# Properties

 Label 135.2.b.b.109.3 Level $135$ Weight $2$ Character 135.109 Analytic conductor $1.078$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(109,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("135.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 135.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: $$1.07798042729$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 1$$ x^4 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 109.3 Root $$-0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 135.109 Dual form 135.2.b.b.109.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.41421i q^{2} +(-2.12132 + 0.707107i) q^{5} +3.00000i q^{7} +2.82843i q^{8} +O(q^{10})$$ $$q+1.41421i q^{2} +(-2.12132 + 0.707107i) q^{5} +3.00000i q^{7} +2.82843i q^{8} +(-1.00000 - 3.00000i) q^{10} +4.24264 q^{11} -3.00000i q^{13} -4.24264 q^{14} -4.00000 q^{16} -2.82843i q^{17} -1.00000 q^{19} +6.00000i q^{22} -7.07107i q^{23} +(4.00000 - 3.00000i) q^{25} +4.24264 q^{26} +4.24264 q^{29} +2.00000 q^{31} +4.00000 q^{34} +(-2.12132 - 6.36396i) q^{35} +9.00000i q^{37} -1.41421i q^{38} +(-2.00000 - 6.00000i) q^{40} -4.24264 q^{41} -6.00000i q^{43} +10.0000 q^{46} -2.82843i q^{47} -2.00000 q^{49} +(4.24264 + 5.65685i) q^{50} +9.89949i q^{53} +(-9.00000 + 3.00000i) q^{55} -8.48528 q^{56} +6.00000i q^{58} +8.48528 q^{59} -13.0000 q^{61} +2.82843i q^{62} -8.00000 q^{64} +(2.12132 + 6.36396i) q^{65} -3.00000i q^{67} +(9.00000 - 3.00000i) q^{70} -12.7279 q^{71} -9.00000i q^{73} -12.7279 q^{74} +12.7279i q^{77} +5.00000 q^{79} +(8.48528 - 2.82843i) q^{80} -6.00000i q^{82} +1.41421i q^{83} +(2.00000 + 6.00000i) q^{85} +8.48528 q^{86} +12.0000i q^{88} +9.00000 q^{91} +4.00000 q^{94} +(2.12132 - 0.707107i) q^{95} +3.00000i q^{97} -2.82843i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q+O(q^{10})$$ 4 * q $$4 q - 4 q^{10} - 16 q^{16} - 4 q^{19} + 16 q^{25} + 8 q^{31} + 16 q^{34} - 8 q^{40} + 40 q^{46} - 8 q^{49} - 36 q^{55} - 52 q^{61} - 32 q^{64} + 36 q^{70} + 20 q^{79} + 8 q^{85} + 36 q^{91} + 16 q^{94}+O(q^{100})$$ 4 * q - 4 * q^10 - 16 * q^16 - 4 * q^19 + 16 * q^25 + 8 * q^31 + 16 * q^34 - 8 * q^40 + 40 * q^46 - 8 * q^49 - 36 * q^55 - 52 * q^61 - 32 * q^64 + 36 * q^70 + 20 * q^79 + 8 * q^85 + 36 * q^91 + 16 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$$.

 $$n$$ $$56$$ $$82$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −2.12132 + 0.707107i −0.948683 + 0.316228i
$$6$$ 0 0
$$7$$ 3.00000i 1.13389i 0.823754 + 0.566947i $$0.191875\pi$$
−0.823754 + 0.566947i $$0.808125\pi$$
$$8$$ 2.82843i 1.00000i
$$9$$ 0 0
$$10$$ −1.00000 3.00000i −0.316228 0.948683i
$$11$$ 4.24264 1.27920 0.639602 0.768706i $$-0.279099\pi$$
0.639602 + 0.768706i $$0.279099\pi$$
$$12$$ 0 0
$$13$$ 3.00000i 0.832050i −0.909353 0.416025i $$-0.863423\pi$$
0.909353 0.416025i $$-0.136577\pi$$
$$14$$ −4.24264 −1.13389
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 2.82843i 0.685994i −0.939336 0.342997i $$-0.888558\pi$$
0.939336 0.342997i $$-0.111442\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416 −0.114708 0.993399i $$-0.536593\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 6.00000i 1.27920i
$$23$$ 7.07107i 1.47442i −0.675664 0.737210i $$-0.736143\pi$$
0.675664 0.737210i $$-0.263857\pi$$
$$24$$ 0 0
$$25$$ 4.00000 3.00000i 0.800000 0.600000i
$$26$$ 4.24264 0.832050
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.24264 0.787839 0.393919 0.919145i $$-0.371119\pi$$
0.393919 + 0.919145i $$0.371119\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 4.00000 0.685994
$$35$$ −2.12132 6.36396i −0.358569 1.07571i
$$36$$ 0 0
$$37$$ 9.00000i 1.47959i 0.672832 + 0.739795i $$0.265078\pi$$
−0.672832 + 0.739795i $$0.734922\pi$$
$$38$$ 1.41421i 0.229416i
$$39$$ 0 0
$$40$$ −2.00000 6.00000i −0.316228 0.948683i
$$41$$ −4.24264 −0.662589 −0.331295 0.943527i $$-0.607485\pi$$
−0.331295 + 0.943527i $$0.607485\pi$$
$$42$$ 0 0
$$43$$ 6.00000i 0.914991i −0.889212 0.457496i $$-0.848747\pi$$
0.889212 0.457496i $$-0.151253\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 10.0000 1.47442
$$47$$ 2.82843i 0.412568i −0.978492 0.206284i $$-0.933863\pi$$
0.978492 0.206284i $$-0.0661372\pi$$
$$48$$ 0 0
$$49$$ −2.00000 −0.285714
$$50$$ 4.24264 + 5.65685i 0.600000 + 0.800000i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 9.89949i 1.35980i 0.733305 + 0.679900i $$0.237977\pi$$
−0.733305 + 0.679900i $$0.762023\pi$$
$$54$$ 0 0
$$55$$ −9.00000 + 3.00000i −1.21356 + 0.404520i
$$56$$ −8.48528 −1.13389
$$57$$ 0 0
$$58$$ 6.00000i 0.787839i
$$59$$ 8.48528 1.10469 0.552345 0.833616i $$-0.313733\pi$$
0.552345 + 0.833616i $$0.313733\pi$$
$$60$$ 0 0
$$61$$ −13.0000 −1.66448 −0.832240 0.554416i $$-0.812942\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 2.82843i 0.359211i
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 2.12132 + 6.36396i 0.263117 + 0.789352i
$$66$$ 0 0
$$67$$ 3.00000i 0.366508i −0.983066 0.183254i $$-0.941337\pi$$
0.983066 0.183254i $$-0.0586631\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 9.00000 3.00000i 1.07571 0.358569i
$$71$$ −12.7279 −1.51053 −0.755263 0.655422i $$-0.772491\pi$$
−0.755263 + 0.655422i $$0.772491\pi$$
$$72$$ 0 0
$$73$$ 9.00000i 1.05337i −0.850060 0.526685i $$-0.823435\pi$$
0.850060 0.526685i $$-0.176565\pi$$
$$74$$ −12.7279 −1.47959
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 12.7279i 1.45048i
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 8.48528 2.82843i 0.948683 0.316228i
$$81$$ 0 0
$$82$$ 6.00000i 0.662589i
$$83$$ 1.41421i 0.155230i 0.996983 + 0.0776151i $$0.0247305\pi$$
−0.996983 + 0.0776151i $$0.975269\pi$$
$$84$$ 0 0
$$85$$ 2.00000 + 6.00000i 0.216930 + 0.650791i
$$86$$ 8.48528 0.914991
$$87$$ 0 0
$$88$$ 12.0000i 1.27920i
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 9.00000 0.943456
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 4.00000 0.412568
$$95$$ 2.12132 0.707107i 0.217643 0.0725476i
$$96$$ 0 0
$$97$$ 3.00000i 0.304604i 0.988334 + 0.152302i $$0.0486686\pi$$
−0.988334 + 0.152302i $$0.951331\pi$$
$$98$$ 2.82843i 0.285714i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −8.48528 −0.844317 −0.422159 0.906522i $$-0.638727\pi$$
−0.422159 + 0.906522i $$0.638727\pi$$
$$102$$ 0 0
$$103$$ 3.00000i 0.295599i −0.989017 0.147799i $$-0.952781\pi$$
0.989017 0.147799i $$-0.0472190\pi$$
$$104$$ 8.48528 0.832050
$$105$$ 0 0
$$106$$ −14.0000 −1.35980
$$107$$ 7.07107i 0.683586i −0.939775 0.341793i $$-0.888966\pi$$
0.939775 0.341793i $$-0.111034\pi$$
$$108$$ 0 0
$$109$$ 8.00000 0.766261 0.383131 0.923694i $$-0.374846\pi$$
0.383131 + 0.923694i $$0.374846\pi$$
$$110$$ −4.24264 12.7279i −0.404520 1.21356i
$$111$$ 0 0
$$112$$ 12.0000i 1.13389i
$$113$$ 1.41421i 0.133038i 0.997785 + 0.0665190i $$0.0211893\pi$$
−0.997785 + 0.0665190i $$0.978811\pi$$
$$114$$ 0 0
$$115$$ 5.00000 + 15.0000i 0.466252 + 1.39876i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 12.0000i 1.10469i
$$119$$ 8.48528 0.777844
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 18.3848i 1.66448i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −6.36396 + 9.19239i −0.569210 + 0.822192i
$$126$$ 0 0
$$127$$ 18.0000i 1.59724i −0.601834 0.798621i $$-0.705563\pi$$
0.601834 0.798621i $$-0.294437\pi$$
$$128$$ 11.3137i 1.00000i
$$129$$ 0 0
$$130$$ −9.00000 + 3.00000i −0.789352 + 0.263117i
$$131$$ 8.48528 0.741362 0.370681 0.928760i $$-0.379124\pi$$
0.370681 + 0.928760i $$0.379124\pi$$
$$132$$ 0 0
$$133$$ 3.00000i 0.260133i
$$134$$ 4.24264 0.366508
$$135$$ 0 0
$$136$$ 8.00000 0.685994
$$137$$ 1.41421i 0.120824i 0.998174 + 0.0604122i $$0.0192415\pi$$
−0.998174 + 0.0604122i $$0.980758\pi$$
$$138$$ 0 0
$$139$$ −13.0000 −1.10265 −0.551323 0.834292i $$-0.685877\pi$$
−0.551323 + 0.834292i $$0.685877\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 18.0000i 1.51053i
$$143$$ 12.7279i 1.06436i
$$144$$ 0 0
$$145$$ −9.00000 + 3.00000i −0.747409 + 0.249136i
$$146$$ 12.7279 1.05337
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −16.9706 −1.39028 −0.695141 0.718873i $$-0.744658\pi$$
−0.695141 + 0.718873i $$0.744658\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −0.0813788 −0.0406894 0.999172i $$-0.512955\pi$$
−0.0406894 + 0.999172i $$0.512955\pi$$
$$152$$ 2.82843i 0.229416i
$$153$$ 0 0
$$154$$ −18.0000 −1.45048
$$155$$ −4.24264 + 1.41421i −0.340777 + 0.113592i
$$156$$ 0 0
$$157$$ 6.00000i 0.478852i 0.970915 + 0.239426i $$0.0769593\pi$$
−0.970915 + 0.239426i $$0.923041\pi$$
$$158$$ 7.07107i 0.562544i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 21.2132 1.67183
$$162$$ 0 0
$$163$$ 9.00000i 0.704934i 0.935824 + 0.352467i $$0.114657\pi$$
−0.935824 + 0.352467i $$0.885343\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −2.00000 −0.155230
$$167$$ 5.65685i 0.437741i 0.975754 + 0.218870i $$0.0702371\pi$$
−0.975754 + 0.218870i $$0.929763\pi$$
$$168$$ 0 0
$$169$$ 4.00000 0.307692
$$170$$ −8.48528 + 2.82843i −0.650791 + 0.216930i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 14.1421i 1.07521i 0.843198 + 0.537603i $$0.180670\pi$$
−0.843198 + 0.537603i $$0.819330\pi$$
$$174$$ 0 0
$$175$$ 9.00000 + 12.0000i 0.680336 + 0.907115i
$$176$$ −16.9706 −1.27920
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.7279 −0.951330 −0.475665 0.879627i $$-0.657792\pi$$
−0.475665 + 0.879627i $$0.657792\pi$$
$$180$$ 0 0
$$181$$ −1.00000 −0.0743294 −0.0371647 0.999309i $$-0.511833\pi$$
−0.0371647 + 0.999309i $$0.511833\pi$$
$$182$$ 12.7279i 0.943456i
$$183$$ 0 0
$$184$$ 20.0000 1.47442
$$185$$ −6.36396 19.0919i −0.467888 1.40366i
$$186$$ 0 0
$$187$$ 12.0000i 0.877527i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 1.00000 + 3.00000i 0.0725476 + 0.217643i
$$191$$ 16.9706 1.22795 0.613973 0.789327i $$-0.289570\pi$$
0.613973 + 0.789327i $$0.289570\pi$$
$$192$$ 0 0
$$193$$ 3.00000i 0.215945i −0.994154 0.107972i $$-0.965564\pi$$
0.994154 0.107972i $$-0.0344358\pi$$
$$194$$ −4.24264 −0.304604
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 22.6274i 1.61214i 0.591822 + 0.806068i $$0.298409\pi$$
−0.591822 + 0.806068i $$0.701591\pi$$
$$198$$ 0 0
$$199$$ 11.0000 0.779769 0.389885 0.920864i $$-0.372515\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 8.48528 + 11.3137i 0.600000 + 0.800000i
$$201$$ 0 0
$$202$$ 12.0000i 0.844317i
$$203$$ 12.7279i 0.893325i
$$204$$ 0 0
$$205$$ 9.00000 3.00000i 0.628587 0.209529i
$$206$$ 4.24264 0.295599
$$207$$ 0 0
$$208$$ 12.0000i 0.832050i
$$209$$ −4.24264 −0.293470
$$210$$ 0 0
$$211$$ −7.00000 −0.481900 −0.240950 0.970538i $$-0.577459\pi$$
−0.240950 + 0.970538i $$0.577459\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 10.0000 0.683586
$$215$$ 4.24264 + 12.7279i 0.289346 + 0.868037i
$$216$$ 0 0
$$217$$ 6.00000i 0.407307i
$$218$$ 11.3137i 0.766261i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −8.48528 −0.570782
$$222$$ 0 0
$$223$$ 6.00000i 0.401790i −0.979613 0.200895i $$-0.935615\pi$$
0.979613 0.200895i $$-0.0643850\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −2.00000 −0.133038
$$227$$ 24.0416i 1.59570i −0.602857 0.797850i $$-0.705971\pi$$
0.602857 0.797850i $$-0.294029\pi$$
$$228$$ 0 0
$$229$$ −16.0000 −1.05731 −0.528655 0.848837i $$-0.677303\pi$$
−0.528655 + 0.848837i $$0.677303\pi$$
$$230$$ −21.2132 + 7.07107i −1.39876 + 0.466252i
$$231$$ 0 0
$$232$$ 12.0000i 0.787839i
$$233$$ 19.7990i 1.29707i −0.761183 0.648537i $$-0.775381\pi$$
0.761183 0.648537i $$-0.224619\pi$$
$$234$$ 0 0
$$235$$ 2.00000 + 6.00000i 0.130466 + 0.391397i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 12.0000i 0.777844i
$$239$$ −4.24264 −0.274434 −0.137217 0.990541i $$-0.543816\pi$$
−0.137217 + 0.990541i $$0.543816\pi$$
$$240$$ 0 0
$$241$$ 5.00000 0.322078 0.161039 0.986948i $$-0.448515\pi$$
0.161039 + 0.986948i $$0.448515\pi$$
$$242$$ 9.89949i 0.636364i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4.24264 1.41421i 0.271052 0.0903508i
$$246$$ 0 0
$$247$$ 3.00000i 0.190885i
$$248$$ 5.65685i 0.359211i
$$249$$ 0 0
$$250$$ −13.0000 9.00000i −0.822192 0.569210i
$$251$$ −12.7279 −0.803379 −0.401690 0.915776i $$-0.631577\pi$$
−0.401690 + 0.915776i $$0.631577\pi$$
$$252$$ 0 0
$$253$$ 30.0000i 1.88608i
$$254$$ 25.4558 1.59724
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 19.7990i 1.23503i −0.786560 0.617514i $$-0.788140\pi$$
0.786560 0.617514i $$-0.211860\pi$$
$$258$$ 0 0
$$259$$ −27.0000 −1.67770
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 12.0000i 0.741362i
$$263$$ 2.82843i 0.174408i −0.996190 0.0872041i $$-0.972207\pi$$
0.996190 0.0872041i $$-0.0277932\pi$$
$$264$$ 0 0
$$265$$ −7.00000 21.0000i −0.430007 1.29002i
$$266$$ 4.24264 0.260133
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 25.4558 1.55207 0.776035 0.630690i $$-0.217228\pi$$
0.776035 + 0.630690i $$0.217228\pi$$
$$270$$ 0 0
$$271$$ −19.0000 −1.15417 −0.577084 0.816685i $$-0.695809\pi$$
−0.577084 + 0.816685i $$0.695809\pi$$
$$272$$ 11.3137i 0.685994i
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 16.9706 12.7279i 1.02336 0.767523i
$$276$$ 0 0
$$277$$ 12.0000i 0.721010i 0.932757 + 0.360505i $$0.117396\pi$$
−0.932757 + 0.360505i $$0.882604\pi$$
$$278$$ 18.3848i 1.10265i
$$279$$ 0 0
$$280$$ 18.0000 6.00000i 1.07571 0.358569i
$$281$$ −8.48528 −0.506189 −0.253095 0.967442i $$-0.581448\pi$$
−0.253095 + 0.967442i $$0.581448\pi$$
$$282$$ 0 0
$$283$$ 6.00000i 0.356663i 0.983970 + 0.178331i $$0.0570699\pi$$
−0.983970 + 0.178331i $$0.942930\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 18.0000 1.06436
$$287$$ 12.7279i 0.751305i
$$288$$ 0 0
$$289$$ 9.00000 0.529412
$$290$$ −4.24264 12.7279i −0.249136 0.747409i
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7.07107i 0.413096i −0.978436 0.206548i $$-0.933777\pi$$
0.978436 0.206548i $$-0.0662230\pi$$
$$294$$ 0 0
$$295$$ −18.0000 + 6.00000i −1.04800 + 0.349334i
$$296$$ −25.4558 −1.47959
$$297$$ 0 0
$$298$$ 24.0000i 1.39028i
$$299$$ −21.2132 −1.22679
$$300$$ 0 0
$$301$$ 18.0000 1.03750
$$302$$ 1.41421i 0.0813788i
$$303$$ 0 0
$$304$$ 4.00000 0.229416
$$305$$ 27.5772 9.19239i 1.57906 0.526355i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −2.00000 6.00000i −0.113592 0.340777i
$$311$$ 8.48528 0.481156 0.240578 0.970630i $$-0.422663\pi$$
0.240578 + 0.970630i $$0.422663\pi$$
$$312$$ 0 0
$$313$$ 21.0000i 1.18699i 0.804838 + 0.593495i $$0.202252\pi$$
−0.804838 + 0.593495i $$0.797748\pi$$
$$314$$ −8.48528 −0.478852
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 11.3137i 0.635441i −0.948184 0.317721i $$-0.897083\pi$$
0.948184 0.317721i $$-0.102917\pi$$
$$318$$ 0 0
$$319$$ 18.0000 1.00781
$$320$$ 16.9706 5.65685i 0.948683 0.316228i
$$321$$ 0 0
$$322$$ 30.0000i 1.67183i
$$323$$ 2.82843i 0.157378i
$$324$$ 0 0
$$325$$ −9.00000 12.0000i −0.499230 0.665640i
$$326$$ −12.7279 −0.704934
$$327$$ 0 0
$$328$$ 12.0000i 0.662589i
$$329$$ 8.48528 0.467809
$$330$$ 0 0
$$331$$ 17.0000 0.934405 0.467202 0.884150i $$-0.345262\pi$$
0.467202 + 0.884150i $$0.345262\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −8.00000 −0.437741
$$335$$ 2.12132 + 6.36396i 0.115900 + 0.347700i
$$336$$ 0 0
$$337$$ 33.0000i 1.79762i 0.438334 + 0.898812i $$0.355569\pi$$
−0.438334 + 0.898812i $$0.644431\pi$$
$$338$$ 5.65685i 0.307692i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.48528 0.459504
$$342$$ 0 0
$$343$$ 15.0000i 0.809924i
$$344$$ 16.9706 0.914991
$$345$$ 0 0
$$346$$ −20.0000 −1.07521
$$347$$ 26.8701i 1.44246i 0.692696 + 0.721230i $$0.256423\pi$$
−0.692696 + 0.721230i $$0.743577\pi$$
$$348$$ 0 0
$$349$$ 5.00000 0.267644 0.133822 0.991005i $$-0.457275\pi$$
0.133822 + 0.991005i $$0.457275\pi$$
$$350$$ −16.9706 + 12.7279i −0.907115 + 0.680336i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 28.2843i 1.50542i −0.658352 0.752710i $$-0.728746\pi$$
0.658352 0.752710i $$-0.271254\pi$$
$$354$$ 0 0
$$355$$ 27.0000 9.00000i 1.43301 0.477670i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 18.0000i 0.951330i
$$359$$ −12.7279 −0.671754 −0.335877 0.941906i $$-0.609033\pi$$
−0.335877 + 0.941906i $$0.609033\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 1.41421i 0.0743294i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6.36396 + 19.0919i 0.333105 + 0.999315i
$$366$$ 0 0
$$367$$ 15.0000i 0.782994i −0.920179 0.391497i $$-0.871957\pi$$
0.920179 0.391497i $$-0.128043\pi$$
$$368$$ 28.2843i 1.47442i
$$369$$ 0 0
$$370$$ 27.0000 9.00000i 1.40366 0.467888i
$$371$$ −29.6985 −1.54187
$$372$$ 0 0
$$373$$ 21.0000i 1.08734i −0.839299 0.543669i $$-0.817035\pi$$
0.839299 0.543669i $$-0.182965\pi$$
$$374$$ 16.9706 0.877527
$$375$$ 0 0
$$376$$ 8.00000 0.412568
$$377$$ 12.7279i 0.655521i
$$378$$ 0 0
$$379$$ 35.0000 1.79783 0.898915 0.438124i $$-0.144357\pi$$
0.898915 + 0.438124i $$0.144357\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 24.0000i 1.22795i
$$383$$ 5.65685i 0.289052i 0.989501 + 0.144526i $$0.0461657\pi$$
−0.989501 + 0.144526i $$0.953834\pi$$
$$384$$ 0 0
$$385$$ −9.00000 27.0000i −0.458682 1.37605i
$$386$$ 4.24264 0.215945
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −33.9411 −1.72088 −0.860442 0.509549i $$-0.829812\pi$$
−0.860442 + 0.509549i $$0.829812\pi$$
$$390$$ 0 0
$$391$$ −20.0000 −1.01144
$$392$$ 5.65685i 0.285714i
$$393$$ 0 0
$$394$$ −32.0000 −1.61214
$$395$$ −10.6066 + 3.53553i −0.533676 + 0.177892i
$$396$$ 0 0
$$397$$ 36.0000i 1.80679i 0.428811 + 0.903394i $$0.358933\pi$$
−0.428811 + 0.903394i $$0.641067\pi$$
$$398$$ 15.5563i 0.779769i
$$399$$ 0 0
$$400$$ −16.0000 + 12.0000i −0.800000 + 0.600000i
$$401$$ −4.24264 −0.211867 −0.105934 0.994373i $$-0.533783\pi$$
−0.105934 + 0.994373i $$0.533783\pi$$
$$402$$ 0 0
$$403$$ 6.00000i 0.298881i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −18.0000 −0.893325
$$407$$ 38.1838i 1.89270i
$$408$$ 0 0
$$409$$ −25.0000 −1.23617 −0.618085 0.786111i $$-0.712091\pi$$
−0.618085 + 0.786111i $$0.712091\pi$$
$$410$$ 4.24264 + 12.7279i 0.209529 + 0.628587i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 25.4558i 1.25260i
$$414$$ 0 0
$$415$$ −1.00000 3.00000i −0.0490881 0.147264i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 6.00000i 0.293470i
$$419$$ 33.9411 1.65813 0.829066 0.559150i $$-0.188873\pi$$
0.829066 + 0.559150i $$0.188873\pi$$
$$420$$ 0 0
$$421$$ 23.0000 1.12095 0.560476 0.828171i $$-0.310618\pi$$
0.560476 + 0.828171i $$0.310618\pi$$
$$422$$ 9.89949i 0.481900i
$$423$$ 0 0
$$424$$ −28.0000 −1.35980
$$425$$ −8.48528 11.3137i −0.411597 0.548795i
$$426$$ 0 0
$$427$$ 39.0000i 1.88734i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ −18.0000 + 6.00000i −0.868037 + 0.289346i
$$431$$ 12.7279 0.613082 0.306541 0.951857i $$-0.400828\pi$$
0.306541 + 0.951857i $$0.400828\pi$$
$$432$$ 0 0
$$433$$ 36.0000i 1.73005i 0.501729 + 0.865025i $$0.332697\pi$$
−0.501729 + 0.865025i $$0.667303\pi$$
$$434$$ −8.48528 −0.407307
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 7.07107i 0.338255i
$$438$$ 0 0
$$439$$ 14.0000 0.668184 0.334092 0.942541i $$-0.391570\pi$$
0.334092 + 0.942541i $$0.391570\pi$$
$$440$$ −8.48528 25.4558i −0.404520 1.21356i
$$441$$ 0 0
$$442$$ 12.0000i 0.570782i
$$443$$ 14.1421i 0.671913i 0.941877 + 0.335957i $$0.109060\pi$$
−0.941877 + 0.335957i $$0.890940\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 8.48528 0.401790
$$447$$ 0 0
$$448$$ 24.0000i 1.13389i
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ −18.0000 −0.847587
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 34.0000 1.59570
$$455$$ −19.0919 + 6.36396i −0.895041 + 0.298347i
$$456$$ 0 0
$$457$$ 12.0000i 0.561336i 0.959805 + 0.280668i $$0.0905560\pi$$
−0.959805 + 0.280668i $$0.909444\pi$$
$$458$$ 22.6274i 1.05731i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 16.9706 0.790398 0.395199 0.918596i $$-0.370676\pi$$
0.395199 + 0.918596i $$0.370676\pi$$
$$462$$ 0 0
$$463$$ 15.0000i 0.697109i 0.937288 + 0.348555i $$0.113327\pi$$
−0.937288 + 0.348555i $$0.886673\pi$$
$$464$$ −16.9706 −0.787839
$$465$$ 0 0
$$466$$ 28.0000 1.29707
$$467$$ 22.6274i 1.04707i 0.852004 + 0.523536i $$0.175387\pi$$
−0.852004 + 0.523536i $$0.824613\pi$$
$$468$$ 0 0
$$469$$ 9.00000 0.415581
$$470$$ −8.48528 + 2.82843i −0.391397 + 0.130466i
$$471$$ 0 0
$$472$$ 24.0000i 1.10469i
$$473$$ 25.4558i 1.17046i
$$474$$ 0 0
$$475$$ −4.00000 + 3.00000i −0.183533 + 0.137649i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 6.00000i 0.274434i
$$479$$ 4.24264 0.193851 0.0969256 0.995292i $$-0.469099\pi$$
0.0969256 + 0.995292i $$0.469099\pi$$
$$480$$ 0 0
$$481$$ 27.0000 1.23109
$$482$$ 7.07107i 0.322078i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.12132 6.36396i −0.0963242 0.288973i
$$486$$ 0 0
$$487$$ 9.00000i 0.407829i −0.978989 0.203914i $$-0.934634\pi$$
0.978989 0.203914i $$-0.0653664\pi$$
$$488$$ 36.7696i 1.66448i
$$489$$ 0 0
$$490$$ 2.00000 + 6.00000i 0.0903508 + 0.271052i
$$491$$ 21.2132 0.957338 0.478669 0.877995i $$-0.341119\pi$$
0.478669 + 0.877995i $$0.341119\pi$$
$$492$$ 0 0
$$493$$ 12.0000i 0.540453i
$$494$$ −4.24264 −0.190885
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 38.1838i 1.71278i
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 18.0000i 0.803379i
$$503$$ 35.3553i 1.57642i 0.615409 + 0.788208i $$0.288991\pi$$
−0.615409 + 0.788208i $$0.711009\pi$$
$$504$$ 0 0
$$505$$ 18.0000 6.00000i 0.800989 0.266996i
$$506$$ 42.4264 1.88608
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −29.6985 −1.31636 −0.658181 0.752860i $$-0.728674\pi$$
−0.658181 + 0.752860i $$0.728674\pi$$
$$510$$ 0 0
$$511$$ 27.0000 1.19441
$$512$$ 22.6274i 1.00000i
$$513$$ 0 0
$$514$$ 28.0000 1.23503
$$515$$ 2.12132 + 6.36396i 0.0934765 + 0.280430i
$$516$$ 0 0
$$517$$ 12.0000i 0.527759i
$$518$$ 38.1838i 1.67770i
$$519$$ 0 0
$$520$$ −18.0000 + 6.00000i −0.789352 + 0.263117i
$$521$$ 12.7279 0.557620 0.278810 0.960346i $$-0.410060\pi$$
0.278810 + 0.960346i $$0.410060\pi$$
$$522$$ 0 0
$$523$$ 9.00000i 0.393543i 0.980449 + 0.196771i $$0.0630456\pi$$
−0.980449 + 0.196771i $$0.936954\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 4.00000 0.174408
$$527$$ 5.65685i 0.246416i
$$528$$ 0 0
$$529$$ −27.0000 −1.17391
$$530$$ 29.6985 9.89949i 1.29002 0.430007i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.7279i 0.551308i
$$534$$ 0 0
$$535$$ 5.00000 + 15.0000i 0.216169 + 0.648507i
$$536$$ 8.48528 0.366508
$$537$$ 0 0
$$538$$ 36.0000i 1.55207i
$$539$$ −8.48528 −0.365487
$$540$$ 0 0
$$541$$ −25.0000 −1.07483 −0.537417 0.843317i $$-0.680600\pi$$
−0.537417 + 0.843317i $$0.680600\pi$$
$$542$$ 26.8701i 1.15417i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −16.9706 + 5.65685i −0.726939 + 0.242313i
$$546$$ 0 0
$$547$$ 3.00000i 0.128271i 0.997941 + 0.0641354i $$0.0204289\pi$$
−0.997941 + 0.0641354i $$0.979571\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 18.0000 + 24.0000i 0.767523 + 1.02336i
$$551$$ −4.24264 −0.180743
$$552$$ 0 0
$$553$$ 15.0000i 0.637865i
$$554$$ −16.9706 −0.721010
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 19.7990i 0.838910i −0.907776 0.419455i $$-0.862221\pi$$
0.907776 0.419455i $$-0.137779\pi$$
$$558$$ 0 0
$$559$$ −18.0000 −0.761319
$$560$$ 8.48528 + 25.4558i 0.358569 + 1.07571i
$$561$$ 0 0
$$562$$ 12.0000i 0.506189i
$$563$$ 11.3137i 0.476816i −0.971165 0.238408i $$-0.923374\pi$$
0.971165 0.238408i $$-0.0766255\pi$$
$$564$$ 0 0
$$565$$ −1.00000 3.00000i −0.0420703 0.126211i
$$566$$ −8.48528 −0.356663
$$567$$ 0 0
$$568$$ 36.0000i 1.51053i
$$569$$ 42.4264 1.77861 0.889304 0.457317i $$-0.151190\pi$$
0.889304 + 0.457317i $$0.151190\pi$$
$$570$$ 0 0
$$571$$ −25.0000 −1.04622 −0.523109 0.852266i $$-0.675228\pi$$
−0.523109 + 0.852266i $$0.675228\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 18.0000 0.751305
$$575$$ −21.2132 28.2843i −0.884652 1.17954i
$$576$$ 0 0
$$577$$ 45.0000i 1.87337i −0.350167 0.936687i $$-0.613875\pi$$
0.350167 0.936687i $$-0.386125\pi$$
$$578$$ 12.7279i 0.529412i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −4.24264 −0.176014
$$582$$ 0 0
$$583$$ 42.0000i 1.73946i
$$584$$ 25.4558 1.05337
$$585$$ 0 0
$$586$$ 10.0000 0.413096
$$587$$ 26.8701i 1.10905i 0.832168 + 0.554523i $$0.187099\pi$$
−0.832168 + 0.554523i $$0.812901\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −0.0824086
$$590$$ −8.48528 25.4558i −0.349334 1.04800i
$$591$$ 0 0
$$592$$ 36.0000i 1.47959i
$$593$$ 9.89949i 0.406524i 0.979124 + 0.203262i $$0.0651542\pi$$
−0.979124 + 0.203262i $$0.934846\pi$$
$$594$$ 0 0
$$595$$ −18.0000 + 6.00000i −0.737928 + 0.245976i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 30.0000i 1.22679i
$$599$$ −29.6985 −1.21345 −0.606724 0.794913i $$-0.707517\pi$$
−0.606724 + 0.794913i $$0.707517\pi$$
$$600$$ 0 0
$$601$$ −40.0000 −1.63163 −0.815817 0.578310i $$-0.803712\pi$$
−0.815817 + 0.578310i $$0.803712\pi$$
$$602$$ 25.4558i 1.03750i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −14.8492 + 4.94975i −0.603708 + 0.201236i
$$606$$ 0 0
$$607$$ 39.0000i 1.58296i −0.611194 0.791481i $$-0.709311\pi$$
0.611194 0.791481i $$-0.290689\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 13.0000 + 39.0000i 0.526355 + 1.57906i
$$611$$ −8.48528 −0.343278
$$612$$ 0 0
$$613$$ 9.00000i 0.363507i −0.983344 0.181753i $$-0.941823\pi$$
0.983344 0.181753i $$-0.0581772\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −36.0000 −1.45048
$$617$$ 7.07107i 0.284670i −0.989819 0.142335i $$-0.954539\pi$$
0.989819 0.142335i $$-0.0454611\pi$$
$$618$$ 0 0
$$619$$ −19.0000 −0.763674 −0.381837 0.924230i $$-0.624709\pi$$
−0.381837 + 0.924230i $$0.624709\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 12.0000i 0.481156i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 7.00000 24.0000i 0.280000 0.960000i
$$626$$ −29.6985 −1.18699
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 25.4558 1.01499
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ 14.1421i 0.562544i
$$633$$ 0 0
$$634$$ 16.0000 0.635441
$$635$$ 12.7279 + 38.1838i 0.505092 + 1.51528i
$$636$$ 0 0
$$637$$ 6.00000i 0.237729i
$$638$$ 25.4558i 1.00781i
$$639$$ 0 0
$$640$$ 8.00000 + 24.0000i 0.316228 + 0.948683i
$$641$$ 16.9706 0.670297 0.335148 0.942165i $$-0.391214\pi$$
0.335148 + 0.942165i $$0.391214\pi$$
$$642$$ 0 0
$$643$$ 42.0000i 1.65632i 0.560493 + 0.828159i $$0.310612\pi$$
−0.560493 + 0.828159i $$0.689388\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −4.00000 −0.157378
$$647$$ 9.89949i 0.389189i 0.980884 + 0.194595i $$0.0623391\pi$$
−0.980884 + 0.194595i $$0.937661\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 16.9706 12.7279i 0.665640 0.499230i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 5.65685i 0.221370i 0.993856 + 0.110685i $$0.0353044\pi$$
−0.993856 + 0.110685i $$0.964696\pi$$
$$654$$ 0 0
$$655$$ −18.0000 + 6.00000i −0.703318 + 0.234439i
$$656$$ 16.9706 0.662589
$$657$$ 0 0
$$658$$ 12.0000i 0.467809i
$$659$$ 16.9706 0.661079 0.330540 0.943792i $$-0.392769\pi$$
0.330540 + 0.943792i $$0.392769\pi$$
$$660$$ 0 0
$$661$$ 23.0000 0.894596 0.447298 0.894385i $$-0.352386\pi$$
0.447298 + 0.894385i $$0.352386\pi$$
$$662$$ 24.0416i 0.934405i
$$663$$ 0 0
$$664$$ −4.00000 −0.155230
$$665$$ 2.12132 + 6.36396i 0.0822613 + 0.246784i
$$666$$ 0 0
$$667$$ 30.0000i 1.16160i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −9.00000 + 3.00000i −0.347700 + 0.115900i
$$671$$ −55.1543 −2.12921
$$672$$ 0 0
$$673$$ 15.0000i 0.578208i −0.957298 0.289104i $$-0.906643\pi$$
0.957298 0.289104i $$-0.0933573\pi$$
$$674$$ −46.6690 −1.79762
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 48.0833i 1.84799i 0.382405 + 0.923995i $$0.375096\pi$$
−0.382405 + 0.923995i $$0.624904\pi$$
$$678$$ 0 0
$$679$$ −9.00000 −0.345388
$$680$$ −16.9706 + 5.65685i −0.650791 + 0.216930i
$$681$$ 0 0
$$682$$ 12.0000i 0.459504i
$$683$$ 15.5563i 0.595247i −0.954683 0.297624i $$-0.903806\pi$$
0.954683 0.297624i $$-0.0961940\pi$$
$$684$$ 0 0
$$685$$ −1.00000 3.00000i −0.0382080 0.114624i
$$686$$ −21.2132 −0.809924
$$687$$ 0 0
$$688$$ 24.0000i 0.914991i
$$689$$ 29.6985 1.13142
$$690$$ 0 0
$$691$$ 50.0000 1.90209 0.951045 0.309053i $$-0.100012\pi$$
0.951045 + 0.309053i $$0.100012\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −38.0000 −1.44246
$$695$$ 27.5772 9.19239i 1.04606 0.348687i
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 7.07107i 0.267644i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −38.1838 −1.44218 −0.721090 0.692841i $$-0.756359\pi$$
−0.721090 + 0.692841i $$0.756359\pi$$
$$702$$ 0 0
$$703$$ 9.00000i 0.339441i
$$704$$ −33.9411 −1.27920
$$705$$ 0 0
$$706$$ 40.0000 1.50542
$$707$$ 25.4558i 0.957366i
$$708$$ 0 0
$$709$$ 17.0000 0.638448 0.319224 0.947679i $$-0.396578\pi$$
0.319224 + 0.947679i $$0.396578\pi$$
$$710$$ 12.7279 + 38.1838i 0.477670 + 1.43301i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 14.1421i 0.529627i
$$714$$ 0 0
$$715$$ 9.00000 + 27.0000i 0.336581 + 1.00974i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 18.0000i 0.671754i
$$719$$ 12.7279 0.474671 0.237336 0.971428i $$-0.423726\pi$$
0.237336 + 0.971428i $$0.423726\pi$$
$$720$$ 0 0
$$721$$ 9.00000 0.335178
$$722$$ 25.4558i 0.947368i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 16.9706 12.7279i 0.630271 0.472703i
$$726$$ 0 0
$$727$$ 42.0000i 1.55769i −0.627214 0.778847i $$-0.715805\pi$$
0.627214 0.778847i $$-0.284195\pi$$
$$728$$ 25.4558i 0.943456i
$$729$$ 0 0
$$730$$ −27.0000 + 9.00000i −0.999315 + 0.333105i
$$731$$ −16.9706 −0.627679
$$732$$ 0 0
$$733$$ 24.0000i 0.886460i 0.896408 + 0.443230i $$0.146168\pi$$
−0.896408 + 0.443230i $$0.853832\pi$$
$$734$$ 21.2132 0.782994
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 12.7279i 0.468839i
$$738$$ 0 0
$$739$$ −10.0000 −0.367856 −0.183928 0.982940i $$-0.558881\pi$$
−0.183928 + 0.982940i $$0.558881\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 42.0000i 1.54187i
$$743$$ 14.1421i 0.518825i 0.965767 + 0.259412i $$0.0835289\pi$$
−0.965767 + 0.259412i $$0.916471\pi$$
$$744$$ 0 0
$$745$$ 36.0000 12.0000i 1.31894 0.439646i
$$746$$ 29.6985 1.08734
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 21.2132 0.775114
$$750$$ 0 0
$$751$$ −7.00000 −0.255434 −0.127717 0.991811i $$-0.540765\pi$$
−0.127717 + 0.991811i $$0.540765\pi$$
$$752$$ 11.3137i 0.412568i
$$753$$ 0 0
$$754$$ 18.0000 0.655521
$$755$$ 2.12132 0.707107i 0.0772028 0.0257343i
$$756$$ 0 0
$$757$$ 27.0000i 0.981332i 0.871348 + 0.490666i $$0.163246\pi$$
−0.871348 + 0.490666i $$0.836754\pi$$
$$758$$ 49.4975i 1.79783i
$$759$$ 0 0
$$760$$ 2.00000 + 6.00000i 0.0725476 + 0.217643i
$$761$$ −4.24264 −0.153796 −0.0768978 0.997039i $$-0.524502\pi$$
−0.0768978 + 0.997039i $$0.524502\pi$$
$$762$$ 0 0
$$763$$ 24.0000i 0.868858i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −8.00000 −0.289052
$$767$$ 25.4558i 0.919157i
$$768$$ 0 0
$$769$$ 11.0000 0.396670 0.198335 0.980134i $$-0.436447\pi$$
0.198335 + 0.980134i $$0.436447\pi$$
$$770$$ 38.1838 12.7279i 1.37605 0.458682i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 41.0122i 1.47511i −0.675289 0.737553i $$-0.735981\pi$$
0.675289 0.737553i $$-0.264019\pi$$
$$774$$ 0 0
$$775$$ 8.00000 6.00000i 0.287368 0.215526i
$$776$$ −8.48528 −0.304604
$$777$$ 0 0
$$778$$ 48.0000i 1.72088i
$$779$$ 4.24264 0.152008
$$780$$ 0 0
$$781$$ −54.0000 −1.93227
$$782$$ 28.2843i 1.01144i
$$783$$ 0 0
$$784$$ 8.00000 0.285714
$$785$$ −4.24264 12.7279i −0.151426 0.454279i
$$786$$ 0 0
$$787$$ 15.0000i 0.534692i 0.963601 + 0.267346i $$0.0861467\pi$$
−0.963601 + 0.267346i $$0.913853\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −5.00000 15.0000i −0.177892 0.533676i
$$791$$ −4.24264 −0.150851
$$792$$ 0 0
$$793$$ 39.0000i 1.38493i
$$794$$ −50.9117 −1.80679
$$795$$ 0