LMFDB - Embedded newform 1690.2.c.c.1689.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(1689,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1690.1689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not 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:	$13.4947179416$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.2
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.c.1689.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.67513i q^{3} +1.00000 q^{4} +(1.48119 - 1.67513i) q^{5} -1.67513i q^{6} +1.80606 q^{7} +1.00000 q^{8} +0.193937 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.67513i q^{3} +1.00000 q^{4} +(1.48119 - 1.67513i) q^{5} -1.67513i q^{6} +1.80606 q^{7} +1.00000 q^{8} +0.193937 q^{9} +(1.48119 - 1.67513i) q^{10} -6.44358i q^{11} -1.67513i q^{12} +1.80606 q^{14} +(-2.80606 - 2.48119i) q^{15} +1.00000 q^{16} -0.481194i q^{17} +0.193937 q^{18} +6.28726i q^{19} +(1.48119 - 1.67513i) q^{20} -3.02539i q^{21} -6.44358i q^{22} +7.11871i q^{23} -1.67513i q^{24} +(-0.612127 - 4.96239i) q^{25} -5.35026i q^{27} +1.80606 q^{28} -2.31265 q^{29} +(-2.80606 - 2.48119i) q^{30} +3.25694i q^{31} +1.00000 q^{32} -10.7938 q^{33} -0.481194i q^{34} +(2.67513 - 3.02539i) q^{35} +0.193937 q^{36} +3.06300 q^{37} +6.28726i q^{38} +(1.48119 - 1.67513i) q^{40} +7.50659i q^{41} -3.02539i q^{42} -2.00000i q^{43} -6.44358i q^{44} +(0.287258 - 0.324869i) q^{45} +7.11871i q^{46} +2.19394 q^{47} -1.67513i q^{48} -3.73813 q^{49} +(-0.612127 - 4.96239i) q^{50} -0.806063 q^{51} +0.906679i q^{53} -5.35026i q^{54} +(-10.7938 - 9.54420i) q^{55} +1.80606 q^{56} +10.5320 q^{57} -2.31265 q^{58} +6.57452i q^{59} +(-2.80606 - 2.48119i) q^{60} -10.9502 q^{61} +3.25694i q^{62} +0.350262 q^{63} +1.00000 q^{64} -10.7938 q^{66} -0.649738 q^{67} -0.481194i q^{68} +11.9248 q^{69} +(2.67513 - 3.02539i) q^{70} +3.66291i q^{71} +0.193937 q^{72} +2.60720 q^{73} +3.06300 q^{74} +(-8.31265 + 1.02539i) q^{75} +6.28726i q^{76} -11.6375i q^{77} +2.29455 q^{79} +(1.48119 - 1.67513i) q^{80} -8.38058 q^{81} +7.50659i q^{82} +13.3380 q^{83} -3.02539i q^{84} +(-0.806063 - 0.712742i) q^{85} -2.00000i q^{86} +3.87399i q^{87} -6.44358i q^{88} -1.15633i q^{89} +(0.287258 - 0.324869i) q^{90} +7.11871i q^{92} +5.45580 q^{93} +2.19394 q^{94} +(10.5320 + 9.31265i) q^{95} -1.67513i q^{96} -13.8315 q^{97} -3.73813 q^{98} -1.24965i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} + 10 q^{14} - 16 q^{15} + 6 q^{16} + 2 q^{18} - 2 q^{20} - 2 q^{25} + 10 q^{28} + 28 q^{29} - 16 q^{30} + 6 q^{32} - 12 q^{33} + 6 q^{35} + 2 q^{36} + 10 q^{37} - 2 q^{40} - 10 q^{45} + 14 q^{47} - 4 q^{49} - 2 q^{50} - 4 q^{51} - 12 q^{55} + 10 q^{56} - 8 q^{57} + 28 q^{58} - 16 q^{60} + 8 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{66} - 24 q^{67} + 28 q^{69} + 6 q^{70} + 2 q^{72} - 12 q^{73} + 10 q^{74} - 8 q^{75} + 28 q^{79} - 2 q^{80} - 26 q^{81} + 8 q^{83} - 4 q^{85} - 10 q^{90} + 52 q^{93} + 14 q^{94} - 8 q^{95} - 52 q^{97} - 4 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 + 10 * q^14 - 16 * q^15 + 6 * q^16 + 2 * q^18 - 2 * q^20 - 2 * q^25 + 10 * q^28 + 28 * q^29 - 16 * q^30 + 6 * q^32 - 12 * q^33 + 6 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^40 - 10 * q^45 + 14 * q^47 - 4 * q^49 - 2 * q^50 - 4 * q^51 - 12 * q^55 + 10 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^60 + 8 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^66 - 24 * q^67 + 28 * q^69 + 6 * q^70 + 2 * q^72 - 12 * q^73 + 10 * q^74 - 8 * q^75 + 28 * q^79 - 2 * q^80 - 26 * q^81 + 8 * q^83 - 4 * q^85 - 10 * q^90 + 52 * q^93 + 14 * q^94 - 8 * q^95 - 52 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.67513i		−	0.967137i	−0.875306	−	0.483569i	$-0.839340\pi$
$3$		−	1.67513i		−	0.967137i	0.875306	−	0.483569i	$-0.160660\pi$
$4$	1.00000			0.500000
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$6$		−	1.67513i		−	0.683869i
$7$	1.80606			0.682628			0.341314	−	0.939949i	$-0.389128\pi$
$7$	1.80606			0.682628			0.341314	+	0.939949i	$0.389128\pi$
$8$	1.00000			0.353553
$9$	0.193937			0.0646455
$10$	1.48119	−	1.67513i	0.468395	−	0.529723i
$11$		−	6.44358i		−	1.94281i	−0.237422	−	0.971407i	$-0.576302\pi$
$11$		−	6.44358i		−	1.94281i	0.237422	−	0.971407i	$-0.423698\pi$
$12$		−	1.67513i		−	0.483569i
$13$		0			0
$13$		0			0
$14$	1.80606			0.482691
$15$	−2.80606	−	2.48119i	−0.724522	−	0.640642i
$16$	1.00000			0.250000
$17$		−	0.481194i		−	0.116707i	−0.998296	−	0.0583534i	$-0.981415\pi$
$17$		−	0.481194i		−	0.116707i	0.998296	−	0.0583534i	$-0.0185850\pi$
$18$	0.193937			0.0457113
$19$			6.28726i			1.44240i	0.692729	+	0.721198i	$0.256408\pi$
$19$			6.28726i			1.44240i	−0.692729	+	0.721198i	$0.743592\pi$
$20$	1.48119	−	1.67513i	0.331205	−	0.374571i
$21$		−	3.02539i		−	0.660195i
$22$		−	6.44358i		−	1.37378i
$23$			7.11871i			1.48435i	0.670204	+	0.742177i	$0.266207\pi$
$23$			7.11871i			1.48435i	−0.670204	+	0.742177i	$0.733793\pi$
$24$		−	1.67513i		−	0.341935i
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$		0			0
$27$		−	5.35026i		−	1.02966i
$28$	1.80606			0.341314
$29$	−2.31265			−0.429448			−0.214724	−	0.976675i	$-0.568885\pi$
$29$	−2.31265			−0.429448			−0.214724	+	0.976675i	$0.568885\pi$
$30$	−2.80606	−	2.48119i	−0.512315	−	0.453002i
$31$			3.25694i			0.584964i	0.956271	+	0.292482i	$0.0944811\pi$
$31$			3.25694i			0.584964i	−0.956271	+	0.292482i	$0.905519\pi$
$32$	1.00000			0.176777
$33$	−10.7938			−1.87897
$34$		−	0.481194i		−	0.0825241i
$35$	2.67513	−	3.02539i	0.452180	−	0.511385i
$36$	0.193937			0.0323228
$37$	3.06300			0.503555			0.251777	−	0.967785i	$-0.418985\pi$
$37$	3.06300			0.503555			0.251777	+	0.967785i	$0.418985\pi$
$38$			6.28726i			1.01993i
$39$		0			0
$40$	1.48119	−	1.67513i	0.234197	−	0.264861i
$41$			7.50659i			1.17233i	0.810191	+	0.586166i	$0.199363\pi$
$41$			7.50659i			1.17233i	−0.810191	+	0.586166i	$0.800637\pi$
$42$		−	3.02539i		−	0.466828i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$		−	6.44358i		−	0.971407i
$45$	0.287258	−	0.324869i	0.0428219	−	0.0484286i
$46$			7.11871i			1.04960i
$47$	2.19394			0.320019			0.160009	−	0.987116i	$-0.448848\pi$
$47$	2.19394			0.320019			0.160009	+	0.987116i	$0.448848\pi$
$48$		−	1.67513i		−	0.241784i
$49$	−3.73813			−0.534019
$50$	−0.612127	−	4.96239i	−0.0865678	−	0.701788i
$51$	−0.806063			−0.112871
$52$		0			0
$53$			0.906679i			0.124542i	0.998059	+	0.0622710i	$0.0198343\pi$
$53$			0.906679i			0.124542i	−0.998059	+	0.0622710i	$0.980166\pi$
$54$		−	5.35026i		−	0.728078i
$55$	−10.7938	−	9.54420i	−1.45544	−	1.28694i
$56$	1.80606			0.241345
$57$	10.5320			1.39499
$58$	−2.31265			−0.303666
$59$			6.57452i			0.855929i	0.903796	+	0.427965i	$0.140769\pi$
$59$			6.57452i			0.855929i	−0.903796	+	0.427965i	$0.859231\pi$
$60$	−2.80606	−	2.48119i	−0.362261	−	0.320321i
$61$	−10.9502			−1.40203			−0.701013	−	0.713149i	$-0.747268\pi$
$61$	−10.9502			−1.40203			−0.701013	+	0.713149i	$0.747268\pi$
$62$			3.25694i			0.413632i
$63$	0.350262			0.0441288
$64$	1.00000			0.125000
$65$		0			0
$66$	−10.7938			−1.32863
$67$	−0.649738			−0.0793782			−0.0396891	−	0.999212i	$-0.512637\pi$
$67$	−0.649738			−0.0793782			−0.0396891	+	0.999212i	$0.512637\pi$
$68$		−	0.481194i		−	0.0583534i
$69$	11.9248			1.43557
$70$	2.67513	−	3.02539i	0.319739	−	0.361604i
$71$			3.66291i			0.434708i	0.976093	+	0.217354i	$0.0697425\pi$
$71$			3.66291i			0.434708i	−0.976093	+	0.217354i	$0.930257\pi$
$72$	0.193937			0.0228556
$73$	2.60720			0.305150			0.152575	−	0.988292i	$-0.451243\pi$
$73$	2.60720			0.305150			0.152575	+	0.988292i	$0.451243\pi$
$74$	3.06300			0.356067
$75$	−8.31265	+	1.02539i	−0.959862	+	0.118402i
$76$			6.28726i			0.721198i
$77$		−	11.6375i		−	1.32622i
$78$		0			0
$79$	2.29455			0.258157			0.129079	−	0.991634i	$-0.458798\pi$
$79$	2.29455			0.258157			0.129079	+	0.991634i	$0.458798\pi$
$80$	1.48119	−	1.67513i	0.165603	−	0.187285i
$81$	−8.38058			−0.931175
$82$			7.50659i			0.828964i
$83$	13.3380			1.46404			0.732020	−	0.681283i	$-0.238578\pi$
$83$	13.3380			1.46404			0.732020	+	0.681283i	$0.238578\pi$
$84$		−	3.02539i		−	0.330097i
$85$	−0.806063	−	0.712742i	−0.0874299	−	0.0773078i
$86$		−	2.00000i		−	0.215666i
$87$			3.87399i			0.415336i
$88$		−	6.44358i		−	0.686888i
$89$		−	1.15633i		−	0.122570i	−0.998120	−	0.0612851i	$-0.980480\pi$
$89$		−	1.15633i		−	0.122570i	0.998120	−	0.0612851i	$-0.0195199\pi$
$90$	0.287258	−	0.324869i	0.0302796	−	0.0342442i
$91$		0			0
$92$			7.11871i			0.742177i
$93$	5.45580			0.565740
$94$	2.19394			0.226287
$95$	10.5320	+	9.31265i	1.08056	+	0.955458i
$96$		−	1.67513i		−	0.170967i
$97$	−13.8315			−1.40437			−0.702186	−	0.711994i	$-0.747792\pi$
$97$	−13.8315			−1.40437			−0.702186	+	0.711994i	$0.747792\pi$
$98$	−3.73813			−0.377609
$99$		−	1.24965i		−	0.125594i
$100$	−0.612127	−	4.96239i	−0.0612127	−	0.496239i
$101$	9.59991			0.955227			0.477613	−	0.878570i	$-0.341502\pi$
$101$	9.59991			0.955227			0.477613	+	0.878570i	$0.341502\pi$
$102$	−0.806063			−0.0798122
$103$			3.07522i			0.303011i	0.988456	+	0.151505i	$0.0484121\pi$
$103$			3.07522i			0.303011i	−0.988456	+	0.151505i	$0.951588\pi$
$104$		0			0
$105$	−5.06793	−	4.48119i	−0.494579	−	0.437320i
$106$			0.906679i			0.0880644i
$107$		−	1.67513i		−	0.161941i	−0.996716	−	0.0809705i	$-0.974198\pi$
$107$		−	1.67513i		−	0.161941i	0.996716	−	0.0809705i	$-0.0258020\pi$
$108$		−	5.35026i		−	0.514829i
$109$		−	10.8872i		−	1.04280i	−0.853312	−	0.521401i	$-0.825410\pi$
$109$		−	10.8872i		−	1.04280i	0.853312	−	0.521401i	$-0.174590\pi$
$110$	−10.7938	−	9.54420i	−1.02915	−	0.910004i
$111$		−	5.13093i		−	0.487007i
$112$	1.80606			0.170657
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	10.5320			0.986410
$115$	11.9248	+	10.5442i	1.11199	+	0.983252i
$116$	−2.31265			−0.214724
$117$		0			0
$118$			6.57452i			0.605233i
$119$		−	0.869067i		−	0.0796673i
$120$	−2.80606	−	2.48119i	−0.256157	−	0.226501i
$121$	−30.5198			−2.77452
$122$	−10.9502			−0.991382
$123$	12.5745			1.13381
$124$			3.25694i			0.292482i
$125$	−9.21933	−	6.32487i	−0.824602	−	0.565713i
$126$	0.350262			0.0312038
$127$			5.18664i			0.460240i	0.973162	+	0.230120i	$0.0739119\pi$
$127$			5.18664i			0.460240i	−0.973162	+	0.230120i	$0.926088\pi$
$128$	1.00000			0.0883883
$129$	−3.35026			−0.294974
$130$		0			0
$131$	−10.8011			−0.943700			−0.471850	−	0.881679i	$-0.656414\pi$
$131$	−10.8011			−0.943700			−0.471850	+	0.881679i	$0.656414\pi$
$132$	−10.7938			−0.939484
$133$			11.3552i			0.984620i
$134$	−0.649738			−0.0561288
$135$	−8.96239	−	7.92478i	−0.771360	−	0.682056i
$136$		−	0.481194i		−	0.0412621i
$137$	−6.14411			−0.524926			−0.262463	−	0.964942i	$-0.584535\pi$
$137$	−6.14411			−0.524926			−0.262463	+	0.964942i	$0.584535\pi$
$138$	11.9248			1.01510
$139$	−10.3380			−0.876861			−0.438431	−	0.898765i	$-0.644466\pi$
$139$	−10.3380			−0.876861			−0.438431	+	0.898765i	$0.644466\pi$
$140$	2.67513	−	3.02539i	0.226090	−	0.255692i
$141$		−	3.67513i		−	0.309502i
$142$			3.66291i			0.307385i
$143$		0			0
$144$	0.193937			0.0161614
$145$	−3.42548	+	3.87399i	−0.284471	+	0.321718i
$146$	2.60720			0.215774
$147$			6.26187i			0.516470i
$148$	3.06300			0.251777
$149$			16.0508i			1.31493i	0.753484	+	0.657466i	$0.228372\pi$
$149$			16.0508i			1.31493i	−0.753484	+	0.657466i	$0.771628\pi$
$150$	−8.31265	+	1.02539i	−0.678725	+	0.0837230i
$151$		−	9.31757i		−	0.758253i	−0.925345	−	0.379127i	$-0.876224\pi$
$151$		−	9.31757i		−	0.758253i	0.925345	−	0.379127i	$-0.123776\pi$
$152$			6.28726i			0.509964i
$153$		−	0.0933212i		−	0.00754457i
$154$		−	11.6375i		−	0.937778i
$155$	5.45580	+	4.82416i	0.438221	+	0.387486i
$156$		0			0
$157$		−	14.7562i		−	1.17768i	−0.808251	−	0.588838i	$-0.799586\pi$
$157$		−	14.7562i		−	1.17768i	0.808251	−	0.588838i	$-0.200414\pi$
$158$	2.29455			0.182545
$159$	1.51881			0.120449
$160$	1.48119	−	1.67513i	0.117099	−	0.132431i
$161$			12.8568i			1.01326i
$162$	−8.38058			−0.658440
$163$	13.5247			1.05934			0.529668	−	0.848205i	$-0.322317\pi$
$163$	13.5247			1.05934			0.529668	+	0.848205i	$0.322317\pi$
$164$			7.50659i			0.586166i
$165$	−15.9878	+	18.0811i	−1.24465	+	1.40761i
$166$	13.3380			1.03523
$167$	23.4241			1.81261			0.906304	−	0.422625i	$-0.138891\pi$
$167$	23.4241			1.81261			0.906304	+	0.422625i	$0.138891\pi$
$168$		−	3.02539i		−	0.233414i
$169$		0			0
$170$	−0.806063	−	0.712742i	−0.0618222	−	0.0546648i
$171$			1.21933i			0.0932444i
$172$		−	2.00000i		−	0.152499i
$173$		−	4.62435i		−	0.351582i	−0.984427	−	0.175791i	$-0.943752\pi$
$173$		−	4.62435i		−	0.351582i	0.984427	−	0.175791i	$-0.0562484\pi$
$174$			3.87399i			0.293687i
$175$	−1.10554	−	8.96239i	−0.0835710	−	0.677493i
$176$		−	6.44358i		−	0.485703i
$177$	11.0132			0.827801
$178$		−	1.15633i		−	0.0866702i
$179$	−8.31265			−0.621317			−0.310658	−	0.950522i	$-0.600549\pi$
$179$	−8.31265			−0.621317			−0.310658	+	0.950522i	$0.600549\pi$
$180$	0.287258	−	0.324869i	0.0214109	−	0.0242143i
$181$	1.02539			0.0762168			0.0381084	−	0.999274i	$-0.487867\pi$
$181$	1.02539			0.0762168			0.0381084	+	0.999274i	$0.487867\pi$
$182$		0			0
$183$			18.3430i			1.35595i
$184$			7.11871i			0.524799i
$185$	4.53690	−	5.13093i	0.333560	−	0.377234i
$186$	5.45580			0.400039
$187$	−3.10062			−0.226739
$188$	2.19394			0.160009
$189$		−	9.66291i		−	0.702873i
$190$	10.5320	+	9.31265i	0.764070	+	0.675611i
$191$	0.355186			0.0257004			0.0128502	−	0.999917i	$-0.495910\pi$
$191$	0.355186			0.0257004			0.0128502	+	0.999917i	$0.495910\pi$
$192$		−	1.67513i		−	0.120892i
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	−13.8315			−0.993041
$195$		0			0
$196$	−3.73813			−0.267010
$197$	14.1065			1.00505			0.502523	−	0.864564i	$-0.332405\pi$
$197$	14.1065			1.00505			0.502523	+	0.864564i	$0.332405\pi$
$198$		−	1.24965i		−	0.0888085i
$199$	−3.14903			−0.223229			−0.111614	−	0.993752i	$-0.535602\pi$
$199$	−3.14903			−0.223229			−0.111614	+	0.993752i	$0.535602\pi$
$200$	−0.612127	−	4.96239i	−0.0432839	−	0.350894i
$201$			1.08840i			0.0767696i
$202$	9.59991			0.675447
$203$	−4.17679			−0.293153
$204$	−0.806063			−0.0564357
$205$	12.5745	+	11.1187i	0.878242	+	0.776565i
$206$			3.07522i			0.214261i
$207$			1.38058i			0.0959569i
$208$		0			0
$209$	40.5125			2.80231
$210$	−5.06793	−	4.48119i	−0.349720	−	0.309232i
$211$	3.09332			0.212953			0.106477	−	0.994315i	$-0.466043\pi$
$211$	3.09332			0.212953			0.106477	+	0.994315i	$0.466043\pi$
$212$			0.906679i			0.0622710i
$213$	6.13586			0.420422
$214$		−	1.67513i		−	0.114510i
$215$	−3.35026	−	2.96239i	−0.228486	−	0.202033i
$216$		−	5.35026i		−	0.364039i
$217$			5.88224i			0.399313i
$218$		−	10.8872i		−	0.737372i
$219$		−	4.36741i		−	0.295122i
$220$	−10.7938	−	9.54420i	−0.727721	−	0.643470i
$221$		0			0
$222$		−	5.13093i		−	0.344366i
$223$	22.1939			1.48622			0.743108	−	0.669172i	$-0.233351\pi$
$223$	22.1939			1.48622			0.743108	+	0.669172i	$0.233351\pi$
$224$	1.80606			0.120673
$225$	−0.118714	−	0.962389i	−0.00791425	−	0.0641592i
$226$		−	14.0000i		−	0.931266i
$227$	13.3357			0.885120			0.442560	−	0.896739i	$-0.354070\pi$
$227$	13.3357			0.885120			0.442560	+	0.896739i	$0.354070\pi$
$228$	10.5320			0.697497
$229$			26.1744i			1.72965i	0.502069	+	0.864827i	$0.332572\pi$
$229$			26.1744i			1.72965i	−0.502069	+	0.864827i	$0.667428\pi$
$230$	11.9248	+	10.5442i	0.786297	+	0.695264i
$231$	−19.4944			−1.28264
$232$	−2.31265			−0.151833
$233$			20.8691i			1.36718i	0.729867	+	0.683589i	$0.239582\pi$
$233$			20.8691i			1.36718i	−0.729867	+	0.683589i	$0.760418\pi$
$234$		0			0
$235$	3.24965	−	3.67513i	0.211984	−	0.239739i
$236$			6.57452i			0.427965i
$237$		−	3.84367i		−	0.249674i
$238$		−	0.869067i		−	0.0563333i
$239$			15.2931i			0.989231i	0.869112	+	0.494615i	$0.164691\pi$
$239$			15.2931i			0.989231i	−0.869112	+	0.494615i	$0.835309\pi$
$240$	−2.80606	−	2.48119i	−0.181131	−	0.160160i
$241$			12.7685i			0.822488i	0.911525	+	0.411244i	$0.134906\pi$
$241$			12.7685i			0.822488i	−0.911525	+	0.411244i	$0.865094\pi$
$242$	−30.5198			−1.96188
$243$		−	2.01222i		−	0.129084i
$244$	−10.9502			−0.701013
$245$	−5.53690	+	6.26187i	−0.353740	+	0.400056i
$246$	12.5745			0.801722
$247$		0			0
$248$			3.25694i			0.206816i
$249$		−	22.3430i		−	1.41593i
$250$	−9.21933	−	6.32487i	−0.583082	−	0.400020i
$251$	4.21203			0.265861			0.132931	−	0.991125i	$-0.457561\pi$
$251$	4.21203			0.265861			0.132931	+	0.991125i	$0.457561\pi$
$252$	0.350262			0.0220644
$253$	45.8700			2.88382
$254$			5.18664i			0.325439i
$255$	−1.19394	+	1.35026i	−0.0747672	+	0.0845567i
$256$	1.00000			0.0625000
$257$		−	18.6253i		−	1.16181i	−0.813970	−	0.580907i	$-0.802698\pi$
$257$		−	18.6253i		−	1.16181i	0.813970	−	0.580907i	$-0.197302\pi$
$258$	−3.35026			−0.208578
$259$	5.53198			0.343740
$260$		0			0
$261$	−0.448507			−0.0277619
$262$	−10.8011			−0.667297
$263$			23.0205i			1.41950i	0.704452	+	0.709751i	$0.251193\pi$
$263$			23.0205i			1.41950i	−0.704452	+	0.709751i	$0.748807\pi$
$264$	−10.7938			−0.664315
$265$	1.51881	+	1.34297i	0.0932995	+	0.0824978i
$266$			11.3552i			0.696231i
$267$	−1.93700			−0.118542
$268$	−0.649738			−0.0396891
$269$	13.4739			0.821518			0.410759	−	0.911744i	$-0.365264\pi$
$269$	13.4739			0.821518			0.410759	+	0.911744i	$0.365264\pi$
$270$	−8.96239	−	7.92478i	−0.545434	−	0.482287i
$271$			17.9003i			1.08737i	0.839290	+	0.543684i	$0.182971\pi$
$271$			17.9003i			1.08737i	−0.839290	+	0.543684i	$0.817029\pi$
$272$		−	0.481194i		−	0.0291767i
$273$		0			0
$274$	−6.14411			−0.371179
$275$	−31.9756	+	3.94429i	−1.92820	+	0.237850i
$276$	11.9248			0.717787
$277$		−	8.48849i		−	0.510024i	−0.966938	−	0.255012i	$-0.917921\pi$
$277$		−	8.48849i		−	0.510024i	0.966938	−	0.255012i	$-0.0820794\pi$
$278$	−10.3380			−0.620035
$279$			0.631640i			0.0378153i
$280$	2.67513	−	3.02539i	0.159870	−	0.180802i
$281$			16.5296i			0.986074i	0.870008	+	0.493037i	$0.164113\pi$
$281$			16.5296i			0.986074i	−0.870008	+	0.493037i	$0.835887\pi$
$282$		−	3.67513i		−	0.218851i
$283$			1.53690i			0.0913595i	0.998956	+	0.0456797i	$0.0145454\pi$
$283$			1.53690i			0.0913595i	−0.998956	+	0.0456797i	$0.985455\pi$
$284$			3.66291i			0.217354i
$285$	15.5999	−	17.6424i	0.924059	−	1.04505i
$286$		0			0
$287$			13.5574i			0.800266i
$288$	0.193937			0.0114278
$289$	16.7685			0.986380
$290$	−3.42548	+	3.87399i	−0.201151	+	0.227489i
$291$			23.1695i			1.35822i
$292$	2.60720			0.152575
$293$	−5.92970			−0.346417			−0.173208	−	0.984885i	$-0.555413\pi$
$293$	−5.92970			−0.346417			−0.173208	+	0.984885i	$0.555413\pi$
$294$			6.26187i			0.365199i
$295$	11.0132	+	9.73813i	0.641212	+	0.566976i
$296$	3.06300			0.178033
$297$	−34.4749			−2.00043
$298$			16.0508i			0.929797i
$299$		0			0
$300$	−8.31265	+	1.02539i	−0.479931	+	0.0592011i
$301$		−	3.61213i		−	0.208200i
$302$		−	9.31757i		−	0.536166i
$303$		−	16.0811i		−	0.923835i
$304$			6.28726i			0.360599i
$305$	−16.2193	+	18.3430i	−0.928716	+	1.05032i
$306$		−	0.0933212i		−	0.00533482i
$307$	17.9756			1.02592			0.512960	−	0.858413i	$-0.328549\pi$
$307$	17.9756			1.02592			0.512960	+	0.858413i	$0.328549\pi$
$308$		−	11.6375i		−	0.663109i
$309$	5.15140			0.293053
$310$	5.45580	+	4.82416i	0.309869	+	0.273994i
$311$	−15.9575			−0.904865			−0.452432	−	0.891799i	$-0.649444\pi$
$311$	−15.9575			−0.904865			−0.452432	+	0.891799i	$0.649444\pi$
$312$		0			0
$313$		−	23.4372i		−	1.32475i	−0.749172	−	0.662376i	$-0.769548\pi$
$313$		−	23.4372i		−	1.32475i	0.749172	−	0.662376i	$-0.230452\pi$
$314$		−	14.7562i		−	0.832742i
$315$	0.518806	−	0.586734i	0.0292314	−	0.0330587i
$316$	2.29455			0.129079
$317$	−20.6507			−1.15986			−0.579929	−	0.814667i	$-0.696920\pi$
$317$	−20.6507			−1.15986			−0.579929	+	0.814667i	$0.696920\pi$
$318$	1.51881			0.0851704
$319$			14.9018i			0.834338i
$320$	1.48119	−	1.67513i	0.0828013	−	0.0936427i
$321$	−2.80606			−0.156619
$322$			12.8568i			0.716484i
$323$	3.02539			0.168337
$324$	−8.38058			−0.465588
$325$		0			0
$326$	13.5247			0.749063
$327$	−18.2374			−1.00853
$328$			7.50659i			0.414482i
$329$	3.96239			0.218454
$330$	−15.9878	+	18.0811i	−0.880098	+	0.995332i
$331$		−	26.6761i		−	1.46625i	−0.680094	−	0.733125i	$-0.738061\pi$
$331$		−	26.6761i		−	1.46625i	0.680094	−	0.733125i	$-0.261939\pi$
$332$	13.3380			0.732020
$333$	0.594028			0.0325526
$334$	23.4241			1.28171
$335$	−0.962389	+	1.08840i	−0.0525809	+	0.0594655i
$336$		−	3.02539i		−	0.165049i
$337$		−	8.40597i		−	0.457902i	−0.973438	−	0.228951i	$-0.926470\pi$
$337$		−	8.40597i		−	0.457902i	0.973438	−	0.228951i	$-0.0735296\pi$
$338$		0			0
$339$	−23.4518			−1.27373
$340$	−0.806063	−	0.712742i	−0.0437149	−	0.0386539i
$341$	20.9864			1.13648
$342$			1.21933i			0.0659338i
$343$	−19.3938			−1.04716
$344$		−	2.00000i		−	0.107833i
$345$	17.6629	−	19.9756i	0.950939	−	1.07545i
$346$		−	4.62435i		−	0.248606i
$347$			21.1514i			1.13547i	0.823213	+	0.567733i	$0.192180\pi$
$347$			21.1514i			1.13547i	−0.823213	+	0.567733i	$0.807820\pi$
$348$			3.87399i			0.207668i
$349$			5.47390i			0.293011i	0.989210	+	0.146506i	$0.0468026\pi$
$349$			5.47390i			0.293011i	−0.989210	+	0.146506i	$0.953197\pi$
$350$	−1.10554	−	8.96239i	−0.0590936	−	0.479060i
$351$		0			0
$352$		−	6.44358i		−	0.343444i
$353$	30.1441			1.60441			0.802204	−	0.597049i	$-0.203660\pi$
$353$	30.1441			1.60441			0.802204	+	0.597049i	$0.203660\pi$
$354$	11.0132			0.585344
$355$	6.13586	+	5.42548i	0.325657	+	0.287955i
$356$		−	1.15633i		−	0.0612851i
$357$	−1.45580			−0.0770492
$358$	−8.31265			−0.439337
$359$		−	8.38787i		−	0.442695i	−0.975195	−	0.221348i	$-0.928954\pi$
$359$		−	8.38787i		−	0.442695i	0.975195	−	0.221348i	$-0.0710455\pi$
$360$	0.287258	−	0.324869i	0.0151398	−	0.0171221i
$361$	−20.5296			−1.08051
$362$	1.02539			0.0538934
$363$			51.1246i			2.68335i
$364$		0			0
$365$	3.86177	−	4.36741i	0.202134	−	0.228600i
$366$			18.3430i			0.958802i
$367$			19.5125i			1.01854i	0.860606	+	0.509271i	$0.170085\pi$
$367$			19.5125i			1.01854i	−0.860606	+	0.509271i	$0.829915\pi$
$368$			7.11871i			0.371089i
$369$			1.45580i			0.0757860i
$370$	4.53690	−	5.13093i	0.235862	−	0.266744i
$371$			1.63752i			0.0850158i
$372$	5.45580			0.282870
$373$		−	8.51388i		−	0.440832i	−0.975406	−	0.220416i	$-0.929259\pi$
$373$		−	8.51388i		−	0.440832i	0.975406	−	0.220416i	$-0.0707415\pi$
$374$	−3.10062			−0.160329
$375$	−10.5950	+	15.4436i	−0.547123	+	0.797503i
$376$	2.19394			0.113144
$377$		0			0
$378$		−	9.66291i		−	0.497007i
$379$			19.7186i			1.01288i	0.862276	+	0.506439i	$0.169038\pi$
$379$			19.7186i			1.01288i	−0.862276	+	0.506439i	$0.830962\pi$
$380$	10.5320	+	9.31265i	0.540279	+	0.477729i
$381$	8.68830			0.445115
$382$	0.355186			0.0181729
$383$	−27.7196			−1.41640			−0.708202	−	0.706010i	$-0.750493\pi$
$383$	−27.7196			−1.41640			−0.708202	+	0.706010i	$0.750493\pi$
$384$		−	1.67513i		−	0.0854837i
$385$	−19.4944	−	17.2374i	−0.993525	−	0.878501i
$386$	−14.0000			−0.712581
$387$		−	0.387873i		−	0.0197167i
$388$	−13.8315			−0.702186
$389$	9.15140			0.463994			0.231997	−	0.972716i	$-0.425474\pi$
$389$	9.15140			0.463994			0.231997	+	0.972716i	$0.425474\pi$
$390$		0			0
$391$	3.42548			0.173234
$392$	−3.73813			−0.188804
$393$			18.0933i			0.912687i
$394$	14.1065			0.710675
$395$	3.39868	−	3.84367i	0.171006	−	0.193396i
$396$		−	1.24965i		−	0.0627971i
$397$	−1.43041			−0.0717902			−0.0358951	−	0.999356i	$-0.511428\pi$
$397$	−1.43041			−0.0717902			−0.0358951	+	0.999356i	$0.511428\pi$
$398$	−3.14903			−0.157847
$399$	19.0214			0.952262
$400$	−0.612127	−	4.96239i	−0.0306063	−	0.248119i
$401$		−	21.6702i		−	1.08216i	−0.840972	−	0.541079i	$-0.818016\pi$
$401$		−	21.6702i		−	1.08216i	0.840972	−	0.541079i	$-0.181984\pi$
$402$			1.08840i			0.0542843i
$403$		0			0
$404$	9.59991			0.477613
$405$	−12.4133	+	14.0386i	−0.616820	+	0.697582i
$406$	−4.17679			−0.207291
$407$		−	19.7367i		−	0.978313i
$408$	−0.806063			−0.0399061
$409$		−	9.08110i		−	0.449032i	−0.974470	−	0.224516i	$-0.927920\pi$
$409$		−	9.08110i		−	0.449032i	0.974470	−	0.224516i	$-0.0720800\pi$
$410$	12.5745	+	11.1187i	0.621011	+	0.549114i
$411$			10.2922i			0.507676i
$412$			3.07522i			0.151505i
$413$			11.8740i			0.584281i
$414$			1.38058i			0.0678518i
$415$	19.7562	−	22.3430i	0.969795	−	1.09677i
$416$		0			0
$417$			17.3176i			0.848045i
$418$	40.5125			1.98153
$419$	15.5428			0.759315			0.379657	−	0.925127i	$-0.376042\pi$
$419$	15.5428			0.759315			0.379657	+	0.925127i	$0.376042\pi$
$420$	−5.06793	−	4.48119i	−0.247290	−	0.218660i
$421$		−	4.96476i		−	0.241968i	−0.992654	−	0.120984i	$-0.961395\pi$
$421$		−	4.96476i		−	0.241968i	0.992654	−	0.120984i	$-0.0386049\pi$
$422$	3.09332			0.150581
$423$	0.425485			0.0206878
$424$			0.906679i			0.0440322i
$425$	−2.38787	+	0.294552i	−0.115829	+	0.0142879i
$426$	6.13586			0.297283
$427$	−19.7767			−0.957062
$428$		−	1.67513i		−	0.0809705i
$429$		0			0
$430$	−3.35026	−	2.96239i	−0.161564	−	0.142859i
$431$		−	32.9706i		−	1.58814i	−0.607826	−	0.794070i	$-0.707958\pi$
$431$		−	32.9706i		−	1.58814i	0.607826	−	0.794070i	$-0.292042\pi$
$432$		−	5.35026i		−	0.257415i
$433$			16.1114i			0.774265i	0.922024	+	0.387133i	$0.126534\pi$
$433$			16.1114i			0.774265i	−0.922024	+	0.387133i	$0.873466\pi$
$434$			5.88224i			0.282357i
$435$	6.48944	+	5.73813i	0.311145	+	0.275123i
$436$		−	10.8872i		−	0.521401i
$437$	−44.7572			−2.14103
$438$		−	4.36741i		−	0.208683i
$439$	−0.0834721			−0.00398390			−0.00199195	−	0.999998i	$-0.500634\pi$
$439$	−0.0834721			−0.00398390			−0.00199195	+	0.999998i	$0.500634\pi$
$440$	−10.7938	−	9.54420i	−0.514576	−	0.455002i
$441$	−0.724961			−0.0345220
$442$		0			0
$443$			40.9135i			1.94386i	0.235271	+	0.971930i	$0.424402\pi$
$443$			40.9135i			1.94386i	−0.235271	+	0.971930i	$0.575598\pi$
$444$		−	5.13093i		−	0.243503i
$445$	−1.93700	−	1.71274i	−0.0918224	−	0.0811918i
$446$	22.1939			1.05091
$447$	26.8872			1.27172
$448$	1.80606			0.0853285
$449$		−	29.1319i		−	1.37482i	−0.726270	−	0.687409i	$-0.758748\pi$
$449$		−	29.1319i		−	1.37482i	0.726270	−	0.687409i	$-0.241252\pi$
$450$	−0.118714	−	0.962389i	−0.00559622	−	0.0453674i
$451$	48.3693			2.27762
$452$		−	14.0000i		−	0.658505i
$453$	−15.6082			−0.733335
$454$	13.3357			0.625874
$455$		0			0
$456$	10.5320			0.493205
$457$	−32.6678			−1.52814			−0.764068	−	0.645135i	$-0.776801\pi$
$457$	−32.6678			−1.52814			−0.764068	+	0.645135i	$0.776801\pi$
$458$			26.1744i			1.22305i
$459$	−2.57452			−0.120168
$460$	11.9248	+	10.5442i	0.555996	+	0.491626i
$461$		−	19.1006i		−	0.889604i	−0.895629	−	0.444802i	$-0.853274\pi$
$461$		−	19.1006i		−	0.889604i	0.895629	−	0.444802i	$-0.146726\pi$
$462$	−19.4944			−0.906960
$463$	8.29218			0.385370			0.192685	−	0.981261i	$-0.438280\pi$
$463$	8.29218			0.385370			0.192685	+	0.981261i	$0.438280\pi$
$464$	−2.31265			−0.107362
$465$	8.08110	−	9.13918i	0.374752	−	0.423819i
$466$			20.8691i			0.966741i
$467$		−	23.5369i		−	1.08916i	−0.838710	−	0.544579i	$-0.816689\pi$
$467$		−	23.5369i		−	1.08916i	0.838710	−	0.544579i	$-0.183311\pi$
$468$		0			0
$469$	−1.17347			−0.0541857
$470$	3.24965	−	3.67513i	0.149895	−	0.169521i
$471$	−24.7186			−1.13897
$472$			6.57452i			0.302617i
$473$	−12.8872			−0.592553
$474$		−	3.84367i		−	0.176546i
$475$	31.1998	−	3.84860i	1.43155	−	0.176586i
$476$		−	0.869067i		−	0.0398336i
$477$			0.175838i			0.00805108i
$478$			15.2931i			0.699492i
$479$			6.55642i			0.299570i	0.988719	+	0.149785i	$0.0478582\pi$
$479$			6.55642i			0.299570i	−0.988719	+	0.149785i	$0.952142\pi$
$480$	−2.80606	−	2.48119i	−0.128079	−	0.113251i
$481$		0			0
$482$			12.7685i			0.581587i
$483$	21.5369			0.979963
$484$	−30.5198			−1.38726
$485$	−20.4871	+	23.1695i	−0.930270	+	1.05207i
$486$		−	2.01222i		−	0.0912761i
$487$	−13.5599			−0.614459			−0.307229	−	0.951635i	$-0.599402\pi$
$487$	−13.5599			−0.614459			−0.307229	+	0.951635i	$0.599402\pi$
$488$	−10.9502			−0.495691
$489$		−	22.6556i		−	1.02452i
$490$	−5.53690	+	6.26187i	−0.250132	+	0.282882i
$491$	−4.95746			−0.223727			−0.111864	−	0.993724i	$-0.535682\pi$
$491$	−4.95746			−0.223727			−0.111864	+	0.993724i	$0.535682\pi$
$492$	12.5745			0.566903
$493$			1.11283i			0.0501195i
$494$		0			0
$495$	−2.09332	−	1.85097i	−0.0940878	−	0.0831949i
$496$			3.25694i			0.146241i
$497$			6.61545i			0.296744i
$498$		−	22.3430i		−	1.00121i
$499$			13.8700i			0.620907i	0.950588	+	0.310454i	$0.100481\pi$
$499$			13.8700i			0.620907i	−0.950588	+	0.310454i	$0.899519\pi$
$500$	−9.21933	−	6.32487i	−0.412301	−	0.282857i
$501$		−	39.2384i		−	1.75304i
$502$	4.21203			0.187992
$503$		−	3.44851i		−	0.153761i	−0.997040	−	0.0768807i	$-0.975504\pi$
$503$		−	3.44851i		−	0.153761i	0.997040	−	0.0768807i	$-0.0244961\pi$
$504$	0.350262			0.0156019
$505$	14.2193	−	16.0811i	0.632752	−	0.715600i
$506$	45.8700			2.03917
$507$		0			0
$508$			5.18664i			0.230120i
$509$			30.9624i			1.37238i	0.727421	+	0.686192i	$0.240719\pi$
$509$			30.9624i			1.37238i	−0.727421	+	0.686192i	$0.759281\pi$
$510$	−1.19394	+	1.35026i	−0.0528684	+	0.0597906i
$511$	4.70877			0.208304
$512$	1.00000			0.0441942
$513$	33.6385			1.48517
$514$		−	18.6253i		−	0.821527i
$515$	5.15140	+	4.55500i	0.226998	+	0.200717i
$516$	−3.35026			−0.147487
$517$		−	14.1368i		−	0.621736i
$518$	5.53198			0.243061
$519$	−7.74638			−0.340029
$520$		0			0
$521$	14.2506			0.624330			0.312165	−	0.950028i	$-0.398946\pi$
$521$	14.2506			0.624330			0.312165	+	0.950028i	$0.398946\pi$
$522$	−0.448507			−0.0196306
$523$			10.5139i			0.459740i	0.973221	+	0.229870i	$0.0738301\pi$
$523$			10.5139i			0.459740i	−0.973221	+	0.229870i	$0.926170\pi$
$524$	−10.8011			−0.471850
$525$	−15.0132	+	1.85192i	−0.655229	+	0.0808246i
$526$			23.0205i			1.00374i
$527$	1.56722			0.0682692
$528$	−10.7938			−0.469742
$529$	−27.6761			−1.20331
$530$	1.51881	+	1.34297i	0.0659727	+	0.0583348i
$531$			1.27504i			0.0553320i
$532$			11.3552i			0.492310i
$533$		0			0
$534$	−1.93700			−0.0838220
$535$	−2.80606	−	2.48119i	−0.121317	−	0.107271i
$536$	−0.649738			−0.0280644
$537$			13.9248i			0.600898i
$538$	13.4739			0.580901
$539$			24.0870i			1.03750i
$540$	−8.96239	−	7.92478i	−0.385680	−	0.341028i
$541$		−	15.5345i		−	0.667882i	−0.942594	−	0.333941i	$-0.891621\pi$
$541$		−	15.5345i		−	0.667882i	0.942594	−	0.333941i	$-0.108379\pi$
$542$			17.9003i			0.768885i
$543$		−	1.71767i		−	0.0737121i
$544$		−	0.481194i		−	0.0206310i
$545$	−18.2374	−	16.1260i	−0.781206	−	0.690762i
$546$		0			0
$547$		−	23.5515i		−	1.00699i	−0.863998	−	0.503495i	$-0.832047\pi$
$547$		−	23.5515i		−	1.00699i	0.863998	−	0.503495i	$-0.167953\pi$
$548$	−6.14411			−0.262463
$549$	−2.12364			−0.0906347
$550$	−31.9756	+	3.94429i	−1.36344	+	0.168185i
$551$		−	14.5402i		−	0.619435i
$552$	11.9248			0.507552
$553$	4.14411			0.176225
$554$		−	8.48849i		−	0.360641i
$555$	−8.59498	−	7.59991i	−0.364837	−	0.322598i
$556$	−10.3380			−0.438431
$557$	20.0459			0.849370			0.424685	−	0.905341i	$-0.360385\pi$
$557$	20.0459			0.849370			0.424685	+	0.905341i	$0.360385\pi$
$558$			0.631640i			0.0267394i
$559$		0			0
$560$	2.67513	−	3.02539i	0.113045	−	0.127846i
$561$			5.19394i			0.219288i
$562$			16.5296i			0.697260i
$563$		−	12.5745i		−	0.529953i	−0.964255	−	0.264976i	$-0.914636\pi$
$563$		−	12.5745i		−	0.529953i	0.964255	−	0.264976i	$-0.0853641\pi$
$564$		−	3.67513i		−	0.154751i
$565$	−23.4518	−	20.7367i	−0.986626	−	0.872400i
$566$			1.53690i			0.0646009i
$567$	−15.1359			−0.635646
$568$			3.66291i			0.153692i
$569$	4.28963			0.179831			0.0899153	−	0.995949i	$-0.471340\pi$
$569$	4.28963			0.179831			0.0899153	+	0.995949i	$0.471340\pi$
$570$	15.5999	−	17.6424i	0.653408	−	0.738961i
$571$	−6.39280			−0.267530			−0.133765	−	0.991013i	$-0.542707\pi$
$571$	−6.39280			−0.267530			−0.133765	+	0.991013i	$0.542707\pi$
$572$		0			0
$573$		−	0.594984i		−	0.0248558i
$574$			13.5574i			0.565874i
$575$	35.3258	−	4.35756i	1.47319	−	0.181723i
$576$	0.193937			0.00808069
$577$	−37.8169			−1.57434			−0.787168	−	0.616738i	$-0.788454\pi$
$577$	−37.8169			−1.57434			−0.787168	+	0.616738i	$0.788454\pi$
$578$	16.7685			0.697476
$579$			23.4518i			0.974625i
$580$	−3.42548	+	3.87399i	−0.142236	+	0.160859i
$581$	24.0894			0.999395
$582$			23.1695i			0.960407i
$583$	5.84226			0.241962
$584$	2.60720			0.107887
$585$		0			0
$586$	−5.92970			−0.244954
$587$	22.5501			0.930741			0.465371	−	0.885116i	$-0.345921\pi$
$587$	22.5501			0.930741			0.465371	+	0.885116i	$0.345921\pi$
$588$			6.26187i			0.258235i
$589$	−20.4772			−0.843749
$590$	11.0132	+	9.73813i	0.453405	+	0.400913i
$591$		−	23.6302i		−	0.972018i
$592$	3.06300			0.125889
$593$	8.38787			0.344449			0.172224	−	0.985058i	$-0.444905\pi$
$593$	8.38787			0.344449			0.172224	+	0.985058i	$0.444905\pi$
$594$	−34.4749			−1.41452
$595$	−1.45580	−	1.28726i	−0.0596821	−	0.0527724i
$596$			16.0508i			0.657466i
$597$			5.27504i			0.215893i
$598$		0			0
$599$	−29.0884			−1.18852			−0.594260	−	0.804273i	$-0.702555\pi$
$599$	−29.0884			−1.18852			−0.594260	+	0.804273i	$0.702555\pi$
$600$	−8.31265	+	1.02539i	−0.339363	+	0.0418615i
$601$	−43.0118			−1.75449			−0.877243	−	0.480046i	$-0.840620\pi$
$601$	−43.0118			−1.75449			−0.877243	+	0.480046i	$0.840620\pi$
$602$		−	3.61213i		−	0.147219i
$603$	−0.126008			−0.00513144
$604$		−	9.31757i		−	0.379127i
$605$	−45.2057	+	51.1246i	−1.83787	+	2.07851i
$606$		−	16.0811i		−	0.653250i
$607$		−	21.7513i		−	0.882858i	−0.897296	−	0.441429i	$-0.854472\pi$
$607$		−	21.7513i		−	0.882858i	0.897296	−	0.441429i	$-0.145528\pi$
$608$			6.28726i			0.254982i
$609$			6.99668i			0.283520i
$610$	−16.2193	+	18.3430i	−0.656701	+	0.742685i
$611$		0			0
$612$		−	0.0933212i		−	0.00377228i
$613$	−30.8129			−1.24452			−0.622261	−	0.782810i	$-0.713786\pi$
$613$	−30.8129			−1.24452			−0.622261	+	0.782810i	$0.713786\pi$
$614$	17.9756			0.725435
$615$	18.6253	−	21.0640i	0.751045	−	0.849381i
$616$		−	11.6375i		−	0.468889i
$617$	−46.0870			−1.85539			−0.927696	−	0.373336i	$-0.878214\pi$
$617$	−46.0870			−1.85539			−0.927696	+	0.373336i	$0.878214\pi$
$618$	5.15140			0.207220
$619$		−	13.5564i		−	0.544878i	−0.962173	−	0.272439i	$-0.912170\pi$
$619$		−	13.5564i		−	0.544878i	0.962173	−	0.272439i	$-0.0878304\pi$
$620$	5.45580	+	4.82416i	0.219110	+	0.193743i
$621$	38.0870			1.52838
$622$	−15.9575			−0.639836
$623$		−	2.08840i		−	0.0836698i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$		−	23.4372i		−	0.936741i
$627$		−	67.8637i		−	2.71021i
$628$		−	14.7562i		−	0.588838i
$629$		−	1.47390i		−	0.0587682i
$630$	0.518806	−	0.586734i	0.0206697	−	0.0233761i
$631$			5.35026i			0.212991i	0.994313	+	0.106495i	$0.0339629\pi$
$631$			5.35026i			0.212991i	−0.994313	+	0.106495i	$0.966037\pi$
$632$	2.29455			0.0912724
$633$		−	5.18172i		−	0.205955i
$634$	−20.6507			−0.820144
$635$	8.68830	+	7.68243i	0.344785	+	0.304868i
$636$	1.51881			0.0602246
$637$		0			0
$638$			14.9018i			0.589966i
$639$			0.710373i			0.0281019i
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	−12.3806			−0.489003			−0.244502	−	0.969649i	$-0.578624\pi$
$641$	−12.3806			−0.489003			−0.244502	+	0.969649i	$0.578624\pi$
$642$	−2.80606			−0.110746
$643$	−11.5247			−0.454489			−0.227245	−	0.973838i	$-0.572972\pi$
$643$	−11.5247			−0.454489			−0.227245	+	0.973838i	$0.572972\pi$
$644$			12.8568i			0.506631i
$645$	−4.96239	+	5.61213i	−0.195394	+	0.220977i
$646$	3.02539			0.119032
$647$		−	3.67021i		−	0.144291i	−0.997394	−	0.0721453i	$-0.977015\pi$
$647$		−	3.67021i		−	0.144291i	0.997394	−	0.0721453i	$-0.0229845\pi$
$648$	−8.38058			−0.329220
$649$	42.3634			1.66291
$650$		0			0
$651$	9.85352			0.386190
$652$	13.5247			0.529668
$653$		−	8.10650i		−	0.317232i	−0.987340	−	0.158616i	$-0.949297\pi$
$653$		−	8.10650i		−	0.317232i	0.987340	−	0.158616i	$-0.0507031\pi$
$654$	−18.2374			−0.713140
$655$	−15.9986	+	18.0933i	−0.625116	+	0.706965i
$656$			7.50659i			0.293083i
$657$	0.505632			0.0197266
$658$	3.96239			0.154470
$659$	−18.5442			−0.722379			−0.361190	−	0.932492i	$-0.617629\pi$
$659$	−18.5442			−0.722379			−0.361190	+	0.932492i	$0.617629\pi$
$660$	−15.9878	+	18.0811i	−0.622324	+	0.703806i
$661$		−	46.4119i		−	1.80521i	−0.430468	−	0.902606i	$-0.641651\pi$
$661$		−	46.4119i		−	1.80521i	0.430468	−	0.902606i	$-0.358349\pi$
$662$		−	26.6761i		−	1.03680i
$663$		0			0
$664$	13.3380			0.517616
$665$	19.0214	+	16.8192i	0.737619	+	0.652222i
$666$	0.594028			0.0230181
$667$		−	16.4631i		−	0.637454i
$668$	23.4241			0.906304
$669$		−	37.1777i		−	1.43737i
$670$	−0.962389	+	1.08840i	−0.0371803	+	0.0420484i
$671$			70.5583i			2.72387i
$672$		−	3.02539i		−	0.116707i
$673$		−	40.4095i		−	1.55767i	−0.627228	−	0.778836i	$-0.715811\pi$
$673$		−	40.4095i		−	1.55767i	0.627228	−	0.778836i	$-0.284189\pi$
$674$		−	8.40597i		−	0.323786i
$675$	−26.5501	+	3.27504i	−1.02191	+	0.126056i
$676$		0			0
$677$		−	14.2473i		−	0.547567i	−0.961791	−	0.273784i	$-0.911725\pi$
$677$		−	14.2473i		−	0.547567i	0.961791	−	0.273784i	$-0.0882752\pi$
$678$	−23.4518			−0.900662
$679$	−24.9805			−0.958663
$680$	−0.806063	−	0.712742i	−0.0309111	−	0.0273324i
$681$		−	22.3390i		−	0.856032i
$682$	20.9864			0.803610
$683$	−5.80351			−0.222065			−0.111033	−	0.993817i	$-0.535416\pi$
$683$	−5.80351			−0.222065			−0.111033	+	0.993817i	$0.535416\pi$
$684$			1.21933i			0.0466222i
$685$	−9.10062	+	10.2922i	−0.347717	+	0.393244i
$686$	−19.3938			−0.740457
$687$	43.8456			1.67281
$688$		−	2.00000i		−	0.0762493i
$689$		0			0
$690$	17.6629	−	19.9756i	0.672416	−	0.760457i
$691$		−	19.2398i		−	0.731916i	−0.930631	−	0.365958i	$-0.880741\pi$
$691$		−	19.2398i		−	0.731916i	0.930631	−	0.365958i	$-0.119259\pi$
$692$		−	4.62435i		−	0.175791i
$693$		−	2.25694i		−	0.0857341i
$694$			21.1514i			0.802896i
$695$	−15.3127	+	17.3176i	−0.580842	+	0.656893i
$696$			3.87399i			0.146843i
$697$	3.61213			0.136819
$698$			5.47390i			0.207190i
$699$	34.9584			1.32225
$700$	−1.10554	−	8.96239i	−0.0417855	−	0.338746i
$701$	−45.3742			−1.71376			−0.856881	−	0.515515i	$-0.827601\pi$
$701$	−45.3742			−1.71376			−0.856881	+	0.515515i	$0.827601\pi$
$702$		0			0
$703$			19.2579i			0.726325i
$704$		−	6.44358i		−	0.242852i
$705$	−6.15633	−	5.44358i	−0.231861	−	0.205017i
$706$	30.1441			1.13449
$707$	17.3380			0.652064
$708$	11.0132			0.413900
$709$			3.97319i			0.149216i	0.997213	+	0.0746082i	$0.0237706\pi$
$709$			3.97319i			0.149216i	−0.997213	+	0.0746082i	$0.976229\pi$
$710$	6.13586	+	5.42548i	0.230275	+	0.203615i
$711$	0.444998			0.0166887
$712$		−	1.15633i		−	0.0433351i
$713$	−23.1852			−0.868294
$714$	−1.45580			−0.0544820
$715$		0			0
$716$	−8.31265			−0.310658
$717$	25.6180			0.956722
$718$		−	8.38787i		−	0.313033i
$719$	45.6991			1.70429			0.852145	−	0.523306i	$-0.175302\pi$
$719$	45.6991			1.70429			0.852145	+	0.523306i	$0.175302\pi$
$720$	0.287258	−	0.324869i	0.0107055	−	0.0121072i
$721$			5.55405i			0.206844i
$722$	−20.5296			−0.764033
$723$	21.3888			0.795459
$724$	1.02539			0.0381084
$725$	1.41564	+	11.4763i	0.0525754	+	0.426218i
$726$			51.1246i			1.89741i
$727$			24.7948i			0.919588i	0.888026	+	0.459794i	$0.152077\pi$
$727$			24.7948i			0.919588i	−0.888026	+	0.459794i	$0.847923\pi$
$728$		0			0
$729$	−28.5125			−1.05602
$730$	3.86177	−	4.36741i	0.142931	−	0.161645i
$731$	−0.962389			−0.0355952
$732$			18.3430i			0.677976i
$733$	45.8651			1.69407			0.847033	−	0.531540i	$-0.178387\pi$
$733$	45.8651			1.69407			0.847033	+	0.531540i	$0.178387\pi$
$734$			19.5125i			0.720218i
$735$	10.4894	+	9.27504i	0.386909	+	0.342115i
$736$			7.11871i			0.262399i
$737$			4.18664i			0.154217i
$738$			1.45580i			0.0535888i
$739$			34.9633i			1.28615i	0.765804	+	0.643074i	$0.222341\pi$
$739$			34.9633i			1.28615i	−0.765804	+	0.643074i	$0.777659\pi$
$740$	4.53690	−	5.13093i	0.166780	−	0.188617i
$741$		0			0
$742$			1.63752i			0.0601152i
$743$	−6.86670			−0.251915			−0.125957	−	0.992036i	$-0.540200\pi$
$743$	−6.86670			−0.251915			−0.125957	+	0.992036i	$0.540200\pi$
$744$	5.45580			0.200019
$745$	26.8872	+	23.7743i	0.985070	+	0.871024i
$746$		−	8.51388i		−	0.311715i
$747$	2.58673			0.0946437
$748$	−3.10062			−0.113370
$749$		−	3.02539i		−	0.110545i
$750$	−10.5950	+	15.4436i	−0.386874	+	0.563920i
$751$	−4.80018			−0.175161			−0.0875806	−	0.996157i	$-0.527914\pi$
$751$	−4.80018			−0.175161			−0.0875806	+	0.996157i	$0.527914\pi$
$752$	2.19394			0.0800046
$753$		−	7.05571i		−	0.257124i
$754$		0			0
$755$	−15.6082	−	13.8011i	−0.568039	−	0.502275i
$756$		−	9.66291i		−	0.351437i
$757$		−	27.7753i		−	1.00951i	−0.863263	−	0.504755i	$-0.831583\pi$
$757$		−	27.7753i		−	1.00951i	0.863263	−	0.504755i	$-0.168417\pi$
$758$			19.7186i			0.716213i
$759$		−	76.8383i		−	2.78905i
$760$	10.5320	+	9.31265i	0.382035	+	0.337805i
$761$			3.16220i			0.114630i	0.998356	+	0.0573149i	$0.0182539\pi$
$761$			3.16220i			0.114630i	−0.998356	+	0.0573149i	$0.981746\pi$
$762$	8.68830			0.314744
$763$		−	19.6629i		−	0.711845i
$764$	0.355186			0.0128502
$765$	−0.156325	−	0.138227i	−0.00565195	−	0.00499760i
$766$	−27.7196			−1.00155
$767$		0			0
$768$		−	1.67513i		−	0.0604461i
$769$		−	8.15633i		−	0.294125i	−0.989127	−	0.147062i	$-0.953018\pi$
$769$		−	8.15633i		−	0.294125i	0.989127	−	0.147062i	$-0.0469818\pi$
$770$	−19.4944	−	17.2374i	−0.702528	−	0.621194i
$771$	−31.1998			−1.12363
$772$	−14.0000			−0.503871
$773$	5.87892			0.211450			0.105725	−	0.994395i	$-0.466284\pi$
$773$	5.87892			0.211450			0.105725	+	0.994395i	$0.466284\pi$
$774$		−	0.387873i		−	0.0139418i
$775$	16.1622	−	1.99366i	0.580564	−	0.0716144i
$776$	−13.8315			−0.496520
$777$		−	9.26679i		−	0.332444i
$778$	9.15140			0.328094
$779$	−47.1958			−1.69097
$780$		0			0
$781$	23.6023			0.844556
$782$	3.42548			0.122495
$783$			12.3733i			0.442185i
$784$	−3.73813			−0.133505
$785$	−24.7186	−	21.8568i	−0.882245	−	0.780104i
$786$			18.0933i			0.645367i
$787$	23.7015			0.844866			0.422433	−	0.906394i	$-0.361176\pi$
$787$	23.7015			0.844866			0.422433	+	0.906394i	$0.361176\pi$
$788$	14.1065			0.502523
$789$	38.5623			1.37285
$790$	3.39868	−	3.84367i	0.120920	−	0.136752i
$791$		−	25.2849i		−	0.899027i
$792$		−	1.24965i		−	0.0444042i
$793$		0			0
$794$	−1.43041			−0.0507633
$795$	2.24965	−	2.54420i	0.0797867	−	0.0902334i
$796$	−3.14903			−0.111614
$797$			48.5198i			1.71866i	0.511423	+	0.859329i	$0.329119\pi$
$797$			48.5198i			1.71866i	−0.511423	+	0.859329i	$0.670881\pi$
$798$	19.0214			0.673351
$799$		−	1.05571i		−	0.0373483i
$800$	−0.612127	−	4.96239i	−0.0216420	−	0.175447i
$801$		−	0.224254i		−	0.00792362i
$802$		−	21.6702i		−	0.765202i
$803$		−	16.7997i		−	0.592849i
$804$			1.08840i			0.0383848i
$805$	21.5369	+	19.0435i	0.759076	+	0.671195i
$806$		0			0
$807$		−	22.5705i		−	0.794521i
$808$	9.59991			0.337724
$809$	17.1187			0.601862			0.300931	−	0.953646i	$-0.402703\pi$
$809$	17.1187			0.601862			0.300931	+	0.953646i	$0.402703\pi$
$810$	−12.4133	+	14.0386i	−0.436158	+	0.493265i
$811$		−	7.67372i		−	0.269461i	−0.990882	−	0.134730i	$-0.956983\pi$
$811$		−	7.67372i		−	0.269461i	0.990882	−	0.134730i	$-0.0430168\pi$
$812$	−4.17679			−0.146577
$813$	29.9854			1.05163
$814$		−	19.7367i		−	0.691772i
$815$	20.0327	−	22.6556i	0.701714	−	0.793592i
$816$	−0.806063			−0.0282179
$817$	12.5745			0.439927
$818$		−	9.08110i		−	0.317513i
$819$		0			0
$820$	12.5745	+	11.1187i	0.439121	+	0.388282i
$821$		−	53.7866i		−	1.87716i	−0.345057	−	0.938582i	$-0.612140\pi$
$821$		−	53.7866i		−	1.87716i	0.345057	−	0.938582i	$-0.387860\pi$
$822$			10.2922i			0.358981i
$823$			9.77575i			0.340761i	0.985378	+	0.170381i	$0.0544997\pi$
$823$			9.77575i			0.340761i	−0.985378	+	0.170381i	$0.945500\pi$
$824$			3.07522i			0.107130i
$825$	6.60720	+	53.5633i	0.230033	+	1.86483i
$826$			11.8740i			0.413149i
$827$	28.1598			0.979213			0.489607	−	0.871943i	$-0.337140\pi$
$827$	28.1598			0.979213			0.489607	+	0.871943i	$0.337140\pi$
$828$			1.38058i			0.0479784i
$829$	20.2130			0.702026			0.351013	−	0.936371i	$-0.385837\pi$
$829$	20.2130			0.702026			0.351013	+	0.936371i	$0.385837\pi$
$830$	19.7562	−	22.3430i	0.685749	−	0.775536i
$831$	−14.2193			−0.493263
$832$		0			0
$833$			1.79877i			0.0623237i
$834$			17.3176i			0.599659i
$835$	34.6956	−	39.2384i	1.20069	−	1.35790i
$836$	40.5125			1.40115
$837$	17.4255			0.602313
$838$	15.5428			0.536917
$839$			12.5926i			0.434745i	0.976089	+	0.217373i	$0.0697487\pi$
$839$			12.5926i			0.434745i	−0.976089	+	0.217373i	$0.930251\pi$
$840$	−5.06793	−	4.48119i	−0.174860	−	0.154616i
$841$	−23.6516			−0.815574
$842$		−	4.96476i		−	0.171097i
$843$	27.6893			0.953669
$844$	3.09332			0.106477
$845$		0			0
$846$	0.425485			0.0146285
$847$	−55.1206			−1.89397
$848$			0.906679i			0.0311355i
$849$	2.57452			0.0883571
$850$	−2.38787	+	0.294552i	−0.0819034	+	0.0101030i
$851$			21.8046i			0.747454i
$852$	6.13586			0.210211
$853$	45.7704			1.56715			0.783574	−	0.621299i	$-0.213395\pi$
$853$	45.7704			1.56715			0.783574	+	0.621299i	$0.213395\pi$
$854$	−19.7767			−0.676745
$855$	2.04254	+	1.80606i	0.0698533	+	0.0617661i
$856$		−	1.67513i		−	0.0572548i
$857$			27.8169i			0.950206i	0.879930	+	0.475103i	$0.157589\pi$
$857$			27.8169i			0.950206i	−0.879930	+	0.475103i	$0.842411\pi$
$858$		0			0
$859$	−25.9706			−0.886107			−0.443053	−	0.896495i	$-0.646105\pi$
$859$	−25.9706			−0.886107			−0.443053	+	0.896495i	$0.646105\pi$
$860$	−3.35026	−	2.96239i	−0.114243	−	0.101017i
$861$	22.7104			0.773967
$862$		−	32.9706i		−	1.12298i
$863$	18.7210			0.637270			0.318635	−	0.947877i	$-0.396776\pi$
$863$	18.7210			0.637270			0.318635	+	0.947877i	$0.396776\pi$
$864$		−	5.35026i		−	0.182020i
$865$	−7.74638	−	6.84955i	−0.263385	−	0.232892i
$866$			16.1114i			0.547488i
$867$		−	28.0894i		−	0.953964i
$868$			5.88224i			0.199656i
$869$		−	14.7851i		−	0.501551i
$870$	6.48944	+	5.73813i	0.220013	+	0.194541i
$871$		0			0
$872$		−	10.8872i		−	0.368686i
$873$	−2.68243			−0.0907863
$874$	−44.7572			−1.51393
$875$	−16.6507	−	11.4231i	−0.562896	−	0.386172i
$876$		−	4.36741i		−	0.147561i
$877$	22.6859			0.766050			0.383025	−	0.923738i	$-0.374882\pi$
$877$	22.6859			0.766050			0.383025	+	0.923738i	$0.374882\pi$
$878$	−0.0834721			−0.00281705
$879$			9.93303i			0.335033i
$880$	−10.7938	−	9.54420i	−0.363860	−	0.321735i
$881$	2.47627			0.0834276			0.0417138	−	0.999130i	$-0.486718\pi$
$881$	2.47627			0.0834276			0.0417138	+	0.999130i	$0.486718\pi$
$882$	−0.724961			−0.0244107
$883$		−	31.4641i		−	1.05885i	−0.848357	−	0.529425i	$-0.822408\pi$
$883$		−	31.4641i		−	1.05885i	0.848357	−	0.529425i	$-0.177592\pi$
$884$		0			0
$885$	16.3127	−	18.4485i	0.548344	−	0.620140i
$886$			40.9135i			1.37452i
$887$			39.7163i			1.33354i	0.745263	+	0.666771i	$0.232324\pi$
$887$			39.7163i			1.33354i	−0.745263	+	0.666771i	$0.767676\pi$
$888$		−	5.13093i		−	0.172183i
$889$			9.36741i			0.314173i
$890$	−1.93700	−	1.71274i	−0.0649283	−	0.0574113i
$891$			54.0010i			1.80910i
$892$	22.1939			0.743108
$893$			13.7938i			0.461593i
$894$	26.8872			0.899241
$895$	−12.3127	+	13.9248i	−0.411567	+	0.465454i
$896$	1.80606			0.0603363
$897$		0			0
$898$		−	29.1319i		−	0.972144i
$899$		−	7.53216i		−	0.251212i
$900$	−0.118714	−	0.962389i	−0.00395713	−	0.0320796i
$901$	0.436289			0.0145349
$902$	48.3693			1.61052
$903$	−6.05079			−0.201358
$904$		−	14.0000i		−	0.465633i
$905$	1.51881	−	1.71767i	0.0504868	−	0.0570972i
$906$	−15.6082			−0.518546
$907$			53.5755i			1.77894i	0.456989	+	0.889472i	$0.348928\pi$
$907$			53.5755i			1.77894i	−0.456989	+	0.889472i	$0.651072\pi$
$908$	13.3357			0.442560
$909$	1.86177			0.0617511
$910$		0			0
$911$	14.6253			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$911$	14.6253			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$912$	10.5320			0.348749
$913$		−	85.9448i		−	2.84436i
$914$	−32.6678			−1.08056
$915$	30.7269	+	27.1695i	1.01580	+	0.898196i
$916$			26.1744i			0.864827i
$917$	−19.5075			−0.644196
$918$	−2.57452			−0.0849717
$919$	−53.0494			−1.74994			−0.874969	−	0.484180i	$-0.839118\pi$
$919$	−53.0494			−1.74994			−0.874969	+	0.484180i	$0.839118\pi$
$920$	11.9248	+	10.5442i	0.393148	+	0.347632i
$921$		−	30.1114i		−	0.992205i
$922$		−	19.1006i		−	0.629045i
$923$		0			0
$924$	−19.4944			−0.641318
$925$	−1.87495	−	15.1998i	−0.0616479	−	0.499767i
$926$	8.29218			0.272498
$927$			0.596398i			0.0195883i
$928$	−2.31265			−0.0759165
$929$			10.4504i			0.342867i	0.985196	+	0.171434i	$0.0548399\pi$
$929$			10.4504i			0.342867i	−0.985196	+	0.171434i	$0.945160\pi$
$930$	8.08110	−	9.13918i	0.264990	−	0.299686i
$931$		−	23.5026i		−	0.770267i
$932$			20.8691i			0.683589i
$933$			26.7308i			0.875128i
$934$		−	23.5369i		−	0.770151i
$935$	−4.59261	+	5.19394i	−0.150195	+	0.169860i
$936$		0			0
$937$			10.5745i			0.345454i	0.984970	+	0.172727i	$0.0552579\pi$
$937$			10.5745i			0.345454i	−0.984970	+	0.172727i	$0.944742\pi$
$938$	−1.17347			−0.0383151
$939$	−39.2605			−1.28122
$940$	3.24965	−	3.67513i	0.105992	−	0.119870i
$941$		−	16.6107i		−	0.541494i	−0.962651	−	0.270747i	$-0.912729\pi$
$941$		−	16.6107i		−	0.541494i	0.962651	−	0.270747i	$-0.0872706\pi$
$942$	−24.7186			−0.805376
$943$	−53.4372			−1.74016
$944$			6.57452i			0.213982i
$945$	−16.1866	−	14.3127i	−0.526552	−	0.465591i
$946$	−12.8872			−0.418998
$947$	−42.4871			−1.38064			−0.690322	−	0.723502i	$-0.742531\pi$
$947$	−42.4871			−1.38064			−0.690322	+	0.723502i	$0.742531\pi$
$948$		−	3.84367i		−	0.124837i
$949$		0			0
$950$	31.1998	−	3.84860i	1.01226	−	0.124865i
$951$			34.5926i			1.12174i
$952$		−	0.869067i		−	0.0281666i
$953$		−	45.0214i		−	1.45839i	−0.684308	−	0.729193i	$-0.739895\pi$
$953$		−	45.0214i		−	1.45839i	0.684308	−	0.729193i	$-0.260105\pi$
$954$			0.175838i			0.00569297i
$955$	0.526100	−	0.594984i	0.0170242	−	0.0192532i
$956$			15.2931i			0.494615i
$957$	24.9624			0.806919
$958$			6.55642i			0.211828i
$959$	−11.0966			−0.358329
$960$	−2.80606	−	2.48119i	−0.0905653	−	0.0800802i
$961$	20.3923			0.657817
$962$		0			0
$963$		−	0.324869i		−	0.0104688i
$964$			12.7685i			0.411244i
$965$	−20.7367	+	23.4518i	−0.667539	+	0.754941i
$966$	21.5369			0.692939
$967$	−24.4763			−0.787104			−0.393552	−	0.919302i	$-0.628754\pi$
$967$	−24.4763			−0.787104			−0.393552	+	0.919302i	$0.628754\pi$
$968$	−30.5198			−0.980942
$969$		−	5.06793i		−	0.162805i
$970$	−20.4871	+	23.1695i	−0.657800	+	0.743928i
$971$	−56.4046			−1.81011			−0.905054	−	0.425296i	$-0.860170\pi$
$971$	−56.4046			−1.81011			−0.905054	+	0.425296i	$0.860170\pi$
$972$		−	2.01222i		−	0.0645419i
$973$	−18.6712			−0.598570
$974$	−13.5599			−0.434488
$975$		0			0
$976$	−10.9502			−0.350506
$977$	−13.5125			−0.432302			−0.216151	−	0.976360i	$-0.569350\pi$
$977$	−13.5125			−0.432302			−0.216151	+	0.976360i	$0.569350\pi$
$978$		−	22.6556i		−	0.724447i
$979$	−7.45088			−0.238131
$980$	−5.53690	+	6.26187i	−0.176870	+	0.200028i
$981$		−	2.11142i		−	0.0674124i
$982$	−4.95746			−0.158199
$983$	−30.1187			−0.960638			−0.480319	−	0.877094i	$-0.659479\pi$
$983$	−30.1187			−0.960638			−0.480319	+	0.877094i	$0.659479\pi$
$984$	12.5745			0.400861
$985$	20.8945	−	23.6302i	0.665753	−	0.752922i
$986$			1.11283i			0.0354399i
$987$		−	6.63752i		−	0.211275i
$988$		0			0
$989$	14.2374			0.452724
$990$	−2.09332	−	1.85097i	−0.0665301	−	0.0588277i
$991$	35.3258			1.12216			0.561081	−	0.827761i	$-0.310386\pi$
$991$	35.3258			1.12216			0.561081	+	0.827761i	$0.310386\pi$
$992$			3.25694i			0.103408i
$993$	−44.6859			−1.41807
$994$			6.61545i			0.209829i
$995$	−4.66433	+	5.27504i	−0.147869	+	0.167230i
$996$		−	22.3430i		−	0.707964i
$997$			16.8169i			0.532596i	0.963891	+	0.266298i	$0.0858004\pi$
$997$			16.8169i			0.532596i	−0.963891	+	0.266298i	$0.914200\pi$
$998$			13.8700i			0.439048i
$999$		−	16.3879i		−	0.518489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.c.1689.2		6
5.4	even	2		1690.2.c.b.1689.5		6
13.2	odd	12		130.2.n.a.9.6	yes	12
13.5	odd	4		1690.2.b.c.339.1		6
13.6	odd	12		130.2.n.a.29.1	yes	12
13.8	odd	4		1690.2.b.b.339.4		6
13.12	even	2		1690.2.c.b.1689.2		6
39.2	even	12		1170.2.bp.h.919.3		12
39.32	even	12		1170.2.bp.h.289.6		12
52.15	even	12		1040.2.dh.b.529.2		12
52.19	even	12		1040.2.dh.b.289.5		12
65.2	even	12		650.2.e.j.451.3		6
65.8	even	4		8450.2.a.ca.1.3		3
65.18	even	4		8450.2.a.bu.1.3		3
65.19	odd	12		130.2.n.a.29.6	yes	12
65.28	even	12		650.2.e.k.451.1		6
65.32	even	12		650.2.e.j.601.3		6
65.34	odd	4		1690.2.b.b.339.3		6
65.44	odd	4		1690.2.b.c.339.6		6
65.47	even	4		8450.2.a.bt.1.1		3
65.54	odd	12		130.2.n.a.9.1	✓	12
65.57	even	4		8450.2.a.cb.1.1		3
65.58	even	12		650.2.e.k.601.1		6
65.64	even	2	inner	1690.2.c.c.1689.5		6
195.119	even	12		1170.2.bp.h.919.6		12
195.149	even	12		1170.2.bp.h.289.3		12
260.19	even	12		1040.2.dh.b.289.2		12
260.119	even	12		1040.2.dh.b.529.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	65.54	odd	12
130.2.n.a.9.6	yes	12	13.2	odd	12
130.2.n.a.29.1	yes	12	13.6	odd	12
130.2.n.a.29.6	yes	12	65.19	odd	12
650.2.e.j.451.3		6	65.2	even	12
650.2.e.j.601.3		6	65.32	even	12
650.2.e.k.451.1		6	65.28	even	12
650.2.e.k.601.1		6	65.58	even	12
1040.2.dh.b.289.2		12	260.19	even	12
1040.2.dh.b.289.5		12	52.19	even	12
1040.2.dh.b.529.2		12	52.15	even	12
1040.2.dh.b.529.5		12	260.119	even	12
1170.2.bp.h.289.3		12	195.149	even	12
1170.2.bp.h.289.6		12	39.32	even	12
1170.2.bp.h.919.3		12	39.2	even	12
1170.2.bp.h.919.6		12	195.119	even	12
1690.2.b.b.339.3		6	65.34	odd	4
1690.2.b.b.339.4		6	13.8	odd	4
1690.2.b.c.339.1		6	13.5	odd	4
1690.2.b.c.339.6		6	65.44	odd	4
1690.2.c.b.1689.2		6	13.12	even	2
1690.2.c.b.1689.5		6	5.4	even	2
1690.2.c.c.1689.2		6	1.1	even	1	trivial
1690.2.c.c.1689.5		6	65.64	even	2	inner
8450.2.a.bt.1.1		3	65.47	even	4
8450.2.a.bu.1.3		3	65.18	even	4
8450.2.a.ca.1.3		3	65.8	even	4
8450.2.a.cb.1.1		3	65.57	even	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.67513i q^{3} +1.00000 q^{4} +(1.48119 - 1.67513i) q^{5} -1.67513i q^{6} +1.80606 q^{7} +1.00000 q^{8} +0.193937 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.67513i q^{3} +1.00000 q^{4} +(1.48119 - 1.67513i) q^{5} -1.67513i q^{6} +1.80606 q^{7} +1.00000 q^{8} +0.193937 q^{9} +(1.48119 - 1.67513i) q^{10} -6.44358i q^{11} -1.67513i q^{12} +1.80606 q^{14} +(-2.80606 - 2.48119i) q^{15} +1.00000 q^{16} -0.481194i q^{17} +0.193937 q^{18} +6.28726i q^{19} +(1.48119 - 1.67513i) q^{20} -3.02539i q^{21} -6.44358i q^{22} +7.11871i q^{23} -1.67513i q^{24} +(-0.612127 - 4.96239i) q^{25} -5.35026i q^{27} +1.80606 q^{28} -2.31265 q^{29} +(-2.80606 - 2.48119i) q^{30} +3.25694i q^{31} +1.00000 q^{32} -10.7938 q^{33} -0.481194i q^{34} +(2.67513 - 3.02539i) q^{35} +0.193937 q^{36} +3.06300 q^{37} +6.28726i q^{38} +(1.48119 - 1.67513i) q^{40} +7.50659i q^{41} -3.02539i q^{42} -2.00000i q^{43} -6.44358i q^{44} +(0.287258 - 0.324869i) q^{45} +7.11871i q^{46} +2.19394 q^{47} -1.67513i q^{48} -3.73813 q^{49} +(-0.612127 - 4.96239i) q^{50} -0.806063 q^{51} +0.906679i q^{53} -5.35026i q^{54} +(-10.7938 - 9.54420i) q^{55} +1.80606 q^{56} +10.5320 q^{57} -2.31265 q^{58} +6.57452i q^{59} +(-2.80606 - 2.48119i) q^{60} -10.9502 q^{61} +3.25694i q^{62} +0.350262 q^{63} +1.00000 q^{64} -10.7938 q^{66} -0.649738 q^{67} -0.481194i q^{68} +11.9248 q^{69} +(2.67513 - 3.02539i) q^{70} +3.66291i q^{71} +0.193937 q^{72} +2.60720 q^{73} +3.06300 q^{74} +(-8.31265 + 1.02539i) q^{75} +6.28726i q^{76} -11.6375i q^{77} +2.29455 q^{79} +(1.48119 - 1.67513i) q^{80} -8.38058 q^{81} +7.50659i q^{82} +13.3380 q^{83} -3.02539i q^{84} +(-0.806063 - 0.712742i) q^{85} -2.00000i q^{86} +3.87399i q^{87} -6.44358i q^{88} -1.15633i q^{89} +(0.287258 - 0.324869i) q^{90} +7.11871i q^{92} +5.45580 q^{93} +2.19394 q^{94} +(10.5320 + 9.31265i) q^{95} -1.67513i q^{96} -13.8315 q^{97} -3.73813 q^{98} -1.24965i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} + 10 q^{14} - 16 q^{15} + 6 q^{16} + 2 q^{18} - 2 q^{20} - 2 q^{25} + 10 q^{28} + 28 q^{29} - 16 q^{30} + 6 q^{32} - 12 q^{33} + 6 q^{35} + 2 q^{36} + 10 q^{37} - 2 q^{40} - 10 q^{45} + 14 q^{47} - 4 q^{49} - 2 q^{50} - 4 q^{51} - 12 q^{55} + 10 q^{56} - 8 q^{57} + 28 q^{58} - 16 q^{60} + 8 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{66} - 24 q^{67} + 28 q^{69} + 6 q^{70} + 2 q^{72} - 12 q^{73} + 10 q^{74} - 8 q^{75} + 28 q^{79} - 2 q^{80} - 26 q^{81} + 8 q^{83} - 4 q^{85} - 10 q^{90} + 52 q^{93} + 14 q^{94} - 8 q^{95} - 52 q^{97} - 4 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 + 10 * q^14 - 16 * q^15 + 6 * q^16 + 2 * q^18 - 2 * q^20 - 2 * q^25 + 10 * q^28 + 28 * q^29 - 16 * q^30 + 6 * q^32 - 12 * q^33 + 6 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^40 - 10 * q^45 + 14 * q^47 - 4 * q^49 - 2 * q^50 - 4 * q^51 - 12 * q^55 + 10 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^60 + 8 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^66 - 24 * q^67 + 28 * q^69 + 6 * q^70 + 2 * q^72 - 12 * q^73 + 10 * q^74 - 8 * q^75 + 28 * q^79 - 2 * q^80 - 26 * q^81 + 8 * q^83 - 4 * q^85 - 10 * q^90 + 52 * q^93 + 14 * q^94 - 8 * q^95 - 52 * q^97 - 4 * q^98

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