LMFDB - Embedded newform 630.2.t.b.551.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.8
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.51897 - 0.832312i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.73162 + 0.0386792i) q^{6} +(2.13731 - 1.55945i) q^{7} -1.00000i q^{8} +(1.61451 + 2.52851i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.51897 - 0.832312i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.73162 + 0.0386792i) q^{6} +(2.13731 - 1.55945i) q^{7} -1.00000i q^{8} +(1.61451 + 2.52851i) q^{9} +(-0.866025 + 0.500000i) q^{10} +0.450472i q^{11} +(-1.48029 + 0.899307i) q^{12} +(4.26160 - 2.46044i) q^{13} +(1.07124 - 2.41918i) q^{14} +(1.51897 + 0.832312i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93285 - 6.81190i) q^{17} +(2.66246 + 1.38250i) q^{18} +(-4.75019 - 2.74252i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-4.54446 + 0.589839i) q^{21} +(0.225236 + 0.390121i) q^{22} +4.86229i q^{23} +(-0.832312 + 1.51897i) q^{24} +1.00000 q^{25} +(2.46044 - 4.26160i) q^{26} +(-0.347881 - 5.18449i) q^{27} +(-0.281867 - 2.63069i) q^{28} +(-8.05558 - 4.65089i) q^{29} +(1.73162 - 0.0386792i) q^{30} +(0.497185 + 0.287050i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.374934 - 0.684252i) q^{33} +(-6.81190 - 3.93285i) q^{34} +(-2.13731 + 1.55945i) q^{35} +(2.99701 - 0.133955i) q^{36} +(-0.721812 + 1.25022i) q^{37} -5.48505 q^{38} +(-8.52108 + 0.190335i) q^{39} +1.00000i q^{40} +(0.956724 + 1.65709i) q^{41} +(-3.64070 + 2.78304i) q^{42} +(-0.459119 + 0.795218i) q^{43} +(0.390121 + 0.225236i) q^{44} +(-1.61451 - 2.52851i) q^{45} +(2.43115 + 4.21087i) q^{46} +(3.71305 + 6.43119i) q^{47} +(0.0386792 + 1.73162i) q^{48} +(2.13623 - 6.66607i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.304239 + 13.6204i) q^{51} -4.92088i q^{52} +(8.30591 - 4.79542i) q^{53} +(-2.89352 - 4.31596i) q^{54} -0.450472i q^{55} +(-1.55945 - 2.13731i) q^{56} +(4.93274 + 8.11944i) q^{57} -9.30178 q^{58} +(4.43278 - 7.67779i) q^{59} +(1.48029 - 0.899307i) q^{60} +(8.54152 - 4.93145i) q^{61} +0.574100 q^{62} +(7.39380 + 2.88646i) q^{63} -1.00000 q^{64} +(-4.26160 + 2.46044i) q^{65} +(-0.0174239 - 0.780047i) q^{66} +(2.32102 - 4.02013i) q^{67} -7.86570 q^{68} +(4.04694 - 7.38565i) q^{69} +(-1.07124 + 2.41918i) q^{70} +3.88571i q^{71} +(2.52851 - 1.61451i) q^{72} +(4.91339 - 2.83675i) q^{73} +1.44362i q^{74} +(-1.51897 - 0.832312i) q^{75} +(-4.75019 + 2.74252i) q^{76} +(0.702489 + 0.962801i) q^{77} +(-7.28430 + 4.42538i) q^{78} +(1.00320 + 1.73760i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.78670 + 8.16461i) q^{81} +(1.65709 + 0.956724i) q^{82} +(-4.76689 + 8.25650i) q^{83} +(-1.76141 + 4.23053i) q^{84} +(3.93285 + 6.81190i) q^{85} +0.918239i q^{86} +(8.36515 + 13.7693i) q^{87} +0.450472 q^{88} +(-1.98445 + 3.43716i) q^{89} +(-2.66246 - 1.38250i) q^{90} +(5.27146 - 11.9045i) q^{91} +(4.21087 + 2.43115i) q^{92} +(-0.516292 - 0.849832i) q^{93} +(6.43119 + 3.71305i) q^{94} +(4.75019 + 2.74252i) q^{95} +(0.899307 + 1.48029i) q^{96} +(-8.69468 - 5.01988i) q^{97} +(-1.48301 - 6.84110i) q^{98} +(-1.13902 + 0.727293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.51897	−	0.832312i	−0.876975	−	0.480536i
$3$	−1.51897	−	0.832312i	−0.876975	−	0.480536i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.73162	+	0.0386792i	−0.706930	+	0.0157907i
$7$	2.13731	−	1.55945i	0.807829	−	0.589417i
$7$	2.13731	−	1.55945i	0.807829	−	0.589417i
$8$		−	1.00000i		−	0.353553i
$9$	1.61451	+	2.52851i	0.538171	+	0.842836i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$			0.450472i			0.135823i	0.997691	+	0.0679113i	$0.0216335\pi$
$11$			0.450472i			0.135823i	−0.997691	+	0.0679113i	$0.978367\pi$
$12$	−1.48029	+	0.899307i	−0.427322	+	0.259607i
$13$	4.26160	−	2.46044i	1.18196	−	0.682403i	0.225490	−	0.974246i	$-0.427602\pi$
$13$	4.26160	−	2.46044i	1.18196	−	0.682403i	0.956466	+	0.291843i	$0.0942684\pi$
$14$	1.07124	−	2.41918i	0.286302	−	0.646553i
$15$	1.51897	+	0.832312i	0.392195	+	0.214902i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.93285	−	6.81190i	−0.953857	−	1.65213i	−0.736963	−	0.675933i	$-0.763741\pi$
$17$	−3.93285	−	6.81190i	−0.953857	−	1.65213i	−0.216894	−	0.976195i	$-0.569593\pi$
$18$	2.66246	+	1.38250i	0.627548	+	0.325857i
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.156254	−	0.987717i	$-0.549942\pi$
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.933515	+	0.358539i	$0.883275\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−4.54446	+	0.589839i	−0.991682	+	0.128713i
$22$	0.225236	+	0.390121i	0.0480205	+	0.0831740i
$23$			4.86229i			1.01386i	0.861988	+	0.506929i	$0.169219\pi$
$23$			4.86229i			1.01386i	−0.861988	+	0.506929i	$0.830781\pi$
$24$	−0.832312	+	1.51897i	−0.169895	+	0.310058i
$25$	1.00000			0.200000
$26$	2.46044	−	4.26160i	0.482532	−	0.835769i
$27$	−0.347881	−	5.18449i	−0.0669498	−	0.997756i
$28$	−0.281867	−	2.63069i	−0.0532678	−	0.497154i
$29$	−8.05558	−	4.65089i	−1.49588	−	0.863648i	−0.495894	−	0.868383i	$-0.665160\pi$
$29$	−8.05558	−	4.65089i	−1.49588	−	0.863648i	−0.999989	+	0.00473444i	$0.998493\pi$
$30$	1.73162	−	0.0386792i	0.316149	−	0.00706182i
$31$	0.497185	+	0.287050i	0.0892970	+	0.0515557i	0.543984	−	0.839096i	$-0.316915\pi$
$31$	0.497185	+	0.287050i	0.0892970	+	0.0515557i	−0.454687	+	0.890652i	$0.650249\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.374934	−	0.684252i	0.0652676	−	0.119113i
$34$	−6.81190	−	3.93285i	−1.16823	−	0.674479i
$35$	−2.13731	+	1.55945i	−0.361272	+	0.263595i
$36$	2.99701	−	0.133955i	0.499501	−	0.0223259i
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	−0.919239	−	0.393700i	$-0.871195\pi$
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	0.800574	+	0.599234i	$0.204528\pi$
$38$	−5.48505			−0.889792
$39$	−8.52108	+	0.190335i	−1.36446	+	0.0304781i
$40$			1.00000i			0.158114i
$41$	0.956724	+	1.65709i	0.149415	+	0.258795i	0.931011	−	0.364990i	$-0.118928\pi$
$41$	0.956724	+	1.65709i	0.149415	+	0.258795i	−0.781596	+	0.623785i	$0.785594\pi$
$42$	−3.64070	+	2.78304i	−0.561772	+	0.429433i
$43$	−0.459119	+	0.795218i	−0.0700151	+	0.121270i	−0.898908	−	0.438138i	$-0.855638\pi$
$43$	−0.459119	+	0.795218i	−0.0700151	+	0.121270i	0.828893	+	0.559408i	$0.188971\pi$
$44$	0.390121	+	0.225236i	0.0588129	+	0.0339556i
$45$	−1.61451	−	2.52851i	−0.240677	−	0.376928i
$46$	2.43115	+	4.21087i	0.358453	+	0.620858i
$47$	3.71305	+	6.43119i	0.541604	+	0.938085i	0.998812	+	0.0487254i	$0.0155159\pi$
$47$	3.71305	+	6.43119i	0.541604	+	0.938085i	−0.457209	+	0.889359i	$0.651151\pi$
$48$	0.0386792	+	1.73162i	0.00558286	+	0.249938i
$49$	2.13623	−	6.66607i	0.305175	−	0.952296i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	0.304239	+	13.6204i	0.0426020	+	1.90724i
$52$		−	4.92088i		−	0.682403i
$53$	8.30591	−	4.79542i	1.14090	−	0.658701i	0.194250	−	0.980952i	$-0.437773\pi$
$53$	8.30591	−	4.79542i	1.14090	−	0.658701i	0.946654	+	0.322251i	$0.104439\pi$
$54$	−2.89352	−	4.31596i	−0.393758	−	0.587328i
$55$		−	0.450472i		−	0.0607417i
$56$	−1.55945	−	2.13731i	−0.208390	−	0.285611i
$57$	4.93274	+	8.11944i	0.653357	+	1.07545i
$58$	−9.30178			−1.22138
$59$	4.43278	−	7.67779i	0.577098	−	0.999564i	−0.418712	−	0.908119i	$-0.637518\pi$
$59$	4.43278	−	7.67779i	0.577098	−	0.999564i	0.995810	−	0.0914445i	$-0.0291484\pi$
$60$	1.48029	−	0.899307i	0.191104	−	0.116100i
$61$	8.54152	−	4.93145i	1.09363	−	0.631407i	0.159089	−	0.987264i	$-0.449144\pi$
$61$	8.54152	−	4.93145i	1.09363	−	0.631407i	0.934540	+	0.355857i	$0.115811\pi$
$62$	0.574100			0.0729107
$63$	7.39380	+	2.88646i	0.931532	+	0.363660i
$64$	−1.00000			−0.125000
$65$	−4.26160	+	2.46044i	−0.528587	+	0.305180i
$66$	−0.0174239	−	0.780047i	−0.00214473	−	0.0960171i
$67$	2.32102	−	4.02013i	0.283558	−	0.491137i	−0.688700	−	0.725046i	$-0.741818\pi$
$67$	2.32102	−	4.02013i	0.283558	−	0.491137i	0.972258	+	0.233909i	$0.0751518\pi$
$68$	−7.86570			−0.953857
$69$	4.04694	−	7.38565i	0.487195	−	0.889128i
$70$	−1.07124	+	2.41918i	−0.128038	+	0.289147i
$71$			3.88571i			0.461149i	0.973055	+	0.230575i	$0.0740606\pi$
$71$			3.88571i			0.461149i	−0.973055	+	0.230575i	$0.925939\pi$
$72$	2.52851	−	1.61451i	0.297987	−	0.190272i
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	−0.184102	−	0.982907i	$-0.558938\pi$
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	0.759171	+	0.650891i	$0.225604\pi$
$74$			1.44362i			0.167818i
$75$	−1.51897	−	0.832312i	−0.175395	−	0.0961071i
$76$	−4.75019	+	2.74252i	−0.544884	+	0.314589i
$77$	0.702489	+	0.962801i	0.0800561	+	0.109721i
$78$	−7.28430	+	4.42538i	−0.824785	+	0.501075i
$79$	1.00320	+	1.73760i	0.112869	+	0.195495i	0.916926	−	0.399058i	$-0.130663\pi$
$79$	1.00320	+	1.73760i	0.112869	+	0.195495i	−0.804057	+	0.594552i	$0.797329\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.78670	+	8.16461i	−0.420744	+	0.907179i
$82$	1.65709	+	0.956724i	0.182995	+	0.105652i
$83$	−4.76689	+	8.25650i	−0.523234	+	0.906268i	0.476400	+	0.879229i	$0.341941\pi$
$83$	−4.76689	+	8.25650i	−0.523234	+	0.906268i	−0.999634	+	0.0270398i	$0.991392\pi$
$84$	−1.76141	+	4.23053i	−0.192186	+	0.461589i
$85$	3.93285	+	6.81190i	0.426578	+	0.738854i
$86$			0.918239i			0.0990162i
$87$	8.36515	+	13.7693i	0.896838	+	1.47622i
$88$	0.450472			0.0480205
$89$	−1.98445	+	3.43716i	−0.210351	+	0.364339i	−0.951824	−	0.306644i	$-0.900794\pi$
$89$	−1.98445	+	3.43716i	−0.210351	+	0.364339i	0.741473	+	0.670982i	$0.234127\pi$
$90$	−2.66246	−	1.38250i	−0.280648	−	0.145728i
$91$	5.27146	−	11.9045i	0.552599	−	1.24793i
$92$	4.21087	+	2.43115i	0.439013	+	0.253464i
$93$	−0.516292	−	0.849832i	−0.0535369	−	0.0881235i
$94$	6.43119	+	3.71305i	0.663326	+	0.382972i
$95$	4.75019	+	2.74252i	0.487359	+	0.281377i
$96$	0.899307	+	1.48029i	0.0917851	+	0.151081i
$97$	−8.69468	−	5.01988i	−0.882811	−	0.509691i	−0.0112270	−	0.999937i	$-0.503574\pi$
$97$	−8.69468	−	5.01988i	−0.882811	−	0.509691i	−0.871584	+	0.490246i	$0.836907\pi$
$98$	−1.48301	−	6.84110i	−0.149807	−	0.691056i
$99$	−1.13902	+	0.727293i	−0.114476	+	0.0730957i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−5.49909			−0.547180			−0.273590	−	0.961846i	$-0.588211\pi$
$101$	−5.49909			−0.547180			−0.273590	+	0.961846i	$0.588211\pi$
$102$	7.07368	+	11.6435i	0.700399	+	1.15288i
$103$			15.5075i			1.52800i	0.645216	+	0.764000i	$0.276767\pi$
$103$			15.5075i			1.52800i	−0.645216	+	0.764000i	$0.723233\pi$
$104$	−2.46044	−	4.26160i	−0.241266	−	0.417885i
$105$	4.54446	−	0.589839i	0.443494	−	0.0575623i
$106$	4.79542	−	8.30591i	0.465772	−	0.806741i
$107$	8.60043	+	4.96546i	0.831435	+	0.480029i	0.854344	−	0.519708i	$-0.173959\pi$
$107$	8.60043	+	4.96546i	0.831435	+	0.480029i	−0.0229088	+	0.999738i	$0.507293\pi$
$108$	−4.66384	−	2.29097i	−0.448779	−	0.220449i
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	0.952784	−	0.303647i	$-0.0982045\pi$
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	−0.739359	+	0.673312i	$0.764871\pi$
$110$	−0.225236	−	0.390121i	−0.0214754	−	0.0371965i
$111$	2.13698	−	1.29826i	0.202833	−	0.123225i
$112$	−2.41918	−	1.07124i	−0.228591	−	0.101223i
$113$	17.4964	−	10.1015i	1.64592	−	0.950271i	0.667247	−	0.744836i	$-0.267472\pi$
$113$	17.4964	−	10.1015i	1.64592	−	0.950271i	0.978671	−	0.205435i	$-0.0658610\pi$
$114$	8.33160	+	4.56527i	0.780326	+	0.427577i
$115$		−	4.86229i		−	0.453411i
$116$	−8.05558	+	4.65089i	−0.747942	+	0.431824i
$117$	13.1016	+	6.80309i	1.21125	+	0.628946i
$118$		−	8.86555i		−	0.816140i
$119$	−19.0286	−	8.42608i	−1.74435	−	0.772418i
$120$	0.832312	−	1.51897i	0.0759794	−	0.138662i
$121$	10.7971			0.981552
$122$	4.93145	−	8.54152i	0.446472	−	0.773313i
$123$	−0.0740106	−	3.31336i	−0.00667331	−	0.298756i
$124$	0.497185	−	0.287050i	0.0446485	−	0.0257778i
$125$	−1.00000			−0.0894427
$126$	7.84645	−	1.19715i	0.699018	−	0.106651i
$127$	3.08808			0.274023			0.137012	−	0.990569i	$-0.456250\pi$
$127$	3.08808			0.274023			0.137012	+	0.990569i	$0.456250\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.35926	−	0.825778i	0.119676	−	0.0727057i
$130$	−2.46044	+	4.26160i	−0.215795	+	0.373767i
$131$	−15.7084			−1.37245			−0.686227	−	0.727388i	$-0.740734\pi$
$131$	−15.7084			−1.37245			−0.686227	+	0.727388i	$0.740734\pi$
$132$	−0.405113	−	0.666828i	−0.0352605	−	0.0580399i
$133$	−14.4295	+	1.54605i	−1.25120	+	0.134060i
$134$		−	4.64204i		−	0.401012i
$135$	0.347881	+	5.18449i	0.0299409	+	0.446210i
$136$	−6.81190	+	3.93285i	−0.584116	+	0.337239i
$137$			13.0632i			1.11606i	0.829821	+	0.558030i	$0.188443\pi$
$137$			13.0632i			1.11606i	−0.829821	+	0.558030i	$0.811557\pi$
$138$	−0.188069	−	8.41963i	−0.0160095	−	0.716727i
$139$	−0.567606	+	0.327707i	−0.0481437	+	0.0277958i	−0.523879	−	0.851793i	$-0.675515\pi$
$139$	−0.567606	+	0.327707i	−0.0481437	+	0.0277958i	0.475735	+	0.879589i	$0.342182\pi$
$140$	0.281867	+	2.63069i	0.0238221	+	0.222334i
$141$	−0.287235	−	12.8592i	−0.0241896	−	1.08294i
$142$	1.94286	+	3.36513i	0.163041	+	0.282395i
$143$	1.10836	+	1.91973i	0.0926857	+	0.160536i
$144$	1.38250	−	2.66246i	0.115208	−	0.221872i
$145$	8.05558	+	4.65089i	0.668979	+	0.386235i
$146$	2.83675	−	4.91339i	0.234771	−	0.406635i
$147$	−8.79311	+	8.34753i	−0.725244	+	0.688492i
$148$	0.721812	+	1.25022i	0.0593326	+	0.102767i
$149$			4.62313i			0.378741i	0.981906	+	0.189371i	$0.0606448\pi$
$149$			4.62313i			0.378741i	−0.981906	+	0.189371i	$0.939355\pi$
$150$	−1.73162	+	0.0386792i	−0.141386	+	0.00315814i
$151$	12.3019			1.00112			0.500559	−	0.865703i	$-0.333128\pi$
$151$	12.3019			1.00112			0.500559	+	0.865703i	$0.333128\pi$
$152$	−2.74252	+	4.75019i	−0.222448	+	0.385291i
$153$	10.8743	−	20.9421i	0.879135	−	1.69307i
$154$	1.08977	+	0.482566i	0.0878165	+	0.0388862i
$155$	−0.497185	−	0.287050i	−0.0399349	−	0.0230564i
$156$	−4.09570	+	7.47464i	−0.327919	+	0.598450i
$157$	16.6593	+	9.61826i	1.32956	+	0.767620i	0.985231	−	0.171230i	$-0.0547740\pi$
$157$	16.6593	+	9.61826i	1.32956	+	0.767620i	0.344326	+	0.938850i	$0.388107\pi$
$158$	1.73760	+	1.00320i	0.138236	+	0.0798104i
$159$	−16.6077	+	0.370966i	−1.31707	+	0.0294195i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	7.58250	+	10.3922i	0.597585	+	0.819024i
$162$	0.802930	+	8.96411i	0.0630841	+	0.704287i
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	−0.717879	−	0.696168i	$-0.754887\pi$
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	0.961839	+	0.273617i	$0.0882200\pi$
$164$	1.91345			0.149415
$165$	−0.374934	+	0.684252i	−0.0291885	+	0.0532689i
$166$			9.53378i			0.739965i
$167$	−3.60660	−	6.24681i	−0.279087	−	0.483393i	0.692071	−	0.721829i	$-0.256698\pi$
$167$	−3.60660	−	6.24681i	−0.279087	−	0.483393i	−0.971158	+	0.238437i	$0.923365\pi$
$168$	0.589839	+	4.54446i	0.0455070	+	0.350612i
$169$	5.60751	−	9.71249i	0.431347	−	0.747114i
$170$	6.81190	+	3.93285i	0.522449	+	0.301636i
$171$	−0.734751	−	16.4387i	−0.0561878	−	1.25710i
$172$	0.459119	+	0.795218i	0.0350075	+	0.0606348i
$173$	7.80001	+	13.5100i	0.593024	+	1.02715i	0.993822	+	0.110982i	$0.0353994\pi$
$173$	7.80001	+	13.5100i	0.593024	+	1.02715i	−0.400798	+	0.916166i	$0.631267\pi$
$174$	14.1291	+	7.74198i	1.07112	+	0.586918i
$175$	2.13731	−	1.55945i	0.161566	−	0.117883i
$176$	0.390121	−	0.225236i	0.0294064	−	0.0169778i
$177$	−13.1236	+	7.97285i	−0.986427	+	0.599276i
$178$			3.96890i			0.297481i
$179$	−3.30274	+	1.90684i	−0.246858	+	0.142524i	−0.618325	−	0.785923i	$-0.712188\pi$
$179$	−3.30274	+	1.90684i	−0.246858	+	0.142524i	0.371466	+	0.928446i	$0.378855\pi$
$180$	−2.99701	+	0.133955i	−0.223384	+	0.00998443i
$181$			4.59480i			0.341529i	0.985312	+	0.170764i	$0.0546237\pi$
$181$			4.59480i			0.341529i	−0.985312	+	0.170764i	$0.945376\pi$
$182$	−1.38703	−	12.9453i	−0.102814	−	0.959571i
$183$	−17.0788	+	0.381489i	−1.26250	+	0.0282005i
$184$	4.86229			0.358453
$185$	0.721812	−	1.25022i	0.0530687	−	0.0919177i
$186$	−0.872038	−	0.477830i	−0.0639409	−	0.0350362i
$187$	3.06857	−	1.77164i	0.224396	−	0.129555i
$188$	7.42609			0.541604
$189$	−8.82849	−	10.5384i	−0.642178	−	0.766555i
$190$	5.48505			0.397927
$191$	−21.7317	+	12.5468i	−1.57245	+	0.907855i	−0.576583	+	0.817039i	$0.695614\pi$
$191$	−21.7317	+	12.5468i	−1.57245	+	0.907855i	−0.995868	+	0.0908162i	$0.971052\pi$
$192$	1.51897	+	0.832312i	0.109622	+	0.0600670i
$193$	8.95240	−	15.5060i	0.644408	−	1.11615i	−0.340030	−	0.940415i	$-0.610437\pi$
$193$	8.95240	−	15.5060i	0.644408	−	1.11615i	0.984438	−	0.175733i	$-0.0562295\pi$
$194$	−10.0398			−0.720812
$195$	8.52108	−	0.190335i	0.610207	−	0.0136302i
$196$	−4.70487	−	5.18306i	−0.336062	−	0.370219i
$197$		−	12.6523i		−	0.901439i	−0.892666	−	0.450720i	$-0.851167\pi$
$197$		−	12.6523i		−	0.901439i	0.892666	−	0.450720i	$-0.148833\pi$
$198$	−0.622776	+	1.19937i	−0.0442588	+	0.0852352i
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.979832	−	0.199823i	$-0.935963\pi$
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.316865	+	0.948471i	$0.602630\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−6.87155	+	4.17462i	−0.484682	+	0.294455i
$202$	−4.76235	+	2.74955i	−0.335078	+	0.193457i
$203$	−24.4701	+	2.62186i	−1.71747	+	0.184019i
$204$	11.9477	+	6.54672i	0.836509	+	0.458362i
$205$	−0.956724	−	1.65709i	−0.0668205	−	0.115736i
$206$	7.75376	+	13.4299i	0.540230	+	0.935705i
$207$	−12.2943	+	7.85023i	−0.854515	+	0.545629i
$208$	−4.26160	−	2.46044i	−0.295489	−	0.170601i
$209$	1.23543	−	2.13983i	0.0854566	−	0.148015i
$210$	3.64070	−	2.78304i	0.251232	−	0.192048i
$211$	10.0132	+	17.3434i	0.689338	+	1.19397i	0.972052	+	0.234764i	$0.0754318\pi$
$211$	10.0132	+	17.3434i	0.689338	+	1.19397i	−0.282714	+	0.959204i	$0.591235\pi$
$212$		−	9.59084i		−	0.658701i
$213$	3.23413	−	5.90226i	0.221599	−	0.404416i
$214$	9.93092			0.678864
$215$	0.459119	−	0.795218i	0.0313117	−	0.0542334i
$216$	−5.18449	+	0.347881i	−0.352760	+	0.0236703i
$217$	1.51028	−	0.161819i	0.102525	−	0.0109850i
$218$	3.85941	+	2.22823i	0.261392	+	0.150915i
$219$	−9.82433	+	0.219446i	−0.663867	+	0.0148288i
$220$	−0.390121	−	0.225236i	−0.0263019	−	0.0151854i
$221$	−33.5205	−	19.3531i	−2.25483	−	1.30183i
$222$	1.20155	−	2.19282i	0.0806425	−	0.147172i
$223$	2.43988	+	1.40867i	0.163387	+	0.0943313i	0.579464	−	0.814998i	$-0.303262\pi$
$223$	2.43988	+	1.40867i	0.163387	+	0.0943313i	−0.416077	+	0.909329i	$0.636595\pi$
$224$	−2.63069	+	0.281867i	−0.175771	+	0.0188330i
$225$	1.61451	+	2.52851i	0.107634	+	0.168567i
$226$	10.1015	−	17.4964i	0.671943	−	1.16384i
$227$	−2.59017			−0.171915			−0.0859577	−	0.996299i	$-0.527395\pi$
$227$	−2.59017			−0.171915			−0.0859577	+	0.996299i	$0.527395\pi$
$228$	9.49801	−	0.212157i	0.629021	−	0.0140505i
$229$		−	21.5183i		−	1.42197i	−0.703206	−	0.710986i	$-0.748249\pi$
$229$		−	21.5183i		−	1.42197i	0.703206	−	0.710986i	$-0.251751\pi$
$230$	−2.43115	−	4.21087i	−0.160305	−	0.277656i
$231$	−0.265706	−	2.04715i	−0.0174822	−	0.134693i
$232$	−4.65089	+	8.05558i	−0.305346	+	0.528875i
$233$	−2.79452	−	1.61342i	−0.183075	−	0.105699i	0.405661	−	0.914023i	$-0.367041\pi$
$233$	−2.79452	−	1.61342i	−0.183075	−	0.105699i	−0.588737	+	0.808325i	$0.700375\pi$
$234$	14.7479	−	0.659177i	0.964101	−	0.0430918i
$235$	−3.71305	−	6.43119i	−0.242212	−	0.419524i
$236$	−4.43278	−	7.67779i	−0.288549	−	0.499782i
$237$	−0.0776060	−	3.47432i	−0.00504105	−	0.225682i
$238$	−20.6923	+	2.21708i	−1.34128	+	0.143712i
$239$	13.9417	−	8.04923i	0.901812	−	0.520661i	0.0240242	−	0.999711i	$-0.492352\pi$
$239$	13.9417	−	8.04923i	0.901812	−	0.520661i	0.877788	+	0.479050i	$0.159019\pi$
$240$	−0.0386792	−	1.73162i	−0.00249673	−	0.111776i
$241$			25.6376i			1.65147i	0.564061	+	0.825733i	$0.309238\pi$
$241$			25.6376i			1.65147i	−0.564061	+	0.825733i	$0.690762\pi$
$242$	9.35054	−	5.39854i	0.601076	−	0.347031i
$243$	12.5474	−	9.25005i	0.804914	−	0.593391i
$244$		−	9.86290i		−	0.631407i
$245$	−2.13623	+	6.66607i	−0.136479	+	0.425880i
$246$	−1.72078	−	2.83245i	−0.109713	−	0.180590i
$247$	−26.9912			−1.71741
$248$	0.287050	−	0.497185i	0.0182277	−	0.0315713i
$249$	14.1127	−	8.57379i	0.894358	−	0.543342i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	12.7547			0.805068			0.402534	−	0.915405i	$-0.368129\pi$
$251$	12.7547			0.805068			0.402534	+	0.915405i	$0.368129\pi$
$252$	6.19665	−	4.95999i	0.390352	−	0.312450i
$253$	−2.19033			−0.137705
$254$	2.67436	−	1.54404i	0.167804	−	0.0968818i
$255$	−0.304239	−	13.6204i	−0.0190522	−	0.852943i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	27.0776			1.68906			0.844528	−	0.535512i	$-0.179881\pi$
$257$	27.0776			1.68906			0.844528	+	0.535512i	$0.179881\pi$
$258$	0.764261	−	1.39477i	0.0475808	−	0.0868348i
$259$	0.406909	+	3.79773i	0.0252841	+	0.235980i
$260$			4.92088i			0.305180i
$261$	−1.24602	−	27.8775i	−0.0771268	−	1.72557i
$262$	−13.6039	+	7.85422i	−0.840453	+	0.485235i
$263$		−	13.3334i		−	0.822172i	−0.911597	−	0.411086i	$-0.865150\pi$
$263$		−	13.3334i		−	0.822172i	0.911597	−	0.411086i	$-0.134850\pi$
$264$	−0.684252	−	0.374934i	−0.0421128	−	0.0230756i
$265$	−8.30591	+	4.79542i	−0.510228	+	0.294580i
$266$	−11.7233	+	8.55366i	−0.718800	+	0.524459i
$267$	5.87510	−	3.56925i	0.359550	−	0.218435i
$268$	−2.32102	−	4.02013i	−0.141779	−	0.245568i
$269$	−7.58415	−	13.1361i	−0.462414	−	0.800924i	0.536667	−	0.843794i	$-0.319683\pi$
$269$	−7.58415	−	13.1361i	−0.462414	−	0.800924i	−0.999081	+	0.0428702i	$0.986350\pi$
$270$	2.89352	+	4.31596i	0.176094	+	0.262661i
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.992542	−	0.121900i	$-0.0388986\pi$
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.390703	+	0.920517i	$0.372232\pi$
$272$	−3.93285	+	6.81190i	−0.238464	+	0.413032i
$273$	−17.9154	+	13.6950i	−1.08429	+	0.828860i
$274$	6.53158	+	11.3130i	0.394587	+	0.683445i
$275$			0.450472i			0.0271645i
$276$	−4.37269	−	7.19758i	−0.263205	−	0.433244i
$277$	23.2800			1.39876			0.699381	−	0.714749i	$-0.253459\pi$
$277$	23.2800			1.39876			0.699381	+	0.714749i	$0.253459\pi$
$278$	−0.327707	+	0.567606i	−0.0196546	+	0.0340427i
$279$	0.0769037	+	1.72058i	0.00460410	+	0.103009i
$280$	1.55945	+	2.13731i	0.0931950	+	0.127729i
$281$	−3.40387	−	1.96523i	−0.203058	−	0.117236i	0.395023	−	0.918671i	$-0.370737\pi$
$281$	−3.40387	−	1.96523i	−0.203058	−	0.117236i	−0.598081	+	0.801436i	$0.704070\pi$
$282$	−6.67833	−	10.9927i	−0.397689	−	0.654608i
$283$	−25.0227	−	14.4469i	−1.48745	−	0.858778i	−0.487550	−	0.873095i	$-0.662109\pi$
$283$	−25.0227	−	14.4469i	−1.48745	−	0.858778i	−0.999898	+	0.0143172i	$0.995443\pi$
$284$	3.36513	+	1.94286i	0.199683	+	0.115287i
$285$	−4.93274	−	8.11944i	−0.292190	−	0.480954i
$286$	1.91973	+	1.10836i	0.113516	+	0.0655387i
$287$	4.62898	+	2.04977i	0.273240	+	0.120994i
$288$	−0.133955	−	2.99701i	−0.00789339	−	0.176600i
$289$	−22.4347	+	38.8580i	−1.31969	+	2.28576i
$290$	9.30178			0.546219
$291$	9.02882	+	14.8617i	0.529279	+	0.871209i
$292$		−	5.67350i		−	0.332016i
$293$	2.16359	+	3.74744i	0.126398	+	0.218928i	0.922279	−	0.386526i	$-0.126325\pi$
$293$	2.16359	+	3.74744i	0.126398	+	0.218928i	−0.795880	+	0.605454i	$0.792992\pi$
$294$	−3.44129	+	11.6257i	−0.200700	+	0.678026i
$295$	−4.43278	+	7.67779i	−0.258086	+	0.447018i
$296$	1.25022	+	0.721812i	0.0726673	+	0.0419545i
$297$	2.33547	−	0.156711i	0.135518	−	0.00909329i
$298$	2.31156	+	4.00375i	0.133905	+	0.231931i
$299$	11.9634	+	20.7212i	0.691859	+	1.19834i
$300$	−1.48029	+	0.899307i	−0.0854644	+	0.0519215i
$301$	0.258821	+	2.41561i	0.0149182	+	0.139233i
$302$	10.6538	−	6.15097i	0.613057	−	0.353948i
$303$	8.35293	+	4.57696i	0.479864	+	0.262940i
$304$			5.48505i			0.314589i
$305$	−8.54152	+	4.93145i	−0.489086	+	0.282374i
$306$	−1.05365	−	23.5736i	−0.0602333	−	1.34761i
$307$			0.419882i			0.0239639i	0.999928	+	0.0119820i	$0.00381407\pi$
$307$			0.419882i			0.0239639i	−0.999928	+	0.0119820i	$0.996186\pi$
$308$	1.18506	−	0.126973i	0.0675248	−	0.00723496i
$309$	12.9071	−	23.5554i	0.734259	−	1.34002i
$310$	−0.574100			−0.0326067
$311$	−3.14218	+	5.44241i	−0.178177	+	0.308611i	−0.941256	−	0.337694i	$-0.890353\pi$
$311$	−3.14218	+	5.44241i	−0.178177	+	0.308611i	0.763079	+	0.646305i	$0.223686\pi$
$312$	0.190335	+	8.52108i	0.0107756	+	0.482411i
$313$	−4.92258	+	2.84206i	−0.278241	+	0.160642i	−0.632627	−	0.774457i	$-0.718023\pi$
$313$	−4.92258	+	2.84206i	−0.278241	+	0.160642i	0.354386	+	0.935099i	$0.384690\pi$
$314$	19.2365			1.08558
$315$	−7.39380	−	2.88646i	−0.416594	−	0.162634i
$316$	2.00640			0.112869
$317$	−8.68744	+	5.01570i	−0.487935	+	0.281710i	−0.723718	−	0.690096i	$-0.757568\pi$
$317$	−8.68744	+	5.01570i	−0.487935	+	0.281710i	0.235782	+	0.971806i	$0.424235\pi$
$318$	−14.1972	+	8.62510i	−0.796139	+	0.483672i
$319$	2.09510	−	3.62881i	0.117303	−	0.203175i
$320$	1.00000			0.0559017
$321$	−8.93094	−	14.7006i	−0.498477	−	0.820508i
$322$	11.7628	+	5.20870i	0.655513	+	0.290269i
$323$			43.1438i			2.40058i
$324$	5.17741	+	7.36168i	0.287634	+	0.408982i
$325$	4.26160	−	2.46044i	0.236391	−	0.136481i
$326$		−	6.22935i		−	0.345012i
$327$	−0.172372	−	7.71690i	−0.00953222	−	0.426745i
$328$	1.65709	−	0.956724i	0.0914977	−	0.0528262i
$329$	17.9651	+	7.95515i	0.990446	+	0.438582i
$330$	0.0174239	+	0.780047i	0.000959155	+	0.0429401i
$331$	−15.8516	−	27.4558i	−0.871282	−	1.50910i	−0.860671	−	0.509161i	$-0.829956\pi$
$331$	−15.8516	−	27.4558i	−0.871282	−	1.50910i	−0.0106106	−	0.999944i	$-0.503378\pi$
$332$	4.76689	+	8.25650i	0.261617	+	0.453134i
$333$	−4.32655	+	0.193381i	−0.237094	+	0.0105972i
$334$	−6.24681	−	3.60660i	−0.341810	−	0.197344i
$335$	−2.32102	+	4.02013i	−0.126811	+	0.219643i
$336$	2.78304	+	3.64070i	0.151827	+	0.198616i
$337$	−7.09612	−	12.2908i	−0.386550	−	0.669525i	0.605433	−	0.795897i	$-0.293000\pi$
$337$	−7.09612	−	12.2908i	−0.386550	−	0.669525i	−0.991983	+	0.126372i	$0.959667\pi$
$338$		−	11.2150i		−	0.610016i
$339$	−34.9840	+	0.781437i	−1.90007	+	0.0424419i
$340$	7.86570			0.426578
$341$	−0.129308	+	0.223968i	−0.00700242	+	0.0121286i
$342$	−8.85568	−	13.8690i	−0.478860	−	0.749949i
$343$	−5.82962	−	17.5788i	−0.314770	−	0.949168i
$344$	0.795218	+	0.459119i	0.0428753	+	0.0247541i
$345$	−4.04694	+	7.38565i	−0.217880	+	0.397630i
$346$	13.5100	+	7.80001i	0.726303	+	0.419331i
$347$	0.634656	+	0.366419i	0.0340701	+	0.0196704i	0.516938	−	0.856023i	$-0.327072\pi$
$347$	0.634656	+	0.366419i	0.0340701	+	0.0196704i	−0.482868	+	0.875693i	$0.660405\pi$
$348$	16.1071	−	0.359785i	0.863433	−	0.0192865i
$349$	−23.1243	−	13.3508i	−1.23782	−	0.714653i	−0.269169	−	0.963093i	$-0.586749\pi$
$349$	−23.1243	−	13.3508i	−1.23782	−	0.714653i	−0.968647	+	0.248440i	$0.920082\pi$
$350$	1.07124	−	2.41918i	0.0572604	−	0.129311i
$351$	−14.2387	−	21.2383i	−0.760003	−	1.13362i
$352$	0.225236	−	0.390121i	0.0120051	−	0.0207935i
$353$	6.00317			0.319516			0.159758	−	0.987156i	$-0.448929\pi$
$353$	6.00317			0.319516			0.159758	+	0.987156i	$0.448929\pi$
$354$	−7.37891	+	13.4665i	−0.392185	+	0.715735i
$355$		−	3.88571i		−	0.206232i
$356$	1.98445	+	3.43716i	0.105176	+	0.182169i
$357$	21.8906	+	28.6366i	1.15857	+	1.51561i
$358$	−1.90684	+	3.30274i	−0.100780	+	0.174555i
$359$	25.3873	+	14.6574i	1.33989	+	0.773587i	0.986791	−	0.161998i	$-0.0517938\pi$
$359$	25.3873	+	14.6574i	1.33989	+	0.773587i	0.353101	+	0.935585i	$0.385127\pi$
$360$	−2.52851	+	1.61451i	−0.133264	+	0.0850923i
$361$	5.54288	+	9.60055i	0.291730	+	0.505292i
$362$	2.29740	+	3.97921i	0.120749	+	0.209143i
$363$	−16.4004	−	8.98654i	−0.860797	−	0.471671i
$364$	−7.67386	−	10.5175i	−0.402220	−	0.551265i
$365$	−4.91339	+	2.83675i	−0.257179	+	0.148482i
$366$	−14.5999	+	8.86977i	−0.763150	+	0.463630i
$367$			20.0340i			1.04576i	0.852405	+	0.522882i	$0.175143\pi$
$367$			20.0340i			1.04576i	−0.852405	+	0.522882i	$0.824857\pi$
$368$	4.21087	−	2.43115i	0.219507	−	0.126732i
$369$	−2.64533	+	5.09448i	−0.137710	+	0.265208i
$370$		−	1.44362i		−	0.0750505i
$371$	10.2741	−	23.2020i	0.533406	−	1.20459i
$372$	−0.994122	+	0.0222057i	−0.0515428	+	0.00115131i
$373$	−6.86717			−0.355568			−0.177784	−	0.984069i	$-0.556893\pi$
$373$	−6.86717			−0.355568			−0.177784	+	0.984069i	$0.556893\pi$
$374$	1.77164	−	3.06857i	0.0916094	−	0.158672i
$375$	1.51897	+	0.832312i	0.0784390	+	0.0429804i
$376$	6.43119	−	3.71305i	0.331663	−	0.191486i
$377$	−45.7729			−2.35742
$378$	−12.9149	−	4.71227i	−0.664271	−	0.242373i
$379$	0.682216			0.0350431			0.0175216	−	0.999846i	$-0.494422\pi$
$379$	0.682216			0.0350431			0.0175216	+	0.999846i	$0.494422\pi$
$380$	4.75019	−	2.74252i	0.243680	−	0.140689i
$381$	−4.69069	−	2.57025i	−0.240312	−	0.131678i
$382$	−12.5468	+	21.7317i	−0.641950	+	1.11189i
$383$	31.6323			1.61634			0.808168	−	0.588952i	$-0.200459\pi$
$383$	31.6323			1.61634			0.808168	+	0.588952i	$0.200459\pi$
$384$	1.73162	−	0.0386792i	0.0883663	−	0.00197384i
$385$	−0.702489	−	0.962801i	−0.0358022	−	0.0490689i
$386$		−	17.9048i		−	0.911331i
$387$	−2.75197	+	0.123003i	−0.139890	+	0.00625259i
$388$	−8.69468	+	5.01988i	−0.441406	+	0.254846i
$389$		−	28.0321i		−	1.42128i	−0.703554	−	0.710641i	$-0.748405\pi$
$389$		−	28.0321i		−	1.42128i	0.703554	−	0.710641i	$-0.251595\pi$
$390$	7.28430	−	4.42538i	0.368855	−	0.224088i
$391$	33.1214	−	19.1227i	1.67502	−	0.967075i
$392$	−6.66607	−	2.13623i	−0.336688	−	0.107896i
$393$	23.8606	+	13.0743i	1.20361	+	0.659513i
$394$	−6.32615	−	10.9572i	−0.318707	−	0.552017i
$395$	−1.00320	−	1.73760i	−0.0504765	−	0.0874279i
$396$	0.0603431	+	1.35007i	0.00303236	+	0.0678435i
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.295682	−	0.955286i	$-0.595547\pi$
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.975143	+	0.221575i	$0.928880\pi$
$398$	−10.5610	+	18.2922i	−0.529374	+	0.916903i
$399$	23.2047	+	9.66144i	1.16169	+	0.483677i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	11.5694i		−	0.577750i	−0.957367	−	0.288875i	$-0.906719\pi$
$401$		−	11.5694i		−	0.577750i	0.957367	−	0.288875i	$-0.0932812\pi$
$402$	−3.86363	+	7.05111i	−0.192700	+	0.351677i
$403$	2.82507			0.140727
$404$	−2.74955	+	4.76235i	−0.136795	+	0.236936i
$405$	3.78670	−	8.16461i	0.188163	−	0.405703i
$406$	−19.8808	+	14.5057i	−0.986669	+	0.719904i
$407$	−0.563188	−	0.325157i	−0.0279162	−	0.0161174i
$408$	13.6204	−	0.304239i	0.674310	−	0.0150621i
$409$	−1.79921	−	1.03878i	−0.0889653	−	0.0513641i	0.454857	−	0.890564i	$-0.349690\pi$
$409$	−1.79921	−	1.03878i	−0.0889653	−	0.0513641i	−0.543823	+	0.839200i	$0.683024\pi$
$410$	−1.65709	−	0.956724i	−0.0818380	−	0.0472492i
$411$	10.8726	−	19.8425i	0.536307	−	0.978757i
$412$	13.4299	+	7.75376i	0.661644	+	0.382000i
$413$	−2.49890	−	23.3226i	−0.122963	−	1.14763i
$414$	−6.72209	+	12.9457i	−0.330373	+	0.636245i
$415$	4.76689	−	8.25650i	0.233998	−	0.405296i
$416$	−4.92088			−0.241266
$417$	1.13493	−	0.0253509i	0.0555777	−	0.00124144i
$418$		−	2.47086i		−	0.120854i
$419$	−3.15211	−	5.45962i	−0.153991	−	0.266720i	0.778700	−	0.627396i	$-0.215879\pi$
$419$	−3.15211	−	5.45962i	−0.153991	−	0.266720i	−0.932691	+	0.360676i	$0.882546\pi$
$420$	1.76141	−	4.23053i	0.0859482	−	0.206429i
$421$	−1.30121	+	2.25376i	−0.0634172	+	0.109842i	−0.895991	−	0.444073i	$-0.853533\pi$
$421$	−1.30121	+	2.25376i	−0.0634172	+	0.109842i	0.832574	+	0.553914i	$0.186867\pi$
$422$	17.3434	+	10.0132i	0.844263	+	0.487436i
$423$	−10.2665	+	19.7717i	−0.499176	+	0.961333i
$424$	−4.79542	−	8.30591i	−0.232886	−	0.403371i
$425$	−3.93285	−	6.81190i	−0.190771	−	0.330426i
$426$	−0.150296	−	6.72857i	−0.00728187	−	0.326000i
$427$	10.5656	−	23.8601i	0.511303	−	1.15467i
$428$	8.60043	−	4.96546i	0.415717	−	0.240015i
$429$	−0.0857409	−	3.83851i	−0.00413961	−	0.185325i
$430$		−	0.918239i		−	0.0442814i
$431$	−8.46126	+	4.88511i	−0.407564	+	0.235307i	−0.689743	−	0.724055i	$-0.742276\pi$
$431$	−8.46126	+	4.88511i	−0.407564	+	0.235307i	0.282178	+	0.959362i	$0.408943\pi$
$432$	−4.31596	+	2.89352i	−0.207652	+	0.139215i
$433$			34.4543i			1.65577i	0.560898	+	0.827885i	$0.310456\pi$
$433$			34.4543i			1.65577i	−0.560898	+	0.827885i	$0.689544\pi$
$434$	1.22703	−	0.895280i	0.0588994	−	0.0429748i
$435$	−8.36515	−	13.7693i	−0.401078	−	0.660187i
$436$	4.45646			0.213426
$437$	13.3349	−	23.0968i	0.637897	−	1.10487i
$438$	−8.39840	+	5.10221i	−0.401291	+	0.243793i
$439$	−17.9508	+	10.3639i	−0.856745	+	0.494642i	−0.862921	−	0.505339i	$-0.831367\pi$
$439$	−17.9508	+	10.3639i	−0.856745	+	0.494642i	0.00617595	+	0.999981i	$0.498034\pi$
$440$	−0.450472			−0.0214754
$441$	20.3042	−	5.36099i	0.966866	−	0.255285i
$442$	−38.7061			−1.84106
$443$	8.25856	−	4.76808i	0.392376	−	0.226538i	−0.290813	−	0.956780i	$-0.593926\pi$
$443$	8.25856	−	4.76808i	0.392376	−	0.226538i	0.683189	+	0.730241i	$0.260592\pi$
$444$	−0.0558382	−	2.49981i	−0.00264997	−	0.118636i
$445$	1.98445	−	3.43716i	0.0940719	−	0.162937i
$446$	2.81733			0.133405
$447$	3.84789	−	7.02237i	0.181999	−	0.332147i
$448$	−2.13731	+	1.55945i	−0.100979	+	0.0736771i
$449$			2.23000i			0.105240i	0.998615	+	0.0526200i	$0.0167572\pi$
$449$			2.23000i			0.105240i	−0.998615	+	0.0526200i	$0.983243\pi$
$450$	2.66246	+	1.38250i	0.125510	+	0.0651715i
$451$	−0.746475	+	0.430978i	−0.0351501	+	0.0202939i
$452$		−	20.2030i		−	0.950271i
$453$	−18.6862	−	10.2390i	−0.877955	−	0.481073i
$454$	−2.24315	+	1.29508i	−0.105276	+	0.0607813i
$455$	−5.27146	+	11.9045i	−0.247130	+	0.558091i
$456$	8.11944	−	4.93274i	0.380228	−	0.230997i
$457$	−6.43820	−	11.1513i	−0.301166	−	0.521635i	0.675234	−	0.737603i	$-0.264043\pi$
$457$	−6.43820	−	11.1513i	−0.301166	−	0.521635i	−0.976400	+	0.215968i	$0.930709\pi$
$458$	−10.7592	−	18.6354i	−0.502743	−	0.870776i
$459$	−33.9481	+	22.7596i	−1.58456	+	1.06233i
$460$	−4.21087	−	2.43115i	−0.196333	−	0.113353i
$461$	1.56738	−	2.71478i	0.0730000	−	0.126440i	−0.827215	−	0.561886i	$-0.810076\pi$
$461$	1.56738	−	2.71478i	0.0730000	−	0.126440i	0.900215	+	0.435446i	$0.143409\pi$
$462$	−1.25368	−	1.64003i	−0.0583267	−	0.0763012i
$463$	−7.25355	−	12.5635i	−0.337101	−	0.583877i	0.646785	−	0.762672i	$-0.276113\pi$
$463$	−7.25355	−	12.5635i	−0.337101	−	0.583877i	−0.983886	+	0.178796i	$0.942780\pi$
$464$			9.30178i			0.431824i
$465$	0.516292	+	0.849832i	0.0239425	+	0.0394100i
$466$	−3.22684			−0.149480
$467$	4.83041	−	8.36651i	0.223525	−	0.387156i	−0.732351	−	0.680927i	$-0.761577\pi$
$467$	4.83041	−	8.36651i	0.223525	−	0.387156i	0.955876	+	0.293771i	$0.0949104\pi$
$468$	12.4425	−	7.94482i	0.575153	−	0.367249i
$469$	−1.30844	−	12.2118i	−0.0604180	−	0.563888i
$470$	−6.43119	−	3.71305i	−0.296648	−	0.171270i
$471$	−17.2995	−	28.4755i	−0.797120	−	1.31208i
$472$	−7.67779	−	4.43278i	−0.353399	−	0.204035i
$473$	−0.358224	−	0.206821i	−0.0164711	−	0.00950962i
$474$	−1.80437	−	2.97005i	−0.0828775	−	0.136419i
$475$	−4.75019	−	2.74252i	−0.217954	−	0.125836i
$476$	−16.8115	+	12.2662i	−0.770553	+	0.562219i
$477$	25.5352	+	13.2593i	1.16918	+	0.607101i
$478$	8.04923	−	13.9417i	0.368163	−	0.637677i
$479$	35.7357			1.63280			0.816402	−	0.577483i	$-0.195965\pi$
$479$	35.7357			1.63280			0.816402	+	0.577483i	$0.195965\pi$
$480$	−0.899307	−	1.48029i	−0.0410475	−	0.0675655i
$481$			7.10390i			0.323910i
$482$	12.8188	+	22.2029i	0.583881	+	1.01131i
$483$	−2.86797	−	22.0965i	−0.130497	−	1.00542i
$484$	5.39854	−	9.35054i	0.245388	−	0.425025i
$485$	8.69468	+	5.01988i	0.394805	+	0.227941i
$486$	6.24132	−	14.2845i	0.283112	−	0.647957i
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	0.569707	−	0.821848i	$-0.307057\pi$
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	−0.996595	+	0.0824564i	$0.973723\pi$
$488$	−4.93145	−	8.54152i	−0.223236	−	0.386656i
$489$	−9.22122	+	5.60210i	−0.416998	+	0.253336i
$490$	1.48301	+	6.84110i	0.0669955	+	0.309050i
$491$	−13.9486	+	8.05323i	−0.629492	+	0.363437i	−0.780555	−	0.625087i	$-0.785064\pi$
$491$	−13.9486	+	8.05323i	−0.629492	+	0.363437i	0.151064	+	0.988524i	$0.451730\pi$
$492$	−2.90646	−	1.59259i	−0.131033	−	0.0717993i
$493$			73.1650i			3.29519i
$494$	−23.3751	+	13.4956i	−1.05170	+	0.607197i
$495$	1.13902	−	0.727293i	0.0511953	−	0.0326894i
$496$		−	0.574100i		−	0.0257778i
$497$	6.05958	+	8.30499i	0.271809	+	0.372530i
$498$	7.93508	−	14.4815i	0.355580	−	0.648931i
$499$	1.35262			0.0605518			0.0302759	−	0.999542i	$-0.490361\pi$
$499$	1.35262			0.0605518			0.0302759	+	0.999542i	$0.490361\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	0.279000	+	12.4905i	0.0124648	+	0.558034i
$502$	11.0459	−	6.37734i	0.493002	−	0.284635i
$503$	39.9065			1.77934			0.889671	−	0.456603i	$-0.150934\pi$
$503$	39.9065			1.77934			0.889671	+	0.456603i	$0.150934\pi$
$504$	2.88646	−	7.39380i	0.128573	−	0.329346i
$505$	5.49909			0.244706
$506$	−1.89688	+	1.09516i	−0.0843266	+	0.0486860i
$507$	−16.6014	+	10.0857i	−0.737296	+	0.447923i
$508$	1.54404	−	2.67436i	0.0685058	−	0.118656i
$509$	−10.8798			−0.482240			−0.241120	−	0.970495i	$-0.577515\pi$
$509$	−10.8798			−0.482240			−0.241120	+	0.970495i	$0.577515\pi$
$510$	−7.07368	−	11.6435i	−0.313228	−	0.515583i
$511$	6.07770	−	13.7252i	0.268861	−	0.607168i
$512$			1.00000i			0.0441942i
$513$	−12.5661	+	25.5814i	−0.554807	+	1.12945i
$514$	23.4499	−	13.5388i	1.03433	−	0.597171i
$515$		−	15.5075i		−	0.683343i
$516$	−0.0355167	−	1.59004i	−0.00156354	−	0.0699976i
$517$	−2.89707	+	1.67263i	−0.127413	+	0.0735620i
$518$	2.25126	+	3.08548i	0.0989147	+	0.135568i
$519$	−0.603396	−	27.0133i	−0.0264862	−	1.18575i
$520$	2.46044	+	4.26160i	0.107897	+	0.186884i
$521$	19.6042	+	33.9555i	0.858877	+	1.48762i	0.873001	+	0.487718i	$0.162171\pi$
$521$	19.6042	+	33.9555i	0.858877	+	1.48762i	−0.0141243	+	0.999900i	$0.504496\pi$
$522$	−15.0178	−	23.5196i	−0.657313	−	1.02943i
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	0.769164	−	0.639052i	$-0.220673\pi$
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	−0.168853	+	0.985641i	$0.554006\pi$
$524$	−7.85422	+	13.6039i	−0.343113	+	0.594290i
$525$	−4.54446	+	0.589839i	−0.198336	+	0.0257427i
$526$	−6.66669	−	11.5471i	−0.290682	−	0.503475i
$527$		−	4.51570i		−	0.196707i
$528$	−0.780047	+	0.0174239i	−0.0339472	+	0.000758278i
$529$	−0.641865			−0.0279072
$530$	−4.79542	+	8.30591i	−0.208300	+	0.360786i
$531$	26.5701	−	1.18759i	1.15305	−	0.0515369i
$532$	−5.87582	+	13.2693i	−0.254749	+	0.575298i
$533$	8.15435	+	4.70792i	0.353204	+	0.203923i
$534$	3.30336	−	6.02862i	0.142950	−	0.260884i
$535$	−8.60043	−	4.96546i	−0.371829	−	0.214676i
$536$	−4.02013	−	2.32102i	−0.173643	−	0.100253i
$537$	6.60383	−	0.147510i	0.284976	−	0.00636552i
$538$	−13.1361	−	7.58415i	−0.566339	−	0.326976i
$539$	3.00288	+	0.962312i	0.129343	+	0.0414497i
$540$	4.66384	+	2.29097i	0.200700	+	0.0985878i
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	−0.988291	−	0.152580i	$-0.951242\pi$
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	0.626284	+	0.779595i	$0.284575\pi$
$542$	26.2938			1.12942
$543$	3.82431	−	6.97934i	0.164117	−	0.299512i
$544$			7.86570i			0.337239i
$545$	−2.22823	−	3.85941i	−0.0954470	−	0.165319i
$546$	−8.66770	+	20.8179i	−0.370943	+	0.890925i
$547$	−13.5255	+	23.4268i	−0.578307	+	1.00166i	0.417366	+	0.908738i	$0.362953\pi$
$547$	−13.5255	+	23.4268i	−0.578307	+	1.00166i	−0.995674	+	0.0929192i	$0.970380\pi$
$548$	11.3130	+	6.53158i	0.483268	+	0.279015i
$549$	26.2596	+	13.6354i	1.12073	+	0.581945i
$550$	0.225236	+	0.390121i	0.00960410	+	0.0166348i
$551$	25.5104	+	44.1852i	1.08678	+	1.88235i
$552$	−7.38565	−	4.04694i	−0.314354	−	0.172249i
$553$	4.85385	+	2.14935i	0.206407	+	0.0913995i
$554$	20.1611	−	11.6400i	0.856563	−	0.494537i
$555$	−2.13698	+	1.29826i	−0.0907097	+	0.0551081i
$556$			0.655415i			0.0277958i
$557$	31.3474	−	18.0984i	1.32823	−	0.766854i	0.343205	−	0.939261i	$-0.388487\pi$
$557$	31.3474	−	18.0984i	1.32823	−	0.766854i	0.985026	+	0.172406i	$0.0551542\pi$
$558$	0.926891	+	1.45162i	0.0392384	+	0.0614518i
$559$			4.51854i			0.191114i
$560$	2.41918	+	1.07124i	0.102229	+	0.0452683i
$561$	−6.13562	+	0.137051i	−0.259046	+	0.00578631i
$562$	−3.93045			−0.165796
$563$	7.00932	−	12.1405i	0.295408	−	0.511661i	−0.679672	−	0.733516i	$-0.737878\pi$
$563$	7.00932	−	12.1405i	0.295408	−	0.511661i	0.975080	+	0.221855i	$0.0712111\pi$
$564$	−11.2800	−	6.18083i	−0.474973	−	0.260260i
$565$	−17.4964	+	10.1015i	−0.736077	+	0.424974i
$566$	−28.8938			−1.21450
$567$	4.63895	+	23.3555i	0.194817	+	0.980840i
$568$	3.88571			0.163041
$569$	−22.2561	+	12.8496i	−0.933024	+	0.538682i	−0.887767	−	0.460294i	$-0.847744\pi$
$569$	−22.2561	+	12.8496i	−0.933024	+	0.538682i	−0.0452575	+	0.998975i	$0.514411\pi$
$570$	−8.33160	−	4.56527i	−0.348972	−	0.191218i
$571$	−7.82510	+	13.5535i	−0.327470	+	0.567195i	−0.982009	−	0.188833i	$-0.939530\pi$
$571$	−7.82510	+	13.5535i	−0.327470	+	0.567195i	0.654539	+	0.756028i	$0.272863\pi$
$572$	2.21672			0.0926857
$573$	43.4526	−	0.970600i	1.81526	−	0.0405474i
$574$	5.03369	−	0.539337i	0.210102	−	0.0225115i
$575$			4.86229i			0.202772i
$576$	−1.61451	−	2.52851i	−0.0672714	−	0.105354i
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.941994	−	0.335629i	$-0.891051\pi$
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.180334	+	0.983605i	$0.557718\pi$
$578$			44.8693i			1.86632i
$579$	−26.5042	+	16.1019i	−1.10148	+	0.669173i
$580$	8.05558	−	4.65089i	0.334490	−	0.193118i
$581$	2.68725	+	25.0805i	0.111486	+	1.04051i
$582$	15.2500	+	8.35621i	0.632135	+	0.346376i
$583$	2.16020	+	3.74158i	0.0894665	+	0.154961i
$584$	−2.83675	−	4.91339i	−0.117385	−	0.203318i
$585$	−13.1016	−	6.80309i	−0.541686	−	0.281273i
$586$	3.74744	+	2.16359i	0.154805	+	0.0893770i
$587$	−2.19821	+	3.80741i	−0.0907299	+	0.157149i	−0.907818	−	0.419363i	$-0.862253\pi$
$587$	−2.19821	+	3.80741i	−0.0907299	+	0.157149i	0.817089	+	0.576512i	$0.195587\pi$
$588$	2.83262	+	11.7888i	0.116815	+	0.486163i
$589$	−1.57448	−	2.72708i	−0.0648754	−	0.112368i
$590$			8.86555i			0.364989i
$591$	−10.5307	+	19.2184i	−0.433174	+	0.790540i
$592$	1.44362			0.0593326
$593$	8.99345	−	15.5771i	0.369317	−	0.639675i	−0.620142	−	0.784489i	$-0.712925\pi$
$593$	8.99345	−	15.5771i	0.369317	−	0.639675i	0.989459	+	0.144814i	$0.0462584\pi$
$594$	1.94422	−	1.30345i	0.0797724	−	0.0534813i
$595$	19.0286	+	8.42608i	0.780095	+	0.345436i
$596$	4.00375	+	2.31156i	0.164000	+	0.0946853i
$597$	36.5752	−	0.816981i	1.49692	−	0.0334368i
$598$	20.7212	+	11.9634i	0.847351	+	0.489218i
$599$	−1.19486	−	0.689852i	−0.0488206	−	0.0281866i	0.475391	−	0.879775i	$-0.342307\pi$
$599$	−1.19486	−	0.689852i	−0.0488206	−	0.0281866i	−0.524212	+	0.851588i	$0.675640\pi$
$600$	−0.832312	+	1.51897i	−0.0339790	+	0.0620115i
$601$	−40.5777	−	23.4275i	−1.65520	−	0.955630i	−0.974885	−	0.222709i	$-0.928510\pi$
$601$	−40.5777	−	23.4275i	−1.65520	−	0.955630i	−0.680314	−	0.732921i	$-0.738157\pi$
$602$	1.43195	+	1.96257i	0.0583618	+	0.0799882i
$603$	13.9122	−	0.621826i	0.566550	−	0.0253227i
$604$	6.15097	−	10.6538i	0.250279	−	0.433496i
$605$	−10.7971			−0.438964
$606$	9.52233	−	0.212701i	0.386818	−	0.00864037i
$607$		−	22.5955i		−	0.917121i	−0.888663	−	0.458561i	$-0.848365\pi$
$607$		−	22.5955i		−	0.917121i	0.888663	−	0.458561i	$-0.151635\pi$
$608$	2.74252	+	4.75019i	0.111224	+	0.192646i
$609$	39.3515	+	16.3843i	1.59460	+	0.663924i
$610$	−4.93145	+	8.54152i	−0.199668	+	0.345836i
$611$	31.6471	+	18.2714i	1.28030	+	0.739183i
$612$	−12.6993	−	19.8885i	−0.513338	−	0.803945i
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	0.996162	−	0.0875282i	$-0.0278968\pi$
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	−0.573883	+	0.818938i	$0.694563\pi$
$614$	0.209941	+	0.363629i	0.00847253	+	0.0146749i
$615$	0.0740106	+	3.31336i	0.00298440	+	0.133608i
$616$	0.962801	−	0.702489i	0.0387924	−	0.0283041i
$617$	−8.43544	+	4.87020i	−0.339598	+	0.196067i	−0.660094	−	0.751183i	$-0.729484\pi$
$617$	−8.43544	+	4.87020i	−0.339598	+	0.196067i	0.320496	+	0.947250i	$0.396150\pi$
$618$	−0.599818	−	26.8531i	−0.0241282	−	1.08019i
$619$			18.2795i			0.734715i	0.930080	+	0.367358i	$0.119737\pi$
$619$			18.2795i			0.734715i	−0.930080	+	0.367358i	$0.880263\pi$
$620$	−0.497185	+	0.287050i	−0.0199674	+	0.0115282i
$621$	25.2085	−	1.69150i	1.01158	−	0.0678775i
$622$			6.28435i			0.251980i
$623$	1.11870	+	10.4410i	0.0448197	+	0.418308i
$624$	4.42538	+	7.28430i	0.177157	+	0.291606i
$625$	1.00000			0.0400000
$626$	−2.84206	+	4.92258i	−0.113591	+	0.196746i
$627$	−3.65758	+	2.22206i	−0.146070	+	0.0887407i
$628$	16.6593	−	9.61826i	0.664779	−	0.383810i
$629$	11.3551			0.452758
$630$	−7.84645	+	1.19715i	−0.312610	+	0.0476957i
$631$	23.4168			0.932209			0.466104	−	0.884730i	$-0.345657\pi$
$631$	23.4168			0.932209			0.466104	+	0.884730i	$0.345657\pi$
$632$	1.73760	−	1.00320i	0.0691178	−	0.0399052i
$633$	−0.774606	−	34.6781i	−0.0307878	−	1.37833i
$634$	−5.01570	+	8.68744i	−0.199199	+	0.345022i
$635$	−3.08808			−0.122547
$636$	−7.98257	+	14.5682i	−0.316530	+	0.577665i
$637$	−7.29770	−	33.6642i	−0.289146	−	1.33382i
$638$		−	4.19019i		−	0.165891i
$639$	−9.82505	+	6.27353i	−0.388673	+	0.248177i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$			3.99917i			0.157958i	0.996876	+	0.0789788i	$0.0251659\pi$
$641$			3.99917i			0.157958i	−0.996876	+	0.0789788i	$0.974834\pi$
$642$	−15.0847	−	8.26563i	−0.595347	−	0.326218i
$643$	−14.6262	+	8.44444i	−0.576801	+	0.333016i	−0.759861	−	0.650085i	$-0.774733\pi$
$643$	−14.6262	+	8.44444i	−0.576801	+	0.333016i	0.183060	+	0.983102i	$0.441400\pi$
$644$	12.7912	−	1.37052i	0.504044	−	0.0540059i
$645$	−1.35926	+	0.825778i	−0.0535207	+	0.0325150i
$646$	21.5719	+	37.3636i	0.848734	+	1.47005i
$647$	−14.0753	−	24.3792i	−0.553358	−	0.958443i	−0.998029	−	0.0627498i	$-0.980013\pi$
$647$	−14.0753	−	24.3792i	−0.553358	−	0.958443i	0.444672	−	0.895694i	$-0.353320\pi$
$648$	8.16461	+	3.78670i	0.320736	+	0.148756i
$649$	3.45863	+	1.99684i	0.135763	+	0.0783830i
$650$	2.46044	−	4.26160i	0.0965063	−	0.167154i
$651$	−2.42875	−	1.01123i	−0.0951902	−	0.0396331i
$652$	−3.11468	−	5.39478i	−0.121980	−	0.211276i
$653$		−	23.4509i		−	0.917704i	−0.888513	−	0.458852i	$-0.848261\pi$
$653$		−	23.4509i		−	0.917704i	0.888513	−	0.458852i	$-0.151739\pi$
$654$	−4.00773	−	6.59684i	−0.156715	−	0.257957i
$655$	15.7084			0.613780
$656$	0.956724	−	1.65709i	0.0373538	−	0.0646987i
$657$	15.1055	+	7.84358i	0.589321	+	0.306007i
$658$	19.5358	−	2.09317i	0.761584	−	0.0816002i
$659$	13.7094	+	7.91513i	0.534043	+	0.308330i	0.742661	−	0.669667i	$-0.233563\pi$
$659$	13.7094	+	7.91513i	0.534043	+	0.308330i	−0.208618	+	0.977997i	$0.566897\pi$
$660$	0.405113	+	0.666828i	0.0157690	+	0.0259563i
$661$	10.3009	+	5.94725i	0.400660	+	0.231321i	0.686769	−	0.726876i	$-0.259028\pi$
$661$	10.3009	+	5.94725i	0.400660	+	0.231321i	−0.286109	+	0.958197i	$0.592362\pi$
$662$	−27.4558	−	15.8516i	−1.06710	−	0.616089i
$663$	34.8087	+	57.2962i	1.35186	+	2.22520i
$664$	8.25650	+	4.76689i	0.320414	+	0.184991i
$665$	14.4295	−	1.54605i	0.559551	−	0.0599533i
$666$	−3.65022	+	2.33075i	−0.141443	+	0.0903147i
$667$	22.6140	−	39.1686i	0.875617	−	1.51661i
$668$	−7.21319			−0.279087
$669$	−2.53365	−	4.17046i	−0.0979565	−	0.161239i
$670$			4.64204i			0.179338i
$671$	2.22148	+	3.84772i	0.0857593	+	0.148540i
$672$	4.23053	+	1.76141i	0.163196	+	0.0679480i
$673$	−2.58993	+	4.48588i	−0.0998343	+	0.172918i	−0.911616	−	0.411043i	$-0.865165\pi$
$673$	−2.58993	+	4.48588i	−0.0998343	+	0.172918i	0.811782	+	0.583961i	$0.198498\pi$
$674$	−12.2908	−	7.09612i	−0.473425	−	0.273332i
$675$	−0.347881	−	5.18449i	−0.0133900	−	0.199551i
$676$	−5.60751	−	9.71249i	−0.215673	−	0.373557i
$677$	−5.58197	−	9.66826i	−0.214533	−	0.371582i	0.738595	−	0.674149i	$-0.235490\pi$
$677$	−5.58197	−	9.66826i	−0.214533	−	0.371582i	−0.953128	+	0.302568i	$0.902156\pi$
$678$	−29.9063	+	18.1687i	−1.14854	+	0.697766i
$679$	−26.4115	+	2.82987i	−1.01358	+	0.108600i
$680$	6.81190	−	3.93285i	0.261224	−	0.150818i
$681$	3.93437	+	2.15583i	0.150766	+	0.0826115i
$682$			0.258616i			0.00990292i
$683$	−31.3199	+	18.0825i	−1.19842	+	0.691909i	−0.960203	−	0.279302i	$-0.909897\pi$
$683$	−31.3199	+	18.0825i	−1.19842	+	0.691909i	−0.238219	+	0.971211i	$0.576564\pi$
$684$	−14.6037	−	7.58305i	−0.558388	−	0.289945i
$685$		−	13.0632i		−	0.499117i
$686$	−13.8380	−	12.3089i	−0.528338	−	0.469956i
$687$	−17.9100	+	32.6856i	−0.683308	+	1.24703i
$688$	0.918239			0.0350075
$689$	23.5977	−	40.8723i	0.898999	−	1.55711i
$690$	0.188069	+	8.41963i	0.00715968	+	0.320530i
$691$	5.80724	−	3.35281i	0.220918	−	0.127547i	−0.385457	−	0.922726i	$-0.625956\pi$
$691$	5.80724	−	3.35281i	0.220918	−	0.127547i	0.606375	+	0.795179i	$0.292623\pi$
$692$	15.6000			0.593024
$693$	−1.30027	+	3.33070i	−0.0493932	+	0.126523i
$694$	0.732838			0.0278181
$695$	0.567606	−	0.327707i	0.0215305	−	0.0124306i
$696$	13.7693	−	8.36515i	0.521924	−	0.317080i
$697$	7.52531	−	13.0342i	0.285041	−	0.493706i
$698$	−26.7017			−1.01067
$699$	2.90192	+	4.77665i	0.109761	+	0.180669i
$700$	−0.281867	−	2.63069i	−0.0106536	−	0.0994309i
$701$			1.39464i			0.0526749i	0.999653	+	0.0263375i	$0.00838445\pi$
$701$			1.39464i			0.0526749i	−0.999653	+	0.0263375i	$0.991616\pi$
$702$	−22.9502	−	11.2736i	−0.866199	−	0.425494i
$703$	6.85749	−	3.95918i	0.258635	−	0.149323i
$704$		−	0.450472i		−	0.0169778i
$705$	0.287235	+	12.8592i	0.0108179	+	0.484304i
$706$	5.19889	−	3.00158i	0.195663	−	0.112966i
$707$	−11.7533	+	8.57557i	−0.442028	+	0.322517i
$708$	0.342912	+	15.3518i	0.0128874	+	0.576954i
$709$	24.8056	+	42.9645i	0.931593	+	1.61357i	0.780599	+	0.625032i	$0.214914\pi$
$709$	24.8056	+	42.9645i	0.931593	+	1.61357i	0.150994	+	0.988535i	$0.451753\pi$
$710$	−1.94286	−	3.36513i	−0.0729141	−	0.126291i
$711$	−2.77384	+	5.34197i	−0.104027	+	0.200340i
$712$	3.43716	+	1.98445i	0.128813	+	0.0743703i
$713$	−1.39572	+	2.41746i	−0.0522701	+	0.0905345i
$714$	33.2761	+	13.8548i	1.24533	+	0.518501i
$715$	−1.10836	−	1.91973i	−0.0414503	−	0.0717940i
$716$			3.81368i			0.142524i
$717$	−27.8764	+	0.622675i	−1.04106	+	0.0232542i
$718$	29.3148			1.09402
$719$	−10.4343	+	18.0727i	−0.389133	+	0.673998i	−0.992333	−	0.123592i	$-0.960559\pi$
$719$	−10.4343	+	18.0727i	−0.389133	+	0.673998i	0.603200	+	0.797590i	$0.293892\pi$
$720$	−1.38250	+	2.66246i	−0.0515226	+	0.0992241i
$721$	24.1832	+	33.1444i	0.900629	+	1.23436i
$722$	9.60055	+	5.54288i	0.357295	+	0.206285i
$723$	21.3385	−	38.9427i	0.793588	−	1.44829i
$724$	3.97921	+	2.29740i	0.147886	+	0.0853821i
$725$	−8.05558	−	4.65089i	−0.299177	−	0.172730i
$726$	−18.6964	+	0.417622i	−0.693889	+	0.0154994i
$727$	−32.1908	−	18.5854i	−1.19389	−	0.689293i	−0.234704	−	0.972067i	$-0.575412\pi$
$727$	−32.1908	−	18.5854i	−1.19389	−	0.689293i	−0.959187	+	0.282773i	$0.908746\pi$
$728$	−11.9045	−	5.27146i	−0.441210	−	0.195373i
$729$	−26.7580	+	3.60718i	−0.991035	+	0.133599i
$730$	−2.83675	+	4.91339i	−0.104993	+	0.181853i
$731$	7.22260			0.267137
$732$	−8.20901	+	14.9814i	−0.303414	+	0.553728i
$733$			11.9964i			0.443096i	0.975149	+	0.221548i	$0.0711109\pi$
$733$			11.9964i			0.443096i	−0.975149	+	0.221548i	$0.928889\pi$
$734$	10.0170	+	17.3499i	0.369733	+	0.640397i
$735$	8.79311	−	8.34753i	0.324339	−	0.307903i
$736$	2.43115	−	4.21087i	0.0896132	−	0.155215i
$737$	1.81096	+	1.04556i	0.0667075	+	0.0385136i
$738$	0.256316	+	5.73462i	0.00943513	+	0.211094i
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	0.990507	+	0.137463i	$0.0438947\pi$
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	−0.376207	+	0.926535i	$0.622772\pi$
$740$	−0.721812	−	1.25022i	−0.0265343	−	0.0459588i
$741$	40.9988	+	22.4651i	1.50613	+	0.825278i
$742$	−2.70334	−	25.2306i	−0.0992426	−	0.926243i
$743$	−42.2679	+	24.4034i	−1.55066	+	0.895273i	−0.552570	+	0.833467i	$0.686353\pi$
$743$	−42.2679	+	24.4034i	−1.55066	+	0.895273i	−0.998088	+	0.0618062i	$0.980314\pi$
$744$	−0.849832	+	0.516292i	−0.0311563	+	0.0189282i
$745$		−	4.62313i		−	0.169378i
$746$	−5.94714	+	3.43358i	−0.217740	+	0.125712i
$747$	−28.5728	+	1.27710i	−1.04542	+	0.0467267i
$748$		−	3.54328i		−	0.129555i
$749$	26.1252	−	2.79919i	0.954595	−	0.102280i
$750$	1.73162	−	0.0386792i	0.0632298	−	0.00141236i
$751$	10.6219			0.387599			0.193799	−	0.981041i	$-0.437919\pi$
$751$	10.6219			0.387599			0.193799	+	0.981041i	$0.437919\pi$
$752$	3.71305	−	6.43119i	0.135401	−	0.234521i
$753$	−19.3739	−	10.6159i	−0.706025	−	0.386864i
$754$	−39.6405	+	22.8864i	−1.44362	+	0.833475i
$755$	−12.3019			−0.447713
$756$	−13.5408	+	2.37650i	−0.492473	+	0.0864326i
$757$	−41.0132			−1.49065			−0.745326	−	0.666701i	$-0.767706\pi$
$757$	−41.0132			−1.49065			−0.745326	+	0.666701i	$0.767706\pi$
$758$	0.590817	−	0.341108i	0.0214594	−	0.0123896i
$759$	3.32703	+	1.82304i	0.120764	+	0.0661720i
$760$	2.74252	−	4.75019i	0.0994818	−	0.172308i
$761$	1.62266			0.0588212			0.0294106	−	0.999567i	$-0.490637\pi$
$761$	1.62266			0.0588212			0.0294106	+	0.999567i	$0.490637\pi$
$762$	−5.34739	+	0.119445i	−0.193715	+	0.00432702i
$763$	10.7810	+	4.77396i	0.390298	+	0.172829i
$764$			25.0936i			0.907855i
$765$	−10.8743	+	20.9421i	−0.393161	+	0.757165i
$766$	27.3944	−	15.8162i	0.989799	−	0.571461i
$767$		−	43.6263i		−	1.57525i
$768$	1.48029	−	0.899307i	0.0534152	−	0.0324509i
$769$	−15.4016	+	8.89210i	−0.555395	+	0.320657i	−0.751295	−	0.659966i	$-0.770570\pi$
$769$	−15.4016	+	8.89210i	−0.555395	+	0.320657i	0.195900	+	0.980624i	$0.437237\pi$
$770$	−1.08977	−	0.482566i	−0.0392727	−	0.0173905i
$771$	−41.1300	−	22.5370i	−1.48126	−	0.811651i
$772$	−8.95240	−	15.5060i	−0.322204	−	0.558074i
$773$	−13.0759	−	22.6481i	−0.470307	−	0.814596i	0.529116	−	0.848549i	$-0.322523\pi$
$773$	−13.0759	−	22.6481i	−0.470307	−	0.814596i	−0.999423	+	0.0339536i	$0.989190\pi$
$774$	−2.32177	+	1.48251i	−0.0834544	+	0.0532877i
$775$	0.497185	+	0.287050i	0.0178594	+	0.0103111i
$776$	−5.01988	+	8.69468i	−0.180203	+	0.312121i
$777$	2.54282	−	6.10730i	0.0912231	−	0.219098i
$778$	−14.0160	−	24.2765i	−0.502499	−	0.870355i
$779$		−	10.4954i		−	0.376035i
$780$	4.09570	−	7.47464i	0.146650	−	0.267635i
$781$	−1.75041			−0.0626344
$782$	19.1227	−	33.1214i	0.683825	−	1.18442i
$783$	−21.3101	+	43.3820i	−0.761562	+	1.55035i
$784$	−6.84110	+	1.48301i	−0.244325	+	0.0529646i
$785$	−16.6593	−	9.61826i	−0.594596	−	0.343290i
$786$	27.2010	−	0.607590i	0.970229	−	0.0216720i
$787$	19.8282	+	11.4478i	0.706800	+	0.408071i	0.809875	−	0.586603i	$-0.199535\pi$
$787$	19.8282	+	11.4478i	0.706800	+	0.408071i	−0.103075	+	0.994674i	$0.532868\pi$
$788$	−10.9572	−	6.32615i	−0.390335	−	0.225360i
$789$	−11.0975	+	20.2530i	−0.395083	+	0.721024i
$790$	−1.73760	−	1.00320i	−0.0618209	−	0.0356923i
$791$	21.6424	−	48.8748i	0.769514	−	1.73779i
$792$	0.727293	+	1.13902i	0.0258432	+	0.0404734i
$793$	24.2670	−	42.0317i	0.861748	−	1.49259i
$794$	−29.2382			−1.03762
$795$	16.6077	−	0.370966i	0.589014	−	0.0131568i
$796$			21.1220i			0.748648i
$797$	−8.74751	−	15.1511i	−0.309853	−	0.536681i	0.668477	−	0.743733i	$-0.266946\pi$
$797$	−8.74751	−	15.1511i	−0.309853	−	0.536681i	−0.978330	+	0.207052i	$0.933613\pi$
$798$	24.9266	−	3.23529i	0.882391	−	0.114528i
$799$	29.2057	−	50.5858i	1.03322	−	1.78960i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−11.8948	+	0.531654i	−0.420283	+	0.0187851i
$802$	−5.78471	−	10.0194i	−0.204265	−	0.353798i
$803$	1.27788	+	2.21335i	0.0450953	+	0.0781073i
$804$	0.179551	+	8.03825i	0.00633226	+	0.283487i
$805$	−7.58250	−	10.3922i	−0.267248	−	0.366278i
$806$	2.44658	−	1.41254i	0.0861773	−	0.0497545i
$807$	0.586697	+	26.2657i	0.0206527	+	0.924597i
$808$			5.49909i			0.193457i
$809$	−3.79610	+	2.19168i	−0.133464	+	0.0770553i	−0.565245	−	0.824923i	$-0.691218\pi$
$809$	−3.79610	+	2.19168i	−0.133464	+	0.0770553i	0.431782	+	0.901978i	$0.357885\pi$
$810$	−0.802930	−	8.96411i	−0.0282121	−	0.314967i
$811$			55.5831i			1.95179i	0.218247	+	0.975893i	$0.429966\pi$
$811$			55.5831i			1.95179i	−0.218247	+	0.975893i	$0.570034\pi$
$812$	−9.96447	+	22.5027i	−0.349684	+	0.789690i
$813$	−23.6462	−	38.9223i	−0.829308	−	1.36507i
$814$	−0.650313			−0.0227935
$815$	−3.11468	+	5.39478i	−0.109102	+	0.188971i
$816$	11.6435	−	7.07368i	0.407604	−	0.247628i
$817$	4.36181	−	2.51829i	0.152600	−	0.0881039i
$818$	−2.07755			−0.0726398
$819$	38.6114	−	5.89103i	1.34919	−	0.205849i
$820$	−1.91345			−0.0668205
$821$	−13.1066	+	7.56707i	−0.457422	+	0.264093i	−0.710960	−	0.703233i	$-0.751739\pi$
$821$	−13.1066	+	7.56707i	−0.457422	+	0.264093i	0.253538	+	0.967325i	$0.418406\pi$
$822$	−0.505272	−	22.6204i	−0.0176234	−	0.788977i
$823$	18.1011	−	31.3520i	0.630964	−	1.09286i	−0.356391	−	0.934337i	$-0.615993\pi$
$823$	18.1011	−	31.3520i	0.630964	−	1.09286i	0.987355	−	0.158525i	$-0.0506739\pi$
$824$	15.5075			0.540230
$825$	0.374934	−	0.684252i	0.0130535	−	0.0238226i
$826$	−13.8254	−	18.9485i	−0.481047	−	0.659302i
$827$		−	3.78131i		−	0.131489i	−0.997836	−	0.0657446i	$-0.979058\pi$
$827$		−	3.78131i		−	0.131489i	0.997836	−	0.0657446i	$-0.0209422\pi$
$828$	0.651329	+	14.5723i	0.0226353	+	0.506423i
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	−0.00776491	−	0.999970i	$-0.502472\pi$
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	0.862117	+	0.506710i	$0.169138\pi$
$830$		−	9.53378i		−	0.330922i
$831$	−35.3616	−	19.3763i	−1.22668	−	0.672155i
$832$	−4.26160	+	2.46044i	−0.147745	+	0.0853003i
$833$	−53.8101	+	11.6649i	−1.86441	+	0.404165i
$834$	0.970201	−	0.589419i	0.0335953	−	0.0204099i
$835$	3.60660	+	6.24681i	0.124811	+	0.216180i
$836$	−1.23543	−	2.13983i	−0.0427283	−	0.0740076i
$837$	1.31525	−	2.67751i	0.0454616	−	0.0925483i
$838$	−5.45962	−	3.15211i	−0.188600	−	0.108888i
$839$	13.6621	−	23.6634i	0.471667	−	0.816951i	−0.527808	−	0.849364i	$-0.676986\pi$
$839$	13.6621	−	23.6634i	0.471667	−	0.816951i	0.999475	+	0.0324131i	$0.0103192\pi$
$840$	−0.589839	−	4.54446i	−0.0203514	−	0.156799i
$841$	28.7615	+	49.8165i	0.991777	+	1.71781i
$842$			2.60242i			0.0896854i
$843$	3.53468	+	5.81820i	0.121741	+	0.200389i
$844$	20.0264			0.689338
$845$	−5.60751	+	9.71249i	−0.192904	+	0.334120i
$846$	0.994764	+	22.2561i	0.0342007	+	0.765179i
$847$	23.0767	−	16.8375i	0.792926	−	0.578544i
$848$	−8.30591	−	4.79542i	−0.285226	−	0.164675i
$849$	25.9844	+	42.7710i	0.891781	+	1.46790i
$850$	−6.81190	−	3.93285i	−0.233646	−	0.134896i
$851$	−6.07891	−	3.50966i	−0.208382	−	0.120310i
$852$	−3.49445	−	5.75197i	−0.119718	−	0.197059i
$853$	−7.91557	−	4.57006i	−0.271024	−	0.156476i	0.358329	−	0.933595i	$-0.383347\pi$
$853$	−7.91557	−	4.57006i	−0.271024	−	0.156476i	−0.629353	+	0.777120i	$0.716680\pi$
$854$	−2.78002	−	25.9463i	−0.0951303	−	0.887863i
$855$	0.734751	+	16.4387i	0.0251280	+	0.562193i
$856$	4.96546	−	8.60043i	0.169716	−	0.293957i
$857$	0.951997			0.0325196			0.0162598	−	0.999868i	$-0.494824\pi$
$857$	0.951997			0.0325196			0.0162598	+	0.999868i	$0.494824\pi$
$858$	−1.99351	−	3.28138i	−0.0680573	−	0.112024i
$859$			35.4135i			1.20829i	0.796873	+	0.604147i	$0.206486\pi$
$859$			35.4135i			1.20829i	−0.796873	+	0.604147i	$0.793514\pi$
$860$	−0.459119	−	0.795218i	−0.0156558	−	0.0271167i
$861$	−5.32521	−	6.96628i	−0.181483	−	0.237410i
$862$	−4.88511	+	8.46126i	−0.166388	+	0.288192i
$863$	−22.9444	−	13.2469i	−0.781036	−	0.450931i	0.0557615	−	0.998444i	$-0.482241\pi$
$863$	−22.9444	−	13.2469i	−0.781036	−	0.450931i	−0.836797	+	0.547513i	$0.815575\pi$
$864$	−2.29097	+	4.66384i	−0.0779405	+	0.158667i
$865$	−7.80001	−	13.5100i	−0.265208	−	0.459354i
$866$	17.2272	+	29.8383i	0.585403	+	1.01395i
$867$	66.4194	−	40.3513i	2.25572	−	1.37040i
$868$	0.615001	−	1.38885i	0.0208745	−	0.0471407i
$869$	−0.782739	+	0.451915i	−0.0265526	+	0.0153301i
$870$	−14.1291	−	7.74198i	−0.479021	−	0.262478i
$871$		−	22.8429i		−	0.774003i
$872$	3.85941	−	2.22823i	0.130696	−	0.0754575i
$873$	−1.34488	−	30.0892i	−0.0455172	−	1.01837i
$874$		−	26.6699i		−	0.902123i
$875$	−2.13731	+	1.55945i	−0.0722544	+	0.0527191i
$876$	−4.72212	+	8.61785i	−0.159546	+	0.291170i
$877$	12.5178			0.422697			0.211349	−	0.977411i	$-0.432214\pi$
$877$	12.5178			0.422697			0.211349	+	0.977411i	$0.432214\pi$
$878$	−10.3639	+	17.9508i	−0.349765	+	0.605810i
$879$	−0.167372	−	7.49302i	−0.00564530	−	0.252733i
$880$	−0.390121	+	0.225236i	−0.0131510	+	0.00759271i
$881$	−32.3516			−1.08995			−0.544977	−	0.838451i	$-0.683462\pi$
$881$	−32.3516			−1.08995			−0.544977	+	0.838451i	$0.683462\pi$
$882$	14.9034	−	14.7948i	0.501825	−	0.498168i
$883$	24.9749			0.840473			0.420237	−	0.907415i	$-0.361947\pi$
$883$	24.9749			0.840473			0.420237	+	0.907415i	$0.361947\pi$
$884$	−33.5205	+	19.3531i	−1.12742	+	0.650914i
$885$	13.1236	−	7.97285i	0.441144	−	0.268004i
$886$	4.76808	−	8.25856i	0.160187	−	0.277452i
$887$	−0.411815			−0.0138274			−0.00691370	−	0.999976i	$-0.502201\pi$
$887$	−0.411815			−0.0138274			−0.00691370	+	0.999976i	$0.502201\pi$
$888$	−1.29826	−	2.13698i	−0.0435668	−	0.0717123i
$889$	6.60021	−	4.81572i	0.221364	−	0.161514i
$890$		−	3.96890i		−	0.133038i
$891$	−3.67793	−	1.70580i	−0.123215	−	0.0571466i
$892$	2.43988	−	1.40867i	0.0816933	−	0.0471657i
$893$		−	40.7325i		−	1.36306i
$894$	−0.178819	−	8.00550i	−0.00598060	−	0.267744i
$895$	3.30274	−	1.90684i	0.110398	−	0.0637386i
$896$	−1.07124	+	2.41918i	−0.0357877	+	0.0808192i
$897$	−0.925466	−	41.4320i	−0.0309004	−	1.38337i
$898$	1.11500	+	1.93123i	0.0372080	+	0.0644461i
$899$	−2.67007	−	4.62470i	−0.0890520	−	0.154243i
$900$	2.99701	−	0.133955i	0.0999003	−	0.00446517i
$901$	−65.3318	−	37.7193i	−2.17652	−	1.25661i
$902$	−0.430978	+	0.746475i	−0.0143500	+	0.0248549i
$903$	1.61740	−	3.88464i	0.0538236	−	0.129273i
$904$	−10.1015	−	17.4964i	−0.335972	−	0.581920i
$905$		−	4.59480i		−	0.152736i
$906$	−21.3023	+	0.475829i	−0.707720	+	0.0158084i
$907$	−40.4316			−1.34251			−0.671254	−	0.741227i	$-0.734244\pi$
$907$	−40.4316			−1.34251			−0.671254	+	0.741227i	$0.734244\pi$
$908$	−1.29508	+	2.24315i	−0.0429789	+	0.0744416i
$909$	−8.87836	−	13.9045i	−0.294476	−	0.461183i
$910$	1.38703	+	12.9453i	0.0459796	+	0.429133i
$911$	−24.9849	−	14.4250i	−0.827786	−	0.477923i	0.0253077	−	0.999680i	$-0.491943\pi$
$911$	−24.9849	−	14.4250i	−0.827786	−	0.477923i	−0.853094	+	0.521757i	$0.825277\pi$
$912$	4.56527	−	8.33160i	0.151171	−	0.275887i
$913$	−3.71932	−	2.14735i	−0.123092	−	0.0710670i
$914$	−11.1513	−	6.43820i	−0.368852	−	0.212957i
$915$	17.0788	−	0.381489i	0.564607	−	0.0126116i
$916$	−18.6354	−	10.7592i	−0.615732	−	0.355493i
$917$	−33.5739	+	24.4965i	−1.10871	+	0.808947i
$918$	−18.0201	+	36.6844i	−0.594752	+	1.21077i
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	−0.831282	−	0.555850i	$-0.812393\pi$
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	0.897022	+	0.441986i	$0.145726\pi$
$920$	−4.86229			−0.160305
$921$	0.349473	−	0.637786i	0.0115155	−	0.0210158i
$922$		−	3.13475i		−	0.103238i
$923$	9.56055	+	16.5594i	0.314689	+	0.545058i
$924$	−1.90574	−	0.793468i	−0.0626942	−	0.0261032i
$925$	−0.721812	+	1.25022i	−0.0237330	+	0.0411068i
$926$	−12.5635	−	7.25355i	−0.412863	−	0.238367i
$927$	−39.2109	+	25.0371i	−1.28785	+	0.822325i
$928$	4.65089	+	8.05558i	0.152673	+	0.264437i
$929$	−21.0976	−	36.5422i	−0.692191	−	1.19891i	−0.971118	−	0.238598i	$-0.923312\pi$
$929$	−21.0976	−	36.5422i	−0.692191	−	1.19891i	0.278927	−	0.960312i	$-0.410021\pi$
$930$	0.872038	+	0.477830i	0.0285952	+	0.0156687i
$931$	−28.4294	+	25.8065i	−0.931735	+	0.845773i
$932$	−2.79452	+	1.61342i	−0.0915377	+	0.0528493i
$933$	9.30264	−	5.65156i	0.304555	−	0.185024i
$934$		−	9.66081i		−	0.316111i
$935$	−3.06857	+	1.77164i	−0.100353	+	0.0579389i
$936$	6.80309	−	13.1016i	0.222366	−	0.428241i
$937$			41.8456i			1.36704i	0.729933	+	0.683519i	$0.239551\pi$
$937$			41.8456i			1.36704i	−0.729933	+	0.683519i	$0.760449\pi$
$938$	−7.23904	−	9.92151i	−0.236363	−	0.323949i
$939$	9.84271	−	0.219857i	0.321205	−	0.00717476i
$940$	−7.42609			−0.242212
$941$	−17.1592	+	29.7207i	−0.559375	+	0.968866i	0.438174	+	0.898890i	$0.355626\pi$
$941$	−17.1592	+	29.7207i	−0.559375	+	0.968866i	−0.997549	+	0.0699758i	$0.977708\pi$
$942$	−29.2196	−	16.0108i	−0.952026	−	0.521660i
$943$	−8.05727	+	4.65187i	−0.262381	+	0.151486i
$944$	−8.86555			−0.288549
$945$	8.82849	+	10.5384i	0.287191	+	0.342814i
$946$	−0.413641			−0.0134486
$947$	−21.0886	+	12.1755i	−0.685289	+	0.395652i	−0.801845	−	0.597532i	$-0.796148\pi$
$947$	−21.0886	+	12.1755i	−0.685289	+	0.395652i	0.116556	+	0.993184i	$0.462815\pi$
$948$	−3.04766	−	1.66995i	−0.0989833	−	0.0542376i
$949$	13.9593	−	24.1782i	0.453138	−	0.784857i
$950$	−5.48505			−0.177958
$951$	17.3705	−	0.388006i	0.563279	−	0.0125820i
$952$	−8.42608	+	19.0286i	−0.273091	+	0.616719i
$953$		−	39.1967i		−	1.26970i	−0.772634	−	0.634852i	$-0.781061\pi$
$953$		−	39.1967i		−	1.26970i	0.772634	−	0.634852i	$-0.218939\pi$
$954$	28.7438	−	1.28474i	0.930615	−	0.0415951i
$955$	21.7317	−	12.5468i	0.703221	−	0.406005i
$956$		−	16.0985i		−	0.520661i
$957$	−6.20269	+	3.76827i	−0.200504	+	0.121811i
$958$	30.9480	−	17.8678i	0.999885	−	0.577284i
$959$	20.3713	+	27.9201i	0.657825	+	0.901586i
$960$	−1.51897	−	0.832312i	−0.0490244	−	0.0268628i
$961$	−15.3352	−	26.5614i	−0.494684	−	0.856818i
$962$	3.55195	+	6.15215i	0.114519	+	0.198353i
$963$	1.33030	+	29.7630i	0.0428683	+	0.959101i
$964$	22.2029	+	12.8188i	0.715106	+	0.412867i
$965$	−8.95240	+	15.5060i	−0.288188	+	0.499156i
$966$	−13.5320	−	17.7021i	−0.435384	−	0.569556i
$967$	7.42308	+	12.8572i	0.238710	+	0.413458i	0.960344	−	0.278816i	$-0.0899421\pi$
$967$	7.42308	+	12.8572i	0.238710	+	0.413458i	−0.721634	+	0.692275i	$0.756609\pi$
$968$		−	10.7971i		−	0.347031i
$969$	35.9091	−	65.5339i	1.15357	−	2.10525i
$970$	10.0398			0.322357
$971$	21.8681	−	37.8766i	0.701780	−	1.21552i	−0.266061	−	0.963956i	$-0.585722\pi$
$971$	21.8681	−	37.8766i	0.701780	−	1.21552i	0.967841	−	0.251562i	$-0.0809444\pi$
$972$	−1.73709	−	15.4914i	−0.0557173	−	0.496886i
$973$	−0.702109	+	1.58557i	−0.0225086	+	0.0508309i
$974$	−16.3170	−	9.42060i	−0.522829	−	0.301855i
$975$	−8.52108	+	0.190335i	−0.272893	+	0.00609561i
$976$	−8.54152	−	4.93145i	−0.273407	−	0.157852i
$977$	36.7089	+	21.1939i	1.17442	+	0.678052i	0.954717	−	0.297514i	$-0.0961576\pi$
$977$	36.7089	+	21.1939i	1.17442	+	0.678052i	0.219704	+	0.975567i	$0.429491\pi$
$978$	−5.18476	+	9.46217i	−0.165790	+	0.302567i
$979$	−1.54835	−	0.893939i	−0.0494854	−	0.0285704i
$980$	4.70487	+	5.18306i	0.150292	+	0.165567i
$981$	−6.16104	+	11.8652i	−0.196707	+	0.378826i
$982$	−8.05323	+	13.9486i	−0.256989	+	0.445118i
$983$	57.2841			1.82708			0.913540	−	0.406748i	$-0.133337\pi$
$983$	57.2841			1.82708			0.913540	+	0.406748i	$0.133337\pi$
$984$	−3.31336	+	0.0740106i	−0.105626	+	0.00235937i
$985$			12.6523i			0.403136i
$986$	36.5825	+	63.3628i	1.16502	+	2.01788i
$987$	−20.6671	−	27.0361i	−0.657842	−	0.860570i
$988$	−13.4956	+	23.3751i	−0.429353	+	0.743661i
$989$	−3.86658	−	2.23237i	−0.122950	−	0.0709853i
$990$	0.622776	−	1.19937i	0.0197931	−	0.0381184i
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	0.569154	−	0.822231i	$-0.307271\pi$
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	−0.996650	+	0.0817862i	$0.973938\pi$
$992$	−0.287050	−	0.497185i	−0.00911384	−	0.0157856i
$993$	1.22625	+	54.8978i	0.0389140	+	1.74213i
$994$	9.40024	+	4.16254i	0.298158	+	0.132028i
$995$	18.2922	−	10.5610i	0.579900	−	0.334806i
$996$	−0.368759	−	16.5089i	−0.0116846	−	0.523104i
$997$		−	59.1431i		−	1.87308i	−0.350561	−	0.936540i	$-0.614009\pi$
$997$		−	59.1431i		−	1.87308i	0.350561	−	0.936540i	$-0.385991\pi$
$998$	1.17141	−	0.676312i	0.0370802	−	0.0214083i
$999$	6.73284	+	3.30730i	0.213018	+	0.104638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.551.8	yes	28
3.2	odd	2		1890.2.t.b.1601.5		28
7.3	odd	6		630.2.bk.b.101.10	yes	28
9.4	even	3		1890.2.bk.b.341.9		28
9.5	odd	6		630.2.bk.b.131.3	yes	28
21.17	even	6		1890.2.bk.b.521.9		28
63.31	odd	6		1890.2.t.b.1151.5		28
63.59	even	6	inner	630.2.t.b.311.8	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.8	✓	28	63.59	even	6	inner
630.2.t.b.551.8	yes	28	1.1	even	1	trivial
630.2.bk.b.101.10	yes	28	7.3	odd	6
630.2.bk.b.131.3	yes	28	9.5	odd	6
1890.2.t.b.1151.5		28	63.31	odd	6
1890.2.t.b.1601.5		28	3.2	odd	2
1890.2.bk.b.341.9		28	9.4	even	3
1890.2.bk.b.521.9		28	21.17	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.51897 - 0.832312i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.73162 + 0.0386792i) q^{6} +(2.13731 - 1.55945i) q^{7} -1.00000i q^{8} +(1.61451 + 2.52851i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.51897 - 0.832312i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.73162 + 0.0386792i) q^{6} +(2.13731 - 1.55945i) q^{7} -1.00000i q^{8} +(1.61451 + 2.52851i) q^{9} +(-0.866025 + 0.500000i) q^{10} +0.450472i q^{11} +(-1.48029 + 0.899307i) q^{12} +(4.26160 - 2.46044i) q^{13} +(1.07124 - 2.41918i) q^{14} +(1.51897 + 0.832312i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93285 - 6.81190i) q^{17} +(2.66246 + 1.38250i) q^{18} +(-4.75019 - 2.74252i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-4.54446 + 0.589839i) q^{21} +(0.225236 + 0.390121i) q^{22} +4.86229i q^{23} +(-0.832312 + 1.51897i) q^{24} +1.00000 q^{25} +(2.46044 - 4.26160i) q^{26} +(-0.347881 - 5.18449i) q^{27} +(-0.281867 - 2.63069i) q^{28} +(-8.05558 - 4.65089i) q^{29} +(1.73162 - 0.0386792i) q^{30} +(0.497185 + 0.287050i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.374934 - 0.684252i) q^{33} +(-6.81190 - 3.93285i) q^{34} +(-2.13731 + 1.55945i) q^{35} +(2.99701 - 0.133955i) q^{36} +(-0.721812 + 1.25022i) q^{37} -5.48505 q^{38} +(-8.52108 + 0.190335i) q^{39} +1.00000i q^{40} +(0.956724 + 1.65709i) q^{41} +(-3.64070 + 2.78304i) q^{42} +(-0.459119 + 0.795218i) q^{43} +(0.390121 + 0.225236i) q^{44} +(-1.61451 - 2.52851i) q^{45} +(2.43115 + 4.21087i) q^{46} +(3.71305 + 6.43119i) q^{47} +(0.0386792 + 1.73162i) q^{48} +(2.13623 - 6.66607i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.304239 + 13.6204i) q^{51} -4.92088i q^{52} +(8.30591 - 4.79542i) q^{53} +(-2.89352 - 4.31596i) q^{54} -0.450472i q^{55} +(-1.55945 - 2.13731i) q^{56} +(4.93274 + 8.11944i) q^{57} -9.30178 q^{58} +(4.43278 - 7.67779i) q^{59} +(1.48029 - 0.899307i) q^{60} +(8.54152 - 4.93145i) q^{61} +0.574100 q^{62} +(7.39380 + 2.88646i) q^{63} -1.00000 q^{64} +(-4.26160 + 2.46044i) q^{65} +(-0.0174239 - 0.780047i) q^{66} +(2.32102 - 4.02013i) q^{67} -7.86570 q^{68} +(4.04694 - 7.38565i) q^{69} +(-1.07124 + 2.41918i) q^{70} +3.88571i q^{71} +(2.52851 - 1.61451i) q^{72} +(4.91339 - 2.83675i) q^{73} +1.44362i q^{74} +(-1.51897 - 0.832312i) q^{75} +(-4.75019 + 2.74252i) q^{76} +(0.702489 + 0.962801i) q^{77} +(-7.28430 + 4.42538i) q^{78} +(1.00320 + 1.73760i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.78670 + 8.16461i) q^{81} +(1.65709 + 0.956724i) q^{82} +(-4.76689 + 8.25650i) q^{83} +(-1.76141 + 4.23053i) q^{84} +(3.93285 + 6.81190i) q^{85} +0.918239i q^{86} +(8.36515 + 13.7693i) q^{87} +0.450472 q^{88} +(-1.98445 + 3.43716i) q^{89} +(-2.66246 - 1.38250i) q^{90} +(5.27146 - 11.9045i) q^{91} +(4.21087 + 2.43115i) q^{92} +(-0.516292 - 0.849832i) q^{93} +(6.43119 + 3.71305i) q^{94} +(4.75019 + 2.74252i) q^{95} +(0.899307 + 1.48029i) q^{96} +(-8.69468 - 5.01988i) q^{97} +(-1.48301 - 6.84110i) q^{98} +(-1.13902 + 0.727293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Introduction

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