−0.353694	−	0.256974i
$162$		0			0
$163$	−620.436	+	450.773i	−0.298137	+	0.216609i	−0.726789	−	0.686860i	$-0.758988\pi$
$163$	−620.436	+	450.773i	−0.298137	+	0.216609i	0.428653	+	0.903469i	$0.358988\pi$
$164$	−870.156	−	632.205i	−0.414316	−	0.301018i
$165$		0			0
$166$	−532.510	+	386.891i	−0.248981	+	0.180895i
$167$	605.341	−	1863.05i	0.280495	−	0.863276i	−0.707217	−	0.706996i	$-0.750050\pi$
$167$	605.341	−	1863.05i	0.280495	−	0.863276i	0.987713	−	0.156280i	$-0.0499502\pi$
$168$		0			0
$169$	−258.594	+	795.871i	−0.117703	+	0.362254i
$170$	1884.07	+	1700.67i	0.850009	+	0.767266i
$171$		0			0
$172$	166.283	+	511.767i	0.0737150	+	0.226871i
$173$	1944.34	+	1412.65i	0.854483	+	0.620818i	0.926378	−	0.376594i	$-0.122905\pi$
$173$	1944.34	+	1412.65i	0.854483	+	0.620818i	−0.0718957	+	0.997412i	$0.522905\pi$
$174$		0			0
$175$	−1231.82	+	544.776i	−0.532095	+	0.235321i
$176$	−4200.08			−1.79883
$177$		0			0
$178$	890.089	+	2739.41i	0.374803	+	1.15353i
$179$	−104.154	−	320.554i	−0.0434908	−	0.133851i	0.926953	−	0.375176i	$-0.122418\pi$
$179$	−104.154	−	320.554i	−0.0434908	−	0.133851i	−0.970444	+	0.241325i	$0.922418\pi$
$180$		0			0
$181$	−324.908	+	999.965i	−0.133427	+	0.410645i	−0.995342	−	0.0964070i	$-0.969265\pi$
$181$	−324.908	+	999.965i	−0.133427	+	0.410645i	0.861915	+	0.507052i	$0.169265\pi$
$182$	1316.58			0.536218
$183$		0			0
$184$	1116.10	−	810.891i	0.447172	−	0.324890i
$185$	−2074.95	−	1872.97i	−0.824612	−	0.744341i
$186$		0			0
$187$	−2949.06	+	2142.62i	−1.15325	+	0.837882i
$188$	−535.282	+	388.905i	−0.207657	+	0.150871i
$189$		0			0
$190$	−133.004	−	120.057i	−0.0507848	−	0.0458412i
$191$	2116.22	−	1537.53i	0.801699	−	0.582468i	−0.109713	−	0.993963i	$-0.534993\pi$
$191$	2116.22	−	1537.53i	0.801699	−	0.582468i	0.911412	+	0.411495i	$0.134993\pi$
$192$		0			0
$193$	1585.88			0.591472			0.295736	−	0.955270i	$-0.404435\pi$
$193$	1585.88			0.591472			0.295736	+	0.955270i	$0.404435\pi$
$194$	−226.711	+	697.746i	−0.0839017	+	0.258223i
$195$		0			0
$196$	−208.670	−	642.221i	−0.0760460	−	0.234045i
$197$	−639.374	−	1967.79i	−0.231236	−	0.711672i	−0.997598	−	0.0692631i	$-0.977935\pi$
$197$	−639.374	−	1967.79i	−0.231236	−	0.711672i	0.766362	−	0.642409i	$-0.222065\pi$
$198$		0			0
$199$	5111.28			1.82075			0.910374	−	0.413786i	$-0.135794\pi$
$199$	5111.28			1.82075			0.910374	+	0.413786i	$0.135794\pi$
$200$	−212.331	−	2069.66i	−0.0750704	−	0.731734i
$201$		0			0
$202$	2146.60	+	1559.60i	0.747696	+	0.543233i
$203$	551.190	+	1696.39i	0.190571	+	0.586518i
$204$		0			0
$205$	2999.35	+	2707.38i	1.02187	+	0.922398i
$206$	−1386.78	+	4268.08i	−0.469038	+	1.44355i
$207$		0			0
$208$	−899.789	+	2769.27i	−0.299948	+	0.923145i
$209$	208.186	−	151.256i	0.0689019	−	0.0500602i
$210$		0			0
$211$	−4179.26	−	3036.41i	−1.36357	−	0.990688i	−0.998209	−	0.0598201i	$-0.980947\pi$
$211$	−4179.26	−	3036.41i	−1.36357	−	0.990688i	−0.365356	−	0.930868i	$-0.619053\pi$
$212$	−1265.13	+	919.170i	−0.409856	+	0.297778i
$213$		0			0
$214$	2709.03	+	1968.22i	0.865352	+	0.628715i
$215$	−417.829	−	1977.81i	−0.132538	−	0.627375i
$216$		0			0
$217$	−1049.04	+	3228.61i	−0.328173	+	1.01001i
$218$	2630.77			0.817331
$219$		0			0
$220$	−1760.20	−	187.216i	−0.539423	−	0.0573733i
$221$	780.925	+	2403.44i	0.237695	+	0.731551i
$222$		0			0
$223$	−3917.06	−	2845.91i	−1.17626	−	0.854602i	−0.184514	−	0.982830i	$-0.559071\pi$
$223$	−3917.06	−	2845.91i	−1.17626	−	0.854602i	−0.991745	+	0.128228i	$0.959071\pi$
$224$	−1383.71			−0.412737
$225$		0			0
$226$	1793.43			0.527865
$227$	−418.579	−	304.115i	−0.122388	−	0.0889200i	0.524907	−	0.851159i	$-0.324100\pi$
$227$	−418.579	−	304.115i	−0.122388	−	0.0889200i	−0.647295	+	0.762239i	$0.724100\pi$
$228$		0			0
$229$	841.230	+	2589.04i	0.242751	+	0.747111i	0.995998	+	0.0893736i	$0.0284865\pi$
$229$	841.230	+	2589.04i	0.242751	+	0.747111i	−0.753247	+	0.657738i	$0.771514\pi$
$230$	2660.75	−	1531.78i	0.762802	−	0.439141i
$231$		0			0
$232$	−2755.20			−0.779690
$233$	1792.83	−	5517.77i	0.504087	−	1.55142i	−0.298212	−	0.954500i	$-0.596390\pi$
$233$	1792.83	−	5517.77i	0.504087	−	1.55142i	0.802300	−	0.596922i	$-0.203610\pi$
$234$		0			0
$235$	2154.11	−	1240.11i	0.597951	−	0.344237i
$236$	−103.899	−	75.4872i	−0.0286579	−	0.0208212i
$237$		0			0
$238$	−1978.97	+	1437.81i	−0.538982	+	0.391593i
$239$	−3885.12	−	2822.71i	−1.05150	−	0.763957i	−0.0790005	−	0.996875i	$-0.525173\pi$
$239$	−3885.12	−	2822.71i	−1.05150	−	0.763957i	−0.972497	+	0.232917i	$0.925173\pi$
$240$		0			0
$241$	−891.648	+	647.821i	−0.238324	+	0.173153i	−0.700536	−	0.713617i	$-0.747056\pi$
$241$	−891.648	+	647.821i	−0.238324	+	0.173153i	0.462212	+	0.886769i	$0.347056\pi$
$242$	1534.69	−	4723.29i	0.407660	−	1.25465i
$243$		0			0
$244$	−570.684	+	1756.38i	−0.149731	+	0.460824i
$245$	524.338	+	2481.97i	0.136729	+	0.647214i
$246$		0			0
$247$	−55.1285	−	169.668i	−0.0142014	−	0.0437074i
$248$	−4242.31	−	3082.22i	−1.08624	−	0.789198i
$249$		0			0
$250$	17.2584	−	4630.06i	0.00436607	−	1.17132i
$251$	−5994.06			−1.50734			−0.753668	−	0.657255i	$-0.771717\pi$
$251$	−5994.06			−1.50734			−0.753668	+	0.657255i	$0.771717\pi$
$252$		0			0
$253$	1362.58	+	4193.58i	0.338595	+	1.04209i
$254$	−1345.27	−	4140.31i	−0.332322	−	1.02278i
$255$		0			0
$256$	1241.37	−	3820.54i	0.303068	−	0.932748i
$257$	4844.17			1.17576			0.587881	−	0.808948i	$-0.299962\pi$
$257$	4844.17			1.17576			0.587881	+	0.808948i	$0.299962\pi$
$258$		0			0
$259$	2179.46	−	1583.47i	0.522878	−	0.379893i
$260$	−500.529	+	1120.46i	−0.119390	+	0.267261i
$261$		0			0
$262$	898.970	−	653.140i	0.211979	−	0.154012i
$263$	−6370.39	+	4628.36i	−1.49359	+	1.08516i	−0.520748	+	0.853711i	$0.674347\pi$
$263$	−6370.39	+	4628.36i	−1.49359	+	1.08516i	−0.972847	+	0.231449i	$0.925653\pi$
$264$		0			0
$265$	5091.19	−	2930.97i	1.18019	−	0.679427i
$266$	139.703	−	101.500i	0.0322021	−	0.0233962i
$267$		0			0
$268$	692.093			0.157747
$269$	−276.633	+	851.389i	−0.0627012	+	0.192974i	−0.977500	−	0.210935i	$-0.932349\pi$
$269$	−276.633	+	851.389i	−0.0627012	+	0.192974i	0.914799	+	0.403910i	$0.132349\pi$
$270$		0			0
$271$	−288.006	−	886.391i	−0.0645576	−	0.198688i	0.913575	−	0.406670i	$-0.133310\pi$
$271$	−288.006	−	886.391i	−0.0645576	−	0.198688i	−0.978133	+	0.207983i	$0.933310\pi$
$272$	−1671.76	−	5145.15i	−0.372667	−	1.14695i
$273$		0			0
$274$	−3985.64			−0.878764
$275$	6501.00	+	1398.72i	1.42554	+	0.306713i
$276$		0			0
$277$	−6357.04	−	4618.66i	−1.37891	−	1.00184i	−0.996981	−	0.0776436i	$-0.975260\pi$
$277$	−6357.04	−	4618.66i	−1.37891	−	1.00184i	−0.381928	−	0.924192i	$-0.624740\pi$
$278$	2004.01	+	6167.70i	0.432347	+	1.33063i
$279$		0			0
$280$	1993.89	+	212.071i	0.425563	+	0.0452631i
$281$	−357.780	+	1101.13i	−0.0759550	+	0.233765i	−0.981824	−	0.189792i	$-0.939219\pi$
$281$	−357.780	+	1101.13i	−0.0759550	+	0.233765i	0.905869	+	0.423557i	$0.139219\pi$
$282$		0			0
$283$	−1284.25	+	3952.50i	−0.269754	+	0.830219i	0.720805	+	0.693137i	$0.243772\pi$
$283$	−1284.25	+	3952.50i	−0.269754	+	0.830219i	−0.990560	+	0.137081i	$0.956228\pi$
$284$	−1526.31	+	1108.93i	−0.318909	+	0.231701i
$285$		0			0
$286$	−5258.67	−	3820.65i	−1.08724	−	0.789928i
$287$	−3150.43	+	2288.92i	−0.647957	+	0.470769i
$288$		0			0
$289$	176.152	+	127.982i	0.0358542	+	0.0260496i
$290$	−6097.18	−	648.500i	−1.23462	−	0.131315i
$291$		0			0
$292$	875.398	−	2694.20i	0.175441	−	0.539952i
$293$	5554.75			1.10755			0.553775	−	0.832666i	$-0.313187\pi$
$293$	5554.75			1.10755			0.553775	+	0.832666i	$0.313187\pi$
$294$		0			0
$295$	358.131	+	323.269i	0.0706821	+	0.0638016i
$296$	1285.91	+	3957.61i	0.252506	+	0.777134i
$297$		0			0
$298$	7023.40	+	5102.80i	1.36528	+	0.991937i
$299$	3056.88			0.591251
$300$		0			0
$301$	1948.22			0.373068
$302$	1508.40	+	1095.92i	0.287413	+	0.208818i
$303$		0			0
$304$	118.016	+	363.216i	0.0222654	+	0.0685258i
$305$	2829.68	−	6334.37i	0.531236	−	1.18920i
$306$		0			0
$307$	−4614.58			−0.857877			−0.428938	−	0.903334i	$-0.641112\pi$
$307$	−4614.58			−0.857877			−0.428938	+	0.903334i	$0.641112\pi$
$308$	527.181	−	1622.50i	0.0975290	−	0.300164i
$309$		0			0
$310$	−8662.64	−	7819.38i	−1.58711	−	1.43262i
$311$	−3714.99	−	2699.10i	−0.677356	−	0.492128i	0.195123	−	0.980779i	$-0.437489\pi$
$311$	−3714.99	−	2699.10i	−0.677356	−	0.492128i	−0.872480	+	0.488651i	$0.837489\pi$
$312$		0			0
$313$	4066.76	−	2954.67i	0.734399	−	0.533572i	−0.156553	−	0.987670i	$-0.550038\pi$
$313$	4066.76	−	2954.67i	0.734399	−	0.533572i	0.890952	+	0.454098i	$0.150038\pi$
$314$	7917.65	+	5752.51i	1.42299	+	1.03386i
$315$		0			0
$316$	2193.03	−	1593.33i	0.390405	−	0.283645i
$317$	−2340.29	+	7202.67i	−0.414649	+	1.27616i	0.497915	+	0.867226i	$0.334099\pi$
$317$	−2340.29	+	7202.67i	−0.414649	+	1.27616i	−0.912564	+	0.408933i	$0.865901\pi$
$318$		0			0
$319$	2721.26	−	8375.19i	0.477622	−	1.46997i
$320$	−940.157	+	2104.59i	−0.164239	+	0.367656i
$321$		0			0
$322$	914.358	+	2814.10i	0.158246	+	0.487031i
$323$	268.154	+	194.825i	0.0461935	+	0.0335615i
$324$		0			0
$325$	2314.95	−	3986.69i	0.395108	−	0.680436i
$326$	2540.76			0.431656
$327$		0			0
$328$	−1858.78	−	5720.75i	−0.312909	−	0.963035i
$329$	740.252	+	2278.26i	0.124047	+	0.381777i
$330$		0			0
$331$	−338.723	+	1042.48i	−0.0562475	+	0.173112i	−0.975233	−	0.221179i	$-0.929010\pi$
$331$	−338.723	+	1042.48i	−0.0562475	+	0.173112i	0.918986	+	0.394291i	$0.129010\pi$
$332$	591.289			0.0977446
$333$		0			0
$334$	−5250.50	+	3814.71i	−0.860163	+	0.624945i
$335$	−2585.37	−	274.981i	−0.421653	−	0.0448472i
$336$		0			0
$337$	146.017	−	106.088i	0.0236025	−	0.0171482i	−0.575921	−	0.817505i	$-0.695357\pi$
$337$	146.017	−	106.088i	0.0236025	−	0.0171482i	0.599524	+	0.800357i	$0.295357\pi$
$338$	2242.95	−	1629.60i	0.360947	−	0.262244i
$339$		0			0
$340$	−471.272	−	2230.79i	−0.0751716	−	0.355828i
$341$	13559.3	−	9851.40i	2.15330	−	1.56447i
$342$		0			0
$343$	−6140.75			−0.966674
$344$	−929.942	+	2862.07i	−0.145753	+	0.448582i
$345$		0			0
$346$	−2460.49	−	7572.62i	−0.382303	−	1.17661i
$347$	2198.19	+	6765.33i	0.340072	+	1.04663i	0.964169	+	0.265287i	$0.0854668\pi$
$347$	2198.19	+	6765.33i	0.340072	+	1.04663i	−0.624097	+	0.781347i	$0.714533\pi$
$348$		0			0
$349$	10139.8			1.55522			0.777612	−	0.628745i	$-0.216431\pi$
$349$	10139.8			1.55522			0.777612	+	0.628745i	$0.216431\pi$
$350$	4362.50	+	938.614i	0.666244	+	0.143346i
$351$		0			0
$352$	5526.79	+	4015.45i	0.836872	+	0.608023i
$353$	1307.23	+	4023.24i	0.197102	+	0.606617i	0.999946	+	0.0104274i	$0.00331921\pi$
$353$	1307.23	+	4023.24i	0.197102	+	0.606617i	−0.802844	+	0.596189i	$0.796681\pi$
$354$		0			0
$355$	6142.26	−	3536.07i	0.918302	−	0.528662i
$356$	799.582	−	2460.86i	0.119039	−	0.366363i
$357$		0			0
$358$	−345.066	+	1062.00i	−0.0509422	+	0.156784i
$359$	−5057.37	+	3674.40i	−0.743504	+	0.540187i	−0.893807	−	0.448453i	$-0.851975\pi$
$359$	−5057.37	+	3674.40i	−0.743504	+	0.540187i	0.150302	+	0.988640i	$0.451975\pi$
$360$		0			0
$361$	5530.12	+	4017.87i	0.806257	+	0.585780i
$362$	2818.13	−	2047.49i	0.409165	−	0.297276i
$363$		0			0
$364$	−956.832	−	695.179i	−0.137779	−	0.100102i
$365$	−4340.57	+	9716.58i	−0.622455	+	1.39339i
$366$		0			0
$367$	4058.64	−	12491.2i	0.577273	−	1.77666i	−0.0510334	−	0.998697i	$-0.516251\pi$
$367$	4058.64	−	12491.2i	0.577273	−	1.77666i	0.628306	−	0.777966i	$-0.283749\pi$
$368$	−6544.01			−0.926983
$369$		0			0
$370$	1914.16	+	9060.75i	0.268952	+	1.27310i
$371$	1749.57	+	5384.63i	0.244834	+	0.753520i
$372$		0			0
$373$	−2397.18	−	1741.65i	−0.332765	−	0.241768i	0.408838	−	0.912607i	$-0.365934\pi$
$373$	−2397.18	−	1741.65i	−0.332765	−	0.241768i	−0.741603	+	0.670839i	$0.765934\pi$
$374$	12076.8			1.66972
$375$		0			0
$376$	−3700.26			−0.507517
$377$	−4939.08	−	3588.46i	−0.674737	−	0.490225i
$378$		0			0
$379$	−2124.88	−	6539.71i	−0.287989	−	0.886338i	−0.985487	−	0.169751i	$-0.945704\pi$
$379$	−2124.88	−	6539.71i	−0.287989	−	0.886338i	0.697498	−	0.716586i	$-0.254296\pi$
$380$	33.2689	+	157.480i	0.00449121	+	0.0212593i
$381$		0			0
$382$	−8666.20			−1.16074
$383$	1713.45	−	5273.46i	0.228599	−	0.703555i	−0.769308	−	0.638879i	$-0.779399\pi$
$383$	1713.45	−	5273.46i	0.228599	−	0.703555i	0.997906	−	0.0646760i	$-0.0206014\pi$
$384$		0			0
$385$	−2613.97	+	5851.51i	−0.346027	+	0.774598i
$386$	−4250.63	−	3088.26i	−0.560495	−	0.407224i
$387$		0			0
$388$	533.185	−	387.382i	0.0697639	−	0.0506864i
$389$	−8335.61	−	6056.17i	−1.08646	−	0.789358i	−0.107660	−	0.994188i	$-0.534336\pi$
$389$	−8335.61	−	6056.17i	−1.08646	−	0.789358i	−0.978798	+	0.204830i	$0.934336\pi$
$390$		0			0
$391$	−4594.83	+	3338.34i	−0.594298	+	0.431783i
$392$	1166.99	−	3591.63i	0.150362	−	0.462767i
$393$		0			0
$394$	−2118.26	+	6519.35i	−0.270854	+	0.833604i
$395$	−8825.31	+	5080.69i	−1.12418	+	0.647182i
$396$		0			0
$397$	4175.65	+	12851.3i	0.527884	+	1.62466i	0.758541	+	0.651625i	$0.225912\pi$
$397$	4175.65	+	12851.3i	0.527884	+	1.62466i	−0.230657	+	0.973035i	$0.574088\pi$
$398$	−13699.7	−	9953.44i	−1.72539	−	1.25357i
$399$		0			0
$400$	−4955.71	+	8534.49i	−0.619463	+	1.06681i
$401$	−6139.20			−0.764531			−0.382266	−	0.924053i	$-0.624856\pi$
$401$	−6139.20			−0.764531			−0.382266	+	0.924053i	$0.624856\pi$
$402$		0			0
$403$	−3590.56	−	11050.6i	−0.443818	−	1.36593i
$404$	−736.557	−	2266.89i	−0.0907056	−	0.279163i
$405$		0			0
$406$	1826.11	−	5620.18i	0.223222	−	0.687007i
$407$	−13300.3			−1.61983
$408$		0			0
$409$	1441.33	−	1047.19i	0.174252	−	0.126602i	−0.497241	−	0.867613i	$-0.665653\pi$
$409$	1441.33	−	1047.19i	0.174252	−	0.126602i	0.671493	+	0.741011i	$0.265653\pi$
$410$	−2766.92	−	13097.4i	−0.333289	−	1.57764i
$411$		0			0
$412$	3261.47	−	2369.60i	0.390003	−	0.283354i
$413$	−376.170	+	273.304i	−0.0448187	+	0.0325627i
$414$		0			0
$415$	−2208.81	−	234.930i	−0.261268	−	0.0277886i
$416$	3831.54	−	2783.78i	0.451579	−	0.328091i
$417$		0			0
$418$	−852.546			−0.0997594
$419$	1708.09	−	5256.97i	0.199155	−	0.612936i	−0.800748	−	0.599001i	$-0.795564\pi$
$419$	1708.09	−	5256.97i	0.199155	−	0.612936i	0.999903	−	0.0139343i	$-0.00443558\pi$
$420$		0			0
$421$	4706.54	+	14485.2i	0.544852	+	1.67688i	0.721342	+	0.692579i	$0.243526\pi$
$421$	4706.54	+	14485.2i	0.544852	+	1.67688i	−0.176490	+	0.984302i	$0.556474\pi$
$422$	5288.70	+	16277.0i	0.610071	+	1.87761i
$423$		0			0
$424$	−8745.50			−1.00170
$425$	874.142	+	8520.53i	0.0997697	+	0.972485i
$426$		0			0
$427$	5409.33	+	3930.10i	0.613058	+	0.445412i
$428$	−929.539	−	2860.83i	−0.104979	−	0.323092i
$429$		0			0
$430$	−2731.58	+	6114.78i	−0.306346	+	0.685770i
$431$	5032.73	−	15489.1i	0.562455	−	1.73106i	−0.112941	−	0.993602i	$-0.536027\pi$
$431$	5032.73	−	15489.1i	0.562455	−	1.73106i	0.675395	−	0.737456i	$-0.263973\pi$
$432$		0			0
$433$	2693.63	−	8290.15i	0.298955	−	0.920090i	−0.682909	−	0.730504i	$-0.739285\pi$
$433$	2693.63	−	8290.15i	0.298955	−	0.920090i	0.981864	−	0.189586i	$-0.0607147\pi$
$434$	9098.98	−	6610.79i	1.00637	−	0.731171i
$435$		0			0
$436$	−1911.92	−	1389.09i	−0.210010	−	0.152581i
$437$	324.367	−	235.666i	0.0355070	−	0.0257974i
$438$		0			0
$439$	4496.39	+	3266.82i	0.488840	+	0.355163i	0.804738	−	0.593630i	$-0.202306\pi$
$439$	4496.39	+	3266.82i	0.488840	+	0.355163i	−0.315898	+	0.948793i	$0.602306\pi$
$440$	−7348.52	−	6633.19i	−0.796198	−	0.718693i
$441$		0			0
$442$	2587.23	−	7962.66i	0.278420	−	0.856889i
$443$	14955.5			1.60397			0.801984	−	0.597346i	$-0.203778\pi$
$443$	14955.5			1.60397			0.801984	+	0.597346i	$0.203778\pi$
$444$		0			0
$445$	−3964.64	+	8875.04i	−0.422342	+	0.945432i
$446$	4956.90	+	15255.8i	0.526269	+	1.61969i
$447$		0			0
$448$	−1797.24	−	1305.77i	−0.189535	−	0.137705i
$449$	−1838.79			−0.193269			−0.0966347	−	0.995320i	$-0.530808\pi$
$449$	−1838.79			−0.193269			−0.0966347	+	0.995320i	$0.530808\pi$
$450$		0			0
$451$	19225.7			2.00732
$452$	−1303.38	−	946.964i	−0.135633	−	0.0985430i
$453$		0			0
$454$	529.696	+	1630.24i	0.0547574	+	0.168526i
$455$	3298.11	+	2977.06i	0.339820	+	0.306740i
$456$		0			0
$457$	2881.50			0.294947			0.147474	−	0.989066i	$-0.452886\pi$
$457$	2881.50			0.294947			0.147474	+	0.989066i	$0.452886\pi$
$458$	2787.02	−	8577.56i	0.284342	−	0.875115i
$459$		0			0
$460$	−2742.51	−	291.695i	−0.277979	−	0.0295660i
$461$	−12021.6	−	8734.19i	−1.21454	−	0.882412i	−0.218901	−	0.975747i	$-0.570247\pi$
$461$	−12021.6	−	8734.19i	−1.21454	−	0.882412i	−0.995635	+	0.0933353i	$0.970247\pi$
$462$		0			0
$463$	2417.11	−	1756.13i	0.242619	−	0.176273i	−0.459830	−	0.888007i	$-0.652090\pi$
$463$	2417.11	−	1756.13i	0.242619	−	0.176273i	0.702449	+	0.711734i	$0.252090\pi$
$464$	10573.3	+	7681.96i	1.05787	+	0.768591i
$465$		0			0
$466$	−15550.3	+	11298.0i	−1.54583	+	1.12311i
$467$	−3260.85	+	10035.9i	−0.323114	+	0.994442i	0.649171	+	0.760642i	$0.275116\pi$
$467$	−3260.85	+	10035.9i	−0.323114	+	0.994442i	−0.972285	+	0.233800i	$0.924884\pi$
$468$		0			0
$469$	774.317	−	2383.10i	0.0762359	−	0.234630i
$470$	−8188.57	−	870.941i	−0.803639	−	0.0854756i
$471$		0			0
$472$	−221.944	−	683.075i	−0.0216437	−	0.0666124i
$473$	−7781.54	−	5653.62i	−0.756439	−	0.549585i
$474$		0			0
$475$	−61.7090	−	601.497i	−0.00596085	−	0.0581022i
$476$	2197.41			0.211593
$477$		0			0
$478$	4916.48	+	15131.4i	0.470449	+	1.44789i
$479$	2070.90	+	6373.57i	0.197540	+	0.607966i	0.999938	+	0.0111759i	$0.00355749\pi$
$479$	2070.90	+	6373.57i	0.197540	+	0.607966i	−0.802397	+	0.596790i	$0.796443\pi$
$480$		0			0
$481$	−2849.34	+	8769.37i	−0.270101	+	0.831287i
$482$	3651.41			0.345057
$483$		0			0
$484$	−3609.32	+	2622.33i	−0.338967	+	0.246274i
$485$	−2145.67	+	1235.25i	−0.200886	+	0.115649i
$486$		0			0
$487$	−7282.87	+	5291.31i	−0.677655	+	0.492345i	−0.872579	−	0.488473i	$-0.837554\pi$
$487$	−7282.87	+	5291.31i	−0.677655	+	0.492345i	0.194924	+	0.980818i	$0.437554\pi$
$488$	−8355.61	+	6070.71i	−0.775083	+	0.563131i
$489$		0			0
$490$	3427.89	−	7673.49i	0.316033	−	0.707455i
$491$	15175.6	−	11025.8i	1.39484	−	1.01341i	0.399527	−	0.916721i	$-0.369174\pi$
$491$	15175.6	−	11025.8i	1.39484	−	1.01341i	0.995314	−	0.0966906i	$-0.0308257\pi$
$492$		0			0
$493$	11342.8			1.03622
$494$	−182.642	+	562.115i	−0.0166345	+	0.0511958i
$495$		0			0
$496$	7686.47	+	23656.5i	0.695832	+	2.14155i
$497$	2110.77	+	6496.28i	0.190505	+	0.586314i
$498$		0			0
$499$	−21413.5			−1.92104			−0.960522	−	0.278203i	$-0.910261\pi$
$499$	−21413.5			−1.92104			−0.960522	+	0.278203i	$0.910261\pi$
$500$	−2457.30	+	3355.80i	−0.219787	+	0.300152i
$501$		0			0
$502$	16065.8	+	11672.5i	1.42839	+	1.03779i
$503$	−3098.09	−	9534.95i	−0.274626	−	0.845213i	−0.989318	−	0.145774i	$-0.953433\pi$
$503$	−3098.09	−	9534.95i	−0.274626	−	0.845213i	0.714692	−	0.699440i	$-0.246567\pi$
$504$		0			0
$505$	1850.79	+	8760.79i	0.163087	+	0.771980i
$506$	4514.25	−	13893.4i	0.396607	−	1.22063i
$507$		0			0
$508$	−1208.48	+	3719.31i	−0.105546	+	0.324838i
$509$	1685.86	−	1224.85i	0.146806	−	0.106661i	−0.511958	−	0.859011i	$-0.671080\pi$
$509$	1685.86	−	1224.85i	0.146806	−	0.106661i	0.658764	+	0.752350i	$0.271080\pi$
$510$		0			0
$511$	−8297.62	−	6028.57i	−0.718327	−	0.521895i
$512$	302.589	−	219.843i	0.0261185	−	0.0189762i
$513$		0			0
$514$	−12983.8	−	9433.28i	−1.11418	−	0.809502i
$515$	−13125.0	+	7555.98i	−1.12302	+	0.646517i
$516$		0			0
$517$	3654.68	−	11247.9i	0.310895	−	0.956836i
$518$	−8925.18			−0.757046
$519$		0			0
$520$	−5947.79	+	3424.11i	−0.501592	+	0.288764i
$521$	6176.74	+	19010.0i	0.519401	+	1.59855i	0.775129	+	0.631803i	$0.217685\pi$
$521$	6176.74	+	19010.0i	0.519401	+	1.59855i	−0.255728	+	0.966749i	$0.582315\pi$
$522$		0			0
$523$	1489.75	+	1082.36i	0.124555	+	0.0904942i	0.648318	−	0.761369i	$-0.275473\pi$
$523$	1489.75	+	1082.36i	0.124555	+	0.0904942i	−0.523764	+	0.851863i	$0.675473\pi$
$524$	−998.199			−0.0832186
$525$		0			0
$526$	26087.6			2.16249
$527$	17465.1	+	12689.1i	1.44363	+	1.04886i
$528$		0			0
$529$	−1636.83	−	5037.63i	−0.134530	−	0.414041i
$530$	−19353.5	−	2058.45i	−1.58616	−	0.168705i
$531$		0			0
$532$	−155.124			−0.0126418
$533$	4118.74	−	12676.2i	0.334713	−	1.03014i
$534$		0			0
$535$	2335.71	+	11056.2i	0.188750	+	0.893457i
$536$	3131.33	+	2275.05i	0.252338	+	0.183334i
$537$		0			0
$538$	2399.41	−	1743.27i	0.192279	−	0.139699i
$539$	9765.12	+	7094.77i	0.780359	+	0.566964i
$540$		0			0
$541$	2538.38	−	1844.24i	0.201725	−	0.146562i	−0.482337	−	0.875986i	$-0.660212\pi$
$541$	2538.38	−	1844.24i	0.201725	−	0.146562i	0.684062	+	0.729424i	$0.260212\pi$
$542$	−954.172	+	2936.64i	−0.0756184	+	0.232730i
$543$		0			0
$544$	−2719.14	+	8368.65i	−0.214305	+	0.659564i
$545$	6590.22	+	5948.70i	0.517970	+	0.467549i
$546$		0			0
$547$	−2473.52	−	7612.71i	−0.193345	−	0.595056i	−0.999992	−	0.00402194i	$-0.998720\pi$
$547$	−2473.52	−	7612.71i	−0.193345	−	0.595056i	0.806646	−	0.591034i	$-0.201280\pi$
$548$	2896.58	+	2104.49i	0.225795	+	0.164050i
$549$		0			0
$550$	−14700.8	−	16408.7i	−1.13972	−	1.27213i
$551$	−800.735			−0.0619101
$552$		0			0
$553$	−3032.79	−	9333.97i	−0.233214	−	0.717759i
$554$	8044.61	+	24758.8i	0.616936	+	1.89873i
$555$		0			0
$556$	1800.23	−	5540.55i	0.137315	−	0.422611i
$557$	−7336.30			−0.558077			−0.279039	−	0.960280i	$-0.590016\pi$
$557$	−7336.30			−0.558077			−0.279039	+	0.960280i	$0.590016\pi$
$558$		0			0
$559$	−5394.68	+	3919.47i	−0.408177	+	0.296558i
$560$	−7060.42	−	6373.13i	−0.532781	−	0.480918i
$561$		0			0
$562$	3103.24	−	2254.64i	0.232922	−	0.169228i
$563$	−1287.19	+	935.199i	−0.0963564	+	0.0700070i	−0.634920	−	0.772578i	$-0.718967\pi$
$563$	−1287.19	+	935.199i	−0.0963564	+	0.0700070i	0.538564	+	0.842585i	$0.318967\pi$
$564$		0			0
$565$	4492.65	+	4055.32i	0.334526	+	0.301962i
$566$	11139.1	−	8093.00i	0.827225	−	0.601014i
$567$		0			0
$568$	−10551.0			−0.779419
$569$	−2067.73	+	6363.82i	−0.152344	+	0.468866i	−0.997882	−	0.0650485i	$-0.979280\pi$
$569$	−2067.73	+	6363.82i	−0.152344	+	0.468866i	0.845538	+	0.533915i	$0.179280\pi$
$570$		0			0
$571$	2180.77	+	6711.72i	0.159829	+	0.491903i	0.998618	−	0.0525535i	$-0.0167360\pi$
$571$	2180.77	+	6711.72i	0.159829	+	0.491903i	−0.838789	+	0.544456i	$0.816736\pi$
$572$	1804.39	+	5553.34i	0.131897	+	0.405938i
$573$		0			0
$574$	12901.4			0.938142
$575$	10129.0	+	2179.30i	0.734622	+	0.158058i
$576$		0			0
$577$	20208.4	+	14682.3i	1.45804	+	1.05933i	0.983869	+	0.178891i	$0.0572510\pi$
$577$	20208.4	+	14682.3i	1.45804	+	1.05933i	0.474168	+	0.880434i	$0.342749\pi$
$578$	−222.914	−	686.058i	−0.0160415	−	0.0493707i
$579$		0			0
$580$	4088.73	+	3690.72i	0.292716	+	0.264222i
$581$	661.537	−	2036.00i	0.0472379	−	0.145383i
$582$		0			0
$583$	8637.76	−	26584.3i	0.613619	−	1.88852i
$584$	12817.1	−	9312.14i	0.908174	−	0.659827i
$585$		0			0
$586$	−14888.4	−	10817.0i	−1.04954	−	0.762539i
$587$	−6989.61	+	5078.25i	−0.491468	+	0.357073i	−0.805749	−	0.592258i	$-0.798237\pi$
$587$	−6989.61	+	5078.25i	−0.491468	+	0.357073i	0.314280	+	0.949330i	$0.398237\pi$
$588$		0			0
$589$	−1232.93	−	895.774i	−0.0862511	−	0.0626651i
$590$	−330.379	−	1563.86i	−0.0230534	−	0.109124i
$591$		0			0
$592$	6099.71	−	18773.0i	0.423474	−	1.30332i
$593$	−196.006			−0.0135733			−0.00678666	−	0.999977i	$-0.502160\pi$
$593$	−196.006			−0.0135733			−0.00678666	+	0.999977i	$0.502160\pi$
$594$		0			0
$595$	−8208.60	−	873.072i	−0.565580	−	0.0601554i
$596$	−2409.91	−	7416.95i	−0.165627	−	0.509749i
$597$		0			0
$598$	−8193.35	−	5952.82i	−0.560286	−	0.407072i
$599$	1180.26			0.0805079			0.0402539	−	0.999189i	$-0.487183\pi$
$599$	1180.26			0.0805079			0.0402539	+	0.999189i	$0.487183\pi$
$600$		0			0
$601$	−14145.6			−0.960083			−0.480042	−	0.877246i	$-0.659378\pi$
$601$	−14145.6			−0.960083			−0.480042	+	0.877246i	$0.659378\pi$
$602$	−5221.81	−	3793.87i	−0.353530	−	0.256855i
$603$		0			0
$604$	−517.572	−	1592.92i	−0.0348671	−	0.107310i
$605$	14524.8	−	8361.85i	0.976061	−	0.561913i
$606$		0			0
$607$	−16501.7			−1.10343			−0.551716	−	0.834032i	$-0.686027\pi$
$607$	−16501.7			−1.10343			−0.551716	+	0.834032i	$0.686027\pi$
$608$	191.954	−	590.775i	0.0128039	−	0.0394064i
$609$		0			0
$610$	−19919.6	+	11467.6i	−1.32216	+	0.761163i
$611$	−6633.23	−	4819.33i	−0.439201	−	0.319098i
$612$		0			0
$613$	−18875.6	+	13714.0i	−1.24369	+	0.903592i	−0.997838	−	0.0657164i	$-0.979067\pi$
$613$	−18875.6	+	13714.0i	−1.24369	+	0.903592i	−0.245849	+	0.969308i	$0.579067\pi$
$614$	12368.4	+	8986.20i	0.812948	+	0.590641i
$615$		0			0
$616$	7718.67	−	5607.94i	0.504861	−	0.366803i
$617$	−4771.61	+	14685.5i	−0.311342	+	0.958212i	0.665892	+	0.746048i	$0.268051\pi$
$617$	−4771.61	+	14685.5i	−0.311342	+	0.958212i	−0.977234	+	0.212164i	$0.931949\pi$
$618$		0			0
$619$	−564.315	+	1736.78i	−0.0366425	+	0.112774i	−0.967705	−	0.252086i	$-0.918883\pi$
$619$	−564.315	+	1736.78i	−0.0366425	+	0.112774i	0.931062	+	0.364860i	$0.118883\pi$
$620$	2166.83	+	10256.8i	0.140358	+	0.664391i
$621$		0			0
$622$	4701.19	+	14468.8i	0.303055	+	0.932708i
$623$	−7578.97	−	5506.45i	−0.487392	−	0.354111i
$624$		0			0
$625$	10512.7	−	11559.5i	0.672816	−	0.739810i
$626$	−16653.9			−1.06330
$627$		0			0
$628$	−2716.76	−	8361.32i	−0.172628	−	0.531294i
$629$	−5293.92	−	16293.0i	−0.335584	−	1.03282i
$630$		0			0
$631$	8156.90	−	25104.4i	0.514613	−	1.58382i	−0.269371	−	0.963036i	$-0.586816\pi$
$631$	8156.90	−	25104.4i	0.514613	−	1.58382i	0.783984	−	0.620781i	$-0.213184\pi$
$632$	15159.9			0.954156
$633$		0			0
$634$	20298.8	−	14747.9i	1.27156	−	0.923841i
$635$	5992.12	−	13413.6i	0.374472	−	0.838274i
$636$		0			0
$637$	6769.83	−	4918.57i	0.421084	−	0.305936i
$638$	−23603.2	+	17148.7i	−1.46467	+	1.06415i
$639$		0			0
$640$	16572.4	−	9540.67i	1.02357	−	0.589263i
$641$	9625.95	−	6993.66i	0.593139	−	0.430941i	−0.250298	−	0.968169i	$-0.580529\pi$
$641$	9625.95	−	6993.66i	0.593139	−	0.430941i	0.843437	+	0.537228i	$0.180529\pi$
$642$		0			0
$643$	−5124.72			−0.314307			−0.157154	−	0.987574i	$-0.550232\pi$
$643$	−5124.72			−0.314307			−0.157154	+	0.987574i	$0.550232\pi$
$644$	821.383	−	2527.96i	0.0502594	−	0.154682i
$645$		0			0
$646$	−339.339	−	1044.38i	−0.0206674	−	0.0636076i
$647$	−6325.15	−	19466.8i	−0.384339	−	1.18287i	−0.936959	−	0.349440i	$-0.886372\pi$
$647$	−6325.15	−	19466.8i	−0.384339	−	1.18287i	0.552620	−	0.833434i	$-0.313628\pi$
$648$		0			0
$649$	2295.60			0.138845
$650$	−13968.2	+	6177.50i	−0.842890	+	0.372772i
$651$		0			0
$652$	−1846.51	−	1341.57i	−0.110912	−	0.0805826i
$653$	525.792	+	1618.22i	0.0315097	+	0.0969769i	0.965574	−	0.260127i	$-0.0837643\pi$
$653$	525.792	+	1618.22i	0.0315097	+	0.0969769i	−0.934065	+	0.357104i	$0.883764\pi$
$654$		0			0
$655$	3728.85	+	396.603i	0.222440	+	0.0236589i
$656$	−8817.16	+	27136.4i	−0.524775	+	1.61509i
$657$		0			0
$658$	2452.48	−	7547.95i	0.145300	−	0.447188i
$659$	10585.8	−	7691.06i	0.625744	−	0.454630i	−0.229179	−	0.973384i	$-0.573604\pi$
$659$	10585.8	−	7691.06i	0.625744	−	0.454630i	0.854923	+	0.518754i	$0.173604\pi$
$660$		0			0
$661$	4396.38	+	3194.16i	0.258698	+	0.187955i	0.709573	−	0.704632i	$-0.248888\pi$
$661$	4396.38	+	3194.16i	0.258698	+	0.187955i	−0.450875	+	0.892587i	$0.648888\pi$
$662$	2937.96	−	2134.55i	0.172488	−	0.125320i
$663$		0			0
$664$	2675.25	+	1943.68i	0.156355	+	0.113599i
$665$	579.477	+	61.6335i	0.0337912	+	0.00359405i
$666$		0			0
$667$	4239.91	−	13049.1i	0.246132	−	0.757516i
$668$	5830.05			0.337682
$669$		0			0
$670$	6394.06	+	5771.64i	0.368693	+	0.332803i
$671$	−10200.9	−	31395.1i	−0.586886	−	1.80625i
$672$		0			0
$673$	18745.6	+	13619.5i	1.07369	+	0.780078i	0.976571	−	0.215195i	$-0.0690386\pi$
$673$	18745.6	+	13619.5i	1.07369	+	0.780078i	0.0971147	+	0.995273i	$0.469039\pi$
$674$	−597.958			−0.0341728
$675$		0			0
$676$	−2490.53			−0.141700
$677$	−2643.89	−	1920.89i	−0.150093	−	0.109049i	0.510205	−	0.860053i	$-0.329570\pi$
$677$	−2643.89	−	1920.89i	−0.150093	−	0.109049i	−0.660297	+	0.751004i	$0.729570\pi$
$678$		0			0
$679$	−737.352	−	2269.34i	−0.0416745	−	0.128261i
$680$	5200.80	−	11642.2i	0.293296	−	0.656558i
$681$		0			0
$682$	−55527.0			−3.11765
$683$	5489.83	−	16896.0i	0.307559	−	0.946568i	−0.671151	−	0.741320i	$-0.734200\pi$
$683$	5489.83	−	16896.0i	0.307559	−	0.946568i	0.978710	−	0.205248i	$-0.0658000\pi$
$684$		0			0
$685$	−9984.24	−	9012.34i	−0.556902	−	0.502691i
$686$	16459.0	+	11958.2i	0.916047	+	0.665547i
$687$		0			0
$688$	11548.6	−	8390.58i	0.639953	−	0.464953i
$689$	−15677.5	−	11390.4i	−0.866859	−	0.629810i
$690$		0			0
$691$	−22646.8	+	16453.8i	−1.24678	+	0.905837i	−0.998030	−	0.0627318i	$-0.980019\pi$
$691$	−22646.8	+	16453.8i	−1.24678	+	0.905837i	−0.248747	+	0.968569i	$0.580019\pi$
$692$	−2210.30	+	6802.61i	−0.121421	+	0.373694i
$693$		0			0
$694$	7282.66	−	22413.7i	0.398337	−	1.22596i
$695$	−8926.27	+	19981.9i	−0.487184	+	1.09058i
$696$		0			0
$697$	7652.39	+	23551.6i	0.415861	+	1.27989i
$698$	−27177.8	−	19745.8i	−1.47377	−	1.07076i
$699$		0			0
$700$	−2674.86	−	2985.62i	−0.144429	−	0.161208i
$701$	12008.1			0.646988			0.323494	−	0.946230i	$-0.395142\pi$
$701$	12008.1			0.646988			0.323494	+	0.946230i	$0.395142\pi$
$702$		0			0
$703$	373.718	+	1150.19i	0.0200499	+	0.0617071i
$704$	3389.23	+	10431.0i	0.181444	+	0.558426i
$705$		0			0
$706$	4330.89	−	13329.1i	0.230872	−	0.710549i
$707$	−8629.71			−0.459057
$708$		0			0
$709$	13731.7	−	9976.69i	0.727371	−	0.528466i	−0.161359	−	0.986896i	$-0.551588\pi$
$709$	13731.7	−	9976.69i	0.727371	−	0.528466i	0.888731	+	0.458430i	$0.151588\pi$
$710$	−23349.0	−	2483.42i	−1.23419	−	0.131269i
$711$		0			0
$712$	11707.0	−	8505.63i	0.616205	−	0.447699i
$713$	21126.3	−	15349.1i	1.10966	−	0.806213i
$714$		0			0
$715$	−4533.99	−	21461.8i	−0.237149	−	1.12256i
$716$	811.535	−	589.614i	0.0423582	−	0.0307750i
$717$		0			0
$718$	20710.6			1.07648
$719$	−90.3053	+	277.931i	−0.00468403	+	0.0144160i	−0.953371	−	0.301800i	$-0.902412\pi$
$719$	−90.3053	+	277.931i	−0.00468403	+	0.0144160i	0.948687	+	0.316216i	$0.102412\pi$
$720$		0			0
$721$	−4510.35	−	13881.4i	−0.232974	−	0.717021i
$722$	−6998.16	−	21538.1i	−0.360727	−	1.11020i
$723$		0			0
$724$	−3129.20			−0.160629
$725$	−13807.4	−	15411.5i	−0.707301	−	0.789474i
$726$		0			0
$727$	−22594.0	−	16415.5i	−1.15263	−	0.837436i	−0.163803	−	0.986493i	$-0.552376\pi$
$727$	−22594.0	−	16415.5i	−1.15263	−	0.837436i	−0.988829	+	0.149057i	$0.952376\pi$
$728$	−2043.94	−	6290.60i	−0.104057	−	0.320254i
$729$		0			0
$730$	30555.6	−	17590.7i	1.54920	−	0.891864i
$731$	3828.46	−	11782.8i	0.193708	−	0.596172i
$732$		0			0
$733$	−11190.6	+	34441.2i	−0.563895	+	1.73549i	0.107316	+	0.994225i	$0.465774\pi$
$733$	−11190.6	+	34441.2i	−0.563895	+	1.73549i	−0.671211	+	0.741266i	$0.734226\pi$
$734$	−35203.1	+	25576.5i	−1.77026	+	1.28617i
$735$		0			0
$736$	8611.10	+	6256.33i	0.431263	+	0.313331i
$737$	−10008.4	+	7271.51i	−0.500222	+	0.363432i
$738$		0			0
$739$	477.123	+	346.650i	0.0237500	+	0.0172554i	0.599597	−	0.800302i	$-0.295328\pi$
$739$	477.123	+	346.650i	0.0237500	+	0.0172554i	−0.575847	+	0.817558i	$0.695328\pi$
$740$	3393.11	−	7595.64i	0.168558	−	0.377326i
$741$		0			0
$742$	5796.38	−	17839.4i	0.286781	−	0.882622i
$743$	15725.6			0.776468			0.388234	−	0.921561i	$-0.373085\pi$
$743$	15725.6			0.776468			0.388234	+	0.921561i	$0.373085\pi$
$744$		0			0
$745$	6055.53	+	28664.1i	0.297795	+	1.40963i
$746$	3033.54	+	9336.28i	0.148882	+	0.458211i
$747$		0			0
$748$	−8776.85	−	6376.75i	−0.429028	−	0.311707i
$749$	−10890.7			−0.531294
$750$		0			0
$751$	−15640.8			−0.759974			−0.379987	−	0.924992i	$-0.624072\pi$
$751$	−15640.8			−0.759974			−0.379987	+	0.924992i	$0.624072\pi$
$752$	14200.1	+	10316.9i	0.688594	+	0.500293i
$753$		0			0
$754$	6250.23	+	19236.2i	0.301883	+	0.929101i
$755$	1300.53	+	6156.13i	0.0626904	+	0.296748i
$756$		0			0
$757$	−31252.3			−1.50051			−0.750255	−	0.661149i	$-0.770069\pi$
$757$	−31252.3			−1.50051			−0.750255	+	0.661149i	$0.770069\pi$
$758$	−7039.78	+	21666.2i	−0.337330	+	1.03820i
$759$		0			0
$760$	−367.144	+	821.870i	−0.0175233	+	0.0392268i
$761$	−11969.7	−	8696.46i	−0.570170	−	0.414253i	0.264997	−	0.964249i	$-0.414629\pi$
$761$	−11969.7	−	8696.46i	−0.570170	−	0.414253i	−0.835167	+	0.549996i	$0.814629\pi$
$762$		0			0
$763$	−6922.17	+	5029.25i	−0.328440	+	0.238625i
$764$	6298.19	+	4575.90i	0.298247	+	0.216689i
$765$		0			0
$766$	−14861.8	+	10797.8i	−0.701018	+	0.509319i
$767$	491.790	−	1513.57i	0.0231519	−	0.0712542i
$768$		0			0
$769$	−12997.7	+	40002.8i	−0.609505	+	1.87586i	−0.147298	+	0.989092i	$0.547058\pi$
$769$	−12997.7	+	40002.8i	−0.609505	+	1.87586i	−0.462207	+	0.886772i	$0.652942\pi$
$770$	18401.1	−	10593.4i	0.861209	−	0.495794i
$771$		0			0
$772$	1458.50	+	4488.81i	0.0679956	+	0.209269i
$773$	23657.9	+	17188.4i	1.10079	+	0.799774i	0.981189	−	0.193047i	$-0.0618371\pi$
$773$	23657.9	+	17188.4i	1.10079	+	0.799774i	0.119605	+	0.992822i	$0.461837\pi$
$774$		0			0
$775$	−4019.16	−	39175.9i	−0.186287	−	1.81580i
$776$	3685.77			0.170504
$777$		0			0
$778$	10548.4	+	32464.7i	0.486091	+	1.49603i
$779$	−540.212	−	1662.60i	−0.0248461	−	0.0764683i
$780$		0			0
$781$	10421.0	−	32072.6i	0.477456	−	1.46946i
$782$	18816.4			0.860453
$783$		0			0
$784$	−14492.5	+	10529.4i	−0.660190	+	0.479656i
$785$	6826.55	+	32313.8i	0.310382	+	1.46921i
$786$		0			0
$787$	−13335.9	+	9689.07i	−0.604030	+	0.438854i	−0.847307	−	0.531103i	$-0.821778\pi$
$787$	−13335.9	+	9689.07i	−0.604030	+	0.438854i	0.243277	+	0.969957i	$0.421778\pi$
$788$	4981.78	−	3619.48i	0.225214	−	0.163628i
$789$		0			0
$790$	33548.3	+	3568.22i	1.51088	+	0.160698i
$791$	−4718.94	+	3428.51i	−0.212119	+	0.154114i
$792$		0			0
$793$	−22885.2			−1.02482
$794$	13834.0	−	42576.8i	0.618327	−	1.90302i
$795$		0			0
$796$	4700.74	+	14467.4i	0.209313	+	0.644200i
$797$	116.610	+	358.888i	0.00518260	+	0.0159504i	0.953614	−	0.301031i	$-0.0973307\pi$
$797$	116.610	+	358.888i	0.00518260	+	0.0159504i	−0.948432	+	0.316981i	$0.897331\pi$
$798$		0			0
$799$	15233.5			0.674498
$800$	14680.4	−	6492.47i	0.648788	−	0.286929i
$801$		0			0
$802$	16454.9	+	11955.2i	0.724491	+	0.526373i
$803$	15647.6	+	48158.3i	0.687661	+	2.11640i
$804$		0			0
$805$	−4072.74	+	9117.03i	−0.178317	+	0.399172i
$806$	−11895.6	+	36611.0i	−0.519858	+	1.59996i
$807$		0			0
$808$	4119.21	−	12677.6i	0.179348	−	0.551976i
$809$	7710.01	−	5601.65i	0.335067	−	0.243441i	−0.407510	−	0.913201i	$-0.633603\pi$
$809$	7710.01	−	5601.65i	0.335067	−	0.243441i	0.742578	+	0.669760i	$0.233603\pi$
$810$		0			0
$811$	−7007.02	−	5090.89i	−0.303390	−	0.220426i	0.425665	−	0.904881i	$-0.360040\pi$
$811$	−7007.02	−	5090.89i	−0.303390	−	0.220426i	−0.729055	+	0.684455i	$0.760040\pi$
$812$	−4294.68	+	3120.27i	−0.185608	+	0.134852i
$813$		0			0
$814$	35648.7	+	25900.3i	1.53500	+	1.11524i
$815$	6364.75	+	5745.18i	0.273555	+	0.246926i
$816$		0			0
$817$	−270.265	+	831.792i	−0.0115733	+	0.0356190i
$818$	−5902.42			−0.252290
$819$		0			0
$820$	−4904.76	+	10979.5i	−0.208880	+	0.467588i
$821$	3769.41	+	11601.0i	0.160235	+	0.493154i	0.998654	−	0.0518736i	$-0.0165193\pi$
$821$	3769.41	+	11601.0i	0.160235	+	0.493154i	−0.838418	+	0.545027i	$0.816519\pi$
$822$		0			0
$823$	17224.2	+	12514.1i	0.729525	+	0.530031i	0.889413	−	0.457104i	$-0.151113\pi$
$823$	17224.2	+	12514.1i	0.729525	+	0.530031i	−0.159888	+	0.987135i	$0.551113\pi$
$824$	22545.7			0.953175
$825$		0			0
$826$	1540.47			0.0648906
$827$	29181.7	+	21201.7i	1.22702	+	0.891483i	0.996663	−	0.0816229i	$-0.0260103\pi$
$827$	29181.7	+	21201.7i	1.22702	+	0.891483i	0.230358	+	0.973106i	$0.426010\pi$
$828$		0			0
$829$	−1650.49	−	5079.70i	−0.0691484	−	0.212817i	0.910511	−	0.413485i	$-0.135689\pi$
$829$	−1650.49	−	5079.70i	−0.0691484	−	0.212817i	−0.979659	+	0.200668i	$0.935689\pi$
$830$	5462.76	+	4931.00i	0.228452	+	0.206214i
$831$		0			0
$832$	7603.59			0.316836
$833$	−4804.36	+	14786.3i	−0.199834	+	0.615024i
$834$		0			0
$835$	−21778.6	−	2316.39i	−0.902611	−	0.0960022i
$836$	619.591	+	450.159i	0.0256328	+	0.0186233i
$837$		0			0
$838$	−14815.4	+	10764.0i	−0.610726	+	0.443718i
$839$	−30433.3	−	22111.1i	−1.25229	−	0.909843i	−0.253939	−	0.967220i	$-0.581726\pi$
$839$	−30433.3	−	22111.1i	−1.25229	−	0.909843i	−0.998353	+	0.0573767i	$0.981726\pi$
$840$		0			0
$841$	−2437.66	+	1771.06i	−0.0999490	+	0.0726172i
$842$	15592.9	−	47990.0i	0.638202	−	1.96419i
$843$		0			0
$844$	4750.93	−	14621.9i	0.193760	−	0.596333i
$845$	9303.55	+	989.531i	0.378760	+	0.0402851i
$846$		0			0
$847$	4991.40	+	15362.0i	0.202487	+	0.623191i
$848$	33561.5	+	24383.9i	1.35909	+	0.987436i
$849$		0			0
$850$	14249.5	−	24539.8i	0.575004	−	0.990244i
$851$	−20722.8			−0.834744
$852$		0			0
$853$	7429.34	+	22865.1i	0.298213	+	0.917805i	0.982123	+	0.188239i	$0.0602779\pi$
$853$	7429.34	+	22865.1i	0.298213	+	0.917805i	−0.683910	+	0.729566i	$0.739722\pi$
$854$	−6845.30	−	21067.7i	−0.274287	−	0.844170i
$855$		0			0
$856$	5198.46	−	15999.2i	0.207570	−	0.638834i
$857$	−19463.5			−0.775800			−0.387900	−	0.921702i	$-0.626799\pi$
$857$	−19463.5			−0.775800			−0.387900	+	0.921702i	$0.626799\pi$
$858$		0			0
$859$	−14558.7	+	10577.5i	−0.578273	+	0.420140i	−0.838101	−	0.545515i	$-0.816334\pi$
$859$	−14558.7	+	10577.5i	−0.578273	+	0.420140i	0.259828	+	0.965655i	$0.416334\pi$
$860$	5213.90	−	3001.62i	0.206735	−	0.119017i
$861$		0			0
$862$	−43652.0	+	31715.0i	−1.72482	+	1.25315i
$863$	9466.85	−	6878.07i	0.373413	−	0.271300i	−0.385212	−	0.922828i	$-0.625872\pi$
$863$	9466.85	−	6878.07i	0.373413	−	0.271300i	0.758625	+	0.651528i	$0.225872\pi$
$864$		0			0
$865$	10959.6	−	24533.5i	0.430793	−	0.964351i
$866$	−23363.5	+	16974.6i	−0.916773	+	0.666074i
$867$		0			0
$868$	−10103.3			−0.395080
$869$	−14973.1	+	46082.5i	−0.584497	+	1.79890i
$870$		0			0
$871$	2650.26	+	8156.67i	0.103101	+	0.317311i
$872$	−4084.15	−	12569.7i	−0.158609	−	0.488148i
$873$		0			0
$874$	−1328.32			−0.0514087
$875$	8805.90	+	12215.8i	0.340221	+	0.471964i
$876$		0			0
$877$	24473.4	+	17781.0i	0.942313	+	0.684631i	0.948976	−	0.315347i	$-0.102121\pi$
$877$	24473.4	+	17781.0i	0.942313	+	0.684631i	−0.00666318	+	0.999978i	$0.502121\pi$
$878$	−5690.02	−	17512.1i	−0.218712	−	0.673125i
$879$		0			0
$880$	9706.12	+	45944.3i	0.371810	+	1.75998i
$881$	7719.26	−	23757.4i	0.295197	−	0.908522i	−0.687958	−	0.725750i	$-0.741493\pi$
$881$	7719.26	−	23757.4i	0.295197	−	0.908522i	0.983155	−	0.182772i	$-0.0585071\pi$
$882$		0			0
$883$	−15226.9	+	46863.7i	−0.580325	+	1.78606i	0.0369593	+	0.999317i	$0.488233\pi$
$883$	−15226.9	+	46863.7i	−0.580325	+	1.78606i	−0.617284	+	0.786740i	$0.711767\pi$
$884$	−6084.70	+	4420.79i	−0.231505	+	0.168198i
$885$		0			0
$886$	−40085.2	−	29123.6i	−1.51996	−	1.10432i
$887$	−5583.54	+	4056.68i	−0.211361	+	0.153562i	−0.688429	−	0.725304i	$-0.741699\pi$
$887$	−5583.54	+	4056.68i	−0.211361	+	0.153562i	0.477069	+	0.878866i	$0.341699\pi$
$888$		0			0
$889$	11454.8	+	8322.38i	0.432149	+	0.313975i
$890$	27909.2	−	16067.2i	1.05114	−	0.605139i
$891$		0			0
$892$	4452.86	−	13704.5i	0.167144	−	0.514418i
$893$	−1075.39			−0.0402986
$894$		0			0
$895$	−3265.82	+	1880.11i	−0.121971	+	0.0702182i
$896$	5695.07	+	17527.6i	0.212342	+	0.653523i
$897$		0			0
$898$	4928.51	+	3580.77i	0.183147	+	0.133064i
$899$	−52152.5			−1.93480
$900$		0			0
$901$	36004.2			1.33127
$902$	−51530.4	−	37439.0i	−1.90219	−	1.38202i
$903$		0			0
$904$	−2784.23	−	8568.97i	−0.102436	−	0.315265i
$905$	11689.4	+	1243.29i	0.429356	+	0.0456666i
$906$		0			0
$907$	−8181.71			−0.299525			−0.149763	−	0.988722i	$-0.547851\pi$
$907$	−8181.71			−0.299525			−0.149763	+	0.988722i	$0.547851\pi$
$908$	475.835	−	1464.47i	0.0173911	−	0.0535244i
$909$		0			0
$910$	−3042.54	−	14402.0i	−0.110834	−	0.524639i
$911$	41559.4	+	30194.7i	1.51144	+	1.09813i	0.965532	+	0.260283i	$0.0838158\pi$
$911$	41559.4	+	30194.7i	1.51144	+	1.09813i	0.545909	+	0.837844i	$0.316184\pi$
$912$		0			0
$913$	−8550.65	+	6212.41i	−0.309951	+	0.225193i
$914$	−7723.26	−	5611.28i	−0.279500	−	0.203069i
$915$		0			0
$916$	−6554.57	+	4762.18i	−0.236429	+	0.171776i
$917$	−1116.79	+	3437.13i	−0.0402178	+	0.123778i
$918$		0			0
$919$	−995.926	+	3065.15i	−0.0357482	+	0.110022i	−0.967338	−	0.253489i	$-0.918422\pi$
$919$	−995.926	+	3065.15i	−0.0357482	+	0.110022i	0.931590	+	0.363510i	$0.118422\pi$
$920$	−11449.5	−	10334.9i	−0.410303	−	0.370362i
$921$		0			0
$922$	15212.9	+	46820.4i	0.543394	+	1.67240i
$923$	−18914.1	−	13741.9i	−0.674502	−	0.490055i
$924$		0			0
$925$	−15693.1	+	27026.0i	−0.557823	+	0.960657i
$926$	−9898.36			−0.351274
$927$		0			0
$928$	−6568.91	−	20217.0i	−0.232365	−	0.715147i
$929$	−4052.06	−	12471.0i	−0.143104	−	0.440430i	0.853658	−	0.520834i	$-0.174379\pi$
$929$	−4052.06	−	12471.0i	−0.143104	−	0.440430i	−0.996762	+	0.0804041i	$0.974379\pi$
$930$		0			0
$931$	339.158	−	1043.82i	0.0119393	−	0.0367453i
$932$	17266.8			0.606859
$933$		0			0
$934$	28283.4	−	20549.1i	0.990856	−	0.719899i
$935$	30253.0	+	27308.1i	1.05816	+	0.955154i
$936$		0			0
$937$	4007.31	−	2911.48i	0.139715	−	0.101509i	−0.515732	−	0.856750i	$-0.672480\pi$
$937$	4007.31	−	2911.48i	0.139715	−	0.101509i	0.655447	+	0.755241i	$0.272480\pi$
$938$	−6716.13	+	4879.55i	−0.233784	+	0.169854i
$939$		0			0
$940$	5491.20	+	4956.67i	0.190535	+	0.171988i
$941$	−40603.6	+	29500.2i	−1.40663	+	1.02198i	−0.412828	+	0.910809i	$0.635459\pi$
$941$	−40603.6	+	29500.2i	−1.40663	+	1.02198i	−0.993802	+	0.111167i	$0.964541\pi$
$942$		0			0
$943$	29954.8			1.03443
$944$	−1052.80	+	3240.17i	−0.0362983	+	0.111715i
$945$		0			0
$946$	9847.25	+	30306.7i	0.338437	+	1.04160i
$947$	1157.97	+	3563.86i	0.0397349	+	0.122291i	0.968956	−	0.247232i	$-0.0795210\pi$
$947$	1157.97	+	3563.86i	0.0397349	+	0.122291i	−0.929221	+	0.369523i	$0.879521\pi$
$948$		0			0
$949$	35104.7			1.20079
$950$	−1005.93	+	1732.36i	−0.0343542	+	0.0591633i
$951$		0			0
$952$	9942.06	+	7223.33i	0.338471	+	0.245913i
$953$	2431.39	+	7483.04i	0.0826447	+	0.254354i	0.983837	−	0.179065i	$-0.0573071\pi$
$953$	2431.39	+	7483.04i	0.0826447	+	0.254354i	−0.901193	+	0.433419i	$0.857307\pi$
$954$		0			0
$955$	−21709.3	−	19596.0i	−0.735598	−	0.663992i
$956$	4416.56	−	13592.8i	0.149416	−	0.459855i
$957$		0			0
$958$	6860.94	−	21115.8i	0.231385	−	0.712130i
$959$	10487.1	−	7619.36i	0.353126	−	0.256561i
$960$		0			0
$961$	−56200.1	−	40831.8i	−1.88648	−	1.37061i
$962$	24714.1	−	17955.8i	0.828290	−	0.601788i
$963$		0			0
$964$	−2653.68	−	1928.01i	−0.0886610	−	0.0644160i
$965$	−3664.86	−	17347.8i	−0.122255	−	0.578699i
$966$		0			0
$967$	11879.3	−	36560.6i	0.395048	−	1.21583i	−0.533877	−	0.845562i	$-0.679265\pi$
$967$	11879.3	−	36560.6i	0.395048	−	1.21583i	0.928924	−	0.370270i	$-0.120735\pi$
$968$	−24950.3			−0.828442
$969$		0			0
$970$	8156.49	+	867.529i	0.269989	+	0.0287162i
$971$	−12524.3	−	38545.9i	−0.413929	−	1.27394i	−0.913205	−	0.407500i	$-0.866401\pi$
$971$	−12524.3	−	38545.9i	−0.413929	−	1.27394i	0.499276	−	0.866443i	$-0.333599\pi$
$972$		0			0
$973$	−17063.8	−	12397.6i	−0.562221	−	0.408478i
$974$	29824.3			0.981141
$975$		0			0
$976$	48991.4			1.60674
$977$	−39686.3	−	28833.8i	−1.29957	−	0.944191i	−0.299616	−	0.954060i	$-0.596859\pi$
$977$	−39686.3	−	28833.8i	−1.29957	−	0.944191i	−0.999951	+	0.00986880i	$0.996859\pi$
$978$		0			0
$979$	14292.4	+	43987.4i	0.466585	+	1.43600i
$980$	−6542.97	+	3766.75i	−0.213273	+	0.122780i
$981$		0			0
$982$	−62146.2			−2.01952
$983$	−10088.9	+	31050.4i	−0.327350	+	1.00748i	0.643018	+	0.765851i	$0.277682\pi$
$983$	−10088.9	+	31050.4i	−0.327350	+	1.00748i	−0.970369	+	0.241630i	$0.922318\pi$
$984$		0			0
$985$	−20047.9	+	11541.5i	−0.648508	+	0.373342i
$986$	−30402.2	−	22088.5i	−0.981950	−	0.713428i
$987$		0			0
$988$	429.542	−	312.081i	0.0138315	−	0.0100492i
$989$	−12124.1	−	8808.71i	−0.389813	−	0.283216i
$990$		0			0
$991$	3786.31	−	2750.91i	0.121368	−	0.0881793i	−0.525445	−	0.850827i	$-0.676101\pi$
$991$	3786.31	−	2750.91i	0.121368	−	0.0881793i	0.646814	+	0.762648i	$0.276101\pi$
$992$	12502.1	−	38477.6i	0.400145	−	1.23152i
$993$		0			0
$994$	6993.03	−	21522.3i	0.223144	−	0.686768i
$995$	−11811.8	−	55911.8i	−0.376342	−	1.78143i
$996$		0			0
$997$	−15137.0	−	46586.8i	−0.480835	−	1.47986i	−0.837923	−	0.545788i	$-0.816230\pi$
$997$	−15137.0	−	46586.8i	−0.480835	−	1.47986i	0.357088	−	0.934071i	$-0.383770\pi$
$998$	57394.6	+	41699.6i	1.82043	+	1.32262i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.91.4	✓	64
3.2	odd	2	inner	225.4.h.d.91.13	yes	64
25.11	even	5	inner	225.4.h.d.136.4	yes	64
75.11	odd	10	inner	225.4.h.d.136.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.91.4	✓	64	1.1	even	1	trivial
225.4.h.d.91.13	yes	64	3.2	odd	2	inner
225.4.h.d.136.4	yes	64	25.11	even	5	inner
225.4.h.d.136.13	yes	64	75.11	odd	10	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68030 - 1.94735i) q^{2} +(0.919680 + 2.83048i) q^{4} +(-2.31093 - 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 + 15.8295i) q^{8} +O(q^{10})\)	\(q+(-2.68030 - 1.94735i) q^{2} +(0.919680 + 2.83048i) q^{4} +(-2.31093 - 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 + 15.8295i) q^{8} +(-15.1079 + 33.8197i) q^{10} +(-43.0382 - 31.2691i) q^{11} +(-29.8370 + 21.6778i) q^{13} +(-28.8808 - 20.9831i) q^{14} +(63.8733 - 46.4067i) q^{16} +(21.1745 - 65.1683i) q^{17} +(-1.49479 + 4.60048i) q^{19} +(28.8371 - 16.6014i) q^{20} +(54.4633 + 167.621i) q^{22} +(-67.0563 - 48.7193i) q^{23} +(-114.319 + 50.5582i) q^{25} +122.186 q^{26} +(9.90977 + 30.4991i) q^{28} +(51.1534 + 157.434i) q^{29} +(-97.3566 + 299.633i) q^{31} -128.416 q^{32} +(-183.659 + 133.436i) q^{34} +(-24.9009 - 117.869i) q^{35} +(202.266 - 146.955i) q^{37} +(12.9652 - 9.41977i) q^{38} +(185.044 + 19.6814i) q^{40} +(-292.377 + 212.424i) q^{41} +180.805 q^{43} +(48.9253 - 150.576i) q^{44} +(84.8573 + 261.164i) q^{46} +(68.6994 + 211.435i) q^{47} -226.894 q^{49} +(404.863 + 87.1085i) q^{50} +(-88.7992 - 64.5164i) q^{52} +(162.370 + 499.723i) q^{53} +(-242.591 + 543.051i) q^{55} +(-55.4206 + 170.567i) q^{56} +(169.473 - 521.583i) q^{58} +(-34.9106 + 25.3641i) q^{59} +(502.015 + 364.735i) q^{61} +(844.434 - 613.517i) q^{62} +(-166.794 - 121.183i) q^{64} +(306.083 + 276.288i) q^{65} +(71.8608 - 221.165i) q^{67} +203.932 q^{68} +(-162.791 + 364.415i) q^{70} +(195.891 + 602.890i) q^{71} +(-770.064 - 559.484i) q^{73} -828.305 q^{74} -14.3963 q^{76} +(-463.747 - 336.932i) q^{77} +(-281.459 - 866.243i) q^{79} +(-655.245 - 591.461i) q^{80} +1197.32 q^{82} +(61.3942 - 188.952i) q^{83} +(-761.802 - 81.0258i) q^{85} +(-484.612 - 352.091i) q^{86} +(716.334 - 520.447i) q^{88} +(-703.370 - 511.028i) q^{89} +(-321.500 + 233.584i) q^{91} +(76.2288 - 234.608i) q^{92} +(227.603 - 700.490i) q^{94} +(53.7785 + 5.71992i) q^{95} +(-68.4303 - 210.607i) q^{97} +(608.144 + 441.842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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