LMFDB - Embedded newform 1155.2.c.d.694.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.2
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.d.694.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.67513 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.67513 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(2.80606 + 2.48119i) q^{10} +1.00000 q^{11} -0.806063i q^{12} -4.48119i q^{13} -1.67513 q^{14} +(-1.67513 - 1.48119i) q^{15} -4.96239 q^{16} +3.15633i q^{17} +1.67513i q^{18} -0.350262 q^{19} +(1.19394 - 1.35026i) q^{20} +1.00000 q^{21} -1.67513i q^{22} -2.19394i q^{23} +2.00000 q^{24} +(-0.612127 - 4.96239i) q^{25} -7.50659 q^{26} -1.00000i q^{27} +0.806063i q^{28} +9.48119 q^{29} +(-2.48119 + 2.80606i) q^{30} -0.0630040 q^{31} +4.31265i q^{32} +1.00000i q^{33} +5.28726 q^{34} +(1.67513 + 1.48119i) q^{35} +0.806063 q^{36} -9.44358i q^{37} +0.586734i q^{38} +4.48119 q^{39} +(3.35026 + 2.96239i) q^{40} -6.86907 q^{41} -1.67513i q^{42} -7.79384i q^{43} -0.806063 q^{44} +(1.48119 - 1.67513i) q^{45} -3.67513 q^{46} -3.98778i q^{47} -4.96239i q^{48} -1.00000 q^{49} +(-8.31265 + 1.02539i) q^{50} -3.15633 q^{51} +3.61213i q^{52} -7.31265i q^{53} -1.67513 q^{54} +(-1.48119 + 1.67513i) q^{55} -2.00000 q^{56} -0.350262i q^{57} -15.8822i q^{58} +5.24965 q^{59} +(1.35026 + 1.19394i) q^{60} -7.73084 q^{61} +0.105540i q^{62} +1.00000i q^{63} -2.70052 q^{64} +(7.50659 + 6.63752i) q^{65} +1.67513 q^{66} -11.1490i q^{67} -2.54420i q^{68} +2.19394 q^{69} +(2.48119 - 2.80606i) q^{70} -1.13093 q^{71} +2.00000i q^{72} -0.649738i q^{73} -15.8192 q^{74} +(4.96239 - 0.612127i) q^{75} +0.282333 q^{76} -1.00000i q^{77} -7.50659i q^{78} +3.93700 q^{79} +(7.35026 - 8.31265i) q^{80} +1.00000 q^{81} +11.5066i q^{82} -4.19394i q^{83} -0.806063 q^{84} +(-5.28726 - 4.67513i) q^{85} -13.0557 q^{86} +9.48119i q^{87} -2.00000i q^{88} +3.35519 q^{89} +(-2.80606 - 2.48119i) q^{90} -4.48119 q^{91} +1.76845i q^{92} -0.0630040i q^{93} -6.68006 q^{94} +(0.518806 - 0.586734i) q^{95} -4.31265 q^{96} +2.64481i q^{97} +1.67513i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} + 16 q^{10} + 6 q^{11} - 8 q^{16} + 18 q^{19} + 8 q^{20} + 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 46 q^{29} - 4 q^{30} + 8 q^{31} + 20 q^{34} + 4 q^{36} + 16 q^{39} - 32 q^{41} - 4 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} - 8 q^{50} + 2 q^{51} + 2 q^{55} - 12 q^{56} - 2 q^{59} - 12 q^{60} - 2 q^{61} + 24 q^{64} + 4 q^{65} + 14 q^{69} + 4 q^{70} - 16 q^{71} - 12 q^{74} + 8 q^{75} - 36 q^{76} + 32 q^{79} + 24 q^{80} + 6 q^{81} - 4 q^{84} - 20 q^{85} - 44 q^{86} + 26 q^{89} - 16 q^{90} - 16 q^{91} - 56 q^{94} + 14 q^{95} + 16 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 + 16 * q^10 + 6 * q^11 - 8 * q^16 + 18 * q^19 + 8 * q^20 + 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 46 * q^29 - 4 * q^30 + 8 * q^31 + 20 * q^34 + 4 * q^36 + 16 * q^39 - 32 * q^41 - 4 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 - 8 * q^50 + 2 * q^51 + 2 * q^55 - 12 * q^56 - 2 * q^59 - 12 * q^60 - 2 * q^61 + 24 * q^64 + 4 * q^65 + 14 * q^69 + 4 * q^70 - 16 * q^71 - 12 * q^74 + 8 * q^75 - 36 * q^76 + 32 * q^79 + 24 * q^80 + 6 * q^81 - 4 * q^84 - 20 * q^85 - 44 * q^86 + 26 * q^89 - 16 * q^90 - 16 * q^91 - 56 * q^94 + 14 * q^95 + 16 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$		−	1.67513i		−	1.18450i	−0.805756	−	0.592248i	$-0.798240\pi$
$2$		−	1.67513i		−	1.18450i	0.805756	−	0.592248i	$-0.201760\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.806063			−0.403032
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$6$	1.67513			0.683869
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	2.00000i		−	0.707107i
$9$	−1.00000			−0.333333
$10$	2.80606	+	2.48119i	0.887355	+	0.784623i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.806063i		−	0.232690i
$13$		−	4.48119i		−	1.24286i	−0.783470	−	0.621430i	$-0.786552\pi$
$13$		−	4.48119i		−	1.24286i	0.783470	−	0.621430i	$-0.213448\pi$
$14$	−1.67513			−0.447698
$15$	−1.67513	−	1.48119i	−0.432517	−	0.382443i
$16$	−4.96239			−1.24060
$17$			3.15633i			0.765521i	0.923848	+	0.382761i	$0.125027\pi$
$17$			3.15633i			0.765521i	−0.923848	+	0.382761i	$0.874973\pi$
$18$			1.67513i			0.394832i
$19$	−0.350262			−0.0803556			−0.0401778	−	0.999193i	$-0.512792\pi$
$19$	−0.350262			−0.0803556			−0.0401778	+	0.999193i	$0.512792\pi$
$20$	1.19394	−	1.35026i	0.266972	−	0.301928i
$21$	1.00000			0.218218
$22$		−	1.67513i		−	0.357139i
$23$		−	2.19394i		−	0.457467i	−0.973489	−	0.228734i	$-0.926541\pi$
$23$		−	2.19394i		−	0.457467i	0.973489	−	0.228734i	$-0.0734585\pi$
$24$	2.00000			0.408248
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$	−7.50659			−1.47216
$27$		−	1.00000i		−	0.192450i
$28$			0.806063i			0.152332i
$29$	9.48119			1.76061			0.880307	−	0.474405i	$-0.157337\pi$
$29$	9.48119			1.76061			0.880307	+	0.474405i	$0.157337\pi$
$30$	−2.48119	+	2.80606i	−0.453002	+	0.512315i
$31$	−0.0630040			−0.0113159			−0.00565793	−	0.999984i	$-0.501801\pi$
$31$	−0.0630040			−0.0113159			−0.00565793	+	0.999984i	$0.501801\pi$
$32$			4.31265i			0.762376i
$33$			1.00000i			0.174078i
$34$	5.28726			0.906757
$35$	1.67513	+	1.48119i	0.283149	+	0.250368i
$36$	0.806063			0.134344
$37$		−	9.44358i		−	1.55252i	−0.630416	−	0.776258i	$-0.717116\pi$
$37$		−	9.44358i		−	1.55252i	0.630416	−	0.776258i	$-0.282884\pi$
$38$			0.586734i			0.0951809i
$39$	4.48119			0.717565
$40$	3.35026	+	2.96239i	0.529723	+	0.468395i
$41$	−6.86907			−1.07277			−0.536384	−	0.843974i	$-0.680210\pi$
$41$	−6.86907			−1.07277			−0.536384	+	0.843974i	$0.680210\pi$
$42$		−	1.67513i		−	0.258478i
$43$		−	7.79384i		−	1.18855i	−0.804262	−	0.594275i	$-0.797439\pi$
$43$		−	7.79384i		−	1.18855i	0.804262	−	0.594275i	$-0.202561\pi$
$44$	−0.806063			−0.121519
$45$	1.48119	−	1.67513i	0.220803	−	0.249714i
$46$	−3.67513			−0.541868
$47$		−	3.98778i		−	0.581678i	−0.956772	−	0.290839i	$-0.906066\pi$
$47$		−	3.98778i		−	0.581678i	0.956772	−	0.290839i	$-0.0939343\pi$
$48$		−	4.96239i		−	0.716259i
$49$	−1.00000			−0.142857
$50$	−8.31265	+	1.02539i	−1.17559	+	0.145012i
$51$	−3.15633			−0.441974
$52$			3.61213i			0.500912i
$53$		−	7.31265i		−	1.00447i	−0.864731	−	0.502235i	$-0.832511\pi$
$53$		−	7.31265i		−	1.00447i	0.864731	−	0.502235i	$-0.167489\pi$
$54$	−1.67513			−0.227956
$55$	−1.48119	+	1.67513i	−0.199724	+	0.225875i
$56$	−2.00000			−0.267261
$57$		−	0.350262i		−	0.0463933i
$58$		−	15.8822i		−	2.08544i
$59$	5.24965			0.683446			0.341723	−	0.939801i	$-0.388990\pi$
$59$	5.24965			0.683446			0.341723	+	0.939801i	$0.388990\pi$
$60$	1.35026	+	1.19394i	0.174318	+	0.154137i
$61$	−7.73084			−0.989833			−0.494916	−	0.868941i	$-0.664801\pi$
$61$	−7.73084			−0.989833			−0.494916	+	0.868941i	$0.664801\pi$
$62$			0.105540i			0.0134036i
$63$			1.00000i			0.125988i
$64$	−2.70052			−0.337565
$65$	7.50659	+	6.63752i	0.931078	+	0.823283i
$66$	1.67513			0.206194
$67$		−	11.1490i		−	1.36207i	−0.732250	−	0.681035i	$-0.761530\pi$
$67$		−	11.1490i		−	1.36207i	0.732250	−	0.681035i	$-0.238470\pi$
$68$		−	2.54420i		−	0.308529i
$69$	2.19394			0.264119
$70$	2.48119	−	2.80606i	0.296559	−	0.335389i
$71$	−1.13093			−0.134217			−0.0671085	−	0.997746i	$-0.521377\pi$
$71$	−1.13093			−0.134217			−0.0671085	+	0.997746i	$0.521377\pi$
$72$			2.00000i			0.235702i
$73$		−	0.649738i		−	0.0760461i	−0.999277	−	0.0380231i	$-0.987894\pi$
$73$		−	0.649738i		−	0.0760461i	0.999277	−	0.0380231i	$-0.0121060\pi$
$74$	−15.8192			−1.83895
$75$	4.96239	−	0.612127i	0.573007	−	0.0706823i
$76$	0.282333			0.0323858
$77$		−	1.00000i		−	0.113961i
$78$		−	7.50659i		−	0.849954i
$79$	3.93700			0.442947			0.221473	−	0.975166i	$-0.428913\pi$
$79$	3.93700			0.442947			0.221473	+	0.975166i	$0.428913\pi$
$80$	7.35026	−	8.31265i	0.821784	−	0.929383i
$81$	1.00000			0.111111
$82$			11.5066i			1.27069i
$83$		−	4.19394i		−	0.460344i	−0.973150	−	0.230172i	$-0.926071\pi$
$83$		−	4.19394i		−	0.460344i	0.973150	−	0.230172i	$-0.0739289\pi$
$84$	−0.806063			−0.0879487
$85$	−5.28726	−	4.67513i	−0.573484	−	0.507089i
$86$	−13.0557			−1.40783
$87$			9.48119i			1.01649i
$88$		−	2.00000i		−	0.213201i
$89$	3.35519			0.355649			0.177825	−	0.984062i	$-0.443094\pi$
$89$	3.35519			0.355649			0.177825	+	0.984062i	$0.443094\pi$
$90$	−2.80606	−	2.48119i	−0.295785	−	0.261541i
$91$	−4.48119			−0.469757
$92$			1.76845i			0.184374i
$93$		−	0.0630040i		−	0.00653321i
$94$	−6.68006			−0.688995
$95$	0.518806	−	0.586734i	0.0532283	−	0.0601977i
$96$	−4.31265			−0.440158
$97$			2.64481i			0.268540i	0.990945	+	0.134270i	$0.0428690\pi$
$97$			2.64481i			0.268540i	−0.990945	+	0.134270i	$0.957131\pi$
$98$			1.67513i			0.169214i
$99$	−1.00000			−0.100504
$100$	0.493413	+	4.00000i	0.0493413	+	0.400000i
$101$	14.6253			1.45527			0.727636	−	0.685964i	$-0.240619\pi$
$101$	14.6253			1.45527			0.727636	+	0.685964i	$0.240619\pi$
$102$			5.28726i			0.523517i
$103$		−	1.09332i		−	0.107728i	−0.998548	−	0.0538641i	$-0.982846\pi$
$103$		−	1.09332i		−	0.107728i	0.998548	−	0.0538641i	$-0.0171538\pi$
$104$	−8.96239			−0.878835
$105$	−1.48119	+	1.67513i	−0.144550	+	0.163476i
$106$	−12.2496			−1.18979
$107$			16.4363i			1.58896i	0.607293	+	0.794478i	$0.292255\pi$
$107$			16.4363i			1.58896i	−0.607293	+	0.794478i	$0.707745\pi$
$108$			0.806063i			0.0775635i
$109$	−2.58673			−0.247764			−0.123882	−	0.992297i	$-0.539534\pi$
$109$	−2.58673			−0.247764			−0.123882	+	0.992297i	$0.539534\pi$
$110$	2.80606	+	2.48119i	0.267548	+	0.236573i
$111$	9.44358			0.896345
$112$			4.96239i			0.468902i
$113$			7.46898i			0.702622i	0.936259	+	0.351311i	$0.114264\pi$
$113$			7.46898i			0.702622i	−0.936259	+	0.351311i	$0.885736\pi$
$114$	−0.586734			−0.0549527
$115$	3.67513	+	3.24965i	0.342708	+	0.303031i
$116$	−7.64244			−0.709583
$117$			4.48119i			0.414287i
$118$		−	8.79384i		−	0.809539i
$119$	3.15633			0.289340
$120$	−2.96239	+	3.35026i	−0.270428	+	0.305836i
$121$	1.00000			0.0909091
$122$			12.9502i			1.17245i
$123$		−	6.86907i		−	0.619363i
$124$	0.0507852			0.00456065
$125$	9.21933	+	6.32487i	0.824602	+	0.565713i
$126$	1.67513			0.149233
$127$			2.33804i			0.207468i	0.994605	+	0.103734i	$0.0330790\pi$
$127$			2.33804i			0.207468i	−0.994605	+	0.103734i	$0.966921\pi$
$128$			13.1490i			1.16222i
$129$	7.79384			0.686210
$130$	11.1187	−	12.5745i	0.975176	−	1.10286i
$131$	−9.25694			−0.808783			−0.404391	−	0.914586i	$-0.632517\pi$
$131$	−9.25694			−0.808783			−0.404391	+	0.914586i	$0.632517\pi$
$132$		−	0.806063i		−	0.0701588i
$133$			0.350262i			0.0303715i
$134$	−18.6761			−1.61337
$135$	1.67513	+	1.48119i	0.144172	+	0.127481i
$136$	6.31265			0.541305
$137$		−	0.806063i		−	0.0688666i	−0.999407	−	0.0344333i	$-0.989037\pi$
$137$		−	0.806063i		−	0.0688666i	0.999407	−	0.0344333i	$-0.0109626\pi$
$138$		−	3.67513i		−	0.312848i
$139$	19.2447			1.63232			0.816158	−	0.577829i	$-0.196100\pi$
$139$	19.2447			1.63232			0.816158	+	0.577829i	$0.196100\pi$
$140$	−1.35026	−	1.19394i	−0.114118	−	0.100906i
$141$	3.98778			0.335832
$142$			1.89446i			0.158980i
$143$		−	4.48119i		−	0.374736i
$144$	4.96239			0.413532
$145$	−14.0435	+	15.8822i	−1.16625	+	1.31895i
$146$	−1.08840			−0.0900763
$147$		−	1.00000i		−	0.0824786i
$148$			7.61213i			0.625713i
$149$	−6.62530			−0.542766			−0.271383	−	0.962471i	$-0.587481\pi$
$149$	−6.62530			−0.542766			−0.271383	+	0.962471i	$0.587481\pi$
$150$	−1.02539	−	8.31265i	−0.0837230	−	0.678725i
$151$	−5.68735			−0.462830			−0.231415	−	0.972855i	$-0.574336\pi$
$151$	−5.68735			−0.462830			−0.231415	+	0.972855i	$0.574336\pi$
$152$			0.700523i			0.0568200i
$153$		−	3.15633i		−	0.255174i
$154$	−1.67513			−0.134986
$155$	0.0933212	−	0.105540i	0.00749574	−	0.00847717i
$156$	−3.61213			−0.289202
$157$		−	5.30043i		−	0.423020i	−0.977376	−	0.211510i	$-0.932162\pi$
$157$		−	5.30043i		−	0.423020i	0.977376	−	0.211510i	$-0.0678382\pi$
$158$		−	6.59498i		−	0.524669i
$159$	7.31265			0.579931
$160$	−7.22425	−	6.38787i	−0.571127	−	0.505006i
$161$	−2.19394			−0.172906
$162$		−	1.67513i		−	0.131611i
$163$			17.1065i			1.33988i	0.742413	+	0.669942i	$0.233681\pi$
$163$			17.1065i			1.33988i	−0.742413	+	0.669942i	$0.766319\pi$
$164$	5.53690			0.432360
$165$	−1.67513	−	1.48119i	−0.130409	−	0.115311i
$166$	−7.02539			−0.545276
$167$		−	3.76845i		−	0.291612i	−0.989313	−	0.145806i	$-0.953423\pi$
$167$		−	3.76845i		−	0.291612i	0.989313	−	0.145806i	$-0.0465775\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−7.08110			−0.544700
$170$	−7.83146	+	8.85685i	−0.600645	+	0.679289i
$171$	0.350262			0.0267852
$172$			6.28233i			0.479023i
$173$			22.2677i			1.69299i	0.532400	+	0.846493i	$0.321290\pi$
$173$			22.2677i			1.69299i	−0.532400	+	0.846493i	$0.678710\pi$
$174$	15.8822			1.20403
$175$	−4.96239	+	0.612127i	−0.375121	+	0.0462724i
$176$	−4.96239			−0.374054
$177$			5.24965i			0.394588i
$178$		−	5.62038i		−	0.421265i
$179$	−25.4191			−1.89992			−0.949958	−	0.312377i	$-0.898875\pi$
$179$	−25.4191			−1.89992			−0.949958	+	0.312377i	$0.898875\pi$
$180$	−1.19394	+	1.35026i	−0.0889908	+	0.100643i
$181$	−11.6629			−0.866897			−0.433449	−	0.901178i	$-0.642703\pi$
$181$	−11.6629			−0.866897			−0.433449	+	0.901178i	$0.642703\pi$
$182$			7.50659i			0.556425i
$183$		−	7.73084i		−	0.571480i
$184$	−4.38787			−0.323478
$185$	15.8192	+	13.9878i	1.16305	+	1.02840i
$186$	−0.105540			−0.00773856
$187$			3.15633i			0.230813i
$188$			3.21440i			0.234435i
$189$	−1.00000			−0.0727393
$190$	−0.982857	−	0.869067i	−0.0713039	−	0.0630488i
$191$	2.76116			0.199790			0.0998952	−	0.994998i	$-0.468149\pi$
$191$	2.76116			0.199790			0.0998952	+	0.994998i	$0.468149\pi$
$192$		−	2.70052i		−	0.194893i
$193$		−	2.31265i		−	0.166468i	−0.996530	−	0.0832341i	$-0.973475\pi$
$193$		−	2.31265i		−	0.166468i	0.996530	−	0.0832341i	$-0.0265249\pi$
$194$	4.43041			0.318085
$195$	−6.63752	+	7.50659i	−0.475323	+	0.537558i
$196$	0.806063			0.0575760
$197$			24.2374i			1.72685i	0.504481	+	0.863423i	$0.331684\pi$
$197$			24.2374i			1.72685i	−0.504481	+	0.863423i	$0.668316\pi$
$198$			1.67513i			0.119046i
$199$	3.79877			0.269288			0.134644	−	0.990894i	$-0.457011\pi$
$199$	3.79877			0.269288			0.134644	+	0.990894i	$0.457011\pi$
$200$	−9.92478	+	1.22425i	−0.701788	+	0.0865678i
$201$	11.1490			0.786392
$202$		−	24.4993i		−	1.72376i
$203$		−	9.48119i		−	0.665449i
$204$	2.54420			0.178130
$205$	10.1744	−	11.5066i	0.710613	−	0.803655i
$206$	−1.83146			−0.127604
$207$			2.19394i			0.152489i
$208$			22.2374i			1.54189i
$209$	−0.350262			−0.0242281
$210$	2.80606	+	2.48119i	0.193637	+	0.171219i
$211$	−1.61213			−0.110983			−0.0554917	−	0.998459i	$-0.517673\pi$
$211$	−1.61213			−0.110983			−0.0554917	+	0.998459i	$0.517673\pi$
$212$			5.89446i			0.404833i
$213$		−	1.13093i		−	0.0774902i
$214$	27.5329			1.88211
$215$	13.0557	+	11.5442i	0.890392	+	0.787308i
$216$	−2.00000			−0.136083
$217$			0.0630040i			0.00427699i
$218$			4.33312i			0.293476i
$219$	0.649738			0.0439052
$220$	1.19394	−	1.35026i	0.0804952	−	0.0910346i
$221$	14.1441			0.951436
$222$		−	15.8192i		−	1.06172i
$223$		−	10.7562i		−	0.720291i	−0.932896	−	0.360145i	$-0.882727\pi$
$223$		−	10.7562i		−	0.720291i	0.932896	−	0.360145i	$-0.117273\pi$
$224$	4.31265			0.288151
$225$	0.612127	+	4.96239i	0.0408085	+	0.330826i
$226$	12.5115			0.832253
$227$			26.6629i			1.76968i	0.465895	+	0.884840i	$0.345732\pi$
$227$			26.6629i			1.76968i	−0.465895	+	0.884840i	$0.654268\pi$
$228$			0.282333i			0.0186980i
$229$	9.33804			0.617075			0.308538	−	0.951212i	$-0.400160\pi$
$229$	9.33804			0.617075			0.308538	+	0.951212i	$0.400160\pi$
$230$	5.44358	−	6.15633i	0.358939	−	0.405936i
$231$	1.00000			0.0657952
$232$		−	18.9624i		−	1.24494i
$233$		−	11.3380i		−	0.742780i	−0.928477	−	0.371390i	$-0.878881\pi$
$233$		−	11.3380i		−	0.742780i	0.928477	−	0.371390i	$-0.121119\pi$
$234$	7.50659			0.490721
$235$	6.68006	+	5.90668i	0.435759	+	0.385309i
$236$	−4.23155			−0.275450
$237$			3.93700i			0.255735i
$238$		−	5.28726i		−	0.342722i
$239$	17.8749			1.15623			0.578117	−	0.815954i	$-0.303788\pi$
$239$	17.8749			1.15623			0.578117	+	0.815954i	$0.303788\pi$
$240$	8.31265	+	7.35026i	0.536579	+	0.474457i
$241$	1.43136			0.0922023			0.0461011	−	0.998937i	$-0.485320\pi$
$241$	1.43136			0.0922023			0.0461011	+	0.998937i	$0.485320\pi$
$242$		−	1.67513i		−	0.107681i
$243$			1.00000i			0.0641500i
$244$	6.23155			0.398934
$245$	1.48119	−	1.67513i	0.0946300	−	0.107020i
$246$	−11.5066			−0.733633
$247$			1.56959i			0.0998707i
$248$			0.126008i			0.00800152i
$249$	4.19394			0.265780
$250$	10.5950	−	15.4436i	0.670086	−	0.976738i
$251$	−0.775746			−0.0489647			−0.0244823	−	0.999700i	$-0.507794\pi$
$251$	−0.775746			−0.0489647			−0.0244823	+	0.999700i	$0.507794\pi$
$252$		−	0.806063i		−	0.0507772i
$253$		−	2.19394i		−	0.137932i
$254$	3.91653			0.245745
$255$	4.67513	−	5.28726i	0.292768	−	0.331101i
$256$	16.6253			1.03908
$257$		−	24.0386i		−	1.49948i	−0.661730	−	0.749742i	$-0.730177\pi$
$257$		−	24.0386i		−	1.49948i	0.661730	−	0.749742i	$-0.269823\pi$
$258$		−	13.0557i		−	0.812813i
$259$	−9.44358			−0.586796
$260$	−6.05079	−	5.35026i	−0.375254	−	0.331809i
$261$	−9.48119			−0.586871
$262$			15.5066i			0.958000i
$263$		−	10.7757i		−	0.664461i	−0.943198	−	0.332230i	$-0.892199\pi$
$263$		−	10.7757i		−	0.664461i	0.943198	−	0.332230i	$-0.107801\pi$
$264$	2.00000			0.123091
$265$	12.2496	+	10.8315i	0.752490	+	0.665371i
$266$	0.586734			0.0359750
$267$			3.35519i			0.205334i
$268$			8.98683i			0.548958i
$269$	−21.9502			−1.33833			−0.669163	−	0.743116i	$-0.733347\pi$
$269$	−21.9502			−1.33833			−0.669163	+	0.743116i	$0.733347\pi$
$270$	2.48119	−	2.80606i	0.151001	−	0.170772i
$271$	19.7064			1.19708			0.598539	−	0.801093i	$-0.295748\pi$
$271$	19.7064			1.19708			0.598539	+	0.801093i	$0.295748\pi$
$272$		−	15.6629i		−	0.949704i
$273$		−	4.48119i		−	0.271214i
$274$	−1.35026			−0.0815723
$275$	−0.612127	−	4.96239i	−0.0369126	−	0.299243i
$276$	−1.76845			−0.106448
$277$		−	14.0303i		−	0.843000i	−0.906828	−	0.421500i	$-0.861504\pi$
$277$		−	14.0303i		−	0.843000i	0.906828	−	0.421500i	$-0.138496\pi$
$278$		−	32.2374i		−	1.93347i
$279$	0.0630040			0.00377195
$280$	2.96239	−	3.35026i	0.177037	−	0.200216i
$281$	−2.18076			−0.130093			−0.0650467	−	0.997882i	$-0.520720\pi$
$281$	−2.18076			−0.130093			−0.0650467	+	0.997882i	$0.520720\pi$
$282$		−	6.68006i		−	0.397792i
$283$			18.0082i			1.07048i	0.844700	+	0.535240i	$0.179779\pi$
$283$			18.0082i			1.07048i	−0.844700	+	0.535240i	$0.820221\pi$
$284$	0.911603			0.0540937
$285$	0.586734	+	0.518806i	0.0347551	+	0.0307314i
$286$	−7.50659			−0.443874
$287$			6.86907i			0.405468i
$288$		−	4.31265i		−	0.254125i
$289$	7.03761			0.413977
$290$	26.6048	+	23.5247i	1.56229	+	1.38142i
$291$	−2.64481			−0.155042
$292$			0.523730i			0.0306490i
$293$		−	10.4617i		−	0.611178i	−0.952164	−	0.305589i	$-0.901147\pi$
$293$		−	10.4617i		−	0.611178i	0.952164	−	0.305589i	$-0.0988533\pi$
$294$	−1.67513			−0.0976956
$295$	−7.77575	+	8.79384i	−0.452721	+	0.511997i
$296$	−18.8872			−1.09779
$297$		−	1.00000i		−	0.0580259i
$298$			11.0982i			0.642904i
$299$	−9.83146			−0.568568
$300$	−4.00000	+	0.493413i	−0.230940	+	0.0284872i
$301$	−7.79384			−0.449230
$302$			9.52705i			0.548220i
$303$			14.6253i			0.840202i
$304$	1.73813			0.0996889
$305$	11.4509	−	12.9502i	0.655675	−	0.741525i
$306$	−5.28726			−0.302252
$307$		−	13.1392i		−	0.749893i	−0.927047	−	0.374946i	$-0.877661\pi$
$307$		−	13.1392i		−	0.749893i	0.927047	−	0.374946i	$-0.122339\pi$
$308$			0.806063i			0.0459297i
$309$	1.09332			0.0621969
$310$	−0.176793	−	0.156325i	−0.0100412	−	0.00887867i
$311$	−17.7743			−1.00789			−0.503945	−	0.863736i	$-0.668119\pi$
$311$	−17.7743			−1.00789			−0.503945	+	0.863736i	$0.668119\pi$
$312$		−	8.96239i		−	0.507395i
$313$			29.9356i			1.69206i	0.533136	+	0.846030i	$0.321013\pi$
$313$			29.9356i			1.69206i	−0.533136	+	0.846030i	$0.678987\pi$
$314$	−8.87892			−0.501066
$315$	−1.67513	−	1.48119i	−0.0943829	−	0.0834558i
$316$	−3.17347			−0.178522
$317$		−	17.0581i		−	0.958077i	−0.877794	−	0.479039i	$-0.840985\pi$
$317$		−	17.0581i		−	0.958077i	0.877794	−	0.479039i	$-0.159015\pi$
$318$		−	12.2496i		−	0.686926i
$319$	9.48119			0.530845
$320$	4.00000	−	4.52373i	0.223607	−	0.252884i
$321$	−16.4363			−0.917384
$322$			3.67513i			0.204807i
$323$		−	1.10554i		−	0.0615139i
$324$	−0.806063			−0.0447813
$325$	−22.2374	+	2.74306i	−1.23351	+	0.152158i
$326$	28.6556			1.58709
$327$		−	2.58673i		−	0.143047i
$328$			13.7381i			0.758562i
$329$	−3.98778			−0.219853
$330$	−2.48119	+	2.80606i	−0.136585	+	0.154469i
$331$	20.9102			1.14933			0.574664	−	0.818389i	$-0.305133\pi$
$331$	20.9102			1.14933			0.574664	+	0.818389i	$0.305133\pi$
$332$			3.38058i			0.185533i
$333$			9.44358i			0.517505i
$334$	−6.31265			−0.345413
$335$	18.6761	+	16.5139i	1.02038	+	0.902250i
$336$	−4.96239			−0.270720
$337$		−	13.9199i		−	0.758263i	−0.925343	−	0.379131i	$-0.876223\pi$
$337$		−	13.9199i		−	0.758263i	0.925343	−	0.379131i	$-0.123777\pi$
$338$			11.8618i			0.645195i
$339$	−7.46898			−0.405659
$340$	4.26187	+	3.76845i	0.231132	+	0.204373i
$341$	−0.0630040			−0.00341186
$342$		−	0.586734i		−	0.0317270i
$343$			1.00000i			0.0539949i
$344$	−15.5877			−0.840432
$345$	−3.24965	+	3.67513i	−0.174955	+	0.197862i
$346$	37.3014			2.00533
$347$			2.25202i			0.120895i	0.998171	+	0.0604473i	$0.0192527\pi$
$347$			2.25202i			0.120895i	−0.998171	+	0.0604473i	$0.980747\pi$
$348$		−	7.64244i		−	0.409678i
$349$	24.6121			1.31746			0.658728	−	0.752381i	$-0.271095\pi$
$349$	24.6121			1.31746			0.658728	+	0.752381i	$0.271095\pi$
$350$	1.02539	+	8.31265i	0.0548095	+	0.444330i
$351$	−4.48119			−0.239188
$352$			4.31265i			0.229865i
$353$		−	14.8119i		−	0.788360i	−0.919033	−	0.394180i	$-0.871029\pi$
$353$		−	14.8119i		−	0.788360i	0.919033	−	0.394180i	$-0.128971\pi$
$354$	8.79384			0.467388
$355$	1.67513	−	1.89446i	0.0889067	−	0.100547i
$356$	−2.70449			−0.143338
$357$			3.15633i			0.167050i
$358$			42.5804i			2.25044i
$359$	−4.20616			−0.221992			−0.110996	−	0.993821i	$-0.535404\pi$
$359$	−4.20616			−0.221992			−0.110996	+	0.993821i	$0.535404\pi$
$360$	−3.35026	−	2.96239i	−0.176574	−	0.156132i
$361$	−18.8773			−0.993543
$362$			19.5369i			1.02684i
$363$			1.00000i			0.0524864i
$364$	3.61213			0.189327
$365$	1.08840	+	0.962389i	0.0569693	+	0.0503737i
$366$	−12.9502			−0.676916
$367$			16.2628i			0.848912i	0.905448	+	0.424456i	$0.139535\pi$
$367$			16.2628i			0.848912i	−0.905448	+	0.424456i	$0.860465\pi$
$368$			10.8872i			0.567533i
$369$	6.86907			0.357589
$370$	23.4314	−	26.4993i	1.21814	−	1.37763i
$371$	−7.31265			−0.379654
$372$			0.0507852i			0.00263309i
$373$			14.8519i			0.769003i	0.923124	+	0.384502i	$0.125627\pi$
$373$			14.8519i			0.769003i	−0.923124	+	0.384502i	$0.874373\pi$
$374$	5.28726			0.273398
$375$	−6.32487	+	9.21933i	−0.326615	+	0.476084i
$376$	−7.97556			−0.411308
$377$		−	42.4871i		−	2.18820i
$378$			1.67513i			0.0861594i
$379$	10.6180			0.545410			0.272705	−	0.962098i	$-0.412082\pi$
$379$	10.6180			0.545410			0.272705	+	0.962098i	$0.412082\pi$
$380$	−0.418190	+	0.472945i	−0.0214527	+	0.0242616i
$381$	−2.33804			−0.119782
$382$		−	4.62530i		−	0.236651i
$383$		−	34.6131i		−	1.76865i	−0.466876	−	0.884323i	$-0.654620\pi$
$383$		−	34.6131i		−	1.76865i	0.466876	−	0.884323i	$-0.345380\pi$
$384$	−13.1490			−0.671009
$385$	1.67513	+	1.48119i	0.0853726	+	0.0754887i
$386$	−3.87399			−0.197181
$387$			7.79384i			0.396183i
$388$		−	2.13189i		−	0.108230i
$389$	28.1343			1.42646			0.713232	−	0.700928i	$-0.247231\pi$
$389$	28.1343			1.42646			0.713232	+	0.700928i	$0.247231\pi$
$390$	12.5745	+	11.1187i	0.636735	+	0.563018i
$391$	6.92478			0.350201
$392$			2.00000i			0.101015i
$393$		−	9.25694i		−	0.466951i
$394$	40.6009			2.04544
$395$	−5.83146	+	6.59498i	−0.293412	+	0.331830i
$396$	0.806063			0.0405062
$397$			28.0567i			1.40812i	0.710139	+	0.704062i	$0.248632\pi$
$397$			28.0567i			1.40812i	−0.710139	+	0.704062i	$0.751368\pi$
$398$		−	6.36344i		−	0.318970i
$399$	−0.350262			−0.0175350
$400$	3.03761	+	24.6253i	0.151881	+	1.23127i
$401$	−35.9937			−1.79744			−0.898719	−	0.438525i	$-0.855501\pi$
$401$	−35.9937			−1.79744			−0.898719	+	0.438525i	$0.855501\pi$
$402$		−	18.6761i		−	0.931479i
$403$			0.282333i			0.0140640i
$404$	−11.7889			−0.586521
$405$	−1.48119	+	1.67513i	−0.0736011	+	0.0832379i
$406$	−15.8822			−0.788222
$407$		−	9.44358i		−	0.468101i
$408$			6.31265i			0.312523i
$409$	−25.7440			−1.27296			−0.636480	−	0.771293i	$-0.719610\pi$
$409$	−25.7440			−1.27296			−0.636480	+	0.771293i	$0.719610\pi$
$410$	−19.2750	−	17.0435i	−0.951926	−	0.841718i
$411$	0.806063			0.0397602
$412$			0.881286i			0.0434179i
$413$		−	5.24965i		−	0.258318i
$414$	3.67513			0.180623
$415$	7.02539	+	6.21203i	0.344863	+	0.304937i
$416$	19.3258			0.947526
$417$			19.2447i			0.942418i
$418$			0.586734i			0.0286981i
$419$	29.9560			1.46345			0.731724	−	0.681601i	$-0.238716\pi$
$419$	29.9560			1.46345			0.731724	+	0.681601i	$0.238716\pi$
$420$	1.19394	−	1.35026i	0.0582581	−	0.0658860i
$421$	19.0508			0.928478			0.464239	−	0.885710i	$-0.346328\pi$
$421$	19.0508			0.928478			0.464239	+	0.885710i	$0.346328\pi$
$422$			2.70052i			0.131459i
$423$			3.98778i			0.193893i
$424$	−14.6253			−0.710267
$425$	15.6629	−	1.93207i	0.759763	−	0.0937192i
$426$	−1.89446			−0.0917869
$427$			7.73084i			0.374122i
$428$		−	13.2487i		−	0.640400i
$429$	4.48119			0.216354
$430$	19.3380	−	21.8700i	0.932563	−	1.05467i
$431$	14.8265			0.714169			0.357084	−	0.934072i	$-0.383771\pi$
$431$	14.8265			0.714169			0.357084	+	0.934072i	$0.383771\pi$
$432$			4.96239i			0.238753i
$433$		−	31.3112i		−	1.50472i	−0.658751	−	0.752361i	$-0.728915\pi$
$433$		−	31.3112i		−	1.50472i	0.658751	−	0.752361i	$-0.271085\pi$
$434$	0.105540			0.00506608
$435$	−15.8822	−	14.0435i	−0.761495	−	0.673334i
$436$	2.08507			0.0998568
$437$			0.768452i			0.0367600i
$438$		−	1.08840i		−	0.0520056i
$439$	34.9511			1.66813			0.834063	−	0.551669i	$-0.186009\pi$
$439$	34.9511			1.66813			0.834063	+	0.551669i	$0.186009\pi$
$440$	3.35026	+	2.96239i	0.159717	+	0.141226i
$441$	1.00000			0.0476190
$442$		−	23.6932i		−	1.12697i
$443$			23.9307i			1.13698i	0.822690	+	0.568490i	$0.192472\pi$
$443$			23.9307i			1.13698i	−0.822690	+	0.568490i	$0.807528\pi$
$444$	−7.61213			−0.361256
$445$	−4.96968	+	5.62038i	−0.235586	+	0.266431i
$446$	−18.0181			−0.853182
$447$		−	6.62530i		−	0.313366i
$448$			2.70052i			0.127588i
$449$	−11.8921			−0.561222			−0.280611	−	0.959822i	$-0.590537\pi$
$449$	−11.8921			−0.561222			−0.280611	+	0.959822i	$0.590537\pi$
$450$	8.31265	−	1.02539i	0.391862	−	0.0483375i
$451$	−6.86907			−0.323452
$452$		−	6.02047i		−	0.283179i
$453$		−	5.68735i		−	0.267215i
$454$	44.6639			2.09618
$455$	6.63752	−	7.50659i	0.311172	−	0.351914i
$456$	−0.700523			−0.0328050
$457$		−	31.7840i		−	1.48679i	−0.668851	−	0.743396i	$-0.733214\pi$
$457$		−	31.7840i		−	1.48679i	0.668851	−	0.743396i	$-0.266786\pi$
$458$		−	15.6424i		−	0.730923i
$459$	3.15633			0.147325
$460$	−2.96239	−	2.61942i	−0.138122	−	0.122131i
$461$	9.06396			0.422151			0.211075	−	0.977470i	$-0.432303\pi$
$461$	9.06396			0.422151			0.211075	+	0.977470i	$0.432303\pi$
$462$		−	1.67513i		−	0.0779341i
$463$			28.4387i			1.32166i	0.750537	+	0.660828i	$0.229795\pi$
$463$			28.4387i			1.32166i	−0.750537	+	0.660828i	$0.770205\pi$
$464$	−47.0494			−2.18421
$465$	0.105540	+	0.0933212i	0.00489430	+	0.00432767i
$466$	−18.9927			−0.879820
$467$			20.4485i			0.946244i	0.880997	+	0.473122i	$0.156873\pi$
$467$			20.4485i			0.946244i	−0.880997	+	0.473122i	$0.843127\pi$
$468$		−	3.61213i		−	0.166971i
$469$	−11.1490			−0.514814
$470$	9.89446	−	11.1900i	0.456397	−	0.516155i
$471$	5.30043			0.244231
$472$		−	10.4993i		−	0.483269i
$473$		−	7.79384i		−	0.358361i
$474$	6.59498			0.302918
$475$	0.214405	+	1.73813i	0.00983756	+	0.0797511i
$476$	−2.54420			−0.116613
$477$			7.31265i			0.334823i
$478$		−	29.9429i		−	1.36956i
$479$	−10.2193			−0.466933			−0.233467	−	0.972365i	$-0.575007\pi$
$479$	−10.2193			−0.466933			−0.233467	+	0.972365i	$0.575007\pi$
$480$	6.38787	−	7.22425i	0.291565	−	0.329741i
$481$	−42.3185			−1.92956
$482$		−	2.39772i		−	0.109213i
$483$		−	2.19394i		−	0.0998276i
$484$	−0.806063			−0.0366392
$485$	−4.43041	−	3.91748i	−0.201175	−	0.177884i
$486$	1.67513			0.0759855
$487$			10.1114i			0.458192i	0.973404	+	0.229096i	$0.0735770\pi$
$487$			10.1114i			0.458192i	−0.973404	+	0.229096i	$0.926423\pi$
$488$			15.4617i			0.699917i
$489$	−17.1065			−0.773582
$490$	−2.80606	−	2.48119i	−0.126765	−	0.112089i
$491$	27.1744			1.22636			0.613182	−	0.789941i	$-0.289889\pi$
$491$	27.1744			1.22636			0.613182	+	0.789941i	$0.289889\pi$
$492$			5.53690i			0.249623i
$493$			29.9257i			1.34779i
$494$	2.62927			0.118296
$495$	1.48119	−	1.67513i	0.0665747	−	0.0752915i
$496$	0.312650			0.0140384
$497$			1.13093i			0.0507293i
$498$		−	7.02539i		−	0.314815i
$499$	−10.3054			−0.461331			−0.230666	−	0.973033i	$-0.574090\pi$
$499$	−10.3054			−0.461331			−0.230666	+	0.973033i	$0.574090\pi$
$500$	−7.43136	−	5.09825i	−0.332341	−	0.228000i
$501$	3.76845			0.168362
$502$			1.29948i			0.0579985i
$503$			44.1900i			1.97033i	0.171600	+	0.985167i	$0.445106\pi$
$503$			44.1900i			1.97033i	−0.171600	+	0.985167i	$0.554894\pi$
$504$	2.00000			0.0890871
$505$	−21.6629	+	24.4993i	−0.963987	+	1.09020i
$506$	−3.67513			−0.163379
$507$		−	7.08110i		−	0.314483i
$508$		−	1.88461i		−	0.0836161i
$509$	−36.6664			−1.62521			−0.812605	−	0.582814i	$-0.801951\pi$
$509$	−36.6664			−1.62521			−0.812605	+	0.582814i	$0.801951\pi$
$510$	−8.85685	−	7.83146i	−0.392188	−	0.346783i
$511$	−0.649738			−0.0287427
$512$		−	1.55149i		−	0.0685669i
$513$			0.350262i			0.0154644i
$514$	−40.2677			−1.77613
$515$	1.83146	+	1.61942i	0.0807036	+	0.0713602i
$516$	−6.28233			−0.276564
$517$		−	3.98778i		−	0.175382i
$518$			15.8192i			0.695057i
$519$	−22.2677			−0.977446
$520$	13.2750	−	15.0132i	0.582149	−	0.658371i
$521$	7.51151			0.329085			0.164543	−	0.986370i	$-0.447385\pi$
$521$	7.51151			0.329085			0.164543	+	0.986370i	$0.447385\pi$
$522$			15.8822i			0.695147i
$523$			14.3488i			0.627431i	0.949517	+	0.313716i	$0.101574\pi$
$523$			14.3488i			0.627431i	−0.949517	+	0.313716i	$0.898426\pi$
$524$	7.46168			0.325965
$525$	−0.612127	−	4.96239i	−0.0267154	−	0.216576i
$526$	−18.0508			−0.787052
$527$		−	0.198861i		−	0.00866253i
$528$		−	4.96239i		−	0.215960i
$529$	18.1866			0.790724
$530$	18.1441	−	20.5198i	0.788130	−	0.891321i
$531$	−5.24965			−0.227815
$532$		−	0.282333i		−	0.0122407i
$533$			30.7816i			1.33330i
$534$	5.62038			0.243217
$535$	−27.5329	−	24.3453i	−1.19035	−	1.05254i
$536$	−22.2981			−0.963130
$537$		−	25.4191i		−	1.09692i
$538$			36.7694i			1.58524i
$539$	−1.00000			−0.0430730
$540$	−1.35026	−	1.19394i	−0.0581060	−	0.0513788i
$541$	−40.8505			−1.75630			−0.878150	−	0.478385i	$-0.841222\pi$
$541$	−40.8505			−1.75630			−0.878150	+	0.478385i	$0.841222\pi$
$542$		−	33.0108i		−	1.41794i
$543$		−	11.6629i		−	0.500503i
$544$	−13.6121			−0.583615
$545$	3.83146	−	4.33312i	0.164122	−	0.185610i
$546$	−7.50659			−0.321252
$547$		−	13.0386i		−	0.557489i	−0.960365	−	0.278744i	$-0.910082\pi$
$547$		−	13.0386i		−	0.557489i	0.960365	−	0.278744i	$-0.0899182\pi$
$548$			0.649738i			0.0277554i
$549$	7.73084			0.329944
$550$	−8.31265	+	1.02539i	−0.354453	+	0.0437229i
$551$	−3.32090			−0.141475
$552$		−	4.38787i		−	0.186760i
$553$		−	3.93700i		−	0.167418i
$554$	−23.5026			−0.998531
$555$	−13.9878	+	15.8192i	−0.593748	+	0.671489i
$556$	−15.5125			−0.657875
$557$		−	44.0625i		−	1.86699i	−0.358591	−	0.933495i	$-0.616743\pi$
$557$		−	44.0625i		−	1.86699i	0.358591	−	0.933495i	$-0.383257\pi$
$558$		−	0.105540i		−	0.00446786i
$559$	−34.9257			−1.47720
$560$	−8.31265	−	7.35026i	−0.351274	−	0.310605i
$561$	−3.15633			−0.133260
$562$			3.65306i			0.154095i
$563$		−	1.47039i		−	0.0619696i	−0.999520	−	0.0309848i	$-0.990136\pi$
$563$		−	1.47039i		−	0.0619696i	0.999520	−	0.0309848i	$-0.00986434\pi$
$564$	−3.21440			−0.135351
$565$	−12.5115	−	11.0630i	−0.526363	−	0.465424i
$566$	30.1662			1.26798
$567$		−	1.00000i		−	0.0419961i
$568$			2.26187i			0.0949058i
$569$	27.4119			1.14916			0.574582	−	0.818447i	$-0.305165\pi$
$569$	27.4119			1.14916			0.574582	+	0.818447i	$0.305165\pi$
$570$	0.869067	−	0.982857i	0.0364012	−	0.0411673i
$571$	−26.5115			−1.10947			−0.554736	−	0.832026i	$-0.687181\pi$
$571$	−26.5115			−1.10947			−0.554736	+	0.832026i	$0.687181\pi$
$572$			3.61213i			0.151031i
$573$			2.76116i			0.115349i
$574$	11.5066			0.480276
$575$	−10.8872	+	1.34297i	−0.454026	+	0.0560056i
$576$	2.70052			0.112522
$577$		−	32.3634i		−	1.34731i	−0.739047	−	0.673654i	$-0.764724\pi$
$577$		−	32.3634i		−	1.34731i	0.739047	−	0.673654i	$-0.235276\pi$
$578$		−	11.7889i		−	0.490354i
$579$	2.31265			0.0961105
$580$	11.3199	−	12.8021i	0.470035	−	0.531578i
$581$	−4.19394			−0.173994
$582$			4.43041i			0.183646i
$583$		−	7.31265i		−	0.302859i
$584$	−1.29948			−0.0537727
$585$	−7.50659	−	6.63752i	−0.310359	−	0.274428i
$586$	−17.5247			−0.723938
$587$			24.6737i			1.01839i	0.860650	+	0.509197i	$0.170057\pi$
$587$			24.6737i			1.01839i	−0.860650	+	0.509197i	$0.829943\pi$
$588$			0.806063i			0.0332415i
$589$	0.0220679			0.000909292
$590$	14.7308	+	13.0254i	0.606459	+	0.536247i
$591$	−24.2374			−0.996995
$592$			46.8627i			1.92605i
$593$		−	3.69323i		−	0.151663i	−0.997121	−	0.0758314i	$-0.975839\pi$
$593$		−	3.69323i		−	0.151663i	0.997121	−	0.0758314i	$-0.0241611\pi$
$594$	−1.67513			−0.0687315
$595$	−4.67513	+	5.28726i	−0.191662	+	0.216756i
$596$	5.34041			0.218752
$597$			3.79877i			0.155473i
$598$			16.4690i			0.673466i
$599$	−0.0507852			−0.00207503			−0.00103751	−	0.999999i	$-0.500330\pi$
$599$	−0.0507852			−0.00207503			−0.00103751	+	0.999999i	$0.500330\pi$
$600$	−1.22425	−	9.92478i	−0.0499799	−	0.405177i
$601$	−31.8061			−1.29740			−0.648698	−	0.761046i	$-0.724686\pi$
$601$	−31.8061			−1.29740			−0.648698	+	0.761046i	$0.724686\pi$
$602$			13.0557i			0.532111i
$603$			11.1490i			0.454024i
$604$	4.58436			0.186535
$605$	−1.48119	+	1.67513i	−0.0602191	+	0.0681038i
$606$	24.4993			0.995216
$607$			10.6351i			0.431667i	0.976430	+	0.215834i	$0.0692469\pi$
$607$			10.6351i			0.431667i	−0.976430	+	0.215834i	$0.930753\pi$
$608$		−	1.51056i		−	0.0612612i
$609$	9.48119			0.384197
$610$	−21.6932	−	19.1817i	−0.878333	−	0.776645i
$611$	−17.8700			−0.722944
$612$			2.54420i			0.102843i
$613$			37.3503i			1.50856i	0.656551	+	0.754281i	$0.272015\pi$
$613$			37.3503i			1.50856i	−0.656551	+	0.754281i	$0.727985\pi$
$614$	−22.0098			−0.888245
$615$	11.5066	+	10.1744i	0.463990	+	0.410272i
$616$	−2.00000			−0.0805823
$617$		−	34.8324i		−	1.40230i	−0.713014	−	0.701150i	$-0.752670\pi$
$617$		−	34.8324i		−	1.40230i	0.713014	−	0.701150i	$-0.247330\pi$
$618$		−	1.83146i		−	0.0736720i
$619$	−18.9986			−0.763618			−0.381809	−	0.924241i	$-0.624699\pi$
$619$	−18.9986			−0.763618			−0.381809	+	0.924241i	$0.624699\pi$
$620$	−0.0752228	+	0.0850719i	−0.00302102	+	0.00341657i
$621$	−2.19394			−0.0880396
$622$			29.7743i			1.19384i
$623$		−	3.35519i		−	0.134423i
$624$	−22.2374			−0.890210
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	50.1460			2.00424
$627$		−	0.350262i		−	0.0139881i
$628$			4.27248i			0.170491i
$629$	29.8070			1.18848
$630$	−2.48119	+	2.80606i	−0.0988531	+	0.111796i
$631$	37.9829			1.51207			0.756037	−	0.654529i	$-0.227133\pi$
$631$	37.9829			1.51207			0.756037	+	0.654529i	$0.227133\pi$
$632$		−	7.87399i		−	0.313211i
$633$		−	1.61213i		−	0.0640763i
$634$	−28.5745			−1.13484
$635$	−3.91653	−	3.46310i	−0.155423	−	0.137429i
$636$	−5.89446			−0.233731
$637$			4.48119i			0.177551i
$638$		−	15.8822i		−	0.628784i
$639$	1.13093			0.0447390
$640$	−22.0263	−	19.4763i	−0.870668	−	0.769867i
$641$	−31.8350			−1.25741			−0.628703	−	0.777646i	$-0.716414\pi$
$641$	−31.8350			−1.25741			−0.628703	+	0.777646i	$0.716414\pi$
$642$			27.5329i			1.08664i
$643$		−	46.3498i		−	1.82786i	−0.405874	−	0.913929i	$-0.633033\pi$
$643$		−	46.3498i		−	1.82786i	0.405874	−	0.913929i	$-0.366967\pi$
$644$	1.76845			0.0696868
$645$	−11.5442	+	13.0557i	−0.454552	+	0.514068i
$646$	−1.85192			−0.0728630
$647$			14.7250i			0.578898i	0.957193	+	0.289449i	$0.0934721\pi$
$647$			14.7250i			0.578898i	−0.957193	+	0.289449i	$0.906528\pi$
$648$		−	2.00000i		−	0.0785674i
$649$	5.24965			0.206067
$650$	4.59498	+	37.2506i	0.180230	+	1.46109i
$651$	−0.0630040			−0.00246932
$652$		−	13.7889i		−	0.540016i
$653$			24.6483i			0.964563i	0.876016	+	0.482282i	$0.160192\pi$
$653$			24.6483i			0.964563i	−0.876016	+	0.482282i	$0.839808\pi$
$654$	−4.33312			−0.169438
$655$	13.7113	−	15.5066i	0.535746	−	0.605892i
$656$	34.0870			1.33087
$657$			0.649738i			0.0253487i
$658$			6.68006i			0.260416i
$659$	7.89938			0.307716			0.153858	−	0.988093i	$-0.450830\pi$
$659$	7.89938			0.307716			0.153858	+	0.988093i	$0.450830\pi$
$660$	1.35026	+	1.19394i	0.0525589	+	0.0464739i
$661$	35.6408			1.38627			0.693134	−	0.720809i	$-0.256229\pi$
$661$	35.6408			1.38627			0.693134	+	0.720809i	$0.256229\pi$
$662$		−	35.0273i		−	1.36137i
$663$			14.1441i			0.549312i
$664$	−8.38787			−0.325513
$665$	−0.586734	−	0.518806i	−0.0227526	−	0.0201184i
$666$	15.8192			0.612983
$667$		−	20.8011i		−	0.805423i
$668$			3.03761i			0.117529i
$669$	10.7562			0.415860
$670$	27.6629	−	31.2849i	1.06871	−	1.20864i
$671$	−7.73084			−0.298446
$672$			4.31265i			0.166364i
$673$		−	43.7245i		−	1.68546i	−0.538340	−	0.842728i	$-0.680948\pi$
$673$		−	43.7245i		−	1.68546i	0.538340	−	0.842728i	$-0.319052\pi$
$674$	−23.3176			−0.898159
$675$	−4.96239	+	0.612127i	−0.191002	+	0.0235608i
$676$	5.70782			0.219531
$677$		−	43.0322i		−	1.65386i	−0.562303	−	0.826931i	$-0.690084\pi$
$677$		−	43.0322i		−	1.65386i	0.562303	−	0.826931i	$-0.309916\pi$
$678$			12.5115i			0.480502i
$679$	2.64481			0.101499
$680$	−9.35026	+	10.5745i	−0.358566	+	0.405514i
$681$	−26.6629			−1.02173
$682$			0.105540i			0.00404133i
$683$			4.87732i			0.186625i	0.995637	+	0.0933127i	$0.0297456\pi$
$683$			4.87732i			0.186625i	−0.995637	+	0.0933127i	$0.970254\pi$
$684$	−0.282333			−0.0107953
$685$	1.35026	+	1.19394i	0.0515908	+	0.0456180i
$686$	1.67513			0.0639568
$687$			9.33804i			0.356269i
$688$			38.6761i			1.47451i
$689$	−32.7694			−1.24841
$690$	6.15633	+	5.44358i	0.234367	+	0.207234i
$691$	−40.3390			−1.53457			−0.767284	−	0.641308i	$-0.778392\pi$
$691$	−40.3390			−1.53457			−0.767284	+	0.641308i	$0.778392\pi$
$692$		−	17.9492i		−	0.682327i
$693$			1.00000i			0.0379869i
$694$	3.77242			0.143199
$695$	−28.5052	+	32.2374i	−1.08126	+	1.22284i
$696$	18.9624			0.718767
$697$		−	21.6810i		−	0.821227i
$698$		−	41.2285i		−	1.56052i
$699$	11.3380			0.428844
$700$	4.00000	−	0.493413i	0.151186	−	0.0186493i
$701$	41.9316			1.58374			0.791868	−	0.610693i	$-0.209109\pi$
$701$	41.9316			1.58374			0.791868	+	0.610693i	$0.209109\pi$
$702$			7.50659i			0.283318i
$703$			3.30773i			0.124753i
$704$	−2.70052			−0.101780
$705$	−5.90668	+	6.68006i	−0.222458	+	0.251585i
$706$	−24.8119			−0.933810
$707$		−	14.6253i		−	0.550041i
$708$		−	4.23155i		−	0.159031i
$709$	3.48356			0.130828			0.0654140	−	0.997858i	$-0.479163\pi$
$709$	3.48356			0.130828			0.0654140	+	0.997858i	$0.479163\pi$
$710$	−3.17347	−	2.80606i	−0.119098	−	0.105310i
$711$	−3.93700			−0.147649
$712$		−	6.71037i		−	0.251482i
$713$			0.138227i			0.00517663i
$714$	5.28726			0.197871
$715$	7.50659	+	6.63752i	0.280730	+	0.248229i
$716$	20.4894			0.765726
$717$			17.8749i			0.667552i
$718$			7.04586i			0.262949i
$719$	8.53927			0.318461			0.159231	−	0.987241i	$-0.449099\pi$
$719$	8.53927			0.318461			0.159231	+	0.987241i	$0.449099\pi$
$720$	−7.35026	+	8.31265i	−0.273928	+	0.309794i
$721$	−1.09332			−0.0407174
$722$			31.6220i			1.17685i
$723$			1.43136i			0.0532330i
$724$	9.40105			0.349387
$725$	−5.80369	−	47.0494i	−0.215544	−	1.74737i
$726$	1.67513			0.0621699
$727$		−	13.1890i		−	0.489153i	−0.969630	−	0.244577i	$-0.921351\pi$
$727$		−	13.1890i		−	0.489153i	0.969630	−	0.244577i	$-0.0786490\pi$
$728$			8.96239i			0.332168i
$729$	−1.00000			−0.0370370
$730$	1.61213	−	1.82321i	0.0596675	−	0.0674799i
$731$	24.5999			0.909860
$732$			6.23155i			0.230325i
$733$			44.8119i			1.65517i	0.561343	+	0.827583i	$0.310285\pi$
$733$			44.8119i			1.65517i	−0.561343	+	0.827583i	$0.689715\pi$
$734$	27.2424			1.00553
$735$	1.67513	+	1.48119i	0.0617881	+	0.0546347i
$736$	9.46168			0.348762
$737$		−	11.1490i		−	0.410680i
$738$		−	11.5066i		−	0.423563i
$739$	38.5402			1.41773			0.708863	−	0.705347i	$-0.249209\pi$
$739$	38.5402			1.41773			0.708863	+	0.705347i	$0.249209\pi$
$740$	−12.7513	−	11.2750i	−0.468747	−	0.414479i
$741$	−1.56959			−0.0576604
$742$			12.2496i			0.449699i
$743$			22.3272i			0.819107i	0.912286	+	0.409553i	$0.134315\pi$
$743$			22.3272i			0.819107i	−0.912286	+	0.409553i	$0.865685\pi$
$744$	−0.126008			−0.00461968
$745$	9.81336	−	11.0982i	0.359534	−	0.406608i
$746$	24.8789			0.910882
$747$			4.19394i			0.153448i
$748$		−	2.54420i		−	0.0930251i
$749$	16.4363			0.600569
$750$	15.4436	+	10.5950i	0.563920	+	0.386874i
$751$	37.1016			1.35386			0.676928	−	0.736049i	$-0.263311\pi$
$751$	37.1016			1.35386			0.676928	+	0.736049i	$0.263311\pi$
$752$			19.7889i			0.721628i
$753$		−	0.775746i		−	0.0282698i
$754$	−71.1714			−2.59191
$755$	8.42407	−	9.52705i	0.306583	−	0.346725i
$756$	0.806063			0.0293162
$757$		−	21.6775i		−	0.787882i	−0.919136	−	0.393941i	$-0.871111\pi$
$757$		−	21.6775i		−	0.787882i	0.919136	−	0.393941i	$-0.128889\pi$
$758$		−	17.7866i		−	0.646037i
$759$	2.19394			0.0796349
$760$	−1.17347	−	1.03761i	−0.0425662	−	0.0376381i
$761$	−26.7123			−0.968319			−0.484160	−	0.874980i	$-0.660875\pi$
$761$	−26.7123			−0.968319			−0.484160	+	0.874980i	$0.660875\pi$
$762$			3.91653i			0.141881i
$763$			2.58673i			0.0936461i
$764$	−2.22567			−0.0805219
$765$	5.28726	+	4.67513i	0.191161	+	0.169030i
$766$	−57.9814			−2.09495
$767$		−	23.5247i		−	0.849427i
$768$			16.6253i			0.599914i
$769$	19.1016			0.688820			0.344410	−	0.938819i	$-0.388079\pi$
$769$	19.1016			0.688820			0.344410	+	0.938819i	$0.388079\pi$
$770$	2.48119	−	2.80606i	0.0894160	−	0.101124i
$771$	24.0386			0.865728
$772$			1.86414i			0.0670920i
$773$		−	34.3488i		−	1.23544i	−0.786397	−	0.617721i	$-0.788056\pi$
$773$		−	34.3488i		−	1.23544i	0.786397	−	0.617721i	$-0.211944\pi$
$774$	13.0557			0.469278
$775$	0.0385664	+	0.312650i	0.00138535	+	0.0112307i
$776$	5.28963			0.189887
$777$		−	9.44358i		−	0.338787i
$778$		−	47.1286i		−	1.68964i
$779$	2.40597			0.0862029
$780$	5.35026	−	6.05079i	0.191570	−	0.216653i
$781$	−1.13093			−0.0404679
$782$		−	11.5999i		−	0.414812i
$783$		−	9.48119i		−	0.338830i
$784$	4.96239			0.177228
$785$	8.87892	+	7.85097i	0.316902	+	0.280213i
$786$	−15.5066			−0.553102
$787$		−	25.7137i		−	0.916594i	−0.888799	−	0.458297i	$-0.848460\pi$
$787$		−	25.7137i		−	0.916594i	0.888799	−	0.458297i	$-0.151540\pi$
$788$		−	19.5369i		−	0.695973i
$789$	10.7757			0.383627
$790$	11.0475	+	9.76845i	0.393051	+	0.347546i
$791$	7.46898			0.265566
$792$			2.00000i			0.0710669i
$793$			34.6434i			1.23022i
$794$	46.9986			1.66792
$795$	−10.8315	+	12.2496i	−0.384152	+	0.434450i
$796$	−3.06205			−0.108531
$797$			25.1392i			0.890476i	0.895412	+	0.445238i	$0.146881\pi$
$797$			25.1392i			0.890476i	−0.895412	+	0.445238i	$0.853119\pi$
$798$			0.586734i			0.0207702i
$799$	12.5867			0.445287
$800$	21.4010	−	2.63989i	0.756641	−	0.0933342i
$801$	−3.35519			−0.118550
$802$			60.2941i			2.12906i
$803$		−	0.649738i		−	0.0229288i
$804$	−8.98683			−0.316941
$805$	3.24965	−	3.67513i	0.114535	−	0.129531i
$806$	0.472945			0.0166588
$807$		−	21.9502i		−	0.772683i
$808$		−	29.2506i		−	1.02903i
$809$	43.6121			1.53332			0.766660	−	0.642053i	$-0.221917\pi$
$809$	43.6121			1.53332			0.766660	+	0.642053i	$0.221917\pi$
$810$	2.80606	+	2.48119i	0.0985950	+	0.0871803i
$811$	−10.9887			−0.385867			−0.192933	−	0.981212i	$-0.561800\pi$
$811$	−10.9887			−0.385867			−0.192933	+	0.981212i	$0.561800\pi$
$812$			7.64244i			0.268197i
$813$			19.7064i			0.691134i
$814$	−15.8192			−0.554464
$815$	−28.6556	−	25.3380i	−1.00376	−	0.887553i
$816$	15.6629			0.548312
$817$			2.72989i			0.0955066i
$818$			43.1246i			1.50782i
$819$	4.48119			0.156586
$820$	−8.20123	+	9.27504i	−0.286399	+	0.323898i
$821$	−30.5002			−1.06447			−0.532233	−	0.846598i	$-0.678647\pi$
$821$	−30.5002			−1.06447			−0.532233	+	0.846598i	$0.678647\pi$
$822$		−	1.35026i		−	0.0470958i
$823$			40.9805i			1.42849i	0.699896	+	0.714245i	$0.253230\pi$
$823$			40.9805i			1.42849i	−0.699896	+	0.714245i	$0.746770\pi$
$824$	−2.18664			−0.0761753
$825$	4.96239	−	0.612127i	0.172768	−	0.0213115i
$826$	−8.79384			−0.305977
$827$			38.1016i			1.32492i	0.749097	+	0.662461i	$0.230488\pi$
$827$			38.1016i			1.32492i	−0.749097	+	0.662461i	$0.769512\pi$
$828$		−	1.76845i		−	0.0614580i
$829$	−11.3258			−0.393362			−0.196681	−	0.980468i	$-0.563016\pi$
$829$	−11.3258			−0.393362			−0.196681	+	0.980468i	$0.563016\pi$
$830$	10.4060	−	11.7685i	0.361197	−	0.408489i
$831$	14.0303			0.486706
$832$			12.1016i			0.419546i
$833$		−	3.15633i		−	0.109360i
$834$	32.2374			1.11629
$835$	6.31265	+	5.58181i	0.218458	+	0.193166i
$836$	0.282333			0.00976470
$837$			0.0630040i			0.00217774i
$838$		−	50.1803i		−	1.73345i
$839$	17.0933			0.590127			0.295063	−	0.955478i	$-0.404659\pi$
$839$	17.0933			0.590127			0.295063	+	0.955478i	$0.404659\pi$
$840$	3.35026	+	2.96239i	0.115595	+	0.102212i
$841$	60.8930			2.09976
$842$		−	31.9126i		−	1.09978i
$843$		−	2.18076i		−	0.0751095i
$844$	1.29948			0.0447298
$845$	10.4885	−	11.8618i	0.360815	−	0.408057i
$846$	6.68006			0.229665
$847$		−	1.00000i		−	0.0343604i
$848$			36.2882i			1.24614i
$849$	−18.0082			−0.618042
$850$	−3.23647	−	26.2374i	−0.111010	−	0.899936i
$851$	−20.7186			−0.710225
$852$			0.911603i			0.0312310i
$853$		−	37.7318i		−	1.29191i	−0.763375	−	0.645956i	$-0.776459\pi$
$853$		−	37.7318i		−	1.29191i	0.763375	−	0.645956i	$-0.223541\pi$
$854$	12.9502			0.443146
$855$	−0.518806	+	0.586734i	−0.0177428	+	0.0200659i
$856$	32.8726			1.12356
$857$		−	44.7729i		−	1.52941i	−0.644378	−	0.764707i	$-0.722884\pi$
$857$		−	44.7729i		−	1.52941i	0.644378	−	0.764707i	$-0.277116\pi$
$858$		−	7.50659i		−	0.256271i
$859$	0.572146			0.0195214			0.00976068	−	0.999952i	$-0.496893\pi$
$859$	0.572146			0.0195214			0.00976068	+	0.999952i	$0.496893\pi$
$860$	−10.5237	−	9.30536i	−0.358856	−	0.317310i
$861$	−6.86907			−0.234097
$862$		−	24.8364i		−	0.845930i
$863$		−	39.4847i		−	1.34407i	−0.740517	−	0.672037i	$-0.765419\pi$
$863$		−	39.4847i		−	1.34407i	0.740517	−	0.672037i	$-0.234581\pi$
$864$	4.31265			0.146719
$865$	−37.3014	−	32.9829i	−1.26829	−	1.12145i
$866$	−52.4504			−1.78234
$867$			7.03761i			0.239010i
$868$		−	0.0507852i		−	0.00172376i
$869$	3.93700			0.133553
$870$	−23.5247	+	26.6048i	−0.797562	+	0.901988i
$871$	−49.9610			−1.69286
$872$			5.17347i			0.175196i
$873$		−	2.64481i		−	0.0895134i
$874$	1.28726			0.0435421
$875$	6.32487	−	9.21933i	0.213820	−	0.311670i
$876$	−0.523730			−0.0176952
$877$		−	43.6072i		−	1.47251i	−0.676704	−	0.736255i	$-0.736592\pi$
$877$		−	43.6072i		−	1.47251i	0.676704	−	0.736255i	$-0.263408\pi$
$878$		−	58.5477i		−	1.97589i
$879$	10.4617			0.352864
$880$	7.35026	−	8.31265i	0.247777	−	0.280219i
$881$	21.7088			0.731387			0.365694	−	0.930735i	$-0.380832\pi$
$881$	21.7088			0.731387			0.365694	+	0.930735i	$0.380832\pi$
$882$		−	1.67513i		−	0.0564046i
$883$			50.9135i			1.71338i	0.515835	+	0.856688i	$0.327482\pi$
$883$			50.9135i			1.71338i	−0.515835	+	0.856688i	$0.672518\pi$
$884$	−11.4010			−0.383459
$885$	−8.79384	−	7.77575i	−0.295602	−	0.261379i
$886$	40.0870			1.34675
$887$			55.3127i			1.85722i	0.371061	+	0.928609i	$0.378994\pi$
$887$			55.3127i			1.85722i	−0.371061	+	0.928609i	$0.621006\pi$
$888$		−	18.8872i		−	0.633812i
$889$	2.33804			0.0784154
$890$	9.41487	+	8.32487i	0.315587	+	0.279050i
$891$	1.00000			0.0335013
$892$			8.67021i			0.290300i
$893$			1.39677i			0.0467410i
$894$	−11.0982			−0.371181
$895$	37.6507	−	42.5804i	1.25852	−	1.42331i
$896$	13.1490			0.439278
$897$		−	9.83146i		−	0.328263i
$898$			19.9208i			0.664766i
$899$	−0.597353			−0.0199228
$900$	−0.493413	−	4.00000i	−0.0164471	−	0.133333i
$901$	23.0811			0.768943
$902$			11.5066i			0.383127i
$903$		−	7.79384i		−	0.259363i
$904$	14.9380			0.496829
$905$	17.2750	−	19.5369i	0.574242	−	0.649429i
$906$	−9.52705			−0.316515
$907$			31.7972i			1.05581i	0.849304	+	0.527904i	$0.177022\pi$
$907$			31.7972i			1.05581i	−0.849304	+	0.527904i	$0.822978\pi$
$908$		−	21.4920i		−	0.713237i
$909$	−14.6253			−0.485091
$910$	−12.5745	−	11.1187i	−0.416841	−	0.368582i
$911$	38.3146			1.26942			0.634709	−	0.772751i	$-0.281120\pi$
$911$	38.3146			1.26942			0.634709	+	0.772751i	$0.281120\pi$
$912$			1.73813i			0.0575554i
$913$		−	4.19394i		−	0.138799i
$914$	−53.2424			−1.76110
$915$	12.9502	+	11.4509i	0.428119	+	0.378554i
$916$	−7.52705			−0.248701
$917$			9.25694i			0.305691i
$918$		−	5.28726i		−	0.174506i
$919$	−39.1392			−1.29108			−0.645541	−	0.763725i	$-0.723368\pi$
$919$	−39.1392			−1.29108			−0.645541	+	0.763725i	$0.723368\pi$
$920$	6.49929	−	7.35026i	0.214275	−	0.242331i
$921$	13.1392			0.432951
$922$		−	15.1833i		−	0.500036i
$923$			5.06793i			0.166813i
$924$	−0.806063			−0.0265175
$925$	−46.8627	+	5.78067i	−1.54084	+	0.190067i
$926$	47.6385			1.56550
$927$			1.09332i			0.0359094i
$928$			40.8891i			1.34225i
$929$	36.7915			1.20709			0.603545	−	0.797329i	$-0.293755\pi$
$929$	36.7915			1.20709			0.603545	+	0.797329i	$0.293755\pi$
$930$	0.156325	−	0.176793i	0.00512610	−	0.00579728i
$931$	0.350262			0.0114794
$932$			9.13918i			0.299364i
$933$		−	17.7743i		−	0.581905i
$934$	34.2539			1.12082
$935$	−5.28726	−	4.67513i	−0.172912	−	0.152893i
$936$	8.96239			0.292945
$937$		−	19.4337i		−	0.634872i	−0.948280	−	0.317436i	$-0.897178\pi$
$937$		−	19.4337i		−	0.634872i	0.948280	−	0.317436i	$-0.102822\pi$
$938$			18.6761i			0.609796i
$939$	−29.9356			−0.976911
$940$	−5.38455	−	4.76116i	−0.175625	−	0.155292i
$941$	22.1441			0.721877			0.360939	−	0.932590i	$-0.382456\pi$
$941$	22.1441			0.721877			0.360939	+	0.932590i	$0.382456\pi$
$942$		−	8.87892i		−	0.289291i
$943$			15.0703i			0.490756i
$944$	−26.0508			−0.847881
$945$	1.48119	−	1.67513i	0.0481833	−	0.0544920i
$946$	−13.0557			−0.424478
$947$			28.0336i			0.910971i	0.890243	+	0.455485i	$0.150534\pi$
$947$			28.0336i			0.910971i	−0.890243	+	0.455485i	$0.849466\pi$
$948$		−	3.17347i		−	0.103069i
$949$	−2.91160			−0.0945146
$950$	2.91160	−	0.359156i	0.0944649	−	0.0116526i
$951$	17.0581			0.553146
$952$		−	6.31265i		−	0.204594i
$953$			42.9986i			1.39286i	0.717624	+	0.696430i	$0.245230\pi$
$953$			42.9986i			1.39286i	−0.717624	+	0.696430i	$0.754770\pi$
$954$	12.2496			0.396597
$955$	−4.08981	+	4.62530i	−0.132343	+	0.149671i
$956$	−14.4083			−0.465999
$957$			9.48119i			0.306483i
$958$			17.1187i			0.553081i
$959$	−0.806063			−0.0260291
$960$	4.52373	+	4.00000i	0.146003	+	0.129099i
$961$	−30.9960			−0.999872
$962$			70.8891i			2.28556i
$963$		−	16.4363i		−	0.529652i
$964$	−1.15377			−0.0371604
$965$	3.87399	+	3.42548i	0.124708	+	0.110270i
$966$	−3.67513			−0.118245
$967$			14.1211i			0.454103i	0.973883	+	0.227052i	$0.0729086\pi$
$967$			14.1211i			0.454103i	−0.973883	+	0.227052i	$0.927091\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	1.10554			0.0355151
$970$	−6.56230	+	7.42152i	−0.210703	+	0.238290i
$971$	16.6448			0.534157			0.267079	−	0.963675i	$-0.413942\pi$
$971$	16.6448			0.534157			0.267079	+	0.963675i	$0.413942\pi$
$972$		−	0.806063i		−	0.0258545i
$973$		−	19.2447i		−	0.616957i
$974$	16.9380			0.542727
$975$	−2.74306	−	22.2374i	−0.0878482	−	0.712168i
$976$	38.3634			1.22798
$977$		−	11.4894i		−	0.367580i	−0.982966	−	0.183790i	$-0.941163\pi$
$977$		−	11.4894i		−	0.367580i	0.982966	−	0.183790i	$-0.0588366\pi$
$978$			28.6556i			0.916306i
$979$	3.35519			0.107232
$980$	−1.19394	+	1.35026i	−0.0381389	+	0.0431325i
$981$	2.58673			0.0825881
$982$		−	45.5207i		−	1.45262i
$983$		−	56.9789i		−	1.81734i	−0.417510	−	0.908672i	$-0.637097\pi$
$983$		−	56.9789i		−	1.81734i	0.417510	−	0.908672i	$-0.362903\pi$
$984$	−13.7381			−0.437956
$985$	−40.6009	−	35.9003i	−1.29365	−	1.14388i
$986$	50.1295			1.59645
$987$		−	3.98778i		−	0.126932i
$988$		−	1.26519i		−	0.0402511i
$989$	−17.0992			−0.543723
$990$	−2.80606	−	2.48119i	−0.0891826	−	0.0788575i
$991$	17.0870			0.542786			0.271393	−	0.962469i	$-0.412516\pi$
$991$	17.0870			0.542786			0.271393	+	0.962469i	$0.412516\pi$
$992$		−	0.271714i		−	0.00862694i
$993$			20.9102i			0.663565i
$994$	1.89446			0.0600886
$995$	−5.62672	+	6.36344i	−0.178379	+	0.201734i
$996$	−3.38058			−0.107118
$997$			40.0381i			1.26802i	0.773325	+	0.634010i	$0.218592\pi$
$997$			40.0381i			1.26802i	−0.773325	+	0.634010i	$0.781408\pi$
$998$			17.2628i			0.546445i
$999$	−9.44358			−0.298782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.d.694.2	✓	6
5.2	odd	4		5775.2.a.bv.1.3		3
5.3	odd	4		5775.2.a.bs.1.1		3
5.4	even	2	inner	1155.2.c.d.694.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.d.694.2	✓	6	1.1	even	1	trivial
1155.2.c.d.694.5	yes	6	5.4	even	2	inner
5775.2.a.bs.1.1		3	5.3	odd	4
5775.2.a.bv.1.3		3	5.2	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.67513 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 + 1.67513i) q^{5} +1.67513 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(2.80606 + 2.48119i) q^{10} +1.00000 q^{11} -0.806063i q^{12} -4.48119i q^{13} -1.67513 q^{14} +(-1.67513 - 1.48119i) q^{15} -4.96239 q^{16} +3.15633i q^{17} +1.67513i q^{18} -0.350262 q^{19} +(1.19394 - 1.35026i) q^{20} +1.00000 q^{21} -1.67513i q^{22} -2.19394i q^{23} +2.00000 q^{24} +(-0.612127 - 4.96239i) q^{25} -7.50659 q^{26} -1.00000i q^{27} +0.806063i q^{28} +9.48119 q^{29} +(-2.48119 + 2.80606i) q^{30} -0.0630040 q^{31} +4.31265i q^{32} +1.00000i q^{33} +5.28726 q^{34} +(1.67513 + 1.48119i) q^{35} +0.806063 q^{36} -9.44358i q^{37} +0.586734i q^{38} +4.48119 q^{39} +(3.35026 + 2.96239i) q^{40} -6.86907 q^{41} -1.67513i q^{42} -7.79384i q^{43} -0.806063 q^{44} +(1.48119 - 1.67513i) q^{45} -3.67513 q^{46} -3.98778i q^{47} -4.96239i q^{48} -1.00000 q^{49} +(-8.31265 + 1.02539i) q^{50} -3.15633 q^{51} +3.61213i q^{52} -7.31265i q^{53} -1.67513 q^{54} +(-1.48119 + 1.67513i) q^{55} -2.00000 q^{56} -0.350262i q^{57} -15.8822i q^{58} +5.24965 q^{59} +(1.35026 + 1.19394i) q^{60} -7.73084 q^{61} +0.105540i q^{62} +1.00000i q^{63} -2.70052 q^{64} +(7.50659 + 6.63752i) q^{65} +1.67513 q^{66} -11.1490i q^{67} -2.54420i q^{68} +2.19394 q^{69} +(2.48119 - 2.80606i) q^{70} -1.13093 q^{71} +2.00000i q^{72} -0.649738i q^{73} -15.8192 q^{74} +(4.96239 - 0.612127i) q^{75} +0.282333 q^{76} -1.00000i q^{77} -7.50659i q^{78} +3.93700 q^{79} +(7.35026 - 8.31265i) q^{80} +1.00000 q^{81} +11.5066i q^{82} -4.19394i q^{83} -0.806063 q^{84} +(-5.28726 - 4.67513i) q^{85} -13.0557 q^{86} +9.48119i q^{87} -2.00000i q^{88} +3.35519 q^{89} +(-2.80606 - 2.48119i) q^{90} -4.48119 q^{91} +1.76845i q^{92} -0.0630040i q^{93} -6.68006 q^{94} +(0.518806 - 0.586734i) q^{95} -4.31265 q^{96} +2.64481i q^{97} +1.67513i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} + 16 q^{10} + 6 q^{11} - 8 q^{16} + 18 q^{19} + 8 q^{20} + 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 46 q^{29} - 4 q^{30} + 8 q^{31} + 20 q^{34} + 4 q^{36} + 16 q^{39} - 32 q^{41} - 4 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} - 8 q^{50} + 2 q^{51} + 2 q^{55} - 12 q^{56} - 2 q^{59} - 12 q^{60} - 2 q^{61} + 24 q^{64} + 4 q^{65} + 14 q^{69} + 4 q^{70} - 16 q^{71} - 12 q^{74} + 8 q^{75} - 36 q^{76} + 32 q^{79} + 24 q^{80} + 6 q^{81} - 4 q^{84} - 20 q^{85} - 44 q^{86} + 26 q^{89} - 16 q^{90} - 16 q^{91} - 56 q^{94} + 14 q^{95} + 16 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 + 16 * q^10 + 6 * q^11 - 8 * q^16 + 18 * q^19 + 8 * q^20 + 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 46 * q^29 - 4 * q^30 + 8 * q^31 + 20 * q^34 + 4 * q^36 + 16 * q^39 - 32 * q^41 - 4 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 - 8 * q^50 + 2 * q^51 + 2 * q^55 - 12 * q^56 - 2 * q^59 - 12 * q^60 - 2 * q^61 + 24 * q^64 + 4 * q^65 + 14 * q^69 + 4 * q^70 - 16 * q^71 - 12 * q^74 + 8 * q^75 - 36 * q^76 + 32 * q^79 + 24 * q^80 + 6 * q^81 - 4 * q^84 - 20 * q^85 - 44 * q^86 + 26 * q^89 - 16 * q^90 - 16 * q^91 - 56 * q^94 + 14 * q^95 + 16 * q^96 - 6 * q^99

Introduction

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