LMFDB - Embedded newform 22.3.d.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,3,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.599456581593$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.2
Root			$0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	22.7
Dual form			22.3.d.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831254 - 1.14412i) q^{2} +(-0.295274 + 0.908759i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42545 + 1.76219i) q^{5} +(0.794285 + 1.09324i) q^{6} +(-3.70473 + 1.20374i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(6.54250 + 4.75340i) q^{9} +O(q^{10})$	\(q+(0.831254 - 1.14412i) q^{2} +(-0.295274 + 0.908759i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42545 + 1.76219i) q^{5} +(0.794285 + 1.09324i) q^{6} +(-3.70473 + 1.20374i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(6.54250 + 4.75340i) q^{9} +4.23984i q^{10} +(-10.2616 - 3.96233i) q^{11} +1.91105 q^{12} +(14.4340 - 19.8667i) q^{13} +(-1.70234 + 5.23927i) q^{14} +(-0.885238 - 2.72448i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(3.79692 + 5.22601i) q^{17} +(10.8770 - 3.53414i) q^{18} +(14.9139 + 4.84581i) q^{19} +(4.85090 + 3.52439i) q^{20} -3.72214i q^{21} +(-13.0634 + 8.44680i) q^{22} -30.3518 q^{23} +(1.58857 - 2.18648i) q^{24} +(-4.94794 + 15.2282i) q^{25} +(-10.7316 - 33.0285i) q^{26} +(-13.2089 + 9.59680i) q^{27} +(4.57929 + 6.30286i) q^{28} +(-14.2561 + 4.63209i) q^{29} +(-3.85300 - 1.25191i) q^{30} +(21.4645 + 15.5949i) q^{31} +5.65685i q^{32} +(6.63078 - 8.15533i) q^{33} +9.13540 q^{34} +(6.86441 - 9.44805i) q^{35} +(4.99802 - 15.3823i) q^{36} +(-1.29043 - 3.97153i) q^{37} +(17.9414 - 13.0352i) q^{38} +(13.7920 + 18.9831i) q^{39} +(8.06466 - 2.62037i) q^{40} +(41.2318 + 13.3970i) q^{41} +(-4.25858 - 3.09404i) q^{42} -56.0236i q^{43} +(-1.19479 + 21.9675i) q^{44} -24.2449 q^{45} +(-25.2301 + 34.7262i) q^{46} +(9.34350 - 28.7563i) q^{47} +(-1.18110 - 3.63504i) q^{48} +(-27.3658 + 19.8824i) q^{49} +(13.3099 + 18.3195i) q^{50} +(-5.87032 + 1.90738i) q^{51} +(-46.7093 - 15.1768i) q^{52} +(-42.1199 - 30.6019i) q^{53} +23.0899i q^{54} +(31.8713 - 8.47245i) q^{55} +11.0178 q^{56} +(-8.80735 + 12.1223i) q^{57} +(-6.55077 + 20.1612i) q^{58} +(29.1737 + 89.7875i) q^{59} +(-4.63516 + 3.36764i) q^{60} +(-54.8450 - 75.4877i) q^{61} +(35.6849 - 11.5947i) q^{62} +(-29.9600 - 9.73460i) q^{63} +(6.47214 + 4.70228i) q^{64} +73.6210i q^{65} +(-3.81884 - 14.3656i) q^{66} +54.0771 q^{67} +(7.59384 - 10.4520i) q^{68} +(8.96210 - 27.5825i) q^{69} +(-5.10366 - 15.7075i) q^{70} +(75.9613 - 55.1891i) q^{71} +(-13.4446 - 18.5050i) q^{72} +(-23.3346 + 7.58189i) q^{73} +(-5.61660 - 1.82494i) q^{74} +(-12.3778 - 8.99297i) q^{75} -31.3627i q^{76} +(42.7859 + 2.32709i) q^{77} +33.1837 q^{78} +(-45.4416 + 62.5450i) q^{79} +(3.70576 - 11.4052i) q^{80} +(17.6701 + 54.3831i) q^{81} +(49.6020 - 36.0379i) q^{82} +(-16.8251 - 23.1578i) q^{83} +(-7.07993 + 2.30041i) q^{84} +(-18.4185 - 5.98453i) q^{85} +(-64.0978 - 46.5698i) q^{86} -14.3231i q^{87} +(24.1404 + 19.6276i) q^{88} +68.2705 q^{89} +(-20.1537 + 27.7392i) q^{90} +(-29.5597 + 90.9753i) q^{91} +(18.7585 + 57.7326i) q^{92} +(-20.5099 + 14.9013i) q^{93} +(-25.1340 - 34.5939i) q^{94} +(-44.7121 + 14.5278i) q^{95} +(-5.14072 - 1.67032i) q^{96} +(-29.1342 - 21.1672i) q^{97} +47.8372i q^{98} +(-48.3018 - 74.7009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9} - 4 q^{11} + 24 q^{12} + 30 q^{13} + 16 q^{14} + 42 q^{15} - 8 q^{16} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 4 q^{20} + 24 q^{22} - 104 q^{23} - 40 q^{24} - 12 q^{25} - 96 q^{26} - 26 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 46 q^{31} - 14 q^{33} + 112 q^{34} + 70 q^{35} - 12 q^{36} + 6 q^{37} + 108 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 56 q^{42} - 12 q^{44} - 136 q^{45} - 160 q^{46} - 54 q^{47} - 8 q^{48} - 144 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 274 q^{53} - 26 q^{55} + 48 q^{56} - 130 q^{57} + 64 q^{58} + 50 q^{59} + 116 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} + 16 q^{64} - 136 q^{66} + 112 q^{67} + 60 q^{68} + 76 q^{69} + 4 q^{70} + 54 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 318 q^{75} + 266 q^{77} + 104 q^{78} + 370 q^{79} + 48 q^{80} + 180 q^{81} - 96 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 72 q^{86} + 72 q^{88} + 24 q^{89} + 160 q^{90} - 294 q^{91} - 112 q^{92} - 134 q^{93} - 20 q^{94} - 330 q^{95} - 18 q^{97} - 308 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9 - 4 * q^11 + 24 * q^12 + 30 * q^13 + 16 * q^14 + 42 * q^15 - 8 * q^16 + 30 * q^17 + 40 * q^18 - 30 * q^19 - 4 * q^20 + 24 * q^22 - 104 * q^23 - 40 * q^24 - 12 * q^25 - 96 * q^26 - 26 * q^27 - 40 * q^28 - 10 * q^29 - 60 * q^30 + 46 * q^31 - 14 * q^33 + 112 * q^34 + 70 * q^35 - 12 * q^36 + 6 * q^37 + 108 * q^38 + 130 * q^39 + 80 * q^40 + 250 * q^41 + 56 * q^42 - 12 * q^44 - 136 * q^45 - 160 * q^46 - 54 * q^47 - 8 * q^48 - 144 * q^49 - 80 * q^50 - 30 * q^51 - 40 * q^52 - 274 * q^53 - 26 * q^55 + 48 * q^56 - 130 * q^57 + 64 * q^58 + 50 * q^59 + 116 * q^60 + 50 * q^61 + 20 * q^62 - 20 * q^63 + 16 * q^64 - 136 * q^66 + 112 * q^67 + 60 * q^68 + 76 * q^69 + 4 * q^70 + 54 * q^71 - 80 * q^72 - 70 * q^73 - 40 * q^74 + 318 * q^75 + 266 * q^77 + 104 * q^78 + 370 * q^79 + 48 * q^80 + 180 * q^81 - 96 * q^82 - 150 * q^83 - 120 * q^84 - 330 * q^85 - 72 * q^86 + 72 * q^88 + 24 * q^89 + 160 * q^90 - 294 * q^91 - 112 * q^92 - 134 * q^93 - 20 * q^94 - 330 * q^95 - 18 * q^97 - 308 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.831254	−	1.14412i	0.415627	−	0.572061i
$2$	0.831254	−	1.14412i	0.415627	−	0.572061i
$3$	−0.295274	+	0.908759i	−0.0984246	+	0.302920i	−0.988131	−	0.153613i	$-0.950909\pi$
$3$	−0.295274	+	0.908759i	−0.0984246	+	0.302920i	0.889706	+	0.456533i	$0.150909\pi$
$4$	−0.618034	−	1.90211i	−0.154508	−	0.475528i
$5$	−2.42545	+	1.76219i	−0.485090	+	0.352439i	−0.803293	−	0.595584i	$-0.796921\pi$
$5$	−2.42545	+	1.76219i	−0.485090	+	0.352439i	0.318203	+	0.948023i	$0.396921\pi$
$6$	0.794285	+	1.09324i	0.132381	+	0.182207i
$7$	−3.70473	+	1.20374i	−0.529247	+	0.171963i	−0.561438	−	0.827519i	$-0.689752\pi$
$7$	−3.70473	+	1.20374i	−0.529247	+	0.171963i	0.0321910	+	0.999482i	$0.489752\pi$
$8$	−2.68999	−	0.874032i	−0.336249	−	0.109254i
$9$	6.54250	+	4.75340i	0.726944	+	0.528156i
$10$			4.23984i			0.423984i
$11$	−10.2616	−	3.96233i	−0.932871	−	0.360212i
$11$	−10.2616	−	3.96233i	−0.932871	−	0.360212i
$12$	1.91105			0.159254
$13$	14.4340	−	19.8667i	1.11031	−	1.52820i	0.289340	−	0.957226i	$-0.406564\pi$
$13$	14.4340	−	19.8667i	1.11031	−	1.52820i	0.820965	−	0.570978i	$-0.193436\pi$
$14$	−1.70234	+	5.23927i	−0.121596	+	0.374234i
$15$	−0.885238	−	2.72448i	−0.0590158	−	0.181632i
$16$	−3.23607	+	2.35114i	−0.202254	+	0.146946i
$17$	3.79692	+	5.22601i	0.223348	+	0.307412i	0.905955	−	0.423373i	$-0.139154\pi$
$17$	3.79692	+	5.22601i	0.223348	+	0.307412i	−0.682607	+	0.730785i	$0.739154\pi$
$18$	10.8770	−	3.53414i	0.604275	−	0.196341i
$19$	14.9139	+	4.84581i	0.784940	+	0.255043i	0.673948	−	0.738779i	$-0.264597\pi$
$19$	14.9139	+	4.84581i	0.784940	+	0.255043i	0.110992	+	0.993821i	$0.464597\pi$
$20$	4.85090	+	3.52439i	0.242545	+	0.176219i
$21$		−	3.72214i		−	0.177245i
$22$	−13.0634	+	8.44680i	−0.593789	+	0.383946i
$23$	−30.3518			−1.31964			−0.659822	−	0.751422i	$-0.729369\pi$
$23$	−30.3518			−1.31964			−0.659822	+	0.751422i	$0.729369\pi$
$24$	1.58857	−	2.18648i	0.0661904	−	0.0911033i
$25$	−4.94794	+	15.2282i	−0.197918	+	0.609127i
$26$	−10.7316	−	33.0285i	−0.412754	−	1.27033i
$27$	−13.2089	+	9.59680i	−0.489217	+	0.355437i
$28$	4.57929	+	6.30286i	0.163546	+	0.225102i
$29$	−14.2561	+	4.63209i	−0.491590	+	0.159727i	−0.544314	−	0.838882i	$-0.683210\pi$
$29$	−14.2561	+	4.63209i	−0.491590	+	0.159727i	0.0527235	+	0.998609i	$0.483210\pi$
$30$	−3.85300	−	1.25191i	−0.128433	−	0.0417305i
$31$	21.4645	+	15.5949i	0.692404	+	0.503061i	0.877450	−	0.479669i	$-0.159243\pi$
$31$	21.4645	+	15.5949i	0.692404	+	0.503061i	−0.185045	+	0.982730i	$0.559243\pi$
$32$			5.65685i			0.176777i
$33$	6.63078	−	8.15533i	0.200933	−	0.247131i
$34$	9.13540			0.268688
$35$	6.86441	−	9.44805i	0.196126	−	0.269944i
$36$	4.99802	−	15.3823i	0.138834	−	0.427287i
$37$	−1.29043	−	3.97153i	−0.0348765	−	0.107339i	0.932103	−	0.362194i	$-0.117972\pi$
$37$	−1.29043	−	3.97153i	−0.0348765	−	0.107339i	−0.966979	+	0.254855i	$0.917972\pi$
$38$	17.9414	−	13.0352i	0.472142	−	0.343031i
$39$	13.7920	+	18.9831i	0.353642	+	0.486746i
$40$	8.06466	−	2.62037i	0.201617	−	0.0655092i
$41$	41.2318	+	13.3970i	1.00565	+	0.326757i	0.765123	−	0.643884i	$-0.222678\pi$
$41$	41.2318	+	13.3970i	1.00565	+	0.326757i	0.240532	+	0.970641i	$0.422678\pi$
$42$	−4.25858	−	3.09404i	−0.101395	−	0.0736676i
$43$		−	56.0236i		−	1.30287i	−0.758703	−	0.651437i	$-0.774167\pi$
$43$		−	56.0236i		−	1.30287i	0.758703	−	0.651437i	$-0.225833\pi$
$44$	−1.19479	+	21.9675i	−0.0271544	+	0.499262i
$45$	−24.2449			−0.538776
$46$	−25.2301	+	34.7262i	−0.548480	+	0.754918i
$47$	9.34350	−	28.7563i	0.198798	−	0.611837i	−0.801113	−	0.598513i	$-0.795759\pi$
$47$	9.34350	−	28.7563i	0.198798	−	0.611837i	0.999911	−	0.0133244i	$-0.00424141\pi$
$48$	−1.18110	−	3.63504i	−0.0246062	−	0.0757300i
$49$	−27.3658	+	19.8824i	−0.558486	+	0.405764i
$50$	13.3099	+	18.3195i	0.266198	+	0.366391i
$51$	−5.87032	+	1.90738i	−0.115104	+	0.0373996i
$52$	−46.7093	−	15.1768i	−0.898256	−	0.291861i
$53$	−42.1199	−	30.6019i	−0.794714	−	0.577394i	0.114644	−	0.993407i	$-0.463427\pi$
$53$	−42.1199	−	30.6019i	−0.794714	−	0.577394i	−0.909359	+	0.416013i	$0.863427\pi$
$54$			23.0899i			0.427591i
$55$	31.8713	−	8.47245i	0.579479	−	0.154044i
$56$	11.0178			0.196746
$57$	−8.80735	+	12.1223i	−0.154515	+	0.212671i
$58$	−6.55077	+	20.1612i	−0.112944	+	0.347607i
$59$	29.1737	+	89.7875i	0.494470	+	1.52182i	0.817781	+	0.575529i	$0.195204\pi$
$59$	29.1737	+	89.7875i	0.494470	+	1.52182i	−0.323312	+	0.946293i	$0.604796\pi$
$60$	−4.63516	+	3.36764i	−0.0772527	+	0.0561274i
$61$	−54.8450	−	75.4877i	−0.899098	−	1.23750i	−0.970755	−	0.240073i	$-0.922828\pi$
$61$	−54.8450	−	75.4877i	−0.899098	−	1.23750i	0.0716564	−	0.997429i	$-0.477172\pi$
$62$	35.6849	−	11.5947i	0.575564	−	0.187012i
$63$	−29.9600	−	9.73460i	−0.475556	−	0.154517i
$64$	6.47214	+	4.70228i	0.101127	+	0.0734732i
$65$			73.6210i			1.13263i
$66$	−3.81884	−	14.3656i	−0.0578612	−	0.217660i
$67$	54.0771			0.807121			0.403560	−	0.914953i	$-0.367773\pi$
$67$	54.0771			0.807121			0.403560	+	0.914953i	$0.367773\pi$
$68$	7.59384	−	10.4520i	0.111674	−	0.153706i
$69$	8.96210	−	27.5825i	0.129886	−	0.399747i
$70$	−5.10366	−	15.7075i	−0.0729095	−	0.224392i
$71$	75.9613	−	55.1891i	1.06988	−	0.777312i	0.0939873	−	0.995573i	$-0.470039\pi$
$71$	75.9613	−	55.1891i	1.06988	−	0.777312i	0.975890	+	0.218262i	$0.0700387\pi$
$72$	−13.4446	−	18.5050i	−0.186731	−	0.257014i
$73$	−23.3346	+	7.58189i	−0.319653	+	0.103861i	−0.464449	−	0.885600i	$-0.653747\pi$
$73$	−23.3346	+	7.58189i	−0.319653	+	0.103861i	0.144796	+	0.989462i	$0.453747\pi$
$74$	−5.61660	−	1.82494i	−0.0758999	−	0.0246614i
$75$	−12.3778	−	8.99297i	−0.165037	−	0.119906i
$76$		−	31.3627i		−	0.412667i
$77$	42.7859	+	2.32709i	0.555662	+	0.0302219i
$78$	33.1837			0.425432
$79$	−45.4416	+	62.5450i	−0.575210	+	0.791709i	−0.993160	−	0.116761i	$-0.962749\pi$
$79$	−45.4416	+	62.5450i	−0.575210	+	0.791709i	0.417950	+	0.908470i	$0.362749\pi$
$80$	3.70576	−	11.4052i	0.0463220	−	0.142564i
$81$	17.6701	+	54.3831i	0.218150	+	0.671397i
$82$	49.6020	−	36.0379i	0.604902	−	0.439487i
$83$	−16.8251	−	23.1578i	−0.202712	−	0.279010i	0.695542	−	0.718485i	$-0.255164\pi$
$83$	−16.8251	−	23.1578i	−0.202712	−	0.279010i	−0.898254	+	0.439476i	$0.855164\pi$
$84$	−7.07993	+	2.30041i	−0.0842848	+	0.0273858i
$85$	−18.4185	−	5.98453i	−0.216688	−	0.0704062i
$86$	−64.0978	−	46.5698i	−0.745324	−	0.541509i
$87$		−	14.3231i		−	0.164633i
$88$	24.1404	+	19.6276i	0.274322	+	0.223041i
$89$	68.2705			0.767085			0.383542	−	0.923523i	$-0.374704\pi$
$89$	68.2705			0.767085			0.383542	+	0.923523i	$0.374704\pi$
$90$	−20.1537	+	27.7392i	−0.223930	+	0.308213i
$91$	−29.5597	+	90.9753i	−0.324831	+	0.999728i
$92$	18.7585	+	57.7326i	0.203896	+	0.627528i
$93$	−20.5099	+	14.9013i	−0.220537	+	0.160229i
$94$	−25.1340	−	34.5939i	−0.267383	−	0.368021i
$95$	−44.7121	+	14.5278i	−0.470654	+	0.152925i
$96$	−5.14072	−	1.67032i	−0.0535492	−	0.0173992i
$97$	−29.1342	−	21.1672i	−0.300353	−	0.218219i	0.427393	−	0.904066i	$-0.359432\pi$
$97$	−29.1342	−	21.1672i	−0.300353	−	0.218219i	−0.727746	+	0.685847i	$0.759432\pi$
$98$			47.8372i			0.488135i
$99$	−48.3018	−	74.7009i	−0.487897	−	0.754555i
$100$	32.0237			0.320237
$101$	1.45687	−	2.00522i	0.0144245	−	0.0198536i	−0.801744	−	0.597668i	$-0.796094\pi$
$101$	1.45687	−	2.00522i	0.0144245	−	0.0198536i	0.816168	+	0.577814i	$0.196094\pi$
$102$	−2.69744	+	8.30188i	−0.0264455	+	0.0813910i
$103$	−9.38014	−	28.8691i	−0.0910693	−	0.280283i	0.895140	−	0.445785i	$-0.147075\pi$
$103$	−9.38014	−	28.8691i	−0.0910693	−	0.280283i	−0.986209	+	0.165502i	$0.947075\pi$
$104$	−56.1914	+	40.8254i	−0.540302	+	0.392552i
$105$	6.55913	+	9.02786i	0.0624679	+	0.0859796i
$106$	−70.0246	+	22.7524i	−0.660609	+	0.214645i
$107$	−72.8287	−	23.6635i	−0.680642	−	0.221154i	−0.0517656	−	0.998659i	$-0.516485\pi$
$107$	−72.8287	−	23.6635i	−0.680642	−	0.221154i	−0.628876	+	0.777505i	$0.716485\pi$
$108$	26.4177	+	19.1936i	0.244609	+	0.177718i
$109$			12.1116i			0.111116i	0.998455	+	0.0555580i	$0.0176938\pi$
$109$			12.1116i			0.111116i	−0.998455	+	0.0555580i	$0.982306\pi$
$110$	16.7997	−	43.5075i	0.152724	−	0.395523i
$111$	3.99020			0.0359477
$112$	9.15859	−	12.6057i	0.0817731	−	0.112551i
$113$	29.3180	−	90.2315i	0.259451	−	0.798509i	−0.733469	−	0.679723i	$-0.762100\pi$
$113$	29.3180	−	90.2315i	0.259451	−	0.798509i	0.992920	−	0.118786i	$-0.0379001\pi$
$114$	6.54823	+	20.1534i	0.0574406	+	0.176784i
$115$	73.6169	−	53.4858i	0.640147	−	0.465094i
$116$	17.6215	+	24.2539i	0.151910	+	0.209086i
$117$	188.868	−	61.3671i	1.61426	−	0.524505i
$118$	126.979	+	41.2579i	1.07609	+	0.349643i
$119$	−20.3573	−	14.7904i	−0.171070	−	0.124289i
$120$			8.10256i			0.0675214i
$121$	89.5999	+	81.3195i	0.740495	+	0.672062i
$122$	−131.957			−1.08162
$123$	−24.3494	+	33.5140i	−0.197962	+	0.272472i
$124$	16.3974	−	50.4661i	0.132237	−	0.406985i
$125$	−37.9950	−	116.937i	−0.303960	−	0.935493i
$126$	−36.0419	+	26.1860i	−0.286047	+	0.207825i
$127$	78.4228	+	107.940i	0.617502	+	0.849919i	0.997168	−	0.0752049i	$-0.0239611\pi$
$127$	78.4228	+	107.940i	0.617502	+	0.849919i	−0.379666	+	0.925124i	$0.623961\pi$
$128$	10.7600	−	3.49613i	0.0840623	−	0.0273135i
$129$	50.9119	+	16.5423i	0.394666	+	0.128235i
$130$	84.2315	+	61.1978i	0.647935	+	0.470752i
$131$		−	42.3750i		−	0.323473i	−0.986834	−	0.161737i	$-0.948290\pi$
$131$		−	42.3750i		−	0.323473i	0.986834	−	0.161737i	$-0.0517095\pi$
$132$	−19.6104	−	7.57222i	−0.148564	−	0.0573653i
$133$	−61.0849			−0.459285
$134$	44.9518	−	61.8708i	0.335461	−	0.461723i
$135$	15.1260	−	46.5531i	0.112045	−	0.344838i
$136$	−5.64599	−	17.3766i	−0.0415146	−	0.127769i
$137$	−110.042	+	79.9503i	−0.803227	+	0.583579i	−0.911859	−	0.410503i	$-0.865353\pi$
$137$	−110.042	+	79.9503i	−0.803227	+	0.583579i	0.108632	+	0.994082i	$0.465353\pi$
$138$	−24.1080	−	33.1818i	−0.174696	−	0.240448i
$139$	−96.2740	+	31.2813i	−0.692619	+	0.225045i	−0.634112	−	0.773242i	$-0.718634\pi$
$139$	−96.2740	+	31.2813i	−0.692619	+	0.225045i	−0.0585070	+	0.998287i	$0.518634\pi$
$140$	−22.2137	−	7.21767i	−0.158669	−	0.0515548i
$141$	23.3737	+	16.9820i	0.165771	+	0.120440i
$142$		−	132.785i		−	0.935107i
$143$	−226.834	+	146.671i	−1.58625	+	1.02567i
$144$	−32.3479			−0.224638
$145$	26.4149	−	36.3569i	0.182171	−	0.250737i
$146$	−10.7224	+	33.0002i	−0.0734411	+	0.226029i
$147$	−9.98794	−	30.7397i	−0.0679452	−	0.209114i
$148$	−6.75678	+	4.90909i	−0.0456539	+	0.0331695i
$149$	30.3729	+	41.8048i	0.203845	+	0.280569i	0.898684	−	0.438597i	$-0.144524\pi$
$149$	30.3729	+	41.8048i	0.203845	+	0.280569i	−0.694839	+	0.719165i	$0.744524\pi$
$150$	−20.5781	+	6.68624i	−0.137188	+	0.0445749i
$151$	−79.6932	−	25.8939i	−0.527770	−	0.171483i	0.0329987	−	0.999455i	$-0.489494\pi$
$151$	−79.6932	−	25.8939i	−0.527770	−	0.171483i	−0.560769	+	0.827973i	$0.689494\pi$
$152$	−35.8828	−	26.0704i	−0.236071	−	0.171516i
$153$			52.2394i			0.341434i
$154$	38.2285	−	47.0180i	0.248237	−	0.305311i
$155$	−79.5424			−0.513177
$156$	27.5841	−	37.9662i	0.176821	−	0.243373i
$157$	−71.8482	+	221.126i	−0.457632	+	1.40845i	0.410386	+	0.911912i	$0.365394\pi$
$157$	−71.8482	+	221.126i	−0.457632	+	1.40845i	−0.868017	+	0.496534i	$0.834606\pi$
$158$	33.7857	+	103.982i	0.213833	+	0.658111i
$159$	40.2466	−	29.2409i	0.253124	−	0.183905i
$160$	−9.96847	−	13.7204i	−0.0623029	−	0.0857526i
$161$	112.445	−	36.5357i	0.698418	−	0.226930i
$162$	76.9094	+	24.9894i	0.474749	+	0.154255i
$163$	260.206	+	189.051i	1.59636	+	1.15982i	0.894072	+	0.447923i	$0.147836\pi$
$163$	260.206	+	189.051i	1.59636	+	1.15982i	0.702284	+	0.711897i	$0.252164\pi$
$164$		−	86.7074i		−	0.528704i
$165$	−1.71136	+	31.4651i	−0.0103719	+	0.190697i
$166$	−40.4813			−0.243863
$167$	73.5229	−	101.196i	0.440257	−	0.605961i	−0.530012	−	0.847990i	$-0.677813\pi$
$167$	73.5229	−	101.196i	0.440257	−	0.605961i	0.970269	+	0.242028i	$0.0778127\pi$
$168$	−3.25327	+	10.0125i	−0.0193647	+	0.0595984i
$169$	−134.121	−	412.781i	−0.793613	−	2.44249i
$170$	−22.1575	+	16.0983i	−0.130338	+	0.0946961i
$171$	74.5398	+	102.595i	0.435905	+	0.599972i
$172$	−106.563	+	34.6245i	−0.619553	+	0.201305i
$173$	120.522	+	39.1600i	0.696660	+	0.226358i	0.635875	−	0.771792i	$-0.280640\pi$
$173$	120.522	+	39.1600i	0.696660	+	0.226358i	0.0607851	+	0.998151i	$0.480640\pi$
$174$	−16.3874	−	11.9061i	−0.0941805	−	0.0684261i
$175$		−	62.3723i		−	0.356413i
$176$	42.5232	−	11.3040i	0.241609	−	0.0642275i
$177$	−90.2094			−0.509658
$178$	56.7501	−	78.1099i	0.318821	−	0.438820i
$179$	61.2907	−	188.633i	0.342406	−	1.05382i	−0.620551	−	0.784166i	$-0.713091\pi$
$179$	61.2907	−	188.633i	0.342406	−	1.05382i	0.962958	−	0.269653i	$-0.0869088\pi$
$180$	14.9842	+	46.1166i	0.0832454	+	0.256203i
$181$	−86.4445	+	62.8056i	−0.477594	+	0.346992i	−0.800393	−	0.599475i	$-0.795376\pi$
$181$	−86.4445	+	62.8056i	−0.477594	+	0.346992i	0.322800	+	0.946467i	$0.395376\pi$
$182$	79.5153	+	109.443i	0.436897	+	0.601337i
$183$	84.7944	−	27.5514i	0.463358	−	0.150554i
$184$	81.6463	+	26.5285i	0.443730	+	0.144176i
$185$	10.1285	+	7.35877i	0.0547485	+	0.0397771i
$186$			35.8527i			0.192756i
$187$	−18.2552	−	68.6717i	−0.0976214	−	0.367229i
$188$	−60.4724			−0.321662
$189$	37.3832	−	51.4535i	0.197795	−	0.272241i
$190$	−20.5455	+	63.2324i	−0.108134	+	0.332802i
$191$	10.6399	+	32.7463i	0.0557064	+	0.171447i	0.975039	−	0.222036i	$-0.0712702\pi$
$191$	10.6399	+	32.7463i	0.0557064	+	0.171447i	−0.919332	+	0.393482i	$0.871270\pi$
$192$	−6.18430	+	4.49315i	−0.0322099	+	0.0234018i
$193$	−125.780	−	173.121i	−0.651710	−	0.897002i	0.347461	−	0.937694i	$-0.387044\pi$
$193$	−125.780	−	173.121i	−0.651710	−	0.897002i	−0.999172	+	0.0406920i	$0.987044\pi$
$194$	−48.4358	+	15.7378i	−0.249669	+	0.0811225i
$195$	−66.9038	−	21.7384i	−0.343097	−	0.111479i
$196$	54.7316	+	39.7649i	0.279243	+	0.202882i
$197$			271.384i			1.37758i	0.724960	+	0.688791i	$0.241858\pi$
$197$			271.384i			1.37758i	−0.724960	+	0.688791i	$0.758142\pi$
$198$	−125.618	−	6.83225i	−0.634435	−	0.0345063i
$199$	249.930			1.25593			0.627966	−	0.778241i	$-0.283888\pi$
$199$	249.930			1.25593			0.627966	+	0.778241i	$0.283888\pi$
$200$	26.6198	−	36.6391i	0.133099	−	0.183195i
$201$	−15.9675	+	49.1431i	−0.0794405	+	0.244493i
$202$	−1.08318	−	3.33369i	−0.00536228	−	0.0165034i
$203$	47.2392	−	34.3213i	0.232705	−	0.169070i
$204$	7.25611	+	9.98718i	0.0355692	+	0.0489568i
$205$	−123.614	+	40.1646i	−0.602995	+	0.195925i
$206$	−40.8271	−	13.2655i	−0.198190	−	0.0643957i
$207$	−198.577	−	144.274i	−0.959308	−	0.696978i
$208$			98.2262i			0.472241i
$209$	−133.839	−	108.819i	−0.640378	−	0.520666i
$210$	15.7813			0.0751490
$211$	−5.23750	+	7.20881i	−0.0248223	+	0.0341650i	−0.821248	−	0.570572i	$-0.806722\pi$
$211$	−5.23750	+	7.20881i	−0.0248223	+	0.0341650i	0.796425	+	0.604737i	$0.206722\pi$
$212$	−32.1767	+	99.0297i	−0.151777	+	0.467121i
$213$	27.7242	+	85.3265i	0.130161	+	0.400594i
$214$	−87.6131	+	63.6546i	−0.409407	+	0.297452i
$215$	98.7243	+	135.882i	0.459183	+	0.632011i
$216$	43.9197	−	14.2704i	0.203332	−	0.0660665i
$217$	−98.2924	−	31.9371i	−0.452960	−	0.147176i
$218$	13.8572	+	10.0679i	0.0635652	+	0.0461828i
$219$		−	23.4443i		−	0.107052i
$220$	−35.8131	−	55.3866i	−0.162787	−	0.251757i
$221$	158.628			0.717774
$222$	3.31687	−	4.56528i	0.0149408	−	0.0205643i
$223$	−63.9823	+	196.917i	−0.286916	+	0.883037i	0.698902	+	0.715218i	$0.253673\pi$
$223$	−63.9823	+	196.917i	−0.286916	+	0.883037i	−0.985818	+	0.167819i	$0.946327\pi$
$224$	−6.80937	−	20.9571i	−0.0303990	−	0.0935585i
$225$	−104.758	+	76.1108i	−0.465589	+	0.338270i
$226$	−78.8652	−	108.549i	−0.348961	−	0.480304i
$227$	92.3282	−	29.9992i	0.406732	−	0.132155i	−0.0985035	−	0.995137i	$-0.531406\pi$
$227$	92.3282	−	29.9992i	0.406732	−	0.132155i	0.505236	+	0.862981i	$0.331406\pi$
$228$	28.5012	+	9.26059i	0.125005	+	0.0406166i
$229$	−46.7820	−	33.9891i	−0.204288	−	0.148424i	0.480937	−	0.876755i	$-0.340296\pi$
$229$	−46.7820	−	33.9891i	−0.204288	−	0.148424i	−0.685226	+	0.728331i	$0.740296\pi$
$230$		−	128.687i		−	0.559509i
$231$	−14.7483	+	38.1950i	−0.0638456	+	0.165346i
$232$	42.3975			0.182748
$233$	−41.2848	+	56.8237i	−0.177188	+	0.243879i	−0.888369	−	0.459131i	$-0.848161\pi$
$233$	−41.2848	+	56.8237i	−0.177188	+	0.243879i	0.711180	+	0.703009i	$0.248161\pi$
$234$	86.7861	−	267.100i	0.370881	−	1.14145i
$235$	28.0120	+	86.2122i	0.119200	+	0.366860i
$236$	152.756	−	110.983i	0.647269	−	0.470269i
$237$	−43.4207	−	59.7634i	−0.183210	−	0.252166i
$238$	−33.8442	+	10.9966i	−0.142202	+	0.0462043i
$239$	62.7924	+	20.4025i	0.262730	+	0.0853660i	0.437420	−	0.899257i	$-0.355892\pi$
$239$	62.7924	+	20.4025i	0.262730	+	0.0853660i	−0.174690	+	0.984623i	$0.555892\pi$
$240$	9.27033	+	6.73529i	0.0386264	+	0.0280637i
$241$		−	49.6438i		−	0.205991i	−0.994682	−	0.102995i	$-0.967157\pi$
$241$		−	49.6438i		−	0.205991i	0.994682	−	0.102995i	$-0.0328427\pi$
$242$	167.520	−	34.9162i	0.692230	−	0.144282i
$243$	−201.582			−0.829556
$244$	−109.690	+	150.975i	−0.449549	+	0.618751i
$245$	31.3378	−	96.4477i	0.127909	−	0.393664i
$246$	18.1037	+	55.7173i	0.0735921	+	0.226493i
$247$	311.536	−	226.344i	1.26128	−	0.916374i
$248$	−44.1090	−	60.7109i	−0.177859	−	0.244802i
$249$	26.0129	−	8.45210i	0.104469	−	0.0339442i
$250$	−165.373	−	53.7331i	−0.661494	−	0.214932i
$251$	53.3991	+	38.7967i	0.212746	+	0.154569i	0.689055	−	0.724709i	$-0.258026\pi$
$251$	53.3991	+	38.7967i	0.212746	+	0.154569i	−0.476309	+	0.879278i	$0.658026\pi$
$252$			63.0036i			0.250014i
$253$	311.458	+	120.264i	1.23106	+	0.475352i
$254$	188.685			0.742856
$255$	10.8770	−	14.9709i	0.0426549	−	0.0587094i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	84.1944	+	259.124i	0.327605	+	1.00826i	0.970251	+	0.242101i	$0.0778364\pi$
$257$	84.1944	+	259.124i	0.327605	+	1.00826i	−0.642647	+	0.766163i	$0.722164\pi$
$258$	61.2472	−	44.4987i	0.237392	−	0.172475i
$259$	9.56137	+	13.1601i	0.0369165	+	0.0508112i
$260$	140.036	−	45.5003i	0.538598	−	0.175001i
$261$	−115.289	−	37.4596i	−0.441719	−	0.143523i
$262$	−48.4822	−	35.2244i	−0.185047	−	0.134444i
$263$		−	66.3839i		−	0.252410i	−0.992004	−	0.126205i	$-0.959720\pi$
$263$		−	66.3839i		−	0.252410i	0.992004	−	0.126205i	$-0.0402797\pi$
$264$	−24.9648	+	16.1423i	−0.0945636	+	0.0611450i
$265$	156.086			0.589004
$266$	−50.7770	+	69.8886i	−0.190891	+	0.262739i
$267$	−20.1585	+	62.0415i	−0.0755000	+	0.232365i
$268$	−33.4215	−	102.861i	−0.124707	−	0.383809i
$269$	−147.830	+	107.405i	−0.549553	+	0.399274i	−0.827621	−	0.561288i	$-0.810306\pi$
$269$	−147.830	+	107.405i	−0.549553	+	0.399274i	0.278067	+	0.960562i	$0.410306\pi$
$270$	−40.6889	−	56.0035i	−0.150700	−	0.207420i
$271$	−380.422	+	123.607i	−1.40377	+	0.456113i	−0.910409	−	0.413710i	$-0.864233\pi$
$271$	−380.422	+	123.607i	−1.40377	+	0.456113i	−0.493363	+	0.869823i	$0.664233\pi$
$272$	−24.5742	−	7.98463i	−0.0903462	−	0.0293553i
$273$	−73.9464	−	53.7252i	−0.270866	−	0.196796i
$274$			192.361i			0.702047i
$275$	111.113	−	136.660i	0.404046	−	0.496945i
$276$	−58.0039			−0.210159
$277$	−27.4031	+	37.7171i	−0.0989282	+	0.136163i	−0.855611	−	0.517619i	$-0.826819\pi$
$277$	−27.4031	+	37.7171i	−0.0989282	+	0.136163i	0.756683	+	0.653782i	$0.226819\pi$
$278$	−44.2385	+	136.152i	−0.159131	+	0.489755i
$279$	66.3028	+	204.059i	0.237644	+	0.731394i
$280$	−26.7231	+	19.4155i	−0.0954397	+	0.0693410i
$281$	−296.043	−	407.468i	−1.05353	−	1.45006i	−0.885706	−	0.464246i	$-0.846325\pi$
$281$	−296.043	−	407.468i	−1.05353	−	1.45006i	−0.167826	−	0.985817i	$-0.553675\pi$
$282$	38.8590	−	12.6260i	0.137798	−	0.0447732i
$283$	−53.4612	−	17.3706i	−0.188909	−	0.0613802i	0.213035	−	0.977045i	$-0.431665\pi$
$283$	−53.4612	−	17.3706i	−0.188909	−	0.0613802i	−0.401944	+	0.915664i	$0.631665\pi$
$284$	−151.923	−	110.378i	−0.534939	−	0.388656i
$285$		−	44.9222i		−	0.157622i
$286$	−20.7465	+	381.446i	−0.0725403	+	1.33373i
$287$	−168.879			−0.588429
$288$	−26.8893	+	37.0099i	−0.0933656	+	0.128507i
$289$	76.4113	−	235.170i	0.264399	−	0.813737i
$290$	−19.6393	−	60.4437i	−0.0677219	−	0.208426i
$291$	27.8385	−	20.2259i	0.0956650	−	0.0695047i
$292$	28.8432	+	39.6993i	0.0987781	+	0.135956i
$293$	177.512	−	57.6771i	0.605843	−	0.196850i	0.00999814	−	0.999950i	$-0.496817\pi$
$293$	177.512	−	57.6771i	0.605843	−	0.196850i	0.595845	+	0.803100i	$0.296817\pi$
$294$	−43.4725	−	14.1251i	−0.147866	−	0.0480445i
$295$	−228.982	−	166.365i	−0.776211	−	0.563950i
$296$			11.8113i			0.0399030i
$297$	173.569	−	46.1404i	0.584409	−	0.155355i
$298$	73.0774			0.245226
$299$	−438.098	+	602.990i	−1.46521	+	2.01669i
$300$	−9.45577	+	29.1019i	−0.0315192	+	0.0970062i
$301$	67.4377	+	207.552i	0.224046	+	0.689541i
$302$	−95.8711	+	69.6545i	−0.317454	+	0.230644i
$303$	1.39208	+	1.91604i	0.00459433	+	0.00632355i
$304$	−59.6555	+	19.3832i	−0.196235	+	0.0637606i
$305$	266.048	+	86.4441i	0.872288	+	0.283423i
$306$	59.7683	+	43.4242i	0.195321	+	0.141909i
$307$		−	495.856i		−	1.61517i	−0.589755	−	0.807583i	$-0.700776\pi$
$307$		−	495.856i		−	1.61517i	0.589755	−	0.807583i	$-0.299224\pi$
$308$	−22.0168	−	82.8219i	−0.0714830	−	0.268902i
$309$	29.0048			0.0938666
$310$	−66.1199	+	91.0063i	−0.213290	+	0.293569i
$311$	114.991	−	353.907i	0.369747	−	1.13796i	−0.577208	−	0.816597i	$-0.695858\pi$
$311$	114.991	−	353.907i	0.369747	−	1.13796i	0.946955	−	0.321366i	$-0.104142\pi$
$312$	−20.5087	−	63.1191i	−0.0657329	−	0.202305i
$313$	198.463	−	144.192i	0.634068	−	0.460677i	−0.223739	−	0.974649i	$-0.571826\pi$
$313$	198.463	−	144.192i	0.634068	−	0.460677i	0.857807	+	0.513972i	$0.171826\pi$
$314$	193.271	+	266.015i	0.615513	+	0.847181i
$315$	89.8208	−	29.1845i	0.285145	−	0.0926493i
$316$	147.052	+	47.7801i	0.465355	+	0.151203i
$317$	48.6657	+	35.3577i	0.153519	+	0.111538i	0.661893	−	0.749598i	$-0.269753\pi$
$317$	48.6657	+	35.3577i	0.153519	+	0.111538i	−0.508374	+	0.861136i	$0.669753\pi$
$318$		−	70.3537i		−	0.221238i
$319$	164.644	+	8.95484i	0.516126	+	0.0280716i
$320$	−23.9842			−0.0749506
$321$	43.0088	−	59.1966i	0.133984	−	0.184413i
$322$	51.6692	−	159.022i	0.160463	−	0.493856i
$323$	31.3025	+	96.3391i	0.0969117	+	0.298264i
$324$	92.5221	−	67.2212i	0.285562	−	0.207473i
$325$	231.115	+	318.102i	0.711122	+	0.978776i
$326$	432.594	−	140.558i	1.32698	−	0.431161i
$327$	−11.0066	−	3.57625i	−0.0336592	−	0.0109365i
$328$	−99.2039	−	72.0759i	−0.302451	−	0.219744i
$329$			117.782i			0.357999i
$330$	34.5773	+	28.1135i	0.104780	+	0.0851923i
$331$	−89.7487			−0.271144			−0.135572	−	0.990767i	$-0.543287\pi$
$331$	−89.7487			−0.271144			−0.135572	+	0.990767i	$0.543287\pi$
$332$	−33.6502	+	46.3156i	−0.101356	+	0.139505i
$333$	10.4357	−	32.1177i	0.0313383	−	0.0964495i
$334$	−54.6640	−	168.238i	−0.163665	−	0.503708i
$335$	−131.161	+	95.2943i	−0.391526	+	0.284460i
$336$	8.75127	+	12.0451i	0.0260454	+	0.0358485i
$337$	−117.112	+	38.0519i	−0.347513	+	0.112914i	−0.477572	−	0.878592i	$-0.658483\pi$
$337$	−117.112	+	38.0519i	−0.347513	+	0.112914i	0.130060	+	0.991506i	$0.458483\pi$
$338$	−583.760	−	189.675i	−1.72710	−	0.561169i
$339$	73.3419	+	53.2860i	0.216348	+	0.157186i
$340$			38.7327i			0.113920i
$341$	−158.468	−	245.078i	−0.464715	−	0.718703i
$342$	179.343			0.524395
$343$	189.642	−	261.020i	0.552893	−	0.760992i
$344$	−48.9664	+	150.703i	−0.142344	+	0.438090i
$345$	26.8686	+	82.6930i	0.0778799	+	0.239690i
$346$	144.988	−	105.340i	0.419041	−	0.304451i
$347$	−186.940	−	257.300i	−0.538731	−	0.741500i	0.449698	−	0.893180i	$-0.351531\pi$
$347$	−186.940	−	257.300i	−0.538731	−	0.741500i	−0.988430	+	0.151681i	$0.951531\pi$
$348$	−27.2442	+	8.85217i	−0.0782879	+	0.0254373i
$349$	252.823	+	82.1472i	0.724421	+	0.235379i	0.647939	−	0.761692i	$-0.275631\pi$
$349$	252.823	+	82.1472i	0.724421	+	0.235379i	0.0764822	+	0.997071i	$0.475631\pi$
$350$	−71.3616	−	51.8472i	−0.203890	−	0.148135i
$351$			400.936i			1.14227i
$352$	22.4143	−	58.0482i	0.0636770	−	0.164910i
$353$	−249.501			−0.706802			−0.353401	−	0.935472i	$-0.614975\pi$
$353$	−249.501			−0.706802			−0.353401	+	0.935472i	$0.614975\pi$
$354$	−74.9869	+	103.211i	−0.211828	+	0.291556i
$355$	−86.9865	+	267.717i	−0.245032	+	0.754132i
$356$	−42.1935	−	129.858i	−0.118521	−	0.364770i
$357$	19.4519	−	14.1327i	0.0544872	−	0.0395873i
$358$	−164.872	−	226.926i	−0.460536	−	0.633873i
$359$	−535.038	+	173.844i	−1.49036	+	0.484246i	−0.937189	−	0.348823i	$-0.886581\pi$
$359$	−535.038	+	173.844i	−1.49036	+	0.484246i	−0.553169	+	0.833069i	$0.686581\pi$
$360$	65.2187	+	21.1908i	0.181163	+	0.0588634i
$361$	−93.1137	−	67.6511i	−0.257933	−	0.187399i
$362$			151.110i			0.417432i
$363$	−100.356	+	57.4132i	−0.276464	+	0.158163i
$364$	191.314			0.525588
$365$	43.2363	−	59.5097i	0.118456	−	0.163040i
$366$	38.9635	−	119.917i	0.106458	−	0.327643i
$367$	8.68220	+	26.7211i	0.0236572	+	0.0728094i	0.962188	−	0.272386i	$-0.0878127\pi$
$367$	8.68220	+	26.7211i	0.0236572	+	0.0728094i	−0.938531	+	0.345195i	$0.887813\pi$
$368$	98.2206	−	71.3614i	0.266904	−	0.193917i
$369$	206.078	+	283.641i	0.558476	+	0.768676i
$370$	16.8387	−	5.47122i	0.0455099	−	0.0147871i
$371$	192.879	+	62.6703i	0.519890	+	0.168923i
$372$	41.0198	+	29.8027i	0.110268	+	0.0801147i
$373$		−	157.016i		−	0.420953i	−0.977599	−	0.210477i	$-0.932498\pi$
$373$		−	157.016i		−	0.420953i	0.977599	−	0.210477i	$-0.0675016\pi$
$374$	−93.7436	−	36.1975i	−0.250651	−	0.0967846i
$375$	117.486			0.313297
$376$	−50.2679	+	69.1879i	−0.133691	+	0.184010i
$377$	−113.748	+	350.081i	−0.301719	+	0.928596i
$378$	−27.7942	−	85.5419i	−0.0735297	−	0.226301i
$379$	−503.479	+	365.799i	−1.32844	+	0.965169i	−0.328656	+	0.944450i	$0.606596\pi$
$379$	−503.479	+	365.799i	−1.32844	+	0.965169i	−0.999785	+	0.0207195i	$0.993404\pi$
$380$	55.2672	+	76.0688i	0.145440	+	0.200181i
$381$	−121.247	+	39.3957i	−0.318235	+	0.103401i
$382$	46.3103	+	15.0471i	0.121231	+	0.0393904i
$383$	278.690	+	202.480i	0.727651	+	0.528670i	0.888820	−	0.458257i	$-0.151526\pi$
$383$	278.690	+	202.480i	0.727651	+	0.528670i	−0.161168	+	0.986927i	$0.551526\pi$
$384$			10.8105i			0.0281525i
$385$	−107.876	+	69.7528i	−0.280197	+	0.181176i
$386$	−302.627			−0.784009
$387$	266.302	−	366.534i	0.688120	−	0.947116i
$388$	−22.2566	+	68.4986i	−0.0573623	+	0.176543i
$389$	−89.6214	−	275.826i	−0.230389	−	0.709065i	−0.997700	−	0.0677892i	$-0.978405\pi$
$389$	−89.6214	−	275.826i	−0.230389	−	0.709065i	0.767311	−	0.641276i	$-0.221595\pi$
$390$	−80.4854	+	58.4761i	−0.206373	+	0.149939i
$391$	−115.243	−	158.619i	−0.294740	−	0.405675i
$392$	90.9918	−	29.5650i	0.232122	−	0.0754210i
$393$	38.5087	+	12.5122i	0.0979865	+	0.0318377i
$394$	310.496	+	225.589i	0.788061	+	0.572560i
$395$		−	231.777i		−	0.586777i
$396$	−112.237	+	138.043i	−0.283428	+	0.348594i
$397$	−238.817			−0.601554			−0.300777	−	0.953694i	$-0.597246\pi$
$397$	−238.817			−0.601554			−0.300777	+	0.953694i	$0.597246\pi$
$398$	207.756	−	285.951i	0.521999	−	0.718470i
$399$	18.0368	−	55.5114i	0.0452049	−	0.139126i
$400$	−19.7918	−	60.9127i	−0.0494794	−	0.152282i
$401$	109.555	−	79.5964i	0.273205	−	0.198495i	−0.442743	−	0.896648i	$-0.645995\pi$
$401$	109.555	−	79.5964i	0.273205	−	0.198495i	0.715948	+	0.698154i	$0.245995\pi$
$402$	42.9526	+	59.1192i	0.106847	+	0.147063i
$403$	619.637	−	201.332i	1.53756	−	0.499584i
$404$	−4.71455	−	1.53185i	−0.0116697	−	0.00379170i
$405$	−138.692	−	100.765i	−0.342449	−	0.248803i
$406$		−	82.5771i		−	0.203392i
$407$	−2.49468	+	45.8673i	−0.00612944	+	0.112696i
$408$	17.4582			0.0427898
$409$	178.874	−	246.199i	0.437345	−	0.601953i	−0.532275	−	0.846572i	$-0.678663\pi$
$409$	178.874	−	246.199i	0.437345	−	0.601953i	0.969619	+	0.244618i	$0.0786627\pi$
$410$	−56.8013	+	174.816i	−0.138540	+	0.426382i
$411$	−40.1630	−	123.609i	−0.0977203	−	0.300752i
$412$	−49.1151	+	35.6842i	−0.119211	+	0.0866121i
$413$	−216.161	−	297.520i	−0.523393	−	0.720388i
$414$	−330.135	+	107.267i	−0.797428	+	0.259100i
$415$	81.6170	+	26.5190i	0.196667	+	0.0639011i
$416$	112.383	+	81.6509i	0.270151	+	0.196276i
$417$		−	96.7264i		−	0.231958i
$418$	−235.757	+	62.6719i	−0.564012	+	0.149933i
$419$	594.131			1.41797			0.708987	−	0.705221i	$-0.249152\pi$
$419$	594.131			1.41797			0.708987	+	0.705221i	$0.249152\pi$
$420$	13.1183	−	18.0557i	0.0312339	−	0.0429898i
$421$	−78.8474	+	242.667i	−0.187286	+	0.576407i	−0.999980	−	0.00628320i	$-0.998000\pi$
$421$	−78.8474	+	242.667i	−0.187286	+	0.576407i	0.812694	+	0.582690i	$0.198000\pi$
$422$	3.89406	+	11.9847i	0.00922764	+	0.0283998i
$423$	197.820	−	143.725i	0.467660	−	0.339775i
$424$	86.5552	+	119.133i	0.204140	+	0.280974i
$425$	−98.3696	+	31.9622i	−0.231458	+	0.0752052i
$426$	120.670	+	39.2080i	0.283263	+	0.0920376i
$427$	294.053	+	213.642i	0.688649	+	0.500333i
$428$			153.153i			0.357835i
$429$	−66.3107	−	249.445i	−0.154570	−	0.581457i
$430$	237.531			0.552398
$431$	388.839	−	535.191i	0.902178	−	1.24174i	−0.0675899	−	0.997713i	$-0.521531\pi$
$431$	388.839	−	535.191i	0.902178	−	1.24174i	0.969768	−	0.244029i	$-0.0784691\pi$
$432$	20.1813	−	62.1118i	0.0467161	−	0.143777i
$433$	33.9998	+	104.641i	0.0785215	+	0.241664i	0.982610	−	0.185681i	$-0.0594490\pi$
$433$	33.9998	+	104.641i	0.0785215	+	0.241664i	−0.904089	+	0.427345i	$0.859449\pi$
$434$	−118.246	+	85.9107i	−0.272456	+	0.197951i
$435$	25.2401	+	34.7400i	0.0580232	+	0.0798621i
$436$	23.0377	−	7.48541i	0.0528388	−	0.0171684i
$437$	−452.663	−	147.079i	−1.03584	−	0.336566i
$438$	−26.8232	−	19.4882i	−0.0612401	−	0.0444936i
$439$			549.236i			1.25111i	0.780181	+	0.625553i	$0.215127\pi$
$439$			549.236i			1.25111i	−0.780181	+	0.625553i	$0.784873\pi$
$440$	−93.1389	−	5.06574i	−0.211679	−	0.0115130i
$441$	−273.550			−0.620295
$442$	131.860	−	181.490i	0.298326	−	0.410611i
$443$	−10.8704	+	33.4556i	−0.0245381	+	0.0755205i	−0.962576	−	0.271013i	$-0.912641\pi$
$443$	−10.8704	+	33.4556i	−0.0245381	+	0.0755205i	0.938038	+	0.346534i	$0.112641\pi$
$444$	−2.46608	−	7.58981i	−0.00555423	−	0.0170942i
$445$	−165.587	+	120.306i	−0.372105	+	0.270350i
$446$	172.112	+	236.892i	0.385901	+	0.531148i
$447$	−46.9588	+	15.2578i	−0.105053	+	0.0341339i
$448$	−29.6378	−	9.62991i	−0.0661558	−	0.0214953i
$449$	456.315	+	331.532i	1.01629	+	0.738379i	0.965519	−	0.260331i	$-0.0838317\pi$
$449$	456.315	+	331.532i	1.01629	+	0.738379i	0.0507723	+	0.998710i	$0.483832\pi$
$450$			183.123i			0.406940i
$451$	−370.020	−	300.849i	−0.820444	−	0.667070i
$452$	−189.750			−0.419801
$453$	47.0627	−	64.7762i	0.103891	−	0.142994i
$454$	42.4253	−	130.572i	0.0934479	−	0.287603i
$455$	−88.6205	−	272.746i	−0.194770	−	0.599441i
$456$	34.2870	−	24.9109i	0.0751907	−	0.0546293i
$457$	399.901	+	550.416i	0.875056	+	1.20441i	0.977766	+	0.209700i	$0.0672487\pi$
$457$	399.901	+	550.416i	0.875056	+	1.20441i	−0.102710	+	0.994711i	$0.532751\pi$
$458$	−77.7755	+	25.2708i	−0.169816	+	0.0551764i
$459$	−100.306	−	32.5914i	−0.218531	−	0.0710052i
$460$	−147.234	−	106.972i	−0.320073	−	0.232547i
$461$		−	202.839i		−	0.439998i	−0.975500	−	0.219999i	$-0.929395\pi$
$461$		−	202.839i		−	0.439998i	0.975500	−	0.219999i	$-0.0706053\pi$
$462$	31.4402	+	48.6236i	0.0680523	+	0.105246i
$463$	−746.270			−1.61182			−0.805908	−	0.592041i	$-0.798322\pi$
$463$	−746.270			−1.61182			−0.805908	+	0.592041i	$0.798322\pi$
$464$	35.2430	−	48.5079i	0.0759548	−	0.104543i
$465$	23.4868	−	72.2849i	0.0505092	−	0.155451i
$466$	30.6951	+	94.4698i	0.0658693	+	0.202725i
$467$	−301.368	+	218.957i	−0.645328	+	0.468858i	−0.861677	−	0.507458i	$-0.830585\pi$
$467$	−301.368	+	218.957i	−0.645328	+	0.468858i	0.216348	+	0.976316i	$0.430585\pi$
$468$	−233.454	−	321.322i	−0.498834	−	0.686586i
$469$	−200.341	+	65.0947i	−0.427166	+	0.138795i
$470$	121.922	+	39.6150i	0.259409	+	0.0842872i
$471$	−179.735	−	130.585i	−0.381604	−	0.277251i
$472$		−	267.027i		−	0.565734i
$473$	−221.984	+	574.890i	−0.469310	+	1.21541i
$474$	−104.470			−0.220401
$475$	−147.586	+	203.134i	−0.310707	+	0.427651i
$476$	−15.5516	+	47.8629i	−0.0326714	+	0.100552i
$477$	−130.106	−	400.425i	−0.272759	−	0.839466i
$478$	75.5394	−	54.8826i	0.158032	−	0.114817i
$479$	336.874	+	463.668i	0.703287	+	0.967991i	0.999916	+	0.0129981i	$0.00413753\pi$
$479$	336.874	+	463.668i	0.703287	+	0.967991i	−0.296629	+	0.954993i	$0.595862\pi$
$480$	15.4120	−	5.00766i	0.0321083	−	0.0104326i
$481$	−97.5271	−	31.6885i	−0.202759	−	0.0658804i
$482$	−56.7986	−	41.2666i	−0.117839	−	0.0856153i
$483$			112.974i			0.233900i
$484$	99.3031	−	220.687i	0.205172	−	0.455966i
$485$	107.964			0.222607
$486$	−167.566	+	230.635i	−0.344786	+	0.474557i
$487$	13.0777	−	40.2489i	0.0268535	−	0.0826467i	−0.936732	−	0.350049i	$-0.886165\pi$
$487$	13.0777	−	40.2489i	0.0268535	−	0.0826467i	0.963585	+	0.267402i	$0.0861651\pi$
$488$	81.5541	+	250.998i	0.167119	+	0.514339i
$489$	−248.634	+	180.643i	−0.508453	+	0.369413i
$490$	−84.2984	−	116.027i	−0.172038	−	0.236789i
$491$	582.692	−	189.328i	1.18675	−	0.385597i	0.351877	−	0.936046i	$-0.385544\pi$
$491$	582.692	−	189.328i	1.18675	−	0.385597i	0.834868	+	0.550450i	$0.185544\pi$
$492$	78.7962	+	25.6024i	0.160155	+	0.0520375i
$493$	−78.3366	−	56.9149i	−0.158898	−	0.115446i
$494$		−	544.585i		−	1.10240i
$495$	248.791	+	96.0663i	0.502608	+	0.194073i
$496$	−106.126			−0.213965
$497$	−214.983	+	295.898i	−0.432561	+	0.595368i
$498$	11.9531	−	36.7878i	0.0240021	−	0.0738710i
$499$	−143.126	−	440.498i	−0.286826	−	0.882761i	−0.985845	−	0.167658i	$-0.946380\pi$
$499$	−143.126	−	440.498i	−0.286826	−	0.882761i	0.699019	−	0.715103i	$-0.253620\pi$
$500$	−198.945	+	144.542i	−0.397889	+	0.289083i
$501$	70.2530	+	96.6950i	0.140226	+	0.193004i
$502$	88.7765	−	28.8452i	0.176846	−	0.0574606i
$503$	717.814	+	233.232i	1.42707	+	0.463682i	0.917840	−	0.396951i	$-0.129932\pi$
$503$	717.814	+	233.232i	1.42707	+	0.463682i	0.509226	+	0.860633i	$0.329932\pi$
$504$	72.0839	+	52.3720i	0.143024	+	0.103913i
$505$			7.43085i			0.0147145i
$506$	396.497	−	256.376i	0.783591	−	0.506672i
$507$	414.721			0.817990
$508$	156.846	−	215.879i	0.308751	−	0.424959i
$509$	216.406	−	666.029i	0.425159	−	1.30850i	−0.477683	−	0.878532i	$-0.658523\pi$
$509$	216.406	−	666.029i	0.425159	−	1.30850i	0.902842	−	0.429972i	$-0.141477\pi$
$510$	−8.08700	−	24.8892i	−0.0158569	−	0.0488024i
$511$	77.3219	−	56.1776i	0.151315	−	0.109937i
$512$	−13.3001	−	18.3060i	−0.0259767	−	0.0357538i
$513$	−243.499	+	79.1177i	−0.474658	+	0.154226i
$514$	366.456	+	119.069i	0.712950	+	0.231651i
$515$	73.6240	+	53.4910i	0.142959	+	0.103866i
$516$		−	107.064i		−	0.207488i
$517$	−209.821	+	258.063i	−0.405844	+	0.499156i
$518$	23.0047			0.0444106
$519$	−71.1741	+	97.9627i	−0.137137	+	0.188753i
$520$	64.3472	−	198.040i	0.123745	−	0.380846i
$521$	72.6318	+	223.538i	0.139408	+	0.429055i	0.996250	−	0.0865255i	$-0.0275764\pi$
$521$	72.6318	+	223.538i	0.139408	+	0.429055i	−0.856841	+	0.515580i	$0.827576\pi$
$522$	−138.693	+	100.766i	−0.265695	+	0.193038i
$523$	−381.075	−	524.505i	−0.728633	−	1.00288i	−0.999193	−	0.0401744i	$-0.987209\pi$
$523$	−381.075	−	524.505i	−0.728633	−	1.00288i	0.270559	−	0.962703i	$-0.412791\pi$
$524$	−80.6021	+	26.1892i	−0.153821	+	0.0499794i
$525$	56.6814	+	18.4169i	0.107965	+	0.0350798i
$526$	−75.9513	−	55.1819i	−0.144394	−	0.104908i
$527$			171.386i			0.325211i
$528$	−2.28332	+	41.9811i	−0.00432446	+	0.0795097i
$529$	392.234			0.741463
$530$	129.747	−	178.582i	0.244806	−	0.336947i
$531$	−235.927	+	726.109i	−0.444307	+	1.36744i
$532$	37.7525	+	116.190i	0.0709634	+	0.218403i
$533$	861.293	−	625.766i	1.61593	−	1.17405i
$534$	54.2263	+	74.6360i	0.101547	+	0.139768i
$535$	218.342	−	70.9436i	0.408116	−	0.132605i
$536$	−145.467	−	47.2651i	−0.271394	−	0.0881812i
$537$	153.325	+	111.397i	0.285521	+	0.207443i
$538$			258.416i			0.480327i
$539$	359.597	−	95.5927i	0.667156	−	0.177352i
$540$	−97.8977			−0.181292
$541$	−194.429	+	267.608i	−0.359388	+	0.494655i	−0.949978	−	0.312317i	$-0.898895\pi$
$541$	−194.429	+	267.608i	−0.359388	+	0.494655i	0.590590	+	0.806972i	$0.298895\pi$
$542$	−174.806	+	537.998i	−0.322521	+	0.992617i
$543$	−31.5504	−	97.1021i	−0.0581038	−	0.178825i
$544$	−29.5628	+	21.4786i	−0.0543433	+	0.0394827i
$545$	−21.3431	−	29.3762i	−0.0391616	−	0.0539013i
$546$	−122.937	+	39.9445i	−0.225158	+	0.0731584i
$547$	−575.496	−	186.990i	−1.05209	−	0.341846i	−0.268604	−	0.963251i	$-0.586562\pi$
$547$	−575.496	−	186.990i	−1.05209	−	0.341846i	−0.783490	+	0.621404i	$0.786562\pi$
$548$	220.084	+	159.901i	0.401614	+	0.291789i
$549$		−	754.578i		−	1.37446i
$550$	−63.9928	−	240.726i	−0.116350	−	0.437683i
$551$	−235.060			−0.426606
$552$	−48.2160	+	66.3636i	−0.0873478	+	0.120224i
$553$	93.0609	−	286.412i	0.168284	−	0.517924i
$554$	20.3741	+	62.7050i	0.0367764	+	0.113186i
$555$	−9.67803	+	7.03150i	−0.0174379	+	0.0126694i
$556$	119.001	+	163.791i	0.214031	+	0.294588i
$557$	−242.301	+	78.7283i	−0.435010	+	0.141343i	−0.518332	−	0.855179i	$-0.673447\pi$
$557$	−242.301	+	78.7283i	−0.435010	+	0.141343i	0.0833221	+	0.996523i	$0.473447\pi$
$558$	288.583	+	93.7663i	0.517174	+	0.168040i
$559$	−1113.00	−	808.642i	−1.99106	−	1.44659i
$560$			46.7137i			0.0834174i
$561$	67.7964	+	3.68738i	0.120849	+	0.00657288i
$562$	−712.280			−1.26740
$563$	−594.763	+	818.621i	−1.05642	+	1.45403i	−0.173308	+	0.984868i	$0.555446\pi$
$563$	−594.763	+	818.621i	−1.05642	+	1.45403i	−0.883110	+	0.469166i	$0.844554\pi$
$564$	17.8559	−	54.9549i	0.0316594	−	0.0974377i
$565$	87.8960	+	270.516i	0.155568	+	0.478789i
$566$	−64.3140	+	46.7268i	−0.113629	+	0.0825562i
$567$	−130.926	−	180.204i	−0.230910	−	0.317821i
$568$	−252.573	+	82.0658i	−0.444670	+	0.144482i
$569$	−418.918	−	136.115i	−0.736236	−	0.239217i	−0.0831875	−	0.996534i	$-0.526510\pi$
$569$	−418.918	−	136.115i	−0.736236	−	0.239217i	−0.653048	+	0.757316i	$0.726510\pi$
$570$	−51.3965	−	37.3418i	−0.0901694	−	0.0655119i
$571$			577.275i			1.01099i	0.862830	+	0.505495i	$0.168690\pi$
$571$			577.275i			1.01099i	−0.862830	+	0.505495i	$0.831310\pi$
$572$	419.176	+	340.815i	0.732825	+	0.595831i
$573$	−32.9002			−0.0574175
$574$	−140.381	+	193.218i	−0.244567	+	0.336618i
$575$	150.179	−	462.203i	0.261181	−	0.803832i
$576$	19.9921	+	61.5293i	0.0347085	+	0.106822i
$577$	666.510	−	484.248i	1.15513	−	0.839251i	0.165976	−	0.986130i	$-0.446923\pi$
$577$	666.510	−	484.248i	1.15513	−	0.839251i	0.989155	+	0.146879i	$0.0469226\pi$
$578$	−205.546	−	282.910i	−0.355616	−	0.489463i
$579$	194.465	−	63.1856i	0.335864	−	0.109129i
$580$	−85.4803	−	27.7742i	−0.147380	−	0.0478866i
$581$	90.2084	+	65.5402i	0.155264	+	0.112806i
$582$		−	48.6635i		−	0.0836142i
$583$	310.962	+	480.916i	0.533382	+	0.824899i
$584$	69.3969			0.118830
$585$	−349.950	+	481.665i	−0.598206	+	0.823360i
$586$	81.5678	−	251.040i	0.139194	−	0.428395i
$587$	−70.2908	−	216.333i	−0.119746	−	0.368540i	0.873161	−	0.487431i	$-0.162066\pi$
$587$	−70.2908	−	216.333i	−0.119746	−	0.368540i	−0.992907	+	0.118891i	$0.962066\pi$
$588$	−52.2975	+	37.9964i	−0.0889414	+	0.0646197i
$589$	244.549	+	336.593i	0.415194	+	0.571465i
$590$	−380.685	+	123.692i	−0.645228	+	0.209647i
$591$	−246.622	−	80.1325i	−0.417297	−	0.135588i
$592$	13.5136	+	9.81817i	0.0228269	+	0.0165847i
$593$		−	154.112i		−	0.259885i	−0.991522	−	0.129942i	$-0.958521\pi$
$593$		−	154.112i		−	0.259885i	0.991522	−	0.129942i	$-0.0414792\pi$
$594$	91.4899	−	236.939i	0.154023	−	0.398887i
$595$	75.4392			0.126789
$596$	60.7459	−	83.6095i	0.101923	−	0.140284i
$597$	−73.7979	+	227.127i	−0.123615	+	0.380446i
$598$	325.724	+	1002.47i	0.544689	+	1.67638i
$599$	−357.063	+	259.422i	−0.596099	+	0.433091i	−0.844492	−	0.535568i	$-0.820097\pi$
$599$	−357.063	+	259.422i	−0.596099	+	0.433091i	0.248393	+	0.968659i	$0.420097\pi$
$600$	25.4360	+	35.0096i	0.0423933	+	0.0583493i
$601$	1074.30	−	349.062i	1.78753	−	0.580802i	0.788128	−	0.615511i	$-0.211050\pi$
$601$	1074.30	−	349.062i	1.78753	−	0.580802i	0.999397	+	0.0347090i	$0.0110504\pi$
$602$	293.523	+	95.3713i	0.487579	+	0.158424i
$603$	353.799	+	257.050i	0.586731	+	0.426285i
$604$			167.589i			0.277465i
$605$	−360.621	−	39.3441i	−0.596067	−	0.0650315i
$606$	3.34935			0.00552699
$607$	156.362	−	215.214i	0.257599	−	0.354554i	−0.660556	−	0.750777i	$-0.729679\pi$
$607$	156.362	−	215.214i	0.257599	−	0.354554i	0.918154	+	0.396223i	$0.129679\pi$
$608$	−27.4120	+	84.3655i	−0.0450856	+	0.138759i
$609$	17.2413	+	53.0632i	0.0283108	+	0.0871317i
$610$	320.056	−	232.534i	0.524682	−	0.381204i
$611$	−436.429	−	600.692i	−0.714286	−	0.983130i
$612$	99.3653	−	32.2857i	0.162362	−	0.0527545i
$613$	−206.889	−	67.2223i	−0.337503	−	0.109661i	0.135362	−	0.990796i	$-0.456780\pi$
$613$	−206.889	−	67.2223i	−0.337503	−	0.109661i	−0.472865	+	0.881135i	$0.656780\pi$
$614$	−567.320	−	412.182i	−0.923974	−	0.671306i
$615$		−	124.195i		−	0.201943i
$616$	−113.060	−	43.6561i	−0.183539	−	0.0708704i
$617$	828.147			1.34222			0.671108	−	0.741360i	$-0.265819\pi$
$617$	828.147			1.34222			0.671108	+	0.741360i	$0.265819\pi$
$618$	24.1103	−	33.1850i	0.0390135	−	0.0536975i
$619$	110.604	−	340.406i	0.178683	−	0.549928i	−0.821100	−	0.570784i	$-0.806639\pi$
$619$	110.604	−	340.406i	0.178683	−	0.549928i	0.999782	+	0.0208561i	$0.00663920\pi$
$620$	49.1599	+	151.299i	0.0792902	+	0.244030i
$621$	400.913	−	291.280i	0.645593	−	0.469051i
$622$	−309.326	−	425.750i	−0.497308	−	0.684486i
$623$	−252.924	+	82.1799i	−0.405977	+	0.131910i
$624$	−89.2639	−	29.0036i	−0.143051	−	0.0464802i
$625$	−25.6267	−	18.6189i	−0.0410027	−	0.0297902i
$626$		−	346.926i		−	0.554195i
$627$	138.410	−	89.4960i	0.220749	−	0.142737i
$628$	465.011			0.740464
$629$	15.8556	−	21.8234i	0.0252077	−	0.0346954i
$630$	41.2732	−	127.026i	0.0655130	−	0.201628i
$631$	193.271	+	594.828i	0.306293	+	0.942674i	0.979191	+	0.202939i	$0.0650493\pi$
$631$	193.271	+	594.828i	0.306293	+	0.942674i	−0.672898	+	0.739735i	$0.734951\pi$
$632$	176.904	−	128.528i	0.279911	−	0.203368i
$633$	−5.00457	−	6.88820i	−0.00790612	−	0.0108818i
$634$	80.9071	−	26.2883i	0.127614	−	0.0414642i
$635$	−380.421	−	123.606i	−0.599088	−	0.194656i
$636$	−80.4933	−	58.4818i	−0.126562	−	0.0919525i
$637$			830.650i			1.30400i
$638$	147.106	−	180.929i	0.230574	−	0.283588i
$639$	759.313			1.18828
$640$	−19.9369	+	27.4408i	−0.0311515	+	0.0428763i
$641$	−184.027	+	566.377i	−0.287094	+	0.883583i	0.698670	+	0.715444i	$0.253776\pi$
$641$	−184.027	+	566.377i	−0.287094	+	0.883583i	−0.985763	+	0.168139i	$0.946224\pi$
$642$	−31.9769	−	98.4148i	−0.0498082	−	0.153294i
$643$	−594.110	+	431.646i	−0.923965	+	0.671300i	−0.944508	−	0.328489i	$-0.893461\pi$
$643$	−594.110	+	431.646i	−0.923965	+	0.671300i	0.0205425	+	0.999789i	$0.493461\pi$
$644$	−138.990	−	191.303i	−0.215823	−	0.297055i
$645$	−152.635	+	49.5941i	−0.236644	+	0.0768902i
$646$	136.244	+	44.2684i	0.210904	+	0.0685269i
$647$	−740.468	−	537.981i	−1.14446	−	0.831501i	−0.156728	−	0.987642i	$-0.550095\pi$
$647$	−740.468	−	537.981i	−1.14446	−	0.831501i	−0.987735	+	0.156141i	$0.950095\pi$
$648$		−	161.735i		−	0.249590i
$649$	56.3992	−	1036.96i	0.0869016	−	1.59778i
$650$	556.063			0.855482
$651$	58.0463	−	79.8939i	0.0891649	−	0.122725i
$652$	198.780	−	611.781i	0.304877	−	0.938314i
$653$	146.502	+	450.888i	0.224353	+	0.690487i	0.998357	+	0.0573062i	$0.0182511\pi$
$653$	146.502	+	450.888i	0.224353	+	0.690487i	−0.774004	+	0.633181i	$0.781749\pi$
$654$	−13.2409	+	9.62010i	−0.0202461	+	0.0147096i
$655$	74.6730	+	102.779i	0.114005	+	0.156914i
$656$	−164.927	+	53.5881i	−0.251414	+	0.0816892i
$657$	−188.707	−	61.3145i	−0.287225	−	0.0933249i
$658$	134.757	+	97.9063i	0.204797	+	0.148794i
$659$			482.603i			0.732326i	0.930551	+	0.366163i	$0.119329\pi$
$659$			482.603i			0.732326i	−0.930551	+	0.366163i	$0.880671\pi$
$660$	60.9078	−	16.1913i	0.0922845	−	0.0245323i
$661$	45.0509			0.0681557			0.0340779	−	0.999419i	$-0.489151\pi$
$661$	45.0509			0.0681557			0.0340779	+	0.999419i	$0.489151\pi$
$662$	−74.6040	+	102.684i	−0.112695	+	0.155111i
$663$	−46.8387	+	144.155i	−0.0706466	+	0.217428i
$664$	25.0188	+	77.0000i	0.0376789	+	0.115964i
$665$	148.158	−	107.643i	0.222794	−	0.161870i
$666$	−28.0719	−	38.6376i	−0.0421500	−	0.0580144i
$667$	432.699	−	140.592i	0.648724	−	0.210783i
$668$	−237.925	−	77.3065i	−0.356175	−	0.115728i
$669$	−160.058	−	116.289i	−0.239250	−	0.173825i
$670$			229.278i			0.342207i
$671$	263.689	+	991.936i	0.392979	+	1.47830i
$672$	21.0556			0.0313327
$673$	−179.880	+	247.583i	−0.267280	+	0.367880i	−0.921469	−	0.388451i	$-0.873010\pi$
$673$	−179.880	+	247.583i	−0.267280	+	0.367880i	0.654189	+	0.756331i	$0.273010\pi$
$674$	−53.8135	+	165.621i	−0.0798421	+	0.245729i
$675$	−80.7852	−	248.631i	−0.119682	−	0.368343i
$676$	−702.265	+	510.225i	−1.03885	+	0.754771i
$677$	−64.6416	−	88.9715i	−0.0954824	−	0.131420i	0.758603	−	0.651553i	$-0.225882\pi$
$677$	−64.6416	−	88.9715i	−0.0954824	−	0.131420i	−0.854085	+	0.520133i	$0.825882\pi$
$678$	121.931	−	39.6179i	0.179840	−	0.0584335i
$679$	133.414	+	43.3489i	0.196486	+	0.0638422i
$680$	44.3149	+	32.1967i	0.0651690	+	0.0473481i
$681$			92.7621i			0.136215i
$682$	−412.126	−	22.4152i	−0.604290	−	0.0328668i
$683$	−490.810			−0.718610			−0.359305	−	0.933220i	$-0.616986\pi$
$683$	−490.810			−0.718610			−0.359305	+	0.933220i	$0.616986\pi$
$684$	149.080	−	205.191i	0.217953	−	0.299986i
$685$	126.014	−	387.831i	0.183962	−	0.566177i
$686$	−140.998	−	433.948i	−0.205537	−	0.632578i
$687$	44.7015	−	32.4775i	0.0650676	−	0.0472744i
$688$	131.719	+	181.296i	0.191452	+	0.263512i
$689$	−1215.91	+	395.074i	−1.76475	+	0.573403i
$690$	116.946	+	37.9979i	0.169486	+	0.0550694i
$691$	632.920	+	459.843i	0.915947	+	0.665475i	0.942512	−	0.334172i	$-0.108457\pi$
$691$	632.920	+	459.843i	0.915947	+	0.665475i	−0.0265646	+	0.999647i	$0.508457\pi$
$692$		−	253.449i		−	0.366256i
$693$	268.865	+	218.604i	0.387973	+	0.315445i
$694$	−449.778			−0.648095
$695$	178.384	−	245.525i	0.256668	−	0.353273i
$696$	−12.5189	+	38.5291i	−0.0179869	+	0.0553579i
$697$	86.5408	+	266.345i	0.124162	+	0.382131i
$698$	304.147	−	220.975i	0.435740	−	0.316584i
$699$	−39.4487	−	54.2965i	−0.0564360	−	0.0776775i
$700$	−118.639	+	38.5482i	−0.169484	+	0.0550688i
$701$	−298.888	−	97.1146i	−0.426374	−	0.138537i	0.0879664	−	0.996123i	$-0.471963\pi$
$701$	−298.888	−	97.1146i	−0.426374	−	0.138537i	−0.514340	+	0.857586i	$0.671963\pi$
$702$	458.720	+	333.279i	0.653447	+	0.474757i
$703$		−	65.4841i		−	0.0931495i
$704$	−47.7823	−	73.8976i	−0.0678726	−	0.104968i
$705$	−86.6173			−0.122861
$706$	−207.399	+	285.460i	−0.293766	+	0.404334i
$707$	−2.98357	+	9.18247i	−0.00422004	+	0.0129879i
$708$	55.7525	+	171.589i	0.0787465	+	0.242357i
$709$	−53.5936	+	38.9380i	−0.0755904	+	0.0549197i	−0.624939	−	0.780674i	$-0.714876\pi$
$709$	−53.5936	+	38.9380i	−0.0755904	+	0.0549197i	0.549348	+	0.835593i	$0.314876\pi$
$710$	233.993	+	322.064i	0.329568	+	0.453611i
$711$	−594.603	+	193.198i	−0.836291	+	0.271728i
$712$	−183.647	−	59.6706i	−0.257932	−	0.0838071i
$713$	−651.488	−	473.334i	−0.913728	−	0.663862i
$714$		−	34.0032i		−	0.0476235i
$715$	291.711	−	755.468i	0.407987	−	1.05660i
$716$	−396.682			−0.554025
$717$	−37.0819	+	51.0388i	−0.0517181	+	0.0711839i
$718$	−245.853	+	756.658i	−0.342414	+	1.05384i
$719$	−310.081	−	954.330i	−0.431267	−	1.32730i	−0.896864	−	0.442306i	$-0.854161\pi$
$719$	−310.081	−	954.330i	−0.431267	−	1.32730i	0.465598	−	0.884997i	$-0.345839\pi$
$720$	78.4582	−	57.0032i	0.108970	−	0.0791711i
$721$	69.5017	+	95.6609i	0.0963963	+	0.132678i
$722$	−154.802	+	50.2983i	−0.214408	+	0.0696652i
$723$	45.1142	+	14.6585i	0.0623987	+	0.0202746i
$724$	172.889	+	125.611i	0.238797	+	0.173496i
$725$		−	240.014i		−	0.331054i
$726$	−17.7338	+	162.545i	−0.0244267	+	0.223891i
$727$	364.375			0.501204			0.250602	−	0.968090i	$-0.419371\pi$
$727$	364.375			0.501204			0.250602	+	0.968090i	$0.419371\pi$
$728$	159.031	−	218.887i	0.218449	−	0.300669i
$729$	−99.5094	+	306.258i	−0.136501	+	0.420108i
$730$	−32.1460	−	98.9353i	−0.0440356	−	0.135528i
$731$	292.780	−	212.717i	0.400519	−	0.290994i
$732$	−104.812	−	144.261i	−0.143185	−	0.197078i
$733$	900.076	−	292.452i	1.22793	−	0.398980i	0.377969	−	0.925818i	$-0.376623\pi$
$733$	900.076	−	292.452i	1.22793	−	0.398980i	0.849965	+	0.526838i	$0.176623\pi$
$734$	37.7893	+	12.2785i	0.0514841	+	0.0167282i
$735$	78.3946	+	56.9570i	0.106659	+	0.0774925i
$736$		−	171.696i		−	0.233282i
$737$	−554.916	−	214.271i	−0.752939	−	0.290734i
$738$	495.823			0.671847
$739$	126.126	−	173.598i	0.170672	−	0.234909i	−0.715110	−	0.699012i	$-0.753623\pi$
$739$	126.126	−	173.598i	0.170672	−	0.234909i	0.885781	+	0.464103i	$0.153623\pi$
$740$	7.73747	−	23.8135i	0.0104560	−	0.0321804i
$741$	113.704	+	349.945i	0.153447	+	0.472261i
$742$	232.034	−	168.583i	0.312714	−	0.227200i
$743$	25.6695	+	35.3310i	0.0345484	+	0.0475518i	0.825942	−	0.563755i	$-0.190644\pi$
$743$	25.6695	+	35.3310i	0.0345484	+	0.0475518i	−0.791393	+	0.611307i	$0.790644\pi$
$744$	68.1958	−	22.1582i	0.0916610	−	0.0297825i
$745$	−147.336	−	47.8724i	−0.197767	−	0.0642583i
$746$	−179.645	−	130.520i	−0.240811	−	0.174959i
$747$		−	231.486i		−	0.309888i
$748$	−119.339	+	77.1649i	−0.159544	+	0.103162i
$749$	298.295			0.398258
$750$	97.6609	−	134.419i	0.130215	−	0.179225i
$751$	157.978	−	486.208i	0.210357	−	0.647414i	−0.789093	−	0.614273i	$-0.789449\pi$
$751$	157.978	−	486.208i	0.210357	−	0.647414i	0.999451	−	0.0331403i	$-0.0105508\pi$
$752$	37.3740	+	115.025i	0.0496995	+	0.152959i
$753$	−51.0243	+	37.0713i	−0.0677613	+	0.0492315i
$754$	305.982	+	421.148i	0.405811	+	0.558551i
$755$	238.922	−	77.6305i	0.316453	−	0.102822i
$756$	−120.974	−	39.3070i	−0.160019	−	0.0519934i
$757$	700.963	+	509.280i	0.925975	+	0.672760i	0.945004	−	0.327059i	$-0.106057\pi$
$757$	700.963	+	509.280i	0.925975	+	0.672760i	−0.0190290	+	0.999819i	$0.506057\pi$
$758$			880.114i			1.16110i
$759$	−201.256	+	247.529i	−0.265160	+	0.326126i
$760$	132.973			0.174965
$761$	770.228	−	1060.13i	1.01213	−	1.39307i	0.0945463	−	0.995520i	$-0.469860\pi$
$761$	770.228	−	1060.13i	1.01213	−	1.39307i	0.917580	−	0.397552i	$-0.130140\pi$
$762$	−55.7139	+	171.470i	−0.0731153	+	0.225026i
$763$	−14.5793	−	44.8703i	−0.0191078	−	0.0588078i
$764$	55.7114	−	40.4767i	0.0729206	−	0.0529799i
$765$	−92.0559	−	126.704i	−0.120335	−	0.165626i
$766$	463.325	−	150.543i	0.604863	−	0.196532i
$767$	2204.87	+	716.406i	2.87467	+	0.934036i
$768$	12.3686	+	8.98631i	0.0161049	+	0.0117009i
$769$		−	1207.32i		−	1.56999i	−0.619503	−	0.784994i	$-0.712666\pi$
$769$		−	1207.32i		−	1.56999i	0.619503	−	0.784994i	$-0.287334\pi$
$770$	−9.86649	+	181.406i	−0.0128136	+	0.235592i
$771$	−260.341			−0.337667
$772$	−251.560	+	346.243i	−0.325855	+	0.448501i
$773$	−247.836	+	762.760i	−0.320615	+	0.986753i	0.652766	+	0.757560i	$0.273609\pi$
$773$	−247.836	+	762.760i	−0.320615	+	0.986753i	−0.973381	+	0.229193i	$0.926391\pi$
$774$	−197.995	−	609.365i	−0.255807	−	0.787294i
$775$	−343.687	+	249.703i	−0.443467	+	0.322198i
$776$	59.8700	+	82.4040i	0.0771521	+	0.106191i
$777$	−14.7826	+	4.80316i	−0.0190252	+	0.00618167i
$778$	−390.077	−	126.744i	−0.501385	−	0.162910i
$779$	550.006	+	399.603i	0.706042	+	0.512969i
$780$			140.694i			0.180377i
$781$	−998.160	+	265.344i	−1.27805	+	0.339749i
$782$	−277.276			−0.354573
$783$	143.854	−	197.998i	0.183721	−	0.252871i
$784$	41.8113	−	128.682i	0.0533307	−	0.164135i
$785$	−215.402	−	662.941i	−0.274398	−	0.844510i
$786$	46.3260	−	33.6578i	0.0589390	−	0.0428217i
$787$	−196.270	−	270.143i	−0.249390	−	0.343256i	0.665907	−	0.746034i	$-0.268045\pi$
$787$	−196.270	−	270.143i	−0.249390	−	0.343256i	−0.915298	+	0.402778i	$0.868045\pi$
$788$	516.202	−	167.724i	0.655079	−	0.212848i
$789$	60.3270	+	19.6014i	0.0764601	+	0.0248434i
$790$	−265.181	−	192.665i	−0.335672	−	0.243880i
$791$			369.574i			0.467224i
$792$	64.6405	+	243.162i	0.0816168	+	0.307023i
$793$	−2291.32			−2.88943
$794$	−198.518	+	273.236i	−0.250022	+	0.344126i
$795$	−46.0881	+	141.845i	−0.0579725	+	0.178421i
$796$	−154.465	−	475.396i	−0.194052	−	0.597231i
$797$	−651.319	+	473.211i	−0.817213	+	0.593740i	−0.915913	−	0.401377i	$-0.868532\pi$
$797$	−651.319	+	473.211i	−0.817213	+	0.593740i	0.0986995	+	0.995117i	$0.468532\pi$
$798$	−48.5188	−	66.7804i	−0.0608005	−	0.0836847i
$799$	185.757	−	60.3563i	0.232487	−	0.0755397i
$800$	−86.1436	−	27.9898i	−0.107680	−	0.0349872i
$801$	446.660	+	324.517i	0.557628	+	0.405140i
$802$		−	191.509i		−	0.238790i
$803$	269.492	+	14.6574i	0.335607	+	0.0182534i
$804$	103.344			0.128537
$805$	−208.347	+	286.766i	−0.258817	+	0.356231i
$806$	284.727	−	876.299i	0.353259	−	1.08722i
$807$	−53.9547	−	166.056i	−0.0668584	−	0.205769i
$808$	−5.67161	+	4.12066i	−0.00701932	+	0.00509983i
$809$	698.652	+	961.612i	0.863600	+	1.18864i	0.980699	+	0.195523i	$0.0626404\pi$
$809$	698.652	+	961.612i	0.863600	+	1.18864i	−0.117099	+	0.993120i	$0.537360\pi$
$810$	−230.576	+	74.9187i	−0.284662	+	0.0924922i
$811$	838.169	+	272.338i	1.03350	+	0.335805i	0.776174	−	0.630519i	$-0.217158\pi$
$811$	838.169	+	272.338i	1.03350	+	0.335805i	0.257328	+	0.966324i	$0.417158\pi$
$812$	−94.4783	−	68.6425i	−0.116353	−	0.0845351i
$813$		−	382.210i		−	0.470123i
$814$	50.4041	+	40.9816i	0.0619215	+	0.0503459i
$815$	−964.261			−1.18314
$816$	14.5122	−	19.9744i	0.0177846	−	0.0244784i
$817$	271.479	−	835.528i	0.332288	−	1.02268i
$818$	−132.992	−	409.307i	−0.162582	−	0.500376i
$819$	−625.836	+	454.696i	−0.764146	+	0.555185i
$820$	152.795	+	210.305i	0.186336	+	0.256469i
$821$	−981.725	+	318.982i	−1.19577	+	0.388528i	−0.838202	−	0.545360i	$-0.816393\pi$
$821$	−981.725	+	318.982i	−1.19577	+	0.388528i	−0.357565	+	0.933888i	$0.616393\pi$
$822$	−174.810	−	56.7991i	−0.212664	−	0.0690987i
$823$	−650.900	−	472.906i	−0.790886	−	0.574613i	0.117340	−	0.993092i	$-0.462563\pi$
$823$	−650.900	−	472.906i	−0.790886	−	0.574613i	−0.908226	+	0.418479i	$0.862563\pi$
$824$			85.8563i			0.104195i
$825$	91.3822	+	141.327i	0.110766	+	0.171305i
$826$	−520.085			−0.629643
$827$	−37.9422	+	52.2230i	−0.0458793	+	0.0631475i	−0.831340	−	0.555764i	$-0.812426\pi$
$827$	−37.9422	+	52.2230i	−0.0458793	+	0.0631475i	0.785461	+	0.618911i	$0.212426\pi$
$828$	−151.699	+	466.882i	−0.183212	+	0.563867i
$829$	188.558	+	580.323i	0.227453	+	0.700028i	0.998033	+	0.0626852i	$0.0199664\pi$
$829$	188.558	+	580.323i	0.227453	+	0.700028i	−0.770581	+	0.637343i	$0.780034\pi$
$830$	98.1854	−	71.3359i	0.118296	−	0.0859468i
$831$	−26.1844	−	36.0397i	−0.0315095	−	0.0433691i
$832$	186.837	−	60.7071i	0.224564	−	0.0729653i
$833$	−207.812	−	67.5221i	−0.249474	−	0.0810589i
$834$	−110.667	−	80.4042i	−0.132694	−	0.0964079i
$835$			375.006i			0.449109i
$836$	−124.269	+	321.831i	−0.148648	+	0.384965i
$837$	−433.183			−0.517542
$838$	493.874	−	679.759i	0.589348	−	0.811168i
$839$	−195.113	+	600.497i	−0.232554	+	0.715729i	0.764882	+	0.644170i	$0.222797\pi$
$839$	−195.113	+	600.497i	−0.232554	+	0.715729i	−0.997436	+	0.0715585i	$0.977203\pi$
$840$	−9.75337	−	30.0178i	−0.0116112	−	0.0357355i
$841$	−498.603	+	362.256i	−0.592869	+	0.430745i
$842$	212.099	+	291.929i	0.251899	+	0.346709i
$843$	457.704	−	148.717i	0.542946	−	0.176414i
$844$	16.9489	+	5.50704i	0.0200817	+	0.00652493i
$845$	1052.70	+	764.833i	1.24580	+	0.905128i
$846$		−	345.803i		−	0.408750i
$847$	−429.830	−	193.412i	−0.507474	−	0.228349i
$848$	208.252			0.245580
$849$	31.5714	−	43.4543i	0.0371866	−	0.0511829i
$850$	−45.2014	+	139.116i	−0.0531781	+	0.163665i
$851$	39.1669	+	120.543i	0.0460246	+	0.141649i
$852$	145.166	−	105.469i	0.170383	−	0.123790i
$853$	253.913	+	349.481i	0.297671	+	0.409709i	0.931487	−	0.363775i	$-0.118512\pi$
$853$	253.913	+	349.481i	0.297671	+	0.409709i	−0.633816	+	0.773484i	$0.718512\pi$
$854$	488.866	−	158.842i	0.572442	−	0.185998i
$855$	−361.585	−	117.486i	−0.422907	−	0.137411i
$856$	175.226	+	127.309i	0.204703	+	0.148726i
$857$		−	137.536i		−	0.160485i	−0.996775	−	0.0802425i	$-0.974431\pi$
$857$		−	137.536i		−	0.160485i	0.996775	−	0.0802425i	$-0.0255695\pi$
$858$	−340.517	−	131.485i	−0.396873	−	0.153246i
$859$	−64.8174			−0.0754568			−0.0377284	−	0.999288i	$-0.512012\pi$
$859$	−64.8174			−0.0754568			−0.0377284	+	0.999288i	$0.512012\pi$
$860$	197.449	−	271.765i	0.229591	−	0.316006i
$861$	49.8656	−	153.471i	0.0579159	−	0.178247i
$862$	−289.100	−	889.759i	−0.335383	−	1.03220i
$863$	817.704	−	594.097i	0.947513	−	0.688409i	−0.00270429	−	0.999996i	$-0.500861\pi$
$863$	817.704	−	594.097i	0.947513	−	0.688409i	0.950217	+	0.311588i	$0.100861\pi$
$864$	−54.2877	−	74.7206i	−0.0628330	−	0.0864822i
$865$	−361.328	+	117.403i	−0.417720	+	0.135726i
$866$	147.984	+	48.0830i	0.170883	+	0.0555231i
$867$	191.151	+	138.879i	0.220474	+	0.160183i
$868$			206.701i			0.238135i
$869$	714.127	−	461.756i	0.821780	−	0.531365i
$870$	60.7278			0.0698020
$871$	780.547	−	1074.33i	0.896150	−	1.23345i
$872$	10.5860	−	32.5803i	0.0121399	−	0.0373627i
$873$	−89.9940	−	276.973i	−0.103086	−	0.317266i
$874$	−544.555	+	395.642i	−0.623060	+	0.452680i
$875$	281.522	+	387.482i	0.321740	+	0.442837i
$876$	−44.5937	+	14.4894i	−0.0509061	+	0.0165404i
$877$	628.136	+	204.094i	0.716233	+	0.232718i	0.644389	−	0.764698i	$-0.277112\pi$
$877$	628.136	+	204.094i	0.716233	+	0.232718i	0.0718438	+	0.997416i	$0.477112\pi$
$878$	628.393	+	456.554i	0.715710	+	0.519994i
$879$			178.346i			0.202897i
$880$	−83.2179	+	102.351i	−0.0945658	+	0.116308i
$881$	1527.49			1.73382			0.866909	−	0.498466i	$-0.166103\pi$
$881$	1527.49			1.73382			0.866909	+	0.498466i	$0.166103\pi$
$882$	−227.389	+	312.975i	−0.257811	+	0.354847i
$883$	−0.133623	+	0.411250i	−0.000151329	+	0.000465742i	−0.951132	−	0.308784i	$-0.900078\pi$
$883$	−0.133623	+	0.411250i	−0.000151329	+	0.000465742i	0.950981	+	0.309250i	$0.100078\pi$
$884$	−98.0375	−	301.728i	−0.110902	−	0.341322i
$885$	218.799	−	158.966i	0.247230	−	0.179623i
$886$	29.2412	+	40.2471i	0.0330037	+	0.0454256i
$887$	−939.334	+	305.208i	−1.05900	+	0.344090i	−0.786195	−	0.617979i	$-0.787952\pi$
$887$	−939.334	+	305.208i	−1.05900	+	0.344090i	−0.272806	+	0.962069i	$0.587952\pi$
$888$	−10.7336	−	3.48756i	−0.0120874	−	0.00392743i
$889$	−420.466	−	305.486i	−0.472965	−	0.343629i
$890$			289.456i			0.325232i
$891$	34.1603	−	628.072i	0.0383392	−	0.704906i
$892$	414.102			0.464240
$893$	278.695	−	383.591i	0.312089	−	0.429554i
$894$	−21.5778	+	66.4098i	−0.0241363	+	0.0742839i
$895$	183.751	+	565.527i	0.205308	+	0.631874i
$896$	−35.6543	+	25.9044i	−0.0397928	+	0.0289112i
$897$	−418.614	−	576.172i	−0.466682	−	0.642333i
$898$	758.627	−	246.493i	0.844796	−	0.274491i
$899$	−378.238	−	122.897i	−0.420732	−	0.136704i
$900$	209.515	+	152.222i	0.232795	+	0.169135i
$901$		−	336.312i		−	0.373265i
$902$	−651.789	+	173.267i	−0.722604	+	0.192092i
$903$	−208.527			−0.230927
$904$	−157.730	+	217.097i	−0.174481	+	0.240152i
$905$	98.9912	−	304.664i	0.109383	−	0.336645i
$906$	−34.9909	−	107.691i	−0.0386213	−	0.118864i
$907$	−581.102	+	422.195i	−0.640685	+	0.465485i	−0.860086	−	0.510150i	$-0.829590\pi$
$907$	−581.102	+	422.195i	−0.640685	+	0.465485i	0.219400	+	0.975635i	$0.429590\pi$
$908$	−114.124	−	157.078i	−0.125687	−	0.172993i
$909$	19.0632	−	6.19401i	0.0209716	−	0.00681409i
$910$	−385.721	−	125.328i	−0.423869	−	0.137723i
$911$	−275.435	−	200.115i	−0.302343	−	0.219665i	0.426261	−	0.904600i	$-0.359831\pi$
$911$	−275.435	−	200.115i	−0.302343	−	0.219665i	−0.728604	+	0.684935i	$0.759831\pi$
$912$		−	59.9358i		−	0.0657191i
$913$	80.8935	+	304.302i	0.0886018	+	0.333299i
$914$	962.162			1.05269
$915$	−157.114	+	216.249i	−0.171709	+	0.236337i
$916$	−35.7383	+	109.991i	−0.0390156	+	0.120078i
$917$	51.0084	+	156.988i	0.0556253	+	0.171197i
$918$	−120.668	+	87.6706i	−0.131447	+	0.0955017i
$919$	590.474	+	812.718i	0.642518	+	0.884350i	0.998747	−	0.0500487i	$-0.0159377\pi$
$919$	590.474	+	812.718i	0.642518	+	0.884350i	−0.356229	+	0.934399i	$0.615938\pi$
$920$	−244.777	+	79.5330i	−0.266062	+	0.0864489i
$921$	450.614	+	146.413i	0.489266	+	0.158972i
$922$	−232.073	−	168.611i	−0.251706	−	0.182875i
$923$		−	2305.70i		−	2.49804i
$924$	81.7662	+	4.44719i	0.0884915	+	0.00481298i
$925$	66.8642			0.0722856
$926$	−620.340	+	853.825i	−0.669914	+	0.922057i
$927$	75.8569	−	233.464i	0.0818305	−	0.251849i
$928$	−26.2031	−	80.6447i	−0.0282361	−	0.0869017i
$929$	273.837	−	198.954i	0.294765	−	0.214159i	−0.430567	−	0.902559i	$-0.641686\pi$
$929$	273.837	−	198.954i	0.294765	−	0.214159i	0.725332	+	0.688399i	$0.241686\pi$
$930$	−63.1793	−	86.9589i	−0.0679347	−	0.0935042i
$931$	−504.477	+	163.914i	−0.541865	+	0.176063i
$932$	133.601	+	43.4094i	0.143348	+	0.0465767i
$933$	287.662	+	208.999i	0.308319	+	0.224007i
$934$			526.811i			0.564037i
$935$	165.290	+	134.391i	0.176781	+	0.143733i
$936$	−561.692			−0.600098
$937$	16.1676	−	22.2528i	0.0172547	−	0.0237490i	−0.800303	−	0.599596i	$-0.795328\pi$
$937$	16.1676	−	22.2528i	0.0172547	−	0.0237490i	0.817557	+	0.575847i	$0.195328\pi$
$938$	−92.0578	+	283.325i	−0.0981426	+	0.302052i
$939$	72.4348	+	222.931i	0.0771404	+	0.237414i
$940$	146.673	−	106.564i	0.156035	−	0.113366i
$941$	−389.897	−	536.648i	−0.414344	−	0.570295i	0.549927	−	0.835212i	$-0.314655\pi$
$941$	−389.897	−	536.648i	−0.414344	−	0.570295i	−0.964271	+	0.264917i	$0.914655\pi$
$942$	−298.812	+	97.0898i	−0.317210	+	0.103068i
$943$	−1251.46	−	406.625i	−1.32711	−	0.431203i
$944$	−305.511	−	221.967i	−0.323635	−	0.235134i
$945$			190.674i			0.201772i
$946$	473.220	+	731.856i	0.500232	+	0.773632i
$947$	−730.987			−0.771898			−0.385949	−	0.922520i	$-0.626126\pi$
$947$	−730.987			−0.771898			−0.385949	+	0.922520i	$0.626126\pi$
$948$	−86.8413	+	119.527i	−0.0916048	+	0.126083i
$949$	−186.185	+	573.018i	−0.196191	+	0.603813i
$950$	109.729	+	337.712i	0.115505	+	0.355487i
$951$	−46.5013	+	33.7852i	−0.0488973	+	0.0355260i
$952$	41.8337	+	57.5791i	0.0439429	+	0.0604823i
$953$	362.664	−	117.837i	0.380550	−	0.123648i	−0.112494	−	0.993652i	$-0.535884\pi$
$953$	362.664	−	117.837i	0.380550	−	0.123648i	0.493045	+	0.870004i	$0.335884\pi$
$954$	−566.287	−	183.998i	−0.593592	−	0.192870i
$955$	−83.5119	−	60.6750i	−0.0874471	−	0.0635340i
$956$		−	132.048i		−	0.138125i
$957$	−56.7529	+	146.978i	−0.0593029	+	0.153582i
$958$	810.521			0.846055
$959$	311.437	−	428.656i	0.324752	−	0.446982i
$960$	7.08190	−	21.7958i	0.00737698	−	0.0227040i
$961$	−79.4400	−	244.491i	−0.0826639	−	0.254413i
$962$	−117.325	+	85.2418i	−0.121960	+	0.0886090i
$963$	−363.999	−	501.002i	−0.377985	−	0.520252i
$964$	−94.4281	+	30.6815i	−0.0979544	+	0.0318273i
$965$	610.147	+	198.249i	0.632276	+	0.205439i
$966$	129.256	+	93.9098i	0.133805	+	0.0972151i
$967$			1791.77i			1.85292i	0.376396	+	0.926459i	$0.377163\pi$
$967$			1791.77i			1.85292i	−0.376396	+	0.926459i	$0.622837\pi$
$968$	−169.947	−	297.062i	−0.175565	−	0.306882i
$969$	−96.7919			−0.0998884
$970$	89.7458	−	123.524i	0.0925214	−	0.127345i
$971$	−194.009	+	597.098i	−0.199803	+	0.614931i	0.800084	+	0.599888i	$0.204788\pi$
$971$	−194.009	+	597.098i	−0.199803	+	0.614931i	−0.999887	+	0.0150426i	$0.995212\pi$
$972$	124.585	+	383.432i	0.128173	+	0.394477i
$973$	319.014	−	231.777i	0.327867	−	0.238209i
$974$	−35.1789	−	48.4196i	−0.0361179	−	0.0497121i
$975$	−357.321	+	116.100i	−0.366483	+	0.119077i
$976$	354.964	+	115.335i	0.363693	+	0.118171i
$977$	−382.101	−	277.613i	−0.391096	−	0.284148i	0.374808	−	0.927102i	$-0.377709\pi$
$977$	−382.101	−	277.613i	−0.391096	−	0.284148i	−0.765905	+	0.642954i	$0.777709\pi$
$978$			434.628i			0.444404i
$979$	−700.563	−	270.510i	−0.715591	−	0.276313i
$980$	−202.822			−0.206962
$981$	−57.5715	+	79.2404i	−0.0586866	+	0.0807751i
$982$	267.750	−	824.051i	0.272658	−	0.839156i
$983$	145.406	+	447.515i	0.147921	+	0.455254i	0.997375	−	0.0724086i	$-0.0230686\pi$
$983$	145.406	+	447.515i	0.147921	+	0.455254i	−0.849454	+	0.527663i	$0.823069\pi$
$984$	94.7920	−	68.8704i	0.0963333	−	0.0699902i
$985$	−478.230	−	658.228i	−0.485513	−	0.668251i
$986$	−130.235	+	42.3160i	−0.132084	+	0.0429168i
$987$	−107.035	−	34.7778i	−0.108445	−	0.0352359i
$988$	−623.073	−	452.689i	−0.630640	−	0.458187i
$989$			1700.42i			1.71933i
$990$	316.720	−	204.792i	0.319919	−	0.206861i
$991$	1639.02			1.65391			0.826955	−	0.562269i	$-0.190071\pi$
$991$	1639.02			1.65391			0.826955	+	0.562269i	$0.190071\pi$
$992$	−88.2180	+	121.422i	−0.0889295	+	0.122401i
$993$	26.5004	−	81.5600i	0.0266873	−	0.0821349i
$994$	159.839	+	491.933i	0.160804	+	0.494902i
$995$	−606.194	+	440.425i	−0.609240	+	0.442639i
$996$	−32.1537	−	44.2558i	−0.0322828	−	0.0444335i
$997$	123.947	−	40.2729i	0.124320	−	0.0403941i	−0.246196	−	0.969220i	$-0.579181\pi$
$997$	123.947	−	40.2729i	0.124320	−	0.0403941i	0.370516	+	0.928826i	$0.379181\pi$
$998$	−622.958	−	202.411i	−0.624206	−	0.202817i
$999$	55.1591	+	40.0754i	0.0552143	+	0.0401155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.3.d.a.7.2	✓	8
3.2	odd	2		198.3.j.a.73.1		8
4.3	odd	2		176.3.n.b.161.1		8
11.2	odd	10		242.3.d.d.215.2		8
11.3	even	5		242.3.d.c.239.1		8
11.4	even	5		242.3.d.d.233.2		8
11.5	even	5		242.3.b.d.241.7		8
11.6	odd	10		242.3.b.d.241.3		8
11.7	odd	10		242.3.d.e.233.1		8
11.8	odd	10	inner	22.3.d.a.19.2	yes	8
11.9	even	5		242.3.d.e.215.1		8
11.10	odd	2		242.3.d.c.161.1		8
33.5	odd	10		2178.3.d.l.1693.1		8
33.8	even	10		198.3.j.a.19.1		8
33.17	even	10		2178.3.d.l.1693.5		8
44.19	even	10		176.3.n.b.129.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.d.a.7.2	✓	8	1.1	even	1	trivial
22.3.d.a.19.2	yes	8	11.8	odd	10	inner
176.3.n.b.129.1		8	44.19	even	10
176.3.n.b.161.1		8	4.3	odd	2
198.3.j.a.19.1		8	33.8	even	10
198.3.j.a.73.1		8	3.2	odd	2
242.3.b.d.241.3		8	11.6	odd	10
242.3.b.d.241.7		8	11.5	even	5
242.3.d.c.161.1		8	11.10	odd	2
242.3.d.c.239.1		8	11.3	even	5
242.3.d.d.215.2		8	11.2	odd	10
242.3.d.d.233.2		8	11.4	even	5
242.3.d.e.215.1		8	11.9	even	5
242.3.d.e.233.1		8	11.7	odd	10
2178.3.d.l.1693.1		8	33.5	odd	10
2178.3.d.l.1693.5		8	33.17	even	10

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831254 - 1.14412i) q^{2} +(-0.295274 + 0.908759i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42545 + 1.76219i) q^{5} +(0.794285 + 1.09324i) q^{6} +(-3.70473 + 1.20374i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(6.54250 + 4.75340i) q^{9} +O(q^{10})\)	\(q+(0.831254 - 1.14412i) q^{2} +(-0.295274 + 0.908759i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42545 + 1.76219i) q^{5} +(0.794285 + 1.09324i) q^{6} +(-3.70473 + 1.20374i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(6.54250 + 4.75340i) q^{9} +4.23984i q^{10} +(-10.2616 - 3.96233i) q^{11} +1.91105 q^{12} +(14.4340 - 19.8667i) q^{13} +(-1.70234 + 5.23927i) q^{14} +(-0.885238 - 2.72448i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(3.79692 + 5.22601i) q^{17} +(10.8770 - 3.53414i) q^{18} +(14.9139 + 4.84581i) q^{19} +(4.85090 + 3.52439i) q^{20} -3.72214i q^{21} +(-13.0634 + 8.44680i) q^{22} -30.3518 q^{23} +(1.58857 - 2.18648i) q^{24} +(-4.94794 + 15.2282i) q^{25} +(-10.7316 - 33.0285i) q^{26} +(-13.2089 + 9.59680i) q^{27} +(4.57929 + 6.30286i) q^{28} +(-14.2561 + 4.63209i) q^{29} +(-3.85300 - 1.25191i) q^{30} +(21.4645 + 15.5949i) q^{31} +5.65685i q^{32} +(6.63078 - 8.15533i) q^{33} +9.13540 q^{34} +(6.86441 - 9.44805i) q^{35} +(4.99802 - 15.3823i) q^{36} +(-1.29043 - 3.97153i) q^{37} +(17.9414 - 13.0352i) q^{38} +(13.7920 + 18.9831i) q^{39} +(8.06466 - 2.62037i) q^{40} +(41.2318 + 13.3970i) q^{41} +(-4.25858 - 3.09404i) q^{42} -56.0236i q^{43} +(-1.19479 + 21.9675i) q^{44} -24.2449 q^{45} +(-25.2301 + 34.7262i) q^{46} +(9.34350 - 28.7563i) q^{47} +(-1.18110 - 3.63504i) q^{48} +(-27.3658 + 19.8824i) q^{49} +(13.3099 + 18.3195i) q^{50} +(-5.87032 + 1.90738i) q^{51} +(-46.7093 - 15.1768i) q^{52} +(-42.1199 - 30.6019i) q^{53} +23.0899i q^{54} +(31.8713 - 8.47245i) q^{55} +11.0178 q^{56} +(-8.80735 + 12.1223i) q^{57} +(-6.55077 + 20.1612i) q^{58} +(29.1737 + 89.7875i) q^{59} +(-4.63516 + 3.36764i) q^{60} +(-54.8450 - 75.4877i) q^{61} +(35.6849 - 11.5947i) q^{62} +(-29.9600 - 9.73460i) q^{63} +(6.47214 + 4.70228i) q^{64} +73.6210i q^{65} +(-3.81884 - 14.3656i) q^{66} +54.0771 q^{67} +(7.59384 - 10.4520i) q^{68} +(8.96210 - 27.5825i) q^{69} +(-5.10366 - 15.7075i) q^{70} +(75.9613 - 55.1891i) q^{71} +(-13.4446 - 18.5050i) q^{72} +(-23.3346 + 7.58189i) q^{73} +(-5.61660 - 1.82494i) q^{74} +(-12.3778 - 8.99297i) q^{75} -31.3627i q^{76} +(42.7859 + 2.32709i) q^{77} +33.1837 q^{78} +(-45.4416 + 62.5450i) q^{79} +(3.70576 - 11.4052i) q^{80} +(17.6701 + 54.3831i) q^{81} +(49.6020 - 36.0379i) q^{82} +(-16.8251 - 23.1578i) q^{83} +(-7.07993 + 2.30041i) q^{84} +(-18.4185 - 5.98453i) q^{85} +(-64.0978 - 46.5698i) q^{86} -14.3231i q^{87} +(24.1404 + 19.6276i) q^{88} +68.2705 q^{89} +(-20.1537 + 27.7392i) q^{90} +(-29.5597 + 90.9753i) q^{91} +(18.7585 + 57.7326i) q^{92} +(-20.5099 + 14.9013i) q^{93} +(-25.1340 - 34.5939i) q^{94} +(-44.7121 + 14.5278i) q^{95} +(-5.14072 - 1.67032i) q^{96} +(-29.1342 - 21.1672i) q^{97} +47.8372i q^{98} +(-48.3018 - 74.7009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9} - 4 q^{11} + 24 q^{12} + 30 q^{13} + 16 q^{14} + 42 q^{15} - 8 q^{16} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 4 q^{20} + 24 q^{22} - 104 q^{23} - 40 q^{24} - 12 q^{25} - 96 q^{26} - 26 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 46 q^{31} - 14 q^{33} + 112 q^{34} + 70 q^{35} - 12 q^{36} + 6 q^{37} + 108 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 56 q^{42} - 12 q^{44} - 136 q^{45} - 160 q^{46} - 54 q^{47} - 8 q^{48} - 144 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 274 q^{53} - 26 q^{55} + 48 q^{56} - 130 q^{57} + 64 q^{58} + 50 q^{59} + 116 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} + 16 q^{64} - 136 q^{66} + 112 q^{67} + 60 q^{68} + 76 q^{69} + 4 q^{70} + 54 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 318 q^{75} + 266 q^{77} + 104 q^{78} + 370 q^{79} + 48 q^{80} + 180 q^{81} - 96 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 72 q^{86} + 72 q^{88} + 24 q^{89} + 160 q^{90} - 294 q^{91} - 112 q^{92} - 134 q^{93} - 20 q^{94} - 330 q^{95} - 18 q^{97} - 308 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9 - 4 * q^11 + 24 * q^12 + 30 * q^13 + 16 * q^14 + 42 * q^15 - 8 * q^16 + 30 * q^17 + 40 * q^18 - 30 * q^19 - 4 * q^20 + 24 * q^22 - 104 * q^23 - 40 * q^24 - 12 * q^25 - 96 * q^26 - 26 * q^27 - 40 * q^28 - 10 * q^29 - 60 * q^30 + 46 * q^31 - 14 * q^33 + 112 * q^34 + 70 * q^35 - 12 * q^36 + 6 * q^37 + 108 * q^38 + 130 * q^39 + 80 * q^40 + 250 * q^41 + 56 * q^42 - 12 * q^44 - 136 * q^45 - 160 * q^46 - 54 * q^47 - 8 * q^48 - 144 * q^49 - 80 * q^50 - 30 * q^51 - 40 * q^52 - 274 * q^53 - 26 * q^55 + 48 * q^56 - 130 * q^57 + 64 * q^58 + 50 * q^59 + 116 * q^60 + 50 * q^61 + 20 * q^62 - 20 * q^63 + 16 * q^64 - 136 * q^66 + 112 * q^67 + 60 * q^68 + 76 * q^69 + 4 * q^70 + 54 * q^71 - 80 * q^72 - 70 * q^73 - 40 * q^74 + 318 * q^75 + 266 * q^77 + 104 * q^78 + 370 * q^79 + 48 * q^80 + 180 * q^81 - 96 * q^82 - 150 * q^83 - 120 * q^84 - 330 * q^85 - 72 * q^86 + 72 * q^88 + 24 * q^89 + 160 * q^90 - 294 * q^91 - 112 * q^92 - 134 * q^93 - 20 * q^94 - 330 * q^95 - 18 * q^97 - 308 * q^99

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