LMFDB - Embedded newform 105.3.c.a.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(71,105)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("105.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.c (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.7
Root			$-0.601965i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.601965i q^{2} +(0.926467 + 2.85336i) q^{3} +3.63764 q^{4} -2.23607i q^{5} +(1.71762 - 0.557701i) q^{6} +2.64575 q^{7} -4.59759i q^{8} +(-7.28332 + 5.28709i) q^{9} +O(q^{10})$	\(q-0.601965i q^{2} +(0.926467 + 2.85336i) q^{3} +3.63764 q^{4} -2.23607i q^{5} +(1.71762 - 0.557701i) q^{6} +2.64575 q^{7} -4.59759i q^{8} +(-7.28332 + 5.28709i) q^{9} -1.34603 q^{10} +13.9110i q^{11} +(3.37015 + 10.3795i) q^{12} +14.4201 q^{13} -1.59265i q^{14} +(6.38030 - 2.07164i) q^{15} +11.7830 q^{16} -26.3516i q^{17} +(3.18264 + 4.38430i) q^{18} -32.8598 q^{19} -8.13401i q^{20} +(2.45120 + 7.54928i) q^{21} +8.37391 q^{22} +6.45011i q^{23} +(13.1186 - 4.25952i) q^{24} -5.00000 q^{25} -8.68040i q^{26} +(-21.8337 - 15.8836i) q^{27} +9.62429 q^{28} +2.47472i q^{29} +(-1.24706 - 3.84072i) q^{30} -15.3304 q^{31} -25.4833i q^{32} +(-39.6929 + 12.8880i) q^{33} -15.8628 q^{34} -5.91608i q^{35} +(-26.4941 + 19.2325i) q^{36} -6.17239 q^{37} +19.7804i q^{38} +(13.3598 + 41.1457i) q^{39} -10.2805 q^{40} -49.4078i q^{41} +(4.54440 - 1.47554i) q^{42} -66.6976 q^{43} +50.6030i q^{44} +(11.8223 + 16.2860i) q^{45} +3.88274 q^{46} -45.1473i q^{47} +(10.9165 + 33.6210i) q^{48} +7.00000 q^{49} +3.00983i q^{50} +(75.1906 - 24.4139i) q^{51} +52.4551 q^{52} -8.37215i q^{53} +(-9.56137 + 13.1431i) q^{54} +31.1058 q^{55} -12.1641i q^{56} +(-30.4435 - 93.7607i) q^{57} +1.48970 q^{58} +34.2807i q^{59} +(23.2092 - 7.53589i) q^{60} -55.3640 q^{61} +9.22834i q^{62} +(-19.2698 + 13.9883i) q^{63} +31.7918 q^{64} -32.2443i q^{65} +(7.75815 + 23.8938i) q^{66} +89.2222 q^{67} -95.8576i q^{68} +(-18.4045 + 5.97582i) q^{69} -3.56127 q^{70} +104.333i q^{71} +(24.3079 + 33.4857i) q^{72} +83.9851 q^{73} +3.71556i q^{74} +(-4.63234 - 14.2668i) q^{75} -119.532 q^{76} +36.8049i q^{77} +(24.7683 - 8.04211i) q^{78} +108.502 q^{79} -26.3475i q^{80} +(25.0934 - 77.0151i) q^{81} -29.7418 q^{82} +107.270i q^{83} +(8.91659 + 27.4615i) q^{84} -58.9240 q^{85} +40.1496i q^{86} +(-7.06127 + 2.29275i) q^{87} +63.9569 q^{88} +77.3193i q^{89} +(9.80360 - 7.11660i) q^{90} +38.1520 q^{91} +23.4632i q^{92} +(-14.2031 - 43.7430i) q^{93} -27.1771 q^{94} +73.4767i q^{95} +(72.7130 - 23.6094i) q^{96} -17.6502 q^{97} -4.21376i q^{98} +(-73.5484 - 101.318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * 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 $

$2$		−	0.601965i		−	0.300983i	−0.988611	−	0.150491i	$-0.951914\pi$
$2$		−	0.601965i		−	0.300983i	0.988611	−	0.150491i	$-0.0480855\pi$
$3$	0.926467	+	2.85336i	0.308822	+	0.951120i
$3$	0.926467	+	2.85336i	0.308822	+	0.951120i
$4$	3.63764			0.909410
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	1.71762	−	0.557701i	0.286270	−	0.0929502i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$		−	4.59759i		−	0.574699i
$9$	−7.28332	+	5.28709i	−0.809257	+	0.587454i
$10$	−1.34603			−0.134603
$11$			13.9110i			1.26463i	0.774711	+	0.632316i	$0.217896\pi$
$11$			13.9110i			1.26463i	−0.774711	+	0.632316i	$0.782104\pi$
$12$	3.37015	+	10.3795i	0.280846	+	0.864957i
$13$	14.4201			1.10924			0.554619	−	0.832104i	$-0.312864\pi$
$13$	14.4201			1.10924			0.554619	+	0.832104i	$0.312864\pi$
$14$		−	1.59265i		−	0.113761i
$15$	6.38030	−	2.07164i	0.425354	−	0.138110i
$16$	11.7830			0.736435
$17$		−	26.3516i		−	1.55010i	−0.631903	−	0.775048i	$-0.717726\pi$
$17$		−	26.3516i		−	1.55010i	0.631903	−	0.775048i	$-0.282274\pi$
$18$	3.18264	+	4.38430i	0.176813	+	0.243572i
$19$	−32.8598			−1.72946			−0.864731	−	0.502236i	$-0.832511\pi$
$19$	−32.8598			−1.72946			−0.864731	+	0.502236i	$0.832511\pi$
$20$		−	8.13401i		−	0.406700i
$21$	2.45120	+	7.54928i	0.116724	+	0.359489i
$22$	8.37391			0.380632
$23$			6.45011i			0.280440i	0.990120	+	0.140220i	$0.0447809\pi$
$23$			6.45011i			0.280440i	−0.990120	+	0.140220i	$0.955219\pi$
$24$	13.1186	−	4.25952i	0.546607	−	0.177480i
$25$	−5.00000			−0.200000
$26$		−	8.68040i		−	0.333862i
$27$	−21.8337	−	15.8836i	−0.808656	−	0.588282i
$28$	9.62429			0.343724
$29$			2.47472i			0.0853352i	0.999089	+	0.0426676i	$0.0135856\pi$
$29$			2.47472i			0.0853352i	−0.999089	+	0.0426676i	$0.986414\pi$
$30$	−1.24706	−	3.84072i	−0.0415686	−	0.128024i
$31$	−15.3304			−0.494528			−0.247264	−	0.968948i	$-0.579531\pi$
$31$	−15.3304			−0.494528			−0.247264	+	0.968948i	$0.579531\pi$
$32$		−	25.4833i		−	0.796353i
$33$	−39.6929	+	12.8880i	−1.20282	+	0.390547i
$34$	−15.8628			−0.466552
$35$		−	5.91608i		−	0.169031i
$36$	−26.4941	+	19.2325i	−0.735946	+	0.534236i
$37$	−6.17239			−0.166821			−0.0834106	−	0.996515i	$-0.526581\pi$
$37$	−6.17239			−0.166821			−0.0834106	+	0.996515i	$0.526581\pi$
$38$			19.7804i			0.520538i
$39$	13.3598	+	41.1457i	0.342558	+	1.05502i
$40$	−10.2805			−0.257013
$41$		−	49.4078i		−	1.20507i	−0.798093	−	0.602534i	$-0.794158\pi$
$41$		−	49.4078i		−	1.20507i	0.798093	−	0.602534i	$-0.205842\pi$
$42$	4.54440	−	1.47554i	0.108200	−	0.0351319i
$43$	−66.6976			−1.55111			−0.775554	−	0.631281i	$-0.782529\pi$
$43$	−66.6976			−1.55111			−0.775554	+	0.631281i	$0.782529\pi$
$44$			50.6030i			1.15007i
$45$	11.8223	+	16.2860i	0.262718	+	0.361911i
$46$	3.88274			0.0844074
$47$		−	45.1473i		−	0.960580i	−0.877110	−	0.480290i	$-0.840531\pi$
$47$		−	45.1473i		−	0.960580i	0.877110	−	0.480290i	$-0.159469\pi$
$48$	10.9165	+	33.6210i	0.227428	+	0.700438i
$49$	7.00000			0.142857
$50$			3.00983i			0.0601965i
$51$	75.1906	−	24.4139i	1.47433	−	0.478704i
$52$	52.4551			1.00875
$53$		−	8.37215i		−	0.157965i	−0.996876	−	0.0789825i	$-0.974833\pi$
$53$		−	8.37215i		−	0.157965i	0.996876	−	0.0789825i	$-0.0251671\pi$
$54$	−9.56137	+	13.1431i	−0.177062	+	0.243391i
$55$	31.1058			0.565561
$56$		−	12.1641i		−	0.217216i
$57$	−30.4435	−	93.7607i	−0.534097	−	1.64492i
$58$	1.48970			0.0256844
$59$			34.2807i			0.581028i	0.956871	+	0.290514i	$0.0938263\pi$
$59$			34.2807i			0.581028i	−0.956871	+	0.290514i	$0.906174\pi$
$60$	23.2092	−	7.53589i	0.386821	−	0.125598i
$61$	−55.3640			−0.907607			−0.453804	−	0.891102i	$-0.649933\pi$
$61$	−55.3640			−0.907607			−0.453804	+	0.891102i	$0.649933\pi$
$62$			9.22834i			0.148844i
$63$	−19.2698	+	13.9883i	−0.305871	+	0.222037i
$64$	31.7918			0.496747
$65$		−	32.2443i		−	0.496067i
$66$	7.75815	+	23.8938i	0.117548	+	0.362027i
$67$	89.2222			1.33167			0.665837	−	0.746097i	$-0.268075\pi$
$67$	89.2222			1.33167			0.665837	+	0.746097i	$0.268075\pi$
$68$		−	95.8576i		−	1.40967i
$69$	−18.4045	+	5.97582i	−0.266732	+	0.0866060i
$70$	−3.56127			−0.0508753
$71$			104.333i			1.46948i	0.678347	+	0.734742i	$0.262697\pi$
$71$			104.333i			1.46948i	−0.678347	+	0.734742i	$0.737303\pi$
$72$	24.3079	+	33.4857i	0.337609	+	0.465079i
$73$	83.9851			1.15048			0.575241	−	0.817984i	$-0.304908\pi$
$73$	83.9851			1.15048			0.575241	+	0.817984i	$0.304908\pi$
$74$			3.71556i			0.0502103i
$75$	−4.63234	−	14.2668i	−0.0617645	−	0.190224i
$76$	−119.532			−1.57279
$77$			36.8049i			0.477986i
$78$	24.7683	−	8.04211i	0.317542	−	0.103104i
$79$	108.502			1.37344			0.686721	−	0.726921i	$-0.259049\pi$
$79$	108.502			1.37344			0.686721	+	0.726921i	$0.259049\pi$
$80$		−	26.3475i		−	0.329344i
$81$	25.0934	−	77.0151i	0.309795	−	0.950803i
$82$	−29.7418			−0.362705
$83$			107.270i			1.29241i	0.763165	+	0.646203i	$0.223644\pi$
$83$			107.270i			1.29241i	−0.763165	+	0.646203i	$0.776356\pi$
$84$	8.91659	+	27.4615i	0.106150	+	0.326923i
$85$	−58.9240			−0.693224
$86$			40.1496i			0.466856i
$87$	−7.06127	+	2.29275i	−0.0811640	+	0.0263534i
$88$	63.9569			0.726783
$89$			77.3193i			0.868756i	0.900731	+	0.434378i	$0.143032\pi$
$89$			77.3193i			0.868756i	−0.900731	+	0.434378i	$0.856968\pi$
$90$	9.80360	−	7.11660i	0.108929	−	0.0790734i
$91$	38.1520			0.419253
$92$			23.4632i			0.255034i
$93$	−14.2031	−	43.7430i	−0.152721	−	0.470355i
$94$	−27.1771			−0.289118
$95$			73.4767i			0.773439i
$96$	72.7130	−	23.6094i	0.757427	−	0.245932i
$97$	−17.6502			−0.181961			−0.0909805	−	0.995853i	$-0.529000\pi$
$97$	−17.6502			−0.181961			−0.0909805	+	0.995853i	$0.529000\pi$
$98$		−	4.21376i		−	0.0429975i
$99$	−73.5484	−	101.318i	−0.742913	−	1.02341i
$100$	−18.1882			−0.181882
$101$			90.7760i			0.898773i	0.893338	+	0.449386i	$0.148357\pi$
$101$			90.7760i			0.898773i	−0.893338	+	0.449386i	$0.851643\pi$
$102$	−14.6963	−	45.2621i	−0.144082	−	0.443746i
$103$	−78.7773			−0.764828			−0.382414	−	0.923991i	$-0.624907\pi$
$103$	−78.7773			−0.764828			−0.382414	+	0.923991i	$0.624907\pi$
$104$		−	66.2978i		−	0.637478i
$105$	16.8807	−	5.48105i	0.160769	−	0.0522005i
$106$	−5.03974			−0.0475447
$107$		−	17.0793i		−	0.159620i	−0.996810	−	0.0798099i	$-0.974569\pi$
$107$		−	17.0793i		−	0.159620i	0.996810	−	0.0798099i	$-0.0254313\pi$
$108$	−79.4232	−	57.7788i	−0.735400	−	0.534989i
$109$	−53.6692			−0.492378			−0.246189	−	0.969222i	$-0.579178\pi$
$109$	−53.6692			−0.492378			−0.246189	+	0.969222i	$0.579178\pi$
$110$		−	18.7246i		−	0.170224i
$111$	−5.71851	−	17.6120i	−0.0515181	−	0.158667i
$112$	31.1748			0.278346
$113$			46.7654i			0.413853i	0.978357	+	0.206926i	$0.0663461\pi$
$113$			46.7654i			0.413853i	−0.978357	+	0.206926i	$0.933654\pi$
$114$	−56.4407	+	18.3259i	−0.495094	+	0.160754i
$115$	14.4229			0.125416
$116$			9.00214i			0.0776047i
$117$	−105.026	+	76.2404i	−0.897660	+	0.651627i
$118$	20.6358			0.174879
$119$		−	69.7198i		−	0.585881i
$120$	−9.52457	−	29.3340i	−0.0793714	−	0.244450i
$121$	−72.5146			−0.599294
$122$			33.3272i			0.273174i
$123$	140.978	−	45.7747i	1.14616	−	0.372152i
$124$	−55.7663			−0.449728
$125$			11.1803i			0.0894427i
$126$	8.42048	+	11.5998i	0.0668292	+	0.0920617i
$127$	114.771			0.903708			0.451854	−	0.892092i	$-0.350763\pi$
$127$	114.771			0.903708			0.451854	+	0.892092i	$0.350763\pi$
$128$		−	121.071i		−	0.945865i
$129$	−61.7932	−	190.312i	−0.479017	−	1.47529i
$130$	−19.4100			−0.149307
$131$		−	182.680i		−	1.39450i	−0.716827	−	0.697251i	$-0.754406\pi$
$131$		−	182.680i		−	1.39450i	0.716827	−	0.697251i	$-0.245594\pi$
$132$	−144.389	+	46.8820i	−1.09385	+	0.355167i
$133$	−86.9388			−0.653675
$134$		−	53.7086i		−	0.400811i
$135$	−35.5168	+	48.8217i	−0.263088	+	0.361642i
$136$	−121.154			−0.890838
$137$			94.0546i			0.686530i	0.939239	+	0.343265i	$0.111533\pi$
$137$			94.0546i			0.686530i	−0.939239	+	0.343265i	$0.888467\pi$
$138$	3.59723	+	11.0789i	0.0260669	+	0.0802815i
$139$	204.250			1.46942			0.734712	−	0.678380i	$-0.237317\pi$
$139$	204.250			1.46942			0.734712	+	0.678380i	$0.237317\pi$
$140$		−	21.5206i		−	0.153718i
$141$	128.821	−	41.8275i	0.913627	−	0.296649i
$142$	62.8050			0.442289
$143$			200.597i			1.40278i
$144$	−85.8190	+	62.2976i	−0.595966	+	0.432622i
$145$	5.53365			0.0381631
$146$		−	50.5561i		−	0.346275i
$147$	6.48527	+	19.9735i	0.0441175	+	0.135874i
$148$	−22.4529			−0.151709
$149$		−	76.1917i		−	0.511354i	−0.966762	−	0.255677i	$-0.917702\pi$
$149$		−	76.1917i		−	0.511354i	0.966762	−	0.255677i	$-0.0822983\pi$
$150$	−8.58811	+	2.78850i	−0.0572541	+	0.0185900i
$151$	−108.592			−0.719151			−0.359576	−	0.933116i	$-0.617079\pi$
$151$	−108.592			−0.719151			−0.359576	+	0.933116i	$0.617079\pi$
$152$			151.076i			0.993920i
$153$	139.323	+	191.927i	0.910610	+	1.25443i
$154$	22.1553			0.143865
$155$			34.2797i			0.221160i
$156$	48.5980	+	149.673i	0.311525	+	0.959444i
$157$	−72.3224			−0.460652			−0.230326	−	0.973114i	$-0.573979\pi$
$157$	−72.3224			−0.460652			−0.230326	+	0.973114i	$0.573979\pi$
$158$		−	65.3144i		−	0.413382i
$159$	23.8887	−	7.75652i	0.150244	−	0.0487832i
$160$	−56.9824			−0.356140
$161$			17.0654i			0.105996i
$162$	−46.3604	−	15.1053i	−0.286175	−	0.0932429i
$163$	−35.3080			−0.216613			−0.108307	−	0.994118i	$-0.534543\pi$
$163$	−35.3080			−0.216613			−0.108307	+	0.994118i	$0.534543\pi$
$164$		−	179.728i		−	1.09590i
$165$	28.8185	+	88.7561i	0.174658	+	0.537916i
$166$	64.5726			0.388992
$167$		−	64.3931i		−	0.385588i	−0.981239	−	0.192794i	$-0.938245\pi$
$167$		−	64.3931i		−	0.385588i	0.981239	−	0.192794i	$-0.0617548\pi$
$168$	34.7085	−	11.2696i	0.206598	−	0.0670811i
$169$	38.9395			0.230411
$170$			35.4702i			0.208648i
$171$	239.328	−	173.732i	1.39958	−	1.01598i
$172$	−242.622			−1.41059
$173$		−	122.944i		−	0.710661i	−0.934741	−	0.355331i	$-0.884368\pi$
$173$		−	122.944i		−	0.710661i	0.934741	−	0.355331i	$-0.115632\pi$
$174$	1.38015	+	4.25064i	0.00793192	+	0.0244289i
$175$	−13.2288			−0.0755929
$176$			163.912i			0.931320i
$177$	−97.8150	+	31.7599i	−0.552627	+	0.179435i
$178$	46.5435			0.261480
$179$			304.544i			1.70136i	0.525683	+	0.850680i	$0.323810\pi$
$179$			304.544i			1.70136i	−0.525683	+	0.850680i	$0.676190\pi$
$180$	43.0052	+	59.2425i	0.238918	+	0.329125i
$181$	51.6184			0.285185			0.142592	−	0.989781i	$-0.454456\pi$
$181$	51.6184			0.285185			0.142592	+	0.989781i	$0.454456\pi$
$182$		−	22.9662i		−	0.126188i
$183$	−51.2930	−	157.973i	−0.280289	−	0.863243i
$184$	29.6550			0.161168
$185$			13.8019i			0.0746047i
$186$	−26.3318	+	8.54976i	−0.141569	+	0.0459664i
$187$	366.576			1.96030
$188$		−	164.229i		−	0.873561i
$189$	−57.7666	−	42.0241i	−0.305643	−	0.222350i
$190$	44.2304			0.232792
$191$		−	234.992i		−	1.23033i	−0.788400	−	0.615163i	$-0.789090\pi$
$191$		−	234.992i		−	1.23033i	0.788400	−	0.615163i	$-0.210910\pi$
$192$	29.4541	+	90.7134i	0.153407	+	0.472466i
$193$	−0.588946			−0.00305153			−0.00152577	−	0.999999i	$-0.500486\pi$
$193$	−0.588946			−0.00305153			−0.00152577	+	0.999999i	$0.500486\pi$
$194$			10.6248i			0.0547671i
$195$	92.0047	−	29.8733i	0.471819	−	0.153197i
$196$	25.4635			0.129916
$197$			257.547i			1.30734i	0.756778	+	0.653672i	$0.226773\pi$
$197$			257.547i			1.30734i	−0.756778	+	0.653672i	$0.773227\pi$
$198$	−60.9898	+	44.2736i	−0.308029	+	0.223604i
$199$	269.961			1.35659			0.678295	−	0.734790i	$-0.262719\pi$
$199$	269.961			1.35659			0.678295	+	0.734790i	$0.262719\pi$
$200$			22.9880i			0.114940i
$201$	82.6614	+	254.583i	0.411251	+	1.26658i
$202$	54.6440			0.270515
$203$			6.54750i			0.0322537i
$204$	273.516	−	88.8090i	1.34077	−	0.435338i
$205$	−110.479			−0.538923
$206$			47.4212i			0.230200i
$207$	−34.1023	−	46.9782i	−0.164745	−	0.226948i
$208$	169.912			0.816883
$209$		−	457.111i		−	2.18713i
$210$	−3.29940	−	10.1616i	−0.0157114	−	0.0483885i
$211$	−72.2378			−0.342359			−0.171180	−	0.985240i	$-0.554758\pi$
$211$	−72.2378			−0.342359			−0.171180	+	0.985240i	$0.554758\pi$
$212$		−	30.4548i		−	0.143655i
$213$	−297.700	+	96.6614i	−1.39765	+	0.453809i
$214$	−10.2811			−0.0480427
$215$			149.140i			0.693676i
$216$	−73.0263	+	100.383i	−0.338085	+	0.464734i
$217$	−40.5603			−0.186914
$218$			32.3070i			0.148197i
$219$	77.8095	+	239.640i	0.355295	+	1.09425i
$220$	113.152			0.514326
$221$		−	379.993i		−	1.71943i
$222$	−10.6018	+	3.44235i	−0.0477560	+	0.0155061i
$223$	−26.1701			−0.117355			−0.0586773	−	0.998277i	$-0.518688\pi$
$223$	−26.1701			−0.117355			−0.0586773	+	0.998277i	$0.518688\pi$
$224$		−	67.4225i		−	0.300993i
$225$	36.4166	−	26.4354i	0.161851	−	0.117491i
$226$	28.1511			0.124562
$227$			58.3117i			0.256880i	0.991717	+	0.128440i	$0.0409969\pi$
$227$			58.3117i			0.256880i	−0.991717	+	0.128440i	$0.959003\pi$
$228$	−110.742	−	341.068i	−0.485712	−	1.49591i
$229$	−0.867142			−0.00378665			−0.00189332	−	0.999998i	$-0.500603\pi$
$229$	−0.867142			−0.00378665			−0.00189332	+	0.999998i	$0.500603\pi$
$230$		−	8.68207i		−	0.0377481i
$231$	−105.018	+	34.0986i	−0.454622	+	0.147613i
$232$	11.3778			0.0490421
$233$		−	40.4900i		−	0.173777i	−0.996218	−	0.0868883i	$-0.972308\pi$
$233$		−	40.4900i		−	0.173777i	0.996218	−	0.0868883i	$-0.0276923\pi$
$234$	45.8940	+	63.2221i	0.196128	+	0.270180i
$235$	−100.952			−0.429585
$236$			124.701i			0.528393i
$237$	100.524	+	309.595i	0.424150	+	1.30631i
$238$	−41.9689			−0.176340
$239$			140.399i			0.587445i	0.955891	+	0.293722i	$0.0948941\pi$
$239$			140.399i			0.587445i	−0.955891	+	0.293722i	$0.905106\pi$
$240$	75.1789	−	24.4101i	0.313245	−	0.101709i
$241$	−321.089			−1.33232			−0.666159	−	0.745809i	$-0.732063\pi$
$241$	−321.089			−1.33232			−0.666159	+	0.745809i	$0.732063\pi$
$242$			43.6512i			0.180377i
$243$	243.000	+	0.248511i	0.999999	+	0.00102268i
$244$	−201.394			−0.825386
$245$		−	15.6525i		−	0.0638877i
$246$	−27.5548	−	84.8640i	−0.112011	−	0.344976i
$247$	−473.841			−1.91839
$248$			70.4827i			0.284205i
$249$	−306.079	+	99.3819i	−1.22923	+	0.399124i
$250$	6.73017			0.0269207
$251$			303.412i			1.20881i	0.796677	+	0.604406i	$0.206589\pi$
$251$			303.412i			1.20881i	−0.796677	+	0.604406i	$0.793411\pi$
$252$	−70.0967	+	50.8844i	−0.278162	+	0.201922i
$253$	−89.7272			−0.354653
$254$		−	69.0881i		−	0.272000i
$255$	−54.5912	−	168.131i	−0.214083	−	0.659339i
$256$	54.2868			0.212058
$257$		−	280.197i		−	1.09026i	−0.838351	−	0.545131i	$-0.816480\pi$
$257$		−	280.197i		−	1.09026i	0.838351	−	0.545131i	$-0.183520\pi$
$258$	−114.561	+	37.1973i	−0.444036	+	0.144176i
$259$	−16.3306			−0.0630525
$260$		−	117.293i		−	0.451128i
$261$	−13.0841	−	18.0242i	−0.0501305	−	0.0690582i
$262$	−109.967			−0.419721
$263$		−	512.262i		−	1.94776i	−0.227053	−	0.973882i	$-0.572909\pi$
$263$		−	512.262i		−	1.94776i	0.227053	−	0.973882i	$-0.427091\pi$
$264$	59.2540	+	182.492i	0.224447	+	0.691257i
$265$	−18.7207			−0.0706441
$266$			52.3341i			0.196745i
$267$	−220.620	+	71.6338i	−0.826291	+	0.268291i
$268$	324.558			1.21104
$269$		−	229.299i		−	0.852413i	−0.904626	−	0.426207i	$-0.859850\pi$
$269$		−	229.299i		−	0.852413i	0.904626	−	0.426207i	$-0.140150\pi$
$270$	29.3889	+	21.3799i	0.108848	+	0.0791847i
$271$	−19.7332			−0.0728161			−0.0364080	−	0.999337i	$-0.511592\pi$
$271$	−19.7332			−0.0728161			−0.0364080	+	0.999337i	$0.511592\pi$
$272$		−	310.500i		−	1.14154i
$273$	35.3466	+	108.861i	0.129475	+	0.398760i
$274$	56.6176			0.206634
$275$		−	69.5548i		−	0.252926i
$276$	−66.9488	+	21.7379i	−0.242568	+	0.0787603i
$277$	278.622			1.00586			0.502928	−	0.864328i	$-0.332256\pi$
$277$	278.622			1.00586			0.502928	+	0.864328i	$0.332256\pi$
$278$		−	122.951i		−	0.442271i
$279$	111.656	−	81.0530i	0.400200	−	0.290512i
$280$	−27.1997			−0.0971418
$281$		−	308.710i		−	1.09861i	−0.835621	−	0.549306i	$-0.814892\pi$
$281$		−	308.710i		−	1.09861i	0.835621	−	0.549306i	$-0.185108\pi$
$282$	−25.1787	−	77.5460i	−0.0892861	−	0.274986i
$283$	−1.14603			−0.00404958			−0.00202479	−	0.999998i	$-0.500645\pi$
$283$	−1.14603			−0.00404958			−0.00202479	+	0.999998i	$0.500645\pi$
$284$			379.527i			1.33636i
$285$	−209.655	+	68.0737i	−0.735633	+	0.238855i
$286$	120.753			0.422212
$287$		−	130.721i		−	0.455473i
$288$	134.732	+	185.603i	0.467821	+	0.644455i
$289$	−405.408			−1.40280
$290$		−	3.33106i		−	0.0114864i
$291$	−16.3523	−	50.3624i	−0.0561936	−	0.173067i
$292$	305.508			1.04626
$293$			549.435i			1.87521i	0.347708	+	0.937603i	$0.386960\pi$
$293$			549.435i			1.87521i	−0.347708	+	0.937603i	$0.613040\pi$
$294$	12.0234	−	3.90391i	0.0408958	−	0.0132786i
$295$	76.6539			0.259844
$296$			28.3781i			0.0958720i
$297$	220.956	−	303.728i	0.743960	−	1.02265i
$298$	−45.8647			−0.153909
$299$			93.0113i			0.311074i
$300$	−16.8508	−	51.8974i	−0.0561692	−	0.172991i
$301$	−176.465			−0.586264
$302$			65.3685i			0.216452i
$303$	−259.017	+	84.1010i	−0.854840	+	0.277561i
$304$	−387.185			−1.27364
$305$			123.798i			0.405894i
$306$	115.533	−	83.8678i	0.377560	−	0.274078i
$307$	190.303			0.619878			0.309939	−	0.950756i	$-0.399691\pi$
$307$	190.303			0.619878			0.309939	+	0.950756i	$0.399691\pi$
$308$			133.883i			0.434685i
$309$	−72.9846	−	224.780i	−0.236196	−	0.727443i
$310$	20.6352			0.0665652
$311$			215.326i			0.692367i	0.938167	+	0.346183i	$0.112522\pi$
$311$			215.326i			0.692367i	−0.938167	+	0.346183i	$0.887478\pi$
$312$	189.171	−	61.4227i	0.606318	−	0.196868i
$313$	112.023			0.357900			0.178950	−	0.983858i	$-0.442730\pi$
$313$	112.023			0.357900			0.178950	+	0.983858i	$0.442730\pi$
$314$			43.5355i			0.138648i
$315$	31.2788	+	43.0887i	0.0992979	+	0.136789i
$316$	394.691			1.24902
$317$		−	75.6312i		−	0.238584i	−0.992859	−	0.119292i	$-0.961938\pi$
$317$		−	75.6312i		−	0.238584i	0.992859	−	0.119292i	$-0.0380625\pi$
$318$	−4.66916	−	14.3802i	−0.0146829	−	0.0452207i
$319$	−34.4257			−0.107918
$320$		−	71.0886i		−	0.222152i
$321$	48.7334	−	15.8234i	0.151817	−	0.0492942i
$322$	10.2728			0.0319030
$323$			865.908i			2.68083i
$324$	91.2807	−	280.153i	0.281731	−	0.864670i
$325$	−72.1005			−0.221848
$326$			21.2542i			0.0651968i
$327$	−49.7228	−	153.138i	−0.152057	−	0.468311i
$328$	−227.157			−0.692552
$329$		−	119.448i		−	0.363065i
$330$	53.4281	−	17.3478i	0.161903	−	0.0525690i
$331$	−136.605			−0.412703			−0.206351	−	0.978478i	$-0.566159\pi$
$331$	−136.605			−0.412703			−0.206351	+	0.978478i	$0.566159\pi$
$332$			390.208i			1.17533i
$333$	44.9554	−	32.6339i	0.135001	−	0.0979998i
$334$	−38.7624			−0.116055
$335$		−	199.507i		−	0.595543i
$336$	28.8824	+	88.9529i	0.0859596	+	0.264741i
$337$	178.151			0.528639			0.264319	−	0.964435i	$-0.414853\pi$
$337$	178.151			0.528639			0.264319	+	0.964435i	$0.414853\pi$
$338$		−	23.4402i		−	0.0693497i
$339$	−133.438	+	43.3266i	−0.393623	+	0.127807i
$340$	−214.344			−0.630424
$341$		−	213.260i		−	0.625396i
$342$	−104.581	−	144.067i	−0.305792	−	0.421249i
$343$	18.5203			0.0539949
$344$			306.648i			0.891420i
$345$	13.3623	+	41.1537i	0.0387314	+	0.119286i
$346$	−74.0082			−0.213897
$347$		−	568.284i		−	1.63771i	−0.574003	−	0.818853i	$-0.694610\pi$
$347$		−	568.284i		−	1.63771i	0.574003	−	0.818853i	$-0.305390\pi$
$348$	−25.6863	+	8.34019i	−0.0738113	+	0.0239661i
$349$	247.824			0.710098			0.355049	−	0.934848i	$-0.384464\pi$
$349$	247.824			0.710098			0.355049	+	0.934848i	$0.384464\pi$
$350$			7.96325i			0.0227521i
$351$	−314.845	−	229.043i	−0.896993	−	0.652545i
$352$	354.497			1.00709
$353$			79.0089i			0.223821i	0.993718	+	0.111911i	$0.0356970\pi$
$353$			79.0089i			0.223821i	−0.993718	+	0.111911i	$0.964303\pi$
$354$	19.1184	+	58.8812i	0.0540067	+	0.166331i
$355$	233.296			0.657173
$356$			281.260i			0.790055i
$357$	198.936	−	64.5931i	0.557243	−	0.180933i
$358$	183.325			0.512080
$359$			565.023i			1.57388i	0.617029	+	0.786941i	$0.288336\pi$
$359$			565.023i			1.57388i	−0.617029	+	0.786941i	$0.711664\pi$
$360$	74.8763	−	54.3541i	0.207990	−	0.150983i
$361$	718.764			1.99104
$362$		−	31.0725i		−	0.0858356i
$363$	−67.1824	−	206.910i	−0.185075	−	0.570000i
$364$	138.783			0.381273
$365$		−	187.796i		−	0.514511i
$366$	−95.0945	+	30.8766i	−0.259821	+	0.0843622i
$367$	−250.538			−0.682663			−0.341332	−	0.939943i	$-0.610878\pi$
$367$	−250.538			−0.682663			−0.341332	+	0.939943i	$0.610878\pi$
$368$			76.0014i			0.206526i
$369$	261.224	+	359.853i	0.707923	+	0.975211i
$370$	8.30825			0.0224547
$371$		−	22.1506i		−	0.0597052i
$372$	−51.6657	−	159.121i	−0.138886	−	0.427745i
$373$	316.476			0.848460			0.424230	−	0.905554i	$-0.360545\pi$
$373$	316.476			0.848460			0.424230	+	0.905554i	$0.360545\pi$
$374$		−	220.666i		−	0.590016i
$375$	−31.9015	+	10.3582i	−0.0850707	+	0.0276219i
$376$	−207.569			−0.552044
$377$			35.6857i			0.0946571i
$378$	−25.2970	+	34.7735i	−0.0669233	+	0.0919933i
$379$	−345.627			−0.911944			−0.455972	−	0.889994i	$-0.650708\pi$
$379$	−345.627			−0.911944			−0.455972	+	0.889994i	$0.650708\pi$
$380$			267.282i			0.703373i
$381$	106.331	+	327.483i	0.279085	+	0.859534i
$382$	−141.457			−0.370307
$383$		−	105.513i		−	0.275490i	−0.990468	−	0.137745i	$-0.956015\pi$
$383$		−	105.513i		−	0.275490i	0.990468	−	0.137745i	$-0.0439854\pi$
$384$	345.458	−	112.168i	0.899631	−	0.292104i
$385$	82.2983			0.213762
$386$			0.354525i			0.000918458i
$387$	485.780	−	352.636i	1.25525	−	0.911205i
$388$	−64.2051			−0.165477
$389$			649.735i			1.67027i	0.550045	+	0.835135i	$0.314610\pi$
$389$			649.735i			1.67027i	−0.550045	+	0.835135i	$0.685390\pi$
$390$	−17.9827	−	55.3836i	−0.0461095	−	0.142009i
$391$	169.971			0.434708
$392$		−	32.1831i		−	0.0820998i
$393$	521.251	−	169.247i	1.32634	−	0.430654i
$394$	155.034			0.393488
$395$		−	242.618i		−	0.614222i
$396$	−267.543	−	368.558i	−0.675613	−	0.930701i
$397$	−434.606			−1.09473			−0.547363	−	0.836896i	$-0.684368\pi$
$397$	−434.606			−1.09473			−0.547363	+	0.836896i	$0.684368\pi$
$398$		−	162.507i		−	0.408310i
$399$	−80.5459	−	248.068i	−0.201870	−	0.621723i
$400$	−58.9148			−0.147287
$401$		−	103.304i		−	0.257616i	−0.991670	−	0.128808i	$-0.958885\pi$
$401$		−	103.304i		−	0.257616i	0.991670	−	0.128808i	$-0.0411150\pi$
$402$	153.250	−	49.7593i	0.381219	−	0.123779i
$403$	−221.065			−0.548549
$404$			330.210i			0.817352i
$405$	−172.211	−	56.1105i	−0.425212	−	0.138545i
$406$	3.94136			0.00970779
$407$		−	85.8638i		−	0.210967i
$408$	−112.245	−	345.696i	−0.275111	−	0.847294i
$409$	636.470			1.55616			0.778081	−	0.628164i	$-0.216193\pi$
$409$	636.470			1.55616			0.778081	+	0.628164i	$0.216193\pi$
$410$			66.5047i			0.162206i
$411$	−268.372	+	87.1385i	−0.652972	+	0.212016i
$412$	−286.563			−0.695542
$413$			90.6981i			0.219608i
$414$	−28.2792	+	20.5284i	−0.0683073	+	0.0495855i
$415$	239.862			0.577982
$416$		−	367.472i		−	0.883346i
$417$	189.231	+	582.798i	0.453791	+	1.39760i
$418$	−275.165			−0.658289
$419$		−	30.8264i		−	0.0735714i	−0.999323	−	0.0367857i	$-0.988288\pi$
$419$		−	30.8264i		−	0.0735714i	0.999323	−	0.0367857i	$-0.0117119\pi$
$420$	61.4059	−	19.9381i	0.146204	−	0.0474717i
$421$	−86.9270			−0.206477			−0.103239	−	0.994657i	$-0.532921\pi$
$421$	−86.9270			−0.206477			−0.103239	+	0.994657i	$0.532921\pi$
$422$			43.4846i			0.103044i
$423$	238.698	+	328.822i	0.564297	+	0.777357i
$424$	−38.4917			−0.0907824
$425$			131.758i			0.310019i
$426$	58.1868	+	179.205i	0.136589	+	0.420670i
$427$	−146.479			−0.343043
$428$		−	62.1284i		−	0.145160i
$429$	−572.376	+	185.847i	−1.33421	+	0.433210i
$430$	89.7773			0.208784
$431$			590.048i			1.36902i	0.729003	+	0.684510i	$0.239984\pi$
$431$			590.048i			1.36902i	−0.729003	+	0.684510i	$0.760016\pi$
$432$	−257.266	−	187.156i	−0.595523	−	0.433231i
$433$	−676.914			−1.56331			−0.781656	−	0.623710i	$-0.785625\pi$
$433$	−676.914			−1.56331			−0.781656	+	0.623710i	$0.785625\pi$
$434$			24.4159i			0.0562578i
$435$	5.12674	+	15.7895i	0.0117856	+	0.0362976i
$436$	−195.229			−0.447774
$437$		−	211.949i		−	0.485009i
$438$	144.255	−	46.8386i	0.329349	−	0.106937i
$439$	−718.820			−1.63740			−0.818702	−	0.574219i	$-0.805306\pi$
$439$	−718.820			−1.63740			−0.818702	+	0.574219i	$0.805306\pi$
$440$		−	143.012i		−	0.325027i
$441$	−50.9832	+	37.0096i	−0.115608	+	0.0839220i
$442$	−228.743			−0.517517
$443$		−	14.8548i		−	0.0335322i	−0.999859	−	0.0167661i	$-0.994663\pi$
$443$		−	14.8548i		−	0.0335322i	0.999859	−	0.0167661i	$-0.00533707\pi$
$444$	−20.8019	−	64.0662i	−0.0468511	−	0.144293i
$445$	172.891			0.388520
$446$			15.7535i			0.0353217i
$447$	217.402	−	70.5891i	0.486359	−	0.157917i
$448$	84.1132			0.187753
$449$		−	861.857i		−	1.91950i	−0.280850	−	0.959752i	$-0.590616\pi$
$449$		−	861.857i		−	1.91950i	0.280850	−	0.959752i	$-0.409384\pi$
$450$	−15.9132	−	21.9215i	−0.0353627	−	0.0487145i
$451$	687.310			1.52397
$452$			170.115i			0.376362i
$453$	−100.607	−	309.852i	−0.222090	−	0.683999i
$454$	35.1016			0.0773163
$455$		−	85.3105i		−	0.187496i
$456$	−431.073	+	139.967i	−0.945337	+	0.306945i
$457$	−516.136			−1.12940			−0.564701	−	0.825296i	$-0.691008\pi$
$457$	−516.136			−1.12940			−0.564701	+	0.825296i	$0.691008\pi$
$458$			0.521989i			0.00113971i
$459$	−418.559	+	575.354i	−0.911892	+	1.25349i
$460$	52.4652			0.114055
$461$			433.972i			0.941370i	0.882301	+	0.470685i	$0.155993\pi$
$461$			433.972i			0.941370i	−0.882301	+	0.470685i	$0.844007\pi$
$462$	20.5261	+	63.2170i	0.0444289	+	0.136833i
$463$	−912.293			−1.97040			−0.985198	−	0.171421i	$-0.945164\pi$
$463$	−912.293			−1.97040			−0.985198	+	0.171421i	$0.945164\pi$
$464$			29.1596i			0.0628439i
$465$	−97.8124	+	31.7590i	−0.210349	+	0.0682990i
$466$	−24.3735			−0.0523037
$467$		−	366.923i		−	0.785701i	−0.919602	−	0.392851i	$-0.871489\pi$
$467$		−	366.923i		−	0.785701i	0.919602	−	0.392851i	$-0.128511\pi$
$468$	−382.047	+	277.335i	−0.816340	+	0.592596i
$469$	236.060			0.503326
$470$			60.7698i			0.129297i
$471$	−67.0043	−	206.362i	−0.142260	−	0.438135i
$472$	157.608			0.333916
$473$		−	927.828i		−	1.96158i
$474$	186.365	−	60.5117i	0.393176	−	0.127662i
$475$	164.299			0.345892
$476$		−	253.615i		−	0.532806i
$477$	44.2643	+	60.9770i	0.0927973	+	0.127834i
$478$	84.5155			0.176811
$479$			281.209i			0.587075i	0.955948	+	0.293538i	$0.0948326\pi$
$479$			281.209i			0.587075i	−0.955948	+	0.293538i	$0.905167\pi$
$480$	−52.7923	−	162.591i	−0.109984	−	0.338732i
$481$	−89.0065			−0.185045
$482$			193.284i			0.401005i
$483$	−48.6937	+	15.8105i	−0.100815	+	0.0327340i
$484$	−263.782			−0.545004
$485$			39.4671i			0.0813754i
$486$	0.149595	−	146.277i	0.000307809	−	0.300982i
$487$	−403.330			−0.828192			−0.414096	−	0.910233i	$-0.635902\pi$
$487$	−403.330			−0.828192			−0.414096	+	0.910233i	$0.635902\pi$
$488$			254.541i			0.521601i
$489$	−32.7117	−	100.746i	−0.0668951	−	0.206025i
$490$	−9.42224			−0.0192291
$491$			99.6221i			0.202896i	0.994841	+	0.101448i	$0.0323476\pi$
$491$			99.6221i			0.202896i	−0.994841	+	0.101448i	$0.967652\pi$
$492$	512.828	−	166.512i	1.04233	−	0.338439i
$493$	65.2129			0.132278
$494$			285.236i			0.577401i
$495$	−226.554	+	164.459i	−0.457684	+	0.332241i
$496$	−180.637			−0.364188
$497$			276.040i			0.555413i
$498$	59.8244	+	184.249i	0.120129	+	0.369978i
$499$	946.177			1.89615			0.948073	−	0.318053i	$-0.103029\pi$
$499$	946.177			1.89615			0.948073	+	0.318053i	$0.103029\pi$
$500$			40.6700i			0.0813401i
$501$	183.737	−	59.6581i	0.366740	−	0.119078i
$502$	182.643			0.363831
$503$		−	445.502i		−	0.885690i	−0.896598	−	0.442845i	$-0.853969\pi$
$503$		−	445.502i		−	0.885690i	0.896598	−	0.442845i	$-0.146031\pi$
$504$	64.3126	+	88.5949i	0.127604	+	0.175783i
$505$	202.981			0.401943
$506$			54.0126i			0.106744i
$507$	36.0761	+	111.108i	0.0711561	+	0.219148i
$508$	417.495			0.821840
$509$		−	341.812i		−	0.671537i	−0.941945	−	0.335768i	$-0.891004\pi$
$509$		−	341.812i		−	0.671537i	0.941945	−	0.335768i	$-0.108996\pi$
$510$	−101.209	+	32.8620i	−0.198449	+	0.0644353i
$511$	222.204			0.434841
$512$		−	516.962i		−	1.00969i
$513$	717.451	+	521.931i	1.39854	+	1.01741i
$514$	−168.669			−0.328150
$515$			176.151i			0.342041i
$516$	−224.781	−	692.287i	−0.435623	−	1.34164i
$517$	628.042			1.21478
$518$			9.83045i			0.0189777i
$519$	350.805	−	113.904i	0.675924	−	0.219468i
$520$	−148.246			−0.285089
$521$			205.431i			0.394302i	0.980373	+	0.197151i	$0.0631690\pi$
$521$			205.431i			0.394302i	−0.980373	+	0.197151i	$0.936831\pi$
$522$	−10.8499	+	7.87615i	−0.0207853	+	0.0150884i
$523$	187.368			0.358257			0.179128	−	0.983826i	$-0.442672\pi$
$523$	187.368			0.358257			0.179128	+	0.983826i	$0.442672\pi$
$524$		−	664.523i		−	1.26817i
$525$	−12.2560	−	37.7464i	−0.0233448	−	0.0718979i
$526$	−308.364			−0.586243
$527$			403.980i			0.766565i
$528$	−467.700	+	151.859i	−0.885796	+	0.287612i
$529$	487.396			0.921354
$530$			11.2692i			0.0212626i
$531$	−181.245	−	249.677i	−0.341327	−	0.470201i
$532$	−316.252			−0.594458
$533$		−	712.466i		−	1.33671i
$534$	43.1211	+	132.805i	0.0807510	+	0.248699i
$535$	−38.1905			−0.0713841
$536$		−	410.207i		−	0.765312i
$537$	−868.972	+	282.150i	−1.61820	+	0.525418i
$538$	−138.030			−0.256562
$539$			97.3767i			0.180662i
$540$	−129.197	+	177.596i	−0.239254	+	0.328881i
$541$	448.915			0.829788			0.414894	−	0.909870i	$-0.363819\pi$
$541$	448.915			0.829788			0.414894	+	0.909870i	$0.363819\pi$
$542$			11.8787i			0.0219164i
$543$	47.8228	+	147.286i	0.0880715	+	0.271245i
$544$	−671.526			−1.23442
$545$			120.008i			0.220198i
$546$	65.5308	−	21.2774i	0.120020	−	0.0389696i
$547$	43.5535			0.0796224			0.0398112	−	0.999207i	$-0.487324\pi$
$547$	43.5535			0.0796224			0.0398112	+	0.999207i	$0.487324\pi$
$548$			342.137i			0.624337i
$549$	403.234	−	292.715i	0.734488	−	0.533178i
$550$	−41.8695			−0.0761264
$551$		−	81.3188i		−	0.147584i
$552$	27.4744	+	84.6163i	0.0497724	+	0.153290i
$553$	287.069			0.519113
$554$		−	167.721i		−	0.302745i
$555$	−39.3817	+	12.7870i	−0.0709580	+	0.0230396i
$556$	742.987			1.33631
$557$		−	88.0769i		−	0.158127i	−0.996870	−	0.0790637i	$-0.974807\pi$
$557$		−	88.0769i		−	0.158127i	0.996870	−	0.0790637i	$-0.0251930\pi$
$558$	−48.7911	−	67.2129i	−0.0874392	−	0.120453i
$559$	−961.787			−1.72055
$560$		−	69.7089i		−	0.124480i
$561$	339.621	+	1045.97i	0.605385	+	1.86448i
$562$	−185.833			−0.330663
$563$			107.789i			0.191455i	0.995408	+	0.0957275i	$0.0305177\pi$
$563$			107.789i			0.191455i	−0.995408	+	0.0957275i	$0.969482\pi$
$564$	468.606	−	152.153i	0.830861	−	0.269775i
$565$	104.571			0.185081
$566$			0.689871i			0.00121885i
$567$	66.3909	−	203.763i	0.117092	−	0.359370i
$568$	479.682			0.844511
$569$		−	364.304i		−	0.640254i	−0.947375	−	0.320127i	$-0.896274\pi$
$569$		−	364.304i		−	0.640254i	0.947375	−	0.320127i	$-0.103726\pi$
$570$	40.9780	+	126.205i	0.0718913	+	0.221413i
$571$	224.369			0.392940			0.196470	−	0.980510i	$-0.437052\pi$
$571$	224.369			0.392940			0.196470	+	0.980510i	$0.437052\pi$
$572$			729.701i			1.27570i
$573$	670.517	−	217.713i	1.17019	−	0.379952i
$574$	−78.6894			−0.137089
$575$		−	32.2505i		−	0.0560879i
$576$	−231.550	+	168.086i	−0.401996	+	0.291816i
$577$	−715.857			−1.24065			−0.620327	−	0.784343i	$-0.713000\pi$
$577$	−715.857			−1.24065			−0.620327	+	0.784343i	$0.713000\pi$
$578$			244.041i			0.422217i
$579$	−0.545639	−	1.68047i	−0.000942382	−	0.00290237i
$580$	20.1294			0.0347059
$581$			283.809i			0.488484i
$582$	−30.3164	+	9.84354i	−0.0520900	+	0.0169133i
$583$	116.465			0.199768
$584$		−	386.129i		−	0.661180i
$585$	170.479	+	234.846i	0.291417	+	0.401446i
$586$	330.741			0.564404
$587$			845.989i			1.44121i	0.693347	+	0.720604i	$0.256135\pi$
$587$			845.989i			1.44121i	−0.693347	+	0.720604i	$0.743865\pi$
$588$	23.5911	+	72.6564i	0.0401209	+	0.123565i
$589$	503.752			0.855267
$590$		−	46.1430i		−	0.0782084i
$591$	−734.874	+	238.609i	−1.24344	+	0.403737i
$592$	−72.7290			−0.122853
$593$		−	129.000i		−	0.217537i	−0.994067	−	0.108769i	$-0.965309\pi$
$593$		−	129.000i		−	0.217537i	0.994067	−	0.108769i	$-0.0346908\pi$
$594$	−182.834	−	133.008i	−0.307801	−	0.223919i
$595$	−155.898			−0.262014
$596$		−	277.158i		−	0.465030i
$597$	250.110	+	770.297i	0.418946	+	1.29028i
$598$	55.9895			0.0936280
$599$		−	843.390i		−	1.40800i	−0.710202	−	0.703998i	$-0.751396\pi$
$599$		−	843.390i		−	1.40800i	0.710202	−	0.703998i	$-0.248604\pi$
$600$	−65.5929	+	21.2976i	−0.109321	+	0.0354960i
$601$	506.266			0.842372			0.421186	−	0.906974i	$-0.361614\pi$
$601$	506.266			0.842372			0.421186	+	0.906974i	$0.361614\pi$
$602$			106.226i			0.176455i
$603$	−649.833	+	471.726i	−1.07767	+	0.782298i
$604$	−395.018			−0.654003
$605$			162.148i			0.268012i
$606$	50.6259	+	155.919i	0.0835411	+	0.257292i
$607$	174.083			0.286793			0.143396	−	0.989665i	$-0.454198\pi$
$607$	174.083			0.286793			0.143396	+	0.989665i	$0.454198\pi$
$608$			837.375i			1.37726i
$609$	−18.6824	+	6.06604i	−0.0306771	+	0.00996066i
$610$	74.5219			0.122167
$611$		−	651.028i		−	1.06551i
$612$	506.808	+	698.162i	0.828117	+	1.14079i
$613$	1012.14			1.65113			0.825563	−	0.564311i	$-0.190858\pi$
$613$	1012.14			1.65113			0.825563	+	0.564311i	$0.190858\pi$
$614$		−	114.556i		−	0.186573i
$615$	−102.355	−	315.237i	−0.166432	−	0.512580i
$616$	169.214			0.274698
$617$			610.435i			0.989359i	0.869075	+	0.494680i	$0.164715\pi$
$617$			610.435i			0.989359i	−0.869075	+	0.494680i	$0.835285\pi$
$618$	−135.310	+	43.9342i	−0.218948	+	0.0710909i
$619$	341.015			0.550913			0.275457	−	0.961313i	$-0.411171\pi$
$619$	341.015			0.550913			0.275457	+	0.961313i	$0.411171\pi$
$620$			124.697i			0.201125i
$621$	102.451	−	140.830i	0.164977	−	0.226779i
$622$	129.619			0.208390
$623$			204.568i			0.328359i
$624$	157.418	+	484.819i	0.252272	+	0.776953i
$625$	25.0000			0.0400000
$626$		−	67.4337i		−	0.107722i
$627$	1304.30	−	423.498i	2.08022	−	0.675436i
$628$	−263.083			−0.418921
$629$			162.652i			0.258589i
$630$	25.9379	−	18.8288i	0.0411712	−	0.0298869i
$631$	−507.868			−0.804862			−0.402431	−	0.915450i	$-0.631835\pi$
$631$	−507.868			−0.804862			−0.402431	+	0.915450i	$0.631835\pi$
$632$		−	498.848i		−	0.789316i
$633$	−66.9260	−	206.120i	−0.105728	−	0.325625i
$634$	−45.5273			−0.0718097
$635$		−	256.635i		−	0.404150i
$636$	86.8986	−	28.2154i	0.136633	−	0.0443639i
$637$	100.941			0.158463
$638$			20.7231i			0.0324813i
$639$	−551.619	−	759.893i	−0.863254	−	1.18919i
$640$	−270.722			−0.423004
$641$		−	198.521i		−	0.309705i	−0.987938	−	0.154852i	$-0.950510\pi$
$641$		−	198.521i		−	0.309705i	0.987938	−	0.154852i	$-0.0494902\pi$
$642$	−9.52515	−	29.3358i	−0.0148367	−	0.0456944i
$643$	−221.828			−0.344988			−0.172494	−	0.985011i	$-0.555183\pi$
$643$	−221.828			−0.344988			−0.172494	+	0.985011i	$0.555183\pi$
$644$			62.0777i			0.0963939i
$645$	−425.551	+	138.174i	−0.659769	+	0.214223i
$646$	521.246			0.806883
$647$		−	689.916i		−	1.06633i	−0.846011	−	0.533165i	$-0.821002\pi$
$647$		−	689.916i		−	1.06633i	0.846011	−	0.533165i	$-0.178998\pi$
$648$	−354.084	−	115.369i	−0.546426	−	0.178039i
$649$	−476.877			−0.734787
$650$			43.4020i			0.0667723i
$651$	−37.5778	−	115.733i	−0.0577232	−	0.177778i
$652$	−128.438			−0.196990
$653$		−	699.877i		−	1.07179i	−0.844286	−	0.535893i	$-0.819975\pi$
$653$		−	699.877i		−	1.07179i	0.844286	−	0.535893i	$-0.180025\pi$
$654$	−92.1835	+	29.9314i	−0.140953	+	0.0457666i
$655$	−408.485			−0.623641
$656$		−	582.171i		−	0.887455i
$657$	−611.690	+	444.037i	−0.931036	+	0.675855i
$658$	−71.9038			−0.109276
$659$		−	456.764i		−	0.693117i	−0.938028	−	0.346558i	$-0.887350\pi$
$659$		−	456.764i		−	0.693117i	0.938028	−	0.346558i	$-0.112650\pi$
$660$	104.831	+	322.863i	0.158835	+	0.489186i
$661$	−1107.62			−1.67568			−0.837838	−	0.545919i	$-0.816181\pi$
$661$	−1107.62			−1.67568			−0.837838	+	0.545919i	$0.816181\pi$
$662$			82.2312i			0.124216i
$663$	1084.26	−	352.051i	1.63538	−	0.530997i
$664$	493.182			0.742745
$665$			194.401i			0.292332i
$666$	−19.6445	−	27.0616i	−0.0294962	−	0.0406330i
$667$	−15.9622			−0.0239314
$668$		−	234.239i		−	0.350657i
$669$	−24.2457	−	74.6727i	−0.0362418	−	0.111618i
$670$	−120.096			−0.179248
$671$		−	770.166i		−	1.14779i
$672$	192.381	−	62.4647i	0.286281	−	0.0929534i
$673$	−83.7969			−0.124513			−0.0622563	−	0.998060i	$-0.519830\pi$
$673$	−83.7969			−0.124513			−0.0622563	+	0.998060i	$0.519830\pi$
$674$		−	107.241i		−	0.159111i
$675$	109.169	+	79.4180i	0.161731	+	0.117656i
$676$	141.648			0.209538
$677$			925.656i			1.36729i	0.729814	+	0.683646i	$0.239607\pi$
$677$			925.656i			1.36729i	−0.729814	+	0.683646i	$0.760393\pi$
$678$	26.0811	+	80.3252i	0.0384677	+	0.118474i
$679$	−46.6981			−0.0687748
$680$			270.909i			0.398395i
$681$	−166.384	+	54.0239i	−0.244323	+	0.0793302i
$682$	−128.375			−0.188233
$683$		−	433.374i		−	0.634516i	−0.948339	−	0.317258i	$-0.897238\pi$
$683$		−	433.374i		−	0.634516i	0.948339	−	0.317258i	$-0.102762\pi$
$684$	870.589	−	631.976i	1.27279	−	0.923941i
$685$	210.313			0.307026
$686$		−	11.1485i		−	0.0162515i
$687$	−0.803379	−	2.47427i	−0.00116940	−	0.00360155i
$688$	−785.896			−1.14229
$689$		−	120.727i		−	0.175221i
$690$	24.7731	−	8.04366i	0.0359030	−	0.0116575i
$691$	−111.697			−0.161645			−0.0808227	−	0.996728i	$-0.525755\pi$
$691$	−111.697			−0.161645			−0.0808227	+	0.996728i	$0.525755\pi$
$692$		−	447.227i		−	0.646282i
$693$	−194.591	−	268.062i	−0.280795	−	0.386814i
$694$	−342.087			−0.492921
$695$		−	456.717i		−	0.657146i
$696$	10.5411	+	32.4648i	0.0151453	+	0.0466449i
$697$	−1301.98			−1.86797
$698$		−	149.182i		−	0.213727i
$699$	115.532	−	37.5126i	0.165282	−	0.0536661i
$700$	−48.1214			−0.0687449
$701$			167.123i			0.238406i	0.992870	+	0.119203i	$0.0380340\pi$
$701$			167.123i			0.238406i	−0.992870	+	0.119203i	$0.961966\pi$
$702$	−137.876	+	189.525i	−0.196405	+	0.269979i
$703$	202.823			0.288511
$704$			442.254i			0.628202i
$705$	−93.5291	−	288.053i	−0.132665	−	0.408586i
$706$	47.5606			0.0673663
$707$			240.171i			0.339704i
$708$	−355.816	+	115.531i	−0.502565	+	0.163179i
$709$	−21.1580			−0.0298420			−0.0149210	−	0.999889i	$-0.504750\pi$
$709$	−21.1580			−0.0298420			−0.0149210	+	0.999889i	$0.504750\pi$
$710$		−	140.436i		−	0.197798i
$711$	−790.254	+	573.660i	−1.11147	+	0.806835i
$712$	355.483			0.499273
$713$		−	98.8825i		−	0.138685i
$714$	−38.8828	−	119.752i	−0.0544577	−	0.167720i
$715$	448.549			0.627342
$716$			1107.82i			1.54723i
$717$	−400.610	+	130.075i	−0.558730	+	0.181416i
$718$	340.124			0.473711
$719$			1179.82i			1.64091i	0.571710	+	0.820456i	$0.306280\pi$
$719$			1179.82i			1.64091i	−0.571710	+	0.820456i	$0.693720\pi$
$720$	139.302	+	191.897i	0.193474	+	0.266524i
$721$	−208.425			−0.289078
$722$		−	432.671i		−	0.599267i
$723$	−297.478	−	916.182i	−0.411450	−	1.26719i
$724$	187.769			0.259350
$725$		−	12.3736i		−	0.0170670i
$726$	−124.553	+	40.4415i	−0.171560	+	0.0557045i
$727$	−1221.16			−1.67973			−0.839865	−	0.542796i	$-0.817366\pi$
$727$	−1221.16			−1.67973			−0.839865	+	0.542796i	$0.817366\pi$
$728$		−	175.407i		−	0.240944i
$729$	224.422	+	693.596i	0.307850	+	0.951435i
$730$	−113.047			−0.154859
$731$			1757.59i			2.40436i
$732$	−186.585	−	574.650i	−0.254898	−	0.785041i
$733$	−1144.56			−1.56147			−0.780733	−	0.624864i	$-0.785154\pi$
$733$	−1144.56			−1.56147			−0.780733	+	0.624864i	$0.785154\pi$
$734$			150.815i			0.205470i
$735$	44.6621	−	14.5015i	0.0607648	−	0.0197299i
$736$	164.370			0.223329
$737$			1241.17i			1.68408i
$738$	216.619	−	157.247i	0.293521	−	0.213072i
$739$	280.928			0.380147			0.190073	−	0.981770i	$-0.439127\pi$
$739$	280.928			0.380147			0.190073	+	0.981770i	$0.439127\pi$
$740$			50.2062i			0.0678462i
$741$	−438.999	−	1352.04i	−0.592441	−	1.82461i
$742$	−13.3339			−0.0179702
$743$		−	893.045i		−	1.20194i	−0.799270	−	0.600972i	$-0.794780\pi$
$743$		−	893.045i		−	1.20194i	0.799270	−	0.600972i	$-0.205220\pi$
$744$	−201.113	+	65.2999i	−0.270313	+	0.0877687i
$745$	−170.370			−0.228684
$746$		−	190.507i		−	0.255372i
$747$	−567.145	−	781.279i	−0.759230	−	1.04589i
$748$	1333.47			1.78272
$749$		−	45.1876i		−	0.0603306i
$750$	6.23529	+	19.2036i	0.00831372	+	0.0256048i
$751$	324.337			0.431874			0.215937	−	0.976407i	$-0.430719\pi$
$751$	324.337			0.431874			0.215937	+	0.976407i	$0.430719\pi$
$752$		−	531.969i		−	0.707405i
$753$	−865.742	+	281.101i	−1.14972	+	0.373308i
$754$	21.4816			0.0284901
$755$			242.819i			0.321614i
$756$	−210.134	−	152.868i	−0.277955	−	0.202207i
$757$	1340.90			1.77133			0.885667	−	0.464320i	$-0.153701\pi$
$757$	1340.90			1.77133			0.885667	+	0.464320i	$0.153701\pi$
$758$			208.055i			0.274479i
$759$	−83.1293	−	256.024i	−0.109525	−	0.337317i
$760$	337.816			0.444494
$761$			1137.24i			1.49441i	0.664595	+	0.747204i	$0.268604\pi$
$761$			1137.24i			1.49441i	−0.664595	+	0.747204i	$0.731396\pi$
$762$	197.133	−	64.0078i	0.258705	−	0.0839998i
$763$	−141.995			−0.186102
$764$		−	854.817i		−	1.11887i
$765$	429.162	−	311.536i	0.560996	−	0.407237i
$766$	−63.5149			−0.0829176
$767$			494.331i			0.644499i
$768$	50.2950	+	154.900i	0.0654883	+	0.201692i
$769$	169.550			0.220482			0.110241	−	0.993905i	$-0.464838\pi$
$769$	169.550			0.220482			0.110241	+	0.993905i	$0.464838\pi$
$770$		−	49.5407i		−	0.0643386i
$771$	799.503	−	259.594i	1.03697	−	0.336697i
$772$	−2.14237			−0.00277509
$773$		−	184.687i		−	0.238922i	−0.992839	−	0.119461i	$-0.961883\pi$
$773$		−	184.687i		−	0.238922i	0.992839	−	0.119461i	$-0.0381166\pi$
$774$	−212.275	−	292.423i	−0.274257	−	0.377807i
$775$	76.6518			0.0989055
$776$			81.1484i			0.104573i
$777$	−15.1298	−	46.5971i	−0.0194720	−	0.0599705i
$778$	391.118			0.502722
$779$			1623.53i			2.08412i
$780$	334.680	−	108.668i	0.429077	−	0.139318i
$781$	−1451.38			−1.85836
$782$		−	102.316i		−	0.130839i
$783$	39.3075	−	54.0324i	0.0502011	−	0.0690069i
$784$	82.4807			0.105205
$785$			161.718i			0.206010i
$786$	−101.881	−	313.775i	−0.129619	−	0.399205i
$787$	310.405			0.394415			0.197208	−	0.980362i	$-0.436813\pi$
$787$	310.405			0.394415			0.197208	+	0.980362i	$0.436813\pi$
$788$			936.863i			1.18891i
$789$	1461.67	−	474.594i	1.85256	−	0.601514i
$790$	−146.047			−0.184870
$791$			123.730i			0.156422i
$792$	−465.818	+	338.146i	−0.588154	+	0.426952i
$793$	−798.355			−1.00675
$794$			261.618i			0.329493i
$795$	−17.3441	−	53.4169i	−0.0218165	−	0.0671910i
$796$	982.022			1.23370
$797$		−	260.415i		−	0.326744i	−0.986565	−	0.163372i	$-0.947763\pi$
$797$		−	260.415i		−	0.326744i	0.986565	−	0.163372i	$-0.0522371\pi$
$798$	−149.328	+	48.4858i	−0.187128	+	0.0607592i
$799$	−1189.70			−1.48899
$800$			127.416i			0.159271i
$801$	−408.794	−	563.141i	−0.510355	−	0.703047i
$802$	−62.1853			−0.0775378
$803$			1168.31i			1.45494i
$804$	300.692	+	926.080i	0.373996	+	1.15184i
$805$	38.1594			0.0474029
$806$			133.074i			0.165104i
$807$	654.273	−	212.438i	0.810747	−	0.263244i
$808$	417.351			0.516524
$809$		−	1459.20i		−	1.80371i	−0.432038	−	0.901855i	$-0.642205\pi$
$809$		−	1459.20i		−	1.80371i	0.432038	−	0.901855i	$-0.357795\pi$
$810$	−33.7766	+	103.665i	−0.0416995	+	0.127981i
$811$	−1017.56			−1.25470			−0.627351	−	0.778737i	$-0.715861\pi$
$811$	−1017.56			−1.25470			−0.627351	+	0.778737i	$0.715861\pi$
$812$			23.8174i			0.0293318i
$813$	−18.2821	−	56.3058i	−0.0224872	−	0.0692568i
$814$	−51.6870			−0.0634975
$815$			78.9510i			0.0968724i
$816$	885.968	−	287.668i	1.08575	−	0.352535i
$817$	2191.67			2.68258
$818$		−	383.133i		−	0.468377i
$819$	−277.873	+	201.713i	−0.339283	+	0.246292i
$820$	−401.884			−0.490102
$821$		−	1247.75i		−	1.51979i	−0.650043	−	0.759897i	$-0.725249\pi$
$821$		−	1247.75i		−	1.51979i	0.650043	−	0.759897i	$-0.274751\pi$
$822$	52.4544	+	161.550i	0.0638131	+	0.196533i
$823$	−1223.50			−1.48663			−0.743315	−	0.668942i	$-0.766747\pi$
$823$	−1223.50			−1.48663			−0.743315	+	0.668942i	$0.766747\pi$
$824$			362.186i			0.439546i
$825$	198.465	−	64.4402i	0.240563	−	0.0781094i
$826$	54.5971			0.0660982
$827$		−	807.623i		−	0.976569i	−0.872684	−	0.488285i	$-0.837623\pi$
$827$		−	807.623i		−	0.976569i	0.872684	−	0.488285i	$-0.162377\pi$
$828$	−124.052	−	170.890i	−0.149821	−	0.206388i
$829$	101.597			0.122554			0.0612769	−	0.998121i	$-0.480483\pi$
$829$	101.597			0.122554			0.0612769	+	0.998121i	$0.480483\pi$
$830$		−	144.389i		−	0.173962i
$831$	258.134	+	795.009i	0.310631	+	0.956690i
$832$	458.441			0.551011
$833$		−	184.461i		−	0.221442i
$834$	350.824	−	113.910i	0.420652	−	0.136583i
$835$	−143.987			−0.172440
$836$		−	1662.80i		−	1.98900i
$837$	334.719	+	243.501i	0.399903	+	0.290922i
$838$	−18.5564			−0.0221437
$839$			903.447i			1.07681i	0.842685	+	0.538407i	$0.180974\pi$
$839$			903.447i			1.07681i	−0.842685	+	0.538407i	$0.819026\pi$
$840$	−25.1997	−	77.6106i	−0.0299996	−	0.0923935i
$841$	834.876			0.992718
$842$			52.3270i			0.0621461i
$843$	880.860	−	286.010i	1.04491	−	0.339276i
$844$	−262.775			−0.311345
$845$		−	87.0713i		−	0.103043i
$846$	197.939	−	143.688i	0.233971	−	0.169844i
$847$	−191.856			−0.226512
$848$		−	98.6487i		−	0.116331i
$849$	−1.06176	−	3.27004i	−0.00125060	−	0.00385164i
$850$	79.3138			0.0933103
$851$		−	39.8126i		−	0.0467833i
$852$	−1082.93	+	351.619i	−1.27104	+	0.412699i
$853$	1047.32			1.22781			0.613906	−	0.789379i	$-0.289597\pi$
$853$	1047.32			1.22781			0.613906	+	0.789379i	$0.289597\pi$
$854$			88.1755i			0.103250i
$855$	−388.478	−	535.154i	−0.454360	−	0.625911i
$856$	−78.5237			−0.0917333
$857$		−	292.707i		−	0.341549i	−0.985310	−	0.170774i	$-0.945373\pi$
$857$		−	292.707i		−	0.341549i	0.985310	−	0.170774i	$-0.0546269\pi$
$858$	111.873	+	344.551i	0.130389	+	0.401574i
$859$	1180.23			1.37396			0.686978	−	0.726679i	$-0.258937\pi$
$859$	1180.23			1.37396			0.686978	+	0.726679i	$0.258937\pi$
$860$			542.519i			0.630836i
$861$	372.993	−	121.109i	0.433210	−	0.140660i
$862$	355.188			0.412051
$863$			585.282i			0.678195i	0.940751	+	0.339097i	$0.110122\pi$
$863$			585.282i			0.678195i	−0.940751	+	0.339097i	$0.889878\pi$
$864$	−404.767	+	556.395i	−0.468480	+	0.643976i
$865$	−274.912			−0.317817
$866$			407.479i			0.470530i
$867$	−375.597	−	1156.77i	−0.433215	−	1.33423i
$868$	−147.544			−0.169981
$869$			1509.37i			1.73690i
$870$	9.50471	−	3.08612i	0.0109250	−	0.00354726i
$871$	1286.59			1.47714
$872$			246.749i			0.282969i
$873$	128.552	−	93.3182i	0.147253	−	0.106894i
$874$	−127.586			−0.145979
$875$			29.5804i			0.0338062i
$876$	283.043	+	871.723i	0.323108	+	0.995117i
$877$	−633.918			−0.722826			−0.361413	−	0.932406i	$-0.617706\pi$
$877$	−633.918			−0.722826			−0.361413	+	0.932406i	$0.617706\pi$
$878$			432.705i			0.492830i
$879$	−1567.74	+	509.034i	−1.78355	+	0.579106i
$880$	366.519			0.416499
$881$			768.947i			0.872812i	0.899750	+	0.436406i	$0.143749\pi$
$881$			768.947i			0.872812i	−0.899750	+	0.436406i	$0.856251\pi$
$882$	22.2785	+	30.6901i	0.0252591	+	0.0347960i
$883$	1399.21			1.58461			0.792307	−	0.610123i	$-0.208880\pi$
$883$	1399.21			1.58461			0.792307	+	0.610123i	$0.208880\pi$
$884$		−	1382.28i		−	1.56366i
$885$	71.0173	+	218.721i	0.0802456	+	0.247142i
$886$	−8.94205			−0.0100926
$887$		−	983.746i		−	1.10907i	−0.832160	−	0.554536i	$-0.812896\pi$
$887$		−	983.746i		−	1.10907i	0.832160	−	0.554536i	$-0.187104\pi$
$888$	−80.9729	+	26.2914i	−0.0911857	+	0.0296074i
$889$	303.655			0.341569
$890$		−	104.074i		−	0.116938i
$891$	1071.35	+	349.073i	1.20242	+	0.391777i
$892$	−95.1973			−0.106723
$893$			1483.53i			1.66129i
$894$	−42.4922	−	130.869i	−0.0475304	−	0.146385i
$895$	680.980			0.760872
$896$		−	320.323i		−	0.357503i
$897$	−265.395	+	86.1719i	−0.295869	+	0.0960668i
$898$	−518.808			−0.577737
$899$		−	37.9384i		−	0.0422006i
$900$	132.470	−	96.1626i	0.147189	−	0.106847i
$901$	−220.620			−0.244861
$902$		−	413.737i		−	0.458688i
$903$	−163.489	−	503.519i	−0.181051	−	0.557607i
$904$	215.008			0.237841
$905$		−	115.422i		−	0.127539i
$906$	−186.520	+	60.5618i	−0.205872	+	0.0668453i
$907$	−492.124			−0.542584			−0.271292	−	0.962497i	$-0.587451\pi$
$907$	−492.124			−0.542584			−0.271292	+	0.962497i	$0.587451\pi$
$908$			212.117i			0.233609i
$909$	−479.941	−	661.150i	−0.527988	−	0.727338i
$910$	−51.3539			−0.0564329
$911$		−	421.958i		−	0.463181i	−0.972813	−	0.231590i	$-0.925607\pi$
$911$		−	421.958i		−	0.463181i	0.972813	−	0.231590i	$-0.0743929\pi$
$912$	−358.715	−	1104.78i	−0.393327	−	1.21138i
$913$	−1492.22			−1.63442
$914$			310.696i			0.339930i
$915$	−353.239	+	114.695i	−0.386054	+	0.125349i
$916$	−3.15435			−0.00344361
$917$		−	483.326i		−	0.527073i
$918$	346.343	+	251.958i	0.377280	+	0.274464i
$919$	418.168			0.455025			0.227513	−	0.973775i	$-0.426941\pi$
$919$	418.168			0.455025			0.227513	+	0.973775i	$0.426941\pi$
$920$		−	66.3105i		−	0.0720766i
$921$	176.309	+	543.002i	0.191432	+	0.589579i
$922$	261.236			0.283336
$923$			1504.50i			1.63001i
$924$	−382.016	+	124.038i	−0.413437	+	0.134240i
$925$	30.8619			0.0333642
$926$			549.169i			0.593055i
$927$	573.760	−	416.502i	0.618942	−	0.449301i
$928$	63.0641			0.0679570
$929$		−	401.518i		−	0.432205i	−0.976371	−	0.216102i	$-0.930665\pi$
$929$		−	401.518i		−	0.432205i	0.976371	−	0.216102i	$-0.0693345\pi$
$930$	19.1178	+	58.8796i	0.0205568	+	0.0633114i
$931$	−230.018			−0.247066
$932$		−	147.288i		−	0.158034i
$933$	−614.402	+	199.493i	−0.658524	+	0.213818i
$934$	−220.875			−0.236482
$935$		−	819.689i		−	0.876673i
$936$	350.522	+	482.868i	0.374489	+	0.515884i
$937$	1064.01			1.13555			0.567777	−	0.823182i	$-0.307803\pi$
$937$	1064.01			1.13555			0.567777	+	0.823182i	$0.307803\pi$
$938$		−	142.100i		−	0.151492i
$939$	103.785	+	319.641i	0.110527	+	0.340406i
$940$	−367.228			−0.390668
$941$		−	1360.41i		−	1.44570i	−0.691003	−	0.722852i	$-0.742831\pi$
$941$		−	1360.41i		−	1.44570i	0.691003	−	0.722852i	$-0.257169\pi$
$942$	−124.222	+	40.3342i	−0.131871	+	0.0428177i
$943$	318.686			0.337949
$944$			403.928i			0.427890i
$945$	−93.9687	+	129.170i	−0.0994377	+	0.136688i
$946$	−558.520			−0.590401
$947$		−	443.635i		−	0.468463i	−0.972181	−	0.234232i	$-0.924743\pi$
$947$		−	443.635i		−	0.468463i	0.972181	−	0.234232i	$-0.0752574\pi$
$948$	365.668	+	1126.20i	0.385726	+	1.18797i
$949$	1211.07			1.27616
$950$		−	98.9022i		−	0.104108i
$951$	215.803	−	70.0698i	0.226922	−	0.0736802i
$952$	−320.543			−0.336705
$953$		−	403.805i		−	0.423720i	−0.977300	−	0.211860i	$-0.932048\pi$
$953$		−	403.805i		−	0.423720i	0.977300	−	0.211860i	$-0.0679521\pi$
$954$	36.7060	−	26.6456i	0.0384759	−	0.0279304i
$955$	−525.459			−0.550219
$956$			510.722i			0.534228i
$957$	−31.8943	−	98.2290i	−0.0333274	−	0.102643i
$958$	169.278			0.176699
$959$			248.845i			0.259484i
$960$	202.841	−	65.8613i	0.211293	−	0.0686055i
$961$	−725.980			−0.755442
$962$			53.5788i			0.0556952i
$963$	90.2998	+	124.394i	0.0937693	+	0.129173i
$964$	−1168.01			−1.21162
$965$			1.31692i			0.00136469i
$966$	9.51738	+	29.3119i	0.00985236	+	0.0303436i
$967$	−175.071			−0.181046			−0.0905229	−	0.995894i	$-0.528854\pi$
$967$	−175.071			−0.181046			−0.0905229	+	0.995894i	$0.528854\pi$
$968$			333.392i			0.344414i
$969$	−2470.75	+	802.236i	−2.54979	+	0.827900i
$970$	23.7578			0.0244926
$971$		−	208.135i		−	0.214351i	−0.994240	−	0.107176i	$-0.965819\pi$
$971$		−	208.135i		−	0.214351i	0.994240	−	0.107176i	$-0.0341807\pi$
$972$	883.946	+	0.903993i	0.909409	+	0.000930034i
$973$	540.394			0.555390
$974$			242.790i			0.249271i
$975$	−66.7988	−	205.729i	−0.0685116	−	0.211004i
$976$	−652.352			−0.668394
$977$		−	1182.66i		−	1.21050i	−0.796034	−	0.605252i	$-0.793072\pi$
$977$		−	1182.66i		−	1.21050i	0.796034	−	0.605252i	$-0.206928\pi$
$978$	−60.6458	+	19.6913i	−0.0620100	+	0.0201342i
$979$	−1075.59			−1.09866
$980$		−	56.9380i		−	0.0581000i
$981$	390.890	−	283.754i	0.398461	−	0.289250i
$982$	59.9690			0.0610683
$983$		−	236.302i		−	0.240389i	−0.992750	−	0.120195i	$-0.961648\pi$
$983$		−	236.302i		−	0.240389i	0.992750	−	0.120195i	$-0.0383518\pi$
$984$	−210.454	−	648.160i	−0.213876	−	0.658700i
$985$	575.892			0.584662
$986$		−	39.2559i		−	0.0398133i
$987$	340.829	−	110.665i	0.345318	−	0.112123i
$988$	−1723.66			−1.74460
$989$		−	430.207i		−	0.434992i
$990$	98.9987	+	136.377i	0.0999987	+	0.137755i
$991$	−1180.48			−1.19120			−0.595598	−	0.803283i	$-0.703085\pi$
$991$	−1180.48			−1.19120			−0.595598	+	0.803283i	$0.703085\pi$
$992$			390.668i			0.393819i
$993$	−126.560	−	389.782i	−0.127452	−	0.392530i
$994$	166.166			0.167169
$995$		−	603.652i		−	0.606686i
$996$	−1113.40	+	361.515i	−1.11788	+	0.362967i
$997$	−727.390			−0.729579			−0.364790	−	0.931090i	$-0.618859\pi$
$997$	−727.390			−0.729579			−0.364790	+	0.931090i	$0.618859\pi$
$998$		−	569.565i		−	0.570707i
$999$	134.766	+	98.0397i	0.134901	+	0.0981379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.7	✓	16
3.2	odd	2	inner	105.3.c.a.71.10	yes	16
4.3	odd	2		1680.3.l.a.1121.9		16
5.2	odd	4		525.3.f.b.449.20		32
5.3	odd	4		525.3.f.b.449.14		32
5.4	even	2		525.3.c.b.176.10		16
12.11	even	2		1680.3.l.a.1121.10		16
15.2	even	4		525.3.f.b.449.13		32
15.8	even	4		525.3.f.b.449.19		32
15.14	odd	2		525.3.c.b.176.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.7	✓	16	1.1	even	1	trivial
105.3.c.a.71.10	yes	16	3.2	odd	2	inner
525.3.c.b.176.7		16	15.14	odd	2
525.3.c.b.176.10		16	5.4	even	2
525.3.f.b.449.13		32	15.2	even	4
525.3.f.b.449.14		32	5.3	odd	4
525.3.f.b.449.19		32	15.8	even	4
525.3.f.b.449.20		32	5.2	odd	4
1680.3.l.a.1121.9		16	4.3	odd	2
1680.3.l.a.1121.10		16	12.11	even	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.601965i q^{2} +(0.926467 + 2.85336i) q^{3} +3.63764 q^{4} -2.23607i q^{5} +(1.71762 - 0.557701i) q^{6} +2.64575 q^{7} -4.59759i q^{8} +(-7.28332 + 5.28709i) q^{9} +O(q^{10})\)	\(q-0.601965i q^{2} +(0.926467 + 2.85336i) q^{3} +3.63764 q^{4} -2.23607i q^{5} +(1.71762 - 0.557701i) q^{6} +2.64575 q^{7} -4.59759i q^{8} +(-7.28332 + 5.28709i) q^{9} -1.34603 q^{10} +13.9110i q^{11} +(3.37015 + 10.3795i) q^{12} +14.4201 q^{13} -1.59265i q^{14} +(6.38030 - 2.07164i) q^{15} +11.7830 q^{16} -26.3516i q^{17} +(3.18264 + 4.38430i) q^{18} -32.8598 q^{19} -8.13401i q^{20} +(2.45120 + 7.54928i) q^{21} +8.37391 q^{22} +6.45011i q^{23} +(13.1186 - 4.25952i) q^{24} -5.00000 q^{25} -8.68040i q^{26} +(-21.8337 - 15.8836i) q^{27} +9.62429 q^{28} +2.47472i q^{29} +(-1.24706 - 3.84072i) q^{30} -15.3304 q^{31} -25.4833i q^{32} +(-39.6929 + 12.8880i) q^{33} -15.8628 q^{34} -5.91608i q^{35} +(-26.4941 + 19.2325i) q^{36} -6.17239 q^{37} +19.7804i q^{38} +(13.3598 + 41.1457i) q^{39} -10.2805 q^{40} -49.4078i q^{41} +(4.54440 - 1.47554i) q^{42} -66.6976 q^{43} +50.6030i q^{44} +(11.8223 + 16.2860i) q^{45} +3.88274 q^{46} -45.1473i q^{47} +(10.9165 + 33.6210i) q^{48} +7.00000 q^{49} +3.00983i q^{50} +(75.1906 - 24.4139i) q^{51} +52.4551 q^{52} -8.37215i q^{53} +(-9.56137 + 13.1431i) q^{54} +31.1058 q^{55} -12.1641i q^{56} +(-30.4435 - 93.7607i) q^{57} +1.48970 q^{58} +34.2807i q^{59} +(23.2092 - 7.53589i) q^{60} -55.3640 q^{61} +9.22834i q^{62} +(-19.2698 + 13.9883i) q^{63} +31.7918 q^{64} -32.2443i q^{65} +(7.75815 + 23.8938i) q^{66} +89.2222 q^{67} -95.8576i q^{68} +(-18.4045 + 5.97582i) q^{69} -3.56127 q^{70} +104.333i q^{71} +(24.3079 + 33.4857i) q^{72} +83.9851 q^{73} +3.71556i q^{74} +(-4.63234 - 14.2668i) q^{75} -119.532 q^{76} +36.8049i q^{77} +(24.7683 - 8.04211i) q^{78} +108.502 q^{79} -26.3475i q^{80} +(25.0934 - 77.0151i) q^{81} -29.7418 q^{82} +107.270i q^{83} +(8.91659 + 27.4615i) q^{84} -58.9240 q^{85} +40.1496i q^{86} +(-7.06127 + 2.29275i) q^{87} +63.9569 q^{88} +77.3193i q^{89} +(9.80360 - 7.11660i) q^{90} +38.1520 q^{91} +23.4632i q^{92} +(-14.2031 - 43.7430i) q^{93} -27.1771 q^{94} +73.4767i q^{95} +(72.7130 - 23.6094i) q^{96} -17.6502 q^{97} -4.21376i q^{98} +(-73.5484 - 101.318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

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