LMFDB - Embedded newform 1205.2.b.c.724.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.5
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36215i q^{2} -2.05253i q^{3} -3.57974 q^{4} +(-0.618559 + 2.14881i) q^{5} -4.84838 q^{6} +3.07728i q^{7} +3.73158i q^{8} -1.21289 q^{9} +O(q^{10})$	\(q-2.36215i q^{2} -2.05253i q^{3} -3.57974 q^{4} +(-0.618559 + 2.14881i) q^{5} -4.84838 q^{6} +3.07728i q^{7} +3.73158i q^{8} -1.21289 q^{9} +(5.07581 + 1.46113i) q^{10} +0.942447 q^{11} +7.34753i q^{12} +1.99403i q^{13} +7.26899 q^{14} +(4.41050 + 1.26961i) q^{15} +1.65507 q^{16} -3.11539i q^{17} +2.86502i q^{18} +6.33222 q^{19} +(2.21428 - 7.69218i) q^{20} +6.31621 q^{21} -2.22620i q^{22} +7.91084i q^{23} +7.65919 q^{24} +(-4.23477 - 2.65833i) q^{25} +4.71020 q^{26} -3.66811i q^{27} -11.0159i q^{28} +1.63432 q^{29} +(2.99901 - 10.4183i) q^{30} +6.96040 q^{31} +3.55366i q^{32} -1.93440i q^{33} -7.35900 q^{34} +(-6.61249 - 1.90348i) q^{35} +4.34182 q^{36} +0.864280i q^{37} -14.9576i q^{38} +4.09282 q^{39} +(-8.01846 - 2.30820i) q^{40} +1.70732 q^{41} -14.9198i q^{42} -10.2266i q^{43} -3.37372 q^{44} +(0.750242 - 2.60626i) q^{45} +18.6866 q^{46} +6.49786i q^{47} -3.39707i q^{48} -2.46965 q^{49} +(-6.27937 + 10.0032i) q^{50} -6.39443 q^{51} -7.13813i q^{52} +2.20905i q^{53} -8.66461 q^{54} +(-0.582959 + 2.02514i) q^{55} -11.4831 q^{56} -12.9971i q^{57} -3.86050i q^{58} +7.69694 q^{59} +(-15.7885 - 4.54488i) q^{60} -3.70322 q^{61} -16.4415i q^{62} -3.73239i q^{63} +11.7044 q^{64} +(-4.28480 - 1.23343i) q^{65} -4.56935 q^{66} +7.96470i q^{67} +11.1523i q^{68} +16.2373 q^{69} +(-4.49630 + 15.6197i) q^{70} -7.02031 q^{71} -4.52599i q^{72} -6.13583i q^{73} +2.04156 q^{74} +(-5.45631 + 8.69200i) q^{75} -22.6677 q^{76} +2.90017i q^{77} -9.66784i q^{78} +14.0583 q^{79} +(-1.02376 + 3.55642i) q^{80} -11.1676 q^{81} -4.03294i q^{82} +3.98789i q^{83} -22.6104 q^{84} +(6.69437 + 1.92705i) q^{85} -24.1566 q^{86} -3.35449i q^{87} +3.51682i q^{88} +11.7782 q^{89} +(-6.15638 - 1.77218i) q^{90} -6.13620 q^{91} -28.3188i q^{92} -14.2864i q^{93} +15.3489 q^{94} +(-3.91685 + 13.6067i) q^{95} +7.29399 q^{96} +17.6694i q^{97} +5.83367i q^{98} -1.14308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.36215i		−	1.67029i	−0.550029	−	0.835145i	$-0.685383\pi$
$2$		−	2.36215i		−	1.67029i	0.550029	−	0.835145i	$-0.314617\pi$
$3$		−	2.05253i		−	1.18503i	−0.805559	−	0.592515i	$-0.798135\pi$
$3$		−	2.05253i		−	1.18503i	0.805559	−	0.592515i	$-0.201865\pi$
$4$	−3.57974			−1.78987
$5$	−0.618559	+	2.14881i	−0.276628	+	0.960977i
$5$	−0.618559	+	2.14881i	−0.276628	+	0.960977i
$6$	−4.84838			−1.97934
$7$			3.07728i			1.16310i	0.813510	+	0.581551i	$0.197554\pi$
$7$			3.07728i			1.16310i	−0.813510	+	0.581551i	$0.802446\pi$
$8$			3.73158i			1.31931i
$9$	−1.21289			−0.404296
$10$	5.07581	+	1.46113i	1.60511	+	0.462049i
$11$	0.942447			0.284159			0.142079	−	0.989855i	$-0.454621\pi$
$11$	0.942447			0.284159			0.142079	+	0.989855i	$0.454621\pi$
$12$			7.34753i			2.12105i
$13$			1.99403i			0.553046i	0.961007	+	0.276523i	$0.0891821\pi$
$13$			1.99403i			0.553046i	−0.961007	+	0.276523i	$0.910818\pi$
$14$	7.26899			1.94272
$15$	4.41050	+	1.26961i	1.13879	+	0.327812i
$16$	1.65507			0.413766
$17$		−	3.11539i		−	0.755592i	−0.925889	−	0.377796i	$-0.876682\pi$
$17$		−	3.11539i		−	0.755592i	0.925889	−	0.377796i	$-0.123318\pi$
$18$			2.86502i			0.675291i
$19$	6.33222			1.45271			0.726355	−	0.687320i	$-0.241213\pi$
$19$	6.33222			1.45271			0.726355	+	0.687320i	$0.241213\pi$
$20$	2.21428	−	7.69218i	0.495128	−	1.72002i
$21$	6.31621			1.37831
$22$		−	2.22620i		−	0.474627i
$23$			7.91084i			1.64952i	0.565479	+	0.824762i	$0.308691\pi$
$23$			7.91084i			1.64952i	−0.565479	+	0.824762i	$0.691309\pi$
$24$	7.65919			1.56343
$25$	−4.23477	−	2.65833i	−0.846954	−	0.531666i
$26$	4.71020			0.923747
$27$		−	3.66811i		−	0.705927i
$28$		−	11.0159i		−	2.08180i
$29$	1.63432			0.303485			0.151742	−	0.988420i	$-0.451512\pi$
$29$	1.63432			0.303485			0.151742	+	0.988420i	$0.451512\pi$
$30$	2.99901	−	10.4183i	0.547542	−	1.90210i
$31$	6.96040			1.25012			0.625062	−	0.780575i	$-0.285074\pi$
$31$	6.96040			1.25012			0.625062	+	0.780575i	$0.285074\pi$
$32$			3.55366i			0.628203i
$33$		−	1.93440i		−	0.336736i
$34$	−7.35900			−1.26206
$35$	−6.61249	−	1.90348i	−1.11771	−	0.321747i
$36$	4.34182			0.723637
$37$			0.864280i			0.142087i	0.997473	+	0.0710434i	$0.0226329\pi$
$37$			0.864280i			0.142087i	−0.997473	+	0.0710434i	$0.977367\pi$
$38$		−	14.9576i		−	2.42645i
$39$	4.09282			0.655375
$40$	−8.01846	−	2.30820i	−1.26783	−	0.364959i
$41$	1.70732			0.266639			0.133319	−	0.991073i	$-0.457436\pi$
$41$	1.70732			0.266639			0.133319	+	0.991073i	$0.457436\pi$
$42$		−	14.9198i		−	2.30218i
$43$		−	10.2266i		−	1.55953i	−0.626069	−	0.779767i	$-0.715337\pi$
$43$		−	10.2266i		−	1.55953i	0.626069	−	0.779767i	$-0.284663\pi$
$44$	−3.37372			−0.508607
$45$	0.750242	−	2.60626i	0.111840	−	0.388519i
$46$	18.6866			2.75519
$47$			6.49786i			0.947811i	0.880576	+	0.473905i	$0.157156\pi$
$47$			6.49786i			0.947811i	−0.880576	+	0.473905i	$0.842844\pi$
$48$		−	3.39707i		−	0.490326i
$49$	−2.46965			−0.352807
$50$	−6.27937	+	10.0032i	−0.888037	+	1.41466i
$51$	−6.39443			−0.895399
$52$		−	7.13813i		−	0.989880i
$53$			2.20905i			0.303436i	0.988424	+	0.151718i	$0.0484805\pi$
$53$			2.20905i			0.303436i	−0.988424	+	0.151718i	$0.951519\pi$
$54$	−8.66461			−1.17910
$55$	−0.582959	+	2.02514i	−0.0786062	+	0.273070i
$56$	−11.4831			−1.53450
$57$		−	12.9971i		−	1.72150i
$58$		−	3.86050i		−	0.506908i
$59$	7.69694			1.00206			0.501028	−	0.865431i	$-0.332955\pi$
$59$	7.69694			1.00206			0.501028	+	0.865431i	$0.332955\pi$
$60$	−15.7885	−	4.54488i	−2.03828	−	0.586742i
$61$	−3.70322			−0.474149			−0.237075	−	0.971491i	$-0.576189\pi$
$61$	−3.70322			−0.474149			−0.237075	+	0.971491i	$0.576189\pi$
$62$		−	16.4415i		−	2.08807i
$63$		−	3.73239i		−	0.470237i
$64$	11.7044			1.46305
$65$	−4.28480	−	1.23343i	−0.531464	−	0.152988i
$66$	−4.56935			−0.562448
$67$			7.96470i			0.973043i	0.873669	+	0.486521i	$0.161734\pi$
$67$			7.96470i			0.973043i	−0.873669	+	0.486521i	$0.838266\pi$
$68$			11.1523i			1.35241i
$69$	16.2373			1.95474
$70$	−4.49630	+	15.6197i	−0.537410	+	1.86691i
$71$	−7.02031			−0.833157			−0.416579	−	0.909100i	$-0.636771\pi$
$71$	−7.02031			−0.833157			−0.416579	+	0.909100i	$0.636771\pi$
$72$		−	4.52599i		−	0.533393i
$73$		−	6.13583i		−	0.718144i	−0.933310	−	0.359072i	$-0.883093\pi$
$73$		−	6.13583i		−	0.718144i	0.933310	−	0.359072i	$-0.116907\pi$
$74$	2.04156			0.237326
$75$	−5.45631	+	8.69200i	−0.630041	+	1.00367i
$76$	−22.6677			−2.60016
$77$			2.90017i			0.330505i
$78$		−	9.66784i		−	1.09467i
$79$	14.0583			1.58168			0.790842	−	0.612021i	$-0.209643\pi$
$79$	14.0583			1.58168			0.790842	+	0.612021i	$0.209643\pi$
$80$	−1.02376	+	3.55642i	−0.114459	+	0.397620i
$81$	−11.1676			−1.24084
$82$		−	4.03294i		−	0.445364i
$83$			3.98789i			0.437728i	0.975755	+	0.218864i	$0.0702351\pi$
$83$			3.98789i			0.437728i	−0.975755	+	0.218864i	$0.929765\pi$
$84$	−22.6104			−2.46700
$85$	6.69437	+	1.92705i	0.726107	+	0.209018i
$86$	−24.1566			−2.60488
$87$		−	3.35449i		−	0.359639i
$88$			3.51682i			0.374894i
$89$	11.7782			1.24849			0.624245	−	0.781229i	$-0.285407\pi$
$89$	11.7782			1.24849			0.624245	+	0.781229i	$0.285407\pi$
$90$	−6.15638	−	1.77218i	−0.648940	−	0.186805i
$91$	−6.13620			−0.643249
$92$		−	28.3188i		−	2.95244i
$93$		−	14.2864i		−	1.48144i
$94$	15.3489			1.58312
$95$	−3.91685	+	13.6067i	−0.401860	+	1.39602i
$96$	7.29399			0.744440
$97$			17.6694i			1.79405i	0.441978	+	0.897026i	$0.354277\pi$
$97$			17.6694i			1.79405i	−0.441978	+	0.897026i	$0.645723\pi$
$98$			5.83367i			0.589290i
$99$	−1.14308			−0.114884
$100$	15.1594	+	9.51614i	1.51594	+	0.951614i
$101$	9.05634			0.901140			0.450570	−	0.892741i	$-0.351221\pi$
$101$	9.05634			0.901140			0.450570	+	0.892741i	$0.351221\pi$
$102$			15.1046i			1.49558i
$103$			2.20110i			0.216881i	0.994103	+	0.108440i	$0.0345857\pi$
$103$			2.20110i			0.216881i	−0.994103	+	0.108440i	$0.965414\pi$
$104$	−7.44090			−0.729641
$105$	−3.90695	+	13.5723i	−0.381279	+	1.32453i
$106$	5.21809			0.506826
$107$			7.08595i			0.685024i	0.939513	+	0.342512i	$0.111278\pi$
$107$			7.08595i			0.685024i	−0.939513	+	0.342512i	$0.888722\pi$
$108$			13.1309i			1.26352i
$109$	7.57661			0.725708			0.362854	−	0.931846i	$-0.381802\pi$
$109$	7.57661			0.725708			0.362854	+	0.931846i	$0.381802\pi$
$110$	4.78368	+	1.37704i	0.456106	+	0.131295i
$111$	1.77396			0.168377
$112$			5.09310i			0.481253i
$113$			17.7967i			1.67418i	0.547069	+	0.837088i	$0.315744\pi$
$113$			17.7967i			1.67418i	−0.547069	+	0.837088i	$0.684256\pi$
$114$	−30.7010			−2.87541
$115$	−16.9989	−	4.89332i	−1.58516	−	0.456305i
$116$	−5.85043			−0.543199
$117$		−	2.41854i		−	0.223594i
$118$		−	18.1813i		−	1.67373i
$119$	9.58691			0.878831
$120$	−4.73766	+	16.4581i	−0.432487	+	1.50242i
$121$	−10.1118			−0.919254
$122$			8.74756i			0.791967i
$123$		−	3.50433i		−	0.315975i
$124$	−24.9164			−2.23756
$125$	8.33171	−	7.45538i	0.745210	−	0.666829i
$126$	−8.81646			−0.785433
$127$		−	19.4716i		−	1.72782i	−0.503642	−	0.863912i	$-0.668007\pi$
$127$		−	19.4716i		−	1.72782i	0.503642	−	0.863912i	$-0.331993\pi$
$128$		−	20.5402i		−	1.81551i
$129$	−20.9903			−1.84810
$130$	−2.91354	+	10.1213i	−0.255534	+	0.887699i
$131$	−8.30848			−0.725915			−0.362958	−	0.931806i	$-0.618233\pi$
$131$	−8.30848			−0.725915			−0.362958	+	0.931806i	$0.618233\pi$
$132$			6.92466i			0.602714i
$133$			19.4860i			1.68965i
$134$	18.8138			1.62526
$135$	7.88206	+	2.26894i	0.678380	+	0.195279i
$136$	11.6253			0.996863
$137$			4.26661i			0.364521i	0.983250	+	0.182261i	$0.0583414\pi$
$137$			4.26661i			0.364521i	−0.983250	+	0.182261i	$0.941659\pi$
$138$		−	38.3548i		−	3.26498i
$139$	4.25699			0.361073			0.180537	−	0.983568i	$-0.442217\pi$
$139$	4.25699			0.361073			0.180537	+	0.983568i	$0.442217\pi$
$140$	23.6710	+	6.81396i	2.00056	+	0.575885i
$141$	13.3371			1.12318
$142$			16.5830i			1.39162i
$143$			1.87927i			0.157153i
$144$	−2.00741			−0.167284
$145$	−1.01092	+	3.51184i	−0.0839524	+	0.291642i
$146$	−14.4937			−1.19951
$147$			5.06903i			0.418086i
$148$		−	3.09390i		−	0.254317i
$149$	−6.80166			−0.557214			−0.278607	−	0.960405i	$-0.589873\pi$
$149$	−6.80166			−0.557214			−0.278607	+	0.960405i	$0.589873\pi$
$150$	20.5318	+	12.8886i	1.67641	+	1.05235i
$151$	−4.11661			−0.335005			−0.167503	−	0.985872i	$-0.553570\pi$
$151$	−4.11661			−0.335005			−0.167503	+	0.985872i	$0.553570\pi$
$152$			23.6292i			1.91658i
$153$			3.77861i			0.305483i
$154$	6.85064			0.552040
$155$	−4.30542	+	14.9566i	−0.345820	+	1.20134i
$156$	−14.6512			−1.17304
$157$		−	19.2876i		−	1.53931i	−0.638457	−	0.769657i	$-0.720427\pi$
$157$		−	19.2876i		−	1.53931i	0.638457	−	0.769657i	$-0.279573\pi$
$158$		−	33.2078i		−	2.64187i
$159$	4.53414			0.359580
$160$	−7.63613	−	2.19815i	−0.603689	−	0.173779i
$161$	−24.3439			−1.91857
$162$			26.3794i			2.07256i
$163$		−	1.77142i		−	0.138749i	−0.997591	−	0.0693743i	$-0.977900\pi$
$163$		−	1.77142i		−	0.138749i	0.997591	−	0.0693743i	$-0.0221003\pi$
$164$	−6.11176			−0.477249
$165$	4.15666	+	1.19654i	0.323596	+	0.0931507i
$166$	9.41999			0.731133
$167$		−	0.0398907i		−	0.00308683i	−0.999999	−	0.00154342i	$-0.999509\pi$
$167$		−	0.0398907i		−	0.00308683i	0.999999	−	0.00154342i	$-0.000491285\pi$
$168$			23.5695i			1.81842i
$169$	9.02383			0.694141
$170$	4.55198	−	15.8131i	0.349121	−	1.21281i
$171$	−7.68027			−0.587325
$172$			36.6084i			2.79137i
$173$			16.1574i			1.22842i	0.789142	+	0.614210i	$0.210525\pi$
$173$			16.1574i			1.22842i	−0.789142	+	0.614210i	$0.789475\pi$
$174$	−7.92379			−0.600701
$175$	8.18043	−	13.0316i	0.618382	−	0.985094i
$176$	1.55981			0.117575
$177$		−	15.7982i		−	1.18747i
$178$		−	27.8219i		−	2.08534i
$179$	−0.727604			−0.0543837			−0.0271918	−	0.999630i	$-0.508656\pi$
$179$	−0.727604			−0.0543837			−0.0271918	+	0.999630i	$0.508656\pi$
$180$	−2.68567	+	9.32975i	−0.200178	+	0.695399i
$181$	13.7237			1.02008			0.510039	−	0.860151i	$-0.329631\pi$
$181$	13.7237			1.02008			0.510039	+	0.860151i	$0.329631\pi$
$182$			14.4946i			1.07441i
$183$			7.60098i			0.561881i
$184$	−29.5200			−2.17624
$185$	−1.85717	−	0.534608i	−0.136542	−	0.0393052i
$186$	−33.7467			−2.47443
$187$		−	2.93609i		−	0.214708i
$188$		−	23.2607i		−	1.69646i
$189$	11.2878			0.821066
$190$	32.1411	+	9.25218i	2.33176	+	0.671224i
$191$	−12.2809			−0.888612			−0.444306	−	0.895875i	$-0.646550\pi$
$191$	−12.2809			−0.888612			−0.444306	+	0.895875i	$0.646550\pi$
$192$		−	24.0236i		−	1.73376i
$193$		−	9.92702i		−	0.714563i	−0.933997	−	0.357281i	$-0.883704\pi$
$193$		−	9.92702i		−	0.714563i	0.933997	−	0.357281i	$-0.116296\pi$
$194$	41.7376			2.99659
$195$	−2.53165	+	8.79469i	−0.181295	+	0.629801i
$196$	8.84070			0.631478
$197$		−	12.1160i		−	0.863229i	−0.902058	−	0.431614i	$-0.857944\pi$
$197$		−	12.1160i		−	0.863229i	0.902058	−	0.431614i	$-0.142056\pi$
$198$			2.70013i			0.191890i
$199$	−13.7540			−0.974995			−0.487498	−	0.873124i	$-0.662090\pi$
$199$	−13.7540			−0.974995			−0.487498	+	0.873124i	$0.662090\pi$
$200$	9.91978	−	15.8024i	0.701435	−	1.11740i
$201$	16.3478			1.15308
$202$		−	21.3924i		−	1.50517i
$203$			5.02925i			0.352984i
$204$	22.8904			1.60265
$205$	−1.05608	+	3.66871i	−0.0737597	+	0.256234i
$206$	5.19932			0.362254
$207$		−	9.59496i		−	0.666896i
$208$			3.30026i			0.228832i
$209$	5.96778			0.412800
$210$	32.0599	+	9.22880i	2.21234	+	0.636847i
$211$	−18.0235			−1.24079			−0.620396	−	0.784289i	$-0.713028\pi$
$211$	−18.0235			−1.24079			−0.620396	+	0.784289i	$0.713028\pi$
$212$		−	7.90781i		−	0.543111i
$213$			14.4094i			0.987316i
$214$	16.7381			1.14419
$215$	21.9749	+	6.32573i	1.49868	+	0.431411i
$216$	13.6878			0.931339
$217$			21.4191i			1.45402i
$218$		−	17.8971i		−	1.21214i
$219$	−12.5940			−0.851022
$220$	2.08684	−	7.24948i	0.140695	−	0.488760i
$221$	6.21219			0.417877
$222$		−	4.19036i		−	0.281239i
$223$		−	27.9985i		−	1.87492i	−0.348098	−	0.937458i	$-0.613172\pi$
$223$		−	27.9985i		−	1.87492i	0.348098	−	0.937458i	$-0.386828\pi$
$224$	−10.9356			−0.730665
$225$	5.13630	+	3.22426i	0.342420	+	0.214950i
$226$	42.0385			2.79636
$227$		−	12.7878i		−	0.848755i	−0.905485	−	0.424378i	$-0.860493\pi$
$227$		−	12.7878i		−	0.848755i	0.905485	−	0.424378i	$-0.139507\pi$
$228$			46.5262i			3.08127i
$229$	15.9201			1.05203			0.526015	−	0.850475i	$-0.323686\pi$
$229$	15.9201			1.05203			0.526015	+	0.850475i	$0.323686\pi$
$230$	−11.5588	+	40.1539i	−0.762162	+	2.64767i
$231$	5.95270			0.391659
$232$			6.09859i			0.400392i
$233$		−	20.1234i		−	1.31833i	−0.751999	−	0.659165i	$-0.770910\pi$
$233$		−	20.1234i		−	1.31833i	0.751999	−	0.659165i	$-0.229090\pi$
$234$	−5.71295			−0.373467
$235$	−13.9627	−	4.01931i	−0.910824	−	0.262191i
$236$	−27.5531			−1.79355
$237$		−	28.8551i		−	1.87434i
$238$		−	22.6457i		−	1.46790i
$239$	−4.68343			−0.302946			−0.151473	−	0.988461i	$-0.548402\pi$
$239$	−4.68343			−0.302946			−0.151473	+	0.988461i	$0.548402\pi$
$240$	7.29967	+	2.10129i	0.471192	+	0.135638i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$			23.8855i			1.53542i
$243$			11.9175i			0.764506i
$244$	13.2566			0.848665
$245$	1.52762	−	5.30680i	0.0975962	−	0.339039i
$246$	−8.27774			−0.527770
$247$			12.6267i			0.803415i
$248$			25.9733i			1.64931i
$249$	8.18528			0.518721
$250$	−17.6107	−	19.6807i	−1.11380	−	1.24472i
$251$	−23.0713			−1.45625			−0.728123	−	0.685447i	$-0.759607\pi$
$251$	−23.0713			−1.45625			−0.728123	+	0.685447i	$0.759607\pi$
$252$			13.3610i			0.841664i
$253$			7.45555i			0.468727i
$254$	−45.9948			−2.88597
$255$	3.95533	−	13.7404i	0.247693	−	0.860458i
$256$	−25.1102			−1.56939
$257$		−	11.6020i		−	0.723715i	−0.932233	−	0.361857i	$-0.882143\pi$
$257$		−	11.6020i		−	0.723715i	0.932233	−	0.361857i	$-0.117857\pi$
$258$			49.5822i			3.08686i
$259$	−2.65963			−0.165261
$260$	15.3385	+	4.41535i	0.951252	+	0.273829i
$261$	−1.98224			−0.122698
$262$			19.6259i			1.21249i
$263$			15.3744i			0.948024i	0.880518	+	0.474012i	$0.157195\pi$
$263$			15.3744i			0.948024i	−0.880518	+	0.474012i	$0.842805\pi$
$264$	7.21838			0.444261
$265$	−4.74682	−	1.36643i	−0.291595	−	0.0839388i
$266$	46.0288			2.82221
$267$		−	24.1752i		−	1.47950i
$268$		−	28.5116i		−	1.74162i
$269$	−9.03287			−0.550744			−0.275372	−	0.961338i	$-0.588801\pi$
$269$	−9.03287			−0.550744			−0.275372	+	0.961338i	$0.588801\pi$
$270$	5.35957	−	18.6186i	0.326173	−	1.13309i
$271$	−25.0727			−1.52306			−0.761528	−	0.648132i	$-0.775550\pi$
$271$	−25.0727			−1.52306			−0.761528	+	0.648132i	$0.775550\pi$
$272$		−	5.15617i		−	0.312639i
$273$			12.5947i			0.762269i
$274$	10.0784			0.608856
$275$	−3.99105	−	2.50534i	−0.240669	−	0.151078i
$276$	−58.1252			−3.49873
$277$			10.5495i			0.633855i	0.948450	+	0.316928i	$0.102651\pi$
$277$			10.5495i			0.633855i	−0.948450	+	0.316928i	$0.897349\pi$
$278$		−	10.0556i		−	0.603097i
$279$	−8.44218			−0.505420
$280$	7.10299	−	24.6750i	0.424485	−	1.47462i
$281$	16.2094			0.966971			0.483485	−	0.875352i	$-0.339371\pi$
$281$	16.2094			0.966971			0.483485	+	0.875352i	$0.339371\pi$
$282$		−	31.5041i		−	1.87604i
$283$		−	8.03684i		−	0.477741i	−0.971051	−	0.238870i	$-0.923223\pi$
$283$		−	8.03684i		−	0.477741i	0.971051	−	0.238870i	$-0.0767771\pi$
$284$	25.1309			1.49124
$285$	27.9282	+	8.03946i	1.65433	+	0.476216i
$286$	4.43912			0.262491
$287$			5.25390i			0.310128i
$288$		−	4.31018i		−	0.253980i
$289$	7.29437			0.429081
$290$	8.29547	+	2.38794i	0.487127	+	0.140225i
$291$	36.2669			2.12600
$292$			21.9647i			1.28539i
$293$			26.1918i			1.53014i	0.643945	+	0.765072i	$0.277297\pi$
$293$			26.1918i			1.53014i	−0.643945	+	0.765072i	$0.722703\pi$
$294$	11.9738			0.698326
$295$	−4.76101	+	16.5393i	−0.277197	+	0.962954i
$296$	−3.22513			−0.187457
$297$		−	3.45700i		−	0.200595i
$298$			16.0665i			0.930709i
$299$	−15.7745			−0.912262
$300$	19.5322	−	31.1151i	1.12769	−	1.79643i
$301$	31.4700			1.81390
$302$			9.72405i			0.559556i
$303$		−	18.5884i		−	1.06788i
$304$	10.4802			0.601083
$305$	2.29066	−	7.95752i	0.131163	−	0.455646i
$306$	8.92564			0.510245
$307$		−	4.41238i		−	0.251828i	−0.992041	−	0.125914i	$-0.959814\pi$
$307$		−	4.41238i		−	0.251828i	0.992041	−	0.125914i	$-0.0401863\pi$
$308$		−	10.3819i		−	0.591562i
$309$	4.51783			0.257010
$310$	35.3296	+	10.1700i	2.00659	+	0.577619i
$311$	−13.2563			−0.751693			−0.375847	−	0.926682i	$-0.622648\pi$
$311$	−13.2563			−0.751693			−0.375847	+	0.926682i	$0.622648\pi$
$312$			15.2727i			0.864646i
$313$			22.1456i			1.25174i	0.779927	+	0.625871i	$0.215256\pi$
$313$			22.1456i			1.25174i	−0.779927	+	0.625871i	$0.784744\pi$
$314$	−45.5601			−2.57110
$315$	8.02020	+	2.30871i	0.451887	+	0.130081i
$316$	−50.3251			−2.83101
$317$		−	3.01320i		−	0.169238i	−0.996413	−	0.0846190i	$-0.973033\pi$
$317$		−	3.01320i		−	0.169238i	0.996413	−	0.0846190i	$-0.0269673\pi$
$318$		−	10.7103i		−	0.600604i
$319$	1.54026			0.0862378
$320$	−7.23986	+	25.1505i	−0.404720	+	1.40596i
$321$	14.5441			0.811774
$322$			57.5038i			3.20456i
$323$		−	19.7273i		−	1.09766i
$324$	39.9770			2.22094
$325$	5.30080	−	8.44427i	0.294036	−	0.468404i
$326$	−4.18436			−0.231750
$327$		−	15.5512i		−	0.859985i
$328$			6.37101i			0.351780i
$329$	−19.9957			−1.10240
$330$	2.82641	−	9.81865i	0.155589	−	0.540499i
$331$	9.41939			0.517736			0.258868	−	0.965913i	$-0.416650\pi$
$331$	9.41939			0.517736			0.258868	+	0.965913i	$0.416650\pi$
$332$		−	14.2756i		−	0.783477i
$333$		−	1.04827i		−	0.0574451i
$334$	−0.0942276			−0.00515591
$335$	−17.1146	−	4.92664i	−0.935072	−	0.269171i
$336$	10.4537			0.570299
$337$			17.0177i			0.927011i	0.886094	+	0.463505i	$0.153409\pi$
$337$			17.0177i			0.927011i	−0.886094	+	0.463505i	$0.846591\pi$
$338$		−	21.3156i		−	1.15942i
$339$	36.5284			1.98395
$340$	−23.9641	−	6.89834i	−1.29964	−	0.374115i
$341$	6.55981			0.355234
$342$			18.1419i			0.981003i
$343$			13.9412i			0.752752i
$344$	38.1612			2.05752
$345$	−10.0437	+	34.8908i	−0.540735	+	1.87846i
$346$	38.1661			2.05182
$347$		−	23.6966i		−	1.27210i	−0.771649	−	0.636049i	$-0.780568\pi$
$347$		−	23.6966i		−	1.27210i	0.771649	−	0.636049i	$-0.219432\pi$
$348$			12.0082i			0.643707i
$349$	−4.05897			−0.217272			−0.108636	−	0.994082i	$-0.534648\pi$
$349$	−4.05897			−0.217272			−0.108636	+	0.994082i	$0.534648\pi$
$350$	−30.7825	−	19.3234i	−1.64539	−	1.03288i
$351$	7.31433			0.390410
$352$			3.34913i			0.178509i
$353$			15.8788i			0.845144i	0.906329	+	0.422572i	$0.138873\pi$
$353$			15.8788i			0.845144i	−0.906329	+	0.422572i	$0.861127\pi$
$354$	−37.3177			−1.98342
$355$	4.34248	−	15.0853i	0.230475	−	0.800645i
$356$	−42.1630			−2.23463
$357$		−	19.6774i		−	1.04144i
$358$			1.71871i			0.0908366i
$359$	4.02791			0.212585			0.106293	−	0.994335i	$-0.466102\pi$
$359$	4.02791			0.212585			0.106293	+	0.994335i	$0.466102\pi$
$360$	9.72549	+	2.79959i	0.512578	+	0.147551i
$361$	21.0970			1.11037
$362$		−	32.4175i		−	1.70383i
$363$			20.7548i			1.08934i
$364$	21.9660			1.15133
$365$	13.1847	+	3.79537i	0.690120	+	0.198659i
$366$	17.9546			0.938504
$367$			38.1519i			1.99151i	0.0920267	+	0.995757i	$0.470665\pi$
$367$			38.1519i			1.99151i	−0.0920267	+	0.995757i	$0.529335\pi$
$368$			13.0930i			0.682518i
$369$	−2.07079			−0.107801
$370$	−1.26282	+	4.38692i	−0.0656511	+	0.228065i
$371$	−6.79785			−0.352927
$372$			51.1418i			2.65158i
$373$		−	20.3518i		−	1.05377i	−0.849935	−	0.526887i	$-0.823359\pi$
$373$		−	20.3518i		−	1.05377i	0.849935	−	0.526887i	$-0.176641\pi$
$374$	−6.93547			−0.358625
$375$	−15.3024	−	17.1011i	−0.790213	−	0.883097i
$376$	−24.2473			−1.25046
$377$			3.25888i			0.167841i
$378$		−	26.6634i		−	1.37142i
$379$	30.2111			1.55184			0.775919	−	0.630833i	$-0.217287\pi$
$379$	30.2111			1.55184			0.775919	+	0.630833i	$0.217287\pi$
$380$	14.0213	−	48.7086i	0.719278	−	2.49870i
$381$	−39.9661			−2.04752
$382$			29.0092i			1.48424i
$383$			23.4619i			1.19885i	0.800431	+	0.599425i	$0.204604\pi$
$383$			23.4619i			1.19885i	−0.800431	+	0.599425i	$0.795396\pi$
$384$	−42.1594			−2.15144
$385$	−6.23192	−	1.79393i	−0.317608	−	0.0914271i
$386$	−23.4491			−1.19353
$387$			12.4037i			0.630513i
$388$		−	63.2517i		−	3.21112i
$389$	−0.990019			−0.0501959			−0.0250980	−	0.999685i	$-0.507990\pi$
$389$	−0.990019			−0.0501959			−0.0250980	+	0.999685i	$0.507990\pi$
$390$	20.7744	+	5.98013i	1.05195	+	0.302816i
$391$	24.6453			1.24637
$392$		−	9.21569i		−	0.465463i
$393$			17.0534i			0.860231i
$394$	−28.6198			−1.44184
$395$	−8.69590	+	30.2086i	−0.437538	+	1.51996i
$396$	4.09194			0.205628
$397$			4.90685i			0.246268i	0.992390	+	0.123134i	$0.0392944\pi$
$397$			4.90685i			0.246268i	−0.992390	+	0.123134i	$0.960706\pi$
$398$			32.4890i			1.62853i
$399$	39.9956			2.00229
$400$	−7.00882	−	4.39971i	−0.350441	−	0.219986i
$401$	−30.6157			−1.52888			−0.764439	−	0.644696i	$-0.776984\pi$
$401$	−30.6157			−1.52888			−0.764439	+	0.644696i	$0.776984\pi$
$402$		−	38.6159i		−	1.92599i
$403$			13.8793i			0.691376i
$404$	−32.4194			−1.61292
$405$	6.90780	−	23.9970i	0.343251	−	1.19242i
$406$	11.8798			0.589586
$407$			0.814538i			0.0403752i
$408$		−	23.8613i		−	1.18131i
$409$	4.00516			0.198043			0.0990213	−	0.995085i	$-0.468429\pi$
$409$	4.00516			0.198043			0.0990213	+	0.995085i	$0.468429\pi$
$410$	8.66603	+	2.49461i	0.427985	+	0.123200i
$411$	8.75735			0.431968
$412$		−	7.87937i		−	0.388189i
$413$			23.6856i			1.16549i
$414$	−22.6647			−1.11391
$415$	−8.56923	−	2.46675i	−0.420647	−	0.121088i
$416$	−7.08611			−0.347425
$417$		−	8.73761i		−	0.427883i
$418$		−	14.0968i		−	0.689496i
$419$	−31.4086			−1.53441			−0.767206	−	0.641401i	$-0.778354\pi$
$419$	−31.4086			−1.53441			−0.767206	+	0.641401i	$0.778354\pi$
$420$	13.9859	−	48.5855i	0.682441	−	2.37073i
$421$	39.1136			1.90628			0.953141	−	0.302526i	$-0.0978298\pi$
$421$	39.1136			1.90628			0.953141	+	0.302526i	$0.0978298\pi$
$422$			42.5743i			2.07248i
$423$		−	7.88117i		−	0.383196i
$424$	−8.24323			−0.400327
$425$	−8.28173	+	13.1929i	−0.401723	+	0.639952i
$426$	34.0372			1.64911
$427$		−	11.3958i		−	0.551484i
$428$		−	25.3659i		−	1.22610i
$429$	3.85727			0.186231
$430$	14.9423	−	51.9080i	0.720582	−	2.50323i
$431$	7.68918			0.370375			0.185188	−	0.982703i	$-0.440711\pi$
$431$	7.68918			0.370375			0.185188	+	0.982703i	$0.440711\pi$
$432$		−	6.07096i		−	0.292089i
$433$		−	4.67921i		−	0.224869i	−0.993659	−	0.112434i	$-0.964135\pi$
$433$		−	4.67921i		−	0.224869i	0.993659	−	0.112434i	$-0.0358648\pi$
$434$	50.5951			2.42864
$435$	7.20815	+	2.07495i	0.345605	+	0.0994861i
$436$	−27.1223			−1.29892
$437$			50.0932i			2.39628i
$438$			29.7488i			1.42145i
$439$	−14.7770			−0.705270			−0.352635	−	0.935761i	$-0.614714\pi$
$439$	−14.7770			−0.705270			−0.352635	+	0.935761i	$0.614714\pi$
$440$	−7.55698	−	2.17536i	−0.360265	−	0.103706i
$441$	2.99540			0.142638
$442$		−	14.6741i		−	0.697976i
$443$			3.71495i			0.176503i	0.996098	+	0.0882513i	$0.0281278\pi$
$443$			3.71495i			0.176503i	−0.996098	+	0.0882513i	$0.971872\pi$
$444$	−6.35033			−0.301373
$445$	−7.28553	+	25.3092i	−0.345367	+	1.19977i
$446$	−66.1365			−3.13165
$447$			13.9606i			0.660315i
$448$			36.0177i			1.70168i
$449$	23.6261			1.11498			0.557492	−	0.830183i	$-0.311764\pi$
$449$	23.6261			1.11498			0.557492	+	0.830183i	$0.311764\pi$
$450$	7.61617	−	12.1327i	0.359030	−	0.571941i
$451$	1.60906			0.0757676
$452$		−	63.7077i		−	2.99656i
$453$			8.44948i			0.396991i
$454$	−30.2066			−1.41767
$455$	3.79560	−	13.1855i	0.177941	−	0.618147i
$456$	48.4997			2.27120
$457$			16.0363i			0.750146i	0.926995	+	0.375073i	$0.122382\pi$
$457$			16.0363i			0.750146i	−0.926995	+	0.375073i	$0.877618\pi$
$458$		−	37.6056i		−	1.75720i
$459$	−11.4276			−0.533393
$460$	60.8517	+	17.5168i	2.83722	+	0.816727i
$461$	23.0734			1.07464			0.537319	−	0.843379i	$-0.319437\pi$
$461$	23.0734			1.07464			0.537319	+	0.843379i	$0.319437\pi$
$462$		−	14.0612i		−	0.654184i
$463$		−	34.0986i		−	1.58470i	−0.610068	−	0.792349i	$-0.708858\pi$
$463$		−	34.0986i		−	1.58470i	0.610068	−	0.792349i	$-0.291142\pi$
$464$	2.70490			0.125572
$465$	30.6989	+	8.83701i	1.42363	+	0.409806i
$466$	−47.5345			−2.20199
$467$			15.2453i			0.705467i	0.935724	+	0.352734i	$0.114748\pi$
$467$			15.2453i			0.705467i	−0.935724	+	0.352734i	$0.885252\pi$
$468$			8.65774i			0.400204i
$469$	−24.5096			−1.13175
$470$	−9.49421	+	32.9819i	−0.437935	+	1.52134i
$471$	−39.5883			−1.82413
$472$			28.7218i			1.32203i
$473$		−	9.63798i		−	0.443155i
$474$	−68.1601			−3.13070
$475$	−26.8155	−	16.8331i	−1.23038	−	0.772357i
$476$	−34.3187			−1.57299
$477$		−	2.67932i		−	0.122678i
$478$			11.0630i			0.506008i
$479$	−41.7622			−1.90816			−0.954082	−	0.299546i	$-0.903165\pi$
$479$	−41.7622			−1.90816			−0.954082	+	0.299546i	$0.903165\pi$
$480$	−4.51176	+	15.6734i	−0.205933	+	0.715390i
$481$	−1.72340			−0.0785805
$482$		−	2.36215i		−	0.107593i
$483$			49.9666i			2.27356i
$484$	36.1976			1.64535
$485$	−37.9681	−	10.9295i	−1.72404	−	0.496285i
$486$	28.1508			1.27695
$487$			33.0645i			1.49830i	0.662402	+	0.749148i	$0.269537\pi$
$487$			33.0645i			1.49830i	−0.662402	+	0.749148i	$0.730463\pi$
$488$		−	13.8189i		−	0.625551i
$489$	−3.63590			−0.164421
$490$	−12.5355	−	3.60847i	−0.566294	−	0.163014i
$491$	−12.6839			−0.572415			−0.286208	−	0.958168i	$-0.592395\pi$
$491$	−12.6839			−0.572415			−0.286208	+	0.958168i	$0.592395\pi$
$492$			12.5446i			0.565554i
$493$		−	5.09153i		−	0.229311i
$494$	29.8260			1.34194
$495$	0.707064	−	2.45627i	0.0317802	−	0.110401i
$496$	11.5199			0.517260
$497$		−	21.6035i		−	0.969047i
$498$		−	19.3348i		−	0.866415i
$499$	15.4405			0.691213			0.345606	−	0.938380i	$-0.387673\pi$
$499$	15.4405			0.691213			0.345606	+	0.938380i	$0.387673\pi$
$500$	−29.8253	+	26.6883i	−1.33383	+	1.19354i
$501$	−0.0818768			−0.00365799
$502$			54.4977i			2.43235i
$503$		−	26.3951i		−	1.17690i	−0.808534	−	0.588450i	$-0.799738\pi$
$503$		−	26.3951i		−	1.17690i	0.808534	−	0.588450i	$-0.200262\pi$
$504$	13.9277			0.620390
$505$	−5.60188	+	19.4604i	−0.249281	+	0.865975i
$506$	17.6111			0.782910
$507$		−	18.5217i		−	0.822577i
$508$			69.7033i			3.09258i
$509$	−13.4761			−0.597318			−0.298659	−	0.954360i	$-0.596539\pi$
$509$	−13.4761			−0.597318			−0.298659	+	0.954360i	$0.596539\pi$
$510$	−32.4569	−	9.34308i	−1.43722	−	0.413718i
$511$	18.8817			0.835275
$512$			18.2336i			0.805817i
$513$		−	23.2272i		−	1.02551i
$514$	−27.4057			−1.20881
$515$	−4.72975	−	1.36151i	−0.208418	−	0.0599953i
$516$	75.1399			3.30785
$517$			6.12389i			0.269328i
$518$			6.28244i			0.276035i
$519$	33.1635			1.45572
$520$	4.60264	−	15.9891i	0.201839	−	0.701168i
$521$	−23.7045			−1.03851			−0.519256	−	0.854619i	$-0.673791\pi$
$521$	−23.7045			−1.03851			−0.519256	+	0.854619i	$0.673791\pi$
$522$			4.68235i			0.204941i
$523$			3.98543i			0.174271i	0.996196	+	0.0871354i	$0.0277713\pi$
$523$			3.98543i			0.174271i	−0.996196	+	0.0871354i	$0.972229\pi$
$524$	29.7422			1.29929
$525$	−26.7477	−	16.7906i	−1.16737	−	0.732802i
$526$	36.3165			1.58348
$527$		−	21.6843i		−	0.944584i
$528$		−	3.20156i		−	0.139330i
$529$	−39.5814			−1.72093
$530$	−3.22770	+	11.2127i	−0.140202	+	0.487048i
$531$	−9.33553			−0.405127
$532$		−	69.7548i		−	3.02426i
$533$			3.40445i			0.147463i
$534$	−57.1053			−2.47119
$535$	−15.2264	−	4.38308i	−0.658293	−	0.189497i
$536$	−29.7209			−1.28375
$537$			1.49343i			0.0644463i
$538$			21.3370i			0.919902i
$539$	−2.32751			−0.100253
$540$	−28.2157	−	8.12222i	−1.21421	−	0.349525i
$541$	14.3140			0.615405			0.307703	−	0.951483i	$-0.400440\pi$
$541$	14.3140			0.615405			0.307703	+	0.951483i	$0.400440\pi$
$542$			59.2253i			2.54394i
$543$		−	28.1684i		−	1.20882i
$544$	11.0710			0.474666
$545$	−4.68658	+	16.2807i	−0.200751	+	0.697389i
$546$	29.7506			1.27321
$547$			25.1893i			1.07702i	0.842621	+	0.538508i	$0.181012\pi$
$547$			25.1893i			1.07702i	−0.842621	+	0.538508i	$0.818988\pi$
$548$		−	15.2734i		−	0.652446i
$549$	4.49159			0.191696
$550$	−5.91798	+	9.42744i	−0.252343	+	0.401987i
$551$	10.3488			0.440876
$552$			60.5907i			2.57891i
$553$			43.2613i			1.83966i
$554$	24.9194			1.05872
$555$	−1.09730	+	3.81191i	−0.0465778	+	0.161807i
$556$	−15.2389			−0.646275
$557$		−	16.4450i		−	0.696798i	−0.937346	−	0.348399i	$-0.886725\pi$
$557$		−	16.4450i		−	0.696798i	0.937346	−	0.348399i	$-0.113275\pi$
$558$			19.9417i			0.844199i
$559$	20.3921			0.862494
$560$	−10.9441	−	3.15038i	−0.462473	−	0.133128i
$561$	−6.02641			−0.254435
$562$		−	38.2890i		−	1.61512i
$563$		−	14.8796i		−	0.627100i	−0.949572	−	0.313550i	$-0.898482\pi$
$563$		−	14.8796i		−	0.627100i	0.949572	−	0.313550i	$-0.101518\pi$
$564$	−47.7433			−2.01035
$565$	−38.2418	−	11.0083i	−1.60884	−	0.463124i
$566$	−18.9842			−0.797966
$567$		−	34.3657i		−	1.44322i
$568$		−	26.1969i		−	1.09920i
$569$	37.4832			1.57138			0.785689	−	0.618622i	$-0.212309\pi$
$569$	37.4832			1.57138			0.785689	+	0.618622i	$0.212309\pi$
$570$	18.9904	−	65.9706i	0.795420	−	2.76321i
$571$	1.58161			0.0661885			0.0330943	−	0.999452i	$-0.489464\pi$
$571$	1.58161			0.0661885			0.0330943	+	0.999452i	$0.489464\pi$
$572$		−	6.72731i		−	0.281283i
$573$			25.2069i			1.05303i
$574$	12.4105			0.518004
$575$	21.0296	−	33.5006i	0.876997	−	1.39707i
$576$	−14.1961			−0.591504
$577$		−	37.7122i		−	1.56998i	−0.619508	−	0.784990i	$-0.712668\pi$
$577$		−	37.7122i		−	1.56998i	0.619508	−	0.784990i	$-0.287332\pi$
$578$		−	17.2304i		−	0.716689i
$579$	−20.3755			−0.846778
$580$	3.61884	−	12.5715i	0.150264	−	0.522002i
$581$	−12.2719			−0.509123
$582$		−	85.6678i		−	3.55105i
$583$			2.08191i			0.0862238i
$584$	22.8963			0.947457
$585$	5.19698	+	1.49601i	0.214869	+	0.0618524i
$586$	61.8690			2.55578
$587$		−	27.6567i		−	1.14151i	−0.821120	−	0.570756i	$-0.806650\pi$
$587$		−	27.6567i		−	1.14151i	0.821120	−	0.570756i	$-0.193350\pi$
$588$		−	18.1458i		−	0.748321i
$589$	44.0748			1.81607
$590$	39.0682	+	11.2462i	1.60841	+	0.462999i
$591$	−24.8685			−1.02295
$592$			1.43044i			0.0587907i
$593$		−	18.1987i		−	0.747329i	−0.927564	−	0.373665i	$-0.878101\pi$
$593$		−	18.1987i		−	0.747329i	0.927564	−	0.373665i	$-0.121899\pi$
$594$	−8.16593			−0.335052
$595$	−5.93007	+	20.6005i	−0.243109	+	0.844536i
$596$	24.3482			0.997341
$597$			28.2305i			1.15540i
$598$			37.2617i			1.52374i
$599$	7.12390			0.291075			0.145537	−	0.989353i	$-0.453509\pi$
$599$	7.12390			0.291075			0.145537	+	0.989353i	$0.453509\pi$
$600$	−32.4349	−	20.3607i	−1.32415	−	0.831221i
$601$	11.3425			0.462672			0.231336	−	0.972874i	$-0.425690\pi$
$601$	11.3425			0.462672			0.231336	+	0.972874i	$0.425690\pi$
$602$		−	74.3367i		−	3.02974i
$603$		−	9.66028i		−	0.393397i
$604$	14.7364			0.599616
$605$	6.25474	−	21.7283i	0.254291	−	0.883382i
$606$	−43.9086			−1.78367
$607$		−	9.88248i		−	0.401117i	−0.979682	−	0.200559i	$-0.935724\pi$
$607$		−	9.88248i		−	0.401117i	0.979682	−	0.200559i	$-0.0642757\pi$
$608$			22.5025i			0.912598i
$609$	10.3227			0.418297
$610$	−18.7968	−	5.41088i	−0.761062	−	0.219080i
$611$	−12.9570			−0.524182
$612$		−	13.5265i		−	0.546775i
$613$		−	6.32265i		−	0.255369i	−0.991815	−	0.127685i	$-0.959245\pi$
$613$		−	6.32265i		−	0.255369i	0.991815	−	0.127685i	$-0.0407546\pi$
$614$	−10.4227			−0.420626
$615$	7.53014	+	2.16763i	0.303644	+	0.0874075i
$616$	−10.8222			−0.436040
$617$		−	28.4003i		−	1.14335i	−0.820480	−	0.571676i	$-0.806293\pi$
$617$		−	28.4003i		−	1.14335i	0.820480	−	0.571676i	$-0.193707\pi$
$618$		−	10.6718i		−	0.429282i
$619$	−14.3962			−0.578633			−0.289316	−	0.957234i	$-0.593428\pi$
$619$	−14.3962			−0.578633			−0.289316	+	0.957234i	$0.593428\pi$
$620$	15.4123	−	53.5407i	0.618972	−	2.15025i
$621$	29.0178			1.16444
$622$			31.3132i			1.25555i
$623$			36.2449i			1.45212i
$624$	6.77388			0.271172
$625$	10.8665	+	22.5148i	0.434662	+	0.900594i
$626$	52.3111			2.09077
$627$		−	12.2491i		−	0.489180i
$628$			69.0445i			2.75517i
$629$	2.69257			0.107360
$630$	5.45350	−	18.9449i	0.217273	−	0.754783i
$631$	−16.4378			−0.654379			−0.327190	−	0.944959i	$-0.606102\pi$
$631$	−16.4378			−0.654379			−0.327190	+	0.944959i	$0.606102\pi$
$632$			52.4597i			2.08674i
$633$			36.9939i			1.47038i
$634$	−7.11761			−0.282677
$635$	41.8408	+	12.0443i	1.66040	+	0.477965i
$636$	−16.2310			−0.643602
$637$		−	4.92456i		−	0.195118i
$638$		−	3.63831i		−	0.144042i
$639$	8.51484			0.336842
$640$	44.1370	+	12.7053i	1.74467	+	0.502222i
$641$	9.38495			0.370683			0.185342	−	0.982674i	$-0.440661\pi$
$641$	9.38495			0.370683			0.185342	+	0.982674i	$0.440661\pi$
$642$		−	34.3554i		−	1.35590i
$643$			2.90484i			0.114556i	0.998358	+	0.0572778i	$0.0182421\pi$
$643$			2.90484i			0.114556i	−0.998358	+	0.0572778i	$0.981758\pi$
$644$	87.1448			3.43399
$645$	12.9838	−	45.1042i	0.511235	−	1.77598i
$646$	−46.5988			−1.83341
$647$		−	16.2707i		−	0.639667i	−0.947474	−	0.319833i	$-0.896373\pi$
$647$		−	16.2707i		−	0.639667i	0.947474	−	0.319833i	$-0.103627\pi$
$648$		−	41.6727i		−	1.63706i
$649$	7.25396			0.284743
$650$	−19.9466	−	12.5213i	−0.782371	−	0.491125i
$651$	43.9634			1.72306
$652$			6.34124i			0.248342i
$653$			11.7812i			0.461035i	0.973068	+	0.230517i	$0.0740418\pi$
$653$			11.7812i			0.461035i	−0.973068	+	0.230517i	$0.925958\pi$
$654$	−36.7343			−1.43643
$655$	5.13929	−	17.8533i	0.200809	−	0.697588i
$656$	2.82573			0.110326
$657$			7.44207i			0.290343i
$658$			47.2329i			1.84133i
$659$	−47.0426			−1.83252			−0.916260	−	0.400583i	$-0.868807\pi$
$659$	−47.0426			−1.83252			−0.916260	+	0.400583i	$0.868807\pi$
$660$	−14.8798	−	4.28331i	−0.579195	−	0.166728i
$661$	−37.3779			−1.45383			−0.726916	−	0.686726i	$-0.759047\pi$
$661$	−37.3779			−1.45383			−0.726916	+	0.686726i	$0.759047\pi$
$662$		−	22.2500i		−	0.864770i
$663$		−	12.7507i		−	0.495197i
$664$	−14.8812			−0.577501
$665$	−41.8717	−	12.0532i	−1.62372	−	0.467405i
$666$	−2.47618			−0.0959500
$667$			12.9288i			0.500606i
$668$			0.142798i			0.00552503i
$669$	−57.4678			−2.22183
$670$	−11.6374	+	40.4273i	−0.449594	+	1.56184i
$671$	−3.49009			−0.134733
$672$			22.4456i			0.865860i
$673$		−	37.3014i		−	1.43786i	−0.695081	−	0.718931i	$-0.744632\pi$
$673$		−	37.3014i		−	1.43786i	0.695081	−	0.718931i	$-0.255368\pi$
$674$	40.1982			1.54838
$675$	−9.75104	+	15.5336i	−0.375318	+	0.597888i
$676$	−32.3030			−1.24242
$677$		−	21.0921i		−	0.810636i	−0.914176	−	0.405318i	$-0.867161\pi$
$677$		−	21.0921i		−	0.810636i	0.914176	−	0.405318i	$-0.132839\pi$
$678$		−	86.2854i		−	3.31377i
$679$	−54.3735			−2.08667
$680$	−7.19095	+	24.9806i	−0.275760	+	0.957962i
$681$	−26.2473			−1.00580
$682$		−	15.4952i		−	0.593343i
$683$		−	30.1078i		−	1.15204i	−0.817434	−	0.576022i	$-0.804604\pi$
$683$		−	30.1078i		−	1.15204i	0.817434	−	0.576022i	$-0.195396\pi$
$684$	27.4934			1.05124
$685$	−9.16813	−	2.63915i	−0.350296	−	0.100837i
$686$	32.9311			1.25731
$687$		−	32.6765i		−	1.24669i
$688$		−	16.9256i		−	0.645283i
$689$	−4.40491			−0.167814
$690$	82.4172	+	23.7247i	3.13757	+	0.903184i
$691$	−22.9001			−0.871162			−0.435581	−	0.900149i	$-0.643457\pi$
$691$	−22.9001			−0.871162			−0.435581	+	0.900149i	$0.643457\pi$
$692$		−	57.8391i		−	2.19871i
$693$		−	3.51758i		−	0.133622i
$694$	−55.9748			−2.12477
$695$	−2.63320	+	9.14747i	−0.0998830	+	0.346983i
$696$	12.5175			0.474476
$697$		−	5.31896i		−	0.201470i
$698$			9.58790i			0.362907i
$699$	−41.3040			−1.56226
$700$	−29.2838	+	46.6496i	−1.10682	+	1.76319i
$701$	−12.7502			−0.481567			−0.240784	−	0.970579i	$-0.577404\pi$
$701$	−12.7502			−0.481567			−0.240784	+	0.970579i	$0.577404\pi$
$702$		−	17.2775i		−	0.652098i
$703$			5.47281i			0.206411i
$704$	11.0308			0.415738
$705$	−8.24976	+	28.6588i	−0.310704	+	1.07935i
$706$	37.5081			1.41164
$707$			27.8689i			1.04812i
$708$			56.5536i			2.12541i
$709$	30.5429			1.14706			0.573531	−	0.819184i	$-0.305573\pi$
$709$	30.5429			1.14706			0.573531	+	0.819184i	$0.305573\pi$
$710$	−35.6337	−	10.2576i	−1.33731	−	0.384960i
$711$	−17.0511			−0.639468
$712$			43.9514i			1.64715i
$713$			55.0626i			2.06211i
$714$	−46.4810			−1.73951
$715$	−4.03820	−	1.16244i	−0.151020	−	0.0434728i
$716$	2.60463			0.0973398
$717$			9.61289i			0.359000i
$718$		−	9.51453i		−	0.355079i
$719$	4.70422			0.175438			0.0877190	−	0.996145i	$-0.472042\pi$
$719$	4.70422			0.175438			0.0877190	+	0.996145i	$0.472042\pi$
$720$	1.24170	−	4.31354i	0.0462754	−	0.160756i
$721$	−6.77340			−0.252255
$722$		−	49.8342i		−	1.85464i
$723$		−	2.05253i		−	0.0763345i
$724$	−49.1275			−1.82581
$725$	−6.92095	−	4.34455i	−0.257038	−	0.161353i
$726$	49.0259			1.81952
$727$		−	34.0042i		−	1.26114i	−0.776130	−	0.630572i	$-0.782820\pi$
$727$		−	34.0042i		−	1.26114i	0.776130	−	0.630572i	$-0.217180\pi$
$728$		−	22.8977i		−	0.848646i
$729$	−9.04171			−0.334878
$730$	8.96523	−	31.1443i	0.331818	−	1.15270i
$731$	−31.8597			−1.17837
$732$		−	27.2096i		−	1.00569i
$733$			16.4990i			0.609406i	0.952447	+	0.304703i	$0.0985572\pi$
$733$			16.4990i			0.609406i	−0.952447	+	0.304703i	$0.901443\pi$
$734$	90.1204			3.32641
$735$	−10.8924	−	3.13549i	−0.401772	−	0.115654i
$736$	−28.1124			−1.03624
$737$			7.50631i			0.276498i
$738$			4.89150i			0.180059i
$739$	−41.0735			−1.51091			−0.755456	−	0.655199i	$-0.772585\pi$
$739$	−41.0735			−1.51091			−0.755456	+	0.655199i	$0.772585\pi$
$740$	6.64820	+	1.91376i	0.244393	+	0.0703512i
$741$	25.9166			0.952071
$742$			16.0575i			0.589490i
$743$			6.32830i			0.232163i	0.993240	+	0.116081i	$0.0370333\pi$
$743$			6.32830i			0.232163i	−0.993240	+	0.116081i	$0.962967\pi$
$744$	53.3110			1.95448
$745$	4.20723	−	14.6155i	0.154141	−	0.535470i
$746$	−48.0739			−1.76011
$747$		−	4.83687i		−	0.176972i
$748$			10.5104i			0.384299i
$749$	−21.8054			−0.796753
$750$	−40.3953	+	36.1465i	−1.47503	+	1.31989i
$751$	53.2850			1.94440			0.972199	−	0.234157i	$-0.0752331\pi$
$751$	53.2850			1.94440			0.972199	+	0.234157i	$0.0752331\pi$
$752$			10.7544i			0.392172i
$753$			47.3545i			1.72569i
$754$	7.69796			0.280343
$755$	2.54637	−	8.84582i	0.0926719	−	0.321932i
$756$	−40.4074			−1.46960
$757$		−	38.5378i		−	1.40068i	−0.713810	−	0.700340i	$-0.753032\pi$
$757$		−	38.5378i		−	1.40068i	0.713810	−	0.700340i	$-0.246968\pi$
$758$		−	71.3630i		−	2.59202i
$759$	15.3028			0.555455
$760$	−50.7746	−	14.6160i	−1.84179	−	0.530180i
$761$	−16.2682			−0.589723			−0.294861	−	0.955540i	$-0.595273\pi$
$761$	−16.2682			−0.589723			−0.294861	+	0.955540i	$0.595273\pi$
$762$			94.4057i			3.41996i
$763$			23.3153i			0.844072i
$764$	43.9623			1.59050
$765$	−8.11952	−	2.33729i	−0.293562	−	0.0845051i
$766$	55.4206			2.00243
$767$			15.3480i			0.554183i
$768$			51.5394i			1.85977i
$769$	35.5516			1.28202			0.641012	−	0.767531i	$-0.278515\pi$
$769$	35.5516			1.28202			0.641012	+	0.767531i	$0.278515\pi$
$770$	−4.23752	+	14.7207i	−0.152710	+	0.530498i
$771$	−23.8135			−0.857623
$772$			35.5362i			1.27898i
$773$		−	0.807556i		−	0.0290458i	−0.999895	−	0.0145229i	$-0.995377\pi$
$773$		−	0.807556i		−	0.0290458i	0.999895	−	0.0145229i	$-0.00462294\pi$
$774$	29.2993			1.05314
$775$	−29.4757	−	18.5031i	−1.05880	−	0.664649i
$776$	−65.9347			−2.36692
$777$			5.45898i			0.195840i
$778$			2.33857i			0.0838418i
$779$	10.8111			0.387349
$780$	9.06265	−	31.4827i	0.324495	−	1.12726i
$781$	−6.61627			−0.236749
$782$		−	58.2159i		−	2.08180i
$783$		−	5.99484i		−	0.214238i
$784$	−4.08743			−0.145980
$785$	41.4453	+	11.9305i	1.47925	+	0.425818i
$786$	40.2827			1.43684
$787$			13.8726i			0.494504i	0.968951	+	0.247252i	$0.0795276\pi$
$787$			13.8726i			0.494504i	−0.968951	+	0.247252i	$0.920472\pi$
$788$			43.3721i			1.54507i
$789$	31.5564			1.12344
$790$	71.3573	+	20.5410i	2.53878	+	0.730816i
$791$	−54.7655			−1.94724
$792$		−	4.26551i		−	0.151568i
$793$		−	7.38435i		−	0.262226i
$794$	11.5907			0.411338
$795$	−2.80463	+	9.74300i	−0.0994700	+	0.345549i
$796$	49.2358			1.74512
$797$			3.24320i			0.114880i	0.998349	+	0.0574400i	$0.0182938\pi$
$797$			3.24320i			0.114880i	−0.998349	+	0.0574400i	$0.981706\pi$
$798$		−	94.4756i		−	3.34440i
$799$	20.2433			0.716158
$800$	9.44680	−	15.0489i	0.333995	−	0.532059i
$801$	−14.2857			−0.504759
$802$			72.3189i			2.55367i
$803$		−	5.78269i		−	0.204067i
$804$	−58.5209			−2.06387
$805$	15.0581	−	52.3104i	0.530729	−	1.84370i
$806$	32.7849			1.15480
$807$			18.5403i			0.652648i
$808$			33.7945i			1.18889i
$809$	−54.4503			−1.91437			−0.957184	−	0.289479i	$-0.906518\pi$
$809$	−54.4503			−1.91437			−0.957184	+	0.289479i	$0.906518\pi$
$810$	−56.6844	−	16.3172i	−1.99169	−	0.573329i
$811$	−20.6483			−0.725059			−0.362530	−	0.931972i	$-0.618087\pi$
$811$	−20.6483			−0.725059			−0.362530	+	0.931972i	$0.618087\pi$
$812$		−	18.0034i		−	0.631796i
$813$			51.4624i			1.80487i
$814$	1.92406			0.0674383
$815$	3.80645	+	1.09573i	0.133334	+	0.0383817i
$816$	−10.5832			−0.370486
$817$		−	64.7567i		−	2.26555i
$818$		−	9.46079i		−	0.330789i
$819$	7.44252			0.260063
$820$	3.78049	−	13.1330i	0.132020	−	0.458625i
$821$	20.0000			0.698006			0.349003	−	0.937122i	$-0.386520\pi$
$821$	20.0000			0.698006			0.349003	+	0.937122i	$0.386520\pi$
$822$		−	20.6862i		−	0.721513i
$823$		−	25.3107i		−	0.882277i	−0.897439	−	0.441138i	$-0.854575\pi$
$823$		−	25.3107i		−	0.882277i	0.897439	−	0.441138i	$-0.145425\pi$
$824$	−8.21359			−0.286134
$825$	−5.14228	+	8.19175i	−0.179031	+	0.285200i
$826$	55.9490			1.94671
$827$			28.9282i			1.00593i	0.864306	+	0.502966i	$0.167758\pi$
$827$			28.9282i			1.00593i	−0.864306	+	0.502966i	$0.832242\pi$
$828$			34.3475i			1.19366i
$829$	−10.9469			−0.380201			−0.190100	−	0.981765i	$-0.560881\pi$
$829$	−10.9469			−0.380201			−0.190100	+	0.981765i	$0.560881\pi$
$830$	−5.82682	+	20.2418i	−0.202252	+	0.702602i
$831$	21.6531			0.751137
$832$			23.3390i			0.809133i
$833$			7.69390i			0.266578i
$834$	−20.6395			−0.714689
$835$	0.0857174	+	0.0246747i	0.00296637	+	0.000853904i
$836$	−21.3631			−0.738859
$837$		−	25.5315i		−	0.882497i
$838$			74.1918i			2.56291i
$839$	−16.6348			−0.574298			−0.287149	−	0.957886i	$-0.592707\pi$
$839$	−16.6348			−0.574298			−0.287149	+	0.957886i	$0.592707\pi$
$840$	−50.6463	−	14.5791i	−1.74746	−	0.503027i
$841$	−26.3290			−0.907897
$842$		−	92.3922i		−	3.18405i
$843$		−	33.2703i		−	1.14589i
$844$	64.5196			2.22086
$845$	−5.58177	+	19.3905i	−0.192019	+	0.667053i
$846$	−18.6165			−0.640048
$847$		−	31.1168i		−	1.06919i
$848$			3.65611i			0.125552i
$849$	−16.4959			−0.566137
$850$	31.1637	+	19.5627i	1.06891	+	0.670994i
$851$	−6.83719			−0.234376
$852$		−	51.5820i		−	1.76717i
$853$			1.31481i			0.0450182i	0.999747	+	0.0225091i	$0.00716547\pi$
$853$			1.31481i			0.0450182i	−0.999747	+	0.0225091i	$0.992835\pi$
$854$	−26.9187			−0.921138
$855$	4.75070	−	16.5034i	0.162470	−	0.564405i
$856$	−26.4418			−0.903762
$857$		−	51.6669i		−	1.76491i	−0.470399	−	0.882454i	$-0.655890\pi$
$857$		−	51.6669i		−	1.76491i	0.470399	−	0.882454i	$-0.344110\pi$
$858$		−	9.11143i		−	0.311059i
$859$	39.7084			1.35483			0.677417	−	0.735599i	$-0.263099\pi$
$859$	39.7084			1.35483			0.677417	+	0.735599i	$0.263099\pi$
$860$	−78.6645	−	22.6445i	−2.68244	−	0.772170i
$861$	10.7838			0.367511
$862$		−	18.1630i		−	0.618634i
$863$		−	28.5307i		−	0.971196i	−0.874182	−	0.485598i	$-0.838602\pi$
$863$		−	28.5307i		−	0.971196i	0.874182	−	0.485598i	$-0.161398\pi$
$864$	13.0352			0.443466
$865$	−34.7191	−	9.99428i	−1.18048	−	0.339816i
$866$	−11.0530			−0.375596
$867$		−	14.9719i		−	0.508473i
$868$		−	76.6748i		−	2.60251i
$869$	13.2492			0.449449
$870$	4.90133	−	17.0267i	0.166171	−	0.577260i
$871$	−15.8819			−0.538137
$872$			28.2727i			0.957436i
$873$		−	21.4309i		−	0.725327i
$874$	118.327			4.00249
$875$	22.9423	+	25.6390i	0.775591	+	0.866756i
$876$	45.0832			1.52322
$877$			4.60926i			0.155644i	0.996967	+	0.0778219i	$0.0247966\pi$
$877$			4.60926i			0.155644i	−0.996967	+	0.0778219i	$0.975203\pi$
$878$			34.9055i			1.17801i
$879$	53.7596			1.81327
$880$	−0.964836	+	3.35174i	−0.0325246	+	0.112987i
$881$	−14.5627			−0.490630			−0.245315	−	0.969443i	$-0.578891\pi$
$881$	−14.5627			−0.490630			−0.245315	+	0.969443i	$0.578891\pi$
$882$		−	7.07559i		−	0.238247i
$883$			4.65262i			0.156573i	0.996931	+	0.0782866i	$0.0249449\pi$
$883$			4.65262i			0.156573i	−0.996931	+	0.0782866i	$0.975055\pi$
$884$	−22.2380			−0.747946
$885$	33.9474	+	9.77213i	1.14113	+	0.328487i
$886$	8.77526			0.294810
$887$			8.77283i			0.294563i	0.989095	+	0.147281i	$0.0470523\pi$
$887$			8.77283i			0.294563i	−0.989095	+	0.147281i	$0.952948\pi$
$888$			6.61969i			0.222142i
$889$	59.9195			2.00964
$890$	59.7840	+	17.2095i	2.00396	+	0.576863i
$891$	−10.5248			−0.352595
$892$			100.227i			3.35586i
$893$			41.1459i			1.37689i
$894$	32.9771			1.10292
$895$	0.450066	−	1.56348i	0.0150441	−	0.0522615i
$896$	63.2079			2.11163
$897$			32.3776i			1.08106i
$898$		−	55.8083i		−	1.86235i
$899$	11.3755			0.379394
$900$	−18.3866	−	11.5420i	−0.612887	−	0.384734i
$901$	6.88203			0.229274
$902$		−	3.80083i		−	0.126554i
$903$		−	64.5931i		−	2.14952i
$904$	−66.4100			−2.20876
$905$	−8.48895	+	29.4897i	−0.282182	+	0.980272i
$906$	19.9589			0.663091
$907$		−	17.5415i		−	0.582457i	−0.956653	−	0.291229i	$-0.905936\pi$
$907$		−	17.5415i		−	0.582457i	0.956653	−	0.291229i	$-0.0940640\pi$
$908$			45.7770i			1.51916i
$909$	−10.9843			−0.364327
$910$	−31.1462	−	8.96577i	−1.03249	−	0.297212i
$911$	−26.2299			−0.869034			−0.434517	−	0.900664i	$-0.643081\pi$
$911$	−26.2299			−0.869034			−0.434517	+	0.900664i	$0.643081\pi$
$912$		−	21.5110i		−	0.712301i
$913$			3.75838i			0.124384i
$914$	37.8801			1.25296
$915$	−16.3331	−	4.70166i	−0.539955	−	0.155432i
$916$	−56.9898			−1.88300
$917$		−	25.5675i		−	0.844314i
$918$			26.9936i			0.890921i
$919$	26.0740			0.860101			0.430051	−	0.902805i	$-0.358496\pi$
$919$	26.0740			0.860101			0.430051	+	0.902805i	$0.358496\pi$
$920$	18.2598	−	63.4328i	0.602009	−	2.09132i
$921$	−9.05655			−0.298424
$922$		−	54.5029i		−	1.79496i
$923$		−	13.9987i		−	0.460774i
$924$	−21.3091			−0.701019
$925$	2.29754	−	3.66003i	0.0755428	−	0.120341i
$926$	−80.5460			−2.64691
$927$		−	2.66969i		−	0.0876840i
$928$			5.80780i			0.190650i
$929$	−22.2068			−0.728582			−0.364291	−	0.931285i	$-0.618689\pi$
$929$	−22.2068			−0.728582			−0.364291	+	0.931285i	$0.618689\pi$
$930$	20.8743	−	72.5152i	0.684496	−	2.37787i
$931$	−15.6383			−0.512526
$932$			72.0367i			2.35964i
$933$			27.2089i			0.890779i
$934$	36.0116			1.17834
$935$	6.30909	+	1.81614i	0.206329	+	0.0593942i
$936$	9.02498			0.294991
$937$		−	39.4539i		−	1.28890i	−0.764645	−	0.644452i	$-0.777086\pi$
$937$		−	39.4539i		−	1.28890i	0.764645	−	0.644452i	$-0.222914\pi$
$938$			57.8953i			1.89035i
$939$	45.4545			1.48335
$940$	49.9828	+	14.3881i	1.63026	+	0.469288i
$941$	7.12527			0.232277			0.116139	−	0.993233i	$-0.462948\pi$
$941$	7.12527			0.232277			0.116139	+	0.993233i	$0.462948\pi$
$942$			93.5135i			3.04683i
$943$			13.5063i			0.439827i
$944$	12.7389			0.414617
$945$	−6.98216	+	24.2553i	−0.227130	+	0.789025i
$946$	−22.7663			−0.740198
$947$			47.2038i			1.53392i	0.641696	+	0.766959i	$0.278231\pi$
$947$			47.2038i			1.53392i	−0.641696	+	0.766959i	$0.721769\pi$
$948$			103.294i			3.35483i
$949$	12.2350			0.397166
$950$	−39.7623	+	63.3421i	−1.29006	+	2.05509i
$951$	−6.18468			−0.200552
$952$			35.7744i			1.15945i
$953$			6.73058i			0.218025i	0.994040	+	0.109013i	$0.0347689\pi$
$953$			6.73058i			0.218025i	−0.994040	+	0.109013i	$0.965231\pi$
$954$	−6.32896			−0.204908
$955$	7.59644	−	26.3892i	0.245815	−	0.853936i
$956$	16.7655			0.542234
$957$		−	3.16143i		−	0.102194i
$958$			98.6485i			3.18719i
$959$	−13.1296			−0.423975
$960$	51.6222	+	14.8600i	1.66610	+	0.479606i
$961$	17.4472			0.562812
$962$			4.07094i			0.131252i
$963$		−	8.59446i		−	0.276952i
$964$	−3.57974			−0.115296
$965$	21.3313	+	6.14045i	0.686678	+	0.197668i
$966$	118.028			3.79750
$967$			51.9356i			1.67014i	0.550146	+	0.835069i	$0.314572\pi$
$967$			51.9356i			1.67014i	−0.550146	+	0.835069i	$0.685428\pi$
$968$		−	37.7330i		−	1.21278i
$969$	−40.4909			−1.30076
$970$	−25.8172	+	89.6862i	−0.828940	+	2.87965i
$971$	21.5150			0.690451			0.345225	−	0.938520i	$-0.387803\pi$
$971$	21.5150			0.690451			0.345225	+	0.938520i	$0.387803\pi$
$972$		−	42.6615i		−	1.36837i
$973$			13.1000i			0.419965i
$974$	78.1033			2.50259
$975$	−17.3321	−	10.8801i	−0.555073	−	0.348441i
$976$	−6.12908			−0.196187
$977$			1.00409i			0.0321238i	0.999871	+	0.0160619i	$0.00511288\pi$
$977$			1.00409i			0.0321238i	−0.999871	+	0.0160619i	$0.994887\pi$
$978$			8.58854i			0.274631i
$979$	11.1004			0.354769
$980$	−5.46849	+	18.9970i	−0.174685	+	0.606836i
$981$	−9.18958			−0.293401
$982$			29.9612i			0.956100i
$983$		−	29.7602i		−	0.949203i	−0.880201	−	0.474601i	$-0.842592\pi$
$983$		−	29.7602i		−	0.949203i	0.880201	−	0.474601i	$-0.157408\pi$
$984$	13.0767			0.416870
$985$	26.0350	+	7.49446i	0.829543	+	0.238793i
$986$	−12.0269			−0.383016
$987$			41.0419i			1.30638i
$988$		−	45.2002i		−	1.43801i
$989$	80.9007			2.57249
$990$	−5.80206	−	1.67019i	−0.184402	−	0.0530821i
$991$	−17.2504			−0.547976			−0.273988	−	0.961733i	$-0.588343\pi$
$991$	−17.2504			−0.547976			−0.273988	+	0.961733i	$0.588343\pi$
$992$			24.7349i			0.785333i
$993$		−	19.3336i		−	0.613533i
$994$	−51.0305			−1.61859
$995$	8.50766	−	29.5547i	0.269711	−	0.936948i
$996$	−29.3012			−0.928444
$997$			36.3908i			1.15251i	0.817271	+	0.576254i	$0.195486\pi$
$997$			36.3908i			1.15251i	−0.817271	+	0.576254i	$0.804514\pi$
$998$		−	36.4728i		−	1.15453i
$999$	3.17027			0.100303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.5	✓	46
5.2	odd	4		6025.2.a.p.1.42		46
5.3	odd	4		6025.2.a.p.1.5		46
5.4	even	2	inner	1205.2.b.c.724.42	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.5	✓	46	1.1	even	1	trivial
1205.2.b.c.724.42	yes	46	5.4	even	2	inner
6025.2.a.p.1.5		46	5.3	odd	4
6025.2.a.p.1.42		46	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.36215i q^{2} -2.05253i q^{3} -3.57974 q^{4} +(-0.618559 + 2.14881i) q^{5} -4.84838 q^{6} +3.07728i q^{7} +3.73158i q^{8} -1.21289 q^{9} +O(q^{10})\)	\(q-2.36215i q^{2} -2.05253i q^{3} -3.57974 q^{4} +(-0.618559 + 2.14881i) q^{5} -4.84838 q^{6} +3.07728i q^{7} +3.73158i q^{8} -1.21289 q^{9} +(5.07581 + 1.46113i) q^{10} +0.942447 q^{11} +7.34753i q^{12} +1.99403i q^{13} +7.26899 q^{14} +(4.41050 + 1.26961i) q^{15} +1.65507 q^{16} -3.11539i q^{17} +2.86502i q^{18} +6.33222 q^{19} +(2.21428 - 7.69218i) q^{20} +6.31621 q^{21} -2.22620i q^{22} +7.91084i q^{23} +7.65919 q^{24} +(-4.23477 - 2.65833i) q^{25} +4.71020 q^{26} -3.66811i q^{27} -11.0159i q^{28} +1.63432 q^{29} +(2.99901 - 10.4183i) q^{30} +6.96040 q^{31} +3.55366i q^{32} -1.93440i q^{33} -7.35900 q^{34} +(-6.61249 - 1.90348i) q^{35} +4.34182 q^{36} +0.864280i q^{37} -14.9576i q^{38} +4.09282 q^{39} +(-8.01846 - 2.30820i) q^{40} +1.70732 q^{41} -14.9198i q^{42} -10.2266i q^{43} -3.37372 q^{44} +(0.750242 - 2.60626i) q^{45} +18.6866 q^{46} +6.49786i q^{47} -3.39707i q^{48} -2.46965 q^{49} +(-6.27937 + 10.0032i) q^{50} -6.39443 q^{51} -7.13813i q^{52} +2.20905i q^{53} -8.66461 q^{54} +(-0.582959 + 2.02514i) q^{55} -11.4831 q^{56} -12.9971i q^{57} -3.86050i q^{58} +7.69694 q^{59} +(-15.7885 - 4.54488i) q^{60} -3.70322 q^{61} -16.4415i q^{62} -3.73239i q^{63} +11.7044 q^{64} +(-4.28480 - 1.23343i) q^{65} -4.56935 q^{66} +7.96470i q^{67} +11.1523i q^{68} +16.2373 q^{69} +(-4.49630 + 15.6197i) q^{70} -7.02031 q^{71} -4.52599i q^{72} -6.13583i q^{73} +2.04156 q^{74} +(-5.45631 + 8.69200i) q^{75} -22.6677 q^{76} +2.90017i q^{77} -9.66784i q^{78} +14.0583 q^{79} +(-1.02376 + 3.55642i) q^{80} -11.1676 q^{81} -4.03294i q^{82} +3.98789i q^{83} -22.6104 q^{84} +(6.69437 + 1.92705i) q^{85} -24.1566 q^{86} -3.35449i q^{87} +3.51682i q^{88} +11.7782 q^{89} +(-6.15638 - 1.77218i) q^{90} -6.13620 q^{91} -28.3188i q^{92} -14.2864i q^{93} +15.3489 q^{94} +(-3.91685 + 13.6067i) q^{95} +7.29399 q^{96} +17.6694i q^{97} +5.83367i q^{98} -1.14308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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