LMFDB - Embedded newform 175.2.e.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	175.151
Dual form			175.2.e.c.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(-1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(-1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(1.41421 + 2.44949i) q^{9} +(0.414214 - 0.717439i) q^{11} +(-0.792893 - 1.37333i) q^{12} +4.82843 q^{13} +(-2.41421 - 5.91359i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(2.41421 - 4.18154i) q^{17} +(-3.41421 + 5.91359i) q^{18} +(-1.41421 - 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} +2.00000 q^{22} +(0.207107 + 0.358719i) q^{23} +(0.914214 - 1.58346i) q^{24} +(5.82843 + 10.0951i) q^{26} -2.41421 q^{27} +(6.20711 - 8.00436i) q^{28} -1.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(0.171573 + 0.297173i) q^{33} +11.6569 q^{34} -10.8284 q^{36} +(3.41421 - 5.91359i) q^{38} +(-1.00000 + 1.73205i) q^{39} -7.82843 q^{41} +(2.62132 + 0.358719i) q^{42} -3.58579 q^{43} +(1.58579 + 2.74666i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.00000 + 1.73205i) q^{47} +1.24264 q^{48} +(6.74264 + 1.88064i) q^{49} +(1.00000 + 1.73205i) q^{51} +(-9.24264 + 16.0087i) q^{52} +(-0.585786 + 1.01461i) q^{53} +(-2.91421 - 5.04757i) q^{54} +(11.5711 + 1.58346i) q^{56} +1.17157 q^{57} +(-1.20711 - 2.09077i) q^{58} +(-2.24264 + 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} +14.4853 q^{62} +(-2.82843 - 6.92820i) q^{63} -9.82843 q^{64} +(-0.414214 + 0.717439i) q^{66} +(4.79289 - 8.30153i) q^{67} +(9.24264 + 16.0087i) q^{68} -0.171573 q^{69} +4.48528 q^{71} +(-6.24264 - 10.8126i) q^{72} +(-0.414214 + 0.717439i) q^{73} +10.8284 q^{76} +(-1.34315 + 1.73205i) q^{77} -4.82843 q^{78} +(-7.41421 - 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-9.44975 - 16.3674i) q^{82} -13.7279 q^{83} +(1.58579 + 3.88437i) q^{84} +(-4.32843 - 7.49706i) q^{86} +(0.207107 - 0.358719i) q^{87} +(-1.82843 + 3.16693i) q^{88} +(4.32843 + 7.49706i) q^{89} +(-12.6569 - 1.73205i) q^{91} -1.58579 q^{92} +(1.24264 + 2.15232i) q^{93} +(-2.41421 + 4.18154i) q^{94} +(-0.328427 - 0.568852i) q^{96} -11.6569 q^{97} +(4.20711 + 16.3674i) q^{98} +2.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{11} - 6 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 4 q^{17} - 8 q^{18} + 14 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 12 q^{26} - 4 q^{27} + 22 q^{28} - 4 q^{29} + 12 q^{31} - 6 q^{32} + 12 q^{33} + 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} - 20 q^{41} + 2 q^{42} - 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 10 q^{49} + 4 q^{51} - 20 q^{52} - 8 q^{53} - 6 q^{54} + 18 q^{56} + 16 q^{57} - 2 q^{58} + 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{66} + 22 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{71} - 8 q^{72} + 4 q^{73} + 32 q^{76} - 28 q^{77} - 8 q^{78} - 24 q^{79} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 12 q^{84} - 6 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 28 q^{91} - 12 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 24 q^{97} + 14 q^{98} + 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 4 * q^11 - 6 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 4 * q^17 - 8 * q^18 + 14 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 12 * q^26 - 4 * q^27 + 22 * q^28 - 4 * q^29 + 12 * q^31 - 6 * q^32 + 12 * q^33 + 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 - 20 * q^41 + 2 * q^42 - 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 10 * q^49 + 4 * q^51 - 20 * q^52 - 8 * q^53 - 6 * q^54 + 18 * q^56 + 16 * q^57 - 2 * q^58 + 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^66 + 22 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^71 - 8 * q^72 + 4 * q^73 + 32 * q^76 - 28 * q^77 - 8 * q^78 - 24 * q^79 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 12 * q^84 - 6 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 28 * q^91 - 12 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 24 * q^97 + 14 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	0.877981	+	0.478696i	$0.158890\pi$
$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	−0.0244272	+	0.999702i	$0.507776\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	−4.41421			−1.56066
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	−0.796800	−	0.604243i	$-0.793476\pi$
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	0.921690	+	0.387927i	$0.126809\pi$
$12$	−0.792893	−	1.37333i	−0.228889	−	0.396447i
$13$	4.82843			1.33916			0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843			1.33916			0.669582	+	0.742738i	$0.266473\pi$
$14$	−2.41421	−	5.91359i	−0.645226	−	1.58047i
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	2.41421	−	4.18154i	0.585533	−	1.01417i	−0.409276	−	0.912411i	$-0.634219\pi$
$17$	2.41421	−	4.18154i	0.585533	−	1.01417i	0.994809	−	0.101762i	$-0.0324480\pi$
$18$	−3.41421	+	5.91359i	−0.804738	+	1.39385i
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$		0			0
$21$	0.671573	−	0.866025i	0.146549	−	0.188982i
$22$	2.00000			0.426401
$23$	0.207107	+	0.358719i	0.0431847	+	0.0747982i	0.886810	−	0.462134i	$-0.152916\pi$
$23$	0.207107	+	0.358719i	0.0431847	+	0.0747982i	−0.843625	+	0.536933i	$0.819583\pi$
$24$	0.914214	−	1.58346i	0.186613	−	0.323223i
$25$		0			0
$26$	5.82843	+	10.0951i	1.14305	+	1.97982i
$27$	−2.41421			−0.464616
$28$	6.20711	−	8.00436i	1.17303	−	1.51268i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−0.792893	+	1.37333i	−0.140165	+	0.242773i
$33$	0.171573	+	0.297173i	0.0298670	+	0.0517312i
$34$	11.6569			1.99913
$35$		0			0
$36$	−10.8284			−1.80474
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	3.41421	−	5.91359i	0.553859	−	0.959311i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$		0			0
$41$	−7.82843			−1.22259			−0.611297	−	0.791401i	$-0.709352\pi$
$41$	−7.82843			−1.22259			−0.611297	+	0.791401i	$0.709352\pi$
$42$	2.62132	+	0.358719i	0.404479	+	0.0553516i
$43$	−3.58579			−0.546827			−0.273414	−	0.961897i	$-0.588153\pi$
$43$	−3.58579			−0.546827			−0.273414	+	0.961897i	$0.588153\pi$
$44$	1.58579	+	2.74666i	0.239066	+	0.414075i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$	1.24264			0.179360
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	−9.24264	+	16.0087i	−1.28172	+	2.22001i
$53$	−0.585786	+	1.01461i	−0.0804640	+	0.139368i	−0.903449	−	0.428695i	$-0.858974\pi$
$53$	−0.585786	+	1.01461i	−0.0804640	+	0.139368i	0.822985	+	0.568063i	$0.192307\pi$
$54$	−2.91421	−	5.04757i	−0.396574	−	0.686887i
$55$		0			0
$56$	11.5711	+	1.58346i	1.54625	+	0.211599i
$57$	1.17157			0.155179
$58$	−1.20711	−	2.09077i	−0.158501	−	0.274532i
$59$	−2.24264	+	3.88437i	−0.291967	+	0.505702i	−0.974275	−	0.225363i	$-0.927643\pi$
$59$	−2.24264	+	3.88437i	−0.291967	+	0.505702i	0.682308	+	0.731065i	$0.260976\pi$
$60$		0			0
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	0.635294	−	0.772271i	$-0.280879\pi$
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	−0.986453	+	0.164045i	$0.947546\pi$
$62$	14.4853			1.83963
$63$	−2.82843	−	6.92820i	−0.356348	−	0.872872i
$64$	−9.82843			−1.22855
$65$		0			0
$66$	−0.414214	+	0.717439i	−0.0509862	+	0.0883106i
$67$	4.79289	−	8.30153i	0.585545	−	1.01419i	−0.409262	−	0.912417i	$-0.634214\pi$
$67$	4.79289	−	8.30153i	0.585545	−	1.01419i	0.994807	−	0.101777i	$-0.0324528\pi$
$68$	9.24264	+	16.0087i	1.12083	+	1.94134i
$69$	−0.171573			−0.0206549
$70$		0			0
$71$	4.48528			0.532305			0.266152	−	0.963931i	$-0.414248\pi$
$71$	4.48528			0.532305			0.266152	+	0.963931i	$0.414248\pi$
$72$	−6.24264	−	10.8126i	−0.735702	−	1.27427i
$73$	−0.414214	+	0.717439i	−0.0484800	+	0.0839699i	−0.889247	−	0.457427i	$-0.848771\pi$
$73$	−0.414214	+	0.717439i	−0.0484800	+	0.0839699i	0.840767	+	0.541397i	$0.182104\pi$
$74$		0			0
$75$		0			0
$76$	10.8284			1.24211
$77$	−1.34315	+	1.73205i	−0.153066	+	0.197386i
$78$	−4.82843			−0.546712
$79$	−7.41421	−	12.8418i	−0.834164	−	1.44481i	−0.894709	−	0.446649i	$-0.852617\pi$
$79$	−7.41421	−	12.8418i	−0.834164	−	1.44481i	0.0605449	−	0.998165i	$-0.480716\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	−9.44975	−	16.3674i	−1.04355	−	1.80748i
$83$	−13.7279			−1.50684			−0.753418	−	0.657542i	$-0.771596\pi$
$83$	−13.7279			−1.50684			−0.753418	+	0.657542i	$0.771596\pi$
$84$	1.58579	+	3.88437i	0.173023	+	0.423819i
$85$		0			0
$86$	−4.32843	−	7.49706i	−0.466746	−	0.808428i
$87$	0.207107	−	0.358719i	0.0222042	−	0.0384588i
$88$	−1.82843	+	3.16693i	−0.194911	+	0.337596i
$89$	4.32843	+	7.49706i	0.458812	+	0.794686i	0.998898	−	0.0469234i	$-0.0149417\pi$
$89$	4.32843	+	7.49706i	0.458812	+	0.794686i	−0.540086	+	0.841610i	$0.681608\pi$
$90$		0			0
$91$	−12.6569	−	1.73205i	−1.32680	−	0.181568i
$92$	−1.58579			−0.165330
$93$	1.24264	+	2.15232i	0.128856	+	0.223185i
$94$	−2.41421	+	4.18154i	−0.249007	+	0.431293i
$95$		0			0
$96$	−0.328427	−	0.568852i	−0.0335200	−	0.0580583i
$97$	−11.6569			−1.18357			−0.591787	−	0.806094i	$-0.701577\pi$
$97$	−11.6569			−1.18357			−0.591787	+	0.806094i	$0.701577\pi$
$98$	4.20711	+	16.3674i	0.424982	+	1.65336i
$99$	2.34315			0.235495
$100$		0			0
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	−0.486758	−	0.873537i	$-0.661821\pi$
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	0.999884	−	0.0152237i	$-0.00484604\pi$
$102$	−2.41421	+	4.18154i	−0.239043	+	0.414034i
$103$	−1.20711	−	2.09077i	−0.118940	−	0.206010i	0.800408	−	0.599456i	$-0.204616\pi$
$103$	−1.20711	−	2.09077i	−0.118940	−	0.206010i	−0.919348	+	0.393446i	$0.871283\pi$
$104$	−21.3137			−2.08998
$105$		0			0
$106$	−2.82843			−0.274721
$107$	5.62132	+	9.73641i	0.543434	+	0.941255i	0.998704	+	0.0509012i	$0.0162093\pi$
$107$	5.62132	+	9.73641i	0.543434	+	0.941255i	−0.455270	+	0.890353i	$0.650457\pi$
$108$	4.62132	−	8.00436i	0.444687	−	0.770220i
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	−0.338282	−	0.941045i	$-0.609846\pi$
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	0.984110	−	0.177562i	$-0.0568210\pi$
$110$		0			0
$111$		0			0
$112$	3.00000	+	7.34847i	0.283473	+	0.694365i
$113$	4.48528			0.421940			0.210970	−	0.977493i	$-0.432338\pi$
$113$	4.48528			0.421940			0.210970	+	0.977493i	$0.432338\pi$
$114$	1.41421	+	2.44949i	0.132453	+	0.229416i
$115$		0			0
$116$	1.91421	−	3.31552i	0.177730	−	0.307838i
$117$	6.82843	+	11.8272i	0.631288	+	1.09342i
$118$	−10.8284			−0.996838
$119$	−7.82843	+	10.0951i	−0.717631	+	0.925419i
$120$		0			0
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$	6.62132	−	11.4685i	0.599466	−	1.03831i
$123$	1.62132	−	2.80821i	0.146190	−	0.253208i
$124$	11.4853	+	19.8931i	1.03141	+	1.78645i
$125$		0			0
$126$	11.0711	−	14.2767i	0.986289	−	1.27187i
$127$	9.31371			0.826458			0.413229	−	0.910627i	$-0.364401\pi$
$127$	9.31371			0.826458			0.413229	+	0.910627i	$0.364401\pi$
$128$	−10.2782	−	17.8023i	−0.908471	−	1.57352i
$129$	0.742641	−	1.28629i	0.0653859	−	0.113252i
$130$		0			0
$131$	9.65685	+	16.7262i	0.843723	+	1.46137i	0.886725	+	0.462297i	$0.152974\pi$
$131$	9.65685	+	16.7262i	0.843723	+	1.46137i	−0.0430021	+	0.999075i	$0.513692\pi$
$132$	−1.31371			−0.114344
$133$	2.82843	+	6.92820i	0.245256	+	0.600751i
$134$	23.1421			1.99918
$135$		0			0
$136$	−10.6569	+	18.4582i	−0.913818	+	1.58278i
$137$	−4.82843	+	8.36308i	−0.412520	+	0.714506i	−0.995165	−	0.0982211i	$-0.968685\pi$
$137$	−4.82843	+	8.36308i	−0.412520	+	0.714506i	0.582644	+	0.812727i	$0.302018\pi$
$138$	−0.207107	−	0.358719i	−0.0176301	−	0.0305362i
$139$	−16.1421			−1.36916			−0.684579	−	0.728939i	$-0.740014\pi$
$139$	−16.1421			−1.36916			−0.684579	+	0.728939i	$0.740014\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$	5.41421	+	9.37769i	0.454351	+	0.786959i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	4.24264	−	7.34847i	0.353553	−	0.612372i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−2.07107	+	2.02922i	−0.170819	+	0.167368i
$148$		0			0
$149$	1.08579	+	1.88064i	0.0889511	+	0.154068i	0.907068	−	0.420984i	$-0.138315\pi$
$149$	1.08579	+	1.88064i	0.0889511	+	0.154068i	−0.818117	+	0.575052i	$0.804982\pi$
$150$		0			0
$151$	−5.82843	+	10.0951i	−0.474311	+	0.821530i	−0.999567	−	0.0294137i	$-0.990636\pi$
$151$	−5.82843	+	10.0951i	−0.474311	+	0.821530i	0.525257	+	0.850944i	$0.323969\pi$
$152$	6.24264	+	10.8126i	0.506345	+	0.877015i
$153$	13.6569			1.10409
$154$	−5.24264	−	0.717439i	−0.422464	−	0.0578129i
$155$		0			0
$156$	−3.82843	−	6.63103i	−0.306519	−	0.530907i
$157$	8.65685	−	14.9941i	0.690892	−	1.19666i	−0.280654	−	0.959809i	$-0.590551\pi$
$157$	8.65685	−	14.9941i	0.690892	−	1.19666i	0.971546	−	0.236851i	$-0.0761154\pi$
$158$	17.8995	−	31.0028i	1.42401	−	2.46645i
$159$	−0.242641	−	0.420266i	−0.0192427	−	0.0333293i
$160$		0			0
$161$	−0.414214	−	1.01461i	−0.0326446	−	0.0799626i
$162$	−18.0711			−1.41980
$163$	6.17157	+	10.6895i	0.483395	+	0.837265i	0.999818	−	0.0190689i	$-0.00607020\pi$
$163$	6.17157	+	10.6895i	0.483395	+	0.837265i	−0.516423	+	0.856333i	$0.672737\pi$
$164$	14.9853	−	25.9553i	1.17015	−	2.02677i
$165$		0			0
$166$	−16.5711	−	28.7019i	−1.28616	−	2.22770i
$167$	−22.4142			−1.73446			−0.867232	−	0.497904i	$-0.834103\pi$
$167$	−22.4142			−1.73446			−0.867232	+	0.497904i	$0.834103\pi$
$168$	−2.96447	+	3.82282i	−0.228714	+	0.294937i
$169$	10.3137			0.793362
$170$		0			0
$171$	4.00000	−	6.92820i	0.305888	−	0.529813i
$172$	6.86396	−	11.8887i	0.523372	−	0.906507i
$173$	1.65685	+	2.86976i	0.125968	+	0.218183i	0.922111	−	0.386925i	$-0.126463\pi$
$173$	1.65685	+	2.86976i	0.125968	+	0.218183i	−0.796143	+	0.605109i	$0.793130\pi$
$174$	1.00000			0.0758098
$175$		0			0
$176$	−2.48528			−0.187335
$177$	−0.928932	−	1.60896i	−0.0698228	−	0.120937i
$178$	−10.4497	+	18.0995i	−0.783242	+	1.35661i
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$		0			0
$181$	2.65685			0.197482			0.0987412	−	0.995113i	$-0.468518\pi$
$181$	2.65685			0.197482			0.0987412	+	0.995113i	$0.468518\pi$
$182$	−11.6569	−	28.5533i	−0.864064	−	2.11651i
$183$	2.27208			0.167957
$184$	−0.914214	−	1.58346i	−0.0673967	−	0.116735i
$185$		0			0
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	−7.65685			−0.558433
$189$	6.32843	+	0.866025i	0.460325	+	0.0629941i
$190$		0			0
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	0.999161	−	0.0409507i	$-0.0130387\pi$
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	−0.535045	+	0.844824i	$0.679705\pi$
$192$	2.03553	−	3.52565i	0.146902	−	0.254442i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−14.0711	−	24.3718i	−1.01024	−	1.74979i
$195$		0			0
$196$	−19.1421	+	18.7554i	−1.36730	+	1.33967i
$197$	12.3431			0.879413			0.439706	−	0.898142i	$-0.355083\pi$
$197$	12.3431			0.879413			0.439706	+	0.898142i	$0.355083\pi$
$198$	2.82843	+	4.89898i	0.201008	+	0.348155i
$199$	4.82843	−	8.36308i	0.342278	−	0.592843i	−0.642577	−	0.766221i	$-0.722135\pi$
$199$	4.82843	−	8.36308i	0.342278	−	0.592843i	0.984855	+	0.173378i	$0.0554682\pi$
$200$		0			0
$201$	1.98528	+	3.43861i	0.140031	+	0.242541i
$202$	24.8995			1.75192
$203$	2.62132	+	0.358719i	0.183981	+	0.0251772i
$204$	−7.65685			−0.536087
$205$		0			0
$206$	2.91421	−	5.04757i	0.203043	−	0.351681i
$207$	−0.585786	+	1.01461i	−0.0407150	+	0.0705204i
$208$	−7.24264	−	12.5446i	−0.502187	−	0.869813i
$209$	−2.34315			−0.162079
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$	−2.24264	−	3.88437i	−0.154025	−	0.266779i
$213$	−0.928932	+	1.60896i	−0.0636494	+	0.110244i
$214$	−13.5711	+	23.5058i	−0.927699	+	1.60682i
$215$		0			0
$216$	10.6569			0.725107
$217$	−9.72792	+	12.5446i	−0.660374	+	0.851584i
$218$	32.5563			2.20499
$219$	−0.171573	−	0.297173i	−0.0115938	−	0.0200811i
$220$		0			0
$221$	11.6569	−	20.1903i	0.784125	−	1.35814i
$222$		0			0
$223$	−0.343146			−0.0229787			−0.0114894	−	0.999934i	$-0.503657\pi$
$223$	−0.343146			−0.0229787			−0.0114894	+	0.999934i	$0.503657\pi$
$224$	2.57107	−	3.31552i	0.171787	−	0.221527i
$225$		0			0
$226$	5.41421	+	9.37769i	0.360148	+	0.623795i
$227$	−3.48528	+	6.03668i	−0.231326	+	0.400669i	−0.958199	−	0.286104i	$-0.907640\pi$
$227$	−3.48528	+	6.03668i	−0.231326	+	0.400669i	0.726872	+	0.686773i	$0.240973\pi$
$228$	−2.24264	+	3.88437i	−0.148523	+	0.257249i
$229$	5.82843	+	10.0951i	0.385153	+	0.667105i	0.991790	−	0.127874i	$-0.0408152\pi$
$229$	5.82843	+	10.0951i	0.385153	+	0.667105i	−0.606637	+	0.794979i	$0.707482\pi$
$230$		0			0
$231$	−0.343146	−	0.840532i	−0.0225773	−	0.0553029i
$232$	4.41421			0.289807
$233$	−8.41421	−	14.5738i	−0.551233	−	0.954764i	−0.998186	−	0.0602067i	$-0.980824\pi$
$233$	−8.41421	−	14.5738i	−0.551233	−	0.954764i	0.446952	−	0.894558i	$-0.352509\pi$
$234$	−16.4853	+	28.5533i	−1.07768	+	1.86659i
$235$		0			0
$236$	−8.58579	−	14.8710i	−0.558887	−	0.968021i
$237$	6.14214			0.398975
$238$	−30.5563	−	4.18154i	−1.98067	−	0.271049i
$239$	−21.3137			−1.37867			−0.689335	−	0.724443i	$-0.742097\pi$
$239$	−21.3137			−1.37867			−0.689335	+	0.724443i	$0.742097\pi$
$240$		0			0
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.0518100	+	0.998657i	$0.516499\pi$
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.838957	+	0.544197i	$0.816834\pi$
$242$	−12.4497	+	21.5636i	−0.800300	+	1.38616i
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$	21.0000			1.34439
$245$		0			0
$246$	7.82843			0.499122
$247$	−6.82843	−	11.8272i	−0.434482	−	0.752546i
$248$	−13.2426	+	22.9369i	−0.840909	+	1.45650i
$249$	2.84315	−	4.92447i	0.180177	−	0.312076i
$250$		0			0
$251$	−9.31371			−0.587876			−0.293938	−	0.955824i	$-0.594966\pi$
$251$	−9.31371			−0.587876			−0.293938	+	0.955824i	$0.594966\pi$
$252$	28.3848	+	3.88437i	1.78807	+	0.244692i
$253$	0.343146			0.0215734
$254$	11.2426	+	19.4728i	0.705426	+	1.22183i
$255$		0			0
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	3.17157	+	5.49333i	0.197837	+	0.342664i	0.947827	−	0.318785i	$-0.103275\pi$
$257$	3.17157	+	5.49333i	0.197837	+	0.342664i	−0.749990	+	0.661450i	$0.769942\pi$
$258$	3.58579			0.223241
$259$		0			0
$260$		0			0
$261$	−1.41421	−	2.44949i	−0.0875376	−	0.151620i
$262$	−23.3137	+	40.3805i	−1.44033	+	2.49472i
$263$	−14.5208	+	25.1508i	−0.895392	+	1.55086i	−0.0620729	+	0.998072i	$0.519771\pi$
$263$	−14.5208	+	25.1508i	−0.895392	+	1.55086i	−0.833319	+	0.552793i	$0.813562\pi$
$264$	−0.757359	−	1.31178i	−0.0466122	−	0.0807348i
$265$		0			0
$266$	−11.0711	+	14.2767i	−0.678811	+	0.875359i
$267$	−3.58579			−0.219447
$268$	18.3492	+	31.7818i	1.12086	+	1.94138i
$269$	−10.2279	+	17.7153i	−0.623607	+	1.08012i	0.365201	+	0.930929i	$0.381000\pi$
$269$	−10.2279	+	17.7153i	−0.623607	+	1.08012i	−0.988808	+	0.149191i	$0.952333\pi$
$270$		0			0
$271$	−8.24264	−	14.2767i	−0.500705	−	0.867246i	−1.00000		0.000813982i	$-0.999741\pi$
$271$	−8.24264	−	14.2767i	−0.500705	−	0.867246i	0.499295	−	0.866432i	$-0.333592\pi$
$272$	−14.4853			−0.878299
$273$	3.24264	−	4.18154i	0.196254	−	0.253078i
$274$	−23.3137			−1.40843
$275$		0			0
$276$	0.328427	−	0.568852i	0.0197690	−	0.0342409i
$277$	8.07107	−	13.9795i	0.484943	−	0.839947i	−0.514907	−	0.857246i	$-0.672174\pi$
$277$	8.07107	−	13.9795i	0.484943	−	0.839947i	0.999850	+	0.0172994i	$0.00550684\pi$
$278$	−19.4853	−	33.7495i	−1.16865	−	2.02416i
$279$	16.9706			1.01600
$280$		0			0
$281$	−30.2843			−1.80661			−0.903304	−	0.429001i	$-0.858866\pi$
$281$	−30.2843			−1.80661			−0.903304	+	0.429001i	$0.858866\pi$
$282$	−1.00000	−	1.73205i	−0.0595491	−	0.103142i
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	−8.58579	+	14.8710i	−0.509473	+	0.882433i
$285$		0			0
$286$	9.65685			0.571022
$287$	20.5208	+	2.80821i	1.21131	+	0.165763i
$288$	−4.48528			−0.264298
$289$	−3.15685	−	5.46783i	−0.185697	−	0.321637i
$290$		0			0
$291$	2.41421	−	4.18154i	0.141524	−	0.245126i
$292$	−1.58579	−	2.74666i	−0.0928011	−	0.160736i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$	−6.74264	−	1.88064i	−0.393239	−	0.109681i
$295$		0			0
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−2.62132	+	4.54026i	−0.151849	+	0.263010i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	9.39949	+	1.28629i	0.541778	+	0.0741406i
$302$	−28.1421			−1.61940
$303$	2.13604	+	3.69973i	0.122712	+	0.212544i
$304$	−4.24264	+	7.34847i	−0.243332	+	0.421464i
$305$		0			0
$306$	16.4853	+	28.5533i	0.942401	+	1.63229i
$307$	4.75736			0.271517			0.135758	−	0.990742i	$-0.456653\pi$
$307$	4.75736			0.271517			0.135758	+	0.990742i	$0.456653\pi$
$308$	−3.17157	−	7.76874i	−0.180717	−	0.442665i
$309$	1.00000			0.0568880
$310$		0			0
$311$	6.58579	−	11.4069i	0.373446	−	0.646827i	−0.616647	−	0.787239i	$-0.711510\pi$
$311$	6.58579	−	11.4069i	0.373446	−	0.646827i	0.990093	+	0.140413i	$0.0448429\pi$
$312$	4.41421	−	7.64564i	0.249906	−	0.432849i
$313$	−3.17157	−	5.49333i	−0.179268	−	0.310501i	0.762362	−	0.647151i	$-0.224040\pi$
$313$	−3.17157	−	5.49333i	−0.179268	−	0.310501i	−0.941630	+	0.336650i	$0.890706\pi$
$314$	41.7990			2.35885
$315$		0			0
$316$	56.7696			3.19354
$317$	−6.89949	−	11.9503i	−0.387514	−	0.671194i	0.604600	−	0.796529i	$-0.293333\pi$
$317$	−6.89949	−	11.9503i	−0.387514	−	0.671194i	−0.992115	+	0.125335i	$0.960000\pi$
$318$	0.585786	−	1.01461i	0.0328493	−	0.0568966i
$319$	−0.414214	+	0.717439i	−0.0231915	+	0.0401689i
$320$		0			0
$321$	−4.65685			−0.259920
$322$	1.62132	−	2.09077i	0.0903527	−	0.116514i
$323$	−13.6569			−0.759888
$324$	−14.3284	−	24.8176i	−0.796024	−	1.37875i
$325$		0			0
$326$	−14.8995	+	25.8067i	−0.825207	+	1.42930i
$327$	2.79289	+	4.83743i	0.154447	+	0.267511i
$328$	34.5563			1.90806
$329$	−2.00000	−	4.89898i	−0.110264	−	0.270089i
$330$		0			0
$331$	−11.4853	−	19.8931i	−0.631288	−	1.09342i	−0.987289	−	0.158937i	$-0.949193\pi$
$331$	−11.4853	−	19.8931i	−0.631288	−	1.09342i	0.356001	−	0.934486i	$-0.384140\pi$
$332$	26.2782	−	45.5151i	1.44220	−	2.49797i
$333$		0			0
$334$	−27.0563	−	46.8630i	−1.48046	−	2.56423i
$335$		0			0
$336$	−3.25736	−	0.445759i	−0.177704	−	0.0243182i
$337$	−9.17157			−0.499607			−0.249804	−	0.968296i	$-0.580366\pi$
$337$	−9.17157			−0.499607			−0.249804	+	0.968296i	$0.580366\pi$
$338$	12.4497	+	21.5636i	0.677177	+	1.17290i
$339$	−0.928932	+	1.60896i	−0.0504527	+	0.0873866i
$340$		0			0
$341$	−2.48528	−	4.30463i	−0.134586	−	0.233109i
$342$	19.3137			1.04437
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	15.8284			0.853412
$345$		0			0
$346$	−4.00000	+	6.92820i	−0.215041	+	0.372463i
$347$	3.96447	−	6.86666i	0.212824	−	0.368621i	−0.739773	−	0.672856i	$-0.765067\pi$
$347$	3.96447	−	6.86666i	0.212824	−	0.368621i	0.952597	+	0.304235i	$0.0984007\pi$
$348$	0.792893	+	1.37333i	0.0425035	+	0.0736183i
$349$	−15.3431			−0.821300			−0.410650	−	0.911793i	$-0.634698\pi$
$349$	−15.3431			−0.821300			−0.410650	+	0.911793i	$0.634698\pi$
$350$		0			0
$351$	−11.6569			−0.622197
$352$	0.656854	+	1.13770i	0.0350104	+	0.0606399i
$353$	−13.4142	+	23.2341i	−0.713967	+	1.23663i	0.249390	+	0.968403i	$0.419770\pi$
$353$	−13.4142	+	23.2341i	−0.713967	+	1.23663i	−0.963357	+	0.268223i	$0.913564\pi$
$354$	2.24264	−	3.88437i	0.119195	−	0.206452i
$355$		0			0
$356$	−33.1421			−1.75653
$357$	−2.00000	−	4.89898i	−0.105851	−	0.259281i
$358$	24.1421			1.27595
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	3.20711	+	5.55487i	0.168562	+	0.291958i
$363$	−4.27208			−0.224226
$364$	29.9706	−	38.6485i	1.57088	−	2.02573i
$365$		0			0
$366$	2.74264	+	4.75039i	0.143360	+	0.248307i
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	−0.899763	−	0.436379i	$-0.856261\pi$
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	0.827797	+	0.561028i	$0.189594\pi$
$368$	0.621320	−	1.07616i	0.0323886	−	0.0560986i
$369$	−11.0711	−	19.1757i	−0.576337	−	0.998245i
$370$		0			0
$371$	1.89949	−	2.44949i	0.0986169	−	0.127171i
$372$	−9.51472			−0.493315
$373$	−10.4853	−	18.1610i	−0.542907	−	0.940343i	−0.998735	−	0.0502752i	$-0.983990\pi$
$373$	−10.4853	−	18.1610i	−0.542907	−	0.940343i	0.455828	−	0.890068i	$-0.349343\pi$
$374$	4.82843	−	8.36308i	0.249672	−	0.432445i
$375$		0			0
$376$	−4.41421	−	7.64564i	−0.227646	−	0.394294i
$377$	−4.82843			−0.248677
$378$	5.82843	+	14.2767i	0.299782	+	0.734313i
$379$	26.8284			1.37808			0.689042	−	0.724722i	$-0.258032\pi$
$379$	26.8284			1.37808			0.689042	+	0.724722i	$0.258032\pi$
$380$		0			0
$381$	−1.92893	+	3.34101i	−0.0988222	+	0.171165i
$382$	−15.4853	+	26.8213i	−0.792296	+	1.37230i
$383$	−1.44975	−	2.51104i	−0.0740786	−	0.128308i	0.826607	−	0.562780i	$-0.190268\pi$
$383$	−1.44975	−	2.51104i	−0.0740786	−	0.128308i	−0.900685	+	0.434472i	$0.856935\pi$
$384$	8.51472			0.434515
$385$		0			0
$386$	−4.82843			−0.245760
$387$	−5.07107	−	8.78335i	−0.257777	−	0.446483i
$388$	22.3137	−	38.6485i	1.13281	−	1.96208i
$389$	−11.8284	+	20.4874i	−0.599725	+	1.03875i	0.393136	+	0.919480i	$0.371390\pi$
$389$	−11.8284	+	20.4874i	−0.599725	+	1.03875i	−0.992861	+	0.119274i	$0.961943\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−29.7635	−	8.30153i	−1.50328	−	0.419291i
$393$	−8.00000			−0.403547
$394$	14.8995	+	25.8067i	0.750626	+	1.30012i
$395$		0			0
$396$	−4.48528	+	7.76874i	−0.225394	+	0.390394i
$397$	−8.31371	−	14.3998i	−0.417253	−	0.722704i	0.578409	−	0.815747i	$-0.303674\pi$
$397$	−8.31371	−	14.3998i	−0.417253	−	0.722704i	−0.995662	+	0.0930434i	$0.970340\pi$
$398$	23.3137			1.16861
$399$	−3.07107	−	0.420266i	−0.153746	−	0.0210396i
$400$		0			0
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	−0.944426	−	0.328725i	$-0.893381\pi$
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	0.187528	−	0.982259i	$-0.439952\pi$
$402$	−4.79289	+	8.30153i	−0.239048	+	0.414043i
$403$	14.4853	−	25.0892i	0.721563	−	1.24978i
$404$	19.7426	+	34.1953i	0.982233	+	1.70128i
$405$		0			0
$406$	2.41421	+	5.91359i	0.119815	+	0.293487i
$407$		0			0
$408$	−4.41421	−	7.64564i	−0.218536	−	0.378516i
$409$	7.39949	−	12.8163i	0.365881	−	0.633725i	−0.623036	−	0.782193i	$-0.714101\pi$
$409$	7.39949	−	12.8163i	0.365881	−	0.633725i	0.988917	+	0.148468i	$0.0474342\pi$
$410$		0			0
$411$	−2.00000	−	3.46410i	−0.0986527	−	0.170872i
$412$	9.24264			0.455352
$413$	7.27208	−	9.37769i	0.357836	−	0.461446i
$414$	−2.82843			−0.139010
$415$		0			0
$416$	−3.82843	+	6.63103i	−0.187704	+	0.325113i
$417$	3.34315	−	5.79050i	0.163715	−	0.283562i
$418$	−2.82843	−	4.89898i	−0.138343	−	0.239617i
$419$	−0.686292			−0.0335275			−0.0167638	−	0.999859i	$-0.505336\pi$
$419$	−0.686292			−0.0335275			−0.0167638	+	0.999859i	$0.505336\pi$
$420$		0			0
$421$	13.4853			0.657232			0.328616	−	0.944464i	$-0.393418\pi$
$421$	13.4853			0.657232			0.328616	+	0.944464i	$0.393418\pi$
$422$	24.7279	+	42.8300i	1.20374	+	2.08493i
$423$	−2.82843	+	4.89898i	−0.137523	+	0.238197i
$424$	2.58579	−	4.47871i	0.125577	−	0.217506i
$425$		0			0
$426$	−4.48528			−0.217313
$427$	5.48528	+	13.4361i	0.265451	+	0.650220i
$428$	−43.0416			−2.08050
$429$	0.828427	+	1.43488i	0.0399968	+	0.0692766i
$430$		0			0
$431$	−8.89949	+	15.4144i	−0.428674	+	0.742484i	−0.996756	−	0.0804875i	$-0.974352\pi$
$431$	−8.89949	+	15.4144i	−0.428674	+	0.742484i	0.568082	+	0.822972i	$0.307686\pi$
$432$	3.62132	+	6.27231i	0.174231	+	0.301777i
$433$	−7.79899			−0.374796			−0.187398	−	0.982284i	$-0.560005\pi$
$433$	−7.79899			−0.374796			−0.187398	+	0.982284i	$0.560005\pi$
$434$	−37.9706	−	5.19615i	−1.82265	−	0.249423i
$435$		0			0
$436$	25.8137	+	44.7107i	1.23625	+	2.14125i
$437$	0.585786	−	1.01461i	0.0280220	−	0.0485355i
$438$	0.414214	−	0.717439i	0.0197919	−	0.0342806i
$439$	16.9706	+	29.3939i	0.809961	+	1.40289i	0.912890	+	0.408205i	$0.133845\pi$
$439$	16.9706	+	29.3939i	0.809961	+	1.40289i	−0.102930	+	0.994689i	$0.532822\pi$
$440$		0			0
$441$	4.92893	+	19.1757i	0.234711	+	0.913126i
$442$	56.2843			2.67717
$443$	15.1066	+	26.1654i	0.717736	+	1.24316i	0.961895	+	0.273420i	$0.0881550\pi$
$443$	15.1066	+	26.1654i	0.717736	+	1.24316i	−0.244158	+	0.969735i	$0.578512\pi$
$444$		0			0
$445$		0			0
$446$	−0.414214	−	0.717439i	−0.0196136	−	0.0339717i
$447$	−0.899495			−0.0425447
$448$	25.7635	+	3.52565i	1.21721	+	0.166571i
$449$	3.82843			0.180675			0.0903373	−	0.995911i	$-0.471205\pi$
$449$	3.82843			0.180675			0.0903373	+	0.995911i	$0.471205\pi$
$450$		0			0
$451$	−3.24264	+	5.61642i	−0.152690	+	0.264467i
$452$	−8.58579	+	14.8710i	−0.403841	+	0.699474i
$453$	−2.41421	−	4.18154i	−0.113430	−	0.196466i
$454$	−16.8284			−0.789797
$455$		0			0
$456$	−5.17157			−0.242181
$457$	12.1421	+	21.0308i	0.567985	+	0.983779i	0.996765	+	0.0803702i	$0.0256102\pi$
$457$	12.1421	+	21.0308i	0.567985	+	0.983779i	−0.428780	+	0.903409i	$0.641056\pi$
$458$	−14.0711	+	24.3718i	−0.657498	+	1.13882i
$459$	−5.82843	+	10.0951i	−0.272048	+	0.471200i
$460$		0			0
$461$	41.3137			1.92417			0.962086	−	0.272748i	$-0.0879324\pi$
$461$	41.3137			1.92417			0.962086	+	0.272748i	$0.0879324\pi$
$462$	1.34315	−	1.73205i	0.0624888	−	0.0805823i
$463$	37.0416			1.72147			0.860735	−	0.509053i	$-0.170004\pi$
$463$	37.0416			1.72147			0.860735	+	0.509053i	$0.170004\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	20.3137	−	35.1844i	0.941014	−	1.62988i
$467$	−1.55025	−	2.68512i	−0.0717371	−	0.124252i	0.827926	−	0.560838i	$-0.189521\pi$
$467$	−1.55025	−	2.68512i	−0.0717371	−	0.124252i	−0.899663	+	0.436586i	$0.856188\pi$
$468$	−52.2843			−2.41684
$469$	−15.5416	+	20.0417i	−0.717646	+	0.925439i
$470$		0			0
$471$	3.58579	+	6.21076i	0.165224	+	0.286177i
$472$	9.89949	−	17.1464i	0.455661	−	0.789228i
$473$	−1.48528	+	2.57258i	−0.0682933	+	0.118287i
$474$	7.41421	+	12.8418i	0.340546	+	0.589843i
$475$		0			0
$476$	−18.4853	−	45.2795i	−0.847271	−	2.07538i
$477$	−3.31371			−0.151724
$478$	−25.7279	−	44.5621i	−1.17677	−	2.03822i
$479$	17.8284	−	30.8797i	0.814602	−	1.41093i	−0.0950120	−	0.995476i	$-0.530289\pi$
$479$	17.8284	−	30.8797i	0.814602	−	1.41093i	0.909614	−	0.415455i	$-0.136378\pi$
$480$		0			0
$481$		0			0
$482$	−66.7696			−3.04127
$483$	0.449747	+	0.0615465i	0.0204642	+	0.00280046i
$484$	−39.4853			−1.79479
$485$		0			0
$486$	12.4853	−	21.6251i	0.566344	−	0.980936i
$487$	2.17157	−	3.76127i	0.0984034	−	0.170440i	−0.812621	−	0.582793i	$-0.801960\pi$
$487$	2.17157	−	3.76127i	0.0984034	−	0.170440i	0.911024	+	0.412353i	$0.135293\pi$
$488$	12.1066	+	20.9692i	0.548040	+	0.949233i
$489$	−5.11270			−0.231204
$490$		0			0
$491$	9.31371			0.420322			0.210161	−	0.977667i	$-0.432601\pi$
$491$	9.31371			0.420322			0.210161	+	0.977667i	$0.432601\pi$
$492$	6.20711	+	10.7510i	0.279838	+	0.484694i
$493$	−2.41421	+	4.18154i	−0.108731	+	0.188327i
$494$	16.4853	−	28.5533i	0.741708	−	1.28468i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	−11.7574	−	1.60896i	−0.527390	−	0.0721716i
$498$	13.7279			0.615163
$499$	0.414214	+	0.717439i	0.0185427	+	0.0321170i	0.875148	−	0.483856i	$-0.160764\pi$
$499$	0.414214	+	0.717439i	0.0185427	+	0.0321170i	−0.856605	+	0.515973i	$0.827431\pi$
$500$		0			0
$501$	4.64214	−	8.04041i	0.207395	−	0.359219i
$502$	−11.2426	−	19.4728i	−0.501784	−	0.869115i
$503$	15.8701			0.707611			0.353805	−	0.935319i	$-0.384887\pi$
$503$	15.8701			0.707611			0.353805	+	0.935319i	$0.384887\pi$
$504$	12.4853	+	30.5826i	0.556139	+	1.36226i
$505$		0			0
$506$	0.414214	+	0.717439i	0.0184140	+	0.0318941i
$507$	−2.13604	+	3.69973i	−0.0948648	+	0.164311i
$508$	−17.8284	+	30.8797i	−0.791009	+	1.37007i
$509$	−6.67157	−	11.5555i	−0.295712	−	0.512189i	0.679438	−	0.733733i	$-0.262224\pi$
$509$	−6.67157	−	11.5555i	−0.295712	−	0.512189i	−0.975150	+	0.221544i	$0.928890\pi$
$510$		0			0
$511$	1.34315	−	1.73205i	0.0594173	−	0.0766214i
$512$	31.2426			1.38074
$513$	3.41421	+	5.91359i	0.150741	+	0.261091i
$514$	−7.65685	+	13.2621i	−0.337729	+	0.584964i
$515$		0			0
$516$	2.84315	+	4.92447i	0.125163	+	0.216788i
$517$	1.65685			0.0728684
$518$		0			0
$519$	−1.37258			−0.0602497
$520$		0			0
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	−0.982102	−	0.188349i	$-0.939686\pi$
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	0.654166	+	0.756351i	$0.273020\pi$
$522$	3.41421	−	5.91359i	0.149436	−	0.258831i
$523$	17.8284	+	30.8797i	0.779583	+	1.35028i	0.932182	+	0.361989i	$0.117902\pi$
$523$	17.8284	+	30.8797i	0.779583	+	1.35028i	−0.152600	+	0.988288i	$0.548765\pi$
$524$	−73.9411			−3.23013
$525$		0			0
$526$	−70.1127			−3.05706
$527$	−14.4853	−	25.0892i	−0.630989	−	1.09290i
$528$	0.514719	−	0.891519i	0.0224003	−	0.0387984i
$529$	11.4142	−	19.7700i	0.496270	−	0.859565i
$530$		0			0
$531$	−12.6863			−0.550538
$532$	−28.3848	−	3.88437i	−1.23064	−	0.168409i
$533$	−37.7990			−1.63726
$534$	−4.32843	−	7.49706i	−0.187309	−	0.324429i
$535$		0			0
$536$	−21.1569	+	36.6447i	−0.913837	+	1.58281i
$537$	2.07107	+	3.58719i	0.0893732	+	0.154799i
$538$	−49.3848			−2.12913
$539$	4.14214	−	4.05845i	0.178414	−	0.174810i
$540$		0			0
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	0.776241	−	0.630436i	$-0.217124\pi$
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	−0.934094	+	0.357026i	$0.883791\pi$
$542$	19.8995	−	34.4669i	0.854756	−	1.48048i
$543$	−0.550253	+	0.953065i	−0.0236136	+	0.0408999i
$544$	3.82843	+	6.63103i	0.164142	+	0.284303i
$545$		0			0
$546$	12.6569	+	1.73205i	0.541663	+	0.0741249i
$547$	−24.8995			−1.06463			−0.532313	−	0.846548i	$-0.678677\pi$
$547$	−24.8995			−1.06463			−0.532313	+	0.846548i	$0.678677\pi$
$548$	−18.4853	−	32.0174i	−0.789652	−	1.36772i
$549$	7.75736	−	13.4361i	0.331076	−	0.573441i
$550$		0			0
$551$	1.41421	+	2.44949i	0.0602475	+	0.104352i
$552$	0.757359			0.0322354
$553$	14.8284	+	36.3221i	0.630569	+	1.54457i
$554$	38.9706			1.65570
$555$		0			0
$556$	30.8995	−	53.5195i	1.31043	−	2.26973i
$557$	11.1421	−	19.2987i	0.472107	−	0.817714i	−0.527383	−	0.849628i	$-0.676827\pi$
$557$	11.1421	−	19.2987i	0.472107	−	0.817714i	0.999491	+	0.0319135i	$0.0101601\pi$
$558$	20.4853	+	35.4815i	0.867211	+	1.50205i
$559$	−17.3137			−0.732292
$560$		0			0
$561$	1.65685			0.0699524
$562$	−36.5563	−	63.3175i	−1.54204	−	2.67089i
$563$	20.8640	−	36.1374i	0.879311	−	1.52301i	0.0272129	−	0.999630i	$-0.491337\pi$
$563$	20.8640	−	36.1374i	0.879311	−	1.52301i	0.852098	−	0.523382i	$-0.175330\pi$
$564$	1.58579	−	2.74666i	0.0667737	−	0.115655i
$565$		0			0
$566$	33.7990			1.42068
$567$	12.1360	−	15.6500i	0.509666	−	0.657238i
$568$	−19.7990			−0.830747
$569$	−3.82843	−	6.63103i	−0.160496	−	0.277987i	0.774551	−	0.632512i	$-0.217976\pi$
$569$	−3.82843	−	6.63103i	−0.160496	−	0.277987i	−0.935047	+	0.354525i	$0.884643\pi$
$570$		0			0
$571$	−4.58579	+	7.94282i	−0.191909	+	0.332396i	−0.945883	−	0.324508i	$-0.894801\pi$
$571$	−4.58579	+	7.94282i	−0.191909	+	0.332396i	0.753974	+	0.656905i	$0.228135\pi$
$572$	7.65685	+	13.2621i	0.320149	+	0.554515i
$573$	−5.31371			−0.221983
$574$	18.8995	+	46.2941i	0.788850	+	1.93228i
$575$		0			0
$576$	−13.8995	−	24.0746i	−0.579146	−	1.00311i
$577$	−21.9706	+	38.0541i	−0.914646	+	1.58421i	−0.107228	+	0.994234i	$0.534198\pi$
$577$	−21.9706	+	38.0541i	−0.914646	+	1.58421i	−0.807418	+	0.589980i	$0.799136\pi$
$578$	7.62132	−	13.2005i	0.317005	−	0.549069i
$579$	−0.414214	−	0.717439i	−0.0172141	−	0.0298157i
$580$		0			0
$581$	35.9853	+	4.92447i	1.49292	+	0.204302i
$582$	11.6569			0.483192
$583$	0.485281	+	0.840532i	0.0200983	+	0.0348113i
$584$	1.82843	−	3.16693i	0.0756609	−	0.131048i
$585$		0			0
$586$	19.3137	+	33.4523i	0.797842	+	1.38190i
$587$	34.2843			1.41506			0.707532	−	0.706682i	$-0.249809\pi$
$587$	34.2843			1.41506			0.707532	+	0.706682i	$0.249809\pi$
$588$	−2.76346	−	10.7510i	−0.113963	−	0.443365i
$589$	−16.9706			−0.699260
$590$		0			0
$591$	−2.55635	+	4.42773i	−0.105154	+	0.182132i
$592$		0			0
$593$	2.10051	+	3.63818i	0.0862574	+	0.149402i	0.905926	−	0.423435i	$-0.139176\pi$
$593$	2.10051	+	3.63818i	0.0862574	+	0.149402i	−0.819669	+	0.572838i	$0.805843\pi$
$594$	−4.82843			−0.198113
$595$		0			0
$596$	−8.31371			−0.340543
$597$	2.00000	+	3.46410i	0.0818546	+	0.141776i
$598$	−2.41421	+	4.18154i	−0.0987245	+	0.170996i
$599$	−3.17157	+	5.49333i	−0.129587	+	0.224451i	−0.923517	−	0.383558i	$-0.874698\pi$
$599$	−3.17157	+	5.49333i	−0.129587	+	0.224451i	0.793930	+	0.608010i	$0.208032\pi$
$600$		0			0
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$	8.65685	+	21.2049i	0.352827	+	0.864246i
$603$	27.1127			1.10411
$604$	−22.3137	−	38.6485i	−0.907932	−	1.57258i
$605$		0			0
$606$	−5.15685	+	8.93193i	−0.209483	+	0.362835i
$607$	19.1066	+	33.0936i	0.775513	+	1.34323i	0.934506	+	0.355948i	$0.115842\pi$
$607$	19.1066	+	33.0936i	0.775513	+	1.34323i	−0.158993	+	0.987280i	$0.550825\pi$
$608$	4.48528			0.181902
$609$	−0.671573	+	0.866025i	−0.0272135	+	0.0350931i
$610$		0			0
$611$	4.82843	+	8.36308i	0.195337	+	0.338334i
$612$	−26.1421	+	45.2795i	−1.05673	+	1.83032i
$613$	17.7279	−	30.7057i	0.716024	−	1.24019i	−0.246539	−	0.969133i	$-0.579293\pi$
$613$	17.7279	−	30.7057i	0.716024	−	1.24019i	0.962563	−	0.271057i	$-0.0873732\pi$
$614$	5.74264	+	9.94655i	0.231754	+	0.401410i
$615$		0			0
$616$	5.92893	−	7.64564i	0.238883	−	0.308052i
$617$	−11.3137			−0.455473			−0.227736	−	0.973723i	$-0.573132\pi$
$617$	−11.3137			−0.455473			−0.227736	+	0.973723i	$0.573132\pi$
$618$	1.20711	+	2.09077i	0.0485570	+	0.0841031i
$619$	−12.7574	+	22.0964i	−0.512762	+	0.888129i	0.487129	+	0.873330i	$0.338044\pi$
$619$	−12.7574	+	22.0964i	−0.512762	+	0.888129i	−0.999890	+	0.0147990i	$0.995289\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	31.7990			1.27502
$623$	−8.65685	−	21.2049i	−0.346830	−	0.849555i
$624$	6.00000			0.240192
$625$		0			0
$626$	7.65685	−	13.2621i	0.306029	−	0.530059i
$627$	0.485281	−	0.840532i	0.0193803	−	0.0335676i
$628$	33.1421	+	57.4039i	1.32252	+	2.29066i
$629$		0			0
$630$		0			0
$631$	−20.1421			−0.801846			−0.400923	−	0.916112i	$-0.631310\pi$
$631$	−20.1421			−0.801846			−0.400923	+	0.916112i	$0.631310\pi$
$632$	32.7279	+	56.6864i	1.30185	+	2.25486i
$633$	−4.24264	+	7.34847i	−0.168630	+	0.292075i
$634$	16.6569	−	28.8505i	0.661528	−	1.14580i
$635$		0			0
$636$	1.85786			0.0736691
$637$	32.5563	+	9.08052i	1.28993	+	0.359783i
$638$	−2.00000			−0.0791808
$639$	6.34315	+	10.9867i	0.250931	+	0.434625i
$640$		0			0
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	0.367354	+	0.930081i	$0.380264\pi$
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	−0.989151	+	0.146903i	$0.953070\pi$
$642$	−5.62132	−	9.73641i	−0.221856	−	0.384266i
$643$	−26.2843			−1.03655			−0.518275	−	0.855214i	$-0.673426\pi$
$643$	−26.2843			−1.03655			−0.518275	+	0.855214i	$0.673426\pi$
$644$	4.15685	+	0.568852i	0.163803	+	0.0224159i
$645$		0			0
$646$	−16.4853	−	28.5533i	−0.648605	−	1.12342i
$647$	−15.5208	+	26.8828i	−0.610186	+	1.05687i	0.381022	+	0.924566i	$0.375572\pi$
$647$	−15.5208	+	26.8828i	−0.610186	+	1.05687i	−0.991209	+	0.132308i	$0.957761\pi$
$648$	16.5208	−	28.6149i	0.648999	−	1.12410i
$649$	1.85786	+	3.21792i	0.0729276	+	0.126314i
$650$		0			0
$651$	−2.48528	−	6.08767i	−0.0974059	−	0.238595i
$652$	−47.2548			−1.85064
$653$	−9.58579	−	16.6031i	−0.375121	−	0.649728i	0.615224	−	0.788352i	$-0.289065\pi$
$653$	−9.58579	−	16.6031i	−0.375121	−	0.649728i	−0.990345	+	0.138624i	$0.955732\pi$
$654$	−6.74264	+	11.6786i	−0.263658	+	0.456669i
$655$		0			0
$656$	11.7426	+	20.3389i	0.458473	+	0.794099i
$657$	−2.34315			−0.0914148
$658$	7.82843	−	10.0951i	0.305184	−	0.393549i
$659$	21.1716			0.824727			0.412364	−	0.911019i	$-0.364703\pi$
$659$	21.1716			0.824727			0.412364	+	0.911019i	$0.364703\pi$
$660$		0			0
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	0.370679	+	0.928761i	$0.379125\pi$
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	−0.989670	+	0.143363i	$0.954208\pi$
$662$	27.7279	−	48.0262i	1.07768	−	1.86659i
$663$	4.82843	+	8.36308i	0.187521	+	0.324795i
$664$	60.5980			2.35166
$665$		0			0
$666$		0			0
$667$	−0.207107	−	0.358719i	−0.00801921	−	0.0138897i
$668$	42.9056	−	74.3147i	1.66007	−	2.87532i
$669$	0.0710678	−	0.123093i	0.00274764	−	0.00475905i
$670$		0			0
$671$	−4.54416			−0.175425
$672$	0.656854	+	1.60896i	0.0253387	+	0.0620669i
$673$	−29.6569			−1.14319			−0.571594	−	0.820537i	$-0.693675\pi$
$673$	−29.6569			−1.14319			−0.571594	+	0.820537i	$0.693675\pi$
$674$	−11.0711	−	19.1757i	−0.426442	−	0.738619i
$675$		0			0
$676$	−19.7426	+	34.1953i	−0.759332	+	1.31520i
$677$	−14.0711	−	24.3718i	−0.540795	−	0.936685i	−0.998859	−	0.0477651i	$-0.984790\pi$
$677$	−14.0711	−	24.3718i	−0.540795	−	0.936685i	0.458064	−	0.888919i	$-0.348543\pi$
$678$	−4.48528			−0.172256
$679$	30.5563	+	4.18154i	1.17265	+	0.160473i
$680$		0			0
$681$	−1.44365	−	2.50048i	−0.0553208	−	0.0958185i
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−17.3787	+	30.1008i	−0.664977	+	1.15177i	0.314315	+	0.949319i	$0.398225\pi$
$683$	−17.3787	+	30.1008i	−0.664977	+	1.15177i	−0.979292	+	0.202455i	$0.935108\pi$
$684$	15.3137	+	26.5241i	0.585534	+	1.01418i
$685$		0			0
$686$	−5.15685	−	44.4135i	−0.196890	−	1.69571i
$687$	−4.82843			−0.184216
$688$	5.37868	+	9.31615i	0.205060	+	0.355175i
$689$	−2.82843	+	4.89898i	−0.107754	+	0.186636i
$690$		0			0
$691$	−0.414214	−	0.717439i	−0.0157574	−	0.0272927i	0.858039	−	0.513584i	$-0.171683\pi$
$691$	−0.414214	−	0.717439i	−0.0157574	−	0.0272927i	−0.873797	+	0.486292i	$0.838349\pi$
$692$	−12.6863			−0.482260
$693$	−6.14214	−	0.840532i	−0.233320	−	0.0319292i
$694$	19.1421			0.726626
$695$		0			0
$696$	−0.914214	+	1.58346i	−0.0346532	+	0.0600211i
$697$	−18.8995	+	32.7349i	−0.715869	+	1.23992i
$698$	−18.5208	−	32.0790i	−0.701023	−	1.21421i
$699$	6.97056			0.263651
$700$		0			0
$701$	−3.20101			−0.120900			−0.0604502	−	0.998171i	$-0.519254\pi$
$701$	−3.20101			−0.120900			−0.0604502	+	0.998171i	$0.519254\pi$
$702$	−14.0711	−	24.3718i	−0.531078	−	0.919854i
$703$		0			0
$704$	−4.07107	+	7.05130i	−0.153434	+	0.265756i
$705$		0			0
$706$	−64.7696			−2.43763
$707$	−16.7218	+	21.5636i	−0.628889	+	0.810982i
$708$	7.11270			0.267312
$709$	−7.84315	−	13.5847i	−0.294556	−	0.510185i	0.680326	−	0.732910i	$-0.261838\pi$
$709$	−7.84315	−	13.5847i	−0.294556	−	0.510185i	−0.974881	+	0.222725i	$0.928505\pi$
$710$		0			0
$711$	20.9706	−	36.3221i	0.786458	−	1.36218i
$712$	−19.1066	−	33.0936i	−0.716050	−	1.24024i
$713$	2.48528			0.0930745
$714$	7.82843	−	10.0951i	0.292972	−	0.377801i
$715$		0			0
$716$	19.1421	+	33.1552i	0.715375	+	1.23907i
$717$	4.41421	−	7.64564i	0.164852	−	0.285532i
$718$	−12.0711	+	20.9077i	−0.450488	+	0.780269i
$719$	−10.5563	−	18.2841i	−0.393685	−	0.681883i	0.599247	−	0.800564i	$-0.295467\pi$
$719$	−10.5563	−	18.2841i	−0.393685	−	0.681883i	−0.992932	+	0.118681i	$0.962133\pi$
$720$		0			0
$721$	2.41421	+	5.91359i	0.0899100	+	0.220234i
$722$	26.5563			0.988325
$723$	−5.72792	−	9.92105i	−0.213024	−	0.368968i
$724$	−5.08579	+	8.80884i	−0.189012	+	0.327378i
$725$		0			0
$726$	−5.15685	−	8.93193i	−0.191389	−	0.331495i
$727$	37.5858			1.39398			0.696990	−	0.717081i	$-0.254522\pi$
$727$	37.5858			1.39398			0.696990	+	0.717081i	$0.254522\pi$
$728$	55.8701	+	7.64564i	2.07068	+	0.283366i
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−8.65685	+	14.9941i	−0.320185	+	0.554577i
$732$	−4.34924	+	7.53311i	−0.160753	+	0.278432i
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	−6.65685			−0.245709
$735$		0			0
$736$	−0.656854			−0.0242120
$737$	−3.97056	−	6.87722i	−0.146258	−	0.253326i
$738$	26.7279	−	46.2941i	0.983868	−	1.70411i
$739$	10.5563	−	18.2841i	0.388322	−	0.672593i	−0.603902	−	0.797058i	$-0.706388\pi$
$739$	10.5563	−	18.2841i	0.388322	−	0.672593i	0.992224	+	0.124466i	$0.0397216\pi$
$740$		0			0
$741$	5.65685			0.207810
$742$	7.41421	+	1.01461i	0.272184	+	0.0372476i
$743$	16.0711			0.589590			0.294795	−	0.955560i	$-0.404749\pi$
$743$	16.0711			0.589590			0.294795	+	0.955560i	$0.404749\pi$
$744$	−5.48528	−	9.50079i	−0.201100	−	0.348316i
$745$		0			0
$746$	25.3137	−	43.8446i	0.926801	−	1.60527i
$747$	−19.4142	−	33.6264i	−0.710329	−	1.23033i
$748$	15.3137			0.559925
$749$	−11.2426	−	27.5387i	−0.410797	−	1.00624i
$750$		0			0
$751$	15.1716	+	26.2779i	0.553619	+	0.958895i	0.998010	+	0.0630625i	$0.0200868\pi$
$751$	15.1716	+	26.2779i	0.553619	+	0.958895i	−0.444391	+	0.895833i	$0.646580\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$	1.92893	−	3.34101i	0.0702942	−	0.121753i
$754$	−5.82843	−	10.0951i	−0.212259	−	0.367643i
$755$		0			0
$756$	−14.9853	+	19.3242i	−0.545009	+	0.702816i
$757$	31.4558			1.14328			0.571641	−	0.820504i	$-0.306307\pi$
$757$	31.4558			1.14328			0.571641	+	0.820504i	$0.306307\pi$
$758$	32.3848	+	56.0921i	1.17627	+	2.03736i
$759$	−0.0710678	+	0.123093i	−0.00257960	+	0.00446800i
$760$		0			0
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	0.769191	−	0.639019i	$-0.220659\pi$
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	−0.938002	+	0.346630i	$0.887326\pi$
$762$	−9.31371			−0.337400
$763$	−21.8640	+	28.1946i	−0.791529	+	1.02071i
$764$	−49.1127			−1.77684
$765$		0			0
$766$	3.50000	−	6.06218i	0.126460	−	0.219035i
$767$	−10.8284	+	18.7554i	−0.390992	+	0.677218i
$768$	6.20711	+	10.7510i	0.223980	+	0.387944i
$769$	−0.627417			−0.0226252			−0.0113126	−	0.999936i	$-0.503601\pi$
$769$	−0.627417			−0.0226252			−0.0113126	+	0.999936i	$0.503601\pi$
$770$		0			0
$771$	−2.62742			−0.0946241
$772$	−3.82843	−	6.63103i	−0.137788	−	0.238656i
$773$	−18.5563	+	32.1405i	−0.667425	+	1.15601i	0.311196	+	0.950346i	$0.399270\pi$
$773$	−18.5563	+	32.1405i	−0.667425	+	1.15601i	−0.978622	+	0.205669i	$0.934063\pi$
$774$	12.2426	−	21.2049i	0.440053	−	0.762194i
$775$		0			0
$776$	51.4558			1.84716
$777$		0			0
$778$	−57.1127			−2.04759
$779$	11.0711	+	19.1757i	0.396662	+	0.687039i
$780$		0			0
$781$	1.85786	−	3.21792i	0.0664796	−	0.115146i
$782$	2.41421	+	4.18154i	0.0863321	+	0.149532i
$783$	2.41421			0.0862770
$784$	−5.22792	−	20.3389i	−0.186712	−	0.726388i
$785$		0			0
$786$	−9.65685	−	16.7262i	−0.344449	−	0.596602i
$787$	1.27817	−	2.21386i	0.0455620	−	0.0789157i	−0.842345	−	0.538939i	$-0.818825\pi$
$787$	1.27817	−	2.21386i	0.0455620	−	0.0789157i	0.887907	+	0.460023i	$0.152159\pi$
$788$	−23.6274	+	40.9239i	−0.841692	+	1.45785i
$789$	−6.01472	−	10.4178i	−0.214130	−	0.370883i
$790$		0			0
$791$	−11.7574	−	1.60896i	−0.418044	−	0.0572080i
$792$	−10.3431			−0.367528
$793$	−13.2426	−	22.9369i	−0.470260	−	0.814514i
$794$	20.0711	−	34.7641i	0.712296	−	1.23373i
$795$		0			0
$796$	18.4853	+	32.0174i	0.655193	+	1.13483i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	−2.82843	−	6.92820i	−0.100125	−	0.245256i
$799$	9.65685			0.341635
$800$		0			0
$801$	−12.2426	+	21.2049i	−0.432572	+	0.749237i
$802$	36.5919	−	63.3790i	1.29210	−	2.23799i
$803$	0.343146	+	0.594346i	0.0121094	+	0.0209740i
$804$	−15.2010			−0.536098
$805$		0			0
$806$	69.9411			2.46357
$807$	−4.23654	−	7.33791i	−0.149133	−	0.258307i
$808$	−22.7635	+	39.4275i	−0.800816	+	1.38705i
$809$	−17.8137	+	30.8542i	−0.626297	+	1.08478i	0.361992	+	0.932181i	$0.382097\pi$
$809$	−17.8137	+	30.8542i	−0.626297	+	1.08478i	−0.988289	+	0.152596i	$0.951237\pi$
$810$		0			0
$811$	−20.6274			−0.724327			−0.362163	−	0.932115i	$-0.617962\pi$
$811$	−20.6274			−0.724327			−0.362163	+	0.932115i	$0.617962\pi$
$812$	−6.20711	+	8.00436i	−0.217827	+	0.280898i
$813$	6.82843			0.239483
$814$		0			0
$815$		0			0
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	5.07107	+	8.78335i	0.177414	+	0.307290i
$818$	35.7279			1.24920
$819$	−13.6569	−	33.4523i	−0.477209	−	1.16892i
$820$		0			0
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	−0.892739	−	0.450575i	$-0.851219\pi$
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	0.0561604	−	0.998422i	$-0.482114\pi$
$822$	4.82843	−	8.36308i	0.168411	−	0.291696i
$823$	1.03553	−	1.79360i	0.0360964	−	0.0625209i	−0.847413	−	0.530935i	$-0.821841\pi$
$823$	1.03553	−	1.79360i	0.0360964	−	0.0625209i	0.883509	+	0.468414i	$0.155174\pi$
$824$	5.32843	+	9.22911i	0.185625	+	0.321511i
$825$		0			0
$826$	28.3848	+	3.88437i	0.987633	+	0.135154i
$827$	26.2132			0.911522			0.455761	−	0.890102i	$-0.349367\pi$
$827$	26.2132			0.911522			0.455761	+	0.890102i	$0.349367\pi$
$828$	−2.24264	−	3.88437i	−0.0779372	−	0.134991i
$829$	−14.6569	+	25.3864i	−0.509054	+	0.881707i	0.490891	+	0.871221i	$0.336671\pi$
$829$	−14.6569	+	25.3864i	−0.509054	+	0.881707i	−0.999945	+	0.0104859i	$0.996662\pi$
$830$		0			0
$831$	3.34315	+	5.79050i	0.115972	+	0.200870i
$832$	−47.4558			−1.64524
$833$	24.1421	−	23.6544i	0.836475	−	0.819575i
$834$	16.1421			0.558956
$835$		0			0
$836$	4.48528	−	7.76874i	0.155127	−	0.268687i
$837$	−7.24264	+	12.5446i	−0.250342	+	0.433606i
$838$	−0.828427	−	1.43488i	−0.0286175	−	0.0495670i
$839$	15.1716			0.523781			0.261890	−	0.965098i	$-0.415654\pi$
$839$	15.1716			0.523781			0.261890	+	0.965098i	$0.415654\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	16.2782	+	28.1946i	0.560983	+	0.971651i
$843$	6.27208	−	10.8636i	0.216022	−	0.374161i
$844$	−39.2132	+	67.9193i	−1.34977	+	2.33788i
$845$		0			0
$846$	−13.6569			−0.469532
$847$	−10.3137	−	25.2633i	−0.354383	−	0.868058i
$848$	3.51472			0.120696
$849$	2.89949	+	5.02207i	0.0995104	+	0.172357i
$850$		0			0
$851$		0			0
$852$	−3.55635	−	6.15978i	−0.121839	−	0.211030i
$853$	−2.54416			−0.0871102			−0.0435551	−	0.999051i	$-0.513868\pi$
$853$	−2.54416			−0.0871102			−0.0435551	+	0.999051i	$0.513868\pi$
$854$	−21.4706	+	27.6873i	−0.734708	+	0.947441i
$855$		0			0
$856$	−24.8137	−	42.9786i	−0.848115	−	1.46898i
$857$	17.1421	−	29.6910i	0.585564	−	1.01423i	−0.409241	−	0.912426i	$-0.634206\pi$
$857$	17.1421	−	29.6910i	0.585564	−	1.01423i	0.994805	−	0.101800i	$-0.0324603\pi$
$858$	−2.00000	+	3.46410i	−0.0682789	+	0.118262i
$859$	−0.686292	−	1.18869i	−0.0234160	−	0.0405576i	0.854080	−	0.520142i	$-0.174121\pi$
$859$	−0.686292	−	1.18869i	−0.0234160	−	0.0405576i	−0.877496	+	0.479584i	$0.840788\pi$
$860$		0			0
$861$	−5.25736	+	6.77962i	−0.179170	+	0.231049i
$862$	−42.9706			−1.46358
$863$	7.27817	+	12.6062i	0.247752	+	0.429119i	0.962902	−	0.269852i	$-0.0869749\pi$
$863$	7.27817	+	12.6062i	0.247752	+	0.429119i	−0.715150	+	0.698971i	$0.753642\pi$
$864$	1.91421	−	3.31552i	0.0651229	−	0.112796i
$865$		0			0
$866$	−9.41421	−	16.3059i	−0.319908	−	0.554097i
$867$	2.61522			0.0888177
$868$	−22.9706	−	56.2662i	−0.779672	−	1.90980i
$869$	−12.2843			−0.416715
$870$		0			0
$871$	23.1421	−	40.0834i	0.784141	−	1.35817i
$872$	−29.7635	+	51.5518i	−1.00792	+	1.74576i
$873$	−16.4853	−	28.5533i	−0.557942	−	0.966384i
$874$	2.82843			0.0956730
$875$		0			0
$876$	1.31371			0.0443861
$877$	12.5858	+	21.7992i	0.424992	+	0.736107i	0.996420	−	0.0845449i	$-0.0269436\pi$
$877$	12.5858	+	21.7992i	0.424992	+	0.736107i	−0.571428	+	0.820652i	$0.693610\pi$
$878$	−40.9706	+	70.9631i	−1.38269	+	2.39489i
$879$	−3.31371	+	5.73951i	−0.111769	+	0.193589i
$880$		0			0
$881$	1.82843			0.0616013			0.0308006	−	0.999526i	$-0.490194\pi$
$881$	1.82843			0.0616013			0.0308006	+	0.999526i	$0.490194\pi$
$882$	−34.1421	+	33.4523i	−1.14963	+	1.12640i
$883$	−18.2843			−0.615315			−0.307657	−	0.951497i	$-0.599545\pi$
$883$	−18.2843			−0.615315			−0.307657	+	0.951497i	$0.599545\pi$
$884$	44.6274	+	77.2970i	1.50098	+	2.59978i
$885$		0			0
$886$	−36.4706	+	63.1689i	−1.22525	+	2.12220i
$887$	14.9645	+	25.9192i	0.502458	+	0.870282i	0.999996	+	0.00284012i	$0.000904038\pi$
$887$	14.9645	+	25.9192i	0.502458	+	0.870282i	−0.497538	+	0.867442i	$0.665763\pi$
$888$		0			0
$889$	−24.4142	−	3.34101i	−0.818826	−	0.112054i
$890$		0			0
$891$	3.10051	+	5.37023i	0.103871	+	0.179910i
$892$	0.656854	−	1.13770i	0.0219931	−	0.0380932i
$893$	2.82843	−	4.89898i	0.0946497	−	0.163938i
$894$	−1.08579	−	1.88064i	−0.0363141	−	0.0628979i
$895$		0			0
$896$	20.5563	+	50.3526i	0.686739	+	1.68216i
$897$	−0.828427			−0.0276604
$898$	4.62132	+	8.00436i	0.154215	+	0.267109i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$		0			0
$901$	2.82843	+	4.89898i	0.0942286	+	0.163209i
$902$	−15.6569			−0.521316
$903$	−2.40812	+	3.10538i	−0.0801371	+	0.103341i
$904$	−19.7990			−0.658505
$905$		0			0
$906$	5.82843	−	10.0951i	0.193637	−	0.335388i
$907$	−7.10660	+	12.3090i	−0.235971	+	0.408713i	−0.959554	−	0.281523i	$-0.909160\pi$
$907$	−7.10660	+	12.3090i	−0.235971	+	0.408713i	0.723584	+	0.690237i	$0.242494\pi$
$908$	−13.3431	−	23.1110i	−0.442808	−	0.766966i
$909$	29.1716			0.967560
$910$		0			0
$911$	−10.2010			−0.337975			−0.168987	−	0.985618i	$-0.554050\pi$
$911$	−10.2010			−0.337975			−0.168987	+	0.985618i	$0.554050\pi$
$912$	−1.75736	−	3.04384i	−0.0581920	−	0.100791i
$913$	−5.68629	+	9.84895i	−0.188189	+	0.325953i
$914$	−29.3137	+	50.7728i	−0.969611	+	1.67942i
$915$		0			0
$916$	−44.6274			−1.47453
$917$	−19.3137	−	47.3087i	−0.637795	−	1.56227i
$918$	−28.1421			−0.928829
$919$	21.5563	+	37.3367i	0.711078	+	1.23162i	0.964453	+	0.264256i	$0.0851262\pi$
$919$	21.5563	+	37.3367i	0.711078	+	1.23162i	−0.253374	+	0.967368i	$0.581540\pi$
$920$		0			0
$921$	−0.985281	+	1.70656i	−0.0324661	+	0.0562330i
$922$	49.8701	+	86.3775i	1.64238	+	2.84469i
$923$	21.6569			0.712844
$924$	3.44365	+	0.471253i	0.113288	+	0.0155031i
$925$		0			0
$926$	44.7132	+	77.4455i	1.46937	+	2.54502i
$927$	3.41421	−	5.91359i	0.112137	−	0.194228i
$928$	0.792893	−	1.37333i	0.0260280	−	0.0450818i
$929$	−2.74264	−	4.75039i	−0.0899831	−	0.155855i	0.817521	−	0.575899i	$-0.195348\pi$
$929$	−2.74264	−	4.75039i	−0.0899831	−	0.155855i	−0.907504	+	0.420044i	$0.862015\pi$
$930$		0			0
$931$	−4.92893	−	19.1757i	−0.161539	−	0.628457i
$932$	64.4264			2.11036
$933$	2.72792	+	4.72490i	0.0893082	+	0.154686i
$934$	3.74264	−	6.48244i	0.122463	−	0.212112i
$935$		0			0
$936$	−30.1421	−	52.2077i	−0.985227	−	1.70646i
$937$	−34.6274			−1.13123			−0.565614	−	0.824670i	$-0.691361\pi$
$937$	−34.6274			−1.13123			−0.565614	+	0.824670i	$0.691361\pi$
$938$	−60.6630	−	8.30153i	−1.98072	−	0.271055i
$939$	2.62742			0.0857425
$940$		0			0
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	−0.191254	−	0.981541i	$-0.561255\pi$
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	0.945666	−	0.325139i	$-0.105411\pi$
$942$	−8.65685	+	14.9941i	−0.282056	+	0.488535i
$943$	−1.62132	−	2.80821i	−0.0527975	−	0.0914479i
$944$	13.4558			0.437950
$945$		0			0
$946$	−7.17157			−0.233168
$947$	16.5919	+	28.7380i	0.539164	+	0.933859i	0.998949	+	0.0458290i	$0.0145929\pi$
$947$	16.5919	+	28.7380i	0.539164	+	0.933859i	−0.459786	+	0.888030i	$0.652074\pi$
$948$	−11.7574	+	20.3643i	−0.381861	+	0.661403i
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	5.71573			0.185345
$952$	34.5563	−	44.5621i	1.11998	−	1.44426i
$953$	13.6569			0.442389			0.221194	−	0.975230i	$-0.429004\pi$
$953$	13.6569			0.442389			0.221194	+	0.975230i	$0.429004\pi$
$954$	−4.00000	−	6.92820i	−0.129505	−	0.224309i
$955$		0			0
$956$	40.7990	−	70.6659i	1.31953	−	2.28550i
$957$	−0.171573	−	0.297173i	−0.00554616	−	0.00960624i
$958$	86.0833			2.78122
$959$	15.6569	−	20.1903i	0.505586	−	0.651978i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	−15.8995	+	27.5387i	−0.512354	+	0.887423i
$964$	−52.9411	−	91.6967i	−1.70512	−	2.95335i
$965$		0			0
$966$	0.414214	+	1.01461i	0.0133271	+	0.0326446i
$967$	−37.5269			−1.20678			−0.603392	−	0.797445i	$-0.706185\pi$
$967$	−37.5269			−1.20678			−0.603392	+	0.797445i	$0.706185\pi$
$968$	−22.7635	−	39.4275i	−0.731645	−	1.26725i
$969$	2.82843	−	4.89898i	0.0908622	−	0.157378i
$970$		0			0
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	0.991783	−	0.127933i	$-0.0408342\pi$
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	−0.606685	+	0.794943i	$0.707501\pi$
$972$	39.5980			1.27011
$973$	42.3137	+	5.79050i	1.35652	+	0.185635i
$974$	10.4853			0.335970
$975$		0			0
$976$	−8.22792	+	14.2512i	−0.263369	+	0.456169i
$977$	−0.656854	+	1.13770i	−0.0210146	+	0.0363984i	−0.876341	−	0.481690i	$-0.840023\pi$
$977$	−0.656854	+	1.13770i	−0.0210146	+	0.0363984i	0.855327	+	0.518089i	$0.173356\pi$
$978$	−6.17157	−	10.6895i	−0.197345	−	0.341812i
$979$	7.17157			0.229204
$980$		0			0
$981$	38.1421			1.21778
$982$	11.2426	+	19.4728i	0.358767	+	0.621403i
$983$	14.1066	−	24.4334i	0.449931	−	0.779303i	−0.548450	−	0.836183i	$-0.684782\pi$
$983$	14.1066	−	24.4334i	0.449931	−	0.779303i	0.998381	+	0.0568803i	$0.0181153\pi$
$984$	−7.15685	+	12.3960i	−0.228152	+	0.395171i
$985$		0			0
$986$	−11.6569			−0.371230
$987$	2.17157	+	0.297173i	0.0691219	+	0.00945912i
$988$	52.2843			1.66338
$989$	−0.742641	−	1.28629i	−0.0236146	−	0.0409017i
$990$		0			0
$991$	2.17157	−	3.76127i	0.0689823	−	0.119481i	−0.829471	−	0.558549i	$-0.811358\pi$
$991$	2.17157	−	3.76127i	0.0689823	−	0.119481i	0.898454	+	0.439069i	$0.144691\pi$
$992$	4.75736	+	8.23999i	0.151046	+	0.261620i
$993$	9.51472			0.301940
$994$	−10.8284	−	26.5241i	−0.343457	−	0.841294i
$995$		0			0
$996$	10.8848	+	18.8530i	0.344897	+	0.597380i
$997$	16.7279	−	28.9736i	0.529779	−	0.917603i	−0.469618	−	0.882870i	$-0.655608\pi$
$997$	16.7279	−	28.9736i	0.529779	−	0.917603i	0.999397	−	0.0347337i	$-0.0110583\pi$
$998$	−1.00000	+	1.73205i	−0.0316544	+	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.e.c.151.2		4
5.2	odd	4		175.2.k.a.74.1		8
5.3	odd	4		175.2.k.a.74.4		8
5.4	even	2		35.2.e.a.11.1	✓	4
7.2	even	3	inner	175.2.e.c.51.2		4
7.3	odd	6		1225.2.a.m.1.1		2
7.4	even	3		1225.2.a.k.1.1		2
15.14	odd	2		315.2.j.e.46.2		4
20.19	odd	2		560.2.q.k.81.1		4
35.2	odd	12		175.2.k.a.149.4		8
35.3	even	12		1225.2.b.h.99.4		4
35.4	even	6		245.2.a.h.1.2		2
35.9	even	6		35.2.e.a.16.1	yes	4
35.17	even	12		1225.2.b.h.99.1		4
35.18	odd	12		1225.2.b.g.99.4		4
35.19	odd	6		245.2.e.e.226.1		4
35.23	odd	12		175.2.k.a.149.1		8
35.24	odd	6		245.2.a.g.1.2		2
35.32	odd	12		1225.2.b.g.99.1		4
35.34	odd	2		245.2.e.e.116.1		4
105.44	odd	6		315.2.j.e.226.2		4
105.59	even	6		2205.2.a.q.1.1		2
105.74	odd	6		2205.2.a.n.1.1		2
140.39	odd	6		3920.2.a.bq.1.2		2
140.59	even	6		3920.2.a.bv.1.1		2
140.79	odd	6		560.2.q.k.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.1	✓	4	5.4	even	2
35.2.e.a.16.1	yes	4	35.9	even	6
175.2.e.c.51.2		4	7.2	even	3	inner
175.2.e.c.151.2		4	1.1	even	1	trivial
175.2.k.a.74.1		8	5.2	odd	4
175.2.k.a.74.4		8	5.3	odd	4
175.2.k.a.149.1		8	35.23	odd	12
175.2.k.a.149.4		8	35.2	odd	12
245.2.a.g.1.2		2	35.24	odd	6
245.2.a.h.1.2		2	35.4	even	6
245.2.e.e.116.1		4	35.34	odd	2
245.2.e.e.226.1		4	35.19	odd	6
315.2.j.e.46.2		4	15.14	odd	2
315.2.j.e.226.2		4	105.44	odd	6
560.2.q.k.81.1		4	20.19	odd	2
560.2.q.k.401.1		4	140.79	odd	6
1225.2.a.k.1.1		2	7.4	even	3
1225.2.a.m.1.1		2	7.3	odd	6
1225.2.b.g.99.1		4	35.32	odd	12
1225.2.b.g.99.4		4	35.18	odd	12
1225.2.b.h.99.1		4	35.17	even	12
1225.2.b.h.99.4		4	35.3	even	12
2205.2.a.n.1.1		2	105.74	odd	6
2205.2.a.q.1.1		2	105.59	even	6
3920.2.a.bq.1.2		2	140.39	odd	6
3920.2.a.bv.1.1		2	140.59	even	6

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(-1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(-1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(1.41421 + 2.44949i) q^{9} +(0.414214 - 0.717439i) q^{11} +(-0.792893 - 1.37333i) q^{12} +4.82843 q^{13} +(-2.41421 - 5.91359i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(2.41421 - 4.18154i) q^{17} +(-3.41421 + 5.91359i) q^{18} +(-1.41421 - 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} +2.00000 q^{22} +(0.207107 + 0.358719i) q^{23} +(0.914214 - 1.58346i) q^{24} +(5.82843 + 10.0951i) q^{26} -2.41421 q^{27} +(6.20711 - 8.00436i) q^{28} -1.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(0.171573 + 0.297173i) q^{33} +11.6569 q^{34} -10.8284 q^{36} +(3.41421 - 5.91359i) q^{38} +(-1.00000 + 1.73205i) q^{39} -7.82843 q^{41} +(2.62132 + 0.358719i) q^{42} -3.58579 q^{43} +(1.58579 + 2.74666i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.00000 + 1.73205i) q^{47} +1.24264 q^{48} +(6.74264 + 1.88064i) q^{49} +(1.00000 + 1.73205i) q^{51} +(-9.24264 + 16.0087i) q^{52} +(-0.585786 + 1.01461i) q^{53} +(-2.91421 - 5.04757i) q^{54} +(11.5711 + 1.58346i) q^{56} +1.17157 q^{57} +(-1.20711 - 2.09077i) q^{58} +(-2.24264 + 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} +14.4853 q^{62} +(-2.82843 - 6.92820i) q^{63} -9.82843 q^{64} +(-0.414214 + 0.717439i) q^{66} +(4.79289 - 8.30153i) q^{67} +(9.24264 + 16.0087i) q^{68} -0.171573 q^{69} +4.48528 q^{71} +(-6.24264 - 10.8126i) q^{72} +(-0.414214 + 0.717439i) q^{73} +10.8284 q^{76} +(-1.34315 + 1.73205i) q^{77} -4.82843 q^{78} +(-7.41421 - 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-9.44975 - 16.3674i) q^{82} -13.7279 q^{83} +(1.58579 + 3.88437i) q^{84} +(-4.32843 - 7.49706i) q^{86} +(0.207107 - 0.358719i) q^{87} +(-1.82843 + 3.16693i) q^{88} +(4.32843 + 7.49706i) q^{89} +(-12.6569 - 1.73205i) q^{91} -1.58579 q^{92} +(1.24264 + 2.15232i) q^{93} +(-2.41421 + 4.18154i) q^{94} +(-0.328427 - 0.568852i) q^{96} -11.6569 q^{97} +(4.20711 + 16.3674i) q^{98} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{11} - 6 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 4 q^{17} - 8 q^{18} + 14 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 12 q^{26} - 4 q^{27} + 22 q^{28} - 4 q^{29} + 12 q^{31} - 6 q^{32} + 12 q^{33} + 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} - 20 q^{41} + 2 q^{42} - 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 10 q^{49} + 4 q^{51} - 20 q^{52} - 8 q^{53} - 6 q^{54} + 18 q^{56} + 16 q^{57} - 2 q^{58} + 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{66} + 22 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{71} - 8 q^{72} + 4 q^{73} + 32 q^{76} - 28 q^{77} - 8 q^{78} - 24 q^{79} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 12 q^{84} - 6 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 28 q^{91} - 12 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 24 q^{97} + 14 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 4 * q^11 - 6 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 4 * q^17 - 8 * q^18 + 14 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 12 * q^26 - 4 * q^27 + 22 * q^28 - 4 * q^29 + 12 * q^31 - 6 * q^32 + 12 * q^33 + 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 - 20 * q^41 + 2 * q^42 - 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 10 * q^49 + 4 * q^51 - 20 * q^52 - 8 * q^53 - 6 * q^54 + 18 * q^56 + 16 * q^57 - 2 * q^58 + 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^66 + 22 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^71 - 8 * q^72 + 4 * q^73 + 32 * q^76 - 28 * q^77 - 8 * q^78 - 24 * q^79 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 12 * q^84 - 6 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 28 * q^91 - 12 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 24 * q^97 + 14 * q^98 + 32 * q^99

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