LMFDB - Embedded newform 105.3.h.a.76.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(76,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.11
Root			$1.31896 - 2.28450i$ of defining polynomial
Character	$\chi$	$=$	105.76
Dual form			105.3.h.a.76.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +2.23607i q^{5} -6.06857i q^{6} +(-6.69736 - 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +2.23607i q^{5} -6.06857i q^{6} +(-6.69736 - 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} +7.83449i q^{10} -2.03112 q^{11} -14.3342i q^{12} +18.0174i q^{13} +(-23.4655 - 7.13352i) q^{14} +3.87298 q^{15} +19.3861 q^{16} -1.07289i q^{17} -10.5111 q^{18} -28.7852i q^{19} +18.5053i q^{20} +(-3.52646 + 11.6002i) q^{21} -7.11640 q^{22} +24.8710 q^{23} -25.9482i q^{24} -5.00000 q^{25} +63.1275i q^{26} +5.19615i q^{27} +(-55.4263 - 16.8496i) q^{28} -38.4300 q^{29} +13.5697 q^{30} +44.0899i q^{31} +7.99812 q^{32} +3.51800i q^{33} -3.75906i q^{34} +(4.55264 - 14.9758i) q^{35} -24.8275 q^{36} +37.2832 q^{37} -100.855i q^{38} +31.2071 q^{39} +33.4990i q^{40} -49.9206i q^{41} +(-12.3556 + 40.6434i) q^{42} -9.58871 q^{43} -16.8092 q^{44} -6.70820i q^{45} +87.1402 q^{46} -55.6978i q^{47} -33.5777i q^{48} +(40.7094 + 27.2717i) q^{49} -17.5184 q^{50} -1.85829 q^{51} +149.109i q^{52} +57.4656 q^{53} +18.2057i q^{54} -4.54171i q^{55} +(-100.335 - 30.5018i) q^{56} -49.8575 q^{57} -134.647 q^{58} -101.697i q^{59} +32.0522 q^{60} +31.9530i q^{61} +154.477i q^{62} +(20.0921 + 6.10801i) q^{63} -49.5215 q^{64} -40.2882 q^{65} +12.3260i q^{66} +95.7318 q^{67} -8.87902i q^{68} -43.0778i q^{69} +(15.9510 - 52.4704i) q^{70} -25.8039 q^{71} -44.9436 q^{72} +95.6803i q^{73} +130.629 q^{74} +8.66025i q^{75} -238.222i q^{76} +(13.6031 + 4.13536i) q^{77} +109.340 q^{78} +28.1212 q^{79} +43.3487i q^{80} +9.00000 q^{81} -174.906i q^{82} +103.374i q^{83} +(-29.1844 + 96.0012i) q^{84} +2.39905 q^{85} -33.5959 q^{86} +66.5628i q^{87} -30.4286 q^{88} -29.3629i q^{89} -23.5035i q^{90} +(36.6835 - 120.669i) q^{91} +205.828 q^{92} +76.3659 q^{93} -195.148i q^{94} +64.3658 q^{95} -13.8531i q^{96} +67.6473i q^{97} +(142.633 + 95.5515i) q^{98} +6.09335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	3.50369			1.75184			0.875922	−	0.482452i	$-0.160254\pi$
$2$	3.50369			1.75184			0.875922	+	0.482452i	$0.160254\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	8.27584			2.06896
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		−	6.06857i		−	1.01143i
$7$	−6.69736	−	2.03600i	−0.956766	−	0.290857i
$7$	−6.69736	−	2.03600i	−0.956766	−	0.290857i
$8$	14.9812			1.87265
$9$	−3.00000			−0.333333
$10$			7.83449i			0.783449i
$11$	−2.03112			−0.184647			−0.0923235	−	0.995729i	$-0.529429\pi$
$11$	−2.03112			−0.184647			−0.0923235	+	0.995729i	$0.529429\pi$
$12$		−	14.3342i		−	1.19451i
$13$			18.0174i			1.38596i	0.720958	+	0.692978i	$0.243702\pi$
$13$			18.0174i			1.38596i	−0.720958	+	0.692978i	$0.756298\pi$
$14$	−23.4655	−	7.13352i	−1.67611	−	0.509537i
$15$	3.87298			0.258199
$16$	19.3861			1.21163
$17$		−	1.07289i		−	0.0631109i	−0.999502	−	0.0315555i	$-0.989954\pi$
$17$		−	1.07289i		−	0.0631109i	0.999502	−	0.0315555i	$-0.0100461\pi$
$18$	−10.5111			−0.583948
$19$		−	28.7852i		−	1.51501i	−0.652828	−	0.757506i	$-0.726417\pi$
$19$		−	28.7852i		−	1.51501i	0.652828	−	0.757506i	$-0.273583\pi$
$20$			18.5053i			0.925267i
$21$	−3.52646	+	11.6002i	−0.167927	+	0.552389i
$22$	−7.11640			−0.323473
$23$	24.8710			1.08135			0.540674	−	0.841232i	$-0.318169\pi$
$23$	24.8710			1.08135			0.540674	+	0.841232i	$0.318169\pi$
$24$		−	25.9482i		−	1.08117i
$25$	−5.00000			−0.200000
$26$			63.1275i			2.42798i
$27$			5.19615i			0.192450i
$28$	−55.4263	−	16.8496i	−1.97951	−	0.601772i
$29$	−38.4300			−1.32517			−0.662587	−	0.748985i	$-0.730542\pi$
$29$	−38.4300			−1.32517			−0.662587	+	0.748985i	$0.730542\pi$
$30$	13.5697			0.452324
$31$			44.0899i			1.42225i	0.703064	+	0.711127i	$0.251815\pi$
$31$			44.0899i			1.42225i	−0.703064	+	0.711127i	$0.748185\pi$
$32$	7.99812			0.249941
$33$			3.51800i			0.106606i
$34$		−	3.75906i		−	0.110561i
$35$	4.55264	−	14.9758i	0.130075	−	0.427879i
$36$	−24.8275			−0.689653
$37$	37.2832			1.00765			0.503827	−	0.863804i	$-0.331925\pi$
$37$	37.2832			1.00765			0.503827	+	0.863804i	$0.331925\pi$
$38$		−	100.855i		−	2.65407i
$39$	31.2071			0.800182
$40$			33.4990i			0.837474i
$41$		−	49.9206i		−	1.21758i	−0.793333	−	0.608788i	$-0.791656\pi$
$41$		−	49.9206i		−	1.21758i	0.793333	−	0.608788i	$-0.208344\pi$
$42$	−12.3556	+	40.6434i	−0.294181	+	0.967700i
$43$	−9.58871			−0.222993			−0.111497	−	0.993765i	$-0.535564\pi$
$43$	−9.58871			−0.222993			−0.111497	+	0.993765i	$0.535564\pi$
$44$	−16.8092			−0.382027
$45$		−	6.70820i		−	0.149071i
$46$	87.1402			1.89435
$47$		−	55.6978i		−	1.18506i	−0.805549	−	0.592529i	$-0.798129\pi$
$47$		−	55.6978i		−	1.18506i	0.805549	−	0.592529i	$-0.201871\pi$
$48$		−	33.5777i		−	0.699536i
$49$	40.7094	+	27.2717i	0.830804	+	0.556565i
$50$	−17.5184			−0.350369
$51$	−1.85829			−0.0364371
$52$			149.109i			2.86749i
$53$	57.4656			1.08426			0.542128	−	0.840296i	$-0.317619\pi$
$53$	57.4656			1.08426			0.542128	+	0.840296i	$0.317619\pi$
$54$			18.2057i			0.337143i
$55$		−	4.54171i		−	0.0825766i
$56$	−100.335	−	30.5018i	−1.79169	−	0.544674i
$57$	−49.8575			−0.874693
$58$	−134.647			−2.32150
$59$		−	101.697i		−	1.72368i	−0.507178	−	0.861841i	$-0.669311\pi$
$59$		−	101.697i		−	1.72368i	0.507178	−	0.861841i	$-0.330689\pi$
$60$	32.0522			0.534203
$61$			31.9530i			0.523819i	0.965092	+	0.261910i	$0.0843523\pi$
$61$			31.9530i			0.523819i	−0.965092	+	0.261910i	$0.915648\pi$
$62$			154.477i			2.49157i
$63$	20.0921	+	6.10801i	0.318922	+	0.0969525i
$64$	−49.5215			−0.773774
$65$	−40.2882			−0.619819
$66$			12.3260i			0.186757i
$67$	95.7318			1.42883			0.714416	−	0.699721i	$-0.246692\pi$
$67$	95.7318			1.42883			0.714416	+	0.699721i	$0.246692\pi$
$68$		−	8.87902i		−	0.130574i
$69$		−	43.0778i		−	0.624316i
$70$	15.9510	−	52.4704i	0.227872	−	0.749577i
$71$	−25.8039			−0.363435			−0.181718	−	0.983351i	$-0.558166\pi$
$71$	−25.8039			−0.363435			−0.181718	+	0.983351i	$0.558166\pi$
$72$	−44.9436			−0.624217
$73$			95.6803i			1.31069i	0.755330	+	0.655345i	$0.227477\pi$
$73$			95.6803i			1.31069i	−0.755330	+	0.655345i	$0.772523\pi$
$74$	130.629			1.76525
$75$			8.66025i			0.115470i
$76$		−	238.222i		−	3.13450i
$77$	13.6031	+	4.13536i	0.176664	+	0.0537059i
$78$	109.340			1.40180
$79$	28.1212			0.355965			0.177982	−	0.984034i	$-0.443043\pi$
$79$	28.1212			0.355965			0.177982	+	0.984034i	$0.443043\pi$
$80$			43.3487i			0.541858i
$81$	9.00000			0.111111
$82$		−	174.906i		−	2.13301i
$83$			103.374i			1.24547i	0.782435	+	0.622733i	$0.213978\pi$
$83$			103.374i			1.24547i	−0.782435	+	0.622733i	$0.786022\pi$
$84$	−29.1844	+	96.0012i	−0.347433	+	1.14287i
$85$	2.39905			0.0282241
$86$	−33.5959			−0.390650
$87$			66.5628i			0.765090i
$88$	−30.4286			−0.345779
$89$		−	29.3629i		−	0.329920i	−0.986300	−	0.164960i	$-0.947250\pi$
$89$		−	29.3629i		−	0.329920i	0.986300	−	0.164960i	$-0.0527496\pi$
$90$		−	23.5035i		−	0.261150i
$91$	36.6835	−	120.669i	0.403116	−	1.32604i
$92$	205.828			2.23726
$93$	76.3659			0.821138
$94$		−	195.148i		−	2.07604i
$95$	64.3658			0.677534
$96$		−	13.8531i		−	0.144304i
$97$			67.6473i			0.697395i	0.937235	+	0.348697i	$0.113376\pi$
$97$			67.6473i			0.697395i	−0.937235	+	0.348697i	$0.886624\pi$
$98$	142.633	+	95.5515i	1.45544	+	0.975016i
$99$	6.09335			0.0615490
$100$	−41.3792			−0.413792
$101$		−	73.3301i		−	0.726040i	−0.931781	−	0.363020i	$-0.881746\pi$
$101$		−	73.3301i		−	0.726040i	0.931781	−	0.363020i	$-0.118254\pi$
$102$	−6.51088			−0.0638321
$103$			57.3431i			0.556729i	0.960476	+	0.278365i	$0.0897923\pi$
$103$			57.3431i			0.556729i	−0.960476	+	0.278365i	$0.910208\pi$
$104$			269.923i			2.59541i
$105$	−25.9388	−	7.88540i	−0.247036	−	0.0750991i
$106$	201.342			1.89945
$107$	−39.8399			−0.372336			−0.186168	−	0.982518i	$-0.559607\pi$
$107$	−39.8399			−0.372336			−0.186168	+	0.982518i	$0.559607\pi$
$108$			43.0025i			0.398171i
$109$	−185.052			−1.69773			−0.848863	−	0.528613i	$-0.822712\pi$
$109$	−185.052			−1.69773			−0.848863	+	0.528613i	$0.822712\pi$
$110$		−	15.9128i		−	0.144661i
$111$		−	64.5764i		−	0.581770i
$112$	−129.836	−	39.4702i	−1.15925	−	0.352412i
$113$	−120.716			−1.06829			−0.534143	−	0.845394i	$-0.679366\pi$
$113$	−120.716			−1.06829			−0.534143	+	0.845394i	$0.679366\pi$
$114$	−174.685			−1.53233
$115$			55.6132i			0.483593i
$116$	−318.041			−2.74173
$117$		−	54.0523i		−	0.461986i
$118$		−	356.316i		−	3.01962i
$119$	−2.18440	+	7.18551i	−0.0183563	+	0.0603824i
$120$	58.0219			0.483516
$121$	−116.875			−0.965906
$122$			111.953i			0.917650i
$123$	−86.4651			−0.702968
$124$			364.880i			2.94258i
$125$		−	11.1803i		−	0.0894427i
$126$	70.3964	+	21.4006i	0.558702	+	0.169846i
$127$	−83.5096			−0.657556			−0.328778	−	0.944407i	$-0.606637\pi$
$127$	−83.5096			−0.657556			−0.328778	+	0.944407i	$0.606637\pi$
$128$	−205.501			−1.60547
$129$			16.6081i			0.128745i
$130$	−141.157			−1.08583
$131$			198.248i			1.51334i	0.653796	+	0.756671i	$0.273175\pi$
$131$			198.248i			1.51334i	−0.653796	+	0.756671i	$0.726825\pi$
$132$			29.1144i			0.220563i
$133$	−58.6068	+	192.785i	−0.440653	+	1.44951i
$134$	335.414			2.50309
$135$	−11.6190			−0.0860663
$136$		−	16.0731i		−	0.118185i
$137$	−24.1635			−0.176376			−0.0881880	−	0.996104i	$-0.528108\pi$
$137$	−24.1635			−0.176376			−0.0881880	+	0.996104i	$0.528108\pi$
$138$		−	150.931i		−	1.09371i
$139$		−	61.6370i		−	0.443432i	−0.975111	−	0.221716i	$-0.928834\pi$
$139$		−	61.6370i		−	0.443432i	0.975111	−	0.221716i	$-0.0711658\pi$
$140$	37.6769	−	123.937i	0.269121	−	0.885264i
$141$	−96.4714			−0.684194
$142$	−90.4088			−0.636682
$143$		−	36.5955i		−	0.255913i
$144$	−58.1583			−0.403877
$145$		−	85.9322i		−	0.592636i
$146$			335.234i			2.29612i
$147$	47.2360	−	70.5107i	0.321333	−	0.479665i
$148$	308.550			2.08480
$149$	−28.8271			−0.193470			−0.0967351	−	0.995310i	$-0.530840\pi$
$149$	−28.8271			−0.193470			−0.0967351	+	0.995310i	$0.530840\pi$
$150$			30.3428i			0.202286i
$151$	248.311			1.64445			0.822223	−	0.569166i	$-0.192734\pi$
$151$	248.311			1.64445			0.822223	+	0.569166i	$0.192734\pi$
$152$		−	431.237i		−	2.83709i
$153$			3.21866i			0.0210370i
$154$	47.6611	+	14.4890i	0.309488	+	0.0940844i
$155$	−98.5879			−0.636051
$156$	258.265			1.65554
$157$		−	41.3848i		−	0.263597i	−0.991277	−	0.131799i	$-0.957925\pi$
$157$		−	41.3848i		−	0.263597i	0.991277	−	0.131799i	$-0.0420752\pi$
$158$	98.5280			0.623595
$159$		−	99.5334i		−	0.625996i
$160$			17.8843i			0.111777i
$161$	−166.570	−	50.6374i	−1.03460	−	0.314518i
$162$	31.5332			0.194649
$163$	−51.8103			−0.317855			−0.158927	−	0.987290i	$-0.550804\pi$
$163$	−51.8103			−0.317855			−0.158927	+	0.987290i	$0.550804\pi$
$164$		−	413.135i		−	2.51912i
$165$	−7.86648			−0.0476756
$166$			362.189i			2.18186i
$167$		−	41.9711i		−	0.251324i	−0.992073	−	0.125662i	$-0.959895\pi$
$167$		−	41.9711i		−	0.251324i	0.992073	−	0.125662i	$-0.0401055\pi$
$168$	−52.8306	+	173.785i	−0.314468	+	1.03443i
$169$	−155.628			−0.920876
$170$	8.40551			0.0494442
$171$			86.3557i			0.505004i
$172$	−79.3546			−0.461364
$173$			98.0199i			0.566589i	0.959033	+	0.283295i	$0.0914274\pi$
$173$			98.0199i			0.566589i	−0.959033	+	0.283295i	$0.908573\pi$
$174$			233.215i			1.34032i
$175$	33.4868	+	10.1800i	0.191353	+	0.0581715i
$176$	−39.3754			−0.223724
$177$	−176.145			−0.995168
$178$		−	102.879i		−	0.577969i
$179$	68.5830			0.383145			0.191573	−	0.981478i	$-0.438641\pi$
$179$	68.5830			0.383145			0.191573	+	0.981478i	$0.438641\pi$
$180$		−	55.5160i		−	0.308422i
$181$			105.124i			0.580798i	0.956906	+	0.290399i	$0.0937880\pi$
$181$			105.124i			0.580798i	−0.956906	+	0.290399i	$0.906212\pi$
$182$	128.528	−	422.788i	0.706196	−	2.32301i
$183$	55.3442			0.302427
$184$	372.597			2.02499
$185$			83.3678i			0.450637i
$186$	267.562			1.43851
$187$			2.17916i			0.0116532i
$188$		−	460.946i		−	2.45184i
$189$	10.5794	−	34.8005i	0.0559755	−	0.184130i
$190$	225.518			1.18693
$191$	229.803			1.20316			0.601579	−	0.798813i	$-0.294539\pi$
$191$	229.803			1.20316			0.601579	+	0.798813i	$0.294539\pi$
$192$			85.7738i			0.446739i
$193$	111.530			0.577877			0.288939	−	0.957348i	$-0.406698\pi$
$193$	111.530			0.577877			0.288939	+	0.957348i	$0.406698\pi$
$194$			237.015i			1.22173i
$195$			69.7812i			0.357852i
$196$	336.904	+	225.696i	1.71890	+	1.15151i
$197$	−172.865			−0.877486			−0.438743	−	0.898613i	$-0.644576\pi$
$197$	−172.865			−0.877486			−0.438743	+	0.898613i	$0.644576\pi$
$198$	21.3492			0.107824
$199$		−	117.944i		−	0.592685i	−0.955082	−	0.296343i	$-0.904233\pi$
$199$		−	117.944i		−	0.592685i	0.955082	−	0.296343i	$-0.0957670\pi$
$200$	−74.9060			−0.374530
$201$		−	165.812i		−	0.824937i
$202$		−	256.926i		−	1.27191i
$203$	257.380	+	78.2437i	1.26788	+	0.385437i
$204$	−15.3789			−0.0753869
$205$	111.626			0.544517
$206$			200.912i			0.975303i
$207$	−74.6130			−0.360449
$208$			349.288i			1.67927i
$209$			58.4662i			0.279742i
$210$	−90.8814	−	27.6280i	−0.432769	−	0.131562i
$211$	−391.940			−1.85754			−0.928769	−	0.370660i	$-0.879131\pi$
$211$	−391.940			−1.85754			−0.928769	+	0.370660i	$0.879131\pi$
$212$	475.576			2.24328
$213$			44.6936i			0.209829i
$214$	−139.587			−0.652274
$215$		−	21.4410i		−	0.0997256i
$216$			77.8446i			0.360392i
$217$	89.7670	−	295.286i	0.413673	−	1.36076i
$218$	−648.365			−2.97415
$219$	165.723			0.756727
$220$		−	37.5865i		−	0.170848i
$221$	19.3306			0.0874690
$222$		−	226.256i		−	1.01917i
$223$			96.2512i			0.431620i	0.976435	+	0.215810i	$0.0692391\pi$
$223$			96.2512i			0.431620i	−0.976435	+	0.215810i	$0.930761\pi$
$224$	−53.5663	−	16.2842i	−0.239135	−	0.0726972i
$225$	15.0000			0.0666667
$226$	−422.952			−1.87147
$227$			91.6962i			0.403948i	0.979391	+	0.201974i	$0.0647357\pi$
$227$			91.6962i			0.403948i	−0.979391	+	0.201974i	$0.935264\pi$
$228$	−412.612			−1.80970
$229$			323.972i			1.41472i	0.706852	+	0.707361i	$0.250115\pi$
$229$			323.972i			1.41472i	−0.706852	+	0.707361i	$0.749885\pi$
$230$			194.852i			0.847180i
$231$	7.16265	−	23.5613i	0.0310071	−	0.101997i
$232$	−575.728			−2.48159
$233$	182.918			0.785055			0.392528	−	0.919740i	$-0.371601\pi$
$233$	182.918			0.785055			0.392528	+	0.919740i	$0.371601\pi$
$234$		−	189.382i		−	0.809327i
$235$	124.544			0.529974
$236$		−	841.630i		−	3.56623i
$237$		−	48.7074i		−	0.205516i
$238$	−7.65345	+	25.1758i	−0.0321573	+	0.105781i
$239$	−42.9240			−0.179598			−0.0897992	−	0.995960i	$-0.528623\pi$
$239$	−42.9240			−0.179598			−0.0897992	+	0.995960i	$0.528623\pi$
$240$	75.0821			0.312842
$241$		−	99.8942i		−	0.414499i	−0.978288	−	0.207249i	$-0.933549\pi$
$241$		−	99.8942i		−	0.414499i	0.978288	−	0.207249i	$-0.0664511\pi$
$242$	−409.492			−1.69212
$243$		−	15.5885i		−	0.0641500i
$244$			264.438i			1.08376i
$245$	−60.9814	+	91.0290i	−0.248904	+	0.371547i
$246$	−302.947			−1.23149
$247$	518.636			2.09974
$248$			660.519i			2.66338i
$249$	179.048			0.719070
$250$		−	39.1724i		−	0.156690i
$251$		−	404.945i		−	1.61333i	−0.591011	−	0.806663i	$-0.701271\pi$
$251$		−	404.945i		−	1.61333i	0.591011	−	0.806663i	$-0.298729\pi$
$252$	166.279	+	50.5489i	0.659837	+	0.200591i
$253$	−50.5159			−0.199668
$254$	−292.592			−1.15194
$255$		−	4.15527i		−	0.0162952i
$256$	−521.924			−2.03876
$257$			102.697i			0.399600i	0.979837	+	0.199800i	$0.0640292\pi$
$257$			102.697i			0.399600i	−0.979837	+	0.199800i	$0.935971\pi$
$258$			58.1897i			0.225542i
$259$	−249.699	−	75.9087i	−0.964090	−	0.293084i
$260$	−333.419			−1.28238
$261$	115.290			0.441725
$262$			694.598i			2.65114i
$263$	281.479			1.07026			0.535132	−	0.844769i	$-0.320262\pi$
$263$	281.479			1.07026			0.535132	+	0.844769i	$0.320262\pi$
$264$			52.7038i			0.199636i
$265$			128.497i			0.484894i
$266$	−205.340	+	675.460i	−0.771955	+	2.53932i
$267$	−50.8581			−0.190480
$268$	792.260			2.95620
$269$		−	176.412i		−	0.655808i	−0.944711	−	0.327904i	$-0.893658\pi$
$269$		−	176.412i		−	0.655808i	0.944711	−	0.327904i	$-0.106342\pi$
$270$	−40.7092			−0.150775
$271$		−	306.041i		−	1.12930i	−0.825330	−	0.564651i	$-0.809011\pi$
$271$		−	306.041i		−	1.12930i	0.825330	−	0.564651i	$-0.190989\pi$
$272$		−	20.7991i		−	0.0764672i
$273$	−209.005	−	63.5378i	−0.765588	−	0.232739i
$274$	−84.6614			−0.308983
$275$	10.1556			0.0369294
$276$		−	356.505i		−	1.29169i
$277$	43.7993			0.158120			0.0790601	−	0.996870i	$-0.474808\pi$
$277$	43.7993			0.158120			0.0790601	+	0.996870i	$0.474808\pi$
$278$		−	215.957i		−	0.776824i
$279$		−	132.270i		−	0.474084i
$280$	68.2040	−	224.355i	0.243586	−	0.801267i
$281$	499.502			1.77759			0.888794	−	0.458307i	$-0.151544\pi$
$281$	499.502			1.77759			0.888794	+	0.458307i	$0.151544\pi$
$282$	−338.006			−1.19860
$283$		−	122.672i		−	0.433470i	−0.976231	−	0.216735i	$-0.930459\pi$
$283$		−	122.672i		−	0.433470i	0.976231	−	0.216735i	$-0.0695407\pi$
$284$	−213.549			−0.751932
$285$		−	111.485i		−	0.391175i
$286$		−	128.219i		−	0.448319i
$287$	−101.639	+	334.337i	−0.354141	+	1.16494i
$288$	−23.9944			−0.0833137
$289$	287.849			0.996017
$290$		−	301.080i		−	1.03821i
$291$	117.169			0.402641
$292$			791.835i			2.71176i
$293$			123.871i			0.422769i	0.977403	+	0.211385i	$0.0677972\pi$
$293$			123.871i			0.422769i	−0.977403	+	0.211385i	$0.932203\pi$
$294$	165.500	−	247.048i	0.562926	−	0.840298i
$295$	227.402			0.770854
$296$	558.547			1.88698
$297$		−	10.5540i		−	0.0355353i
$298$	−101.001			−0.338930
$299$			448.112i			1.49870i
$300$			71.6708i			0.238903i
$301$	64.2191	+	19.5226i	0.213352	+	0.0648593i
$302$	870.006			2.88081
$303$	−127.011			−0.419180
$304$		−	558.034i		−	1.83564i
$305$	−71.4490			−0.234259
$306$			11.2772i			0.0368535i
$307$		−	225.577i		−	0.734778i	−0.930067	−	0.367389i	$-0.880252\pi$
$307$		−	225.577i		−	0.734778i	0.930067	−	0.367389i	$-0.119748\pi$
$308$	112.577	+	34.2235i	0.365511	+	0.111115i
$309$	99.3211			0.321428
$310$	−345.421			−1.11426
$311$		−	52.9648i		−	0.170305i	−0.996368	−	0.0851525i	$-0.972862\pi$
$311$		−	52.9648i		−	0.170305i	0.996368	−	0.0851525i	$-0.0271377\pi$
$312$	467.520			1.49846
$313$		−	374.563i		−	1.19669i	−0.801240	−	0.598343i	$-0.795826\pi$
$313$		−	374.563i		−	1.19669i	0.801240	−	0.598343i	$-0.204174\pi$
$314$		−	144.999i		−	0.461782i
$315$	−13.6579	+	44.9273i	−0.0433585	+	0.142626i
$316$	232.727			0.736477
$317$	12.0550			0.0380283			0.0190142	−	0.999819i	$-0.493947\pi$
$317$	12.0550			0.0380283			0.0190142	+	0.999819i	$0.493947\pi$
$318$		−	348.734i		−	1.09665i
$319$	78.0559			0.244689
$320$		−	110.734i		−	0.346042i
$321$			69.0048i			0.214968i
$322$	−583.610	−	177.418i	−1.81245	−	0.550987i
$323$	−30.8833			−0.0956138
$324$	74.4825			0.229884
$325$		−	90.0872i		−	0.277191i
$326$	−181.527			−0.556832
$327$			320.520i			0.980183i
$328$		−	747.871i		−	2.28009i
$329$	−113.401	+	373.028i	−0.344683	+	1.13382i
$330$	−27.5617			−0.0835203
$331$	−376.184			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$331$	−376.184			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$332$			855.503i			2.57682i
$333$	−111.850			−0.335885
$334$		−	147.054i		−	0.440281i
$335$			214.063i			0.638993i
$336$	−68.3643	+	224.882i	−0.203465	+	0.669293i
$337$	−108.973			−0.323363			−0.161682	−	0.986843i	$-0.551692\pi$
$337$	−108.973			−0.323363			−0.161682	+	0.986843i	$0.551692\pi$
$338$	−545.272			−1.61323
$339$			209.087i			0.616775i
$340$	19.8541			0.0583944
$341$		−	89.5516i		−	0.262615i
$342$			302.564i			0.884689i
$343$	−217.120	−	265.533i	−0.633004	−	0.774148i
$344$	−143.650			−0.417588
$345$	96.3250			0.279203
$346$			343.431i			0.992576i
$347$	−206.351			−0.594671			−0.297335	−	0.954773i	$-0.596098\pi$
$347$	−206.351			−0.594671			−0.297335	+	0.954773i	$0.596098\pi$
$348$			550.863i			1.58294i
$349$			373.475i			1.07013i	0.844811	+	0.535064i	$0.179713\pi$
$349$			373.475i			1.07013i	−0.844811	+	0.535064i	$0.820287\pi$
$350$	117.327	+	35.6676i	0.335221	+	0.101907i
$351$	−93.6213			−0.266727
$352$	−16.2451			−0.0461509
$353$		−	646.142i		−	1.83043i	−0.402964	−	0.915216i	$-0.632020\pi$
$353$		−	646.142i		−	1.83043i	0.402964	−	0.915216i	$-0.367980\pi$
$354$	−617.157			−1.74338
$355$		−	57.6992i		−	0.162533i
$356$		−	243.003i		−	0.682592i
$357$	12.4457	+	3.78349i	0.0348618	+	0.0105980i
$358$	240.294			0.671211
$359$	175.261			0.488192			0.244096	−	0.969751i	$-0.421509\pi$
$359$	175.261			0.488192			0.244096	+	0.969751i	$0.421509\pi$
$360$		−	100.497i		−	0.279158i
$361$	−467.590			−1.29526
$362$			368.323i			1.01747i
$363$			202.433i			0.557666i
$364$	303.587	−	998.640i	0.834030	−	2.74352i
$365$	−213.948			−0.586158
$366$	193.909			0.529805
$367$			106.477i			0.290127i	0.989422	+	0.145063i	$0.0463386\pi$
$367$			106.477i			0.290127i	−0.989422	+	0.145063i	$0.953661\pi$
$368$	482.152			1.31020
$369$			149.762i			0.405859i
$370$			292.095i			0.789446i
$371$	−384.868	−	117.000i	−1.03738	−	0.315364i
$372$	631.991			1.69890
$373$	223.324			0.598723			0.299362	−	0.954140i	$-0.403226\pi$
$373$	223.324			0.598723			0.299362	+	0.954140i	$0.403226\pi$
$374$			7.63508i			0.0204147i
$375$	−19.3649			−0.0516398
$376$		−	834.419i		−	2.21920i
$377$		−	692.411i		−	1.83663i
$378$	37.0668	−	121.930i	0.0980604	−	0.322567i
$379$	119.075			0.314183			0.157092	−	0.987584i	$-0.449788\pi$
$379$	119.075			0.314183			0.157092	+	0.987584i	$0.449788\pi$
$380$	532.680			1.40179
$381$			144.643i			0.379640i
$382$	805.159			2.10775
$383$		−	494.637i		−	1.29148i	−0.763557	−	0.645740i	$-0.776549\pi$
$383$		−	494.637i		−	1.29148i	0.763557	−	0.645740i	$-0.223451\pi$
$384$			355.937i			0.926920i
$385$	−9.24694	+	30.4175i	−0.0240180	+	0.0790065i
$386$	390.767			1.01235
$387$	28.7661			0.0743311
$388$			559.838i			1.44288i
$389$	−270.578			−0.695574			−0.347787	−	0.937574i	$-0.613067\pi$
$389$	−270.578			−0.695574			−0.347787	+	0.937574i	$0.613067\pi$
$390$			244.492i			0.626902i
$391$		−	26.6837i		−	0.0682448i
$392$	609.875	+	408.563i	1.55580	+	1.04225i
$393$	343.375			0.873728
$394$	−605.664			−1.53722
$395$			62.8810i			0.159192i
$396$	50.4276			0.127342
$397$			37.1881i			0.0936727i	0.998903	+	0.0468364i	$0.0149139\pi$
$397$			37.1881i			0.0936727i	−0.998903	+	0.0468364i	$0.985086\pi$
$398$		−	413.240i		−	1.03829i
$399$	333.914	+	101.510i	0.836877	+	0.254411i
$400$	−96.9306			−0.242326
$401$	−36.7102			−0.0915467			−0.0457733	−	0.998952i	$-0.514575\pi$
$401$	−36.7102			−0.0915467			−0.0457733	+	0.998952i	$0.514575\pi$
$402$		−	580.955i		−	1.44516i
$403$	−794.386			−1.97118
$404$		−	606.868i		−	1.50215i
$405$			20.1246i			0.0496904i
$406$	901.780	+	274.141i	2.22113	+	0.675225i
$407$	−75.7266			−0.186060
$408$	−27.8394			−0.0682339
$409$			495.325i			1.21106i	0.795821	+	0.605532i	$0.207040\pi$
$409$			495.325i			1.21106i	−0.795821	+	0.605532i	$0.792960\pi$
$410$	391.103			0.953909
$411$			41.8524i			0.101831i
$412$			474.562i			1.15185i
$413$	−207.056	+	681.104i	−0.501346	+	1.64916i
$414$	−261.421			−0.631451
$415$	−231.151			−0.556989
$416$			144.106i			0.346408i
$417$	−106.758			−0.256016
$418$			204.847i			0.490065i
$419$		−	269.297i		−	0.642713i	−0.946958	−	0.321357i	$-0.895861\pi$
$419$		−	269.297i		−	0.642713i	0.946958	−	0.321357i	$-0.104139\pi$
$420$	−214.665	−	65.2583i	−0.511107	−	0.155377i
$421$	756.722			1.79744			0.898719	−	0.438524i	$-0.144499\pi$
$421$	756.722			1.79744			0.898719	+	0.438524i	$0.144499\pi$
$422$	−1373.24			−3.25412
$423$			167.093i			0.395020i
$424$	860.904			2.03043
$425$			5.36443i			0.0126222i
$426$			156.593i			0.367588i
$427$	65.0563	−	214.001i	0.152357	−	0.501173i
$428$	−329.709			−0.770347
$429$	−63.3853			−0.147751
$430$		−	75.1226i		−	0.174704i
$431$	185.182			0.429657			0.214828	−	0.976652i	$-0.431081\pi$
$431$	185.182			0.429657			0.214828	+	0.976652i	$0.431081\pi$
$432$			100.733i			0.233179i
$433$			642.846i			1.48463i	0.670049	+	0.742317i	$0.266273\pi$
$433$			642.846i			1.48463i	−0.670049	+	0.742317i	$0.733727\pi$
$434$	314.516	−	1034.59i	0.724691	−	2.38385i
$435$	−148.839			−0.342158
$436$	−1531.46			−3.51253
$437$		−	715.918i		−	1.63826i
$438$	580.643			1.32567
$439$		−	464.239i		−	1.05749i	−0.848780	−	0.528745i	$-0.822663\pi$
$439$		−	464.239i		−	1.05749i	0.848780	−	0.528745i	$-0.177337\pi$
$440$		−	68.0403i		−	0.154637i
$441$	−122.128	−	81.8151i	−0.276935	−	0.185522i
$442$	67.7286			0.153232
$443$	−115.228			−0.260109			−0.130054	−	0.991507i	$-0.541515\pi$
$443$	−115.228			−0.260109			−0.130054	+	0.991507i	$0.541515\pi$
$444$		−	534.424i		−	1.20366i
$445$	65.6575			0.147545
$446$			337.234i			0.756130i
$447$			49.9299i			0.111700i
$448$	331.664	+	100.826i	0.740321	+	0.225058i
$449$	333.955			0.743774			0.371887	−	0.928278i	$-0.378711\pi$
$449$	333.955			0.743774			0.371887	+	0.928278i	$0.378711\pi$
$450$	52.5553			0.116790
$451$			101.395i			0.224822i
$452$	−999.028			−2.21024
$453$		−	430.088i		−	0.949421i
$454$			321.275i			0.707654i
$455$	269.825	+	82.0269i	0.593022	+	0.180279i
$456$	−746.925			−1.63799
$457$	354.152			0.774949			0.387474	−	0.921880i	$-0.373348\pi$
$457$	354.152			0.774949			0.387474	+	0.921880i	$0.373348\pi$
$458$			1135.10i			2.47837i
$459$	5.57488			0.0121457
$460$			460.246i			1.00053i
$461$		−	128.906i		−	0.279623i	−0.990178	−	0.139811i	$-0.955350\pi$
$461$		−	128.906i		−	0.279623i	0.990178	−	0.139811i	$-0.0446497\pi$
$462$	25.0957	−	82.5515i	0.0543197	−	0.178683i
$463$	−302.175			−0.652645			−0.326322	−	0.945259i	$-0.605810\pi$
$463$	−302.175			−0.652645			−0.326322	+	0.945259i	$0.605810\pi$
$464$	−745.009			−1.60562
$465$			170.759i			0.367224i
$466$	640.887			1.37530
$467$			808.227i			1.73068i	0.501186	+	0.865339i	$0.332897\pi$
$467$			808.227i			1.73068i	−0.501186	+	0.865339i	$0.667103\pi$
$468$		−	447.328i		−	0.955829i
$469$	−641.151	−	194.910i	−1.36706	−	0.415587i
$470$	436.363			0.928433
$471$	−71.6805			−0.152188
$472$		−	1523.55i		−	3.22785i
$473$	19.4758			0.0411750
$474$		−	170.656i		−	0.360033i
$475$			143.926i			0.303003i
$476$	−18.0777	+	59.4661i	−0.0379784	+	0.124929i
$477$	−172.397			−0.361419
$478$	−150.392			−0.314628
$479$		−	48.8836i		−	0.102053i	−0.998697	−	0.0510267i	$-0.983751\pi$
$479$		−	48.8836i		−	0.102053i	0.998697	−	0.0510267i	$-0.0162494\pi$
$480$	30.9766			0.0645345
$481$			671.748i			1.39657i
$482$		−	349.998i		−	0.726137i
$483$	−87.7066	+	288.508i	−0.181587	+	0.597325i
$484$	−967.235			−1.99842
$485$	−151.264			−0.311884
$486$		−	54.6171i		−	0.112381i
$487$	334.433			0.686720			0.343360	−	0.939204i	$-0.388435\pi$
$487$	334.433			0.686720			0.343360	+	0.939204i	$0.388435\pi$
$488$			478.694i			0.980930i
$489$			89.7381i			0.183514i
$490$	−213.660	+	318.937i	−0.436040	+	0.650892i
$491$	−549.151			−1.11843			−0.559217	−	0.829021i	$-0.688898\pi$
$491$	−549.151			−1.11843			−0.559217	+	0.829021i	$0.688898\pi$
$492$	−715.571			−1.45441
$493$			41.2310i			0.0836329i
$494$	1817.14			3.67842
$495$			13.6251i			0.0275255i
$496$			854.731i			1.72325i
$497$	172.818	+	52.5368i	0.347722	+	0.105708i
$498$	627.330			1.25970
$499$	−462.450			−0.926754			−0.463377	−	0.886161i	$-0.653362\pi$
$499$	−462.450			−0.926754			−0.463377	+	0.886161i	$0.653362\pi$
$500$		−	92.5267i		−	0.185053i
$501$	−72.6961			−0.145102
$502$		−	1418.80i		−	2.82630i
$503$		−	676.817i		−	1.34556i	−0.739842	−	0.672781i	$-0.765100\pi$
$503$		−	676.817i		−	1.34556i	0.739842	−	0.672781i	$-0.234900\pi$
$504$	301.004	+	91.5053i	0.597229	+	0.181558i
$505$	163.971			0.324695
$506$	−176.992			−0.349786
$507$			269.556i			0.531668i
$508$	−691.112			−1.36046
$509$		−	31.5959i		−	0.0620744i	−0.999518	−	0.0310372i	$-0.990119\pi$
$509$		−	31.5959i		−	0.0620744i	0.999518	−	0.0310372i	$-0.00988104\pi$
$510$		−	14.5588i		−	0.0285466i
$511$	194.805	−	640.806i	0.381224	−	1.25402i
$512$	−1006.66			−1.96613
$513$	149.572			0.291564
$514$			359.819i			0.700036i
$515$	−128.223			−0.248977
$516$			137.446i			0.266369i
$517$			113.129i			0.218817i
$518$	−874.869	−	265.961i	−1.68894	−	0.513437i
$519$	169.775			0.327120
$520$	−603.566			−1.16070
$521$			793.420i			1.52288i	0.648236	+	0.761440i	$0.275507\pi$
$521$			793.420i			1.52288i	−0.648236	+	0.761440i	$0.724493\pi$
$522$	403.941			0.773833
$523$		−	593.508i		−	1.13481i	−0.823438	−	0.567407i	$-0.807947\pi$
$523$		−	593.508i		−	1.13481i	0.823438	−	0.567407i	$-0.192053\pi$
$524$			1640.67i			3.13104i
$525$	17.6323	−	58.0009i	0.0335853	−	0.110478i
$526$	986.216			1.87494
$527$	47.3034			0.0897597
$528$			68.2003i			0.129167i
$529$	89.5666			0.169313
$530$			450.214i			0.849460i
$531$			305.092i			0.574561i
$532$	−485.020	+	1595.46i	−0.911692	+	2.99898i
$533$	899.442			1.68751
$534$	−178.191			−0.333691
$535$		−	89.0848i		−	0.166514i
$536$	1434.18			2.67570
$537$		−	118.789i		−	0.221209i
$538$		−	618.094i		−	1.14887i
$539$	−82.6855	−	55.3920i	−0.153405	−	0.102768i
$540$	−96.1565			−0.178068
$541$	217.690			0.402385			0.201192	−	0.979552i	$-0.435518\pi$
$541$	217.690			0.402385			0.201192	+	0.979552i	$0.435518\pi$
$542$		−	1072.27i		−	1.97836i
$543$	182.081			0.335324
$544$		−	8.58106i		−	0.0157740i
$545$		−	413.789i		−	0.759246i
$546$	−732.290	−	222.617i	−1.34119	−	0.407723i
$547$	−137.891			−0.252085			−0.126043	−	0.992025i	$-0.540228\pi$
$547$	−137.891			−0.252085			−0.126043	+	0.992025i	$0.540228\pi$
$548$	−199.973			−0.364915
$549$		−	95.8589i		−	0.174606i
$550$	35.5820			0.0646945
$551$			1106.22i			2.00766i
$552$		−	645.358i		−	1.16913i
$553$	−188.338	−	57.2549i	−0.340575	−	0.103535i
$554$	153.459			0.277002
$555$	144.397			0.260175
$556$		−	510.098i		−	0.917442i
$557$	−316.337			−0.567930			−0.283965	−	0.958835i	$-0.591650\pi$
$557$	−316.337			−0.567930			−0.283965	+	0.958835i	$0.591650\pi$
$558$		−	463.431i		−	0.830522i
$559$		−	172.764i		−	0.309059i
$560$	88.2580	−	290.322i	0.157604	−	0.518432i
$561$	3.77441			0.00672800
$562$	1750.10			3.11406
$563$			151.482i			0.269063i	0.990909	+	0.134531i	$0.0429529\pi$
$563$			151.482i			0.269063i	−0.990909	+	0.134531i	$0.957047\pi$
$564$	−798.381			−1.41557
$565$		−	269.930i		−	0.477752i
$566$		−	429.804i		−	0.759371i
$567$	−60.2763	−	18.3240i	−0.106307	−	0.0323175i
$568$	−386.573			−0.680586
$569$	−213.993			−0.376086			−0.188043	−	0.982161i	$-0.560214\pi$
$569$	−213.993			−0.376086			−0.188043	+	0.982161i	$0.560214\pi$
$570$		−	390.608i		−	0.685277i
$571$	−204.492			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$571$	−204.492			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$572$		−	302.858i		−	0.529473i
$573$		−	398.031i		−	0.694643i
$574$	−356.110	+	1171.41i	−0.620400	+	2.04079i
$575$	−124.355			−0.216270
$576$	148.565			0.257925
$577$		−	957.823i		−	1.66001i	−0.557759	−	0.830003i	$-0.688339\pi$
$577$		−	957.823i		−	1.66001i	0.557759	−	0.830003i	$-0.311661\pi$
$578$	1008.53			1.74487
$579$		−	193.176i		−	0.333638i
$580$		−	711.161i		−	1.22614i
$581$	210.469	−	692.331i	0.362253	−	1.19162i
$582$	410.522			0.705364
$583$	−116.719			−0.200205
$584$			1433.41i			2.45446i
$585$	120.865			0.206606
$586$			434.007i			0.740626i
$587$			981.279i			1.67168i	0.548969	+	0.835842i	$0.315020\pi$
$587$			981.279i			1.67168i	−0.548969	+	0.835842i	$0.684980\pi$
$588$	390.917	−	583.535i	0.664825	−	0.992407i
$589$	1269.14			2.15473
$590$	796.746			1.35042
$591$			299.410i			0.506617i
$592$	722.777			1.22091
$593$		−	708.384i		−	1.19458i	−0.802026	−	0.597288i	$-0.796245\pi$
$593$		−	708.384i		−	1.19458i	0.802026	−	0.597288i	$-0.203755\pi$
$594$		−	36.9779i		−	0.0622523i
$595$	−16.0673	−	4.88446i	−0.0270038	−	0.00820918i
$596$	−238.568			−0.400282
$597$	−204.286			−0.342187
$598$			1570.04i			2.62549i
$599$	−928.994			−1.55091			−0.775454	−	0.631404i	$-0.782479\pi$
$599$	−928.994			−1.55091			−0.775454	+	0.631404i	$0.782479\pi$
$600$			129.741i			0.216235i
$601$		−	466.882i		−	0.776842i	−0.921482	−	0.388421i	$-0.873021\pi$
$601$		−	466.882i		−	0.776842i	0.921482	−	0.388421i	$-0.126979\pi$
$602$	225.004	+	68.4012i	0.373760	+	0.113623i
$603$	−287.195			−0.476277
$604$	2054.98			3.40229
$605$		−	261.339i		−	0.431966i
$606$	−445.009			−0.734338
$607$			988.757i			1.62892i	0.580216	+	0.814462i	$0.302968\pi$
$607$			988.757i			1.62892i	−0.580216	+	0.814462i	$0.697032\pi$
$608$		−	230.228i		−	0.378664i
$609$	135.522	−	445.795i	0.222532	−	0.732012i
$610$	−250.335			−0.410386
$611$	1003.53			1.64244
$612$			26.6371i			0.0435246i
$613$	469.962			0.766660			0.383330	−	0.923612i	$-0.374777\pi$
$613$	469.962			0.766660			0.383330	+	0.923612i	$0.374777\pi$
$614$		−	790.351i		−	1.28722i
$615$		−	193.342i		−	0.314377i
$616$	203.791	+	61.9526i	0.330830	+	0.100572i
$617$	1081.72			1.75320			0.876598	−	0.481223i	$-0.159807\pi$
$617$	1081.72			1.75320			0.876598	+	0.481223i	$0.159807\pi$
$618$	347.990			0.563091
$619$		−	553.956i		−	0.894921i	−0.894304	−	0.447461i	$-0.852328\pi$
$619$		−	553.956i		−	0.894921i	0.894304	−	0.447461i	$-0.147672\pi$
$620$	−815.897			−1.31596
$621$			129.234i			0.208105i
$622$		−	185.572i		−	0.298348i
$623$	−59.7829	+	196.654i	−0.0959598	+	0.315657i
$624$	604.985			0.969527
$625$	25.0000			0.0400000
$626$		−	1312.35i		−	2.09641i
$627$	101.266			0.161509
$628$		−	342.494i		−	0.545372i
$629$		−	40.0006i		−	0.0635940i
$630$	−47.8531	+	157.411i	−0.0759573	+	0.249859i
$631$	−77.8822			−0.123427			−0.0617133	−	0.998094i	$-0.519656\pi$
$631$	−77.8822			−0.123427			−0.0617133	+	0.998094i	$0.519656\pi$
$632$	421.290			0.666597
$633$			678.861i			1.07245i
$634$	42.2369			0.0666197
$635$		−	186.733i		−	0.294068i
$636$		−	823.722i		−	1.29516i
$637$	−491.366	+	733.479i	−0.771375	+	1.15146i
$638$	273.484			0.428658
$639$	77.4117			0.121145
$640$		−	459.513i		−	0.717989i
$641$	−360.619			−0.562589			−0.281294	−	0.959622i	$-0.590764\pi$
$641$	−360.619			−0.562589			−0.281294	+	0.959622i	$0.590764\pi$
$642$			241.771i			0.376591i
$643$			793.158i			1.23353i	0.787148	+	0.616764i	$0.211557\pi$
$643$			793.158i			1.23353i	−0.787148	+	0.616764i	$0.788443\pi$
$644$	−1378.51	−	419.067i	−2.14054	−	0.650725i
$645$	−37.1369			−0.0575766
$646$	−108.205			−0.167501
$647$		−	405.244i		−	0.626344i	−0.949696	−	0.313172i	$-0.898608\pi$
$647$		−	405.244i		−	0.626344i	0.949696	−	0.313172i	$-0.101392\pi$
$648$	134.831			0.208072
$649$			206.559i			0.318273i
$650$		−	315.637i		−	0.485596i
$651$	−511.450	−	155.481i	−0.785638	−	0.238834i
$652$	−428.774			−0.657629
$653$	493.508			0.755755			0.377877	−	0.925856i	$-0.376654\pi$
$653$	493.508			0.755755			0.377877	+	0.925856i	$0.376654\pi$
$654$			1123.00i			1.71713i
$655$	−443.295			−0.676787
$656$		−	967.767i		−	1.47526i
$657$		−	287.041i		−	0.436896i
$658$	−397.321	+	1306.97i	−0.603831	+	1.98628i
$659$	−1120.88			−1.70088			−0.850441	−	0.526070i	$-0.823665\pi$
$659$	−1120.88			−1.70088			−0.850441	+	0.526070i	$0.823665\pi$
$660$	−65.1017			−0.0986389
$661$			1134.48i			1.71631i	0.513393	+	0.858154i	$0.328388\pi$
$661$			1134.48i			1.71631i	−0.513393	+	0.858154i	$0.671612\pi$
$662$	−1318.03			−1.99098
$663$		−	33.4817i		−	0.0505002i
$664$			1548.66i			2.33232i
$665$	−431.081	−	131.049i	−0.648242	−	0.197066i
$666$	−391.887			−0.588418
$667$	−955.794			−1.43297
$668$		−	347.346i		−	0.519979i
$669$	166.712			0.249196
$670$			750.009i			1.11942i
$671$		−	64.9002i		−	0.0967216i
$672$	−28.2050	+	92.7796i	−0.0419718	+	0.138065i
$673$	−763.267			−1.13413			−0.567063	−	0.823674i	$-0.691920\pi$
$673$	−763.267			−1.13413			−0.567063	+	0.823674i	$0.691920\pi$
$674$	−381.809			−0.566482
$675$		−	25.9808i		−	0.0384900i
$676$	−1287.95			−1.90525
$677$		−	456.611i		−	0.674463i	−0.941422	−	0.337232i	$-0.890509\pi$
$677$		−	456.611i		−	0.674463i	0.941422	−	0.337232i	$-0.109491\pi$
$678$			732.575i			1.08049i
$679$	137.730	−	453.058i	0.202842	−	0.667244i
$680$	35.9406			0.0528538
$681$	158.822			0.233219
$682$		−	313.761i		−	0.460060i
$683$	−219.276			−0.321049			−0.160524	−	0.987032i	$-0.551319\pi$
$683$	−219.276			−0.321049			−0.160524	+	0.987032i	$0.551319\pi$
$684$			714.666i			1.04483i
$685$		−	54.0313i		−	0.0788777i
$686$	−760.722	−	930.345i	−1.10892	−	1.35619i
$687$	561.135			0.816791
$688$	−185.888			−0.270186
$689$			1035.38i			1.50273i
$690$	337.493			0.489120
$691$			396.801i			0.574242i	0.957894	+	0.287121i	$0.0926982\pi$
$691$			396.801i			0.574242i	−0.957894	+	0.287121i	$0.907302\pi$
$692$			811.197i			1.17225i
$693$	−40.8094	−	12.4061i	−0.0588880	−	0.0179020i
$694$	−722.989			−1.04177
$695$	137.825			0.198309
$696$			997.190i			1.43274i
$697$	−53.5591			−0.0768424
$698$			1308.54i			1.87470i
$699$		−	316.823i		−	0.453252i
$700$	277.131	+	84.2481i	0.395902	+	0.120354i
$701$	−493.156			−0.703503			−0.351752	−	0.936093i	$-0.614414\pi$
$701$	−493.156			−0.703503			−0.351752	+	0.936093i	$0.614414\pi$
$702$	−328.020			−0.467265
$703$		−	1073.21i		−	1.52661i
$704$	100.584			0.142875
$705$		−	215.717i		−	0.305981i
$706$		−	2263.88i		−	3.20663i
$707$	−149.300	+	491.118i	−0.211174	+	0.694651i
$708$	−1457.75			−2.05896
$709$	859.326			1.21202			0.606012	−	0.795455i	$-0.292768\pi$
$709$	859.326			1.21202			0.606012	+	0.795455i	$0.292768\pi$
$710$		−	202.160i		−	0.284733i
$711$	−84.3637			−0.118655
$712$		−	439.892i		−	0.617825i
$713$			1096.56i			1.53795i
$714$	43.6057	+	13.2562i	0.0610724	+	0.0185661i
$715$	81.8300			0.114448
$716$	567.582			0.792712
$717$			74.3466i			0.103691i
$718$	614.060			0.855237
$719$		−	385.539i		−	0.536216i	−0.963389	−	0.268108i	$-0.913602\pi$
$719$		−	385.539i		−	0.536216i	0.963389	−	0.268108i	$-0.0863983\pi$
$720$		−	130.046i		−	0.180619i
$721$	116.751	−	384.048i	0.161929	−	0.532660i
$722$	−1638.29			−2.26910
$723$	−173.022			−0.239311
$724$			869.992i			1.20165i
$725$	192.150			0.265035
$726$			709.261i			0.976944i
$727$		−	114.722i		−	0.157802i	−0.996882	−	0.0789012i	$-0.974859\pi$
$727$		−	114.722i		−	0.157802i	0.996882	−	0.0789012i	$-0.0251412\pi$
$728$	549.563	−	1807.77i	0.754895	−	2.48320i
$729$	−27.0000			−0.0370370
$730$	−749.606			−1.02686
$731$			10.2876i			0.0140733i
$732$	458.019			0.625710
$733$		−	140.433i		−	0.191586i	−0.995401	−	0.0957932i	$-0.969461\pi$
$733$		−	140.433i		−	0.191586i	0.995401	−	0.0957932i	$-0.0305388\pi$
$734$			373.061i			0.508257i
$735$	157.667	+	105.623i	0.214513	+	0.143705i
$736$	198.921			0.270273
$737$	−194.442			−0.263830
$738$			524.719i			0.711002i
$739$	−50.8609			−0.0688239			−0.0344120	−	0.999408i	$-0.510956\pi$
$739$	−50.8609			−0.0688239			−0.0344120	+	0.999408i	$0.510956\pi$
$740$			689.939i			0.932349i
$741$		−	898.304i		−	1.21229i
$742$	−1348.46	−	409.932i	−1.81733	−	0.552469i
$743$	930.694			1.25262			0.626309	−	0.779575i	$-0.284565\pi$
$743$	930.694			1.25262			0.626309	+	0.779575i	$0.284565\pi$
$744$	1144.05			1.53770
$745$		−	64.4593i		−	0.0865225i
$746$	782.457			1.04887
$747$		−	310.121i		−	0.415155i
$748$			18.0343i			0.0241101i
$749$	266.822	+	81.1142i	0.356238	+	0.108297i
$750$	−67.8486			−0.0904649
$751$	−446.702			−0.594809			−0.297404	−	0.954752i	$-0.596121\pi$
$751$	−446.702			−0.594809			−0.297404	+	0.954752i	$0.596121\pi$
$752$		−	1079.76i		−	1.43586i
$753$	−701.385			−0.931455
$754$		−	2425.99i		−	3.21750i
$755$			555.241i			0.735419i
$756$	87.5532	−	288.003i	0.115811	−	0.380957i
$757$	27.2042			0.0359369			0.0179684	−	0.999839i	$-0.494280\pi$
$757$	27.2042			0.0359369			0.0179684	+	0.999839i	$0.494280\pi$
$758$	417.203			0.550400
$759$			87.4961i			0.115278i
$760$	964.276			1.26878
$761$			333.536i			0.438287i	0.975693	+	0.219143i	$0.0703262\pi$
$761$			333.536i			0.438287i	−0.975693	+	0.219143i	$0.929674\pi$
$762$			506.784i			0.665070i
$763$	1239.36	+	376.767i	1.62433	+	0.493796i
$764$	1901.81			2.48928
$765$	−7.19714			−0.00940802
$766$		−	1733.05i		−	2.26247i
$767$	1832.32			2.38895
$768$			903.998i			1.17708i
$769$		−	56.3903i		−	0.0733294i	−0.999328	−	0.0366647i	$-0.988327\pi$
$769$		−	56.3903i		−	0.0733294i	0.999328	−	0.0366647i	$-0.0116734\pi$
$770$	−32.3984	+	106.574i	−0.0420758	+	0.138407i
$771$	177.877			0.230709
$772$	923.006			1.19560
$773$		−	296.398i		−	0.383438i	−0.981450	−	0.191719i	$-0.938594\pi$
$773$		−	296.398i		−	0.383438i	0.981450	−	0.191719i	$-0.0614063\pi$
$774$	100.788			0.130217
$775$		−	220.449i		−	0.284451i
$776$			1013.44i			1.30598i
$777$	−131.478	+	432.492i	−0.169212	+	0.556618i
$778$	−948.022			−1.21854
$779$	−1436.98			−1.84464
$780$			577.498i			0.740382i
$781$	52.4107			0.0671072
$782$		−	93.4915i		−	0.119554i
$783$		−	199.688i		−	0.255030i
$784$	789.197	+	528.692i	1.00663	+	0.674352i
$785$	92.5392			0.117884
$786$	1203.08			1.53064
$787$			226.427i			0.287709i	0.989599	+	0.143854i	$0.0459497\pi$
$787$			226.427i			0.287709i	−0.989599	+	0.143854i	$0.954050\pi$
$788$	−1430.60			−1.81548
$789$		−	487.537i		−	0.617917i
$790$			220.315i			0.278880i
$791$	808.481	+	245.779i	1.02210	+	0.310719i
$792$	91.2857			0.115260
$793$	−575.711			−0.725991
$794$			130.295i			0.164100i
$795$	222.563			0.279954
$796$		−	976.088i		−	1.22624i
$797$		−	305.282i		−	0.383038i	−0.981489	−	0.191519i	$-0.938659\pi$
$797$		−	305.282i		−	0.383038i	0.981489	−	0.191519i	$-0.0613414\pi$
$798$	1169.93	+	355.659i	1.46608	+	0.445688i
$799$	−59.7573			−0.0747901
$800$	−39.9906			−0.0499882
$801$			88.0887i			0.109973i
$802$	−128.621			−0.160375
$803$		−	194.338i		−	0.242015i
$804$		−	1372.24i		−	1.70676i
$805$	113.229	−	372.462i	0.140657	−	0.462686i
$806$	−2783.28			−3.45320
$807$	−305.555			−0.378631
$808$		−	1098.57i		−	1.35962i
$809$	592.651			0.732573			0.366286	−	0.930502i	$-0.380629\pi$
$809$	592.651			0.732573			0.366286	+	0.930502i	$0.380629\pi$
$810$			70.5104i			0.0870498i
$811$			731.348i			0.901785i	0.892578	+	0.450893i	$0.148894\pi$
$811$			731.348i			0.901785i	−0.892578	+	0.450893i	$0.851106\pi$
$812$	2130.04	+	647.532i	2.62320	+	0.797453i
$813$	−530.078			−0.652003
$814$	−265.322			−0.325949
$815$		−	115.851i		−	0.142149i
$816$	−36.0251			−0.0441484
$817$			276.013i			0.337838i
$818$			1735.47i			2.12160i
$819$	−110.051	+	362.008i	−0.134372	+	0.442012i
$820$	923.798			1.12658
$821$	268.560			0.327114			0.163557	−	0.986534i	$-0.447703\pi$
$821$	268.560			0.327114			0.163557	+	0.986534i	$0.447703\pi$
$822$			146.638i			0.178392i
$823$	1213.35			1.47430			0.737151	−	0.675728i	$-0.236170\pi$
$823$	1213.35			1.47430			0.737151	+	0.675728i	$0.236170\pi$
$824$			859.068i			1.04256i
$825$		−	17.5900i		−	0.0213212i
$826$	−725.459	+	2386.37i	−0.878280	+	2.88907i
$827$	−1238.49			−1.49757			−0.748785	−	0.662813i	$-0.769363\pi$
$827$	−1238.49			−1.49757			−0.748785	+	0.662813i	$0.769363\pi$
$828$	−617.485			−0.745755
$829$		−	873.056i		−	1.05314i	−0.850131	−	0.526572i	$-0.823477\pi$
$829$		−	873.056i		−	1.05314i	0.850131	−	0.526572i	$-0.176523\pi$
$830$	−809.879			−0.975758
$831$		−	75.8626i		−	0.0912908i
$832$		−	892.251i		−	1.07242i
$833$	29.2594	−	43.6765i	0.0351253	−	0.0524328i
$834$	−374.048			−0.448499
$835$	93.8503			0.112396
$836$			483.856i			0.578776i
$837$	−229.098			−0.273713
$838$		−	943.532i		−	1.12593i
$839$		−	100.572i		−	0.119871i	−0.998202	−	0.0599355i	$-0.980910\pi$
$839$		−	100.572i		−	0.119871i	0.998202	−	0.0599355i	$-0.0190895\pi$
$840$	−388.594	−	118.133i	−0.462612	−	0.140634i
$841$	635.869			0.756086
$842$	2651.32			3.14883
$843$		−	865.163i		−	1.02629i
$844$	−3243.63			−3.84317
$845$		−	347.995i		−	0.411828i
$846$			585.443i			0.692013i
$847$	782.752	+	237.957i	0.924146	+	0.280941i
$848$	1114.03			1.31372
$849$	−212.474			−0.250264
$850$			18.7953i			0.0221121i
$851$	927.271			1.08963
$852$			369.877i			0.434128i
$853$			1162.30i			1.36260i	0.732003	+	0.681302i	$0.238586\pi$
$853$			1162.30i			1.36260i	−0.732003	+	0.681302i	$0.761414\pi$
$854$	227.937	−	749.792i	0.266905	−	0.877977i
$855$	−193.097			−0.225845
$856$	−596.850			−0.697254
$857$		−	87.8213i		−	0.102475i	−0.998686	−	0.0512376i	$-0.983683\pi$
$857$		−	87.8213i		−	0.102475i	0.998686	−	0.0512376i	$-0.0163166\pi$
$858$	−222.082			−0.258837
$859$		−	200.580i		−	0.233504i	−0.993161	−	0.116752i	$-0.962752\pi$
$859$		−	200.580i		−	0.233504i	0.993161	−	0.116752i	$-0.0372482\pi$
$860$		−	177.442i		−	0.206328i
$861$	579.088	+	176.043i	0.672576	+	0.204464i
$862$	648.820			0.752691
$863$	−617.914			−0.716007			−0.358004	−	0.933720i	$-0.616542\pi$
$863$	−617.914			−0.716007			−0.358004	+	0.933720i	$0.616542\pi$
$864$			41.5594i			0.0481012i
$865$	−219.179			−0.253386
$866$			2252.33i			2.60085i
$867$		−	498.569i		−	0.575051i
$868$	742.897	−	2443.74i	0.855872	−	2.81537i
$869$	−57.1175			−0.0657278
$870$	−521.485			−0.599408
$871$			1724.84i			1.98030i
$872$	−2772.30			−3.17925
$873$		−	202.942i		−	0.232465i
$874$		−	2508.35i		−	2.86997i
$875$	−22.7632	+	74.8788i	−0.0260151	+	0.0855758i
$876$	1371.50			1.56564
$877$	−638.649			−0.728220			−0.364110	−	0.931356i	$-0.618627\pi$
$877$	−638.649			−0.728220			−0.364110	+	0.931356i	$0.618627\pi$
$878$		−	1626.55i		−	1.85256i
$879$	214.551			0.244086
$880$		−	88.0462i		−	0.100052i
$881$			148.009i			0.168001i	0.996466	+	0.0840003i	$0.0267697\pi$
$881$			148.009i			0.168001i	−0.996466	+	0.0840003i	$0.973230\pi$
$882$	−427.899	−	286.655i	−0.485146	−	0.325005i
$883$	−784.505			−0.888454			−0.444227	−	0.895914i	$-0.646522\pi$
$883$	−784.505			−0.888454			−0.444227	+	0.895914i	$0.646522\pi$
$884$	159.977			0.180970
$885$		−	393.872i		−	0.445053i
$886$	−403.724			−0.455670
$887$			1466.40i			1.65321i	0.562783	+	0.826605i	$0.309731\pi$
$887$			1466.40i			1.65321i	−0.562783	+	0.826605i	$0.690269\pi$
$888$		−	967.433i		−	1.08945i
$889$	559.294	+	170.026i	0.629127	+	0.191255i
$890$	230.043			0.258476
$891$	−18.2800			−0.0205163
$892$			796.559i			0.893003i
$893$	−1603.27			−1.79538
$894$			174.939i			0.195681i
$895$			153.356i			0.171348i
$896$	1376.31	+	418.400i	1.53606	+	0.466964i
$897$	776.152			0.865276
$898$	1170.07			1.30298
$899$		−	1694.38i		−	1.88473i
$900$	124.138			0.137931
$901$		−	61.6540i		−	0.0684284i
$902$			355.255i			0.393853i
$903$	33.8142	−	111.231i	0.0374465	−	0.123179i
$904$	−1808.48			−2.00053
$905$	−235.065			−0.259741
$906$		−	1506.89i		−	1.66324i
$907$	488.454			0.538538			0.269269	−	0.963065i	$-0.413218\pi$
$907$	488.454			0.538538			0.269269	+	0.963065i	$0.413218\pi$
$908$			758.863i			0.835752i
$909$			219.990i			0.242013i
$910$	945.382	+	287.397i	1.03888	+	0.315821i
$911$	1329.44			1.45932			0.729658	−	0.683812i	$-0.239679\pi$
$911$	1329.44			1.45932			0.729658	+	0.683812i	$0.239679\pi$
$912$	−966.543			−1.05981
$913$		−	209.964i		−	0.229971i
$914$	1240.84			1.35759
$915$			123.753i			0.135250i
$916$			2681.14i			2.92700i
$917$	403.633	−	1327.74i	0.440167	−	1.44791i
$918$	19.5326			0.0212774
$919$	1369.52			1.49023			0.745113	−	0.666938i	$-0.232395\pi$
$919$	1369.52			1.49023			0.745113	+	0.666938i	$0.232395\pi$
$920$			833.153i			0.905601i
$921$	−390.710			−0.424224
$922$		−	451.647i		−	0.489856i
$923$		−	464.920i		−	0.503705i
$924$	59.2769	−	194.989i	0.0641525	−	0.211028i
$925$	−186.416			−0.201531
$926$	−1058.73			−1.14333
$927$		−	172.029i		−	0.185576i
$928$	−307.368			−0.331216
$929$			909.289i			0.978783i	0.872064	+	0.489391i	$0.162781\pi$
$929$			909.289i			0.978783i	−0.872064	+	0.489391i	$0.837219\pi$
$930$			598.287i			0.643320i
$931$	785.022	−	1171.83i	0.843203	−	1.25868i
$932$	1513.80			1.62425
$933$	−91.7378			−0.0983256
$934$			2831.78i			3.03188i
$935$	−4.87274			−0.00521149
$936$		−	809.768i		−	0.865137i
$937$			184.883i			0.197313i	0.995122	+	0.0986566i	$0.0314545\pi$
$937$			184.883i			0.197313i	−0.995122	+	0.0986566i	$0.968545\pi$
$938$	−2246.39	−	682.904i	−2.39487	−	0.728043i
$939$	−648.762			−0.690907
$940$	1030.71			1.09650
$941$			884.454i			0.939909i	0.882691	+	0.469955i	$0.155730\pi$
$941$			884.454i			0.939909i	−0.882691	+	0.469955i	$0.844270\pi$
$942$	−251.146			−0.266610
$943$		−	1241.58i		−	1.31662i
$944$		−	1971.51i		−	2.08847i
$945$	77.8163	+	23.6562i	0.0823453	+	0.0250330i
$946$	68.2371			0.0721322
$947$	−651.331			−0.687784			−0.343892	−	0.939009i	$-0.611745\pi$
$947$	−651.331			−0.687784			−0.343892	+	0.939009i	$0.611745\pi$
$948$		−	403.094i		−	0.425205i
$949$	−1723.91			−1.81656
$950$			504.273i			0.530813i
$951$		−	20.8798i		−	0.0219557i
$952$	−32.7249	+	107.647i	−0.0343749	+	0.113075i
$953$	1622.61			1.70263			0.851316	−	0.524654i	$-0.175805\pi$
$953$	1622.61			1.70263			0.851316	+	0.524654i	$0.175805\pi$
$954$	−604.025			−0.633150
$955$			513.855i			0.538069i
$956$	−355.232			−0.371582
$957$		−	135.197i		−	0.141271i
$958$		−	171.273i		−	0.178782i
$959$	161.832	+	49.1970i	0.168751	+	0.0513003i
$960$	−191.796			−0.199788
$961$	−982.915			−1.02280
$962$			2353.60i			2.44657i
$963$	119.520			0.124112
$964$		−	826.708i		−	0.857581i
$965$			249.389i			0.258435i
$966$	−307.297	+	1010.84i	−0.318112	+	1.04642i
$967$	−1491.24			−1.54213			−0.771067	−	0.636754i	$-0.780276\pi$
$967$	−1491.24			−1.54213			−0.771067	+	0.636754i	$0.780276\pi$
$968$	−1750.92			−1.80880
$969$			53.4914i			0.0552027i
$970$	−529.982			−0.546373
$971$		−	1739.36i		−	1.79130i	−0.444756	−	0.895652i	$-0.646709\pi$
$971$		−	1739.36i		−	1.79130i	0.444756	−	0.895652i	$-0.353291\pi$
$972$		−	129.008i		−	0.132724i
$973$	−125.493	+	412.806i	−0.128975	+	0.424261i
$974$	1171.75			1.20303
$975$	−156.036			−0.160036
$976$			619.444i			0.634676i
$977$	−62.8973			−0.0643780			−0.0321890	−	0.999482i	$-0.510248\pi$
$977$	−62.8973			−0.0643780			−0.0321890	+	0.999482i	$0.510248\pi$
$978$			314.414i			0.321487i
$979$			59.6395i			0.0609188i
$980$	−504.672	+	753.341i	−0.514971	+	0.768715i
$981$	555.156			0.565909
$982$	−1924.06			−1.95932
$983$			1214.68i			1.23569i	0.786299	+	0.617846i	$0.211994\pi$
$983$			1214.68i			1.23569i	−0.786299	+	0.617846i	$0.788006\pi$
$984$	−1295.35			−1.31641
$985$		−	386.537i		−	0.392424i
$986$			144.461i			0.146512i
$987$	646.104	+	196.416i	0.654614	+	0.199003i
$988$	4292.15			4.34428
$989$	−238.481			−0.241133
$990$			47.7383i			0.0482205i
$991$	114.216			0.115253			0.0576266	−	0.998338i	$-0.481647\pi$
$991$	114.216			0.115253			0.0576266	+	0.998338i	$0.481647\pi$
$992$			352.636i			0.355480i
$993$			651.570i			0.656163i
$994$	605.501	+	184.072i	0.609156	+	0.185184i
$995$	263.732			0.265057
$996$	1481.78			1.48773
$997$		−	178.000i		−	0.178536i	−0.996008	−	0.0892678i	$-0.971547\pi$
$997$		−	178.000i		−	0.178536i	0.996008	−	0.0892678i	$-0.0284527\pi$
$998$	−1620.28			−1.62353
$999$			193.729i			0.193923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.h.a.76.11	✓	12
3.2	odd	2		315.3.h.d.181.1		12
4.3	odd	2		1680.3.s.c.1441.12		12
5.2	odd	4		525.3.e.c.349.10		24
5.3	odd	4		525.3.e.c.349.23		24
5.4	even	2		525.3.h.d.76.2		12
7.6	odd	2	inner	105.3.h.a.76.12	yes	12
21.20	even	2		315.3.h.d.181.2		12
28.27	even	2		1680.3.s.c.1441.3		12
35.13	even	4		525.3.e.c.349.9		24
35.27	even	4		525.3.e.c.349.24		24
35.34	odd	2		525.3.h.d.76.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.11	✓	12	1.1	even	1	trivial
105.3.h.a.76.12	yes	12	7.6	odd	2	inner
315.3.h.d.181.1		12	3.2	odd	2
315.3.h.d.181.2		12	21.20	even	2
525.3.e.c.349.9		24	35.13	even	4
525.3.e.c.349.10		24	5.2	odd	4
525.3.e.c.349.23		24	5.3	odd	4
525.3.e.c.349.24		24	35.27	even	4
525.3.h.d.76.1		12	35.34	odd	2
525.3.h.d.76.2		12	5.4	even	2
1680.3.s.c.1441.3		12	28.27	even	2
1680.3.s.c.1441.12		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +2.23607i q^{5} -6.06857i q^{6} +(-6.69736 - 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +2.23607i q^{5} -6.06857i q^{6} +(-6.69736 - 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} +7.83449i q^{10} -2.03112 q^{11} -14.3342i q^{12} +18.0174i q^{13} +(-23.4655 - 7.13352i) q^{14} +3.87298 q^{15} +19.3861 q^{16} -1.07289i q^{17} -10.5111 q^{18} -28.7852i q^{19} +18.5053i q^{20} +(-3.52646 + 11.6002i) q^{21} -7.11640 q^{22} +24.8710 q^{23} -25.9482i q^{24} -5.00000 q^{25} +63.1275i q^{26} +5.19615i q^{27} +(-55.4263 - 16.8496i) q^{28} -38.4300 q^{29} +13.5697 q^{30} +44.0899i q^{31} +7.99812 q^{32} +3.51800i q^{33} -3.75906i q^{34} +(4.55264 - 14.9758i) q^{35} -24.8275 q^{36} +37.2832 q^{37} -100.855i q^{38} +31.2071 q^{39} +33.4990i q^{40} -49.9206i q^{41} +(-12.3556 + 40.6434i) q^{42} -9.58871 q^{43} -16.8092 q^{44} -6.70820i q^{45} +87.1402 q^{46} -55.6978i q^{47} -33.5777i q^{48} +(40.7094 + 27.2717i) q^{49} -17.5184 q^{50} -1.85829 q^{51} +149.109i q^{52} +57.4656 q^{53} +18.2057i q^{54} -4.54171i q^{55} +(-100.335 - 30.5018i) q^{56} -49.8575 q^{57} -134.647 q^{58} -101.697i q^{59} +32.0522 q^{60} +31.9530i q^{61} +154.477i q^{62} +(20.0921 + 6.10801i) q^{63} -49.5215 q^{64} -40.2882 q^{65} +12.3260i q^{66} +95.7318 q^{67} -8.87902i q^{68} -43.0778i q^{69} +(15.9510 - 52.4704i) q^{70} -25.8039 q^{71} -44.9436 q^{72} +95.6803i q^{73} +130.629 q^{74} +8.66025i q^{75} -238.222i q^{76} +(13.6031 + 4.13536i) q^{77} +109.340 q^{78} +28.1212 q^{79} +43.3487i q^{80} +9.00000 q^{81} -174.906i q^{82} +103.374i q^{83} +(-29.1844 + 96.0012i) q^{84} +2.39905 q^{85} -33.5959 q^{86} +66.5628i q^{87} -30.4286 q^{88} -29.3629i q^{89} -23.5035i q^{90} +(36.6835 - 120.669i) q^{91} +205.828 q^{92} +76.3659 q^{93} -195.148i q^{94} +64.3658 q^{95} -13.8531i q^{96} +67.6473i q^{97} +(142.633 + 95.5515i) q^{98} +6.09335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Introduction

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