LMFDB - Embedded newform 343.2.k.a.100.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(2,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

chi = DirichletCharacter(H, H._module([194]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("343.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.k (of order $147$, degree $84$, 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$2688$
Relative dimension:	$32$ over $\Q(\zeta_{147})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{147}]$

Embedding invariants

Embedding label			100.4
Character	$\chi$	$=$	343.100
Dual form			343.2.k.a.319.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37080 - 1.87829i) q^{2} +(0.115205 - 2.15419i) q^{3} +(-1.03897 + 3.24476i) q^{4} +(-0.517175 + 0.0110544i) q^{5} +(-4.20410 + 2.73657i) q^{6} +(-2.60550 + 0.459747i) q^{7} +(3.10511 - 1.03097i) q^{8} +(-1.64436 - 0.176383i) q^{9} +(0.729705 + 0.956248i) q^{10} +(-0.590941 + 5.00428i) q^{11} +(6.87012 + 2.61195i) q^{12} +(-0.782394 - 1.49970i) q^{13} +(4.43515 + 4.26365i) q^{14} +(-0.0357676 + 1.11536i) q^{15} +(-0.646188 - 0.461095i) q^{16} +(-4.42480 + 1.05980i) q^{17} +(1.92279 + 3.33036i) q^{18} +(1.19784 - 2.07472i) q^{19} +(0.501462 - 1.68959i) q^{20} +(0.690215 + 5.66570i) q^{21} +(10.2095 - 5.74990i) q^{22} +(-5.68078 + 4.43180i) q^{23} +(-1.86318 - 6.80776i) q^{24} +(-4.72809 + 0.202215i) q^{25} +(-1.74437 + 3.52534i) q^{26} +(0.463498 - 2.86690i) q^{27} +(1.21528 - 8.93188i) q^{28} +(0.110231 - 0.0446275i) q^{29} +(2.14400 - 1.46176i) q^{30} +(2.51404 - 2.33269i) q^{31} +(-0.0501970 - 4.69741i) q^{32} +(10.7121 + 1.84951i) q^{33} +(8.05611 + 6.85826i) q^{34} +(1.34242 - 0.266572i) q^{35} +(2.28077 - 5.15229i) q^{36} +(-4.39978 - 4.64136i) q^{37} +(-5.53892 + 0.594135i) q^{38} +(-3.32077 + 1.51265i) q^{39} +(-1.59449 + 0.567516i) q^{40} +(0.254392 - 0.691265i) q^{41} +(9.69566 - 9.06294i) q^{42} +(9.15264 + 3.03889i) q^{43} +(-15.6237 - 7.11678i) q^{44} +(0.852372 + 0.0730435i) q^{45} +(16.1114 + 4.59503i) q^{46} +(-2.95791 - 1.58358i) q^{47} +(-1.06773 + 1.33889i) q^{48} +(6.57727 - 2.39574i) q^{49} +(6.86106 + 8.60350i) q^{50} +(1.77325 + 9.65394i) q^{51} +(5.67905 - 0.980526i) q^{52} +(-2.92960 - 1.73340i) q^{53} +(-6.02021 + 3.05935i) q^{54} +(0.250300 - 2.59462i) q^{55} +(-7.61639 + 4.11375i) q^{56} +(-4.33134 - 2.81939i) q^{57} +(-0.234927 - 0.145870i) q^{58} +(-6.78328 + 8.14273i) q^{59} +(-3.58193 - 1.27489i) q^{60} +(-10.2562 + 0.878897i) q^{61} +(-7.82770 - 1.52444i) q^{62} +(4.36547 - 0.296423i) q^{63} +(-10.0266 + 7.48308i) q^{64} +(0.421213 + 0.766959i) q^{65} +(-11.2102 - 22.6557i) q^{66} +(-7.60362 + 2.34541i) q^{67} +(1.15845 - 15.4585i) q^{68} +(8.89247 + 12.7480i) q^{69} +(-2.34088 - 2.15603i) q^{70} +(-3.72918 - 1.50978i) q^{71} +(-5.28777 + 1.14759i) q^{72} +(-7.27431 + 3.89445i) q^{73} +(-2.68660 + 14.6264i) q^{74} +(-0.109089 + 10.2085i) q^{75} +(5.48744 + 6.04229i) q^{76} +(-0.761007 - 13.3103i) q^{77} +(7.39329 + 4.16383i) q^{78} +(9.91547 - 1.49452i) q^{79} +(0.339290 + 0.231324i) q^{80} +(-10.9709 - 2.38100i) q^{81} +(-1.64711 + 0.469763i) q^{82} +(11.5122 - 2.24199i) q^{83} +(-19.1009 - 3.64693i) q^{84} +(2.27668 - 0.597016i) q^{85} +(-6.83851 - 21.3570i) q^{86} +(-0.0834369 - 0.242599i) q^{87} +(3.32432 + 16.1481i) q^{88} +(-7.50914 + 7.58981i) q^{89} +(-1.03123 - 1.70112i) q^{90} +(2.72801 + 3.54777i) q^{91} +(-8.47792 - 23.0373i) q^{92} +(-4.73542 - 5.68445i) q^{93} +(1.08028 + 7.72656i) q^{94} +(-0.596559 + 1.08624i) q^{95} +(-10.1249 - 0.433029i) q^{96} +(0.845738 + 3.70542i) q^{97} +(-13.5160 - 9.06991i) q^{98} +(1.85439 - 8.12462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 84 q^{8} - 98 q^{9} - 84 q^{10} - 91 q^{11} - 119 q^{12} - 84 q^{13} - 119 q^{14} - 98 q^{15} - 84 q^{16} - 91 q^{17} - 42 q^{18}+ \cdots - 182 q^{99}+O(q^{100}) $ 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 84 * q^8 - 98 * q^9 - 84 * q^10 - 91 * q^11 - 119 * q^12 - 84 * q^13 - 119 * q^14 - 98 * q^15 - 84 * q^16 - 91 * q^17 - 42 * q^18 + 126 * q^19 + 84 * q^20 - 84 * q^21 - 98 * q^22 - 105 * q^23 - 126 * q^24 - 84 * q^25 - 98 * q^26 - 105 * q^27 - 126 * q^28 - 126 * q^29 - 91 * q^30 - 133 * q^31 - 126 * q^32 - 84 * q^33 - 168 * q^34 - 98 * q^35 - 42 * q^36 - 105 * q^37 + 28 * q^38 - 77 * q^39 - 56 * q^40 - 56 * q^41 - 126 * q^42 - 84 * q^43 - 28 * q^44 - 105 * q^45 - 119 * q^47 - 14 * q^48 - 28 * q^49 - 196 * q^50 - 28 * q^51 - 28 * q^52 - 91 * q^53 + 126 * q^54 + 301 * q^55 - 70 * q^56 + 21 * q^57 + 308 * q^58 + 28 * q^59 - 112 * q^60 - 105 * q^61 - 70 * q^62 - 133 * q^63 - 140 * q^64 - 84 * q^65 - 252 * q^66 - 91 * q^67 - 175 * q^68 - 168 * q^69 - 168 * q^70 - 161 * q^71 - 21 * q^72 + 42 * q^73 - 210 * q^75 - 21 * q^76 + 42 * q^77 + 280 * q^78 - 91 * q^79 - 168 * q^80 - 126 * q^81 - 84 * q^82 - 98 * q^83 - 14 * q^84 - 140 * q^85 - 28 * q^86 + 14 * q^87 + 28 * q^88 - 84 * q^89 + 329 * q^90 + 406 * q^91 + 336 * q^92 + 14 * q^93 - 112 * q^94 + 238 * q^95 + 560 * q^96 + 196 * q^97 + 63 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{76}{147}\right)$

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 $

$2$	−1.37080	−	1.87829i	−0.969300	−	1.32815i	−0.944520	−	0.328455i	$-0.893472\pi$
$2$	−1.37080	−	1.87829i	−0.969300	−	1.32815i	−0.0247800	−	0.999693i	$-0.507889\pi$
$3$	0.115205	−	2.15419i	0.0665134	−	1.24372i	−0.748049	−	0.663644i	$-0.769009\pi$
$3$	0.115205	−	2.15419i	0.0665134	−	1.24372i	0.814562	−	0.580077i	$-0.196977\pi$
$4$	−1.03897	+	3.24476i	−0.519487	+	1.62238i
$5$	−0.517175	+	0.0110544i	−0.231288	+	0.00494369i	−0.136870	−	0.990589i	$-0.543704\pi$
$5$	−0.517175	+	0.0110544i	−0.231288	+	0.00494369i	−0.0944175	+	0.995533i	$0.530099\pi$
$6$	−4.20410	+	2.73657i	−1.71632	+	1.11720i
$7$	−2.60550	+	0.459747i	−0.984787	+	0.173768i
$7$	−2.60550	+	0.459747i	−0.984787	+	0.173768i
$8$	3.10511	−	1.03097i	1.09782	−	0.364502i
$9$	−1.64436	−	0.176383i	−0.548120	−	0.0587944i
$10$	0.729705	+	0.956248i	0.230753	+	0.302392i
$11$	−0.590941	+	5.00428i	−0.178175	+	1.50885i	0.556738	+	0.830688i	$0.312053\pi$
$11$	−0.590941	+	5.00428i	−0.178175	+	1.50885i	−0.734914	+	0.678161i	$0.762777\pi$
$12$	6.87012	+	2.61195i	1.98323	+	0.754006i
$13$	−0.782394	−	1.49970i	−0.216997	−	0.415943i	0.753364	−	0.657604i	$-0.228430\pi$
$13$	−0.782394	−	1.49970i	−0.216997	−	0.415943i	−0.970361	+	0.241662i	$0.922308\pi$
$14$	4.43515	+	4.26365i	1.18534	+	1.13951i
$15$	−0.0357676	+	1.11536i	−0.00923515	+	0.287986i
$16$	−0.646188	−	0.461095i	−0.161547	−	0.115274i
$17$	−4.42480	+	1.05980i	−1.07317	+	0.257039i	−0.730846	−	0.682542i	$-0.760874\pi$
$17$	−4.42480	+	1.05980i	−1.07317	+	0.257039i	−0.342325	+	0.939581i	$0.611215\pi$
$18$	1.92279	+	3.33036i	0.453205	+	0.784974i
$19$	1.19784	−	2.07472i	0.274804	−	0.475974i	−0.695282	−	0.718737i	$-0.744720\pi$
$19$	1.19784	−	2.07472i	0.274804	−	0.475974i	0.970086	+	0.242763i	$0.0780538\pi$
$20$	0.501462	−	1.68959i	0.112130	−	0.377804i
$21$	0.690215	+	5.66570i	0.150617	+	1.23636i
$22$	10.2095	−	5.74990i	2.17668	−	1.22588i
$23$	−5.68078	+	4.43180i	−1.18452	+	0.924093i	−0.998293	−	0.0584126i	$-0.981396\pi$
$23$	−5.68078	+	4.43180i	−1.18452	+	0.924093i	−0.186231	+	0.982506i	$0.559627\pi$
$24$	−1.86318	−	6.80776i	−0.380319	−	1.38963i
$25$	−4.72809	+	0.202215i	−0.945617	+	0.0404429i
$26$	−1.74437	+	3.52534i	−0.342098	+	0.691377i
$27$	0.463498	−	2.86690i	0.0892002	−	0.551735i
$28$	1.21528	−	8.93188i	0.229666	−	1.68797i
$29$	0.110231	−	0.0446275i	0.0204693	−	0.00828712i	−0.365009	−	0.931004i	$-0.618934\pi$
$29$	0.110231	−	0.0446275i	0.0204693	−	0.00828712i	0.385479	+	0.922717i	$0.374036\pi$
$30$	2.14400	−	1.46176i	0.391440	−	0.266879i
$31$	2.51404	−	2.33269i	0.451535	−	0.418963i	−0.421343	−	0.906901i	$-0.638441\pi$
$31$	2.51404	−	2.33269i	0.451535	−	0.418963i	0.872878	+	0.487938i	$0.162251\pi$
$32$	−0.0501970	−	4.69741i	−0.00887366	−	0.830393i
$33$	10.7121	+	1.84951i	1.86473	+	0.321959i
$34$	8.05611	+	6.85826i	1.38161	+	1.17618i
$35$	1.34242	−	0.266572i	0.226910	−	0.0450588i
$36$	2.28077	−	5.15229i	0.380128	−	0.858715i
$37$	−4.39978	−	4.64136i	−0.723319	−	0.763035i	0.255711	−	0.966753i	$-0.417691\pi$
$37$	−4.39978	−	4.64136i	−0.723319	−	0.763035i	−0.979030	+	0.203718i	$0.934697\pi$
$38$	−5.53892	+	0.594135i	−0.898531	+	0.0963814i
$39$	−3.32077	+	1.51265i	−0.531749	+	0.242218i
$40$	−1.59449	+	0.567516i	−0.252111	+	0.0897322i
$41$	0.254392	−	0.691265i	0.0397293	−	0.107957i	−0.917050	−	0.398772i	$-0.869436\pi$
$41$	0.254392	−	0.691265i	0.0397293	−	0.107957i	0.956779	+	0.290815i	$0.0939263\pi$
$42$	9.69566	−	9.06294i	1.49607	−	1.39844i
$43$	9.15264	+	3.03889i	1.39576	+	0.463426i	0.911429	−	0.411457i	$-0.134980\pi$
$43$	9.15264	+	3.03889i	1.39576	+	0.463426i	0.484335	+	0.874883i	$0.339062\pi$
$44$	−15.6237	−	7.11678i	−2.35536	−	1.07289i
$45$	0.852372	+	0.0730435i	0.127064	+	0.0108887i
$46$	16.1114	+	4.59503i	2.37549	+	0.677500i
$47$	−2.95791	−	1.58358i	−0.431455	−	0.230988i	0.241909	−	0.970299i	$-0.422226\pi$
$47$	−2.95791	−	1.58358i	−0.431455	−	0.230988i	−0.673365	+	0.739311i	$0.735152\pi$
$48$	−1.06773	+	1.33889i	−0.154113	+	0.193252i
$49$	6.57727	−	2.39574i	0.939609	−	0.342249i
$50$	6.86106	+	8.60350i	0.970300	+	1.21672i
$51$	1.77325	+	9.65394i	0.248305	+	1.35182i
$52$	5.67905	−	0.980526i	0.787543	−	0.135975i
$53$	−2.92960	−	1.73340i	−0.402411	−	0.238101i	0.293908	−	0.955834i	$-0.405044\pi$
$53$	−2.92960	−	1.73340i	−0.402411	−	0.238101i	−0.696319	+	0.717732i	$0.745180\pi$
$54$	−6.02021	+	3.05935i	−0.819247	+	0.416325i
$55$	0.250300	−	2.59462i	0.0337505	−	0.349859i
$56$	−7.61639	+	4.11375i	−1.01778	+	0.549723i
$57$	−4.33134	−	2.81939i	−0.573701	−	0.373438i
$58$	−0.234927	−	0.145870i	−0.0308475	−	0.0191536i
$59$	−6.78328	+	8.14273i	−0.883108	+	1.06009i	0.114666	+	0.993404i	$0.463420\pi$
$59$	−6.78328	+	8.14273i	−0.883108	+	1.06009i	−0.997774	+	0.0666886i	$0.978757\pi$
$60$	−3.58193	−	1.27489i	−0.462425	−	0.164588i
$61$	−10.2562	+	0.878897i	−1.31317	+	0.112531i	−0.720805	−	0.693138i	$-0.756228\pi$
$61$	−10.2562	+	0.878897i	−1.31317	+	0.112531i	−0.592365	+	0.805669i	$0.701806\pi$
$62$	−7.82770	−	1.52444i	−0.994118	−	0.193605i
$63$	4.36547	−	0.296423i	0.549998	−	0.0373458i
$64$	−10.0266	+	7.48308i	−1.25333	+	0.935385i
$65$	0.421213	+	0.766959i	0.0522450	+	0.0951296i
$66$	−11.2102	−	22.6557i	−1.37988	−	2.78872i
$67$	−7.60362	+	2.34541i	−0.928930	+	0.286537i	−0.722059	−	0.691831i	$-0.756804\pi$
$67$	−7.60362	+	2.34541i	−0.928930	+	0.286537i	−0.206871	+	0.978368i	$0.566328\pi$
$68$	1.15845	−	15.4585i	0.140483	−	1.87462i
$69$	8.89247	+	12.7480i	1.07053	+	1.53468i
$70$	−2.34088	−	2.15603i	−0.279788	−	0.257694i
$71$	−3.72918	−	1.50978i	−0.442572	−	0.179177i	0.143130	−	0.989704i	$-0.454283\pi$
$71$	−3.72918	−	1.50978i	−0.442572	−	0.179177i	−0.585702	+	0.810526i	$0.699181\pi$
$72$	−5.28777	+	1.14759i	−0.623170	+	0.135245i
$73$	−7.27431	+	3.89445i	−0.851394	+	0.455811i	−0.839012	−	0.544112i	$-0.816867\pi$
$73$	−7.27431	+	3.89445i	−0.851394	+	0.455811i	−0.0123818	+	0.999923i	$0.503941\pi$
$74$	−2.68660	+	14.6264i	−0.312311	+	1.70028i
$75$	−0.109089	+	10.2085i	−0.0125965	+	1.17877i
$76$	5.48744	+	6.04229i	0.629453	+	0.693098i
$77$	−0.761007	−	13.3103i	−0.0867247	−	1.51686i
$78$	7.39329	+	4.16383i	0.837126	+	0.471460i
$79$	9.91547	−	1.49452i	1.11558	−	0.168146i	0.434722	−	0.900565i	$-0.356847\pi$
$79$	9.91547	−	1.49452i	1.11558	−	0.168146i	0.680855	+	0.732418i	$0.261608\pi$
$80$	0.339290	+	0.231324i	0.0379337	+	0.0258628i
$81$	−10.9709	−	2.38100i	−1.21899	−	0.264556i
$82$	−1.64711	+	0.469763i	−0.181893	+	0.0518766i
$83$	11.5122	−	2.24199i	1.26362	−	0.246091i	0.485520	−	0.874226i	$-0.338630\pi$
$83$	11.5122	−	2.24199i	1.26362	−	0.246091i	0.778105	+	0.628135i	$0.216181\pi$
$84$	−19.1009	−	3.64693i	−2.08408	−	0.397913i
$85$	2.27668	−	0.597016i	0.246941	−	0.0647554i
$86$	−6.83851	−	21.3570i	−0.737416	−	2.30298i
$87$	−0.0834369	−	0.242599i	−0.00894538	−	0.0260094i
$88$	3.32432	+	16.1481i	0.354374	+	1.72139i
$89$	−7.50914	+	7.58981i	−0.795967	+	0.804518i	−0.984098	−	0.177626i	$-0.943158\pi$
$89$	−7.50914	+	7.58981i	−0.795967	+	0.804518i	0.188131	+	0.982144i	$0.439757\pi$
$90$	−1.03123	−	1.70112i	−0.108701	−	0.179314i
$91$	2.72801	+	3.54777i	0.285973	+	0.371908i
$92$	−8.47792	−	23.0373i	−0.883884	−	2.40180i
$93$	−4.73542	−	5.68445i	−0.491040	−	0.589450i
$94$	1.08028	+	7.72656i	0.111423	+	0.796933i
$95$	−0.596559	+	1.08624i	−0.0612056	+	0.111445i
$96$	−10.1249	−	0.433029i	−1.03337	−	0.0441959i
$97$	0.845738	+	3.70542i	0.0858717	+	0.376229i	0.999543	−	0.0302251i	$-0.00962241\pi$
$97$	0.845738	+	3.70542i	0.0858717	+	0.376229i	−0.913671	+	0.406454i	$0.866765\pi$
$98$	−13.5160	−	9.06991i	−1.36532	−	0.916199i
$99$	1.85439	−	8.12462i	0.186373	−	0.816555i
$100$	4.25622	−	15.5516i	0.425622	−	1.55516i
$101$	−1.40745	−	3.37237i	−0.140046	−	0.335563i	0.837451	−	0.546513i	$-0.184045\pi$
$101$	−1.40745	−	3.37237i	−0.140046	−	0.335563i	−0.977497	+	0.210950i	$0.932344\pi$
$102$	15.7021	−	16.5643i	1.55474	−	1.64011i
$103$	2.11154	−	2.76709i	0.208056	−	0.272649i	−0.679173	−	0.733978i	$-0.737661\pi$
$103$	2.11154	−	2.76709i	0.208056	−	0.272649i	0.887229	+	0.461329i	$0.152627\pi$
$104$	−3.97556	−	3.85012i	−0.389836	−	0.377535i
$105$	−0.419593	−	2.92253i	−0.0409481	−	0.285210i
$106$	0.760055	+	7.87876i	0.0738231	+	0.765253i
$107$	7.39028	+	11.6232i	0.714445	+	1.12366i	0.986875	+	0.161485i	$0.0516285\pi$
$107$	7.39028	+	11.6232i	0.714445	+	1.12366i	−0.272430	+	0.962176i	$0.587827\pi$
$108$	8.82082	+	4.48257i	0.848784	+	0.431335i
$109$	−0.193146	+	0.303775i	−0.0185000	+	0.0290963i	−0.852994	−	0.521920i	$-0.825216\pi$
$109$	−0.193146	+	0.303775i	−0.0185000	+	0.0290963i	0.834494	+	0.551017i	$0.185760\pi$
$110$	−5.21655	+	3.08656i	−0.497379	+	0.294292i
$111$	−10.5052	+	8.94324i	−0.997113	+	0.848855i
$112$	1.89563	+	0.904301i	0.179120	+	0.0854484i
$113$	−18.0047	−	4.72138i	−1.69374	−	0.444150i	−0.724299	−	0.689485i	$-0.757837\pi$
$113$	−18.0047	−	4.72138i	−1.69374	−	0.444150i	−0.969438	+	0.245335i	$0.921102\pi$
$114$	0.641769	+	12.0003i	0.0601072	+	1.12393i
$115$	2.88896	−	2.35481i	0.269397	−	0.219587i
$116$	0.0302785	+	0.404039i	0.00281129	+	0.0375141i
$117$	1.02202	+	2.60405i	0.0944853	+	0.240745i
$118$	24.5929	+	1.57891i	2.26396	+	0.145351i
$119$	11.0416	−	4.79560i	1.01218	−	0.439612i
$120$	1.03884	+	3.50021i	0.0948330	+	0.319524i
$121$	−13.9962	−	3.35229i	−1.27238	−	0.304753i
$122$	15.7100	+	18.0593i	1.42231	+	1.63501i
$123$	−1.45981	−	0.627644i	−0.131626	−	0.0565928i
$124$	4.95699	+	10.5811i	0.445151	+	0.950207i
$125$	5.02416	−	0.322562i	0.449375	−	0.0288508i
$126$	−6.54094	−	7.79327i	−0.582714	−	0.694280i
$127$	−1.74614	−	10.8005i	−0.154945	−	0.958390i	−0.940548	−	0.339659i	$-0.889688\pi$
$127$	−1.74614	−	10.8005i	−0.154945	−	0.958390i	0.785603	−	0.618730i	$-0.212353\pi$
$128$	18.8219	+	5.80579i	1.66364	+	0.513164i
$129$	7.60075	−	19.3664i	0.669209	−	1.70512i
$130$	0.863171	−	1.84250i	0.0757051	−	0.161598i
$131$	9.35544	−	8.31569i	0.817389	−	0.726545i	−0.147540	−	0.989056i	$-0.547136\pi$
$131$	9.35544	−	8.31569i	0.817389	−	0.726545i	0.964929	+	0.262511i	$0.0845506\pi$
$132$	−17.1308	+	32.8365i	−1.49104	+	2.85805i
$133$	−2.16713	+	5.95640i	−0.187914	+	0.516485i
$134$	14.8284	+	11.0667i	1.28098	+	0.956017i
$135$	−0.208018	+	1.48781i	−0.0179033	+	0.128050i
$136$	−12.6469	+	7.85263i	−1.08446	+	0.673357i
$137$	−8.13324	−	0.173845i	−0.694870	−	0.0148526i	−0.327397	−	0.944887i	$-0.606171\pi$
$137$	−8.13324	−	0.173845i	−0.694870	−	0.0148526i	−0.367473	+	0.930034i	$0.619777\pi$
$138$	11.7547	−	34.1775i	1.00062	−	2.90938i
$139$	6.68506	+	0.861944i	0.567020	+	0.0731091i	0.406051	−	0.913850i	$-0.366906\pi$
$139$	6.68506	+	0.861944i	0.567020	+	0.0731091i	0.160969	+	0.986960i	$0.448538\pi$
$140$	−0.529775	+	4.63278i	−0.0447742	+	0.391541i
$141$	−3.75208	+	6.18945i	−0.315982	+	0.521246i
$142$	2.27615	+	9.07405i	0.191010	+	0.761478i
$143$	7.96728	−	3.02909i	0.666258	−	0.253305i
$144$	0.981237	+	0.872184i	0.0817698	+	0.0726820i
$145$	−0.0565153	+	0.0242988i	−0.00469334	+	0.00201790i
$146$	17.2865	+	8.32474i	1.43064	+	0.688960i
$147$	−4.40314	−	14.4447i	−0.363165	−	1.19138i
$148$	19.6313	−	9.45396i	1.61369	−	0.777110i
$149$	−7.20747	+	8.28528i	−0.590459	+	0.678757i	−0.969066	−	0.246801i	$-0.920621\pi$
$149$	−7.20747	+	8.28528i	−0.590459	+	0.678757i	0.378608	+	0.925557i	$0.376403\pi$
$150$	19.3240	−	13.7888i	1.57780	−	1.12585i
$151$	2.95899	+	4.44127i	0.240799	+	0.361426i	0.932753	−	0.360516i	$-0.117399\pi$
$151$	2.95899	+	4.44127i	0.240799	+	0.361426i	−0.691954	+	0.721942i	$0.743250\pi$
$152$	1.58046	−	7.67718i	0.128192	−	0.622702i
$153$	7.46290	−	0.962234i	0.603340	−	0.0777920i
$154$	−23.9574	+	19.6752i	−1.93055	+	1.58547i
$155$	−1.27441	+	1.23420i	−0.102363	+	0.0991333i
$156$	−1.45798	−	12.3467i	−0.116732	−	0.988527i
$157$	5.05398	−	20.1481i	0.403352	−	1.60799i	−0.340905	−	0.940098i	$-0.610733\pi$
$157$	5.05398	−	20.1481i	0.403352	−	1.60799i	0.744256	−	0.667894i	$-0.232804\pi$
$158$	−16.3992	−	16.5754i	−1.30465	−	1.31867i
$159$	−4.07158	+	6.11120i	−0.322897	+	0.484650i
$160$	0.0778878	+	2.42883i	0.00615757	+	0.192016i
$161$	12.7638	−	14.1588i	1.00593	−	1.11587i
$162$	10.5667	+	23.8704i	0.830201	+	1.87544i
$163$	−5.50523	+	13.1910i	−0.431203	+	1.03320i	0.549110	+	0.835750i	$0.314967\pi$
$163$	−5.50523	+	13.1910i	−0.431203	+	1.03320i	−0.980313	+	0.197450i	$0.936734\pi$
$164$	1.97868	+	1.54364i	0.154509	+	0.120538i
$165$	−5.56047	−	0.838106i	−0.432882	−	0.0652464i
$166$	−19.9919	−	18.5498i	−1.55168	−	1.43975i
$167$	0.332729	−	0.366371i	0.0257473	−	0.0283507i	−0.727269	−	0.686353i	$-0.759211\pi$
$167$	0.332729	−	0.366371i	0.0257473	−	0.0283507i	0.753016	+	0.658002i	$0.228598\pi$
$168$	7.98435	+	16.8810i	0.616006	+	1.30240i
$169$	5.80055	−	8.31552i	0.446196	−	0.639656i
$170$	−4.24223	−	3.45787i	−0.325364	−	0.265206i
$171$	−2.33563	+	3.20031i	−0.178610	+	0.244734i
$172$	−19.3698	+	26.5408i	−1.47693	+	2.02371i
$173$	14.7794	+	12.0468i	1.12366	+	0.915899i	0.997103	−	0.0760603i	$-0.0242342\pi$
$173$	14.7794	+	12.0468i	1.12366	+	0.915899i	0.126554	+	0.991960i	$0.459608\pi$
$174$	−0.341295	+	0.489272i	−0.0258735	+	0.0370916i
$175$	12.2261	−	2.70059i	0.924203	−	0.204146i
$176$	2.68931	−	2.96123i	0.202714	−	0.223211i
$177$	16.7595	+	15.5505i	1.25972	+	1.16885i
$178$	24.5493	+	3.70021i	1.84005	+	0.277343i
$179$	−16.4545	−	12.8368i	−1.22986	−	0.959465i	−0.229958	−	0.973200i	$-0.573859\pi$
$179$	−16.4545	−	12.8368i	−1.22986	−	0.959465i	−0.999906	+	0.0137355i	$0.995628\pi$
$180$	−1.12260	+	2.68985i	−0.0836736	+	0.200489i
$181$	−7.66031	−	17.3048i	−0.569387	−	1.28625i	−0.934723	−	0.355378i	$-0.884352\pi$
$181$	−7.66031	−	17.3048i	−0.569387	−	1.28625i	0.365336	−	0.930876i	$-0.380954\pi$
$182$	2.92418	−	9.98725i	0.216755	−	0.740305i
$183$	0.711750	+	22.1950i	0.0526141	+	1.64070i
$184$	−13.0704	+	19.6179i	−0.963563	+	1.44625i
$185$	2.32676	+	2.35176i	0.171067	+	0.172905i
$186$	−4.18572	+	16.6867i	−0.306912	+	1.22353i
$187$	−2.68875	−	22.7692i	−0.196621	−	1.66505i
$188$	8.21151	−	7.95240i	0.598886	−	0.579988i
$189$	0.110403	+	7.68280i	0.00803061	+	0.558841i
$190$	2.85802	−	0.368501i	0.207343	−	0.0267339i
$191$	2.40101	−	11.6631i	0.173731	−	0.843911i	−0.797044	−	0.603921i	$-0.793604\pi$
$191$	2.40101	−	11.6631i	0.173731	−	0.843911i	0.970775	−	0.239990i	$-0.0771441\pi$
$192$	14.9648	+	22.4614i	1.07999	+	1.62101i
$193$	0.726759	−	0.518587i	0.0523132	−	0.0373287i	−0.554391	−	0.832256i	$-0.687049\pi$
$193$	0.726759	−	0.518587i	0.0523132	−	0.0373287i	0.606705	+	0.794927i	$0.292491\pi$
$194$	5.80050	−	6.66792i	0.416452	−	0.478728i
$195$	1.70070	−	0.819014i	0.121790	−	0.0586508i
$196$	0.939988	+	23.8307i	0.0671420	+	1.70220i
$197$	−14.5329	−	6.99867i	−1.03543	−	0.498635i	−0.162613	−	0.986690i	$-0.551992\pi$
$197$	−14.5329	−	6.99867i	−1.03543	−	0.498635i	−0.872813	+	0.488055i	$0.837706\pi$
$198$	−17.8023	+	7.65412i	−1.26516	+	0.543955i
$199$	11.0942	+	9.86121i	0.786448	+	0.699043i	0.958201	−	0.286097i	$-0.0923580\pi$
$199$	11.0942	+	9.86121i	0.786448	+	0.699043i	−0.171753	+	0.985140i	$0.554943\pi$
$200$	−14.4728	+	5.50240i	−1.02338	+	0.389079i
$201$	4.17647	+	16.6498i	0.294586	+	1.17439i
$202$	−4.40495	+	7.26642i	−0.309931	+	0.511264i
$203$	−0.266689	+	0.166955i	−0.0187179	+	0.0117180i
$204$	−33.1670	−	4.27642i	−2.32216	−	0.299409i
$205$	−0.123923	+	0.360317i	−0.00865519	+	0.0251656i
$206$	−8.09187	−	0.172961i	−0.563787	−	0.0120507i
$207$	10.1229	−	6.28548i	0.703593	−	0.436871i
$208$	−0.185932	+	1.32985i	−0.0128921	+	0.0922084i
$209$	9.67465	+	7.22038i	0.669210	+	0.499444i
$210$	−4.91416	+	4.79431i	−0.339110	+	0.330839i
$211$	−2.78861	+	5.34524i	−0.191976	+	0.367982i	−0.963286	−	0.268478i	$-0.913479\pi$
$211$	−2.78861	+	5.34524i	−0.191976	+	0.367982i	0.771310	+	0.636460i	$0.219602\pi$
$212$	8.66825	−	7.70487i	0.595338	−	0.529173i
$213$	−3.68196	+	7.85941i	−0.252284	+	0.538518i
$214$	11.7012	−	29.8141i	0.799877	−	2.03805i
$215$	−4.76711	−	1.47046i	−0.325114	−	0.100284i
$216$	−1.51647	−	9.37989i	−0.103183	−	0.638221i
$217$	−5.47789	+	7.23365i	−0.371863	+	0.491052i
$218$	0.835339	−	0.0536305i	0.0565763	−	0.00363232i
$219$	7.55134	+	16.1189i	0.510272	+	1.08921i
$220$	8.15886	+	3.50791i	0.550070	+	0.236503i
$221$	5.05132	+	5.80670i	0.339789	+	0.390601i
$222$	31.1985	+	7.47247i	2.09391	+	0.501519i
$223$	0.249725	+	0.841405i	0.0167228	+	0.0563446i	0.966615	−	0.256232i	$-0.0824812\pi$
$223$	0.249725	+	0.841405i	0.0167228	+	0.0563446i	−0.949892	+	0.312577i	$0.898808\pi$
$224$	2.29041	+	12.2160i	0.153034	+	0.816218i
$225$	7.81035	+	0.501441i	0.520690	+	0.0334294i
$226$	15.8127	+	40.2900i	1.05184	+	2.68005i
$227$	1.29066	+	17.2226i	0.0856640	+	1.14311i	0.859987	+	0.510316i	$0.170471\pi$
$227$	1.29066	+	17.2226i	0.0856640	+	1.14311i	−0.774323	+	0.632790i	$0.781910\pi$
$228$	13.6484	−	11.1249i	0.903887	−	0.736763i
$229$	−0.962784	−	18.0029i	−0.0636225	−	1.18967i	−0.833885	−	0.551938i	$-0.813888\pi$
$229$	−0.962784	−	18.0029i	−0.0636225	−	1.18967i	0.770262	−	0.637727i	$-0.220125\pi$
$230$	−8.38319	−	2.19833i	−0.552771	−	0.144954i
$231$	−28.7607	+	0.105938i	−1.89231	+	0.00697022i
$232$	0.296269	−	0.252218i	0.0194510	−	0.0165589i
$233$	20.2287	−	11.9691i	1.32523	−	0.784119i	0.337652	−	0.941271i	$-0.390367\pi$
$233$	20.2287	−	11.9691i	1.32523	−	0.784119i	0.987574	+	0.157152i	$0.0502312\pi$
$234$	3.49018	−	5.48926i	0.228160	−	0.358844i
$235$	1.54726	+	0.786288i	0.100932	+	0.0512918i
$236$	−19.3735	−	30.4702i	−1.26111	−	1.98344i
$237$	−2.07716	−	21.5319i	−0.134926	−	1.39865i
$238$	−24.1433	−	14.1654i	−1.56497	−	0.918209i
$239$	−12.4920	−	12.0979i	−0.808043	−	0.782546i	0.171200	−	0.985236i	$-0.445236\pi$
$239$	−12.4920	−	12.0979i	−0.808043	−	0.782546i	−0.979243	+	0.202690i	$0.935031\pi$
$240$	0.537402	−	0.704244i	0.0346892	−	0.0454587i
$241$	17.9311	−	18.9156i	1.15504	−	1.21846i	0.183136	−	0.983088i	$-0.441375\pi$
$241$	17.9311	−	18.9156i	1.15504	−	1.21846i	0.971905	−	0.235374i	$-0.0756316\pi$
$242$	12.8894	+	30.8842i	0.828563	+	1.98531i
$243$	−4.09317	+	14.9558i	−0.262577	+	0.959417i
$244$	7.80410	−	34.1920i	0.499606	−	2.18892i
$245$	−3.37511	+	1.31172i	−0.215628	+	0.0838030i
$246$	0.822203	+	3.60230i	0.0524217	+	0.229675i
$247$	−4.04865	−	0.173156i	−0.257609	−	0.0110176i
$248$	5.40145	−	9.83516i	0.342992	−	0.624533i
$249$	−3.50342	−	25.0577i	−0.222020	−	1.58796i
$250$	−7.49297	−	8.99464i	−0.473897	−	0.568871i
$251$	−10.5500	−	28.6678i	−0.665912	−	1.80950i	−0.582259	−	0.813003i	$-0.697831\pi$
$251$	−10.5500	−	28.6678i	−0.665912	−	1.80950i	−0.0836527	−	0.996495i	$-0.526659\pi$
$252$	−3.57379	+	14.4729i	−0.225128	+	0.911705i
$253$	−18.8210	−	31.0472i	−1.18326	−	1.95192i
$254$	−17.8928	+	18.0850i	−1.12270	+	1.13476i
$255$	−1.02380	−	4.97317i	−0.0641128	−	0.311432i
$256$	−6.75800	−	19.6494i	−0.422375	−	1.22809i
$257$	6.79610	+	21.2245i	0.423929	+	1.32395i	0.896651	+	0.442737i	$0.145993\pi$
$257$	6.79610	+	21.2245i	0.423929	+	1.32395i	−0.472722	+	0.881212i	$0.656729\pi$
$258$	−46.7947	+	12.2710i	−2.91331	+	0.763960i
$259$	13.5975	+	10.0703i	0.844906	+	0.625737i
$260$	−2.92622	+	0.569882i	−0.181477	+	0.0353426i
$261$	−0.189131	+	0.0539409i	−0.0117069	+	0.00333886i
$262$	−28.4436	−	6.17307i	−1.75725	−	0.381373i
$263$	5.72364	+	3.90231i	0.352935	+	0.240627i	0.726789	−	0.686860i	$-0.241012\pi$
$263$	5.72364	+	3.90231i	0.352935	+	0.240627i	−0.373854	+	0.927487i	$0.621964\pi$
$264$	35.1690	−	5.30088i	2.16450	−	0.326246i
$265$	1.53428	+	0.864088i	0.0942498	+	0.0530805i
$266$	14.1585	−	4.09452i	0.868114	−	0.251051i
$267$	15.4848	+	17.0505i	0.947653	+	1.04347i
$268$	0.289686	−	27.1087i	0.0176954	−	1.65593i
$269$	3.75916	−	20.4656i	0.229200	−	1.24781i	−0.645731	−	0.763565i	$-0.723447\pi$
$269$	3.75916	−	20.4656i	0.229200	−	1.24781i	0.874931	−	0.484247i	$-0.160906\pi$
$270$	3.07968	−	1.64877i	0.187424	−	0.100341i
$271$	−17.9587	+	3.89755i	−1.09091	+	0.236759i	−0.721437	−	0.692480i	$-0.756518\pi$
$271$	−17.9587	+	3.89755i	−1.09091	+	0.236759i	−0.369478	+	0.929239i	$0.620464\pi$
$272$	3.34792	+	1.35542i	0.202998	+	0.0821847i
$273$	7.95684	−	5.46792i	0.481570	−	0.330934i
$274$	10.8225	+	15.5149i	0.653811	+	0.937287i
$275$	1.78208	−	23.7802i	0.107463	−	1.43400i
$276$	−50.6032	+	15.6090i	−3.04596	+	0.939553i
$277$	7.01352	+	14.1743i	0.421402	+	0.851648i	0.999367	+	0.0355869i	$0.0113300\pi$
$277$	7.01352	+	14.1743i	0.421402	+	0.851648i	−0.577965	+	0.816062i	$0.696153\pi$
$278$	−7.54489	−	13.7380i	−0.452512	−	0.823951i
$279$	−4.54544	+	3.39235i	−0.272128	+	0.203095i
$280$	3.89353	−	2.21172i	0.232683	−	0.132176i
$281$	−14.8864	−	2.89913i	−0.888050	−	0.172948i	−0.273544	−	0.961860i	$-0.588196\pi$
$281$	−14.8864	−	2.89913i	−0.888050	−	0.172948i	−0.614506	+	0.788912i	$0.710645\pi$
$282$	16.7689	−	1.43700i	0.998574	−	0.0855721i
$283$	−9.65417	−	3.43614i	−0.573881	−	0.204258i	0.0324457	−	0.999474i	$-0.489670\pi$
$283$	−9.65417	−	3.43614i	−0.573881	−	0.204258i	−0.606326	+	0.795216i	$0.707357\pi$
$284$	8.77337	−	10.5317i	0.520604	−	0.624938i
$285$	2.27123	+	1.41024i	0.134536	+	0.0835353i
$286$	−16.6110	−	10.8126i	−0.982230	−	0.639361i
$287$	−0.345011	+	1.91805i	−0.0203654	+	0.113219i
$288$	−0.746003	+	7.73310i	−0.0439586	+	0.455677i
$289$	3.30033	−	1.67716i	0.194137	−	0.0986566i
$290$	0.123111	+	0.0728431i	0.00722932	+	0.00427750i
$291$	8.07960	−	1.39500i	0.473635	−	0.0817762i
$292$	−5.07872	−	27.6496i	−0.297210	−	1.61807i
$293$	7.41743	+	9.30116i	0.433331	+	0.543379i	0.949772	−	0.312943i	$-0.101315\pi$
$293$	7.41743	+	9.30116i	0.433331	+	0.543379i	−0.516441	+	0.856323i	$0.672744\pi$
$294$	−21.0954	+	28.0710i	−1.23031	+	1.63714i
$295$	3.41813	−	4.28620i	0.199011	−	0.249552i
$296$	−18.4469	−	9.87592i	−1.07220	−	0.574026i
$297$	14.0729	+	4.01364i	0.816591	+	0.232895i
$298$	25.4421	+	2.18024i	1.47382	+	0.126298i
$299$	11.0910	+	5.05206i	0.641408	+	0.292168i
$300$	−33.0107	−	10.9603i	−1.90587	−	0.632793i
$301$	−25.2443	−	3.70992i	−1.45506	−	0.213836i
$302$	4.28580	−	11.6459i	0.246620	−	0.670147i
$303$	−7.42686	+	2.64339i	−0.426662	+	0.151859i
$304$	−1.73068	+	0.788343i	−0.0992611	+	0.0452145i
$305$	5.29453	−	0.567920i	0.303164	−	0.0325190i
$306$	−12.0375	−	12.6984i	−0.688136	−	0.725921i
$307$	−11.4604	+	25.8892i	−0.654077	+	1.47757i	0.211799	+	0.977313i	$0.432068\pi$
$307$	−11.4604	+	25.8892i	−0.654077	+	1.47757i	−0.865876	+	0.500259i	$0.833238\pi$
$308$	43.9795	+	11.3598i	2.50596	+	0.647286i
$309$	−5.71756	−	4.86743i	−0.325261	−	0.276899i
$310$	4.06514	+	0.701873i	0.230884	+	0.0398637i
$311$	−0.0145528	−	1.36184i	−0.000825212	−	0.0772230i	−0.999610	−	0.0279340i	$-0.991107\pi$
$311$	−0.0145528	−	1.36184i	−0.000825212	−	0.0772230i	0.998785	−	0.0492890i	$-0.0156955\pi$
$312$	−8.75188	+	8.12056i	−0.495478	+	0.459736i
$313$	−2.95574	+	2.01519i	−0.167068	+	0.113905i	−0.643968	−	0.765053i	$-0.722713\pi$
$313$	−2.95574	+	2.01519i	−0.167068	+	0.113905i	0.476899	+	0.878958i	$0.341761\pi$
$314$	−44.7718	+	18.1261i	−2.52662	+	1.02292i
$315$	−2.25444	+	0.201560i	−0.127023	+	0.0113566i
$316$	−5.45256	+	33.7260i	−0.306731	+	1.89724i
$317$	−6.80977	+	13.7625i	−0.382475	+	0.772978i	−0.999907	−	0.0136463i	$-0.995656\pi$
$317$	−6.80977	+	13.7625i	−0.382475	+	0.772978i	0.617432	+	0.786624i	$0.288173\pi$
$318$	17.0599	−	0.729631i	0.956671	−	0.0409157i
$319$	0.158189	+	0.577999i	0.00885688	+	0.0323617i
$320$	5.10281	−	3.98090i	0.285256	−	0.222539i
$321$	25.8900	−	14.5810i	1.44504	−	0.813832i
$322$	−44.0907	−	4.56520i	−2.45708	−	0.254409i
$323$	−3.10142	+	10.4497i	−0.172568	+	0.581437i
$324$	19.1243	−	33.1243i	1.06246	−	1.84024i
$325$	4.00249	+	6.93251i	0.222018	+	0.384546i
$326$	32.3230	−	7.74181i	1.79021	−	0.428779i
$327$	0.632136	+	0.451068i	0.0349572	+	0.0249441i
$328$	0.0772431	−	2.40872i	0.00426504	−	0.133000i
$329$	8.43488	+	2.76612i	0.465030	+	0.152501i
$330$	6.04807	+	11.5930i	0.332935	+	0.638174i
$331$	7.50345	+	2.85274i	0.412427	+	0.156801i	0.552831	−	0.833294i	$-0.313548\pi$
$331$	7.50345	+	2.85274i	0.412427	+	0.156801i	−0.140404	+	0.990094i	$0.544840\pi$
$332$	−4.68611	+	39.6836i	−0.257184	+	2.17792i
$333$	6.41616	+	8.40812i	0.351604	+	0.460762i
$334$	−1.14425	−	0.122739i	−0.0626107	−	0.00671597i
$335$	3.90648	−	1.29704i	0.213434	−	0.0708648i
$336$	2.16642	−	3.97936i	0.118188	−	0.217092i
$337$	16.9076	−	11.0056i	0.921017	−	0.599516i	0.00470876	−	0.999989i	$-0.498501\pi$
$337$	16.9076	−	11.0056i	0.921017	−	0.599516i	0.916309	+	0.400473i	$0.131154\pi$
$338$	−23.5703	+	0.503806i	−1.28206	+	0.0274035i
$339$	−12.2450	+	38.2415i	−0.665055	+	2.07699i
$340$	−0.428239	+	8.00755i	−0.0232245	+	0.434271i
$341$	10.1878	+	13.9595i	0.551700	+	0.755947i
$342$	9.21278			0.498170
$343$	−16.0356	+	9.26598i	−0.865843	+	0.500316i
$344$	31.5530			1.70122
$345$	−4.73988	−	6.49465i	−0.255187	−	0.349660i
$346$	2.36772	−	44.2736i	0.127290	−	2.38016i
$347$	−5.42566	+	16.9446i	−0.291265	+	0.909632i	0.691116	+	0.722743i	$0.257119\pi$
$347$	−5.42566	+	16.9446i	−0.291265	+	0.909632i	−0.982381	+	0.186888i	$0.940160\pi$
$348$	0.873864	−	0.0186785i	0.0468440	−	0.00100127i
$349$	−27.3938	+	17.8314i	−1.46636	+	0.954493i	−0.468899	+	0.883252i	$0.655349\pi$
$349$	−27.3938	+	17.8314i	−1.46636	+	0.954493i	−0.997459	+	0.0712411i	$0.977304\pi$
$350$	−21.8319	−	19.2621i	−1.16697	−	1.02960i
$351$	−4.66213	+	1.54793i	−0.248846	+	0.0826226i
$352$	23.5369	+	2.52469i	1.25452	+	0.134567i
$353$	6.05510	+	7.93496i	0.322281	+	0.422336i	0.927558	−	0.373679i	$-0.121904\pi$
$353$	6.05510	+	7.93496i	0.322281	+	0.422336i	−0.605278	+	0.796015i	$0.706938\pi$
$354$	6.23448	−	52.7957i	0.331359	−	2.80606i
$355$	1.94533	+	0.739594i	0.103247	+	0.0392536i
$356$	−16.8253	−	32.2509i	−0.891738	−	1.70930i
$357$	−9.05857	−	24.3381i	−0.479431	−	1.28811i
$358$	−1.55539	+	48.5028i	−0.0822049	+	2.56345i
$359$	−7.75462	−	5.53340i	−0.409273	−	0.292042i	0.357558	−	0.933891i	$-0.383610\pi$
$359$	−7.75462	−	5.53340i	−0.409273	−	0.292042i	−0.766831	+	0.641850i	$0.778167\pi$
$360$	2.72202	−	0.651960i	0.143463	−	0.0343613i
$361$	6.63035	+	11.4841i	0.348966	+	0.604426i
$362$	−22.0026	+	38.1096i	−1.15643	+	2.00300i
$363$	−8.83388	+	29.7643i	−0.463658	+	1.56222i
$364$	−14.3460	+	5.16569i	−0.751934	+	0.270756i
$365$	3.71904	−	2.09453i	0.194664	−	0.109632i
$366$	40.7129	−	31.7617i	2.12810	−	1.66021i
$367$	−5.24021	−	19.1469i	−0.273536	−	0.999461i	−0.961745	−	0.273948i	$-0.911670\pi$
$367$	−5.24021	−	19.1469i	−0.273536	−	0.999461i	0.688208	−	0.725513i	$-0.258398\pi$
$368$	5.71433	−	0.244395i	0.297880	−	0.0127400i
$369$	−0.540239	+	1.09182i	−0.0281237	+	0.0568378i
$370$	1.22776	−	7.59411i	0.0638280	−	0.394799i
$371$	8.42999	+	3.16951i	0.437664	+	0.164553i
$372$	23.3646	−	9.45929i	1.21140	−	0.490441i
$373$	11.7252	−	7.99413i	0.607110	−	0.413920i	−0.220370	−	0.975416i	$-0.570726\pi$
$373$	11.7252	−	7.99413i	0.607110	−	0.413920i	0.827479	+	0.561496i	$0.189774\pi$
$374$	−39.0814	+	36.2622i	−2.02085	+	1.87508i
$375$	−0.116053	−	10.8601i	−0.00599293	−	0.560816i
$376$	−10.8173	−	1.86767i	−0.557857	−	0.0963178i
$377$	−0.153172	−	0.130397i	−0.00788875	−	0.00671579i
$378$	14.2791	−	10.7389i	0.734440	−	0.552350i
$379$	−8.96190	+	20.2451i	−0.460342	+	1.03992i	0.522021	+	0.852933i	$0.325178\pi$
$379$	−8.96190	+	20.2451i	−0.460342	+	1.03992i	−0.982362	+	0.186987i	$0.940128\pi$
$380$	−2.90476	−	3.06426i	−0.149011	−	0.157193i
$381$	−23.4675	+	2.51725i	−1.20227	+	0.128963i
$382$	−25.1979	+	11.4779i	−1.28924	+	0.587262i
$383$	17.5868	−	6.25954i	0.898642	−	0.319848i	0.154597	−	0.987978i	$-0.450592\pi$
$383$	17.5868	−	6.25954i	0.898642	−	0.319848i	0.744045	+	0.668130i	$0.232905\pi$
$384$	14.6751	−	39.8770i	0.748886	−	2.03497i
$385$	0.540712	+	6.87537i	0.0275572	+	0.350401i
$386$	−1.97029	−	0.654182i	−0.100285	−	0.0332970i
$387$	−14.5142	−	6.61140i	−0.737800	−	0.336076i
$388$	−12.9019	−	1.10562i	−0.654994	−	0.0561293i
$389$	17.2952	+	4.93266i	0.876901	+	0.250096i	0.682552	−	0.730837i	$-0.260870\pi$
$389$	17.2952	+	4.93266i	0.876901	+	0.250096i	0.194349	+	0.980932i	$0.437741\pi$
$390$	−3.86965	−	2.07170i	−0.195948	−	0.104904i
$391$	20.4395	−	25.6303i	1.03367	−	1.29618i
$392$	17.9532	−	14.2200i	0.906774	−	0.718218i
$393$	−16.8358	−	21.1114i	−0.849252	−	1.06493i
$394$	6.77614	+	36.8907i	0.341377	+	1.85852i
$395$	−5.11151	+	0.882536i	−0.257188	+	0.0444052i
$396$	24.4357	+	14.4583i	1.22794	+	0.726557i
$397$	−22.7758	+	11.5742i	−1.14308	+	0.580892i	−0.919226	−	0.393730i	$-0.871185\pi$
$397$	−22.7758	+	11.5742i	−1.14308	+	0.580892i	−0.223857	+	0.974622i	$0.571865\pi$
$398$	3.31426	−	34.3558i	0.166129	−	1.72210i
$399$	12.5815	+	5.35461i	0.629864	+	0.268066i
$400$	3.14847	+	2.04943i	0.157424	+	0.102471i
$401$	−3.01142	−	1.86983i	−0.150383	−	0.0933751i	0.450239	−	0.892908i	$-0.351339\pi$
$401$	−3.01142	−	1.86983i	−0.150383	−	0.0933751i	−0.600622	+	0.799533i	$0.705080\pi$
$402$	25.5480	−	30.6681i	1.27422	−	1.52959i
$403$	−5.46531	−	1.94523i	−0.272246	−	0.0968989i
$404$	12.4048	−	1.06302i	0.617163	−	0.0528874i
$405$	5.70022	+	1.11012i	0.283246	+	0.0551622i
$406$	0.679166	+	0.272056i	0.0337064	+	0.0135019i
$407$	25.8267	−	19.2750i	1.28018	−	0.955425i
$408$	15.4590	+	28.1484i	0.765337	+	1.39355i
$409$	−13.0144	−	26.3020i	−0.643521	−	1.30055i	−0.938577	−	0.345069i	$-0.887856\pi$
$409$	−13.0144	−	26.3020i	−0.643521	−	1.30055i	0.295057	−	0.955480i	$-0.404661\pi$
$410$	0.846652	−	0.261157i	0.0418131	−	0.0128976i
$411$	−1.31148	+	17.5005i	−0.0646906	+	0.863236i
$412$	6.78469	+	9.72636i	0.334258	+	0.479183i
$413$	13.9303	−	24.3345i	0.685463	−	1.19742i
$414$	−25.6824	−	10.3977i	−1.26222	−	0.511017i
$415$	−5.92902	+	1.28676i	−0.291044	+	0.0631647i
$416$	−7.00545	+	3.75051i	−0.343470	+	0.183884i
$417$	2.62694	−	14.3016i	0.128642	−	0.700351i
$418$	0.299953	−	28.0694i	0.0146712	−	1.37292i
$419$	22.9422	+	25.2619i	1.12080	+	1.23412i	0.969356	+	0.245659i	$0.0790044\pi$
$419$	22.9422	+	25.2619i	1.12080	+	1.23412i	0.151443	+	0.988466i	$0.451608\pi$
$420$	9.91884	+	1.67495i	0.483990	+	0.0817293i
$421$	14.5315	+	8.18401i	0.708224	+	0.398864i	0.802476	−	0.596684i	$-0.203515\pi$
$421$	14.5315	+	8.18401i	0.708224	+	0.398864i	−0.0942522	+	0.995548i	$0.530046\pi$
$422$	13.8625	−	2.08944i	0.674816	−	0.101712i
$423$	4.58455	+	3.12570i	0.222909	+	0.151977i
$424$	−10.8838	−	2.36209i	−0.528565	−	0.114713i
$425$	20.7065	−	5.90559i	1.00441	−	0.286463i
$426$	19.8094	−	3.85789i	0.959770	−	0.186915i
$427$	26.3184	−	7.00521i	1.27364	−	0.339006i
$428$	−45.3929	+	11.9034i	−2.19415	+	0.575373i
$429$	−5.60735	−	17.5120i	−0.270725	−	0.845487i
$430$	3.77280	+	10.9697i	0.181940	+	0.529005i
$431$	3.39273	+	16.4804i	0.163422	+	0.793832i	0.977144	+	0.212578i	$0.0681860\pi$
$431$	3.39273	+	16.4804i	0.163422	+	0.793832i	−0.813722	+	0.581254i	$0.802562\pi$
$432$	−1.62142	+	1.63884i	−0.0780106	+	0.0788487i
$433$	16.9081	+	27.8918i	0.812554	+	1.34039i	0.937414	+	0.348218i	$0.113213\pi$
$433$	16.9081	+	27.8918i	0.812554	+	1.34039i	−0.124860	+	0.992174i	$0.539848\pi$
$434$	21.0959	+	0.373183i	1.01264	+	0.0179133i
$435$	0.0458333	+	0.124544i	0.00219754	+	0.00597142i
$436$	−0.785001	−	0.942324i	−0.0375947	−	0.0451292i
$437$	2.39008	+	17.0946i	0.114333	+	0.817747i
$438$	19.9245	−	36.2793i	0.952030	−	1.73349i
$439$	−0.000917779	0	3.92523e-5i	−4.38032e−5	0	1.87341e-6i	0.0427078	−	0.999088i	$-0.486402\pi$
$439$	−0.000917779	0	3.92523e-5i	−4.38032e−5	0	1.87341e-6i	−0.0427516	+	0.999086i	$0.513612\pi$
$440$	−1.89776	−	8.31464i	−0.0904723	−	0.396385i
$441$	−11.2380	+	2.77934i	−0.535141	+	0.132350i
$442$	3.98231	−	17.4476i	0.189419	−	0.829899i
$443$	3.71111	−	13.5598i	0.176320	−	0.644247i	−0.820989	−	0.570943i	$-0.806578\pi$
$443$	3.71111	−	13.5598i	0.176320	−	0.644247i	0.997310	−	0.0733041i	$-0.0233544\pi$
$444$	−18.1040	−	43.3787i	−0.859176	−	2.05866i
$445$	3.79963	−	4.00827i	0.180120	−	0.190010i
$446$	1.23808	−	1.62245i	0.0586246	−	0.0768252i
$447$	17.0177	+	16.4807i	0.804910	+	0.779512i
$448$	22.6841	−	24.1069i	1.07172	−	1.13894i
$449$	2.27945	+	23.6289i	0.107574	+	1.11512i	0.878353	+	0.478013i	$0.158643\pi$
$449$	2.27945	+	23.6289i	0.107574	+	1.11512i	−0.770779	+	0.637103i	$0.780133\pi$
$450$	−9.76455	−	15.3574i	−0.460305	−	0.723956i
$451$	3.30895	+	1.68155i	0.155813	+	0.0791809i
$452$	34.0261	−	53.5154i	1.60045	−	2.51715i
$453$	9.90823	−	5.86257i	0.465529	−	0.275447i
$454$	30.5798	−	26.0329i	1.43518	−	1.22179i
$455$	−1.45008	−	1.80466i	−0.0679806	−	0.0846039i
$456$	−16.3560	−	4.28905i	−0.765940	−	0.200853i
$457$	−0.749335	−	14.0117i	−0.0350524	−	0.655439i	−0.960791	−	0.277274i	$-0.910569\pi$
$457$	−0.749335	−	14.0117i	−0.0350524	−	0.655439i	0.925738	−	0.378164i	$-0.123445\pi$
$458$	−32.4948	+	26.4867i	−1.51838	+	1.23764i
$459$	0.987455	+	13.1767i	0.0460904	+	0.615034i
$460$	4.63923	+	11.8206i	0.216305	+	0.551137i
$461$	−40.7925	−	2.61897i	−1.89990	−	0.121977i	−0.930318	−	0.366755i	$-0.880469\pi$
$461$	−40.7925	−	2.61897i	−1.89990	−	0.121977i	−0.969579	+	0.244777i	$0.921285\pi$
$462$	39.6240	+	53.8755i	1.84347	+	2.50651i
$463$	9.21894	+	31.0617i	0.428441	+	1.44356i	0.845155	+	0.534521i	$0.179508\pi$
$463$	9.21894	+	31.0617i	0.428441	+	1.44356i	−0.416714	+	0.909037i	$0.636819\pi$
$464$	−0.0918074	−	0.0219891i	−0.00426205	−	0.00102082i
$465$	2.51188	+	2.88751i	0.116486	+	0.133905i
$466$	−50.2108	−	21.5881i	−2.32597	−	1.00005i
$467$	−7.08291	−	15.1190i	−0.327758	−	0.699623i	0.671381	−	0.741112i	$-0.265701\pi$
$467$	−7.08291	−	15.1190i	−0.327758	−	0.699623i	−0.999139	+	0.0414890i	$0.986790\pi$
$468$	−9.51136	+	0.610650i	−0.439663	+	0.0282273i
$469$	18.7330	−	9.60670i	0.865007	−	0.443596i
$470$	−0.644108	−	3.98404i	−0.0297105	−	0.183770i
$471$	−42.8205	−	13.2084i	−1.97306	−	0.608610i
$472$	−12.6680	+	32.2774i	−0.583090	+	1.48569i
$473$	−20.6161	+	44.0066i	−0.947930	+	2.02343i
$474$	−37.5958	+	33.4174i	−1.72683	+	1.53491i
$475$	−5.24396	+	10.0517i	−0.240609	+	0.461203i
$476$	4.08864	+	40.8097i	0.187402	+	1.87051i
$477$	4.51157	+	3.36707i	0.206571	+	0.154168i
$478$	−5.59919	+	40.0473i	−0.256101	+	1.83172i
$479$	27.6867	−	17.1911i	1.26504	−	0.785481i	0.280367	−	0.959893i	$-0.409544\pi$
$479$	27.6867	−	17.1911i	1.26504	−	0.785481i	0.984673	+	0.174412i	$0.0558024\pi$
$480$	5.24113	+	0.112027i	0.239224	+	0.00511332i
$481$	−3.51830	+	10.2297i	−0.160421	+	0.466435i
$482$	−60.1087	−	7.75016i	−2.73788	−	0.353010i
$483$	−29.0302	−	29.1267i	−1.32092	−	1.32531i
$484$	25.4190	−	41.9314i	1.15541	−	1.90597i
$485$	−0.478356	−	1.90700i	−0.0217210	−	0.0865925i
$486$	33.7022	−	12.8133i	1.52876	−	0.581221i
$487$	−20.9651	−	18.6351i	−0.950020	−	0.844436i	0.0379185	−	0.999281i	$-0.487927\pi$
$487$	−20.9651	−	18.6351i	−0.950020	−	0.844436i	−0.987939	+	0.154845i	$0.950512\pi$
$488$	−30.9405	+	13.3029i	−1.40061	+	0.602193i
$489$	27.7817	+	13.3790i	1.25633	+	0.605017i
$490$	7.09039	+	4.54132i	0.320311	+	0.205156i
$491$	−3.83242	+	1.84559i	−0.172955	+	0.0832905i	−0.518358	−	0.855164i	$-0.673456\pi$
$491$	−3.83242	+	1.84559i	−0.172955	+	0.0832905i	0.345403	+	0.938454i	$0.387742\pi$
$492$	3.55325	−	4.08461i	0.160193	−	0.184148i
$493$	−0.440453	+	0.314290i	−0.0198370	+	0.0141549i
$494$	5.22464	+	7.84188i	0.235068	+	0.352823i
$495$	−0.869231	+	4.22235i	−0.0390690	+	0.189780i
$496$	−2.70014	+	0.348144i	−0.121240	+	0.0156321i
$497$	10.4105	+	2.21925i	0.466974	+	0.0995468i
$498$	−42.2629	+	40.9294i	−1.89385	+	1.83409i
$499$	5.01806	+	42.4946i	0.224639	+	1.90232i	0.397873	+	0.917440i	$0.369748\pi$
$499$	5.01806	+	42.4946i	0.224639	+	1.90232i	−0.173234	+	0.984881i	$0.555422\pi$
$500$	−4.17334	+	16.6373i	−0.186637	+	0.744043i
$501$	−0.750900	−	0.758967i	−0.0335478	−	0.0339082i
$502$	−39.3844	+	59.1137i	−1.75781	+	2.63838i
$503$	0.301152	+	9.39101i	0.0134277	+	0.418725i	0.984027	+	0.178022i	$0.0569697\pi$
$503$	0.301152	+	9.39101i	0.0134277	+	0.418725i	−0.970599	+	0.240703i	$0.922622\pi$
$504$	13.2497	−	5.42109i	0.590188	−	0.241475i
$505$	0.765176	+	1.72855i	0.0340499	+	0.0769193i
$506$	−32.5157	+	77.9105i	−1.44550	+	3.46354i
$507$	−17.2449	−	13.4535i	−0.765875	−	0.597489i
$508$	36.8592	+	5.55563i	1.63536	+	0.246491i
$509$	5.69000	+	5.27955i	0.252205	+	0.234012i	0.796136	−	0.605118i	$-0.206874\pi$
$509$	5.69000	+	5.27955i	0.252205	+	0.234012i	−0.543931	+	0.839130i	$0.683065\pi$
$510$	−7.93761	+	8.74020i	−0.351483	+	0.387022i
$511$	17.1628	−	13.4913i	0.759236	−	0.596821i
$512$	−5.10538	+	7.31895i	−0.225628	+	0.323455i
$513$	−5.39282	−	4.39572i	−0.238099	−	0.194076i
$514$	30.5496	−	41.8595i	1.34749	−	1.84634i
$515$	−1.06145	+	1.45441i	−0.0467729	+	0.0640889i
$516$	54.9423	+	44.7838i	2.41870	+	1.97150i
$517$	9.67261	−	13.8664i	0.425401	−	0.609844i
$518$	0.275503	−	39.3443i	0.0121049	−	1.72869i
$519$	27.6537	−	30.4498i	1.21386	−	1.33660i
$520$	2.09862	+	1.94724i	0.0920307	+	0.0853920i
$521$	−4.66731	−	0.703484i	−0.204479	−	0.0308202i	0.0460041	−	0.998941i	$-0.485351\pi$
$521$	−4.66731	−	0.703484i	−0.204479	−	0.0308202i	−0.250483	+	0.968121i	$0.580589\pi$
$522$	0.360576	+	0.281300i	0.0157820	+	0.0123121i
$523$	1.07123	−	2.56677i	0.0468417	−	0.112237i	−0.897725	−	0.440556i	$-0.854781\pi$
$523$	1.07123	−	2.56677i	0.0468417	−	0.112237i	0.944567	+	0.328319i	$0.106482\pi$
$524$	17.2623	+	38.9959i	0.754108	+	1.70354i
$525$	−4.40908	−	26.6483i	−0.192428	−	1.16303i
$526$	−0.516293	−	16.0999i	−0.0225114	−	0.701989i
$527$	−8.65195	+	12.9861i	−0.376885	+	0.565682i
$528$	−6.06922	−	6.13443i	−0.264129	−	0.266967i
$529$	7.03442	−	28.0432i	0.305844	−	1.21927i
$530$	−0.480176	−	4.06630i	−0.0208575	−	0.176629i
$531$	12.5904	−	12.1931i	0.546377	−	0.529136i
$532$	−17.0755	−	13.2203i	−0.740315	−	0.573175i
$533$	−1.23573	+	0.159329i	−0.0535252	+	0.00690131i
$534$	10.7991	−	52.4575i	0.467325	−	2.27006i
$535$	−3.95055	−	5.92955i	−0.170797	−	0.256357i
$536$	−21.1921	+	15.1218i	−0.915358	+	0.653164i
$537$	−29.5484	+	33.9671i	−1.27511	+	1.46579i
$538$	−43.5933	+	20.9935i	−1.87944	+	0.905092i
$539$	8.10219	+	34.3303i	0.348986	+	1.47871i
$540$	−4.61146	−	2.22076i	−0.198446	−	0.0955664i
$541$	−5.87603	+	2.52640i	−0.252630	+	0.108619i	−0.517553	−	0.855651i	$-0.673157\pi$
$541$	−5.87603	+	2.52640i	−0.252630	+	0.108619i	0.264923	+	0.964270i	$0.414654\pi$
$542$	31.9385	+	28.3889i	1.37187	+	1.21941i
$543$	−38.1602	+	14.5082i	−1.63761	+	0.622605i
$544$	5.20043	+	20.7319i	0.222967	+	0.888874i
$545$	0.0965321	−	0.159240i	0.00413498	−	0.00682108i
$546$	−21.1775	−	7.44981i	−0.906315	−	0.318822i
$547$	−36.4910	−	4.70499i	−1.56024	−	0.201171i	−0.701158	−	0.713006i	$-0.747333\pi$
$547$	−36.4910	−	4.70499i	−1.56024	−	0.201171i	−0.859084	+	0.511835i	$0.828966\pi$
$548$	9.01431	−	26.2098i	0.385072	−	1.11963i
$549$	17.0199	+	0.363794i	0.726391	+	0.0155263i
$550$	−47.1088	+	29.2505i	−2.00873	+	1.24725i
$551$	0.0394494	−	0.282155i	0.00168060	−	0.0120202i
$552$	40.7549	+	30.4162i	1.73464	+	1.29460i
$553$	−25.1477	+	8.45256i	−1.06939	+	0.359440i
$554$	17.0092	−	32.6034i	0.722651	−	1.38519i
$555$	5.33418	−	4.74135i	0.226423	−	0.201259i
$556$	−9.74240	+	20.7959i	−0.413170	+	0.881941i
$557$	9.61665	−	24.5028i	0.407471	−	1.03822i	−0.568956	−	0.822368i	$-0.692652\pi$
$557$	9.61665	−	24.5028i	0.407471	−	1.03822i	0.976426	−	0.215850i	$-0.0692523\pi$
$558$	12.6027	+	3.88741i	0.533514	+	0.164567i
$559$	−2.60354	−	16.1038i	−0.110118	−	0.681120i
$560$	−0.990369	−	0.446727i	−0.0418507	−	0.0188777i
$561$	−49.3590	+	3.16895i	−2.08394	+	0.133793i
$562$	14.9609	+	31.9351i	0.631086	+	1.34710i
$563$	−16.7228	−	7.18996i	−0.704780	−	0.303021i	0.0123854	−	0.999923i	$-0.496058\pi$
$563$	−16.7228	−	7.18996i	−0.704780	−	0.303021i	−0.717166	+	0.696903i	$0.754561\pi$
$564$	−16.1850	−	18.6053i	−0.681509	−	0.783423i
$565$	9.36376	+	2.24275i	0.393936	+	0.0943532i
$566$	6.77984	+	22.8435i	0.284978	+	0.960185i
$567$	29.6795	+	1.15985i	1.24642	+	0.0487091i
$568$	−13.1360	−	0.843362i	−0.551176	−	0.0353867i
$569$	4.53120	+	11.5453i	0.189958	+	0.484004i	0.993845	−	0.110777i	$-0.0353339\pi$
$569$	4.53120	+	11.5453i	0.189958	+	0.484004i	−0.803888	+	0.594781i	$0.797239\pi$
$570$	−0.464563	−	6.19917i	−0.0194584	−	0.259654i
$571$	−26.1782	+	21.3380i	−1.09552	+	0.892967i	−0.994790	−	0.101946i	$-0.967493\pi$
$571$	−26.1782	+	21.3380i	−1.09552	+	0.892967i	−0.100734	+	0.994913i	$0.532119\pi$
$572$	1.55085	+	28.9990i	0.0648443	+	1.21251i
$573$	−24.8478	−	6.51587i	−1.03803	−	0.272205i
$574$	4.07558	−	1.98122i	0.170111	−	0.0826946i
$575$	25.9630	−	22.1026i	1.08273	−	0.921744i
$576$	17.8073	−	10.5364i	0.741971	−	0.439015i
$577$	20.8986	−	32.8688i	0.870019	−	1.36834i	−0.0589784	−	0.998259i	$-0.518784\pi$
$577$	20.8986	−	32.8688i	0.870019	−	1.36834i	0.928998	−	0.370085i	$-0.120671\pi$
$578$	−7.67427	−	3.89991i	−0.319207	−	0.162215i
$579$	−1.03341	−	1.62532i	−0.0429470	−	0.0675459i
$580$	−0.0201257	−	0.208624i	−0.000835675	−	0.00866264i
$581$	−28.9642	+	11.1342i	−1.20164	+	0.461924i
$582$	−13.6957	−	13.2635i	−0.567705	−	0.549791i
$583$	10.4057	−	13.6362i	0.430959	−	0.564754i
$584$	−18.5725	+	19.5923i	−0.768536	+	0.810735i
$585$	−0.557347	−	1.33545i	−0.0230435	−	0.0552142i
$586$	7.30244	−	26.6820i	0.301661	−	1.10222i
$587$	1.61525	−	7.07686i	0.0666684	−	0.292093i	−0.930593	−	0.366057i	$-0.880708\pi$
$587$	1.61525	−	7.07686i	0.0666684	−	0.292093i	0.997261	+	0.0739634i	$0.0235648\pi$
$588$	51.4441	+	0.720498i	2.12152	+	0.0297128i
$589$	−1.82826	−	8.01013i	−0.0753322	−	0.330052i
$590$	−12.7363	−	0.544715i	−0.524344	−	0.0224256i
$591$	−16.7507	+	30.5003i	−0.689032	+	1.25461i
$592$	0.702975	+	5.02791i	0.0288921	+	0.206646i
$593$	11.0953	+	13.3189i	0.455628	+	0.546941i	0.945828	−	0.324669i	$-0.105253\pi$
$593$	11.0953	+	13.3189i	0.455628	+	0.546941i	−0.490200	+	0.871610i	$0.663076\pi$
$594$	−11.7523	−	31.9348i	−0.482202	−	1.31030i
$595$	−5.65741	+	2.60222i	−0.231931	+	0.106681i
$596$	−19.3953	−	31.9947i	−0.794464	−	1.31055i
$597$	22.5210	−	22.7629i	0.921723	−	0.931625i
$598$	−5.71426	−	27.7574i	−0.233673	−	1.13508i
$599$	6.82592	+	19.8469i	0.278899	+	0.810921i	0.993748	+	0.111642i	$0.0356111\pi$
$599$	6.82592	+	19.8469i	0.278899	+	0.810921i	−0.714849	+	0.699279i	$0.753505\pi$
$600$	10.1859	+	31.8109i	0.415837	+	1.29868i
$601$	17.7245	−	4.64792i	0.722999	−	0.189593i	0.126225	−	0.992002i	$-0.459714\pi$
$601$	17.7245	−	4.64792i	0.722999	−	0.189593i	0.596774	+	0.802409i	$0.296449\pi$
$602$	27.6365	+	52.5016i	1.12638	+	2.13980i
$603$	12.9168	−	2.51554i	0.526012	−	0.102441i
$604$	−17.4852	+	4.98684i	−0.711461	+	0.202912i
$605$	7.27555	+	1.57900i	0.295793	+	0.0641954i
$606$	15.1458	+	10.3262i	0.615254	+	0.419473i
$607$	−11.4868	+	1.73136i	−0.466237	+	0.0702738i	−0.377960	−	0.925822i	$-0.623374\pi$
$607$	−11.4868	+	1.73136i	−0.466237	+	0.0702738i	−0.0882770	+	0.996096i	$0.528136\pi$
$608$	−9.80596	−	5.52261i	−0.397684	−	0.223972i
$609$	0.328929	+	0.593732i	0.0133289	+	0.0240592i
$610$	−8.32443	−	9.16613i	−0.337046	−	0.371126i
$611$	−0.0606432	+	5.67496i	−0.00245336	+	0.229584i
$612$	−4.63154	+	25.2150i	−0.187219	+	1.01926i
$613$	−13.3098	+	7.12568i	−0.537579	+	0.287804i	−0.718303	−	0.695730i	$-0.755081\pi$
$613$	−13.3098	+	7.12568i	−0.537579	+	0.287804i	0.180725	+	0.983534i	$0.442156\pi$
$614$	64.3370	−	13.9629i	2.59643	−	0.563498i
$615$	0.761913	+	0.308465i	0.0307233	+	0.0124385i
$616$	−16.0856	−	40.5455i	−0.648106	−	1.63363i
$617$	−3.08890	−	4.42816i	−0.124354	−	0.178271i	0.753137	−	0.657864i	$-0.228540\pi$
$617$	−3.08890	−	4.42816i	−0.124354	−	0.178271i	−0.877491	+	0.479592i	$0.840785\pi$
$618$	−1.30481	+	17.4115i	−0.0524871	+	0.700392i
$619$	9.01384	−	2.78040i	0.362297	−	0.111754i	−0.108262	−	0.994122i	$-0.534529\pi$
$619$	9.01384	−	2.78040i	0.362297	−	0.111754i	0.470559	+	0.882369i	$0.344052\pi$
$620$	−2.68060	−	5.41746i	−0.107655	−	0.217570i
$621$	10.0725	+	18.3403i	0.404195	+	0.735972i
$622$	−2.53798	+	1.89414i	−0.101764	+	0.0759482i
$623$	16.0757	−	23.2275i	0.644058	−	0.930592i
$624$	2.84332	+	0.553737i	0.113824	+	0.0221672i
$625$	20.9808	−	1.79794i	0.839233	−	0.0719176i
$626$	7.83683	+	2.78931i	0.313223	+	0.111483i
$627$	16.6686	−	20.0092i	0.665680	−	0.799090i
$628$	60.1247	+	37.3323i	2.39923	+	1.48972i
$629$	24.3871	+	15.8742i	0.972376	+	0.632946i
$630$	3.46896	+	3.95818i	0.138207	+	0.157698i
$631$	3.08464	−	31.9755i	0.122798	−	1.27293i	−0.703908	−	0.710291i	$-0.748563\pi$
$631$	3.08464	−	31.9755i	0.122798	−	1.27293i	0.826706	−	0.562634i	$-0.190212\pi$
$632$	29.2478	−	14.8632i	1.16342	−	0.591225i
$633$	11.1934	+	6.62298i	0.444897	+	0.263240i
$634$	35.1847	−	6.07487i	1.39736	−	0.241264i
$635$	1.02245	+	5.56645i	0.0405748	+	0.220898i
$636$	−15.5991	−	19.5607i	−0.618545	−	0.775631i
$637$	−8.73891	−	7.98953i	−0.346248	−	0.316557i
$638$	0.868801	−	1.08944i	0.0343962	−	0.0431314i
$639$	5.86581	+	3.14038i	0.232048	+	0.124232i
$640$	−9.79839	−	2.79454i	−0.387315	−	0.110464i
$641$	40.7049	+	3.48818i	1.60775	+	0.137775i	0.854316	−	0.519754i	$-0.173976\pi$
$641$	40.7049	+	3.48818i	1.60775	+	0.137775i	0.753430	+	0.657529i	$0.228398\pi$
$642$	−62.8772	−	28.6413i	−2.48157	−	1.13038i
$643$	−12.9411	−	4.29673i	−0.510346	−	0.169446i	0.0483320	−	0.998831i	$-0.484609\pi$
$643$	−12.9411	−	4.29673i	−0.510346	−	0.169446i	−0.558678	+	0.829385i	$0.688691\pi$
$644$	32.6805	+	56.1259i	1.28779	+	2.21167i
$645$	−3.71683	+	10.0998i	−0.146350	+	0.397681i
$646$	23.8789	−	8.49908i	0.939504	−	0.334392i
$647$	−41.1145	+	18.7281i	−1.61638	+	0.736278i	−0.998740	−	0.0501846i	$-0.984019\pi$
$647$	−41.1145	+	18.7281i	−1.61638	+	0.736278i	−0.617638	+	0.786463i	$0.711910\pi$
$648$	−36.5208	+	3.91742i	−1.43467	+	0.153891i
$649$	−36.7400	−	38.7573i	−1.44217	−	1.52136i
$650$	7.53463	−	17.0209i	0.295533	−	0.667613i
$651$	14.9515	+	12.6337i	0.585997	+	0.495156i
$652$	−37.0819	−	31.5682i	−1.45224	−	1.23631i
$653$	−15.3504	−	2.65034i	−0.600706	−	0.103716i	−0.138309	−	0.990389i	$-0.544167\pi$
$653$	−15.3504	−	2.65034i	−0.600706	−	0.103716i	−0.462397	+	0.886673i	$0.653010\pi$
$654$	−0.0192954	−	1.80565i	−0.000754510	−	0.0706067i
$655$	−4.74647	+	4.40408i	−0.185460	+	0.172082i
$656$	−0.483124	+	0.329388i	−0.0188628	+	0.0128605i
$657$	12.6485	−	5.12082i	0.493465	−	0.199782i
$658$	−6.36694	−	19.6349i	−0.248209	−	0.765448i
$659$	3.41076	−	21.0968i	0.132864	−	0.821814i	−0.831167	−	0.556024i	$-0.812326\pi$
$659$	3.41076	−	21.0968i	0.132864	−	0.821814i	0.964031	−	0.265790i	$-0.0856328\pi$
$660$	8.49662	−	17.1716i	0.330731	−	0.668403i
$661$	−32.6480	+	1.39632i	−1.26986	+	0.0543104i	−0.667922	−	0.744232i	$-0.732816\pi$
$661$	−32.6480	+	1.39632i	−1.26986	+	0.0543104i	−0.601939	+	0.798542i	$0.705605\pi$
$662$	−4.92744	−	18.0041i	−0.191511	−	0.699751i
$663$	13.0907	−	10.2125i	0.508399	−	0.396622i
$664$	33.4351	−	18.8303i	1.29754	−	0.730758i
$665$	1.05494	−	3.10445i	0.0409089	−	0.120386i
$666$	6.99759	−	23.5772i	0.271151	−	0.913598i
$667$	−0.428417	+	0.742039i	−0.0165884	+	0.0287319i
$668$	0.843089	+	1.46027i	0.0326201	+	0.0564997i
$669$	1.84131	−	0.441020i	0.0711893	−	0.0170508i
$670$	−7.79119	−	5.55950i	−0.301000	−	0.214782i
$671$	1.66254	−	51.8443i	0.0641818	−	2.00143i
$672$	26.5795	−	3.52662i	1.02533	−	0.136043i
$673$	12.4431	+	23.8510i	0.479644	+	0.919389i	0.997938	+	0.0641858i	$0.0204450\pi$
$673$	12.4431	+	23.8510i	0.479644	+	0.919389i	−0.518294	+	0.855203i	$0.673433\pi$
$674$	−43.8487	−	16.6708i	−1.68899	−	0.642137i
$675$	−1.61173	+	13.6487i	−0.0620355	+	0.525337i
$676$	20.9552	+	27.4610i	0.805971	+	1.05619i
$677$	−16.2106	−	1.73884i	−0.623023	−	0.0668289i	−0.210228	−	0.977652i	$-0.567420\pi$
$677$	−16.2106	−	1.73884i	−0.623023	−	0.0668289i	−0.412796	+	0.910824i	$0.635448\pi$
$678$	88.6138	−	29.4218i	3.40319	−	1.12994i
$679$	−3.90713	−	9.26565i	−0.149942	−	0.355583i
$680$	6.45384	−	4.20098i	0.247493	−	0.161100i
$681$	37.2495	−	0.796193i	1.42740	−	0.0305102i
$682$	12.2545	−	38.2712i	0.469247	−	1.46548i
$683$	1.59833	−	29.8870i	0.0611586	−	1.14359i	−0.788076	−	0.615577i	$-0.788923\pi$
$683$	1.59833	−	29.8870i	0.0611586	−	1.14359i	0.849235	−	0.528015i	$-0.177064\pi$
$684$	−7.95758	−	10.9036i	−0.304266	−	0.416909i
$685$	4.20823			0.160788
$686$	39.3857	+	17.4177i	1.50375	+	0.665012i
$687$	−38.8925			−1.48384
$688$	−4.51311	−	6.18393i	−0.172061	−	0.235760i
$689$	−0.307492	+	5.74973i	−0.0117145	+	0.219047i
$690$	−5.70140	+	17.8057i	−0.217048	+	0.677851i
$691$	17.7732	−	0.379896i	0.676126	−	0.0144519i	0.317952	−	0.948107i	$-0.397005\pi$
$691$	17.7732	−	0.379896i	0.676126	−	0.0144519i	0.358174	+	0.933655i	$0.383400\pi$
$692$	−54.4443	+	35.4393i	−2.06966	+	1.34720i
$693$	−1.09635	+	22.0212i	−0.0416470	+	0.836518i
$694$	39.2642	−	13.0366i	1.49045	−	0.494863i
$695$	−3.46688	−	0.371876i	−0.131506	−	0.0141061i
$696$	−0.509193	−	0.667276i	−0.0193009	−	0.0252930i
$697$	−0.393030	+	3.32831i	−0.0148871	+	0.126069i
$698$	71.0438	+	27.0102i	2.68905	+	1.02235i
$699$	−23.4532	−	44.9553i	−0.887080	−	1.70037i
$700$	−3.93979	+	42.4764i	−0.148910	+	1.60546i
$701$	1.03772	−	32.3598i	0.0391940	−	1.22221i	−0.771302	−	0.636469i	$-0.780394\pi$
$701$	1.03772	−	32.3598i	0.0391940	−	1.22221i	0.810496	−	0.585744i	$-0.199198\pi$
$702$	9.29830	+	6.63491i	0.350942	+	0.250419i
$703$	−14.8998	+	3.56870i	−0.561956	+	0.134596i
$704$	−31.5223	−	54.5983i	−1.18804	−	2.05775i
$705$	1.87206	−	3.24251i	0.0705059	−	0.122120i
$706$	6.60381	−	22.2504i	0.248538	−	0.837406i
$707$	5.21754	+	8.13964i	0.196226	+	0.306123i
$708$	−67.8704	+	38.2239i	−2.55072	+	1.43654i
$709$	−9.90392	+	7.72644i	−0.371950	+	0.290172i	−0.783719	−	0.621116i	$-0.786680\pi$
$709$	−9.90392	+	7.72644i	−0.371950	+	0.290172i	0.411769	+	0.911288i	$0.364911\pi$
$710$	−1.27748	−	4.66771i	−0.0479429	−	0.175176i
$711$	−16.5682	+	0.708603i	−0.621357	+	0.0265747i
$712$	−15.4919	+	31.3089i	−0.580582	+	1.17335i
$713$	−3.94370	+	24.3932i	−0.147693	+	0.913533i
$714$	−33.2964	+	50.3772i	−1.24609	+	1.88532i
$715$	−4.08699	+	1.65464i	−0.152845	+	0.0618801i
$716$	58.7479	−	40.0537i	2.19551	−	1.49688i
$717$	−27.5002	+	25.5165i	−1.02701	+	0.952930i
$718$	0.236703	+	22.1505i	0.00883367	+	0.826651i
$719$	−42.9329	−	7.41265i	−1.60113	−	0.276445i	−0.701357	−	0.712810i	$-0.747422\pi$
$719$	−42.9329	−	7.41265i	−1.60113	−	0.276445i	−0.899770	+	0.436365i	$0.856266\pi$
$720$	−0.517113	−	0.440225i	−0.0192717	−	0.0164062i
$721$	−4.22946	+	8.18042i	−0.157513	+	0.304655i
$722$	12.4816	−	28.1961i	0.464515	−	1.04935i
$723$	−38.6820	−	40.8060i	−1.43860	−	1.51759i
$724$	64.1086	−	6.87664i	2.38258	−	0.255568i
$725$	−0.512156	+	0.233293i	−0.0190210	+	0.00866428i
$726$	68.0152	−	24.2082i	2.52428	−	0.898451i
$727$	−2.95472	+	8.02892i	−0.109584	+	0.297776i	−0.981375	−	0.192103i	$-0.938469\pi$
$727$	−2.95472	+	8.02892i	−0.109584	+	0.297776i	0.871790	+	0.489879i	$0.162959\pi$
$728$	12.1284	+	8.20374i	0.449509	+	0.304051i
$729$	−0.217180	−	0.0721087i	−0.00804370	−	0.00267069i
$730$	−9.03216	−	4.11425i	−0.334295	−	0.152275i
$731$	−43.7192	−	3.74649i	−1.61701	−	0.138569i
$732$	−72.7568	−	20.7506i	−2.68917	−	0.766962i
$733$	16.6296	+	8.90298i	0.614228	+	0.328839i	0.749535	−	0.661965i	$-0.230277\pi$
$733$	16.6296	+	8.90298i	0.614228	+	0.328839i	−0.135308	+	0.990804i	$0.543202\pi$
$734$	−28.7801	+	36.0891i	−1.06229	+	1.33207i
$735$	2.43687	+	7.42174i	0.0898853	+	0.273755i
$736$	21.1031	+	26.4625i	0.777872	+	0.975421i
$737$	−7.24380	−	39.4367i	−0.266829	−	1.45267i
$738$	2.79130	−	0.481937i	0.102749	−	0.0177403i
$739$	31.8114	+	18.8224i	1.17020	+	0.692394i	0.958542	−	0.284950i	$-0.0919769\pi$
$739$	31.8114	+	18.8224i	1.17020	+	0.692394i	0.211660	+	0.977343i	$0.432113\pi$
$740$	−10.0483	+	5.10636i	−0.369384	+	0.187714i
$741$	−0.839433	+	8.70160i	−0.0308373	+	0.319661i
$742$	−5.60256	−	20.1787i	−0.205676	−	0.740783i
$743$	39.4927	+	25.7069i	1.44885	+	0.943095i	0.998743	+	0.0501186i	$0.0159599\pi$
$743$	39.4927	+	25.7069i	1.44885	+	0.943095i	0.450104	+	0.892976i	$0.351387\pi$
$744$	−20.5645	−	12.7688i	−0.753931	−	0.468127i
$745$	3.63593	−	4.36461i	0.133210	−	0.159907i
$746$	−31.0882	−	11.0650i	−1.13822	−	0.405119i
$747$	−19.3256	+	1.65610i	−0.707087	+	0.0605934i
$748$	76.6742	+	14.9323i	2.80349	+	0.545979i
$749$	−24.5991	−	26.8867i	−0.898832	−	0.982419i
$750$	−20.2394	+	15.1050i	−0.739037	+	0.551558i
$751$	−11.0189	−	20.0635i	−0.402084	−	0.732129i	0.595369	−	0.803452i	$-0.297006\pi$
$751$	−11.0189	−	20.0635i	−0.402084	−	0.732129i	−0.997453	+	0.0713233i	$0.977278\pi$
$752$	1.18119	+	2.38717i	0.0430735	+	0.0870510i
$753$	−62.9713	+	19.4241i	−2.29480	+	0.707853i
$754$	−0.0349555	+	0.466448i	−0.00127300	+	0.0169870i
$755$	−1.57941	−	2.26421i	−0.0574807	−	0.0824029i
$756$	−25.0435	−	7.62399i	−0.910824	−	0.277282i
$757$	−3.64921	−	1.47740i	−0.132633	−	0.0536970i	0.307989	−	0.951390i	$-0.400344\pi$
$757$	−3.64921	−	1.47740i	−0.132633	−	0.0536970i	−0.440622	+	0.897693i	$0.645242\pi$
$758$	50.3110	−	10.9189i	1.82738	−	0.396592i
$759$	−69.0496	+	36.9671i	−2.50634	+	1.34182i
$760$	−0.732507	+	3.98792i	−0.0265708	+	0.144657i
$761$	0.147910	−	13.8414i	0.00536173	−	0.501749i	−0.965280	−	0.261218i	$-0.915876\pi$
$761$	0.147910	−	13.8414i	0.00536173	−	0.501749i	0.970642	−	0.240531i	$-0.0773214\pi$
$762$	36.8972	+	40.6280i	1.33665	+	1.47180i
$763$	0.363582	−	0.880283i	0.0131625	−	0.0318684i
$764$	35.3493	+	19.9083i	1.27889	+	0.720258i
$765$	−3.84899	+	0.580141i	−0.139160	+	0.0209751i
$766$	−35.8651	−	24.4524i	−1.29586	−	0.883501i
$767$	17.5189	+	3.80208i	0.632569	+	0.137285i
$768$	−43.1070	+	12.2943i	−1.55549	+	0.443632i
$769$	53.3411	−	10.3882i	1.92353	−	0.374607i	0.923569	−	0.383432i	$-0.125258\pi$
$769$	53.3411	−	10.3882i	1.92353	−	0.374607i	0.999961	+	0.00882427i	$0.00280889\pi$
$770$	12.1727	−	10.4403i	0.438673	−	0.376244i
$771$	46.5045	−	12.1949i	1.67482	−	0.439189i
$772$	0.927606	+	2.89695i	0.0333853	+	0.104264i
$773$	−6.64776	−	19.3289i	−0.239103	−	0.695211i	−0.998980	−	0.0451443i	$-0.985625\pi$
$773$	−6.64776	−	19.3289i	−0.239103	−	0.695211i	0.759877	−	0.650067i	$-0.225259\pi$
$774$	7.47798	+	36.3247i	0.268790	+	1.30567i
$775$	−11.4149	+	11.5375i	−0.410035	+	0.414440i
$776$	6.44628	+	10.6338i	0.231408	+	0.381732i
$777$	23.2598	−	28.1314i	0.834440	−	1.00921i
$778$	−14.4433	−	39.2470i	−0.517816	−	1.40707i
$779$	−1.12946	−	1.35582i	−0.0404672	−	0.0485772i
$780$	0.890519	+	6.36929i	0.0318857	+	0.228057i
$781$	9.75907	−	17.7697i	0.349207	−	0.635849i
$782$	−76.1594	−	3.25725i	−2.72345	−	0.116479i
$783$	−0.0768508	−	0.336705i	−0.00274642	−	0.0120329i
$784$	−5.35482	−	1.48465i	−0.191243	−	0.0530231i
$785$	−2.39107	+	10.4759i	−0.0853408	+	0.373903i
$786$	−16.5748	+	60.5618i	−0.591203	+	2.16017i
$787$	17.3089	+	41.4736i	0.616995	+	1.47837i	0.861002	+	0.508601i	$0.169837\pi$
$787$	17.3089	+	41.4736i	0.616995	+	1.47837i	−0.244007	+	0.969773i	$0.578462\pi$
$788$	37.8083	−	39.8842i	1.34686	−	1.42082i
$789$	9.06570	−	11.8802i	0.322748	−	0.422947i
$790$	8.66449	+	8.39109i	0.308269	+	0.298542i
$791$	49.0818	+	4.02398i	1.74515	+	0.143076i
$792$	−2.61813	−	27.1397i	−0.0930312	−	0.964366i
$793$	9.34246	+	14.6936i	0.331760	+	0.521784i
$794$	52.9606	+	26.9135i	1.87950	+	0.955125i
$795$	2.03816	−	3.20557i	0.0722862	−	0.113690i
$796$	−43.5238	+	25.7525i	−1.54266	+	0.912772i
$797$	−8.77512	+	7.47036i	−0.310831	+	0.264614i	−0.789998	−	0.613110i	$-0.789918\pi$
$797$	−8.77512	+	7.47036i	−0.310831	+	0.264614i	0.479167	+	0.877724i	$0.340939\pi$
$798$	−7.18923	−	30.9718i	−0.254496	−	1.09639i
$799$	14.7664	+	3.87221i	0.522399	+	0.136989i
$800$	1.18722	+	22.1996i	0.0419746	+	0.784875i
$801$	13.6864	−	11.1559i	0.483587	−	0.394174i
$802$	0.615964	+	8.21947i	0.0217505	+	0.290240i
$803$	−15.1903	−	38.7041i	−0.536052	−	1.36584i
$804$	−58.3639	−	3.74708i	−2.05834	−	0.132149i
$805$	−6.44458	+	7.46365i	−0.227142	+	0.263059i
$806$	3.83813	+	12.9319i	0.135192	+	0.455508i
$807$	−43.6537	−	10.4557i	−1.53668	−	0.368057i
$808$	−7.84709	−	9.02055i	−0.276060	−	0.317342i
$809$	−43.9665	−	18.9034i	−1.54578	−	0.664608i	−0.559371	−	0.828918i	$-0.688957\pi$
$809$	−43.9665	−	18.9034i	−1.54578	−	0.664608i	−0.986409	+	0.164309i	$0.947460\pi$
$810$	−5.72872	−	12.2284i	−0.201287	−	0.429662i
$811$	−13.5735	+	0.871446i	−0.476629	+	0.0306006i	−0.300531	−	0.953772i	$-0.597164\pi$
$811$	−13.5735	+	0.871446i	−0.476629	+	0.0306006i	−0.176098	+	0.984373i	$0.556348\pi$
$812$	−0.264646	−	1.03880i	−0.00928726	−	0.0364548i
$813$	6.32712	+	39.1355i	0.221902	+	1.37254i
$814$	−71.6071	−	22.0879i	−2.50983	−	0.774179i
$815$	2.70135	−	6.88292i	0.0946241	−	0.241098i
$816$	3.30553	−	7.05590i	0.115717	−	0.247006i
$817$	17.2683	−	15.3491i	0.604140	−	0.536997i
$818$	−31.5625	+	60.4994i	−1.10356	+	2.11531i
$819$	−3.86007	−	6.31499i	−0.134882	−	0.220664i
$820$	−1.04039	−	0.776461i	−0.0363319	−	0.0271152i
$821$	−1.56186	+	11.1710i	−0.0545094	+	0.389870i	0.943738	+	0.330694i	$0.107283\pi$
$821$	−1.56186	+	11.1710i	−0.0545094	+	0.389870i	−0.998248	+	0.0591760i	$0.981153\pi$
$822$	34.6687	−	21.5263i	1.20921	−	0.750815i
$823$	19.2351	+	0.411143i	0.670493	+	0.0143315i	0.355379	−	0.934722i	$-0.384352\pi$
$823$	19.2351	+	0.411143i	0.670493	+	0.0143315i	0.315114	+	0.949054i	$0.397957\pi$
$824$	3.70379	−	10.7690i	0.129028	−	0.375157i
$825$	−51.0217	−	6.57851i	−1.77635	−	0.229034i
$826$	−64.8026	+	7.19262i	−2.25477	+	0.250263i
$827$	4.77314	−	7.87380i	0.165978	−	0.273799i	−0.761124	−	0.648606i	$-0.775352\pi$
$827$	4.77314	−	7.87380i	0.165978	−	0.273799i	0.927103	+	0.374807i	$0.122291\pi$
$828$	9.87738	+	39.3769i	0.343263	+	1.36844i
$829$	−47.9036	+	18.2125i	−1.66376	+	0.632546i	−0.993935	−	0.109972i	$-0.964924\pi$
$829$	−47.9036	+	18.2125i	−1.66376	+	0.632546i	−0.669826	+	0.742518i	$0.733631\pi$
$830$	10.5444	+	9.37250i	0.366001	+	0.325324i
$831$	31.3420	−	13.4755i	1.08724	−	0.467460i
$832$	19.0672	+	9.18227i	0.661035	+	0.318338i
$833$	−26.5641	+	17.5713i	−0.920391	+	0.608808i
$834$	−30.4634	+	14.6704i	−1.05486	+	0.507995i
$835$	−0.168029	+	0.193156i	−0.00581488	+	0.00668444i
$836$	−33.4801	+	23.8901i	−1.15793	+	0.826256i
$837$	−5.52233	−	8.28870i	−0.190880	−	0.286499i
$838$	16.0000	−	77.7209i	0.552710	−	2.68482i
$839$	31.4713	−	4.05777i	1.08651	−	0.140090i	0.436268	−	0.899817i	$-0.356300\pi$
$839$	31.4713	−	4.05777i	1.08651	−	0.140090i	0.650242	+	0.759727i	$0.274667\pi$
$840$	−4.31592	−	8.64219i	−0.148913	−	0.298184i
$841$	−20.8220	+	20.1650i	−0.717999	+	0.695343i
$842$	−4.54788	−	38.5130i	−0.156730	−	1.32725i
$843$	−7.96026	+	31.7342i	−0.274166	+	1.09298i
$844$	−14.4467	−	14.6019i	−0.497276	−	0.502619i
$845$	−2.90798	+	4.36470i	−0.100037	+	0.150150i
$846$	−0.413543	−	12.8958i	−0.0142179	−	0.443366i
$847$	38.0084	+	2.29967i	1.30598	+	0.0790177i
$848$	1.09381	+	2.47093i	0.0375615	+	0.0848521i
$849$	−8.51430	+	20.4010i	−0.292210	+	0.700161i
$850$	−39.4768	−	30.7974i	−1.35404	−	1.05634i
$851$	45.5637	+	6.86763i	1.56190	+	0.235419i
$852$	−21.6764	−	20.1128i	−0.742622	−	0.689052i
$853$	−27.1868	+	29.9356i	−0.930857	+	1.02498i	0.0687693	+	0.997633i	$0.478093\pi$
$853$	−27.1868	+	29.9356i	−0.930857	+	1.02498i	−0.999626	+	0.0273441i	$0.991295\pi$
$854$	−49.2350	−	39.8308i	−1.68479	−	1.36298i
$855$	1.17255	−	1.68094i	0.0401004	−	0.0574870i
$856$	34.9308	+	28.4723i	1.19391	+	0.973164i
$857$	28.3880	−	38.8977i	0.969716	−	1.32872i	0.0254010	−	0.999677i	$-0.491914\pi$
$857$	28.3880	−	38.8977i	0.969716	−	1.32872i	0.944315	−	0.329042i	$-0.106726\pi$
$858$	−25.2060	+	34.5376i	−0.860517	+	1.17909i
$859$	4.79458	+	3.90809i	0.163589	+	0.133342i	0.710075	−	0.704126i	$-0.248661\pi$
$859$	4.79458	+	3.90809i	0.163589	+	0.133342i	−0.546486	+	0.837468i	$0.684035\pi$
$860$	9.72417	−	13.9403i	0.331592	−	0.475362i
$861$	4.09208	+	0.964187i	0.139458	+	0.0328594i
$862$	26.3041	−	28.9638i	0.895922	−	0.986509i
$863$	7.56876	+	7.02278i	0.257644	+	0.239058i	0.798410	−	0.602115i	$-0.205675\pi$
$863$	7.56876	+	7.02278i	0.257644	+	0.239058i	−0.540766	+	0.841173i	$0.681866\pi$
$864$	−13.4903	−	2.03333i	−0.458948	−	0.0691754i
$865$	−7.77671	−	6.06691i	−0.264416	−	0.206281i
$866$	29.2110	−	69.9922i	0.992631	−	2.37843i
$867$	−3.23271	−	7.30274i	−0.109789	−	0.248014i
$868$	−17.7800	−	25.2900i	−0.603494	−	0.858398i
$869$	1.61953	+	50.5030i	0.0549389	+	1.71320i
$870$	0.171101	−	0.256812i	0.00580086	−	0.00870675i
$871$	9.46644	+	9.56814i	0.320758	+	0.324204i
$872$	−0.286557	+	1.14238i	−0.00970405	+	0.0386859i
$873$	−0.737125	−	6.24222i	−0.0249479	−	0.211267i
$874$	28.8323	−	27.9225i	0.975266	−	0.944493i
$875$	−12.9422	+	3.15028i	−0.437525	+	0.106499i
$876$	−60.1475	+	7.75516i	−2.03220	+	0.262023i
$877$	3.16247	−	15.3619i	0.106789	−	0.518735i	−0.891101	−	0.453805i	$-0.850066\pi$
$877$	3.16247	−	15.3619i	0.106789	−	0.518735i	0.997890	−	0.0649292i	$-0.0206822\pi$
$878$	0.00118436	+	0.00177766i	3.99703e−5	+	5.99930e-5i
$879$	20.8910	−	14.9070i	0.704634	−	0.502800i
$880$	−1.35811	+	1.56120i	−0.0457819	+	0.0526281i
$881$	5.01275	−	2.41401i	0.168884	−	0.0813301i	−0.347532	−	0.937668i	$-0.612980\pi$
$881$	5.01275	−	2.41401i	0.168884	−	0.0813301i	0.516416	+	0.856338i	$0.327266\pi$
$882$	20.6254	+	17.2982i	0.694492	+	0.582460i
$883$	12.6251	+	6.07995i	0.424870	+	0.204607i	0.634085	−	0.773263i	$-0.281377\pi$
$883$	12.6251	+	6.07995i	0.424870	+	0.204607i	−0.209216	+	0.977870i	$0.567091\pi$
$884$	−24.0895	+	10.3573i	−0.810218	+	0.348354i
$885$	−8.83949	−	7.85708i	−0.297136	−	0.264113i
$886$	−30.5564	+	11.6173i	−1.02656	+	0.390289i
$887$	−3.65821	−	14.5837i	−0.122831	−	0.489674i	−0.999956	−	0.00941195i	$-0.997004\pi$
$887$	−3.65821	−	14.5837i	−0.122831	−	0.489674i	0.877125	−	0.480262i	$-0.159459\pi$
$888$	−23.3997	+	38.6003i	−0.785244	+	1.29534i
$889$	9.51507	+	27.3379i	0.319125	+	0.916885i
$890$	−12.7372	−	1.64228i	−0.426952	−	0.0550493i
$891$	18.3984	−	53.4947i	0.616370	−	1.79214i
$892$	−2.98961	−	0.0639018i	−0.100100	−	0.00213959i
$893$	−6.82859	+	4.23997i	−0.228510	+	0.141885i
$894$	7.62770	−	54.5558i	0.255108	−	1.82462i
$895$	8.65174	+	6.45696i	0.289196	+	0.215832i
$896$	−51.7097	−	6.47368i	−1.72750	−	0.216270i
$897$	12.1608	−	23.3100i	0.406038	−	0.778299i
$898$	41.2571	−	36.6718i	1.37677	−	1.22375i
$899$	0.173023	−	0.369330i	0.00577063	−	0.0123178i
$900$	−9.74179	+	24.8217i	−0.324726	+	0.827389i
$901$	14.7999	+	4.56518i	0.493058	+	0.152088i
$902$	−1.37748	−	8.52022i	−0.0458652	−	0.283692i
$903$	−10.9001	+	53.9536i	−0.362734	+	1.79546i
$904$	−60.7741	+	3.90183i	−2.02132	+	0.129773i
$905$	4.15302	+	8.86492i	0.138051	+	0.294680i
$906$	−24.5937	−	10.5741i	−0.817072	−	0.351300i
$907$	4.01837	+	4.61928i	0.133428	+	0.153381i	0.817282	−	0.576238i	$-0.195480\pi$
$907$	4.01837	+	4.61928i	0.133428	+	0.153381i	−0.683854	+	0.729619i	$0.739698\pi$
$908$	−57.2242	−	13.7060i	−1.89905	−	0.454849i
$909$	1.71952	+	5.79364i	0.0570330	+	0.192163i
$910$	−1.40191	+	5.19748i	−0.0464728	+	0.172295i
$911$	−24.1224	−	1.54871i	−0.799209	−	0.0513110i	−0.340895	−	0.940101i	$-0.610730\pi$
$911$	−24.1224	−	1.54871i	−0.799209	−	0.0513110i	−0.458314	+	0.888790i	$0.651547\pi$
$912$	1.49886	+	3.81902i	0.0496321	+	0.126460i
$913$	4.41657	+	58.9351i	0.146167	+	1.95047i
$914$	−25.2907	+	20.6146i	−0.836543	+	0.681871i
$915$	−0.613452	−	11.4708i	−0.0202801	−	0.379214i
$916$	59.4154	+	15.5805i	1.96314	+	0.514796i
$917$	−20.5525	+	25.9677i	−0.678703	+	0.857528i
$918$	23.3959	−	19.9173i	0.772181	−	0.657367i
$919$	−2.27242	+	1.34456i	−0.0749603	+	0.0443530i	−0.546222	−	0.837640i	$-0.683935\pi$
$919$	−2.27242	+	1.34456i	−0.0749603	+	0.0443530i	0.471262	+	0.881993i	$0.343799\pi$
$920$	6.54282	−	10.2904i	0.215710	−	0.339264i
$921$	54.4498	+	27.6703i	1.79418	+	0.911768i
$922$	50.9991	+	80.2100i	1.67957	+	2.64158i
$923$	0.653469	+	6.77389i	0.0215092	+	0.222965i
$924$	29.5378	−	93.4314i	0.971722	−	3.07367i
$925$	21.7411	+	21.0551i	0.714842	+	0.692286i
$926$	45.7054	−	59.8950i	1.50197	−	1.96827i
$927$	−3.96020	+	4.17765i	−0.130070	+	0.137212i
$928$	−0.215167	−	0.515560i	−0.00706321	−	0.0169241i
$929$	−13.7859	+	50.3715i	−0.452300	+	1.65264i	0.271359	+	0.962478i	$0.412527\pi$
$929$	−13.7859	+	50.3715i	−0.452300	+	1.65264i	−0.723659	+	0.690158i	$0.757541\pi$
$930$	1.98029	−	8.67621i	0.0649362	−	0.284504i
$931$	2.90803	−	16.5157i	0.0953068	−	0.541281i
$932$	17.8196	+	78.0728i	0.583700	+	2.55736i
$933$	−2.93534	−	0.125541i	−0.0960987	−	0.00411003i
$934$	−18.6885	+	34.0288i	−0.611508	+	1.11346i
$935$	1.64225	+	11.7460i	0.0537075	+	0.384134i
$936$	5.85817	+	7.03221i	0.191480	+	0.229855i
$937$	7.77922	+	21.1387i	0.254136	+	0.690570i	0.999708	+	0.0241452i	$0.00768641\pi$
$937$	7.77922	+	21.1387i	0.254136	+	0.690570i	−0.745572	+	0.666425i	$0.767824\pi$
$938$	−43.7232	−	22.0170i	−1.42761	−	0.718880i
$939$	4.00058	+	6.59938i	0.130554	+	0.215363i
$940$	−4.15887	+	4.20355i	−0.135648	+	0.137105i
$941$	4.91524	+	23.8761i	0.160232	+	0.778338i	0.978943	+	0.204132i	$0.0654373\pi$
$941$	4.91524	+	23.8761i	0.160232	+	0.778338i	−0.818711	+	0.574206i	$0.805311\pi$
$942$	33.8891	+	98.5351i	1.10417	+	3.21045i
$943$	1.61840	+	5.05433i	0.0527024	+	0.164592i
$944$	8.13785	−	2.13400i	0.264864	−	0.0694556i
$945$	−0.142026	−	3.97213i	−0.00462012	−	0.129213i
$946$	110.917	−	21.6012i	3.60624	−	0.702315i
$947$	0.924158	−	0.263574i	0.0300311	−	0.00856499i	−0.259219	−	0.965819i	$-0.583465\pi$
$947$	0.924158	−	0.263574i	0.0300311	−	0.00856499i	0.289250	+	0.957254i	$0.406594\pi$
$948$	72.0240	+	15.6312i	2.33923	+	0.507679i
$949$	11.5319	+	7.86231i	0.374341	+	0.255221i
$950$	26.0683	−	3.92917i	0.845769	−	0.127479i
$951$	28.8624	+	16.2550i	0.935929	+	0.527105i
$952$	29.3412	−	26.2744i	0.950955	−	0.851558i
$953$	2.36711	+	2.60645i	0.0766781	+	0.0844311i	0.777412	−	0.628991i	$-0.216532\pi$
$953$	2.36711	+	2.60645i	0.0766781	+	0.0844311i	−0.700734	+	0.713422i	$0.747144\pi$
$954$	0.139877	−	13.0896i	0.00452867	−	0.423791i
$955$	−1.11282	+	6.05839i	−0.0360099	+	0.196045i
$956$	52.2335	−	27.9643i	1.68935	−	0.904429i
$957$	1.26334	−	0.274180i	0.0408380	−	0.00886300i
$958$	−70.2427	−	28.4381i	−2.26944	−	0.918794i
$959$	21.2711	−	3.28628i	0.686879	−	0.106119i
$960$	−7.98774	−	11.4510i	−0.257803	−	0.369580i
$961$	−1.43767	+	19.1844i	−0.0463764	+	0.618850i
$962$	24.0372	−	7.41450i	0.774991	−	0.239053i
$963$	−10.1021	−	20.4163i	−0.325537	−	0.657907i
$964$	42.7467	+	77.8347i	1.37678	+	2.50689i
$965$	−0.370129	+	0.276234i	−0.0119149	+	0.00889229i
$966$	−14.9137	+	94.4537i	−0.479842	+	3.03900i
$967$	23.8362	+	4.64209i	0.766520	+	0.149280i	0.559244	−	0.829003i	$-0.311091\pi$
$967$	23.8362	+	4.64209i	0.766520	+	0.149280i	0.207275	+	0.978283i	$0.433540\pi$
$968$	−46.9159	+	4.02043i	−1.50793	+	0.129221i
$969$	22.1533	+	7.88489i	0.711667	+	0.253299i
$970$	−2.92616	+	3.51260i	−0.0939535	+	0.112783i
$971$	−27.1965	−	16.8867i	−0.872777	−	0.541920i	0.0162011	−	0.999869i	$-0.494843\pi$
$971$	−27.1965	−	16.8867i	−0.872777	−	0.541920i	−0.888979	+	0.457949i	$0.848584\pi$
$972$	−44.2753	−	28.8200i	−1.42013	−	0.924404i
$973$	−17.8142	+	0.827641i	−0.571097	+	0.0265329i
$974$	−6.26308	+	64.9234i	−0.200682	+	2.08028i
$975$	15.3950	−	7.82345i	0.493035	−	0.250551i
$976$	7.03268	+	4.16115i	0.225111	+	0.133195i
$977$	−10.1609	+	1.75434i	−0.325075	+	0.0561263i	−0.330346	−	0.943860i	$-0.607166\pi$
$977$	−10.1609	+	1.75434i	−0.325075	+	0.0561263i	0.00527154	+	0.999986i	$0.498322\pi$
$978$	−12.9536	−	70.5218i	−0.414209	−	2.25504i
$979$	−33.5441	−	42.0630i	−1.07207	−	1.34434i
$980$	−0.749573	−	12.3143i	−0.0239442	−	0.393365i
$981$	0.371182	−	0.465447i	0.0118509	−	0.0148606i
$982$	8.72002	+	4.66844i	0.278267	+	0.148976i
$983$	−23.0467	−	6.57302i	−0.735076	−	0.209647i	−0.114092	−	0.993470i	$-0.536396\pi$
$983$	−23.0467	−	6.57302i	−0.735076	−	0.209647i	−0.620984	+	0.783824i	$0.713267\pi$
$984$	−5.17994	−	0.443892i	−0.165131	−	0.0141508i
$985$	7.59341	+	3.45888i	0.241946	+	0.110209i
$986$	1.19410	+	0.396468i	0.0380278	+	0.0126261i
$987$	6.93047	−	17.8516i	0.220599	−	0.568224i
$988$	4.76829	−	12.9570i	0.151699	−	0.412216i
$989$	−65.4618	+	23.2994i	−2.08156	+	0.740878i
$990$	9.12231	−	4.15531i	0.289926	−	0.132065i
$991$	18.6295	−	1.99830i	0.591786	−	0.0634782i	0.194071	−	0.980987i	$-0.437831\pi$
$991$	18.6295	−	1.99830i	0.591786	−	0.0634782i	0.397714	+	0.917509i	$0.369803\pi$
$992$	−11.0838	−	11.6924i	−0.351911	−	0.371234i
$993$	7.00977	−	15.8352i	0.222448	−	0.502514i
$994$	−10.1023	−	22.5960i	−0.320425	−	0.716701i
$995$	−5.84666	−	4.97733i	−0.185351	−	0.157792i
$996$	84.9459	+	14.6665i	2.69161	+	0.464725i
$997$	−0.291093	−	27.2403i	−0.00921900	−	0.862710i	−0.906729	−	0.421715i	$-0.861428\pi$
$997$	−0.291093	−	27.2403i	−0.00921900	−	0.862710i	0.897510	−	0.440995i	$-0.145374\pi$
$998$	72.9383	−	67.6768i	2.30882	−	2.14227i
$999$	−15.3456	+	10.4625i	−0.485513	+	0.331017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.k.a.100.4	✓	2688
343.319	even	147	inner	343.2.k.a.319.4	yes	2688

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.2.k.a.100.4	✓	2688	1.1	even	1	trivial
343.2.k.a.319.4	yes	2688	343.319	even	147	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.k (of order \(147\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37080 - 1.87829i) q^{2} +(0.115205 - 2.15419i) q^{3} +(-1.03897 + 3.24476i) q^{4} +(-0.517175 + 0.0110544i) q^{5} +(-4.20410 + 2.73657i) q^{6} +(-2.60550 + 0.459747i) q^{7} +(3.10511 - 1.03097i) q^{8} +(-1.64436 - 0.176383i) q^{9} +(0.729705 + 0.956248i) q^{10} +(-0.590941 + 5.00428i) q^{11} +(6.87012 + 2.61195i) q^{12} +(-0.782394 - 1.49970i) q^{13} +(4.43515 + 4.26365i) q^{14} +(-0.0357676 + 1.11536i) q^{15} +(-0.646188 - 0.461095i) q^{16} +(-4.42480 + 1.05980i) q^{17} +(1.92279 + 3.33036i) q^{18} +(1.19784 - 2.07472i) q^{19} +(0.501462 - 1.68959i) q^{20} +(0.690215 + 5.66570i) q^{21} +(10.2095 - 5.74990i) q^{22} +(-5.68078 + 4.43180i) q^{23} +(-1.86318 - 6.80776i) q^{24} +(-4.72809 + 0.202215i) q^{25} +(-1.74437 + 3.52534i) q^{26} +(0.463498 - 2.86690i) q^{27} +(1.21528 - 8.93188i) q^{28} +(0.110231 - 0.0446275i) q^{29} +(2.14400 - 1.46176i) q^{30} +(2.51404 - 2.33269i) q^{31} +(-0.0501970 - 4.69741i) q^{32} +(10.7121 + 1.84951i) q^{33} +(8.05611 + 6.85826i) q^{34} +(1.34242 - 0.266572i) q^{35} +(2.28077 - 5.15229i) q^{36} +(-4.39978 - 4.64136i) q^{37} +(-5.53892 + 0.594135i) q^{38} +(-3.32077 + 1.51265i) q^{39} +(-1.59449 + 0.567516i) q^{40} +(0.254392 - 0.691265i) q^{41} +(9.69566 - 9.06294i) q^{42} +(9.15264 + 3.03889i) q^{43} +(-15.6237 - 7.11678i) q^{44} +(0.852372 + 0.0730435i) q^{45} +(16.1114 + 4.59503i) q^{46} +(-2.95791 - 1.58358i) q^{47} +(-1.06773 + 1.33889i) q^{48} +(6.57727 - 2.39574i) q^{49} +(6.86106 + 8.60350i) q^{50} +(1.77325 + 9.65394i) q^{51} +(5.67905 - 0.980526i) q^{52} +(-2.92960 - 1.73340i) q^{53} +(-6.02021 + 3.05935i) q^{54} +(0.250300 - 2.59462i) q^{55} +(-7.61639 + 4.11375i) q^{56} +(-4.33134 - 2.81939i) q^{57} +(-0.234927 - 0.145870i) q^{58} +(-6.78328 + 8.14273i) q^{59} +(-3.58193 - 1.27489i) q^{60} +(-10.2562 + 0.878897i) q^{61} +(-7.82770 - 1.52444i) q^{62} +(4.36547 - 0.296423i) q^{63} +(-10.0266 + 7.48308i) q^{64} +(0.421213 + 0.766959i) q^{65} +(-11.2102 - 22.6557i) q^{66} +(-7.60362 + 2.34541i) q^{67} +(1.15845 - 15.4585i) q^{68} +(8.89247 + 12.7480i) q^{69} +(-2.34088 - 2.15603i) q^{70} +(-3.72918 - 1.50978i) q^{71} +(-5.28777 + 1.14759i) q^{72} +(-7.27431 + 3.89445i) q^{73} +(-2.68660 + 14.6264i) q^{74} +(-0.109089 + 10.2085i) q^{75} +(5.48744 + 6.04229i) q^{76} +(-0.761007 - 13.3103i) q^{77} +(7.39329 + 4.16383i) q^{78} +(9.91547 - 1.49452i) q^{79} +(0.339290 + 0.231324i) q^{80} +(-10.9709 - 2.38100i) q^{81} +(-1.64711 + 0.469763i) q^{82} +(11.5122 - 2.24199i) q^{83} +(-19.1009 - 3.64693i) q^{84} +(2.27668 - 0.597016i) q^{85} +(-6.83851 - 21.3570i) q^{86} +(-0.0834369 - 0.242599i) q^{87} +(3.32432 + 16.1481i) q^{88} +(-7.50914 + 7.58981i) q^{89} +(-1.03123 - 1.70112i) q^{90} +(2.72801 + 3.54777i) q^{91} +(-8.47792 - 23.0373i) q^{92} +(-4.73542 - 5.68445i) q^{93} +(1.08028 + 7.72656i) q^{94} +(-0.596559 + 1.08624i) q^{95} +(-10.1249 - 0.433029i) q^{96} +(0.845738 + 3.70542i) q^{97} +(-13.5160 - 9.06991i) q^{98} +(1.85439 - 8.12462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 84 q^{8} - 98 q^{9} - 84 q^{10} - 91 q^{11} - 119 q^{12} - 84 q^{13} - 119 q^{14} - 98 q^{15} - 84 q^{16} - 91 q^{17} - 42 q^{18}+ \cdots - 182 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 84 * q^8 - 98 * q^9 - 84 * q^10 - 91 * q^11 - 119 * q^12 - 84 * q^13 - 119 * q^14 - 98 * q^15 - 84 * q^16 - 91 * q^17 - 42 * q^18 + 126 * q^19 + 84 * q^20 - 84 * q^21 - 98 * q^22 - 105 * q^23 - 126 * q^24 - 84 * q^25 - 98 * q^26 - 105 * q^27 - 126 * q^28 - 126 * q^29 - 91 * q^30 - 133 * q^31 - 126 * q^32 - 84 * q^33 - 168 * q^34 - 98 * q^35 - 42 * q^36 - 105 * q^37 + 28 * q^38 - 77 * q^39 - 56 * q^40 - 56 * q^41 - 126 * q^42 - 84 * q^43 - 28 * q^44 - 105 * q^45 - 119 * q^47 - 14 * q^48 - 28 * q^49 - 196 * q^50 - 28 * q^51 - 28 * q^52 - 91 * q^53 + 126 * q^54 + 301 * q^55 - 70 * q^56 + 21 * q^57 + 308 * q^58 + 28 * q^59 - 112 * q^60 - 105 * q^61 - 70 * q^62 - 133 * q^63 - 140 * q^64 - 84 * q^65 - 252 * q^66 - 91 * q^67 - 175 * q^68 - 168 * q^69 - 168 * q^70 - 161 * q^71 - 21 * q^72 + 42 * q^73 - 210 * q^75 - 21 * q^76 + 42 * q^77 + 280 * q^78 - 91 * q^79 - 168 * q^80 - 126 * q^81 - 84 * q^82 - 98 * q^83 - 14 * q^84 - 140 * q^85 - 28 * q^86 + 14 * q^87 + 28 * q^88 - 84 * q^89 + 329 * q^90 + 406 * q^91 + 336 * q^92 + 14 * q^93 - 112 * q^94 + 238 * q^95 + 560 * q^96 + 196 * q^97 + 63 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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